Tux Machines Bulletin for Tuesday, March 10, 2026 ┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅ Generated Wed 11 Mar 02:49:45 GMT 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 - Android Leftovers ⦿ Tux Machines - Applications and Internet Utility in GNU/Linux ⦿ Tux Machines - Audiocasts/Shows: Late Night Linux, LINUX Unplugged, and More ⦿ Tux Machines - Best Free and Open Source Software ⦿ Tux Machines - Calamares Linux Graphical Installer Now Supports KDE’s Plasma Login Manager ⦿ Tux Machines - Claws Mail 4.4.0 unleashed ⦿ Tux Machines - Congrats to Rianne ⦿ Tux Machines - Debian: Colin Watson, Sven Hoexter, LibreOffice at MiniDebConf Kanpur ⦿ Tux Machines - Devices: Unraid, Raspberry Pi Zero, and Samsung DeX ⦿ Tux Machines - Distributions and Operating Systems: NixOS, ReactOS, and More ⦿ Tux Machines - Fedora Linux 44 Beta Released with Linux 6.19, GNOME 50, and KDE Plasma 6.6 ⦿ Tux Machines - Free and Open Source Software ⦿ Tux Machines - FreeBSD 14.4 Released ⦿ Tux Machines - Free, Libre, and Open Source Software and Open Data Leftovers ⦿ Tux Machines - Games: SiN Reloaded, Less DRM, PRAGMATA, and More ⦿ Tux Machines - Games: SteamOS and Common PCs Running Steam ⦿ Tux Machines - Geminispace Will Soon Have 5,000 Capsules ⦿ Tux Machines - GNU/Linux Devices and Open Hardware Projects ⦿ Tux Machines - GNU/Linux Leftovers ⦿ Tux Machines - GNU/Linux Perils on Desktop/Laptop: Common Mistakes, Terminal, Wayland, and More ⦿ Tux Machines - GNU/Linux terminals and "Kitty is the most powerful tool in my workflow" ⦿ Tux Machines - I’ve helped friends and family move to Linux—here are my top 5 gateway distros ⦿ Tux Machines - I’ve used dozens of Linux distros—these 3 offer the best nostalgia trip ⦿ Tux Machines - KDE: Kate and KDE Connect in Review ⦿ Tux Machines - KDE Plasma 6.5.6 Released as the Last Update in the Series with More Fixes ⦿ Tux Machines - KeePassXC 2.7.12 Password Manager Adds Support for Bitwarden’s Nested Folders ⦿ Tux Machines - Latest Steam Client Update Improves Support for Proton Games on Linux ⦿ Tux Machines - Linux distros are quietly abandoning their own desktops for KDE Plasma, and I get why ⦿ Tux Machines - Linux PC vendor System76 tries to talk Colorado down over OS age checks ⦿ Tux Machines - Linux Virtualization With Xen and Running Windows Under GNU/Linux ⦿ Tux Machines - Mamma Mia! The Party at Manchester City’s Campus ⦿ Tux Machines - NVIDIA 580.142 Production-Ready Linux Graphics Driver Released with Bug Fixes ⦿ Tux Machines - One of the best Arch-based Linux distros out there just got even easier to set up ⦿ Tux Machines - Open Hardware/Modding: Raspberry Pi, Arduino, and More ⦿ Tux Machines - OpenSSL 4.0 Promises Support for Encrypted Client Hello, SNMP KDF, and SRTP KDF ⦿ Tux Machines - Programming Leftovers ⦿ Tux Machines - Programming Leftovers ⦿ Tux Machines - Red Hat/RHEL: Libvirt, Slop Hype, and AlmaLinux ⦿ Tux Machines - Security and Standards: NTP Security, New Attack Against Wi-Fi, AirSnitch, and More ⦿ Tux Machines - Security Leftovers ⦿ Tux Machines - Servers: Slop Promoted by Kubernetes, Hetzner Prices Soar After Slop Grifting (Hoarding Hardware) ⦿ Tux Machines - Today in Techrights ⦿ Tux Machines - today's howtos ⦿ Tux Machines - today's howtos ⦿ Tux Machines - today's leftovers ⦿ Tux Machines - Using the Terminal in GNU/Linux: Coding, Scripting, Studying Logs ⦿ Tux Machines - Web Browsers: Curl, Blocking HTTP1.1, and Mozilla Peddling Slop via Firefox ䷼ Bulletin articles (as HTML) to comment on (requires login): https://tuxmachines.org/n/2026/03/10/Android_Leftovers.shtml https://tuxmachines.org/n/2026/03/10/Applications_and_Internet_Utility_in_GNU_Linux.shtml https://tuxmachines.org/n/2026/03/10/Audiocasts_Shows_Late_Night_Linux_LINUX_Unplugged_and_More.shtml https://tuxmachines.org/n/2026/03/10/Best_Free_and_Open_Source_Software.shtml https://tuxmachines.org/n/2026/03/10/Calamares_Linux_Graphical_Installer_Now_Supports_KDE_s_Plasma_L.shtml https://tuxmachines.org/n/2026/03/10/Claws_Mail_4_4_0_unleashed.shtml https://tuxmachines.org/n/2026/03/10/Congrats_to_Rianne.shtml https://tuxmachines.org/n/2026/03/10/Debian_Colin_Watson_Sven_Hoexter_LibreOffice_at_MiniDebConf_Kan.shtml https://tuxmachines.org/n/2026/03/10/Devices_Unraid_Raspberry_Pi_Zero_and_Samsung_DeX.shtml https://tuxmachines.org/n/2026/03/10/Distributions_and_Operating_Systems_NixOS_ReactOS_and_More.shtml https://tuxmachines.org/n/2026/03/10/Fedora_Linux_44_Beta_Released_with_Linux_6_19_GNOME_50_and_KDE_.shtml https://tuxmachines.org/n/2026/03/10/Free_and_Open_Source_Software.shtml https://tuxmachines.org/n/2026/03/10/FreeBSD_14_4_Released.shtml https://tuxmachines.org/n/2026/03/10/Free_Libre_and_Open_Source_Software_and_Open_Data_Leftovers.shtml https://tuxmachines.org/n/2026/03/10/Games_SiN_Reloaded_Less_DRM_PRAGMATA_and_More.shtml https://tuxmachines.org/n/2026/03/10/Games_SteamOS_and_Common_PCs_Running_Steam.shtml https://tuxmachines.org/n/2026/03/10/Geminispace_Will_Soon_Have_5_000_Capsules.shtml https://tuxmachines.org/n/2026/03/10/GNU_Linux_Devices_and_Open_Hardware_Projects.shtml https://tuxmachines.org/n/2026/03/10/GNU_Linux_Leftovers.shtml https://tuxmachines.org/n/2026/03/10/GNU_Linux_Perils_on_Desktop_Laptop_Common_Mistakes_Terminal_Way.shtml https://tuxmachines.org/n/2026/03/10/GNU_Linux_terminals_and_Kitty_is_the_most_powerful_tool_in_my_w.shtml https://tuxmachines.org/n/2026/03/10/I_ve_helped_friends_and_family_move_to_Linux_here_are_my_top_5_.shtml https://tuxmachines.org/n/2026/03/10/I_ve_used_dozens_of_Linux_distros_these_3_offer_the_best_nostal.shtml https://tuxmachines.org/n/2026/03/10/KDE_Kate_and_KDE_Connect_in_Review.shtml https://tuxmachines.org/n/2026/03/10/KDE_Plasma_6_5_6_Released_as_the_Last_Update_in_the_Series_with.shtml https://tuxmachines.org/n/2026/03/10/KeePassXC_2_7_12_Password_Manager_Adds_Support_for_Bitwarden_s_.shtml https://tuxmachines.org/n/2026/03/10/Latest_Steam_Client_Update_Improves_Support_for_Proton_Games_on.shtml https://tuxmachines.org/n/2026/03/10/Linux_distros_are_quietly_abandoning_their_own_desktops_for_KDE.shtml https://tuxmachines.org/n/2026/03/10/Linux_PC_vendor_System76_tries_to_talk_Colorado_down_over_OS_ag.shtml https://tuxmachines.org/n/2026/03/10/Linux_Virtualization_With_Xen_and_Running_Windows_Under_GNU_Lin.shtml https://tuxmachines.org/n/2026/03/10/Mamma_Mia_The_Party_at_Manchester_City_s_Campus.shtml https://tuxmachines.org/n/2026/03/10/NVIDIA_580_142_Production_Ready_Linux_Graphics_Driver_Released_.shtml https://tuxmachines.org/n/2026/03/10/One_of_the_best_Arch_based_Linux_distros_out_there_just_got_eve.shtml https://tuxmachines.org/n/2026/03/10/Open_Hardware_Modding_Raspberry_Pi_Arduino_and_More.shtml https://tuxmachines.org/n/2026/03/10/OpenSSL_4_0_Promises_Support_for_Encrypted_Client_Hello_SNMP_KD.shtml https://tuxmachines.org/n/2026/03/10/Programming_Leftovers.1.shtml https://tuxmachines.org/n/2026/03/10/Programming_Leftovers.shtml https://tuxmachines.org/n/2026/03/10/Red_Hat_RHEL_Libvirt_Slop_Hype_and_AlmaLinux.shtml https://tuxmachines.org/n/2026/03/10/Security_and_Standards_NTP_Security_New_Attack_Against_Wi_Fi_Ai.shtml https://tuxmachines.org/n/2026/03/10/Security_Leftovers.shtml https://tuxmachines.org/n/2026/03/10/Servers_Slop_Promoted_by_Kubernetes_Hetzner_Prices_Soar_After_S.shtml https://tuxmachines.org/n/2026/03/10/Today_in_Techrights.shtml https://tuxmachines.org/n/2026/03/10/today_s_howtos.1.shtml https://tuxmachines.org/n/2026/03/10/today_s_howtos.shtml https://tuxmachines.org/n/2026/03/10/today_s_leftovers.shtml https://tuxmachines.org/n/2026/03/10/Using_the_Terminal_in_GNU_Linux_Coding_Scripting_Studying_Logs.shtml https://tuxmachines.org/n/2026/03/10/Web_Browsers_Curl_Blocking_HTTP1_1_and_Mozilla_Peddling_Slop_vi.shtml ䷩ 𝚕𝚒𝚗𝚎 154 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/10/Android_Leftovers.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/10/Android_Leftovers.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Android Leftovers⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Rianne Schestowitz on Mar 10, 2026 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇device_details⦈_ * ⚓ I_found_the_best_budget_Android_phone_and_earbuds_combination,_and_it's glorious⠀⇛ * ⚓ Android_Auto_Update_Causing_Control_Issues_for_Some_Drivers⠀⇛ * ⚓ Google_adding_a_WebGPU_kill_switch_for_Chrome_on_Android_16⠀⇛ * ⚓ OnePlus'_next_Android_phone_is_coming_with_a_monster_of_a_battery_–_and that's_official_|_T3⠀⇛ * ⚓ Lenovo_confirms_key_detail_about_new_high-end_Android_tablet_before imminent_release_-_NotebookCheck.net_News⠀⇛ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⠒⣶⣶⣶⣶⣶⣲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠋⠁⠀⢀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠰⡛⢿⣿⣿⡿⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣱⣧⣿⣿⡟⠃⠀⢀⣠⡶⠟⠃⠀⠉⢢⠒⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠃⣠⠔⠛⠻⣷⠀⠀⢰⣶⣛⡲⢠⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠋⠀⡃⠀⠀⣠⣤⡀⠀⣀⣭⣽⣾⣿⣷⡄⠀⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠿⠿⠀⠀⠁⠀⢰⣟⡽⣿⣾⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣻⣯⣶⣿⣿⣿⣷⣄⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⢻⣿⣿⣿⣿⣿⣿⣷⡀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠼⢯⣿⣿⣿⣿⣿⣿⣿⣦⣽⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣂⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢁⠃⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡿⠿⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡄⢠⠤⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠁⠀ ䷩ 𝚕𝚒𝚗𝚎 218 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/10/Applications_and_Internet_Utility_in_GNU_Linux.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/10/Applications_and_Internet_Utility_in_GNU_Linux.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Applications and Internet Utility in GNU/ Linux⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Mar 10, 2026 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Krita⦈_ * § Applications⠀➾ o ⚓ XDA ☛ Linux_distros_can't_agree_on_how_to_install_apps,_but Distrobox_makes_that_problem_disappear⠀⇛ As great as Linux is, some aspects of the platform can drive away potential users due to making things too convoluted. One such example is app support, because Linux-based operating systems (or distros) aren't all created equal. Some, like Debian and Ubuntu, can install DEB packages and use a package manager called APT. Fedora and it derivatives typically run RPM packages and use DNF as the primary package manager. And then Arch relies on its package manager (pacman) to install essentially all of its apps. Platforms like Flatpak and portable AppImage packages make cross-platform apps easier, but there are some things you just need to install with a package manager, and no Linux distro can support all of them. Well, not without Distrobox, that is. This tool lets you run apps for any Linux distro inside any other distro, so your Debian apps work in Arch, your Arch apps work in Fedora, and your Fedora apps work in Ubuntu. It's an amazing tool to have for multiple reasons, and it comes highly recommended. o ⚓ XDA ☛ 6_powerful_Linux_tools_that_make_Windows_alternatives_look outdated⠀⇛ The base of Linux and Windows users have strong arguments for their preferred operating system and software. However, some Linux tools have features that make Windows alternatives seem left in the dust. While a Windows tool may look modern and have fancy graphical effects, it doesn’t mean the feature set compares to Linux tools. Some Linux software tools have always been more powerful, while others have been included with the OS with more features and capabilities. On the other hand, certain Windows alternatives weren’t ever really that great to begin with. * § Internet⠀➾ o ⚓ HowTo Geek ☛ How_to_build_an_automatic_internet_speed_tracker_for your_home_network⠀⇛ Have you been experiencing frequent internet connection issues, but whenever you do an internet speed test, the results show you're getting the speeds your internet service provider promised? If you can relate to that, consider building an automatic internet speed tracker and logger. § Your ISP doesn't want you to know this about your internet speed Fact: the internet speeds promised by most ISPs are 'up to speeds.' In other words, the internet speed you pay for is the uppermost threshold. You'll rarely get the advertised speed all the time. For example, if you're paying for a 'gigabit' connection, you'll not get that speed consistently. o ⚓ HowTo Geek ☛ The_internet_is_disappearing,_so_I_repurposed_an_old laptop_to_save_it⠀⇛ Every day, parts of the web are disappearing. Content that isn't taken down is being edited and paywalled. What can you do about it? You can install this open source server and browser extension, which is what I did. Archiving media is one of the most time-honored methods of preservation. You might have heard of the Wayback Machine, which is a service run by the non-profit called the Internet Archive. It lets you retrieve old versions of websites, plus websites that don't exist at all anymore, thanks to people who archived it when it was still live. Knowledge is power, and the Wayback Machine isn't the only way to collect and review historical knowledge of online content. ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⠀⠘⠀⠀⠇⠿⠇⠠⠀⠀⠇⠘⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠸⠗⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠂⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠰⠆⠀⠸⠂⠀⠀⠂⠀⠀⠀⠀⠀⠈⠁ ⢀⠀⢠⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠂⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀ ⣨⠄⣨⡀⣾⣿⣿⣿⣿⣷⣶⣶⣤⣤⣠⣤⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⣭⠄⠀⠀⠀⠀⠤⠤⡀⠀⠀⠀⠀⠁⠀ ⣥⡄⢁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡙⠖⠀⠀⣤⣀⣶⣴⣶⣶⣯⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠐⠞⠓⠃⠀⠀⠀⠀⠀⠀ ⡿⡅⡠⡀⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⡿⣿⢿⣿⣄⠆⠀⠿⢛⣻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣤⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⡩⡅⣭⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣀⣀⣀⣀⡀⠀⣀⠀⠀⠀⢾⣿⣿⣿⣿⡇⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀ ⡭⡄⢥⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⡇⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄ ⢐⠄⢤⠆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠄ ⡤⡄⣠⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠿⣿⣿⠟⠛⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠠⠀⠠⠦⠶⣶⣶⣶⣶⣶⠶⠶⡶⠶⡶ ⢬⡅⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⣿⠘⣷⣶⣤⣤⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡄⢠⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠛⠁⠈⠉⠛⠛⠃⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢨⠅⣤⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣷⣬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⠀⠀⡤⠀⡀⠀⠀⢀⡀⠀⠀⠀⢀⡄ ⢤⡀⣤⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣀⠀⠀⠉⢀⡀⠀⠀⠀⠀⠀⠀⠀⠌⠁ ⢠⡄⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠲⠀⠀ ⢠⠄⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⡇⠀⣿⣿⣏⣼⣿⣟⣵⣿⣿⣏⣼⣿⣿⣽⠀ ⠀⠄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⢿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⢿⣿⣿⠿⣿⣿⣿⣧⣤⣿⡿⠀ ⠀⡁⢤⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣾⣿⣿⣿⣧⢠⣷⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣵⢿⣿⣡⡾⣿⣿⣿⣿⣿⣿⣿⠀ ⠴⡀⡲⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣴⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⡿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣷⣶⣿⣿⣿⣾⣿⣿⣿⣾⣿⣿⢟⠀ ⠒⠂⡒⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣗⠀⠀⠀⠠⠀⠀⠀⣀⠀⠀⢻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣯⠿⣻⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⠀ ⠐⠀⠀⠀⠛⠛⠛⠛⠛⠻⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠚⠉⠛⠀⠀⠀⠀⠈⠛⠀⠀⠛⠀⠀⠚⠛⠛⠛⠛⠛⠛⠙⠛⠛⠋⠉⠛⠛⠛⠂⠀⠙⠛⠛⠛⠛⠛⠃⠀⠉⠉⠉⠉⠉⠉⠁⠉⠙⠏⠍⠿⠛⠍⠀ ⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⠠⠀⠄⠠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀ ䷩ 𝚕𝚒𝚗𝚎 361 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/10/Audiocasts_Shows_Late_Night_Linux_LINUX_Unplugged_and_More.