Tux Machines Bulletin for Thursday, April 09, 2026 ┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅ Generated Fri 10 Apr 02:49:40 BST 2026 Created by Dr. Roy Schestowitz (𝚛𝚘𝚢 (at) 𝚜𝚌𝚑𝚎𝚜𝚝𝚘𝚠𝚒𝚝𝚣 (dot) 𝚌𝚘𝚖) Full hyperlinks for navigation omitted but are fully available in the originals The corresponding HTML versions are at http://news.tuxmachines.org ╒═══════════════════ 𝐈𝐍𝐃𝐄𝐗 ═══════════════════════════════════════════════════╕ ⦿ Tux Machines - 5 open-source projects that secretly power the world ⦿ Tux Machines - Android Leftovers ⦿ Tux Machines - Android Leftovers ⦿ Tux Machines - Applications nvim-µwiki and macOS app Little Snitch is now available on Linux ⦿ Tux Machines - Best Free and Open Source Software ⦿ Tux Machines - Canonical/Ubuntu: FunOS 25.10 (with Calamares Installer), Canonical Upselling Canonical, and How to "Stop Installing Ubuntu [Software] One at a Time" ⦿ Tux Machines - Desktop Environments: tiling window manager and XFCE tip ⦿ Tux Machines - Dynamic Music Pill brings lyrics to your GNOME desktop ⦿ Tux Machines - Free and Open Source Software, howtos and Installations ⦿ Tux Machines - FreeBSD 14.4 on Raspberry Pi Zero 2W and OpenBSD on Motorola 88000 Processors ⦿ Tux Machines - Free, Libre, and Open Source Software Leftovers ⦿ Tux Machines - Games: New Steam Games with Native GNU/Linux Builds, Why Windows Users Should Become GNU/Linux Gamers, and More ⦿ Tux Machines - GNU Projects: GNU Health Control Center 5.0.3 and Parted 3.7 Released ⦿ Tux Machines - I ditched Windows for SteamOS on my PC, and gaming is way better now ⦿ Tux Machines - Introducing our Art Contest winner! ⦿ Tux Machines - KDE Linux is the purest form of Plasma I've tested - but the install isn't for the meek ⦿ Tux Machines - Krita 5.3.1.1 Released (Android-only) ⦿ Tux Machines - Linux-centric Devices and Open Hardware Stories ⦿ Tux Machines - LWN is Promoting LLM Slop, Makes Excuses for "Age Verification" (Surveillance), Promotes Rust (Microsoft GitHub) ⦿ Tux Machines - New Issue of Linux Magazine, #306 ⦿ Tux Machines - Openwashing: Anthropic Buys PR/Promotion (of Slop) From Apache Software Foundation and 'Linux' Foundation, PyTorch Foundation Likewise, Facebook Pretends Private Models Are 'Open' ⦿ Tux Machines - PipeWire 1.6.3 Improves RAOP Compatibility to Make It Work on More Devices ⦿ Tux Machines - Programming Leftovers ⦿ Tux Machines - Red Hat Summit 2026 and Red Hat Trying Hard to Sell Slop (to Help IBM Fake Novelty) ⦿ Tux Machines - Relicensing versus license compatibility ⦿ Tux Machines - Rofi and Wofi: Keyboard Launchers That Keep Your Hands on the Keys ⦿ Tux Machines - Security Leftovers ⦿ Tux Machines - ShredOS – disk eraser operating system ⦿ Tux Machines - ShrikeLinux – Arch-based Linux distribution ⦿ Tux Machines - Stop believing these 4 myths about Linux—they're all outdated now ⦿ Tux Machines - Super Lite Linux – lightweight distribution ⦿ Tux Machines - Syndicator, RSS, and Web Browsers ⦿ Tux Machines - This Linux distro will give your old Windows 10 PC a new lease on life ⦿ Tux Machines - Today in Techrights ⦿ Tux Machines - today's howtos ⦿ Tux Machines - today's leftovers ⦿ Tux Machines - Ubuntu is still the only Linux distro I recommend to beginners—here are 3 reasons why ⦿ Tux Machines - Video: GNU/Linux, Office Suites, Slop, and More ⦿ Tux Machines - Why I returned to Enlightenment Linux after 30 years: Testing the new Elive beta ䷼ Bulletin articles (as HTML) to comment on (requires login): https://tuxmachines.org/n/2026/04/09/5_open_source_projects_that_secretly_power_the_world.shtml https://tuxmachines.org/n/2026/04/09/Android_Leftovers.1.shtml https://tuxmachines.org/n/2026/04/09/Android_Leftovers.shtml https://tuxmachines.org/n/2026/04/09/Applications_nvim_%CE%BCwiki_and_macOS_app_Little_Snitch_is_now_avai.shtml https://tuxmachines.org/n/2026/04/09/Best_Free_and_Open_Source_Software.shtml https://tuxmachines.org/n/2026/04/09/Canonical_Ubuntu_FunOS_25_10_with_Calamares_Installer_Canonical.shtml https://tuxmachines.org/n/2026/04/09/Desktop_Environments_tiling_window_manager_and_XFCE_tip.shtml https://tuxmachines.org/n/2026/04/09/Dynamic_Music_Pill_brings_lyrics_to_your_GNOME_desktop.shtml https://tuxmachines.org/n/2026/04/09/Free_and_Open_Source_Software_howtos_and_Installations.shtml https://tuxmachines.org/n/2026/04/09/FreeBSD_14_4_on_Raspberry_Pi_Zero_2W_and_OpenBSD_on_Motorola_88.shtml https://tuxmachines.org/n/2026/04/09/Free_Libre_and_Open_Source_Software_Leftovers.shtml https://tuxmachines.org/n/2026/04/09/Games_New_Steam_Games_with_Native_GNU_Linux_Builds_Why_Windows_.shtml https://tuxmachines.org/n/2026/04/09/GNU_Projects_GNU_Health_Control_Center_5_0_3_and_Parted_3_7_Rel.shtml https://tuxmachines.org/n/2026/04/09/I_ditched_Windows_for_SteamOS_on_my_PC_and_gaming_is_way_better.shtml https://tuxmachines.org/n/2026/04/09/Introducing_our_Art_Contest_winner.shtml https://tuxmachines.org/n/2026/04/09/KDE_Linux_is_the_purest_form_of_Plasma_I_ve_tested_but_the_inst.shtml https://tuxmachines.org/n/2026/04/09/Krita_5_3_1_1_Released_Android_only.shtml https://tuxmachines.org/n/2026/04/09/Linux_centric_Devices_and_Open_Hardware_Stories.shtml https://tuxmachines.org/n/2026/04/09/LWN_is_Promoting_LLM_Slop_Makes_Excuses_for_Age_Verification_Su.shtml https://tuxmachines.org/n/2026/04/09/New_Issue_of_Linux_Magazine_306.shtml https://tuxmachines.org/n/2026/04/09/Openwashing_Anthropic_Buys_PR_Promotion_of_Slop_From_Apache_Sof.shtml https://tuxmachines.org/n/2026/04/09/PipeWire_1_6_3_Improves_RAOP_Compatibility_to_Make_It_Work_on_M.shtml https://tuxmachines.org/n/2026/04/09/Programming_Leftovers.shtml https://tuxmachines.org/n/2026/04/09/Red_Hat_Summit_2026_and_Red_Hat_Trying_Hard_to_Sell_Slop_to_Hel.shtml https://tuxmachines.org/n/2026/04/09/Relicensing_versus_license_compatibility.shtml https://tuxmachines.org/n/2026/04/09/Rofi_and_Wofi_Keyboard_Launchers_That_Keep_Your_Hands_on_the_Ke.shtml https://tuxmachines.org/n/2026/04/09/Security_Leftovers.shtml https://tuxmachines.org/n/2026/04/09/ShredOS_disk_eraser_operating_system.shtml https://tuxmachines.org/n/2026/04/09/ShrikeLinux_Arch_based_Linux_distribution.shtml https://tuxmachines.org/n/2026/04/09/Stop_believing_these_4_myths_about_Linux_they_re_all_outdated_n.shtml https://tuxmachines.org/n/2026/04/09/Super_Lite_Linux_lightweight_distribution.shtml https://tuxmachines.org/n/2026/04/09/Syndicator_RSS_and_Web_Browsers.shtml https://tuxmachines.org/n/2026/04/09/This_Linux_distro_will_give_your_old_Windows_10_PC_a_new_lease_.shtml https://tuxmachines.org/n/2026/04/09/Today_in_Techrights.shtml https://tuxmachines.org/n/2026/04/09/today_s_howtos.shtml https://tuxmachines.org/n/2026/04/09/today_s_leftovers.shtml https://tuxmachines.org/n/2026/04/09/Ubuntu_is_still_the_only_Linux_distro_I_recommend_to_beginners_.shtml https://tuxmachines.org/n/2026/04/09/Video_GNU_Linux_Office_Suites_Slop_and_More.shtml https://tuxmachines.org/n/2026/04/09/Why_I_returned_to_Enlightenment_Linux_after_30_years_Testing_th.shtml ䷩ 𝚕𝚒𝚗𝚎 130 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/04/09/5_open_source_projects_that_secretly_power_the_world.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/04/09/5_open_source_projects_that_secretly_power_the_world.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 5 open-source projects that secretly power the world⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Rianne Schestowitz on Apr 09, 2026 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇FFmpeg⦈_ Quoting: 5 open-source projects that secretly power the world — FFmpeg is an open-source tool that can encode, decode, transcode, and filter multiple kinds of files including video, audio, and images. If you need to isolate the audio from a video file, say an MP4, and save it as an MP3 file, FFmpeg can do it. If you need to convert a WAV into an MP4, FFmpeg can do that too. It is a multimedia Swiss army knife. Read_on ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣟⣻⣿⣻⣿⣿⣿⣿⣟⣛⣿⣛⣿⣛⣛⣻⣿⣝⣛⣛⣟⣿⣛⣛⣛⣙⣿⣏⣛⣛⣉⣿⣟⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣯⣿⣿⣿⣽⣻⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣻⣿⣿⣻⣿⣿⣟⣿⣿⣹⣿⣿⣿⣯⣯⣯⣉⣿⣿⣍⣛⣭⣿⣹⣏⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⡿⣿⣷⣾⣾⣿⣿⢼⣿⢾⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⢾⣿⣿⣿⣿⣿⢿⣷⣿⣿⣿⣿⠿⠿⠿⠾⠷⢿⣷⣿⢿⣿⣿⢿⣿⠿⠷⠷⠷⠷⣷⣿⢶⢶⢶⠶⡶⡶⣿⣿⡿⠿⢿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡿⠛⢻⣿⣿⣏⠁⠁⠙⠀⠀⠀⠀⠀⠀⠀⠀⡠⡾⡷⡾⣿⣿⣿⢾⣿⠶⣶⡶⣶⡶⡿⠿⢾⣾⢾⠶⠶⡷⣾⣿⣿⠶⢾⡿⣶⢶⢿⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣀⣈⣿⡿⠃⠀⠀⠀⠀⠀⠄⠀⠀⠀⢠⠾⣿⡷⡷⠷⠿⣿⠿⠻⢾⣿⣿⠷⡿⠷⠶⣾⢻⣿⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⣾⣾⣾⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡿⢿⠀⠉⠀⠐⠀⠀⢀⠐⠁⠀⠀⢀⠜⠁⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⣿⡟⣛⣻⠀⠀⠘⠻⠻⢿⡇⠀⠘⠿⠟⢙⡻⠙⠛⠟⠛⠹⠋⠋⠛⠻⣿⡿⠛⠛⠟⠛⠿⢿⣿⣿⠿⠛⠛⠿⣿⣿⡿⠿⠛⠻⠟⠻⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⣿⣟⡟⣿⠀⠀⠀⠀⠀⣛⡇⠀⠀⠀⠀⢸⡁⠀⠀⣠⡄⠀⠀⣠⡄⠀⠈⡇⠀⠀⣠⣤⡀⠀⠛⠁⠀⡠⣤⠀⠈⠟⠀⢀⣤⣄⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⢀⡀⠀⠀⠀⢀⠔⠁⠀⠀⣀⡆⠀⠀⠀⣿⣿⣋⣏⠀⠀⢨⣽⣹⣻⡇⠀⢸⣿⣿⣿⡇⠀⠀⣿⡇⠀⠀⣿⣿⠀⠀⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠸⣿⢿⠅⠀⢸⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠁⠀⠀⢀⡶⠋⠀⠀⠀⠐⠛⢻⣯⣷⠀⠀⢈⣹⣹⣉⡇⠀⢸⣿⣿⣿⡇⠀⠀⣿⡇⠀⠀⣿⣿⠀⠀⡇⠀⠀⠀⠀⠀⣠⣾⣄⠀⠀⠀⠀⢈⣷⣀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣿⣿⣯⣿⣿⣿⣯⣤⣤⣄⣀⣀⣀⣀⣠⡔⠃⠀⠀⠀⠀⠀⠀⠀⢸⣯⣽⣏⣿⣷⣩⣩⣽⣧⣏⣇⣯⣿⣽⣵⣩⣽⣼⣟⣿⣇⣭⣍⣿⣭⡇⠀⠀⣽⣽⣿⣿⣯⣿⣿⣭⣭⣿⣽⣿⠋⠙⠛⠋⠀⠀⣼⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣷⣿⣿⣽⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣼⣿⣿⣿⣿⣿⣧⣧⣷⣷⣿⣴⣾⣷⣮⣷⣧⡷⣿⣷⣼⣿⣾⣼⣷⣴⣦⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣷⣾⣿⡷⣶⣶⣾⣿⣿⣿⣿⣿⡷⡷⣷⣴⢶⢿⣶⢾⢶⡾⡧⣷⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⢿⣿⣾⣷⣿⡿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣾⣾⣿⣶⣾⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣷⢿⢿⢿⣿⠿⢿⡿⢷⣿⡿⣿⠿⢿⣿⢿⣿⡿⠿⠿⠿⣿⡿⡿⢿⢿⢿⠿⢿⣿⣿⣿⣿⡿⠿⠿⣿⣿⢿⡿⡿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡟⣿⣿⢿⢿⢿⣿⠻⣾⡿⣿⣿⣿⣿⠛⢻⣿⢾⣿⡿⠷⠾⣿⣿⡿⠿⢾⢾⢾⢻⣾⣿⡿⣿⡿⠷⠾⢿⣿⣿⢺⣿⣿⠷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡟⣟⡟⠻⣿⣿⢻⣻⢻⣟⡛⠛⣿⣛⢛⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ䷩ 𝚕𝚒𝚗𝚎 188 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/04/09/Android_Leftovers.1.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/04/09/Android_Leftovers.1.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Android Leftovers⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Rianne Schestowitz on Apr 09, 2026 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇android_phone_with_bugdroid⦈_ * ⚓ Android_17:_These_Phones_Will_be_Upgraded_-_Tech_Advisor⠀⇛ * ⚓ Gamers_will_love_what_Google_is_adding_to_Android_17_-_PhoneArena⠀⇛ * ⚓ Android_17_Will_Finally_Let_You_Remap_Your_Gaming_Controllers_| Lifehacker⠀⇛ * ⚓ The_best_Android_phones_2025:_top_Google-powered_phones_|_TechRadar⠀⇛ * ⚓ 5_hidden_Pixel_settings_I_wish_I’d_changed_years_ago⠀⇛ * ⚓ 8_Hidden_Android_Features_That_Quietly_Save_You_Time_Every_Day⠀⇛ * ⚓ The_latest_Pixel_update_tackles_Android_16's_early_stability_woes_| Android_Central⠀⇛ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⣿⣿⠟⡛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣧⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⡀⠝⠧⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣛⢿⣿⣿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣶⣶⣶⣶⣶⣤⡶⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⠛⠛⠛⠙⠋⠀⣿⣿⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⠛⠛⠋⠉⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢰⠀⠀⠸⠁⠸⣿⡿⠉⠛⠛⠛⠿⠟⢱⣿⣧⠰⠿⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀ ⠉⠉⠉⠉⠉⠉⠈⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠙⠲⠦⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠈⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠉⠀⠀⢠⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⣯⣽⢿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣏⣹⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣽⣿⣿⣿⣿⣿⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⠶⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣦⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⣿⣿⣿⣿⣿ ䷩ 𝚕𝚒𝚗𝚎 253 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/04/09/Android_Leftovers.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/04/09/Android_Leftovers.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Android Leftovers⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Rianne Schestowitz on Apr 09, 2026, updated Apr 09, 2026 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Google_Photos⦈_ * ⚓ Why_three_buttons_beat_Android's_gesture_system_every_single_time⠀⇛ * ⚓ Many_of_you_think_Google_is_slowly_turning_Android_into_the_one_thing it_was_never_supposed_to_be_-_PhoneArena⠀⇛ * ⚓ Google_owes_Android_users_$135_million,_and_you_can_now_claim_your_cut -_PhoneArena⠀⇛ * ⚓ Android_17_Will_Finally_Let_You_Remap_Your_Gaming_Controllers⠀⇛ * ⚓ Android_17_will_fix_one_of_Android_gaming’s_oldest_problems⠀⇛ * ⚓ I'm_excited_for_Android_17_on_my_Google_Pixel_just_because_of_this_one major_productivity_feature⠀⇛ * ⚓ Android_finally_gets_a_controller_feature_mobile_gamers_have_been begging_for⠀⇛ * ⚓ The_Android_dark_mode_upgrade_you_deserve_–_Computerworld⠀⇛ * ⚓ Google_Photos_On_Android_Just_Got_A_Feature_It's_Needed_For_Years⠀⇛ * ⚓ Qt_for_Android_Automotive_6.8.7_is_released⠀⇛ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢤⢴⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⠶⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣦⢤⣾⣻⡟⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣠⣤⡄⠻⡏⠘⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡹⣿⣆⠀⠀⠀⠀⢠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣴⣟⣿⡿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡽⣿⣧⠀⠀⠀⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⣣⣼⣏⣿⠓⠚⠘⠛⠁⠀⢠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣷⣦⡀⠀⠀⠀⠑⠒⠋⠀⠀⠀⢀⣄⣤⠱⠼⠚⠉⠀⣀⣤⣴⠦⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣿⣿⡄⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⡤⣤⣶⠶⠿⠟⠉⢀⣀⣤⠦⠋⠋⠉⠀⠀⠀⠀⠀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠉⠉⠀⠀⣤⣶⠷⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠈⠛⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⡄⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠻⢿⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣾⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⣴⠿⠏⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤ ䷩ 𝚕𝚒𝚗𝚎 330 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/04/09/Applications_nvim_%CE%BCwiki_and_macOS_app_Little_Snitch_is_now_avai.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/04/09/Applications_nvim_%CE%BCwiki_and_macOS_app_Little_Snitch_is_now_avai.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Applications nvim-µwiki and macOS app Little Snitch is now available on Linux⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Apr 09, 2026 * ⚓ Jonathan Dowland ☛ Jonathan_Dowland:_nvim-µwiki⠀⇛ In January 2025, as a pre-requisite for something else, I published a minimal neovim plugin called nvim-µwiki. It's essentially just the features from vimwiki that I regularly use, which is a small fraction them. I forgot to blog about it. I recently dusted it off and cleaned it up. * ⚓ OMG Ubuntu ☛ macOS_app_Little_Snitch_is_now_available_on_Linux⠀⇛ Little Snitch is now on Linux. See which apps are making network connections, block unwanted ones and find out how chatty your system really is. ䷩ 𝚕𝚒𝚗𝚎 365 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/04/09/Best_Free_and_Open_Source_Software.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/04/09/Best_Free_and_Open_Source_Software.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Best Free and Open Source Software⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Rianne Schestowitz on Apr 09, 2026 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇a_woman_playing_violin⦈_ * ⚓ mpdscribble_-_MPD_client_-_LinuxLinks⠀⇛ mpdscribble is a client for Music Player Daemon that submits information about tracks being played to scrobbler services such as Last.fm. It is designed to run alongside MPD and automatically report listening activity, making it useful for users who want their local music server playback logged to online scrobbling services. This is free and open source software. * ⚓ 5_Useful_Free_and_Open_Source_Linux_Background_Noise_Generators_- LinuxLinks⠀⇛ Their appeal is practical as much as aesthetic. A writer might use rain or waves to soften household distractions, a developer might layer wind, stream, or white noise to create a steadier background for deep work, and a remote worker might reach for coffee-shop ambience to make a quiet room feel less sterile. These programs are also handy for reading, studying, meditation, evening relaxation, or covering irregular background sounds without switching to music. Blanket suits users who want an easy graphical mixer; Tanin and onsen are natural fits for terminal enthusiasts who like staying in the shell; Noisedash is ideal for people who want browser access, self-hosting, and elaborate customization; and aNoise remains attractive for users who prefer a minimal, low-overhead player that sits neatly in the desktop environment. Together, they show how Linux offers ambient tools for every taste, from straightforward sound playback to personalized soundscape creation. Here’s our verdict captured in a legendary LinuxLinks-style ratings chart. Only free and open source software is eligible for inclusion. * ⚓ Gloomberb_-_keyboard-driven_financial_terminal_-_LinuxLinks⠀⇛ Gloomberb is a keyboard-driven financial terminal that runs inside your terminal emulator. It offers a full-screen interface for monitoring markets, managing portfolios and watchlists, viewing quotes and company data, reading news and SEC filings, exploring options chains, comparing charts, and keeping local notes. The project is built around plugins, which lets it extend its interface and add integrations such as broker connectivity and extra commands. This is free and open source software. * ⚓ Purple_-_terminal-based_SSH_host_manager_-_LinuxLinks⠀⇛ Purple is a terminal-based SSH host manager that helps administrators work with large or frequently changing server inventories from a single text user interface. Rather than storing hosts in a separate database, it reads and edits ~/.ssh/config directly while preserving existing formatting, comments, Include files, and other directives. This is free and open source software. * ⚓ OneFile_-_file_organiser_-_LinuxLinks⠀⇛ OneFile is a Python command-line utility that helps keep cluttered directories tidy by automatically placing files into structured subfolders. It’s designed for routine housekeeping tasks such as cleaning a Downloads folder, and it can work with configurable organisation rules so users can tailor how files are sorted. The project can be run for a one-off cleanup or used in a background watch mode to keep folders organised as new files appear. This is free and open source software. * ⚓ Solitaire_-_play_patience_games_-_LinuxLinks⠀⇛ Solitaire is a lightweight GNOME application that provides a simple implementation of classic solitaire card games for the Linux desktop. It is designed to integrate cleanly with the GNOME environment, offering a distraction-free interface and smooth gameplay. The application focuses on delivering a straightforward card- playing experience without unnecessary complexity, making it suitable for casual play. This is free and open source software. * ⚓ rusti-cal_-_cal_clone_-_LinuxLinks⠀⇛ rusti-cal is a Rust command line utility for generating text calendars from the terminal. It is a lightweight clone of cal(1) that focuses on speed and minimalism while offering useful formatting options for displaying yearly calendars. This is free and open source software. * ⚓ deadbranch_-_keep_Git_repositories_tidy_-_LinuxLinks⠀⇛ deadbranch is a command-line utility that helps keep Git repositories tidy by identifying stale branches and cleaning them up with a safety-first workflow. It can scan local and remote branches, show details such as age, merge status, last commit date, and author, and then remove branches after confirmation. This is free and open source software. * ⚓ s5cmd_-_S3_and_local_filesystem_execution_tool_-_LinuxLinks⠀⇛ s5cmd is a command-line utility for working with Amazon S3 and other S3-compatible object storage services from a terminal. It’s designed for high-throughput workflows, handling large numbers of objects with parallel execution across cloud storage and local filesystems. The software is suited to tasks such as transferring data, managing buckets and objects, and running batch commands efficiently in storage-heavy environments. This is free and open source software. * ⚓ otel-tui_-_terminal-based_observability_viewer_-_LinuxLinks⠀⇛ otel-tui is a terminal-based observability viewer that lets you inspect telemetry data directly from a text user interface. It can receive OpenTelemetry data over OTLP, ingest Zipkin traces, scrape Prometheus metrics, and accept Datadog traces, metrics, and logs, making it a handy local tool for exploring application behaviour without needing a full browser-based observability stack. This is free and open source software. ⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⠿⠃⣄⠝⣟⢏⣩⣉⡿⠂⠠⣭⠼⡟⠁⠛⠋⣈⣵⣾⡀⠀⠀⢠⣼⡟⢻⣿⠇⠭⠯⠠⠠⠽⣿⡿⣿⣼⣿⣏⡀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡇⠠⠘⣿⣯⣿⢿⣿⣿⣿⣿⢿ ⣿⣿⣿⣿⣿⣿⠃⠀⢻⡽⠅⠀⣀⣸⣇⠙⢾⣿⣿⣟⠄⠀⠀⠐⠿⠻⣿⢶⣘⣿⣏⠀⠀⠀⢠⣼⣿⣼⡟⠀⠁⠐⠆⢄⡆⠟⢿⣿⣿⣻⣿⣿⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣮⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡀⣀⡀⠀⣴⠾⣯⣹⢛⡂⠀⡚⠩⠀⠀⠀⠀⠲⠂⢀⠸⣿⡻⡿⠀⠉⠀⢀⣀⣛⡇⣿⣤⡀⠀⠀⣾⣷⣄⣄⠀⣻⣶⣿⣿⣿⠿⣿⣯⣿⣿⣿⣞⣿⡻⡯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡿⣿⣋⠀⠀⠉⣿⣿⠷⠇⠈⠀⢃⠀⠀⠀⠐⠉⠀⠀⡠⢰⣿⣦⣿⣆⠄⠀⢼⣿⣿⣿⣿⣿⡇⠀⠒⢉⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣧⣮⣽⣾⣿⣷⣿⣿⣷⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿ ⣿⣿⣿⣿⣿⣾⣿⣿⠻⣶⣾⡉⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⣼⣿⣷⣿⡯⢀⣵⣿⣿⣏⡿⢿⣿⠚⣧⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢿⠿⠼⢄⣄⡹⣧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢿⣿⠯⣤⣿⣟⣿⣿⣿⣿⡇⢠⢽⣵⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿ ⣿⣿⣿⣿⣿⡇⠀⠀⠸⣿⣋⣠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠩⢭⠤⣾⣿⣿⣿⡿⣿⡿⢇⢶⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣏⠯⣿⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿ ⢯⣥⣿⣿⣯⠞⣄⡰⡆⣚⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⣥⡟⡉⢻⣿⣶⣿⠤⠽⣿⣿⣿⣷⡿⢿⠝⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣾⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡿⠿⠿⠉⠀⣻⣿⡿⠓⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠋⠉⢹⣿⣿⣿⣼⣿⠞⠻⠟⠿⣿⣿⣦⡁⠶⢍⢻⣿⣿⣻⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿ ⠈⡄⠀⠀⠰⡾⣿⢿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠑⣬⡿⠛⠀⠁⢈⣧⣶⣶⣤⣤⣤⣄⣈⡀⢉⣉⣻⣾⡟⠋⠂⠀⠽⠚⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿ ⣀⢁⡴⠶⠶⠂⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠾⢿⠗⠨⠍⠀⠈⠉⠉⠛⠿⠿⣿⠿⣻⣷⣿⣿⣿⣿⣇⣂⠈⠀⠀⠀⠁⠈⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣟⠃⠈⠈⢠⣴⢏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⡞⣢⢻⣿⢢⣤⣀⣄⣼⢟⣾⡿⠹⠿⠉⢩⣿⣻⡅⠘⢓⣂⣐⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣶⢀⡄⠀⠀⠀⣲⣦⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⢊⠃⠃⣰⠿⣿⣾⣿⣿⣿⠿⢿⣿⠿⣦⠀⢀⢺⣿⡋⢁⣀⣉⣋⣫⣽⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿ ⡿⣿⠿⠧⡀⠀⢸⣿⡭⠭⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠂⢠⠄⠀⣰⣻⣻⣦⠀⠀⠀⠉⠋⠋⢀⣁⡺⠁⠀⠀⣵⡀⣨⣿⣏⣥⣸⣯⣾⣿⣿⣿⣿⣿⣿⣯⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⣿⣿ ⣷⣿⢧⣼⡇⣾⣿⢯⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣮⢥⠀⠀⠘⣿⣿⡅⠀⠀⠀⠀⠂⠨⣢⡋⣁⣄⡠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⣿⣯⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿ ⣷⣦⣼⣼⣿⣿⡟⢿⡿⣶⣦⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢈⡛⡘⣦⠀⠀⢨⣿⡇⣶⣤⣄⡋⠌⣈⢠⣄⡹⢻⣿⣿⣭⣿⣿⢿⣿⣿⡿⣿⣻⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣥⣿⣿⣿⣿⣿⣷⣻⣿⣿⣧ ⣿⣿⣿⣿⠛⠏⠻⠟⣫⣽⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⠴⣾⣽⣇⠐⣋⣿⣠⣿⣿⣿⣿⣿⣿⣿⣿⣷⡾⣿⣼⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣷⣼⣿⣿⢿⣇⡀⠀⠀⠀⠀⠀⣄⣀⢄⣴⣦⣶⣷⢨⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿ ⣿⣿⣿⡿⣿⣿⠟⣿⣿⣯⣤⣇⣀⠀⠀⣌⠀⠀⠀⡀⠀⠀⠉⠁⣠⣉⡉⠙⠻⣟⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡞⠈⠄⢀⣼⣟⣛⣿⣿⣿⣿⠄⠰⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠢⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣶⡆⣤⣻⣿⣿⣿⣿⣾⡏⡔⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ䷩ 𝚕𝚒𝚗𝚎 598 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/04/09/Canonical_Ubuntu_FunOS_25_10_with_Calamares_Installer_Canonical.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/04/09/Canonical_Ubuntu_FunOS_25_10_with_Calamares_Installer_Canonical.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Canonical/Ubuntu: FunOS 25.10 (with Calamares Installer), Canonical Upselling Canonical, and How to "Stop Installing Ubuntu [Software] One at a Time"⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Apr 09, 2026 * ⚓ FunOS_25.10_(with_Calamares_Installer)⠀⇛ Release Date: 9 April 2026Base: Ubuntu 25.10 (Questing Quokka) Introduction FunOS 25.10 is now available as an updated ISO featuring the Calamares installer, replacing the previous Ubiquity-based installer used in the original release. This refreshed ISO provides a more modern and flexible installation experience, along with updated packages and new visual improvements. * ⚓ Ubuntu ☛ Ubuntu_Pro_comes_to_Nutanix_bare-metal_Kubernetes⠀⇛ Nutanix and Canonical expand partnership to offer more choice for containerized workloads Enterprise Kubernetes® is maturing into a highly flexible, multi-architecture model. As AI/ML and data-intensive workloads continue to demand maximum hardware throughput, organizations are seeking the performance of bare metal without sacrificing the operational consistency of cloud platforms. * ⚓ HowTo Geek ☛ Stop_installing_Ubuntu_apps_one_at_a_time—here_are_3 faster_ways⠀⇛ The beauty of Linux is that it gives you a minimal base on top of which you can build a customized system exactly how you like. However, that also means going through the painstakingly long process of installing all your apps and packages one at a time. Thankfully, there's a better way—a few actually—that allows you to install everything you need in a single shot. ䷩ 𝚕𝚒𝚗𝚎 652 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/04/09/Desktop_Environments_tiling_window_manager_and_XFCE_tip.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/04/09/Desktop_Environments_tiling_window_manager_and_XFCE_tip.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Desktop Environments: tiling window manager and XFCE tip⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Apr 09, 2026 * ⚓ ZDNet ☛ Love_window_snapping_on_Linux?_You_should_try_a_tiling_window manager_-_here's_why⠀⇛ For those who've never experienced a tiling window manager, you're in for a treat. Tiling window managers depend on keyboard shortcuts to interact with the interface. Instead of using the mouse, you use the keyboard to open apps, move windows around, cycle through windows, and just about everything you do on the desktop. This reliance on the keyboard can prevent new Linux users from adopting a tiling window manager. That's a shame, because although these window managers have a steeper learning curve, they are amazingly efficient. * ⚓ [Old] Mitesh Singh Jat ☛ Stopping_Tumblerd_in_XFCE⠀⇛ Tumbler is a D-Bus service for applications to request thumbnails for various URI schemes and MIME types. It is an implementation of the thumbnail management D-Bus specification described here. ䷩ 𝚕𝚒𝚗𝚎 698 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/04/09/Dynamic_Music_Pill_brings_lyrics_to_your_GNOME_desktop.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/04/09/Dynamic_Music_Pill_brings_lyrics_to_your_GNOME_desktop.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Dynamic Music Pill brings lyrics to your GNOME desktop⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Rianne Schestowitz on Apr 09, 2026 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Music_Pill⦈_ Quoting: Dynamic Music Pill brings lyrics to your GNOME desktop - OMG! Ubuntu — The lyrics are shown in a freely scrollable widget, with the active line bolder in white for more emphasis. You can scroll up and down whilst tracks are playing. If you click a lyric line, your music player jumps to that part of the track. Of course, having a dedicated place to see lyrics is all well and good, but the popover hides when it loses focus. Not great for a passive sing-a-long while you work, right? ;) There is an option to show lyrics appear in the panel pill itself, still in time with what you’re listening to. This feature is not enabled by default. As the pill width isn’t huge, lyrics auto-scroll, and the speed depends on how long it takes to transition to the next line... Read_on ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⣻ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⡿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⡟⡟⢹⢈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡇⠇⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⣿⡟⣿⣿⣿⣿⣿⣿⣿⢹⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠘⡇⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣄⣀⣀⣀⣀⣀⣴⡇⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⠿⠃⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⡀⣴⢀⢀⣀⣴⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠘⠠⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⢻⠙⠋⠋⠉⠀⠀⠀⠀⢠⡎⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠠⠀⠀⠀⠀⠀⠀⡆⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢤⣤⣤⣤⠤⠤⠤⠤⠭⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⠤⠤⠤⠤⣤⣤⣤⡤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ䷩ 𝚕𝚒𝚗𝚎 762 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/04/09/Free_and_Open_Source_Software_howtos_and_Installations.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/04/09/Free_and_Open_Source_Software_howtos_and_Installations.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Free and Open Source Software, howtos and Installations⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Rianne Schestowitz on Apr 09, 2026 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Radio⦈_ * ⚓ RadioGoGo_-_surf_global_radio_waves_-_LinuxLinks⠀⇛ Its appeal lies in both its accessibility and its breadth of content. Most internet radio services can be accessed without subscription or registration fees, making them available to a wide audience. Listeners can choose from tens of thousands of stations worldwide, offering an extensive range of programming, including music, news, sport, cultural content, and talk shows. Genres span everything from classical and jazz to pop, folk, and specialist interests, giving users far greater choice than is typically available through local terrestrial broadcasting. With a stable internet connection, listeners can access this content from almost anywhere, making internet radio a flexible and convenient alternative to conventional radio services. RadioGoGo is a terminal application for browsing and playing internet radio stations. Written in Go, it uses the RadioBrowser API to discover stations and relies on FFmpeg tools for playback and optional recording. * ⚓ Siggy_-_terminal-based_client_for_the_Signal_messaging_service_- LinuxLinks⠀⇛ Siggy is a terminal-based client for the Signal messaging service that uses signal-cli as its messaging backend and presents conversations in a text user interface with an IRC- inspired look and feel. The application is designed for keyboard-driven use, offers vim-style modal editing, guides users through linking a Signal account as a secondary device with QR code pairing, and keeps local conversation data so message history, unread markers, and settings persist across sessions. This is free and open source software. * ⚓ lazyjira_-_terminal_user_interface_for_Jira_-_LinuxLinks⠀⇛ lazyjira is a terminal user interface for Jira designed to reduce the friction of working with tickets through the browser. It provides a fast, keyboard-driven interface for browsing issues and projects, reading ticket details, and carrying out common updates from a text-based application. This is free and open source software. * ⚓ uncover_-_quickly_discover_exposed_hosts_on_the_internet_-_LinuxLinks⠀⇛ Uncover is a command-line reconnaissance tool that helps you discover exposed internet-facing hosts by querying multiple external search engines and asset discovery services from one interface. It is designed for automation workflows, making it easy to feed queries from files or standard input, combine results with other security tools, and quickly surface systems that may warrant further investigation. This is free and open source software. ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣿⣧⣴⣾⠇⣀⠀⠀⠀⠀⠀⢀⠀⢿⣦⣀⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠆⠀⠀⠀⠀⠀⠀⠀⠿⠆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣽⣿⣧⣼⣿⣧⣴⣶⣶⡄⢿⣧⠀⣿⣿⣿⣿⡇⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣀⢳⡁⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⢿⣿⡯⢻⣿⡿⠿⠿⠿⠃⣼⡿⢀⣿⡿⢿⣿⡇⠀⣀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢼⣿⣿⣷⠀⠀⢰⠄⠘⠃⠀⠠⠀⢨⠟⠟⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡌⠻⣿⣯⠛⡁⠸⣶⡆⠀⠉⢹⣾⠿⢿⣿⣿⣿⠃⠉⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⢀⠀⣊⣽⣿⣿⣿⣾⣧⣷⣭⣴⣶⣦⣀⣴⠦⠀⠀⠀⠀⠀⢀⣤⣄⠀⢀⠀⠀⠀⠀⠹⢿⡆⠀⠀⠀⠀⠀⣿⡇⠀⠀⡀⠀⢠⣾⣿⢿⠋⠀⡀⣀⣦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⣂⣀⠞⠉⠉⠤⠈⢷⣀⢀⠤⠔⡄⣂⠰⠉⠀⠀⠀⣿⡇⠀⠂⡒⢠⣬⣽⣽⣉⣄⣸⣷⠿⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣽⣾⣿⣿⣿⣿⣬⣿⣿⣿⣶⣿⣿⣾⣇⣤⣾⣾⣿⣇⣳⣷⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⢽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣤⣤⣤⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠒⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣼⣿⣷⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣧⣟⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠰⢹⣿⣿⣿⣿⣿⣿⣿⡟⣻⣿⣿⣿⡛⠿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠆⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⠟⠫⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢈⡀⠳⠆⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⠂⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢝⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢐⡐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢤⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠯⡁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣈⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡙⠅⠈⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⣿⡞⠛⠭⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠛⠂⠠⠒⠀⠒⠀⠤⠀⠒⠂⠐⠒⠀⠀⠀⠀⠐⢻⡖⠶⠞⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠁⣀⣂⣿⡿⠋⢉⣻⣿⠟⠁⠀⠈⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠀⠀⠁⠀⠀⠀⢻⣿⣿⣟⣻⢿⣿⣿⠛⡿⠻⢟⠁⠉⠉⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠀⣿⣿⣷⣶⣾⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⠐⠀⠀⠐⠀⠀⠉⠻⣿⣿⣿⣿⣿⠆⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ䷩ 𝚕𝚒𝚗𝚎 882 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/04/09/FreeBSD_14_4_on_Raspberry_Pi_Zero_2W_and_OpenBSD_on_Motorola_88.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/04/09/FreeBSD_14_4_on_Raspberry_Pi_Zero_2W_and_OpenBSD_on_Motorola_88.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ FreeBSD 14.4 on Raspberry Pi Zero 2W and OpenBSD on Motorola 88000 Processors⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Apr 09, 2026 * ⚓ TuMFatig ☛ FreeBSD_14.4_on_Raspberry_Pi_Zero_2W⠀⇛ Not convinced lately with OpenBSD on this board , I went searching for another BSD OS to run on the Raspberry Pi Zero 2 W. According to the documentation, FreeBSD should do fine. Let’s have a look. Spoiler Alert: it does work nicely. * ⚓ Miod Vallat ☛ OpenBSD_on_Motorola_88000_processors⠀⇛ This allowed him to run a Luna-88K system using a PCMCIA wireless interface, which got demonstrated later that year at the OSC Conference. ䷩ 𝚕𝚒𝚗𝚎 921 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/04/09/Free_Libre_and_Open_Source_Software_Leftovers.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/04/09/Free_Libre_and_Open_Source_Software_Leftovers.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Free, Libre, and Open Source Software Leftovers⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Apr 09, 2026 * ⚓ Ruben Schade ☛ My_A–Z_toolbox:_ExifTool⠀⇛ That leaves us with Phil Harvey’s excellent ExifTool. It can do a tonne of stuff, but my primary use case is removing EXIF metadata before uploading an image to the interwebs. * § SaaS/Back End/Databases⠀➾ o ⚓ [Repeat] RedMonk ☛ Two_Years_of_Valkey_–_tecosystems⠀⇛ Two years ago last month, a group of former contributors to the Redis project announced their intention to collaborate instead on a competitive fork. Triggered by the decision to shift Redis away from the permissive open source BSD license to source available alternatives – the Redis Source Available License (RSALv2) and Server Side Public License (SSPLv1) – the new fork, Valkey, attracted attention without recent precedent. A lot has happened since, including the return to the project of its original author and the decision by Redis a little over a year after the relicensing to return to an open source license, albeit the copyleft AGPL rather than the more permissive [sic], original BSD. Given the two year anniversary, it’s worth taking stock of the two projects via their commit metrics. This is only one facet of the project’s health, obviously, and does not reflect usage, but as forks typically enter a decline phase shortly after their inception, comparing the two projects contributions should be a useful exercise. * § Content Management Systems (CMS) / Static Site Generators (SSG)⠀➾ o ⚓ Andrew Shell ☛ Working_on_the_RSS_Cloud_WordPress_Plugin_–_Andrew Shell's_Weblog⠀⇛ I’ve been continuing to work on the modern testing infrastructure so I can make sure the RSS Cloud plugin for WordPress is up to date. The maintainer rightfully wants to keep it as simple as possible, so I want to respect his wishes. * § Standards/Consortia⠀➾ o ⚓ Ruben Schade ☛ The_NMS_Ceefax_teletext_reproduction!⠀⇛ I’m just old enough to remember Teletext, the standard that encoded text information on standard analogue TV signals. Now thanks to Nathan Media Services and Alistair Cree, we can now interact with it again in the browser: [...] ䷩ 𝚕𝚒𝚗𝚎 1002 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/04/09/Games_New_Steam_Games_with_Native_GNU_Linux_Builds_Why_Windows_.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/04/09/Games_New_Steam_Games_with_Native_GNU_Linux_Builds_Why_Windows_.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Games: New Steam Games with Native GNU/ Linux Builds, Why Windows Users Should Become GNU/Linux Gamers, and More⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Apr 09, 2026 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Linux_gamers⦈_ * ⚓ Boiling Steam ☛ New_Steam_Games_with_Native_GNU/Linux_Builds,_including Wasteland_Bites_and_Stiff_Neck_-_2026-04-08_Edition⠀⇛ Between 2026-04-01 and 2026-04-08 there were 61 New Steam games released with Native GNU/Linux builds. For reference, during the same time, there were 451 games released for backdoored Windows on Steam, so the GNU/Linux versions represent about 13.5 % of total released titles. No major release in this week, but Wasteland Bites takes cooking games into a new spin with your customers being mutants and decayed humans of the post- apocalypse Wasteland. * ⚓ PC World ☛ Try_out_an_open-source_app_to_access_GeForce_Now,_while_you can⠀⇛ OpenNow is an unauthorized open-source client for Nvidia’s GeForce Now cloud gaming service, available on Windows, Mac, Linux, and Steam Deck. * ⚓ XDA ☛ Linux_gamers_didn't_do_anything_wrong,_but_they_might_pay_for Windows_piracy_anyway⠀⇛ Gaming on Linux has come a long way. Valve's Proton compatibility layer and the Steam Deck have done more for Linux gaming in the last few years than the previous two decades of community effort combined, and we've reached a point where the vast majority of single-player PC games run on Linux without much fuss. ProtonDB data suggests practically every Windows game works in some form on Linux now, and for a lot of people, that's more than enough to make the switch. * ⚓ Sentinel_Adds_Steam_Achievements_to_Non-Steam_Linux_Games⠀⇛ A new open-source tool called Sentinel brings achievement tracking to non-Steam games on Linux, pulling data from the Steam Web API and SteamHunters to fire real-time notifications. A Reddit user going by m0rpheus23 just dropped something that sits firmly at the intersection of two passionate but niche communities: achievement hunters and Linux gamers. The tool is called Sentinel, and as PC Gamer reports, it adds a fully functional achievement system to games played outside of Steam on Linux. * ⚓ Gamer Network Limited ☛ From_the_C:_to_the_/Mnt/s,_Linux_is_better_than ever_for_PC_gaming_–_and_easier_to_switch_to_from_Windows⠀⇛ A few months ago, I did something radical. For radical, picture me skateboarding ungainly while installing Linux - or, to be more precise CachyOS - on my PC. Windows 11 had just been bugging me too much. On top of Microsoft's forced AI implementation growing ever more obscene, I was starting to get unexplained slowdown; something that would usually just prompt a Windows reinstall, as I've done countless times all the way back to Windows Vista. However, prompted by my good friend (and writer at cheery RPS fanzine PC Gamer) Joshua Wolens deciding to boldly try out Linux, this time, I would not-so-boldly join him. What I've found is a genuinely fantastic OS: a real, viable alternative to Windows, and one that's far more accessible than it was just a few years ago. ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⠉⠉⠉⠙⠛⠛⠛⡛⣻⣿⣛⠿⠿⣿⣿⠿⠿⠿⢿ ⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠭⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⡀⢀⡀⠘⠀⠁⣀⢩⣭⣯⣾⡇⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⣤⣶⣶⣶⣦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⡍⢸⣿⣻⡟⠂⣆⠀⠀⠀ ⠀⠀⠀⠀⠐⠢⠀⣠⣿⣦⣴⣶⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠖⠀⠀⠘⢙⣼⡄⠀⠁⠀⠀⠄ ⠀⠀⠀⢀⡀⢰⣌⢙⣿⣿⡛⢉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠀⠀⠀⠀⠀⠀⠠⣤⠠⠐⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠖⡦⢹⠱⡄⠀⠀⠀⠀ ⡁⠀⠀⠀⠀⢨⡤⠠⠀⠀⠟⠀⢐⡂⠀⠀⠀⠀⣴⠞⠛⠳⣆⠀⠀⣰⣐⢂⣶⡔⠤⠤⠤⠄⠤⠤⠆⠀⢀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⣘⡁⢆⠙⡛⠚⠄⠀⣠⣤⣤ ⡅⠀⠤⢀⠄⠐⢆⠂⢀⣺⠂⠀⡘⠀⠀⠀⠀⠀⣿⡀⠀⠀⣼⠠⠄⠀⠀⠀⠀⠀⠂⣿⣦⣦⣿⣤⡤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⠇⠀⠀⠀⠀⠀⠀⠀⠰⣿⠷⠶⠇⠠⠤⣤⠤⠬⣭⣡ ⠡⡀⠀⠚⢀⠀⢶⠙⢫⠟⠿⣿⡦⡄⠀⠀⠀⠀⠈⠛⠒⠛⠁⢐⠒⠒⠒⠀⠃⠉⠍⣿⣿⣿⣼⣏⡀⠙⠛⠿⣟⣿⣯⣿⣿⣿⣿⣿⣿⣼⣻⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡄⡀⣶⣀⣀⣀⣀⣀⣉ ⣦⠂⠀⠀⠀⠀⢀⠀⠀⡄⠀⠰⢠⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⣶⡶⠂⠀⠀⠀⣿⣿⣿⣿⣿⣿⣾⠄⠀⠛⢫⣭⣿⣾⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣯⢞⢀⣸⣿⣿⣿⣿⣿ ⣹⣀⣀⣀⣤⠤⣶⡶⠒⠛⠛⢻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⣛⠓⠒⠂⢿⣿⣿⣿⣿⣿⣣⡆⠀⠀⠈⠉⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⡿⠛⣡⡦⠄⠈⢰⣿⣿⣿⣿ ⠟⢋⣋⢀⢠⣾⣯⣽⠀⠀⠀⠈⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠦⠭⢥⣄⡐⠒⢺⣿⣿⣿⣿⣿⣿⡃⢤⡤⠤⢮⡽⠿⠻⠿⠿⠿⠿⠿⠟⠛⠉⠉⠛⠉⠉⠀⣤⣄⠀⠀⠀⠀⠀⢈⠘⠰⠋⣥⣀⣤⣼⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡿⣆⣀⣀⠀⡀⢙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣒⣲⣶⣦⣤⣄⡘⣿⣿⣛⢻⢛⣈⡄⠄⠀⠤⠤⠄⠀⠒⣚⣛⣛⣛⣀⣈⣭⣥⣤⣤⣤⣤⡀⣿⡿⠀⠀⠀⠀⠀⢸⠆⠀⠈⠙⢘⡟⢟⣟⣿⣿⢿ ⣿⣿⣿⣿⣿⣿⣿⣏⠙⠃⠉⠠⠀⠠⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⢛⣝⣟⣉⠉⠉⠀⠀⣯⣭⣥⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⢟⡛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⣤⣶⣈⣀⠸⠿⠈⣽⡟⠃⢨ ⣿⣿⣿⣿⣿⣿⠞⣿⣆⡐⠀⠠⠀⠶⡾⠀⠀⠀⠘⠛⠀⠀⠀⠀⠸⡧⣯⣍⣁⣀⣀⠀⢟⣻⣛⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⣶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠿⣿⣿⣿⣶⣾ ⣿⣿⣿⣿⣿⣿⣧⣤⣭⣤⣀⣀⣤⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⠶⠤⠤⠄⠀⠀⢂⣒⣀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠒⠒⠛⠛⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⣭⣝⣛⣛⣛⣾⣶⠶⠿⣧⣼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣉⣉⠀⠀⠀⠀⠈⠿⠿⠖⠒⠛⠛⠍⠉⠀⠉⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣟⣿⣿⣿⣿⣿⣿⣟⣍⣩⣬⣤⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡿⢿⡿⠿⠿⠛⢛⣋⣉⣥⣤⣤⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⣥⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢀⠀⢀⡀⠀⠠⠤⠀⠀⢀⡀⠂⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⠀⠐⠀⠀⠈⠘⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠄⠀⠐⠆⠀⠉⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢙⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠐⢠⠀⠀⠢⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠑⠓⠛⢿⣿ ䷩ 𝚕𝚒𝚗𝚎 1124 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/04/09/GNU_Projects_GNU_Health_Control_Center_5_0_3_and_Parted_3_7_Rel.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/04/09/GNU_Projects_GNU_Health_Control_Center_5_0_3_and_Parted_3_7_Rel.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ GNU Projects: GNU Health Control Center 5.0.3 and Parted 3.7 Released⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Apr 09, 2026 * ⚓ GNU ☛ health_@_Savannah:_GNU_Health_control_center_5.0.3_released⠀⇛ Dear community I'm happy to announce the release of the gnuhealth-control version 5.0.3 This version fixes some dependency issues in the context of the the initial HIS instance creation. * ⚓ GNU ☛ parted_@_Savannah:_parted-3.7_released_[stable]⠀⇛ I have released parted 3.7 Here are the compressed sources and a GPG detached signature[*]: [...] ䷩ 𝚕𝚒𝚗𝚎 1162 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/04/09/I_ditched_Windows_for_SteamOS_on_my_PC_and_gaming_is_way_better.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/04/09/I_ditched_Windows_for_SteamOS_on_my_PC_and_gaming_is_way_better.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ I ditched Windows for SteamOS on my PC, and gaming is way better now⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Rianne Schestowitz on Apr 09, 2026 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇SteamOS⦈_ Quoting: I ditched Windows for SteamOS on my PC, and gaming is way better now — I've been a big fan of SteamOS for quite a while now, especially on my handheld gaming PC. And seeing as when I'm not working, I'm playing games on my PC, I figured that it was time to give it a test run on my desktop. While I've tried Nobara and other gaming-centric Linux distros in the past, I always tend to flock back to SteamOS. After installing it on my desktop, I'm reminded exactly why I love using SteamOS as my gaming-centric Linux installation. While it may not be as endlessly customizable as other distros that I've tried, sometimes you just want things to work like you already know and trust. Read_on ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠐⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣾⠭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢿⣶⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣛⣿⣯⣩⣉⣩⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣉⣉⣿⣿⣿⣇⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠾⡿⢻⣿⣽⣹⣿⣿⣿⣿⢻⣿⣿⣿⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣻⣶⣶⣒⠀⠀⢨⣿⣿⣿⣽⣿⣿⣿⡿⠿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣜⣒⣒⡚⠒⠃⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡓⡜⣯⣽⡟⠀⠀⢸⣿⣿⡿⠿⠟⠋⠁⠀⢠⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡇⠶⢸⣿⢰⣧⢸⣿⣿⣿⡗⣒⣒⣒⣂⡀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣛⣂⠀⠀⠈⠩⣇⠀⠀⣀⡤⠶⠚⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣇⣂⣷⣈⣀⡀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠍⠉⠙⠒⠀⠀⠀⣠⡴⠒⠋⠁⢀⣀⣤⣤⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⢄⣀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⠽⠿⠏⠡⣴⣼⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣀⡀⠀⠀⠀⣨⣾⣿⣤⣶⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠉⠀⠀⠀⠈⠉⠲⠀⢹⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡭⠭⠭⠉⢡⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠄⠀⠀⠀⠀⠀⠼⠁⢺⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⠐⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣲⣸⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⢭⡭⡭⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣡⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠭⠭⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠄⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⡖⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣻⣭⣭⣿⡿⠿⠿⠿⠿⠿⠿⣟⣛⣛⣻⣷⡶⠂⣀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣄⠀⠀ ⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⡿⣟⣫⣵⣿⣿⣿⣾⡿⠿⠿⢿⣿⣿⣻⡿⠯⠭⠿⠿⠟⠀⢀⠄⠀⠈⠓⢶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠿⠯⠥⠀⠀⠀⠀⠀⠀⠉⠀⣀⣀⠀⢀⣀⣀⣀⣠⣤⣤⣄⠀⠀⣴ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠛⠛⠛⠛⠉⠙⠋⠉⠁⠀⠀⠀⠀⡀⠀⡀⢠⣶⣶⣴⣶⣿⣾⣿⣿⣿⣿⣿⣿⢉⣍⡀⠰⣶⠄⠀⠘⠻⢀⡻ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠉⠉⠉⠁⠀⣀⣀⡀⢠⣤⣤⣀⣴⣶⣦⠄⠐⠀⠐⠀⠈⠈⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⠐⠒⠈⠀⠀⡀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣯⣽⣯⣾⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣀⣠⣄⣠⣤⣶⣤⣶⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣤⣤⣤⣿ ⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠋ ⣤⡶⠞⠛⠋⢁⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⠀⠀ ⠁⠀⠀⠀⠘⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠒⠒⠠⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠆⠀⠀⢀ ⠀⣿⣷⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣛⣻⣏⠩⣭⣀⣄⡙⠈ ⠀⠉⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠰⠔⠒⠊⠃⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⠛⣛⣹⠉⠉⠀⠀⠀⠀⠀⣠⡺⢳⣿⡼⢿⣿⣇⣀ ⠀⠀⠠⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⡀⢠⣤⡍⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⢛⡋⠉⣉⠀⠄⠆⠂⠋⠒⠉⠁⠀⠀⠀⠀⠀⠀⢸⣁⣠⣭⣿⣿⣿⣿⣿⣿ ䷩ 𝚕𝚒𝚗𝚎 1228 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/04/09/Introducing_our_Art_Contest_winner.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/04/09/Introducing_our_Art_Contest_winner.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Introducing our Art Contest winner!⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Rianne Schestowitz on Apr 09, 2026 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇“Welcome_Screen”⦈_ Quoting: Introducing our Art Contest winner! | Mageia Blog (English) — Now that voting for the Mageia 10 art competition has closed, we are delighted to present what will be the official desktop wallpaper for our new release. Many thanks to our contributor Davide Dallara for this excellent work. In his words, our new desktop background depicts “our beloved Mageia, born of the entire team that makes this great distro possible, alongside Tux, the Linux mascot, and the bubbling cauldron that represents the Mageia development branch”. Read_on ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢉⠉⠉⠉⢉⣾⣿⣿⣿⣿⣿⣯⡎⠻⠟⢁⡋⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠑⠉⠉⠛⠛⠊⠁⠒⠚⠉⠁⠀⠔⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣦⠀⡰⠁⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⡯⠊⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠠⠭⠭⠍⠉⠋⣡⡴⠊⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⢰⣶⣤⣄⣀⠀⠈⠀⣀⣀⣤⣴⡆⠀⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣼⣿⣿⣿⣷⠆⢠⠸⣼⣻⣿⣿⣧⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ䷩ 𝚕𝚒𝚗𝚎 1288 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/04/09/KDE_Linux_is_the_purest_form_of_Plasma_I_ve_tested_but_the_inst.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/04/09/KDE_Linux_is_the_purest_form_of_Plasma_I_ve_tested_but_the_inst.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ KDE Linux is the purest form of Plasma I've tested - but the install isn't for the meek⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Rianne Schestowitz on Apr 09, 2026 Quoting: KDE Linux is the purest form of Plasma I've tested - but the install isn't for the meek | ZDNET — Over the past few years, I've become a big fan of KDE Plasma. Not only has it become one of the most stable Linux desktop environments, but it's also incredibly user-friendly, fast, and beautiful. But did you know that most Linux distributions present KDE Plasma with a version of the desktop usually customized to meet the aesthetic and functionality of that particular OS? For example, when you use KDE Plasma on Kubuntu, it looks and feels different from what the KDE Plasma developers created. Read_on ䷩ 𝚕𝚒𝚗𝚎 1324 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/04/09/Krita_5_3_1_1_Released_Android_only.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/04/09/Krita_5_3_1_1_Released_Android_only.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Krita 5.3.1.1 Released (Android- only)⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Rianne Schestowitz on Apr 09, 2026 Quoting: Krita 5.3.1.1 Released (Android-only) | Krita — Krita 5.3.1.1 is an Android-only fix for 5.3.1. It is exactly the same as Krita 5.3.1, but with two fixes: fixed a crash on Android 12 and older when trying to access any text controls fix stylus workarounds for Xiaomi and OnePlus to work properly Check out the release notes for a full overview of all the new features in Krita 5.3 and 6.0. Note: this release is only relevant for Android, so only Android APK's and source archives are available. You only need the source archive when building for Android yourself. Read_on ䷩ 𝚕𝚒𝚗𝚎 1365 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/04/09/Linux_centric_Devices_and_Open_Hardware_Stories.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/04/09/Linux_centric_Devices_and_Open_Hardware_Stories.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Linux-centric Devices and Open Hardware Stories⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Apr 09, 2026 * § Devices/Embedded⠀➾ o ⚓ Dark Reading ☛ Iran_Disrupts_US_Critical_Infrastructure_Via Exposed_PLCs⠀⇛ Iran-affiliated threat actors are disrupting US critical infrastructure through attacks on Internet-exposed operational technology (OT) devices across numerous sectors, the US government is warning. o ⚓ Linux Gizmos ☛ RealSense_ID_Pro_F500_Combines_Depth_Sensing_and On-Device_Biometrics⠀⇛ RealSense has introduced the RealSense ID Pro F500, a facial authentication module designed for access control, kiosks, and identity verification systems. The solution combines depth sensing, vision processing, and local computation to support secure biometric authentication without relying on cloud-based processing. o ⚓ Yonathan Gashu ☛ ygashu_·_From_UART_to_Root:_Vendor_Shell_Escape on_a_Uniview_IP_Camera⠀⇛ But the thing that immediately stood out to me was the unpopulated 4-pin header in the corner labeled J4. Unpopulated headers on embedded hardware are usually there for good reason, whether that’s debugging, manufacturing, or both. The next step was probing each pin with a multimeter to map the pinout. * § Open Hardware/Modding⠀➾ o ⚓ CNX Software ☛ WeAct_STM32U585CIU6_Core_Mini_–_An_$8_STM32U5 board_supported_by_MicroPython_v1.28⠀⇛ While checking out MicroPython v1.28 changelog, I noticed a board from WeAct Studio based on ST’s STM32U5 Cortex- M33 microcontroller: the WeAct STM32U585CIU6 Mini Core board (WEACTSTUDIO_MINI_STM32U585 in MicroPython code). o ⚓ Arduino ☛ The_Arduino_Marketing_Team_receives_Best_Digital Strategy_award_for_“From_Blink_to_Think”⠀⇛ At Arduino, our mission has always been clear: make complex technology accessible to everyone. But accessibility also means reaching people, inspiring them, and helping them understand what’s possible. o ⚓ CNX Software ☛ Flash_Bee_–_An_ESP32-C3-based_DIY_handheld lightning_detector⠀⇛ Flash Bee is an easy-to-make DIY handheld lightning detector based on off-the-shelf parts such as the XIAO ESP32C3 board and the Round Display for XIAO, as well as a 3D-printed enclosure. The design relies on the AMS AS3935 Franklin lightning sensor that’s been around for years, and found in kits like Sparkfun’s Arduino IoT weather station, which is capable of detecting lightning up to 40 km away with 1km accuracy. While it’s not quite new technology, I found the Flash Bee design to be rather cute and convenient, and it looks really easy to reproduce. o ⚓ Hackaday ☛ Bending_Faux-Neon_LEDs_Make_For_Animations_Glass_Tubes Can’t_Match⠀⇛ Back in the day, you’d have needed dozens of tubes for a flickery animation, but [David] figured that since these LED strips are flexible, why not flex them? He’s using addressable LEDs — WS2812s, specifically — so activating and deactivating the pupil of the eye is easy-peasy. Opening and closing the lid is accomplished with a geared motor driven by a TB6612 driver turning a barrel cam. The ends of the stiff LED strip being brought together and pulled apart result in the blinking effect here, but as [David] points out you’re hardly limited that specific motion. There’s a whole world of Tron-like glowing animatronics that can be created with this technique. Code and STLs are available on GitHub, though, if you want to replicate the eye exactly. o ⚓ Hackaday ☛ Espressif’s_New_ESP32-S31:_Dual-Core_RISC-V_With_WiFi 6_And_GBit_Ethernet⠀⇛ In a move that’s no doubt going to upset and confuse many, Espressif has released its newest microcontroller — the ESP32-S31. The confusing part here is that the ESP32- S series was always the one based on Tensilica Xtensa LX7 cores, while the ESP32-C series was the one using RISC- V cores. o ⚓ Ruben Schade ☛ Assembling_a_new_study_desk_from_shelves⠀⇛ But then a thought dawned on me: is a phrase with seven words. AAAAAAH! I was walking past a line of IKEA desks, and noticed they were at least 30 cm narrower than the kitchen tables we were using as desks. We scurried back to the shelving department, and noted a BILLY bookshelf case was… about 30 cm deep. o ⚓ Electropages ☛ Secure_Linux_edge_platform_for_automotive_and industrial_applications⠀⇛ Kvaser has announced Kvaser Edge, an open, secure Linux‑based edge computing platform that transforms how automotive and industrial teams collect, process, and act on data. Designed for harsh environments and real‑time performance, it runs analytics directly where data is generated: on the vehicle, test bench, or machine. ䷩ 𝚕𝚒𝚗𝚎 1517 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/04/09/LWN_is_Promoting_LLM_Slop_Makes_Excuses_for_Age_Verification_Su.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/04/09/LWN_is_Promoting_LLM_Slop_Makes_Excuses_for_Age_Verification_Su.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ LWN is Promoting LLM Slop, Makes Excuses for "Age Verification" (Surveillance), Promotes Rust (Microsoft GitHub)⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Apr 09, 2026 * § Slop Inside Kernels⠀➾ o ⚓ LWN ☛ The_role_of_LLMs_in_patch_review [Ed: Slop entering Linux little by little]⠀⇛ Discussion of a memory-management patch set intended to clean up a helper function for handling huge pages spiraled into something else entirely after it was posted on March 19. Memory-management maintainer Andrew Morton proposed making changes to the subsystem's review process, to require patch authors to respond to feedback from Sashiko, the recently released LLM-based kernel patch review system. Other sub-maintainers, particularly Lorenzo Stoakes, objected. The resulting discussion about how and when to adopt Sashiko is potentially relevant to many other parts of the kernel. Morton began by saying that the current way Sashiko integrates into the memory-management workflow isn't working. He merges patches to his tree, and ""then half a day later a bunch of potential issues are identified."" Morton stated that he was going to further increase the lag between seeing a patch set on the mailing list and merging it to his tree, to give Sashiko time to produce feedback and patch authors time to respond to it. He also wanted its reviews distributed to a wider audience — partly to better determine how useful its comments are, which he is ""paying close attention to"". o ⚓ LWN ☛ Vibe-coded_ext4_for_OpenBSD [Ed: Slop makes worthless code that is unmaintainable, but LWN is connected to LF, which is paid by Microsoft et al to market slop]⠀⇛ A number of projects have been struggling with the question of which submissions created by large language models (LLMs), if any, should be accepted into their code base. This discussion has been further muddied by efforts to use LLM-driven reimplemention as a way to remove copyleft restrictions from a body of existing code, as recently happened with the Python chardet module. In this context, an attempt to introduce an LLM-generated implementation of the Linux ext4 filesystem into OpenBSD was always going to create some fireworks, but that project has its own, clearly defined reasons for looking askance at such submissions. * § Applications⠀➾ o ⚓ LWN ☛ Pandoc:_a_workhorse_for_document_conversion_[LWN.net]⠀⇛ Pandoc is a document-conversion program that can translate among a myriad of formats, including LaTeX, HTML, Office Open XML (docx), plain text, and Markdown. It is also extensible by writing Lua filters that can manipulate the document structure and perform arbitrary computations. Pandoc has appeared in various LWN articles over the years, such as my look at Typst and at the importance of free software to science in 2025, but we have missed providing an overview of the tool. The February release of Pandoc 3.9, which comes with the ability to compile the program to WebAssembly (Wasm), allowing Pandoc to run in web browsers, will likely also be of interest. * § Distributions and Operating Systems⠀➾ o § IBM⠀➾ # ⚓ LWN ☛ Objections_to_systemd_age-attestation_changes_go overboard [Ed: One person from Red Hat (Joe Brockmeier) covering up for another person from Red Hat]⠀⇛ In early March, Dylan M. Taylor submitted a pull request to add a field to store a user's birth date in systemd's JSON user records. This was done to allow applications to store the date to facilitate compliance with age-attestation and -verification laws. It was to be expected that some members of the community would object; the actual response, however, has been shockingly hostile. Some of this has been fueled by a misinformation campaign that has targeted the systemd project and Taylor specifically, resulting in Taylor being doxxed and receiving death threats. Such behavior is not just problematic; it is also deeply misguided given the actual nature of the changes. Age-attestation and -verification laws that place requirements on operating-system providers have passed in California and Brazil, and are being discussed in many other states and locations. This has led a number of Linux distributions to consider ways that they can comply with the laws if necessary. One idea that is being worked on is to add parental controls to the XDG Accounts portal which is a mechanism that allows applications to query for information about users, such as their name or avatar image. It can gather this information from various data sources, including systemd. * § Anti-Copyleft⠀➾ o § Programming/Development⠀➾ # § Rust⠀➾ # ⚓ LWN ☛ Rust's_next-generation_trait_solver [Ed: LWN promoting the Microsoft-controlled Rust, as usual]⠀⇛ Rust's compiler team has been working on a long-term project to rewrite the trait solver — the part of the compiler that determines which concrete function should be called when a programmer uses a trait method that is implemented for multiple types. The rewrite is intended to simplify future changes to the trait system, fix a handful of tricky soundness bugs, and provide faster compile times. It's also nearly finished, with a relatively small number of remaining blocking bugs. * § Slop, Entrapment (Microsoft GitHub) and Security Failures⠀➾ o ⚓ LWN ☛ The_many_failures_leading_to_the_LiteLLM_compromise⠀⇛ This story starts with a different project, Trivy, which is a widely used security scanner, distributed under the Apache-2.0 license. As is often the case with these scanners, Trivy releases normally include tests for newly discovered vulnerabilities, so projects that depend on Trivy to detect potential security problems in their code have every reason to want to rerun their scans when a new release is made. Many projects hosted on GitHub thus set up an action so that, when a new release tag shows up for Trivy, new scans are automatically run, just in case Trivy has any new problems to point out. On March 20, Paul McCarty announced that Trivy had been compromised; Philipp Burckhardt wrote up a detailed report on what was done. Somebody had managed to obtain credentials giving write access to the Trivy repository. This attacker then placed commits with malware in that repository, but they did so without changing any existing branches, avoiding the notifications that would have normally gone out in response to such changes. Instead, a large number of release tags were force-pushed to point to the new commits, which was sufficient to cause other projects to perform automatic Trivy runs. The Trivy malware was of the information-stealing variety; whenever it ran within a project's context, it would sweep up everything it could get its virtual hands on and send it back to the attackers. Trivy itself was never the primary target; it was just a stepping stone giving access to other projects of interest. Just how many projects this exploit was able to hit may not become clear for some time. ䷩ 𝚕𝚒𝚗𝚎 1719 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/04/09/New_Issue_of_Linux_Magazine_306.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/04/09/New_Issue_of_Linux_Magazine_306.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ New Issue of Linux Magazine, #306⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Apr 09, 2026 * ⚓ Introduction⠀⇛ This month in GNU/Linux Voice and Elvie. * ⚓ Darktable_5.4's_Scene-Referred_Workflow⠀⇛ Darktable 5.4's scene-referred workflow promises predictable results across different imaging outputs, but it requires a shift in perspective. We help you navigate this image- processing pipeline. * ⚓ Display_Web_Traffic_on_a_World_Map⠀⇛ To discover where the traffic to his website comes from, Mike Schilli displays it live on an interactive world map. * ⚓ Exploring_the_OpenWrt_router_OS⠀⇛ The OpenWrt router OS includes features you won't find with over-the-counter home routers – and you can use it on old hardware that the vendor has abandoned. * ⚓ The_Latest_Quirky_and_Creative_GNU/Linux_Distros⠀⇛ This month we explore Lilidog 26.02.06, KaOS 2026.02, NuTyX 26.02.2, and ParrotOS 7.1. * ⚓ Where_to_Start?⠀⇛ A look at its origins shows GNU/Linux isn't necessarily meant to be user-friendly for novices. * ⚓ Stash_Interesting_Reads_in_Readeck⠀⇛ Don't let interesting articles and blog posts linger in your browser's bookmarking purgatory. Use Readeck to read and manage them instead. * ⚓ Divorcing_KWallet_from_KMail⠀⇛ KDE's password manager, KWallet, can be an annoyance. While it can't be completely disabled, the nuisance can be minimized. * ⚓ Comparing_Four_Leading_Immutable_Distros⠀⇛ Immutable GNU/Linux distributions protect your system files in ways that an ordinary distro can't. We take a look at four promising alternatives: Aurora, blendOS, NixOS, and Vanilla OS. * ⚓ Oh_Why_Not⠀⇛ We are all accustomed to rapid evolution of the high-tech space, and I'm one of many journalists who have made a career out of talking about it. Computers were an important accessory when I first started doing this, then they became a necessary accessory, and then, for many industries, the server room became the centerpiece for everything – everything else was an accessory as long as the servers kept churning. * ⚓ Keep_Your_Digital_Comics_in_Easy_ Reach_with_Komga⠀⇛ Use the Komga comic server to organize and access your digital comic collection. * ⚓ Keep_Files_in_Sync⠀⇛ FreeFileSync and Syncthing let you keep your files in sync between two computers on your local network or across the Internet. * ⚓ Sparkling_Gems_and_New_Releases_from_the_world_of_Free_and_Open_Source Software⠀⇛ This month we explore the top FOSS, including the latest version of the KDE app ecosystem and Firefox browser, a font downloader, and an orbital game that's out of this world. * ⚓ Plug-and-Play_System_Monitor_for_Rasp_Pi_and_Others⠀⇛ A tiny screen plugged into a USB port displays current performance data for your Raspberry Pi, as well as most other machines that can run a Python script. * ⚓ Note-Taking_App_for_GNU/Linux_Desktop⠀⇛ You don't need a complex, feature-packed app to take notes. Iotas is a simple but flexible package for recording your ideas, important information, and more. * ⚓ Updates_on_Technologies,_Trends,_and_Tools⠀⇛ In the news: UN Creates Open Source Portal; Latest GNU/Linux Kernel RC Contains Changes Galore; Nitrux 6.0 Now Ready to Rock Your World; 'Linux' Foundation Reports that Open Source Delivers Better ROI; Keep Android Open; Kernel 7.0 Now in Testing; Introducing matrixOS, an Immutable Gentoo-Based GNU/ Linux Distro; and Chaos Comes to KDE in KaOS. * ⚓ Setting_up_a_home_desktop_system_with_FreeBSD⠀⇛ FreeBSD is steady and stable – will it work as a desktop system? * ⚓ Creating_a_Status_Dashboard_for_Your_Home_Server⠀⇛ If you run a VPS or a home server, you might like to know the status of your services. Gatus provides you with a status dashboard and sends you alerts when something's amiss. * ⚓ Raspberry_Pi_Imager_2.0:_Update_for_the_Official_Installer⠀⇛ Raspberry Pi Imager 2.0 features a modern interface, cloud- init, and Raspberry Pi Connect. Installation, configuration, and headless operation are now easier to implement. * ⚓ kernel_News⠀⇛ Chronicler Zack Brown reports on compiler optimizations and compatibility. ䷩ 𝚕𝚒𝚗𝚎 1896 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/04/09/Openwashing_Anthropic_Buys_PR_Promotion_of_Slop_From_Apache_Sof.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/04/09/Openwashing_Anthropic_Buys_PR_Promotion_of_Slop_From_Apache_Sof.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Openwashing: Anthropic Buys PR/Promotion (of Slop) From Apache Software Foundation and 'Linux' Foundation, PyTorch Foundation Likewise, Facebook Pretends Private Models Are 'Open'⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Apr 09, 2026 * ⚓ Unicorn Media ☛ Does_Acting_Like_Good_Guys_Actually_Make_Anthropic_Good Guys?⠀⇛ Anthropic just dropped $1.5 million on the Apache Software Foundation. Is it paying back the open source world -- or buying goodwill? * ⚓ It's FOSS ☛ Anthropic_Just_Handed_Apache_$1.5M_to_Secure_the_Open Source_Stack_Hey_Hi_(AI)_Depends_On⠀⇛ Apache Software Foundation's Ruth Suehle says this kind of sustained investment is what keeps critical open source up and running. * ⚓ It's FOSS ☛ PyTorch_Foundation_Expands_Its_Open_Source_Hey_Hi_(AI) Portfolio_With_Helion_and_Safetensors⠀⇛ Meta's Helion and Hugging Face's Safetensors are now hosted projects under the PyTorch umbrella. * ⚓ New York Times ☛ Meta_Unveils_New_Hey_Hi_(AI)_Model,_Its_First_From_the Superintelligence_Lab⠀⇛ The model, Muse Spark, performed better than Meta’s previous Hey Hi (AI) models but lags rivals on coding ability. * ⚓ The Register UK ☛ Meta's_new_model_is_as_open_as_Zuckerberg's_private school⠀⇛ Meta's decision not to release Muse Spark's weights comes in stark contrast to Zuckerberg's earlier position that "open source AI represents the world's best shot at harnessing this technology to create the greatest economic opportunity and security for everyone." ䷩ 𝚕𝚒𝚗𝚎 1960 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/04/09/PipeWire_1_6_3_Improves_RAOP_Compatibility_to_Make_It_Work_on_M.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/04/09/PipeWire_1_6_3_Improves_RAOP_Compatibility_to_Make_It_Work_on_M.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ PipeWire 1.6.3 Improves RAOP Compatibility to Make It Work on More Devices⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Marius Nestor on Apr 09, 2026 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇PipeWire⦈_ Coming three weeks after PipeWire 1.6.2, the PipeWire 1.6.3 release is here to align RTP timestamps to make RAOP work on more devices, avoid crashes in RTP streams because of concurrent event emission, and avoid MIDI conversions to and from UMP. PipeWire 1.6.3 also avoids loading plugins from absolute paths that aren’t in the search path, avoids OOB reading in the mix matrix, makes sure the timebase callback for JACK is never called with 0 frames, and increases the notify queue for JACK to avoid losing notifications. Read_on ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣏⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢾⡿⣧⣿⠲⣷⢺⡇⠀⠀⢸⣿⣿⣿⠀⢠⡄⠘⡇⢸⡇⢠⡄⠈⡏⠀⠀⠈⣧⠀⠇⠀⠛⠀⡇⠀⡇⠀⣤⠋⠀⠄⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣧⠿⣿⡴⣯⠾⠃⠀⠀⢸⣿⣿⣿⠀⢈⣁⣼⣇⣸⡇⢈⣁⣠⣷⣀⣉⣩⣿⣄⣀⣧⣀⣸⣇⣀⣇⣀⣿⣧⣈⣉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣼⡇⠀⠈⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣤⣼⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ䷩ 𝚕𝚒𝚗𝚎 2017 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/04/09/Programming_Leftovers.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/04/09/Programming_Leftovers.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Programming Leftovers⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Apr 09, 2026 * ⚓ Rlang ☛ Collaborating_between_Bioconductor_and_R-universe_on Development_of_Common_Infrastructure⠀⇛ * ⚓ [Old] Feldera ☛ Nobody_ever_got_fired_for_using_a_struct⠀⇛ When a few variables belong together, we put them in a struct. Programmers do this automatically without thinking about it much. And most of the time it's the right choice. Structs are simple, fast, and predictable. But once in a while they break down. This is the story of one of those cases. * ⚓ Andrew Nesbitt ☛ Package_Security_Problems_for_AI_Agents⠀⇛ I went through the recent OWASP Top 10 for Agentic Applications and pulled out the scenarios related to package management, which turn up in all ten categories and don’t sort neatly into any one of them, since a typosquatted MCP server is simultaneously a name attack, a registry attack, and a metadata poisoning vector. * ⚓ Simon Hartcher ☛ Applying_"Programming_Without_Pointers"_to_an_mbox indexer_using_Zig⠀⇛ I must have watched Programming without pointers (or PWP) roughly 10 times by now. In garbage collected languages where memory allocations are mostly invisible, it can be so easy to forget that memory allocations are often poison for high performance software. In the video, Zig’s creator Andrew Kelley shows us how to structure our programs so that they only need to do minimal memory allocations, reducing the number of total pointers that we need to manage. Memory allocations are expensive, so reducing them can improve the overall complexity of our programs. I think that the pattern of PWP can make the code a little bit more complex if you’re not used to writing code that way. But once you’re used to it, I think that complexity can go away as you’ll recognise the pattern when you see it. Here’s how I applied it to a real problem that I had. * § Python⠀➾ o ⚓ [Old] Polars ☛ Multiprocessing⠀⇛ TLDR: if you find that using Python's built-in multiprocessing module together with Polars results in a Polars error about multiprocessing methods, you should make sure you are using spawn, not fork, as the starting method: [...] o ⚓ [Old] Elementl Inc ☛ What_Is_Multiprocessing⠀⇛ Multiprocessing refers to a paradigm where multiple processes are employed to execute different tasks simultaneously in order to optimize the execution time and improve the efficiency of a pipeline, particularly for large volumes of data or heavy compute requirements. This is achieved using the multiprocessing module in Python which allows the creation of process-based parallelism. Here are some important points about multiprocessing in Python: [...] o ⚓ [Old] Martin Mirakyan ☛ Thread_Pools_and_Process_Pools_in_Python_ (75/100_Days_of_Python)_|_by_Martin_Mirakyan_|_Medium⠀⇛ When using multiprocessing in Python, it’s important to consider the number of processes you create versus the number of CPUs available on your machine to achieve the best performance. o ⚓ Towards Dev ☛ What’s_the_Best_Way_to_Handle_Concurrency_in Python:_ThreadPoolExecutor_or_asyncio?⠀⇛ Coming from Go to Python, learning multithreading and async programming model was nothing short of unpleasant for me. A part of that may have something to do with me not having any respect for Python’s syntax but mostly because Python’s GIL (Global Interpreter Lock) which controls resource access for concurrency scenarios, is dumb. In Go, I can simply specify go primitive in front of any synchronous function et. voila. Python is not that and the implementation of asyncio library seemed like a crazy talk. On top of that my existing code base was fully synchronous (like a regular human being) and I was too lazy to covert a whole bunch of things just to run some functions parallelly. So yeah, blah blah blabbitty- blah, TL;DR there are two built-in libraries that can get you through most of your day-to-day needs — o ⚓ Bruce Schneier ☛ Python_Supply-Chain_Compromise⠀⇛ There are a lot of really boring things we need to do to help secure all of these critical libraries: SBOMs, SLSA, SigStore. But we have to do them. * § Java/Golang⠀➾ o ⚓ The New Stack ☛ In_the_AI_Age,_Java_is_More_Relevant_Than_Ever⠀⇛ Java is the language used throughout enterprise platforms: ERPs, your ecommerce backends, analytics, logistics, and business workflows. You have decades of code, build pipelines, deployment practices, and operational runbooks all built around the JVM. When it comes to a language for AI though, your first thought might be Python, Node.js and TypeScript, or even Go. When you’re figuring out what AI features are useful to add to those critical enterprise systems, it may well make sense to experiment in a language like Python. But when it’s time to move from experimentation to production, Java is ready for building AI – and the AI tools that are speeding up developers across the industry are now ready for Java too. o ⚓ Vikash Patel ☛ Part_2:_Decoupling_the_Renderer:_Terminal_to Raylib_in_One_Interface_|_Lorbic⠀⇛ If your game logic knows about OpenGL, your architecture has failed. This post dissects the Interface Segregation Principle in Go, demonstrating how the Derelict Facility engine swapped an ANSI terminal renderer for hardware- accelerated Raylib without changing a single line of game simulation code. o ⚓ Vikash Patel ☛ Part_3:_Casting_Shadows_Without_Trigonometry:_The Beauty_of_Integer_Math_|_Lorbic⠀⇛ To calculate Field of View in a grid-based game engine, you have to cast rays. The naive approach uses heavy floating-point trigonometry. This post explores Bresenham's Line Algorithm: a 60-year-old technique from the era of hardware plotters that draws perfect lines using only integer addition and comparison. o ⚓ Blain Smith ☛ Building_Go_APIs_with_Huma,_sqlc,_and_Goose⠀⇛ I've been building an API recently with a stack that I think hits a sweet spot of just enough structure to keep a team productive, not so much that you're fighting the tools. The stack is Huma for the HTTP layer, sqlc for database queries, and Goose for migrations. Each tool does one thing well and stays out of your way for everything else. o ⚓ Andrew Nesbitt ☛ Who_Built_This?⠀⇛ Michael Stapelberg wrote last week about Go’s automatic VCS stamping: since Go 1.18, every binary built from a git checkout embeds the commit hash, timestamp, and dirty flag, queryable with go version -m or runtime/ debug.ReadBuildInfo() at runtime. His argument is that every program should do this, so you can always answer “what version is running in production?” without guessing. Go is unusual in doing this by default, and the rest of the package management landscape varies wildly in how it handles this, if it handles it at all. o ⚓ Jakub Ciolek ☛ cloud_security,_system_engineering_and_compilers⠀⇛ Early in March, I reported two compiler bugs affecting Go releases up to 1.26.1 which broke the Go memory safety guarantees using only safe Go code. This means the proof-of-concepts did not import unsafe, did not use CGO and did not rely on custom assembly nor data races. Using specially constructed code, I was able to turn both bugs into control-flow hijack, and with the loop bug I also got execution of injected instructions. * § Rust⠀➾ o ⚓ Rust Weekly Updates ☛ This_Week_In_Rust:_This_Week_in_Rust_646⠀⇛ Hello and welcome to another issue of This Week in Rust! ䷩ 𝚕𝚒𝚗𝚎 2257 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/04/09/Red_Hat_Summit_2026_and_Red_Hat_Trying_Hard_to_Sell_Slop_to_Hel.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/04/09/Red_Hat_Summit_2026_and_Red_Hat_Trying_Hard_to_Sell_Slop_to_Hel.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Red Hat Summit 2026 and Red Hat Trying Hard to Sell Slop (to Help IBM Fake Novelty)⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Apr 09, 2026 * ⚓ Red Hat Official ☛ What’s_new_at_Red_Hat_Summit_2026⠀⇛ The expo hall is your hub for 1-on-1 access to the experts building the future of IT. This year, we’re introducing lightning labs: 20-minute self-service sessions right in the hall that cover our four pillar products—Red Hat Enterprise Linux, Red Hat AI, Red Hat OpenShift, and Red Hat Ansible. While you're there, you can visit our expanded product booths, explore our new AI quickstarts (ready-to-run, industry- specific use cases), or find a spot to refuel in one of our dedicated networking lounges. * ⚓ Red Hat Official ☛ Navigating_the_Mythos-haunted_world_of_platform security [Ed: Red Hat pushing slop, as usual]⠀⇛ This dramatically compounds and expands the outsize role currently played by AI-driven vulnerability scanning both in corporate IT security teams and open source communities. Mythos, however, represents more than a deluge of AI vulnerability reports; it’s an avenue to potentially industrialize cyberattacks. It is positioned to lower the barrier to entry for sophisticated bug research and chaining related vulnerabilities. As an industry, we cannot react to this shift with panic; instead, we need to reinforce the need for system resilience through context, skill and, ultimately, using AI ourselves. * ⚓ Red Hat Official ☛ MCP_security:_Logging_and_runtime_security_measures [Ed: Red Hat pushing slop, as usual]⠀⇛ As discussed in our previous blog post, MCP security: Implementing robust authentication and authorization, an important aspect of MCP security is the ability to monitor autonomous agent behaviour and identify potential threats in real-time. By maintaining a detailed audit trail of tool invocations, authentication events, and errors, organizations can investigate security incidents more effectively, enforce compliance with the principle of least privilege, and mitigate risks like prompt injection or unauthorized code execution.  * ⚓ Red Hat ☛ Manage_Hey_Hi_(AI)_context_with_the_Lola_package_manager [Ed: Red Hat pushing slop, as usual]⠀⇛ As developers build agents that do more than just talk, they increasingly rely on tools like the Model Context Protocol (MCP) and agent skills—portable packages of markdown and scripts that provide LLMs with on-demand procedural knowledge. While MCP and Skills provide the standardized framework for these agents, developers still lack a unified way to distribute and version them. Lola fixes this problem by acting as a universal package manager for Hey Hi (AI) context. By using Lola, you can treat your Hey Hi (AI) context as versioned, auditable code. Lola includes two major components: modules and marketplaces. ䷩ 𝚕𝚒𝚗𝚎 2343 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/04/09/Relicensing_versus_license_compatibility.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/04/09/Relicensing_versus_license_compatibility.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Relicensing versus license compatibility⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Rianne Schestowitz on Apr 09, 2026 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇FSF_Free_Software⦈_ Quoting: Relicensing versus license compatibility — Some copyright holders, however, do permit recipients to further distribute the copy in their possession under a different license. For example, the copyright holder can release a work under a GNU GPL and add the option for recipients to follow a later version of the GNU GPL; however, this is optional and at the discretion of the copyright holder. They may also license the work without adding the option for others to upgrade to a newer version of the license. If a copyright holder licenses the work under "GNU GPL version 2 or any later version," it means the work is effectively licensed under either the GNU GPLv2 or the GNU GPLv3 (or any later version that the FSF releases). Recipients of such a work can choose to further distribute their copy under the GNU GPLv3 instead of the GNU GPLv2, taking advantage of an existing licensing option explicitly granted to them by the copyright holder. Note the subtle difference here: true relicensing can only be done by the copyright holder, since only they can freely change the license of the work to any other license. Relicensing explicitly permitted by copyright holder(s), in contrast, is when a non-copyright holder exercises the right given to them by the copyright holder(s) to further distribute the work under a different license. The non- copyright holder is limited to the permitted changes in licensing. Read_on ⠀⢠⣦⣤⣤⣤⣤⣤⠔⠒⢂⣩⠭⠝⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⣿⠛⠛⠀⣿⠛⢷⡄⢸⡟⠛⠃⢸⡟⠛⠃⠀⠀⢠⡞⠛⠀⢠⡞⠛⢳⡄⢸⡟⠛⠛⠘⠛⣿⠛⠃⢷⠀⣸⡆⢠⡟⠀⣼⡆⠀⢸⡟⠛⣦⠀⣿⠛⠛ ⣀⣠⣿⣀⣀⣠⡏⠀⠠⣊⣥⢤⣤⣀⣤⣀⣀⣀⣀⣀⡀⠀⠀⠀⡿⠛⠃⠀⣿⠻⣏⠀⢸⡟⠛⠀⢸⡟⠛⠀⠀⠀⠀⠙⢷⡄⢸⡀⠀⢸⡇⢸⡟⠛⠀⠀⠀⣿⠀⠀⠘⣧⡏⢻⣾⠁⣰⣏⣿⡄⢸⡟⢿⡁⠀⣿⠛⠃ ⠛⠛⡟⠛⠛⠛⠓⠶⠆⠀⠀⠀⢸⡿⣿⠛⠛⠛⠛⠛⠃⠀⠀⠀⠃⠀⠀⠀⠛⠀⠘⠃⠘⠓⠒⠂⠘⠓⠒⠂⠀⠀⠐⠳⠞⠁⠈⠛⠖⠋⠀⠘⠃⠀⠀⠀⠀⠛⠀⠀⠀⠙⠀⠈⠃⠀⠛⠀⠈⠓⠘⠃⠀⠛⠀⠛⠒⠒ ⠀⠀⡇⠀⠀⠀⠀⠀⢀⣀⣤⣶⠟⠃⣿⠷⠿⠿⠿⠆⠀⠀⠀⠀⠀⡤⠤⠀⠀⠀⢀⠤⡀⠀⠀⠀⢠⠀⡄⠀⠀⠀⢀⠀⡄⠀⠀⠀⠠⢤⡀⠀⠀⠀⢀⡀⠀⠀⠀⠤⡤⠄⠀⠀⠀⡄⠀⠀⠀⢀⠤⡀⠀⠀⠀⢀⠀⡄ ⠀⠀⠓⠒⠒⠒⠚⠛⠋⠉⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢸⣀⡔⠀⠀⠀⢸⣀⡇⠀⠀⠀⠸⠑⡇⠀⠀⠀⢀⣠⠇⠀⠀⠀⡼⢵⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⢣⣀⠄⠀⠀⠀⠸⠑⡇ ䷩ 𝚕𝚒𝚗𝚎 2401 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/04/09/Rofi_and_Wofi_Keyboard_Launchers_That_Keep_Your_Hands_on_the_Ke.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/04/09/Rofi_and_Wofi_Keyboard_Launchers_That_Keep_Your_Hands_on_the_Ke.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Rofi and Wofi: Keyboard Launchers That Keep Your Hands on the Keys⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Rianne Schestowitz on Apr 09, 2026 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Rofi_running_in_-show_run_mode⦈_ Quoting: Rofi and Wofi: Keyboard Launchers That Keep Your Hands on the Keys - FOSS Force — Rofi is a handy little Linux keyboard launcher. Any chance I can get to make Linux a bit more efficient, I’m going to take it. Sometimes that’s simply a matter of configurations, while other times it requires the installation of an app or two. One way to do this is by adding a keyboard launcher. If you hit the Super key (sometimes called the “Windows” key — I know, boo hiss), your desktop menu will open, where you can search for the app you want and then launch it. Now, imagine you could install a small app that would do the same thing… and more. That’s what keyboard launchers are; they allow you to launch applications, run commands, some of them even have the ability to search for files. They are very, very handy. Read_on ⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢸⣷⣶⣶⣶⡷⣿⣻⣇⣿⣷⣶⣶⢟⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡏⠙⠿⣿⠿⠋⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠛⠟⠻⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣧⣿⣿⣤⣿⣿⣽⣿⣯⣿⣿⣯⣧⣿⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ䷩ 𝚕𝚒𝚗𝚎 2476 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/04/09/Security_Leftovers.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/04/09/Security_Leftovers.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Security Leftovers⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Apr 09, 2026 * ⚓ SANS ☛ TeamPCP_Supply_Chain_Campaign:_Update_007_-_Cisco_Source_Code Stolen_via_Trivy-Linked_Breach,_Surveillance_Giant_Google_GTIG_Tracks TeamPCP_as_UNC6780,_and_CISA_KEV_Deadline_Arrives_with_No_Standalone Advisory,_(Wed,_Apr_8th)⠀⇛ * ⚓ LWN ☛ Security_updates_for_Wednesday⠀⇛ Security updates have been issued by Debian (openssl), Fedora (corosync, goose, kea, pspp, and rauc), Mageia (python- pygments, roundcubemail, and tigervnc), SUSE (bind, gimp, google-cloud-sap-agent, govulncheck-vulndb, ignition, ImageMagick, python, python-PyJWT, and python-pyOpenSSL), and Ubuntu (adsys, juju-core, lxd, python-django, and salt). * ⚓ Security Week ☛ Data_Leakage_Vulnerability_Patched_in_OpenSSL⠀⇛ A total of seven vulnerabilities, most of which can be exploited for DoS attacks, have been patched in OpenSSL. * ⚓ Security Week ☛ Evasive_Masjesu_DDoS_Botnet_Targets_IoT_Devices⠀⇛ Focused on persistence, the botnet does not engage in widespread infection and avoids blacklisted IPs and critical infrastructure entities. * ⚓ Security Week ☛ Massachusetts_Hospital_Diverts_Ambulances_as Cyberattack_Causes_Disruption⠀⇛ Signature Healthcare was forced to cancel some services, and pharmacies are unable to fill prescriptions due to the hacker attack. * ⚓ SANS ☛ More_Honeypot_Fingerprinting_Scans,_(Wed,_Apr_8th)⠀⇛ One question that often comes up when I talk about honeypots: Are attackers able to figure out if they are connected to a honeypot? The answer is pretty simple: Yes! * ⚓ SANS ☛ Number_Usage_in_Passwords:_Take_Two,_(Thu,_Apr_9th)⠀⇛ In a previous diary [1], we looked to see how numbers were used within passwords submitted to honeypots. One of the items of interest was how dates, and more specifically years, were represented within the data and how that changed over time. It is often seen that years and seasons are used in passwords, especially when password change requirements include frequenty password changes. * ⚓ LWN ☛ Nix_privilege_escalation_security_advisory⠀⇛ The NixOS project has announced_a_critical_vulnerability in many versions of the Nix package manager's daemon. The flaw was introduced as part of a fix for a_prior_vulnerability_in_2024. According to the advisory, all default configurations of NixOS and systems building untrusted derivations are impacted. * ⚓ Security Week ☛ Hackers_Targeting_Ninja_Forms_Vulnerability_That Exposes_WordPress_Sites_to_Takeover⠀⇛ The vulnerability allows hackers to upload arbitrary files to a site’s server and achieve remote code execution. * ⚓ AccessNow ☛ Espionage_for_repression:_hack-for-hire_phishing_campaign targets_civil_society_in_MENA⠀⇛ A new investigation by Access Now’s Digital Security Helpline has exposed a hack-for-hire campaign targeting two prominent Egyptian journalists and government critics. * ⚓ Security Week ☛ RCE_Bug_Lurked_in_Apache_ActiveMQ_Classic_for_13 Years⠀⇛ The vulnerability requires authentication for successful exploitation, but another flaw exposes the Jolokia API without authentication. * ⚓ Adafruit ☛ Claude_Code_found_a_Linux_vulnerability_hidden_for_23 years⠀⇛ Nicholas Carlini, a research scientist at Anthropic, reported at the [un]prompted AI security conference that he used Claude Code to find multiple remotely exploitable security vulnerabilities in the Linux kernel, including one that sat undiscovered for 23 years. * ⚓ Help Net Security ☛ Chaos_malware_expands_from_routers_to_Linux_cloud servers⠀⇛ Chaos, Go-based malware first documented by Lumen’s Black Lotus Labs, has historically targeted routers and edge devices. A new variant observed in March 2026 shows the malware operating against misconfigured Linux cloud servers, a category of infrastructure the botnet had not previously prioritized. Darktrace’s malware research team documented the compromise through its CloudyPots program, a global honeypot network the company runs to capture attacker behavior across a range of services and cloud platforms. One honeypot in that network runs Apache Hadoop, an open-source distributed data processing framework, deliberately misconfigured to allow remote code execution. That misconfiguration gave attackers a foothold and gave researchers a documented look at the updated malware. * § Windows TCO / Windows Bot Nets⠀➾ o ⚓ The Record ☛ Minnesota_governor_sends_national_guard_to_county after_cyberattack⠀⇛ Walz previously activated the state’s national guard in response to a ransomware attack last year on the city of St. Paul, which is about two hours north of Winona County. The state’s other large city, Minneapolis, has also faced several cyberattacks over the last three years. o ⚓ Meduza ☛ Russia’s_internet_regulator_blames_Rostelecom_network fault_for_widespread_outages⠀⇛ Users also reported that Rostelecom’s home internet service had stopped working in Moscow. The company stated that it had detected a major DDoS attack on its network and had quickly neutralized it. ䷩ 𝚕𝚒𝚗𝚎 2647 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/04/09/ShredOS_disk_eraser_operating_system.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/04/09/ShredOS_disk_eraser_operating_system.