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/10/Audiocasts_Shows_Late_Night_Linux_LINUX_Unplugged_and_More.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Audiocasts/Shows: Late Night Linux, LINUX Unplugged, and More⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Mar 10, 2026 * ⚓ Late_Night_Linux_–_Episode_376⠀⇛ Discord delays their age-gating rollout but legislators are pushing for operating systems including GNU/Linux to verify ages, LLM licence laundering might mean the end of copyleft, and how and why you might want to detect Meta’s spy camera glasses. * ⚓ Jupiter Broadcasting ☛ Slop_to_Slap_|_LINUX_Unplugged_657⠀⇛ After experiencing Planet Nix and SCaLE, we come back convinced that the next phase of GNU/Linux is already taking shape. * ⚓ Becky Spratford ☛ RA_for_All:_Annual_Circulating_Ideas_Podcast_with_the ALA_Presdential_Candidates⠀⇛ ALA Election ballots went out this morning and Steve Thomas has his annual podcast interviewing the ALA President candidates on Circulation Ideas. This is a must listen podcast for all library workers whether you are an ALA member or not. Why? Because you need to know what the biggest issues are for our profession. And Steve makes it very easy. * ⚓ Austin White ☛ Podcast_Retirement⠀⇛ The other day, I woke up and started my podcast player. I clicked on Under the Radar show about independent app developers and their business. I learned that this was the last show. It had been recorded for 10 years, twice a month. Even though I’m not a developer by trade, it was a fantastic show that taught me a lot about things that could apply to marketing and different ways of thinking. I understand why they are shutting down the show. They had a fantastic run, and I thoroughly enjoyed it, but I will miss it. Other shows that have been retired that I still miss are: [...] ䷩ 𝚕𝚒𝚗𝚎 425 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/10/Best_Free_and_Open_Source_Software.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/10/Best_Free_and_Open_Source_Software.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Best Free and Open Source Software⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Rianne Schestowitz on Mar 10, 2026, updated Mar 10, 2026 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇doot⦈_ * ⚓ doot_-_simple_dotfiles_manager_-_LinuxLinks⠀⇛ doot is billed as a fast, simple and intuitive dotfiles manager that just gets the job done. Simply run doot (or doot install) from anywhere in your system. It will symlink all files in your dotfiles directory to your home directory, creating directories as needed. The subsequent runs will incrementally update the symlinks, adding the new files and directories, and removing references to files that are no longer in the dotfiles directory. This is free and open source software. * ⚓ PixelBatch_-_batch_image_optimization_tool_-_LinuxLinks⠀⇛ PixelBatch is a powerful, user-friendly desktop application for batch image optimization on Linux. Optimize hundreds of images at once while preserving quality, reducing file sizes, and saving disk space. This is free and open source software. * ⚓ Bobby_-_browse_SQLite_files_-_LinuxLinks⠀⇛ Bobby lets you open SQLite database files (.db, .sqlite) and browse the tables inside. It’s useful for app development or inspecting downloaded databases. This is free and open source software. * ⚓ Chuwi_CoreBook_Air_Plus_running_Linux:_Battery_Life_-_LinuxLinks⠀⇛ When looking at battery life, it doesn’t really matter what a laptop idles at or what usage is under full load. As indicated in my power consumption article, the screen brightness plays a big part in how many hours you’ll get from a full charge. There are many other factors that play a part including CPU, iGPU, backlight, draw from USB devices etc. To give an idea of battery life, I have maintained LinuxLinks with the laptop over many days. Maintaining the website involves a wide range of software including web browsers, RStudio, building and evaluating software, manipulating images, etc. Here’s the Info Centre output showing the energy consumption for an hour. * ⚓ ytdl-gui_-_graphical_interface_for_yt-dlp_-_LinuxLinks⠀⇛ ytdl-gui is a simple-to-use, cross-platform graphical interface for yt-dlp. This is a fork of the original youtubedl-gui by JaGoLi. This is a simple-to-use tool to download videos or audios from various sources including Youtube, Dailymotion, Vimeo… It support more than 1000 websites and 8 different formats including mp3, mp4 and webm. You can chose between different resolutions and audio quality. It also support downloading whole playlists. This is free and open source software. * ⚓ voxcii_-_terminal-based_ASCII_3D_model_viewer_-_LinuxLinks⠀⇛ voxcii is a terminal-based ASCII 3D model viewer written in C++. This is free and open source software. * ⚓ FreeShow_-_Linux_presentation_application_-_LinuxLinks⠀⇛ FreeShow is a presentation application designed for displaying lyrics, scriptures, announcements, and multimedia content on large screens. It is commonly used in churches and live events to present song lyrics, sermon notes, and other information to audiences. The software provides tools for creating, organising, and presenting slides while supporting multiple display outputs and flexible presentation workflows. The application offers a modern interface for building presentations and managing media such as images and videos. FreeShow supports features useful in live environments including stage displays for presenters, remote control from mobile devices, and automation tools such as timers and slide transitions. It aims to provide a powerful open source alternative to commercial worship presentation software while remaining easy to use. This is free and open source software. * ⚓ gohan_-_static_site_generator_written_in_Go_-_LinuxLinks⠀⇛ gohan is a simple, fast static site generator written in Go featuring incremental builds, syntax highlighting, Mermaid diagrams, and a live-reload dev server. This is free and open source software. * ⚓ 39_Best_Free_and_Open_Source_Linux_Backup_Tools_-_LinuxLinks⠀⇛ Linux offers a wide range of backup solutions. Traditional command line tools such as rsync, tar, and dump provide powerful and flexible methods for creating backups, but they may be intimidating for beginners. To address this, many projects provide graphical interfaces that simplify scheduling, managing backup locations, and restoring files. Other tools focus on advanced techniques such as incremental backups, deduplication, encryption, and filesystem snapshots. In this article we explore a diverse range of Linux backup utilities, including user-friendly graphical applications, snapshot-based backup systems, and robust command line tools designed for automation and scripting. To provide an insight into the quality of software available for Linux, we have compiled a list of 39 high quality free backup tools. These programs help individuals and organisations protect their data and ensure that important files can be recovered quickly when problems occur. * ⚓ Walt_-_wallpaper_manager_for_Hyprland_-_LinuxLinks⠀⇛ Walt is a wallpaper manager for Hyprland with both a terminal UI and a native desktop GUI. It lets you browse, preview, apply, randomize, and rotate wallpapers using hyprpaper, while keeping the TUI fast for keyboard-heavy workflows and the GUI focused on preview-driven browsing. This is free and open source software. * ⚓ conceal_-_operate_the_recycle_bin_-_LinuxLinks⠀⇛ conceal is a command line recycle bin utility that follows the FreeDesktop.org Trash specification and offers a safer alternative to permanent deletion by moving files into a trash location. Users can send files to the trash, inspect discarded items, restore entries to their original location, remove selected items permanently, and clean the trash when needed. The project also supports integration with fuzzy finders such as fzf and skim for interactive selection when restoring or deleting files. This is free and open source software. * ⚓ Nibble_-_local_network_scanning_tool_-_LinuxLinks⠀⇛ Nibble is a CLI tool for local network scanning that focuses on speed and ease of use. Select a network interface, and Nibble scans your local subnet. Lists hosts, hardware manufacturer, open ports and their services. This is free and open source software. * ⚓ Color_My_Desktop_-_personalize_your_Linux_desktop_with_custom_generated themes_-_LinuxLinks⠀⇛ Color My Desktop is an easy to use tool for creating, managing, and applying custom color palettes to custom generated themes for the gnome-shell/ KDE-Plasma / GTK4 apps. It also includes options for creating Vesktop, Zen-browser, and YouTube themes with your colors, allowing for easy and uniform customization of your desktop environment. This is free and open source software. * ⚓ Backup_with_these_Linux_DeDuplicating_Encryption_Tools_-_LinuxLinks⠀⇛ With data growing in volume, improving storage utilization is pretty important. In computing, data deduplication is a specialized data compression technique for eliminating duplicate copies of repeating data. This technique therefore improves storage utilization. Data is not only of interest to its creator. Governments, competitors, criminals, snoopers may be very keen to access your data. They might want to steal your data, extort money from you, or see what you are up to. Encryption is essential to protect your data. So the solution is a deduplicating encrypting backup software. Making file backups is an essential activity for all users, yet many users do not take adequate steps to protect their data. Whether a computer is being used in a corporate environment, or for private use, the machine’s hard disk may fail without any warning signs. Alternatively, some data loss occurs as a result of human error. Without regular backups being made, data will inevitably be lost even if the services of a specialist recovery organisation are used. ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠛⠉⠁⠈⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿⣿⣿⡿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⣿⣿⣿⣿⣇⠀⠀⠀⣸⠛⠛⢿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠁⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⢛⣲⣶⡶⣾⣿⣖⡲⠀⠈⠉⠉⠛⠛⠿⣷⣶⣶⣇⠀⠀⢈⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⠀⢸⣿⢙⣿⣷⠸⣿⠛⣿⡦⠐⡢⠀⠀⠀⠀⠀⠉⠻⣿⣶⣶⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⠋⠱⣿⣾⣿⣏⣹⣿⣟⣰⣿⣏⣹⣿⣾⡿⠁⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⠙⠁⠀⠀⠀⠀⠀⠘⢿⣿⣬⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣷⣤⣀⣀⠀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠛⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣾⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣶⣦⣤⣴⣾⣷⣶⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣤⡀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢀⣀⣿⣿⣿⡿⠁⠀⠀⠀⠀⣠⠂⠻⣿⣿⣿⣿⣿⣿⡿⠛⠃⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⣦⡀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⣿⣿⣿⣿⠁⠀⠀⠀⢀⣼⣿⣶⣾⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣶⠀⠀⣠⣶⣶⠀⣶⣶⣶⣶⣶⣶⢸⣿⣿⣿⣿⠐⠀⠀⠐⠲⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣶⣶⠄⣠⣾⣿⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡟⠶⣿⣿⣿⣿⣇⣉⣉⣉⣉⣉⣉⠈⣉⣉⣉⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣤⣿⣿⣿⢸⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡄⣿⣦⠹⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⡇⢿⣿⣟⣥⣾⢡⣶⣌⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢣⡅⢸⣿⠇⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⣿⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⡇⠇⠘⣿⣿⣿⡟⠰⣦⡹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡈⠃⠈⢉⣁⢈⣋⣛⣛⣛⠛⠁⠀⠀⠀⠀⠐⠀⢀⣀⣀⣀⡀⠀⠀⠀⢸⣿⣿⢸⣿⣿⣿⣇⠀⠈⠙⠻⢿⣿⣿⣿⣧⢰⡀⠉⠛⠛⠱⢷⡬⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠼⠃⠼⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⢸⣿⣿⠘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠿⣃⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠘⣿⣿⣤⣭⣭⣭⣭⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢸⡿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠻⠿⠿⠿⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣠⣴⣿⣿⣶⣤⣀⣀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ䷩ 𝚕𝚒𝚗𝚎 738 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/10/Calamares_Linux_Graphical_Installer_Now_Supports_KDE_s_Plasma_L.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/10/Calamares_Linux_Graphical_Installer_Now_Supports_KDE_s_Plasma_L.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Calamares Linux Graphical Installer Now Supports KDE’s Plasma Login Manager⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Marius Nestor on Mar 10, 2026 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Calamares⦈_ Calamares 3.4.2 is a small update, but an important one as it introduces support for KDE’s Plasma Login Manager (PLM) display manager, allowing distributions that use Calamares as their default graphical installer and offer the KDE Plasma desktop environment to install Plasma Login Manager. This release also adds support for alternate greeter paths to the LightDM display manager,  adds support for recognizing NVMe and MMC drivers as SSDs, and updates the Partition screen to force 4K alignment of disk partitions, which is a performance boost for SSD drives. Read_on ⣿⣿⣿⣿⣿⣿⣿⡿⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠋⣀⣀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠙⠛⠿⣿⣿⣿⣿⠇⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣾⣥⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣼⣿⣿⣷⠀⠈⣽⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣴⣿⣿⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⢻⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠛⠻⠿⠿⠿⠿⠆⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠻⠛⠀⠀⠀⠀⣿⣿⣿⣿⠂⠀⠿⠿⠿⠿⠿⠿⠿⠿⠄⠀⠀⠸⠿⠿⠿⠆⠼⠿⠿⠿⡿⣿⣿⣿⣿⠆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿ ⠿⠿⠿⠿⢹⣿⣿⣿⣿⣿⣿⠁⠈⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠉⠿⣿⣿⡆⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿ ⣤⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⢠⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⡇⠀⠀⠀⠈⠉⠉⢋⣾⣿⣿ ⣿⣷⡄⠀⠀⢿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣇⣀⠀⣀⣀⣀⠀⣀⣀⠀⠶⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀⠀⢀⡀⠀⠀⠀⠀⢰⣶⡶⠿⠓⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿ ⣿⣿⣿⣦⡄⠀⠩⣽⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣶⣤⣤⣤⣤⣔⠂⠀⠀⠀⠘⢻⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡂⠀⠀⠀⠀⣴⣿⣾⣿⣿⣿⣿ ⣿⣿⣿⠛⠀⠀⠀⢺⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣇⠀⠀⣠⣾⣿⣿⣿⡇⠛⠛⢻ ⣿⣿⡟⠃⠀⣠⣶⣾⣷⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢿⣷⠀⠀⢿⡿⣿⣿⣿⡇⠀⣠⣾ ⣿⣿⣧⣧⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠛⡳⠀⠀⠀⠉⠒⠒⢛⠅⣠⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡛⠁⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⣴⣿⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣧⣀⠀⢀⢺⡍⢿⣦⡙⢿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣭⠭⠁⣽⡆⢈⠘⣷⣈⠻⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠘⠀⠸⣄⠘⢿⣷⣮⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣛⣳⣟⣳⣟⣛⣓⣟⣙⣻⣚⣛⡛⠛⠛⠛⠚⠛⠛⠚⠚⠛⠛⠛⠛⠛⠓⠓⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⢀⣀⣀⣤⣤⠀⣄⠹⣿⣮⣙⡻⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠐⠂⠀⠐⠒⠒⠀⣿⣿⣿⣿⣿⣷⡘⢷⣤⣉⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣘⣛⣛⣀⣀⣚⣛⣂⣀⣘⣛⣛⣀⣿⣿⣿⣿⣇⣘⣛⣛⣀⣀⣛⡛⠀⠀⠘⢛⣓⣀⣤⣜⣓⣰⣶⣾⣿⣷⣶⣶⣿⣿⣶⣶⣶⣿⣆⣰⣿⣿⣿⣿⣿⣿⣿⣧⣽⣛⢿⣿⣿⣯ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣍ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣟⣿⣏⣿⣿⣿⣋⣉⣉⣉⣉⣛⣛⣋⣉⣉⣙⣛⣛⣛⣛⣋⣉⣛⣛⣛⣉⣉⣛⣉⣙⣋⣉⣛⣉⣉⣙⣛⣉⣉⣉⣉⣉⣉⣉⣉⠉⠉⢙⣛⣛⣛⣙⣉⣉⣉⣉⣉⡉⠉⠉⠉⣉⣉⣹⡩⡍⢍⣽⢽⡩⢩⣿⣯⣹⣽ ䷩ 𝚕𝚒𝚗𝚎 795 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/10/Claws_Mail_4_4_0_unleashed.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/10/Claws_Mail_4_4_0_unleashed.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Claws Mail 4.4.0 unleashed⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Mar 10, 2026 9th March 2026 Claws Mail 4.4.0 CLAWS MAIL RELEASE NOTES http://www.claws-mail.org Claws Mail is a GTK+ based, user-friendly, lightweight, and fast email client. This release marks 25 years of Claws Mail. ~~~~~~~~~~~~~~~~~~~ UI * Several updates to strings and icons. * The word 'Write' is now used in place of 'Compose'. e.g. 'Write email'; 'Write' preferences page, etc. * Hide Message List's horizontal scrollbar by default if not using GENERIC_UMPC. * Added a new hidden preference, 'mainwin_toolbar_always_enable_actions', (turned off by default). Activating this option means that toolbar items bound to user Actions (in the main window) will be active even when no messages are selected. * Navigation using the numpad arrow keys is now possible. * A new Colour preference has been added: 'Messages marked for moving or deletion'. This is used when 'execute immediately' is switched off. * Compose window: When re-editing a drafted message, the user will now be prompted to save any changes made to the message headers. * Compose window: when the contents of a header field are cleared, the Clear button becomes a Delete button, enabling the now empty row to be removed completely. * Folder properties: two new options to handle HTML content have been added to the General page: 'Render HTML messages as text' and 'Render HTML messages with plugin if possible'. * Folder properties: a new option, 'Show tags' has been added. This controls whether any message tags are displayed at the top of the Message View. Plugins * SpamAssassin: updated third-party code to 4.0.1. * Mail Archiver: added support for Zstandard compression (zstd) (libarchive >= 3.4.0 required). * RSSyl: the default User-Agent string has been changed to ClawsMailRSSyl/$VERSION ($URL); this can be changed in the plugin's preferences, and can be further set on a per-feed basis on the 'Feed properties' page. * RSSyl: added a preference so that feeds configured for manual updates only are not updated when refreshing all feeds (recursively by the context menu, timer or at start-up, if enabled). * RSSyl: store and send ETag and Last-Modified headers. * RSSyl: postpone auto-updates if the server sends a Retry-After: header. A successful manual update clears the Retry-After value. * PGP: display a specific message, ("This key is not in your keyring") in the NoticeView area when a key is not in the keyring. * PGP: added an option to automatically locate missing keys when sending encrypted messages. * PGP: a missing key can now optionally be retrieved by clicking the NoticeView icon. * PGP: added a 'Search for PGP key' context menu item to email addresses in the Message View. * Notification: Ayatana indicator can now be configured to limit notifications to certain folders only. * Notification: added 'Open address book' entry to Ayatana indicator's tray menu. OAUTH2 * Configuration is now stored in a dedicated file: oauth2rc, located in the configuration directory. This file allows a user to accommodate an API change by a service provider, or to add a completely new Oauth2-based email provider of their choice. Setting protected=1 within an edited or bespoke block protects it from being overwritten by a new version of Claws Mail. Build System * GnuTLS >= 3.4.0 is now the minimum requirement. * libetpan >= 1.9.4 is now the minimum requirement. * dbus-glib support has been migrated to GDBus (GIO) >= 2.26 and D-Bus (>= 0.60). * The summary of the configure output has been completed. Other * A new hidden preference has been added: "show_contact_pic". When viewing a message, if the sender is in your address book and you have saved a picture for the contact there, this option will display that picture unless the Header Pane is displayed or you have chosen not to display (X-)Face or "enable_avatars" is set to '0'. If you have a large address book it is recommended that you leave this option turned off to avoid delays in displaying messages. * The wizard now uses secure defaults. * Various code cleanups, fixes, and enhancements. * The English, French and Spanish manuals have been updated. * Updated translations: British English, Catalan, Czech, Dutch, French, German, Romanian, Slovak, Spanish, Swedish, Turkish. * bug fixes: * bug 4498, 'About window resizing issues' * bug 4586, 'PDF Viewer view breaks in Three Column layout' * bug 4764, 'Wrapped UTF8 encoded subject line displayed with nonexistent quotation marks' * bug 4834, 'Long email addresses in vCalendar invites cause the attachments bar on the right side to be hidden until restart' * bug 4841, 'qutoted-printable encoding breaks text/html file with extraordinarily long lines, base64 does not' * bug 4846, 'Preferences-> Toolbars: always show icon preview on button' * bug 4848, 'The new ayatana tray icon displays no icon when there are new messages' * bug 4850, 'Show error dialog on receive error translation' * bug 4852, 'Cancel messages contain Approved-header' * bug 4854, 'auto-wrapping off not respected when using external editor' * bug 4856, 'Build fails with gettext 0.24' * bug 4863, 'Account Preferences Minor UI inconsistency' * bug 4882, 'IMAP can not use client certificate with passphrase' * bug 4887, 'Dillo processes are not killed when an HTML message is no longer being viewed' * bug 4893, 'Clamd plugin not checking any mail' * bug 4897, ''small screen' view: crash when exiting view message list after deleting all messages/mails in folder.' * bug 4898, 'When entering folder message list is not scrolling to selected message' * bug 4902, 'memory leak in the spam_report plug-in' * bug 4930, 'remove duplicate signature flag from MimeView' * bug 4931, 'avoid memory leak in summary_set_header' * fix bug where viewing msgs in the separate msg view are not marked as read when the msgview panel is hidden * litehtml plugin build failure on Windows * 'Save email as...' from the separate message view would save whatever was selected in the summaryview rather than what was open in the message view. * when message view is closed 1. select a msg; 2. hit [v] (key), 3. open the mime structure list 4. select a part in the structure tree 5. hit [v] --[crash]-- * fix header pane bug whereby a very long header value would push the mime icons panel out of the visible area. * do not attempt to delete a tag from list when the edit tag entry has focus. For further details of the numbered bugs and RFEs listed above see https://www.claws-mail.org/bug/[BUG NUMBER] --------------------------------------------------------------------- See ChangeLog for full information regarding changes in this release. Read_on ䷩ 𝚕𝚒𝚗𝚎 953 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/10/Congrats_to_Rianne.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/10/Congrats_to_Rianne.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Congrats to Rianne⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Mar 10, 2026 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Irish_Sea⦈_ Today Rianne accomplished something that she had worked towards for over 2 years. She excelled at it. A week from now it'll be another half_anniversary and next month we expect everything to turn green, with resumption of gardening at long last. We've had a very good week and today I've had a lot of coffee. Tomorrow I plan to stay home (for a change) and get back to posting more articles. We_have enjoyed_strong_momentum_this_year. There's also a lot of GNU/Linux we can locate and curate. The number of adopters continues to grow. █ =============================================================================== Image source: Irish_Sea ⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣼⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠿⢧⣀⣠⠶⠄⠀⠀⠤⣤⡤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠇⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⢀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⢸⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣿⣟⣿⣀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡎⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⣀⣀⠀⢸⣿⣷⣾⠀⠀⣶⡄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⡇⠀⠀⠀⢠⣿⣿⣿⡆⣺⣿⣿⣿⠀⠀⣿⣇⠀⠠⣶⡦⠀⠀⠘⢣⠀⢀⣷⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⡇⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠘⣿⣿⣧⠀⠀⠀⢸⣿⣿⣿⡟⢹⣿⣿⣿⣄⡰⣟⣉⠑⢶⣿⡷⠀⠀⠀⠈⠀⣿⣧⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⡄⡆⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⣿⣿⡿⠀⠀⠀⠈⠉⠀⠀⠀⢸⣿⣿⠻⣿⣿⣿⣿⠃⠀⠙⠀⠀⠀⠀⠀⠀⢿⢁⢹⣿⣿⣾⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢰⣿⡇⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⠿⢂⡀⣤⣾⣿⡄⣀⠀⠀⠀⠀⣀⠀⠀⣹⠀⢹⣿⡿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⢿⠀⢸⣿⡇⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣿⣿⣿⣿⡿⣿⡀⠀⠀⣀⣠⣤⣿⡀⣼⣿⣿⡆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡈⠀⣸⣿⢀⣆⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⡟⣸⡟⠉⠉⡍⠀⣮⣿⣯⢻⣿⣿⠿⣿⢳⣿⣿⣿⡇⠀⠠⡀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠀⠀⣿⣿⢸⡏⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⣿⣧⠀⣄⠅⣶⠻⡿⠟⠀⡈⣿⣀⣿⣧⣿⣿⣿⡀⠀⠀⠙⢷⣜⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⡟⠀⠀⣿⣿⣽⡏⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⢀⡠⠄⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣏⣿⣿⣂⠛⠂⠁⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⢠⣿⣷⣮⡻⣿⣿⣿⣿⣿⣿⣿⡇⣿⣇⠀⢸⣿⣿⣿⠇⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣋⣤⠶⠛⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡹⣿⣿⣿⠏⠀⠀⢀⣤⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣮⡙⢿⣿⣿⣿⣿⣷⣿⣿⠀⢸⣿⣿⣿⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⠟⢋⣡⡴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠘⣿⠙⢻⠂⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⣝⠻⣿⣿⢿⣿⡏⠀⣾⣿⣿⣿⢸⠀ ⣿⣿⣿⡿⠿⠛⢉⣤⠶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠁⠸⠀⠂⠀⠀⠀⠘⠃⠋⠉⠉⠉⠙⢻⠿⠛⠀⢃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣗⣱⡌⢻⢹⣿⠃⠀⣿⣿⣿⡏⣾⠀ ⠟⠋⠁⣠⡴⠞⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣸⣿⠀⢀⣿⣿⣿⡧⣿⠀ ⣠⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢸⣿⣿⣿⡇⡏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⡟⡿⠀⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣿⠃⠈⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢠⢠⡄⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢺⣻⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠀⠠⠿⠸⠿⣀⣶⣤⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⠸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣴⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ䷩ 𝚕𝚒𝚗𝚎 1018 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/10/Debian_Colin_Watson_Sven_Hoexter_LibreOffice_at_MiniDebConf_Kan.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/10/Debian_Colin_Watson_Sven_Hoexter_LibreOffice_at_MiniDebConf_Kan.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Debian: Colin Watson, Sven Hoexter, LibreOffice at MiniDebConf Kanpur⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Mar 10, 2026 * ⚓ Chiark ☛ Colin_Watson:_Free_software_activity_in_February 2026⠀⇛ My Debian contributions this month were all sponsored by Freexian. * ⚓ Sven_Hoexter:_Latest_pflogsumm_from_unstable_on_trixie⠀⇛ If you want the latest pflogsumm release form unstable on your Debian trixie/stable mailserver you've to rely on pining (Hint for the future: Starting with apt 3.1 there is a new Include and Exclude option for your sources.list). * ⚓ Document Foundation ☛ LibreOffice_at_MiniDebConf_Kanpur_(India)_2026⠀⇛ MiniDebConf Kanpur 2026 is being organised by Debian India. The event will be hosted at the Indian Institute of Technology Kanpur on 14 – 15 March 2026 – and the LibreOffice community will be there! ䷩ 𝚕𝚒𝚗𝚎 1060 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/10/Devices_Unraid_Raspberry_Pi_Zero_and_Samsung_DeX.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/10/Devices_Unraid_Raspberry_Pi_Zero_and_Samsung_DeX.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Devices: Unraid, Raspberry Pi Zero, and Samsung DeX⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Mar 10, 2026 * § Hardware⠀➾ o ⚓ XDA ☛ I_paid_for_Unraid_after_using_TrueNAS_for_free,_and_I'd_do it_again⠀⇛ When building my own custom network-attached storage (NAS) device, it was difficult to resist the often- recommended powerful and free option, TrueNAS. It seemed to have it all, including a solid reputation, enterprise- grade roots, full ZFS support, and it was available for absolutely nothing. Using TrueNAS felt like I was running some serious storage software that enthusiasts preferred over alternatives, such as Unraid. I tried Unraid in the past and even had it running with an all-SSD NAS from LincPlus. It was great, allowing me to mix and match drives to suit my immediate storage needs. It was easy, intuitive, and allowed me to get a centralized storage space up and running for the home with scope to run a few services. Strangely enough, the free choice isn't always best, and depending on what you need from your NAS, paying for the OS could be the answer. In fact, if I were to start fresh today, I would pick Unraid and pay for it over TrueNAS. o ⚓ HowTo Geek ☛ Got_a_Raspberry_Pi_Zero?_Here's_the_first_project you_should_do⠀⇛ The Raspberry Pi Zero and the Pi Zero 2 aren't powerful devices, even by the standards of Raspberry Pis. However, their tiny form factor and negligible power draw make them excellent for low-power applications and services. This is how I use mine. § Run a Pi-hole on your Pi Zero The Raspberry Pi Zero, and its newer, slightly more powerful sibling, the Pi Zero 2, aren't going to win any performance awards, but they're still useful for certain lightweight self-hosted services. The very first project I set up on my Pi Zero was a Pi- hole. A Pi-hole is a self-hosted, network-wide adblocker that protects every device on your network. It works by acting as a DNS sinkhole, which selectively blocks domains only known to serve up ads. * § Mobile⠀➾ o ⚓ Make Use Of ☛ I_finally_found_a_real_reason_to_use_Samsung_DeX⠀⇛ Samsung Desktop Experience (DeX), which is Samsung's attempt to give you the ability to run apps in discreet Windows similar to a desktop operating system, ushered in an era of great promise: your phone could be a phone, but could also get real work done if you connected a display with a mouse and keyboard. Today, DeX is widely available on most Samsung devices, even my relatively old S22+. Many think DeX is a solution in search of a problem because while it looks like a desktop UI, it's pretty slow and cumbersome when you try to use it as one, and windowed Android apps only get you so far. But I've found a reason to use DeX that has little to do with its intended purpose. ䷩ 𝚕𝚒𝚗𝚎 1162 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/10/Distributions_and_Operating_Systems_NixOS_ReactOS_and_More.