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ ShredOS – disk eraser operating system⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Rianne Schestowitz on Apr 09, 2026 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇ShredOS⦈_ Quoting: ShredOS - disk eraser operating system - LinuxLinks — It starts nwipe automatically and gives technicians a dedicated environment for wiping storage devices on PCs, servers, and Intel- powered Macs without needing to install a full operating system first. The project provides prebuilt images for quick deployment, source for custom builds, and a set of storage-related tools that make it useful for refurbishment, decommissioning, and data sanitization workflows. This is free and open source software. Read_on ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⣤⠀⠀⠀⠁⠁⢉⠀⠠⠁⠩⠈⠁⠀⡈⠃⠙⠐⠀⡄⠑⠁⠘⠀⠙⠓⠀⠀⠀⠀⢒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠨⠁⠂⠁⠀⠈⠀⠂⠓⡂⣃⠑⢀⠀⠒⠀⠂⠀⠀⠐⢁⠀⠄⠀⠀⠀⠀⢐⠀⠀⠈⠀⠈⠀ ⠑⠀⠀⠨⠀⠀⢐⠀⡐⠀⠁⠠⠄⠀⠀⠐⢐⢚⢂⢀⠀⠈⠀⠀⡀⢠⡀⠀⠀⠠⠄⠀⠀⠒⠋⠁⢠⠈⠉⠉⠉⠸⢎⠥⠉⠁⠣⠟⢍⠡⠉⠤⠬⠍⠋⠩⠙⠙⡉⣛⠉⢉⣉⠉⢉⣉⠈⢡⠄⠁⠁⠣⠓⠀⠀⡀⢀⠈ ⠀⢠⠠⠀⣀⣀⠀⠒⢐⢒⡦⠐⡒⢐⠓⠂⠐⢂⠀⠂⠀⠤⠨⢄⠍⣅⢐⣤⡄⠄⠀⠠⡤⠀⠂⠀⠀⠀⠀⢀⡄⡀⠀⠀⠀⠃⠀⠀⠀⡀⢀⠀⢀⠈⠄⠀⠀⠀⠨⠄⠈⡈⠀⠁⡁⠨⠨⠉⢁⣀⡀⣠⠄⠤⠀⠑⠀⠀ ⠁⡀⠂⡀⢀⡑⠀⠀⠀⠁⠠⢀⠀⡠⠀⠀⠀⠀⠀⢀⠂⠈⠈⠡⠀⠀⠀⠁⠁⠀⠀⠙⡀⠁⠁⢄⠀⠀⢠⠀⠁⠀⠀⠀⠀⠀⠀⠊⠄⠀⡀⠀⠈⠀⠀⠀⠂⠘⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠈⣄⡀⠒⣄⡢⡀⠠⠄⠠ ⠑⠂⠤⠂⠄⠂⠂⠐⠈⣊⠒⠰⠒⠀⠀⠂⠀⠉⠓⠒⠖⠐⠓⠠⠣⠀⠊⠂⠚⠐⠀⡌⠂⠐⠂⠈⠂⠃⠒⠑⠑⡙⡚⡚⣈⠲⣀⢉⠈⡀⠀⠀⣐⢶⠁⠂⢂⣂⠐⠐⠐⠂⠀⠂⠀⢀⠁⡺⡐⠀⠀⠠⡉⠀⠁⠂⢒⠓ ⣂⠀⠀⢀⠀⠈⣀⠀⠐⠨⠀⣂⢒⠢⠀⠑⠠⠶⠄⠟⠐⠂⠄⣼⣀⣀⡠⢀⣠⣀⢀⡀⢀⢀⠀⠐⠄⠬⠀⠂⡀⠀⠀⢀⠈⣐⢗⣐⣒⢓⣀⣂⣂⣐⣀⣁⣓⠒⠂⠀⠀⠀⠀⠀⠀⠂⡑⢀⠓⠃⢐⣂⠀⠰⠂⠐⠒⠠ ⠢⠤⠄⠌⠀⡡⡇⢂⠀⠀⠮⡅⠠⠄⠁⢉⠠⠀⠀⠀⠀⠈⠠⠀⠪⠁⠀⣀⡥⡉⠀⠀⢐⠈⡀⠁⠉⣉⠀⠀⠉⠊⠉⠐⠁⠈⠀⠀⢁⢀⠀⠈⠒⠙⠚⠃⠊⠈⠛⠁⠉⠙⠉⠛⠁⠀⠡⠊⠀⠀⠘⠆⠀⡠⠠⠜⠒⠠ ⠀⠃⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠤⠶⠀⠐⠌⠃⠤⠂⠄⢠⠖⠄⠀⠁⠀⠀⠦⠀⠀⠀⠀⠀⠐⠀⠂⠀⡀⠂⠀⡀⠀⠀⠀⠡⡀⢀⡀⡀⢢⠨⠢⠀⠀⡠⠀⠀⠀⠀⠀⠀⢀⠀⠀⢐⠗⠀⠄⠄⠂⠠⠠⠀⠐⠄⠀⣀ ⠀⠠⠀⢈⠀⠈⠁⠀⠀⠀⠀⠈⢐⠀⠀⠌⢐⠐⠂⠀⠗⠀⢒⠀⠀⠂⠐⠂⠄⠀⠁⠀⠀⠰⡁⠀⠰⠰⢀⠂⠐⡀⠀⠀⠠⠠⢀⠀⠄⠂⢐⢒⠒⠒⠆⢲⠠⡒⠒⡒⣂⢊⠄⠄⡄⢢⡀⠄⠀⣁⠄⡄⠀⠁⡀⠨⠀⡐ ⠀⠀⠀⠐⠐⡠⠒⠊⡀⠁⠀⠀⠀⠀⠀⠀⠡⠐⢈⠂⢠⠀⠀⠈⠀⠀⠀⢀⢀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠠⠀⠁⠀⠂⡀⠂⠘⠄⠀⠀⠨⠀⠀⠈⠀⠉⠁⠠⠄⠀⠌⠉⠁⠀⠀⠀⠐⠀⠀⠑⠠⠀⢀⠀⠁ ⠬⠤⠥⠅⠉⠌⠁⠀⠑⠐⠀⠐⠑⠚⠷⠓⠒⠰⠲⠲⠂⠚⠐⠘⠘⢂⠀⠄⡠⠂⠄⠈⢐⠀⠂⠐⠠⠂⠒⠒⠢⠘⠀⠐⠀⠐⠑⠈⠛⠤⠀⠁⠀⠀⠀⠀⠄⠀⠠⠀⠄⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠐⠐⠄⠢⠠ ⠀⡃⠁⡐⠈⠀⠀⢑⠀⠀⠀⠂⠁⠁⠀⠐⡐⠁⢀⠀⡀⢁⠀⠀⠂⠄⠀⠀⠈⠀⠀⠀⣡⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⠐⠄⠀⠐⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⢀⠃⠀⠀⠁⡄⠐ ⠰⠐⢀⠐⠀⠂⠄⠀⠣⠀⠀⠈⡀⡀⠀⠈⠀⠤⠀⢀⠀⠂⠳⠔⣀⠂⠐⠠⠀⣀⠀⠀⠀⢀⠀⠀⠀⢠⠀⠀⠀⠀⠂⠀⠐⠂⢒⠐⠀⠀⠐⠀⠙⠂⠑⠑⠈⠈⠈⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠑⠀⠀⣀⠠ ⠀⠀⠀⠀⠂⡄⠢⠡⠖⠄⠠⠄⠠⠀⠀⠀⠄⠀⠈⠂⠀⠀⠀⠉⠀⠠⠀⠄⠂⠱⠀⠈⠀⠁⠀⠀⠀⠃⠀⠄⠀⠂⠀⠀⢀⠀⠀⡀⠀⢈⠀⠠⢐⠈⠂⠄⠀⠀⠅⠀⠀⠀⡀⠀⠀⡁⠀⠀⠀⡀⠂⠀⠀⢐⠀⠀⠀⠀ ⠠⠆⠰⠢⡂⠐⠀⠲⠂⠀⠄⠄⢰⡀⠄⠐⠀⠂⠀⠀⠀⠐⠐⠂⠚⠑⠀⠐⠀⠀⠀⠀⠂⠀⠀⠀⠨⠙⠋⠨⠑⡌⠉⠀⠀⠀⠂⢉⠓⠐⠐⡀⠐⠀⠀⠈⠀⠁⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⡐⠨⡀⠂ ⠀⠀⡀⢐⠀⠀⠄⠀⠐⠈⠉⠉⠉⠀⡀⠀⠀⠐⠀⠁⠀⢐⠀⠅⠀⠒⠒⠈⠁⠀⠀⠁⠀⠐⠄⠠⠀⠐⠈⠀⠄⠀⠀⠀⠰⠀⠀⠀⠀⢄⢀⠄⠁⠀⠄⠈⠉⠤⠀⠁⠀⠀⢀⠀⡐⠆⠀⠀⠀⠀⠀⠄⠀⠴⡂⠃⠀⠱ ⡀⡐⢀⠂⡤⠀⠂⠤⠊⠄⠂⠶⠀⠐⠠⠀⠀⠀⠀⠂⠐⠠⠢⠀⠀⠐⢀⡈⢐⢀⣀⡀⡖⠀⢆⡀⠁⠂⠠⠄⠀⠄⠤⠀⠀⡠⡤⠄⠨⠄⠄⠄⠀⠄⠀⠐⠠⠂⠀⠀⠒⠔⠒⠐⠠⡐⠆⡀⣀⠀⠀⠀⠀⠀⠀⠂⠀⠀ ⠀⠰⠀⠀⠀⡀⢄⡄⡄⠀⣀⢄⢈⠀⠅⠀⣁⡀⠀⠀⠠⢀⠀⠀⠡⠀⡀⠀⠀⠂⠐⠀⠠⠈⠀⠀⠀⣀⠀⠀⠀⠀⠀⠁⡠⠂⠂⠑⡲⠀⠂⠁⠀⣊⠀⠀⠀⠀⢂⠀⠀⠀⠁⡀⠀⠈⠈⠀⢀⠀⠁⢉⠐⠁⠀⠀⠆⠀ ⠀⡆⠀⠀⠀⡀⠡⠀⠀⠀⠉⢨⠁⠘⠁⠁⠈⠈⠈⠁⠀⠈⠀⠂⠀⠀⠀⠂⠊⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠄⠀⠀⠀⢠⠀⠠⠄⠄⠄⢠⠤⠂⠀⠄⠀⢥⠘⠀⠀⠀⠀⠠⠀⠀⠠⠀⠀⠈⠀⠀⠁ ⣶⣿⣿⡾⡟⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣵⣾⣿⣯⣿⣿⣿⣭⣿⣿⣿⣷⣿⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣾⡷⣶⣿⣾⣾⣿⣿⣿⣻⣛⣿⣿⣯⣿⣼⣿⣿⣿⣾⣿⣷⣾⣿⣿⣸⣷⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣶ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠓⠓⡃⠒⠃⢗⡘⠖⠂⠺⠒⡳⡰⡂⠊⡲⠒⠣⠭⣿⡶⣷⢶⣾⣶⠀⡀⠀⠐⠀⠀⡀⢁⠀⠚⠀⠄⠀⣀⠂⠀⠈⠈⡜⢢⠶⡐⠂⠒⠺⠐⢐⢒⠂⠲⠺⠫⢷⠖⠶⡒⠊⠲⠅⡾⡗⠄⠀⠀⢊⠺⡊⠠⠖⠄⢰⠀⠶ ⠀⢱⢷⣿⠕⢶⢲⠺⠠⢁⠰⠔⠷⠔⠒⠘⠶⡪⢵⣿⢧⢄⠄⣾⠵⢷⠶⡷⢶⠶⠿⢑⠂⠈⡀⠀⠀⠀⠀⡀⡀⠀⢀⡟⢻⠶⢟⣧⢦⣶⠦⠖⠀⠂⠀⠀⠀⠈⠂⠁⠀⡁⠀⢀⠀⠄⡀⠠⠄⠀⠀⠀⠠⠁⠂⠀⠀⠀ ⢀⡁⢷⠿⢾⠮⠀⠣⠀⠴⣷⢲⡲⠲⢶⠶⠶⠓⠚⣆⡟⠶⠶⠽⠞⢢⠂⠴⠟⠟⡺⠶⠿⠾⢞⠒⢰⢳⠖⠭⠲⠁⡍⡍⣿⡾⠟⠏⣅⢟⡖⡶⣶⢜⠦⠈⡀⠀⠐⠀⠀⠐⠀⠀⠀⠀⠀⠀⠉⠀⠀⠂⠀⠈⠀⠘⠨⠀ ⠪⠷⠿⠿⡟⢶⠗⡆⠑⠹⠿⠺⠷⠼⠹⠿⠻⠞⡆⠁⠀⠀⠄⠀⠀⠀⠀⠁⠀⠌⠁⠀⠀⠠⠀⠰⠀⠈⠈⠁⠐⠄⢀⣿⠶⢹⠶⡾⠃⠻⡿⠳⠲⠖⠞⡿⠷⠆⠠⠸⠈⠠⠀⠈⠀⠀⠡⠈⠀⠄⠀⠄⠀⠀⠀⠐⠌⠄ ⠑⡻⠿⠷⠧⢿⡏⡓⠂⠀⠶⢖⡧⠗⠄⠙⠹⡻⠇⠨⠠⠁⠄⠀⢀⠀⡀⡀⢀⢀⠀⠠⠀⢀⢠⣀⠂⠀⠀⡂⠘⠀⡂⣟⣝⢾⣗⠺⢟⠿⣾⠳⠟⢓⠾⠡⠐⠀⠈⠀⠈⡀⠀⠀⠀⠀⠈⠀⢐⠀⠀⡂⠀⢂⠂⣈⢀⡊ ⠿⡿⢿⠗⡾⠒⡷⠣⠀⠤⠆⠠⡰⢶⠶⢑⢚⠱⣒⠶⠟⠟⠎⠲⠶⢖⠚⡝⠲⡿⠶⠄⠀⡀⠂⠀⠄⡀⠄⠀⠀⠐⠅⡧⠿⠾⠋⡽⢞⠚⠦⠒⠄⠀⠂⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⢠⠀⠀⡀⠂⠠⠀⠠⢀⠄⠈⠈⠀ ⠁⠐⠋⡗⠚⠟⢒⠗⢂⢰⠐⠈⠀⣀⠅⡀⠐⠀⣀⠀⢁⡈⠀⠀⣂⠁⠀⠄⠀⣀⢲⣇⡄⣈⠀⠙⠰⡉⡂⣕⣰⠄⣗⢓⢚⠚⡢⠐⠁⠡⠖⠨⠨⠀⠀⠁⡀⠐⢀⢂⢠⣀⠀⣃⢠⠀⠁⡁⣀⡙⢠⠂⠠⡑⠈⣢⠄⢐ ⠒⠚⠍⠿⠞⠚⠒⠆⠃⠳⠇⠒⠗⢒⠒⢖⡂⢟⡳⢒⡖⠲⠻⠒⡲⠿⠷⡶⠀⠾⠟⠟⠷⠸⠒⠠⠽⠳⠓⠈⠛⠙⠃⠓⠈⠗⠞⠓⠿⠋⠔⠒⠑⠒⠴⢃⠔⢞⠒⢟⣂⠲⠶⠥⠖⡒⠲⠶⠗⢒⠆⠺⠖⠏⠒⠆⠲⠟ ⠠⡀⠀⠈⢌⡀⠠⠀⠀⡃⢀⣍⠈⠈⡑⠁⠘⠃⠑⠀⠐⡅⠠⠩⢄⣠⡀⡤⠂⢠⢑⡅⣀⣄⣀⠈⣈⡠⢂⠀⣀⡂⢂⡁⢀⣈⠀⣁⣁⣀⣁⠩⠁⣢⡉⠌⣁⣈⠐⢀⠰⢁⣉⣆⣤⣀⠈⠀⠠⣄⠔⢄⠠⠀⡥⠀⠀⠀ ⡀⠀⠈⢅⣊⠀⡐⠁⢀⠀⠌⢀⠐⠐⡛⠟⠍⢩⠹⣉⣻⢏⠚⡉⡃⣽⠉⣇⣀⢍⠹⠙⣹⣻⠟⠻⣕⡝⡏⡈⡉⣗⡜⣟⣙⢿⣯⢗⣟⣏⢳⣓⠙⢾⢏⣙⡻⣻⣟⣿⣷⣗⣟⣁⣋⢿⢋⡑⡁⠃⠀⠐⠀⠐⠤⠀⠠⠂ ⠀⠄⠈⠠⠛⡆⠀⠀⡢⡁⠒⡛⡁⢀⣙⡟⣻⡛⠙⣛⡛⣏⠋⢙⢙⣙⢍⠃⠱⢟⣙⣻⣇⣗⡮⢸⣟⠻⢯⣭⣛⣿⣻⣯⣟⡿⣛⡿⣛⠅⣚⣽⣺⣝⣉⣽⣛⣽⣛⣟⣿⣟⣋⣳⢚⠕⠐⠂⠡⠀⠈⡀⠀⠀⠄⠄⠡⠠ ⠀⠈⠀⢀⣀⠁⠀⠁⢐⢋⢑⣸⠀⢒⡛⣛⣉⣛⢓⣛⢛⠛⣩⣒⣻⣛⣫⠀⠊⣺⣻⡆⡏⣋⣺⣚⣙⣛⣛⣻⣙⣛⣟⣻⣉⢻⡓⡛⣛⣩⣳⣃⣁⣋⣉⣩⣛⣹⢙⣻⣟⢛⠉⣋⣒⡌⣇⣔⣭⣄⡸⢀⡄⡄⢀⠈⣨⠂ ⡀⢀⠀⢀⡹⠩⡠⠀⠁⠍⡉⢑⠀⠈⠈⣉⡟⣭⢹⣋⣟⣍⡁⠺⣿⣏⡉⣁⡑⢿⣹⠁⢉⣯⣳⣈⣋⣙⡏⡉⡉⣛⠟⣉⣉⢩⣅⣉⣭⣫⣍⡻⠟⡋⠏⠋⢹⠏⠙⡋⠯⠏⠹⠙⠿⠻⠳⠸⠅⠑⠑⠐⠀⠁⠀⠀⡀⠌ ⠁⠍⠋⠐⠁⠨⡠⠈⠁⠕⣎⡃⡁⡈⢕⡍⠑⡋⠝⣩⠫⠩⠓⣭⣹⠫⢈⠈⢏⠝⣝⣋⡍⡉⣣⣺⣍⢉⢋⡙⢍⣐⣁⣛⣩⣫⣏⣻⣯⢿⣷⣉⡄⣟⣠⢼⣀⣄⣄⣀⣠⣐⠀⠀⣂⠀⠇⠀⢀⠀⠀⠂⠀⠘⠀⠀⠂⠀ ⠀⠀⠀⠔⠁⠀⠂⠀⡂⠸⠀⠘⠈⠈⠛⠍⠙⡃⠝⠣⠛⠋⠂⠙⡻⠓⠟⠒⠈⠐⠍⠨⠏⠋⠍⢡⠁⠈⠫⠻⢀⠛⠚⠉⠟⠉⡋⠉⠹⠛⠋⠛⢿⠁⠂⠜⠹⠭⠩⠋⠻⠙⠫⠀⠐⠀⠰⠐⠀⠂⠀⠀⢀⡀⡀⠄⢀⠀ ⠀⠂⠀⠀⠒⠄⠂⡁⠈⠀⠠⠐⡃⠈⢀⠀⠡⠈⠐⠁⠁⠐⠈⠠⡀⠀⡔⠀⣠⠠⠐⢢⠠⠐⡀⠊⠸⢡⡀⢨⠀⠑⡀⠁⠄⠀⠠⠀⠁⡀⠈⠂⠀⡁⠀⠀⠂⠨⢰⠀⡀⠴⠀⠷⠁⠀⡂⠀⣐⠀⠀⠔⠀⠀⠀⠠⠐⠁ ⢀⠄⠆⠠⠐⠀⡄⠀⠠⠈⠀⢰⠀⠁⡀⠀⠂⠊⠀⠨⠀⠠⠁⢨⠀⠀⠀⠄⡢⢀⠂⠄⠀⠒⠄⠠⠀⡁⠠⠁⠈⠈⠆⠋⠔⢀⢱⠀⠀⠀⠀⠠⠅⠀⠂⠀⠀⠀⠠⠂⠀⠆⡠⢁⠀⠀⢀⠀⠀⠥⠈⠠⠁⠠⠀⠈⡐⠈ ⠠⠀⠅⠀⠈⡀⠠⠀⠊⡨⠊⢁⠀⠀⠄⠈⢁⠀⠠⡊⠐⠀⠡⠌⣠⡀⡅⠀⠀⠂⠔⠁⠤⠀⠀⠐⡄⠁⠈⠠⠄⠁⢅⠠⡠⠀⢃⠀⢀⠐⢐⡀⠄⠁⠁⠠⠀⠀⡪⠄⠅⠁⠀⢠⠀⡀⠀⠐⢀⠀⢠⠁⠈⠀⠀⠀⢔⠄ ⠀⠀⡀⠀⡘⠀⠀⠃⢀⢐⢀⠐⢀⠈⣂⠀⠂⡂⠂⢢⠀⠠⠀⠀⠠⢠⠐⡐⠀⠀⠐⡀⠄⡐⠀⠀⠂⠄⠔⠐⠀⠂⠁⢀⠘⠐⠁⠀⡐⡠⠀⠀⠀⡀⠀⠐⠠⠀⠊⠈⡀⠀⠀⠂⡀⡀⠀⠀⠀⠀⡂⠀⡐⠀⠀⠀⠠⡐ ⠀⠈⠀⠀⡀⠀⠌⠀⠀⠠⠘⠁⠀⠀⠄⠀⠈⠀⠀⠀⠀⠨⠨⠀⠆⠑⡨⠀⢌⠀⡐⠠⠀⠀⡀⠀⠁⠠⡁⠕⠁⠠⠀⡅⢠⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠡⠀⡄⡀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠁⠀⠑⠈⡤⠀⠀⠀⡄ ⠀⡈⠇⠀⢀⠀⠀⠀⠀⠀⠀⢔⠀⠀⡀⡐⡃⠇⢨⠂⠁⡊⠀⠘⠈⢠⠂⠄⠀⠠⡒⠂⠀⡀⠈⠀⠐⡀⡁⠠⡂⠀⠄⠐⢀⠀⠀⡀⠀⠘⠀⠘⠀⠃⠂⡀⢠⠁⢀⡀⢠⠀⠐⠐⠀⠁⠈⡀⠀⠂⢀⠀⠀⠀⠀⠈⢘⠀ ⠀⠡⠔⠠⠈⠀⠰⠀⠈⠀⠡⢆⠊⠀⡑⠀⠂⠀⠀⠐⠐⠂⠀⠀⠀⠊⠕⠀⠀⠀⠀⠰⠀⠊⢀⠘⠌⠃⠀⠅⠀⠎⠀⠀⡀⠈⠌⠂⠉⠠⠀⠢⠀⠉⠂⢐⠌⠀⠕⠤⠀⠐⠀⡀⠁⠀⠆⠀⠁⠨⢁⠀⠆⠊⠀⢈⠌⠂ ⠈⢂⠌⠀⡈⠀⡐⠰⠀⡃⠅⠑⠁⠘⠂⠈⠈⠀⠀⠀⠀⠐⢀⠀⠀⠠⢒⠀⠆⠀⠐⠀⠃⠀⡁⢠⠒⠈⠐⡀⠚⡐⠀⠀⡀⠀⠀⠀⡄⢅⡈⢂⠀⢒⡀⢢⠀⠈⠀⠀⠀⠓⠈⠂⠉⠈⠌⠁⠀⠀⢠⠀⠠⡊⠁⠈⠀⠀ ⠠⠓⡀⠀⠐⠂⠀⠁⠀⠊⠀⠄⠅⡐⠈⠀⠁⡀⠈⠄⠀⠄⡀⠐⠐⢀⢀⠅⡀⡀⠌⠀⠠⠅⠂⠈⢀⠄⢠⠀⠈⠀⠀⠀⠆⢄⠀⠀⡠⠠⠀⠀⠀⠠⠀⠀⡂⠀⡠⠀⢀⠆⠀⠁⠄⢀⠰⠂⠔⡀⢀⠂⠀⠂⠀⠡⠠⠪ ⠈⠀⠈⠀⡘⠁⠀⡈⣁⠉⠀⡀⠀⢀⠁⡀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠄⠀⢁⠀⠀⠀⠀⠃⢀⠈⢁⡈⢂⣀⠈⡅⢁⠁⢀⠄⠀⡄⠄⢠⠨⢠⠀⠀⠄⡀⡌⠠⠀⡠⠀⠅⠀⡄⠀⢂⠔⠀⠀⠀⠑⠁⠀⠡⠀⠄⠠⠡ ⠀⠁⠀⠀⠂⠀⡀⠀⠐⢀⠄⢀⡀⣀⡄⠠⡠⣀⢢⢪⠀⠐⠆⠐⠈⠒⠄⡒⠄⠂⠀⠊⠀⠘⠁⠈⡀⠂⠁⠀⠀⠆⠀⢀⠀⠀⡀⠂⠠⠀⠄⠀⠀⠁⠠⠊⠀⡀⢁⠊⠈⢎⢐⣐⠠⠤⠐⠀⠐⠀⠀⠂⠀⠢⠀⠀⠀⠀ ⡀⡀⣠⠤⢤⠤⠱⠄⢠⠛⠞⠁⠁⠪⠜⢯⡕⣢⠒⠱⠠⢵⠆⠌⠤⠤⢦⢤⢩⢦⣴⢎⣦⢎⡄⡈⢤⠀⢦⠰⠴⡈⠂⠨⢠⠈⡀⠠⡥⠴⠬⠔⡩⠄⠠⠀⠦⢄⠨⠐⠼⡇⠦⢄⠠⠤⠴⠔⠰⠤⠀⠠⢠⠮⠲⠤⠪⠤ ⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣥⠘⠀⠀⠋⠁⠈⠉⠐⠙⠑⠈⠉⠉⠈⠀⠈⠹⢷⠶⠿⠵⠵⠶⠌⠈⠃⠊⠚⠀⠈⠈⠙⠈⠋⠈⠃⠘⠀⠁⠀⠁⣤⡼⠀⠁⠀⠑⠒⠀⠁⠀⠀⠘⠘⠸⠷⠿⠿⠮⠶⠺⠻⠿⠲⠇⠀⠈⠐⠈⠀⠂⠚⠈⠂⠁⠊⢡ ⣗⠿⠶⠷⠶⠶⠶⡦⠆⠸⠧⠶⠶⠶⠆⠸⠿⠶⠶⠶⠶⠀⠰⠶⠶⠶⠴⠾⠷⠶⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠷⠶⠶⠧⠶⠶⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠟⠻⠿⠗⠀⠀⠀⠀⠸⠷⠲⠲⠒⠶⠶⠶⠂⠸⠷⠶⠶⠐⠶⠖⠂⠰⠲⠲⠸⠝⠚⠹⠹⠶⠖⠒⠂⠖⠷⠐⠀⣿⡗⠷⠒⠶⠖⠖⠂⠖⠶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣷⠿⠖⠓⠗⠶⠗⠅⠀⠸⠷⠿⠗⠨⠿⠷⠶⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣳⠧⠖⠶⠿⠐⠛⠶⠶⠒⠶⠶⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼ ⡗⠟⠶⠆⠗⠗⠖⠁⠀⠸⠷⠶⠞⠆⠸⠳⠲⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣭⠋⠗⠖⠶⠶⠮⠷⠶⠶⠇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠟⠛⠓⠛⠟⠋⠁⠀⠀⠃⠐⠰⠛⠛⠚⠂⠘⠛⠛⠚⠛⠛⠛⠺⠆⠶⠓⠒⠛⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⠛⠛⠛⠛⠛⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⡶⠐⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠈⠀⠉⠀⠀⠈⠀⠀⠈⠈⠀⠀⠀⠁⠀⠀⠛⠙⠚⠛⠙⠀⠚⠛⠛⠀⠛⠛⠛⠛⠉⠃⠋⠛⠛⠋⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⢰ ⡗⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⢀⢀⣀⠀⢀⠀⣀⢀⡀⢀⣀⢀⠀⣀⣀⣀⠀⡀⣀⣀⣀⡀⡀⣀⠀⣀⣀⣀⡀⠀⣀⡀⢀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⠀⡃⠀⠀⠀⠀⡓⠒⡓⠀⠐⠙⡛⠛⠋⠑⠛⣛⠃⠀⢙⢛⡋⠃⢘⢀⢈⣙⠀⣛⣛⢚⠀⡛⣛⣓⠐⣛⣛⡋⡛⠛⡛⡛⠈⣙⡛⢛⡓⢙⢛⡋⠘⣛⡛⣛⡛⣓⣓⣓⣛⡛⣛⣙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡃⠀⠀⠀⠀⡃⠐⡃⠀⠐⠉⡛⠚⡛⢘⠛⡛⠂⠁⢊⣛⣛⡁⢈⠙⣛⣛⠀⣛⣛⣚⠀⣛⣛⣃⣀⡛⣛⣛⣛⣛⣛⣛⣛⡃⣋⢑⡓⢙⣛⣋⣙⣛⣛⢛⣛⡛⣘⣋⡛⠋⠛⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡏⠀⠀⠀⡃⠀⠀⠀⠀⡃⡀⡃⠀⠀⠉⡋⠋⠋⠘⠛⣛⡁⠀⠉⣛⣋⡃⢈⠀⢑⣛⠈⣙⣙⣘⠀⣙⣂⣈⠋⣓⣏⢋⡋⠉⣋⣋⣛⢉⣃⣉⣋⣙⣋⡉⢁⣉⡙⠚⣋⣉⣉⣛⣁⣀⡀⢀⢀⣀⢀⡀⠀⠀⠀⠀⠀⠀⢸ ⡧⠀⠀⠀⡃⠁⠀⠀⠀⡃⢠⣃⠀⠈⣉⣙⣛⠉⣉⣛⣛⡂⠀⢘⣓⣛⡀⢈⠀⣙⣙⠀⣻⣛⢘⠀⣋⡋⣃⡀⣋⡛⠋⡋⠈⣃⣋⣏⣉⣙⡛⠛⠛⠉⠁⠙⠋⠋⠉⠙⠛⠛⠛⠊⠓⠛⠉⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡁⠀⠀⠀⠀⡁⢁⡉⠀⠈⣈⣙⣉⡉⡈⣉⣉⠀⠀⢉⣁⣋⠁⢈⠀⠉⣘⠀⡉⣉⢉⠀⣉⣉⢉⠉⣉⣉⢀⢉⣀⣁⠉⣉⣉⣉⣁⡀⣀⢀⣀⡀⡀⡀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡗⠀⠀⠀⠁⠀⠀⠀⠀⠁⠈⠃⠀⠈⠙⠙⠉⠋⠈⠉⠙⠀⠀⠙⠙⠙⠁⠈⠁⠀⠈⠀⠉⠙⠈⠀⠉⠉⠋⠀⠁⠉⠉⠈⠉⠁⠋⠋⠙⠋⠉⠁⠋⠉⠋⠉⠙⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹ ⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼ ⠧⠄⠄⠄⠄⠠⠠⠠⠠⠀⠄⠠⠤⠀⠤⠄⠄⠄⠄⠄⠀⠠⠠⠤⠠⠠⠤⠤⠠⠀⠤⠠⠀⠄⠄⠠⠄⠀⠤⠠⠠⠠⠀⠄⠤⠀⠄⠀⠠⠄⠀⠀⠠⠄⠤⠠⠠⠄⠄⠄⠠⠠⠀⠄⠄⠠⠠⠀⠤⠄⠠⠄⠠⠠⠠⠄⠠⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣄⠦⠒⠑⠊⠛⠂⠀⠑⠐⠛⠃⠒⠒⠐⠐⠃⠺⢿⠾⠼⠷⠿⠶⠆⠸⠀⠃⠐⠀⠀⠀⠒⠐⠂⠐⠂⠂⠠⠁⠐⠀⣧⣵⠐⠒⠒⠒⠐⠒⠒⠒⠒⠒⠂⠸⠿⠷⠾⠿⠿⠾⠿⠿⠶⠅⠐⠒⠒⠒⠲⠐⠐⠂⠀⠒⠀⢢ ⡿⡿⡶⠷⠖⠶⡶⡶⠂⠸⠇⠷⠶⠶⠦⠸⠷⠶⠲⠶⠾⠂⠰⠴⠶⠶⠶⠾⠶⠶⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠷⠶⠗⠷⠶⠦⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠟⠿⠿⠯⠊⠀⠀⠀⠸⠿⠶⠓⠶⠖⠶⠖⠆⠚⠿⠾⠰⠺⠶⠶⠀⠐⠶⠰⠸⠻⠻⠻⠙⠶⠖⠒⠶⠶⠷⠚⠀⣿⡿⠿⠷⠷⠖⠗⠖⠖⢶⡆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠻⠖⠧⠗⠶⠃⠃⠀⠰⠷⠾⠇⠺⠿⠷⠶⠚⠆⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡿⠷⠶⠶⠟⠰⠻⠗⠶⠖⠾⠶⠶⠖⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⡛⠷⠆⠇⠿⠾⠂⠀⠘⠷⠖⠟⠇⠸⠱⠶⠗⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⠏⠿⠖⠶⠶⠿⠷⠷⠮⠇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡏⠿⠿⠒⠓⠛⠇⠀⠀⠀⠃⠐⠳⠞⠻⠚⠓⠸⠚⠒⠚⠻⠚⠚⠾⠆⠶⠺⠲⠒⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡗⠟⠛⠒⠟⠖⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠉⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊ ⡖⠛⠀⠀⠀⠀⠈⠁⠁⠂⠋⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠁⠃⠈⠁⠀⠀⠛⠚⠛⠛⠚⠀⠚⠛⠛⠀⠋⠛⠃⠓⠓⠓⠓⠛⠛⠓⠐⠒⠂⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠂⠀⠀⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠂⢰ ⣏⠀⠀⠠⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⢀⠀⣀⣀⢀⠀⣀⣀⡀⠀⢀⣀⣀⣀⡀⣀⣀⠀⡀⣀⣀⡀⢀⣀⡀⢀⣀⣀⢀⣀⣀⣀⣀⣀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣗⠀⠉⠀⡓⠀⠀⠀⠀⡃⢀⡃⠂⠀⠙⡛⠛⠓⠙⠛⣛⠃⠀⢙⢛⣛⠃⢘⢀⠘⣙⠀⣛⣛⠘⠀⣛⣛⣛⠈⣛⣛⡋⡙⣛⡛⡋⡉⣛⡛⢛⡓⢙⣛⡋⢙⣛⣛⣛⣛⣚⣓⣛⣙⣛⣛⢛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣏⠀⠀⠀⡃⠀⠀⠀⠀⡃⠘⡃⠀⠀⠙⡛⢛⠓⠙⠛⡛⠃⠀⢘⣛⣋⠁⢘⠘⢛⣛⠁⣛⣛⣙⠀⢛⣛⣃⡀⡛⣋⣛⣛⣛⣛⣛⣙⣛⡋⠙⡒⢙⣛⣋⣙⣛⣛⢛⣛⣛⣘⣉⡋⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡃⠀⠀⠀⠀⡃⠐⡃⠂⠐⠙⡛⠋⠋⠉⢛⣛⡁⠀⠈⣙⣉⡁⢘⠀⣙⣛⠁⣋⣛⢈⠀⣘⣑⣚⠛⣛⣛⣛⣋⢛⣋⣓⣉⢋⣁⣉⣛⣁⣋⡛⢁⣋⡙⢛⣓⣘⣉⣛⣃⣀⣀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸ ⡗⠀⠀⠀⡃⠀⠀⠀⠀⡁⢀⡃⠀⠈⣉⣛⡙⡋⠘⢛⣛⡁⠀⡘⣙⣛⡁⢈⠀⣙⣋⠀⣛⣛⣉⠀⣙⠙⣑⡀⣋⡛⠙⡉⠈⣋⣋⣋⣉⣋⡋⠋⠋⠋⠋⠙⠙⠁⠈⠙⠙⠛⠛⠊⠛⠙⠙⠘⠛⠉⠁⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡁⠀⠀⠀⠀⡅⢀⡁⠀⠈⣉⣙⣉⡉⡉⣉⣉⠀⠀⢈⣻⣙⡁⢈⠀⠉⢙⠀⣉⣋⣈⠀⣉⣉⢉⡉⣭⣉⣈⠉⣀⣍⡉⣉⡙⡉⣉⣀⡄⣀⣀⡀⣀⡀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣇⠀⠀⠀⠁⠀⠀⠀⠀⠁⠈⠉⠁⠈⠈⠙⠉⠉⠈⠉⠙⠁⠀⠈⠉⠋⠁⠈⠀⠀⠈⠀⠉⠉⠉⠀⠉⠉⠉⠁⠉⠉⠋⠀⠉⠉⠉⠉⠉⠉⠋⠉⠁⠉⠉⠉⠉⠉⠉⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠠⠄⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠤⠤⠤⠤⠤⠤⠤⠄⠤⠤⠤⠠⠤⠤⠤⠤⠤⠤⠄⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣬⠛⠛⠉⠋⠓⠊⠐⠐⠉⠙⠀⠒⠙⠈⠙⠃⠸⢿⠿⠽⠷⠿⠷⠌⠐⠁⠐⠉⠋⠈⠁⠂⠙⠓⠒⠀⠀⠈⠉⠁⠃⣭⣅⠑⠓⠒⠚⠒⠒⠛⠚⠛⠒⠂⠸⠟⠷⠿⠿⠿⠿⠹⠶⠺⠎⠐⠈⠋⠛⠁⠚⠒⠛⠓⠒⠙⢪ ⡷⠿⠶⠶⠶⠶⡶⡴⠄⠸⠧⠶⠶⠶⠆⠸⠷⠶⠲⠶⠺⠆⠰⠶⠶⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠶⠶⠦⠷⠶⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡯⠿⠿⠿⠟⠀⠀⠀⠀⠸⠿⠶⠲⠶⠶⠶⠶⠆⠸⠷⠶⠰⠾⠲⠶⠂⠰⠶⠶⠼⠻⠿⠿⠟⠶⠖⠒⠶⠶⠷⠔⠀⣿⣿⠿⠶⠶⠦⠗⠖⠖⠶⡆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠻⠗⠿⠷⠶⠷⠂⠀⠸⠷⠾⠇⠸⠿⠶⠶⠺⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⡷⠶⠶⠇⠸⠷⠖⠶⠶⠶⡶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠛⠶⠆⠇⠷⠶⠁⠀⠸⠷⠶⠞⠇⠸⠳⠷⠺⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠿⠞⠶⠶⠾⠷⠷⠞⠇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠻⠛⠒⠓⠓⠆⠃⠀⠀⠇⠘⠳⠇⠛⠚⠂⠘⠒⠻⠚⠻⠚⠺⠿⠆⠼⠚⠺⠻⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠛⠛⠗⠟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠙⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠐⠀⠀⠀⠀⠀⠀⢀⢀⠀⡀⠀⠀⠀⠀⢂⠀⣀⠀⠀⠋⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠂⠀⠀⠀⠀⠂⠐⠀⠀⠂⠀⠀⠀⠀⠀⠂⠀⠈ ⡆⠀⠀⠀⠀⠁⠀⠂⠀⠀⠀⠈⠐⠐⠀⠁⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠀⠛⠛⠛⠀⠋⠛⠋⠓⠛⠃⠛⠛⠛⠃⠀⠂⠂⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠈⠐⠀⠀⠂⠉⠀⠀⠀⠂⠀⠒⠂⠒⠂⢰ ⡇⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⢀⣀⣀⠀⢀⠀⣀⣀⠀⣀⣀⡀⠀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⡀⠀⡀⣀⣀⡀⠀⣀⡀⢀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠁⠀⡃⠀⠀⠀⠀⡃⢐⡃⠂⠘⠙⡛⠛⠛⠙⠛⣛⠃⠀⢙⢛⣛⠃⢘⣀⣘⣙⠀⣛⣛⢛⠀⣛⣛⡓⠈⣛⣛⣋⡛⡛⣛⡛⡉⣛⡛⢛⡓⢙⣛⡋⢘⣛⣛⣛⣛⣛⣛⣛⣙⣛⣛⣛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣇⠀⠀⠀⡃⠀⠀⠀⠀⡃⠐⡃⠂⠐⠙⡛⠛⠛⠙⢛⡛⠁⠀⢛⣛⣛⠃⢘⠘⢛⣛⠁⣛⣛⢙⠀⣛⣛⣓⡀⡛⣛⣛⣛⣛⣛⣛⣙⣛⣋⢑⡓⢙⣛⣋⣙⣛⣛⢋⣛⣛⣛⣋⡛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡃⠀⠀⠀⠀⡃⢐⡃⠂⠀⢙⣛⠛⠋⡙⢛⣛⡃⠀⣉⣛⣋⡁⢈⠀⣘⣛⡁⣛⣛⣘⠀⣙⣓⣚⠛⣛⣛⣛⣛⠛⣋⣛⣛⢋⣃⣉⣛⣓⣋⡙⢃⣉⡙⢛⣛⣙⣙⣙⣂⣀⣀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡃⠀⠀⠀⠀⡃⢈⡃⠀⠘⣙⣙⣛⡉⣘⣛⣛⡃⠀⣘⣟⣛⡁⢈⠀⣙⣙⠁⣙⣛⢉⠀⣛⣋⣓⡀⣛⣋⠋⡋⠀⣋⣏⣛⣉⣋⡋⠛⠋⠙⠛⠙⠛⠋⠘⠙⠛⠙⠛⠋⠛⠙⠛⠚⠙⠉⠁⠀⠀⠀⠀⠀⠀⢸ ⡧⠀⠀⠀⡁⠀⠀⠀⠀⡁⢀⡃⠀⠈⣉⣙⢉⡉⣙⣋⣉⡀⠀⣉⣍⣩⡁⢈⠀⠉⢉⡀⡉⣫⢈⠀⣍⣉⣉⣙⣽⣃⣈⢉⣀⣋⡋⣉⣍⣉⣍⣀⡄⣀⣀⡀⣀⡀⣀⣄⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡗⠀⠀⠀⠁⠀⠀⠀⠀⠁⠈⠁⠀⠈⠉⠉⠉⠉⠈⠙⠛⠃⠀⠉⠙⠙⠁⠈⠀⠀⠈⠀⠉⠉⠈⠀⠉⠋⠉⠉⠁⠉⠉⠈⠉⠁⠋⠋⠉⠋⠉⠉⠉⠉⠋⠉⠉⠛⠋⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣤⠀⠨⠐⠀⠀⠀⠂⠀⠐⠂⠐⠀⠀⠀⠒⠀⠸⢷⠾⠿⠷⠷⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠀⠀⠀⠐⣤⣤⠔⠀⠀⠀⠂⠀⠂⠀⠂⠐⠀⠸⠿⠷⠾⠿⠷⠾⠾⠿⠶⠆⠀⠑⠐⠀⠐⠢⠒⠀⠀⠐⠐⢠ ⡿⠿⠶⠶⠶⠶⡶⡶⠆⠸⠧⠷⠶⠶⠆⠸⠷⠶⠲⠶⠾⠇⠸⠶⠶⠶⠶⠾⠶⠶⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠶⠶⠇⠷⠶⠆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡿⠟⠿⠻⠧⠄⠀⠀⠀⠸⠿⠶⠲⠶⠶⠶⠶⠆⠸⠷⠶⠶⠾⠶⠶⠂⠸⠲⠾⠸⠻⠻⠿⠝⠶⠖⠒⠶⠶⠷⠕⠀⣿⣿⠿⠶⠶⠖⠷⠖⠗⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡿⠿⠶⠷⠷⠷⠇⠂⠀⠸⠷⠾⠇⠸⠿⠶⠶⠺⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠷⠷⠶⠿⠰⠷⠶⠷⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠟⠿⠇⠇⠿⠶⠇⠀⠸⠷⠶⠟⠇⠸⠳⠖⠾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⠯⠿⠖⠷⠶⠾⠷⠷⠞⠇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠻⠛⠛⠓⠟⠇⠃⠀⠀⠇⠘⠻⠛⠗⠟⠃⠘⠚⠛⠺⠛⠻⠘⠾⠆⠾⠺⠺⠛⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠗⠛⠟⠛⠇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢂⠀⡂⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠊ ⡖⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠛⠙⠛⠛⠛⠀⠛⠛⠛⠀⠋⠛⠋⠃⠋⠃⠓⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢲ ⡇⠀⠀⠀⡀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⢀⣀⣀⠀⢀⠀⣀⣀⠀⢀⣀⢀⠀⣀⣀⣀⠀⣀⣀⣀⣀⡀⣀⡀⠀⣀⣀⣀⡀⢀⣀⡀⢀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⠀⡃⠀⠀⠀⠀⡃⢈⡃⠂⠐⠙⡛⠛⠛⠙⢛⣛⠃⠀⢛⢛⣛⠃⢘⢀⣘⢙⠀⣛⣛⢚⠀⣛⣛⣓⠀⣛⣛⣋⡛⣛⣛⡛⡘⣛⡛⠛⡓⢙⣛⡋⢙⣛⣛⣛⣛⣛⣓⣛⣙⣛⣛⣛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡧⠀⠀⠀⡃⠀⠀⠀⠀⡃⠘⡃⠀⠐⠙⡛⠛⠛⠙⢛⡛⠃⠀⢉⣛⣋⠃⢘⠘⢛⣛⠁⣛⣛⢘⠀⣛⣛⣓⣀⡛⣛⣛⣛⣛⣛⣛⣛⣛⣋⢙⡓⢙⣛⣋⣙⣛⣛⢛⣛⣚⣙⣋⡛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡃⠀⠀⠀⠀⡃⠀⡃⠀⠀⠙⣛⠙⠋⠙⢛⣛⡀⠀⣙⣛⣋⡁⢈⠀⣛⣛⠀⣙⣛⢊⠀⣛⣓⣛⠙⣓⣛⣛⣛⠉⣉⣛⣛⢋⣋⣉⣋⣙⣋⡛⢙⣋⡛⢚⣛⣉⣉⣛⣂⣀⣀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡃⠀⠀⠀⠀⡃⢈⡃⠀⠈⣙⣛⣛⡉⣙⢛⣙⡁⠀⣙⣛⣛⡁⢈⠀⣛⣛⠁⣙⣛⢈⠀⣛⡛⡓⣀⣛⣛⢛⡋⠈⣋⣋⣋⣈⣋⡋⠛⠙⠉⠋⠙⠛⠋⠙⠛⠛⠛⠛⠋⠛⠛⠙⠙⠙⠙⠁⠀⠀⠀⠀⠀⠀⢸ ⡏⠀⠀⠀⡇⠀⠀⠀⠀⡁⢀⡁⠀⠈⣉⣙⣉⡉⣈⣉⣙⡀⠀⣉⣙⣽⡁⢈⠀⠉⢙⡀⣉⣽⢈⠀⣉⣋⢉⣉⣭⣃⣈⢉⣤⣏⣋⣉⣋⣍⣉⣀⡄⣀⣀⡀⡀⡀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠀⠀⠀⠀⠁⠈⠉⠀⠈⠉⠉⠉⠉⠈⠉⠙⠃⠀⠉⠉⠉⠁⠈⠀⠀⠈⠁⠉⠉⠈⠀⠁⠉⠉⠉⠉⠉⠉⠈⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡤⠚⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠸⢿⠾⠿⠶⠷⠷⠇⠐⠒⠚⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠒⠒⠒⣤⣴⠒⠒⠒⠒⠒⠒⠓⠒⠐⠒⠂⠸⠿⠿⠾⠿⠷⠾⠿⠽⠾⠇⠐⠒⠒⠓⠒⠒⠚⠒⠒⠒⠚⢧ ⡿⠿⠶⠷⠶⠶⡶⡶⠆⠸⠇⠷⠶⠶⠆⠸⠷⠶⠲⠶⠾⠆⠸⠴⠶⠶⠶⠾⠶⠶⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠶⠶⠧⠷⠶⠆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡏⠟⠿⠿⠗⠄⠀⠀⠀⠸⠷⠶⠲⠶⠶⠶⠶⠆⠸⠷⠾⠶⠾⠶⠶⠂⠸⠶⠺⠼⠻⠻⠿⠻⠶⠖⠒⠶⠶⠷⠗⠀⡿⣿⠿⠶⠶⠶⠷⠆⠗⢶⡆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡿⠿⠖⠷⠷⠶⠇⠁⠀⠸⠷⠾⠇⠸⠿⠶⠶⠺⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠷⠶⠶⠷⠰⠳⠶⠶⠲⠶⡶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠟⠶⠆⠇⠿⡶⠁⠀⠸⠷⠶⠞⠇⠸⠳⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠷⠗⠶⠶⠾⠷⠶⠞⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡿⠛⠟⠞⠓⠗⠇⠁⠀⠀⠇⠘⠻⠟⠛⠺⠃⠘⠚⠛⠺⠚⠺⠚⠿⠆⠾⠺⠚⠺⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠛⠛⠛⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠉⠀⠀⠐⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈ ⡖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠀⠛⠛⠛⠀⠋⠛⠋⠓⠛⠃⠓⠛⠛⠓⠀⠀⠀⠀⠀⠁⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠁⠈⢲ ⡇⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⢀⢀⣀⠀⢀⠀⣀⣀⠀⣀⣀⠀⠀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀⡀⢀⢀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⠀⡃⠀⠀⠀⠀⡃⢀⡃⠂⠐⠙⡛⠛⠛⠙⢛⣛⠃⠀⢙⢛⣛⠃⢘⢀⣘⢙⠀⣛⣛⢚⠀⣛⣛⣓⠀⣛⣛⣋⡛⣛⡛⡋⡙⣛⡛⢛⡓⢙⣛⡋⢘⣛⣛⣛⣛⣛⣓⣛⣛⣛⣛⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡃⠀⠀⠀⠀⡃⢘⡃⠀⠐⠙⡛⠛⠛⡙⢛⡛⠃⠀⢙⣛⣛⠃⢘⠘⢛⣛⠁⣛⣛⢘⠀⣛⣛⣓⡀⡛⣛⣛⣛⣛⣛⣛⣛⣛⣋⢙⡓⢙⣛⣋⣙⣛⣛⢛⣛⣚⣘⣛⡛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡃⠀⠀⠀⠀⡃⢐⡃⠀⠘⠙⡛⠛⠉⣙⢛⣛⡁⠀⣉⣛⣋⡁⢈⠀⣚⣛⡁⣛⣛⢈⠀⣙⣓⣚⠛⣛⣛⣛⣛⢛⣋⣛⣛⢋⣋⣉⣛⣉⣋⡙⢁⣋⡙⢛⣛⣙⣉⣛⣂⣀⣀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡃⠀⠀⠀⠀⡃⢈⡃⠀⠘⣙⣛⣛⡋⣙⣛⣛⡁⠀⣙⣛⣛⡁⢈⠀⣙⣛⠁⣙⣛⢈⠀⣛⡋⣓⡀⣛⣋⢋⡋⠈⣋⣋⣋⣉⣋⡋⠛⠛⠉⠛⠙⠛⠋⠙⠛⠛⠛⠛⠋⠛⠛⠙⠚⠛⠙⠁⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡁⠀⠀⠀⠀⡁⢈⡁⠀⠈⣙⣉⣉⡉⣘⣉⣙⡀⠀⣙⣙⣹⡁⢈⠀⠉⢙⡀⣉⣉⢈⠀⣉⣉⢉⣙⣍⣉⣈⢉⣀⣍⣉⣋⣉⣉⣍⣀⡄⣀⣀⡀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠀⠀⠀⠀⠁⠈⠁⠀⠈⠉⠉⠉⠉⠘⠉⠙⠃⠀⠉⠉⠉⠁⠈⠀⠀⠈⠁⠉⠉⠈⠀⠉⠉⠉⠉⠉⠉⠉⠈⠉⠉⠋⠉⠉⠋⠉⠉⠉⠉⠉⠉⠉⠉⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡤⠐⠒⠂⠒⠂⠐⠀⠐⠂⠂⠒⠀⠀⠀⠀⠀⠹⢿⠾⠿⠷⠶⠾⠆⠀⠐⠐⠐⠐⠀⠀⠐⠀⠂⠐⠀⠀⠀⠐⠀⠒⣤⣴⠐⠐⠐⠂⠂⠀⠐⠀⠀⠀⠂⠸⠿⠿⠾⠿⠷⠾⠿⠿⠶⠇⠐⠀⠀⠒⠐⠐⠀⠒⠀⠀⠀⢠ ⡿⠿⠶⠷⠶⢶⡶⡶⠆⠸⠧⠷⠶⠶⠆⠸⠷⠶⠲⠶⠾⠆⠸⠶⠶⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠶⠶⠧⠷⠶⠆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡿⠿⠿⠿⠧⠀⠀⠀⠀⠸⠷⠶⠲⠶⠶⠶⠶⠆⠸⠷⠾⠶⠾⠶⠶⠂⠸⠶⠾⠸⠻⠻⠿⠹⠶⠖⠒⠶⠶⠷⠗⠀⣿⡿⠿⠶⠶⠖⠷⠖⠗⠶⡆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡿⠿⠷⠿⠷⠶⠇⠃⠀⠸⠷⠾⠇⠸⠿⠶⠶⠺⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠷⠶⠶⠿⠰⠷⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠟⠷⠇⠇⠿⠶⠁⠀⠸⠷⠷⠞⠇⠸⠳⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠷⠗⠶⠶⠾⠷⠶⠞⠇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠛⠛⠛⠓⠗⠃⠁⠀⠀⠃⠘⠻⠗⠛⠚⠃⠘⠚⠛⠚⠛⠛⠚⠿⠆⠾⠚⠺⠛⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠑⠒⠒⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⢀⠀⡀⠐⠀⠀⠀⢀⠀⡀⠀⠐⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠀⠐⠈ ⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠛⠛⠛⠛⠛⠀⠛⠛⠛⠀⠋⠛⠋⠓⠛⠃⠓⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢲ ⡇⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⢀⣀⣀⠀⢀⠀⣀⣀⠀⣀⣀⢀⠀⣀⣀⣀⠀⣀⣀⣀⣀⡀⣀⡀⠀⣀⣀⣀⡀⢀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⠀⡃⠀⠀⠀⠀⡃⢘⡃⠂⠐⠙⡛⠛⠛⠙⢛⣛⠃⠀⢛⣛⣛⠃⢘⢀⢘⣙⠀⣛⣛⢚⠀⣛⣛⣓⠀⣛⣛⣋⡛⣛⣛⡛⡙⣛⡛⠛⡓⢙⣛⡋⢙⣛⣛⣛⣛⣛⣛⣛⣙⣛⣛⣛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡃⠀⠀⠀⠀⡃⠐⡃⠀⠐⠙⡛⠛⠛⠙⢛⡛⠃⠀⢙⣛⣛⠃⢘⠘⢛⣛⠁⣛⣛⢘⠀⣛⣛⣓⡀⡛⣛⣛⣛⣛⣛⣛⣛⣛⡋⢙⡓⢙⣛⣋⣙⣛⣛⢛⣛⣛⣙⣛⡛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡃⠀⠀⠀⠀⡃⢐⡃⠂⠈⢙⡛⠛⠋⠙⢛⣛⡃⠀⣉⣛⣋⡁⢘⠀⣚⣛⠁⣙⣛⣈⠀⣙⣓⣚⠛⣛⣛⣛⣛⠛⣋⣛⣛⢋⣋⣉⣋⣙⣋⡙⢁⣋⡙⢛⣋⣉⣉⣛⣂⣀⣀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡃⠀⠀⠀⠀⡃⢈⡃⠀⠈⣙⣛⣛⡋⣙⢛⣛⡁⠀⣙⣛⣛⡁⢈⠀⣙⣛⠁⣙⣛⢈⠀⣛⣛⣛⡀⣛⣛⢛⡋⠈⣋⣛⣋⣉⣋⡋⠚⠛⠙⠛⠙⠛⠋⠙⠛⠛⠛⠛⠋⠛⠛⠛⠛⠙⠙⠁⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡁⠀⠀⠀⠀⡁⢀⡃⠀⠈⣉⣋⣉⡉⣘⣙⣉⡀⠀⣙⣙⣹⡁⢈⠀⠙⢙⡀⣩⣻⢈⠀⣍⣋⢉⣉⣯⣃⣈⢋⣄⣍⣉⣋⣍⣍⣉⣀⡄⣀⣀⡀⣄⣄⣀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠀⠀⠀⠀⠁⠈⠉⠀⠈⠉⠉⠉⠉⠘⠉⠙⠃⠀⠉⠙⠙⠁⠈⠀⠀⠈⠀⠉⠉⠉⠀⠋⠉⠉⠉⠉⠉⠋⠈⠉⠉⠉⠋⠉⠉⠋⠉⠉⠉⠉⠉⠋⠉⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠐⠀⠀⠐⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠸⢷⠾⠿⠷⠶⠶⠆⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠂⠀⠀⠐⣄⣤⠐⠒⠂⠂⠐⠀⠃⠒⠂⠂⠈⠸⠿⠷⠾⠿⠷⠾⠿⠵⠶⠆⠐⠀⠂⠂⠀⠀⠈⠀⠀⠐⠀⢠ ⡷⠿⠶⠷⠶⠶⡶⡶⠆⠸⠧⠷⠶⠶⠆⠸⠷⠶⠲⠶⠾⠆⠸⠴⠶⠶⠶⠾⠶⠶⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠷⠶⠶⠇⠷⠶⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡗⠟⠿⠻⠷⠀⠀⠀⠀⠸⠷⠶⠲⠶⠶⠶⠶⠆⠸⠷⠾⠶⠺⠶⠶⠂⠸⠶⠾⠸⠻⠻⠿⠝⠶⠖⠒⠶⠶⠷⠓⠀⣿⣿⠿⠶⠶⠦⠗⠖⠗⠶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠻⠖⠿⠷⠶⠇⠀⠀⠸⠷⠾⠇⠸⠿⠶⠶⠺⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿⠷⠶⠶⠗⠰⠷⠶⠶⠲⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠟⠶⠆⠇⠿⠶⠀⠀⠸⠷⠶⠞⠇⠸⠱⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⣿⠟⠷⠖⠶⠶⠾⠷⠶⠞⠇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠛⠛⠚⠓⠛⠃⠁⠀⠀⠃⠘⠻⠗⠟⠚⠂⠘⠚⠛⠚⠛⠚⠚⠿⠆⠾⠚⠺⠛⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡿⠟⠓⠛⠟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠀⠛⠛⠛⠀⠋⠛⠋⠓⠓⠃⠓⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡇⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⢀⢀⣀⠀⢀⠀⣀⣀⠀⣀⣀⢀⠀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀⡀⢀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⠀⡃⠀⠀⠀⠀⡃⢈⡃⠂⠐⠙⡛⠛⠛⠙⢛⣛⠃⠀⢛⣛⣛⠃⢘⢀⣚⣙⠀⣛⣛⢘⠀⣛⣛⣓⠀⣛⣛⣋⡛⣛⣛⡛⡙⣛⡛⠛⡓⢙⣛⡋⢘⣛⣛⣛⣛⣛⣓⣛⣙⣛⣛⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡃⠀⠀⠀⠀⡃⠘⡃⠀⠐⠙⡛⠛⠛⠙⢛⡛⠃⠀⢙⣛⣛⠁⢘⠘⢛⣛⠁⣛⣛⢘⠀⣛⣛⣓⡀⡛⣛⣛⣛⣛⣛⣛⣛⣛⣋⢙⡓⢙⣛⣋⣙⣛⣛⢛⣛⣛⣙⣛⡛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡃⠀⠀⠀⠀⡃⢀⡃⠂⠀⠙⡛⠛⠋⠙⢛⣛⡀⠀⣉⣛⣋⡁⢘⠀⣚⣛⠁⣙⣛⢈⠀⣙⣓⣛⠛⣛⣛⣛⣛⠛⣋⣛⣛⢋⣋⣉⣛⣉⣋⡛⢁⣋⡙⢛⣛⣙⣉⣛⣂⣀⣀⢀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡃⠀⠀⠀⠀⡃⢈⡃⠀⠈⣙⣛⣛⡉⣙⢛⣛⡁⠀⣙⣛⣛⡁⢈⠀⣙⣙⠁⣙⣛⢈⠀⣛⣋⡓⣀⣛⣛⢋⡋⠈⣋⣋⣋⣉⣋⡋⠚⠛⠙⠋⠙⠛⠋⠙⠛⠛⠛⠛⠋⠛⠛⠙⠚⠙⠙⠁⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡁⠀⠀⠀⠀⡁⢀⡁⠀⠈⣉⣙⣉⡉⣈⣉⣙⡀⠀⣙⣉⣹⡁⢈⠀⠉⢙⡀⣉⣙⢈⠀⣍⣉⢉⣉⣩⣉⣈⢉⣀⣍⣍⣉⣍⣍⣉⣀⡄⣀⣀⡀⡀⣀⣀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠀⠀⠀⠀⠁⠈⠁⠀⠈⠉⠉⠉⠉⠈⠉⠙⠃⠀⠉⠉⠉⠁⠈⠀⠀⠈⠁⠉⠉⠈⠀⠁⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢷⠾⠿⠷⠶⠶⠄⠐⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⠿⠷⠾⠿⠷⠾⠿⠵⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⡿⠿⠶⠷⠶⢶⡶⡶⠆⠸⠇⠷⠶⠶⠆⠸⠷⠶⠲⠶⠾⠆⠸⠴⠶⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠶⠶⠧⠷⠶⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠟⠿⠿⠧⠀⠀⠀⠀⠸⠷⠶⠲⠶⠶⠶⠶⠆⠸⠷⠶⠶⠺⠶⠶⠂⠸⠶⠾⠸⠻⠻⠿⠙⠶⠖⠒⠶⠶⠷⠗⠀⣿⣿⠿⠶⠶⠶⠷⠖⠗⠶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡿⠿⠖⠿⠷⠶⠇⠀⠀⠸⠷⠾⠇⠸⠿⠶⠶⠺⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠷⠶⠶⠿⠰⠷⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠟⠶⠆⠇⠿⠶⠀⠀⠸⠷⠶⠞⠇⠸⠳⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠷⠖⠶⠶⠾⠷⠶⠞⠇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠛⠛⠚⠓⠛⠇⠁⠀⠀⠇⠘⠻⠗⠟⠚⠃⠘⠚⠻⠚⠛⠚⠚⠿⠆⠾⠚⠚⠺⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠛⠛⠟⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠀⠛⠛⠛⠀⠋⠛⠋⠃⠓⠃⠓⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡇⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⢀⢀⣀⠀⢀⠀⣀⣀⠀⣀⣀⢀⠀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀⡀⢀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⠀⡃⠀⠀⠀⠀⡃⢘⡃⠂⠐⠙⡛⠛⠛⠙⢛⣛⠃⠀⢛⣛⣛⠃⢘⢀⣘⣙⠀⣛⣛⢚⠀⣛⣛⣓⠀⣛⣛⣋⡛⣛⣛⡛⡘⣛⡛⠛⡓⢙⣛⡋⢙⣛⣛⣛⣛⣛⣓⣛⣙⣛⣛⣛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡃⠀⠀⠀⠀⡃⠐⡃⠀⠐⠙⡛⠛⠛⠙⢛⡛⠃⠀⢙⣛⣛⠃⢘⠘⢛⣛⠁⣛⣛⢘⠀⣛⣛⣓⡀⡛⣛⣛⣛⣛⣛⣛⣛⣛⡋⢙⡓⢙⣛⣋⣙⣛⣛⢛⣛⣛⣙⣛⡛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡃⠀⠀⠀⠀⡃⢐⡃⠀⠈⠙⡛⠛⠋⠙⢛⣛⡀⠀⣉⣛⣋⡁⢘⠀⣛⣛⠁⣙⣛⢈⠀⣙⣓⣛⠛⣛⣛⣛⣛⠛⣉⣛⣛⢋⣋⣉⣛⣙⣋⡛⢁⣋⡙⢛⣛⣙⣉⣛⣂⣀⣀⢀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡃⠀⠀⠀⠀⡃⢈⡃⠀⠈⣙⣛⣛⡋⣙⢛⣛⡃⠀⣙⣛⣛⡁⢈⠀⣙⣙⠁⣙⣛⢈⠀⣛⣋⡓⣀⣛⣋⠛⡋⠈⣋⣋⣋⣉⣋⡋⠛⠛⠉⠛⠙⠛⠋⠙⠛⠛⠛⠛⠋⠛⠛⠙⠚⠙⠙⠁⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡁⠀⠀⠀⠀⡁⢀⡁⠀⠈⣉⣉⣉⡉⣈⣉⣉⡀⠀⣉⣉⣹⡁⢈⠀⠙⢙⡀⣉⣉⢈⠀⣩⣉⢉⣉⣭⣁⣈⢉⣀⣍⣍⣍⣍⣉⣍⣀⡄⣀⣀⡀⡀⡀⣀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠀⠀⠀⠀⠁⠈⠁⠀⠈⠉⠉⠉⠉⠈⠉⠙⠃⠀⠉⠉⠙⠁⠈⠀⠀⠈⠁⠉⠉⠈⠀⠉⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠋⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠂⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠸⢷⠿⠿⠿⠶⠾⠆⠀⠐⠂⠀⠀⠂⠀⠀⠀⠀⠂⠐⠐⠀⠀⠂⠀⣦⣴⠐⠐⠂⠂⠀⠐⠀⠀⠂⠐⠀⠸⠿⠷⠾⠿⠷⠾⠿⠵⠾⠆⠀⠀⠀⠀⠀⠂⠀⠀⠀⠂⠀⢠ ⡷⠿⠶⠷⠶⠶⡶⡶⠆⠸⠧⠷⠶⠶⠆⠸⠷⠶⠲⠶⠾⠆⠸⠴⠶⠶⠶⠾⠶⠶⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠟⠿⠿⠇⠀⠀⠀⠀⠸⠷⠶⠲⠶⠶⠶⠶⠆⠸⠷⠾⠶⠺⠶⠶⠂⠸⠶⠾⠸⠻⠻⠿⠙⠶⠖⠒⠶⠶⠷⠗⠀⣿⣿⠿⠶⠶⠖⠷⠖⠗⠶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡿⠻⠖⠿⠷⠶⠇⠂⠀⠸⠷⠾⠇⠸⠿⠶⠶⠺⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠷⠶⠶⠷⠰⠷⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠟⠶⠆⠇⠿⠶⠂⠀⠸⠷⠶⠞⠇⠸⠳⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠷⠖⠶⠶⠾⠷⠶⠞⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠛⠟⠒⠓⠛⠇⠁⠀⠀⠇⠘⠻⠗⠛⠚⠃⠘⠚⠛⠚⠛⠚⠚⠿⠆⠾⠺⠚⠛⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠛⠛⠛⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠀⠛⠛⠛⠀⠋⠛⠋⠃⠓⠃⠓⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡇⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⢀⢀⣀⠀⢀⠀⣀⣀⠀⣀⣀⢀⠀⣀⣀⣀⠀⣀⣀⣀⣀⡀⣀⡀⠀⣀⣀⣀⡀⢀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⠀⡃⠀⠀⠀⠀⡃⢘⡃⠂⠐⠙⡛⠛⠛⠙⢛⣛⠃⠀⢛⣛⣛⠃⢘⢀⣘⣙⠀⣛⣛⢚⠀⣛⣛⣓⠀⣛⣛⣋⡛⣛⣛⡋⡙⣛⡛⢛⡓⢙⣛⡋⢙⣛⣛⣛⣛⣛⣛⣛⣙⣛⣛⣛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡃⠀⠀⠀⠀⡃⢘⡃⠀⠘⠙⡛⠛⠛⠙⢛⡛⠃⠀⢙⣛⣛⠁⢘⠘⢛⣛⠁⣛⣛⢘⠀⣛⣛⣓⡀⡛⣛⣛⣛⣛⣛⣛⣛⣛⣋⢙⡓⢙⣛⣋⣙⣛⣛⢛⣛⣛⣙⣛⡛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡃⠀⠀⠀⠀⡃⢀⡃⠀⠈⠙⡛⠛⠋⡙⢛⣛⡀⠀⣉⣛⣋⡁⢈⠀⣛⣛⠁⣙⣛⢈⠀⣙⣓⣚⠛⣛⣛⣛⣛⠛⣋⣛⣛⢋⣋⣉⣛⣙⣋⡛⢁⣋⡙⢛⣛⣙⣉⣛⣂⣀⣀⢀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡃⠀⠀⠀⠀⡃⢈⡃⠀⠈⣙⣛⣛⡋⣙⢛⣛⡁⠀⣙⣛⣛⡁⢈⠀⣙⣙⠁⣙⣛⢈⠀⣛⣛⣓⣀⣛⣋⢛⡋⠈⣋⣋⣋⣉⣋⡋⠛⠛⠙⠋⠙⠛⠋⠙⠛⠛⠛⠛⠋⠛⠛⠛⠛⠙⠙⠁⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡁⠀⠀⠀⠀⡁⢀⡁⠀⠈⣉⣉⣉⡉⣈⣉⣉⡀⠀⣙⣩⣹⡁⢈⠀⠙⢙⡀⣉⣩⢈⠀⣩⣉⢉⣉⣭⣩⣈⢉⣀⣍⣍⣍⣍⣍⣅⣀⡄⣀⣀⡀⡀⡀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠀⠀⠀⠀⠁⠈⠁⠀⠈⠉⠉⠉⠉⠈⠉⠙⠃⠀⠉⠉⠉⠁⠈⠀⠀⠈⠁⠉⠉⠉⠀⠁⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢷⠾⠿⠷⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠾⠿⠷⠾⠾⠷⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⡿⠿⠶⠷⠶⠶⡶⡶⠆⠸⠧⠷⠶⠶⠆⠸⠷⠶⠲⠶⠾⠆⠸⠶⠶⠶⠶⠾⠶⠶⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠟⠿⠿⠷⠀⠀⠀⠀⠸⠷⠶⠲⠶⠶⠶⠶⠆⠸⠷⠾⠶⠺⠶⠶⠂⠸⠶⠾⠸⠻⠻⠿⠙⠶⠖⠒⠶⠶⠷⠗⠀⣿⣿⠿⠶⠶⠶⠷⠖⠷⠶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡿⠻⠖⠿⠷⠶⠇⠂⠀⠸⠷⠾⠇⠸⠿⠶⠶⠺⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠷⠶⠶⠗⠰⠷⠶⠶⠲⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠟⠷⠆⠇⠿⠶⠁⠀⠸⠷⠶⠞⠇⠸⠳⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡯⠟⠷⠖⠶⠶⠾⠷⠶⠞⠇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠛⠟⠒⠓⠛⠇⠁⠀⠀⠇⠘⠻⠗⠛⠚⠃⠘⠚⠛⠚⠛⠚⠚⠿⠆⠾⠚⠺⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠟⠛⠛⠟⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠀⠛⠛⠛⠀⠋⠛⠋⠃⠓⠃⠓⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲ ⡇⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⢀⢀⣀⠀⢀⠀⣀⣀⠀⣀⣀⢀⠀⣀⣀⣀⠀⣀⣀⣀⣀⡀⣀⡀⠀⣀⣀⣀⡀⢀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⠀⡃⠀⠀⠀⠀⡃⢘⡃⠂⠐⠙⡛⠛⠛⠙⢛⣛⠃⠀⢛⢛⣛⠃⢘⢀⣘⣙⠀⣛⣛⢚⠀⣛⣛⣓⠀⣛⣛⣋⡛⣛⣛⡋⡙⣛⡛⢛⡓⢙⣛⡋⢙⣛⣛⣛⣛⣛⣛⣛⣙⣛⣛⣛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡃⠀⠀⠀⠀⡃⢘⡃⠀⠐⠙⡛⠛⠛⠙⢛⡛⠃⠀⢙⣛⣛⠁⢘⠘⢛⣛⠁⣛⣛⢘⠀⣛⣛⣓⡀⡛⣛⣛⣛⣛⣛⣛⣛⣛⣋⢙⡓⢙⣛⣋⣙⣛⣛⢛⣛⣛⣙⣛⡛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡃⠀⠀⠀⠀⡃⢐⡃⠀⠈⠙⡛⠛⠋⡙⢛⣛⡀⠀⣉⣛⣋⡁⢈⠀⣚⣛⠁⣙⣛⢈⠀⣙⣓⣛⠛⣛⣛⣛⣛⠋⣉⣛⣛⢋⣋⣉⣋⣙⣋⡙⢁⣋⡙⢛⣛⣙⣉⣛⣂⣀⣀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡃⠀⠀⠀⠀⡃⢈⡃⠀⠈⣙⣛⣛⡋⣘⢛⣛⡁⠀⣙⣛⣛⡁⢈⠀⣙⣛⠁⣙⣛⢈⠀⣛⣛⣓⣀⣛⣛⢛⡋⠈⣋⣋⣋⣉⣋⡋⠛⠛⠙⠋⠙⠛⠋⠙⠛⠋⠛⠛⠋⠛⠛⠙⠚⠙⠙⠁⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡁⠀⠀⠀⠀⡁⢀⡁⠀⠈⣉⣉⣉⡉⣈⣙⣉⡀⠀⣉⣉⣹⡁⢈⠀⠙⢙⡀⣉⣉⢈⠀⣩⣉⢉⣉⣭⣁⣈⢉⣀⣍⡉⣋⣍⣉⣉⣀⡄⣀⣀⡀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠀⠀⠀⠀⠁⠈⠁⠀⠈⠉⠉⠉⠉⠈⠉⠙⠃⠀⠉⠉⠉⠁⠈⠀⠀⠈⠁⠉⠉⠈⠀⠁⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠹⢷⠾⠿⠷⠶⠶⠆⠀⠂⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠾⠿⠷⠾⠿⠷⠶⠆⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⢢ ⡿⠿⠶⠷⠶⢶⡶⡶⠆⠸⠧⠷⠶⠶⠆⠸⠷⠶⠲⠶⠾⠆⠸⠶⠶⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡿⠟⠿⠿⠧⠀⠀⠀⠀⠸⠷⠶⠲⠶⠶⠶⠶⠆⠸⠷⠾⠶⠾⠶⠶⠂⠸⠶⠾⠸⠻⠻⠿⠙⠶⠖⠒⠶⠶⠷⠗⠀⣿⣿⠿⠶⠶⠶⠷⠖⠷⠶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡿⠿⠶⠿⠷⠶⠇⠁⠀⠸⠷⠾⠇⠸⠿⠶⠶⠺⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠷⠶⠶⠿⠰⠷⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠟⠷⠆⠇⠿⠶⠃⠀⠸⠷⠶⠞⠇⠸⠳⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠷⠖⠶⠶⠾⠷⠶⠞⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠛⠛⠚⠓⠛⠇⠁⠀⠀⠇⠘⠻⠗⠛⠚⠃⠘⠚⠛⠚⠛⠚⠚⠿⠆⠾⠚⠺⠻⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠛⠛⠛⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠀⠛⠛⠛⠀⠋⠛⠋⠓⠛⠃⠓⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡇⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⢀⢀⣀⠀⢀⠀⣀⣀⠀⣀⣀⢀⠀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀⡀⢀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⠀⡃⠀⠀⠀⠀⡃⢐⡃⠂⠐⠙⡛⠛⠛⠙⢛⣛⠃⠀⢛⣛⣛⠃⢘⢀⣘⣙⠀⣛⣛⢚⠀⣛⣛⣓⠀⣛⣛⣋⡛⣛⣛⡛⡘⣛⡛⠛⡓⢙⣛⡋⢙⣛⣛⣛⣛⣛⣛⣛⣙⣛⣛⣛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡃⠀⠀⠀⠀⡃⢘⡃⠀⠐⠙⡛⠛⠛⠙⢛⡛⠃⠀⢙⣛⣛⠃⢘⠘⢛⣛⠁⣛⣛⢘⠀⣛⣛⣓⣀⡛⣛⣛⣛⣛⣛⣛⣛⣛⣋⢙⡓⢙⣛⣋⣙⣛⣛⢛⣛⣛⣙⣛⡛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡃⠀⠀⠀⠀⡃⢀⡃⠂⠈⠙⡛⠛⠋⠙⢛⣛⡀⠀⣉⣛⣋⡁⢘⠀⣛⣛⠁⣙⣛⢈⠀⣙⣓⣛⠛⣛⣛⣛⣛⠛⣋⣛⣛⢋⣋⣉⣋⣙⣋⡛⢁⣋⡙⢛⣛⣙⣉⣛⣂⣀⣀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡃⠀⠀⠀⠀⡃⢈⡃⠀⠈⣙⣛⣛⡉⣘⢛⣛⡁⠀⣙⣛⣛⡁⢈⠀⣙⣙⠁⣙⣛⢈⠀⣛⣛⣓⣀⣛⣋⢛⡋⠈⣋⣋⣋⣉⣋⡋⠛⠛⠙⠛⠙⠛⠋⠙⠛⠛⠛⠛⠛⠛⠛⠙⠚⠙⠙⠁⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡁⠀⠀⠀⠀⡁⢀⡁⠀⠈⣉⣉⣉⡉⣈⣉⣙⡀⠀⣉⣉⣹⡁⢈⠀⠉⢙⡀⣉⣉⢈⠀⣭⣉⢉⣉⣭⣍⣈⢉⣀⣍⣉⣉⣉⣉⣉⣀⡄⣀⣀⡀⡀⣀⣀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠀⠀⠀⠀⠁⠈⠁⠀⠈⠉⠉⠉⠉⠈⠉⠙⠃⠀⠉⠉⠉⠁⠈⠀⠀⠈⠁⠉⠉⠈⠀⠁⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠹⢷⠾⠿⠷⠶⠶⠆⠀⠂⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠾⠿⠷⠾⠿⠷⠶⠆⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⢢ ⡿⠿⠶⠷⠶⢶⡶⡶⠆⠸⠧⠷⠶⠶⠆⠸⠷⠶⠲⠶⠾⠆⠸⠶⠶⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡿⠟⠿⠿⠧⠀⠀⠀⠀⠸⠷⠶⠲⠶⠶⠶⠶⠆⠸⠷⠾⠶⠾⠶⠶⠂⠸⠶⠾⠸⠻⠻⠿⠙⠶⠖⠒⠶⠶⠷⠗⠀⣿⣿⠿⠶⠶⠶⠷⠖⠷⠶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡿⠿⠶⠿⠷⠶⠇⠁⠀⠸⠷⠾⠇⠸⠿⠶⠶⠺⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠷⠶⠶⠿⠰⠷⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠟⠷⠆⠇⠿⠶⠃⠀⠸⠷⠶⠞⠇⠸⠳⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠷⠖⠶⠶⠾⠷⠶⠞⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠛⠛⠚⠓⠛⠇⠁⠀⠀⠇⠘⠻⠗⠛⠚⠃⠘⠚⠛⠚⠛⠚⠚⠿⠆⠾⠚⠺⠻⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠛⠛⠛⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠀⠛⠛⠛⠀⠋⠛⠋⠓⠛⠃⠓⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡇⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⢀⢀⣀⠀⢀⠀⣀⣀⠀⣀⣀⢀⠀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀⡀⢀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⠀⡃⠀⠀⠀⠀⡃⢐⡃⠂⠐⠙⡛⠛⠛⠙⢛⣛⠃⠀⢛⣛⣛⠃⢘⢀⣘⣙⠀⣛⣛⢚⠀⣛⣛⣓⠀⣛⣛⣋⡛⣛⣛⡛⡘⣛⡛⠛⡓⢙⣛⡋⢙⣛⣛⣛⣛⣛⣛⣛⣙⣛⣛⣛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡃⠀⠀⠀⠀⡃⢘⡃⠀⠐⠙⡛⠛⠛⠙⢛⡛⠃⠀⢙⣛⣛⠃⢘⠘⢛⣛⠁⣛⣛⢘⠀⣛⣛⣓⣀⡛⣛⣛⣛⣛⣛⣛⣛⣛⣋⢙⡓⢙⣛⣋⣙⣛⣛⢛⣛⣛⣙⣛⡛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡃⠀⠀⠀⠀⡃⢀⡃⠂⠈⠙⡛⠛⠋⠙⢛⣛⡀⠀⣉⣛⣋⡁⢘⠀⣛⣛⠁⣙⣛⢈⠀⣙⣓⣛⠛⣛⣛⣛⣛⠛⣋⣛⣛⢋⣋⣉⣋⣙⣋⡛⢁⣋⡙⢛⣛⣙⣉⣛⣂⣀⣀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡃⠀⠀⠀⠀⡃⢈⡃⠀⠈⣙⣛⣛⡉⣘⢛⣛⡁⠀⣙⣛⣛⡁⢈⠀⣙⣙⠁⣙⣛⢈⠀⣛⣛⣓⣀⣛⣋⢛⡋⠈⣋⣋⣋⣉⣋⡋⠛⠛⠙⠛⠙⠛⠋⠙⠛⠛⠛⠛⠛⠛⠛⠙⠚⠙⠙⠁⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡁⠀⠀⠀⠀⡁⢀⡁⠀⠈⣉⣉⣉⡉⣈⣉⣙⡀⠀⣉⣉⣹⡁⢈⠀⠉⢙⡀⣉⣉⢈⠀⣭⣉⢉⣉⣭⣍⣈⢉⣀⣍⣉⣉⣉⣉⣉⣀⡄⣀⣀⡀⡀⣀⣀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠀⠀⠀⠀⠁⠈⠁⠀⠈⠉⠉⠉⠉⠈⠉⠙⠃⠀⠉⠉⠉⠁⠈⠀⠀⠈⠁⠉⠉⠈⠀⠁⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠸⢷⠾⠿⠷⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠾⠿⠷⠾⠿⠵⠶⠆⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⢢ ⡿⠿⠶⠷⠶⠶⡶⡶⠆⠸⠧⠷⠶⠶⠆⠸⠷⢶⠲⠶⠾⠆⠸⠶⠶⠶⠶⠾⠶⠶⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠟⠿⠿⠧⠀⠀⠀⠀⠸⠷⠶⠲⠶⠶⠶⠶⠆⠸⠳⠾⠶⠺⠶⠶⠂⠸⠶⠾⠸⠻⠻⠿⠙⠶⠖⠒⠶⠶⠷⠗⠀⣿⣿⠿⠶⠶⠖⠷⠖⠗⠶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡿⠿⠖⠿⠷⠶⠇⠁⠀⠸⠷⠾⠇⠸⠿⠶⠶⠺⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠷⠶⠶⠷⠰⠷⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠟⠷⠆⠇⠿⠶⠃⠀⠸⠷⠶⠞⠇⠸⠳⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠟⠷⠖⠶⠶⠾⠷⠶⠞⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠛⠛⠒⠓⠛⠃⠁⠀⠀⠇⠘⠻⠗⠛⠚⠃⠘⠚⠃⢸⡟⠚⠚⠿⠆⠾⠚⠺⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠟⠛⠛⠛⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⡖⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠀⠛⠛⠛⠀⠋⠛⠋⠓⠛⠃⠓⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⣇⡀⠀⠀⡀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⢀⢀⣀⠀⢀⠀⣀⣀⠀⣀⣀⢀⠀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀⡀⢀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠄⠉⠀⡃⠀⠀⠀⠀⡃⢐⡃⠂⠐⠙⡛⠛⠛⠙⢛⣛⠃⠀⢛⢛⣛⠃⢘⢀⣘⣙⠀⣛⣛⢚⠀⣛⣛⣓⠀⣛⣛⣃⡛⣛⡛⡋⡈⣛⡛⠛⡓⢙⣛⡋⢙⣛⣛⣛⣛⣛⣛⣛⣙⣛⣛⣛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡃⠀⠀⠀⠀⡃⢘⡃⠀⠐⠙⡛⠛⠛⠙⢛⡛⠃⠀⢙⣛⣛⠃⢘⠘⢛⣛⠁⣛⣛⢘⠀⣛⣛⣓⡀⡛⣛⣛⣛⣛⣛⣛⣛⣛⣋⢙⡓⢙⣛⣋⣙⣛⣛⢛⣛⣛⣙⣛⡛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣇⠀⠀⠀⡃⣀⠀⠀⠀⡃⣆⡃⠂⠈⠙⡛⠛⠋⠙⢛⣛⡀⠀⣉⣛⣋⡁⢘⠀⣛⣛⠁⣙⣛⢈⠀⣙⣓⣚⠛⣛⣛⣓⣟⠛⣋⣛⣛⢋⣋⣉⣋⣙⣋⡛⢁⣋⡙⢚⣛⣙⣉⣛⣂⣀⣀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡃⠀⠀⠀⠀⡃⢈⡃⠀⠈⣙⣛⣛⡉⣘⢛⣛⡁⠀⣙⣛⣛⡁⢈⠀⣙⣙⠁⣙⣛⢈⠀⣛⣛⣃⣀⣛⣋⣋⡋⠈⣋⣋⣋⣉⣋⡋⠛⠛⠙⠛⠙⠛⠋⠙⠛⠛⠛⠛⠋⠛⠛⠙⠘⠙⠙⠁⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡁⠀⠀⠀⠀⡁⢀⡁⠀⠈⣉⣉⣉⡉⣈⣉⣉⡀⠀⣉⣉⣹⡁⢈⠀⠉⢙⡀⣉⣉⢈⠀⣭⣉⢉⣉⣭⣉⣈⢉⣀⣍⣉⣉⣉⣉⣁⣀⡄⣀⣀⡀⡀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠀⠀⠀⠀⠁⠈⠁⠀⠈⠉⠉⠉⠉⠈⠉⠙⠃⠀⠉⠉⠉⠁⠈⠀⠀⠈⠁⠉⠉⠈⠀⠁⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠄⠀⣤⣤⣦⣤⣄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠁⠀⠛⠛⠻⠟⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⢦⣤⣦⣤⡄⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠊⠋⠻⠟⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣢⣤⣧⣦⡆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠈⠉⠹⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⢶⣶⣷⣶⠆⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡈⠁⡙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠄⣷⣶⣷⣶⡆⠆⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⡧⡁⠁⡙⠃⢁⡼⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠸⢷⠾⠿⠷⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠾⠿⠷⠾⠿⠵⠶⠆⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⢢ ⡿⠿⠶⠷⠶⠶⡶⡶⠆⠸⠧⠷⠶⠶⠆⠸⠷⢲⠲⠶⠾⠆⠸⠶⠶⠶⠶⠾⠶⠶⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠟⠿⠿⠧⠀⠀⠀⠀⠈⠀⠠⠲⠶⠶⠶⠶⠎⠸⠳⠾⠶⠺⠶⠶⠂⠸⠶⠾⠸⠻⠻⠿⠙⠶⠖⠒⠶⠶⠷⠗⠀⣿⣿⠿⠶⠶⠖⠷⠖⠗⠶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡿⠿⠶⠿⠷⠶⠇⠁⠀⠸⠷⠾⠇⠸⠿⠶⠶⠺⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠷⠶⢶⠷⠰⠷⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠟⠷⠆⠇⠿⠶⠃⠀⠸⠷⠶⠞⠇⠸⠳⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠟⠓⠛⠶⠶⠾⠷⠶⠞⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠛⠛⠚⠓⠛⠇⠁⠀⠀⠇⠐⡢⢔⠛⠚⠃⠘⠚⢣⣼⡖⠚⠚⠿⠆⠾⠚⠺⠛⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠟⠛⢛⠛⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠚⠀⠀⠈⠀⠑⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⡆⢮⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠀⠛⠛⠛⠀⠋⠛⠋⡃⡯⠃⡓⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⣇⠈⠀⠀⡀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⢀⢀⣀⠀⢀⠀⣀⣀⠀⣀⣀⢀⠀⣀⣀⣀⠀⣀⣀⡤⣀⠀⣀⡀⠀⣀⢀⣀⡀⢀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣏⣗⠍⠀⡃⠀⠀⠀⠀⡃⢐⡃⠂⠐⠙⡛⠛⠛⠙⢛⣛⠃⠀⢛⢛⣛⠃⢘⢀⣘⣙⠀⣛⣛⢚⠀⣛⣛⣓⠀⣛⣛⡒⡟⣟⡛⡛⡈⣻⣟⠗⡓⢙⣛⡋⢙⣛⣛⣛⣛⣛⣛⣛⣙⣛⣛⣛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠃⠀⠀⠀⠀⠃⢘⡃⠀⠐⠙⡛⠛⠛⠙⢛⡛⠃⠀⢙⣛⣛⠃⢘⠘⢛⣛⠁⣛⣛⢘⠀⣛⣛⣓⡀⡛⣛⣛⣋⡛⣛⣛⣛⣛⡋⢙⡓⢙⣛⣋⣙⣛⣛⢛⣛⣛⣙⣛⡛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣇⠀⠀⠀⣒⣆⠀⠀⠀⡃⣆⡃⠂⠈⠙⡛⠛⠋⠙⢛⣛⡀⠀⣉⣛⣋⡁⢘⠀⣛⣛⠁⣙⣛⢈⠀⣙⣓⣚⠛⣛⣛⣓⣟⠟⣏⣛⣛⢋⣋⣉⣋⣙⣋⡛⢁⣋⡙⢚⣛⣙⣉⣛⣂⣀⣀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡃⠁⠀⠀⠀⡃⢉⡃⠀⠈⠙⠛⠛⠉⣘⢛⣛⡁⠀⠙⠛⣛⡁⢈⠀⣙⣙⠁⣙⣛⢈⠀⣛⣛⣓⣀⣛⣋⡋⡋⠉⣉⣋⣋⣉⣋⡋⠛⠛⠙⠛⠙⠛⠋⠙⠛⠛⠛⠛⠋⠛⠛⠙⠘⠙⠙⠁⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡁⠀⠀⠀⠀⡁⢀⡧⠠⠤⠤⠤⠄⠤⠤⠤⠤⠤⠤⠤⠄⣼⡥⢈⠀⠉⢙⡀⣉⣉⢈⠀⣭⣉⢉⣉⣭⣉⣈⢉⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠈⠁⠉⠉⠈⠀⠁⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠄⠀⣤⣤⣄⣤⣄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠁⠀⠛⠛⠻⠟⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⢦⣤⣦⣤⡄⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠊⠋⠻⠟⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠈⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣢⣤⣧⣦⡆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡈⠉⠹⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⢶⣶⣷⣶⠆⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡈⠁⡙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠀⣗⣶⣷⣶⡆⠆⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⡠⡋⠁⠙⠃⢁⡼⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠸⢷⡾⢿⠷⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠾⠿⠷⠾⠿⠵⠶⠆⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⢢ ⡿⠿⠶⠷⠶⠶⡶⡶⠆⠐⡀⢰⠶⢶⣆⡸⠷⢲⢲⡶⠾⠆⠸⠶⠶⠶⠶⠾⠶⠶⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠟⠿⠿⠧⠀⠀⠀⠀⠈⠀⠠⠲⠶⠶⠶⠶⠎⠸⠳⠾⠶⠺⠶⠶⠂⠸⠶⠾⠸⠻⠻⠿⠙⠶⠖⠒⠶⠶⠷⠗⠀⣿⣿⠿⠖⠖⠖⠷⠖⠗⠶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡿⠿⠖⠿⠷⠶⠇⠁⠀⠸⠷⠾⠇⠸⠿⠶⠶⠺⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠷⠶⢶⠷⠰⠷⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠟⠷⠆⠇⠿⠶⠃⠀⠸⠷⠶⠞⠇⠸⠳⠶⠶⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠟⠃⠙⠶⠶⠾⠷⠶⠞⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠛⠛⠚⠓⠛⠇⠁⠀⠀⠇⠐⡢⢔⠛⠚⠃⠘⠚⢣⣼⡖⠚⠚⠿⠆⠾⠚⠺⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⠛⢛⠛⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠚⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⣟⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⣶⣮⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠀⠛⠛⠛⠀⠋⠛⠋⡃⡯⡣⡓⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⣇⠈⠀⠀⡀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⢀⢀⣀⠀⢀⠀⣀⣀⠀⣀⣀⢀⠀⣀⣀⣀⠀⣀⣀⡤⣨⠀⣀⡀⠀⣀⢀⣀⡀⢀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣏⣗⠍⠀⡃⠀⠀⠀⠀⡃⢐⡃⠂⠐⠙⡛⠛⠛⠙⢛⣛⠃⠀⢛⢛⣛⠃⢘⢀⣘⣙⠀⣛⣛⢚⠀⣛⣛⣓⠀⣛⣛⡒⡟⣛⡻⡛⡈⣻⣿⡗⡗⢙⣛⡋⢙⣛⣛⣛⣛⣛⣛⣛⣙⣛⣛⣛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠃⠀⠀⠀⠀⠁⢘⡃⠀⠐⠙⡛⠛⠛⠙⢛⡛⠃⠀⢙⣛⣛⠃⢘⠘⢛⣛⠁⣛⣛⢘⠀⣛⣛⣓⡀⡛⣛⣛⣋⡋⣛⣛⣛⣛⡋⢑⡓⢙⣛⣋⣙⣛⣛⢛⣛⣛⣙⣛⡛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣇⠀⠀⠀⣲⣆⠀⠀⠀⡃⣆⡃⠂⠈⠙⡛⠛⠋⠙⢛⣛⡀⠀⣉⣛⣋⡁⢘⠀⣛⣛⠁⣙⣛⢈⠀⣙⣓⣚⠛⣛⣛⣓⣟⠟⣏⣛⣛⢋⣋⣉⣋⣙⣋⡛⢁⣋⡙⢚⣛⣙⣉⣛⣂⣀⣀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡃⠀⠀⠀⠀⡃⢉⡃⠀⠈⠙⠛⠛⠉⣘⢛⣛⡁⠀⠙⠙⣛⡁⢈⠀⣙⣙⠁⣙⣛⢈⠀⣛⣛⣃⣀⣛⣋⡋⡋⠉⣉⣋⣋⣉⣋⡋⠛⠛⠙⠛⠙⠛⠋⠙⠛⠛⠛⠛⠋⠛⠛⠙⠘⠙⠙⠁⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡁⠀⠀⠀⠀⡁⢀⡧⠠⠤⠤⠤⠄⠤⠤⠤⠤⠤⠤⠤⠄⢸⡥⢈⠀⠉⢙⡀⣉⣉⢈⠀⣭⣉⢉⣉⣭⣉⣈⢉⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠈⠁⠉⠉⠈⠀⠁⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⡄⠀⣤⣤⣄⣤⣄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠁⠀⠛⠛⠻⠟⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⢦⣤⣦⣤⡄⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠊⠋⠻⠟⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠉⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣢⣤⣧⣦⡆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡈⠉⠹⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⢶⣶⣷⣶⠆⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡈⠁⡙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠀⣗⣶⣷⣶⡆⠆⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⢤⠤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⡠⡋⠁⠙⠃⢁⡼⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠸⢷⡾⢿⠷⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠾⠿⠷⠾⠿⠵⠶⠆⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⢢ ⡿⠿⠶⠷⠶⠶⡶⡶⠆⠐⡀⢰⠶⢶⣆⡸⠷⢲⢲⡶⠾⠆⠸⠶⠶⠶⠶⠾⠶⠶⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠟⠿⠿⠧⠀⠀⠀⠀⠈⠀⠠⠲⠶⠶⠶⠶⠎⠸⠳⠾⠶⠾⠶⠶⠂⠸⠶⠾⠸⠻⠻⠿⠙⠶⠖⠒⠶⠶⠷⠗⠀⣿⣿⠿⠖⠖⠖⠷⠖⠗⠶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡿⠿⠶⠿⠷⠶⠇⠁⠀⠸⠷⢾⠇⠸⠿⠶⠶⠺⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠷⠶⢶⠷⠰⠷⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠟⠷⠆⠇⠿⠶⠃⠀⠸⠷⠶⠞⠇⠸⠳⠶⠶⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠟⠃⠙⠶⠶⠾⠷⠶⠞⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠛⠛⠚⠓⠛⠇⠁⠀⠀⠇⠐⡢⢔⠛⠚⠃⠘⠚⢣⣼⡗⠂⠘⠧⠀⠾⠚⠂⣈⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⠛⢛⠚⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠚⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⢑⠆⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⣟⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⣶⣮⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠀⠛⠛⠛⠀⠋⠛⠋⡃⡿⡣⡓⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⣇⠈⠀⠀⡀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⢀⢀⣀⠀⢀⠀⣀⣀⠀⣀⣀⢀⠀⣀⣀⣀⠀⣀⣀⡤⣨⠀⣀⡀⠀⠀⢀⣀⡀⢀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣏⣗⠍⠀⡃⠀⠀⠀⠀⡃⢐⡃⠂⠐⠙⡛⠛⠛⠙⢛⣛⠃⠀⢛⢛⣛⠃⢘⢀⣘⣙⠀⣛⣛⢚⠀⣛⣛⣓⠀⣛⣛⡒⡟⣟⡻⡛⡈⣢⣤⡐⡗⢙⣛⡋⢙⣛⣛⣛⣛⣛⣛⣛⣙⣛⣛⣛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠃⠀⠀⠀⠀⠁⢘⡃⠀⠐⠙⡛⠛⠛⠙⢛⡛⠃⠀⢙⣛⣛⠃⢘⠘⢛⣛⠁⣛⣛⢘⠀⣛⣛⣓⡀⡛⣛⣛⣋⡋⣛⣛⣛⡋⠋⠑⡓⢙⣛⣋⣙⣛⣛⢛⣛⣛⣙⣛⡛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣇⠀⠀⠀⣲⣆⠀⠀⠀⡃⣆⡃⠂⠈⠙⡛⠛⠋⠙⢛⣛⡀⠀⣉⣛⣋⡁⢘⠀⣛⣛⠁⣙⣛⢈⠀⣙⣓⣚⠛⣛⣛⣓⣟⠟⣏⣛⣓⢋⣂⣉⣋⣙⣋⡛⢁⣋⡙⢚⣛⣙⣉⣛⣂⣀⣀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡃⠀⠀⠀⠀⡃⢉⡃⠀⠈⠙⠛⠛⠉⣘⢛⣛⡁⠀⠙⠙⣛⡁⢈⠀⣙⣙⠁⣙⣛⢈⠀⣛⣛⣓⣀⣛⣋⡋⡋⠉⣉⣋⣋⣉⣋⡋⠛⠛⠙⠛⠙⠛⠋⠙⠛⠛⠛⠛⠋⠛⠛⠙⠚⠙⠙⠁⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡁⠀⠀⠀⠀⡁⢀⡧⠠⠤⠤⠤⠄⠤⠤⠤⠤⠤⠤⠤⠄⢸⡥⢈⠀⠉⢙⡀⣉⣉⢈⠀⣭⣉⢉⣉⣭⣉⣈⢉⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠈⠁⠉⠉⠈⠀⠁⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⡄⠀⣤⣤⣄⣤⣄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠁⠀⠛⠋⣻⠟⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⢦⣤⣶⣤⡄⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣠⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠊⠋⡻⠟⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠉⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣢⣤⣃⣦⡆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡈⠉⠻⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⢶⣶⣷⣶⠆⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡈⠁⡹⡋⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠀⣗⣶⣗⣶⡒⠆⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⢤⠤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⡠⡋⠁⠛⠃⢁⡼⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠸⢷⡾⢿⠷⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠾⠿⠷⠾⠿⠵⠶⠆⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⢢ ⡿⠿⠶⠷⠶⠶⡶⡶⠆⠐⡀⢰⠶⢶⣆⡸⠷⢲⢲⡶⠾⠆⠸⠶⠶⠶⠶⢶⣶⣶⣼⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣰ ⡟⠟⠿⠿⠧⠀⠀⠀⠀⠈⠀⠠⠲⠶⠶⠶⠶⠎⠸⠳⠾⠶⠺⠶⠶⠂⠘⠶⠾⠸⠻⠻⠿⠙⠶⠖⠒⠶⠶⠷⠗⠀⣶⣾⠿⠖⠖⠖⠷⠖⠗⠶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡿⠿⠶⠿⠶⢶⠇⠁⠀⠸⠷⢿⠇⠸⠿⠶⠶⠺⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠷⠶⢶⠷⠰⠷⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠟⠷⠆⠇⠋⠖⠃⠀⠸⠗⠂⠘⠇⠸⠳⠶⠶⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠟⠃⠉⠶⠶⠞⠷⠶⠞⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠛⠛⠚⢓⠓⠇⠁⠀⠀⠇⠐⡢⢔⠛⠚⠃⠘⠚⢣⣼⡖⠂⢼⠧⠀⠶⠚⠂⣸⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⠛⢛⠚⠛⠇⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠚⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⢑⠆⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⣟⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⣶⣮⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠀⠛⠛⠛⠀⠋⠛⠋⡃⡿⡣⡓⠛⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⣇⠈⠀⠀⡀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⢀⢀⣀⠀⢀⠀⣀⣀⠀⣀⣀⢀⠀⣀⣀⣀⠀⣀⣀⡤⣨⠀⣀⡀⠀⠀⢀⣀⡀⢀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣏⣗⠍⠀⡃⠀⠀⠀⠀⡃⢐⡃⠂⠐⠙⡛⠛⠛⠙⢛⣛⠃⠀⢛⢛⣛⠃⢘⢀⣘⣙⠀⣛⣛⢚⠀⣛⣛⣓⠀⣛⣛⡒⡟⣟⡻⡛⡈⣢⣤⡐⡗⢙⣛⡋⢙⣛⣛⣛⣛⣛⣛⣛⣙⣛⣛⣛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠃⠀⠀⠀⠀⠁⢘⡃⠀⠐⠙⡛⠛⠛⠙⢛⡛⠃⠀⢙⣛⣛⠃⢘⠘⢛⣛⠁⣛⣛⢘⠀⣛⣛⣓⡀⡛⣛⣛⣋⡋⣛⣛⣋⡋⠋⠑⡓⢙⣛⣋⣙⣛⣛⢛⣛⣛⣙⣛⡛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣇⠀⠀⠀⣲⣆⠀⠀⠀⡃⣆⡃⠂⠈⠙⡛⠛⠋⠙⢛⣛⡀⠀⣉⣛⣋⡁⢘⠀⣛⣛⠁⣙⣛⢈⠀⣙⣓⣚⠛⣛⣛⣓⣟⠟⣏⣛⣓⢋⣂⣉⣋⣙⣋⡛⢁⣋⡙⢚⣛⣙⣉⣛⣂⣀⣀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡃⠀⠀⠀⠀⡃⢉⡃⠀⠈⠙⠛⠛⠉⣘⢛⣛⡁⠀⠙⠙⣛⡁⢈⠀⣙⣙⠁⣙⣛⢈⠀⣛⣛⣓⣀⣛⣋⡋⡋⠉⣉⣉⣋⣉⣋⡋⠛⠛⠙⠛⠙⠛⠋⠙⠛⠛⠛⠛⠋⠛⠛⠙⠘⠙⠙⠁⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡁⠀⠀⠀⠀⡁⢀⡧⠠⠤⠤⠤⠄⠤⠤⠤⠤⠤⠤⠤⠄⢸⡥⢈⠀⠉⢙⡀⣉⣉⢈⠀⣭⣉⢉⣉⣭⣉⣈⢉⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠈⠁⠉⠉⠈⠀⠁⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠚ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⡄⠀⣤⣄⣄⣤⣄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠁⠀⠛⠛⣻⠟⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠰⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⢦⣤⣶⣤⡄⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣠⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠊⠋⡻⠟⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠉⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣢⣤⣇⣦⡆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡈⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⢶⣶⡧⣶⢆⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡈⠁⡱⡋⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠀⣗⣶⣗⣶⡒⠆⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⢤⠤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⡠⡋⠁⠛⠃⢁⡼⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠹⢷⡾⢿⠷⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠾⠿⠷⠾⠿⠵⠶⠆⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⢢ ⡿⠿⠶⠷⠶⠶⡶⡶⠆⠐⡀⢰⠶⢶⣆⡸⠷⢲⢲⡶⠾⠆⠸⠶⠶⠶⠆⢠⣶⣶⣼⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠐ ⡟⠟⠿⠿⠧⠀⠀⠀⠀⠈⠀⠠⠲⠶⠶⠶⠶⠎⠸⠳⠾⠶⠾⠶⠶⠂⠙⠿⠿⠹⠹⠻⠿⠙⠿⠟⠛⠿⠿⠿⠟⠉⣶⣾⠿⠖⠖⠖⠷⠖⠗⠶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠄⠀⠀⠈⠉⠀⠉⠉⠉⠉⢹ ⡿⠿⠶⠿⠶⢶⠇⠁⠀⠸⠷⠟⠇⠸⠿⠶⠶⠺⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠷⠶⢶⠷⠰⠷⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡟⠟⠷⠆⠇⠋⠖⠃⠀⠸⠗⠁⠟⠇⠸⠳⠶⠶⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠃⠉⠶⠶⠞⠷⠶⠞⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠛⠛⠚⢒⠓⠇⠁⠀⠀⠇⠐⡢⢔⠛⠚⠃⠘⠚⢣⣼⡗⠀⢬⠠⠄⠶⠒⠀⣰⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠛⢒⠂⠐⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠚⠀⠀⠈⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⣟⠀⠁⠄⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⣶⣮⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠀⠛⠛⠛⠀⠋⠛⠋⡃⡿⡣⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⣇⠈⠀⠀⡀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⢀⢀⣀⠀⢀⠀⣀⣀⠀⣀⣀⢀⠀⣀⣀⣀⠀⣀⣀⡤⣨⠀⣀⠀⠂⠀⢀⣀⡀⢀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣏⣗⠍⠀⡃⠀⠀⠀⠀⡃⢐⡃⠂⠐⠙⡛⠛⠛⠙⢛⣛⠃⠀⢛⣛⣛⠃⢘⢀⣘⣙⠀⣛⣛⢚⠀⣛⣛⣓⠀⣛⣛⡒⡟⢻⡷⡒⡀⣀⣠⡐⡗⢙⣛⡋⢙⣛⣛⣛⣛⣛⣛⣛⣙⣛⣛⣛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠃⠀⠀⠀⠀⠁⢘⡃⠀⠐⠙⡛⠛⠛⠙⢛⡛⠃⠀⢙⣛⣛⠃⢘⠘⢛⣛⠁⣛⣛⢘⠀⣛⣛⣓⣀⡛⣛⣛⣛⡫⡛⣻⣯⠋⠋⠑⡓⢙⣛⣋⣙⣛⣛⢛⣛⣛⣙⣛⡛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣇⠀⠀⠀⣲⣦⠀⠀⠀⡃⣆⡃⠂⠈⠙⡛⠛⠋⠙⢛⣛⡀⠀⣉⣛⣋⡁⢘⠀⣛⣛⠁⣙⣛⢈⠀⣙⣓⣚⠛⣛⣛⣓⣟⠟⣌⣁⣀⢀⣀⣈⣋⣙⣋⡛⢁⣋⡙⢚⣛⣙⣉⣛⣂⣀⣀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡃⠀⠀⠀⠀⡃⢉⡃⠀⠈⠙⠛⠛⠉⣘⢛⣛⡁⠀⠙⠙⣛⡁⢈⠀⣙⣙⠁⣙⣛⢈⠀⣛⣛⣓⣀⣛⣋⡋⡋⢘⣉⢉⣋⣉⣋⡋⠛⠛⠙⠛⠙⠛⠋⠙⠛⠛⠛⠛⠋⠛⠛⠙⠚⠙⠙⠁⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡁⠀⠀⠀⠀⡁⢀⡧⠠⠤⠤⠤⠄⠤⠤⠤⠤⠤⠤⠤⠄⢸⡥⢈⠀⠉⢙⡀⣉⣉⢈⠀⣭⣉⢉⣉⣭⣉⣈⢉⠈⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠈⠁⠉⠉⠈⠀⠁⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠘ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡇⠀⡄⠀⣤⣄⣄⣤⣄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠁⠀⠛⠛⡋⠛⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠰⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⢦⣤⣶⣤⡄⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠂⠀⠀⠀⣠⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠊⠋⠹⠟⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠉⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣢⣤⣇⣦⡦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡈⠉⡛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣶⣶⡧⣶⣆⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡈⠁⡡⡉⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠀⣗⣶⣇⣶⡒⠆⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⢤⠤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⡠⡋⠁⠓⠃⢀⡼⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠹⢷⡾⢿⠷⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠾⠿⠷⠾⠿⠵⠶⠆⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⢢ ⡿⠿⠶⠷⠶⠶⡶⡶⠆⠐⡀⢰⠶⢶⣆⡸⠷⢲⢲⡶⠾⠆⠸⠶⠶⠶⠆⢠⣶⣶⣼⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠐ ⡟⠟⠿⠿⠧⠀⠀⠀⠀⠈⠀⠠⠲⠶⠶⠶⠶⠎⠸⠳⠾⠶⠾⠶⠶⠂⠙⠿⠿⠹⠹⠻⠿⠙⠿⠟⠛⠿⠿⠿⠟⠉⣶⣾⠿⠖⠖⠖⠷⠖⠗⠶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠄⠀⠀⠈⠉⠀⠉⠉⠉⠉⢹ ⡿⠿⠶⠿⠶⢶⠇⠁⠀⠸⠷⠟⠇⠸⠿⠶⠶⠺⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠷⠶⢶⠷⠰⠷⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡟⠟⠷⠆⠇⠋⠖⠃⠀⠸⠗⠁⠟⠇⠸⠳⠶⠶⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠃⠉⠶⠶⠞⠷⠶⠞⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠛⠛⠚⢒⠓⠇⠁⠀⠀⠇⠐⡢⢔⠛⠚⠃⠘⠚⢣⣼⡗⠀⢬⠠⠄⠶⠒⠀⣰⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠛⢒⠂⠐⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠚⠀⠀⠈⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⣟⠀⠁⠄⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⣶⣮⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠀⠛⠛⠛⠀⠋⠛⠋⡃⡿⡣⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⣇⠈⠀⠀⡀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⢀⢀⣀⠀⢀⠀⣀⣀⠀⣀⣀⢀⠀⣀⣀⣀⠀⣀⣀⡤⣨⠀⣀⠀⠂⠀⢀⣀⡀⢀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣏⣗⠍⠀⡃⠀⠀⠀⠀⡃⢐⡃⠂⠐⠙⡛⠛⠛⠙⢛⣛⠃⠀⢛⣛⣛⠃⢘⢀⣘⣙⠀⣛⣛⢚⠀⣛⣛⣓⠀⣛⣛⡒⡟⢻⡷⡒⡀⣀⣠⡐⡗⢙⣛⡋⢙⣛⣛⣛⣛⣛⣛⣛⣙⣛⣛⣛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠃⠀⠀⠀⠀⠁⢘⡃⠀⠐⠙⡛⠛⠛⠙⢛⡛⠃⠀⢙⣛⣛⠃⢘⠘⢛⣛⠁⣛⣛⢘⠀⣛⣛⣓⣀⡛⣛⣛⣛⡫⡛⣻⣯⠋⠋⠑⡓⢙⣛⣋⣙⣛⣛⢛⣛⣛⣙⣛⡛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣇⠀⠀⠀⣲⣦⠀⠀⠀⡃⣆⡃⠂⠈⠙⡛⠛⠋⠙⢛⣛⡀⠀⣉⣛⣋⡁⢘⠀⣛⣛⠁⣙⣛⢈⠀⣙⣓⣚⠛⣛⣛⣓⣟⠟⣌⣁⣀⢀⣀⣈⣋⣙⣋⡛⢁⣋⡙⢚⣛⣙⣉⣛⣂⣀⣀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡃⠀⠀⠀⠀⡃⢉⡃⠀⠈⠙⠛⠛⠉⣘⢛⣛⡁⠀⠙⠙⣛⡁⢈⠀⣙⣙⠁⣙⣛⢈⠀⣛⣛⣓⣀⣛⣋⡋⡋⢘⣉⢉⣋⣉⣋⡋⠛⠛⠙⠛⠙⠛⠋⠙⠛⠛⠛⠛⠋⠛⠛⠙⠚⠙⠙⠁⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡁⠀⠀⠀⠀⡁⢀⡧⠠⠤⠤⠤⠄⠤⠤⠤⠤⠤⠤⠤⠄⢸⡥⢈⠀⠉⢙⡀⣉⣉⢈⠀⣭⣉⢉⣉⣭⣉⣈⢉⠈⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠈⠁⠉⠉⠈⠀⠁⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠘ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠛ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡇⠀⡄⠀⣤⣄⣄⣤⣄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠁⠀⠛⠛⡋⠛⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠰⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⢦⣤⣶⣤⡄⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠂⠀⠀⠀⣠⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠊⠋⠹⠟⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠉⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣢⣤⣇⣦⡦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡈⠉⡛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣶⣶⡧⣶⣆⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡈⠁⡡⡉⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠀⣗⣶⣇⣶⡒⠆⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⢤⠤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⡠⡋⠁⠓⠃⢀⡼⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠹⢷⡾⢿⠷⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠾⠿⠷⠾⠿⠵⠶⠆⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⢢ ⡿⠿⠶⠷⠶⠶⡶⡶⠆⠐⡀⢰⠶⢶⣆⡸⠷⢲⢲⡶⠾⠆⠸⠶⠶⠶⠆⢠⣶⣶⣼⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠐ ⡟⠟⠿⠿⠧⠀⠀⠀⠀⠈⠀⠠⠲⠶⠶⠶⠶⠎⠸⠳⠾⠶⠾⠶⠶⠂⠙⠿⠿⠹⠹⠻⠿⠙⠿⠟⠛⠿⠿⠿⠟⠉⣶⣾⠿⠖⠖⠖⠷⠖⠗⠶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠄⠀⠀⠈⠉⠀⠉⠉⠉⠉⢹ ⡿⠿⠶⠿⠶⢶⠇⠁⠀⠸⠷⠟⠇⠸⠿⠶⠶⠺⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠷⠶⢶⠷⠰⠷⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡟⠟⠷⠆⠇⠋⠖⠃⠀⠸⠗⠁⠟⠇⠸⠳⠶⠶⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠃⠉⠶⠶⠞⠷⠶⠞⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠛⠛⠚⢒⠓⠇⠁⠀⠀⠇⠐⡢⢔⠛⠚⠃⠘⠚⢣⣼⡗⠀⢬⠠⠄⠶⠒⠀⣰⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠛⢒⠂⠐⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠚⠀⠀⠈⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⣟⠀⠁⠄⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⣶⣮⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠀⠛⠛⠛⠀⠋⠛⠋⡃⡿⡣⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⣇⠈⠀⠀⡀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⢀⢀⣀⠀⢀⠀⣀⣀⠀⣀⣀⢀⠀⣀⣀⣀⠀⣀⣀⡤⣨⠀⣀⠀⠂⠀⢀⣀⡀⢀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣏⣗⠍⠀⡃⠀⠀⠀⠀⡃⢐⡃⠂⠐⠙⡛⠛⠛⠙⢛⣛⠃⠀⢛⣛⣛⠃⢘⢀⣘⣙⠀⣛⣛⢚⠀⣛⣛⣓⠀⣛⣛⡒⡟⢻⡷⡒⡀⣀⣠⡐⡗⢙⣛⡋⢙⣛⣛⣛⣛⣛⣛⣛⣙⣛⣛⣛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠃⠀⠀⠀⠀⠁⢘⡃⠀⠐⠙⡛⠛⠛⠙⢛⡛⠃⠀⢙⣛⣛⠃⢘⠘⢛⣛⠁⣛⣛⢘⠀⣛⣛⣓⣀⡛⣛⣛⣛⡫⡛⣻⣯⠋⠋⠑⡓⢙⣛⣋⣙⣛⣛⢛⣛⣛⣙⣛⡛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣇⠀⠀⠀⣲⣦⠀⠀⠀⡃⣆⡃⠂⠈⠙⡛⠛⠋⠙⢛⣛⡀⠀⣉⣛⣋⡁⢘⠀⣛⣛⠁⣙⣛⢈⠀⣙⣓⣚⠛⣛⣛⣓⣟⠟⣌⣁⣀⢀⣀⣈⣋⣙⣋⡛⢁⣋⡙⢚⣛⣙⣉⣛⣂⣀⣀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡃⠀⠀⠀⠀⡃⢉⡃⠀⠈⠙⠛⠛⠉⣘⢛⣛⡁⠀⠙⠙⣛⡁⢈⠀⣙⣙⠁⣙⣛⢈⠀⣛⣛⣓⣀⣛⣋⡋⡋⢘⣉⢉⣋⣉⣋⡋⠛⠛⠙⠛⠙⠛⠋⠙⠛⠛⠛⠛⠋⠛⠛⠙⠚⠙⠙⠁⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡁⠀⠀⠀⠀⡁⢀⡧⠠⠤⠤⠤⠄⠤⠤⠤⠤⠤⠤⠤⠄⢸⡥⢈⠀⠉⢙⡀⣉⣉⢈⠀⣭⣉⢉⣉⣭⣉⣈⢉⠈⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠈⠁⠉⠉⠈⠀⠁⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠘ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠘ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⡇⠀⡄⠀⣤⣄⣄⣤⣄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠁⠀⠛⠛⡋⠛⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠰⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⢦⣤⣶⣤⡄⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠂⠀⠀⠀⣠⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠊⠋⠹⠟⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠉⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣢⣤⣇⣦⡦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡈⠉⡛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣶⣶⡧⣶⣆⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡈⠁⡡⡉⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠀⣗⣶⣇⣶⡒⠆⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⢤⠤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⡠⡋⠁⠓⠃⢀⡼⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠹⢷⡾⢿⠷⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠾⠿⠷⠾⠿⠵⠶⠆⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⢢ ⡿⠿⠶⠷⠶⠶⡶⡶⠆⠐⡀⢰⠶⢶⣆⡸⠷⢲⢲⡶⠾⠆⠸⠶⠶⠶⠆⢠⣶⣶⣼⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠐ ⡟⠟⠿⠿⠧⠀⠀⠀⠀⠈⠀⠠⠲⠶⠶⠶⠶⠎⠸⠳⠾⠶⠾⠶⠶⠂⠙⠿⠿⠹⠹⠻⠿⠙⠿⠟⠛⠿⠿⠿⠟⠉⣶⣾⠿⠖⠖⠖⠷⠖⠗⠶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠄⠀⠀⠈⠉⠀⠉⠉⠉⠉⢹ ⡿⠿⠶⠿⠶⢶⠇⠁⠀⠸⠷⠟⠇⠸⠿⠶⠶⠺⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠷⠶⢶⠷⠰⠷⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡟⠟⠷⠆⠇⠋⠖⠃⠀⠸⠗⠁⠟⠇⠸⠳⠶⠶⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠃⠉⠶⠶⠞⠷⠶⠞⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠛⠛⠚⢒⠓⠇⠁⠀⠀⠇⠐⡢⢔⠛⠚⠃⠘⠚⢣⣼⡗⠀⢬⠠⠄⠶⠒⠀⣰⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠛⢒⠂⠐⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠚⠀⠀⠈⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⣟⠀⠁⠄⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⣶⣮⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠀⠛⠛⠛⠀⠋⠛⠋⡃⡿⡣⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⣇⠈⠀⠀⡀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⢀⢀⣀⠀⢀⠀⣀⣀⠀⣀⣀⢀⠀⣀⣀⣀⠀⣀⣀⡤⣨⠀⣀⠀⠂⠀⢀⣀⡀⢀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣏⣗⠍⠀⡃⠀⠀⠀⠀⡃⢐⡃⠂⠐⠙⡛⠛⠛⠙⢛⣛⠃⠀⢛⣛⣛⠃⢘⢀⣘⣙⠀⣛⣛⢚⠀⣛⣛⣓⠀⣛⣛⡒⡟⢻⡷⡒⡀⣀⣠⡐⡗⢙⣛⡋⢙⣛⣛⣛⣛⣛⣛⣛⣙⣛⣛⣛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠃⠀⠀⠀⠀⠁⢘⡃⠀⠐⠙⡛⠛⠛⠙⢛⡛⠃⠀⢙⣛⣛⠃⢘⠘⢛⣛⠁⣛⣛⢘⠀⣛⣛⣓⣀⡛⣛⣛⣛⡫⡛⣻⣯⠋⠋⠑⡓⢙⣛⣋⣙⣛⣛⢛⣛⣛⣙⣛⡛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣇⠀⠀⠀⣲⣦⠀⠀⠀⡃⣆⡃⠂⠈⠙⡛⠛⠋⠙⢛⣛⡀⠀⣉⣛⣋⡁⢘⠀⣛⣛⠁⣙⣛⢈⠀⣙⣓⣚⠛⣛⣛⣓⣟⠟⣌⣁⣀⢀⣀⣈⣋⣙⣋⡛⢁⣋⡙⢚⣛⣙⣉⣛⣂⣀⣀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡃⠀⠀⠀⠀⡃⢉⡃⠀⠈⠙⠛⠛⠉⣘⢛⣛⡁⠀⠙⠙⣛⡁⢈⠀⣙⣙⠁⣙⣛⢈⠀⣛⣛⣓⣀⣛⣋⡋⡋⢘⣉⢉⣋⣉⣋⡋⠛⠛⠙⠛⠙⠛⠋⠙⠛⠛⠛⠛⠋⠛⠛⠙⠚⠙⠙⠁⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡁⠀⠀⠈⠀⡁⢀⡧⠠⠤⠤⠤⠄⠤⠤⠤⠤⠤⠤⠤⠄⢸⡥⢈⠀⠉⢙⡀⣉⣉⢈⠀⣭⣉⢉⣉⣭⣉⣈⢉⠈⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠈⠁⠉⠉⠈⠀⠁⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠘ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠘ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⡇⠀⡄⠀⣤⣄⣄⣤⣄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠁⠀⠛⠛⡋⠛⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠰⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⢦⣤⣶⣤⡄⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠂⠀⠀⠀⣠⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠊⠋⠹⠟⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠉⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣢⣤⣇⣦⡦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡈⠉⡛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣶⣶⡧⣶⣆⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡈⠁⡡⡉⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠀⣗⣶⣇⣶⡒⠆⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⢤⠤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⡠⡋⠁⠓⠃⢀⡼⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠹⢷⡾⢿⠷⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠾⠿⠷⠾⠿⠵⠶⠆⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⢢ ⡿⠿⠶⠷⠶⠶⡶⡶⠆⠐⡀⢰⠶⢶⣆⡸⠷⢲⢲⡶⠾⠆⠸⠶⠶⠶⠆⢠⣶⣶⣼⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠐ ⡟⠟⠿⠿⠧⠀⠀⠀⠀⠈⠀⠠⠲⠶⠶⠶⠶⠎⠸⠳⠾⠶⠾⠶⠶⠂⠙⠿⠿⠹⠹⠻⠿⠙⠿⠟⠛⠿⠿⠿⠟⠉⣶⣾⠿⠖⠖⠖⠷⠖⠗⠶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠄⠀⠀⠈⠉⠀⠉⠉⠉⠉⢹ ⡿⠿⠶⠿⠶⢶⠇⠁⠀⠸⠷⠟⠇⠸⠿⠶⠶⠺⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠷⠶⢶⠷⠰⠷⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡟⠟⠷⠆⠇⠋⠖⠃⠀⠸⠗⠁⠟⠇⠸⠳⠶⠶⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠃⠉⠶⠶⠞⠷⠶⠞⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠛⠛⠚⢒⠓⠇⠁⠀⠀⠇⠐⡢⢔⠛⠚⠃⠘⠚⢣⣼⡗⠀⢬⠠⠄⠶⠒⠀⣰⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠛⢒⠂⠐⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠚⠀⠀⠈⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⣟⠀⠁⠄⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⣶⣮⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠀⠛⠛⠛⠀⠋⠛⠋⡃⡿⡣⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⣇⠈⠀⠀⡀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⢀⢀⣀⠀⢀⠀⣀⣀⠀⣀⣀⢀⠀⣀⣀⣀⠀⣀⣀⡤⣨⠀⣀⠀⠂⠀⢀⣀⡀⢀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣏⣗⠍⠀⡃⠀⠀⠀⠀⡃⢐⡃⠂⠐⠙⡛⠛⠛⠙⢛⣛⠃⠀⢛⣛⣛⠃⢘⢀⣘⣙⠀⣛⣛⢚⠀⣛⣛⣓⠀⣛⣛⡒⡟⢻⡷⡒⡀⣀⣠⡐⡗⢙⣛⡋⢙⣛⣛⣛⣛⣛⣛⣛⣙⣛⣛⣛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠃⠀⠀⠀⠀⠁⢘⡃⠀⠐⠙⡛⠛⠛⠙⢛⡛⠃⠀⢙⣛⣛⠃⢘⠘⢛⣛⠁⣛⣛⢘⠀⣛⣛⣓⣀⡛⣛⣛⣛⡫⡛⣻⣯⠋⠋⠑⡓⢙⣛⣋⣙⣛⣛⢛⣛⣛⣙⣛⡛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣇⠀⠀⠀⣲⣦⠀⠀⠀⡃⣆⡃⠂⠈⠙⡛⠛⠋⠙⢛⣛⡀⠀⣉⣛⣋⡁⢘⠀⣛⣛⠁⣙⣛⢈⠀⣙⣓⣚⠛⣛⣛⣓⣟⠟⣌⣁⣀⢀⣀⣈⣋⣙⣋⡛⢁⣋⡙⢚⣛⣙⣉⣛⣂⣀⣀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡃⠀⠀⠀⠀⡃⢉⡃⠀⠈⠙⠛⠛⠉⣘⢛⣛⡁⠀⠙⠙⣛⡁⢈⠀⣙⣙⠁⣙⣛⢈⠀⣛⣛⣓⣀⣛⣋⡋⡋⢘⣉⢉⣋⣉⣋⡋⠛⠛⠙⠛⠙⠛⠋⠙⠛⠛⠛⠛⠋⠛⠛⠙⠚⠙⠙⠁⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡁⠀⠀⠈⠀⡁⢀⡧⠠⠤⠤⠤⠄⠤⠤⠤⠤⠤⠤⠤⠄⢸⡥⢈⠀⠉⢙⡀⣉⣉⢈⠀⣭⣉⢉⣉⣭⣉⣈⢉⠈⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠈⠁⠉⠉⠈⠀⠁⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠘ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠘ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⡇⠀⡄⠀⣤⣄⣄⣤⣄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠁⠀⠛⠛⡋⠛⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠰⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⢦⣤⣶⣤⡄⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠂⠀⠀⠀⣠⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠊⠋⠹⠟⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠉⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣢⣤⣇⣦⡦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡈⠉⡛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣶⣶⡧⣶⣆⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡈⠁⡡⡉⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠀⣗⣶⣇⣶⡒⠆⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⢤⠤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⡠⡋⠁⠓⠃⢀⡼⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠹⢷⡾⢿⠷⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠾⠿⠷⠾⠿⠵⠶⠆⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⢢ ⡿⠿⠶⠷⠶⠶⡶⡶⠆⠐⡀⢰⠶⢶⣆⡸⠷⢲⢲⡶⠾⠆⠸⠶⠶⠶⠆⢠⣶⣶⣼⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠐ ⡟⠟⠿⠿⠧⠀⠀⠀⠀⠈⠀⠠⠲⠶⠶⠶⠶⠎⠸⠳⠾⠶⠾⠶⠶⠂⠙⠿⠿⠹⠹⠻⠿⠙⠿⠟⠛⠿⠿⠿⠟⠉⣶⣾⠿⠖⠖⠖⠷⠖⠗⠶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠄⠀⠀⠈⠉⠀⠉⠉⠉⠉⢹ ⡿⠿⠶⠿⠶⢶⠇⠁⠀⠸⠷⠟⠇⠸⠿⠶⠶⠺⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠷⠶⢶⠷⠰⠷⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡟⠟⠷⠆⠇⠋⠖⠃⠀⠸⠗⠁⠟⠇⠸⠳⠶⠶⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠃⠉⠶⠶⠞⠷⠶⠞⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠛⠛⠚⢒⠓⠇⠁⠀⠀⠇⠐⡢⢔⠛⠚⠃⠘⠚⢣⣼⡗⠀⢬⠠⠄⠶⠒⠀⣰⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠛⢒⠂⠐⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠚⠀⠀⠈⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⣟⠀⠁⠄⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⣶⣮⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠀⠛⠛⠛⠀⠋⠛⠋⡃⡿⡣⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⣇⠈⠀⠀⡀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⢀⢀⣀⠀⢀⠀⣀⣀⠀⣀⣀⢀⠀⣀⣀⣀⠀⣀⣀⡤⣨⠀⣀⠀⠂⠀⢀⣀⡀⢀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣏⣗⠍⠀⡃⠀⠀⠀⠀⡃⢐⡃⠂⠐⠙⡛⠛⠛⠙⢛⣛⠃⠀⢛⣛⣛⠃⢘⢀⣘⣙⠀⣛⣛⢚⠀⣛⣛⣓⠀⣛⣛⡒⡟⢻⡷⡒⡀⣀⣠⡐⡗⢙⣛⡋⢙⣛⣛⣛⣛⣛⣛⣛⣙⣛⣛⣛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠃⠀⠀⠀⠀⠁⢘⡃⠀⠐⠙⡛⠛⠛⠙⢛⡛⠃⠀⢙⣛⣛⠃⢘⠘⢛⣛⠁⣛⣛⢘⠀⣛⣛⣓⣀⡛⣛⣛⣛⡫⡛⣻⣯⠋⠋⠑⡓⢙⣛⣋⣙⣛⣛⢛⣛⣛⣙⣛⡛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣇⠀⠀⠀⣲⣦⠀⠀⠀⡃⣆⡃⠂⠈⠙⡛⠛⠋⠙⢛⣛⡀⠀⣉⣛⣋⡁⢘⠀⣛⣛⠁⣙⣛⢈⠀⣙⣓⣚⠛⣛⣛⣓⣟⠟⣌⣁⣀⢀⣀⣈⣋⣙⣋⡛⢁⣋⡙⢚⣛⣙⣉⣛⣂⣀⣀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡃⠀⠀⠀⠀⡃⢉⡃⠀⠈⠙⠛⠛⠉⣘⢛⣛⡁⠀⠙⠙⣛⡁⢈⠀⣙⣙⠁⣙⣛⢈⠀⣛⣛⣓⣀⣛⣋⡋⡋⢘⣉⢉⣋⣉⣋⡋⠛⠛⠙⠛⠙⠛⠋⠙⠛⠛⠛⠛⠋⠛⠛⠙⠚⠙⠙⠁⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡁⠀⠀⠈⠀⡁⢀⡧⠠⠤⠤⠤⠄⠤⠤⠤⠤⠤⠤⠤⠄⢸⡥⢈⠀⠉⢙⡀⣉⣉⢈⠀⣭⣉⢉⣉⣭⣉⣈⢉⠈⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠈⠁⠉⠉⠈⠀⠁⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠘ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠘ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⡇⠀⡄⠀⣤⣄⣄⣤⣄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠁⠀⠛⠛⡋⠛⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠰⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⢦⣤⣶⣤⡄⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠂⠀⠀⠀⣠⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠊⠋⠹⠟⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠉⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣢⣤⣇⣦⡦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡈⠉⡛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣶⣶⡧⣶⣆⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡈⠁⡡⡉⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠀⣗⣶⣇⣶⡒⠆⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⢤⠤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⡠⡋⠁⠓⠃⢀⡼⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠹⢷⡾⢿⠷⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠾⠿⠷⠾⠿⠵⠶⠆⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⢢ ⡿⠿⠶⠷⠶⠶⡶⡶⠆⠐⡀⢰⠶⢶⣆⡸⠷⢲⢲⡶⠾⠆⠸⠶⠶⠶⠆⢠⣶⣶⣼⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠐ ⡟⠟⠿⠿⠧⠀⠀⠀⠀⠈⠀⠠⠲⠶⠶⠶⠶⠎⠸⠳⠾⠶⠾⠶⠶⠂⠙⠿⠿⠹⠹⠻⠿⠙⠿⠟⠛⠿⠿⠿⠟⠉⣶⣾⠿⠖⠖⠖⠷⠖⠗⠶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠄⠀⠀⠈⠉⠀⠉⠉⠉⠉⢹ ⡿⠿⠶⠿⠶⢶⠇⠁⠀⠸⠷⠟⠇⠸⠿⠶⠶⠺⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠷⠶⢶⠷⠰⠷⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡟⠟⠷⠆⠇⠋⠖⠃⠀⠸⠗⠁⠟⠇⠸⠳⠶⠶⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠃⠉⠶⠶⠞⠷⠶⠞⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠛⠛⠚⢒⠓⠇⠁⠀⠀⠇⠐⡢⢔⠛⠚⠃⠘⠚⢣⣼⡗⠀⢬⠠⠄⠶⠒⠀⣰⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠛⢒⠂⠐⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠚⠀⠀⠈⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⣟⠀⠁⠄⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⣶⣮⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠀⠛⠛⠛⠀⠋⠛⠋⡃⡿⡣⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⣇⠈⠀⠀⡀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⢀⢀⣀⠀⢀⠀⣀⣀⠀⣀⣀⢀⠀⣀⣀⣀⠀⣀⣀⡤⣨⠀⣀⠀⠂⠀⢀⣀⡀⢀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣏⣗⠍⠀⡃⠀⠀⠀⠀⡃⢐⡃⠂⠐⠙⡛⠛⠛⠙⢛⣛⠃⠀⢛⣛⣛⠃⢘⢀⣘⣙⠀⣛⣛⢚⠀⣛⣛⣓⠀⣛⣛⡒⡟⢻⡷⡒⡀⣀⣠⡐⡗⢙⣛⡋⢙⣛⣛⣛⣛⣛⣛⣛⣙⣛⣛⣛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠃⠀⠀⠀⠀⠁⢘⡃⠀⠐⠙⡛⠛⠛⠙⢛⡛⠃⠀⢙⣛⣛⠃⢘⠘⢛⣛⠁⣛⣛⢘⠀⣛⣛⣓⣀⡛⣛⣛⣛⡫⡛⣻⣯⠋⠋⠑⡓⢙⣛⣋⣙⣛⣛⢛⣛⣛⣙⣛⡛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣇⠀⠀⠀⣲⣦⠀⠀⠀⡃⣆⡃⠂⠈⠙⡛⠛⠋⠙⢛⣛⡀⠀⣉⣛⣋⡁⢘⠀⣛⣛⠁⣙⣛⢈⠀⣙⣓⣚⠛⣛⣛⣓⣟⠟⣌⣁⣀⢀⣀⣈⣋⣙⣋⡛⢁⣋⡙⢚⣛⣙⣉⣛⣂⣀⣀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡃⠀⠀⠀⠀⡃⢉⡃⠀⠈⠙⠛⠛⠉⣘⢛⣛⡁⠀⠙⠙⣛⡁⢈⠀⣙⣙⠁⣙⣛⢈⠀⣛⣛⣓⣀⣛⣋⡋⡋⢘⣉⢉⣋⣉⣋⡋⠛⠛⠙⠛⠙⠛⠋⠙⠛⠛⠛⠛⠋⠛⠛⠙⠚⠙⠙⠁⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡁⠀⠀⠈⠀⡁⢀⡧⠠⠤⠤⠤⠄⠤⠤⠤⠤⠤⠤⠤⠄⢸⡥⢈⠀⠉⢙⡀⣉⣉⢈⠀⣭⣉⢉⣉⣭⣉⣈⢉⠈⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠈⠁⠉⠉⠈⠀⠁⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠘ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠘ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⡇⠀⡄⠀⣤⣄⣄⣤⣄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠁⠀⠛⠛⡋⠛⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠰⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⢦⣤⣶⣤⡄⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠂⠀⠀⠀⣠⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠊⠋⠹⠟⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠉⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣢⣤⣇⣦⡦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡈⠉⡛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣶⣶⡧⣶⣆⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡈⠁⡡⡉⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠀⣗⣶⣇⣶⡒⠆⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⢤⠤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⡠⡋⠁⠓⠃⢀⡼⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠐⠂⠀⠀⠐⠀⠸⢷⠾⠾⠷⠶⠶⠆⠀⠒⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠒⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⠿⠶⠾⠾⠷⠾⠽⠵⠶⠆⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡ ⡏⠿⠶⠷⠶⢶⣶⡶⠀⠸⠅⠷⠶⠶⠆⠸⠷⠲⠲⠶⠺⠆⠸⠲⠶⠶⠶⠾⠶⠶⠼⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣿⣿⠿⠶⠶⠇⠷⠶⠆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⢐ ⡯⠟⠿⠻⠧⠀⠀⠀⠀⠈⠓⠲⠲⠶⠶⠶⠶⠂⠸⠷⠶⠶⠺⠶⠶⠂⠸⠶⠾⠸⠹⠻⠽⠙⠶⠖⠒⠶⠶⠷⠖⠀⣿⣿⠿⠶⠶⠆⠗⠖⠗⠶⡆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠄⠀⠀⠈⠉⠀⠉⠉⠉⠉⢸ ⡿⠻⠖⠯⠷⠶⠇⠀⠀⠸⠷⠾⠃⠸⠿⠶⠶⠺⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠷⠶⠶⠗⠰⠓⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡟⠟⠷⠆⠇⠟⠶⠀⠀⠘⠷⠶⠞⠇⠸⠳⠶⠶⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡿⠋⠗⠒⠷⠶⠾⠷⠶⠞⠇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠛⠛⠖⠓⠓⠇⠁⠀⠀⠇⠐⠳⠗⠛⠛⠃⠘⠚⠛⠾⠺⠚⠚⠲⠆⠾⠒⠐⠺⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠛⠛⠟⠟⠅⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⡆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠓⠀⠛⠛⠛⠀⠋⠛⠋⠓⠋⡃⠓⠛⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡇⠈⠀⠀⡀⠀⡀⠀⠀⡀⠀⡀⠀⠀⠀⡀⠀⠀⠀⢀⡀⠀⠀⢀⢀⣀⠀⠀⠀⣀⢀⠀⣀⣀⣀⠀⢀⣀⣀⠀⣀⣀⣀⢈⢀⣀⡀⠂⡀⣀⣀⡀⢀⣀⡀⢀⣀⣀⢀⣀⣀⣀⣀⣀⣀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⢀⠉⠀⡛⠛⠻⠛⠁⡃⢐⡃⠂⠐⠙⡛⠛⠛⠙⢛⣛⠃⠀⢛⣛⣛⠃⢘⢀⠘⣙⠀⣛⣛⢚⠀⢛⣛⣓⠀⣛⣛⣋⡛⣛⡛⡛⡙⣓⡛⢛⡓⢙⢛⡋⢘⣛⣛⣛⣛⣛⣓⣓⣙⣛⣛⢛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡛⠛⡚⠛⠃⡃⠘⡃⠀⠐⠙⡛⠙⠋⠙⢛⡛⠃⠀⢙⢛⣛⠃⢘⠘⢛⣛⠁⣛⣛⢘⠀⣛⣛⣓⡀⡛⣛⣛⣋⣛⣛⣙⣙⣛⣋⠙⡓⢙⣛⣋⣙⣛⣛⢛⣛⣛⣙⣛⡋⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡋⠋⡋⠛⠀⡃⠐⡃⠀⠈⠙⡛⠋⠉⠉⢛⣛⡀⠀⣉⣙⣋⡁⢈⠀⣚⣛⠀⣙⣛⢚⠀⣉⣓⣛⠛⣛⣛⣉⣛⠉⣉⣛⣉⢋⣃⣉⣃⣙⡋⡛⢁⣋⡙⢛⣋⣉⣉⣛⣂⣀⣀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡋⠉⠛⢛⡃⡃⢈⡃⠀⠈⣙⣛⡛⠉⣘⢛⣛⡃⠀⣙⣛⣛⡁⢘⠀⣙⣙⠁⣙⣛⢉⠀⣛⠛⡓⣀⣛⣋⠛⡋⠈⣋⣋⣋⣉⣋⡋⠚⠙⠉⠋⠙⠛⠉⠙⠋⠛⠛⠛⠊⠛⠛⠙⠚⠛⠙⠁⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡍⠋⢙⣋⡁⡅⢀⡃⠀⠈⡉⣉⣉⠉⣘⣉⣉⡀⠀⣉⣉⢙⡁⢈⠀⠉⢉⠀⡉⣉⢈⠀⣭⣋⢉⣉⣩⣅⣈⢉⣀⣅⣉⢉⣍⣉⣁⣀⡄⣀⢀⡀⡀⡀⡀⡀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠉⠉⠑⠋⠁⠁⠈⠁⠀⠈⠉⠉⠈⠉⠈⠉⠙⠂⠀⠙⠉⠉⠁⠈⠀⠀⠈⠁⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⠉⠈⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠉⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢘ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⡄⠀⣤⣄⣄⣤⣄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠁⠀⠙⠛⠉⠙⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠆⠤⠒⠤⠄⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠊⠋⠙⠛⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠢⠤⠇⠦⠦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡀⠁⡓⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣤⣤⡥⣤⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡈⠁⡡⡉⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠜ ⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠐⠂⠀⠀⠐⠀⠸⢷⠾⠾⠷⠶⠶⠆⠀⠒⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠒⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⠿⠶⠾⠾⠷⠾⠽⠽⠶⠆⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡ ⡏⠿⠶⠷⠶⢶⣶⡶⠀⠸⠅⠷⠶⠶⠆⠸⠷⠲⠲⠶⠺⠆⠸⠲⠶⠶⠶⠾⠶⠶⠼⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣿⡿⠿⠶⠶⠇⠷⠶⠆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⢐ ⡯⠟⠿⠿⠧⠀⠀⠀⠀⠈⠓⠲⠲⠶⠶⠶⠶⠂⠸⠷⠶⠶⠺⠶⠷⠂⠸⠶⠾⠸⠹⠿⠽⠙⠶⠖⠒⠶⠶⠷⠖⠀⣿⡇⢾⠰⠶⠆⠗⠖⠗⠶⡆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠄⠀⠀⠈⠉⠀⠉⠉⠉⠉⢸ ⡿⠻⠖⠯⠷⠶⠇⠀⠀⠸⠷⠾⠃⠸⠿⠶⠶⠺⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢷⢲⠶⠗⠰⠓⠶⠶⠖⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡟⠟⠷⠆⠇⠟⠶⠀⠀⠘⠷⠶⠞⠇⠸⠳⠶⠶⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡿⠛⢿⠚⠷⠶⠾⠷⠶⠞⠇⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠛⠓⠖⠓⠓⠇⠁⠀⠀⠇⠐⠳⠗⠛⠛⠃⠘⠚⠛⠾⠺⠚⠚⠲⠆⠾⠒⠐⠺⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠛⠛⠛⠟⠟⠅⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⡆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠓⠀⠛⠛⠛⠀⠋⠛⠋⠓⠋⡃⠛⠛⠙⠒⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡇⠈⠀⠀⡀⠀⣀⠀⠀⡀⠀⡀⠀⠀⠀⡀⠀⠀⠀⢀⡀⠀⠀⢀⢀⣀⠀⠀⠀⣀⢀⠀⣀⣀⣀⠀⢀⣀⣀⠀⣀⣀⣀⢈⢀⣀⡀⠂⡀⣀⣀⡀⢀⣀⡀⢀⣀⣀⢀⣀⣀⣀⣀⣀⣀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⢀⠉⠀⡛⠛⠻⠛⠁⡃⢐⡃⠂⠐⠙⡛⠛⠛⠙⢛⣛⠃⠀⢛⣛⣛⠃⢘⢀⠘⣙⠀⣛⣛⢚⠀⢛⣛⣓⠀⣛⣛⣋⡛⣛⣛⣛⣙⣓⡛⢛⡓⢙⢛⡋⢘⣛⣛⣛⣛⣛⣓⣓⣙⣛⣛⢛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡛⠛⡚⠛⠃⡃⠘⡃⡀⠐⠙⡛⠙⠋⠙⢛⡛⠃⠀⢙⢛⣛⠃⢘⠘⢛⣛⠁⣛⣛⢘⠀⣛⣛⣓⡀⡛⣛⣛⣋⣛⣛⣙⣙⣛⣋⠙⡓⢙⣛⣋⣙⣛⣛⢙⣛⣛⣙⣛⡋⠛⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡋⠋⡋⠛⠀⡃⠐⡃⠀⠈⠙⡛⠋⠉⠉⢛⣛⡀⠀⣉⣙⣋⡁⢈⠀⣚⣛⠀⣙⣛⢚⠀⣉⣓⣛⠛⣛⣛⣉⣛⠉⣉⣛⣉⢋⣃⣉⣃⣙⡋⡛⢁⣋⡙⢛⣋⣉⣉⣛⣀⣀⣀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡋⠉⠛⢛⡃⡃⢈⡃⠀⠈⣙⣛⡛⠉⣘⢛⣛⡃⠀⣙⣛⣛⡁⢘⠀⣙⣙⠉⣙⣛⢉⢀⣛⠛⣓⣀⣛⣋⠛⡋⠈⣋⣋⣋⣉⣋⡋⠚⠙⠉⠋⠙⠛⠉⠙⠋⠛⠛⠛⠊⠛⠛⠙⠛⠛⠙⠁⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡍⠋⢙⣋⡁⡅⢀⡃⠀⠈⡉⣉⣉⠉⣘⣉⣉⡀⠀⣉⣉⢙⡁⢈⠀⠉⢉⠀⡉⣉⢈⠀⣍⣋⢉⣉⣩⣅⣈⢉⣀⣅⣉⢉⣍⣍⣁⡀⡄⣀⢀⡀⡀⡀⡀⡀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠉⠉⠑⠋⠁⠁⠈⠁⠀⠈⠉⠉⠈⠉⠈⠉⠙⠂⠀⠙⠉⠉⠁⠈⠀⠀⠈⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢘ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⡄⠀⣤⣄⣄⣤⣄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠁⠀⠙⠛⠉⠙⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠆⠤⠒⠤⠄⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠊⠋⠙⠛⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠢⠤⠇⠦⠦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡀⠁⡓⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣤⣤⡥⣤⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡈⠁⡡⡉⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠜ ⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠐⠂⠀⠀⠐⠀⠸⢷⠾⠾⠷⠶⠶⠆⠀⠒⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠒⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⠿⠶⠾⠾⠷⠾⠿⠽⠶⠆⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡ ⡏⠿⠶⠷⠶⢶⣶⡶⠀⠸⠅⠷⠶⠶⠆⠸⠷⠲⠲⠶⠺⠆⠸⠲⠶⠶⠶⠾⠶⠶⠼⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣿⡿⠿⠶⠷⠇⠷⠶⠆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⢐ ⡯⠟⠿⠿⠇⠀⠀⠀⠀⠈⠓⠲⠲⠶⠶⠶⠶⠂⠸⠷⠶⠶⠺⠶⠷⠂⠸⠶⠾⠸⠹⠿⠽⠙⠶⠖⠐⠶⠶⠷⠖⠀⣿⡇⢾⠰⠶⠆⠗⠆⠗⠶⡆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠄⠀⠀⠈⠉⠀⠉⠉⠉⠉⢸ ⡿⠻⠖⠯⠷⠶⠇⠀⠀⠸⠷⠾⠃⠸⠿⠶⠶⠺⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢷⢲⠶⠗⠰⠓⠶⠶⠖⠶⠶⠶⠆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡟⠟⠷⠆⠇⠟⠶⠀⠀⠘⠷⠶⠞⠇⠸⠳⠶⠶⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡿⠛⢿⠚⠷⠶⠾⠷⠶⠞⠇⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠛⠓⠖⠓⠓⠇⠁⠀⠀⠇⠐⠳⠗⠛⠛⠃⠘⠚⠛⠾⠺⠚⠚⠲⠆⠾⠒⠐⠺⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠛⠛⠛⠟⠛⠅⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⡆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠓⠀⠛⠛⠛⠀⠋⠛⠋⠓⠋⡓⠛⠛⠙⠒⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡇⠈⠀⠀⡀⠀⣀⠀⠀⡀⠀⡀⠀⠀⠀⡀⠀⠀⠀⢀⡀⠀⠀⢀⢀⣀⠀⠀⠀⣀⢀⠀⣀⣀⣀⠀⢀⣀⣀⠀⣀⣀⣀⢈⢀⣀⡀⠂⡀⣀⣀⡀⢀⣀⡀⢀⣀⣀⢀⣀⣀⣀⣀⣀⣀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⢀⠉⠀⡛⠛⠻⠛⠁⡃⢐⡃⠂⠐⠉⡛⠛⠛⠙⢛⣛⠃⠀⢛⣛⣛⠃⢘⢀⠘⣙⠀⣙⣛⢚⠀⢛⣛⣓⠀⣛⣛⣋⣛⣛⣛⣛⣙⣓⡛⢛⡓⢙⢛⡋⢘⣛⣛⣛⣛⣛⣓⣓⣙⣛⣛⢛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡛⠛⡚⠛⠃⡃⠘⣃⡀⠐⠉⡛⠙⠋⠙⢛⡛⠃⠀⢙⢛⣛⠃⢘⠘⢛⣛⠁⣛⣛⢘⠀⣛⣛⣓⡀⡛⣛⣛⣋⣛⣛⣙⣙⣛⣋⠙⡓⢙⣛⣋⣙⣛⣛⢙⣛⣛⣙⣛⡋⡛⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡋⠋⡋⠛⠀⡃⠐⡃⠀⠈⠙⡛⠋⠉⠉⢛⣛⡀⠀⣉⣙⣋⡁⢈⠀⣚⣛⠁⣙⣛⣚⠀⣈⣓⣛⠛⣛⣛⣉⣛⠉⣉⣛⣉⢋⣃⣉⣃⣙⡋⡛⢁⣋⡙⢛⣋⣉⣉⣛⣀⣀⣀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡋⠉⠛⢛⡃⡃⢈⡃⠀⠈⢙⣛⡛⠉⣘⢛⣛⡃⠀⣙⣛⣛⡁⢘⠀⣙⣙⠉⣙⣛⢉⡀⣛⠛⣓⣀⣛⣋⠛⡋⠈⣋⣋⣋⣉⣋⡋⠚⠙⠉⠋⠙⠛⠉⠙⠋⠛⠛⠛⠊⠛⠛⠙⠛⠛⠙⠁⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡍⠋⢙⣋⡁⡅⢀⡃⠀⠈⠉⣉⣉⠉⣘⣉⣉⡀⠀⣉⣉⢙⣁⢈⠀⠉⢉⠀⡉⣉⢉⠀⣉⣋⢉⣉⣩⣅⣈⢉⣀⣥⣉⢉⡍⣍⣁⡀⡄⣀⢀⡀⡀⡀⡀⡀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠉⠉⠑⠋⠁⠁⠈⠁⠀⠈⠉⠉⠉⠉⠈⠉⠙⠂⠀⠙⠉⠉⠉⠈⠀⠀⠈⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢘ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⡄⠀⣤⣄⣄⣤⣄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠁⠀⠙⠛⠉⠙⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠆⠤⠒⠤⠄⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠊⠋⠙⠛⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠢⠤⠇⠦⠦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡀⠁⡓⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣤⣤⡥⣤⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡈⠁⡡⡉⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠜ ⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠐⠂⠀⠀⠐⠀⠸⢷⠾⠾⠷⠶⠶⠆⠀⠒⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠒⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⠿⠶⠾⠾⠷⠾⠿⠽⠶⠆⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡ ⡏⠿⠶⠷⠶⢶⣶⡶⠀⠸⠅⠷⠶⠶⠆⠸⠷⠲⠲⠶⠺⠆⠸⠲⠶⠶⠶⠾⠶⠶⠼⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣿⡿⠿⠶⠷⠇⠷⠶⠆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⢐ ⡯⠟⠿⠿⠇⠀⠀⠀⠀⠈⠓⠲⠲⠶⠶⠶⠶⠂⠸⠷⠶⠶⠺⠶⠷⠂⠸⠶⠾⠸⠹⠿⠽⠙⠶⠖⠐⠶⠶⠷⠖⠀⣿⣷⢸⠰⠶⠆⠗⠆⠗⠶⡆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠄⠀⠀⠈⠉⠀⠉⠉⠉⠉⢸ ⡿⠻⠖⠯⠷⠶⠇⠀⠀⠸⠷⠾⠃⠸⠿⠶⠶⠺⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢰⢲⠶⠗⠰⠓⠶⠶⠖⠶⠶⠶⠆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡟⠟⠷⠆⠇⠟⠶⠀⠀⠘⠷⠶⠞⠇⠸⠳⠶⠶⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡿⠻⢿⠚⠷⠶⠾⠷⠶⠞⠇⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠛⠓⠖⠓⠓⠇⠁⠀⠀⠇⠐⠳⠗⠛⠛⠃⠘⠚⠛⠾⠺⠚⠚⠲⠆⠾⠒⠐⠺⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠙⠛⠛⠟⠛⠅⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⡆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠓⠀⠛⠛⠛⠀⠋⠛⠋⠓⠋⡓⠛⠛⠙⠒⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡇⠈⠀⠀⡀⠀⣀⠀⠀⡀⠀⡀⠀⠀⠀⡀⠀⠀⠀⢀⡀⠀⠀⢀⢀⣀⠀⠀⠀⣀⢀⠀⣀⣀⣀⠀⢀⣀⣀⠀⣀⣀⣀⢈⢀⣀⡀⠂⡀⣀⣀⡀⢀⣀⡀⢀⣀⣀⢀⣀⣀⣀⣀⣀⣀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⢀⠉⠀⡛⠛⠻⠛⠁⡃⢐⡃⠂⠐⠉⡛⠛⠛⠙⢛⣛⠃⠀⢛⢛⣛⠃⢘⢀⠘⣙⠀⣙⣛⢚⠀⢛⣛⣓⠀⢛⣛⣋⣛⣛⢛⣛⣙⢓⠛⢛⡓⢙⢛⡋⢘⣛⣛⣛⣛⣛⣓⣛⣙⣛⣛⢛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡛⠛⡚⠛⠃⡃⠘⣃⡀⠐⠉⡛⠙⠋⠙⢛⡛⠃⠀⢙⢛⢛⠃⢘⠘⢛⣛⠁⣛⣛⢘⠀⢛⣛⣓⡀⡛⣛⣛⣋⣛⣛⣛⣙⣛⣋⠙⡓⢙⣛⣋⣙⣛⣛⢙⣛⣛⣙⣛⣋⡛⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡋⠋⡋⠛⠀⡃⠐⡃⠀⠈⠙⡛⠋⠉⠉⢛⣛⠀⠀⣉⣙⣋⡁⢈⠀⣚⣛⠁⣙⣛⣚⠀⣈⣓⣛⠛⣛⣛⣉⣛⠉⣉⣋⣉⢋⣃⣉⣃⣙⡋⡛⢁⣋⡙⢛⣋⣉⣉⣛⣈⣀⣀⣀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡋⠉⠛⢛⡃⡃⢈⡃⠀⠈⢙⣛⡛⠉⣘⢛⣛⡃⠀⣉⣛⣛⡁⢘⠀⣙⣙⠉⣙⣛⣉⠀⣛⠛⣓⣀⣛⣋⠛⡋⡈⣋⣋⣛⣉⣋⡋⢚⠙⠉⠋⠙⠛⠉⠙⠋⠛⠛⠛⠊⠛⠛⠙⠛⠛⠙⠁⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡍⠋⢙⣋⡁⡅⢀⡃⠀⠈⠉⣉⣉⠉⣘⣉⣉⡀⠀⣉⣉⢙⣁⢈⠀⠉⢉⠀⡉⣉⢉⠀⢉⣋⢉⣉⣩⣅⣈⢉⣀⣅⣉⢉⡉⣍⣁⡀⡀⣀⢀⡀⡀⡀⡀⡀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠉⠉⠑⠋⠁⠁⠈⠁⠀⠈⠉⠉⠉⠉⠈⠉⠙⠂⠀⠙⠉⠉⠉⠈⠀⠀⠈⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠙⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢘ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⡄⠀⣤⣄⣄⣤⣄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠁⠀⠙⠛⠉⠙⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠆⠤⠒⠤⠄⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠊⠋⠙⠛⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠢⠤⠇⠦⠦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡀⠁⡓⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣤⣤⡥⣤⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡈⠁⡡⡉⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠜ ⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠐⠂⠀⠀⠐⠀⠸⢷⠾⠾⠷⠶⠶⠆⠀⠒⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠒⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⠿⠶⠾⠾⠷⠾⠿⠽⠶⠆⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡ ⡏⠿⠶⠷⠶⢶⣶⡶⠀⠸⠅⠷⠶⠶⠆⠸⠷⠲⠲⠶⠺⠆⠸⠲⠶⠶⠶⠾⠶⠶⠼⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣿⡿⠿⠶⠷⠇⠷⠶⠆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⢐ ⡯⠟⠿⠿⠇⠀⠀⠀⠀⠈⠓⠲⠲⠶⠶⠶⠶⠂⠸⠷⠶⠶⠺⠶⠷⠂⠸⠶⠾⠸⠹⠿⠽⠙⠶⠖⠐⠶⠶⠷⠖⠀⣿⣷⢸⠰⠶⠆⠗⠆⠗⠶⡆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠄⠀⠀⠈⠉⠀⠉⠉⠉⠉⢸ ⡿⠻⠖⠯⠷⠶⠇⠀⠀⠸⠷⠾⠃⠸⠿⠶⠶⠺⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢰⢲⠶⠗⠰⠓⠶⠶⠖⠶⠶⠶⠆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡟⠟⠷⠆⠇⠟⠶⠀⠀⠘⠷⠶⠞⠇⠸⠳⠶⠶⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡿⠻⢿⠚⠷⠶⠾⠷⠶⠞⠇⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠛⠓⠖⠓⠓⠇⠁⠀⠀⠇⠐⠳⠗⠛⠛⠃⠘⠚⠛⠾⠺⠚⠚⠲⠆⠾⠒⠐⠺⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠙⠛⠛⠟⠛⠅⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⡆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠓⠀⠛⠛⠛⠀⠋⠛⠋⠓⠋⡓⠛⠛⠙⠒⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡇⠈⠀⠀⡀⠀⣀⠀⠀⡀⠀⡀⠀⠀⠀⡀⠀⠀⠀⢀⡀⠀⠀⢀⢀⣀⠀⠀⠀⣀⢀⠀⣀⣀⣀⠀⢀⣀⣀⠀⣀⣀⣀⢈⢀⣀⡀⠂⡀⣀⣀⡀⢀⣀⡀⢀⣀⣀⢀⣀⣀⣀⣀⣀⣀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⢀⠉⠀⡛⠛⠻⠛⠁⡃⢐⡃⠂⠐⠉⡛⠛⠛⠙⢛⣛⠃⠀⢛⢛⣛⠃⢘⢀⠘⣙⠀⣙⣛⢚⠀⢛⣛⣓⠀⢛⣛⣋⣛⣛⢛⣛⣙⢓⠛⢛⡓⢙⢛⡋⢘⣛⣛⣛⣛⣛⣓⣛⣙⣛⣛⢛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡛⠛⡚⠛⠃⡃⠘⣃⡀⠐⠉⡛⠙⠋⠙⢛⡛⠃⠀⢙⢛⢛⠃⢘⠘⢛⣛⠁⣛⣛⢘⠀⢛⣛⣓⡀⡛⣛⣛⣋⣛⣛⣛⣙⣛⣋⠙⡓⢙⣛⣋⣙⣛⣛⢙⣛⣛⣙⣛⣋⡛⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡋⠋⡋⠛⠀⡃⠐⡃⠀⠈⠙⡛⠋⠉⠉⢛⣛⠀⠀⣉⣙⣋⡁⢈⠀⣚⣛⠁⣙⣛⣚⠀⣈⣓⣛⠛⣛⣛⣉⣛⠉⣉⣋⣉⢋⣃⣉⣃⣙⡋⡛⢁⣋⡙⢛⣋⣉⣉⣛⣈⣀⣀⣀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡋⠉⠛⢛⡃⡃⢈⡃⠀⠈⢙⣛⡛⠉⣘⢛⣛⡃⠀⣉⣛⣛⡁⢘⠀⣙⣙⠉⣙⣛⣉⠀⣛⠛⣓⣀⣛⣋⠛⡋⡈⣋⣋⣛⣉⣋⡋⢚⠙⠉⠋⠙⠛⠉⠙⠋⠛⠛⠛⠊⠛⠛⠙⠛⠛⠙⠁⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡍⠋⢙⣋⡁⡅⢀⡃⠀⠈⠉⣉⣉⠉⣘⣉⣉⡀⠀⣉⣉⢙⣁⢈⠀⠉⢉⠀⡉⣉⢉⠀⢉⣋⢉⣉⣩⣅⣈⢉⣀⣅⣉⢉⡉⣍⣁⡀⡀⣀⢀⡀⡀⡀⡀⡀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠉⠉⠑⠋⠁⠁⠈⠁⠀⠈⠉⠉⠉⠉⠈⠉⠙⠂⠀⠙⠉⠉⠉⠈⠀⠀⠈⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠙⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢘ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⡄⠀⣤⣄⣄⣤⣄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠁⠀⠙⠛⠉⠙⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠆⠤⠒⠤⠄⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠊⠋⠙⠛⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠢⠤⠇⠦⠦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡀⠁⡓⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣤⣤⡥⣤⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡈⠁⡡⡉⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠜ ⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠐⠂⠀⠀⠐⠀⠸⢷⠾⠾⠷⠶⠶⠆⠀⠒⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠒⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⠿⠶⠾⠾⠷⠾⠿⠽⠶⠆⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡ ⡏⠿⠶⠷⠶⢶⣶⡶⠀⠸⠅⠷⠶⠶⠆⠸⠷⠲⠲⠶⠺⠆⠸⠲⠶⠶⠶⠾⠶⠶⠼⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣿⡿⠿⠶⠷⠇⠷⠶⠆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⢐ ⡯⠟⠿⠿⠇⠀⠀⠀⠀⠈⠓⠲⠲⠶⠶⠶⠶⠂⠸⠷⠶⠶⠺⠶⠷⠂⠸⠶⠾⠸⠹⠿⠽⠙⠶⠖⠐⠶⠶⠷⠖⠀⣿⣷⢸⠰⠶⠆⠗⠆⠗⠶⡆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠄⠀⠀⠈⠉⠀⠉⠉⠉⠉⢸ ⡿⠻⠖⠯⠷⠶⠇⠀⠀⠸⠷⠾⠃⠸⠿⠶⠶⠺⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢰⢲⠶⠗⠰⠓⠶⠶⠖⠶⠶⠶⠆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡟⠟⠷⠆⠇⠟⠶⠀⠀⠘⠷⠶⠞⠇⠸⠳⠶⠶⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡿⠻⢿⠚⠷⠶⠾⠷⠶⠞⠇⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠛⠓⠖⠓⠓⠇⠁⠀⠀⠇⠐⠳⠗⠛⠛⠃⠘⠚⠛⠾⠺⠚⠚⠲⠆⠾⠒⠐⠺⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠙⠛⠛⠟⠛⠅⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⡆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠓⠀⠛⠛⠛⠀⠋⠛⠋⠓⠋⡓⠛⠛⠙⠒⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡇⠈⠀⠀⡀⠀⣀⠀⠀⡀⠀⡀⠀⠀⠀⡀⠀⠀⠀⢀⡀⠀⠀⢀⢀⣀⠀⠀⠀⣀⢀⠀⣀⣀⣀⠀⢀⣀⣀⠀⣀⣀⣀⢈⢀⣀⡀⠂⡀⣀⣀⡀⢀⣀⡀⢀⣀⣀⢀⣀⣀⣀⣀⣀⣀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⢀⠉⠀⡛⠛⠻⠛⠁⡃⢐⡃⠂⠐⠉⡛⠛⠛⠙⢛⣛⠃⠀⢛⢛⣛⠃⢘⢀⠘⣙⠀⣙⣛⢚⠀⢛⣛⣓⠀⢛⣛⣋⣛⣛⢛⣛⣙⢓⠛⢛⡓⢙⢛⡋⢘⣛⣛⣛⣛⣛⣓⣛⣙⣛⣛⢛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡛⠛⡚⠛⠃⡃⠘⣃⡀⠐⠉⡛⠙⠋⠙⢛⡛⠃⠀⢙⢛⢛⠃⢘⠘⢛⣛⠁⣛⣛⢘⠀⢛⣛⣓⡀⡛⣛⣛⣋⣛⣛⣛⣙⣛⣋⠙⡓⢙⣛⣋⣙⣛⣛⢙⣛⣛⣙⣛⣋⡛⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡋⠋⡋⠛⠀⡃⠐⡃⠀⠈⠙⡛⠋⠉⠉⢛⣛⠀⠀⣉⣙⣋⡁⢈⠀⣚⣛⠁⣙⣛⣚⠀⣈⣓⣛⠛⣛⣛⣉⣛⠉⣉⣋⣉⢋⣃⣉⣃⣙⡋⡛⢁⣋⡙⢛⣋⣉⣉⣛⣈⣀⣀⣀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡋⠉⠛⢛⡃⡃⢈⡃⠀⠈⢙⣛⡛⠉⣘⢛⣛⡃⠀⣉⣛⣛⡁⢘⠀⣙⣙⠉⣙⣛⣉⠀⣛⠛⣓⣀⣛⣋⠛⡋⡈⣋⣋⣛⣉⣋⡋⢚⠙⠉⠋⠙⠛⠉⠙⠋⠛⠛⠛⠊⠛⠛⠙⠛⠛⠙⠁⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡍⠋⢙⣋⡁⡅⢀⡃⠀⠈⠉⣉⣉⠉⣘⣉⣉⡀⠀⣉⣉⢙⣁⢈⠀⠉⢉⠀⡉⣉⢉⠀⢉⣋⢉⣉⣩⣅⣈⢉⣀⣅⣉⢉⡉⣍⣁⡀⡀⣀⢀⡀⡀⡀⡀⡀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠉⠉⠑⠋⠁⠁⠈⠁⠀⠈⠉⠉⠉⠉⠈⠉⠙⠂⠀⠙⠉⠉⠉⠈⠀⠀⠈⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠙⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢘ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⡄⠀⣤⣄⣄⣤⣄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠁⠀⠙⠛⠉⠙⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠆⠤⠒⠤⠄⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠊⠋⠙⠛⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠢⠤⠇⠦⠦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡀⠁⡓⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣤⣤⡥⣤⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡈⠁⡡⡉⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠜ ⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠐⠂⠀⠀⠐⠀⠸⢷⠾⠾⠶⠶⠶⠆⠀⠒⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠒⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⠿⠶⠶⠾⠷⠿⠿⠽⠶⠆⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡ ⡏⠿⠶⠷⠶⢶⣶⡶⠀⠸⠅⠷⠶⠶⠆⠸⠷⠲⠲⠶⠺⠆⠸⠲⠶⠶⠶⠾⠶⠶⠼⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣿⡿⠿⠶⠷⠇⠷⠶⠆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠿⠿⠇⠀⠀⠀⠀⠈⠳⠲⠲⠶⠶⠶⠶⠂⠸⠷⠶⠶⠺⠶⠷⠂⠸⠶⠾⠸⠹⠿⠽⠙⠶⠖⠒⠶⠶⠷⠔⠀⣿⣧⠺⠰⠶⠆⠗⠆⠗⠶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠉⠉⠀⢸ ⡟⠻⠶⠫⠷⠶⠇⠀⠀⠸⠗⠾⠃⠸⠿⠶⠶⠚⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⠲⢲⠶⠗⠐⠓⠶⠶⠲⠶⠶⠶⠆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡟⠟⠷⠆⠇⠟⠶⠀⠀⠘⠷⠶⠞⠇⠸⠱⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⠻⢿⠒⠶⠶⠾⠷⠶⠞⠇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠛⠛⠚⠓⠓⠇⠁⠀⠀⠇⠐⠳⠗⠛⠛⠂⠘⠚⠻⠾⠺⠚⠚⠲⠂⠾⠲⠒⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡿⠙⠟⠛⠟⠓⠇⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡒⠀⠀⠀⠀⠀⠀⡀⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⡆⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠛⠛⠛⠛⠓⠀⠛⠛⠛⠀⠋⠛⠋⠃⠓⡃⠓⠛⠉⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢰ ⡇⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⢀⢀⣀⠀⢀⠀⣀⢀⠀⣀⣀⣀⠀⣀⣀⣀⠀⣀⣀⣀⣈⣀⣀⡀⠂⣀⣀⣀⡀⢀⣀⡀⢀⣀⣀⢀⣀⣀⣀⣀⣀⣀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⢀⠉⠀⡛⠋⡻⠟⠃⡃⠐⡃⠂⠐⠙⡛⠛⠛⠙⢛⣛⠃⠀⢛⢛⣛⠃⢘⢀⡘⣙⠀⣛⣛⢘⠀⢛⣛⣓⠀⣛⣛⡋⡛⣛⣛⡋⡘⣛⡛⢛⡓⢙⣛⡋⢙⣛⡛⣛⣛⣛⣛⣛⣙⣛⣛⣛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡛⠛⡛⠛⠃⡃⠘⡃⠀⠐⠙⡛⠛⠛⠙⢛⡛⠃⠀⢙⣛⣛⠃⢘⠘⢛⣛⠁⣛⣛⢘⠀⣛⣛⣓⡀⡛⣛⣛⣛⣛⣛⣛⣙⣋⣋⠑⡓⢙⣛⣋⣙⣛⣛⢛⣛⣛⣙⣛⡛⠛⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡋⠋⡛⠛⠂⡃⢐⡃⠀⠈⠙⡛⠙⠋⡙⢛⣛⠀⠀⣉⣛⣋⡁⢘⠀⣚⣛⠁⣙⣛⣈⠀⣉⣑⣙⠛⣛⣛⣛⣛⠛⣋⣛⣛⢋⣋⣉⣋⣙⣋⡛⢁⣋⡙⢛⣋⣉⣉⣛⣂⣀⣀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡋⢋⠛⢛⡃⡃⢈⡃⠀⠈⢙⣛⣛⡉⣘⢛⣛⡁⠀⣙⣙⣛⡁⢈⠀⣙⣙⠁⣙⣛⢈⠀⣛⣋⣓⣀⣛⣋⢛⡋⠈⣋⣋⣋⣉⣋⡋⢛⠛⠙⠋⠙⠛⠋⠘⠛⠋⠙⠙⠋⠛⠛⠙⠚⠛⠙⠁⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡉⣋⡛⣋⡁⡁⢀⡃⠀⠈⣉⣉⣉⡉⣈⣉⣉⡀⠀⣉⣉⣍⡁⢈⠀⠉⢉⡀⣉⣉⢈⠀⣍⣉⢉⣉⣉⣁⣈⢉⣀⣍⡉⣉⣉⣉⣉⣀⡄⣀⣀⡀⡀⣄⡄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠉⠉⠛⠋⠁⠁⠈⠁⠀⠈⠉⠉⠉⠉⠈⠉⠙⠃⠀⠉⠉⠉⠁⠈⠀⠀⠈⠀⠉⠉⠈⠀⠉⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⡄⠀⣤⣄⣄⣤⣄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠁⠀⠙⠛⠉⠙⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠆⠤⠒⠤⠄⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠊⠋⠙⠛⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠢⠤⠇⠦⠆⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡀⠁⡓⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣤⣤⡥⣤⢄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡈⠁⡡⡉⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠠⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠂⠐⠒⠀⠀⠐⠀⠸⢷⠾⠾⠶⠶⠶⠆⠀⠒⠀⠐⠂⠀⠐⠀⠀⠀⠀⠀⠀⠉⠀⠁⠒⣤⣴⠒⠀⠀⠀⠀⠀⠁⠀⠁⠀⠂⠸⠿⠶⠾⠾⠿⠿⠾⠽⠶⠆⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢡ ⡏⠿⠶⠷⠶⢶⣶⡶⠀⠸⠅⠷⠶⠶⠆⠸⠷⠲⠲⠶⠺⠆⠸⠲⠶⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠿⣿⠿⠾⠷⠇⠷⠶⠆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣀⡀⢀⠀⠀⠀⠀⢸ ⡟⠿⠿⠿⠷⠀⠀⠀⠀⠈⠻⠲⠲⠶⠶⠶⠶⠂⠸⠷⠶⠶⠺⠷⠷⠂⠸⠶⠾⠽⠿⠿⠽⠹⠶⠖⠒⠶⠶⠷⠔⠀⠀⣿⠺⠰⠶⠆⠗⠆⠗⠶⡆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠉⠉⠀⢸ ⡟⠻⠶⠻⠷⠶⠇⠀⠀⠸⠗⠾⠇⠸⠿⠶⠶⠚⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣤⢲⠶⠗⠐⠒⠶⠶⠶⠶⠶⠶⠆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡟⠟⠷⠆⠇⠟⠶⠀⠀⠘⠷⠶⠞⠇⠸⠱⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⠿⢿⠒⠶⠶⠾⠷⠶⠞⠇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠛⠛⠚⠓⠓⠇⠁⠀⠀⠇⠘⠳⠗⠛⠛⠂⠘⠚⠻⠾⠺⠚⠚⠲⠆⠾⠲⠒⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿⠛⠟⠛⠟⠗⠇⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⣀⡀⠀⠀⠀⣀⠀⡀⡋⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⡆⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠈⠉⠉⠉⠁⠀⠛⠛⠟⠛⠀⠛⠛⠛⠛⠛⡛⠀⠉⠉⠉⠉⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠉⢹ ⡇⠀⠀⠀⣀⠀⠀⠀⠀⣀⡀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠀⠀⡀⠂⠀⣀⠀⠈⣀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⢀⠀⣀⠀⢀⠀⡀⠀⠀⣀⣀⠀⠀⠀⢸ ⡗⢀⠀⠀⣛⣛⣋⣛⠀⣃⣓⣛⣛⣀⠀⣀⣀⣀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⠟⠛⠛⠛⡛⡛⠛⠐⡛⠋⠟⠀⣀⠛⠛⣛⠛⣉⡀⠛⠛⠛⣟⣛⠀⠉⠉⠛⠛⠛⠛⣛⠛⠀⠛⠛⠙⠛⠛⠛⠋⠛⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣛⣛⣙⠃⣀⡋⣛⣛⡋⠋⠀⠛⠃⠛⠁⠃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠋⠋⠛⠛⠀⠓⠛⠛⠛⠙⠀⠀⠛⠛⠛⠛⠛⠛⠀⠉⠚⠀⠛⠛⠛⠛⠛⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⠀⣏⣛⣏⢀⡏⣋⣛⣋⠁⣀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⢀⣋⣋⣋⣀⡋⣛⣛⢋⣀⣛⣛⣈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠈⣭⣭⣭⡍⠉⣍⣉⣈⣉⣉⣋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⢀⣥⣉⣉⣍⣤⣉⠉⣭⣍⣉⣉⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⢀⣭⣭⣥⠉⣭⣿⣄⠉⣭⣉⣍⣉⣀⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸ ⡇⠀⠀⠀⠉⠉⠉⠀⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸ ⡇⠀⣤⣄⣀⢀⣤⣀⣀⣀⣄⣀⣀⣀⠀⣤⣀⣀⣀⣀⣄⣀⣀⣀⡄⠀⣀⡤⠀⣤⣀⣤⣀⣀⣀⣀⠠⣤⡤⣤⣤⠀⣤⡤⣀⣤⠀⣀⣄⣀⣀⡄⠀⣀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣭⣍⡅⣄⢈⣍⣍⡅⣅⣍⣭⠉⣄⣍⢉⣍⣍⣅⣍⣭⣍⣍⣭⢀⣍⡥⠀⣍⣉⣅⣍⣍⣍⠉⣤⠉⠉⡭⠉⣤⠉⣭⠀⡭⣤⣭⣍⠉⡥⣭⣄⠉⣍⣭⣉⣄⣤⣀⣤⣤⠀⣀⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠁⠁⠁⠁⠀⠈⠁⠀⠉⠉⠁⠀⠁⠁⠀⠁⠉⠉⠉⠉⠉⠁⠉⠀⠁⠁⠀⠉⢉⠉⠉⠁⠁⠀⠉⠁⠀⠉⠀⠉⠀⠀⠀⠁⠁⠉⠉⠀⠈⠉⠁⠀⠉⠈⠉⠉⠉⠉⠁⠉⠀⠉⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠦⠤⠒⠤⠄⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠊⠋⠙⠛⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠣⠤⠇⠦⠦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡀⠁⡓⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣤⣤⡥⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡈⠁⡡⡉⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠠⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠂⠐⠒⠀⠀⠐⠀⠸⢷⠾⠾⠶⠶⠶⠆⠀⠒⠀⠐⠂⠀⠐⠀⠀⠀⠀⠀⠀⠉⠉⠁⠒⣤⣴⠒⠀⠀⠀⠀⠀⠁⠀⠁⠀⠂⠸⠿⠶⠾⠾⠿⠿⠾⠽⠶⠎⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢡ ⡏⠿⠶⠷⠶⢶⣶⡶⠀⠸⠅⠷⠶⠶⠆⠸⠷⠲⠲⠶⠺⠆⠸⠲⠶⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠿⣿⠿⠾⠷⠇⠿⠶⠆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣀⡀⢀⠀⠀⠀⠀⢸ ⡟⠿⠿⠿⠷⠀⠀⠀⠀⠈⠻⠳⠲⠶⠶⠶⠶⠂⠸⠷⠶⠶⠺⠴⠷⠀⠺⠶⠾⠽⠿⠿⠽⠹⠶⠖⠒⠶⠶⠷⠔⠀⠀⣿⠺⠰⠶⠆⠗⠆⠗⠶⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠉⠉⠀⢸ ⡟⠿⠶⠻⠷⠶⠇⠀⠀⠸⠗⠾⠗⠺⠿⠶⠶⠚⠍⠙⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣤⢲⠶⠗⠐⠒⠶⠶⠶⠶⠶⠶⠆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡟⠟⠷⠆⠇⠟⠶⠀⠀⠘⠷⠶⠞⠇⠸⠱⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⠿⢿⠒⠶⠶⠾⠷⠶⠞⠇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠛⠛⠚⠓⠓⠇⠁⠀⠀⠇⠘⠳⠗⠛⠛⠂⠘⠚⠻⠾⠺⠚⠚⠲⠆⠾⠲⠒⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿⠛⠟⠛⠟⠗⠇⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⣀⡀⠀⠀⠀⣀⠀⡀⡋⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⡆⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠈⠉⠛⠉⠁⠀⠛⠛⠟⠛⠀⠛⠛⠛⠛⠛⡛⠀⠉⠉⠉⠉⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠉⢹ ⡇⠀⠀⠀⣀⠀⠀⠀⠀⣀⡀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠀⠀⡀⠂⠀⣀⠀⠈⣀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⢀⠀⣀⠀⢀⠀⡀⠀⠀⣀⣀⠀⠀⠀⢸ ⡗⢀⠀⠀⣛⣛⣋⣛⠀⣃⣓⣛⣛⣀⠀⣀⣀⣀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⠟⠛⠛⠛⡛⡛⠛⠐⡛⠋⠟⠀⣀⠛⠛⣛⠛⣉⡀⠛⠛⠛⣟⣛⠀⠉⠉⠛⠛⠛⠛⣛⠛⠀⠛⠛⠙⠛⠛⠛⠋⠛⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣛⣛⣙⠃⣀⡋⣛⣛⡋⠋⠀⠛⠃⠋⠀⠃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠋⠋⠛⠛⠀⠓⠛⠛⠛⠙⠀⠀⠛⠛⠛⠛⠛⠛⠀⠉⠚⠀⠛⠛⠛⠛⠛⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⠀⣍⣛⣏⢀⡏⣋⣛⣋⠁⣀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣛⣉⣋⣀⡋⣛⣛⢋⣀⣛⣛⣈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣩⣭⣭⡍⠉⣍⣉⣈⣉⣉⣋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣡⣉⣉⣍⣤⣉⠉⣭⣍⣉⣉⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣩⣭⣥⠉⣭⣿⣄⠉⣭⣉⣍⣉⣀⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸ ⡇⠀⠀⠀⠉⠉⠉⠀⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸ ⡇⠀⣤⣄⣀⢀⣤⣀⣀⣀⣄⣀⣀⣀⠀⣤⣀⣀⣀⣀⣄⣀⣀⣀⡄⠀⣀⡤⠀⣤⣀⣤⣀⣀⣀⣀⠠⣤⡤⣤⣤⠄⣤⡤⣀⣤⠀⣀⣄⣀⣀⡄⠀⣀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢭⣍⡅⣄⢈⣍⣍⡅⣅⣍⣭⠉⣄⣍⢉⣍⣍⣅⣍⣭⣍⣍⣭⢀⣍⡥⠀⣍⣉⣅⣍⣍⣍⠉⣤⠉⠉⡭⠉⣤⠉⣩⠀⡭⣤⣭⣍⠉⡥⣭⣄⠉⣍⣭⣉⣄⣤⣀⣤⣤⢠⣀⣀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠁⠉⠁⠀⠈⠉⠀⠉⠉⠁⠀⠁⠁⠀⠁⠉⠉⠉⠉⠉⠁⠉⠀⠁⠁⠀⠉⢉⠉⠉⠁⠁⠀⠉⠁⠀⠉⠀⠉⠀⠀⠀⠁⠁⠉⠉⠀⠈⠉⠁⠀⠉⠈⠉⠉⠀⠉⠁⠉⠀⠉⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠦⠤⠒⠤⠄⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠊⠋⠙⠛⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠣⠤⠇⠦⠦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡀⠁⡓⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣤⣤⡥⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡈⠁⡡⡉⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠠⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠂⠐⠒⠀⠀⠐⠀⠸⢷⠾⠾⠶⠶⠶⠆⠀⠒⠀⠐⠂⠀⠐⠀⠀⠀⠀⠀⠀⠉⠉⠉⠓⣤⣴⠒⠀⠀⠀⠀⠀⠁⠀⠁⠀⠂⠸⠿⠶⠾⠾⠿⠿⠾⠿⠶⠎⠘⠌⠂⠀⠀⠀⠀⠀⠀⠀⠀⢡ ⡏⠿⠶⠷⠶⢶⣶⡶⠀⠸⠅⠷⠶⠶⠆⠸⠷⠲⠲⠶⠺⠆⠸⠀⠶⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠿⣿⠿⠾⠷⠇⠿⠶⠆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣀⡀⢀⠀⠀⠀⠀⢸ ⡟⠿⠿⠿⠗⠀⠀⠀⠀⠈⠻⠳⠲⠶⠶⠶⠶⠂⠸⠷⠶⠶⠺⠴⠷⠂⠺⠶⠾⠽⠿⠿⠽⠻⠶⠖⠒⠶⠶⠷⠔⠀⠀⣿⠺⠰⠶⡇⠗⠆⠗⠶⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠉⠉⠀⢸ ⡟⠿⠶⠻⠷⠶⠇⠀⠀⠸⠗⠾⠗⠺⠿⠶⠶⠚⠍⠹⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣤⢲⢾⡇⡔⠒⠶⠶⠶⠶⠶⠶⠆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡟⠟⠷⠆⠇⠟⠶⠀⠀⠘⠷⠶⠞⠇⠸⠱⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⠿⢿⠒⠾⡷⠾⠷⠶⠞⠇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠛⠛⠚⠓⠓⠇⠁⠀⠀⠇⠘⠳⠗⠛⠛⠂⠘⠚⠻⠾⠺⠚⠚⠲⠆⠾⠲⠒⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿⠛⠟⠛⠟⠟⠇⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⣀⡀⠀⠀⠀⣀⠀⡀⡋⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⡆⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠈⠉⠛⠉⠁⠀⠛⠛⠟⠛⠀⠛⠛⠛⠛⠛⡛⠀⠉⠉⠉⠉⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠉⢹ ⡇⠀⠀⠀⣀⠀⠀⠀⠀⣀⡀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠀⠀⡀⠂⠀⣀⠀⠈⣀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⢀⠀⣀⠀⢀⠀⡀⠀⠀⣀⣀⠀⠀⠀⢸ ⡗⢀⠀⠀⣛⣛⣋⣛⠀⣃⣓⣛⣛⣀⠀⣀⣀⣀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⠟⠛⠛⠛⡛⡛⠛⠐⡛⠋⠟⠀⣀⠛⠛⣛⠛⣉⡀⠛⠛⠛⣟⣛⠀⠉⠉⠛⠛⠛⠛⣛⠛⠀⠛⠛⠙⠛⠛⠛⠋⠛⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣛⣛⣙⠃⣀⡋⣛⣛⡋⠋⠀⠛⠃⠋⠀⠃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠋⠋⠛⠛⠀⠓⠛⠛⠛⠙⠀⠀⠛⠛⠛⠛⠛⠛⠀⠉⠚⠀⠛⠛⠛⠛⠛⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⠀⣉⣛⣏⢀⡏⣋⣛⣋⠁⣀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣙⣉⣋⣀⡋⣛⣛⢋⣀⣛⣛⣈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣩⣭⣭⡍⠉⣍⣉⣈⣉⣉⣋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣠⣉⣉⣍⣤⣉⠉⣭⣍⣉⣉⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣩⣭⣥⠉⣭⣿⣄⠉⣭⣉⣍⣉⣀⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸ ⡇⠀⠀⠀⠉⠉⠉⠀⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸ ⡇⠀⣤⣄⣀⢀⣤⣀⣀⣀⣄⣀⣀⣀⠀⣤⣀⣀⣀⣀⣄⣀⣀⣀⡄⠀⣀⡤⠀⣤⢀⣤⣀⣀⣀⣀⠠⣤⡤⣤⣤⢄⣤⡤⣀⣤⠀⣀⣄⣀⣀⡄⠀⣀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢭⣍⡅⣄⢈⣍⣍⡅⣅⣍⣭⠉⣄⣍⢉⣍⣍⣅⣍⣭⣍⣍⣭⢀⣍⡥⠀⣍⣉⣅⣍⣍⣍⠉⣤⠉⠉⡭⠉⣤⠉⣩⠀⡭⣤⣭⣍⠉⡤⣭⣄⠉⣍⣭⣉⣄⣤⣀⣤⣤⢠⣀⣀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠁⠉⠁⠀⠈⠈⠁⠉⠉⠁⠀⠁⠁⠀⠁⠉⠉⠉⠉⠉⠁⠉⠀⠁⠁⠀⠉⢉⠉⠉⠁⠁⠀⠉⠁⠀⠉⠀⠉⠀⠀⠀⠁⠁⠉⠉⠀⠈⠉⠁⠀⠉⠈⠉⠉⠀⠉⠁⠉⠀⠉⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠦⠤⠒⠤⠄⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠊⠋⠙⠛⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠣⠤⠇⠦⠦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡀⠁⡓⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣤⣤⡥⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡈⠁⡡⡉⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠠⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠐⠒⠀⠀⠐⠀⠸⢷⠾⠾⠶⠶⠶⠆⠀⠒⠀⠐⠂⠀⠐⠀⠀⠀⠀⠀⠀⠉⠈⠉⠓⣤⣴⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⠿⠶⠾⠾⠿⠿⠾⠿⠶⠎⠘⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡ ⡏⠿⠶⠷⠶⢶⣶⡶⠀⠸⠅⠷⠶⠶⠆⠸⠷⠲⠲⠶⠺⠆⠸⠀⠶⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠿⣿⠿⠾⠷⠇⠿⠶⠆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣀⡀⢀⠀⠀⠀⠀⢸ ⡟⠿⠿⠿⠗⠀⠀⠀⠀⠈⠻⠳⠲⠶⠶⠶⠶⠂⠸⠷⠶⠶⠺⠴⠷⠂⠺⠶⠾⠽⠿⠿⠽⠻⠶⠖⠒⠶⠶⠷⠔⠀⠀⣿⠺⠰⠶⡇⠗⠆⠷⠆⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠉⠉⠀⢸ ⡟⠿⠶⠻⠷⠶⠇⠀⠀⠸⠗⠾⠗⠺⠿⠶⠶⠚⠍⠹⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⣤⢲⢾⡇⡔⠒⠶⡗⠲⠶⠶⠶⠆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡟⠟⠷⠆⠇⠟⠶⠀⠀⠘⠷⠶⠞⠇⠸⠱⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⠿⢿⠒⠾⡷⠾⠷⡆⡞⠇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠛⠛⠚⠓⠓⠇⠁⠀⠀⠇⠐⠳⠗⠛⠛⠂⠘⠚⠻⠾⠺⠚⠚⠲⠆⠾⠲⠒⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿⠛⠟⠛⠟⠟⠇⠀⡤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⣀⡀⠀⠀⠀⣀⠀⡀⡋⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⡆⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠈⠉⠛⠉⠁⠀⠛⠛⠟⠛⠀⠛⠛⠛⠛⠛⡛⠀⠉⠉⢉⠉⠉⠉⡉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠉⢹ ⡇⠀⠀⠀⣀⠀⠀⠀⠀⣀⡀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⠀⠐⠈⠀⠀⡀⠂⠀⣀⠀⠈⣈⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⢀⠀⣀⠀⢀⠀⡀⠀⠀⣀⣀⠀⠀⠀⢸ ⡗⢀⠀⠀⣛⣛⣋⣛⠀⣃⣓⣛⣛⣀⠀⣀⣀⣀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⠟⠛⠛⠛⡛⡛⠛⠐⡛⡋⠟⠀⣀⠛⠛⣛⢛⣉⡀⠛⠛⠛⣟⣛⠀⠉⠉⠛⠛⠛⠛⣛⠛⠀⠛⠛⠙⠛⠛⠛⠋⠛⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣛⡛⣙⠃⣀⡋⣙⣓⡋⠋⠐⠛⠃⠋⠀⠃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠉⠋⠙⠟⠀⠓⠛⠛⠛⠙⠄⠀⠛⠛⠛⠛⠛⠛⠀⠉⠚⠀⠛⠛⠛⠛⠛⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠂⠀⠀⠀⢸ ⡇⠀⠉⠀⡉⡛⣟⢃⡿⣉⣛⣋⠁⣐⣀⢀⣀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸ ⡇⠀⠀⠀⣙⣉⣫⣀⡋⣛⣛⢋⣠⣛⣛⣈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣩⣭⣭⡍⠉⣍⣉⣈⣉⣉⣋⠉⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣠⣉⣉⣟⣤⣉⠉⣭⣍⣉⣉⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣩⣭⣥⡉⣭⣯⣄⠏⣭⣉⣍⣉⣀⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸ ⡇⠀⠀⠀⠉⠉⠉⠀⠉⠉⠋⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸ ⡇⠀⣤⣄⣀⢀⣤⣀⣀⣀⣬⣇⣀⣀⠀⣤⣀⣀⣀⣀⣄⣀⣀⣀⡄⠀⣀⡤⠀⣤⢀⣤⣀⣀⣀⣀⠠⣤⡤⣤⣤⢄⣤⡤⣀⣤⠀⣀⣄⣀⣀⡄⠀⣀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢭⣍⡅⣄⢈⣍⣍⡅⣍⣍⣭⠉⣄⣍⢉⣍⣍⣅⣍⣭⣍⣍⣭⢀⣍⡥⠀⣍⣉⣅⣍⣍⣍⠉⣤⠉⠉⡭⠉⣤⠉⣩⠀⡭⣤⣭⣍⠉⡤⣭⣄⠉⣍⣭⣉⣄⣤⣀⣤⣤⢠⣀⣀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠁⠉⠁⠀⠈⠈⠁⠉⠉⠁⠀⠁⠁⠀⠁⠉⠉⠉⠉⠉⢡⠉⠀⠁⠁⣀⠉⢉⠉⠉⠁⠁⠀⠉⠁⠀⠉⠀⠉⠀⠀⠀⠁⠁⠉⠁⠀⠈⠉⠁⠀⠉⠈⠉⠉⠀⠉⠁⠉⠀⠉⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠄⠦⠄⠒⠤⠄⠆⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠐⠀⠀⠀⠀⠤⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠊⠋⠙⠛⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠣⠤⠇⠦⠦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡀⠁⡓⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣤⣤⡥⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡈⠁⡡⡉⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠠⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠐⠒⠀⠀⠐⠀⠸⢷⠾⠾⠶⠶⠶⠆⠀⠒⠀⠐⠂⠀⠐⠀⠀⠀⠀⠀⠀⠉⠈⠉⠓⣤⣴⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⠿⠶⠾⠾⠷⠿⠾⠿⠶⠎⠘⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡ ⡏⠿⠶⠷⠶⢶⣶⡶⠀⠸⠅⠷⠶⠶⠆⠸⠷⠲⠲⠶⠺⠆⠸⠀⠶⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠿⣿⠿⠾⠷⠇⠿⠶⠆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣀⡀⢀⠀⠀⠀⠀⢸ ⡟⠿⠿⠿⠗⠀⠀⠀⠀⠈⠻⠳⠲⠶⠶⠶⠶⠂⠸⠷⠶⠶⠺⠴⠷⠂⠺⠶⠾⠹⠿⠿⠽⠻⠶⠖⠒⠶⠶⠷⠔⠀⠀⣿⠪⠰⠶⡇⠗⠆⠷⠆⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠉⠉⠀⢸ ⡟⠿⠶⠫⠷⠶⠇⠀⠀⠸⠗⠾⠗⠺⠿⠶⠶⠚⠍⠹⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⣤⢲⢾⡇⡔⠒⠶⡗⠲⠶⠶⠶⠆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡟⠟⠷⠆⠇⠟⠶⠀⠀⠘⠷⠶⠞⠇⠸⠱⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⠿⢿⠒⠾⡷⠾⠷⡆⡞⠇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠛⠛⠚⠓⠓⠇⠁⠀⠀⠇⠐⠳⠗⠛⠛⠂⠘⠚⠻⠾⠺⠚⠚⠲⠆⠾⠲⠒⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿⠛⠟⠛⠟⠟⠇⠀⡤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⣀⡀⠀⠀⠀⣀⠀⡀⡋⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⡆⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠈⠉⠛⠉⠁⠀⠛⠛⠟⠛⠀⠛⠛⠛⠛⠛⡛⠀⠉⠉⢉⠉⠉⠉⡉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠉⢹ ⡇⠀⠀⠀⣀⠀⠀⠀⠀⣀⡀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⠀⠐⠈⠀⠀⡀⠂⠀⣀⠀⠈⣈⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⢀⠀⣀⠀⢀⠀⡀⠀⠀⣀⣀⠀⠀⠀⢸ ⡗⢀⠀⠀⣛⣛⣋⣛⠀⣃⣃⣛⣛⣀⠀⣀⣀⣀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⠟⠛⠛⠛⡛⡛⠛⠐⡛⡋⠟⠀⣀⠛⠛⣛⢛⣉⡀⠛⠛⠛⣟⣛⠀⠉⠉⠛⠛⠛⠛⣛⠛⠀⠛⠛⠙⠛⠛⠛⠋⠛⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣛⡛⣙⠃⣀⡃⣙⣓⡋⠋⠐⠛⠃⠋⠀⠃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠉⠋⠙⠟⠀⠓⠛⠛⠛⠙⠄⠀⠛⠛⠛⠛⠛⠛⠀⠉⠚⠀⠛⠛⠛⠛⠛⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠂⠀⠀⠀⢸ ⡇⠀⠉⠀⡉⡛⣟⢃⡿⣉⣛⣋⠁⣐⣀⢀⣀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸ ⡇⠀⠀⠀⣙⣉⡫⣀⡋⡛⣛⢋⣠⣛⣛⣈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⡀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣩⣭⣭⡍⠉⣅⣉⣈⣍⣉⣋⠉⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠁⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣠⡉⣙⡛⣥⣉⠉⣭⣍⣉⣉⣄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣩⣭⡥⡉⣭⣯⣄⠏⣭⣉⣍⣉⣀⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸ ⡇⠀⠀⠀⠉⠉⠉⠀⠉⠉⠋⠠⠙⠉⠉⠉⡋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸ ⡇⠀⣤⣄⢀⢄⣤⣈⣀⣀⣬⣇⣀⣀⠀⣤⣈⣀⡀⣀⣄⣀⣀⣀⡄⠀⣀⡤⠀⣤⢀⣤⣀⣀⣀⣀⠠⣤⡤⣤⣤⢄⣤⡤⣀⣤⠀⣀⣄⣀⣀⡄⠀⣀⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢭⣅⡘⣄⢈⣍⣍⡅⣍⣍⣭⠉⣄⣍⠉⣏⣍⣅⣍⣭⣍⣍⣭⢀⣍⡥⠀⣍⣉⣅⣍⣍⣍⠉⣤⠉⠉⡭⠉⣤⠉⣩⠀⡭⣤⣭⣍⠉⡤⣭⣄⠉⣍⣭⣉⣄⣤⣀⣤⣤⢠⣀⣀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠁⠉⠁⠀⠈⠺⠁⠉⠉⠁⠀⠁⠁⠀⠁⠉⠉⠉⠉⠉⢡⠉⠀⠁⠁⣀⠉⢉⠉⠉⠁⠁⠀⠉⠁⠀⠉⠀⠉⠀⠀⠀⠁⠁⠉⠁⠀⠈⠉⠁⠀⠉⠈⠉⠉⠀⠉⠁⠉⠀⠉⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠄⠢⠄⠒⠤⠄⠆⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠐⠀⠀⠀⠀⠤⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠊⠋⠙⠛⠃⢀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠣⠤⠇⠦⠦⠇⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡀⠁⡓⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣤⣤⡥⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡈⡁⡡⡉⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠤⠤⠤⠤⠤⠤⢤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠬⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠠⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠐⠒⠀⠀⠐⠀⠸⢷⠾⠾⠶⠶⠶⠆⠀⠒⠀⠐⠂⠀⠐⠀⠀⠀⠀⠀⠀⠉⠈⠉⠓⣤⣴⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⠿⠶⠾⠾⠷⠿⠾⠿⠶⠆⠘⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡ ⡏⠿⠶⠷⠶⢶⣶⡶⠀⠸⠅⠷⠶⠶⠆⠸⠷⠲⠲⠶⠺⠆⠸⠀⠶⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠿⣿⠿⠾⠷⠇⠿⠶⠆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣀⡀⢀⠀⠀⠀⠀⢸ ⡟⠿⠿⠿⠗⠀⠀⠀⠀⠈⠻⠳⠲⠶⠶⠶⠶⠂⠸⠷⠶⠶⠺⠴⠷⠂⠺⠶⠾⠹⠿⠿⠽⠻⠶⠖⠒⠶⠶⠷⠔⠀⠀⣿⠪⠰⠶⡇⠗⠆⠷⠆⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠉⠉⠀⢸ ⡟⠿⠶⠫⠷⠶⠇⠀⠀⠸⠗⠶⠗⠺⠿⠶⠶⠚⠍⠹⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⣤⢲⢾⡇⡔⠒⠶⡗⠲⠶⠶⠶⠆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡟⠟⠷⠆⠇⠟⠶⠀⠀⠘⠷⠶⠞⠇⠸⠱⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⠿⢿⠒⠾⡷⠾⠷⡆⡞⠇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠛⠛⠚⠓⠓⠇⠁⠀⠀⠇⠐⠳⠗⠛⠛⠂⠘⠚⠻⠾⠺⠚⠚⠲⠆⠾⠲⠒⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿⠛⠟⠛⠟⠟⠇⠀⡤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⣀⡀⠀⠀⠀⣀⠀⡀⡋⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⡆⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠈⠉⠛⠉⠁⠀⠛⠛⠟⠛⠀⠛⠛⠛⠛⠛⡛⠀⠉⠉⢉⠉⠉⠉⡉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠉⢹ ⡇⠀⠀⠀⣀⠀⠀⠀⠀⣀⡀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⠀⠐⠈⠀⠀⡀⠂⠀⣀⠀⠈⣈⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⢀⠀⣀⠀⢀⠀⡀⠀⠀⣀⣀⠀⠀⠀⢸ ⡗⢀⠀⠀⣛⣛⣋⣛⠀⣃⣃⣛⣛⣀⠀⣀⣀⣀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⠟⠛⠛⠛⡛⡛⠛⠐⡛⣋⡛⠀⣀⠛⠛⣛⢛⣉⡀⠛⠛⠛⣟⣛⠀⠉⠉⠛⠛⠛⠛⣛⠛⠀⠛⠛⠙⠛⠛⠛⠋⠛⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣛⡛⣙⠃⣀⡃⣙⣓⡋⠋⠐⠛⠃⠋⠀⠃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠉⠋⠙⠟⠀⠓⠛⠻⠛⠙⠄⠀⠛⠛⠛⠛⠛⠋⠀⠉⠚⠀⠛⠛⠛⠛⠛⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠂⠀⠀⠀⢸ ⡇⠀⠉⠀⡉⡛⣟⢃⡿⣉⣛⣋⠁⣐⣀⢀⣀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸ ⡇⠀⠀⠀⣙⣉⡫⣀⡋⠛⣛⢃⣠⣎⣛⣈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⡀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣩⣍⣍⡉⢉⣀⣉⣨⣅⣍⣉⠉⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠁⠀⠀⠈⠀⠁⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⢠⡉⣙⡛⣭⣉⠉⣭⣍⣉⣉⣀⠀⠀⠐⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠑⠊⠁⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣩⣭⡥⡉⣭⣯⣤⠏⣭⣉⣍⣉⣀⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸ ⡇⠀⠀⠀⠉⠁⠀⠐⠀⠉⠫⠠⠝⠉⠉⠉⡋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸ ⡇⠀⣤⣄⢀⢄⣤⣈⣀⣀⣬⣇⣀⣀⠀⣥⣈⣀⡀⣀⣄⣀⣀⣀⡄⠀⣀⡤⠀⣤⢀⣤⣀⣀⣀⣀⠠⣤⡤⣤⣤⢄⣤⡤⣀⣤⠀⣀⣄⣀⣀⡄⠀⣀⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢭⣁⡘⡄⠈⢍⣍⠅⣍⣍⣭⠉⣄⣍⠉⡛⣉⣅⣍⣭⣍⣍⣭⢀⣍⡥⠀⣍⣉⣅⣍⣍⣍⠉⣤⠉⠉⡭⠉⣤⠉⣩⠀⡭⣤⣭⣍⠉⡤⣭⣄⠉⣍⣭⣉⣄⣤⣀⣤⣤⢠⣀⣀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠁⠉⠁⠀⠈⠺⠁⠉⠉⠅⠀⠁⠁⠀⠁⠉⠉⠉⠉⠉⢡⠉⠀⠁⠁⣀⠉⢉⠉⠉⠁⠁⠀⠉⠁⠀⠉⠀⠉⠀⠀⠀⠁⠁⠉⠁⠀⠈⠉⠁⠀⠉⠈⠉⠉⠀⠉⠁⠉⠀⠉⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠲⠄⢒⡤⠄⠂⡀⠀⠠⠄⡄⠀⢀⠀⠀⠀⠀⠀⠀⠈⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠐⠀⠀⠀⠀⠤⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠈⠋⠉⠫⠁⢀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠣⠤⠇⠤⠦⠇⠒⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡀⠁⡓⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣤⣤⡥⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠄⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣈⡅⡡⡉⢁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠤⠤⠤⠤⠤⠤⢤⠄⠠⠠⠀⠄⠤⠤⠤⠤⠤⠤⠠⠈⠤⠤⠄⠀⠀⠂⠂⠀⠀⠀⠥⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠥⠬⠤⠤⠄⠠⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠐⠒⠀⠀⠐⠀⠸⢷⠾⠾⠶⠶⠶⠆⠀⠒⠀⠐⠂⠀⠐⠀⠀⠀⠀⠀⠀⠉⠈⠉⠓⣤⣴⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⠿⠶⠾⠾⠷⠿⠾⠿⠶⠆⠘⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡ ⡏⠿⠶⠷⠶⢶⣶⡶⠀⠸⠅⠷⠶⠶⠆⠸⠷⠲⠲⠶⠺⠆⠸⠀⠶⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠿⣿⠿⠾⠷⠇⠿⠶⠆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣀⡀⢀⠀⠀⠀⠀⢸ ⡟⠿⠿⠿⠗⠀⠀⠀⠀⠈⠻⠳⠲⠶⠶⠶⠶⠂⠸⠷⠶⠶⠺⠴⠷⠂⠺⠶⠾⠹⠿⠿⠽⠻⠶⠖⠒⠶⠶⠷⠔⠀⠀⣿⠪⠰⠶⡇⠗⠆⠷⠆⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠉⠉⠀⢸ ⡟⠿⠶⠫⠷⠶⠇⠀⠀⠸⠗⠶⠗⠺⠿⠶⠶⠚⠍⠹⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⣤⢲⢾⡇⡔⠒⠶⡗⠲⠶⠶⠶⠆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡟⠟⠷⠆⠇⠟⠶⠀⠀⠘⠷⠶⠞⠇⠸⠱⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⠿⢿⠒⠾⡷⠾⠷⡆⡞⠇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠛⠛⠚⠓⠓⠇⠁⠀⠀⠇⠐⠳⠗⠛⠛⠂⠘⠚⠻⠾⠺⠚⠚⠲⠆⠾⠲⠒⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿⠛⠟⠛⠟⠟⠇⠀⡤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⣀⡀⠀⠀⠀⣀⠀⡀⡋⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⡆⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠈⠉⠛⠉⠁⠀⠛⠛⠟⠛⠀⠛⠛⠛⠛⠛⡛⠀⠉⠉⢉⠉⠉⠉⡉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠉⢹ ⡇⠀⠀⠀⣀⠀⠀⠀⠀⣀⡀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⠀⠐⠈⠀⠀⡀⠂⠀⣀⠀⠈⣈⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⢀⠀⣀⠀⢀⠀⡀⠀⠀⣀⣀⠀⠀⠀⢸ ⡗⢀⠀⠀⣛⣛⣋⣛⠀⣃⣃⣛⣛⣀⠀⣀⣀⣀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⠟⠛⠛⠛⡛⡛⠛⠐⡛⣋⡛⠀⣀⠛⠛⣛⢛⣉⡀⠛⠛⠛⣟⣛⠀⠉⠉⠛⠛⠛⠛⣛⠛⠀⠛⠛⠙⠛⠛⠛⠋⠛⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣛⡛⣙⠃⣀⡃⣙⣓⡋⠋⠐⠛⠃⠋⠀⠃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠉⠋⠙⠟⠀⠓⠛⠻⠛⠙⠄⠀⠛⠛⠛⠛⠛⠋⠀⠉⠚⠀⠛⠛⠛⠛⠛⠛⠈⠀⠀⠀⠀⠅⠀⠀⠀⠁⠐⠂⠀⠀⠀⢸ ⡇⠀⠉⠀⡉⡛⣟⢃⡿⣉⣛⣋⠁⣐⣀⢀⣀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸ ⡇⠀⠀⠀⣙⣉⡫⣀⡋⠛⣛⢃⣠⣎⣛⣈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⡀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣩⣍⣍⡉⢉⣀⣉⣨⣅⣍⣉⠉⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠁⠀⠀⠈⠀⠁⠈⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⢠⡉⣙⡛⣭⣉⠉⣭⣍⣉⣉⣀⠀⠀⠐⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠑⠊⠁⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣩⣭⡥⡉⣭⣯⣤⠏⣭⣉⣍⣉⣀⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸ ⡇⠀⠀⠀⠉⠁⠀⠐⠀⠉⠫⠠⠝⠉⠉⠉⡋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸ ⡇⠀⣤⣄⢀⢄⣤⣈⣀⣀⣬⣇⣀⣀⠀⣥⣈⣀⡀⣀⣄⣀⣀⣀⡄⠀⣀⡤⠀⣤⢀⣤⣀⣀⣀⣀⠠⣤⡤⣤⣤⢄⣤⡤⣀⣤⠀⣀⣄⣀⣀⡄⠀⣀⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢭⣁⡘⡄⠈⢍⣍⠅⣍⣍⣭⠉⣄⣍⠉⡛⣉⣅⣍⣭⣍⣍⣭⢀⣍⡥⠀⣍⣉⣅⣍⣍⣍⠉⣤⠉⠉⡭⠉⣤⠉⣩⠀⡭⣤⣭⣍⠉⡤⣭⣄⠉⣍⣭⣉⣄⣤⣀⣤⣤⢠⣀⣀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠁⠉⠁⠀⠈⠺⠁⠉⠉⠅⠀⠁⠁⠀⠁⠉⠉⠉⠉⠉⢡⠉⠀⠁⠁⣀⠉⢉⠉⠉⠁⠁⠀⠉⠁⠀⠉⠀⠉⠀⠀⠀⠁⠁⠉⠁⠀⠈⠉⠁⠀⠉⠈⠉⠉⠀⠉⠁⠉⠀⠉⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠲⠄⢒⡤⠄⠂⡀⠀⠠⠄⡄⠀⢀⠀⠀⠀⠀⠀⠀⠈⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠐⠀⠀⠀⠀⠤⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠈⠋⠉⠫⠁⢀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠣⠤⠇⠤⠦⠇⠒⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡀⠁⡓⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣤⣤⡥⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠄⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣈⡅⡡⡉⢁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠤⠤⠤⠤⠤⠤⢤⠄⠠⠠⠀⠄⠤⠤⠤⠤⠤⠤⠠⠈⠠⠤⠄⠀⠀⠂⠂⠀⠀⠀⠥⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠥⠬⠤⠠⠄⠠⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠐⠒⠀⠀⠐⠀⠸⢷⠾⠾⠶⠶⠶⠆⠀⠒⠀⠐⠂⠀⠐⠀⠀⠀⠀⠀⠀⠉⠈⠉⠓⣤⣴⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⠿⠶⠾⠾⠷⠿⠾⠿⠶⠆⠘⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡ ⡏⠿⠶⠷⠶⢶⣶⡶⠀⠸⠅⠷⠶⠶⠆⠸⠷⠲⠲⠶⠺⠆⠸⠀⠶⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠿⣿⠿⠾⠷⠇⠿⠶⠆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣀⡀⢀⠀⠀⠀⠀⢸ ⡟⠿⠿⠿⠗⠀⠀⠀⠀⠈⠻⠳⠲⠶⠶⠶⠶⠂⠸⠷⠶⠶⠺⠴⠷⠂⠺⠶⠾⠹⠿⠿⠽⠻⠶⠖⠒⠶⠶⠷⠔⠀⠀⣿⠪⠰⠶⡇⠗⠆⠷⠆⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠉⠉⠀⢸ ⡟⠿⠶⠫⠷⠶⠇⠀⠀⠸⠗⠾⠗⠺⠿⠶⠶⠚⠍⠹⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⣤⢲⢾⡇⡔⠒⠶⡗⠲⠶⠶⠶⠆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡟⠟⠷⠆⠇⠟⠶⠀⠀⠘⠷⠶⠞⠇⠸⠱⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⠿⢿⠒⠾⡷⠾⠷⡆⡞⠇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠛⠛⠚⠓⠓⠇⠁⠀⠀⠇⠐⠳⠗⠛⠛⠂⠘⠚⠻⠾⠺⠚⠚⠲⠆⠾⠲⠒⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿⠛⠟⠛⠟⠟⠇⠀⡤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⣀⡀⠀⠀⠀⣀⠀⡀⡋⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⡆⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠈⠉⠛⠉⠁⠀⠛⠛⠟⠛⠀⠛⠛⠛⠛⠛⡛⠀⠉⠉⢉⠉⠉⠉⡉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠉⢹ ⡇⠀⠀⠀⣀⠀⠀⠀⠀⣀⡀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⠀⠐⠈⠀⠀⡀⠂⠀⣀⠀⠈⣈⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⢀⠀⣀⠀⢀⠀⡀⠀⠀⣀⣀⠀⠀⠀⢸ ⡗⢀⠀⠀⣛⣛⣋⣛⠀⣃⣃⣛⣛⣀⠀⣀⣀⣀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⠟⠛⠛⠛⡛⡛⠛⠐⡛⣋⡛⠀⣀⠛⠛⣛⢛⣉⡀⠛⠛⠛⣟⣛⠀⠉⠉⠛⠛⠛⠛⣛⠛⠀⠛⠛⠙⠛⠛⠛⠋⠛⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣛⡛⣙⠃⣀⡃⣙⣓⡋⠋⠐⠛⠃⠋⠀⠃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠉⠋⠙⠟⠀⠓⠛⠻⠛⠙⠄⠀⠛⠛⠛⠛⠛⠋⠀⠉⠚⠀⠛⠛⠛⠛⠛⠛⠈⠀⠀⠀⠀⠅⠀⠀⠀⠁⠐⠂⠀⠀⠀⢸ ⡇⠀⠉⠀⡉⡛⣟⢃⡿⣉⣛⣋⠁⣐⣀⢀⣀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸ ⡇⠀⠀⠀⣙⣉⡫⣀⡋⠛⣛⢃⣠⣎⣛⣈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⡀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣩⣍⣍⡉⢉⣀⣉⣨⣅⣍⣉⠉⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠈⠀⠁⠈⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⢠⡉⣙⡛⣭⣉⠉⣭⣍⣉⣉⣀⠀⠀⠐⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠑⠈⠁⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣩⣭⡥⡉⣭⣯⣤⠏⣭⣉⣍⣉⣀⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸ ⡇⠀⠀⠀⠉⠁⠀⠐⠀⠉⠫⠠⠝⠉⠉⠉⡋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸ ⡇⠀⣤⣄⢀⢄⣤⣈⣀⣀⣬⣇⣀⣀⠀⣥⣈⣀⡀⣀⣄⣀⣀⣀⡄⠀⣀⡤⠀⣤⢀⣤⣀⣀⣀⣀⠠⣤⡤⣤⣤⢄⣤⡤⣀⣤⠀⣀⣄⣀⣀⡄⠀⣀⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢭⣁⡘⡄⠈⢍⣍⠅⣍⣍⣭⠉⣄⣍⠉⡛⣉⣅⣍⣭⣍⣍⣭⢀⣍⡥⠀⣍⣉⣅⣍⣍⣍⠉⣤⠉⠉⡭⠉⣤⠉⣩⠀⡭⣤⣭⣍⠉⡤⣭⣄⠉⣍⣭⣉⣄⣤⣀⣤⣤⢠⣀⣀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠁⠉⠁⠀⠈⠺⠁⠉⠉⠅⠀⠁⠁⠀⠁⠉⠉⠉⠉⠉⢡⠉⠀⠁⠁⣀⠉⢉⠉⠉⠁⠁⠀⠉⠁⠀⠉⠀⠉⠀⠀⠀⠁⠁⠉⠁⠀⠈⠉⠁⠀⠉⠈⠉⠉⠀⠉⠁⠉⠀⠉⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠲⠄⢒⡤⠄⠂⡀⠀⠠⠄⡄⠀⢀⠀⠀⠀⠀⠀⠀⠈⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠐⠀⠀⠀⠀⠤⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠈⠋⠉⠫⠁⢀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠣⠤⠇⠤⠦⠇⠒⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡀⠁⡓⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣤⣤⡥⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠄⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣈⡅⡡⡉⢁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠤⠤⠤⠤⠤⠤⢤⠄⠀⠀⠀⠀⠀⠤⠤⠤⠤⠄⠀⠈⠠⠤⠄⠀⠀⠂⠂⠀⠀⠀⠁⠀⠀⠄⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠤⠤⠤⠥⠬⠤⠠⠄⠠⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠐⠒⠀⠀⠐⠀⠸⢷⠾⠾⠶⠶⠶⠆⠀⠒⠀⠐⠂⠀⠐⠀⠀⠀⠀⠀⠀⠉⠈⠉⠓⣤⣴⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⠿⠶⠾⠾⠷⠿⠾⠿⠶⠎⠘⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡ ⡏⠿⠶⠷⠶⢶⣶⡶⠀⠸⠅⠷⠶⠶⠆⠸⠷⠲⠲⠶⠺⠆⠸⠀⠶⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠿⣿⠿⠾⠷⠇⠿⠶⠆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣀⡀⢀⠀⠀⠀⠀⢸ ⡟⠿⠿⠿⠗⠀⠀⠀⠀⠈⠻⠳⠲⠶⠶⠶⠶⠂⠸⠷⠶⠶⠺⠴⠷⠂⠺⠶⠾⠹⠿⠿⠽⠻⠶⠖⠒⠶⠶⠷⠔⠀⠀⣿⠪⠰⠶⡇⠗⠆⠷⠆⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠉⠉⠀⢸ ⡟⠿⠶⠫⠷⠶⠇⠀⠀⠸⠗⠾⠗⠺⠿⠶⠶⠚⠍⠹⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⣤⢲⢾⡇⡔⠒⠶⡗⠲⠶⠶⠶⠆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡟⠟⠷⠆⠇⠟⠶⠀⠀⠘⠷⠶⠞⠇⠸⠱⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⠿⢿⠒⠾⡷⠾⠷⡆⡞⠇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠛⠛⠚⠓⠓⠇⠁⠀⠀⠇⠐⠳⠗⠛⠛⠂⠘⠚⠻⠾⠺⠚⠚⠲⠆⠾⠲⠒⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿⠛⠟⠛⠟⠟⠇⠀⡤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⣀⡀⠀⠀⠀⣀⠀⡀⡋⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⡆⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠈⠉⠛⠉⠁⠀⠛⠛⠟⠛⠀⠛⠛⠛⠛⠛⡛⠀⠉⠉⢉⠉⠉⠉⡉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠉⢹ ⡇⠀⠀⠀⣀⠀⠀⠀⠀⣀⡀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⠀⠐⠈⠀⠀⡀⠂⠀⣀⠀⠈⣈⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⢀⠀⣀⠀⢀⠀⡀⠀⠀⣀⣀⠀⠀⠀⢸ ⡗⢀⠀⠀⣛⣛⣋⣛⠀⣃⣃⣛⣛⣀⠀⣀⣀⣀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⠟⠛⠛⠛⡛⡛⠛⠐⡛⣋⡛⠀⣀⠛⠛⣛⢛⣉⡀⠛⠛⠛⣟⣛⠀⠉⠉⠛⠛⠛⠛⣛⠛⠀⠛⠛⠙⠛⠛⠛⠋⠛⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣛⡛⣙⠃⣀⡃⣙⣓⡋⠋⠐⠛⠃⠋⠀⠃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠉⠋⠙⠟⠀⠓⠛⠻⠛⠙⠄⠀⠛⠛⠛⠛⠟⠋⠀⠉⠚⠀⠛⠛⠛⠛⠛⠛⠈⠀⠀⠀⠀⠅⠀⠀⠀⠁⠐⠂⠀⠀⠀⢸ ⡇⠀⠉⠀⡉⡛⣟⢃⡿⣉⣛⣋⠁⣐⣀⢀⣀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸ ⡇⠀⠀⠀⣙⣉⡫⣀⡋⠛⣛⢃⣠⣎⣒⣈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⡀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣩⣍⣍⡉⢉⣀⣉⣨⣅⣍⣉⠉⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠈⠀⠁⠈⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⢠⡉⣙⡛⣭⣉⠉⣭⣍⣉⣉⣀⠀⠀⠐⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠑⠈⠁⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣩⣭⡥⡉⣭⣯⣤⠏⣭⣉⣍⣉⣀⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸ ⡇⠀⠀⠀⠉⠁⠀⠐⠀⠉⠫⠠⠝⠉⠉⠉⡋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸ ⡇⠀⣤⡄⢀⢄⣤⣈⣀⣀⣬⣇⣀⣀⠀⣥⣈⣀⡀⣀⣄⣀⣀⣀⡄⠀⣀⡤⠀⣤⢀⣤⣀⣀⣀⣀⠠⣤⡤⣤⣤⢄⣤⡤⣀⣤⠀⣀⣄⣀⣀⡄⠀⣀⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢭⣁⡘⡇⠈⢍⣍⠕⣏⣍⣭⠉⣄⣍⠉⡛⣉⣅⣍⣭⣍⣍⣭⢀⣍⡥⠀⣍⣉⣅⣍⣍⣍⠉⣤⠉⠉⡭⠉⣤⠉⣩⠀⡭⣤⣭⣍⠉⡤⣭⣄⠉⣍⣭⣉⣄⣤⣀⣤⣤⢠⣀⣀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠁⠉⠁⠀⠈⠺⠁⠉⠉⠅⠀⠁⠁⠀⠁⠉⠉⠉⠉⠉⢡⠉⠀⠁⠁⣀⠉⢉⠉⠉⠁⠁⠀⠉⠁⠀⠉⠀⠉⠀⠀⠀⠁⠁⠉⠁⠀⠈⠉⠁⠀⠉⠈⠉⠉⠀⠉⠁⠉⠀⠉⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠲⠄⢒⡤⠄⠂⡀⠀⠠⠄⡄⠀⢀⠀⠀⠀⠀⠀⠀⠈⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠐⠀⠀⠀⠀⠤⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠈⠋⠉⠫⠁⢀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠣⠤⠇⠤⠦⠇⠒⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡀⠁⡓⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣤⣤⡥⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠄⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣈⡅⡡⡉⢁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠤⠤⠤⠤⠤⠤⢤⠄⠀⠀⠀⠀⠀⠤⠤⠤⠤⠄⠀⠈⠠⠤⠄⠀⠀⠂⠂⠀⠀⠀⠁⠀⠀⠄⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠽⠴⠄⠥⠬⠤⠠⠄⠠⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠐⠂⠀⠀⠐⠀⠸⢷⠾⠾⠶⠶⠶⠆⠀⠒⠀⠐⠂⠀⠐⠀⠀⠀⠀⠀⠀⠉⠈⠉⠓⣤⣴⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⠿⠶⠾⠾⠷⠿⠾⠿⠶⠆⠘⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡ ⡏⠿⠶⠷⠶⢶⣶⡶⠀⠸⠅⠷⠶⠶⠆⠸⠷⠲⠲⠶⠺⠆⠸⠀⠶⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠿⣿⠿⠾⠷⠇⠿⠶⠆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣀⡀⢀⠀⠀⠀⠀⢸ ⡟⠿⠿⠿⠗⠀⠀⠀⠀⠈⠻⠳⠲⠶⠶⠶⠶⠂⠸⠷⠶⠶⠺⠴⠷⠂⠺⠶⠾⠹⠿⠿⠽⠻⠶⠖⠒⠶⠶⠷⠔⠀⠀⣿⠪⠰⠶⡇⠗⠆⠷⠆⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠉⠉⠀⢸ ⡟⠿⠶⠫⠷⠶⠇⠀⠀⠸⠗⠶⠗⠺⠿⠶⠶⠚⠍⠹⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⣤⢲⢾⡇⡔⠒⠶⡗⠲⠶⠶⠶⠆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡟⠟⠷⠆⠇⠟⠶⠀⠀⠘⠷⠶⠞⠇⠸⠱⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⠿⢿⠒⠾⡷⠾⠷⡆⡞⠇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠛⠛⠚⠓⠓⠇⠁⠀⠀⠇⠐⠳⠗⠛⠛⠂⠘⠚⠻⠾⠺⠚⠚⠲⠆⠾⠲⠒⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿⠛⠟⠛⠟⠟⠇⠀⡤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⣀⡀⠀⠀⠀⣀⠀⡀⡋⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⡆⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠈⠉⠛⠉⠁⠀⠛⠛⠟⠛⠀⠛⠛⠛⠛⠛⡛⠀⠉⠉⢉⠉⠉⠉⡉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠉⢹ ⡇⠀⠀⠀⣀⠀⠀⠀⠀⣀⡀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⠀⠐⠈⠀⠀⡀⠂⠀⣀⠀⠈⣈⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⢀⠀⣀⠀⢀⠀⡀⠀⠀⣀⣀⠀⠀⠀⢸ ⡗⢀⠀⠀⣛⣛⣋⣛⠀⣃⣃⣛⣛⣀⠀⣀⣀⣀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⠟⠛⠛⠛⡛⡛⠛⠐⡛⣋⡛⠀⣀⠛⠛⣛⢛⣉⡀⠛⠛⠛⣟⣛⠀⠉⠉⠛⠛⠛⠛⣛⠛⠀⠛⠛⠙⠛⠛⠛⠋⠛⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣛⡛⣙⠃⣀⡃⣙⣓⡋⠋⠐⠛⠃⠋⠀⠃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠉⠋⠙⠟⠀⠓⠛⠻⠛⠙⠄⠀⠛⠛⠛⠛⠛⠋⠀⠉⠚⠀⠛⠛⠛⠛⠛⠛⠈⠀⠀⠀⠀⠅⠀⠀⠀⠁⠐⠂⠀⠀⠀⢸ ⡇⠀⠉⠀⡉⡛⣟⢃⡿⣉⣛⣋⠁⣐⣀⢀⣀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸ ⡇⠀⠀⠀⣙⣉⡫⣀⡋⠛⣛⢃⣠⣎⣒⣈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⡀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣩⣍⣍⡉⢉⣀⣉⣨⣅⣍⣉⠉⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠈⠀⠁⠈⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⢠⡉⣙⡛⣭⣉⠉⣭⣍⣉⣉⣀⠀⠀⠐⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠑⠈⠁⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣩⣭⡥⡉⣭⣯⣤⠏⣭⣉⣍⣉⣀⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸ ⡇⠀⠀⠀⠉⠁⠀⠐⠀⠉⠫⠠⠝⠉⠉⠉⡋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸ ⡇⠀⣤⡄⢀⢄⣤⣈⣀⣀⣬⣇⣀⣀⠀⣥⣈⣀⡀⣀⣄⣀⣀⣀⡄⠀⣀⡤⠀⣤⢀⣤⣀⣀⣀⣀⠠⣤⡤⣤⣤⢄⣤⡤⣀⣤⠀⣀⣄⣀⣀⡄⠀⣀⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢭⣁⡘⡇⠈⢍⣍⠕⣏⣍⣭⠉⣄⣍⠉⡛⣉⣅⣍⣭⣍⣍⣭⢀⣍⡥⠀⣍⣉⣅⣍⣍⣍⠉⣤⠉⠉⡭⠉⣤⠉⣩⠀⡭⣤⣭⣍⠉⡤⣭⣄⠉⣍⣭⣉⣄⣤⣀⣄⣤⢠⣀⠀⠀⢠⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠁⠉⠁⠀⠈⠺⠁⠉⠉⠅⠀⠁⠁⠀⠁⠉⠉⠉⠉⠉⢡⠉⠀⠁⠁⣀⠉⢉⠉⠉⠁⠁⠀⠉⠁⠀⠉⠀⠉⠀⠀⠀⠁⠁⠉⠁⠀⠈⠉⠁⠀⠉⠈⠉⠉⠀⠉⠁⠉⠀⢉⠀⣶⣶⣶⣽⠉⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠲⠄⢒⡤⠄⠂⡀⠀⠠⠄⡄⠀⢀⠀⠀⠀⠀⠀⠀⠈⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠐⠀⠀⠀⠀⠤⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠉⠋⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠶⠀⠙⠏⠉⠫⠁⢀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠠⡤⠀⠀⠀⠀⠀⠀⠑⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡡⠤⠇⠤⠦⠇⠒⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡛⠁⡓⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣠⣤⡥⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠄⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣨⡥⡡⡉⢁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠤⠤⠤⠤⠤⠤⢤⠄⠀⠀⠀⠀⠀⠤⠤⠤⠤⠄⠀⠈⠠⠤⠄⠀⠀⠂⠂⠀⠀⠀⠁⠀⠀⠄⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠽⠴⠄⠥⠬⠤⠠⠄⠠⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠐⠂⠀⠀⠐⠀⠸⢷⠾⠾⠶⠶⠶⠆⠀⠒⠀⠐⠂⠀⠐⠀⠀⠀⠀⠀⠀⠉⠈⠉⠓⣤⣤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⠿⠶⠾⠾⠷⠿⠾⠿⠶⠆⠘⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡ ⡏⠿⠶⠷⠶⢶⣶⡶⠀⠸⠅⠷⠶⠶⠆⠸⠷⠲⠲⠶⠺⠆⠸⠀⠶⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠿⣿⠿⠾⠷⠇⠿⠶⠆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⢸ ⡟⠿⠿⠿⠗⠀⠀⠀⠀⠈⠻⠳⠲⠶⠶⠶⠶⠂⠸⠷⠶⠶⠺⠴⠷⠂⠺⠶⠾⠹⠿⠿⠭⠻⠶⠖⠒⠶⠶⠷⠔⠀⠀⣿⠪⠰⠶⡇⠗⠆⠷⠆⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠉⠉⠀⢸ ⡟⠿⠶⠫⠷⠶⠇⠀⠀⠸⠗⠶⠗⠺⠿⠶⠶⠚⠍⠹⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⣤⢲⢾⡇⡔⠒⠶⡗⠲⠶⠶⠶⠆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡟⠟⠷⠆⠇⠟⠶⠀⠀⠘⠷⠶⠞⠇⠸⠱⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⠿⢿⠒⠾⡷⠾⠷⡆⡞⠇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠛⠛⠚⠓⠓⠇⠁⠀⠀⠇⠐⠳⠗⠛⠛⠂⠘⠚⠻⠾⠺⠚⠚⠲⠆⠾⠲⠒⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿⠛⠟⠛⠟⠟⠇⠀⡤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⣀⡀⠀⠀⠀⣀⠀⡀⡋⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⡆⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠈⠉⠛⠉⠁⠀⠛⠛⠟⠛⠀⠛⠛⠛⠛⠛⡛⠀⠉⠉⢉⠉⠉⠉⡉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠉⢹ ⡇⠀⠀⠀⣀⠀⠀⠀⠀⣀⡀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⠀⠐⠈⠀⠀⡀⠂⠀⣀⠀⠈⣈⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⢀⠀⣀⠀⢀⠀⡀⠀⠀⣀⣀⠀⠀⠀⢸ ⡗⢀⠀⠀⣛⣛⣋⣛⠀⣃⣃⣛⣛⣀⠀⣀⣀⣀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⠟⠛⠛⠛⡛⡛⠛⠐⡛⣋⡛⠀⣀⠛⠛⣛⢛⣉⡀⠛⠛⠛⣟⣛⠀⠉⠉⠛⠛⠛⠛⣛⠛⠀⠛⠛⠙⠛⠛⠛⠋⠛⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣛⡛⣙⠃⣀⡃⣙⣓⡋⠋⠐⠛⠃⠋⠀⠃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠉⠋⠙⠟⠀⠓⠛⠻⠛⠙⠄⠀⠛⠛⠛⠛⠛⠋⠀⠉⠚⠀⠛⠛⠛⠛⠛⠛⠈⠀⠀⠀⠀⠅⠀⠀⠀⠁⠐⠂⠀⠀⠀⢸ ⡇⠀⠉⠀⡉⡛⣟⢃⡿⣉⣛⣋⠁⣐⣀⢀⣀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸ ⡇⠀⠀⠀⣙⣉⡫⣀⡋⠛⣛⢃⣠⣎⣒⣈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⡀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣩⣍⣍⡉⢉⣀⣉⣨⣅⣍⣉⠉⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠈⠀⠁⠈⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⢠⡉⣙⡛⣭⣉⠉⣭⣍⣉⣉⣀⠀⠀⠐⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠑⠈⠁⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣩⣭⡥⡉⣭⣯⣤⠏⣭⣉⣍⣉⣀⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸ ⡇⠀⠀⠀⠉⠁⠀⠐⠀⠉⠋⠠⠝⠉⠉⠉⡋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸ ⡇⠀⣤⡄⢀⢄⣤⣈⣀⣀⣬⣇⣀⣀⠀⣥⣈⣀⡀⣀⣄⣀⣀⣀⡄⠀⣀⡤⠀⣤⢀⣤⣀⣀⣀⣀⠀⣤⡤⣤⣤⢄⣤⡤⣀⣤⠀⣀⣄⣀⣀⡄⠀⣀⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢭⣁⡘⡇⠈⢍⣍⠕⣏⣍⣭⠉⣄⣍⠉⡛⣉⣅⣍⣭⣍⣍⣭⢀⣍⡥⠀⣍⣉⣅⣍⣍⣍⠉⣤⠉⠉⡭⠉⣤⠉⣩⠀⡭⣤⣭⣍⠉⡤⣭⣄⠉⣍⣭⣉⣄⣤⣀⣄⣤⢠⣀⠀⠀⢠⠀⠆⣀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠁⠉⠁⠀⠈⠺⠁⠉⠉⠅⠀⠁⠁⠀⠁⠉⠉⠉⠉⠉⢡⠉⠀⠁⠁⣀⠉⢉⠉⠉⠁⠁⠀⠉⠁⠀⠉⠀⠉⠀⠀⠀⠁⠁⠉⠁⠀⠈⠉⠁⠀⠉⠈⠉⠉⠀⠉⠁⠉⠐⢉⠀⣶⣶⣶⣽⠉⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣤⠀⠳⠄⢒⡤⠄⠂⡀⠀⠠⠄⡄⠀⢀⠀⠀⠀⠀⠀⠀⠈⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠐⠀⠀⠀⠀⠤⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠉⠋⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠙⠏⠉⠫⠁⢀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠠⡤⠀⠀⠀⠀⠀⠀⠑⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡡⠴⠇⠤⠦⠇⠒⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣉⠁⡓⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣠⣤⡥⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠄⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣨⡥⡡⡉⢁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠬⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠤⠤⠤⠤⠤⠤⢤⠄⠀⠀⠀⠀⠀⠤⠤⠤⠤⠄⠀⠈⠠⠤⠄⠀⠀⠂⠂⠀⠀⠀⠁⠀⠀⠄⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠽⠴⠄⠥⠬⠤⠠⠄⠠⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠐⠂⠀⠀⠐⠀⠸⢷⠾⠾⠶⠶⠶⠆⠀⠒⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠓⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⠿⠶⠾⠾⠷⠿⠾⠿⠶⠆⠘⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡ ⡏⠿⠶⠷⠶⢶⣶⡶⠀⠸⠅⠷⠶⠶⠆⠸⠷⠲⠲⠶⠺⠆⠸⠀⠶⠶⠶⠾⠶⠶⠼⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠿⢿⠿⠾⠷⠇⠿⠶⠆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⢸ ⡟⠿⠿⠿⠗⠀⠀⠀⠀⠈⠻⠳⠲⠶⠶⠶⠶⠂⠸⠷⠶⠶⠺⠴⠷⠂⠺⠶⠾⠹⠿⠿⠭⠛⠶⠖⠒⠶⠶⠷⠔⠀⠀⣽⠪⠰⠶⡇⠗⠆⠷⠆⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠉⠉⠀⢸ ⡟⠿⠶⠫⠷⠶⠇⠀⠀⠸⠗⠶⠓⠺⠿⠶⠶⠚⠍⠹⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⣤⢲⢾⡇⡔⠒⠶⡗⠲⠶⠶⠶⠆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡟⠟⠷⠆⠇⠟⠶⠀⠀⠘⠷⠶⠞⠇⠸⠱⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡿⠿⢿⠒⠾⡷⠾⠷⡆⡞⠇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠛⠛⠚⠓⠓⠇⠁⠀⠀⠇⠐⠳⠗⠛⠛⠂⠘⠚⠻⠾⠺⠚⠚⠲⠂⠾⠲⠒⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿⠛⠟⠛⠟⠟⠇⠀⡤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⣀⡀⠀⠀⠀⣀⠀⡀⡋⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⡆⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠈⠉⠛⠉⠁⠀⠛⠛⠟⠛⠀⠛⠛⠛⠛⠛⡛⠀⠉⠉⢉⠉⠉⠉⡉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠉⢹ ⡇⠀⠀⠀⣀⠀⠀⠀⠀⣀⡀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⠀⠐⠈⠀⠀⡀⠂⠀⣀⠀⠀⣈⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⢀⠀⣀⠀⢀⠀⡀⠀⠀⣀⣀⠀⠀⠀⢸ ⡗⢀⠀⠀⣛⣛⣋⣛⠀⣃⣃⣛⣛⣀⠀⣀⣀⣀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⠟⠛⠛⠛⡛⡛⠛⠐⡛⣋⡛⠀⣀⠛⠛⣛⢛⣉⡀⠛⠛⠛⣟⣛⠀⠉⠉⠛⠛⠛⠛⣛⠛⠀⠛⠛⠙⠛⠛⠛⠋⠛⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣛⡛⣙⠃⣀⡃⡙⣓⡋⠋⠐⠛⠃⠋⠀⠃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠉⠋⠙⠟⠀⠓⠛⠻⠋⠙⠄⠀⠛⠛⠛⠛⠛⠋⠀⠉⠚⠀⠛⠛⠛⠛⠛⠛⠈⠀⠀⠀⠀⠁⠀⠀⠀⠁⠐⠂⠀⠀⠀⢸ ⡇⠀⠉⠀⡉⡛⣟⢃⡿⣉⣛⣋⠁⣐⣀⢀⣀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸ ⡇⠀⠀⠀⣙⣉⡫⣀⡋⠛⣛⢃⣠⣎⣒⣈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⡀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣩⣍⣍⡉⢉⣀⣉⣨⣅⣍⣉⠉⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠈⠀⠁⠈⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⢠⡉⣙⡛⣭⣉⠉⣭⣍⣉⣉⣀⠀⠀⠐⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠑⠈⠁⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣩⣭⡥⡉⣭⣯⣤⠏⣭⣉⣍⣉⣀⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸ ⡇⠀⠀⠀⠉⠁⠀⠐⠀⠉⠋⠠⠝⠉⠉⠉⡋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸ ⡇⠀⠤⠄⢀⢄⣤⣈⣀⣀⣬⣇⣀⣀⠀⣥⣈⣀⡀⣀⣄⣀⣀⣀⡄⠀⣀⡤⠀⣤⢀⣤⣀⣀⣀⣀⠀⣤⡤⡤⣤⠄⣤⡤⣀⣤⠀⣀⣄⣀⣀⡄⠀⣀⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣤⠐⡛⡅⠈⢍⡍⠕⣏⣍⣭⠉⣄⣍⠉⡛⣉⣅⣍⣭⣍⣍⣭⠀⣍⡥⠀⣍⣉⣅⣍⣍⣍⠉⣤⠉⠉⡭⠉⣤⠉⣩⠀⡭⣤⣭⣍⠉⡤⣭⣄⠉⣍⣭⣉⣄⣤⣀⣄⣤⢠⣀⠄⠠⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠉⠁⠀⠈⠺⠁⠉⠉⠅⠀⠁⠁⠀⠁⠉⠉⠉⠉⠉⢡⠁⠀⠁⠁⣀⠉⢉⠉⠉⠁⠁⠀⠉⠁⠀⠉⠀⠉⠀⠀⠀⠁⠁⠉⠁⠀⠈⠉⠁⠀⠉⠈⠉⠉⠀⠉⠁⠉⠐⠉⠂⡈⣋⠋⠋⠋⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡻⠄⢒⡤⠄⠂⡀⠀⠠⠄⡄⠀⢀⠀⠀⠀⠀⠀⠀⠈⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠐⠀⠀⠀⠀⢸⣰⣶⡆⢰⣿⡇⢰⣶⡶⡶⡆⡇⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠙⠏⠉⠫⠁⢀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠃⠀⠀⠈⠉⠉⠁⠀⠉⠁⠘⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡡⠴⠇⠤⠦⠇⠒⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣁⠁⡓⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣩⣦⡥⣤⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠄⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣠⡥⡡⡉⢁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠬⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠤⠤⠤⠤⠤⠤⢤⠄⠀⠀⠀⠀⠀⠤⠤⠤⠤⠄⠀⠈⠠⠤⠄⠀⠀⠂⠂⠀⠀⠀⠁⠀⠀⠄⠀⠄⠤⠤⠤⠤⠤⠤⠤⠤⠀⠽⠴⠄⠥⠬⠤⠠⠄⠠⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠐⠂⠀⠀⠐⠀⠸⢷⠾⠾⠶⠶⠶⠆⠀⠒⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠓⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⠿⠶⠾⠾⠷⠿⠾⠿⠶⠆⠘⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡ ⡏⠿⠶⠷⠶⢶⣶⡶⠀⠸⠅⠷⠶⠶⠆⠸⠷⠲⠲⠶⠺⠆⠸⠀⠶⠶⠶⠾⠶⠶⠼⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠿⢿⠿⠾⠷⠇⠿⠶⠆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⢸ ⡟⠿⠿⠿⠗⠀⠀⠀⠀⠈⠻⠳⠲⠶⠶⠶⠶⠂⠸⠷⠶⠶⠺⠴⠷⠂⠺⠶⠾⠹⠿⠿⠭⠛⠶⠖⠒⠶⠶⠷⠔⠀⠀⣽⠪⠰⠶⡇⠗⠆⠷⠆⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠉⠉⠀⢸ ⡟⠿⠶⠫⠷⠶⠇⠀⠀⠸⠗⠶⠓⠺⠿⠶⠶⠚⠍⠹⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⣤⢲⢾⡇⡔⠒⠶⡗⠲⠶⠶⠶⠆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡟⠟⠷⠆⠇⠟⠶⠀⠀⠘⠷⠶⠞⠇⠸⠱⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡿⠿⢿⠒⠾⡷⠾⠷⡆⡞⠇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠛⠛⠚⠓⠓⠇⠁⠀⠀⠇⠐⠳⠗⠛⠛⠂⠘⠚⠻⠾⠺⠚⠚⠲⠂⠾⠲⠒⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿⠛⠟⠛⠟⠟⠇⠀⡤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⣀⡀⠀⠀⠀⣀⠀⡀⡋⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⡆⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠈⠉⠛⠉⠁⠀⠛⠛⠟⠛⠀⠛⠛⠛⠛⠛⡛⠀⠉⠉⢉⠉⠉⠉⡉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠉⢹ ⡇⠀⠀⠀⣀⠀⠀⠀⠀⣀⡀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⠀⠐⠈⠀⠀⡀⠂⠀⣀⠀⠀⣈⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⢀⠀⣀⠀⢀⠀⡀⠀⠀⣀⣀⠀⠀⠀⢸ ⡗⢀⠀⠀⣛⣛⣋⣛⠀⣃⣃⣛⣛⣀⠀⣀⣀⣀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⠟⠛⠛⠛⡛⡛⠛⠐⡛⣋⡛⠀⣀⠛⠛⣛⢛⣉⡀⠛⠛⠛⣟⣛⠀⠉⠉⠛⠛⠛⠛⣛⠛⠀⠛⠛⠙⠛⠛⠛⠋⠛⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣛⡛⣙⠃⣀⡃⡙⣓⡋⠋⠐⠛⠃⠋⠀⠃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠉⠋⠙⠟⠀⠓⠛⠻⠋⠙⠄⠀⠛⠛⠛⠛⠛⠋⠀⠉⠚⠀⠛⠛⠛⠛⠛⠛⠈⠀⠀⠀⠀⠁⠀⠀⠀⠁⠐⠂⠀⠀⠀⢸ ⡇⠀⠉⠀⡉⡛⣟⢃⡿⣉⣛⣋⠁⣐⣀⢀⣀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸ ⡇⠀⠀⠀⣙⣉⡫⣀⡋⠛⣛⢃⣠⣎⣒⣈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⡀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣩⣍⣍⡉⢉⣀⣉⣨⣅⣍⣉⠉⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠈⠀⠁⠈⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⢠⡉⣙⡛⣭⣉⠉⣭⣍⣉⣉⣀⠀⠀⠐⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠑⠈⠁⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣩⣭⡥⡉⣭⣯⣤⠏⣭⣉⣍⣉⣀⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸ ⡇⠀⠀⠀⠉⠁⠀⠐⠀⠉⠋⠠⠝⠉⠉⠉⡋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸ ⡇⠀⠤⠄⢀⢄⣤⣈⣀⣀⣬⣇⣀⣀⠀⣥⣈⣀⡀⣀⣄⣀⣀⣀⡄⠀⣀⡤⠀⣤⢀⣤⣀⣀⣀⣀⠀⣤⡤⡤⣤⠄⣤⡤⣀⣤⠀⣀⣄⣀⣀⡄⠀⣀⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣤⠐⡛⡅⠈⢍⡍⠕⣏⣍⣭⠉⣄⣍⠉⡛⣉⣅⣍⣭⣍⣍⣭⠀⣍⡥⠀⣍⣉⣅⣍⣍⣍⠉⣤⠉⠉⡭⠉⣤⠉⣩⠀⡭⣤⣭⣍⠉⡤⣭⣄⠉⣍⣭⣉⣄⣤⣀⣄⣤⢠⣀⠄⠠⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠉⠁⠀⠈⠺⠁⠉⠉⠅⠀⠁⠁⠀⠁⠉⠉⠉⠉⠉⢡⠁⠀⠁⠁⣀⠉⢉⠉⠉⠁⠁⠀⠉⠁⠀⠉⠀⠉⠀⠀⠀⠁⠁⠉⠁⠀⠈⠉⠁⠀⠉⠈⠉⠉⠀⠉⠁⠉⠐⠉⠂⡈⣋⠋⠋⠋⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡻⠄⢒⡤⠄⠂⡀⠀⠠⠄⡄⠀⢀⠀⠀⠀⠀⠀⠀⠈⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠐⠀⠀⠀⠀⢸⣰⣶⡆⢰⣿⡇⢰⣶⡶⡶⡆⡇⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠙⠏⠉⠫⠁⢀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠃⠀⠀⠈⠉⠉⠁⠀⠉⠁⠘⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡡⠴⠇⠤⠦⠇⠒⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣁⠁⡓⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣩⣦⡥⣤⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠄⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣠⡥⡡⡉⢁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠬⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠤⠤⠤⠤⠤⠤⢤⠄⠀⠀⠀⠀⠀⠤⠤⠤⠤⠄⠀⠈⠠⠤⠄⠀⠀⠂⠂⠀⠀⠀⠁⠀⠀⠄⠀⠄⠤⠤⠤⠤⠤⠤⠤⠤⠀⠽⠴⠄⠥⠬⠤⠠⠄⠠⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠐⠂⠀⠀⠐⠀⠸⢷⠾⠾⠶⠶⠶⠆⠀⠒⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠓⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⠿⠶⠾⠾⠷⠿⠾⠿⠶⠆⠘⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡ ⡏⠿⠶⠷⠶⢶⣶⡶⠀⠸⠅⠷⠶⠶⠆⠸⠷⠲⠲⠶⠺⠆⠸⠀⠶⠶⠶⠾⠶⠶⠼⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠿⢿⠿⠾⠷⠇⠿⠶⠆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⢸ ⡟⠿⠿⠿⠗⠀⠀⠀⠀⠈⠻⠳⠲⠶⠶⠶⠶⠂⠸⠷⠶⠶⠺⠴⠷⠂⠺⠶⠾⠹⠿⠿⠭⠛⠶⠖⠒⠶⠶⠷⠔⠀⠀⣽⠪⠰⠶⡇⠗⠆⠷⠆⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠉⠉⠀⢸ ⡟⠿⠶⠫⠷⠶⠇⠀⠀⠸⠗⠶⠓⠺⠿⠶⠶⠚⠍⠹⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⣤⢲⢾⡇⡔⠒⠶⡗⠲⠶⠶⠶⠆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡟⠟⠷⠆⠇⠟⠶⠀⠀⠘⠷⠶⠞⠇⠸⠱⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡿⠿⢿⠒⠾⡷⠾⠷⡆⡞⠇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠛⠛⠚⠓⠓⠇⠁⠀⠀⠇⠐⠳⠗⠛⠛⠂⠘⠚⠻⠾⠺⠚⠚⠲⠂⠾⠲⠒⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿⠛⠟⠛⠟⠟⠇⠀⡤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⣀⡀⠀⠀⠀⣀⠀⡀⡋⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⡆⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠈⠉⠛⠉⠁⠀⠛⠛⠟⠛⠀⠛⠛⠛⠛⠛⡛⠀⠉⠉⢉⠉⠉⠉⡉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠉⢹ ⡇⠀⠀⠀⣀⠀⠀⠀⠀⣀⡀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⠀⠐⠈⠀⠀⡀⠂⠀⣀⠀⠀⣈⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⢀⠀⣀⠀⢀⠀⡀⠀⠀⣀⣀⠀⠀⠀⢸ ⡗⢀⠀⠀⣛⣛⣋⣛⠀⣃⣃⣛⣛⣀⠀⣀⣀⣀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⠟⠛⠛⠛⡛⡛⠛⠐⡛⣋⡛⠀⣀⠛⠛⣛⢛⣉⡀⠛⠛⠛⣟⣛⠀⠉⠉⠛⠛⠛⠛⣛⠛⠀⠛⠛⠙⠛⠛⠛⠋⠛⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣛⡛⣙⠃⣀⡃⡙⣓⡋⠋⠐⠛⠃⠋⠀⠃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠉⠋⠙⠟⠀⠓⠛⠻⠋⠙⠄⠀⠛⠛⠛⠛⠛⠋⠀⠉⠚⠀⠛⠛⠛⠛⠛⠛⠈⠀⠀⠀⠀⠁⠀⠀⠀⠁⠐⠂⠀⠀⠀⢸ ⡇⠀⠉⠀⡉⡛⣟⢃⡿⣉⣛⣋⠁⣐⣀⢀⣀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸ ⡇⠀⠀⠀⣙⣉⡫⣀⡋⠛⣛⢃⣠⣎⣒⣈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⡀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣩⣍⣍⡉⢉⣀⣉⣨⣅⣍⣉⠉⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠈⠀⠁⠈⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⢠⡉⣙⡛⣭⣉⠉⣭⣍⣉⣉⣀⠀⠀⠐⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠑⠈⠁⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣩⣭⡥⡉⣭⣯⣤⠏⣭⣉⣍⣉⣀⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸ ⡇⠀⠀⠀⠉⠁⠀⠐⠀⠉⠋⠠⠝⠉⠉⠉⡋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸ ⡇⠀⠤⠄⢀⢄⣤⣈⣀⣀⣬⣇⣀⣀⠀⣥⣈⣀⡀⣀⣄⣀⣀⣀⡄⠀⣀⡤⠀⣤⢀⣤⣀⣀⣀⣀⠀⣤⡤⡤⣤⠄⣤⡤⣀⣤⠀⣀⣄⣀⣀⡄⠀⣀⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣤⠐⡛⡅⠈⢍⡍⠕⣏⣍⣭⠉⣄⣍⠉⡛⣉⣅⣍⣭⣍⣍⣭⠀⣍⡥⠀⣍⣉⣅⣍⣍⣍⠉⣤⠉⠉⡭⠉⣤⠉⣩⠀⡭⣤⣭⣍⠉⡤⣭⣄⠉⣍⣭⣉⣄⣤⣀⣄⣤⢠⣀⠄⠠⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠉⠁⠀⠈⠺⠁⠉⠉⠅⠀⠁⠁⠀⠁⠉⠉⠉⠉⠉⢡⠁⠀⠁⠁⣀⠉⢉⠉⠉⠁⠁⠀⠉⠁⠀⠉⠀⠉⠀⠀⠀⠁⠁⠉⠁⠀⠈⠉⠁⠀⠉⠈⠉⠉⠀⠉⠁⠉⠐⠉⠂⡈⣋⠋⠋⠋⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡻⠄⢒⡤⠄⠂⡀⠀⠠⠄⡄⠀⢀⠀⠀⠀⠀⠀⠀⠈⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠐⠀⠀⠀⠀⢸⣰⣶⡆⢰⣿⡇⢰⣶⡶⡶⡆⡇⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠙⠏⠉⠫⠁⢀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠃⠀⠀⠈⠉⠉⠁⠀⠉⠁⠘⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡡⠴⠇⠤⠦⠇⠒⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣁⠁⡓⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣩⣦⡥⣤⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠄⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣠⡥⡡⡉⢁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠬⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠤⠤⠤⠤⠤⠤⢤⠄⠀⠀⠀⠀⠀⠤⠤⠤⠤⠄⠀⠈⠠⠤⠄⠀⠀⠂⠂⠀⠀⠀⠁⠀⠀⠄⠀⠄⠤⠤⠤⠤⠤⠤⠤⠤⠀⠽⠴⠄⠥⠬⠤⠠⠄⠠⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠐⠂⠀⠀⠀⠀⠹⢷⠾⠴⠶⠶⠶⠆⠀⠀⠒⠂⠒⠂⠒⠂⠒⠂⠒⠂⠒⠂⠚⠒⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠸⠿⠶⠾⠮⠾⠿⠼⠵⠲⠆⠀⠈⠂⠐⠀⠐⠐⠒⠀⠐⠒⢠ ⡏⠿⠶⠷⠶⢶⣶⡶⠀⠸⠅⠷⠶⠶⠆⠸⠷⠲⠲⠶⠺⠆⠸⠀⠖⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣿⡿⠿⠶⠶⠇⠷⠶⠆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠿⠿⠷⠀⠀⠀⠀⠈⠻⠳⠲⠶⠶⠶⠶⠂⠸⠷⠶⠰⠺⠴⠷⠂⠸⠶⠺⠸⠿⠻⠽⠛⠶⠖⠒⠶⠶⠷⠔⠀⣾⣿⠻⠰⠶⠆⠗⠆⠷⠆⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠉⠉⠀⢸ ⡟⠿⠖⠫⠷⠶⠇⠀⠀⠸⠷⠾⠇⠸⠿⠶⠶⠺⠄⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠤⠶⠾⠇⠐⠳⠶⠶⠶⠶⡶⠶⠆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡟⠟⠷⠆⠇⠿⠶⠀⠀⠘⠷⠶⠞⠇⠸⠱⠶⠾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠷⠒⠾⠷⠾⠷⡆⡞⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠛⠛⠚⠓⠓⠇⠁⠀⠀⠃⠐⠳⠓⠛⠛⠂⠸⠚⠻⠾⠺⠺⠚⠲⠂⠾⠲⠒⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡿⠟⠛⠓⠟⠓⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈ ⡆⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠈⠉⠁⠀⠛⠛⠟⠛⠀⠛⠛⠛⠛⠛⠛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢰ ⡇⠀⠀⠀⣀⠀⠀⠀⢀⡀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠐⠈⠀⡀⠀⠂⡀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⢀⡀⡀⠀⠀⣀⣀⠀⠀⠀⢸ ⡇⢀⠉⢐⣛⣛⣛⡓⢘⣃⣂⡋⣃⡀⢀⣀⣀⡀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠛⠚⠘⠛⡛⠛⠀⡓⠋⠏⠋⡀⠛⠛⡛⠛⠉⠘⡛⡋⠻⠛⠓⠀⠁⠉⠛⠛⠛⠛⠛⠃⠘⠛⠛⠙⠃⠐⠛⠛⠃⠒⠀⠀⠀⠀⢸ ⡇⠀⠀⢀⣛⢛⡙⢁⣀⡃⠛⠋⡋⠃⠘⠚⠙⠋⠙⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠂⠛⠛⠛⠋⠙⠛⠟⠀⠓⠛⠛⠛⠋⠈⠀⠛⠛⠛⠀⠃⠃⠘⠛⠛⠛⠂⠁⠚⠛⠛⠛⠛⠈⠀⠀⠀⠀⠁⠀⠀⠀⠁⠐⠂⠀⠀⠀⢸ ⡇⠀⠉⠀⣋⢛⣋⢐⣛⡛⣛⡉⠁⣐⡀⢀⣀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸ ⡇⠀⠀⠀⣋⣛⠋⡀⣛⣛⡛⢁⣈⣙⣁⡙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⡀⠀⠀⠀⠀⢸ ⡇⠀⠀⠈⣍⣅⣉⠉⢉⣉⣁⣈⣋⣙⡋⠁⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠈⠀⠁⠈⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⢠⣉⣉⡉⡙⣈⡉⢉⡍⣉⣉⣉⡀⠀⠀⠐⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠑⠈⠁⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⢀⣭⣭⡅⠉⣽⣧⡌⢉⡍⣩⣉⣁⣀⣀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸ ⡇⠀⠀⠈⠉⠉⠁⠀⠉⠁⠁⠨⠉⠉⠉⠉⡉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸ ⡇⠀⣤⣄⢀⡀⢀⣈⣀⣠⣈⣁⡄⢠⠄⡅⣠⣀⠀⢠⢀⣀⡀⢀⣄⣀⣠⡀⣀⡀⢀⢠⣀⣀⢀⣀⣀⣀⣀⣀⠀⢀⣤⣀⣀⣀⠀⣤⣄⣀⡄⣄⣄⣀⡀⢀⣀⡀⠀⠀⣀⡀⢀⠀⠠⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⢀⣭⠉⡍⠁⢀⣉⣁⣍⡉⢉⣅⠀⢠⣭⣉⣉⡁⣈⣉⣩⢤⣈⣩⠀⠈⢨⣭⣡⣉⠈⣈⣭⣭⣍⣩⡡⠉⣉⣤⣠⣈⣉⡌⠉⣀⣉⣉⡅⢁⣁⣉⡍⢁⣉⣈⣉⣩⡍⢀⣤⢀⣙⠌⠉⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠁⠀⠁⠀⠈⠉⠡⠉⠁⠀⠀⠀⠀⠉⠈⠉⠁⠈⠉⠈⠉⢉⠉⠀⠀⠀⣀⠈⢉⠀⠉⠉⠈⠉⠁⠁⠀⠉⠁⠉⠉⠉⠁⠀⠁⠉⠉⠁⠀⠉⠁⠁⠈⠈⠉⠉⠉⠁⠀⠉⠐⠉⠂⡈⣋⠋⠋⠋⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢀⢀⡍⠀⣤⣄⣤⡄⢀⡄⣤⣤⣤⣤⡄⢠⣠⡀⢠⣠⣠⣈⣥⠀⣠⠠⣠⣤⣠⠀⣄⣤⣤⣠⣤⣄⠀⣤⡤⣄⣤⡀⡤⣀⡌⢀⣤⣄⣤⣥⣅⢤⣤⣠⡤⣤⣅⡀⠀⢀⡠⠄⠀⠩⢩⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣤⢄⣤⣄⡤⢀⡄⡄⡀⢤⣤⠄⢰⣤⣤⣠⢤⣤⣠⣠⢤⠀⣤⣠⣤⣄⣠⣠⣈⠀⢤⣤⠀⣠⣥⣤⡠⢤⣤⠀⣄⣤⣄⢀⣀⡤⣀⡄⠀⣬⣡⢤⣬⡅⢀⣠⣄⢠⡄⢠⣤⣤⡀⢠⠤⣤⠤⡤⢤⠀⠀⠀⠀⠀⠀⢸ ⡇⢀⣤⡆⡄⡄⡦⡤⣄⠀⣄⣄⣬⣡⡤⢤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣀⠀⡀⠈⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣩⣦⡥⣤⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠄⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣠⡥⡡⡉⢁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠤⠤⠤⠤⠤⠄⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠐⠂⠀⠀⠀⠀⠹⢷⠾⠴⠶⠶⠶⠆⠀⠀⠒⠂⠒⠂⠒⠂⠒⠂⠒⠂⠒⠂⠚⠒⠀⡤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠸⠿⠶⠾⠾⠾⠿⠼⠵⠲⠆⠀⠂⠂⠐⠀⠐⠐⠒⠀⠐⠒⢠ ⡏⠿⠶⠷⠶⢶⣶⡶⠀⠸⠅⠷⠶⠶⠆⠸⠷⠲⠲⠶⠺⠆⠸⠀⠖⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣷⣿⠿⠶⠶⠇⠷⠶⠆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠿⠿⠗⠀⠀⠀⠀⠈⠻⠳⠲⠶⠶⠶⠶⠂⠸⠷⠶⠲⠺⠴⠷⠂⠸⠶⠺⠸⠿⠻⠽⠛⠶⠖⠒⠶⠶⠷⠔⠀⣶⣿⠻⠰⠶⠆⠗⠆⠷⠆⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠉⠉⠀⢸ ⡟⠿⠖⠫⠷⠶⠇⠀⠀⠸⠷⠾⠇⠸⠿⠶⠶⠺⠄⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠤⠶⠾⠇⠐⠳⠶⠶⠶⠶⡶⠶⠆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡟⠟⠷⠆⠇⠿⠶⠀⠀⠘⠷⠶⠞⠇⠸⠱⠶⠾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠷⠒⠾⠷⠾⠷⡆⡞⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠛⠛⠚⠓⠓⠇⠁⠀⠀⠃⠐⠳⠓⠛⠛⠂⠸⠚⠻⠾⠺⠺⠚⠲⠂⠾⠲⠒⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠟⠛⠓⠟⠓⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈ ⡆⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠈⠉⠁⠀⠛⠛⠟⠛⠀⠛⠛⠛⠛⠛⠛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢰ ⡇⠀⠀⠀⣀⠀⠀⠀⢀⡀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠐⠈⠀⡀⠀⠂⡀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⢀⡀⡀⠀⠀⣀⣀⠀⠀⠀⢸ ⡇⢀⠉⢐⣛⣛⣛⡓⢘⣃⣂⡋⣃⡀⢀⣀⣀⡀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠛⠚⠘⠛⡛⠛⠀⡓⠋⠏⠋⡀⠛⠛⡛⠛⠉⠘⡛⡋⠻⠛⠓⠀⠁⠉⠛⠛⠛⠛⠛⠃⠘⠛⠛⠙⠃⠐⠛⠛⠃⠒⠀⠀⠀⠀⢸ ⡇⠀⠀⢀⣛⢛⡙⢁⣀⡃⠛⠋⡋⠃⠘⠚⠙⠋⠙⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠂⠛⠛⠛⠋⠙⠛⠟⠀⠓⠛⠛⠛⠋⠈⠀⠛⠛⠛⠀⠃⠃⠘⠛⠛⠛⠂⠁⠚⠛⠛⠛⠛⠈⠀⠀⠀⠀⠁⠀⠀⠀⠁⠐⠂⠀⠀⠀⢸ ⡇⠀⠉⠀⣋⢛⣋⢐⣛⡛⣛⡉⠁⣐⡀⢀⣀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸ ⡇⠀⠀⠀⣋⣛⠋⡀⣛⣛⡛⢁⣈⣙⣁⡙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⡀⠀⠀⠀⠀⢸ ⡇⠀⠀⠈⣍⣅⣉⠉⢉⣉⣁⣈⣋⣙⡋⠁⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠈⠀⠁⠈⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⢠⣍⣉⡉⡙⣈⡉⢉⡍⣉⣉⣉⡀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠑⠈⠁⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⢀⣩⣭⡁⠉⡽⣧⡌⢉⡍⣩⣉⣁⣀⣀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸ ⡇⠀⠀⠈⠉⠉⠁⠀⠉⠁⠁⠨⠉⠉⠉⠉⡉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸ ⡇⠀⣤⣄⢄⡀⢀⣈⣀⣠⣈⣁⡄⢠⠄⡅⣠⣀⠀⢠⢀⣀⡀⢠⣄⣀⣠⡀⣀⡀⢀⢠⣀⣀⢀⣀⣀⣀⣀⣀⠀⢀⣤⣀⣀⣀⠀⣤⣄⣀⡄⣄⣄⣀⡀⢀⣀⡀⠀⠀⣄⡀⢀⠀⡠⠠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⢀⣭⠉⡍⠁⢀⣉⣁⣍⡉⢉⣅⠀⢠⣥⣉⣉⡁⣈⣉⣩⢤⣈⣩⠀⠈⢨⣭⣡⣉⠈⣈⣭⣬⣍⣩⡡⠉⣉⣤⣠⣈⣉⡌⠉⣀⣉⣉⡅⢁⣁⣉⡍⢁⣉⣈⣉⣩⡍⢀⣤⢀⣙⠌⠉⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠀⠈⠉⠁⠉⠁⠀⠀⠀⠀⠉⠈⠁⠀⠈⠉⠈⠉⢉⠉⠀⠀⠀⣀⠈⢉⠀⠉⠁⠈⠁⠉⠁⠀⠉⠁⠉⠁⠉⠁⠀⠁⠉⠉⠀⠀⠉⠁⠁⠈⠈⠉⠉⠉⠁⠀⠉⠐⠉⠂⡈⣋⠋⠋⠋⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢀⢀⡍⠀⣤⣄⣤⡄⢀⡄⣤⣤⣤⣤⡄⢠⣠⡀⢠⣠⣠⣈⣥⠀⣠⠠⣠⣤⣠⠀⣄⣤⣤⣠⣤⣄⠀⣤⡤⣄⣤⡀⡤⣀⡌⢀⣤⣄⣤⣤⣅⢤⣤⣠⡤⣤⣅⡀⠀⢀⡠⠄⠀⠠⢩⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣤⢄⣤⣄⡤⢀⡄⡄⡤⣤⣤⠄⢰⣤⣤⣠⢤⣤⣠⣠⢤⠀⣤⣠⣤⣄⣠⣠⣀⠀⢤⣤⠀⣠⣥⣤⡠⢤⣤⠀⣄⣤⣄⢀⣀⡤⣀⡄⠀⣬⣡⢤⣬⡅⢀⣠⣄⢠⡄⢠⣤⣤⡀⢠⠤⣤⠤⡤⢤⠀⠀⠀⠀⠀⠀⢸ ⡇⢀⣤⡆⡄⡄⡦⡤⣄⠀⣄⣄⣬⣡⡤⢤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣀⠀⡀⠈⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣩⣦⡥⣤⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠄⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣠⡥⡡⡉⢁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠤⠤⠤⠤⠤⠄⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠐⠂⠀⠀⠀⠀⠹⢷⠾⠴⠶⠶⠶⠆⠀⠀⠒⠂⠒⠂⠒⠂⠒⠂⠒⠂⠒⠂⠚⠒⠀⡤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠸⠿⠶⠾⠾⠾⠿⠼⠵⠲⠆⠀⠂⠐⠒⠀⠒⠒⠒⠀⠐⠒⢠ ⡏⠿⠶⠷⠶⢶⣶⡶⠀⠸⠅⠷⠶⠶⠆⠸⠷⠲⠲⠶⠺⠆⠸⠀⠖⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣷⣿⠿⠶⠶⠇⠷⠶⠆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠿⠿⠗⠀⠀⠀⠀⠈⠻⠳⠲⠶⠶⠶⠶⠂⠸⠷⠶⠢⠺⠶⠷⠂⠸⠶⠺⠸⠿⠻⠽⠛⠶⠖⠒⠶⠶⠷⠔⠀⣶⣿⠻⠰⠶⠆⠗⠆⠷⠆⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠉⠉⠀⢸ ⡿⠿⠖⠫⠷⠶⠇⠀⠀⠸⠷⠾⠇⠸⠿⠶⠶⠺⠄⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠤⠶⠶⠇⠐⠳⠶⠖⠶⠶⡶⠶⠆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡟⠟⠷⠆⠇⠟⠶⠀⠀⠘⠷⠶⠞⠇⠸⠱⠶⠾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠷⠒⠾⠷⠾⠷⡆⡞⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠛⠛⠚⠓⠓⠇⠁⠀⠀⠃⠐⠳⠓⠛⠛⠂⠸⠚⠻⠾⠺⠺⠚⠲⠂⠾⠲⠒⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡟⠟⠛⠓⠟⠓⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈ ⡆⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠈⠉⠁⠀⠛⠛⠟⠛⠀⠛⠛⠛⠛⠛⠛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢰ ⡇⠀⠀⠀⣀⠀⠀⠀⢀⡀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠐⠈⠀⡀⠀⠂⡀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⢀⡀⡀⠀⠀⣀⣀⠀⠀⠀⢸ ⡇⢀⠉⢐⣛⣛⣛⡓⢘⣃⣂⡋⣃⡀⢀⣀⣀⡀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠛⠚⠙⠛⡛⠛⠀⡓⠋⠏⠋⡀⠛⠛⡛⠛⠉⠘⡛⡋⠻⠛⠓⠀⠁⠉⠛⠛⠛⠛⠛⠃⠘⠛⠛⠙⠃⠐⠛⠛⠃⠒⠀⠀⠀⠀⢸ ⡇⠀⠀⢀⣛⢛⡙⢁⣀⡃⠛⠋⡋⠃⠘⠚⠙⠋⠙⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠂⠛⠛⠛⠋⠙⠙⠟⠀⠓⠛⠛⠛⠋⠈⠀⠛⠛⠛⠀⠃⠃⠘⠛⠛⠛⠂⠁⠚⠛⠛⠛⠛⠈⠀⠀⠀⠀⠁⠀⠀⠀⠁⠐⠂⠀⠀⠀⢸ ⡇⠀⠉⠀⣋⢛⣋⢐⣛⡛⣛⡉⠁⣐⡀⢀⣀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸ ⡇⠀⠀⠀⣋⣛⠋⡀⣛⣛⡛⢁⣈⣙⣁⡙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⡀⠀⠀⠀⠀⢸ ⡇⠀⠀⠈⣭⣅⣉⠉⢉⣉⣁⣈⣋⣙⡋⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠈⠀⠁⠈⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⢀⣍⣉⡉⡙⣈⡉⢉⡍⣉⣉⣉⡀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠑⠈⠁⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⢀⣩⣭⡁⠉⡽⣧⡌⢉⡍⣩⣉⣁⣀⣀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸ ⡇⠀⠀⠈⠉⠉⠁⠀⠉⠁⠁⠨⠉⠉⠉⠉⡉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸ ⡇⠀⣤⣄⢄⡀⢀⣈⣀⣠⣈⣀⡄⢠⠄⡅⣠⣀⠀⢠⢀⣀⡀⢠⣄⣀⣠⡀⣀⡀⢀⢠⣀⣀⢀⣀⣀⣀⣀⣀⠀⢀⣤⣀⣀⣀⠀⣤⣄⣀⡄⣄⣄⣀⡀⢀⣀⡀⠀⠀⣄⡀⢀⠀⡠⠠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⢀⣭⠉⡍⠁⢀⣉⣁⣍⡉⢉⣅⠀⢠⣥⣉⣉⡁⣈⣉⣩⢤⣈⣩⠀⠈⢨⣭⣡⣉⠈⣉⣭⣬⣍⣉⡡⠉⣉⣤⣠⣈⣉⡌⠉⣀⣉⣉⡅⢁⣁⣉⡍⢁⣉⣈⣉⣩⡍⢀⣤⢀⣙⠌⠉⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠀⠈⠉⠁⠉⠁⠀⠀⠀⠀⠉⠈⠁⠀⠈⠉⠈⠉⢉⠉⠀⠀⠀⣀⠈⢉⠀⠉⠉⠉⠁⠉⠁⠀⠉⠁⠉⠁⠉⠁⠀⠁⠉⠉⠀⠀⠉⠁⠁⠈⠈⠉⠉⠉⠁⠀⠉⠐⠉⠂⡈⣋⠋⠋⠋⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢀⢀⡍⠀⣤⣄⣤⡄⢀⡄⣤⣤⣤⣤⡄⢠⣠⡀⢠⣠⣠⣈⣥⠀⣠⠠⣠⣤⣠⠀⣄⣤⣤⣠⣤⣄⠀⣤⡤⣄⣤⡀⡤⣀⡌⢀⣤⣄⣤⣤⣅⢤⣤⣠⡤⣤⣅⡀⠀⢀⡠⠄⠀⠠⢩⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣤⢄⣤⣄⡤⢀⡅⡄⡤⣤⣤⠄⢰⣤⣤⣠⢤⣤⣠⣠⢤⠀⣤⣠⣤⣄⣠⣠⣀⠀⢤⣤⠀⣠⣥⣤⡠⢤⣤⠀⣄⣤⣄⢀⣀⡤⣀⡄⠀⣬⣩⢤⣬⡅⢀⣠⣄⢠⡄⢠⣤⣤⡀⢠⠤⣤⠤⡤⢤⠀⠀⠀⠀⠀⠀⢸ ⡇⢀⣤⡆⡄⡄⡦⡤⣄⠀⣄⣄⣬⣡⡤⢤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣀⠀⡀⠈⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣩⣦⡥⣤⢄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠄⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣠⡥⡡⡉⢁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠤⠤⠤⠤⠤⠄⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠹⢷⠾⠶⠶⠶⠶⠆⠀⠐⠒⠒⠒⠂⠒⠒⠒⠂⠒⠊⠒⠂⠚⠒⠀⣦⣥⠒⠒⠂⠐⠀⠒⠐⠂⠐⠐⠂⠸⠿⠶⠾⠾⠿⠿⠿⠽⠳⠆⠐⠂⠐⠒⠒⠒⠒⠒⠀⠐⠒⢠ ⡟⠿⠶⠷⠶⢶⣶⡶⠂⠸⠅⠷⠶⠶⠆⠸⠷⠲⠲⠶⠾⠆⠸⠀⠶⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⠿⠶⠶⠇⠷⠶⠆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢼ ⡟⠿⠿⠿⠷⠀⠀⠀⠀⠈⠻⠳⠲⠶⠶⠶⠶⠂⠸⠷⠶⠢⠾⠼⠷⠂⠸⠶⠾⠼⠿⠻⠽⠿⠶⠖⠒⠶⠶⠷⠕⠀⣿⣿⠻⠴⠶⠆⠷⠖⠷⠆⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠉⠉⠀⢸ ⡿⠿⠖⠿⠷⠶⠇⠀⠀⠸⠷⠾⠇⠸⠿⠶⠶⠺⠅⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠤⠶⠾⠇⠘⠷⠶⠶⠶⠶⡶⠶⠆⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡟⠟⠷⠆⠇⠿⠶⠀⠀⠘⠷⠶⠞⠇⠸⠳⠶⠾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠷⠲⠾⠷⠾⢷⡦⡞⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠻⠛⠛⠓⠻⠇⠃⠀⠈⠃⠘⠳⠓⠛⠛⠃⠸⠞⠻⠾⠺⠺⠚⠲⠇⠾⠲⠒⠺⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠛⠛⠟⠓⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠂⠒⠐⠒⠒⠐⠒⠐⠐⠒⠀⠒⠐⠒⠀⠂⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠋⠙⠀⠀⠂⠐⠀⠐⠐⠀⠀⠐⠀⠐⠀⠂⠀⠐⠀⠀⠀⠀⠐⠀⠀⠂⠂⠀⠀⠀⠂⠀⠐⠀⠀⠈ ⡆⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠈⠉⠁⠁⠛⠛⠟⠛⠀⠛⠛⠛⠛⠛⠛⡀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢰ ⡇⠀⠀⢀⣀⠀⠀⠀⢀⡀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠐⠈⠀⡀⠀⠂⡀⠀⠀⡈⠈⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀⢀⡀⡀⠀⠀⣀⣀⠀⠀⠀⢸ ⡷⢀⠉⢐⣛⣛⣛⡛⢘⣃⣂⡋⣃⡀⢀⣀⣀⡀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠛⠚⠙⢛⡛⠛⠀⡓⠋⠯⠋⡀⠛⠛⡛⠛⠉⠘⡛⡋⠻⠛⠓⠀⠉⡉⠛⠛⠛⠛⠛⠃⠘⠛⠛⠙⠃⠐⠛⠛⠃⠓⠀⠀⠀⠀⢸ ⣇⠀⠀⢀⣛⣛⡛⢁⣀⡃⠛⠋⡋⠃⠘⠚⠙⠋⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠛⠛⠋⠙⠛⠿⠀⠓⠛⠛⠛⠛⠉⠀⠛⠛⠛⠀⠃⠃⠘⠛⠛⠛⠂⠃⠚⠛⠛⠛⠛⠈⠀⠀⠀⠀⠅⠀⠀⠀⠁⠐⠂⠀⠀⠀⢸ ⡗⠀⠉⠀⣋⢛⣋⢐⣛⣛⣟⡉⠁⣐⡀⢀⣀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸ ⡇⠀⠀⠈⣋⣛⣋⣀⣛⣛⡛⢁⣈⣙⣁⡙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⣀⠀⠀⠀⠀⢸ ⡇⠀⠀⠈⣍⣉⣛⣋⡉⡍⢁⡈⠋⠙⣋⣁⣀⡀⣀⣀⣀⡀⠀⣀⣤⣤⡀⢀⠀⠀⢠⡀⣠⣤⢀⠀⣤⣀⢈⣀⣥⣤⣀⢈⣄⣅⣈⣄⣄⣄⣄⣀⡄⣀⣁⡀⣤⣄⣄⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⢸ ⡇⠀⠀⠀⠉⠉⠛⠋⠁⠁⠈⠁⠀⠈⠉⠉⠉⠉⠈⠉⠛⠃⠀⠙⠙⠙⠁⠈⠀⠀⠉⠁⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⠋⡈⠉⠉⠉⠉⠉⠉⠋⠉⠉⠉⠉⠉⠉⠋⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸ ⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⢀⣀⠀⠀⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠉⠂⡈⣛⠋⠋⠋⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣩⣦⣥⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠄⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣨⡭⡡⡉⢁⡀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠐⠂⠀⠀⠀⠀⠹⢷⠾⠴⠶⠶⠶⠆⠀⠀⠒⠂⠒⠂⠒⠂⠒⠂⠒⠊⠒⠂⠚⠒⠀⡤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠸⠿⠶⠾⠾⠾⠿⠼⠵⠲⠆⠀⠂⠐⠒⠒⠒⠒⠒⠀⠐⠒⢠ ⡏⠿⠶⠷⠶⢶⣶⡶⠀⠸⠅⠷⠶⠶⠆⠸⠷⠲⠲⠶⠺⠆⠸⠀⠖⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡇⠰⡷⠶⠶⠇⠷⠶⠆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠿⠿⠗⠀⠀⠀⠀⠈⠻⠳⠲⠶⠶⠶⠶⠂⠸⠷⠶⠢⠺⠴⠷⠂⠸⠶⠺⠸⠿⠻⠽⠛⠶⠖⠒⠶⠶⠷⠔⠀⣇⢸⡗⠷⠶⠆⠗⠆⠷⠆⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠉⠉⠀⢸ ⡿⠿⠖⠫⠷⠶⠇⠀⠀⠈⣲⣤⣤⣤⠀⣶⢰⢰⢰⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣾⡯⠷⠶⠇⠐⠳⠶⠖⠶⠶⡶⠶⠆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡟⠟⠷⠆⠇⠟⠶⠀⠀⠐⠦⠦⠔⠆⠰⠰⣤⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠷⠒⠾⠷⠾⠷⡆⡞⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠻⠛⠚⠓⠓⠇⠁⠀⠀⠃⠐⠳⠓⠛⠛⠃⠸⠚⠻⠾⠺⠺⠚⠲⠂⠾⠲⠒⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⣿⡟⠓⠟⠓⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠋⠙⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈ ⡆⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⢀⠈⢠⣤⣠⣭⣠⡀⢀⣀⣩⡅⢠⣅⣀⣭⣠⣤⣤⣄⣀⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢰ ⡇⠀⠀⠀⣀⠀⠀⠀⢀⡀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢈⠉⠉⠁⠈⠉⠉⣁⠈⠈⠉⠈⠉⡁⠉⠉⡉⠉⠁⡀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⢀⡀⡀⠀⠀⣀⣀⠀⠀⠀⢸ ⡇⢀⠉⠀⡭⣉⣩⣁⣈⢡⠀⢡⠁⠀⢀⣠⣀⣀⣀⣀⣠⣀⠀⠀⣠⣤⣤⡀⢠⠈⢡⣭⡌⣡⣬⣭⡁⢠⣤⣭⠍⢩⣤⣭⣥⣭⣭⣭⣄⣨⣥⣥⣭⠁⣠⣤⣌⣩⣭⣭⣭⣬⡥⡬⣭⣭⣭⣤⣤⣄⠀⠃⠒⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡭⣉⣩⣋⣉⢨⠀⢬⠈⠀⢁⣩⣉⣉⢁⣉⣩⣭⠀⠀⣩⣩⣭⡁⢨⢠⣨⣨⡁⣨⣭⣭⡀⢨⣭⣭⠅⢨⣭⣭⣤⣩⣭⣭⣡⡌⣭⣍⣨⡍⣨⣭⣅⣨⣭⣍⣭⣭⣭⣭⣍⣭⣭⣭⣭⡅⠀⠁⠐⠂⠀⠀⠀⢸ ⡇⠀⠉⠀⡉⣉⣉⣋⣉⢨⠀⢭⠀⠀⢁⣩⣉⣉⢁⣈⣩⣉⠀⠀⣩⣩⣭⡁⢨⠈⢩⣭⡁⣨⣭⣭⡁⢨⣩⢭⣥⣨⢩⣭⣭⣍⣩⣭⣭⣭⡭⡅⢨⡍⣨⣭⣥⣬⣭⣩⣩⣭⣭⣍⣭⡅⠉⠉⠉⠁⠀⠀⠀⠁⠀⠀⠀⢸ ⡇⠀⠀⠀⣉⣉⣉⣛⣉⢨⠀⣉⠀⠀⢁⣩⣉⣉⢉⣉⣩⣉⠀⠀⣉⣭⣭⡁⢈⠀⣩⣩⡁⣨⣭⣉⡁⢈⣭⣩⠉⢉⣭⣩⣭⡉⢉⡉⣭⡍⢉⣁⣈⢭⣌⣉⡉⣁⣩⣍⢉⣋⣅⣁⣭⣅⣀⣄⡄⡄⣄⣄⣀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣉⠉⣉⣛⢉⢨⠀⡈⠀⠀⢉⣉⣉⣉⢉⣉⢉⣉⠀⠀⣉⣉⣩⡁⢈⠀⣩⣉⠁⣉⣩⣉⡁⢈⣉⠉⣀⣈⣉⡉⢉⠁⢈⣉⣉⣉⣩⣉⡉⢉⣉⡉⣉⣉⣉⣉⣈⡉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠙⠛⢙⠛⠛⠘⠀⠛⠀⠀⠉⢙⠛⠙⠉⠙⠛⠙⠀⠀⠙⠛⠛⠁⠈⠀⠙⠙⠀⠙⣛⠉⠁⠈⠛⠋⠉⠙⠛⢁⡘⠃⡈⠉⢙⢋⣛⡉⠁⢈⠉⠉⠉⡋⠉⡉⡉⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠂⠀⠐⠀⠀⠈⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸ ⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢀⣀⠀⠀⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠉⠂⡈⣋⠋⠋⠋⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣩⣦⡥⣤⢄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠄⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣠⡥⡡⡉⢁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠤⠤⠤⠤⠤⠄⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠐⠂⠀⠀⠀⠀⠹⢷⠾⠴⠶⠶⠶⠆⠀⠀⠒⠂⠒⠂⠒⠂⠒⠂⠒⠊⠒⠂⠚⠒⠀⡤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠸⠿⠶⠾⠾⠾⠿⠼⠽⠲⠆⠀⠂⠐⠒⠒⠒⠒⠒⠀⠐⠒⢠ ⡏⠿⠶⠷⠶⢶⣶⡶⠀⠸⠅⠷⠶⠶⠆⠸⠷⠲⠲⠶⠺⠆⠸⠀⠖⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡇⠰⡷⠶⠶⠇⠷⠶⠆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠿⠿⠗⠀⠀⠀⠀⠈⠻⠳⠲⠶⠶⠶⠶⠂⠸⠷⠶⠢⠺⠴⠷⠂⠸⠶⠺⠸⠿⠻⠽⠛⠶⠖⠒⠶⠶⠷⠔⠀⣗⢸⡗⠷⠶⠆⠗⠆⠷⠆⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠉⠉⠀⢸ ⡿⠿⠖⠫⠷⠶⠇⠀⠀⠈⣲⣤⣤⣤⠀⣶⢠⢠⢰⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣾⡿⠷⠾⠇⠐⠳⠶⠶⠶⠶⡶⠶⠆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡟⠟⠷⠆⠇⠿⠶⠀⠀⠀⠄⠦⠔⠆⠰⠠⣤⡎⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠷⠒⠾⠷⠾⠷⡆⡞⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠻⠛⠚⠓⠓⠇⠁⠀⠀⠃⠐⠳⠓⠛⠛⠃⠸⠚⠻⠾⠺⠺⠚⠲⠂⠾⠲⠒⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠓⠟⠓⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠋⠙⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈ ⡆⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⢀⠈⢠⣀⢀⣉⣀⡀⢀⣀⣩⡅⢠⣅⣀⣩⢀⣠⣤⣀⣀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢰ ⡇⠀⠀⠀⣀⠀⠀⠀⢀⡀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠈⢈⠉⠉⠁⠈⠉⠉⣁⠈⠈⠉⠈⠉⡁⠉⠉⡉⠉⠁⡀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⢀⡀⡀⠀⠀⣀⣀⠀⠀⠀⢸ ⡗⢀⠉⠀⡭⠉⢩⣁⣈⢡⠀⠡⠁⠀⠀⣀⡀⣀⣀⣀⡠⣀⠀⠀⣠⠀⠀⠀⠀⠈⢁⠉⠈⢡⣌⡉⠁⢠⣤⠭⠍⢩⣤⠭⣡⣍⠉⣉⠀⣨⣥⢡⣍⠁⡀⣤⣌⣉⣭⣍⣉⣬⡥⠌⣭⡍⢭⢀⠀⠀⠀⠃⠒⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡭⣹⣩⣋⣉⢨⠀⣬⠈⠀⢁⣩⣉⣉⢁⣉⣩⣭⠀⠀⣩⣩⣭⠀⢨⢠⣸⣨⡁⣪⣭⣽⡀⢨⣭⣭⠅⢨⣭⣭⣤⣹⣭⣍⣡⡌⣭⣍⣸⡍⣨⣭⣅⣨⣭⣍⣭⣭⣭⣭⣍⣭⣽⣭⣭⡅⠀⠁⠐⠂⠀⠀⠀⢸ ⡇⠀⠉⠀⡃⣉⢉⣋⣉⢨⠀⢭⠀⠀⢁⣩⣉⣉⢁⣈⣩⣉⠁⠀⣩⣩⣭⡁⢨⠈⢩⣭⡁⣨⣭⣭⡁⢨⣩⢭⣥⣬⢩⣭⣭⣍⣩⣭⣭⣭⡭⡅⢨⡍⣨⣭⣥⣬⣭⣩⣩⣭⣭⣍⣭⡅⠉⠉⠉⠁⠀⠀⠀⠁⠀⠀⠀⢸ ⡇⠀⠀⠀⣁⣋⣈⣛⣉⢨⠀⣉⠀⠀⢁⣩⣉⣉⢉⣉⣩⣉⠀⠀⣉⣭⣭⡁⢈⠀⣩⣩⡁⣨⣭⣉⡁⢈⣭⣩⠉⢉⣭⣩⣭⡉⢉⡉⣭⡍⢉⣁⣈⢭⣌⣉⡉⣁⣩⣍⢉⣋⣅⣁⣭⣅⣀⣄⠄⡄⣄⣄⣀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣀⡩⢉⣛⢉⢨⠀⡈⠀⠀⢉⣉⣉⣉⢉⣉⢉⣉⠀⠀⣉⣉⣩⡁⢈⠀⣩⣉⠁⣉⣩⣉⡁⣈⣉⠉⣀⣈⣉⡉⢉⠁⢈⣉⣉⣉⣩⣉⡉⢉⣉⡉⠫⣉⣉⣉⣈⡉⠉⠉⠉⠉⠉⠉⠀⠀⠈⠉⡍⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠑⠛⢙⠛⠛⠘⠀⠛⠀⠀⠉⢙⠛⠙⠉⠙⠛⠙⠀⠀⠙⠛⠛⠁⠈⠀⠙⢙⠀⠙⣛⠉⠁⠈⠛⠋⠉⠙⠛⢁⡘⠃⡈⠉⢛⢋⣛⡉⠁⢈⠉⠉⠉⡋⠉⡉⡉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠤⣀⠀⠐⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠁⡁⠀⠀⠲⠁⠀⡒⠐⢐⠴⠀⠀⠐⠈⠀⠀⢐⡠⠂⡰⠆⠀⠈⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸ ⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢀⣀⠀⠀⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠉⠂⡈⣋⠋⠋⠋⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣩⣦⡥⣤⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠄⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣠⡥⡡⡉⢁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠤⠤⠤⠤⠤⠄⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠐⠂⠀⠀⠀⠀⠹⢷⠾⠴⠶⠶⠶⠆⠀⠀⠒⠂⠒⠂⠒⠂⠒⠂⠒⠊⠒⠂⠚⠒⠀⡤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠸⠿⠶⠾⠾⠾⠿⠼⠵⠲⠆⠀⠂⠐⠒⠒⠒⠒⠒⠀⠐⠒⢠ ⡏⠿⠶⠷⠶⢶⣶⡶⠀⠸⠅⠷⠶⠶⠆⠸⠷⠲⠲⠶⠺⠆⠸⠀⠖⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡇⠀⡇⠶⠶⠇⠷⠶⠆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠿⠿⠗⠀⠀⠀⠀⠈⠻⠳⠲⠶⠶⠶⠶⠂⠸⠷⠶⠢⠺⠴⠷⠂⠸⠶⠺⠸⠿⠻⠽⠛⠶⠖⠒⠶⠶⠷⠔⠀⣗⠀⡇⠷⠶⠆⠗⠆⠷⠆⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠉⠉⠀⢸ ⡿⠿⠖⠫⠷⠶⠇⠀⠀⠈⣲⣤⣤⣤⠀⣶⢠⢰⢰⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⡧⠷⠾⠇⠐⠳⠶⠶⠶⠶⡶⠶⠆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡟⠟⠷⠆⠇⠿⠶⠀⠀⠀⠄⠦⠔⠆⠰⠠⣤⡄⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠷⠒⠾⠷⠾⠷⡆⡞⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠻⠛⠚⠓⠓⠇⠁⠀⠀⠃⠐⠳⠓⠛⠛⠃⠸⠚⠻⠾⠺⠺⠚⠲⠂⠾⠲⠒⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⡟⠓⠟⠓⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠋⠙⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈ ⡆⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⢀⠈⢠⣀⣀⣉⣀⡀⢀⣀⣩⡅⢠⣅⣀⣩⢀⣠⣤⣀⣀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢰ ⡇⠀⠀⠀⣀⠀⠀⠀⢀⡀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠈⢉⠉⠉⠁⠈⠉⠉⣁⠈⠈⠉⠈⠉⡁⠉⠉⡉⠉⠁⡀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⢀⡀⡀⠀⠀⣀⣀⠀⠀⠀⢸ ⡗⢀⠉⠀⡭⡉⢩⣁⣈⢡⠀⠡⠁⠀⠀⣀⡀⣀⣀⣀⡠⣀⠀⠀⣠⠠⢠⠀⠀⠈⢁⠉⠈⢡⣌⡉⠁⢠⣤⠭⠍⢩⣤⠭⣡⣍⢉⣉⠀⣨⣥⢡⣍⠁⡀⣤⣌⣉⣭⣭⣉⣬⡥⠌⣭⡍⢭⢀⠀⠀⠀⠃⠒⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡭⣹⣩⣋⣉⢨⠀⣬⠈⠀⢁⣩⣉⣉⢁⣉⣩⣭⠀⠀⣩⣩⣭⠀⢨⢠⣸⣨⡁⣪⣭⣭⡁⢨⣭⣭⠅⢨⣭⣭⣤⣹⣭⣍⣡⡌⣭⣍⣸⡍⣨⣭⣅⣨⣭⣍⣭⣭⣭⣭⣍⣭⣽⣭⣭⡅⠀⠁⠐⠂⠀⠀⠀⢸ ⡇⠀⠉⠀⡃⣉⢉⣋⣉⢨⠀⢭⠀⠀⢁⣩⣉⣉⢁⣈⣩⣉⠁⠀⣩⣩⣭⡁⢨⠈⢩⣭⡁⣨⣭⣭⡁⢨⣩⢭⣥⣨⢩⣭⣭⣍⣩⣭⣭⣭⡭⡅⢨⡍⣨⣭⣥⣬⣭⣩⣩⣭⣭⣍⣭⡅⠉⠉⠉⠁⠀⠀⠀⠁⠀⠀⠀⢸ ⡇⠀⠀⠀⣁⣋⣈⣛⣉⢨⠀⣉⠀⠀⢁⣩⣉⣉⢉⣉⣩⣉⠀⠀⣉⣭⣭⡁⢈⠀⣩⣩⡁⣨⣭⣉⡁⢈⣭⣩⠉⢉⣭⣩⣭⡉⢉⡉⣭⡍⢉⣁⣈⢭⣌⣉⣉⢁⣩⣍⢉⣋⣅⣁⣭⣅⣀⣄⠄⡄⣄⣄⣀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣀⡩⢉⣛⢉⢨⠀⡈⠀⠀⢉⣉⣉⣉⢉⣉⢉⣉⠀⠀⣉⣉⣩⡁⢈⠀⣩⣉⡁⣉⣩⣉⡁⣈⣉⠉⣀⣈⣉⡉⢉⠁⢈⣉⣉⣉⣩⣉⡉⢉⣉⡉⠫⣉⣉⣉⣈⡉⠉⠉⠉⠉⠉⠉⠀⠀⠈⠉⡉⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠑⠛⣙⠛⠛⠘⠀⠛⠀⠀⠉⢙⠛⠙⠉⠙⠛⠙⠀⠀⠙⠛⠛⠁⢈⠀⠙⢙⠃⢙⣛⡉⠁⠈⠛⠋⠉⠙⠛⢁⡘⠃⡈⠉⣙⣋⡛⡉⠁⠈⠉⠉⠉⠋⢉⣉⡉⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠤⣘⠀⠈⠀⠀⠀⠀⠀⠈⠒⠀⠀⠀⠁⡁⠀⠀⠲⠁⠀⠒⠐⢐⠤⠀⠀⠐⠈⠀⠀⢙⡢⠂⡰⠟⠀⠈⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸ ⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢀⣀⠀⠀⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠉⠂⡈⣋⠋⠋⠋⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣩⣦⡥⣤⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠄⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣠⡥⡡⡉⢁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠤⠤⠤⠤⠤⠄⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠐⠂⠀⠀⠀⠀⠹⢷⠾⠴⠶⠶⠶⠆⠀⠀⠒⠂⠒⠂⠒⠂⠒⠂⠒⠊⠒⠂⠚⠒⠀⡤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠸⠿⠶⠾⠾⠾⠿⠼⠵⠲⠆⠀⠂⠐⠒⠒⠒⠒⠒⠀⠐⠒⢠ ⡏⠿⠶⠷⠶⢶⣶⡶⠀⠸⠅⠷⠶⠶⠆⠸⠷⠲⠲⠶⠺⠆⠸⠀⠖⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡇⠀⡇⠦⠀⠹⠱⠶⠆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠿⠿⠗⠀⠀⠀⠀⠈⠻⠳⠲⠶⠶⠶⠶⠂⠸⠷⠶⠢⠺⠴⠷⠂⠸⠶⠺⠸⠿⠻⠽⠛⠶⠖⠒⠶⠶⠷⠔⠀⣗⠀⡇⠷⠂⢸⠹⠆⠷⠆⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠉⠉⠀⢸ ⡿⠿⠖⠫⠷⠶⠇⠀⠀⠈⣲⣤⣤⣤⠀⣶⢠⢰⢰⡄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⡧⠷⠶⢞⠘⠳⠶⠶⠶⠶⡶⠶⠆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡟⠟⠷⠆⠇⠿⠶⠀⠀⠀⠄⠦⠔⠆⠰⠠⣤⡄⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠷⠒⢾⠷⠾⠷⡆⡞⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠻⠛⠚⠓⠓⠇⠁⠀⠀⠃⠐⠳⠓⠛⠛⠃⠸⠚⠻⠾⠺⠺⠚⠲⠂⠾⠲⠒⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⡟⠓⢿⢱⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠋⠙⠃⠁⠀⠚⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈ ⡆⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⢀⠈⢠⣀⣀⣉⡀⡀⢀⣀⣩⡅⢠⣅⣀⣩⢀⣠⣤⣀⣀⠀⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢰ ⡇⠀⠀⠀⣀⠀⠀⠀⢀⡀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠈⢉⠉⠁⠁⠈⠉⠉⣁⠈⠈⠉⠈⠉⡁⠉⠉⡉⠉⠁⡈⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⢀⡀⡀⠀⠀⣀⣀⠀⠀⠀⢸ ⡗⢀⠉⠀⡭⡉⢩⣁⣈⢡⠀⠡⠁⠀⠀⣀⡀⣀⣀⣀⡠⣀⠀⣀⣠⠠⢠⠀⠀⠈⢁⠉⠈⢡⣌⡉⠁⢠⣤⠭⠍⢩⣤⠭⣡⣍⢉⣉⠀⣨⣥⢡⣍⠁⡀⣤⣌⣉⣭⣭⣉⣨⡥⠌⣭⡍⣭⢀⠀⠀⠀⠃⠒⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡭⣹⣉⣋⣉⢨⠀⣬⠈⠀⢁⣩⣉⣉⢁⣉⣩⣭⠀⠉⣩⣩⣭⠀⢨⢠⣰⣨⡁⣪⣭⣭⡁⣨⣭⣭⠅⢨⣭⣭⣤⣹⣭⣍⣡⡌⣩⣍⣹⡍⣨⣭⣅⣨⣭⣍⣭⣉⣭⣭⣍⣭⣽⣭⣭⡅⠀⠁⠐⠂⠀⠀⠀⢸ ⡇⠀⠉⠀⡃⣉⢉⣋⣉⢨⠀⢭⠀⠀⢁⣩⣉⣉⢁⣈⣩⣉⠁⠀⣩⣩⣭⡁⢨⠈⢩⣭⡁⣨⣭⣭⡅⢨⣩⢭⣥⣨⢩⣭⣭⣍⣭⣭⣭⣭⡭⡅⢨⡍⣨⣭⣥⣌⣩⣩⣩⣭⣭⣍⣭⡅⠉⠉⠉⠁⠀⠀⠀⠁⠀⠀⠀⢸ ⡇⠀⠀⠀⣁⣋⣈⣛⣉⢨⠀⣉⠀⠀⢁⣩⣉⣉⢉⣉⣩⣉⠀⠀⣉⣭⣭⡁⢈⠀⣩⣩⡁⣈⣭⣉⡁⢈⣭⣩⠉⢉⣩⣩⣭⡉⢉⡉⣭⡍⢉⣁⣈⢍⣈⣉⣉⢁⣩⣍⢉⣋⣅⣁⣭⣅⣀⣄⠄⡄⣄⣄⣀⠀⠀⠀⡀⢸ ⡇⠀⠀⠀⣀⡩⢉⣚⢉⢨⠀⡈⠀⠀⢉⣉⣉⣉⢉⣉⢉⣉⠀⠀⣉⣉⣩⡁⢈⠀⣩⣉⡁⣉⡉⣉⡁⣈⣉⠉⣀⣈⣉⡉⢉⠁⢈⣉⣉⣉⣩⣩⡉⢉⣉⡉⠫⣉⣉⣉⣈⡉⠈⠉⠉⠉⠉⠉⠀⠀⠈⠉⡉⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠑⠛⣉⠛⠛⠘⠀⠛⠀⠀⠉⢙⠛⠙⠉⠙⠛⠙⠀⠀⠙⠛⠛⠁⢈⠀⠙⣙⠃⢙⣛⡈⠁⠈⠛⠋⠉⠙⠛⢁⡘⠃⡈⠉⣙⣋⡛⣙⢁⠈⠉⠉⡉⠋⢉⣉⡉⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠔⠀⠤⣘⠀⠈⠀⠀⠀⠀⠀⠈⠒⠀⠀⠀⠁⡁⠀⠀⠲⠁⠀⠒⠐⠐⠤⠀⠀⠐⠈⠀⠀⢙⡢⠂⡰⠟⠀⠈⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸ ⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢀⣀⠀⠀⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠉⠂⡈⣋⠋⠋⠋⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣩⣦⡥⣤⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠄⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣠⡥⡡⡉⢁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠤⠤⠤⠤⠤⠄⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠐⠂⠀⠀⠀⠀⠹⢷⠾⠴⠶⠶⠶⠆⠀⠀⠒⠂⠒⠂⠒⠂⠒⠂⠒⠊⠒⠂⠚⠒⠀⡤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠸⠿⠶⠾⠾⠾⠿⠼⠵⠲⠆⠀⠂⠐⠒⠒⠒⠒⠒⠀⠐⠒⢠ ⡏⠿⠶⠷⠶⢶⣶⡶⠀⠸⠅⠷⠶⠶⠆⠸⠷⠲⠲⠶⠺⠆⠸⠀⠖⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡇⠀⡇⠦⠀⠹⠱⠶⠆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠿⠿⠗⠀⠀⠀⠀⠈⠻⠳⠲⠶⠶⠶⠶⠂⠸⠷⠶⠢⠺⠴⠷⠂⠸⠶⠺⠸⠿⠻⠽⠛⠶⠖⠒⠶⠶⠷⠔⠀⣗⠀⡇⠷⠂⢸⠹⠆⠷⠆⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠉⠉⠀⢸ ⡿⠿⠖⠫⠷⠶⠇⠀⠀⠈⣲⣤⣤⣤⠀⣶⢠⢰⢰⣄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⡧⠷⠶⢞⠘⠳⠶⠶⠶⠶⡶⠶⠆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡟⠟⠷⠆⠇⠿⠶⠀⠀⠀⠄⠦⠔⠆⠰⠠⣤⡄⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠷⠒⢾⠷⠾⠷⡆⡞⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠻⠛⠚⠓⠓⠇⠁⠀⠀⠃⠐⠳⠓⠛⠛⠃⠸⠚⠻⠾⠺⠺⠚⠲⠂⠾⠲⠒⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⡟⠓⢿⢱⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠋⠙⠃⠁⠀⠚⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈ ⡆⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⢀⠈⢠⣀⣀⣉⡀⡀⢀⣀⣩⡅⢠⣅⣀⣉⠀⣠⣤⣀⣀⢀⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢰ ⡇⠀⠀⠀⣀⠀⠀⠀⢀⡀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠈⢉⠉⠀⠁⠈⠉⠉⣁⠈⠈⠉⠋⠉⡁⠉⠉⡉⠉⠁⡈⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⢀⡀⡀⠀⠀⣀⣀⠀⠀⠀⢸ ⡗⢀⠉⠀⡭⡉⢩⣁⣈⢡⠀⠡⠁⠀⠀⣀⡀⣀⣀⣀⡠⣀⠀⠀⢠⠠⢠⠀⠀⠈⢁⠉⠈⢡⣌⡉⠁⢠⣤⠩⠍⢩⣤⠭⣡⣍⢉⣉⠀⣨⣥⢡⣍⠁⡀⣤⣌⣉⣭⣭⣉⣨⡥⠌⣍⡍⣭⢀⠀⠀⠀⠃⠒⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡭⣹⣉⢋⣉⢨⠀⣬⠈⠀⢁⣩⣉⣉⢁⣉⣩⣭⠀⠁⣨⣩⣭⠀⢨⢠⣰⣨⡁⣪⣭⣽⡁⣨⣭⣭⠏⢨⣭⣭⣤⣹⣭⣍⣱⡚⣩⣍⢹⡍⣨⣭⣅⣨⣭⣍⢭⣉⣭⣭⣍⣭⣽⣍⣭⡅⠀⠁⠐⠂⠀⠀⠀⢸ ⡇⠀⠉⠀⡃⣉⢉⣛⣉⢨⠀⢭⠀⠀⢁⣩⣉⣉⢁⣈⣩⣉⠁⠀⡉⣹⣯⡁⢨⠈⢩⣭⡁⢈⣭⣬⡅⢨⣩⢭⣥⣬⢩⣉⣝⣍⣭⣭⣭⣍⡹⡅⢨⡍⣨⣭⣥⡌⣩⣩⣠⣭⣭⣍⣭⡅⠉⠉⠉⠁⠀⠂⠀⠁⠀⠀⠀⢸ ⡇⠀⠀⠀⣁⣋⣈⣛⣉⢨⠀⣉⠀⠀⢁⣩⣉⣉⢉⣉⣩⣉⠀⠀⣉⣭⣭⡁⢈⠀⣩⣩⡁⢨⣭⣁⡁⢈⣭⣡⠋⢉⣩⣩⣭⡉⢉⡙⣭⡍⢉⣁⣈⢍⣈⣉⣉⢁⣩⣍⢉⣋⣅⣁⣭⣅⣀⣄⠤⡄⣄⣄⣀⠀⠀⠀⡀⢸ ⡇⠀⠀⠀⣀⡩⢉⣚⢉⢨⠀⡈⠀⠀⢉⣉⣉⣉⢉⣉⢉⣉⠀⠀⣉⣉⣩⡁⢈⠀⣩⣉⡁⣉⡉⣩⡁⣈⣉⠉⣀⣉⣉⡉⢉⠁⢈⣉⣉⣘⣩⣩⡉⢉⣍⡉⠫⣉⣉⣋⣈⡉⠈⠊⠯⠉⠉⠉⠀⠀⠈⠉⡉⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠑⠛⣁⠛⠛⠘⠀⠛⡀⠀⠉⢙⠛⠙⠉⠙⠛⠙⠈⠀⠙⠛⠛⠁⢘⠀⠙⣙⠃⢙⣛⡈⠁⠈⠛⠻⠉⠝⠛⢁⡘⠃⡈⠉⣛⣋⡛⣙⢁⠈⠉⠉⡉⠋⢉⣉⡉⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠧⡀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠔⠀⠤⣘⠀⠈⠀⠀⠀⠀⠀⠈⠒⠀⠀⠀⠁⡁⠀⠀⠲⠁⠀⠒⠐⠐⠴⠀⠀⠐⠈⢀⡀⢙⡢⠂⡰⠟⠀⠈⠊⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸ ⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢀⣀⠀⠀⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠉⠂⡈⣋⠋⠋⠋⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣩⣦⡥⣤⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠄⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣠⡥⡡⡉⢁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠤⠤⠤⠤⠤⠄⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠐⠂⠀⠀⠀⠀⠹⢷⠾⠴⠶⠶⠶⠆⠀⠀⠒⠂⠒⠂⠒⠂⠒⠂⠒⠊⠒⠂⠚⠒⠀⡤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠸⠿⠶⠾⠾⠾⠿⠼⠵⠲⠆⠀⠂⠐⠒⠒⠒⠒⠒⠀⠐⠒⢠ ⡏⠿⠶⠷⠶⢶⣶⡶⠀⠸⠅⠷⠶⠶⠆⠸⠷⠲⠲⠶⠺⠆⠸⠀⠖⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡇⠀⡇⠀⢼⠹⠱⠶⠆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠿⠿⠗⠀⠀⠀⠀⠈⠻⠳⠲⠶⠶⠶⠶⠂⠸⠷⠶⠢⠺⠴⠷⠂⠸⠶⠺⠸⠿⠻⠽⠛⠶⠖⠒⠶⠶⠷⠔⠀⣗⠀⡇⠀⢾⢸⠹⠆⠷⠆⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠉⠉⠀⢸ ⡿⠿⠖⠫⠷⠶⠇⠀⠀⠈⣲⣤⣤⣤⠀⣶⢠⢰⢰⣤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⡧⠶⢿⢜⠘⠳⠶⠶⠶⠶⡶⠶⠆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡟⠟⠷⠆⠇⠿⠶⠀⠀⠀⠄⠦⠔⠆⠰⠠⣤⡄⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠷⣻⢾⠷⠾⠷⡆⡞⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠻⠛⠚⠓⠓⠇⠁⠀⠀⠃⠐⠳⠓⠛⠛⠃⠸⠚⠻⠾⠺⠺⠚⠲⠂⠾⠲⠒⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⡟⣿⢹⢱⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠋⠙⠃⠁⠓⠸⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈ ⡆⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⢀⠈⢠⣀⣀⣉⡀⡀⢀⣀⣩⡅⢠⣅⣀⣩⠀⣠⣤⣠⣀⢀⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢰ ⡇⠀⠀⠀⣀⠀⠀⠀⢀⡀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠈⢉⠈⠀⠁⠈⠉⠉⣁⠈⠈⠉⠋⠉⡁⠉⠉⡉⠉⠁⡈⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⢀⡀⡀⠀⠀⣀⣀⠀⠀⠀⢸ ⡗⢀⠉⠀⡭⡉⢩⣁⣈⢡⠀⠡⠅⠀⠀⣀⡀⣀⣀⣀⡠⣀⠀⠀⢠⠠⢠⠀⠀⠈⢁⠉⠈⢡⣌⡉⠁⢠⡄⢩⠍⢩⣤⠭⣡⣍⢉⣉⢠⣨⣥⢡⣍⠁⡀⣤⣌⣉⣩⣭⣉⣨⡥⠌⣍⡭⣭⢀⠀⠀⠀⠃⠒⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡭⣹⣉⢋⡉⢨⠀⣬⠈⠀⢁⣩⣉⣉⢁⣉⣩⣍⠠⠁⡈⢩⣭⠀⢨⢠⣹⣬⡁⣪⣭⣭⡁⣨⣥⣬⠏⢩⡭⣩⣤⣹⣭⣍⣹⣚⣩⣍⢹⡍⣨⣭⣅⣨⣭⣍⢉⣉⣭⣭⣍⣭⣽⣍⣭⡅⢀⠁⠰⠂⠀⠀⠀⢸ ⡇⠀⠉⠀⡃⣉⢉⣛⣉⢨⠀⢩⠀⠀⢁⣩⣉⣉⢁⣈⣩⣉⠁⠀⡉⣹⣯⡁⢨⠈⢩⣭⡁⢈⣭⣬⡅⢨⣩⢭⣥⣨⢩⣉⣝⣉⣭⣭⣭⣍⡩⡅⢨⡍⣨⣭⣥⡬⣩⣩⣠⣭⣭⣍⣭⡅⠉⠉⠉⠁⠀⠂⠀⠁⠀⠀⠀⢸ ⡇⠀⠀⠀⣁⣋⣈⣛⣉⢨⠀⣈⠈⠀⢁⣩⣉⣉⢉⣉⣩⣉⠀⠀⣉⣭⣭⡁⢈⠀⣩⣩⡁⢨⣭⣁⡁⢈⣉⣠⠋⢉⣩⣩⣭⡉⢩⡙⣭⣩⢉⣁⣈⢩⣈⣉⣉⣁⣩⣍⢉⣋⣅⣁⣭⣅⣀⣄⠤⡄⣄⣄⣀⠀⠀⠀⡀⢸ ⡇⠀⠀⠀⣀⡩⢉⣚⢉⢨⠀⡈⠀⠀⢉⣉⣉⣉⢉⣉⢉⣉⠀⠄⣉⣉⣩⡁⢈⠀⣩⣉⡁⣉⡉⣩⠁⣈⡉⠉⣀⣉⣉⡉⢉⠁⢈⣉⣉⣙⣩⣩⡁⢈⣍⡉⠫⣉⣉⣋⣈⡉⠈⠋⠯⠉⠉⠉⠀⠀⠉⠉⡉⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠑⠛⣁⠛⠛⠘⠀⠛⡀⠀⠉⢙⠛⠙⠉⠙⠛⠙⠈⠀⠙⠛⠛⠁⢘⠀⢙⣙⠃⢙⣛⡈⠁⠈⠛⠻⠉⠝⠛⢁⡘⠃⡈⠉⣉⣛⣙⣙⣑⠈⢉⡉⡉⠋⢉⣉⡉⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠧⡀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠀⠐⠀⠤⣘⠀⠈⠀⠁⠀⠀⠀⠈⠒⠀⠀⠀⠁⡁⠀⠀⠲⠁⠀⠒⠐⠐⠴⠀⠀⠘⠈⢀⡀⢙⡢⠂⡰⠟⠀⠈⠊⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸ ⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢀⣀⠀⠀⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠉⠂⡈⣋⠋⠋⠋⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣩⣦⡥⣤⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠄⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣠⡥⡡⡉⢁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠤⠤⠤⠤⠤⠄⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠐⠂⠀⠀⠀⠀⠹⢷⠾⠴⠶⠶⠶⠆⠀⠀⠒⠂⠒⠂⠒⠂⠒⠂⠒⠊⠒⠂⠚⠒⠀⡤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠸⠿⠶⠾⠾⠾⠿⠼⠵⠲⠆⠀⠂⠐⠒⠒⠒⠒⠒⠀⠐⠒⢠ ⡏⠿⠶⠷⠶⢶⣶⡶⠀⠸⠅⠷⠶⠶⠆⠸⠷⠲⠲⠶⠺⠆⠸⠀⠖⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡇⠀⡇⠀⢼⠹⠱⠶⠆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡇⠠⠀⠀⣀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠿⠿⠗⠀⠀⠀⠀⠈⠻⠳⠲⠶⠶⠶⠶⠂⠸⠷⠶⠢⠺⠴⠷⠂⠸⠶⠺⠸⠿⠻⠽⠛⠶⠖⠒⠶⠶⠷⠔⠀⣇⠀⡇⠀⢾⢸⠹⠆⠷⠆⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡇⠸⠀⠀⠈⠉⠀⠉⠉⠉⠀⢸ ⡿⠿⠖⠫⠷⠶⠇⠀⠀⠈⣲⣤⣤⣤⠀⣶⢠⢰⢰⣤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⡧⠶⢿⢜⠘⠳⠶⠖⠶⠶⡶⠶⠆⠀⠀⠁⠀⠀⠀⠀⠀⠀⡃⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡟⠟⠷⠆⠇⠟⠶⠀⠀⠀⠄⠦⠔⠆⠰⠠⣤⡄⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠷⣻⢾⠷⠾⠷⡆⡞⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠻⠛⠚⠓⠓⠇⠁⠀⠀⠃⠐⠳⠓⠛⠛⠃⠸⠚⠻⠾⠺⠺⠚⠲⠂⠾⠲⠒⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⣇⡟⣿⢹⢱⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠋⠙⠃⠁⠓⠸⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠨⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈ ⡆⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⢀⠈⢠⣀⣀⣉⡀⡀⢀⣀⣩⡅⢠⣅⣀⣩⠀⣠⣤⣠⣀⢀⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢰ ⡇⠀⠀⠀⣀⠀⠀⠀⢀⡀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠈⢉⠈⠀⠁⠈⠉⠉⣁⠈⠈⠉⠋⠉⡁⠉⠉⡉⠉⠁⡈⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⢀⡀⡀⠀⠀⣀⣀⠀⠀⠀⢸ ⡇⢀⠉⠀⡭⡉⢩⣁⣈⢡⠀⠡⠅⠀⠀⣀⡀⣀⣀⣀⡠⣀⠀⠀⢠⠠⢠⠀⠀⠈⢁⠉⠈⢡⣌⡉⠁⢠⡄⢩⠍⢩⣤⠭⣡⣍⢉⣉⢠⣨⣥⢡⣍⠁⡀⣤⣌⣉⣩⣭⣉⣨⡥⠌⣍⡭⣭⢀⠀⠀⠀⠃⠒⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡭⣹⣉⢋⡉⢨⠀⢬⠈⠀⢁⣩⣉⣉⢁⣉⣩⣍⠠⠁⡈⢩⣭⠀⢨⢠⣹⣬⡁⣪⣭⣭⡁⣨⣥⣬⠏⢩⡭⣩⣤⣹⣭⣍⣹⣚⣩⣍⢹⡍⣨⣭⣅⣨⣭⣍⢉⣉⣭⣭⣍⣭⣽⣍⣭⡅⢀⠁⠰⠂⠀⠀⠀⢸ ⡇⠀⠉⠀⡃⣉⢉⣛⣉⢨⠀⢩⠀⠀⢁⣩⣉⣉⢁⣈⣩⣉⠀⠀⡉⣹⣯⡁⢨⠈⢩⣭⡁⢈⣭⣬⡅⢨⣩⢭⣥⣨⢩⣉⣝⣉⣭⣭⣭⣍⡩⡅⢨⡍⣨⣭⣥⡬⣩⣩⣠⣭⣭⣍⣭⡅⠉⠉⠉⠁⠀⠂⠀⠁⠀⠀⠀⢸ ⡇⠀⠀⠀⣁⣋⣈⣛⣉⢨⠀⣈⠈⠀⢁⣩⣉⣉⢉⣉⣩⣉⠀⠀⣉⣭⣭⡁⢈⠀⣩⣩⡁⢨⣭⣁⡁⢈⣉⣠⠋⢉⣩⣩⣭⡉⢩⡙⣭⣩⢉⣁⣈⢩⣈⣉⣉⣁⣩⣍⢉⣋⣅⣁⣭⣅⣀⣄⠤⡄⣄⣄⣀⠀⠀⠀⡀⢸ ⡇⠀⠀⠀⣀⡩⢉⣚⢉⢨⠀⡈⠀⠀⢉⣉⣉⣉⢉⣉⢉⣉⠀⠄⣉⣉⣩⡁⢈⠀⣩⣉⡁⣉⡉⣡⠁⢈⡉⠉⣀⣉⣉⡉⢉⠁⢈⣉⣉⣙⣩⣩⡁⢈⣍⡉⠫⣉⣉⣋⣈⡉⠈⠋⠯⠉⠉⠉⠀⠀⠉⠉⡉⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠑⠛⣁⠛⠛⠘⠀⠛⡀⠀⠉⢙⠛⠙⠉⠙⠛⠙⠈⠀⠙⠛⠛⠁⢈⠀⢙⣙⠃⢙⣛⡈⠁⠈⠛⠻⢉⠝⠛⢁⡘⠃⡈⠉⣉⣛⣙⣙⣑⠈⢉⡉⡉⠋⢉⣉⡉⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢸ ⡇⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠧⡀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠀⠐⠀⠤⣘⠀⠈⠀⠁⠀⠀⠀⠈⠒⠀⠀⠀⠁⡁⠀⠀⠲⠁⠀⠒⠐⠐⠴⠀⠀⠘⠈⢀⡀⢙⡢⠂⡰⠟⠀⠈⠊⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸ ⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢀⣀⠀⠀⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠉⠂⡈⣋⠋⠋⠋⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣩⣦⡥⣤⢄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠄⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣠⡥⡡⡉⢁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠤⠤⠤⠤⠤⠄⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠐⠂⠀⠀⠀⠀⠹⢷⠾⠴⠶⠶⠶⠆⠀⠀⠒⠂⠒⠂⠒⠂⠒⠂⠒⠊⠒⠂⠚⠒⠀⡤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠸⠿⠶⠾⠮⠾⠿⠼⠵⠲⠆⠀⠂⠐⠒⠒⠒⠒⠒⠀⠐⠒⢠ ⡏⠿⠶⠷⠶⢶⣶⡶⠀⠸⠅⠷⠶⠶⠆⠸⠷⠲⠲⠶⠺⠆⠸⠀⠖⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡇⠀⡇⠀⢼⠹⠱⠶⠆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡇⠠⠀⠀⣀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠿⠿⠗⠀⠀⠀⠀⠈⠻⠳⠲⠶⠶⠶⠶⠂⠸⠷⠶⠢⠺⠴⠷⠂⠸⠶⠺⠸⠿⠻⠽⠛⠶⠖⠒⠶⠶⠷⠔⠀⣇⠀⡇⠀⢾⢸⠹⠆⠷⠆⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡇⠸⠀⠀⠈⠉⠀⠉⠉⠉⠀⢸ ⡿⠿⠖⠫⠷⠶⠇⠀⠀⠈⣲⣤⣤⣤⠀⣶⢠⢰⢰⣤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⡧⠶⢿⢜⠘⠳⠶⠖⠶⠶⡶⠶⠆⠀⠀⠁⠀⠀⠀⠀⠀⠀⡃⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡟⠟⠷⠆⠇⠟⠶⠀⠀⠀⠄⠦⠔⠆⠰⠠⣤⡄⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠷⣻⢾⠷⠾⠷⡆⡞⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠻⠛⠚⠓⠓⠇⠁⠀⠀⠃⠐⠳⠓⠛⠛⠃⠸⠚⠻⠾⠺⠺⠚⠲⠂⠾⠲⠒⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⣇⡟⣿⢹⢱⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠋⠙⠃⠁⠓⠸⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠨⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈ ⡆⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⢀⠈⢠⣀⣀⣉⡀⡀⢀⣀⣩⡅⢠⣅⣀⣩⠀⣠⣤⣠⣀⢀⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢰ ⡇⠀⠀⠀⣀⠀⠀⠀⢀⡀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠈⢉⠈⠀⠁⠈⠉⠉⣁⠈⠈⠉⠋⠉⡁⠉⠉⡉⠉⠁⡈⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⢀⡀⡀⠀⠀⣀⣀⠀⠀⠀⢸ ⡇⢀⠉⠀⡭⡉⢩⣁⣈⢡⠀⠡⠅⠀⠀⣀⡀⣀⣀⣀⡠⣀⠀⠀⢠⠠⢠⠀⠀⠈⢁⠉⠈⢡⣌⡉⠁⢠⡄⢩⠍⢩⣤⠭⣡⣍⢉⣉⢠⣨⣥⢡⣍⠁⡀⣤⣌⢉⣩⣭⣉⣨⡥⠌⣍⡭⣭⢀⠀⠀⠀⠃⠒⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡭⣹⣉⢋⡉⢨⠀⢬⠈⠀⢁⣩⣉⣉⢁⣉⣩⣍⠠⠁⡈⢩⣭⠀⢨⢠⣹⣬⡁⣪⣭⣭⡁⣨⣥⣬⠏⢩⡭⣩⣤⣹⣭⣍⣹⣚⣩⣍⢹⡍⣨⣭⣅⣨⣭⣍⢉⣉⣭⣭⣍⣭⣽⣍⣭⡅⢀⠁⠰⠂⠀⠀⠀⢸ ⡇⠀⠉⠀⡃⣉⢉⣛⣉⢨⠀⢩⠀⠀⢁⣩⣉⣉⢁⣈⣩⣉⠀⠀⡉⣹⣯⡁⢨⠈⢩⣭⡁⢈⣭⣬⡅⢨⣩⢭⣥⣨⢩⣉⣝⣉⣭⣭⣭⣍⡩⡅⢨⡍⣨⣭⣥⡬⣩⣩⣠⣭⣭⣍⣭⡅⠉⠉⠉⠁⠀⠂⠀⠁⠀⠀⠀⢸ ⡇⠀⠀⠀⣁⣋⣈⣛⣉⢨⠀⣈⠈⠀⢁⣩⣉⣉⢉⣉⣩⣉⠀⠀⣉⣭⣭⡁⢈⠀⣩⣩⡁⢨⣭⣁⡁⢈⣉⣠⠋⢉⣩⣩⣭⡉⢩⡙⣭⣩⢉⣁⣈⢩⣈⣉⣉⣁⣩⣍⢉⣋⣅⣁⣭⣅⣀⣄⠤⡄⣄⣄⣀⠀⠀⠀⡀⢸ ⡇⠀⠀⠀⣀⡩⢉⣚⢉⢨⠀⡈⠀⠀⢉⣉⣉⣉⢉⣉⢉⣉⠀⠄⣉⣉⣩⡁⢈⠀⣩⣉⡁⣉⡉⣡⠁⢈⡉⠉⣀⣉⣉⡉⢉⠁⢈⣉⣉⣙⣩⣩⡁⢈⣍⡉⠫⣉⣉⣋⣈⡉⠈⠋⠯⠉⠉⠉⣀⣀⡉⡉⡉⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠑⠛⣁⠛⠛⠘⠀⠛⡀⠀⠉⢙⠛⠙⠉⠙⠛⠙⠈⠀⠙⠛⠛⠁⢈⠀⠉⢙⠃⢙⣛⡈⠁⠈⠛⠻⢉⠝⠛⢁⡘⠃⡈⠉⣉⣛⣙⣙⣑⠈⢉⡉⡉⠋⢉⣉⡉⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⣀⠀⢸ ⡇⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠧⡀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠀⠐⠀⠤⣘⠀⠈⠀⠁⠀⠀⠀⠈⠒⠀⠀⠀⠁⡁⠀⠀⠲⠁⠀⠒⠐⠐⠴⠀⠀⠘⠈⢀⡀⢙⡢⠂⡰⠟⠀⠈⠊⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸ ⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢀⣀⠀⠀⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠉⠂⡈⣋⠋⠋⠋⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⢺ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣩⣦⡥⣤⢄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠄⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣠⡥⡡⡉⢁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠤⠤⠤⠤⠤⠄⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠐⠂⠀⠀⠀⠀⠹⢷⠾⠴⠶⠶⠶⠆⠀⠀⠒⠂⠒⠂⠒⠂⠒⠂⠒⠊⠒⠂⠚⠒⠀⡤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠸⠿⠶⠾⠮⠾⠿⠼⠵⠲⠆⠀⠂⠐⠒⠒⠒⠒⠒⠀⠐⠒⢠ ⡏⠿⠶⠷⠶⢶⣶⡶⠀⠸⠅⠷⠶⠶⠆⠸⠷⠲⠲⠶⠺⠆⠸⠀⠖⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡇⠀⡇⠄⢼⠹⠱⠶⠆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡇⠠⠀⠀⣀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠿⠿⠗⠀⠀⠀⠀⠈⠻⠳⠲⠶⠶⠶⠶⠂⠸⠷⠶⠢⠺⠴⠷⠂⠸⠶⠺⠸⠿⠻⠽⠛⠶⠖⠒⠶⠶⠷⠔⠀⣇⠀⡇⠂⢾⢸⠹⠆⠷⠆⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡇⠸⠀⠀⠈⠉⠀⠉⠉⠉⠀⢸ ⡿⠿⠖⠫⠷⠶⠇⠀⠀⠈⣲⣤⣤⣤⠀⣶⢠⢰⢰⣤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⡧⠷⢿⢜⠘⠳⠶⠖⠶⠶⡶⠶⠆⠀⠀⠁⠀⠀⠀⠀⠀⠀⡃⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡟⠟⠷⠆⠇⠟⠶⠀⠀⠀⠄⠦⠔⠆⠰⠠⣤⡄⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷⠷⣻⢾⠷⠾⠷⡆⡞⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠻⠛⠚⠓⠓⠇⠁⠀⠀⠃⠐⠳⠓⠛⠛⠃⠸⠚⠻⠾⠺⠺⠚⠲⠂⠾⠲⠒⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⡇⡟⣿⢹⢱⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠋⠙⠓⠅⠓⠸⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠨⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈ ⡆⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⢀⠈⢠⣀⣀⣉⡀⡀⢀⣀⣩⡅⢠⣅⣀⣩⠀⣠⣤⣠⣀⢀⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢰ ⡇⠀⠀⠀⣀⠀⠀⠀⢀⡀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠈⢉⠈⠀⠁⠈⠉⠉⣁⠈⠈⠉⠋⠉⡁⠉⠉⡉⠉⠁⡈⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⢀⡀⡀⠀⠀⣀⣀⠀⠀⠀⢸ ⡇⢀⠉⠀⡭⡉⢩⣁⣈⢡⠀⠡⠅⠀⠀⣀⡀⣀⣀⣀⡠⣀⠀⠀⢠⠠⢠⠀⠀⠈⢁⠉⠈⢡⣌⡉⠁⢠⡄⢩⠍⢩⣤⠭⣡⣍⢉⣉⢠⢨⣥⢡⣍⠁⡀⣤⣬⢉⣩⣭⣉⣨⡥⠌⣍⡭⣭⢀⠀⠀⠀⠃⠒⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡭⣹⣉⢋⡉⢨⠀⢬⠈⠀⢁⣩⣉⣉⢁⣉⣩⣍⠠⠁⡈⢩⣭⠀⢨⢠⣹⣬⡁⣪⣭⣭⡁⣨⣥⣬⠏⢩⡭⣩⣤⣹⣭⣍⣹⣒⣩⣍⢹⡍⣨⣭⣅⣨⣭⣍⢉⣉⣭⣭⣍⣭⣽⣍⣭⡅⢀⠁⠰⠂⠀⠀⠀⢸ ⡇⠀⠉⠀⡃⣉⢉⣛⣉⢨⠀⢩⠀⠀⢁⣩⣉⣉⢁⣈⣩⣉⠀⠀⡉⣹⣯⡁⢨⠈⢩⣭⡁⢈⣭⣬⡅⢨⣩⢭⣥⣨⢩⣉⣝⣉⣭⣭⣭⣍⡩⡅⢨⡍⣨⣭⣥⡬⣩⣩⣠⣭⣭⣍⣭⡅⠉⠉⠉⠁⠀⠂⠀⠁⠀⠀⠀⢸ ⡇⠀⠀⠀⣁⣋⣈⣛⣉⢨⠀⣈⠈⠀⢁⣩⣉⣉⢉⣉⣩⣉⠀⠀⣉⣭⣭⡁⢈⠀⣩⣩⡁⢨⣭⣁⡁⢈⣉⣠⠋⢉⣩⣩⣭⡉⢩⡙⣭⣩⢉⣁⣈⢩⣈⣉⣉⣁⣩⣍⠉⣋⣅⣁⣭⣅⣀⣄⠤⡄⣄⣄⣀⠀⠀⠀⡀⢸ ⡇⠀⠀⠀⣀⡩⢉⣚⢉⢨⠀⡈⠀⠀⢉⣉⣉⣉⢉⣉⢉⣉⠀⠄⣉⣉⣩⡁⢈⠀⣩⣉⡁⢉⡉⣡⠁⢈⡉⠉⣀⣉⣉⡉⢉⠁⢈⣉⣉⣙⣩⣩⡁⢈⣍⡉⠫⣉⣉⣋⣉⡉⠈⠋⠯⠉⠉⠉⣀⣀⡉⡉⡉⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠑⠛⣁⠛⠛⠘⠀⠛⡀⠀⠉⢙⠛⠙⠉⠙⠛⠙⠈⠀⠙⠛⢛⠁⢈⠀⠉⢙⠃⢘⣛⡈⠁⠈⠛⠻⢉⠝⠛⢁⡘⠃⡈⠉⣉⣛⣙⣙⣑⠈⢉⡉⡉⠋⢉⣉⡉⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⣀⠀⢸ ⡇⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠧⡀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠀⠐⠀⠤⣘⠀⠈⠀⠁⠀⠀⠀⠈⠒⠀⠀⠀⠁⡁⠀⠀⠲⠁⠀⠒⠐⠐⠴⠀⠀⠘⠈⢀⡀⢙⡢⠂⡰⠟⠀⠈⠊⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸ ⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢀⣀⠀⠀⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠉⠂⡈⣋⠋⠋⠋⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⢺ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣩⣦⡥⣤⢄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠄⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣠⡥⡡⡉⢁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠤⠤⠤⠤⠤⠄⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠐⠂⠀⠀⠀⠀⠹⢷⠾⠴⠶⠶⠶⠆⠀⠀⠒⠂⠒⠂⠒⠂⠒⠂⠒⠊⠒⠂⠚⠒⠀⡤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠸⠿⠶⠾⠮⠾⠿⠼⠵⠲⠆⠀⠂⠐⠒⠒⠒⠒⠒⠀⠐⠒⢠ ⡏⠿⠶⠷⠶⢶⣶⡶⠀⠸⠅⠷⠶⠶⠆⠸⠷⠲⠲⠶⠺⠆⠸⠀⠖⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡇⠀⡇⠄⢼⠹⠱⠶⠆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡇⠠⠀⠀⣀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠿⠿⠗⠀⠀⠀⠀⠈⠻⠳⠲⠶⠶⠶⠶⠂⠸⠷⠶⠢⠺⠴⠷⠂⠸⠶⠺⠸⠿⠻⠽⠛⠶⠖⠒⠶⠶⠷⠔⠀⣇⠀⡇⠂⢾⢸⠹⠆⠷⠆⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡇⠸⠀⠀⠈⠉⠀⠉⠉⠉⠀⢸ ⡿⠿⠖⠫⠷⠶⠇⠀⠀⠈⣲⣤⣤⣤⠀⣶⢠⢰⢰⣤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⡧⠷⢿⢜⠘⠳⠶⠖⠶⠶⡶⠶⠆⠀⠀⠁⠀⠀⠀⠀⠀⠀⡃⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡟⠟⠷⠆⠇⠟⠶⠀⠀⠀⠄⠦⠔⠆⠰⠠⣤⡄⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷⠷⣻⢾⠷⠾⠷⡆⡞⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠻⠛⠚⠓⠓⠇⠁⠀⠀⠃⠐⠳⠓⠛⠛⠃⠸⠚⠻⠾⠺⠺⠚⠲⠂⠾⠲⠒⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⡇⡟⣿⢹⢱⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠋⠙⠓⠅⠓⠸⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠨⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈ ⡆⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⢀⠈⢠⣀⣀⣉⡀⡀⢀⣀⣩⡅⢠⣅⣀⣩⠀⣠⣤⣠⣀⢀⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢰ ⡇⠀⠀⠀⣀⠀⠀⠀⢀⡀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠈⢉⠈⠀⠁⠈⠉⠉⣁⠈⠈⠉⠋⠉⡁⠉⠉⡉⠉⠁⡈⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⢀⡀⡀⠀⠀⣀⣀⠀⠀⠀⢸ ⡇⢀⠉⠀⡭⡉⢩⣁⣈⢡⠀⠡⠅⠀⠀⣀⡀⣀⣀⣀⡠⣀⠀⠀⢠⠠⢠⠀⠀⠈⢁⠉⠈⢡⣌⡉⠁⢠⡄⢩⠍⢩⣤⠭⣡⣍⢉⣉⢠⢨⣥⢡⣍⠁⡀⣤⣬⢉⣩⣭⣉⣨⡥⠌⣍⡭⣭⢀⠀⠀⠀⠃⠒⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡭⣹⣉⢋⡉⢨⠀⢬⠈⠀⢁⣩⣉⣉⢁⣉⣩⣍⠠⠁⡈⢩⣭⠀⢨⢠⣹⣬⡁⣪⣭⣭⡁⣨⣥⣬⠏⢩⡭⣩⣤⣹⣭⣍⣹⣒⣩⣍⢹⡍⣨⣭⣅⣨⣭⣍⢉⣉⣭⣭⣍⣭⣽⣍⣭⡅⢀⠁⠰⠂⠀⠀⠀⢸ ⡇⠀⠉⠀⡃⣉⢉⣛⣉⢨⠀⢩⠀⠀⢁⣩⣉⣉⢁⣈⣩⣉⠀⠀⡉⣹⣯⡁⢨⠈⢩⣭⡁⢈⣭⣬⡅⢨⣩⢭⣥⣨⢩⣉⣝⣉⣭⣭⣭⣍⡩⡅⢨⡍⣨⣭⣥⡬⣩⣩⣠⣭⣭⣍⣭⡅⠉⠉⠉⠁⠀⠂⠀⠁⠀⠀⠀⢸ ⡇⠀⠀⠀⣁⣋⣈⣛⣉⢨⠀⣈⠈⠀⢁⣩⣉⣉⢉⣉⣩⣉⠀⠀⣉⣭⣭⡁⢈⠀⣩⣩⡁⢨⣭⣁⡁⢈⣉⣠⠋⢉⣩⣩⣭⡉⢩⡙⣭⣩⢉⣁⣈⢩⣈⣉⣉⣁⣩⣍⠉⣋⣅⣁⣭⣅⣀⣄⠤⡄⣄⣄⣀⠀⠀⠀⡀⢸ ⡇⠀⠀⠀⣀⡩⢉⣚⢉⢨⠀⡈⠀⠀⢉⣉⣉⣉⢉⣉⢉⣉⠀⠄⣉⣉⣩⡁⢈⠀⣩⣉⡁⢉⡉⣡⠁⢈⡉⠉⣀⣉⣉⡉⢉⠁⢈⣉⣉⣙⣩⣩⡁⢈⣍⡉⠫⣉⣉⣋⣉⡉⠈⠋⠯⠉⠉⠉⣀⣀⡉⡉⡉⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠑⠛⣁⠛⠛⠘⠀⠛⡀⠀⠉⢙⠛⠙⠉⠙⠛⠙⠈⠀⠙⠛⢛⠁⢈⠀⠉⢙⠃⢘⣛⡈⠁⠈⠛⠻⢉⠝⠛⢁⡘⠃⡈⠉⣉⣛⣙⣙⣑⠈⢉⡉⡉⠋⢉⣉⡉⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⣀⠀⢸ ⡇⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠧⡀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠀⠐⠀⠤⣘⠀⠈⠀⠁⠀⠀⠀⠈⠒⠀⠀⠀⠁⡁⠀⠀⠲⠁⠀⠒⠐⠐⠴⠀⠀⠘⠈⢀⡀⢙⡢⠂⡰⠟⠀⠈⠊⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸ ⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢀⣀⠀⠀⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠉⠂⡈⣋⠋⠋⠋⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⢺ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣩⣦⡥⣤⢄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠄⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣠⡥⡡⡉⢁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠤⠤⠤⠤⠤⠄⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠂⠀⠀⠀⠀⠹⢷⠾⠴⠷⠶⠶⠆⠀⠀⠒⠂⠒⠂⠒⠂⠒⠂⠒⠊⠒⠂⠚⠒⠀⡤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠸⠿⠶⠾⠮⠷⠾⠼⠵⠲⠆⠐⠂⠐⠒⠒⠒⠒⠒⠒⠒⠒⢠ ⡇⠿⠶⠷⠶⢶⣶⡶⠀⠸⠄⠷⠶⠶⠆⠸⠷⠲⠲⠶⠺⠆⠸⠀⠖⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠄⢴⠹⠱⠶⠆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡇⠠⠀⠀⣀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠿⠿⠗⠀⠀⠀⠀⠈⠻⠳⠲⠶⠶⠶⠶⠂⠸⠷⠶⠲⠺⠶⠶⠀⠸⠶⠾⠸⠻⠻⠽⠛⠶⠖⠒⠖⠶⠷⠔⠀⣿⡂⡇⠂⢺⢸⠳⠖⠷⠆⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡇⠸⠀⠀⠈⠉⠀⠉⠉⠉⠀⢸ ⡿⠿⠖⠫⠗⠶⠇⠀⠀⠨⠷⠶⠲⠆⠸⠳⠾⢞⠂⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣷⡧⠷⢿⢔⠘⠳⠶⠶⠲⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡟⠟⠳⠆⠃⠟⠶⠀⠀⠀⠖⠦⠔⠇⠸⠠⣦⡤⢮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷⠷⣻⢾⠷⠾⠷⠆⡞⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡗⠛⠓⠚⠓⠓⠇⠁⠀⠀⠃⠐⠳⠛⠛⠛⠃⠸⠚⠺⠶⠺⠚⠘⠲⠂⠾⠒⠐⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⡇⠟⠟⢹⠱⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⡆⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠛⢚⠚⢋⠛⠀⠛⢛⠒⣀⠋⢛⢋⠃⠃⠃⠃⠛⠛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡇⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⡀⠀⠀⠀⢀⡀⠀⠀⢀⠀⣀⠀⠀⠁⣀⢈⠈⣉⣈⢀⠁⢈⣉⣉⠁⣈⣈⣉⣋⡉⣁⡉⠉⣉⣉⣁⡈⢈⢀⡀⢀⣀⣀⣀⣀⡀⢀⣀⣀⣀⣀⢀⡀⠀⡀⠀⠀⣀⣀⠀⠀⠀⢸ ⡇⢀⠉⠀⡛⠋⡻⠟⠃⡃⢘⡃⠂⠐⠐⡒⠓⠓⠈⢓⣛⢂⠀⠉⢛⣉⠃⢘⢀⣘⣙⠀⢛⣛⢚⠀⢛⣛⡓⠀⣛⣛⣋⡛⡛⡛⡋⡘⣛⡛⠛⡃⠉⣛⡉⢘⣛⣛⣛⣛⣛⣙⣋⣉⣙⣛⣚⡁⠀⠀⠀⠃⠒⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡛⠋⡛⠛⠃⡃⢀⣃⠀⠀⠑⡛⠉⠛⡉⢛⠙⢋⠀⢉⣙⣛⢃⢐⠘⢛⣛⠁⣛⣛⢈⠀⢛⣛⣓⡀⡛⣉⣛⣛⣛⣛⣛⣙⣛⡋⢙⡓⢙⣛⣋⣙⣓⣙⢛⣛⡛⣙⣋⡋⣛⣋⣋⣀⣬⡅⢀⠁⠰⠀⠀⠀⠀⢸ ⡇⠀⠉⠀⡋⠋⡛⠛⠃⡃⠀⡃⠂⠐⠙⡛⠉⠉⠑⢋⣙⡈⠀⣀⣈⣋⡀⢈⠀⣚⣋⠁⣙⢚⢈⠀⢙⣁⣛⠛⣁⣛⣛⣛⠙⣉⣋⣋⢋⣃⣉⣉⣙⣋⡙⢁⣋⡙⢘⣛⣙⣉⣛⣃⣈⣁⢉⢉⣉⣁⠀⠂⠀⠁⠀⠀⠀⢸ ⡇⠀⠀⠀⣉⡋⡙⣛⡁⡃⢀⡁⠂⠈⣑⣛⣙⡉⣘⢙⣉⣁⠀⣙⣉⣙⣁⠈⠀⣐⣙⠁⣙⣛⢈⡀⣛⢉⡑⣀⠛⡛⢘⡋⠈⣋⣉⣉⣉⣋⣋⢋⣙⢋⣛⣙⣛⣉⣉⣛⠛⣙⣉⣉⣛⣙⣉⣘⠉⡙⣁⣄⣀⠀⠀⠀⡀⢸ ⡇⠀⠀⠀⡉⠉⣛⣋⡁⡁⢀⡁⠀⠈⢉⣉⣉⡉⢈⢙⣉⡀⠀⣙⣉⣉⡁⢈⠀⠁⢈⡀⡉⣛⢈⠀⣭⣉⢉⣉⣁⣡⣈⢉⣀⣉⡋⣍⣉⣉⣉⣉⡅⣈⣉⡉⡉⣉⡉⣋⣩⡉⠈⠋⠫⠉⠉⠉⣀⣀⡉⡉⡉⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠉⠉⣙⠋⠃⠁⠈⠉⡀⠈⠈⢉⠉⠉⠈⠉⠙⠃⠀⠉⠉⠉⢁⠈⢈⠀⠈⢀⠉⢉⣈⡀⠁⠉⠉⠉⢉⠉⠉⢈⡉⠉⡉⠉⣉⣋⣉⣉⣉⠈⢁⡉⡋⠋⢁⣉⡉⢁⡀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⣀⠀⢸ ⡇⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠧⡀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠀⠐⠀⠤⣘⠀⠈⠀⠁⠀⠀⠀⠈⠒⠀⠀⠀⠁⡁⠀⠀⠲⠁⠀⠒⠐⠐⠴⠀⠀⠘⠈⢀⡀⢙⡢⠂⡰⠟⠀⠈⠊⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸ ⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢀⣀⠀⠀⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠉⠂⡈⣋⠋⠋⠋⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣩⣦⡥⣤⢄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠄⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣠⡥⡡⡉⢁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠂⠀⠀⠀⠀⠹⢷⠾⠴⠷⠶⠶⠆⠀⠀⠒⠂⠒⠂⠒⠂⠒⠂⠒⠊⠒⠂⠚⠒⠀⡤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠸⠿⠶⠾⠮⠷⠾⠼⠵⠲⠆⠐⠂⠐⠒⠒⠒⠒⠒⠒⠒⠒⢠ ⡇⠿⠶⠷⠶⢶⣶⡶⠀⠸⠄⠷⠶⠶⠆⠸⠷⠲⠲⠶⠺⠆⠸⠀⠖⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠄⢴⠹⠱⠶⠆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡇⠠⠀⠀⣀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠿⠿⠗⠀⠀⠀⠀⠈⠻⠳⠲⠶⠶⠶⠶⠂⠸⠷⠶⠲⠺⠶⠶⠀⠸⠶⠾⠻⠻⠻⠽⠛⠶⠖⠒⠖⠶⠷⠔⠀⠀⣺⣞⠂⢺⢸⠳⠖⠷⠆⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡇⠸⠀⠀⠈⠉⠀⠉⠉⠉⠀⢸ ⡿⠿⠖⠫⠷⠶⠇⠀⠀⠨⠷⠶⠲⠆⠸⠳⠾⢖⠂⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣷⡯⠷⢿⢔⠘⠳⠶⠶⠲⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡟⠟⠳⠆⠇⠟⠶⠀⠀⠀⠖⠦⠔⠇⠸⠠⣦⡤⢮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠶⠷⣻⢾⠷⠾⠷⠆⡞⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡗⠛⠛⠚⠓⠓⠇⠁⠀⠀⠃⠐⠳⠟⠛⠛⠃⠸⠚⠺⠶⠺⠚⠘⠲⠂⠾⠲⠐⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⠉⠟⠟⢹⠱⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⡆⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠛⢚⠚⢋⠛⠀⠛⢛⠒⣀⠋⢛⢋⠃⠃⠃⠃⠛⠛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡇⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⡀⠀⠀⠀⢀⡀⠀⠀⢀⠀⣀⠀⠀⠁⣀⢈⠈⣉⣈⢀⠁⢈⣉⣉⠁⣈⣈⣉⣋⡉⣁⡉⠉⣉⣉⣁⡈⢈⢀⡀⢀⣀⣀⣀⣀⡀⢀⣀⣀⣀⣀⢀⡀⠀⡀⠀⠀⣀⣀⠀⠀⠀⢸ ⡇⢀⠉⠀⡛⠋⡻⠟⠃⡃⢘⡋⠂⠐⠐⡒⠓⠓⠈⢓⣛⢂⠀⠉⣛⣉⠃⢘⢀⣘⣙⠀⢛⣛⢚⠀⢛⣛⡓⠀⢛⣛⣋⡛⡛⡛⡋⡈⣛⡛⠛⡃⠉⣛⡉⢘⣛⣛⣛⣛⣛⣙⣋⣉⣙⣛⣚⡁⠀⠀⠀⠃⠒⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡛⠋⡛⠛⠃⡃⢀⣃⠀⠀⠑⡛⠉⠛⡉⢛⠙⢋⠀⢉⣙⣛⢃⢐⠘⢛⣛⠃⣛⣛⢊⠀⢛⣛⣓⡀⡛⣉⣛⣛⣛⣛⣛⣙⣛⡋⢙⡑⢙⣛⣋⣙⣁⣙⢛⣛⡛⣙⣋⡋⣛⣋⣋⣀⣬⡅⢀⠁⠰⠀⠀⠀⠀⢸ ⡇⠀⠉⠀⡋⠋⡛⠛⠃⡃⠀⡃⠂⠐⠙⡛⠉⠉⠑⢋⡙⠈⠀⣀⣈⣋⡀⢈⠀⣚⣋⠁⣙⢚⢈⠀⢙⣁⣛⠛⣁⣛⣛⣛⠙⣉⣋⣋⢋⣃⣉⣉⣙⣋⡙⢁⣋⡙⢘⣛⣙⣉⣛⣃⣈⣁⢉⢉⣉⣁⠀⠂⠀⠁⠀⠀⠀⢸ ⡇⠀⠀⠀⣉⡋⡙⣛⡁⡃⢀⡁⠀⠈⣑⣛⣙⡉⣘⢙⣉⣁⠀⣙⣉⣙⣁⠈⠀⣐⣙⢁⣙⣛⢈⡀⣛⢉⡑⣀⢛⡛⢘⡋⠈⣋⣉⣉⣉⣋⣋⢋⣙⢋⣛⣙⣛⣉⣉⣛⠛⣙⣉⣉⣛⣙⣉⣘⠙⡙⣁⣄⣀⠀⠀⠀⡀⢸ ⡇⠀⠀⠀⡉⠉⣛⣋⡁⡁⢀⡁⠀⠈⢉⣉⣉⡉⢈⢙⣉⡀⠀⣙⣉⣉⡁⢈⠀⠁⢈⡈⡈⣛⢈⠀⣭⣉⢉⣉⢡⣡⣈⢉⣀⣉⡋⡍⣉⣉⣉⣉⡅⣈⣉⡉⡉⣉⡉⣋⣩⡉⠈⠋⠫⠉⠉⠉⣀⣀⡉⡉⡉⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠉⠉⣙⠋⠃⠁⠈⠉⡀⠈⠈⢉⠉⠉⠈⠉⠙⠃⠀⠉⠉⠉⢁⠈⢈⠀⠈⢀⠉⢉⣈⡀⠁⠉⠉⠉⢉⠉⠉⢉⡉⠉⡉⠉⣉⣋⣉⣉⣉⠈⢁⡉⡋⠉⢁⣉⡉⢁⡀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⣀⠀⢸ ⡇⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠧⡀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠀⠐⠀⠤⣘⠀⠈⠀⠁⠀⠀⠀⠈⠒⠀⠀⠀⠁⡁⠀⠀⠲⠁⠀⠒⠐⠐⠴⠀⠀⠘⠈⢀⡀⢙⡢⠂⡰⠟⠀⠈⠊⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸ ⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢀⣀⠀⠀⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠉⠂⡈⣋⠋⠋⠋⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣩⣦⡥⣤⢄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠄⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣠⡥⡡⡉⢁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠂⠀⠀⠀⠀⠹⢷⠾⠴⠷⠶⠶⠆⠀⠀⠒⠂⠒⠂⠒⠂⠒⠂⠒⠂⠒⠂⠚⠒⠀⡤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠸⠿⠶⠾⠮⠷⠾⠽⠵⠲⠆⠐⠂⠐⠒⠒⠒⠒⠒⠒⠒⠒⢠ ⡇⠿⠶⠷⠶⢶⣶⡶⠀⠸⠄⠷⠶⠶⠆⠸⠷⠲⠲⠶⠺⠆⠸⠀⠖⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠄⢴⠹⠱⠶⠆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡇⠠⠀⠀⣀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠿⠿⠗⠀⠀⠀⠀⠈⠻⠳⠲⠶⠶⠶⠶⠂⠸⠷⠶⠲⠾⠶⠶⠀⠸⠶⠾⠺⠻⠻⠽⠛⠶⠖⠒⠖⠶⠷⠔⠀⠀⣺⣞⠂⢺⢸⠳⠖⠶⠆⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡇⠸⠀⠀⠈⠉⠀⠉⠉⠉⠀⢸ ⡿⠿⠖⠫⠷⠶⠇⠀⠀⠨⠷⠶⠲⠆⠸⠳⠾⢖⠂⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣷⡯⠷⢿⢔⠘⠳⠶⠶⠲⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡟⠟⠳⠆⠃⠟⠶⠀⠀⠀⠖⠦⠔⠇⠸⠠⣦⡤⢮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠶⠷⣻⢾⠷⠾⠷⠆⡞⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡗⠛⠛⠚⠓⠓⠇⠁⠀⠀⠃⠐⠳⠛⠛⠛⠃⠸⠚⠺⠶⠺⠚⠘⠲⠂⠾⠒⠐⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⠉⠟⠟⢹⠱⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⡆⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠛⢚⠚⢋⠛⠀⠛⢛⠒⣀⠋⢛⢋⠃⠃⠓⠃⠛⠛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡇⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⢀⠀⣀⠀⠀⠁⣀⢈⠈⣉⣈⢀⠁⢈⣉⣉⠁⣈⣈⣉⣋⡉⣁⡉⠉⣉⣉⣁⡈⢈⢀⡀⢀⣀⣀⣀⣀⡀⢀⣀⣀⣀⣀⢀⡀⠀⡀⠀⠀⣀⣀⠀⠀⠀⢸ ⡇⢀⠉⠀⡛⠋⠻⠟⠃⡃⢘⡋⠂⠐⠐⡒⠓⠓⠈⢓⣛⢂⠀⠉⣛⣉⠃⢘⢀⣘⣙⠀⢛⣛⢚⠀⢛⣛⡓⠀⢛⣛⣋⡛⣛⡛⡋⡈⣛⡛⠛⡃⠉⣛⡉⢘⣛⣛⣛⣛⣛⣙⣋⣉⣙⣛⣚⡁⠀⠀⠀⠃⠒⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡛⠋⡛⠛⠃⡃⢀⣃⠀⠀⠑⡛⠉⠛⡉⢛⠙⢋⠀⢉⣙⣛⢊⢑⠘⢛⣛⠓⣛⣛⢊⠀⢛⣛⣓⣀⡛⣉⣛⣛⣛⣛⣛⣙⣛⡋⢙⡑⢙⣛⣋⣙⣁⣙⢛⣛⡛⣙⣋⡋⣛⣋⣋⣀⣬⡅⢀⠁⠰⠀⠀⠀⠀⢸ ⡇⠀⠉⠀⡋⠋⡛⠛⠃⡃⠀⣃⠂⠐⠘⡛⠉⠉⠑⢋⡙⠈⠀⣀⣈⣋⡀⢈⠀⣚⣋⠁⣙⢚⢈⠀⢙⣁⣛⠛⣁⣛⣛⣛⠙⣉⣋⣋⢋⣃⣉⣉⣙⣋⡙⢃⣋⡙⢘⣛⣙⣉⣛⣃⣈⣁⢉⢉⣉⣁⠀⠂⠀⠁⠀⠀⠀⢸ ⡇⠀⠀⠀⣉⡋⡙⣛⡁⡃⢀⡁⠀⠈⣙⣛⣙⡉⣘⢙⣉⣁⠀⢙⣉⣙⣁⠈⠀⣐⣙⢁⣙⣛⢈⡀⣛⢉⡑⣀⢛⡛⢘⡋⠈⣋⣉⣉⣉⣋⣋⢋⣙⢋⣛⣙⣛⣉⣉⣛⠛⣙⣉⣉⣛⣙⣉⣘⠙⡛⣁⣄⣀⠀⠀⠀⡀⢸ ⡇⠀⠀⠀⡉⠉⣛⣋⡁⡁⢀⡁⠀⠈⢉⣉⣉⡉⢈⢙⣉⡀⠀⣉⣉⣉⡁⢈⠀⠁⢈⡈⡈⣛⢈⠀⣩⣉⢉⣉⢡⣡⣈⢉⣀⣉⡋⡍⣉⣉⣉⣩⡅⣈⣉⡉⡉⣍⡉⣋⣩⡉⠈⠋⠫⠉⠉⠉⣀⣀⡉⡉⡉⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠉⠉⣙⠋⠃⠁⠈⠉⡀⠈⠈⢉⠉⠉⠈⠉⠙⠃⠀⠉⠉⠉⢁⠈⢈⠀⠈⢀⠉⢉⣈⡀⠁⠉⠉⠉⢉⠉⠉⢉⡉⠉⡉⠉⣉⣋⣉⣉⣉⠈⢁⡉⡋⠉⢁⣉⡉⢁⡀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⣀⠀⢸ ⡇⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠧⡀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠀⠐⠀⠤⣘⠀⠈⠀⠁⠀⠀⠀⠈⠒⠀⠀⠀⠁⡁⠀⠀⠲⠁⠀⠒⠐⠐⠴⠀⠀⠘⠈⢀⡀⢙⡢⠂⡰⠟⠀⠈⠊⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸ ⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢀⣀⠀⠀⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠉⠂⡈⣋⠋⠋⠋⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣩⣦⡥⣤⢄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠄⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣠⡥⡡⡉⢁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠂⠀⠀⠀⠀⠹⢷⠾⠴⠷⠶⠶⠆⠀⠀⠒⠂⠒⠂⠒⠂⠒⠂⠒⠂⠒⠂⠚⠒⠀⡤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠸⠿⠶⠾⠮⠷⠾⠽⠴⠶⠆⠐⠂⠐⠒⠒⠒⠒⠒⠒⠒⠒⢠ ⡇⠿⠶⠷⠶⢶⣶⡶⠀⠸⠄⠷⠶⠶⠆⠸⠷⠲⠲⠶⠺⠆⠸⠀⠖⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣇⡄⢴⠹⠱⠶⠆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡇⠠⠀⠀⣀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠿⠿⠗⠀⠀⠀⠀⠈⠻⠳⠲⠶⠶⠶⠶⠂⠸⠷⠶⠲⠸⠶⠶⠀⠸⠶⠾⠺⠻⠻⠽⠛⠶⠖⠒⠖⠶⠷⠔⠀⠀⢸⡇⡇⢺⢸⠳⠖⠶⠆⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡇⠸⠀⠀⠈⠉⠀⠉⠉⠉⠀⢸ ⡿⠿⠖⠫⠷⠶⠇⠀⠀⠨⠷⠶⠲⠆⠸⠳⠾⢶⠀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⡯⠷⢿⢔⠘⠳⠶⠶⠲⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡟⠟⠳⠆⠃⠟⠶⠀⠀⠀⠖⠦⠔⠇⠸⠠⣦⡤⢮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷⠷⣻⢾⠷⠾⠷⠆⡞⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡗⠛⠛⠚⠓⠓⠇⠁⠀⠀⠃⠐⠳⠛⠛⠛⠃⠸⠚⠺⠶⠺⠚⠘⠲⠂⠾⠒⠐⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⡏⠟⠟⢹⠱⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⡆⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠛⢚⠚⢋⠛⠀⠛⢛⠒⣀⠋⢛⢋⠃⠃⠓⠃⠛⠛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡇⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⢀⠀⣀⠀⠀⠁⠀⢈⠈⣉⣈⢀⠁⢈⣉⣉⠁⣈⣈⣉⣋⡉⣁⡉⠉⣉⣉⣁⡈⢈⢀⡀⢀⣀⣀⣀⣀⡀⢀⣀⣀⣀⣀⢀⡀⠀⡀⠀⠀⣀⣀⠀⠀⠀⢸ ⡇⢀⠉⠀⡛⠋⠻⠟⠃⡃⢘⡋⠂⠐⠀⡒⠓⠓⠈⢓⣛⢂⠀⠉⣛⣉⠃⢘⢈⣀⣙⢀⢛⣛⢚⠀⢛⣛⡓⠀⢛⣛⣋⣛⣛⡛⡋⡈⣛⡛⢛⡃⠉⣛⡉⢘⣛⣛⣛⣛⣛⣙⣋⣉⣙⣛⣚⡁⠀⡀⠀⠃⠒⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡛⠋⡛⠛⠃⡃⢀⣃⠀⠀⠑⡛⠉⠛⡉⢛⢙⢋⠀⢉⣙⣛⢊⢑⠘⢛⣛⠓⣛⣛⢊⠀⢛⣛⣓⣀⡛⣉⣛⣛⣛⣛⣛⣙⣛⡋⢙⡓⢙⣛⣋⣙⣁⣙⢛⣛⡛⣙⣋⡋⣛⣋⣋⣀⣬⡅⢀⠁⠰⠀⠀⠀⠀⢸ ⡇⠀⠉⠀⡋⠋⡛⠛⠃⡃⠀⣃⠂⠐⠘⡛⠉⠉⠑⢋⣙⠈⠀⣀⣈⣋⡀⢈⠀⣚⣋⠁⣙⢚⢈⡀⢙⣁⣛⠛⣁⣛⣛⣛⠙⣉⣋⣋⢋⣃⣉⣉⣙⣋⡘⢋⣋⡙⢈⣛⣙⣉⣛⣃⣈⣁⢉⢉⣉⣁⠀⠂⠀⠁⠀⠀⠀⢸ ⡇⠀⠀⠀⣉⡋⡙⣛⡁⡃⢀⡁⠀⠈⢙⣛⣙⡉⣘⢙⣉⣁⠀⢙⣉⣙⣁⠈⠀⣐⣙⢁⣙⣛⢈⡀⣛⢉⡑⣀⢛⡛⢘⡋⢈⣋⣉⣉⣉⣋⣋⢋⣙⢋⣛⣙⣛⣉⣉⣛⠛⣙⣉⣉⣛⣙⣉⣘⠙⡛⣁⣄⣀⠀⠀⠀⡀⢸ ⡇⠀⠀⠀⡉⠉⣛⣋⡁⡁⢀⡁⠀⠈⢉⣉⣉⡉⢈⢙⣉⡀⠀⣉⣉⣉⡁⢈⠀⠁⢈⡈⡈⣛⢈⠀⣩⣉⢉⣉⢡⣡⣈⢉⣀⣉⡋⣍⡉⣉⣉⣩⡅⣈⡉⡉⡉⣉⡉⣋⣩⡉⠈⠋⠫⠉⠉⠉⣀⣀⡉⡉⡉⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠉⠉⣙⠋⠃⠁⠈⠉⡀⠈⠈⢉⠉⠉⠈⠉⠙⠃⠀⠉⠉⠉⢁⠈⢈⠀⠈⢀⠉⢉⣈⡀⠁⠉⠉⠉⢉⠉⠉⢉⡉⠉⡉⠉⣉⣋⣉⣉⣉⠈⢁⡉⡋⠉⢁⣉⡉⢁⡀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⣀⠀⢸ ⡇⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠧⡀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠀⠐⠀⠤⣘⠀⠈⠀⠁⠀⠀⠀⠈⠒⠀⠀⠀⠁⡁⠀⠀⠲⠁⠀⠒⠐⠐⠴⠀⠀⠘⠈⢀⡀⢙⡢⠂⡰⠟⠀⠈⠊⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸ ⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢀⣀⠀⠀⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠉⠂⡈⣋⠋⠋⠋⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣩⣦⡥⣤⢄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠄⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣠⡥⡡⡉⢁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠂⠀⠀⠀⠀⠹⢷⠾⠴⠷⠶⠶⠆⠀⠀⠒⠂⠒⠂⠒⠂⠒⠂⠒⠂⠒⠂⠚⠒⠀⡤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠸⠿⠶⠾⠮⠷⠾⠽⠴⠶⠆⠐⠂⠐⠒⠒⠒⠒⠒⠒⠒⠒⢠ ⡇⠿⠶⠷⠶⢶⣶⡶⠀⠸⠄⠷⠶⠶⠆⠸⠷⠲⠲⠶⠺⠆⠸⠀⠖⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣇⡄⢴⠹⠱⠶⠆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡇⠠⠀⠀⣀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠿⠿⠗⠀⠀⠀⠀⠈⠻⠳⠲⠶⠶⠶⠶⠂⠸⠷⠶⠲⠸⠶⠶⠀⠸⠶⠾⠺⠻⠻⠽⠛⠶⠖⠒⠖⠶⠷⠔⠀⠀⢸⡇⡇⢺⢸⠳⠖⠶⠆⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡇⠸⠀⠀⠈⠉⠀⠉⠉⠉⠀⢸ ⡿⠿⠖⠫⠷⠶⠇⠀⠀⠨⠷⠶⠲⠆⠸⠳⠾⢶⠀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⡯⠷⢿⢔⠘⠳⠶⠶⠲⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡟⠟⠳⠆⠃⠟⠶⠀⠀⠀⠖⠦⠔⠇⠸⠠⣦⡤⢮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷⠷⣻⢾⠷⠾⠷⠆⡞⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡗⠛⠛⠚⠓⠓⠇⠁⠀⠀⠃⠐⠳⠛⠛⠛⠃⠸⠚⠺⠶⠺⠚⠘⠲⠂⠾⠒⠐⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⡏⠟⠟⢹⠱⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⡆⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠛⢚⠚⢋⠛⠀⠛⢛⠒⣀⠋⢛⢋⠃⠃⠓⠃⠛⠛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡇⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⢀⠀⣀⠀⠀⠁⠀⢈⠈⣉⣈⢀⠁⢈⣉⣉⠁⣈⣈⣉⣋⡉⣁⡉⠉⣉⣉⣁⡈⢈⢀⡀⢀⣀⣀⣀⣀⡀⢀⣀⣀⣀⣀⢀⡀⠀⡀⠀⠀⣀⣀⠀⠀⠀⢸ ⡇⢀⠉⠀⡛⠋⠻⠟⠃⡃⢘⡋⠂⠐⠀⡒⠓⠓⠈⢓⣛⢂⠀⠉⣛⣉⠃⢘⢈⣀⣙⢀⢛⣛⢚⠀⢛⣛⡓⠀⢛⣛⣋⣛⣛⡛⡋⡈⣛⡛⢛⡃⠉⣛⡉⢘⣛⣛⣛⣛⣛⣙⣋⣉⣙⣛⣚⡁⠀⡀⠀⠃⠒⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡛⠋⡛⠛⠃⡃⢀⣃⠀⠀⠑⡛⠉⠛⡉⢛⢙⢋⠀⢉⣙⣛⢊⢑⠘⢛⣛⠓⣛⣛⢊⠀⢛⣛⣓⣀⡛⣉⣛⣛⣛⣛⣛⣙⣛⡋⢙⡓⢙⣛⣋⣙⣁⣙⢛⣛⡛⣙⣋⡋⣛⣋⣋⣀⣬⡅⢀⠁⠰⠀⠀⠀⠀⢸ ⡇⠀⠉⠀⡋⠋⡛⠛⠃⡃⠀⣃⠂⠐⠘⡛⠉⠉⠑⢋⣙⠈⠀⣀⣈⣋⡀⢈⠀⣚⣋⠁⣙⢚⢈⡀⢙⣁⣛⠛⣁⣛⣛⣛⠙⣉⣋⣋⢋⣃⣉⣉⣙⣋⡘⢋⣋⡙⢈⣛⣙⣉⣛⣃⣈⣁⢉⢉⣉⣁⠀⠂⠀⠁⠀⠀⠀⢸ ⡇⠀⠀⠀⣉⡋⡙⣛⡁⡃⢀⡁⠀⠈⢙⣛⣙⡉⣘⢙⣉⣁⠀⢙⣉⣙⣁⠈⠀⣐⣙⢁⣙⣛⢈⡀⣛⢉⡑⣀⢛⡛⢘⡋⢈⣋⣉⣉⣉⣋⣋⢋⣙⢋⣛⣙⣛⣉⣉⣛⠛⣙⣉⣉⣛⣙⣉⣘⠙⡛⣁⣄⣀⠀⠀⠀⡀⢸ ⡇⠀⠀⠀⡉⠉⣛⣋⡁⡁⢀⡁⠀⠈⢉⣉⣉⡉⢈⢙⣉⡀⠀⣉⣉⣉⡁⢈⠀⠁⢈⡈⡈⣛⢈⠀⣩⣉⢉⣉⢡⣡⣈⢉⣀⣉⡋⣍⡉⣉⣉⣩⡅⣈⡉⡉⡉⣉⡉⣋⣩⡉⠈⠋⠫⠉⠉⠉⣀⣀⡉⡉⡉⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠉⠉⣙⠋⠃⠁⠈⠉⡀⠈⠈⢉⠉⠉⠈⠉⠙⠃⠀⠉⠉⠉⢁⠈⢈⠀⠈⢀⠉⢉⣈⡀⠁⠉⠉⠉⢉⠉⠉⢉⡉⠉⡉⠉⣉⣋⣉⣉⣉⠈⢁⡉⡋⠉⢁⣉⡉⢁⡀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⣀⠀⢸ ⡇⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠧⡀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠀⠐⠀⠤⣘⠀⠈⠀⠁⠀⠀⠀⠈⠒⠀⠀⠀⠁⡁⠀⠀⠲⠁⠀⠒⠐⠐⠴⠀⠀⠘⠈⢀⡀⢙⡢⠂⡰⠟⠀⠈⠊⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸ ⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢀⣀⠀⠀⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠉⠂⡈⣋⠋⠋⠋⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣩⣦⡥⣤⢄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠄⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣠⡥⡡⡉⢁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠂⠀⠀⠀⠀⠹⢷⠾⠴⠷⠶⠶⠆⠀⠀⠒⠂⠒⠂⠒⠂⠒⠂⠒⠂⠒⠂⠚⠒⠀⡤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠸⠿⠶⠾⠮⠷⠾⠽⠴⠶⠆⠐⠂⠐⠒⠒⠒⠒⠒⠒⠒⠒⢠ ⡇⠿⠶⠷⠶⢶⣶⡶⠀⠸⠄⠷⠶⠶⠆⠸⠷⠲⠲⠶⠺⠆⠸⠀⠖⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣇⡄⢴⠹⠱⠶⠆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡇⠠⠀⠀⣀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠿⠿⠗⠀⠀⠀⠀⠈⠻⠳⠲⠶⠶⠶⠶⠂⠸⠷⠶⠲⠸⠶⠶⠀⠸⠶⠾⠺⠻⠻⠽⠛⠶⠖⠒⠖⠶⠷⠔⠀⠀⢸⡇⡇⢺⢸⠳⠖⠶⠆⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡇⠸⠀⠀⠈⠉⠀⠉⠉⠉⠀⢸ ⡿⠿⠖⠫⠷⠶⠇⠀⠀⠨⠷⠶⠲⠆⠸⠳⠾⢶⠀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⡯⠷⢿⢔⠘⠳⠶⠶⠲⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡟⠟⠳⠆⠃⠟⠶⠀⠀⠀⠖⠦⠔⠇⠸⠠⣦⡤⢮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷⠷⣻⢾⠷⠾⠷⠆⡞⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡗⠛⠛⠚⠓⠓⠇⠁⠀⠀⠃⠐⠳⠛⠛⠛⠃⠸⠚⠺⠶⠺⠚⠘⠲⠂⠾⠒⠐⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⡏⠟⠟⢹⠱⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⡆⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠛⢚⠚⢋⠛⠀⠛⢛⠒⣀⠋⢛⢋⠃⠃⠓⠃⠛⠛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡇⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⢀⠀⣀⠀⠀⠁⠀⢈⠈⣉⣈⢀⠁⢈⣉⣉⠁⣈⣈⣉⣋⡉⣁⡉⠉⣉⣉⣁⡈⢈⢀⡀⢀⣀⣀⣀⣀⡀⢀⣀⣀⣀⣀⢀⡀⠀⡀⠀⠀⣀⣀⠀⠀⠀⢸ ⡇⢀⠉⠀⡛⠋⠻⠟⠃⡃⢘⡋⠂⠐⠀⡒⠓⠓⠈⢓⣛⢂⠀⠉⣛⣉⠃⢘⢈⣀⣙⢀⢛⣛⢚⠀⢛⣛⡓⠀⢛⣛⣋⣛⣛⡛⡋⡈⣛⡛⢛⡃⠉⣛⡉⢘⣛⣛⣛⣛⣛⣙⣋⣉⣙⣛⣚⡁⠀⡀⠀⠃⠒⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡛⠋⡛⠛⠃⡃⢀⣃⠀⠀⠑⡛⠉⠛⡉⢛⢙⢋⠀⢉⣙⣛⢊⢑⠘⢛⣛⠓⣛⣛⢊⠀⢛⣛⣓⣀⡛⣉⣛⣛⣛⣛⣛⣙⣛⡋⢙⡓⢙⣛⣋⣙⣁⣙⢛⣛⡛⣙⣋⡋⣛⣋⣋⣀⣬⡅⢀⠁⠰⠀⠀⠀⠀⢸ ⡇⠀⠉⠀⡋⠋⡛⠛⠃⡃⠀⣃⠂⠐⠘⡛⠉⠉⠑⢋⣙⠈⠀⣀⣈⣋⡀⢈⠀⣚⣋⠁⣙⢚⢈⡀⢙⣁⣛⠛⣁⣛⣛⣛⠙⣉⣋⣋⢋⣃⣉⣉⣙⣋⡘⢋⣋⡙⢈⣛⣙⣉⣛⣃⣈⣁⢉⢉⣉⣁⠀⠂⠀⠁⠀⠀⠀⢸ ⡇⠀⠀⠀⣉⡋⡙⣛⡁⡃⢀⡁⠀⠈⢙⣛⣙⡉⣘⢙⣉⣁⠀⢙⣉⣙⣁⠈⠀⣐⣙⢁⣙⣛⢈⡀⣛⢉⡑⣀⢛⡛⢘⡋⢈⣋⣉⣉⣉⣋⣋⢋⣙⢋⣛⣙⣛⣉⣉⣛⠛⣙⣉⣉⣛⣙⣉⣘⠙⡛⣁⣄⣀⠀⠀⠀⡀⢸ ⡇⠀⠀⠀⡉⠉⣛⣋⡁⡁⢀⡁⠀⠈⢉⣉⣉⡉⢈⢙⣉⡀⠀⣉⣉⣉⡁⢈⠀⠁⢈⡈⡈⣛⢈⠀⣩⣉⢉⣉⢡⣡⣈⢉⣀⣉⡋⣍⡉⣉⣉⣩⡅⣈⡉⡉⡉⣉⡉⣋⣩⡉⠈⠋⠫⠉⠉⠉⣀⣀⡉⡉⡉⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠉⠉⣙⠋⠃⠁⠈⠉⡀⠈⠈⢉⠉⠉⠈⠉⠙⠃⠀⠉⠉⠉⢁⠈⢈⠀⠈⢀⠉⢉⣈⡀⠁⠉⠉⠉⢉⠉⠉⢉⡉⠉⡉⠉⣉⣋⣉⣉⣉⠈⢁⡉⡋⠉⢁⣉⡉⢁⡀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⣀⠀⢸ ⡇⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠧⡀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠀⠐⠀⠤⣘⠀⠈⠀⠁⠀⠀⠀⠈⠒⠀⠀⠀⠁⡁⠀⠀⠲⠁⠀⠒⠐⠐⠴⠀⠀⠘⠈⢀⡀⢙⡢⠂⡰⠟⠀⠈⠊⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸ ⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢀⣀⠀⠀⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠉⠂⡈⣋⠋⠋⠋⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣩⣦⡥⣤⢄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠄⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣠⡥⡡⡉⢁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠂⠀⠀⠀⠀⠹⢷⠾⠴⠷⠶⠶⠆⠀⠀⠒⠂⠒⠂⠒⠂⠒⠂⠒⠂⠒⠂⠚⠒⠀⡤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠸⠿⠶⠾⠮⠷⠾⠽⠴⠶⠆⠐⠂⠐⠒⠒⠒⠒⠒⠒⠒⠒⢠ ⡇⠿⠶⠷⠶⢶⣶⡶⠀⠸⠄⠷⠶⠶⠆⠸⠷⠲⠲⠶⠺⠆⠸⠀⠖⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣇⡄⢴⠹⠱⠶⠆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡇⠠⠀⠀⣀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠿⠿⠗⠀⠀⠀⠀⠈⠻⠳⠲⠶⠶⠶⠶⠂⠸⠷⠶⠲⠸⠶⠶⠀⠸⠶⠾⠺⠻⠻⠽⠛⠶⠖⠒⠖⠶⠷⠔⠀⠀⢸⡇⡇⢺⢸⠳⠖⠶⠆⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡇⠸⠀⠀⠈⠉⠀⠉⠉⠉⠀⢸ ⡿⠿⠖⠫⠷⠶⠇⠀⠀⠨⠷⠶⠲⠆⠸⠳⠾⢶⠀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⡯⠷⢿⢔⠘⠳⠶⠶⠲⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡟⠟⠳⠆⠃⠟⠶⠀⠀⠀⠖⠦⠔⠇⠸⠠⣦⡤⢮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷⠷⣻⢾⠷⠾⠷⠆⡞⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡗⠛⠛⠚⠓⠓⠇⠁⠀⠀⠃⠐⠳⠛⠛⠛⠃⠸⠚⠺⠶⠺⠚⠘⠲⠂⠾⠒⠐⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⡏⠟⠟⢹⠱⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⡆⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠛⢚⠚⢋⠛⠀⠛⢛⠒⣀⠋⢛⢋⠃⠃⠓⠃⠛⠛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡇⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⢀⠀⣀⠀⠀⠁⠀⢈⠈⣉⣈⢀⠁⢈⣉⣉⠁⣈⣈⣉⣋⡉⣁⡉⠉⣉⣉⣁⡈⢈⢀⡀⢀⣀⣀⣀⣀⡀⢀⣀⣀⣀⣀⢀⡀⠀⡀⠀⠀⣀⣀⠀⠀⠀⢸ ⡇⢀⠉⠀⡛⠋⠻⠟⠃⡃⢘⡋⠂⠐⠀⡒⠓⠓⠈⢓⣛⢂⠀⠉⣛⣉⠃⢘⢈⣀⣙⢀⢛⣛⢚⠀⢛⣛⡓⠀⢛⣛⣋⣛⣛⡛⡋⡈⣛⡛⢛⡃⠉⣛⡉⢘⣛⣛⣛⣛⣛⣙⣋⣉⣙⣛⣚⡁⠀⡀⠀⠃⠒⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡛⠋⡛⠛⠃⡃⢀⣃⠀⠀⠑⡛⠉⠛⡉⢛⢙⢋⠀⢉⣙⣛⢊⢑⠘⢛⣛⠓⣛⣛⢊⠀⢛⣛⣓⣀⡛⣉⣛⣛⣛⣛⣛⣙⣛⡋⢙⡓⢙⣛⣋⣙⣁⣙⢛⣛⡛⣙⣋⡋⣛⣋⣋⣀⣬⡅⢀⠁⠰⠀⠀⠀⠀⢸ ⡇⠀⠉⠀⡋⠋⡛⠛⠃⡃⠀⣃⠂⠐⠘⡛⠉⠉⠑⢋⣙⠈⠀⣀⣈⣋⡀⢈⠀⣚⣋⠁⣙⢚⢈⡀⢙⣁⣛⠛⣁⣛⣛⣛⠙⣉⣋⣋⢋⣃⣉⣉⣙⣋⡘⢋⣋⡙⢈⣛⣙⣉⣛⣃⣈⣁⢉⢉⣉⣁⠀⠂⠀⠁⠀⠀⠀⢸ ⡇⠀⠀⠀⣉⡋⡙⣛⡁⡃⢀⡁⠀⠈⢙⣛⣙⡉⣘⢙⣉⣁⠀⢙⣉⣙⣁⠈⠀⣐⣙⢁⣙⣛⢈⡀⣛⢉⡑⣀⢛⡛⢘⡋⢈⣋⣉⣉⣉⣋⣋⢋⣙⢋⣛⣙⣛⣉⣉⣛⠛⣙⣉⣉⣛⣙⣉⣘⠙⡛⣁⣄⣀⠀⠀⠀⡀⢸ ⡇⠀⠀⠀⡉⠉⣛⣋⡁⡁⢀⡁⠀⠈⢉⣉⣉⡉⢈⢙⣉⡀⠀⣉⣉⣉⡁⢈⠀⠁⢈⡈⡈⣛⢈⠀⣩⣉⢉⣉⢡⣡⣈⢉⣀⣉⡋⣍⡉⣉⣉⣩⡅⣈⡉⡉⡉⣉⡉⣋⣩⡉⠈⠋⠫⠉⠉⠉⣀⣀⡉⡉⡉⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠉⠉⣙⠋⠃⠁⠈⠉⡀⠈⠈⢉⠉⠉⠈⠉⠙⠃⠀⠉⠉⠉⢁⠈⢈⠀⠈⢀⠉⢉⣈⡀⠁⠉⠉⠉⢉⠉⠉⢉⡉⠉⡉⠉⣉⣋⣉⣉⣉⠈⢁⡁⡊⠉⢁⣉⡉⢁⡀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⣀⠀⢸ ⡇⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠧⡀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠀⠐⠀⠤⣘⠀⠈⠀⠁⠀⠀⠀⠈⠒⠀⠀⠀⠁⡁⠀⠀⠲⠁⠀⠒⠐⠐⠴⠀⠀⠘⠈⢀⡀⢙⡢⠂⡰⠟⠀⠈⠊⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸ ⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢀⣀⠀⠀⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠉⠂⡈⣋⠋⠋⠋⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣩⣦⡥⣤⢄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠄⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣠⡥⡡⡉⢁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠂⠀⠀⠀⠀⠹⢷⠾⠴⠷⠶⠶⠆⠀⠀⠒⠂⠒⠂⠒⠂⠒⠂⠒⠂⠒⠂⠚⠒⠀⡤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠸⠿⠶⠾⠮⠷⠾⠽⠴⠶⠆⠐⠂⠐⠒⠒⠒⠒⠒⠒⠒⠒⢠ ⡇⠿⠶⠷⠶⢶⣶⡶⠀⠸⠄⠷⠶⠶⠆⠸⠷⠲⠲⠶⠺⠆⠸⠀⠖⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣇⡄⢴⠹⠱⠶⠆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡇⠠⠀⠀⣀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠿⠿⠗⠀⠀⠀⠀⠈⠻⠳⠲⠶⠶⠶⠶⠂⠸⠷⠶⠲⠸⠶⠶⠀⠸⠶⠾⠺⠻⠻⠽⠛⠶⠖⠒⠖⠶⠷⠔⠀⠀⢸⡇⡇⢺⢸⠳⠖⠶⠆⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡇⠸⠀⠀⠈⠉⠀⠉⠉⠉⠀⢸ ⡿⠿⠖⠫⠷⠶⠇⠀⠀⠨⠷⠶⠲⠆⠸⠳⠾⢶⠀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⡯⠷⢿⢔⠘⠳⠶⠶⠲⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡟⠟⠳⠆⠃⠟⠶⠀⠀⠀⠖⠦⠔⠇⠸⠠⣦⡤⢮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷⠷⣻⢾⠷⠾⠷⠆⡞⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡗⠛⠛⠚⠓⠓⠇⠁⠀⠀⠃⠐⠳⠛⠛⠛⠃⠸⠚⠺⠶⠺⠚⠘⠲⠂⠾⠒⠐⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⡏⠟⠟⢹⠱⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⡆⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠛⢚⠚⢋⠛⠀⠛⢛⠒⣀⠋⢛⢋⠃⠃⠓⠃⠛⠛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡇⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⢀⠀⣀⠀⠀⠁⠀⢈⠈⣉⣈⢀⠁⢈⣉⣉⠁⣈⣈⣉⣋⡉⣁⡉⠉⣉⣉⣁⡈⢈⢀⡀⢀⣀⣀⣀⣀⡀⢀⣀⣀⣀⣀⢀⡀⠀⡀⠀⠀⣀⣀⠀⠀⠀⢸ ⡇⢀⠉⠀⡛⠋⠻⠟⠃⡃⢘⡋⠂⠐⠀⡒⠓⠓⠈⢓⣛⢂⠀⠉⣛⣉⠃⢘⢈⣀⣙⢀⢛⣛⢚⠀⢛⣛⡓⠀⢛⣛⣋⣛⣛⡛⡋⡈⣛⡛⢛⡃⠉⣛⡉⢘⣛⣛⣛⣛⣛⣙⣋⣉⣙⣛⣚⡁⠀⡀⠀⠃⠒⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡛⠋⡛⠛⠃⡃⢀⣃⠀⠀⠑⡛⠉⠛⡉⢛⢙⢋⠀⢉⣙⣛⢊⢑⠘⢛⣛⠓⣛⣛⢊⠀⢛⣛⣓⣀⡛⣉⣛⣛⣛⣛⣛⣙⣛⡋⢙⡓⢙⣛⣋⣙⣁⣙⢛⣛⡛⣙⣋⡋⣛⣋⣋⣀⣬⡅⢀⠁⠰⠀⠀⠀⠀⢸ ⡇⠀⠉⠀⡋⠋⡛⠛⠃⡃⠀⣃⠂⠐⠘⡛⠉⠉⠑⢋⣙⠈⠀⣀⣈⣋⡀⢈⠀⣚⣋⠁⣙⢚⢈⡀⢙⣁⣛⠛⣁⣛⣛⣛⠙⣉⣋⣋⢋⣃⣉⣉⣙⣋⡘⢋⣋⡙⢈⣛⣙⣉⣛⣃⣈⣁⢉⢉⣉⣁⠀⠂⠀⠁⠀⠀⠀⢸ ⡇⠀⠀⠀⣉⡋⡙⣛⡁⡃⢀⡁⠀⠈⢙⣛⣙⡉⣘⢙⣉⣁⠀⢙⣉⣙⣁⠈⠀⣐⣙⢁⣙⣛⢈⡀⣛⢉⡑⣀⢛⡛⢘⡋⢈⣋⣉⣉⣉⣋⣋⢋⣙⢋⣛⣙⣛⣉⣉⣛⠛⣙⣉⣉⣛⣙⣉⣘⠙⡛⣁⣄⣀⠀⠀⠀⡀⢸ ⡇⠀⠀⠀⡉⠉⣛⣋⡁⡁⢀⡁⠀⠈⢉⣉⣉⡉⢈⢙⣉⡀⠀⣉⣉⣉⡁⢈⠀⠁⢈⡈⡈⣛⢈⠀⣩⣉⢉⣉⢡⣡⣈⢉⣀⣉⡋⣍⡉⣉⣉⣩⡅⣈⡉⡉⡉⣉⡉⣋⣩⡉⠈⠋⠫⠉⠉⠉⣀⣀⡉⡉⡉⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠉⠉⣙⠋⠃⠁⠈⠉⡀⠈⠈⢉⠉⠉⠈⠉⠙⠃⠀⠉⠉⠉⢁⠈⢈⠀⠈⢀⠉⢉⣈⡀⠁⠉⠉⠉⢉⠉⠉⢉⡉⠉⡉⠉⣉⣋⣉⣉⣉⠈⢁⡁⡊⠉⢁⣉⡉⢁⡀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⣀⠀⢸ ⡇⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠧⡀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠀⠐⠀⠤⣘⠀⠈⠀⠁⠀⠀⠀⠈⠒⠀⠀⠀⠁⡁⠀⠀⠲⠁⠀⠒⠐⠐⠴⠀⠀⠘⠈⢀⡀⢙⡢⠂⡰⠟⠀⠈⠊⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸ ⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢀⣀⠀⠀⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠉⠂⡈⣋⠋⠋⠋⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣩⣦⡥⣤⢄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠄⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣠⡥⡡⡉⢁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠂⠀⠀⠀⠀⠹⢷⠾⠴⠷⠶⠶⠆⠀⠀⠒⠂⠒⠂⠒⠂⠒⠂⠒⠂⠒⠂⠚⠒⠀⡤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠸⠿⠶⠾⠮⠷⠾⠽⠴⠶⠆⠐⠂⠐⠒⠒⠒⠒⠒⠒⠒⠒⢠ ⡇⠿⠶⠷⠶⢶⣶⡶⠀⠸⠄⠷⠶⠶⠆⠸⠷⠲⠲⠶⠺⠆⠸⠀⠖⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣇⡄⢴⠹⠱⠶⠆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡇⠠⠀⠀⣀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠿⠿⠗⠀⠀⠀⠀⠈⠻⠳⠲⠶⠶⠶⠶⠂⠸⠷⠶⠲⠸⠶⠶⠀⠸⠶⠾⠺⠻⠻⠽⠛⠶⠖⠒⠖⠶⠷⠔⠀⠀⢸⡇⡇⢺⢸⠳⠖⠶⠆⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡇⠸⠀⠀⠈⠉⠀⠉⠉⠉⠀⢸ ⡿⠿⠖⠫⠷⠶⠇⠀⠀⠨⠷⠶⠲⠆⠸⠳⠾⢶⠀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⡯⠷⢿⢔⠘⠳⠶⠶⠲⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡟⠟⠳⠆⠃⠟⠶⠀⠀⠀⠖⠦⠔⠇⠸⠠⣦⡤⢮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷⠷⣻⢾⠷⠾⠷⠆⡞⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡗⠛⠛⠚⠓⠓⠇⠁⠀⠀⠃⠐⠳⠛⠛⠛⠃⠸⠚⠺⠶⠺⠚⠘⠲⠂⠾⠒⠐⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⡏⠟⠟⢹⠱⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⡆⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠛⢚⠚⢋⠛⠀⠛⢛⠒⣀⠋⢛⢋⠃⠃⠓⠃⠛⠛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡇⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⢀⠀⣀⠀⠀⠁⠀⢈⠈⣉⣈⢀⠁⢈⣉⣉⠁⣈⣈⣉⣋⡉⣁⡉⠉⣉⣉⣁⡈⢈⢀⡀⢀⣀⣀⣀⣀⡀⢀⣀⣀⣀⣀⢀⡀⠀⡀⠀⠀⣀⣀⠀⠀⠀⢸ ⡇⢀⠉⠀⡛⠋⠻⠟⠃⡃⢘⡋⠂⠐⠀⡒⠓⠓⠈⢓⣛⢂⠀⠉⣛⣉⠃⢘⢈⣀⣙⢀⢛⣛⢚⠀⢛⣛⡓⠀⢛⣛⣋⣛⣛⡛⡋⡈⣛⡛⢛⡃⠉⣛⡉⢘⣛⣛⣛⣛⣛⣙⣋⣉⣙⣛⣚⡁⠀⡀⠀⠃⠒⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡛⠋⡛⠛⠃⡃⢀⣃⠀⠀⠑⡛⠉⠛⡉⢛⢙⢋⠀⢉⣙⣛⢊⢑⠘⢛⣛⠓⣛⣛⢊⠀⢛⣛⣓⣀⡛⣉⣛⣛⣛⣛⣛⣙⣛⡋⢙⡓⢙⣛⣋⣙⣁⣙⢛⣛⡛⣙⣋⡋⣛⣋⣋⣀⣬⡅⢀⠁⠰⠀⠀⠀⠀⢸ ⡇⠀⠉⠀⡋⠋⡛⠛⠃⡃⠀⣃⠂⠐⠘⡛⠉⠉⠑⢋⣙⠈⠀⣀⣈⣋⡀⢈⠀⣚⣋⠁⣙⢚⢈⡀⢙⣁⣛⠛⣁⣛⣛⣛⠙⣉⣋⣋⢋⣃⣉⣉⣙⣋⡘⢋⣋⡙⢈⣛⣙⣉⣛⣃⣈⣁⢉⢉⣉⣁⠀⠂⠀⠁⠀⠀⠀⢸ ⡇⠀⠀⠀⣉⡋⡙⣛⡁⡃⢀⡁⠀⠈⢙⣛⣙⡉⣘⢙⣉⣁⠀⢙⣉⣙⣁⠈⠀⣐⣙⢁⣙⣛⢈⡀⣛⢉⡑⣀⢛⡛⢘⡋⢈⣋⣉⣉⣉⣋⣋⢋⣙⢋⣛⣙⣛⣉⣉⣛⠛⣙⣉⣉⣛⣙⣉⣘⠙⡛⣁⣄⣀⠀⠀⠀⡀⢸ ⡇⠀⠀⠀⡉⠉⣛⣋⡁⡁⢀⡁⠀⠈⢉⣉⣉⡉⢈⢙⣉⡀⠀⣉⣉⣉⡁⢈⠀⠁⢈⡈⡈⣛⢈⠀⣩⣉⢉⣉⢡⣡⣈⢉⣀⣉⡋⣍⡉⣉⣉⣩⡅⣈⡉⡉⡉⣉⡉⣋⣩⡉⠈⠋⠫⠉⠉⠉⣀⣀⡉⡉⡉⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠉⠉⣙⠋⠃⠁⠈⠉⡀⠈⠈⢉⠉⠉⠈⠉⠙⠃⠀⠉⠉⠉⢁⠈⢈⠀⠈⢀⠉⢉⣈⡀⠁⠉⠉⠉⢉⠉⠉⢉⡉⠉⡉⠉⣉⣋⣉⣉⣉⠈⢁⡁⡊⠉⢁⣉⡉⢁⡀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⣀⠀⢸ ⡇⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠧⡀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠀⠐⠀⠤⣘⠀⠈⠀⠁⠀⠀⠀⠈⠒⠀⠀⠀⠁⡁⠀⠀⠲⠁⠀⠒⠐⠐⠴⠀⠀⠘⠈⢀⡀⢙⡢⠂⡰⠟⠀⠈⠊⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸ ⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢀⣀⠀⠀⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠉⠂⡈⣋⠋⠋⠋⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣩⣦⡥⣤⢄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠄⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣠⡥⡡⡉⢁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠂⠀⠀⠀⠀⠹⢷⠾⠴⠷⠶⠶⠆⠀⠀⠒⠂⠒⠂⠒⠂⠒⠂⠒⠂⠒⠂⠚⠒⠀⡤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠸⠿⠶⠾⠮⠷⠾⠽⠴⠶⠆⠐⠂⠐⠒⠒⠒⠒⠒⠒⠒⠒⢠ ⡇⠿⠶⠷⠶⢶⡶⡶⠀⠸⠄⠷⠶⠶⠆⠸⠷⠲⠲⠶⠺⠆⠸⠀⠖⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣇⡄⢴⠹⠱⠶⠆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡇⠠⠀⠀⣀⠀⠀⠀⠀⠀⢀⡸ ⡟⠿⠿⠿⠗⠀⠀⠀⠀⠈⠻⠳⠲⠶⠶⠶⠶⠂⠸⠷⠶⠲⠸⠶⠶⠀⠸⠶⠾⠺⠻⠻⠽⠛⠶⠖⠒⠖⠶⠷⠔⠀⠀⢸⡇⡇⢺⢸⠳⠖⠶⠆⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡇⠸⠀⠀⠈⠉⠀⠉⠁⠀⢸⡇ ⡿⠿⠖⠫⠷⠶⠇⠀⠀⠨⠷⠶⠲⠆⠸⠳⠾⢶⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⡯⠷⢿⢔⠘⠳⠶⠶⠲⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠘⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇ ⡟⠟⠳⠆⠃⠟⠶⠀⠀⠀⠖⠦⠔⠇⠸⠠⣦⡤⢮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷⠷⣻⢾⠷⠾⠷⠆⡞⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇ ⡗⠛⠛⠚⠓⠓⠇⠁⠀⠀⠃⠐⠳⠛⠛⠛⠃⠸⠚⠺⠶⠺⠚⠘⠲⠂⠾⠒⠐⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⡏⠟⠟⢹⠱⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⢨⡅ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃ ⡆⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠛⢚⠚⢋⠛⠀⠛⢛⠒⣀⠋⢛⢋⠃⠃⠓⠃⠛⠛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣇ ⡇⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⢀⠀⣀⠀⠀⠁⠀⢈⠈⣉⣈⢀⠁⢈⣉⣉⠁⣈⣈⣉⣋⡉⣁⡉⠉⣉⣉⣁⡈⢈⢀⡀⢀⣀⣀⣀⣀⡀⢀⣀⣀⣀⣀⢀⠀⠀⡀⠀⠀⣀⣀⠀⠀⢘⡇ ⡇⢀⠉⠀⡛⠋⠻⠟⠃⡃⢘⡋⠂⠐⠀⡒⠓⠓⠈⢓⣛⢂⠀⠉⣛⣉⠃⢘⢈⣀⣙⢀⢛⣛⢚⠀⢛⣛⡓⠀⢛⣛⣋⣛⣛⡛⡋⡈⣛⡛⢛⡃⠉⣛⡉⢘⣛⣛⣛⣛⣛⣙⣋⣉⣙⣛⣚⡁⠀⡀⠀⠃⠒⠀⠀⠀⢸⣫ ⡇⠀⠀⠀⡛⠋⡛⠛⠃⡃⢀⣃⠀⠀⠑⡛⠉⠛⡉⢛⢙⢋⠀⢉⣙⣛⢊⢑⠘⢛⣛⠓⣛⣛⢊⠀⢛⣛⣓⣀⡛⣉⣛⣛⣛⣛⣛⣙⣛⡋⢙⡓⢙⣛⣋⣙⣁⣙⢛⣛⡛⣙⣋⡋⣛⣋⣋⣀⣬⡅⢀⠁⠰⠀⠀⠀⠀⢸ ⡇⠀⠉⠀⡋⠋⡛⠛⠃⡃⠀⣃⠂⠐⠘⡛⠉⠉⠑⢋⣙⠈⠀⣀⣈⣋⡀⢈⠀⣚⣋⠁⣙⢚⢈⡀⢙⣁⣛⠛⣁⣛⣛⣛⠙⣉⣋⣋⢋⣃⣉⣉⣙⣋⡘⢋⣋⡙⢈⣛⣙⣉⣛⣃⣈⣁⢉⢉⣉⣁⠀⠂⠀⠁⠀⠀⠀⢸ ⡇⠀⠀⠀⣉⡋⡙⣛⡁⡃⢀⡁⠀⠈⢙⣛⣙⡉⣘⢙⣉⣁⠀⢙⣉⣙⣁⠈⠀⣐⣙⢁⣙⣛⢈⡀⣛⢉⡑⣀⢛⡛⢘⡋⢈⣋⣉⣉⣉⣋⣋⢋⣙⢋⣛⣙⣛⣉⣉⣛⠛⣙⣉⣉⣛⣙⣉⣘⠙⡛⣁⣄⣀⠀⠀⠀⡀⢸ ⡇⠀⠀⠀⡉⠉⣛⣋⡁⡁⢀⡁⠀⠈⢉⣉⣉⡉⢈⢙⣉⡀⠀⣉⣉⣉⡁⢈⠀⠁⢈⡈⡈⣛⢈⠀⣩⣉⢉⣉⢡⣡⣈⢉⣀⣉⡋⣍⡉⣉⣉⣩⡅⣈⡉⡉⡉⣉⡉⣋⣩⡉⠈⠋⠫⠉⠉⠉⣀⣀⡉⡉⡉⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠉⠉⣙⠋⠃⠁⠈⠉⠀⠈⠈⢉⠉⠉⠈⠉⠙⠃⠀⠉⠉⠉⢁⠈⢈⠀⠈⢀⠉⢉⣈⡀⠁⠉⠉⠉⢉⠉⠉⢉⡉⠉⡉⠉⣉⣋⣉⣉⣉⠈⢁⡁⡊⠉⢁⣉⡉⢁⡀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⣀⠀⢸ ⡇⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠧⡀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠀⠐⠀⠤⣘⠀⠈⠀⠁⠀⠀⠀⠈⠒⠀⠀⠀⠁⡁⠀⠀⠲⠁⠀⠒⠐⠐⠴⠀⠀⠘⠈⢀⡀⢙⡢⠂⡰⠟⠀⠈⠊⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢀⣀⠀⠀⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠉⠂⡈⣋⠋⠋⠋⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣩⣦⡥⣤⢄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠄⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣠⡥⡡⡉⢁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠂⠀⠀⠀⠀⠹⢷⠾⠴⠷⠶⠶⠆⠀⠀⠒⠂⠒⠂⠒⠂⠒⠂⠒⠂⠒⠂⠚⠒⠀⡤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠸⠿⠶⠾⠮⠷⠾⠽⠴⠶⠆⠐⠂⠐⠒⠒⠒⠒⠒⠒⠒⠒⢠ ⡇⠿⠶⠷⠶⢶⡶⡶⠀⠸⠄⠷⠶⠶⠆⠸⠷⠲⠲⠶⠺⠆⠸⠀⠖⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣇⡄⢴⠹⠱⠶⠆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡇⠠⠀⠀⣀⠀⠀⠀⠀⠀⢀⡸ ⡟⠿⠿⠿⠗⠀⠀⠀⠀⠈⠻⠳⠲⠶⠶⠶⠶⠂⠸⠷⠶⠲⠸⠶⠶⠀⠸⠶⠾⠺⠻⠻⠽⠛⠶⠖⠒⠖⠶⠷⠔⠀⠀⢸⡇⡇⢺⢸⠳⠖⠶⠆⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡇⠸⠀⠀⠈⠉⠀⠉⠁⠀⢸⡇ ⡿⠿⠖⠫⠷⠶⠇⠀⠀⠨⠷⠶⠲⠆⠸⠳⠾⢶⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⡯⠷⢿⢔⠘⠳⠶⠶⠲⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠘⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇ ⡟⠟⠳⠆⠃⠟⠶⠀⠀⠀⠖⠦⠔⠇⠸⠠⣦⡤⢮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷⠷⣻⢾⠷⠾⠷⠆⡞⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇ ⡗⠛⠛⠚⠓⠓⠇⠁⠀⠀⠃⠐⠳⠛⠛⠛⠃⠸⠚⠺⠶⠺⠚⠘⠲⠂⠾⠒⠐⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⡏⠟⠟⢹⠱⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⢨⡅ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃ ⡆⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠛⢚⠚⢋⠛⠀⠛⢛⠒⣀⠋⢛⢋⠃⠃⠓⠃⠛⠛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣇ ⡇⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⢀⠀⣀⠀⠀⠁⠀⢈⠈⣉⣈⢀⠁⢈⣉⣉⠁⣈⣈⣉⣋⡉⣁⡉⠉⣉⣉⣁⡈⢈⢀⡀⢀⣀⣀⣀⣀⡀⢀⣀⣀⣀⣀⢀⠀⠀⡀⠀⠀⣀⣀⠀⠀⢘⡇ ⡇⢀⠉⠀⡛⠋⠻⠟⠃⡃⢘⡋⠂⠐⠀⡒⠓⠓⠈⢓⣛⢂⠀⠉⣛⣉⠃⢘⢈⣀⣙⢀⢛⣛⢚⠀⢛⣛⡓⠀⢛⣛⣋⣛⣛⡛⡋⡈⣛⡛⢛⡃⠉⣛⡉⢘⣛⣛⣛⣛⣛⣙⣋⣉⣙⣛⣚⡁⠀⡀⠀⠃⠒⠀⠀⠀⢸⣫ ⡇⠀⠀⠀⡛⠋⡛⠛⠃⡃⢀⣃⠀⠀⠑⡛⠉⠛⡉⢛⢙⢋⠀⢉⣙⣛⢊⢑⠘⢛⣛⠓⣛⣛⢊⠀⢛⣛⣓⣀⡛⣉⣛⣛⣛⣛⣛⣙⣛⡋⢙⡓⢙⣛⣋⣙⣁⣙⢛⣛⡛⣙⣋⡋⣛⣋⣋⣀⣬⡅⢀⠁⠰⠀⠀⠀⠀⢸ ⡇⠀⠉⠀⡋⠋⡛⠛⠃⡃⠀⣃⠂⠐⠘⡛⠉⠉⠑⢋⣙⠈⠀⣀⣈⣋⡀⢈⠀⣚⣋⠁⣙⢚⢈⡀⢙⣁⣛⠛⣁⣛⣛⣛⠙⣉⣋⣋⢋⣃⣉⣉⣙⣋⡘⢋⣋⡙⢈⣛⣙⣉⣛⣃⣈⣁⢉⢉⣉⣁⠀⠂⠀⠁⠀⠀⠀⢸ ⡇⠀⠀⠀⣉⡋⡙⣛⡁⡃⢀⡁⠀⠈⢙⣛⣙⡉⣘⢙⣉⣁⠀⢙⣉⣙⣁⠈⠀⣐⣙⢁⣙⣛⢈⡀⣛⢉⡑⣀⢛⡛⢘⡋⢈⣋⣉⣉⣉⣋⣋⢋⣙⢋⣛⣙⣛⣉⣉⣛⠛⣙⣉⣉⣛⣙⣉⣘⠙⡛⣁⣄⣀⠀⠀⠀⡀⢸ ⡇⠀⠀⠀⡉⠉⣛⣋⡁⡁⢀⡁⠀⠈⢉⣉⣉⡉⢈⢙⣉⡀⠀⣉⣉⣉⡁⢈⠀⠁⢈⡈⡈⣛⢈⠀⣩⣉⢉⣉⢡⣡⣈⢉⣀⣉⡋⣍⡉⣉⣉⣩⡅⣈⡉⡉⡉⣉⡉⣋⣩⡉⠈⠋⠫⠉⠉⠉⣀⣀⡉⡉⡉⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠉⠉⣙⠋⠃⠁⠈⠉⠀⠈⠈⢉⠉⠉⠈⠉⠙⠃⠀⠉⠉⠉⢁⠈⢈⠀⠈⢀⠉⢉⣈⡀⠁⠉⠉⠉⢉⠉⠉⢉⡉⠉⡉⠉⣉⣋⣉⣉⣉⠈⢁⡁⡊⠉⢁⣉⡉⢁⡀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⣀⠀⢸ ⡇⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠧⡀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠀⠐⠀⠤⣘⠀⠈⠀⠁⠀⠀⠀⠈⠒⠀⠀⠀⠁⡁⠀⠀⠲⠁⠀⠒⠐⠐⠴⠀⠀⠘⠈⢀⡀⢙⡢⠂⡰⠟⠀⠈⠊⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢀⣀⠀⠀⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠉⠂⡈⣋⠋⠋⠋⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣩⣦⡥⣤⢄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠄⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣠⡥⡡⡉⢁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠂⠀⠀⠀⠀⠹⢷⠾⠴⠷⠶⠶⠆⠀⠀⠒⠂⠒⠂⠒⠂⠒⠂⠒⠂⠒⠂⠚⠒⠀⡤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠸⠿⠶⠾⠮⠷⠾⠽⠴⠶⠆⠐⠂⠐⠒⠒⠒⠒⠒⠒⠒⠒⢠ ⡇⠿⠶⠷⠶⢶⡶⡶⠀⠸⠄⠷⠶⠶⠆⠸⠷⠲⠲⠶⠺⠆⠸⠀⠖⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣇⡄⢴⠹⠱⠶⠆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡇⠠⠀⠀⣀⠀⠀⠀⠀⠀⢀⡸ ⡟⠿⠿⠿⠗⠀⠀⠀⠀⠈⠻⠳⠲⠶⠶⠶⠶⠂⠸⠷⠶⠲⠸⠶⠶⠀⠸⠶⠾⠺⠻⠻⠽⠛⠶⠖⠒⠖⠶⠷⠔⠀⠀⢸⡇⡇⢺⢸⠳⠖⠶⠆⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡇⠸⠀⠀⠈⠉⠀⠉⠁⠀⢸⡇ ⡿⠿⠖⠫⠷⠶⠇⠀⠀⠨⠷⠶⠲⠆⠸⠳⠾⢶⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⡯⠷⢿⢔⠘⠳⠶⠶⠲⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠘⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇ ⡟⠟⠳⠆⠃⠟⠶⠀⠀⠀⠖⠦⠔⠇⠸⠠⣦⡤⢮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷⠷⣻⢾⠷⠾⠷⠆⡞⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇ ⡗⠛⠛⠚⠓⠓⠇⠁⠀⠀⠃⠐⠳⠛⠛⠛⠃⠸⠚⠺⠶⠺⠚⠘⠲⠂⠾⠒⠐⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⡏⠟⠟⢹⠱⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⢨⡅ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃ ⡆⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠛⢚⠚⢋⠛⠀⠛⢛⠒⣀⠋⢛⢋⠃⠃⠓⠃⠛⠛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣇ ⡇⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⢀⠀⣀⠀⠀⠁⠀⢈⠈⣉⣈⢀⠁⢈⣉⣉⠁⣈⣈⣉⣋⡉⣁⡉⠉⣉⣉⣁⡈⢈⢀⡀⢀⣀⣀⣀⣀⡀⢀⣀⣀⣀⣀⢀⠀⠀⡀⠀⠀⣀⣀⠀⠀⢘⡇ ⡇⢀⠉⠀⡛⠋⠻⠟⠃⡃⢘⡋⠂⠐⠀⡒⠓⠓⠈⢓⣛⢂⠀⠉⣛⣉⠃⢘⢈⣀⣙⢀⢛⣛⢚⠀⢛⣛⡓⠀⢛⣛⣋⣛⣛⡛⡋⡈⣛⡛⢛⡃⠉⣛⡉⢘⣛⣛⣛⣛⣛⣙⣋⣉⣙⣛⣚⡁⠀⡀⠀⠃⠒⠀⠀⠀⢸⣫ ⡇⠀⠀⠀⡛⠋⡛⠛⠃⡃⢀⣃⠀⠀⠑⡛⠉⠛⡉⢛⢙⢋⠀⢉⣙⣛⢊⢑⠘⢛⣛⠓⣛⣛⢊⠀⢛⣛⣓⣀⡛⣉⣛⣛⣛⣛⣛⣙⣛⡋⢙⡓⢙⣛⣋⣙⣁⣙⢛⣛⡛⣙⣋⡋⣛⣋⣋⣀⣬⡅⢀⠁⠰⠀⠀⠀⠀⢸ ⡇⠀⠉⠀⡋⠋⡛⠛⠃⡃⠀⣃⠂⠐⠘⡛⠉⠉⠑⢋⣙⠈⠀⣀⣈⣋⡀⢈⠀⣚⣋⠁⣙⢚⢈⡀⢙⣁⣛⠛⣁⣛⣛⣛⠙⣉⣋⣋⢋⣃⣉⣉⣙⣋⡘⢋⣋⡙⢈⣛⣙⣉⣛⣃⣈⣁⢉⢉⣉⣁⠀⠂⠀⠁⠀⠀⠀⢸ ⡇⠀⠀⠀⣉⡋⡙⣛⡁⡃⢀⡁⠀⠈⢙⣛⣙⡉⣘⢙⣉⣁⠀⢙⣉⣙⣁⠈⠀⣐⣙⢁⣙⣛⢈⡀⣛⢉⡑⣀⢛⡛⢘⡋⢈⣋⣉⣉⣉⣋⣋⢋⣙⢋⣛⣙⣛⣉⣉⣛⠛⣙⣉⣉⣛⣙⣉⣘⠙⡛⣁⣄⣀⠀⠀⠀⡀⢸ ⡇⠀⠀⠀⡉⠉⣛⣋⡁⡁⢀⡁⠀⠈⢉⣉⣉⡉⢈⢙⣉⡀⠀⣉⣉⣉⡁⢈⠀⠁⢈⡈⡈⣛⢈⠀⣩⣉⢉⣉⢡⣡⣈⢉⣀⣉⡋⣍⡉⣉⣉⣩⡅⣈⡉⡉⡉⣉⡉⣋⣩⡉⠈⠋⠫⠉⠉⠉⣀⣀⡉⡉⡉⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠉⠉⣙⠋⠃⠁⠈⠉⠀⠈⠈⢉⠉⠉⠈⠉⠙⠃⠀⠉⠉⠉⢁⠈⢈⠀⠈⢀⠉⢉⣈⡀⠁⠉⠉⠉⢉⠉⠉⢉⡉⠉⡉⠉⣉⣋⣉⣉⣉⠈⢁⡁⡊⠉⢁⣉⡉⢁⡀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⣀⠀⢸ ⡇⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠧⡀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠀⠐⠀⠤⣘⠀⠈⠀⠁⠀⠀⠀⠈⠒⠀⠀⠀⠁⡁⠀⠀⠲⠁⠀⠒⠐⠐⠴⠀⠀⠘⠈⢀⡀⢙⡢⠂⡰⠟⠀⠈⠊⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢀⣀⠀⠀⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠉⠂⡈⣋⠋⠋⠋⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣩⣦⡥⣤⢄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠄⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣠⡥⡡⡉⢁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠂⠀⠀⠀⠀⠹⢷⠾⠴⠷⠶⠶⠆⠀⠀⠒⠂⠒⠂⠒⠂⠒⠂⠒⠂⠒⠂⠚⠒⠀⡤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠸⠿⠶⠾⠮⠷⠾⠽⠴⠶⠆⠐⠂⠐⠒⠒⠒⠒⠒⠒⠒⠒⢠ ⡇⠿⠶⠷⠶⢶⡶⡶⠀⠸⠄⠷⠶⠶⠆⠸⠷⠲⠲⠶⠺⠆⠸⠀⠖⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣇⡄⢴⠹⠱⠶⠆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡇⠠⠀⠀⣀⠀⠀⠀⠀⠀⢀⡸ ⡟⠿⠿⠿⠗⠀⠀⠀⠀⠈⠻⠳⠲⠶⠶⠶⠶⠂⠸⠷⠶⠲⠸⠶⠶⠀⠸⠶⠾⠺⠻⠻⠽⠛⠶⠖⠒⠖⠶⠷⠔⠀⠀⢸⡇⡇⢺⢸⠳⠖⠶⠆⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡇⠸⠀⠀⠈⠉⠀⠉⠁⠀⢸⡇ ⡿⠿⠖⠫⠷⠶⠇⠀⠀⠨⠷⠶⠲⠆⠸⠳⠾⢶⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⡯⠷⢿⢔⠘⠳⠶⠶⠲⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠘⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇ ⡟⠟⠳⠆⠃⠟⠶⠀⠀⠀⠖⠦⠔⠇⠸⠠⣦⡤⢮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷⠷⣻⢾⠷⠾⠷⠆⡞⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇ ⡗⠛⠛⠚⠓⠓⠇⠁⠀⠀⠃⠐⠳⠛⠛⠛⠃⠸⠚⠺⠶⠺⠚⠘⠲⠂⠾⠒⠐⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⡏⠟⠟⢹⠱⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⢨⡅ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃ ⡆⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠛⢚⠚⢋⠛⠀⠛⢛⠒⣀⠋⢛⢋⠃⠃⠓⠃⠛⠛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣇ ⡇⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⢀⠀⣀⠀⠀⠁⠀⢈⠈⣉⣈⢀⠁⢈⣉⣉⠁⣈⣈⣉⣋⡉⣁⡉⠉⣉⣉⣁⡈⢈⢀⡀⢀⣀⣀⣀⣀⡀⢀⣀⣀⣀⣀⢀⠀⠀⡀⠀⠀⣀⣀⠀⠀⢘⡇ ⡇⢀⠉⠀⡛⠋⠻⠟⠃⡃⢘⡋⠂⠐⠀⡒⠓⠓⠈⢓⣛⢂⠀⠉⣛⣉⠃⢘⢈⣀⣙⢀⢛⣛⢚⠀⢛⣛⡓⠀⢛⣛⣋⣛⣛⡛⡋⡈⣛⡛⢛⡃⠉⣛⡉⢘⣛⣛⣛⣛⣛⣙⣋⣉⣙⣛⣚⡁⠀⡀⠀⠃⠒⠀⠀⠀⢸⣫ ⡇⠀⠀⠀⡛⠋⡛⠛⠃⡃⢀⣃⠀⠀⠑⡛⠉⠛⡉⢛⢙⢋⠀⢉⣙⣛⢊⢑⠘⢛⣛⠓⣛⣛⢊⠀⢛⣛⣓⣀⡛⣉⣛⣛⣛⣛⣛⣙⣛⡋⢙⡓⢙⣛⣋⣙⣁⣙⢛⣛⡛⣙⣋⡋⣛⣋⣋⣀⣬⡅⢀⠁⠰⠀⠀⠀⠀⢸ ⡇⠀⠉⠀⡋⠋⡛⠛⠃⡃⠀⣃⠂⠐⠘⡛⠉⠉⠑⢋⣙⠈⠀⣀⣈⣋⡀⢈⠀⣚⣋⠁⣙⢚⢈⡀⢙⣁⣛⠛⣁⣛⣛⣛⠙⣉⣋⣋⢋⣃⣉⣉⣙⣋⡘⢋⣋⡙⢈⣛⣙⣉⣛⣃⣈⣁⢉⢉⣉⣁⠀⠂⠀⠁⠀⠀⠀⢸ ⡇⠀⠀⠀⣉⡋⡙⣛⡁⡃⢀⡁⠀⠈⢙⣛⣙⡉⣘⢙⣉⣁⠀⢙⣉⣙⣁⠈⠀⣐⣙⢁⣙⣛⢈⡀⣛⢉⡑⣀⢛⡛⢘⡋⢈⣋⣉⣉⣉⣋⣋⢋⣙⢋⣛⣙⣛⣉⣉⣛⠛⣙⣉⣉⣛⣙⣉⣘⠙⡛⣁⣄⣀⠀⠀⠀⡀⢸ ⡇⠀⠀⠀⡉⠉⣛⣋⡁⡁⢀⡁⠀⠈⢉⣉⣉⡉⢈⢙⣉⡀⠀⣉⣉⣉⡁⢈⠀⠁⢈⡈⡈⣛⢈⠀⣩⣉⢉⣉⢡⣡⣈⢉⣀⣉⡋⣍⡉⣉⣉⣩⡅⣈⡉⡉⡉⣉⡉⣋⣩⡉⠈⠋⠫⠉⠉⠉⣀⣀⡉⡉⡉⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠉⠉⣙⠋⠃⠁⠈⠉⠀⠈⠈⢉⠉⠉⠈⠉⠙⠃⠀⠉⠉⠉⢁⠈⢈⠀⠈⢀⠉⢉⣈⡀⠁⠉⠉⠉⢉⠉⠉⢉⡉⠉⡉⠉⣉⣋⣉⣉⣉⠈⢁⡁⡊⠉⢁⣉⡉⢁⡀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⣀⠀⢸ ⡇⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠧⡀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠀⠐⠀⠤⣘⠀⠈⠀⠁⠀⠀⠀⠈⠒⠀⠀⠀⠁⡁⠀⠀⠲⠁⠀⠒⠐⠐⠴⠀⠀⠘⠈⢀⡀⢙⡢⠂⡰⠟⠀⠈⠊⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢀⣀⠀⠀⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠉⠂⡈⣋⠋⠋⠋⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣩⣦⡥⣤⢄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠄⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣠⡥⡡⡉⢁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠂⠀⠀⠀⠀⠹⢷⠾⠴⠷⠶⠶⠆⠀⠀⠒⠂⠒⠂⠒⠂⠒⠂⠒⠂⠒⠂⠚⠒⠀⡤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠸⠿⠶⠾⠮⠷⠾⠽⠴⠶⠆⠐⠂⠐⠒⠒⠒⠒⠒⠒⠒⠒⢠ ⡇⠿⠶⠷⠶⢶⡶⡶⠀⠸⠄⠷⠶⠶⠆⠸⠷⠲⠲⠶⠺⠆⠸⠀⠖⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣇⡄⢴⠹⠱⠶⠆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡇⠠⠀⠀⣀⠀⠀⠀⠀⠀⢀⡸ ⡟⠿⠿⠿⠗⠀⠀⠀⠀⠈⠻⠳⠲⠶⠶⠶⠶⠂⠸⠷⠶⠲⠸⠶⠶⠀⠸⠶⠾⠺⠻⠻⠽⠛⠶⠖⠒⠖⠶⠷⠔⠀⠀⢸⡇⡇⢺⢸⠳⠖⠶⠆⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡇⠸⠀⠀⠈⠉⠀⠉⠁⠀⢸⡇ ⡿⠿⠖⠫⠷⠶⠇⠀⠀⠨⠷⠶⠲⠆⠸⠳⠾⢶⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⡯⠷⢿⢔⠘⠳⠶⠶⠲⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠘⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇ ⡟⠟⠳⠆⠃⠟⠶⠀⠀⠀⠖⠦⠔⠇⠸⠠⣦⡤⢮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷⠷⣻⢾⠷⠾⠷⠆⡞⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇ ⡗⠛⠛⠚⠓⠓⠇⠁⠀⠀⠃⠐⠳⠛⠛⠛⠃⠸⠚⠺⠶⠺⠚⠘⠲⠂⠾⠒⠐⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⡏⠟⠟⢹⠱⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⢨⡅ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃ ⡆⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠛⢚⠚⢋⠛⠀⠛⢛⠒⣀⠋⢛⢋⠃⠃⠓⠃⠛⠛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣇ ⡇⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⢀⠀⣀⠀⠀⠁⠀⢈⠈⣉⣈⢀⠁⢈⣉⣉⠁⣈⣈⣉⣋⡉⣁⡉⠉⣉⣉⣁⡈⢈⢀⡀⢀⣀⣀⣀⣀⡀⢀⣀⣀⣀⣀⢀⠀⠀⡀⠀⠀⣀⣀⠀⠀⢘⡇ ⡇⢀⠉⠀⡛⠋⠻⠟⠃⡃⢘⡋⠂⠐⠀⡒⠓⠓⠈⢓⣛⢂⠀⠉⣛⣉⠃⢘⢈⣀⣙⢀⢛⣛⢚⠀⢛⣛⡓⠀⢛⣛⣋⣛⣛⡛⡋⡈⣛⡛⢛⡃⠉⣛⡉⢘⣛⣛⣛⣛⣛⣙⣋⣉⣙⣛⣚⡁⠀⡀⠀⠃⠒⠀⠀⠀⢸⣫ ⡇⠀⠀⠀⡛⠋⡛⠛⠃⡃⢀⣃⠀⠀⠑⡛⠉⠛⡉⢛⢙⢋⠀⢉⣙⣛⢊⢑⠘⢛⣛⠓⣛⣛⢊⠀⢛⣛⣓⣀⡛⣉⣛⣛⣛⣛⣛⣙⣛⡋⢙⡓⢙⣛⣋⣙⣁⣙⢛⣛⡛⣙⣋⡋⣛⣋⣋⣀⣬⡅⢀⠁⠰⠀⠀⠀⠀⢸ ⡇⠀⠉⠀⡋⠋⡛⠛⠃⡃⠀⣃⠂⠐⠘⡛⠉⠉⠑⢋⣙⠈⠀⣀⣈⣋⡀⢈⠀⣚⣋⠁⣙⢚⢈⡀⢙⣁⣛⠛⣁⣛⣛⣛⠙⣉⣋⣋⢋⣃⣉⣉⣙⣋⡘⢋⣋⡙⢈⣛⣙⣉⣛⣃⣈⣁⢉⢉⣉⣁⠀⠂⠀⠁⠀⠀⠀⢸ ⡇⠀⠀⠀⣉⡋⡙⣛⡁⡃⢀⡁⠀⠈⢙⣛⣙⡉⣘⢙⣉⣁⠀⢙⣉⣙⣁⠈⠀⣐⣙⢁⣙⣛⢈⡀⣛⢉⡑⣀⢛⡛⢘⡋⢈⣋⣉⣉⣉⣋⣋⢋⣙⢋⣛⣙⣛⣉⣉⣛⠛⣙⣉⣉⣛⣙⣉⣘⠙⡛⣁⣄⣀⠀⠀⠀⡀⢸ ⡇⠀⠀⠀⡉⠉⣛⣋⡁⡁⢀⡁⠀⠈⢉⣉⣉⡉⢈⢙⣉⡀⠀⣉⣉⣉⡁⢈⠀⠁⢈⡈⡈⣛⢈⠀⣩⣉⢉⣉⢡⣡⣈⢉⣀⣉⡋⣍⡉⣉⣉⣩⡅⣈⡉⡉⡉⣉⡉⣋⣩⡉⠈⠋⠫⠉⠉⠉⣀⣀⡉⡉⡉⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠉⠉⣙⠋⠃⠁⠈⠉⠀⠈⠈⢉⠉⠉⠈⠉⠙⠃⠀⠉⠉⠉⢁⠈⢈⠀⠈⢀⠉⢉⣈⡀⠁⠉⠉⠉⢉⠉⠉⢉⡉⠉⡉⠉⣉⣋⣉⣉⣉⠈⢁⡁⡊⠉⢁⣉⡉⢁⡀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⣀⠀⢸ ⡇⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠧⡀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠀⠐⠀⠤⣘⠀⠈⠀⠁⠀⠀⠀⠈⠒⠀⠀⠀⠁⡁⠀⠀⠲⠁⠀⠒⠐⠐⠴⠀⠀⠘⠈⢀⡀⢙⡢⠂⡰⠟⠀⠈⠊⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢀⣀⠀⠀⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠉⠂⡈⣋⠋⠋⠋⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣩⣦⡥⣤⢄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠄⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣠⡥⡡⡉⢁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠐⠂⠀⠀⠀⠀⠹⢷⠾⠴⠷⠶⠶⠆⠀⠀⠒⠂⠒⠂⠒⠂⠒⠂⠒⠊⠒⠂⠚⠒⠀⡤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠸⠿⠶⠾⠾⠿⠿⠽⠴⠶⠆⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⡏⠿⠶⠷⠶⢶⣶⡶⠀⠸⠅⠷⠶⠶⠆⠸⠷⠲⠲⠶⠲⠆⠸⠀⠖⠶⠶⠾⠶⠶⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣇⡄⢴⠹⠱⠶⠆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡇⠠⠀⠀⣀⠀⠀⠀⠀⠀⠀⡸ ⡇⠟⠿⠿⠷⠀⠀⠀⠀⠈⠻⠳⠲⠶⠶⠶⠶⠂⠸⠷⠶⠲⠸⠶⠶⠀⠸⠶⠺⠺⠹⠻⠿⠻⠶⠖⠒⠦⠶⠷⠔⠀⣾⣺⡇⡇⢾⠼⠳⠖⠖⠆⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠃⠘⠀⠀⠈⠉⠀⠉⠁⠀⢸⡇ ⡿⠿⠖⠫⠷⠶⠇⠀⠀⠸⠷⠶⠲⠆⠸⠳⠾⠾⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⡯⠷⢿⢔⠘⠳⠶⠶⠲⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇ ⡟⠟⠳⠆⠃⠗⠶⠀⠀⠐⠶⠦⠔⠇⠸⠠⡆⠴⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷⠷⣻⠾⠷⠾⠷⠆⡞⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇ ⡇⠟⠛⠒⠒⠛⠃⠁⠀⠀⠇⠘⠳⠟⠛⠛⠃⠘⠚⠛⠺⠺⠚⠚⠲⠂⠾⠲⠐⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣿⠋⠟⠛⠱⠑⠇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢅ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠉⠀⠄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋ ⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠚⠛⠛⠛⠀⠛⠛⠛⠀⠋⠛⠋⠃⠃⠃⠓⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳ ⡇⠀⠀⠀⡀⠀⡀⠀⠀⡀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⢀⠀⣀⠀⢀⠀⡀⢀⠀⣀⣀⢀⠀⢀⣀⣀⠀⣀⣀⣀⣀⡀⣀⡀⠀⣀⣀⣀⠀⢀⢀⡀⢀⣀⣀⣀⣀⡀⢀⣀⣀⣀⣀⢀⠀⠀⡀⠀⠀⣀⣀⠀⠀⠀⢸ ⡇⢀⠁⠀⡛⠛⡻⠟⠃⡃⠈⡃⠂⠐⠘⡛⠛⠛⠙⢓⣛⠃⠀⠉⢛⣙⠃⠘⢀⠀⣙⠀⣛⣛⢚⠀⢛⣛⣓⠀⣛⣛⣋⡛⣛⣛⡋⡈⣋⡛⠛⡃⢉⣛⡉⢘⣛⣛⣛⣛⣛⣙⣋⣙⣛⣛⣛⡃⠀⡀⠀⠀⠀⠀⠀⠀⠀⢨ ⡇⠀⠀⠀⡛⠋⡻⠛⠃⡃⢘⡃⠀⠐⠙⡛⠛⠛⡙⢛⡛⠋⠀⢈⣛⣛⢁⢀⠘⢛⣛⠁⢛⣛⢈⠀⣛⣛⣃⡀⡛⣋⣛⣛⣛⣛⣛⣙⣛⣋⢑⡓⢙⣛⣋⣙⣛⣛⢛⣛⣚⣙⣛⡓⣛⣛⣛⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⠀⡋⠋⡙⠛⠃⡃⠀⡃⠂⠈⠙⡛⠛⠋⠙⢛⣙⡂⠀⣉⣉⣋⡁⢈⠀⣚⣛⠁⣙⢛⢈⠀⣚⣓⣛⠛⡋⣛⣛⣛⠉⣋⣋⣋⢋⣋⣉⣋⣙⣋⡙⢁⣋⡙⢚⣋⣁⣉⣛⣂⣈⣁⢉⣉⣉⣁⠀⠂⠀⠁⠀⠀⠀⢸ ⡇⠀⠀⠀⣉⡋⡛⣛⡁⡃⢈⡃⠀⠈⣙⣛⡙⡋⣘⢙⣙⡁⠀⣙⣛⣛⣁⠈⠀⣙⣙⠁⣙⣛⢈⠀⣙⢋⡛⡀⢛⣛⠋⡋⠈⣋⣉⣋⣉⣋⡋⠋⠙⠙⠛⠙⠛⠉⠙⠛⠋⠙⠙⠉⠛⠛⠉⠘⠉⠛⠁⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡍⣋⡙⣋⡁⡁⢀⡁⠀⠈⣉⣉⣉⡉⣈⣉⣙⡀⠀⣉⣉⣩⡁⢈⠀⠁⢈⠀⣈⣉⢈⠀⣭⣉⢉⣉⣩⣩⣈⢉⣀⣉⣉⢉⣉⣍⣁⣀⡄⣀⣀⡀⣀⣀⡤⣀⣠⡀⠀⠀⠀⠀⠀⠀⣀⣀⡀⡀⡀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠉⠉⣙⠋⠁⠁⠈⠉⡀⠈⠈⢉⠉⠉⠈⠉⠙⠃⠀⠉⠉⠙⢁⠈⢀⠀⠈⢀⠉⢉⣈⡀⠉⠉⠉⠉⢉⠉⠉⢈⡉⠉⡉⠉⣉⣉⣉⣉⣉⠉⢁⡉⡋⠉⢉⣉⡉⢁⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢸ ⡇⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠧⡀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠀⠐⠀⠤⣘⠀⠈⠀⠁⠀⠀⠀⠈⠒⠀⠀⠀⠁⡁⠀⠀⠲⠁⠀⠒⠐⠐⠴⠀⠀⠘⠈⢀⡀⢙⡢⠂⡰⠟⠀⠈⠊⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸ ⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣩⣦⡥⣤⢄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠄⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣠⡥⡡⡉⢁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠤⠤⠤⠄⠀⠤⠤⠀⠤⠤⠄⠠⠤⠄⠀⠤⠤⠀⠄⠤⠄⠠⠤⠤⠤⠄⠤⠄⠤⠤⠀⠤⠀⠤⠤⠀⠠⠤⠄⠠⠤⠄⠀⠤⠤⠤⠤⠤⠤⠤⠄⠠⠤⠤⠀⠤⠤⠤⠤⠀⠤⠤⠠⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠐⠂⠀⠀⠀⠀⠹⢷⠾⠴⠶⠶⠶⠆⠀⠀⠒⠂⠒⠂⠒⠂⠒⠂⠒⠊⠒⠂⠒⠒⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠸⠿⠶⠾⠾⠷⠿⠽⠴⠶⠆⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⡏⠿⠶⠷⠶⢶⣶⡶⠀⠸⠅⠷⠶⠶⠆⠸⠷⠲⠲⠶⠲⠆⠸⠀⠖⠶⠶⠾⠶⠶⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣇⡄⢴⠹⠱⠶⠆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡇⠠⠀⠀⣀⠀⠀⠀⠀⠀⠀⡸ ⡇⠟⠿⠿⠷⠀⠀⠀⠀⠈⠻⠳⠲⠶⠶⠶⠶⠂⠸⠷⠶⠲⠸⠶⠶⠀⠸⠶⠺⠾⠽⠻⠿⠻⠶⠖⠒⠦⠶⠷⠔⠀⢸⣸⡇⡇⢾⠼⠳⠖⠖⠆⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠃⠘⠀⠀⠈⠉⠀⠉⠁⠀⢸⡇ ⡿⠿⠖⠫⠷⠶⠇⠀⠀⠸⠷⠶⠲⠆⠸⠳⠾⠶⠁⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣾⡮⠷⢿⢔⠘⠳⠶⠶⠲⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇ ⡟⠟⠳⠆⠃⠟⠶⠀⠀⠐⠶⠦⠔⠇⠸⠠⡆⠴⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢼⡷⠷⣻⠾⠷⠾⠷⠆⡞⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇ ⡇⠟⠛⠒⠒⠛⠃⠁⠀⠀⠇⠘⠳⠟⠛⠛⠃⠘⠚⠛⠺⠺⠚⠚⠲⠂⠾⠲⠐⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⠋⠟⠛⠱⠑⠇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢅ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠈⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉ ⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠚⠚⠛⠛⠀⠛⠛⠛⠀⠋⠛⠋⠃⠃⠃⠚⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳ ⡇⠀⠀⠀⡀⠀⡀⠀⠀⡀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⢀⠀⣀⠀⢀⠀⡀⢀⠀⣀⡀⢀⠀⢀⣀⣀⠀⣀⣀⣀⣀⡀⣀⡀⠀⣀⣀⣀⠀⢀⢀⡀⢀⣀⣀⡀⣀⡀⢀⣀⣀⣀⣀⢀⠀⠀⡀⠀⠀⣀⣀⠀⠀⠀⢸ ⡇⢀⠁⠀⡛⠛⡻⠟⠃⡃⠈⡃⠂⠐⠘⡛⠛⠛⠙⢓⣛⠃⠀⠉⢛⣙⠁⠘⢀⠀⣉⠃⣛⣛⢚⠀⢛⣛⣓⠀⣛⣛⣋⡛⣛⣛⡋⡈⣋⡛⠛⡒⢉⣛⡉⢘⣛⣛⣛⣛⣛⣙⣋⣙⣛⣛⣛⡃⠀⡀⠀⠀⠀⠀⠀⠀⠀⢨ ⡇⠀⠀⠀⡛⠋⡻⠛⠃⡃⢘⡃⠀⠐⠙⡛⠛⠛⡙⢛⡛⠋⠀⢈⣛⣛⢁⢀⠘⢛⣛⠁⢛⣛⢈⠀⣛⣛⣃⡀⡛⣋⣛⣛⣛⣛⣛⣙⣛⣋⢑⡓⢙⣛⣋⣙⣛⣛⢛⣛⣚⣙⣛⡓⣛⣛⣛⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⠀⡋⠋⡙⠛⠃⡃⠀⡃⠂⠈⠙⡛⠛⠋⠙⢛⣙⡂⠀⣉⣉⣋⡁⢈⡀⣚⣛⠁⣙⢛⢈⠀⣚⣓⣛⠛⡋⣛⣛⣛⠉⣋⣋⣋⢋⣋⣉⣋⣙⣋⣙⢁⣋⡙⢚⣋⣁⣉⣛⣂⣈⣁⢉⣉⣉⣁⠀⠂⠀⠁⠀⠀⠀⢸ ⡇⠀⠀⠀⣁⡋⡛⣛⡁⡃⢈⡃⠀⠈⣙⣛⡙⡋⣘⢙⣙⡁⠀⣙⣛⣛⣁⠈⠀⣙⣙⠁⣙⣛⣈⠀⣙⢋⡛⡀⢛⣛⠋⡋⠈⣋⣙⣉⣉⣋⣋⠋⠙⠙⠛⠙⠛⠉⠙⠛⠋⠙⠙⠉⠛⠛⠉⠘⠉⠛⠁⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡍⣋⡙⣋⡁⡁⢀⡁⠀⠈⣉⣉⣉⡉⣈⣉⣉⡀⠀⣉⣉⣩⡁⢀⠀⠁⢈⠀⣈⣉⢈⠀⣭⣉⢉⢩⣩⢩⣈⢉⣀⣉⣉⢉⣋⣭⣩⣀⡄⣀⣀⡀⣀⣀⡤⣀⣠⡀⠀⠀⠀⠀⠀⠀⣀⣀⡀⡀⡀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠉⠉⣙⠋⠁⠁⠈⠉⡀⠈⠈⢉⠉⠉⠈⠉⠙⠃⠀⠉⠉⠙⢁⠈⢀⠀⠈⢀⠉⢉⣈⡀⠉⠉⠉⠉⢉⠉⠉⢈⡉⠉⡉⠉⣉⣉⣉⣉⣁⠉⢉⡉⡋⠉⢉⣉⡉⢁⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢸ ⡇⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠧⡀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠀⠐⠀⠤⣘⠀⠈⠀⠁⠀⠀⠀⠈⠒⠀⠀⠀⠁⡁⠀⠀⠲⠁⠀⠒⠐⠐⠴⠀⠀⠘⠈⢀⡀⢙⡢⠂⡰⠟⠀⠈⠊⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸ ⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣩⣦⡥⣤⢄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠄⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣠⡥⡡⡉⢁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠤⠤⠤⠄⠀⠤⠤⠀⠤⠤⠄⠠⠤⠄⠀⠤⠤⠀⠄⠤⠄⠠⠤⠤⠤⠄⠤⠄⠤⠤⠀⠤⠀⠤⠤⠀⠠⠤⠄⠠⠤⠄⠀⠤⠤⠤⠤⠤⠤⠤⠄⠠⠤⠤⠀⠤⠤⠤⠤⠀⠤⠤⠠⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠐⠂⠀⠀⠀⠀⠹⢷⠾⠴⠶⠶⠶⠆⠀⠀⠒⠂⠒⠂⠒⠂⠒⠂⠒⠂⠒⠂⠒⠒⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠸⠿⠶⠾⠾⠷⠿⠽⠴⠶⠆⠀⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⢠ ⡏⠿⠶⠷⠶⢶⣶⡶⠀⠸⠅⠷⠶⠶⠆⠸⠷⠲⠲⠶⠲⠆⠸⠀⠖⠶⠶⠾⠶⠶⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣇⡄⢴⠱⠱⠶⠆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠠⠀⠀⣀⠀⠀⠀⠀⠀⠀⡸ ⡇⠟⠿⠿⠷⠀⠀⠀⠀⠈⠻⠳⠲⠶⠶⠶⠶⠂⠸⠷⠶⠲⠸⠶⠶⠀⠸⠶⠺⠿⠽⠻⠿⠻⠶⠖⠒⠦⠶⠷⠔⠀⢸⣸⡇⡇⢾⠼⠳⠖⠖⠆⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠃⠘⠀⠀⠈⠉⠀⠉⠁⠀⢸⡇ ⡟⠻⠖⠫⠷⠶⠇⠀⠀⠸⠷⠶⠲⠆⠸⠳⠾⠶⠁⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣾⡮⠷⢿⢔⠘⠳⠶⠶⠲⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇ ⡟⠟⠳⠆⠃⠟⠶⠀⠀⠐⠶⠦⠔⠇⠸⠠⡆⠴⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢼⡷⠷⣻⠾⠷⠾⠷⠆⡞⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇ ⡇⠟⠛⠒⠒⠛⠃⠁⠀⠀⠇⠘⠳⠟⠛⠛⠃⠘⠚⠛⠺⠺⠚⠚⠲⠂⠾⠲⠐⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢘⠋⠟⠛⠱⠑⠇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢅ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠒⠀⠂⠐⠒⠒⠂⠐⠒⠀⠐⠀⠀⠒⢂⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉ ⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠚⠚⠛⠛⠀⠛⠛⠛⠀⠋⠛⠋⠃⠃⠃⠚⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳ ⡇⠀⠀⠀⡀⠀⡀⠀⠀⡀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⢀⠀⣀⠀⢀⠀⡀⢀⠀⣀⡀⢀⠀⢀⣀⣀⠀⣀⣀⣀⣀⡀⣀⡀⠀⣀⣀⣀⠀⢀⢀⡀⢀⣀⣀⡀⣀⡀⢀⣀⣀⣀⣀⢀⠀⠀⡀⠀⠀⣀⣀⠀⠀⠀⢸ ⡇⢀⠁⠀⡛⠛⡻⠟⠃⡃⠈⡃⠂⠐⠘⡛⠛⠛⠙⢓⣛⠃⠀⠉⢛⣙⠁⠘⢀⠀⣉⠃⣛⣛⢚⠀⢛⣛⣓⠀⣛⣛⣋⡛⣛⣛⡋⡈⣋⡛⠛⡒⢉⣛⡉⢘⣛⣛⣛⣛⣛⣙⣋⣙⣛⣛⣛⡃⠀⡀⠀⠀⠀⠀⠀⠀⠀⢨ ⡇⠀⠀⠀⡛⠋⡻⠛⠃⡃⢘⡃⠀⠐⠙⡛⠛⠛⡙⢛⡛⠋⠀⢈⣛⣛⢁⢀⠘⢛⣛⠁⢛⣛⢈⠀⣛⣛⣃⡀⡛⣋⣛⣛⣛⣛⣛⣙⣛⣋⢑⡓⢙⣛⣋⣙⣛⣛⢛⣛⣚⣙⣛⡓⣛⣛⣛⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⠀⡋⠋⡙⠛⠃⡃⠀⡃⠂⠈⠙⡛⠛⠋⠙⢛⣙⡂⠀⣉⣉⣋⡁⢈⡀⣚⣛⠁⣙⢛⢈⠀⣚⣓⣛⠛⡋⣛⣛⣛⠉⣋⣋⣋⢋⣋⣉⣋⣙⣋⣙⢁⣋⡙⢚⣋⣁⣉⣛⣂⣈⣁⢉⣉⣉⣁⠀⠂⠀⠁⠀⠀⠀⢸ ⡇⠀⠀⠀⣁⡋⡛⣛⡁⡃⢈⡃⠀⠈⣙⣛⡙⡋⣘⢙⣙⡁⠀⣙⣛⣛⣁⠈⠀⣙⣙⠁⣙⣛⣈⠀⣙⢋⡛⡀⢛⣛⠋⡋⠈⣋⣙⣉⣉⣋⣋⠋⠙⠙⠛⠙⠛⠉⠙⠛⠋⠙⠙⠉⠛⠛⠉⠘⠉⠛⠁⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡍⣋⡙⣋⡁⡁⢀⡁⠀⠈⣉⣉⣉⡉⣈⣉⣉⡀⠀⣉⣉⣩⡁⢀⠀⠁⢈⠀⣈⣉⢈⠀⣭⣉⢉⢩⣩⢩⣈⢉⣀⣉⣉⢉⣋⣭⣩⣀⡄⣀⣀⡀⣀⣀⡤⣀⣠⡀⠀⠀⠀⠀⠀⠀⣀⣀⡀⡀⡀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠉⠉⣙⠋⠁⠁⠈⠉⡀⠈⠈⢉⠉⠉⠈⠉⠙⠃⠀⠉⠉⠙⢁⠈⢀⠀⠈⢀⠉⢉⣈⡀⠉⠉⠉⠉⢉⠉⠉⢈⡉⠉⡉⠉⣉⣉⣉⣉⣁⠉⢉⡉⡋⠉⢉⣉⡉⢁⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢸ ⡇⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠧⡀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠀⠐⠀⠤⣘⠀⠈⠀⠁⠀⠀⠀⠈⠒⠀⠀⠀⠁⡁⠀⠀⠲⠁⠀⠒⠐⠐⠴⠀⠀⠘⠈⢀⡀⢙⡢⠂⡰⠟⠀⠈⠊⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸ ⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣩⣦⡥⣤⢄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠄⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣠⡥⡡⡉⢁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠤⠤⠤⠄⠀⠤⠤⠀⠤⠤⠄⠠⠤⠄⠀⠤⠤⠀⠄⠤⠄⠠⠤⠤⠤⠄⠤⠄⠤⠤⠀⠤⠀⠤⠤⠀⠠⠤⠄⠠⠤⠄⠀⠤⠤⠤⠤⠤⠤⠤⠄⠠⠤⠤⠀⠤⠤⠤⠤⠀⠤⠤⠠⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠸⢷⠾⠴⠶⠶⠶⠆⠀⠀⠒⠀⠒⠂⠒⠂⠒⠂⠒⠂⠒⠂⠒⠒⠀⡤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠸⠷⠶⠶⠮⠷⠾⠸⠴⠶⠂⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⡇⠿⠶⠷⠶⠶⡶⡶⠀⠰⠄⠶⠶⠶⠆⠸⠷⠲⠲⠶⠲⠆⠰⠀⠖⠶⠶⠾⠶⠶⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣪⣇⡄⢴⠱⠱⠶⠆⠄⠀⠀⠀⠀⠀⠀⠀⠾⠾⠲⠾⠾⠲⠾⠾⠠⠀⠀⣀⠀⠀⠀⠀⠀⠀⡸ ⡇⠏⠿⠿⠗⠀⠀⠀⠀⠈⠻⠲⠲⠶⠲⠶⠶⠂⠸⠷⠶⠶⠸⠷⠶⠀⠸⠶⠺⠷⠽⠻⠽⠻⠶⠖⠒⠦⠶⠷⠔⠀⢸⣻⡇⡇⢺⠴⠓⠖⠖⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠃⠘⠀⠀⠈⠉⠀⠉⠁⠀⢰⡇ ⡟⠻⠖⠫⠷⠶⠇⠀⠀⠨⠵⠶⠲⠆⠸⠣⠞⠆⠇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣾⡮⠷⢿⢄⠘⠳⠶⠶⠲⠶⠶⠶⠆⠀⠀⠸⠠⠹⠿⠀⠸⠢⠸⠷⠀⠽⠠⠙⠿⠀⠀⠀⢨⡇ ⡟⠛⠳⠆⠃⠗⠶⠀⠀⠐⠦⠦⠔⠆⠸⠠⡆⠠⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⡶⠷⣻⠾⠷⠾⠷⠆⡞⠇⠁⠀⠀⠀⠀⠀⠀⠻⠂⠻⠖⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇ ⡇⠛⠛⠒⠒⠓⠃⠁⠀⠀⠃⠐⠳⠓⠛⠛⠃⠘⠚⠚⠲⠺⠚⠐⠲⠂⠾⠒⠐⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⠋⠟⠛⠱⠑⠇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢅ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉ ⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳ ⡇⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⡀⣀⡀⠀⡀⢀⡀⡀⠀⣀⡀⡀⢀⣀⣀⡀⢀⣀⣀⡀⣀⣀⣀⡀⢀⣀⣀⣀⠀⢀⣀⡀⢀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⢨ ⡇⢀⠊⠛⠛⠛⣋⠛⡛⡓⠀⠘⠛⠛⠛⠀⠃⡀⠋⡃⠈⠛⡛⠃⡘⠛⠛⠂⠘⠛⠓⢋⡛⠛⢛⡃⢘⡛⡛⢙⡒⠙⠛⢃⢙⢛⠛⠛⠛⢚⡚⢛⠛⠛⢛⠛⣁⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨ ⡇⠀⠀⠀⠁⠀⠛⠈⠋⠓⠓⠂⠀⠋⠛⠋⠛⠋⠀⠃⠘⠛⠃⠀⠃⠂⠸⠛⠛⠛⠃⠈⠃⠘⠛⠃⠘⠃⠃⠘⠀⠘⠛⠙⠛⠚⠛⠻⠃⠘⠃⠘⠀⠀⠙⠁⠙⠋⠙⠘⠀⠀⠘⠀⠀⠀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⣀⠀⠀⠀⠀⣀⡀⠀⠀⣀⣀⡀⠀⡀⣀⣀⡀⢀⣀⣀⡀⢀⣀⣀⡀⢀⣀⣀⣀⢀⣀⣀⣀⡀⣀⡀⢀⡀⣀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠁⠀⠂⠀⠁⠀⠀⠀⢸ ⡇⠀⠉⠛⡋⠋⣉⠛⣋⣋⡀⠈⠉⣛⣉⡀⡁⡛⠋⡋⠈⣛⡋⠁⡈⠛⠋⡂⣘⣛⡃⢛⡛⢋⣛⡛⢛⡙⡋⢙⡊⢙⣛⣉⣙⢋⢋⣋⠙⢛⡘⢉⠙⠙⣙⡛⣀⡀⣀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠀⠉⠈⠉⠉⠁⠂⠀⠉⠉⠉⠉⠉⠀⠃⠈⠉⠁⠀⠃⠀⠘⠋⠉⠉⠁⠀⠁⠈⠉⠁⠈⠁⠁⠈⠀⠈⠉⠈⠉⠈⠉⠙⠃⠈⠁⠈⠀⠀⠉⠁⠉⠉⠈⠈⠀⠀⠈⠀⠀⠀⠀⠀⣀⡀⡀⡀⠀⠀⠀⠀⠀⢸ ⡇⠀⢀⣀⣀⣀⢀⣀⣀⡀⠀⢀⣄⣄⣀⠀⡄⠀⣄⣄⢀⣤⣄⡀⠀⣄⠄⣤⣤⢀⣄⣄⣀⣀⣠⣤⣄⣠⡄⣀⡀⣠⣄⣤⣤⣄⣠⢠⣤⣤⣀⣠⡀⠀⢀⡀⡀⠀⢀⣀⡀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢸ ⡇⠀⠁⠉⡍⠉⣅⢉⣍⣅⣀⠈⠉⣉⣉⣀⣁⣌⠉⡅⢈⣉⡍⠁⡄⠉⢉⣉⣉⣉⡉⢉⡍⢉⣉⡍⢉⡉⡄⢨⠉⢈⣉⣉⣨⢉⣉⣙⡋⢨⡈⢩⠀⠀⣠⡀⢩⣀⣀⢰⠉⠀⢈⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠀⠉⠀⠉⠉⠁⠁⠀⠉⠉⠉⡉⠁⠀⠁⠈⠉⠁⠀⠁⠁⠘⠉⠉⠉⠁⠈⠁⠈⠉⠁⠈⠁⠁⠈⠁⠈⠉⠈⠉⠉⠉⠙⠁⠈⠁⠈⠀⠀⠈⠁⠉⠉⠈⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸ ⡇⠀⣀⣤⣀⣀⣀⣀⣤⣤⠈⢠⣤⣤⣤⠁⡄⢠⣤⣄⢀⣤⣤⡄⢠⣤⣤⠄⢠⣤⣤⣤⡄⢠⣄⣤⣄⣠⣤⣤⢤⣤⣠⣀⣤⣤⣄⣠⣤⣤⣤⣤⣤⣤⣤⣠⢤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠁⠉⡍⠉⣤⢉⣭⡍⡀⠀⠉⣉⣉⣀⣁⣌⠉⡅⢀⣉⡅⠁⡌⠉⢉⣁⣈⣉⡉⠩⡅⢈⣩⡍⢡⡌⡍⢩⠍⢉⣉⣡⣨⢩⣀⣈⡉⢡⡍⢩⠉⠉⣩⡍⣩⣌⣈⢠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠀⠁⠀⠁⠉⠈⠁⠀⠁⠉⠁⠉⠁⠀⠁⠀⠁⠁⢀⠁⠁⠈⠉⢉⠉⢁⠀⠁⠈⠉⠀⠈⠁⠁⠈⠀⠈⠉⠈⠀⠈⡈⢉⠁⠈⠀⠈⠀⠀⠈⠀⠈⠁⠈⠈⠀⠀⠀⠀⠀⡈⣉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣠⣤⣭⣠⡠⣄⣤⡤⠀⢠⣤⣤⣤⠀⡄⢠⣤⡄⢠⣤⣤⡌⢡⣤⣄⣤⣤⣤⡄⢠⡄⠠⣤⣤⣤⣤⢤⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡄⠀⣤⢠⣤⣤⡤⡀⠀⣤⣤⣤⣤⣤⠀⡄⢀⣤⡄⠀⡄⡀⢠⣤⣤⣤⡄⢠⡄⢠⣤⡄⢠⡄⡄⢠⡀⢠⣤⢤⣤⣤⣤⣤⡄⢠⡄⢠⠀⠀⣤⡄⣰⣤⢤⢠⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣩⣦⡥⣤⢄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠄⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡠⡥⡡⡉⢁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣶⣤⡤⣤⠀⣼ ⠧⠤⠤⠤⠤⠤⠤⠤⠄⠤⠠⠤⠄⠀⠤⠤⠤⠄⠀⠤⠤⠀⠤⠤⠄⠠⠤⠄⠀⠤⠤⠀⠄⠤⠄⠠⠤⠤⠤⠄⠤⠄⠤⠤⠀⠤⠀⠤⠤⠀⠠⠤⠄⠠⠤⠄⠀⠤⠤⠤⠤⠤⠠⠤⠄⠠⠤⠤⠀⠤⠤⠤⠤⠀⠤⠤⠠⠴ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠸⢷⠾⠴⠶⠶⠶⠆⠀⠀⠒⠀⠒⠂⠒⠂⠒⠂⠒⠂⠒⠂⠒⠒⠀⡤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠸⠷⠶⠶⠮⠷⠾⠸⠴⠶⠂⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⡇⠿⠶⠷⠶⠶⡶⡶⠀⠰⠄⠶⠶⠶⠆⠸⠷⠲⠲⠶⠲⠆⠰⠀⠖⠶⠶⠾⠶⠶⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡾⣇⡄⢴⠱⠱⠶⠆⠄⠀⠀⠀⠀⠀⠀⠀⠾⠾⠲⠾⠾⢰⠾⠮⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡸ ⡇⠏⠿⠿⠗⠀⠀⠀⠀⠈⠻⠲⠲⠶⠲⠶⠶⠂⠸⠷⠶⠶⠸⠷⠶⠀⠸⠶⠺⠷⠽⠻⠽⠻⠶⠖⠒⠦⠶⠷⠔⠀⠀⡷⠃⡇⢺⠴⠓⠖⠖⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠈⠉⠀⠉⠁⠀⢰⡇ ⡟⠻⠖⠫⠷⠶⠇⠀⠀⠨⠵⠶⠲⠆⠸⠣⠞⠆⠇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⡯⠷⢿⢄⠘⠳⠶⠶⠲⠶⠶⠶⠆⠀⠀⠸⠤⠹⠿⠄⠸⠢⠸⠷⠀⠹⠤⠝⠿⠤⠀⠀⢨⡇ ⡟⠛⠳⠆⠃⠗⠶⠀⠀⠐⠦⠦⠔⠆⠸⠠⡆⠠⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⡶⠷⣻⠾⠷⠾⠷⠆⡞⠇⠁⠀⠀⠀⠀⠀⠀⠋⣂⠛⢒⠒⡀⠀⠈⠀⠀⠀⠁⠀⠀⠀⢨⡇ ⡇⠛⠛⠒⠒⠓⠃⠁⠀⠀⠃⠐⠳⠓⠛⠛⠃⠘⠚⠚⠲⠺⠚⠐⠲⠂⠾⠒⠐⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠋⠟⠛⠱⠑⠇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⣋⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢅ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠟⡓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉ ⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳ ⡇⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⡀⣀⡀⠀⡀⢀⡀⡀⠀⣀⡀⡀⢀⣀⣀⡀⢀⣀⣀⡀⣀⣀⣀⡀⢀⣀⣀⣀⠀⢀⣀⡀⢀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⢨ ⡇⢀⠊⠛⠛⠛⣋⠛⡛⡓⠀⠘⠛⠛⠛⠀⠃⡀⠋⡃⠈⠛⡛⠃⡘⠛⠛⠂⠘⠛⠓⠋⡛⠛⢛⡃⠘⠛⡛⢙⡒⠙⠛⢃⢙⢛⠛⠛⠛⢚⡚⢛⠛⠛⢛⠛⣁⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨ ⡇⠀⠀⠀⠁⠀⠛⠀⠃⠓⠓⠂⠀⠋⠛⠋⠛⠋⠀⠆⠈⠛⠃⠀⠃⠂⠸⠛⠛⠛⠃⠐⠢⠘⠛⠃⠀⠒⠓⠘⠀⠘⠛⠙⠛⠚⠛⠻⠃⠘⠃⢘⠀⠀⠙⠁⠙⠋⠙⠘⠀⠀⠘⠀⠀⠀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⣀⠀⠀⠀⠀⣂⡄⠀⠀⣀⣀⡀⠀⡀⣀⣀⡀⢀⣀⣖⡀⡆⡀⣀⡀⢀⣀⣀⣀⡂⣀⣀⡀⡀⡄⡀⢀⡀⣀⣀⡀⣀⣀⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠁⠀⠂⠀⠁⠀⠀⠀⢸ ⡇⠀⠉⠛⡋⠋⣉⠃⣀⣀⡀⠈⠉⣛⣉⡀⡁⡛⠋⡋⠈⣛⡋⠁⡈⠛⠋⡂⣘⣛⡃⢛⡛⢋⣛⡛⢛⡙⡋⢙⡊⢙⣛⣉⣙⢋⢋⣋⠙⢛⡘⢉⠙⠙⣙⡉⣀⡀⣀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠀⠉⠈⠉⠉⠁⠂⠀⠉⠉⠉⠉⠉⠀⠃⠈⠉⠁⠀⠃⠀⠘⠋⠉⠉⠁⠀⠁⠈⠉⠁⠈⠁⠁⠈⠀⠈⠉⠈⠉⠈⠉⠙⠃⠈⠁⡌⠀⠀⠉⠁⠉⠉⠈⠈⠀⠀⠈⠀⠀⠀⠀⠀⣀⡀⡀⡀⠀⠀⠀⠀⠀⢸ ⡇⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⢀⣄⣄⣀⠀⡄⠀⣄⡈⢀⣤⣄⡀⠀⣄⠄⣤⣤⢀⣄⣄⣀⣀⣠⣤⣄⣠⡄⣀⡁⣠⣌⣤⣤⣍⣠⢠⣤⣤⣀⣠⡈⠀⢀⡀⡀⠀⢀⣀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢸ ⡇⠀⠁⠉⡍⠉⣅⢉⣉⣁⣀⠊⠉⣉⣉⣀⣁⣌⠉⡅⢈⣉⡍⠁⡅⠉⢉⣉⣉⣉⡉⢉⡍⢉⣉⡅⢉⡉⡄⢨⠉⢈⣉⣉⣨⢉⣉⣙⡋⢨⡈⢩⠀⠀⣀⡀⢩⣀⣀⢰⠉⠀⢀⠘⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠀⠉⠀⠉⠉⠁⠁⠀⠉⠉⠉⡉⠁⠀⡁⠈⠉⠁⠀⠁⠁⠘⠉⠉⠉⠁⠈⠁⠈⠉⠁⠈⠁⠁⠈⠁⠈⠉⠈⠉⠉⠉⠙⠁⠈⠁⠈⠀⠀⠈⠁⠉⠉⠈⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸ ⡇⠀⣀⣤⣀⣀⣀⣀⣤⣤⠈⢠⣤⣤⣤⠁⡄⢠⣤⣄⢀⣤⡤⡄⢠⣤⣤⠄⢠⣤⣤⣤⡄⢠⣄⣤⡄⠠⣤⣤⢤⣤⣠⣀⣤⣤⣆⣠⣤⣤⣤⣤⣤⣤⣤⣠⢠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠁⠉⡍⠩⣇⠉⢭⡍⡂⠀⠉⣉⣉⣀⣁⣌⠉⡅⢀⣉⡅⠁⠍⠉⢉⣁⣈⣉⡉⠩⡇⢈⣩⡍⢠⡍⠍⢩⠍⢉⣉⣡⣬⠭⢒⣌⡉⢡⡍⢩⠉⠉⣩⡍⣩⣌⣈⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠀⠁⠀⠁⠉⠈⠁⠀⠁⠉⠁⠉⠁⠀⠁⠀⠁⠁⢀⠁⠁⠈⠉⢉⠉⢁⠀⠁⠈⠉⠀⠈⠁⠁⠈⠀⠈⠁⠈⠀⠈⡈⢉⠁⠈⠀⠈⠀⠀⠈⠀⠈⠁⠈⠈⠀⠀⠀⠀⠀⡈⣉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢠⣤⣭⣠⡠⣄⣤⡤⠀⢠⣤⣶⣤⠀⡄⢠⣤⡆⢠⣤⣤⡌⢡⣤⣄⣤⣤⣤⡄⢢⡄⠠⣤⣤⣤⣤⣤⡦⠐⢢⡆⠀⠀⠀⠈⠀⠀⠐⢀⠆⢅⠄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡄⠀⣦⢠⣤⣤⡤⡀⠀⣤⣤⣤⣤⣤⠀⡄⢀⣤⡄⠀⡆⡀⢠⣤⣤⣤⡄⠠⡄⢠⣤⡄⢀⡤⡄⢠⡀⢠⣤⢤⣤⣤⣠⣤⡄⢠⡄⢠⠀⠀⢀⡄⣰⣤⢤⢠⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠄⠀⠀⠀⠀⠤⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠈⠀⣩⣦⡤⣄⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣤⠀⠀⠀⠀⠄⠀⣀⣀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡠⡥⡡⡉⢋⠑⠀⠂⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣶⣤⡤⣤⠀⣼ ⠧⠤⠤⠤⠤⠤⠤⠤⠄⠤⠠⠤⠄⠀⠤⠤⠤⠄⠀⠤⠤⠀⠤⠤⠄⠠⠤⠄⠀⠤⠤⠀⠄⠤⠄⠠⠤⠤⠤⠄⠤⠄⠤⠤⠀⠤⠀⠤⠤⠀⠠⠤⠄⠠⠤⠄⠀⠤⠤⠤⠤⠤⠠⠤⠄⠠⠤⠤⠀⠤⠤⠤⠤⠀⠤⠤⠠⠴ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠸⢷⠾⠴⠶⠶⠶⠆⠀⠀⠒⠀⠒⠂⠒⠂⠒⠂⠒⠂⠒⠂⠒⠒⠀⡤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠸⠷⠶⠶⠮⠦⠾⠸⠴⠶⠂⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⡇⠿⠶⠷⠶⠶⡶⡶⠀⠰⠄⠶⠶⠶⠆⠸⠷⠲⠲⠶⠲⠆⠰⠀⠖⠶⠶⠾⠶⠶⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡾⣇⡄⢴⠱⠱⠶⠆⠄⠀⠀⠀⠀⠀⠀⠀⠾⠾⠲⠾⡾⢰⠾⠮⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡸ ⡇⠏⠿⠿⠗⠀⠀⠀⠀⠈⠻⠲⠲⠶⠲⠶⠶⠂⠸⠷⠶⠶⠸⠷⠶⠀⠸⠶⠺⠷⠽⠳⠽⠻⠶⠖⠒⠦⠶⠷⠔⠀⠀⡷⠇⡇⢺⠴⠓⠖⠖⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠁⠀⢰⡇ ⡟⠻⠖⠫⠷⠶⠇⠀⠀⠨⠵⠶⠲⠆⠸⠣⠞⠆⠇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⡯⠷⢿⢄⠘⠳⠶⠶⠲⠶⠶⠶⠆⠀⠀⠸⠠⠹⠿⠄⠸⠄⠸⠷⠀⠹⡤⠝⡿⠤⠀⠀⢨⡇ ⡟⠛⠳⠆⠃⠗⠶⠀⠀⠐⠦⠦⠔⠆⠸⠠⡆⠠⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⡶⠷⣻⠾⠷⠾⠷⠆⡞⠇⠁⠀⠀⠀⠀⠀⠁⠁⡂⠋⣒⠐⡀⠀⠈⠀⠀⠀⠁⠀⠀⠀⢨⡇ ⡇⠛⠛⠒⠒⠓⠃⠁⠀⠀⠃⠐⠳⠓⠓⠛⠃⠘⠚⠚⠲⠺⠚⠐⠲⠂⠾⠒⠐⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠋⠟⠛⠱⠑⠇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢅ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠟⡓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉ ⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳ ⡇⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⡀⣀⡀⠀⡀⢀⡀⡀⠀⣀⡀⡀⢀⣀⣀⡀⢀⣀⣀⡀⣀⣀⣀⡀⢀⣀⣀⣀⠀⢀⣀⡀⢀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⢨ ⡇⢀⠊⠛⠛⠛⣋⠛⡛⡓⠀⠘⠛⠛⠛⠀⠃⡀⠋⡃⠈⠛⡛⠃⡘⠛⠛⠂⠘⠛⠓⠋⡛⠛⠛⡃⠘⠛⡛⢙⡒⠙⠛⢃⢙⢛⠛⠛⠛⢚⡚⢛⠛⠛⢛⠛⣁⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨ ⡇⠀⠀⠀⠁⠀⠛⠀⠃⠓⠓⠂⠀⠋⠛⠋⠛⠋⠀⠆⠈⢛⠃⠀⠃⠂⠸⠛⠛⠛⠃⠐⠢⠈⠓⠃⠀⠒⠓⠘⠀⠘⠛⠙⠛⠚⠓⠻⠃⠘⠃⢘⠀⠒⠛⡑⠛⠋⠙⠘⠀⠀⠘⠀⠀⠀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⣀⠀⠀⠂⠀⣦⣦⡀⠀⣀⣀⡀⠀⡀⣀⣀⡀⢀⣀⣖⡀⡆⡀⣀⡀⢀⣀⣀⣀⡆⣀⣀⡀⡀⡄⡀⢀⡀⣀⣀⡀⣀⣀⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠁⠀⠂⠀⠁⠀⠀⠀⢸ ⡇⠀⠉⠛⡋⠋⣁⠃⣀⣀⡀⠈⠉⣛⣉⡀⡁⡛⠋⡋⠈⣛⡋⠁⡈⠛⠋⡂⣘⣛⡃⢛⡛⢋⣛⡙⢛⡙⡋⢙⡊⢙⣛⣉⣙⢃⢋⣋⠑⢛⡘⢉⠙⠁⣘⡉⣀⡀⣀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠀⠉⠈⠉⠉⠁⠂⠀⠉⠉⠉⠉⠉⠀⠃⠈⠉⠁⠀⠁⡀⠘⠋⠉⠉⠁⠀⠁⠈⠉⠁⠈⠁⠁⠈⠀⠈⠉⢌⠉⠈⠉⠙⠃⠈⢁⡌⣤⠀⢉⠁⠉⠉⠈⠈⠀⠀⠈⠀⠀⠀⠀⠀⣀⡀⡀⡀⠀⠀⠀⠀⠀⢸ ⡇⠀⢀⣀⣀⣀⣀⣀⣄⡀⠀⢀⣄⣄⣀⠀⡀⠀⣄⡀⢀⣤⣄⡀⡀⣄⠄⣤⣤⢀⣄⣄⣀⣀⣠⣤⣄⣠⡄⣀⡁⣠⣌⣌⣤⡉⣠⢠⣤⣤⣀⣠⠈⠁⢁⡉⡀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢸ ⡇⠀⠁⠉⡉⠉⣅⢉⣉⣓⣁⠊⠉⣉⣉⣀⣁⣌⠉⡅⢈⣉⡍⠁⡅⠉⢉⣉⣉⣉⡉⢉⡍⢉⣉⡄⢉⡉⡄⢨⠉⢈⣉⣁⣨⢉⣉⣙⡋⢨⡈⢩⠀⠀⣀⡀⢩⣀⣀⢰⠉⠀⢀⠁⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠀⠉⠀⠉⠉⠁⠁⠀⠉⠉⠉⡉⠁⠀⡁⠈⠉⠁⠀⠁⠁⠘⠉⠉⠉⠁⠈⠁⠈⠉⠁⠈⠁⠁⠈⠁⠈⠉⠈⠉⠉⠉⠙⠁⠈⠁⠈⠀⠀⠈⠁⠉⠉⠈⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸ ⡇⠀⣀⣤⣀⣀⡀⡀⠤⠤⠈⢠⣤⣤⣤⠁⡄⢠⣤⡄⢀⣤⡤⡄⢠⣤⣤⠄⢠⣤⣤⣤⡄⢠⣄⣤⡄⠠⣤⣤⢤⣤⣠⣀⣤⣤⣆⣠⣤⣤⣤⣤⣤⡤⠤⡠⠠⠤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠁⠉⡍⠩⣇⠉⠝⠯⡂⠀⠉⣉⣁⣀⣁⣌⠉⡅⢀⡉⡅⠁⠍⠉⢉⣁⣈⣉⡉⠩⡇⢈⣩⠍⢠⡯⠍⢩⠍⢉⣉⣁⢬⠭⢒⣌⡉⢡⡍⢩⠉⠐⠯⠅⠸⠿⠷⠲⠆⠇⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠀⠁⠀⠁⠀⠈⠁⠀⠁⠉⠁⠉⠁⠀⠁⠀⠁⠁⢀⠁⠁⠈⠉⢉⠉⢁⠀⠁⠈⠉⠀⠈⠁⠀⠀⠀⠈⠁⠈⠀⠈⡈⢉⠁⠈⠀⠈⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡈⣉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢠⣤⣭⣠⡠⣄⣤⡤⠀⢠⣤⣴⣤⠀⡄⢠⡤⡖⢠⣴⣤⡈⢡⣤⣄⣶⣤⣤⡄⢢⡄⠠⣦⣤⣤⣤⣤⡤⠐⢢⡆⠀⢀⠀⠈⠀⠀⠐⢐⠆⢅⠄⠰⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡄⠀⣦⢠⣦⣦⡤⡀⠀⣤⣤⣤⣤⣤⠀⡄⢀⣤⡆⠀⡄⡀⢠⣤⣤⣤⡄⠀⡄⢠⣤⡄⢀⡆⡄⢠⡀⢠⣤⢤⣤⣤⣠⣤⡄⢠⡄⢠⠀⢰⣦⡆⢰⣶⣆⢤⡄⡆⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡀⠀⣀⠀⠀⠄⠀⠀⠠⠤⠀⠀⠄⠀⣄⠀⠀⠤⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠈⠀⣩⣦⡄⣄⡀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⣤⠀⠀⠀⠁⠄⠀⣀⣀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⣄⡄⢀⣤⡄⣀⡀⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡠⡥⡡⡉⢛⠛⠁⠂⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠈⠁⠀⠁⠀⠀⠀⠀⠃⠀⢀⡀⠀⠀⠀⠂⢤⠁⠀⠀⠀⠀⠀⠀⠀⠋⠃⠈⠙⠋⠉⠃⠃⠀⠀⠁⠀⢀⡀⠀⠀⠀⠀⣶⣤⡤⣤⠀⣼ ⠧⠤⠤⠤⠤⠤⠤⠤⠄⠤⠠⠤⠄⠀⠤⠤⠤⠄⠀⠤⠤⠀⠤⠤⠄⠠⠤⠄⠀⠤⠤⠀⠄⠤⠄⠠⠤⠤⠤⠄⠤⠄⠤⠤⠀⠤⠀⠤⠤⠀⠠⠤⠄⠠⠤⠄⠀⠤⠤⠤⠤⠤⠠⠤⠄⠠⠤⠤⠀⠤⠤⠤⠄⠀⠤⠤⠠⠴ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠸⢷⠾⠴⠶⠶⠶⠆⠀⠀⠒⠀⠒⠂⠒⠂⠒⠂⠒⠂⠒⠂⠒⠒⠀⡤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠸⠷⠶⠶⠮⠦⠾⠸⠴⠶⠂⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⡇⠿⠶⠷⠶⠶⠶⡶⠀⠰⠄⠶⠶⠶⠆⠸⠷⠲⠲⠶⠲⠂⠰⠀⠖⠶⠶⠾⠶⠶⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡎⣇⡄⢴⠱⠱⠶⠆⠄⠀⠀⠀⠀⠀⠀⠀⠾⠾⠲⡾⡾⢤⢾⣆⡆⠀⠀⣀⠀⠀⠀⠀⠀⠀⡸ ⡇⠏⠿⠿⠗⠀⠀⠀⠀⠈⠻⠲⠲⠶⠲⠶⠶⠂⠸⠷⠶⠶⠸⠷⠶⠀⠸⠶⠺⠷⠽⠳⠽⠻⠶⠖⠒⠦⠶⠷⠔⠀⠀⡇⠧⡇⢺⠴⠓⠖⠖⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠁⠀⠀⠈⠉⠀⠉⠁⠀⢰⡇ ⡟⠻⠖⠫⠷⠶⠇⠀⠀⠨⠵⠶⠲⠆⠸⠣⠞⠄⠇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⡯⠷⢿⢄⠘⠳⠶⠶⠲⠶⠶⠶⠆⠀⠀⠸⡀⠹⡿⠄⠸⠄⠘⠧⠀⠹⡄⠝⡿⠤⠀⠀⢨⡇ ⡟⠛⠳⠆⠃⠗⠶⠀⠀⠐⠦⠦⠔⠆⠸⠠⡆⠠⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡶⠷⣻⠾⠷⠾⠷⠆⡞⠇⠁⠀⠀⠀⠀⠀⣁⡀⡄⢁⣠⡕⣀⡀⠈⠀⠀⠀⠉⠀⠀⠀⢨⡇ ⡇⠛⠛⠒⠒⠓⠃⠁⠀⠀⠃⠐⠱⠓⠓⠛⠃⠘⠚⠚⠲⠺⠚⠐⠲⠂⠾⠒⠐⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡗⡋⠟⠛⠱⠑⠇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⠛⠋⡁⠘⠙⠛⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢅ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⡓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉ ⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡ ⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⠀⡀⢀⡀⡀⠀⣀⡀⡀⢀⣀⣀⡀⢀⣀⣀⡀⣀⣀⣀⡀⢀⣀⣀⣀⠀⢀⣀⡀⢀⣀⣀⢀⣀⣀⣀⣀⣀⣀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⢨ ⡇⢀⠊⠛⠛⠛⣋⠛⡛⡓⠀⠘⠛⠛⠛⠀⠃⡀⠋⡃⠈⠛⡛⠃⡘⠛⠛⠂⠘⠛⠓⠋⡛⠛⠛⡃⠘⠛⡛⢙⡒⠙⠛⢃⢙⢛⠛⠛⠛⢚⡚⢛⠛⠛⢛⠛⣁⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨ ⡇⠀⠀⠀⠁⠀⠛⠀⠃⠃⠓⠂⠀⠋⠛⠋⠛⠋⠀⠆⠈⢛⠃⠀⠃⠂⠸⠛⠛⠛⠃⠐⠢⠈⠓⠃⠀⠓⠓⠘⠀⠘⠛⠙⠛⠚⠓⠺⠃⠘⠃⢘⠀⠒⠛⡑⠛⠋⠙⠘⠀⠀⠘⠀⠀⠀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⣀⠀⠀⠒⡀⣆⣶⠄⠀⣀⣀⡀⠀⡀⣀⣀⡀⢀⣀⣖⡀⡆⡀⣀⡀⢀⣀⣀⣀⡆⣀⣀⡀⠀⡆⡀⢀⡀⣀⣀⡀⢀⡀⣆⣀⣀⣀⣀⣀⣀⠐⡖⡆⢰⣶⣦⢤⡄⡆⠀⠀⡆⠁⠉⠉⠉⠁⠀⠂⠀⠁⠀⠀⠀⢸ ⡇⠀⠉⠛⡋⠋⣁⠃⣀⣀⡀⠈⠉⣛⣉⡀⡁⡛⠋⡋⠈⣛⡋⠁⡈⠛⠋⡂⣘⣛⡃⢛⡛⢋⣛⡙⢓⡐⡂⢙⡊⢙⣛⣉⣙⢃⢋⣋⠑⢛⡘⢉⠙⠁⣀⡀⣀⡀⣀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠀⠉⠈⠉⠉⠁⠂⠀⠉⠉⠉⠉⠉⠀⣃⠈⠉⠁⠀⠁⡀⠘⠋⠉⠉⠁⠀⠁⠈⠉⠁⠈⠁⠁⠈⡀⠈⠉⣮⠉⠈⠉⠙⠃⠈⢡⡎⣤⠄⣉⡁⠉⠉⠈⠈⠀⠀⠈⠀⠀⠀⠀⠀⣀⡀⡀⡀⠀⠀⠀⠀⠀⢸ ⡇⠀⢀⣀⣀⢀⣄⣀⣤⣤⡀⢀⣄⣄⣀⠀⡀⠀⡄⡄⢀⣤⣄⡀⡀⣄⠄⣤⣤⢀⣄⣤⣄⣀⣠⡤⣄⡠⡄⣈⡁⣠⣌⣄⣤⡉⣄⢠⣤⣤⣀⣠⠄⠡⡥⡍⢡⣤⣄⣀⡀⡄⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢸ ⡇⠀⠁⠉⡉⠈⣅⢉⣉⣉⣁⠉⠉⣉⣉⣀⣁⡌⠉⡅⢈⣉⡍⠁⡅⠁⢉⣉⣉⣉⡉⢉⡍⢉⣉⡅⢉⡉⡄⢨⠉⢈⣉⣁⣩⢉⣉⣙⡋⢨⡈⢩⠀⠀⣉⡁⢈⣉⣉⢈⠁⠁⢀⠀⠁⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠀⠉⠀⠉⠉⠁⠁⠀⠉⠉⠉⡉⠁⢀⡁⠈⠉⠁⠀⠁⠁⠘⠉⠉⠉⠁⠀⠁⠈⠉⠁⠈⠁⠁⠈⠁⠈⠉⠈⠉⠉⠉⠙⠁⠈⠁⠈⠀⠀⠈⠁⠉⠉⠈⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸ ⡇⠀⣀⣤⣀⣀⡀⡀⠤⠤⠈⢠⣤⣤⣤⠁⡄⢠⣤⡄⢀⣤⡤⡄⣠⣤⣤⠄⢠⣤⣤⣤⡄⢠⣄⣤⡄⡠⣤⣤⢤⣥⣠⣀⣤⣤⣂⣠⣤⣤⣤⣤⣤⡄⣀⡀⠀⣀⠠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠁⠉⡍⠩⣇⠉⠝⠏⡂⠀⠉⣉⣁⣀⣁⡌⠉⡅⢀⡉⡅⠁⠅⠏⢉⣁⣈⣉⡉⠩⡇⢈⣩⠍⢠⡯⠍⢩⠉⢉⠉⠁⢮⠍⢓⣌⡉⢡⡍⢩⠉⠐⠗⠃⠸⠿⠷⠲⠆⠇⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠀⠁⠀⠁⠀⠈⠁⠀⠁⠉⠁⠉⠁⠀⠁⠀⠁⠁⢀⠁⠁⠈⠉⢉⠉⢁⠀⠁⠈⠉⠀⠈⠁⠀⠀⠀⠈⠁⠈⠀⠈⡈⢉⠁⠈⠀⠈⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡈⣉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢠⣤⣭⣠⡠⣄⣤⡤⠀⢠⣤⣼⣤⠀⡄⢨⠼⡗⢠⣽⣥⠀⢡⣤⣅⣾⣤⣤⡄⢫⡄⠨⣧⣤⣤⣤⣬⡾⠙⢻⠗⠃⢠⠀⠈⠀⠀⠐⢰⠖⢇⠌⠸⠁⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡄⠀⣦⠠⡦⡦⠤⠀⠀⣤⣤⣤⣤⣄⠀⡅⢀⣤⡆⠀⡇⠀⢠⣤⣤⣤⡄⠀⡆⢠⣤⡄⢀⡇⡄⢠⡀⢠⣤⢄⣶⣤⣠⣤⡄⢠⡄⢠⠀⠰⠦⠆⢰⣶⣆⢤⡄⡆⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⢀⡀⠀⡀⠀⢀⠀⠀⠆⠀⠀⠠⠦⠂⠀⠆⠀⣤⠀⠀⠦⠀⠀⠠⠦⠀⠀⢀⡀⠀⠀⠀⠀⡀⠄⢠⠄⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠈⠀⡉⢠⡄⣄⡀⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡂⣤⡀⠀⠀⠁⠄⠀⣀⣀⡀⠀⠀⡀⠀⡀⠀⠀⡀⠀⠀⠀⠀⡄⡄⠀⠀⠀⠀⠀⡀⠠⡤⡄⢀⣤⡄⣀⡀⡄⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡠⡤⡡⡉⢙⠛⠁⠂⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠃⠀⢀⡀⠀⠀⠀⠂⢤⠁⠀⠀⠀⠀⠀⠀⠀⠁⠁⠈⠉⠉⠁⠃⠃⠀⠀⠁⠀⢀⡀⠀⠀⠀⠀⣶⣤⡤⣤⠀⣼ ⠧⠤⠤⠤⠤⠤⠤⠤⠄⠤⠠⠤⠄⠀⠤⠤⠤⠄⠀⠤⠤⠀⠤⠤⠄⠠⠤⠄⠀⠤⠤⠀⠄⠤⠄⠠⠤⠤⠤⠄⠤⠄⠤⠤⠀⠤⠀⠤⠤⠀⠠⠤⠄⠠⠤⠄⠀⠤⠤⠤⠤⠤⠠⠤⠄⠠⠤⠤⠀⠤⠤⠤⠄⠀⠤⠤⠠⠴ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠸⢷⠾⠴⠶⠶⠶⠆⠀⠀⠒⠀⠒⠂⠒⠂⠒⠂⠒⠂⠒⠂⠒⠒⠀⡤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠸⠷⠶⠶⠮⠦⠾⠸⠴⠶⠂⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⡇⠿⠶⠷⠶⠶⠶⡶⠀⠰⠄⠶⠶⠶⠆⠸⠷⠲⠲⠶⠲⠂⠰⠀⠖⠶⠶⠾⠶⠶⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡎⣇⡄⢴⠱⠁⠀⡆⠄⠀⠀⠀⠀⠀⠀⠀⠾⠾⠲⡾⡾⢤⢾⣆⡆⠀⠀⣀⠀⠀⠀⠀⠀⠀⡸ ⡇⠏⠿⠿⠗⠀⠀⠀⠀⠈⠻⠲⠲⠶⠲⠶⠶⠂⠸⠷⠶⠶⠸⠷⠶⠀⠸⠶⠺⠷⠽⠳⠽⠻⠶⠖⠒⠦⠶⠷⠔⠀⠀⡇⠧⡇⢺⠴⠃⠄⡇⣖⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠁⠀⠀⠈⠉⠀⠉⠁⠀⢰⡇ ⡟⠻⠖⠫⠷⠶⠇⠀⠀⠨⠵⠶⠲⠆⠸⠣⠞⠄⠇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⡯⠷⢿⢄⠘⠳⡇⡶⠲⠶⠶⠶⠆⠀⠀⠸⡀⠹⡿⠄⠸⠄⠘⠧⠀⠹⡄⠝⡿⠤⠀⠀⢨⡇ ⡟⠛⠲⠆⠃⠗⠶⠀⠀⠐⠦⠦⠔⠆⠸⠠⡆⠠⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡶⠷⣻⠾⠷⠮⠇⠇⡞⠇⠁⠀⠀⠀⠀⠀⣁⡀⡄⢁⣠⡕⣀⡀⠈⠀⠀⠀⠉⠀⠀⠀⢨⡇ ⡇⠛⠛⠒⠒⠓⠃⠁⠀⠀⠃⠐⠱⠓⠓⠛⠃⠘⠚⠚⠲⠺⠚⠐⠲⠂⠾⠒⠐⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡗⡋⠟⠛⠱⠑⠇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⠛⠋⡁⠘⠙⠛⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢅ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⡓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉ ⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡ ⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⠀⡀⢀⡀⡀⠀⣀⡀⡀⢀⣀⣀⡀⢀⣀⣀⡀⣀⣀⣀⡀⢀⣀⣀⣀⠀⢀⣀⡀⢀⣀⣀⢀⣀⣀⣀⣀⣀⣀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⢨ ⡇⢀⠊⠛⠛⠛⣋⠛⡛⡓⠀⠘⠛⠛⠛⠀⠃⡀⠋⡃⠈⠛⡛⠃⡘⠛⠛⠂⠘⠛⠓⠋⡛⠛⠛⡃⠘⠛⡛⢙⡒⠙⠛⢃⢙⢛⠛⠛⠛⢚⡚⢛⠛⠛⢛⠛⣁⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨ ⡇⠀⠀⠀⠁⠀⠛⠀⠃⠃⠓⠂⠀⠋⠛⠋⠛⠋⠀⠆⠈⢛⠃⠀⠃⠂⠘⠛⠛⠛⠃⠐⠢⠈⠓⠃⠀⠳⠓⠘⠀⠘⠋⠻⠿⠚⠓⠺⠃⠘⠃⢘⠀⣒⢛⡕⠛⠋⠙⠘⠀⠀⠘⠀⠀⠀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⣀⠀⠀⠒⡀⣆⣶⠄⠀⣀⣀⡀⠀⡀⣀⣀⡀⢀⣀⣖⡀⡆⡀⣀⡀⢀⣀⣀⣀⡆⣀⣀⡀⠀⡆⡀⢀⡀⣀⣀⡀⢀⡀⣆⣀⣀⣀⣀⣀⣀⠐⡟⡄⢰⣶⣦⢤⡄⡆⠀⠀⡆⠁⣭⠍⠉⠁⠀⠂⠀⠁⢀⠀⠀⢸ ⡇⠀⠉⠛⡋⠋⣁⠃⣀⣀⡀⠈⠉⣛⣉⡀⡁⡛⠋⡋⠈⣛⡋⠁⡈⠛⠋⡂⣘⣛⡃⢛⡛⢋⣛⡙⢓⡐⡂⢙⡊⢙⣛⣉⣙⢃⢋⢋⠑⢛⡘⢉⠙⠁⣀⡀⣀⡀⣀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠀⠉⠈⠉⠉⠁⠂⠀⠉⠉⠉⠉⠉⢀⣃⠈⠉⠁⠀⠁⡀⠘⠋⠉⠉⠁⠀⠁⠈⠉⠁⠈⠁⠁⠈⡀⠈⠉⣮⠉⠈⠉⠙⠃⠈⢡⡎⣤⠄⣉⡁⠉⠉⠈⠈⠀⠀⠈⠀⠀⠀⠀⠀⣀⡀⡀⡀⠀⠀⠀⠀⠀⢸ ⡇⠀⢀⣀⣀⢀⣄⣀⣤⣤⡀⢀⣄⣄⣀⠀⡀⠀⡄⡄⢀⣤⣄⡀⡀⣄⠄⣤⣤⢀⣄⣤⣄⣀⣠⡤⣄⡠⡄⣈⡁⣠⣌⣄⣤⡉⣄⢠⣤⣤⣀⣠⠄⠡⡥⡍⢡⣤⣄⣀⡀⡄⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠁⠉⡉⠈⣅⢉⣉⣉⠁⠉⠉⣉⣉⣀⣁⡌⠉⡅⢈⣉⡍⠁⡅⠁⢉⣉⣉⣉⡉⢉⡍⢉⣉⡅⢉⡉⡄⢨⠉⢈⣉⣁⣩⢉⣉⣉⡋⢨⡈⢩⠀⠀⣉⡁⢈⣉⣉⢈⠁⠁⠀⠀⠁⠀⠠⠖⠀⠀⠀⠀⠀⠀⠘⠀⠀⢸ ⡇⠀⠀⠀⠁⠀⠉⠀⠉⠉⠁⠁⠀⠉⠉⠉⡉⠁⢀⡁⠈⠉⠁⠀⠁⠁⠘⠉⠉⠉⠁⠀⠁⠈⠉⠁⠈⠁⠁⠈⠁⠈⠉⠈⠉⠉⠉⠙⠁⠈⠁⠈⠀⠀⠈⠁⠉⠉⠈⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸ ⡇⠀⣀⣤⣀⣀⡀⡀⠤⠤⠈⢠⣤⣤⣤⠁⡄⢠⣤⡀⢈⣤⡤⡄⣠⣤⣤⠄⢠⣤⣤⣤⡄⢠⣄⣤⡄⡠⣤⣤⢤⣥⣠⣀⣤⣤⣂⣠⣤⣤⣤⣤⣤⡄⣀⡀⠀⣀⠠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠁⠉⡍⠩⣇⠉⠝⠏⡂⠀⠉⣉⣁⣀⣁⡌⠉⡅⢀⡉⡅⠁⠅⠏⢉⣁⣈⣉⡉⠩⡇⢈⣩⠍⢠⡯⠍⢩⠉⢉⠉⠁⢮⠍⢓⣌⡉⢡⡍⢩⠉⠐⠗⠃⠸⠿⠷⠲⠆⠇⠐⠂⡃⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠀⠁⠀⠁⠀⠈⠁⠀⠁⠉⠁⠉⠁⠀⠁⠀⠁⠁⢀⠁⠁⠈⠉⢉⠉⢁⠀⠁⠈⠉⠀⠈⠁⠀⠀⠀⠈⠁⠈⠀⠈⡈⢉⠁⠈⠀⠈⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡈⣉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢠⣤⣭⣠⡠⣄⣤⡤⠀⢠⣤⣼⣤⠀⡄⢨⠼⡗⢠⣭⣥⠀⢡⣤⣥⣬⣤⣤⡤⡫⡄⠨⣧⣤⣤⣤⣬⣴⡝⢻⠗⠃⢠⠀⠈⠀⠠⠐⡰⠖⢇⠌⠸⠁⠀⠀⠅⡆⣄⠀⠀⠀⠀⠄⢉⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡄⠀⣦⠠⡦⡦⠤⠀⠀⣤⣤⣤⣤⣄⠀⡅⢀⣭⡆⠀⡇⠀⢠⣤⣤⣤⡄⠀⡆⢠⣤⡄⢀⡇⡄⢠⡀⢠⣤⢄⣶⣤⣠⣤⡄⢠⡄⢠⠁⠰⠦⠆⢰⣶⣆⢤⡄⡆⠀⠀⠄⠀⠤⠀⠀⠀⠀⠀⠀⠀⢠⠘⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⢀⡀⠀⡀⠀⢀⠀⠀⠆⠀⠀⠠⠦⠂⠀⠆⠀⡤⠀⠀⠆⠀⠀⢀⡦⠀⠀⢀⡀⠀⠀⠀⠀⡀⠄⢠⠄⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠈⠀⡉⢠⡄⣄⡀⣖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡂⣤⡀⠀⠀⠁⠄⠀⣀⣀⡀⠀⠀⡀⠀⡀⠀⠀⡀⠀⠀⠀⠀⡄⡀⠀⠀⠀⠀⠀⡀⠠⡤⡄⢀⣤⡄⣀⡀⡀⠀⡀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡠⡤⡡⡉⢙⠛⠁⠂⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠃⠀⢀⡀⠀⠀⠀⠂⢤⠑⠀⠀⠀⠀⠀⠀⠀⠁⠁⠈⠉⠉⠁⠃⠃⠀⠁⠁⠀⢀⡔⠀⠀⠀⠀⣶⡤⠄⡤⠀⣼ ⠧⠤⠤⠤⠤⠤⠤⠤⠄⠤⠠⠤⠄⠀⠤⠤⠤⠄⠀⠤⠤⠀⠤⠤⠄⠠⠤⠄⠀⠤⠤⠀⠄⠤⠀⠠⠤⠤⠤⠄⠤⠄⠤⠤⠀⠤⠀⠤⠤⠀⠠⠤⠄⠠⠤⠄⠀⠤⠤⠤⠤⠤⠠⠤⠄⠠⠤⠤⠀⠤⠤⠤⠄⠀⠤⠤⠠⠴ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠸⢷⠾⠴⠶⠶⠶⠆⠀⠀⠒⠀⠒⠂⠒⠂⠒⠂⠒⠂⠒⠂⠒⠒⠀⡤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠸⠷⠶⠶⠮⠦⠾⠸⠴⠶⠂⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⡇⠿⠶⠷⠶⠶⠶⡶⠀⠰⠄⠶⠶⠶⠆⠸⠷⠲⠲⠶⠲⠂⠰⠀⠖⠶⠶⠾⠶⠶⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡎⣇⡄⢴⠱⠁⠀⡆⠄⠀⠀⠀⠀⠀⠀⠀⠾⠾⠢⡾⡾⢤⢾⣆⡆⠀⠀⣀⠀⡀⠀⠀⠀⠀⡸ ⡇⠏⠿⠿⠗⠀⠀⠀⠀⠈⠻⠲⠲⠶⠲⠶⠶⠂⠸⠷⠶⠶⠸⠷⠶⠀⠸⠶⠺⠷⠽⠳⠽⠻⠶⠖⠒⠦⠶⠷⠔⠀⠀⡇⠧⡇⢺⠴⠃⠄⡇⣖⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠁⠀⠀⠈⠉⠀⠉⠁⠀⢰⡇ ⡟⠻⠖⠫⠷⠶⠇⠀⠀⠨⠵⠶⠲⠆⠸⠣⠞⠄⠇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⡯⠷⢿⢄⠘⠳⡇⡶⠲⠶⠶⠶⠆⠀⠀⠸⡀⠹⡿⠄⠸⠄⠘⠧⠀⠹⡄⠝⡿⠤⠀⠀⢨⡇ ⡟⠛⠲⠆⠃⠗⠶⠀⠀⠐⠦⠦⠔⠆⠸⠠⡆⠠⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡶⠷⣻⠾⠷⠮⠇⠇⡞⠇⠁⠀⠀⠀⠀⠀⣁⡀⡄⢁⣠⡕⣀⡀⠈⠀⠀⠀⠉⠀⠀⠀⢨⡇ ⡇⠛⠛⠒⠒⠓⠃⠁⠀⠀⠃⠐⠱⠓⠓⠛⠃⠘⠚⠚⠲⠺⠚⠐⠲⠂⠾⠒⠐⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡗⡋⠟⠛⠱⠑⠇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⠛⠋⡁⠘⠙⠛⠉⠃⠀⠀⠺⠿⠿⠗⠈⠁⠈⠅ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⡓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉ ⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡ ⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⠀⡀⢀⡀⡀⠀⣀⡀⡀⢀⣀⣀⡀⢀⣀⣀⡀⣀⣀⣀⡀⢀⣀⣀⣀⠀⢀⣀⡀⢀⣀⣀⢀⣀⣀⣀⣀⣀⣀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⢨ ⡇⢀⠊⠛⠛⠛⣋⠛⡛⡓⠀⠘⠛⠛⠛⠀⠃⡀⠋⡃⠈⠛⡛⠃⡘⠛⠛⠂⠘⠛⠓⠋⡛⠛⠛⡃⠘⠛⡛⢙⡒⠙⠛⢃⢙⢛⠛⠛⠛⢚⡚⢛⠛⠛⢛⠛⢁⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨ ⡇⠀⠀⠀⠁⠀⠛⠀⠃⠃⠓⠂⠀⠋⠛⠋⠛⠋⠀⠆⠈⢛⢃⠀⠃⠂⠘⠛⠛⠛⠃⠐⠢⠈⠓⠁⠀⡓⠓⠘⠀⠘⠋⢛⢿⡚⠓⠺⠃⠘⠃⢘⠀⣒⢛⡕⠊⠋⠙⠘⠀⠀⠘⠀⠀⠀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⣀⠀⠀⠒⡀⣆⣶⠀⠀⣀⣀⡀⠀⡀⣀⣀⡀⢀⣀⢞⡀⡆⡀⣀⡀⢀⣀⣀⣀⡆⣀⣀⡀⠀⡂⡀⢀⡀⣀⣀⡀⢀⡀⣄⣀⣀⣀⣀⣀⣀⠐⡛⡂⢰⣶⣦⢤⡄⡆⠀⠀⢆⠁⣭⠍⠉⠁⠀⠂⠀⠁⠀⠀⠀⢸ ⡇⠀⠉⠛⡋⠋⣁⠃⣀⠸⠻⠟⠏⣛⣉⠄⡋⡻⠏⡛⠈⣛⡋⠁⡈⠛⠋⡂⣘⣛⡃⢛⡛⢋⣛⡙⢓⡐⡂⢘⡊⢙⣛⣉⢙⢃⢋⢋⠑⢛⡘⢉⠙⠁⣀⡐⣤⡀⣀⢀⠀⠄⠀⠿⠻⠃⠈⠛⠀⠈⠁⠀⠀⠀⠀⠊⠀⢸ ⡇⠀⠀⠀⠁⠀⠉⠈⠉⠉⠀⠂⠀⠉⠉⠉⠉⠉⢀⣃⠈⠉⠁⠀⠁⡀⠘⠋⠉⠉⠁⠀⠁⠈⠉⠁⠈⠁⠁⠈⡀⠈⠉⣮⠉⠈⠉⠙⠃⠈⢡⡎⣤⠄⣉⡁⠉⠉⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⡀⠀⠀⠀⠀⠀⢸ ⡇⠀⢀⣀⣀⢀⣄⣀⣤⣤⡀⢀⣄⣄⣀⠀⡀⠀⡄⡆⢂⣤⣄⡀⡀⣄⠄⣤⣤⢀⣄⣤⣄⣀⣠⡤⣄⡠⡄⣈⡁⢠⣌⣄⣤⡉⣄⢠⣠⣤⣀⣠⠄⠡⡥⡌⢡⣤⣄⣀⡀⡄⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠁⠉⡉⠈⣅⢉⣉⣁⠀⢈⠉⣉⣉⣀⣁⡌⠉⡅⢈⣉⡍⠁⡅⠁⢉⣉⣉⣉⡉⢉⡍⢉⣉⡅⢉⡉⡄⢨⠉⢈⣉⣁⣩⢉⣉⣉⡋⢨⡈⢩⠀⠀⣉⡁⢈⣉⣉⢈⠁⠄⠀⣶⣶⡆⠠⠖⠀⠀⠀⠀⠀⠀⠀⡠⠀⢘ ⡇⠀⠀⠀⠁⠀⠉⠀⠉⠀⠈⠀⠀⠉⠉⠉⠉⠁⢀⡁⠈⠉⠁⠀⠁⠁⠘⠉⠉⠉⠁⠀⠁⠈⠉⠁⠈⠁⠁⠈⠁⠈⠉⠈⠉⠉⠉⠙⠁⠈⠁⠈⠀⠀⠈⠁⠉⠁⠈⠈⠀⠀⠁⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢨ ⡇⠀⣀⣤⣀⣀⡀⡀⠤⠤⠈⢠⣤⣤⣤⠁⡀⢠⣄⡀⢈⣤⡤⡄⣠⣤⣤⠄⢠⣤⣤⣤⡄⢠⣄⣤⡄⡠⣤⣤⢤⣥⣠⣀⣠⣤⣂⣠⣤⣤⣤⣤⣤⡄⣀⡀⠀⣀⠠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠁⠉⡍⠩⣇⠉⠝⠏⣂⡀⠉⣉⣁⣀⣉⡌⠉⡅⢀⡉⡅⠁⠅⠏⢉⣁⣈⣉⡉⠩⡇⢈⣩⠍⢠⡯⠍⢩⠉⢉⠉⠁⢮⠍⢓⣌⡉⢡⡍⢩⠉⠐⠗⠃⠸⠿⠧⠲⠆⠃⠐⠂⣃⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠀⠁⠀⠁⠐⠛⠓⠀⠁⠁⠁⠉⠁⠀⠁⠀⠁⠁⢀⠁⠁⠈⠉⢉⠉⢁⠀⠁⠈⠉⠀⠈⠁⠀⠀⠀⠈⠁⠈⠀⠈⡈⢉⠁⠈⠀⠈⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠘⠛⠃⣉⠉⠉⠉⠀⠀⠀⠀⠀⠊⠀⢨ ⡇⠀⢠⣤⣭⣠⡠⣄⣤⡤⠀⢠⣤⣼⣤⠀⡄⢨⠼⡗⢠⣭⣥⠀⢡⣤⣥⣬⣤⣤⡤⡫⡄⠨⣧⣤⣤⣤⣬⡴⠝⢻⠗⠃⠠⠀⠈⠀⠠⠐⡰⠖⢇⠌⠸⠁⠀⠀⠅⡆⣄⠀⠀⠀⠀⠄⢉⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡄⠀⣦⠠⡦⡦⠤⠀⠀⣤⣤⣿⣴⣆⠀⡅⢀⣭⡆⠀⡏⠁⢠⣦⣤⣤⣅⠀⡆⢠⣤⡄⢀⡏⡄⢠⡀⢠⣤⢄⣶⣤⣤⣤⡄⣰⠴⢠⢁⠰⠦⠆⢰⣶⣆⢤⡄⡆⠀⠀⠆⠘⠧⠀⠀⠂⠀⠀⠀⠀⢠⠘⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⡄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠄⠀⢸ ⡇⢀⡀⠀⡀⠀⢀⠀⠀⠂⠀⠀⠀⠂⠀⠀⠂⠀⡀⠀⠀⠂⠀⠀⢀⡀⠀⠀⢀⡀⠀⠀⠀⠀⡀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘ ⡇⠀⠈⠀⡉⢠⡄⣄⡀⣖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡂⣄⡀⠀⠀⠁⠄⠀⣀⣀⡀⠀⠀⡀⠀⡀⠀⠀⡀⠀⠀⠠⠀⡄⣀⠀⠀⠀⠀⠀⡀⠠⡤⡄⢀⣤⡄⣀⡀⡀⠀⡀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡠⡤⡡⡉⢉⠛⠁⠂⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠃⠀⢀⡀⠀⠀⠀⠂⢤⠑⠀⠀⠀⠀⠀⠀⠀⠁⠁⠈⠉⠉⠁⠃⠃⠀⢁⢁⡀⢀⡔⠀⠀⠀⠀⡶⡤⠀⠀⠀⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠄⠤⠠⠤⠄⠀⠤⠤⠤⠄⠀⠤⠤⠀⠤⠤⠄⠠⠤⠄⠀⠤⠤⠀⠄⠤⠀⠠⠤⠤⠤⠄⠤⠄⠤⠤⠀⠤⠀⠤⠤⠀⠠⠤⠄⠠⠤⠄⠀⠤⠤⠤⠤⠤⠠⠈⠙⠣⠤⠽⠁⠤⠤⠤⠄⠀⠄⠉⠀⠰ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠸⢷⠾⠴⠶⠶⠶⠆⠀⠀⠒⠀⠒⠂⠒⠂⠒⠂⠒⠂⠒⠂⠒⠒⠀⡤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠸⠷⠶⠶⠮⠦⠾⠸⠴⠶⠂⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⡇⠿⠶⠷⠶⠶⠶⡶⠀⠰⠄⠶⠶⠶⠆⠸⠷⠲⠲⠶⠲⠂⠰⠀⠖⠶⠶⠾⠦⠶⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡎⣇⡄⢴⠡⠁⠀⡆⠄⠀⠀⠀⠀⠀⠀⠀⠾⠾⠢⡾⡾⢤⢾⣆⡆⠀⠀⣀⡄⠀⠀⠀⠀⠀⡸ ⡇⠏⠿⠿⠗⠀⠀⠀⠀⠈⠻⠲⠲⠶⠲⠶⠶⠂⠸⠷⠶⠶⠸⠷⠶⠀⠸⠶⠺⠷⠽⠳⠽⠻⠶⠖⠒⠦⠶⠷⠔⠀⠀⡇⠧⡇⢺⠴⠃⠄⡆⣆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠁⠀⠀⠈⠉⠀⠉⠁⠀⢰⡇ ⡟⠻⠖⠫⠷⠶⠇⠀⠀⠨⠵⠶⠲⠆⠸⠣⠞⠄⠇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⡯⠷⢿⢄⠘⠳⡇⡷⠲⠶⠶⠶⠆⠀⠀⠸⡀⠹⡿⠄⠸⠄⠘⠧⠀⠸⡄⠝⡿⠤⠀⠀⢨⡇ ⡟⠛⠲⠆⠃⠗⠶⠀⠀⠐⠦⠦⠔⠆⠸⠠⡆⠠⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡶⠷⣻⠾⠷⠮⠇⠇⡞⠇⠁⠀⠀⠀⠀⠀⣁⡀⡄⢁⣠⡕⣀⡀⠈⢀⣀⣀⡉⠀⠀⠀⠈⡇ ⡇⠛⠛⠒⠒⠓⠃⠁⠀⠀⠃⠐⠱⠓⠓⠛⠃⠘⠚⠚⠲⠺⠚⠐⠲⠂⠾⠒⠐⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡗⡋⠟⠛⠱⠑⠇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⠛⠋⡁⠘⠙⠛⠉⠃⠀⠀⠚⠛⠣⠗⠉⠁⠊⠁ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⡓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉ ⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡ ⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⠀⡀⢀⡀⡀⠀⣀⡀⡀⢀⣀⣀⡀⢀⣀⣀⡀⣀⣀⣀⡀⢀⣀⣀⣀⠀⢀⣀⡀⢀⣀⣀⢀⣀⣀⣀⣀⣀⣀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⢨ ⡇⢀⠊⠛⠛⠛⣋⠛⡛⡓⠀⠘⠛⠛⠛⠀⠃⡀⠋⡃⠈⠛⡛⠃⡘⠛⠛⠂⠘⠛⠓⠋⡛⠛⠛⡃⠘⠛⡛⢙⡒⠙⠛⢃⢙⢛⠛⠛⠛⢚⡚⢛⠛⠛⢛⠛⢁⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨ ⡇⠀⠀⠀⠁⠀⠛⠀⠃⠃⠓⠂⠀⠋⠛⠋⠛⠋⠀⠆⠈⢛⢄⠀⠃⠂⠘⠛⠛⠛⠃⠔⠠⠈⠓⠁⠀⠳⠓⠘⠀⠈⠉⢛⢿⡚⠓⠺⠃⠘⠃⢘⠠⣲⢻⡕⠪⡋⠙⠘⠀⠀⠘⠀⠀⠀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⣀⠀⠀⠒⡀⣆⣤⣤⠀⣀⣀⠀⠀⡀⣀⣀⡀⢀⣀⢞⠀⡆⡀⣀⡀⢀⣀⣉⣀⡆⣀⣀⡀⠀⡀⡀⢀⡀⣀⣀⡀⢀⡀⣄⣀⣀⣀⣀⣀⣀⠐⡛⡂⢰⣶⣦⢤⡄⢤⣤⣬⡆⠁⣭⠍⠉⠁⠀⠂⠀⠡⡀⠀⠀⢸ ⡇⠀⠉⠛⡋⠋⣁⠃⣀⠨⠉⠉⠅⣛⣉⠄⡋⡻⠏⡛⠈⣛⡋⠀⡈⠛⠋⡂⣘⣛⡃⢛⡋⢋⣛⡙⢓⡐⡂⢘⡊⢙⣛⣉⢙⢃⢋⢋⠑⢛⡘⢉⠙⠁⣀⡐⣤⡀⣀⢀⠀⠉⠉⠉⠡⠂⠈⠛⠀⠈⠁⠀⠀⠀⠈⠈⠀⢸ ⡇⠀⠀⠀⠁⠀⠉⠈⠉⠉⠀⠂⠀⠉⠉⠉⠉⠉⢀⣃⠈⠉⠁⠀⠁⡀⠘⠋⠉⠉⠁⠀⠁⠈⠉⠁⠈⠁⠁⠈⡀⠈⠉⣮⠉⠈⠉⠙⠃⠈⢡⡎⣤⠄⣉⡁⠉⠉⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⡀⠀⠀⠀⠀⠀⢸ ⡇⠀⢀⣀⣀⢀⣄⣀⣤⡤⢀⢀⣀⣄⣀⠀⡀⠀⡄⡆⢂⣤⣄⡀⡀⣄⠄⣤⣤⢀⣄⣤⣄⣀⣠⡤⣔⡤⡌⣈⡁⢠⣌⣄⣤⡉⣄⢠⣠⣤⣀⣠⠄⠡⡥⡌⢠⣤⣄⡀⡀⢀⢀⡀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠁⠉⡉⠈⣅⢉⡉⠓⠺⢛⠉⣉⣉⣀⣁⡌⠉⡅⢈⣉⡍⠁⡅⠁⢉⣉⣉⣉⡉⢉⡉⢉⣉⡅⢉⡉⡄⢨⠉⢈⣉⣁⣩⢉⣉⣉⡋⢨⡈⢩⠀⠀⣉⡁⢈⣉⣉⢀⠁⠹⠾⠻⣶⡆⠨⠖⠀⠀⠀⠀⠀⠈⠓⠀⠀⢘ ⡇⠀⠀⠀⠁⠀⠉⠀⠉⠀⠈⠀⠀⠉⠉⠉⠉⠁⢀⡁⠈⠉⠁⠀⠁⠁⠘⠉⠉⠉⠁⠀⠁⠈⠉⠁⠈⠁⠁⠈⠁⠈⠉⠈⠉⠉⠉⠙⠁⠈⠁⠈⠀⠀⠈⠁⠉⠁⠈⠈⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢨ ⡇⠀⣀⣤⣀⣀⡀⡀⠤⠤⠈⢠⣤⣤⣤⠁⡂⢠⣜⡁⢈⣤⡤⡄⣠⣤⣤⠄⢠⣤⣤⣤⡄⢠⣄⣤⡄⡠⣤⣤⢤⣥⣠⣀⣠⣤⣂⣠⣤⣤⣤⣤⣤⡄⣀⡀⠀⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠁⠉⡍⠩⣇⠉⠝⢯⢦⣆⠉⣉⣁⣀⣉⡌⠉⡅⢀⡉⡅⠁⠅⠏⢉⣁⣈⣉⡉⠩⡇⢈⣩⠍⢠⡯⠍⢩⠉⢉⠉⠁⢮⠍⢓⣌⡉⢡⡍⢩⠉⠐⠗⠃⠸⠿⠧⠲⠆⠁⣶⣴⡆⠀⠐⠇⠀⠀⠀⠀⠀⠐⢤⠀⠀⢸ ⡇⠀⠀⠀⠁⠀⠁⠀⠁⠐⠒⠐⠀⠁⠁⠁⠉⠁⠀⠁⠀⠁⠁⢀⠁⠀⠈⠉⢉⠉⢁⠀⠁⠈⠉⠀⠈⠁⠀⠀⠀⠈⠁⠈⠀⠈⡈⢉⠁⠈⠀⠈⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠐⠚⠃⣉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢨ ⡇⠀⢠⣤⣭⣠⡠⣄⣤⡤⠀⢠⣤⣼⣤⠀⡤⢨⠼⡗⢠⣭⣥⠀⢡⣤⣥⣬⣤⣤⡤⡭⡀⠨⣧⣤⣤⣤⣬⣴⡝⢻⠗⠃⠠⡀⡌⠀⢠⡀⡴⠖⢇⠌⠸⠁⠀⠀⠅⡄⣄⡀⢀⠀⠀⡄⢋⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡄⠀⣦⠠⡦⡦⠤⠀⠀⣤⣤⣿⣴⣆⠀⡅⢀⣭⡎⠀⡏⠀⢠⣦⣤⣤⣅⠀⡄⢠⣤⡄⢀⡍⡄⢠⡀⢠⣤⢄⣶⣤⣥⣤⡄⣰⠴⢠⢁⠰⠦⠆⢰⣦⣆⢤⡄⡆⠀⣠⡀⢘⣧⢀⠀⠂⠀⠀⠀⢀⡀⠈⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⠄⠀⠠⠀⠀⠀⠀⠀⠀⠉⠀⠀⠸ ⡇⢀⡀⠀⡀⠀⢀⠀⠀⠂⠀⠀⠀⠂⠀⠀⠂⠀⣀⠀⠀⠂⠀⠀⢀⡀⠀⠀⢀⡀⠀⠀⠀⠀⡀⠀⢀⠀⢀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘ ⡇⠀⠈⠀⡉⢠⡄⣄⡀⣖⡀⠀⠀⠐⠒⠀⠀⠀⠀⠁⠀⠀⡂⣄⡀⠀⠀⠁⠄⠀⣀⣀⡀⠀⠀⡀⠀⡀⠀⠀⡀⠀⠀⠠⠀⡜⣀⠀⠀⠀⠀⠀⠀⠠⡤⡄⢀⣤⡄⣀⡀⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡠⡤⡡⠉⢉⠛⠁⠂⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠃⠀⢀⡀⠀⠀⠀⠂⢤⠓⠀⠀⠀⠀⠀⠀⠀⠁⠁⠈⠉⠉⠁⠃⠃⠘⠫⠇⡀⢐⡔⠀⠀⠀⠀⡶⡌⠓⠀⠀⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠄⠤⠠⠤⠄⠀⠤⠤⠤⠄⠀⠤⠤⠀⠤⠤⠄⠠⠤⠄⠀⠤⠤⠀⠄⠤⠀⠠⠤⠤⠤⠄⠤⠄⠤⠤⠀⠤⠀⠤⠤⠀⠠⠤⠄⠠⠤⠄⠀⠤⠤⠤⠤⠤⠠⠈⠙⠣⠤⠽⠁⠤⠤⠤⠄⠀⠄⠉⠀⠰ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠸⢷⠾⠴⠶⠶⠶⠆⠀⠀⠒⠀⠒⠂⠒⠂⠐⠀⠒⠂⠒⠂⠒⠒⠀⡄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠸⠷⠶⠶⠮⠦⠾⠸⠴⠶⠂⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⡇⠿⠶⠷⠶⠶⠶⡶⠀⠰⠄⠶⠶⠶⠆⠸⠷⠲⠲⠶⠲⠂⠰⠀⠖⠶⠶⠾⠦⠶⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡎⣇⡄⢴⠡⠁⢀⡆⠄⠀⠀⠀⠀⠀⠀⠀⠾⠾⠢⡾⡮⢤⢾⣆⡆⠀⠀⣀⡄⠀⠀⠀⠀⠀⡸ ⡇⠏⠿⠿⠗⠀⠀⠀⠀⠈⠻⠲⠲⠶⠲⠶⠶⠂⠸⠷⠶⠶⠸⠷⠶⠀⠸⠶⠺⠷⠽⠳⠽⠻⠶⠖⠒⠦⠶⠷⠔⠀⠀⡇⠧⡇⢸⠴⠀⠘⡇⣆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠁⠀⠀⠈⠉⠀⠉⠁⠀⢰⡇ ⡟⠻⠖⠫⠷⠶⠇⠀⠀⠨⠵⠶⠲⠆⠸⠣⠞⠄⠇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⡯⠷⢿⢄⠘⢫⡇⡷⠲⠶⠶⠶⠆⠀⠀⠸⡀⠹⡿⠄⠸⠄⠘⠧⠀⠸⡄⠝⡿⠤⠀⠀⢨⡇ ⡟⠛⠲⠆⠃⠗⠶⠀⠀⠐⠦⠦⠔⠆⠸⠠⡆⠠⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡶⠷⣻⠾⠷⠮⠇⡇⡞⠇⠁⠀⠀⠀⠀⠀⣁⡀⡄⢁⣠⡑⣀⡀⠈⢀⣀⣀⡉⠀⠀⠀⠈⡇ ⡇⠛⠛⠒⠒⠓⠃⠁⠀⠀⠃⠐⠱⠓⠓⠛⠃⠘⠚⠚⠲⠺⠚⠐⠲⠂⠾⠒⠐⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡗⡋⠟⠛⠱⠑⠇⠀⠄⠁⠀⠀⠀⠀⠀⠀⠐⠛⠋⡁⠘⠙⠛⠉⠃⠀⣀⣈⣛⡃⢓⣉⡁⠊⠁ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⡓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠟⠛⠛⠂⠐⠉⠀⠀⠉ ⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠈⢡ ⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⠀⡀⢀⡀⡀⠀⣀⡀⡀⢀⣀⣀⡀⢀⣀⣀⡀⣀⣀⣀⡀⢀⣀⣀⣀⠀⢀⣀⡀⢀⣀⣀⢀⣀⣀⣀⣀⣀⣀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⢨ ⡇⢀⠊⠛⠛⠛⣋⠛⡛⡓⠀⠘⠛⠛⠛⠀⠃⡀⠋⡃⠈⠛⡛⠃⡘⠛⠛⠂⠘⠛⠓⠋⡛⠛⠛⡃⠘⠛⡛⢙⡒⠙⠛⢃⢙⢛⠛⠛⠛⢚⡚⢛⠛⠛⢛⠛⢁⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨ ⡇⠀⠀⠀⠁⠀⠛⠀⠃⠃⠓⠂⠀⠋⠚⠋⠛⠃⠀⠆⠈⢛⢄⠀⠃⠂⠘⠛⠛⠛⠃⠔⠠⠈⠓⠁⠀⠳⠓⠘⠀⠈⠉⢛⢿⡚⠑⠺⠃⠘⠃⢘⠠⣲⢻⡕⠪⡋⠙⠘⠀⠀⠘⠀⠀⠀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⣀⠀⠀⠒⡀⣆⣤⣤⠀⣀⣀⠀⠀⡀⣀⣀⡀⢀⣀⢞⠀⡆⡀⣀⡀⢀⣀⣉⣀⡆⣀⣀⡀⠀⡀⡀⢀⡀⣀⣀⡀⢀⡀⣄⣀⣀⣀⣀⣀⣀⠐⡛⡂⢰⣶⣦⢤⡄⢤⣤⣌⡆⠁⣭⠍⠉⠁⠀⠂⠀⠡⡀⠀⠀⢸ ⡇⠀⠉⠛⡋⠋⣁⠃⣀⠨⠉⠉⠅⣛⣉⠄⡋⡻⠏⡛⠈⣛⡋⠀⡀⠻⠋⡀⣘⣛⡃⢛⡋⢋⣛⡙⢓⡐⡂⢘⡊⢐⣛⣁⢙⢃⢋⢋⠑⢛⡘⢉⠙⠳⣀⡐⣤⡀⣀⢀⠀⠉⠉⠉⠡⠂⠈⠛⠀⠈⠁⠀⠀⠀⠈⠈⠀⢸ ⡇⠀⠀⠀⠁⠀⠉⠈⠉⠉⠠⠀⠀⠉⠉⠉⠉⠉⢀⣃⠈⠉⠁⠀⠁⡀⠘⠋⠉⠉⠁⠀⠁⠈⠉⠁⠈⠁⠁⠈⡀⠈⠉⣮⠉⠈⠉⠙⠃⠈⢡⡎⣤⠄⣈⡁⠉⠉⠈⠈⠀⢀⢠⣨⠀⠀⠀⠀⣀⡀⡀⠀⠀⠀⡄⠀⠀⢸ ⡇⠀⢀⣀⣀⢀⣄⣀⣤⡄⠀⢀⣂⣄⣀⠀⡀⠀⡄⡆⢂⣤⣄⡀⡀⣄⠄⣤⣤⢀⣄⣤⣄⣀⣠⡤⣄⡤⡌⣈⡁⢠⣌⣄⣤⡉⣄⢠⣠⣤⣀⣠⠄⠡⡭⡌⢠⣤⣄⡀⡀⢀⠘⠛⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢸ ⡇⠀⠁⠉⡉⠈⣅⢉⡉⠓⠲⢛⠉⣉⣉⣀⣁⡌⠉⡅⢈⣉⡍⠁⡅⠁⢉⣉⣉⣉⡉⢉⡉⢉⣉⡅⢉⡉⡄⢨⠉⢈⣉⣁⣩⢉⣉⣉⡋⢨⡈⢩⠀⠀⣉⡁⢈⣉⣉⢀⠁⠹⠾⠻⣶⡆⠨⠖⠀⠀⠀⠀⠀⠈⠓⠀⠀⢘ ⡇⠀⠀⠀⠁⠀⠉⠀⠉⠀⠈⠀⠀⠉⠉⠉⠉⠁⢀⡑⠊⠉⠁⠀⠁⠁⠘⠉⠉⠉⠁⠀⠁⠈⠉⠁⠈⠁⠁⠈⠁⠈⠉⠈⠉⠉⠉⠙⠁⠈⠁⠈⠀⠀⠈⠁⠉⠁⠈⠈⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢨ ⡇⠀⣀⣤⣀⣀⡀⡀⠤⠤⠈⢠⣤⣤⣤⠁⡂⢠⣜⡀⢈⣤⡤⡄⣠⣤⣤⠄⢠⣤⣤⣤⡄⢠⣄⣤⡄⡠⣤⣤⢤⣥⣠⣀⣠⣤⣂⣠⣤⣤⣤⣤⣤⡄⣀⡀⠀⣀⠠⠀⠀⠠⣠⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢸ ⡇⠀⠁⠉⡍⠩⣇⠉⠝⢋⢈⣆⠉⣉⣁⣀⣉⡌⠉⡁⢀⡉⡅⠁⠅⠏⢉⣁⣈⣉⡉⠩⡇⢈⣩⠍⢠⡯⠍⢩⠉⢉⠉⠁⢮⠍⢓⣌⡉⢡⡍⢩⠉⠐⠗⠃⠸⠿⠧⠲⠆⠁⣈⣈⡁⠀⠐⠇⠀⠀⠀⠀⠀⠀⢅⠀⠀⢸ ⡇⠀⠀⠀⠁⠀⠁⠀⠁⠐⠒⠐⠀⠁⠁⠁⠉⠁⠀⠁⠀⠁⠁⢀⠁⠀⠈⠉⢉⠉⢁⠀⠁⠈⠉⠀⠀⠁⠀⠀⠀⠈⠁⠈⠀⠈⡈⢉⠁⠈⠀⠈⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠐⠚⠃⣉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢨ ⡇⠀⢠⣤⣭⣠⡠⣄⣤⡤⠀⢠⣤⣼⣤⣀⡤⢨⠼⡗⢠⣭⣥⠀⢡⣤⣥⣬⣤⣤⡤⡭⡀⠨⣧⣤⣤⣤⣬⣴⡝⢻⠗⠃⠠⡀⡄⠀⢠⡀⡴⠖⢇⠌⠸⠁⠀⠀⠅⡄⣀⡀⢀⠀⠀⡄⢋⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡄⠀⣦⠠⠄⣤⣴⣤⠀⣤⣤⣿⣴⣆⠀⡅⢀⣭⡎⠀⡏⠀⢠⣦⣤⣤⣅⠀⡄⢠⣤⡄⢀⡍⡄⢠⡀⢠⣤⢄⣶⣤⣥⣤⡄⣰⠴⢠⢁⠰⠦⠆⢰⣦⣆⢤⡄⡆⢀⣴⡄⢘⣧⢀⠀⠂⠀⠀⠀⠀⡆⠈⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠡⠄⠀⠠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠸ ⡇⢀⡀⠀⡀⠀⢀⠀⠀⠂⠀⠀⠀⠂⠀⠀⠂⠀⣀⠀⠀⠂⠀⠀⢀⡀⠀⠀⢀⡀⠀⠀⠀⠀⡀⠀⢀⠀⢀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘ ⡇⠀⠈⠀⡉⢠⡄⣄⡀⣖⡀⠀⠀⠐⠒⠀⠀⠀⠀⠁⠀⠖⡾⣄⡀⠀⠀⠁⠄⠀⣀⢆⡀⠀⠀⡀⠀⡐⠀⠀⡀⠀⠀⠠⠀⡝⢃⠐⠆⠈⠆⠠⠄⠠⡤⡄⢀⣨⠼⣀⡀⡀⠊⠁⠂⠀⠀⠙⠒⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡠⡤⡡⠁⢉⠛⠁⠂⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠃⠀⢀⡀⠀⠀⠀⠂⢤⠓⠀⠀⠀⠀⠀⠀⠀⠁⠁⠈⠉⠉⠁⠃⠃⠘⠫⠇⡀⢐⡔⠀⠀⠀⠀⡂⠀⡆⠀⠀⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠄⠤⠠⠤⠄⠀⠤⠤⠤⠄⠀⠤⠤⠀⠤⠤⠄⠠⠤⠄⠀⠤⠤⠀⠄⠤⠀⠠⠤⠤⠤⠄⠤⠄⠤⠤⠀⠤⠀⠤⠤⠀⠠⠤⠄⠠⠤⠄⠀⠤⠤⠤⠤⠤⠠⠈⠙⠣⠤⠝⠁⠤⠤⠤⠄⠀⠁⠀⠀⠰ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠸⢷⠾⠴⠶⠶⠶⠆⠀⠀⠒⠀⠒⠂⠒⠂⠐⠀⠒⠂⠒⠂⠒⠒⠀⡄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠸⠷⠶⠶⠮⠦⠾⠸⠴⠶⠂⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⡇⠿⠶⠷⠶⠶⠶⡶⠀⠰⠄⠶⠶⠶⠆⠸⠷⠲⠲⠶⠲⠂⠰⠀⠖⠶⠶⠾⠦⠶⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡎⣇⡄⢴⠡⠁⢀⡆⠄⠀⠀⠀⠀⠀⠀⠀⠾⠾⠢⡾⡮⢤⢾⣆⡆⠀⠀⣀⡄⠀⠀⠀⠀⠀⡸ ⡇⠏⠿⠿⠗⠀⠀⠀⠀⠈⠻⠲⠲⠶⠲⠶⠶⠂⠸⠷⠖⠶⠸⠷⠶⠀⠸⠶⠺⠷⠽⠳⠽⠻⠶⠖⠒⠦⠶⠷⠔⠀⠀⡇⠧⡇⢸⠴⠀⠘⠇⣆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠃⠁⠀⠀⠈⠉⠀⠉⠁⠀⢰⡇ ⡟⠻⠖⠫⠷⠶⠇⠀⠀⠨⠵⠶⠲⠆⠸⠣⠞⠄⠇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⡯⠷⢿⢄⠘⢫⡇⡷⠲⠶⠶⠶⠆⠀⠀⠸⡀⠹⡿⠄⠸⠄⠘⠧⠀⠸⡄⠝⡿⠤⠀⠀⢠⡇ ⡟⠛⠲⠆⠃⠗⠶⠀⠀⠐⠦⠦⠔⠆⠸⠠⡆⠠⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⡶⠷⣻⠾⠷⠮⠇⡇⡞⠇⠁⠀⠀⠀⠀⠀⣁⡀⡄⢁⣠⡑⣀⡀⠈⢀⣀⣀⡉⠀⠀⠀⠈⡇ ⡇⠛⠛⠒⠒⠓⠃⠁⠀⠀⠃⠐⠱⠓⠓⠛⠃⠘⠚⠚⠲⠺⠚⠐⠲⠂⠾⠒⠐⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡗⡋⠟⠛⠱⠑⠇⠀⠄⠁⠀⠀⠀⠀⠀⠀⠐⠛⠋⡁⠘⠙⠛⠉⣃⣀⠀⢈⣛⡃⢓⣉⡁⠊⠁ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⡓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⠼⠻⠓⠛⠛⠃⠀⠉⠀⠀⠉ ⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠘⠆⠀⠈⠂⠀⠀⠀⠈⢡ ⡇⠀⢀⢀⣀⢀⣀⢀⣀⣀⠀⣀⡀⣀⡀⠀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⢨ ⡇⢀⠂⠛⠛⠛⣋⠛⡛⡛⠀⠐⠛⠛⠛⠀⠂⡀⠊⡃⠀⠓⡓⠃⡘⠛⠛⠂⠘⠛⠓⠂⡓⠛⠛⡃⠘⠛⡛⢙⡒⠘⠓⢃⢘⢛⠛⠛⠛⢚⡚⢛⠛⠛⢛⠛⢁⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨ ⡇⠀⠀⠀⠁⠀⠛⠀⠃⠃⠓⠂⠀⠋⠚⠋⠛⠃⠀⠆⠈⢛⢄⠀⠃⠂⠘⠛⠛⠛⠃⠔⠠⠈⠓⠁⠀⠳⠓⠘⠀⠈⠉⢛⢿⡚⠑⠺⠃⠘⠃⢘⠠⣲⢻⡕⠪⡋⠙⠘⠀⠀⠘⠀⠀⠀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⣀⠀⠀⠒⡀⣆⣤⣤⠀⣀⣀⠀⠀⡀⣀⣀⡀⢀⣀⢞⠀⡆⡀⣀⡀⢀⣀⣉⣀⡆⣀⣀⡀⠀⡀⡀⢀⡀⣀⣀⡀⢀⡀⣄⣀⣀⣀⣀⣀⣀⠐⡛⡂⢰⣶⣦⢤⡄⢤⣤⣌⡆⠁⣭⠍⠉⠁⠀⠂⠀⠡⡀⠀⠀⢸ ⡇⠀⠉⠛⡋⠋⣁⠃⣀⠨⠉⠉⠅⣛⣉⠄⡋⡻⠏⡛⠀⣝⡃⠀⣀⠻⠋⡀⣘⣙⡃⢛⡋⢋⣛⡙⢓⡐⡂⢘⡊⢐⣛⣁⢙⢃⢋⢋⠑⢛⣼⣉⠝⠳⣀⡐⣤⡀⣀⢀⠀⠉⠉⠉⠡⠂⠈⠛⠀⠈⠁⠀⠀⠀⠈⠈⠀⢸ ⡇⠀⠀⠀⠁⠀⠉⠈⠉⢉⡀⠀⠀⠉⠉⠉⠉⠉⢀⣃⠈⠉⠁⠀⠁⡀⠘⠋⠉⠉⠁⠀⠁⠈⠉⠁⠈⠁⠁⠈⡀⠈⠉⣮⠉⠈⠉⠙⠃⠈⢡⡌⣤⠄⣈⡁⠈⠉⠈⢈⣀⡀⢠⣨⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡄⠀⠀⢸ ⡇⠀⢀⣀⣀⢀⣄⣀⡌⠚⠋⢀⣆⣄⣀⠀⡀⠀⡄⡆⢂⣤⣄⡀⡀⣄⠄⣤⣤⢀⣄⣤⣄⣀⣠⡤⣄⡠⡌⣈⡁⢠⣌⣄⣤⡉⣄⢠⣠⣤⣀⣠⠄⠡⡭⡌⢠⣤⣌⠺⠅⢃⠘⠛⡀⢀⡀⠀⠀⠀⠐⠁⠀⠀⠃⠀⠀⢸ ⡇⠀⠁⠉⡉⠈⣅⢉⡁⠓⠲⢛⠉⣉⣉⣀⣁⡌⠉⡅⢈⣉⡍⠁⡅⠁⢉⣉⣉⣉⡉⢉⡉⢉⣉⡅⢉⡉⡄⢨⠉⢈⣉⣁⣉⢉⣉⣉⡋⢨⡈⢩⠀⠀⣉⡁⢈⣉⣉⢀⠀⠸⠾⠻⣶⡆⠨⠖⠀⠀⠀⠀⠀⠀⠒⠀⠀⢐ ⡇⠀⠀⠀⠁⠀⠉⠀⠉⠀⠈⠀⠀⠉⠉⠉⠉⠁⢀⡑⠊⠉⠁⠀⠁⠁⠘⠉⠉⠉⠁⠀⠁⠈⠉⠁⠈⠁⠁⠈⠁⠈⠉⠈⠉⠉⠉⠙⠁⠈⠁⠈⠀⠀⠈⠁⠉⡥⠈⠈⠠⡀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢨ ⡇⠀⣀⣤⣀⣀⡀⡀⠀⠤⠈⢠⣤⣤⣤⠁⡂⢠⣝⡀⢈⣤⡤⡄⣠⣤⣤⠄⢠⣤⣤⣤⡄⢠⣄⣤⡄⡠⣤⣤⢤⣥⣠⣀⣠⣤⣂⣠⣤⣤⣤⣤⣤⡄⣀⡀⠀⣀⠠⣈⣁⡀⣠⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢸ ⡇⠀⠁⠉⡍⠩⣇⠉⠝⢋⢘⣆⠉⣉⣁⣀⣉⡌⠉⡁⢀⡉⡅⠁⠅⠏⢉⣁⣈⣉⡉⠩⡇⢈⣩⠍⢠⡯⠍⢩⠉⢉⠉⠁⢮⠍⢓⣌⡉⢡⡍⢩⠉⠐⠗⠃⠸⠿⠧⠈⠋⠃⣈⣈⡁⠀⠐⠇⠀⠀⠐⠁⠀⠀⢅⠀⠀⢸ ⡇⠀⠀⠀⠁⠀⠁⠀⠁⠐⠒⠐⠀⠁⠁⠁⠈⠁⠀⠁⠀⠁⠁⢀⠁⠀⠈⠉⢉⠉⢁⠀⠁⠈⠉⠀⠀⠁⠀⠀⠀⠈⠁⠈⠀⠈⡈⢉⠁⠈⠀⠈⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠐⠚⠃⣉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢨ ⡇⠀⢠⣤⣭⣠⡠⣄⣤⡤⠀⢠⣤⣴⣤⣀⡤⢨⠶⡗⢠⣭⣥⠀⢡⣤⣥⣬⣤⣤⡤⡭⡀⠨⣧⣤⣤⣤⣬⣴⡝⢻⠗⠃⠲⠀⡀⠀⢠⡀⡴⠖⢇⠌⠸⠁⠀⠀⠅⡄⣀⡀⢀⠀⠀⡄⢋⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡄⠀⣦⠀⠀⡀⡀⢀⠀⣤⣤⣿⣴⣆⠀⡅⢀⣭⡎⠀⡏⠀⢠⣦⣤⣤⣅⠀⡄⢠⣤⡄⢀⡍⡄⢠⡀⢠⣤⢄⣶⣤⣥⣤⡄⣰⠴⢠⢁⠰⠦⠆⢰⣦⡆⢀⢀⠀⢀⣴⡄⢘⣧⢀⠀⠀⠀⠀⠀⠀⡆⠈⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠃⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠃⠀⠉⠡⠄⠀⠠⠀⠀⠈⠁⠀⠀⠁⠀⠀⠸ ⡇⢀⡀⠀⡀⠀⢀⠀⠀⠂⠀⠀⠀⠂⠀⠀⠂⠀⣀⠀⠀⠂⠀⠀⢀⡀⠀⠀⢀⡀⠀⠀⠀⠀⡀⠀⢀⠀⢀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘ ⡇⠀⠈⠀⡉⢠⡄⣄⡀⣖⡀⠀⠀⠐⠒⠀⠀⠀⠀⠁⣀⢶⡼⣔⡄⠂⠀⠀⠆⠠⣀⢆⡀⠀⠀⡀⠀⡐⠀⠀⡄⠀⠠⣦⠀⡝⢁⢐⠆⠈⠂⡠⡄⠠⡤⡆⣖⣌⠸⣀⡒⡀⠊⠁⠢⡄⠀⠙⠒⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡠⡤⡡⠁⢉⠛⠁⠂⠀⠀⠀⠀⢠⠀⠀⠈⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠃⠀⢀⡁⠀⠀⠀⠁⢤⠓⠀⠀⠈⠈⠁⠀⠀⠁⠁⠈⠉⠉⠁⣡⡅⠘⠣⠇⡀⢐⡔⠀⠀⠀⠀⠂⠀⡆⠀⠀⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠄⠤⠠⠤⠄⠀⠤⠤⠤⠄⠀⠤⠤⠀⠤⠤⠄⠠⠤⠄⠀⠤⠤⠀⠄⠤⠀⠠⠤⠤⠤⠄⠤⠄⠤⠤⠀⠤⠀⠤⠤⠀⠠⠤⠄⠠⠤⠄⠀⠤⠤⠌⠙⠁⠠⠈⠙⠢⠤⠝⠁⠤⠈⠁⠀⠀⠁⠀⠀⠰ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠸⢷⠾⠴⠶⠶⠶⠆⠀⠀⠒⠀⠒⠂⠒⠂⠐⠀⠒⠂⠒⠂⠒⠒⠀⡄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠸⠷⠶⠶⠮⠦⠾⠸⠴⠶⠂⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⡇⠿⠶⠷⠶⠶⠶⡶⠀⠰⠄⠶⠶⠶⠆⠸⠷⠲⠲⠶⠲⠂⠰⠀⠖⠶⠶⠾⠦⠶⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡎⣇⡄⠴⡅⠁⢀⡆⠄⠀⠀⠀⠀⠀⠀⠀⠾⠾⠢⡾⡮⢤⢾⣆⡆⠀⠀⣀⡄⠀⠀⠀⠀⠀⡸ ⡇⠏⠿⠿⠗⠀⠀⠀⠀⠈⠻⠲⠲⠶⠲⠶⠶⠂⠸⠷⠶⠶⠸⠷⠶⠀⠸⠶⠺⠷⠽⠳⠽⠻⠶⠖⠒⠦⠶⠷⠔⠀⠀⡇⠧⡇⠀⡇⡀⠘⡇⣆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠃⠁⠀⠀⠈⠉⠀⠉⠁⠀⢰⡇ ⡟⠻⠖⠫⠷⠶⠇⠀⠀⠨⠵⠶⠲⠆⠸⠣⠞⠄⠇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⡯⠷⢿⠅⡘⢫⡇⡷⠲⠶⠶⠶⠆⠀⠀⠸⡀⠹⡿⠄⠸⠄⠘⠧⠀⠸⡄⠝⡿⠤⠀⠀⢨⡇ ⡟⠛⠲⠆⠃⠗⠶⠀⠀⠐⠦⠦⠔⠆⠸⠠⡆⠠⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡶⠷⣻⠷⠷⠮⠇⡇⡞⠇⠁⠀⠀⠀⠀⠀⣁⡀⡄⢁⣠⡑⣀⡀⠈⢀⣀⣀⡉⠀⠀⠀⠈⡇ ⡇⠛⠛⠒⠒⠓⠃⠁⠀⠀⠃⠐⠱⠓⠓⠛⠃⠘⠚⠚⠲⠺⠚⠐⠲⠂⠾⠒⠐⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡗⡋⠟⠛⠱⠕⠇⠀⠄⠁⠀⠀⠀⠀⠀⠀⠐⠛⠋⡁⠘⠙⠛⣉⣃⠀⣀⣈⣛⡃⢓⣉⡁⠊⠁ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⡓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠙⠛⠺⠒⠛⠛⠂⠀⠉⠀⠀⠉ ⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠛⠘⠆⠀⠈⠂⠀⠀⠀⠈⢡ ⡇⠀⢀⠀⣀⢀⣀⢀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⢨ ⡇⢀⠀⠀⠀⠀⣀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⡀⠀⡀⠀⠛⠂⠘⠛⠓⠂⡓⠛⠛⡃⠘⠛⡛⢙⡒⠘⠓⢃⢘⢛⠛⠛⠛⢚⡚⢛⠛⠛⢛⠛⢁⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨ ⡇⠀⠀⠀⠁⠀⠛⠀⠃⠃⠓⠂⠀⠋⠚⠋⠛⠃⠀⠆⠈⢛⢄⠀⠃⠂⠘⠛⠛⠛⠃⠔⠠⠈⠓⠁⠀⠳⠓⠘⠀⠈⠉⢛⢿⡚⠑⠺⠃⠘⠃⢘⠠⣲⢻⡕⠪⡋⠙⠘⠀⠀⠘⠀⠀⠀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⣀⠀⠀⠒⡀⣆⣤⣤⠀⣀⣀⠀⠀⡀⣀⣀⡀⢀⣀⢞⠀⡆⡀⣀⡀⢀⣀⣉⣀⡆⣀⣀⡀⠀⡀⡀⠀⡀⣀⣀⡀⢀⡀⣄⣀⣀⣀⣀⣀⣀⠐⡛⡂⢰⣶⣦⢤⡄⢤⣤⣌⡆⠁⣭⠍⠉⠁⠀⠂⠀⠡⡀⠀⠀⢸ ⡇⠀⠉⠛⡋⠋⣁⠃⣀⠨⠉⠉⠅⣛⣉⠄⡋⡻⠏⡓⠀⣝⡃⠐⣂⠻⠋⡀⣘⣙⡃⢛⡋⢋⣛⡙⢓⡐⡂⢘⡊⢐⣛⣁⢙⢃⢋⢋⠑⢛⣼⣭⠝⢳⣀⡐⣤⡀⣀⢀⠀⠉⠉⠉⠡⠂⠈⠛⠀⠈⠁⠀⠀⠀⠈⠈⠀⢸ ⡇⠀⠀⠀⠁⠀⠉⠈⠉⢉⡀⠀⠀⠉⠉⠉⠉⠉⢀⣃⠈⠉⠁⠀⠁⡀⠘⠋⠉⠉⠁⠀⠁⠈⠉⠁⠈⠁⠁⠈⡀⠈⠉⣮⠉⠈⠉⠙⠃⠀⢠⡄⣤⠄⣈⡁⠉⠉⢨⣤⡄⡀⢠⣨⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡄⠀⠀⢸ ⡇⠀⢀⣀⣀⢀⣄⣀⡌⠋⠋⢀⣆⣄⣀⠀⡀⠀⡄⡆⢂⣤⣄⡀⡀⣄⠄⣤⣤⢀⣄⣤⣄⣀⣠⡤⣄⡤⡌⣈⡁⢠⣌⣄⣤⡉⣄⢠⣠⣤⣀⣠⠄⠡⡭⡌⢠⣤⣌⠁⠁⢃⠘⠛⡀⢀⡀⠀⠀⠈⠁⠀⠀⠀⠃⠀⠀⢸ ⡇⠀⠁⠉⡉⠈⣅⢉⡁⠓⠲⢛⠉⣉⣉⣀⣁⠌⠉⡅⢈⣉⡍⠁⡅⠁⢉⣉⣉⣉⡉⢉⡉⢉⣉⡅⢉⡉⡄⢨⠉⢈⣉⣁⣩⢉⣉⣉⡋⢨⡈⢩⠀⠀⣉⡁⢈⣉⣉⢀⠀⠸⠾⠻⣶⡆⠨⠖⠀⠀⠀⠀⠀⠀⠒⠀⠀⢐ ⡇⠀⠀⠀⠁⠀⠉⠀⠉⠀⠈⠀⠀⠉⠉⠉⠉⢁⢘⡑⠊⠉⠁⠀⠁⠁⠘⠉⠉⠉⠁⠀⠁⠈⠉⠁⠈⠁⠁⠈⠁⠈⠉⠈⠉⠉⠉⠙⠁⠈⠁⠈⠀⠀⠈⠁⠙⡧⠈⡈⢠⡀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢨ ⡇⠀⣀⣤⣀⣀⡀⡀⠀⢤⡮⢠⣤⣤⣤⠁⡂⢠⣝⡀⢈⣤⡤⡄⣠⣤⣤⠄⢠⣤⣤⣤⡄⢠⣄⣤⡄⡠⣤⣤⢤⣥⣠⣀⣠⣤⣂⣠⣤⣤⣤⣤⣤⡄⣀⡀⢰⣀⣰⡖⡆⡀⣠⣠⡀⠀⠀⠀⠀⢤⡀⠀⠀⠀⡄⠀⠀⢸ ⡇⠀⠁⠉⡍⠩⣇⠉⠍⢁⢉⣆⠉⣉⣁⣀⣉⡌⠉⡁⢀⡉⡅⠁⠅⠏⢉⣁⣈⣉⡉⠩⡇⢈⣩⠍⢠⡯⠍⢩⠉⢉⠉⠁⢮⠍⢓⣌⡉⢡⡍⢩⠉⠐⠗⠃⠸⠋⠉⠉⠁⠃⣈⣈⡁⠀⠐⠇⠀⠀⠁⠀⠀⠀⢅⠀⠀⢸ ⡇⠀⠀⠀⠁⠀⠁⠀⠁⠐⠒⠐⠀⠁⠁⠁⠉⠁⠀⠁⠀⠁⠁⢀⠁⠀⠈⠉⢉⠉⢁⠀⠁⠈⠉⠀⠀⠁⠀⠀⠀⠈⠁⠈⠀⠈⡈⢉⠁⠈⠀⠈⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠐⠚⠃⣉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢨ ⡇⠀⢠⣤⣭⣠⡠⣄⡤⡤⠀⢀⣠⢴⣤⣀⡤⢨⠰⡖⢠⣭⣥⠀⢡⣤⣥⣬⣤⣤⡤⡭⡀⠨⣧⣤⣤⣤⣬⣴⡝⢻⠗⠃⠳⡀⡄⠀⢠⡀⡴⠖⢇⠌⠸⠁⠀⠀⠅⡄⣀⡀⢀⠀⠀⡄⢋⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡄⠀⣦⠀⠀⣐⣖⣄⠀⣤⣤⣿⣴⣆⠀⡅⢀⣭⡎⠀⡏⠀⢠⣦⣤⣤⣅⠀⡄⢠⣤⡄⢀⡍⡄⢠⡀⢠⣤⢄⣶⣤⣥⣤⡄⣰⠴⢠⢁⠰⠦⠆⢰⣦⢐⣶⡆⠀⢀⣴⡄⢘⣧⢀⠀⢠⡀⠀⠀⠀⡆⠈⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠉⠡⠄⠀⠠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠸ ⡇⢀⡀⠀⡀⠀⢀⠀⠀⠂⠀⠀⠀⠂⠀⠀⠂⠀⣀⠀⠀⠂⠀⠀⢀⡀⠀⢀⠀⡀⠀⠀⠀⠀⡀⡀⢀⠀⢀⠀⠀⢀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘ ⡇⠀⠈⠀⡉⢠⡄⣄⡀⣖⡀⠀⠀⠐⠒⠀⠀⠀⠀⠙⣒⢶⡼⣔⡄⠂⠀⠀⠦⠡⢀⢆⡀⠀⠀⡀⠀⡐⠀⠀⡄⠈⠸⣶⠀⡝⢃⢐⠆⠈⠂⡠⡄⠠⡤⡇⣖⣬⠸⠁⠒⠀⠊⠁⠫⠄⠀⠙⠒⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡠⡤⡡⠁⢉⠛⠁⠂⠀⠀⠀⠀⢠⠀⠀⠈⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠃⠀⢀⡁⠀⠀⠀⠁⢤⠓⠀⠀⠈⠈⠁⠀⠀⠁⠁⠈⠉⠉⠁⣡⡅⠘⠣⢇⡀⢐⡔⠀⠲⡄⠀⠂⠀⡆⠀⠀⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠄⠤⠠⠤⠄⠀⠤⠤⠤⠄⠀⠤⠤⠀⠤⠤⠄⠠⠤⠄⠀⠤⠤⠀⠄⠤⠀⠠⠤⠤⠤⠄⠤⠄⠤⠤⠀⠤⠀⠤⠤⠀⠠⠤⠄⠠⠤⠄⠀⠤⠤⠄⠁⠁⠠⠈⠙⠢⠤⠝⠁⠤⠀⠀⠀⠀⠁⠀⠀⠰ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣽⣿⣿⣿⣿⣭⣭⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠸⢷⠾⠴⠶⠶⠶⠆⠀⠀⠒⠀⠒⠂⠒⠂⠐⠀⠒⠂⠒⠂⠒⠒⠀⡄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠸⠷⠶⠶⠮⠦⠾⠸⠴⠶⠂⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⡇⠿⠶⠷⠶⠶⠶⡶⠀⠰⠄⠶⠶⠶⠆⠸⠷⠲⠲⠶⠲⠂⠰⠀⠖⠶⠶⠾⠦⠶⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡎⣇⡄⠴⡅⠁⢀⡆⠄⠀⠀⠀⠀⠀⢀⠀⠾⠾⠢⡾⡮⢤⢾⣆⡆⠀⠀⣀⡄⠀⠀⠀⠀⠀⡸ ⡇⠏⠿⠿⠗⠀⠀⠀⠀⠈⠻⠲⠲⠶⠲⠶⠶⠂⠸⠷⠶⠶⠸⠷⠶⠀⠸⠶⠺⠷⠽⠳⠽⠻⠶⠖⠒⠦⠶⠷⠔⠀⠀⡇⠧⡇⠀⡇⡀⠘⡇⣆⠄⠀⠀⠀⠀⠸⠀⡀⠀⠀⠈⠀⠀⠀⠃⠁⠀⠀⠈⠉⠀⠉⠁⠀⢰⡇ ⡟⠻⠖⠫⠷⠶⠇⠀⠀⠨⠵⠶⠲⠆⠸⠣⠞⠄⠇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⡯⠷⢯⠅⡘⢫⡇⡷⠲⠶⠶⠶⠆⢸⠀⡹⡀⠹⡿⠄⠸⠄⠘⠧⠀⠸⡄⠝⡿⠤⠀⠀⢨⡇ ⡟⠛⠲⠆⠃⠗⠶⠀⠀⠐⠦⠦⠔⠆⠸⠠⡆⠠⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡶⠷⣻⠷⠷⠮⠇⡇⡞⠇⠁⠀⠀⠈⠀⠅⡁⡀⡄⢁⣠⡑⣀⡀⠈⢀⣀⣀⡉⠀⠀⠀⠈⡇ ⡇⠛⠛⠒⠒⠓⠃⠁⠀⠀⠃⠐⠱⠓⠓⠛⠃⠘⠚⠚⠲⠺⠚⠐⠲⠂⠾⠒⠐⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡗⡋⠟⠛⠱⠕⠇⠀⠄⠁⠀⠀⠀⠀⠀⠀⠔⠛⠋⡁⠘⠙⠛⣉⣃⠀⣀⣈⣛⡃⢓⣉⡁⠊⠁ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⡓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠙⠛⠺⠒⠛⠛⠂⠀⠉⠀⠀⠉ ⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠛⠘⠆⠀⠈⠂⠀⠀⠀⠈⢡ ⡇⠀⢀⠀⣀⢀⣀⢀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⢨ ⡇⢀⠀⠀⠀⠀⣀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⡀⠀⡀⠀⠛⠂⠘⠛⠓⠂⡓⠛⠛⡃⠘⠛⡛⢙⡒⠘⠓⢃⢘⢛⠛⠛⠛⢚⡚⢛⠛⠛⢛⠛⢁⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨ ⡇⠀⠀⠀⠁⠀⠛⠀⠃⠃⠓⠂⠀⠋⠚⠋⠛⠃⠀⠆⠈⢛⢄⠀⠃⠂⠘⠛⠛⠛⠃⠔⠠⠈⠓⠁⠀⠳⠓⠘⠀⠈⠉⢛⢿⡚⠑⠺⠃⠘⠃⢘⠠⣲⢻⡕⠪⡋⠙⠘⠀⠀⠘⠀⠀⠀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⣀⠀⠀⠒⡀⣆⣤⣤⠀⣀⣀⠀⠀⡀⣀⣀⡀⢀⣀⢞⠀⡆⡀⣀⡀⢀⣀⣉⣀⡆⣀⣀⡀⠀⡀⡀⠀⡀⣀⣀⡀⢀⡀⣄⣀⣀⣀⣀⣀⣀⠐⡛⡂⢰⣶⣦⢤⡄⢤⣤⣌⡆⠁⣭⠍⠉⠁⠀⠂⠀⠡⡀⠀⠀⢸ ⡇⠀⠉⠛⡋⠋⣁⠃⣀⠨⠉⠉⠅⣛⣉⠄⡋⡻⠏⡓⠀⣝⡃⠐⣂⠻⠋⡀⣘⣙⡃⢛⡋⢋⣛⡙⢓⡐⡂⢘⡊⢐⣛⣁⢙⢃⢋⢋⠑⢛⣼⣭⠝⢳⣀⡐⣤⡀⣀⢀⠀⠉⠉⠉⠡⠂⠈⠛⠀⠈⠁⠀⠀⠀⠈⠈⠀⢸ ⡇⠀⠀⠀⠁⠀⠉⠈⠉⢉⡀⠀⠀⠉⠉⠉⠉⠉⢀⣃⠈⠉⠁⠀⠁⡀⠘⠋⠉⠉⠁⠀⠁⠈⠉⠁⠈⠁⠁⠈⡀⠈⠉⣮⠉⠈⠉⠙⠃⠀⢠⡄⣤⠄⣈⡁⠉⠉⢨⣤⡄⡀⢠⣨⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡄⠀⠀⢸ ⡇⠀⢀⣀⣀⢀⣄⣀⡌⠋⠋⠀⣆⣀⣀⠀⡀⠀⡄⡆⢂⣤⣄⡀⡀⣄⠄⣤⣤⢀⣄⣤⣄⣀⣠⡤⣄⡤⡌⣈⡁⢠⣌⣄⣤⡉⣄⢠⣠⣤⣀⣠⠄⠡⡭⡌⢠⣤⣌⠁⠁⢃⠘⠛⡀⢀⡀⠀⠀⠈⠁⠀⠀⠀⠃⠀⠀⢸ ⡇⠀⠁⠉⡉⠈⣅⢉⡁⠓⠲⢛⠉⣉⣉⣀⣁⠌⠉⡅⢈⣉⡍⠁⡅⠁⢉⣉⣉⣉⡉⢉⡉⢉⣉⡅⢉⡉⡄⢨⠉⢈⣉⣁⣩⢉⣉⣉⡋⢨⡈⢩⠀⠀⣉⡁⢈⣉⣉⢀⠀⠸⠾⠻⣶⡆⠨⠖⠀⠀⠀⠀⠀⠀⠒⠀⠀⢐ ⡇⠀⠀⠀⠁⠀⠉⠀⠉⠀⠈⠀⠀⠉⠉⠉⠉⢁⢘⡑⠊⠉⠁⠀⠁⠁⠘⠉⠉⠉⠁⠀⠁⠈⠉⠁⠈⠁⠁⠈⠁⠈⠉⠈⠉⠉⠉⠙⠁⠈⠁⠈⠀⠀⠈⠁⠙⡧⠈⡈⢠⡀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢨ ⡇⠀⣀⣤⣀⣀⡀⡀⠀⢤⡮⢠⣤⣤⣤⠁⡂⢠⣝⡀⢈⣤⡤⡄⣠⣤⣤⠄⢠⣤⣤⣤⡄⢠⣄⣤⡄⡠⣤⣤⢤⣥⣠⣀⣠⣤⣂⣠⣤⣤⣤⣤⣤⡄⣀⡀⢰⣀⣰⡖⡆⡀⣠⣠⡀⠀⠀⠀⠀⢤⡀⠀⠀⠀⡄⠀⠀⢸ ⡇⠀⠁⠉⡍⠩⣇⠉⠍⢁⢉⣆⠉⣉⣁⣀⣉⡌⠉⡁⢀⡉⡅⠁⠅⠏⢉⣁⣈⣉⡉⠩⡇⢈⣩⠍⢠⡯⠍⢩⠉⢉⠉⠁⢮⠍⢓⣌⡉⢡⡍⢩⠉⠐⠗⠃⠸⠋⠉⠉⠁⠃⣈⣈⡁⠀⠐⠇⠀⠀⠁⠀⠀⠀⢅⠀⠀⢸ ⡇⠀⠀⠀⠁⠀⠁⠀⠁⠐⠒⠐⠀⠁⠁⠁⠉⠁⠀⠁⠀⠁⠁⢀⠁⠀⠈⠉⢉⠉⢁⠀⠁⠈⠉⠀⠀⠁⠀⠀⠀⠈⠁⠈⠀⠈⡈⢉⠁⠈⠀⠈⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠐⠚⠃⣉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢨ ⡇⠀⢠⣤⣭⣠⡠⣄⡤⡤⠀⢀⣠⢴⣤⣀⡤⢨⠰⡖⢠⣭⣥⠀⢡⣤⣥⣬⣤⣤⡤⡭⡀⠨⣧⣤⣤⣤⣬⣴⡝⢻⠗⠃⠳⡀⡄⠀⢠⡀⡴⠖⢇⠌⠸⠁⠀⠀⠅⡄⣀⡀⢀⠀⠀⡄⢋⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡄⠀⣦⠀⠀⣐⣦⣆⠀⣤⣤⣿⣴⣆⠀⡅⢀⣭⡎⠀⡏⠀⢠⣦⣤⣤⣅⠀⣤⢠⣤⡄⢀⡍⡄⢠⡀⢠⣤⢄⣶⣤⣥⣤⡄⣰⠴⢠⢁⠰⠦⠆⢰⣦⢐⣶⡆⠀⢀⣴⡄⢘⣧⢀⠀⢠⡀⠀⠀⠀⡆⠈⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠉⠡⠄⠀⠠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠸ ⡇⢀⡀⠀⡀⠀⢀⠀⠀⠂⠀⠀⠀⠂⠀⠀⠂⠀⣀⠀⠀⠂⠀⠀⢀⡀⠀⢀⠀⡀⠀⠀⠀⠀⡀⡀⢀⠀⢀⠀⠀⢀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘ ⡇⠀⠈⠀⡉⢠⡄⣄⡀⣖⡀⠀⠀⠐⠒⠀⠀⠀⠀⠙⣒⢶⡼⣔⡄⠂⠀⠀⠦⠡⢀⢆⡀⠀⠀⡀⠀⡐⠀⠀⡄⠈⠸⣶⠀⡝⢃⢐⠆⠈⠂⡠⡄⠠⡤⡇⣖⣬⠸⠁⠒⠀⠊⠁⠫⠄⠀⠙⠒⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡠⡤⡡⠁⢉⠛⠁⠂⠀⠀⠀⠀⢠⠀⠀⠈⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠃⠀⢀⡁⠀⠀⠀⠁⢤⠓⠀⠀⠈⠈⠁⠀⠀⠁⠁⠈⠉⠉⠁⣡⡅⠘⠣⢇⡀⢐⡔⠀⠲⡄⠀⠂⠀⡆⠀⠀⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠄⠤⠠⠤⠄⠀⠤⠤⠤⠄⠀⠤⠤⠀⠤⠤⠄⠠⠤⠄⠀⠤⠤⠀⠄⠤⠀⠠⠤⠤⠤⠄⠤⠄⠤⠤⠀⠤⠀⠤⠤⠀⠠⠤⠄⠠⠤⠄⠀⠤⠤⠄⠁⠁⠠⠈⠙⠢⠤⠝⠁⠤⠀⠀⠀⠀⠁⠀⠀⠰ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣽⣿⣿⣿⣿⣭⣭⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠸⢷⠾⠴⠶⠶⠶⠆⠀⠀⠒⠀⠒⠂⠒⠂⠐⠀⠒⠂⠒⠂⠒⠒⠀⡄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠸⠷⠶⠶⠮⠦⠾⠸⠴⠶⠂⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⡇⠿⠶⠷⠶⠶⠶⡶⠀⠰⠄⠶⠶⠶⠆⠸⠷⠲⠲⠶⠲⠂⠰⠀⠖⠶⠶⠾⠦⠶⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡎⣇⡄⠴⡅⠁⢀⡆⠄⠀⠀⠀⠀⠀⢀⠀⠾⠾⠢⡾⡮⢤⢾⣆⡆⠀⠀⣀⡄⠀⠀⠀⠀⠀⡸ ⡇⠏⠿⠿⠗⠀⠀⠀⠀⠈⠻⠲⠲⠶⠲⠶⠶⠂⠸⠷⠖⠶⠸⠷⠶⠀⠸⠶⠺⠷⠽⠳⠽⠻⠶⠖⠒⠦⠶⠷⠔⠀⠀⡇⠧⡇⠀⡇⡀⠘⠇⣆⠄⠀⠀⠀⠀⠸⠀⡀⠀⠀⠈⠀⠀⠀⠃⠁⠀⠀⠈⠉⠀⠉⠁⠀⢰⡇ ⡟⠻⠖⠫⠷⠶⠇⠀⠀⠨⠵⠶⠲⠆⠸⠣⠞⠄⠇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⡯⠷⢯⠅⡘⢫⡇⡷⠲⠶⠶⠶⠆⢸⠀⡹⡀⠹⡿⠄⠸⠄⠘⠧⠀⠸⡄⠝⡿⠤⠀⠀⢠⡇ ⡟⠛⠲⠆⠃⠗⠶⠀⠀⠐⠦⠦⠔⠆⠸⠠⡆⠠⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⡶⠷⣻⠷⠷⠮⠇⡇⡞⠇⠁⠀⠀⠈⠀⠅⡁⡀⡄⢁⣠⡑⣀⡀⠈⢀⣀⣀⡉⠀⠀⠀⠈⡇ ⡇⠛⠛⠒⠒⠓⠃⠁⠀⠀⠃⠐⠱⠓⠓⠛⠃⠘⠚⠚⠲⠺⠚⠐⠲⠂⠾⠒⠐⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡗⡋⠟⠛⠱⠕⠇⠀⠄⠁⠀⠀⠀⠀⠀⠀⠔⠛⠋⡁⠘⠙⠛⣉⣃⠀⣀⣈⣛⡃⢓⣉⡁⠊⠁ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⡓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠙⠛⠺⠒⠛⠓⠂⠀⠉⠀⠀⠉ ⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠛⠘⠆⠀⠈⠂⠀⠀⠀⠈⢡ ⡇⠀⢀⠀⣀⢀⣀⢀⣀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⢨ ⡇⢀⠀⠀⠀⠀⣀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⡀⠀⡀⠀⠛⠂⠘⠛⠓⠂⡓⠛⠛⡃⠘⠛⡛⢙⡒⠘⠓⢃⢘⢛⠛⠛⠛⢚⡚⢛⠛⠛⢛⠛⢁⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨ ⡇⠀⠀⠀⠁⠀⠛⠀⠃⠃⠓⠂⠀⠋⠚⠋⠛⠃⠀⠆⠈⢛⢄⠀⠃⠂⠘⠛⠛⠛⠃⠔⠠⠈⠓⠁⠀⠳⠓⠘⠀⠈⠉⢛⢿⡚⠑⠺⠃⠘⠃⢘⠠⣲⢻⡕⠪⡋⠙⠘⠀⠀⠘⠀⠀⠀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⣀⠀⠀⠒⡀⣆⣤⣤⠀⣀⣀⠀⠀⡀⣀⣀⡀⢀⣀⢞⠀⡆⡀⣀⡀⢀⣀⣉⣀⡆⣀⣀⡀⠀⡀⡀⠀⡀⣀⣀⡀⢀⡀⣄⣀⣀⣀⣀⣀⣀⠐⡛⡂⢰⣶⣦⢤⡄⢤⣤⣌⡆⠁⣭⠍⠉⠁⠀⠂⠀⠡⡀⠀⠀⢸ ⡇⠀⠉⠛⡋⠋⣁⠃⣀⠨⠉⠉⠅⣛⣉⠄⡋⡻⠏⡓⠀⣝⡃⠐⣂⠻⠋⡀⣘⣙⡃⢛⡋⢋⣛⡙⢓⡐⡂⢘⡊⢐⣛⣁⢙⢃⢋⢋⠑⢛⣼⣭⠝⢳⣀⡐⣤⡀⣀⢀⠀⠉⠉⠉⠡⠂⠈⠛⠀⠈⠁⠀⠀⠀⠈⠈⠀⢸ ⡇⠀⠀⠀⠁⠀⠉⠈⠉⢉⡀⠀⠀⠉⠉⠉⠉⠉⢀⣃⠈⠉⠁⠀⠁⡀⠘⠋⠉⠉⠁⠀⠁⠈⠉⠁⠈⠁⠁⠈⡀⠈⠉⣮⠉⠈⠉⠙⠃⠀⢠⡄⣤⠄⣈⡁⠈⠉⢨⣤⡄⡀⢠⣨⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡄⠀⠀⢸ ⡇⠀⢀⣀⣀⢀⣄⣀⡌⠋⠋⠀⠆⣀⣀⠀⡀⠀⡄⡆⢂⣤⣄⡀⡀⣄⠄⣤⣤⢀⣄⣤⣄⣀⣠⡤⣄⡠⡌⣈⡁⢠⣌⣄⣤⡉⣄⢠⣠⣤⣀⣠⠄⠡⡭⡌⢠⣤⣌⠁⠁⢃⠘⠛⡀⢀⡀⠀⠀⠈⠁⠀⠀⠀⠃⠀⠀⢸ ⡇⠀⠁⠉⡉⠈⣅⢉⡁⠓⢲⣫⢤⡍⣉⣀⣁⠌⠉⡅⢈⣉⡍⠁⡅⠁⢉⣉⣉⣉⡉⢉⡉⢉⣉⡅⢉⡉⡄⢨⠉⢈⣉⣁⣉⢉⣉⣉⡋⢨⡈⢩⠀⠀⣉⡁⢈⣉⣉⢀⠀⠸⠾⠻⣶⡆⠨⠖⠀⠀⠀⢀⣤⣤⠒⠀⠀⢐ ⡇⠀⠀⠀⠁⠀⠉⠀⠉⠀⠈⠋⠛⠚⠉⠉⠉⢁⢘⡑⠊⠉⠁⠀⠁⠁⠘⠉⠉⠉⠁⠀⠁⠈⠉⠁⠈⠁⠁⠈⠁⠈⠉⠈⠉⠉⠉⠙⠁⠈⠁⠈⠀⠀⠈⠁⠙⡧⠈⡈⢠⡀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠉⠛⠛⠀⠀⠄⢨ ⡇⠀⣀⣤⣀⣀⡀⡀⠀⢤⡮⢠⣤⣤⣤⠁⡂⢠⣝⡀⢈⣤⡤⡄⣠⣤⣤⠄⢠⣤⣤⣤⡄⢠⣄⣤⡄⡠⣤⣤⢤⣥⣠⣀⣠⣤⣂⣠⣤⣤⣤⣤⣤⡄⣀⡀⢰⣀⣰⡖⡆⡀⣠⣠⡀⠀⠀⠀⠀⢤⡀⠀⠀⠀⡄⠀⠀⢰ ⡇⠀⠁⠉⡍⠩⣇⠉⠍⢁⢉⣆⠉⣉⣁⣀⣉⡌⠉⡁⢀⡉⡅⠁⠅⠏⢉⣁⣈⣉⡉⠩⡇⢈⣩⠍⢠⡯⠍⢩⠉⢉⠉⠁⢮⠍⢓⣌⡉⢡⡍⢩⠉⠐⠗⠃⠸⠋⠉⠉⠁⠃⣈⣈⡁⠀⠐⠇⠀⠀⠁⠀⠀⠀⢅⠀⠀⢸ ⡇⠀⠀⠀⠁⠀⠁⠀⠁⠐⠒⠐⠀⠁⠁⠁⠈⠁⠀⠁⠀⠁⠁⢀⠁⠀⠈⠉⢉⠉⢁⠀⠁⠈⠉⠀⠀⠁⠀⠀⠀⠈⠁⠈⠀⠈⡈⢉⠁⠈⠀⠈⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠐⠚⠃⣉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢨ ⡇⠀⢠⣤⣭⣠⡠⣄⡤⡤⠀⢀⣠⢴⣤⣀⡤⢨⠰⡖⢠⣭⣥⠀⢡⣤⣥⣬⣤⣤⡤⡭⡀⠨⣧⣤⣤⣤⣬⣴⡝⢻⠗⠃⠳⠀⡀⠀⢠⡀⡴⠖⢇⠌⠸⠁⠀⠀⠅⡄⣀⡀⢀⠀⠀⡄⢋⢀⣤⠀⢀⣘⡿⣷⠀⠀⠀⢸ ⡇⠀⠀⠀⡄⠀⣦⠀⠀⣐⣦⣆⠀⣤⣤⣿⣴⣆⠀⡅⢀⣭⡎⠀⡏⠀⢠⣦⣤⣤⣅⠀⣤⢠⣤⡄⢀⡍⡄⢠⡀⢠⣤⢄⣶⣤⣥⣤⡄⣰⠴⢠⢁⠰⠦⠆⢰⣦⢐⣶⡆⠀⢀⣴⡄⢘⣧⢀⠀⢠⡀⠀⠀⠀⡆⠈⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠉⠡⠄⠀⠠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠸ ⡇⢀⡀⠀⡀⠀⢀⠀⠀⠂⠀⠀⠀⠂⠀⠀⠂⠀⣀⠀⠀⠂⠀⠀⢀⡀⠀⢀⠀⡀⠀⠀⠀⠀⡀⡀⢀⠀⢀⠀⠀⢀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘ ⡇⠀⠈⠀⡉⢠⡄⣄⡀⣖⡠⡆⠀⢀⠒⠀⠀⠀⠀⠙⣒⢶⡼⣔⡄⠂⠀⠀⠦⠡⢀⢆⡄⠀⠀⡀⠀⡐⠀⠀⡄⠈⠸⣶⠀⡝⢃⢐⠆⠈⠂⡠⡄⠠⡤⡇⣖⣌⠸⠁⠒⠀⠊⠁⠫⠄⠀⠙⠒⠀⠀⠀⣦⣤⠀⠀⠀⢸ ⡇⠀⠀⠀⡠⡤⡡⠁⢉⠛⠁⠀⠀⠈⠀⠀⢠⠀⠀⠈⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠃⠀⢀⡁⠀⠀⠀⠁⢤⠓⠀⠀⠈⠈⠁⠀⠀⠁⠁⠈⠉⠉⠁⣡⡅⠘⠣⠇⡀⢐⡔⠀⠲⡄⠀⠁⠘⠀⠀⠀⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠄⠤⠠⠤⠄⠀⠤⠤⠤⠄⠀⠤⠤⠀⠤⠤⠄⠠⠤⠄⠀⠤⠤⠀⠄⠤⠀⠠⠤⠤⠤⠄⠤⠄⠤⠤⠀⠤⠀⠤⠤⠀⠠⠤⠄⠠⠤⠄⠀⠤⠤⠄⠁⠁⠠⠈⠙⠢⠤⠝⠁⠤⠀⠀⠀⠀⠁⠀⠀⠰ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣽⣿⣿⣿⣿⣭⣭⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣻⣿⣿⣿⣿⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠸⢷⠾⠴⠶⠶⠶⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠗⠶⠶⠾⠶⠾⠱⠴⠲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⡇⠿⠶⠷⠶⢶⡶⡶⠀⠰⠄⠶⠶⠶⠆⠸⠷⠲⠲⠶⠲⠆⠰⠀⠖⠴⠶⠾⠶⠶⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡯⠗⠶⠶⠅⠗⠦⠆⠀⠀⠀⠀⠀⠀⠀⠸⠿⠆⠼⠾⠦⠸⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸ ⡇⠏⠿⠿⠗⠀⠀⠀⠀⠈⠳⠲⠲⠶⠲⠶⠶⠆⠸⠷⠞⠴⠺⠶⠶⠂⠸⠶⠺⠸⠹⠻⠼⠙⠶⠖⠒⠦⠶⠗⠕⠀⡃⡷⠯⠦⠔⠆⠕⠐⠗⠆⠄⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇ ⡟⠻⠖⠯⠷⠶⠇⠀⠀⠸⠷⠶⠲⠆⠸⠱⠞⠾⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⡧⠧⠶⠦⠅⠰⠷⠆⠶⠲⠶⠶⠶⠆⠸⠰⠆⠰⠹⠆⠨⠧⠸⠿⠀⠸⠣⠀⠿⠻⠤⠀⠀⢨⡇ ⡟⠟⠶⠂⠇⠗⠶⠀⠀⠸⠶⠖⠞⠇⠸⠑⠖⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡇⠃⠷⠖⠗⠷⠮⠧⠶⠖⠇⠀⠀⠀⠀⠨⠽⠿⠇⠸⠿⠗⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇ ⡇⠛⠛⠒⠓⠃⠃⠁⠀⠀⠃⠐⠳⠟⠛⠚⠃⠸⠚⠛⠚⠚⠘⠐⠺⠆⠾⠒⠘⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡇⠛⠓⠓⠛⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠉ ⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡇⠀⠀⠀⡀⠀⣀⢀⡀⠀⠀⡀⣀⡀⠀⠀⠀⢀⡀⡀⢀⣀⣀⠀⠀⣀⢀⠀⣀⣀⣀⢀⣀⣀⣀⠀⣀⣀⣀⡀⠀⣀⡀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⢨ ⡇⢐⠋⠃⡛⠒⡀⢘⢙⡃⠀⠐⠙⠊⠀⠈⠂⠘⠉⠁⠘⢛⡛⢁⠛⠚⠓⠀⠛⠛⠋⢉⠛⠛⢛⠉⣛⢛⠃⠓⠊⠙⠛⡈⡙⠙⠛⠛⠓⡒⠛⡛⢛⣛⡋⢃⣀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨ ⡇⠀⠀⠀⠃⠈⠋⠚⠋⠓⠃⠀⠘⠙⠛⠛⠛⠁⠈⠃⠘⢙⢀⠘⠐⠀⠻⠛⠙⠙⠀⠘⠀⠛⠋⠀⠛⠘⠀⠁⠀⠛⠋⠋⢃⡂⠛⠇⠀⠁⠀⠃⠀⠛⢃⡘⠙⡛⠘⠃⠃⠀⠘⠁⠀⠀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⣀⠀⠀⠀⠀⣀⡀⠀⢀⣀⣀⡀⢀⣀⣀⢀⡀⢀⣀⢊⠀⣂⣀⣀⠀⣀⣀⣉⣀⣂⣀⣀⣀⢀⡀⠀⣀⢀⣀⣀⢀⣀⣀⣂⣀⣀⣀⣀⣀⣀⣐⣛⡂⢐⣲⣦⢤⡄⢤⣤⣬⡆⠁⣭⠍⠉⠁⠀⠂⠀⢡⡀⠀⠀⢸ ⡇⠀⠉⠉⡋⢋⣉⢛⣃⣃⡉⠈⢁⣋⡁⢀⣀⡚⢛⡁⠈⢙⡉⢀⠙⠛⢙⠀⢛⢙⠙⢛⠙⠙⣉⠉⢛⢛⠁⠁⠉⢛⣋⣉⡛⡙⣙⡉⠛⡋⠋⡋⡋⣛⡛⢑⣀⡀⢀⢀⡀⠉⠉⠉⠡⠂⠈⠛⠀⠈⠁⠀⠀⠀⠈⠈⠀⢸ ⡇⠀⠀⠀⠁⠈⠉⠈⠉⢉⡁⠀⠈⠉⠉⠉⠉⠁⢈⣁⠉⠉⠀⠈⠀⡀⠚⠉⠉⠉⠀⠘⠀⠉⠉⠀⠈⠈⠀⠁⡀⠉⠉⣁⠁⠁⠉⠃⠀⠁⢀⡁⣥⠍⣁⡈⠉⠉⢉⣤⡀⡀⢠⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡄⠀⠀⢸ ⡇⠀⢀⣀⣀⣀⣀⡀⡌⠋⠋⢀⡀⣀⡀⢀⠀⠀⣀⡀⣂⣤⣀⡀⢀⣠⢀⣄⣀⣀⣠⣠⣀⣀⣠⣤⣤⢤⠈⣈⢁⣤⣨⣄⣤⣉⢀⣤⣤⣄⣀⡄⠀⠡⡭⡍⢡⣤⣌⠁⠁⢃⠚⠛⡀⢀⡀⠈⠀⠈⠁⠀⠀⠀⠃⠀⠀⢸ ⡇⠀⠈⠉⡉⢉⣅⠉⣅⡅⠀⠉⢁⣉⣁⣀⣀⡈⢩⡁⢈⣉⠉⢀⠈⠉⣉⣉⣉⣉⠉⢩⠉⣉⣡⠉⣉⢡⠀⡉⠁⣉⣉⣁⡁⣉⣉⣋⠁⡁⠉⠁⢀⣄⡍⢡⣬⡍⣉⠀⡄⠈⢈⠉⠐⡆⠨⠖⠀⠀⠀⢀⣤⣤⠒⠀⠀⢐ ⡇⠀⠀⠀⠁⠀⠉⠁⠁⠉⠀⠁⠈⠈⠉⠉⡉⢁⢈⡁⠈⠉⠀⠈⠈⠀⠈⠉⠉⠈⠀⠈⠀⠉⠁⠀⠈⠈⠀⠁⠀⠈⠁⠁⠁⠁⠉⠋⠀⠁⠀⠁⠀⠉⠁⠈⠉⡥⠈⡁⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠀⠀⠄⢨ ⡇⠀⣀⣤⣀⣀⡀⣀⣄⡄⠈⢠⣤⣤⡄⠁⠄⢠⣽⡄⣨⣤⣤⡀⣤⣤⡤⠀⣤⣤⣤⣤⡀⢤⣠⣤⣀⣤⣤⡤⣤⣄⣄⣠⣤⣄⣀⣠⢄⣤⣤⣄⣤⣤⣀⡤⢤⣄⡄⠔⡆⡀⣠⣠⡀⠀⠀⠀⠀⢤⡀⠀⠀⠀⡄⠀⠀⢰ ⡇⠀⠀⠉⡍⢩⣄⢩⣍⣥⡀⠈⢉⣍⣁⣀⣀⡌⢩⡅⢈⣩⠉⢠⠀⠉⣨⣀⣈⣉⡉⢩⠀⣨⣩⠉⣤⢩⠉⡍⠉⣉⣉⡄⡍⣉⣄⣉⠉⠀⠉⠅⢉⣬⡍⢁⣥⣅⣁⡈⡅⠁⢈⠈⠁⠀⠐⠇⠀⠀⠁⠀⠀⠀⢅⠀⠀⢸ ⡇⠀⠀⠀⠁⠀⠁⠀⠁⠁⠂⠀⠀⠈⠉⠉⠉⠁⠀⠁⠈⠉⠀⢈⠈⠀⠈⠈⢀⠈⢀⠈⠁⠉⠀⠀⠈⠈⠀⠁⠀⠉⠁⠀⠁⠀⡉⢁⠀⠀⠀⠁⠀⠁⠁⠀⠉⠁⠈⠀⠁⠀⠀⠀⠘⠃⣉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢨ ⡇⠀⣠⣤⣭⣀⡠⣤⡤⡄⠀⢠⣤⣤⡄⢠⠀⢨⢤⡄⢠⣭⣥⡀⣡⣤⣁⢠⣠⣤⠀⣭⠀⢬⣥⣤⣤⡤⣤⠰⡝⢻⠗⠃⠳⡀⡄⠀⢠⡀⡴⠖⢇⠌⠸⠁⠀⠀⠅⡄⣄⡀⢀⠀⠀⡄⢋⢀⣤⠀⢀⣘⡿⣷⠀⠀⠀⢸ ⡇⠀⠀⠀⡄⢠⣤⢀⣤⣤⣄⡂⢠⢤⣤⣤⣄⡄⠠⡄⢠⣠⠀⢠⢀⠀⢤⣀⣠⣠⠄⢠⠀⣤⣤⠀⣤⢠⠀⣄⠀⣠⡄⡄⡄⡄⣤⣄⠀⡀⠀⡄⢁⢄⡆⢄⣤⣄⢤⡄⡄⠀⠀⠀⠀⢘⣧⢀⠀⢠⡀⠀⠀⠀⡆⠈⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠸ ⡇⢀⡀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠀⣀⠀⠀⠂⠀⠀⢀⡀⠀⢀⠀⡀⠀⠀⠀⠀⡀⡀⢀⠀⢀⠀⠀⢀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘ ⡇⠀⠈⠀⡉⢠⡄⣄⡀⣖⡠⡆⠀⢀⠒⠀⠀⠀⠀⠙⣒⢶⡼⣔⡄⠂⠀⠀⠦⠡⢀⢆⡄⠀⠀⡀⠀⡐⠀⠀⡄⠌⠸⣶⠀⡝⢃⢐⠆⠈⠂⡠⡄⠠⡤⡇⣖⣬⠸⠁⠒⠀⠊⠁⠫⠄⠀⠙⠒⠀⠀⠀⣦⣤⠀⠀⠀⢸ ⡇⠀⠀⠀⠠⠤⠡⠉⠙⠛⠁⠀⠀⠈⠀⠀⠠⠀⠀⠈⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠃⠀⠀⠁⠀⠀⠀⠁⠤⠓⠀⠀⠈⠈⠁⠀⠀⠁⠁⠈⠉⠉⠁⠡⠅⠘⠣⢇⠀⠐⠔⠀⠲⠀⡴⣦⡄⠤⠀⠠⢸ ⠣⠄⠠⠠⠄⠠⠄⠄⠄⠠⠀⠄⠀⠄⠄⠠⠠⠄⠄⠄⠄⠠⠠⠠⠠⠀⠀⠤⠤⠄⠄⠠⠤⠤⠠⠠⠀⠤⠤⠤⠤⠤⠤⠄⠄⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠠⠠⠤⠤⠠⠁⠥⠤⠬⠭⠠⠠⠭⠡⠤⠄⠤⠤⠤⠤⠤⠤⠸ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠸⢷⠾⠴⠶⠶⠶⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠗⠶⠶⠾⠶⠾⠵⠴⠲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⡇⠿⠶⠷⠶⢶⡶⡶⠀⠰⠄⠶⠶⠶⠆⠸⠷⠲⠲⠶⠲⠖⠰⠀⠖⠴⠶⠾⠶⠶⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢸⠶⠶⠅⠗⠦⠆⠄⠀⠀⠀⠀⠀⠀⠸⠿⠆⠼⠾⠦⠸⠿⠎⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸ ⡇⠏⠿⠿⠗⠀⠀⠀⠀⠈⠳⠲⠲⠶⠲⠶⠶⠆⠸⠷⠞⠴⠲⠶⠶⠂⠸⠶⠺⠸⠻⠻⠼⠙⠶⠖⠒⠦⠶⠗⠕⠀⡃⣟⠼⠦⠔⠆⠕⠐⠖⠆⠄⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇ ⡟⠻⠖⠯⠷⠶⠇⠀⠀⠸⠷⠶⠲⠆⠸⠱⠞⠾⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⡾⠸⠶⠦⠅⠰⠷⠖⠶⠲⠶⠶⠶⠆⠸⠰⠆⠰⠹⠆⠨⠧⠸⠿⠀⠸⠣⠀⠿⠻⠤⠀⠀⢨⡇ ⡟⠟⠶⠂⠇⠗⠶⠀⠀⠸⠶⠖⠞⠇⠸⠑⠖⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡇⠃⠷⠖⠗⠷⠮⠧⠶⠖⠇⠀⠀⠀⠀⠨⠽⠿⠛⠟⠇⠐⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇ ⡇⠛⠛⠒⠓⠃⠃⠁⠀⠀⠃⠐⠳⠟⠛⠚⠃⠸⠚⠛⠚⠚⠘⠐⠺⠆⠾⠒⠘⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣇⠛⠓⠓⠛⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠊⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠉ ⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡇⠀⠀⠀⡀⠀⣀⢀⡀⠀⠀⡀⣀⡀⠀⠀⠀⢀⡀⡀⢀⣀⣀⠀⠀⣀⢀⠀⣀⣀⣀⢀⣀⣀⣀⢀⢀⣀⣀⡀⠀⣀⡀⠀⣀⣀⡀⣀⣀⣀⣀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⢨ ⡇⢐⠋⠃⡛⠒⡀⠘⣙⣃⠀⠐⠙⠊⠀⠈⠂⠘⠉⠁⠘⢛⡛⢁⠛⠚⠓⠀⠛⠛⠋⢉⠛⠛⢛⠉⣛⢛⠃⠓⠊⠙⠛⡈⡙⢙⠛⠛⠓⡒⠛⡛⢛⡛⢋⣃⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨ ⡇⠀⠀⠀⠃⠈⠋⠊⠛⠛⠃⠀⠘⠙⠛⠛⠛⠁⠈⠃⠘⢙⢀⠘⠐⠀⠻⠛⠙⠙⠀⠘⠀⠛⠋⠀⠛⠘⠀⠁⠀⠛⠋⠃⢃⡒⠛⠇⠀⠁⠀⠃⠀⠃⠙⡛⠛⡛⠘⠃⠃⠀⠈⠀⠈⠃⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⣀⠀⠀⠀⠀⣀⡀⠀⢀⣀⣀⡀⢀⣀⣀⢀⡀⢀⣀⢊⠀⣂⣀⣀⠀⣀⣀⣉⣀⣂⣀⣀⣀⢀⡀⠀⣀⢀⣀⣀⢀⣀⣀⣂⣀⣀⣀⣀⣀⣀⣐⣛⡂⢐⣲⣦⢤⡄⢤⣤⣬⡆⠁⣭⠍⠉⠁⠀⠂⠀⠡⡀⠀⠀⢸ ⡇⠀⠉⠉⡋⢋⣉⢛⣃⣃⡉⠈⢁⣋⡁⢀⣀⡚⢛⣁⠈⢙⡉⢀⠙⠛⢙⠀⢛⢙⠙⢛⠙⠙⣉⠉⢛⢛⠁⠁⠉⢛⣋⣉⡛⡙⣙⡉⠛⡋⠋⡋⡋⣛⢛⣑⠀⡀⢀⢀⡀⠉⠉⠉⢁⠀⠈⠛⠀⠈⠁⠀⠀⠀⠈⠈⠀⢸ ⡇⠀⠀⠀⠁⠈⠉⠈⠉⢉⡁⠀⠈⠉⠉⠉⠉⠁⢈⣁⠉⠉⠀⠈⠈⡀⠚⠉⠉⠉⠀⠘⠀⠉⠉⠀⠈⠈⠀⠁⡀⠉⠉⣁⠁⠁⠉⠃⠀⠁⢀⡁⣥⠍⣈⡉⠁⠉⢉⣤⡀⡀⢠⣀⠈⠁⠀⠀⠀⢀⠀⠀⠀⠀⡄⠀⠀⢸ ⡇⠀⢀⣀⣀⣀⣀⡀⡌⠋⠋⢀⡀⣀⡀⢀⠀⠀⣀⡀⣂⣤⣀⡀⢀⣠⢀⣄⣀⣀⣠⣠⣀⣀⣠⣤⣤⢤⠈⣈⢁⣤⣨⣄⣤⣉⢀⣤⣤⣄⣀⡄⠀⠡⡭⡍⢡⣤⣌⠁⠁⢃⠘⠛⡀⢀⡀⠈⠀⠈⠁⠀⠀⠀⠃⠀⠀⢸ ⡇⠀⠈⠉⡉⢉⣅⠉⣁⣅⠀⠉⢁⣉⣁⣀⣀⡈⢩⣅⢈⣉⠉⢀⣈⠉⣉⣉⣉⣉⠉⢩⠉⣉⣡⢩⣉⢡⠀⡉⠁⣉⣉⣁⡁⣉⣉⣋⠁⡁⠉⠁⢀⣄⡉⢡⣈⡍⣉⠀⡄⠈⢈⠉⢀⠀⠈⠖⠀⠀⠀⢀⣤⣤⠒⠀⠀⢐ ⡇⠀⠀⠀⠁⠀⠉⠀⠁⠉⠀⠁⠈⠈⠉⠉⠉⢁⢈⡁⠈⠉⠁⠈⠈⠀⠈⠉⠉⠈⠀⠈⠈⠉⠁⠀⠈⠈⠀⠁⠀⠈⠁⠁⠁⠁⠉⠋⠀⠁⠀⠁⠀⠉⠁⠈⠁⡥⠈⡁⢡⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠛⠛⠀⠀⠄⢨ ⡇⠀⣀⣤⣀⣀⡀⣀⣄⡄⠈⢠⣤⣤⡄⠁⡄⢠⣽⡄⣨⣤⣤⡀⣤⣤⡤⠀⣤⣤⣤⣤⡀⢤⣠⣤⣀⣤⣤⡤⣤⣄⣄⣠⢠⣄⣀⣠⢄⣤⣤⣄⣤⣤⣀⡤⢤⣄⡄⠔⡆⡀⣠⣠⡀⠀⠀⠀⠀⢤⡀⠀⠀⠀⡄⠀⠀⢰ ⡇⠀⠀⠉⡍⢩⣄⢩⣍⣥⡀⠈⢉⣍⣁⣀⣀⡌⢩⣅⢈⣩⠉⢠⠄⠉⣨⣀⣈⣉⡉⢩⠀⣨⣩⠉⣤⢩⠉⡍⠉⣉⣉⡄⣍⣉⣄⣉⠉⠀⠉⠅⢉⣬⡍⢁⣥⣅⣁⡈⡅⠁⢈⠈⢡⡀⠐⠇⠀⠀⠁⠀⠀⠀⢅⠀⠀⢸ ⡇⠀⠀⠀⠁⠀⠁⠀⠁⠁⠂⠀⠀⠈⠉⠉⠉⠁⠀⠁⠈⠉⠀⢈⠉⠀⠈⠈⢀⠈⢀⠈⠁⠉⠀⠀⠈⠈⠀⠁⠀⠉⠁⠀⠉⠀⡉⢁⠀⠀⠀⠁⠀⠁⠁⠀⠉⠁⠈⠀⠁⠀⠀⠀⠀⠀⣈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢨ ⡇⠀⣠⣤⣭⣀⡠⣤⡤⡄⠀⢠⣤⣤⡄⢠⠀⢨⣤⣄⢠⣭⣥⡀⣡⣤⣁⢠⣠⣤⠀⣭⠀⢬⣥⣤⣤⡤⣤⠰⡝⢻⠗⠃⠳⡀⡄⠀⢠⡀⡴⠖⢇⠌⠸⠁⠀⠀⠅⡄⣄⡀⢀⠀⠀⡄⢋⢀⣤⠀⢀⣘⡿⣷⠀⠀⠀⢸ ⡇⠀⠀⠀⡄⢠⣤⢀⣤⣤⣄⡂⢠⢤⣤⣤⣄⡄⠠⡄⢠⣠⠀⢀⣄⠀⢤⣀⣠⣠⠄⢠⠤⣤⣤⠤⣤⢠⠀⣄⠀⣠⡄⡄⡄⡄⣤⣄⠀⡀⠀⡄⢁⢄⡆⢄⢤⣄⢤⡄⡄⠀⠀⠀⢠⡀⠀⢀⠀⢠⡀⠀⠀⠀⡆⠈⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠸ ⡇⢀⡀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠀⣀⠀⠀⠂⠀⠀⢀⡀⠀⢀⠀⡀⠀⠀⠀⠀⡀⡀⢀⠀⢀⠀⠀⢀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘ ⡇⠀⠈⠀⡉⢠⡄⣄⡀⣖⡠⡆⠀⢀⠒⠀⠀⠀⠀⠙⣒⢶⡼⣔⡄⠂⠀⠀⠦⠡⢀⢆⡄⠀⠀⡀⠀⡐⠀⠀⡄⠌⠸⣶⠀⡝⢃⢐⠆⠈⠂⡠⡄⠠⡤⡇⣖⣬⠸⠁⠒⠀⠊⠁⠫⠄⠀⠙⠒⠀⠀⠀⣦⣤⠀⠀⠀⢸ ⡇⠀⠀⠀⠠⠤⠡⠉⠙⠛⠁⠀⠀⠈⠀⠀⠠⠀⠀⠈⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠃⠀⠀⠁⠀⠀⠀⠁⠤⠓⠀⠀⠈⠈⠁⠀⠀⠁⠁⠈⠉⠉⠁⠡⠅⠘⠣⢇⠀⠐⠔⠀⠲⠀⡴⣦⡄⠤⠀⠠⢸ ⠣⠄⠠⠠⠄⠠⠄⠄⠄⠠⠀⠄⠀⠄⠄⠠⠠⠄⠄⠄⠄⠠⠠⠠⠠⠀⠀⠤⠤⠄⠄⠠⠤⠤⠠⠠⠀⠤⠤⠤⠤⠤⠤⠄⠄⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠠⠠⠤⠤⠠⠁⠥⠤⠬⠭⠠⠠⠭⠡⠤⠄⠤⠤⠤⠤⠤⠤⠸ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠸⢷⠾⠴⠶⠶⠶⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠗⠶⠶⠾⠶⠾⠵⠴⠲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⡇⠿⠶⠷⠶⢶⡶⡶⠀⠰⠄⠷⠶⠶⠆⠸⠷⠲⠲⠶⠲⠖⠰⠀⠖⠴⠶⠾⠶⠶⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢸⡶⠶⠅⠗⠦⠆⠄⠀⠀⠀⠀⠀⠀⠸⠿⠆⠼⠾⠦⠸⠿⠎⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸ ⡇⠏⠿⠿⠗⠀⠀⠀⠀⠈⠳⠲⠲⠶⠲⠶⠶⠆⠸⠷⠞⠴⠲⠾⠶⠂⠸⠶⠺⠸⠹⠻⠼⠙⠶⠖⠒⠦⠶⠗⠕⠀⡃⣟⠼⠦⠔⠆⠕⠀⠖⠆⠄⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇ ⡟⠻⠖⠯⠷⠶⠇⠀⠀⠸⠷⠶⠲⠆⠸⠱⠞⠾⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⡾⠸⠶⠦⠅⠰⠷⠖⠶⠲⠶⠶⠶⠆⠸⠰⠆⠰⠟⠆⠨⠧⠸⠿⠀⠸⠣⠀⠿⠻⠤⠀⠀⢨⡇ ⡟⠟⠶⠂⠇⠗⠶⠀⠀⠸⠶⠖⠞⠇⠸⠑⠖⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡇⠃⠷⠖⠗⠷⠮⠧⠶⠖⠇⠀⠀⠀⠀⠨⠽⠏⠟⠟⠋⠐⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇ ⡇⠛⠛⠒⠓⠃⠃⠁⠀⠀⠃⠐⠳⠟⠓⠚⠃⠸⠚⠛⠚⠚⠘⠐⠺⠆⠾⠒⠘⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣇⠛⠓⠓⠛⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠉ ⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡇⠀⠀⠀⡀⠀⣀⢀⡀⠀⠀⡀⣀⡀⠀⠀⠀⢀⡀⡀⢀⣀⣀⠀⠀⣀⢀⠀⣀⣀⣀⢀⣀⣀⣀⢀⢀⣀⣀⡀⠀⣀⡀⠀⣀⣀⡀⣀⣀⣀⣀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⢨ ⡇⢐⠋⠃⡛⠒⡀⠘⣙⣃⠀⠐⠙⠊⠀⠈⠂⠘⠉⠁⠘⢛⡛⢁⠛⠚⠓⠀⠛⠛⠋⢉⢛⠛⢛⠉⣛⢛⠃⠓⠊⠙⠛⡈⡙⢙⢛⠛⠓⡒⠛⡛⢛⡛⢋⣃⡀⡀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨ ⡇⠀⠀⠀⠃⠈⠋⠊⠛⠛⠃⠀⠘⠙⠛⠛⠛⠁⠈⠛⠘⢙⢀⠘⠘⠀⠻⠛⠙⠙⠀⠘⠀⠛⠋⠀⠛⠘⠀⠁⠀⠛⠋⠃⢓⡒⠛⠇⠀⠁⠀⠃⠀⠃⠈⡛⠃⡚⠘⠃⠃⠀⠈⠀⠀⠃⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⣀⠀⠀⠀⠀⣀⡀⠀⢀⣀⣀⡀⢀⣀⣀⢀⡀⢀⣀⢊⠀⣂⣀⣀⠀⣀⣀⣉⣀⣂⣀⣀⣀⢀⡀⠀⣀⢀⣀⣀⢀⣀⣀⣂⣀⣀⣀⣀⣀⣀⣐⣛⡂⢐⣲⣦⢤⡄⢤⣤⣬⡆⠁⣭⠍⠉⠁⠀⠂⠀⠡⡀⠀⠀⢸ ⡇⠀⠉⠉⡋⢋⣉⢛⣃⣃⡉⠈⢁⣋⡁⢀⣀⡚⢛⣁⠈⢙⡉⢀⢙⠛⢙⠀⢛⢙⠙⢛⢙⠙⣉⠉⢛⢛⠁⠁⠉⢛⣋⣉⡙⡙⣙⡉⠛⡋⠋⡋⡋⣛⣛⣑⡀⡀⢀⢀⡀⠉⠉⠉⠁⡀⠈⠛⠀⠈⠁⠀⠀⠀⠈⠈⠀⢸ ⡇⠀⠀⠀⠁⠈⠉⠀⠉⢉⡁⠀⠈⠉⠉⠉⠉⠁⢈⣁⠉⠉⠀⠈⠈⡀⠚⠉⠉⠉⠀⠘⠀⠉⠉⠀⠈⠈⠀⠁⡀⠉⠉⣁⠁⠁⠉⠃⠀⠁⢀⡁⣥⠍⣉⡉⠁⠉⢉⣤⡀⡀⢠⣀⠀⠁⠀⠀⠀⢀⠀⠀⠀⠀⡄⠀⠀⢸ ⡇⠀⢀⣀⣀⣀⣀⡀⡌⠋⠋⢀⡀⣀⡀⢀⡀⠀⣤⡀⣂⣤⣀⡀⢀⣠⢀⣄⣀⣀⣠⣠⣀⣀⣠⣤⣤⢤⠈⣈⢁⣤⣨⣄⣤⣉⢀⣤⣤⣄⣀⡄⠀⠡⡭⡍⢡⣤⣌⠁⠁⢃⠘⠛⡀⢀⡀⠈⠀⠈⠁⠀⠀⠀⠃⠀⠀⢸ ⡇⠀⠈⠉⡉⢉⣅⠉⣁⣅⠀⠉⢁⣉⣁⣀⣀⡈⢩⣅⢈⣉⠉⢀⣈⠉⣉⣉⣉⣉⠉⢩⠉⣉⣡⢩⣉⢡⠀⡉⠁⣉⣉⣁⡁⣉⣉⢋⠁⡁⠉⠁⢀⣄⡉⣥⡌⡍⣉⠀⡄⠈⢈⠉⠀⡀⠈⠖⠀⠀⠀⢀⣤⣤⠒⠀⠀⢐ ⡇⠀⠀⠀⠁⠀⠉⠀⠁⠉⠀⠁⠈⠈⠉⠉⠉⢁⢈⡁⠈⠉⠁⠈⠈⠀⠈⠉⠉⠈⠀⠈⠈⠉⠁⠀⠈⠈⠀⠁⠀⠈⠁⠁⠁⠁⠉⠊⠉⠁⠀⠁⠀⠉⠁⠈⠁⡥⠈⡁⢡⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠛⠛⠀⠀⠄⢨ ⡇⠀⣀⣤⣀⣀⡀⣀⣄⡄⠈⢠⣤⣤⡄⠁⡀⢠⣽⡄⣨⣤⣤⡀⣠⣤⡤⠀⣤⣤⣤⣤⡀⢤⣠⣤⣀⣤⣤⡤⣤⣄⣄⣠⢠⣄⣀⣠⢄⣤⣤⣄⣤⣤⣀⡤⢤⣄⡄⣔⡆⡀⣠⣠⡀⠀⠀⠀⠀⢤⡀⠀⠀⠀⡄⠀⠀⢰ ⡇⠀⠀⠉⡍⢩⣄⢩⣍⣥⡀⠈⢉⣍⣁⣀⣀⡌⢩⣅⢈⣩⠉⢠⢄⠉⣨⣀⣈⣉⡉⢩⠀⣨⣩⠉⢤⢩⠉⡍⠉⣉⣉⡄⣍⣉⣄⣉⠉⠀⠉⠅⢉⣬⡍⣡⡅⣅⣁⡈⡅⠁⠈⠈⠁⡀⠐⠇⠀⠀⠁⠀⠀⠀⢅⠀⠀⢸ ⡇⠀⠀⠀⠁⠀⠁⠀⠁⠁⠂⠀⠀⠈⠉⠉⠉⠁⠀⠁⠈⠉⠀⢈⠉⠀⠈⠈⢀⠈⢀⠈⠁⠉⠀⠀⠈⠈⠀⠁⠀⠉⠁⠀⠉⠀⡉⢁⠀⠀⠀⠁⠀⠁⠁⠈⠁⠁⠈⠀⠁⠀⠀⠀⠀⠀⣀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢨ ⡇⠀⣠⣤⣭⣀⡠⣤⡤⡄⠀⢠⣤⣤⡄⢠⠀⢨⣤⣄⢠⣭⣥⡀⣡⣤⣁⢠⣠⣤⠀⣭⠀⢬⢥⣤⣤⡤⣤⠰⡝⢻⠗⠃⠳⡀⡄⠀⢠⡀⡴⠖⢇⠌⠸⠁⠀⠀⠅⡄⣄⡀⢀⠀⠀⡄⢋⢀⣤⠀⢀⣘⡿⣷⠀⠀⠀⢸ ⡇⠀⠀⠀⡄⢠⣤⢀⣤⣤⣄⡂⢠⢤⣤⣤⣄⡄⠠⣄⢠⣠⠀⢀⣤⠀⢤⣀⣠⣠⠄⢠⢤⣤⣤⠤⣤⢠⢀⣄⠀⣠⡄⡄⣄⡄⣤⣄⠀⡀⠀⡄⢁⢄⡆⠠⡤⣄⢤⡄⡄⠀⠀⠀⢀⡄⠀⢀⠀⢠⡀⠀⠀⠀⡆⠈⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠸ ⡇⢀⡀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠀⣀⠀⠀⠂⠀⠀⢀⡀⠀⢀⠀⡀⠀⠀⠀⠀⡀⡀⢀⠀⢀⠀⠀⢀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘ ⡇⠀⠈⠀⡉⢠⡄⣄⡀⣖⡠⡆⠀⢀⠒⠀⠀⠀⠀⠙⣒⢶⡼⣔⡄⠂⠀⠀⠦⠡⢀⢆⡄⠀⠀⡀⠀⡐⠀⠀⡄⠌⠸⣶⠀⡝⢃⢐⠆⠈⠂⡠⡄⠠⡤⡇⣖⣬⠸⠁⠒⠀⠊⠁⠫⠄⠀⠙⠒⠀⠀⠀⣦⣤⠀⠀⠀⢸ ⡇⠀⠀⠀⠠⠤⠡⠉⠙⠛⠁⠀⠀⠈⠀⠀⠠⠀⠀⠈⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠃⠀⠀⠁⠀⠀⠀⠁⠤⠓⠀⠀⠈⠈⠁⠀⠀⠁⠁⠈⠉⠉⠁⠡⠅⠘⠣⢇⠀⠐⠔⠀⠲⠀⡴⣦⡄⠤⠀⠠⢸ ⠣⠄⠠⠠⠄⠠⠄⠄⠄⠠⠀⠄⠀⠄⠄⠠⠠⠄⠄⠄⠄⠠⠠⠠⠠⠀⠀⠤⠤⠄⠄⠠⠤⠤⠠⠠⠀⠤⠤⠤⠤⠤⠤⠄⠄⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠠⠠⠤⠤⠠⠁⠥⠤⠬⠭⠠⠠⠭⠡⠤⠄⠤⠤⠤⠤⠤⠤⠸ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠸⢷⠾⠴⠾⠶⠶⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠗⠶⠶⠾⠶⠾⠵⠴⠲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⡇⠿⠶⠷⠶⢶⡶⡶⠀⠰⠄⠷⠶⠶⠆⠸⠷⠲⠲⠶⠲⠖⠰⠀⠖⠴⠶⠾⠶⠶⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡷⠶⠅⠗⠦⠆⠤⠀⠀⠀⠀⠀⠀⠸⠿⠆⠼⠾⠦⠸⠿⠎⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸ ⡇⠏⠿⠿⠗⠀⠀⠀⠀⠈⠳⠲⠲⠶⠲⠶⠶⠆⠸⠷⠞⠴⠲⠾⠶⠂⠸⠶⠺⠸⠹⠻⠽⠙⠶⠖⠒⠦⠶⠗⠕⠀⡃⣿⡺⠦⠔⠆⠕⠀⠖⠆⠄⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇ ⡟⠻⠖⠯⠷⠶⠇⠀⠀⠸⠷⠶⠲⠆⠸⠱⠞⠺⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⡾⠙⠷⠦⠅⠸⠷⠖⠿⠒⠶⠶⠶⠆⠸⠀⠆⠰⠛⠆⠨⠧⠸⠿⠀⠸⠣⠀⠿⠻⠤⠀⠀⢨⡇ ⡟⠟⠶⠂⠗⠗⠶⠀⠀⠸⠶⠖⠞⠇⠸⠑⠖⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡇⠃⠷⠖⠗⠷⠮⠧⠶⠖⠇⠀⠀⠀⠀⠨⠽⠏⠛⠋⡇⠐⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇ ⡇⠛⠛⠒⠓⠃⠃⠁⠀⠀⠃⠐⠳⠟⠛⠚⠃⠸⠚⠛⠚⠚⠘⠐⠺⠆⠾⠒⠘⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣧⡛⠓⠓⠛⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠉ ⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡇⠀⠀⠀⡀⠀⣀⢀⡀⠀⠀⡀⣀⡀⠀⠀⠀⢀⡀⡀⢀⣀⣀⠀⠀⣀⢀⠀⣀⣀⣀⢀⣀⣀⣀⢀⣀⣀⣀⡀⠀⣀⡀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⢨ ⡇⢐⠋⠃⡛⠒⣀⠘⣙⣃⠀⠐⠙⠊⠀⠈⠂⠘⠉⢁⠘⢛⡛⢁⠛⠚⠓⠀⠛⠛⠋⢉⢛⠛⢛⠉⣛⢛⠁⠑⠊⠙⠛⡈⡙⢙⠛⠛⠓⡒⠛⡛⢛⡛⢋⣃⡀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨ ⡇⠀⠀⠀⠃⠈⠋⠂⠋⠘⠃⠀⠘⠙⠛⠛⠛⠁⠈⠛⠘⢙⢀⠘⠘⠀⠻⠛⠙⠙⠀⠘⠀⠛⠋⠀⠚⠘⠀⠁⠀⠛⠋⠋⢓⡒⠓⠇⠀⠁⠀⠃⠀⠃⠀⡙⠃⡚⠘⠃⠃⠀⠈⠀⠀⠁⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⣀⠀⠀⠀⠀⣀⡀⠀⢀⣀⣀⡀⢀⣀⣀⢀⡀⢀⣀⢊⠀⣂⣀⣀⠀⣀⣀⣉⣀⣂⣀⣀⣀⢀⡀⠀⣀⢀⣀⣀⢀⣀⣀⣂⣀⣀⣀⣀⣀⣀⣐⣛⡂⢐⣲⣦⢤⡄⢤⣤⣬⡆⠁⣭⠍⠉⠁⠀⠂⠀⢡⡀⠀⠀⢸ ⡇⠀⠉⠉⡋⢋⣉⢛⣃⣃⡉⠈⢁⣋⡁⢀⣀⡚⢛⣁⠈⢙⡉⢀⢙⠛⢙⠀⢛⢙⠙⢛⢙⠙⣉⠉⢛⢛⠁⠁⠉⢛⣋⣉⡉⡙⣙⡉⠛⡋⠋⡋⡋⣛⡛⣑⡀⡀⢀⢀⡀⠉⠉⠉⠁⠀⠈⠛⠀⠈⠁⠀⠀⠀⠈⠈⠀⢸ ⡇⠀⠀⠀⠁⠈⠉⠀⠉⢉⡁⠀⠈⠉⠉⠉⠉⠁⢈⣁⠉⠉⠀⠈⠈⡀⠚⠉⠉⠉⠀⠘⠀⠉⠉⠀⠈⠈⠀⠁⡀⠉⠉⣁⠁⠁⠉⠃⠀⠁⢀⡁⣥⠍⣁⡉⠁⠉⢉⣤⡀⡀⢠⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡄⠀⠀⢸ ⡇⠀⢀⣀⣀⣀⣀⡀⡌⠋⠋⢀⡀⣀⡀⢀⣀⠀⣤⡀⣂⣤⣀⡀⢀⣠⢀⣄⣀⣀⣠⣠⣀⣀⣠⣤⣤⢤⠈⣈⢁⣤⣨⣄⣤⣉⢀⣤⣤⣄⣀⡄⠀⠡⡭⡍⢡⣤⣌⠁⠁⢃⠚⠛⡀⢀⡀⠈⠀⠈⠁⠀⠀⠀⠃⠀⠀⢸ ⡇⠀⠈⠉⡉⢉⣅⠉⣅⢥⠀⠉⢁⣉⣁⣀⣀⡈⢩⣅⢈⣉⠉⢀⣈⠉⣉⣉⣉⣉⠉⢩⠉⣉⣡⢩⣉⢡⠀⡉⠁⣉⣉⣁⡁⣉⣉⢋⠁⡁⠉⠁⢀⣄⢩⣥⡌⡍⣉⠀⡄⠈⢈⠉⠀⡀⠈⠖⠀⠀⠀⢀⣤⣤⠒⠀⠀⢐ ⡇⠀⠀⠀⠁⠀⠉⠀⠁⠁⠁⠁⠈⠈⠉⠉⡉⢁⢈⡁⠈⠉⠀⠈⠈⠀⠈⠉⠉⠈⠀⠈⠈⠉⠁⠀⠈⠈⠁⠁⠀⠈⠁⠁⠁⠁⠉⠊⠉⠁⠀⠁⠀⠉⠈⠉⠁⡥⠈⡁⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠀⠀⠄⢨ ⡇⠀⣀⣤⣀⣀⡀⣀⣄⡄⠈⢠⣤⣤⡄⠁⡀⢠⣽⡤⣨⣤⣤⡀⣤⣤⡤⠀⣤⣤⣤⣤⡀⢤⣠⣤⣀⣤⣤⡤⣤⣄⣄⣠⢠⣄⣀⣠⢄⣤⣤⣄⣤⣤⣀⡤⢤⣄⡄⣔⡆⡀⣠⣠⡀⠀⠀⠀⠀⢤⡀⠀⠀⠀⡄⠀⠀⢰ ⡇⠀⠀⠉⡍⠩⣄⠩⣍⣥⡀⠈⢉⣍⣁⣀⣀⣌⢩⣅⢈⣩⠉⢠⢤⠉⣨⣀⣈⣉⡉⢩⠠⣨⣩⠉⢠⢩⠉⡍⠉⣈⣉⡄⣭⣍⣄⣉⠉⠀⠉⠅⢉⣬⡍⣡⡅⣅⣁⡈⡅⠁⠈⠈⠁⡀⠐⠇⠀⠀⠁⠀⠀⠀⢅⠀⠀⢸ ⡇⠀⠀⠀⠁⠀⠁⠀⠁⠁⠂⠀⠀⠈⠉⠉⠉⠁⠀⠁⠈⠉⠀⢈⠉⠀⠈⠈⢀⠈⢀⠈⠁⠉⠀⠀⠈⠈⠁⠁⠀⠉⠁⠀⠉⠀⡉⢁⠀⠀⠀⠁⠀⠁⠁⠈⠁⠁⠈⠀⠁⠀⠀⠀⠀⠀⣀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢨ ⡇⠀⣠⣤⣭⣀⡠⣤⡤⡄⠀⢠⣤⣤⡄⢠⠀⢨⣤⣤⢠⣭⣥⡀⣡⣤⣁⢠⣠⣤⠀⣭⠀⢬⢥⣤⣤⡤⣤⠰⡝⢻⠗⠃⠳⡀⡄⠀⢠⡀⡴⠖⢇⠌⠸⠁⠀⠀⠅⡄⣄⡀⢀⠀⠀⡄⢋⢀⣤⠀⢀⣘⡿⣷⠀⠀⠀⢸ ⡇⠀⠀⠀⡄⢠⣤⢀⣤⣤⣄⡂⢠⢤⣤⣤⣄⡄⠠⣄⢠⣠⠀⢀⣤⠀⢤⣀⣠⣠⠄⢠⢤⣤⣤⠤⣤⢠⣀⣄⠀⣠⡄⡄⣄⡄⣤⣄⠀⡀⠀⡄⢁⢄⡄⠠⡤⣄⢤⡄⡄⠀⠀⠀⠀⠀⠀⢀⠀⢠⡀⠀⠀⠀⡆⠈⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠸ ⡇⢀⡀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠀⣀⠀⠀⠂⠀⠀⢀⡀⠀⢀⠀⡀⠀⠀⠀⠀⡀⡀⢀⠀⢀⠀⠀⢀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘ ⡇⠀⠈⠀⡉⢠⡄⣄⡀⣖⡠⡆⠀⢀⠒⠀⠀⠀⠀⠙⣒⢶⡼⣔⡄⠂⠀⠀⠦⠡⢀⢆⡄⠀⠀⡀⠀⡐⠀⠀⡄⠌⠸⣶⠀⡝⢃⢐⠆⠈⠂⡠⡄⠠⡤⡇⣖⣬⠸⠁⠒⠀⠊⠁⠫⠄⠀⠙⠒⠀⠀⠀⣦⣤⠀⠀⠀⢸ ⡇⠀⠀⠀⠠⠤⠡⠉⠙⠛⠁⠀⠀⠈⠀⠀⠠⠀⠀⠈⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠃⠀⠀⠁⠀⠀⠀⠁⠤⠓⠀⠀⠈⠈⠁⠀⠀⠁⠁⠈⠉⠉⠁⠡⠅⠘⠣⢇⠀⠐⠔⠀⠲⠀⡴⣦⡄⠤⠀⠠⢸ ⠣⠄⠠⠠⠄⠠⠄⠄⠄⠠⠀⠄⠀⠄⠄⠠⠠⠄⠄⠄⠄⠠⠠⠠⠠⠀⠀⠤⠤⠄⠄⠠⠤⠤⠠⠠⠀⠤⠤⠤⠤⠤⠤⠄⠄⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠠⠠⠤⠤⠠⠁⠥⠤⠬⠭⠠⠠⠭⠡⠤⠄⠤⠤⠤⠤⠤⠤⠸ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠸⢷⠾⠴⠾⠶⠶⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠗⠶⠶⠾⠶⠾⠵⠴⠲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⡇⠿⠶⠷⠶⢶⡶⡶⠀⠰⠄⠷⠶⠶⠆⠸⠷⠲⠲⠶⠲⠖⠰⠀⠖⠴⠶⠾⠶⠶⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡷⠶⠅⠗⠦⠆⠤⠀⡀⢀⠀⠀⠀⠸⠿⠆⠼⠾⠦⠸⠿⠎⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸ ⡇⠏⠿⠿⠗⠀⠀⠀⠀⠈⠳⠲⠲⠶⠲⠶⠶⠆⠸⠷⠞⠴⠲⠾⠶⠂⠸⠶⠺⠸⠹⠻⠽⠙⠶⠖⠒⠦⠶⠗⠕⠀⡃⣿⡲⠦⠔⠆⠕⠀⠖⠆⠀⡇⠛⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇ ⡟⠻⠖⠯⠷⠶⠇⠀⠀⠸⠷⠶⠲⠆⠸⠱⠞⠺⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⡾⠙⠷⠦⠅⠸⠷⠖⠿⠂⡟⠾⠶⠆⠸⠀⠆⠰⠛⠆⠨⠧⠸⠿⠀⠸⠣⠀⠿⠻⠤⠀⠀⢨⡇ ⡟⠟⠶⠂⠔⠗⠶⠀⠀⠸⠶⠖⠞⠇⠸⠑⠖⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡇⠃⠷⠖⠗⠷⠮⠧⠶⠖⠇⣤⠀⠀⠀⠨⠽⠏⠛⠋⡇⠐⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇ ⡇⠛⠛⠒⠓⠃⠃⠁⠀⠀⠃⠐⠳⠟⠛⠚⠃⠸⠚⠛⠚⠚⠘⠐⠺⠆⠾⠒⠘⠒⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣧⡛⠓⠓⠛⠙⠃⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠘⠃⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠛⠚⠀ ⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡇⠀⠀⠀⡀⠀⣀⢀⡀⠀⠀⡀⣀⡀⠀⠀⠀⢀⡀⡀⢀⣀⣀⠀⠀⣀⢀⠀⣀⣀⣀⢀⣀⣀⣀⢀⣀⣀⣀⡀⠀⣀⡀⠀⣀⣀⡀⣀⣀⣀⣀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⢨ ⡇⢐⠋⠃⡛⠒⣀⠘⣙⣃⠀⠐⠙⠊⠀⠈⠂⠘⠉⢁⠘⢛⡛⢁⠛⠚⠓⠀⠛⠛⠋⢉⢛⠛⢛⠉⣛⢛⠁⠑⠊⠙⠛⡈⡙⠙⠛⠛⠓⡒⠛⡛⢛⡛⢋⣃⡀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨ ⡇⠀⠀⠀⠃⠈⠋⠂⠋⠘⠃⠀⠘⠙⠛⠛⠛⠁⠈⠛⠘⢙⢀⠘⠘⠀⠻⠛⠙⠙⠀⠘⠀⠛⠋⠀⠚⠘⠀⠁⠀⠛⠋⠃⢓⡒⠓⠇⠀⠁⠀⠃⠀⠃⠀⡙⠃⡚⠘⠃⠃⠀⠈⠀⠀⠁⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⣀⠀⠀⠀⠀⣀⡀⠀⢀⣀⣀⡀⢀⣀⣀⢀⡀⢀⣀⢊⠀⣂⣀⣀⠀⣀⣀⣉⣀⣂⣀⣀⣀⢀⡀⠀⣀⢀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⣛⡂⢐⣲⣦⢤⡄⢤⣤⣬⡆⠁⣭⠍⠉⠁⠀⠂⠀⠡⡀⠀⠀⢸ ⡇⠀⠉⠉⡋⢋⣉⢛⣃⣃⡉⠈⢁⣋⡁⢀⣀⡚⢛⣁⠈⢙⡉⢀⢙⠛⢙⠀⢛⢙⠙⢛⢙⠙⣉⠉⢛⢛⠁⠁⠉⢛⣋⣉⡉⡙⣙⡉⠛⡋⠋⡋⡋⣛⡛⣑⡀⡀⢀⢀⡀⠉⠉⠉⠁⠀⠈⠛⠀⠈⠁⠀⠀⠀⠈⠈⠀⢸ ⡇⠀⠀⠀⠁⠈⠉⠀⠉⢉⣁⠠⠈⡉⠉⠉⠉⠁⢈⣁⠉⠉⠀⠈⠈⡀⠚⠉⠉⠉⠀⠘⠀⠉⠉⠀⠈⠈⠀⠁⡀⠉⠉⣁⠁⠁⠉⠃⠀⠁⢀⡁⣥⠍⣁⡉⠁⠉⢉⣤⡀⡀⢠⣀⠀⣤⣤⣤⡄⢀⠀⠀⠀⠀⡄⠀⠀⠈ ⡇⠀⢀⣀⣀⣀⣀⡀⡌⠉⠋⢀⡀⣀⡀⢀⣀⠀⣤⡀⣂⣤⣀⡀⢀⣠⢀⣄⣀⣀⣠⣠⣀⣀⣠⣤⣠⢄⠈⣈⢁⣤⣨⣄⣄⣉⢀⣤⣤⣄⣀⡄⠀⠡⡭⡌⢡⣤⣌⠁⠁⢃⠘⠛⡀⢙⡙⠙⠃⠈⠁⠀⠀⠀⠃⠀⠀⢸ ⡇⠀⠈⠉⡉⢉⣅⠉⣅⢥⠀⠉⢁⣉⣁⣀⣀⡈⢩⣅⢈⣉⠉⢀⣈⠉⣉⣉⣉⣉⠉⢩⠉⣉⣡⢩⣉⢡⠀⡉⠁⣉⣉⡁⡁⣉⣉⢋⠁⡁⠉⠁⢀⣄⢩⣥⡌⡍⣉⠀⡄⠈⢈⠉⠀⠀⠈⠖⠀⠀⠀⢀⣤⣤⠒⠀⠀⢐ ⡇⠀⠀⠀⠁⠀⠉⠀⠁⠁⠁⠁⠈⠈⠉⠉⠉⢉⢈⡁⠈⠉⠀⠈⠈⠀⠈⠉⠉⠈⠀⠈⠈⠉⠁⠀⠈⠈⠁⠁⠀⠈⠁⠁⠁⠁⠉⠊⠉⠁⠀⠁⠀⠉⠈⠉⠁⡥⠈⡁⢡⡀⠀⠀⠀⠫⠄⠀⠀⡀⠀⠉⠛⠛⠀⠀⠄⢨ ⡇⠀⣀⣤⣀⣀⡀⣀⣄⡄⠈⢠⣤⣤⡄⠁⡀⢠⣽⡤⣨⣤⣤⡀⣤⣤⡤⠀⣤⣤⣤⣤⡀⢤⣠⣤⣀⣤⣤⡤⣤⣄⣄⣠⢠⣄⣀⣠⢄⣤⣤⣄⣤⣤⣀⡤⢤⣄⡄⣔⡆⡀⣠⣠⡀⢠⣠⣤⡄⢤⡀⠀⠀⠀⡄⠀⠀⢀ ⡇⠀⠀⠉⡍⠩⣄⠉⣍⣥⡀⠈⢉⣍⣁⣀⣀⣌⢩⣅⢈⣩⠉⢠⢤⠉⣨⣀⣈⣉⡉⢩⠠⣨⣩⠉⢠⢩⠉⡍⠉⣈⣉⡄⣭⣍⣄⣉⠉⠀⠉⠅⢉⣬⡍⣡⡅⣅⣁⡈⡅⠁⠈⠈⠁⡈⠈⠉⠁⠀⠁⠀⠀⠀⠅⠀⠀⠸ ⡇⠀⠀⠀⠁⠀⠁⠀⠁⠁⠂⠀⠀⠈⠉⠉⠉⠁⠀⠁⠈⠉⠀⢈⠉⠀⠈⠈⢀⠈⢀⠈⠁⠉⠀⠀⠈⠈⠁⠁⠀⠉⠁⠀⠉⠀⡉⢁⠀⠀⠀⠁⠀⠁⠁⠈⠁⠁⠈⠀⠁⠀⠀⠀⠀⠀⣀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢨ ⡇⠀⣠⣤⣭⣀⡠⣤⡤⡄⠀⢠⣤⣤⡄⢡⠀⢨⣤⣤⢠⣥⣥⡀⣥⣤⣁⢠⣠⣤⠀⣭⠀⢬⢥⣤⣤⡤⣤⠰⡝⢻⠗⠃⠳⡏⡄⠀⢠⡀⡴⠖⢇⠌⠸⠁⠀⠀⠅⡄⣄⡀⢀⠀⠀⡄⢋⠀⣤⠀⢀⣘⡿⣷⠀⠀⠀⢸ ⡇⠀⠀⠀⡄⢠⡤⢀⣤⣤⣄⡀⢠⢤⣤⣤⣄⡄⠠⣄⢠⣠⠀⢀⣤⠀⢤⣀⣠⣠⠄⢠⢤⣤⣤⠤⣤⢠⣀⣄⠀⣠⡄⡄⣄⡄⣤⣄⠀⡀⠀⡄⢁⢄⡄⠠⡤⣄⢤⡄⡄⠀⠀⠀⠀⠀⠶⣶⡆⢠⡀⠀⠀⠀⡆⠈⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠉⠈⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀ ⡇⢀⡀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠀⣀⠀⠀⠂⠀⠀⢀⡀⠀⢀⠀⡀⠀⠀⠀⠀⡀⡀⢀⠀⢀⠀⠀⢀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘ ⡇⠀⠈⠀⡉⢠⡄⣄⡀⣖⡠⡆⠀⢀⠒⠀⠀⠀⠀⠙⣒⢶⡼⣔⡄⠂⠀⠀⠦⠡⢀⢆⡴⠃⠀⡀⠀⡐⠀⠀⡄⠌⠸⣶⠀⡝⢃⢐⠆⠈⠂⡠⡄⠠⡤⡇⣖⣭⠸⠁⠒⠀⠊⠁⠫⠄⠒⠛⠒⠀⠀⠀⡾⢦⠀⠀⠀⢸ ⡇⠀⠀⠀⠠⠤⠡⠉⠉⠛⠁⠀⠀⠈⠀⠀⠠⠀⠀⠈⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠃⠀⠀⠁⠀⠀⠀⠁⠤⠓⠀⠀⠈⠈⠁⠀⠀⠁⠁⠈⠉⠉⠁⠡⠅⠘⠣⢇⠀⠐⠔⠀⠲⠀⡴⣦⡄⠤⠀⠠⠀ ⠣⠄⠠⠠⠄⠠⠄⠄⠄⠠⠀⠄⠀⠄⠄⠠⠠⠄⠄⠄⠀⠠⠠⠠⠠⠀⠀⠤⠤⠄⠄⠠⠤⠤⠠⠠⠀⠤⠤⠤⠤⠤⠤⠄⠄⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠠⠠⠤⠤⠠⠁⠥⠤⠬⠭⠠⠠⠭⠡⠤⠄⠤⠤⠤⠤⠤⠤⠰ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠸⢷⠾⠴⠾⠶⠶⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠗⠶⠶⠾⠶⠾⠵⠴⠲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⡇⠿⠶⠷⠶⢶⡶⡶⠀⠰⠄⠷⠶⠶⠆⠸⠷⠲⠲⠶⠲⠖⠰⠀⠖⠴⠶⠾⠶⠶⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡷⠶⠅⠗⠦⠆⠤⠀⡀⢀⠀⠀⠀⠸⠿⠆⠼⠾⠦⠸⠿⠎⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸ ⡇⠏⠿⠿⠗⠀⠀⠀⠀⠈⠳⠲⠲⠶⠲⠶⠶⠆⠸⠷⠞⠴⠲⠾⠶⠂⠸⠶⠺⠸⠹⠻⠽⠙⠶⠖⠒⠦⠶⠗⠕⠀⡃⣿⡲⠦⠔⠆⠕⠀⠖⠆⠀⡇⠛⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇ ⡟⠻⠖⠯⠷⠶⠇⠀⠀⠸⠷⠶⠲⠆⠸⠱⠞⠺⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⡾⠙⠷⠦⠅⠸⠷⠖⠿⠂⡟⠾⠶⠆⠸⠀⠆⠰⠛⠆⠨⠧⠸⠿⠀⠸⠣⠀⠿⠻⠤⠀⠀⢨⡇ ⡟⠟⠶⠂⠐⠗⠶⠀⠀⠸⠶⠖⠞⠇⠸⠑⠖⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡇⠃⠷⠖⠗⠷⠮⠧⠶⠖⠇⣤⠀⠀⠀⠨⠽⠏⠛⠋⡇⠐⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇ ⡇⠛⠛⠒⠃⠛⠃⠁⠀⠀⠃⠐⠳⠟⠛⠚⠃⠸⠚⠛⠚⠚⠘⠐⠺⠆⠾⠒⠘⠒⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣧⡛⠓⠓⠛⠙⠃⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠘⠃⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠌⠟⠚⠀ ⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐ ⡇⠀⠀⠀⡀⠀⣀⢀⡀⠀⠀⡀⣀⡀⠀⠀⠀⢀⡀⡀⢀⣀⣀⠀⠀⣀⢀⠀⣀⣀⣀⢀⣀⣀⣀⢀⣀⣀⣀⡀⠀⣀⡀⠀⣀⣀⡀⣀⣀⣀⣀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⢨ ⡇⢐⠋⠃⡛⠒⣀⠘⣙⣃⠀⠐⠙⠊⠀⠈⠂⠘⠉⢁⠘⢛⡛⢁⠛⠚⠓⠀⠛⠛⠋⢉⢛⠛⢛⠉⣛⢛⠁⠑⠊⠙⠛⡈⡙⠙⠛⠛⠓⡒⠛⡛⢛⡛⢋⣃⡀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨ ⡇⠀⠀⠀⠃⠈⠋⠂⠋⠘⠃⠀⠘⠙⠛⠛⠛⠁⠈⠛⠘⢙⢀⠘⠘⠀⠻⠛⠙⠙⠀⠘⠀⠛⠋⠀⠚⠘⠀⠁⠀⠛⠋⠃⢓⡒⠓⠇⠀⠁⠀⠃⠀⠃⠀⡙⠃⡚⠘⠃⠃⠀⠈⠀⠀⠁⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⣀⠀⠀⠀⠀⣀⡀⠀⢀⣀⣀⡀⢀⣀⣀⢀⡀⢀⣀⢊⠀⣂⣀⣀⠀⣀⣀⣉⣀⣂⣀⣀⣀⢀⡀⠀⣀⢀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⣛⡂⢐⣲⣦⢤⡄⢤⣤⣬⡆⠁⣭⠍⠉⠁⠀⠂⠀⠡⡀⠀⠀⢸ ⡇⠀⠉⠉⡋⢋⣉⢛⣃⣃⡉⠈⢁⣋⡁⢀⣀⡚⢛⣁⠈⢙⡉⢀⢙⠛⢙⠀⢛⢙⠙⢛⢙⠙⣉⠉⢛⢛⠁⠁⠉⢛⣋⣉⡉⡙⣙⡉⠛⡋⠋⡋⡋⣛⡛⣑⡀⡀⢀⢀⡀⠉⠉⠉⠁⠀⠈⠛⠀⠈⠁⠀⠀⠀⠈⠈⠀⢸ ⡇⠀⠀⠀⠁⠈⠉⠀⠉⢉⣁⠠⠈⡉⠉⠉⠉⠁⢈⣁⠉⠉⠀⠈⠈⡀⠚⠉⠉⠉⠀⠘⠀⠉⠉⠀⠈⠈⠀⠁⡀⠉⠉⣁⠁⠁⠉⠃⠀⠁⢀⡁⣥⠍⣁⡉⠁⠉⢉⣤⡀⡀⢠⣀⠀⣤⣤⣤⡄⢀⠀⠀⠀⠀⡄⠀⠀⠈ ⡇⠀⢀⣀⣀⣀⣀⡀⡌⠉⠋⢀⡀⣀⡀⢀⣀⠀⣤⡀⣂⣤⣀⡀⢀⣠⢀⣄⣀⣀⣠⣠⣀⣀⣠⣤⣠⢄⠈⣈⢁⣤⣨⣄⣄⣉⢀⣤⣤⣄⣀⡄⠀⠡⡭⡌⢡⣤⣌⠁⠁⢃⠘⠛⡀⢙⡙⠙⠃⠈⠁⠀⠀⠀⠃⠀⠀⢸ ⡇⠀⠈⠉⡉⢉⣅⠉⣅⢵⠐⠉⢁⣉⣁⣀⣀⡈⢩⣅⢈⣉⠉⢀⣈⠉⣉⣉⣉⣉⠉⢩⠉⣉⣡⢩⣉⢡⠀⡉⠁⣉⣉⡁⡁⣉⣉⢋⠁⡁⠉⠁⢀⣄⢩⣥⡌⡍⣉⠀⡄⠈⢈⠉⠄⠀⠈⠖⠀⠀⠀⢀⣤⣤⠒⠀⠀⢐ ⡇⠀⠀⠀⠁⠀⠉⠀⠁⠁⠀⠁⠈⠈⠉⠉⠉⢉⢈⡁⠈⠉⠀⠈⠈⠀⠈⠉⠉⠈⠀⠈⠈⠉⠁⠀⠈⠈⠁⠁⠀⠈⠁⠁⠁⠁⠉⠊⠉⠁⠀⠁⠀⠉⠈⠉⠁⡥⠈⡁⢡⡀⠀⠀⠀⠫⠄⠀⠀⡀⠀⠉⠛⠛⠀⠀⠄⢨ ⡇⠀⣀⣤⣀⣀⡀⣀⣄⡄⠈⢠⣤⣤⡄⠁⡀⢠⣽⡤⣨⣤⣤⡀⣤⣤⡤⠀⣤⣤⣤⣤⡀⢤⣠⣤⣀⣤⣤⡤⣤⣄⣄⣠⢠⣄⣀⣠⢄⣤⣤⣄⣤⣤⣀⡤⢤⣄⡄⣔⡆⡀⣠⣠⡀⢤⣠⣤⡄⢤⡀⠀⠀⠀⡄⠀⠀⢀ ⡇⠀⠀⠉⡍⠩⣄⠉⣍⣥⡀⠈⢉⣍⣁⣀⣀⣌⢩⣅⢈⣩⠉⢠⢤⠉⣨⣀⣈⡉⡉⢩⠠⣨⣩⠉⢠⢩⠉⡍⠉⣈⣉⡄⣭⣍⣄⣉⠉⠀⠉⠅⢉⣬⡍⣡⡅⣅⣁⡈⡅⠁⠈⠈⠁⡈⠈⠉⠁⠀⠁⠀⠀⠀⠅⠀⠀⠸ ⡇⠀⠀⠀⠁⠀⠁⠀⠁⠁⠂⠀⠀⠈⠉⠉⠉⠁⠀⠁⠈⠉⠀⢈⠉⠀⠈⠈⢀⠈⢀⠈⠁⠉⠀⠀⠈⠈⠁⠁⠀⠉⠁⠀⠉⠀⡉⢁⠀⠀⠀⠁⠀⠁⠁⠈⠁⠁⠈⠀⠁⠀⠀⠀⠀⠥⢀⠉⡏⠉⠀⠀⠀⠀⠀⠀⠀⢠ ⡇⠀⣠⣤⣭⣀⡠⣤⡤⡄⠀⢠⣤⣤⡄⢡⠀⢨⣤⣤⢠⣥⣥⡀⣥⣤⣁⢠⣠⣤⠀⣥⠀⢬⢥⣤⣤⡤⣤⠰⡝⢻⠗⠃⠳⡏⡄⠀⢠⡀⡴⠖⢇⠌⠸⠁⠀⠀⠅⡄⣄⡀⢀⠀⠀⡄⢈⠀⣤⠀⢀⣘⡿⣷⠀⠀⠀⢸ ⡇⠀⠀⠀⡄⢠⡤⢀⣤⣤⣄⡀⢠⢤⣤⣤⣄⡄⠠⣄⢠⣠⠀⢀⢤⠀⢤⣀⣠⣠⠄⢠⢤⣤⣤⠤⣤⢠⣀⣄⠀⣠⡄⡄⣄⡄⣤⣄⠀⡀⠀⡄⢁⢄⡄⠠⡤⣄⢤⡄⡄⠀⠀⠀⠀⠀⠶⣶⡆⢠⡀⠀⠀⠀⡆⠈⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠉⠈⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀ ⡇⢀⡀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠀⣀⠀⠀⠂⠀⠀⢀⡀⠀⢀⠀⡀⠀⠀⠀⠀⡀⡀⢀⠀⢀⠀⠀⢀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘ ⡇⠀⠈⠀⡉⢠⡄⣄⡀⣖⡠⡄⠀⢀⠒⠀⠀⠀⠀⠙⣒⢶⡘⣔⡄⠂⠀⠀⠦⠡⢀⢆⡴⠃⠀⡀⠀⡐⠀⠀⡄⠌⠸⣶⠀⡝⢃⢐⠆⠈⠂⡠⡄⠠⡤⡇⣖⣭⠸⠁⠒⠀⠊⠁⠫⠄⠀⠘⠒⠀⠀⠀⡾⢦⠀⠀⠀⢠ ⡇⠀⠀⠀⠠⠤⠡⠉⠉⠛⠁⠀⠀⠈⠀⠀⠠⠀⠀⠈⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠃⠀⠀⠁⠀⠀⠀⠁⠤⠓⠀⠀⠈⠈⠁⠀⠀⠁⠁⠈⠉⠉⠁⠡⠅⠘⠣⢇⠀⠐⠔⠀⠲⠀⡴⣦⡄⠤⠀⠠⠀ ⠣⠄⠠⠠⠄⠠⠄⠄⠄⠠⠀⠄⠀⠄⠄⠠⠠⠄⠄⠄⠀⠠⠠⠠⠢⠀⠀⠤⠤⠄⠄⠠⠤⠌⠠⠠⠀⠤⠤⠤⠤⠤⠤⠄⠄⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠠⠠⠤⠤⠠⠁⠥⠤⠬⠭⠰⠩⠽⠡⠤⠄⠤⠤⠦⠤⠤⠤⠰ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠸⢷⠾⠴⠾⠶⠶⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠗⠶⠶⠾⠶⠾⠵⠴⠲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⡇⠿⠶⠷⠶⢶⡶⡶⠀⠰⠄⠷⠶⠶⠆⠸⠷⠲⠲⠶⠲⠖⠰⠀⠖⠴⠶⠾⠶⠶⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡷⠶⠅⠗⠦⠆⠤⢀⠀⢀⠀⠀⠀⠸⠿⠆⠼⠾⠦⠸⠿⠎⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸ ⡇⠏⠿⠿⠗⠀⠀⠀⠀⠈⠳⠲⠲⠶⠲⠶⠶⠆⠸⠷⠞⠴⠲⠾⠶⠂⠸⠶⠺⠸⠹⠻⠽⠙⠶⠖⠒⠦⠶⠗⠕⠀⡃⣿⡲⠦⠔⠆⠕⠀⠖⠀⢸⠀⠛⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇ ⡟⠻⠖⠯⠷⠶⠇⠀⠀⠸⠷⠶⠲⠆⠸⠱⠞⠺⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⡾⠙⠷⠦⠅⠸⠷⠖⠿⢚⡜⠾⠶⠆⠸⠀⠆⠰⠛⠆⠨⠧⠸⠿⠀⠸⠣⠀⠿⠻⠤⠀⠀⢨⡇ ⡟⠟⠶⠂⠐⡗⠶⠀⠀⠸⠶⠖⠞⠇⠸⠑⠖⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡇⠃⠷⠖⠗⠷⠮⠧⠶⠖⢧⣅⠀⠀⠀⠨⠽⠏⠛⠋⡇⠐⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇ ⡇⠛⠛⠒⠃⠛⠃⠁⠀⠀⠃⠐⠳⠟⠛⠚⠃⠸⠚⠛⠚⠚⠘⠐⠺⠆⠾⠒⠘⠒⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣧⡛⠓⠓⠛⠙⠃⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠘⠃⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⢀⡀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠹⠸⠛⠃⠐ ⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐ ⡇⠀⠀⠀⡀⠀⣀⢀⡀⠀⠀⡀⣀⡀⠀⠀⠀⢀⡀⡀⢀⣀⣀⠀⠀⣀⢀⠀⣀⣀⣀⢀⣀⣀⣀⢀⣀⣀⣀⡀⠀⣀⡀⠀⣀⣀⡀⣀⣀⣀⣀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⢨ ⡇⢐⠋⠃⡛⠒⣀⠘⣙⣃⠀⠐⠙⠊⠀⠈⠂⠘⠉⢁⠘⢛⡛⢁⠛⠚⠓⠀⠛⠛⠋⢉⢛⠛⢛⠉⣛⢛⠁⠑⠊⠙⠛⡈⡙⠙⠛⠛⠓⡒⠛⡛⢛⡛⢋⣃⡀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨ ⡇⠀⠀⠀⠃⠈⠋⠂⠋⠘⠃⠀⠘⠙⠛⠛⠛⠁⠈⠛⠘⢙⢀⠘⠘⠀⠻⠛⠙⠙⠀⠘⠀⠛⠋⠀⠚⠘⠀⠁⠀⠛⠋⠃⢓⡒⠓⠇⠀⠁⠀⠃⠀⠃⠀⡙⠃⡚⠘⠃⠃⠀⠈⠀⠀⠁⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⣀⠀⠀⠀⠀⣀⡀⠀⢀⣀⣀⡀⢀⣀⣀⢀⡀⢀⣀⢊⠀⣂⣀⣀⠀⣀⣀⣉⣀⣂⣀⣀⣀⢀⡀⠀⣀⢀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⣛⡂⢐⣲⣦⢤⡄⢤⣤⣬⡆⠁⣭⠍⠉⠁⠀⠂⠀⠡⡀⠀⠀⢸ ⡇⠀⠉⠉⡋⢋⣉⢛⣃⣃⡉⠈⢁⣋⡁⢀⣀⡚⢛⣁⠈⢙⡉⢀⢙⠛⢙⠀⢛⢙⠙⢛⢙⠙⣉⠉⢛⢛⠁⠁⠉⢛⣋⣉⡉⡙⣙⡉⠛⡋⠋⡋⡋⣛⡛⣑⡀⡀⢀⢀⡀⠉⠉⠉⠁⠀⠈⠛⠀⠈⠁⠀⠀⠀⠈⠈⠀⢸ ⡇⠀⠀⠀⠁⠈⠉⠀⠉⠩⣅⣤⢈⠉⠉⠉⠉⠁⢈⣁⠉⠉⠀⠈⠈⡀⠚⠉⠉⠉⠀⠘⠀⠉⠉⠀⠈⠈⠀⠁⡀⠉⠉⣁⠁⠁⠉⠃⠀⠁⢀⡁⣥⠍⣁⡉⠁⠉⢉⣤⡀⡀⢠⣀⠀⣠⣤⣄⠀⢀⠀⠀⠀⠀⡄⠀⠀⠈ ⡇⠀⢀⣀⣀⣀⣀⡀⡌⠀⠋⢋⡀⣀⡀⢀⣀⠀⣤⡀⣂⣤⣀⡀⢀⣠⢀⣄⣀⣀⣠⣠⣀⣀⣠⣤⣤⢤⠈⣈⢁⣤⣨⣄⣄⣉⢀⣤⣤⣄⣀⡄⠀⠡⡭⡌⢡⣤⣌⠁⠁⢃⠘⠛⡀⢉⡉⠋⠀⠈⠁⠀⠀⠀⠃⠀⠀⢀ ⡇⠀⠈⠉⡉⢉⣅⠉⣅⢵⠐⠉⢁⣉⣁⣀⣀⠈⢩⣅⢈⣉⠉⢀⣈⠉⣉⣉⣉⣉⠉⢩⠉⣉⣡⢩⣉⢡⠀⡉⠁⣉⣉⣁⡁⣉⣉⢋⠁⡁⠉⠁⢀⣄⢩⣥⡌⡍⣉⠀⡄⠈⢈⠉⠄⠀⠈⠖⠀⠀⠀⢀⣤⣤⠒⠀⠀⢐ ⡇⠀⠀⠀⠁⠀⠉⠀⠁⠁⠀⠁⠈⠈⠉⠉⠉⢩⢈⡁⠈⠉⠀⠈⠈⠀⠈⠉⠉⠈⠀⠈⠈⠉⠁⠀⠈⠈⠁⠁⠀⠈⠁⠁⠁⠁⠉⠊⠉⠁⠀⠁⠀⠉⠈⠉⠁⡥⠈⡁⢡⡀⠀⠀⠀⠮⠄⠀⢀⡀⠀⠉⠛⠛⠀⠀⠄⢨ ⡇⠀⣀⣤⣀⣀⡀⣀⣄⡄⠈⢠⣤⣤⡄⠁⡀⢠⣽⡤⣨⣤⣤⡀⣤⣤⡤⠀⣤⣤⣤⣤⡀⢤⣠⣤⣀⣤⣤⡤⣤⣄⣄⣠⢠⣄⣀⣠⢄⣤⣤⣄⣤⣤⣀⡤⢤⣄⡄⣔⡆⡀⣠⣠⡀⢤⣦⣆⠀⢤⡀⠀⠀⠀⡄⠀⠀⠀ ⡇⠀⠀⠉⠍⠩⣄⠩⢍⡥⡀⠈⢉⣍⣁⣀⣀⣌⢩⡅⢈⡩⠉⢠⢤⠉⣨⣀⣈⡉⠉⢩⠠⣨⡩⠉⢠⢩⠉⡍⠉⣈⣉⡄⣭⠍⣄⣉⠉⠀⠉⠅⢉⣬⡍⣡⡅⣅⣁⠈⡅⠁⠈⠈⠁⡁⠉⠉⠀⠀⠁⠀⠀⠀⠅⠀⠀⠠ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⡇⠀⣠⣤⣭⣀⡠⣤⡤⡄⠀⢠⣤⣤⡌⢣⠀⢨⣤⣤⢠⣥⣥⡨⣤⣤⣁⢠⣠⣤⠀⣥⠀⢬⢥⣤⣤⡤⣤⠰⡝⢻⠗⠃⠷⠏⡄⠀⢠⡀⡴⠖⢇⠌⠸⠁⠀⠀⠅⡄⣄⡀⢀⠀⠀⡄⢈⠀⣤⠀⢀⣘⡿⣷⠀⠀⠀⢸ ⡇⠀⠀⠀⡄⢠⣤⢀⣤⡀⡶⣶⡤⢤⣤⣤⣄⡄⠠⣄⢠⣠⠀⢀⢤⠀⢤⣀⣠⣠⠄⢠⢤⣤⣤⠤⣤⢠⣀⣄⠀⣠⡄⡄⣄⡄⣤⣄⠀⡀⠀⡄⢁⢄⡄⠠⡤⣄⢤⡄⡄⠀⠀⠀⠀⠠⣦⣦⠀⢠⡀⠀⠀⠀⡆⠈⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀ ⡇⢀⡀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠀⣀⠀⠀⠂⠀⠀⢀⡀⠀⢀⠀⡀⠀⠀⠀⡀⡀⡀⢀⠀⢀⠀⠀⢀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢐ ⡇⠀⠈⠀⡉⢠⡄⣄⡀⣖⡠⡄⠀⢀⠒⠀⠀⠀⠀⠙⣒⢶⡘⣔⡄⠂⠀⠀⠦⠡⢀⢆⡾⠁⠀⡀⠀⡐⠀⠀⡄⠌⠸⣶⠀⡝⢃⢐⠆⠈⠂⡠⡄⠠⡤⡇⣞⣭⠸⠁⠒⠀⠊⠁⠫⠄⠂⠚⠒⠀⠀⠀⠾⢤⠀⠀⠀⢠ ⡇⠀⠀⠀⠠⠤⠡⠉⠙⠛⠁⠀⠀⠈⠀⠀⠠⠀⠀⠈⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠃⠀⠀⠁⠀⠀⠀⠁⠤⠓⠀⠀⠈⠈⠁⠀⠀⠁⠁⠈⠉⠉⠁⠡⠅⠘⠣⢇⠀⠐⠔⠀⠲⠀⡴⣦⡄⠤⠀⠀⠀ ⠣⠄⠠⠠⠄⠠⠄⠄⠄⠠⠀⠄⠀⠄⠄⠠⠠⠄⠄⠄⠄⠠⠠⠠⠢⠀⠀⠤⠤⠄⠄⠠⠤⠌⠠⠠⠀⠤⠤⠤⠤⠤⠤⠄⠄⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠠⠠⠤⠤⠠⠁⠥⠤⠬⠭⠰⠩⠽⠡⠤⠄⠤⠤⠦⠤⠤⠤⠰ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠸⢷⠾⠴⠾⠶⠶⠂⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠤⠭⡅⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠗⠶⠶⠾⠶⠾⠵⠴⠲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⡇⠿⠶⠷⠶⢶⡶⡶⠀⠰⠄⠷⠶⠶⠆⠸⠷⠲⠲⠶⠲⠖⠰⠀⠖⠴⠶⠶⠶⠶⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⣷⣦⣴⣴⠰⠤⣤⡄⢀⠀⢀⠀⠀⠀⠰⠺⢆⠼⠾⠦⠸⠿⠎⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸ ⡇⠆⠿⠾⠗⠀⠀⠀⠀⠈⠳⠲⠲⠶⠲⠶⠶⠆⠸⠷⠞⠴⠲⠾⠶⠂⠸⠶⠺⠸⠹⠿⠵⠙⠶⠖⠀⠤⠤⠖⠕⠀⣺⢸⡷⣤⣄⣦⣤⣠⣴⢤⢨⠀⠒⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇ ⡟⠳⠔⠦⠶⠶⠇⠀⠀⠸⠷⠶⠲⠆⠸⠱⠞⠺⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢺⡴⡠⣤⡐⠄⠴⠆⡼⢚⡜⠾⠶⠄⠸⠀⠄⠰⠛⠆⠨⠥⠨⠶⠐⠸⠣⠀⠤⠰⠤⠀⠀⢨⡇ ⡟⠟⠶⠆⠐⡗⠶⠀⠀⠸⠶⠖⠞⠇⠸⠑⠖⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢾⢴⣦⠠⠔⠶⠦⠧⠶⠖⢧⣅⠀⠀⠀⠨⠽⣽⢽⡉⡄⠐⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇ ⡇⠛⠛⠒⠓⠛⠃⠁⠀⠀⠃⠐⠳⠟⠛⠚⠃⠸⠚⠛⠚⠚⠚⠐⠺⠆⠾⠒⠚⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢺⣦⢄⠐⠚⠙⠇⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⢀⡀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣹⠫⠉⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠁⠐ ⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐ ⡇⠀⠀⠀⡀⠀⣀⢀⡀⠀⠀⡀⣀⡀⠀⠀⠀⢀⡀⡀⢀⣀⣀⠀⠀⣀⢀⠀⣀⣀⣀⢀⣀⣀⣀⢀⣀⣀⣀⡀⠀⣀⡀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⢨ ⡇⢐⠋⠃⡛⠒⣀⠘⣙⣃⠀⠐⠙⠊⠀⠈⠂⠘⠉⢁⠘⢛⡛⢁⠛⠚⠓⠀⠛⠛⠋⢉⢛⠛⢛⠉⣛⢛⠁⠑⠊⠙⠛⡈⡙⢙⠛⠛⠓⣲⣯⡝⢛⡛⢋⣃⡀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨ ⡇⠀⠀⠀⠃⠈⠋⠀⠋⠘⠃⠀⠘⠙⠛⠛⠛⠁⠈⠛⠘⢙⢀⠘⠘⠀⠻⠛⠙⠙⠀⠘⠀⠛⠋⠀⠚⠘⠀⠁⠀⠛⠋⠋⢓⡒⠓⠇⠀⠉⠀⠁⠀⢁⣀⠙⠃⡚⠘⠃⠃⠀⠈⠀⠀⠁⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⣀⠀⠀⠀⠀⣀⡀⠀⢀⣀⣀⡀⢀⣀⣀⢀⡀⢀⣀⢊⠀⣂⣀⣀⠀⣀⣀⣉⣀⣂⣀⣀⣀⢀⡀⠀⣀⢀⣀⣀⢀⣀⣀⣂⣘⣃⣈⣀⣀⣀⣘⡈⡁⢐⣒⣀⢀⡀⢤⣤⣌⡄⠁⣭⠍⠉⠁⠀⠂⠀⢡⡀⠀⠀⢸ ⡇⠀⠉⠉⡋⢋⣉⢛⣃⣃⡉⠈⢁⣋⡁⢀⣀⡚⢛⣁⠈⢙⡉⣀⢙⣛⣙⡀⢛⣙⠙⢛⢙⢙⣉⠉⢛⢛⠁⠁⠉⢛⣋⣉⡉⣙⣙⡉⠛⡋⡋⡋⣋⣛⡛⡑⡀⡀⣀⢀⡀⠉⠉⠉⠁⠀⠈⠛⠀⠈⠁⠀⠀⠀⠈⠈⠀⢸ ⡇⠀⠀⠀⠁⠈⠉⠀⢉⣉⠅⣄⢈⠉⠉⠉⠉⠁⢈⣁⠙⠋⠂⠊⠘⡒⠛⠂⠘⠋⠀⠘⠀⠉⠉⠀⠉⠈⠀⠁⡀⠉⠉⣁⠁⠁⠛⠋⠀⠁⢘⡁⢅⣉⣁⡉⠁⠉⢉⣀⡀⠀⠠⠀⠀⣠⣤⣄⠀⢀⠀⠀⠀⠀⡄⠀⠀⠈ ⡇⠀⢀⣀⣀⣀⣀⡀⡈⠃⠃⢊⡐⣂⡀⢀⠀⠀⣄⡀⢂⣄⣀⡀⢀⣀⢀⣄⣀⣀⣠⣠⣀⣀⣠⣤⣤⢤⠈⣈⢁⣤⣨⣄⣤⣉⢀⣤⣤⣄⣀⡄⠀⠘⡛⡃⢡⣤⣌⠁⠁⢀⠐⠈⡀⢉⡉⠋⠀⠈⠁⠀⠀⠀⠃⠀⠀⢀ ⡇⠀⠉⠉⡉⢉⡁⠉⡅⢵⠐⠉⢁⡉⡁⣀⣀⠈⢉⡅⢈⣉⠉⢀⣈⠉⣉⣉⣉⣉⠉⢩⠉⣉⣩⢩⣉⢡⠀⡉⠁⣉⣉⣁⡁⣉⣉⢋⠁⡁⠉⠁⢀⣄⢩⣥⡌⡍⣉⠀⡄⠈⢈⠉⠄⠀⠈⠖⠀⠀⠀⣀⣤⣤⠒⠀⠀⢐ ⡇⠀⠀⠀⠁⠐⠈⠑⠙⠃⠀⠙⠛⠈⠓⠉⡉⢩⢈⡁⠈⠉⠀⠈⠈⠀⠈⠉⠉⠉⠀⠈⠈⠉⠁⠀⠈⠈⠁⠁⠀⠈⠁⠉⠁⠁⠉⠊⠉⠁⠀⠁⠀⠉⠈⠉⠁⡥⠈⡁⢡⠀⠀⠀⠀⠯⠄⠀⢀⡀⠀⠉⠛⠛⠀⠀⠄⢨ ⡇⠀⡀⢤⣇⣈⡑⡀⠅⠄⠈⢠⣤⡤⠄⠁⠀⢠⣽⡤⣨⢤⣤⡠⣤⣤⡤⠀⣤⣤⣤⣤⡀⢤⣠⣤⣀⣤⣤⡤⣤⣄⣄⣠⢠⣄⣀⣠⢄⡤⠤⣄⣤⣤⣽⡧⢤⣄⡄⣔⡆⡀⣠⡀⡀⢠⣦⣆⠀⢤⡀⠀⠀⠀⡄⠀⠀⠀ ⡇⠀⠀⠉⠍⠩⡄⠩⠍⡥⠀⠈⠉⢍⣁⣀⠀⠌⠩⡅⢈⠩⠉⢠⢤⠉⡨⣀⣈⡉⡉⢩⠠⣩⡩⠉⢠⢩⠉⡍⠉⣈⣉⡄⣭⠍⣄⣉⠉⠀⠉⠅⢉⡬⠍⢡⡅⣅⡁⠈⠅⠁⠈⠈⠁⡁⠉⠉⠀⠀⠁⠀⠀⠀⠅⠀⠀⠠ ⡇⠀⠀⠉⠀⠔⠀⠀⠢⠀⠀⠈⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠙⠁⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠤⢀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⡇⠀⣠⣤⣧⡀⠤⣤⡴⡤⠀⢠⣤⣤⡌⠣⠀⢨⣤⣤⢠⠥⢥⡨⣤⣤⣁⢨⢠⣤⠀⣥⠀⢬⢥⣤⣤⡤⣤⠰⡝⢻⠗⠃⠷⠏⡄⠀⢠⡀⡴⠖⢇⠌⠿⠆⠀⠘⠄⡄⣄⡀⠀⠐⠀⠀⢈⠀⣤⠀⢀⣘⡿⣷⠀⠀⠀⢸ ⡇⠀⠀⠀⠄⠠⠤⢀⡤⠀⡶⣶⡤⢤⡤⣤⣄⠄⢠⡄⠠⣠⠀⢀⢤⠀⢤⣀⣠⣠⠄⢠⢤⣤⣤⠤⣤⢠⣀⣄⠀⣠⡄⡄⣄⡄⣤⣄⠀⡀⠀⡄⢁⣆⡄⠠⡤⣄⢤⡄⡄⠀⠀⠀⠀⠠⣦⣦⠀⢠⡀⠀⠀⠀⡆⠈⠀⠀ ⡇⠀⠀⠀⠄⠀⠀⠀⠀⠂⠀⠁⠀⠀⠀⠃⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀ ⡇⢀⡀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠀⣀⠀⠀⠂⠀⠀⢀⡀⠀⢀⠀⡀⠀⠀⠀⡀⡀⡀⢀⠀⢀⠀⠀⢀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢾⠂⠀⠐⠂⢀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢐ ⡇⠀⠈⠀⡀⢠⡄⣄⡀⣖⡠⡄⠀⢀⠒⠀⠀⠀⠀⠙⣒⢶⡘⣔⡄⠂⠀⠀⠦⠡⢀⢆⡾⠁⠀⡀⠀⡐⠀⠀⡄⠌⠸⣶⠀⡝⢃⢐⠆⠈⠂⡠⡄⠠⡤⡇⣞⣭⠸⠁⠒⠀⠂⠀⠫⠄⠂⠚⠒⠀⠀⠀⠾⢦⠀⠀⠀⢠ ⡇⠀⠀⠀⠠⠤⠡⡉⠙⠛⠀⠀⠀⠈⠀⠀⠠⠀⠀⠈⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠃⠀⠀⠁⠀⠀⠀⠁⠤⠓⠀⠀⠈⠈⠁⠀⠀⠁⠁⠈⠉⠉⠁⠡⠅⠘⠣⢇⠀⠐⠔⠀⠲⠀⡴⣦⡄⠤⠀⠀⠀ ⠃⠀⠠⠠⠤⠠⠄⠄⠄⠠⠀⠄⠀⠄⠄⠠⠠⠄⠄⠄⠄⠠⠠⠠⠢⠀⠀⠤⠤⠄⠄⠠⠤⠌⠠⠠⠀⠤⠤⠤⠤⠤⠤⠤⠄⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠠⠠⠤⠤⠤⠁⠥⠤⠬⠭⠰⠩⠽⠡⠤⠄⠤⠤⠦⠤⠤⠤⠰ ⡇⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⡯ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠺⢶⠾⠸⠶⠶⠶⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠒⡄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠶⠾⠸⠶⠾⠰⠴⠲⠂⠀⠀⠐⠒⠒⠒⠒⠒⠒⠂⠉⢭ ⡇⠿⠶⠷⠶⠶⠶⡶⠀⠰⠄⠷⠶⠶⠆⠸⠷⠶⠲⠶⠸⠀⠸⠶⠖⠶⠶⠾⠶⠶⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡿⠷⠶⠶⠆⠷⠶⠆⠀⠀⠀⢀⠀⠀⠀⠸⠾⠆⠺⠾⠢⠸⠾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸ ⡇⠆⠿⠾⠗⠀⠀⠀⠀⠈⠳⠲⠲⠶⠶⠶⠶⠂⠸⠷⠾⠲⠺⠶⠖⠀⠺⠶⠲⠸⠻⠻⠽⠝⠶⠖⠒⠶⠶⠇⠇⠀⡇⡿⠷⠶⠶⠆⠷⠆⠷⢶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇ ⡟⠳⠔⠦⠶⠶⠇⠀⠀⠸⠷⠶⠲⠆⠸⠹⠸⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡿⠷⠶⠶⠇⠸⠳⠶⠶⠲⠶⠶⠶⠆⠀⠸⠅⠸⠻⠂⠸⠣⠸⠻⠑⠸⠣⠻⠻⠰⠤⠀⠀⢨⡇ ⡟⠟⠶⠂⠐⡗⠶⠀⠀⠸⠶⠶⠞⠄⠸⠳⠶⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡏⠟⠷⠒⠶⠶⠾⠷⠶⠞⠄⠀⠀⠀⠀⠸⠭⠿⠃⠛⠿⠗⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇ ⡇⠛⠛⠒⠃⠛⠃⠁⠀⠀⠃⠐⠻⠛⠓⠚⠂⠘⠚⠚⠚⠛⠘⠚⠾⠀⠾⠒⠛⠛⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡟⢛⠓⠓⠟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠡⠉⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊ ⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡀⡀⣀⠀⠀⠀⠐⠐⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢒ ⡇⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⢀⣀⣀⡀⢀⠀⢀⣀⠀⢀⣀⢀⠀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⠀⣀⣀⣀⡀⢀⣀⡀⢀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⢨ ⡇⢀⠉⠛⡋⢛⡉⠛⡛⡃⠀⠘⠙⠋⠃⠈⢀⡘⢙⠃⠙⢛⠙⢀⠛⠛⠑⠀⠛⠛⠋⣙⠛⠛⣋⠉⡋⣛⠃⡓⠉⠛⠋⡙⡛⡛⠛⠛⠛⡓⠓⡛⢛⣛⡛⢃⣀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨ ⡇⠀⠀⠀⠃⠈⠋⠀⠃⠋⠁⠂⠈⠙⠛⠙⠛⠁⠘⠀⠙⢙⢀⠘⠐⠀⠛⠛⠙⠙⠀⠙⠀⠋⠃⠀⠃⠈⠀⠃⠈⠛⠁⠃⠃⠋⠛⠃⠀⠃⠈⠃⠐⠙⠃⠘⠛⠋⠙⠚⠃⠀⠈⠀⠀⠁⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢉⣀⣀⠀⢀⡀⣀⡀⠀⢀⣀⣄⡀⢀⢀⣀⣀⡀⣀⣠⣈⠀⣀⣀⡀⠀⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⠀⣄⢀⣀⣄⢀⣀⣀⣀⣈⣁⣈⣀⣀⣀⣈⣈⡁⢐⣒⣀⢀⡀⢤⣤⣌⡄⠁⣭⠍⠉⠁⠀⠂⠀⠡⡀⠀⠀⢸ ⡇⠀⠉⠉⡍⢉⣍⢉⣭⣅⡉⠈⢉⣉⣁⣈⣈⡉⢉⠁⢉⣉⠉⢀⠉⠉⣉⣀⣉⣉⠉⣉⠉⣉⣉⠉⡉⣉⠈⡉⠉⣉⡉⡈⡉⣉⣉⡉⠉⡜⢋⣃⣉⣛⡛⢂⣀⡀⣀⢀⡀⠉⢉⠉⠁⠀⠈⠛⠀⠈⠁⠀⠀⠀⠈⠈⠀⢸ ⡇⠀⠀⠀⠁⠈⠉⠈⠁⢉⠁⣁⢈⠈⠉⠉⠉⠁⢈⣀⠉⠉⠀⠈⠈⡀⠛⠉⠉⠉⠀⠉⠀⠉⠁⠀⠉⠉⠀⠁⡈⠉⠁⣁⠁⠉⠙⠃⠀⠁⢈⡁⢉⣉⣁⡈⠉⠉⢈⣉⡁⠀⠨⠀⠀⣠⣤⣄⠀⢀⠀⠀⠀⠀⡄⠀⠀⠈ ⡇⠀⣀⣄⣀⣀⣀⣀⣌⡁⠁⢈⣤⣤⡄⢀⠀⢠⣤⡀⣠⣤⣠⠀⢠⡤⢤⣤⡄⣤⣤⣤⣤⣤⣤⣤⣤⣤⢈⣌⣁⣤⣨⡤⣤⣭⣠⣤⡤⣄⣤⡄⠀⠘⡛⡃⢠⣤⣌⠁⠁⢀⠐⠈⡀⢉⡉⠋⠀⠈⠁⠀⠀⠀⠃⠀⠀⢀ ⡇⠀⠀⠉⡍⢉⣄⠉⣭⣅⡀⠈⢉⣉⣁⣈⣠⡈⢩⠀⣈⣩⠈⢠⠈⠉⣉⣉⣉⣉⠉⢭⠉⣉⡭⠉⡍⢥⠀⡍⢁⣉⣉⡅⡅⣍⣉⡉⠉⡅⢉⡅⢀⣤⡉⢡⣬⡍⣉⣠⡀⠈⢈⠉⠀⠀⠈⠖⠀⠀⠀⢀⣤⣤⠒⠀⠀⢐ ⡇⠀⠀⠀⠁⠀⠁⠈⠉⠉⠁⠁⠚⠈⠉⠉⠉⢀⢈⡀⠈⠈⠀⠈⠈⠀⠉⠉⠉⠉⠀⠉⠀⠉⠁⠀⠉⠉⠀⠁⠀⠉⠁⠁⠁⠁⠉⠃⠀⠁⠀⠁⠀⠉⠁⠈⠉⡭⠈⡉⢡⠀⠀⠁⠀⠮⠄⠀⠀⡀⠀⠉⠛⠛⠀⠀⠄⢨ ⡇⠀⣀⣤⣀⣀⣀⣀⣄⡄⠀⢠⣤⣤⡄⢠⠄⢠⣤⡄⣤⣤⣠⠀⣤⣤⡤⠀⣤⣤⣤⣤⠀⣤⣠⣤⢀⣤⣤⡤⣤⣤⡄⣠⣤⣄⣠⣤⢤⣤⣤⣄⣤⣤⣠⡤⣤⣤⡄⣐⡆⡀⣠⡀⡀⢠⣦⣆⠀⢤⡀⠀⠀⠀⡄⠀⠀⠀ ⡇⠀⠀⠉⡅⢡⣤⢩⣭⣥⡄⠀⢩⣭⣥⣤⣤⡌⢩⡄⣨⣩⠄⢠⠈⠉⣨⣠⣭⣭⠉⣥⠀⣥⡥⠁⡄⣥⠁⡅⢉⣨⡅⡤⡍⣅⣈⡉⠉⡍⢩⡅⠩⣭⡍⢩⡍⣅⣁⡈⡅⠁⢨⡈⠁⡁⠉⠉⠀⠀⠁⠀⠀⠀⠅⠀⠀⠠ ⡇⠀⠀⠀⠀⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠉⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠁⡉⢁⠀⠁⠀⠁⠀⠁⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠤⢀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⡇⠀⣠⣤⣤⡀⠤⣤⡴⡄⠀⢠⣴⣶⡆⢠⠄⢰⣤⡄⢰⣵⣥⠀⣤⣤⣠⢠⣤⣤⠀⣴⠀⢼⣥⣶⣶⡦⣤⠰⡝⢻⠗⠃⠷⠏⡀⠀⢠⡀⡴⠖⢇⠌⠿⠆⠀⠘⠄⡄⣀⡀⠀⠐⠀⠀⢈⠀⣤⠀⢀⣘⡿⣷⠀⠀⠀⢸ ⡇⠀⠀⠀⡄⠠⠤⢀⡤⠀⡤⣴⡤⢤⡤⣤⣄⠄⢠⡄⠠⣠⠀⢀⢤⠀⢤⣀⣠⣠⠄⢠⢤⣤⣤⠤⣤⢠⣀⣄⠀⣠⡄⡄⣄⡄⣤⣄⠀⡀⠀⡄⢁⣄⡄⠠⡤⣆⢤⡄⡄⠀⢠⡀⠀⠠⣦⣦⠀⢠⡀⠀⠀⠀⡆⠈⠀⠀ ⡇⠀⠀⠀⠄⠀⠀⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀ ⡇⢀⡀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠀⣀⠀⠀⠂⠀⠀⢀⡀⠀⢀⠀⡀⠀⠀⠀⡀⡀⡀⢀⠀⢀⠀⠀⢀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢾⠂⠀⠐⠂⢀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢐ ⡇⠀⠈⠀⡀⢠⡄⣄⡀⣖⡠⡀⠀⢀⠒⠀⠀⠀⠀⠙⣒⢶⡘⣔⡄⠂⠀⠀⠦⠡⢀⢆⡞⠁⠀⡀⠀⡐⠀⠀⡄⠈⠸⣶⠀⡝⢃⢐⠆⠈⠂⡠⡄⠠⡤⡇⣞⣭⠸⠁⠒⠀⠂⠀⠫⠄⠂⠚⠒⠀⠀⠀⠾⢤⠀⠀⠀⢠ ⡇⠀⠀⠀⠠⠤⠡⠁⠉⠛⠀⠀⠀⠈⠀⠀⠠⠀⠀⠈⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠃⠀⠀⠁⠀⠀⠀⠁⠤⠓⠀⠀⠈⠈⠁⠀⠀⠁⠁⠈⠉⠉⠁⠡⠅⠘⠣⠇⠀⠐⠔⠀⠲⠀⡴⣦⡄⠤⠀⣰⠀ ⠃⠀⠠⠠⠄⠠⠄⠄⠄⠠⠀⠄⠀⠄⠄⠠⠠⠄⠄⠄⠀⠠⠠⠠⠢⠀⠀⠤⠤⠄⠄⠠⠤⠌⠠⠠⠀⠤⠤⠤⠤⠤⠤⠄⠄⠤⠤⠤⠄⠤⠤⠤⠤⠤⠤⠠⠠⠤⠤⠠⠁⠥⠤⠬⠭⠰⠩⠽⠡⠤⠄⠤⠤⠦⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣷⠿⠸⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⢩⣭⡍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠻⠿⠽⠽⠹⠽⠿⠹⠽⠿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢭ ⡧⠿⠶⠷⠶⢶⠶⡆⠄⠸⠴⠶⠶⠶⠀⠿⠶⠶⠶⠶⠸⠀⠶⠶⠖⠶⠶⠿⠶⠶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠶⠶⠶⠴⠴⠶⠢⠀⠀⠀⠀⠀⠀⠀⠾⠾⠶⠾⠶⠀⠶⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠟⠿⠻⠗⠀⠀⠀⠀⠸⠷⠲⠲⠶⠲⠶⠶⠀⠸⠲⠺⠶⠷⠶⠖⠀⠷⠶⠇⠇⠟⠿⠿⠿⠶⠖⠲⠶⠾⠆⠆⢸⣿⡿⠷⠶⠶⠶⠴⠶⠶⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠛⠟⠛⠓⠗⠃⠁⠀⠸⠟⠻⠻⠂⠛⠸⠘⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠴⠶⠶⠇⠸⠦⠶⠶⠴⢶⠶⠶⠠⠀⠼⠠⠺⠾⠀⠸⠀⠸⠿⠀⠼⠀⠾⠺⠀⠀⠀⠀⠀⢸ ⡟⡛⠛⠃⠃⠛⠇⠂⠀⠸⠚⠚⠛⠀⠛⠛⠚⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠿⠶⠲⠶⢶⠶⢶⠶⠲⠀⠀⠀⠀⠀⠸⠾⠿⠄⠿⠿⠔⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠛⠛⠛⠛⠛⠃⠀⠀⠘⠃⠘⠸⠛⠛⠛⠀⠙⠚⠚⠛⠛⠘⠛⠿⠀⠗⠓⠓⠃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠷⠲⠲⠶⠲⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠉⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠚⠉⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚ ⡎⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠈⠉⠉⠉⠁⠈⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢲ ⡇⠀⢀⣀⣀⠀⢀⡀⡀⡀⠀⢀⣀⣀⡀⢀⠀⢀⣀⡀⣀⣀⣀⠀⣀⣀⣀⠀⣀⣀⣀⢀⣀⣀⣀⠀⡀⡀⣀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⠉⡋⢉⣉⠉⡉⣁⡀⠈⢉⣉⣁⢈⣀⡈⢈⠁⢉⢛⠙⢀⠛⠛⠑⠀⠛⠛⠋⣙⠛⠛⣛⠈⡛⠛⠋⡓⠚⠛⠛⠚⠟⠛⠛⠻⠿⠉⠋⠻⠿⠿⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠈⠉⠀⠁⠉⠁⠁⠈⠉⠉⠉⠉⠁⠈⠀⠉⠉⠀⠘⠐⠀⠛⠛⠛⠛⠀⠛⠀⠛⠃⠀⠓⠛⠀⠃⠘⠛⠃⠋⠃⠛⠻⠇⠀⠃⠘⠇⠘⠟⠇⠸⠻⠗⠳⠆⠃⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣀⣀⣀⣀⣀⣤⡀⠀⢀⣠⣄⡀⢀⢀⣠⣠⡀⣠⣤⣀⡀⣀⣠⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⠀⣀⠀⣀⡀⠀⢀⣀⡀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣧⠀⠉⠉⡍⢉⣌⢉⣭⣥⡀⠈⢉⣉⣁⣈⣉⡍⢉⡅⢈⣩⡍⢁⡉⠉⢉⣀⣉⣉⠙⢛⠙⢙⣙⠛⢛⢛⠉⣓⠋⠛⠛⠙⠛⠛⠛⠛⠛⠋⠛⡛⡛⡛⡓⢃⣀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠀⠁⠀⠉⠉⠁⠉⠁⠁⠈⠉⠉⠉⠉⠁⠈⠁⠈⠉⠀⠈⠉⠀⠘⠉⠉⠉⠀⠘⠀⠉⠉⠀⠘⠘⠀⠙⠀⠛⠋⠛⠛⠛⠛⠟⠀⠛⠀⠃⠃⠃⠃⠘⠛⠛⠙⠃⠃⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⣀⣤⣀⣀⣀⣀⣄⡀⠀⢀⣤⣤⡄⠀⡄⢠⣤⡄⢠⣤⡤⡄⠀⣤⠤⣤⣤⣠⣠⣠⣀⣀⣤⣤⣀⣀⡀⣀⡀⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠉⡍⢉⣤⠉⣭⡥⡀⠀⠀⣉⣁⣀⣁⡌⠉⡅⢀⣩⡅⠡⡄⠉⢉⣉⣉⣉⡉⢩⠉⢉⣩⠉⢉⢉⡈⢉⠉⣉⣉⢋⣘⢉⠓⡛⠉⢊⠛⡛⠀⣀⣀⢀⣀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠀⠀⠀⠁⠀⠉⠉⠀⠁⠀⠁⠁⠁⠈⠁⠀⠁⠀⠁⠀⠀⠁⠁⠘⠉⠉⠉⠁⠈⠁⠈⠉⠀⠈⠉⠁⠈⠀⠉⠉⠘⠘⠘⠉⠛⠀⠘⠀⠓⠀⠙⠛⠈⠛⠛⠉⠃⠃⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⣠⣤⣤⣠⡠⣤⣤⣤⠀⢠⣤⣦⣦⠀⡄⢠⣤⣤⢠⣦⣤⡄⢠⣤⣤⠄⢠⣤⣤⣤⡄⢠⣄⣤⡄⣠⣠⣠⣤⣠⣀⢀⣀⣀⡀⣀⡀⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠀⡄⠠⣦⠀⣤⣤⡤⡀⠀⣤⣤⣤⣤⣤⠀⡄⢀⣭⡅⠀⡌⠉⢡⣥⣬⣉⡉⠩⡅⢈⣩⡍⢡⡌⡍⢩⠉⢉⣉⣉⢉⢉⣁⣉⠉⢩⠉⣛⠙⣋⣉⠙⣋⣏⢉⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠁⠀⠁⠈⠉⠀⠈⠉⠁⠈⠁⠈⠉⠈⠈⠈⠉⠙⠀⠈⠀⠉⠀⠉⠉⠀⠉⠋⠁⠉⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⡠⣴⣤⣤⡤⣤⣴⡖⠀⠠⣶⣶⣶⠀⡆⢠⣦⡆⢠⣶⣦⡤⢠⣦⣄⣤⣤⣤⡄⢠⡄⠠⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠀⡆⠀⣦⠀⣶⣶⣤⡀⠀⡤⣤⣤⣤⣦⠀⡆⢠⣤⡆⠀⡆⡀⢀⣤⣤⣤⡄⠠⡄⢠⣤⡄⢡⡌⡌⢠⠀⢀⣀⣠⢠⢠⣀⣀⠀⢠⠀⢠⠀⣤⣤⠀⣤⣤⣀⣀⣤⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠈⠀⠈⠉⠉⠀⠈⠀⠈⠀⠉⠉⠀⠉⠉⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣤⣤⠄⢰⢸ ⠻⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡶⠧⠧⠶⠾⠯⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢩⢩⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠿⠿⠷⠿⠿⠶⠿⠹⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⡏⠿⠶⠷⠶⠶⠶⠶⠀⠸⠴⠲⠶⠶⠀⠿⠶⠖⠶⠶⠇⠀⠶⠶⠶⠦⠶⠷⠶⠆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠶⠶⠴⠶⠰⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠰⠿⠿⠀⠿⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡏⠟⠿⠻⠇⠀⠀⠀⠀⠛⠷⠲⠲⠶⠲⠶⠶⠀⠹⠶⠇⠶⠷⠶⠆⠀⠶⠶⠆⠟⠖⠶⠦⠶⠶⠂⠴⠶⠶⠴⠂⢸⢸⠶⠶⠶⠶⠰⠶⠴⠶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠛⠋⠛⠛⡛⠃⠀⠀⢘⠻⠛⠺⠂⢛⠘⠸⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⢸⣴⠶⠴⠀⠶⠦⠶⠶⠶⢶⠶⠶⠰⠀⠿⠠⠹⠿⠀⠸⠀⠘⠛⠀⠹⠀⠛⠛⠀⠀⠀⠀⠀⢸ ⡏⣛⠛⠃⠃⡛⠇⠃⠀⠘⡚⠛⠛⠀⠛⠛⠚⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⡶⠶⠶⠶⠶⢶⠶⢶⠶⠺⠀⠀⠀⠀⠀⠹⠻⠽⠃⠛⠛⠊⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠛⠛⠛⠛⠛⠃⠂⠀⠘⠃⠘⠸⠛⠛⠛⠂⠙⠚⠚⠚⠛⠸⠲⠶⠀⡶⠶⠶⠶⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡿⠷⠲⠲⠶⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠉⠉⠈⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠃⠃⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉ ⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠀⠉⠁⠈⠁⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠁⠁⠈⠉⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢹ ⣿⠀⢀⣀⣀⣀⢀⣀⣀⡀⠀⢀⣀⣀⡀⠀⡀⢀⣀⡀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠁⠉⡍⢉⣅⠉⣍⣥⣀⠈⠉⣉⣉⣀⡁⣀⠋⡃⠘⠛⡃⠃⡘⠛⠛⠁⠸⠿⠏⠛⠿⠿⠿⠗⠺⠿⠿⠹⠔⠿⠿⠒⠿⠿⠿⠿⠿⠿⠽⠛⠛⠛⠛⠙⣀⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠀⠁⠀⠉⠀⠉⠉⠉⠁⠀⠉⠉⠉⠉⠋⠀⠃⠈⠛⠃⠀⠃⠂⠰⠟⠓⠷⠇⠨⠇⠰⠶⠇⠸⠧⠇⠸⠄⠰⠶⠺⠸⠼⠶⢶⠀⠸⠀⠹⠀⠛⠛⠀⠛⠛⠋⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⣀⣤⣄⣀⣀⣄⣤⣄⠀⠀⣄⣤⣀⠀⡀⣀⣀⣀⠀⣀⣀⠀⠀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠁⡅⠈⣤⠉⣭⣭⣀⠀⠉⣉⣉⣀⣉⣉⠉⣉⠀⣛⣛⠈⡀⠛⠛⠃⠘⠛⠛⠛⠟⠟⠟⠻⠳⠿⠗⠲⠧⠺⠿⠗⠚⠛⠛⠛⠛⠛⡙⢛⢛⢛⢛⡛⣀⣀⢀⡀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠁⠉⠉⠉⠉⠀⠉⠀⠉⠁⠀⠓⠂⠀⠟⠛⠛⠛⠀⠗⠐⠗⠃⠀⠇⠇⠀⠇⠰⠶⠂⠛⠃⠛⠻⠇⠀⠃⠘⠘⠘⠛⠁⠋⠛⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⡠⣤⣤⣤⡠⣤⣤⣤⠀⠀⣤⢤⣤⠀⡤⠀⣤⣤⠀⣠⣄⢀⠀⣀⣀⣀⡀⡀⣀⣀⡀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠀⣄⠀⣶⢀⣦⣤⣤⠀⠀⣌⣉⣀⣈⣠⠉⡍⠀⣉⣉⠈⡀⠋⠓⡛⠛⠓⠛⠛⡛⠛⠛⡛⠛⡛⡋⠘⠓⠛⠟⠛⠉⠛⠛⠚⠟⢙⡙⢛⠀⢀⣀⠀⣀⣠⢀⣀⢤⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠉⠀⠉⠁⠀⠉⠂⠀⠋⠛⠛⠃⠀⠃⠘⠛⠃⠀⠃⠃⠘⠃⠘⠛⠙⠛⠛⠛⠻⠃⠘⠃⠘⠀⠘⠉⠀⠉⠉⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⡠⣤⣤⣤⡠⣤⣤⣤⠀⢠⣴⣦⣦⠀⡄⢠⣤⣤⢀⣤⣤⡄⢠⣀⣀⠀⢀⣀⣀⣀⡀⢀⡀⣀⡀⢀⣀⣀⣀⣀⢀⠀⣀⣀⠀⣀⣀⣀⣀⣠⣀⣀⣀⣀⢤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠀⡆⠠⣦⡠⡦⣶⡤⡀⠀⣤⣤⣤⣤⡄⠁⡅⢀⣩⡅⠁⡌⠉⢉⣁⣈⣙⠉⢉⡁⠘⢛⡛⢋⢙⡙⢙⠚⠛⠛⢊⢛⢛⠉⣉⠑⢉⠙⡩⠉⣍⡍⢉⣭⣭⣈⡀⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠁⠁⠘⠉⠉⠉⠁⠈⠀⠉⠛⠀⠘⠘⠀⠘⠀⠛⠋⠘⠙⠘⠉⠛⠀⠈⠀⠁⠀⠉⠉⠀⠉⠉⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠀⠤⣶⡤⣤⠤⣤⣦⡆⠀⢰⣶⣶⡆⢠⡄⢰⣦⡄⢠⣤⣤⡀⣤⣄⣀⣠⣀⣀⠀⣀⠀⣠⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡆⠰⡦⡰⣶⣶⡄⡀⢠⢤⣤⣤⣤⡄⢰⠀⣠⣤⠀⢠⢀⠉⣉⣈⣉⣉⠀⣭⠀⣈⡭⠉⡍⣭⠉⡄⢀⣀⡀⣄⡄⣄⣀⡀⠀⡄⢠⡄⢠⡤⡄⢠⣤⣄⢤⣤⡄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠉⠉⠉⠉⠀⠉⠈⠉⠁⠀⠁⠁⠀⠁⠈⠉⠀⠉⠁⠉⠙⠃⠀⠁⠈⠁⠈⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣦⡤⣤⠀⢴⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⡿⠏⠯⠿⠿⠏⠉⠭⠉⠉⠉⠉⠉⠉⠭⠉⠉⠉⠉⠉⠉⠉⠉⢭⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠷⠶⠇⠇⠶⠧⠿⠶⠶⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⢭ ⡯⠿⠶⠷⠲⠶⠶⠆⠀⠹⠼⠶⠶⠶⠀⠿⠶⠖⠶⠆⠆⠀⠦⠴⠦⠴⠴⠶⠶⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠿⠶⠶⠶⠺⠶⠶⠀⠀⠀⠀⠀⠀⠀⠐⠟⠿⠀⠿⠟⠐⠷⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡗⠋⠛⠛⠃⠀⠀⠀⠀⠛⠷⠲⠲⠶⠶⠶⠶⠀⠻⠶⠦⠶⠶⠶⡆⠀⣦⠴⡖⡶⡶⡖⡶⢶⡶⠂⠴⠶⠶⠶⠂⢸⢸⠹⠶⠶⠶⠸⠲⠺⠒⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣟⣛⠋⠛⡛⡛⠃⠀⠀⢘⠻⠺⠺⠆⠺⠹⠸⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡾⡾⠴⠚⠚⠂⠘⢛⠛⠛⢛⠻⠟⠛⠈⠀⢚⣀⣙⠛⠀⠸⠀⠹⠻⠀⠽⠠⠿⠺⠀⠀⠀⠀⠀⢸ ⣏⣛⠛⠋⠃⡛⠟⠃⠀⠘⡒⠚⠛⠂⠸⠱⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡏⠟⠛⠛⠛⠻⠟⠻⠛⠛⠂⠀⠀⠀⠀⠘⠛⢛⡃⠛⠻⠓⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠛⠛⠛⠛⠛⠓⠀⠀⠀⠃⠀⠻⠗⠛⠒⠆⠸⠆⠷⠶⠾⠶⠶⢶⡄⢰⣴⣴⣴⡔⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢹⠛⠋⠋⠛⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠈⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠂⠀⠀⠠⠤⠤⠤⠤⠤⠤⠄⠀⠀⠐⠒⠒⠒⠒⠒⠒⠈⠈⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠂⠀⠀⠘ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠈⠀⠀⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠈⠀⠀⠒⠒⠒⠒⠒⠒⠀⠀⠀⢠ ⣿⠀⣀⣠⣀⣀⢀⣀⣀⣀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⣀⣀⣠⣠⡤⡤⣤⣤⣠⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠉⡍⠉⣥⠉⣭⢩⣀⠀⠙⠙⠛⠀⠙⠀⠘⠻⠀⠿⠿⠰⠀⠶⠿⠶⠀⠶⠶⠼⠺⠾⠾⠿⠒⠿⠟⠋⠓⠚⠛⠋⡉⡋⡉⣉⡉⠉⡍⢩⠌⢩⣭⡍⢤⣤⣄⣀⢠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠀⠀⠀⠉⠀⠉⠉⠉⠈⠀⠉⠙⠛⠛⠛⠀⠸⠀⠶⠾⠀⠸⠠⠀⣶⠶⠶⠶⠀⠸⠀⠶⠟⠀⠿⠘⠀⠃⠀⠛⠋⠃⠁⠉⠉⠃⠀⠁⠈⠀⠈⠉⠁⠀⠉⠁⠈⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⣠⣤⣤⣤⡠⣀⣠⣄⠀⠀⣀⣠⣀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⡀⢀⣠⣄⣤⣤⢤⢤⣤⡤⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠀⡄⠀⣤⠉⣭⣭⣄⠀⠉⣈⣙⡀⠑⣛⠛⠛⠀⠟⠿⠔⠀⠿⠿⠯⠰⠿⠷⠷⠷⠿⠿⠿⠓⠛⡓⢑⡓⠙⣛⣋⣈⢉⣉⣉⡉⢩⠌⢰⢠⣠⣤⠀⣴⣦⡠⣄⣠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠁⠉⠉⠛⠛⠀⠃⠐⠓⠋⠀⠇⠄⢰⠶⠶⠶⠆⠰⠇⠰⠾⠃⠘⠓⠃⠘⠂⠘⠉⠈⠈⠈⠉⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡿⠀⣠⣴⣤⣤⢤⣤⣤⡄⠀⢀⣤⣤⡄⢀⡀⢀⣀⡀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣀⢀⣀⣀⣤⣤⣤⣄⣤⡤⡦⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡆⠠⡦⣀⣖⣦⡄⠈⢉⣉⣁⣈⣀⡘⢙⠁⠙⢛⠛⠀⠸⠫⠽⠿⠿⠿⠿⠿⠛⠛⠿⠛⡛⡋⠉⡋⢉⣉⣉⣅⡅⣅⣉⡍⠀⡆⢠⡂⢠⣶⡄⣰⣶⡦⢤⣴⡄⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠉⠀⠘⠀⠛⠛⠀⠛⠀⠀⠗⠓⠗⠇⠀⠇⠐⠛⠃⠀⠃⠃⠈⠃⠈⠉⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠤⣶⡦⣤⢤⣴⣦⡆⠀⣤⣤⣤⡀⡠⠀⣄⣀⠀⣀⣀⡀⢀⣀⡀⡀⠀⢀⢀⠀⠀⢀⢀⣀⡀⢀⣀⣀⣀⣠⣠⢀⣤⣤⡀⣤⣔⣤⣶⣶⢶⣶⡦⢶⢰⠶⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡆⢰⡆⢰⡶⣦⢀⠀⣬⣭⣄⣈⣠⠉⡍⠈⡉⡋⢃⡘⠛⠛⠂⠘⠛⠛⢛⠃⠘⢛⠛⢋⢙⠉⣉⠉⣉⣉⣡⣭⣭⣤⣤⠀⢰⠀⡆⠀⣲⣶⠀⣶⣶⠤⣤⡶⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠁⠈⠉⠁⠀⠃⠂⠸⠛⠛⠛⠃⠘⠀⠛⠛⠀⠘⠈⠀⠉⠀⠉⠁⠈⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠴⠶⡶⠤⢦⣴⣶⠀⠀⣶⣶⣶⠀⡄⠀⣤⣄⢀⣤⣄⡄⢀⣀⡀⣀⠀⠀⠀⢀⠀⢀⣀⣀⣠⣠⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡇⠰⠆⢰⢶⣦⢄⠀⢤⣤⣤⣤⣠⠁⣭⠀⣉⡭⠁⡈⠉⠉⣉⣉⣙⡁⢈⡁⢈⣉⡙⢩⣩⡉⢠⠀⣀⣠⢠⢤⢰⣤⣤⠀⢰⠀⠶⠀⣖⢲⠀⠶⣷⠤⣤⢰⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠉⠁⠀⠁⠁⠀⠋⠉⠉⠁⠀⠁⠈⠉⠁⠈⠉⠁⠈⠀⠈⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣦⣤⣤⠀⢠⢸ ⠻⠤⠠⠤⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡖⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠹⣿⡿⡏⣯⡭⣭⡍⠉⠉⠩⠍⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠒⠒⣦⣴⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠈⠹⡿⠯⠿⡏⡯⡭⡏⡯⡭⡭⠉⠉⠭⠉⠍⠉⠉⠉⠉⠉⠀⠀⢠ ⡏⡟⠒⠷⠲⠶⠶⠆⠀⠺⠼⠶⠶⠴⠀⠶⠶⡶⢦⡦⡆⠀⢦⣤⣴⣴⣶⠶⠶⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⢟⠶⠒⠷⠷⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠀⣶⣶⠀⣶⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣟⣋⠛⡛⠓⠀⠀⠀⠀⠸⠷⠶⠲⠶⠶⠶⢶⠀⢲⢤⢴⣤⢶⣤⡤⠀⢦⡴⠦⠖⠿⠷⠿⠷⠶⠒⠒⠔⠛⠋⠃⠸⡼⣟⠛⠛⠚⠚⠒⠾⠲⢶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⣛⠋⠛⠛⣛⠃⠁⠀⠘⠷⠶⠶⠆⠸⠇⠔⠖⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢻⣛⡛⠛⠃⠘⠛⠚⠷⠖⠶⡶⠶⠆⠄⠰⠆⠐⣶⡆⢐⡆⢐⡶⠆⢐⠆⠾⠶⠄⠀⠀⠀⠀⢸ ⣿⣉⡋⠋⠃⢋⠟⠁⠀⠀⠷⠶⠶⠇⠀⠗⠶⡦⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⣘⡙⠛⠛⠛⠻⠛⠿⠶⠳⠀⠀⠀⠀⠀⣶⣶⣦⠰⣶⣦⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠋⠋⠛⠙⠛⠛⠀⠀⠀⠛⠀⠚⠶⠾⠶⢶⠀⢶⢴⣤⣤⣦⢰⢤⣤⠀⣤⠴⠶⠶⠽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡟⠛⠙⠙⠛⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⢀⣀⣀⣀⡀⠀⠉⠉⠉⠁⠀⠀⠒⠒⠒⠒⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠒⠒⠒⠒⠀⠀⠈⠉⠉⠉⠀⢀⣀⣀⣀⣀⣀⡀⠀⠉⠉⠉⠀⠀⠀⠒⠒⠒⠂⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠒⠒⠒⠂⠀⠀⠉ ⣿⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠒⠒⠒⠂⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠐⠒⠒⠒⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠒⠒⠒⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠒⠒⠒⠂⠀⠀⢹ ⣿⠀⣀⣠⣀⣀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣀⠀⣠⣤⡤⡄⣠⣤⣤⢀⣤⣤⣤⣤⡄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠁⡍⠉⣥⠉⣉⣉⠀⠀⠛⠙⠿⠀⠲⠀⠴⢶⠀⣶⣶⠰⠀⡶⡶⠮⠀⠿⠟⠛⡙⠛⠛⡋⠀⡍⡍⠁⡍⢠⣭⢅⣤⣍⣍⣈⡉⢉⡅⢉⠙⣛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠀⠀⠀⠉⠀⠉⠉⠉⠂⠀⠛⠗⠶⠶⠗⠀⠆⠠⡦⠆⠀⡆⠀⢠⠶⠶⠶⠇⠀⠃⠘⠋⠁⠈⠁⠁⠀⠁⠀⠀⠀⠀⠀⠈⠉⠁⠈⠀⠈⠀⠘⠛⠀⠻⠿⠔⠆⠖⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡏⠀⣤⣤⣤⣄⣤⣀⣤⡀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⣀⣤⣤⢀⣤⣠⣴⡦⢠⣴⣶⣤⣤⣤⣤⣄⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡆⢠⡄⢩⣭⣅⡀⠘⠛⠛⠃⠘⠸⠾⠾⠀⠾⠿⠰⠠⠶⠷⠯⠰⠿⠟⠛⡛⠛⣋⡍⢩⣭⡅⢠⠀⣤⣤⢤⢰⢠⣤⣤⠀⢨⠈⣩⢩⣙⣙⠛⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠀⠛⠛⠛⠛⠾⠀⠇⠠⠶⠇⠀⠆⠄⢰⠶⠶⠶⠂⠘⠃⠘⠉⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠉⠉⠉⠀⠛⠛⠂⠖⠞⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢤⣦⣤⣄⢤⣤⣤⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣀⣤⣤⣤⡠⢠⣦⡤⣶⣶⡖⡶⣶⣦⣶⡶⡦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡆⢰⡆⣰⢬⣄⠀⠉⣉⡛⠀⠃⠐⠿⠗⠸⠿⠇⠂⠸⠿⠽⠿⠿⠛⠛⢛⠛⣉⣩⠉⣅⢤⠀⣆⠠⣤⡦⡆⠆⡦⢤⡤⠀⡆⠀⡅⢀⣤⣄⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠙⠛⠛⠛⠀⠇⠐⠖⠇⠈⠇⠄⠰⠾⠚⠛⠂⠘⠀⠉⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠙⠛⠉⠃⠓⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠴⠶⠦⠤⢤⣤⣦⡄⠀⣤⣤⣠⡀⢀⠀⣀⢀⠀⠀⠀⠀⠀⠀⡀⡀⠀⣀⣀⣀⣀⢀⣄⣤⡄⢴⣴⣶⢶⡶⠶⠠⠶⠶⠦⢶⢶⣶⣶⣶⣤⣤⣤⣠⢀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡆⠰⡦⣠⡦⣤⡄⠈⢉⣉⣁⠈⠀⡙⠛⠃⠛⠻⠘⢀⠛⠛⠓⠈⠛⢋⠋⢉⠈⣉⣥⠀⣆⢦⠀⠆⠠⡶⠆⠖⠆⡦⢤⡆⠀⡆⠠⡄⠩⣭⡍⢩⣙⡙⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠉⠛⠃⠈⠃⠘⠛⠃⠘⠃⠂⠸⠛⠛⠋⠁⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠈⠉⠛⠉⠃⠃⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠔⠶⠶⠤⠤⣤⣴⡶⠀⠀⣤⣤⣤⠀⣀⠀⣀⣀⠀⣀⣀⢀⠀⣀⠀⢀⣀⣀⣀⠀⣄⠀⣤⣶⣶⣶⡶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠀⠆⠀⢶⠀⢶⣶⣤⢀⠉⣉⣉⣀⣈⣀⠙⢙⠀⢙⢛⠘⢀⠋⠛⢉⣉⣉⣁⠀⢭⠀⣤⣴⠀⢲⢰⠀⠦⠀⠴⠖⠇⠆⠦⣦⣄⠀⡆⠠⡆⢀⣤⡄⢠⣤⡀⣀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠉⠁⠘⠀⠉⠉⠀⠘⠈⠀⠘⠉⠉⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠈⠉⠉⠈⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣤⣤⠄⢰⢸ ⠻⠄⠄⠄⠠⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠠⠤⠄⠠⠄⠤⠤⠠⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡖⠒⠒⠒⠒⠀⠀⠀⠀⠉⠉⠉⠉⠍⠉⠍⠹⣿⡽⡏⣯⣭⣽⡍⠉⠉⠉⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⣄⣤⠀⠉⠉⠉⠉⠍⠉⠩⠉⠉⠍⠙⡿⣯⡽⡏⠯⠿⠇⠷⠶⠆⠀⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⢠ ⡟⠿⠛⠷⠲⠶⠶⠆⠄⠰⠴⠶⠶⢤⠀⢶⣤⡤⢥⣤⢦⠀⠦⠤⠶⠶⠶⠷⠶⠆⠇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣸⡿⠶⠶⠶⠰⢶⣤⠄⠀⠀⠀⠀⠀⠀⠀⠶⠶⠠⠿⠿⠀⠿⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣷⣛⠛⠛⡓⠂⠀⠀⠀⠸⠷⠶⠦⣤⣤⣤⣤⡄⠰⣦⡴⡤⡴⡴⠶⠂⠸⠶⠶⠹⠙⠙⠛⠛⠛⠃⠈⠒⠛⠓⠓⠀⢧⢿⠷⠶⠶⣦⠦⣤⣦⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⡀⢀⢀⠀⠀⠀⠀⠀⢸ ⣿⣛⠋⠓⠛⣛⠛⠀⠀⠀⠿⠶⠶⣦⠀⡶⢤⢢⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡞⡾⠴⠶⠴⡆⢰⣤⣤⣭⢤⣤⣤⢤⠀⠀⠷⠄⠿⠗⠀⣓⠀⠓⠃⠐⠃⠚⠋⠃⠀⠀⠀⠀⢸ ⣿⣍⣋⠋⠛⢛⠿⠐⠀⠀⠷⠴⢶⢴⡀⢲⢦⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢳⠿⠶⠶⣦⣤⣴⣦⣤⣤⡎⠀⠀⠀⠀⠸⠾⠿⠂⠛⠛⠋⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⢿⠉⠉⠙⠉⠛⠛⠐⠀⠀⠸⠄⠰⢠⣴⣤⣤⡄⢰⡄⣦⣤⣴⠆⠶⢶⠆⠸⠛⠛⠛⠁⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠿⠶⠶⣤⡤⣭⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢸ ⢀⣀⣀⣀⡀⠈⠉⠁⠀⠐⠒⠒⠀⠤⠤⠤⠀⠀⠀⠀⠤⠤⠤⠀⠒⠒⠂⠀⠈⠉⠁⢀⣀⣀⣀⣀⣀⣀⣀⡀⠉⠉⠁⠈⠘⠒⠂⠀⠤⠤⠄⠀⠀⠀⠀⠤⠤⠤⠀⠒⠒⠀⠀⠉⠉⠁⣀⣀⣀⣀⣀⣀⣀⣀⡀⠉⠉⠈ ⣿⠀⠀⠀⠀⠀⠀⠀⠁⠐⠒⠂⠀⠀⠠⠤⠤⠤⠠⠤⠤⠤⠄⠀⠐⠒⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠒⠒⠂⠀⠠⠤⠤⠤⠄⠤⠤⠤⠤⠀⠀⠒⠒⠂⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹ ⣿⠀⣀⣤⣀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣠⣤⣤⣤⣤⣴⡄⣤⣤⣤⡤⢀⣀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠁⡅⢉⡄⢙⣛⡃⠀⠰⠿⠷⠆⢰⠀⢰⢶⠀⣴⣶⠲⠀⠿⠟⠓⠀⣉⡉⠉⡌⢨⣤⡆⢀⡆⡆⢡⠍⣁⣉⢋⢙⠛⠻⠿⠿⢶⣖⣶⣶⣶⣶⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠈⠁⠈⠑⠛⠡⠀⠖⠶⠤⣤⣴⠀⡆⢠⡤⠆⠀⠇⠄⠸⠛⠛⠉⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠘⠚⠻⠶⠀⠴⠀⡆⠀⣶⣦⢠⣶⡶⠔⠶⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢤⣦⣤⣄⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣤⣤⣤⣦⣶⣦⢦⡶⡶⢄⣆⢤⣤⣄⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⢰⡆⢠⡌⣩⣙⡀⠀⠛⠿⠷⠀⠆⣶⣴⡆⢰⢶⠶⠀⠿⠟⠓⠀⣋⣉⠉⣄⠀⣤⡖⠀⡆⡆⠰⡆⢠⣬⡁⣌⡉⡛⠛⠻⠿⠻⠶⡖⣶⣶⣶⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠈⠉⠉⠐⠀⠖⠶⠶⠶⠦⠀⡆⠠⠶⠆⠸⠤⠀⠻⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠛⠛⠇⠀⠇⠀⠆⣆⡶⡆⠰⠶⠷⠒⠆⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠤⣶⣤⣄⢤⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣶⣶⠶⠾⠿⠾⠾⠂⢴⣆⢴⣤⣤⣤⣄⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣧⠀⠀⠀⡆⠠⣦⠉⣭⣄⡀⠘⠛⠿⠇⠐⠄⠰⠶⠆⠸⠿⠞⠂⡘⠑⢈⣉⣩⣠⡀⢰⠀⠶⠾⠀⠳⠰⠀⢦⠀⣤⣉⢁⣉⢋⠛⠿⠏⠗⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠒⠀⠓⠶⠶⠶⠶⠀⠷⠀⠶⠇⠀⠓⠂⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠉⠘⠛⠻⠆⠘⠆⠸⠀⠳⠾⠀⠟⠟⠊⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠔⠶⢶⢤⡠⢤⣠⣠⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢀⣤⣤⡄⢤⣶⠶⠶⠆⠺⠾⠿⠆⠶⢶⢖⣶⣤⣤⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠀⢶⠀⣴⠌⣬⣭⣅⠀⠙⠛⠻⠃⠘⠀⠸⠿⠃⠘⠛⡃⢃⡈⠉⢉⣤⣤⣤⡄⠰⠆⠰⠾⠇⠰⠆⠆⢰⠀⢠⣌⣡⣉⢛⠁⠛⠋⠛⠿⠿⠻⠿⠗⠃⣛⡋⢃⡀⡄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠐⠀⠘⠛⠛⠛⠚⠃⠘⠃⠘⠛⠁⠀⠁⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠘⠙⠿⠀⠚⠀⠃⠀⠛⠃⠘⠛⠋⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠔⠶⠶⢤⠤⣤⣤⡤⠀⠀⣀⣀⣀⠀⠀⠀⣀⠀⠀⣀⣀⢀⠀⣤⣀⣄⣤⣤⡴⠀⠶⠀⠾⠿⠿⠿⠞⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠀⠆⠠⡶⢠⣦⣤⡀⠀⢉⣛⣋⠀⠃⡀⢛⡃⠈⢛⡋⢉⡄⠉⢩⣤⣤⣤⠄⠰⠃⠰⠶⠃⠰⠢⠃⠰⠀⣤⡤⣠⡤⣠⣀⡀⠀⡀⠀⡀⠀⣀⡀⢀⣀⡀⣀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠈⠈⠉⠉⠛⠁⠘⠀⠉⠉⠀⠈⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠃⠀⠁⠀⠁⠘⠛⠃⠈⠉⠉⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠷⠶⠶⡶⠀⢴⢸ ⠣⠤⠤⠤⠄⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠠⠄⠤⠤⠠⠤⠄⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠄⠠⠤⠄⠤⠤⠠⠠⠀⠄⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡖⠒⠒⠒⠂⠀⠀⠈⠉⠉⠍⠉⠉⠉⠭⠭⠹⣿⡽⡏⡿⡿⠷⠆⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠉⠉⠉⠉⢭⢭⠩⠭⠍⠩⠉⠉⠍⠉⠉⠁⠀⠘⠟⠷⠾⠇⠓⠖⠇⠷⠷⠆⠀⠀⠉⠉⠩⠉⠍⠉⠩⠭⠭⠭⢭ ⣏⣿⡓⠗⠖⠶⡶⡦⠄⠰⡄⡦⣤⣤⡄⢰⣦⣤⢤⡶⠰⠀⠲⠶⠖⠖⠒⠻⠛⢓⢃⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⢞⣶⣦⣤⣴⡔⣴⡶⠆⠀⠀⠀⠀⠀⠀⠀⠛⠛⠚⠻⠻⠀⠻⠺⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⣋⠛⠛⠓⠀⠀⠀⠀⠀⣶⣤⣤⣤⣤⣤⣤⣤⠀⢶⠶⠶⠶⠷⠖⠃⠈⠛⠛⠋⠋⠋⠛⠛⠓⠶⠖⠲⠶⢶⣄⡆⠘⡜⣶⣦⣤⣤⡴⣴⠴⠶⢶⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⣛⠛⠛⢛⠻⠺⠠⠀⠀⢲⣦⣤⢤⡄⢰⢦⡴⡔⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⣆⣤⣤⣴⠀⠶⠶⠶⠗⠛⠟⠛⠃⠀⠘⣂⣘⠙⢀⣘⠀⠽⠽⠀⠲⠰⡦⡆⠀⠀⠀⠀⢸ ⣿⣉⣉⠉⠘⢘⠷⠆⠀⠀⢰⣠⣤⣤⡄⢰⢦⣤⣤⡆⠀⠀⠀⠀⡀⠀⠀⢀⣀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣤⢤⠤⣶⠿⠶⠛⠛⠀⠀⠀⠀⠀⠉⢉⡁⠘⠛⠓⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⢿⣉⠉⠙⠙⠛⠛⠀⠀⠀⢰⠀⢠⢠⣤⣤⣤⡄⢰⡄⠶⠶⠟⠃⠋⠛⠃⢘⡋⢉⠉⡁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⣷⡤⡤⣤⡴⠶⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣀⣀⣀⣀⠈⠉⠀⠐⠒⠂⠤⠤⠀⠉⠀⠀⠀⠀⠤⠤⠐⠒⠂⠈⠉⢀⣀⣀⣀⣀⣀⣀⣀⣀⠈⠉⠀⠐⠒⠀⠤⠄⠠⠏⠏⠀⠀⠠⠤⠄⠐⠒⠀⠈⠉⢁⣀⣀⣀⣀⣀⣀⣀⣀⠉⠁⠀⠐⠒⠠⠤⠄⠀⠀⠀⠀⠀⠸ ⡟⠀⠀⠀⠀⠀⠀⠐⠒⠀⠠⠤⠄⠀⡀⡀⠀⠠⠤⠄⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠠⠤⠀⠀⣀⡀⠀⠤⠄⠀⠐⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠤⠤⠀⢀⡀⡀⠀⢤ ⡇⠀⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠄⣤⣶⣶⢶⣶⣤⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⢩⡍⣡⡘⢛⠲⠀⠀⢶⣶⣄⠀⠄⢰⢶⡆⠼⠿⠛⢀⠉⠉⣉⣤⣤⡄⠀⡆⢠⣤⡅⠀⡍⡛⠙⠅⠺⢶⠦⢤⣦⣦⣴⣶⣲⣲⠮⠿⢛⣛⠁⣡⣤⣄⢤⣤⠆⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠈⠁⠘⠸⠶⠀⠀⣤⣤⣤⣤⡄⢰⡀⠴⠾⠀⠘⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠘⠀⠰⠶⢴⣰⣠⣠⣤⡄⢰⠄⠸⠀⠙⠛⠁⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢤⣦⣤⡀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⢀⣤⣴⡀⢶⠶⠶⠦⢶⢶⣦⣤⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣀⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡆⢉⣌⠛⡛⠂⠀⠰⣶⣶⡄⠰⢰⣶⠶⠄⠛⢛⡉⢨⠉⠀⢤⢤⠶⠦⠀⠦⠠⣤⣄⠉⣍⢋⠙⠥⠲⣶⡦⠴⣶⣦⣴⡶⡺⠻⠛⡛⡋⣭⡅⢴⣶⡤⠲⠼⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠀⠀⠀⠉⠈⠛⠿⠖⠀⠀⡤⣤⣤⣤⣶⠀⠧⠘⠛⠃⠈⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠂⠘⠄⠰⣤⡴⡴⡴⡤⣴⡄⠸⠀⠓⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠔⢶⣤⣄⣀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⡄⠐⡶⠼⠿⠿⠾⠾⠶⣶⣦⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠀⢴⠈⣥⡘⢛⣻⠀⠀⠰⠶⣶⠆⠰⠆⠨⠟⡃⠈⣉⡅⠀⡆⠄⢐⡶⠶⠶⠆⠀⠆⢠⣌⡍⢉⡓⡃⠺⠧⠶⡶⢶⠲⠶⠶⠿⠟⢙⠙⢩⠀⣶⡶⠐⠿⠷⠒⠆⠇⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠀⠀⠀⠈⠁⠘⠛⠓⠢⠀⠠⢤⢤⠴⠶⠇⠀⠃⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠃⠃⠸⠁⠴⠶⢰⢲⠰⠶⡶⠀⠘⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠖⠶⣤⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⣤⡠⠀⡶⠾⠮⠁⠿⠿⠿⠾⠀⣶⣴⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣶⠴⠾⠿⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠀⠀⠀⡆⢠⣤⢉⣍⡋⠀⠘⠿⠿⠇⠐⠃⠸⠛⠋⠈⣩⠁⢰⢀⠀⡴⠶⠶⠶⠀⠸⠀⠶⡔⠀⡄⡌⠙⡙⠛⠛⠾⠰⠿⠟⠒⠟⠛⡛⢋⠉⠨⣥⡆⠰⠿⠿⠲⠆⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠈⠉⠋⠑⠀⠒⠶⠶⠶⠞⠀⠛⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠛⠛⠸⠺⠼⠶⠶⠀⠘⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠠⠲⠷⢶⣤⢤⣠⣠⠀⠀⣀⣀⡀⠀⠀⢀⣀⠀⢀⣠⢠⠀⣴⣤⠴⠶⠶⠖⠐⠗⠀⠿⠷⢶⣶⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠰⠆⢴⡄⣬⣥⣀⠈⠛⠛⠃⠘⠃⡘⢛⠀⢉⣩⠀⢤⢀⠀⡶⠶⠶⠦⠀⠇⠰⠶⠇⠐⡆⡆⢠⠄⢀⣀⡀⢀⠀⠀⠀⠀⢀⡀⢀⠀⢠⣴⡀⠶⠿⠶⠲⠾⠇⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠀⠋⠛⠛⠛⠃⠈⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠋⠋⠛⠛⠇⠀⠁⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⡀⢠⢸ ⠻⠤⠤⠤⠠⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠠⠤⠤⠶⠦⠄⠄⠠⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠄⠤⠶⠄⠄⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠸ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣾⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡖⠒⠒⠒⠀⠀⠉⠉⠉⠉⠭⠭⠭⠭⠭⠉⠙⡿⣿⠧⠷⠾⠶⠆⠐⠒⠒⠒⠒⠒⠀⠀⠉⠉⠍⠉⠭⠭⠭⠭⠭⢭⢩⡉⠉⠀⠀⠒⠒⠒⠒⠒⠒⠂⠈⠿⠧⠾⠯⠯⣯⢏⢯⣍⣭⠉⠩⠩⠉⠍⠉⠁⠀⠐⠒⠒⠒⢲ ⣿⣛⡖⠣⠖⠶⡶⣤⠀⠀⣆⣦⣤⣤⣄⠐⣶⠶⠖⠶⠎⠆⠘⠒⠚⠒⠒⠚⠶⠶⠞⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡱⡷⠶⠶⠳⠻⠛⠓⠀⠀⠀⠀⠀⠀⠀⠐⠶⣦⠰⣶⣦⢴⡦⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⣋⠛⠛⠻⠠⠀⠀⠀⠀⣶⣤⣤⢤⣤⣤⣤⠴⠆⠘⠶⠚⠚⠛⠛⠛⠀⠘⠛⠛⠙⠟⠟⠶⡶⣦⣤⡄⢤⢤⣤⡴⠄⢱⣱⡿⠶⠓⢓⠋⢛⠋⠛⠇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⣙⡛⠙⠛⠶⠶⠆⠀⠀⢰⣦⣤⣤⣄⠰⡆⠆⠇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡟⣞⠛⠛⣃⣉⣹⣙⣉⢙⠻⠛⠷⠀⠀⡖⠀⣦⡄⢠⡄⢰⣶⠀⠲⠠⠿⠃⠀⠀⠀⠀⢸ ⣿⣭⣙⠋⠘⠸⢷⠖⠀⠀⢠⣡⣬⢤⠄⢰⢶⠶⠶⠆⠀⠀⣀⣀⣀⣀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢧⠏⠛⠛⣉⣉⣙⠉⠙⠉⠉⠀⠀⠀⠀⠀⣶⣆⡆⣠⣬⣄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⢿⣉⠉⠛⠛⠛⠶⠐⠀⠀⡤⠈⡬⣤⣤⣤⣤⠀⠾⠚⠛⠉⢉⣉⡉⠉⣁⣘⠉⠙⠛⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⠾⠟⠛⠋⠉⡁⣁⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸ ⡀⢀⣀⡀⠉⠀⠒⠂⠤⠀⢀⣀⣉⣁⡀⠀⠤⠐⠒⠀⠉⢀⣀⣀⠀⠀⠀⢀⣀⡀⠉⠀⠒⠂⠤⠀⠀⣀⣀⣀⠀⠠⠊⠟⠒⠀⠉⠁⣀⡀⠀⠀⠀⢀⣀⡀⠁⠁⠐⠂⠤⠀⠀⣀⣀⣀⡀⠀⠠⠄⠒⠀⠉⠁⣀⣀⠀⢀ ⡇⠀⠀⠀⠈⠀⠒⠂⠠⠄⢀⣀⣀⣀⡀⠠⠄⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠠⠄⢀⣀⣀⣀⡀⠠⠄⠀⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠠⠤⢀⣀⣀⣀⡀⠠⠄⠀⠒⠀⠁⠀⠀⠀⠀⢸ ⡇⢀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⠠⣴⡶⠆⢰⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⡲⣶⡶⣦⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⢩⡍⢉⠹⠾⢤⠀⠀⣤⣤⣄⠀⡄⠠⠚⠆⠙⣩⠁⢠⢀⠀⣦⢦⣤⣤⠀⣍⠙⠻⠗⠰⣶⣤⣤⡀⣠⣴⡤⠶⠿⠟⠛⡉⠩⡄⠰⡀⠲⠶⡆⢲⣤⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠘⠃⠸⠖⣦⡄⠁⢈⣭⣤⣤⠴⠀⠓⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠾⠆⠐⣄⢅⠩⡄⢠⣤⠴⠶⠙⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠓⠹⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠤⣤⣀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⣠⡀⣴⣶⠢⠐⠾⠶⠄⠐⣤⣤⣀⣀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⡶⠳⠾⠿⠷⢶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠀⢭⠙⢛⠳⠶⢶⡄⠀⢠⡴⣦⡆⠐⠜⠛⠋⡅⠠⡴⠆⠈⠇⠄⠐⣦⣤⣌⣙⠛⠛⠶⣶⣤⣤⣤⣄⢐⡦⠶⠿⠋⣉⣩⣠⣴⡄⠸⠀⠣⠳⢳⣦⠁⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠀⠈⠀⠙⠃⠰⢶⣦⡄⡀⢠⣤⡴⠶⠖⠛⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠛⠀⣦⡖⠀⡅⡥⠀⡆⠰⠾⠃⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠂⠦⠆⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠔⣴⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⢰⠾⠇⠇⠀⠿⠭⠷⣶⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣾⠟⠙⠻⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡿⠀⠀⠀⡆⢉⣉⠛⠾⠆⠀⢠⣦⣶⠶⠀⠎⠀⢛⡍⢠⡤⠎⠀⠏⠂⠠⠶⠶⢦⠄⢩⠙⠛⠻⠷⢶⡶⠦⣴⡦⠶⠿⠛⡁⡡⣠⣤⠀⠰⠃⠘⠀⠼⠵⢠⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠉⠒⠿⠶⢠⠀⡤⣤⡤⠶⠞⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠛⠃⠰⠢⠂⡰⠀⡤⠖⠲⠙⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠘⠁⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠠⠲⢦⣤⡀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣠⣶⠰⠀⠿⠟⠃⠐⠿⠿⠶⡆⢠⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣤⣔⡶⠾⠿⠛⢛⠻⠺⠽⠶⢦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⢰⡂⣠⡉⣛⠛⠀⠐⠶⠶⠆⠐⠀⠘⢛⠀⣩⣴⠀⠧⠄⠀⠟⠗⠶⠆⠐⡆⢈⣉⡙⠃⠻⠾⠾⠶⠶⠾⠔⠛⢛⣁⣩⠀⠰⠀⠺⠀⠘⠹⠀⠿⢷⡤⢤⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠈⠀⠙⠙⠓⠠⠀⠖⠶⠶⠞⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠃⠧⠘⠇⠐⠶⠞⠚⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣇⠀⠶⠶⣤⣤⣀⡀⣀⡀⠀⠀⠀⠀⠀⠀⡀⢠⣤⡄⠶⠶⠴⠈⠛⠗⠚⠳⠶⠶⠀⢦⡀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠀⢖⠀⣤⠉⣛⣃⡀⠀⠛⠛⠛⠀⢁⣠⡁⢰⡀⠶⠿⠀⠱⠠⠀⢲⠶⠶⢤⡀⢡⡀⢋⢛⡛⠛⠛⠓⢀⠀⢀⣀⢀⣄⢤⠶⣦⠈⠆⠘⠀⠸⠷⠄⢲⣶⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠀⠀⠀⠈⠀⠉⠙⠛⠃⠂⠘⠙⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠋⠃⠈⠃⠃⠈⠂⠈⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⡴⠶⠂⠸⢸ ⠓⠠⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠠⠄⠀⠀⠀⠠⠤⠠⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠄⠄⠄⠀⠚ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡆⠒⠒⠂⠀⠉⠩⠉⠭⠭⠭⠭⠭⠍⠉⠉⠉⠿⢾⠃⠳⠶⠶⠆⠀⠒⠂⠀⠉⠉⠉⠭⠩⠍⠭⠭⠍⠉⠉⠉⠀⠐⣴⡖⠐⠒⠂⠒⠒⠂⠀⠉⠉⠉⠉⢻⣯⣩⣯⣩⣭⡿⠹⠶⠶⠀⠒⠐⠒⠒⠐⠒⠒⠀⠈⠉⠉⢭ ⣿⣛⠒⠳⠖⠶⣶⣤⡀⠀⢦⣠⢤⣤⡴⠀⠾⠶⠖⢓⡓⠓⠀⠛⠒⠗⠶⠶⠷⠶⣤⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢺⢿⣛⠛⠛⠞⠶⠶⠆⠄⠀⠀⠀⠀⠀⠀⢶⣶⠔⠷⠷⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⣋⠛⠛⠿⠔⠀⠈⠀⠀⢠⣤⣤⡤⣤⠶⠶⠖⠃⢀⠛⠛⠋⠛⠓⠛⠓⠀⠲⠶⢦⢶⢶⣤⣤⣶⣤⡤⠀⠶⠾⠃⠃⠀⣏⣟⡛⠛⠛⠚⠶⠶⠤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⡀⣀⠀⡀⠀⠀⠀⠀⠀⢸ ⣿⣛⠛⠛⠿⠶⢴⠆⠀⠀⢠⣤⣤⢤⡤⠀⠏⠛⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣏⣽⣛⡛⠃⠐⠷⠶⡬⣥⣤⣤⣤⠀⢀⡖⠀⠿⠇⣐⡃⣐⠉⠀⠈⠀⠋⠛⠀⠀⠀⠀⢸ ⣿⣍⡛⠋⠸⠾⣦⠀⠀⠀⡌⣉⣠⣴⠀⠜⠷⠚⡛⣁⣀⣀⡄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⣼⣬⣉⣉⣉⠛⠗⠷⠶⢤⠀⠉⠉⠁⠀⢰⣶⠶⠂⠟⠛⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠏⣉⠉⠛⠓⠷⠆⠀⠀⢠⠍⢩⣥⣰⣤⠴⠂⠘⠉⠉⡉⠉⠀⠈⢙⠁⠚⠛⠶⠆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢪⠊⠉⠁⡀⠉⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢸ ⡀⢀⣀⠉⠀⠒⠠⠀⢀⣈⣀⣈⣉⠀⠄⠐⠂⠉⢀⣀⠀⠀⠀⠀⢀⣀⠈⠁⠐⠀⠄⢀⣀⣀⣀⣀⠀⠠⠀⠀⠀⢁⣀⠀⠀⠀⠀⠀⣀⠈⠁⠐⠂⠄⠀⣀⣀⣀⣀⠀⠠⠄⠂⠈⠁⣀⠀⠀⠀⠀⠀⣀⡈⠁⠐⠂⠄⠼ ⡇⠀⠀⠈⠀⠒⠠⠄⢀⣀⣀⣀⣀⠠⠄⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠤⠀⣀⠀⣀⣀⠀⠤⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠠⠀⣀⡀⠀⣀⠀⠄⠀⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠠⢀ ⡇⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⢰⡶⡶⠀⠶⣶⣤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠠⣶⠶⠶⠶⣖⣦⣤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣧⠀⠀⠉⡛⠓⠖⣤⣄⣀⠀⠀⣤⣶⡦⠘⠀⣈⠀⡄⠰⠾⠄⠰⡄⡀⠁⡈⠻⠷⡶⣤⣤⣤⣤⣀⢤⡶⠟⢒⡉⢉⣤⠲⠦⠶⠶⢦⡀⢨⠙⠛⠿⢶⣤⣤⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠀⠑⠀⠷⠄⢨⣩⣄⡀⠁⢠⠴⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠛⠶⣤⣄⠈⡍⠉⣡⡄⠐⠜⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠧⢲⣦⣬⠁⣤⣄⡤⡔⠆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⡠⣠⡀⠀⠀⠀⠈⠁⠉⠁⠁⠀⠀⠀⠀⡀⣤⡦⠾⠀⠻⠿⠰⠀⣤⣄⣀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⣀⢀⣴⡴⠾⠷⠚⠿⠷⢶⣤⣄⣀⠀⠀⠀⠉⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠈⣙⠛⠦⢢⣤⣤⡀⠀⣠⣶⡷⠛⢀⣀⡄⠀⠏⠐⠗⠏⠀⣆⡈⢉⠃⠠⢶⣦⣤⣤⣤⣤⣦⡶⢞⠛⢠⠄⠠⢶⠖⠳⠳⠷⣦⠄⢩⠙⠻⠳⣦⣄⡤⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡿⠀⠀⠀⠉⠀⠿⠠⡮⣬⡀⠀⢠⢤⠶⠞⠋⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠋⠛⠶⠆⢠⠌⣉⣨⠄⣠⠢⠎⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠹⢴⡶⢨⣥⣤⣠⡄⡔⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢠⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⠰⠞⠛⢊⠀⠳⢴⣦⣤⣀⡀⠀⠀⠀⠁⠁⠀⠀⠀⠀⢀⣤⣶⠞⠝⠛⠛⠟⠛⠗⣶⡄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⢠⠉⣑⠳⠶⣤⠀⢠⣤⣶⡆⠘⢁⠈⢥⠀⠶⠏⠀⠛⠂⢰⠦⣤⣉⠙⠻⠷⢶⣶⣴⣴⡶⠤⠾⠋⢉⡡⣴⠶⠘⠛⠿⠀⠸⠀⡆⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠙⠁⠽⠶⣄⡀⠠⡤⠶⠞⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⠄⠠⣴⠀⢰⡰⠀⠻⠀⠋⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠙⠛⠀⠶⣶⣠⢤⢰⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣴⠦⠘⠛⢋⠂⠙⠻⠿⣀⠠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣤⡦⠜⠟⠓⡙⠛⠸⠿⢶⣦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣷⠀⠀⠀⣭⠉⣉⠷⠶⠶⠀⠐⠾⠿⠓⢈⣁⣤⠀⠧⠘⠛⠂⠈⠂⠠⠀⢤⣉⠛⠛⠾⠦⠰⠦⠶⠦⢛⢛⠉⣅⠰⠶⠙⠑⠙⠛⠳⡄⠐⡌⠉⡙⠻⠷⢶⠰⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠀⠈⠀⠙⠃⠸⠖⠶⠆⠄⠘⠛⠋⠁⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠈⠉⠋⠓⠦⠀⠦⠀⠶⠇⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠻⠲⠐⠶⠶⠒⠂⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠔⢴⣤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠀⡄⠀⠿⠻⠀⠛⠛⠻⠀⢶⣤⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠀⡤⠉⣉⠙⡛⠻⠁⠀⠘⠛⣛⣁⣠⣤⠆⠠⠃⠘⠛⠃⠠⠧⠀⣠⣀⣉⡛⠃⡰⠃⠠⠛⠛⡛⣩⠁⡰⠀⠴⠞⠑⠙⠙⠲⠶⠀⡴⢀⠄⢀⣀⠀⠀⠀⠀⠀⢀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠀⠀⠀⠀⠀⠉⠀⠋⠛⠃⠂⠐⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠁⠐⠁⠒⠚⠁⠐⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠋⠐⠛⠛⠘⠋⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⢦⡤⣤⠀⣠⢸ ⠓⠀⠠⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠄⠠⠀⠀⠀⠀⠀⠄⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠀⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣶⠒⠂⠀⠉⠉⠭⠭⠭⠍⠉⠩⠉⠉⠁⠐⠂⠻⠶⠗⠑⠶⠶⠶⠌⠉⠍⠭⠭⠩⠍⠭⠭⠉⠉⠁⠐⠒⠂⠒⠒⠒⢢⣶⡂⠈⠉⠍⠭⠭⠭⠭⠭⠭⠉⠻⠿⠴⠟⠔⠶⠟⠜⠒⠾⠄⠈⠉⠉⠭⠭⠭⠭⠭⠭⠉⠉⢡ ⣿⣻⠶⠶⠶⢦⣤⣤⡄⡀⢰⣰⡴⠶⠶⠆⠙⠛⠛⠛⣛⠊⠂⠘⠶⠶⡦⣤⣤⣦⣤⣤⢠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠙⡝⡷⠶⣦⣴⡰⣤⣤⡀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠛⠛⠂⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⣋⠻⠿⠿⠄⠈⠈⠁⠀⢠⣶⣤⡶⠶⠞⣛⢛⢛⢀⠘⠛⠚⠰⠺⠶⢤⠄⢠⣬⣭⢰⢴⣶⠶⠿⠛⠚⠀⠙⠛⠛⠘⠀⢹⢹⠷⣦⣤⣄⡄⣄⣤⣤⡄⠂⠀⠀⠀⠀⢀⠀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⣛⠛⠻⠶⢦⣤⠠⠀⠀⢠⣦⣤⠶⠖⣐⠃⢋⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣣⠿⠷⣤⣤⢀⣤⣀⣥⢬⣤⡶⠞⠛⠀⢠⣭⣤⠍⣉⣐⠃⠼⠷⠀⣤⢠⣤⡄⠀⠀⠀⠀⢸ ⡟⣍⠛⠃⠆⢶⡄⠀⠀⢠⣉⣠⢴⠂⠰⠛⠋⣩⣩⣀⣀⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⣷⡛⠻⠲⣤⣤⣤⣉⣉⣩⠀⠀⠀⠀⠀⠀⠉⣭⠅⠈⠉⠉⠙⠂⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⢸ ⠇⠉⠛⠛⠶⢮⠡⠀⠀⡍⠉⣤⣤⠶⠖⠃⠈⡁⠁⠀⠈⠈⠉⠛⠡⠶⣤⣤⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠱⠉⡉⠙⠳⠖⡤⠁⠙⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡀⢀⡀⠀⠀⠀⠀⣀⡀⠁⣀⡉⠠⠔⠀⠉⣀⠀⠠⠤⠤⠀⢀⠈⠀⠂⠄⢀⣈⣀⢀⣀⡀⠀⠐⠀⠁⣀⠀⠠⠤⠀⠀⢀⠈⠀⠂⠄⢀⣀⡀⣀⣀⡀⠀⠐⠀⠁⣀⠀⠠⠤⠄⠀⢀⠉⠀⠂⠄⢀⣀⠀⢀⣀⡀⠄⠒⠈ ⡇⠀⠀⠀⠒⠠⠀⣀⠀⠀⠀⣀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠀⠀⠀⢀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⢀⠀⠀⠀⣀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⢀⡀⠀⠀⡀⠀⠄⠐⢰ ⣷⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢄⠀⠖⠦⠐⢶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠢⠼⠲⣶⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠙⠳⢦⣄⣀⡀⣄⡀⠀⠰⠞⠛⣁⣤⡤⠧⠀⠧⠀⣤⣥⠃⠘⢶⣦⣤⠀⣀⣤⣤⠶⠿⠛⣡⠀⠢⠳⠈⠆⠀⣤⣀⠙⠿⢶⣤⣤⡄⡤⣤⣴⡶⠟⠋⣤⣶⠄⠆⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠀⠸⠀⢠⡌⢉⣉⣅⡠⡀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠸⢀⠈⣈⣁⣈⣉⠀⠰⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠴⣄⡉⠉⡉⢩⠄⠰⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⡀⣀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⣀⠀⢰⠰⠻⠛⠋⠰⢴⣦⠀⡀⠀⠀⠉⠉⠉⠉⠀⠀⠀⣀⣠⡤⠾⠋⠒⠓⠶⠶⣀⣀⠀⠀⠈⠁⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡏⠀⠀⢉⡛⠦⢤⣄⣤⡀⠀⣤⣾⠟⢋⣠⣴⠃⠘⠁⠚⠟⢁⣄⠘⠛⠗⣠⣤⣤⣠⣠⣤⡾⠟⣫⣡⠒⠠⠋⠐⠿⠶⠆⣨⡙⠛⢷⡦⣤⣠⣤⡤⣴⡾⢉⣠⣠⠴⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠈⠁⠺⢆⣭⣭⡀⠀⢡⠶⠟⠋⠁⠀⠀⠀⣀⡀⠀⠀⠈⠐⠛⠶⣤⠉⢩⠉⣁⡵⠂⠘⠁⠁⠀⠀⣀⣀⡀⠀⠀⠀⠛⠀⠔⠀⡌⣍⣭⡭⢠⠾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠠⢤⣄⡀⠀⠀⠀⠈⠀⠁⠀⠀⠀⢀⠀⠾⠟⠈⠛⣃⠃⠐⣦⠤⣀⠀⠀⠀⠈⠀⠁⠀⠀⢀⣠⠠⠶⠚⠛⠛⢋⠛⠶⣦⣄⡀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠉⡙⠢⢢⣤⣄⠀⠀⢴⠾⠛⣀⣠⡦⠈⠂⠙⠛⠀⠘⣄⠈⠙⠷⣶⣠⣤⣤⣤⡶⠿⢛⠩⡰⠈⠂⠘⠛⠋⠚⠆⡦⣉⠻⠏⢢⠤⣤⠀⠀⠀⠀⢀⣤⡠⠮⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠀⠁⠀⢷⠀⣩⣥⣤⠀⠀⠋⠉⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠂⠀⢦⣤⣨⣩⡀⠢⠐⠛⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠉⠙⠲⣆⠀⢍⠡⡄⠐⠗⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠠⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠀⠃⢈⠛⢛⠈⠻⢶⣤⡀⠀⠀⠁⠀⠀⠀⠀⢀⡀⣠⣴⠿⢈⢛⡛⢚⠻⠷⣦⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡰⠿⠛⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠈⢙⠓⠦⢢⣤⣦⡆⠀⠐⢋⣉⡤⠶⠞⠛⠀⠘⠀⠶⡴⠈⣁⠻⠿⢶⠀⣴⡶⠾⠛⠃⣨⡴⠀⠘⠘⠁⠘⠀⠶⠦⣄⡙⠛⠲⢶⣢⣶⣶⠗⢟⣫⠁⡶⠿⠋⠛⠘⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠀⠉⠀⠿⠀⠶⠶⠶⠤⠀⠈⠀⠀⠀⠀⣀⡀⢀⣀⠀⠀⠀⠑⠀⠶⠶⠄⠄⠀⠜⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠻⠆⠠⠆⠠⠂⠤⠋⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢤⣦⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⡄⠀⠟⠛⠀⢛⠛⠂⢰⣦⣀⡀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⢠⠈⣉⠛⡚⠏⠀⠘⠛⢛⣁⣠⣴⠀⠜⠀⠛⠋⠀⠧⠄⢠⣉⢙⠛⠂⠾⠀⠸⠛⠛⡍⡤⠀⠎⠀⠛⠋⠊⠋⠶⢦⡄⠀⡀⠀⠀⠀⠀⠀⢀⣀⣤⡠⡤⠼⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠉⠐⠛⠙⠂⠀⠘⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠙⠂⠸⠀⠚⠛⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠃⠀⠟⠛⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣠⡄⢠⢸ ⠛⠀⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠄⠀⠀⠀⠀⠀⠠⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠀⠀⠀⠀⠀⠀⠄⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠀⠀⠀⠀⠈⠁⠀⠀⠤⠼ ⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣴⠒⠀⠉⠉⠉⠩⠍⠩⠍⠍⠉⠉⠀⠒⠒⠂⠘⠷⠾⠾⠶⠿⠯⣭⡉⠉⠩⠭⠭⠉⠉⠀⠒⠐⠒⠒⠒⠂⠒⠀⠉⠭⢍⢭⠍⠩⠭⠭⠉⠉⠐⠒⠒⠂⠈⠿⠲⠾⠮⠯⢿⢏⢯⣭⣍⠉⠭⠉⠉⠀⠒⠒⠒⠒⠒⠒⢲ ⣿⡻⠶⠶⢠⢤⣤⣤⣀⠄⠐⡆⠶⠶⠖⠓⠈⠛⠛⠛⠲⠶⠰⠀⠰⣤⣤⣤⣤⣴⡶⠶⠴⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢳⢳⣶⣤⣤⠆⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠷⢶⠤⣦⣦⢤⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⣋⠻⠿⢶⡆⠈⠉⠉⠀⢰⡶⠶⠖⠛⠛⡻⡉⡙⡁⠘⠳⠶⢦⣤⣤⣨⠀⢠⣤⠴⠲⠏⠋⠓⠃⠉⠛⠁⠚⠲⠶⠶⠀⡸⡼⣤⣤⣤⡤⠖⠶⠛⢛⢃⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢸ ⣿⣛⠛⠶⢶⣤⡤⠀⠀⢀⣶⡴⠖⠞⢃⣈⣀⣉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣺⣿⣉⣉⡡⢀⠴⠶⠚⢛⡋⠙⠋⠉⠁⢀⡒⠅⢶⡦⠠⡄⢠⣤⠆⠀⠟⠘⠋⠃⠀⠀⠀⠀⢸ ⡏⣝⠛⠂⢶⣆⡁⠀⠀⡌⣅⡴⠞⠀⢋⠉⣩⢩⣄⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣪⢺⣮⣉⣉⣉⣀⣴⡴⠶⠏⠋⠀⠀⠀⠀⠀⠙⡛⠟⢰⣦⢍⣁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠇⠙⠛⠲⢶⣍⠀⠀⠀⡍⠡⢰⠾⠛⠉⠀⠤⠤⠤⠉⠁⠛⢷⠄⢠⣀⣀⢀⢀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⢠⡧⡷⢧⣬⣉⣉⣙⠋⠈⠁⠀⠀⠀⠀⠠⠤⠄⠀⠈⠋⠀⠀⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⣸ ⡀⢀⠁⠐⠠⢈⡈⠀⠀⢁⡀⠄⠂⠈⣀⠀⠀⠤⠄⠀⣀⠁⠀⠀⢈⡉⠉⠉⢈⡀⠀⠀⠈⣀⠀⠠⠤⠄⠀⢀⠁⠑⠀⢈⡉⠉⠁⢁⡀⠀⠂⠈⡀⠀⠠⠤⠤⠀⣀⠁⠐⠀⢀⡀⠀⠀⢀⡀⠀⠂⠈⣀⠀⠤⠤⠄⠀⣀ ⣷⠀⠀⠐⠀⢀⠀⠀⠀⠀⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣀⢤⠶⠀⠣⠀⢰⢤⡄⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⣠⡴⡶⠿⠷⠂⢶⣤⣀⡀⠀⠀⠀⠈⠁⠀⠀⠀⢀⣠⢴⠶⠾⠷⠗⠄⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠉⠻⢧⣄⡀⡀⢀⣀⡀⠀⠀⠋⡤⠴⠶⠒⠾⠃⢨⠁⠸⢷⣦⠀⣀⣀⡠⠄⠸⠟⠋⢱⠂⠰⠚⠃⠰⢢⠙⠹⠤⣤⣄⢀⣀⣤⣤⡾⠟⡏⠁⠆⠘⠛⠃⠰⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠀⠖⢈⣍⠘⣙⡭⡁⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⡄⠈⠛⠙⢁⣠⡄⠁⠀⠀⠀⠀⠀⡀⠀⠀⠈⠁⠦⢌⡁⣙⡋⣉⠁⠠⠊⠀⠀⠀⠀⡀⠀⠀⠀⠈⠓⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⢀⣀⡀⠀⠀⠁⠐⠁⠉⠀⠀⣀⡀⠀⠎⠞⢛⠋⠰⣶⣄⠀⠀⠀⠐⠉⠉⠉⠁⠀⢀⣠⡴⠶⢓⠛⠑⠊⢤⣤⠀⠀⠈⠉⠉⠋⠀⠀⠀⣀⣤⣲⠿⢊⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠈⢛⢦⣤⣀⣀⣀⠀⣠⡾⢟⣡⣴⠾⠀⠋⠐⠳⠆⢠⡸⣷⣦⡀⣄⣄⣤⣤⠾⢛⡅⠀⠇⠋⠀⠃⠰⢦⣈⠙⠷⣦⣄⣀⣠⣤⡤⠾⢛⣡⡂⠘⠛⠛⠉⠃⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠘⠂⢶⡝⢛⣻⣀⢀⠘⠛⠉⠀⠀⠀⣀⡀⠀⠀⠘⠓⠢⠈⢁⣛⢛⣉⠑⠄⠛⠁⠀⠀⣀⣀⠀⠀⠀⠉⠙⠦⣠⣉⣉⡈⠠⡀⠢⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣧⠀⣀⣀⠀⠀⠀⠈⠁⠁⠀⠀⢀⣤⡦⠈⠀⢙⡛⠂⠰⣤⣄⠀⠀⠀⠛⠉⠁⠀⠀⣀⣤⡾⠟⣛⠋⢂⠙⠲⣄⠀⠀⠀⠈⠉⠉⠀⠀⢀⣀⣤⡀⠀⣀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠙⠲⢤⣄⣀⣀⣤⡄⠀⠈⠁⠖⠛⠋⠙⠃⠀⠳⠀⠙⠷⠤⡄⢠⣠⢤⣶⠿⢋⡁⠲⠈⠛⠁⠀⠳⢱⡈⢃⠛⢲⣤⣤⢤⣤⣶⠿⠉⢄⠐⠄⠙⠁⠈⠛⠷⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠀⠸⠀⢠⡄⢉⡥⠶⠂⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠘⠳⠃⢠⠀⠉⣡⡴⠖⠋⠁⠀⠀⣀⢀⣀⠀⠀⠀⠘⠀⢤⣤⡨⡌⡤⣴⠾⠀⠀⠀⢀⣀⣀⢀⠀⠀⠀⠘⠸⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⢠⣀⠀⠀⠀⠀⠈⠀⠀⢀⣠⣴⡾⠃⠀⡁⢘⡛⠃⣤⣄⠀⠀⠀⠀⠈⠁⠀⢀⣀⡴⠂⢘⠙⣉⢉⠘⠷⣦⣄⡀⠀⠀⠀⠁⠀⠀⢀⣠⣶⠏⣛⡋⢉⣋⡛⠳⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⢉⡛⠦⣤⣤⣤⠀⠀⠚⣉⣤⠖⠛⠋⠀⠈⠐⠶⠂⡩⠰⠿⡖⢠⣤⣶⠾⠛⣉⣤⠖⠁⠐⠁⠁⠘⠡⣬⢉⠓⠶⠦⣤⣤⡲⠾⠛⠉⣡⠊⠛⠁⠉⠛⠁⠆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠈⠀⠿⠀⡶⣶⠄⠀⠘⠈⠀⠀⠀⣀⡀⢀⡀⠀⠀⠁⠀⠴⠤⣤⣤⠀⠞⠀⠉⠀⠀⢀⣀⡀⠀⠀⠀⠀⠁⠓⠳⢦⡄⠀⠆⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢤⣄⡀⠀⠀⠀⠀⠀⠀⣀⣤⣦⠘⠀⡛⢁⡈⠛⠷⢦⡀⣀⡀⠀⠀⠀⠀⠀⠀⠠⡶⠿⠛⡋⣛⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣧⠀⠀⠈⣉⠓⠒⠶⠶⢇⠀⠉⠉⡤⠶⠞⠛⠂⠙⠀⠰⢤⣄⠈⢛⠲⠶⠶⠶⠖⢈⠡⣄⠺⠇⠈⠒⠓⠈⠢⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⡀⠦⠘⠝⠂⠙⠛⠚⠒⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠀⠉⠀⠛⠂⠘⠋⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠱⠠⠀⠲⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠊⠊⠊⠚⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠶⠖⠾⠀⠼⢸ ⠓⠠⠤⠤⠄⠀⠀⠀⠀⠀⠀⠠⠤⠤⠠⠀⠂⠀⠀⠀⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⠀⠂⠀⠀⠀⠠⠤⠤⠄⠀⠀⠀⠀⠀⠀⠠⠤⠤⠄⠀⠀⠀⠐⠀⠄⠤⠤⠄⠀⠀⠀⠀⠀⠀⠠⠤⠤⠄⠀⠂⠀⠀⠀⠜ ⣿⣿⣿⣿⣿⣿⣷⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣴⠒⠈⠉⠉⠭⠉⠉⠩⠍⠉⠁⠐⠒⠒⠒⠒⠈⠻⠾⡿⣿⣭⣭⣭⣍⠉⠉⠉⠐⠒⠒⠒⠒⠒⠒⠂⠈⠉⠭⠍⠉⠍⠭⡩⡍⠁⠒⠒⠒⠒⠒⠒⠒⠀⠉⠛⣿⣭⣽⡽⡽⡿⠷⠶⠖⠀⠒⠒⠒⠒⠐⠉⠉⠭⠍⠉⢩ ⣿⠿⠶⢶⣤⢤⣤⣤⣀⠀⠀⠧⠲⠚⠛⠛⠀⠙⠲⠶⠲⣤⡄⡆⠀⣤⣤⡴⠶⠶⠟⡛⣃⣃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡾⡿⠖⠛⠓⢛⠛⠓⠁⠀⠀⠀⠀⠀⠀⢰⣴⠖⠷⠷⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⡋⠿⢷⣶⠀⠉⠉⠁⠀⠰⠿⠚⢋⠛⢹⢝⢛⢛⠀⠴⣦⣤⢄⣄⣀⠄⠀⠴⠿⠛⠛⠑⠉⠛⠓⠓⠖⢤⣤⣠⢄⠄⣀⢾⡾⠿⠟⢛⠋⣩⣙⡛⠻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸ ⣟⡛⠷⢶⣦⣀⡄⠀⠀⣰⡶⠶⠛⠋⣤⣅⣉⡉⠃⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣮⣿⣥⠶⠞⢋⣀⣍⣉⣉⡍⠻⠷⠶⠀⠀⠤⢀⣤⡴⠀⠴⠃⠐⠉⠀⠈⠁⠘⠛⠁⠀⠀⠀⠀⢸ ⣏⣝⠳⢲⢨⣉⠀⠀⢠⢠⡴⠞⢃⣈⣨⠉⣄⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢪⢪⣭⣉⣤⠶⠾⠛⠙⠉⠁⠈⠀⠀⠀⠀⢀⢭⡄⡈⢩⣤⡾⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠏⠙⠳⢶⣤⣛⠀⠀⠈⢅⠐⠼⠋⠉⠤⠤⠤⠈⠉⠛⠶⢆⣀⣀⠀⣀⣠⣴⠗⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠈⢎⢎⣍⣉⣤⠶⠛⠀⠀⠤⠤⠤⠀⠀⠀⠀⠀⠁⠁⢁⡈⠁⠀⠀⠀⠀⠠⠤⠄⠄⠀⠀⠀⠀⠀⠀⠀⢸ ⣀⡀⠀⠀⢈⡉⠃⠀⠀⡀⠀⠀⢁⠀⠀⠀⠀⠀⢀⠀⠂⠀⡉⠙⠓⠈⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⡈⠀⠀⢀⠀⠁⠻⡫⠀⠀⠈⠀⠀⠄⠀⠀⠀⡀⠁⠀⠀⡀⠀⠈⠁⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠀⠀⢸ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⢀⡴⠸⠛⠂⠰⠀⢀⠀⠀⠀⠈⠉⠁⠀⠀⢀⡀⣠⠾⠟⠋⠷⢦⣤⠀⠀⠀⠈⠉⠉⠀⠀⠀⢀⣴⡶⠾⠿⠿⢲⣦⣀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹ ⡿⠀⠉⠶⣄⡀⠀⠀⣀⡀⠀⠀⢀⠖⠖⠛⠒⠶⢀⠍⠃⣶⢄⠀⣀⣀⣤⠀⠉⣀⠐⠀⠐⠁⠲⠒⣉⡛⠷⡦⢀⣀⡀⢀⣴⠿⢋⡡⠒⠀⠊⠑⠃⣬⠙⠳⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠰⠂⣉⠙⣛⡉⡁⡀⠀⠀⠀⠀⣀⡀⠀⠀⠘⠓⢀⡄⠘⠛⢛⣁⡴⠞⠀⠀⠀⡀⡀⠀⠀⠈⠑⢃⣄⡙⠉⠙⣉⣤⡔⠋⠀⠀⠀⣀⢀⠀⠀⠐⠻⠆⡀⡀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⡀⠀⠀⠉⠀⠓⠉⠀⠀⢠⣴⡀⠃⢋⠛⠃⢰⣄⡀⠀⠀⠀⠟⠋⠁⠀⢀⣠⡶⠛⣋⠓⡛⠇⠠⣀⠀⠈⠘⠘⠘⠈⠉⢀⣠⢴⠞⣛⣙⣛⡶⡀⠀⠀⠀⠁⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠘⠳⣤⣀⣀⣀⣤⣀⣀⣉⣥⡾⣛⢙⢀⢹⣦⣉⣻⣶⣤⣀⣀⣠⣄⣾⣟⣉⠢⠙⠛⠀⠙⢯⡢⡙⢀⠀⣄⣀⡀⢠⡶⠟⢋⡐⠆⠑⠙⠙⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠀⢾⠛⢛⡛⢻⡿⠟⠛⠛⠙⣓⣓⠓⠒⠊⠛⠒⠺⣟⣛⠛⢛⠛⠻⠟⠁⠀⢀⣀⣀⣀⠀⠈⠉⠑⢌⠉⡉⠛⣁⣤⠎⠉⠀⠀⣀⡀⡀⡀⠀⠀⠢⠰⣤⣀⠀⣀⣄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠟⢘⣉⡀⠘⠀⢠⣀⠀⠈⠉⠀⠈⠁⠀⣀⣴⠾⠚⡉⠉⡛⠻⣦⣄⠀⠀⠁⠈⠀⠈⠀⢀⣤⡶⠗⣛⡁⢉⠙⠴⠀⠀⠀⠈⠙⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠉⠻⣤⣀⣀⣀⣠⣦⠀⠀⠀⠀⠃⠉⠉⠛⠖⢈⠙⠡⣤⣄⡀⢀⣴⠎⢂⢁⠖⠋⠁⠈⠁⠲⠎⣙⠳⠐⣠⢀⣠⣤⡶⠋⣨⠾⠿⠋⠀⠉⠐⠁⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡏⠀⠀⠀⠇⢨⡉⢩⣭⡶⠀⠁⠀⠀⠀⡀⢀⣀⠀⠀⠘⠒⢠⠅⠀⣁⣡⠾⠋⠀⠀⢀⣀⣠⡀⠀⠀⠉⠁⢂⣉⣈⢍⢤⠀⠊⠁⠀⢀⣀⣄⣀⡀⠀⠈⠘⠷⢄⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢄⡀⠀⠀⠈⠉⠀⠀⢀⣤⡾⠃⣈⣀⠉⡋⠰⣦⣀⠀⠀⠁⠈⠁⠀⠀⣠⡦⠀⢋⡉⢉⣀⡻⢶⣤⡀⠀⠀⠁⠉⠀⠀⣀⣰⡾⢟⠉⣩⣍⡳⢷⣦⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠈⠙⠦⣤⣤⣤⣤⠀⠘⠡⡴⠟⠉⠉⠀⠃⠀⣤⣁⠃⠠⣤⣤⣄⠲⠟⣉⠣⠈⠛⠁⠈⠁⠣⠀⢭⡛⠶⣦⢠⢤⣤⠘⢋⡁⠂⠘⠀⠉⠉⠃⠘⢮⣉⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣧⠀⠀⠀⠃⠀⣦⠀⠶⠲⠁⠀⠀⢀⣀⡀⢀⠀⠀⠀⠙⠓⠄⠐⢄⠀⠰⠞⠉⠀⠀⠀⣀⠀⢀⠀⠀⠀⠈⠢⠀⠠⣤⠶⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⡠⢄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⣀⣀⡀⠀⠀⠀⠀⠀⡀⠀⠐⠟⠋⢁⡀⠁⠀⢶⣄⡀⠀⠀⠀⠀⠀⢀⣀⡴⠖⠓⡈⠉⡀⠹⣷⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠙⠻⠶⠦⠰⠶⢟⡃⡀⡀⠀⠈⠙⠙⠛⠶⠂⣡⠃⠰⠷⠆⠆⠘⠙⣡⣤⠖⠛⠃⠀⠃⠰⢦⠈⡙⡛⠳⠆⠀⠀⠀⡠⡴⠰⠘⠟⠁⠘⠀⠆⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡿⠀⠀⠀⠈⠀⠞⠀⠞⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠁⠔⠀⠠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠊⠰⠖⠚⠊⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠛⠃⠖⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⣤⣤⣀⠀⢠⢸ ⠛⠤⠤⠄⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠤⠤⠄⠀⠀⠀⠀⠀⠀⠤⠤⠄⠀⠂⠀⠀⠀⠤⠤⠄⠀⠀⠀⠀⠀⠀⠠⠤⠤⠄⠀⠀⠀⠀⠠⠤⠤⠄⠈⠀⠈⠸ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣴⠂⠉⠉⠭⠉⠉⠩⠍⠉⠁⠒⠒⠂⠀⠒⠒⠊⠻⢿⣭⣯⠫⣭⣭⠭⠁⠒⠒⠒⠀⠒⠒⠂⠉⠩⠩⠉⠍⠉⠍⠉⠅⠐⢔⠖⢀⠒⠒⠂⠉⠉⠩⠉⠉⠩⠝⠿⠿⠿⠾⢚⠟⠑⠶⠶⠍⠉⠭⠉⠍⠉⠍⠉⠁⠐⠒⢲ ⣿⠿⠶⢶⣤⣤⣤⣤⣤⠀⠀⠷⠚⢚⢛⠛⠃⠸⠶⢦⢬⣅⡄⡤⠀⠶⠶⠞⠓⣛⡛⡛⡓⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢇⢟⡛⠓⠶⠶⢦⡤⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠛⠛⠓⠷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠟⠿⢶⣬⠈⠙⠉⠁⠀⠞⠛⠛⡉⢉⣟⡛⠓⠂⣴⣆⣩⣈⣤⣤⠔⠒⠐⠊⠙⠉⠛⠛⠛⠷⡶⢄⣀⣀⣠⠴⠀⣋⣴⣿⣃⣋⣋⠛⠓⠷⣶⡄⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠻⠶⣶⣀⣠⠀⠀⢀⡺⠟⢋⠉⡡⣬⣉⡉⠋⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢁⢄⠬⠿⢛⣋⣩⣍⣄⣙⠓⠶⣮⣄⣀⡀⠀⢀⡔⠨⡀⢈⣭⣤⠈⡁⠚⠛⢀⠄⢠⣄⡄⠀⠀⠀⠀⠀⢸ ⣏⡛⠶⢤⢩⡉⠀⠀⢰⡰⠞⢋⢠⣥⣤⠡⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢸⠲⠟⣋⣉⣥⢭⡱⠛⠛⠷⠼⠉⠉⠀⠀⢠⡲⠟⡃⠈⠁⠈⠈⠁⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⢸ ⡇⠛⠶⣄⡘⡙⠃⠀⠀⠰⠀⠉⠡⠄⠀⠄⠈⠘⠶⣤⡀⣀⠀⢀⣠⠰⠞⠋⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣿⡋⠡⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼ ⣀⠀⠀⢀⡉⠛⠛⠀⡀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠉⠛⠛⠉⡁⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠒⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠂⠀⠀⠈⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⣿⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸ ⡿⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⢀⠴⠛⠛⠃⠄⢀⡀⠀⠀⠁⠀⠁⠀⠀⣀⠀⠈⠐⠛⠛⢶⣄⡀⠀⠀⠁⠀⠁⠀⠀⣀⠴⠶⠖⠛⠻⢶⣄⡀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⠀⠀⢸ ⡇⠀⠱⣦⡀⠀⠀⣀⡀⠀⠀⢰⠚⠛⠛⠓⠂⡘⠋⣦⡄⠀⢀⣀⣰⠚⢁⣤⠚⠐⠊⠑⠶⢉⠛⢦⣄⠀⠀⣀⣄⠚⢛⢠⠿⠟⠋⠑⠃⠉⠛⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⢠⠙⠋⠛⣋⣥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⡉⠀⠛⠛⢁⠖⠋⠀⠀⠀⣀⡀⠀⠈⠸⠀⠙⡋⠛⠛⠠⠦⠈⠀⠀⣀⣀⣀⠀⠀⠸⠲⡈⠀⢀⡀⡀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣇⠀⠀⠈⠀⠙⠂⠈⠁⠀⠀⠰⠙⣁⡈⠈⢲⣆⠀⠀⠁⠀⠑⠀⠈⢀⣀⡰⠟⣋⡉⠛⡲⣄⡀⠀⠀⠁⠂⠉⠁⠀⣀⠴⠟⣉⣁⠛⠥⣦⡀⠀⠁⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠒⢴⣤⣤⣤⣀⣴⣿⣤⣤⣤⣉⣉⣟⣶⣬⣿⣦⣤⣤⣄⣠⣤⣽⣫⣤⣿⠋⠉⠃⠙⠫⣻⢧⣀⡀⠀⣀⡀⠾⠋⠰⠟⠛⠉⠙⠳⣌⠻⠗⢄⢀⣀⣀⣠⠀⣠⡄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠈⢛⠛⢛⡟⠻⠿⠛⠛⠛⣻⢻⣟⠛⠛⠻⠟⢛⠛⠛⢛⠟⠛⠛⠛⢛⣤⣄⢀⠀⠀⠙⢀⣉⡛⢛⠊⡅⠀⠁⠀⠀⣠⢤⣀⡀⠈⠁⠠⠈⡙⡛⡉⠥⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡿⠀⠀⠀⠈⠀⠘⠁⠀⠀⠀⠀⣘⣁⣉⢉⠐⢀⣀⠀⠈⠐⠛⠃⠀⢀⣤⡮⠛⣉⠉⣙⠛⣦⣄⠀⠀⠐⠀⠊⠀⢀⣠⡴⢟⣁⣀⡙⠺⢦⣄⠀⠈⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠙⠧⣄⣀⣀⣠⣀⠀⠀⠠⠋⠉⠉⠙⠃⡈⠉⢶⡄⠀⢀⡀⣔⠟⣡⡶⠋⠁⠉⠁⠛⢊⣙⠓⣠⣄⣀⣠⣴⠛⢁⠔⠋⠙⠉⠀⠉⠄⢉⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⢰⠈⣉⠋⢭⡶⠐⠀⠀⢀⠀⠀⠀⡀⠀⠘⠲⠈⢀⠉⠉⢥⠞⠁⠀⣀⣄⠀⣄⠀⠈⠘⠀⠨⠉⠉⣉⠠⠛⠀⠀⢀⣤⢤⣀⡀⠀⠘⠰⠀⢀⣀⡀⠠⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣇⠀⠀⠀⠀⠈⠀⠁⠀⡀⠀⠺⠋⣡⣀⡀⠙⢦⣄⠀⠀⠀⠉⠁⠀⣀⣤⠚⢋⣉⡀⣌⡛⣷⣄⡀⠀⠈⠀⠉⠀⣀⣄⠾⣂⣍⣈⣉⠻⢶⣄⡀⡀⠀⠉⠉⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠉⠻⣤⣄⣄⣤⡼⣏⣤⠆⠂⠉⢉⠉⠳⢦⣉⣻⣦⡄⢠⣤⡴⠉⣅⡄⠛⠉⠉⠀⠈⠢⡉⠻⣴⣤⣄⣠⡼⠛⡁⠴⠋⠉⠉⠉⠛⢦⡉⠻⢷⣄⣤⣤⡴⢉⣥⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠀⢠⠀⢡⡦⠀⠋⠀⠀⠀⣀⣤⣀⠀⠀⠉⠃⠀⠄⢀⡤⠎⠀⠁⠀⠀⢀⣀⡀⠀⠀⠉⠀⠤⠄⢁⡄⠔⠀⠁⠀⠀⠀⠀⠀⠀⠈⠁⠠⠀⡈⢈⡐⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡿⠀⣀⣀⠀⠀⠀⠀⠀⡀⠀⠀⠘⣉⣉⠉⠐⢠⣤⠀⠀⠀⠀⠀⠀⣀⣠⠴⠁⣉⠉⣉⠐⢠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠈⠛⠶⠤⣤⠼⡞⡀⠀⠀⠉⠉⠉⠙⠃⡔⢀⣘⠿⠖⠠⠶⠟⡉⣥⡶⠋⠀⠈⠐⠒⢀⣌⡙⠷⠂⠀⠀⠀⣠⣄⠔⠛⠟⠁⠀⠁⠔⣠⡀⠀⠀⠀⠀⠄⡀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠘⠀⠶⠀⠗⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠰⠀⠀⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠀⠲⠖⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠓⠾⠄⠘⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⢤⠄⠸⢸ ⠻⠤⠤⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⠤⠤⠄⠀⠀⠀⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⠀⠐⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⠘ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣴⠈⠉⠉⠉⠉⠉⠭⠉⠁⠒⠒⠀⠂⠒⠒⠈⠩⠭⢿⣭⣽⣽⠿⠶⠖⠀⠐⠀⠒⠒⠈⠩⠉⠉⠉⠉⠭⠉⠐⠒⠂⠂⠀⠒⡔⡌⠩⠍⠉⠉⠉⠉⠉⠐⠐⠊⠹⠗⠾⠷⠿⢽⣯⢯⡭⢍⠉⠉⠐⠒⠂⠐⠐⠂⠂⠉⢩ ⣿⠿⢶⢶⢤⣄⣤⣤⡤⠀⢀⣛⣚⡚⠛⠲⠆⢰⣶⣤⣀⣁⢤⠶⠀⠚⠛⠛⢚⠚⠺⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠢⡦⠷⣦⣤⡤⣠⣤⠤⠀⠀⠀⠀⠀⠀⠀⠰⠷⠦⣦⡴⢠⡦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⢷⣾⡅⠉⠋⠀⠀⠰⠛⣛⣉⠘⡻⠳⠶⠂⣨⣍⠉⣡⣴⠶⠾⠋⠁⠐⠉⠙⠛⠻⠶⣦⣀⠀⢠⣤⠶⠿⠛⠁⣵⣿⡛⠛⠶⠦⣆⣈⣉⡱⠄⠀⠀⠀⠀⠀⠠⢂⡀⠐⠂⠀⠈⠉⠁⠀⠀⠀⣀⣠⠀⠀⠀⠀⠀⢸ ⣟⠻⢶⢯⡓⣀⠂⠀⠠⠿⠛⣤⠀⡆⣘⠙⠊⠀⠈⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⡐⡐⡤⣯⣍⣍⠋⠲⢦⣈⡛⠓⣀⡤⡶⠟⠂⢤⢤⢠⠉⣛⠠⠆⠠⡄⡀⠀⢴⠠⠚⠋⠃⠀⠀⠀⠀⠀⢸ ⡟⡻⢦⡌⡋⡛⠀⠀⠐⢜⠛⡦⡴⠤⣬⡙⠳⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠑⠴⣦⣤⢭⡛⠳⣶⣝⠛⠛⢛⠃⠀⠀⠀⠀⠀⠀⢤⡙⠓⣾⡟⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠻⢶⣀⠓⠛⠓⠀⠀⠈⠃⠀⠰⠂⠔⠙⠢⢄⠠⡀⠀⠐⢠⡶⠻⠂⠵⠒⠐⠌⠙⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⠣⠋⠓⢾⡉⠛⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠉⠚⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⢀⠀⠀⠈⠙⠛⠋⠁⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠈⠓⠋⠁⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠀⠀⠀⠒⠒⠀⠀⠀⠀⠘⠛⠛⠉⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⠐⠂⠀⠀⠀⠸ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⡇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⠞⠛⡛⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠳⣄⣀⠀⠀⠀⠀⠈⠀⠀⣠⠴⢋⣉⠚⢳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠐⢢⡄⠀⠀⠀⣀⠅⠀⡀⠚⠛⠛⠳⠆⠙⠂⢀⡀⠀⠀⣰⡞⣛⡵⠛⠃⠘⠓⢨⡛⠃⣀⠀⠀⣀⣱⠟⢋⠆⠛⠛⠙⢟⠙⠛⢷⠒⠀⠀⢀⡴⠀⣠⠐⠚⠘⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣇⠀⠀⠉⡓⠒⠛⠫⠜⠋⠁⠀⣀⡀⡈⠈⠀⠀⠈⡛⠛⠃⡈⠔⠉⠀⢀⠀⠀⠀⠀⠙⠢⠉⠙⠛⢛⢙⠂⠉⠀⢀⣀⠀⠀⠀⠠⣀⠑⠛⠛⠋⠥⠈⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠀⠙⠀⠙⠀⠀⣀⠤⢀⡉⡉⠛⢦⡀⠀⠀⠈⠀⠈⠁⠀⣀⣈⣛⠁⠀⣈⢢⡀⠀⠀⠈⠛⠂⠀⠀⣠⠄⠊⡍⠉⢲⣄⡀⠀⠉⢦⡀⡂⠀⢀⣤⡎⣂⢀⣄⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠤⣀⣤⣤⣤⣤⣾⣧⣾⣯⣭⣥⣼⣦⣭⣤⣤⣤⣤⣬⣤⣾⣽⣥⣽⣤⣬⠛⢦⣙⢷⣁⣈⣈⢀⣤⢞⠇⠘⠉⠉⠀⠛⢮⡙⢷⣄⠀⠀⢁⡴⢛⡹⠞⠋⠀⠉⠋⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠀⠀⠘⡛⠟⠛⢻⠟⠛⠛⢻⢿⣿⠛⠛⠛⠟⡻⠛⠛⡛⠛⠛⠛⠛⣿⣿⣿⡁⠀⠁⢊⣉⠛⠛⢋⠁⠊⠀⠀⣀⡤⣤⡀⠀⠐⠆⠉⠛⠋⣀⡴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠈⠀⠚⠀⠀⡀⠀⠐⢋⣡⣄⡈⢀⣄⠀⠀⠛⠁⢀⠀⠀⣴⠛⢉⡁⢨⠙⢶⣄⡀⠀⠈⢈⠀⠀⢀⣤⠞⣁⣠⣄⡱⢶⣄⠀⠀⠃⡛⠁⠀⠀⠀⠀⣀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠈⠱⣆⡀⠀⣀⣤⢄⣀⠄⠉⠁⠉⢙⢣⡈⢧⣀⣀⣀⡈⠰⠗⡩⡞⠉⠁⠉⠁⠀⠉⠙⢤⣀⣀⣀⣤⠉⣡⠙⠉⠁⠉⠛⢄⠉⠓⢄⣀⠀⠀⠀⠀⠴⠎⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣧⠀⠀⠈⢉⠋⢩⡁⠋⠁⠀⠀⢠⣤⣀⠈⠉⠢⡀⠈⡉⠁⡠⠉⠁⠀⣠⣤⡀⠀⠀⠀⠠⠈⠙⠛⡉⠀⠀⠀⠀⣤⣤⣄⠀⠀⠘⠢⣌⡁⠑⠀⠀⠋⠀⠀⣀⢤⣄⣀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠀⠈⠀⠀⠀⣀⣴⠖⢀⡀⡈⠉⢳⡄⠀⡀⠀⠈⢀⠀⠀⣴⡤⣨⠀⠀⣐⠀⣤⡀⣀⠁⠈⠉⠀⣠⡤⣟⠉⣤⠀⡉⣆⣀⣀⠈⢙⠂⠀⣀⣠⡴⢟⣭⣀⣬⡉⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠒⢤⣄⣀⣠⣴⢫⣥⡞⠈⠈⠀⢉⣲⣄⢐⣠⣤⡀⣠⡴⠏⣁⠄⠉⠀⠘⠹⠣⠍⠻⠦⣠⢀⣤⣾⣋⠄⠋⠀⠁⠈⠉⠱⡈⠛⣤⢄⣀⣤⡾⠋⠁⠙⠉⠀⠉⠁⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⢠⠁⣩⠀⠔⠋⠁⠀⣀⢤⠄⠀⠈⠈⠁⠂⣀⠨⠁⠠⠈⠁⠀⢀⡀⠀⡀⠀⠈⠐⠂⡩⡁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠨⠉⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⡀⠀⠀⠀⠀⢀⡄⠀⠙⢃⣉⣀⡁⠰⡄⡀⠀⠀⢀⢠⠀⠀⡴⣗⢉⡀⢨⡁⠰⣤⡀⠀⠀⠀⠀⠄⠀⠀⠀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠘⠳⡦⣤⠤⠾⣣⣤⠄⠈⠉⠉⠙⢶⣦⡑⠠⠲⢶⣦⠌⢩⣀⠺⢋⠉⠀⠈⠠⢀⠉⠳⣶⠶⠶⢂⠠⡀⠂⠅⠉⠉⠙⡶⣄⣀⠀⠀⠀⠀⢀⣤⡐⠳⠅⠅⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠀⠰⠀⠰⠂⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠢⠀⠢⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠰⠦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⠀⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠵⠶⠀⣴⢸ ⠣⠤⠄⠀⠀⠀⠀⠀⠤⠤⠄⠀⠂⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⠤⠤⠄⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠤⠤⠄⠀⠀⠀⠀⠤⠤⠄⠀⠀⠀⠀⠀⠤⠤⠀⠐⠀⠂⠀⠤⠤⠀⠀⠀⠀⠀⠀⠤⠤⠀⠐⠀⠀⠀⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣴⠈⠩⠉⠉⠉⠉⠉⠑⠒⠂⢐⠂⠒⠂⠈⠉⠩⢿⠹⣿⣽⠿⠶⠒⠒⠂⠀⠒⠉⠩⠉⠉⠉⠉⠉⠁⠒⠂⠐⠀⠒⠂⠭⠩⢉⢉⠉⠩⠉⠑⠐⠀⠂⠂⠒⠛⠹⣿⡏⡽⡽⡭⠿⠷⠆⠂⠀⠒⠒⠂⠉⠍⠉⠉⠉⠉⢩ ⣿⠿⣦⡦⣄⣤⣤⣴⠆⠈⣀⣚⡞⠺⠶⠴⢦⣴⣠⣶⣤⠄⠲⠚⢀⢚⠻⠾⠶⠶⣶⡄⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⣀⢶⣾⣾⣆⣤⠶⠖⠚⠋⡁⠀⠀⠀⠀⠀⢪⣥⡴⣤⠶⠞⠛⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⣿⣿⠅⠉⠁⠀⠀⣘⣻⣻⠓⢻⠳⠶⠖⣠⠈⠩⢥⠴⠾⠛⠛⠀⠈⠛⠻⠾⢾⢭⠔⡀⣰⠴⠒⠒⠛⠋⠩⡀⠿⣿⣷⠛⡯⠋⣧⡦⠶⢟⣏⣀⡀⠀⠀⠀⠀⠛⠁⠐⠓⠂⠀⢢⠄⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠻⢦⢯⠓⢀⠇⠀⠐⢛⣵⢶⠰⡇⠹⠳⠆⠙⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠆⠄⣍⡛⠦⡇⠓⡛⠋⣰⡷⠖⠟⠁⠂⠖⠐⠊⠀⢤⣄⡈⠠⡀⠸⠇⠁⠐⠀⠈⠉⠻⠆⠀⠀⠀⠀⠀⢸ ⣟⠿⠆⡋⠛⣛⢀⠀⠀⠩⡅⠲⠦⣧⠘⠳⣄⡀⠀⠀⠀⠀⠀⣀⡄⡀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⢭⣓⠊⠛⣳⣶⠟⠒⠂⠀⠀⠀⠀⠀⠀⠘⠛⡀⠸⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠻⣾⠛⠚⠛⣋⡄⠀⠀⠄⠐⠰⠎⠛⠳⡄⠙⠛⠓⣐⠾⠛⠉⠶⠀⠰⠚⠙⢶⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠛⢟⢟⣛⡋⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠙⠓⠛⠉⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠛⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠚⠚⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⡏⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢴ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢉⡉⡀⡀⠀⠀⠀⠀⠀⠀⢀⣀⡶⠀⣐⡛⠳⢄⣀⠀⠀⠀⠀⠀⠀⡀⡰⠛⡋⠑⢶⣄⠀⠀⠀⠀⠀⠀⠀⣀⡤⢉⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠄⠃⠀⠂⢀⡲⢓⡂⠀⠈⠛⠻⣇⠀⠂⠀⠀⠀⠀⡞⠉⡀⠙⠛⠛⠲⣘⢻⣆⠈⠉⠁⣊⠼⣋⡓⠋⠛⠈⠛⠋⢳⣿⠙⠙⠑⡓⡞⠋⠚⠛⠙⠛⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠙⠗⠚⢋⡇⠈⠉⣁⠀⠀⠀⠙⠻⣍⠈⠉⠛⠁⠀⠉⠀⣁⢀⠈⠀⠘⠳⣌⠛⠞⠛⢉⠘⠋⠁⢀⢀⢀⠀⠈⠢⣀⠙⠻⠟⡁⠤⠀⠀⣀⣀⣀⠀⠈⠳⣄⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠀⠀⠅⠀⠀⣀⡜⣩⣀⡀⡐⣤⠀⠈⠓⠲⠞⠀⢀⣀⠞⡋⣈⡀⠸⣦⡀⢈⠑⢰⢀⠀⠀⣠⡞⠉⣉⠈⢀⣀⠀⢈⣃⠔⢋⢀⣀⣀⡈⣁⣡⣁⡫⡄⠀⠈⠛⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠀⠄⣈⣤⣤⣤⣼⣯⣿⣥⣬⣥⣿⣦⣥⣤⣤⣥⣤⣤⣾⣯⣤⣬⣭⣥⣶⣬⣻⢎⣁⢉⠉⣉⣟⠋⠚⠁⠁⠈⠹⠍⠩⣏⠉⠉⠀⠠⠟⠉⠑⠋⠉⠙⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⢙⠿⠟⢻⡿⠛⠛⢻⣿⣿⠛⠛⠛⢻⠛⠿⠿⠛⠿⠛⠛⡿⣿⣿⡛⠛⠋⢄⢛⠛⠛⠉⠉⠀⠀⣠⣤⠄⡀⠀⠰⡌⠁⠛⠀⠁⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠘⠀⠋⠀⠀⣀⠀⠁⠀⣄⣀⠠⠄⠀⠀⠐⠒⠀⢀⡀⠂⢁⣤⣄⡱⢤⣀⠈⡛⣀⡀⠀⣀⣀⢆⠁⣠⣄⣉⣢⡄⡑⢠⠀⠀⠁⢀⣀⠀⣠⣀⠤⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⢈⡀⠀⣀⡜⢉⣟⡀⠀⠈⠙⣤⡀⡀⢀⣈⢀⣠⠙⢡⠄⡈⠀⢈⠙⢬⣹⣅⡁⠁⢀⣠⠟⣥⣉⠀⠉⠀⠉⠉⠙⣦⣀⡀⣁⣐⠏⠉⠁⠀⠀⠀⠨⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠈⠛⠋⠉⠟⠀⠀⢠⠀⠀⡀⠈⠙⢧⡀⠁⠀⠁⠘⠀⠀⣤⠠⠀⡀⠀⠸⢤⠙⠚⠋⠩⠂⠀⠁⣠⠄⣀⡀⠀⠀⢌⡙⠋⠉⣀⠞⠁⢀⣠⣤⢤⡀⠀⠀⢦⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡿⠀⠀⢀⠘⠀⠀⢀⣴⡟⠁⠀⣠⣩⡗⠀⠀⠈⡉⡀⠀⢠⣴⠋⢁⣠⣬⠙⢠⣄⡀⡈⠀⣀⢀⢀⣐⣋⣀⡤⣌⣑⣦⣀⣀⡀⠁⣉⠀⣠⣴⠏⣀⣤⡄⡹⣤⣄⡀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠠⣄⡀⣀⣤⣏⣩⢤⡀⠀⠉⢙⣦⣄⣶⣄⣠⣠⡠⠉⠀⡀⡌⠉⢈⠁⢨⠩⠡⣠⣀⢠⡤⠋⣤⡌⠁⠀⠉⠉⢍⡉⠥⢄⣀⣠⡔⠉⡁⠙⠉⠀⠈⠉⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠨⠉⢡⠀⠋⠁⠀⠠⣤⣤⡀⠀⠉⠀⠀⠉⢩⡄⠁⠀⢀⣀⣠⠀⠀⠀⠀⠀⠌⣉⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⠦⣈⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣷⠀⠀⣀⠀⠀⠀⣀⣤⡆⣀⣀⠈⢹⣷⣄⡀⠀⠀⠀⠀⢠⣴⢄⡩⣄⣀⠠⢦⣄⠀⡄⠀⠠⢄⣠⣴⡿⣤⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠐⠠⣦⡤⡴⣈⡡⡿⠉⠁⠈⠀⢠⣌⣡⠄⠤⠀⢶⣹⠀⢲⠁⠀⢉⢠⠀⣀⠑⢤⡤⣄⠰⠀⣤⠓⠀⠁⠉⠀⢰⣀⡀⡄⡀⢀⡀⣀⡄⠀⠀⠀⠀⠸⢶⣄⠀⠀⠀⠀⠠⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡿⠀⠀⠀⠐⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠂⠠⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠑⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠠⡴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣄⣄⣤⠀⢠⢸ ⠻⠤⠀⠀⠀⠀⠀⠠⠤⠄⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠠⠤⠄⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠤⠤⠄⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠤⠤⠄⠀⠀⠀⠀⠤⠤⠄⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠤⠤⠈⠉⠈⠁⠀⠸ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣤⠉⠉⠉⠉⠉⠉⠁⠒⠂⠒⢒⠂⠂⠉⠉⠉⠩⢿⠿⠿⠶⠷⠷⠓⠒⠶⠍⠉⠉⠉⠉⠉⠁⠂⠂⠐⠀⠐⠂⠉⠉⣍⡍⠉⢩⢩⠒⠂⠐⠐⠐⠂⠉⠉⠩⢽⠭⢿⠿⠿⠾⠚⠻⠾⠖⠹⠉⠉⠉⠉⠩⠉⠐⠂⠒⠒⢰ ⡿⢷⣦⡦⣆⣤⣶⡶⠆⠈⣄⡟⠾⠶⠦⢰⣶⣴⣠⣶⠶⠖⢙⣡⡔⠲⠶⢶⣴⣶⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣷⡶⠾⠟⢿⡿⠂⠛⠀⠀⠀⠀⠀⠀⠐⠦⠞⠛⠙⠋⠻⠻⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡿⢷⣿⡿⠍⠉⠀⠀⢀⣸⡿⠷⠛⡷⢶⠖⢿⠂⠩⣷⠶⠓⠛⠙⠒⠀⠺⠶⢾⢽⣱⡘⠴⠚⠚⠛⠁⠋⠛⠧⠶⣤⣍⣉⠛⡶⠶⠖⣋⢇⣟⣿⡆⠀⠀⠀⠀⠀⠐⠒⠂⢰⠶⠂⡴⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⢿⣎⣛⠓⢲⠇⠀⠀⣩⡵⡶⠘⠃⢸⠄⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡛⠛⢯⣖⠶⢛⣸⡶⠾⠟⠓⠶⡖⠒⠀⠀⠰⠷⠨⡭⡅⠨⠏⠠⠒⠂⡀⠀⣰⡆⠀⠀⠀⠀⠀⢸ ⣿⠿⣇⠛⠛⢋⣤⡄⠀⠀⠲⠆⠘⢆⢘⠱⢛⠓⠂⢀⠀⢀⠤⠄⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡟⠯⠷⠶⢛⠷⠾⠷⣞⠟⠧⣌⡁⠐⠀⠁⠸⠛⠠⠜⠛⠃⠙⠂⡀⠀⠂⠉⠀⠀⠀⠀⠀⠀⢸ ⣿⠿⡝⠛⠓⠃⡷⠖⠀⠀⠂⠀⠠⠊⢓⡃⠀⠛⠛⠑⠛⠛⠐⠒⠲⠄⠹⢶⠐⠐⠐⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠃⠻⠻⠛⠆⠂⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠉⠓⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠂⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨ ⡏⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠀⢳⣀⠀⠀⠀⠀⠀⠀⢀⣀⢚⠁⠀⢀⢀⠀⠀⠀⠀⠀⠀⢀⣤⠊⣀⢈⣓⣄⠀⠀⡀⠀⠀⡀⢀⣀⣍⢉⡉⠂⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣗⠀⠀⠓⠋⠂⣀⡛⠛⡃⠀⠘⠁⠛⢳⢀⠀⠀⠈⠡⠘⡙⠓⠀⠙⢛⣑⢢⣘⢛⠀⢘⣙⠛⢛⠁⣉⡋⠃⡛⢢⣛⠋⠀⠛⡙⠟⠳⠓⠃⠉⠙⠛⠻⣆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠈⠰⠷⠋⠙⠋⠈⢉⣥⠀⠀⠈⠉⠛⠳⠈⠙⡸⠀⠀⠀⣁⡡⠀⠘⠂⠙⠻⠁⠘⠡⠟⠉⣀⣭⣏⡀⠉⠃⠈⠹⠀⠘⠁⠈⠀⠀⣠⡤⠀⠀⠀⠈⠳⠶⢈⣠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠀⠀⠀⠄⠀⠀⢀⣔⡁⠁⠀⣐⣄⡀⠈⠲⠐⢀⠀⢀⣴⣋⠁⠀⣐⣆⠀⢈⣒⢐⠀⣀⣀⣴⣁⢠⣈⠉⣄⠀⢀⡒⠢⢀⣀⣀⣴⣁⣅⣀⣀⣄⣀⠀⠉⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⢉⣥⣥⣤⣿⣿⣧⣤⣬⣿⣯⣧⣤⣤⣬⣭⣵⣽⣿⣭⣤⣭⣿⣭⣷⣭⡉⠈⣁⣉⠛⣝⣉⠉⠈⢸⢏⠡⣏⠉⠀⠉⢹⠋⠉⠊⠁⠉⠛⢩⡁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠈⠺⠿⠿⡿⠟⠛⠛⠻⢿⡟⠛⠻⠟⠿⠿⠛⠻⠟⠛⠛⠿⢿⠟⠛⠻⡟⠛⠖⠛⠉⠁⠉⣩⡀⠆⡀⠈⠳⡈⠳⠖⠋⢀⠀⠀⠀⢤⡀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⡀⡐⠀⠀⢀⡔⣡⢤⢠⡙⣦⡀⠈⠒⠰⢂⡀⢠⣄⣁⣀⢄⡈⠀⡀⠈⣠⠴⣀⣀⣠⡼⣁⣤⣄⠀⣦⡀⣀⢀⡶⣾⢀⣀⡄⣣⣤⡀⠉⠠⡀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠉⠀⣉⣤⡍⢉⣀⡀⠀⠁⢉⣁⣄⡀⢈⣈⣀⣈⠙⢁⠀⡈⠁⢠⢨⣭⣉⠁⢉⡹⢉⣡⠉⣁⣀⠁⣉⠩⢊⠁⠁⢀⡥⠋⠟⠁⠁⠉⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡏⠀⠀⠚⠓⢋⠟⠁⠀⠀⠀⣀⡀⠈⠙⢉⠉⠉⠈⠉⠁⠀⠀⣡⣥⠄⠈⠙⠍⠙⠋⢉⡀⠉⠈⣀⣠⡭⢀⠀⠈⠄⠐⠋⠁⣠⠀⠀⢠⡤⢤⣀⠀⠀⢀⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣀⣀⠁⠀⣀⣆⡄⠀⣤⣉⣠⡄⠀⠀⢁⣌⡀⣠⢰⡁⢠⣤⣴⣦⡀⢀⣤⡢⡉⠀⣠⣾⣭⡀⣠⣍⣤⣤⣀⡄⢻⣫⡄⣠⣶⢋⣠⣤⡍⣤⣄⠀⠁⡥⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠄⡀⡀⣄⣤⣭⢛⣁⡀⠀⠉⢏⣑⣀⡀⢀⣠⣘⢈⠉⠁⡀⡍⠩⣬⣽⣯⣤⣀⣠⠐⢡⡩⠁⣤⣄⠉⢁⢉⠀⠀⠀⣁⠐⢉⡁⠉⠀⠈⠉⠃⡉⠁⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠉⠁⡁⠘⠁⠀⢠⢤⠀⠀⠀⠉⠨⣈⡀⣈⠌⠁⠀⠀⢀⣤⡀⠀⠈⠀⠈⣉⡉⠀⠁⠀⠀⠠⣄⣀⠀⠈⠀⠌⠁⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⣄⢀⣀⠀⣠⣶⣅⡤⢠⡄⣤⣄⠀⠈⢩⡤⠀⣠⣼⣠⡀⠬⣅⢠⣤⣀⡈⠉⡅⠀⣠⣼⣥⣤⡤⣍⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡏⠀⠠⢤⣤⡤⠆⡡⠿⠋⠀⠀⢀⢤⣍⣀⣠⡄⠰⠁⢠⢠⠁⢠⠀⠁⢤⣈⢲⣠⠀⢠⠀⣠⡀⠀⠀⠀⠀⢤⠀⣄⠀⡀⣀⡄⣀⣤⡀⠀⠀⠀⢠⣄⡀⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠒⠀⠁⠀⠀⠀⠀⠀⠀⠈⠁⠰⠀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠤⡄⠀⠀⠀⠁⠀⠀⠀⠀⠈⠃⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣴⡴⠶⠁⢸⢸ ⠧⠄⠀⠀⠀⠀⠤⠤⠄⠀⠐⠀⠀⠤⠤⠀⠀⠀⠀⠠⠤⠄⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠠⠤⠄⠀⠀⠀⠀⠤⠤⠄⠀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠚ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣤⠉⠉⠉⠉⠉⠉⠐⠂⠐⠐⠐⠂⠉⠉⠉⠉⠹⢿⠿⠻⠿⠿⠾⠖⠮⠭⠍⠉⠉⠉⠁⠀⠂⠒⠀⠒⠈⠉⠉⠉⠉⡭⠍⠒⠒⢖⠂⠒⠂⠉⠉⠉⠉⠉⠩⠗⠢⠿⠟⠷⠿⠿⢽⢿⡍⢩⠉⠀⠒⠂⠒⠀⠐⠈⠉⠉⢩ ⡿⢷⣆⣦⡆⣶⣶⡶⠂⢨⣔⠗⠶⠶⠆⣸⣶⢶⡴⠶⠚⠋⣸⠰⠶⠶⣴⣶⣴⠶⠴⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⡷⠿⠖⠾⠏⠿⠶⠦⠄⠀⠀⠀⠀⠀⠀⠰⠶⠛⠻⠾⠦⣨⡽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡷⠿⣿⡻⠋⠁⠀⠀⠀⠸⡿⡚⠳⠶⣾⠛⣶⠃⡸⠷⠚⠹⠘⠐⠲⠒⡸⢿⠩⠼⢾⠿⠛⠙⠲⠒⠓⠖⠶⢷⢛⠀⣧⡷⠿⡷⡶⣇⠿⠆⠆⠶⠆⠀⠀⠀⠀⠀⣴⡶⠂⠰⠒⠂⠘⠒⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⢸ ⡿⢿⡟⠛⠓⢶⠇⠀⠀⠠⠷⠾⠒⠓⢼⠃⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣧⡷⢧⡶⠶⠧⣹⠳⢶⡖⠒⠲⣶⠶⠆⠀⠰⠧⢬⡈⠃⠤⠃⠠⠵⠀⠼⠃⠺⠶⠀⠀⠀⠀⠀⢸ ⣿⠾⡟⠓⠟⠛⡶⠇⠀⠀⠐⠾⡟⠦⠘⠙⠚⢚⠄⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡏⠛⠷⠶⠶⣾⠿⢷⡟⠛⠟⢉⡀⠀⠀⠀⠐⠙⠉⠾⠿⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣟⢿⠛⠳⠓⢃⠗⠃⠀⠀⠃⠀⠱⠢⠛⠛⠀⠛⠚⠒⠒⠚⠒⠐⠻⠃⡴⠒⠐⠐⢘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡇⠃⠒⠛⠓⠂⠋⠄⠉⠒⠗⠁⠀⠀⠀⠀⠀⠘⠃⠠⠀⠈⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠉⠈⠑⠒⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢺ ⣧⠀⠀⠀⠀⠀⠀⠀⡂⢀⣀⠀⢄⡀⠀⠀⠀⠀⠀⡀⢈⢀⣀⠁⢀⣀⠀⠀⠀⣀⢀⢀⣐⢀⣈⠁⢂⡀⡀⡀⠀⠀⡀⢀⣐⣋⣉⣙⣁⣀⡀⡀⡀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠛⡉⣂⣘⡛⠛⡃⠀⠚⠃⠛⡁⠀⠀⠀⠉⢃⠘⠛⠋⠁⣚⣛⣓⢀⢙⢛⠘⢙⠟⠛⢛⠀⣋⣛⠇⠓⠈⠛⠋⠌⠛⠛⠛⠛⠳⠛⢧⡈⠛⠛⢂⠟⣀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡯⠀⠀⠴⠗⠋⠟⠃⠈⠍⠁⠀⠈⠈⠛⠛⠁⠚⠙⠉⢀⡀⠔⠁⠁⠓⠘⠛⠚⠍⠀⠛⠀⣙⣽⡀⠉⠛⠊⠛⠚⠈⠁⠀⠀⢠⣤⣄⠀⠈⠀⠁⠀⠞⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣀⠀⠈⠀⡠⣀⠀⠀⠀⣄⣀⡑⠂⢠⢀⢀⡀⢈⣀⡀⠈⠂⣀⣀⠀⣀⣀⢀⣀⣎⣁⡀⣀⢀⣀⠀⢢⢄⣀⡀⢀⣔⣁⣀⢀⢐⣄⡀⣁⣠⣴⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠈⢉⣭⣭⣼⣿⣯⣥⣤⣭⣥⣭⣥⣤⣤⣬⣽⣥⣬⣽⣥⣤⣿⣽⣥⣤⣭⣉⠸⣋⣉⠉⣉⣉⠛⡙⣄⠁⠀⠉⠫⠋⠛⠉⠉⠉⠛⠉⠣⠁⠁⠁⠈⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣧⠀⠀⠸⠿⠛⠛⠛⢻⠿⠿⠟⠛⠻⠻⠿⠟⠻⠿⠛⢻⠿⠿⠿⠛⠻⢿⠿⠿⠋⡀⠉⠈⣀⠿⣏⠁⠉⠈⠀⠠⠀⠁⠈⠀⡀⠒⢄⠀⠀⠀⠉⠒⠒⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⡀⡀⠃⠀⡀⣀⡠⠄⢀⣀⣀⡀⢢⠴⠂⣀⡀⣈⣴⣀⡀⢠⡀⢀⡡⣀⣠⢁⣠⣀⣀⣠⣄⣱⣄⠀⣀⠀⣀⢀⣀⣤⣀⣄⣤⡤⣄⡀⡀⠀⠀⠂⠀⠀⠀⠴⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡏⠀⡀⠉⡉⣉⣀⡉⢉⣀⡀⡈⢉⣛⣁⣀⣀⣈⣊⣁⠈⠉⠀⡀⣈⡩⣤⣀⢉⢩⡙⢩⠉⢉⠉⠉⣩⣍⢀⣉⢀⢈⡉⠁⠉⠁⠉⠉⠁⠁⠉⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠘⠒⠋⠁⠉⠁⡀⠉⠱⠀⠈⠩⠉⠙⠛⠉⠈⠉⠀⠠⠾⣥⠁⠉⠈⠉⠙⠋⠀⠉⠀⠸⠮⢤⡀⠙⢄⠉⠙⠛⠠⠊⠀⢠⠤⣦⡀⠀⠀⢄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣈⣀⡀⢀⣔⣥⡄⠄⢠⣤⣤⡄⠙⠂⢠⣤⡄⣡⣤⣄⡈⢷⣤⡠⠀⣠⣤⣤⣤⠀⣤⢤⣤⣑⣤⣄⡍⣶⣄⡄⣠⣤⣥⣤⣤⣝⣤⣄⡌⣥⣤⠀⡀⡴⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣷⠀⠀⠀⡄⣤⣬⡝⢉⣅⡄⠀⢈⢩⣥⣀⣀⣀⣡⣡⠈⠉⠠⣄⡿⡍⢤⢠⣨⣤⠈⣩⠀⠨⠠⠉⣤⣭⠣⣄⢉⣀⠬⠉⠙⠁⠀⠁⠉⠈⠻⡅⠁⣀⡄⠋⠑⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡿⠀⠀⠈⠉⠁⠀⠀⠠⠠⠀⠀⠀⠀⢉⠙⠉⠀⠘⠁⠀⣀⠠⠀⠀⠀⠀⠉⠉⡁⠀⠁⠀⠀⠀⢄⠀⠉⠀⠉⠉⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⡀⣄⣀⣀⣀⣄⣄⡄⠀⣨⡶⣤⡄⠈⠁⢠⣤⡴⢠⣤⡀⡀⢧⣄⢀⢠⣈⡀⠀⣤⠊⢤⣤⣤⣯⡤⣤⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠠⣄⡤⣤⡧⠾⠧⡀⠀⠈⢠⣌⣤⣠⣤⡄⢩⡄⢠⢡⠀⢸⠢⠈⢦⣤⣠⣤⠈⢡⠀⣠⡄⠈⢤⢠⠀⠀⠀⣄⣀⣤⣤⡄⡄⣄⡀⡄⠀⡀⠀⢄⠄⣠⣴⡇⢀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣷⠀⠀⠀⠠⠀⠁⠀⠀⠀⠀⠀⠀⠈⠐⠀⠤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠶⠶⡤⠀⣰⢸ ⠧⠤⠄⠀⠀⠤⠤⠤⠀⠀⠀⠀⠤⠤⠄⠀⠀⠀⠤⠤⠄⠀⠀⠀⠠⠤⠤⠀⠀⠀⠠⠤⠄⠀⠀⠀⠠⠤⠄⠀⠀⠠⠄⠤⠤⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠤⠤⠄⠀⠀⠠⠤⠤⠄⠀⠀⠀⠠⠤⠄⠉⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡬⠉⠉⠉⠉⠉⠉⠉⠉⠀⠐⠒⠐⠒⠒⠐⠀⠹⢿⠿⣿⡽⠿⠿⠏⠴⠆⠀⠒⠐⠒⠂⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⡆⡔⠒⠄⠖⠂⠂⠀⠉⠉⠉⠉⠉⠩⠿⠿⠿⠷⠷⠾⠺⠷⠷⠇⠉⠉⠉⠉⠉⠉⠉⠉⠀⠐⠐⢲ ⡿⠷⢶⠦⠶⣶⣶⣴⠆⠰⠄⠗⠾⠶⠆⠸⠷⠶⠶⢶⣬⠁⠰⠰⠶⠶⠶⠾⠷⠷⠻⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣃⠷⢶⠶⠗⠷⠶⠦⡄⠀⠀⠀⠀⠀⠀⠰⠮⠓⠻⠟⠛⠻⠿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡿⠿⢿⣿⠇⠁⠁⠀⠀⠸⠻⠳⠓⠿⡿⠲⠶⠂⢸⠷⠮⢰⠴⠴⠶⠂⠐⠲⠻⠹⠙⠛⠻⠿⠶⠖⠒⣆⠶⠧⠒⠀⣷⣟⠿⠟⠿⠗⠗⠶⢦⠶⠆⠀⠀⠀⠀⠀⠐⠻⣆⡸⠺⠆⠸⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡿⠿⠶⠯⠓⢶⠇⠀⠀⠸⠿⠶⠒⠆⠸⠙⠚⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡟⣏⣧⣷⠶⡏⠘⠳⠶⢶⣒⢶⠶⠖⠆⠂⠰⠏⢹⡾⡅⠠⠃⠸⠷⠀⠸⠠⢲⠶⠀⠀⠀⠀⠀⢸ ⡟⠾⠶⡃⠋⠛⠶⠀⠀⠘⠟⠶⡾⠅⡸⠑⠲⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⣏⠯⠷⢟⠿⠻⠿⢷⠿⠛⠋⠀⠀⠀⠀⠉⢹⠙⠁⠘⠛⠓⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡿⠿⡟⠃⠓⢛⠃⠀⠀⠈⠃⠀⠱⠆⠗⠚⠂⠘⠞⠒⠒⠚⠐⠐⠶⠆⠻⠺⠰⠐⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡿⠇⠂⠒⠖⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠈⠉⠚⠋⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠉⠐⠘⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⡖⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢈⡈⠀⠀⠀⠀⡀⠀⢀⢀⠀⠀⠀⣀⢀⠀⠐⣂⣀⢠⣀⣀⣀⠀⠀⠀⣀⡀⠀⢀⣀⠠⢔⣊⠓⣆⣀⣀⡀⣀⡀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠈⠛⡋⡒⣀⡻⠛⣃⡀⠘⠛⠛⠓⠄⢀⠘⢉⢃⠘⠚⣃⣠⣞⣛⣑⣂⢙⢛⠙⢹⠛⠛⢻⣀⣛⣛⢃⣳⠊⠛⠛⠘⠛⠛⠙⠛⠓⠛⠳⠏⠛⠛⠊⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠉⠓⠋⠋⠃⠞⠋⠃⠁⡈⠈⠛⠛⠋⠛⠉⠙⠓⠀⠘⠛⠳⠛⠙⠘⠘⠈⠀⠈⠀⠙⠙⠀⠙⠛⠋⠋⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣇⠀⠀⡀⠀⠈⠀⠀⣀⣀⠀⠈⣀⣉⡀⠐⢄⢀⢀⡀⢀⣀⣀⠀⠀⣠⣤⠀⣁⣀⣀⡀⣦⣀⣀⣀⢀⣀⠀⢀⠀⣀⣤⠐⣋⣉⣀⢐⣢⣄⡀⣀⣀⢀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⢉⣭⣭⣤⣽⣿⣧⣤⣬⣧⣭⣧⣦⣬⣿⣽⣥⣬⣭⣥⣤⣽⣿⣥⣤⣽⣝⠙⣻⣉⠙⣻⣍⣉⡈⢀⠑⠀⠛⡋⠘⠛⠙⠙⠛⠛⠉⠋⢃⠉⠉⠙⡀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣟⠀⠀⠘⢛⠛⠻⠿⠟⠛⠛⠛⠻⠿⡿⠛⠛⠻⠿⠟⡛⠛⠻⠿⠟⠛⠛⢻⠿⡏⠀⠉⠉⠀⠋⠉⠉⠙⡉⠁⠀⠀⠀⠀⢀⡀⣀⠀⠀⠘⠀⠀⠀⠈⢈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡗⠀⠀⣀⣀⠀⠀⡀⣀⡀⠀⢀⣀⣄⡀⠀⠀⢀⣀⡀⢀⢀⣀⠀⢀⡀⢠⣀⣀⣀⣀⣰⣠⣄⣀⣀⣀⢀⠀⣀⠀⣠⣤⣄⣤⣀⣀⢰⣤⣄⡀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⢉⡉⣉⣤⡽⢋⣄⣀⡈⢉⣉⣉⣂⣀⣈⣩⣁⡈⠉⢡⣄⡬⣉⣼⢉⢉⢉⠁⢹⠉⢩⢿⠉⣩⣅⣀⣍⢵⠉⠉⠁⠉⠉⠉⠋⠁⠁⠉⠁⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠉⢉⠉⠁⠉⠉⠁⠀⢈⡈⠉⠙⠉⠉⠈⠉⡉⠀⠈⠉⠉⠉⠈⢉⣉⡀⠀⠈⠀⠈⠉⠀⠉⠉⠉⠩⠘⠀⠀⠀⠀⢀⠀⡀⠀⠀⠈⠤⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣀⣀⣀⡀⣀⣄⡄⠀⢀⡤⣥⡄⠁⠄⢠⣤⡀⢠⣠⡀⠀⣀⣤⡤⠈⣡⣬⣤⣦⠀⣠⢠⣤⠁⣄⣤⡄⣤⣤⡤⢈⣡⣬⣁⣠⢤⣤⣤⡄⣤⣥⡀⡄⡤⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⢡⣅⣥⣤⡍⢩⣥⡔⡈⢁⢉⣉⣠⣤⣀⣩⢠⣬⡈⢠⡴⡍⡭⣤⢤⢭⢩⠉⢩⠀⠩⠩⠹⣤⣤⣁⡠⢿⠉⠁⠈⠉⠁⠈⠉⠉⠈⠙⠓⠭⠍⢠⠥⠉⠉⠥⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⢡⠁⠠⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠂⠊⠨⠀⠀⠈⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡏⠀⣀⣄⣀⣀⠀⣀⣤⡄⠀⢠⣤⣤⡍⠁⠄⣠⣤⠀⢠⣠⡄⠀⣤⣤⢤⢠⣁⡁⠈⣤⠀⣤⣤⣤⣤⡤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠐⠃⡤⡤⡶⠺⣤⣤⡄⠀⢉⢭⣥⣶⣠⡌⢠⠦⢤⣤⠀⢹⢉⡠⢴⣠⢡⢠⠀⢰⠄⣨⣽⠃⢶⢠⠀⡄⠀⣤⣦⣄⣔⡏⡄⣄⡤⡆⢀⡄⢀⢄⠄⢠⣤⣄⣤⡄⡄⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠐⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⠀⠐⠒⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣤⣤⣤⠀⢰⢸ ⠷⠤⠤⠤⠠⠤⠠⠤⠤⠤⠤⠄⠄⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠄⠠⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠜ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡬⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠒⠂⠸⢿⠾⠾⠶⠶⠶⠆⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⠀⠀⠐⠒⠒⡄⡤⠐⠒⠒⠂⠀⠈⠉⠉⠉⠉⠉⠹⠿⠿⠿⠿⠿⠿⠾⠽⠶⠆⠀⠀⠀⠀⠀⠒⠀⠀⠉⠉⠉⢩ ⡿⠿⠶⠶⠶⢶⣶⡦⡄⠸⠴⠶⠶⠶⠆⠸⠷⠶⠲⠶⠺⠂⠸⠰⠶⠶⠶⠾⠶⠶⠼⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠷⠶⠶⠇⠷⠶⠶⠄⠀⠀⠀⠀⠀⠀⠸⠿⠷⠾⠾⠷⠨⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡿⠟⠿⠿⠷⠀⠀⠀⠀⠸⠷⠶⠲⠶⠶⠶⠶⠂⠸⠷⠞⠲⠺⠶⠶⠂⠰⠲⠶⠼⠽⠿⠿⠟⠶⠖⠒⠖⠶⠷⠓⠀⡏⣷⠷⠶⠷⠖⠷⠶⠶⠶⡦⠄⠀⠀⠀⠀⠘⠿⠂⠸⠺⠂⠸⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡿⠿⠶⠷⠷⠶⠧⠀⠀⠨⠷⠶⠲⠖⠸⠋⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡿⠷⠖⠷⠗⠐⠳⠶⠶⠶⣶⡶⠶⠆⠀⠰⠇⠸⠿⠃⠠⠃⠸⠿⠂⠸⠃⠺⠿⠃⠀⠀⠀⠀⢸ ⡟⠿⠶⠆⠇⢿⠖⠀⠀⠸⠴⠶⠾⠆⠸⠙⠺⡜⠆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣧⠏⠿⠚⠛⠶⠾⠷⠶⠖⠇⠁⠀⠀⠀⠀⠸⠿⠁⠛⠿⠓⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡗⠿⠷⠖⠷⠟⠃⠀⠀⠀⠃⠐⠷⠟⠛⠓⠂⠘⠚⠛⠛⠛⠘⠛⠲⠆⠶⠲⠖⠞⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡏⠋⠛⠛⠛⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣀⣀⠀⠀⢀⡀⡀⢀⣀⣀⠀⠀⣀⢀⠀⠀⣀⣀⢀⣀⢀⣀⠀⣀⣀⣀⡀⢀⢀⡀⠀⢀⣤⣀⣀⣀⣀⣀⣀⡀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠘⠻⡛⣛⣉⣛⢛⣃⡀⠘⠛⠛⢃⣈⢀⡐⢉⠃⠘⠚⢛⡁⣙⣛⣛⣂⣛⢛⡘⣙⠛⣟⣛⠉⣛⣛⠋⠓⢊⠛⠛⠈⠟⠛⠛⠛⠛⠓⠋⠛⠛⠛⠋⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠃⠋⠋⠋⠘⠛⠛⠃⠘⠘⠛⠛⠋⠘⠙⠘⠁⠀⠘⠛⠃⠓⠚⠚⠚⢈⠀⠙⠀⠛⠙⠀⠛⠛⠉⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⡀⠀⠀⠀⠀⣀⡀⠀⢀⣀⣀⡀⠀⢀⢀⢀⡀⢀⣀⣀⡀⡀⣀⣀⠀⣀⣀⣀⡀⣀⣀⣀⣀⢀⣀⠀⣀⢀⣀⣀⠀⣀⣠⣄⣤⣀⣀⡀⣀⣀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⢻⣯⣭⣥⣯⣯⣧⣤⣬⣯⣭⣥⣤⣴⣿⣭⣥⣬⣿⣽⣥⣽⣿⣿⣤⣽⣿⠙⣍⣉⠹⣿⣟⢛⣋⢉⠓⠃⠙⠛⠈⠛⠛⠙⠉⠛⠙⠋⠓⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠘⠟⠻⠿⠿⠿⠿⠿⠟⠛⠛⠛⠟⠻⠛⠻⠟⠟⠟⠻⠿⠟⠿⠿⠿⠿⠋⠀⠉⠉⠀⠋⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣀⣀⠀⢀⡀⣀⠀⠀⢀⣀⣄⡀⠀⠀⢠⣀⡀⢠⣤⣀⡀⢠⣀⢀⣠⡀⣀⣀⣀⣀⣀⣠⣄⣀⣤⠀⣠⢀⣤⣠⣄⣤⣤⡄⣤⣤⣄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⠋⡍⣍⣤⣭⢉⣀⣀⡈⢉⣉⣁⣈⡀⢈⣈⢁⡉⠉⢩⣀⡈⡉⢹⢽⢯⣩⠅⣭⠉⢭⣿⠉⣩⣭⢀⣩⢅⠉⠉⠁⠓⠋⠉⠋⠁⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠁⠉⠁⠈⠉⠁⠀⠈⠉⠉⠙⠁⠈⠈⠉⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠈⠀⠈⠈⠀⠉⠉⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣄⣀⣀⣀⣀⣄⡄⠀⢠⣤⣤⡄⢀⠄⢠⣦⡀⢠⣤⣤⡄⢤⣤⡠⠀⣤⣤⣤⣤⠀⣤⢠⣤⣀⣤⣤⡤⣶⣤⡄⢠⣦⣄⢠⣤⢤⣤⣤⣄⣤⣤⡀⡤⡤⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠈⠉⡅⣥⣤⣭⢩⣥⡄⡀⢉⢩⣥⣤⡠⢌⣩⣁⡈⠉⢬⣄⡬⡭⢭⢥⢬⢩⠍⢭⠀⡬⠩⠉⣥⣥⣁⣍⢩⠈⠉⠁⠉⠁⠀⠉⠈⠉⠉⠉⠉⠋⠡⠁⠁⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠁⠁⠁⠈⠉⠉⠁⠀⠀⠁⠈⠀⠈⠀⠀⠀⠀⠀⠈⠀⠉⠈⠈⠈⠀⠀⠀⠀⠉⠉⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣤⣄⣀⡀⣀⡄⡄⠀⢠⣤⣤⡆⢠⠀⢠⣤⡄⢠⣠⣦⡄⡤⣤⣀⢠⣀⡀⠀⣄⠀⢤⣤⣤⣤⣤⣤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠉⡧⣶⡦⠰⣾⣦⡄⠀⢠⣤⣤⣤⣤⡎⢠⠀⢠⣴⠄⢠⣀⠈⢩⣨⢨⣤⠀⢠⠀⣤⣼⠉⣭⢤⠀⡄⠀⣄⣖⣄⣤⡆⡦⣤⡄⡄⠀⡄⢀⣄⡄⢠⣤⣄⢤⡄⡄⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠁⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠙⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⡤⣤⠀⢰⢸ ⠧⠤⠤⠤⠤⠤⠤⠄⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠤⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠤⠄⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠁⠈⠀⠉⠉⠈⠁⠈⠉⠁⠉⠀⠁⠈⠀⠀⠹⢿⠿⠿⠿⠿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⡤⡤⠀⠀⠀⠀⠀⠈⠉⠀⠀⠈⠉⠹⠿⠿⠿⠿⠿⠿⠿⠿⠿⠏⠈⠈⠈⠉⠁⠉⠉⠁⠀⠀⠀⢠ ⡿⠿⠶⠧⠶⠶⡶⡦⠄⠸⠆⠶⠶⠶⠆⠸⠷⠶⠲⠶⠶⠄⠰⠶⠶⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡏⠿⠶⠶⠦⠷⠶⠆⠄⠀⠀⠀⠀⠀⠀⠸⠿⠧⠸⠿⠷⠸⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡿⠟⠿⠿⠧⠀⠀⠀⠀⠸⠷⠶⠶⠶⠶⠶⠶⠆⠸⠷⠶⠲⠲⠶⠶⠂⠘⠶⠾⠸⠻⠻⠹⠙⠶⠖⠒⠖⠶⠷⠓⠀⡇⡿⠿⠶⠶⠶⠗⠖⠖⠶⠦⠄⠀⠀⠀⠀⠸⠿⠂⠸⠺⠂⠸⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡿⠿⠖⠷⠷⠶⠷⠀⠀⠨⠷⠶⠲⠆⠸⠳⠶⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡿⠷⠶⠶⠗⠰⠳⠶⠶⠶⠶⠶⠶⠆⠀⠰⠅⠸⠾⠃⠨⠧⠸⠿⠆⠸⠣⠾⠿⠂⠀⠀⠀⠀⢸ ⡟⠟⠶⠖⠇⠿⠶⠀⠀⠘⠶⠶⠾⠇⠸⠳⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡏⠏⠷⠗⠶⠶⠾⠷⠶⠾⠇⠂⠀⠀⠀⠀⠸⠿⠇⠘⠿⠷⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠛⠷⠖⠷⠿⠇⠀⠀⠀⠇⠀⠳⠆⠓⠾⠂⠘⠾⠻⠾⠞⠾⠘⠾⠆⠸⠞⠚⠛⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡗⠟⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡇⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡀⠀⠀⠀⢀⡀⡀⢀⣀⢀⠀⠀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⠀⣀⣀⣀⡀⠀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠛⠛⡛⡛⣙⡛⠛⣃⡀⠘⠛⠛⠃⠘⠀⠐⢙⠃⠙⠛⢛⣀⣛⣛⣓⣀⣛⣛⠙⣙⠛⣛⢛⠀⣛⣛⠃⠓⢊⠛⠋⠈⠛⠛⠛⠛⠛⠓⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠃⠛⠋⠋⠚⠛⠋⠁⠘⠚⠛⠻⠛⠙⠙⠛⠓⠀⠘⠛⠓⠓⠛⠛⠛⠉⠀⠙⠀⠛⠙⠀⠙⠛⠈⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⡀⠀⠀⠀⠀⣀⡀⠀⢀⣀⣀⡀⠀⢀⣀⢀⡀⢀⣀⣀⠀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⠀⣀⢀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⢻⣿⣯⣥⣿⣿⣧⣤⣼⣿⣿⣥⣬⣾⣿⣿⣥⣽⣿⣯⣤⣽⣿⣵⣤⣽⣝⠙⣙⣉⠙⣉⣹⢛⡊⢀⠓⠉⠛⠋⠉⠋⠙⠉⠋⠛⠋⠋⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠋⠀⠉⠉⠀⠉⠉⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢀⣀⣀⠀⢀⡀⣀⠀⠀⢀⣀⣄⡀⢀⠀⢀⣀⡀⢀⣠⣀⠀⢠⣠⣠⣤⣀⣠⣤⣤⣠⣤⣤⣤⣤⢤⢀⣄⢀⣤⣤⣤⣤⣤⣄⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⠉⡍⣉⣁⣍⢋⣄⣀⡈⢉⣉⣁⣈⣀⣈⣉⢁⡈⠉⢩⣄⡬⡉⣭⣭⣩⣩⠁⣩⠉⢭⣉⠉⣭⣅⢀⣉⢡⠉⠉⠁⠁⠉⠉⠉⠁⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠉⠉⠁⠉⠉⠉⠁⠈⠉⠉⠙⠉⠉⠉⠉⠉⠀⠈⠉⠉⠉⠉⠉⠉⠈⠀⠈⠀⠈⠈⠀⠉⠉⠁⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣄⣀⣀⣀⣀⣄⡄⠀⢠⣤⣤⡄⢀⠀⢠⣤⡄⢠⣤⣤⡀⣀⣤⣤⠀⣤⣤⣤⣤⠀⣤⣠⣤⣀⣤⣤⡤⣤⣤⣤⣠⣤⣤⣠⣤⣤⣤⣤⣤⣤⣤⡀⡤⣤⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠉⡍⣍⣤⡍⢩⣥⣄⡈⢉⢉⣁⣀⣁⣈⣩⣁⡈⠉⢩⣤⡬⡭⣭⣤⣬⣭⠉⢩⠀⣩⣭⠉⣤⣭⡁⣩⢩⠈⠉⠀⠉⠁⠀⠉⠉⠉⠉⠁⠉⠉⠉⠁⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠁⠉⠁⠉⠉⠉⠀⠀⠉⠉⠙⠉⠉⠀⠉⠈⠀⠈⠈⠉⠉⠈⠉⠈⠀⠀⠀⠀⠈⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣤⣄⣀⡀⣀⣄⡄⠀⢠⣤⣤⡄⢀⠀⢠⣤⡀⢠⣤⣤⡀⣤⣤⣠⢤⣠⣤⠀⣤⠀⢤⣤⣴⣴⡤⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠁⡥⣥⣤⠨⣽⣤⡄⠀⢩⣭⣥⣠⣤⡄⢨⠀⢠⣨⠀⢠⢀⠀⢠⣤⣤⣤⠀⢠⠀⣤⣴⠀⢤⢠⠀⡄⠀⣄⣤⣤⣄⣄⣄⣤⡄⡄⠀⡄⢀⣄⡄⢠⣤⣄⣤⡄⡄⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⣤⣤⠀⢰⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠄⠤⠤⠤⠤⠤⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢷⠾⠾⠷⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠾⠿⠷⠾⠾⠷⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⡧⠿⠶⠷⠶⠶⡶⡶⠄⠸⠆⠷⠶⠶⠆⠸⠷⠶⠲⠶⠾⠆⠸⠴⠶⠶⠶⠾⠶⠶⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⠀⠀⠀⠀⠸⠿⠇⠸⠿⠧⠸⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠟⠿⠿⠇⠀⠀⠀⠀⠸⠷⠶⠲⠶⠶⠶⠶⠆⠸⠷⠶⠶⠺⠶⠶⠂⠸⠶⠺⠸⠹⠻⠽⠙⠶⠖⠒⠶⠶⠷⠕⠀⣿⡿⠿⠶⠶⠆⠷⠖⠗⠶⡆⠀⠀⠀⠀⠀⠸⠿⠇⠸⠺⠂⠸⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠻⠖⠿⠷⠶⠇⠃⠀⠸⠷⠶⠲⠆⠸⠳⠾⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠷⠶⠶⠗⠰⠷⠶⠶⠲⠶⠶⠶⠆⠀⠸⠇⠼⠿⠃⠸⠧⠼⠿⠂⠸⠣⠿⠿⠀⠀⠀⠀⠀⢸ ⡟⠟⠶⠆⠇⠿⠶⠀⠀⠸⠷⠶⠞⠇⠸⠳⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠏⠷⠖⠶⠶⠾⠷⠶⠞⠇⠀⠀⠀⠀⠀⠸⠿⠇⠸⠿⠗⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡗⠛⠛⠒⠓⠓⠃⠁⠀⠀⠃⠘⠻⠗⠛⠚⠃⠘⠚⠛⠚⠛⠚⠘⠿⠆⠾⠚⠚⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠟⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡇⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⢀⣀⡀⢀⣀⣀⠀⠀⣀⣀⠀⣀⣀⣀⢀⣀⣀⣀⠀⣀⣀⣀⡀⠀⣀⣀⠀⣀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠙⠛⡛⡛⣉⡛⢛⣃⡀⠘⠛⠛⠃⠈⢂⡘⢉⠃⠙⠛⢛⣁⣛⣛⣓⣀⣛⢛⠛⢙⠛⡛⢛⠉⣛⣛⠋⠓⢊⠛⠛⠈⠛⠛⠛⠛⠓⠓⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠃⠋⠛⠋⠚⠛⠓⠃⠘⠛⠛⠻⠛⠛⠙⠛⠑⠀⠘⠛⠓⠓⠛⠛⠛⠘⠀⠘⠀⠛⠙⠀⠛⠛⠈⠛⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣀⠀⠀⠀⠀⣀⡀⠀⢀⣀⣀⡀⢀⣀⣀⢀⡀⢀⣀⣀⠀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⠀⣀⢀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⢻⣯⣯⣭⣿⣿⣧⣤⣬⣯⣿⣥⣬⣼⣿⣿⣥⣽⣿⣭⣥⣽⣿⣽⣤⣽⣟⠙⣛⣙⠙⣛⣛⢛⣛⢁⠓⠉⠛⠋⠉⠛⠙⠉⠉⠛⠋⠋⠃⠋⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠋⠀⠉⠉⠀⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢀⣀⣀⣀⣀⣀⣄⡀⠀⢀⣠⣄⡀⢀⠀⢠⣤⡀⢠⣤⣀⡀⢠⣠⢤⣤⣀⣠⣠⣠⣀⣤⣤⣤⣤⣤⠀⣀⢀⣤⣠⣄⣤⣠⣀⣤⣤⣄⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⠉⡍⣉⣅⣍⢉⣅⣄⡈⢉⣉⣁⣈⣁⣈⣩⣁⡈⠉⢩⣄⡬⡩⣩⢩⣩⢩⠉⢩⠉⢩⣩⠉⣭⣥⢀⣉⢁⠉⠉⠁⠉⠉⠉⠋⠁⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠉⠉⠁⠉⠉⠉⠁⠈⠉⠉⠙⠉⠉⠉⠉⠉⠀⠈⠉⠉⠉⠉⠉⠉⠈⠀⠈⠀⠉⠉⠀⠉⠉⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣤⣀⣀⣀⣀⣄⡄⠀⢠⣤⣤⡄⢀⠄⢠⣤⡄⣠⣤⣤⡀⣤⣤⡤⠀⣤⣤⣤⣤⠀⣤⣠⣤⣀⣤⣤⡤⣤⣄⣄⣠⣤⣄⣠⣤⢤⣤⣤⣤⣤⣤⡄⡤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠉⡍⣍⣤⣍⢩⣥⣤⡈⢉⣉⣁⣀⣠⣌⣩⣁⡈⠉⢩⣤⡬⡭⣭⣤⣭⣩⠉⢩⠀⣩⣭⠉⣤⣭⠉⣉⢩⠉⠉⠀⠉⠁⠀⠉⠉⠉⠉⠁⠉⠉⠉⠉⠁⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠁⠁⠁⠁⠁⠁⠀⠈⠉⠉⠉⠉⠈⠈⠉⠈⠀⠈⠈⠈⠈⠉⠉⠉⠈⠀⠈⠀⠉⠉⠀⠈⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣠⣤⣤⣀⣠⣄⣤⡄⠀⢠⣤⣤⡄⢠⡄⢠⣤⡄⢠⣤⣤⡀⣤⣤⣠⢤⣠⣤⠀⣤⠀⢤⣤⣤⣤⡤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡤⣤⣦⠠⣦⣤⡄⡀⢠⣤⣤⣤⣤⡄⢠⡄⢠⣤⠀⢠⢀⠀⣤⣠⣠⣤⠀⢠⠀⣤⣤⠀⣤⢠⠀⡄⠀⣤⣤⣤⣤⣄⣄⣤⡄⡄⠀⡄⢀⣆⡄⢰⣤⣄⢤⡄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⡤⣤⠀⢰⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢷⠾⠾⠷⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠾⠿⠷⠾⠾⠵⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⡧⠿⠶⠷⠶⠶⠶⡶⠆⠸⠆⠷⠶⠶⠆⠸⠷⠶⠲⠶⠾⠆⠸⠴⠶⠶⠶⠾⠶⠶⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⠀⠀⠀⠀⠸⠿⠇⠸⠿⠧⠸⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠟⠿⠻⠇⠀⠀⠀⠀⠸⠷⠶⠲⠶⠶⠶⠶⠆⠸⠷⠶⠲⠺⠶⠶⠂⠸⠶⠺⠸⠻⠻⠿⠙⠶⠖⠒⠶⠶⠷⠑⠀⣿⡿⠿⠶⠶⠆⠷⠖⠗⠶⡆⠀⠀⠀⠀⠀⠸⠿⠇⠸⠿⠂⠸⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠻⠖⠿⠷⠶⠇⠁⠀⠸⠷⠶⠲⠆⠸⠓⠾⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠷⠶⠶⠗⠰⠳⠶⠶⠲⠶⠶⠶⠆⠀⠸⠇⠼⠿⠃⠸⠧⠼⠿⠂⠸⠣⠿⠿⠀⠀⠀⠀⠀⢸ ⡟⠟⠶⠆⠇⠿⠶⠀⠀⠸⠷⠶⠞⠇⠸⠳⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠏⠷⠖⠶⠶⠾⠷⠶⠞⠇⠀⠀⠀⠀⠀⠸⠿⠅⠘⠿⠗⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠛⠛⠒⠓⠓⠇⠁⠀⠀⠃⠘⠻⠗⠛⠚⠃⠘⠚⠛⠚⠛⠚⠘⠿⠆⠾⠚⠚⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠟⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡇⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⢀⣀⡀⢀⣀⣀⠀⠀⣀⣀⠀⣀⣀⣀⢀⣀⣀⣀⠀⣀⣀⣀⡀⠀⣀⡀⠀⣀⣀⡀⣀⣀⣀⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠙⠛⡛⡛⣙⡛⢛⣃⡀⠘⠛⠛⠃⠈⢂⠘⢉⠃⠙⠛⢛⣁⣛⣛⣛⣀⣛⢛⠛⢙⠛⡛⢛⠉⣛⣛⠋⠓⣋⠛⠛⠈⠛⠛⠛⠛⠛⠓⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠃⠋⠛⠋⠚⠛⠛⠃⠘⠛⠛⠻⠛⠛⠙⠛⠑⠀⠘⠛⠓⠓⠛⠚⠛⠙⠀⠘⠀⠛⠙⠀⠛⠛⠊⠛⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣀⠀⠀⠀⠀⣀⡀⠀⢀⣀⣀⡀⢀⣀⣀⢀⡀⢀⣀⣀⠀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⠀⣀⢀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⢻⣯⣯⣭⣿⣿⣧⣤⣬⣯⣿⣥⣬⣽⣿⣿⣥⣽⣿⣭⣥⣽⣿⣽⣤⣽⣟⠙⣛⣙⠙⣛⣛⢛⣛⢁⠓⠉⠛⠋⠉⠛⠙⠉⠛⠛⠋⠋⠃⠋⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠋⠀⠉⠉⠀⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢀⣀⣀⣀⣀⣀⣄⡀⠀⢀⣠⣄⡀⢀⠀⢠⣤⡀⢠⣠⣀⡀⢠⣠⢠⣤⣄⣠⣠⣠⣀⣄⣤⣤⣤⣤⢀⣀⢀⣤⣠⣄⣤⣠⣀⣤⣤⣄⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⠉⡍⣍⣅⣍⢉⣅⣄⡈⢉⣉⣁⣈⣁⣈⣩⣁⡈⠉⢩⣄⡬⡩⣭⢭⣩⢩⠉⢩⠉⢩⣩⠉⣭⣭⢀⣉⢁⠉⠉⠁⠉⠉⠉⠋⠁⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠉⠉⠁⠉⠉⠉⠁⠈⠉⠉⠙⠉⠉⠉⠉⠈⠀⠈⠉⠉⠉⠉⠉⠉⠈⠀⠈⠀⠉⠉⠀⠉⠉⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣄⣀⣀⣀⣀⣄⡄⠀⢠⣤⣤⡄⢀⠄⢠⣤⡄⣠⣤⣤⡀⣤⣤⡤⠀⣤⣤⣤⣤⠀⣤⣠⣤⣀⣤⣤⡤⣤⣄⣄⣠⣤⣄⣠⣤⢤⣤⣤⣤⣤⣤⡄⡤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠉⡍⣭⣤⣍⢩⣥⣄⡈⢉⣉⣁⣀⣠⣌⣩⣁⡈⠉⢩⣤⡬⡭⣭⣤⣭⢭⠉⢩⠀⣩⣭⠉⣤⣭⣉⣉⢩⠉⠉⠀⠉⠁⠀⠉⠉⠉⠉⠁⠉⠉⠉⠉⠁⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠁⠁⠁⠁⠁⠁⠁⠈⠉⠉⠉⠁⠈⠈⠉⠈⠀⠈⠉⠈⠈⠉⠉⠉⠈⠀⠈⠀⠉⠉⠀⠈⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣠⣤⣤⣀⡠⣄⣤⡄⠀⢠⣤⣤⡄⢠⠄⢠⣤⡄⢠⣤⣤⡀⣤⣤⣠⢤⣠⣤⠀⣤⠀⢤⣤⣤⣤⡤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡤⣤⣤⠠⣤⣤⡄⡀⢠⣤⣤⣤⣤⡄⢠⡄⢠⣤⠀⢠⢀⠀⣠⣠⣠⣤⠀⢠⠀⣤⣤⠀⣤⢠⠀⡄⠀⣄⣤⣤⣤⣄⣄⣤⡄⡄⠀⡄⢀⣄⡄⢠⣤⣄⢤⡄⡄⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⡤⣤⠀⢰⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢷⠾⠾⠷⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣤⡤⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠾⠿⠷⠾⠾⠴⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⡇⠿⠶⠷⠶⠶⠶⡶⠆⠸⠆⠷⠶⠶⠆⠸⠷⠶⠲⠶⠾⠆⠸⠴⠶⠶⠶⠾⠶⠶⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡿⠷⠶⠶⠇⠷⠶⠆⠄⠀⠀⠀⠀⠀⠀⠸⠿⠇⠸⠟⠧⠸⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠟⠿⠻⠧⠀⠀⠀⠀⠸⠷⠶⠲⠶⠶⠶⠶⠆⠸⠷⠶⠰⠺⠶⠶⠂⠸⠴⠺⠸⠻⠻⠿⠙⠶⠖⠒⠶⠶⠷⠐⠀⡧⡿⠿⠶⠶⠆⠗⠆⠗⠶⡆⠀⠀⠀⠀⠀⠸⠿⠇⠸⠿⠇⠺⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠻⠖⠿⠷⠶⠇⠃⠀⠸⠷⠶⠲⠆⠸⠓⠾⠾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡿⠷⠶⠶⠗⠸⠳⠶⠶⠲⠶⠶⠶⠆⠀⠸⠇⠸⠞⠁⠸⠧⠼⠿⠂⠸⠣⠷⠿⠀⠀⠀⠀⠀⢸ ⡟⠟⠶⠆⠇⠿⠶⠀⠀⠸⠷⠶⠞⠇⠸⠳⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡏⠟⠷⠖⠶⠶⠾⠷⠶⠞⠇⠀⠀⠀⠀⠀⠸⠽⠅⠘⠿⠗⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠛⠛⠒⠓⠓⠇⠁⠀⠀⠃⠐⠻⠗⠓⠚⠃⠘⠚⠛⠚⠛⠚⠘⠿⠆⠾⠚⠚⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡿⠟⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡇⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⢀⣀⡀⢀⣀⣀⠀⢀⣀⣀⠀⡀⣀⣀⢀⣀⢀⣀⠀⣀⣀⣀⡀⠀⣀⡀⠀⣀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠙⠛⡛⡛⣙⡛⠛⣃⡀⠘⠛⠛⠃⠈⢂⡐⢉⠃⠙⠛⢛⣀⣛⣛⣛⣀⣛⢛⠛⢙⠛⣛⢛⠁⣛⣛⠃⠓⣋⠛⠛⠈⠛⠛⠛⠛⠛⠓⠃⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠃⠋⠛⠋⠚⠛⠛⠃⠘⠘⠛⠻⠋⠛⠛⠛⠑⠀⠘⠛⠃⠓⠛⠚⠛⠘⠀⠙⠀⠛⠙⠀⠛⠛⠋⠛⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣀⠀⠀⠀⠀⣀⡀⠀⢀⣀⣀⡀⢀⣀⣀⢀⡀⢀⣀⣀⠀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⠀⣀⢀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⢻⣿⣯⣭⣿⣿⣧⣤⣬⣥⣿⣧⣬⣽⣿⣿⣥⣽⣿⣭⣤⣽⣿⣽⣤⣽⣟⠙⣛⣙⠙⣙⣛⢛⡛⢁⠓⠉⠛⠋⠉⠛⠙⠙⠛⠛⠋⠋⠃⠋⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠋⠀⠉⠉⠀⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢀⣀⣀⣀⣀⣀⣄⡀⠀⢀⣠⣄⡀⢀⠀⢠⣤⡀⢠⣠⣀⡀⢠⣠⢠⣤⣄⣠⣠⣀⣀⣄⣤⣤⣤⣤⢀⣀⢀⣤⣠⣄⣤⣀⣀⣤⣤⣄⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⠉⡍⣍⣅⣍⢉⣄⣄⡈⢉⢉⣁⣈⣡⣈⣉⣁⡈⠉⢩⣄⡬⡩⣭⣭⣭⢩⠉⢩⠉⢩⣩⠉⣭⣭⢀⣉⢡⠉⠉⠁⠉⠉⠉⠋⠁⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠉⠉⠁⠈⠉⠉⠁⠈⠉⠉⠙⠉⠉⠉⠉⠈⠀⠈⠉⠉⠉⠉⠉⠉⠈⠀⠈⠀⠈⠉⠀⠉⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣄⣀⣀⣀⣀⣄⡄⠀⢠⣤⣤⡄⢀⠄⢠⣤⡄⢠⣤⣤⡀⣤⣤⡤⠀⣤⣤⣤⣤⠀⣤⣠⣤⣀⣤⣤⡤⣤⣤⣄⣠⣤⣄⣠⣤⢤⣤⣤⣤⣤⣤⡠⡤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠉⡍⣭⣤⣍⢩⣥⣤⡈⢉⣍⣁⣀⣀⣈⣩⣁⡈⠉⢩⣤⡬⣭⣭⢤⣭⢭⠉⣩⠀⣭⣩⠉⣤⣭⣉⣉⢩⠉⠉⠁⠉⠁⠈⠉⠉⠉⠉⠁⠉⠉⠉⠉⠁⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠁⠁⠁⠁⠁⠉⠁⠈⠉⠉⠉⠁⠈⠉⠉⠈⠀⠈⠉⠉⠈⠉⠉⠈⠀⠀⠈⠀⠉⠉⠀⠉⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣠⣤⣤⣀⡠⣄⣤⡄⠀⢠⣤⣤⡄⢠⠄⢠⣤⡄⢠⣤⣤⡀⣤⣤⣠⢤⣠⣤⠀⣤⠀⢤⣤⣤⣤⡤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡤⣤⡤⠠⣤⣤⡄⡀⢠⢤⣤⣤⣤⡄⢠⡄⢠⣤⠀⢠⢀⠀⣠⣠⣠⣤⠀⢠⠀⣤⣤⠀⣤⢠⠀⡄⠀⣄⣤⣤⣤⣄⣤⣤⡄⡄⠀⡄⢀⣄⡄⢠⣦⣄⢤⡄⡄⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⡤⣤⠀⢰⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢷⠾⠾⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠈⠀⠀⠀⣤⡭⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠾⠿⠷⠶⠾⠴⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⡧⠿⠶⠷⠶⠶⡶⡶⠄⠸⠆⠷⠶⠶⠆⠸⠷⠶⠲⠶⠾⠆⠸⠴⠶⠶⠶⠾⠶⠶⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⠀⠀⠀⠀⠸⠿⠇⠸⠟⠧⠘⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠏⠿⠻⠧⠀⠀⠀⠀⠸⠷⠶⠲⠶⠶⠶⠶⠆⠸⠷⠶⠲⠲⠶⠶⠂⠸⠶⠲⠸⠹⠻⠿⠙⠶⠖⠒⠶⠶⠷⠐⠀⡧⡿⠿⠶⠶⠆⠗⠖⠖⠶⡆⠀⠀⠀⠀⠀⠸⠿⠇⠸⠿⠇⠺⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠻⠖⠯⠷⠶⠇⠂⠀⠨⠷⠶⠲⠆⠸⠓⠾⠾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡿⠷⠶⠶⠟⠸⠳⠶⠶⠲⠶⠶⠶⠆⠀⠸⠇⠼⠿⠃⠸⠧⠸⠿⠂⠸⠣⠷⠿⠀⠀⠀⠀⠀⢸ ⡟⠟⠶⠆⠇⠿⠴⠀⠀⠸⠷⠶⠞⠇⠸⠳⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡏⠏⠷⠖⠶⠶⠾⠷⠶⠞⠇⠀⠀⠀⠀⠀⠸⠽⠅⠘⠿⠗⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠛⠛⠒⠓⠓⠇⠁⠀⠀⠇⠐⠻⠗⠛⠚⠃⠘⠚⠚⠛⠛⠚⠘⠿⠆⠾⠚⠚⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡿⠟⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡇⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⢀⣀⡀⢀⣀⣀⠀⠀⣀⣀⠀⡀⣀⣀⢀⣀⢀⣀⠀⣀⣀⣀⡀⠀⣀⡀⠀⣀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠙⠛⡛⡛⣙⡛⢛⣃⡀⠘⠛⠛⠃⠈⠂⠐⢉⠃⠙⠛⢛⣀⣛⣛⣛⣀⣛⣛⠛⢙⠛⡛⢛⠁⣛⣛⠃⠓⣋⠛⠛⠉⠛⠛⠛⠛⠛⠓⠃⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠃⠋⠛⠋⠚⠛⠛⠃⠘⠛⠛⠻⠛⠛⠛⠛⠑⠀⠘⠛⠛⠛⠛⠚⠛⠘⠀⠘⠀⠛⠙⠀⠛⠛⠋⠛⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣀⠀⠀⠀⠀⣀⡀⠀⢀⣀⣀⡀⢀⣀⣀⢀⡀⢀⣀⣀⠀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⠀⣀⢀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⢫⣿⣯⣭⣿⣿⣧⣤⣬⣥⣯⣥⣬⣼⣬⣿⣥⣽⣿⣭⣥⣽⣿⣽⣤⣽⣟⠙⣛⣙⠙⣙⣛⢛⡛⢁⠓⠉⠛⠋⠉⠛⠙⠙⠛⠛⠋⠋⠃⠋⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠋⠀⠉⠉⠀⠉⠉⠉⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢀⣀⣀⡀⣀⣀⣄⡀⠀⢀⣠⣄⡀⢀⠀⢠⣤⡀⢠⣠⣀⡀⢠⣠⢠⣤⣄⣠⣀⣠⣀⣄⣤⣤⣤⣤⢀⣀⢀⣤⣠⣄⣤⣀⣀⣤⣤⣄⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⠉⡉⣍⣅⣍⢩⣄⣄⡈⢉⢉⣁⣈⣡⣈⣉⣁⡈⠉⢩⣄⣬⡭⣭⢭⣭⢩⠉⢉⠉⢭⣉⠉⣭⣥⢀⣉⢡⠉⠉⠁⠉⠉⠉⠉⠁⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠉⠉⠁⠉⠉⠉⠁⠈⠉⠉⠙⠉⠉⠉⠉⠉⠀⠈⠉⠉⠉⠉⠉⠉⠈⠀⠈⠀⠈⠉⠀⠉⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣄⣀⣀⣀⣀⣄⡄⠀⢠⣤⣤⡄⢀⠄⢠⣤⡄⢠⣤⣤⡀⣤⣤⡤⠀⣤⣤⣤⣤⠀⣤⣠⣤⣀⣤⣤⡤⣤⣤⣄⣠⣤⣄⣠⣠⢤⣤⣤⣤⣤⣤⡄⡤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠉⡍⣭⣤⣍⢩⣥⣤⡌⢉⢍⣁⣀⣠⣨⣩⣁⡈⠉⢩⣤⡬⡭⣭⢤⢭⢩⠉⢩⠀⣩⣭⠉⣤⣭⣩⣉⣭⠉⠉⠁⠉⠁⠈⠉⠉⠈⠉⠁⠉⠉⠁⠉⠁⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠁⠁⠁⠁⠁⠉⠁⠀⠉⠉⠉⠁⠉⠉⠉⠉⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠈⠀⠉⠉⠀⠉⠉⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣠⣤⣤⣀⡠⣄⣄⡄⠀⢠⣤⣤⡄⢠⠄⢠⣤⡄⢠⣤⣤⡄⣤⣤⣠⢤⣠⣤⠀⣤⠀⢤⣤⣤⣤⡤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠁⡤⣤⣦⠠⣦⣤⡄⡀⢠⢤⣤⣤⣤⡄⢠⡄⢠⣤⠀⢠⢀⠀⣠⣤⣠⣤⠀⢠⠀⣤⣤⠀⣤⢠⠀⡄⠀⣄⣤⣠⣤⣤⣄⣤⡄⡄⠀⡄⢀⣄⡄⢠⣦⣄⢤⡄⡄⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⡤⣤⠀⢰⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢷⠾⠾⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠈⠀⠀⠀⣤⡬⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠀⠸⠿⠷⠾⠿⠷⠶⠾⠴⠾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⡯⠿⠶⠷⠶⠶⡶⡶⠄⠸⠆⠷⠶⠶⠆⠸⠷⠶⠲⠶⠾⠀⠸⠶⠶⠶⠶⠾⠶⠶⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⠀⠀⠀⠀⠸⠿⠇⠘⠟⠧⠸⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠏⠿⠻⠧⠀⠀⠀⠀⠸⠷⠶⠲⠶⠶⠶⠶⠆⠸⠷⠶⠲⠺⠶⠶⠂⠸⠶⠾⠸⠹⠻⠿⠙⠶⠖⠒⠶⠶⠧⠑⠀⣷⡿⠷⠶⠶⠆⠗⠖⠆⠶⡆⠀⠀⠀⠀⠀⠸⠿⠇⠺⠿⠇⠺⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠻⠖⠧⠷⠶⠧⠂⠀⠨⠗⠶⠲⠆⠸⠓⠾⠾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠷⠶⠶⠏⠸⠳⠶⠶⠒⠶⠶⠶⠆⠀⠸⠇⠼⠞⠁⠸⠧⠸⠿⠂⠸⠣⠷⠿⠀⠀⠀⠀⠀⢸ ⡟⠟⠶⠆⠇⠿⠶⠀⠀⠸⠷⠶⠞⠇⠸⠳⠒⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⠏⠷⠖⠶⠶⠾⠷⠶⠞⠇⠀⠀⠀⠀⠀⠸⠽⠅⠘⠿⠗⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠛⠛⠒⠓⠛⠇⠁⠀⠀⠃⠘⠳⠗⠗⠚⠂⠘⠚⠚⠛⠛⠚⠘⠿⠆⠾⠚⠚⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⠟⠛⠛⠟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⡆⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⢲ ⡇⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⢀⣀⡀⢀⣀⣀⠀⠀⣀⣀⠀⣀⣀⣀⢀⣀⢀⣀⠀⣀⣀⣀⡀⠀⣀⡀⠀⣀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠙⠛⡛⡛⣉⡛⢛⣃⡀⠘⠛⠛⠃⠈⢂⠐⢉⠃⠙⠛⢛⣀⣛⣛⣛⣀⣛⣛⠛⢙⠛⡛⢛⠁⣛⣛⠃⠓⣊⠛⠛⠉⠛⠛⠛⠛⠓⠓⠃⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠃⠋⠛⠋⠊⠛⠛⠃⠘⠛⠛⠻⠛⠛⠛⠛⠑⠀⠘⠛⠛⠛⠚⠚⠛⠘⠀⠙⠀⠛⠙⠀⠛⠛⠋⠛⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣀⠀⠀⠀⠀⣀⡀⠀⢀⣀⣀⡀⢀⣀⣀⢀⡀⢀⣀⣀⠀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⠀⣀⢀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⢫⣯⣯⣭⣿⣿⣧⣤⣬⣭⣯⣥⣬⣼⣬⣽⣥⣽⣿⣭⣥⣽⣿⣽⣤⣽⣟⠙⣛⣙⠙⣙⣛⢛⡛⢁⠓⠉⠛⠋⠉⠛⠙⠉⠙⠛⠉⠋⠃⠋⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠋⠀⠉⠉⠀⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢀⣄⣀⡀⣀⣀⣀⡀⠀⢀⣠⣄⡀⢀⠀⢠⣤⡀⢠⣠⣀⡀⢠⣠⢠⣤⣄⣠⣀⣠⣀⣤⣤⣤⣠⣤⢀⣀⢀⣠⣠⣄⣄⣠⣄⣤⣤⣄⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⠉⡍⣍⣅⣍⢉⣤⣄⡈⢉⢉⣁⣈⣁⣈⣉⣁⡈⠉⢩⣄⣬⡩⣭⢭⢭⢩⠉⢉⠉⢩⣉⠉⣭⣅⢀⣉⣡⠉⠉⠁⠉⠉⠉⠉⠁⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠉⠉⠁⠉⠉⠉⠁⠈⠉⠉⠙⠉⠉⠉⠉⠉⠀⠈⠉⠉⠉⠉⠉⠉⠈⠀⠈⠀⠈⠈⠀⠉⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣄⣀⣀⣀⣀⣄⡄⠀⢠⣤⣤⡄⢀⠀⢠⣤⡄⢠⣤⣤⡀⣤⣤⡤⠀⣤⣤⣤⣤⠀⣤⢠⣤⣀⣤⣤⡤⣤⣄⣄⣠⣤⣄⣠⣠⢤⣤⣤⣤⣤⣤⡀⡤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠉⡅⣍⣤⣍⢩⣥⣤⡌⢉⢉⣁⣄⣀⣈⣩⣁⡈⠉⢩⣤⡬⡭⣭⢤⣭⢭⠉⣩⠀⣩⣭⠉⣤⣭⡉⣉⢭⠉⠉⠁⠉⠁⠈⠉⠉⠈⠉⠁⠉⠉⠁⠉⠁⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠁⠁⠁⠀⠀⠁⠁⠀⠉⠉⠙⠉⠈⠈⠉⠈⠀⠈⠉⠉⠈⠉⠉⠀⠈⠀⠈⠀⠉⠉⠀⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣤⣤⣀⡠⣄⣤⡄⠀⢠⣤⣤⡄⢠⠀⢠⣤⡀⢠⣤⣤⡄⣤⣤⣠⢤⣠⣤⠀⣤⠀⢤⣤⣤⣤⡤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡤⣦⣦⠠⣦⣤⡄⡀⢠⢤⣤⣤⣤⡄⢠⡄⢠⣤⠀⢠⢀⠀⣠⣤⣠⣤⠀⢠⠀⣤⣤⠀⣤⢠⠀⡄⠀⣄⣄⣤⣤⣄⣄⣤⡄⡄⠀⡄⢀⣄⡄⢠⣦⣄⢤⡄⡄⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⡤⣤⠀⢰⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢷⠾⠾⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠈⠀⠀⠀⣤⡬⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠀⠸⠿⠷⠾⠿⠷⠶⠾⠴⠾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⡯⠿⠶⠷⠶⠶⡶⡶⠄⠸⠆⠷⠶⠶⠆⠸⠷⠶⠲⠶⠾⠀⠸⠶⠶⠶⠶⠾⠶⠶⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⠀⠀⠀⠀⠸⠿⠇⠘⠟⠧⠸⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠏⠿⠻⠧⠀⠀⠀⠀⠸⠷⠶⠲⠶⠶⠶⠶⠆⠸⠷⠶⠲⠺⠶⠶⠂⠸⠶⠾⠸⠻⠻⠿⠙⠶⠖⠒⠶⠶⠧⠑⠀⠀⣿⠿⠷⠶⠆⠗⠖⠆⠶⡆⠀⠀⠀⠀⠀⠸⠿⠇⠺⠿⠇⠲⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠻⠖⠧⠷⠶⠧⠂⠀⠨⠗⠶⠲⠆⠸⠓⠾⠾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣗⠶⠶⠏⠸⠳⠶⠶⠒⠶⠶⠶⠆⠀⠸⠇⠼⠞⠁⠸⠦⠸⠿⠂⠶⠣⠷⠿⠀⠀⠀⠀⠀⢸ ⡟⠟⠶⠆⠇⠿⠶⠀⠀⠸⠷⠶⠞⠇⠸⠳⠒⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣮⣿⠷⠖⠶⠶⠾⠷⠶⠞⠇⠀⠀⠀⠀⠀⠸⠽⠍⠘⠿⠟⠱⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠛⠛⠒⠓⠛⠇⠁⠀⠀⠧⠘⠻⠗⠗⠚⠂⠘⠚⠚⠛⠛⠚⠚⠿⠆⠾⠚⠚⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠛⠛⠛⠟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⡆⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⢲ ⡇⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⢀⣀⡀⢀⣀⣀⠀⠀⣀⣀⠀⣀⣀⣀⢀⣀⢀⣀⠀⣀⣀⣀⡀⠀⣀⡀⠀⣀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠙⠛⡛⡛⣉⡛⢛⣃⡀⠘⠛⠛⠋⠈⢂⠐⢉⠃⠙⠛⢛⣀⣛⣛⣛⣀⣛⣛⠛⢙⠛⡛⢛⠁⣛⣛⠃⠓⣋⠛⠛⠉⠛⠛⠛⠛⠓⠓⠃⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠃⠋⠛⠋⠊⠛⠛⠃⠘⠛⠛⠻⠛⠛⠛⠛⠑⠀⠘⠛⠛⠛⠚⠚⠛⠘⠀⠙⠀⠛⠙⠀⠛⠛⠋⠛⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣀⠀⠀⠀⠀⣀⡀⠀⢀⣀⣀⡀⢀⣀⣀⢀⡀⢀⣀⣀⠀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⢀⣀⠀⢀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⢫⣯⣯⣭⣿⣿⣧⣤⣬⣭⣯⣧⣬⣼⣬⣽⣥⣽⣿⣭⣥⣽⣿⣽⣤⣽⣟⠙⣛⣙⠙⣙⣛⢛⡋⢀⠓⠉⠛⠋⠉⠛⠙⠉⠙⠛⠉⠋⠃⠋⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠿⠿⠿⠿⠿⠿⠿⠿⠋⠀⠉⠉⠀⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢀⣄⣀⡀⣀⣀⣀⡀⠀⢀⣠⣄⡀⢀⡀⢠⣤⡀⢠⣠⣀⡀⢠⣠⢠⣤⡀⣠⣀⣠⣀⣤⣠⣤⣠⣤⢀⣀⢀⣠⣠⣄⣄⣠⣄⣤⣤⣄⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⠉⡍⣍⣅⣍⢉⣤⣄⡈⢉⢉⣁⣈⣁⣈⣉⣁⡈⠉⢩⣄⣬⡩⣭⢭⢭⢩⠉⢉⠉⢩⣉⠉⣭⣅⢀⣉⣡⠉⠉⠁⠁⠉⠉⠉⠁⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠉⠉⠁⠉⠉⠉⠁⠈⠉⠉⠙⠉⠉⠉⠉⠉⠀⠈⠉⠉⠉⠉⠉⠉⠈⠀⠈⠀⠈⠈⠀⠉⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣄⣀⣀⣀⣀⣄⡄⠀⢠⣤⣤⡄⢀⠀⢠⣤⡄⢠⣤⣤⡀⣤⣤⡤⠀⣤⣤⣤⣤⠀⣤⣠⣤⣀⣤⣤⡤⣤⣄⣄⣠⣤⣄⣠⣠⢤⣤⣤⣤⣤⣤⡀⡤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠉⡅⣍⣤⣍⢩⣥⣤⡌⢉⢉⣁⣄⣁⣈⣩⣁⡈⠉⢩⣤⡬⡭⣭⢤⣭⢭⠉⣩⠀⣩⣭⠉⣤⣭⡉⣉⢭⠉⠉⠁⠉⠁⠈⠉⠉⠈⠉⠁⠉⠉⠁⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠁⠁⠁⠀⠀⠁⠁⠀⠉⠉⠙⠉⠈⠈⠉⠈⠀⠈⠉⠉⠈⠉⠉⠀⠈⠀⠈⠀⠉⠉⠀⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣤⣤⣀⡠⣄⣤⡄⠀⢠⣤⣤⡄⢠⠀⢠⣤⡀⢠⣤⣤⡄⣤⣤⣠⢤⣠⣤⠀⣤⠀⢤⣤⣤⣤⡤⣤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡤⣦⣦⠠⣦⣄⡄⡀⢠⢤⣤⣤⣤⡄⢠⡄⢠⣤⠀⢠⢀⠀⣠⣤⣠⣤⠀⢠⠀⣤⣤⠀⣤⢠⠀⡄⠀⣄⣄⣤⣤⣄⣄⣤⡄⡄⠀⡄⢀⣄⡄⢠⣦⣄⢤⡄⡄⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⡤⣤⠀⢰⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢷⠾⠾⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠈⠀⠀⠀⣤⣌⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠸⠿⠷⠾⠿⠴⠶⠾⠴⠾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡ ⡯⠿⠶⠷⠶⠶⡶⡶⠄⠸⠆⠷⠶⠶⠆⠸⠷⠶⠲⠶⠾⠃⠰⠲⠶⠶⠶⠾⠶⠶⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⠀⠀⠀⠀⠸⠿⠇⠘⠟⠧⠸⠿⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠏⠿⠻⠧⠀⠀⠀⠀⠸⠷⠶⠲⠶⠶⠶⠶⠆⠸⠷⠶⠲⠺⠶⠶⠂⠸⠶⠶⠹⠿⠛⠿⠙⠶⠖⠒⠶⠶⠧⠑⠀⠀⣿⠿⠷⠶⠆⠗⠖⠆⠶⡆⠀⠀⠀⠀⠀⠸⠿⠗⠺⠿⠇⠲⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠻⠖⠧⠷⠶⠧⠂⠀⠨⠗⠶⠲⠆⠸⠓⠾⠾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⡗⠶⠶⠏⠸⠳⠶⠶⠒⠶⠶⠶⠆⠀⠸⠇⠼⠞⠓⠻⠦⠸⠿⠾⠂⠠⠂⠿⠶⠆⠀⠀⠀⢸ ⡟⠟⠶⠆⠇⠿⠔⠀⠀⠸⠷⠶⠞⠇⠸⠳⠒⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠷⠶⠶⠶⠾⠷⠶⠞⠇⠀⠀⠀⠀⠀⠸⠽⠍⠘⠿⠟⠱⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠛⠛⠒⠓⠛⠇⠁⠀⠀⠧⠈⠻⠗⠓⠚⠂⠘⠊⠚⠛⠛⠚⠓⠿⠆⠾⠺⠓⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡿⡟⠛⠛⠟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⡆⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⢲ ⡇⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⢀⣀⡀⢀⣀⣀⠀⠀⣀⣀⠀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⣀⡀⠀⣀⡀⠀⢀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠙⠛⡛⡛⣉⡛⢛⣃⡀⠘⠛⠛⠃⠈⢂⡐⢉⠃⠙⠛⢛⣀⣛⣛⣛⣀⣛⣛⠛⢙⠋⡛⢛⡁⣛⣛⠃⠓⣋⠛⠛⠁⠛⠛⠛⠛⠓⠓⠃⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠃⠋⠛⠋⠈⠛⠛⠃⠘⠛⠛⠻⠛⠛⠛⠛⠑⠀⠘⠛⠛⠚⠚⠚⠛⠘⠀⠙⠀⠛⠙⠀⠛⠛⠂⠛⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣀⠀⠀⠀⠀⣀⡀⠀⢀⣀⣀⡀⢀⣀⣀⢀⡀⢀⣀⣀⠀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⣀⡀⣀⠀⢀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⢫⣯⣯⣭⣿⣿⣧⣤⣬⣥⣯⣧⣬⣼⣬⣽⣥⣽⣿⣭⣥⣽⣿⣽⣤⣽⣟⠙⣛⣙⠙⣙⣛⡛⡛⢃⠛⠁⠉⠋⠉⠙⠙⠉⠙⠙⠉⠋⠃⠋⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠻⠻⠿⠿⠿⠿⠿⠿⠿⠿⠋⠀⠉⠉⠀⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢀⣄⣀⡀⣀⣀⣀⡀⠀⢀⣠⣄⡀⢀⡀⢠⣤⡀⢀⣤⣀⡀⢠⣠⢠⣤⣀⣠⣀⣠⣀⣤⣠⣤⣠⣤⢀⣀⢀⣠⣠⣄⣤⣤⣄⣤⣤⣄⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⠉⡍⣍⣄⣍⢉⣤⣄⡈⢉⢉⣁⣈⣁⣈⣉⣁⡈⠉⢡⣄⣬⡩⣭⢭⢭⢩⠉⢉⠉⢩⢉⠉⣭⣅⢀⣉⣡⠉⠉⠁⠀⠉⠉⠉⠁⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠉⠉⠁⠉⠉⠉⠁⠈⠉⠉⠙⠉⠉⠉⠉⠉⠀⠈⠉⠉⠉⠉⠉⠉⠈⠀⠈⠀⠈⠈⠀⠉⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣄⣀⣀⣀⣀⣄⡄⠀⢠⣤⣤⡄⢀⡀⢠⣤⡄⢠⣤⣤⡀⣤⣤⡤⠀⣤⣤⣤⣤⠄⢠⣠⣤⣀⣤⣤⡤⣤⣄⣄⣠⣤⣤⣤⣠⢤⣤⣤⣤⣤⣤⡀⡤⢤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠉⡅⣭⣤⣍⢩⣥⣤⡌⢉⢉⣁⣄⣁⣈⣩⣁⡈⠉⢩⣤⡬⡭⣭⢤⣭⢭⠉⣩⠀⣨⣭⠉⣤⣭⡉⣉⢭⠉⠉⠁⠉⠁⠈⠉⠉⠈⠉⠁⠉⠉⠁⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠁⠁⠁⠀⠀⠁⠁⠀⠉⠉⠙⠉⠈⠈⠉⠈⠀⠈⠉⠉⠈⠉⠉⠀⠈⠀⠈⠀⠉⠉⠀⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣤⣤⣀⡠⣄⣤⡄⠀⢠⣤⣤⡄⢠⡀⢠⣤⡀⢠⣤⣤⡄⣤⣄⣠⢠⣤⣤⠀⣤⠀⢤⣤⣤⣤⡤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡤⣦⣦⠠⣦⣤⡄⡀⢠⢤⣤⣤⣤⡄⢠⡄⢠⣤⠀⢠⢀⠀⣠⣤⣠⣤⠀⢠⠀⣤⣤⠀⣤⢠⠀⡄⠀⣄⣄⣤⣤⣄⣄⣤⡄⡄⠀⡄⢀⣄⡄⢠⣦⣄⢤⡄⡄⠀⠠⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⡤⣤⠀⢰⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⢷⠾⠿⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠈⠀⠀⠀⣤⡌⠔⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠸⠿⠷⠾⠾⠴⠴⠾⠴⠾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡ ⡯⠿⠶⠷⠶⠶⠶⡶⠄⠸⠆⠷⠶⠶⠆⠸⠷⠶⠲⠶⠾⠃⠰⠳⠶⠶⠶⠾⠶⠶⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠯⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⠀⠀⠀⠀⠸⠿⠆⠘⠟⠧⠸⠯⠾⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠏⠿⠻⠧⠀⠀⠀⠀⠸⠷⠶⠲⠶⠶⠶⠶⠆⠸⠷⠶⠲⠺⠶⠶⠂⠸⠶⠲⠫⠿⠛⠿⠙⠶⠖⠒⠶⠶⠧⠑⠀⠀⣟⡿⠷⠶⠆⠗⠖⠆⠶⡆⠀⠀⠀⠀⠀⠸⠿⠗⠺⠿⠇⠢⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠻⠖⠧⠷⠶⠧⠂⠀⠨⠗⠶⠲⠆⠸⠓⠾⠾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡗⠴⠶⠏⠸⠻⠶⠶⠒⠶⠶⠶⠆⠀⠸⠇⠼⠞⠓⠹⠦⠸⠿⠾⠂⠸⠆⠿⠶⠆⠀⠀⠀⢸ ⡟⠟⠶⠆⠇⠟⠔⠀⠀⠸⠷⠶⠞⠇⠸⠳⠒⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⡟⠷⠶⠶⠶⠾⠷⠶⠞⠇⠀⠀⠀⠀⠀⠸⠽⠍⠘⠽⠟⠱⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠛⠛⠒⠓⠛⠇⠁⠀⠀⠧⠈⠻⠇⠓⠛⠃⠘⠊⠚⠛⠛⠚⠓⠿⠆⠾⠚⠓⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⡟⠛⠛⠟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡆⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⢲ ⡇⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⢀⣀⡀⢀⣀⣀⠀⠀⣀⣀⠀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⣀⡀⠀⣀⡀⠀⢀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠙⠛⡛⡛⣉⡛⢛⣃⡀⠘⠛⠛⠃⠈⢂⡐⢉⠃⠙⠛⢛⣀⣛⣛⣛⣀⣛⣛⡛⢙⠋⡛⠛⡁⣛⣛⠃⠓⣋⠛⠛⠁⠛⠛⠙⠛⠓⠓⠃⠛⠛⠛⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠃⠋⠛⠋⠈⠛⠛⠃⠘⠛⠛⠻⠛⠙⠛⠛⠑⠀⠘⠛⠛⠚⠚⠚⠛⠘⠀⠉⠀⠛⠙⠁⠛⠛⠂⠛⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣀⠀⠀⠀⠀⣀⡀⠀⢀⣀⣀⡀⠀⣀⣀⢀⡀⢀⣀⣀⠀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⣀⡀⣀⠀⢀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⢫⣯⣯⣭⣿⣿⣧⣤⣬⣥⣯⣧⣬⣼⣬⣽⣥⣽⣿⣭⣥⣽⣿⣽⣤⣽⣟⠙⣛⣙⠙⣙⣛⡛⡛⢃⠛⠁⠉⠋⠉⠙⠛⠉⠙⠙⠋⠋⠃⠋⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠻⠿⠿⠻⠛⠿⠿⠻⠿⠿⠿⠿⠿⠋⠀⠉⠉⠀⠉⠉⠉⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢀⣄⣀⣀⢀⣀⣀⡀⠀⢀⣠⣄⡀⢀⡀⢀⣤⡀⢀⣠⣀⡀⢠⣠⢠⣤⣤⣠⣀⣠⣀⣤⣠⣤⣠⣤⢀⣀⢀⣠⣠⣄⣤⣤⣄⣤⣤⣄⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⠉⡍⡍⣅⣍⢉⣤⣄⡈⢉⢉⣁⣈⣁⣈⣉⣉⡈⠉⢡⣅⣬⡩⣭⢭⢭⢩⠉⢉⠉⢩⢉⠉⣭⣅⢀⣉⣡⠉⠉⠁⠀⠉⠉⠉⠁⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠉⠉⠁⠉⠉⠉⠁⠈⠉⠉⠙⠉⠉⠉⠉⠉⠀⠈⠉⠉⠉⠉⠉⠉⠈⠀⠈⠀⠈⠈⠀⠉⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣄⣀⣀⣀⣀⣄⡄⠀⢠⣤⣤⡄⢀⡀⢠⣤⡄⢠⣤⣤⡀⣤⣤⡤⠀⣤⣤⣤⣤⠄⢠⣠⣤⣀⣤⣤⡤⣤⣄⣄⣠⣤⣤⣤⣠⢤⣤⣤⣤⣤⣤⡀⡤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠉⡅⣍⣤⣍⢩⣥⣤⡌⢉⢉⣁⣄⣁⣈⣩⣁⡈⠉⢩⣤⡬⡭⣭⢤⣭⢭⠉⣩⠀⣨⣭⠉⣤⣭⡉⣉⢭⠉⠉⠁⠉⠁⠀⠈⠉⠈⠉⠁⠉⠉⠉⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠁⠁⠁⠁⠀⠁⠁⠀⠉⠉⠙⠉⠈⠈⠉⠈⠀⠈⠉⠉⠈⠉⠉⠀⠈⠀⠈⠀⠉⠉⠀⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣤⣤⣀⡠⣄⣤⡄⠀⢠⣤⣤⡄⢠⡀⢠⣤⡀⢠⣤⣤⡄⣤⣤⣄⡠⣤⣤⠀⣤⠀⢤⣤⣤⣤⡤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡤⣦⣦⠠⣦⣤⡄⡀⢠⢤⣤⣤⣤⡄⢠⡄⢠⣤⠀⢠⢀⠀⣠⣤⣠⣤⠀⢠⠀⣤⣤⠄⣤⢠⠀⡄⠀⣄⣄⣤⣤⣄⣄⣤⡄⡄⠀⡄⢀⣄⡄⢠⣦⣄⢤⡄⡄⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⡤⣤⠀⢰⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⢷⠾⠿⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠈⠀⠀⠀⣤⡌⠔⠐⠒⠒⠀⠐⠒⠒⠒⠂⠀⠸⠿⠷⠾⠾⠴⠴⠾⠴⠾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡ ⡯⠿⠶⠷⠶⠶⠶⡶⠄⠸⠆⠷⠶⠶⠆⠸⠷⠶⠲⠶⠾⠃⠰⠷⠶⠶⠶⠾⠶⠶⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⠀⠀⠀⠀⠸⠿⠆⠚⠟⠧⠸⠯⠾⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠏⠿⠻⠧⠀⠀⠀⠀⠸⠷⠶⠲⠶⠖⠶⠶⠆⠸⠷⠶⠲⠺⠶⠶⠂⠸⠶⠲⠫⠻⠛⠽⠙⠶⠖⠒⠶⠶⠦⠑⠀⠀⡇⡇⠷⠶⠆⠗⠖⠆⠶⡆⠀⠀⠀⠀⠀⠸⠿⠗⠺⠿⠇⠲⠟⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠻⠖⠧⠷⠶⠧⠂⠀⠨⠗⠶⠲⠆⠸⠓⠾⠾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡗⠤⠶⠏⠸⠻⠶⠶⠒⠶⠶⠶⠆⠀⠸⠇⠼⠞⠓⠹⠦⠸⠿⠾⠂⠸⠆⠿⠶⠆⠀⠀⠀⢸ ⡟⠟⠶⠆⠇⠟⠔⠀⠀⠸⠷⠶⠞⠇⠸⠳⠒⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡜⠷⠶⠶⠶⠾⠷⠶⠞⠇⠀⠀⠀⠀⠀⠸⠽⠍⠘⠽⠟⠳⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠛⠛⠒⠓⠛⠇⠁⠀⠀⠇⠈⠻⠇⠓⠛⠃⠘⠊⠚⠛⠛⠚⠓⠿⠆⠾⠚⠓⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡘⠟⠛⠟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡆⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⢲ ⡇⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⢀⣀⡀⢀⣀⣀⠀⠀⣀⣀⠀⣀⣀⣀⠀⣀⢀⣀⠀⣀⣀⣀⡀⠀⣀⡀⠀⢀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠙⠛⡛⡛⣉⡛⢛⣃⡀⠘⠛⠛⠃⠈⢂⡐⢉⠃⠙⠛⢛⣀⣛⣛⣛⣀⣛⣛⡛⢙⠋⡛⠛⡁⣛⣛⠃⠓⣋⠛⠛⠁⠛⠛⠛⠛⠓⠓⠃⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠃⠋⠛⠋⠈⠛⠛⠃⠘⠛⠛⠻⠛⠙⠛⠛⠑⠀⠘⠛⠓⠚⠚⠚⠛⠘⠀⠉⠀⠛⠙⠁⠛⠛⠂⠛⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣀⠀⠀⠀⠀⣀⡀⠀⢀⣀⣀⡀⠀⣀⣀⢀⡀⢀⣀⣀⠀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⡀⣀⠀⢀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⢫⣯⣯⣭⣿⣿⣧⣤⣬⣥⣯⣧⣬⣼⣬⣽⣥⣽⣿⣭⣥⣽⣿⣽⣤⣽⣟⠙⣛⣙⠙⣙⣛⡛⡛⢃⠛⠁⠉⠋⠉⠙⠛⠉⠙⠙⠋⠋⠃⠋⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠘⠻⠟⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠻⠿⠿⠻⠛⠛⠻⠻⠿⠿⠿⠿⠿⠋⠀⠉⠉⠀⠉⠉⠉⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢀⣄⣀⣀⢀⣀⣀⡀⠀⢀⣠⣄⡀⢀⡀⢀⣤⣀⢀⣠⣀⡀⢠⣠⢠⣤⣤⣠⣀⣠⣀⣤⣠⣤⣠⣤⢀⣀⢀⣠⣠⣄⣤⣤⣄⣤⣤⣄⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⠉⡍⡍⣅⣍⢉⣤⣄⡈⢉⢉⣁⣈⣁⣈⣉⣉⡈⠉⢡⣅⣬⡩⣭⢭⢭⢩⠉⢉⠉⢩⢉⠉⣭⣅⢀⣉⣡⠉⠉⠁⠀⠉⠉⠉⠁⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠉⠉⠁⠉⠉⠉⠁⠈⠉⠉⠙⠉⠉⠉⠉⠉⠀⠈⠉⠉⠉⠉⠉⠉⠈⠀⠈⠀⠈⠈⠀⠉⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣄⣀⣀⣀⣀⣄⡄⠀⢠⣤⣤⡄⢀⡀⢠⣤⡄⢠⣤⣤⡀⣤⣤⡤⠀⣤⣤⣤⣤⠄⢠⣠⣤⣀⣤⣤⡤⣤⣄⣄⣠⣤⣤⣤⣠⢤⣤⣤⣤⣤⣤⡀⡤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠉⡅⣍⣤⣍⢩⣥⣤⡌⢉⢉⣁⣄⣁⣈⣩⣁⡈⠉⢩⣤⡬⡭⣭⢤⣭⢭⠉⣩⠀⣨⣭⠉⣤⣭⡉⣉⢭⠉⠉⠁⠉⠁⠀⠈⠉⠈⠉⠁⠉⠉⠉⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠁⠁⠁⠁⠀⠁⠁⠀⠉⠉⠙⠉⠈⠈⠉⠈⠀⠈⠉⠉⠈⠉⠉⠀⠈⠀⠈⠀⠉⠉⠀⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣤⣤⣀⡠⣄⣤⡄⠀⢠⣤⣤⡄⢠⡀⢠⣤⡀⢠⣤⣤⡄⣤⣤⣄⡠⣤⣤⠀⣤⠀⢤⣤⣤⣤⡤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡤⣦⣦⠠⣤⣤⡄⡀⢠⢤⣤⣤⣤⡄⢠⡄⢠⣤⠀⢠⢀⠀⣠⣤⣠⣤⠀⢠⠀⣤⣤⠆⣤⢠⠀⡄⠀⣄⣄⣤⣤⣄⣄⣤⡄⡄⠀⡄⢀⣄⡄⢠⣦⣄⢤⡄⡄⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⡤⣤⠀⢰⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⢷⠾⠿⠶⠶⠦⠆⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠈⠀⠀⠀⣤⡌⠔⠐⠒⠒⠀⠐⠒⠒⠒⠂⠐⠐⠲⠶⠶⠶⠴⠴⠾⠴⠾⠆⠩⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡ ⡯⠿⠶⠷⠶⠶⠶⡶⠔⠸⠆⠷⠶⠶⠆⠸⠷⠶⠲⠶⠾⠃⠰⠷⠶⠶⠾⠾⠶⠶⠼⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⣿⠿⠿⠶⠶⠇⠷⠶⡦⠆⠠⠀⠀⠀⠀⠀⠸⠿⠆⠚⠟⠧⠸⠯⠾⠄⠀⠒⠂⠀⠀⠀⠀⠀⠀⢸ ⡇⠏⠿⠻⠷⠂⠀⠀⠀⠸⠷⠿⠶⠶⠖⠶⠶⠆⠸⠷⠶⠲⠺⠶⠶⠂⠸⠶⠲⠫⠻⠟⠟⠓⠾⠞⠚⠷⠶⠦⠑⠀⠀⠇⡆⠶⠶⠆⠇⣷⠬⠶⡦⠀⠀⠀⠀⠀⠸⠿⠗⠺⠿⠇⠲⠟⠗⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠻⠖⠧⠷⠶⠧⠂⠀⠨⠗⠶⠲⠆⠸⠓⠾⠾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡗⠤⠶⠏⠸⠿⢶⠶⠒⠶⠶⠶⠆⠀⠸⠇⠼⠞⠓⠹⠦⠸⠿⠾⠂⠸⠆⠿⠶⠆⠀⠀⠀⢸ ⡟⠟⠶⠆⠇⠟⠔⠀⠀⠸⠷⠶⠞⠇⠸⠳⠒⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡜⠷⠶⠶⠆⣂⠲⠖⠜⠇⠀⠀⠀⠀⠀⠸⠽⠍⠘⠽⠟⠳⠂⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⢸ ⡇⠛⠛⠒⠓⠛⠇⠁⠀⠀⠇⠈⠻⠇⠓⠛⠃⠘⠊⠚⠛⠛⠚⠓⠿⠆⠾⠚⠓⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡘⠟⠛⠟⠃⠧⠆⠐⠀⠁⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡆⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⢲ ⡇⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⢀⣀⡀⢀⣀⣀⠀⠀⣀⣀⠀⣀⣀⣀⠀⣀⢀⣀⠀⡀⣀⣀⡀⠀⣀⡀⠀⢀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠙⠛⡛⡛⣉⡛⢛⣃⡀⠘⠛⠛⠃⠈⢂⡐⢉⠃⠙⠛⢛⣀⣛⣛⣛⣀⣛⣛⡛⢙⠋⡛⠛⡁⣛⣛⠃⠓⣋⠛⠛⠁⠛⠛⠛⠛⠓⠓⠃⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠃⠋⠛⠋⠈⠛⠛⠃⠘⠛⠛⠻⠛⠙⠛⠛⠑⠀⠘⠛⠓⠚⠚⠛⠛⠘⠀⠉⠀⠛⠙⠁⠛⠛⠂⠛⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣀⠀⠀⠀⠀⣀⡀⠀⢀⣀⣀⡀⠀⣀⣀⢀⠀⢀⣀⣀⠀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⡀⣀⠀⢀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⢫⣯⣯⣭⣿⣿⣧⣤⣬⣥⣯⣧⣬⣼⣬⣽⣵⣽⣽⣭⣥⣽⣿⣽⣤⣽⣟⠙⣛⣙⠙⣙⣛⡛⡛⢃⠛⠁⠉⠛⠉⠙⠛⠉⠙⠙⠋⠋⠃⠋⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠘⠻⠟⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠻⠿⠿⠻⠻⠛⠻⠛⠻⠿⠿⠿⠻⠋⠀⠉⠉⠀⠉⠉⠉⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢀⣄⣀⣀⢀⣀⣀⡀⠀⢀⣠⣄⡀⢀⡀⢀⣤⣀⢀⣠⣀⡀⢠⣠⢠⣤⣤⣠⣀⣠⣀⣤⣠⣤⣠⣤⢀⣀⢀⣠⣠⣄⣤⣤⣄⣤⣤⣄⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⠉⡍⡍⣅⣍⢉⣤⣄⡈⢉⢉⣁⣈⣁⣈⣉⣉⡈⠉⢡⣅⣬⡉⣩⢭⢭⢩⠉⢉⠉⢩⢉⠉⣭⣅⢀⣉⣡⠉⢉⡁⠀⠉⠉⠉⠁⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠉⠉⠁⠉⠉⠉⠁⠈⠉⠉⠙⠉⠉⠉⠉⠉⠀⠈⠉⠉⠉⠉⠉⠉⠈⠀⠈⠀⠈⠈⠀⠉⠉⠁⠉⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣄⣀⣀⡀⣀⣄⡄⠀⢠⣤⣤⡄⢀⡀⢠⣠⠄⢠⣤⣤⡀⣤⣤⡤⠀⣤⣤⣤⣤⠄⢠⣠⣤⣀⣤⣤⡤⣤⣄⣄⣠⣤⣤⣤⣠⢤⣤⣤⣤⣤⣤⡀⡤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠉⡅⣍⣤⣍⢩⣥⣤⡌⢉⢉⣁⣄⣁⣈⣩⣁⡈⠉⢩⣤⡬⡭⣭⢤⣭⢭⠉⣩⠀⣨⣭⠉⣤⣩⡉⣉⢭⠉⠉⠁⠉⠁⠀⠈⠉⠈⠉⠁⠉⠉⠉⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠁⠁⠁⠁⠀⠁⠁⠀⠉⠉⠙⠉⠈⠈⠉⠈⠀⠈⠉⠉⠈⠉⠉⠀⠈⠀⠈⠀⠉⠉⠀⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣤⣤⣀⡠⣄⣤⡄⠀⢠⣤⣤⡄⢠⡀⢠⣤⡀⢠⣤⣤⡄⣤⣤⣄⡠⣤⣤⠀⣤⠀⢤⣤⣤⣤⡤⣤⡤⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡤⣦⣦⠠⣤⣤⣰⢄⢠⢤⣤⣤⣤⡄⢠⡄⣠⣤⠀⢠⢀⠀⣠⣤⣠⣤⠀⢠⠀⣤⣤⠆⣤⢠⢀⡄⠀⣄⣄⣤⣤⣄⣄⣤⡄⡄⠀⡄⢀⣄⡄⢠⣦⣄⢤⡄⡄⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⡤⣤⠀⢰⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⢷⠾⠿⠶⠶⠦⠆⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠈⠀⠀⠀⣤⠬⠔⠐⠒⠒⠀⠒⠒⠒⠒⠂⠐⠐⠲⠶⠶⠶⠴⠴⠾⠼⠾⠆⠩⠠⠀⠀⠀⠀⠀⠀⠀⠀⠁⢡ ⡯⠿⠶⠷⠶⠶⠶⡶⠔⠸⠆⠷⠶⠶⠆⠸⠷⠶⠲⠶⠾⠂⠰⠷⠶⠶⠾⠾⠶⠶⠼⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣷⠿⠶⠶⠇⠷⠶⡦⠆⠠⠀⠀⠀⠀⠀⠸⠿⠆⠚⠟⠧⠸⠯⠾⠄⠀⠒⠂⠀⠀⠀⠀⠀⠀⢸ ⡇⠏⠿⠻⠷⠀⠀⠀⠀⠸⠷⠿⠶⠶⠶⠶⠶⠆⠸⠷⠶⠲⠺⠶⠶⠂⠸⠶⠺⠫⠻⠟⠝⠓⠾⠞⠚⠷⠶⠦⠑⠀⢀⡿⡦⠶⠶⠆⠇⣷⠬⠶⡦⠀⠀⠀⠀⠀⠸⠿⠗⠺⠿⠇⠲⠿⠄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠻⠖⠧⠷⠶⠧⠂⠀⠨⠗⠶⠲⠆⠸⠓⠾⠾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡗⠤⠶⠏⠸⠿⢶⠶⠒⠶⠶⠶⠆⠀⠸⠇⠼⠞⠓⠹⠦⠸⠿⠾⠂⠸⠆⠿⠶⠆⠀⠀⠀⢸ ⡟⠟⠶⠆⠇⠟⠔⠀⠀⠸⠷⠶⠞⠇⠸⠳⠒⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡜⠷⠶⠶⠆⣂⠲⠖⠜⠇⠀⠀⠀⠀⠀⠸⠽⠍⠘⠽⠟⠳⠂⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⢸ ⡇⠛⠛⠒⠓⠛⠇⠁⠀⠀⠇⠘⠻⠇⠓⠛⠂⠘⠊⠚⠛⠛⠚⠓⠿⠆⠾⠚⠓⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⡛⠟⠛⠟⠃⠧⠆⠐⠀⠁⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡆⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⢲ ⡇⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⢀⣀⡀⢀⣀⣀⠀⠀⣀⣀⠀⣀⣀⣀⠀⣀⢀⣀⠀⡀⣀⣀⡀⠀⣀⡀⠀⢀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠙⠛⡛⡛⣉⡛⢛⣃⡀⠘⠛⠛⠁⠈⢂⡐⢉⠃⠙⠛⢛⣀⣛⣛⣛⣀⣛⣛⡛⢙⠋⡛⠛⡁⣛⣛⠃⠓⣋⠛⠛⠁⠛⠛⠛⠛⠓⠓⠃⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠃⠋⠛⠋⠈⠛⠛⠃⠘⠛⠛⠻⠛⠙⠛⠛⠑⠀⠘⠛⠛⠚⠚⠛⠛⠘⠀⠉⠀⠛⠙⠁⠛⠛⠂⠛⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣀⠀⠀⠀⠀⣀⡀⠀⢀⣀⣀⡀⠀⣀⣀⢀⠀⢀⣀⣀⠀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⡀⣀⠀⢀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⢫⣯⣯⣭⣿⣿⣧⣤⣬⣥⣯⣧⣬⣼⣬⣽⣵⣽⣽⣭⣥⣽⣿⣽⣤⣽⣟⠙⣛⣙⠙⣙⣛⡛⡛⢃⠛⠁⠉⠛⠉⠙⠛⠉⠙⠙⠋⠋⠃⠋⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠘⠻⠟⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠻⠿⠟⠿⠿⠛⠿⠿⠿⠿⠿⠿⠻⠋⠀⠉⠉⠀⠉⠉⠉⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢀⣄⣀⣀⢀⣀⣀⡀⠀⢀⣠⣄⡀⢀⡀⢀⣤⣀⢀⣠⣀⡀⢠⣠⢠⣤⣤⣠⣀⣠⣀⣤⣠⣤⣠⣤⢀⣀⢀⣠⣠⣄⣤⣤⣄⣤⣤⣄⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⠉⡍⡍⣅⣍⢉⣤⣄⡈⢉⢉⣁⣈⣁⣈⣉⣉⡈⠉⢡⣅⣬⡉⣩⢭⢭⢩⠉⢉⠉⢩⢉⠉⣭⣅⢀⣉⣡⠉⢉⡁⠀⠉⠉⠉⠁⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠉⠉⠁⠉⠉⠉⠁⠈⠉⠉⠙⠉⠉⠉⠉⠉⠀⠈⠉⠉⠉⠉⠉⠉⠈⠀⠈⠀⠈⠈⠀⠉⠉⠁⠉⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣄⣀⣀⡀⣀⣄⡄⠀⢠⣤⣤⡄⢀⡀⢠⣤⠄⢠⣤⣤⡀⣤⣤⡤⠀⣤⣤⣤⣤⠄⢠⣠⣤⣀⣤⣤⡤⣤⣄⣄⣠⣤⣤⣤⣠⢤⣤⣤⣤⣤⣤⡀⡤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠉⡅⣍⣤⣍⢩⣥⣤⡌⢉⢉⣁⣄⣁⣈⣩⣁⡈⠉⢩⣤⡬⡭⣭⢤⣭⢭⠉⣩⠀⣨⣭⠉⣤⣩⡉⣉⢭⠉⠉⠁⠉⠁⠀⠈⠉⠈⠉⠁⠉⠉⠉⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠁⠁⠁⠁⠀⠁⠁⠀⠉⠉⠙⠉⠈⠈⠉⠈⠀⠈⠉⠉⠈⠉⠉⠀⠈⠀⠈⠀⠉⠉⠀⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣤⣤⣀⡠⣄⣤⡄⠀⢠⣤⣤⡄⢠⡀⢠⣤⡀⢠⣤⣤⡄⣤⣤⣄⡠⣤⣤⠀⣤⠀⢤⣤⣤⣤⡤⣤⠤⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡤⣦⣦⠠⣤⣤⣰⢄⢠⢤⣤⣤⣤⡄⢠⡄⣠⣤⠀⢠⢀⠀⣠⣤⣠⣤⠀⢠⠀⣤⣤⠄⣤⢠⢀⡄⠀⣄⣄⣤⣤⣄⣄⣤⡄⡄⠀⡄⢀⣄⡄⢠⣦⣄⢤⡄⡄⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⡤⣤⠀⢰⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⢷⠾⠿⠶⠶⠦⠆⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠈⠀⠀⠀⣤⠬⠔⠐⠒⠒⠀⠒⠒⠒⠒⠂⠐⠐⠲⠶⠶⠶⠴⠴⠾⠼⠾⠆⠩⠠⠀⠀⠀⠀⠀⠀⠀⠀⠁⢡ ⡯⠿⠶⠷⠶⠶⠶⡶⠔⠸⠆⠷⠶⠶⠆⠸⠷⠶⠲⠶⠾⠂⠰⠷⠶⠶⠾⠾⠶⠶⠼⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣷⠿⠶⠶⠇⠷⠶⡦⠆⠠⠀⠀⠀⠀⠀⠸⠿⠆⠚⠟⠧⠸⠯⠾⠄⠀⠒⠂⠀⠀⠀⠀⠀⠀⢸ ⡇⠏⠿⠻⠷⠀⠀⠀⠀⠸⠷⠿⠶⠶⠶⠶⠶⠆⠸⠷⠶⠲⠺⠶⠶⠂⠸⠶⠺⠫⠻⠟⠝⠓⠾⠞⠚⠷⠶⠦⠑⠀⢀⡿⡦⠶⠶⠆⠇⣷⠬⠀⢸⢰⡆⠀⠀⠀⠸⠿⠗⠺⠿⠇⠲⠿⠄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠻⠖⠧⠷⠶⠧⠂⠀⠨⠗⠶⠲⠆⠸⠓⠾⠾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡗⠤⠶⠏⠸⠿⢶⠀⢸⢸⢷⠶⠆⠀⠸⠇⠼⠞⠓⠹⠦⠸⠿⠾⠂⠸⠆⠿⠶⠆⠀⠄⠀⢸ ⡟⠟⠶⠆⠁⠟⠴⠀⠀⠸⠷⠶⠞⠇⠸⠳⠒⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡜⠷⠶⠶⠆⣂⠲⠀⢘⢘⠀⠀⠀⠀⠀⠸⠽⠍⠘⠽⠟⠳⠂⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⢸ ⡇⠛⠛⠒⠓⠛⠇⠁⠀⠀⠇⠘⠻⠇⠓⠛⠂⠘⠊⠚⠛⠛⠚⠓⠿⠆⠾⠚⠓⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⡛⠟⠛⠟⠃⠧⠆⠀⢨⠘⠢⠄⠀⠀⠀⢀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡆⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⢲ ⡇⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⢀⣀⡀⢀⣀⣀⠀⠀⣀⣀⠀⣀⣀⣀⠀⣀⢀⣀⠀⡀⣀⣀⡀⠀⣀⡀⠀⢀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠙⠛⡛⡛⣉⡛⢛⣃⡀⠘⠛⠛⠁⠈⢂⡐⢉⠃⠙⠛⢛⣀⣛⣛⣛⣀⣛⣛⡛⢙⠋⡛⠛⡁⣛⣛⠃⠓⣋⠛⠛⠁⠛⠛⠛⠛⠓⠓⠃⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠃⠋⠛⠋⠈⠛⠛⠃⠘⠛⠛⠻⠛⠙⠛⠛⠑⠀⠘⠛⠛⠚⠚⠛⠛⠘⠀⠉⠀⠛⠙⠁⠛⠛⠂⠛⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣀⠀⠀⠀⠀⣀⡀⠀⢀⣀⣀⡀⠀⣀⣀⢀⠀⢀⣀⣀⠀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⡀⣀⠀⢀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⢫⣯⣯⣭⣿⣿⣧⣤⣬⣥⣯⣧⣬⣼⣬⣽⣵⣽⣽⣭⣥⣽⣿⣽⣤⣽⣟⠙⣛⣙⠙⣙⣛⡛⡛⢃⠛⠁⠉⠛⠉⠙⠛⠉⠙⠙⠋⠋⠃⠋⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠘⠻⠟⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠻⠿⠟⠿⠿⠛⠿⠿⠿⠿⠿⠿⠻⠋⠀⠉⠉⠀⠉⠉⠉⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢀⣄⣀⣀⢀⣂⣀⣄⣀⣀⣠⣄⡀⢀⡀⢀⣤⣀⢀⣠⣀⡀⢠⣠⢠⣤⣤⣠⣀⣠⣀⣤⣠⣤⣠⣤⢀⣀⢀⣠⣠⣄⣤⣤⣄⣤⣤⣄⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⠉⡍⡍⣅⣅⢀⣤⣄⡈⢉⢉⣁⣈⣁⣈⣉⣉⡈⠉⢡⣅⣬⡁⣨⢬⢭⢩⠉⢉⠉⢩⢉⠉⣭⣅⢀⣉⣡⠉⢉⡁⠀⠉⠉⠉⠁⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠉⠉⠁⠉⠉⠉⠁⠈⠉⠉⠙⠉⠉⠉⠉⠉⠀⠈⠉⠉⠉⠉⠉⠉⠈⠀⠈⠀⠈⠈⠀⠉⠉⠁⠉⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣄⣀⣀⡀⣀⣄⡄⠀⢠⣤⣤⡄⢀⡀⢠⣤⠄⢠⣤⣤⡀⣤⣤⡤⠀⣤⣤⣤⣤⠄⢠⣠⣤⣀⣤⣤⡤⣤⣄⣄⣠⣤⣤⣤⣠⢤⣤⣤⣤⣤⣤⡀⡤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠉⡅⣍⣤⣍⢩⣥⣤⡌⢉⢉⣁⣄⣁⣈⣩⣁⡈⠉⢩⣤⡬⡭⣭⢤⣭⢭⠉⣩⠀⣨⣭⠉⣤⣩⡉⣉⢭⠉⠉⠁⠉⠁⠀⠈⠉⠈⠉⠁⠉⠉⠉⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠁⠁⠁⠁⠀⠁⠁⠀⠉⠉⠙⠉⠈⠈⠉⠈⠀⠈⠉⠉⠈⠉⠉⠀⠈⠀⠈⠀⠉⠉⠀⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣤⣤⣀⣀⣄⣤⡄⠀⢠⣤⣤⡄⢠⡀⢠⣤⡀⢠⣤⣤⡄⣤⣤⣄⡠⣤⣤⠀⣤⠀⢤⣤⣤⣤⡤⣤⠤⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡤⣦⣦⠠⣤⣤⣰⢄⢠⢤⣤⣤⣤⡄⢠⡄⣠⣤⠀⢠⢀⠀⣠⣤⣠⣤⠀⢠⠀⣤⣤⠄⣤⢠⢀⡄⠀⣄⣄⣤⣤⣄⣄⣤⡄⡄⠀⡄⢀⣄⡄⢠⣦⣄⢤⡄⡄⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⡤⣤⠀⢰⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⢷⠾⠿⠶⠶⠦⠆⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠈⠀⠀⠀⣤⠬⠔⠐⠒⠒⠀⠒⠒⠒⠒⠂⠐⠐⠲⠶⠶⠶⠴⠴⠾⠼⠾⠆⠩⠠⠀⠀⠀⠀⠀⠀⠀⠀⠁⢡ ⡯⠿⠶⠷⠶⠶⠶⡶⠔⠸⠆⠷⠶⠶⠆⠸⠷⠶⠲⠶⠾⠂⠰⠷⠶⠶⠾⠾⠶⠶⠼⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣷⠿⠶⠶⠇⠷⠶⡦⠆⠠⠀⠀⠀⠀⠀⠸⠿⠆⠚⠟⠧⠸⠯⠾⠄⠀⠒⠂⠀⠀⠀⠀⠀⠀⢸ ⡇⠏⠿⠻⠷⠀⠀⠀⠀⠸⠷⠿⠶⠶⠶⠶⠶⠆⠸⠷⠶⠲⠺⠶⠶⠂⠸⠶⠺⠫⠻⠟⠝⠓⠾⠞⠚⠷⠶⠦⠑⠀⢀⡿⡦⠶⠶⠆⠇⣷⠬⠀⢸⢰⠄⠀⠀⠀⠸⠿⠗⠺⠿⠇⠲⠿⠄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠻⠖⠧⠷⠶⠧⠂⠀⠨⠗⠶⠲⠆⠸⠓⠾⠾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡗⠤⠶⠏⠸⠿⢶⠀⢸⢸⢶⠴⠆⠀⠸⠇⠼⠞⠓⠹⠦⠸⠿⠾⠂⠸⠆⠿⠶⠆⠀⠦⠀⢸ ⡟⠟⠶⠆⠁⠟⠴⠀⠀⠸⠷⠶⠞⠇⠸⠳⠒⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡜⠷⠶⠶⠆⣂⠲⠀⢘⢘⠀⠀⠀⠀⠀⠸⠽⠍⠘⠽⠟⠳⠂⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⢸ ⡇⠛⠛⠒⠓⠛⠇⠁⠀⠀⠇⠘⠻⠇⠓⠛⠂⠘⠊⠚⠛⠛⠚⠓⠿⠆⠾⠚⠓⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⡛⠟⠛⠟⠃⠧⠆⠀⢨⠘⠲⠄⠀⠀⠀⢀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡆⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⢲ ⡇⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⢀⣀⡀⢀⣀⣀⠀⠀⣀⣀⠀⣀⣀⣀⠀⣀⢀⣀⠀⡀⣀⣀⡀⠀⣀⡀⠀⢀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠙⠛⡛⡛⣉⡛⢛⣃⡀⠘⠛⠛⠁⠈⢂⡐⢉⠃⠙⠛⢛⣀⣛⣛⣛⣀⣛⣛⡛⢙⠋⡛⠛⡁⣛⣛⠃⠓⣪⠛⠛⠁⠛⠛⠛⠛⠓⠓⠃⠛⠛⠛⠛⠋⠀⠀⢠⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠃⠋⠛⠋⠈⠛⠛⠃⠘⠛⠛⠻⠛⠙⠛⠛⠑⠀⠘⠛⠛⠚⠚⠛⠛⠘⠀⠉⠀⠛⠙⠁⠛⠛⠂⠛⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣀⠀⠀⠀⠀⣀⡀⠀⢀⣀⣀⡀⠀⣀⣀⢀⠀⢀⣀⣀⠀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⡀⣀⠀⢀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⢫⣯⣯⣭⣿⣿⣧⣤⣬⣥⣯⣧⣬⣼⣬⣽⣵⣽⣽⣭⣥⣽⣿⣽⣤⣽⣟⠙⣛⣙⠙⣙⣛⡛⡛⢃⠛⠁⠉⠛⠉⠙⠛⠉⠙⠙⠋⠋⠃⠋⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠘⠻⠟⢿⣿⠿⢿⠿⣿⠿⠿⠿⠟⠻⠿⠟⠿⠿⠛⠿⠿⠿⠿⠿⠿⠻⠋⠀⠉⠉⠀⠉⠉⠉⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢀⣄⣀⣀⢀⣋⣀⣍⣀⣁⣠⣄⡀⢀⡀⢀⣤⣀⢀⣠⣀⡀⢠⣠⢠⣤⣤⣠⣀⣠⣀⣤⣠⣤⣠⣤⢀⣀⢀⣠⣠⣄⣤⣤⣄⣤⣤⣄⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⠉⡍⡍⣅⣅⢀⣤⣄⡈⢉⢉⣁⣈⣁⣈⣉⣉⡈⠉⢡⣅⣬⡁⣨⢬⢭⢩⠉⢉⠉⢩⢉⠉⣭⣅⢀⣉⣡⠉⢉⡁⠀⠉⠉⠉⠁⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠉⠉⠁⠉⠉⠉⠁⠈⠉⠉⠙⠉⠉⠉⠉⠉⠀⠈⠉⠉⠉⠉⠉⠉⠈⠀⠈⠀⠈⠈⠀⠉⠉⠁⠉⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣄⣀⣀⡀⣀⣄⡄⠀⢠⣤⣤⡄⢀⡀⢠⣤⠄⢠⣤⣤⡀⣤⣤⡤⠀⣤⣤⣤⣤⠄⢠⢠⣤⣀⣤⣤⡤⣤⣄⣄⣠⣤⣤⣤⣠⢤⣤⣤⣤⣤⣤⡀⡤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠉⡅⣍⣤⣍⢩⣥⣤⡌⢉⢉⣁⣄⣁⣈⣩⣁⡈⠉⢩⣤⡬⡭⣭⢤⣭⢭⠉⣩⠀⣨⣭⠉⣤⣩⡉⣉⢭⠉⠉⠁⠉⠁⠀⠈⠉⠈⠉⠁⠉⠉⠉⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠁⠁⠁⠁⠀⠁⠁⠀⠉⠉⠙⠉⠈⠈⠉⠈⠀⠈⠉⠉⠈⠉⠉⠀⠈⠀⠈⠀⠉⠉⠀⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣤⣤⣀⣀⣄⣤⡄⠀⢠⣤⣤⡄⢠⡀⢠⣤⡀⢠⣤⣤⡄⣤⣤⣄⡠⣤⣤⠀⣤⠀⢤⣤⣤⣤⡤⣤⠤⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡤⣦⣦⠠⣤⣤⣰⢄⢠⢤⣤⣤⣤⡄⢠⡄⣠⣤⠀⢠⢀⠀⣠⣤⣠⣤⠀⢠⠀⣤⣤⠄⣤⢠⢀⡄⠀⣄⣄⣴⣤⣄⣄⣤⡄⡄⠀⡄⢀⣄⡄⢠⣦⣄⢤⡄⡄⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⡤⣤⠀⢰⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⢷⠾⠿⠶⠶⠦⠆⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠈⠀⠀⠀⣤⠬⠔⠐⠒⠒⠀⠒⠒⠒⠒⠂⠐⠐⠲⠶⠶⠶⠴⠴⠾⠼⠾⠆⠩⠠⠀⠀⠀⠀⠀⠀⠀⠀⠁⢡ ⡯⠿⠶⠷⠶⠶⠶⡶⠔⠸⠆⠷⠶⠶⠆⠸⠷⠶⠲⠶⠾⠂⠰⠷⠶⠶⠾⠾⠶⠶⠼⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣷⠿⠶⠶⠇⠷⠶⡦⠆⠠⠀⡀⠀⠀⠀⠸⠿⠆⠚⠟⠧⠸⠯⠾⠄⠀⠒⠂⠀⠀⠀⠀⠀⠀⢸ ⡇⠏⠿⠻⠷⠀⠀⠀⠀⠸⠷⠿⠶⠶⠶⠶⠶⠆⠸⠷⠶⠲⠺⠶⠶⠂⠸⠶⠺⠫⠻⠟⠝⠓⠾⠞⠚⠷⠶⠦⠑⠀⢀⡿⡦⠶⠶⠆⠇⣷⠬⠀⢸⡙⡅⠂⠀⠀⠸⠿⠗⠺⠿⠇⠲⠿⠄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠻⠖⠧⠷⠶⠧⠂⠀⠨⠗⠶⠲⠆⠸⠓⠾⠾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡗⠤⠶⠏⠸⠿⢶⠀⢸⡇⡷⠴⠆⠀⠸⠇⠼⠞⠓⠹⠦⠸⠿⠾⠂⠸⠆⠿⠶⠆⠀⠦⠀⢸ ⡟⠟⠶⠆⠀⠟⠴⠀⠀⠸⠷⠶⠞⠇⠸⠳⠒⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡜⠷⠶⠶⠆⣂⠲⠀⠈⠀⡇⠀⠀⠀⠀⠸⠽⠍⠘⠽⠟⠳⠂⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⢸ ⡇⠛⠛⠒⠓⠛⠇⠁⠀⠀⠇⠘⠻⠇⠓⠛⠂⠘⠊⠚⠛⠛⠚⠓⠿⠆⠾⠚⠓⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⡛⠟⠛⠟⠃⠧⠆⠀⢨⡇⡷⠄⠀⠀⠀⢀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⠠⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡆⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⢲ ⡇⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⢀⣀⡀⢀⣀⣀⠀⠀⣀⣀⠀⣀⣀⣀⠀⣀⢀⣀⠀⡀⣀⣀⠀⠀⣀⡀⠀⢀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠙⠛⡛⡛⣉⡛⢛⣃⡀⠘⠛⠛⠁⠈⢂⡐⢉⠃⠙⠛⢛⣀⣛⣛⣛⣀⣛⣛⡛⢙⠋⡛⠛⡁⣛⣛⠃⠓⣪⠛⠛⠁⠛⠛⠛⠛⠓⠓⠃⠛⠛⠛⠛⠋⠐⠂⢠⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠃⠋⠛⠋⠈⠛⠛⠃⠘⠛⠛⠻⠛⠙⠛⠛⠑⠀⠘⠛⠛⠚⠚⠛⠛⠘⠀⠉⠀⠛⠙⠁⠛⠛⠂⠛⠚⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣀⠀⠀⠀⠀⣀⡀⠀⢀⣀⣀⡀⠀⣀⣀⢀⠀⢀⣀⣀⠀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⡀⣀⠀⢀⣀⠀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⢫⣯⣯⣭⣿⣿⣧⣤⣬⣥⣯⣧⣬⣬⣬⣽⣵⣽⣽⣭⣥⣽⣿⣽⣤⣽⣟⠙⣛⣙⠙⣙⣛⡛⡛⢃⠛⠁⠉⠛⠉⠙⠛⠉⠙⠙⠋⠋⠃⠋⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠘⠻⠟⢿⣿⠿⣿⡿⣿⢿⠿⠿⠟⠻⠿⠟⠿⠿⠛⠿⠿⠿⠿⠿⠿⠻⠋⠀⠉⠉⠀⠉⠉⠉⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢀⣄⣀⣀⢀⣋⣀⣄⣀⣁⣠⣄⡀⢀⡀⢀⣤⣀⢀⣠⣀⡀⢠⣠⢠⣤⣤⣠⣀⣠⣀⣤⣠⣤⣠⣤⢀⣀⢀⣠⣠⣄⣤⣤⣄⣤⣤⣄⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⠉⡍⡍⣅⣅⢀⣤⣄⡈⢉⢉⣁⣈⣁⣈⣉⣉⡈⠉⢡⣅⣬⡁⣨⢬⢭⢩⠉⢉⠉⢩⢉⠉⣭⣅⢀⣉⣡⠉⢉⡁⠀⠉⠉⠉⠁⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠉⠉⠁⠉⠉⠉⠁⠈⠉⠉⠙⠉⠉⠉⠉⠉⠀⠈⠉⠉⠉⠉⠉⠉⠈⠀⠈⠀⠈⠈⠀⠉⠉⠁⠉⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣄⣀⣀⡀⣀⣄⡄⠀⢠⣤⣤⡄⢀⡀⢠⣤⠄⢠⣤⣤⡀⣤⣤⡤⠀⣤⣤⣤⣤⠄⢠⢠⣤⣀⣤⣤⡤⣤⣄⣄⣠⣤⣤⣤⣠⢤⣤⣤⣤⣤⣤⡀⡤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠉⡅⣍⣤⣍⢩⣥⣤⡌⢉⢉⣁⣄⣁⣈⣩⣁⡈⠉⢩⣤⡬⡭⣭⢤⣭⢭⠉⣩⠀⣨⣭⠉⣤⣩⡉⣉⢭⠉⠉⠁⠉⠁⠀⠈⠉⠈⠉⠁⠉⠉⠉⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠁⠁⠁⠁⠀⠁⠁⠀⠉⠉⠙⠉⠈⠈⠉⠈⠀⠈⠉⠉⠈⠉⠉⠀⠈⠀⠈⠀⠉⠉⠀⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣤⣤⣀⣀⣄⣤⡄⠀⢠⣤⣤⡄⢠⡀⢠⣤⡀⢠⣤⣤⡄⣤⣤⣄⡠⣤⣤⠀⣤⠀⢤⣤⣤⣤⡤⣤⠤⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠤⣦⣦⠠⣤⣤⣰⢄⢠⢤⣤⣤⣤⡄⢠⡄⣠⣤⠀⢠⢀⠀⣠⣤⣠⣤⠀⢠⠀⣤⣤⠄⣤⢠⢀⡄⠀⣄⣄⣴⣵⣄⣄⣤⡄⡄⠀⡄⢀⣄⡄⢠⣦⣄⢤⡄⡄⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⡤⣤⠀⢰⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⢷⠾⠿⠶⠶⠦⠆⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠈⠀⠀⠀⣤⠬⠔⠐⠒⠒⠀⠒⠒⠒⠒⠂⠐⠐⠲⠶⠶⠶⠴⠴⠾⠼⠾⠆⠩⠠⠀⠀⠀⠀⠀⠀⠀⠀⠁⢡ ⡯⠿⠶⠷⠶⠶⠶⡶⠔⠸⠆⠷⠶⠶⠆⠸⠷⠶⠲⠶⠾⠂⠰⠷⠶⠶⠾⠾⠶⠶⠼⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣷⠿⠶⠶⠇⠷⠶⡦⠆⠠⠀⡀⠀⠀⠀⠸⠿⠆⠚⠟⠧⠸⠯⠾⠄⠀⠒⠂⠀⠀⣀⡀⠀⠀⢸ ⡇⠏⠿⠻⠷⠀⠀⠀⠀⠸⠷⠿⠶⠶⠶⠶⠶⠆⠸⠷⠶⠲⠺⠶⠶⠂⠸⠶⠺⠫⠛⠟⠝⠓⠾⠞⠚⠗⠶⠦⠑⠀⢀⡿⡦⠶⠶⠦⢇⣷⠬⠀⢸⡙⡅⠂⠀⠀⠸⠿⠗⠺⠿⠇⠢⠿⠄⠀⠀⠐⠀⠀⠀⠵⠅⠀⠀⢸ ⡟⠻⠖⠧⠷⠶⠧⠂⠀⠨⠗⠶⠲⠆⠸⠓⠾⠾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡗⠤⠀⢸⢸⠾⢶⠀⢸⡇⡷⠴⠆⠀⠸⠇⠼⠞⠓⠹⠦⠸⠿⠾⠂⠸⠆⠿⠶⠆⠀⠦⠀⢸ ⡟⠟⠶⠆⠀⠟⠴⠀⠀⠸⠷⠶⠞⠇⠸⠳⠒⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡜⠷⠀⢸⢨⣰⠰⠀⠈⠀⡇⠀⠀⠀⠀⠸⠽⠍⠘⠽⠟⠳⠂⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⢸ ⡇⠛⠛⠒⠓⠛⠇⠁⠀⠀⠇⠘⠻⠇⠓⠛⠂⠘⠊⠚⠛⠛⠚⠓⠿⠆⠾⠚⠓⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⡛⠟⠀⢸⠨⢤⠆⠀⢨⡇⡷⠄⠀⠀⠀⢀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠸⢸⠀⠀⠀⠸⠠⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡆⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠘⢰⠉⠁⠈⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⢲ ⡇⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⢀⣀⡀⢀⣀⣀⠀⠀⣀⣀⠀⣀⣀⣀⠀⣀⢀⣀⠀⡀⣀⣀⠀⠀⣀⡀⠀⢀⣀⡀⣀⡘⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠙⠛⡛⡛⣉⡛⢛⣃⡀⠘⠛⠛⠁⠈⢂⡐⢉⠃⠙⠛⢛⣀⣛⣛⣛⣀⣛⣛⡛⢙⠋⡛⠛⡁⣛⣛⠃⠓⣪⠛⠛⠁⠛⠛⠛⠛⠓⠓⠃⠛⠛⠛⠛⠋⠐⠂⢠⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠃⠋⠛⠋⠈⠛⠛⠃⠘⠛⠛⠻⠛⠙⠛⠛⠑⠀⠘⠛⠓⠚⠚⠛⠛⠘⠀⠉⠀⠛⠙⠁⠛⠛⠂⠛⠚⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣀⠀⠀⠀⠀⣀⡀⠀⢀⣀⣀⡀⠀⣀⣀⢀⠀⢀⣀⣀⠀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⡀⣀⠀⢀⣀⠀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⢫⣯⣯⣭⣿⣿⣧⣤⣬⣥⣯⣧⣬⣬⣬⣽⣵⣽⣽⣭⣥⣽⣿⣽⣤⣽⣟⠙⣛⣙⠙⣙⣛⡛⡛⢃⠛⠁⠉⠛⠉⠙⠛⠉⠙⠙⠋⠋⠃⠋⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠘⠻⠟⢿⣿⠿⣿⡿⣿⢿⠿⠿⠟⠻⠿⠟⠿⠿⠛⠿⠿⠿⠿⠿⠿⠻⠋⠀⠉⠉⠀⠉⠉⠉⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢀⣄⣀⣀⢀⣋⣀⣄⣀⣁⣠⣄⡀⢀⡀⢀⣤⣀⢀⣠⣀⡀⢠⣠⢠⣤⣤⣠⣀⣠⣀⣤⣠⣤⣠⣤⠀⣀⢀⣠⣠⣄⣤⣤⣄⣤⣤⣄⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⠉⡍⡍⣅⣅⢀⣄⣄⡈⢉⢉⣁⣈⣁⣈⣉⣉⡈⠉⢡⣅⣬⡁⣨⢬⢭⢩⠉⢉⠉⢩⢉⠉⣭⣅⢀⣉⣡⠉⢉⡁⠀⠉⠉⠉⠁⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠉⠉⠁⠉⠉⠉⠁⠈⠉⠉⠙⠉⠉⠉⠉⠉⠀⠈⠉⠉⠉⠉⠉⠉⠈⠀⠈⠀⠈⠈⠀⠉⠉⠁⠉⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣄⣀⣀⡀⣀⣄⡄⠀⢠⣤⣤⡄⢀⡀⢠⣤⠄⢠⣤⣤⡀⣤⣤⡤⠀⣤⣤⣤⣤⠄⢠⢠⣤⣀⣤⣤⡤⣤⣄⣄⣠⣤⣤⣤⣠⢤⣤⣤⣤⣤⣤⡀⡤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠉⡅⣍⣤⣍⢩⣥⣤⡌⢉⢉⣁⣄⣁⣈⣩⣁⡈⠉⢩⣤⡬⡭⣭⢤⣭⢭⠉⣩⠀⣨⣭⠉⣤⣩⡉⣉⢭⠉⠉⠁⠉⠁⠀⠈⠉⠈⠉⠁⠉⠉⠉⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠁⠁⠁⠀⠀⠁⠁⠀⠉⠉⠙⠉⠈⠈⠉⠈⠀⠈⠉⠉⠈⠉⠉⠀⠈⠀⠈⠀⠉⠉⠀⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣤⣤⣀⣀⣄⣤⡄⠀⢠⣤⣤⡄⢠⡀⢠⣤⡀⢠⣤⣤⡄⣤⣤⣄⡠⣤⣤⠀⣤⠀⢤⣤⣤⣤⡤⣤⠤⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠤⣦⣤⠠⣤⣤⣰⢄⢠⢤⣤⣤⣤⡄⢠⡄⣠⣤⠀⢠⢀⠀⣠⣤⣠⣤⠀⢠⠀⣤⣤⠄⣤⢠⢀⡄⠀⣄⣄⣴⣵⣄⣄⣤⡄⡄⠀⡄⢀⣄⡄⢠⣦⣄⢤⡄⡄⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⡤⣤⠀⢰⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⢷⠾⠾⠶⠶⠦⠆⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠈⠀⠀⠀⣤⠬⠔⠐⠒⠒⠀⠒⠒⠒⠒⠂⠐⠐⠲⠶⠶⠶⠴⠴⠾⠼⠾⠆⠩⠠⠀⠀⠀⠀⠀⠀⠀⠀⠁⢡ ⡯⠿⠶⠷⠶⠶⠶⡶⠔⠸⠆⠷⠶⠶⠆⠸⠷⠶⠲⠶⠾⠂⠰⠷⠶⠶⠾⠾⠶⠶⠼⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣷⠿⠶⠶⠇⠷⠶⡦⠆⠠⠀⡀⠀⠀⠀⠸⠿⠆⠚⠟⠧⠸⠯⠾⠄⠀⠒⠂⠀⠀⣀⡀⠀⠀⢸ ⡇⠏⠿⠻⠷⠀⠀⠀⠀⠸⠷⠿⠶⠶⠶⠶⠶⠆⠸⠷⠶⠲⠺⠶⠶⠂⠸⠶⠺⠫⠛⠟⠝⠓⠾⠞⠚⠗⠶⠦⠑⠀⢀⡿⡦⠶⠶⠦⢇⠷⠬⠀⢸⡙⡅⠂⠀⠀⠸⠿⠗⠺⠿⠇⠢⠿⠄⠀⠀⠐⠀⠀⠀⠵⠅⠀⠀⢸ ⡟⠻⠖⠧⠷⠶⠧⠂⠀⠨⠗⠶⠲⠆⠸⠓⠾⠾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡗⠤⠀⢸⢸⠽⢷⠀⢸⡇⡷⠴⠆⠀⠸⠇⠼⠞⠓⠹⠦⠸⠿⠾⠂⠸⠆⠿⠶⠆⠀⠦⠀⢸ ⡟⠟⠶⠆⠀⠟⠴⠀⠀⠸⠷⠶⠞⠇⠸⠳⠒⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡜⠷⠀⢸⢨⣰⠰⠀⠈⠀⡇⠀⠀⠀⠀⠸⠽⠍⠘⠽⠟⠳⠂⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⢸ ⡇⠛⠛⠒⠓⠛⠇⠁⠀⠀⠇⠘⠻⠇⠓⠛⠂⠘⠊⠚⠛⠛⠚⠓⠿⠆⠾⠚⠓⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⡛⠟⠀⢸⢨⢤⠆⠀⢨⡇⡷⠄⠀⠀⠀⢀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⢸⢸⠀⠀⠀⠸⠠⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡆⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⢸⢰⠙⠅⠈⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⢲ ⡇⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⢀⣀⡀⢀⣀⣀⠀⠀⣀⣀⠀⣀⣀⣀⠀⣀⢀⣀⠀⡀⣀⣀⠀⠀⣀⡀⠀⢀⣀⡀⣈⣘⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠙⠛⡛⡛⣉⡛⢛⣃⡀⠘⠛⠛⠁⠈⢂⡐⢉⠃⠙⠛⢛⣀⣛⣛⣛⣀⣛⣛⡛⢙⠋⡛⠛⡁⣛⣛⠃⠓⣪⠛⠛⠁⠛⠛⠛⠛⠓⠓⠃⠛⠛⠛⠛⠋⠐⠂⢠⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠃⠋⠛⠋⠈⠛⠛⠃⠘⠛⠛⠻⠛⠙⠛⠛⠑⠀⠘⠛⠓⠚⠚⠛⠛⠘⠀⠉⠀⠛⠙⠁⠛⠛⠂⠛⠚⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣀⠀⠀⠀⠀⣀⡀⠀⢀⣀⣀⡀⠀⣀⣀⢀⠀⢀⣀⣀⠀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⡀⣀⠀⢀⣀⠀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⢫⣯⣯⣭⣿⣿⣧⣤⣬⣥⣯⣧⣬⣬⣬⣽⣵⣽⣽⣭⣥⣽⣿⣽⣤⣽⣟⠙⣛⣙⠙⣙⣛⡛⡛⢃⠛⠁⠉⠛⠉⠙⠛⠉⠙⠙⠋⠋⠃⠋⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠘⠻⠟⢿⣿⠿⣿⡿⣿⢿⠿⠿⠟⠻⠿⠟⠿⠿⠛⠿⠿⠿⠿⠿⠿⠻⠋⠀⠉⠉⠀⠉⠉⠉⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢀⣄⣀⣀⢀⣋⣀⣄⣀⣁⣠⣄⡀⢀⡀⢀⣤⣀⢀⣠⣀⡀⢠⣠⢠⣤⣤⣠⣀⣠⣀⣤⣠⣤⣠⣤⠀⣀⢀⣠⣠⣄⣤⣤⣄⣤⣤⣄⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⠉⡍⡍⣅⣅⢀⣄⣄⡈⢉⢉⣁⣈⣁⣈⣉⣉⡈⠉⢡⣅⣬⡁⣨⢬⢭⢩⠉⢉⠉⢩⢉⠉⣭⣅⢀⣉⣡⠉⢉⡁⠀⠉⠉⠉⠁⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠉⠉⠁⠉⠉⠉⠁⠈⠉⠉⠙⠉⠉⠉⠉⠉⠀⠈⠉⠉⠉⠉⠉⠉⠈⠀⠈⠀⠈⠈⠀⠉⠉⠁⠉⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣄⣀⣀⡀⣀⣄⡄⠀⢠⣤⣤⡄⢀⡀⢠⣤⠄⢠⣤⣤⡀⣤⣤⡤⠀⣤⣤⣤⣤⠄⢠⢠⣤⣀⣤⣤⡤⣤⣄⣄⣠⣤⣤⣤⣠⢤⣤⣤⣤⣤⣤⡀⡤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠉⡅⣍⣤⣍⢩⣥⣤⡌⢉⢉⣁⣄⣁⣈⣩⣁⡈⠉⢩⣤⡬⡭⣭⢤⣭⢭⠉⣩⠀⣨⣭⠉⣤⣩⡉⣉⢭⠉⠉⠁⠉⠁⠀⠈⠉⠈⠉⠁⠉⠉⠉⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠁⠁⠁⠀⠀⠁⠁⠀⠉⠉⠙⠉⠈⠈⠉⠈⠀⠈⠉⠉⠈⠉⠉⠀⠈⠀⠈⠀⠉⠉⠀⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣤⣤⣀⣀⣄⣤⡄⠀⢠⣤⣤⡄⢠⡀⢠⣤⡀⢠⣤⣤⡄⣤⣤⣄⡠⣤⣤⠀⣤⠀⢤⣤⣤⣤⡤⣤⠤⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠤⣦⣤⠠⣤⣤⣰⢄⢠⢤⣤⣤⣤⡄⢠⡄⣠⣤⠀⢠⢀⠀⣠⣤⣠⣤⠀⢠⠀⣤⣤⠄⣤⢠⢀⡄⠀⣄⣄⣴⣵⣄⣄⣤⡄⡄⠀⡄⢀⣄⡄⢠⣦⣄⢤⡄⡄⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⡤⣤⠀⢰⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⢷⠶⠴⠶⠶⠦⠄⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣄⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠷⠾⠖⠶⠾⠶⠴⠶⠄⠀⠐⠐⠀⠂⠀⠐⠀⠀⠂⠒⢤ ⡇⠯⠶⠧⠶⢶⡶⡤⠆⠸⠆⠷⠶⠶⠆⠸⠷⠶⠲⠶⠺⠆⠸⠷⠶⠶⠶⠾⠶⠶⠼⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⡀⠀⠀⠀⠸⠷⠇⠸⠿⠧⠸⠿⠥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠟⠿⠻⠧⠀⠀⠀⠀⠸⠷⠶⠲⠶⠶⠶⠶⠆⠸⠷⠶⠲⠸⠶⠶⠂⠸⠶⠺⠸⠹⠛⠽⠙⠶⠖⠐⠗⠶⠗⠐⠀⣗⡿⠷⠶⠶⠆⠷⠖⠗⠂⡆⠘⠅⠂⠀⠀⠸⠿⠇⠸⠻⠇⠺⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠻⠖⠧⠷⠖⠇⠀⠀⠸⠷⠶⠲⠆⠸⠱⠾⠺⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠷⠶⠂⠞⠰⠿⠶⠶⠴⠖⠶⠶⠆⠀⠸⠇⠸⠾⠃⠸⠆⠼⠿⠆⠘⠣⠟⠿⠠⠀⠀⠀⠀⢸ ⡟⠟⠒⠆⠇⠗⠶⠀⠀⠸⠷⠖⠞⠇⠸⠱⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡟⠏⠷⠒⠶⠶⠾⠷⠴⠞⠇⠀⠀⠀⠀⠀⠸⠿⠅⠘⠿⠗⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡏⠛⠛⠚⠓⠓⠂⠁⠀⠀⠇⠐⠳⠓⠓⠚⠂⠘⠚⠛⠒⠛⠚⠐⠾⠆⠾⠚⠚⠺⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⠛⠓⠒⠛⠂⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⡆⠀⠀⠀⠈⠀⠀⠀⠀⠐⠀⠀⠂⠈⠘⠀⠈⠒⠐⠀⠀⠀⠀⠐⠀⠀⠀⠂⠁⠀⠀⠀⠑⠈⠀⠀⠈⠐⠐⠀⠀⠐⠂⠀⠒⠁⠀⢲⢲⠒⠆⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠀⠀⢳ ⡇⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⢀⡀⡀⢀⣀⡀⠀⠀⣀⢀⠀⢀⣀⣀⢀⣀⢀⡀⠀⡀⣀⣀⡀⠀⣀⡀⠀⣀⣀⡀⣈⣈⣀⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠐⠛⠛⡛⡛⣉⡛⢛⣃⡀⠘⠛⠛⠃⠘⢃⠘⢉⠃⠙⠛⢛⣁⡛⣛⣓⣀⣛⢛⠘⢙⠛⡛⢛⠈⣛⣛⠃⠓⣋⠛⠛⠈⠛⠛⠛⠛⠓⠓⠓⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠃⠋⠛⠋⠈⠛⠛⠃⠘⠙⠛⠻⠋⠙⠙⠛⠁⠀⠘⠛⠑⠓⠛⠚⠚⠙⠀⠙⠀⠛⠙⠀⠛⠛⠋⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣀⠀⠀⢀⠀⣀⡀⠀⢀⣀⣀⡀⠀⣀⢀⢀⡀⢀⣀⣀⠀⣀⣀⣀⠀⣀⣀⣀⡀⣀⣀⣀⣀⢀⣀⠀⣀⢀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⢻⣯⣯⣭⣿⣿⣧⣤⣼⣥⣯⣧⣬⣼⣿⣭⣥⣼⣽⣭⣥⣽⣿⣽⣤⣽⣟⠙⣛⣉⠙⣛⣛⢛⡛⢁⠓⠉⠛⠋⠉⠛⠙⠙⠉⠛⠃⠋⠃⠋⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠘⠟⠟⢿⣿⠿⣿⡿⣻⢿⠿⠿⠿⠻⠟⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠋⠀⠉⠉⠀⠉⠉⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣀⣀⣀⣀⣋⣀⡀⡀⢁⣠⣄⡀⢀⠀⢠⣄⡀⢀⣠⣀⡀⢠⡠⢠⣠⣀⣠⣠⣠⣀⣄⣠⣤⣠⣠⠀⣄⢀⣀⣀⣄⣄⣠⣀⣄⡄⣄⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⠉⡍⡍⣁⣍⢀⣄⣄⡈⢉⢉⣁⣈⣁⣈⣉⣁⡈⠉⢩⣀⣬⡍⣭⣭⣭⢩⠉⢩⠉⢩⣉⠉⣭⣥⢀⣉⢡⠉⠉⠁⠀⠉⠉⠋⠁⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠉⠉⠁⠉⠉⠉⠁⠈⠉⠉⠙⠉⠈⠉⠉⠈⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠉⠀⠉⠉⠀⠉⠉⠁⠉⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣄⣀⣀⡀⣀⣄⡄⠀⢠⣤⣤⡄⢀⠀⢠⣤⡄⣠⣤⣤⡀⣤⣤⡤⠀⣤⣤⣤⣤⠀⣠⣠⣤⡀⣤⣤⡤⣤⣄⡄⣠⣤⣄⣠⣤⢤⣤⣤⣄⣤⣤⡤⡤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠉⡍⣍⣤⣍⢩⣥⣤⡈⢉⣉⣡⣀⣠⣈⣩⣁⡈⠉⢩⣤⣬⡭⣭⢤⢭⢭⠉⢭⠀⣭⣭⠉⣤⣥⣩⣉⣭⠉⠉⠀⠉⠁⠀⠉⠉⠈⠉⠁⠉⠉⠁⠉⠁⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠁⠀⠁⠀⠀⠈⠀⠀⠉⠉⠘⠁⠀⠀⠈⠀⠀⠀⠈⠈⠈⠉⠉⠈⠀⠀⠈⠀⠉⠉⠀⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣠⣤⣤⣀⠠⣄⣤⡄⠀⢠⣤⣤⡄⢠⠀⢠⣤⡄⢠⣤⣤⠀⣤⣤⣠⠠⣠⣠⠀⣤⠀⢤⣤⣤⣤⡤⣤⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡤⣤⡤⠠⣤⣤⡄⠀⢠⣤⣤⣤⣤⡄⢠⡄⢠⣠⠀⢠⢀⠀⣠⣠⣤⣤⠀⢠⠀⣤⡤⠀⣤⢠⠀⡄⠀⣄⣄⣄⣤⣄⣄⣤⡄⡄⠀⡆⢀⣆⡄⢠⣦⣄⢤⡄⡄⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⣤⢤⠀⢴⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⢷⠶⠴⠶⠶⠦⠄⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣄⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠷⠾⠖⠶⠾⠶⠴⠶⠄⠀⠐⠐⠀⠂⠀⠐⠀⠀⠂⠒⢤ ⡇⠯⠶⠧⠶⢶⡶⡤⠆⠸⠆⠷⠶⠶⠆⠸⠷⠶⠲⠶⠺⠆⠸⠷⠶⠶⠶⠾⠶⠶⠼⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⡀⠀⠀⠀⠸⠷⠇⠸⠿⠧⠸⠿⠥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠟⠿⠻⠧⠀⠀⠀⠀⠸⠷⠶⠲⠶⠶⠶⠶⠆⠸⠷⠶⠲⠸⠶⠶⠂⠸⠶⠺⠻⠻⠛⠽⠙⠶⠖⠐⠗⠶⠗⠐⠀⣗⡿⠷⠶⠶⠆⠷⠖⠗⠂⡆⠘⠅⠂⠀⠀⠸⠿⠇⠸⠻⠇⠺⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠻⠖⠧⠷⠖⠇⠀⠀⠸⠷⠶⠲⠆⠸⠱⠾⠪⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠷⠶⠂⠞⠰⠿⠶⠶⠴⠖⠶⠶⠆⠀⠸⠇⠸⠾⠃⠸⠆⠼⠿⠎⠘⠣⠟⠿⠠⠀⠀⠀⠀⢸ ⡟⠟⠒⠆⠇⠗⠶⠀⠀⠸⠷⠖⠞⠇⠸⠱⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡟⠏⠷⠒⠶⠶⠾⠷⠴⠞⠇⠀⠀⠀⠀⠀⠸⠿⠅⠘⠿⠗⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡏⠛⠛⠚⠓⠓⠂⠁⠀⠀⠇⠐⠳⠓⠓⠚⠂⠘⠚⠛⠖⠛⠚⠐⠾⠆⠾⠚⠚⠺⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⠛⠓⠒⠛⠂⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⡆⠀⠀⠀⠈⠀⠀⠀⠀⠐⠀⠀⠂⠈⠘⠀⠈⠒⠐⠀⠀⠀⠀⠐⠀⠀⠀⠂⠁⠀⠀⠀⠑⠈⠀⠀⠈⠐⠐⠀⠀⠐⠂⠀⠒⠁⠀⢲⢲⠒⠆⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠀⠀⢳ ⡇⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⢀⡀⡀⢀⣀⡀⠀⠀⣀⢀⠀⢀⣀⣀⢀⣀⢀⡀⠀⡀⣀⣀⡀⠀⣀⡀⠀⣀⣀⡀⣈⣈⣀⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠐⠛⠛⡛⡛⣉⡛⢛⣃⡀⠘⠛⠛⠃⠘⢃⠘⢉⠇⠙⠛⢛⣁⡛⣛⣓⣀⣛⢛⠘⢙⠛⡻⢛⠈⣛⣟⠃⠓⣋⠛⠛⠈⠛⠛⠛⠛⠓⠃⠓⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠃⠋⠛⠋⠈⠻⠛⠃⠘⠙⠛⠻⠋⠙⠙⠟⠁⠀⠘⠛⠑⠓⠛⠚⠚⠙⠀⠙⠀⠛⠙⠀⠛⠛⠋⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣀⠀⠀⢀⠀⣀⡀⠀⢀⣀⣀⡀⠀⣀⢀⢀⡀⢀⣀⣀⠀⣀⣀⣀⠀⣀⣀⣀⡀⣀⣀⣀⣀⢀⣀⠀⣀⢀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⢻⣯⣯⣭⣿⣿⣧⣤⣼⣥⣯⣧⣬⣼⣿⣭⣥⣼⣽⣭⣥⣽⣿⣽⣤⣽⣟⠙⣛⣉⠙⣛⣛⢛⡛⢁⠓⠉⠛⠋⠉⠛⠙⠙⠉⠛⠃⠋⠃⠋⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠘⠟⠟⢿⣿⠿⣿⡿⣻⢿⠿⠿⠿⠻⠟⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠋⠀⠉⠉⠀⠉⠉⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣀⣀⣀⣀⣋⣀⡀⡀⢁⣠⣄⡀⢀⠀⢠⣄⡀⢀⣠⣀⡀⢠⡠⢠⣠⣀⣠⣠⣠⣀⣄⣠⣤⣠⣠⠀⣄⢀⣀⣀⣄⣄⣠⣀⣄⡄⣄⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⠉⡍⡍⣁⣍⢀⣄⣄⡈⢉⢉⣁⣈⣁⣈⣉⣁⡈⠉⢩⣀⣬⡍⣭⣭⣭⢩⠉⢩⠉⢩⣉⠉⣭⣅⢀⣉⢡⠉⠉⠁⠀⠉⠉⠋⠁⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠉⠉⠁⠉⠉⠉⠁⠈⠉⠉⠙⠉⠈⠉⠉⠈⠀⠈⠉⠉⠉⠉⠉⠉⠀⠁⠉⠀⠉⠉⠀⠉⠙⠁⠉⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣄⣀⣀⡀⣀⣄⡄⠀⢠⣤⣤⡄⢀⠀⢠⣤⡄⣠⣤⣤⡀⣤⣤⡤⠀⣤⣤⣤⣤⠀⣠⣠⣤⡀⣤⣤⡤⣤⣄⡄⣠⣤⣄⣠⣤⢤⣤⣤⣄⣤⣤⡤⡤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠉⡍⣍⣤⣍⢩⣥⣤⡈⢉⣉⣡⣀⣠⣈⣩⣁⡈⠉⢩⣤⣬⡭⣭⢤⢭⢭⠉⢭⠀⣭⣭⠉⣤⣥⣩⣉⣭⠉⠉⠄⠉⠁⠀⠉⠉⠈⠉⠁⠉⠉⠁⠉⠁⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠁⠀⠁⠀⠂⠈⠀⠀⠉⠉⠘⠁⠀⠀⠈⠀⠀⠀⠈⠈⠈⠉⠉⠈⠀⠁⠈⠀⠉⠉⠀⠉⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣠⣤⣤⣀⠠⣄⣤⡄⠀⢠⣤⣤⡄⢠⠀⢠⣤⡄⢠⣤⣤⠀⣤⣤⣠⠠⣠⣠⠀⣤⠀⢤⣤⣤⣤⡤⣤⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡤⣤⡤⠠⣤⣤⡄⠀⢠⣤⣤⣤⣤⡄⢠⡆⢠⣠⠀⢠⢀⠀⣠⣠⣤⣤⠀⢠⠀⣤⡤⠀⣤⢠⠀⡄⠀⣄⣄⣄⣤⣄⣄⣤⡄⡄⠀⡆⢀⣆⡄⢠⣦⣄⢤⡄⡄⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⡤⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⣤⢤⠀⢴⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⢷⠶⠴⠶⠶⠦⠄⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣄⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠷⠾⠖⠶⠾⠶⠴⠶⠄⠀⠐⠐⠀⠂⠀⠐⠀⠀⠂⠒⢤ ⡇⠯⠶⠧⠶⢶⡶⡤⠆⠸⠄⠷⠶⠶⠆⠸⠷⠶⠲⠶⠺⠆⠸⠷⠶⠶⠶⠾⠶⠶⠼⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⡀⠀⠀⠀⠸⠷⠇⠘⠿⠧⠸⠏⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠟⠿⠻⠧⠀⠀⠀⠀⠸⠷⠶⠲⠶⠶⠶⠶⠆⠸⠷⠶⠲⠸⠶⠶⠂⠸⠶⠲⡾⠻⠛⠽⠙⠶⠖⠐⠗⠶⠗⠐⠀⣗⡿⠷⠶⠶⠆⠷⠖⠗⠂⡆⠘⠅⠂⠀⠀⠸⠿⠇⠸⠻⠧⠺⠷⠔⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠻⠖⠧⠷⠖⠇⠀⠀⠸⠷⠶⠲⠆⠸⠱⠾⠪⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠷⠶⠂⠞⠰⠿⠶⠶⠴⠖⠶⠶⠆⠀⠸⠇⠸⠾⠃⠸⠆⠼⠿⠦⠘⠣⠛⠿⠠⠀⠀⠀⠀⢸ ⡟⠟⠒⠆⠇⠗⠶⠀⠀⠸⠷⠖⠞⠇⠸⠱⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡟⠏⠷⠒⠶⠶⠾⠷⠴⠞⠇⠀⠀⠀⠀⠀⠸⠿⠅⠘⠿⠗⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡏⠛⠛⠚⠓⠓⠂⠁⠀⠀⠇⠐⠳⠓⠓⠚⠂⠘⠚⠛⠖⠛⠚⠐⠾⠆⠾⠚⠚⠺⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣗⠛⠓⠒⠛⠂⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⡆⠀⠀⠀⠈⠀⠀⠀⠀⠐⠀⠀⠂⠈⠘⠀⠈⠒⠐⠀⠀⠀⠀⠐⠀⠀⠀⠂⠁⠀⠀⠀⠑⠈⠀⠀⠈⠐⠐⠀⠀⠐⠂⠀⠒⠁⠀⢲⢲⠒⠆⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠀⠀⢲ ⡇⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⢀⡀⡀⢀⣀⡀⠀⠀⣀⢀⠀⢀⣀⣀⢀⣀⢀⡀⠀⡀⣀⣀⡀⠀⣀⡀⠀⣀⣀⡀⣈⣈⣀⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠐⠛⠛⡛⡛⣉⡛⢛⣃⡀⠘⠛⠛⠃⠈⢀⠘⠉⠇⠙⠛⢛⣁⡛⣛⣓⣀⣛⢛⠘⢙⠛⡻⢛⠈⣛⣟⠃⠓⣋⠛⠛⠈⠛⠛⠛⠛⠓⠃⠓⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠃⠋⠛⠃⠈⠿⠛⠃⠘⠙⠛⠻⠋⠙⠱⠟⠁⠀⠘⠛⠑⠓⠛⠚⠚⠙⠀⠙⠀⠛⠙⠀⠛⠛⠋⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣀⠀⠀⢀⠀⣀⡀⠀⢀⣀⣀⡀⠀⣀⢀⢀⡀⢀⣀⣀⠀⣀⣀⣀⠀⣀⣀⣀⡀⣀⣀⣀⣀⢀⣀⠀⣀⢀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⢻⣯⣯⣭⣧⣿⣧⣤⣼⣥⣯⣧⣬⣼⣿⣭⣥⣼⣽⣭⣥⣽⣿⣽⣤⣽⣟⠙⣛⣉⠙⣛⣛⢛⡛⢁⠓⠉⠛⠋⠉⠛⠙⠙⠉⠛⠃⠋⠃⠋⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠘⠟⠟⢿⣿⠿⣿⡿⣻⢿⠿⠿⠿⠻⠟⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠋⠀⠉⠉⠀⠉⠉⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣀⣀⣀⣀⣋⣀⡀⡀⢁⣠⣄⡀⢀⠀⢠⣄⡀⢀⣠⣀⡀⢠⡠⢠⣠⣀⣠⣠⣠⣀⣄⣠⣤⣠⣠⠀⣄⢀⣀⣀⣄⣄⣠⣀⣄⡄⣄⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⠉⡍⡍⣁⣍⢀⣄⣄⡈⢉⢉⣁⣈⣁⣈⣍⣁⡈⠉⢩⣀⣬⡍⣭⣭⣭⢩⠉⢩⠉⢩⣉⠉⣭⣅⢀⣉⢡⠉⠉⠁⠀⠉⠉⠋⠁⠁⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠉⠉⠁⠉⠉⠉⠁⠈⠉⠉⠙⠉⠈⠉⠉⠈⠀⠈⠉⠉⠉⠉⠉⠉⠀⠁⠉⠀⠉⠉⠀⠉⠛⠁⠉⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣄⣀⣀⡀⣀⣄⡄⠀⢠⣤⣤⡄⢀⠀⢠⣤⡄⣠⣤⣤⡀⣤⣤⡤⠀⣤⣤⣤⣤⠀⣠⣠⣤⡀⣤⣤⡤⣤⣄⡄⣠⣤⣄⣠⣤⢤⣤⣤⣄⣤⣤⡤⡤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠉⡍⣍⣤⣍⢩⣥⣤⡈⢉⣉⣡⣀⣠⣈⣩⣁⡈⠉⢩⣤⣬⡭⣭⢤⢭⢭⠉⢭⠀⣭⣭⠉⣤⣥⣩⣉⣭⠉⠉⠄⠉⠁⠀⠉⠉⠈⠉⠁⠉⠉⠁⠅⡃⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠁⠀⠁⠀⠂⠈⠀⠀⠉⠉⠘⠁⠀⠀⠈⠀⠀⠀⠈⠈⠈⠉⠉⠈⠀⠁⠈⠀⠉⢉⠀⠑⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣠⣤⣤⣀⠠⣄⣤⡄⠀⢠⣤⣤⡄⢠⠀⢠⣤⡄⢠⣤⣤⠀⣤⣤⣠⠠⣠⣠⠀⣤⠀⢤⣤⣤⣤⡤⣤⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡤⣤⡤⠠⣤⣤⡄⠀⢠⣤⣤⣤⣤⡄⢠⡄⢠⣠⠀⢠⢀⠀⣠⣠⣤⣤⠀⢠⠀⣤⡤⠀⣤⢠⠀⡄⠀⣄⣄⣄⣤⣄⣄⣤⡄⡄⠀⡆⢀⣆⡄⢠⣦⣄⢤⡄⡄⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⡤⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠌⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⣤⢤⠀⢴⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⢷⠶⠴⠶⠶⠦⠄⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣄⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠷⠾⠖⠶⠾⠶⠴⠶⠄⠀⠐⠐⠀⠂⠀⠐⠀⠀⠂⠒⢤ ⡇⠯⠶⠧⠶⢶⡶⡤⠆⠸⠄⠷⠶⠶⠆⠸⠷⠶⠲⠶⠺⠆⠸⠷⠶⠶⠶⠾⠶⠶⠼⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⡀⠀⠀⠀⠸⠷⠇⠘⠿⠧⠸⠏⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠟⠿⠻⠧⠀⠀⠀⠀⠸⠷⠶⠲⠶⠶⠶⠶⠆⠸⠷⠶⠲⠸⠶⠶⠂⠸⠶⠲⡾⠻⠛⠽⠙⠶⠖⠐⠗⠶⠗⠐⠀⣗⡿⠷⠶⠶⠆⠷⠖⠗⠂⡆⠘⠅⠂⠀⠀⠸⠿⠇⠸⠻⠧⠺⠷⠔⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠻⠖⠧⠷⠖⠇⠀⠀⠸⠷⠶⠲⠆⠸⠱⠾⠪⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠷⠶⠂⠶⠰⠿⠶⠶⠴⠖⠶⠶⠆⠀⠸⠇⠸⠾⠃⠸⠆⠼⠿⠦⠘⠣⠛⠿⠠⠀⠀⠀⠀⢸ ⡟⠟⠒⠆⠇⠗⢶⠀⠀⠸⠷⠖⠞⠇⠸⠱⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡟⠏⠷⠒⠶⠶⠾⠷⠴⠞⠇⠀⠀⠀⠀⠀⠸⠿⠅⠘⠿⠗⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡏⠛⠛⠚⠓⠓⠂⠁⠀⠀⠇⠐⠳⠓⠓⠚⠂⠘⠚⠛⠖⠛⠚⠐⠾⠆⠾⠚⠚⠺⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣗⠛⠓⠒⠛⠂⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⡆⠀⠀⠀⠈⠀⠀⠀⠀⠐⠀⠀⠂⠈⠘⠀⠈⠒⠐⠀⠀⠀⠀⠐⠀⠀⠀⠂⠁⠀⠀⠀⠑⠈⠀⠀⠀⠐⠐⠀⠀⠐⠂⠀⠒⠁⠀⢲⢲⠒⠆⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠀⠀⢲ ⡇⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⢀⡀⡀⢀⣀⡀⠀⠀⣀⢀⠀⢀⣀⣀⢀⣀⢀⡀⠀⡀⣀⣀⡀⠀⣀⡀⠀⣀⣀⡀⣈⣈⣀⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠐⠛⠛⡛⡛⣉⡛⢛⣃⡀⠘⠛⠛⠃⠀⢀⠘⠉⠇⠙⠛⢛⣁⡛⣛⣓⣀⣛⢛⠘⢙⠛⡻⢛⠈⣛⣟⠃⠓⣋⠛⠛⠈⠛⠛⠛⠛⠓⠃⠓⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠃⠋⠛⠃⠈⠿⠛⠃⠘⠙⠛⠻⠋⠛⠱⠟⠁⠀⠘⠛⠑⠓⠛⠚⠚⠘⠀⠙⠀⠛⠙⠀⠛⠛⠋⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣀⠀⠀⢀⠀⣀⡀⠀⢀⣀⣀⡀⠀⣀⢀⢀⡀⢀⣀⣀⠀⣀⣀⣀⠀⣀⣀⣀⡀⣀⣀⣀⣀⢀⣀⠀⣀⢀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⢻⣯⣯⣭⣧⣿⣧⣤⣼⣥⣯⣧⣬⣼⣿⣭⣥⣼⣽⣭⣥⣽⣿⣽⣤⣽⣟⠙⣛⣉⠙⣛⣛⢟⡛⢁⠓⠉⠛⠋⠈⠛⠙⠙⠉⠛⠃⠋⠃⠋⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠘⠟⠟⢿⣿⠿⣿⡿⣻⢿⠿⠿⠿⠻⠟⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠋⠀⠉⠉⠀⠉⠉⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣀⣀⣀⣀⣋⣀⡀⡀⢁⣠⣄⡀⢀⠀⢠⣄⡀⢀⣠⣀⡀⢠⡠⢠⣠⣀⣠⣠⣠⣀⣄⣠⣤⣠⣠⠀⣄⢀⣀⣀⣄⣄⣠⣀⣄⡄⣄⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⠉⡍⡍⣁⣍⢀⣄⣄⡈⢉⢉⣁⣈⣁⣨⣍⣁⡈⠉⢩⣀⣬⡍⣭⣭⣭⢩⠉⢩⠉⢩⣉⠉⣭⣅⢀⣉⢡⠉⠉⠁⠀⠉⠉⠋⠁⠁⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠉⠉⠁⠉⠉⠉⠁⠈⠉⠉⠙⠉⠈⠉⠉⠈⠀⠈⠉⠉⠙⠉⠉⠉⠀⠃⠉⠀⠉⠉⠀⠉⠛⠁⠉⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣄⣀⣀⡀⣀⣄⡄⠀⢠⣤⣤⡄⢀⠀⢠⣤⡄⣠⣤⣤⡀⣤⣤⡤⠀⣤⣤⣤⣤⠀⣠⣠⣤⡀⣤⣤⡤⣤⣄⡄⣠⣤⣄⣠⣤⢤⣤⣤⣄⣤⣤⡤⡤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠉⡍⣍⣤⣍⢩⣥⣤⡈⢉⣉⣡⣀⣠⣈⣩⣁⡈⠉⢩⣤⣬⡭⣭⢤⢭⢭⠉⢭⠀⣭⣭⠉⣤⣥⣩⣉⣭⠉⠉⠀⠉⠁⠀⠉⠉⠈⠉⠁⠉⠉⠁⠅⡃⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠁⠀⠁⠀⠂⠈⠀⠀⠉⠉⠘⠁⠀⠀⠈⠀⠀⠀⠈⠈⠈⠉⠉⠈⠀⠃⠈⠀⠉⠉⠂⠑⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣠⣤⣤⣀⠠⣄⣤⡄⠀⢠⣤⣤⡄⢠⠀⢠⣤⡄⢠⣤⣤⠀⣤⣤⣀⠠⣠⣠⠀⣤⠀⢤⣤⣤⣤⡤⣤⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡤⣤⡤⠠⣤⣤⡄⠀⢠⣤⣤⣤⣤⡄⢠⡄⢠⣠⠀⢠⢀⠀⣠⣠⣤⣤⠀⢠⠀⣤⡤⠀⣤⢠⠀⡄⠀⣄⣄⣄⣤⣄⣄⣤⡄⡄⠀⡆⢀⣆⡄⢠⣦⣄⢤⡄⡄⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⡤⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠌⠀⠉⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⣤⢤⠀⢴⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⢷⠶⠴⠶⠶⠦⠄⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣄⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠷⠾⠖⠶⠾⠶⠴⠶⠄⠀⠐⠐⠀⠂⠀⠐⠀⠀⠂⠒⢤ ⡇⠯⠶⠧⠶⢶⡶⡤⠆⠸⠄⠷⠶⠶⠆⠸⠷⠶⠲⠶⠺⠆⠸⠷⠶⠶⠶⠾⠶⠶⠼⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⡀⠀⠀⠀⠸⠷⠇⠘⠿⠧⠸⠏⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠟⠿⠻⠧⠀⠀⠀⠀⠸⠷⠶⠲⠶⠶⠶⠶⠆⠸⠷⠶⠲⠸⠶⠶⠂⠸⠶⠲⡾⠻⠛⠽⠙⠶⠖⠐⠗⠶⠗⠐⠀⣗⡿⠷⠶⠶⠆⠷⠖⠗⠂⡆⠘⠅⠂⠀⠀⠸⠿⠇⠸⠻⠧⠺⠷⠔⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠻⠖⠧⠷⠖⠇⠀⠀⠸⠷⠶⠲⠆⠸⠱⠾⠪⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠷⠶⠂⠶⠰⠿⠶⠶⠴⠖⠶⠶⠆⠀⠸⠇⠸⠾⠃⠸⠆⠼⠿⠦⠘⠣⠛⠿⠠⠀⠀⠀⠀⢸ ⡟⠟⠒⠆⠇⠗⢶⠀⠀⠸⠷⠖⠞⠇⠸⠱⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡟⠏⠷⠒⠶⠶⠾⠷⠴⠖⠇⠀⠀⠀⠀⠀⠸⠿⠅⠘⠿⠗⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡘ ⡏⠛⠛⠚⠓⠓⠂⠁⠀⠀⠇⠐⠳⠓⠓⠚⠂⠘⠚⠛⠖⠛⠚⠐⠾⠆⠾⠚⠚⠺⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣗⠛⠓⠒⠛⠂⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢃ ⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⡆⠀⠀⠀⠈⠀⠀⠀⠀⠐⠀⠀⠂⠈⠘⠀⠈⠒⠐⠀⠀⠀⠀⠐⠀⠀⠀⠂⠁⠀⠀⠀⠑⠈⠀⠀⠀⠐⠐⠀⠀⠐⠂⠀⠒⠁⠀⢲⢲⠒⠆⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠀⠀⢲ ⡇⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⢀⡀⡀⢀⣀⡀⠀⠀⣀⢀⠀⢀⣀⣀⢀⣀⢀⡀⠀⡀⣀⣀⡀⠀⣀⡀⠀⣀⣀⡀⣈⣈⣀⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠐⠛⠛⡛⡛⣉⡛⢛⣃⡀⠘⠛⠛⠃⠀⢀⠘⠉⠇⠙⠛⢛⣁⡛⣛⣓⣀⣛⢛⠘⢙⠛⡻⢛⠈⣛⣟⠃⠓⣋⠛⠛⠈⠛⠛⠛⠛⠓⠃⠓⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠃⠋⠛⠃⠈⠿⠛⠃⠘⠙⠛⠻⠋⠛⠱⠟⠁⠀⠘⠛⠑⠓⠛⠚⠚⠘⠀⠙⠀⠛⠙⠀⠛⠛⠋⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣀⠀⠀⢀⠀⣀⡀⠀⢀⣀⣀⡀⠀⣀⢀⢀⡀⢀⣀⣀⠀⣀⣀⣀⠀⣀⣀⣀⡀⣀⣀⣀⣀⢀⣀⠀⣀⢀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⢻⣯⣯⣭⣧⣿⣧⣤⣼⣥⣯⣧⣬⣼⣿⣭⣥⣼⣽⣭⣥⣽⣿⣽⣤⣽⣟⠙⣛⣉⠙⣋⣛⢟⡛⢁⠓⠉⠛⠋⠈⠛⠙⠙⠉⠛⠃⠋⠃⠋⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠘⠟⠟⢿⣿⠿⣿⡿⣻⢿⠿⠿⠿⠻⠟⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠋⠀⠉⠉⠀⠉⠉⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣀⣀⣀⣀⣋⣀⡀⡀⢁⣠⣄⡀⢀⠀⢠⣄⡀⢀⣠⣀⡀⢠⡠⢠⣠⣀⣠⣠⣠⣀⣄⣠⣤⣠⣠⠀⣄⢀⣀⣀⣄⣄⣠⣀⣄⡄⣄⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⠉⡍⡍⣁⣍⢀⣄⣄⡈⢉⢉⣁⣈⣁⣨⣍⣁⡈⠉⢩⣀⣬⡍⣭⣭⣭⢩⠉⢩⠉⢩⣉⠉⣭⣅⢀⣉⢡⠉⠉⠁⠀⠉⠉⠋⠁⠁⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠉⠉⠁⠉⠉⠉⠁⠈⠉⠉⠙⠉⠈⠉⠉⠈⠀⠈⠉⠉⠙⠉⠉⠉⠀⠃⠉⠀⠉⠉⠀⠉⠛⠁⠉⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣄⣀⣀⡀⣀⣄⡄⠀⢠⣤⣤⡄⢀⠀⢠⣤⡄⣠⣤⣤⡀⣤⣤⡤⠀⢤⣤⣤⣤⠀⣠⣠⣤⡀⣤⣤⡤⣤⣄⡄⣠⣤⣄⣠⣤⢤⣤⣤⣄⣤⣤⡤⡤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠉⡍⣍⣤⣍⢩⣥⣤⡈⢉⣉⣡⣀⣠⣈⣩⣁⡈⠉⢩⣤⣬⡭⣭⢤⢭⢭⠉⢭⠀⣭⣭⠉⣤⣥⣉⣉⣭⠉⠉⠀⠉⠁⠀⠉⠉⠈⠉⠁⠉⠉⠁⠅⡃⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠁⠀⠁⠀⠂⠈⠀⠀⠉⠉⠘⠁⠀⠀⠈⠀⠀⠀⠈⠈⠈⠉⠉⠈⠀⠃⠈⠀⠉⠉⠂⠑⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣠⣤⣤⣀⠠⣄⣤⡄⠀⢠⣤⣤⡄⢠⠀⢠⣤⡄⢠⣤⣤⠀⣤⣤⣀⠠⢠⣠⠀⣤⠀⢤⣤⣤⣤⡤⣤⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡤⣤⡤⠠⣤⣤⡄⠀⢠⣤⣤⣤⣤⡄⢠⡄⢠⣠⠀⢠⢀⠀⣠⣠⣬⣤⠀⢠⠀⣤⡤⠀⣤⢠⠀⡄⠀⣄⣄⣄⣤⣄⣄⣤⡄⡄⠀⡆⢀⣆⡄⢠⣦⣄⢤⡄⡄⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⡤⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠌⠀⠉⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⣤⢤⠀⢴⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⢷⠶⠴⠶⠶⠦⠄⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣄⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠷⠾⠖⠶⠾⠶⠴⠶⠄⠀⠐⠐⠀⠂⠀⠐⠀⠀⠂⠒⢤ ⡇⠯⠶⠧⠶⢶⡶⡤⠆⠸⠄⠷⠶⠶⠆⠸⠷⠶⠲⠶⠺⠆⠸⠷⠶⠶⠶⠾⠶⠶⠼⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⡀⠀⠀⠀⠸⠷⠇⠘⠿⠧⠸⠏⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠟⠿⠻⠧⠀⠀⠀⠀⠸⠷⠶⠲⠶⠶⠶⠶⠆⠸⠷⠶⠲⠸⠶⠶⠂⠸⠶⠲⡾⠻⠛⠽⠙⠶⠖⠐⠗⠶⠗⠐⠀⣗⡿⠷⠶⠶⠆⠷⠖⠗⠂⡆⠘⠅⠂⠀⠀⠸⠿⠇⠸⠻⠧⠺⠷⠔⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠻⠖⠧⠷⠖⠇⠀⠀⠸⠷⠶⠲⠆⠸⠱⠾⠪⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠷⠶⠂⠶⠰⠿⠶⠶⠴⠖⠶⠶⠆⠀⠸⠇⠸⠾⠃⠸⠆⠼⠿⠦⠘⠣⠛⠿⠠⠀⠀⠀⠀⢸ ⡟⠟⠒⠆⠇⠗⢶⠀⠀⠸⠷⠖⠞⠇⠸⠱⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡟⠏⠷⠒⠶⠶⠾⠷⠴⠖⠇⠀⠀⠀⠀⠀⠸⠿⠅⠘⠿⠗⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡘ ⡏⠛⠛⠚⠓⠓⠂⠁⠀⠀⠇⠐⠳⠓⠓⠚⠂⠘⠚⠛⠖⠛⠚⠐⠾⠆⠾⠚⠚⠺⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣗⠛⠓⠒⠛⠂⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢃ ⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙ ⡆⠀⠀⠀⠈⠀⠀⡀⠀⠐⠀⠀⠂⠈⠘⠀⠈⠒⠐⠀⠀⠀⠀⠐⠀⠀⠀⠂⠁⠀⠀⠀⠑⠈⠀⠀⠀⠐⠐⠀⠀⠐⠂⠀⠒⠁⠀⢲⢲⠒⠆⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠀⠀⢲ ⡇⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⢀⡀⡀⢀⣀⡀⠀⠀⣀⢀⠀⢀⣀⣀⢀⣀⢀⡀⠀⡀⣀⣀⡀⠀⣀⡀⠀⣀⣀⡀⣈⣈⣀⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠐⠛⠛⡛⡛⣉⡛⢛⣃⡀⠘⠛⠛⠃⠀⢀⠘⠉⠇⠙⠛⢛⣁⡛⣛⣓⣀⣛⢛⠘⢙⠛⡻⢛⠈⣛⣟⠃⠓⣋⠛⠛⠈⠛⠛⠛⠛⠓⠃⠓⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠃⠋⠛⠃⠈⠿⠛⠃⠘⠙⠛⠻⠋⠛⠱⠟⠁⠀⠘⠛⠑⠓⠛⠚⠚⠘⠀⠙⠀⠛⠙⠀⠛⠛⠋⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣀⠀⠀⢀⠀⣀⡀⠀⢀⣀⣀⡀⠀⣀⢀⢀⡀⢀⣀⣀⠀⣀⣀⣀⠀⣀⣀⣀⡀⣀⣀⣀⣀⢀⣀⠀⣀⢀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⢻⣯⣯⣭⣧⣿⣧⣤⣼⣥⣯⣧⣬⣼⣿⣭⣥⣼⣽⣭⣥⣽⣿⣽⣤⣽⣟⠙⣛⣉⠙⣋⣛⢟⡛⢁⠓⠉⠛⠋⠈⠛⠙⠙⠉⠛⠃⠋⠃⠋⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠘⠟⠟⢿⣿⠿⣿⡿⣻⢿⠿⠿⠿⠻⠟⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠋⠀⠉⠉⠀⠉⠉⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣀⣀⣀⣀⣋⣀⡀⡀⢁⣠⣄⡀⢀⠀⢠⣄⡀⢀⣠⣀⡀⢠⡠⢠⣠⣀⣠⣠⣠⣀⣄⣠⣤⣠⣠⠀⣄⢀⣀⣀⣄⣄⣠⣀⣄⡄⣄⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⠉⡍⡍⣁⣍⢀⣄⣄⡈⢉⢉⣁⣈⣁⣨⣍⣁⡈⠉⢩⣀⣬⡍⣭⣭⣭⢩⠉⢩⠉⢩⣉⠉⣭⣅⢀⣉⢡⠉⠉⠁⠀⠉⠉⠋⠁⠁⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠉⠉⠁⠉⠉⠉⠁⠈⠉⠉⠙⠉⠈⠉⠉⠈⠀⠈⠉⠉⠙⠉⠉⠉⠀⠃⠉⠀⠉⠉⠀⠉⠛⠁⠉⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣄⣀⣀⡀⣀⣄⡄⠀⢠⣤⣤⡄⢀⠀⢠⣤⡄⣠⣤⣤⡀⣤⣤⡤⠀⢤⣤⣤⣤⠀⣠⣠⣤⡀⣤⣤⡤⣤⣄⡄⣠⣤⣄⣠⣤⢤⣤⣤⣄⣤⣤⡤⡤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠉⡍⣍⣤⣍⢩⣥⣤⡈⢉⣉⣡⣀⣠⣈⣩⣁⡈⠉⢩⣤⣬⡭⣭⢤⢭⢭⠉⢭⠀⣭⣭⠉⣤⣥⣉⣉⣭⠉⠉⠀⠉⠁⠀⠉⠉⠈⠉⠁⠉⠉⠁⠅⡃⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠁⠀⠁⠀⠂⠈⠀⠀⠉⠉⠘⠁⠀⠀⠈⠀⠀⠀⠈⠈⠈⠉⠉⠈⠀⠃⠈⠀⠉⠉⠂⠑⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣠⣤⣤⣀⠠⣄⣤⡄⠀⢠⣤⣤⡄⢠⠀⢠⣤⡄⢠⣤⣤⠀⣤⣤⣀⠠⢤⣠⠀⣤⠀⢤⣤⣤⣤⡤⣤⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡤⣤⣤⡠⣤⣤⡄⠀⢠⣤⣤⣤⣤⡄⢠⡄⢠⣠⠀⢠⢀⠀⣠⣠⣬⣤⠀⢠⠀⣤⡤⠀⣤⢠⠀⡄⠀⣄⣄⣄⣤⣄⣄⣤⡄⡄⠀⡆⢀⣆⡄⢠⣦⣄⢤⡄⡄⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⡤⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠌⠀⠉⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⣤⢤⠀⢴⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⢷⠶⠴⠶⠶⠦⠄⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣄⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠷⠾⠖⠶⠾⠶⠴⠶⠄⠀⠐⠐⠀⠂⠀⠐⠀⠀⠂⠒⢤ ⡇⠯⠶⠧⠶⢶⡶⡤⠆⠸⠄⠷⠶⠶⠆⠸⠷⠶⠲⠶⠺⠆⠸⠷⠶⠶⠶⠾⠶⠶⠼⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⡀⠀⠀⠀⠸⠷⠇⠘⠿⠧⠸⠏⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠟⠿⠻⠧⠀⠀⠀⠀⠸⠷⠶⠲⠶⠶⠶⠶⠆⠸⠷⠶⠲⠸⠶⠶⠂⠸⠶⠲⡾⠻⠛⠽⠙⠶⠖⠐⠗⠶⠗⠐⠀⣗⡿⠷⠶⠶⠆⠷⠖⠗⠂⡆⠘⠅⠂⠀⠀⠸⠿⠇⠸⠻⠧⠺⠷⠔⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠻⠖⠧⠷⠖⠇⠀⠀⠸⠷⠶⠲⠆⠸⠱⠾⠪⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠷⠶⠂⠶⠰⠿⠶⠶⠴⠖⠶⠶⠆⠀⠸⠇⠸⠾⠃⠸⠆⠼⠿⠦⠘⠣⠛⠿⠠⠀⠀⠀⠀⢸ ⡟⠟⠒⠆⠇⠗⢶⠀⠀⠸⠷⠖⠞⠇⠸⠱⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡟⠏⠷⠒⠶⠶⠾⠷⠴⠖⠇⠀⠀⠀⠀⠀⠸⠿⠅⠘⠿⠗⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡘ ⡏⠛⠛⠚⠓⠓⠂⠁⠀⠀⠇⠐⠳⠓⠓⠚⠂⠘⠚⠛⠖⠛⠚⠐⠾⠆⠾⠚⠚⠺⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣗⠛⠓⠒⠛⠂⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢃ ⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙ ⡆⠀⠀⠀⠈⠀⠀⡠⠀⠀⠀⠀⠂⠈⠘⠀⠈⠒⠐⠀⠀⠀⠀⠐⠀⠀⠀⠂⠁⠀⠀⠀⠑⠈⠀⠀⠀⠐⠐⠀⠀⠐⠂⠀⠒⠁⠀⢲⢲⠒⠆⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠀⠀⢲ ⡇⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⢀⡀⡀⢀⣀⡀⠀⠀⣀⢀⠀⢀⣀⣀⢀⣀⢀⡀⠀⡀⣀⣀⡀⠀⣀⡀⠀⣀⣀⡀⣈⣈⣀⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠐⠛⠛⡛⡛⣉⡛⢛⣃⡀⠘⠛⠛⠃⠀⢀⠘⠉⠇⠙⠛⢛⣁⡛⣛⣓⣀⣛⢛⠘⢙⠛⡻⢛⠈⣛⣟⠃⠓⣋⠛⠛⠈⠛⠛⠛⠛⠓⠃⠓⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠃⠋⠛⠃⠈⠿⠛⠃⠘⠙⠛⠻⠋⠛⠱⠟⠁⠀⠘⠛⠑⠓⠛⠚⠚⠘⠀⠙⠀⠛⠙⠀⠛⠛⠋⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣀⠀⠀⢀⠀⣀⡀⠀⢀⣀⣀⡀⠀⣀⢀⢀⡀⢀⣀⣀⠀⣀⣀⣀⠀⣀⣀⣀⡀⣀⣀⣀⣀⢀⣀⠀⣀⢀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⢻⣯⣯⣭⣧⣿⣧⣤⣼⣥⣯⣧⣬⣼⣿⣭⣥⣼⣽⣭⣥⣽⣿⣽⣤⣽⣟⠙⣛⣉⠙⣋⣛⢟⡛⢁⠓⠉⠛⠋⠈⠛⠙⠙⠉⠛⠃⠋⠃⠋⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠘⠟⠟⢿⣿⠿⣿⡿⣻⢿⠿⠿⠿⠻⠟⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠋⠀⠉⠉⠀⠉⠉⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣀⣀⣀⣀⣋⣀⡀⡀⢁⣠⣄⡀⢀⠀⢠⣄⡀⢀⣠⣀⡀⢠⡠⢠⣠⣀⣠⣠⣠⣀⣄⣠⣤⣠⣠⠀⣄⢀⣀⣀⣄⣄⣠⣀⣄⡄⣄⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⠉⡍⡍⣁⣍⢀⣄⣄⡈⢉⢉⣁⣈⣁⣨⣍⣁⡈⠉⢩⣀⣬⡍⣭⣭⣭⢩⠉⢩⠉⢩⣉⠉⣭⣅⢀⣉⢡⠉⠉⠁⠀⠉⠉⠋⠁⠁⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠉⠉⠁⠉⠉⠉⠁⠈⠉⠉⠙⠉⠈⠉⠉⠈⠀⠈⠉⠉⠙⠉⠉⢉⠀⠃⠉⠀⠉⠉⠀⠉⠛⠁⠉⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣄⣀⣀⡀⣀⣄⡄⠀⢠⣤⣤⡄⢀⠀⢠⣤⡄⣠⣤⣤⡀⣤⣤⡤⠀⢤⣤⣤⣤⠀⣠⣠⣤⡀⣤⣤⡤⣤⣄⡄⣠⣤⣄⣠⣤⢤⣤⣤⣄⣤⣤⡤⡤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠉⡍⣍⣤⣍⢩⣥⣤⡈⢉⣉⣡⣀⣠⣈⣩⣁⡈⠉⢩⣤⣬⡭⣭⢤⢭⢭⠉⢭⠀⣭⣭⠉⣤⣥⣉⣉⣭⠉⠉⠀⠉⠁⠀⠉⠉⠈⠉⠁⠉⠉⠁⠅⡃⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠁⠀⠁⠀⠂⠈⠀⠀⠉⠉⠘⠁⠀⠀⠈⠀⠀⠀⠈⠈⠈⠉⠉⠈⠀⠃⠈⠀⠉⠉⠂⠑⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣠⣤⣤⣀⠠⣄⣤⡄⠀⢠⣤⣤⡄⢠⠀⢠⣤⡄⢠⣤⣤⠀⣤⣤⣀⠠⢴⣠⠀⣤⠀⢤⣤⣤⣤⡤⣤⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡤⣤⣴⡠⣤⣤⡄⠀⢠⣤⣤⣤⣤⡄⢠⡄⢠⣠⠀⢠⢀⠀⣠⣠⣬⣤⠀⢠⠀⣤⡤⠀⣤⢠⠀⡄⠀⣄⣄⣄⣤⣄⣄⣤⡄⡄⠀⡆⢀⣆⡄⢠⣦⣄⢤⡄⡄⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⡤⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠌⠀⠉⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⣤⢤⠀⢴⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⢷⠶⠴⠶⠶⠦⠄⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣄⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠷⠾⠖⠶⠾⠶⠴⠶⠄⠀⠐⠐⠀⠂⠀⠐⠀⠀⠂⠒⢤ ⡇⠯⠶⠧⠶⢶⡶⡤⠆⠸⠄⠷⠶⠶⠆⠸⠷⠶⠲⠶⠺⠆⠸⠷⠶⠶⠶⠾⠶⠶⠼⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⡀⠀⠀⠀⠸⠷⠇⠘⠿⠧⠸⠏⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠟⠿⠻⠧⠀⠀⠀⠀⠸⠷⠶⠲⠶⠶⠶⠶⠆⠸⠷⠶⠲⠸⠶⠶⠂⠸⠶⠲⡾⠻⠛⠽⠙⠶⠖⠐⠗⠶⠗⠐⠀⣗⡿⠷⠶⠶⠆⠷⠖⠗⠂⡆⠘⠅⠂⠀⠀⠸⠿⠇⠸⠻⠧⠺⠷⠔⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠻⠖⠧⠷⠖⠇⠀⠀⠸⠷⠶⠲⠆⠸⠱⠾⠪⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠷⠶⠂⠶⠰⠿⠶⠶⠴⠖⠶⠶⠆⠀⠸⠇⠸⠾⠃⠸⠆⠼⠿⠦⠘⠣⠛⠿⠠⠀⠀⠀⠀⢸ ⡟⠟⠒⠆⠇⠗⢶⠀⠀⠸⠷⠖⠞⠇⠸⠱⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡟⠏⠷⠒⠶⠶⠾⠷⠴⠖⠇⠀⠀⠀⠀⠀⠸⠿⠅⠘⠿⠗⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡘ ⡏⠛⠛⠚⠓⠓⠂⠁⠀⠀⠇⠐⠳⠓⠓⠚⠂⠘⠚⠛⠖⠛⠚⠐⠾⠆⠾⠚⠚⠺⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣗⠛⠓⠒⠛⠂⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢃ ⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙ ⡆⠀⠀⠀⠈⠀⠀⡠⠀⠀⠀⠀⠂⠈⠘⠀⠈⠒⠐⠀⠀⠀⠀⠐⠀⠀⠀⠂⠁⠀⠀⠀⠑⠈⠀⠀⠀⠐⠐⠀⠀⠐⠂⠀⠒⠁⠀⢲⢲⠒⠆⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠀⠀⢲ ⡇⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⢀⡀⡀⢀⣀⡀⠀⠀⣀⢀⠀⢀⣀⣀⢀⣀⢀⡀⠀⡀⣀⣀⡀⠀⣀⡀⠀⣀⣀⡀⣈⣈⣀⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠐⠛⠛⡛⡛⣉⡛⢛⣃⡀⠘⠛⠛⠃⠀⢀⠘⠉⠇⠙⠛⢛⣁⡛⣛⣓⣀⣛⢛⠘⢙⠛⡻⢛⠈⣛⣟⠃⠓⣋⠛⠛⠈⠛⠛⠛⠛⠓⠃⠓⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠃⠋⠛⠃⠈⠿⠛⠃⠘⠙⠛⠻⠋⠛⠱⠟⠁⠀⠘⠛⠑⠓⠛⠚⠚⠘⠀⠙⠀⠛⠙⠀⠛⠛⠋⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣀⠀⠀⢀⠀⣀⡀⠀⢀⣀⣀⡀⠀⣀⢀⢀⡀⢀⣀⣀⠀⣀⣀⣀⠀⣀⣀⣀⡀⣀⣀⣀⣀⢀⣀⠀⣀⢀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⢻⣯⣯⣭⣧⣿⣧⣤⣼⣥⣯⣧⣬⣼⣿⣭⣥⣼⣽⣭⣥⣽⣿⣽⣤⣽⣟⠙⣛⣉⠙⣋⣛⢟⡛⢁⠓⠉⠛⠋⠈⠛⠙⠙⠉⠛⠃⠋⠃⠋⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠘⠟⠟⢿⣿⠿⣿⡿⣻⢿⠿⠿⠿⠻⠟⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠋⠀⠉⠉⠀⠉⠉⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣀⣀⣀⣀⣋⣀⡀⡀⢁⣠⣄⡀⢀⠀⢠⣄⡀⢀⣠⣀⡀⢠⡠⢠⣠⣀⣠⣠⣠⣀⣄⣠⣤⣠⣠⠀⣄⢀⣀⣀⣄⣄⣠⣀⣄⡄⣄⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⠉⡍⡍⣁⣍⢀⣄⣄⡈⢉⢉⣁⣈⣁⣨⣍⣁⡈⠉⢩⣀⣬⡍⣭⣭⣭⢩⠉⢩⠉⢩⣉⠉⣭⣅⢀⣉⢡⠉⠉⠁⠀⠉⠉⠋⠁⠁⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠉⠉⠁⠉⠉⠉⠁⠈⠉⠉⠙⠉⠈⠉⠉⠈⠀⠈⠉⠉⠙⠉⠉⢉⠀⠃⠉⠀⠉⠉⠀⠉⠛⠁⠉⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣄⣀⣀⡀⣀⣄⡄⠀⢠⣤⣤⡄⢀⠀⢠⣤⡄⣠⣤⣤⡀⣤⣤⡤⠀⢤⣤⣤⣤⠀⣠⣠⣤⡀⣤⣤⡤⣤⣄⡄⣠⣤⣄⣠⣤⢤⣤⣤⣄⣤⣤⡤⡤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠉⡍⣍⣤⣍⢩⣥⣤⡈⢉⣉⣡⣀⣠⣈⣩⣁⡈⠉⢩⣤⣬⡭⣭⢤⢭⢭⠉⢭⠀⣭⣭⠉⣤⣥⣉⣉⣭⠉⠉⠀⠉⠁⠀⠉⠉⠈⠉⠁⠉⠉⠁⠅⡃⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠁⠀⠁⠀⠂⠈⠀⠀⠉⠉⠘⠁⠀⠀⠈⠀⠀⠀⠈⠈⠈⠉⠉⠈⠀⠃⠈⠀⠉⠉⠂⠑⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣠⣤⣤⣀⠠⣄⣤⡄⠀⢠⣤⣤⡄⢠⠀⢠⣤⡄⢠⣤⣤⠀⣤⣤⣀⠠⢴⣠⠀⣤⠀⢤⣤⣤⣤⡤⣤⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡤⣤⣴⡠⣤⣤⡄⠀⢠⣤⣤⣤⣤⡄⢠⡄⢠⣠⠀⢠⢀⠀⣠⣠⣬⣤⠀⢠⠀⣤⡤⠀⣤⢠⠀⡄⠀⣄⣄⣄⣤⣄⣄⣤⡄⡄⠀⡆⢀⣆⡄⢠⣦⣄⢤⡄⡄⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⡤⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠌⠀⠉⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⣤⢤⠀⢴⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⢷⠶⠴⠶⠶⠦⠄⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣄⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠷⠾⠖⠶⠾⠶⠴⠶⠄⠀⠐⠐⠀⠂⠀⠐⠀⠀⠂⠒⢤ ⡇⠯⠶⠧⠶⢶⡶⡤⠆⠸⠄⠷⠶⠶⠆⠸⠷⠶⠲⠶⠺⠆⠸⠷⠶⠶⠶⠾⠶⠶⠼⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⡀⠀⠀⠀⠸⠷⠇⠘⠿⠧⠸⠏⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠟⠿⠻⠧⠀⠀⠀⠀⠸⠷⠶⠲⠶⠶⠶⠶⠆⠸⠷⠶⠲⠸⠶⠶⠂⠸⠶⠲⡾⠻⠛⠽⠙⠶⠖⠐⠗⠶⠗⠐⠀⣗⡿⠷⠶⠶⠆⠷⠖⠗⠂⡆⠘⠅⠂⠀⠀⠸⠿⠇⠸⠻⠧⠺⠷⠔⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠻⠖⠧⠷⠖⠇⠀⠀⠸⠷⠶⠲⠆⠸⠱⠾⠪⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠷⠶⠂⠶⠰⠿⠶⠶⠴⠖⠶⠶⠆⠀⠸⠇⠸⠾⠃⠸⠆⠼⠿⠦⠘⠣⠛⠿⠠⠀⠀⠀⠀⢸ ⡟⠟⠒⠆⠇⠗⢶⠀⠀⠸⠷⠖⠞⠇⠸⠱⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡟⠏⠷⠒⠶⠶⠾⠷⠴⠖⠇⠀⠀⠀⠀⠀⠸⠿⠅⠘⠿⠗⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡘ ⡏⠛⠛⠚⠓⠓⠂⠁⠀⠀⠇⠐⠳⠓⠓⠚⠂⠘⠚⠛⠖⠛⠚⠐⠾⠆⠾⠚⠚⠺⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣗⠛⠓⠒⠛⠂⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢃ ⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙ ⡆⠀⠀⠀⠈⠀⠀⡠⠀⠀⠀⠀⠂⠈⠘⠀⠈⠒⠐⠀⠀⠀⠀⠐⠀⠀⠀⠂⠁⠀⠀⠀⠑⠈⠀⠀⠀⠐⠐⠀⠀⠐⠂⠀⠒⠁⠀⢲⢲⠒⠆⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠀⠀⢲ ⡇⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⢀⡀⡀⢀⣀⡀⠀⠀⣀⢀⠀⢀⣀⣀⢀⣀⢀⡀⠀⡀⣀⣀⡀⠀⣀⡀⠀⣀⣀⡀⣈⣈⣀⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠐⠛⠛⡛⡛⣉⡛⢛⣃⡀⠘⠛⠛⠃⠀⢀⠘⠉⠇⠙⠛⢛⣁⡛⣛⣓⣀⣛⢛⠘⢙⠛⡻⢛⠈⣛⣟⠃⠓⣋⠛⠛⠈⠛⠛⠛⠛⠓⠃⠓⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠃⠋⠛⠃⠈⠿⠛⠃⠘⠙⠛⠻⠋⠛⠱⠟⠁⠀⠘⠛⠑⠓⠛⠚⠚⠘⠀⠙⠀⠛⠙⠀⠛⠛⠋⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣀⠀⠀⢀⠀⣀⡀⠀⢀⣀⣀⡀⠀⣀⢀⢀⡀⢀⣀⣀⠀⣀⣀⣀⠀⣀⣀⣀⡀⣀⣀⣀⣀⢀⣀⠀⣀⢀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⢻⣯⣯⣭⣧⣿⣧⣤⣼⣥⣯⣧⣬⣼⣿⣭⣥⣼⣽⣭⣥⣽⣿⣽⣤⣽⣟⠙⣛⣉⠙⣋⣛⢟⡛⢁⠓⠉⠛⠋⠈⠛⠙⠙⠉⠛⠃⠋⠃⠋⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠘⠟⠟⢿⣿⠿⣿⡿⣻⢿⠿⠿⠿⠻⠟⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠋⠀⠉⠉⠀⠉⠉⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣀⣀⣀⣀⣋⣀⡀⡀⢁⣠⣄⡀⢀⠀⢠⣄⡀⢀⣠⣀⡀⢠⡠⢠⣠⣀⣠⣠⣠⣀⣄⣠⣤⣠⣠⠀⣄⢀⣀⣀⣄⣄⣠⣀⣄⡄⣄⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⠉⡍⡍⣁⣍⢀⣄⣄⡈⢉⢉⣁⣈⣁⣨⣍⣁⡈⠉⢩⣀⣬⡍⣭⣭⣭⢩⠉⢩⠉⢩⣉⠉⣭⣅⢀⣉⢡⠉⠉⠁⠀⠉⠉⠋⠁⠁⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠉⠉⠁⠉⠉⠉⠁⠈⠉⠉⠙⠉⠈⠉⠉⠈⠀⠈⠉⠉⠙⠉⠉⢉⠀⠃⠉⠀⠉⠉⠀⠉⠛⠁⠉⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣄⣀⣀⡀⣀⣄⡄⠀⢠⣤⣤⡄⢀⠀⢠⣤⡄⣠⣤⣤⡀⣤⣤⡤⠀⢤⣤⣤⣤⠀⣠⣠⣤⡀⣤⣤⡤⣤⣄⡄⣠⣤⣄⣠⣤⢤⣤⣤⣄⣤⣤⡤⡤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠉⡍⣍⣤⣍⢩⣥⣤⡈⢉⣉⣡⣀⣠⣈⣩⣁⡈⠉⢩⣤⣬⡭⣭⢤⢭⢭⠉⢭⠀⣭⣭⠉⣤⣥⣉⣉⣭⠉⠉⠀⠉⠁⠀⠉⠉⠈⠉⠁⠉⠉⠁⠅⡃⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠁⠀⠁⠀⠂⠈⠀⠀⠉⠉⠘⠁⠀⠀⠈⠀⠀⠀⠈⠈⠈⠉⠉⠈⠀⠃⠈⠀⠉⠉⠂⠑⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣠⣤⣤⣀⠠⣄⣤⡄⠀⢠⣤⣤⡄⢠⠀⢠⣤⡄⢠⣤⣤⠀⣤⣤⣀⠠⢴⣠⠀⣤⠀⢤⣤⣤⣤⡤⣤⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡤⣤⣴⡠⣤⣤⡄⠀⢠⣤⣤⣤⣤⡄⢠⡄⢠⣠⠀⢠⢀⠀⣠⣠⣬⣤⠀⢠⠀⣤⡤⠀⣤⢠⠀⡄⠀⣄⣄⣄⣤⣄⣄⣤⡄⡄⠀⡆⢀⣆⡄⢠⣦⣄⢤⡄⡄⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⡤⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠌⠀⠉⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⣤⢤⠀⢴⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⢷⠶⠴⠶⠶⠦⠄⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣄⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠷⠾⠖⠶⠾⠶⠴⠶⠄⠀⠐⠐⠀⠂⠀⠐⠀⠀⠂⠒⢤ ⡇⠯⠶⠧⠶⢶⡶⡤⠆⠸⠄⠷⠶⠶⠆⠸⠷⠶⠲⠶⠺⠆⠸⠷⠶⠶⠶⠾⠶⠶⠼⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⡀⠀⠀⠀⠸⠷⠇⠘⠿⠧⠸⠏⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠟⠿⠻⠧⠀⠀⠀⠀⠸⠷⠶⠲⠶⠶⠶⠶⠆⠸⠷⠶⠲⠸⠶⠶⠂⠸⠶⠲⡾⠻⠛⠽⠙⠶⠖⠐⠗⠶⠗⠐⠀⣗⡿⠷⠶⠶⠆⠷⠖⠗⠂⡆⠘⠅⠂⠀⠀⠸⠿⠇⠸⠻⠧⠺⠷⠔⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠻⠖⠧⠷⠖⠇⠀⠀⠸⠷⠶⠲⠆⠸⠱⠾⠪⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠷⠶⠂⠶⠰⠿⠶⠶⠴⠖⠶⠶⠆⠀⠸⠇⠸⠾⠃⠸⠆⠼⠿⠦⠘⠣⠛⠿⠠⠀⠀⠀⠀⢸ ⡟⠟⠒⠆⠇⠗⢶⠀⠀⠸⠷⠖⠞⠇⠸⠱⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡟⠏⠷⠒⠶⠶⠾⠷⠴⠖⠇⠀⠀⠀⠀⠀⠸⠿⠅⠘⠿⠗⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡘ ⡏⠛⠛⠚⠓⠓⠂⠁⠀⠀⠇⠐⠳⠓⠓⠚⠂⠘⠚⠛⠖⠛⠚⠐⠾⠆⠾⠚⠚⠺⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣗⠛⠓⠒⠛⠂⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢃ ⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙ ⡆⠀⠀⠀⠈⠀⠀⡠⠀⠀⠀⠀⠂⠈⠘⠀⠈⠒⠐⠀⠀⠀⠀⠐⠀⠀⠀⠂⠁⠀⠀⠀⠑⠈⠀⠀⠀⠐⠐⠀⠀⠐⠂⠀⠒⠁⠀⢲⢲⠒⠆⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠀⠀⢲ ⡇⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⢀⡀⡀⢀⣀⡀⠀⠀⣀⢀⠀⢀⣀⣀⢀⣀⢀⡀⠀⡀⣀⣀⡀⠀⣀⡀⠀⣀⣀⡀⣈⣈⣀⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠐⠛⠛⡛⡛⣉⡛⢛⣃⡀⠘⠛⠛⠃⠀⢀⠘⠉⠇⠙⠛⢛⣁⡛⣛⣓⣀⣛⢛⠘⢙⠛⡻⢛⠈⣛⣟⠃⠓⣋⠛⠛⠈⠛⠛⠛⠛⠓⠃⠓⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠃⠋⠛⠃⠈⠿⠛⠃⠘⠙⠛⠻⠋⠛⠱⠟⠁⠀⠘⠛⠑⠓⠛⠚⠚⠘⠀⠙⠀⠛⠙⠀⠛⠛⠋⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣀⠀⠀⢀⠀⣀⡀⠀⢀⣀⣀⡀⠀⣀⢀⢀⡀⢀⣀⣀⠀⣀⣀⣀⠀⣀⣀⣀⡀⣀⣀⣀⣀⢀⣀⠀⣀⢀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⢻⣯⣯⣭⣧⣿⣧⣤⣼⣥⣯⣧⣬⣼⣿⣭⣥⣼⣽⣭⣥⣽⣿⣽⣤⣽⣟⠙⣛⣉⠙⣋⣛⢟⡛⢁⠓⠉⠛⠋⠈⠛⠙⠙⠉⠛⠃⠋⠃⠋⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠘⠟⠟⢿⣿⠿⣿⡿⣻⢿⠿⠿⠿⠻⠟⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠋⠀⠉⠉⠀⠉⠉⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣀⣀⣀⣀⣋⣀⡀⡀⢁⣠⣄⡀⢀⠀⢠⣄⡀⢀⣠⣀⡀⢠⡠⢠⣠⣀⣠⣠⣠⣀⣄⣠⣤⣠⣠⠀⣄⢀⣀⣀⣄⣄⣠⣀⣄⡄⣄⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⠉⡍⡍⣁⣍⢀⣄⣄⡈⢉⢉⣁⣈⣁⣨⣍⣁⡈⠉⢩⣀⣬⡍⣭⣭⣭⢩⠉⢩⠉⢩⣉⠉⣭⣅⢀⣉⢡⠉⠉⠁⠀⠉⠉⠋⠁⠁⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠉⠉⠁⠉⠉⠉⠁⠈⠉⠉⠙⠉⠈⠉⠉⠈⠀⠈⠉⠉⠙⠉⠉⢉⠀⠃⠉⠀⠉⠉⠀⠉⠛⠁⠉⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣄⣀⣀⡀⣀⣄⡄⠀⢠⣤⣤⡄⢀⠀⢠⣤⡄⣠⣤⣤⡀⣤⣤⡤⠀⢤⣤⣤⣤⠀⣠⣠⣤⡀⣤⣤⡤⣤⣄⡄⣠⣤⣄⣠⣤⢤⣤⣤⣄⣤⣤⡤⡤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠉⡍⣍⣤⣍⢩⣥⣤⡈⢉⣉⣡⣀⣠⣈⣩⣁⡈⠉⢩⣤⣬⡭⣭⢤⢭⢭⠉⢭⠀⣭⣭⠉⣤⣥⣉⣉⣭⠉⠉⠀⠉⠁⠀⠉⠉⠈⠉⠁⠉⠉⠁⠅⡃⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠁⠀⠁⠀⠂⠈⠀⠀⠉⠉⠘⠁⠀⠀⠈⠀⠀⠀⠈⠈⠈⠉⠉⠈⠀⠃⠈⠀⠉⠉⠂⠑⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣠⣤⣤⣀⠠⣄⣤⡄⠀⢠⣤⣤⡄⢠⠀⢠⣤⡄⢠⣤⣤⠀⣤⣤⣀⠠⢴⣠⠀⣤⠀⢤⣤⣤⣤⡤⣤⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡤⣤⣴⡠⣤⣤⡄⠀⢠⣤⣤⣤⣤⡄⢠⡄⢠⣠⠀⢠⢀⠀⣠⣠⣬⣤⠀⢠⠀⣤⡤⠀⣤⢠⠀⡄⠀⣄⣄⣄⣤⣄⣄⣤⡄⡄⠀⡆⢀⣆⡄⢠⣦⣄⢤⡄⡄⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⡤⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠌⠀⠉⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⣤⢤⠀⢴⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⢷⠶⠴⠶⠶⠦⠄⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣄⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠷⠾⠖⠶⠾⠶⠴⠶⠄⠀⠐⠐⠀⠂⠀⠐⠀⠀⠂⠒⢤ ⡇⠯⠶⠧⠶⢶⡶⡤⠆⠸⠄⠷⠶⠶⠆⠸⠷⠶⠲⠶⠺⠆⠸⠷⠶⠶⠶⠾⠶⠶⠼⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⡀⠀⠀⠀⠸⠷⠇⠘⠿⠧⠸⠏⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠟⠿⠻⠧⠀⠀⠀⠀⠸⠷⠶⠲⠶⠶⠶⠶⠆⠸⠷⠶⠲⠸⠶⠶⠂⠸⠶⠲⡾⠻⠛⠽⠙⠶⠖⠐⠗⠶⠗⠐⠀⣗⡿⠷⠶⠶⠆⠷⠖⠗⠂⡆⠘⠅⠂⠀⠀⠸⠿⠇⠸⠻⠧⠺⠷⠔⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠻⠖⠧⠷⠖⠇⠀⠀⠸⠷⠶⠲⠆⠸⠱⠾⠪⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠷⠶⠂⠶⠰⠿⠶⠶⠴⠖⠶⠶⠆⠀⠸⠇⠸⠾⠃⠸⠆⠼⠿⠦⠘⠣⠛⠿⠠⠀⠀⠀⠀⢸ ⡟⠟⠒⠆⠇⠗⢶⠀⠀⠸⠷⠖⠞⠇⠸⠱⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡟⠏⠷⠒⠶⠶⠾⠷⠴⠖⠇⠀⠀⠀⠀⠀⠸⠿⠅⠘⠿⠗⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡘ ⡏⠛⠛⠚⠓⠓⠂⠁⠀⠀⠇⠐⠳⠓⠓⠚⠂⠘⠚⠛⠖⠛⠚⠐⠾⠆⠾⠚⠚⠺⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣗⠛⠓⠒⠛⠂⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢃ ⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙ ⡆⠀⠀⠀⠈⠀⠀⡠⠀⠀⠀⠀⠂⠈⠘⠀⠈⠒⠐⠀⠀⠀⠀⠐⠀⠀⠀⠂⠁⠀⠀⠀⠑⠈⠀⠀⠀⠐⠐⠀⠀⠐⠂⠀⠒⠁⠀⢲⢲⠒⠆⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠀⠀⢲ ⡇⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⢀⡀⡀⢀⣀⡀⠀⠀⣀⢀⠀⢀⣀⣀⢀⣀⢀⡀⠀⡀⣀⣀⡀⠀⣀⡀⠀⣀⣀⡀⣈⣈⣀⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠐⠛⠛⡛⡛⣉⡛⢛⣃⡀⠘⠛⠛⠃⠀⢀⠘⠉⠇⠙⠛⢛⣁⡛⣛⣓⣀⣛⢛⠘⢙⠛⡻⢛⠈⣛⣟⠃⠓⣋⠛⠛⠈⠛⠛⠛⠛⠓⠃⠓⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠃⠋⠛⠃⠈⠿⠛⠃⠘⠙⠛⠻⠋⠛⠱⠟⠁⠀⠘⠛⠑⠓⠛⠚⠚⠘⠀⠙⠀⠛⠙⠀⠛⠛⠋⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣀⠀⠀⢀⠀⣀⡀⠀⢀⣀⣀⡀⠀⣀⢀⢀⡀⢀⣀⣀⠀⣀⣀⣀⠀⣀⣀⣀⡀⣀⣀⣀⣀⢀⣀⠀⣀⢀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⢻⣯⣯⣭⣧⣿⣧⣤⣼⣥⣯⣧⣬⣼⣿⣭⣥⣼⣽⣭⣥⣽⣿⣽⣤⣽⣟⠙⣛⣉⠙⣋⣛⢟⡛⢁⠓⠉⠛⠋⠈⠛⠙⠙⠉⠛⠃⠋⠃⠋⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠘⠟⠟⢿⣿⠿⣿⡿⣻⢿⠿⠿⠿⠻⠟⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠋⠀⠉⠉⠀⠉⠉⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣀⣀⣀⣀⣋⣀⡀⡀⢁⣠⣄⡀⢀⠀⢠⣄⡀⢀⣠⣀⡀⢠⡠⢠⣠⣀⣠⣠⣠⣀⣄⣠⣤⣠⣠⠀⣄⢀⣀⣀⣄⣄⣠⣀⣄⡄⣄⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⠉⡍⡍⣁⣍⢀⣄⣄⡈⢉⢉⣁⣈⣁⣨⣍⣁⡈⠉⢩⣀⣬⡍⣭⣭⣭⢩⠉⢩⠉⢩⣉⠉⣭⣅⢀⣉⢡⠉⠉⠁⠀⠉⠉⠋⠁⠁⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠉⠉⠁⠉⠉⠉⠁⠈⠉⠉⠙⠉⠈⠉⠉⠈⠀⠈⠉⠉⠙⠉⠉⢉⠀⠃⠉⠀⠉⠉⠀⠉⠛⠁⠉⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣄⣀⣀⡀⣀⣄⡄⠀⢠⣤⣤⡄⢀⠀⢠⣤⡄⣠⣤⣤⡀⣤⣤⡤⠀⢤⣤⣤⣤⠀⣠⣠⣤⡀⣤⣤⡤⣤⣄⡄⣠⣤⣄⣠⣤⢤⣤⣤⣄⣤⣤⡤⡤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠉⡍⣍⣤⣍⢩⣥⣤⡈⢉⣉⣡⣀⣠⣈⣩⣁⡈⠉⢩⣤⣬⡭⣭⢤⢭⢭⠉⢭⠀⣭⣭⠉⣤⣥⣉⣉⣭⠉⠉⠀⠉⠁⠀⠉⠉⠈⠉⠁⠉⠉⠁⠅⡃⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠁⠀⠁⠀⠂⠈⠀⠀⠉⠉⠘⠁⠀⠀⠈⠀⠀⠀⠈⠈⠈⠉⠉⠈⠀⠃⠈⠀⠉⠉⠂⠑⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣠⣤⣤⣀⠠⣄⣤⡄⠀⢠⣤⣤⡄⢠⠀⢠⣤⡄⢠⣤⣤⠀⣤⣤⣀⠠⢴⣠⠀⣤⠀⢤⣤⣤⣤⡤⣤⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡤⣤⣴⡠⣤⣤⡄⠀⢠⣤⣤⣤⣤⡄⢠⡄⢠⣠⠀⢠⢀⠀⣠⣠⣬⣤⠀⢠⠀⣤⡤⠀⣤⢠⠀⡄⠀⣄⣄⣄⣤⣄⣄⣤⡄⡄⠀⡆⢀⣆⡄⢠⣦⣄⢤⡄⡄⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⡤⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠌⠀⠉⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⣤⢤⠀⢴⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⢷⠶⠴⠶⠶⠦⠄⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣄⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠷⠾⠖⠶⠾⠶⠴⠶⠄⠀⠐⠐⠀⠂⠀⠐⠀⠀⠂⠒⢤ ⡇⠯⠶⠧⠶⢶⡶⡤⠆⠸⠄⠷⠶⠶⠆⠸⠷⠶⠲⠶⠺⠆⠸⠷⠶⠶⠶⠾⠶⠶⠼⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⡀⠀⠀⠀⠸⠷⠇⠘⠿⠧⠸⠏⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠟⠿⠻⠧⠀⠀⠀⠀⠸⠷⠶⠲⠶⠶⠶⠶⠆⠸⠷⠶⠲⠸⠶⠶⠂⠸⠶⠲⡾⠻⠛⠽⠙⠶⠖⠐⠗⠶⠗⠐⠀⣗⡿⠷⠶⠶⠆⠷⠖⠗⠂⡆⠘⠅⠂⠀⠀⠸⠿⠇⠸⠻⠧⠺⠷⠔⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠻⠖⠧⠷⠖⠇⠀⠀⠸⠷⠶⠲⠆⠸⠱⠾⠪⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠷⠶⠂⠶⠰⠿⠶⠶⠴⠖⠶⠶⠆⠀⠸⠇⠸⠾⠃⠸⠆⠼⠿⠦⠘⠣⠛⠿⠠⠀⠀⠀⠀⢸ ⡟⠟⠒⠆⠇⠗⢶⠀⠀⠸⠷⠖⠞⠇⠸⠱⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡟⠏⠷⠒⠶⠶⠾⠷⠴⠖⠇⠀⠀⠀⠀⠀⠸⠿⠅⠘⠿⠗⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡘ ⡏⠛⠛⠚⠓⠓⠂⠁⠀⠀⠇⠐⠳⠓⠓⠚⠂⠘⠚⠛⠖⠛⠚⠐⠾⠆⠾⠚⠚⠺⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣗⠛⠓⠒⠛⠂⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢃ ⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙ ⡆⠀⠀⠀⠈⠀⠀⡠⠀⠀⠀⠀⠂⠈⠘⠀⠈⠒⠐⠀⠀⠀⠀⠐⠀⠀⠀⠂⠁⠀⠀⠀⠑⠈⠀⠀⠀⠐⠐⠀⠀⠐⠂⠀⠒⠁⠀⢲⢲⠒⠆⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠀⠀⢲ ⡇⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⢀⡀⡀⢀⣀⡀⠀⠀⣀⢀⠀⢀⣀⣀⢀⣀⢀⡀⠀⡀⣀⣀⡀⠀⣀⡀⠀⣀⣀⡀⣈⣈⣀⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠐⠛⠛⡛⡛⣉⡛⢛⣃⡀⠘⠛⠛⠃⠀⢀⠘⠉⠇⠙⠛⢛⣁⡛⣛⣓⣀⣛⢛⠘⢙⠛⡻⢛⠈⣛⣟⠃⠓⣋⠛⠛⠈⠛⠛⠛⠛⠓⠃⠓⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠃⠋⠛⠃⠈⠿⠛⠃⠘⠙⠛⠻⠋⠛⠱⠟⠁⠀⠘⠛⠑⠓⠛⠚⠚⠘⠀⠙⠀⠛⠙⠀⠛⠛⠋⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣀⠀⠀⢀⠀⣀⡀⠀⢀⣀⣀⡀⠀⣀⢀⢀⡀⢀⣀⣀⠀⣀⣀⣀⠀⣀⣀⣀⡀⣀⣀⣀⣀⢀⣀⠀⣀⢀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⢻⣯⣯⣭⣧⣿⣧⣤⣼⣥⣯⣧⣬⣼⣿⣭⣥⣼⣽⣭⣥⣽⣿⣽⣤⣽⣟⠙⣛⣉⠙⣋⣛⢟⡛⢁⠓⠉⠛⠋⠈⠛⠙⠙⠉⠛⠃⠋⠃⠋⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠘⠟⠟⢿⣿⠿⣿⡿⣻⢿⠿⠿⠿⠻⠟⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠋⠀⠉⠉⠀⠉⠉⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣀⣀⣀⣀⣋⣀⡀⡀⢁⣠⣄⡀⢀⠀⢠⣄⡀⢀⣠⣀⡀⢠⡠⢠⣠⣀⣠⣠⣠⣀⣄⣠⣤⣠⣠⠀⣄⢀⣀⣀⣄⣄⣠⣀⣄⡄⣄⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⠉⡍⡍⣁⣍⢀⣄⣄⡈⢉⢉⣁⣈⣁⣨⣍⣁⡈⠉⢩⣀⣬⡍⣭⣭⣭⢩⠉⢩⠉⢩⣉⠉⣭⣅⢀⣉⢡⠉⠉⠁⠀⠉⠉⠋⠁⠁⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠉⠉⠁⠉⠉⠉⠁⠈⠉⠉⠙⠉⠈⠉⠉⠈⠀⠈⠉⠉⠙⠉⠉⢉⠀⠃⠉⠀⠉⠉⠀⠉⠛⠁⠉⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣄⣀⣀⡀⣀⣄⡄⠀⢠⣤⣤⡄⢀⠀⢠⣤⡄⣠⣤⣤⡀⣤⣤⡤⠀⢤⣤⣤⣤⠀⣠⣠⣤⡀⣤⣤⡤⣤⣄⡄⣠⣤⣄⣠⣤⢤⣤⣤⣄⣤⣤⡤⡤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠉⡍⣍⣤⣍⢩⣥⣤⡈⢉⣉⣡⣀⣠⣈⣩⣁⡈⠉⢩⣤⣬⡭⣭⢤⢭⢭⠉⢭⠀⣭⣭⠉⣤⣥⣉⣉⣭⠉⠉⠀⠉⠁⠀⠉⠉⠈⠉⠁⠉⠉⠁⠅⡃⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠁⠀⠁⠀⠂⠈⠀⠀⠉⠉⠘⠁⠀⠀⠈⠀⠀⠀⠈⠈⠈⠉⠉⠈⠀⠃⠈⠀⠉⠉⠂⠑⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣠⣤⣤⣀⠠⣄⣤⡄⠀⢠⣤⣤⡄⢠⠀⢠⣤⡄⢠⣤⣤⠀⣤⣤⣀⠠⢴⣠⠀⣤⠀⢤⣤⣤⣤⡤⣤⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡤⣤⣴⡠⣤⣤⡄⠀⢠⣤⣤⣤⣤⡄⢠⡄⢠⣠⠀⢠⢀⠀⣠⣠⣬⣤⠀⢠⠀⣤⡤⠀⣤⢠⠀⡄⠀⣄⣄⣄⣤⣄⣄⣤⡄⡄⠀⡆⢀⣆⡄⢠⣦⣄⢤⡄⡄⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⡤⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠌⠀⠉⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⣤⢤⠀⢴⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⢷⠶⠴⠶⠶⠦⠄⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣄⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠷⠾⠖⠶⠾⠶⠴⠶⠄⠀⠐⠐⠀⠂⠀⠐⠀⠀⠂⠒⢤ ⡇⠯⠶⠧⠶⢶⡶⡤⠆⠸⠄⠷⠶⠶⠆⠸⠷⠶⠲⠶⠺⠆⠸⠷⠶⠶⠶⠾⠶⠶⠼⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⡀⠀⠀⠀⠸⠷⠇⠘⠿⠧⠸⠏⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠟⠿⠻⠧⠀⠀⠀⠀⠸⠷⠶⠲⠶⠶⠶⠶⠆⠸⠷⠶⠲⠸⠶⠶⠂⠸⠶⠲⡾⠻⠛⠽⠙⠶⠖⠐⠗⠶⠗⠐⠀⣗⡿⠷⠶⠶⠆⠷⠖⠗⠂⡆⠘⠅⠂⠀⠀⠸⠿⠇⠸⠻⠧⠺⠷⠔⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠻⠖⠧⠷⠖⠇⠀⠀⠸⠷⠶⠲⠆⠸⠱⠾⠪⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠷⠶⠂⠶⠰⠿⠶⠶⠴⠖⠶⠶⠆⠀⠸⠇⠸⠾⠃⠸⠆⠼⠿⠦⠘⠣⠛⠿⠠⠀⠀⠀⠀⢸ ⡟⠟⠒⠆⠇⠗⢶⠀⠀⠸⠷⠖⠞⠇⠸⠱⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡟⠏⠷⠒⠶⠶⠾⠷⠴⠖⠇⠀⠀⠀⠀⠀⠸⠿⠅⠘⠿⠗⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡘ ⡏⠛⠛⠚⠓⠓⠂⠁⠀⠀⠇⠐⠳⠓⠓⠚⠂⠘⠚⠛⠖⠛⠚⠐⠾⠆⠾⠚⠚⠺⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣗⠛⠓⠒⠛⠂⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢃ ⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙ ⡆⠀⠀⠀⠈⠀⠀⡠⠀⠀⠀⠀⠂⠈⠘⠀⠈⠒⠐⠀⠀⠀⠀⠐⠀⠀⠀⠂⠁⠀⠀⠀⠑⠈⠀⠀⠀⠐⠐⠀⠀⠐⠂⠀⠒⠁⠀⢲⢲⠒⠆⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠀⠀⢲ ⡇⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⢀⡀⡀⢀⣀⡀⠀⠀⣀⢀⠀⢀⣀⣀⢀⣀⢀⡀⠀⡀⣀⣀⡀⠀⣀⡀⠀⣀⣀⡀⣈⣈⣀⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠐⠛⠛⡛⡛⣉⡛⢛⣃⡀⠘⠛⠛⠃⠀⢀⠘⠉⠇⠙⠛⢛⣁⡛⣛⣓⣀⣛⢛⠘⢙⠛⡻⢛⠈⣛⣟⠃⠓⣋⠛⠛⠈⠛⠛⠛⠛⠓⠃⠓⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠃⠋⠛⠃⠈⠿⠛⠃⠘⠙⠛⠻⠋⠛⠱⠟⠁⠀⠘⠛⠑⠓⠛⠚⠚⠘⠀⠙⠀⠛⠙⠀⠛⠛⠋⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣀⠀⠀⢀⠀⣀⡀⠀⢀⣀⣀⡀⠀⣀⢀⢀⡀⢀⣀⣀⠀⣀⣀⣀⠀⣀⣀⣀⡀⣀⣀⣀⣀⢀⣀⠀⣀⢀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⢻⣯⣯⣭⣧⣿⣧⣤⣼⣥⣯⣧⣬⣼⣿⣭⣥⣼⣽⣭⣥⣽⣿⣽⣤⣽⣟⠙⣛⣉⠙⣋⣛⢟⡛⢁⠓⠉⠛⠋⠈⠛⠙⠙⠉⠛⠃⠋⠃⠋⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠘⠟⠟⢿⣿⠿⣿⡿⣻⢿⠿⠿⠿⠻⠟⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠋⠀⠉⠉⠀⠉⠉⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣀⣀⣀⣀⣋⣀⡀⡀⢁⣠⣄⡀⢀⠀⢠⣄⡀⢀⣠⣀⡀⢠⡠⢠⣠⣀⣠⣠⣠⣀⣄⣠⣤⣠⣠⠀⣄⢀⣀⣀⣄⣄⣠⣀⣄⡄⣄⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⠉⡍⡍⣁⣍⢀⣄⣄⡈⢉⢉⣁⣈⣁⣨⣍⣁⡈⠉⢩⣀⣬⡍⣭⣭⣭⢩⠉⢩⠉⢩⣉⠉⣭⣅⢀⣉⢡⠉⠉⠁⠀⠉⠉⠋⠁⠁⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠉⠉⠁⠉⠉⠉⠁⠈⠉⠉⠙⠉⠈⠉⠉⠈⠀⠈⠉⠉⠙⠉⠉⢉⠀⠃⠉⠀⠉⠉⠀⠉⠛⠁⠉⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣄⣀⣀⡀⣀⣄⡄⠀⢠⣤⣤⡄⢀⠀⢠⣤⡄⣠⣤⣤⡀⣤⣤⡤⠀⢤⣤⣤⣤⠀⣠⣠⣤⡀⣤⣤⡤⣤⣄⡄⣠⣤⣄⣠⣤⢤⣤⣤⣄⣤⣤⡤⡤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠉⡍⣍⣤⣍⢩⣥⣤⡈⢉⣉⣡⣀⣠⣈⣩⣁⡈⠉⢩⣤⣬⡭⣭⢤⢭⢭⠉⢭⠀⣭⣭⠉⣤⣥⣉⣉⣭⠉⠉⠀⠉⠁⠀⠉⠉⠈⠉⠁⠉⠉⠁⠅⡃⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠁⠀⠁⠀⠂⠈⠀⠀⠉⠉⠘⠁⠀⠀⠈⠀⠀⠀⠈⠈⠈⠉⠉⠈⠀⠃⠈⠀⠉⠉⠂⠑⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣠⣤⣤⣀⠠⣄⣤⡄⠀⢠⣤⣤⡄⢠⠀⢠⣤⡄⢠⣤⣤⠀⣤⣤⣀⠠⢴⣠⠀⣤⠀⢤⣤⣤⣤⡤⣤⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡤⣤⣴⡠⣤⣤⡄⠀⢠⣤⣤⣤⣤⡄⢠⡄⢠⣠⠀⢠⢀⠀⣠⣠⣬⣤⠀⢠⠀⣤⡤⠀⣤⢠⠀⡄⠀⣄⣄⣄⣤⣄⣄⣤⡄⡄⠀⡆⢀⣆⡄⢠⣦⣄⢤⡄⡄⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⡤⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠌⠀⠉⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⣤⢤⠀⢴⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⢷⠶⠴⠶⠶⠦⠄⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣄⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠷⠾⠖⠶⠾⠶⠴⠶⠄⠀⠐⠐⠀⠂⠀⠐⠀⠀⠂⠒⢤ ⡇⠯⠶⠧⠶⢶⡶⡤⠆⠸⠄⠷⠶⠶⠆⠸⠷⠶⠲⠶⠺⠆⠸⠷⠶⠶⠶⠾⠶⠶⠼⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⡀⠀⠀⠀⠸⠷⠇⠘⠿⠧⠸⠏⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠟⠿⠻⠧⠀⠀⠀⠀⠸⠷⠶⠲⠶⠶⠶⠶⠆⠸⠷⠶⠲⠸⠶⠶⠂⠸⠶⠲⡾⠻⠛⠽⠙⠶⠖⠐⠗⠶⠗⠐⠀⣗⡿⠷⠶⠶⠆⠷⠖⠗⠂⡆⠘⠅⠂⠀⠀⠸⠿⠇⠸⠻⠧⠺⠷⠔⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠻⠖⠧⠷⠖⠇⠀⠀⠸⠷⠶⠲⠆⠸⠱⠾⠪⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠷⠶⠂⠶⠰⠿⠶⠶⠴⠖⠶⠶⠆⠀⠸⠇⠸⠾⠃⠸⠆⠼⠿⠦⠘⠣⠛⠿⠠⠀⠀⠀⠀⢸ ⡟⠟⠒⠆⠇⠗⢶⠀⠀⠸⠷⠖⠞⠇⠸⠱⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡟⠏⠷⠒⠶⠶⠾⠷⠴⠖⠇⠀⠀⠀⠀⠀⠸⠿⠅⠘⠿⠗⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡘ ⡏⠛⠛⠚⠓⠓⠂⠁⠀⠀⠇⠐⠳⠓⠓⠚⠂⠘⠚⠛⠖⠛⠚⠐⠾⠆⠾⠚⠚⠺⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣗⠛⠓⠒⠛⠂⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢃ ⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙ ⡆⠀⠀⠀⠈⠀⠀⡠⠀⠀⠀⠀⠂⠈⠘⠀⠈⠒⠐⠀⠀⠀⠀⠐⠀⠀⠀⠂⠁⠀⠀⠀⠑⠈⠀⠀⠀⠐⠐⠀⠀⠐⠂⠀⠒⠁⠀⢲⢲⠒⠆⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠀⠀⢲ ⡇⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⢀⡀⡀⢀⣀⡀⠀⠀⣀⢀⠀⢀⣀⣀⢀⣀⢀⡀⠀⡀⣀⣀⡀⠀⣀⡀⠀⣀⣀⡀⣈⣈⣀⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠐⠛⠛⡛⡛⣉⡛⢛⣃⡀⠘⠛⠛⠃⠀⢀⠘⠉⠇⠙⠛⢛⣁⡛⣛⣓⣀⣛⢛⠘⢙⠛⡻⢛⠈⣛⣟⠃⠓⣋⠛⠛⠈⠛⠛⠛⠛⠓⠃⠓⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠃⠋⠛⠃⠈⠿⠛⠃⠘⠙⠛⠻⠋⠛⠱⠟⠁⠀⠘⠛⠑⠓⠛⠚⠚⠘⠀⠙⠀⠛⠙⠀⠛⠛⠋⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣀⠀⠀⢀⠀⣀⡀⠀⢀⣀⣀⡀⠀⣀⢀⢀⡀⢀⣀⣀⠀⣀⣀⣀⠀⣀⣀⣀⡀⣀⣀⣀⣀⢀⣀⠀⣀⢀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⢻⣯⣯⣭⣧⣿⣧⣤⣼⣥⣯⣧⣬⣼⣿⣭⣥⣼⣽⣭⣥⣽⣿⣽⣤⣽⣟⠙⣛⣉⠙⣋⣛⢟⡛⢁⠓⠉⠛⠋⠈⠛⠙⠙⠉⠛⠃⠋⠃⠋⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠘⠟⠟⢿⣿⠿⣿⡿⣻⢿⠿⠿⠿⠻⠟⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠋⠀⠉⠉⠀⠉⠉⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣀⣀⣀⣀⣋⣀⡀⡀⢁⣠⣄⡀⢀⠀⢠⣄⡀⢀⣠⣀⡀⢠⡠⢠⣠⣀⣠⣠⣠⣀⣄⣠⣤⣠⣠⠀⣄⢀⣀⣀⣄⣄⣠⣀⣄⡄⣄⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⠉⡍⡍⣁⣍⢀⣄⣄⡈⢉⢉⣁⣈⣁⣨⣍⣁⡈⠉⢩⣀⣬⡍⣭⣭⣭⢩⠉⢩⠉⢩⣉⠉⣭⣅⢀⣉⢡⠉⠉⠁⠀⠉⠉⠋⠁⠁⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠉⠉⠁⠉⠉⠉⠁⠈⠉⠉⠙⠉⠈⠉⠉⠈⠀⠈⠉⠉⠙⠉⠉⢉⠀⠃⠉⠀⠉⠉⠀⠉⠛⠁⠉⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣄⣀⣀⡀⣀⣄⡄⠀⢠⣤⣤⡄⢀⠀⢠⣤⡄⣠⣤⣤⡀⣤⣤⡤⠀⢤⣤⣤⣤⠀⣠⣠⣤⡀⣤⣤⡤⣤⣄⡄⣠⣤⣄⣠⣤⢤⣤⣤⣄⣤⣤⡤⡤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠉⡍⣍⣤⣍⢩⣥⣤⡈⢉⣉⣡⣀⣠⣈⣩⣁⡈⠉⢩⣤⣬⡭⣭⢤⢭⢭⠉⢭⠀⣭⣭⠉⣤⣥⣉⣉⣭⠉⠉⠀⠉⠁⠀⠉⠉⠈⠉⠁⠉⠉⠁⠅⡃⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠁⠀⠁⠀⠂⠈⠀⠀⠉⠉⠘⠁⠀⠀⠈⠀⠀⠀⠈⠈⠈⠉⠉⠈⠀⠃⠈⠀⠉⠉⠂⠑⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣠⣤⣤⣀⠠⣄⣤⡄⠀⢠⣤⣤⡄⢠⠀⢠⣤⡄⢠⣤⣤⠀⣤⣤⣀⠠⢴⣠⠀⣤⠀⢤⣤⣤⣤⡤⣤⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡤⣤⣴⡠⣤⣤⡄⠀⢠⣤⣤⣤⣤⡄⢠⡄⢠⣠⠀⢠⢀⠀⣠⣠⣬⣤⠀⢠⠀⣤⡤⠀⣤⢠⠀⡄⠀⣄⣄⣄⣤⣄⣄⣤⡄⡄⠀⡆⢀⣆⡄⢠⣦⣄⢤⡄⡄⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⡤⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠌⠀⠉⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⣤⢤⠀⢴⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⢷⠶⠴⠶⠶⠦⠄⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣄⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠷⠾⠖⠶⠾⠶⠴⠶⠄⠀⠐⠐⠀⠂⠀⠐⠀⠀⠂⠒⢤ ⡇⠯⠶⠧⠶⢶⡶⡤⠆⠸⠄⠷⠶⠶⠆⠸⠷⠶⠲⠶⠺⠆⠸⠷⠶⠶⠶⠾⠶⠶⠼⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⡀⠀⠀⠀⠸⠷⠇⠘⠿⠧⠸⠏⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠟⠿⠻⠧⠀⠀⠀⠀⠸⠷⠶⠲⠶⠶⠶⠶⠆⠸⠷⠶⠲⠸⠶⠶⠂⠸⠶⠲⡾⠻⠛⠽⠙⠶⠖⠐⠗⠶⠗⠐⠀⣗⡿⠷⠶⠶⠆⠷⠖⠗⠂⡆⠘⠅⠂⠀⠀⠸⠿⠇⠸⠻⠧⠺⠷⠔⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠻⠖⠧⠷⠖⠇⠀⠀⠸⠷⠶⠲⠆⠸⠱⠾⠪⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠷⠶⠂⠶⠰⠿⠶⠶⠴⠖⠶⠶⠆⠀⠸⠇⠸⠾⠃⠸⠆⠼⠿⠦⠘⠣⠛⠿⠠⠀⠀⠀⠀⢸ ⡟⠟⠒⠆⠇⠗⢶⠀⠀⠸⠷⠖⠞⠇⠸⠱⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡟⠏⠷⠒⠶⠶⠾⠷⠴⠖⠇⠀⠀⠀⠀⠀⠸⠿⠅⠘⠿⠗⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡘ ⡏⠛⠛⠚⠓⠓⠂⠁⠀⠀⠇⠐⠳⠓⠓⠚⠂⠘⠚⠛⠖⠛⠚⠐⠾⠆⠾⠚⠚⠺⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣗⠛⠓⠒⠛⠂⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢃ ⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙ ⡆⠀⠀⠀⠈⠀⠀⡠⠀⠀⠀⠀⠂⠈⠘⠀⠈⠒⠐⠀⠀⠀⠀⠐⠀⠀⠀⠂⠁⠀⠀⠀⠑⠈⠀⠀⠀⠐⠐⠀⠀⠐⠂⠀⠒⠁⠀⢲⢲⠒⠆⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠀⠀⢲ ⡇⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⢀⡀⡀⢀⣀⡀⠀⠀⣀⢀⠀⢀⣀⣀⢀⣀⢀⡀⠀⡀⣀⣀⡀⠀⣀⡀⠀⣀⣀⡀⣈⣈⣀⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠐⠛⠛⡛⡛⣉⡛⢛⣃⡀⠘⠛⠛⠃⠀⢀⠘⠉⠇⠙⠛⢛⣁⡛⣛⣓⣀⣛⢛⠘⢙⠛⡻⢛⠈⣛⣟⠃⠓⣋⠛⠛⠈⠛⠛⠛⠛⠓⠃⠓⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠃⠋⠛⠃⠈⠿⠛⠃⠘⠙⠛⠻⠋⠛⠱⠟⠁⠀⠘⠛⠑⠓⠛⠚⠚⠘⠀⠙⠀⠛⠙⠀⠛⠛⠋⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣀⠀⠀⢀⠀⣀⡀⠀⢀⣀⣀⡀⠀⣀⢀⢀⡀⢀⣀⣀⠀⣀⣀⣀⠀⣀⣀⣀⡀⣀⣀⣀⣀⢀⣀⠀⣀⢀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⢻⣯⣯⣭⣧⣿⣧⣤⣼⣥⣯⣧⣬⣼⣿⣭⣥⣼⣽⣭⣥⣽⣿⣽⣤⣽⣟⠙⣛⣉⠙⣋⣛⢟⡛⢁⠓⠉⠛⠋⠈⠛⠙⠙⠉⠛⠃⠋⠃⠋⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠘⠟⠟⢿⣿⠿⣿⡿⣻⢿⠿⠿⠿⠻⠟⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠋⠀⠉⠉⠀⠉⠉⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣀⣀⣀⣀⣋⣀⡀⡀⢁⣠⣄⡀⢀⠀⢠⣄⡀⢀⣠⣀⡀⢠⡠⢠⣠⣀⣠⣠⣠⣀⣄⣠⣤⣠⣠⠀⣄⢀⣀⣀⣄⣄⣠⣀⣄⡄⣄⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⠉⡍⡍⣁⣍⢀⣄⣄⡈⢉⢉⣁⣈⣁⣨⣍⣁⡈⠉⢩⣀⣬⡍⣭⣭⣭⢩⠉⢩⠉⢩⣉⠉⣭⣅⢀⣉⢡⠉⠉⠁⠀⠉⠉⠋⠁⠁⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠉⠉⠁⠉⠉⠉⠁⠈⠉⠉⠙⠉⠈⠉⠉⠈⠀⠈⠉⠉⠙⠉⠉⢉⠀⠃⠉⠀⠉⠉⠀⠉⠛⠁⠉⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣄⣀⣀⡀⣀⣄⡄⠀⢠⣤⣤⡄⢀⠀⢠⣤⡄⣠⣤⣤⡀⣤⣤⡤⠀⢤⣤⣤⣤⠀⣠⣠⣤⡀⣤⣤⡤⣤⣄⡄⣠⣤⣄⣠⣤⢤⣤⣤⣄⣤⣤⡤⡤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠉⡍⣍⣤⣍⢩⣥⣤⡈⢉⣉⣡⣀⣠⣈⣩⣁⡈⠉⢩⣤⣬⡭⣭⢤⢭⢭⠉⢭⠀⣭⣭⠉⣤⣥⣉⣉⣭⠉⠉⠀⠉⠁⠀⠉⠉⠈⠉⠁⠉⠉⠁⠅⡃⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠁⠀⠁⠀⠂⠈⠀⠀⠉⠉⠘⠁⠀⠀⠈⠀⠀⠀⠈⠈⠈⠉⠉⠈⠀⠃⠈⠀⠉⠉⠂⠑⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣠⣤⣤⣀⠠⣄⣤⡄⠀⢠⣤⣤⡄⢠⠀⢠⣤⡄⢠⣤⣤⠀⣤⣤⣀⠠⢴⣠⠀⣤⠀⢤⣤⣤⣤⡤⣤⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡤⣤⣴⡠⣤⣤⡄⠀⢠⣤⣤⣤⣤⡄⢠⡄⢠⣠⠀⢠⢀⠀⣠⣠⣬⣤⠀⢠⠀⣤⡤⠀⣤⢠⠀⡄⠀⣄⣄⣄⣤⣄⣄⣤⡄⡄⠀⡆⢀⣆⡄⢠⣦⣄⢤⡄⡄⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⡤⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠌⠀⠉⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⣤⢤⠀⢴⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⢷⠶⠴⠶⠶⠦⠄⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠷⠾⠖⠶⠾⠶⠴⠶⠄⠀⠐⠐⠀⠂⠒⠐⠐⠀⠂⠒⢤ ⡇⠯⠶⠧⠶⢶⡶⡤⠆⠸⠆⠷⠶⠶⠆⠸⠷⠶⠲⠶⠺⠆⠸⠷⠶⠶⠶⠾⠶⠶⠼⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⡀⠀⠀⠀⠸⠷⠇⠘⠿⠷⠸⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠟⠿⠿⠧⠀⠀⠀⠀⠸⠷⠶⠲⠶⠶⠶⠶⠆⠸⠷⠶⠲⠸⠶⠶⠂⠸⠶⠲⡺⠻⠛⠽⠙⠶⠖⠐⠗⠶⠗⠐⠀⣗⡿⠷⠶⠶⠆⠧⠶⠗⠂⡆⠂⠄⠀⠀⠀⠘⠓⠂⠘⠛⠣⠒⠒⠔⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡿⠻⠖⠷⠷⠖⠇⠄⠀⠸⠷⠲⠲⠆⠸⠱⠾⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠧⠶⠦⠗⠰⠷⠶⠶⠴⢶⡶⠶⠆⠀⠸⠃⠸⠶⠆⠨⠇⠼⠿⠄⠸⠦⠶⠾⠠⠀⠀⠀⠀⢸ ⡟⠿⠶⠆⠇⠗⠶⠄⠀⠸⠦⠶⠖⠇⠸⠳⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡝⠏⠷⠖⠶⢶⡾⠶⡴⠖⠆⠄⠀⠀⠀⠀⠸⠿⠃⠸⠿⠗⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡘ ⡏⠛⠛⠚⠓⠓⠂⠁⠀⠀⠇⠐⠳⠓⠓⠛⠆⠸⠚⠾⠖⠺⠲⠘⠾⠆⠾⠚⠚⠺⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡟⠧⠖⠲⠖⠖⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢃ ⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙ ⡆⠀⠀⠀⠈⠀⠀⡠⠀⠀⠀⠀⠂⠈⠘⠀⠈⠒⠐⠀⠀⠀⠀⠐⠀⠀⠀⠂⠁⠀⠀⠀⠑⠈⠀⠀⠈⠐⠐⠀⠀⠐⠂⠀⠒⠁⠀⢲⢲⠒⠆⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠀⠀⢠ ⡇⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⢀⡀⡀⢀⣀⠀⠀⠀⣀⢀⠀⠀⣀⣀⢀⣀⢀⡀⠀⡀⣀⣀⡀⠀⣀⡀⠀⣀⣀⡀⣈⣈⣀⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠐⠓⠳⠖⠛⠉⡻⠓⡂⡀⠸⠛⠛⠃⠀⢀⠘⠉⠃⠙⠛⢛⡁⡟⠛⠏⠀⢿⢛⠚⢘⠻⠻⠟⠈⣻⡟⠋⠃⠋⠛⠛⠈⠻⠟⠿⠻⠃⠃⠓⠻⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠇⠛⠗⠃⠄⠷⠖⠂⠐⠀⠓⠳⠚⠻⠐⠞⠀⠀⠸⠛⠑⠛⠚⠟⠛⠚⠀⠸⠀⠓⠙⠀⠟⠛⠆⠣⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣀⠀⠀⢀⠀⣀⡀⠀⢀⣀⣀⡀⠀⣀⢀⢀⡀⢀⣀⣀⠀⣀⣀⣀⠀⣀⣀⣀⡀⣀⣀⣀⣀⢀⣀⠀⣀⠀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⢿⣯⣯⣭⣧⣿⣧⣤⣼⣥⣯⣧⣬⣼⣿⣭⣥⣽⣽⣽⣤⣽⣿⣽⣤⣽⣟⠙⠻⠿⠿⢗⠚⠟⠟⠁⠓⠀⠟⠃⠘⠛⠛⠿⠍⠛⠃⠋⠃⠟⠵⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠘⠟⣿⣿⣿⣿⣿⡿⣻⢿⣿⣿⣿⣿⢟⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠿⠸⠀⠛⠩⠄⠆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢀⣀⣀⣀⣀⡂⣀⡀⡀⢀⣠⣄⡀⢀⠀⢠⣄⡀⢀⣠⣁⠀⢠⡠⢠⣠⡀⣠⣠⣠⣀⣄⣠⣤⣠⢠⠀⣄⢀⣀⣀⣄⣄⣠⣀⣄⣄⣄⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠄⠉⡍⡍⣁⣍⡠⣄⣄⡈⢉⢉⣁⣈⣁⣸⣍⣁⡈⠉⢩⣀⣨⡍⣭⠭⠥⠩⠉⠩⠾⠿⣉⠙⢿⠕⢀⣋⣡⠙⠛⠃⠁⠉⠉⠏⠁⠇⠥⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠅⠗⠑⠄⠉⠉⠉⠁⠈⠉⠉⠙⠉⠈⠉⠉⠈⠀⠈⠉⠉⠛⠉⠉⢁⠘⠀⠘⠀⠘⠹⠀⠸⠟⠄⠉⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣄⣀⣀⡀⣀⣄⡄⠀⢠⣤⣤⡄⢀⠀⢠⣤⡄⣠⣤⣤⡀⢤⣤⡤⠀⢤⣤⣤⣤⠀⣠⣠⣤⡀⣤⣤⡤⣤⣄⡄⣠⣤⣄⣠⣤⢤⣤⣤⣄⣤⣤⡤⠤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠩⠍⣍⣤⣍⢭⣥⡄⠈⠉⠭⢡⣘⣡⣈⣩⡁⠈⠉⢡⠀⠦⠯⠬⠠⠭⠭⠭⠭⠀⣭⣭⠉⣤⠥⢭⣉⣭⠉⠒⠀⠉⠁⠀⠉⠉⠈⠉⠁⠉⠙⠃⠅⡃⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠁⠀⠁⠌⠳⠈⠀⠀⠈⠵⠐⠀⠵⠀⠐⠂⠀⠈⠨⠀⠈⠉⠋⠈⠘⠃⠈⠀⠉⠙⠀⠓⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣠⣤⣤⣀⠠⣄⣤⡄⠀⢠⣤⣤⡄⢠⠀⢠⣤⡄⢠⣤⡤⠀⣤⣤⠠⠠⢴⣠⠀⣤⠀⢤⣤⣤⣤⡤⡤⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠶⡤⠰⠠⠤⠄⠄⠀⠠⠴⢦⡤⢤⠄⢠⠆⢠⣠⠰⢤⢀⠶⠠⢠⠬⠤⠀⢠⠀⣤⠤⠠⠦⠰⠔⠀⠀⣄⠄⡄⣤⡄⡄⣤⠄⠄⠀⠆⠀⠆⠄⢠⣦⡄⠤⠄⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠂⠷⠷⠗⠰⠷⠶⠆⠰⠶⠶⢶⠶⠶⠶⠶⠦⠀⠸⠷⠿⠾⠿⠿⠾⠼⠀⠸⠀⠼⠽⠀⠿⠿⠔⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⣤⢤⠀⢴⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠦⠤⠤⠤⠤⠴⢼ ⣿⡿⠿⢿⡿⢿⡿⠿⠿⠽⠿⠽⠿⠿⠿⢿⣿⠿⠿⠿⣿⠿⡿⣿⠿⢿⡿⡿⠿⠿⠿⡿⠿⠻⣿⠿⠿⠟⠛⠟⠛⠛⠛⠛⠟⠛⠛⠛⠛⡟⡟⠛⠛⣻⣻⣿⠛⠛⠛⣻⣿⡿⠿⠿⠛⠻⠟⠛⢻⣿⣿⠿⠿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⢷⠾⠴⠶⠶⠦⠄⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠾⠖⠶⠾⠶⠴⠶⠄⠀⠐⠐⠀⠂⠒⠐⠐⠀⠂⠒⢤ ⡇⠯⠶⠧⠶⢶⡶⡤⠆⠸⠆⠷⠶⠶⠆⠸⠷⠶⠲⠶⠺⠆⠸⠷⠶⠶⠶⠾⠶⠶⠼⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⡀⠀⠀⠀⠸⠷⠇⠸⠿⠷⠸⠾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠟⠿⠿⠧⠀⠀⠀⠀⠸⠷⠶⠲⠶⠶⠶⠶⠆⠸⠷⠶⠲⠸⠶⠶⠂⠸⠶⠲⡾⠻⠛⠽⠙⠶⠖⠐⠗⠶⠗⠐⠀⣷⡿⠷⠶⠶⠆⠧⠶⠗⠂⡆⠂⠄⠀⠀⠀⠘⠓⠂⠘⠛⠣⠒⠒⠔⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡿⠻⠖⠷⠷⠖⠇⠄⠀⠸⠷⠲⠲⠆⠸⠳⠾⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠶⠆⠇⠗⠶⠄⠀⠸⠦⠶⠖⠇⠸⠳⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡝⠇⠷⠖⠶⢶⡾⠶⡶⠖⠆⠄⠀⠀⠀⠀⠀⠸⠆⠸⠷⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡘ ⡏⠛⠛⠚⠓⠓⠂⠁⠀⠀⠇⠐⠳⠓⠓⠛⠆⠸⠚⠿⠖⠺⠲⠘⠾⠆⠾⠚⠚⠺⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡟⠧⠖⠲⠖⠖⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢃ ⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙ ⡆⠈⠐⠉⠈⠉⠁⡩⠉⠀⠉⠙⠋⠉⠘⠉⠉⠛⠙⠉⠀⠙⠉⠙⠉⠉⠑⠃⠉⠋⠉⠉⠑⠈⠋⠉⠉⠙⠙⠈⠉⠙⠊⠉⠛⠉⠉⢻⢳⠓⠎⠉⠙⠐⠚⠉⠋⠀⠉⠉⠉⠉⠉⠉⠑⠉⠉⠉⠉⠉⠙⠉⠉⠛⠉⠉⠁⢠ ⡇⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⢀⡀⡀⢀⣀⠀⠀⠀⣀⢀⠀⠀⣀⣀⢀⣀⢀⡀⠀⡀⣀⣀⡀⠀⣀⡀⢀⣀⣀⡀⣈⣈⣀⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠐⠓⠳⠖⠛⠉⡻⠓⡂⡀⠸⠛⠛⠃⠈⢀⠘⠉⠃⠙⠛⢛⡁⡟⠛⠏⠀⢿⢛⠚⢘⠿⠻⠟⠈⣻⡟⠋⠃⠋⠛⠛⠈⠻⠟⠿⠻⠃⠃⠓⠻⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠇⠛⠗⠃⠄⠷⠖⠂⠐⠀⠓⠳⠚⠻⠘⠞⠀⠀⠸⠛⠑⠛⠚⠟⠛⠚⠀⠸⠀⠓⠙⠀⠟⠛⠆⠣⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣀⠀⠀⢀⠀⣀⡀⠀⢀⣀⣀⡀⠀⣀⣀⢀⡀⢀⣀⣀⠀⣀⣀⣀⠀⣀⣀⣀⡀⣀⣀⣀⣀⢀⣀⠀⣀⠀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⢿⣯⣯⣭⣧⣿⣧⣤⣼⣥⣯⣧⣬⣼⣿⣭⣥⣽⣽⣽⣤⣽⣿⣽⣤⣽⣟⠙⠻⠿⠿⢗⠻⠟⠟⠁⠓⠀⠟⠃⠘⠛⠛⠿⠍⠛⠃⠋⠃⠟⠵⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠘⠟⣿⣿⣿⣿⣿⡿⣻⢿⣿⣿⣿⣿⢟⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠿⠸⠀⠛⠩⠄⠆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢀⣀⣀⣀⣀⡂⣀⡀⡀⢀⣠⣄⡀⢀⠀⢠⣄⡀⢀⣠⣁⠀⢠⡠⢠⣠⡀⣠⣠⣠⣀⣄⣠⣤⣠⢠⠀⣄⢀⣀⣀⣄⣄⣠⣀⣤⣄⣄⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠄⠉⡍⡍⣁⣍⡠⣆⣄⡈⢉⢉⣁⣈⣁⣸⣍⣁⡈⠉⢩⣀⣬⡍⣭⠭⠥⠩⠉⠩⠾⠿⣉⠙⢿⠕⢀⣋⣡⠙⠛⠃⠁⠉⠉⠏⠁⠇⠥⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠅⠗⠑⠄⠉⠉⠉⠁⠈⠉⠉⠙⠉⠈⠉⠉⠈⠀⠈⠉⠉⠛⠉⠉⢁⠸⠀⠘⠀⠘⠹⠀⠸⠟⠄⠉⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣄⣀⣀⡀⣀⣄⡄⠀⢠⣤⣤⡄⢀⠀⢠⣤⡄⣠⣤⣤⡀⢤⣤⡤⠀⢤⣤⣤⣤⠀⣠⣠⣤⡀⣤⣤⡤⣤⣄⡄⣠⣤⣄⣠⣤⢤⣤⣤⣄⣤⣤⡤⠤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠩⠍⣍⣤⣅⠭⣥⡄⠈⠉⠭⢡⣜⣡⣈⣩⡁⠈⠉⢡⠀⠦⠯⠬⠠⠭⠭⠭⠭⠀⣭⣭⠉⣤⠥⢭⣉⣭⠉⠲⠀⠉⠁⠀⠉⠉⠈⠉⠁⠉⠙⠃⠇⡃⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠁⠀⠁⠜⠳⠈⠀⠀⠈⠵⠐⠀⠵⠀⠐⠂⠀⠈⠨⠀⠈⠉⠋⠈⠘⠃⠈⠀⠉⠝⠀⠓⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣠⣤⣤⣀⠠⣄⣤⡄⠀⢠⣤⣤⡄⢠⠀⢠⣤⠄⢠⣤⡤⠀⣤⣤⠠⠠⢴⣠⠀⣤⠀⢤⣤⣤⣤⡤⡤⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠶⡤⠰⠠⠤⠄⠄⠀⠠⠴⢦⡤⢤⠔⠠⠄⢠⣠⠰⢤⢀⠶⠠⢠⠬⠤⠀⢠⠀⣤⠤⠠⠦⠰⠔⠀⠀⣄⠄⡄⣤⡄⡄⣤⠄⠄⠀⠆⠀⠆⠄⢠⣦⡄⠤⠄⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠂⠷⠷⠗⠴⠷⠶⠆⠰⠶⠶⢶⠶⠶⠶⠶⠢⠀⠸⠷⠿⠾⠿⠿⠾⠼⠀⠸⠀⠼⠵⠀⠿⠿⠔⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⣤⢤⠀⢴⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠦⠤⠤⠤⠤⠴⢼ ⠿⠿⠿⠿⠿⠿⠿⠿⠿⠽⠿⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠿⠿⠿⠟⠛⠟⠛⠛⠛⠛⠟⠛⠛⠛⠛⠟⠟⠛⠛⠻⠻⣿⠛⠛⠛⣻⠿⠿⠿⠿⠛⠻⠟⠛⠻⠿⠿⠿⠿⠿⠿⢿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⢷⠾⠴⠶⠶⠦⠄⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠾⠖⠶⠾⠶⠴⠶⠄⠀⠐⠐⠀⠂⠒⠐⠐⠀⠂⠒⢤ ⡇⠯⠶⠧⠶⢶⡶⡤⠆⠸⠆⠷⠶⠶⠆⠸⠷⠶⠲⠶⠺⠆⠸⠷⠶⠶⠶⠾⠶⠶⠼⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⡀⠀⠀⠀⠸⠷⠇⠸⠿⠷⠸⠾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠟⠿⠿⠧⠀⠀⠀⠀⠸⠷⠶⠲⠶⠶⠶⠶⠆⠸⠷⠶⠲⠸⠶⠶⠂⠸⠶⢲⠺⠻⠛⠽⠙⠶⠖⠐⠗⠶⠗⠐⠀⣷⡿⠷⠶⠶⠆⠧⠶⠗⠂⡆⠂⠄⠀⠀⠀⠘⠓⠂⠘⠛⠣⠒⠒⠔⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡿⠻⠖⠷⠷⠖⠇⠄⠀⠸⠷⠲⠲⠆⠸⠳⠾⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠶⠆⠇⠗⠶⠄⠀⠸⠦⠶⠖⠇⠸⠳⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡝⠇⠶⠖⠶⢶⡾⠶⡶⠖⠆⠄⠀⠀⠀⠀⠀⠸⠆⠸⠷⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡘ ⡏⠛⠛⠚⠓⠓⠂⠁⠀⠀⠇⠐⠳⠓⠓⠛⠆⠸⠚⠿⠖⠺⠲⠘⠾⠆⠾⠚⠚⠺⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡟⠧⠖⠲⠖⠖⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢃ ⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙ ⡆⠈⠐⠉⠈⠉⠁⡩⠉⠀⠉⠙⠋⠉⠘⠉⠉⠛⠙⠉⠀⠙⠉⠙⠉⠉⠑⠃⠉⠋⠉⠉⠑⠈⠋⠉⠉⠙⠙⠈⠉⠙⠊⠉⠛⠉⠉⢻⢳⠓⠎⠉⠙⠐⠚⠉⠋⠀⠉⠉⠉⠉⠉⠉⠑⠉⠉⠉⠉⠉⠙⠉⠉⠛⠉⠉⠁⢠ ⡇⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⢀⡀⡀⢀⣀⠀⠀⠀⣀⢀⠀⠀⣀⣀⢀⣀⢀⡀⠀⡀⣀⣀⡀⠀⣀⡀⢀⣀⣀⡀⣈⣈⣀⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠐⠓⠳⠖⠛⠉⡻⠓⡂⡀⠸⠛⠛⠃⠈⢀⠘⠉⠃⠙⠛⢛⡁⡟⠛⠏⠀⢿⢛⠚⢘⠿⠻⠟⠈⣻⡟⠋⠃⠋⠛⠛⠈⠻⠟⠿⠻⠗⠃⠓⠻⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠇⠛⠗⠃⠄⠷⠖⠂⠐⠀⠓⠳⠚⠻⠘⠞⠀⠀⠸⠛⠑⠛⠚⠟⠛⠚⠀⠸⠀⠓⠙⠀⠟⠛⠆⠣⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣀⠀⠀⢀⠀⣀⡀⠀⢀⣀⣀⡀⠀⣀⣀⢀⡀⢀⣀⣀⠀⣀⣀⣀⠀⣀⣀⣀⡀⣀⣀⣀⣀⢀⣀⠀⣀⠀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⢿⣯⣯⣭⣧⣿⣧⣤⣼⣥⣯⣧⣬⣼⣿⣭⣥⣽⣽⣽⣤⣽⣿⣽⣤⣽⣟⠙⠻⠿⠿⢗⠾⡿⠟⠁⠓⠀⠟⠃⠘⠛⠛⠿⠍⠛⠃⠋⠃⠟⠵⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠘⠟⣿⣿⣿⣿⣿⡿⣻⢿⣿⣿⣿⣿⢟⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠿⠸⠀⠛⠩⠄⠆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢀⣀⣀⣀⣀⡂⣀⡀⡀⢀⣠⣄⡀⢀⠀⢠⣄⡀⢀⣠⣁⠀⢠⡠⢠⣠⡀⣠⣠⣠⣀⣄⣠⣤⣠⢠⠀⣄⢀⣀⣀⣄⣄⣠⣀⣤⣄⣄⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠄⠉⡍⡍⣁⣍⡠⣆⣄⡈⢉⢉⣁⣈⣁⣸⣍⣁⡈⠉⢩⣀⣬⡍⣭⠭⠥⠩⠉⠩⠾⠿⣉⠙⢿⠕⢀⣋⣡⠙⠛⠃⠁⠉⠉⠏⠁⠇⢥⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠅⠗⠑⠄⠉⠉⠉⠁⠈⠉⠉⠙⠉⠈⠉⠉⠈⠀⠈⠉⠉⠛⠉⠉⢁⠸⠀⠘⠀⠘⠙⠀⠸⠟⠄⠉⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣄⣀⣀⡀⣀⣄⡄⠀⢠⣤⣤⡄⢀⠀⢠⣤⡄⣠⣤⣤⡀⢤⣤⡤⠀⢤⣤⣤⣤⠀⣠⣠⣤⡀⣤⣤⡤⣤⣄⡄⣠⣤⣄⣠⣤⢤⣤⣤⣄⣤⣤⡤⠤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠩⠍⣍⣤⣅⠭⣥⡄⠈⠉⠭⢡⣜⣡⣈⣩⡁⠈⠉⢡⠀⠦⠯⠬⠠⠭⠭⠭⠭⠀⣭⣭⠉⣤⠥⢭⣉⣭⠉⠲⠀⠉⠁⠀⠉⠉⠈⠉⠁⠉⠙⠂⠇⡃⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠁⠀⠁⠜⠳⠈⠀⠀⠈⠵⠐⠀⠵⠀⠐⠂⠀⠈⠨⠀⠈⠉⠋⠈⠘⠃⠈⠀⠋⠝⠀⠓⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣠⣤⣤⣀⠠⣄⣤⡄⠀⢠⣤⣤⡄⢠⠀⢠⣤⠄⢠⣤⡤⠀⣤⣤⠠⠠⢴⣠⠀⣤⠀⢤⣤⣤⣤⡤⡤⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠶⡤⠰⠠⠤⠄⠄⠀⠠⠴⢦⡤⢤⠔⠠⠄⢠⣠⠰⢤⢀⠶⠠⢠⠬⠤⠀⢠⠀⣤⠤⠠⠦⠰⠔⠀⠀⣄⠄⡄⣤⡄⡄⣤⠄⠄⠀⠆⠀⠆⠄⢠⣦⡄⠤⠄⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠂⠷⠷⠗⠴⠷⠶⠆⠰⠶⠶⢶⠶⠶⠴⠶⠢⠀⠸⠷⢿⠾⢿⠿⢾⠼⠀⠸⠀⠼⢥⠀⠿⠿⠔⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⣤⢤⠀⢴⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠦⠤⠤⠤⠤⠴⢼ ⠿⠿⠿⠿⠿⠿⠿⠿⠿⠽⠿⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠿⠿⠿⠟⠛⠟⠛⠛⠛⠛⠟⠛⠛⠛⠛⠟⠟⠛⠛⠻⠻⣿⠛⠛⠛⣻⠿⠿⠿⠿⠛⠻⠟⠛⠻⠿⠿⠿⠿⠿⠿⢿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⢷⠾⠴⠶⠶⠦⠄⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠾⠖⠶⠾⠶⠴⠶⠄⠀⠐⠐⠀⠂⠒⠐⠐⠀⠂⠒⢤ ⡇⠯⠶⠧⠶⢶⡶⡤⠆⠸⠆⠷⠶⠶⠆⠸⠷⠶⠲⠶⠺⠆⠸⠷⠶⠶⠶⠾⠶⠶⠼⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⡀⠀⠀⠀⠸⠷⠇⠸⠿⠷⠸⠾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠟⠿⠿⠧⠀⠀⠀⠀⠸⠷⠶⠲⠶⠶⠶⠶⠆⠸⠷⠶⠲⠸⠶⠶⠂⠸⠶⢶⠺⠺⠛⠽⠙⠶⠖⠐⠗⠶⠗⠐⠀⣷⡿⠷⠶⠶⠆⠧⠶⠗⠂⡆⠂⠄⠀⠀⠀⠘⠓⠂⠘⠛⠣⠒⠒⠔⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡿⠻⠖⠷⠷⠖⠇⠄⠀⠸⠷⠲⠲⠆⠸⠳⠾⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠶⠆⠇⠗⠶⠄⠀⠸⠦⠶⠖⠇⠸⠳⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡝⠇⠶⠖⠶⢶⡾⠶⡶⠖⠆⠄⠀⠀⠀⠀⠀⠸⠆⠸⠷⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡘ ⡏⠓⠛⠚⠓⠓⠂⠁⠀⠀⠇⠐⠳⠓⠓⠛⠆⠸⠚⠿⠖⠺⠲⠘⠾⠆⠾⠚⠚⠺⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡟⠧⠖⠲⠖⠖⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢃ ⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙ ⡆⠈⠐⠉⠈⠉⠁⡩⠉⠀⠉⠙⠋⠉⠘⠉⠉⠛⠙⠉⠀⠙⠉⠙⠉⠉⠑⠃⠉⠋⠉⠉⠑⠈⠋⠉⠉⠙⠙⠈⠉⠙⠊⠉⠛⠉⠉⢻⢳⠓⠎⠉⠙⠐⠚⠉⠋⠀⠉⠉⠉⠉⠉⠉⠑⠉⠉⠉⠉⠉⠙⠉⠉⠛⠉⠉⠁⢠ ⡇⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⢀⡀⡀⢀⣀⠀⠀⠀⣀⢀⠀⠀⣀⣀⢀⣀⢀⡀⠀⡀⣀⣀⡀⠀⣀⡀⢀⣀⣀⡀⣈⣈⣀⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠐⠓⠳⠖⠛⠉⡻⠓⡂⡀⠸⠛⠛⠃⠈⢀⠘⠉⠇⠙⠛⢛⡁⡟⠛⠏⠀⢿⢛⠚⢘⢿⠻⢟⠈⣻⡟⠋⠃⠋⠛⠛⠈⠻⠟⠿⠻⠷⠇⠓⠻⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠇⠛⠗⠃⠔⠷⠖⠆⠐⠀⠓⠳⠚⠻⠘⠞⠀⠀⠸⠛⠑⠛⠚⠗⠛⠚⠀⠸⠀⠓⠙⠀⠟⠛⠆⠣⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣀⠀⠀⢀⠀⣀⡀⠀⢀⣀⣀⡀⠀⣀⣀⢀⡀⢀⣀⣀⠀⣀⣀⣀⠀⣀⣀⣀⡀⣀⣀⣀⣀⢀⣀⠀⣀⠀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⢿⣯⣯⣭⣧⣿⣧⣤⣼⣥⣯⣧⣬⣼⣿⣭⣥⣽⣽⣽⣤⣽⣿⣽⣤⣽⣟⠙⠻⠿⠿⢗⠾⡿⠟⠁⠓⠀⠟⠃⠘⠛⠛⠿⠍⠛⠃⠋⠃⠟⠵⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠘⠟⣿⣿⣿⣿⣿⡿⣻⢿⣿⣿⣿⣿⢟⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠿⠸⠀⠛⠩⠄⠆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢀⣀⣀⣀⣀⡂⣀⡀⡀⢀⣠⣄⡀⢀⠀⢠⣄⡀⢀⣠⣁⠀⢠⡠⢠⣠⡀⣠⣠⣠⣀⣄⣠⣤⣠⢠⠀⣄⢀⣀⣀⣄⣄⣠⣀⣤⣄⣄⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠄⠉⡍⡍⣁⣍⡠⣆⣄⡈⢉⢉⣁⣈⣁⣸⣍⣁⡈⠉⢩⣀⣬⡍⣭⠭⠥⠩⠉⠩⠾⠿⣉⠙⠿⠕⢀⣋⣡⠙⠛⠃⠁⠉⠉⠏⠁⠇⢥⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠅⠖⠑⠀⠀⠉⡉⠁⠈⠉⠉⠙⠉⠈⠉⠉⠈⠀⠈⠉⠉⢖⠉⠉⢁⠸⠀⠘⠀⠘⠙⠀⠰⠟⠄⠉⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣄⣀⣀⡀⣀⣄⡄⠀⢠⣤⣤⡄⢀⠀⢠⣤⡄⣠⣤⣤⡀⢤⣤⡤⠀⢤⣤⣤⣤⠀⣠⣠⣤⡀⣤⣤⡤⣤⣄⡄⣠⣤⣄⣠⣤⢤⣤⣤⣄⣤⣤⡤⠤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠩⠍⣍⣤⣅⠭⣥⡄⠈⠉⠭⢡⣜⣡⣈⣩⡁⠈⠉⢡⠀⠦⠯⠬⠠⠭⠭⠭⠭⠀⣭⣭⠉⣤⠥⢭⣉⣭⠉⠢⠀⠉⠁⠀⠉⠉⠈⠉⠁⠉⠙⠂⡇⡃⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠁⠠⠅⠄⠲⠈⠀⠀⠈⠵⠐⠀⠵⠀⠐⠂⠀⠈⠨⠀⠜⠙⠋⠈⠘⠁⠈⠀⠋⠝⠀⠓⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣠⣤⣤⣀⠠⣄⣤⡄⠀⢠⣤⣤⡄⢠⠀⢠⣤⠄⢠⣤⡤⠀⣤⣤⠠⠠⢴⣠⠀⣤⠀⢤⣤⣤⣤⡤⡤⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠶⡤⠰⠠⠤⡄⠄⠀⠠⠴⢦⡤⢤⠔⠠⠄⢠⣠⠰⢤⢀⠶⠠⢠⠬⠤⠀⢠⠀⣤⠤⠠⠦⠰⠔⠀⠀⣄⠄⡄⣤⡄⡄⣤⠄⠄⠀⠆⠀⠆⠄⢠⣦⡄⠤⠄⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠂⠷⠷⠗⠰⡷⠶⠂⠰⠶⠶⢶⠶⠦⠴⠶⠢⠀⠸⠷⢿⠾⢾⡻⣾⠴⠀⠸⠀⠼⢧⠀⠿⠿⠔⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⣤⢤⠀⢴⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠦⠤⠤⠤⠤⠴⢼ ⠿⠿⠿⠿⠿⠿⠿⠿⠿⠽⠿⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠿⠿⠿⠟⠛⠟⠛⠛⠛⠛⠟⠛⠛⠛⠛⠟⠟⠛⠛⠻⠻⣿⠛⠛⠛⣻⠿⠿⠿⠿⠛⠻⠟⠛⠻⠿⠿⠿⠿⠿⠿⢿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⢷⠾⠴⠶⠶⠦⠄⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠾⠖⠶⠾⠶⠴⠶⠄⠀⠐⠐⠀⠂⠒⠐⠐⠀⠂⠒⢤ ⡇⠯⠶⠧⠶⢶⡶⡤⠆⠸⠆⠷⠶⠶⠆⠸⠷⠶⠲⠶⠺⠆⠸⠷⠶⠶⠶⠾⠶⠶⠼⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⡀⠀⠀⠀⠸⠷⠇⠸⠿⠷⠸⠾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠟⠿⠿⠧⠀⠀⠀⠀⠸⠷⠶⠲⠶⠶⠶⠶⠆⠸⠷⠶⠲⠸⠶⠶⠂⠸⠶⢶⠺⠺⠛⠽⠙⠶⠖⠐⠗⠶⠗⠐⠀⣷⡿⠷⠶⠶⠆⠧⠶⠗⠂⡆⠂⠄⠀⠀⠀⠘⠓⠂⠘⠛⠣⠒⠒⠔⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡿⠻⠖⠷⠷⠖⠇⠄⠀⠸⠷⠲⠲⠆⠸⠳⠾⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠶⠆⠇⠗⠶⠄⠀⠸⠦⠶⠖⠇⠸⠳⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡝⠇⠶⠖⠶⢶⡾⠶⡶⠖⠆⠄⠀⠀⠀⠀⠀⠸⠆⠸⠷⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡘ ⡏⠓⠛⠚⠓⠓⠂⠁⠀⠀⠇⠐⠳⠓⠓⠛⠆⠸⠚⠿⠖⠺⠲⠘⠾⠆⠾⠚⠚⠺⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡟⠧⠖⠲⠖⠖⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢃ ⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙ ⡆⠈⠐⠉⠈⠉⠁⡩⠉⠀⠉⠙⠋⠉⠘⠉⠉⠛⠙⠉⠀⠙⠉⠙⠉⠉⠑⠃⠉⠋⠉⠉⠑⠈⠋⠉⠉⠙⠙⠈⠉⠙⠊⠉⠛⠉⠉⢻⢳⠓⠎⠉⠙⠐⠚⠉⠋⠀⠉⠉⠉⠉⠉⠉⠑⠉⠉⠉⠉⠉⠙⠉⠉⠛⠉⠉⠁⢠ ⡇⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⢀⡀⡀⢀⣀⠀⠀⠀⣀⢀⠀⠀⣀⣀⢀⣀⢀⡀⠀⡀⣀⣀⡀⠀⣀⡀⢀⣀⣀⡀⣈⣈⣀⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠐⠓⠳⠖⠛⠉⡻⠓⡂⡀⠸⠛⠛⠃⠈⢀⠘⠉⠇⠙⠛⢛⡁⡟⠛⠏⠀⢿⢛⠚⢘⢿⠻⢟⠈⣻⡟⠋⠃⠋⠛⠛⠈⠻⠟⠿⠻⠷⠇⠓⠻⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠇⠛⠗⠃⠔⠷⠖⠆⠐⠀⠓⠳⠚⠻⠘⠞⠀⠀⠸⠛⠑⠛⠚⠗⠛⠚⠀⠸⠀⠓⠙⠀⠟⠛⠆⠣⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣀⠀⠀⢀⠀⣀⡀⠀⢀⣀⣀⡀⠀⣀⣀⢀⡀⢀⣀⣀⠀⣀⣀⣀⠀⣀⣀⣀⡀⣀⣀⣀⣀⢀⣀⠀⣀⠀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⢿⣯⣯⣭⣧⣿⣧⣤⣼⣥⣯⣧⣬⣼⣿⣭⣥⣽⣽⣽⣤⣽⣿⣽⣤⣽⣟⠙⠻⠿⠿⢗⠾⡿⠟⠁⠓⠀⠟⠃⠘⠛⠛⠿⠍⠛⠃⠋⠃⠟⠵⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠘⠟⣿⣿⣿⣿⣿⡿⣻⢿⣿⣿⣿⣿⢟⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠿⠸⠀⠛⠩⠄⠆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢀⣀⣀⣀⣀⡂⣀⡀⡀⢀⣠⣄⡀⢀⠀⢠⣄⡀⢀⣠⣁⠀⢠⡠⢠⣠⡀⣠⣠⣠⣀⣄⣠⣤⣠⢠⠀⣄⢀⣀⣀⣄⣄⣠⣀⣤⣄⣄⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠄⠉⡍⡍⣁⣍⡠⣆⣄⡈⢉⢉⣁⣈⣁⣸⣍⣁⡈⠉⢩⣀⣬⡍⣭⠭⠥⠩⠉⠩⠾⠿⣉⠙⠿⠕⢀⣋⣡⠙⠛⠃⠁⠉⠉⠏⠁⠇⢥⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠅⠖⠑⠀⠀⠉⡉⠁⠈⠉⠉⠙⠉⠈⠉⠉⠈⠀⠈⠉⠉⢖⠉⠉⢁⠸⠀⠘⠀⠘⠙⠀⠰⠟⠄⠉⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣄⣀⣀⡀⣀⣄⡄⠀⢠⣤⣤⡄⢀⠀⢠⣤⡄⣠⣤⣤⡀⢤⣤⡤⠀⢤⣤⣤⣤⠀⣠⣠⣤⡀⣤⣤⡤⣤⣄⡄⣠⣤⣄⣠⣤⢤⣤⣤⣄⣤⣤⡤⠤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠩⠍⣍⣤⣅⠭⣥⡄⠈⠉⠭⢡⣜⣡⣈⣩⡁⠈⠉⢡⠀⠦⠯⠬⠠⠭⠭⠭⠭⠀⣭⣭⠉⣤⠥⢭⣉⣭⠉⠢⠀⠉⠁⠀⠉⠉⠈⠉⠁⠉⠙⠂⡇⡃⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠁⠠⠅⠄⠲⠈⠀⠀⠈⠵⠐⠀⠵⠀⠐⠂⠀⠈⠨⠀⠜⠙⠋⠈⠘⠁⠈⠀⠋⠝⠀⠓⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣠⣤⣤⣀⠠⣄⣤⡄⠀⢠⣤⣤⡄⢠⠀⢠⣤⠄⢠⣤⡤⠀⣤⣤⠠⠠⢴⣠⠀⣤⠀⢤⣤⣤⣤⡤⡤⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠶⡤⠰⠠⠤⡄⠄⠀⠠⠴⢦⡤⢤⠔⠠⠄⢠⣠⠰⢤⢀⠶⠠⢠⠬⠤⠀⢠⠀⣤⠤⠠⠦⠰⠔⠀⠀⣄⠄⡄⣤⡄⡄⣤⠄⠄⠀⠆⠀⠆⠄⢠⣦⡄⠤⠄⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠂⠷⠷⠗⠰⡷⠶⠂⠰⠶⠶⢶⠶⠦⠴⠶⠢⠀⠸⠷⢿⠾⢾⡻⣾⠴⠀⠸⠀⠼⢧⠀⠿⠿⠔⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⣤⢤⠀⢴⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠦⠤⠤⠤⠤⠴⢼ ⠿⠿⠿⠿⠿⠿⠿⠿⠿⠽⠿⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠿⠿⠿⠟⠛⠟⠛⠛⠛⠛⠟⠛⠛⠛⠛⠟⠟⠛⠛⠻⠻⣿⠛⠛⠛⣻⠿⠿⠿⠿⠛⠻⠟⠛⠻⠿⠿⠿⠿⠿⠿⢿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⢷⠾⠴⠶⠶⠦⠄⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠾⠖⠶⠾⠶⠴⠶⠄⠀⠐⠐⠀⠂⠒⠐⠐⠀⠂⠒⢤ ⡇⠯⠶⠧⠶⢶⡶⡤⠆⠸⠆⠷⠶⠶⠆⠸⠷⠶⠲⠶⠺⠆⠸⠷⠶⠶⠶⠾⠶⠶⠼⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⡀⠀⠀⠀⠸⠷⠇⠸⠿⠷⠸⠾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠟⠿⠿⠧⠀⠀⠀⠀⠸⠷⠶⠲⠶⠶⠶⠶⠆⠸⠷⠶⠲⠸⠶⠶⠂⠸⠶⢶⠺⠺⠛⠽⠙⠶⠖⠐⠗⠶⠗⠐⠀⣷⡿⠷⠶⠶⠆⠧⠶⠗⠂⡆⠂⠄⠀⠀⠀⠘⠓⠂⠘⠛⠣⠒⠒⠔⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡿⠻⠖⠷⠷⠖⠇⠄⠀⠸⠷⠲⠲⠆⠸⠳⠾⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠶⠆⠇⠗⠶⠄⠀⠸⠦⠶⠖⠇⠸⠳⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡝⠇⠶⠖⠶⢶⡾⠶⡶⠖⠆⠄⠀⠀⠀⠀⠀⠸⠆⠸⠷⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡘ ⡏⠓⠛⠚⠓⠓⠂⠁⠀⠀⠇⠐⠳⠓⠓⠛⠆⠸⠚⠿⠖⠺⠲⠘⠾⠆⠾⠚⠚⠺⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡟⠧⠖⠲⠖⠖⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢃ ⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙ ⡆⠈⠐⠉⠈⠉⠁⡩⠉⠀⠉⠙⠋⠉⠘⠉⠉⠛⠙⠉⠀⠙⠉⠙⠉⠉⠑⠃⠉⠋⠉⠉⠑⠈⠋⠉⠉⠙⠙⠈⠉⠙⠊⠉⠛⠉⠉⢻⢳⠓⠎⠉⠙⠐⠚⠉⠋⠀⠉⠉⠉⠉⠉⠉⠑⠉⠉⠉⠉⠉⠙⠉⠉⠛⠉⠉⠁⢠ ⡇⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⢀⡀⡀⢀⣀⠀⠀⠀⣀⢀⠀⠀⣀⣀⢀⣀⢀⡀⠀⡀⣀⣀⡀⠀⣀⡀⢀⣀⣀⡀⣈⣈⣀⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠐⠓⠳⠖⠛⠉⡻⠓⡂⡀⠸⠛⠛⠃⠈⢀⠘⠉⠇⠙⠛⢛⡁⡟⠛⠏⠀⢿⢛⠚⢘⢿⠻⢟⠈⣻⡟⠋⠃⠋⠛⠛⠈⠻⠟⠿⠻⠷⠇⠓⠻⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠇⠛⠗⠃⠔⠷⠖⠆⠐⠀⠓⠳⠚⠻⠘⠞⠀⠀⠸⠛⠑⠛⠚⠗⠛⠚⠀⠸⠀⠓⠙⠀⠟⠛⠆⠣⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣀⠀⠀⢀⠀⣀⡀⠀⢀⣀⣀⡀⠀⣀⣀⢀⡀⢀⣀⣀⠀⣀⣀⣀⠀⣀⣀⣀⡀⣀⣀⣀⣀⢀⣀⠀⣀⠀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⢿⣯⣯⣭⣧⣿⣧⣤⣼⣥⣯⣧⣬⣼⣿⣭⣥⣽⣽⣽⣤⣽⣿⣽⣤⣽⣟⠙⠻⠿⠿⢗⠾⡿⠟⠁⠓⠀⠟⠃⠘⠛⠛⠿⠍⠛⠃⠋⠃⠟⠵⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠘⠟⣿⣿⣿⣿⣿⡿⣻⢿⣿⣿⣿⣿⢟⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠿⠸⠀⠛⠩⠄⠆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢀⣀⣀⣀⣀⡂⣀⡀⡀⢀⣠⣄⡀⢀⠀⢠⣄⡀⢀⣠⣁⠀⢠⡠⢠⣠⡀⣠⣠⣠⣀⣄⣠⣤⣠⢠⠀⣄⢀⣀⣀⣄⣄⣠⣀⣤⣄⣄⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠄⠉⡍⡍⣁⣍⡠⣆⣄⡈⢉⢉⣁⣈⣁⣸⣍⣁⡈⠉⢩⣀⣬⡍⣭⠭⠥⠩⠉⠩⠾⠿⣉⠙⠿⠕⢀⣋⣡⠙⠛⠃⠁⠉⠉⠏⠁⠇⢥⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠅⠖⠑⠀⠀⠉⡉⠁⠈⠉⠉⠙⠉⠈⠉⠉⠈⠀⠈⠉⠉⢖⠉⠉⢁⠸⠀⠘⠀⠘⠙⠀⠰⠟⠄⠉⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣄⣀⣀⡀⣀⣄⡄⠀⢠⣤⣤⡄⢀⠀⢠⣤⡄⣠⣤⣤⡀⢤⣤⡤⠀⢤⣤⣤⣤⠀⣠⣠⣤⡀⣤⣤⡤⣤⣄⡄⣠⣤⣄⣠⣤⢤⣤⣤⣄⣤⣤⡤⠤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠩⠍⣍⣤⣅⠭⣥⡄⠈⠉⠭⢡⣜⣡⣈⣩⡁⠈⠉⢡⠀⠦⠯⠬⠠⠭⠭⠭⠭⠀⣭⣭⠉⣤⠥⢭⣉⣭⠉⠢⠀⠉⠁⠀⠉⠉⠈⠉⠁⠉⠙⠂⡇⡃⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠁⠠⠅⠄⠲⠈⠀⠀⠈⠵⠐⠀⠵⠀⠐⠂⠀⠈⠨⠀⠜⠙⠋⠈⠘⠁⠈⠀⠋⠝⠀⠓⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣠⣤⣤⣀⠠⣄⣤⡄⠀⢠⣤⣤⡄⢠⠀⢠⣤⠄⢠⣤⡤⠀⣤⣤⠠⠠⢴⣠⠀⣤⠀⢤⣤⣤⣤⡤⡤⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠶⡤⠰⠠⠤⡄⠄⠀⠠⠴⢦⡤⢤⠔⠠⠄⢠⣠⠰⢤⢀⠶⠠⢠⠬⠤⠀⢠⠀⣤⠤⠠⠦⠰⠔⠀⠀⣄⠄⡄⣤⡄⡄⣤⠄⠄⠀⠆⠀⠆⠄⢠⣦⡄⠤⠄⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠂⠷⠷⠗⠰⡷⠶⠂⠰⠶⠶⢶⠶⠦⠴⠶⠢⠀⠸⠷⢿⠾⢾⡻⣾⠴⠀⠸⠀⠼⢧⠀⠿⠿⠔⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⣤⢤⠀⢴⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠦⠤⠤⠤⠤⠴⢼ ⠿⠿⠿⠿⠿⠿⠿⠿⠿⠽⠿⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠿⠿⠿⠟⠛⠟⠛⠛⠛⠛⠟⠛⠛⠛⠛⠟⠟⠛⠛⠻⠻⣿⠛⠛⠛⣻⠿⠿⠿⠿⠛⠻⠟⠛⠻⠿⠿⠿⠿⠿⠿⢿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⢷⠾⠴⠶⠶⠦⠄⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠾⠖⠶⠾⠶⠴⠶⠄⠀⠐⠐⠀⠂⠒⠐⠐⠀⠂⠒⢤ ⡇⠯⠶⠧⠶⢶⡶⡤⠆⠸⠆⠷⠶⠶⠆⠸⠷⠶⠲⠶⠺⠆⠸⠷⠶⠶⠶⠾⠶⠶⠼⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⡀⠀⠀⠀⠸⠷⠇⠸⠿⠷⠸⠾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠟⠿⠿⠧⠀⠀⠀⠀⠸⠷⠶⠲⠶⠶⠶⠶⠆⠸⠷⠶⠲⠸⠶⠶⠂⠸⠶⢶⠺⠺⠛⠽⠙⠶⠖⠐⠗⠶⠗⠐⠀⣷⡿⠷⠶⠶⠆⠧⠶⠗⠂⡆⠂⠄⠀⠀⠀⠘⠓⠂⠘⠛⠣⠒⠒⠔⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡿⠻⠖⠷⠷⠖⠇⠄⠀⠸⠷⠲⠲⠆⠸⠳⠾⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠶⠆⠇⠗⠶⠄⠀⠸⠦⠶⠖⠇⠸⠳⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡝⠇⠶⠖⠶⢶⡾⠶⡶⠖⠆⠄⠀⠀⠀⠀⠀⠸⠆⠸⠷⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡘ ⡏⠓⠛⠚⠓⠓⠂⠁⠀⠀⠇⠐⠳⠓⠓⠛⠆⠸⠚⠿⠖⠺⠲⠘⠾⠆⠾⠚⠚⠺⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡟⠧⠖⠲⠖⠖⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢃ ⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙ ⡆⠈⠐⠉⠈⠉⠁⡩⠉⠀⠉⠙⠋⠉⠘⠉⠉⠛⠙⠉⠀⠙⠉⠙⠉⠉⠑⠃⠉⠋⠉⠉⠑⠈⠋⠉⠉⠙⠙⠈⠉⠙⠊⠉⠛⠉⠉⢻⢳⠓⠎⠉⠙⠐⠚⠉⠋⠀⠉⠉⠉⠉⠉⠉⠑⠉⠉⠉⠉⠉⠙⠉⠉⠛⠉⠉⠁⢠ ⡇⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⢀⡀⡀⢀⣀⠀⠀⠀⣀⢀⠀⠀⣀⣀⢀⣀⢀⡀⠀⡀⣀⣀⡀⠀⣀⡀⢀⣀⣀⡀⣈⣈⣀⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠐⠓⠳⠖⠛⠉⡻⠓⡂⡀⠸⠛⠛⠃⠈⢀⠘⠉⠇⠙⠛⢛⡁⡟⠛⠏⠀⢿⢛⠚⢘⢿⠻⢟⠈⣻⡟⠋⠃⠋⠛⠛⠈⠻⠟⠿⠻⠷⠇⠓⠻⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠇⠛⠗⠃⠔⠷⠖⠆⠐⠀⠓⠳⠚⠻⠘⠞⠀⠀⠸⠛⠑⠛⠚⠗⠛⠚⠀⠸⠀⠓⠙⠀⠟⠛⠆⠣⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣀⠀⠀⢀⠀⣀⡀⠀⢀⣀⣀⡀⠀⣀⣀⢀⡀⢀⣀⣀⠀⣀⣀⣀⠀⣀⣀⣀⡀⣀⣀⣀⣀⢀⣀⠀⣀⠀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⢿⣯⣯⣭⣧⣿⣧⣤⣼⣥⣯⣧⣬⣼⣿⣭⣥⣽⣽⣽⣤⣽⣿⣽⣤⣽⣟⠙⠻⠿⠿⢗⠾⡿⠟⠁⠓⠀⠟⠃⠘⠛⠛⠿⠍⠛⠃⠋⠃⠟⠵⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠘⠟⣿⣿⣿⣿⣿⡿⣻⢿⣿⣿⣿⣿⢟⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠿⠸⠀⠛⠩⠄⠆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢀⣀⣀⣀⣀⡂⣀⡀⡀⢀⣠⣄⡀⢀⠀⢠⣄⡀⢀⣠⣁⠀⢠⡠⢠⣠⡀⣠⣠⣠⣀⣄⣠⣤⣠⢠⠀⣄⢀⣀⣀⣄⣄⣠⣀⣤⣄⣄⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠄⠉⡍⡍⣁⣍⡠⣆⣄⡈⢉⢉⣁⣈⣁⣸⣍⣁⡈⠉⢩⣀⣬⡍⣭⠭⠥⠩⠉⠩⠾⠿⣉⠙⠿⠕⢀⣋⣡⠙⠛⠃⠁⠉⠉⠏⠁⠇⢥⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠅⠖⠑⠀⠀⠉⡉⠁⠈⠉⠉⠙⠉⠈⠉⠉⠈⠀⠈⠉⠉⢖⠉⠉⢁⠸⠀⠘⠀⠘⠙⠀⠰⠟⠄⠉⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣄⣀⣀⡀⣀⣄⡄⠀⢠⣤⣤⡄⢀⠀⢠⣤⡄⣠⣤⣤⡀⢤⣤⡤⠀⢤⣤⣤⣤⠀⣠⣠⣤⡀⣤⣤⡤⣤⣄⡄⣠⣤⣄⣠⣤⢤⣤⣤⣄⣤⣤⡤⠤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠩⠍⣍⣤⣅⠭⣥⡄⠈⠉⠭⢡⣜⣡⣈⣩⡁⠈⠉⢡⠀⠦⠯⠬⠠⠭⠭⠭⠭⠀⣭⣭⠉⣤⠥⢭⣉⣭⠉⠢⠀⠉⠁⠀⠉⠉⠈⠉⠁⠉⠙⠂⡇⡃⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠁⠠⠅⠄⠲⠈⠀⠀⠈⠵⠐⠀⠵⠀⠐⠂⠀⠈⠨⠀⠜⠙⠋⠈⠘⠁⠈⠀⠋⠝⠀⠓⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣠⣤⣤⣀⠠⣄⣤⡄⠀⢠⣤⣤⡄⢠⠀⢠⣤⠄⢠⣤⡤⠀⣤⣤⠠⠠⢴⣠⠀⣤⠀⢤⣤⣤⣤⡤⡤⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠶⡤⠰⠠⠤⡄⠄⠀⠠⠴⢦⡤⢤⠔⠠⠄⢠⣠⠰⢤⢀⠶⠠⢠⠬⠤⠀⢠⠀⣤⠤⠠⠦⠰⠔⠀⠀⣄⠄⡄⣤⡄⡄⣤⠄⠄⠀⠆⠀⠆⠄⢠⣦⡄⠤⠄⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠂⠷⠷⠗⠰⡷⠶⠂⠰⠶⠶⢶⠶⠦⠴⠶⠢⠀⠸⠷⢿⠾⢾⡻⣾⠴⠀⠸⠀⠼⢧⠀⠿⠿⠔⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⣤⢤⠀⢴⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠦⠤⠤⠤⠤⠴⢼ ⠿⠿⠿⠿⠿⠿⠿⠿⠿⠽⠿⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠿⠿⠿⠟⠛⠟⠛⠛⠛⠛⠟⠛⠛⠛⠛⠟⠟⠛⠛⠻⠻⣿⠛⠛⠛⣻⠿⠿⠿⠿⠛⠻⠟⠛⠻⠿⠿⠿⠿⠿⠿⢿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⢷⠾⠴⠶⠶⠦⠄⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠾⠖⠶⠾⠶⠴⠶⠄⠀⠐⠐⠀⠂⠒⠐⠐⠀⠂⠒⢤ ⡇⠯⠶⠧⠶⢶⡶⡤⠆⠸⠆⠷⠶⠶⠆⠸⠷⠶⠲⠶⠺⠆⠸⠷⠶⠶⠶⠾⠶⠶⠼⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⡀⠀⠀⠀⠸⠷⠇⠸⠿⠷⠸⠾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠟⠿⠿⠧⠀⠀⠀⠀⠸⠷⠶⠲⠶⠶⠶⠶⠆⠸⠷⠶⠲⠸⠶⠶⠂⠸⠶⢶⠺⠺⠛⠽⠙⠶⠖⠐⠗⠶⠗⠐⠀⣷⡿⠷⠶⠶⠆⠧⠶⠗⠂⡆⠂⠄⠀⠀⠀⠘⠓⠂⠘⠛⠣⠒⠒⠔⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡿⠻⠖⠷⠷⠖⠇⠄⠀⠸⠷⠲⠲⠆⠸⠳⠾⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠶⠆⠇⠗⠶⠄⠀⠸⠦⠶⠖⠇⠸⠳⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡝⠇⠶⠖⠶⢶⡾⠶⡶⠖⠆⠄⠀⠀⠀⠀⠀⠸⠆⠸⠷⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡘ ⡏⠓⠛⠚⠓⠓⠂⠁⠀⠀⠇⠐⠳⠓⠓⠛⠆⠸⠚⠿⠖⠺⠲⠘⠾⠆⠾⠚⠚⠺⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡟⠧⠖⠲⠖⠖⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢃ ⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙ ⡆⠈⠐⠉⠈⠉⠁⡩⠉⠀⠉⠙⠋⠉⠘⠉⠉⠛⠙⠉⠀⠙⠉⠙⠉⠉⠑⠃⠉⠋⠉⠉⠑⠈⠋⠉⠉⠙⠙⠈⠉⠙⠊⠉⠛⠉⠉⢻⢳⠓⠎⠉⠙⠐⠚⠉⠋⠀⠉⠉⠉⠉⠉⠉⠑⠉⠉⠉⠉⠉⠙⠉⠉⠛⠉⠉⠁⢠ ⡇⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⢀⡀⡀⢀⣀⠀⠀⠀⣀⢀⠀⠀⣀⣀⢀⣀⢀⡀⠀⡀⣀⣀⡀⠀⣀⡀⢀⣀⣀⡀⣈⣈⣀⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠐⠓⠳⠖⠛⠉⡻⠓⡂⡀⠸⠛⠛⠃⠈⢀⠘⠉⠇⠙⠛⢛⡁⡟⠛⠏⠀⢿⢛⠚⢘⢿⠻⢟⠈⣻⡟⠋⠃⠋⠛⠛⠈⠻⠟⠿⠻⠷⠇⠓⠻⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠇⠛⠗⠃⠔⠷⠖⠆⠐⠀⠓⠳⠚⠻⠘⠞⠀⠀⠸⠛⠑⠛⠚⠗⠛⠚⠀⠸⠀⠓⠙⠀⠟⠛⠆⠣⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣀⠀⠀⢀⠀⣀⡀⠀⢀⣀⣀⡀⠀⣀⣀⢀⡀⢀⣀⣀⠀⣀⣀⣀⠀⣀⣀⣀⡀⣀⣀⣀⣀⢀⣀⠀⣀⠀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⢿⣯⣯⣭⣧⣿⣧⣤⣼⣥⣯⣧⣬⣼⣿⣭⣥⣽⣽⣽⣤⣽⣿⣽⣤⣽⣟⠙⠻⠿⠿⢗⠾⡿⠟⠁⠓⠀⠟⠃⠘⠛⠛⠿⠍⠛⠃⠋⠃⠟⠵⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠘⠟⣿⣿⣿⣿⣿⡿⣻⢿⣿⣿⣿⣿⢟⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠿⠸⠀⠛⠩⠄⠆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢀⣀⣀⣀⣀⡂⣀⡀⡀⢀⣠⣄⡀⢀⠀⢠⣄⡀⢀⣠⣁⠀⢠⡠⢠⣠⡀⣠⣠⣠⣀⣄⣠⣤⣠⢠⠀⣄⢀⣀⣀⣄⣄⣠⣀⣤⣄⣄⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠄⠉⡍⡍⣁⣍⡠⣆⣄⡈⢉⢉⣁⣈⣁⣸⣍⣁⡈⠉⢩⣀⣬⡍⣭⠭⠥⠩⠉⠩⠾⠿⣉⠙⠿⠕⢀⣋⣡⠙⠛⠃⠁⠉⠉⠏⠁⠇⢥⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠅⠖⠑⠀⠀⠉⡉⠁⠈⠉⠉⠙⠉⠈⠉⠉⠈⠀⠈⠉⠉⢖⠉⠉⢁⠸⠀⠘⠀⠘⠙⠀⠰⠟⠄⠉⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣄⣀⣀⡀⣀⣄⡄⠀⢠⣤⣤⡄⢀⠀⢠⣤⡄⣠⣤⣤⡀⢤⣤⡤⠀⢤⣤⣤⣤⠀⣠⣠⣤⡀⣤⣤⡤⣤⣄⡄⣠⣤⣄⣠⣤⢤⣤⣤⣄⣤⣤⡤⠤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠩⠍⣍⣤⣅⠭⣥⡄⠈⠉⠭⢡⣜⣡⣈⣩⡁⠈⠉⢡⠀⠦⠯⠬⠠⠭⠭⠭⠭⠀⣭⣭⠉⣤⠥⢭⣉⣭⠉⠢⠀⠉⠁⠀⠉⠉⠈⠉⠁⠉⠙⠂⡇⡃⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠁⠠⠅⠄⠲⠈⠀⠀⠈⠵⠐⠀⠵⠀⠐⠂⠀⠈⠨⠀⠜⠙⠋⠈⠘⠁⠈⠀⠋⠝⠀⠓⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣠⣤⣤⣀⠠⣄⣤⡄⠀⢠⣤⣤⡄⢠⠀⢠⣤⠄⢠⣤⡤⠀⣤⣤⠠⠠⢴⣠⠀⣤⠀⢤⣤⣤⣤⡤⡤⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠶⡤⠰⠠⠤⡄⠄⠀⠠⠴⢦⡤⢤⠔⠠⠄⢠⣠⠰⢤⢀⠶⠠⢠⠬⠤⠀⢠⠀⣤⠤⠠⠦⠰⠔⠀⠀⣄⠄⡄⣤⡄⡄⣤⠄⠄⠀⠆⠀⠆⠄⢠⣦⡄⠤⠄⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠂⠷⠷⠗⠰⡷⠶⠂⠰⠶⠶⢶⠶⠦⠴⠶⠢⠀⠸⠷⢿⠾⢾⡻⣾⠴⠀⠸⠀⠼⢧⠀⠿⠿⠔⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⣤⢤⠀⢴⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠦⠤⠤⠤⠤⠴⢼ ⠿⠿⠿⠿⠿⠿⠿⠿⠿⠽⠿⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠿⠿⠿⠟⠛⠟⠛⠛⠛⠛⠟⠛⠛⠛⠛⠟⠟⠛⠛⠻⠻⣿⠛⠛⠛⣻⠿⠿⠿⠿⠛⠻⠟⠛⠻⠿⠿⠿⠿⠿⠿⢿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⢷⠾⠴⠶⠶⠦⠄⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠾⠖⠶⠾⠶⠴⠶⠄⠀⠐⠐⠀⠂⠒⠐⠐⠀⠂⠒⢤ ⡇⠯⠶⠧⠶⢶⡶⡤⠆⠸⠆⠷⠶⠶⠆⠸⠷⠶⠲⠶⠺⠆⠸⠷⠶⠶⠶⠾⠶⠶⠼⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⡀⠀⠀⠀⠸⠷⠇⠸⠿⠷⠸⠾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠟⠿⠿⠧⠀⠀⠀⠀⠸⠷⠶⠲⠶⠶⠶⠶⠆⠸⠷⠶⠲⠸⠶⠶⠂⠸⠶⢶⠺⠺⠛⠽⠙⠶⠖⠐⠗⠶⠗⠐⠀⣷⡿⠷⠶⠶⠆⠧⠶⠗⠂⡆⠂⠄⠀⠀⠀⠘⠓⠂⠘⠛⠣⠒⠒⠔⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡿⠻⠖⠷⠷⠖⠇⠄⠀⠸⠷⠲⠲⠆⠸⠳⠾⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠶⠆⠇⠗⠶⠄⠀⠸⠦⠶⠖⠇⠸⠳⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡝⠇⠶⠖⠶⢶⡾⠶⡶⠖⠆⠄⠀⠀⠀⠀⠀⠸⠆⠸⠷⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡘ ⡏⠓⠛⠚⠓⠓⠂⠁⠀⠀⠇⠐⠳⠓⠓⠛⠆⠸⠚⠿⠖⠺⠲⠘⠾⠆⠾⠚⠚⠺⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡟⠧⠖⠲⠖⠖⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢃ ⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙ ⡆⠈⠐⠉⠈⠉⠁⡩⠉⠀⠉⠙⠋⠉⠘⠉⠉⠛⠙⠉⠀⠙⠉⠙⠉⠉⠑⠃⠉⠋⠉⠉⠑⠈⠋⠉⠉⠙⠙⠈⠉⠙⠊⠉⠛⠉⠉⢻⢳⠓⠎⠉⠙⠐⠚⠉⠋⠀⠉⠉⠉⠉⠉⠉⠑⠉⠉⠉⠉⠉⠙⠉⠉⠛⠉⠉⠁⢠ ⡇⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⢀⡀⡀⢀⣀⠀⠀⠀⣀⢀⠀⠀⣀⣀⢀⣀⢀⡀⠀⡀⣀⣀⡀⠀⣀⡀⢀⣀⣀⡀⣈⣈⣀⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠐⠓⠳⠖⠛⠉⡻⠓⡂⡀⠸⠛⠛⠃⠈⢀⠘⠉⠇⠙⠛⢛⡁⡟⠛⠏⠀⢿⢛⠚⢘⢿⠻⢟⠈⣻⡟⠋⠃⠋⠛⠛⠈⠻⠟⠿⠻⠷⠇⠓⠻⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠇⠛⠗⠃⠔⠷⠖⠆⠐⠀⠓⠳⠚⠻⠘⠞⠀⠀⠸⠛⠑⠛⠚⠗⠛⠚⠀⠸⠀⠓⠙⠀⠟⠛⠆⠣⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣀⠀⠀⢀⠀⣀⡀⠀⢀⣀⣀⡀⠀⣀⣀⢀⡀⢀⣀⣀⠀⣀⣀⣀⠀⣀⣀⣀⡀⣀⣀⣀⣀⢀⣀⠀⣀⠀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⢿⣯⣯⣭⣧⣿⣧⣤⣼⣥⣯⣧⣬⣼⣿⣭⣥⣽⣽⣽⣤⣽⣿⣽⣤⣽⣟⠙⠻⠿⠿⢗⠾⡿⠟⠁⠓⠀⠟⠃⠘⠛⠛⠿⠍⠛⠃⠋⠃⠟⠵⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠘⠟⣿⣿⣿⣿⣿⡿⣻⢿⣿⣿⣿⣿⢟⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠿⠸⠀⠛⠩⠄⠆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢀⣀⣀⣀⣀⡂⣀⡀⡀⢀⣠⣄⡀⢀⠀⢠⣄⡀⢀⣠⣁⠀⢠⡠⢠⣠⡀⣠⣠⣠⣀⣄⣠⣤⣠⢠⠀⣄⢀⣀⣀⣄⣄⣠⣀⣤⣄⣄⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠄⠉⡍⡍⣁⣍⡠⣆⣄⡈⢉⢉⣁⣈⣁⣸⣍⣁⡈⠉⢩⣀⣬⡍⣭⠭⠥⠩⠉⠩⠾⠿⣉⠙⠿⠕⢀⣋⣡⠙⠛⠃⠁⠉⠉⠏⠁⠇⢥⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠅⠖⠑⠀⠀⠉⡉⠁⠈⠉⠉⠙⠉⠈⠉⠉⠈⠀⠈⠉⠉⢖⠉⠉⢁⠸⠀⠘⠀⠘⠙⠀⠰⠟⠄⠉⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣄⣀⣀⡀⣀⣄⡄⠀⢠⣤⣤⡄⢀⠀⢠⣤⡄⣠⣤⣤⡀⢤⣤⡤⠀⢤⣤⣤⣤⠀⣠⣠⣤⡀⣤⣤⡤⣤⣄⡄⣠⣤⣄⣠⣤⢤⣤⣤⣄⣤⣤⡤⠤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠩⠍⣍⣤⣅⠭⣥⡄⠈⠉⠭⢡⣜⣡⣈⣩⡁⠈⠉⢡⠀⠦⠯⠬⠠⠭⠭⠭⠭⠀⣭⣭⠉⣤⠥⢭⣉⣭⠉⠢⠀⠉⠁⠀⠉⠉⠈⠉⠁⠉⠙⠂⡇⡃⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠁⠠⠅⠄⠲⠈⠀⠀⠈⠵⠐⠀⠵⠀⠐⠂⠀⠈⠨⠀⠜⠙⠋⠈⠘⠁⠈⠀⠋⠝⠀⠓⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣠⣤⣤⣀⠠⣄⣤⡄⠀⢠⣤⣤⡄⢠⠀⢠⣤⠄⢠⣤⡤⠀⣤⣤⠠⠠⢴⣠⠀⣤⠀⢤⣤⣤⣤⡤⡤⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠶⡤⠰⠠⠤⡄⠄⠀⠠⠴⢦⡤⢤⠔⠠⠄⢠⣠⠰⢤⢀⠶⠠⢠⠬⠤⠀⢠⠀⣤⠤⠠⠦⠰⠔⠀⠀⣄⠄⡄⣤⡄⡄⣤⠄⠄⠀⠆⠀⠆⠄⢠⣦⡄⠤⠄⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠂⠷⠷⠗⠰⡷⠶⠂⠰⠶⠶⢶⠶⠦⠴⠶⠢⠀⠸⠷⢿⠾⢾⡻⣾⠴⠀⠸⠀⠼⢧⠀⠿⠿⠔⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⣤⢤⠀⢴⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠦⠤⠤⠤⠤⠴⢼ ⠿⠿⠿⠿⠿⠿⠿⠿⠿⠽⠿⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠿⠿⠿⠟⠛⠟⠛⠛⠛⠛⠟⠛⠛⠛⠛⠟⠟⠛⠛⠻⠻⣿⠛⠛⠛⣻⠿⠿⠿⠿⠛⠻⠟⠛⠻⠿⠿⠿⠿⠿⠿⢿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⢷⠾⠴⠶⠶⠦⠄⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠾⠖⠶⠾⠶⠴⠶⠄⠀⠐⠐⠀⠂⠒⠐⠐⠀⠂⠒⢤ ⡇⠯⠶⠧⠶⢶⡶⡤⠆⠸⠆⠷⠶⠶⠆⠸⠷⠶⠲⠶⠺⠆⠸⠷⠶⠶⠶⠾⠶⠶⠼⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⡀⠀⠀⠀⠸⠷⠇⠸⠿⠷⠸⠾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠟⠿⠿⠧⠀⠀⠀⠀⠸⠷⠶⠲⠶⠶⠶⠶⠆⠸⠷⠶⠲⠸⠶⠶⠂⠸⠶⢶⠺⠺⠛⠽⠙⠶⠖⠐⠗⠶⠗⠐⠀⣷⡿⠷⠶⠶⠆⠧⠶⠗⠂⡆⠂⠄⠀⠀⠀⠘⠓⠂⠘⠛⠣⠒⠒⠔⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡿⠻⠖⠷⠷⠖⠇⠄⠀⠸⠷⠲⠲⠆⠸⠳⠾⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠶⠆⠇⠗⠶⠄⠀⠸⠦⠶⠖⠇⠸⠳⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡝⠇⠶⠖⠶⢶⡾⠶⡶⠖⠆⠄⠀⠀⠀⠀⠀⠸⠆⠸⠷⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡘ ⡏⠓⠛⠚⠓⠓⠂⠁⠀⠀⠇⠐⠳⠓⠓⠛⠆⠸⠚⠿⠖⠺⠲⠘⠾⠆⠾⠚⠚⠺⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡟⠧⠖⠲⠖⠖⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢃ ⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙ ⡆⠈⠐⠉⠈⠉⠁⡩⠉⠀⠉⠙⠋⠉⠘⠉⠉⠛⠙⠉⠀⠙⠉⠙⠉⠉⠑⠃⠉⠋⠉⠉⠑⠈⠋⠉⠉⠙⠙⠈⠉⠙⠊⠉⠛⠉⠉⢻⢳⠓⠎⠉⠙⠐⠚⠉⠋⠀⠉⠉⠉⠉⠉⠉⠑⠉⠉⠉⠉⠉⠙⠉⠉⠛⠉⠉⠁⢠ ⡇⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⢀⡀⡀⢀⣀⠀⠀⠀⣀⢀⠀⠀⣀⣀⢀⣀⢀⡀⠀⡀⣀⣀⡀⠀⣀⡀⢀⣀⣀⡀⣈⣈⣀⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠐⠓⠳⠖⠛⠉⡻⠓⡂⡀⠸⠛⠛⠃⠈⢀⠘⠉⠇⠙⠛⢛⡁⡟⠛⠏⠀⢿⢛⠚⢘⢿⠻⢟⠈⣻⡟⠋⠃⠋⠛⠛⠈⠻⠟⠿⠻⠷⠇⠓⠻⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠇⠛⠗⠃⠔⠷⠖⠆⠐⠀⠓⠳⠚⠻⠘⠞⠀⠀⠸⠛⠑⠛⠚⠗⠛⠚⠀⠸⠀⠓⠙⠀⠟⠛⠆⠣⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣀⠀⠀⢀⠀⣀⡀⠀⢀⣀⣀⡀⠀⣀⣀⢀⡀⢀⣀⣀⠀⣀⣀⣀⠀⣀⣀⣀⡀⣀⣀⣀⣀⢀⣀⠀⣀⠀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⢿⣯⣯⣭⣧⣿⣧⣤⣼⣥⣯⣧⣬⣼⣿⣭⣥⣽⣽⣽⣤⣽⣿⣽⣤⣽⣟⠙⠻⠿⠿⢗⠾⡿⠟⠁⠓⠀⠟⠃⠘⠛⠛⠿⠍⠛⠃⠋⠃⠟⠵⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠘⠟⣿⣿⣿⣿⣿⡿⣻⢿⣿⣿⣿⣿⢟⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠿⠸⠀⠛⠩⠄⠆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢀⣀⣀⣀⣀⡂⣀⡀⡀⢀⣠⣄⡀⢀⠀⢠⣄⡀⢀⣠⣁⠀⢠⡠⢠⣠⡀⣠⣠⣠⣀⣄⣠⣤⣠⢠⠀⣄⢀⣀⣀⣄⣄⣠⣀⣤⣄⣄⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠄⠉⡍⡍⣁⣍⡠⣆⣄⡈⢉⢉⣁⣈⣁⣸⣍⣁⡈⠉⢩⣀⣬⡍⣭⠭⠥⠩⠉⠩⠾⠿⣉⠙⠿⠕⢀⣋⣡⠙⠛⠃⠁⠉⠉⠏⠁⠇⢥⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠅⠖⠑⠀⠀⠉⡉⠁⠈⠉⠉⠙⠉⠈⠉⠉⠈⠀⠈⠉⠉⢖⠉⠉⢁⠸⠀⠘⠀⠘⠙⠀⠰⠟⠄⠉⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣄⣀⣀⡀⣀⣄⡄⠀⢠⣤⣤⡄⢀⠀⢠⣤⡄⣠⣤⣤⡀⢤⣤⡤⠀⢤⣤⣤⣤⠀⣠⣠⣤⡀⣤⣤⡤⣤⣄⡄⣠⣤⣄⣠⣤⢤⣤⣤⣄⣤⣤⡤⠤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠩⠍⣍⣤⣅⠭⣥⡄⠈⠉⠭⢡⣜⣡⣈⣩⡁⠈⠉⢡⠀⠦⠯⠬⠠⠭⠭⠭⠭⠀⣭⣭⠉⣤⠥⢭⣉⣭⠉⠢⠀⠉⠁⠀⠉⠉⠈⠉⠁⠉⠙⠂⡇⡃⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠁⠠⠅⠄⠲⠈⠀⠀⠈⠵⠐⠀⠵⠀⠐⠂⠀⠈⠨⠀⠜⠙⠋⠈⠘⠁⠈⠀⠋⠝⠀⠓⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣠⣤⣤⣀⠠⣄⣤⡄⠀⢠⣤⣤⡄⢠⠀⢠⣤⠄⢠⣤⡤⠀⣤⣤⠠⠠⢴⣠⠀⣤⠀⢤⣤⣤⣤⡤⡤⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠶⡤⠰⠠⠤⡄⠄⠀⠠⠴⢦⡤⢤⠔⠠⠄⢠⣠⠰⢤⢀⠶⠠⢠⠬⠤⠀⢠⠀⣤⠤⠠⠦⠰⠔⠀⠀⣄⠄⡄⣤⡄⡄⣤⠄⠄⠀⠆⠀⠆⠄⢠⣦⡄⠤⠄⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠂⠷⠷⠗⠰⡷⠶⠂⠰⠶⠶⢶⠶⠦⠴⠶⠢⠀⠸⠷⢿⠾⢾⡻⣾⠴⠀⠸⠀⠼⢧⠀⠿⠿⠔⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⣤⢤⠀⢴⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠦⠤⠤⠤⠤⠴⢼ ⠿⠿⠿⠿⠿⠿⠿⠿⠿⠽⠿⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠿⠿⠿⠟⠛⠟⠛⠛⠛⠛⠟⠛⠛⠛⠛⠟⠟⠛⠛⠻⠻⣿⠛⠛⠛⣻⠿⠿⠿⠿⠛⠻⠟⠛⠻⠿⠿⠿⠿⠿⠿⢿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠸⢷⠾⠴⠶⠶⠦⠅⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠾⠶⠶⠾⠶⠴⠶⠄⠀⠐⠐⠐⠂⠒⠐⠒⠀⠂⠒⢤ ⡇⠯⠶⠧⠶⢶⡶⡤⠆⠸⠆⠷⠶⠶⠆⠸⠷⠶⠲⠶⠺⠆⠸⠷⠶⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⡀⠀⠀⠀⠸⠷⠇⠸⠿⠷⠸⠾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠟⠿⠿⠧⠀⠀⠀⠀⠸⠷⠶⠲⠶⠶⠶⠶⠆⠸⠷⠶⠲⠸⠶⠶⠂⠸⠶⢶⠸⠻⠛⠽⠙⠶⠖⠐⠗⠶⠷⠱⠀⣷⡿⠿⠶⠶⠆⠧⠶⠗⠂⡆⠂⠄⠀⠀⠀⠘⠓⠂⠘⠛⠣⠒⠒⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡿⠻⠶⠷⠷⠶⠇⠆⠀⠸⠷⠲⠲⠆⠸⠳⠾⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠶⠆⠇⠟⠴⠄⠀⠰⠦⠶⠔⠆⠸⠳⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡝⠷⠷⠖⠶⢶⡶⢶⡶⠶⠆⠄⠀⠀⠀⠀⠀⠸⠆⠸⠶⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡘ ⡟⠛⠛⠾⠓⠷⠂⠁⠀⠀⠇⠐⢲⠆⠳⠞⠆⠸⠚⠾⠖⠺⠲⠘⠾⠆⠾⠚⠚⠺⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡟⠧⠖⠲⠖⠖⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢃ ⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠃⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙ ⡆⠈⠓⠛⠛⠛⠓⡻⠛⠊⠉⠙⠛⠋⠛⠛⠉⠛⠛⠙⠚⠛⠛⠛⠙⠛⠓⠓⠛⠛⠙⠛⠓⠋⠛⠙⠛⠛⠛⠚⠛⠛⠚⠛⠛⠙⠙⢻⢳⠛⠞⠛⠛⠛⠚⠛⠛⠓⠛⠛⠛⠙⠛⠛⠓⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠛⠁⢠ ⡇⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⢀⠀⠀⡀⣀⠀⠀⢀⡀⠀⡀⠀⢀⡀⠀⣀⣀⢀⣀⣀⡀⣈⡈⠀⠀⣀⢀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠐⠓⠳⠖⠛⠙⡻⠓⠂⠀⠰⠓⠿⠃⠈⠂⠨⠳⠇⠸⠝⠚⠂⠶⠿⠮⠀⠷⠿⠿⠺⠾⠶⠿⠒⠿⠿⠟⠃⠀⠷⠿⠈⠻⠿⠷⠿⠯⠧⠯⠿⠿⠿⠞⠆⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠇⠷⠷⠳⠰⠷⠷⠆⠐⠲⠖⢲⠶⠶⠾⠶⠂⠀⠸⠷⠿⠯⠽⠿⠿⠾⠀⠼⠀⠷⠺⠀⠿⠟⠄⠦⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣀⠀⠀⢀⠀⣀⡀⠀⢀⣀⣀⡀⠀⢀⢀⢀⡀⢀⣀⡀⠀⣀⣀⠀⠀⣀⣀⣀⡀⣀⣀⣀⠀⢀⡀⠀⣀⠀⢀⣀⠀⣀⣀⡀⣀⠀⠀⡀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⢿⣯⣯⣭⣷⣿⡦⠄⠸⠷⢿⠇⠰⠷⠶⠾⣦⣽⣽⣽⣤⠶⢿⠾⠀⠿⠿⠾⠶⠿⠾⠶⠶⠼⠟⠀⠟⠔⠾⠳⠰⠞⠿⠿⠞⠿⠿⠷⠟⠟⠿⠮⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠿⠺⠀⠾⠿⠔⠶⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢀⣀⣀⣀⣀⡂⣀⡀⡀⢀⣠⣄⡀⠀⠀⢠⣄⡀⢀⣤⡀⠀⢠⡠⢤⡠⠀⣠⠠⠠⠀⣄⣠⣤⣠⢠⠀⠄⠀⠀⠀⢄⣄⣠⣄⣤⣄⣄⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠄⠉⠍⡍⣁⠭⠠⢆⣄⠐⠺⠶⠆⠀⠀⠸⠿⠄⠸⠶⠲⠂⠸⠾⠽⠿⠶⠾⠞⠾⠶⠾⠿⠿⠿⠕⠐⠦⠖⠿⠾⠗⠟⠾⠶⡿⠟⠗⠧⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠄⠷⠵⠄⠤⠚⠩⠆⠐⠐⠂⠚⠈⠰⠦⠀⠀⠀⠘⠖⠌⢞⠊⠎⠻⠸⠀⠸⠀⠘⠒⠀⠿⠟⠄⠅⠍⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣄⣀⣀⡀⡀⣄⠄⠀⢠⣤⣤⡄⢀⠀⢠⠤⠄⣠⣤⣤⡀⠤⡤⠤⠀⠤⣤⢤⣤⠀⡠⢠⣤⠀⠤⠤⠤⠤⠄⠄⠀⠠⠄⠠⠤⠤⠤⠤⠄⠤⠄⡤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠩⠍⢍⣤⡄⠧⠇⠀⠀⠩⠥⠁⠘⣡⡼⠾⠆⠨⠉⠥⠀⠦⠿⠾⠀⠶⠿⠯⠷⠀⠿⠴⠿⠐⠷⠤⠬⠾⠷⠷⠔⠾⠷⠰⠾⠴⠷⠶⠗⠿⠻⠆⠧⠟⠗⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠃⠰⠕⠄⠳⠤⠀⠀⠈⠷⠒⠄⠵⠖⠐⠂⠀⠠⠬⠖⠞⠙⠫⠸⠜⠀⠈⠀⠉⠽⠀⠛⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣠⣤⣤⣀⠠⣄⡤⡄⠀⢠⣤⣤⡄⢠⡄⢠⡤⠀⣠⣤⡀⠀⠠⠄⠀⠀⠐⠀⠀⠀⠀⢤⡤⠠⠤⠤⠤⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠶⡦⠰⠴⠶⠆⠄⠀⠬⢴⢦⡤⢤⠼⠼⠆⢠⢠⠰⢀⠾⠶⠶⠰⠶⠶⠀⢲⠀⠩⠼⠮⠷⠿⠟⠀⠀⣄⠄⡤⣤⡄⡄⣤⠄⠄⠀⠆⠀⠆⠄⢠⣦⡄⠤⠄⡄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠂⠷⠷⠷⠰⠷⠶⠆⠰⠶⠶⢶⠾⠶⠶⠶⠢⠀⠰⠷⠯⠦⠾⠯⢾⠼⠀⠸⠀⠼⠽⠀⠟⠿⠔⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⣤⢤⠀⢴⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠶⠦⠴⠶⠀⠼⢸ ⠿⠚⠛⠛⠛⠛⠛⠛⠛⠙⠛⠙⠛⠛⠛⠛⠛⠛⠛⠓⠛⠛⠛⠛⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠸⢷⠾⠴⠶⠶⠦⠅⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠾⠶⠶⠾⠶⠴⠶⠄⠀⠐⠐⠐⠂⠒⠐⠒⠀⠂⠒⢤ ⡇⠯⠶⠧⠶⢶⡶⡤⠆⠸⠆⠷⠶⠶⠆⠸⠷⠶⠲⠶⠺⠆⠸⠷⠶⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⡀⠀⠀⠀⠸⠷⠇⠘⠿⠷⠸⠾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠟⠿⠿⠧⠀⠀⠀⠀⠸⠷⠶⠲⠶⠶⠶⠶⠆⠸⠷⠶⠲⠸⠶⠶⠂⠸⠶⢶⠿⠿⠛⠽⠙⠶⠖⠐⠗⠶⠷⠱⠀⣷⡿⠿⠶⠶⠆⠧⠶⠗⠂⡆⠂⠄⠀⠀⠀⠘⠓⠂⠘⠛⠣⠒⠒⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡿⠻⠶⠷⠷⠶⠆⠆⠀⠸⠷⠲⠲⠆⠸⠳⠾⠨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠶⠆⠇⠟⠴⠄⠀⠰⠦⠶⠔⠆⠸⠳⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡝⠷⠷⠖⠶⢶⡶⢶⡶⠶⠆⠄⠀⠀⠀⠀⠀⠸⠆⠸⠶⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡘ ⡟⠛⠛⠾⠓⠷⠂⠁⠀⠀⠇⠐⢲⠆⠳⠞⠆⠸⠚⠾⠖⠺⠲⠘⠾⠆⠾⠚⠚⠺⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡟⠧⠖⠲⠖⠖⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢃ ⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠃⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙ ⡆⠈⠓⠛⠛⠛⠓⡻⠛⠊⠉⠙⠛⠋⠛⠛⠉⠛⠛⠙⠚⠛⠛⠛⠙⠛⠓⠓⠛⠛⠙⠛⠓⠋⠛⠙⠛⠛⠛⠚⠛⠛⠚⠛⠛⠙⠙⢻⢳⠛⠞⠛⠛⠛⠚⠛⠛⠓⠛⠛⠛⠙⠛⠛⠓⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠛⠁⢠ ⡇⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⢀⠀⠀⡀⣀⠀⠀⢀⡀⠀⡀⠀⢀⡀⠀⣀⣀⢀⣀⣀⡀⣈⡈⠀⠀⣀⢀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠐⠓⠳⠖⠛⠙⡻⠓⠂⠀⠰⠓⠿⠃⠈⠂⠨⠳⠇⠸⠝⠚⠂⠶⠿⠮⠀⠷⠿⠿⠺⠾⠶⠿⠒⠿⠿⠟⠃⠀⠷⠿⠈⠻⠿⠷⠿⠯⠧⠯⠿⠿⠿⠞⠆⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠇⠷⠷⠳⠰⠷⠷⠆⠐⠲⠖⢲⠶⠶⠾⠶⠂⠀⠸⠷⠿⠿⠿⠿⠿⠮⠀⠼⠀⠷⠻⠀⠿⠟⠗⠦⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣀⠀⠀⢀⠀⡀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⡀⢀⣀⡀⠀⡀⢀⠀⠀⣀⣀⡀⡀⣀⣀⣀⠀⠀⡀⠀⣀⠀⢀⣀⠀⠀⢀⡀⣀⠀⠀⡀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⢿⣯⣯⣭⣷⣾⠧⠄⠸⢷⢿⠇⠐⠖⠶⠾⣆⣽⣽⣽⣤⠶⠿⠾⠀⠿⠿⠾⠷⠿⠾⠶⠶⠾⠟⠄⠟⠔⠾⠷⠰⠞⠿⠿⠞⠿⠿⠷⠟⠟⠿⠮⠇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠿⠺⠀⠾⠿⠔⠶⠄⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢀⣀⣀⣀⣀⡂⡀⡀⡀⢀⣠⣄⠀⠀⠀⢠⣄⡀⢀⣤⡀⠀⢠⡠⢤⡠⠀⣠⠠⠠⠀⣄⣠⣤⣠⢠⠀⠄⠀⠀⠀⢄⣄⣠⣄⣤⠄⣄⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠄⠉⠍⡍⣁⠭⠠⠆⠄⠐⠺⠶⠆⠀⠀⠰⠿⠄⠸⠶⠲⠂⠰⠦⠽⠿⠶⠾⠖⠶⠶⠾⠿⠿⠿⠕⠐⠦⠖⠿⠾⠗⠟⠾⠶⡿⠗⠇⠧⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠄⠧⠽⠄⠠⠚⠩⠆⠐⠐⠂⠚⠈⠰⠦⠀⠀⠀⠘⠶⠎⢾⠋⠎⠻⠨⠀⠸⠁⠘⠒⠂⠿⠟⠄⠅⠍⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣄⣀⣀⡀⡀⠄⠄⠀⢠⣤⣤⡄⢀⠀⢠⠤⠄⣠⣤⣤⡀⠤⡤⠤⠀⠤⣤⢤⣤⠀⡠⠠⠤⠀⠤⠤⠤⠤⠄⠄⠀⠠⠄⠠⠤⠤⠤⠤⠄⠤⠄⡤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠩⠍⢍⣤⡄⠧⠇⠀⠀⠩⠥⠁⠘⣡⡼⠿⠇⠨⠉⠥⠀⠦⠿⠾⠀⠾⠿⠿⠷⠀⠷⠴⠿⠴⠶⠅⠤⠾⠶⠳⠤⠾⠷⠰⠾⠴⠷⠷⠗⠿⠻⠆⠧⠟⠗⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠃⠰⠕⠄⠳⠴⠀⠀⠈⠷⠒⠄⠵⠖⠐⠂⠀⠠⠬⠖⠚⠙⠫⠸⠕⠀⠈⠀⠉⠽⠀⠛⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣠⣤⣤⣀⠠⡄⠤⠄⠀⢠⣤⣤⡄⢠⡄⢠⡤⠀⣠⣤⡀⠀⠠⠄⠀⠀⠐⠀⠀⠀⠀⢤⡤⠠⠤⠤⠤⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠶⡦⠰⠴⠶⠇⠄⠀⠬⢴⢦⡤⢤⠼⠵⠆⢠⢠⠰⢀⠰⠷⠶⠰⠷⠶⠀⢲⠀⠩⠼⠦⠷⠿⠟⠀⠀⣄⠄⡤⣤⡄⡄⣤⠄⠄⠀⠆⠀⠆⠄⢠⣦⡄⠤⠄⡄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠂⠷⠷⠷⠰⠷⠶⠆⠰⠶⠶⢶⠾⠶⠶⠶⠢⠄⠰⠷⠦⠦⠾⠯⢾⠵⠂⠸⠀⠼⠽⠀⠟⠿⠔⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⣤⢤⠀⢴⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠶⠦⠴⠶⠂⠼⢨ ⠿⠚⠛⠛⠛⠛⠛⠛⠛⠙⠛⠙⠛⠛⠛⠛⠛⠛⠛⠓⠛⠛⠛⠛⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠸⢷⠾⠴⠶⠶⠦⠅⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠾⠶⠶⠾⠶⠴⠶⠄⠀⠐⠐⠐⠂⠒⠐⠒⠀⠂⠒⢤ ⡇⠯⠶⠧⠶⢶⡶⡤⠆⠸⠆⠷⠶⠶⠆⠸⠷⠶⠲⠶⠺⠆⠸⠶⠶⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⡀⠀⠀⠀⠸⠷⠇⠚⠿⠷⠸⠾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠟⠿⠿⠧⠀⠀⠀⠀⠸⠷⠶⠲⠶⠶⠶⠶⠆⠸⠷⠶⠲⠸⠶⠶⠂⠸⠶⢶⡞⡾⠛⠹⠙⠶⠖⠐⠗⠶⠷⠱⠀⣷⡿⠿⠶⠶⠆⠧⠶⠗⠂⡆⠂⠄⠀⠀⠀⠘⠓⠂⠘⠛⠣⠒⠒⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡿⠻⠶⠷⠷⠶⠖⠆⠀⠸⠷⠲⠲⠆⠸⠳⠾⠨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠶⠆⠇⠟⠴⠄⠀⠰⠦⠶⠔⠆⠸⠳⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡝⠷⠷⠖⠶⢶⡶⢶⡶⠶⠆⠄⠀⠀⠀⠀⠀⠸⠆⠸⠶⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡘ ⡟⠛⠛⠾⠓⠷⠂⠁⠀⠀⠇⠐⢲⠆⠳⠞⠆⠸⠚⠾⠖⠺⠲⠘⠾⠆⠾⠚⠚⠺⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡟⠧⠖⠲⠖⠖⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠧⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢃ ⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠃⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙ ⡆⠈⠓⠛⠛⠛⠓⡻⠛⠊⠉⠙⠛⠋⠛⠛⠉⠛⠛⠙⠚⠛⠛⠛⠙⠛⠓⠓⠛⠛⠙⠛⠓⠋⠛⠙⠛⠛⠛⠚⠛⠛⠚⠛⠛⠙⠙⢻⢳⠛⠞⠛⠛⠛⠚⠛⠛⠓⠛⠛⠛⠙⠛⠛⠓⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠛⠁⢠ ⡇⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⢀⠀⠀⡀⣀⠀⠀⢀⡀⠀⡀⠀⢀⡀⠀⣀⣀⢀⣀⣀⡀⣈⡈⠀⠀⣀⢀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠐⠓⠳⠖⠛⠙⡻⠓⠂⠀⠰⠓⠿⠃⠈⠂⠨⠳⠇⠸⠝⠚⠂⠶⠿⠮⠀⠷⠿⠿⠺⠾⠶⠿⠒⠷⠿⠟⠃⠀⠷⠿⠈⠻⠿⠷⠿⠯⠧⠯⠿⠿⠿⠞⠆⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡇⠀⠀⠀⠇⠷⠷⠳⠰⠷⠷⠆⠐⠲⠖⢲⠶⠶⠾⠶⠂⠀⠸⠷⠿⠿⠿⠿⠿⠮⠀⠼⠀⠷⠻⠀⠿⠟⠗⠦⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣀⠀⠀⢀⠀⡀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⡀⢀⣀⡀⠀⡀⢀⠀⠀⣀⣀⡀⡀⣀⣀⣀⠀⠀⡀⠀⣀⠀⢀⣀⠀⠀⢀⡀⣀⠀⠀⡀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⢿⣯⣯⣭⣧⣴⠦⠄⠸⢷⢿⢇⠐⠖⠶⢶⣆⣽⣽⣽⡤⠶⠿⠾⠀⠿⠿⠾⠶⠿⠾⡶⠶⠶⠟⠄⠟⠔⠾⠷⠠⠞⠾⠿⠞⠿⠿⠶⠟⠟⠿⠮⠇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠿⠺⠀⠾⠿⠔⠶⠄⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢀⣀⣁⣉⣁⡋⡁⡀⡉⢈⣡⣅⠉⠉⠁⢠⣍⡀⢉⣬⡀⠉⢩⡩⢥⡠⠀⣠⠠⠠⠀⣄⣠⣤⣠⢠⠀⠄⠀⠀⠀⢄⣄⣠⣄⣤⠄⣄⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠄⠉⠍⡍⣁⠭⠠⠆⠄⠐⠺⠶⠆⠀⠀⠰⠿⠄⠸⠶⠲⠂⠰⠦⠵⠿⠶⠾⠖⠶⠶⠶⠿⠷⠿⠔⠐⠦⠖⠿⠶⠗⠟⠾⠶⡿⠗⠇⠧⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠄⠇⠽⠔⠠⠚⠫⠄⠐⠐⠂⠚⠈⠰⠦⠀⠀⠀⠘⠶⠎⢶⠊⢎⠻⠨⠀⠸⠃⠘⠒⠂⠿⠟⠄⠅⠍⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣄⣀⣀⡀⡀⠄⠄⠀⢠⣤⣤⡄⢀⠀⢠⠤⠄⣠⣤⣤⡀⠤⡤⠤⠀⠤⣤⢤⣤⠀⡠⠠⠤⠀⠤⠤⠤⠤⠄⠄⠀⠠⠄⠠⠤⠤⠤⠤⠄⠤⠄⡤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠩⠍⢍⣤⡄⠧⠆⠀⠀⠩⠥⠁⠘⣡⡼⠿⠇⠨⠉⠥⠀⠦⠿⠾⠀⠶⠿⠷⠷⡀⠷⠴⠷⠴⠶⠆⠤⠾⠶⠷⠤⠾⠷⠰⠾⢴⡷⠶⠗⠿⠻⠆⠧⠟⠗⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠃⠰⠕⠄⠳⡴⠀⠀⠈⠷⠒⠄⠵⠖⠐⠆⠀⠠⠬⠖⡞⠙⠫⠸⠗⠂⠈⠀⠁⠿⡀⠛⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣠⣤⣤⣀⠠⡄⠤⠄⠀⢠⣤⣤⡄⢠⡄⢠⡤⠀⣠⣤⡀⠀⠠⠄⠀⠀⠐⠀⠀⠀⠀⢤⡤⠠⠤⠤⠤⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠶⡦⠰⠴⠶⠆⠄⠀⠬⢴⢦⡤⢤⠼⡴⠆⢠⢠⠰⢀⠰⠷⠶⠰⠶⠶⠀⢲⠀⠩⠼⠦⠷⠿⠟⠀⠀⣄⠄⡤⣤⡄⡄⣤⠄⠄⠀⠆⠀⠆⠄⢠⣦⡄⠤⠄⡄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠂⠷⠷⠷⠰⠷⠶⠆⠰⠶⠶⢶⠾⠦⠶⠶⡢⠄⠰⠷⠦⠦⠾⠮⢶⠵⠂⠸⠀⠤⠽⠀⠟⠿⠔⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⣤⢤⠀⢴⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠶⠦⠴⠶⠂⠼⢨ ⠿⠚⠛⠛⠛⠛⠛⠛⠛⠙⠛⠙⠛⠛⠛⠛⠛⠛⠛⠓⠛⠛⠛⠛⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠸⢷⠾⠴⠶⠶⠦⠅⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠾⠶⠶⠾⠶⠴⠶⠄⠀⠐⠐⠐⠂⠒⠐⠒⠀⠂⠒⢤ ⡇⠯⠶⠧⠶⢶⡶⡤⠆⠸⠆⠷⠶⠶⠆⠸⠷⠶⠲⠶⠺⠆⠸⠶⠶⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⡀⠀⠀⠀⠸⠷⠇⠚⠿⠷⠸⠾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠟⠿⠿⠧⠀⠀⠀⠀⠸⠷⠶⠲⠶⠶⠶⠶⠆⠸⠷⠶⠲⠰⠶⠶⠂⠸⠶⢶⡞⡾⠛⠹⠙⠶⠖⠐⠗⠶⠷⠱⠀⣷⡿⠿⠶⠶⠆⠧⠶⠗⠂⡆⠂⠄⠀⠀⠀⠘⠓⠂⠘⠛⠣⠒⠒⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡿⠻⠶⠷⠷⠶⠖⠆⠀⠸⠷⠲⠲⠆⠸⠳⠾⠨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠶⠆⠇⠟⠴⠄⠀⠰⠦⠶⠔⠆⠸⠳⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡝⠷⠷⠖⠶⢶⡶⢶⡶⠶⠆⠄⠀⠀⠀⠀⠀⠸⠆⠸⠶⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡘ ⡟⠓⠛⠾⠓⠷⠂⠁⠀⠀⠆⠐⢲⠆⠳⠞⠆⠸⠚⠾⠖⠺⠲⠘⠾⠆⠾⠚⠚⠺⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡟⠧⠖⠲⠖⠖⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠧⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢃ ⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠃⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙ ⡆⠈⠓⠛⠛⠛⠓⡻⠛⠊⠉⠙⠛⠋⠛⠛⠉⠛⠛⠙⠚⠛⠛⠛⠙⠛⠓⠓⠛⠛⠙⠛⠓⠋⠛⠙⠛⠛⠛⠚⠛⠛⠚⠛⠛⠙⠙⢻⢳⠛⠞⠛⠛⠛⠚⠛⠛⠓⠛⠛⠛⠙⠛⠛⠓⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠛⠁⢠ ⡇⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⢀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⣶⢶⠄⠰ ⡇⠐⠓⠳⡖⠛⠙⡻⡓⡦⠀⠰⠓⡿⠃⠈⠂⣶⡶⡶⠸⠝⠚⠂⠶⠿⠮⠀⠷⠿⠗⣶⣶⠶⣶⣶⣦⣶⡦⢰⣦⠷⠿⠈⠻⠿⠷⡷⢶⣶⢶⡶⡖⢶⣶⢴⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠰⠶⡆⢰⢶⡦⠶⡆⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣀⠉⠉⢉⠉⡉⠉⠉⢉⣉⣉⡉⠉⠉⠉⠉⡉⢉⣉⡉⠉⡉⢉⠉⠉⣉⣁⡀⡀⣀⣀⣀⠀⠀⡀⠀⣀⠀⢀⣀⠀⠀⢀⡀⣀⠀⠀⡀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⠿⣯⢯⠭⣧⠤⡄⠀⠸⠷⢿⠇⠐⠆⢠⡶⠆⣽⣽⢽⡤⠀⡶⡒⣶⣶⡶⣶⣶⣶⠶⢶⣶⣶⡶⠦⠴⡦⢔⡶⢶⠒⡶⢶⣰⣶⠶⠶⣶⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⡆⡶⡶⡶⡰⡶⡶⢄⠠⡦⣦⣦⡦⣦⡶⡦⡆⡀⠐⣶⡶⡶⣶⣶⣶⡆⠆⠰⡆⢀⡖⡆⢰⣶⡦⢴⡆⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢀⣀⣀⣀⣀⡀⡀⡀⡀⢀⣠⣄⠀⠀⠀⠠⣄⡀⢀⣤⡀⠀⢠⡠⢤⡠⠀⣠⠠⠠⠀⣄⣠⣤⣠⢠⠀⠄⠀⠀⠀⢄⣄⣠⡄⣤⠄⢄⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠄⠉⠍⡍⣁⠭⡠⡦⠀⠰⣶⣶⡶⠀⠆⠰⡾⠆⠸⠶⠲⠂⠰⣶⡶⡂⢰⣶⣶⡶⠖⠰⣦⣶⡧⠴⣶⡶⣲⣶⣶⡦⢶⣶⡦⢴⣶⣲⣶⣶⡶⣶⣶⣴⣶⣶⠶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠄⠆⠽⠔⠠⠒⠢⠄⠐⠀⠂⠚⠈⠰⠆⠀⠀⠀⠘⠶⠆⢶⠀⢖⢺⠠⠂⠸⠃⢰⣶⡆⠽⠞⠄⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣄⣀⣀⡀⡀⠄⠄⠀⢠⣤⣤⡄⢀⠀⢠⠤⠄⣠⣤⣤⡀⠤⠤⠤⠀⠤⠤⠤⢤⠀⠠⠠⠤⠀⠤⠤⠤⠤⠄⠄⠀⠠⠄⠠⠤⠤⠤⠤⠄⠤⠄⡤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠩⠍⢍⣤⡄⠇⡖⠀⠀⠩⠥⠁⠘⣡⡼⠷⡆⠨⠉⠥⠀⢰⣶⣤⡴⣦⣤⡄⢰⡆⠐⣶⣶⣶⣶⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠃⠰⠔⠄⠲⡴⠀⠀⠈⠷⠒⠄⠵⠖⠐⠆⠀⠠⠤⠖⡦⠀⠢⠰⠗⠂⠀⠀⠀⢶⡀⠒⠶⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣠⣤⣤⣀⠠⡄⠤⠄⠀⢠⣤⣤⡄⢠⡄⢠⡤⠀⣠⣤⡀⠀⠠⠄⠀⠀⠐⠀⠀⠀⠀⢤⡤⠠⠤⠤⠤⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠶⡦⠰⠴⣦⡤⠄⠀⠬⢴⢦⡤⢤⠀⠀⡦⢠⢠⠰⢀⢰⣶⣶⡆⡖⣖⣶⡦⢰⣶⠶⣒⡶⢗⣶⣶⡖⣦⢴⣶⣶⣶⣶⣒⡶⣶⡆⠀⠀⠆⠄⢠⣦⡄⠤⠄⡄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠂⠷⠷⠷⠰⠷⠶⠖⠰⠶⠶⢶⠾⠦⠶⣶⡢⠄⠰⠷⠦⠦⠶⠦⢶⠶⠆⠰⠀⠐⣶⡆⠐⠶⠄⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⣤⢤⠀⢴⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠚⠛⠛⠛⠛⠛⠛⠛⠙⠛⠙⠛⠛⠛⠛⠛⠛⠛⠓⠛⠛⠛⠛⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣿⣷ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠸⢷⠾⠴⠶⠶⠦⠅⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠾⠶⠶⠾⠶⠴⠶⠄⠀⠐⠐⠐⠂⠒⠐⠒⠀⠂⠒⢤ ⡇⠯⠶⠧⠶⢶⡶⡤⠆⠸⠆⠷⠶⠶⠆⠸⠷⠶⠲⠶⠺⠆⠸⠶⠶⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⡀⠀⠀⠀⠸⠷⠇⠚⠿⠷⠸⠾⠆⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠟⠿⠿⠧⠀⠀⠀⠀⠸⠷⠶⠲⠶⠶⠶⠶⠆⠸⠷⠶⠲⠰⠶⠶⠂⠸⠶⢶⡞⡾⠛⠹⠙⠶⠖⠐⠗⠶⠷⠱⠀⣷⡿⠿⠶⠶⠆⠧⠶⠗⠂⡆⠂⠄⠀⠀⠀⠘⠓⠂⠘⠛⠣⠒⠒⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡿⠻⠶⠷⠷⠶⠖⠆⠀⠸⠷⠲⠲⠆⠸⠳⠾⠨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠶⠆⠇⠟⠴⠄⠀⠰⠦⠶⠔⠆⠸⠳⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡝⠷⠷⠖⠶⢶⡶⢶⡶⠶⠆⠄⠀⠀⠀⠀⠀⠸⠆⠸⠶⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡘ ⡟⠓⠛⠾⠓⠷⠂⠁⠀⠀⠆⠐⢲⠆⠳⠞⠆⠸⠚⠾⠖⠺⠲⠘⠾⠆⠾⠚⠚⠺⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡟⠧⠖⠲⠖⠖⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠧⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢃ ⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠃⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙ ⡆⠈⠓⠛⠛⠛⠓⡻⠛⠊⠉⠙⠛⠋⠚⠛⠉⠛⠛⠙⠚⠛⠛⠛⠙⠛⠓⠓⠛⠛⠙⠛⠓⠋⠛⠙⠛⠛⠛⠚⠛⠛⠚⠛⠛⠙⠙⢻⢳⠛⠞⠛⠛⠓⠚⠛⠛⠓⠛⠛⠛⠙⠛⠛⠓⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠛⠁⢠ ⡇⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⢀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⣶⢶⠄⠰ ⡇⠐⠓⠳⡖⠛⠙⡻⡓⡦⠀⠰⠓⡿⠃⠈⠂⣶⡶⡶⠘⠝⠚⠂⠶⠿⠮⠀⠷⠿⠗⣶⣶⠶⣶⣶⣦⣶⡢⢰⣦⠷⠛⠈⠻⠿⠷⡷⢶⣶⢶⡶⣖⢶⣶⢴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠰⠶⡆⢰⣶⡦⠶⡆⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣀⠙⠙⢉⠉⡉⠉⠋⢙⣻⣉⡙⠛⠏⠉⠉⡉⢉⣉⡉⠉⡉⢹⠙⠉⣉⣍⡙⡀⣀⣈⣀⠀⠀⡀⠀⣀⠀⢀⣀⠀⠀⢀⡀⣀⠀⠀⡀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⠿⣯⢯⠭⣧⠤⡄⠀⠸⠷⢿⠇⠐⠆⢠⡶⠆⣽⣽⢽⡤⠀⡶⡒⣶⣶⡶⣶⣶⣶⢶⢶⣶⣶⠶⠢⠴⡦⢔⡶⢶⠒⡶⢶⣰⣶⠶⠶⣶⡂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣆⡶⣶⡶⡰⡶⡶⢄⠠⡦⣦⣦⡦⣦⡶⡮⡆⡀⠐⣶⡯⡶⣖⣶⣶⣆⡆⠰⠆⢑⡟⡆⣸⢶⣤⢴⡆⡆⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢀⣀⣀⣀⣐⡀⡁⡀⡀⢈⣠⣄⠀⠀⠀⠠⣅⡀⢀⣤⡀⠀⢠⡠⢤⡠⠀⣠⠠⠠⠀⣄⣠⣤⣨⢠⠀⠅⠀⠀⠀⢄⣄⣠⡀⣤⠄⢄⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠄⠉⠍⡍⣁⠭⡠⡦⠀⠰⣶⣲⡲⠀⠆⠰⡾⠆⠸⠶⠲⠂⠰⣶⡶⣂⣰⣶⣶⡶⠖⠰⣦⣶⡧⠴⣶⡶⣲⣶⣶⡂⢶⡶⡦⢴⡶⢲⣶⣶⡶⣶⣶⣴⣶⣶⠶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠄⠆⠽⠔⠠⠒⠢⠄⠐⠀⠂⠚⠈⠰⠖⠉⠀⠀⠘⠶⠆⢶⠂⢞⢳⠠⠂⠸⠋⢹⣶⡆⠽⠞⠄⠰⠕⠚⠀⠀⠁⠂⠀⠀⠀⠀⠈⠀⠀⠐⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣄⣀⣀⡀⡀⠄⠄⠀⢠⣤⣤⡄⢀⠀⢠⠤⠄⣠⣤⣤⡀⠤⠤⠤⠀⠤⠤⠤⢤⠀⠠⠠⠤⠈⠤⠤⠤⠤⠄⠀⠀⠠⠄⠠⠤⠤⠤⠤⠄⠤⠄⡤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠩⠍⢍⣤⡄⠇⡖⠀⠀⠩⠥⠁⠘⣡⡼⠷⡆⠨⠉⠥⠀⢰⣶⣤⡴⣦⣤⡄⢰⡆⠐⣶⣶⣶⢶⡦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠃⠰⠔⠄⠲⡴⠀⠀⠈⠷⠒⠄⠵⠖⠐⠆⠀⠠⠤⠖⡮⠃⠢⠲⠗⠓⠀⠀⠀⢶⡀⠒⠖⢐⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣠⣤⣤⣀⠠⡄⠤⠄⠀⢠⣤⣤⡄⢠⡄⢠⡤⠀⣠⣤⡀⠀⠠⠄⠀⠀⠐⠀⠁⠈⠀⢤⡤⠠⠌⠄⠨⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠶⡦⠰⠴⣦⡤⠄⠀⠬⢴⢦⡤⢤⠀⠀⡦⢠⢠⠰⢀⢰⣶⣶⡆⡖⣖⣶⡦⢰⣶⠶⣒⡶⢗⣶⣶⡖⡦⢴⡶⣶⣶⣶⣒⡶⣶⡆⠀⠀⠆⠄⢠⣦⡄⠤⠄⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠂⠷⠷⠷⠰⠷⠶⠖⠰⠶⠶⢶⠾⠦⠶⣶⡢⠄⠰⠷⠦⠦⠶⠦⢶⠶⠗⠼⠰⠐⣶⡇⠐⠶⠄⠶⠶⠀⠀⠂⠈⠁⠀⠀⠀⠄⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⣤⢤⠀⢴⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠚⠛⠛⠛⠛⠛⠛⠛⠙⠛⠙⠛⠛⠛⠛⠛⠛⠛⠓⠛⠛⠛⠛⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣿⣷ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠸⢷⠾⠴⠶⠶⠦⠅⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠾⠶⠶⠾⠶⠴⠶⠄⠀⠐⠐⠀⠂⠒⠐⠒⠀⠂⠒⢤ ⡇⠯⠶⠧⠶⢶⡶⡤⠆⠸⠆⠷⠶⠶⠆⠸⠷⠶⠲⠶⠺⠆⠸⠶⠶⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⡀⠀⠀⠀⠸⠷⠇⠚⠿⠷⠸⠾⠆⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠟⠿⠿⠧⠀⠀⠀⠀⠸⠷⠶⠲⠶⠶⠶⠶⠆⠸⠷⠶⠲⠰⠶⠶⠂⠸⠶⢶⡞⡾⠛⠹⠙⠶⠖⠐⠗⠶⠷⠱⠀⣷⡿⠿⠶⠶⠆⠧⠶⠗⠂⡆⠂⠄⠀⠀⠀⠘⠓⠂⠘⠛⠣⠒⠒⠔⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡿⠻⠶⠷⠷⠶⠖⠆⠀⠸⠷⠲⠲⠆⠸⠳⠾⠨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠶⠆⠇⠟⠴⠄⠀⠰⠦⠶⠔⠆⠸⠳⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡝⠷⠷⠖⠶⢶⡶⢶⡶⠶⠆⠄⠀⠀⠀⠀⠀⠸⠆⠸⠶⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡘ ⡟⠓⠛⠾⠓⠷⠂⠀⠀⠀⠆⠐⢲⠆⠳⠞⠆⠸⠚⠾⠖⠺⠲⠘⠾⠆⠾⠚⠚⠺⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡟⠧⠖⠲⠖⠖⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠧⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢃ ⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠃⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙ ⡆⠈⠓⠛⠛⠛⠓⡻⠛⠊⠉⠙⠛⠋⠚⠛⠉⠛⠛⠙⠚⠛⠛⠛⠙⠛⠓⠓⠛⠛⠙⠛⠓⠋⠛⠙⠛⠛⠛⠚⠛⠛⠚⠛⠛⠙⠙⢻⢳⠛⠞⠛⠛⠓⠚⠛⠛⠓⠛⠛⠛⠙⠛⠛⠓⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠛⠁⢠ ⡇⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⢀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⣶⢦⠀⠰ ⡇⠐⠓⠳⡖⠛⠙⡻⡓⡦⠀⠰⠃⣿⣇⠈⠂⣶⡶⡶⠘⠝⠚⠂⠶⠿⠮⠀⠷⠿⠗⣶⣶⠶⣶⣶⣦⣖⡢⢰⣦⢳⠛⠈⠻⠿⠷⡷⢶⣶⢶⣶⣖⢶⣶⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡇⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠰⠶⣦⢔⣶⡦⠾⡆⡏⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠈⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣀⠛⠛⢉⠙⡉⠛⠛⢙⣛⣉⡛⠛⠛⠉⠋⡉⢉⣉⡉⠉⡉⢿⠙⠛⣉⣍⡙⡁⣀⣈⣁⠀⠀⡀⠀⣀⠀⢀⣀⠀⠀⢀⡀⣀⠀⠀⡀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⠿⣯⢯⠭⣧⠤⡄⠀⠸⠷⢿⠇⠐⠆⢠⡶⠆⣽⣽⣽⡤⠀⡶⡒⣶⣖⡶⣖⣶⣶⣶⠶⣶⣶⢶⡦⠴⡦⢔⡶⢶⠒⡶⢶⣰⣶⠶⠶⣶⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣆⣖⣲⣶⡰⡶⡶⢄⠠⡦⣦⣦⡦⣦⠂⡬⡆⡀⠐⣰⡭⡶⣖⣲⣶⣄⡄⠉⠋⢑⡟⣆⢘⢷⣄⢴⠆⡆⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢀⣀⣀⣐⣒⡀⡁⡀⡀⢈⣠⣄⠀⠀⠀⠠⣅⡁⢐⣤⡀⠀⢘⡨⢤⡠⠀⣠⠨⠠⠀⣄⣠⣤⣉⢠⠈⠅⠀⠀⠀⢄⣄⣠⡀⣤⠄⢄⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠄⠉⠍⡍⣁⠭⡠⡦⠀⠰⣶⣲⣲⠀⠆⠰⡾⠆⠸⠶⠲⠂⠰⣶⡶⡂⢰⣶⣶⡶⠖⠰⣦⣶⡧⠴⣶⡶⣲⣶⣶⣂⢖⠶⡦⢴⠶⢲⣶⣶⡶⣶⣶⣴⣶⣶⠶⡆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠄⠆⠽⠔⠠⠒⠠⠄⠐⠂⠂⠘⠈⠰⠖⠉⠀⠀⠘⠶⠆⢶⠂⢞⢲⠠⠂⠸⠋⢹⣶⡆⢽⠟⠄⠸⠝⠒⠀⠈⠙⠂⠐⠂⠀⠂⠈⠀⠀⠓⠀⠈⠐⠁⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣄⣀⣀⡀⡀⠄⠄⠀⢠⣤⣤⡄⢀⠀⢠⠤⠄⣠⣤⣤⡀⠤⠤⠤⠀⠤⠤⠤⢤⠀⠠⠠⠤⠉⠤⠤⠤⠤⠄⠀⠀⠠⠄⠠⠤⠤⠤⠤⠄⠤⠄⡤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠩⠍⢍⣤⡄⠇⡖⠀⠀⠩⠥⠁⠘⣡⡼⠷⡆⠨⠉⠥⠀⢰⣶⡤⠴⡦⣤⡄⢰⡆⠐⣶⣶⣶⢶⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠃⠰⠔⠄⠲⡴⠀⠀⠈⠷⠒⠄⠵⠖⠐⠆⠀⠠⠤⠖⡮⠋⠓⡢⠗⠓⠀⠀⠀⢶⡀⡒⠖⢑⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣠⣤⣤⣀⠀⡀⠤⠄⠀⢠⣤⣤⡄⢠⡄⢠⡤⠀⣠⣤⡀⠀⠠⠄⠐⠈⠐⠀⠁⠈⠀⢤⡤⠠⠌⠄⠨⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠶⡦⠰⠴⣦⡤⠄⠀⠬⢴⢦⡤⢤⠀⠀⡦⢠⢠⠰⢀⢰⣶⣶⡆⡖⣖⣶⡦⢰⣶⠶⣒⡶⢗⣶⣶⠖⡦⢴⡶⣶⣶⣶⣒⡶⣶⡆⠀⠀⠆⠄⢠⣦⡄⠤⠄⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠂⠷⠷⠷⠰⠷⠶⠖⠰⠶⠶⢶⠾⠦⠶⣶⡢⠄⠰⠶⠦⠦⠶⠦⢶⠆⠗⠽⠰⠐⠶⡇⠑⠶⠄⠶⠶⠀⠐⠂⠈⠙⠄⠀⠀⠄⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠲⠂⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⣤⢤⠀⢴⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠚⠛⠛⠛⠛⠛⠛⠛⠙⠛⠙⠛⠛⠛⠛⠛⠛⠛⠓⠛⠛⠛⠛⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣿⣷ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠸⢷⠾⠴⠶⠶⠦⠅⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠾⠶⠶⠾⠶⠤⠶⠄⠀⠐⠐⠀⠂⠒⠐⠒⠀⠂⠒⢤ ⡇⠯⠶⠧⠶⢶⡶⡤⠆⠸⠆⠷⠶⠶⠆⠸⠷⠶⠲⠶⠺⠆⠸⠶⠶⠶⠶⠾⠶⠶⠼⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⡀⠀⠀⠀⠸⠷⠇⠚⠿⠷⠸⠾⠆⠀⠀⠶⠄⠀⠀⠀⠀⠀⠀⢸ ⡇⠟⠿⠿⠧⠀⠀⠀⠀⠸⠷⠶⠲⠶⠶⠶⠶⠆⠸⠷⠶⠲⠰⠶⠶⠂⠸⠶⢶⡞⡾⠛⠹⠙⠶⠖⠐⠗⠶⠷⠱⠀⣷⡿⠿⠶⠶⠆⠧⠶⠗⠂⡆⠂⠄⠀⠀⠀⠘⠓⠂⠘⠛⠣⠒⠒⠔⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡿⠻⠶⠷⠷⠶⠖⠆⠀⠸⠷⠲⠲⠆⠸⠳⠾⠨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠶⠆⠇⠟⠤⠄⠀⠰⠦⠶⠔⠆⠸⠳⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡝⠷⠷⠖⠶⢶⡶⢶⡶⠶⠆⠄⠀⠀⣄⠀⠀⠸⠆⠸⠶⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡘ ⡟⠓⠛⠾⠓⠷⠂⠀⠀⠀⠆⠐⢲⠆⠳⠞⠆⠸⠚⠾⠖⠺⠲⠘⠾⠆⠾⠚⠚⠺⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡟⠧⠖⠲⠖⠖⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠧⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢃ ⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠃⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙ ⡆⠈⠓⠛⠛⠛⠓⡻⠛⠊⠉⠙⠛⠋⠚⠛⠉⠛⠛⠙⠚⠛⠛⠛⠙⠛⠓⠓⠛⠛⠙⠛⠓⠋⠛⠙⠛⠛⠛⠚⠛⠛⠚⠛⠛⠙⠙⢻⢳⠛⠞⠛⠛⠓⠚⠛⠛⠓⠛⠛⠛⠙⠛⠛⠓⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠛⠁⢠ ⡇⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⢀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⣶⢦⠀⠰ ⡇⠐⠓⠳⡖⠛⠉⡻⡓⡦⠀⠰⠃⣿⣇⠈⠂⣶⡴⡄⠘⠝⠚⠂⠶⠿⠮⠀⠷⠿⠗⣶⣶⠶⣶⢶⣦⣖⣢⢰⣢⢳⠛⠈⠻⠿⠷⣷⣶⣲⢶⣶⡶⢶⣶⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡇⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠰⠒⣦⣴⣷⡦⠾⡆⡏⠀⠈⠁⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⠀⠀⠉⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣀⠛⠛⢋⠙⡟⠛⠛⢛⣻⣿⡟⠛⠟⠉⠛⡉⢉⣉⡙⠉⡉⢿⠛⠛⣉⣋⡙⡁⣀⣈⣁⠀⠀⡀⠀⣀⠀⢀⣀⠀⠀⢀⡀⣀⠀⠀⡀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⠿⣯⢯⠭⣧⠤⡄⠀⠸⠷⢿⠇⠐⠄⢠⡶⠆⣽⣽⣽⡤⠀⡶⡒⣶⣖⡶⣖⣶⣶⢶⣶⢶⣶⢶⡢⢴⡦⢔⡶⢶⠒⡶⢶⣰⣶⠶⠶⣶⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣆⣖⣒⣶⡰⡶⡶⢄⠠⡦⣦⣦⡦⣦⡂⡮⡆⡀⠑⣰⡥⡲⣒⣲⣦⣄⡄⡉⠃⢑⡟⣆⠘⢿⣅⢸⠆⡆⠀⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢀⣀⣀⣐⣒⡀⡁⡀⡐⢈⣠⣄⠐⠀⠐⠀⣁⡀⢐⣠⡀⠀⢘⡈⢀⡠⠀⣠⠨⠡⠀⣄⣠⣤⣈⢠⠈⠅⠂⠀⠀⢄⣄⣠⡀⣤⠄⢄⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠄⠉⠍⡍⣁⠭⡠⡆⠀⠰⣶⣲⣒⠀⠆⠰⠾⠆⡸⠶⠲⠂⠰⣶⡶⣂⣰⣶⡖⡶⠖⡰⣦⣶⡧⠴⣶⡶⣲⣶⣶⣂⢖⠶⡦⢴⡶⢲⣶⣶⡶⣶⣶⣴⣖⡶⠶⢆⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠄⠆⠽⠔⠠⠒⠠⠄⠐⠂⠃⠘⠈⠠⠐⠉⠂⠀⠘⠶⠆⢶⠂⢞⢲⠠⠃⠸⠋⢹⣶⡆⢽⠟⠄⠹⠝⠒⠈⠀⠙⠂⠐⠃⠀⠂⠈⠀⠀⠓⠀⠈⠒⠁⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣄⣀⣀⡀⡀⠄⠄⠀⢠⣤⣤⡄⢀⠀⢠⠤⠄⣠⣤⣤⡀⠤⠤⠠⠀⠤⠤⠤⢤⠀⠠⠠⠤⠋⠤⠤⠤⠤⠄⠀⠀⠠⠄⠠⠤⠤⠤⠤⠄⠤⠄⡤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠩⠍⢍⣤⡄⠇⡖⠀⠀⠩⠥⠁⠘⣡⡼⠷⡆⠨⠉⠥⠀⢰⢶⡤⠴⡦⢤⡄⢰⡆⠐⣶⣶⡶⢶⢦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠃⠰⠔⠄⠒⡴⠀⠀⠈⠷⠒⠄⠵⠖⠐⠆⠀⠠⠤⠖⡮⠛⠓⡣⠗⠓⠀⠀⠀⢶⡀⡒⠖⢓⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣠⣤⣤⣀⠀⡀⠤⠄⠀⢠⣤⣤⡄⢠⡄⢠⡤⠀⢠⣤⡀⠀⠢⠘⠐⠈⠐⠀⠉⠉⠀⢤⡤⠠⠌⠄⠨⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠶⡦⠰⠴⣦⡤⠄⠀⠬⢴⢦⡤⢤⠀⠀⡦⢠⢠⠰⢀⢰⣶⣶⡆⡖⣖⣶⡦⢰⣶⠶⣒⡶⢗⣶⣶⠖⡦⢴⡶⣶⡶⠶⢒⡶⣶⡆⠀⠀⠆⠄⢠⣦⡄⠤⠄⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠂⠷⠷⠷⠰⠷⠶⠖⠰⠲⠶⢶⠾⠦⠶⢶⡢⠄⠰⠶⠦⠦⠶⠦⢴⠆⠇⠽⠰⠐⠿⡟⠓⠶⠄⠦⠴⠀⠐⠂⠈⠙⠮⠁⠡⠄⠀⠞⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠲⠊⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠀⠀⠐⠀⠂⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⣤⢤⠀⢴⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠚⠛⠛⠛⠛⠛⠛⠛⠙⠛⠙⠛⠛⠛⠛⠛⠛⠛⠓⠛⠛⠛⠛⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣿⣷ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠸⢷⠾⠴⠶⠶⠦⠅⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠾⠶⠶⠾⠶⠤⠶⠄⠀⠐⠐⠀⠂⠒⠐⠒⠀⠂⠒⢤ ⡇⠯⠶⠧⠶⢶⡶⡤⠆⠸⠆⠷⠶⠶⠆⠸⠷⠶⠲⠶⠺⠆⠸⠶⠶⠶⠶⠾⠶⠶⠼⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⡀⠀⠀⠀⠸⠷⠇⠚⠿⠷⠸⠾⠆⠀⠀⠶⠄⠀⠀⠀⠀⠀⠀⢸ ⡇⠟⠿⠿⠧⠀⠀⠀⠀⠸⠷⠶⠲⠶⠶⠶⠶⠆⠸⠷⠶⠲⠰⠶⠶⠂⠸⠶⢶⡞⡾⠛⠹⠙⠶⠖⠐⠗⠶⠷⠱⠀⣷⡿⠿⠶⠶⠆⠧⠶⠗⠂⡆⠂⠄⠀⠀⠀⠘⠓⠂⠘⠛⠣⠒⠒⠔⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡿⠻⠶⠷⠷⠶⠖⠆⠀⠘⠷⠲⠲⠆⠸⠳⠾⠨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠶⠆⠇⠟⠤⠄⠀⠰⠦⠶⠔⠆⠸⠳⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡝⠷⠷⠖⠶⢶⡶⢶⡶⠶⠆⠄⠀⠀⣄⠀⠀⠸⠆⠸⠶⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡘ ⡟⠓⠛⠾⠓⠷⠂⠀⠀⠀⠆⠐⢲⠆⠳⠞⠆⠸⠚⠾⠖⠺⠲⠘⠾⠆⠾⠚⠚⠺⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡟⠧⠖⠲⠖⠖⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠧⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢃ ⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠃⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙ ⡆⠈⠓⠛⠛⠛⠓⡻⠛⠊⠉⠙⠛⠋⠚⠛⠉⠛⠛⠙⠚⠛⠛⠛⠙⠛⠓⠓⠛⠛⠙⠛⠓⠋⠛⠙⠛⠛⠛⠚⠛⠛⠚⠛⠛⠙⠙⢻⢳⠛⠞⠛⠛⠓⠚⠛⠛⠓⠛⠛⠛⠙⠛⠛⠓⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠛⠁⢠ ⡇⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⢀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⣶⢦⠀⠰ ⡇⠐⠓⠳⡖⠛⠉⡻⡓⡦⠀⠰⠃⣿⣇⠈⠂⣶⡴⡄⠘⠝⠚⠂⠶⠿⠮⠀⠷⠿⠗⣶⣶⠶⣶⢶⣦⣖⣢⢰⣢⢳⠛⠈⠻⠿⠷⣷⣶⣲⢶⣶⡶⢶⣶⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡇⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⡆⠰⠒⣦⣴⣷⡦⠾⡆⡏⠀⠈⠁⠀⠦⠀⠀⠈⠀⠀⠈⠁⠀⠀⠀⠉⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣀⠛⠛⢋⠙⡟⠛⠛⢛⣻⣿⡟⠛⠟⠉⠛⡉⢉⣉⡙⠉⡉⢿⠛⠛⣉⣋⡙⡁⣀⣈⣁⠀⠀⡀⠀⣀⠀⢀⣀⠀⠀⢀⡀⣀⠀⠀⡀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⠿⣯⢯⠭⣧⠤⡄⠀⠸⠷⢿⠇⠐⠄⢠⡶⠆⣽⣽⣽⡤⠀⡶⡒⣶⣖⡶⣖⣶⣶⢶⣶⢶⣶⢶⡢⢴⡦⢔⡶⢶⠒⡶⢶⣰⣶⠶⠶⣶⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣆⣖⣒⣶⡰⡶⡶⢄⠠⡦⣦⣦⡦⣦⡂⡮⡆⡀⠑⣰⡥⡲⣒⣲⣦⣄⡄⡉⠃⢑⡟⣆⠘⢿⣅⢸⠆⡆⠀⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢀⣀⣀⣐⣒⡀⡁⡀⡐⢈⣠⣄⠐⠀⠐⠀⣁⡀⢐⣠⡀⠀⢘⡈⢀⡠⠀⣠⠨⠡⠀⣄⣠⣤⣈⢠⠈⠅⠂⠀⠀⢄⣄⣠⡀⣤⠄⢄⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠄⠉⠍⡍⣁⠭⡠⡆⠀⠰⣶⣲⣒⠀⠆⠰⠾⠆⡸⠶⠲⠂⠰⣶⡶⣂⣰⣶⡖⡶⠖⡸⣦⣶⡧⠴⣶⡆⣲⣶⣶⣂⢖⠶⡦⢴⡶⢲⣶⣶⡶⣶⣶⣴⣖⡶⠶⢆⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠄⠆⠽⠔⠠⠒⠠⠄⠐⠂⠃⠘⠈⠠⠐⠉⠂⠀⠘⠶⠆⢶⠂⢞⢲⠠⠃⠸⠋⢹⣶⡆⢽⠟⠄⠹⠝⠒⠈⠀⠙⠂⠐⠃⠀⠂⠈⠀⠀⠓⠀⠈⠒⠁⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣄⣀⣀⡀⡀⠄⠄⠀⢠⣤⣤⡄⢀⠀⢠⠤⠄⣠⣤⣤⡀⠤⠤⠠⠀⠤⠤⠤⢤⠀⠠⠠⠤⠃⠤⠤⠤⠦⠄⠀⠀⠠⠄⠠⠤⠤⠤⠤⠄⠤⠄⡤⠤⠤⠤⠄⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠩⠍⢍⣤⡄⠇⡖⠀⠀⠩⠥⠁⠘⣡⡼⠷⡆⠨⠉⠥⠀⢰⢶⡤⠴⡦⢤⡄⢰⡆⠐⣶⣶⡶⢶⢦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠃⠰⠔⠄⠒⡴⠀⠀⠈⠷⠒⠄⠵⠖⠐⠆⠀⠠⠤⠖⡮⠛⠓⡣⠗⠓⠀⠀⠀⢶⡀⡒⠖⢓⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣠⣤⣤⣀⠀⡀⠤⠄⠀⢠⣤⣤⡄⢠⡄⢠⡤⠀⢠⣤⡀⠀⠢⠘⠐⠈⠐⠀⠉⠉⠀⢤⡤⠠⠌⠄⠨⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠶⡦⠰⠰⣦⡤⠄⠀⠬⢴⢦⡤⢤⠀⠀⡦⢠⢠⠰⢀⢰⣶⣶⡆⡖⣖⣶⡦⢰⣶⠶⣒⡶⢗⣶⣶⠖⡦⢴⡶⣶⡶⠶⢒⡶⣶⡆⠀⠀⠆⠄⢠⣦⡄⠤⠄⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠂⠷⠷⠷⠰⠷⠶⠖⠰⠲⠶⢶⠾⠦⠶⢶⡢⠄⠰⠶⠦⠦⠶⠦⢴⠆⠇⠽⠰⠐⠿⡟⠓⠶⠄⠦⠴⠀⠐⠂⠈⠙⠮⠁⠡⠄⠀⠞⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠲⠊⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠀⠀⠐⠀⠂⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠁⠀⠀⠀⠐⠀⠀⠀⠈⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⣤⢤⠀⢴⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠚⠛⠛⠛⠛⠛⠛⠛⠙⠛⠙⠛⠛⠛⠛⠛⠛⠛⠓⠛⠛⠛⠛⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣿⣷ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠸⢷⠾⠴⠶⠶⠦⠅⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠾⠶⠶⠾⠶⠤⠶⠄⠀⠐⠐⠀⠂⠒⠐⠒⠀⠂⠒⢤ ⡇⠯⠶⠧⠶⢶⡶⡤⠆⠸⠆⠷⠶⠶⠆⠸⠷⠶⠲⠶⠺⠆⠸⠶⠶⠶⠶⠾⠶⠶⠼⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⡀⠀⠀⠀⠸⠷⠇⠚⠿⠷⠸⠾⠆⠀⠀⠶⠄⠀⠀⠀⠀⠀⠀⢸ ⡇⠟⠿⠿⠧⠀⠀⠀⠀⠸⠷⠶⠲⠶⠶⠶⠶⠆⠸⠷⠶⠲⠰⠶⠶⠂⠸⠶⢶⡞⡾⠛⠹⠙⠶⠖⠐⠗⠶⠷⠱⠀⣷⡿⠿⠶⠶⠆⠧⠶⠗⠂⡆⠂⠄⠀⠀⠀⠘⠓⠂⠘⠛⠣⠒⠒⠔⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡿⠻⠶⠷⠷⠶⠖⠆⠀⠘⠷⠲⠲⠆⠸⠳⠾⠨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠶⠆⠇⠟⠤⠄⠀⠰⠦⠶⠔⠆⠸⠳⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡝⠷⠷⠖⠶⢶⡶⢶⡶⠶⠆⠄⠀⠀⣄⠀⠀⠸⠆⠸⠶⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡘ ⡟⠓⠛⠾⠓⠷⠂⠀⠀⠀⠆⠐⢲⠆⠳⠞⠆⠸⠚⠾⠖⠺⠲⠘⠾⠆⠾⠚⠚⠺⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡟⠧⠖⠲⠖⠖⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠧⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢃ ⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠃⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙ ⡆⠈⠑⠛⠛⠛⠓⡻⠛⠊⠉⠙⠛⠋⠚⠛⠉⠛⠛⠙⠚⠛⠛⠛⠙⠛⠓⠓⠛⠋⠙⠛⠓⠋⠛⠉⠛⠛⠛⠚⠛⠛⠚⠛⠛⠙⠙⢻⢳⠛⠞⠛⠛⠓⠚⠛⠛⠓⠛⠛⠛⠙⠛⠛⠓⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠛⠁⢠ ⡇⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⢀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⣶⢦⠀⠰ ⡇⠐⠓⠳⡖⠛⠉⡻⡓⡦⠀⠰⠃⣿⣇⠈⠂⣶⡴⡄⠘⠝⠚⠂⠶⠿⠮⠀⠷⠿⠗⣶⣶⠶⣶⢶⣦⣖⣢⢰⣢⢳⠛⠈⠻⠿⠷⣷⣶⣲⢶⣶⡶⢶⣶⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡇⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⡆⠰⠒⣦⣴⣷⡦⠾⡆⡏⠀⠈⠁⠀⠦⡀⠀⠈⠀⠀⠈⠁⠀⠀⠀⠉⠈⠉⠉⠀⠤⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣀⠛⠛⢋⠙⡟⠛⠛⢛⣻⣿⡟⠛⠟⠉⠛⡉⢉⣉⡙⠉⡉⢿⠛⠛⣉⣋⡙⡁⣀⣈⣁⠀⠀⡀⠀⣀⠀⢀⣄⠀⠀⢀⡀⣀⠀⠀⡀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⠿⣯⢯⠭⣧⠤⡄⠀⠸⠷⢿⠇⠐⠄⢠⡶⠆⣽⣽⣽⡤⠀⡶⡒⣶⣖⡶⣖⣶⣶⢶⣶⢶⣶⢶⡢⢴⡦⢔⡶⢶⠒⡶⢶⣰⣶⠶⠶⣶⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣆⣖⣒⣶⡰⡶⡶⢄⠠⡦⣦⣦⡦⣦⡂⡮⡆⡀⠑⣰⡥⡲⣒⣲⣦⣄⡄⡉⠃⢑⡟⣆⠘⢿⣅⢸⠆⡆⠀⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢀⣀⣀⣐⣒⡀⡁⡀⡐⢈⣠⣄⠐⠀⠐⠀⣁⡀⢐⣠⡀⠀⢘⡈⢀⡠⠀⢠⠨⠡⠀⣄⣠⣤⣈⢠⠈⠅⠂⠀⠀⢄⣄⣠⡀⣤⠄⢄⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠄⠉⠍⡍⣁⠭⡠⡆⠀⠰⣶⣲⣒⠀⠆⠰⠾⠆⡸⠶⠲⠂⠰⣶⡶⣂⣰⣶⡖⡶⠖⡸⣧⣶⡧⠴⣶⡆⣒⢶⣶⣂⢖⠶⡦⢴⡶⢲⣶⣶⡶⣶⣶⣴⣖⡶⠶⢆⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠄⠆⠽⠔⠠⠒⠠⠄⠐⠂⠃⠘⠈⠠⠐⠉⠂⠀⠘⠶⠆⢶⠂⢞⢲⠠⠃⠸⠋⢹⣶⡆⢽⠟⠄⠹⠝⠒⠈⠀⠙⠂⠐⠃⠀⠂⠈⠀⠀⠓⠀⠈⠒⠁⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣄⣀⣀⡀⡀⠄⠄⠀⢠⣤⣤⡄⢀⠀⢠⠤⠄⣠⣤⡤⠀⠤⠤⠠⠀⠤⠤⠤⢤⠀⠠⠠⠤⠳⠤⠴⠤⠦⠔⠀⠂⠠⠄⠠⠤⠤⠤⠤⠄⠤⠄⡤⠤⠤⠤⠄⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠩⠍⢍⣤⡄⠇⡖⠀⠀⠩⠥⠁⠘⣡⡼⠷⡆⠨⠉⠥⠀⢰⢶⡤⠴⡦⢤⡄⢰⡆⠐⣶⣶⡶⢶⢦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠃⠰⠔⠄⠒⡴⠀⠀⠈⠷⠒⠄⠵⠖⠐⠆⠀⠠⠤⠖⡮⠛⠓⡣⠗⠓⠀⠀⠀⢶⡀⡒⠖⢓⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣠⣤⣤⣀⠀⡀⠤⠄⠀⢠⣤⣤⡄⢠⡄⢠⡤⠀⢠⣤⡀⠀⠢⠘⠐⠈⠐⠀⠉⠉⠀⢤⡤⠠⠌⠄⠨⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠶⡦⢰⡰⣦⡤⠄⠀⠬⢴⢦⡤⢤⠀⠀⡦⢠⢠⠰⢀⢰⣶⣶⡆⡖⣖⣶⡦⢰⢶⠶⣒⡶⢗⣶⣶⠖⡦⢴⡶⣶⡶⠶⢒⡶⣶⡆⠀⠀⠆⠄⢠⣦⡄⠤⠄⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠂⠷⠷⠷⠰⠷⠶⠖⠰⠲⠶⢶⠾⠦⠶⢶⡢⠄⠰⠶⠦⠦⠶⠦⢴⠆⠇⠽⠰⠐⠿⡟⠓⠶⠄⠦⠴⠀⠐⠂⠈⠙⠮⠁⠡⠄⠀⠞⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠲⠊⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠀⠀⠐⠀⠂⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠘⠈⠀⠀⠂⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠁⠀⠀⠀⠐⠀⠀⠀⠘⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⣤⢤⠀⢴⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠚⠛⠛⠛⠛⠛⠛⠛⠙⠛⠙⠛⠛⠛⠛⠛⠛⠛⠓⠛⠛⠛⠛⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣿⣷ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠸⢷⠾⠴⠶⠶⠦⠄⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠾⠶⠶⠾⠶⠤⠶⠄⠀⠐⠐⠀⠂⠒⠐⠒⠀⠂⠒⢤ ⡇⠯⠶⠧⠶⢶⡶⡤⠆⠸⠆⠷⠶⠶⠆⠸⠷⠶⠲⠶⠺⠆⠸⠶⠶⠶⠶⠾⠶⠶⠼⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⡀⠀⠀⠀⠸⠷⠇⠚⠿⠷⠸⠾⠆⠀⠀⠶⠄⠀⠀⠀⠀⠀⠀⢸ ⡇⠟⠿⠿⠧⠀⠀⠀⠀⠸⠷⠶⠲⠶⠶⠶⠶⠆⠸⠷⠶⠲⠰⠶⠶⠂⠸⠶⢶⡞⡾⠛⠹⠙⠶⠖⠐⠗⠶⠷⠱⠀⣷⡿⠿⠶⠶⠆⠧⠶⠗⠂⡆⠂⠄⠀⠀⠀⠘⠓⠂⠘⠛⠣⠒⠒⠔⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡿⠻⠶⠷⠷⠶⠖⠆⠀⠘⠷⠲⠲⠆⠸⠳⠾⠨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠶⠆⠇⠟⠤⠄⠀⠰⠦⠶⠔⠆⠸⠳⠶⠶⠆⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡝⠷⠷⠖⠶⢶⡶⢶⡶⠶⠆⠄⠀⠀⣄⠀⠀⠸⠆⠸⠶⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡘ ⡟⠓⠛⠾⠓⠷⠂⠀⠀⠀⠆⠐⢲⠆⠳⠞⠆⠸⠚⠾⠖⠺⠲⠘⠾⠆⠾⠚⠚⠺⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡟⠧⠖⠲⠖⠖⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠧⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢃ ⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠃⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙ ⡆⠈⠑⠛⠛⠛⠓⡻⠛⠂⠉⠙⠛⠋⠚⠛⠉⠛⠛⠙⠚⠛⠛⠛⠙⠛⠓⠓⠛⠋⠙⠛⠓⠋⠛⠉⠛⠛⠛⠚⠛⠛⠚⠛⠛⠙⠙⢻⢳⠛⠞⠛⠛⠒⠚⠛⠛⠓⠛⠛⠛⠙⠛⠛⠓⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠛⠁⢠ ⡇⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⢀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⣶⢦⠀⠰ ⡇⠐⠓⠳⡖⠛⠉⡻⡓⡦⠀⠰⠃⣿⣇⠈⠂⣶⡴⡄⠘⠝⠚⠂⠶⠿⠮⠀⠷⠿⠗⣶⣶⠶⣶⢶⣦⣖⣢⢰⣢⢳⠛⠈⠻⠿⠷⣷⣶⣲⢶⣶⡶⢶⣶⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡇⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⡆⠰⠒⣦⣴⣷⡦⠾⡆⡏⠀⠈⠁⠀⢦⡀⠀⠈⠀⠀⠈⠁⠀⠀⠀⠉⢈⡉⠩⠤⠤⠀⠀⠀⠀⠀⢒⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣀⠛⠛⢋⠙⡟⠛⠛⢛⣻⣿⡟⠛⠟⠉⠛⡉⢉⣉⡙⠉⡉⢿⠛⠛⣉⣋⡙⡁⣀⣈⣁⠀⠀⡀⠀⣀⠀⢠⡀⠀⠀⢀⡀⣀⠀⠀⡀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⠿⣯⢿⠽⣷⠤⡄⠀⠸⠷⢿⠇⠐⠄⢠⡶⠆⣽⣽⣽⡤⠀⡶⡒⣶⣖⡶⣖⣶⣶⢶⣶⢶⣶⢶⡢⢴⡦⢔⡶⢶⠒⡶⢶⣰⣶⠶⠶⣶⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣆⣖⣒⣶⡰⡶⡶⢄⠠⡦⣦⣦⡦⣦⡂⡮⡆⡀⠑⣰⡥⡲⣒⣲⣦⣄⡄⡉⠃⢑⡟⣆⠘⢿⣅⢸⠆⡆⠀⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢀⣀⣀⣐⣒⡀⡁⡀⡐⢈⣠⣄⠐⠀⠐⠀⣁⡀⢐⣠⡀⠀⢘⡈⢀⡠⠀⢠⠨⠡⠀⣄⣠⣤⣈⢠⠈⠅⠂⠀⠀⣄⣄⣠⡀⣤⠄⢄⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠄⠉⠍⡍⣁⠭⡠⡆⠀⠰⣶⣲⣒⠀⠆⠰⠾⠆⡸⠶⠲⠂⠰⣶⡶⣂⣰⣶⡖⡶⠖⡸⣧⣶⡧⠴⣤⡆⣓⢴⣶⣂⢖⠶⡦⢴⡶⢲⣶⣶⡶⣶⣶⣴⣖⡶⠶⢆⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠄⠆⠽⠔⠠⠒⠠⠄⠐⠂⠃⠘⠈⠠⠐⠉⠂⠀⠘⠶⠆⢶⠂⢞⢲⠠⠃⠰⠋⢹⣶⡆⠽⠟⠄⠹⠝⠒⠈⠀⠙⠂⠐⠃⠀⠂⠈⠀⠀⠓⠀⠈⠒⠁⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣄⣀⣀⡀⡀⠄⠄⠀⢠⣤⣤⡄⢀⠀⢠⠤⠀⣠⣤⡤⠀⠥⠤⠠⠀⠤⠤⠤⢤⠀⠠⠠⠠⠷⠦⠴⠤⠦⠐⠀⠂⠠⠄⠠⠤⠤⠤⠤⠄⠤⠄⡤⠤⠤⠤⠄⠀⠀⠀⠈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠩⠍⢍⣤⡄⠇⡖⠀⠀⠩⠥⠁⠘⣡⡼⠶⡆⠨⠉⠥⠀⢰⢶⡤⠴⡦⢤⡄⢰⡆⠐⣶⣶⠷⢶⢦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠃⠰⠔⠄⠒⡴⠀⠀⠈⠷⠒⠄⠵⠖⠐⠆⠀⠠⠤⠖⡮⠛⠓⡣⠗⠓⠀⠀⠀⢶⡀⡒⠖⢓⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣠⣤⣤⣀⠀⡀⠤⠄⠀⢠⣤⣤⡄⢠⡄⢠⡤⠀⢠⣤⡀⠀⠢⠘⠐⠈⠐⠀⠉⠉⠀⢤⡤⠠⠌⠄⠨⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠶⡦⢰⡰⣦⡤⠄⠀⠬⢴⢦⡤⢤⠀⠀⡦⢠⢠⠰⢀⢰⣶⣶⡆⡖⣖⣶⡦⢰⢶⠶⣒⡶⢗⣶⣶⠖⡦⢴⡶⣶⡶⠶⢒⡶⣶⡆⠀⠀⠆⠄⢠⣦⡄⠤⠄⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠂⠷⠷⠷⠰⠷⠶⠖⠰⠲⠶⢶⠾⠦⠶⢶⡢⠄⠰⠶⠦⠦⠶⠦⢴⠆⠇⠽⠰⠐⠿⡟⠓⠶⠄⠦⠴⠀⠐⠂⠈⠙⠦⠁⠡⠄⠀⠞⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠲⠊⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠀⠀⠐⠀⠂⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠈⠀⠀⠚⠈⠀⠀⠊⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠋⠁⠀⠀⠀⠐⠀⠀⠀⠘⠀⠐⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⣤⢤⠀⢴⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠚⠛⠛⠛⠛⠛⠛⠛⠙⠛⠙⠛⠛⠛⠛⠛⠛⠛⠓⠛⠛⠛⠛⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣿⣷ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠸⢷⠾⠴⠶⠶⠦⠄⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠾⠶⠶⠾⠶⠤⠶⠄⠀⠐⠐⠀⠂⠒⠐⠒⠀⠂⠒⢤ ⡇⠯⠶⠧⠶⢶⡶⡤⠆⠸⠆⠷⠶⠶⠆⠸⠷⠶⠲⠶⠺⠆⠸⠶⠶⠶⠶⠾⠶⠶⠼⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⡀⠀⠀⠀⠸⠷⠇⠚⠿⠷⠸⠾⠆⠀⠀⠶⠄⠀⠀⠀⠀⠀⠀⢸ ⡇⠟⠿⠿⠧⠀⠀⠀⠀⠸⠷⠶⠲⠶⠶⠶⠶⠆⠸⠷⠶⠲⠰⠶⠶⠂⠸⠶⢶⡞⡾⠛⠹⠙⠶⠖⠐⠗⠶⠷⠱⠀⣷⡿⠿⠶⠶⠆⠧⠶⠗⠂⡆⠂⠄⠀⠀⠀⠘⠓⠂⠘⠛⠣⠒⠒⠔⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡿⠻⠶⠷⠷⠶⠖⠆⠀⠘⠷⠲⠲⠆⠸⠳⠾⠨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠶⠆⠇⠟⠤⠄⠀⠰⠦⠶⠔⠆⠸⠳⠶⠶⠆⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡝⠷⠷⠖⠶⢶⡶⢶⡶⠶⠆⠄⠀⠀⣄⠀⠀⠸⠆⠸⠶⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡘ ⡟⠓⠛⠾⠓⠷⠂⠀⠀⠀⠆⠐⢲⠆⠳⠞⠆⠸⠚⠾⠖⠺⠲⠘⠾⠆⠾⠚⠚⠺⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡟⠧⠖⠲⠖⠖⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠧⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢃ ⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠃⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙ ⡆⠈⠑⠛⠛⠛⠓⡻⠛⠂⠉⠙⠛⠋⠚⠛⠉⠛⠛⠙⠚⠛⠛⠛⠙⠛⠓⠓⠛⠋⠙⠛⠓⠋⠛⠉⠛⠛⠛⠚⠛⠛⠚⠛⠛⠙⠙⢻⢳⠛⠞⠛⠛⠒⠚⠛⠛⠓⠛⠛⠛⠙⠛⠛⠓⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠛⠁⢠ ⡇⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⢀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⣶⢦⠀⠰ ⡇⠐⠓⠳⡖⠛⠉⡻⡓⡦⠀⠰⠃⣿⣇⠈⠂⣶⡴⡄⠘⠝⠚⠂⠶⠿⠮⠀⠷⠿⠗⣶⣶⠶⣶⢶⣦⣖⣢⢰⣢⢳⠛⠈⠻⠿⠷⣷⣶⣲⢶⣶⡶⢶⣶⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡇⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⡆⠰⠒⣦⣴⣷⡦⠾⡆⡏⠀⠈⠁⠀⢦⡀⠀⠈⠀⠀⠈⠁⠀⠀⠀⠉⢈⡉⠩⠤⠤⠀⠀⠀⠀⠀⢒⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣀⠛⠛⢋⠙⡟⠛⠛⢛⣻⣿⡟⠛⠟⠉⠛⡉⢉⣉⡙⠉⡉⢿⠛⠛⣉⣋⡙⡁⣀⣈⣁⠀⠀⡀⠀⣀⠀⢠⡀⠀⠀⢀⡀⣀⠀⠀⡀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⠿⣯⢿⠽⣷⠤⡄⠀⠸⠷⢿⠇⠐⠄⢠⡶⠆⣽⣽⣽⡤⠀⡶⡒⣶⣖⡶⣖⣶⣶⢶⣶⢶⣶⢶⡢⢴⡦⢔⡶⢶⠒⡶⢶⣰⣶⠶⠶⣶⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣆⣖⣒⣶⡰⡶⡶⢄⠠⡦⣦⣦⡦⣦⡂⡮⡆⡀⠑⣰⡥⡲⣒⣲⣦⣄⡄⡉⠃⢑⡟⣆⠘⢿⣅⢸⠆⡆⠀⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢀⣀⣀⣐⣒⡀⡁⡀⡐⢈⣠⣄⠐⠀⠐⠀⣁⡀⢐⣠⡀⠀⢘⡈⢀⡠⠀⢠⠨⠡⠀⣄⣠⣤⣈⢠⠈⠅⠂⠀⠀⣄⣄⣠⡀⣤⠄⢄⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠄⠉⠍⡍⣁⠭⡠⡆⠀⠰⣶⣲⣒⠀⠆⠰⠾⠆⡸⠶⠲⠂⠰⣶⡶⣂⣰⣶⡖⡶⠖⡸⣧⣶⡧⠴⣤⡆⣓⢴⣶⣂⢖⠶⡦⢴⡶⢲⣶⣶⡶⣶⣶⣴⣖⡶⠶⢆⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠄⠆⠽⠔⠠⠒⠠⠄⠐⠂⠃⠘⠈⠠⠐⠉⠂⠀⠘⠶⠆⢶⠂⢞⢲⠠⠃⠰⠋⢹⣶⡆⠽⠟⠄⠹⠝⠒⠈⠀⠙⠂⠐⠃⠀⠂⠈⠀⠀⠓⠀⠈⠒⠁⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣄⣀⣀⡀⡀⠄⠄⠀⢠⣤⣤⡄⢀⠀⢠⠤⠀⣠⣤⡤⠀⠥⠤⠠⠀⠤⠤⠤⢤⠀⠠⠠⠠⠷⠦⠴⠤⠦⠐⠀⠂⠠⠄⠠⠤⠤⠤⠤⠄⠤⠄⡤⠤⠤⠤⠄⠀⠀⠀⠈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠩⠍⢍⣤⡄⠇⡖⠀⠀⠩⠥⠁⠘⣡⡼⠶⡆⠨⠉⠥⠀⢰⢶⡤⠴⡦⢤⡄⢰⡆⠐⣶⣶⠷⢶⢦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠃⠰⠔⠄⠒⡴⠀⠀⠈⠷⠒⠄⠵⠖⠐⠆⠀⠠⠤⠖⡮⠛⠓⡣⠗⠓⠀⠀⠀⢶⡀⡒⠖⢓⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣠⣤⣤⣀⠀⡀⠤⠄⠀⢠⣤⣤⡄⢠⡄⢠⡤⠀⢠⣤⡀⠀⠢⠘⠐⠈⠐⠀⠉⠉⠀⢤⡤⠠⠌⠄⠨⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠶⡦⢰⡰⣦⡤⠄⠀⠬⢴⢦⡤⢤⠀⠀⡦⢠⢠⠰⢀⢰⣶⣶⡆⡖⣖⣶⡦⢰⢶⠶⣒⡶⢗⣶⣶⠖⡦⢴⡶⣶⡶⠶⢒⡶⣶⡆⠀⠀⠆⠄⢠⣦⡄⠤⠄⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠂⠷⠷⠷⠰⠷⠶⠖⠰⠲⠶⢶⠾⠦⠶⢶⡢⠄⠰⠶⠦⠦⠶⠦⢴⠆⠇⠽⠰⠐⠿⡟⠓⠶⠄⠦⠴⠀⠐⠂⠈⠙⠦⠁⠡⠄⠀⠞⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠲⠊⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠀⠀⠐⠀⠂⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠈⠀⠀⠚⠈⠀⠀⠊⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠋⠁⠀⠀⠀⠐⠀⠀⠀⠘⠀⠐⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⣤⢤⠀⢴⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠚⠛⠛⠛⠛⠛⠛⠛⠙⠛⠙⠛⠛⠛⠛⠛⠛⠛⠓⠛⠛⠛⠛⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣿⣷ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠸⢷⠾⠴⠶⠶⠦⠄⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠾⠶⠶⠾⠶⠤⠶⠄⠀⠐⠐⠀⠂⠒⠐⠒⠀⠂⠒⢤ ⡇⠯⠶⠧⠶⢶⡶⡤⠆⠸⠆⠷⠶⠶⠆⠸⠷⠶⠲⠶⠺⠆⠸⠶⠶⠶⠶⠾⠶⠶⠼⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⡀⠀⠀⠀⠸⠷⠇⠚⠿⠷⠸⠾⠆⠀⠀⠶⠄⠀⠀⠀⠀⠀⠀⢸ ⡇⠟⠿⠿⠧⠀⠀⠀⠀⠸⠷⠶⠲⠶⠶⠶⠶⠆⠸⠷⠶⠲⠰⠶⠶⠂⠸⠶⢶⡞⡾⠛⠹⠙⠶⠖⠐⠗⠶⠷⠱⠀⣷⡿⠿⠶⠶⠆⠧⠶⠗⠂⡆⠂⠄⠀⠀⠀⠘⠓⠂⠘⠛⠣⠒⠒⠔⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡿⠻⠶⠷⠷⠶⠖⠆⠀⠘⠷⠲⠲⠆⠸⠳⠾⠨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠶⠆⠇⠟⠤⠄⠀⠰⠦⠶⠔⠆⠸⠳⠶⠶⠆⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡝⠷⠷⠖⠶⢶⡶⢶⡶⠶⠆⠄⠀⠀⣄⠀⠀⠸⠆⠸⠶⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡘ ⡟⠓⠛⠾⠓⠷⠂⠀⠀⠀⠆⠐⢲⠆⠳⠞⠆⠸⠚⠾⠖⠺⠲⠘⠾⠆⠾⠚⠚⠺⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡟⠧⠖⠲⠖⠖⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠧⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢃ ⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠃⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙ ⡆⠈⠑⠛⠛⠛⠓⡻⠛⠂⠉⠙⠛⠋⠚⠛⠉⠛⠛⠙⠚⠛⠛⠛⠙⠛⠓⠓⠛⠋⠙⠛⠓⠋⠛⠉⠛⠛⠛⠚⠛⠛⠚⠛⠛⠙⠙⢻⢳⠛⠞⠛⠛⠒⠚⠛⠛⠓⠛⠛⠛⠙⠛⠛⠓⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠛⠁⢠ ⡇⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⢀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⣶⢦⠀⠰ ⡇⠐⠓⠳⡖⠛⠉⡻⡓⡦⠀⠰⠃⣿⣇⠈⠂⣶⡴⡄⠘⠝⠚⠂⠶⠿⠮⠀⠷⠿⠗⣶⣶⠶⣶⢶⣦⣖⣢⢰⣢⢳⠛⠈⠻⠿⠷⣷⣶⣲⢶⣶⡶⢶⣶⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡇⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⡆⠰⠒⣦⣴⣷⡦⠾⡆⡏⠀⠈⠁⠀⢦⡀⠀⠈⠀⠀⠈⠁⠀⠀⠀⠉⢈⡉⠩⠤⠤⠀⠀⠀⠀⠀⢒⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣀⠛⠛⢋⠙⡟⠛⠛⢛⣻⣿⡟⠛⠟⠉⠛⡉⢉⣉⡙⠉⡉⢿⠛⠛⣉⣋⡙⡁⣀⣈⣁⠀⠀⡀⠀⣀⠀⢠⡀⠀⠀⢀⡀⣀⠀⠀⡀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⠿⣯⢿⠽⣷⠤⡄⠀⠸⠷⢿⠇⠐⠄⢠⡶⠆⣽⣽⣽⡤⠀⡶⡒⣶⣖⡶⣖⣶⣶⢶⣶⢶⣶⢶⡢⢴⡦⢔⡶⢶⠒⡶⢶⣰⣶⠶⠶⣶⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣆⣖⣒⣶⡰⡶⡶⢄⠠⡦⣦⣦⡦⣦⡂⡮⡆⡀⠑⣰⡥⡲⣒⣲⣦⣄⡄⡉⠃⢑⡟⣆⠘⢿⣅⢸⠆⡆⠀⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢀⣀⣀⣐⣒⡀⡁⡀⡐⢈⣠⣄⠐⠀⠐⠀⣁⡀⢐⣠⡀⠀⢘⡈⢀⡠⠀⢠⠨⠡⠀⣄⣠⣤⣈⢠⠈⠅⠂⠀⠀⣄⣄⣠⡀⣤⠄⢄⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠄⠉⠍⡍⣁⠭⡠⡆⠀⠰⣶⣲⣒⠀⠆⠰⠾⠆⡸⠶⠲⠂⠰⣶⡶⣂⣰⣶⡖⡶⠖⡸⣧⣶⡧⠴⣤⡆⣓⢴⣶⣂⢖⠶⡦⢴⡶⢲⣶⣶⡶⣶⣶⣴⣖⡶⠶⢆⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠄⠆⠽⠔⠠⠒⠠⠄⠐⠂⠃⠘⠈⠠⠐⠉⠂⠀⠘⠶⠆⢶⠂⢞⢲⠠⠃⠰⠋⢹⣶⡆⠽⠟⠄⠹⠝⠒⠈⠀⠙⠂⠐⠃⠀⠂⠈⠀⠀⠓⠀⠈⠒⠁⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣄⣀⣀⡀⡀⠄⠄⠀⢠⣤⣤⡄⢀⠀⢠⠤⠀⣠⣤⡤⠀⠥⠤⠠⠀⠤⠤⠤⢤⠀⠠⠠⠠⠷⠦⠴⠤⠦⠐⠀⠂⠠⠄⠠⠤⠤⠤⠤⠄⠤⠄⡤⠤⠤⠤⠄⠀⠀⠀⠈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠩⠍⢍⣤⡄⠇⡖⠀⠀⠩⠥⠁⠘⣡⡼⠶⡆⠨⠉⠥⠀⢰⢶⡤⠴⡦⢤⡄⢰⡆⠐⣶⣶⠷⢶⢦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠃⠰⠔⠄⠒⡴⠀⠀⠈⠷⠒⠄⠵⠖⠐⠆⠀⠠⠤⠖⡮⠛⠓⡣⠗⠓⠀⠀⠀⢶⡀⡒⠖⢓⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣠⣤⣤⣀⠀⡀⠤⠄⠀⢠⣤⣤⡄⢠⡄⢠⡤⠀⢠⣤⡀⠀⠢⠘⠐⠈⠐⠀⠉⠉⠀⢤⡤⠠⠌⠄⠨⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠶⡦⢰⡰⣦⡤⠄⠀⠬⢴⢦⡤⢤⠀⠀⡦⢠⢠⠰⢀⢰⣶⣶⡆⡖⣖⣶⡦⢰⢶⠶⣒⡶⢗⣶⣶⠖⡦⢴⡶⣶⡶⠶⢒⡶⣶⡆⠀⠀⠆⠄⢠⣦⡄⠤⠄⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠂⠷⠷⠷⠰⠷⠶⠖⠰⠲⠶⢶⠾⠦⠶⢶⡢⠄⠰⠶⠦⠦⠶⠦⢴⠆⠇⠽⠰⠐⠿⡟⠓⠶⠄⠦⠴⠀⠐⠂⠈⠙⠦⠁⠡⠄⠀⠞⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠲⠊⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠀⠀⠐⠀⠂⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠈⠀⠀⠚⠈⠀⠀⠊⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠋⠁⠀⠀⠀⠐⠀⠀⠀⠘⠀⠐⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⣤⢤⠀⢴⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠚⠛⠛⠛⠛⠛⠛⠛⠙⠛⠙⠛⠛⠛⠛⠛⠛⠛⠓⠛⠛⠛⠛⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣿⣷ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠸⢷⠾⠴⠶⠶⠦⠄⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠾⠶⠶⠾⠶⠤⠶⠄⠀⠐⠐⠀⠂⠒⠐⠒⠀⠂⠒⢤ ⡇⠯⠶⠧⠶⢶⡶⡤⠆⠸⠆⠷⠶⠶⠆⠸⠷⠶⠲⠶⠺⠆⠸⠶⠶⠶⠶⠾⠶⠶⠼⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⡀⠀⠀⠀⠸⠷⠇⠚⠿⠷⠸⠾⠆⠀⠀⠶⠄⠀⠀⠀⠀⠀⠀⢸ ⡇⠟⠿⠿⠧⠀⠀⠀⠀⠸⠷⠶⠲⠶⠶⠶⠶⠆⠸⠷⠶⠲⠰⠶⠶⠂⠸⠶⢶⡞⡾⠛⠹⠙⠶⠖⠐⠗⠶⠷⠱⠀⣷⡿⠿⠶⠶⠆⠧⠶⠗⠂⡆⠂⠄⠀⠀⠀⠘⠓⠂⠘⠛⠣⠒⠒⠔⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡿⠻⠶⠷⠷⠶⠖⠆⠀⠘⠷⠲⠲⠆⠸⠳⠾⠨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠶⠆⠇⠟⠤⠄⠀⠰⠦⠶⠔⠆⠸⠳⠶⠶⠆⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡝⠷⠷⠖⠶⢶⡶⢶⡶⠶⠆⠄⠀⠀⣄⠀⠀⠸⠆⠸⠶⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡘ ⡟⠓⠛⠾⠓⠷⠂⠀⠀⠀⠆⠐⢲⠆⠳⠞⠆⠸⠚⠾⠖⠺⠲⠘⠾⠆⠾⠚⠚⠺⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡟⠧⠖⠲⠖⠖⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠧⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢃ ⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠃⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙ ⡆⠈⠑⠛⠛⠛⠓⡻⠛⠂⠉⠙⠛⠋⠚⠛⠉⠛⠛⠙⠚⠛⠛⠛⠙⠛⠓⠓⠛⠋⠙⠛⠓⠋⠛⠉⠛⠛⠛⠚⠛⠛⠚⠛⠛⠙⠙⢻⢳⠛⠞⠛⠛⠒⠚⠛⠛⠓⠛⠛⠛⠙⠛⠛⠓⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠛⠁⢠ ⡇⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⢀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⣶⢦⠀⠰ ⡇⠐⠓⠳⡖⠛⠉⡻⡓⡦⠀⠰⠃⣿⣇⠈⠂⣶⡴⡄⠘⠝⠚⠂⠶⠿⠮⠀⠷⠿⠗⣶⣶⠶⣶⢶⣦⣖⣢⢰⣢⢳⠛⠈⠻⠿⠷⣷⣶⣲⢶⣶⡶⢶⣶⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡇⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⡆⠰⠒⣦⣴⣷⡦⠾⡆⡏⠀⠈⠁⠀⢦⡀⠀⠈⠀⠀⠈⠁⠀⠀⠀⠉⢈⡉⠩⠤⠤⠀⠀⠀⠀⠀⢒⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣀⠛⠛⢋⠙⡟⠛⠛⢛⣻⣿⡟⠛⠟⠉⠛⡉⢉⣉⡙⠉⡉⢿⠛⠛⣉⣋⡙⡁⣀⣈⣁⠀⠀⡀⠀⣀⠀⢠⡀⠀⠀⢀⡀⣀⠀⠀⡀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠉⠿⣯⢿⠽⣷⠤⡄⠀⠸⠷⢿⠇⠐⠄⢠⡶⠆⣽⣽⣽⡤⠀⡶⡒⣶⣖⡶⣖⣶⣶⢶⣶⢶⣶⢶⡢⢴⡦⢔⡶⢶⠒⡶⢶⣰⣶⠶⠶⣶⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣆⣖⣒⣶⡰⡶⡶⢄⠠⡦⣦⣦⡦⣦⡂⡮⡆⡀⠑⣰⡥⡲⣒⣲⣦⣄⡄⡉⠃⢑⡟⣆⠘⢿⣅⢸⠆⡆⠀⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢀⣀⣀⣐⣒⡀⡁⡀⡐⢈⣠⣄⠐⠀⠐⠀⣁⡀⢐⣠⡀⠀⢘⡈⢀⡠⠀⢠⠨⠡⠀⣄⣠⣤⣈⢠⠈⠅⠂⠀⠀⣄⣄⣠⡀⣤⠄⢄⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠄⠉⠍⡍⣁⠭⡠⡆⠀⠰⣶⣲⣒⠀⠆⠰⠾⠆⡸⠶⠲⠂⠰⣶⡶⣂⣰⣶⡖⡶⠖⡸⣧⣶⡧⠴⣤⡆⣓⢴⣶⣂⢖⠶⡦⢴⡶⢲⣶⣶⡶⣶⣶⣴⣖⡶⠶⢆⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠄⠆⠽⠔⠠⠒⠠⠄⠐⠂⠃⠘⠈⠠⠐⠉⠂⠀⠘⠶⠆⢶⠂⢞⢲⠠⠃⠰⠋⢹⣶⡆⠽⠟⠄⠹⠝⠒⠈⠀⠙⠂⠐⠃⠀⠂⠈⠀⠀⠓⠀⠈⠒⠁⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣄⣀⣀⡀⡀⠄⠄⠀⢠⣤⣤⡄⢀⠀⢠⠤⠀⣠⣤⡤⠀⠥⠤⠠⠀⠤⠤⠤⢤⠀⠠⠠⠠⠷⠦⠴⠤⠦⠐⠀⠂⠠⠄⠠⠤⠤⠤⠤⠄⠤⠄⡤⠤⠤⠤⠄⠀⠀⠀⠈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠩⠍⢍⣤⡄⠇⡖⠀⠀⠩⠥⠁⠘⣡⡼⠶⡆⠨⠉⠥⠀⢰⢶⡤⠴⡦⢤⡄⢰⡆⠐⣶⣶⠷⢶⢦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠁⠃⠰⠔⠄⠒⡴⠀⠀⠈⠷⠒⠄⠵⠖⠐⠆⠀⠠⠤⠖⡮⠛⠓⡣⠗⠓⠀⠀⠀⢶⡀⡒⠖⢓⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣠⣤⣤⣀⠀⡀⠤⠄⠀⢠⣤⣤⡄⢠⡄⢠⡤⠀⢠⣤⡀⠀⠢⠘⠐⠈⠐⠀⠉⠉⠀⢤⡤⠠⠌⠄⠨⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠶⡦⢰⡰⣦⡤⠄⠀⠬⢴⢦⡤⢤⠀⠀⡦⢠⢠⠰⢀⢰⣶⣶⡆⡖⣖⣶⡦⢰⢶⠶⣒⡶⢗⣶⣶⠖⡦⢴⡶⣶⡶⠶⢒⡶⣶⡆⠀⠀⠆⠄⢠⣦⡄⠤⠄⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠂⠷⠷⠷⠰⠷⠶⠖⠰⠲⠶⢶⠾⠦⠶⢶⡢⠄⠰⠶⠦⠦⠶⠦⢴⠆⠇⠽⠰⠐⠿⡟⠓⠶⠄⠦⠴⠀⠐⠂⠈⠙⠦⠁⠡⠄⠀⠞⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠲⠊⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠀⠀⠐⠀⠂⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠈⠀⠀⠚⠈⠀⠀⠊⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠋⠁⠀⠀⠀⠐⠀⠀⠀⠘⠀⠐⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⣤⢤⠀⢴⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠚⠛⠛⠛⠛⠛⠛⠛⠙⠛⠙⠛⠛⠛⠛⠛⠛⠛⠓⠛⠛⠛⠛⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣿⣷ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠸⢷⠾⠴⠶⠶⠦⠅⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠾⠶⠶⠾⠶⠴⠶⠄⠀⠐⠐⠒⠂⠒⠐⠐⠀⠂⠀⢬ ⡇⠯⠶⠧⠶⢶⣶⡤⠆⠸⠆⠷⠶⠶⠆⠸⠷⠶⠲⠶⠺⠆⠸⠶⠶⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⡀⠀⠀⠀⠸⠷⠗⢚⠿⠆⠐⠶⠆⠀⠀⠶⠄⠀⠀⠀⠀⠀⠀⢸ ⡇⠟⠿⠿⠧⠂⠀⠀⠀⠰⠶⠶⠢⠶⠶⠶⠶⠆⠸⠷⠶⠲⠰⠶⠶⠂⠰⠶⠶⠾⡺⠓⠲⠶⠶⠖⠐⠗⠶⠷⠰⠀⣷⡿⠿⠶⠶⠆⠧⠖⠗⠂⡆⠂⠄⠀⠀⠀⠘⠓⠃⠘⠓⠣⠒⠒⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡷⠻⠖⠷⠷⠶⠆⠆⠀⠰⠷⠶⠲⠆⢸⠢⠴⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠶⠖⠇⠖⡦⠀⠀⠰⠢⠶⡴⠆⠰⠲⠶⠶⠄⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡟⠒⠶⠖⠶⢶⡶⢶⡶⠶⠆⠆⠀⠀⣄⠀⠀⠰⠆⠰⠦⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡘ ⡟⠗⠓⠾⠲⠧⠆⠀⠀⠀⠆⠐⢲⡆⠶⠖⠆⠰⠐⠾⠖⠺⠴⠐⢾⠆⠾⠚⠚⠺⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣏⡧⠆⠲⠖⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢃ ⠑⠰⠶⠒⠖⠲⠀⠤⠠⠄⠠⠀⠤⠠⠄⠠⠀⠤⠠⠄⠠⠀⠄⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠆⠇⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠽ ⡆⠈⠓⠛⠛⠛⠓⡻⠛⠊⠉⠙⠛⠋⠛⠛⠉⠛⠛⠙⠚⠛⠛⠛⠙⠛⠓⠓⠛⠛⠙⠛⠓⠋⠛⠙⠛⠛⠛⠚⠛⠛⠚⠛⠛⠙⠙⢻⢳⠛⠞⠛⠛⠛⠚⠛⠛⠓⠛⠛⠛⠙⠛⠛⠓⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠛⠁⢠ ⡇⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠶⠶⠀⠲⢰ ⡇⠀⠤⡷⠖⠳⠔⡻⡿⡆⠀⠰⠶⡷⠆⠰⠴⢶⠶⠆⠺⠿⠖⠂⠶⠿⢾⠀⠷⠷⢾⠶⠶⠶⠶⠶⠼⠶⠀⡗⠔⠷⠟⠨⠿⠾⠶⠾⡷⠶⠷⡗⠿⠼⢤⠷⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠶⠶⠀⠾⠿⠔⠶⠰⡆⠀⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠤⠤⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣀⠛⠛⢂⠙⡟⠚⠛⢛⣻⣿⡟⠛⠟⠉⠛⡉⢉⣉⡙⠉⡉⢿⠛⠛⣉⣂⡘⡀⣀⣀⣀⠀⠀⡀⠀⣀⠀⢠⡀⠀⠀⢀⡀⣀⠀⠀⡀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠁⠷⡶⠴⠤⠦⠶⠂⠀⠰⠶⡶⠆⠐⠆⠸⡾⠆⠲⣾⠽⠄⠰⠦⠼⠿⠶⠾⠾⠶⠶⠶⠶⠿⠶⠴⠀⠶⠔⠿⠶⠗⠿⠾⢷⡿⠟⠗⠦⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠆⠖⠶⠷⠰⠶⠖⠆⠰⠶⠶⢶⠶⠶⠶⠶⠢⠀⠸⠶⠾⠾⠾⠺⠾⠶⠀⠰⠀⠴⠶⠀⠲⠶⠔⠶⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢀⣀⣀⡐⠒⠀⡁⡀⠐⢈⣠⣄⠐⠀⠐⠀⣁⡀⢐⢤⡀⠀⢐⠀⠀⠠⠀⠠⠠⠠⠀⠄⠠⡤⠀⠠⠀⠄⠂⠀⠀⠄⠄⠠⠄⠤⠄⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠔⠉⠍⠥⠄⠴⠴⠆⠀⠰⠶⠿⠇⠠⠆⠰⠶⠆⠶⠶⠲⠀⠶⠾⠾⢀⠶⠷⠶⠶⠀⠶⠼⠷⠰⠶⠶⠦⠷⠲⠶⠴⠶⠷⠰⠶⠴⠶⠷⠷⠶⠶⠶⠆⠖⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠅⠷⠵⠕⠤⠲⠳⠆⠐⠖⡆⠾⠆⠰⠐⠀⠀⠀⠸⠶⠶⢾⠲⢞⠿⠺⠂⠸⠃⠼⠽⠀⠿⠿⠔⠦⠾⠐⠀⠀⠐⠂⠐⠂⠀⠂⠀⠀⠀⠒⠀⠀⠒⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣄⣀⣀⡀⠀⠄⠄⠀⢠⣤⣤⡄⢀⠀⢠⠤⠀⣠⡤⠤⠀⠤⠤⠠⠀⠤⠤⠤⠤⠀⠠⠠⠠⠶⠦⠴⠤⠦⠐⠀⠂⠠⠄⠠⠤⠤⠤⠤⠄⠤⠄⠤⠤⠤⠤⠄⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠩⠍⠝⠤⡤⠷⠇⠀⠀⠩⠴⠇⠰⠆⠰⠿⠆⠸⠴⠤⠀⠶⠿⠾⠀⠶⠿⠾⠾⠀⠾⠼⠿⠀⠶⠶⠧⠷⠶⠷⠴⠾⠷⠰⠶⠵⠶⠿⠷⠿⠷⠶⠦⠟⠷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠆⠗⠳⠔⠠⠷⠷⠀⠠⠒⠶⢂⠔⠶⠖⠐⢢⠀⠰⠤⠶⠮⠿⠟⠾⠞⠀⠨⠀⠽⠼⠀⠻⠿⠔⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣠⣤⣤⣀⠀⡀⠤⠄⠀⢠⣤⣤⡄⢠⠄⢠⠤⠀⢠⣤⡀⠀⠢⠘⠐⠀⠐⠀⠀⠀⠀⠤⡤⠠⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠩⠶⡦⠐⠰⠷⠇⠀⠈⠌⢼⢦⠴⠄⠸⠿⠆⠨⠡⠲⠂⠾⠶⠶⠲⠶⠶⠀⠶⠀⠺⠿⠷⠾⠟⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠇⠷⠶⠷⠰⠷⠷⠆⠰⠴⠶⢶⠶⠶⠲⠶⠦⠀⠰⠶⠾⠮⠿⠷⠾⠞⠂⠾⠀⠼⠼⠀⠾⠶⠔⠶⠶⠀⠐⠂⠀⠐⠦⠀⠠⠄⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠲⠊⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠂⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠈⠀⠀⠛⠈⠀⠀⠊⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠋⠁⠀⠀⠀⠐⠀⠀⠀⠘⠀⠐⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⣤⢤⠀⠄⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠿⠶⠶⠶⠀⠼⢠ ⠣⠚⠛⠛⠛⠛⠛⠛⠛⠙⠛⠙⠛⠛⠛⠛⠛⠛⠛⠓⠛⠛⠛⠛⠛⠂⠒⠒⠒⠂⠒⠒⠐⠂⠂⠒⠒⠐⠂⠒⠒⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣶⣾ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠸⢷⠾⠴⠶⠶⠦⠅⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠾⠶⠶⠾⠶⠴⠶⠄⠀⠐⠐⠒⠂⠒⠐⠐⠀⠂⠀⢬ ⡇⠯⠶⠧⠶⢶⣶⡤⠆⠸⠆⠷⠶⠶⠆⠸⠷⠶⠲⠶⠺⠆⠸⠶⠶⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⡀⠀⠀⠀⠸⠷⠗⢚⠿⠆⠐⠶⠖⠂⠀⠶⠄⠀⠀⠀⠀⠀⠀⢸ ⡇⠟⠿⠿⠧⠂⠀⠀⠀⠰⠶⠶⠢⠶⠶⠶⠶⠆⠸⠷⠶⠲⠰⠶⠶⠂⠰⠶⠶⠾⡺⠓⠲⠶⠶⠖⠐⠗⠶⠷⠰⠀⣷⡿⠿⠶⠶⠆⠧⠖⠗⠂⡆⠂⠄⠀⠀⠀⠘⠓⠃⠘⠓⠣⠒⠒⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡷⠻⠖⠷⠷⠶⠖⠆⠀⠰⠷⠶⠲⠆⢸⠢⠴⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠶⠖⠇⠖⡦⠀⠀⠰⠢⠶⡴⠆⠰⠲⠶⠶⠄⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡟⠒⠶⠖⠶⢶⡶⢶⡶⠶⠆⠆⠀⠀⣄⠀⠀⠰⠆⠰⠦⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡘ ⡟⠗⠓⠾⠲⠧⠆⠀⠀⠀⠆⠐⢲⡆⠶⠖⠆⠰⠐⠾⠖⠺⠴⠐⢾⠆⠾⠚⠚⠺⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣏⡧⠆⠲⠖⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢃ ⠑⠰⠶⠒⠖⠲⠀⠤⠠⠄⠠⠀⠤⠠⠄⠠⠀⠤⠠⠄⠠⠀⠄⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠆⠇⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠽ ⡆⠈⠓⠛⠛⠛⠓⡻⠛⠊⠉⠙⠛⠋⠛⠛⠉⠛⠛⠙⠚⠛⠛⠛⠙⠛⠓⠓⠛⠛⠙⠛⠓⠋⠛⠙⠛⠛⠛⠚⠛⠛⠚⠛⠛⠙⠙⢻⢳⠛⠞⠛⠛⠛⠚⠛⠛⠓⠛⠛⠛⠙⠛⠛⠓⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠛⠁⠠ ⡇⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀ ⡇⠀⠤⡷⠖⠳⠔⠳⠶⠦⠀⠰⠶⠷⠆⠰⠄⠀⠗⠷⠺⠿⠖⠂⠶⠿⠾⠀⠷⠷⠖⠟⠷⠶⠿⠷⠰⠷⠿⠿⠧⠶⠞⠨⠿⠾⠶⠾⠿⠯⠧⠿⠿⠾⠷⠷⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡇⠀⠀⠀⠇⠷⠷⠷⠐⠷⠷⠶⠠⠶⠶⢶⡶⠷⠖⠶⠖⠄⠠⠿⠿⠿⠿⠿⠿⠷⠇⠀⠇⠰⠷⠷⠸⠿⠷⠖⠆⠇⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠤⠤⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣀⠒⠒⢂⠐⡖⠒⠒⢒⣲⣶⡖⠒⠖⠀⠒⡀⢀⣀⡐⠀⠀⢶⠒⠒⣀⡂⠘⠀⣀⡀⠀⠀⠀⡀⠀⣀⠀⢠⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠁⢷⡶⠴⠤⠦⠦⡷⠀⠰⠶⠶⠆⠐⠂⡷⡷⠇⠲⢾⠽⠅⠰⡿⡷⡧⠰⡿⠷⠷⠷⠷⠷⠷⠷⠿⠧⠠⠧⠲⠾⠷⠸⠿⠿⠿⠾⠿⠿⠷⠿⠿⠿⠯⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠰⠷⠷⠰⠿⠷⠖⠆⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢀⣀⣀⡐⠒⠀⡀⡀⠐⠀⠠⠄⠐⠀⠐⠀⣀⡀⢐⢤⡀⠀⠐⠀⠀⠠⠀⠠⠠⠠⠀⠄⠠⠤⠀⠠⠀⠄⠂⠀⠀⠄⠄⠠⠄⠤⠄⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠔⠉⠍⠥⠄⠴⠴⠆⠀⠰⠶⠿⠶⠀⠄⠠⠷⠆⠶⠶⠲⠀⠀⠷⠯⠿⠿⠷⠷⠷⠷⠷⠾⠿⠶⠿⠗⠲⠷⠖⠿⠾⠗⠿⠾⠶⡿⠟⠗⠷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠅⠷⠵⠕⠤⠲⠷⠆⠐⠶⡆⠾⠆⠐⠒⠃⠀⠀⠸⠶⠶⢿⠻⢞⠿⠾⠂⠸⠃⠤⠷⠃⠾⠿⠴⠦⠾⠐⠀⠀⠐⠂⠐⠂⠀⠂⠀⠀⠀⠒⠀⠀⠒⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣄⣀⣀⡀⠀⠄⠄⠀⢠⣤⣤⡄⢀⠀⢠⠤⠀⣠⡤⠤⠀⠤⠤⠠⠀⠤⠤⠤⠤⠀⠠⠠⠠⠶⠦⠴⠤⠦⠐⠀⠂⠠⠄⠠⠤⠤⠤⠤⠄⠤⠄⠤⠤⠤⠤⠄⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠩⠍⠝⠤⡤⠷⠇⠀⠀⠩⠴⠇⠰⠆⠰⠿⠆⠸⠴⠤⠀⠶⠿⠾⠀⠶⠿⠾⠾⠀⠾⠾⠿⠀⠶⠶⠧⠷⠶⠷⠖⠾⠷⠰⠶⠵⠶⠿⠷⠿⠷⠶⠦⠗⠿⠇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠆⠗⠳⠔⠠⠷⠷⠀⠠⠒⠶⢂⠔⠶⠖⠒⢢⠄⠰⠤⠶⠮⠿⠟⠾⠟⠀⠨⠀⠽⠼⠀⠻⠿⠔⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣠⣤⣤⣀⠀⡀⠤⠄⠀⢠⣤⣤⡄⢠⠄⢠⠤⠀⢠⣤⡀⠀⠢⠘⠐⠀⠐⠀⠀⠀⠀⠤⡤⠠⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠩⠶⡦⠐⠰⠷⠇⠀⠈⠌⢼⢦⠴⠄⠸⠿⠆⠨⠡⠲⠂⠾⠶⠶⠲⠶⠶⠀⠶⠀⠺⠿⠷⠾⠟⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠇⠶⠶⠷⠰⠷⠷⠆⠰⠴⠶⢶⠶⠶⠲⠶⠦⠀⠰⠶⠾⠮⠿⠷⠾⠞⠂⠾⠀⠼⠼⠄⠾⠶⠔⠶⠶⠀⠐⠂⠀⠐⠦⠀⠠⠄⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠲⠊⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠂⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠈⠀⠀⠛⠈⠀⠀⠊⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠋⠁⠀⠀⠀⠐⠀⠀⠀⠘⠀⠐⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⣤⢤⠀⠄⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠿⠶⠶⠶⠀⠼⢠ ⠣⠚⠛⠛⠛⠛⠛⠛⠛⠙⠛⠙⠛⠛⠛⠛⠛⠛⠛⠓⠛⠛⠛⠛⠛⠂⠒⠒⠒⠂⠒⠒⠐⠂⠂⠒⠒⠐⠂⠒⠒⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣶⣾ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠸⢷⠾⠴⠶⠶⠦⠅⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠾⠶⠶⠾⠶⠴⠶⠄⠀⠐⠐⠒⠂⠒⠐⠐⠀⠂⠀⢬ ⡇⠯⠶⠧⠶⢶⣶⡤⠆⠸⠆⠷⠶⠶⠆⠸⠷⠶⠲⠶⠺⠆⠸⠶⠶⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⡀⠀⠀⠀⠸⠷⠗⢚⠿⠆⠐⠶⠖⠆⠀⠶⠄⠀⠀⠀⠀⠀⠀⢸ ⡇⠟⠿⠿⠧⠂⠀⠀⠀⠰⠶⠶⠢⠶⠶⠶⠶⠆⠸⠷⠶⠲⠰⠶⠶⠂⠰⠶⠶⢶⡺⠳⠶⠶⠶⠖⠐⠗⠶⠷⠰⠀⣷⡿⠿⠶⠶⠆⠧⠖⠗⠂⡆⠂⠄⠀⠀⠀⠘⠓⠃⠘⠓⠣⠒⠒⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡷⠻⠖⠷⠷⠶⠖⠆⠀⠰⠷⠶⠲⠆⢸⠢⠴⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠶⠖⠇⠖⡦⠀⠀⠰⠢⠶⡴⠆⠰⠲⠶⠶⠄⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡟⠒⠶⠖⠶⢶⡶⢶⡶⠶⠆⠆⠀⠀⣄⠀⠀⠰⠆⠰⠦⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡘ ⡟⠗⠒⠾⠲⠧⠆⠀⠀⠀⠆⠐⢲⡆⠶⠖⠆⠰⠐⠾⠖⠺⠴⠐⢾⠆⠾⠚⠚⠺⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣏⡧⠆⠲⠖⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢃ ⠑⠰⠶⠒⠖⠲⠀⠤⠠⠄⠠⠀⠤⠠⠄⠠⠀⠤⠠⠄⠠⠀⠄⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠆⠇⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠽ ⡆⠈⠓⠛⠛⠛⠓⡻⠛⠊⠉⠙⠛⠋⠛⠛⠉⠛⠛⠙⠚⠛⠛⠛⠙⠛⠓⠓⠛⠛⠙⠛⠓⠋⠛⠙⠛⠛⠛⠚⠛⠛⠚⠛⠛⠙⠙⢻⢳⠛⠞⠛⠛⠛⠚⠛⠛⠓⠛⠛⠛⠙⠛⠛⠓⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠛⠁⠠ ⡇⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀ ⡇⠀⠤⡷⠖⠳⠔⠳⠶⠦⠀⠰⠶⠷⠆⠰⠄⠀⠗⠷⠺⠿⠖⠂⠶⠿⠾⠀⠷⠷⠖⠟⠷⠶⠿⠷⠰⠷⠷⠿⠧⠶⠞⠨⠿⠾⠶⠾⠿⠯⠧⠿⠿⠾⠷⠷⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡇⠀⠀⠀⠆⠷⠷⠷⠐⠷⠷⠶⠠⠶⠶⢶⡶⠷⠖⠶⠖⢄⠠⠿⠿⠿⠿⠷⠿⠷⠇⠀⠇⠰⠷⠷⠸⠿⠷⠖⠆⠇⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠤⠤⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣀⠒⠒⢂⠐⡖⠒⠒⢒⣲⣶⡖⠒⠖⠀⠒⡀⢀⣀⡐⠀⠀⢶⠒⠒⣀⡂⠘⠀⣀⡀⠀⠀⠀⡀⠀⣀⠀⢠⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠁⢷⡶⠴⠤⠦⠦⡷⠀⠰⠶⠶⠆⠐⠂⡷⡷⠇⠲⢾⠽⠥⠰⡿⡷⡧⠰⡿⠷⠷⠷⠷⠷⠷⠷⠿⠧⠠⠧⠲⠾⠷⠸⠶⠿⠿⠾⠿⠿⠳⠿⠿⠿⠯⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠰⠷⠷⠰⠿⠷⠖⠆⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢀⣀⣁⡙⠛⠉⡉⡉⠙⠁⠨⠄⠐⠀⠐⠀⣀⡀⢐⢤⡀⠀⠐⠀⠉⠩⠉⠩⠠⠠⠀⠄⠠⠤⠀⠠⠀⠄⠂⠀⠀⠄⠄⠠⠀⠤⠄⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠔⠉⠍⠥⠄⠴⠴⠆⠀⠰⠶⠿⠶⠀⠆⠀⡶⠆⠶⠶⠲⠀⠀⠷⠧⠿⠿⠷⠷⠷⢷⠶⠶⠾⠶⢷⠖⠲⠶⠶⠷⠾⠗⠷⠾⠶⡷⠞⠗⠷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠄⠷⠵⠕⠠⠲⣷⠆⠐⠶⡆⠾⠆⠐⠒⠂⠀⠀⠸⠶⠶⢷⠺⢞⠾⠾⠂⠸⠃⠤⠷⠃⠾⠿⠴⠦⠾⠐⠀⠀⠐⠂⠐⠂⠀⠂⠀⠀⠀⠒⠀⠀⠒⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣄⣀⣀⡀⠀⠄⠄⠀⢠⣤⣤⡄⢀⠀⢠⠤⠀⣠⡤⠤⠀⠤⠤⠠⠀⠤⠤⠤⠤⠀⠠⠠⠠⠶⠦⠴⠤⠦⠀⠀⠂⠠⠄⠠⠤⠤⠤⠤⠄⠤⠄⠤⠤⠤⠤⠄⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠩⠍⠝⠤⡤⠶⠇⠀⠀⠩⠴⠇⠰⠆⠰⠿⠆⠸⠴⠤⠀⠶⠿⠾⠀⠶⠿⠾⠾⠒⠾⠾⠿⣀⠶⠶⠧⠷⠶⠷⠶⠼⠷⠰⠶⠵⠶⠿⠷⠿⠷⠶⠶⠗⠿⠇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠆⠗⠳⠔⠠⠷⠷⠀⠠⠒⠶⢂⠔⠶⠖⠒⢦⠄⠰⠤⠶⠮⠿⠟⠾⠟⠀⠨⠀⠽⠾⠀⠻⠿⠔⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣠⣤⣤⣀⠀⡀⠤⠄⠀⢠⣤⣤⡄⢠⠄⢠⠤⠀⢠⣤⡀⠀⠢⠘⠐⠀⠐⠀⠀⠀⠀⠤⡤⠠⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠩⠶⡦⠐⠰⠦⠇⠀⠈⠌⢼⢦⠴⠄⠸⠿⠆⠨⠡⠲⠂⠾⠶⠶⠲⠶⠶⠀⠶⠀⠺⢿⢷⠾⠟⠷⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠇⠶⠶⠷⠰⠷⠷⠆⠰⠴⠶⢶⠶⠶⠲⠶⠦⠀⠰⠶⠾⠮⠿⠷⠾⠞⠂⠾⠀⠼⠼⣤⠺⠶⠔⠴⠶⠀⠐⠂⠀⠐⠦⠀⠠⠄⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠲⠊⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠂⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠈⠀⠀⠛⠈⠀⠀⠊⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠋⠁⠀⠀⠀⠐⠀⠀⠀⠘⠀⠐⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⣤⢤⠀⠄⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠿⠶⠶⠶⠀⠼⢠ ⠣⠚⠛⠛⠛⠛⠛⠛⠛⠙⠛⠙⠛⠛⠛⠛⠛⠛⠛⠓⠛⠛⠛⠛⠛⠂⠒⠒⠒⠂⠒⠒⠐⠂⠂⠒⠒⠐⠂⠒⠒⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣶⣾ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠸⢷⠾⠴⠶⠶⠦⠅⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠾⠶⠶⠾⠶⠴⠶⠄⠀⠐⠐⠒⠂⠒⠐⠐⠀⠂⠀⢬ ⡇⠯⠶⠧⠶⢶⣶⡤⠆⠸⠆⠷⠶⠶⠆⠸⠷⠶⠲⠶⠺⠆⠸⠶⠶⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⡀⠀⠀⠀⠸⠷⠗⢚⠿⠆⠐⠶⠖⠆⠀⠶⠄⠀⠀⠀⠀⠀⠀⢸ ⡇⠟⠿⠿⠧⠂⠀⠀⠀⠰⠶⠶⠢⠶⠶⠶⠶⠆⠸⠷⠶⠲⠰⠶⠶⠂⠰⠶⠶⢶⡺⠳⠶⠶⠶⠖⠐⠗⠶⠷⠰⠀⣷⡿⠿⠶⠶⠆⠧⠖⠗⠂⡆⠂⠄⠀⠀⠀⠘⠓⠃⠘⠓⠣⠒⠒⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡷⠻⠖⠷⠷⠶⠖⠆⠀⠰⠷⠶⠲⠆⢸⠢⠴⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠶⠖⡇⠖⡦⠀⠀⠰⠢⠶⡴⠆⠰⠲⠶⠶⠄⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡟⠒⠶⠖⠶⢶⡶⢶⡶⠶⠆⠆⠀⠀⣄⠀⠀⠰⠆⠰⠦⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡘ ⡟⠗⠒⡾⡲⠧⠆⠀⠀⠀⠆⠐⢲⡆⠶⠖⠆⠰⠐⠾⠖⠺⠴⠐⢾⠆⠾⠚⠚⠺⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣏⡧⠆⠲⠖⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢃ ⠑⠰⠶⠒⠖⠲⠀⠤⠠⠄⠠⠀⠤⠠⠄⠠⠀⠤⠠⠄⠠⠀⠄⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠆⠇⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠽ ⡆⠈⠓⠛⠛⠛⠓⡻⠛⠊⠉⠙⠛⠋⠛⠛⠉⠛⠛⠙⠚⠛⠛⠛⠙⠛⠓⠓⠛⠛⠙⠛⠓⠋⠛⠙⠛⠛⠛⠚⠛⠛⠚⠛⠛⠙⠙⢻⢳⠛⠞⠛⠛⠛⠚⠛⠛⠓⠛⠛⠛⠙⠛⠛⠓⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠛⠁⠠ ⡇⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀ ⡇⠀⠤⡷⠖⠳⠔⠳⠶⠦⠀⠰⠶⠷⠆⠰⠄⠀⠗⠷⠺⠿⠖⠂⠶⠿⠾⠀⠷⠷⠖⠟⠷⠶⠿⠷⠰⠷⠷⠿⠧⠶⠞⠨⠿⠾⠶⠶⠿⠯⠧⠿⠿⠾⠷⠷⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡇⠀⠀⠀⠆⠷⠷⠷⠐⠷⠷⠶⠠⠶⠶⢶⡶⠷⠖⠶⠖⠄⠠⠿⠿⠿⠿⠷⠿⠷⠇⠀⠇⠰⠷⠷⠸⠿⠷⠖⠆⠇⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠤⠤⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣀⠒⠒⢂⠐⡖⠒⠒⢒⣲⣶⡖⠒⠖⠀⠒⡀⢀⣀⡐⠀⠀⢶⠒⠒⣀⡂⠘⠀⣀⡀⠀⠀⠀⡀⠀⣀⠀⢠⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠁⢷⡶⠴⠤⠦⠦⡷⠀⠰⠶⠶⠆⠐⠂⡷⡷⠇⠲⢾⠽⠥⠰⡿⡷⡧⠰⡿⠷⠷⠷⠷⠷⠷⠷⠿⠧⠠⠧⠲⠾⠷⠸⠶⠿⠿⠾⠿⠿⠳⠿⠿⠿⠯⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠰⠷⠷⠰⠿⠷⠖⠆⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢀⣀⣁⡙⠛⠉⡉⡉⠙⠁⠨⠄⠐⠀⠐⠀⣈⡉⢑⢤⡀⠀⠐⠀⠉⠩⠉⠩⠠⠠⠀⠄⠠⠤⠀⠠⠀⠄⠂⠀⠀⠄⠄⠠⠀⠤⠄⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠔⠉⠍⠥⠄⠴⠴⠆⠀⠰⠶⠿⠶⠀⠆⠀⡶⠆⠶⠶⠲⠀⠀⠷⠧⠿⠿⠷⠷⠷⢷⠶⠶⠾⠶⢶⠖⠲⠶⠶⠷⠾⠗⠷⠾⠶⡷⠞⠗⢷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠄⠷⠵⠕⠠⠲⣷⠆⠐⠶⡆⠾⠆⠐⠒⠂⠀⠀⠸⠶⠶⢷⠺⢞⠶⠾⠂⠸⠃⠤⠷⠃⠾⠿⠴⠦⠾⠐⠀⠀⠐⠂⠐⠂⠀⠂⠀⠀⠀⠒⠀⠀⠒⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣄⣀⣀⡀⠀⠄⠄⠀⢠⣤⣤⡄⢀⠀⢠⠤⠀⣠⡤⠤⠀⠤⠤⠠⠀⠤⠤⠤⠤⠀⠠⠠⠠⠶⠦⠴⠤⠦⠀⠀⠂⠠⠄⠠⠤⠤⠤⠤⠄⠤⠄⠤⠤⠤⠤⠄⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠩⠍⠝⠤⡤⠶⡇⠀⠀⠩⠴⠇⠰⠆⠰⠿⠆⠸⠴⠤⠀⠶⠿⠾⠀⠶⠿⠾⠾⠒⠶⠾⠿⣀⠶⠶⠧⢷⠶⢷⡶⠼⠷⠰⠶⠵⠶⠿⠷⠿⠷⠶⠶⠗⠾⠇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠆⠗⠳⠄⠠⠶⠷⠀⠠⠒⠶⢂⠔⠶⠖⠲⢦⠄⠰⠤⠶⠮⠿⠟⠾⠗⠀⠨⠀⠵⠾⠀⠻⠿⠖⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣠⣤⣤⣀⠀⡀⠤⠄⠀⢠⣤⣤⡄⢠⠄⢠⠤⠀⢠⣤⡀⠀⠢⠘⠐⠀⠐⠀⠀⠀⠀⠤⡤⠠⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠩⠶⡦⠐⠰⠦⠇⠀⠈⠌⢼⢦⠴⠄⠸⠿⠆⠨⠡⠲⠂⠾⠶⠶⠲⠶⠶⠀⠶⠀⠺⣿⢷⠾⠟⠶⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠇⠶⠶⠷⠰⠷⠷⠆⠰⠴⠶⢶⠶⠶⠲⠶⠦⠀⠰⠶⠾⠮⠿⠷⠶⠞⠂⠾⠀⠼⢼⣤⠺⠶⠔⠴⠶⠀⠐⠂⠀⠐⠦⠀⠠⠄⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠲⠊⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠂⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠈⠀⠀⠛⠈⠀⠀⠊⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠋⠁⠀⠀⠀⠐⠀⠀⠀⠘⠀⠐⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⣤⢤⠀⠄⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠿⠶⠶⠶⠀⠼⢠ ⠣⠚⠛⠛⠛⠛⠛⠛⠛⠙⠛⠙⠛⠛⠛⠛⠛⠛⠛⠓⠛⠛⠛⠛⠛⠂⠒⠒⠒⠂⠒⠒⠐⠂⠂⠒⠒⠐⠂⠒⠒⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣶⣾ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠸⢷⠾⠴⠶⠶⠦⠅⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠾⠶⠶⠾⠶⠴⠶⠄⠀⠐⠐⠒⠂⠒⠐⠐⠀⠂⠀⢬ ⡇⠯⠶⠧⠶⢶⣶⡤⠆⠸⠆⠷⠶⠶⠆⠸⠷⠶⠲⠶⠺⠆⠸⠶⠶⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⡀⠀⠀⠀⠸⠷⠗⢚⠿⠆⠐⠶⠖⠆⠀⠶⠄⠀⠀⠀⠀⠀⠀⢸ ⡇⠟⠿⠿⠧⠂⠀⠀⠀⠰⠶⠶⠢⠶⠶⠶⠶⠆⠸⠷⠶⠲⠰⠶⠶⠂⠰⠶⠶⢶⡺⠳⠶⠶⠶⠖⠐⠗⠶⠷⠰⠀⣷⡿⠿⠶⠶⠆⠧⠖⠗⠂⡆⠂⠄⠀⠀⠀⠘⠓⠃⠘⠓⠣⠒⠒⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡷⠻⠖⠷⠷⠶⠖⠆⠀⠰⠷⠶⠲⠆⢸⠢⠴⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠶⠖⡇⠖⡦⠀⠀⠰⠢⠶⡴⠆⠰⠲⠶⠶⠄⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡟⠒⠶⠖⠶⢶⡶⢶⡶⠶⠆⠆⠀⠀⣄⠀⠀⠰⠆⠰⠦⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡘ ⡟⠗⠒⡾⡲⠧⠆⠀⠀⠀⠆⠐⢲⡆⠶⠖⠆⠰⠐⠾⠖⠺⠴⠐⢾⠆⠾⠚⠚⠺⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣏⡧⠆⠲⠖⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢃ ⠑⠰⠶⠒⠖⠲⠀⠤⠠⠄⠠⠀⠤⠠⠄⠠⠀⠤⠠⠄⠠⠀⠄⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠆⠇⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠽ ⡆⠈⠓⠛⠛⠛⠓⡻⠛⠊⠉⠙⠛⠋⠛⠛⠉⠛⠛⠙⠚⠛⠛⠛⠙⠛⠓⠓⠛⠛⠙⠛⠓⠋⠛⠙⠛⠛⠛⠚⠛⠛⠚⠛⠛⠙⠙⢻⢳⠛⠞⠛⠛⠛⠚⠛⠛⠓⠛⠛⠛⠙⠛⠛⠓⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠛⠁⠠ ⡇⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀ ⡇⠀⠤⡷⠖⠳⠔⠳⠶⠦⠀⠰⠶⠷⠆⠰⠄⠀⠗⠷⠺⠿⠖⠂⠶⠿⠾⠀⠷⠷⠖⠟⠷⠶⠿⠷⠰⠷⠷⠿⠧⠶⠞⠨⠿⠾⠶⠶⠿⠯⠧⠿⠿⠾⠷⠷⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡇⠀⠀⠀⠆⠷⠷⠷⠐⠷⠷⠶⠠⠶⠶⢶⡶⠷⠖⠶⠖⠄⠠⠿⠿⠿⠿⠷⠿⠷⠇⠀⠇⠰⠷⠷⠸⠿⠷⠖⠆⠇⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠤⠤⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣀⠒⠒⢂⠐⡖⠒⠒⢒⣲⣶⡖⠒⠖⠀⠒⡀⢀⣀⡐⠀⠀⢶⠒⠒⣀⡂⠘⠀⣀⡀⠀⠀⠀⡀⠀⣀⠀⢠⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠁⢷⡶⠴⠤⠦⠦⡷⠀⠰⠶⠶⠆⠐⠂⡷⡷⠇⠲⢾⠽⠥⠰⡿⡷⡧⠰⡿⠷⠷⠷⠷⠷⠷⠷⠿⠧⠠⠧⠲⠾⠷⠸⠶⠿⠿⠾⠿⠿⠳⠿⠿⠿⠯⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠰⠷⠷⠰⠿⠷⠖⠆⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢀⣀⣁⡙⠛⠉⡉⡉⠙⠁⠨⠄⠐⠀⠐⠀⣈⡉⢑⢤⡀⠀⠐⠀⠉⠩⠉⠩⠠⠠⠀⠄⠠⠤⠀⠠⠀⠄⠂⠀⠀⠄⠄⠠⠀⠤⠄⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠔⠉⠍⠥⠄⠴⠴⠆⠀⠰⠶⠿⠶⠀⠆⠀⡶⠆⠶⠶⠲⠀⠀⠷⠧⠿⠿⠷⠷⠷⢷⠶⠶⠾⠶⢶⠖⠲⠶⠶⠷⠾⠗⠷⠾⠶⡷⠞⠗⢷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠄⠷⠵⠕⠠⠲⣷⠆⠐⠶⡆⠾⠆⠐⠒⠂⠀⠀⠸⠶⠶⢷⠺⢞⠶⠾⠂⠸⠃⠤⠷⠃⠾⠿⠴⠦⠾⠐⠀⠀⠐⠂⠐⠂⠀⠂⠀⠀⠀⠒⠀⠀⠒⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣄⣀⣀⡀⠀⠄⠄⠀⢠⣤⣤⡄⢀⠀⢠⠤⠀⣠⡤⠤⠀⠤⠤⠠⠀⠤⠤⠤⠤⠀⠠⠠⠠⠶⠦⠴⠤⠦⠀⠀⠂⠠⠄⠠⠤⠤⠤⠤⠄⠤⠄⠤⠤⠤⠤⠄⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠩⠍⠝⠤⡤⠶⡇⠀⠀⠩⠴⠇⠰⠆⠰⠿⠆⠸⠴⠤⠀⠶⠿⠾⠀⠶⠿⠾⠾⠒⠶⠾⠿⣀⠶⠶⠧⢷⠶⢷⡶⠼⠷⠰⠶⠵⠶⠿⠷⠿⠷⠶⠶⠗⠾⠇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠆⠗⠳⠄⠠⠶⠷⠀⠠⠒⠶⢂⠔⠶⠖⠲⢦⠄⠰⠤⠶⠮⠿⠟⠾⠗⠀⠨⠀⠵⠾⠀⠻⠿⠖⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣠⣤⣤⣀⠀⡀⠤⠄⠀⢠⣤⣤⡄⢠⠄⢠⠤⠀⢠⣤⡀⠀⠢⠘⠐⠀⠐⠀⠀⠀⠀⠤⡤⠠⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠩⠶⡦⠐⠰⠦⠇⠀⠈⠌⢼⢦⠴⠄⠸⠿⠆⠨⠡⠲⠂⠾⠶⠶⠲⠶⠶⠀⠶⠀⠺⣿⢷⠾⠟⠶⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠇⠶⠶⠷⠰⠷⠷⠆⠰⠴⠶⢶⠶⠶⠲⠶⠦⠀⠰⠶⠾⠮⠿⠷⠶⠞⠂⠾⠀⠼⢼⣤⠺⠶⠔⠴⠶⠀⠐⠂⠀⠐⠦⠀⠠⠄⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠲⠊⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠂⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠈⠀⠀⠛⠈⠀⠀⠊⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠋⠁⠀⠀⠀⠐⠀⠀⠀⠘⠀⠐⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⣤⢤⠀⠄⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠿⠶⠶⠶⠀⠼⢠ ⠣⠚⠛⠛⠛⠛⠛⠛⠛⠙⠛⠙⠛⠛⠛⠛⠛⠛⠛⠓⠛⠛⠛⠛⠛⠂⠒⠒⠒⠂⠒⠒⠐⠂⠂⠒⠒⠐⠂⠒⠒⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣶⣾ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠸⢷⠾⠴⠶⠶⠦⠅⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠾⠶⠶⠾⠶⠴⠶⠄⠀⠐⠐⠒⠂⠒⠐⠐⠀⠂⠀⢬ ⡇⠯⠶⠧⠶⢶⣶⡤⠆⠸⠆⠷⠶⠶⠆⠸⠷⠶⠲⠶⠺⠆⠸⠶⠶⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⡀⠀⠀⠀⠸⠷⠗⢚⠿⠆⠐⠶⠖⠆⠀⠶⠄⠀⠀⠀⠀⠀⠀⢸ ⡇⠟⠿⠿⠧⠂⠀⠀⠀⠰⠶⠶⠢⠶⠶⠶⠶⠆⠸⠷⠶⠲⠰⠶⠶⠂⠰⠶⠶⢶⡺⠳⠶⠶⠶⠖⠐⠗⠶⠷⠰⠀⣷⡿⠿⠶⠶⠆⠧⠖⠗⠂⡆⠂⠄⠀⠀⠀⠘⠓⠃⠘⠓⠣⠒⠒⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡷⠻⠖⠷⠷⠶⠖⠆⠀⠰⠷⠶⠲⠆⢸⠢⠴⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠶⠖⡇⠖⡦⠀⠀⠰⠢⠶⡴⠆⠰⠲⠶⠶⠄⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡟⠒⠶⠖⠶⢶⡶⢶⡶⠶⠆⠆⠀⠀⣄⠀⠀⠰⠆⠰⠦⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡘ ⡟⠗⠒⡾⡲⠧⠆⠀⠀⠀⠆⠐⢲⡆⠶⠖⠆⠰⠐⠾⠖⠺⠴⠐⢾⠆⠾⠚⠚⠺⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣏⡧⠆⠲⠖⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢃ ⠑⠰⠶⠒⠖⠲⠀⠤⠠⠄⠠⠀⠤⠠⠄⠠⠀⠤⠠⠄⠠⠀⠄⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠆⠇⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠽ ⡆⠈⠓⠛⠛⠛⠓⡻⠛⠊⠉⠙⠛⠋⠚⠛⠉⠛⠛⠙⠚⠛⠛⠛⠙⠛⠓⠓⠛⠛⠙⠛⠓⠋⠛⠙⠛⠛⠛⠚⠛⠛⠚⠛⠛⠙⠙⢻⢳⠛⠞⠛⠛⠓⠚⠛⠛⠓⠛⠛⠛⠙⠛⠛⠓⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠛⠁⠠ ⡇⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀ ⡇⠀⠤⡷⠖⠳⠔⠳⠶⠦⠀⠰⠶⠷⠆⠰⠄⠀⠗⠷⠺⠿⠖⠂⠶⠿⠾⠀⠷⠷⠖⠟⠷⠶⠿⠷⠰⠷⠷⠿⠧⠶⠞⠨⠿⠾⠶⠶⠿⠯⠧⠿⠿⠾⠷⠷⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡇⠀⠀⠀⠆⠷⠷⠷⠐⠷⠷⠶⠠⠶⠶⢶⡶⠷⠖⠶⠖⠄⠠⠿⠿⠿⠿⠷⠿⠷⠇⠀⠇⠰⠷⠷⠸⠿⠷⠖⠆⠇⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠤⠤⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣀⠒⠒⢂⠐⡖⠒⠒⢒⣲⣶⡖⠒⠖⠀⠒⡀⢀⣀⡐⠀⠀⢶⠒⠒⣀⡂⠘⠀⣀⡀⠀⠀⠀⡀⠀⣀⠀⢠⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠁⢷⡶⠴⠤⠦⠦⡷⠀⠰⠶⠶⠆⠐⠂⡷⡷⠇⠲⢾⠽⠥⠰⡿⡷⡧⠰⡿⠷⠷⠷⠷⠷⠷⠷⠿⠧⠠⠧⠲⠾⠷⠸⠶⠿⠿⠾⠿⠿⠳⠿⠿⠿⠯⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠰⠷⠷⠰⠿⠷⠖⠆⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢀⣀⣁⡙⠛⠉⡉⡉⠙⠁⠨⠄⠐⠀⠐⠀⣈⡉⢑⢤⡀⠀⠐⠀⠉⠩⠉⠩⠠⠠⠀⠄⠠⠤⠀⠠⠀⠄⠂⠀⠀⠄⠄⠠⠀⠤⠄⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠔⠉⠍⠥⠄⠴⠴⠆⠀⠰⠶⠿⠶⠀⠆⠀⡶⠆⠶⠶⠲⠀⠀⠷⠧⠿⠿⠷⠷⠷⢷⠶⠶⠾⠶⢶⠖⠲⠶⠶⠷⠾⠗⠷⠾⠶⡷⠞⠗⢷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠄⠷⠵⠕⠠⠲⣷⠆⠐⠶⡆⠾⠆⠐⠒⠂⠀⠀⠸⠶⠶⢷⠺⢞⠶⠾⠂⠸⠃⠤⠷⠃⠾⠿⠴⠦⠾⠐⠀⠀⠐⠂⠐⠂⠀⠂⠀⠀⠀⠒⠀⠀⠒⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣄⣀⣀⡀⠀⠄⠄⠀⢠⣤⣤⡄⢀⠀⢠⠤⠀⣠⡤⠤⠀⠤⠤⠠⠀⠤⠤⠤⠤⠀⠠⠠⠠⠶⠦⠴⠤⠦⠀⠀⠂⠠⠄⠠⠤⠤⠤⠤⠄⠤⠄⠤⠤⠤⠤⠄⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠩⠍⠝⠤⡤⠶⡇⠀⠀⠩⠴⠇⠰⠆⠰⠿⠆⠸⠴⠤⠀⠶⠿⠾⠀⠶⠿⠾⠾⠒⠶⠾⠿⣀⠶⠶⠧⢷⠶⢷⡶⠼⠷⠰⠶⠵⠶⠿⠷⠿⠷⠶⠶⠗⠾⠇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠆⠗⠳⠄⠠⠶⠷⠀⠠⠒⠶⢂⠔⠶⠖⠲⢦⠄⠰⠤⠶⠮⠿⠟⠾⠗⠀⠨⠀⠵⠾⠀⠻⠿⠖⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣠⣤⣤⣀⠀⡀⠤⠄⠀⢠⣤⣤⡄⢠⠄⢠⠤⠀⢠⣤⡀⠀⠢⠘⠐⠀⠐⠀⠀⠀⠀⠤⡤⠠⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠩⠶⡦⠐⠰⠦⠇⠀⠈⠌⢼⢦⠴⠄⠸⠿⠆⠨⠡⠲⠂⠾⠶⠶⠲⠶⠶⠀⠶⠀⠺⣿⢷⠾⠟⠶⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠇⠶⠶⠷⠰⠷⠷⠆⠰⠴⠶⢶⠶⠶⠲⠶⠦⠀⠰⠶⠾⠮⠿⠷⠶⠞⠂⠾⠀⠼⢼⣤⠺⠶⠔⠴⠶⠀⠐⠂⠀⠐⠦⠀⠠⠄⠀⠖⠀⠀⠀⠀⠀⠤⠸⠣⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠲⠊⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠂⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠀⠄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣴⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠈⠀⠀⠛⠈⠀⠀⠊⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠋⠁⠀⠀⠀⠐⠀⠀⠀⠘⠀⠔⠐⠀⠂⠀⠀⠀⠀⠠⠅⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⣤⢤⠀⠄⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠿⠶⠶⠶⠀⠼⢠ ⠣⠚⠛⠛⠛⠛⠛⠛⠛⠙⠛⠙⠛⠛⠛⠛⠛⠛⠛⠓⠛⠛⠛⠛⠛⠂⠒⠐⠂⠂⠒⠒⠐⠂⠂⠒⠐⠐⠂⠒⠒⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣶⣾ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠸⢷⠾⠴⠶⠶⠦⠅⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠾⠶⠶⠾⠶⠴⠶⠄⠀⠐⠐⠒⠂⠒⠐⠐⠀⠂⠀⢬ ⡇⠯⠶⠧⠶⢶⣶⡤⠆⠸⠆⠷⠶⠶⠆⠸⠷⠶⠲⠶⠺⠆⠸⠶⠶⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⡀⠀⠀⠀⠸⠷⠗⢚⠿⠆⠐⠶⠖⠆⠀⠶⠄⠀⠀⠀⠀⠀⠀⢸ ⡇⠟⠿⠿⠧⠂⠀⠀⠀⠰⠶⠶⠢⠶⠶⠶⠶⠆⠸⠷⠶⠲⠰⠶⠶⠂⠰⠶⠶⢶⡺⠳⠶⠶⠶⠖⠐⠗⠶⠷⠰⠀⣷⡿⠿⠶⠶⠆⠧⠖⠗⠂⡆⠂⠄⠀⠀⠀⠘⠓⠃⠘⠓⠣⠒⠒⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡷⠻⠖⠷⠷⠶⠖⠆⠀⠰⠷⠶⠲⠆⢸⠢⠴⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠶⠖⡇⠖⡦⠀⠀⠰⠢⠶⡴⠆⠰⠲⠶⠶⠄⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡟⠒⠶⠖⠶⢶⡶⢶⡶⠶⠆⠆⠀⠀⣄⠀⠀⠰⠆⠰⠦⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡘ ⡟⠗⠒⡾⡲⠧⠆⠀⠀⠀⠆⠐⢲⡆⠶⠖⠆⠰⠐⠾⠖⠺⠴⠐⢾⠆⠾⠚⠚⠺⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣏⡧⠆⠲⠖⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢃ ⠑⠰⠶⠒⠖⠲⠀⠤⠠⠄⠠⠀⠤⠠⠄⠠⠀⠤⠠⠄⠠⠀⠄⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠆⠇⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠽ ⡆⠈⠓⠛⠛⠛⠓⡻⠛⠊⠉⠙⠛⠋⠚⠛⠉⠛⠛⠙⠚⠛⠛⠛⠙⠛⠓⠓⠛⠛⠙⠛⠓⠋⠛⠙⠛⠛⠛⠚⠛⠛⠚⠛⠛⠙⠙⢻⢳⠛⠞⠛⠛⠓⠚⠛⠛⠓⠛⠛⠛⠙⠛⠛⠓⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠛⠁⠠ ⡇⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀ ⡇⠀⠤⡷⠖⠳⠔⠳⠶⠦⠀⠰⠶⠷⠆⠰⠄⠀⠗⠷⠺⠿⠖⠂⠶⠿⠾⠀⠷⠷⠖⠟⠷⠶⠿⠷⠰⠷⠷⠿⠧⠶⠞⠨⠿⠾⠶⠶⠿⠯⠧⠿⠿⠾⠷⠷⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡇⠀⠀⠀⠆⠷⠷⠷⠐⠷⠷⠶⠠⠶⠶⢶⡶⠷⠖⠶⠖⠄⠠⠿⠿⠿⠿⠷⠿⠷⠇⠀⠇⠰⠷⠷⠸⠿⠷⠖⠆⠇⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠤⠤⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣀⠒⠒⢂⠐⡖⠒⠒⢒⣲⣶⡖⠒⠖⠀⠒⡀⢀⣀⡐⠀⠀⢶⠒⠒⣀⡂⠘⠀⣀⡀⠀⠀⠀⡀⠀⣀⠀⢠⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠁⢷⡶⠴⠤⠦⠦⡷⠀⠰⠶⠶⠆⠐⠂⡷⡷⠇⠲⢾⠽⠥⠰⡿⡷⡧⠰⡿⠷⠷⠷⠷⠷⠷⠷⠿⠧⠠⠧⠲⠾⠷⠸⠶⠿⠿⠾⠿⠿⠳⠿⠿⠿⠯⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠰⠷⠷⠰⠿⠷⠖⠆⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢀⣀⣁⡙⠛⠉⡉⡉⠙⠁⠨⠄⠐⠀⠐⠀⣈⡉⢑⢤⡀⠀⠐⠀⠉⠩⠉⠩⠠⠠⠀⠄⠠⠤⠀⠠⠀⠄⠂⠀⠀⠄⠄⠠⠀⠤⠄⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠔⠉⠍⠥⠄⠴⠴⠆⠀⠰⠶⠿⠶⠀⠆⠀⡶⠆⠶⠶⠲⠀⠀⠷⠧⠿⠿⠷⠷⠷⢷⠶⠶⠾⠶⢶⠖⠲⠶⠶⠷⠾⠗⠷⠾⠶⡷⠞⠗⢷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠄⠷⠵⠕⠠⠲⣷⠆⠐⠶⡆⠾⠆⠐⠒⠂⠀⠀⠸⠶⠶⢷⠺⢞⠶⠾⠂⠸⠃⠤⠷⠃⠾⠿⠴⠦⠾⠐⠀⠀⠐⠂⠐⠂⠀⠂⠀⠀⠀⠒⠀⠀⠒⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣄⣀⣀⡀⠀⠄⠄⠀⢠⣤⣤⡄⢀⠀⢠⠤⠀⣠⡤⠤⠀⠤⠤⠠⠀⠤⠤⠤⠤⠀⠠⠠⠠⠶⠦⠴⠤⠦⠀⠀⠂⠠⠄⠠⠤⠤⠤⠤⠄⠤⠄⠤⠤⠤⠤⠄⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠩⠍⠝⠤⡤⠶⡇⠀⠀⠩⠴⠇⠰⠆⠰⠿⠆⠸⠴⠤⠀⠶⠿⠾⠀⠶⠿⠾⠾⠒⠶⠾⠿⣀⠶⠶⠧⢷⠶⢷⡶⠼⠷⠰⠶⠵⠶⠿⠷⠿⠷⠶⠶⠗⠾⠇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠆⠗⠳⠄⠠⠶⠷⠀⠠⠒⠶⢂⠔⠶⠖⠲⢦⠄⠰⠤⠶⠮⠿⠟⠾⠗⠀⠨⠀⠵⠾⠀⠻⠿⠖⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣠⣤⣤⣀⠀⡀⠤⠄⠀⢠⣤⣤⡄⢠⠄⢠⠤⠀⢠⣤⡀⠀⠢⠘⠐⠀⠐⠀⠀⠀⠀⠤⡤⠠⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠩⠶⡦⠐⠰⠦⠇⠀⠈⠌⢼⢦⠴⠄⠸⠿⠆⠨⠡⠲⠂⠾⠶⠶⠲⠶⠶⠀⠶⠀⠺⣿⢷⠾⠟⠶⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠇⠶⠶⠷⠰⠷⠷⠆⠰⠴⠶⢶⠶⠶⠲⠶⠦⠀⠰⠶⠾⠮⠿⠷⠶⠞⠂⠾⠀⠼⢼⣤⠺⠶⠔⠴⠶⠀⠐⠂⠀⠐⠦⠀⠠⠄⠀⠖⠀⠀⠀⠀⠀⠤⠸⠣⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠲⠊⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠂⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠀⠄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣴⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠈⠀⠀⠛⠈⠀⠀⠊⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠋⠁⠀⠀⠀⠐⠀⠀⠀⠘⠀⠔⠐⠀⠂⠀⠀⠀⠀⠠⠅⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⣤⢤⠀⠄⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠿⠶⠶⠶⠀⠼⢠ ⠣⠚⠛⠛⠛⠛⠛⠛⠛⠙⠛⠙⠛⠛⠛⠛⠛⠛⠛⠓⠛⠛⠛⠛⠛⠂⠒⠐⠂⠂⠒⠒⠐⠂⠂⠒⠐⠐⠂⠒⠒⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣶⣾ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠸⢷⠾⠴⠶⠶⠦⠅⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠾⠶⠶⠾⠶⠴⠶⠄⠀⠐⠐⠒⠂⠒⠐⠐⠀⠂⠀⢬ ⡇⠯⠶⠧⠶⢶⣶⡤⠆⠸⠆⠷⠶⠶⠆⠸⠷⠶⠲⠶⠺⠆⠸⠶⠶⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⡀⠀⠀⠀⠸⠷⠗⢚⠿⠆⠐⠶⠖⠆⠀⠶⠄⠀⠀⠀⠀⠀⠀⢸ ⡇⠟⠿⠿⠧⠂⠀⠀⠀⠰⠶⠶⠢⠶⠶⠶⠶⠆⠸⠷⠶⠲⠰⠶⠶⠂⠰⠶⠶⢶⡺⠳⠶⠶⠶⠖⠐⠗⠶⠷⠰⠀⣷⡿⠿⠶⠶⠆⠧⠖⠗⠂⡆⠂⠄⠀⠀⠀⠘⠓⠃⠘⠓⠣⠒⠒⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡷⠻⠖⠷⠷⠶⠖⠆⠀⠰⠷⠶⠲⠆⢸⠢⠴⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠶⠖⡇⠖⡦⠀⠀⠰⠢⠶⡴⠆⠰⠲⠶⠶⠄⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡟⠒⠶⠖⠶⢶⡶⢶⡶⠶⠆⠆⠀⠀⣄⠀⠀⠰⠆⠰⠦⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡘ ⡟⠗⠒⡾⡲⠧⠆⠀⠀⠀⠆⠐⢲⡆⠶⠖⠆⠰⠐⠾⠖⠺⠴⠐⢾⠆⠾⠚⠚⠺⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣏⡧⠆⠲⠖⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢃ ⠑⠰⠶⠒⠖⠲⠀⠤⠠⠄⠠⠀⠤⠠⠄⠠⠀⠤⠠⠄⠠⠀⠄⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠆⠇⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠽ ⡆⠈⠓⠛⠛⠛⠓⡻⠛⠊⠉⠙⠛⠋⠚⠛⠉⠛⠛⠙⠚⠛⠛⠛⠙⠛⠓⠓⠛⠛⠙⠛⠓⠋⠛⠙⠛⠛⠛⠚⠛⠛⠚⠛⠛⠙⠙⢻⢳⠛⠞⠛⠛⠓⠚⠛⠛⠓⠛⠛⠛⠙⠛⠛⠓⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠛⠁⠠ ⡇⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀ ⡇⠀⠤⡷⠖⠳⠔⠳⠶⠦⠀⠰⠶⠷⠆⠰⠄⠀⠗⠷⠺⠿⠖⠂⠶⠿⠾⠀⠷⠷⠖⠟⠷⠶⠿⠷⠰⠷⠷⠿⠧⠶⠞⠨⠿⠾⠶⠶⠿⠯⠧⠿⠿⠾⠷⠷⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡇⠀⠀⠀⠆⠷⠷⠷⠐⠷⠷⠶⠠⠶⠶⢶⡶⠷⠖⠶⠖⠄⠠⠿⠿⠿⠿⠷⠿⠷⠇⠀⠇⠰⠷⠷⠸⠿⠷⠖⠆⠇⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠤⠤⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣀⠒⠒⢂⠐⡖⠒⠒⢒⣲⣶⡖⠒⠖⠀⠒⡀⢀⣀⡐⠀⠀⢶⠒⠒⣀⡂⠘⠀⣀⡀⠀⠀⠀⡀⠀⣀⠀⢠⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠁⢷⡶⠴⠤⠦⠦⡷⠀⠰⠶⠶⠆⠐⠂⡷⡷⠇⠲⢾⠽⠥⠰⡿⡷⡧⠰⡿⠷⠷⠷⠷⠷⠷⠷⠿⠧⠠⠧⠲⠾⠷⠸⠶⠿⠿⠾⠿⠿⠳⠿⠿⠿⠯⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠰⠷⠷⠰⠿⠷⠖⠆⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢀⣀⣁⡙⠛⠉⡉⡉⠙⠁⠨⠄⠐⠀⠐⠀⣈⡉⢑⢤⡀⠀⠐⠀⠉⠩⠉⠩⠠⠠⠀⠄⠠⠤⠀⠠⠀⠄⠂⠀⠀⠄⠄⠠⠀⠤⠄⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠔⠉⠍⠥⠄⠴⠴⠆⠀⠰⠶⠿⠶⠀⠆⠀⡶⠆⠶⠶⠲⠀⠀⠷⠧⠿⠿⠷⠷⠷⢷⠶⠶⠾⠶⢶⠖⠲⠶⠶⠷⠾⠗⠷⠾⠶⡷⠞⠗⢷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠄⠷⠵⠕⠠⠲⣷⠆⠐⠶⡆⠾⠆⠐⠒⠂⠀⠀⠸⠶⠶⢷⠺⢞⠶⠾⠂⠸⠃⠤⠷⠃⠾⠿⠴⠦⠾⠐⠀⠀⠐⠂⠐⠂⠀⠂⠀⠀⠀⠒⠀⠀⠒⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣄⣀⣀⡀⠀⠄⠄⠀⢠⣤⣤⡄⢀⠀⢠⠤⠀⣠⡤⠤⠀⠤⠤⠠⠀⠤⠤⠤⠤⠀⠠⠠⠠⠶⠦⠴⠤⠦⠀⠀⠂⠠⠄⠠⠤⠤⠤⠤⠄⠤⠄⠤⠤⠤⠤⠄⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠩⠍⠝⠤⡤⠶⡇⠀⠀⠩⠴⠇⠰⠆⠰⠿⠆⠸⠴⠤⠀⠶⠿⠾⠀⠶⠿⠾⠾⠒⠶⠾⠿⣀⠶⠶⠧⢷⠶⢷⡶⠼⠷⠰⠶⠵⠶⠿⠷⠿⠷⠶⠶⠗⠾⠇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠆⠗⠳⠄⠠⠶⠷⠀⠠⠒⠶⢂⠔⠶⠖⠲⢦⠄⠰⠤⠶⠮⠿⠟⠾⠗⠀⠨⠀⠵⠾⠀⠻⠿⠖⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣠⣤⣤⣀⠀⡀⠤⠄⠀⢠⣤⣤⡄⢠⠄⢠⠤⠀⢠⣤⡀⠀⠢⠘⠐⠀⠐⠀⠀⠀⠀⠤⡤⠠⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠩⠶⡦⠐⠰⠦⠇⠀⠈⠌⢼⢦⠴⠄⠸⠿⠆⠨⠡⠲⠂⠾⠶⠶⠲⠶⠶⠀⠶⠀⠺⣿⢷⠾⠟⠶⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠇⠶⠶⠷⠰⠷⠷⠆⠰⠴⠶⢶⠶⠶⠲⠶⠦⠀⠰⠶⠾⠮⠿⠷⠶⠞⠂⠾⠀⠼⢼⣤⠺⠶⠔⠴⠶⠀⠐⠂⠀⠐⠦⠀⠠⠄⠀⠖⠀⠀⠀⠀⠀⠤⠸⠣⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠲⠊⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠂⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠀⠄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣴⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠈⠀⠀⠛⠈⠀⠀⠊⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠋⠁⠀⠀⠀⠐⠀⠀⠀⠘⠀⠔⠐⠀⠂⠀⠀⠀⠀⠠⠅⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⣤⢤⠀⠄⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠿⠶⠶⠶⠀⠼⢠ ⠣⠚⠛⠛⠛⠛⠛⠛⠛⠙⠛⠙⠛⠛⠛⠛⠛⠛⠛⠓⠛⠛⠛⠛⠛⠂⠒⠐⠂⠂⠒⠒⠐⠂⠂⠒⠐⠐⠂⠒⠒⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣶⣾ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠸⢷⠾⠴⠶⠶⠦⠅⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠾⠶⠶⠾⠶⠴⠶⠄⠀⠐⠐⠒⠂⠒⠐⠐⠀⠂⠀⢬ ⡇⠯⠶⠧⠶⢶⣶⡤⠆⠸⠆⠷⠶⠶⠆⠸⠷⠶⠲⠶⠺⠆⠸⠶⠶⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⡀⠀⠀⠀⠸⠷⠗⢚⠿⠆⠐⠶⠖⠆⠀⠶⠄⠀⠀⠀⠀⠀⠀⢸ ⡇⠟⠿⠿⠧⠂⠀⠀⠀⠰⠶⠶⠢⠶⠶⠶⠶⠆⠸⠷⠶⠲⠰⠶⠶⠂⠰⠶⠶⢶⡺⠳⠶⠶⠶⠖⠐⠗⠶⠷⠰⠀⣷⡿⠿⠶⠶⠆⠧⠖⠗⠂⡆⠂⠄⠀⠀⠀⠘⠓⠃⠘⠓⠣⠒⠒⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡷⠻⠖⠷⠷⠶⠖⠆⠀⠰⠷⠶⠲⠆⢸⠢⠴⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠶⠖⡇⠖⡦⠀⠀⠰⠢⠶⡴⠆⠰⠲⠶⠶⠄⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡟⠒⠶⠖⠶⢶⡶⢶⡶⠶⠆⠆⠀⠀⣄⠀⠀⠰⠆⠰⠦⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡘ ⡟⠗⠒⡾⡲⠧⠆⠀⠀⠀⠆⠐⢲⡆⠶⠖⠆⠰⠐⠾⠖⠺⠴⠐⢾⠆⠾⠚⠚⠺⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣏⡧⠆⠲⠖⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢃ ⠑⠰⠶⠒⠖⠲⠀⠤⠠⠄⠠⠀⠤⠠⠄⠠⠀⠤⠠⠄⠠⠀⠄⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠆⠇⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠽ ⡆⠈⠓⠛⠛⠛⠓⡻⠛⠊⠉⠙⠛⠋⠚⠛⠉⠛⠛⠙⠚⠛⠛⠛⠙⠛⠓⠓⠛⠛⠙⠛⠓⠋⠛⠙⠛⠛⠛⠚⠛⠛⠚⠛⠛⠙⠙⢻⢳⠛⠞⠛⠛⠓⠚⠛⠛⠓⠛⠛⠛⠙⠛⠛⠓⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠛⠁⠠ ⡇⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀ ⡇⠀⠤⡷⠖⠳⠔⠳⠶⠦⠀⠰⠶⠷⠆⠰⠄⠀⠗⠷⠺⠿⠖⠂⠶⠿⠾⠀⠷⠷⠖⠟⠷⠶⠿⠷⠰⠷⠷⠿⠧⠶⠞⠨⠿⠾⠶⠶⠿⠯⠧⠿⠿⠾⠷⠷⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡇⠀⠀⠀⠆⠷⠷⠷⠐⠷⠷⠶⠠⠶⠶⢶⡶⠷⠖⠶⠖⠄⠠⠿⠿⠿⠿⠷⠿⠷⠇⠀⠇⠰⠷⠷⠸⠿⠷⠖⠆⠇⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠤⠤⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣀⠒⠒⢂⠐⡖⠒⠒⢒⣲⣶⡖⠒⠖⠀⠒⡀⢀⣀⡐⠀⠀⢶⠒⠒⣀⡂⠘⠀⣀⡀⠀⠀⠀⡀⠀⣀⠀⢠⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠁⢷⡶⠴⠤⠦⠦⡷⠀⠰⠶⠶⠆⠐⠂⡷⡷⠇⠲⢾⠽⠥⠰⡿⡷⡧⠰⡿⠷⠷⠷⠷⠷⠷⠷⠿⠧⠠⠧⠲⠾⠷⠸⠶⠿⠿⠾⠿⠿⠳⠿⠿⠿⠯⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠰⠷⠷⠰⠿⠷⠖⠆⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢀⣀⣁⡙⠛⠉⡉⡉⠙⠁⠨⠄⠐⠀⠐⠀⣈⡉⢑⢤⡀⠀⠐⠀⠉⠩⠉⠩⠠⠠⠀⠄⠠⠤⠀⠠⠀⠄⠂⠀⠀⠄⠄⠠⠀⠤⠄⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠔⠉⠍⠥⠄⠴⠴⠆⠀⠰⠶⠿⠶⠀⠆⠀⡶⠆⠶⠶⠲⠀⠀⠷⠧⠿⠿⠷⠷⠷⢷⠶⠶⠾⠶⢶⠖⠲⠶⠶⠷⠾⠗⠷⠾⠶⡷⠞⠗⢷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠄⠷⠵⠕⠠⠲⣷⠆⠐⠶⡆⠾⠆⠐⠒⠂⠀⠀⠸⠶⠶⢷⠺⢞⠶⠾⠂⠸⠃⠤⠷⠃⠾⠿⠴⠦⠾⠐⠀⠀⠐⠂⠐⠂⠀⠂⠀⠀⠀⠒⠀⠀⠒⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣄⣀⣀⡀⠀⠄⠄⠀⢠⣤⣤⡄⢀⠀⢠⠤⠀⣠⡤⠤⠀⠤⠤⠠⠀⠤⠤⠤⠤⠀⠠⠠⠠⠶⠦⠴⠤⠦⠀⠀⠂⠠⠄⠠⠤⠤⠤⠤⠄⠤⠄⠤⠤⠤⠤⠄⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠩⠍⠝⠤⡤⠶⡇⠀⠀⠩⠴⠇⠰⠆⠰⠿⠆⠸⠴⠤⠀⠶⠿⠾⠀⠶⠿⠾⠾⠒⠶⠾⠿⣀⠶⠶⠧⢷⠶⢷⡶⠼⠷⠰⠶⠵⠶⠿⠷⠿⠷⠶⠶⠗⠾⠇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠆⠗⠳⠄⠠⠶⠷⠀⠠⠒⠶⢂⠔⠶⠖⠲⢦⠄⠰⠤⠶⠮⠿⠟⠾⠗⠀⠨⠀⠵⠾⠀⠻⠿⠖⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣠⣤⣤⣀⠀⡀⠤⠄⠀⢠⣤⣤⡄⢠⠄⢠⠤⠀⢠⣤⡀⠀⠢⠘⠐⠀⠐⠀⠀⠀⠀⠤⡤⠠⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠩⠶⡦⠐⠰⠦⠇⠀⠈⠌⢼⢦⠴⠄⠸⠿⠆⠨⠡⠲⠂⠾⠶⠶⠲⠶⠶⠀⠶⠀⠺⣿⢷⠾⠟⠶⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠇⠶⠶⠷⠰⠷⠷⠆⠰⠴⠶⢶⠶⠶⠲⠶⠦⠀⠰⠶⠾⠮⠿⠷⠶⠞⠂⠾⠀⠼⢼⣤⠺⠶⠔⠴⠶⠀⠐⠂⠀⠐⠦⠀⠠⠄⠀⠖⠀⠀⠀⠀⠀⠤⠸⠣⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠲⠊⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠂⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠀⠄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣴⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠈⠀⠀⠛⠈⠀⠀⠊⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠋⠁⠀⠀⠀⠐⠀⠀⠀⠘⠀⠔⠐⠀⠂⠀⠀⠀⠀⠠⠅⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⣤⢤⠀⠄⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠿⠶⠶⠶⠀⠼⢠ ⠣⠚⠛⠛⠛⠛⠛⠛⠛⠙⠛⠙⠛⠛⠛⠛⠛⠛⠛⠓⠛⠛⠛⠛⠛⠂⠒⠐⠂⠂⠒⠒⠐⠂⠂⠒⠐⠐⠂⠒⠒⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣶⣾ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠸⢷⠾⠴⠶⠶⠦⠅⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠾⠶⠶⠾⠶⠴⠶⠄⠀⠐⠐⠒⠂⠒⠐⠐⠀⠂⠀⢬ ⡇⠯⠶⠧⠶⢶⣶⡤⠆⠸⠆⠷⠶⠶⠆⠸⠷⠶⠲⠶⠺⠆⠸⠶⠶⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⡀⠀⠀⠀⠸⠷⠗⢚⠿⠆⠐⠶⠖⠆⠀⠶⠄⠀⠀⠀⠀⠀⠀⢸ ⡇⠟⠿⠿⠧⠂⠀⠀⠀⠰⠶⠶⠢⠶⠶⠶⠶⠆⠸⠷⠶⠲⠰⠶⠶⠂⠰⠶⠶⢶⡺⠳⠶⠶⠶⠖⠐⠗⠶⠷⠰⠀⣷⡿⠿⠶⠶⠆⠧⠖⠗⠂⡆⠂⠄⠀⠀⠀⠘⠓⠃⠘⠓⠣⠒⠒⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡷⠻⠖⠷⠷⠶⠖⠆⠀⠰⠷⠶⠲⠆⢸⠢⠴⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠶⠖⡇⠖⡦⠀⠀⠰⠢⠶⡴⠆⠰⠲⠶⠶⠄⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡟⠒⠶⠖⠶⢶⡶⢶⡶⠶⠆⠆⠀⠀⣄⠀⠀⠰⠆⠰⠦⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡘ ⡟⠗⠒⡾⡲⠧⠆⠀⠀⠀⠆⠐⢲⡆⠶⠖⠆⠰⠐⠾⠖⠺⠴⠐⢾⠆⠾⠚⠚⠺⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣏⡧⠆⠲⠖⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢃ ⠑⠰⠶⠒⠖⠲⠀⠤⠠⠄⠠⠀⠤⠠⠄⠠⠀⠤⠠⠄⠠⠀⠄⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠆⠇⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠽ ⡆⠈⠓⠛⠛⠛⠓⡻⠛⠊⠉⠙⠛⠋⠚⠛⠉⠛⠛⠙⠚⠛⠛⠛⠙⠛⠓⠓⠛⠛⠙⠛⠓⠋⠛⠙⠛⠛⠛⠚⠛⠛⠚⠛⠛⠙⠙⢻⢳⠛⠞⠛⠛⠓⠚⠛⠛⠓⠛⠛⠛⠙⠛⠛⠓⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠛⠁⠠ ⡇⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀ ⡇⠀⠤⡷⠖⠳⠔⠳⠶⠦⠀⠰⠶⠷⠆⠰⠄⠀⠗⠷⠺⠿⠖⠂⠶⠿⠾⠀⠷⠷⠖⠟⠷⠶⠿⠷⠰⠷⠷⠿⠧⠶⠞⠨⠿⠾⠶⠶⠿⠯⠧⠿⠿⠾⠷⠷⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡇⠀⠀⠀⠆⠷⠷⠷⠐⠷⠷⠶⠠⠶⠶⢶⡶⠷⠖⠶⠖⠄⠠⠿⠿⠿⠿⠷⠿⠷⠇⠀⠇⠰⠷⠷⠸⠿⠷⠖⠆⠇⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠤⠤⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣀⠒⠒⢂⠐⡖⠒⠒⢒⣲⣶⡖⠒⠖⠀⠒⡀⢀⣀⡐⠀⠀⢶⠒⠒⣀⡂⠘⠀⣀⡀⠀⠀⠀⡀⠀⣀⠀⢠⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠁⢷⡶⠴⠤⠦⠦⡷⠀⠰⠶⠶⠆⠐⠂⡷⡷⠇⠲⢾⠽⠥⠰⡿⡷⡧⠰⡿⠷⠷⠷⠷⠷⠷⠷⠿⠧⠠⠧⠲⠾⠷⠸⠶⠿⠿⠾⠿⠿⠳⠿⠿⠿⠯⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠰⠷⠷⠰⠿⠷⠖⠆⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢀⣀⣁⡙⠛⠉⡉⡉⠙⠁⠨⠄⠐⠀⠐⠀⣈⡉⢑⢤⡀⠀⠐⠀⠉⠩⠉⠩⠠⠠⠀⠄⠠⠤⠀⠠⠀⠄⠂⠀⠀⠄⠄⠠⠀⠤⠄⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠔⠉⠍⠥⠄⠴⠴⠆⠀⠰⠶⠿⠶⠀⠆⠀⡶⠆⠶⠶⠲⠀⠀⠷⠧⠿⠿⠷⠷⠷⢷⠶⠶⠾⠶⢶⠖⠲⠶⠶⠷⠾⠗⠷⠾⠶⡷⠞⠗⢷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠄⠷⠵⠕⠠⠲⣷⠆⠐⠶⡆⠾⠆⠐⠒⠂⠀⠀⠸⠶⠶⢷⠺⢞⠶⠾⠂⠸⠃⠤⠷⠃⠾⠿⠴⠦⠾⠐⠀⠀⠐⠂⠐⠂⠀⠂⠀⠀⠀⠒⠀⠀⠒⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣄⣀⣀⡀⠀⠄⠄⠀⢠⣤⣤⡄⢀⠀⢠⠤⠀⣠⡤⠤⠀⠤⠤⠠⠀⠤⠤⠤⠤⠀⠠⠠⠠⠶⠦⠴⠤⠦⠀⠀⠂⠠⠄⠠⠤⠤⠤⠤⠄⠤⠄⠤⠤⠤⠤⠄⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠩⠍⠝⠤⡤⠶⡇⠀⠀⠩⠴⠇⠰⠆⠰⠿⠆⠸⠴⠤⠀⠶⠿⠾⠀⠶⠿⠾⠾⠒⠶⠾⠿⣀⠶⠶⠧⢷⠶⢷⡶⠼⠷⠰⠶⠵⠶⠿⠷⠿⠷⠶⠶⠗⠾⠇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠆⠗⠳⠄⠠⠶⠷⠀⠠⠒⠶⢂⠔⠶⠖⠲⢦⠄⠰⠤⠶⠮⠿⠟⠾⠗⠀⠨⠀⠵⠾⠀⠻⠿⠖⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣠⣤⣤⣀⠀⡀⠤⠄⠀⢠⣤⣤⡄⢠⠄⢠⠤⠀⢠⣤⡀⠀⠢⠘⠐⠀⠐⠀⠀⠀⠀⠤⡤⠠⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠩⠶⡦⠐⠰⠦⠇⠀⠈⠌⢼⢦⠴⠄⠸⠿⠆⠨⠡⠲⠂⠾⠶⠶⠲⠶⠶⠀⠶⠀⠺⣿⢷⠾⠟⠶⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠇⠶⠶⠷⠰⠷⠷⠆⠰⠴⠶⢶⠶⠶⠲⠶⠦⠀⠰⠶⠾⠮⠿⠷⠶⠞⠂⠾⠀⠼⢼⣤⠺⠶⠔⠴⠶⠀⠐⠂⠀⠐⠦⠀⠠⠄⠀⠖⠀⠀⠀⠀⠀⠤⠸⠣⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠲⠊⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠂⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠀⠄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣴⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠈⠀⠀⠛⠈⠀⠀⠊⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠋⠁⠀⠀⠀⠐⠀⠀⠀⠘⠀⠔⠐⠀⠂⠀⠀⠀⠀⠠⠅⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⣤⢤⠀⠄⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠿⠶⠶⠶⠀⠼⢠ ⠣⠚⠛⠛⠛⠛⠛⠛⠛⠙⠛⠙⠛⠛⠛⠛⠛⠛⠛⠓⠛⠛⠛⠛⠛⠂⠒⠐⠂⠂⠒⠒⠐⠂⠂⠒⠐⠐⠂⠒⠒⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣶⣾ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠸⢷⠾⠴⠶⠶⠦⠅⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠾⠶⠶⠾⠶⠴⠶⠄⠀⠐⠐⠒⠂⠒⠐⠐⠀⠂⠀⢬ ⡇⠯⠶⠧⠶⢶⣶⡤⠆⠸⠆⠷⠶⠶⠆⠸⠷⠶⠲⠶⠺⠆⠸⠶⠶⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⡀⠀⠀⠀⠸⠷⠗⢚⠿⠆⠐⠶⠖⠆⠀⠶⠄⠀⠀⠀⠀⠀⠀⢸ ⡇⠟⠿⠿⠧⠂⠀⠀⠀⠰⠶⠶⠢⠶⠶⠶⠶⠆⠸⠷⠶⠲⠰⠶⠶⠂⠰⠶⠶⢶⡺⠳⠶⠶⠶⠖⠐⠗⠶⠷⠰⠀⣷⡿⠿⠶⠶⠆⠧⠖⠗⠂⡆⠂⠄⠀⠀⠀⠘⠓⠃⠘⠓⠣⠒⠒⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡷⠻⠖⠷⠷⠶⠖⠆⠀⠰⠷⠶⠲⠆⢸⠢⠴⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠶⠖⡇⠖⡦⠀⠀⠰⠢⠶⡴⠆⠰⠲⠶⠶⠄⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡟⠒⠶⠖⠶⢶⡶⢶⡶⠶⠆⠆⠀⠀⣄⠀⠀⠰⠆⠰⠦⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡘ ⡟⠗⠒⡾⡲⠧⠆⠀⠀⠀⠆⠐⢲⡆⠶⠖⠆⠰⠐⠾⠖⠺⠴⠐⢾⠆⠾⠚⠚⠺⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣏⡧⠆⠲⠖⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢃ ⠑⠰⠶⠒⠖⠲⠀⠤⠠⠄⠠⠀⠤⠠⠄⠠⠀⠤⠠⠄⠠⠀⠄⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠆⠇⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠽ ⡆⠈⠓⠛⠛⠛⠓⡻⠛⠊⠉⠙⠛⠋⠚⠛⠉⠛⠛⠙⠚⠛⠛⠛⠙⠛⠓⠓⠛⠛⠙⠛⠓⠋⠛⠙⠛⠛⠛⠚⠛⠛⠚⠛⠛⠙⠙⢻⢳⠛⠞⠛⠛⠓⠚⠛⠛⠓⠛⠛⠛⠙⠛⠛⠓⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠛⠁⠠ ⡇⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀ ⡇⠀⠤⡷⠖⠳⠔⠳⠶⠦⠀⠰⠶⠷⠆⠰⠄⠀⠗⠷⠺⠿⠖⠂⠶⠿⠾⠀⠷⠷⠖⠟⠷⠶⠿⠷⠰⠷⠷⠿⠧⠶⠞⠨⠿⠾⠶⠶⠿⠯⠧⠿⠿⠾⠷⠷⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡇⠀⠀⠀⠆⠷⠷⠷⠐⠷⠷⠶⠠⠶⠶⢶⡶⠷⠖⠶⠖⠄⠠⠿⠿⠿⠿⠷⠿⠷⠇⠀⠇⠰⠷⠷⠸⠿⠷⠖⠆⠇⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠤⠤⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣀⠒⠒⢂⠐⡖⠒⠒⢒⣲⣶⡖⠒⠖⠀⠒⡀⢀⣀⡐⠀⠀⢶⠒⠒⣀⡂⠘⠀⣀⡀⠀⠀⠀⡀⠀⣀⠀⢠⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠁⢷⡶⠴⠤⠦⠦⡷⠀⠰⠶⠶⠆⠐⠂⡷⡷⠇⠲⢾⠽⠥⠰⡿⡷⡧⠰⡿⠷⠷⠷⠷⠷⠷⠷⠿⠧⠠⠧⠲⠾⠷⠸⠶⠿⠿⠾⠿⠿⠳⠿⠿⠿⠯⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠰⠷⠷⠰⠿⠷⠖⠆⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢀⣀⣁⡙⠛⠉⡉⡉⠙⠁⠨⠄⠐⠀⠐⠀⣈⡉⢑⢤⡀⠀⠐⠀⠉⠩⠉⠩⠠⠠⠀⠄⠠⠤⠀⠠⠀⠄⠂⠀⠀⠄⠄⠠⠀⠤⠄⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠔⠉⠍⠥⠄⠴⠴⠆⠀⠰⠶⠿⠶⠀⠆⠀⡶⠆⠶⠶⠲⠀⠀⠷⠧⠿⠿⠷⠷⠷⢷⠶⠶⠾⠶⢶⠖⠲⠶⠶⠷⠾⠗⠷⠾⠶⡷⠞⠗⢷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠄⠷⠵⠕⠠⠲⣷⠆⠐⠶⡆⠾⠆⠐⠒⠂⠀⠀⠸⠶⠶⢷⠺⢞⠶⠾⠂⠸⠃⠤⠷⠃⠾⠿⠴⠦⠾⠐⠀⠀⠐⠂⠐⠂⠀⠂⠀⠀⠀⠒⠀⠀⠒⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣄⣀⣀⡀⠀⠄⠄⠀⢠⣤⣤⡄⢀⠀⢠⠤⠀⣠⡤⠤⠀⠤⠤⠠⠀⠤⠤⠤⠤⠀⠠⠠⠠⠶⠦⠴⠤⠦⠀⠀⠂⠠⠄⠠⠤⠤⠤⠤⠄⠤⠄⠤⠤⠤⠤⠄⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠩⠍⠝⠤⡤⠶⡇⠀⠀⠩⠴⠇⠰⠆⠰⠿⠆⠸⠴⠤⠀⠶⠿⠾⠀⠶⠿⠾⠾⠒⠶⠾⠿⣀⠶⠶⠧⢷⠶⢷⡶⠼⠷⠰⠶⠵⠶⠿⠷⠿⠷⠶⠶⠗⠾⠇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠆⠗⠳⠄⠠⠶⠷⠀⠠⠒⠶⢂⠔⠶⠖⠲⢦⠄⠰⠤⠶⠮⠿⠟⠾⠗⠀⠨⠀⠵⠾⠀⠻⠿⠖⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣠⣤⣤⣀⠀⡀⠤⠄⠀⢠⣤⣤⡄⢠⠄⢠⠤⠀⢠⣤⡀⠀⠢⠘⠐⠀⠐⠀⠀⠀⠀⠤⡤⠠⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠩⠶⡦⠐⠰⠦⠇⠀⠈⠌⢼⢦⠴⠄⠸⠿⠆⠨⠡⠲⠂⠾⠶⠶⠲⠶⠶⠀⠶⠀⠺⣿⢷⠾⠟⠶⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠇⠶⠶⠷⠰⠷⠷⠆⠰⠴⠶⢶⠶⠶⠲⠶⠦⠀⠰⠶⠾⠮⠿⠷⠶⠞⠂⠾⠀⠼⢼⣤⠺⠶⠔⠴⠶⠀⠐⠂⠀⠐⠦⠀⠠⠄⠀⠖⠀⠀⠀⠀⠀⠤⠸⠣⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠲⠊⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠂⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠀⠄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣴⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠈⠀⠀⠛⠈⠀⠀⠊⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠋⠁⠀⠀⠀⠐⠀⠀⠀⠘⠀⠔⠐⠀⠂⠀⠀⠀⠀⠠⠅⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⣤⢤⠀⠄⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠿⠶⠶⠶⠀⠼⢠ ⠣⠚⠛⠛⠛⠛⠛⠛⠛⠙⠛⠙⠛⠛⠛⠛⠛⠛⠛⠓⠛⠛⠛⠛⠛⠂⠒⠐⠂⠂⠒⠒⠐⠂⠂⠒⠐⠐⠂⠒⠒⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣶⣾ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠸⢷⠾⠴⠶⠶⠦⠅⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠾⠶⠶⠾⠶⠴⠶⠄⠀⠐⠐⠒⠂⠒⠐⠐⠀⠂⠀⢬ ⡇⠯⠶⠧⠶⢶⣶⡤⠆⠸⠆⠷⠶⠶⠆⠸⠷⠶⠲⠶⠺⠆⠸⠶⠶⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⡀⠀⠀⠀⠸⠷⠗⢚⠿⠆⠐⠶⠖⠆⠀⠶⠄⠀⠀⠀⠀⠀⠀⢸ ⡇⠟⠿⠿⠧⠂⠀⠀⠀⠰⠶⠶⠢⠶⠶⠶⠶⠆⠸⠷⠶⠲⠰⠶⠶⠂⠰⠶⠶⢶⡺⠳⠶⠶⠶⠖⠐⠗⠶⠷⠰⠀⣷⡿⠿⠶⠶⠆⠧⠖⠗⠂⡆⠂⠄⠀⠀⠀⠘⠓⠃⠘⠓⠣⠒⠒⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡷⠻⠖⠷⠷⠶⠖⠆⠀⠰⠷⠶⠲⠆⢸⠢⠴⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠶⠖⡇⠖⡦⠀⠀⠰⠢⠶⡴⠆⠰⠲⠶⠶⠄⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡟⠒⠶⠖⠶⢶⡶⢶⡶⠶⠆⠆⠀⠀⣄⠀⠀⠰⠆⠰⠦⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡘ ⡟⠗⠒⡾⡲⠧⠆⠀⠀⠀⠆⠐⢲⡆⠶⠖⠆⠰⠐⠾⠖⠺⠴⠐⢾⠆⠾⠚⠚⠺⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣏⡧⠆⠲⠖⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢃ ⠑⠰⠶⠒⠖⠲⠀⠤⠠⠄⠠⠀⠤⠠⠄⠠⠀⠤⠠⠄⠠⠀⠄⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠆⠇⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠽ ⡆⠈⠓⠛⠛⠛⠓⡻⠛⠊⠉⠙⠛⠋⠚⠛⠉⠛⠛⠙⠚⠛⠛⠛⠙⠛⠓⠓⠛⠛⠙⠛⠓⠋⠛⠙⠛⠛⠛⠚⠛⠛⠚⠛⠛⠙⠙⢻⢳⠛⠞⠛⠛⠓⠚⠛⠛⠓⠛⠛⠛⠙⠛⠛⠓⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠛⠁⠠ ⡇⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀ ⡇⠀⠤⡷⠖⠳⠔⠳⠶⠦⠀⠰⠶⠷⠆⠰⠄⠀⠗⠷⠺⠿⠖⠂⠶⠿⠾⠀⠷⠷⠖⠟⠷⠶⠿⠷⠰⠷⠷⠿⠧⠶⠞⠨⠿⠾⠶⠶⠿⠯⠧⠿⠿⠾⠷⠷⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡇⠀⠀⠀⠆⠷⠷⠷⠐⠷⠷⠶⠠⠶⠶⢶⡶⠷⠖⠶⠖⠄⠠⠿⠿⠿⠿⠷⠿⠷⠇⠀⠇⠰⠷⠷⠸⠿⠷⠖⠆⠇⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠤⠤⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⣀⠒⠒⢂⠐⡖⠒⠒⢒⣲⣶⡖⠒⠖⠀⠒⡀⢀⣀⡐⠀⠀⢶⠒⠒⣀⡂⠘⠀⣀⡀⠀⠀⠀⡀⠀⣀⠀⢠⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠁⢷⡶⠴⠤⠦⠦⡷⠀⠰⠶⠶⠆⠐⠂⡷⡷⠇⠲⢾⠽⠥⠰⡿⡷⡧⠰⡿⠷⠷⠷⠷⠷⠷⠷⠿⠧⠠⠧⠲⠾⠷⠸⠶⠿⠿⠾⠿⠿⠳⠿⠿⠿⠯⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠰⠷⠷⠰⠿⠷⠖⠆⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢀⣀⣁⡙⠛⠉⡉⡉⠙⠁⠨⠄⠐⠀⠐⠀⣈⡉⢑⢤⡀⠀⠐⠀⠉⠩⠉⠩⠠⠠⠀⠄⠠⠤⠀⠠⠀⠄⠂⠀⠀⠄⠄⠠⠀⠤⠄⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠔⠉⠍⠥⠄⠴⠴⠆⠀⠰⠶⠿⠶⠀⠆⠀⡶⠆⠶⠶⠲⠀⠀⠷⠧⠿⠿⠷⠷⠷⢷⠶⠶⠾⠶⢶⠖⠲⠶⠶⠷⠾⠗⠷⠾⠶⡷⠞⠗⢷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠄⠷⠵⠕⠠⠲⣷⠆⠐⠶⡆⠾⠆⠐⠒⠂⠀⠀⠸⠶⠶⢷⠺⢞⠶⠾⠂⠸⠃⠤⠷⠃⠾⠿⠴⠦⠾⠐⠀⠀⠐⠂⠐⠂⠀⠂⠀⠀⠀⠒⠀⠀⠒⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣀⣄⣀⣀⡀⠀⠄⠄⠀⢠⣤⣤⡄⢀⠀⢠⠤⠀⣠⡤⠤⠀⠤⠤⠠⠀⠤⠤⠤⠤⠀⠠⠠⠠⠶⠦⠴⠤⠦⠀⠀⠂⠠⠄⠠⠤⠤⠤⠤⠄⠤⠄⠤⠤⠤⠤⠄⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠩⠍⠝⠤⡤⠶⡇⠀⠀⠩⠴⠇⠰⠆⠰⠿⠆⠸⠴⠤⠀⠶⠿⠾⠀⠶⠿⠾⠾⠒⠶⠾⠿⣀⠶⠶⠧⢷⠶⢷⡶⠼⠷⠰⠶⠵⠶⠿⠷⠿⠷⠶⠶⠗⠾⠇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠆⠗⠳⠄⠠⠶⠷⠀⠠⠒⠶⢂⠔⠶⠖⠲⢦⠄⠰⠤⠶⠮⠿⠟⠾⠗⠀⠨⠀⠵⠾⠀⠻⠿⠖⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⣠⣤⣤⣀⠀⡀⠤⠄⠀⢠⣤⣤⡄⢠⠄⢠⠤⠀⢠⣤⡀⠀⠢⠘⠐⠀⠐⠀⠀⠀⠀⠤⡤⠠⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠩⠶⡦⠐⠰⠦⠇⠀⠈⠌⢼⢦⠴⠄⠸⠿⠆⠨⠡⠲⠂⠾⠶⠶⠲⠶⠶⠀⠶⠀⠺⣿⢷⠾⠟⠶⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠇⠶⠶⠷⠰⠷⠷⠆⠰⠴⠶⢶⠶⠶⠲⠶⠦⠀⠰⠶⠾⠮⠿⠷⠶⠞⠂⠾⠀⠼⢼⣤⠺⠶⠔⠴⠶⠀⠐⠂⠀⠐⠦⠀⠠⠄⠀⠖⠀⠀⠀⠀⠀⠤⠸⠣⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠲⠊⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠂⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠀⠄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣴⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠈⠀⠀⠛⠈⠀⠀⠊⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠋⠁⠀⠀⠀⠐⠀⠀⠀⠘⠀⠔⠐⠀⠂⠀⠀⠀⠀⠠⠅⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⣤⢤⠀⠄⢸ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠿⠶⠶⠶⠀⠼⢠ ⠣⠚⠛⠛⠛⠛⠛⠛⠛⠙⠛⠙⠛⠛⠛⠛⠛⠛⠛⠓⠛⠛⠛⠛⠛⠂⠒⠐⠂⠂⠒⠒⠐⠂⠂⠒⠐⠐⠂⠒⠒⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣶⣾ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠸⢷⠾⠴⠶⠶⠦⠅⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠾⠶⠶⠾⠶⠴⠶⠄⠀⠐⠐⠒⠒⠒⠐⠒⠀⠂⠀⢌ ⡇⠿⠶⠧⠶⢶⣶⡤⠆⠸⠆⠷⠶⠶⠆⠸⠷⠶⠲⠶⠺⠆⠰⠶⠶⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⡀⠀⠀⠀⠸⠷⠗⠚⠿⠆⠐⠾⠖⠆⠀⠶⠄⠀⠀⠀⠀⠀⠀⢸ ⡇⠗⠿⠿⠷⠂⠀⠀⠀⠰⠶⠶⠢⠶⠦⠶⠶⠆⠸⠷⠶⠲⠰⠶⠶⠂⠰⠶⠶⠶⠺⠳⠶⠶⠶⠖⠒⠗⠶⠷⠴⠀⣷⡿⠿⠶⠶⠆⠧⠖⠗⠂⡆⠂⠄⠀⠀⠀⠘⠓⠃⠚⠓⠣⠒⠒⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡷⠻⠖⠷⠷⠶⠗⠆⠀⠰⠷⠶⠲⠆⢸⠂⠴⠆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠶⠖⠇⠆⣦⠀⠀⠐⠢⠶⠔⠆⠰⠲⠶⠶⠄⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡟⠒⠶⠖⠶⢶⡶⢶⡶⠶⠆⠆⠀⠀⣄⠀⠀⠰⠆⠰⠦⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡘ ⡟⠗⠓⡾⠲⠷⠆⠀⠀⠀⠆⠐⢲⡆⠶⠖⠆⠰⡀⠾⠖⠲⠄⠔⢾⡆⠾⠚⠚⠺⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣏⡧⠆⠲⠖⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠞⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢃ ⠑⠰⠶⠒⠖⠲⠀⠤⠠⠄⠠⠀⠤⠠⠄⠠⠀⠤⠠⠄⠠⠀⠄⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠆⠏⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠽ ⡆⠈⠓⠛⠛⠛⠓⡻⠛⠋⠉⠙⠛⠋⠛⠛⠉⠛⠛⠙⠚⠛⠛⠛⠙⠛⠓⠓⠛⠛⠙⠛⠓⠋⠛⠙⠛⠛⠛⠚⠛⠛⠚⠛⠛⠙⠙⢻⢳⠛⠞⠛⠛⠛⠚⠛⠛⠓⠛⠛⠛⠙⠛⠛⠓⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠛⠁⠠ ⡇⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀ ⡇⠀⠤⠷⠖⠳⠔⠣⠶⡦⠀⠰⠖⠷⠆⠐⠆⠀⠗⠆⠰⠿⠖⠂⠰⠿⠷⡄⠷⠷⠶⠖⠶⠶⠼⠦⠰⠶⠷⠻⠤⠶⠖⠪⠿⠾⠶⠾⠿⠿⠾⠧⠿⠾⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⡇⠀⠀⠀⠇⠶⠷⠶⠰⠷⠷⠆⠠⠲⠶⢶⡦⠶⠂⠶⠆⠄⠰⠶⠶⠶⠴⠿⠷⠇⠆⠐⠂⠰⠖⠆⠐⠾⠧⠒⠆⠇⠀⠀⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⣀⠒⠒⢂⠐⡖⠒⠒⢒⣲⣶⡖⠒⠖⠀⠒⡀⢀⣀⡐⠀⠀⢶⠒⠒⣀⡂⠘⠀⣀⡀⠀⠀⠀⡀⠀⣀⠀⢠⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠠⠷⡶⠤⠄⡦⡶⡧⠀⠰⠖⠶⠦⠀⠂⠷⠶⠗⠲⢾⠷⠄⠰⠾⠷⡆⠰⠾⠗⠶⠶⠷⠷⠶⠦⠷⠇⠰⠢⠶⠾⠶⠰⠶⠷⠶⠶⠺⠓⠳⠖⠿⠿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠰⠷⠆⠸⠾⠧⠲⠆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⢀⣀⣁⡙⠛⠉⡉⡉⠙⠁⠩⠅⠐⠀⠑⠀⣈⡉⢙⢤⡉⠉⠙⠉⠉⠩⠉⠡⠠⠠⠀⠄⠠⠤⠀⠠⠀⠄⠂⠀⠀⠄⠄⠠⠄⠤⠄⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⡇⠀⠔⠍⠍⠥⠄⠤⠶⠆⠀⠰⠶⠶⠶⠀⠆⠠⠷⠦⠰⠶⠶⠄⠀⠶⠄⠾⠷⠶⠶⠶⠶⠶⠾⠿⠷⠶⠖⠰⠦⠲⠶⠾⠚⠶⠾⠴⡦⠎⠗⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠄⠶⠵⠷⠀⠻⠷⠖⠰⠶⡦⠶⡶⠃⠒⠂⠄⠀⠠⠶⠶⠵⠷⣾⠿⠇⠂⠸⠂⠠⠷⠇⠸⠷⠦⠢⠌⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⣀⣄⣀⣀⠀⠀⠄⠄⠀⠠⣤⣤⡄⢀⠀⢠⠤⠀⣠⡤⠤⠀⠤⠤⠠⠀⠤⠤⠤⠤⠀⠤⠠⠠⠶⠦⠴⠤⠦⠀⠀⠂⠠⠄⠠⠤⠤⠤⠤⠄⠤⠄⠤⠤⠤⠤⠄⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠ ⡇⠀⠀⠭⠍⠽⠄⠤⠶⠦⠀⠀⠩⠶⠗⠰⠆⠰⠿⠆⠰⠵⠦⠖⠰⠿⠾⠅⠰⠾⠾⠾⠒⠶⠷⠿⡇⠴⠶⠧⢵⠶⠶⡦⠴⠶⠂⠰⠶⠶⠾⠾⠷⠾⠾⠴⠎⠿⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠆⠗⠳⠔⠠⠷⠷⠀⠠⠒⠶⢂⠔⠶⠆⠲⢦⠄⠰⠬⠶⠶⠽⠟⠿⠇⠀⠠⠄⠼⠿⠆⠲⠾⠗⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⣠⣤⣤⣀⠀⡀⠤⠄⠀⢠⣤⣤⡄⢠⠄⢠⠤⠀⣠⣤⡀⠀⠢⠘⠐⠀⠐⠀⠀⠀⠀⠤⡤⠠⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠭⠶⡦⠐⠰⠗⠇⠀⠘⠼⠽⢦⠤⠄⠸⠿⠇⠨⠡⠢⠃⠸⠷⠶⠶⠶⠶⠀⠶⠀⠚⣿⠷⠾⠟⠷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠇⠶⠷⠷⠰⠷⠷⠆⠰⠰⠶⢶⠶⠶⠒⠶⠦⠀⠰⠶⠶⠥⠵⠿⠷⠗⠂⠾⠅⠼⠴⢇⠺⠷⠔⠴⠶⠀⠐⠂⠀⠐⠦⠀⠠⠄⠀⠖⠐⠀⠀⠀⠀⠤⠸⠣⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⡇⠀⠀⠀⠀⠀⠲⠊⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠂⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⡇⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠀⠄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣴⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠ ⡇⠀⠀⠀⠀⠈⠀⠀⠛⠈⠀⠀⠊⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠋⠁⠀⠀⠀⠒⠀⠀⠀⠘⠀⠔⠐⠀⠂⠀⠀⠀⠀⠠⠅⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⣤⢤⠀⠄⢨ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠿⠶⠶⠶⠤⠼⠰ ⠣⠚⠛⠛⠛⠛⠛⠛⠛⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠛⠛⠛⠛⠛⠂⠒⠒⠒⠂⠒⠒⠐⠂⠒⠒⠒⠒⠂⠒⠒⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣶⣶ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠸⢷⠾⠴⠶⠶⠦⠅⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠾⠶⠶⠾⠶⠴⠶⠄⠀⠐⠐⠒⠒⠒⠐⠒⠀⠀⠀⢌ ⡇⠿⠶⠧⠶⢶⣶⡤⠆⠸⠆⠷⠶⠶⠆⠸⠷⠶⠲⠶⠺⠆⠰⠶⠶⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⡀⠀⠀⠀⠸⠷⠗⠚⠿⠆⠐⠾⠖⠆⠀⠶⠄⠀⠁⠀⠀⠀⠀⢹ ⡇⠟⠿⠿⠷⠂⠀⠀⠀⠰⠶⠶⠢⠶⠦⠶⠶⠆⠸⠷⠶⠲⠰⠶⠶⠂⠰⠶⠶⠶⠺⠳⠶⠶⠶⠖⠒⠗⠶⠷⠴⠀⣷⡿⠿⠶⠶⠆⠧⠖⠗⠂⡆⠂⠄⠀⠀⠀⠘⠓⠃⠚⠓⠣⠒⠒⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡷⠻⠖⠷⠷⠶⠗⠆⠀⠰⠷⠶⠲⠆⢸⠂⠴⠆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠶⠖⠇⠆⣦⠀⠀⠐⠢⠶⠔⠆⠰⠲⠶⠶⠄⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡟⠒⠶⠖⠶⢶⡶⢶⡶⠶⠆⠆⠀⠀⣄⠀⠀⠰⠆⠰⠦⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡘ ⡟⠗⠓⡾⠲⠷⠆⠀⠀⠀⠆⠐⢲⡆⠶⠖⠆⠰⡀⠾⠖⠲⠄⠔⢾⡆⠾⠚⠚⠺⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣏⡧⠆⠲⠖⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠞⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠛⠛⢃ ⠑⠰⠶⠒⠖⠲⠀⠤⠠⠄⠠⠀⠤⠠⠄⠠⠀⠤⠠⠄⠠⠀⠄⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠆⠏⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠽ ⡆⠈⠓⠛⠛⠛⠓⡻⠛⠋⠉⠙⠛⠋⠛⠛⠉⠛⠛⠙⠚⠛⠛⠛⠙⠛⠓⠓⠛⠛⠙⠛⠓⠋⠛⠙⠛⠛⠛⠚⠛⠛⠚⠛⠛⠙⠙⢻⢳⠛⠞⠛⠛⠛⠚⠛⠛⠓⠛⠛⠛⠙⠛⠛⠓⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠛⠁⠠ ⡇⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀ ⡇⠀⠤⠷⠖⠳⠔⠣⠶⡦⠀⠰⠖⠷⠆⠐⠆⠀⠗⠆⠰⠿⠖⠂⠰⠿⠷⡄⠷⠷⠶⠖⠶⠶⠼⠦⠰⠶⠷⠻⠤⠶⠖⠪⠿⠾⠶⠾⠿⠿⠾⠧⠿⠾⠶⠶⠆⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⡇⠀⠀⠀⠇⠶⠷⠶⠰⠷⠷⠆⠠⠲⠶⢶⡦⠶⠂⠶⠆⠄⠰⠶⠶⠶⠴⠿⠷⠇⠆⠐⠂⠰⠖⠎⠐⠾⠧⠒⠆⠇⠀⠐⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⣀⠒⠒⢂⠐⡖⠒⠒⢒⣲⣶⡖⠒⠖⠀⠒⡀⢀⣀⡐⠀⠀⢶⠒⠒⣀⡂⠘⠀⣀⡀⠀⠀⠀⡀⠀⣀⠀⢠⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠠⠷⡶⠤⠄⡦⡶⡯⠐⠰⠖⠶⠦⠀⠂⠷⠶⠗⠲⢾⠷⠄⠰⠾⠷⡆⠰⠾⠗⠶⠶⠷⠷⠶⠦⠷⠇⠰⠢⠶⠾⠶⠰⠶⠷⠶⠶⠺⠓⠳⠖⠿⠿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠰⢷⡆⠸⠾⠧⠲⠆⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⢀⣀⣁⡙⠛⠉⡉⡉⠙⠁⠩⠅⠐⠀⠑⠀⣈⡉⢙⢤⡀⠈⠙⠉⠉⠡⠉⠡⠠⠠⠀⠄⠠⠤⠀⠠⠀⠄⠂⠀⠀⠄⠄⠠⠄⠤⠄⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⡇⠀⠔⠍⠍⠥⠄⠤⠶⠆⠀⠰⠶⠶⠶⠀⠆⠠⠷⠦⠰⠶⠶⠄⠀⠶⠄⠾⠷⠶⠶⠶⠶⠶⠾⠿⠷⠶⠖⠰⠦⠲⠶⠾⠚⠶⠾⠴⡦⠎⠗⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠄⠶⠵⠷⠐⠺⠷⠖⠰⠶⡦⠶⡶⠃⠒⠂⠄⠀⠠⠶⠶⠵⠷⣾⠿⠇⠂⠸⠂⠨⠷⠇⠸⠷⠦⠢⠌⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⣀⣄⣀⣀⠀⠀⠄⠄⠀⠠⣤⣤⡄⢀⠀⢠⠤⠀⣠⡤⠤⠀⠤⠤⠠⠀⠤⠤⠤⠤⠀⠤⠠⠠⠶⠦⠴⠤⠦⠀⠀⠂⠠⠄⠠⠤⠤⠤⠤⠄⠤⠄⠤⠤⠤⠤⠄⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠ ⡇⠀⠀⠭⠍⠽⠄⠤⠶⠦⠀⠀⠩⠶⠗⠰⠆⠰⠿⠆⠰⠵⠦⠖⠰⠿⠾⠅⠰⠾⠾⠾⠒⠶⠷⠿⡇⠴⠶⠧⢵⠶⠶⡦⠴⠶⠂⠰⠶⠶⠾⠾⠷⠾⠾⠴⠎⠿⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠆⠗⠳⠔⠠⠷⠷⠄⠠⠒⠶⢂⠔⠶⠆⠲⢦⠄⠰⠬⠶⠶⠽⠟⠿⠇⠀⠠⠄⠼⠿⠆⠲⠾⠗⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⣠⣤⣤⣀⠀⡀⠤⠄⠀⢠⣤⣤⡄⢠⠄⢠⠤⠀⣠⣤⡀⠀⠢⠘⠐⠀⠐⠀⠀⠀⠀⠤⡤⠠⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠭⠶⡦⠐⠰⠗⠆⠀⠘⠼⠽⢦⠤⠄⠸⠿⠇⠨⠡⠢⠃⠸⠷⠶⠶⠶⠶⠀⠶⠀⠚⣿⠷⠾⠟⠷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠇⠶⠷⠷⠰⠷⠷⠆⠰⠰⠶⢶⠶⠶⠒⠶⠦⠀⠰⠶⠶⠥⠵⠿⠷⠗⠂⠾⠅⠼⠴⢇⠺⠷⠔⠴⠶⠤⠐⠂⠀⠐⠢⠀⠠⠄⠀⠖⠐⠀⠀⠀⠀⠤⠸⠣⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⡇⠀⠀⠀⠀⠀⠲⠊⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠂⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⡇⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠀⠄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣴⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠ ⡇⠀⠀⠀⠀⠈⠀⠀⠛⠈⠀⠀⠊⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠋⠁⠀⠀⠀⠒⠀⠀⠀⠘⠀⠔⠐⠀⠂⠀⠀⠀⠀⠠⠅⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⣤⢤⠀⠄⢨ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠿⠶⠶⠶⠤⠼⠰ ⠣⠚⠛⠛⠛⠛⠛⠛⠛⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠛⠛⠛⠛⠛⠂⠒⠒⠒⠂⠒⠒⠐⠂⠒⠒⠒⠒⠂⠒⠒⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣶⣶ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠸⢷⠾⠴⠶⠶⠦⠅⠁⠒⠒⠒⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠾⠶⠶⠾⠶⠴⠶⠄⠀⠐⠐⠒⠒⠒⠐⠒⠀⠀⠀⢌ ⡇⠿⠶⠧⠶⢶⣶⡤⠆⠸⠆⠷⠶⠶⠆⠸⠷⠶⠲⠶⠺⠆⠰⠶⠶⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⡀⠀⠀⠀⠸⠷⠗⠚⠿⠆⠐⠾⠖⠆⠀⠶⠄⠀⠁⠂⠀⠀⠀⢻ ⡇⠟⠿⠿⠷⠂⠀⠀⠀⠰⠶⠶⠢⠶⠦⠶⠶⠆⠸⠷⠶⠲⠰⠶⠶⠂⠰⠶⠶⠶⠺⠳⠶⠶⠶⠖⠒⠗⠶⠷⠰⠀⣷⡿⠿⠶⠶⠆⠧⠖⠗⠂⡆⠂⠄⠀⠀⠀⠘⠓⠃⠚⠓⠣⠒⠒⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡷⠻⠖⠷⠷⠶⠗⠆⠀⠰⠷⠶⠲⠆⢸⠂⠴⠆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠶⠖⠇⠆⣦⠀⠀⠐⠢⠶⠔⠆⠰⠲⠶⠶⠄⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡟⠒⠶⠖⠶⢶⡶⢶⡶⠶⠆⠆⠀⠀⣄⠀⠀⠰⠆⠰⠦⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡘ ⡟⠗⠓⡾⠲⠷⠆⠀⠀⠀⠆⠐⢲⡆⠶⠖⠆⠰⡀⠾⠖⠲⠄⠔⢾⡆⠾⠚⠚⠺⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣏⡧⠆⠲⠖⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠞⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠛⠛⢃ ⠑⠰⠶⠒⠖⠲⠀⠤⠠⠄⠠⠀⠤⠠⠄⠠⠀⠤⠠⠄⠠⠀⠄⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠆⠇⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠽ ⡆⠈⠓⠛⠛⠛⠓⡻⠛⠋⠉⠙⠛⠋⠛⠛⠉⠛⠛⠙⠚⠛⠛⠛⠙⠛⠓⠓⠛⠛⠙⠛⠓⠋⠛⠙⠛⠛⠛⠚⠛⠛⠚⠛⠛⠙⠙⢻⢳⠛⠞⠛⠛⠛⠚⠛⠛⠓⠛⠛⠛⠙⠛⠛⠓⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠛⠁⠠ ⡇⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀ ⡇⠀⠤⠷⠖⠳⠔⠣⠶⡦⠀⠰⠖⠷⠆⠐⠆⠀⠗⠆⠰⠿⠖⠂⠰⠿⠷⡄⠷⠷⠖⠖⠶⠶⠼⠦⠰⠶⠷⠻⠤⠶⠖⠪⠿⠾⠶⠾⠿⠿⠾⠧⠿⠾⠶⠶⠆⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⡇⠀⠀⠀⠇⠶⠷⠶⠰⠷⠷⠆⠠⠲⠶⢶⡦⠶⠂⠶⠆⠄⠰⠶⠶⠶⠴⠿⠷⠇⠆⠐⠂⠰⠖⠞⠐⠾⠧⠒⠆⠇⠀⠰⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⣀⠒⠒⢂⠐⡖⠒⠒⢒⣲⣶⡖⠒⠖⠀⠒⡀⢀⣀⡐⠀⠀⢶⠒⠒⣀⡂⠘⠀⣀⡀⠀⠀⠀⡀⠀⣀⠀⢠⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠠⠷⡶⠤⠄⡦⡶⡯⠔⠰⠖⠶⠦⠀⠂⠷⠶⠗⠲⢾⠷⠄⠰⠾⠷⡆⠰⠾⠗⠶⠶⠷⠷⠶⠦⠷⠇⠰⠢⠶⠾⠶⠰⠶⠷⠶⠶⠺⠓⠳⠖⠿⠿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠰⢷⡦⠸⠾⠧⠲⠆⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⢀⣀⣁⡙⠛⠉⡉⡉⠙⠁⠩⠅⠐⠀⠑⠀⣈⡉⢙⢤⡀⠈⠙⠉⠉⠡⠉⠡⠠⠠⠈⠅⠠⠤⠀⠠⠀⠄⠂⠀⠀⠄⠄⠠⠄⠤⠄⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⡇⠀⠔⠍⠍⠥⠄⠤⠶⠆⠂⡰⠶⠶⠶⠀⠆⠠⠷⠦⠰⠶⠶⠄⠀⠶⠄⠾⠷⠶⠶⠶⠶⠶⠾⠿⠷⠶⠖⠰⠦⠲⠶⠾⠚⠶⠾⠴⡦⠎⠗⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠄⠶⠵⠷⠐⠲⠷⠖⠐⠶⡦⠶⡶⠃⠒⠂⠄⠄⠠⠶⠶⠵⠷⣾⠿⠇⠂⠸⠂⠸⠷⠧⠸⠷⠦⠢⠌⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⣀⣄⣀⣀⠀⠀⠄⠄⠀⠠⣤⣤⡄⢀⠀⢠⠤⠀⣠⡤⠤⠀⠤⠤⠠⠀⠤⠤⠤⠤⠀⠤⠠⠠⠶⠦⠴⠤⠦⠀⠀⠂⠠⠄⠠⠤⠤⠤⠤⠄⠤⠄⠤⠤⠤⠤⠄⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠ ⡇⠀⠀⠭⠍⠽⠄⠤⠶⠦⠀⠀⠩⠶⠗⠰⠆⠰⠿⠆⠰⠵⠦⠆⠰⠿⠾⠅⠰⠾⠾⠾⠒⠶⠷⠿⡇⠴⠶⠧⢵⠶⠶⡦⠴⠶⠂⠰⠶⠶⠾⠶⠷⠾⠾⠴⠎⠿⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠆⠗⠳⠄⠠⠷⠷⠆⠠⠒⠶⢂⠔⠶⠆⠲⢦⠄⠰⠬⠶⠶⠽⠟⠿⠇⠀⠠⠄⠾⠿⠦⠲⠾⠗⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⣠⣤⣤⣀⠀⡀⠤⠄⠀⢠⣤⣤⡄⢠⠄⢠⠤⠀⢠⣤⡀⠀⠢⠘⠐⠀⠐⠀⠀⠀⠀⠤⡤⠠⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠭⠶⡦⠐⠰⠗⠆⠀⠘⠼⠽⢦⠤⠄⠸⠿⠇⠨⠡⠢⠃⠸⠷⠶⠶⠶⠶⠀⠶⠀⠚⣿⠷⠾⠟⠷⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠇⠶⠷⠷⠰⠶⠷⠆⠰⠰⠶⢶⠶⠶⠒⠶⠦⠀⢰⡶⠶⠥⠵⠿⠷⠗⠂⠾⠅⠼⠴⢷⠺⠷⠔⠴⠶⣤⠐⠂⠀⠂⠢⠀⠠⠄⠀⠖⠀⠀⠀⠀⠀⠤⠸⠣⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⡇⠀⠀⠀⠀⠀⠲⠊⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠂⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⡇⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠀⠄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣴⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠ ⡇⠀⠀⠀⠀⠈⠀⠀⠛⠈⠀⠀⠊⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠋⠁⠀⠀⠀⠒⠀⠀⠀⠘⠀⠔⠐⠀⠂⠀⠀⠀⠀⠠⠅⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⣤⢤⠀⠄⢨ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠿⠶⠶⠶⠤⠼⠰ ⠣⠚⠛⠛⠛⠛⠛⠛⠛⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠛⠛⠛⠛⠛⠂⠒⠒⠒⠂⠒⠒⠐⠂⠒⠒⠒⠒⠂⠒⠒⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣶⣶ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠸⢷⠾⠴⠶⠶⠦⠅⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠾⠶⠶⠾⠶⠴⠶⠄⠀⠐⠐⠒⠒⠒⠐⠒⠀⠀⠀⢌ ⡇⠿⠶⠧⠶⢶⣶⡤⠆⠸⠆⠷⠶⠶⠆⠸⠷⠶⠲⠶⠺⠆⠰⠶⠶⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⡀⠀⠀⠀⠸⠷⠗⠚⠿⠆⠐⠾⠖⠆⠀⠶⠄⠀⠀⠂⠀⠀⠀⢻ ⡇⠟⠿⠿⠷⠂⠀⠀⠀⠰⠶⠶⠢⠶⠦⠶⠶⠆⠸⠷⠶⠲⠰⠶⠶⠂⠰⠶⠶⠶⠺⠳⠶⠶⠶⠖⠒⠗⠶⠷⠰⠀⣷⡿⠿⠶⠶⠆⠧⠖⠗⠂⡆⠂⠄⠀⠀⠀⠘⠓⠃⠘⠓⠣⠒⠒⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡷⠻⠖⠷⠷⠶⠗⠆⠀⠰⠷⠶⠲⠆⢸⠂⠴⠆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠶⠖⠇⠆⣦⠀⠀⠐⠢⠶⠔⠆⠰⠲⠶⠶⠄⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡟⠒⠶⠖⠶⢶⡶⢶⡶⠶⠆⠆⠀⠀⣄⠀⠀⠰⠆⠰⠦⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡘ ⡟⠗⠓⡾⠲⠷⠆⠀⠀⠀⠆⠐⢲⡆⠶⠖⠆⠰⡀⠾⠖⠲⠄⠔⢾⡆⠾⠚⠚⠺⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣏⡧⠆⠲⠖⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠞⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠛⠛⢃ ⠑⠰⠶⠒⠖⠲⠀⠤⠠⠄⠠⠀⠤⠠⠄⠠⠀⠤⠠⠄⠠⠀⠄⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠆⠇⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠽ ⡆⠈⠓⠛⠛⠛⠓⡻⠛⠋⠉⠙⠛⠋⠛⠛⠉⠛⠛⠙⠚⠛⠛⠛⠙⠛⠓⠓⠛⠛⠙⠛⠓⠋⠛⠙⠛⠛⠛⠚⠛⠛⠚⠛⠛⠙⠙⢻⢳⠛⠞⠛⠛⠛⠚⠛⠛⠓⠛⠛⠛⠙⠛⠛⠓⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠛⠁⠠ ⡇⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀ ⡇⠀⠤⠷⠖⠳⠔⠣⠶⡦⠀⠰⠖⠷⠆⠐⠆⠀⠗⠆⠰⠿⠖⠂⠰⠿⠷⡄⠷⠷⠖⠖⠶⠶⠼⠦⠰⠶⠷⠻⠤⠶⠖⠪⠿⠾⠶⠾⠿⠿⠾⠧⠿⠾⠶⠶⠆⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⡇⠀⠀⠀⠇⠶⠷⠶⠰⠷⠷⠆⠠⠲⠶⢶⡦⠶⠂⠶⠆⠄⠰⠶⠶⠶⠴⠿⠷⠇⠆⠐⠂⠰⠖⠞⠐⠾⠧⠒⠆⠇⠀⠰⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⣀⠒⠒⢂⠐⡖⠒⠒⢒⣲⣶⡖⠒⠖⠀⠒⡀⢀⣀⡐⠀⠀⢶⠒⠒⣀⡂⠘⠀⣀⡀⠀⠀⠀⡀⠀⣀⠀⢠⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠠⠷⡶⠤⠄⡦⡶⡯⠔⠰⠖⠶⠦⠀⠂⠷⠶⠗⠲⢾⠷⠄⠰⠾⠷⡆⠰⠾⠗⠶⠶⠷⠷⠶⠦⠷⠇⠰⠢⠶⠾⠶⠰⠶⠷⠶⠶⠺⠓⠳⠖⠿⠿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠰⢷⡦⠸⠾⠧⠲⠆⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⢀⣀⣁⡙⠛⠉⡉⡉⠙⠁⠩⠅⠐⠀⠑⠀⣈⡉⢙⢤⡈⠈⠙⠉⠉⠡⠉⠡⠠⠨⠈⠅⠠⠤⠀⠠⠀⠄⠂⠀⠀⠄⠄⠠⠄⠤⠄⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⡇⠀⠔⠍⠍⠥⠄⠤⠶⠆⠆⡰⠶⠶⠶⠀⠆⠠⠷⠦⠰⠶⠶⠄⠀⠶⠄⠾⠷⠶⠶⠶⠶⠶⠾⠿⠷⠶⠖⠰⠦⠲⠶⠾⠚⠶⠾⠴⡦⠎⠗⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠄⠶⠵⠷⠐⠲⠿⠖⠐⠶⡦⠶⡶⠃⠒⠂⠄⠆⠠⠶⠶⠵⠷⣾⠿⠇⠂⠸⠂⠸⠷⠧⠸⠷⠦⠢⠌⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⣀⣄⣀⣀⠀⠀⠄⠄⠀⠠⣤⣤⡄⢀⠀⢠⠤⠀⣠⡤⠤⠀⠤⠤⠠⠀⠤⠤⠤⠤⠀⠤⠠⠠⠶⠦⠴⠤⠦⠀⠀⠂⠠⠄⠠⠤⠤⠤⠤⠄⠤⠄⠤⠤⠤⠤⠄⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠ ⡇⠀⠀⠭⠍⠽⠄⠤⠶⠦⠀⠀⠩⠶⠗⠰⠆⠰⠿⠆⠰⠵⠦⠆⠰⠿⠾⠅⠰⠾⠾⠾⠒⠶⠷⠿⡇⠴⠶⠧⢵⠶⠶⡦⠴⠶⠂⠰⠶⠶⠾⠶⠷⠾⠾⠴⠎⠿⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠆⠗⠳⠄⠠⠷⠷⠆⠠⠒⠶⢂⠔⠶⠆⠲⢦⠆⠰⠬⠶⠶⠽⠟⠿⠇⠀⠠⠔⠾⠿⠆⠲⠾⠗⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⣠⣤⣤⣀⠀⡀⠤⠄⠀⢠⣤⣤⡄⢠⠄⢠⠤⠀⢠⣤⡀⠀⠢⠘⠐⠀⠐⠀⠀⠀⠀⠤⡤⠠⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠭⠶⡦⠐⠰⠗⠆⠀⠘⠼⠽⢦⠤⠄⠸⠿⠇⠨⠡⠢⠃⠸⠷⠶⠶⠶⠶⠀⠶⠀⠚⣿⠷⠾⠟⠷⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠇⠶⠷⠷⠰⠶⠷⠆⠰⠰⠶⢶⠶⠶⠒⠶⠦⠀⠴⡶⠶⠥⠵⠿⠷⠗⠂⠾⠅⠼⠴⢶⠺⠷⠔⠴⠶⣤⠐⠂⠀⠂⠢⠀⠠⠄⠀⠖⠀⠀⠀⠀⠀⠤⠸⠣⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⡇⠀⠀⠀⠀⠀⠲⠊⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠂⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⡇⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠀⠄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣴⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠ ⡇⠀⠀⠀⠀⠈⠀⠀⠛⠈⠀⠀⠊⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠋⠁⠀⠀⠀⠒⠀⠀⠀⠘⠀⠔⠐⠀⠂⠀⠀⠀⠀⠠⠅⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⣤⢤⠀⠄⢨ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠿⠶⠶⠶⠤⠼⠰ ⠣⠚⠛⠛⠛⠛⠛⠛⠛⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠛⠛⠛⠛⠛⠂⠒⠒⠒⠂⠒⠒⠐⠂⠒⠒⠒⠒⠂⠒⠒⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣶⣶ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠸⢷⠾⠴⠶⠶⠦⠅⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠾⠶⠶⠾⠶⠴⠶⠄⠀⠐⠐⠒⠒⠒⠐⠒⠀⠀⠀⢌ ⡇⠿⠶⠧⠶⢶⣶⡤⠆⠸⠆⠷⠶⠶⠆⠸⠷⠶⠲⠶⠺⠆⠰⠶⠶⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⡀⠀⠀⠀⠸⠷⠗⠚⠿⠆⠐⠾⠖⠆⠀⠶⠄⠀⠀⠂⠀⠀⠀⢻ ⡇⠟⠿⠿⠷⠂⠀⠀⠀⠰⠶⠶⠢⠶⠦⠶⠶⠆⠸⠷⠶⠲⠰⠶⠶⠂⠰⠶⠶⠶⠺⠳⠶⠶⠶⠖⠒⠗⠶⠷⠰⠀⣷⡿⠿⠶⠶⠆⠧⠖⠗⠂⡆⠂⠄⠀⠀⠀⠘⠓⠃⠘⠓⠣⠒⠒⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡷⠻⠖⠷⠷⠶⠗⠆⠀⠰⠷⠶⠲⠆⢸⠂⠴⠆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠶⠖⠇⠆⣦⠀⠀⠐⠢⠶⠔⠆⠰⠲⠶⠶⠄⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡟⠒⠶⠖⠶⢶⡶⢶⡶⠶⠆⠆⠀⠀⣄⠀⠀⠰⠆⠰⠦⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡘ ⡟⠗⠓⡾⠲⠷⠆⠀⠀⠀⠆⠐⢲⡆⠶⠖⠆⠰⡀⠾⠖⠲⠄⠔⢾⡆⠾⠚⠚⠺⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣏⡧⠆⠲⠖⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠞⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠛⠛⢃ ⠑⠰⠶⠒⠖⠲⠀⠤⠠⠄⠠⠀⠤⠠⠄⠠⠀⠤⠠⠄⠠⠀⠄⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠆⠇⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠽ ⡆⠈⠓⠛⠛⠛⠓⡻⠛⠋⠉⠙⠛⠋⠛⠛⠉⠛⠛⠙⠚⠛⠛⠛⠙⠛⠓⠓⠛⠛⠙⠛⠓⠋⠛⠙⠛⠛⠛⠚⠛⠛⠚⠛⠛⠙⠙⢻⢳⠛⠞⠛⠛⠛⠚⠛⠛⠓⠛⠛⠛⠙⠛⠛⠓⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠛⠁⠠ ⡇⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀ ⡇⠀⠤⠷⠖⠳⠔⠣⠶⡦⠀⠰⠖⠷⠆⠐⠆⠀⠗⠆⠰⠿⠖⠂⠰⠿⠷⡄⠷⠷⠖⠖⠶⠶⠼⠦⠰⠶⠷⠻⠤⠶⠖⠪⠿⠾⠶⠾⠿⠿⠾⠧⠿⠾⠶⠶⠆⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⡇⠀⠀⠀⠇⠶⠷⠶⠰⠷⠷⠆⠠⠲⠶⢶⡦⠶⠂⠶⠆⠄⠰⠶⠶⠶⠴⠿⠷⠇⠆⠐⠂⠰⠖⠞⠐⠾⠧⠒⠆⠇⠀⠰⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⣀⠒⠒⢂⠐⡖⠒⠒⢒⣲⣶⡖⠒⠖⠀⠒⡀⢀⣀⡐⠀⠀⢶⠒⠒⣀⡂⠘⠀⣀⡀⠀⠀⠀⡀⠀⣀⠀⢠⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠠⠷⡶⠤⠄⡦⡶⡯⠔⠰⠖⠶⠦⠀⠂⠷⠶⠗⠲⢾⠷⠄⠰⠾⠷⡆⠰⠾⠗⠶⠶⠷⠷⠶⠦⠷⠇⠰⠢⠶⠾⠶⠰⠶⠷⠶⠶⠺⠓⠳⠖⠿⠿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠰⢷⡦⠸⠾⠧⠲⠆⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⢀⣀⣁⡙⠛⠉⡉⡉⠙⠁⠩⠅⠐⠀⠑⠀⣈⡉⢙⢤⡈⠈⠙⠉⠉⠡⠉⠡⠠⠨⠈⠅⠠⠤⠀⠠⠀⠄⠂⠀⠀⠄⠄⠠⠄⠤⠄⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⡇⠀⠔⠍⠍⠥⠄⠤⠶⠆⠆⡰⠶⠶⠶⠀⠆⠠⠷⠦⠰⠶⠶⠄⠀⠶⠄⠾⠷⠶⠶⠶⠶⠶⠾⠿⠷⠶⠖⠰⠦⠲⠶⠾⠚⠶⠾⠴⡦⠎⠗⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠄⠶⠵⠷⠐⠲⠿⠖⠐⠶⡦⠶⡶⠃⠒⠂⠄⠆⠠⠶⠶⠵⠷⣾⠿⠇⠂⠸⠂⠸⠷⠧⠸⠷⠦⠢⠌⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⣀⣄⣀⣀⠀⠀⠄⠄⠀⠠⣤⣤⡄⢀⠀⢠⠤⠀⣠⡤⠤⠀⠤⠤⠠⠀⠤⠤⠤⠤⠀⠤⠠⠠⠶⠦⠴⠤⠦⠀⠀⠂⠠⠄⠠⠤⠤⠤⠤⠄⠤⠄⠤⠤⠤⠤⠄⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠ ⡇⠀⠀⠭⠍⠽⠄⠤⠶⠦⠀⠀⠩⠶⠗⠰⠆⠰⠿⠆⠰⠵⠦⠆⠰⠿⠾⠅⠰⠾⠾⠾⠒⠶⠷⠿⡇⠴⠶⠧⢵⠶⠶⡦⠴⠶⠂⠰⠶⠶⠾⠶⠷⠾⠾⠴⠎⠿⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠆⠗⠳⠄⠠⠷⠷⠆⠠⠒⠶⢂⠔⠶⠆⠲⢦⠆⠰⠬⠶⠶⠽⠟⠿⠇⠀⠠⠔⠾⠿⠆⠲⠾⠗⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⣠⣤⣤⣀⠀⡀⠤⠄⠀⢠⣤⣤⡄⢠⠄⢠⠤⠀⢠⣤⡀⠀⠢⠘⠐⠀⠐⠀⠀⠀⠀⠤⡤⠠⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠭⠶⡦⠐⠰⠗⠆⠀⠘⠼⠽⢦⠤⠄⠸⠿⠇⠨⠡⠢⠃⠸⠷⠶⠶⠶⠶⠀⠶⠀⠚⣿⠷⠾⠟⠷⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠇⠶⠷⠷⠰⠶⠷⠆⠰⠰⠶⢶⠶⠶⠒⠶⠦⠀⠴⡶⠶⠥⠵⠿⠷⠗⠂⠾⠅⠼⠴⢶⠺⠷⠔⠴⠶⣤⠐⠂⠀⠂⠢⠀⠠⠄⠀⠖⠀⠀⠀⠀⠀⠤⠸⠣⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⡇⠀⠀⠀⠀⠀⠲⠊⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠂⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⡇⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠀⠄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣴⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠ ⡇⠀⠀⠀⠀⠈⠀⠀⠛⠈⠀⠀⠊⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠋⠁⠀⠀⠀⠒⠀⠀⠀⠘⠀⠔⠐⠀⠂⠀⠀⠀⠀⠠⠅⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⣤⢤⠀⠄⢨ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠿⠶⠶⠶⠤⠼⠰ ⠣⠚⠛⠛⠛⠛⠛⠛⠛⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠛⠛⠛⠛⠛⠂⠒⠒⠒⠂⠒⠒⠐⠂⠒⠒⠒⠒⠂⠒⠒⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣶⣶ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠸⢷⠾⠴⠶⠶⠦⠅⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠾⠶⠶⠾⠶⠴⠶⠄⠀⠐⠐⠒⠒⠒⠐⠒⠀⠀⠀⢌ ⡇⠿⠶⠧⠶⢶⣶⡤⠆⠸⠆⠷⠶⠶⠆⠸⠷⠶⠲⠶⠺⠆⠰⠶⠶⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⡀⠀⠀⠀⠸⠷⠗⠚⠿⠆⠐⠾⠖⠆⠀⠶⠄⠀⠀⠂⠀⠀⠀⢻ ⡇⠟⠿⠿⠷⠂⠀⠀⠀⠰⠶⠶⠢⠶⠦⠶⠶⠆⠸⠷⠶⠲⠰⠶⠶⠂⠰⠶⠶⠶⠺⠳⠶⠶⠶⠖⠒⠗⠶⠷⠰⠀⣷⡿⠿⠶⠶⠆⠧⠖⠗⠂⡆⠂⠄⠀⠀⠀⠘⠓⠃⠘⠓⠣⠒⠒⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡷⠻⠖⠷⠷⠶⠗⠆⠀⠰⠷⠶⠲⠆⢸⠂⠴⠆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠶⠖⠇⠆⣦⠀⠀⠐⠢⠶⠔⠆⠰⠲⠶⠶⠄⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡟⠒⠶⠖⠶⢶⡶⢶⡶⠶⠆⠆⠀⠀⣄⠀⠀⠰⠆⠰⠦⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡘ ⡟⠗⠓⡾⠲⠷⠆⠀⠀⠀⠆⠐⢲⡆⠶⠖⠆⠰⡀⠾⠖⠲⠄⠔⢾⡆⠾⠚⠚⠺⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣏⡧⠆⠲⠖⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠞⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠛⠛⢃ ⠑⠰⠶⠒⠖⠲⠀⠤⠠⠄⠠⠀⠤⠠⠄⠠⠀⠤⠠⠄⠠⠀⠄⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠆⠇⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠽ ⡆⠈⠓⠛⠛⠛⠓⡻⠛⠋⠉⠙⠛⠋⠛⠛⠉⠛⠛⠙⠚⠛⠛⠛⠙⠛⠓⠓⠛⠛⠙⠛⠓⠋⠛⠙⠛⠛⠛⠚⠛⠛⠚⠛⠛⠙⠙⢻⢳⠛⠞⠛⠛⠛⠚⠛⠛⠓⠛⠛⠛⠙⠛⠛⠓⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠛⠁⠠ ⡇⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀ ⡇⠀⠤⠷⠖⠳⠔⠣⠶⡦⠀⠰⠖⠷⠆⠐⠆⠀⠗⠆⠰⠿⠖⠂⠰⠿⠷⡄⠷⠷⠖⠖⠶⠶⠼⠦⠰⠶⠷⠻⠤⠶⠖⠪⠿⠾⠶⠾⠿⠿⠾⠧⠿⠾⠶⠶⠆⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⡇⠀⠀⠀⠇⠶⠷⠶⠰⠷⠷⠆⠠⠲⠶⢶⡦⠶⠂⠶⠆⠄⠰⠶⠶⠶⠴⠿⠷⠇⠆⠐⠂⠰⠖⠞⠐⠾⠧⠒⠆⠇⠀⠰⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⣀⠒⠒⢂⠐⡖⠒⠒⢒⣲⣶⡖⠒⠖⠀⠒⡀⢀⣀⡐⠀⠀⢶⠒⠒⣀⡂⠘⠀⣀⡀⠀⠀⠀⡀⠀⣀⠀⢠⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠠⠷⡶⠤⠄⡦⡶⡯⠔⠰⠖⠶⠦⠀⠂⠷⠶⠗⠲⢾⠷⠄⠰⠾⠷⡆⠰⠾⠗⠶⠶⠷⠷⠶⠦⠷⠇⠰⠢⠶⠾⠶⠰⠶⠷⠶⠶⠺⠓⠳⠖⠿⠿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠰⢷⡦⠸⠾⠧⠲⠆⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⢀⣀⣁⡙⠛⠉⡉⡉⠙⠁⠩⠅⠐⠀⠑⠀⣈⡉⢙⢤⡈⠈⠙⠉⠉⠡⠉⠡⠠⠨⠈⠅⠠⠤⠀⠠⠀⠄⠂⠀⠀⠄⠄⠠⠄⠤⠄⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⡇⠀⠔⠍⠍⠥⠄⠤⠶⠆⠆⡰⠶⠶⠶⠀⠆⠠⠷⠦⠰⠶⠶⠄⠀⠶⠄⠾⠷⠶⠶⠶⠶⠶⠾⠿⠷⠶⠖⠰⠦⠲⠶⠾⠚⠶⠾⠴⡦⠎⠗⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠄⠶⠵⠷⠐⠲⠿⠖⠐⠶⡦⠶⡶⠃⠒⠂⠄⠆⠠⠶⠶⠵⠷⣾⠿⠇⠂⠸⠂⠸⠷⠧⠸⠷⠦⠢⠌⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⣀⣄⣀⣀⠀⠀⠄⠄⠀⠠⣤⣤⡄⢀⠀⢠⠤⠀⣠⡤⠤⠀⠤⠤⠠⠀⠤⠤⠤⠤⠀⠤⠠⠠⠶⠦⠴⠤⠦⠀⠀⠂⠠⠄⠠⠤⠤⠤⠤⠄⠤⠄⠤⠤⠤⠤⠄⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠ ⡇⠀⠀⠭⠍⠽⠄⠤⠶⠦⠀⠀⠩⠶⠗⠰⠆⠰⠿⠆⠰⠵⠦⠆⠰⠿⠾⠅⠰⠾⠾⠾⠒⠶⠷⠿⡇⠴⠶⠧⢵⠶⠶⡦⠴⠶⠂⠰⠶⠶⠾⠶⠷⠾⠾⠴⠎⠿⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠆⠗⠳⠄⠠⠷⠷⠆⠠⠒⠶⢂⠔⠶⠆⠲⢦⠆⠰⠬⠶⠶⠽⠟⠿⠇⠀⠠⠔⠾⠿⠆⠲⠾⠗⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⣠⣤⣤⣀⠀⡀⠤⠄⠀⢠⣤⣤⡄⢠⠄⢠⠤⠀⢠⣤⡀⠀⠢⠘⠐⠀⠐⠀⠀⠀⠀⠤⡤⠠⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠭⠶⡦⠐⠰⠗⠆⠀⠘⠼⠽⢦⠤⠄⠸⠿⠇⠨⠡⠢⠃⠸⠷⠶⠶⠶⠶⠀⠶⠀⠚⣿⠷⠾⠟⠷⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠇⠶⠷⠷⠰⠶⠷⠆⠰⠰⠶⢶⠶⠶⠒⠶⠦⠀⠴⡶⠶⠥⠵⠿⠷⠗⠂⠾⠅⠼⠴⢶⠺⠷⠔⠴⠶⣤⠐⠂⠀⠂⠢⠀⠠⠄⠀⠖⠀⠀⠀⠀⠀⠤⠸⠣⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⡇⠀⠀⠀⠀⠀⠲⠊⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠂⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⡇⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠀⠄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣴⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠ ⡇⠀⠀⠀⠀⠈⠀⠀⠛⠈⠀⠀⠊⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠋⠁⠀⠀⠀⠒⠀⠀⠀⠘⠀⠔⠐⠀⠂⠀⠀⠀⠀⠠⠅⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⣤⢤⠀⠄⢨ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠿⠶⠶⠶⠤⠼⠰ ⠣⠚⠛⠛⠛⠛⠛⠛⠛⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠛⠛⠛⠛⠛⠂⠒⠒⠒⠂⠒⠒⠐⠂⠒⠒⠒⠒⠂⠒⠒⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣶⣶ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠸⢷⠾⠴⠶⠶⠦⠅⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠾⠶⠶⠾⠶⠴⠶⠄⠀⠐⠐⠒⠒⠒⠐⠒⠀⠀⠀⢌ ⡇⠿⠶⠧⠶⢶⣶⡤⠆⠸⠆⠷⠶⠶⠆⠸⠷⠶⠲⠶⠺⠆⠰⠶⠶⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⡀⠀⠀⠀⠸⠷⠗⠚⠿⠆⠐⠾⠖⠆⠀⠶⠄⠀⠀⠂⠀⠀⠀⢻ ⡇⠟⠿⠿⠷⠂⠀⠀⠀⠰⠶⠶⠢⠶⠦⠶⠶⠆⠸⠷⠶⠲⠰⠶⠶⠂⠰⠶⠶⠶⠺⠳⠶⠶⠶⠖⠒⠗⠶⠷⠰⠀⣷⡿⠿⠶⠶⠆⠧⠖⠗⠂⡆⠂⠄⠀⠀⠀⠘⠓⠃⠘⠓⠣⠒⠒⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡷⠻⠖⠷⠷⠶⠗⠆⠀⠰⠷⠶⠲⠆⢸⠂⠴⠆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠶⠖⠇⠆⣦⠀⠀⠐⠢⠶⠔⠆⠰⠲⠶⠶⠄⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡟⠒⠶⠖⠶⢶⡶⢶⡶⠶⠆⠆⠀⠀⣄⠀⠀⠰⠆⠰⠦⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡘ ⡟⠗⠓⡾⠲⠷⠆⠀⠀⠀⠆⠐⢲⡆⠶⠖⠆⠰⡀⠾⠖⠲⠄⠔⢾⡆⠾⠚⠚⠺⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣏⡧⠆⠲⠖⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠞⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠛⠛⢃ ⠑⠰⠶⠒⠖⠲⠀⠤⠠⠄⠠⠀⠤⠠⠄⠠⠀⠤⠠⠄⠠⠀⠄⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠆⠇⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠽ ⡆⠈⠓⠛⠛⠛⠓⡻⠛⠋⠉⠙⠛⠋⠛⠛⠉⠛⠛⠙⠚⠛⠛⠛⠙⠛⠓⠓⠛⠛⠙⠛⠓⠋⠛⠙⠛⠛⠛⠚⠛⠛⠚⠛⠛⠙⠙⢻⢳⠛⠞⠛⠛⠛⠚⠛⠛⠓⠛⠛⠛⠙⠛⠛⠓⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠛⠁⠠ ⡇⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀ ⡇⠀⠤⠷⠖⠳⠔⠣⠶⡦⠀⠰⠖⠷⠆⠐⠆⠀⠗⠆⠰⠿⠖⠂⠰⠿⠷⡄⠷⠷⠖⠖⠶⠶⠼⠦⠰⠶⠷⠻⠤⠶⠖⠪⠿⠾⠶⠾⠿⠿⠾⠧⠿⠾⠶⠶⠆⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⡇⠀⠀⠀⠇⠶⠷⠶⠰⠷⠷⠆⠠⠲⠶⢶⡦⠶⠂⠶⠆⠄⠰⠶⠶⠶⠴⠿⠷⠇⠆⠐⠂⠰⠖⠞⠐⠾⠧⠒⠆⠇⠀⠰⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⣀⠒⠒⢂⠐⡖⠒⠒⢒⣲⣶⡖⠒⠖⠀⠒⡀⢀⣀⡐⠀⠀⢶⠒⠒⣀⡂⠘⠀⣀⡀⠀⠀⠀⡀⠀⣀⠀⢠⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠠⠷⡶⠤⠄⡦⡶⡯⠔⠰⠖⠶⠦⠀⠂⠷⠶⠗⠲⢾⠷⠄⠰⠾⠷⡆⠰⠾⠗⠶⠶⠷⠷⠶⠦⠷⠇⠰⠢⠶⠾⠶⠰⠶⠷⠶⠶⠺⠓⠳⠖⠿⠿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠰⢷⡦⠸⠾⠧⠲⠆⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⢀⣀⣁⡙⠛⠉⡉⡉⠙⠁⠩⠅⠐⠀⠑⠀⣈⡉⢙⢤⡈⠈⠙⠉⠉⠡⠉⠡⠠⠨⠈⠅⠠⠤⠀⠠⠀⠄⠂⠀⠀⠄⠄⠠⠄⠤⠄⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⡇⠀⠔⠍⠍⠥⠄⠤⠶⠆⠆⡰⠶⠶⠶⠀⠆⠠⠷⠦⠰⠶⠶⠄⠀⠶⠄⠾⠷⠶⠶⠶⠶⠶⠾⠿⠷⠶⠖⠰⠦⠲⠶⠾⠚⠶⠾⠴⡦⠎⠗⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠄⠶⠵⠷⠐⠲⠿⠖⠐⠶⡦⠶⡶⠃⠒⠂⠄⠆⠠⠶⠶⠵⠷⣾⠿⠇⠂⠸⠂⠸⠷⠧⠸⠷⠦⠢⠌⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⣀⣄⣀⣀⠀⠀⠄⠄⠀⠠⣤⣤⡄⢀⠀⢠⠤⠀⣠⡤⠤⠀⠤⠤⠠⠀⠤⠤⠤⠤⠀⠤⠠⠠⠶⠦⠴⠤⠦⠀⠀⠂⠠⠄⠠⠤⠤⠤⠤⠄⠤⠄⠤⠤⠤⠤⠄⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠ ⡇⠀⠀⠭⠍⠽⠄⠤⠶⠦⠀⠀⠩⠶⠗⠰⠆⠰⠿⠆⠰⠵⠦⠆⠰⠿⠾⠅⠰⠾⠾⠾⠒⠶⠷⠿⡇⠴⠶⠧⢵⠶⠶⡦⠴⠶⠂⠰⠶⠶⠾⠶⠷⠾⠾⠴⠎⠿⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠆⠗⠳⠄⠠⠷⠷⠆⠠⠒⠶⢂⠔⠶⠆⠲⢦⠆⠰⠬⠶⠶⠽⠟⠿⠇⠀⠠⠔⠾⠿⠆⠲⠾⠗⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⣠⣤⣤⣀⠀⡀⠤⠄⠀⢠⣤⣤⡄⢠⠄⢠⠤⠀⢠⣤⡀⠀⠢⠘⠐⠀⠐⠀⠀⠀⠀⠤⡤⠠⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠭⠶⡦⠐⠰⠗⠆⠀⠘⠼⠽⢦⠤⠄⠸⠿⠇⠨⠡⠢⠃⠸⠷⠶⠶⠶⠶⠀⠶⠀⠚⣿⠷⠾⠟⠷⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠇⠶⠷⠷⠰⠶⠷⠆⠰⠰⠶⢶⠶⠶⠒⠶⠦⠀⠴⡶⠶⠥⠵⠿⠷⠗⠂⠾⠅⠼⠴⢶⠺⠷⠔⠴⠶⣤⠐⠂⠀⠂⠢⠀⠠⠄⠀⠖⠀⠀⠀⠀⠀⠤⠸⠣⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⡇⠀⠀⠀⠀⠀⠲⠊⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠂⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⡇⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠀⠄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣴⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠ ⡇⠀⠀⠀⠀⠈⠀⠀⠛⠈⠀⠀⠊⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠋⠁⠀⠀⠀⠒⠀⠀⠀⠘⠀⠔⠐⠀⠂⠀⠀⠀⠀⠠⠅⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⣤⢤⠀⠄⢨ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠿⠶⠶⠶⠤⠼⠰ ⠣⠚⠛⠛⠛⠛⠛⠛⠛⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠛⠛⠛⠛⠛⠂⠒⠒⠒⠂⠒⠒⠐⠂⠒⠒⠒⠒⠂⠒⠒⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣶⣶ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠸⢷⠾⠴⠶⠶⠦⠅⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠾⠶⠶⠾⠶⠴⠶⠄⠀⠐⠐⠒⠒⠒⠐⠒⠀⠀⠀⢌ ⡇⠿⠶⠧⠶⢶⣶⡤⠆⠸⠆⠷⠶⠶⠆⠸⠷⠶⠲⠶⠺⠆⠰⠶⠶⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⡀⠀⠀⠀⠸⠷⠗⠚⠿⠆⠐⠾⠖⠆⠀⠶⠄⠀⠀⠂⠀⠀⠀⢻ ⡇⠟⠿⠿⠷⠂⠀⠀⠀⠰⠶⠶⠢⠶⠦⠶⠶⠆⠸⠷⠶⠲⠰⠶⠶⠂⠰⠶⠶⠶⠺⠳⠶⠶⠶⠖⠒⠗⠶⠷⠴⠀⣷⡿⠿⠶⠶⠆⠧⠖⠗⠂⡆⠂⠄⠀⠀⠀⠘⠓⠃⠚⠓⠣⠒⠒⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡷⠻⠖⠷⠷⠶⠗⠆⠀⠰⠷⠶⠲⠆⢸⠂⠴⠆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠶⠖⠇⠆⣦⠀⠀⠐⠢⠶⠔⠆⠰⠲⠶⠶⠄⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡟⠒⠶⠖⠶⢶⡶⢶⡶⠶⠆⠆⠀⠀⣄⠀⠀⠰⠆⠰⠦⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡘ ⡟⠗⠓⡾⠲⠷⠆⠀⠀⠀⠆⠐⢲⡆⠶⠖⠆⠰⡀⠾⠖⠲⠄⠔⢾⡆⠾⠚⠚⠺⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣏⡧⠆⠲⠖⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠞⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠛⠛⢃ ⠑⠰⠶⠒⠖⠲⠀⠤⠠⠄⠠⠀⠤⠠⠄⠠⠀⠤⠠⠄⠠⠀⠄⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠆⠏⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠽ ⡆⠈⠓⠛⠛⠛⠓⡻⠛⠋⠉⠙⠛⠋⠛⠛⠉⠛⠛⠙⠚⠛⠛⠛⠙⠛⠓⠓⠛⠛⠙⠛⠓⠋⠛⠙⠛⠛⠛⠚⠛⠛⠚⠛⠛⠙⠙⢻⢳⠛⠞⠛⠛⠛⠚⠛⠛⠓⠛⠛⠛⠙⠛⠛⠓⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠛⠁⠠ ⡇⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀ ⡇⠀⠤⠷⠖⠳⠔⠣⠶⡦⠀⠰⠖⠷⠆⠐⠆⠀⠗⠆⠰⠿⠖⠂⠰⠿⠷⡄⠷⠷⠶⠖⠶⠶⠼⠦⠰⠶⠷⠻⠤⠶⠖⠪⠿⠾⠶⠾⠿⠿⠾⠧⠿⠾⠶⠶⠆⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⡇⠀⠀⠀⠇⠶⠷⠶⠰⠷⠷⠆⠠⠲⠶⢶⡦⠶⠂⠶⠆⠄⠰⠶⠶⠶⠴⠿⠷⠇⠆⠐⠂⠰⠖⠞⠐⠾⠧⠒⠆⠇⠀⠰⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⣀⠒⠒⢂⠐⡖⠒⠒⢒⣲⣶⡖⠒⠖⠀⠒⡀⢀⣀⡐⠀⠀⢶⠒⠒⣀⡂⠘⠀⣀⡀⠀⠀⠀⡀⠀⣀⠀⢠⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠠⠷⡶⠤⠄⡦⡶⡯⠔⠰⠖⠶⠦⠀⠂⠷⠶⠗⠐⢸⠷⠀⠰⠾⠷⡆⠰⠾⠗⠶⠶⠷⠷⠶⠦⠷⠇⠐⠂⠶⠾⠶⠰⠶⠷⠶⠶⠺⠓⠳⠖⠿⠿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⢸⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣖⠂⠐⢖⡢⠐⠶⠆⠒⠂⠓⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⢀⣀⣁⡙⠛⠉⠉⠉⠙⠁⠩⠅⠐⠀⠑⠀⠈⠉⠙⠤⠈⠈⠙⠉⠉⠡⠉⠡⠠⠨⠈⠅⠠⠤⠀⠠⠀⠄⠂⠀⠀⠄⠄⠠⠄⠤⠄⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⡇⠀⠔⠍⠍⠥⠄⠴⠶⠖⠆⡰⠶⠶⠶⠐⠆⠠⠷⠶⠰⠶⠶⠆⠀⠶⠄⠶⠷⠶⠶⠶⠶⠶⠾⠿⠷⠶⠖⠲⠶⠲⠶⠾⠚⠶⠾⠶⡶⠎⠗⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠄⠶⠵⠷⠐⠲⠿⠖⠐⠶⡦⠶⡶⠃⠒⠂⠄⠆⠠⠶⠶⠵⠷⣾⠿⠇⠂⠸⠂⠸⠷⠧⠸⠷⠦⠢⠌⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⣀⣄⣀⣀⠀⠀⠄⠄⠀⠠⣤⣤⡄⢀⠀⢠⠤⠀⣠⡤⠤⠀⠤⠤⠠⠀⠤⠤⠤⠤⠀⠤⠠⠠⠶⠦⠴⠤⠦⠀⠀⠂⠠⠄⠠⠤⠤⠤⠤⠄⠤⠄⠤⠤⠤⠤⠄⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠ ⡇⠀⠀⠭⠍⠽⠄⠤⠶⠦⠀⠀⠩⠶⠗⠰⠆⠰⠿⠆⠰⠵⠦⠖⠰⠿⠾⠅⠰⠾⠾⠾⠒⠶⠷⠿⡇⠴⠶⠧⢵⠶⠶⡦⠴⠶⠂⠰⠶⠶⠾⠾⠷⠾⠾⠴⠎⠿⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠆⠗⠳⠔⠠⠷⠷⠆⠠⠒⠶⢂⠔⠶⠆⠲⢦⠆⠰⠬⠶⠶⠽⠟⠿⠇⠀⠠⠔⠾⠿⠆⠲⠾⠗⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⣠⣤⣤⣀⠀⡀⠤⠄⠀⢠⣤⣤⡄⢠⠄⢠⠤⠀⣠⣤⡀⠀⠢⠘⠐⠀⠐⠀⠀⠀⠀⠤⡤⠠⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠭⠶⡦⠐⠰⠗⠆⠀⠘⠼⠽⢦⠤⠄⠸⠿⠇⠨⠡⠢⠃⠸⠷⠶⠶⠶⠶⠀⠶⠀⠚⣿⠷⠾⠟⠷⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠇⠶⠷⠷⠰⠶⠷⠆⠰⠰⠶⢶⠶⠶⠒⠶⠦⠀⠴⡶⠶⠥⠵⠿⠷⠗⠂⠾⠅⠼⠴⢶⠺⠷⠔⠴⠶⣤⠐⠂⠀⠂⠢⠀⠠⠄⠀⠖⠐⠀⠀⠀⠀⠤⠸⠣⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⡇⠀⠀⠀⠀⠀⠲⠊⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠂⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⡇⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠀⠄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣴⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠ ⡇⠀⠀⠀⠀⠈⠀⠀⠛⠈⠀⠀⠊⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠋⠁⠀⠀⠀⠒⠀⠀⠀⠘⠀⠔⠐⠀⠂⠀⠀⠀⠀⠠⠅⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⣤⢤⠀⠄⢨ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠿⠶⠶⠶⠤⠼⠰ ⠣⠚⠛⠛⠛⠛⠛⠛⠛⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠛⠛⠛⠛⠛⠂⠒⠒⠒⠂⠒⠒⠐⠂⠒⠒⠒⠒⠂⠒⠒⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣶⣶ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠸⢷⠾⠴⠶⠶⠦⠅⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠾⠶⠶⠾⠶⠴⠶⠄⠀⠐⠐⠒⠒⠒⠐⠒⠀⠀⠀⢌ ⡇⠿⠶⠧⠶⢶⣶⡤⠆⠸⠆⠷⠶⠶⠆⢸⠷⠶⠲⠶⠺⠆⠰⠶⠶⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⡀⠀⠀⠀⠸⠷⠗⠚⠿⠆⠐⠾⠖⠆⠀⠶⠄⠀⠀⠂⠀⠀⠀⢻ ⡇⠟⠿⠿⠷⠂⠀⠀⠀⠰⠶⠦⠀⠲⠦⠶⠶⠆⠸⠷⠶⠲⠰⠶⠶⠂⠰⠶⠶⠶⠺⠳⠶⠶⠶⠖⠒⠗⠶⠷⠰⠀⣷⡿⠿⠶⠶⠆⠧⠖⠗⠂⡆⠂⠄⠀⠀⠀⠘⠓⠃⠘⠓⠣⠒⠒⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡷⠻⠖⠷⠷⠶⠗⠆⠀⠰⠷⠶⠲⠆⢸⠂⠴⠆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠶⠖⠇⠆⣦⠀⠀⠐⠢⠶⠔⠆⠰⠲⠶⠶⠄⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡟⠒⠶⠖⠶⢶⡶⢶⡶⠶⠆⠆⠀⠀⣄⠀⠀⠰⠆⠰⠦⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡘ ⡟⠗⠓⡾⠲⠷⠆⠀⠀⠀⠆⠐⢲⡆⠶⠖⠆⠰⡀⠾⠖⠲⠄⠔⢾⡆⠾⠚⠚⠺⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣏⡧⠆⠲⠖⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠞⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠛⠛⢃ ⠑⠰⠶⠒⠖⠲⠀⠤⠠⠄⠠⠀⠤⠠⠄⠠⠀⠤⠠⠄⠠⠀⠄⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠆⠇⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠽ ⡆⠈⠓⠛⠛⠛⠓⡻⠛⠋⠉⠙⠛⠋⠛⠛⠉⠛⠛⠙⠚⠛⠛⠛⠙⠛⠓⠓⠛⠛⠙⠛⠓⠋⠛⠙⠛⠛⠛⠚⠛⠛⠚⠛⠛⠙⠙⢻⢳⠛⠞⠛⠛⠛⠚⠛⠛⠓⠛⠛⠛⠙⠛⠛⠓⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠛⠁⠠ ⡇⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀ ⡇⠀⠤⠷⠖⠳⠔⠣⠶⡦⠀⠰⠖⠷⠆⠐⠆⠀⠗⠆⠰⠿⠖⠂⠰⠿⠷⡄⠷⠷⠖⠖⠶⠶⠼⠦⠰⠶⠷⠻⠤⠶⠖⠪⠿⠾⠶⠾⠿⠿⠾⠧⠿⠾⠶⠶⠆⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⡇⠀⠀⠀⠇⠶⠷⠶⠰⠷⠷⠆⠠⠲⠶⢶⡦⠶⠂⠶⠆⠄⠰⠶⠶⠶⠴⠿⠷⠇⠆⠐⠂⠰⠖⠞⠐⠾⠧⠒⠆⠇⠀⠰⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⣀⠒⠒⠂⠐⡖⠒⠒⢒⣲⣶⡖⠒⠒⠀⠒⡀⠀⠀⡐⠀⠀⢶⠒⠒⣀⡂⠘⠀⣀⡀⠀⠀⠀⠀⠀⣀⠀⢠⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠠⠷⡶⠤⠄⡤⣤⣯⣔⣠⣆⣶⣦⣀⠂⢷⠤⠄⠀⢠⢷⣀⣠⣾⣷⣄⣰⣾⣇⣶⣤⣷⣷⣶⡦⡶⣇⣐⣂⣶⠾⠶⠰⠶⠷⠶⠶⠺⠓⠳⠖⠿⠿⠭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⢸⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠒⣶⣶⣶⣶⣶⣶⣖⠂⠐⢖⡢⠐⠶⠆⠒⠂⠓⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⢀⣀⣁⡙⠿⠭⠭⠭⠽⠥⠭⠥⠴⠤⠵⠤⠌⠭⠷⠤⠄⠤⠽⠭⠭⠥⠭⠥⠤⠬⠬⠥⠤⠤⠤⠤⠤⠤⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴ ⡇⠀⠔⠍⠍⠥⠄⠴⠶⠖⠆⡰⠶⠶⠶⠐⠆⠠⠷⠶⠰⠶⠶⠆⠀⠶⠄⠶⠷⠶⠶⠶⠶⠶⠶⠿⠷⠶⠖⠲⠶⠲⠶⠾⠒⠶⠾⠶⡶⠎⠗⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠄⠶⠵⠷⠐⠲⠿⠖⠐⠶⡦⠶⡶⠃⠒⠂⠄⠆⠠⠶⠶⠵⠷⣾⠿⠇⠂⠸⠂⠸⠷⠧⠸⠷⠦⠢⠌⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⣀⣄⣀⣀⠀⠀⠄⠄⠀⠠⣤⣤⡄⢀⠀⢠⠤⠀⣠⡤⠤⠀⠤⠤⠠⠀⠤⠤⠤⠤⠀⠤⠠⠠⠶⠦⠴⠤⠦⠀⠀⠂⠠⠄⠠⠤⠤⠤⠤⠄⠤⠄⠤⠤⠤⠤⠄⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠ ⡇⠀⠀⠭⠍⠽⠄⠤⠶⠦⠀⠀⠩⠶⠗⠰⠆⠰⠿⠆⠰⠵⠦⠆⠰⠿⠾⠅⠰⠾⠾⠾⠒⠶⠷⠿⡇⠴⠶⠧⢵⠶⠶⡦⠴⠶⠂⠰⠶⠶⠾⠶⠷⠾⠾⠴⠎⠿⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠆⠗⠳⠄⠠⠷⠷⠆⠠⠒⠶⢂⠔⠶⠆⠲⢦⠆⠰⠬⠶⠶⠽⠟⠿⠇⠀⠠⠔⠾⠿⠆⠲⠾⠗⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⣠⣤⣤⣀⠀⡀⠤⠄⠀⢠⣤⣤⡄⢠⠄⢠⠤⠀⢠⣤⡀⠀⠢⠘⠐⠀⠐⠀⠀⠀⠀⠤⡤⠠⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠭⠶⡦⠐⠰⠗⠆⠀⠘⠼⠽⢦⠤⠄⠸⠿⠇⠨⠡⠢⠃⠸⠷⠶⠶⠶⠶⠀⠶⠀⠚⣿⠷⠾⠟⠷⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠇⠶⠷⠷⠰⠶⠷⠆⠰⠰⠶⢶⠶⠶⠒⠶⠦⠀⠴⡶⠶⠥⠵⠿⠷⠗⠂⠾⠅⠼⠴⢶⠺⠷⠔⠴⠶⣤⠐⠂⠀⠂⠢⠀⠠⠄⠀⠖⠀⠀⠀⠀⠀⠤⠸⠣⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⡇⠀⠀⠀⠀⠀⠲⠊⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠂⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⡇⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠀⠄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣴⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠ ⡇⠀⠀⠀⠀⠈⠀⠀⠛⠈⠀⠀⠊⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠋⠁⠀⠀⠀⠒⠀⠀⠀⠘⠀⠔⠐⠀⠂⠀⠀⠀⠀⠠⠅⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⣤⢤⠀⠄⢨ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠿⠶⠶⠶⠤⠼⠰ ⠣⠚⠛⠛⠛⠛⠛⠛⠛⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠛⠛⠛⠛⠛⠂⠒⠒⠒⠂⠒⠒⠐⠂⠒⠒⠒⠒⠂⠒⠒⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣶⣶ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠸⢷⠾⠴⠶⠶⠦⠅⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠾⠶⠶⠾⠶⠴⠶⠄⠀⠐⠐⠒⠂⠒⠐⠐⠀⠀⠀⢌ ⡇⠯⠶⠧⠶⢶⣶⡤⠆⠸⠆⠧⠤⠴⠦⢼⠷⠶⠲⠶⠺⠆⠰⠶⠶⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⡀⠀⠀⠀⠸⠷⠗⠚⠿⠆⠐⠾⠖⠆⠀⠶⠄⠀⠀⠂⠀⠀⠀⢻ ⡇⠟⠿⠿⠧⠂⠀⠀⠀⠰⠶⠦⠀⠲⠦⠶⠶⠆⠸⠷⠶⠲⠰⠶⠶⠂⠰⠶⠶⠶⠺⠳⠶⠶⠶⠖⠐⠗⠶⠷⠰⠀⣷⡿⠿⠶⠶⠆⠧⠖⠗⠂⡆⠂⠄⠀⠀⠀⠘⠓⠃⠘⠓⠣⠒⠒⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡷⠻⠖⠷⠷⠶⠗⠆⠀⠰⠷⠶⠲⠖⢸⠂⠴⠆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠶⠖⠇⠆⣦⠀⠀⠐⠢⠶⠔⠆⠰⠲⠶⠶⠄⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡟⠒⠶⠖⠶⢶⡶⢶⡶⠶⠆⠆⠀⠀⣄⠀⠀⠰⠆⠰⠦⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡘ ⡟⠗⠓⡾⠲⠷⠆⠀⠀⠀⠆⠐⢲⡆⠶⠖⠆⠰⡀⠾⠖⠲⠄⠔⢾⡆⠾⠚⠚⠺⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣏⡧⠆⠲⠖⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠞⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠛⠛⢃ ⠑⠰⠶⠒⠖⠲⠀⠤⠠⠄⠠⠀⠤⠠⠄⠠⠀⠤⠠⠄⠠⠀⠄⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠆⠇⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠽ ⡆⠈⠓⠛⠛⠛⠓⡻⠛⠊⠉⠙⠛⠋⠚⠛⠉⠛⠛⠙⠚⠛⠛⠛⠙⠛⠓⠓⠛⠛⠙⠛⠓⠋⠛⠙⠛⠛⠛⠚⠛⠛⠚⠛⠛⠙⠙⢻⢳⠛⠞⠛⠛⠓⠚⠛⠛⠓⠛⠛⠛⠙⠛⠛⠓⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠛⠁⠠ ⡇⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀ ⡇⠀⠤⠷⠖⠳⠔⠣⠶⡦⠀⠰⠖⠷⠆⠐⠆⠀⠗⠆⠰⠿⠖⠂⠰⠿⠷⡄⠷⠷⠖⠖⠶⠶⠼⠦⠰⠶⠷⠻⠤⠶⠖⠪⠿⠾⠶⠾⠿⠿⠾⠧⠿⠾⠶⠶⠆⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⡇⠀⠀⠀⠇⠶⠷⠶⠰⠷⠷⠆⠠⠲⠶⠶⡦⠶⠂⠶⠆⠄⠰⠶⠶⠶⠴⠿⠷⠇⠆⠐⠂⠰⠖⠞⠐⠾⠧⠒⠆⠇⠀⠰⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⣀⠒⠒⣂⡐⡖⠒⠒⢒⣲⣶⡖⠒⠒⢀⣒⣀⣀⢀⣐⣀⣀⣶⣒⣒⣀⣂⣘⣀⣀⣀⣀⡀⣀⢀⣀⣀⣀⣠⡀⠀⠀⠀⠀⢀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀ ⡇⠀⠠⠷⡶⠤⠄⠤⠤⠯⠔⠠⠆⠶⠦⠀⠂⠷⠤⠄⠀⠠⠶⢀⣠⣶⣶⣄⣰⣶⣆⣶⣤⣶⣶⣶⡦⡶⣆⣐⣃⣶⠾⠶⠰⠶⠷⠶⠶⠺⠓⠳⠗⠿⠽⠭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⢸⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣶⣶⣤⠶⣶⣶⣶⣶⣶⣶⣶⠦⠴⢶⡦⠴⠶⠦⠶⠦⠷⠶⠶⠶⠶⠶⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀ ⡇⠀⢀⣀⣁⡙⠿⠭⠭⠭⠽⠥⠭⠥⠴⠤⠵⠤⠌⠭⠷⠤⠄⠤⠽⠭⠭⠥⠭⠥⠤⠬⠬⠥⠤⠤⠤⠤⠤⠤⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴ ⡇⠀⠔⠍⠍⠥⠄⠴⠶⠖⠆⡰⠶⠶⠶⠐⠆⠠⠷⠶⠰⠶⠶⠆⠀⠶⠄⠶⠷⠶⠶⠶⠶⠶⠶⠿⠷⠶⠖⠲⠶⠲⠶⠾⠒⠶⠾⠶⡶⠎⠗⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠄⠶⠵⠷⠐⠲⠿⠖⠐⠶⡦⠶⡶⠃⠒⠂⠄⠆⠠⠶⠶⠵⠷⣾⠿⠇⠂⠸⠂⠸⠷⠧⠸⠷⠦⠢⠌⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⣀⣄⣀⣀⠀⠀⠄⠄⠀⠠⣤⣤⡄⢀⠀⢠⠤⠀⣠⡤⠤⠀⠤⠤⠠⠀⠤⠤⠤⠤⠀⠠⠠⠠⠶⠦⠴⠤⠦⠀⠀⠂⠠⠄⠠⠤⠤⠤⠤⠄⠤⠄⠤⠤⠤⠤⠄⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠ ⡇⠀⠀⠭⠍⠽⠄⠤⠶⠦⠀⠀⠩⠴⠗⠰⠆⠰⠿⠆⠰⠵⠦⠆⠰⠿⠾⠅⠰⠾⠾⠾⠒⠶⠷⠿⡆⠴⠶⠧⢵⠶⠶⡦⠴⠶⠂⠰⠶⠶⠾⠶⠷⠾⠾⠴⠎⠿⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠆⠗⠳⠄⠠⠷⠷⠆⠠⠒⠶⢂⠔⠶⠆⠲⢦⠆⠰⠬⠶⠶⠽⠟⠿⠇⠀⠠⠔⠾⠿⠆⠲⠾⠗⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⣠⣤⣤⣀⠀⡀⠤⠄⠀⢠⣤⣤⡄⢠⠄⢠⠤⠀⢠⣤⡀⠀⠢⠘⠐⠀⠐⠀⠀⠀⠀⠤⡤⠠⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠭⠶⡦⠐⠰⠗⠆⠀⠘⠼⠽⢦⠤⠄⠸⠿⠇⠨⠡⠢⠃⠸⠷⠶⠶⠶⠶⠀⠶⠀⠚⣿⠷⠾⠟⠷⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠇⠶⠷⠷⠰⠶⠷⠆⠰⠰⠶⢶⠶⠶⠒⠶⠦⠀⠰⡶⠶⠥⠵⠿⠷⠗⠂⠾⠅⠼⠴⢶⠺⠶⠔⠴⠶⣤⠐⠂⠀⠂⠢⠀⠠⠄⠀⠖⠀⠀⠀⠀⠀⠤⠸⠣⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⡇⠀⠀⠀⠀⠀⠲⠊⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠂⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⡇⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠀⠄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣴⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠ ⡇⠀⠀⠀⠀⠈⠀⠀⠛⠈⠀⠀⠊⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠋⠁⠀⠀⠀⠐⠀⠀⠀⠘⠀⠔⠐⠀⠂⠀⠀⠀⠀⠠⠅⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⣤⢤⠀⠄⢨ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠿⠶⠶⠶⠤⠼⠰ ⠣⠚⠛⠛⠛⠛⠛⠛⠛⠙⠛⠙⠛⠟⠛⠛⠛⠛⠛⠓⠛⠛⠛⠛⠛⠂⠒⠐⠂⠂⠒⠒⠐⠂⠂⠒⠐⠐⠂⠒⠒⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣶⣶ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠀⠒⠒⠒⠒⠒⠀⠒⠒⠒⠒⠂⠂⠸⢷⠾⠴⠶⠶⠦⠅⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠾⠶⠶⠾⠶⠴⠶⠄⠀⠐⠐⠒⠂⠒⠐⠐⠀⠀⠀⢌ ⡇⠯⠶⠧⠶⢶⣶⡤⠆⠸⠆⠧⠤⠴⠦⢼⠷⠶⠲⠶⠺⠆⠰⠶⠶⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⡀⠀⠀⠀⠸⠷⠗⠚⠿⠆⠐⠾⠖⠆⠀⠶⠄⠀⠀⠂⠀⠀⠀⢻ ⡇⠟⠿⠿⠧⠂⠀⠀⠀⠰⠶⠦⠀⠲⠦⠶⠶⠆⠸⠷⠶⠲⠰⠶⠶⠂⠰⠶⠶⠶⠺⠳⠶⠶⠶⠖⠐⠗⠶⠷⠰⠀⣷⡿⠿⠶⠶⠆⠧⠖⠗⠂⡆⠂⠄⠀⠀⠀⠘⠓⠃⠘⠓⠣⠒⠒⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡷⠻⠖⠷⠷⠶⠗⠆⠀⠰⠷⠶⠲⠖⢸⠂⠴⠆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠶⠖⠇⠆⣦⠀⠀⠐⠢⠶⠔⠆⠰⠲⠶⠶⠄⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡟⠒⠶⠖⠶⢶⡶⢶⡶⠶⠆⠆⠀⠀⣄⠀⠀⠰⠆⠰⠦⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡘ ⡟⠗⠓⡾⠲⠷⠆⠀⠀⠀⠆⠐⢲⡆⠶⠖⠆⠰⡀⠾⠖⠲⠄⠔⢾⡆⠾⠚⠚⠺⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣏⡧⠆⠲⠖⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠞⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠛⠛⢃ ⠑⠰⠖⠀⠐⠐⠒⠒⠒⠒⠠⠐⠒⠒⠒⠂⠀⠴⠖⠲⠒⠀⠀⠒⠒⠒⠒⠒⠒⠐⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠆⠇⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹ ⡆⠈⠓⠛⠛⠛⠓⡻⠛⠊⠉⠙⠛⠋⠛⠛⠉⠛⠛⠙⠚⠛⠛⠛⠙⠛⠓⠓⠛⠛⠙⠛⠓⠋⠛⠙⠛⠛⠛⠚⠛⠛⠚⠛⠛⠙⠙⢻⢳⠛⠞⠛⠛⠛⠚⠛⠛⠓⠛⠛⠛⠙⠛⠛⠓⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠛⠁⠠ ⡇⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀ ⡇⠀⠤⠷⠖⠳⠔⠣⠶⡦⠀⠰⠖⠷⠆⠐⠆⠀⠗⠆⠰⠿⠖⠂⠰⠿⠷⡄⠷⠷⠖⠖⠶⠶⠼⠦⠰⠶⠷⠻⠤⠶⠖⠪⠿⠾⠶⠾⠿⠿⠾⠧⠿⠾⠶⠶⠆⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⡇⠀⠀⠀⠇⠶⠷⠶⠰⠷⠷⠆⠠⠲⠶⠶⡦⠶⠂⠶⠆⠄⠰⠶⠶⠶⠴⠿⠷⠇⠆⠐⠂⠰⠖⠞⠐⠾⠧⠒⠆⠇⠀⠰⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⣀⠒⠒⣂⡐⡖⠒⠒⢒⣲⣶⡖⠒⠒⢀⣒⣀⣀⢀⣐⣀⣀⣶⣒⣒⣀⣂⣘⣀⣀⣀⣀⡀⣀⢀⣀⣀⣀⣠⡀⠀⠀⠀⠀⢀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀ ⡇⠀⠠⠷⡶⠤⠄⠤⠤⠯⠔⠠⠆⠶⠦⠀⠂⠷⠤⠄⠀⠠⠶⢀⣠⣶⣶⣄⣰⣶⣆⣶⣤⣶⣶⣶⡦⡶⣆⣐⣃⣶⠾⠶⠰⠶⠷⠶⠶⠺⠓⠳⠗⠿⠽⠭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⢸⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣶⣶⣤⠶⣶⣶⣶⣶⣶⣶⣶⠦⠴⢶⡦⠴⠶⠦⠶⠦⠷⠶⠶⠶⠶⠶⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀ ⡇⠀⢀⣀⣁⡙⠿⠭⠭⠭⠽⠥⠭⠥⠴⠤⠵⠤⠌⠭⠷⠤⠄⠤⠽⠭⠭⠥⠭⠥⠤⠬⠬⠥⠤⠤⠤⠤⠤⠤⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴ ⡇⠀⠔⠍⠍⠥⠄⠴⠶⠖⠆⡰⠶⠶⠶⠐⠆⠠⠷⠶⠰⠶⠶⠆⠀⠶⠄⠶⠷⠶⠶⠶⠶⠶⠶⠿⠷⠶⠖⠲⠶⠲⠶⠾⠒⠶⠾⠶⡶⠎⠗⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠄⠶⠵⠷⠐⠲⠿⠖⠐⠶⡦⠶⡶⠃⠒⠂⠄⠆⠠⠶⠶⠵⠷⣾⠿⠇⠂⠸⠂⠸⠷⠧⠸⠷⠦⠢⠌⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⣀⣄⣀⣀⠀⠀⠄⠄⠀⠠⣤⣤⡄⢀⠀⢠⠤⠀⣠⡤⠤⠀⠤⠤⠠⠀⠤⠤⠤⠤⠀⠠⠠⠠⠶⠦⠴⠤⠦⠀⠀⠂⠠⠄⠠⠤⠤⠤⠤⠄⠤⠄⠤⠤⠤⠤⠄⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠ ⡇⠀⠀⠭⠍⠽⠄⠤⠶⠦⠀⠀⠩⠴⠗⠰⠆⠰⠿⠆⠰⠵⠦⠆⠰⠿⠾⠅⠰⠾⠾⠾⠒⠶⠷⠿⡆⠴⠶⠧⢵⠶⠶⡦⠴⠶⠂⠰⠶⠶⠾⠶⠷⠾⠾⠴⠎⠿⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠆⠗⠳⠄⠠⠷⠷⠆⠠⠒⠶⢂⠔⠶⠆⠲⢦⠆⠰⠬⠶⠶⠽⠟⠿⠇⠀⠠⠔⠾⠿⠆⠲⠾⠗⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⣠⣤⣤⣀⠀⡀⠤⠄⠀⢠⣤⣤⡄⢠⠄⢠⠤⠀⢠⣤⡀⠀⠢⠘⠐⠀⠐⠀⠀⠀⠀⠤⡤⠠⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠠⠀⠭⠶⡦⠐⠰⠗⠆⠀⠘⠼⠽⢦⠤⠄⠸⠿⠇⠨⠡⠢⠃⠸⠷⠶⠶⠶⠶⠀⠶⠀⠚⣿⠷⠾⠟⠷⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠇⠶⠷⠷⠰⠶⠷⠆⠰⠰⠶⢶⠶⠶⠒⠶⠦⠀⠴⡶⠶⠥⠵⠿⠷⠗⠂⠾⠅⠼⠴⢶⠺⠶⠔⠴⠶⣤⠐⠂⠀⠂⠢⠀⠠⠄⠀⠖⠀⠀⠀⠀⠀⠤⠸⠣⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⡇⠀⠀⠀⠀⠀⠲⠊⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠂⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⡇⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠀⠄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣴⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠ ⡇⠀⠀⠀⠀⠈⠀⠀⠛⠈⠀⠀⠊⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠋⠁⠀⠀⠀⠐⠀⠀⠀⠘⠀⠔⠐⠀⠂⠀⠀⠀⠀⠠⠅⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⣤⢤⠀⠄⢨ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠿⠶⠶⠶⠤⠼⠰ ⠣⠚⠛⠛⠛⠛⠛⠛⠛⠙⠛⠙⠛⠟⠛⠛⠛⠛⠛⠓⠛⠛⠛⠛⠻⠂⠒⠒⠒⠂⠒⠒⠔⠂⠂⠒⠒⠐⠂⠲⠒⠐⠒⠒⠒⠒⠒⠒⠒⠲⠒⠖⠒⠒⠒⠲⠒⠒⠒⠒⠒⠂⠒⠒⠲⠒⠒⠒⠖⠒⠲⠒⠒⠒⠖⠒⠶⠶ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠒⠂⠀⠀⠀⠀⠒⠂⠀⠐⠒⠂⠂⠸⢷⠾⠴⠶⠶⠦⠅⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠾⠶⠶⠾⠶⠴⠶⠄⠀⠐⠐⠒⠂⠒⠐⠐⠀⠀⠀⢌ ⡇⠯⠶⠧⠶⢶⣶⡤⠆⠸⠆⠧⠤⠴⠦⢼⠷⠶⠲⠶⠺⠆⠰⠶⠶⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⡀⠀⠀⠀⠸⠷⠗⠚⠿⠆⠐⠾⠖⠆⠀⠶⠄⠀⠀⠂⠀⠀⠀⢻ ⡇⠟⠿⠿⠧⠂⠀⠀⠀⠰⠶⠦⠀⠲⠦⠶⠶⠆⠸⠷⠶⠲⠰⠶⠶⠂⠰⠶⠶⠶⠺⠳⠶⠶⠶⠖⠐⠗⠶⠷⠰⠀⣷⡿⠿⠶⠶⠆⠧⠖⠗⠂⡆⠂⠄⠀⠀⠀⠘⠓⠃⠘⠓⠣⠒⠒⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡷⠻⠖⠷⠷⠶⠗⠆⠀⠰⠷⠶⠲⠖⢸⠂⠴⠆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠶⠖⠇⠆⣦⠀⠀⠐⠢⠶⠔⠆⠰⠲⠶⠶⠄⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡟⠒⠶⠖⠶⢶⡶⢶⡶⠶⠆⠆⠀⠀⣄⠀⠀⠰⠆⠰⠦⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡘ ⡟⠗⠓⡾⠲⠷⠆⠀⠀⠀⠆⠐⢲⡆⠶⠖⠆⠰⡀⠾⠖⠲⠄⠔⢾⡆⠾⠚⠚⠺⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣏⡧⠆⠲⠖⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠞⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠛⠛⢃ ⠑⠐⠀⠀⠐⠐⠖⠒⠒⠒⠒⠂⠒⠒⠂⠒⠂⠐⠒⠒⠒⠀⠀⠒⠒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠂⠃⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹ ⡆⠈⠓⠛⠛⠛⠓⡳⠒⠂⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠚⠛⠛⠛⠙⠛⠓⠓⠛⠛⠙⠛⠓⠋⠛⠙⠛⠛⠛⠚⠛⠛⠚⠛⠛⠙⠙⢻⢳⠛⠞⠛⠛⠛⠚⠛⠛⠓⠛⠛⠛⠙⠛⠛⠓⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠛⠁⠠ ⡇⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀ ⡇⠀⠤⠷⠖⠳⠔⠣⠶⡦⠀⠰⠖⠷⠆⠐⠆⠀⠗⠆⠰⠿⠖⠂⠰⠿⠷⡄⠷⠷⠖⠖⠶⠶⠼⠦⠰⠶⠷⠻⠤⠶⠖⠪⠿⠾⠶⠾⠿⠿⠾⠧⠿⠾⠶⠶⠆⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⡇⠀⠀⠀⠇⠶⠷⠶⠰⠷⠷⠆⠠⠲⠶⠶⡦⠶⠂⠶⠆⠄⠰⠶⠶⠶⠴⠿⠷⠇⠆⠐⠂⠰⠖⠞⠐⠾⠧⠒⠆⠇⠀⠰⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⣀⠒⠒⣂⡐⡖⠒⠒⢒⣲⣶⡖⠒⠒⢀⣒⣀⣀⢀⣐⣀⣀⣶⣒⣒⣀⣂⣘⣀⣀⣀⣀⡀⣀⢀⣀⣀⣀⣠⡀⠀⠀⠀⠀⢀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀ ⡇⠀⠠⠷⡶⠤⠄⠤⠤⠯⠔⠠⠆⠶⠦⠀⠂⠷⠤⠄⠀⠠⠶⢀⣠⣶⣶⣄⣰⣶⣆⣶⣤⣶⣶⣶⡦⡶⣆⣐⣃⣶⠾⠶⠰⠶⠷⠶⠶⠺⠓⠳⠗⠿⠽⠭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⢸⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣶⣶⣤⠶⣶⣶⣶⣶⣶⣶⣶⠦⠴⢶⡦⠴⠶⠦⠶⠦⠷⠶⠶⠶⠶⠶⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀ ⡇⠀⢀⣀⣁⡙⠿⠭⠭⠭⠽⠥⠭⠥⠴⠤⠵⠤⠌⠭⠷⠤⠄⠤⠽⠭⠭⠥⠭⠥⠤⠬⠬⠥⠤⠤⠤⠤⠤⠤⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴ ⡇⠀⠔⠍⠍⠥⠄⠴⠶⠖⠆⡰⠶⠶⠶⠐⠆⠠⠷⠶⠰⠶⠶⠆⠀⠶⠄⠶⠷⠶⠶⠶⠶⠶⠶⠿⠷⠶⠖⠲⠶⠲⠶⠾⠒⠶⠾⠶⡶⠎⠗⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠄⠶⠵⠷⠐⠲⠿⠖⠐⠶⡦⠶⡶⠃⠒⠂⠄⠆⠠⠶⠶⠵⠷⣾⠿⠇⠂⠸⠂⠸⠷⠧⠸⠷⠦⠢⠌⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⣀⣄⣀⣀⠀⠀⠄⠄⠀⠠⣤⣤⡄⢀⠀⢠⠤⠀⣠⡤⠤⠀⠤⠤⠠⠀⠤⠤⠤⠤⠀⠠⠠⠠⠶⠦⠴⠤⠦⠀⠀⠂⠠⠄⠠⠤⠤⠤⠤⠄⠤⠄⠤⠤⠤⠤⠄⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠ ⡇⠀⠀⠭⠍⠽⠄⠤⠶⠦⠀⠀⠩⠴⠗⠰⠆⠰⠿⠆⠰⠵⠦⠆⠰⠿⠾⠅⠰⠾⠾⠾⠒⠶⠷⠿⡆⠴⠶⠧⢵⠶⠶⡦⠴⠶⠂⠰⠶⠶⠾⠶⠷⠾⠾⠴⠎⠿⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠆⠗⠳⠄⠠⠷⠷⠆⠠⠒⠶⢂⠔⠶⠆⠲⢦⠆⠰⠬⠶⠶⠽⠟⠿⠇⠀⠠⠔⠾⠿⠆⠲⠾⠗⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⣠⣤⣤⣀⠀⡀⠤⠄⠀⢠⣤⣤⡄⢠⠄⢠⠤⠀⢠⣤⡀⠀⠢⠘⠐⠀⠐⠀⠀⠀⠀⠤⡤⠠⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠠⠀⠭⠶⡦⠐⠰⠗⠆⠀⠘⠼⠽⢦⠤⠄⠸⠿⠇⠨⠡⠢⠃⠸⠷⠶⠶⠶⠶⠀⠶⠀⠚⣿⠷⠾⠟⠷⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠇⠶⠷⠷⠰⠶⠷⠆⠰⠰⠶⢶⠶⠶⠒⠶⠦⠀⠴⡶⠶⠥⠵⠿⠷⠗⠂⠾⠅⠼⠴⢶⠺⠶⠔⠴⠶⣤⠐⠂⠀⠂⠢⠀⠠⠄⠀⠖⠀⠀⠀⠀⠀⠤⠸⠣⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⡇⠀⠀⠀⠀⠀⠲⠊⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠂⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⡇⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠀⠄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣴⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠ ⡇⠀⠀⠀⠀⠈⠀⠀⠛⠈⠀⠀⠊⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠋⠁⠀⠀⠀⠐⠀⠀⠀⠘⠀⠔⠐⠀⠂⠀⠀⠀⠀⠠⠅⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⣤⢤⠀⠄⢨ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠿⠶⠶⠶⠤⠼⠰ ⠣⠚⠛⠛⠛⠛⠻⠛⠛⠙⠛⠙⠛⠟⠛⠛⠛⠛⠛⠓⠛⠛⠛⠛⠛⠂⠒⠒⠒⠂⠒⠒⠐⠂⠂⠒⠒⠐⠂⠒⠒⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠶⠶ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠄⠄⠤⠤⠀⠀⠤⠄⠀⠠⠤⠤⠂⠸⢷⠾⠴⠶⠶⠦⠅⠀⠒⠒⠒⠂⠀⠀⠀⠠⠤⠦⠤⠤⠤⠤⠤⠤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠾⠶⠶⠾⠶⠴⠶⠄⠀⠐⠐⠒⠂⠒⠐⠐⠀⠀⠀⢌ ⡇⠯⠶⠧⠶⢶⣶⡤⠆⠸⠆⠧⠤⠴⠦⢼⠷⠶⠲⠶⠺⠆⠰⠶⠶⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⡀⠀⠀⠀⠸⠷⠗⠚⠿⠆⠐⠾⠖⠆⠀⠶⠄⠀⠀⠂⠀⠀⠀⢻ ⡇⠟⠿⠿⠧⠂⠀⠀⠀⠰⠶⠦⠀⠲⠦⠶⠶⠆⠸⠷⠶⠲⠰⠶⠶⠂⠰⠶⠶⠶⠺⠳⠶⠶⠶⠖⠐⠗⠶⠷⠰⠀⣷⡿⠿⠶⠶⠆⠧⠖⠗⠂⡆⠂⠄⠀⠀⠀⠘⠓⠃⠘⠓⠣⠒⠒⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡷⠻⠖⠷⠷⠶⠗⠆⠀⠰⠷⠶⠲⠖⢸⠂⠴⠆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠶⠖⠇⠆⣦⠀⠀⠐⠢⠶⠔⠆⠰⠲⠶⠶⠄⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡟⠒⠶⠖⠶⢶⡶⢶⡶⠶⠆⠆⠀⠀⣄⠀⠀⠰⠆⠰⠦⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡘ ⡟⠗⠓⡾⠲⠷⠆⠀⠀⠀⠆⠐⢲⡆⠶⠖⠆⠰⡀⠾⠖⠲⠄⠔⢾⡆⠾⠚⠚⠺⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣏⡧⠆⠲⠖⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠞⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠛⠛⢃ ⠑⠐⠀⠀⣀⡀⣒⣀⠀⣐⣒⡂⣀⣀⣀⣐⢂⣀⠀⠰⣶⡤⣄⣒⣒⣒⣒⣒⣒⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣆⡃⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⣀⣀⣀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡹ ⡆⠈⠓⠛⠛⠛⠓⡣⣀⠀⠙⠛⠛⠛⠚⠛⠛⠛⠛⠛⠚⠛⠛⠛⠙⠛⠓⠓⠛⠛⠙⠛⠓⠋⠛⠙⠛⠛⠛⠚⠛⠛⠚⠛⠛⠙⠙⢻⢳⠛⠞⠛⠛⠓⠚⠛⠛⠓⠛⠛⠛⠙⠛⠛⠓⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠛⠁⠠ ⡇⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀ ⡇⠀⠤⠷⠖⠳⠔⠣⠶⡦⠀⠰⠖⠷⠆⠐⠆⠀⠗⠆⠰⠿⠖⠂⠰⠿⠷⡄⠷⠷⠖⠖⠶⠶⠼⠦⠰⠶⠷⠻⠤⠶⠖⠪⠿⠾⠶⠾⠿⠿⠾⠧⠿⠾⠶⠶⠆⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⡇⠀⠀⠀⠇⠶⠷⠶⠰⠷⠷⠆⠠⠲⠶⠶⡦⠶⠂⠶⠆⠄⠰⠶⠶⠶⠴⠿⠷⠇⠆⠐⠂⠰⠖⠞⠐⠾⠧⠒⠆⠇⠀⠰⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⣀⠒⠒⣂⡐⡖⠒⠒⢒⣲⣶⡖⠒⠒⢀⣒⣀⣀⢀⣐⣀⣀⣶⣒⣒⣀⣂⣘⣀⣀⣀⣀⡀⣀⢀⣀⣀⣀⣠⡀⠀⠀⠀⠀⢀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀ ⡇⠀⠠⠷⡶⠤⠄⠤⠤⠯⠔⠠⠆⠶⠦⠀⠂⠷⠤⠄⠀⠠⠶⢀⣠⣶⣶⣄⣰⣶⣆⣶⣤⣶⣶⣶⡦⡶⣆⣐⣃⣶⠾⠶⠰⠶⠷⠶⠶⠺⠓⠳⠗⠿⠽⠭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⢸⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣶⣶⣤⠶⣶⣶⣶⣶⣶⣶⣶⠦⠴⢶⡦⠴⠶⠦⠶⠦⠷⠶⠶⠶⠶⠶⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀ ⡇⠀⢀⣀⣁⡙⠿⠭⠭⠭⠽⠥⠭⠥⠴⠤⠵⠤⠌⠭⠷⠤⠄⠤⠽⠭⠭⠥⠭⠥⠤⠬⠬⠥⠤⠤⠤⠤⠤⠤⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴ ⡇⠀⠔⠍⠍⠥⠄⠴⠶⠖⠆⡰⠶⠶⠶⠐⠆⠠⠷⠶⠰⠶⠶⠆⠀⠶⠄⠶⠷⠶⠶⠶⠶⠶⠶⠿⠷⠶⠖⠲⠶⠲⠶⠾⠒⠶⠾⠶⡶⠎⠗⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠄⠶⠵⠷⠐⠲⠿⠖⠐⠶⡦⠶⡶⠃⠒⠂⠄⠆⠠⠶⠶⠵⠷⣾⠿⠇⠂⠸⠂⠸⠷⠧⠸⠷⠦⠢⠌⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⣀⣄⣀⣀⠀⠀⠄⠄⠀⠠⣤⣤⡄⢀⠀⢠⠤⠀⣠⡤⠤⠀⠤⠤⠠⠀⠤⠤⠤⠤⠀⠠⠠⠠⠶⠦⠴⠤⠦⠀⠀⠂⠠⠄⠠⠤⠤⠤⠤⠄⠤⠄⠤⠤⠤⠤⠄⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠ ⡇⠀⠀⠭⠍⠽⠄⠤⠶⠦⠀⠀⠩⠴⠗⠰⠆⠰⠿⠆⠰⠵⠦⠆⠰⠿⠾⠅⠰⠾⠾⠾⠒⠶⠷⠿⡆⠴⠶⠧⢵⠶⠶⡦⠴⠶⠂⠰⠶⠶⠾⠶⠷⠾⠾⠴⠎⠿⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠆⠗⠳⠄⠠⠷⠷⠆⠠⠒⠶⢂⠔⠶⠆⠲⢦⠆⠰⠬⠶⠶⠽⠟⠿⠇⠀⠠⠔⠾⠿⠆⠲⠾⠗⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⣠⣤⣤⣀⠀⡀⠤⠄⠀⢠⣤⣤⡄⢠⠄⢠⠤⠀⢠⣤⡀⠀⠢⠘⠐⠀⠐⠀⠀⠀⠀⠤⡤⠠⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠠⠀⠭⠶⡦⠐⠰⠗⠆⠀⠘⠼⠽⢦⠤⠄⠸⠿⠇⠨⠡⠢⠃⠸⠷⠶⠶⠶⠶⠀⠶⠀⠚⣿⠷⠾⠟⠷⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠇⠶⠷⠷⠰⠶⠷⠆⠰⠰⠶⢶⠶⠶⠒⠶⠦⠀⠰⡶⠶⠥⠵⠿⠷⠗⠂⠾⠅⠼⠴⢶⠺⠶⠔⠴⠶⣤⠐⠂⠀⠂⠢⠀⠠⠄⠀⠖⠀⠀⠀⠀⠀⠤⠸⠣⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⡇⠀⠀⠀⠀⠀⠲⠊⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠂⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⡇⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠀⠄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣴⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠ ⡇⠀⠀⠀⠀⠈⠀⠀⠛⠈⠀⠀⠊⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠋⠁⠀⠀⠀⠐⠀⠀⠀⠘⠀⠔⠐⠀⠂⠀⠀⠀⠀⠠⠅⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⣤⢤⠀⠄⢨ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠿⠶⠶⠶⠤⠼⠰ ⠣⠚⠛⠛⠛⠛⠻⠛⠛⠙⠛⠙⠛⠟⠛⠛⠛⠛⠛⠓⠛⠛⠛⠛⠛⠂⠒⠒⠂⠂⠒⠒⠐⠂⠂⠒⠐⠐⠂⠒⠒⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠶⠶ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠄⠄⠶⠤⠀⠰⠦⠄⠒⠢⠤⠤⠂⠸⢷⠾⠴⠶⠶⠦⠅⠀⠒⠒⠒⠂⠀⠀⠀⠠⠤⠦⠤⠤⠤⠤⠤⠤⣤⣤⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠸⠿⠷⠾⠶⠶⠾⠶⠴⠶⠄⠀⠐⠐⠀⠂⠒⠐⠐⠀⠀⠀⢌ ⡇⠯⠶⠧⠶⢶⣶⡤⠆⠸⠆⠧⠤⠴⠦⢼⠷⠶⠲⠶⠺⠆⠰⠶⠶⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⡀⠀⠀⠀⠸⠷⠗⠚⠿⠆⠐⠾⠖⠆⠀⠶⠄⠀⠀⠂⠀⠀⠀⢻ ⡇⠟⠿⠿⠧⠂⠀⠀⠀⠰⠷⠦⠀⠲⠦⠶⠶⠆⠸⠷⠶⠲⠰⠶⠶⠂⠰⠶⠶⠶⠺⠳⠶⠶⠶⠖⠐⠗⠶⠷⠰⠀⣷⡿⠿⠶⠶⠆⠧⠖⠗⠂⡆⠂⠄⠀⠀⠀⠘⠓⠃⠘⠓⠣⠒⠒⠔⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡷⠻⠖⠷⠷⠶⠗⠆⠀⠰⠷⠶⠲⠖⢸⠂⠴⠆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠶⠖⠇⠆⣦⠀⠀⠐⠢⠶⠔⠆⠰⠲⠶⠶⠄⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡟⠒⠶⠖⠶⢶⡶⢶⡶⠶⠆⠆⠀⠀⣄⠀⠀⠰⠆⠰⠦⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡘ ⡟⠗⠓⡾⠲⠷⠆⠀⠀⠀⠆⠐⢲⡆⠶⠖⠆⠰⡀⠾⠖⠲⠄⠔⢾⡆⠾⠚⠚⠺⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣏⡧⠆⠲⠖⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠞⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠛⠛⢃ ⠑⠐⠀⠒⠒⠐⠀⢀⠀⣐⣒⡂⣀⡀⠀⠐⠂⠀⠀⠰⣲⡐⣒⡒⠒⠒⠒⠒⣒⠂⣐⡂⠒⠒⠂⠂⠒⠒⠒⢒⣒⣒⡓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⣀⣀⣀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡹ ⡆⠈⠒⠒⠒⠒⠒⡲⣀⠀⠙⠛⠒⠒⠒⠒⠒⠒⠚⠛⠚⠛⠛⠓⠛⠛⠓⠓⠛⠓⠓⠓⠒⠂⠒⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠐⠐⢲⢲⠒⠞⠛⠛⠓⠚⠛⠛⠓⠛⠛⠛⠙⠛⠛⠓⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠛⠁⠠ ⡇⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀ ⡇⠀⠤⠷⠖⠳⠔⠣⠶⡦⠀⠰⠖⠷⠆⠐⠆⠀⠗⠆⠰⠿⠖⠂⠰⠿⠷⡄⠷⠷⠖⠖⠶⠶⠼⠦⠰⠶⠷⠻⠤⠶⠖⠪⠿⠾⠶⠾⠿⠿⠾⠧⠿⠾⠶⠶⠆⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⡇⠀⠀⠀⠇⠶⠷⠶⠰⠷⠷⠆⠠⠲⠶⠶⡦⠶⠂⠶⠆⠄⠰⠶⠶⠶⠴⠿⠷⠇⠆⠐⠂⠰⠖⠞⠐⠾⠧⠒⠆⠇⠀⠰⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⣀⠒⠒⣂⡐⡖⠒⠒⠒⢒⣶⡖⠒⠒⢀⣒⣀⣀⢀⠐⢀⣀⣶⣒⢒⣀⣂⣘⣀⣀⣀⣀⡀⣀⢀⣀⣀⣀⣠⡀⠀⠀⠀⠀⢀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀ ⡇⠀⠠⠷⡶⠤⠄⠤⠤⠯⠄⠠⠆⠶⠦⠀⠂⠷⠤⠄⠀⠠⠶⢀⣠⣶⣶⣄⣰⣶⣆⣶⣤⣶⣶⣶⡦⡶⣆⣐⣃⣶⠾⠶⠰⠶⠷⠶⠶⠺⠓⠳⠗⠿⠽⠭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⢸⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣶⣶⣤⠶⣶⣶⣶⣶⣶⣶⣶⠦⠴⢶⡦⠴⠶⠦⠶⠦⠷⠶⠶⠶⠶⠶⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀ ⡇⠀⢀⣀⣁⡙⠿⠭⠭⠥⠼⠤⠬⠥⠴⠤⠵⠤⠌⠭⠷⠤⠄⠤⠽⠭⠭⠥⠭⠥⠤⠬⠬⠥⠤⠤⠤⠤⠤⠤⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴ ⡇⠀⠄⠍⠍⠥⠄⠴⠶⠖⠆⡰⠶⠶⠶⠐⠆⠠⠷⠶⠰⠶⠶⠆⠀⠶⠄⠶⠷⠶⠶⠶⠶⠶⠶⠿⠷⠶⠖⠲⠶⠲⠶⠾⠒⠶⠾⠶⡶⠎⠗⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠄⠶⠵⠷⠐⠲⠿⠖⠐⠶⠦⠶⡶⠃⠒⠂⠄⠆⠠⠶⠶⠵⠷⣾⠿⠇⠂⠸⠂⠸⠷⠧⠸⠷⠦⠢⠌⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⣀⣄⣀⣀⠀⠀⠄⠄⠀⠠⣤⣤⡄⢀⠀⢠⠤⠀⣠⡤⠤⠀⠤⠤⠠⠀⠤⠤⠤⠤⠀⠠⠠⠠⠶⠦⠴⠤⠦⠀⠀⠂⠠⠄⠠⠤⠤⠤⠤⠄⠤⠄⠤⠤⠤⠤⠄⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠ ⡇⠀⠀⠭⠍⠽⠄⠤⠶⠆⠀⠀⠩⠴⠗⠰⠆⠰⠿⠆⠰⠵⠦⠆⠰⠿⠾⠅⠰⠾⠾⠾⠒⠶⠷⠿⡆⠴⠶⠧⢴⠶⠶⡦⠴⠶⠂⠰⠶⠶⠾⠶⠷⠾⠾⠴⠎⠿⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠆⠗⠳⠄⠠⠷⠷⠆⠠⠒⠶⢂⠔⠶⠆⠲⢦⠆⠰⠬⠶⠶⠽⠟⠿⠇⠀⠠⠔⠾⠿⠆⠲⠾⠗⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⣠⣤⣤⣀⠀⡀⠤⠄⠀⢠⣤⣤⡄⢠⠄⢠⠤⠀⢠⣤⡀⠀⠢⠘⠐⠀⠐⠀⠀⠀⠀⠤⡤⠠⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠠⠀⠭⠶⡦⠐⠰⠗⠆⠀⠘⠼⠽⢦⠤⠄⠸⠿⠇⠨⠡⠢⠃⠸⠷⠶⠶⠶⠶⠀⠶⠀⠚⣿⠷⠾⠟⠷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠇⠖⠷⠷⠰⠶⠷⠆⠰⠰⠶⢶⠶⠶⠒⠶⠦⠀⠰⡶⠶⠥⠵⠿⠷⠗⠂⠾⠅⠼⠴⢶⠺⠶⠔⠴⠶⣤⠐⠂⠀⠂⠢⠀⠠⠄⠀⠖⠀⠀⠀⠀⠀⠤⠸⠣⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⡇⠀⠀⠀⠀⠀⠲⠊⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠂⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⡇⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠀⠄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣴⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠ ⡇⠀⠀⠀⠀⠈⠀⠀⠛⠈⠀⠀⠊⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠋⠁⠀⠀⠀⠐⠀⠀⠀⠘⠀⠔⠐⠀⠂⠀⠀⠀⠀⠠⠅⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⣤⢤⠀⠄⢨ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠿⠶⠶⠶⠤⠼⠰ ⠣⠚⠛⠛⠛⠛⠻⠛⠛⠛⠛⠛⠛⠟⠚⠛⠛⠛⠛⠓⠛⠛⠛⠛⠛⠂⠒⠐⠂⠂⠒⠒⠐⠂⠒⠒⠒⠐⠒⠒⠂⠒⠐⠒⠒⠒⠒⠒⠒⠂⠐⠒⠒⠒⠒⠒⠒⠒⠒⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠶⠶ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠀⠄⠄⠀⠀⠤⠰⠦⠄⠀⠠⠤⠤⠂⠸⢷⠾⠴⠶⠶⠦⠅⠀⠒⠒⠒⠂⠀⠀⠀⠠⠤⠦⠤⠄⠀⠀⠀⠀⣤⣤⠀⠀⠀⠐⠒⠂⠀⠀⠂⠀⠀⠸⠿⠷⠾⠶⠶⠾⠶⠴⠶⠄⠀⠐⠐⠀⠂⠒⠐⠐⠀⠀⠀⢌ ⡇⠯⠶⠧⠶⢶⣶⡤⠆⠸⠆⠧⠤⠴⠦⢼⠷⠶⠲⠶⠺⠆⠰⠶⠶⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡿⣿⠿⠶⠶⠇⠷⠶⠆⠄⠀⠀⡀⠀⠀⠀⠸⠷⠗⠚⠿⠆⠐⠾⠶⠆⠀⠶⠄⠀⠀⠂⠀⠀⠀⢻ ⡇⠟⠿⠿⠧⠂⠀⠀⠀⠰⠷⠦⠀⠲⠦⠶⠶⠆⠸⠷⠶⠲⠰⠶⠶⠂⠰⠶⠶⠶⠺⠳⠶⠶⠶⠖⠐⠗⠶⠷⠰⠀⣷⡿⠿⠶⠶⠆⠧⠖⠗⠂⡆⠂⠄⠀⠀⠀⠘⠓⠃⠘⠓⠣⠒⠒⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡷⠻⠖⠷⠷⠶⠗⠆⠀⠰⠷⠶⠲⠖⢸⠂⠴⠆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠶⠖⠇⠆⣦⠀⠀⠐⠢⠶⠔⠆⠰⠲⠶⠶⠄⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡟⠒⠶⠖⠶⢶⡶⢶⡶⠶⠆⠆⠀⠀⣄⠀⠀⠀⠆⠰⠦⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡘ ⡟⠗⠓⡾⠲⠷⠆⠀⠀⠀⠆⠐⢲⡆⠶⠖⠆⠰⡀⠾⠖⠲⠄⠔⢾⡆⠾⠚⠚⠺⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣏⡧⠆⠲⠖⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠞⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠛⠛⢃ ⠑⠐⠀⠤⠤⠔⠀⢀⠀⣐⣒⡂⣀⡀⠀⠐⠂⠀⠀⠠⣀⡀⣤⡤⠤⠤⠤⠤⣶⠦⣤⡤⠤⠄⠠⠄⠶⠖⠒⢒⣒⣒⡓⠋⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⣀⣀⣀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡹ ⡆⠈⠤⠤⠤⠤⠠⡤⣤⠤⠽⠟⠤⠤⠠⠤⠤⠴⠾⠟⠾⠟⠛⠃⠤⠀⠤⠄⠉⠁⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠶⠴⠴⢶⢶⠖⠞⠛⠛⠓⠚⠛⠛⠓⠛⠛⠛⠙⠛⠛⠓⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠛⠁⠠ ⡇⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀ ⡇⠀⠤⠷⠖⠳⠔⠣⠶⡦⠀⠰⠖⠷⠆⠐⠆⠀⠗⠆⠰⠿⠖⠂⠰⠿⠷⡄⠷⠷⠖⠖⠶⠶⠼⠦⠰⠶⠷⠻⠤⠶⠖⠪⠿⠾⠶⠾⠿⠿⠾⠧⠿⠾⠶⠶⠆⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⡇⠀⠀⠀⠇⠶⠷⠶⠰⠷⠷⠆⠠⠲⠶⠶⡦⠶⠂⠶⠆⠄⠰⠶⠶⠶⠴⠿⠷⠇⠆⠐⠂⠰⠖⠞⠐⠾⠧⠒⠆⠇⠀⠰⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⣀⠒⠒⣂⡐⡖⠒⠒⠒⢒⣶⡖⠒⠒⢀⣒⣀⣀⢀⠐⢀⣀⣶⣒⢒⣀⣂⣘⣀⣀⣀⣀⡀⣀⢀⣀⣀⣀⣠⡀⠀⠀⠀⠀⢀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀ ⡇⠀⠠⠷⡶⠤⠄⠤⠤⠯⠄⠠⠆⠶⠦⠀⠂⠷⠤⠄⠀⠠⠶⢀⣠⣶⣶⣄⣰⣶⣆⣶⣤⣶⣶⣶⡦⡶⣆⣐⣃⣶⠾⠶⠰⠶⠷⠶⠶⠺⠓⠳⠗⠿⠽⠭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⢸⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣶⣶⣤⠶⣶⣶⣶⣶⣶⣶⣶⠦⠴⢶⡦⠴⠶⠦⠶⠦⠷⠶⠶⠶⠶⠶⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀ ⡇⠀⢀⣀⣁⡙⠿⠭⠭⠽⠭⠷⠬⠥⠴⠤⠵⠤⠌⠭⠷⠤⠄⠤⠽⠭⠭⠥⠭⠥⠤⠬⠬⠥⠤⠤⠤⠤⠤⠤⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴ ⡇⠀⠔⠍⠍⠥⠄⠴⠶⠖⠆⡰⠶⠶⠶⠐⠆⠠⠷⠶⠰⠶⠶⠆⠀⠶⠄⠶⠷⠶⠶⠶⠶⠶⠶⠿⠷⠶⠖⠲⠶⠲⠶⠾⠒⠶⠾⠶⡶⠎⠗⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠄⠶⠵⠷⠐⠲⠿⠖⠐⠶⠦⠶⡶⠃⠒⠂⠄⠆⠠⠶⠶⠵⠷⣾⠿⠇⠂⠸⠂⠸⠷⠧⠸⠷⠦⠢⠌⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⣀⣄⣀⣀⠀⠀⠄⠄⠀⠠⣤⣤⡄⢀⠀⢠⠤⠀⣠⡤⠤⠀⠤⠤⠠⠀⠤⠤⠤⠤⠀⠠⠠⠠⠶⠦⠴⠤⠦⠀⠀⠂⠠⠄⠠⠤⠤⠤⠤⠄⠤⠄⠤⠤⠤⠤⠄⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠ ⡇⠀⠀⠭⠍⠽⠄⠤⠶⠆⠀⠀⠩⠴⠗⠰⠆⠰⠿⠆⠰⠵⠦⠆⠰⠿⠾⠅⠰⠾⠾⠾⠒⠶⠷⠿⡆⠴⠶⠧⢴⠶⠶⡦⠴⠶⠂⠰⠶⠶⠾⠶⠷⠾⠾⠴⠎⠿⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠆⠗⠳⠄⠠⠷⠷⠄⠠⠒⠶⢂⠔⠶⠆⠲⢦⠆⠰⠬⠶⠶⠽⠟⠿⠇⠀⠠⠔⠾⠿⠆⠲⠾⠗⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⣠⣤⣤⣀⠀⡀⠤⠄⠀⢠⣤⣤⡄⢠⠄⢠⠤⠀⢠⣤⡀⠀⠢⠘⠐⠀⠐⠀⠀⠀⠀⠤⡤⠠⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠠⠀⠭⠶⡦⠐⠰⠗⠆⠀⠘⠼⠽⢦⠤⠄⠸⠿⠇⠨⠡⠢⠃⠸⠷⠶⠶⠶⠶⠀⠶⠀⠚⣿⠷⠾⠟⠷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠇⠖⠷⠷⠰⠶⠷⠄⠰⠰⠶⢶⠶⠶⠒⠶⠦⠀⠰⡶⠶⠥⠵⠿⠷⠗⠂⠾⠅⠼⠴⢶⠺⠶⠔⠴⠴⣤⠐⠂⠀⠂⠢⠀⠠⠄⠀⠖⠀⠀⠀⠀⠀⠤⠸⠣⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⡇⠀⠀⠀⠀⠀⠲⠊⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠂⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⡇⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠀⠄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣴⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠ ⡇⠀⠀⠀⠀⠈⠀⠀⠛⠈⠀⠀⠊⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠋⠁⠀⠀⠀⠐⠀⠀⠀⠘⠀⠔⠐⠀⠂⠀⠀⠀⠀⠠⠅⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⣤⢤⠀⠄⢨ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠿⠶⠶⠶⠤⠼⠰ ⠣⠚⠛⠛⠛⠛⠻⠛⠛⠛⠛⠛⠛⠟⠚⠛⠛⠛⠛⠓⠛⠛⠛⠛⠛⠂⠒⠐⠂⠂⠒⠒⠐⠂⠒⠒⠒⠐⠒⠒⠂⠒⠐⠒⠒⠒⠒⠒⠒⠂⠐⠒⠒⠒⠒⠒⠒⠒⠒⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠶⠶ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡽⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠹⢿⠿⠿⠿⠿⠿⠏⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣯⣽⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠹⠿⠿⠿⠿⠿⠿⠿⠿⠿⠏⠙⠛⠛⠛⠛⠛⠛⠓⠛⠚⠛⢯ ⡿⠿⠶⠷⠶⢶⣶⡶⠆⠸⠧⠷⠶⠶⠆⠸⠷⠶⠲⠶⠾⠆⠸⠶⠶⠶⠶⠾⠶⠶⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠶⠶⠧⠷⠶⠆⠆⠀⠀⠀⠀⠀⠀⠸⠿⠇⠾⠿⠷⠼⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡿⠿⠿⠿⠷⠄⠀⠀⠀⠸⠷⠶⠲⠶⠶⠶⠶⠆⠸⠷⠾⠶⠾⠶⠶⠂⠸⠶⠾⠼⠿⠿⠿⠽⠶⠖⠒⠶⠶⠷⠿⠀⣿⣿⠿⠶⠶⠶⠷⠶⠷⢶⡆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡿⠿⠷⠿⠷⠷⠇⠇⠀⠸⠷⠶⠲⠆⠸⠻⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠿⠇⠗⠿⠶⠃⠀⠸⠷⠶⠾⠇⠸⠳⠶⠾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠷⠗⠷⠶⠿⠷⠷⠞⠇⠃⠀⠀⠀⠀⠀⠸⠇⠸⠗⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡟⠿⠟⠟⠿⠟⠇⠃⠀⠀⠇⠘⠿⠟⠿⠿⠃⠸⠺⠻⠻⠿⠻⠚⠿⠆⠾⠺⠺⠻⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠟⠟⠿⠟⠇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠑⠒⠒⠒⠒⠂⠒⠒⠂⠒⠒⠂⠂⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠒⠒⠂⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠋⠙⠒⠒⠒⠂⠂⠒⠒⠒⠒⠒⠒⠐⠒⠒⠒⠐⠒⠒⠒⠒⠒⠒⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠊ ⡞⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢳ ⡇⠀⠛⠛⠛⠛⠛⠛⠛⠃⠀⠘⠛⠛⠃⠸⠂⠐⠙⠃⠙⠚⠛⠁⠛⠛⠓⠀⠛⠛⠛⠙⠛⠛⠛⠉⠛⠛⠋⠓⠋⠛⠛⠙⠛⠛⠛⠛⠓⠓⠓⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠐⠛⠛⠛⠛⠙⠛⠛⠃⠀⠘⠛⠛⠃⠘⠚⠛⠛⠃⠙⠛⠛⠁⠛⠛⠛⠂⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠛⠋⠛⠛⠙⠛⠛⠛⠛⠛⠓⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠓⠚⠒⠒⠐⠓⠚⠂⠀⠐⠒⠚⠂⠀⠂⠐⠒⠃⠐⠚⠒⠀⠐⠒⠒⠒⠒⠒⠓⠒⠓⠛⠒⠚⠓⠂⠀⠛⠂⠚⠒⠃⠒⠓⠒⠒⠃⠂⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠒⠒⠒⠀⠒⠒⠂⠀⠐⠒⠒⠂⠀⠂⠐⠒⠂⠐⠒⠒⠀⠘⠒⠐⠀⠚⠒⠒⠒⠀⠐⠒⠒⠀⠒⠂⠒⠒⠒⠒⠀⠒⠂⠀⠒⠒⠐⠒⠂⠒⠒⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠒⠂⠂⠀⠒⠒⠂⠀⠐⠒⠒⠂⠀⠀⠐⠒⠂⠐⠒⠐⠀⠀⠒⠒⠐⠒⠂⠀⠒⠀⠐⠐⠒⠒⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⢀⢸ ⡅⣤⣄⣄⣄⣀⣄⡄⣠⣤⡄⢀⣄⡄⣀⣤⡀⢠⣤⡤⡄⢀⣀⣀⢠⣀⣀⢀⠀⣤⣀⣀⣀⣠⠀⢀⣠⣀⣀⢀⣀⣤⡀⠀⠀⢀⣄⣤⣄⠀⢠⣤⣄⠄⢠⣤⣤⣄⣤⣤⣤⡀⣠⣠⣠⣤⠀⠀⠀⢠⣠⠉⣩⣭⠙⠀⣭⢘ ⡍⣭⣭⣭⣍⣉⣍⡍⡩⣭⡅⠀⣍⡅⢉⣩⡅⢨⣭⡩⡅⢈⣉⣩⢨⣉⣉⠈⠀⣭⣉⣉⣉⣩⠀⢁⣩⣉⣉⢁⣉⣭⣍⠁⠀⢈⣍⣭⣍⠁⢨⣭⣭⠅⢨⣭⣍⣠⣩⣭⣭⣡⣈⣭⣍⢨⠉⠀⢠⣨⣨⡀⣩⣭⠉⠀⣭⢁ ⣭⣨⣭⣭⣬⣭⣭⣭⣭⡭⣍⣥⡍⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠄⠤⠤⠀⠀⠌⠉⠉⠩⠭⠉⠡⠁⠠⠀⠀⠈⠠⠡⠀⠩⠭⠀⠀⠨⠁ ⡍⣭⣭⣭⣥⣥⣍⣭⣭⣭⡥⢭⣭⡥⢬⣥⡤⠬⣬⡌⡀⢈⣈⣈⢈⣈⣈⠀⠀⣀⣈⣉⣁⣉⠀⣀⣉⣉⣀⣀⣁⣉⡁⠁⠀⢀⣁⣉⣁⠁⢀⣍⣁⣁⣈⣉⡀⢁⡀⢀⣀⣀⣀⣀⣀⡀⠀⠀⣀⣀⠀⣀⣀⠀⠀⢀⣀⣀ ⡍⣩⣭⣩⣭⣠⣥⣍⣨⣭⡁⠠⡭⡅⠨⣭⡅⠈⣭⡉⡅⢨⣩⣩⢨⣩⣩⠠⠀⣡⣭⣉⣉⣩⠀⣁⣩⣉⣉⣡⣍⣭⣅⠁⠀⢠⣭⣭⣅⠁⢨⣭⣍⡍⡭⣭⣤⡌⢡⣬⣭⢉⣭⣍⣌⣭⣠⠀⠈⠉⠀⢉⠉⣌⣤⠉⠁⣍ ⡄⣬⣤⣭⣭⣩⣭⣍⣡⣭⡅⠠⡤⡄⣤⣤⡄⢠⣤⡠⡄⢠⣠⣠⢄⣠⣩⢠⠀⣥⣉⣩⣩⣉⣤⣤⣩⣭⣭⣄⣉⠉⣅⢀⣤⣠⠉⣉⠅⠁⠌⠨⠉⠁⠅⠉⠉⠁⠈⠉⠈⠉⠉⠈⠉⠉⠉⠈⠀⠀⠀⠈⠀⠈⠉⠈⠀⠉ ⡅⣭⣭⣭⣥⣠⣥⣍⣬⡭⡅⠠⡭⡅⢨⣭⡄⠨⣭⣩⡄⢨⣭⣬⢨⣭⣭⢀⠀⣨⣌⣭⣭⣤⣬⣉⣥⣭⣬⣭⣭⡤⣄⣀⣄⣥⣥⡅⠀⡄⢠⣤⣤⣄⡄⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣆⣦⣦⣦⣦⣤⣦⣆⣄⣶⡄⠠⣥⡄⣤⣤⡄⢰⣶⣀⡄⢠⣤⣤⢠⣤⣤⠠⠀⣤⣭⣥⣤⣤⣤⣀⣤⣤⢄⣤⠀⣤⢠⣤⣤⡄⠀⣤⣤⣤⣤⣤⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀ ⣆⣶⣶⣦⣦⣤⣦⣆⣴⣶⡆⢠⣦⡆⣤⣴⡆⣰⣶⣔⡆⢠⣤⣤⣰⣤⣤⢠⠀⣦⣤⣤⣤⣦⣤⣤⡤⣴⠀⣤⣤⡤⣤⣤⣤⣤⠀⡄⠀⡄⣠⡤⠀⠐⠒⠂⠐⠒⠒⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣆⣶⣶⣶⣦⣤⣦⣦⢴⣶⡆⠀⣦⡆⣠⣶⡆⢰⣶⣔⡆⢠⣤⣴⢰⣤⣤⢀⠀⣦⣤⣤⣤⣦⢠⣤⠤⣴⣤⣤⣤⡄⣤⡦⣤⣦⣤⣤⡄⠀⠄⠂⣤⡴⢢⣤⡔⢢⢴⣶⣤⣤⣦⡔⢢⣤⡔⣤⣜⣦⣒⣤⠀⠀⠀⠀⠀⠀ ⣆⣶⣶⣶⣦⠴⡦⣦⢴⣶⡆⢀⣶⡆⢴⣶⡆⢰⣶⣔⡆⢠⣤⣴⣰⣤⣤⠠⠀⣤⣦⣤⣤⣤⢴⣤⠤⣤⣭⡥⣤⣦⣤⠤⣤⣤⣤⣶⣤⡜⠃⠄⠐⣦⡆⢢⣦⡄⢢⢴⣦⣤⣴⣦⡔⢢⣶⡆⣤⣄⣤⢀⣤⢀⠀⠀⠀⠀ ⣆⣶⣶⣶⣦⠴⡶⣦⢴⣶⡆⠐⣖⡆⢰⣶⡆⢐⣶⣔⡆⢠⣤⣴⢰⣤⣤⠀⠀⣤⡤⣤⣤⣤⣤⣤⣤⡤⠤⣶⣤⣤⣦⣦⣤⣥⣤⡤⢦⣤⡄⠀⡔⡂⣴⣦⣤⠤⡄⢀⢀⠀⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣆⣶⣶⣶⡶⠶⡶⣦⢴⣶⡆⠐⣖⡆⠒⣶⠆⢀⣶⡄⠆⢰⣴⣴⢰⣴⣴⠀⠀⢴⣴⣴⡴⣴⣤⠴⣤⡦⠤⡖⣦⣦⣤⠤⡦⣦⣦⡤⡀⡄⠠⠖⠶⣶⡆⠰⢶⣶⠆⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡆⣶⣶⡶⡶⠴⡶⣦⢴⣶⡆⠐⣶⡆⢶⣶⡆⢰⣶⡔⠆⢰⣴⢶⢰⢴⢴⠐⠀⠠⢾⣶⢦⠴⣶⣶⣦⠀⣤⣦⡦⠗⣧⣴⡦⡶⡦⡴⠶⣶⣤⣴⣴⣦⠆⢶⣶⠖⢶⡤⣦⠶⢶⣶⢴⠤⣶⢶⢶⣶⠶⠀⠀⠀⠀⠀⠀⠀ ⠧⠷⠷⠷⠷⠶⠷⠦⠶⠿⠇⠰⠶⠆⠶⠶⠆⠸⠿⠾⠆⠰⠶⠶⠸⠶⠶⠰⠀⠶⠶⠶⠶⠶⠶⠶⠶⠶⠲⠶⠶⠖⠶⠶⠶⠶⠒⠖⠒⠶⠦⠴⠦⠤⠷⠖⠖⠲⠦⠤⠴⠤⠠⠤⠤⠤⠀⠠⠤⠤⠄⠤⠤⠤⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠶⠷⠧⠮⠿⠇⠰⠷⠇⠶⠿⠇⠺⠿⠦⠇⠰⠶⠾⠼⠶⠶⠰⠀⠶⠶⠶⠶⠖⠶⠤⠶⠶⠶⠾⠶⠶⠶⠤⠶⠶⠶⠶⠲⠦⠤⠭⠿⠿⠷⠮⠿⠷⠲⠶⠶⠶⠶⠦⠤⠤⠠⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠯⠿⠿⠿⠷⠶⠷⠷⠺⠿⠇⠰⠿⠇⠾⠿⠇⠼⠿⠯⠇⠰⠶⠾⠼⠶⠶⠰⠀⠔⠾⠶⠶⠖⠶⠾⠶⠤⠀⠶⠶⠶⠧⠖⠷⠷⠷⠶⠷⠶⠖⠸⠿⠿⠧⠒⠿⠿⠿⠶⠺⠓⠿⠿⠿⠿⠿⠿⠿⠿⠾⠆⠀⠀⠀⠀⠀⠀ ⠯⠿⠿⠿⠷⠚⠟⠷⠺⠿⠇⠠⠿⠇⠸⠿⠇⠸⠿⠿⠇⠰⠶⠾⠸⠶⠶⠢⠀⠔⠾⠶⠶⠖⠶⠾⠶⠤⠓⠶⠶⠤⠶⠖⠶⠧⠶⠣⠴⠶⠖⠺⠶⠶⠦⠘⠿⠿⠿⠿⠻⠿⠿⠿⠿⠿⠭⠬⠬⠬⠬⠈⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠚⠟⠷⠺⠿⠇⠨⠿⠇⠻⠿⠇⠸⠿⠿⠇⠰⠶⠾⠼⠾⠶⠚⠀⠔⠾⠶⠶⠖⠶⠾⡿⠀⠶⠶⠶⠒⠷⠾⠗⠿⠷⠖⠻⠶⠶⠼⠿⠿⠇⠺⠿⠿⠿⠶⠿⠟⠿⠟⠛⠛⠛⠛⠙⠛⠛⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠿⠚⠟⠷⠺⠿⠇⠈⠿⠇⠺⠿⠇⠸⠿⠿⠇⠸⠾⠾⠸⠾⠾⠘⠀⠿⠻⠾⠞⠻⠸⠾⠶⠀⠶⠷⠿⠷⠛⠬⠃⠽⠟⠃⠄⠧⠼⠿⠗⠱⠿⠳⠷⠖⠻⠶⠟⠃⠠⠤⠤⠌⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⡟⡟⡟⡟⠚⡟⡗⠻⣟⡇⠈⠟⠇⠙⢿⡇⢸⣿⠛⠃⠸⠿⠻⠸⠻⠻⠈⠀⢹⠻⠺⠟⠻⠸⠻⠿⠀⠟⠟⠟⠟⠉⠶⠃⠆⠃⠙⠚⠟⠖⠿⠇⠀⠗⠋⠇⠀⠙⠿⠋⠑⠲⠶⠲⠒⠰⠲⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⡟⡟⡟⡟⠛⡟⡗⢛⣟⡇⠘⡟⡇⠛⢿⡇⢻⣿⣚⠃⠘⠻⠛⢸⠻⠻⠘⠀⢹⠛⠻⠻⠛⠻⠛⠿⠀⠛⠗⠛⠛⠖⡗⠊⡓⠖⠖⠛⠟⠛⠓⡇⠎⡃⠋⠓⠒⠚⠛⠳⠲⠛⠛⠳⠳⠻⢚⢙⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⡛⠛⡛⡓⢛⣛⡃⠘⡛⡃⢛⣛⡃⢚⣛⣛⡃⠘⠛⢛⢘⠛⠛⠘⠀⢙⠛⠛⠛⡛⢚⠛⠿⠀⠛⠛⠓⠛⠚⠛⠈⡑⠓⠛⠛⠛⠘⠃⡃⡋⡃⠈⠙⠛⠋⠘⠛⠛⠛⠛⠙⠛⠛⠊⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣓⣛⣛⣛⡛⢛⡛⡓⢛⣛⡃⢘⣛⡃⢛⣛⡃⢘⣛⣓⡃⠘⠛⢛⢚⠛⠛⠙⠀⣚⣛⢛⣛⣛⡛⣛⣿⡀⣛⠛⡛⠛⡛⠉⠒⠀⠛⠋⡙⡃⡘⠓⠓⢑⡓⠒⠚⠛⡓⠒⠛⠛⢉⡉⠙⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⡛⢙⣋⡛⢙⣛⡃⢘⣛⡃⢛⣛⡁⢚⣛⣛⡃⠘⠛⢛⢚⠛⠛⠘⠀⣚⡙⠛⢛⢛⠛⣛⠛⠉⠟⡒⡛⠛⡉⠛⠋⣚⠋⠙⠛⠛⡛⠛⠃⡘⠛⠑⠒⠋⢙⡛⠋⠙⠙⠛⠓⠒⠐⠒⠲⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⣛⢉⣋⡛⢙⣛⡃⢐⣛⡃⣚⣛⡃⢘⣛⢛⡃⢘⢛⢛⢘⢛⢛⢑⠀⣛⣛⠛⢛⣛⣛⠛⢛⠛⣞⡓⠀⡛⡛⡛⠛⢛⣘⡛⡋⠃⡃⡛⡛⠋⠈⠛⠋⠘⠙⠛⠛⡛⠙⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⣛⢉⣋⡛⢙⣛⡃⢐⣛⡃⣙⣛⡁⢘⣛⣛⡃⢘⠛⢛⢚⢛⢛⢉⠀⣙⣛⣛⣛⣛⣛⣛⣛⣒⣉⣋⠛⡋⠛⡋⡒⡛⠛⠉⡛⣛⣛⡛⡁⡐⢒⡂⠀⠐⣒⣲⡂⠀⡐⢀⣐⠂⠲⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⣛⣉⣋⡛⣙⣛⡃⢀⣛⡃⣑⣛⡃⢈⣛⣛⡃⢘⣛⣛⢚⣛⣛⢈⠀⣋⣙⣛⣙⣛⣛⣛⣛⠈⢛⡛⣛⣛⡈⡛⠉⣃⣋⣉⣋⢛⣛⡛⡋⠙⠛⢙⢃⡊⠙⠛⠋⠙⠙⠛⠛⠃⠐⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⣏⣏⣏⣏⣉⣏⡏⣙⣯⡇⢀⣋⡃⣀⣩⣅⣸⣿⡍⡁⢘⣛⣙⢘⣙⣙⢈⠀⢩⣹⣏⣸⣩⣽⣽⣭⣛⣀⣭⣙⠋⣁⣀⣉⣋⣋⢋⣉⡋⣋⣃⣀⣋⡃⢌⣛⡛⠋⣛⣃⣀⡀⣀⣀⣀⠐⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡭⣯⣍⣏⣍⣉⣍⡍⣩⣯⡅⢈⣏⡇⣉⣍⡅⣩⣩⣩⡁⢈⣙⣉⢨⣙⣙⢈⠀⣬⣹⣉⣩⣉⣍⣉⣩⠉⣫⣉⣉⣂⣍⣋⠉⣋⣋⣈⣍⣃⣍⣉⡉⠏⠁⡌⠙⠃⠈⠉⠙⠍⠉⠈⠉⠹⢥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡍⣭⣭⣭⣍⣉⣍⣍⣩⣭⡅⢈⣭⡅⣩⣭⡅⢩⣩⡭⡅⢈⣉⣩⢩⣉⣉⣈⠀⢩⣭⣭⡭⡭⣿⣭⣭⢺⠉⣭⣍⣉⣉⣍⣀⣍⠉⣍⣉⣉⣍⣉⡉⠀⣀⣄⣀⡐⣀⣐⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡍⣭⣭⣭⣍⣩⣍⣍⣩⣭⡅⢨⣭⡅⣩⡭⡅⢨⣭⡭⡅⢈⣉⣩⢩⣉⣉⢈⠀⣭⣭⣉⣩⣉⣍⣉⣩⠉⣭⣉⣀⣉⣟⣉⣉⣉⣈⣉⣍⡁⣍⣉⣉⡍⠨⡍⢁⣈⡈⠉⣉⣅⣈⣉⣉⣡⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡭⣭⣭⣭⣍⣠⣥⣍⣨⣭⡅⢨⣭⡅⢩⣭⡅⢩⣭⡭⡅⢈⣉⣩⢩⣉⣉⠈⠀⣭⢭⣉⣩⣉⣍⣉⣹⠀⡉⣉⣉⣉⣋⠍⣈⣍⣉⣉⡉⠈⡉⢉⣅⡠⠄⡠⢄⣀⡀⢀⣀⣀⣠⣄⣀⣀⣀⠠⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⡍⣭⣭⣭⣭⣠⣥⣍⣨⣭⡅⢨⣭⡅⣭⣭⡁⢨⣭⣭⡅⣨⣩⣩⣩⣭⡩⠈⣠⣉⣨⣩⣩⡉⣩⣭⣋⣤⣭⣍⣉⣩⣭⣅⣍⣭⣉⠍⢁⣄⣅⣍⣍⠄⣀⣥⣬⣍⣥⡌⣬⣭⣩⢩⣌⣭⠈⣠⣠⣠⣠⣤⠀⠀⠀⠀⠀⠀ ⡍⣭⣭⣭⣭⣠⣥⣍⣨⣭⡅⢨⣭⡅⣤⣭⡅⢠⣭⣬⡅⢨⣩⣨⢨⣩⣠⣠⠈⢭⣍⣉⣬⣭⣄⣬⣉⢀⠁⣭⣭⣍⣄⡅⣥⣭⣍⠀⣌⣌⣭⡍⢉⣌⣍⣍⣁⣸⣥⣔⡀⢀⣠⡀⢠⣤⣠⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⡍⣭⣭⣯⣭⣤⣥⣍⣬⣭⡅⠠⣥⡅⣬⣭⡄⢴⣥⣭⡅⢨⣭⣭⢨⣭⣭⠠⠀⣨⣭⣭⣭⡭⣭⣭⣭⢨⠀⣤⣭⣥⣭⣥⣥⣭⢁⣤⣭⣍⣥⣥⡄⢈⣭⣭⣭⣌⣭⣭⣥⠌⠉⠁⠈⠉⠉⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠁⠁⠁⠀⠀⠁⠁⠀⠁⠀⠀⠁⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠁⠀⠀⠉⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⡀⡀⠀⠄⢀⣆⠀⣀⢀⢀⡀⠀⠀⠰⢲⠀⠀⠀⣀⠀⢀⠀⠠⠀⠀⢦⠀⢂⠲⠀⢒⠖⠀⠀⠀⢀⡀⡀⠀⡆⡀⠆⡀⡀⣄⡀⠆⠀⢀⢀⡐⠀⢀⠀⢀⠀⡀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⣤⣦⡄⠀⡆⢰⣦⢤⣤⣤⣤⡆⢰⡄⠀⢰⣶⡀⣴⣶⣦⣤⠀⢰⠀⣴⣴⢀⣲⣶⢀⣲⣶⠀⣤⠀⣶⣖⣶⣶⣦⣶⣶⣦⣶⣶⣶⣶⣶⡦⢴⣆⢴⣶⣶⢶⣶⣶⣴⣶⢶⢶⣶⡒⠐⠒⠒⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣤⣦⡆⠀⡆⢰⣦⢤⣤⣤⣤⡆⢰⡆⠀⢰⣶⡆⣶⣶⡦⣤⠀⢰⠀⣶⣶⢠⣲⣶⠠⣶⣶⠀⣦⠀⡶⣤⡤⡆⣤⣴⣴⢢⣶⣶⣖⣶⣶⣶⣦⣤⣤⢤⣴⣤⣤⣤⣤⣴⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⠶⠶⠶⠦⠤⠦⠦⠴⠶⠦⠴⠦⠦⠴⠶⠦⠴⠶⠶⠦⠴⠦⠴⠤⠴⠤⠶⠶⠤⠤⠤⠤⠦⠤⠤⠶⠤⠶⠶⠦⠴⠶⠶⠤⠤⠤⠴⠶⠤⠤⠤⠴⠶⠶⠶⠦⠤⠴⠶⠦⠴⠦⠶⠶⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠷⠷⠷⠷⠶⠷⠦⠶⠿⠇⠰⠶⠆⠶⠶⠆⠸⠿⠾⠆⠰⠶⠶⠸⠶⠶⠰⠀⠶⠶⠶⠶⠶⠶⠶⠶⠶⠲⠶⠶⠖⠶⠶⠶⠶⠂⠖⠒⠶⠦⠴⠦⠤⠷⠖⠖⠲⠦⠤⠴⠤⠠⠤⠤⠤⠀⠠⠤⠤⠄⠤⠤⠤⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠶⠷⠧⠮⠿⠇⠰⠷⠇⡶⠿⠇⠸⠿⠦⠇⠰⠶⠾⠼⠶⠶⠰⠀⠶⠶⠶⠶⠖⠶⠤⠶⠶⠶⠾⠶⠶⠶⠤⠶⠶⠶⠶⠲⠦⠤⠭⠿⠿⠷⠮⠿⠷⠲⠶⠶⠶⠶⠦⠤⠤⠠⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠯⠿⠿⠿⠷⠶⠷⠷⠺⠿⠇⠰⠿⠇⡮⡿⠇⠼⠿⠯⠇⠰⠶⠾⠼⠶⠶⠰⠀⠔⠾⠶⠶⠖⠶⠾⠶⠤⠀⠶⠶⠶⠧⠖⠷⠷⠷⠶⠷⠶⠖⠸⠿⠿⠧⠒⠿⠿⠿⠶⠺⠓⠿⠿⠿⠿⠿⠿⠿⠿⠾⠆⠀⠀⠀⠀⠀⠀ ⠯⠿⠿⠿⠷⠚⠟⠷⠺⠿⠇⠠⠷⠇⡸⠿⠇⠸⠿⠿⠇⠰⠶⠾⠸⠶⠶⠢⠀⠐⠾⠶⠶⠖⠶⠾⠶⠤⠓⠶⠶⠤⠶⠖⠶⠧⠶⠣⠴⠶⠖⠺⠶⠶⠦⠘⠿⠿⠿⠿⠻⠿⠿⠿⠿⠿⠭⠬⠬⠬⠬⠈⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠚⠟⠷⠺⠿⠇⠨⠯⠇⠻⠿⠇⠸⠿⠿⠇⠰⠶⠾⠼⠾⠶⠚⠀⠔⠾⠶⠶⠖⠶⠾⡿⠀⠶⠶⠶⠒⠷⠾⠗⠿⠷⠖⠻⠶⠶⠼⠿⠿⠇⠺⠿⠿⠿⠶⠿⠟⠿⠟⠛⠛⠛⠛⠙⠛⠛⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠿⠚⠟⠷⠺⠿⠇⠈⠯⠅⡝⠿⠇⠸⠿⠿⠇⠸⠾⠾⠸⠾⠾⠘⠀⠿⠻⠶⠞⠻⠸⠾⠶⠀⠶⠷⠿⠷⠛⠬⠃⠽⠟⠃⠄⠧⠼⠿⢗⡵⠿⠳⠷⠖⠻⠶⠟⠃⠠⠤⠤⠌⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⡟⡟⡟⡟⠚⡟⡗⠛⣟⡇⠈⢟⡇⠙⢿⡇⢸⣿⠛⠃⠸⠿⠛⢈⠻⠻⠈⠀⠹⠻⠺⠟⠻⠸⠛⡿⠀⠟⠟⠟⠟⠉⠶⠃⠆⠃⠙⠚⠟⠶⠿⠇⠀⠗⠋⠇⠀⠙⠟⠋⠑⠲⠶⠲⠒⠰⠲⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⡟⡟⡟⡟⠛⡟⡗⢛⣟⡇⠘⡟⡇⡛⢿⡇⢻⣿⣚⠃⠘⠻⠛⢋⠻⠻⠘⠀⢹⠛⠛⠻⠛⠺⠛⠿⠀⠛⠗⠛⠛⠖⡗⠊⡓⠖⠖⠛⠟⠛⠓⡇⠎⡃⠋⠓⠒⠚⠛⠓⠲⠛⠛⠳⠳⠻⠚⢙⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⡛⠛⡛⡓⢛⣛⡃⠘⡛⡃⣛⣛⡃⢚⣛⣛⡃⠘⠛⢛⢘⠛⠛⠘⠀⢙⠛⠛⠛⡛⠚⠛⠿⠀⠛⠛⠓⠛⠚⠛⠈⡑⠓⠛⠛⠛⠘⠃⡃⠋⡃⠈⠙⠛⠋⠘⠛⠛⠛⠛⠙⠛⠛⠊⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣓⣛⣛⣛⡛⢛⡛⣓⢛⣛⡃⢘⣓⡃⢛⣛⡃⢘⣛⣓⡃⠘⠛⢛⢚⠛⠛⠙⠀⣚⣛⢛⣛⡛⡛⣛⣿⡀⣛⠟⡛⠛⡛⠉⠒⠀⠛⠋⡙⡃⡘⠓⠓⢑⡓⠒⠚⠛⡓⠒⠛⠛⢉⡉⠙⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⡛⢙⣋⡛⢙⣛⡃⢘⢛⡃⢛⣛⡁⢚⣛⣛⡃⠘⠛⢛⢚⠛⠛⠘⠀⣚⡙⠛⢛⢛⠛⣛⠛⠉⠟⡒⡛⠛⡉⠛⠋⣚⠋⠙⠛⠛⡛⠛⠓⡘⠛⠑⠒⠋⢙⡛⠋⠙⠙⠛⠓⠒⠐⠒⠲⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⣛⢉⣋⡛⢙⣛⡃⢐⣛⡇⣚⣛⡃⢘⣛⢛⡃⠘⢛⢛⢘⢛⢛⢑⠀⣛⣛⠛⢛⣛⣛⠛⢛⠛⣞⡓⠀⡛⡛⠛⠛⢛⣘⡛⡋⠃⡃⡛⡛⠋⠈⠛⠋⠘⠙⠛⠛⡛⠙⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⣛⢉⣋⡛⢙⣛⡃⢐⣋⡃⣙⣛⡁⢘⣛⣛⡃⢘⠛⢛⢚⢛⢛⢁⠀⣙⣛⣛⣛⣛⣛⣛⣛⣒⣉⣋⠛⡋⠛⡋⡒⠛⠛⠉⡛⣛⣛⡛⡁⠐⢒⡂⠀⠐⣒⣲⠂⠀⡐⢀⡐⠂⠲⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⣛⣉⣋⡛⣙⣛⡃⢀⣛⡃⣑⣛⡃⢈⣛⣛⡃⢘⣛⣛⢘⣛⣛⢈⠀⣋⣙⣛⣙⣛⣛⣛⣛⠈⢛⡛⣛⣛⡈⡛⠉⣃⣋⣉⣋⢛⣛⡛⡋⠙⠛⢙⢃⡊⠙⠛⠋⠉⠙⠛⠛⠃⠐⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⣟⣏⣏⣏⣉⣏⡏⣙⣯⡇⢀⣫⡇⣄⣩⣁⣸⣿⡍⡁⢘⣛⣙⢘⣙⣙⢈⠀⢩⣹⣏⣸⣩⣽⣽⣭⣛⣀⣭⣙⠋⣁⣀⣉⣋⣋⢋⣉⡋⣋⣃⣀⣋⡃⢈⣋⡛⠋⣛⣃⣀⡀⣀⣀⣀⠐⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡭⣯⣍⣏⣍⣉⣍⡍⣩⣯⡅⢈⣏⡇⣉⣍⡅⣩⣩⣩⡁⢈⣙⣉⢨⣙⣙⢈⠀⣬⣩⣉⣉⣉⣍⣉⣩⠉⣫⣉⣉⣂⣍⣋⠉⣋⣋⣈⣍⣃⣍⣉⡉⠏⠁⡌⠙⠃⠈⠉⠙⠍⠉⠈⠉⠹⢥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡍⣭⣭⣭⣍⣉⣍⣍⣩⣭⡅⢈⣭⡅⣩⣭⡅⢩⣩⡭⡅⢈⣉⣩⢩⣉⣉⣈⠀⢩⣭⣭⡭⡭⣿⣭⣭⢺⠉⣭⣍⣉⣉⣍⣀⣍⠉⣍⣉⣉⣍⣉⡉⠀⣀⣄⣀⡐⣀⣐⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡍⣭⣭⣭⣍⣩⣍⣍⣩⣭⡅⢨⣭⡅⣩⡭⡅⢨⣭⡭⡅⢈⣉⣩⢩⣉⣉⢈⠀⣭⣭⣉⣩⣉⣍⣉⣩⠉⣭⣉⣀⣉⣟⣉⣉⣉⣈⣉⣅⡁⣍⣉⣉⡅⠨⡍⢁⣈⡈⠉⣉⣅⣈⣉⣉⣡⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡭⣭⣭⣭⣍⣠⣥⣍⣨⣭⡅⢨⣭⡅⢩⣭⡅⢨⣭⡭⡅⢈⣉⣩⢩⣉⣉⠈⠀⣭⢭⣉⣩⣉⣍⣉⣹⠀⡉⣉⣉⣉⣋⠍⣈⣍⣉⣉⡉⠈⡉⢉⣅⡠⠄⡠⢄⣀⡀⢀⣀⣀⣠⣄⣀⣀⣀⠠⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⡍⣭⣭⣭⣭⣠⣥⣍⣨⣭⡅⢨⣭⡅⣭⣭⡁⢨⣭⡭⡅⣨⣩⣩⣩⣩⡩⠈⣠⣉⣨⣩⣩⡉⣩⣭⣋⣤⣭⣍⣉⣉⣭⣅⣍⣭⣉⠍⢁⣄⣅⣍⣍⠄⣀⣥⣨⣍⣥⠌⣬⣍⣩⢩⣄⣭⠈⣠⣠⣠⣠⣠⠀⠀⠀⠀⠀⠀ ⡍⣭⣭⣭⣭⣠⣥⣍⣨⣭⡅⠨⣭⡅⣤⣭⡅⢠⣭⣬⡅⢨⣩⣨⢨⣩⣠⢠⠈⢭⣍⣉⣬⣭⣄⣬⣉⢀⠁⣭⣭⣍⣄⡅⣁⣭⣍⠀⣄⣌⣭⡍⢉⣌⣍⣍⣁⣨⣥⣰⡀⢀⣠⡀⢠⣤⣠⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⡍⣭⣭⣯⣭⣤⣥⣍⣬⣭⡅⠠⣥⡅⣬⣭⡄⢴⣥⣭⡄⢨⣭⣭⢨⣭⣭⠠⠀⣨⣭⣭⣭⡬⣭⣭⣭⢨⠀⣤⣭⣥⣭⣥⣥⣭⢁⣤⣭⣍⣥⣥⡄⢈⣭⣭⣭⣌⣭⣭⣥⠌⠉⠁⠈⠉⠉⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠁⠁⠁⠀⠀⠁⠁⠀⠁⠀⠀⠁⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⡀⡀⠀⠄⢀⣆⠀⣀⢀⢀⡀⠀⠀⠰⢲⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⢂⠀⢂⠲⠀⢒⠖⠀⠀⠀⢀⡀⡀⠀⡆⡀⠆⡀⡀⣄⡀⠆⠀⢀⢀⡐⠀⢀⠀⢀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⣤⣦⡄⠀⡆⢰⣦⢤⣤⣤⣤⡆⢰⡄⠀⢲⣶⡀⣴⣶⣤⣤⠀⢰⠀⣴⣴⢀⣲⣶⢀⣲⣶⠀⣤⠀⣶⣖⣶⣶⣦⣶⣶⣦⣶⣶⣶⣶⣶⡦⢴⣆⢴⣶⣶⢶⣶⣶⣴⣶⢶⢶⣶⡒⠐⠒⠒⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣤⣦⡆⠀⡆⢰⣦⢤⣤⣤⣤⡆⢰⡄⠀⢰⣶⡆⣶⣶⡦⣤⠀⢰⠀⣶⣶⢠⣲⣶⠠⣶⣶⠀⣦⠀⡶⣤⡤⡆⣄⣴⣴⢢⣶⣶⣖⣶⣶⣶⣦⣤⣤⢤⣴⣤⣤⣤⣤⣴⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⠶⠶⠶⠦⠤⠦⠦⠴⠶⠦⠴⠦⠦⠴⠶⠦⠴⠶⠶⠦⠴⠦⠴⠤⠴⠤⠶⠶⠤⠤⠤⠤⠦⠤⠤⠶⠤⠶⠶⡦⠴⠶⠶⠤⠤⠤⠴⠶⠤⠤⠤⠴⠶⠶⠶⠦⠤⠴⠶⠦⠴⠦⠶⠶⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠷⠷⠷⠷⠶⠷⠦⠶⠿⠇⠰⢶⡇⠶⢾⠇⠰⠾⠾⠆⠰⠶⠶⠸⠶⠶⠰⠀⢾⢶⣺⣶⢶⢺⠶⣿⡻⡷⡶⠀⣶⣶⠶⠶⠦⠠⡶⠆⠗⡖⠶⠶⠆⠰⢶⡆⠠⢶⣷⠶⠦⢲⢶⢶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠶⠷⠧⠮⠿⠇⠰⢷⡗⡶⣿⡆⢴⠾⠶⠇⠰⠶⠾⠼⠶⠶⠰⠀⡿⢲⣶⢴⣶⣶⣶⣶⠀⣶⣦⣶⣶⠀⣦⠔⡆⡄⢠⣶⣶⣶⣦⡇⠐⣦⢖⡆⡀⢰⣶⠆⠠⢶⣶⣦⡤⢶⣴⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠯⠿⠿⠿⠷⠶⠷⠷⠺⠿⠇⠰⢷⡆⡮⣷⡆⢴⣶⡾⠇⠰⠶⠾⠼⠶⠶⠰⠀⢶⢲⣶⢴⣶⣶⣶⠶⠀⡶⣶⣶⣶⡶⠀⡦⣷⣦⣶⠗⠐⡆⠠⣶⡆⠐⡆⢰⣶⡆⠰⢶⣶⣦⡦⢶⣴⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠯⠿⠿⠿⠷⠚⠟⠷⠺⠿⠇⠠⢷⡆⡰⣶⡇⢰⣶⡾⠇⠰⠶⠾⠸⠶⠶⠢⠀⣶⣶⣤⣤⣶⣴⣤⣤⠀⣴⣤⣤⣦⣶⣤⢀⡴⣶⣤⣤⢤⣤⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠚⠟⠷⠺⠿⠇⠠⣶⡆⠻⢷⡆⢰⣶⠼⠇⠰⠶⠾⠼⠾⠶⠚⠀⢶⣦⣴⢰⣴⣤⣶⣭⣦⠀⣆⣦⣤⣖⠀⣤⣶⣤⣤⣤⣦⢶⡆⠀⣦⡄⢠⣤⣤⣴⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠿⠚⠟⠷⠺⠿⠇⠀⢾⡇⡭⣷⣄⢰⣶⠿⠇⣼⣬⢬⣬⣤⢠⠀⣤⣤⣽⣤⣤⠀⣭⣶⣤⣯⣤⣤⠀⣤⣤⡤⡆⣶⣤⡄⢠⣤⣤⣤⣆⡄⠀⣦⣶⣬⣴⣬⢥⣤⣴⣤⣤⣴⡀⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀ ⡇⡟⡟⡟⡟⠚⡟⡗⠛⣟⡇⠘⣿⡇⠠⣶⡄⢰⣶⠞⠃⣤⣤⣤⣤⣤⢤⠀⣶⣦⣤⣯⢰⣭⠀⣤⣤⠀⣤⣤⣭⣶⠀⣶⣤⣤⣥⠀⢂⣤⣦⣤⣤⣤⣤⣶⡜⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⡟⡟⡟⡟⠛⡟⡗⢛⣟⡇⠘⣷⡆⡒⣶⡄⢰⣴⣾⠃⠐⠲⠒⢂⠲⠲⠐⠀⣴⣤⣤⢰⣴⣤⣴⣤⣤⠀⣤⣦⣤⣆⠁⣤⣶⣦⣤⣤⣤⣦⡆⠀⣦⡄⢠⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⡛⠛⡛⡓⢛⣛⡃⠘⣣⡆⣛⣫⡅⢠⣴⣜⡃⠘⠛⢛⢘⠛⠛⠘⠀⣤⣤⣤⢠⣴⣭⣤⣤⣭⠀⣬⣤⣥⣤⠀⣠⣦⣥⣥⣤⣥⣦⡇⠀⣥⡄⢨⣤⣬⣥⣭⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣓⣛⣛⣛⡛⢛⡛⣓⢛⣛⡃⢘⣫⡇⣭⡷⡇⢨⣭⣗⡃⠘⠛⢛⢚⠛⠛⠙⠀⣲⣼⣦⣼⣴⣿⣶⣶⢻⠀⣴⣤⡤⣤⡤⣄⣄⣥⠉⣤⣅⣤⡄⢀⣥⣧⣤⣄⣬⣤⣯⡇⢠⣠⡀⣠⣤⣤⣤⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⡛⢙⣋⡛⢙⣛⡃⢈⣣⡅⣨⣭⡅⢠⣥⣗⡃⠘⠛⢋⢚⠛⠛⠘⠀⢨⢽⣭⡭⡭⣭⣿⣭⢨⠀⣤⣭⣅⣭⣥⣍⣭⢁⣤⣭⣉⣥⣽⡖⢈⣭⣭⣭⣌⣭⣭⣥⡌⠈⠁⠈⠉⠉⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⣛⢉⣋⡛⢙⣛⡃⢘⣣⡅⣨⣭⡅⢠⣭⣝⡃⠘⢛⢙⢘⢛⢛⢑⠀⢺⣽⣭⡭⡭⣭⣭⣭⢭⠀⣭⣉⣉⣍⡭⣍⣉⣤⠉⣥⣅⣉⡍⢁⣈⣌⣉⣉⣅⣨⣭⡍⢡⣀⡀⢀⣀⣀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⣛⢉⣋⡛⢙⣛⡃⢐⣣⡅⢨⣭⡅⢘⣫⣝⡃⢘⠛⢛⢚⢛⢛⢁⠀⣸⢭⣭⡭⡭⣭⣭⣭⢨⠀⣭⣭⣁⣩⣅⣉⣍⢉⣤⣉⣉⣅⣁⣈⠈⣉⣍⣉⣈⣉⣨⣥⡌⠁⠁⠘⠉⠹⠉⠹⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣻⣛⣛⣛⣉⣋⡟⣙⣛⡃⢀⣳⡅⣨⣭⡅⢨⣿⣛⡃⣘⣛⣛⣘⣛⢛⠈⣤⣌⣩⣉⣙⠋⣋⣛⣩⣌⣀⣩⠉⣉⣍⣩⣍⠉⣬⣉⣍⡁⡟⢉⣁⣈⣈⣉⣉⡉⢈⣉⡉⢀⣄⣀⣠⣀⣀⡀⢀⠀⢀⣠⣀⣀⣀⣀⣠⣄ ⠃⠛⠋⠋⠋⠉⠋⠋⠙⠋⠃⠀⠃⠁⠉⠉⠁⠈⠉⠉⠁⠉⠉⠈⠉⠉⠈⠀⠉⠉⠉⠛⠉⠀⠉⠉⠉⠉⠉⠉⠀⠉⠉⠉⠉⠀⠉⠉⠉⠃⠁⠈⠉⠈⠉⠉⠈⠁⠈⠉⠁⠈⠉⠉⠉⠉⠉⠀⠀⠀⠁⠉⠉⠉⠁⠉⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⣉⢉⣍⣉⡉⡉⣉⡉⠉⡉⢉⣍⣉⣉⣉⣉⡉⢉⡉⢩⣭⣉⣉⠉⢉⣉⣉⠉⢉⠉⣉⣍⢉⣭⣭⣉⣭⣍⣍⣉⠉⣉⣉⣉⣉⡉⢉⣍⣉⡉⡍⡉⡉⢉⣉⣉⣩⣉⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉ ⠁⠈⠛⠋⠉⠋⠚⠃⠀⠃⠘⠋⠛⠋⠛⠛⠃⠈⠁⠘⠛⠛⠙⠉⠛⠛⠙⠀⠘⠀⠋⠋⠈⠛⠛⠉⠛⠈⠀⠉⠀⠙⠛⠛⠋⠃⠉⠛⠛⠁⠛⠃⠃⠘⠙⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠉⠉⠉⠉⡉⠉⠉⡉⢉⣉⠉⠉⠉⢉⡉⢉⡉⠉⢉⢉⡉⣉⣉⡉⠉⠉⢉⠉⣉⣉⢉⣉⣉⣉⣉⣉⠉⣁⠉⣉⣉⣉⢉⣉⣉⣉⣉⣉⣉⡉⢉⣉⣉⣉⠉⣉⣩⡉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⡉⠉⠉⠉⠉⠉ ⣀⠀⠀⠀⠀⡛⣛⡃⠀⡃⢘⣛⣙⣛⢛⣛⡃⢘⡁⠀⢙⣛⡃⣙⣛⡋⢙⠀⢘⠀⣛⣛⢀⣛⣋⢀⣙⣋⠀⣋⠀⣛⣛⣓⢈⣛⣛⣋⣛⣛⣛⣋⡙⣛⡛⢙⡚⢙⣛⡋⢙⣛⣛⣛⣛⣛⣚⣛⣛⣛⣛⣛⠁⠀⠀⠀⠀⠀ ⠃⠀⠀⠀⠘⠛⡛⠋⠀⡋⢙⡙⠛⠛⠚⠛⡋⢙⡃⠀⢙⣛⠃⣙⣛⡫⠿⠀⢘⠀⣛⣟⠐⣞⣙⠐⣛⣛⠀⡛⠀⣛⣛⣓⣈⡛⣛⣛⣛⣛⣛⣛⣛⣛⡋⢙⡓⢙⣛⣋⣙⣛⣛⢛⣛⣛⣚⣛⡛⠛⠛⠛⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⡛⡃⠀⡃⢘⡛⠙⠙⠛⠛⡃⢘⠃⠀⢘⣛⡂⢛⣛⡛⠛⠀⢘⠀⣛⣙⠐⣚⣛⠐⣚⣛⠀⠛⠀⣛⣓⣛⢛⣛⣛⣛⡛⠛⡛⣛⡛⢛⣋⣉⣁⡙⢛⣛⡙⢛⣛⣛⣟⣙⣙⣛⣂⢀⣀⣀⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠛⡛⡃⠀⡃⢘⡛⠛⠛⠛⠛⡃⢘⠃⠀⢚⣛⡃⢛⣛⠛⠛⠀⢘⠀⢛⣛⠘⣛⣚⠘⣛⣛⠀⠛⠀⣛⠛⠓⠘⠛⠛⠛⡋⠘⣛⣛⣛⣙⣛⡛⠚⠓⠙⠛⠋⠛⠛⠛⠛⠛⠛⠛⠛⠛⠚⠛⠙⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⡛⠃⠀⡃⢘⡛⠛⠛⠛⠛⡃⠘⠃⠀⢘⢛⠁⢛⣛⠛⠛⠀⢘⠀⢛⣛⠘⠛⣛⠑⢛⡛⠀⡛⠀⣛⠛⢛⡛⣛⣋⠘⢓⣀⡛⣛⣛⣛⣙⡓⢁⡀⢀⡀⢀⣀⣀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠟⠿⠇⠀⠇⠘⠿⠛⠿⠿⠻⠇⠘⠃⠀⠸⠻⠃⠻⠿⠗⠻⠀⠘⠀⠻⠿⠘⠽⠿⠚⠻⠛⠀⠛⠀⠟⠿⠟⠇⠟⠟⠟⠘⠻⠛⠟⠟⠿⠿⠿⠛⠓⠛⠻⠿⠿⠿⠿⠛⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢒⠒⠒⠒⠒⠒⢒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒ ⠧⠿⠿⠿⠿⠚⠟⠷⠺⠿⠇⠨⠟⠇⠻⠿⠇⠹⠿⠻⠇⠸⠿⠿⠾⠾⠀⠸⠿⠿⠿⠷⠿⠿⡿⠿⠿⠀⠿⠿⠷⠈⠿⠿⠚⠷⠆⠸⠿⠿⠻⠗⠸⠋⠇⠇⠇⠄⠸⠿⠗⠺⠗⠻⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠈⠠⠈⠀⠐⠒⠐⠒⠂⠰⠂⠀⠀⠀⠀⠂⠀⠀⠘⠒⠒⠇⠑⠓⠀⠀⠒⠐⠀⠀⠀⠐⠛⠃⠒⠂⠀⠐⠒⠒⠚⠘⠒⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠷⠷⠷⠷⠶⠷⠦⠶⠿⠇⠰⢶⡇⠶⢾⠇⠰⠾⠾⠆⠰⠶⠶⠸⠶⠶⠰⠀⢾⢶⣺⣶⢶⢺⠶⣿⡻⡷⡶⠀⣶⣶⠶⠶⠦⠠⡶⠆⠖⡖⠶⠶⠆⠰⢶⡆⠠⢶⣷⠶⠦⢲⢶⢶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠶⠷⠧⠮⠿⠇⠰⢷⡗⡶⣿⡆⢴⠾⠶⠇⠰⠶⠾⠼⠶⠶⠰⠀⡿⢲⣶⢴⣶⣶⣶⣶⠀⣶⣦⣶⣶⠀⣦⠔⡆⡄⢠⣶⣶⣶⣦⡇⠐⣦⢖⡖⠀⢰⣶⠆⠠⢶⣶⣦⡤⢶⣴⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠯⠿⠿⠿⠷⠶⠷⠷⠺⠿⠇⠰⢷⡆⡮⣷⡆⢴⣶⡾⠇⠰⠶⠾⠼⠶⠶⠰⠀⢶⢲⣶⢴⣶⣶⣶⠶⠀⡶⣶⣶⣶⡶⠀⡦⣷⣦⣶⠗⠐⡆⠠⣶⡆⠐⡆⢰⣶⡆⠰⢶⣶⣦⡦⢶⣴⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠯⠿⠿⠿⠷⠚⠟⠷⠺⠿⠇⠠⢷⡆⡰⣶⡇⢰⣶⡾⠇⠰⠶⠾⠸⠶⠶⠢⠀⣶⣶⣤⣤⣶⣴⣤⣤⠀⣴⣤⣤⣦⣶⣤⢀⡴⣶⣤⣤⢤⣤⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠚⠟⠷⠺⠿⠇⠠⣶⡆⠻⢷⡆⢰⣶⠼⠇⠰⠶⠾⠼⠾⠶⠚⠀⢶⣦⣴⢰⣴⣤⣶⣭⣦⠀⣆⣦⣤⣖⠀⣤⣶⣤⣤⣤⣦⢶⡆⠀⣦⡄⢠⣤⣤⣴⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠿⠚⠟⠷⠺⠿⠇⠀⢾⡇⡭⣷⣄⢰⣶⠿⠇⣼⣬⢬⣬⣤⢠⠀⣤⣤⣽⣤⣤⠀⣭⣶⣤⣯⣤⣤⠀⣤⣤⡤⡖⣶⣤⡄⢠⣤⣤⣤⣆⡄⠀⣦⣶⣬⣴⣬⢥⣤⣴⣤⣤⣴⡀⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀ ⡇⡟⡟⡟⡟⠚⡟⡗⠛⣟⡇⠈⣿⡇⠠⣶⡄⢰⣶⠞⠃⣤⣤⣤⣤⣤⢤⠀⣶⣦⣤⣯⢰⣭⠀⣤⣤⠀⣤⣤⣭⣶⠀⣶⣤⣤⣥⠀⢂⣤⣦⣤⣤⣤⣤⣶⡜⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⡟⡟⡟⡟⠛⡟⡗⢛⣟⡇⠘⣷⡆⡒⣶⡄⢰⣴⣾⠃⠐⠲⠒⢂⠲⠲⠐⠀⣴⣤⣤⢰⣴⣤⣴⣤⣤⠀⣤⣦⣤⣆⠁⣤⣶⣦⣤⣤⣤⣦⡆⠀⣦⡄⢠⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⡛⠛⡛⡛⢛⣛⡃⠘⣣⡆⣛⣫⡅⢠⣴⣜⡃⠘⠛⢛⢘⠛⠛⠘⠀⣤⣤⣤⢠⣴⣭⣤⣤⣭⠀⣬⣤⣥⣤⠀⣠⣦⣥⣥⣤⣥⣦⡇⠀⣥⡄⢨⣤⣬⣥⣭⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣓⣛⣛⣛⡛⢛⡛⣓⢛⣛⡃⢐⣫⡇⣭⡷⡇⢨⣭⣗⡃⠘⠛⢛⢚⠛⠛⠙⠀⣲⣼⣦⣼⣴⣿⣶⣶⢻⠀⣴⣤⡤⣤⡤⣄⣄⣥⠉⣤⣅⣤⡄⢀⣥⣧⣤⣄⣬⣤⣯⡇⢠⣠⡀⣠⣤⣤⣤⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⡛⢙⣋⡛⢙⣛⡃⢈⣣⡅⣨⣭⡅⢠⣥⣗⡃⠘⠛⢋⢚⠛⠛⠘⠀⢨⢽⣭⡭⡭⣭⣿⣭⢨⠀⣤⣭⣅⣭⣥⣍⣭⢁⣤⣭⣉⣥⣽⡖⢈⣭⣭⣭⣌⣭⣭⣥⡌⠈⠁⠈⠉⠉⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⣛⢉⣋⡛⢙⣛⡃⢘⣣⡅⣨⣭⡅⢠⣭⣝⡃⠘⢛⢙⢘⢛⢛⢑⠀⢺⣽⣭⡭⡭⣭⣭⣭⢭⠀⣭⣉⣉⣍⡭⣍⣉⣤⠉⣥⣅⣉⡍⢁⣈⣌⣉⣉⣅⣨⣭⡏⢡⣀⡀⢀⣀⣀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⣛⢉⣋⡛⢙⣛⡃⢐⣣⡅⢨⣭⡅⢘⣫⣝⡃⢘⠛⢛⢚⢛⢛⢁⠀⣸⢭⣭⡭⡭⣭⣭⣭⢨⠀⣭⣭⣁⣩⣅⣉⣍⢉⣤⣉⣉⣅⣁⣈⠈⣉⣍⣉⣈⣉⣨⣥⡌⠁⠁⠘⠉⠹⠉⠹⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣻⣛⣛⣛⣉⣋⡟⣙⣛⡃⢀⣳⡅⣨⣭⡅⢨⣿⣛⡃⣘⣛⣛⣘⣛⢛⠈⣤⣌⣩⣉⣙⠋⣋⣛⣩⣌⣀⣩⠉⣉⣍⣩⣍⠉⣬⣉⣍⡁⡟⢉⣁⣈⣈⣉⣉⡉⢈⣉⡉⢀⣄⣀⣠⣀⣀⡀⢀⠀⢀⣠⣀⣀⣀⣀⣠⣄ ⠃⠛⠋⠋⠋⠉⠋⠋⠙⠋⠃⠀⠃⠁⠉⠉⠁⠈⠉⠉⠁⠉⠉⠈⠉⠉⠈⠀⠉⠉⠉⠛⠉⠀⠉⠉⠉⠉⠉⠉⠀⠉⠉⠉⠉⠀⠉⠉⠉⠃⠁⠈⠉⠈⠉⠉⠈⠁⠈⠉⠁⠈⠉⠉⠉⠉⠉⠀⠀⠀⠁⠉⠉⠉⠁⠉⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⣉⢉⣍⣉⡉⡉⣉⡉⠉⡉⢉⣍⣉⣉⣉⣉⡉⢉⡉⢩⣭⣉⣉⠉⢉⣉⣉⠉⢉⠉⣉⣍⢉⣭⣭⣉⣭⣍⣍⣉⠉⣉⣉⣉⣉⡉⢉⣍⣉⡉⡍⡉⡉⢉⣉⣉⣩⣉⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉ ⠁⠈⠛⠋⠉⠋⠚⠃⠀⠃⠘⠋⠛⠋⠛⠛⠃⠈⠁⠘⠛⠛⠙⠉⠛⠛⠙⠀⢘⡀⠋⠋⠈⠛⠛⠉⠛⠈⠀⠉⠀⠙⠛⠛⠋⠃⠉⠛⠛⠁⠛⠃⠃⠘⠙⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠉⠉⠉⠉⡉⠉⠉⡉⢉⣉⠉⠉⠉⢉⡉⢉⡉⠉⢉⢉⡉⣉⣉⡉⠉⠉⢉⠉⣉⣉⢉⣉⣉⣉⣉⣉⠉⣁⠉⣉⣉⣉⢉⣉⣉⣉⣉⣉⣉⡉⢉⣉⣩⣉⠉⣉⣩⡉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⡉⠉⠉⠉⠉⠉ ⣀⠀⠀⠀⠀⡛⣛⡃⠀⡃⢘⣛⣙⣛⢛⣛⡃⢘⡁⠀⢙⣛⡃⣙⣛⡋⢙⠀⢸⠀⣛⣛⢀⣛⣋⢀⣙⣋⠀⣋⠀⣛⣛⣓⢈⣛⣛⣋⣝⣛⣛⣋⡙⣛⡛⢙⡚⢙⣛⡋⢙⣛⣛⣛⣛⣛⣚⣛⣛⣛⣛⣛⠁⠀⠀⠀⠀⠀ ⠃⠀⠀⠀⠘⠛⡛⠋⠀⡋⢙⡙⠛⠛⠚⠛⡋⢙⡃⠀⢙⣛⠃⣙⣛⡫⠿⠀⢘⠀⣛⣟⠐⣞⣙⠐⣛⣛⠀⡛⠀⣛⣛⣓⣈⡛⣛⣛⣛⣛⣛⣛⣛⣛⡋⢙⡓⢙⣛⣋⣙⣛⣛⢛⣛⣛⣚⣛⡛⠛⠛⠛⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⡛⡃⠀⡃⢘⡛⠙⠙⠛⠛⡃⢘⠃⠀⢘⣛⡂⢛⣛⡛⠛⠀⢘⠀⣛⣙⠐⣚⣛⠐⣚⣛⠀⠿⠀⣛⣓⣛⢛⣛⣛⣛⡛⠛⡛⣛⡛⢛⣋⣉⣁⡙⢛⣛⡙⢛⣛⣛⣟⣙⣙⣛⣂⢀⣀⣀⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠛⡛⡃⠀⡃⢘⡛⠛⠛⠛⠛⡃⢘⠃⠀⢚⣛⡃⢛⣛⠛⠛⠀⢘⠀⢛⣛⠘⣛⣚⠘⣛⣛⠀⠛⠀⣛⠛⠓⠘⠛⠛⠛⡋⠘⣛⣛⣛⣙⣛⡛⠚⠓⠙⠛⠏⠛⠛⠛⠛⠛⠛⠛⠛⠛⠚⠛⠙⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⡛⠃⠀⡃⢘⡛⠛⠛⠛⠛⡃⠘⠃⠀⢘⢛⠁⢛⣛⠛⠛⠀⢘⠀⢛⣛⠘⠛⣛⠑⢛⡛⠀⡛⠀⣛⠛⢛⡛⣛⣋⠘⢓⣀⡛⣛⣛⣛⣙⡓⢁⡀⢀⡀⢀⣀⣀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠟⠿⠇⠀⠇⠘⢿⠟⠿⠿⠻⠇⠘⠃⠀⠸⠻⠃⠻⠿⠗⠻⢀⠘⠀⠻⠿⠘⠽⠿⠚⠻⠛⠀⠛⠀⠟⠿⠟⠇⠟⠋⠟⠘⠻⠛⠟⠟⠿⠿⠿⠛⡓⠛⠿⠿⠿⠿⠿⠛⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢒⠒⠒⠒⠒⠒⢒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠐⠒⠒⠒⠒⠒⠒⠒⠖⡲⠖⠶⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒ ⠧⠿⠿⠿⠿⠚⠟⠷⠺⠿⠇⠨⠟⠇⠻⠿⠇⠹⠿⠻⠇⠸⠿⠿⠾⠾⠀⠸⠿⠿⠿⠷⠿⠿⡿⠿⠿⠀⠿⠿⠷⠈⠿⠿⠚⠷⠆⠸⠿⠿⠻⠗⠸⠋⠇⠇⠇⠄⠸⠿⠗⠺⠗⠻⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠈⠠⠈⠀⠐⠒⠐⠒⠂⠰⠂⠀⠀⠀⠀⠂⠀⠀⠘⠒⠒⠇⠑⠓⠀⠀⠒⠐⠀⠀⠀⠐⠛⠃⠒⠂⠀⠐⠒⠒⠚⠘⠒⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠷⠷⠷⠷⠶⠷⠦⠶⠿⠇⠰⢶⡇⠶⢾⠇⠰⠾⠾⠆⠰⠶⠶⠸⠶⠶⠰⠀⢾⢶⣺⣶⢶⢺⠶⣿⡻⡷⡶⠀⣶⣶⠶⠶⠦⠠⡶⠆⠖⡖⠶⠶⠆⠰⢶⡆⠠⢶⣷⠶⠦⢲⢶⢶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠶⠷⠧⠮⠿⠇⠰⢷⡗⡶⣿⡆⢴⠾⠶⠇⠰⠶⠾⠼⠶⠶⠰⠀⡿⢲⣶⢴⣶⣶⣶⣶⠀⣶⣦⣶⣶⠀⣦⠔⡦⡄⢠⣶⣶⣶⣦⡇⠐⣦⢖⡖⠀⢰⣶⠆⠠⢶⣶⣦⡤⢶⣴⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠯⠿⠿⠿⠷⠶⠷⠷⠺⠿⠇⠰⢷⡆⡮⣷⡆⢴⣶⡾⠇⠰⠶⠾⠼⠶⠶⠰⠀⢶⢲⣶⢴⣶⣶⣶⠶⠀⡶⣶⣶⣶⡶⠀⣦⣷⣦⣶⠗⠐⡆⠠⣶⡆⠐⡆⢰⣶⡆⠰⢶⣶⣦⡦⢶⣴⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠯⠿⠿⠿⠷⠚⠟⠷⠺⠿⠇⠠⢷⡆⡰⣶⡇⢰⣶⡾⠇⠰⠶⠾⠸⠶⠶⠢⠀⣶⣶⣤⣤⣶⣴⣤⣤⠀⣴⣤⣤⣦⣶⣤⢀⡴⣶⣤⣤⢤⣤⣶⡆⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠚⠟⠷⠺⠿⠇⠠⣶⡆⠻⢷⡆⢰⣶⠼⠇⠰⠶⠾⠼⠾⠶⠚⠀⢶⣦⣴⢴⣴⣤⣶⣭⣦⠀⣆⣦⣤⣖⠀⣤⣶⣤⣤⣤⣦⢶⡆⠀⣦⡄⢠⣤⣤⣴⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠿⠚⠟⠷⠺⠿⠇⠀⢾⡇⡭⣷⣄⢰⣶⠿⠇⣼⣬⢬⣬⣤⢠⠀⣤⣤⣽⣤⣤⠀⣭⣶⣤⣯⣤⣤⠀⣤⣤⡤⡖⣶⣤⡄⢠⣤⣤⣤⣆⡄⠀⣦⣶⣬⣴⣬⢥⣤⣴⣤⣤⣴⡀⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀ ⡇⡟⡟⡟⡟⠚⡟⡗⠛⣟⡇⠈⣿⡇⠠⣶⡄⢰⣲⠞⠃⣤⣤⣤⣤⣤⢤⠀⣶⣦⣤⣯⢰⣭⠀⣤⣤⠀⣤⣤⣭⣶⠀⣶⣤⣤⣥⠀⢂⣤⣦⣤⣤⣤⣤⣶⡜⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⡟⡟⡟⡟⠛⡟⡗⢻⣟⡇⠘⣷⡆⡒⣶⡄⢰⣴⣾⠃⠐⠲⠒⢂⠲⠲⠐⠀⣴⣤⣤⢰⣴⣤⣶⣤⣤⠀⣤⣦⣤⣆⠁⣤⣶⣦⣤⣤⣤⣦⡆⠀⣦⡄⢠⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⡛⠛⡛⡛⢛⣛⡃⠘⣣⡆⣛⣫⣅⢠⣴⣜⡃⠘⠛⢛⢘⠛⠛⠘⠀⣤⣤⣤⢠⣴⣍⣤⣤⣭⠀⣬⣤⣥⣤⠀⣠⣦⣥⣥⣤⣥⣦⡇⠀⣥⡄⢨⣤⣬⣥⣭⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣓⣛⣛⣛⡛⢛⡛⣓⢛⣛⡃⢐⣫⡇⣭⡷⡇⢬⣭⣷⡃⠘⠛⢛⢚⠛⠛⠙⠀⣲⣼⣦⣼⣴⣿⣶⣶⢻⠀⣴⣤⡤⣤⡤⣤⣄⣥⠉⣤⣅⣤⡄⢀⣥⣧⣤⣄⣬⣤⣯⡇⢠⣠⡀⣠⣤⣤⣤⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⡛⢙⣋⡛⢙⣛⡃⢈⣣⡅⣨⣭⡅⢠⣥⣗⡃⠘⠛⢋⢚⠛⠛⠘⠀⢨⢽⣭⡭⡭⣭⣿⣭⢬⠤⣤⣭⣅⣭⣥⣍⣭⢁⣤⣭⣉⣥⣽⡖⢈⣭⣭⣭⣌⣭⣭⣥⡌⠈⠁⠈⠉⠉⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⣛⢉⣋⡛⢙⣛⡃⢘⣣⡅⣨⣭⡅⢠⣥⣝⡃⠘⢛⢙⢘⢛⢛⢑⠀⢺⣽⣭⡭⡭⣭⣭⣭⣭⠀⣭⣉⣉⣍⡭⣍⣉⣤⢉⣥⣅⣉⡍⢁⣈⣌⣉⣉⣅⣨⣭⡏⢡⣀⡀⢀⣀⣀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⣛⢉⣋⡛⢙⣛⡃⢐⣣⡅⢨⣭⡄⢘⣫⣝⡃⢘⠛⢛⢚⢛⢛⢁⠀⣸⢭⣭⡭⡭⣭⣭⣭⢨⠀⣭⣭⣁⣩⣅⣉⣍⢉⣤⣉⣉⣅⣁⣈⠈⣉⣍⣉⣈⣉⣨⣥⡌⠁⠁⠘⠉⠹⠉⠹⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣻⣛⣛⣛⣉⣋⡟⣙⣛⡃⢀⣳⡅⣨⣭⡅⢨⣿⣛⡃⣘⣛⣛⣘⣛⢛⠈⣤⣌⣩⣉⣙⠋⣋⣛⣩⣌⣀⣩⠉⣉⣍⣩⣍⠉⣬⣉⣍⡁⡟⢉⣁⣈⣈⣉⣉⡉⢈⣉⡉⢀⣄⣀⣠⣀⣀⡀⢀⠀⢀⣠⣀⣀⣀⣀⣠⣄ ⠃⠛⠋⠋⠋⠉⠋⠋⠙⠋⠃⠀⠃⠁⠉⠉⠁⠈⠉⠉⠁⠉⠉⠈⠉⠉⠈⠀⠉⠉⠉⠛⠉⠀⠉⠉⠉⠉⠉⠉⠀⠉⠉⠉⠉⠀⠉⠉⠉⠃⠁⠈⠉⠈⠉⠉⠈⠁⠈⠉⠁⠈⠉⠉⠉⠉⠉⠀⠀⠀⠁⠉⠉⠉⠁⠉⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⣉⢉⣍⣉⡉⣉⣉⡉⠉⡉⢉⣍⣉⣉⣉⣉⡉⢉⡉⢩⣭⣉⣉⠉⣉⣉⣉⠉⢉⠉⣉⣍⢉⣭⣭⣉⣭⣍⡍⣉⠉⣉⣉⣉⣉⡉⢉⣍⣉⡉⡍⡉⡉⢉⣉⣉⣩⣉⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉ ⠁⠈⠛⠋⠉⠋⠚⠃⠀⠃⠘⠋⠛⠋⠛⠛⠃⠈⠁⠘⠛⠛⠙⠉⠛⠙⠙⠀⢘⡀⠋⠋⠈⠛⠛⠉⠛⠈⠀⠉⠀⠙⠛⠛⠋⠃⠉⠛⠛⠁⠛⠃⠃⠘⠙⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠉⠉⠉⠉⡉⠉⠉⡉⢉⣉⠉⠉⠉⢉⡉⢉⣉⠉⢉⢉⡉⣉⣉⡉⠉⠉⢉⠉⡉⣉⢉⣉⣉⣉⣉⣉⠉⣁⠉⣉⣉⣉⢉⣉⣉⣉⣉⣉⣉⡉⢉⣉⣩⣉⠉⣉⣩⡉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⡉⠉⠉⠉⠉⠉ ⣀⠀⠀⠀⠀⡛⣛⡃⠀⡃⢘⣛⣙⣛⢛⣛⡃⢘⡁⠀⢙⣛⡃⣙⣛⡋⢙⠀⢲⠀⣙⣛⢀⣛⣋⢈⣙⣋⠀⣋⠀⣛⣛⣓⢈⣛⣛⣋⣝⣛⣛⣋⡙⣛⡛⢙⡚⢙⣛⡋⢙⣛⣛⣛⣛⣛⣚⣛⣛⣛⣛⣛⠁⠀⠀⠀⠀⠀ ⠃⠀⠀⠀⠘⠛⡛⠋⠀⡋⢙⡙⠛⠛⠚⠛⡋⢙⡃⠀⠙⢛⠃⣙⣛⡫⠿⠀⢘⠀⣛⣟⠘⣞⣙⠐⣛⣛⠀⡛⠀⣛⣛⣓⣈⡛⣛⣛⣛⣛⣛⣛⣛⣛⡋⢙⡛⢙⣛⣋⣙⣛⣛⢛⣛⣛⣚⣛⡛⠛⠛⠛⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⡛⡃⠀⣛⢘⡛⠙⠙⠛⠛⡃⢘⠃⠀⢀⣘⡂⢛⣛⡛⠛⠀⢘⠀⣛⣙⠐⣚⣛⠐⣚⣛⠀⠿⠀⣛⣀⣚⢛⣛⣛⣛⡛⠛⡛⣛⡛⢛⣋⣉⣁⡙⢛⣛⡙⢛⣛⣛⣟⣙⣙⣛⣂⢀⣀⣀⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠛⡛⡃⠀⡛⢘⡛⠛⠛⠛⠛⡃⢘⠃⠀⢚⣛⡃⢛⣛⠛⠛⠀⢘⠀⢛⣛⠘⣛⣚⠘⣛⣛⠀⠛⠀⣛⠛⠓⠘⠛⠛⠛⡋⠘⣛⣛⣛⣙⣛⡛⠚⠓⠙⠛⠏⠛⠛⠛⠛⠛⠛⠛⠛⠛⠚⠛⠙⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⡛⠃⠀⡚⢘⡛⠛⠛⠛⠛⡃⠘⠃⠀⢘⢛⠁⢛⣛⠛⠛⠀⢘⠀⢛⣛⠘⠛⣛⠑⢛⡛⠀⡛⠀⣛⠃⢛⡛⣛⣋⠘⢓⣀⡛⣛⣛⣛⣙⡓⢁⡀⢀⡀⢀⣀⣀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠟⠿⠇⠀⠇⠘⢿⠟⠿⠿⠻⠇⠘⠃⠀⠸⠻⠃⠻⠿⠗⠻⢀⠘⠀⠻⠿⠘⠽⠿⠟⠿⠛⠀⠛⠀⠟⠿⠟⠣⠟⠋⠟⠘⠻⠛⠟⠟⠿⠿⠿⠛⡓⠛⠿⠿⠿⠿⠿⠛⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢒⠒⠒⠒⠒⠒⢒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠐⠒⠒⠒⠒⠒⠒⠒⠖⡲⠖⠶⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒ ⠧⠿⠿⠿⠿⠚⠟⠷⠺⠿⠗⠨⠟⠇⠻⠿⠇⠹⠿⠻⠇⠸⠿⠿⠾⠾⠀⠸⠙⠿⠿⠷⠿⠿⡿⠿⠿⠀⠿⠿⠷⠈⠿⠿⠚⠷⠆⠸⠿⠿⠻⠗⠸⠋⠇⠇⠇⠄⠸⠿⠗⠺⠗⠻⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠒⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠂⠀⠈⠠⠈⠀⠐⠒⠒⠒⠂⠰⠂⠀⠀⠀⠀⠂⠀⠀⠘⠒⠒⠇⠑⠓⠀⠀⠒⠐⠀⠀⠀⠐⠛⠃⠒⠂⠀⠐⠒⠒⠚⠘⠒⠚⠂⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠷⠷⠷⠷⠶⠷⠦⠶⠿⠇⠰⢶⡇⠶⢾⠇⠴⠾⠶⠆⠰⠶⠶⠸⠶⠶⠰⠀⢾⢶⣺⣶⠶⢻⠶⣿⡻⡷⡶⠀⣶⣶⠶⠶⠦⠠⣶⠆⠖⡖⠶⠶⠆⠰⣶⡆⠠⢶⣷⠶⠦⢲⢶⢶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠶⠷⠧⠮⠿⠇⠰⢷⡗⡶⣿⡆⢴⡾⠶⠇⠰⠶⠾⠼⠶⠶⠰⠀⡿⢲⣶⢴⣶⣶⣶⣶⠀⣶⣦⣶⣶⠀⣦⠔⡦⡄⢤⣶⣶⣶⣦⡇⠐⣦⢖⡖⠀⢰⣶⠆⠠⢶⣶⣦⡤⢶⣴⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠯⠿⠿⠿⠷⠶⠷⠷⠺⠿⠇⠰⢷⡆⡮⣷⡆⢴⣶⡾⠇⠰⠶⠾⠼⠶⠶⠰⠀⢶⢲⣶⢴⣶⣶⣶⠶⠀⡶⣶⣶⣶⡶⠀⣦⣵⣦⣶⠗⠐⡆⠠⣾⡆⠐⡆⢰⣶⡆⠰⢶⣶⣶⡦⢶⣴⣶⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠯⠿⠿⠿⠷⠚⠟⠷⠺⠿⠇⠠⢷⡆⡴⣾⡇⢰⣶⡾⠇⠰⠶⠾⠸⠶⠶⠢⠀⣶⣶⣤⣤⣶⣴⣤⣤⠀⣴⣤⣤⣦⣶⣤⢀⡴⣶⣤⣤⢤⣤⣶⡆⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠿⠚⠟⠷⠺⠿⠇⠠⣶⡆⠻⢷⡆⢰⣶⠼⠇⠰⠶⠾⠼⠾⠶⠚⠀⢶⣦⣴⢴⣴⣤⣶⣭⣦⠀⣆⣦⣤⣖⠀⣤⣶⣦⣤⣤⣦⢶⡆⠀⣦⡄⢰⣦⣤⣴⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠿⠚⠟⠷⠺⠿⠇⠀⢾⡇⡭⣷⣄⢰⣶⠿⠇⣼⣬⢬⣬⣤⢠⠀⣤⣤⣽⣤⣤⠀⡭⣶⣤⣯⣤⣤⠀⣤⣤⡤⡖⣶⣤⡄⢠⣤⣤⣤⣆⡄⠀⣦⣶⣼⣴⣬⢥⣤⣴⣤⣤⣴⡀⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀ ⡇⡟⡟⡟⡛⠚⡟⡗⠻⣟⡇⠈⣿⡇⠀⣶⡄⢠⣶⠞⠃⣤⣤⣤⣤⣤⢤⠀⣶⣦⣤⣫⢰⣭⠀⣤⣤⠀⣤⣤⣭⣶⠀⣶⣤⣤⣧⠀⢂⣤⣦⣤⣤⣴⣤⣶⡜⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⡟⡟⡟⡟⠛⡟⡗⢻⣟⡇⠘⣷⡆⡒⡲⠄⢸⣴⣽⡃⠐⠲⠒⢂⠲⠲⠐⠀⣴⣤⣤⢰⣴⡤⣼⣤⣤⠀⣤⣦⣤⣆⠁⣤⣶⣦⣤⣤⣤⣦⡆⠀⣦⡄⢠⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⡛⠛⡛⡛⢛⣛⡃⠘⣣⡆⣛⣩⣅⢠⣴⣜⡃⠘⠛⢛⢘⠛⠛⠘⠀⣤⣬⣥⢠⣴⣍⣤⣤⣭⡀⣬⣦⣥⣤⠀⣠⣦⣥⣥⣤⣥⣧⡇⠀⣥⡄⢨⣤⣬⣥⣭⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣓⣛⣛⣛⡛⢛⡛⣓⢛⣛⡃⢐⣫⡇⣥⡷⡇⢬⣭⣿⡃⠘⠛⢛⢚⠛⠛⠙⠀⣲⣼⣦⣼⣴⣿⣶⣶⣻⠀⣴⣤⡂⣤⡤⣤⣄⣥⠩⣤⣅⣤⡄⢀⣥⣧⣤⣄⣬⣤⣯⡇⢠⣠⡀⣠⣤⣤⣤⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⡛⢙⣋⡛⢙⣛⡃⢈⣣⣅⢨⣭⡅⢠⣭⣗⡃⠘⠛⢋⢚⠛⠛⠘⠀⢨⢽⣭⡭⡭⣭⣿⣥⢭⠇⣤⣭⣥⣭⣥⣍⣭⠁⣤⣭⣉⣥⣽⡖⢈⣭⣭⣭⣌⣭⣭⣥⡌⠈⡃⠈⠉⠉⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⣛⢉⣋⡛⢙⣛⡃⢘⣣⡕⣨⣭⠅⢠⣥⣝⡃⢘⢛⢙⢘⢛⢛⢑⠀⢺⣽⣭⡩⡭⣭⣭⣭⣭⢂⣭⣉⣉⣍⡭⣉⣉⣴⢉⣥⣅⣉⡍⢁⣈⣌⣉⣉⣍⣩⣭⡏⢡⣀⡀⢀⣙⣂⣠⣀⡁⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⣛⢉⣋⡛⢙⣛⡃⢐⣣⡅⢨⣭⡄⢘⣻⣟⡃⢘⠛⢛⢚⢛⢛⢉⠀⣸⢭⣅⡭⡭⣭⣭⣭⢨⠀⣭⣭⣁⣩⣅⣉⣍⢉⣤⣉⣉⣅⣁⣈⠈⣉⣍⣉⣈⣉⣨⣥⡌⠁⠁⠙⠉⠹⠉⠹⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣻⣛⣛⣛⣉⣋⡟⣙⣛⡃⢀⣳⡅⣨⣭⡅⣨⣿⣛⡃⣘⣛⣛⣚⣛⣛⠈⣤⣌⣩⣉⣙⠋⣋⣛⣩⣌⣀⣩⠉⣉⣍⣩⣍⠉⣬⣉⣍⡁⡟⢉⣁⣈⣈⣉⣉⡉⢈⣉⡉⢀⣄⣀⣠⣀⣀⡀⢀⠀⢀⣠⣀⣀⣀⣀⣠⣄ ⠃⠛⠋⠋⠋⠉⠋⠋⠙⠋⠃⠀⠃⠁⠉⠉⠁⠈⠉⠉⠁⠉⠉⠈⠉⠉⠈⠀⠉⠉⠉⠛⠉⠀⠉⠉⠉⠉⠉⠉⠀⠉⠉⠉⠉⠀⠉⠉⠉⠃⠁⠈⠉⠈⠉⠉⠈⠁⠈⠉⠁⠈⠉⠉⠉⠉⠉⠀⠀⠀⠉⠉⠉⠉⠁⠉⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣄⡀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⣁⢉⣍⣉⡉⣉⣉⡉⠉⡉⢉⣍⣉⣉⣉⣉⡉⢉⡉⢉⣉⠉⠉⠉⠉⠉⣉⠉⢉⠉⣉⣍⢉⣭⣭⢉⣉⣍⡍⣉⠉⢉⣉⣉⣉⡉⢉⣍⣉⡉⡍⡉⡉⢉⣉⣉⣩⣉⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉ ⠁⠈⠛⠋⠉⠋⠛⠃⠀⠃⠘⠋⠛⠋⠛⠛⠃⠈⠡⠀⠀⢀⠀⠀⠐⠀⠀⠀⢀⡀⠉⠋⠈⠛⠛⠉⠛⠈⠀⠉⠀⠙⠛⠛⠋⠃⠉⢛⠻⠃⠛⠃⠃⠘⠙⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀ ⠉⠉⠉⠉⠉⠉⡉⠉⠉⡉⢉⣉⠉⠉⠉⢉⡉⢉⣉⠁⠀⢈⡉⣉⣉⡉⠉⠉⢉⠉⡍⣉⣍⣉⣉⣉⣉⣉⠉⣁⠉⣉⣉⣉⢉⣭⡉⣉⣉⣉⣉⡉⢉⣉⣩⣉⠉⣍⣩⡉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⡉⠉⠉⠉⠉⠉ ⣀⠀⠀⠀⠀⡛⣛⡃⠀⡃⢘⣛⣙⣛⢛⣛⡃⢘⡁⠀⢀⣘⡁⠙⣛⡋⢙⠀⡲⠀⣝⣈⢁⣛⣋⢈⣝⣋⠁⣋⠀⣛⣛⣷⢈⣛⣛⣋⣝⣛⣛⣋⡙⣛⡛⢙⡚⢑⣛⡋⢙⣛⣛⣛⣛⣛⣚⣛⣛⣛⣛⣟⠁⠀⠀⠀⠀⠀ ⠃⠀⠀⠀⠘⠛⡛⠋⠀⡋⢙⡙⠋⠉⠈⠛⣋⠉⠉⠀⠐⢺⠳⣑⣛⡫⠷⠨⠁⠀⢘⣟⠰⣞⣙⠐⣛⣛⠀⣛⠀⣛⣋⣓⣈⡝⠋⣛⣛⣛⣛⣛⣛⣛⡋⢙⡙⢙⣛⣋⣙⣛⣛⢛⣛⣛⣚⣛⡛⠋⠛⠛⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⡟⡣⠀⣛⢘⡛⠁⠀⠀⠀⡁⠀⠂⠀⢀⣘⡂⢛⣛⡛⠛⠀⢘⠀⣙⣙⠐⣚⣻⠖⣂⣈⠀⠿⠀⣛⣁⣚⢓⣒⣒⣋⡉⠈⣄⣛⡛⢻⣋⣉⣁⡙⢛⣟⡙⢛⣛⣛⣟⣙⣙⣛⣂⢀⣀⣀⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣛⡻⡃⠀⡛⢘⡛⠛⠛⠛⠻⡃⢐⠀⠀⢚⣛⡃⢛⣛⠛⠛⠀⠘⠀⡛⣛⠘⣛⣊⡜⣛⣛⣄⠛⠀⣛⠛⡒⠚⠛⠛⠒⡓⠐⣚⣛⣛⣑⣒⡟⠚⠓⠙⠛⠏⠛⠛⠛⠛⠛⢟⠛⠛⠛⠚⠛⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⡛⠃⠀⡚⢘⡛⠛⠛⠛⠛⡃⠘⠃⠀⢘⢛⠁⢛⣛⠛⠛⠀⢐⠀⢛⣛⠘⠛⣛⠙⢒⣒⠀⡛⠀⣛⠃⢛⡓⣛⣃⠐⢒⣀⡛⣛⣛⣛⣛⣒⢁⡀⢀⡀⣀⡀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡀⠀⠘⠟⠿⠇⠀⠇⠸⢿⠟⠿⠿⠻⠇⠐⠂⠀⠸⠻⠃⢻⡿⡅⠳⡀⠘⠀⢻⡿⠘⠽⠿⠟⠿⠛⠀⠛⠀⠟⠿⠟⠣⠟⠋⠟⠈⠻⠛⠟⠟⠿⠿⠿⢛⠱⠹⢯⠭⠵⠶⠾⠛⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠒⠒⠒⠲⠖⠖⠒⠲⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⠖⠶⠂⠐⠂⠀⠐⠲⠴⠶⠲⠤⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠐⠒⠒⠒⠒⠒⠒⠒⠖⡲⠖⠶⠲⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒ ⠧⠿⠿⠷⠿⠒⠖⠶⠲⠶⠆⠠⠆⠆⠺⠿⠇⠹⠿⠳⠆⠰⠾⠿⠾⠾⠀⠸⠙⠶⠾⠷⠿⠿⡿⠿⠿⠀⠿⠿⠷⠈⠿⠿⠚⠷⠆⠸⠿⠷⠲⠗⠸⠋⠇⠇⠇⠄⠸⠶⠗⠺⠗⠻⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⠀⠒⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠂⠀⠈⠠⠈⠀⠐⠒⠒⠒⠂⠰⠂⠀⠀⠀⠀⠂⠀⠀⠘⠒⠒⠇⠑⠓⠀⠀⠒⠐⠀⠀⠀⠐⠛⠃⠒⠃⠀⠐⠒⠒⠚⠘⠒⠚⠂⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠷⠷⠷⠷⠶⠷⠦⠶⠿⠇⠰⢶⡇⠶⢾⠇⠴⠾⠶⠆⠰⠶⠶⠸⠶⠶⠰⠀⢾⢶⣺⣶⠶⢻⠶⣿⡻⡷⡶⠀⣶⣶⠶⠶⠦⠠⣶⠆⠗⡖⠶⠶⠆⠰⣶⡆⠠⢶⣷⠶⠦⢲⢶⢶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠶⠷⠧⠮⠿⠇⠰⢷⡗⡶⣿⡆⢴⡾⠶⠇⠰⠶⠾⠼⠶⠶⠰⠀⡿⢲⣶⢴⣶⣶⣶⣶⠀⣶⣦⣶⣶⠀⣦⠔⣆⡀⢤⣶⣶⣶⣦⡇⠐⣦⢖⡖⠀⢰⣶⠆⠠⢶⣶⣦⡤⢶⣴⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠯⠿⠿⠿⠷⠶⠷⠷⠺⠿⠇⠰⢷⡆⡮⣷⡆⠴⣶⡾⠇⠰⠶⠾⠼⠶⠶⠰⠀⢶⢲⣶⢴⣶⣶⣶⠶⠀⡶⣶⣶⣶⡶⠀⣦⣵⣦⣶⠗⠐⡆⠠⣾⡆⠐⡆⢰⣶⡆⠰⢶⣶⣶⡦⢶⣴⣶⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠚⠟⠷⠺⠿⠇⠠⢷⡆⡴⣾⡇⢰⣶⡾⠇⠰⠶⠾⠸⠶⠶⠢⠀⣶⣶⣤⣤⣶⣴⣤⣤⠀⣴⣤⣤⣦⣶⣤⢀⡴⣶⣤⣤⢤⣤⣶⡆⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠿⠚⠟⠷⠺⠿⠇⠠⣶⡆⠻⢷⡆⢰⣶⠼⠇⠰⠶⠾⠼⠾⠶⠚⠀⢶⣦⣴⢴⣴⣤⣶⣭⣦⠀⣆⣦⣤⣖⠀⣤⣶⣦⣤⣤⣦⢶⡆⠠⣦⡄⢰⣦⣤⣴⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠿⠚⠟⠷⠺⠿⠇⠀⢾⡇⡭⣷⣄⢰⣶⠿⠇⣼⣬⢬⣬⣤⢠⠀⣤⣤⣽⣤⣤⠀⣭⣦⣤⣯⣤⣤⠀⣤⣤⡤⣖⣶⣤⡄⢠⣤⣤⣤⣆⡄⠀⣦⣶⣼⣴⣬⢥⣤⣴⣤⣤⣴⡀⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀ ⡇⣟⡟⡟⡛⠚⡟⡗⠻⣟⡇⠈⣿⡇⠀⣶⣄⢠⣶⠞⠃⣤⣤⣤⣤⣤⢄⠀⣶⣦⣤⣫⢰⣭⠀⣤⣤⠀⣤⣤⣭⣶⠀⣶⣤⣤⣧⠀⢂⣤⣦⣤⣤⣴⣤⣶⡜⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⡟⡟⡟⡟⠛⡟⡗⢻⣟⡇⠘⣷⡆⡒⡲⠄⢸⣶⣽⡃⠐⠲⠒⢂⠲⠲⠐⠀⣴⣤⣤⢰⣴⡤⣼⣤⣤⠀⣤⣦⣤⣆⠁⣤⣶⣦⣤⣤⣤⣦⡆⠀⣦⡄⢠⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⡛⠛⡛⡛⢛⣛⡃⠘⣣⡆⣛⣩⣅⢠⣴⣞⡃⠘⠛⢛⢘⠛⠛⠘⠀⣤⣬⣥⢠⣴⣍⣤⣤⣭⡀⣬⣦⣥⣤⠀⣠⣦⣥⣥⣤⣥⣧⡇⠀⣥⡄⢨⣤⣬⣥⣭⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣓⣛⣛⣛⡛⢛⡛⣓⢛⣛⡃⢐⣫⡇⣥⡷⡇⢬⣭⣿⡃⠘⠛⢛⢚⠛⠛⠙⠀⣲⣼⣦⣼⣴⣿⣶⣶⣻⠀⣴⣤⡂⣤⡤⣤⣄⣥⠩⣤⣅⣤⡄⢀⣥⣧⣤⣄⣬⣤⣯⡇⢠⣠⡀⣠⣤⣤⣤⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⡛⢙⣋⡛⢙⣛⡃⢈⣣⣅⢨⣭⡅⢠⣭⣗⡃⠘⠛⢋⢚⠛⠛⠘⠀⢨⢽⣭⡭⡭⣭⣿⣥⢭⠇⣤⣭⣥⣭⣥⣍⣭⠁⣤⣭⣉⣥⣽⡖⢈⣭⣭⣭⣌⣭⣭⣥⡌⠈⡃⠈⠉⠉⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⣛⢉⣋⡛⢙⣛⡃⢘⣣⡕⣨⣭⠅⢠⣥⣝⡃⢘⢛⢙⢘⢛⢛⢑⠀⢺⣽⣭⡩⡭⣭⣭⣭⣭⢂⣭⣉⣉⣍⡭⣉⣉⣴⢉⣥⣅⣉⡍⢁⣈⣌⣉⣉⣍⣩⣭⡏⢡⣀⡀⢀⣙⣂⣠⣀⡁⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⣛⢉⣋⡛⢙⣛⡃⢐⣣⡅⢨⣭⡄⢘⣻⣟⡃⢘⠛⢛⢚⢛⢛⢉⠀⣸⢭⣅⡭⡭⣭⣭⣭⢨⠀⣭⣭⣁⣩⣅⣉⣍⢉⣤⣉⣉⣅⣁⣈⠈⣉⣍⣉⣈⣉⣨⣥⡌⠁⠁⠙⠉⠹⠉⠹⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣻⣛⣛⣛⣉⣋⡟⣙⣛⡃⢀⣳⡅⣨⣭⡅⣨⣿⣛⡃⣘⣛⣛⣚⣛⣛⠈⣤⣌⣩⣉⣙⠋⣋⣛⣩⣌⣀⣩⠉⣉⣍⣩⣍⠉⣬⣉⣍⡁⡟⢉⣁⣈⣈⣉⣉⡉⢈⣉⡉⢀⣄⣀⣠⣀⣀⡀⢀⠀⢀⣠⣀⣀⣀⣀⣠⣄ ⠃⠛⠋⠋⠋⠉⠋⠋⠙⠋⠃⠀⠃⠁⠉⠉⠁⠈⠉⠉⠁⠉⠉⠈⠉⠉⠈⠀⠉⠉⠉⠛⠉⠀⠉⠉⠉⠉⠉⠉⠀⠉⠉⠉⠉⠀⠉⠉⠉⠃⠁⠈⠉⠈⠉⠉⠈⠁⠈⠉⠁⠈⠉⠉⠉⠉⠉⠀⠀⠀⠉⠉⠉⠉⠁⠉⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣄⡀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⣁⢉⣍⣉⡉⣉⣉⡉⠉⡉⢉⣍⣉⣉⣉⣉⡉⢉⡉⢉⣉⠉⡉⠉⠉⠉⣉⠉⢩⠉⣉⣍⢉⣭⣭⢉⣉⣍⡍⣉⠉⢉⣉⣉⣉⡉⢉⣍⣉⡉⡍⡉⡉⢉⣉⣉⣩⣉⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉ ⠁⠈⠛⠋⠉⠋⠛⠃⠀⠃⠘⠋⠛⠋⠛⠛⠃⠈⠡⠀⠀⢀⠀⠀⠐⠀⠀⠀⢀⡀⠉⠋⠈⠛⠛⠉⠛⠈⠀⠉⠀⠙⠛⠛⠋⠃⠉⢛⠻⠃⠛⠃⠃⠘⠙⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀ ⠉⠉⠉⠉⠉⠉⡉⠉⠉⡉⢉⣉⠉⠉⠉⢉⡉⢉⣉⠀⠀⢈⡉⣉⣉⡉⠉⠉⢉⠉⡍⣉⣍⣉⣉⣉⣉⣉⠉⣁⠉⣉⣉⣉⢉⣭⡉⣉⣉⣉⣉⡍⢉⣉⣩⣉⠉⣍⣩⡉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⠉⠉⠉⠉⠉⠉ ⣀⠀⠀⠀⠀⡛⣛⡃⠀⡃⢘⣛⣙⣛⢛⣛⡃⢘⡁⠀⢀⣘⡁⠙⣛⡋⢙⠀⡲⠀⣝⣈⢁⣛⣋⢈⣝⣋⠁⣋⠀⣛⣛⣷⢈⣛⣛⣋⣝⣛⣛⣋⡙⣛⡛⢙⡚⢑⣛⡋⢙⣛⣛⣛⣛⣛⣚⣛⣛⣛⣛⣟⠀⠀⠀⠀⠀⠀ ⠃⠀⠀⠀⠘⠛⡛⠋⠀⡋⢙⡙⠋⠉⠈⠛⣋⠉⠉⠀⠐⢊⠳⣑⣛⡫⠷⠨⠁⠀⢛⣛⠰⣞⣙⠐⣛⣛⠀⣛⠀⣛⣋⣓⣈⡝⠋⣛⣛⣛⣛⣛⣛⣛⡋⢙⡙⢙⣛⣋⣙⣛⣛⢛⣛⣛⣚⣛⡛⠋⠛⠛⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⡟⡣⠀⣛⢘⡛⠁⠀⠀⠀⡁⠀⠂⠀⠀⣘⡂⢛⣛⡛⠛⠀⢘⠀⣙⣙⠐⣚⣻⠖⣂⣈⠀⠿⠀⣛⣁⣚⢓⣒⣒⣋⡉⠈⣄⣛⡛⢻⣋⣉⣁⡙⢛⣟⡙⢛⣛⣛⣟⣙⣙⣛⣂⢀⣀⣀⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣛⡻⡃⠀⡛⢘⡛⠙⠛⠛⠻⡃⢐⠀⠀⢚⣛⡃⢛⣛⠛⠛⠀⠘⠀⡛⣛⠘⣛⣊⡝⣛⣛⣄⠛⠀⣛⠛⡒⠚⠛⠛⠒⡓⠐⣚⣛⣛⣑⣒⡟⠚⠓⠙⠛⠏⠛⠛⠛⠛⠛⢟⠛⠛⠛⠚⠛⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⡛⠃⠀⡚⢘⡛⠛⠛⠛⠛⡃⢘⠃⠀⢘⢛⠁⢛⣛⠛⠛⠀⢘⠀⢛⣛⠘⠛⣛⠙⢒⣒⠀⡛⠀⣛⠃⢛⡓⣛⣃⠐⢒⣀⡛⣛⣛⣛⣛⣒⢁⡀⢀⡀⢀⡀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡀⠀⠘⠟⠿⠇⠀⠇⠸⢿⠟⠿⠿⠻⠇⠐⠂⠀⠸⠻⠃⢻⡿⡅⠳⡀⠘⠀⢻⡿⠘⠻⠿⠟⠿⠛⠀⠛⠀⠟⠿⠟⠣⠟⠋⠟⠈⠻⠛⠟⠟⠿⠿⠿⢛⠱⠹⢯⠭⠵⠶⠾⠛⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠒⠒⠒⠲⠖⠖⠒⠲⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⠖⠶⠂⠐⠂⠀⢐⠲⠴⠶⠲⠤⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠐⠒⢒⠒⠒⠒⠒⠖⡲⠖⠶⠲⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒ ⠧⠿⠿⠷⠿⠒⠖⠶⠲⠶⠆⠸⠆⠆⠺⠿⠇⠹⠿⠳⠆⠰⠾⠿⠾⠾⠀⠸⠙⠶⠾⠷⠿⠿⡿⠿⠿⠀⠿⠿⠷⠈⠿⠿⠚⠷⠆⠸⠿⠷⠲⠗⠸⠋⠇⠇⠇⠄⠸⠶⠗⠺⠗⠻⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⠀⠒⠓⠈⠈⠁⠐⠋⠀⠀⠐⠂⠀⠀⠀⠀⠐⠚⠂⠀⠈⠠⠈⠀⠐⠒⠒⠒⠂⠰⠂⠀⠀⠀⠀⠂⠀⠀⠘⠒⠒⠇⠑⠓⠀⠀⠒⠐⠀⠀⠀⠐⠛⠃⠒⠃⠀⠐⠒⠒⠚⠘⠒⠚⠂⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠷⠷⠷⠷⠶⠷⠦⠶⠿⠇⠰⢶⡇⠶⢾⠇⠴⠾⠶⠆⠰⠶⠶⠸⠶⠶⠰⠀⢾⢶⣺⣶⠶⢻⠶⣿⡻⡷⡶⠀⣶⣶⠶⠶⠦⠠⣶⠆⠗⡖⠶⠶⠆⠰⣶⡆⠠⢶⣷⠶⠦⢲⢶⢶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠶⠷⠧⠮⠿⠇⠰⢷⡗⡶⣿⡆⢴⡾⠶⠇⠰⠶⠾⠼⠶⠶⠰⠀⡿⢲⣶⢴⣶⣶⣶⣶⠀⣶⣦⣶⣶⠀⣦⠔⣆⡀⢤⣶⣶⣶⣦⡇⠐⣦⢖⡖⠀⢰⣶⠆⠠⢶⣶⣦⡤⢶⣴⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠯⠿⠿⠿⠷⠶⠷⠷⠺⠿⠇⠰⢷⡆⡮⣷⡆⠴⣶⡾⠇⠰⠶⠾⠼⠶⠶⠰⠀⢶⢲⣶⢴⣶⣶⣶⠶⠀⡶⣶⣶⣶⡶⠀⣦⣵⣦⣶⠗⠐⡆⠠⣾⡆⠐⡆⢰⣶⡆⠰⢶⣶⣶⡦⢶⣴⣶⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠚⠟⠷⠺⠿⠇⠠⢷⡆⡴⣾⡇⢰⣶⡾⠇⠰⠶⠾⠸⠶⠶⠢⠀⣶⣶⣤⣤⣶⣴⣤⣤⠀⣴⣤⣤⣦⣶⣤⢀⡴⣶⣤⣤⢤⣤⣶⡆⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠿⠚⠟⠷⠺⠿⠇⠠⣶⡆⠻⢷⡆⢰⣶⠼⠇⠰⠶⠾⠼⠾⠶⠚⠀⢶⣦⣴⢴⣴⣤⣶⣭⣦⠀⣆⣦⣤⣖⠀⣤⣶⣦⣤⣤⣦⢶⡆⠠⣦⡄⢰⣦⣤⣴⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠿⠚⠟⠷⠺⠿⠇⠀⢾⡇⡭⣷⣄⢰⣶⠿⠇⣼⣬⢬⣬⣤⢠⠀⣤⣤⣽⣤⣤⠀⣭⣦⣤⣯⣤⣤⠀⣤⣤⡤⣖⣶⣤⡄⢠⣤⣤⣤⣆⡄⠀⣦⣶⣼⣴⣬⢥⣤⣴⣤⣤⣴⡀⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀ ⡇⣟⡟⡟⡛⠚⡟⡗⠻⣟⡇⠈⣿⡇⠀⣶⣄⢠⣶⠞⠃⣤⣤⣤⣤⣤⢄⠀⣶⣦⣤⣫⢰⣭⠀⣤⣤⠀⣤⣤⣭⣶⠀⣶⣤⣤⣧⠀⢂⣤⣦⣤⣤⣴⣤⣶⡜⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⡟⡟⡟⡟⠛⡟⡗⢻⣟⡇⠘⣷⡆⡒⡲⠄⢸⣶⣽⡃⠐⠲⠒⢂⠲⠲⠐⠀⣴⣤⣤⢰⣴⡤⣼⣤⣤⠀⣤⣦⣤⣆⠁⣤⣶⣦⣬⣤⣤⣦⡆⠀⣦⡄⢠⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⡛⠛⡛⡛⢛⣛⡃⠘⣣⡆⣛⣩⣅⢠⣴⣞⡃⠘⠛⢛⢘⠛⠛⠘⠀⣤⣬⣥⢠⣴⣍⣤⣤⣭⡀⣬⣦⣥⣤⠀⣠⣦⣥⣥⣤⣥⣧⡇⠀⣥⡄⢨⣤⣬⣥⣭⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣓⣛⣛⣛⡛⢛⡛⣓⢛⣛⡃⢐⣫⡇⣥⡷⡇⢬⣭⣿⡃⠘⠛⢛⢚⠛⠛⠙⠀⣲⣼⣦⣼⣴⣿⣶⣶⣻⠀⣴⣤⡂⣤⡤⣤⣄⣥⠩⣤⣅⣤⡄⢀⣥⣧⣤⣄⣬⣤⣯⡇⢠⣠⡀⣠⣤⣤⣤⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⡟⢙⣋⡛⢙⣛⡃⢈⣣⣅⢨⣭⡅⢠⣭⣗⡃⠘⠛⢋⢚⠛⠛⠘⠀⢨⢽⣭⡭⡭⣭⣿⣥⢭⠇⣤⣭⣥⣭⣥⣍⣭⠁⣤⣭⣉⣥⣽⡖⢈⣭⣭⣭⣌⣭⣭⣥⡌⠈⡃⠈⠉⠉⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⣛⢉⣋⡛⢙⣛⡃⢘⣣⡕⣨⣭⠅⢠⣥⣝⡃⢘⢛⢙⢘⢛⢛⢑⠀⢺⣽⣭⡩⡭⣭⣭⣭⣭⢂⣭⣉⣉⣍⡭⣉⣉⣴⢉⣥⣅⣉⡍⢁⣈⣌⣉⣉⣍⣩⣭⡏⢡⣀⡀⢀⣙⣂⣠⣀⡁⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⣛⢉⣋⡛⢙⣻⡃⢐⣣⡅⢨⣭⡄⢘⣻⣟⡃⢘⠛⢛⢚⢛⢛⢉⠀⣸⢭⣅⡭⡭⣭⣭⣭⢨⠀⣭⣭⣁⣩⣅⣉⣍⢉⣤⣉⣉⣅⣁⣈⠈⣉⣍⣉⣈⣉⣨⣥⡌⠁⠁⠙⠉⠹⠉⠹⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣻⣛⣛⣛⣉⣋⡟⣙⣛⡃⢀⣳⡅⣨⣭⡅⣨⣿⣛⡃⣘⣛⣛⣚⣛⣛⠈⣤⣌⣩⣉⣙⠋⣋⣛⣩⣌⣀⣩⠉⣉⣍⣩⣍⠉⣬⣉⣍⡁⡟⢉⣁⣈⣈⣉⣉⡉⢈⣉⡉⢀⣄⣀⣠⣀⣀⡀⢀⠀⢀⣠⣀⣀⣀⣀⣠⣄ ⠃⠛⠋⠋⠋⠉⠋⠋⠙⠋⠃⠀⠃⠁⠉⠉⠁⠈⠉⠉⠁⠉⠉⠈⠉⠉⠈⠀⠉⠉⠉⠛⠉⠀⠉⠉⠉⠉⠉⠉⠀⠉⠉⠉⠉⠀⠉⠉⠉⠃⠁⠈⠉⠈⠉⠉⠈⠁⠈⠉⠁⠈⠉⠉⠉⠉⠉⠀⠀⠀⠉⠉⠉⠉⠁⠉⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣄⡀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⣁⢉⣍⣉⡉⣉⣉⡉⠉⡉⢉⣍⣉⣉⣉⣉⡉⢉⡉⢉⣉⠉⡉⠉⠉⠉⣉⠉⢩⠉⣉⣍⢉⣭⣭⢉⣉⣍⡍⣉⠉⢉⣉⣉⣉⡉⢉⣍⣉⡉⡍⡉⡉⢉⣉⣉⣩⣉⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉ ⠁⠈⠛⠋⠉⠋⠛⠃⠀⠃⠘⠋⠛⠋⠛⠛⠃⠈⠡⠀⠀⢀⠀⠀⠐⠀⠀⠀⢀⡀⠉⠋⠈⠛⠛⠉⠛⠈⠀⠉⠀⠙⠛⠛⠋⠃⠉⢛⠻⠃⠛⠃⠃⠘⠙⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀ ⠉⠉⠉⠉⠉⠉⡉⠉⠉⡉⢉⣉⠉⠉⠉⢉⡉⢉⣉⠀⠀⢈⡉⣉⣉⡉⠉⠉⢉⠉⡍⣉⣍⣉⣉⣉⣉⣉⠉⣁⠉⣉⣉⣉⢉⣭⡉⣉⣉⣉⣉⡍⢉⣉⣩⣉⠉⣍⣩⡉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⠉⠉⠉⠉⠉⠉ ⣀⠀⠀⠀⠀⡛⣛⡃⠀⡃⢘⣛⣙⣛⢛⣛⡃⢘⡁⠀⢀⣘⡁⠙⣛⡋⢙⠀⡲⠀⣝⣈⢁⣛⣋⢈⣝⣋⠁⣋⠀⣛⣛⣷⢈⣛⣛⣋⣝⣛⣛⣋⡙⣛⡛⢙⡚⢑⣛⡋⢙⣛⣛⣛⣛⣛⣚⣛⣛⣛⣛⣟⠀⠀⠀⠀⠀⠀ ⠃⠀⠀⠀⠘⠛⡛⠋⠀⡋⢙⡙⠋⠉⠈⠛⣋⠉⠉⠀⠐⢊⠳⣑⣛⡫⠷⠨⠁⠀⢛⣛⠰⣞⣙⠐⣛⣛⠀⣛⠀⣛⣋⣓⣈⡝⠋⣛⣛⣛⣛⣛⣛⣛⡋⢙⡙⢙⣛⣋⣙⣛⣛⢛⣛⣛⣚⣛⡛⠋⠛⠛⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⡟⡣⠀⣛⢘⡛⠁⠀⠀⠀⡁⠀⠂⠀⠀⣘⡂⢛⣛⡛⠛⠀⢘⠀⣙⣙⠐⣚⣻⠖⣂⣈⠀⠿⠀⣛⣁⣚⢓⣒⣒⣋⡉⠈⣄⣛⡛⢻⣋⣉⣁⡙⢛⣟⡙⢛⣛⣛⣟⣙⣙⣛⣂⢀⣀⣀⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣛⡻⡃⠀⡛⢘⡛⠙⠛⠛⠻⡃⢐⠀⠀⢚⣛⡃⢛⣛⠛⠛⠀⠘⠀⡛⣛⠘⣛⣊⡝⣛⣛⣄⠛⠀⣛⠛⡒⠚⠛⠛⠒⡓⠐⣚⣛⣛⣑⣒⡟⠚⠓⠙⠛⠏⠛⠛⠛⠛⠛⢟⠛⠛⠛⠚⠛⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⡛⠃⠀⡚⢘⡛⠿⠛⠛⠛⡃⢘⠃⠀⢘⢛⠁⢛⣛⠛⠛⠀⢘⠀⢛⣛⠘⠛⣛⠙⢒⣒⠀⡛⠀⣛⠃⢛⡓⣛⣃⠐⢒⣀⡛⣛⣛⣛⣛⣒⢁⡀⢀⡀⢀⡀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡀⠀⠘⠟⠿⠇⠀⠇⠸⢿⠟⠿⠿⠻⠇⠐⠂⠀⠸⠻⠃⢻⡿⡅⠳⡀⠘⠀⢻⡿⠘⠻⠿⠟⠿⠛⠀⠛⠀⠟⠿⠟⠣⠟⠋⠟⠈⠻⠛⠟⠟⠿⠿⠿⢛⠱⠹⢯⠭⠵⠶⠾⠻⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⠄⠄⠒⠲⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⠖⠶⠂⠐⠂⠀⢐⠲⠴⠶⠲⠤⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠐⠒⢒⠒⠒⠒⡒⠖⡲⠖⠶⠲⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀ ⠧⠿⠿⠷⠿⠒⠖⠶⠲⠶⠆⠸⠆⠆⠺⠿⠇⠹⠿⠳⠆⠰⠾⠿⠾⠾⠀⠸⠙⠶⠾⠷⠿⠿⡿⠿⠿⠀⠿⠿⠷⠈⠿⠿⠚⠷⠆⠸⠿⠷⠲⠗⠸⠋⠇⠇⠇⠄⠸⠶⠗⠺⠗⠻⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⠀⠒⠓⠈⠈⠁⠐⠋⠀⠀⠐⠂⠀⠀⠀⠀⠐⠚⠂⠀⠈⠠⠈⠀⠐⠒⠒⠒⠂⠰⠂⠀⠀⠀⠀⠂⠀⠀⠘⠒⠒⠇⠑⠓⠀⠀⠒⠐⠀⠀⠀⠐⠛⠃⠒⠃⠀⠐⠒⠒⠚⠘⠒⠚⠂⠀⠐⠂⠀⠀⠀⠐⠀⠀⠀⠀⠀ ⠧⠷⠷⠷⠷⠶⠷⠦⠶⠿⠇⠰⢶⡇⠶⢾⠇⠴⠾⠶⠆⠰⠶⠶⠸⠶⠶⠰⠀⢾⢶⣺⣶⠶⢻⠶⣿⡻⡷⡶⠀⣶⣶⠶⠶⠦⠠⣶⠆⠗⡖⠶⠶⠆⠰⣶⡆⠠⢶⣷⠶⠦⢲⢶⢶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠶⠷⠧⠮⠿⠇⠰⢷⡗⡶⣿⡆⢴⡾⠶⠇⠰⠶⠾⠼⠶⠶⠰⠀⡿⢲⣶⢴⣶⣶⣶⣶⠀⣶⣦⣶⣶⠀⣦⠔⣆⡀⢤⣶⣶⣶⣦⡇⠐⣦⢖⡖⠀⢰⣶⠆⠠⢶⣶⣦⡤⢶⣴⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠯⠿⠿⠷⠶⠶⠷⠷⠺⠿⠇⠰⢷⡆⡮⣷⡆⠴⣶⡾⠇⠰⠶⠾⠼⠶⠶⠰⠀⢶⢲⣶⢴⣶⣶⣶⠶⠀⡶⣶⣶⣶⡶⠀⣦⣵⣦⣶⠗⠐⡆⠠⣾⡆⠐⡆⢰⣶⡆⠰⢶⣶⣶⡦⢶⣴⣶⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠚⠟⠷⠺⠿⠇⠠⢷⡆⡴⣾⡇⢰⣶⡾⠇⠰⠶⠾⠸⠶⠶⠢⠀⣶⣶⣤⣤⣶⣴⣤⣤⠀⣴⣤⣤⣦⣶⣤⢀⡴⣶⣤⣤⢤⣤⣶⡆⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠿⠚⠟⠷⠺⠿⠇⠠⣶⡆⠻⢷⡆⢰⣶⠼⠇⠰⠶⠾⠼⠾⠶⠚⠀⢶⣦⣴⢴⣴⣤⣶⣭⣦⠀⣆⣦⣤⣖⠀⣤⣶⣦⣤⣤⣦⢶⡆⠠⣦⡄⢰⣦⣤⣴⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠿⠚⠟⠷⠺⠿⠇⠀⢾⡇⡭⣷⣄⢰⣶⠿⠇⣼⣬⢬⣬⣤⢠⠀⣤⣤⣽⣤⣤⠀⣭⣦⣤⣯⣤⣤⠀⣤⣤⡤⣖⣶⣤⡄⢠⣤⣤⣤⣆⡄⠀⣦⣶⣼⣴⣬⢥⣤⣴⣤⣤⣴⡀⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀ ⡇⣟⡟⡟⡛⠚⡟⡗⠻⣟⡇⠈⣿⡇⠀⣶⣄⢠⣶⠞⠃⣤⣤⣤⣤⣤⢄⠀⣶⣦⣤⣫⢰⣭⠀⣤⣤⠀⣤⣤⣭⣶⠀⣶⣤⣤⣧⠀⢂⣤⣦⣤⣤⣴⣤⣶⡜⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⡟⡟⡟⡟⠛⡟⡗⢻⣟⡇⠘⣷⡆⡒⡲⠄⢸⣶⣽⡃⠐⠲⠒⢂⠲⠲⠐⠀⣴⣤⣤⢰⣴⡤⣼⣤⣤⠀⣤⣦⣤⣆⠁⣤⣶⣦⣬⣤⣤⣦⡆⠀⣦⡄⢠⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⡛⣛⡛⠛⡛⡛⢛⣛⡃⠘⣣⡆⣛⣩⣅⢠⣴⣞⡃⠘⠛⢛⢘⠛⠛⠘⠀⣤⣬⣥⢠⣴⣍⣤⣤⣭⡀⣬⣦⣥⣤⠀⣠⣦⣥⣥⣤⣥⣧⡇⠀⣥⡄⢨⣤⣬⣥⣭⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣓⣛⣛⣛⡛⢛⡛⣓⢛⣛⡃⢐⣫⡇⣥⡷⡇⢬⣭⣿⡃⠘⠛⢛⢚⠛⠛⠙⠀⣲⣼⣦⣼⣴⣿⣶⣶⣻⠀⣴⣤⡂⣤⡬⣤⣄⣥⠩⣤⣅⣤⡄⢀⣥⣧⣤⣄⣬⣤⣯⡇⢠⣠⡀⣠⣤⣤⣤⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⡟⢙⣋⡛⢙⣛⡃⢈⣣⣅⢨⣭⡅⢠⣭⣗⡃⠘⠛⢋⢚⠛⠛⠘⠀⢨⢽⣭⡭⡭⣭⣿⣥⢭⠇⣤⣭⣥⣭⣥⣍⣭⠁⣤⣭⣉⣥⣽⡖⢈⣭⣭⣭⣌⣭⣭⣥⡌⠈⡃⠈⠉⠉⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⣛⢙⣋⡛⢙⣻⡃⢘⣣⡕⣨⣭⠅⢠⣥⣝⡃⢘⢛⢙⢘⢛⢛⢑⠀⢺⣽⣭⡩⡭⣭⣭⣭⣭⢂⣭⣉⣉⣍⡭⣉⣉⣴⢉⣥⣅⣉⡍⢁⣈⣌⣉⣉⣍⣩⣭⡏⢡⣀⡀⢀⣙⣂⣠⣀⡁⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⣛⢉⣋⡛⢙⣻⡃⢐⣣⡅⢨⣭⡄⢘⣻⣟⡃⢘⠛⢛⢚⢛⢛⢉⠀⣸⢭⣅⡭⡭⣭⣭⣭⢨⠀⣭⣭⣁⣩⣅⣉⣍⢉⣤⣉⣉⣅⣁⣈⠈⣉⣍⣉⣈⣉⣨⣥⡌⠁⠁⠙⠉⠹⠉⠹⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣻⣛⣛⣛⣉⣋⡟⣙⣛⡃⢀⣳⡅⣨⣭⡅⣨⣿⣛⡃⣘⣛⣛⣚⣛⣛⠈⣤⣌⣩⣉⣙⠋⣋⣛⣩⣌⣀⣩⠉⣉⣍⣩⣍⠉⣬⣉⣍⡁⡟⢉⣁⣈⣈⣉⣉⡉⢈⣉⡉⢀⣄⣀⣠⣀⣀⡀⢀⠀⢀⣠⣀⣀⣀⣀⣠⣄ ⠃⠛⠋⠋⠋⠉⠋⠋⠙⠋⠃⠀⠃⠁⠉⠉⠁⠈⠉⠉⠁⠉⠉⠈⠉⠉⠈⠀⠉⠉⠉⠛⠉⠀⠉⠉⠉⠉⠉⠉⠀⠉⠉⠉⠉⠀⠉⠉⠉⠃⠁⠈⠉⠈⠈⠉⠈⠁⠈⠉⠁⠈⠉⠉⠉⠉⠉⠀⠀⠀⠉⠉⠉⠉⠁⠉⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣄⡀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⣁⢉⣍⣉⡉⣉⣉⡉⠉⡉⢉⣍⣉⣉⣉⣉⡉⢉⡉⢉⣉⠉⡉⠉⠉⠉⣉⠉⢩⠉⣉⣍⢉⣭⣭⢉⣉⣍⡍⣉⠉⢉⣉⣉⣉⡉⢉⣍⣉⡉⡍⡉⡉⢉⣉⣉⣩⣉⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉ ⠁⠈⠛⠋⠉⠋⠛⠃⠀⠃⠘⠋⠛⠋⠛⠛⠃⠈⠡⠀⠀⢀⠀⠀⠐⠀⠀⠀⢀⡀⠉⠋⠈⠛⠛⠉⠛⠈⠀⠉⠀⠙⠛⠛⠋⠃⠉⢛⠻⠃⠛⠃⠃⠘⠙⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀ ⠉⠉⠉⠉⠉⠉⡉⠉⠉⡉⢉⣉⠉⠉⠉⢉⡉⢉⣉⠀⠀⢈⡉⣉⣉⡉⠉⠉⢉⠉⡍⣉⣍⣉⣉⣉⣉⣉⠉⣁⠉⣉⣉⣉⢉⣭⡉⣉⣉⣉⣉⡍⢉⣉⣩⣉⠉⣍⣩⡉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⠉⠉⠉⠉⠉⠉ ⣀⠀⠀⠀⠀⡛⣛⡃⠀⡃⢘⣛⣙⣛⢛⣛⡃⢘⡁⠀⢀⣘⡁⠙⣛⡋⢙⠀⡲⠀⣝⣈⢁⣛⣋⢈⣝⣋⠁⣋⠀⣛⣛⢷⢈⣛⣛⣋⣝⣛⣛⣋⡙⣛⡛⢙⡚⢑⣛⡋⢙⣛⣛⣛⣛⣛⣚⣛⣛⣛⣛⣟⠀⠀⠀⠀⠀⠀ ⠃⠀⠀⠀⠘⠛⡛⠋⠀⡋⢙⡙⠏⠉⠈⠛⣋⠉⠉⠀⠐⢊⠳⣙⣛⡫⠷⠨⠁⠀⢛⣛⠰⣞⣙⠐⣛⣛⠀⣛⠀⣛⡋⢀⣈⡝⠋⣛⣛⣛⣛⣛⣛⣛⡋⢙⡙⢙⣛⣋⣙⣛⣛⢛⣛⣛⣚⣛⡛⠋⠛⠛⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⡟⡣⠀⣛⢘⡛⠁⠀⠀⠀⡁⠀⠂⠀⠀⣘⡂⢛⣛⡛⠛⠀⢘⠀⣙⣙⠐⣞⢳⠖⠂⣄⠀⠿⢁⣒⡐⠀⢓⣒⣒⣋⡉⠈⣄⣛⡛⢻⣋⣉⣁⡙⢛⣟⡙⢛⣛⣟⠟⣙⣙⣛⢂⢀⣀⣀⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣛⡻⡃⠀⡛⢘⡛⠙⠛⠛⠻⡃⢐⠀⠀⢚⣛⡃⢛⣛⠛⠛⠀⠘⠀⡛⣛⠘⣛⣊⡝⣛⣚⣄⠛⠀⣒⠒⡒⠚⠛⠛⠒⡷⠐⣚⣛⣛⣑⣒⡟⠚⠓⠚⠛⠏⠛⠛⠟⠛⠛⢟⠛⠛⠛⠚⠛⠻⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⡛⠃⠀⡚⢘⡛⠿⠛⠛⠛⡃⢘⠃⠀⢘⢛⠁⢛⣛⠛⠛⠀⢘⠀⢛⣛⠘⠛⣛⠙⢒⣒⠀⡛⢀⣛⠃⢛⡓⣛⣃⠐⢒⣀⡛⣛⡋⠑⣛⣒⣁⡀⢀⡀⢀⡀⠠⢀⡀⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⡀⠀⠘⠟⠿⠇⠀⠇⠸⢿⠟⠿⠿⠻⠇⠐⠂⠀⠸⠻⠃⢻⡿⡅⠳⡀⢘⠀⢻⡿⠘⠛⠿⠟⠻⠛⠀⠛⠀⠟⠿⠟⠣⠟⠋⠟⢈⠻⠛⠟⠟⠶⠶⠾⢛⠱⠹⢯⠭⠵⠶⠾⠻⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⠄⠄⠒⠲⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⠖⠶⠂⠐⠂⠀⢐⠲⠴⠶⠲⠤⠒⠒⠒⠒⠒⠚⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠐⠒⢂⠒⠒⠒⡒⠖⡲⠖⠶⠲⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀ ⠧⠿⠿⠷⠿⠒⠖⠶⠲⠶⠆⠸⠆⠆⠺⠿⠇⠹⠿⠳⠆⠰⠾⠿⠾⠾⠀⠸⠙⠶⠾⠷⠿⠿⡿⠿⠿⠀⠿⠿⠷⠈⠿⠿⠚⠷⠆⠸⠿⠷⠲⠗⠸⠋⠇⠇⠇⠄⠸⠶⠗⠺⠗⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⠀⠒⠓⠈⠈⠁⠐⠋⠀⠀⠐⠂⠀⠀⠀⠀⠐⠒⠂⠀⠀⠠⠈⠀⠐⠒⠒⠒⠂⠰⠂⠀⠀⠀⠀⠂⠀⠀⠘⠒⠒⠇⠑⠓⠀⠀⠒⠐⠀⠀⠀⠐⠛⠃⠘⠃⠀⠐⠒⠒⠚⠘⠒⠚⠂⠀⠐⠂⠀⠀⠀⠐⠀⠀⠀⠀⠀ ⠧⠷⠷⠷⠷⠶⠷⠦⠶⠿⠇⠰⢶⡇⠶⢾⠇⠴⠾⠶⠆⠰⠶⠶⠸⠶⠶⠰⠀⢾⢶⣺⣶⠶⢻⠶⣿⡻⡷⡶⠀⣶⣶⠶⠶⠦⠠⣶⠆⠗⡖⠶⠶⠆⠰⣶⡆⠠⢶⣷⠶⠦⢲⢶⢶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠶⠷⠧⠮⠿⠇⠰⢷⡗⡶⣿⡆⢴⡾⠶⠇⠰⠶⠾⠼⠶⠶⠰⠀⡿⢲⣶⢴⣶⣶⣶⣶⠀⣶⣦⣶⣶⠀⣦⠔⣆⡀⢤⣶⣶⣶⣦⡇⠐⣦⢖⡖⠀⢰⣶⠆⠠⢶⣶⣦⡤⢶⣴⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠯⠿⠿⠶⠶⠶⠷⠷⠺⠿⠇⠰⢷⡆⡮⣷⡆⠴⣶⡾⠇⠰⠶⠾⠼⠶⠶⠰⠀⢶⢲⣶⢴⣶⣶⣶⠶⠀⡶⣶⣶⣶⡶⠀⣦⣵⣦⣶⠗⠐⡆⠠⣾⡆⠐⡆⢰⣶⡆⠰⢶⣶⣶⡦⢶⣴⣶⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠚⠟⠷⠺⠿⠇⠠⢷⡆⡴⣾⡇⢰⣶⡾⠇⠰⠶⠾⠸⠶⠶⠢⠀⣶⣶⣤⣤⣶⣴⣤⣤⠀⣴⣤⣤⣦⣶⣤⢀⡴⣶⣤⣤⢤⣤⣶⡆⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠿⠚⠟⠷⠺⠿⠇⠠⣶⡆⠻⢷⡆⢰⣶⠼⠇⠰⠶⠾⠼⠾⠶⠚⠀⢶⣦⣴⢴⣴⣤⣶⣭⣦⠀⣆⣦⣤⣖⠀⣤⣶⣦⣤⣤⣦⢶⡆⠠⣦⡄⢰⣦⣤⣴⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠿⠚⠟⠷⠺⠿⠇⠀⢾⡇⡭⣷⣄⢰⣶⠿⠇⣼⣬⢬⣬⣤⢠⠀⣤⣤⣽⣤⣤⠀⣭⣦⣤⣯⣤⣤⠀⣤⣤⡤⣖⣶⣤⡄⢠⣤⣤⣤⣆⡄⠀⣦⣶⣼⣴⣬⢥⣤⣴⣤⣤⣴⡀⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀ ⡇⣟⡟⡟⡛⠚⡟⡗⠻⣟⡇⠈⣿⡇⠀⣶⣄⢠⣶⠞⠃⣤⣤⣤⣤⣤⢄⠀⣶⣦⣤⣫⢰⣭⠀⣤⣤⠀⣤⣤⣭⣶⠀⣶⣤⣤⣧⠀⢃⣤⣦⣤⣤⣴⣤⣶⡜⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⡟⡟⡟⡟⠛⡟⡗⢻⣟⡇⠘⣷⡆⡒⡲⠄⢸⣶⣽⡃⠐⠲⠒⢂⠲⠲⠐⠀⣴⣤⣤⢰⣴⡤⣼⣤⣤⠀⣤⣦⣤⣆⠁⣤⣶⣦⣬⣤⣤⣦⡆⠀⣦⡄⢠⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⡛⣛⡛⠛⡛⡛⢛⣛⡃⠘⣣⡆⣛⣩⣅⢠⣴⣞⡃⠘⠛⢛⢘⠛⠛⠘⠀⣤⣬⣥⢠⣴⣍⣤⣤⣭⡀⣬⣦⣥⣤⠀⣠⣦⣥⣥⣤⣥⣧⡇⠀⣥⡄⢨⣤⣬⣥⣭⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣓⣛⣛⣛⡛⢛⡛⣓⢛⣛⡃⢐⣫⡇⣥⡷⡇⢬⣭⣿⡃⠘⠛⢛⢚⠛⠛⠙⠀⣲⣼⣦⣼⣴⣿⣶⣶⣻⠀⣴⣤⡂⣤⡬⣤⣄⣥⠩⣤⣅⣤⡄⢀⣥⣧⣤⣄⣬⣤⣯⡇⢠⣠⡀⣠⣤⣤⣤⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⡟⢙⣋⡛⢙⣛⡃⢈⣣⣅⢨⣭⡅⢠⣭⣗⡃⠘⠛⢋⢚⠛⠛⠘⠀⢨⢽⣭⡭⡭⣭⣿⣥⢭⠇⣤⣭⣥⣭⣥⣍⣭⠁⣤⣭⣉⣥⣽⡖⢈⣭⣭⣭⣌⣭⣭⣥⡌⠈⡃⠈⠉⠉⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⣛⢙⣋⡛⢙⣻⡃⢘⣣⡕⣨⣭⠅⢠⣥⣝⡃⢘⢛⢙⢘⢛⢛⢑⠀⢺⣽⣭⡩⡭⣭⣭⣭⣭⢂⣭⣉⣉⣍⡭⣉⣉⣴⢉⣥⣅⣉⡍⢁⣈⣌⣉⣉⣍⣩⣭⡏⢡⣀⡀⢀⣙⣂⣠⣀⡁⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⣛⢉⣋⡛⢙⣻⡃⢐⣣⡅⢨⣭⡄⢘⣻⣟⡃⢘⠛⢛⢚⢛⢛⢉⠀⣸⢭⣅⡭⡭⣭⣭⣭⢨⠀⣭⣭⣁⣩⣅⣉⣍⢉⣤⣉⣉⣅⣁⣈⠈⣉⣍⣉⣈⣉⣨⣥⡌⠁⠁⠙⠉⠹⠉⠹⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣻⣛⣛⣛⣉⣋⡟⣙⣛⡃⢀⣳⡅⣨⣭⡅⣨⣿⣛⡃⣘⣛⣛⣚⣛⣛⠈⣤⣌⣩⣉⣙⠋⣋⣛⣩⣌⣀⣩⠉⣉⣍⣩⣍⠉⣬⣉⣍⡁⡟⢉⣁⣈⣈⣉⣉⡉⢈⣉⡉⢀⣄⣀⣠⣀⣀⡀⢀⠀⢀⣠⣀⣀⣀⣀⣠⣄ ⠃⠛⠋⠋⠋⠉⠋⠋⠙⠋⠃⠀⠃⠁⠉⠉⠁⠈⠉⠉⠁⠉⠉⠈⠉⠉⠈⠀⠉⠉⠉⠛⠉⠀⠉⠉⠉⠉⠉⠉⠀⠉⠉⠉⠉⠀⠉⠉⠉⠃⠁⠈⠉⠈⠈⠉⠈⠁⠈⠉⠁⠈⠉⠉⠉⠉⠉⠀⠀⠀⠉⠉⠉⠉⠁⠉⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣄⡀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⣁⢉⣍⣉⡉⣉⣉⡉⠉⡉⢉⣍⣉⣉⣉⣉⡉⢉⡉⢉⣉⠉⡉⠉⠉⠉⣉⠉⢩⠉⣉⣍⢉⣭⣭⢉⣉⣍⡍⣉⠉⢉⣉⣉⣉⡉⢉⣍⣉⡉⡍⡉⡉⢉⣉⣉⢩⣉⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉ ⠁⠈⠛⠋⠉⠋⠛⠃⠀⠃⠘⠋⠛⠋⠛⠛⠃⠈⠡⠀⠀⢀⠀⠀⠐⠀⠀⠀⢀⡀⠉⠋⠈⠛⠛⠉⠛⠈⠀⠉⠀⠙⠛⠛⠋⠃⠉⢛⠻⠃⠛⠃⠃⠘⠙⠓⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀ ⠉⠉⠉⠉⠉⠉⡉⠉⠉⡉⢉⣉⠉⠉⠉⢉⡉⢉⣉⠀⠀⢈⡉⣉⣉⡉⠉⠉⢉⠉⡍⣉⣍⣉⣉⣉⣉⣉⠉⣁⠉⣉⣉⣉⢉⣭⡉⣉⣉⣉⣉⡍⢉⣉⣩⣉⠉⣍⣩⡉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⠉⠉⠉⠉⠉⠉ ⣀⠀⠀⠀⠀⡛⣛⡃⠀⡃⢘⣛⣙⣛⢛⣛⡃⢘⡁⠀⢀⣘⡁⠙⣛⡋⢙⠀⡲⠀⣝⣈⢁⣛⣋⢈⣝⣋⠁⣋⠀⣛⣛⢷⢈⣛⣛⣋⣝⣛⣛⣋⡙⣛⡛⢙⡚⢑⣛⡋⢙⣛⣛⣛⣛⣛⣚⣛⣛⣛⣛⣟⠀⠀⠀⠀⠀⠀ ⠃⠀⠀⠀⠘⠛⡛⠋⠀⡋⢙⡙⠏⠉⠈⠛⣋⠉⠉⠀⠐⢊⠳⣙⣛⡫⠷⠨⠁⠀⢛⣛⠰⣞⣙⠐⣛⣛⠀⣛⠀⣛⡋⢀⣈⡝⠋⣛⣛⣛⣛⣛⣛⣛⡋⢙⡙⢙⣛⣋⣙⣛⣛⢛⣛⣿⣚⣛⡛⠋⠛⠛⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⡟⡣⠀⣛⢘⡛⠁⠀⠀⠀⡁⠀⠂⠀⠀⣘⡂⢛⣛⡛⠛⠀⢘⠀⣙⣙⠐⣞⢳⠖⠂⣄⠀⠿⢁⣒⡐⠀⢓⣒⣒⣋⡉⠈⣄⣛⡛⢻⣋⣉⣁⡙⢛⣟⡙⢛⣛⣟⠟⣙⣙⣛⢂⢀⣀⣀⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣛⡻⡃⠀⡛⢘⡛⠙⠛⠛⠻⡃⢐⠀⠀⢚⣛⡃⢛⣛⠛⠛⠀⠘⠀⡛⣛⠘⣛⣊⡝⣛⣚⣄⠛⠀⣖⠒⡒⠚⠛⠛⠒⡷⠐⣚⣛⣛⣑⣒⡟⠚⠓⠚⠛⠏⠛⠛⠟⠛⠛⢟⠛⠛⠛⠚⠛⠻⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⡛⠃⠀⡚⢘⡛⠿⠛⠛⠛⡃⢘⠃⠀⢘⢛⠁⢛⣛⠛⠛⠀⢘⠀⢛⣛⠘⠛⣛⠙⢒⣒⠀⡛⢀⣛⠃⢛⡓⣛⣃⠐⢒⣀⡛⣛⡋⠑⣛⣒⣁⡀⢀⣀⣀⡀⠠⢀⡀⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⡀⠀⠘⠟⠿⠇⠀⠇⠸⢿⠟⠿⠿⠻⠇⠐⠂⠀⠸⠻⠃⢻⡿⡅⠳⡀⢘⠀⢻⡿⠘⠛⠿⠟⠻⠛⠀⠛⠀⠟⠿⠟⠣⠟⠋⠟⢈⠻⠛⠟⠟⠶⠶⠾⢛⠱⠹⢯⠭⠵⠶⠾⠻⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⠄⠄⠒⠲⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⠖⠶⠂⠐⠂⠀⢐⠲⠴⠶⠲⠤⠒⠒⠒⠒⠒⠚⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠐⠒⢂⠒⠒⠒⡒⠖⠲⠖⠶⠲⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀ ⠧⠿⠿⠷⠿⠒⠖⠶⠲⠶⠆⠸⠆⠆⠺⠿⠇⠹⠿⠳⠆⠰⠾⠿⠾⠾⠀⠸⠙⠶⠾⠷⠿⠿⡿⠿⠿⠀⠿⠿⠷⠈⠿⠿⠚⠷⠆⠸⠿⠷⠲⠗⠸⠋⠇⠇⠇⠄⠸⠶⠗⠺⠗⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⠀⠒⠓⠈⠈⠁⠐⠋⠀⠀⠐⠂⠀⠀⠀⠀⠐⠒⠂⠀⠀⠠⠈⠀⠐⠒⠒⠒⠂⠰⠂⠀⠀⠀⠀⠂⠀⠀⠘⠒⠒⠇⠑⠓⠀⠀⠒⠐⠀⠀⠀⠐⠛⠃⠘⠃⠀⠐⠒⠒⠚⠘⠒⠚⠂⠀⠐⠂⠀⠀⠀⠐⠀⠀⠀⠀⠀ ⠧⠷⠷⠷⠷⠶⠷⠦⠶⠿⠇⠰⢶⡇⠶⢾⠇⠴⠾⠶⠆⠰⠶⠶⠸⠶⠶⠰⠀⢾⢶⣺⣶⠶⢻⠶⣿⡻⡷⡶⠀⣶⣶⠶⠶⠦⠠⣶⠆⠗⡖⠶⠶⠆⠰⣶⡆⠠⢶⣷⠶⠦⢲⢶⢶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠶⠷⠧⠮⠿⠇⠰⢷⡗⡶⣿⡆⢴⡾⠶⠇⠰⠶⠾⠼⠶⠶⠰⠀⡿⢲⣶⢴⣶⣶⣶⣶⠀⣶⣦⣶⣶⠀⣦⠔⣆⡀⢤⣶⣶⣶⣦⡇⠐⣦⢖⡖⠀⢰⣶⠆⠠⢶⣶⣦⡤⢶⣴⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠯⠿⠿⠶⠶⠶⠷⠷⠺⠿⠇⠰⢷⡆⡮⣷⡆⠴⣶⡾⠇⠰⠶⠾⠼⠶⠶⠰⠀⢶⢲⣶⢴⣶⣶⣶⠶⠀⡶⣶⣶⣶⡶⠀⣦⣵⣦⣶⠗⠐⡆⠠⣾⡆⠐⡆⢰⣶⡆⠰⢶⣶⣶⡦⢶⣴⣶⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠚⠟⠷⠺⠿⠇⠠⢷⡆⡴⣾⡇⢰⣶⡾⠇⠰⠶⠾⠸⠶⠶⠢⠀⣶⣶⣤⣤⣶⣴⣤⣤⠀⣴⣤⣤⣦⣶⣤⢀⡴⣶⣤⣤⢤⣤⣶⡆⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠿⠚⠟⠷⠺⠿⠇⠠⣶⡆⠻⢷⡆⢰⣶⠼⠇⠰⠶⠾⠼⠾⠶⠚⠀⢶⣦⣴⢴⣴⣤⣶⣭⣦⠀⣆⣦⣤⣖⠀⣤⣶⣦⣤⣤⣦⢶⡆⠠⣦⡄⢰⣦⣤⣴⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠿⠚⠟⠷⠺⠿⠇⠀⢾⡇⡭⣷⣄⢰⣶⠿⠇⣼⣬⢬⣬⣤⢠⠀⣤⣤⣽⣤⣤⠀⣭⣦⣤⣯⣤⣤⠀⣤⣤⡤⣖⣶⣤⡄⢠⣤⣤⣤⣆⡄⠀⣦⣶⣼⣴⣬⢥⣤⣴⣤⣤⣴⡀⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀ ⡇⣟⡟⡟⡛⠚⡟⡗⠻⣟⡇⠈⣿⡇⠀⣶⣄⢠⣶⠞⠃⣤⣤⣤⣤⣤⢄⠀⣶⣦⣤⣫⢰⣭⠀⣤⣤⠀⣤⣤⣭⣶⠀⣶⣤⣤⣧⠀⢃⣤⣦⣤⣤⣴⣤⣶⡜⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⡟⡟⡟⡟⠛⡟⡗⢻⣟⡇⠘⣷⡆⡒⡲⠄⢸⣶⣽⡃⠐⠲⠒⢂⠲⠲⠐⠀⣴⣤⣤⢰⣴⡤⣼⣤⣤⠀⣤⣦⣤⣆⠁⣤⣶⣦⣬⣤⣤⣦⡆⠀⣦⡄⢠⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⡛⣛⡛⠛⡛⡛⢛⣛⡃⠘⣣⡆⣛⣩⣅⢠⣴⣞⡃⠘⠛⢛⢘⠛⠛⠘⠀⣤⣬⣥⢠⣴⣍⣤⣤⣭⡀⣬⣦⣥⣤⠀⣠⣦⣥⣥⣤⣥⣧⡇⠀⣥⡄⢨⣤⣬⣥⣭⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣓⣛⣛⣛⡛⢛⡛⣓⢛⣛⡃⢐⣫⡇⣥⡷⡇⢬⣭⣿⡃⠘⠛⢛⢚⠛⠛⠙⠀⣲⣼⣦⣼⣴⣿⣶⣶⣻⠀⣴⣤⡂⣤⡬⣤⣄⣥⠩⣤⣅⣤⡄⢀⣥⣧⣤⣄⣬⣤⣯⡇⢠⣠⡀⣠⣤⣤⣤⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⡟⢙⣋⡛⢙⣛⡃⢈⣣⣅⢨⣭⡅⢠⣭⣗⡃⠘⠛⢋⢚⠛⠛⠘⠀⢨⢽⣭⡭⡭⣭⣿⣥⢭⠇⣤⣭⣥⣭⣥⣍⣭⠁⣤⣭⣉⣥⣽⡖⢈⣭⣭⣭⣌⣭⣭⣥⡌⠈⡃⠈⠉⠉⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⣛⢙⣋⡛⢙⣻⡃⢘⣣⡕⣨⣭⠅⢠⣥⣝⡃⢘⢛⢙⢘⢛⢛⢑⠀⢺⣽⣭⡩⡭⣭⣭⣭⣭⢂⣭⣉⣉⣍⡭⣉⣉⣴⢉⣥⣅⣉⡍⢁⣈⣌⣉⣉⣍⣩⣭⡏⢡⣀⡀⢀⣙⣂⣠⣀⡁⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⣛⢉⣋⡛⢙⣻⡃⢐⣣⡅⢨⣭⡄⢘⣻⣟⡃⢘⠛⢛⢚⢛⢛⢉⠀⣸⢭⣅⡭⡭⣭⣭⣭⢨⠀⣭⣭⣁⣩⣅⣉⣍⢉⣤⣉⣉⣅⣁⣈⠈⣉⣍⣉⣈⣉⣨⣥⡌⠁⠁⠙⠉⠹⠉⠹⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣻⣛⣛⣛⣉⣋⡟⣙⣛⡃⢀⣳⡅⣨⣭⡅⣨⣿⣛⡃⣘⣛⣛⣚⣛⣛⠈⣤⣌⣩⣉⣙⠋⣋⣛⣩⣌⣀⣩⠉⣉⣍⣩⣍⠉⣬⣉⣍⡁⡟⢉⣁⣈⣈⣉⣉⡉⢈⣉⡉⢀⣄⣀⣠⣀⣀⡀⢀⠀⢀⣠⣀⣀⣀⣀⣠⣄ ⠃⠛⠋⠋⠋⠉⠋⠋⠙⠋⠃⠀⠃⠁⠉⠉⠁⠈⠉⠉⠁⠉⠉⠈⠉⠉⠈⠀⠉⠉⠉⠛⠉⠀⠉⠉⠉⠉⠉⠉⠀⠉⠉⠉⠉⠀⠉⠉⠉⠃⠁⠈⠉⠈⠈⠉⠈⠁⠈⠉⠁⠈⠉⠉⠉⠉⠉⠀⠀⠀⠉⠉⠉⠉⠁⠉⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣄⡀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⣁⢉⣍⣉⡉⣉⣉⡉⠉⡉⢉⣍⣉⣉⣉⣉⡉⢉⡉⢉⣉⠉⡉⠉⠉⠉⣉⠉⢩⠉⣉⣍⢉⣭⣭⢉⣉⣍⡍⣉⠉⢉⣉⣉⣉⡉⢉⣍⣉⡉⡍⡉⡉⢉⣉⣉⢩⣉⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉ ⠁⠈⠛⠋⠉⠋⠛⠃⠀⠃⠘⠋⠛⠋⠛⠛⠃⠈⠡⠀⠀⢀⠀⠀⠐⠀⠀⠀⢀⡀⠉⠋⠈⠛⠛⠉⠛⠈⠀⠉⠀⠙⠛⠛⠋⠃⠉⢛⠻⠃⠛⠃⠃⠘⠙⠓⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀ ⠉⠉⠉⠉⠉⠉⡉⠉⠉⡉⢉⣉⠉⠉⠉⢉⡉⢉⣉⠀⠀⢈⡉⣉⣉⡉⠉⠉⢉⠉⡍⣉⣍⣉⣉⣉⣉⣉⠉⣁⠉⣉⣉⣉⢉⣭⡉⣉⣉⣉⣉⡍⢉⣉⣩⣉⠉⣍⣩⡉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⠉⠉⠉⠉⠉⠉ ⣀⠀⠀⠀⠀⡛⣛⡃⠀⡃⢘⣛⣙⣛⢛⣛⡃⢘⡁⠀⢀⣘⡁⠙⣛⡋⢙⠀⡲⠀⣝⣈⢁⣛⣋⢈⣝⣋⠁⣋⠀⣛⣛⢷⢈⣛⣛⣋⣝⣛⣛⣋⡙⣛⡛⢙⡚⢑⣛⡋⢙⣛⣛⣛⣛⣛⣚⣛⣛⣛⣛⣟⠀⠀⠀⠀⠀⠀ ⠃⠀⠀⠀⠘⠛⡛⠋⠀⡋⢙⡙⠏⠉⠈⠛⣋⠉⠉⠀⠐⢊⠳⣙⣛⡫⠷⠨⠁⠀⢛⣛⠰⣞⣙⠐⣛⣛⠀⣛⠀⣛⡋⢀⣈⡝⠋⣛⣛⣛⣛⣛⣛⣛⡋⢙⡙⢙⣛⣋⣙⣛⣛⢛⣛⣿⣚⣛⡛⠋⠛⠛⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⡟⡣⠀⣛⢘⡛⠁⠀⠀⠀⡁⠀⠂⠀⠀⣘⡂⢛⣛⡛⠛⠀⢘⠀⣙⣙⠐⣞⢳⠖⠂⣄⠀⠿⢁⣒⡐⠀⢓⣒⣒⣋⡉⠈⣄⣛⡛⢻⣋⣉⣁⡙⢛⣟⡙⢛⣛⣟⠟⣙⣙⣛⢂⢀⣀⣀⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣛⡻⡃⠀⡛⢘⡛⠙⠛⠛⠻⡃⢐⠀⠀⢚⣛⡃⢛⣛⠛⠛⠀⠘⠀⡛⣛⠘⣛⣊⡝⣛⣚⣄⠛⠀⣖⠒⡚⠚⠛⠛⠒⡷⠐⣚⣛⣛⣑⣒⡟⠚⠓⠚⠛⠏⠛⠛⠟⠛⠛⢟⠛⠛⠛⠚⠛⠻⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⡛⠃⠀⡚⢘⡛⠿⠛⠛⠛⡃⢘⠃⠀⢘⢛⠁⢛⣛⠛⠛⠀⢘⠀⢛⣛⠘⠛⣛⠙⢒⣒⠀⡛⢀⣛⠃⢛⡓⣛⣃⠐⢒⣀⡛⣛⡋⠑⣛⣒⣁⡀⢀⣀⣀⡀⠠⢀⡀⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⡀⠀⠘⠟⠿⠇⠀⠇⠸⢿⠟⠿⠿⠻⠇⠐⠂⠀⠸⠻⠃⢻⡿⡅⠳⡀⢘⠀⢻⡿⠘⠛⠿⠟⠻⠛⠀⠛⠀⠟⠿⠟⠣⠟⠋⠟⢈⠻⠛⠟⠟⠶⠶⠾⢛⠱⠹⢯⠭⠵⠶⠾⠻⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⠄⠄⠒⠲⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⠖⠶⠂⠐⠂⠀⢐⠲⠴⠶⠲⠤⠒⠒⠒⠒⠒⠚⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠐⠒⢂⠒⠒⠒⡒⠖⠲⠖⠶⠲⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀ ⠧⠿⠿⠷⠿⠒⠖⠶⠲⠶⠆⠸⠆⠆⠺⠿⠇⠹⠿⠳⠆⠰⠾⠿⠾⠾⠀⠸⠙⠶⠾⠷⠿⠿⡿⠿⠿⠀⠿⠿⠷⠈⠿⠿⠚⠷⠆⠸⠿⠷⠲⠗⠸⠋⠇⠇⠇⠄⠸⠶⠗⠺⠗⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⠀⠒⠓⠈⠈⠁⠐⠋⠀⠀⠐⠂⠀⠀⠀⠀⠐⠒⠂⠀⠀⠠⠈⠀⠐⠒⠒⠒⠂⠰⠂⠀⠀⠀⠀⠂⠀⠀⠘⠒⠒⠇⠑⠓⠀⠀⠒⠐⠀⠀⠀⠐⠛⠃⠘⠃⠀⠐⠒⠒⠚⠘⠒⠚⠂⠀⠐⠂⠀⠀⠀⠐⠀⠀⠀⠀⠀ ⠧⠷⠷⠷⠷⠶⠷⠦⠶⠿⠇⠰⢶⡇⠶⢾⠇⠴⠾⠶⠆⠰⠶⠶⠸⠶⠶⠰⠀⢾⢶⣺⣶⠶⢻⠶⣿⡻⡷⡶⠀⣶⣶⠶⠶⠦⠠⣶⠆⠗⡖⠶⠶⠆⠰⣶⡆⠠⢶⣷⠶⠦⢲⢶⢶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠶⠷⠧⠮⠿⠇⠰⢷⡗⡶⣿⡆⢴⡾⠶⠇⠰⠶⠾⠼⠶⠶⠰⠀⡿⢲⣶⢴⣶⣶⣶⣶⠀⣶⣦⣶⣶⠀⣦⠔⣆⡀⢤⣶⣶⣶⣦⡇⠐⣦⢖⡖⠀⢰⣶⠆⠠⢶⣶⣦⡤⢶⣴⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠯⠿⠿⠶⠶⠶⠷⠷⠺⠿⠇⠰⢷⡆⡮⣷⡆⠴⣶⡾⠇⠰⠶⠾⠼⠶⠶⠰⠀⢶⢲⣶⢴⣶⣶⣶⠶⠀⡶⣶⣶⣶⡶⠀⣦⣵⣦⣶⠗⠐⡆⠠⣾⡆⠐⡆⢰⣶⡆⠰⢶⣶⣶⡦⢶⣴⣶⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠚⠟⠷⠺⠿⠇⠠⢷⡆⡴⣾⡇⢰⣶⡾⠇⠰⠶⠾⠸⠶⠶⠢⠀⣶⣶⣤⣤⣶⣴⣤⣤⠀⣴⣤⣤⣦⣶⣤⢀⡴⣶⣤⣤⢤⣤⣶⡆⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠿⠚⠟⠷⠺⠿⠇⠠⣶⡆⠻⢷⡆⢰⣶⠼⠇⠰⠶⠾⠼⠾⠶⠚⠀⢶⣦⣴⢴⣴⣤⣶⣭⣦⠀⣆⣦⣤⣖⠀⣤⣶⣦⣤⣤⣦⢶⡆⠠⣦⡄⢰⣦⣤⣴⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠿⠚⠟⠷⠺⠿⠇⠀⢾⡇⡭⣷⣄⢰⣶⠿⠇⣼⣬⢬⣬⣤⢠⠀⣤⣤⣽⣤⣤⠀⣭⣦⣤⣯⣤⣤⠀⣤⣤⡤⣖⣶⣤⡄⢠⣤⣤⣤⣆⡄⠀⣦⣶⣼⣴⣬⢥⣤⣴⣤⣤⣴⡀⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀ ⡇⣟⡟⡟⡛⠚⡟⡗⠻⣟⡇⠈⣿⡇⠀⣶⣄⢠⣶⠞⠃⣤⣤⣤⣤⣤⢄⠀⣶⣦⣤⣫⢰⣭⠀⣤⣤⠀⣤⣤⣭⣶⠀⣶⣤⣤⣧⠀⢃⣤⣦⣤⣤⣴⣤⣶⡜⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⡟⡟⡟⡟⠛⡟⡗⢻⣟⡇⠘⣷⡆⡒⡲⠄⢸⣶⣽⡃⠐⠲⠒⢂⠲⠲⠐⠀⣴⣤⣤⢰⣴⡤⣼⣤⣤⠀⣤⣦⣤⣆⠁⣤⣶⣦⣬⣤⣤⣦⡆⠀⣦⡄⢠⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⡛⣛⡛⠛⡛⡛⢛⣛⡃⠘⣣⡆⣛⣩⣅⢠⣴⣞⡃⠘⠛⢛⢘⠛⠛⠘⠀⣤⣬⣥⢠⣴⣍⣤⣤⣭⡀⣬⣦⣥⣤⠀⣠⣦⣥⣥⣤⣥⣧⡇⠀⣥⡄⢨⣤⣬⣥⣭⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣓⣛⣛⣛⡛⢛⡛⣓⢛⣛⡃⢐⣫⡇⣥⡷⡇⢬⣭⣿⡃⠘⠛⢛⢚⠛⠛⠙⠀⣲⣼⣦⣼⣴⣿⣶⣶⣻⠀⣴⣤⡂⣤⡬⣤⣄⣥⠩⣤⣅⣤⡄⢀⣥⣧⣤⣄⣬⣤⣯⡇⢠⣠⡀⣠⣤⣤⣤⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⡟⢙⣋⡛⢙⣛⡃⢈⣣⣅⢨⣭⡅⢠⣭⣗⡃⠘⠛⢋⢚⠛⠛⠘⠀⢨⢽⣭⡭⡭⣭⣿⣥⢭⠇⣤⣭⣥⣭⣥⣍⣭⠁⣤⣭⣉⣥⣽⡖⢈⣭⣭⣭⣌⣭⣭⣥⡌⠈⡃⠈⠉⠉⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⣛⢙⣋⡛⢙⣻⡃⢘⣣⡕⣨⣭⠅⢠⣥⣝⡃⢘⢛⢙⢘⢛⢛⢑⠀⢺⣽⣭⡩⡭⣭⣭⣭⣭⢂⣭⣉⣉⣍⡭⣉⣉⣴⢉⣥⣅⣉⡍⢁⣈⣌⣉⣉⣍⣩⣭⡏⢡⣀⡀⢀⣙⣂⣠⣀⡁⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⣛⢉⣋⡛⢙⣻⡃⢐⣣⡅⢨⣭⡄⢘⣻⣟⡃⢘⠛⢛⢚⢛⢛⢉⠀⣸⢭⣅⡭⡭⣭⣭⣭⢨⠀⣭⣭⣁⣩⣅⣉⣍⢉⣤⣉⣉⣅⣁⣈⠈⣉⣍⣉⣈⣉⣨⣥⡌⠁⠁⠙⠉⠹⠉⠹⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣻⣛⣛⣛⣉⣋⡟⣙⣛⡃⢀⣳⡅⣨⣭⡅⣨⣿⣛⡃⣘⣛⣛⣚⣛⣛⠈⣤⣌⣩⣉⣙⠋⣋⣛⣩⣌⣀⣩⠉⣉⣍⣩⣍⠉⣬⣉⣍⡁⡟⢉⣁⣈⣈⣉⣉⡉⢈⣉⡉⢀⣄⣀⣠⣀⣀⡀⢀⠀⢀⣠⣀⣀⣀⣀⣠⣄ ⠃⠛⠋⠋⠋⠉⠋⠋⠙⠋⠃⠀⠃⠁⠉⠉⠁⠈⠉⠉⠁⠉⠉⠈⠉⠉⠈⠀⠉⠉⠉⠛⠉⠀⠉⠉⠉⠉⠉⠉⠀⠉⠉⠉⠉⠀⠉⠉⠉⠃⠁⠈⠉⠈⠈⠉⠈⠁⠈⠉⠁⠈⠉⠉⠉⠉⠉⠀⠀⠀⠉⠉⠉⠉⠁⠉⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣄⡀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⣁⢉⣍⣉⡉⣉⣉⡉⠉⡉⢉⣍⣉⣉⣉⣉⡉⢉⡉⢉⣉⠉⡉⠉⠉⠉⣉⠉⢩⠉⣉⣍⢉⣭⣭⢉⣉⣍⡍⣉⠉⢉⣉⣉⣉⡉⢉⣍⣉⡉⡍⡉⡉⢉⣉⣉⢩⣉⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉ ⠁⠈⠛⠋⠉⠋⠛⠃⠀⠃⠘⠋⠛⠋⠛⠛⠃⠈⠡⠀⠀⢀⠀⠀⠐⠀⠀⠀⢀⡀⠉⠋⠈⠛⠛⠉⠛⠈⠀⠉⠀⠙⠛⠛⠋⠃⠉⢛⠻⠃⠛⠃⠃⠘⠙⠓⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀ ⠉⠉⠉⠉⠉⠉⡉⠉⠉⡉⢉⣉⠉⠉⠉⢉⡉⢉⣉⠀⠀⢈⡉⣉⣉⡉⠉⠉⢉⠉⡍⣉⣍⣉⣉⣉⣉⣉⠉⣁⠉⣉⣉⣉⢉⣭⡉⣉⣉⣉⣉⡍⢉⣉⣩⣉⠉⣍⣩⡉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⠉⠉⠉⠉⠉⠉ ⣀⠀⠀⠀⠀⡛⣛⡃⠀⡃⢘⣛⣙⣛⢛⣛⡃⢘⡁⠀⢀⣘⡁⠙⣛⡋⢙⠀⡲⠀⣝⣈⢁⣛⣋⢈⣝⣋⠁⣋⠀⣛⣛⢷⢈⣛⣛⣋⣝⣛⣛⣋⡙⣛⡛⢙⡚⢑⣛⡋⢙⣛⣛⣛⣛⣛⣚⣛⣛⣛⣛⣟⠀⠀⠀⠀⠀⠀ ⠃⠀⠀⠀⠘⠛⡛⠋⠀⡋⢙⡙⠏⠉⠈⠛⣋⠉⠉⠀⠐⢊⠳⣙⣛⡫⠷⠨⠁⠀⢛⣛⠰⣞⣙⠐⣛⣛⠀⣛⠀⣛⡋⢀⣈⡝⠋⣛⣛⣛⣛⣛⣛⣛⡋⢙⡙⢙⣛⣋⣙⣛⣛⢛⣛⣿⣚⣛⡛⠋⠛⠛⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⡟⡣⠀⣛⢘⡛⠁⠀⠀⠀⡁⠀⠂⠀⠀⣘⡂⢛⣛⡛⠛⠀⢘⠀⣙⣙⠐⣞⢳⠖⠂⣄⠀⠿⢁⣒⡐⠀⢓⣒⣒⣋⡉⠈⣄⣛⡛⢻⣋⣉⣁⡙⢛⣟⡙⢛⣛⣟⠟⣙⣙⣛⢂⢀⣀⣀⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣛⡻⡃⠀⡛⢘⡛⠙⠛⠛⠻⡃⢐⠀⠀⢚⣛⡃⢛⣛⠛⠛⠀⠘⠀⡛⣛⠘⣛⣊⡝⣛⣚⣄⠛⠀⣖⠒⡚⠚⠛⠛⠒⣷⠐⣚⣛⣛⣑⣒⡟⠚⠓⠚⠛⠏⠛⠛⠟⠛⠛⢟⠛⠛⠛⠚⠛⠻⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⡛⠃⠀⡚⢘⡛⠿⠛⠛⠛⡃⢘⠃⠀⢘⢛⠁⢛⣛⠛⠛⠀⢘⠀⢛⣛⠘⠛⣛⠙⢒⣒⠀⡛⢀⣛⠃⢛⡓⣛⣃⠘⢒⣀⡛⣛⡋⠑⣛⣒⣁⡀⢀⣀⣀⡀⠠⢀⡀⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⡀⠀⠘⠟⠿⠇⠀⠇⠸⢿⠟⠿⠿⠻⠇⠐⠂⠀⠸⠻⠃⢻⡿⡅⠳⡀⢘⠀⢻⡿⠘⠛⠿⠟⠻⠛⠀⠛⠀⠟⠿⠟⠣⠟⠋⠟⢈⠻⠛⠟⠟⠶⠶⠾⢛⠱⠹⢯⠭⠵⠶⠾⠻⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⠄⠄⠒⠲⠖⠒⠒⢒⠒⠒⠒⠒⠒⠒⠲⠖⠶⠂⠐⠂⠀⢐⠲⠴⠶⠲⠤⠒⠒⠒⠒⠒⠚⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⡐⠒⢂⠒⠒⠒⡒⠖⠲⠖⠶⠲⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀ ⠧⠿⠿⠷⠿⠒⠖⠶⠲⠶⠆⠸⠆⠆⠺⠿⠇⠹⠿⠳⠆⠰⠾⠿⠾⠾⠀⠸⠙⠶⠾⠷⠿⠿⡿⠿⠿⠀⠿⠿⠷⠈⠿⠿⠚⠷⠆⠸⠿⠷⠲⠗⠸⠋⠇⠇⠇⠄⠸⠶⠗⠺⠗⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⠀⠒⠓⠈⠈⠁⠐⠋⠀⠀⠐⠂⠀⠀⠀⠀⠐⠒⠂⠀⠀⠠⠈⠀⠐⠒⠒⠒⠂⠰⠂⠀⠀⠀⠀⠂⠀⠀⠘⠒⠒⠇⠑⠓⠀⠀⠒⠐⠀⠀⠀⠐⠛⠃⠘⠃⠀⠐⠒⠒⠚⠘⠒⠚⠂⠀⠐⠂⠀⠀⠀⠐⠀⠀⠀⠀⠀ ⠧⠷⠷⠷⠷⠶⠷⠦⠶⠿⠇⠰⢶⡇⠶⢾⠇⠴⠾⠶⠆⠰⠶⠶⠸⠶⠶⠰⠀⢾⢶⣺⣶⠶⢻⠶⣿⡻⡷⡶⠀⣶⣶⠶⠶⠦⠠⣶⠆⠗⡖⠶⠶⠆⠰⣶⡆⠠⢶⣷⠶⠦⢲⢶⢶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠶⠷⠧⠮⠿⠇⠰⢷⡗⡶⣿⡆⢴⡾⠶⠇⠰⠶⠾⠼⠶⠶⠰⠀⡿⢲⣶⢴⣶⣶⣶⣶⠀⣶⣦⣶⣶⠀⣦⠔⣆⡀⢤⣶⣶⣶⣦⡇⠐⣦⢖⡖⠀⢰⣶⠆⠠⢶⣶⣦⡤⢶⣴⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠯⠿⠿⠶⠶⠶⠷⠷⠺⠿⠇⠰⢷⡆⡮⣷⡆⠴⣶⡾⠇⠰⠶⠾⠼⠶⠶⠰⠀⢶⢲⣶⢴⣶⣶⣶⠶⠀⡶⣶⣶⣶⡶⠀⣦⣵⣦⣶⠗⠐⡆⠠⣾⡆⠐⡆⢰⣶⡆⠰⢶⣶⣶⡦⢶⣴⣶⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠚⠟⠷⠺⠿⠇⠠⢷⡆⡴⣾⡇⢰⣶⡾⠇⠰⠶⠾⠸⠶⠶⠢⠀⣶⣶⣤⣤⣶⣴⣤⣤⠀⣴⣤⣤⣦⣶⣤⢀⡴⣶⣤⣤⢤⣤⣶⡆⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠿⠚⠟⠷⠺⠿⠇⠠⣶⡆⠻⢷⡆⢰⣶⠼⠇⠰⠶⠾⠼⠾⠶⠚⠀⢶⣦⣴⢴⣴⣤⣶⣭⣦⠀⣆⣦⣤⣖⠀⣤⣶⣦⣤⣤⣦⢶⡆⠠⣦⡄⢰⣦⣤⣴⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠿⠚⠟⠷⠺⠿⠇⠀⢾⡇⡭⣷⣄⢰⣶⠿⠇⣼⣬⢬⣬⣤⢠⠀⣤⣤⣽⣤⣤⠀⣭⣦⣤⣯⣤⣤⠀⣤⣤⡤⣖⣶⣤⡄⢠⣤⣤⣤⣆⡄⠀⣦⣶⣼⣴⣬⢥⣤⣴⣤⣤⣴⡀⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀ ⡇⣟⡟⡟⡛⠚⡟⡗⠻⣟⡇⠈⣿⡇⠀⣶⣄⢠⣶⠞⠃⣤⣤⣤⣤⣤⢄⠀⣶⣦⣤⣫⢰⣭⠀⣤⣤⠀⣤⣤⣭⣶⠀⣶⣤⣤⣧⠀⢃⣤⣦⣤⣤⣴⣤⣶⡜⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⡟⡟⡟⡟⠛⡟⡗⢻⣟⡇⠘⣷⡆⡒⡲⠄⢸⣶⣽⡃⠐⠲⠒⢂⠲⠲⠐⠀⣴⣤⣤⢰⣴⡤⣼⣤⣤⠀⣤⣦⣤⣆⠁⣤⣶⣦⣬⣤⣤⣦⡆⠀⣦⡄⢠⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⡛⣛⡛⠛⡛⡛⢛⣛⡃⠘⣣⡆⣛⣩⣅⢠⣴⣞⡃⠘⠛⢛⢘⠛⠛⠘⠀⣤⣬⣥⢠⣴⣍⣤⣤⣭⡀⣬⣦⣥⣤⠀⣠⣦⣥⣥⣤⣥⣧⡇⠀⣥⡄⢨⣤⣬⣥⣭⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣓⣛⣛⣛⡛⢛⡛⣓⢛⣛⡃⢐⣫⡇⣥⡷⡇⢬⣭⣿⡃⠘⠛⢛⢚⠛⠛⠙⠀⣲⣼⣦⣼⣴⣿⣶⣶⣻⠀⣴⣤⡂⣤⡬⣤⣄⣥⠩⣤⣅⣤⡄⢀⣥⣧⣤⣄⣬⣤⣯⡇⢠⣠⡀⣠⣤⣤⣤⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⡟⢙⣋⡛⢙⣛⡃⢈⣣⣅⢨⣭⡅⢠⣭⣗⡃⠘⠛⢋⢚⠛⠛⠘⠀⢨⢽⣭⡭⡭⣭⣿⣥⢭⠇⣤⣭⣥⣭⣥⣍⣭⠁⣤⣭⣉⣥⣽⡖⢈⣭⣭⣭⣌⣭⣭⣥⡌⠈⡃⠈⠉⠉⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⣛⢙⣋⡛⢙⣻⡃⢘⣣⡕⣨⣭⠅⢠⣥⣝⡃⢘⢛⢙⢘⢛⢛⢑⠀⢺⣽⣭⡩⡭⣭⣭⣭⣭⢂⣭⣉⣉⣍⡭⣉⣉⣴⢉⣥⣅⣉⡍⢁⣈⣌⣉⣉⣍⣩⣭⡏⢡⣀⡀⢀⣙⣂⣠⣀⡁⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⣛⢉⣋⡛⢙⣻⡃⢐⣣⡅⢨⣭⡄⢘⣻⣟⡃⢘⠛⢛⢚⢛⢛⢉⠀⣸⢭⣅⡭⡭⣭⣭⣭⢨⠀⣭⣭⣁⣩⣅⣉⣍⢉⣤⣉⣉⣅⣁⣈⠈⣉⣍⣉⣈⣉⣨⣥⡌⠁⠁⠙⠉⠹⠉⠹⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣻⣛⣛⣛⣉⣋⡟⣙⣛⡃⢀⣳⡅⣨⣭⡅⣨⣿⣛⡃⣘⣛⣛⣚⣛⣛⠈⣤⣌⣩⣉⣙⠋⣋⣛⣩⣌⣀⣩⠉⣉⣍⣩⣍⠉⣬⣉⣍⡁⡟⢉⣁⣈⣈⣉⣉⡉⢈⣉⡉⢀⣄⣀⣠⣀⣀⡀⢀⠀⢀⣠⣀⣀⣀⣀⣠⣄ ⠃⠛⠋⠋⠋⠉⠋⠋⠙⠋⠃⠀⠃⠁⠉⠉⠁⠈⠉⠉⠁⠉⠉⠈⠉⠉⠈⠀⠉⠉⠉⠛⠉⠀⠉⠉⠉⠉⠉⠉⠀⠉⠉⠉⠉⠀⠉⠉⠉⠃⠁⠈⠉⠈⠈⠉⠈⠁⠈⠉⠁⠈⠉⠉⠉⠉⠉⠀⠀⠀⠉⠉⠉⠉⠁⠉⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣄⡀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⣁⢉⣍⣉⡉⣉⣉⡉⠉⡉⢉⣍⣉⣉⣉⣉⡉⢉⡉⢉⣉⠉⡉⠉⠉⠉⣉⠉⢩⠉⣉⣍⢉⣭⣭⢉⣉⣍⡍⣉⠉⢉⣉⣉⣉⡉⢉⣍⣉⡉⡍⡉⡉⢉⣉⣉⢩⣉⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉ ⠁⠈⠛⠋⠉⠋⠛⠃⠀⠃⠘⠋⠛⠋⠛⠛⠃⠈⠡⠀⠀⢀⠀⠀⠐⠀⠀⠀⢀⡀⠉⠋⠈⠛⠛⠉⠛⠈⠀⠉⠀⠙⠛⠛⠋⠃⠉⢛⠻⠃⠛⠃⠃⠘⠙⠓⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀ ⠉⠉⠉⠉⠉⠉⡉⠉⠉⡉⢉⣉⠉⠉⠉⢉⡉⢉⣉⠀⠀⢈⡉⣉⣉⡉⠉⠉⢉⠉⡍⣉⣍⣉⣉⣉⣉⣉⠉⣁⠉⣉⣉⣉⢉⣭⡉⣉⣉⣉⣉⡍⢉⣉⣩⣉⠉⣍⣩⡉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⠉⠉⠉⠉⠉⠉ ⣀⠀⠀⠀⠀⡛⣛⡃⠀⡃⢘⣛⣙⣛⢛⣛⡃⢘⡁⠀⢀⣘⡁⠙⣛⡋⢙⠀⡲⠀⣝⣈⢁⣛⣋⢈⣝⣋⠁⣋⠀⣛⣛⢷⢈⣛⣛⣋⣝⣛⣛⣋⡙⣛⡛⢙⡚⢑⣛⡋⢙⣛⣛⣛⣛⣛⣚⣛⣛⣛⣛⣟⠀⠀⠀⠀⠀⠀ ⠃⠀⠀⠀⠘⠛⡛⠋⠀⡋⢙⡙⠏⠉⠈⠛⣋⠉⠉⠀⠐⢊⠳⣙⣛⡫⠷⠨⠁⠀⢛⣛⠰⣞⣙⠐⣛⣛⠀⣛⠀⣛⡋⢀⣈⡝⠋⣛⣛⣛⣛⣛⣛⣛⡋⢙⡙⢙⣛⣋⣙⣛⣛⢛⣛⣿⣚⣛⡛⠋⠛⠛⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⡟⡣⠀⣛⢘⡛⠁⠀⠀⠀⡁⠀⠂⠀⠀⣘⡂⢛⣛⡛⠛⠀⢘⠀⣙⣙⠐⣞⢳⠖⠂⣄⠀⠿⢁⣒⡐⠀⢓⣒⣒⣋⡉⠈⣄⣛⡛⢻⣋⣉⣁⡙⢛⣟⡙⢛⣛⣟⠟⣙⣙⣛⢂⢀⣀⣀⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣛⡻⡃⠀⡛⢘⡛⠙⠛⠛⠻⡃⢐⠀⠀⢚⣛⡃⢛⣛⠛⠛⠀⠘⠀⡛⣛⠘⣛⣊⡝⣛⣚⣄⠛⠀⣖⠒⡚⠚⠛⠛⠒⣷⠐⣚⣛⣛⣑⣒⡟⠚⠓⠚⠛⠏⠛⠛⠟⠛⠛⢟⠛⠛⠛⠚⠛⠻⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⡛⠃⠀⡚⢘⡛⠿⠛⠛⠛⡃⢘⠃⠀⢘⢛⠁⢛⣛⠛⠛⠀⢘⠀⢛⣛⠘⠛⣛⠙⢒⣒⠀⡛⢀⣛⠃⢛⡓⣛⣃⠘⢒⣀⡛⣛⡋⠑⣛⣒⣁⡀⢀⣀⣀⡀⠠⢀⡀⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⡀⠀⠘⠟⠿⠇⠀⠇⠸⢿⠟⠿⠿⠻⠇⠐⠂⠀⠸⠻⠃⢻⡿⡅⠳⡀⢘⠀⢻⡿⠘⠛⠿⠟⠻⠛⠀⢛⠀⢟⠿⠟⠣⠟⠋⠟⢈⠻⠛⠟⠟⠶⠶⠾⢛⠱⠹⢯⠭⠵⠶⠾⠻⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⠄⠄⠒⠲⠖⠒⠒⢒⠒⠒⠒⠒⠒⠒⠲⠖⠶⠂⠐⠂⠀⢐⠲⠴⠶⠲⠤⠒⠒⠒⠒⠒⠚⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⡐⠒⢂⠒⠒⠒⡒⠖⠲⠖⠶⠲⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀ ⠧⠿⠿⠷⠿⠒⠖⠶⠲⠶⠆⠸⠆⠆⠺⠿⠇⠹⠿⠳⠆⠰⠾⠿⠾⠾⠀⠸⠙⠶⠾⠷⠿⠿⡿⠿⠿⠀⠿⠿⠷⠈⠿⠿⠚⠷⠆⠸⠿⠷⠲⠗⠸⠋⠇⠇⠇⠄⠸⠶⠗⠺⠗⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⠀⠒⠓⠈⠈⠁⠐⠋⠀⠀⠐⠂⠀⠀⠀⠀⠐⠒⠂⠀⠀⠠⠈⠀⠐⠒⠒⠒⠂⠰⠂⠀⠀⠀⠀⠂⠀⠀⠘⠒⠒⠇⠑⠓⠀⠀⠒⠐⠀⠀⠀⠐⠛⠃⠘⠃⠀⠐⠒⠒⠚⠘⠒⠚⠂⠀⠐⠂⠀⠀⠀⠐⠀⠀⠀⠀⠀ ⠇⠷⠷⠷⠷⠶⠷⠧⠶⠿⠇⠰⠿⠇⠶⠾⠇⠾⠾⠿⠆⠰⠶⠶⠸⠶⠶⠰⠀⠾⠾⠺⠾⠾⠿⠾⠿⠿⠷⠶⠀⠷⣶⠶⠶⠦⠰⠶⠆⠗⠖⠶⠶⠦⠰⠶⠆⠠⠶⠷⠶⠦⠲⠶⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠶⠷⠧⠾⠿⠇⠰⠯⠇⠶⠿⠇⠺⠿⠿⠇⠰⠶⠾⠼⠶⠶⠲⠀⠿⠸⠶⠶⠶⠷⠶⠾⠀⡶⠶⠶⠶⠀⠧⠖⠇⠄⠰⠶⠶⠶⠶⠇⠰⠧⠲⠇⠄⠰⠶⠆⠠⠲⠷⠶⠶⠲⠾⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠯⠿⠿⠿⠷⠶⠷⠷⠺⠿⠇⠰⠿⠇⠾⠿⠇⠾⠿⠿⠇⠰⠶⠾⠼⠶⠶⠰⠀⠿⠹⠶⠼⠶⠷⠶⠾⠀⠿⠶⠶⠶⠷⠀⠶⠶⠶⠶⠷⠀⠇⠰⠶⠇⠠⠇⠰⠶⠆⠰⠲⠷⠶⠶⠲⠾⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠺⠟⠷⠺⠿⠇⠠⠿⠇⠼⠿⠇⠸⠿⠿⠇⠰⠶⠾⠼⠶⠶⠂⠀⠿⠿⠶⠶⠷⠾⠶⣶⠀⠾⠶⠶⠷⠶⠶⠀⠶⠿⠶⠶⠲⠶⠷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠿⠚⠟⠷⠺⠿⠇⠸⠿⠇⠹⠿⠇⠹⠿⠾⠇⠰⠾⠾⠼⠾⠶⠚⠀⠻⠷⠶⠸⠿⣶⠿⠶⡶⠀⠷⠷⠶⠧⠠⠒⠿⠷⠶⠲⠶⠿⠗⠀⠷⠆⠰⠶⢶⠾⢷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠯⠿⠿⠿⠿⠚⠟⠷⠺⠿⠇⠘⠿⠇⠛⠿⠆⠘⠿⠻⠇⠺⠾⠺⠺⠾⠘⠀⠺⠶⠺⡾⠾⠤⠶⠿⠶⠿⠻⠧⠤⠶⠷⠗⠇⠟⠶⠇⠰⠷⠷⠷⠇⠇⠀⠷⢶⠷⠾⠷⠻⠷⠾⠾⠶⠾⠀⠺⠾⠺⠾⠾⠀⠀⠀⠀⠀⠀ ⡇⡿⡿⡟⡟⠛⡟⡗⠻⣟⡇⠘⠿⡇⠛⠿⠂⠘⢟⠛⠃⠺⠛⠛⠻⠿⠘⠀⠻⠛⠿⠿⠺⢻⠀⠻⠿⠀⠟⠟⡷⠟⠀⠟⠟⠟⠓⠀⠁⠚⡟⡟⠗⠛⠿⠟⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡗⡟⡟⡟⡟⠛⡟⡗⠛⣟⡇⠘⣟⡏⠛⠟⡇⠚⢿⣛⠃⠘⠻⠛⢸⠻⠻⠘⠀⠛⠻⠟⠘⢛⠿⠛⠛⠿⠀⠛⡛⠟⠛⠀⠚⡟⠟⠟⠚⠗⡟⡇⠀⡟⠇⠘⠟⠻⠟⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⡛⠛⡛⡓⢛⣛⡃⠈⡛⡃⢛⣛⡃⠘⣛⣛⡃⠘⠛⢛⢘⠛⠛⠘⠀⢛⣛⡛⣘⣛⣿⣛⣛⣿⠀⣛⠛⠛⡓⣀⠛⠛⡛⠛⣛⡛⠛⡃⠀⠛⡃⠘⠛⠻⠛⡻⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣓⣛⣛⣛⡛⢛⡛⡓⢓⣛⡃⢘⡋⡃⢛⣛⡃⢙⣛⣓⡃⠘⠛⢛⢚⠛⠛⠙⠀⢘⣛⣛⣓⣓⣛⣛⣛⣚⠀⣛⡛⠋⠛⡃⠛⡛⠛⡈⠛⠛⡛⠃⠐⠛⠛⡛⠓⠙⠛⠛⡃⡘⠛⠃⠘⠛⠻⠛⠻⠓⠀⠀⠀⠀⠀⠀⠀⠀ ⣓⣛⣛⣛⡛⢙⣛⡛⢙⣛⡃⢘⡋⡃⢛⣛⡃⢛⣛⣛⡃⠘⠛⢛⢚⠛⠛⠘⠀⢘⣛⣛⣓⣓⣛⣛⣛⣚⠀⣛⠛⠛⡛⣛⡛⠛⣘⠛⣛⡋⠛⡛⠃⠐⡙⠛⠛⠛⢙⣛⡛⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⣛⢉⣋⡛⢙⣛⡃⢘⣋⡃⣚⣛⡃⣘⣛⣛⡃⢘⢛⢛⢘⢛⢛⢑⠀⢘⣚⣛⣓⣓⣛⣛⣛⢘⠀⣛⣛⠋⢛⡃⡛⣛⠛⣀⡛⠛⡋⡃⡐⠙⠛⡛⠛⠙⡛⢛⣁⡘⠛⠃⠘⠛⠻⠛⠻⠓⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⣛⢉⣋⡛⢙⣛⡃⢘⣋⡃⣘⣛⡃⣘⣛⣛⡃⢘⢛⢛⢚⢛⢛⠉⣀⡙⢛⠛⠓⠓⠛⠛⣛⣚⡀⣛⠛⠛⣛⣛⡛⠛⣈⣛⡛⡋⡛⠛⠃⡘⣙⠛⠛⠛⠙⠛⠛⢁⣀⠀⢀⢀⢀⠀⢀⠀⠀⢀⣀⠀⢀⣀⢀⣀ ⠓⠛⠛⠛⠛⠉⠋⠛⠙⠛⠃⠈⠋⠃⠙⠛⠃⠙⠛⠛⠃⠙⠛⠙⠙⠛⠈⠀⠛⠛⠙⠛⠛⠀⠛⠛⠛⠛⠛⠛⠀⠛⠛⠛⠛⠀⠋⠋⠛⠃⠃⠘⠛⠙⠙⠛⠙⠃⠘⠛⠃⠘⠛⠛⠙⠛⠛⠁⠈⠀⠈⠛⠛⠙⠋⠛⠛⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⣍⢉⣍⣉⣉⣍⣉⣉⠉⡍⢩⣍⣉⣉⣉⣉⡉⢩⡉⢩⣭⣉⣉⣉⣉⣉⣩⠉⢩⠉⣭⣭⢉⣭⣭⣉⣭⣭⠉⣉⠉⣭⣉⣍⣉⡍⣉⣍⣉⣉⣍⡉⡍⢩⣍⣉⣩⣉⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉ ⣁⣀⣉⣉⣉⣉⣉⣁⣀⣁⣈⣉⣉⣉⣉⣉⣁⣈⣁⣈⣉⣉⣉⣁⣙⣉⣉⣀⣈⣀⣉⣉⣈⣉⣉⣉⣉⣉⣀⣉⣀⣉⣉⣉⣉⣉⣁⣉⣉⣁⣉⣁⣁⣈⣉⣉⣉⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⠀⠀⠀⠀⢀⣀⣄⡀⠀⡄⢠⣤⣀⣀⣀⣀⡄⢠⡄⠀⣠⣠⡄⣤⣤⣄⣀⠀⢠⠀⣤⣤⠀⣤⣤⠀⣤⣤⠀⣤⠀⣤⣤⡤⢠⣤⣤⣤⣤⣤⣤⣄⣠⣤⣤⣤⢀⣠⣤⣄⣠⣤⣤⣤⣤⣤⢤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀ ⡤⠀⠀⠀⢀⣍⣭⣅⠀⣅⣨⣭⣬⣭⢩⣭⣅⣨⡅⠀⣨⣭⡅⣭⣭⣅⣬⠀⢨⠀⣭⣭⠨⢭⣥⠨⣬⣥⠀⣥⠀⣭⣭⡭⢠⣭⣭⣥⣭⣭⣭⣥⣌⣭⣍⣨⣍⣬⣭⣅⣨⣭⣭⣭⣭⣭⢭⣭⣭⣭⣭⣭⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⢀⣍⣭⡅⠀⡅⢨⣬⣭⣩⣭⣩⡅⢨⡄⠀⢨⣭⠁⣤⣭⣅⣬⠀⢨⠀⣬⣭⢠⢭⣬⢠⣭⣭⠀⣤⠀⣭⣭⣥⣤⣭⣥⣭⣭⣥⣭⣭⣭⣭⣅⣨⣍⣬⣭⣥⢬⣭⣭⣩⣭⢭⣬⣬⠍⠉⠉⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣭⣭⡅⠀⡅⢨⣯⣬⣭⣭⣭⡅⢠⡄⠀⢨⣬⠅⣤⣽⣅⣬⠀⢨⠀⣬⣬⢠⣽⣯⢤⣭⢭⠀⣤⠀⣭⣯⡭⢩⣭⣭⣭⣭⢠⣭⣭⣭⣡⣤⣤⣭⣌⣥⣬⣌⣥⣬⣭⣭⣼⣬⣭⣥⣠⢤⣤⣤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣥⣧⡇⠀⡄⢰⣯⣤⣤⣭⣬⡄⢠⡄⠀⢸⣼⡄⣴⣿⣤⣬⠀⢰⠀⣴⣼⢠⣶⣶⣤⣼⣶⠀⣤⠀⣷⣥⣥⣤⣥⡥⢡⣅⠠⣦⣦⣧⣶⣦⣆⡅⠀⠈⠉⠀⠈⠀⠀⠉⠉⠀⠈⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣤⣦⡄⠀⡆⢰⣦⢤⣤⣤⣤⡆⢰⡄⠀⢰⣴⡄⣴⣶⣤⣤⠀⢰⠀⣴⣶⢠⣴⣶⣠⣶⣶⠀⣤⠀⡶⣶⣶⡆⣶⣶⣶⢰⣶⣶⣶⣶⣶⣶⣦⣴⣆⢴⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⠤⠤⠤⠤⠤⠬⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤ ⣆⣶⣶⣶⣦⠴⡶⣦⢴⣶⡆⢰⡦⡆⣴⣶⡆⢴⣶⣖⡆⢰⣦⣴⣤⣴⠀⢰⣶⣤⣤⣤⣤⣦⣤⣤⣶⠀⣶⣶⣦⠠⣶⣶⡤⣤⡀⢐⣶⣤⣤⡤⢰⡖⡆⡆⣆⡀⢰⣶⡦⢴⡦⢴⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠤⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠇⠷⠷⠷⠷⠶⠷⠧⠶⠿⠇⠰⠿⠇⠶⠾⠇⠾⠾⠿⠆⠰⠶⠶⠸⠶⠶⠰⠀⠾⠾⠺⠾⠾⠿⠾⠿⠿⠷⠶⠀⠷⣶⠶⠶⠦⠰⠶⠆⠗⠖⠶⠶⠦⠰⠶⠆⠠⠶⠷⠶⠦⠲⠶⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠶⠷⠯⠾⠿⠇⠰⠯⠇⠶⠿⠇⠺⠿⠿⠇⠰⠶⠾⠼⠶⠶⠲⠀⠿⠸⠶⠶⠶⠷⠶⠾⠀⡶⠶⠶⠶⠀⠧⠖⠇⠤⡰⠶⠶⠶⠶⠇⠰⠧⠲⠇⠄⠰⡶⠆⠠⠲⠷⠶⠶⠲⠾⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠯⠿⠿⠿⠷⠶⠷⠷⠺⠿⠇⠰⠿⠇⠾⠿⠇⠾⠿⠿⠇⠰⠶⠾⠼⠶⠶⠰⠀⠿⠹⠶⠼⠶⠷⠶⠾⠀⠿⠶⠶⠶⠷⠀⠶⢶⠶⠶⠷⠀⠇⠰⠶⠇⠲⠇⠰⠶⠆⠰⠲⠷⠶⠶⠲⠾⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠺⠟⠷⠺⠿⠇⠠⠿⠇⠾⠿⠇⠸⠿⠿⠇⠰⠶⠾⠼⠶⠶⠂⠀⠿⠿⠶⠶⠷⠾⠶⣶⠀⠾⠶⠶⠷⠶⠶⠀⠶⠿⠶⠶⠲⠶⠷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠿⠚⠟⠷⠺⠿⠇⠸⠿⠇⠻⠿⠇⠹⠿⠾⠇⠰⠾⠾⠼⢾⠶⠚⠀⠻⠷⠶⠸⠿⣶⠿⠶⡶⠀⠷⠷⠶⠧⠠⠒⠿⠷⠶⠲⠶⠿⠗⠀⠷⠆⠰⠶⢶⠾⢷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠯⠿⠿⠿⠿⠚⠟⠷⠺⠿⠇⠘⢿⡇⠛⠿⠆⠘⠿⠻⠇⠺⠾⠺⠺⠾⠘⠀⠺⠶⠺⡾⠾⠤⠶⠿⠶⠿⠻⠧⠤⠶⠷⠗⠇⠟⠶⠇⠰⠷⠷⠷⠇⠇⠀⠷⢶⠷⠾⠷⠻⠷⠾⠾⠶⠾⠀⠺⠾⠺⠾⠾⠀⠀⠀⠀⠀⠀ ⡇⡿⡿⡟⡟⠛⡟⡗⠻⣟⡇⠘⢿⡇⠛⠿⠂⠚⢟⠛⠃⠺⠛⠛⠻⠿⠘⠀⠻⠛⠿⠿⠺⢻⠀⠻⠿⠀⠟⠟⡷⠟⠀⠟⠟⠟⠓⠀⠁⠚⡟⡟⠗⠛⠿⠟⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡗⡟⡟⡟⡟⠛⡟⡗⠛⣟⡇⠘⣿⡏⠛⠟⡇⠚⢿⣛⠃⠘⠻⠛⢸⠻⠻⠘⠀⠛⠻⠟⠘⢛⠿⠛⠛⠿⠂⠛⡛⠟⠛⠀⠚⡟⠟⠟⠚⠗⡟⡇⠀⡟⠇⠘⠟⠻⠟⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⡛⠛⡛⡓⢛⣛⡃⠈⡛⡃⢛⣛⡃⠘⣛⣙⡃⠘⠛⢛⢘⠛⠛⠘⠀⢛⣛⡛⣘⣛⣿⣛⣛⣿⠀⣛⠛⠛⡓⣀⠛⠛⡛⠛⣛⡛⠛⡃⠀⠛⡃⠘⠛⠿⠛⡻⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣓⣛⣛⣛⡛⢛⡛⡓⢓⣛⡃⢘⡋⡃⢛⣟⡇⢙⣛⣓⡃⠘⠛⢛⢚⠛⠛⠙⠀⢘⣛⣛⣓⣓⣛⣛⣛⣚⠀⣛⡛⠋⠛⡃⠛⡛⠛⡈⠛⠛⡛⠃⠐⠛⠛⡛⠓⠙⠛⠛⡃⡘⠛⠃⠘⠛⠻⠛⠻⠓⠀⠀⠀⠀⠀⠀⠀⠀ ⣓⣛⣛⣫⡛⢙⣛⡛⢙⣛⡃⢘⡋⡃⢛⣛⡃⢙⣛⣛⡃⠘⠛⢛⢚⠛⠛⠘⠀⢘⣛⣛⣓⣓⣛⣛⣛⣚⠀⣛⠛⠛⡛⣛⡛⠛⣘⠛⣛⡋⠛⡛⠃⠐⡙⠛⠛⠛⢙⣛⡛⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⣛⢉⣋⡛⢙⣛⡃⢘⣋⡇⣚⣛⡃⣘⣛⣛⡃⢘⢛⢛⢘⢛⢛⢑⠀⢘⣚⣛⣓⣓⣻⣟⣛⢘⠀⣛⣛⠋⢛⡃⡛⣛⠛⣀⡛⠛⡋⡃⡐⠙⠛⡛⠛⠙⡛⢛⣁⡘⠛⠃⠘⠛⠻⠛⠻⠓⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⣛⢉⣋⡛⢙⣛⡃⢘⣫⡇⣘⣛⡃⣘⣛⣛⡃⢘⢛⢛⢚⢛⢛⠉⣀⡙⢛⠛⠓⠓⠛⠛⣛⣚⡀⣛⠛⠛⣛⣛⡛⠛⣈⣛⡛⡋⡛⠛⠃⡘⣙⠛⠛⠛⠙⠛⠛⢁⣀⠀⢀⢀⢀⠀⢀⠀⠀⢀⣀⠀⢀⣀⢀⣀ ⠓⠛⠛⠛⠛⠉⠋⠛⠙⠛⠃⠈⠋⡃⠙⠛⡇⠙⠛⠛⠃⠙⠛⠙⠙⠛⠈⠀⠛⠛⠙⠛⠛⠀⠛⠛⠛⠛⠛⠛⠀⠛⠛⠛⠛⠀⢫⠋⠛⠃⠃⠘⠛⠙⠙⠛⠙⠃⠘⠛⠃⠘⠛⠛⠙⠛⠛⠁⠈⠀⠈⠛⠛⠙⠋⠛⠛⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⣍⢉⣍⣉⣉⣍⣉⣉⠉⡍⢩⣍⣉⣉⣉⣉⡉⢩⡉⢩⣭⣉⣉⣉⣉⣉⣩⠉⢩⠉⣭⣭⢉⣭⣭⣉⣭⣭⠉⣉⠉⣭⣉⣍⣉⡍⣉⣍⣉⣉⣍⡉⡍⢩⣍⣉⣩⣉⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉ ⣁⣀⣉⣉⣉⣉⣉⣁⣀⣁⢈⣉⣉⣉⣉⣉⣁⣈⡁⣈⣉⣉⣉⣁⣙⣉⣉⣀⣈⣀⣉⣉⣈⣉⣉⣉⣉⣉⣀⣉⣀⣉⣉⣉⣉⣉⣁⣉⣉⣁⣉⣁⣁⣈⣉⣉⣉⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⠀⠀⠀⠀⢀⣀⣄⡀⠀⡄⢠⣤⣀⣀⣀⣀⡄⢠⡄⠁⣠⣱⡄⣤⣤⣄⣀⠀⢠⠀⣤⣥⠀⣤⣤⠀⣤⣤⠀⣤⠀⣤⣤⡤⢠⣤⣤⣤⣤⣤⣤⣄⣠⣤⣤⣤⢀⣠⣤⣄⣠⣤⣤⣤⣤⣤⢤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀ ⡤⠀⠀⠀⢀⣍⣭⣅⠀⣅⣨⣭⣬⣭⢩⣭⣅⣨⡅⡀⣨⣭⡅⣭⣭⣅⣬⡀⢨⠀⣭⣭⠨⢭⣥⠨⣬⣥⠀⣥⠀⣭⣭⡭⢠⣭⣭⣥⣭⣭⣭⣥⣬⣭⣍⣨⣍⣬⣭⣅⣨⣭⣭⣭⣭⣭⢭⣭⣩⣭⣭⣭⠀⠀⠀⠀⡀⠀ ⠁⠀⠀⠀⢀⣍⣭⡅⠀⡍⢩⣬⣭⣩⣭⣩⡅⢨⡄⠀⢨⣭⠁⣤⣭⣅⣬⠀⢨⠀⣬⣭⢠⢭⣬⢠⣭⣭⠀⣤⠀⣭⣭⣥⣤⣭⣥⣭⣭⣥⣭⣭⣭⣭⣅⣨⣍⣬⣭⣥⢬⣭⣭⣩⣭⢭⣬⣬⠍⠉⠉⠉⠀⠀⢀⠀⠈⠀ ⠀⠀⠀⠀⠀⣭⣭⡅⠀⡅⢨⣯⣬⣭⣭⣭⡅⢠⡄⠁⢨⣬⠅⣤⣽⣅⣬⠀⢨⠀⣬⣬⢠⣽⣯⢤⣭⢭⠀⣤⠀⣭⣯⡭⢩⣭⣭⣭⣭⢠⣭⣭⣭⣡⣤⣤⣭⣌⣥⣬⣌⣥⣬⣭⣭⣼⣬⣭⣥⣠⢤⣤⣤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣥⣧⡇⠀⡄⢰⣯⣤⣤⣭⣬⡄⢠⡄⠀⢸⣼⡄⣴⣿⣤⣬⠀⢰⠀⣴⣼⢠⣶⣶⣤⣼⣶⠀⣤⠀⣷⣥⣥⣤⣥⡥⢡⣅⠠⣦⣦⣧⣶⣦⣆⡅⠀⠈⠉⠀⠈⠀⠀⠉⠉⠀⠈⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣤⣦⡄⠀⡆⢰⣦⢤⣤⣤⣤⡆⢰⡄⠀⢰⣴⡄⣴⣶⣤⣤⠀⢰⠀⣴⣶⢠⣴⣶⣠⣶⣶⠀⣤⠀⡶⣶⣶⡆⣶⣶⣶⢰⣶⣶⣶⣶⣶⣶⣦⣴⣆⢴⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⠤⠤⠤⠤⠤⠬⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤ ⣆⣶⣶⣶⣦⠴⡶⣦⢴⣶⡆⢰⡦⡆⣴⣶⡆⢴⣆⣗⡆⢰⣦⣴⣤⣴⠀⢰⣶⣤⣤⣤⣤⣦⣤⣤⣶⠀⣶⣶⣦⠠⣶⣶⡤⣤⡀⢐⣶⣤⣤⡤⢰⡖⡆⡆⣆⡀⢰⣶⡦⢴⡦⢴⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠤⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠇⠷⠷⠷⠷⠶⠷⠧⠶⠿⠇⠰⠿⠇⠶⠾⠇⠾⠾⠿⠆⠰⠶⠶⠸⠶⠶⠰⠀⠾⠾⠾⠾⠾⠿⠾⠿⠿⠷⠶⠀⠷⣶⠶⠶⠦⠰⠶⠆⠗⠖⠶⠶⠦⠰⠶⠆⠠⠶⠷⠶⠦⠲⠶⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠶⠷⠯⠾⠿⠇⠰⠧⠗⠶⠿⠇⠺⠿⠿⠇⠰⠶⠾⠼⠶⠶⠲⠀⠿⠸⠶⠶⠴⠷⠶⠾⠀⡶⠶⠶⠶⠀⠧⠖⠇⠤⡰⠶⠶⠶⠶⠇⠰⢧⠲⠆⠄⠰⡶⠆⠠⠲⠷⠶⠶⠲⠾⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠯⠿⠿⠿⠷⠶⠷⠷⠺⠿⠇⠐⡿⠧⠾⠿⠇⠾⠿⠿⠇⠰⠶⠾⠼⠶⠶⠰⠀⠿⠹⠶⠼⠶⠷⠶⠾⠀⠿⠶⠶⠶⠧⠀⠶⢶⠶⠶⠷⠀⠇⠰⠶⠇⠲⠇⠰⠶⠆⠰⠲⠷⠶⠶⠲⠾⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠺⠟⠷⠺⠿⠇⠠⠿⠇⠾⠿⠇⠸⠿⠿⠇⠰⠶⠾⠼⠶⠶⠂⠀⠿⠿⠴⠶⠷⠾⠴⣶⠀⠾⠶⠶⠷⠶⠶⠀⠶⠿⠶⠶⠲⠶⠵⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠿⠚⠟⠷⠺⠿⠇⠸⠿⠅⠻⠿⠇⠹⠿⠾⠇⠰⠾⠾⠼⢾⠶⠚⠀⠻⠷⠶⠸⠿⣶⠿⠶⡶⠀⠷⠷⠶⠧⠠⠒⠿⠷⠶⠲⠶⠿⠗⠀⠷⠆⠰⠶⢶⠾⢷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠯⠿⠿⠿⠿⠚⠟⠷⠺⠿⠇⢐⣿⡅⠛⠿⠆⠘⠿⠻⠇⠺⠾⠺⠺⠾⠘⠀⠺⠶⠺⡾⠾⠤⠶⠿⠶⠿⠻⠧⠤⠶⠷⠗⠇⠟⠶⠇⠰⠷⠷⠷⠇⠆⠀⠷⢶⠷⠾⠷⠻⠷⠾⠾⠶⠾⠀⠺⠾⠺⠾⠾⠀⠀⠀⠀⠀⠀ ⡇⡿⡿⡟⡟⠛⡟⡗⠻⣟⡇⠘⢿⡇⠛⠿⠎⠛⢟⠛⠃⠺⠛⠛⠻⠿⠘⠀⠻⠛⠿⠿⠺⢻⠀⠻⠿⠀⠟⠟⡷⠟⠀⠛⠟⠟⠓⠀⠁⠚⡟⡟⠗⠛⠿⠟⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡗⡟⣟⡟⡟⠛⡟⡗⠛⣟⡇⠘⣿⡏⠛⠟⡇⠚⢿⣛⠃⠘⠻⠛⢸⠻⠻⠘⠀⠛⠻⠟⠘⢛⠿⢻⠛⠿⠂⢛⡛⠟⠛⠀⠚⡟⠟⠟⠚⠗⡟⡇⠀⡟⠇⠘⠟⠻⠟⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⡛⠛⡛⡓⢛⣛⡃⠈⡛⡃⢛⣛⡃⠘⣛⣙⡃⠘⠛⢛⢘⠛⠛⠘⠀⢛⣛⡛⣘⣛⣿⣛⣛⣿⠀⣛⠛⠛⡓⣀⠛⠛⡛⠛⣛⡛⠛⡃⠀⠛⡃⠘⠛⠿⠛⡻⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣓⣛⣛⣛⡛⢛⡛⡓⢓⣛⡃⢀⡋⡃⢛⣟⡇⢙⣛⣓⡃⠘⠛⢛⢚⠛⠛⠙⠀⢘⣛⣛⣓⣓⣛⣛⣛⣚⠀⣛⡛⠋⠛⡃⠛⡛⠛⡈⠛⠛⡛⠃⠐⠛⠛⡛⠓⠙⠛⠛⡃⡘⠛⠃⠘⠛⠻⠛⠻⠓⠀⠀⠀⠀⠀⠀⠀⠀ ⣓⣛⣛⣫⡛⢙⣛⡛⢙⣛⡃⢘⡋⡃⢛⣛⠃⢙⣛⣛⡃⠘⠛⢛⢚⠛⠛⠘⠀⢘⣛⣛⣓⣓⣛⣛⣛⣚⠀⣛⠛⠛⡛⣛⡛⠛⣘⠛⣛⡋⠛⡛⠃⠐⡙⠛⠛⠛⢙⣛⡛⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⣛⢉⣋⡛⢙⣛⡃⢈⣋⡇⣚⣛⡃⣘⣛⣛⡃⢘⢛⢻⢘⢛⢛⢑⠀⢘⣛⣛⣓⣓⣻⣟⣛⢘⠀⣛⣛⠋⢛⡃⡛⣛⠛⣀⡛⠛⡋⡃⡐⠙⠛⡛⠛⠙⡛⢛⣁⡘⠛⠃⠘⠛⠻⠛⠻⠓⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⣛⢉⣋⡛⢙⣛⡃⢘⣯⡇⣘⣛⡃⣘⣛⣛⡃⢘⢛⢛⢚⢛⢛⠉⣀⡙⢛⠛⠛⠓⠛⠛⣛⣚⡀⣛⠛⠛⣛⣛⡛⠛⣈⣛⡛⡋⡛⠛⠃⡘⣙⠛⠛⠛⠙⠛⠛⢁⣀⠀⢀⢀⢀⠀⢀⠀⠀⢀⣀⠀⢀⣀⢀⣀ ⠃⠛⠛⠛⠛⠉⠋⠛⠙⠛⠃⠘⡋⡃⠙⠛⡇⠙⠛⠛⠃⠙⠛⠙⠙⠛⠈⠀⠛⠛⠙⠛⠛⠀⠛⠛⠛⠛⠛⠛⠀⠛⠛⠛⠛⠀⢫⠋⠛⠃⠃⠘⠛⠙⠙⠛⠙⠃⠘⠛⠃⠘⠛⠛⠙⠛⠛⠁⠈⠀⠈⠛⠛⠙⠋⠛⠛⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⣍⢉⣍⣉⣉⣍⣉⣉⠉⡍⢩⣍⣉⣉⣉⣉⡉⢩⡉⢩⣭⣉⣉⣉⣉⣉⣩⠉⢩⠉⣭⣭⢉⣭⣭⣉⣭⣭⠉⣉⠉⣭⣉⣍⣉⡍⣉⣍⣉⣉⣍⡉⡍⢩⣍⣉⣩⣉⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉ ⣁⣀⣉⣉⣉⣉⣉⣁⣀⣁⢈⣉⣉⣉⣉⣉⣁⣈⡁⣈⣉⣉⣉⣁⣙⣉⣉⣀⣈⣀⣉⣉⣈⣉⣉⣉⣉⣉⣀⣉⣀⣉⣉⣉⣉⣉⣁⣉⣉⣁⣉⣁⣁⣈⣉⣉⣉⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⠀⠀⠀⠀⢀⣀⣄⡀⠀⡄⢠⣤⣀⣀⣀⣀⡄⢠⡄⠁⣠⣱⡄⣤⣤⣄⣀⠀⢠⠀⣤⣥⠀⣤⣤⠀⣤⣤⠀⣤⠀⣤⣤⡤⢠⣤⣤⣤⣤⣤⣤⣄⣠⣤⣤⣤⢀⣠⣤⣄⣠⣤⣤⣤⣤⣤⢤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀ ⡤⠀⠀⠀⢀⣍⣭⣅⠀⣅⣨⣭⣬⣭⢩⣭⣅⣨⡅⡀⣨⣭⡅⣭⣭⣅⣬⡀⢨⠀⣭⣭⠨⢭⣥⠨⣬⣥⠀⣥⠀⣭⣭⡭⢠⣭⣭⣥⣭⣭⣭⣥⣬⣭⣍⣨⣍⣬⣭⣅⣨⣭⣭⣭⣭⣭⢭⣭⣩⣭⣭⣭⠀⠀⠀⠀⡀⠀ ⠁⠀⠀⠀⢀⣍⣭⡅⠀⡍⢩⣬⣭⣩⣭⣩⡅⢨⡄⠀⢨⣭⠁⣤⣭⣅⣬⠀⢨⠀⣬⣭⢠⢭⣬⢠⣭⣭⠀⣤⠀⣭⣭⣥⣤⣭⣥⣭⣭⣥⣭⣭⣭⣭⣅⣨⣍⣬⣭⣥⢬⣭⣭⣉⣭⢭⣬⣬⠍⠉⠉⠉⠀⠀⢀⠀⠈⠀ ⠀⠀⠀⠀⠀⣭⣭⡅⠀⡅⢨⣯⣬⣭⣭⣭⡅⢠⡄⠁⢨⣬⠅⣤⣽⣅⣬⠀⢨⠀⣬⣬⢠⣽⣯⢤⣭⣭⠀⣤⠀⣭⣯⡭⢩⣭⣭⣭⣭⢠⣭⣭⣭⣡⣤⣤⣭⣌⣥⣬⣌⣥⣬⣭⣭⣼⣬⣭⣥⣠⢤⣤⣤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣥⣧⡇⠀⡄⢰⣯⣤⣤⣭⣌⡄⢠⡄⠀⢸⣼⡄⣴⣟⣤⣬⠀⢰⠀⣴⣼⢠⣶⣶⣤⣼⣶⠀⣤⠀⣷⣥⣥⣤⣥⡭⠡⣁⠠⣦⣦⣧⣶⣦⣆⡅⠀⠈⠉⢀⠈⠈⠁⠉⠉⠈⠈⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣤⣦⡄⠀⡆⢰⣦⢤⣤⣤⡤⡆⢰⡄⠀⢰⣴⡄⣴⣿⣤⣤⠀⢰⠀⣴⣶⢠⣴⣶⣠⣶⣶⠀⣤⠀⡶⣶⣶⡆⣶⣶⣶⢰⣶⣶⣶⣶⣶⣶⣦⣴⣆⢴⣶⣶⣶⣶⣶⣾⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⠤⠤⠤⠤⠤⠬⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼⠤⠤⠤⠤⠥⠭⠤⠬⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤ ⣆⣶⣶⣶⣦⠴⡿⣦⢴⣶⡆⢰⡦⡆⣴⣶⡆⢴⣆⣗⡆⢰⣦⣴⣤⣴⠀⢰⣶⣤⣤⣤⣤⣦⣤⣥⣶⠀⣶⣶⣦⠨⣷⣶⡤⣤⡀⢐⣶⣤⣤⡤⢰⡖⡆⡆⣆⡀⢰⣶⡦⢴⡦⢴⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡤⠤⠤⠤⠤⠤⠤⠤⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠤⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠇⠷⠷⠷⠷⠶⠷⠧⠶⠿⠇⠰⡿⠇⠶⠾⠇⠾⠾⠿⠆⠰⠶⠶⠸⠶⠶⠰⠀⠾⠾⠾⠾⠾⠿⠾⠿⠿⠷⠶⠀⠷⣶⠶⠶⠦⠰⠶⠆⠗⠖⠶⠶⠦⠰⠶⠆⠠⠶⠷⠶⠦⠲⠶⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠶⠷⠯⠾⠿⠇⠰⠯⠗⠶⠿⠇⠺⠿⠿⠇⠰⠶⠾⠼⠶⠶⠲⠀⠿⠸⠶⠶⠴⠷⠶⠾⠀⡶⠶⠶⠶⠀⠧⠖⢇⡤⡰⠶⠶⠶⠶⠇⠰⢧⠲⠆⠄⠰⡶⠆⠠⠲⠷⠶⠶⠲⠾⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠯⠿⠿⠿⠷⠶⠷⠷⠺⠿⠇⠐⡿⠧⠾⠿⠇⠾⠿⠿⠇⠰⠶⠾⠼⠶⠶⠰⠀⠿⠹⠶⠼⠶⠷⠶⠾⠀⠿⠶⠶⠶⠧⠀⠶⢶⠶⠶⠷⠀⠇⠰⠶⠇⠲⠇⠰⠶⠆⠰⠲⠷⠶⠶⠲⠾⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠺⠗⠷⠺⠿⠇⠠⠿⠇⠾⠿⠇⠸⠿⠿⠇⠰⠶⠾⠼⠴⠶⠂⠀⠿⠿⠴⠶⠷⠾⠴⣶⠀⠾⠶⠶⠷⠶⠶⠀⠖⠿⠶⠶⠲⠶⠵⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠿⠚⠟⠷⠺⠿⠇⠸⠿⠅⠻⠿⠇⠹⠿⠾⠇⠰⠾⠾⠼⢾⠶⠚⠀⠻⠷⠶⠸⠿⣶⠿⠶⡶⠀⠷⠷⠶⠧⠠⠒⠿⠷⠶⠲⠶⠿⠗⠀⠷⠆⠰⠶⢶⠾⢷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠯⠿⠿⠿⠿⠚⠟⠷⠺⠿⠇⢐⣿⡇⠛⠿⠆⠘⠿⠻⠇⠺⠾⠺⠺⠾⠸⠄⠺⠶⠺⡾⠾⠤⠶⠿⠶⠿⠻⠧⠤⠶⠷⠗⠇⠟⠶⠇⠰⠷⠷⠷⠇⠆⠀⢷⢶⠷⠾⠷⠻⠷⠾⠾⠶⠾⠀⠺⠾⠺⠾⠾⠀⠀⠀⠀⠀⠀ ⡇⡿⡿⡟⡟⠛⡟⡗⠻⣟⡇⠘⢿⡇⠛⠿⠎⠛⢟⠛⠃⠺⠛⠛⠻⠿⠘⠀⠻⠛⠿⠿⠺⢻⠀⠻⠿⠀⠟⠟⡷⠟⠀⠛⠟⠟⠓⠀⠁⠚⡟⡟⠗⠛⠿⠟⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡗⡟⣟⡟⡟⠛⡟⡗⠛⣟⡇⠘⣿⡏⠛⠟⡇⠚⢿⣛⠃⠘⠻⠛⢸⢺⠻⠘⠀⠛⠻⠟⠘⣛⠿⢻⠛⠿⠂⢛⡛⠟⠛⠀⠚⡟⠟⠟⠚⠗⡟⡇⠀⡟⠇⠘⠟⠻⠟⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⡛⠛⡋⡓⢛⣛⡃⠈⡛⡃⢛⣋⡃⠘⣛⣙⡃⠘⠛⢛⢘⠛⠛⠘⠀⢛⣛⡛⣘⣛⣿⣛⣛⣿⠀⣛⠛⠛⡓⣀⠛⠛⡛⠛⣛⡛⠛⡃⠀⠛⡃⠘⠛⠿⠛⡻⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣓⣛⣛⣛⡛⢛⡛⡓⢓⣛⡃⢀⡏⡃⢛⣟⡇⢙⣛⣓⡃⠘⠛⢛⢚⠛⠛⠙⠀⢘⣻⣛⣓⣓⣛⣛⣛⣚⠀⣛⡛⠋⠛⡃⠛⡛⠛⡈⠛⠛⡛⠃⠐⠛⠛⡛⠓⠙⠛⠛⡃⡘⠛⠃⠘⠛⠻⠛⠻⠓⠀⠀⠀⠀⠀⠀⠀⠀ ⣓⣛⣛⣫⡛⢙⣛⡛⢙⣛⡃⢘⡏⡃⢛⣛⠇⢙⣛⣛⡃⠘⠛⢛⢚⠛⠛⠘⠀⢘⣛⣛⣓⣓⣛⣛⣛⣚⠀⣛⠛⠛⡛⣛⡛⠛⣘⠛⣛⡋⠛⡛⠃⠐⡙⠛⠛⠛⢙⣛⡛⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣻⣟⣟⣛⢉⣋⡛⢙⣛⡃⢈⣋⡇⣚⣛⡃⣘⣛⣛⡃⢘⢛⢻⢘⢛⢛⢑⠀⢘⣛⣛⣳⣓⣻⣟⣛⢘⠀⣛⣛⠋⢛⡣⡛⣛⠛⣀⡛⠛⡋⡃⡐⠙⠛⡛⠛⠙⡛⢛⣁⡘⠛⠃⠘⠛⠻⠛⠻⠓⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⣛⢉⣋⡛⢙⣛⡃⢘⣯⡇⣘⡛⡃⣘⣛⣛⡃⢘⢛⢛⢚⢛⢛⠉⣀⡙⢛⠛⠛⠓⠛⠛⣛⣚⡀⣛⠛⠛⣛⣛⡛⠛⣈⣛⡛⡋⡛⠛⠃⡘⣙⠛⠛⠛⠙⠛⠛⢁⣀⠀⢀⢀⢀⠀⢀⠀⠀⢀⣀⠀⢀⣀⢀⣀ ⠃⠛⠛⠟⠛⠉⠫⠛⠙⠛⠃⠘⡋⡇⠙⠛⡇⠙⠛⠛⠃⠙⠛⠙⠙⠛⠈⠀⠛⠛⠙⠛⠛⠀⠛⠛⠛⠛⠛⠛⠀⠛⠛⠛⠛⠀⢫⠋⠛⠃⠃⠘⠛⠙⠙⠛⠙⠃⠘⠛⠃⠘⠛⠛⠙⠛⠛⠁⠈⠀⠈⠛⠛⠙⠋⠛⠛⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⣍⢉⣍⣉⣉⣍⣉⣉⠉⡍⢩⣍⣉⣉⣉⣉⡉⢩⡉⢩⣭⣉⣉⣉⣉⣉⣩⠉⢩⠉⣭⣭⢉⣭⣭⣉⣭⣭⠉⣉⠉⣭⣉⣍⣉⡍⣉⣍⣉⣉⣍⡉⡍⢩⣍⣉⣩⣉⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉ ⣁⣀⣉⣉⣉⣉⣉⣁⣀⣁⢈⣉⣉⣉⣉⣉⣁⣈⡁⣈⣉⣉⣉⣁⣙⣉⣉⣀⣈⢀⣉⣉⣈⣉⣉⣉⣉⣉⣀⣉⣀⣉⣉⣉⣉⣉⣁⣉⣉⣁⣉⣁⣁⣈⣉⣉⣉⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⠀⠀⠀⠀⢀⣀⣄⡀⠀⡄⢠⣤⣀⣀⣀⣀⡄⢠⡄⠁⣠⣱⡄⣤⣤⣄⣀⠀⢠⠀⣤⣥⠀⣤⣤⠀⣤⣤⠀⣤⠀⣤⣤⡤⢠⣤⣤⣤⣤⣤⣤⣄⣠⣤⣤⣤⢀⣠⣤⣄⣠⣤⣤⣤⣤⣤⢤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀ ⡤⠀⠀⠀⢀⣍⣭⣅⠀⣅⣨⣭⣬⣭⢩⣭⣅⣨⡅⡀⣨⣭⡅⣭⣭⣅⣬⡀⢨⠀⣭⣭⠨⢭⣥⠨⣬⣥⠀⣥⠀⣭⣭⡭⢠⣭⣭⣥⣭⣭⣭⣥⣬⣭⣍⣨⣍⣬⣭⣅⣨⣭⣭⣍⣭⣭⢭⣭⣩⣭⣭⣭⠀⠀⠀⠀⡀⠀ ⠁⠀⠀⠀⢀⣍⣭⡅⠀⡍⢩⣬⣍⣩⣭⣩⡅⢨⡄⠀⢨⣭⠁⣤⣭⣅⣬⠀⢨⠀⣬⣭⢠⢭⣬⢠⣭⣭⠀⣤⠀⣭⣭⣥⣤⣭⣥⣭⣭⣥⣭⣭⣭⣭⣅⣨⣍⣬⣭⣥⢬⣭⣭⣉⣭⢭⣬⣬⠍⠉⠉⠉⠀⠀⢀⠀⠈⠀ ⠀⠀⠀⠀⠀⣭⣭⡅⠀⡅⢨⣯⣬⣭⣭⣭⡅⢠⡄⠁⢨⣬⠅⣤⣽⣅⣬⠀⢨⠀⣬⣬⢠⣽⣯⢤⣭⣭⠀⣤⠀⣭⣯⡭⢩⣭⣭⣭⣍⢠⣭⣭⣭⣡⣤⣤⣭⣌⣥⣬⣌⣥⣬⣭⣭⣼⣤⣭⣥⣠⢤⣤⣤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣥⣧⡇⠀⡄⢰⣯⣤⣤⣭⣌⡄⢠⡄⠀⢸⣼⡄⣴⣟⣤⣬⠀⢰⠀⣴⣼⢠⣶⣶⣤⣼⣶⠀⢤⠀⣷⣥⣥⣤⣥⡭⠡⣁⠠⣦⣦⣧⣶⣦⣆⡅⠀⠈⠉⢀⠈⠈⠁⠉⢈⠈⠈⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣤⣦⡄⠀⡆⢰⣦⢤⣤⣤⡤⡆⠰⡄⠀⢰⣴⡄⣴⣿⣤⣤⠀⢰⠀⣴⣶⢠⣴⣶⣠⣶⣶⠀⣤⠀⡶⣶⣶⡆⣶⣶⣶⢰⣶⣶⣶⣶⣶⣶⣦⣴⣆⢴⣶⣶⣶⣶⣶⣾⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⠤⠤⠤⠤⠤⠬⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼⠤⠤⠤⠤⠥⠭⠤⣬⡤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤ ⣆⣶⣶⣶⣦⠴⡿⣦⢴⣶⡆⢰⡦⡆⣴⣶⡆⢴⣆⣗⡆⢰⣦⣴⣤⣴⠀⢰⣶⣤⣤⣤⣤⣶⣤⣥⣶⠀⣶⣶⣦⠨⣷⣶⡤⣤⡀⢐⣶⣤⣦⡤⢰⡖⡆⡆⣆⡀⢰⣶⡦⢴⡦⢴⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡤⠤⠤⠤⠤⠤⠤⠤⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠤⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠇⠷⠷⠷⠷⠶⠷⠧⠶⠿⠇⠰⡿⠇⠶⠾⠇⠾⠾⠿⠆⠰⠶⠶⠸⠶⠶⠰⠀⠾⠾⠺⠾⠾⠿⠾⠿⠿⠷⠶⠀⠷⣶⠶⠶⠦⠰⠶⠆⠗⠖⠶⠶⠦⠰⠶⠆⠠⠶⠷⠶⠦⠲⠶⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠶⠷⠮⠾⠿⠇⠰⡯⠗⠶⡿⠇⠺⠿⠿⠇⠰⠶⠾⠼⠶⠶⠲⠀⠿⠸⠶⠶⠴⠷⠶⠾⠀⡶⠶⠶⠶⠀⣧⠖⢇⡤⡰⠶⠶⠶⠶⠇⠰⢧⠲⠆⠄⠰⡶⠆⠠⠲⠷⠶⠶⠲⠾⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠯⠿⠷⠿⠷⠶⠷⠷⠺⠿⠇⠐⡿⠧⠾⠿⠇⠾⠾⠾⠇⠰⠶⢾⠼⠶⠶⠰⠀⠿⠹⠶⠼⠶⠷⠶⠾⠀⠿⠶⠶⠶⠷⠀⠶⢶⠶⠶⠷⠀⠇⠰⠶⠇⠒⠇⠰⠶⠆⠰⠲⠷⠶⠶⠲⠾⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠺⠗⠷⠺⠿⠇⠠⠿⠇⠾⠿⠇⠸⠿⠿⠇⠰⠶⢾⠼⠴⠶⠒⠀⠿⠿⠴⠶⠷⠾⠴⣶⠀⠾⠶⠶⠷⠶⠶⠀⠖⠿⠶⠶⠲⠶⠵⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠿⠚⠟⠷⠺⠿⠇⠸⠷⠆⠻⠿⠇⠹⠿⠾⠇⠰⠾⢾⠼⢾⠶⠚⠀⠻⠷⠶⠸⠿⣶⠿⠶⡶⠀⠷⠷⠶⠧⠠⠒⠿⠷⠶⠲⠶⠿⠗⠀⠷⠆⠰⠶⢶⠾⢷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠯⠿⠿⠿⠷⠚⠟⠷⠺⠿⠇⢰⣿⡇⠟⠿⢆⡘⠿⠻⠇⠺⠾⠺⠺⠾⠘⠀⠺⠶⠺⡾⠾⠤⠾⠿⠶⠿⠻⠧⠤⠶⠷⠗⠇⠟⠶⠇⠰⠷⠷⠷⠇⠆⢀⣷⢶⠷⠾⠷⠻⠷⠾⠾⠶⠾⠀⠺⠾⠺⠾⠾⠀⠀⠀⠀⠀⠀ ⡇⡿⡿⡟⡟⠛⡟⡗⠻⣟⡇⠸⣿⡇⠛⠷⠎⠛⢟⠛⠃⠺⠛⠛⠻⠿⠘⠀⠻⠛⠿⠿⠺⢻⠀⠹⠿⠀⠟⠟⡷⠟⠀⠛⠟⠟⠓⠀⠁⠚⡟⡟⠗⠛⠿⠟⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡗⡟⣟⡟⡟⠛⡟⡗⠛⣟⡇⠘⣿⡏⠛⠟⡇⠚⢿⣛⠃⠘⠻⢛⢸⣺⠻⠘⠀⠛⠻⠟⢸⣛⠿⢻⠛⠿⠂⢛⡛⠟⠛⠀⠚⡟⠟⠟⠚⠗⡟⡇⠀⡟⠇⠘⠟⠻⠟⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣋⣛⡋⠛⡋⡓⢛⣛⡃⢨⡟⡃⢛⣋⡃⢘⣛⣙⡃⠘⠛⢛⢘⠛⠛⠘⠀⢛⣛⡛⣘⣛⣿⣛⣛⣿⠀⣛⠛⠛⡓⣀⠛⠛⡛⠛⣛⡛⠛⡃⠀⠛⡃⠘⠛⠿⠛⡻⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣓⣛⣻⣛⡛⢛⡛⡓⢓⣟⡃⢠⡏⡃⢛⣟⡇⢙⣛⣓⡃⠘⠛⢛⢚⠛⠛⠙⠀⢘⣿⣛⣓⣓⣛⣛⣛⣚⠀⣛⡛⠋⠛⡃⠛⡛⠛⡈⠛⠛⡛⠃⠐⠛⠛⡛⠓⠙⠛⠛⡃⡘⠛⠃⠘⠛⠻⠛⠻⠓⠀⠀⠀⠀⠀⠀⠀⠀ ⣓⣛⣛⣍⡛⢙⣏⡛⢙⣛⡃⢘⡏⡃⢻⣫⠅⢙⣛⣛⡃⠘⠛⢛⢚⠙⠛⠘⠀⢘⣟⣛⣓⣓⣛⣛⣛⣚⠀⣛⠛⠛⡛⣛⡛⠛⣘⠛⣛⡋⠛⡛⠃⠐⡙⠛⠛⠛⢙⣛⡛⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣫⣏⣝⣛⢉⣋⡛⢙⣛⡃⢈⣏⡇⣚⣛⡃⢘⣛⣛⡃⢘⢛⢻⢘⢛⢛⢑⠀⢘⣻⣛⣷⣓⣻⣟⣛⢘⠀⣛⣛⠋⢛⡣⡛⣛⠛⣀⡟⠛⡋⡃⡐⠙⠛⡛⠛⠙⡛⢛⣁⡘⠛⠃⠘⠛⠻⠛⠻⠓⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⣛⢉⣋⡛⢙⣛⡃⠘⣯⡇⣘⡛⡃⣘⣛⣛⡃⢘⢛⢛⢚⢛⢛⠉⣀⡙⢙⠛⠛⠓⠛⠛⣟⣚⡀⣛⠛⠛⣛⣛⡛⠛⣈⣛⡛⡋⡛⠛⠃⡘⣙⠛⠛⠛⠙⠛⠛⢁⣀⠀⢀⢀⢀⠀⢀⠀⠀⢀⣀⠀⢀⣀⢀⣀ ⠃⠛⠻⠟⠛⠉⠫⠛⠙⠛⠃⠐⡋⡇⠹⡟⡇⠙⠛⠛⠃⠙⠛⠙⠙⠛⠈⠀⠛⠛⠙⠛⠛⠀⠛⠛⠛⠛⠛⠛⠀⠛⠛⠟⠛⠀⢯⠋⠛⠃⠃⠘⠛⠙⠙⠛⠙⠃⠘⠛⠃⠘⠛⠛⠙⠛⠛⠁⠈⠀⠈⠛⠛⠙⠋⠛⠛⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⣍⢉⣍⣉⣉⣍⣉⣉⠉⡍⢩⣍⣉⣉⣉⣉⡉⢩⡉⢩⣭⣉⣉⣉⣉⣉⣩⠉⢩⠉⣭⣭⢉⣭⣭⣉⣭⣭⠉⣉⠉⣭⣉⣍⣉⡍⣉⣍⣉⣉⣍⡉⡍⢩⣍⣉⣩⣉⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉ ⣁⣀⣉⣉⣉⣉⣉⣁⣀⣁⢈⣉⣉⣉⣉⣉⣁⣈⡁⣈⣉⣉⣉⣁⣙⣉⣉⣀⣨⢀⣉⣉⣈⣉⣉⣉⣉⣉⣀⣉⣀⣉⣉⣉⣉⣍⣁⣉⣉⣁⣉⣁⣁⣈⣉⣉⣉⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⠀⠀⠀⠀⢀⣀⣄⡀⠀⡄⢠⣤⣀⣀⣀⣀⡄⢨⡄⠙⣠⣱⡄⣤⣤⣄⣀⠀⢸⠀⣤⣥⠀⣤⣤⠀⣤⣤⠀⣤⠀⣤⣤⡤⢠⣤⣤⣤⣤⣤⣤⣄⣠⣤⣤⣤⢀⣠⣤⣄⣠⣤⣤⣤⣤⣤⢤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀ ⡤⠀⠀⠀⢀⣍⣭⣅⠀⣅⣨⣭⣬⣭⢩⣭⣅⣨⡅⡀⣨⣭⡅⣭⣭⣅⣬⡀⢨⠀⣭⣭⠨⢭⣥⠨⣬⣥⠀⣥⠀⣭⣭⡭⢠⣭⣭⣥⣍⣍⣭⣥⣌⣭⣍⣨⣍⣬⣭⣅⣨⣭⣍⣉⣭⣭⢭⣩⣩⣭⣭⣭⡀⠀⠀⠀⡀⠀ ⠁⠀⠀⠀⢀⣍⣭⡅⠀⡅⢩⣬⣉⣩⣭⣩⡅⢨⡄⠀⢨⣭⠁⣤⣭⣅⣬⠀⢸⠀⣬⣭⢠⢭⣬⢠⣭⣩⠀⣤⠀⣭⣭⣥⣤⣭⣥⣭⣭⣥⣭⣭⣭⣭⣅⣨⣍⣬⣭⣥⢬⣭⣩⣉⣭⢭⣬⣬⠍⠉⠉⠉⠀⠀⢀⠀⠈⠀ ⠀⠀⠀⠀⠀⣍⣭⡅⠀⡅⢨⣯⣬⣭⣭⣭⡅⢸⡄⠁⢨⣼⠅⣤⣝⣅⣬⠀⢨⠀⣬⣬⢠⣽⣯⢤⣭⣭⠀⣤⠀⣭⣯⡭⢩⣭⣭⣭⣍⢠⣭⣭⣍⣡⣤⣤⣭⣌⣥⣬⣌⣥⣬⣭⣭⣼⣤⣭⣥⣠⢤⣤⣤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣥⣧⡇⠀⡆⢰⣯⣤⣤⣭⣌⡄⢠⡄⠀⢸⣼⡄⣴⣟⣤⣬⠀⢰⠀⣴⣼⢠⣶⣶⣤⣼⣶⠀⣤⠀⣷⣥⣥⣤⣥⣭⠡⣁⠠⣦⣦⣧⣶⣦⣆⡅⠀⠈⠉⢀⠈⠈⠁⠉⢈⠈⠈⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣤⣦⡄⠀⡆⢰⣦⢤⣤⣤⡤⡆⠰⡄⠀⢰⣴⡄⣴⣿⣤⣤⠀⢰⠀⣴⣶⢠⣴⣶⣠⣶⣶⠀⣤⠀⣶⣶⣶⡆⣶⣶⣶⢰⣶⣶⣶⣶⣶⣶⣦⣴⣆⢴⣶⣶⣶⣶⣶⣾⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⠤⠤⠤⠤⠤⠬⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⢼⡤⡤⠤⢤⠤⠤⠤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠧⠤⠤⠼⠤⠤⠤⢤⠥⠭⣤⣬⣤⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤ ⣆⣶⣶⣶⣦⠴⡿⣆⢴⣶⡆⢰⡦⡆⣴⣶⡆⢼⣇⣗⡆⢰⣦⣴⣤⣴⠀⢰⣶⣤⣤⣤⣤⣾⣤⣥⣶⠀⣶⣶⣦⠨⣷⣶⡤⣤⡀⢐⣶⣤⣦⡤⢹⡖⡆⡆⣆⡀⢰⣶⡦⢴⡦⢴⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⢤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡤⡤⠤⠤⠤⠤⠤⠤⠤⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠤⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠇⠷⠷⠷⠷⠶⠷⠧⠶⠿⠇⠰⡿⠇⠶⠾⠇⠾⠾⠿⠆⠰⠶⠶⠸⠶⠶⠰⠀⠾⠾⠺⠾⠾⠿⠾⠿⠿⠷⠶⠀⠷⣶⠶⠶⠦⠰⠶⠆⠗⠖⠶⠶⠦⠰⠶⠆⠠⠶⠷⠶⠦⠲⠶⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠶⠷⠮⠾⠿⠇⠰⡯⠗⠶⡿⠇⠺⠿⠿⠇⠰⠶⠾⠼⠶⠶⠲⠀⠿⠸⠶⠶⠴⠷⠶⠾⠀⡶⠶⠶⠶⠀⣧⠖⢇⡤⡰⠶⠶⠶⠶⠇⠰⢧⠲⠆⠄⠰⡶⠆⠠⠲⠷⠶⠶⠲⠾⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠯⠿⠷⠿⠷⠶⠷⠷⠺⠿⠇⠐⡿⠧⠾⠿⠇⠾⠾⠾⠇⠰⠶⢾⠼⠶⠶⠰⠀⠿⠹⠶⠼⠶⠷⠶⠾⠀⠿⠶⠶⠶⠷⠀⠶⢶⠶⠶⠷⠀⠇⠰⠶⠇⠒⠇⠰⠶⠆⠰⠲⠷⠶⠶⠲⠾⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠺⠗⠷⠺⠿⠇⠠⠿⠆⠾⠿⠇⠸⠿⠿⠇⠰⠶⢾⠼⠴⠶⠒⠀⠿⠿⠴⠶⠷⠾⠴⣶⠀⠾⠶⠶⠷⠶⠶⠀⠖⠿⠶⠶⠲⠶⠵⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠿⠚⠟⠷⠺⠿⠇⠸⠷⠆⠻⠿⠇⠹⠿⠾⠇⠰⠾⢾⠼⢾⠶⠚⠀⠻⠷⠶⠸⠿⣶⠿⠶⡶⠀⠷⠷⠶⠧⠠⠒⠿⠷⠶⠲⠶⠿⠗⠀⠷⠆⠰⠶⢶⠾⢷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠯⠿⠿⠿⠷⠚⠟⠷⠺⠿⠇⢰⣿⡇⠟⠿⢆⡘⠿⠻⠇⠺⠾⠺⠺⠾⠘⠀⠺⠶⠺⡾⠾⠤⠾⠿⠶⠿⠻⠧⠤⠶⠷⠗⠇⠟⠶⠇⠰⠷⠷⠷⠇⠆⢀⣷⢶⠷⠾⠷⠻⠷⠾⠾⠶⠾⠀⠺⠾⠺⠾⠾⠀⠀⠀⠀⠀⠀ ⡇⡿⡿⡟⡟⠛⡟⡗⠻⣟⡇⠸⣿⡇⠛⠷⠎⠛⢟⠛⠃⠺⠛⠛⠻⠿⠘⠀⠻⠛⠿⠿⠺⢻⠀⠹⠿⠀⠟⠟⡷⠟⠀⠛⠟⠟⠓⠀⠁⠚⡟⡟⠗⠛⠿⠟⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡗⡟⣟⡟⡟⠛⡟⡗⠛⣟⡇⠘⣿⡏⠛⠟⡇⠚⢿⣛⠃⠘⠻⢛⢸⣺⠻⠘⠀⠛⠻⠟⢸⣛⠿⢻⠛⠿⠂⢛⡛⠟⠛⠀⠚⡟⠟⠟⠚⠗⡟⡇⠀⡟⠇⠘⠟⠻⠟⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣋⣛⡋⠛⡋⡓⢛⣛⡃⢨⡟⡃⢛⣋⡃⢘⣛⣙⡃⠘⠛⢛⢘⠛⠛⠘⠀⢛⣛⡛⣘⣛⣿⣛⣛⣿⠀⣛⠛⠛⡓⣀⠛⠛⡛⠛⣛⡛⠛⡃⠀⠛⡃⠘⠛⠿⠛⡻⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣓⣛⣻⣛⡛⢛⡛⡓⢓⣟⡃⢠⡏⡃⢛⣟⡇⢙⣛⣓⡃⠘⠛⢛⢚⠛⠛⠙⠀⢘⣿⣛⣓⣓⣛⣛⣛⣚⠀⣛⡛⠋⠛⡃⠛⡛⠛⡈⠛⠛⡛⠃⠐⠛⠛⡛⠓⠙⠛⠛⡃⡘⠛⠃⠘⠛⠻⠛⠻⠓⠀⠀⠀⠀⠀⠀⠀⠀ ⣓⣛⣛⣭⡛⢙⣏⡛⢙⣛⡃⢘⡏⡃⢻⣫⠅⢙⣛⣛⡃⠘⠛⢛⢚⠙⠛⠘⠀⢘⣟⣛⣓⣓⣛⣛⣛⣚⠀⣛⠛⠛⡛⣛⡛⠛⣘⠛⣛⡋⠛⡛⠃⠐⡙⠛⠛⠛⢙⣛⡛⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣫⣏⣝⣛⢉⣋⡛⢙⣛⡃⢈⣏⡇⣚⣛⡃⢘⣛⣛⡃⢘⢛⢻⢘⢛⢛⢑⠀⢘⣻⣛⣷⣓⣻⣟⣛⢘⠀⣛⣛⠋⢛⡣⡛⣛⠛⣀⡟⠛⡋⡃⡐⠙⠛⡛⠛⠙⡛⢛⣁⡘⠛⠃⠘⠛⠻⠛⠻⠓⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⣛⢉⣋⡛⢙⣛⡃⠘⣯⡇⣘⡛⡃⣘⣛⣛⡃⢘⢛⢛⢚⢛⢛⠉⣀⡙⢙⠛⠛⠓⠛⠛⣟⣚⡀⣛⠛⠛⣛⣛⡛⠛⣈⣛⡛⡋⡛⠛⠃⡘⣙⠛⠛⠛⠙⠛⠛⢁⣀⠀⢀⢀⢀⠀⢀⠀⠀⢀⣀⠀⢀⣀⢀⣀ ⠃⠛⠻⠟⠛⠉⠫⠛⠙⠛⠃⠐⡋⡇⠹⠟⡇⠙⠛⠛⠃⠙⠛⠙⠙⠛⠈⠀⠛⠛⠙⠛⠛⠀⠛⠛⠛⠛⠛⠛⠀⠛⠛⠟⠛⠀⢫⠋⠛⠃⠃⠘⠛⠙⠙⠛⠙⠃⠘⠛⠃⠘⠛⠛⠙⠛⠛⠁⠈⠀⠈⠛⠛⠙⠋⠛⠛⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⣍⢉⣍⣉⣉⣍⣉⣉⠉⡍⢩⣍⣉⣉⣉⣉⡉⢩⡉⢩⣭⣉⣉⣉⣉⣉⣩⠉⢩⠉⣭⣭⢉⣭⣭⣉⣭⣭⠉⣉⠉⣭⣉⣍⣉⡍⣉⣍⣉⣉⣍⡉⡍⢩⣍⣉⣩⣉⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉ ⣁⣀⣉⣉⣉⣉⣉⣁⣀⣁⢈⣉⣉⣉⣉⣉⣁⣈⡁⣈⣉⣉⣉⣁⣙⣉⣉⣀⣨⢀⣉⣉⣈⣉⣉⣉⣉⣉⣀⣉⣀⣉⣉⣉⣉⣍⣁⣉⣉⣁⣉⣁⣁⣈⣉⣉⣉⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⠀⠀⠀⠀⢀⣀⣄⡀⠀⡄⢠⣤⣀⣀⣀⣀⡄⢨⡄⠙⣠⣱⡄⣤⣤⣄⣀⠀⢸⠀⣤⣥⠀⣤⣤⠀⣤⣤⠀⣤⠀⣤⣤⡤⢠⣤⣤⣤⣤⣤⣤⣄⣠⣤⣤⣤⢀⣠⣤⣄⣠⣤⣤⣤⣤⣤⢤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀ ⡤⠀⠀⠀⢀⣍⣭⣅⠀⣅⣨⣭⣬⣭⢩⣭⣅⣨⡅⡀⣨⣭⡅⣭⣭⣅⣬⡀⢨⠀⣭⣭⠨⢭⣥⠨⣬⣥⠀⣥⠀⣭⣭⡭⢠⣭⣭⣥⣍⣍⣭⣥⣬⣭⣍⣨⣍⣬⣭⣅⣨⣭⣍⣉⣭⣭⢭⣩⣩⣭⣭⣭⡀⠀⠀⠀⡀⠀ ⠁⠀⠀⠀⢀⣍⣭⡅⠀⡍⢩⣬⣉⣩⣭⣩⡅⢨⡄⠀⢨⣭⠁⣤⣭⣅⣬⠀⢸⠀⣬⣭⢠⢭⣬⢠⣭⣩⠀⣤⠀⣭⣭⣥⣤⣭⣥⣭⣭⣥⣭⣭⣭⣭⣅⣨⣍⣬⣭⣥⢬⣭⣩⣉⣭⢭⣬⣬⠍⠉⠉⠉⠀⠀⢀⠀⠈⠀ ⠀⠀⠀⠀⠀⣍⣭⡅⠀⡅⢨⣯⣬⣭⣭⣭⡅⢸⡄⠁⢨⣼⠅⣤⣝⣅⣬⠀⢨⠀⣬⣬⢠⣽⣯⢤⣭⣭⠀⣤⠀⣭⣯⡭⢩⣭⣭⣭⣍⢠⣭⣭⣍⣡⣤⣤⣭⣌⣥⣬⣌⣥⣬⣭⣭⣼⣤⣭⣥⣠⢤⣤⣤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣥⣧⡇⠀⡆⢰⣯⣤⣤⣭⣌⡄⢠⡄⠀⢸⣼⡄⣴⣟⣤⣬⠀⢰⠀⣴⣼⢠⣶⣶⣤⣼⣶⠀⣤⠀⣷⣥⣥⣤⣥⣭⠡⣁⠠⣦⣦⣧⣶⣦⣆⡅⠀⠈⠉⢀⠈⠈⠁⠉⢈⠈⠈⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣤⣦⡄⠀⡆⢰⣦⢤⣤⣤⡤⡆⠰⡄⠀⢰⣴⡄⣴⣿⣤⣤⠀⢰⠀⣴⣶⢠⣴⣶⣠⣶⣶⠀⣤⠀⣶⣶⣶⡆⣶⣶⣶⢰⣶⣶⣶⣶⣶⣶⣦⣴⣆⢴⣶⣶⣶⣶⣶⣾⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⠤⠤⠤⠤⠤⠬⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⢼⡤⡤⠤⢤⠤⠤⠤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠧⠤⠤⠼⠤⠤⠤⢤⠥⠭⣤⣬⣤⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤ ⣆⣶⣶⣶⣦⠴⡿⣆⢴⣶⡆⢰⡦⡆⣴⣶⡆⢼⣇⣗⡆⢰⣦⣴⣤⣴⠀⢰⣶⣤⣤⣤⣤⣾⣤⣥⣶⠀⣶⣶⣦⠨⣷⣶⡤⣤⡀⢐⣶⣤⣦⡤⢹⡖⡆⡆⣆⡀⢰⣶⡦⢴⡦⢴⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⢤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡤⡤⠤⠤⠤⠤⠤⠤⠤⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠤⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠇⠷⠷⠷⠷⠶⠷⠧⠶⠿⠇⠰⡿⠇⠶⠾⠇⠾⠾⠿⠆⠰⠶⠶⠸⠶⠶⠰⠀⠾⠾⠾⠾⠾⠿⠾⠿⠿⠷⠶⠀⠷⣶⠶⠶⠦⠰⠶⠆⠗⠖⠶⠶⠦⠰⠶⠆⠠⠶⠷⠶⠦⠲⠶⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠶⠷⠮⠾⠿⠇⠰⡯⠗⠶⡿⠇⠺⠿⠿⠇⠰⠶⠾⠼⠶⠶⠲⠀⠿⠸⠶⠶⠴⠷⠶⠾⠀⡶⠶⠶⠶⠀⣧⠖⢇⡤⡰⠶⠶⠶⠶⠇⠰⢧⠲⠆⠄⠰⡶⠆⠠⠲⠷⠶⠶⠲⠾⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠯⠿⠷⠿⠷⠶⠷⠷⠺⠿⠇⠐⡿⠧⠾⠿⠇⠾⠾⠾⠇⠰⠶⢾⠼⠶⠶⠰⠀⠿⠹⠶⠼⠶⠷⠶⠾⠀⠿⠶⠶⠶⠧⠀⠶⢶⠶⠶⠷⠀⠇⠰⠶⠇⠒⠇⠰⠶⠆⠰⠲⠷⠶⠶⠲⠾⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠺⠗⠷⠺⠿⠇⠠⠿⠇⠾⠿⠇⠸⠿⠿⠇⠰⠶⢾⠼⠴⠶⠒⠀⠿⠿⠴⠶⠷⠾⠴⣶⠀⠾⠶⠶⠷⠶⠶⠀⠖⠿⠶⠶⠲⠶⠵⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠿⠚⠟⠷⠺⠿⠇⠸⠷⠆⠻⠿⠇⠹⠿⠾⠇⠰⠾⢾⠼⢾⠶⠚⠀⠻⠷⠶⠸⠿⣶⠿⠶⡶⠀⠷⠷⠶⠧⠠⠒⠿⠷⠶⠲⠶⠿⠗⠀⠷⠆⠰⠶⢶⠾⢷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠯⠿⠿⠿⠷⠚⠟⠷⠺⠿⠇⢰⣿⡅⠟⠿⢆⡘⠿⠻⠇⠺⠾⠺⠺⠾⠘⠀⠺⠶⠺⡾⠾⠤⠾⠿⠶⠿⠻⠧⠤⠶⠷⠗⠇⠟⠶⠇⠰⠷⠷⠷⠇⠆⢀⣷⢶⠷⠾⠷⠻⠷⠾⠾⠶⠾⠀⠺⠾⠺⠾⠾⠀⠀⠀⠀⠀⠀ ⡇⡿⡿⡟⡟⠛⡟⡗⠻⣟⡇⠸⣿⡇⠛⠷⠎⠛⢟⠛⠃⠺⠛⠛⠻⠿⠘⠀⠻⠛⠿⠿⠺⢻⠀⠹⠿⠀⠟⠟⡷⠟⠀⠛⠟⠟⠓⠀⠁⠚⡟⡟⠗⠛⠿⠟⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡗⡟⣟⡟⡟⠛⡟⡗⠛⣟⡇⠘⣿⡏⠛⠟⡇⠚⢿⣛⠃⠘⠻⢛⢸⣺⠻⠘⠀⠛⠻⠟⢸⣛⠿⢻⠛⠿⠂⢛⡛⠟⠛⠀⠚⡟⠟⠟⠚⠗⡟⡇⠀⡟⠇⠘⠟⠻⠟⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣋⣛⡋⠛⡋⡓⢛⣛⡃⢨⡟⡃⢛⣋⡃⢘⣛⣙⡃⠘⠛⢛⢘⠛⠛⠘⠀⢛⣛⡛⣘⣛⣿⣛⣛⣿⠀⣛⠛⠛⡓⣀⠛⠛⡛⠛⣛⡛⠛⡃⠀⠛⡃⠘⠛⠿⠛⡻⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣓⣛⣻⣛⡛⢛⡛⡓⢓⣟⡃⢠⡏⡃⢛⣟⡇⢙⣛⣓⡃⠘⠛⢛⢚⠛⠛⠙⠀⢘⣿⣛⣓⣓⣛⣛⣛⣚⠀⣛⡛⠋⠛⡃⠛⡛⠛⡈⠛⠛⡛⠃⠐⠛⠛⡛⠓⠙⠛⠛⡃⡘⠛⠃⠘⠛⠻⠛⠻⠓⠀⠀⠀⠀⠀⠀⠀⠀ ⣓⣛⣛⣭⡛⢙⣏⡛⢙⣛⡃⢘⡏⡃⢻⣫⠅⢙⣛⣛⡃⠘⠛⢛⢚⠙⠛⠘⠀⢘⣟⣛⣓⣓⣛⣛⣛⣚⠀⣛⠛⠛⡛⣛⡛⠛⣘⠛⣛⡋⠛⡛⠃⠐⡙⠛⠛⠛⢙⣛⡛⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣫⣏⣝⣛⢉⣋⡛⢙⣛⡃⢈⣏⡇⣚⣛⡃⢘⣛⣛⡃⢘⢛⢻⢘⢛⢛⢑⠀⢘⣻⣛⣷⣓⣻⣟⣛⢘⠀⣛⣛⠋⢛⡣⡛⣛⠛⣀⡟⠛⡋⡃⡐⠙⠛⡛⠛⠙⡛⢛⣁⡘⠛⠃⠘⠛⠻⠛⠻⠓⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⣛⢉⣋⡛⢙⣛⡃⠘⣯⡇⣘⡛⡃⣘⣛⣛⡃⢘⢛⢛⢚⢛⢛⠉⣀⡙⢙⠛⠛⠓⠛⠛⣟⣚⡀⣛⠛⠛⣛⣛⡛⠛⣈⣛⡛⡋⡛⠛⠃⡘⣙⠛⠛⠛⠙⠛⠛⢁⣀⠀⢀⢀⢀⠀⢀⠀⠀⢀⣀⠀⢀⣀⢀⣀ ⠃⠛⠻⠟⠛⠉⠫⠛⠙⠛⠃⠐⡋⡇⠹⠟⡇⠙⠛⠛⠃⠙⠛⠙⠙⠛⠈⠀⠛⠛⠙⠛⠛⠀⠛⠛⠛⠛⠛⠛⠀⠛⠛⠟⠛⠀⢫⠋⠛⠃⠃⠘⠛⠙⠙⠛⠙⠃⠘⠛⠃⠘⠛⠛⠙⠛⠛⠁⠈⠀⠈⠛⠛⠙⠋⠛⠛⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⣍⢉⣍⣉⣉⣍⣉⣉⠉⡍⢩⣍⣉⣉⣉⣉⡉⢩⡉⢩⣭⣉⣉⣉⣉⣉⣩⠉⢩⠉⣭⣭⢉⣭⣭⣉⣭⣭⠉⣉⠉⣭⣉⣍⣉⡍⣉⣍⣉⣉⣍⡉⡍⢩⣍⣉⣩⣉⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉ ⣁⣀⣉⣉⣉⣉⣉⣁⣀⣁⢈⣉⣉⣉⣉⣉⣁⣈⡁⣈⣉⣉⣉⣁⣙⣉⣉⣀⣨⢀⣉⣉⣈⣉⣉⣉⣉⣉⣀⣉⣀⣉⣉⣉⣉⣍⣁⣉⣉⣁⣉⣁⣁⣈⣉⣉⣉⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⠀⠀⠀⠀⢀⣀⣄⡀⠀⡄⢠⣤⣀⣀⣀⣀⡄⢨⡄⠙⣠⣱⡄⣤⣤⣄⣀⠀⢸⠀⣤⣥⠀⣤⣤⠀⣤⣤⠀⣤⠀⣤⣤⡤⢠⣤⣤⣤⣤⣤⣤⣄⣠⣤⣤⣤⢀⣠⣤⣄⣠⣤⣤⣤⣤⣤⢤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀ ⡤⠀⠀⠀⢀⣍⣭⣅⠀⣅⣨⣭⣬⣭⢩⣭⣅⣨⡅⡀⣨⣭⡅⣭⣭⣅⣬⡀⢨⠀⣭⣭⠨⢭⣥⠨⣬⣥⠀⣥⠀⣭⣭⡭⢠⣭⣭⣥⣍⣍⣭⣥⣬⣭⣍⣨⣍⣬⣭⣅⣨⣭⣍⣉⣭⣭⢭⣩⣩⣭⣭⣭⡀⠀⠀⠀⡀⠀ ⠁⠀⠀⠀⢀⣍⣭⡅⠀⡍⢩⣬⣉⣩⣭⣩⡅⢨⡄⠀⢨⣭⠁⣤⣭⣅⣬⠀⢸⠀⣬⣭⢠⢭⣬⢠⣭⣩⠀⣤⠀⣭⣭⣥⣤⣭⣥⣭⣭⣥⣭⣭⣭⣭⣅⣨⣍⣬⣭⣥⢬⣭⣩⣉⣭⢭⣬⣬⠍⠉⠉⠉⠀⠀⢀⠀⠈⠀ ⠀⠀⠀⠀⠀⣍⣭⡅⠀⡅⢨⣯⣬⣭⣭⣭⡅⢸⡄⠁⢨⣼⠅⣤⣝⣅⣬⠀⢨⠀⣬⣬⢠⣽⣯⢤⣭⣭⠀⣤⠀⣭⣯⡭⢩⣭⣭⣭⣍⢠⣭⣭⣍⣡⣤⣤⣭⣌⣥⣬⣌⣥⣬⣭⣭⣼⣤⣭⣥⣠⢤⣤⣤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣥⣧⡇⠀⡆⢰⣯⣤⣤⣭⣌⡄⢠⡄⠀⢸⣼⡄⣴⣟⣤⣬⠀⢰⠀⣴⣼⢠⣶⣶⣤⣼⣶⠀⣤⠀⣷⣥⣥⣤⣥⣭⠡⣁⠠⣦⣦⣧⣶⣦⣆⡅⠀⠈⠉⢀⠈⠈⠁⠉⢈⠈⠈⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣤⣦⡄⠀⡆⢰⣦⢤⣤⣤⡤⡆⠰⡄⠀⢰⣴⡄⣴⣿⣤⣤⠀⢰⠀⣴⣶⢠⣴⣶⣠⣶⣶⠀⣤⠀⣶⣶⣶⡆⣶⣶⣶⢰⣶⣶⣶⣶⣶⣶⣦⣴⣆⢴⣶⣶⣶⣶⣶⣾⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⠤⠤⠤⠤⠤⠬⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⢼⡤⡤⠤⢤⠤⠤⠤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠧⠤⠤⠼⠤⠤⠤⢤⠥⠭⣤⣬⣤⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤ ⣆⣶⣶⣶⣦⠴⡿⣆⢴⣶⡆⢰⡦⡆⣴⣶⡆⢼⣇⣗⡆⢰⣦⣴⣤⣴⠀⢰⣶⣤⣤⣤⣤⣾⣤⣥⣶⠀⣶⣶⣦⠨⣷⣶⡤⣤⡀⢐⣶⣤⣦⡤⢹⡖⡆⡆⣆⡀⢰⣶⡦⢴⡦⢴⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⢤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡤⡤⠤⠤⠤⠤⠤⠤⠤⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠤⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠇⠷⠷⠷⠷⠶⠷⠧⠶⠿⠇⠰⡿⠇⠶⠾⠇⠾⠾⠿⠆⠰⠶⠶⠸⠶⠶⠰⠀⠾⠾⠾⠾⠾⠿⠾⠿⠿⠷⠶⠀⠷⣶⠶⠶⠦⠰⠶⠆⠗⠖⠶⠶⠦⠰⠶⠆⠠⠶⠷⠶⠦⠲⠶⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠶⠷⠮⠾⠿⠇⠰⡯⠗⠶⡿⠇⠺⠿⠿⠇⠰⠶⠾⠼⠶⠶⠲⠀⠿⠸⠶⠶⠴⠷⠶⠾⠀⡶⠶⠶⠶⠀⣧⠖⢇⡤⡰⠶⠶⠶⠶⠇⠰⢧⠲⠆⠄⠰⡶⠆⠠⠲⠷⠶⠶⠲⠾⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠯⠿⠷⠿⠷⠶⠷⠷⠺⠿⠇⠐⡿⠧⠾⠿⠇⠾⠾⠾⠇⠰⠶⢾⠼⠶⠶⠰⠀⠿⠹⠶⠼⠶⠷⠶⠾⠀⠿⠶⠶⠶⠧⠀⠶⢶⠶⠶⠷⠀⠇⠰⠶⠇⠒⠇⠰⠶⠆⠰⠲⠷⠶⠶⠲⠾⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠺⠗⠷⠺⠿⠇⠠⠿⠇⠾⠿⠇⠸⠿⠿⠇⠰⠶⢾⠼⠴⠶⠒⠀⠿⠿⠴⠶⠷⠾⠴⣶⠀⠾⠶⠶⠷⠶⠶⠀⠖⠿⠶⠶⠲⠶⠵⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠿⠚⠟⠷⠺⠿⠇⠸⠷⠆⠻⠿⠇⠹⠿⠾⠇⠰⠾⢾⠼⢾⠶⠚⠀⠻⠷⠶⠸⠿⣶⠿⠶⡶⠀⠷⠷⠶⠧⠠⠒⠿⠷⠶⠲⠶⠿⠗⠀⠷⠆⠰⠶⢶⠾⢷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠯⠿⠿⠿⠷⠚⠟⠷⠺⠿⠇⢰⣿⡇⠟⠿⢆⡘⠿⠻⠇⠺⠾⠺⠺⠾⠸⠄⠺⠶⠺⡾⠾⠤⠾⠿⠶⠿⠻⠧⠤⠶⠷⠗⠇⠟⠶⠇⠰⠷⠷⠷⠇⠆⢀⣷⢶⠷⠾⠷⠻⠷⠾⠾⠶⠾⠀⠺⠾⠺⠾⠾⠀⠀⠀⠀⠀⠀ ⡇⡿⡿⡟⡟⠛⡟⡗⠻⣟⡇⠸⢿⡇⠛⠷⠎⠛⢟⠛⠃⠺⠛⠛⠻⠿⠘⠀⠻⠛⠿⠿⠺⢻⠀⠹⠿⠀⠟⠟⡷⠟⠀⠛⠟⠟⠓⠀⠁⠚⡟⡟⠗⠛⠿⠟⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡗⡟⣟⡟⡟⠛⡟⡗⠛⣟⡇⠘⣿⡏⠛⠟⡇⠚⢿⣛⠃⠘⠻⢛⢸⣺⠻⠘⠀⠛⠻⠟⢸⣛⠿⢻⠛⠿⠂⢛⡛⠟⠛⠀⠚⡟⠟⠟⠚⠗⡟⡇⠀⡟⠇⠘⠟⠻⠟⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣋⣛⡋⠛⡋⡓⢛⣛⡃⠨⡟⡃⢛⣋⡃⠘⣛⣙⡃⠘⠛⢛⢘⠛⠛⠘⠀⢛⣛⡛⣘⣛⣿⣛⣛⣿⠀⣛⠛⠛⡓⣀⠛⠛⡛⠛⣛⡛⠛⡃⠀⠛⡃⠘⠛⠿⠛⡻⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣓⣛⣻⣛⡛⢛⡛⡓⢓⣟⡃⢠⡏⡃⢛⣟⡇⢙⣛⣓⡃⠘⠛⢛⢚⠛⠛⠙⠀⢘⣿⣛⣓⣓⣛⣛⣛⣚⠀⣛⡛⠋⠛⡃⠛⡛⠛⡈⠛⠛⡛⠃⠐⠛⠛⡛⠓⠙⠛⠛⡃⡘⠛⠃⠘⠛⠻⠛⠻⠓⠀⠀⠀⠀⠀⠀⠀⠀ ⣓⣛⣛⣭⡛⢙⣏⡛⢙⣛⡃⢘⡏⡃⢻⣫⠅⢙⣛⣛⡃⠘⠛⢛⢚⠙⠛⠘⠀⢘⣟⣛⣓⣓⣛⣛⣛⣚⠀⣛⠛⠛⡛⣛⡛⠛⣘⠛⣛⡋⠛⡛⠃⠐⡙⠛⠛⠛⢙⣛⡛⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣫⣏⣝⣛⢉⣋⡛⢙⣛⡃⢈⣏⡇⣚⣛⡃⢘⣛⣛⡃⢘⢛⢻⢘⢛⢛⢑⠀⢘⣻⣛⣷⣓⣻⣟⣛⢘⠀⣛⣛⠋⢛⡣⡛⣛⠛⣀⡟⠛⡋⡃⡐⠙⠛⡛⠛⠙⡛⢛⣁⡘⠛⠃⠘⠛⠻⠛⠻⠓⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⣛⢉⣋⡛⢙⣛⡃⠘⣯⡇⣘⡛⡃⣘⣛⣛⡃⢘⢛⢛⢚⢛⢛⠉⣀⡙⢙⠛⠛⠓⠛⠛⣟⣚⡀⣛⠛⠛⣛⣛⡛⠛⣈⣛⡛⡋⡛⠛⠃⡘⣙⠛⠛⠛⠙⠛⠛⢁⣀⠀⢀⢀⢀⠀⢀⠀⠀⢀⣀⠀⢀⣀⢀⣀ ⠃⠛⠻⠟⠛⠉⠫⠛⠙⠛⠃⠐⡋⡇⠹⠟⡇⠙⠛⠛⠃⠙⠛⠙⠙⠛⠈⠀⠛⠛⠙⠛⠛⠀⠛⠛⠛⠛⠛⠛⠀⠛⠛⠟⠛⠀⢫⠋⠛⠃⠃⠘⠛⠙⠙⠛⠙⠃⠘⠛⠃⠘⠛⠛⠙⠛⠛⠁⠈⠀⠈⠛⠛⠙⠋⠛⠛⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⣍⢉⣍⣉⣉⣍⣉⣉⠉⡍⢩⣍⣉⣉⣉⣉⡉⢩⡉⢩⣭⣉⣉⣉⣉⣉⣩⠉⢩⠉⣭⣭⢉⣭⣭⣉⣭⣭⠉⣉⠉⣭⣉⣍⣉⡍⣉⣍⣉⣉⣍⡉⡍⢩⣍⣉⣩⣉⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉ ⣁⣀⣉⣉⣉⣉⣉⣁⣀⣁⢈⣉⣉⣉⣉⣉⣁⣈⡁⣈⣉⣉⣉⣁⣙⣉⣉⣀⣨⢀⣉⣉⣈⣉⣉⣉⣉⣉⣀⣉⣀⣉⣉⣉⣉⣍⣁⣉⣉⣁⣉⣁⣁⣈⣉⣉⣉⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⠀⠀⠀⠀⢀⣀⣄⡀⠀⡄⢠⣤⣀⣀⣀⣀⡄⢨⡄⠙⣠⣱⡄⣤⣤⣄⣀⠀⢸⠀⣤⣥⠀⣤⣤⠀⣤⣤⠀⣤⠀⣤⣤⡤⢠⣤⣤⣤⣤⣤⣤⣄⣠⣤⣤⣤⢀⣠⣤⣄⣠⣤⣤⣤⣤⣤⢤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀ ⡤⠀⠀⠀⢀⣍⣭⣅⠀⣅⣨⣭⣬⣭⢩⣭⣅⣨⡅⡀⣨⣭⡅⣭⣭⣅⣬⡀⢨⠀⣭⣭⠨⢭⣥⠨⣬⣥⠀⣥⠀⣭⣭⡭⢠⣭⣭⣥⣍⣭⣭⣥⣬⣭⣍⣨⣍⣬⣭⣅⣨⣭⣍⣉⣭⣭⢭⣩⣩⣭⣭⣭⡀⠀⠀⠀⡀⠀ ⠁⠀⠀⠀⢀⣍⣭⡅⠀⡍⢩⣬⣉⣩⣭⣩⡅⢨⡄⠀⢨⣭⠁⣤⣭⣅⣬⠀⢸⠀⣬⣭⢠⢭⣬⢠⣭⣩⠀⣤⠀⣭⣭⣥⣤⣭⣥⣭⣭⣥⣭⣭⣭⣭⣅⣨⣍⣬⣭⣥⢬⣭⣩⣉⣭⢭⣬⣬⠍⠉⠉⠉⠀⠀⢀⠀⠈⠀ ⠀⠀⠀⠀⠀⣍⣭⡅⠀⡅⢨⣯⣬⣭⣭⣭⡅⢸⡄⠁⢨⣼⠅⣤⣝⣅⣬⠀⢨⠀⣬⣬⢠⣽⣯⢤⣭⣭⠀⣤⠀⣭⣯⡭⢩⣭⣭⣭⣍⢠⣭⣭⣍⣡⣤⣤⣭⣌⣥⣬⣌⣥⣬⣭⣭⣼⣤⣭⣥⣠⢤⣤⣤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣥⣧⡇⠀⡆⢰⣯⣤⣤⣭⣌⡄⢠⡄⠀⢸⣼⡄⣴⣟⣤⣬⠀⢰⠀⣴⣼⢠⣶⣶⣤⣼⣶⠀⢤⠀⣷⣥⣥⣤⣥⣭⠡⣁⠠⣦⣦⣧⣶⣦⣆⡅⠀⠈⠉⢀⠈⠈⠁⠉⢈⠈⠈⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣤⣦⡄⠀⡆⢰⣦⢤⣤⣤⡤⡆⠰⡄⠀⢰⣴⡄⣴⣿⣤⣤⠀⢰⠀⣴⣶⢠⣴⣶⣠⣶⣶⠀⣤⠀⣶⣶⣶⡆⣶⣶⣶⢰⣶⣶⣶⣶⣶⣶⣦⣴⣆⢴⣶⣶⣶⣶⣶⣾⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⠤⠤⠤⠤⠤⠬⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⢼⡤⡤⠤⢤⠤⠤⠤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠧⠤⠤⠼⠤⠤⠤⢤⠥⠭⣤⣬⣤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤ ⣆⣶⣶⣶⣦⠴⡿⣦⢴⣶⡆⢰⡦⡆⣴⣶⡆⢼⣇⣗⡆⢰⣦⣴⣤⣴⠀⢰⣶⣤⣤⣤⣤⣾⣤⣥⣶⠀⣶⣶⣦⠨⣷⣶⡤⣤⡀⢐⣶⣤⣦⡤⢹⡖⡆⡆⣆⡀⢰⣶⡦⢴⡦⢴⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⢤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡤⡤⠤⠤⠤⠤⠤⠤⠤⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠤⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠇⠷⠷⠷⠷⠶⠷⠧⠶⠿⠇⠰⡿⠇⠶⠾⠇⠾⠾⠿⠆⠰⠶⠶⠸⠶⠶⠰⠀⠾⠾⠺⠾⠾⠿⠾⠿⠿⠷⠶⠀⠷⣶⠶⠶⠦⠰⠶⠆⠗⠖⠶⠶⠦⠰⠶⠆⠠⠶⠷⠶⠦⠲⠶⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠶⠷⠮⠾⠿⠇⠰⡯⠗⠶⡿⠇⠺⠿⠿⠇⠰⠶⠾⠼⠶⠶⠲⠀⠿⠸⠶⠶⠴⠷⠶⠾⠀⡶⠶⠶⠶⠀⣧⠖⢇⡤⡰⠶⠶⠶⠶⠇⠰⢧⠲⠆⠄⠰⡶⠆⠠⠲⠷⠶⠶⠲⠾⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠯⠿⠷⠿⠷⠶⠷⠷⠺⠿⠇⠐⡿⠧⠾⠿⠇⠾⠾⠾⠇⠰⠶⢾⠼⠶⠶⠰⠀⠿⠹⠶⠼⠶⠷⠶⠾⠀⠿⠶⠶⠶⠷⠀⠶⢶⠶⠶⠷⠀⠇⠰⠶⠇⠒⠇⠰⠶⠆⠰⠲⠷⠶⠶⠲⠾⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠺⠗⠷⠺⠿⠇⠠⠿⠇⠾⠿⠇⠸⠿⠿⠇⠰⠶⢾⠼⠴⠶⠒⠀⠿⠿⠴⠶⠷⠾⠴⣶⠀⠾⠶⠶⠷⠶⠶⠀⠖⠿⠶⠶⠲⠶⠵⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠿⠚⠟⠷⠺⠿⠇⠸⠷⠆⠻⠿⠇⠹⠿⠾⠇⠰⠾⢾⠼⢾⠶⠚⠀⠻⠷⠶⠸⠿⣶⠿⠶⡶⠀⠷⠷⠶⠧⠠⠒⠿⠷⠶⠲⠶⠿⠗⠀⠷⠆⠰⠶⢶⠾⢷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠯⠿⠿⠿⠷⠚⠟⠷⠺⠿⠇⢰⣿⡇⠟⠿⢆⡘⠿⠻⠇⠺⠾⠺⠺⠾⠘⠀⠺⠶⠺⡾⠾⠤⠾⠿⠶⠿⠻⠧⠤⠶⠷⠗⠇⠟⠶⠇⠰⠷⠷⠷⠇⠆⢀⣷⢶⠷⠾⠷⠻⠷⠾⠾⠶⠾⠀⠺⠾⠺⠾⠾⠀⠀⠀⠀⠀⠀ ⡇⡿⡿⡟⡟⠛⡟⡗⠻⣟⡇⠸⣿⡇⠛⠷⠎⠛⢟⠛⠃⠺⠛⠛⠻⠿⠘⠀⠻⠛⠿⠿⠺⢻⠀⠹⠿⠀⠟⠟⡷⠟⠀⠛⠟⠟⠓⠀⠁⠚⡟⡟⠗⠛⠿⠟⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡗⡟⣟⡟⡟⠛⡟⡗⠛⣟⡇⠘⣿⡏⠛⠟⡇⠚⢿⣛⠃⠘⠻⢛⢸⣺⠻⠘⠀⠛⠻⠟⢸⣛⠿⢻⠛⠿⠂⢛⡛⠟⠛⠀⠚⡟⠟⠟⠚⠗⡟⡇⠀⡟⠇⠘⠟⠻⠟⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣋⣛⡋⠛⡋⡓⢛⣛⡃⢨⡟⡃⢛⣋⡃⢘⣛⣙⡃⠘⠛⢛⢘⠛⠛⠘⠀⢛⣛⡛⣘⣛⣿⣛⣛⣿⠀⣛⠛⠛⡓⣀⠛⠛⡛⠛⣛⡛⠛⡃⠀⠛⡃⠘⠛⠿⠛⡻⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣓⣛⣻⣛⡛⢛⡛⡓⢓⣟⡃⢠⡏⡃⢛⣟⡇⢙⣛⣓⡃⠘⠛⢛⢚⠛⠛⠙⠀⢘⣿⣛⣓⣓⣛⣛⣛⣚⠀⣛⡛⠋⠛⡃⠛⡛⠛⡈⠛⠛⡛⠃⠐⠛⠛⡛⠓⠙⠛⠛⡃⡘⠛⠃⠘⠛⠻⠛⠻⠓⠀⠀⠀⠀⠀⠀⠀⠀ ⣓⣛⣛⣍⡛⢙⣏⡛⢙⣛⡃⢘⡏⡃⢻⣫⠅⢙⣛⣛⡃⠘⠛⢛⢚⠙⠛⠘⠀⢘⣟⣛⣓⣓⣛⣛⣛⣚⠀⣛⠛⠛⡛⣛⡛⠛⣘⠛⣛⡋⠛⡛⠃⠐⡙⠛⠛⠛⢙⣛⡛⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣫⣏⣝⣛⢉⣋⡛⢙⣛⡃⢈⣏⡇⣚⣛⡃⢘⣛⣛⡃⢘⢛⢻⢘⢛⢛⢑⠀⢘⣻⣛⣷⣓⣻⣟⣛⢘⠀⣛⣛⠋⢛⡣⡛⣛⠛⣀⡟⠛⡋⡃⡐⠙⠛⡛⠛⠙⡛⢛⣁⡘⠛⠃⠘⠛⠻⠛⠻⠓⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⣛⢉⣋⡛⢙⣛⡃⠘⣯⡇⣘⡛⡃⣘⣛⣛⡃⢘⢛⢛⢚⢛⢛⠉⣀⡙⢙⠛⠛⠓⠛⠛⣟⣚⡀⣛⠛⠛⣛⣛⡛⠛⣈⣛⡛⡋⡛⠛⠃⡘⣙⠛⠛⠛⠙⠛⠛⢁⣀⠀⢀⢀⢀⠀⢀⠀⠀⢀⣀⠀⢀⣀⢀⣀ ⠃⠛⠻⠟⠛⠉⠫⠛⠙⠛⠃⠐⡋⡇⠹⡟⡇⠙⠛⠛⠃⠙⠛⠙⠙⠛⠈⠀⠛⠛⠙⠛⠛⠀⠛⠛⠛⠛⠛⠛⠀⠛⠛⠟⠛⠀⢯⠋⠛⠃⠃⠘⠛⠙⠙⠛⠙⠃⠘⠛⠃⠘⠛⠛⠙⠛⠛⠁⠈⠀⠈⠛⠛⠙⠋⠛⠛⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⣍⢉⣍⣉⣉⣍⣉⣉⠉⡍⢩⣍⣉⣉⣉⣉⡉⢩⡉⢩⣭⣉⣉⣉⣉⣉⣩⠉⢩⠉⣭⣭⢉⣭⣭⣉⣭⣭⠉⣉⠉⣭⣉⣍⣉⡍⣉⣍⣉⣉⣍⡉⡍⢩⣍⣉⣩⣉⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉ ⣁⣀⣉⣉⣉⣉⣉⣁⣀⣁⢈⣉⣉⣉⣉⣉⣁⣈⡁⣈⣉⣉⣉⣁⣙⣉⣉⣀⣨⢀⣉⣉⣈⣉⣉⣉⣉⣉⣀⣉⣀⣉⣉⣉⣉⣍⣁⣉⣉⣁⣉⣁⣁⣈⣉⣉⣉⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⠀⠀⠀⠀⢀⣀⣄⡀⠀⡄⢠⣤⣀⣀⣀⣀⡄⢨⡄⠙⣠⣱⡄⣤⣤⣄⣀⠀⢸⠀⣤⣥⠀⣤⣤⠀⣤⣤⠀⣤⠀⣤⣤⡤⢠⣤⣤⣤⣤⣤⣤⣄⣠⣤⣤⣤⢀⣠⣤⣄⣠⣤⣤⣤⣤⣤⢤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀ ⡤⠀⠀⠀⢀⣍⣭⣅⠀⣅⣨⣭⣬⣭⢩⣭⣅⣨⡅⡀⣨⣭⡅⣭⣭⣅⣬⡀⢨⠀⣭⣭⠨⢭⣥⠨⣬⣥⠀⣥⠀⣭⣭⡭⢠⣭⣭⣥⣍⣍⣭⣥⣌⣭⣍⣨⣍⣬⣭⣅⣨⣭⣍⣉⣭⣭⢭⣩⣩⣭⣭⣭⡀⠀⠀⠀⡀⠀ ⠁⠀⠀⠀⢀⣍⣭⡅⠀⡅⢩⣬⣉⣩⣭⣩⡅⢨⡄⠀⢨⣭⠁⣤⣭⣅⣬⠀⢸⠀⣬⣭⢠⢭⣬⢠⣭⣩⠀⣤⠀⣭⣭⣥⣤⣭⣥⣭⣭⣥⣭⣭⣭⣭⣅⣨⣍⣬⣭⣥⢬⣭⣩⣉⣭⢭⣬⣬⠍⠉⠉⠉⠀⠀⢀⠀⠈⠀ ⠀⠀⠀⠀⠀⣍⣭⡅⠀⡅⢨⣯⣬⣭⣭⣭⡅⢸⡄⠁⢨⣼⠅⣤⣝⣅⣬⠀⢨⠀⣬⣬⢠⣽⣯⢤⣭⣭⠀⣤⠀⣭⣯⡭⢩⣭⣭⣭⣍⢠⣭⣭⣍⣡⣤⣤⣭⣌⣥⣬⣌⣥⣬⣭⣭⣼⣤⣭⣥⣠⢤⣤⣤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣥⣧⡇⠀⡆⢰⣯⣤⣤⣭⣌⡄⢠⡄⠀⢸⣼⡄⣴⣟⣤⣬⠀⢰⠀⣴⣼⢠⣶⣶⣤⣼⣶⠀⣤⠀⣷⣥⣥⣤⣥⣭⠡⣁⠠⣦⣦⣧⣶⣦⣆⡅⠀⠈⠉⢀⠈⠈⠁⠉⢈⠈⠈⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣤⣦⡄⠀⡆⢰⣦⢤⣤⣤⡤⡆⠰⡄⠀⢰⣴⡄⣴⣿⣤⣤⠀⢰⠀⣴⣶⢠⣴⣶⣠⣶⣶⠀⣤⠀⣶⣶⣶⡆⣶⣶⣶⢰⣶⣶⣶⣶⣶⣶⣦⣴⣆⢴⣶⣶⣶⣶⣶⣾⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⠤⠤⠤⠤⠤⠬⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⢼⡤⡤⠤⢤⠤⠤⠤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠧⠤⠤⠼⠤⠤⠤⢤⠥⠭⣤⣬⣤⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤ ⣆⣶⣶⣶⣦⠴⡿⣆⢴⣶⡆⢰⡦⡆⣴⣶⡆⢼⣇⣗⡆⢰⣦⣴⣤⣴⠀⢰⣶⣤⣤⣤⣤⣾⣤⣥⣶⠀⣶⣶⣦⠨⣷⣶⡤⣤⡀⢐⣶⣤⣦⡤⢹⡖⡆⡆⣆⡀⢰⣶⡦⢴⡦⢴⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⢤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡤⡤⠤⠤⠤⠤⠤⠤⠤⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠤⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠇⠷⠷⠷⠷⠶⠷⠧⠶⠿⠇⠰⡿⠇⠶⠾⠇⠾⠾⠿⠆⠰⠶⠶⠸⠶⠶⠰⠀⠾⠾⠺⠾⠾⠿⠾⠿⠿⠷⠶⠀⠷⣶⠶⠶⠦⠰⠶⠆⠗⠖⠶⠶⠦⠰⠶⠆⠠⠶⠷⠶⠦⠲⠶⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠶⠷⠮⠾⠿⠇⠰⡯⠗⠶⡿⠇⠺⠿⠿⠇⠰⠶⠾⠼⠶⠶⠲⠀⠿⠸⠶⠶⠴⠷⠶⠾⠀⡶⠶⠶⠶⠀⣧⠖⢇⡤⡰⠶⠶⠶⠶⠇⠰⢧⠲⠆⠄⠰⡶⠆⠠⠲⠷⠶⠶⠲⠾⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠯⠿⠷⠿⠷⠶⠷⠷⠺⠿⠇⠐⡿⠧⠾⠿⠇⠾⠾⠾⠇⠰⠶⢾⠼⠶⠶⠰⠀⠿⠹⠶⠼⠶⠷⠶⠾⠀⠿⠶⠶⠶⠷⠀⠶⢶⠶⠶⠷⠀⠇⠰⠶⠇⠒⠇⠰⠶⠆⠰⠲⠷⠶⠶⠲⠾⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠺⠗⠷⠺⠿⠇⠠⠿⠆⠾⠿⠇⠸⠿⠿⠇⠰⠶⢾⠼⠴⠶⠒⠀⠿⠿⠴⠶⠷⠾⠴⣶⠀⠾⠶⠶⠷⠶⠶⠀⠖⠿⠶⠶⠲⠶⠵⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠿⠚⠟⠷⠺⠿⠇⠸⠷⠆⠻⠿⠇⠹⠿⠾⠇⠰⠾⢾⠼⢾⠶⠚⠀⠻⠷⠶⠸⠿⣶⠿⠶⡶⠀⠷⠷⠶⠧⠠⠒⠿⠷⠶⠲⠶⠿⠗⠀⠷⠆⠰⠶⢶⠾⢷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠯⠿⠿⠿⠷⠚⠟⠷⠺⠿⠇⢰⣿⡇⠟⠿⢆⡘⠿⠻⠇⠺⠾⠺⠺⠾⠘⠀⠺⠶⠺⡾⠾⠤⠾⠿⠶⠿⠻⠧⠤⠶⠷⠗⠇⠟⠶⠇⠰⠷⠷⠷⠇⠆⢀⣷⢶⠷⠾⠷⠻⠷⠾⠾⠶⠾⠀⠺⠾⠺⠾⠾⠀⠀⠀⠀⠀⠀ ⡇⡿⡿⡟⡟⠛⡟⡗⠻⣟⡇⠸⣿⡇⠛⠷⠎⠛⢟⠛⠃⠺⠛⠛⠻⠿⠘⠀⠻⠛⠿⠿⠺⢻⠀⠹⠿⠀⠟⠟⡷⠟⠀⠛⠟⠟⠓⠀⠁⠚⡟⡟⠗⠛⠿⠟⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡗⡟⣟⡟⡟⠛⡟⡗⠛⣟⡇⠘⣿⡏⠛⠟⡇⠚⢿⣛⠃⠘⠻⢛⢸⣺⠻⠘⠀⠛⠻⠟⢸⣛⠿⢻⠛⠿⠂⢛⡛⠟⠛⠀⠚⡟⠟⠟⠚⠗⡟⡇⠀⡟⠇⠘⠟⠻⠟⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣋⣛⡋⠛⡋⡓⢛⣛⡃⢨⡟⡃⢛⣋⡃⢘⣛⣙⡃⠘⠛⢛⢘⠛⠛⠘⠀⢛⣛⡛⣘⣛⣿⣛⣛⣿⠀⣛⠛⠛⡓⣀⠛⠛⡛⠛⣛⡛⠛⡃⠀⠛⡃⠘⠛⠿⠛⡻⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣓⣛⣻⣛⡛⢛⡛⡓⢓⣟⡃⢠⡏⡃⢛⣟⡇⢙⣛⣓⡃⠘⠛⢛⢚⠛⠛⠙⠀⢘⣿⣛⣓⣓⣛⣛⣛⣚⠀⣛⡛⠋⠛⡃⠛⡛⠛⡈⠛⠛⡛⠃⠐⠛⠛⡛⠓⠙⠛⠛⡃⡘⠛⠃⠘⠛⠻⠛⠻⠓⠀⠀⠀⠀⠀⠀⠀⠀ ⣓⣛⣛⣭⡛⢙⣏⡛⢙⣛⡃⢘⡏⡃⢻⣫⠅⢙⣛⣛⡃⠘⠛⢛⢚⠙⠛⠘⠀⢘⣟⣛⣓⣓⣛⣛⣛⣚⠀⣛⠛⠛⡛⣛⡛⠛⣘⠛⣛⡋⠛⡛⠃⠐⡙⠛⠛⠛⢙⣛⡛⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣫⣏⣝⣛⢉⣋⡛⢙⣛⡃⢈⣏⡇⣚⣛⡃⢘⣛⣛⡃⢘⢛⢻⢘⢛⢛⢑⠀⢘⣻⣛⣷⣓⣻⣟⣛⢘⠀⣛⣛⠋⢛⡣⡛⣛⠛⣀⡟⠛⡋⡃⡐⠙⠛⡛⠛⠙⡛⢛⣁⡘⠛⠃⠘⠛⠻⠛⠻⠓⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⣛⢉⣋⡛⢙⣛⡃⠘⣯⡇⣘⡛⡃⣘⣛⣛⡃⢘⢛⢛⢚⢛⢛⠉⣀⡙⢙⠛⠛⠓⠛⠛⣟⣚⡀⣛⠛⠛⣛⣛⡛⠛⣈⣛⡛⡋⡛⠛⠃⡘⣙⠛⠛⠛⠙⠛⠛⢁⣀⠀⢀⢀⢀⠀⢀⠀⠀⢀⣀⠀⢀⣀⢀⣀ ⠃⠛⠻⠟⠛⠉⠫⠛⠙⠛⠃⠐⡋⡇⠹⠟⡇⠙⠛⠛⠃⠙⠛⠙⠙⠛⠈⠀⠛⠛⠙⠛⠛⠀⠛⠛⠛⠛⠛⠛⠀⠛⠛⠟⠛⠀⢫⠋⠛⠃⠃⠘⠛⠙⠙⠛⠙⠃⠘⠛⠃⠘⠛⠛⠙⠛⠛⠁⠈⠀⠈⠛⠛⠙⠋⠛⠛⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⣍⢉⣍⣉⣉⣍⣉⣉⠉⡍⢩⣍⣉⣉⣉⣉⡉⢩⡉⢩⣭⣉⣉⣉⣉⣉⣩⠉⢩⠉⣭⣭⢉⣭⣭⣉⣭⣭⠉⣉⠉⣭⣉⣍⣉⡍⣉⣍⣉⣉⣍⡉⡍⢩⣍⣉⣩⣉⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉ ⣁⣀⣉⣉⣉⣉⣉⣁⣀⣁⢈⣉⣉⣉⣉⣉⣁⣈⡁⣈⣉⣉⣉⣁⣙⣉⣉⣀⣨⢀⣉⣉⣈⣉⣉⣉⣉⣉⣀⣉⣀⣉⣉⣉⣉⣍⣁⣉⣉⣁⣉⣁⣁⣈⣉⣉⣉⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⠀⠀⠀⠀⢀⣀⣄⡀⠀⡄⢠⣤⣀⣀⣀⣀⡄⢨⡄⠙⣠⣱⡄⣤⣤⣄⣀⠀⢸⠀⣤⣥⠀⣤⣤⠀⣤⣤⠀⣤⠀⣤⣤⡤⢠⣤⣤⣤⣤⣤⣤⣄⣠⣤⣤⣤⢀⣠⣤⣄⣠⣤⣤⣤⣤⣤⢤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀ ⡤⠀⠀⠀⢀⣍⣭⣅⠀⣅⣨⣭⣬⣭⢩⣭⣅⣨⡅⡀⣨⣭⡅⣭⣭⣅⣬⡀⢨⠀⣭⣭⠨⢭⣥⠨⣬⣥⠀⣥⠀⣭⣭⡭⢠⣭⣭⣥⣍⣍⣭⣥⣬⣭⣍⣨⣍⣬⣭⣅⣨⣭⣍⣉⣭⣭⢭⣩⣩⣭⣭⣭⡀⠀⠀⠀⡀⠀ ⠁⠀⠀⠀⢀⣍⣭⡅⠀⡍⢩⣬⣉⣩⣭⣩⡅⢨⡄⠀⢨⣭⠁⣤⣭⣅⣬⠀⢸⠀⣬⣭⢠⢭⣬⢠⣭⣩⠀⣤⠀⣭⣭⣥⣤⣭⣥⣭⣭⣥⣭⣭⣭⣭⣅⣨⣍⣬⣭⣥⢬⣭⣩⣉⣭⢭⣬⣬⠍⠉⠉⠉⠀⠀⢀⠀⠈⠀ ⠀⠀⠀⠀⠀⣍⣭⡅⠀⡅⢨⣯⣬⣭⣭⣭⡅⢸⡄⠁⢨⣼⠅⣤⣝⣅⣬⠀⢨⠀⣬⣬⢠⣽⣯⢤⣭⣭⠀⣤⠀⣭⣯⡭⢩⣭⣭⣭⣍⢠⣭⣭⣍⣡⣤⣤⣭⣌⣥⣬⣌⣥⣬⣭⣭⣼⣤⣭⣥⣠⢤⣤⣤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣥⣧⡇⠀⡆⢰⣯⣤⣤⣭⣌⡄⢠⡄⠀⢸⣼⡄⣴⣟⣤⣬⠀⢰⠀⣴⣼⢠⣶⣶⣤⣼⣶⠀⣤⠀⣷⣥⣥⣤⣥⣭⠡⣁⠠⣦⣦⣧⣶⣦⣆⡅⠀⠈⠉⢀⠈⠈⠁⠉⢈⠈⠈⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣤⣦⡄⠀⡆⢰⣦⢤⣤⣤⡤⡆⠰⡄⠀⢰⣴⡄⣴⣿⣤⣤⠀⢰⠀⣴⣶⢠⣴⣶⣠⣶⣶⠀⣤⠀⣶⣶⣶⡆⣶⣶⣶⢰⣶⣶⣶⣶⣶⣶⣦⣴⣆⢴⣶⣶⣶⣶⣶⣾⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⠤⠤⠤⠤⠤⠬⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⢼⡤⡤⠤⢤⠤⠤⠤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠧⠤⠤⠼⠤⠤⠤⢤⠥⠭⣤⣬⣤⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤ ⣆⣶⣶⣶⣦⠴⡿⣆⢴⣶⡆⢰⡦⡆⣴⣶⡆⢼⣇⣗⡆⢰⣦⣴⣤⣴⠀⢰⣶⣤⣤⣤⣤⣾⣤⣥⣶⠀⣶⣶⣦⠨⣷⣶⡤⣤⡀⢐⣶⣤⣦⡤⢹⡖⡆⡆⣆⡀⢰⣶⡦⢴⡦⢴⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⢤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡤⡤⠤⠤⠤⠤⠤⠤⠤⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠤⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠇⠷⠷⠷⠷⠶⠷⠧⠶⠿⠇⠰⡿⠇⠶⠾⠇⠾⠾⠿⠆⠰⠶⠶⠸⠶⠶⠰⠀⠾⠾⠾⠾⠾⠿⠾⠿⠿⠷⠶⠀⠷⣶⠶⠶⠦⠰⠶⠆⠗⠖⠶⠶⠦⠰⠶⠆⠠⠶⠷⠶⠦⠲⠶⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠶⠷⠮⠾⠿⠇⠰⡯⠗⠶⡿⠇⠺⠿⠿⠇⠰⠶⠾⠼⠶⠶⠲⠀⠿⠸⠶⠶⠴⠷⠶⠾⠀⡶⠶⠶⠶⠀⣧⠖⢇⡤⡰⠶⠶⠶⠶⠇⠰⢧⠲⠆⠄⠰⡶⠆⠠⠲⠷⠶⠶⠲⠾⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠯⠿⠷⠿⠷⠶⠷⠷⠺⠿⠇⠐⡿⠧⠾⠿⠇⠾⠾⠾⠇⠰⠶⢾⠼⠶⠶⠰⠀⠿⠹⠶⠼⠶⠷⠶⠾⠀⠿⠶⠶⠶⠧⠀⠶⢶⠶⠶⠷⠀⠇⠰⠶⠇⠒⠇⠰⠶⠆⠰⠲⠷⠶⠶⠲⠾⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠺⠗⠷⠺⠿⠇⠠⠿⠇⠾⠿⠇⠸⠿⠿⠇⠰⠶⢾⠼⠴⠶⠒⠀⠿⠿⠴⠶⠷⠾⠴⣶⠀⠾⠶⠶⠷⠶⠶⠀⠖⠿⠶⠶⠲⠶⠵⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠿⠚⠟⠷⠺⠿⠇⠸⠷⠆⠻⠿⠇⠹⠿⠾⠇⠰⠾⢾⠼⢾⠶⠚⠀⠻⠷⠶⠸⠿⣶⠿⠶⡶⠀⠷⠷⠶⠧⠠⠒⠿⠷⠶⠲⠶⠿⠗⠀⠷⠆⠰⠶⢶⠾⢷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠯⠿⠿⠿⠷⠚⠟⠷⠺⠿⠇⢰⣿⡅⠟⠿⢆⡘⠿⠻⠇⠺⠾⠺⠺⠾⠘⠀⠺⠶⠺⡾⠾⠤⠾⠿⠶⠿⠻⠧⠤⠶⠷⠗⠇⠟⠶⠇⠰⠷⠷⠷⠇⠆⢀⣷⢶⠷⠾⠷⠻⠷⠾⠾⠶⠾⠀⠺⠾⠺⠾⠾⠀⠀⠀⠀⠀⠀ ⡇⡿⡿⡟⡟⠛⡟⡗⠻⣟⡇⠸⣿⡇⠛⠷⠎⠛⢟⠛⠃⠺⠛⠛⠻⠿⠘⠀⠻⠛⠿⠿⠺⢻⠀⠹⠿⠀⠟⠟⡷⠟⠀⠛⠟⠟⠓⠀⠁⠚⡟⡟⠗⠛⠿⠟⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡗⡟⣟⡟⡟⠛⡟⡗⠛⣟⡇⠘⣿⡏⠛⠟⡇⠚⢿⣛⠃⠘⠻⢛⢸⣺⠻⠘⠀⠛⠻⠟⢸⣛⠿⢻⠛⠿⠂⢛⡛⠟⠛⠀⠚⡟⠟⠟⠚⠗⡟⡇⠀⡟⠇⠘⠟⠻⠟⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣋⣛⡋⠛⡋⡓⢛⣛⡃⢨⡟⡃⢛⣋⡃⢘⣛⣙⡃⠘⠛⢛⢘⠛⠛⠘⠀⢛⣛⡛⣘⣛⣿⣛⣛⣿⠀⣛⠛⠛⡓⣀⠛⠛⡛⠛⣛⡛⠛⡃⠀⠛⡃⠘⠛⠿⠛⡻⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣓⣛⣻⣛⡛⢛⡛⡓⢓⣟⡃⢠⡏⡃⢛⣟⡇⢙⣛⣓⡃⠘⠛⢛⢚⠛⠛⠙⠀⢘⣿⣛⣓⣓⣛⣛⣛⣚⠀⣛⡛⠋⠛⡃⠛⡛⠛⡈⠛⠛⡛⠃⠐⠛⠛⡛⠓⠙⠛⠛⡃⡘⠛⠃⠘⠛⠻⠛⠻⠓⠀⠀⠀⠀⠀⠀⠀⠀ ⣓⣛⣛⣭⡛⢙⣏⡛⢙⣛⡃⢘⡏⡃⢻⣫⠅⢙⣛⣛⡃⠘⠛⢛⢚⠙⠛⠘⠀⢘⣟⣛⣓⣓⣛⣛⣛⣚⠀⣛⠛⠛⡛⣛⡛⠛⣘⠛⣛⡋⠛⡛⠃⠐⡙⠛⠛⠛⢙⣛⡛⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣫⣏⣝⣛⢉⣋⡛⢙⣛⡃⢈⣏⡇⣚⣛⡃⢘⣛⣛⡃⢘⢛⢻⢘⢛⢛⢑⠀⢘⣻⣛⣷⣓⣻⣟⣛⢘⠀⣛⣛⠋⢛⡣⡛⣛⠛⣀⡟⠛⡋⡃⡐⠙⠛⡛⠛⠙⡛⢛⣁⡘⠛⠃⠘⠛⠻⠛⠻⠓⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⣛⢉⣋⡛⢙⣛⡃⠘⣯⡇⣘⡛⡃⣘⣛⣛⡃⢘⢛⢛⢚⢛⢛⠉⣀⡙⢙⠛⠛⠓⠛⠛⣟⣚⡀⣛⠛⠛⣛⣛⡛⠛⣈⣛⡛⡋⡛⠛⠃⡘⣙⠛⠛⠛⠙⠛⠛⢁⣀⠀⢀⢀⢀⠀⢀⠀⠀⢀⣀⠀⢀⣀⢀⣀ ⠃⠛⠻⠟⠛⠉⠫⠛⠙⠛⠃⠐⡋⡇⠹⠟⡇⠙⠛⠛⠃⠙⠛⠙⠙⠛⠈⠀⠛⠛⠙⠛⠛⠀⠛⠛⠛⠛⠛⠛⠀⠛⠛⠟⠛⠀⢫⠋⠛⠃⠃⠘⠛⠙⠙⠛⠙⠃⠘⠛⠃⠘⠛⠛⠙⠛⠛⠁⠈⠀⠈⠛⠛⠙⠋⠛⠛⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⣍⢉⣍⣉⣉⣍⣉⣉⠉⡍⢩⣍⣉⣉⣉⣉⡉⢩⡉⢩⣭⣉⣉⣉⣉⣉⣩⠉⢩⠉⣭⣭⢉⣭⣭⣉⣭⣭⠉⣉⠉⣭⣉⣍⣉⡍⣉⣍⣉⣉⣍⡉⡍⢩⣍⣉⣩⣉⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉ ⣁⣀⣉⣉⣉⣉⣉⣁⣀⣁⢈⣉⣉⣉⣉⣉⣁⣈⡁⣈⣉⣉⣉⣁⣙⣉⣉⣀⣨⢀⣉⣉⣈⣉⣉⣉⣉⣉⣀⣉⣀⣉⣉⣉⣉⣍⣁⣉⣉⣁⣉⣁⣁⣈⣉⣉⣉⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⠀⠀⠀⠀⢀⣀⣄⡀⠀⡄⢠⣤⣀⣀⣀⣀⡄⢨⡄⠙⣠⣱⡄⣤⣤⣄⣀⠀⢸⠀⣤⣥⠀⣤⣤⠀⣤⣤⠀⣤⠀⣤⣤⡤⢠⣤⣤⣤⣤⣤⣤⣄⣠⣤⣤⣤⢀⣠⣤⣄⣠⣤⣤⣤⣤⣤⢤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀ ⡤⠀⠀⠀⢀⣍⣭⣅⠀⣅⣨⣭⣬⣭⢩⣭⣅⣨⡅⡀⣨⣭⡅⣭⣭⣅⣬⡀⢨⠀⣭⣭⠨⢭⣥⠨⣬⣥⠀⣥⠀⣭⣭⡭⢠⣭⣭⣥⣍⣍⣭⣥⣬⣭⣍⣨⣍⣬⣭⣅⣨⣭⣍⣉⣭⣭⢭⣩⣩⣭⣭⣭⡀⠀⠀⠀⡀⠀ ⠁⠀⠀⠀⢀⣍⣭⡅⠀⡍⢩⣬⣉⣩⣭⣩⡅⢨⡄⠀⢨⣭⠁⣤⣭⣅⣬⠀⢸⠀⣬⣭⢠⢭⣬⢠⣭⣩⠀⣤⠀⣭⣭⣥⣤⣭⣥⣭⣭⣥⣭⣭⣭⣭⣅⣨⣍⣬⣭⣥⢬⣭⣩⣉⣭⢭⣬⣬⠍⠉⠉⠉⠀⠀⢀⠀⠈⠀ ⠀⠀⠀⠀⠀⣍⣭⡅⠀⡅⢨⣯⣬⣭⣭⣭⡅⢸⡄⠁⢨⣼⠅⣤⣝⣅⣬⠀⢨⠀⣬⣬⢠⣽⣯⢤⣭⣭⠀⣤⠀⣭⣯⡭⢩⣭⣭⣭⣍⢠⣭⣭⣍⣡⣤⣤⣭⣌⣥⣬⣌⣥⣬⣭⣭⣼⣤⣭⣥⣠⢤⣤⣤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣥⣧⡇⠀⡆⢰⣯⣤⣤⣭⣌⡄⢠⡄⠀⢸⣼⡄⣴⣟⣤⣬⠀⢰⠀⣴⣼⢠⣶⣶⣤⣼⣶⠀⣤⠀⣷⣥⣥⣤⣥⣭⠡⣁⠠⣦⣦⣧⣶⣦⣆⡅⠀⠈⠉⢀⠈⠈⠁⠉⢈⠈⠈⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣤⣦⡄⠀⡆⢰⣦⢤⣤⣤⡤⡆⠰⡄⠀⢰⣴⡄⣴⣿⣤⣤⠀⢰⠀⣴⣶⢠⣴⣶⣠⣶⣶⠀⣤⠀⣶⣶⣶⡆⣶⣶⣶⢰⣶⣶⣶⣶⣶⣶⣦⣴⣆⢴⣶⣶⣶⣶⣶⣾⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⠤⠤⠤⠤⠤⠬⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⢼⡤⡤⠤⢤⠤⠤⠤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠧⠤⠤⠼⠤⠤⠤⢤⠥⠭⣤⣬⣤⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤ ⣆⣶⣶⣶⣦⠴⡿⣆⢴⣶⡆⢰⡦⡆⣴⣶⡆⢼⣇⣗⡆⢰⣦⣴⣤⣴⠀⢰⣶⣤⣤⣤⣤⣾⣤⣥⣶⠀⣶⣶⣦⠨⣷⣶⡤⣤⡀⢐⣶⣤⣦⡤⢹⡖⡆⡆⣆⡀⢰⣶⡦⢴⡦⢴⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⢤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡤⡤⠤⠤⠤⠤⠤⠤⠤⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠤⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠇⠷⠷⠷⠷⠶⠷⠧⠶⠿⠇⠰⡿⠇⠶⠾⠇⠾⠾⠿⠆⠰⠶⠶⠸⠶⠶⠰⠀⠾⠾⠾⠾⠾⠿⠾⠿⠿⠷⠶⠀⠷⣶⠶⠶⠦⠰⠶⠆⠗⠖⠶⠶⠦⠰⠶⠆⠠⠶⠷⠶⠦⠲⠶⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠶⠷⠮⠾⠿⠇⠰⡯⠗⠶⡿⠇⠺⠿⠿⠇⠰⠶⠾⠼⠶⠶⠲⠀⠿⠸⠶⠶⠴⠷⠶⠾⠀⡶⠶⠶⠶⠀⣧⠖⢇⡤⡰⠶⠶⠶⠶⠇⠰⢧⠲⠆⠄⠰⡶⠆⠠⠲⠷⠶⠶⠲⠾⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠯⠿⠷⠿⠷⠶⠷⠷⠺⠿⠇⠐⡿⠧⠾⠿⠇⠾⠾⠾⠇⠰⠶⢾⠼⠶⠶⠰⠀⠿⠹⠶⠼⠶⠷⠶⠾⠀⠿⠶⠶⠶⠧⠀⠶⢶⠶⠶⠷⠀⠇⠰⠶⠇⠒⠇⠰⠶⠆⠰⠲⠷⠶⠶⠲⠾⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠺⠗⠷⠺⠿⠇⠠⠿⠇⠾⠿⠇⠸⠿⠿⠇⠰⠶⢾⠼⠴⠶⠒⠀⠿⠿⠴⠶⠷⠾⠴⣶⠀⠾⠶⠶⠷⠶⠶⠀⠖⠿⠶⠶⠲⠶⠵⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠿⠚⠟⠷⠺⠿⠇⠸⠷⠆⠻⠿⠇⠹⠿⠾⠇⠰⠾⢾⠼⢾⠶⠚⠀⠻⠷⠶⠸⠿⣶⠿⠶⡶⠀⠷⠷⠶⠧⠠⠒⠿⠷⠶⠲⠶⠿⠗⠀⠷⠆⠰⠶⢶⠾⢷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠯⠿⠿⠿⠷⠚⠟⠷⠺⠿⠇⢰⣿⡇⠟⠿⢆⡘⠿⠻⠇⠺⠾⠺⠺⠾⠸⠄⠺⠶⠺⡾⠾⠤⠾⠿⠶⠿⠻⠧⠤⠶⠷⠗⠇⠟⠶⠇⠰⠷⠷⠷⠇⠆⢀⣷⢶⠷⠾⠷⠻⠷⠾⠾⠶⠾⠀⠺⠾⠺⠾⠾⠀⠀⠀⠀⠀⠀ ⡇⡿⡿⡟⡟⠛⡟⡗⠻⣟⡇⠸⢿⡇⠛⠷⠎⠛⢟⠛⠃⠺⠛⠛⠻⠿⠘⠀⠻⠛⠿⠿⠺⢻⠀⠹⠿⠀⠟⠟⡷⠟⠀⠛⠟⠟⠓⠀⠁⠚⡟⡟⠗⠛⠿⠟⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡗⡟⣟⡟⡟⠛⡟⡗⠛⣟⡇⠘⣿⡏⠛⠟⡇⠚⢿⣛⠃⠘⠻⢛⢸⣺⠻⠘⠀⠛⠻⠟⢸⣛⠿⢻⠛⠿⠂⢛⡛⠟⠛⠀⠚⡟⠟⠟⠚⠗⡟⡇⠀⡟⠇⠘⠟⠻⠟⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣋⣛⡋⠛⡋⡓⢛⣛⡃⠨⡟⡃⢛⣋⡃⠘⣛⣙⡃⠘⠛⢛⢘⠛⠛⠘⠀⢛⣛⡛⣘⣛⣿⣛⣛⣿⠀⣛⠛⠛⡓⣀⠛⠛⡛⠛⣛⡛⠛⡃⠀⠛⡃⠘⠛⠿⠛⡻⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣓⣛⣻⣛⡛⢛⡛⡓⢓⣟⡃⢠⡏⡃⢛⣟⡇⢙⣛⣓⡃⠘⠛⢛⢚⠛⠛⠙⠀⢘⣿⣛⣓⣓⣛⣛⣛⣚⠀⣛⡛⠋⠛⡃⠛⡛⠛⡈⠛⠛⡛⠃⠐⠛⠛⡛⠓⠙⠛⠛⡃⡘⠛⠃⠘⠛⠻⠛⠻⠓⠀⠀⠀⠀⠀⠀⠀⠀ ⣓⣛⣛⣭⡛⢙⣏⡛⢙⣛⡃⢘⡏⡃⢻⣫⠅⢙⣛⣛⡃⠘⠛⢛⢚⠙⠛⠘⠀⢘⣟⣛⣓⣓⣛⣛⣛⣚⠀⣛⠛⠛⡛⣛⡛⠛⣘⠛⣛⡋⠛⡛⠃⠐⡙⠛⠛⠛⢙⣛⡛⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣫⣏⣝⣛⢉⣋⡛⢙⣛⡃⢈⣏⡇⣚⣛⡃⢘⣛⣛⡃⢘⢛⢻⢘⢛⢛⢑⠀⢘⣻⣛⣷⣓⣻⣟⣛⢘⠀⣛⣛⠋⢛⡣⡛⣛⠛⣀⡟⠛⡋⡃⡐⠙⠛⡛⠛⠙⡛⢛⣁⡘⠛⠃⠘⠛⠻⠛⠻⠓⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⣛⢉⣋⡛⢙⣛⡃⠘⣯⡇⣘⡛⡃⣘⣛⣛⡃⢘⢛⢛⢚⢛⢛⠉⣀⡙⢙⠛⠛⠓⠛⠛⣟⣚⡀⣛⠛⠛⣛⣛⡛⠛⣈⣛⡛⡋⡛⠛⠃⡘⣙⠛⠛⠛⠙⠛⠛⢁⣀⠀⢀⢀⢀⠀⢀⠀⠀⢀⣀⠀⢀⣀⢀⣀ ⠃⠛⠻⠟⠛⠉⠫⠛⠙⠛⠃⠐⡋⡇⠹⠟⡇⠙⠛⠛⠃⠙⠛⠙⠙⠛⠈⠀⠛⠛⠙⠛⠛⠀⠛⠛⠛⠛⠛⠛⠀⠛⠛⠟⠛⠀⢫⠋⠛⠃⠃⠘⠛⠙⠙⠛⠙⠃⠘⠛⠃⠘⠛⠛⠙⠛⠛⠁⠈⠀⠈⠛⠛⠙⠋⠛⠛⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⣍⢉⣍⣉⣉⣍⣉⣉⠉⡍⢩⣍⣉⣉⣉⣉⡉⢩⡉⢩⣭⣉⣉⣉⣉⣉⣩⠉⢩⠉⣭⣭⢉⣭⣭⣉⣭⣭⠉⣉⠉⣭⣉⣍⣉⡍⣉⣍⣉⣉⣍⡉⡍⢩⣍⣉⣩⣉⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉ ⣁⣀⣉⣉⣉⣉⣉⣁⣀⣁⢈⣉⣉⣉⣉⣉⣁⣈⡁⣈⣉⣉⣉⣁⣙⣉⣉⣀⣨⢀⣉⣉⣈⣉⣉⣉⣉⣉⣀⣉⣀⣉⣉⣉⣉⣍⣁⣉⣉⣁⣉⣁⣁⣈⣉⣉⣉⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⠀⠀⠀⠀⢀⣀⣄⡀⠀⡄⢠⣤⣀⣀⣀⣀⡄⢨⡄⠙⣠⣱⡄⣤⣤⣄⣀⠀⢸⠀⣤⣥⠀⣤⣤⠀⣤⣤⠀⣤⠀⣤⣤⡤⢠⣤⣤⣤⣤⣤⣤⣄⣠⣤⣤⣤⢀⣠⣤⣄⣠⣤⣤⣤⣤⣤⢤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀ ⡤⠀⠀⠀⢀⣍⣭⣅⠀⣅⣨⣭⣬⣭⢩⣭⣅⣨⡅⡀⣨⣭⡅⣭⣭⣅⣬⡀⢨⠀⣭⣭⠨⢭⣥⠨⣬⣥⠀⣥⠀⣭⣭⡭⢠⣭⣭⣥⣍⣭⣭⣥⣬⣭⣍⣨⣍⣬⣭⣅⣨⣭⣍⣉⣭⣭⢭⣩⣩⣭⣭⣭⡀⠀⠀⠀⡀⠀ ⠁⠀⠀⠀⢀⣍⣭⡅⠀⡍⢩⣬⣉⣩⣭⣩⡅⢨⡄⠀⢨⣭⠁⣤⣭⣅⣬⠀⢸⠀⣬⣭⢠⢭⣬⢠⣭⣩⠀⣤⠀⣭⣭⣥⣤⣭⣥⣭⣭⣥⣭⣭⣭⣭⣅⣨⣍⣬⣭⣥⢬⣭⣩⣉⣭⢭⣬⣬⠍⠉⠉⠉⠀⠀⢀⠀⠈⠀ ⠀⠀⠀⠀⠀⣍⣭⡅⠀⡅⢨⣯⣬⣭⣭⣭⡅⢸⡄⠁⢨⣼⠅⣤⣝⣅⣬⠀⢨⠀⣬⣬⢠⣽⣯⢤⣭⣭⠀⣤⠀⣭⣯⡭⢩⣭⣭⣭⣍⢠⣭⣭⣍⣡⣤⣤⣭⣌⣥⣬⣌⣥⣬⣭⣭⣼⣤⣭⣥⣠⢤⣤⣤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣥⣧⡇⠀⡆⢰⣯⣤⣤⣭⣌⡄⢠⡄⠀⢸⣼⡄⣴⣟⣤⣬⠀⢰⠀⣴⣼⢠⣶⣶⣤⣼⣶⠀⢤⠀⣷⣥⣥⣤⣥⣭⠡⣁⠠⣦⣦⣧⣶⣦⣆⡅⠀⠈⠉⢀⠈⠈⠁⠉⢈⠈⠈⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣤⣦⡄⠀⡆⢰⣦⢤⣤⣤⡤⡆⠰⡄⠀⢰⣴⡄⣴⣿⣤⣤⠀⢰⠀⣴⣶⢠⣴⣶⣠⣶⣶⠀⣤⠀⣶⣶⣶⡆⣶⣶⣶⢰⣶⣶⣶⣶⣶⣶⣦⣴⣆⢴⣶⣶⣶⣶⣶⣾⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⠤⠤⠤⠤⠤⠬⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⢼⡤⡤⠤⢤⠤⠤⠤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠧⠤⠤⠼⠤⠤⠤⢤⠥⠭⣤⣬⣤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤ ⣆⣶⣶⣶⣦⠴⡿⣦⢴⣶⡆⢰⡦⡆⣴⣶⡆⢼⣇⣗⡆⢰⣦⣴⣤⣴⠀⢰⣶⣤⣤⣤⣤⣾⣤⣥⣶⠀⣶⣶⣦⠨⣷⣶⡤⣤⡀⢐⣶⣤⣦⡤⢹⡖⡆⡆⣆⡀⢰⣶⡦⢴⡦⢴⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⢤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡤⡤⠤⠤⠤⠤⠤⠤⠤⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠤⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠇⠷⠷⠷⠶⠶⠷⠷⠶⠾⠇⠰⠦⠆⠰⠾⠇⠰⠾⠿⠆⠰⠶⠶⠸⠶⠶⠰⠀⠾⠾⠺⠶⠶⠺⠶⠷⠿⠿⠶⠀⠷⣶⠶⠶⠶⠰⠶⠆⠗⠖⠶⠶⠦⠰⠶⠆⠠⠶⠷⠶⠦⠲⠾⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠷⠷⠶⠷⠧⠾⠿⠆⠰⠿⠗⠾⠿⠆⠺⠿⠯⠆⠰⠶⠾⠼⠶⠶⠐⠀⠿⠸⠶⠶⠴⠷⠶⠾⠀⡶⠶⠶⠶⠀⠷⠔⠇⡄⠰⠶⠶⠶⠶⠇⠀⢇⠲⠇⠄⠰⠶⠆⠠⠲⠷⠶⠶⠶⠾⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠯⠿⠷⠿⠷⠶⠷⠷⠺⠿⠇⠐⡿⠇⠖⠿⠇⠾⠿⠿⠇⠰⠶⢾⠼⠶⠶⠰⠀⠿⠹⠶⠼⠶⠷⠶⠾⠀⠿⠶⠶⠶⠟⠀⠶⠶⠶⠶⠷⠀⠇⠰⠶⠇⠚⠇⠰⠶⠆⠰⠲⠷⠶⠶⠲⠾⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠚⠗⠷⠺⠿⠇⠸⠿⠇⠺⠿⠇⠸⠿⠯⠇⠰⠶⢾⠼⠶⠶⠲⠀⠿⠿⠶⠶⠿⠾⠴⣶⠀⠾⠶⠶⠷⠶⠖⠀⠶⠷⠶⠶⠖⠶⠵⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠿⠚⠟⠷⠺⠿⠇⠸⠷⠏⠻⠿⠇⠹⠿⠾⠇⠰⠾⢾⠼⠾⠶⠚⠀⠻⠷⠷⠸⠿⢶⠿⠶⡶⠀⠷⠷⠶⠷⠠⠒⠿⠷⠶⠲⠶⠿⠗⠀⠷⠆⠰⠾⢶⠞⢷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠯⠿⠿⠿⠿⠚⠟⠷⠺⠿⠇⠈⠿⠇⠛⠿⢆⠘⠿⠻⠇⠺⠾⠺⠻⠾⠰⠀⠸⠲⠺⡾⠿⠤⠾⠿⠶⠿⠿⠷⠤⠶⠷⠗⠇⠿⠶⠇⠰⠷⠷⠷⠇⠇⠀⢷⢷⠷⠾⠷⠻⠷⠾⠾⠶⠾⠄⠺⠾⠺⠾⠾⠀⠀⠀⠀⠀⠀ ⠇⡿⡿⡟⡟⠛⠟⡗⠻⣯⡇⠘⠻⡃⠘⠻⠃⠛⢛⢛⠃⠺⠻⠛⠻⠿⠘⠀⠻⠛⠻⠻⠸⢻⠀⠻⠿⠀⠛⠛⡷⠟⠀⠛⠛⠟⠓⠀⠁⠚⠿⠗⠓⠛⠛⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡗⣿⡿⠟⡟⠛⡟⡗⠛⣟⡇⠈⣿⡏⠛⠟⡏⢙⢻⡛⠃⠘⠻⢛⢺⠻⠻⠘⠀⠛⠻⠟⢸⢛⠿⢻⠿⠿⠂⢛⡛⠟⡛⠀⠚⠟⠟⠟⠚⠗⡟⡇⠐⡟⠇⠘⠟⠿⠟⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣓⣛⣋⣛⡋⠛⡛⡓⢛⣛⡃⠈⡛⡃⢋⣋⡓⠘⡛⣙⡃⠘⠛⢛⢘⠛⠛⠙⠀⢛⣛⡛⣘⣛⣿⣛⣛⣿⠀⣛⠛⠛⠓⡀⡛⠛⡛⠛⣛⠛⠛⡃⠀⠛⡃⠘⠛⠿⠛⡻⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣓⣛⣻⣛⡛⢛⡛⡓⢓⣟⡃⢘⡟⡛⢛⣛⡃⢘⣛⣛⡃⠘⠛⢛⢚⠛⠛⠙⠀⢘⣛⣛⣓⣓⣛⣛⣛⣚⠀⣛⡛⠋⠛⡃⠛⣛⠓⣈⠛⠛⡛⠃⠐⠛⠛⡛⠓⠙⠛⠛⡃⡘⠛⠃⠙⠛⠻⠛⠻⠓⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣿⡛⢙⣏⡛⢙⣛⡃⢘⡋⡃⢺⣋⠑⢛⢛⣛⠃⠘⠛⢛⢚⠛⠛⠛⠀⢙⣛⣛⣓⣓⣛⣛⣛⣚⠀⣛⠛⠛⡛⣛⡛⠛⣘⠛⣛⡋⠛⡛⠃⠐⡙⠛⠛⠛⢙⣛⡛⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣻⣋⣛⡛⢉⣋⡛⢙⣛⡃⢀⣋⡃⣚⣛⡃⢘⣛⣛⡃⢘⢛⢻⢘⢛⢛⢑⠀⢘⣚⣛⣓⣓⣛⣛⣛⢘⠀⣛⣛⡋⢛⡃⠛⣛⠋⣀⡟⠛⡋⡃⡐⠙⠛⣛⠛⠙⡛⢛⣁⡘⠙⠃⠘⠛⠻⠙⠻⠓⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣟⣛⣛⣋⢉⣋⡛⢙⣛⡃⢈⣋⡃⣙⡓⡃⣘⣛⣛⡃⠘⢛⢛⢚⠙⢛⠀⣀⡙⢉⠛⠛⠓⠛⠛⣛⣘⡀⣛⠛⠛⣛⣛⡛⠛⣌⣛⡋⠋⡛⠛⡃⡘⢙⠛⠛⠛⠙⠛⠛⢀⣀⠀⢀⢀⢀⠀⠀⠀⠀⢀⡀⠀⢀⣀⢀⣀ ⠃⠛⠛⠛⠛⠉⠋⠛⠙⠛⠃⠀⠋⡃⠉⠛⠃⠙⠛⠛⠃⠙⠛⠙⠙⠛⠈⠀⠛⠛⠙⠛⠛⠀⠛⠛⠛⠛⠛⠛⠀⠛⠛⠛⠛⠀⢋⠋⠛⠃⠃⠈⠛⠙⠙⠛⠙⠃⠘⠛⠃⠘⠛⠛⠙⠛⠛⠀⠈⠀⠈⠛⠛⠛⠋⠛⠛⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⣍⢉⣍⣉⣉⣉⣉⡉⠉⡍⢩⣭⣉⣉⣉⣉⡉⢉⡉⢩⣭⣉⣉⣉⣉⣉⣩⠉⢩⠉⣭⣭⢉⣭⣭⣉⣭⣭⠉⣉⠉⣭⣉⣉⣉⡍⣉⣭⣉⣉⣉⡉⡍⢩⣍⣉⣩⣉⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉ ⡁⡀⣉⡉⠉⠉⠉⡁⠀⡁⠈⡉⠉⢉⠉⢉⠁⠈⠁⣈⡉⠉⢉⠁⠙⠉⢈⠀⢈⢀⠉⢉⣈⠉⡉⢀⣉⠉⢀⠉⣀⣉⣉⡉⡉⣉⡁⠉⡉⡁⠉⠉⡁⢈⢉⡉⣉⣉⣉⢀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀ ⠀⠀⠀⠀⢀⣀⣄⡀⠀⡄⢠⣤⣀⣀⣀⣀⡄⢠⡄⠀⣠⣠⡄⣤⣤⣄⣀⠀⢠⠀⣤⣤⠀⣤⣤⠀⣤⣤⠀⣤⠀⣤⣤⡤⢠⣤⣤⣤⣤⣤⣤⣄⣠⣤⣤⣤⢀⣠⣤⣄⣠⣤⣤⣤⣤⣤⢤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀ ⡤⠀⠀⠀⢀⣍⣭⣅⠀⣅⣨⣭⣬⣭⢩⣭⣅⢠⡅⡀⣨⣭⡅⣭⣭⣅⣬⡀⢨⠀⣭⣭⠠⣭⣥⠠⣬⣥⠀⣅⠀⣭⣭⡭⢠⣭⣭⣥⣭⣭⣭⣥⣌⣭⣍⣨⣍⣬⣭⣅⣬⣭⣭⣉⣭⣭⢭⣭⣭⣭⣭⣭⡀⠀⠀⠀⡀⠀ ⠁⠀⠀⠀⢀⣍⣭⡅⠀⡍⢩⣮⣉⣩⣭⣉⡄⢨⡄⠀⢨⣭⠁⣤⣭⣅⣬⠀⢨⠀⣬⣭⢠⢭⣬⢠⣭⣭⠀⣤⠀⣭⣭⣥⣤⣍⣭⣭⣭⣥⣭⣭⣯⣭⣅⣨⣍⣬⣭⣥⢬⣭⣭⣩⣭⢭⣬⣬⠍⠉⠉⠉⠀⠀⢀⠀⠈⠀ ⠀⠀⠀⠀⠀⣍⣭⡇⠀⡅⢨⣯⣬⣭⣭⣭⡅⢨⡄⠀⢨⣽⠅⣤⣭⣅⣬⠀⢨⠀⣼⣬⢠⢽⣭⢄⣭⣽⠀⣤⠀⣭⣯⣭⢩⣭⣭⣭⣧⢠⣬⣭⣯⣥⣤⣬⣭⣌⣭⣽⣌⣥⣬⣭⣭⣼⣬⣭⣤⣠⢤⣤⣤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣥⣧⡇⠀⡄⢰⣯⣤⣤⣭⣌⡄⢠⡄⠀⢸⣽⡄⣴⣿⣤⣬⠀⢰⠀⣼⣿⠠⣦⣶⠤⣬⣤⠀⣤⠀⣿⣥⣥⣤⣥⣥⢡⣄⠠⣧⣦⣧⣶⣷⣇⡅⠀⠈⠈⢀⠈⠈⠁⠉⢉⠈⠈⠈⠈⠈⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣤⣦⡄⠀⡆⢰⣦⢤⣤⣤⣤⡄⠠⡄⠀⢰⣴⡄⣴⣿⣤⣤⠀⢰⠀⣼⣶⢠⣰⣶⣀⣵⣶⠀⣤⠀⣶⣴⣶⡆⣷⣶⣶⢰⣶⣶⣶⣶⣦⣶⣦⣴⣆⢴⣶⣶⣶⣶⣴⣾⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⠤⠤⠤⠄⠤⠌⠥⠤⠠⠤⠤⠤⠤⠠⠤⠤⠤⠤⠤⠤⠠⠤⠤⠤⠤⠤⠠⠠⠀⠤⠤⠀⠠⠤⠤⠤⠠⠄⠥⠤⠤⠍⠤⠤⠤⢄⠡⠉⣤⣌⣤⡤⠄⠤⠤⠠⠤⠤⠤⠄⠠⠠⠤⠀⠠⠠⠤⠤⠤⠤⠠⠤⠤⠄⠠⠤⠤ ⣆⣶⣶⣶⣦⠴⡦⣆⢴⣶⡆⢰⡦⡆⠴⣶⡆⢴⣖⣖⡆⢰⣦⣴⣤⣴⠀⢰⣶⣤⣤⣤⣤⣦⣤⣤⣶⠀⣖⣶⣦⢰⣶⣶⡤⣤⡀⢐⣶⣤⣦⡤⢹⣆⣆⡆⣆⡀⢰⣶⡦⢴⡦⢴⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⠤⠤⠤⠤⠤⠤⢤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠤⢥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⢤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠇⠷⠷⠷⠶⠶⠷⠷⠶⠾⠇⠰⠦⠆⠰⠾⠇⠰⠾⠿⠆⠰⠶⠶⠸⠶⠶⠰⠀⠾⠾⠺⠶⠶⠺⠶⠷⠿⠿⠶⠀⠷⣶⠶⠶⠶⠰⠶⠆⠗⠖⠶⠶⠦⠰⠶⠆⠠⠶⠷⠶⠦⠲⠾⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠷⠷⠶⠷⠧⠾⠿⠆⠰⠯⠗⠾⠿⠆⠺⠿⠯⠆⠰⠶⠾⠼⠶⠶⠐⠀⠿⠸⠶⠶⠴⠷⠶⠾⠀⡶⠶⠶⠶⠀⠷⠔⠇⡄⠰⠶⠶⠶⠶⠇⠀⢇⠲⠇⠄⠰⠶⠆⠠⠲⠷⠶⠶⠶⠾⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠯⠿⠷⠿⠷⠶⠷⠷⠺⠿⠇⠐⡿⠇⠖⠿⠇⠾⠿⠿⠇⠰⠶⢾⠼⠶⠶⠰⠀⠿⠹⠶⠼⠶⠷⠶⠾⠀⠿⠶⠶⠶⡿⠀⠶⠶⠶⠶⠷⠀⠇⠰⠶⠇⠚⠇⠰⠶⠆⠰⠲⠷⠶⠶⠲⠾⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠚⠗⠷⠺⠿⠇⠸⠿⠇⠺⠿⠇⠸⠿⠯⠇⠰⠶⢾⠼⠶⠶⠲⠀⠿⠿⠶⠶⠿⠾⠴⣶⠀⠾⠶⠶⠷⠶⠖⠀⠶⠷⠶⠶⠖⠶⠵⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠿⠚⠟⠷⠺⠿⠇⠸⠷⠏⠻⠿⠇⠹⠿⠾⠇⠰⠾⢾⠼⠾⠶⠚⠀⠻⠷⠶⠸⠿⢶⠿⠶⡶⠀⠷⠷⠶⠷⠠⠒⠿⠷⠶⠲⠶⠿⠗⠀⠷⠆⠰⠾⢶⠞⢷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠯⠿⠿⠿⠿⠚⠟⠷⠺⠿⠇⠈⠿⠇⠛⠿⢆⠘⠿⠻⠇⠺⠾⠺⠻⠾⠰⠀⠸⠲⠺⡾⠿⠤⠾⠿⠶⠿⠿⠷⠤⠶⠷⠇⠇⠿⠶⠇⠰⠷⠷⠷⠇⠇⠀⢷⢷⠷⠾⠷⠻⠷⠾⠾⠶⠾⠄⠺⠾⠺⠾⠾⠀⠀⠀⠀⠀⠀ ⠇⡿⡿⡟⡟⠛⠟⡗⠻⣯⡇⠘⠻⡃⠘⠻⠃⠛⢛⢛⠃⠺⠻⠛⠻⠿⠘⠀⠻⠛⠻⠻⠸⢻⠀⠻⠿⠀⠛⠛⡷⠟⠀⠛⠛⠟⠓⠀⠁⠚⠿⠗⠓⠛⠛⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡗⣿⡿⠟⡟⠛⡟⡗⠛⣟⡇⠈⣿⡏⠛⠟⡏⢙⢻⡛⠃⠘⠻⢛⢺⠻⠻⠘⠀⠛⠻⠟⢸⢛⠿⢻⠿⠿⠂⢛⡛⠟⡛⠀⠚⠟⠟⠟⠚⠗⡟⡇⠐⡟⠇⠘⠟⠿⠟⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣓⣛⣋⣛⡋⠛⡛⡓⢛⣛⡃⠈⡛⡃⢋⣋⡓⠘⡛⢙⡃⠘⠛⢛⢘⠛⠛⠘⠀⢛⣛⡛⣘⣛⣿⣛⣛⣿⠀⣛⠛⠛⠓⡀⡛⠛⡛⠛⣛⠛⠛⡃⠀⠛⡃⠘⠛⠿⠛⡻⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣓⣛⣻⣛⡛⢛⡛⡓⢓⣟⡃⠘⡟⡛⢛⣛⡃⢘⣛⣛⡃⠘⠛⢛⢚⠛⠛⠙⠀⢘⣛⣛⣓⣓⣛⣛⣛⣚⠀⣛⡛⠋⠛⡃⠛⣛⠓⣈⠛⠛⡛⠃⠐⠛⠛⡛⠓⠙⠛⠛⡃⡘⠛⠃⠙⠛⠻⠛⠻⠓⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣿⡛⢙⣏⡛⢙⣛⡃⢘⡋⡃⢺⣋⠑⢛⢛⣛⠃⠘⠛⢛⢚⠛⠛⠛⠀⢙⣛⣛⣓⣓⣛⣛⣛⣚⠀⣛⠛⠛⡛⣛⡛⠛⣘⠛⣛⡋⠛⡛⠃⠐⡙⠛⠛⠛⢙⣛⡛⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣻⣋⣛⡛⢉⣋⡛⢙⣛⡃⢀⣋⡃⣚⣛⡃⢘⣛⣛⡃⢘⢛⢻⢘⢛⢛⢑⠀⢘⣚⣛⣓⣓⣛⣛⣛⢘⠀⣛⣛⡋⢛⡃⠛⣛⠋⣀⡟⠛⡋⡃⡐⠙⠛⣛⠛⠙⡛⢛⣁⡘⠙⠃⠘⠛⠻⠙⠻⠓⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣟⣛⣛⣋⢉⣋⡛⢙⣛⡃⢈⣋⡃⣙⡓⡃⣘⣛⣛⡃⠘⢛⢛⢚⠙⢛⠀⣀⡙⢉⠛⠛⠓⠛⠛⣛⣘⡀⣛⠛⠛⣛⣛⡛⠛⣌⣛⡋⠋⡛⠛⡃⡘⢙⠛⠛⠛⠙⠛⠛⢀⣀⠀⢀⢀⢀⠀⠀⠀⠀⢀⡀⠀⢀⣀⢀⣀ ⠃⠛⠛⠛⠛⠉⠋⠛⠙⠛⠃⠀⠋⡃⠉⠛⠃⠙⠛⠛⠃⠙⠛⠙⠙⠛⠈⠀⠛⠛⠙⠛⠛⠀⠛⠛⠛⠛⠛⠛⠀⠛⠛⠛⠛⠀⢋⠋⠛⠃⠃⠈⠛⠙⠙⠛⠙⠃⠘⠛⠃⠘⠛⠛⠙⠛⠛⠀⠈⠀⠈⠛⠛⠛⠋⠛⠛⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⣍⢉⣍⣉⣉⣉⣉⡉⠉⡍⢩⣭⣉⣉⣉⣉⡉⢉⡉⢩⣭⣉⣉⣉⣉⣉⣩⠉⢩⠉⣭⣭⢉⣭⣭⣉⣭⣭⠉⣉⠉⣭⣉⣉⣉⡍⣉⣭⣉⣉⣉⡉⡍⢩⣍⣉⣩⣉⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉ ⡁⡀⣉⡉⠉⠉⠉⡁⠀⡁⢈⡉⠉⢉⠉⢉⠁⠈⠁⣈⡉⠉⢉⠁⠙⠉⢈⠀⢈⢀⠉⢉⣈⠉⡉⢀⣉⠉⢀⣉⣀⣉⣉⡉⡉⣉⡁⠉⡉⡁⠉⠉⡁⢈⢉⡉⣉⣉⣉⢀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀ ⠀⠀⠀⠀⢀⣀⣄⡀⠀⡇⢠⣧⣀⣀⣀⣀⡄⢠⡄⠀⣠⣠⡄⠤⠤⠄⠀⠀⠘⠀⣤⣀⠀⣤⣤⠀⣤⣤⠀⣥⠀⣤⣤⡤⢠⣤⣤⣤⣤⣤⣤⣄⣠⣤⣤⣤⢀⣠⣤⣄⣠⣤⣤⣤⣤⣤⢤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀ ⡤⠀⠀⠀⢀⣍⣭⣍⠈⣍⣩⣭⣭⣭⢩⣭⣍⢩⡍⡉⣩⣭⡍⣭⣭⣍⣉⡉⢉⠉⣭⣭⠩⣭⣭⠩⣭⣭⠉⣍⠉⣭⣭⣭⢩⣭⣍⣉⣭⣭⣭⣭⣉⣭⣍⣩⣍⣭⣭⣍⣩⣭⣭⣉⣭⣭⢭⣍⣩⣭⣭⣉⡉⠉⠉⠉⡉⠉ ⠁⠀⠀⠀⢀⣍⣭⡅⠀⡏⢩⣮⣉⣩⣭⣉⡄⢸⡇⠀⢨⣭⠁⣤⣭⣅⣬⠀⢸⠀⣬⣭⢠⢭⣬⢠⣭⣋⠀⣥⠀⣭⣭⣇⣤⣍⣭⣭⣭⣥⣭⣭⣯⣭⣅⣨⣍⣬⣭⣥⢬⣭⣭⣩⣭⢭⣬⣬⠍⠉⠉⠉⠀⠀⢀⠀⠈⠀ ⠀⠀⠀⠀⠀⣍⣭⡇⠀⡇⢨⣯⣬⣭⣭⣭⡅⢸⡄⠀⢨⣽⠅⣤⣭⣅⣬⠀⢸⠀⣼⣬⢠⢽⣭⢄⣿⣿⠀⣧⠀⣭⣯⣭⢩⣭⣭⣭⣧⢠⣬⣭⣯⣥⣤⣬⣭⣌⣭⣽⣌⣥⣬⣭⣭⣼⣬⣭⣤⣠⢤⣤⣤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣥⣧⡇⠀⡇⢰⣯⣤⣤⣭⣌⡄⢸⡆⠀⢸⣽⡄⣴⣿⣤⣬⠀⢸⠀⣼⣿⠠⣦⣶⠴⣬⣾⠀⣧⠀⣿⣥⣥⣤⣥⣥⢡⣄⠠⣧⣦⣧⣶⣷⣇⡅⠀⠈⠈⢀⠈⠈⠁⠉⢉⠈⠈⠈⠈⠈⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣤⣦⡄⠀⡇⢰⣦⢤⣤⣤⣤⡄⢸⡇⠀⢸⣿⡆⣴⣿⣤⣤⠀⢸⠀⣼⣶⢠⣰⣶⣂⣿⣶⠀⣧⠀⣶⣴⣶⡆⣷⣶⣶⢰⣶⣶⣶⣶⣦⣶⣦⣴⣆⢴⣶⣶⣶⣶⣴⣾⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⠤⠤⠤⠄⠤⠌⠥⠤⠧⠤⠤⠤⠤⠠⠤⠤⠼⠧⠄⠚⠹⠥⠤⠤⠤⠤⠠⢸⠀⠤⠤⠀⠠⠤⠤⠤⠠⠄⠯⠤⠤⠍⠤⠤⠤⢄⠡⠉⣤⣌⣤⡤⠄⠤⠤⠠⠤⠤⠤⠄⠠⠠⠤⠀⠠⠠⠤⠤⠤⠤⠠⠤⠤⠄⠠⠤⠤ ⣆⣶⣶⣶⣦⠴⡦⣆⢴⣷⡆⢰⡦⡆⠴⣶⡆⢼⣗⣖⡮⢶⣦⣴⣤⣴⠀⢰⣾⣤⣤⣤⣤⣦⣤⣤⣶⠀⣖⣻⣦⢰⣶⣶⡄⣦⡀⢐⣶⣤⣦⡤⢹⣆⣆⡆⣆⡀⢰⣶⡦⢴⡦⢴⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⠤⠤⠤⠤⠤⠦⠼⠶⡶⠶⠦⠶⠦⢶⣦⡶⠶⠶⠶⠶⠴⠴⠴⠶⢾⠶⠴⠶⠶⠾⠶⠿⠾⢿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠷⠶⠶⠶⠷⠷⠦⠧⣮⢦⠦⡶⡦⠴⠦⠶⠶⠶⠴⠦⢦⠶⠦⠴⠴⠶⠶⠶⠴⠶⠶⠶⠶⠴ ⠀⠀⠀⠀⠀⠀⠀⠰⠺⠇⠀⠀⠀⠀⠋⠷⠅⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠘⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠇⠇⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠷⠷⠷⠷⠶⠷⠦⠾⠿⠇⠰⠿⠇⠶⠾⠇⠾⠾⠿⠇⠰⠶⠶⠸⠶⠶⠰⠀⠾⠾⠻⠶⠾⠿⠿⠿⠿⠷⠶⠀⠷⣶⠶⠶⠦⠰⠶⠆⠗⠖⠶⠶⠦⠰⠶⠆⠠⠶⠷⠶⠦⠲⠶⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠶⠷⠧⠾⠿⠇⠰⠿⠇⠾⠿⠇⠺⠿⠯⠇⠰⠶⠾⠼⠶⠶⠲⠀⠿⠸⠶⠶⠶⠷⠶⠾⠀⡶⠶⠶⠶⠀⠷⠖⠇⠄⠰⠶⠶⠶⠶⠇⠐⠧⠲⠇⠄⠰⠶⠆⠠⠲⠷⠶⠶⠶⠾⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠯⠿⠿⠿⠷⠶⠷⠷⠺⠿⠇⠰⠿⠇⠾⠿⠇⠾⠿⠿⠇⠰⠶⠾⠼⠶⠶⠲⠀⠿⠹⠶⠾⠶⠷⠶⠾⠀⠟⠷⠶⠶⠷⠀⠶⠶⠶⠶⠗⠀⠇⠰⠶⠇⠰⠇⠰⠶⠆⠰⠲⠷⠶⠶⠲⠾⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠺⠟⠷⠺⠿⠇⠨⠿⠇⠼⠿⠇⠸⠿⠯⠇⠰⠶⠾⠼⠶⠶⠢⠀⠿⠿⠶⠶⠿⠼⠶⣶⠀⠾⠶⠶⠷⠶⠶⠀⠶⠿⠶⠶⠲⠶⠷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠿⠚⠟⠷⠺⠿⠇⠨⠿⠇⠹⠿⠇⠹⠿⠾⠇⠰⠾⠾⠼⠶⠶⠚⠀⠻⠷⠶⠸⠿⢶⠿⠶⣶⠀⠷⠷⠶⠧⠠⠒⠿⠶⠶⠲⠶⠿⠇⠀⠷⠆⠰⠶⢶⠾⢷⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠯⠿⠿⠿⠿⠚⠟⠷⠺⠿⠇⠈⠿⠇⠛⠿⠇⠘⠿⠻⠇⠺⠾⠺⠺⠾⠘⠀⠺⠶⠺⠾⠿⠤⠾⠿⠶⠿⠿⠷⠤⠾⠿⠇⠇⠟⠶⠃⠰⠷⠷⠷⠇⠃⠀⠿⢷⠷⠾⠷⠻⠷⠾⠾⠷⠾⠀⠺⠾⠺⠺⠿⠀⠀⠀⠀⠀⠀ ⡇⡟⡿⡟⡟⠛⡟⡷⠻⣟⡇⠈⠿⡇⠛⠿⠇⠘⢿⠛⠃⠺⠻⠻⠻⠿⠈⠀⠻⠛⠿⠿⠺⢻⠀⠻⠿⠀⠟⠟⡷⠟⠀⠟⠟⠿⠓⠀⠁⠚⡟⡟⠗⠛⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣟⡟⡟⡛⠛⡟⡗⠛⣟⡇⠘⣟⡟⠻⠟⡇⠹⢿⣛⡃⠘⠻⠛⢸⠻⠻⠘⠀⢛⠻⠟⠸⢛⠿⠻⠛⠿⠀⠛⡛⠟⠓⠀⠚⡟⠟⠞⠚⠟⡟⡇⠀⡟⠇⠘⠛⠻⠟⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⡛⠛⡛⡛⢛⣛⡃⠘⡛⡋⢛⣛⡃⢘⣛⣛⡃⠘⠛⢛⢘⠛⠛⠘⠀⢛⣛⣛⣘⣛⣿⣛⣛⣿⠀⣛⠛⠛⡓⡀⡛⠛⡛⠛⣛⡛⠛⡃⠀⠛⡃⠘⠛⠻⠛⡻⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣓⣛⣛⣛⡛⢛⡛⡓⢛⣛⡃⢘⡋⡃⢛⣛⡃⢙⣛⣓⡃⠘⠛⢛⢚⠛⠛⠙⠀⢘⣛⣛⣓⣓⣛⣛⣛⣚⠀⣛⡛⠋⠛⡃⠛⡛⠛⡈⠛⠛⡛⠃⠐⠙⠛⡛⠓⠙⠛⠛⣃⡘⠛⠃⠘⠛⠿⠛⠻⠓⠀⠀⠀⠀⠀⠀⠀⠀ ⣓⣛⣛⣛⡛⢛⣛⡛⢙⣛⡃⢘⣋⡃⢛⣛⡃⢘⣛⣛⡃⠘⠛⢛⢚⠛⠛⠘⠀⢙⣛⣛⣓⣓⣛⣛⣛⣚⠀⣛⠛⠛⡛⣛⡛⠛⡘⠛⣛⡋⠛⡛⠃⠐⡙⠛⠛⠛⢙⣛⡛⢃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⣛⢉⣋⡛⢙⣛⡃⢈⣋⡃⣘⣛⡃⣘⣛⣛⡃⢘⢛⢛⢚⢛⢛⢑⠀⢙⣛⣛⣓⣓⣛⣛⣛⢘⠀⣛⣛⠋⢛⡃⡛⣛⠛⣀⡛⠛⡋⡃⠐⠙⠛⡛⠛⠙⣛⢛⣃⡘⠛⠃⠙⠛⠻⠛⠻⠓⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⣛⢉⣋⡛⢙⣛⡃⢐⣋⡃⣘⣛⡃⢘⣛⣛⡃⢘⠛⢛⢚⢛⢛⠉⣀⡙⢛⢛⢛⠓⢛⠛⣛⣚⡀⣛⠛⠛⣛⣛⡛⠛⣈⢛⡛⠋⡛⠛⡃⡘⡙⡛⠛⠛⠙⠛⠛⢁⣀⠀⢀⣀⢀⠀⢀⠀⠀⢀⣀⠀⢀⣀⢀⣀ ⠓⠛⠛⠛⠛⠉⠋⠛⠙⠛⠃⠐⠋⠃⠙⠛⠃⠙⠛⠛⠃⠙⠛⠙⠙⠛⠈⠀⠛⠛⠙⠛⠛⠀⠛⠛⠛⠙⠛⠛⠀⠛⠋⠛⠛⠀⠋⠋⠛⠃⠃⠘⠛⠙⠙⠛⠙⠃⠘⠛⠃⠘⠛⠛⠙⠛⠛⠁⠈⠀⠈⠛⠛⠛⠋⠛⠛⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⣍⢉⣍⣉⣉⣍⣉⡉⠉⡍⢩⣍⣉⣉⣉⣉⡉⢩⡉⢩⣭⣉⣉⣉⣉⣉⣩⠉⢩⠉⣭⣭⢉⣭⣭⣉⣭⣭⠉⣉⠉⣭⣉⣍⣉⡍⣉⣍⣉⣉⣍⡉⡍⢩⣍⣉⣩⣉⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉ ⣁⣀⣉⡉⣉⣉⣉⣁⣀⣁⣈⣉⣉⣉⣉⣉⣁⣈⣁⣈⣉⣉⣉⣁⣛⣉⣉⣀⣈⣀⣉⣉⣈⣉⣉⣉⣉⣉⣀⣉⣀⣉⣉⣉⡉⣉⣉⣉⣉⣁⣉⣉⣁⣈⣉⣉⣉⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⠀⠀⠀⠀⢀⣀⣄⡀⠀⡄⢠⣄⣀⣀⣀⣀⡄⢠⡄⠀⣠⣠⡄⣤⣤⣄⣀⠀⢠⠀⣤⣤⠀⣤⣤⢀⣤⣤⠀⣄⠀⣤⣤⡤⢠⣤⣤⣤⣤⣤⣤⣄⣠⣤⣤⣤⣀⣠⣤⣄⣠⣤⣤⣤⣤⣤⢤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀ ⡤⠀⠀⠀⢀⣍⣭⣅⠀⣅⣨⣭⣬⣭⢩⣭⣅⣨⡅⠀⣨⣭⡅⣭⣭⣅⣬⠀⢨⠀⣭⣭⠨⢭⣥⠨⣬⣥⠀⣥⠀⣭⣭⡭⢠⣭⣭⣥⣭⣭⣭⣥⣌⣭⣍⣨⣍⣬⣭⣅⣨⣭⣭⣭⣭⣭⢭⣭⣭⣭⣭⣭⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⢀⣍⣭⡅⠀⡅⢨⣬⣭⣭⣭⣩⡅⢨⡄⠀⢨⣭⠁⣬⣭⣅⣬⠀⢨⠀⣬⣭⢠⣭⣬⢠⢭⣭⠀⣤⠀⣭⣭⣭⣤⣭⣥⣭⣭⣥⣭⣭⣭⣭⣅⣨⣍⣬⣭⣥⢬⣭⣭⣭⣭⣭⣬⣬⠍⠉⠉⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣭⣭⡅⠀⡅⢨⣭⣬⣭⣭⣭⡅⢠⡄⠀⢨⣭⠄⣤⣽⣅⣬⠀⢨⠀⣬⣭⢠⣽⣯⢤⣭⢭⠀⣤⠀⣭⣯⣭⢩⣭⣭⣭⣭⢡⣭⣭⣭⣡⣤⣬⣭⣌⣥⣬⣌⣥⣬⣭⣭⣼⣬⣭⣤⣠⣴⣤⣤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣥⣧⡆⠀⡄⢰⣧⣤⣬⣥⣤⡆⢠⡄⠀⢸⣿⡄⣴⣿⣤⣬⠀⢰⠀⣼⣼⢠⣶⣶⣤⣾⣶⠀⣤⠀⣿⣥⣥⣤⣥⡥⢡⣇⠠⣦⣦⣧⣶⣧⣆⡌⠀⠀⠉⠀⠈⠀⠀⠈⠈⠀⠈⠈⠈⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣤⣦⡄⠀⡆⢰⣦⣤⣤⣤⣤⡆⢰⡄⠀⢰⣴⡄⣴⣶⣤⣤⠀⢰⠀⣴⣶⢠⣴⣶⣠⣴⣶⠀⣤⠀⡶⣶⣶⡆⣶⣶⣶⢰⣶⣶⣶⣶⣶⣶⣦⣴⣆⢴⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⠤⠤⠤⠤⠤⠬⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤ ⣆⣶⣶⣶⣦⢴⡶⣦⢴⣶⡆⢰⡦⡆⣴⣶⡆⢴⣶⣶⡆⢰⣦⣴⣤⣴⠀⢰⣶⣤⣤⣤⣤⣦⣤⣤⣶⠀⣶⣶⣦⠠⣶⣶⡤⣤⡀⢐⣶⣤⣤⡤⢰⡖⡆⡆⣆⡀⢰⣶⡦⢴⡦⢴⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠤⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠷⠷⠷⠷⠶⠷⠷⠶⠿⠇⠰⠷⠇⠶⠾⠇⠾⠾⠾⠆⠰⠶⠶⠸⠶⠶⠰⠀⠾⠾⠺⠶⠾⠿⠾⠿⠿⠷⠶⠀⠷⣶⠶⠶⠦⠰⠶⠆⠗⠖⠶⠶⠦⠰⠶⠆⠠⠲⠷⠶⠦⠲⠶⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠶⠷⠷⠮⠿⠇⠰⠯⠇⠶⠿⠇⠺⠿⠯⠇⠰⠶⠾⠼⠶⠶⠲⠀⠿⠸⠶⠶⠶⠷⠶⠾⠀⡶⠶⠶⠶⠀⠧⠖⠇⠄⠰⠶⠶⠶⠶⠇⠐⠧⠲⠇⠄⠰⠶⠆⠠⠲⠷⠶⠶⠶⠾⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠶⠷⠷⠺⠿⠇⠸⠿⠇⠾⠿⠇⠾⠿⠯⠇⠰⠶⠾⠼⠶⠶⠰⠀⠿⠹⠶⠼⠶⠷⠶⠾⠀⠟⠶⠶⠶⠷⠀⠶⠶⠶⠶⠇⠀⠇⠰⠶⠇⠠⠇⠰⠶⠆⠠⠲⠷⠶⠶⠲⠾⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠚⠟⠷⠺⠿⠇⠠⠿⠇⠼⠿⠇⠸⠿⠯⠇⠰⠶⠾⠸⠶⠶⠂⠀⠿⠿⠶⠶⠷⠾⠶⣶⠀⠾⠶⠶⠷⠶⠶⠀⠖⠿⠶⠶⠲⠶⠷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠚⠟⠷⠺⠿⠇⠨⠿⠇⠹⠿⠇⠸⠿⠮⠇⠰⠶⠾⠼⠶⠶⠺⠀⠻⠷⠶⠸⠿⢶⠿⠶⡶⠀⠷⠷⠶⠷⠀⠒⠿⠶⠶⠲⠶⠿⠗⠀⠷⠆⠰⠶⢶⠾⢷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠯⠿⠿⠿⠿⠚⠟⠷⠺⠿⠇⠈⠿⠇⠛⠿⠆⠘⠿⠫⠇⠺⠾⠺⠺⠾⠘⠀⠺⠶⠺⠶⠿⠤⠶⠻⠶⠿⠿⠦⠤⠾⠷⠇⠇⠿⠶⠃⡰⠷⠷⠷⠇⠃⠀⠷⢷⠶⠾⠷⠻⠶⠾⠶⠷⠾⠀⠺⠾⠺⠲⠾⠀⠀⠀⠀⠀⠀ ⡇⡿⡿⡟⡟⠚⡟⡗⠻⣟⡇⠈⠿⡇⠛⠿⠃⠘⢟⠛⠃⠺⠻⠛⠻⠿⠈⠀⠻⠛⠿⠻⠸⢻⠀⠻⠟⠀⠟⠟⠗⠟⠀⠟⠟⠿⠓⠀⠑⠚⡟⡟⠓⠛⠿⠟⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⡟⣟⡟⡛⠛⡛⡓⠛⣟⡇⠘⣟⡓⠛⠟⡋⠸⢻⣛⠃⠘⠻⠛⢸⠻⠻⠘⠀⢛⠻⠟⠸⢛⠿⠛⠛⠿⠀⠛⡛⠛⠓⠀⠚⡛⠟⠟⠚⠗⡟⡃⠀⡟⠇⠘⠛⠻⠟⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⡛⠛⡛⡓⢛⣛⡃⠘⡛⡃⢛⣛⡃⠘⣛⣛⡃⠘⠛⢛⢘⠛⠛⠘⠀⢛⣛⣛⣘⣛⣿⣛⣛⢿⠀⣛⠛⠛⡓⣀⠛⠛⡛⠛⣛⡛⠛⡃⠀⠛⡃⠘⠛⠻⠛⡻⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣓⣛⣛⣛⡛⢛⡛⡓⢛⣛⡃⢘⡋⡃⢛⣛⡃⢙⣛⣓⡃⠘⠛⢛⢚⠛⠛⠙⠀⢘⣛⣛⣓⣓⣛⣛⣛⣚⠀⣛⡛⠋⠛⡃⠛⡛⠛⡈⠛⠛⡛⠃⠐⠛⠛⡛⠓⠙⠛⠛⣃⡘⠛⠃⠘⠛⠿⠛⠻⠓⠀⠀⠀⠀⠀⠀⠀⠀ ⣓⣛⣛⣛⡛⢛⣋⡛⢙⣛⡃⠘⡋⡃⢛⣛⡃⢚⣛⣛⡃⠘⠛⢛⢚⠛⠛⠘⠀⢙⣛⣛⣓⣓⣛⣛⣛⣚⠀⣛⠛⠛⡛⣛⡛⠛⡐⠛⣛⡋⠛⡛⠃⠐⡙⠛⠛⠛⢙⣛⡛⢃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⣛⢉⣋⡛⢙⣛⡃⢐⣋⡃⣚⣛⡃⣘⣛⣓⡃⠘⢛⢛⢚⢛⠛⠑⠀⢘⣛⣛⣓⣓⣛⣛⣛⢘⠀⣛⣛⡋⢛⡃⡛⣛⠛⣈⡛⠛⡋⡃⡐⠙⠛⡛⠛⠙⣛⢛⣃⡘⠛⠃⠙⠛⠻⠛⠻⠓⠀⠀⠀⠀⠀⠀⠀⠀ ⣓⣛⣛⣛⣛⢉⣋⡛⢙⣛⡃⢘⣋⡃⣘⣛⡃⢘⣛⣛⡃⠘⢛⢛⠘⠛⢛⠉⣀⡘⢛⠛⠓⠓⠛⠛⣛⣚⠀⣛⠛⠛⣛⣛⡛⠛⣈⢛⡛⠋⡛⠛⠃⠐⠙⡛⠛⠋⠙⠛⠛⢁⣀⠀⢀⢀⢀⠀⠀⠀⠀⢀⡀⠀⠀⡀⢀⣀ ⠓⠛⠛⠛⠛⠉⠋⠛⠙⠛⠃⠀⠋⠃⠙⠛⠃⠙⠛⠙⠃⠙⠛⠙⠙⠛⠈⠀⠛⠛⠙⠛⠛⠀⠛⠛⠛⠙⠛⠛⠀⠛⠋⠛⠛⠀⠋⠋⠛⠃⠃⠘⠛⠙⠙⠛⠙⠃⠘⠛⠃⠘⠛⠛⠙⠛⠛⠁⠈⠀⠉⠛⠛⠙⠋⠛⠛⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⣍⢉⣍⣉⣉⣍⣉⣉⠉⡍⢩⣍⣉⣉⣉⣉⡉⢩⡉⢩⣭⣉⣉⣉⣉⣉⣩⠉⢩⠉⣭⣭⢉⣭⣭⣉⣭⣭⠉⣉⠉⣭⣉⣉⣉⡍⣉⣍⣉⡉⣍⡉⡍⢩⣍⣉⣩⣉⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉ ⣁⣀⡉⣉⡉⡉⡉⣁⣀⣁⣈⣉⣉⣉⣉⣉⣁⣈⣁⣈⣉⢉⣉⣁⣙⣉⢉⣀⢈⢀⣉⣉⣈⣉⢉⣉⣉⣉⡀⣉⣀⣉⣉⡉⡉⣉⡁⣉⣉⡁⡉⡉⣁⣈⣉⣉⣉⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⢀⢀⣀⣀⣀⣀⢀⢀⣀⣀⣀ ⠀⠀⠀⠀⢀⣀⣄⡀⠀⡄⢠⣤⣀⣀⣀⣀⡄⢠⡄⠀⣠⣠⡄⣤⣤⣄⣀⠀⢠⠀⣤⣤⠀⣤⣤⠀⣤⣤⠀⣤⠀⣤⣤⡤⢠⣤⣤⣤⣤⣤⣤⣄⣠⣤⣤⣤⢀⣠⣤⣄⣠⣤⣤⣤⣤⣤⢤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀ ⡤⠀⠀⠀⢀⣍⣭⣅⠀⣅⣨⣭⣬⣭⢩⣭⣅⣨⡅⠀⣬⣭⡅⣭⣭⣅⣬⠀⢨⠀⣭⣭⠨⢭⣥⠨⣬⣥⠀⣥⠀⣭⣭⡭⢠⣭⣭⣥⣭⣭⣭⣥⣌⣭⣍⣨⣍⣬⣭⣅⣨⣭⣭⣭⣭⣭⢭⣭⣭⣭⣭⣭⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⣍⣭⡅⠀⡅⢨⣬⣍⣭⣭⣩⡅⢠⡄⠀⢨⣭⠁⣤⣭⣅⣬⠀⢨⠀⣬⣭⢠⢭⣬⢠⢭⣭⠀⣤⠀⣭⣭⣭⣤⣭⣥⣭⣭⣥⣭⣭⣭⣭⣅⣨⣍⣬⣭⣥⢬⣭⣭⣩⣭⢭⣬⣬⠍⠈⠉⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣭⣭⡅⠀⡅⢨⣯⣬⣭⣭⣭⡅⢠⡄⠀⢨⣭⠄⣤⣭⣅⣬⠀⢨⠀⣬⣬⢠⣭⣭⠤⣭⢭⠀⣤⠀⣭⣭⡭⢩⣭⣭⣭⣭⢠⣭⣭⣭⣡⣥⣬⣭⣌⣭⣼⣄⣤⣬⣭⣭⣼⣬⣭⣥⣠⢤⣤⣤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣥⣦⡇⠀⡄⢰⣯⣤⣤⣥⣤⡆⢠⡄⠀⢸⣼⡄⣴⣿⣄⣬⠀⢠⠀⣴⣵⢠⣶⣶⢤⣲⣦⠀⣤⠀⣿⣥⣤⣤⣥⡥⢡⣄⠠⣦⣦⣧⣶⣧⣆⡄⠁⠈⠉⠀⠈⠀⠀⠈⠈⠀⠈⠈⠈⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⣦⡄⠀⡆⢰⣦⢤⣤⣤⣤⡆⢠⡄⠀⢰⣴⡄⣴⣶⣤⣤⠀⢰⠀⣴⣶⢠⢴⣶⣠⣶⣶⠀⣤⠀⡶⣶⣶⡆⣶⣶⣦⢰⣶⣶⣖⣶⣶⣶⣦⣴⣆⢴⣶⣶⣶⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⠤⠤⠤⠤⠤⠬⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤ ⣆⣶⣶⣶⣦⠴⡶⣦⢴⣶⡆⢰⡦⡆⣴⣶⡆⢰⣶⣶⡆⢰⣦⣴⣤⣴⠀⢰⣶⣤⣤⣤⣤⣦⣤⣤⣦⠀⣶⣶⣦⠠⣶⣶⡤⣤⡀⢐⣶⣤⣤⡤⢰⡖⡆⡆⣆⡀⢰⣶⡦⢴⡦⢴⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠤⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠷⠷⠷⠷⠶⠷⠷⠶⠿⠇⠰⠿⠇⠶⠾⠇⠺⠾⠿⠆⠰⠶⠶⠸⠶⠶⠰⠀⠾⠾⠺⠾⠾⠿⠾⠿⠿⠷⠶⠀⠷⣶⠶⠶⠦⠠⠶⠖⠗⠖⠶⠶⠦⠰⠶⠆⠠⠲⠷⠶⠦⠲⠶⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠶⠷⠧⠮⠿⠇⠰⠯⠇⠶⠿⠇⠺⠿⠷⠆⠰⠶⠾⠼⠶⠶⠲⠀⠾⠸⠶⠼⠶⠷⠶⠾⠀⡶⠶⠶⠶⠀⠷⠖⠇⠄⠰⠶⠶⠶⠶⠇⠐⠧⠲⠇⠄⠰⠶⠆⠠⠲⠷⠶⠶⠶⠾⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠯⠿⠿⠿⠷⠶⠷⠷⠺⠿⠇⠸⠿⠇⠾⠿⠇⠺⠿⠿⠇⠰⠶⠾⠼⠶⠶⠰⠀⠿⠹⠶⠾⠶⠷⠶⠾⠀⠟⠷⠶⠶⠷⠀⠶⠶⠶⠶⠇⠀⠇⠰⠶⠇⠠⠇⠰⠶⠆⠰⠲⠷⠶⠶⠲⠾⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠯⠿⠿⠿⠷⠚⠟⠷⠺⠿⠇⠈⠿⠇⠬⠿⠇⠸⠿⠯⠇⠰⠶⠾⠼⠶⠶⠢⠀⠿⠿⠶⠶⠿⠾⠶⣶⠀⠾⠶⠶⠷⠶⠖⠀⠶⠿⠶⠶⠲⠶⠷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠿⠚⠟⠷⠺⠿⠇⠨⠿⠇⠹⠿⠇⠸⠿⠾⠇⠰⠶⠾⠼⠾⠶⠘⠀⠻⠷⠶⠸⠾⣶⠿⠶⡶⠀⠿⠷⠶⠷⠀⠒⠿⠶⠶⠲⠷⠿⠇⠀⠷⠆⠰⠶⢶⠾⢷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠿⠚⠟⠷⠺⠿⠇⠈⠿⠇⠚⠿⠇⠘⠿⠫⠇⠺⠾⠺⠺⠾⠘⠀⠺⠶⠺⠶⠾⠤⠾⠿⠶⠿⠿⠧⠤⠶⠷⠗⠇⠿⠶⠃⡰⠷⠷⠷⠇⠇⠀⠷⠷⠷⠾⠷⠻⠷⠾⠾⠷⠾⠀⠺⠾⠺⠾⠾⠀⠀⠀⠀⠀⠀ ⡇⡟⡟⡟⡟⠚⡟⡗⠻⣟⡇⠘⣿⡇⠛⠿⠃⠘⢟⠛⠃⠺⠻⠻⠻⠟⠈⠀⠻⠻⠿⠿⠸⢿⠀⠻⠟⠀⠟⠟⡷⠟⠀⠟⠟⠿⠛⠀⠁⠚⡿⡟⠗⠛⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡃⡟⣟⡟⡟⠛⡟⡗⢛⣟⡇⠘⣟⡇⠛⠟⡇⠙⢿⣛⠃⠘⠻⠛⢚⠻⠻⠚⠀⢛⠻⠟⢸⢛⠿⠻⠛⠿⠀⠛⡛⠛⠓⠀⠚⡛⠟⠟⠛⠟⡟⡃⠀⡟⠇⠘⠛⠻⠟⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⡛⠛⡛⡓⢛⣛⡃⠈⡛⡓⢛⣛⡃⢘⣛⣛⡃⠘⠛⢛⢘⠛⠛⠘⠀⢛⣛⣛⣘⣛⣿⣛⣛⢿⠀⣛⠛⠛⡓⡀⠚⠛⡛⠛⣛⡛⠛⡃⠀⠛⡃⠘⠛⠻⠟⡻⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣓⣛⣛⣛⡛⠛⡛⡛⢓⣛⡃⢘⡋⡃⢛⣛⡃⢘⣛⣓⡃⠘⠛⢛⢚⠛⠛⠙⠀⢙⣛⣛⣓⣓⣛⣛⣛⣚⠀⣛⡛⠋⢛⡃⠛⡛⠛⡈⠛⠛⡛⠃⠐⠛⠛⡛⠓⠙⠛⠛⡃⡘⠛⠃⠚⠛⠻⠛⠻⠓⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⡛⢙⣛⡛⢙⣛⡃⢘⡋⡃⢛⣛⡃⢚⣛⣓⡃⠘⠛⢛⢚⠛⠛⠘⠀⢙⣛⣛⣓⣓⣛⣛⣛⣚⠀⣛⠛⠛⡛⣛⡛⠛⡘⠛⣛⡋⠛⡛⠃⠐⡙⠛⠛⠛⢙⣛⡛⢃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⣛⢉⣋⡛⢙⣛⡃⢘⣋⡃⣚⣛⡃⢘⣛⣛⡃⠘⠛⢛⢚⢛⢛⢑⠀⢙⣚⣛⣓⣓⣛⣛⣛⢘⠀⣛⣛⠋⢛⡃⡛⣛⠛⣀⡛⠛⡋⡃⠐⠙⠛⡛⠛⠙⣛⢛⣃⡘⠛⠃⠙⠛⠻⠛⠻⠓⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⣛⢉⣋⡛⢙⣛⡃⢐⣋⡃⣘⣛⡃⢘⣛⣛⡃⢘⢛⢛⢘⢛⢛⠉⣀⡙⢛⠛⠓⠓⢛⠛⣛⣚⡀⣛⠛⠛⣛⣛⡛⠛⣈⠛⡛⠋⡛⠛⡃⡘⠙⢛⠛⠛⠙⢛⠛⢁⡀⠀⢀⠀⢀⠀⠀⠀⠀⢀⣀⡀⢀⡀⢀⣀ ⠓⠛⠛⠛⠛⠉⠋⠛⠙⠛⠃⠐⠋⠃⠙⠛⠃⠙⠛⠛⠃⠙⠛⠙⠙⠛⠈⠀⠛⠛⠙⠛⠛⠀⠛⠛⠛⠙⠛⠛⠀⠛⠋⠛⠛⠀⠋⠋⠛⠃⠃⠘⠛⠙⠙⠛⠙⠃⠘⠛⠃⠘⠛⠛⠙⠛⠛⠁⠈⠀⠈⠙⠛⠛⠋⠛⠛⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⣍⠉⣍⣉⣉⣍⣉⣉⠉⡍⢩⣍⣉⣉⣉⣉⡉⢩⡉⢩⣭⣉⣉⣉⣉⣉⣩⠉⢩⠉⣭⣭⢉⣭⣭⣉⣭⣭⠉⣉⠉⣭⣉⣍⣉⡍⣉⣍⣉⣉⣍⡉⡍⢩⣍⣉⣩⣉⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉ ⡁⣀⣉⡉⡉⣉⣉⣁⣀⣁⡈⣉⣉⣉⣉⣉⣁⣈⣁⣈⣉⣉⢉⢁⣛⣉⢉⣀⢈⣀⣉⣉⣈⣉⣉⣉⣉⣉⣀⣉⣀⣉⣉⣉⡉⣉⣁⣉⡉⣁⣉⡉⣁⣈⣉⣉⣉⣉⣉⣀⣀⣀⢀⣀⣀⣀⣀⢀⣀⢀⣀⣀⣀⢀⢀⣀⣀⣀ ⠀⠀⠀⠀⠀⣀⣄⡀⠀⡄⢠⣤⣀⣀⣀⣀⡄⢠⡄⠀⣠⣠⡄⣤⣤⣄⣀⠀⢠⠀⣤⣤⠀⣤⣤⠀⣤⣤⠀⣤⠀⣤⣤⡤⢠⣤⣤⣤⣤⣤⣤⣄⣠⣤⣤⣤⣀⣠⣤⣄⣠⣤⣤⣤⣤⣤⢤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀ ⡤⠀⠀⠀⢀⣍⣭⣅⠀⣅⣨⣭⣬⣭⣩⣭⣅⣨⡄⠀⣨⣭⡅⣭⣭⣅⣬⠀⢨⠀⣭⣭⠨⢭⣥⠠⣬⣥⠀⣤⠀⣭⣭⡭⢠⣭⣭⣥⣭⣭⣭⣥⣌⣭⣍⣨⣍⣬⣭⣅⣨⣭⣭⣭⣭⣭⢭⣭⣭⣭⣭⣭⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⣍⣭⡅⠀⡅⢨⣬⣍⣩⣭⣩⡅⢨⡄⠀⢨⣭⠁⣬⣭⣅⣬⠀⢨⠀⣬⣭⢠⢭⣬⢠⣭⣭⠀⣤⠀⣭⣭⣭⣤⣭⣥⣭⣭⣥⣭⣭⣭⣭⣅⣨⣍⣬⣭⣥⣬⣭⣭⣩⣭⢭⣬⣬⠍⠈⠉⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣭⣭⡅⠀⡅⢨⣯⣬⣭⣭⣭⡅⢠⡄⠀⢨⣽⠅⣤⣽⣥⣬⠀⢨⠀⣬⣬⢠⣽⣽⢤⣭⢭⠀⣤⠀⣭⣭⡭⢩⣭⣯⣭⣭⢠⣭⣭⣯⣡⣤⣤⣭⣌⣥⣬⣌⣥⣬⣭⣭⣼⣬⣽⣥⣠⢤⣤⣤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣥⣧⡇⠀⡄⢰⣯⣤⣥⣥⣤⡆⢠⡄⠀⢸⣽⡄⣴⣿⣄⣬⠀⢰⠀⣴⣷⢠⣶⣶⢤⣼⣶⠀⣤⠀⣿⣥⣤⣤⣥⡥⢡⣆⠠⣧⣦⣧⣶⣦⣆⡌⠀⠈⠉⠀⠈⠀⠀⠈⠈⠀⠈⠈⠈⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⣦⡄⠀⡆⢰⣧⣤⣤⣤⣤⡆⢠⡄⠀⢸⣴⡄⣴⣶⣤⢤⡀⢰⠀⣴⣶⢠⣴⣶⣠⣶⣶⠀⣤⠀⡶⣴⣴⡆⣶⣶⣴⢰⣶⣶⣶⣶⣶⣶⣦⣴⣆⢴⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⠤⠤⠤⠤⠤⠬⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤ ⣖⣶⣶⣶⣦⠴⡦⣦⢴⣶⡆⢰⡦⡆⣴⣶⡆⢴⣶⣶⡆⢰⣦⣴⣤⣴⠀⢰⣶⣤⣤⣤⣤⣦⣤⣤⣦⠀⣶⣶⣦⢠⣶⣶⡤⣤⡀⢐⣶⣤⣤⡤⢰⡆⡆⣆⡆⡀⢰⣶⡦⢴⡦⢴⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠤⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠷⠷⠷⠷⠶⠷⠧⠾⠿⠇⠰⠿⠇⠶⠾⠇⠾⠾⠿⠆⠰⠶⠶⠸⠶⠶⠰⠀⠾⠾⠺⠾⠶⠿⠶⠿⠷⠷⠶⠀⠷⣶⠶⠶⠖⠰⠶⠖⠗⠖⠶⠶⠦⠰⠶⠆⠠⠶⠷⠶⠦⠲⠶⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠶⠷⠧⠶⠿⠇⠰⠯⠇⠶⠿⠇⠺⠿⠿⠇⠰⠶⠾⠼⠶⠶⠰⠀⠾⠸⠶⠴⠶⠷⠶⠾⠀⡶⠶⠶⠶⠀⠧⠖⠇⠄⠰⠶⠶⠶⠶⠇⠐⠧⠒⠇⠄⠰⠶⠆⠠⠲⠶⠶⠶⠶⠾⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠺⠷⠷⠺⠿⠇⠰⠿⠇⠾⠿⠇⠾⠿⠯⠇⠰⠶⠾⠼⠶⠶⠰⠀⠿⠹⠶⠼⠶⠷⠶⠾⠀⠟⠶⠶⠶⠷⠀⠶⠶⠶⠶⠇⠀⠇⠰⠶⠇⠰⠇⠰⠶⠆⠠⠲⠷⠶⠶⠲⠾⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠚⠟⠷⠺⠿⠇⠠⠿⠇⠸⠿⠇⠺⠿⠿⠇⠰⠶⠾⠼⠶⠶⠂⠀⠿⠿⠶⠶⠷⠼⠶⣶⠀⠾⠶⠶⠷⠶⠶⠀⠖⠷⠶⠶⠲⠶⠷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠿⠚⠟⠷⠺⠿⠇⠨⠿⠇⠸⠿⠇⠸⠿⠾⠇⠰⠶⠾⠼⠾⠶⠒⠀⠻⠿⠶⠸⠿⢶⠿⠶⡶⠀⠷⠷⠶⠧⠀⠚⠿⠶⠶⠲⠶⠿⠇⠀⠷⠆⠰⠶⢶⠾⢷⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠿⠚⠟⠷⠺⠿⠇⠈⠿⠇⠛⠿⠆⠘⠿⠫⠇⠺⠾⠺⠺⠾⠸⠀⠺⠶⠺⠶⠿⠤⠾⠻⠶⠿⠾⠷⠤⠾⠷⠗⠇⠿⠶⠃⠰⠷⠷⠷⠇⠃⠀⠷⢿⠷⠾⠷⠻⠷⠾⠾⠷⠾⠀⠺⠾⠺⠺⠾⠀⠀⠀⠀⠀⠀ ⡃⡟⡿⡟⡟⠛⡟⡗⠻⣿⡇⠈⠿⡇⠛⠿⠇⠘⢿⠛⠃⠺⠿⠻⠻⠟⠈⠀⠻⠛⠿⠿⠘⢿⠀⠻⠟⠀⠟⠟⠷⠟⠀⠟⠟⠟⠓⠀⠁⠚⡟⡟⠗⠛⠿⠟⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣟⡟⡟⡛⠛⡛⡗⢛⣟⡇⠘⣟⡟⠛⠛⠇⠘⢛⣛⠃⠘⠻⠛⢸⠻⠻⠘⠀⠛⠻⠟⠘⢛⠿⢛⠛⠿⠀⠻⡛⠛⡓⠀⠚⡟⠟⠟⠛⠟⡟⡇⠀⡟⠃⠘⠟⠻⠟⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⡛⠛⡛⡓⢛⣛⡃⠈⡛⡃⢛⣛⡃⢘⣛⣛⡃⠘⠛⢛⢘⠛⠛⠘⠀⢛⣛⡛⣘⣛⣿⣛⣛⢿⠀⣛⠛⠛⡓⡀⠛⠛⡛⠛⣛⠛⠛⡃⠀⠛⡃⠘⠛⠻⠛⡻⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⡛⠛⡛⡓⢓⣛⡃⢘⡋⡃⢛⣛⡃⢙⣛⣛⡃⠘⠛⢛⢚⠛⠛⠙⠀⢘⣛⣛⣓⣓⣛⣛⣛⢚⠀⣛⡛⠋⠛⡃⠛⡛⠛⡈⠛⠛⡛⠃⠐⠛⠛⡛⠓⠙⠛⠛⡃⡘⠛⠃⠘⠛⠻⠛⠻⠓⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⡛⢛⣋⡛⢙⣛⡃⢘⡋⡃⢛⣛⡃⢘⣛⣛⡃⠘⠛⢛⢚⠛⠛⠐⠀⢘⣛⣛⣓⣓⣛⣛⣛⢚⠀⣛⠛⠛⡛⣛⡛⠛⣐⠛⣛⡋⠛⡛⠃⠐⡙⠛⠛⠛⢙⣛⡛⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⣛⢙⣋⡛⢙⣛⡃⢀⣋⡃⣘⣛⡃⢘⣛⣛⡃⢘⢛⢛⢚⢛⢛⢁⠀⢘⣚⣛⣓⣓⣛⣛⣛⢘⠀⣛⣛⠋⢛⡃⡛⣛⠋⣀⡛⠛⡋⡃⡐⠙⠛⡛⠛⠙⣛⢛⣁⡘⠛⠃⠙⠛⠻⠛⠻⠓⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⣛⢉⣋⡛⢙⣛⡃⢐⣋⡃⣘⣛⡃⢘⣛⣛⡃⢘⢛⢛⠚⣛⢛⠉⣀⡘⢛⠛⠓⠓⢛⠛⣛⣘⠀⣛⠛⠛⣛⣛⡛⠛⣈⡛⡛⠋⡛⠛⠃⡘⠙⢛⠛⠛⠙⡛⠛⢁⣀⡀⢀⢀⢀⠀⢀⠀⠀⣀⣀⠀⠀⡀⢀⣀ ⠓⠛⠛⠛⠛⠉⠋⠛⠙⠛⠃⠐⠋⠃⠙⠛⠃⠙⠛⠛⠁⠙⠛⠙⠙⠛⠈⠀⠛⠛⠙⠛⠛⠀⠛⠛⠛⠛⠛⠛⠀⠛⠛⠛⠛⠀⠋⠋⠛⠃⠃⠘⠛⠙⠙⠛⠙⠃⠘⠛⠃⠘⠛⠛⠙⠛⠛⠁⠈⠀⠈⠛⠛⠙⠋⠛⠛⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⣍⢉⣍⣉⣉⣍⣉⡉⠉⡍⢩⣍⣉⣉⣉⣉⡉⢩⡉⢩⣭⣉⣉⣉⣉⣉⣩⠉⢩⠉⣭⣭⢉⣭⣭⡉⣭⣭⠉⣉⠉⣭⣉⣍⣉⡍⣉⣍⣉⣉⣍⡉⡍⢩⣍⣉⣩⣉⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉ ⣁⣈⣉⣉⣉⣉⣉⣁⣀⣁⣈⣉⣉⣉⣉⣉⣁⣈⣁⣈⣉⣉⢉⣁⣙⣉⣉⣀⣈⣀⣉⣉⣈⣉⣉⣉⣉⣉⣀⣉⣀⣉⣉⣉⣉⣉⣉⣉⣉⣁⣉⣉⣁⣈⣉⣉⣉⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⠀⠀⠀⠀⠀⣀⣄⡀⠀⡄⢠⣄⣀⣀⣀⣀⡄⢠⡄⠀⣠⣠⡄⣤⣤⣄⣀⠀⢠⠀⣤⣤⠀⣤⣤⢀⣤⣤⠀⣤⠀⣤⣤⡤⢠⣤⣤⣤⣤⣤⣤⣄⣠⣤⣤⣤⣀⣠⣤⣄⣠⣤⣤⣤⣤⣤⢤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀ ⡤⠀⠀⠀⢀⣍⣭⣅⠀⣅⣨⣭⣬⣭⢩⣭⣅⣨⡅⠀⣬⣭⡅⣬⣭⣅⣬⠀⢨⠀⣭⣭⠠⢭⣥⠠⣬⣥⠀⣥⠀⣭⣭⡭⢠⣭⣭⣥⣭⣭⣭⣥⣌⣭⣍⣨⣍⣬⣭⣅⣨⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⣍⣭⡅⠀⡅⢨⣬⣩⣉⣭⣩⡅⢠⡄⠀⢨⣥⠁⣤⣭⣅⣬⠀⢨⠀⣬⣬⢠⢭⣬⢠⢭⣭⠀⣤⠀⣭⣭⣭⣤⣭⣥⣭⣭⣭⣭⣭⣭⣭⣅⣨⣍⣬⣭⣥⢬⣭⣭⣭⣭⣭⣬⣬⠍⠈⠉⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣭⣭⡇⠀⡅⢨⣭⣬⣭⣭⣭⡅⢠⡄⠀⢨⣬⠄⣤⣽⣅⣬⠀⢨⠀⣬⣬⠠⢭⣽⢀⣭⢭⠀⣤⠀⣭⣯⡭⢩⣭⣭⣯⣭⢠⣬⣭⣭⣡⣤⣤⣭⣌⣥⣬⣌⣥⣬⣭⣽⣼⣤⣽⣤⣠⢤⣤⣤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⣥⣧⡆⠀⡄⢰⣧⣤⣤⣤⣤⡄⢠⡄⠀⢰⣴⡄⣴⣶⣄⣤⠀⢠⠀⣼⣵⢠⣶⣶⢤⣼⣶⠀⣤⠀⣷⣥⣤⣤⣥⡥⢠⣆⠠⣦⣦⣧⣶⣦⣆⠄⠀⠀⠈⠀⠈⠀⠀⠀⠉⠀⠀⠈⠈⠈⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⣤⣦⡄⠀⡆⢰⣦⣤⣤⣤⣤⡆⢰⡄⠀⢰⣴⡄⣴⣶⣤⣤⠀⢰⠀⣴⣾⢠⢴⣶⣠⣴⣶⠀⣤⠀⣶⣴⣴⣆⣶⣶⣴⢰⣶⣦⣶⣶⣶⣶⣦⣴⣆⢴⣶⣶⣶⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⠤⠤⠤⠤⠤⠬⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤ ⣆⣶⣶⣶⣦⠴⡶⣦⢴⣶⡆⢰⡦⡆⣴⣶⡆⢴⣶⣶⡆⢰⣦⣴⣤⣴⠀⢰⣶⣤⣤⣤⣤⣦⣤⣤⣶⠀⣶⣶⣦⠠⣶⣶⡤⣤⡀⢐⣶⣤⣤⡤⢰⡆⡆⣆⡆⡀⢰⣶⡦⢴⡦⢴⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠤⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠷⠷⠷⠶⠷⠦⠶⠿⠇⠐⠾⠇⠴⠾⠇⠲⠾⠶⠆⠰⠶⠶⠰⠶⠶⠰⠀⠾⠾⠺⠶⠶⠾⠾⠾⠿⠷⠶⠀⠶⣶⠶⠶⠦⠠⠶⠆⠖⠶⠶⠶⠦⠰⠶⠆⠠⠲⠷⠶⠦⠲⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠶⠷⠷⠾⠿⠇⠰⠯⠇⠶⠿⠆⠺⠿⠯⠇⠰⠶⠾⠼⠶⠶⠰⠀⠾⠺⠶⠶⠶⠷⠶⠾⠀⡶⠶⠶⠶⠀⠷⠔⠇⠄⠰⠶⠶⠶⠶⠇⠐⠧⠲⠇⠄⠰⠶⠆⠠⠲⠶⠶⠶⠲⠾⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠯⠿⠿⠿⠷⠶⠗⠷⠺⠿⠇⠰⠿⠇⠾⠿⠇⠺⠿⠯⠇⠰⠶⠾⠼⠶⠶⠰⠀⠿⠸⠶⠾⠶⠷⠶⠾⠀⠞⠷⠶⠶⠷⠠⠶⠶⠶⠶⠇⠀⠇⠰⠶⠇⠐⠇⠰⠶⠆⠠⠲⠷⠶⠶⠲⠾⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠚⠟⠷⠺⠿⠇⠠⠿⠇⠨⠿⠇⠸⠿⠯⠇⠰⠶⠾⠼⠶⠶⠂⠀⠿⠿⠶⠶⠷⠺⠶⣶⠀⠾⠶⠶⠷⠶⠶⠀⠶⠷⠶⠶⠲⠶⠷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠚⠟⠷⠺⠿⠇⠨⠿⠇⠸⠿⠇⠸⠿⠾⠇⠰⠶⠾⠼⠶⠶⠂⠀⠻⠷⠶⠸⠾⢷⠿⠶⡶⠀⠷⠷⠶⠧⠀⠒⠿⠶⠶⠲⠷⠿⠇⠀⠷⠇⠰⠶⠶⠾⢷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠿⠚⠟⠷⠺⠿⠇⠈⠿⠇⠙⠿⠆⠘⠿⠫⠃⠺⠾⠺⠺⠾⠘⠀⠺⠶⠺⠶⠶⠤⠾⠻⠶⠿⠶⠧⠤⠶⠷⠇⠇⠟⠶⠇⠰⠶⠶⠶⠇⠃⠀⠷⠶⠷⠾⠷⠻⠶⠾⠴⠶⠾⠀⠺⠾⠺⠺⠾⠀⠀⠀⠀⠀⠀ ⡇⡟⡿⡟⡟⠚⡟⡗⠛⣟⡇⠈⠿⡇⠛⠿⠆⠘⢟⠋⠃⠺⠻⠛⠻⠟⠈⠀⠻⠛⠟⠻⠸⢛⠀⠻⠛⠀⠛⠛⡳⠛⠀⠏⠟⠿⠓⠀⠁⠒⡟⠟⠒⡛⠿⠛⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡃⡟⡟⡟⡛⠛⡟⡗⠛⣟⡇⠈⣗⡋⠛⠛⠋⠘⢛⣛⠃⠘⠻⠛⢺⠺⠻⠘⠀⢛⠻⠛⢘⢛⠿⠛⠛⠿⠀⠛⡛⠟⠓⠀⠚⡟⠛⠞⠚⠗⡛⡃⠀⡟⠃⠘⠛⠻⠛⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⡛⠛⡛⡛⠛⣛⡃⠘⡓⡃⢛⣛⡃⢘⡛⣛⡃⠘⠛⢛⢘⠛⠛⠘⠀⢛⣛⡛⣘⣛⣿⣛⣛⢿⠀⣛⠛⠛⡓⣀⠚⠛⡛⠛⣛⡛⠛⠃⠀⠛⡃⠘⠛⠻⠛⡻⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣓⣛⣛⣛⡛⢛⡛⡓⢛⣛⡃⠐⡋⡃⢛⣋⡃⢘⣛⣓⡃⠘⠛⢛⢚⠛⠛⠘⠀⢘⣛⣛⣓⣓⣛⣛⣛⢘⠀⣛⡛⠋⠛⡃⠛⡛⠛⡈⠛⠛⡛⠃⠐⠙⠛⡛⠓⠙⠛⠛⣃⡘⠛⠃⠘⠛⠻⠛⠻⠗⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⡛⢙⣋⡛⢙⣛⡃⢘⡋⡃⢛⣛⡃⢚⣛⣓⡃⠘⠛⢛⢚⠛⠛⠘⠀⢘⣛⣛⣓⣓⣛⣛⣛⢚⠀⣛⠛⠛⡛⣛⡛⠛⡘⠛⣛⡋⠛⡛⠃⠐⡙⠛⠛⠛⠙⣛⡛⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⣛⢉⣋⡛⢙⣛⡃⢐⣋⡃⣘⣛⡃⢘⣛⣃⡃⢘⢛⢛⢘⢛⠛⢐⠀⢘⣛⣛⣓⣓⣛⣛⣛⢘⠀⣛⣛⠋⢛⡃⠛⣛⠋⣀⡛⠛⡋⡃⡐⠙⠛⡛⠛⠙⡛⢛⣁⡘⠛⠃⠘⠛⠻⠛⠻⠓⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⣛⢉⣋⡛⢙⣛⡃⢀⣋⡃⣘⣛⡃⢘⣛⣛⡃⢘⢛⢛⠚⠛⢛⠁⣀⡘⢛⠛⡛⠓⢛⠛⢛⣘⡀⣛⠛⠛⣛⣛⡛⠋⣈⡛⡛⠋⡛⠛⡃⠈⠙⢛⠛⠋⠙⠛⠛⢁⣀⡀⢀⠀⢀⠀⠀⠀⠀⢀⢀⠀⠀⡀⢀⣀ ⠃⠛⠛⠛⠛⠉⠋⠛⠙⠛⠃⠀⠋⠃⠙⠛⠃⠘⠛⠛⠁⠙⠛⠙⠙⠛⠈⠀⠛⠛⠙⠛⠛⠀⠛⠛⠛⠙⠛⠛⠀⠛⠋⠛⠛⠀⠋⠛⠛⠃⠃⠈⠛⠙⠙⠛⠙⠃⠘⠛⠃⠘⠛⠛⠙⠛⠛⠁⠈⠀⠈⠙⠛⠙⠋⠙⠛⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⡍⠉⣍⣉⣉⣍⣉⣉⠉⡍⢩⣍⣉⣉⣉⣉⡉⢉⡉⢩⣭⣉⣉⣉⣉⣉⣩⠉⢩⠉⣭⣭⢉⣭⣭⡉⣭⣭⠉⣉⠉⣭⣉⣍⣉⡍⣉⣍⣉⣉⣍⡉⡍⢩⣍⣉⣩⣉⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉ ⣁⣀⣉⣉⡉⣉⣉⡁⣀⣁⣈⣉⣉⣉⣉⣉⣁⣈⣁⣈⣉⣉⢉⣁⣙⢉⢈⢀⣈⣀⣉⢉⣈⣉⣉⣈⣉⣉⣀⣉⣀⣉⣉⣉⡉⡉⡁⡉⣉⡁⣉⣁⡁⣈⣉⣉⣉⣉⣉⣀⢀⢀⣀⣀⢀⣀⢀⢀⣀⢀⣀⢀⣀⢀⣀⢀⢀⣀ ⠀⠀⠀⠀⢀⣀⣄⡀⠀⡄⢠⣄⣀⣀⣀⣀⡄⢠⡀⠀⣠⣠⡄⣤⣤⣄⣀⠀⢠⠀⣤⣤⠀⣤⣤⢀⣤⣤⠀⣄⠀⣤⣤⡤⢠⣤⣤⣤⣤⣤⣤⣄⣠⣤⣤⣤⢀⣠⣤⣄⣠⣤⣤⣤⣤⣤⢤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀ ⡤⠀⠀⠀⠀⣍⣭⣅⠀⣅⣨⣭⣬⣭⢩⣭⣅⣨⡅⠀⣬⣭⡅⣬⣭⣅⣬⠀⢨⠀⣭⣭⠨⢭⣥⠠⣬⣥⠀⣄⠀⣭⣭⡭⢠⣭⣭⣥⣭⣭⣭⣥⣌⣭⣍⣨⣍⣬⣭⣅⣨⣭⣭⣭⣭⣭⢭⣭⣭⣭⣭⣭⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⣍⣭⡅⠀⡅⢨⣬⣍⣩⣩⣍⡅⢨⡄⠀⢨⣥⠁⣬⣭⣅⣨⠀⢨⠀⣬⣬⢠⢭⣬⢠⢭⣭⠀⣤⠀⣭⣥⣭⣤⣭⣥⣭⣭⣥⣭⣭⣭⣭⡅⣨⣍⣬⣭⣥⢬⣭⣭⣭⣬⢭⣬⣬⠍⠉⠉⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣥⣭⡅⠀⡅⢨⣭⣬⣭⣭⣭⡅⢠⡄⠀⢨⣬⠄⣤⣭⣅⣬⠀⢨⠀⣬⣭⢠⢭⣭⠠⣭⢭⠀⣤⠀⣥⣭⡍⢩⣭⣭⣭⣭⢠⣭⣭⣭⣡⣤⣤⢭⣌⣭⣬⣄⣥⣬⣭⣭⣬⣤⣭⣤⣠⢤⣤⣤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣤⣦⡆⠀⡄⢰⣧⣤⣤⣤⣤⡄⢠⡄⠀⢰⣴⡄⣴⣿⣄⣤⠀⢠⠀⣴⣶⢠⣶⣴⡤⣺⣶⠀⣤⠀⣯⣥⣤⣄⣥⡥⢠⣆⠀⣦⣦⣦⣶⣦⣆⠄⠀⠀⠉⠀⠈⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⣤⣦⡄⠀⡆⢰⣦⣤⣤⣤⣤⡆⢠⡄⠀⢰⣴⡄⣴⣶⣤⣤⠀⢰⠀⣴⣶⢠⣴⣶⣠⣴⣶⠀⣤⠀⣶⣴⣴⡆⣶⣶⣤⢰⣶⣶⣖⣶⣶⣶⣦⣴⣆⢴⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⠤⠤⠤⠤⠤⠬⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤ ⣆⣶⣶⣶⣦⠴⡶⣦⢴⣶⡆⢰⡦⡆⣴⣶⡆⢰⣶⣖⡆⢰⣦⣴⣤⣴⠀⢰⣦⣤⣤⣤⣤⣦⣤⣤⣶⠀⣶⣶⣦⠠⣶⣶⡤⣤⡀⢐⣶⣤⣤⡄⢰⡦⡆⡆⡆⡀⢰⣶⡦⢴⡦⢴⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠤⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠷⠷⠷⠷⠶⠷⠧⠶⠿⠇⠐⠾⠇⠴⠾⠇⠴⠾⠾⠆⠰⠶⠶⠰⠶⠶⠰⠀⠾⠾⠺⠾⠲⠿⠾⠿⠷⠿⠶⠀⠶⣶⠶⠶⠦⠠⠶⠆⠗⠖⠶⠶⠦⠰⠶⠆⠠⠶⠷⠶⠦⠲⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠶⠷⠧⠶⠿⠇⠐⠯⠇⠶⠿⠇⠺⠿⠷⠇⠰⠶⠾⠸⠶⠶⠶⠀⠾⠸⠶⠶⠶⠷⠶⠾⠀⡶⠶⠶⠶⠀⠷⠔⠇⠄⠰⠶⠶⠶⠶⠇⠐⠧⠲⠆⠄⠰⠶⠆⠠⠲⠷⠶⠶⠲⠾⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠯⠿⠿⠿⠷⠶⠷⠷⠺⠿⠇⠰⠿⠇⠼⠿⠇⠺⠿⠿⠇⠰⠶⠾⠼⠶⠶⠰⠀⠿⠸⠶⠼⠶⠷⠶⠾⠀⠟⠷⠶⠶⠷⠀⠶⠶⠶⠶⠇⠀⠇⠰⠶⠇⠀⠇⠰⠶⠆⠰⠲⠷⠶⠶⠲⠾⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠞⠟⠷⠺⠿⠇⠠⠿⠇⠬⠿⠇⠺⠿⠿⠇⠰⠶⠾⠸⠶⠶⠂⠀⠿⠿⠶⠶⠷⠼⠶⣶⠀⠾⠶⠶⠷⠶⠶⠀⠖⠷⠶⠶⠒⠶⠷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠿⠚⠟⠷⠺⠿⠇⠨⠿⠇⠹⠿⠇⠸⠿⠾⠇⠰⠶⠺⠼⠶⠶⠂⠀⠻⠷⠖⠸⠾⠶⠾⠶⡶⠀⠻⠷⠶⠧⠠⠒⠿⠶⠶⠲⠶⠿⠇⠀⠷⠆⠰⠶⢶⠾⢷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠇⠿⠿⠿⠿⠚⠟⠷⠺⠿⠇⠨⠿⠇⠚⠿⠇⠸⠿⠫⠇⠺⠶⠺⠺⠾⠊⠀⠺⠶⠺⠶⠶⠤⠶⠻⠶⠿⠲⠦⠤⠾⠷⠇⠇⠟⠶⠃⠰⠗⠷⠷⠇⠇⠀⠿⢶⠶⠾⠷⠺⠶⠾⠵⠶⠾⠀⠺⠾⠲⠾⠶⠀⠀⠀⠀⠀⠀ ⠃⡟⡛⡟⡟⠚⡟⡷⠚⣟⡇⠘⡿⡇⠛⠿⠆⠘⢛⠋⠃⠺⠻⠛⠻⠟⠈⠀⠻⠻⠿⠻⠸⢿⠀⠛⠛⠀⠟⠟⡷⠟⠀⠟⠛⠟⠓⠀⠁⠚⠟⠛⠗⠛⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⡛⡟⡛⡛⠛⡛⠗⠛⣟⡃⠈⣳⡛⠛⠟⠃⠸⢛⣛⠃⠘⠻⠛⠚⠚⠛⠚⠀⠛⠻⠟⠘⢛⠿⠛⠛⠿⠀⠛⡛⠟⠓⠀⠚⡛⠛⠖⠛⠟⡛⡃⠀⡛⠇⠘⠛⠻⠟⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⡛⠛⡛⡛⢛⣛⡃⠘⡃⡓⢛⣛⡓⠘⣛⡛⠃⠘⠛⢛⢘⠛⠛⠘⠀⢛⣛⣛⣘⣛⣿⣛⣛⢿⠀⣛⠛⠛⠓⡀⡚⠛⡛⠛⣛⡛⠛⡃⠀⠛⡃⠘⠛⠻⠛⡻⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣓⣛⣛⣛⡛⠛⡛⡓⢛⣛⡃⠘⡛⡃⢛⣛⡃⢘⣛⣓⡃⠘⠛⢛⢚⠛⠛⠑⠀⢘⣛⣛⣓⣓⣛⣛⣛⣘⠀⣛⡛⠋⠛⡋⠛⡛⠓⡀⠛⠛⡛⠃⠐⠙⠛⡛⠓⠙⠛⠛⡃⡘⠛⠃⠘⠛⠿⠛⠻⠓⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⡛⢛⡋⡛⢙⣛⡃⠘⣋⡃⢛⣛⡃⢘⣛⣓⡃⠘⠛⢛⢚⠛⠛⠛⠀⢘⣛⣛⣓⣓⣛⣛⣛⢚⠀⣛⠛⠛⡛⣛⡛⠛⡐⠛⣛⡋⠛⡛⠃⠐⡙⠛⠛⠛⠙⣛⡛⢃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⡛⢉⣋⡛⢙⣛⡃⢀⣋⡃⢈⣓⡃⢘⣛⣛⡃⠘⠛⢛⢚⢛⢛⢁⠀⢘⣚⣛⣓⣓⣛⣛⣛⣘⠀⣛⣛⠋⢛⡃⠛⣛⠛⣀⠛⠛⡛⡃⠐⠙⠛⡛⠛⠙⣛⢛⣁⡘⠛⠃⠘⠛⠻⠛⠻⠓⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⣛⢉⣋⡛⢙⣛⡃⢈⣋⡃⣘⣛⡃⣘⣛⣛⡁⢘⢛⢛⠚⢛⢛⠁⣀⡘⢛⠛⠓⠓⢛⠛⢛⣘⡀⣛⠋⠛⣛⣛⡛⠋⣈⡛⡛⠋⡛⠛⡃⡘⠙⢛⠛⠛⠙⠛⠛⢁⣀⠀⢀⢀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣀ ⠃⠛⠛⠛⠛⠉⠋⠛⠙⠛⠃⠘⠋⠃⠑⠛⠋⠙⠛⠙⠁⠙⠛⠙⠙⠛⠈⠀⠛⠛⠙⠛⠛⠀⠛⠛⠛⠙⠛⠛⠀⠛⠋⠛⠛⠀⠋⠋⠛⠃⠃⠈⠛⠙⠙⠛⠙⠃⠘⠛⠃⠘⠛⠛⠙⠛⠛⠁⠈⠀⠈⠛⠛⠙⠋⠛⠛⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⣍⢉⣍⣉⣉⣍⣉⣉⠉⡍⢩⣍⣉⣉⣉⣉⡉⢉⡉⢩⣭⣉⣉⣉⣉⣉⣩⠉⢩⠉⣭⣭⢉⣭⣭⢉⣭⣭⠉⣉⠉⣭⣉⣍⣉⡍⣉⣍⣉⣉⣍⡉⡍⢩⣍⣉⣩⣉⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉ ⡁⡀⣉⡉⡉⡉⡉⣁⣀⡁⡈⢉⣉⣉⣉⣉⣁⢈⣁⣈⣉⢉⢉⣁⢙⣉⢉⣀⢈⢀⣉⣉⣈⢉⡉⣉⣉⢉⡀⣉⣀⣉⣉⡉⡉⡉⣁⡉⡉⡁⡉⡁⡁⣈⣉⣉⡉⣉⣉⣀⣀⢀⢀⣀⣀⣀⢀⢀⢀⣀⣀⣀⢀⢀⢀⢀⣀⣀ ⠀⠀⠀⠀⠀⣀⣄⡀⠀⡄⢠⣄⣀⣀⣀⣀⡄⢠⡄⠀⣠⣠⡄⣤⣤⣄⣀⠀⢠⠀⣤⣤⠀⣤⣤⢀⣠⣤⠀⣠⠀⣤⣤⡤⢠⣤⣤⣤⣤⣤⣤⣄⣠⣤⣤⣤⢀⣠⣤⣄⣠⣤⣤⣤⣤⢤⢤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀ ⡤⠀⠀⠀⢀⣍⣭⣅⠀⣅⣨⣭⣬⣭⣩⣭⣅⣨⡄⠀⣨⣥⡅⣬⣭⣍⣬⠀⢨⠀⣭⣭⠈⢭⣥⠨⣬⣥⠀⣥⢀⣭⣭⡭⢠⣭⣭⣥⣭⣭⣭⣥⣌⣭⣍⣨⣍⣬⣭⣅⣨⣭⣭⣭⣭⣭⢭⣭⣬⣭⣭⣭⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣍⣭⡅⠀⡅⢨⣬⣩⣩⣍⣭⡄⢠⡄⠀⢨⣬⠁⣤⣭⣅⣨⡀⢨⠀⣬⣬⢠⢬⣬⠨⢭⣭⠀⣤⠀⣭⣭⣥⣤⣭⣥⣭⣭⣥⣭⣭⣭⣭⣅⣨⣅⣬⣭⣥⢬⣭⣭⣩⣬⢭⣬⣬⠍⠉⠉⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣭⣭⡅⠀⡅⢨⣭⣬⣭⣭⣭⡅⢠⡄⠀⢨⣬⠄⣤⣭⣅⣬⠀⢨⠀⣬⣬⢠⣭⣭⠠⣭⢭⠀⣤⠀⣥⣭⡭⢩⣭⣥⣭⣭⢠⣭⣭⣭⣡⣤⣤⣭⣌⣥⣬⣄⣥⣬⣭⣭⣬⣬⣭⣤⣠⢤⣤⣤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⣤⣦⡆⠀⡄⢰⣦⣤⣤⣤⣤⡄⢠⡄⠀⢸⣴⡄⣴⣾⣄⣬⠀⢠⠀⣬⣷⢠⣶⣶⣤⣰⣶⠀⣤⠀⣷⣥⣤⣤⣥⡥⢠⣆⠠⣦⣦⣧⣶⣦⣆⠄⠀⠀⠉⠀⠈⠀⠀⠀⠈⠀⠈⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣤⣦⡄⠀⡆⢰⣦⢤⣤⣤⣤⡆⢠⡄⠀⢰⣴⡄⣴⣶⣤⢤⠀⢰⠀⣴⣶⢀⣰⣶⣠⣶⣶⠀⣤⠀⡶⣴⣴⡆⣶⣶⣤⢰⣶⣦⣖⣶⣶⣶⣦⣴⣆⢴⣶⣶⣶⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⠤⠤⠄⠤⠄⠤⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤ ⣆⣶⣶⣶⣦⠴⡶⣦⢴⣶⡆⢰⡦⡆⢴⣶⡆⢴⣶⣶⡆⢰⣦⣴⣤⣴⠀⢰⣲⣤⣤⣤⣤⣦⣤⣤⣦⠀⣶⣶⣦⠠⣶⣶⡤⣤⡀⢐⣶⣤⣤⡤⢰⠆⡆⣆⡆⡀⢰⣶⡦⢴⡦⢴⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠤⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠆⠷⠷⠷⠶⠶⠷⠦⠦⠿⠇⠰⠶⠇⠴⠾⠇⠲⠾⠞⠆⠰⠶⠶⠰⠶⠶⠲⠀⠾⠶⠺⠶⠶⠼⠶⠿⠷⠺⠶⠀⠶⣶⠶⠶⠦⠰⠶⠆⠖⠖⠶⠶⠆⠰⠶⠆⠠⠶⠷⠶⠦⠲⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠶⠷⠧⠦⠿⠇⠰⠯⠇⠶⠿⠇⠾⠿⠧⠆⠰⠶⠾⠾⠶⠶⠲⠀⠾⠸⠶⠴⠶⠷⠶⠾⠀⡶⠶⠶⠶⠀⠧⠔⠧⠄⠰⠶⠶⠶⠶⠇⠀⠧⠲⠇⠄⠰⠶⠆⠠⠲⠷⠶⠶⠲⠾⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠯⠿⠿⠿⠷⠶⠗⠷⠾⠿⠧⠐⠿⠇⠾⠿⠇⠺⠿⠯⠇⠰⠶⠾⠼⠶⠶⠲⠀⠿⠸⠶⠼⠶⠷⠶⠾⠀⠟⠶⠶⠶⠷⠀⠶⠶⠶⠶⠇⠀⠇⠰⠶⠇⠰⠇⠰⠶⠆⠠⠲⠷⠶⠶⠲⠾⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠚⠗⠷⠺⠿⠇⠀⠿⠇⠸⠿⠇⠸⠿⠯⠇⠰⠶⠾⠼⠶⠶⠂⠀⠿⠿⠶⠶⠷⠼⠶⣶⠀⠾⠶⠶⠿⠶⠶⠀⠖⠷⠶⠶⠲⠶⠷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠯⠿⠿⠿⠿⠚⠟⠷⠺⠿⠇⠈⠿⠇⠸⠿⠇⠸⠿⠾⠇⠰⠶⠾⠼⠶⠶⠊⠀⠻⠷⠖⠸⠟⢶⠾⠶⡶⠀⠧⠷⠶⠧⠀⠞⠿⠶⠶⠲⠶⠿⠗⠀⠷⠆⠰⠶⠶⠞⠷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠯⠿⠿⠿⠿⠚⠟⠷⠺⠿⠇⠈⠿⠇⠘⠿⠆⠘⠿⠫⠃⠺⠾⠲⠲⠾⠀⠀⠺⠶⠺⠶⠶⠤⠶⠿⠶⠿⠳⠦⠄⠶⠷⠖⠇⠟⠶⠇⠰⠷⠷⠶⠇⠇⠀⠷⢶⠶⠿⠷⠺⠶⠾⠴⠶⠾⠄⠺⠾⠺⠾⠶⠀⠀⠀⠀⠀⠀ ⡇⡟⡛⡟⡟⠚⡟⡗⠛⣿⠇⠈⠿⡃⠛⠿⠂⠙⢟⠓⠃⠺⠛⠻⢻⠻⠘⠀⠻⠻⠿⠛⠚⢿⠀⠻⠟⠀⠟⠟⠳⠟⠀⠟⠟⠟⠓⠀⠁⠚⡟⡟⠗⠛⠻⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣟⣛⡛⡟⠚⡟⡓⠛⣿⡃⠈⢓⡋⠛⠿⡇⠚⢛⢛⠃⠘⠻⠛⢘⠛⠻⠘⠀⠛⠛⠛⢘⢛⠿⢟⠛⠿⠀⠻⡛⠛⠓⠀⠚⡟⠟⠓⠛⠛⡗⡇⠀⡛⠃⠘⠟⠻⠟⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⡛⣛⡛⠛⡛⡓⢛⣛⡃⠘⡓⡓⢛⣛⡃⠚⡛⣛⡃⠘⠛⢛⢘⠛⠛⠚⠀⢛⣛⡛⣘⣛⣿⣛⣛⢿⠀⣛⠛⠛⠓⣀⠚⠛⡛⠛⣛⡛⠛⠃⠀⠛⡃⠘⠛⠻⠛⡻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣓⣛⣛⣛⡛⠛⡛⡓⢙⣛⡃⢀⡋⡃⢛⣛⡋⢙⣛⣓⡃⠘⠛⢛⢚⠛⠛⠛⠀⢘⣛⣛⣓⣓⣛⣛⣛⢘⠀⣛⡛⠋⠛⡃⠛⣛⠛⡈⠛⠛⡛⠃⠐⠛⠛⡛⠓⠙⠛⠛⣃⡘⠚⠃⠘⠛⠻⠛⠻⠓⠀⠀⠀⠀⠀⠀⠀⠀ ⣓⣛⣛⣛⡛⢙⣋⡛⢙⣛⡃⢘⡋⡃⢛⣛⡃⢘⣋⣛⡃⠘⠛⢛⢚⠛⠛⠑⠀⢘⣛⣛⣓⣓⣛⣛⣛⣚⠀⣛⠛⠛⡛⣛⡛⠛⡐⠛⣛⡃⠛⡛⠃⠐⡙⠛⠛⠛⢙⣛⡛⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣓⣛⣛⣛⣛⢉⣋⡛⢙⣛⡃⢀⣋⡃⣘⣓⡃⢘⣛⣓⡃⢘⠛⢛⢚⠛⢛⢑⠀⢘⣚⣛⣓⣓⣛⣛⣛⣘⠀⣛⣛⠋⠛⡃⠛⣛⠛⣀⠛⠛⡋⡃⠐⠙⠛⡛⡛⠙⢛⠛⣃⡘⠛⠃⠘⠛⠻⠛⠻⠓⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⣛⢉⣋⡛⢙⣛⡃⢘⣋⡃⣘⣛⡃⣘⣛⣛⡃⢘⢛⢛⢘⠛⢛⠈⣀⡘⢛⡛⠛⠑⢛⠛⣛⣘⠀⣛⠛⠛⣛⣛⡛⠛⣈⡛⡋⠋⡛⠛⠃⡐⢙⢛⠋⠋⠙⢛⠛⢁⡀⠀⢀⠀⢀⠀⠀⠀⠀⢀⢀⠀⠀⠀⢀⣀ ⠓⠛⠛⠛⠛⠉⠋⠛⠙⠛⠃⠐⠋⠃⠈⠛⠃⠘⠑⠋⠃⠙⠛⠙⠙⠛⠘⠀⠙⠛⠙⠛⠛⠀⠛⠛⠙⠙⠛⠛⠀⠛⠋⠛⠋⠀⠋⠋⠛⠃⠃⠘⠛⠙⠙⠛⠙⠃⠘⠛⠃⠘⠛⠛⠛⠛⠛⠁⠈⠁⠈⠛⠛⠛⠋⠛⠛⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⣍⢉⣍⣉⣉⣍⣉⡉⠉⡍⢩⣍⣉⣉⣉⣉⡉⢩⡉⢩⣭⣉⣉⣉⣉⣉⣩⠉⢩⠉⣍⣭⣉⣭⣭⡉⣭⣭⠉⣉⠉⣭⣉⣍⣉⡍⣉⣍⣉⣉⣍⡉⡍⢩⣍⣉⣩⣉⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉ ⣁⣀⣉⣉⣁⣉⣉⣁⣀⡁⣈⣉⣉⣉⣉⣉⣁⣈⣁⣈⣉⢉⢉⣁⣙⣉⣈⢀⣈⣀⣉⣉⣈⣉⣉⡉⣉⣉⣀⣀⣀⣉⣉⣉⣉⣉⣁⣉⣉⣁⣉⣉⣁⣈⣉⣉⣉⣉⣉⣀⣀⣀⣀⣀⣀⣀⢀⣀⢀⣀⣀⣀⢀⣀⣀⣀⣀⣀ ⠀⠀⠀⠀⠀⣀⣄⡀⠀⡄⢠⣤⣀⣀⣀⣀⡄⢠⡄⠀⣠⣠⡄⣤⣤⣄⣀⠀⢠⠀⣤⣤⠠⣤⣤⢀⣤⣤⠀⣠⠀⣤⣤⡤⢠⣤⣤⣤⣤⣤⣤⣄⣠⣤⣤⣤⢀⣠⣤⣄⣠⣤⣤⣤⣤⣤⢤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀ ⡤⠀⠀⠀⢀⣍⣭⡅⠀⣅⣨⣭⣬⣭⢩⣭⣅⣨⡄⠀⣬⣥⡅⣬⣭⣅⣬⠀⢨⠀⣭⣭⠨⢭⣥⢠⣬⣥⠀⣤⠀⣭⣭⡭⢠⣭⣭⣥⣭⣭⣭⣥⣌⣭⣍⣨⣍⣬⣭⣅⣨⣭⣭⣭⣭⣭⢭⣭⣭⣭⣭⣭⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣍⣭⡅⠀⡅⢨⣬⣉⣉⣩⣉⡄⢠⡄⠀⢨⣥⠁⣥⣭⣅⣬⠀⢨⠀⣬⣬⢠⢭⣬⢠⢭⣭⠀⣤⠀⣭⣥⣥⣤⣭⣥⣭⣭⣥⣭⣭⣭⣭⡅⣨⣅⣬⣭⣥⢬⣭⣭⣭⣬⢭⣬⣬⠍⠈⠉⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣭⣭⡅⠀⡅⢨⣯⣬⣭⣭⣭⡅⢠⡄⠀⢸⣼⠅⣤⣭⣅⣬⠀⢨⠀⣬⣬⢠⣭⣽⠤⣭⢯⠀⣤⠀⣥⣭⡭⢩⣭⣭⣯⣏⢠⣭⣭⣭⣡⣤⣬⣥⣌⣥⣼⣌⣤⣬⣭⣭⣬⣬⣽⣥⣠⢴⣴⣤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣤⣤⡇⠀⡄⢠⣦⣤⣤⣤⣤⡄⢠⡄⠀⢸⣤⡄⣴⣾⣤⣤⠀⢠⠀⣴⣴⠠⣦⣶⢤⣴⣦⠀⣤⠀⣦⣤⣤⣤⣥⡤⢠⣆⠠⣦⣤⣧⣤⣦⣄⡄⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣤⣦⡄⠀⡆⢰⣦⢤⣤⣤⣤⡆⢠⡄⠀⢸⣴⡄⣴⣶⣤⣤⡀⢰⠀⣴⣶⢠⣴⣶⣀⣴⣶⠀⣤⠀⣶⣶⣴⡖⣶⣶⣤⢰⣶⣦⣶⣶⣶⣶⣦⣴⣆⢴⣦⣶⣶⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⠤⠤⠤⠤⠤⠬⠥⠤⠤⠤⠤⠄⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤ ⣆⣶⣶⣶⣦⠴⡦⣦⢴⣶⡆⢰⡦⡆⢰⣶⡆⢰⣶⣶⡆⢰⣦⣴⣠⣴⠀⢰⣶⣤⣤⣤⣤⣦⣤⣤⣶⠀⣶⣲⣦⠠⣶⣶⡤⣤⡀⢐⣶⣤⣤⡤⢰⡦⡆⣆⡆⡀⢰⣶⡦⢴⡦⢴⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠤⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠆⠷⠶⠷⠶⠶⠶⠦⠦⠟⠇⠐⠶⠃⠴⠾⠇⠰⠾⠞⠆⠰⠶⠶⠰⠶⠶⠀⠀⠶⠾⠲⠶⠶⠰⠷⠿⠳⠷⠶⠀⠶⣴⠶⠖⠦⠠⠶⠆⠖⠖⠶⠶⠆⠐⠶⠆⠠⠲⠶⠶⠦⠲⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠇⠿⠿⠿⠷⠶⠷⠷⠢⠿⠆⠐⠧⠇⠶⠾⠆⠺⠿⠧⠆⠰⠶⠶⠴⠶⠶⠠⠀⠞⠰⠶⠰⠶⠷⠶⠾⠀⡶⠶⠶⠶⠀⠷⠆⠇⠄⠰⠶⠶⠶⠶⠇⠀⠧⠒⠆⠄⠰⠶⠆⠠⠲⠶⠶⠦⠲⠾⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠖⠗⠷⠺⠿⠇⠰⠿⠇⠴⠿⠆⠸⠿⠯⠇⠰⠶⠾⠼⠶⠶⠐⠀⠿⠸⠶⠲⠶⠷⠶⠾⠀⠾⠶⠶⠶⠷⠀⠖⠶⠶⠶⠇⠀⠇⠰⠶⠇⠀⠇⠰⠶⠆⠠⠲⠷⠶⠶⠲⠾⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠞⠟⠷⠪⠿⠇⠀⠿⠇⠀⠿⠇⠸⠿⠯⠆⠰⠶⠾⠸⠶⠶⠀⠀⠿⠾⠶⠶⠷⠾⠶⡶⠀⠾⠶⠶⠶⠶⠖⠀⠖⠷⠶⠶⠒⠶⠷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠇⠿⠿⠟⠗⠚⠟⠷⠺⠿⠇⠈⠿⠇⠸⠿⠆⠸⠿⠮⠇⠰⠶⠾⠸⠶⠶⠀⠀⠻⠷⠶⠸⠾⠶⠾⠶⢶⠀⠷⠷⠶⠧⠀⠒⠿⠶⠶⠒⠶⠿⠇⠀⠷⠆⠰⠶⢶⠾⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠚⠟⠷⠺⠯⠇⠈⠿⠇⠙⠿⠆⠘⠿⠉⠇⠺⠾⠲⠺⠷⠀⠀⠰⠶⠺⠶⠾⠀⠲⠿⠶⠻⠶⠦⠀⠶⠶⠆⠇⠟⠶⠂⠐⠶⠷⠶⠏⠁⠀⠟⠶⠶⠾⠕⠺⠷⠾⠴⠶⠾⠀⠲⠾⠲⠶⠶⠀⠀⠀⠀⠀⠀ ⠃⡛⡛⡛⡛⠚⡛⠓⠒⣟⡃⠈⠓⡃⠙⠛⠂⠘⢛⡋⠃⠘⠛⠛⠛⠛⠀⠀⠛⠛⠚⠛⠚⢛⠀⠛⠛⠀⠛⠛⠓⠛⠀⠛⠛⠻⠓⠀⠁⠒⠛⠛⠗⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣃⡟⡛⡛⡛⠚⡛⠓⠚⣛⡃⠈⣓⡃⠛⠛⠇⠘⢛⡓⠃⠘⠛⠚⠚⠚⠚⠚⠀⠛⠛⠚⠘⢛⠿⠺⠛⠷⠀⠛⡛⠛⠓⠀⠒⠛⠛⠒⠚⠓⠓⡃⠀⡛⠃⠐⠛⠻⠟⠳⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠃⣛⡛⣛⡛⠛⡛⡓⠛⣛⠃⠈⡓⡃⢈⣋⡃⠘⣋⠃⠃⠘⠛⢛⠘⠛⠛⠐⠀⢛⣛⡛⣘⣛⣿⣛⣛⢿⠀⣛⠛⠛⠃⡀⠊⠛⡛⠛⣋⡛⠛⠃⠀⠛⡃⠘⠛⠻⠛⡻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡃⣛⣛⣛⡛⠛⡛⡓⢓⣛⡃⠐⡋⡃⢛⣋⡃⢘⣛⣓⡃⠘⠛⢛⢘⠛⠛⠀⠀⢘⣛⣛⣓⣓⣛⣛⣛⣘⠀⣛⡛⠋⠛⡃⠓⡛⠛⡀⠛⠛⠋⠃⠀⠛⠛⡛⠓⠙⠛⠛⡃⡘⠛⠂⠘⠛⠻⠛⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⡛⠉⡋⡛⢙⣛⡃⠈⡋⡃⢛⡋⡃⢘⣋⣃⡃⠘⠛⢛⢘⠛⠛⠐⠀⢘⣛⣛⣓⣓⣛⣛⣛⢘⠀⣛⠛⠛⡛⣛⡛⠓⡀⠛⣛⡃⠛⡛⠃⠐⡙⠛⠛⠛⠙⣛⡛⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⣛⢉⣋⡛⢙⣛⡃⢀⣋⡃⣂⣛⠃⣘⣛⣓⡃⢘⠛⢛⢘⠛⠛⠀⠀⢘⣚⣛⣓⣓⣛⣛⣛⢘⠀⣛⣛⠋⠛⡃⠋⣛⠃⡀⠛⠛⡋⡃⠐⠙⠛⣛⠓⠙⠛⠛⣁⡈⠛⠃⠘⠛⠛⠛⠻⠓⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⡋⢉⣋⡛⢙⣛⡃⢈⣋⡃⣙⣛⡃⢘⣛⣃⡃⠘⠛⠛⠚⠛⠛⠁⣀⡙⢛⠛⠓⠓⠛⠛⣛⣘⠀⣛⠛⠛⡛⣛⡋⠛⣈⡛⡋⠋⡛⠛⠃⠐⠙⠛⠛⠋⠙⠛⠛⢁⡀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⡀ ⠃⠛⠛⠛⠛⠉⠋⠙⠙⠛⠃⠀⠋⠃⠘⠛⠂⠘⠙⠁⠃⠙⠛⠙⠙⠛⠀⠀⠉⠛⠙⠛⠛⠀⠛⠋⠛⠙⠛⠛⠀⠛⠋⠋⠋⠀⠃⠋⠛⠃⠃⠈⠛⠙⠙⠛⠙⠃⠘⠋⠃⠘⠙⠛⠙⠙⠛⠀⠈⠀⠈⠙⠛⠙⠉⠙⠛⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⣍⠉⣍⣉⣁⣉⣉⡉⠉⡉⢡⣍⣉⣉⣉⣉⡉⢩⡉⢩⣭⣉⣉⣉⣉⣉⣉⠈⢩⠉⣍⣭⢉⣬⣭⣉⣭⣭⠉⡉⠉⣭⣉⣉⣉⡍⣩⣍⣉⡁⡉⡉⡍⢩⣍⣉⣩⣉⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉ ⠁⡀⠉⠉⠉⡉⡉⠁⣀⠁⡀⠉⣉⢉⡉⠉⢁⠈⡁⢈⠉⢉⢉⣁⠛⢉⢈⢀⠈⡀⢉⠉⢀⡉⣉⡀⡉⠉⣀⠀⣀⠉⡉⠉⡁⡁⡁⠉⡉⠁⡉⢁⠁⡈⡉⡉⠉⣉⡉⡀⠀⠀⢀⣀⠀⢀⠀⠀⢀⠀⣀⢀⣀⠀⡀⢀⢀⡀ ⠀⠀⠀⠀⠀⣀⣄⡀⠀⡄⢠⣄⣀⣀⣀⣀⡄⢠⡀⠀⣠⣠⡄⣠⣤⣄⣀⠀⢠⠀⣤⣤⠀⣤⣤⠀⣠⣤⠀⡀⠀⣤⣤⡤⢀⣤⣤⣤⣤⣤⣤⣄⣠⣤⣤⣤⠀⣠⣤⣄⣠⣤⣤⣤⣤⣤⢤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀ ⡄⠀⠀⠀⠀⣍⣭⣅⠀⣅⣨⣭⣌⣭⢩⣭⣅⢨⡀⠀⣨⣭⠁⣬⣭⣅⣨⠀⢨⠀⣭⣭⠀⢭⣥⠀⣬⡥⠀⡀⠀⣭⣭⡅⢀⣭⣥⣥⣭⣭⣭⣥⣌⣭⣍⣨⣍⣨⣭⣅⣨⣭⣭⣭⣭⣭⢭⣭⣭⣭⣭⣩⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣅⣭⡅⠀⡄⢨⣬⣤⣩⣩⣩⡄⢠⡄⠀⢨⣥⠀⢤⣭⣅⣈⠀⢠⠀⣬⣬⢀⢬⣬⢠⢭⣭⠀⡄⠀⣭⡥⣥⣤⣭⣥⣭⣭⣥⣭⣬⣬⣭⡅⣨⣅⣬⣭⣥⢬⣭⣭⣡⣬⣭⣬⣬⠍⠈⠉⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣍⣭⡅⠀⡅⢨⣭⣌⣭⣭⣭⡅⢨⡄⠀⢨⣬⠄⢤⣭⣅⣬⠀⢠⠀⣬⣬⢀⢭⣭⢄⣭⢭⠀⡄⠀⣥⣭⡍⢩⣭⣭⣭⣭⢠⣍⣭⣭⢡⣤⣤⣭⣌⣥⣬⣌⣡⣬⣭⣭⣬⣤⣭⣥⣠⢠⣤⣤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣅⣥⡇⠀⡄⢠⣧⣤⣥⣤⣬⡄⢠⡄⠀⢈⣼⡄⣴⣾⣅⣬⠀⢠⠀⣼⣵⠠⣮⢴⢤⣲⣶⠀⣤⠀⣿⣥⣥⣤⣥⡥⢠⣅⠀⣧⣦⣦⣶⣦⣄⠄⠁⠈⠉⠀⠈⠀⠀⠀⠉⠀⠈⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣤⣦⡄⠀⡄⢰⣦⣤⣤⣤⣤⡆⢠⡀⠀⢰⣴⡄⢴⣶⣤⣤⠀⢰⠀⣴⣶⢠⢰⣶⡀⣴⣶⠀⡤⠀⣶⣤⣤⡆⣶⣶⣤⢰⣶⣦⣖⣦⣶⣶⣦⣴⣆⢴⣦⣶⣶⣶⣶⣦⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠄⠄⠄⠄⠠⠌⠅⠄⠤⠤⠤⠤⠤⠤⠤⠠⠤⠤⠠⠤⠠⠤⠠⠤⠠⠠⠤⠠⠤⠠⠤⠤⠀⠤⠠⠄⠄⠄⠤⠤⠀⠄⠄⠄⠄⠄⠄⠄⠤⠤⠤⠤⠄⠤⠤⠄⠤⠤⠤⠤⠠⠠⠠⠤⠠⠠⠠⠤⠠⠠⠤⠤⠠⠤⠠⠠⠤ ⡆⣶⣶⣶⣦⠴⡦⣦⢴⣶⡆⢐⡶⡆⣴⣶⡆⢰⣶⣆⡆⢰⣦⣴⣠⣴⠀⢰⣦⡤⣤⣤⣤⣦⣤⣤⢦⠀⣶⣶⣦⠠⢶⣶⡤⣤⡀⢐⣶⣤⣤⡤⢰⠆⡆⡆⡆⠀⢰⣶⡦⢴⡦⢴⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠤⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠦⠷⠷⠷⠶⠶⠶⠦⠶⠟⠇⠐⠶⠇⠴⠾⠆⠸⠶⠧⠇⠰⠶⠶⠰⠶⠶⠀⠀⠾⠾⠺⠶⠶⠺⠶⠶⠿⠷⠶⠀⠶⣶⠶⠶⠦⠰⠶⠖⠖⠖⠶⠶⠆⠰⠶⠆⠠⠶⠶⠶⠦⠲⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠶⠷⠷⠾⠿⠇⠰⠧⠇⠖⠿⠆⠸⠿⠧⠆⠰⠶⠶⠶⠶⠶⠂⠀⠾⠸⠶⠴⠶⠷⠶⠾⠀⡶⠶⠶⠶⠀⠷⠖⠇⠄⠰⠶⠶⠶⠶⠇⠀⠧⠲⠇⠄⠰⠶⠆⠠⠲⠶⠶⠦⠲⠶⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠯⠿⠿⠿⠷⠖⠷⠷⠺⠿⠇⠰⠿⠇⠾⠿⠇⠺⠿⠏⠇⠰⠶⠾⠼⠶⠶⠲⠀⠿⠸⠶⠸⠶⠷⠶⠾⠀⠿⠖⠶⠶⠷⠀⠖⠶⠶⠶⠗⠀⠇⠰⠶⠇⠀⠇⠰⠶⠆⠠⠲⠶⠶⠶⠲⠾⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠏⠿⠿⠿⠷⠖⠿⠷⠲⠿⠇⠰⠿⠇⠸⠿⠇⠸⠿⠏⠇⠰⠶⠾⠸⠶⠶⠂⠀⠻⠾⠶⠶⠿⠺⠶⣶⠀⠾⠶⠶⠶⠶⠖⠀⠖⠿⠶⠶⠖⠶⠷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠯⠿⠿⠿⠿⠚⠟⠷⠺⠿⠇⠨⠿⠇⠹⠿⠇⠽⠿⠮⠇⠸⠾⠾⠼⠶⠶⠺⠀⠻⠷⠶⠸⠛⠷⠾⠶⢶⠀⠧⠷⠶⠧⠀⠺⠿⠷⠶⠲⠷⠿⠗⠀⠷⠆⠰⠿⢶⠾⠷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠷⠿⠿⠿⠿⠚⠟⠷⠺⠯⠇⠈⠿⠇⠘⠿⠇⠘⠿⠫⠇⠺⠶⠺⠲⠷⠐⠀⠲⠶⠾⠶⠶⠀⠶⠿⠶⠿⠾⠦⠤⠶⠶⠖⠆⠿⠶⠇⠰⠲⠷⠶⠇⠂⠀⠿⠾⠷⠾⠗⠺⠶⠾⠾⠶⠾⠀⠲⠾⠲⠲⠾⠀⠀⠀⠀⠀⠀ ⡟⡛⡛⡟⡛⠛⡟⡓⠻⣏⡃⠈⠿⡃⠛⠛⠃⢘⢛⡃⠃⠘⠛⠛⠛⠻⠘⠀⠻⠛⠺⠻⠺⢛⠀⠛⠿⠀⠛⠛⡳⠛⠀⠟⠟⠿⠓⠀⠁⠚⡟⠛⠖⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡛⡛⡛⡛⡛⠛⡛⠛⠚⣛⡇⠘⣓⡓⠛⠛⠃⠙⣻⠓⠃⠘⠚⠛⠻⠛⠚⠚⠀⠛⠛⠛⠘⢛⠿⠟⠛⠿⠀⠛⠛⠛⠓⠀⠚⠛⠛⠓⠚⠓⡛⡃⠀⡓⠃⠘⠛⠻⠟⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡃⣛⣛⣛⡛⠛⡛⡛⠙⣛⡃⠈⡓⡃⢚⣛⡃⠘⣻⡓⠃⠘⠛⢛⠘⠛⠛⠊⠀⢛⣛⣛⣘⣛⣿⣛⣛⣿⠀⣛⠛⠛⠓⣀⠚⠛⠛⠛⣋⡛⠛⠃⠀⠛⡃⠘⠛⠻⠟⡻⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⣛⠛⡛⡛⢓⣋⡃⠈⡛⡃⢙⣛⡃⢘⣛⡓⠃⠘⠛⢛⢙⠛⠛⠘⠀⢘⣛⣛⣓⣓⣛⣛⣛⣚⠀⣛⡛⠋⠓⡃⠛⡛⠓⡀⠛⠛⡋⠃⠐⠙⠛⡛⠓⠛⠛⠛⡃⠘⠛⠃⠘⠛⠻⠛⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⣃⣛⣛⣛⡛⢉⣛⡛⢙⣛⡃⠘⡋⡃⠛⡛⠃⢘⣋⣓⡃⠘⠛⢛⢚⠛⠛⠐⠀⢘⣛⣛⣛⣓⣛⣛⣛⣘⠀⣛⠛⠛⡛⡛⠛⠛⡀⠛⣛⡋⢛⡛⠃⠀⡙⠛⠛⠓⠙⣛⡛⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⣛⢉⣋⣛⢙⣛⡃⢀⣋⡃⢘⣓⡃⢘⣛⣓⡃⠘⠛⢛⢚⠛⠛⢀⠀⢘⣛⣛⣛⣛⣛⣛⣛⢘⠀⣛⣛⠋⢛⡃⠋⡛⠓⣀⠛⠛⡋⠃⠐⠙⡛⡛⠛⠙⠛⡛⣃⡘⠛⠃⠘⠛⠻⠛⠻⠓⠀⠀⠀⠀⠀⠀⠀⠀ ⡓⣛⣛⣛⣛⢉⣋⡛⢙⣛⡃⢀⣋⡃⣘⣛⡃⣘⣛⣓⡃⠘⠛⠛⢚⠛⠛⠁⣀⣘⢛⠛⠛⠑⠛⠛⢛⣚⠀⣛⠛⠛⣛⣛⡋⠛⣀⠛⡛⠋⡛⠛⢃⡀⡙⠛⠛⠛⠙⡛⠛⢁⡀⠀⢀⢀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀⢀⣀ ⠛⠛⠛⠛⠛⠉⠋⠛⠙⠛⠃⠀⠋⠃⠙⠛⠊⠘⠛⠑⠃⠙⠛⠙⠉⠛⠀⠀⠉⠛⠙⠛⠛⠀⠛⠛⠙⠙⠛⠛⠀⠋⠋⠋⠋⠀⠋⠛⠛⠃⠃⠈⠋⠙⠙⠛⠙⠃⠘⠛⠃⠘⠛⠛⠛⠙⠛⠃⠈⠀⠈⠙⠙⠙⠋⠙⠛⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⣍⢉⣍⣉⣉⣍⣉⡉⠉⡍⢩⣍⣉⣉⣉⣉⡉⢩⡉⢩⣭⣉⣉⣉⣉⣉⣉⠉⢩⠉⣍⣍⢉⣭⣭⣉⣭⣭⠉⣉⠉⣭⣉⣍⣉⡍⣉⣍⣉⣉⡍⡉⡍⢩⣍⣉⣩⣉⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉ ⠁⠀⠉⡉⠁⠉⡉⡁⣀⠁⣈⢉⢉⢉⡉⠉⠁⣈⡁⡈⣉⢉⠉⣁⡙⢉⠈⣀⢈⠀⢉⢉⡈⡉⢉⡉⡉⡉⡀⣈⡀⡉⡉⣉⡁⠉⠁⡉⡉⠁⡉⢉⡁⢈⡉⠉⢉⠉⠉⠀⠀⠀⠀⡀⢀⡀⡀⠀⢀⢀⣀⢀⣀⠀⡀⢀⠀⠀ ⠀⠀⠀⠀⠀⣀⣄⡀⠀⡄⢠⣤⣀⣀⣀⣀⡄⢠⡀⠀⣠⣠⡄⣠⣤⣄⣀⠀⢠⠀⣤⣤⣀⣤⣤⠀⣠⣤⠀⣄⠀⣤⣤⡄⢠⣤⣤⣤⣤⣤⣤⣄⣠⣤⣤⣤⡀⣠⣤⣄⣠⣤⣤⣤⣤⣤⢤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀ ⣤⠀⠀⠀⠀⣍⣭⡅⠀⣅⣨⣭⣬⣭⢩⣭⣅⢨⡀⠀⣨⣭⡅⣨⣭⣅⣨⠀⢨⠀⣭⣭⠈⢭⣥⠠⣬⣥⠀⣄⠀⣭⣭⡭⢠⣭⣭⣥⣭⣭⣭⣥⣌⣭⣍⣨⣍⣬⣭⣅⣨⣭⣭⣭⣭⣭⢭⣭⣭⣭⣭⣭⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⣍⣭⡅⠀⡅⢨⣬⣍⣭⣩⣩⡅⢨⡄⠀⢨⣥⠁⣤⣭⣅⣨⠀⢠⠀⣬⣭⢠⣭⣬⢀⢭⣭⠀⣤⠀⣭⣭⣭⣤⣭⣥⣭⣭⣥⣭⣯⣭⣭⡅⣨⣍⣬⣭⣥⣬⣭⣭⣭⣬⣭⣬⣤⠍⠉⠉⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣭⣭⡅⠀⡅⢨⣭⣬⣭⣭⣭⡅⢨⡄⠀⢨⣬⡄⢤⣭⣅⢬⠀⢨⠀⣬⣭⠠⣭⣬⢤⣭⢬⠀⠠⠀⣬⣯⡭⢩⣥⣭⣭⣭⢠⣬⣭⣭⣩⣥⣤⣭⣌⣥⣭⣌⣤⣬⣭⣭⣬⣬⣭⣤⣠⣤⣤⣤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣤⣭⡆⠀⡄⢠⣯⣤⣭⣭⣬⡄⢠⡄⠀⢨⣬⠄⣴⣾⣄⢬⠀⢰⠀⣼⣵⢠⣦⢶⠤⣰⣶⠀⢤⠀⣷⣥⣤⣤⣥⡥⢠⣅⠠⣯⣷⣷⣴⣧⣄⠅⠀⠈⠉⠀⠈⠀⠀⠉⠈⠀⠈⠈⠈⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣤⣦⣄⠀⡆⢠⣦⣤⣤⣤⣤⡆⢠⡄⠀⢰⣴⡆⣴⣶⣤⢤⠀⢰⠀⣴⣶⢠⣴⣶⣀⣴⣶⠀⡄⠀⣶⣴⣶⡶⣶⣶⣤⢰⣶⣶⣶⣶⣶⣶⣶⣴⣆⢴⣦⣶⣶⣶⣶⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⠤⠤⠤⠤⠤⠬⠥⠤⠤⠤⠤⠤⠤⠤⠤⠠⠠⠤⠤⠤⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠤⠠⠤⠄⠄⠀⠤⠄⠤⠄⠤⠤⠤⠤⠄⠤⠤⠤⠤⠤⠄⠤⠤⠬⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠠⠤⠤ ⣖⣶⣶⣶⣶⢴⡦⣦⢴⣶⡆⢰⡦⡆⢴⣶⡆⢴⣶⣆⠆⢰⢦⣴⣤⣴⠀⢰⣦⣤⣤⣤⣤⣦⣤⣤⣦⠀⣶⣶⣦⢠⣶⣶⣤⣤⡀⢀⣶⣤⣤⣤⢰⠦⡆⡆⡆⡀⢰⣶⡦⢴⡦⢴⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⠤⠤⠤⠤⠤⡤⠤⠤⠤⡤⠤⠤⠤⠤⠤⠤⠤⢤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠤⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠆⠿⠶⠷⠷⠶⠶⠦⠶⠞⠧⠀⠿⠃⠔⠞⠄⠰⠾⠶⠆⠰⠶⠶⠰⠶⠶⠦⠀⠶⠶⠲⠶⠲⠾⠶⠞⠳⠷⠶⠀⠶⣶⠶⠶⠆⠠⠶⠆⠖⠆⠶⠶⠆⠰⠶⠆⠠⠲⠶⠶⠦⠲⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠿⠿⠿⠷⠶⠗⠧⠢⠿⠆⠐⠯⠇⠖⠾⠖⠸⠿⠿⠆⠰⠶⠾⠰⠶⠶⠐⠀⠚⠲⠶⠲⠶⠶⠶⠾⠀⡶⠶⠶⠶⠀⠷⠔⠇⠄⠐⠶⠶⠶⠶⠇⠀⠆⠒⠇⠄⠰⠶⠆⠠⠲⠷⠦⠦⠶⠶⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠇⠿⠿⠿⠷⠖⠷⠧⠦⠿⠇⠐⠿⠇⠰⠿⠆⠺⠿⠷⠇⠰⠶⠾⠴⠶⠶⠄⠀⠿⠰⠶⠴⠶⠷⠶⠾⠀⠾⠖⠶⠶⠧⠀⠖⠶⠶⠶⠇⠀⠇⠰⠶⠇⠀⠇⠰⠶⠆⠠⠲⠷⠶⠦⠲⠶⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠇⠿⠿⠿⠗⠒⠟⠷⠶⠿⠇⠀⠯⠏⠀⠿⠆⠸⠿⠿⠇⠰⠶⠾⠰⠶⠶⠀⠀⠺⠾⠶⠶⠷⠐⠶⡶⠀⠾⠶⠶⠿⠶⠖⠀⠖⠷⠶⠶⠒⠶⠗⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠇⠿⠿⠿⠿⠚⠟⠷⠾⠿⠇⠀⠿⠇⠨⠿⠆⠸⠾⠮⠇⠰⠶⠾⠸⠶⠲⠪⠀⠻⠿⠷⠖⠞⠶⠾⠖⡶⠀⠳⠷⠶⠧⠀⠒⠿⠶⠶⠲⠶⠿⠇⠀⠷⠆⠰⠶⠶⠾⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠇⠿⠿⠟⠿⠘⠟⠷⠺⠯⠇⠈⠿⠅⠘⠿⠖⠘⠿⠋⠇⠰⠻⠲⠺⠾⠠⠀⠰⠶⠺⠶⠶⠀⠶⠿⠶⠻⠻⠆⠀⠶⠷⠆⠆⠟⠶⠅⡐⠶⠶⠶⠇⠂⠀⠗⠶⠶⠾⠗⠲⠶⠾⠶⠷⠾⠀⠲⠶⠺⠺⠾⠀⠀⠀⠀⠀⠀ ⠃⠛⡛⡛⡓⠚⡛⠳⠒⣛⠃⠀⠓⠃⠚⠛⠂⠘⢳⠉⠃⠚⠛⠛⠛⠛⠂⠀⠛⠓⠚⠛⠚⠛⠀⠛⠞⠀⠛⠓⠛⠟⠀⠛⠟⠛⠛⠀⠁⠚⠛⠓⠒⠛⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡃⡟⣟⡟⠛⠛⡟⠓⠚⣟⡃⠘⢟⡃⠘⠛⠃⠘⢛⠛⠃⠘⠺⠛⠘⠚⠛⠈⠀⢙⠛⠛⠘⢻⠺⢚⠛⠷⠀⠓⠛⠛⠛⠀⠚⠛⠓⠒⠊⠟⠛⡇⠀⠛⠃⠘⠟⠻⠟⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡃⢛⣛⣛⠓⠘⡛⡓⠛⣛⠓⠀⠛⠃⠉⢛⡃⠘⠛⠋⠃⠘⠛⢛⠙⠛⠛⠐⠀⠛⢛⣛⣘⢚⡿⣛⣛⠿⠀⣓⠛⠛⠓⠀⠚⠛⠛⠛⠋⠛⠛⠃⠀⠛⠃⠘⠛⠻⠛⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡃⣛⣛⡛⡛⠋⡛⡓⠑⣛⣋⠘⡛⡃⢚⣋⡋⠘⡛⣓⠃⠘⠛⢛⠙⠛⠛⠀⠀⢘⣚⣛⣛⣓⣛⣛⣛⣙⠀⣛⣛⠋⠛⡋⠛⠛⠛⠀⠛⠛⠛⠃⠐⠙⠛⡛⠓⠙⠛⠛⡃⡀⠛⠃⠘⠛⠻⠛⠻⠓⠀⠀⠀⠀⠀⠀⠀⠀ ⣓⣛⣛⣛⡛⠙⡋⡛⢓⣛⡃⠈⡋⡋⠛⡋⠋⢊⣋⣃⡃⠘⠛⢛⢘⠛⠛⠘⠀⢘⢛⣛⣓⣛⣛⣛⣛⢚⠀⣛⠓⠛⡛⣛⡛⠛⡐⠛⣛⡋⠛⡛⠃⠀⡙⠛⠛⠓⠙⣛⡛⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡃⣛⣛⣛⣛⢛⣋⡛⢙⣓⡋⠀⣋⡃⢀⣛⠃⣊⣛⣓⡃⠘⠛⢛⣘⠙⠛⠑⠀⢘⣚⣛⣛⣓⣓⣛⣛⢘⠀⣛⡛⢋⠛⡓⡛⡛⠛⣀⠛⠛⡛⠃⡀⠙⠛⡛⡛⠙⣛⠛⣁⡀⠛⠃⠘⠛⠛⠛⠻⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⣃⣛⣛⣋⣛⠋⣋⡛⢙⣛⡇⢀⣋⡃⠈⣓⡃⢘⣛⡋⡁⠘⠛⠛⠛⠛⠛⠁⣀⡘⢚⠛⠑⠑⠛⠛⣛⣋⡀⢛⠛⠛⡛⣛⡋⠓⡀⠛⡋⠛⡛⠛⠃⠀⠙⠛⠋⠋⠙⠛⠛⢁⡀⠀⢀⣀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⢀⣀ ⠃⠛⠛⠋⠋⠉⠋⠙⠙⠛⠃⠈⠉⠃⠈⠙⠃⠘⠙⠁⠁⠘⠋⠉⠙⠛⠈⠀⠙⠛⠙⠛⠛⠀⠛⠉⠙⠙⠛⠛⠀⠛⠉⠃⠋⠀⠋⠋⠙⠃⠁⠈⠛⠙⠉⠛⠙⠃⠘⠛⠃⠘⠙⠙⠙⠙⠛⠀⠈⠀⠈⠙⠛⠛⠉⠙⠛⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⡉⢉⣍⣉⣉⣁⣉⡉⠉⡉⠡⣉⣍⣉⣉⣉⡉⢉⡉⢩⣭⣉⣉⣉⣉⣉⣉⠉⢉⠉⣍⣭⠉⣭⣭⣉⣭⣭⠉⢉⠉⣭⣉⣉⣁⡍⣉⣭⣉⡁⡉⡉⡍⢩⣍⣉⣉⣉⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉ ⠁⠀⠉⠉⠉⠉⠉⠁⠀⠁⠀⠉⢉⠉⠉⠉⠁⠈⠁⡈⠉⠉⠉⠁⠙⠉⠈⠁⢈⠀⠉⠉⡀⠉⠉⢈⠉⠉⠀⡀⠀⠉⡉⡉⠁⠁⠁⡉⠉⠁⡉⡁⠁⠈⡉⣉⠉⠉⠉⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⡀⢀⠀⠀ ⠀⠀⠀⠀⠀⣀⣄⡀⠀⡄⢠⣤⣀⣀⣀⣀⡄⢠⡀⠀⣀⣠⡀⢠⣤⣄⣀⡀⢠⠀⣠⣤⠀⣤⣤⠀⣠⣤⠀⢀⠀⣤⣤⡄⢀⣤⣤⣤⣤⣤⣤⣄⣀⣤⣤⣤⢀⣠⣤⣄⣠⣤⣤⣤⣤⣤⢤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀ ⡄⠀⠀⠀⢀⣍⣭⣅⠀⣅⣨⣭⣭⣭⣭⣭⣅⣨⡀⠀⢬⣥⡄⣬⣭⣅⣬⠀⢨⠀⣭⣭⠄⢩⣥⠀⡬⣥⠀⣀⠀⣩⣭⡍⢠⣭⣭⣥⣭⣭⣭⣥⣄⣭⣍⣩⣍⣨⣭⣅⣨⣭⣭⣭⣭⣭⢭⣩⣬⣭⣭⣭⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⣅⣭⡁⠀⡄⢨⣬⣁⣉⣉⣍⡄⢨⡅⠀⠨⣥⠀⢤⣭⣅⣬⠀⢨⠀⣬⣬⢠⢩⣬⢀⢭⣭⠀⢌⠀⣭⡭⣥⣤⣥⣥⣭⣥⣭⣥⣭⣬⣭⡅⣨⣥⣬⣭⣥⣤⣭⣥⣥⣬⢥⢬⣤⠈⠉⠈⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣍⣭⣇⠀⡅⢨⣭⣤⣭⣭⣭⡅⢠⡄⠀⢨⣬⠄⢤⣭⣅⣬⠀⢠⠀⣬⣬⠀⣭⡭⠤⣭⣭⠀⢤⠀⣭⣭⣍⢩⣭⣭⣯⣭⢩⣬⣭⣍⣠⣤⣤⢭⣌⢥⣬⣄⣡⣬⢭⣭⣼⣬⣭⣥⣠⣤⣤⣤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣤⣥⡇⠀⡄⢠⣧⣤⣤⣤⣥⡄⢠⡄⠀⢠⣕⡄⢰⣾⣄⣬⠀⢠⠀⣤⣥⠤⢤⢶⠤⢠⣤⠀⢠⠀⣴⣥⣤⣤⣥⡅⢠⡄⠀⣧⣧⣴⣤⣤⣄⠄⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣤⣦⡄⠀⡄⢠⣦⣤⣤⣤⣤⡄⢠⠄⠀⢰⣴⡄⢰⣶⣤⢤⡀⢠⠀⣴⣤⠀⢤⣦⣠⣤⣤⠀⣤⠀⡶⣤⣤⡆⣦⣶⣤⢠⢶⣦⣔⣦⣦⣦⣦⣴⣆⢤⣤⣴⣴⣶⢶⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠤⠄⠄⠠⠤⠌⠥⠤⠄⠤⠤⠤⠤⠤⠠⠤⠤⠠⠤⠠⠠⠤⠠⠤⠠⠤⠠⠤⠤⠤⠠⠤⠤⠠⠠⠠⠤⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠠⠤⠤⠄⠀⠤⠤⠤⠄⠠⠤⠄⠤⠤⠠⠤⠠⠤⠤⠤⠠⠠⠤⠄⠤⠠⠠⠤⠄ ⣖⣶⣶⣶⡦⠤⡶⣦⢄⣶⡆⢠⡶⡆⣠⣴⡆⢰⢶⣆⠆⢰⣦⣴⣤⣰⠀⢰⣦⣤⢤⣤⣤⣦⣤⣤⣶⠀⣶⣲⣤⠀⢶⣶⡤⣤⡀⢀⣶⣤⣤⡤⢰⠆⡆⡆⡄⡀⢰⣶⡦⢴⡦⢴⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠬⠤⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠂⠐⠲⠤⠦⠲⠲⠦⠠⠂⠖⠐⠦⠆⠀⠲⠤⠲⠔⠤⠆⠰⠶⠶⠲⠀⠴⠢⠀⠴⠶⠐⠶⠢⠤⠦⠶⠒⠆⠶⠄⠲⡴⠢⡒⠀⠀⠤⠔⠄⠢⠲⠶⠶⠄⠦⠂⠀⠠⠆⠲⠤⠤⠴⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠬⠲⠕⠶⠶⠿⠶⠤⠕⠧⠐⠿⠥⠄⠟⠆⠴⠷⠷⠂⠰⠶⠐⠤⠆⠶⠂⠐⠲⠲⠦⠤⠐⠶⠗⠆⠄⠲⠦⠦⠂⠀⠂⠁⠒⠀⠀⠒⠦⠖⠶⠆⠢⠆⠓⠢⠀⠠⠶⠤⠠⠴⠶⠲⠦⠢⠴⠭⠠⠠⠀⠀⠀⠀⠀⠀⠀ ⠂⠱⠲⠾⠳⠆⠳⠶⠀⠗⠂⠄⠼⠵⠀⠚⠲⠴⠓⠞⠣⠴⠴⠂⠲⠄⠢⠐⠀⠼⠎⠐⠠⠖⠎⠏⠆⠸⠒⠄⠂⠖⠡⠐⠶⠰⠲⠶⠖⠒⠒⠁⠖⠷⠂⠓⠰⠴⠦⠀⠒⠖⠶⠆⠒⠆⠼⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⠨⠳⠿⠙⠚⠳⠿⠄⠣⠗⠰⠤⠀⠎⠟⠀⠩⠾⠟⠅⠰⠶⠢⠢⠶⠶⠠⠂⠲⠶⠰⠲⠶⠂⠖⠤⠢⠾⠶⠾⠷⠐⠲⠐⠒⠶⠶⠢⠌⠤⠂⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠃⠨⠒⠛⠽⠚⠚⠗⠲⠥⠛⠚⠒⠄⠈⠭⠅⠓⠞⠺⠒⠸⠒⠖⠜⠲⠲⠶⠀⠓⠗⠴⠻⠶⠳⠒⠶⢢⠶⠦⠒⠲⠊⠂⠂⠒⠒⠂⠒⠐⠖⠂⠐⠂⠂⠒⠒⠲⠜⠒⠆⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠨⠑⠬⠓⠷⠛⠿⠰⠗⠆⠤⠢⠍⠐⠙⠩⠹⠿⠡⠗⠢⠻⠶⠖⠶⠐⠀⠲⠴⠜⠔⠣⠀⠶⠾⠆⠩⠌⠧⠎⠳⠖⠜⠀⠶⠕⠓⠆⠴⠿⠚⠄⠁⠈⠑⠲⠤⠟⠜⠞⠳⠃⠵⠾⠾⠺⠪⠥⠀⠨⠖⠢⠀⠀⠀⠀⠀ ⠂⠘⠙⡛⡃⠛⠛⠻⠓⠛⠋⠊⠒⡑⠚⠓⠉⠘⠓⠋⠓⠘⠋⠒⠛⠒⠀⠁⠋⠛⠂⠛⠚⠑⠒⢀⠑⠐⠙⠑⠐⠚⠀⠈⠓⠛⠛⠁⠁⠚⠓⠚⠚⠂⠒⠚⠛⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠂⠐⠟⠊⢛⠒⠙⠓⠒⠛⠃⠉⠋⠒⠙⠙⠓⠙⠓⠃⠃⠙⠒⠒⠒⠒⠒⠚⠐⠐⠚⠐⠈⠓⠳⠼⠛⠶⠐⠟⠲⠒⠂⠂⠐⠓⠚⠓⠀⠊⠓⠃⠚⠆⠐⠒⠂⠒⠒⠐⠊⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⢘⠛⡃⡛⠊⡙⡋⠐⡑⠑⠐⡛⠙⢂⡃⠋⢉⢘⡘⠉⠈⠊⠈⡛⠙⠙⠐⠅⢉⡛⠃⠈⠁⣂⠺⡑⡓⠩⠓⠻⠺⡂⠏⠲⠓⠛⠂⠁⡃⠁⠑⠈⠃⠑⠈⠛⠓⠟⡒⠶⣐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡛⠚⠚⠙⠉⠙⡙⠀⠙⠙⠐⡉⠁⢛⡋⠉⠛⠈⢓⠃⠙⠛⠈⠐⠋⠈⠉⠊⠘⢚⣙⢙⠘⣁⠋⡃⠙⠐⠙⣋⠈⢀⡁⠑⡓⠚⢐⠉⠓⠉⠂⠉⠐⠚⠑⠑⠁⠑⠃⡃⠁⠛⠉⠐⠚⠛⠛⠺⠐⠒⠀⠉⠀⠀⠀⠀⠀ ⠂⢐⠛⡚⣈⠊⠋⡛⠚⣉⠋⠐⠛⢋⠉⠋⡙⠙⢛⠘⡃⠋⠛⠉⠓⠛⠘⠉⠒⠑⢛⢉⠑⢃⣛⢚⡛⡉⠈⢛⠛⠛⠛⡙⢋⠋⡁⠙⠉⡋⠈⠐⠋⠀⠋⠙⠋⠈⠋⠂⡛⠉⠈⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⠓⢙⣁⡑⣙⣚⠋⣊⡁⡀⢐⠊⣈⡂⡃⠃⣋⣈⡑⡃⠐⠛⠃⠃⠘⠊⠈⠀⠐⢐⣛⣑⣓⡙⣛⣢⠑⡉⢋⠑⠛⠂⠃⠓⠋⠋⠑⠛⠋⠛⠑⠀⠈⠛⢚⠋⠘⠉⠛⡙⠀⠀⠓⠑⠛⠛⠛⠑⠃⠐⠐⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ䷩ 𝚕𝚒𝚗𝚎 9790 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/04/09/ShrikeLinux_Arch_based_Linux_distribution.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/04/09/ShrikeLinux_Arch_based_Linux_distribution.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ ShrikeLinux – Arch-based Linux distribution⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Rianne Schestowitz on Apr 09, 2026 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇ShrikeLinux⦈_ Quoting: ShrikeLinux - Arch-based Linux distribution - LinuxLinks — ShrikeLinux is an Arch-based distribution with a customised Xfce desktop and Nordic-inspired theming, designed to deliver a minimal, fast, and polished Linux experience. The project is available with three kernel options: LTS for maximum stability, rolling stable for the latest reliable software, and Zen for higher performance, gaming, and power use. Developed by the Shrike Linux Uganda FOSS community and maintained by root1 in Kampala, it also emphasises privacy, free and open source software, and a telemetry-free design. Read_on ⠛⠘⠛⠛⠛⠀⠛⠈⠛⠀⠛⠃⠙⠛⠁⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠈⠁⠉⠀⠃⠛⠘⠃⠛⠘⠃⠛⠘⠃⠛⠛⠉⠛ ⠀⣀⢀⡀⣀⡀⡀⢀⣀⣀⢀⣀⠀⠀⠀⠀⠀⠒⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠰⠀⠄⠤⠰⠄⠶⠴⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀ ⠀⢩⣍⣀⣀⠀⠀⠀⠀⣶⣶⡄⠀⠀⢰⣶⣦⠀⠀⠀⣶⣶⡄⠀⠀⢰⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠗⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⢾⣻⠶⠶⠶⠶⠆⠀⠩⠯⠁⠀⠀⠈⠽⠏⠀⠀⠀⠹⠭⠁⠀⠀⠈⠭⠭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣯⣥⣤⣄⠀⠀⢰⣶⣤⣤⡤⠤⠤⢠⣶⣶⣤⣤⠀⠀⠀⣴⣶⣤⣤⣤⡄⠀⠀⠀⠀⠀ ⠀⢨⡯⠭⠍⠀⠀⠀⠀⣿⣷⡆⠀⠀⢸⣿⣶⠀⠀⠀⣾⣷⡆⠀⠀⢰⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣯⣀⡀⠀⠀⠀⣸⣿⣄⣀⣀⣀⣀⢀⣿⣯⣀⣀⣀⣀⠀⣨⣿⣥⣤⣤⣤⡄⠀⠀⠀⠀ ⠀⣘⣛⡐⠀⠀⠀⠀⠀⠹⠿⠁⠀⠀⢈⣿⠏⠀⠀⠀⣉⣟⠁⠀⠀⠈⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣯⣀⠀⠀⠀⠀⣸⣿⣅⢀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠘⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠰⠖⠂⠒⠂⠀⠀⠀⣿⣿⡆⠀⠀⢸⣿⣿⠀⠀⢠⣿⣿⠧⠤⠤⠼⣿⡿⠤⠤⠤⠤⠤⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠬⠿⠿⠭⠭⠭⠤⠤⠽⠿⠯⠭⠭⠭⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢩⣭⠥⠤⠤⠤⠀⠀⣛⣛⠃⠀⠀⢚⣛⣓⠂⠀⢸⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⡇⠰⣶⣶⠤⠤⠄⠀⠀⢰⣿⠠⠤⠤⠤⠤⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⣿⣧⣤⣤⣼⣿⣿⣤⣤⣼⡿⠿⠒⠒⠐⠒⠛⠓⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⠀⠀⠀⠀⠀⢀⣖⠀⠀⠀⠈⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣉⡉⣉⢉⣈⣉⢉⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠴⢠⠒⠀⠐⠀⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠅⠀⠀⠀⠀⠀⠀⠯⠀⠀⠀⠀⠀⠐⢿⡿⠒⠒⠒⠒⠂⠸⡿⠓⠒⠒⠒⠒⠂⠀⠀⠀ ⠀⠀⠀⣼⣽⣼⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣟⣻⣿⠭⠭⢭⠨⠭⠥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠀⢠⣄⡀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢒⣐⡒⢒⣐⣒⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⡂⠒⠒⠒⠒⠒⠒⠒⠒⠒⡖⠒⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠑⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣴⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠷⠿⠿⠿⣿⣿⠳⠿⠿⠿⢏⣀⣠⣴⣾ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣤⣤⣤⣤⣽⣭⣿⣴⣥⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ䷩ 𝚕𝚒𝚗𝚎 9851 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/04/09/Stop_believing_these_4_myths_about_Linux_they_re_all_outdated_n.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/04/09/Stop_believing_these_4_myths_about_Linux_they_re_all_outdated_n.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Stop believing these 4 myths about Linux—they're all outdated now⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Rianne Schestowitz on Apr 09, 2026 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Rocky_Linux_installation_summary⦈_ Quoting: Stop believing these 4 myths about Linux—they're all outdated now — Linux has been popular with enthusiasts and enterprise users for decades, but it still has a negative reputation among Windows users. However, most of that negative reputation is based on outdated information. Linux is the best it has been. Read_on ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠛⠛⠛⠻⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⡿⠛⠟⡟⢻⡟⠛⠛⠿⠟⠛⠛⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣍⣉⣉⣉⣩⣉⣭⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⣭⣍⣉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣭⣩⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡛⡻⡿⠿⠿⠿⠿⠿⡿⠿⠿⢿⣿⣿⣿⡟⠛⠛⠿⠿⠿⠿⠿⠿⠟⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣴⣯⣡⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣴⣯⣭⣭⣽⣭⣭⣭⣽⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⢿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⠛⢿⡿⠿⠿⡿⢿⠿⠿⡿⠿⣿⣿⣿⣿⣿⢿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣴⣗⣒⣲⣒⣒⣗⣒⣲⣶⣾⣿⣿⣿⣿⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣗⣒⣲⣚⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⢿⡿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⡿⣿⣿⢿⢿⢿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣑⣡⣗⣒⣒⣒⣒⣒⣚⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣼⣖⣒⣒⣒⣚⣚⣲⣶⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⡟⠛⠛⠻⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣹⡤⠤⠬⠬⠤⠥⠤⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢻⡭⣭⢭⠭⡭⡭⠭⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣽⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣽⣿⣯⣿⣽⣿⣿⣿⣽⣽⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣻⣙⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢛⣛⣙⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ䷩ 𝚕𝚒𝚗𝚎 9910 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/04/09/Super_Lite_Linux_lightweight_distribution.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/04/09/Super_Lite_Linux_lightweight_distribution.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Super Lite Linux – lightweight distribution⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Rianne Schestowitz on Apr 09, 2026 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Super_Lite_Linux⦈_ Quoting: Super Lite Linux - lightweight distribution - LinuxLinks — Super Lite Linux is a lightweight Linux distribution that aims to make lightweight systems more visually appealing to new users. The project notes describe it as a distribution focused on improving the interface of light distributions, and the current release is based on antiX (which in turn is based on Debian) with zzzFM and Rox- filer as its file managers. Read_on ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠀⠀⠀⣴⣶⡄⢰⡆⠀⣶⣦⠀⣶⡆⢰⣶⡆⢠⣶⠀⣧⣄⣤⣀⠀⠀⠀⠀⢀⣀⣀⣰⣶⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⣾⣿⣿⣿⣤⣤⣤⣬⣍⣥⣀⢀⡀⢉⣭⣤⣭⣥⠌⠉⠁⠀⠁⢀⡉⠛⠉⠀⠀⢀⣀⣤⣿⢿⡿⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣷⣶⣷⣯⣍⣥⣶⣄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠒⣐⡐⠒⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣉⣡⢤⣤⣤⠭⢭⠩⠥⠤⠤⠤⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⠉⠈⠉⠉⠈⠁⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⡂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧ ⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣛⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⣿⡿⠛⠛⢿⣿⣿⣿⣿⡿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣉⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⣴⣿⣆⠀⢀⣀⣿⡿⠿⣿⣄⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏ ⠀⣻⡃⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⢗⣶⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷ ⠀⣛⠃⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠉⠉⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇ ⠀⣛⠁⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢉ ⠀⣋⡀⢠⢠⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⢀⡄⢸⣿⣿⣿⣿⣿⣿⣿⡿⠁⢀⡠⢀⠀⠀⠀⠀⢀⠀⢠⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼ ⠀⣙⡁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠁⢱⠯⠠⠔⢁⠀⣀⢚⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠈⣛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠃⠀⠘⠤⢐⡿⠿⠿⠿⠿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠛⠃⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡏⠀⠀⠮⠕⠋⠀⠀⠀⠀⢠⡀⠀⠉⠩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⠐⠲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠈⠉⢹⣿⣿⠏⠉⠉⠩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⢍⠈⠁ ⠀⣛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⠀⢴⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠳⣦ ⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⣿⣿⣿⣿⣿⣿⠋⠛⢿⣿⣿⠿⡿⠿⠿⠟⠟⠛⠛⢛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⢴⠄⠀⠀⡆⢖⡆⠶⠰⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈⠁⠀⠀⠠⡆⠖⠀⠀⠀⠄⠀⠀⠀⠄ ䷩ 𝚕𝚒𝚗𝚎 9968 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/04/09/Syndicator_RSS_and_Web_Browsers.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/04/09/Syndicator_RSS_and_Web_Browsers.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Syndicator, RSS, and Web Browsers⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Apr 09, 2026 * ⚓ Yury Molodtsov ☛ Why_I've_Built_Syndicator⠀⇛ Syndicator is a ranked, personalized reading app. It pulls news sites, blogs, YouTube videos and Substacks into one place, then learns from what you actually read, skip, save, and share. Algorithms have a bad rep, but I 100% believe they can be fantastic when they’re optimized to help you. I don’t want the app to be “engaging”. I want you to open it, scan everything that happened, and close it for the day. Follow everything, miss nothing. * ⚓ Six Colors ☛ Rethinking_RSS,_newsletters,_and_how_I_read_every morning⠀⇛ Every morning, I start my day with breakfast, a cup of tea, and my iPad. This is the latest version of a ritual that began years ago with an actual newspaper that an actual human being left in my driveway. For the last five years, it’s all been mediated by my RSS reader, but it’s an experience that integrates newsletters and RSS feeds together in one place. o § Chromium⠀➾ # ⚓ N Recursions ☛ N_Recursions:_How_to_set_Google_search_as the_default_in_Chromium⠀⇛ Somebody either had something against Google or somebody on the Chromium team understood UI/UX so poorly that it left people frustrated at not being able to add Google as the default search engine on Chromium. This is all you need to do: [...] o § Mozilla⠀➾ # ⚓ Firefox_Tooling_Announcements:_MozPhab_2.12.0_Released⠀⇛ Bugs resolved in Moz-Phab 2.12.0: [...] # ⚓ Waterfox ☛ 6.6.11_-_Security_fixes_and_feature_preview_- Waterfox_Release⠀⇛ ䷩ 𝚕𝚒𝚗𝚎 10039 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/04/09/This_Linux_distro_will_give_your_old_Windows_10_PC_a_new_lease_.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/04/09/This_Linux_distro_will_give_your_old_Windows_10_PC_a_new_lease_.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ This Linux distro will give your old Windows 10 PC a new lease on life⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Rianne Schestowitz on Apr 09, 2026 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇MX_Linux⦈_ Quoting: This Linux distro will give your old Windows 10 PC a new lease on life — You might have heard that Linux is perfect for reviving older hardware that Windows no longer supports. That claim is very true in my experience, but you have to pick the right distribution for that hardware. This kind of distribution usually falls in one of two camps. For ancient computers (I'm talking Pentium III and Pentium 4 PCs from the early 2000s), you'll want a distro like Puppy Linux. This weird little OS looks like it was "Frankenstein'd" together using packages from multiple mainline distros. It even has its own PPM package manager. Read_on ⡟⡍⠉⠉⠉⠙⣯⣻⡿⣏⠉⢉⠉⠉⢻⣿⠉⣿⢿⣯⠉⡿⡉⠉⡋⢹⣏⠉⣋⠉⠻⢿⣿⡉⠉⣽⡿⣿⣿⣏⠹⣯⠉⣽⣯⢹⣿⠉⠻⢿⡿⠉⢍⠉⠉⢉⣿⣩⡿⣿⣿⠉⠿⣻⣿⢿⣽⡟⣹⡿⠋⠉⣩⣿⠏⠉⡉⢙ ⡇⠹⠆⣿⣧⠈⣽⢿⡖⠑⡀⢸⣷⡀⠸⠋⠘⡟⡒⠻⣆⠀⢰⣄⡿⣽⡕⠀⣤⡀⣴⡆⣹⣷⠀⡛⢻⣿⣿⣿⣧⠀⢸⣿⣿⢾⡟⠀⢀⣾⡇⠀⢻⡇⣰⡿⠝⣻⣿⣿⠿⠀⣴⡟⣣⡎⣼⣾⠟⠁⣀⢰⣿⠟⠀⢾⠁⠾ ⡇⠈⠀⠈⣬⣤⠀⠀⠀⠀⠀⠀⠹⢱⡀⠀⠀⡷⣄⢀⠁⢀⣿⣿⣆⠹⠃⢠⣿⣧⣿⢇⠻⠫⢿⣿⠿⠿⠷⠟⣿⡁⢸⢿⡏⢸⡇⣴⣿⢻⠇⢀⠟⠳⠿⡇⣰⣿⠋⠛⠀⣼⠻⣩⡿⠣⠫⣿⣴⠚⠋⠈⣋⠀⠀⠀⡠⠂ ⣇⠀⠀⠀⢿⣿⠁⠀⠀⣄⢰⢰⣄⠸⣿⣦⡀⠀⣿⣆⠀⣸⣿⣿⣷⡠⠆⣸⣿⣎⣍⠀⠀⠀⢏⣿⡂⠀⠀⠀⠙⠀⢠⣾⠉⣿⣿⣟⢿⠉⠀⣰⡇⢀⣼⡇⣼⡿⠀⠀⣼⡿⢰⣿⢁⡀⠷⣿⡻⠂⠁⠘⢉⠀⢠⣾⢇⡴ ⡇⠁⠀⠀⠘⠅⠀⠀⠀⢻⢷⡈⠙⢠⣬⣿⢷⢀⠙⠽⣤⡉⡹⣿⣿⡿⢠⣬⠀⣿⣿⠀⣀⠀⣸⡿⣇⢀⣼⣿⠄⠀⣼⣿⣿⣿⣿⣿⠁⠀⢰⣿⣷⠈⢙⣶⠉⠀⠀⣼⡿⠀⠿⡿⠙⠁⣿⡟⠀⢰⠇⢰⡏⠰⡿⠉⡏⠀ ⣇⠀⠀⠀⢸⣧⣄⠀⠀⢸⣌⡓⠀⢘⣿⣿⠎⠉⠀⠀⣿⣿⣹⣿⣷⡌⢸⢿⣨⠏⣻⣾⣿⣇⡉⣱⣧⡘⣿⡷⠁⠸⡟⢙⣾⣿⣧⣿⡄⢀⢸⡿⣿⣠⣾⣿⠀⠀⢘⠻⠁⡯⠀⠀⠀⠸⡟⠀⣀⡄⣠⠆⠀⡰⠀⠀⢀⡀ ⡏⠀⢰⣦⣜⡻⡙⢂⠀⣼⠉⣆⠀⢸⣿⡉⠈⠀⠀⠀⢿⠈⠹⣿⢻⡧⠀⠈⠊⠀⢽⣿⣿⣇⣀⣿⣿⡯⠟⠇⠀⠀⣰⣾⡿⣿⣿⣿⣿⣿⡿⣼⣶⣿⡯⠛⠀⣀⣾⠀⠀⣠⣴⠀⣠⣾⠁⡶⣿⠁⣠⡄⢀⣠⡆⣀⣽⠂ ⡷⠄⠀⠙⣿⣶⣀⠀⠀⠙⠂⢻⡄⠸⡏⣛⠂⠀⠀⢀⣸⣷⣄⡀⠁⠀⠀⠀⢸⡇⠺⠫⠹⣿⣯⣿⣿⣋⣶⡄⠀⢠⣿⣿⣧⣟⣼⣿⣿⣿⣟⣿⣧⣶⠃⠀⢐⣿⣷⠿⢰⣿⡏⠁⠀⠀⣠⣴⠀⢴⠿⣀⠚⠀⠚⢛⡿⠴ ⡇⠀⠀⠀⠿⢻⡓⠀⠀⠀⠀⠀⣤⡀⠀⢀⣄⠀⠀⣾⣿⣯⢹⠿⠄⠀⠸⠇⢼⣷⡄⠀⠈⠉⠭⢹⡟⠧⣿⡧⠀⢾⣿⣿⣿⠙⣿⣿⣿⣿⣿⠿⣻⣿⢣⣾⣸⣷⣿⠀⢾⡿⠇⠀⠀⢚⣿⠟⠀⠁⣠⡇⠀⠀⠀⠀⠀⠀ ⡇⠀⢲⣄⠀⠁⢿⣧⠄⣶⡄⠀⣿⡿⣆⠘⡿⠣⠀⣿⣿⢿⣷⡀⠀⠀⠀⠀⣾⣿⣷⣀⡀⠀⠀⣾⣟⠈⣿⣧⠀⠈⠈⢧⠁⠈⢿⠿⣾⣿⡅⠀⠀⣰⣿⣿⣿⣿⣏⡄⠠⠀⠀⠀⢀⣽⣟⣤⡆⡄⠉⠂⠀⠏⠈⢀⣴⣾ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣈⠁⢿⣿⣗⠀⠀⣰⣷⢟⢟⠇⣸⣿⡀⢰⣿⣿⢴⣿⣿⡄⠀⠈⠀⠀⠀⠀⣸⣿⣿⣀⣴⠀⠸⢳⣷⣿⣿⠋⠃⠀⢴⡇⠀⢺⣿⡿⠿⣣⡅⠀⠀⠀⢠⣾⠀⢸⠁ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠙⠨⠀⠀⣿⣿⣧⠌⠀⢛⣿⣿⣾⣿⣿⣾⣿⣿⣿⢲⠀⠀⠀⠀⠸⠿⡛⣷⡾⣿⣥⡄⠘⣿⠋⠀⡀⠿⣧⣾⡇⠐⠻⢟⣁⣶⡏⢁⡀⠀⠀⠀⠁⣠⣼⣄ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⡀⢼⣷⣄⢀⣿⣆⢻⠀⠀⠾⣿⣿⠿⣿⣿⣻⣿⡿⠏⢀⣤⠀⢀⡀⢁⢼⣼⣷⠈⣿⣿⣿⡎⠉⣠⣾⣧⡾⠺⡟⣋⡰⣾⣿⡅⠛⠀⢻⠃⢀⣠⣾⢾⡿⠋⠘ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠓⠚⠋⠡⠀⠝⠻⠀⢠⣿⣷⡐⢱⣿⣟⠛⣽⣿⣇⠀⢺⡟⠷⣿⡷⢾⣿⣿⡟⠉⣿⣿⣿⡇⠘⣯⠿⠉⠋⠀⢿⡿⠃⢈⣋⠀⠀⠀⠀⠀⡿⡿⠁⠣⠼⠿⢷ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⣄⠁⠀⠀⠀⢀⣀⢀⡀⠘⣫⣿⣷⣾⣿⣿⡀⠙⠛⠀⠀⠉⠀⠚⡿⠯⠨⣽⡟⠂⢀⣾⣿⣿⠀⠀⠉⠀⠀⠀⣤⡦⢩⣵⣾⡟⢀⣾⠆⣀⣤⠀⠀⢠⣀⠀⠀⣰ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿⢷⣠⣄⠀⣾⣿⣾⣿⣾⣿⣿⣿⡩⢻⣟⡉⠀⠀⠀⠀⣴⡀⠀⠁⠀⠀⠁⢀⣰⣾⣿⡌⠛⠀⠀⠀⣀⣤⣿⣿⣇⠠⡿⣿⠃⠝⠁⠞⡿⠇⠠⡴⣿⡏⢀⣠⣤ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⠏⠈⠙⢛⠆⠼⠟⠋⣋⠘⠫⣿⠎⠉⣰⣶⡈⠀⡀⠀⠀⠉⠀⠀⠀⣀⠀⠀⢘⣿⣿⣿⡀⠀⠀⠀⠰⢹⣿⣿⣿⡅⢸⣦⣮⠀⠀⣠⣤⠀⣀⣴⣶⣿⠀⠸⠛⠉ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⡄⠀⠁⣤⣘⠿⠀⠘⠣⠀⠀⡀⠀⠐⣾⣿⠄⠀⣾⣿⣿⣥⣤⣤⣶⡤⠁⠘⠛⠏⠁⠐⢻⢿⣿⢿⠿⣿⡿⢴⣿⣿⡿⠧⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣰⣦⣠⣿⣿⢙⡯⠫⠅⠀⢺⣿⣿⣇⣠⣄⠀⢀⣾⡷⠀⢾⣿⣿⡀⠈⣿⣿⡿⣳⣿⣿⡟⣹⣿⣿⠶⠿⠀⢀⣠⣤⣠⡔⠀⠳⣶⣮⡤⠉⠉⠠⡶⠀⠀⣤ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠿⢿⠻⢿⣿⣯⣤⠀⢠⣶⣿⡉⠿⠉⢛⣿⡋⣿⡿⣿⣅⣾⣿⣿⠀⠀⠘⠉⣠⣼⣿⣿⠉⠐⠈⠉⠀⢀⣼⣿⣿⡿⠛⠀⠀⠟⢛⣿⠃⠐⠲⠆⢠⣴⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡟⡦⠁⠀⠈⠋⠙⠋⠁⣿⣿⣿⡿⠁⠀⠀⠀⠀⠁⢃⠁⠌⣿⣿⡃⢀⣤⡀⢀⣿⠿⣿⠓⠀⣀⣤⡄⠀⠐⠛⠛⠿⠂⠀⠀⠀⣈⡀⠀⢀⣠⣶⡆⣬⡍⠀⠁ ⣿⣿⣿⡏⣿⡿⣿⡏⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠉⠀⠀⢰⣤⣄⠀⠀⠀⠀⠀⠀⠀⠙⠻⠇⠀⠀⠀⢀⣴⣆⠀⠀⢹⡿⠉⠉⠙⣿⣇⡀⠁⠀⠘⣀⣤⡎⠋⢁⡀⠀⠀⣠⣾⣿⣷⣤⣽⢿⣧⢤⣴⣶⢮⡶⣶⣷⢽⣶ ䷩ 𝚕𝚒𝚗𝚎 10102 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/04/09/Today_in_Techrights.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/04/09/Today_in_Techrights.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Today in Techrights⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Apr 09, 2026 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇sequel_to_The_Wonderful_Electric_Elephant⦈_ ⚓ Updated This Past Day⠀⇛ 1. ⚓ Slopfarms_Marginalised,_Some_Suspend_Operations⠀⇛ some people who become lazy and prompt LLMs are just signalling that they throw in the towel ⚓ New⠀⇛ 2. ⚓ Countries_Where_Windows_is_Measured_Below_1%⠀⇛ Windows' monoculture is going away 3. ⚓ SLAPP_Censorship_-_Part_39_Out_of_200:_Recycled_Text_for_Garrett_and Graveley_(Buy_One,_Get_One_Free?)⠀⇛ perhaps thousands of pounds per hour 4. ⚓ Microsoft_Azure_is_Now_“Perpetually_on_Life_Support”,_Even_Microsoft Sites_Express_Concerns⠀⇛ Less than a decade ago Microsoft-connected sites kept saying that AWS was doomed and Microsoft would replace AWS with Azure 5. ⚓ IBM's_Fedora_Project_Sees_Sharp_Increase_(Over_25%)_in_Code_of_Conduct Complaints,_i.e._Censorship_Demands⠀⇛ Remember that IBM lawyered up against its own community in an effort to shut down a site critical of it 6. ⚓ Malicious_Bots⠀⇛ Tackling corruption in the world is never easy 7. ⚓ Gemini_Links_08/04/2026:_"Managing_Dotfiles_with_GNU_Stow"_and "Observations_on_Blocking_Various_Webbots"⠀⇛ Links for the day 8. ⚓ Links_08/04/2026:_GAFAM_"Abandons_Multi-Billion_Dollar_Data_Centres_in US_as_Investors_Demand_Energy,_Water_Usage";_Artemis_II_Astronauts Updates⠀⇛ Links for the day 9. ⚓ Links_08/04/2026:_Dems_Call_for_25th_Amendment_Remedy,_Bill_Epsteingate Summoned_in_Jeffrey_Epstein_Investigation⠀⇛ Links for the day 10. ⚓ A_Lot_of_Law_Firms_Are_Collapsing⠀⇛ There has been a lot of discussion about this lately 11. ⚓ IBM_Red_Hat_Profited_From_5+_Weeks_of_War_in_Iran⠀⇛ remember that IBM's current CEO comes from a military family (on both sides) 12. ⚓ Associated_Press_Failed_Financially,_Now_It's_Offloading_What's_Left_to Slop_(How_Sites_Die_'Cheaply')⠀⇛ LLMs are not intelligent or any form of intelligence, they are just falsely marketed as such 13. ⚓ Microsoft_Shares_Down_35%_in_5_Months,_Executives_Leave_Microsoft⠀⇛ Many people leave (or flee) Microsoft because, seeing what goes on insider, they know what's coming 14. ⚓ Are_Some_Obscure_or_Chinese_Operating_Systems_(Like_Huawei's)_Taking Over_in_"Unknown"_Clothing?⠀⇛ statCounter still cannot detect many operating systems 15. ⚓ SLAPP_Censorship_-_Part_38_Out_of_200:_Advertisement_or_£10,000+ Classified_Ad_in_the_Form_of_Court_Filing_in_Another_Continent⠀⇛ Graveley fancies himself some world-renown something 16. ⚓ Software_Freedom_is_Closely_Connected_to_Privacy⠀⇛ privacy can be a matter of life and death 17. ⚓ What_Communities_Mean_and_Look_Like_(If_They're_Effective_and Focused)⠀⇛ Last week we wrote about this in the context of distros and alleged "inclusion" 18. ⚓ April_2026_FSF_LibreLocal_Concludes_in_Atlanta⠀⇛ Happy Hacking 19. ⚓ Gemini_Links_08/04/2026:_GPG_Symmetric_Encryption_and_Slop_in_USENET⠀⇛ Links for the day 20. ⚓ Over_at_Tux_Machines...⠀⇛ GNU/Linux news for the past day 21. ⚓ IRC_Proceedings:_Tuesday,_April_07,_2026⠀⇛ IRC logs for Tuesday, April 07, 2026 ========================================================================= The corresponding text-only bulletin for Wednesday contains all the text. 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⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣭⣶⢶⣶⡶⢿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣶⣟⣽⣿⡿⣿⣿⣿⣿⣟⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⣨⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠁⡇⢸⣿⣿⣿⣿⣿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡂⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠙⣭⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠉⢛⣻⣭⡙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠁⠀⠁⢸⣿⠏⠀⣨⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⢉⢘⣿⣿⣿⣿⣿⣿⣿⡇⠀⡇⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⡉⠛⡿⠀⠀⠠⠶⠄⡀⢸⣿⠀⣰⡿⡏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⢠⣼⣯⣽⣿⣿⣿⣿⣿⣇⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⡼⠑⠋⠁⠀⢹⣷⣡⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠆⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⣀⡇⠀⠀⠀⠀⣸⢏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⡇⢸⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⠒⠙⢤⡀⠂⣨⣿⠟⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠠⠀⡄⣴⠤⢾⣿⣿⣿⣿⣿⣿⣿⣿⠇⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠳⠜⠿⠃⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠁⣁⣳⣮⠭⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⢀⢌⣻⣳⢿⢏⣹⣿⣿⣿⣿⣿⣿⡿⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⢻⠙⡏⠧⠌⣘⣿⣿⣿⣿⣿⣿⣧⠠⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣀⣤⡞⠀⠀⠀⠀⠀⣰⣦⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⡌⠀⠁⠀⢊⣸⣿⣿⣿⣿⣿⣿⣿⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣼⠛⢿⡻⠄⠀⠀⠀⠀⣰⣿⣿⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⡀⠺⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⣀⢘⣦⠸⣟⣶⣀⠀⠀⢰⣿⠟⠋⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⢸⣿⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠟⢸⣿⣿⣿⣿⣶⣾⡿⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⠀ ⠀⠀⠀⠀⠀⢠⣤⠀⢻⣿⣿⣿⣿⣿⣿⣿⡬⣗⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢸⣿⣿⣿⣿⣿⣿⣷⠀⢠⣤⣤⣴⣾⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⣀⣀⣠⣤⣥⣦⣼⣿⣿⣿⣿⣿⣿⣿⣇⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡆⠀⢹⣿⠋⣱⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠛⠿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⣿⡌⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠹⣿⣿⣾⡿⢿⣿⣿⣿⣿⣿⠀⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣹⠸⣿⣿⣷⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀ ⠀⠀⠀⠀⢴⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⢸⣿⣿⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀ ⠀⠀⠀⠀⠈⢀⣿⣿⡟⣹⣿⣿⣿⣿⣿⣿⣿⣗⢹⣷⣟⠁⠀⣠⣴⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⢷⣿⣿⣿⣿⣿⣿⣿⣿⠀⠸⠏⢹⠀⢈⣭⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⢀⣀⣴⣶⣿⣿⣵⣿⣿⣿⣿⣿⢿⣿⣿⡆⢠⣤⣈⣀⣠⣆⣽⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠀⠉⠈⠀⠉⠙⠀⠀⠐⠊⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀ ䷩ 𝚕𝚒𝚗𝚎 10518 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/04/09/today_s_howtos.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/04/09/today_s_howtos.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ today's howtos⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Apr 09, 2026 * ⚓ LinuxConfig ☛ How_to_Configure_Dracut_Initramfs_on_Ubuntu_26.04⠀⇛ * ⚓ Linux Capable ☛ How_to_Install_Zsh_on_Debian_13,_12_and_11⠀⇛ Zsh becomes easier to live in than plain Bash once you want better completion, shared history, and prompts that surface useful context without extra busywork. Debian’s default APT sources already make it straightforward to install Zsh on Debian 13, 12, and 11. * ⚓ Linux Capable ☛ How_to_Install_Clang_on_Debian_13,_12_and_11⠀⇛ Debian already packages Clang in its default repositories, but it is not installed by default and the compiler branch changes sharply between Debian 13, 12, and 11. That matters when you need newer LLVM diagnostics, sanitizers, or the same toolchain branch your CI pipeline uses. * ⚓ ID Root ☛ How_To_Install_Alacritty_on_Fedora_43⠀⇛ If you have ever felt limited by GNOME Terminal’s sluggish rendering when tailing large log files or running a busy multiplexer session, you are not alone. * ⚓ ID Root ☛ How_To_Install_Etherpad_on_Fedora_43⠀⇛ If your team needs a self-hosted, real-time collaborative document editor that respects your data privacy, Etherpad is one of the best tools available. * ⚓ ID Root ☛ How_To_Install_OpenToonz_on_Fedora_43⠀⇛ If you want to run professional 2D animation software on GNU/ Linux without paying a cent, OpenToonz is one of the best tools available. * ⚓ Unix Men ☛ Converting_Office_Documents_on_Linux_Without_MS_Office⠀⇛ Linux has solid tools for document conversion. Some work great. Some have quirks. Here’s what actually works. * ⚓ [Old] CubePath ☛ System_Limits_Optimization_(ulimit,_limits.conf)⠀⇛ System resource limits in Linux control how much of a given resource a process or user can consume. These limits are critical for system stability, security, and performance. By default, Linux distributions set conservative limits that protect the system from resource exhaustion but often restrict the performance of production applications. Understanding and optimizing these limits is essential for running high- performance applications, databases, web servers, and other resource-intensive services. * ⚓ Mitchell Hashimoto ☛ The_Building_Block_Economy⠀⇛ Experiencing this firsthand as well as witnessing it in other ecosystems has fundamentally shifted how I view the practice of product and software development today, regardless of commercial vs non-commercial goals. * ⚓ Busybee ☛ Code:_Specification_vs._implementation⠀⇛ There are a lot of times when the specification says one thing but common implementations do another. Here are some especially common examples to watch out for. * ⚓ Linuxize ☛ tail_Cheatsheet⠀⇛ Quick reference for viewing the end of files, following logs, and using tail with lines, bytes, and pipelines in Linux * ⚓ Simultaneously_build_several_python_3D_plots_via_Multi-threaded_Python 3.14t_on_Arch_Linux⠀⇛ ䷩ 𝚕𝚒𝚗𝚎 10631 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/04/09/today_s_leftovers.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/04/09/today_s_leftovers.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ today's leftovers⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Apr 09, 2026 * § Audiocasts/Shows⠀➾ o ⚓ Graham Cluley ☛ Smashing_Security_podcast_#462:_LinkedIn_is spying_on_you,_and_you_agreed_to_nothing⠀⇛ LinkedIn has been secretly scanning your browser for over 6,000 installed extensions – on every single click you make. It can tell if you’re job hunting, what religion you are, and whether you have ADHD. And none of this is mentioned anywhere in their privacy policy. o ⚓ The Ask Noah Show ☛ Ask_Noah_Show:_Ask_Noah_Show_486⠀⇛ This week Noah and Steve address the blueprint OpenAI CEO Scam Altman published. * § Kernel Space / File Systems / Virtualization⠀➾ o ⚓ Klara ☛ The_Hidden_Value_of_CPU-Intensive_Compression⠀⇛ Compression in storage systems is often viewed as a trade-off between CPU overhead and capacity savings. On modern hardware, however, compression can improve overall system performance. This article examines how compression in OpenZFS reduces I/O pressure, improves caching efficiency, and leverages abundant CPU resources to increase storage throughput. o ⚓ Matthias Petermann ☛ Cells_for_NetBSD_-_Kernel-enforced,_jail- like_Isolation_with_User-friendly_Operations⠀⇛ Cells for NetBSD is an early-stage but steadily maturing system for lightweight, kernel-enforced isolation on NetBSD. It closes the operational gap between simple chroot environments and full virtualization platforms such as Xen. o ⚓ Ars Technica ☛ Linux_kernel_maintainers_are_following_through_on removing_Intel_486_support⠀⇛ One point in favor of the sprawling Linux ecosystem is its broad hardware support—the kernel officially supports everything from ’90s-era PC hardware to Arm-based Apple Silicon chips, thanks to decades of combined effort from hardware manufacturers and motivated community members. But nothing can last forever, and for a few years now, Linux maintainers (including Linus Torvalds) have been pushing to drop kernel support for Intel’s 80486 processor. This chip was originally introduced in 1989, was replaced by the first Intel Pentium in 1993, and was fully discontinued in 2007. Code commits suggest that Linux kernel version 7.1 will be the first to follow through, making it impossible to build a version of the kernel that will support the 486; Phoronix says that additional kernel changes to remove 486-related code will follow in subsequent kernel versions. Although these chips haven’t changed in decades, maintaining support for them in modern software isn’t free. * § Distributions and Operating Systems⠀➾ o § Arch Family⠀➾ # ⚓ Caio Bianchi ☛ Omarchy_on_a_Kamrui_Pinova_P2:_Two_Hundred Dollars_of_Chaos_and_Joy⠀⇛ The plan was to install Omarchy. If you haven’t heard of it: Omarchy is DHH’s “opinionated” Arch Linux setup built around Hyprland, the Wayland tiling compositor that the r/ unixporn crowd won’t shut up about. Version 2.0 shipped with an actual ISO installer and dropped the AUR dependency, which made it a lot more approachable than the original script-based approach. I’d been following it since the initial release in June and finally had an excuse to try it properly on dedicated hardware rather than a VM. o § Debian Family⠀➾ # ⚓ Tor ☛ New_Release:_Tails_7.6.1_|_The_Tor_Project⠀⇛ This release is an emergency release to fix important security vulnerabilities in Tor Browser. ䷩ 𝚕𝚒𝚗𝚎 10762 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/04/09/Ubuntu_is_still_the_only_Linux_distro_I_recommend_to_beginners_.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/04/09/Ubuntu_is_still_the_only_Linux_distro_I_recommend_to_beginners_.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Ubuntu is still the only Linux distro I recommend to beginners—here are 3 reasons why⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Rianne Schestowitz on Apr 09, 2026 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇ubuntu_logo⦈_ Quoting: Ubuntu is still the only Linux distro I recommend to beginners—here are 3 reasons why — The first hurdle newcomers will face is onboarding. There are a multitude of distros to choose from, and it's undeniably overwhelming for beginners, especially when they don't realize distros are more like flavors than entirely different dishes. However, there are some defining qualities about distros that serve users well—qualities that don't concern fancy features but simplify usability instead. For many reasons, I recommend Ubuntu: it's tried and tested, stable, and just works. Read_on ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⠛⠛⠛⠛⢿⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠙⠐⢀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⢄⠀⠀⠀⠀⠠⡀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡿⢿⠿⠟⠛⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠁⠛⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⣸⣷⣀⠀⠀⠀⠐⠂⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣤⣤⣄⣀⠀⠀⣀⣠⣤⣄⣸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣧⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡺⢿⣷⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⡒⠄⠀⠀⠀⠀⠂⠀⠁⠀⠀⠈⠁⠰⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠨⠠⠚⠓⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⡋⠁⠀⠄⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⣀⣀⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠄⣇⠈⠀⠀⠀⠀⠀⠸⣧⠀⠄⠀⢀⠀⠀⠀⠂⠀⠀⠐⠀⠀⠀⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣀⠤⠺⠃⠀⢀⡀⠀⠀⠀⠀⢿⡆⠀⠀⠠⠀⠀⢐⠀⠠⠄⠀⡃⣀⡀⠤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢢⠀⠀⢧⣔⣪⣥⡜⡀⠀⠀⠀⠘⣿⡀⠀⠒⠀⠤⣼⣍⣐⣒⣩⣧⣤⣶⣒ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠤⣷⣄⡠⣶⢵⣦⢷⣇⠀⠀⠀⠀⢻⣷⣤⣴⣾⣿⣷⣷⣾⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡀⠁⢤⣤⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣀⣘⣶⣋⣵⣿⣷⣼⣿⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠢⣽⣿⡛⣛⣛⣻⣿⣿⣿⣂⣹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢠⡀⠷⣶⣬⣙⠛⠻⠭⡭⢟⣻⣭⣿⢷⣶⣏⣛⣿⠿⠿⠿⠿⣿⡏⢁⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣀⠀⣀⣠⣀⣀⣤⣤⣤⣤⣶⣶⣶⣿⣷⣿⣦⡘⢿⣿⣿⣶⣴⡾⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣖⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ䷩ 𝚕𝚒𝚗𝚎 10822 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/04/09/Video_GNU_Linux_Office_Suites_Slop_and_More.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/04/09/Video_GNU_Linux_Office_Suites_Slop_and_More.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Video: GNU/Linux, Office Suites, Slop, and More⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Apr 09, 2026 * ⚓ 2026-04-06_[Older]_What_is_happening_to_our_Office_Suites?!_-_Linux Weekly_News⠀⇛ * ⚓ 2026-04-05_[Older]_Session_Restore_Finally_Exists_On_Wayland⠀⇛ * ⚓ 2026-04-05_[Older]_how_to_install_a_linux_in_2026⠀⇛ * ⚓ 2026-04-05_[Older]_A_Unique_Idea_To_Solve_The_AI_Slop_Code_Problem⠀⇛ * ⚓ 2026-04-05_[Older]_Software_Freedom_Day_Is_Your_Time_To_Make_A_Change⠀⇛ * ⚓ 2026-04-05_[Older]_Ubuntu_26.04_LTS_FIRST_LOOK!_This_Might_Be_the GREATEST_Ubuntu_Ever_Made!_(No,_Seriously)⠀⇛ * ⚓ 2026-04-04_[Older]_Just_Microslop_things_😂_#microslop⠀⇛ * ⚓ 2026-04-04_[Older]_Ranking_Linux_distributions_for_2026:_not_your average_tier_list_!⠀⇛ * ⚓ 2026-04-04_[Older]_'cal'_-_display_a_calendar_-_Video_Man_Pages⠀⇛ * ⚓ 2026-04-04_[Older]_Archinstall_4.0:_Does_It_Make_Installing_Arch_Linux Easier?⠀⇛ * ⚓ 2026-04-04_[Older]_The_Ubuntu_Linux_Grub_Situation_Is_Hilarious⠀⇛ * ⚓ 2026-04-03_[Older]_'date'_-_print_or_set_date_and_time_-_Video_Man Pages⠀⇛ * ⚓ 2026-04-01_[Older]_Meet_Sloppix_—_The_New_AI-Powered_Linux_Distro!⠀⇛ * ⚓ 2026-03-29_[Older]_Linux_gatekeepers_#linux_#community⠀⇛ * ⚓ 2026-03-29_[Older]_This_1_Command_Freed_2.6GB_on_My_Linux_Server⠀⇛ ䷩ 𝚕𝚒𝚗𝚎 10889 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/04/09/Why_I_returned_to_Enlightenment_Linux_after_30_years_Testing_th.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/04/09/Why_I_returned_to_Enlightenment_Linux_after_30_years_Testing_th.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Why I returned to Enlightenment Linux after 30 years: Testing the new Elive beta⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Rianne Schestowitz on Apr 09, 2026 Quoting: Why I returned to Enlightenment Linux after 30 years: Testing the new Elive beta | ZDNET — There's a lot to love about Linux, including its flexibility. No matter the distribution, you can tweak and customize it to perfectly fit your needs and aesthetic. I learned this back in the late '90s, when I discovered the Enlightenment desktop. I spent hours upon hours on customization, and always found myself in awe at what it could do. Although Enlightenment (also called E) doesn't enjoy nearly the popularity it once had, it's still available, thanks to distributions such as Elive. Elive is based on Debian, so it inherits the rock- solid reliability from the "Mother of all distributions." Elive is also configured, out of the box, to be one very cool-looking desktop OS. Read_on ╘══════════════════════════════════════════════════════════════════════════════╛ ¶ Lines in total: 10931 ➮ Generation completed at 02:50, i.e. 79 seconds to (re)generate ⟲