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/10/Distributions_and_Operating_Systems_NixOS_ReactOS_and_More.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Distributions and Operating Systems: NixOS, ReactOS, and More⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Mar 10, 2026 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Whonix⦈_ * ⚓ XDA ☛ 3_wacky_Linux_distros_you_should_check_out_this_weekend⠀⇛ Thanks to their simple UIs, stable nature, and beginner- friendly app collection, Ubuntu, Debian, and Fedora are among the most popular Linux flavors out there. However, the best perk of the Linux ecosystem is being able to tinker with hundreds of distributions out there, not just the user-friendly ones. In fact, the deeper you go down the Linux iceberg, the wackier the distros start to become. And on that note, here are some cool yet quirky Linux flavors you can experiment with over the weekend if you’re tired of similar-looking Debian and Arch reskins. * ⚓ XDA ☛ 4_things_NixOS_gets_right_that_every_other_distro_should_copy⠀⇛ NixOS isn't everyone's cup of tea, and I say that with absolute honesty and personal experience. The simple thought of managing a Linux distro via a single configuration file might urge you to look elsewhere. But after spending some time with it, there are multiple things that NixOS gets perfectly right. I didn't even know that I needed such features until I used NixOS and then switched to another Linux distro. NixOS's declarative approach, generation management, and reproducibility make it a better OS in my opinion. These features are rarely a part of most mainstream Linux distros. Let's discuss the elements NixOS gets right that other distros can copy. * ⚓ XDA ☛ Proxmox-NixOS_is_a_real_thing,_and_it_changes_everything_about declarative_server_management⠀⇛ Have you been in my shows when you awake during the night and notice your Proxmox node is in a weird state? By weird, I mean it's not quite working right, and it's a similar problem you fixed months ago without effectively documenting the changes and commands you used. Sure, Proxmox backups can help here by resetting the entire node or specific VMs, but it's not great if you don't have it saving these regularly enough to avoid data loss. That's where NixOS comes into play. The issue with your typical server setup is that a package, kernel change, or something as small as a network config alteration could upset the delicate balance you managed to perfect. The system may be running, but perhaps a VM isn't booting up for some reason. I had this with my dual GPU setup with Ollama and Frigate running on the same box. If the GPUs aren't passing through correctly, it can upset the other VM. The same goes for the order in which they can launch. Oddities like that can cause some serious headaches. * ⚓ XDA ☛ Don't_install_Ubuntu_as_your_first_Linux_distro;_there's_a_better option_now⠀⇛ Ubuntu has long been the most recognizable name in the Linux space, and it's the most popular distro out there, something I've argued is actually a net negative for Linux adoption. Ubuntu is a beginner-friendly distro, but it's not the most friendly to users coming from Windows, and it makes a bad first impression. The good news is there's no reason for Ubuntu to be your first Linux distro, and a relatively recent member of the Linux family may just be the new best option for Linux newcomers; it's called Pop! OS, and it brings some cool new ideas to the table while building on the foundation of Ubuntu. Taking the latest iteration of Pop! OS for a spin, I came away fairly impressed and happy with what's possible here. * ⚓ HowTo Geek ☛ I_tried_using_"open-source_Windows,"_but_it_still_doesn't measure_up_to_the_real_thing⠀⇛ When we talk about Windows app compatibilty, we usually think of Linux running some sort of WINE configuration. That's not all the wonderful world of open-source has to offer though. Some really talented developers have managed to reverse engineer the Windows NT architecture. They've been working on it for almost 30 years. The project is called ReactOS, and it's directly compatible with Windows software and drivers (no compatibility layers or emulation required). ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⠇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⡄⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠇⠸⣿⣿⠰⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠄⠤⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠈⠁⠀⡩⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⠤⣴⣤⣴⣶⣦⣴⣶⣶⣶⣦⠄⠤⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⠀⣠⠀⠾⠷⠀⠉⠺⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠈⠄⢫⠩⠩⠭⠍⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠁⢀⣀⣄⣠⣾⣾⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⠀⠀⢠⠤⢤⠄⠠⠄⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⢸⣿⣿⣿⣧⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⣿⣿⣿⣿⠀⠀⠃⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠙⠻⢯⢿⢫⣛⣿⣿⣿⣿⣦ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⡟⢻⢻⠀⡛⢻⠋⠃⢯⢉⠉⡏⢹⠈⢸⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⡀⠀⠀⠀⡀⠀⠴⣾⢯⣿⣛⠋⠻⠛⢽ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢁⡀⣸⣆⣿⣸⣴⣖⣿⣬⣧⣧⣼⣼⣶⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣟⠂⠀⢌⠀⢁⢡⣤⣾⣿⣿⠿⠀⠀⠀⢠ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣤⡄⢸⡯⣿⣯⠀⠀⣶⣷⡼⣿⣿⣿⠃⠁⠐⢀⡀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠘⡏⣿⡿⠀⠀⣿⣷⣿⣾⣽⣛⡷⠰⠆⠒⠀⣩⡵ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢰⣶⣶⣶⣶⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣧⣿⣯⣿⣿⣿⣿⡇⠀⠀⠀⡥⠈⡏⠀⠀⡟⢿⣿⣿⢿⣿⣻⡦⠀⠀⠩⠤⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⠛⠛⠛⠉⠉⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠛⠃⠀⠀⠀⢀⣀⡗⠀⠀⣇⣼⠿⠃⠘⢿⣋⣻⣿⢰⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠠⠤⠉⠉⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠻⡯⠀⢠⣿⣧⢠⡄⠈⠈⠣⠉⠀⠀⠀⠀⣀ ⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⡿⠿⠿⠿⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⣶⠀⠀⢿⣿⣟⢿⡄⠀⡀⠀⠃⠀⠀⠀⠈ ⣧⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠝⡶⣾⣏⢋⠸⠗⠳⡀⠀⠀⠀⠀⠀⠀ ⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠈⠙⢉⣿⣿⣦⣄⡀⠀⠄⠀⠀⠀⠀⠀ ⣆⣮⣽⢹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠈⣭⣽⣿⣛⢷⣦⣈⡬⢄⠤⡀ ⠯⠀⡥⢫⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⢐⠋⣩⠠⠴⢾⣾⡽⢿⣮⣍⡁ ䷩ 𝚕𝚒𝚗𝚎 1298 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/10/Fedora_Linux_44_Beta_Released_with_Linux_6_19_GNOME_50_and_KDE_.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/10/Fedora_Linux_44_Beta_Released_with_Linux_6_19_GNOME_50_and_KDE_.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Fedora Linux 44 Beta Released with Linux 6.19, GNOME 50, and KDE Plasma 6.6⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Marius Nestor on Mar 10, 2026, updated Mar 10, 2026 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Fedora_Linux_44_beta⦈_ Powered by the latest and greatest Linux 6.19 kernel series, the Fedora Linux 44 beta ships with the soon-to-be-released GNOME 50 desktop environment for the flagship Fedora Workstation edition, as well as the latest KDE Plasma 6.6 desktop environment for the Fedora KDE Plasma Desktop edition. Powered by the latest and greatest Linux 6.19 kernel series, the Fedora Linux 44 beta ships with the soon-to-be-released GNOME 50 desktop environment for the flagship Fedora Workstation edition, as well as the latest KDE Plasma 6.6 desktop environment for the Fedora KDE Plasma Desktop edition. Read_on More Updates: * ⚓ Fedora_44_Beta_now_available⠀⇛ Today, the Fedora Project is excited to announce that the beta version of Fedora Linux 44 - the latest version of the free and open source operating system - is now available. Learn more about the new and updated features of Fedora 44 Beta below and don’t forget to make sure that your system is fully up-to-date before upgrading from a previous release. * ⚓ Fedora_44_Beta_is_out_with_KDE_improvements,_better_live_media_and_more |_GamingOnLinux⠀⇛ The Fedora team have put up Fedora 44 Beta for you to get testing and report bugs, ahead of the full release due out around April 14th. Quite a few improvements across the desktop are coming with this release, including for my favourite the Fedora KDE Plasma edition that I think you should try out for yourself. * ⚓ Announcing_Fedora_Linux_44_Beta_-_Fedora_Magazine⠀⇛ On Tuesday, 10 March 2026, it is our pleasure to announce the availability of Fedora Linux 44 Beta! As with every beta release, this is your opportunity to contribute by testing out the upcoming Fedora Linux 44 Beta release. Testing the beta release is a vital way you can contribute to the Fedora Project. Your testing is invaluable feedback that helps us refine what the final F44 experience will be for all users. How-To Geek: * ⚓ Fedora_Linux_44_Beta_has_GNOME_50,_KDE_Plasma_6.6,_and_installer improvements⠀⇛ Fedora Linux 44 is just around the corner, with Gnome 50, KDE Plasma 6.6, compatibility updates, and many other changes. Now, the first beta release has arrived with the new desktop environments and some helpful changes to the system installer. The Fedora Linux 44 Beta includes most of the changes expected for the final release of Fedora 44, which is scheduled for April 14, 2026—around the same time as Ubuntu 26.04 LTS. This version uses the latest Linux 6.19 kernel, adding the usual mix of performance improvements and expanded hardware support. The main editions have been updated to the GNOME 50 desktop environment, and the KDE versions are now using KDE Plasma 6.6. The Budgie desktop edition has switched to Budgie 10.10, which now supports Wayland. KDE Plasma 6.6 is a massive update in its own right, with custom global themes, text recognition in the Spectacle screenshot tool, a revamped on-screen keyboard, automatic screen brightness for devices with ambient light sensors, QR code scanning for Wi-Fi networks, and much more. GNOME 50 includes better support for variable refresh rate and HiDPI monitors, the end of X11 support, and many small changes that add up to a great update. ⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⠀⠀⠀⠀⠀⣀⣀⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢰⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠸⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢰⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢠⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣗⠿⣿⣿⣿⣿⠀⠀⠀⠀⢠⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣦⣽⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠿⠿⠿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠈⠈⠁⠉⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⣦⢠⣤⣤⠀⣶⣶⠀⢰⣶⡆⠀⣴⣲⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠉⠉⠀⠙⠛⠀⠘⠛⠁⠀⠛⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ䷩ 𝚕𝚒𝚗𝚎 1428 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/10/Free_and_Open_Source_Software.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/10/Free_and_Open_Source_Software.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Free and Open Source Software⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Rianne Schestowitz on Mar 10, 2026 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇youtube_logo⦈_ * ⚓ musicfetch-ng_-_download_and_tag_music_from_YouTube_-_LinuxLinks⠀⇛ With Musicfetch you can use the power of yt-dlp to search for Albums, Songs or Playlists, download them, and then add an Album Cover, as well as Metadata for the Title, Artist, Album etc. This is free and open source software. * ⚓ Arf_-_fzf_Pacman_wrapper_and_AUR_helper_-_LinuxLinks⠀⇛ Arf is an fzf Pacman wrapper and AUR helper. This is free and open source software. * ⚓ TrID_-_identify_file_types_from_their_binary_signatures_-_LinuxLinks⠀⇛ TrID is a command-line utility designed to identify file types by analysing their binary signatures rather than relying on filename extensions. It determines the most probable file format by comparing a file’s contents against a database of known file type definitions. The program uses an extensible definitions database containing patterns that describe different file formats. These definitions can be updated or expanded to support additional formats, allowing TrID to recognize a large and continually growing range of file types. TrID is useful for identifying files with missing, incorrect, or unknown extensions, making it valuable for file analysis, digital forensics, and data recovery tasks. Results are presented with probability percentages indicating how closely a file matches known format signatures. * ⚓ Deletor_-_file_deletion_tool_-_LinuxLinks⠀⇛ Deletor is a file deletion tool that combines a powerful text interface (TUI) with visual directory navigation, and classic command line mode (CLI). With it, you can quickly find and delete files by filters, send them to the trash or completely erase them, as well as clear the cache, both interactively and through scripts. This is free and open source software. * ⚓ Firm_-_terminal-based_work_management_system_-_LinuxLinks⠀⇛ Firm is a text-based work management system for technologists. Think of your business as a graph: organizations link to people, people link to projects, projects link to tasks, and so on. Firm lets you define these relationships in plain text files. Version controlled, locally stored and structured as code with the Firm DSL. This structured representation of your work, business-as-code, makes your business accessible to yourself and to the robots that help you run it. This is free and open source software. ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠉⠁⠈⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣴⣿⣿⢦⡀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡄⠀⡀⠘⠂⠀⢐⣿⣷⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣸⣻⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡇⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣏⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣎⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡟⢀⠠⣤⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢀⡀⠀⠘⠀⠀⠀⠀⣀⣀⡉⠉⠙⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠨⢻⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⠃⠀⠀⠀⠀⠀⠀⢻⠏⠀⠀⠀⠀⠀⠈⠻⢿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣶⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢷⣿⣿⡟⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⠿⠛ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠛⠟⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⠛⢻⣿⣿⣿⣿⣿⡿⢃⣾⣿⣿⣿⣥⣿⣷⡆⣀⠀⢘⠂⠀⠀⠀⠀⢹⡏⠉⠉⠁⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢠⢬⣿⣿⣿⣿⡿⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡊⣂⣒⣤⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣄⣽⣿⣿⣿⣿⠃⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠠⢸⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⢿⣿⣿⣿⣿⣿⣿⣿⠃⡀⠀⠀⠀⢀⣀⣄⣀⡤⠤⠤⠤⠀⠒⠒⠒⠈⠉⠁⠀⠈⢿⣿⣿⠆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡏⠄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠛⣿⣿⣿⣿⠏⠀⣀⣀⣤⣶⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠟⢹⣿⡿⠁⠁⠀⠀⠀⠀⣠⣤⠤⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⢀⣤⣾⣿⣿⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⢠⢶⣿⣹⣿⣿⣿⣃⡀⠀⠙⠿⠿⠟⠉⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡇⠀⠀⣵⣿⣿⣿⣿⣯⣿⣟⠂⠀⠀⠀⠀⠀⣼⠿⣿⠞⠉⠉⠉⢂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠟⠀⠀⢰⣿⣿⣿⣿⣿⣿⣷⢿⣷⣀⡀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡝⣿⣿⠃⠀⣀⣀⣰⣿⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀ ⣤⣤⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠆⠀⠀⠀⠀⠀⠘⢿⣻⣿⣿⣿⣯⢱⢻⣿⣆⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠨⠁⠀⠀⠀⠀ ䷩ 𝚕𝚒𝚗𝚎 1559 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/10/FreeBSD_14_4_Released.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/10/FreeBSD_14_4_Released.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ FreeBSD 14.4 Released⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Mar 10, 2026 * ⚓ FreeBSD_News_Flash⠀⇛ FreeBSD 14.4-RELEASE is now available. Please be sure to check the Release Notes and Release Errata before installation for any late-breaking news and/or issues with 14.4. More information about FreeBSD releases can be found on the Release Information page. * ⚓ FreeBSD_14.4-RELEASE_Release_Notes⠀⇛ The release notes for FreeBSD 14.4-RELEASE contain a summary of the changes made to the FreeBSD base system on the 14-STABLE development line. This document lists applicable security advisories that were issued since the last release, as well as significant changes to the FreeBSD kernel and userland. Some brief remarks on upgrading are also presented. ䷩ 𝚕𝚒𝚗𝚎 1597 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/10/Free_Libre_and_Open_Source_Software_and_Open_Data_Leftovers.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/10/Free_Libre_and_Open_Source_Software_and_Open_Data_Leftovers.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Free, Libre, and Open Source Software and Open Data Leftovers⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Mar 10, 2026 * ⚓ PowerDNS ☛ PowerDNS_Recursor_5.4.0_Released⠀⇛ Compared to the latest 5.3 release, this release includes the following changes: [...] * ⚓ GamingOnLinux ☛ CoolerControl_v4_adds_new_security_features,_brings hardware_support_and_more_|_GamingOnLinux⠀⇛ Monitor and manage various different cooling devices on Linux with CoolerControl. Version 4.0.0 brings a bunch more advanced features for you. For those of you who just love to tinker with your system to get the most out of it, CoolerControl rocks. * § Content Management Systems (CMS) / Static Site Generators (SSG)⠀➾ o ⚓ Mark Dastmalchi-Round ☛ Returning_To_Rails_in_2026⠀⇛ I know, right? Rails. That old thing ? People still use that ? But as I was doing this purely for fun, I decided to forgo the usual stacks-du-jour at $DAYJOB, and go back to my “first love” of Ruby. I also figured it would be a great opportunity to get re-acquainted with the framework that shook things up so much in the early 2000s. I’d been keeping half an eye on it over the years but it’s been a long time since I’ve done anything serious with Rails. The last time I properly sat down with it was probably around the Rails 3-4 era about 13-14 years ago now. Life moved on, I got deep into infrastructure and DevOps work, and Rails faded into the background of my tech stack. * § Licensing / Legal⠀➾ o ⚓ HOPE ☛ Is_legal_the_same_as_legitimate:_AI_reimplementation_and the_erosion_of_copyleft⠀⇛ In the chardet case, the distinction is sharper still. What the LGPL protected was not Blanchard's labor alone. It was a social compact agreed to by everyone who contributed to the library over twelve years. The terms of that compact were: if you take this and build on it, you share back under the same terms. This compact operated as a legal instrument, yes, but it was also the foundation of trust that made contribution rational. The fact that a reimplementation may qualify legally as a new work, and the fact that it breaks faith with the original contributors, are separate questions. If a court eventually rules in Blanchard's favor, that ruling will tell us what the law permits. It will not tell us that the act was right. * § Openness/Sharing/Collaboration⠀➾ o § Open Data⠀➾ # ⚓ Rlang ☛ Formula_1_Analysis_in_R_with_f1dataR:_Lap_Times, Pit_Stops,_and_Driver_Performance⠀⇛ This is where Formula 1 becomes much more than a sports topic. It becomes a practical case study in data wrangling, time-series thinking, feature engineering, visualization, and prediction. And because the R blog space has relatively little deep Formula 1 content compared with more general analytics topics, a strong tutorial here can help position your site as a serious source of expertise. ䷩ 𝚕𝚒𝚗𝚎 1695 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/10/Games_SiN_Reloaded_Less_DRM_PRAGMATA_and_More.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/10/Games_SiN_Reloaded_Less_DRM_PRAGMATA_and_More.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Games: SiN Reloaded, Less DRM, PRAGMATA, and More⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Mar 10, 2026 * ⚓ SiN_Reloaded_from_Nightdive_Studios_arrives_this_year_and_there's_a_new trailer_|_GamingOnLinux⠀⇛ Nightdive Studios have announced today that SiN Reloaded will release this year, and there's a new trailer available to watch right now. * ⚓ Denuvo_has_been_removed_from_DRAGON_QUEST_I_-_II_HD-2D_Remake_| GamingOnLinux⠀⇛ Haters of DRM will be happy about this one - as Square Enix appear to have removed Denuvo from DRAGON QUEST I & II HD-2D Remake. It was originally released on Steam in October 2025, so it didn't last very long. * ⚓ You_can_grab_the_Mafia:_Trilogy,_Far_Cry_Primal,_Pentiment_and_more_in this_game_bundle_|_GamingOnLinux⠀⇛ The ESA All-Star Alliance Humble Bundle is live and includes a really great set of games to add to your collection including the Mafia: Trilogy. Below the cut we'll list all the available games and their various ratings, along with the status on ProtonDB and store links to make it easier for you. * ⚓ DG2:_Defense_Grid_2_-_Aftermath_DLC_finally_comes_to_PC_| GamingOnLinux⠀⇛ 12 years after the original release of DG2: Defense Grid 2, a first DLC has been released for the well-received Tower Defense game. Defense Grid 2 - Aftermath was originally released for Oculus Rift and Nintendo Switch but was never on Steam until now. Good to finally see it. * ⚓ Valve_give_Team_Fortress_2_a_big_bug-fix_update_|_GamingOnLinux⠀⇛ Team Fortress 2 still lives on, somehow after 18 years and Valve just released one of the biggest bug-fix updates in some time. Quite a lot of the fixes came from the community, since the game source code is available now as part of the Source SDK. * ⚓ PRAGMATA_from_Capcom_has_the_release_date_moved_closer_in_April_| GamingOnLinux⠀⇛ Capcom recently announced that the brand new science fiction action-adventure PRAGMATA is actually going to release earlier than expected. Originally due out April 24th, they've moved the release date up to April 17th so you can get it a whole week earlier now. * ⚓ The_deep_strategy_RPG_Heart_of_the_Machine_1.0_is_out_now_| GamingOnLinux⠀⇛ From Hooded Horse and Arcen Games, the high-concept strategy RPG Heart of the Machine has now left Early Access for the big 1.0 release. ䷩ 𝚕𝚒𝚗𝚎 1783 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/10/Games_SteamOS_and_Common_PCs_Running_Steam.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/10/Games_SteamOS_and_Common_PCs_Running_Steam.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Games: SteamOS and Common PCs Running Steam⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Mar 10, 2026 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Bazzite⦈_ * ⚓ Make Use Of ☛ My_SteamOS_handheld_now_has_the_ultimate_library_thanks to_this_launcher⠀⇛ I've had my ROG Ally X for just about a year now, and shortly after SteamOS became available for it, I quickly converted this Windows 11 machine to a more handheld-friendly OS. Since then, I've been using it far more often than I ever did before, thanks in part to the more user-friendly experience that SteamOS has to offer for devices like this. But there was only one problem. Using SteamOS limited me to just using Steam games. Or so I thought. Enter Heroic Launcher. It's got all the things I like in one small package. It's open-source, gives me access to my Epic, GOG, and Amazon Prime Games library, and still lets me primarily use Steam as I see fit. Honestly, while it would be counterintuitive to Steam, I wish Heroic Launcher were included with a SteamOS install. It's just that good. * ⚓ XDA ☛ Linux_runs_most_PC_games_now,_and_you_don't_need_SteamOS_to_do it⠀⇛ Linux gaming is slowly gaining prominence, and while it's definitely not mainstream, it has crossed a line of viability that sounded ridiculous even a few years ago. It's no longer a hobby project, but a real way to enjoy most of your favorite games. Not every title works, and a handful of popular multiplayer games still treat Linux like a second-class citizen, but by and large, even games that aren't supported by Linux natively will run perfectly fine. The best part is: none of this has to do with distro. You don’t need SteamOS to get the modern Linux gaming experience. SteamOS is a great product, and it’s getting more important every year, but it’s not the secret sauce. The real story is that the tech stack underneath Linux gaming has matured to the point where your distro choice matters far less than the pieces it ships. * ⚓ XDA ☛ I_installed_SteamOS_on_a_regular_PC,_and_it_runs_better_than you'd_think⠀⇛ SteamOS is one of the main drivers of Linux adoption these days thanks to its inclusion with the Steam Deck and recent Lenovo gaming handhelds, but Valve has kept official support for it to a very limited number of devices. Of course, you can try to mimic the SteamOS experience with alternatives like Bazzite, but what would happen if you were to try and run proper SteamOS on a PC that isn't even designed for gaming in the first place? That's what I set out to discover, and, surprising as it may be, the results were pretty positive. I put the official SteamOS release on a Minisforum V3 tablet, and I had a pretty good experience using it this way. At the end of the day, it's Linux, and it works as well as you could expect it to. Let's take a look. ⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣵⣶⣶⣶⣶⣾⣭⣭⣭⣭⣍⣛⣛⣛⣛⡛⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠶⠶⠶⠶⠶⠦⠤⢬⣭⣭⣭⣍⣉⡙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣦⣤⢀⣤⣄⣄⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠻⢾⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠺⠓⣖⣒⡒⠲⠖⣠⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠉⠂⠸⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣉⣿⣿⣷⡢⠋⠉⠙⠉⠋⢄⡫⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠂⠐⠀⠉⠙⠿⠏⠿⣿⠿⢿⠻⠟⠇⠈⣀⣤⡴⠖⠀⠀⠀⠀⠈⠁⠤⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⣠⣴⢾⣟⣩⣵⣶⣏⡂⠀⠀⠀⠀⠀⠀⠈⠈⠻⡿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⡏⠉⠀⠉⠙⠻⠿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡟⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⡈⠋⢟⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣼⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⠁⠀⣀⣠⣄⣀⡀⠀⠀⠀⢰⣿⣿⣿⣿⣶⠀⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢨⣯⣿⣬⣴⣿⣗⣶⣶⣀⣐⡀⠀⠠⠼⠿⣿⣿⡀⢸⣿⣿⡿⠙⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⢸⠃⡁⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣠⣤⢠⣌⡻⣿⣿⣿⣿⣿⣿⣿⡿⠀⢘⣛⣻⣿⣏⣻⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣀⡬⣿⣶⡿⠖⠉⠁⠀⠀⣶⣼⣿⣿⣿⣿⡇⢸⡄⠁⠘⠛⠻⣿⣿⣿⣿⣿⡟⡇⠀⠀⢸⣿⣿⡏⠀⣀⠀⠀⠀⠀⠊⠈⢺ ⡿⠸⠿⢚⣳⣄⠉⠛⢿⣿⣿⣿⣿⡇⠀⢐⣺⣏⢉⢏⣺⣿⣿⣿⣻⣿⣿⣿⣟⣿⣻⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⢿⣿⣿⣿⣿⠛⠁⢈⠁⠀⠀⠀⠀⠊⠿⠿⣿⡿⠁⠀⠀⠀⣾⣿⣿⡇⠀⢻⠙⣶⣄⠀⠀⠻⣀ ⣿⣧⣷⣭⣿⣿⣿⡆⠀⠈⠉⠉⠉⠁⠀⣒⣾⡭⢔⣯⣿⣿⣿⣿⡿⣿⣯⢾⡿⢟⣿⣿⣯⠀⡄⠀⠀⠀⠀⠀⠀⠀⠈⠓⢭⡻⢿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⣿⣿⣿⣿⣶⡀⠁⠈⢻⣦⠀⠀⠈ ⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣒⣿⠿⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠣⣤⡀⠐⡶⢠⣀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠿⠉⣿⣿⣌⣦⣰⣦⣽⡧⠀⢀ ⠟⠛⣋⣉⣉⣩⣽⣿⠀⠀⠀⠀⠀⠀⠀⣖⣿⣮⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠂⠈⠐⠈⠃⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⢿⣿⡔⣫⠝⢦⣜ ⣼⡛⠛⠛⠋⣉⣥⣿⠄⠀⠀⠀⠀⠀⠀⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣌⠻⣦⣥⣭⠟ ⣿⣿⣿⣯⣯⣽⣿⣿⡀⠀⠀⠀⠀⠀⠀⠋⠛⠛⠳⠲⠶⠦⠾⣭⣭⣽⣙⣛⣛⡻⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣍⡻⢷⣤⠍⠁⠀ ⣿⣿⣿⢿⡿⠿⠟⠛⠃⠀⠀⢀⠐⠈⠀⠒⠒⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠒⠒⠶⢦⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣦⣌⡙⠲⠦⣤⣴ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠁⠀⠀⠁⠀⠁⠂⠐⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⠿⠿⠶⣦⣤⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣿⣿⣿⣿⣏⠑⢢⣤⣉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠬⠁⠀⡐⠀⠀⠀⠀⠈⠅⠀⠀⠀⠁⠄⠀⠀⠀⠠⠀⠀⡀⠜⠈⠀⠢⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⣿⣿⣿⣿⡷⣟⠲⢤ ⠀⠀⠀⠀⠀⠀⠀⠀⣔⡟⠀⠀⠀⠉⠀⠀⠀⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⢀⠀⠀⠒⠒⠀⠀⠤⢀⡂⠀⠀⠀⠀⠐⣿⣦⣺⢿⡿⠋⠹⠿⠣⣈⠙⣶ ⠀⠀⠀⠀⠀⠀⢀⣌⠟⠀⠀⠈⠉⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠀⠀⠈⠀⠀⢀⠀⠀⠀⡀⠀⠉⠀⠈⠐⠀⢘⢀⠀⠀⠀⠀⠙⢻⣽⣿⣾⣿⣿⣶⣠⣀⡈⠙⠒ ⠀⠀⠀⠀⠀⢀⢾⠊⡀⠀⠐⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠂⠀⠀⢰⠀⠀⢠⠀⠀⠀⠀⠀⠀⠁⠀⠀⢹⢸⠀⠀⠀⠀⠀⠉⠛⠻⠿⢷⣻⣯⣻⣿⣋⡐⡦ ⠀⠀⠀⠀⣠⣿⠉⠀⠀⠤⠀⠀⢀⡀⠀⢂⠀⠀⠀⠀⠁⠀⠀⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠀⠀⠀⠀⠀⠀⠒⠄⠐⠁⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⢷⣿⣿⣿⣅⣳ ䷩ 𝚕𝚒𝚗𝚎 1894 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/10/Geminispace_Will_Soon_Have_5_000_Capsules.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/10/Geminispace_Will_Soon_Have_5_000_Capsules.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Geminispace Will Soon Have 5,000 Capsules⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Mar 10, 2026 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Library_At_Trinity_College⦈_ About two thirds of them online 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇There_are_4857_capsules._We_successfully_connected_recently to_3317_of_them.⦈_ Speaking of accomplishments, the steadily-growing Geminispace bears fruit as it seems like another record week for us, traffic-wise, and Lupa lists us as top today. About a week ago Lupa saw a total of about 4,950 capsules, so 5k isn't far away. █ =============================================================================== Image source: Library_At_Trinity_College ⠀⠀⠀⠀⣼⣿⣿⣯⡙⣛⠛⣛⣛⢛⣿⣿⣛⠁⣭⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⣀⣀⣀⡼⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣽⣿⣿⣿⡆⢩⣶⣿⣿⣿⣿⣷⣾⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣸⣿⠃⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢨⣿⡇⠀⠀⠀⠀⠙⢿⣷⠀⠀⠀⠀⠀⠀⠀⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀ ⠀⠀⠀⠀⣶⣿⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠘⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠘⣟⣀⠀⣼⡆⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀ ⠀⠀⠀⠀⢹⢹⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢹⣿⡇⠉⠁⢸⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⠀⠀⠀⠀⢸⢸⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠄⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⡅⠀⠀⠀⠀⣀⣸⣿⡇⠀⠀⠀⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆ ⠀⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡁⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠉⠁⠈⠁⠀⠀⠀⠙⠁⠀⠀⢰⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇ ⠀⠀⠀⠀⢸⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠠⠄⠀⠿⠀⠀⠀⣼⡆⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇ ⠀⠀⠀⠀⢸⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⣀⠀⠀⢀⣿⠇⠀⠀⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢼⣿⣷⢠⣷⣼⣿⠀⠀⠀⠛⣶⣦⠀⠻⠃⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇ ⠀⠀⠀⠀⢸⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣯⠀⡀⢀⣴⣆⠀⠀⠀⠘⣿⡇⠀⠀⢿⠟⠀⠀⠀⠀⠀⠀⠀⣾⣿⣦⠀⠿⠃ ⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣿⡏⠀⠀⢀⣰⣿⠀⠀⠀⠀⠀⠀⢰⣷⠀⠀⠀⢀⣼⣿⣯⡀⠀⠀ ⠀⠀⡀⡇⡎⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⡀⠀⠀⠀⠀⠘⣿⣿⢸⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣿⡇⠀⠀⢈⠙⠁⢰⠀⠀⠀⠀⠀⣘⣁⣀⠀⠀⣸⣿⣿⣿⡷⠀⠀ ⠀⠀⡅⡇⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠉⠀⠀⠀⠀⠀⣿⣿⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⢻⡧⠤⠀⠟⠀⠀⠀⠀⡀⠾⢶⣾⡟⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀ ⠀⢀⣇⡇⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⢸⣧⣀⣀⡀⠀⠀⠈⢿⣟⠀⠈⠛⠀⢀⣤⠀⠀⠀⠀⣤⣄⠀⠀⣤ ⠀⢸⣿⡇⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⢸⣿⠻⠟⣿⡄⠀⠀⢘⣿⠀⠀⠀⠀⢸⣿⣷⡄⠀⣠⣍⠁⣶⣶⡧ ⠰⠈⢻⡷⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⢸⣿⢿⣿⣿⠇⠀⠀⠻⠟⠀⠠⠦⣤⠄⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀ ⠀⠀⠀⠠⣿⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣼⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠈⣿⢸⣿⣿⡧⠀⠆⠀⠀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⣿⠺⡗⣿⣧⣤⡄⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠸⢸⠸⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣸⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⣿⠀⠀⢹⣿⣩⣷⠀⠀⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠈⢸⠀⣸⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⣿⠀⠀⢸⣿⠈⣿⠄⠄⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⢰⢸⣤⣿⣿⣿⣿⣿⠧⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⣿⠀⠀⢸⣿⠀⣿⣦⣦⠀⣠⡟⠀⠀⠀⠀⠀⠀⢰⣿⡆⠀⠀⠀ ⣯⠀⠀⢈⢸⢺⢹⣿⣿⣿⣿⣧⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⡃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⣿⠀⠀⠸⣿⠀⣿⡅⣿⣦⡉⠙⣶⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀ ⣿⠀⠀⠈⣿⣿⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⢹⠀⠀⠀⣿⠀⢸⠁⣿⣿⡄⠠⡇⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⣀ ⣿⠀⠀⠀⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⢸⡆⠀⠀⣿⠀⠈⠀⢹⣿⣿⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡟⠀⠀⠀⣟⣯⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣾⣶⣦⣄⣿⣿⡇⠀⠀⠀⢸⡇⠀⠀⢻⠀⠀⠀⠘⣿⣿⣆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡇⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠣⠀⠀⡇⠀⠀⡀⠀⠸⡟⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡇⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⠀⣿⣿⣧⣤⣾⣿⣿⣿⣿⠟⠋⠁⠀⠉⠉ ⠁⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢀⠀⠀⡇⠀⠀⡇⠀⠰⣧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⡇⠀⠀⠁⠀⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣸⡇⠀⠀⢸⠀⠀⠀⠀⠀⠈⠇⣿⣿⣿⣿⠇⠀⠲⣶⣶⣶⡄⠀ ⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠃⠀⠀⠀⠀⠀⣿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣴⣿⣿⣿⣦⠀⢸⡇⠀⠂⠀⠀⠀⠀⢿⣿⣤⣄⠀⠀⢀⣤⣤⣤⣄⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇⠀⡀⠀⠀⠀⠀⢸⣿⣿⣿⡁⠀⢸⣿⣿⣿⡯⠀ ⠀⠀⠄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢀⠀⠀⠀⠀⠀⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⡂⠀⠀⠀⠀⠀⢿⠻⣿⡇⠀⠘⢿⣿⣿⠇⠀ ⠀⠀⠆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢰⣿⡿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠈⠀⢿⠀⠀⠀⠘⠋⠀⠀⠀ ⠀⠀⠀⠘⠟⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠈⠀⠀⠀⠀⣴⣿⣦⠀ ⠀⠀⠀⠀⠀⠀⣠⡀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠉⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⢀⣸⣿⣿⣀ ⠀⠀⠀⠀⠀⠀⣾⣷⣦⣄⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⢿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⣿⣿⢹⣿⣶⣄⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⠀⠀⣿⣇⣬⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⣄⣀⣹⣿⣿⣅ ⠀⠀⠀⠀⠀⢀⢻⣇⣸⣿⣿⣿⣿⠀⠀⠈⠻⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿⣿⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠠⠈⠉⠹⣿⣿⣿⣿⡆⠀⠀⠀⠈⠛⠛⠻⣶⣾⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿⣿⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⡇⠀⠀⠈⢿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠠⢰⢠⡤⠛⠉⠉⠉⠁⠀⣀⣤⣤⣤⣬⣬⣭⣿⣿⣿⣏⡉⠀⠀⠀⠀⠀⠀⠀⢸⡀⢸⣿⣿⣿⠅⠀⠀⠀⠀⢈⣻⣿⣿⢿⡇⠀⠀⠀⣠⣼⣿⣿⡿⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢰⢸⢘⡀⠒⠒⠚⠚⠛⠛⠛⠛⠛⠛⠋⠛⠛⢻⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⡟⠓⠐⠚⠛⠻⢿⣿⡿⠁⢸⡇⠀⢀⣤⣤⣭⣼⡇⠀⢠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⢙⣿⠛⠿ ⠀⠀⠀⠀⠀⢸⢸⢸⣿⣦⢀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣶⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⠋⠳⠀⣴⣶⣶⣶⣾⣿⡇⠀⠘⣃⣠⣾⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⡿⠿⠋⠉⠉⠁⠀⠀⠀⠀⠸⠟⠀⠀ ⠐⠀⠀⠀⢀⢸⢸⢸⣿⣿⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠠⣿⣠⣴⣶⣿⣿⣿⣿⣿⣿⣷⣤⣄⢻⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⠛⠛⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⢸⢸⢸⣿⠟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠲⠀⠀ ⠀⠀⠀⠀⢸⢸⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⢸⣸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢉⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀ ⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⢹⣿⣿⣿⣿⣏⠁⣀⢸⣿⣿⣿⡆⠤⢤⣤⣤⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆⣾⡏⠀⠀⠀⠀⠀⠀⠈⣉⠀⠀⠀ ⠀⠀⠀⠛⠛⠙⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠃⢐⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⣿⠇⣿⠇⠀⠀⠰⡶⠋⠀⣞⣻⣿⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⣿⠀⠉⠀⠀⢠⣶⠋⠀⠀⢛⢻⣿⡟⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⣇⠀⢠⡿⠀⠀⠀⢀⣀⡙⠃⠀⢰⣿⣿⣿⣷⠶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⢸⡇⠀⠀⠴⠟⠋⠀⠀⠀⣀⣩⣭⣭⣀⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⢸⠇⠀⣀⣀⣤⣤⣀⣠⣼⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡟⢀⡦⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣀⣀⣿⡟⠋⠀⠀⠉⣻⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢟⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣸⠃⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠉⠉⠈⠻⠆⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⡿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢠⣤⣤⣤⡶⠂⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠈⠂⠖⠲⠀⠆⠗⠒⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠰⠆⠀⠂⠀⠀⠂⠀⢲⠂⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⡀⡀⡀⡀⠀⡀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠂⠀⠀⠒⠚⠐⠐⠂⠀⠂⠘⠓⠀⠐⠃⠐⠐⠙⠀⠊⠈⠈⠈⠀⠑⠈⠚⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⢀⡀⠀⠀⣀⣀⢀⠀⣀⣀⣀⣤⡠⢀⢀⠀⠀⡂⡂⡢⠂⢂⢰⡀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⢀⢀⢀⢀⢀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠐⠂⠀⠀⠒⠒⠚⠊⠘⠒⠀⠒⠀⠀⠂⠐⠐⠑⠑⠑⠈⠂⠓⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⢀⣀⠀⠀⣀⣠⢀⡀⣀⡀⢀⠀⢀⡀⢀⠀⡀⠀⣐⢔⢔⢐⠀⡐⡲⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⢀⢀⢀⢀⢀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠚⠐⠀⠒⠂⠂⠀⠒⠂⠒⠒⠐⠐⠀⠐⠐⠀⠒⠑⠓⠂⠀⠂⠐⠐⠑⠑⠑⠈⠂⠓⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⢀⣀⠀⢀⢀⠀⡠⢠⡄⡀⢀⡄⢀⠀⡀⢀⣀⢰⠠⠠⠠⡠⢀⢂⠆⡂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠂⠀⠐⠐⠂⠀⠒⠁⠃⠂⠀⠙⠑⠐⠈⠂⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⡀⢀⣀⡠⠠⠀⠠⠤⡀⡄⢀⢰⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⠀⠀⠀⠈⠀⠑⠐⠐⠀⠒⠃⠂⠈⠁⠙⠁⠁⠃⠚⠃⠑⠙⠋⠙⠀⠂⠙⠛⠀⠃⠂⠁⠀⠂⠈⠘⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠄⠀⠀⠀⠠⠀⠀⠠⠤⠀⠀⠐⠀⠀⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ䷩ 𝚕𝚒𝚗𝚎 2023 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/10/GNU_Linux_Devices_and_Open_Hardware_Projects.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/10/GNU_Linux_Devices_and_Open_Hardware_Projects.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ GNU/Linux Devices and Open Hardware Projects⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Mar 10, 2026 * § GNU/Linux Devices⠀➾ o ⚓ Linux Gizmos ☛ BeagleBadge_wearable_platform_boasts_TI_AM62L_SoC, ePaper_display,_and_GNU/Linux_support⠀⇛ The BeagleBoard.org Foundation has introduced BeagleBadge, an open-source wearable development platform for IoT and embedded applications. The badge integrates a 4.2-inch ePaper display, onboard sensors, wireless connectivity, and expansion interfaces in a compact board for prototyping wearable and interactive systems. o ⚓ Hackaday ☛ Last_Year_In_SBCs⠀⇛ While it might not be comprehensive, [Bret.dk] recently posted a retrospective titled “Every Single Board Computer I Tested in 2025.” The post covers 15 boards from 8 different companies. The cheapest board was $42, but the high-end topped out at $590. We like the structure of the post. The boards are grouped in an under $50 category, another group for $50-100, and a final group for everything north of $100. Then there’s some analysis of what RAM prices are doing to the market, and commentary about CIX P1, Qualcomm, RISC-V, and more. o ⚓ [Old] Troy Press ☛ Sinclair_4K_BASIC_for_the_ZX80⠀⇛ In my study of Tiny BASICs, one I overlooked reviewing was Sinclair 4K BASIC, which stands out for its unique keyboard, its approach to graphics, and its memory usage. A friend’s family bought their first computer, which was either a ZX80 (4K BASIC) or ZX81 (8K BASIC), but I can’t recall which it was. I do remember learning the keyboard’s unique layout when we got together to help type in BASIC programs, which was a team effort when I was a kid. * § Open Hardware/Modding⠀➾ o ⚓ Ubuntu ☛ Canonical_and_Arduino_collaborate_to_enable_Ubuntu_on the_VENTUNO_Q,_the_next_generation_platform_for_AI⠀⇛ Today, Arduino announced the launch of the Arduino® VENTUNO™ Q, a dual-brain board designed for high- performance computing and physical actuation. VENTUNO Q represents a significant step in the Arduino-Qualcomm Technologies, Inc.-Canonical collaboration, embracing a developer-first philosophy with Ubuntu. o ⚓ Raspberry Pi ☛ Maker_Monday:_Your_Raspberry_Pi_builds⠀⇛ Maker Monday is the fun way we keep in touch with the maker community from all over the world. We’ve piggybacked on Raspberry Pi Official Magazine’s habit, and every Monday, we ask the question: have you made something with a Raspberry Pi over the weekend? Every Monday, our followers send us amazing photos and videos of the things they’ve made using the hashtag #MakerMonday. o ⚓ Hackaday ☛ Real-Time_ISS_Tracker_Shows_Off_The_Goods⠀⇛ Conceptually, it’s very similar to the International Space Station tracking lamp that [Will Dana] built in 2025. In fact, [wyojustin] cites it specifically as one of the inspirations for this project. But unlike that build, which saw a small model of the ISS moving across the surface of the globe, a transparent globe is rotated around the internal mechanism. This not only looks gorgeous, but solves a key problem in [Will]’s design — that is, there’s no trailing servo wiring that needs to be kept track of. o ⚓ Hackaday ☛ Building_A_Class_100_Semiconductor_Cleanroom_Inside_A Shed⠀⇛ Key to everything is HEPA filtration along with positive pressure, to constantly push clean air into the cleanroom, while preventing dirty air from flowing in. The shed was also split into two sections, the first room once you enter it being the the gowning room. This is where you change into cleanroom gear before you transition into the cleanroom. ䷩ 𝚕𝚒𝚗𝚎 2144 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/10/GNU_Linux_Leftovers.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/10/GNU_Linux_Leftovers.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ GNU/Linux Leftovers⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Mar 10, 2026 * § Graphics Stack⠀➾ o ⚓ James Randall ☛ Path_Tracer⠀⇛ A real-time path tracer built entirely in WebGPU compute shaders — no RT cores, no ML denoisers, just maths and triangles. Woke up one morning and wanted to follow up the Wolfenstein 3D raycaster with a ray tracer… obviously Doom levels were an obvious starting point. * § Distributions and Operating Systems⠀➾ o ⚓ Barry Kauler ☛ Have_brought_back_mount-FULL_utility⠀⇛ EasyOS uses the busybox 'mount' utility, instead of the full utility in util-linux (mount is split out to the 'mount' DEB package in Devuan/Debian). One reason the full mount is not used: https://bkhome.org/news/202210/problem-with-mount- utility-when-non-root.html woofQ2 has woofq2/builtin/deb/fixes/mount, which replaces the full mount with a script. Ditto for 'umount'. The script calls the busybox mount. o § SUSE/OpenSUSE⠀➾ # ⚓ Updating_perltidy_(and_other_dependencies)_in_os-autoinst⠀⇛ When updating the dependecies.yaml file in os- autoinst, e.g. when you’d like to fix_the_outdated perltidy_version_in_the_repo the recommended workflow is to: # Update dependencies.yaml # Run make update-deps This will update the cpanfile for you and you only need to make your changes in one single file (dependencies.yaml). ䷩ 𝚕𝚒𝚗𝚎 2213 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/10/GNU_Linux_Perils_on_Desktop_Laptop_Common_Mistakes_Terminal_Way.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/10/GNU_Linux_Perils_on_Desktop_Laptop_Common_Mistakes_Terminal_Way.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ GNU/Linux Perils on Desktop/Laptop: Common Mistakes, Terminal, Wayland, and More⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Mar 10, 2026 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇A_popular_newcomer_mistake⦈_ * ⚓ Make Use Of ☛ 3_Linux_mistakes_even_experienced_users_still_make⠀⇛ If you have been running Linux for a few years, you already know the obvious ways to break things. You are not pasting mystery commands from page four of a forum thread, and you are not casually torching your bootloader for weekend entertainment. At this point, you have scars, backups, and at least one opinion about package managers that borders on philosophical. I still keep seeing the same quiet mistakes show up in otherwise very competent Linux setups. Not beginner stuff. Not “help I deleted /usr” energy, but just habit mistakes. The kind that feels completely reasonable in the moment and only shows its teeth months later when your system starts behaving… off. These three in particular still ambush experienced users. I know because I have personally done all of them. With confidence, and more than once. * ⚓ Make Use Of ☛ You_don’t_need_the_terminal_to_use_Linux_anymore⠀⇛ If you hang around Linux spaces long enough, you start to notice a vibe. The terminal is not just a tool. It is practically a personality trait. Screenshots glow with neon green text. Dotfiles get treated like family heirlooms. And somewhere off to the side, a perfectly normal newcomer is quietly wondering if they just signed up for a lifetime of memorizing spells that look like they were created by a caffeinated octopus. I get the anxiety; I have been using Linux for years. Yes, I can navigate a terminal without breaking into a stress shimmer. But here is the part that doesn't get said nearly enough: in my actual day-to-day life, the terminal barely makes a cameo. Modern Linux desktops have quietly grown up while nobody was looking. You can now get through most of your week without living inside a black rectangle full-time. If you have been curious about Linux but worried it requires permanent command- line residency, here is what my real week actually looks like. * ⚓ XDA ☛ Linux_desktops_silently_fixed_their_biggest_problem,_but_most people_missed_it⠀⇛ I'm not talking about gaming! Though it has come a long way since Proton came about and driver support improved over recent years, the largest problem had already been fixed in the background. No, it's not the steep learning curve for those coming from macOS or Windows and diving straight into the console, nor is it fragmented software ecosystems and package managers. It's not the plethora of choice when it comes to picking a distro, nor is it the fact that Linux still has a very small desktop market share. * ⚓ XDA ☛ Most_people_install_Linux_wrong,_and_it_ruins_their_first impression_forever⠀⇛ Every so often, you hear of users trying to make the leap from Windows or macOS to Linux, drawn in by the allure of its flexibility, control, and freedom to choose how their OS looks and feels like. Unfortunately, many of them just crawl back within a week or two. They will tell you how Linux "just isn't for them", or that it's too complicated or too different. The truth is seldom about Linux itself, and a lot of it is about how it's installed. Unlike Windows or macOS where installation is a passive experience, Linux hands you the keys to make every decision right from the very beginning, whether it's about your choice of distro, the desktop environment, and even the hardware you have. It's true that the freedom that comes with the process is the whole point, but it's also unmistakably daunting for the unprepared who come seeking a plug-and-play experience. If your migration to Linux fails, it could be because of these reasons. ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢁⣀⣈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠉⠛⠿⠁⠀⣼⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣀⣀⣤⣶⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣹⣿⣿⣿⢟⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠁⠀⠈⡙⢿⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠯⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣐⣋⣽⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠙⠛⠛⠉⠀⠔⠻⠿⢉⣁⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠂⢀⡔⠀⠀⠀⠀⣿⣿⣿⣿⣿ ⣿⣿⣿⡏⣶⣶⣶⣶⣶⣶⣶⡶⠤⠴⠴⠤⠤⠤⠤⠤⠤⠤⠴⠦⠤⠤⠤⠤⢤⣤⣤⣤⣴⣶⣶⡆⣿⣿⣿⣿⣿⣿⣿⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠈⠁⠀⠀⢀⠀⠛⠛⠛⢻⣿ ⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⠀⠉⢠⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡂⠁⠀⢨⣘⣒⠂⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠀⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡟⠀⠀⠻⣀⡸⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⡀⠀⢀⠀⠀⣀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣼⣿ ⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡿⠄⢈⣏⠀⣼⡅⠘⡿⠀⣾⣶⣦⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⣿⣿⡗⢿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠠⠀⠐⠒⠂⢸⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⠁⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡋⠀⢘⡋⠀⣛⠃⢰⡿⠀⠛⠟⠛⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⣿⣿⣿⢸⣾⣿⣬⣿⣿⠀⠀⣀⠀⣀⠐⡓⢘⡀⣛⢈⡃⣩⠀⠁⢀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⢿⣿⠃⠀⠸⣿⠃⣨⣤⠀⠀⢠⣄⢀⠀⠀⠀⣀⠀⠨⠄⠀⢈⡑⠀⠛⠄⠼⠧⠀⠈⣶⠄⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⣿⣿⣿⣤⣿⣿⣿⣃⣃⣢⠤⢽⣯⡽⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣼⣾⣿⣷⣿⣿⣿⣿⣿⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⢩⠍⠘⠀⠉⠀⠁⠀⠈⠁⠀⠞⣇⠀⣀⣀⠀⠀⠀⠄⠋⠀⠀⣤⣄⠀⠀⠀⢀⣿⣇ ⣿⣿⣿⣿⢰⣶⣾⣿⣼⣯⣬⣄⣠⣤⣀⠀⡶⠦⠄⠀⠠⠤⠤⠘⠂⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⢨⣿⣿ ⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠭⠭⠭⠭⠀⠭⠭⠿⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿ ⣿⣿⣿⣿⢾⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣤⠶⠶⠦⢤⣤⠤⠤⠤⠤⠼⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⢠⣄⣀⣄⢀⣀⠀⠍⠁⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠏ ⣿⣿⣿⣿⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⣾⣷⣄ ⣿⣿⣿⣿⠂⠛⢻⣿⠳⣗⢓⣳⠓⠢⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⠈⠉⠈⠁⡀⠁⠈⠁⣤⣼⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣿⣿⣿⡯⠼⠄⠀⠈⠧⠨⠭⠀⠥⠀⠩⠀⠠⢄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢐⡂⢹⡿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⣿⣿ ⣿⣿⡯⠭⠍⠀⠤⠀⠬⠁⠨⣅⢄⣁⣀⣈⣀⣀⣀⣀⣀⣀⣀⢀⣂⡀⢒⢀⣀⡒⢀⣒⣂⠐⡂⣸⣯⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠰⠓⠈⠈⠉⠉⠀⠀⠀⠀⠉⢻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠟⠷⠰⠀⠐⣒⣒⣀⠀⢀⣀⣀⠠⠼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠛⠛⠛⠛⠛⠛⠛⢉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣁⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣦⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠩⠭⠭⠭⠭⠭⠝⠛⠛⠛⣛⡛⠛⢛⣛⠻⢿⡿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣦⣤ ⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿ ䷩ 𝚕𝚒𝚗𝚎 2344 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/10/GNU_Linux_terminals_and_Kitty_is_the_most_powerful_tool_in_my_w.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/10/GNU_Linux_terminals_and_Kitty_is_the_most_powerful_tool_in_my_w.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ GNU/Linux terminals and "Kitty is the most powerful tool in my workflow"⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Mar 10, 2026 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Konsole⦈_ * ⚓ HowTo Geek ☛ I_tried_the_top_8_Linux_terminal_emulators_so_you_don't have_to⠀⇛ Even though most Linux distros have become less terminal- dependent in recent years, everyone winds up using the terminal eventually. I tested seven of the most popular terminal emulators out there to see which was the best. * ⚓ HowTo Geek ☛ Forget_the_standard_terminal—Kitty_is_the_most_powerful tool_in_my_workflow⠀⇛ When you think of a terminal app, it might seem like a program stuck in time—just a solid window that interacts with your shell and displays text. However, modern terminal apps have come a long way. And I've found no terminal app better than Kitty. Give me a chance to convince you to switch to it. ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠻⡛⣿⣿⡿⠿⢿⣿⣿⣟⣿⣿⣿⡟⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⢻⣿⣿⣿⠻⠻⢟⠛⢻⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣄⢠⢠⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⣠⣤⡀⢸⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⠶⠶⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢒⣖⢲⣖⠒⠒⠒⠒⠒⠒⠂⠀⠐⠲⠀⠀⠀⠀⠸⢖⣦⢸⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡿⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡯⢸⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣦⣠⣤⣀⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⢸⣿⠀⠀⠀⡀⡀⠀⠀⢀⣀⡀⠀⡀⠀⡂⠀⣬⣿⢹⣯⠀⡀⠀⠀⠀⢀⠀⢀⣀⠀⠀⠀⠀⡀⠀⢨⣽⢸⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠧⡤⠤⠤⠤⠤⠿⠿⠿⠶⠿⠼⠿⠷⠿⠿⠿⠧⠤⠤⠤⠤⠤⠤⠤⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣟⢺⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣗⢸⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⣀⠀⠀⠁⠀⠀⠀⠀⠁⠈⠀⠀⠀⠉⠀⢀⡈⠸⠿⠶⢱⣶⣏⢀⢀⣶⠷⠎⠀⠿⣴⣞⡁⡰⣴⣖⢸⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⣭⠨⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠤⠭⠥⠄⠰⢦⢈⣉⣉⡈⢩⣭⠄⣶⣶⠄⣉⣈⡀⢹⡯⠭⢸⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣠⣤⣠⣄⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠒⠚⣒⣒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢒⣒⣒⡒⠒⠒⠒⠒⠒⠒⠒⣒⠒⠒⠒⢒⣒⣒⡒⢒⣒⣒⣒⠒⠒⠒⠒⠒⠒⠒⠒⢒⣒⣒⣒⡒⢒⣒⣒⠒⠒⣒⣒⢲⣒⣒⠒⠒⠊⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⣷⠿⡿⠅⠀⠀⠀⢰⣶⣴⢰⣶⡆⢁⣿⡿⠏⠉⠁⠀⠀⠀⠀⠀⠷⠿⠇⣿⠉⢁⣹⣿⣯⠱⠿⣿⣿⢿⠠⡶⣶⢶⣶⠄⠈⠈⢉⠉⠿⢿⠯⠉⢷⣿⣶⠉⠉⠈⠩⣿⢶⢭⣿⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡏⣛⣛⣋⣀⣀⣀⣀⣈⣛⣉⢸⣽⡇⢸⢻⣥⣤⣤⣤⣤⣤⣤⣤⣤⢠⣤⣤⣿⠀⢸⣿⣿⣿⢸⣿⣭⣿⡍⠀⣽⣯⣿⣿⣿⣽⢿⣯⡏⣽⣿⣭⠀⢸⣯⣭⢀⣀⣐⠀⢹⣸⠝⢻⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠛⠛⠛⠛⠛⠓⠀⠘⠓⠛⢘⣿⡃⢀⢛⣻⣇⣀⣀⣀⣀⣀⣀⣀⢘⣿⣧⣿⠀⠘⣿⣿⣿⢘⣟⣒⣛⠛⠀⣛⣛⣚⣛⣛⣛⣛⣛⡃⣛⣛⣛⠀⢸⣿⣟⠀⠀⠀⠀⢸⢚⡀⢸⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠿⠿⠿⠿⠉⠉⠉⠹⠿⠿⢰⣷⡆⢈⣼⡷⠶⠶⠶⠶⠀⠀⠀⠀⠶⠿⠆⣿⠀⠀⣷⣿⣷⠰⡶⢾⡶⠀⠀⣾⣿⢷⡷⣶⡾⣾⣶⡆⢶⣿⡶⠀⢸⣿⣶⠀⠀⠀⠀⢸⢴⠂⢸⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠿⢿⡯⠉⠉⠉⠉⢹⣿⣿⢸⣽⡇⢨⢩⣥⡤⠤⠤⠤⠤⠤⠤⠤⢠⣴⣶⣿⠀⠀⣯⣭⣯⢨⠭⢭⣭⠀⠀⢭⣭⣭⣭⠭⣭⢭⠭⡅⢭⣭⡭⠀⢨⣭⡭⠀⠀⠀⠀⢨⠩⠅⢸⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠐⠒⠒⠒⠒⠒⠒⠒⠒⠂⠘⠛⠃⢠⣿⡟⠛⠛⠃⠀⠀⠀⠀⠀⠛⠛⠃⣿⠀⢠⣼⣿⣿⢘⣟⣻⣘⠛⠁⣟⣛⣻⣛⣟⣛⣿⣇⡃⣩⣛⣃⠀⢸⣿⣯⠀⠀⠀⠀⢸⣸⡀⢸⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠓⠒⣒⣒⠒⠒⠒⠒⠒⣒⣒⡒⠒⣒⣓⠒⢒⣒⡒⠒⣒⢒⣖⣒⣒⣒⢒⠒⢻⠀⠀⣟⣺⣿⢐⣒⣒⣓⠒⠂⣲⣿⣖⣒⣖⣚⣒⣗⡂⣒⣒⣒⠀⢸⣿⣓⠀⠀⠀⠀⢸⢐⠂⢸⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠰⡷⡏⠉⠁⢴⣶⣴⡌⡏⣯⢹⠈⠉⡉⠁⣈⠉⡉⠁⠈⠈⠉⠉⠉⠉⠈⠈⢸⠀⠀⡹⢯⡿⠸⠭⠬⠩⠶⠀⠬⠯⠽⠯⠭⠯⠬⠅⠅⠼⠭⠧⠀⠸⢾⡷⠀⠀⠀⠀⢸⠸⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡅⣇⡀⠀⣽⣿⣽⡅⡇⣿⢸⢠⡌⣿⣿⣽⣿⣯⣤⢠⣄⣤⡄⣤⣤⣤⡄⢸⠀⠀⣭⣭⡭⢨⣭⣭⡭⡄⠀⢭⡿⢩⣭⣭⣭⣭⣭⠅⢭⣭⡭⠀⢨⢭⡭⠀⠀⠀⠀⢨⢨⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⠃⣿⣀⡇⢘⣟⣸⣠⣇⡟⠘⢘⡃⣟⣟⣠⡀⠀⠀⠀⠛⢛⣃⣻⢻⣻⡇⢸⠀⢘⣛⣛⣛⢘⣃⡀⣚⣂⠀⣒⣒⠈⣒⣛⣓⢉⣂⡂⣒⣒⣒⠀⢀⣛⣋⠀⠀⠀⠀⢘⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠉⣿⡏⠉⡏⢻⢿⡟⣻⠉⠀⠀⣈⡈⣀⣀⡀⡀⢀⡀⣀⡉⣈⣀⣈⡁⢸⠀⢀⣶⣲⡶⢰⠂⠆⠀⠀⠀⠒⠶⠀⠀⢀⠀⢀⠀⠀⠰⠶⠒⠀⠐⣰⡒⠀⠀⠀⠀⢰⠐⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠁⠀⡇⢸⢸⠁⠀⠀⢨⡅⣯⡭⠉⠋⠉⠉⠸⢏⢿⡧⣿⣿⣭⡇⢸⠀⠨⠭⠭⠍⠨⠤⠤⠄⠭⠀⠨⠅⠀⠈⠭⠭⠀⠁⠅⠨⠭⠥⠀⠨⠭⠅⠀⠀⠀⠀⠨⠨⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠁⠘⠘⠀⠀⠀⠘⠃⣿⣿⣿⡅⠀⠀⠀⠀⠀⠘⠛⠘⠛⠃⢸⠀⠀⠈⠉⣉⠀⠁⡀⣁⠀⠀⢈⣓⠀⠀⡀⣀⡀⡁⡀⢈⣀⠁⠀⠈⠀⠁⠀⠀⠀⠀⢈⠈⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡸⠟⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣄⠀⣀⣄⣀⡀⢀⣀⠂⠀⠀⢰⡄⠀⠀⣀⠀⠀⠀⠀⣐⣀⣀⣀⣀⣐⣂⣀⣀⣀⣀⣐⣀⣐⣾⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ䷩ 𝚕𝚒𝚗𝚎 2418 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/10/I_ve_helped_friends_and_family_move_to_Linux_here_are_my_top_5_.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/10/I_ve_helped_friends_and_family_move_to_Linux_here_are_my_top_5_.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ I’ve helped friends and family move to Linux—here are my top 5 gateway distros⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Rianne Schestowitz on Mar 10, 2026 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇penguin_side_by_side_with_human⦈_ Quoting: These are the top 5 gateway Linux distros, ranked — Getting someone to try Linux is one thing—getting them to stay is another. After helping several friends and family members make the switch, I’ve found that some distros do a better job of keeping people around and encouraging them to explore the OS further. I call these “gateway” Linux distros—and here are my top five picks. Read_on ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⢰⣿⣷⣦⣤⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠼⠿⠿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⡶⢆⠀⠀⣴⡿⣷⡄⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡀⠀⢠⣤⣤⢀⡄⣤⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡁⠈⣀⣀⣿⡀⢁⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠉⠛⠙⠛⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢶⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠑⠒⠂⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢀⠈⠉⣉⣥⣤⣶⣿⡇⠀⠀⠀⠀⢿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⡠⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣼⣷⣤⣭⣽⣿⣿⣿⡇⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠘⠛⠻⠛⠛⠉⠙⠛⠻⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣷⡴⠀⠀⢀⣿⣿⠟⠛⠛⠛⠛⠛⠛⠉⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠈⢾⡟⠀⠀⣼⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠙⠀⢰⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣦⣤⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣠⣀⣠⣶⣿⣿⣿⣿⣶⣦⣤⣤⣤⣴⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠑⠎⣿⣿⣿⣿⢿⣿⣷⠿⢧⣄⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠁⠈⠂⣣⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ䷩ 𝚕𝚒𝚗𝚎 2473 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/10/I_ve_used_dozens_of_Linux_distros_these_3_offer_the_best_nostal.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/10/I_ve_used_dozens_of_Linux_distros_these_3_offer_the_best_nostal.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ I’ve used dozens of Linux distros—these 3 offer the best nostalgia trip⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Rianne Schestowitz on Mar 10, 2026 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇old_penguin⦈_ Quoting: These 3 classic Linux distros are a blast from the past — Here is a fact-based summary of the story contents: Linux has evolved dramatically over the years—so much so that it's often unrecognizable from how it started. Whether you're new to Linux or a veteran who's simply moved along with the times, sometimes it's worth taking a look back to see how far we've come. These three distros let you relive the past and re-experience the classics that shaped everything we use today. Read_on ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠴⠾⠿⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣴⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣤⣴⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠰⠾⠷⠦⠀⠀⠀⠴⠾⣶⣿⣿⣿⣿⣿⣟⣉⡉⠉⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⡿⢿⣿⣿⣿⣷⣶⣶⣶⣶⣴⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡀⠀⡄⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠁⢠⣶⣶⣄⠋⠁⠀⢀⠀⢲⣦⣤⣤⣤⣄⣀⡀⠀⠀⢸⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠚⠻⢿⣿⣿⣦⣤⡤⠘⣧⡀⠹⠿⠿⠛⠉⠁⠀⠀⠀⢸⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣯⣥⣤⡀⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢠⣶⣶⣶⣀⣀⣀⣠⣼⣿⣿⣿⣿⣧⠀⠙⢿⣷⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠹⣿⣿⣿⠿⠛⠛⠋⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⣠⣤⡀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠈⠁⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣶⣌⡆⢨⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿ ⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣶⣽⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⣤⣤⣤⣤⣴⣿⣿⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⢛⡛⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ䷩ 𝚕𝚒𝚗𝚎 2532 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/10/KDE_Kate_and_KDE_Connect_in_Review.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/10/KDE_Kate_and_KDE_Connect_in_Review.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ KDE: Kate and KDE Connect in Review⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Mar 10, 2026 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Kate⦈_ * ⚓ HowTo Geek ☛ Why_I'm_learning_to_code_in_Kate_instead_of_VS_Code⠀⇛ I use Linux as my primary desktop, and I have for years. My favorite desktop environment to work in is KDE Plasma. Kate is developed under the same roof, so to speak, at the KDE Project. In fact, Kate is sometimes packaged with KDE Plasma desktop environments. It integrates the Konsole terminal emulator, which I already use for command line work, and its theming options match the standard KDE Plasma themes. A single cohesive ecosystem makes me feel at home and in tune with my PC, and since it's KDE-based, I don't have Microsoft looking over my shoulder. * ⚓ XDA ☛ KDE_Connect_does_something_between_my_phone_and_PC_that_even Apple_hasn't_figured_out⠀⇛ Over the years, many solutions have come around for linking your phone to your PC in an attempt to improve your productivity or simply make things more seamless as you move from one device to another. Apple is arguably the most notorious and successful in this endeavour, though Microsoft has been trying hard to replicate it with its Phone Link app. But unbeknownst to most people, there's a solution that may be even better than both of those. It's called KDE Connect, and it has some features you won't even find in Apple's tightly integrated ecosystem, which I've found fascinating. I tested KDE Connect between my phone running Android 16 (specifically, LineageOS 23.2) and my laptop running Arch Linux with KDE Plasma, and frankly, the setup process was incredibly easy. With the app installed on both devices, my laptop immediately appeared as an available device on my phone, and linking the two was instant. I was also able to access the features I'm going to talk about immediately without much setup, either. ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠉ ⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢀⣤⣶⣦ ⠀⠀⠀⠀⠉⠛⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⢿⣿⣿⠿⠛⠛⠻⢿⣿⡿⠿⠛⠁⣠⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠰⠶⠚⠻⠿⠿⠿⠿⠿⠿⠿⠿⢿⡿⠿⠿⠿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣏⣹⣿⣿⣉⣿⣯⣿⣿⣿⣿⣿⣿⣿⣟⣿⣏⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ䷩ 𝚕𝚒𝚗𝚎 2621 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/10/KDE_Plasma_6_5_6_Released_as_the_Last_Update_in_the_Series_with.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/10/KDE_Plasma_6_5_6_Released_as_the_Last_Update_in_the_Series_with.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ KDE Plasma 6.5.6 Released as the Last Update in the Series with More Fixes⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Marius Nestor on Mar 10, 2026, updated Mar 10, 2026 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇KDE_Plasma_6.5.6⦈_ Coming almost a month after KDE Plasma 6.5.5, the KDE Plasma 6.5.6 release is here to update the HDR calibration wizard to temporarily disable the Night Light feature while calibrating your monitor to ensure that you get an accurate result. KDE Plasma 6.5.6 also updates the Spectacle screenshot tool by bringing back the ability to remember the location where you last saved a screenshot the next time you save one, and it adds support for third-party wallpaper plugins that include translations to show that translated text. Read_on Planet KDE: * ⚓ KDE_Plasma_6.5.6,_Bugfix_Release_for_March_-_KDE_Community⠀⇛ Today KDE releases a bugfix update to KDE Plasma 6, versioned 6.5.6. Plasma 6.5 was released in October 2025 with many feature refinements and new modules to complete the desktop experience. This release adds two months’ worth of new translations and fixes from KDE’s contributors. The bugfixes are typically small but important and include... ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡉⠳⢯⣓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⢻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣌⠙⠲⢭⣒⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠉⠉⠙ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡈⠓⠮⣝⡲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠅⠀⠀⣩⡓⠪⣑⠦⣄⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠻⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢿⣦⡆⠀⠙⠲⢍⡒⠤⣀⣠⣴⣾⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣽⡻⣿⣿⣿⣿⣿⣿⣟⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⢈⣵⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣍⡻⠻⠟⠄⡈⠙⠻⣿⣿⣿⣅⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⡿⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣤⡀⠀⢰⣶⡀⠈⠓⠈⠋⠀⠀⠈⢙⣵⣿⢳⠀⠈⠈⣙⠿⢦⣄⠀⠀⠙⢿⣿⣿⣿⠿⠟⠋⠀⠁⠒⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢬⣿⣿⡆⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣂⢀⣤⣬⡷⢤⣬⣤⣠⣄⠀⠙⠛⠛⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⣤⣄⠀⢀⣀⣀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢤⣀⠀⠀⠀⣼⣿⣿⣿⣿⣷⢽⣿⡷⠶⠆⣸⣿⣽⢿⣿⣾⣿⡶⣾⣷⣼⡞⣶⢻⣖⣾⣷⠀⢸⡷⢿⡅⢸⡷⢶⡀⢸⡷⢾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⢽⡛⠛⠃⠘⠛⠀⠈⠛⠛⠛⠋⠛⠛⠛⣣⣿⣾⣿⣗⣿⠀⠈⠛⠛⠙⠊⠛⠛⠘⠋⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⠿⠋⠉⠀⠉⠓⠤⡀⠀⢠⠂⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣼⣿⣿⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠉⠉⠂⠀⠀⠀⠀⠀⠀⠈⠑⠸⣷⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡿⠏⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠿⠟⠉⠀⠀⠈⠀⠀⠀⠈⠢⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⡶⡶⡶⡶⡶⡶⡶⡶⡶⡶⡶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣏⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷ ䷩ 𝚕𝚒𝚗𝚎 2698 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/10/KeePassXC_2_7_12_Password_Manager_Adds_Support_for_Bitwarden_s_.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/10/KeePassXC_2_7_12_Password_Manager_Adds_Support_for_Bitwarden_s_.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ KeePassXC 2.7.12 Password Manager Adds Support for Bitwarden’s Nested Folders⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Marius Nestor on Mar 10, 2026 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇KeePassXC_2.7.12⦈_ Coming more than three months after KeePassXC 2.7.11, the new release adds support for nested folders when importing passwords from Bitwarden, adds support for TIMEOTP autotype and entry placeholder, and adds support for setting BE and BS flags to true for Passkeys. KeePassXC 2.7.12 also improves the password browser to display URLs in the browser access dialog, correctly display the checkbox value in the entry Browser Integration settings, and correctly set browser-related values to customData. Read_on ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣾⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣷⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿ ⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠻⣷⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⠏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⡏⠉⠉⢉⣿⡏⠉⠉⠹⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣴⠿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⢀⡀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⢻⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣶⠀⣾⣶⠀⣶⡦⠀⢶⠆⠀⣿⣇⣴⣿⡏⠀⣿⡆⠀⣶⡆⢰⣶⡆⢸⣿⡆⢰⣷⡆⢰⣶⠀⠠⡶⠀⢰⣿⡇⢸⣷⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠈⠻⣧⡤⠤⠤⠤⠀⠠⠤⠄⠦⠤⠀ ䷩ 𝚕𝚒𝚗𝚎 2755 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/10/Latest_Steam_Client_Update_Improves_Support_for_Proton_Games_on.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/10/Latest_Steam_Client_Update_Improves_Support_for_Proton_Games_on.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Latest Steam Client Update Improves Support for Proton Games on Linux⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Marius Nestor on Mar 10, 2026 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Steam_Client⦈_ The new Steam Client update introduces an option to attach hardware specs when writing or updating a Steam User Review on a game’s store page, adds notification settings for showing a toast and playing a sound when an achievement is unlocked, and adds an option to provide anonymized framerate data. The new Steam Client update also adds an icon on tools in the game list with a tooltip to explain what they are, as well as a warning dialog that is displayed when a user selects “Tools” in their Steam library filter for the first time, which will explain to them what tools are and why they are showing up in their Steam game list. Read_on ⠰⠒⠂⢀⣂⡐⠂⡀⠒⠀⢒⡀⡀⠀⣀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠐⠀⠐⠐⠒⠒⠀⠂⠀⠀⠂⠀ ⣈⣀⣀⣉⣉⣁⣘⣛⣛⡃⠈⠉⠉⠉⠉⠁⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠙⠛⠛⠛⠛⠛⠛⠛⢛⣃⣉⡀⠀⠒⠒⠒⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⢈⠉⠉⠉⠉⠉⠀⠈⠈⠉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⣠⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣶⣾⠰⢴⣶⣤⣦⣤⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⠿⠿⠿⠰⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣜⣛⣛⣛⣛⣛⣛⡛⠛⠛⠛⠀⢠⣿⣿⣿⣿⣿⣿⠇⠐⢻⣿⣿⣿⠋⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠰⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠰⣷⣒⣒⣒⣒⣒⣀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠿⠏⠀⠀⠀⠁⠀⠉⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢘⣟⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠰⡷⠆⠾⠖⠗⠶⠶⠒⠖⠶⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⡸⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⡿⠭⠭⠭⠭⠭⠭⠭⠭⠭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⡿⠭⠭⠭⠭⠭⠭⠭⠭⠭⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⣛⣛⣛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡍⠃⠀⠀⠀⠀⠀⠀⢠⣄⣠⣄⣀⣤⣤⣀⠀ ⠐⣓⣒⣂⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⠁⠀⠀⠸⠿⠀⠀⠀⠘⠛⡿⣿⣿⣿⣿⣿⡀ ⠀⣿⠶⠲⠶⠶⠆⢀⠀⠀⠀⠀⠀⠻⣿⣿⣧⡀⠿⠶⡶⠶⠶⠴⠶⠷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⡿⣛⣿⠀⣈⣉⣉⣉⣀⣀⠀⢹⣿⣿⣾⣿⣿⣿⠃ ⠀⠭⠭⠭⠬⠍⠉⠉⠉⠉⠉⠀⠀⠀⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣟⣻⡀⠀⣛⠻⠛⠿⣿⢰⣿⣿⣿⢻⣿⣿⣇⠀ ⠀⣏⢭⢭⡭⡭⠧⠀⠀⠀⠀⠀⢠⣶⣶⡶⢶⣶⣶⣶⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠸⢿⣿⣷⣶⣶⣿⢸⣿⣏⣿⢻⣿⣿⡍⠁ ⠀⣆⣗⣻⣛⣛⠚⠀⠀⠀⠀⠀⠸⣿⣿⡇⠚⠛⠛⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⠏⠀⠀⠉⠉⠉⠛⠋⢸⣿⣿⠿⠿⣿⣿⣿⠂ ⠀⡀⣒⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣿⣿⣿⣿⣿⣿⣧⣤⡄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠉⠉⠉⠀ ⠰⡷⡶⠶⠶⢶⢶⠀⢀⣀⠀⠀⠀⠂⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠹⠍⠭⠭⠍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠏⠭⠭⠭⠭⠍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠭⠭⠩⠍⠏ ⣰⣶⣶⣿⣿⡿⣿⡦⢀⣶⣶⠆⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⣿⣷⣿⣿⣶⣶⣶⣿⣿⣿⣧⣶⣷⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⠀⠶⡀⠤⠦⠦⠦⠤⠤⠀⠰⠦⠄⠦⠦⠄ ䷩ 𝚕𝚒𝚗𝚎 2814 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/10/Linux_distros_are_quietly_abandoning_their_own_desktops_for_KDE.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/10/Linux_distros_are_quietly_abandoning_their_own_desktops_for_KDE.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Linux distros are quietly abandoning their own desktops for KDE Plasma, and I get why⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Rianne Schestowitz on Mar 10, 2026 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇KDE_plasma⦈_ Quoting: Linux distros are quietly abandoning their own desktops for KDE Plasma, and I get why — Here is a fact-based summary of the story contents: There has been a gradual but noticeable shift in the Linux scene where distro developers are adopting KDE Plasma as the default desktop environment. Granted, there are a few examples of distros going the opposite way, but it feels like we don't go a few months without another operating system adopting KDE Plasma as the norm. Usually, I'd say that the shift toward KDE Plasma is a sign of stagnation, that the alternatives are just not putting up a strong enough fight to justify using them. However, as a huge KDE Plasma fan myself, I have to say that I do, in fact, understand why developers are abandoning their stock desktop environment for it. Read_on ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⢯⣿⡇⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠐⠀⠂⠀⠂⢰⣿⣶⡄⠀⢸⣿⣿⣿⣿⣿⣿⡿ ⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⣿⣿⣿⣀⣸⣿⣿⣟⣿⣿⣯⢽ ⣿⢿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⠿⣿⣿⡇⠀⠀⠀⠀⣠⠤⢤⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⠉⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣾⣿⣿⣿⣿⣯⣿⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⡇⠀⠀⢹⠀⠀⠀⠀⠐⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⣀⠀⠀⢠⣤⡄⠀⢡⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⢁⣸⢠⣿⣿⢿⣿⣿⢿⣿⣿ ⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠈⠳⠦⠴⠋⠀⠀⡇⢅⠀⠀⠘⠿⠃⠀⠀⠿⠇⠀⠀⠛⠛⠀⠀⠀⠘⠟⠀⠀⠼⣿⠅⠀⠸⠭⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⣿⣿⣿⣿⣽⣿⣾⣶⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣄⣀⠀⢰⣶⡆⠀⠀⣶⡦⠀⠀⢶⡶⠀⠀⠀⢐⣶⠀⠀⢸⣿⡆⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢹⠻⣉⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠅⠀⠀⢨⣈⡁⠀⠠⣄⠠⠀⠀⡄⠤⠀⠀⠀⢛⣛⠂⠀⢈⣭⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⠙ ⣿⣿⣿⣿⣿⢿⣿⣿⣭⣟⠸⠀⣴⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠈⠩⠥⠀⠐⠛⠔⠀⠀⠘⠂⠀⠀⠀⣠⢷⡀⠀⣸⢿⡀⠀⣠⣻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⡟⢻⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣍⣿⣷⣿⣿⣿⢟⣽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠷⠀⠀⠿⠿⠀⠀⠿⢟⡀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇⠀⠄⣿⣿⣿⣧⣽ ⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⠻⣿⣷⣿⣿⡇⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⣬⣄⠀⠀⣤⣬⠁⠀⣤⣭⠁⠀⠀⠘⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣶⣿⡟⣯⣬⢹⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠉⣹⡿⢵⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⠭⠀⠠⠭⠭⠄⠰⠟⠟⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠀⠀⣈⣩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠠⠀⠀⣀⣀⣀⠤⠀⠀⠀⠐⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡛⠛⡿⣿⣿⣧⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢸⣿⣿⣿⣶⣶⣬⣟⣻⡾⣷⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠒⠀⠒⠒⠂⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠂⠀⠀⠂⠀⠀⠂⠀⡀⠀⠀⠁⠁⠀⠀⠀⠀⠉⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠒⠀⠀⠐⠀⠀⠀⠀⠀⠀⠁⠀⣀⠈⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠂⠀⠀⠁⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠤⠄⠀⠒⠂⠒⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠤⠀⠀⠀⠀⠀⠈⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⠀⠀⠀⢀⢹⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠑⠛⢿⣿⣿ ䷩ 𝚕𝚒𝚗𝚎 2884 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/10/Linux_PC_vendor_System76_tries_to_talk_Colorado_down_over_OS_ag.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/10/Linux_PC_vendor_System76_tries_to_talk_Colorado_down_over_OS_ag.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Linux PC vendor System76 tries to talk Colorado down over OS age checks⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Rianne Schestowitz on Mar 10, 2026 Quoting: System76 tries to talk Colorado down over OS age checks — As more US states push to mandate OS-level age checks, System76 is taking its fight directly to lawmakers. Last week, The Reg reported that some US states are enacting legislation that would oblige OS vendors to include mandatory age verification. There is some very limited good news on that front from the state of Colorado. On the other hand, multiple US states are also considering it. We mentioned that one of the more insightful commentaries that we've read was "System76 on Age Verification Laws" by CEO Carl Richell. System76 is one of the most visible companies in the world that makes PCs specifically to run Linux, and The Register first mentioned Richell all the way back in 2009. Read_on ䷩ 𝚕𝚒𝚗𝚎 2925 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/10/Linux_Virtualization_With_Xen_and_Running_Windows_Under_GNU_Lin.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/10/Linux_Virtualization_With_Xen_and_Running_Windows_Under_GNU_Lin.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Linux Virtualization With Xen and Running Windows Under GNU/Linux⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Mar 10, 2026 * ⚓ XDA ☛ The_Xen_hypervisor_ain’t_dead_yet_–_two_of_the_coolest_Linux distros_still_use_it⠀⇛ Back when ESXi used to dominate the home server ecosystem, Xen was the other key player for Linux-centric setups. But with the rise of KVM, the situation is a lot different from what it used to be. These days, most folks tend to prefer KVM-powered home labs, with Hyper-V and ESXi being the other popular options. Meanwhile, Xen is no longer as popular as it used to be – to the point where you might come across folks who consider it a dead hypervisor. Now, I’m a staunch member of the KVM faction with multiple Proxmox nodes, but Xen is far from the outdated relic that many tinkerers consider it to be. Sure, it’s mostly used in commercial setups and production environments. But you can just as easily configure it on your favorite distro and use it to spin up a few VMs. And once you dig a little deeper, you’ll come across these slick distros that are centered around the Xen hypervisor. * ⚓ XDA ☛ WSL_convinced_me_Linux_works_on_Windows,_so_I_flipped_it_and_run Windows_on_Linux_instead⠀⇛ For many people, the Windows Subsystem for Linux, or WSL, is a great way to use the tools you need in Linux while staying on Windows most of the time. You can just use Windows for most of your tasks, and then boot up WSL whenever you need something from a Linux distro. WSL was my first exposure to Linux, and it showed me that it can, in fact, do a lot of the things Windows can. And that's true to the point that, today, I'd rather use Linux full-time. So, instead of using WSL to run Linux on Windows, I'm doing the opposite and running Windows on Linux. ䷩ 𝚕𝚒𝚗𝚎 2984 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/10/Mamma_Mia_The_Party_at_Manchester_City_s_Campus.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/10/Mamma_Mia_The_Party_at_Manchester_City_s_Campus.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Mamma Mia! The Party at Manchester City’s Campus⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Mar 10, 2026, updated Mar 10, 2026 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_world-renowned_immersive_experience_Mamma_Mia!⦈_ Lately we've listening to a_lot of ABBA, so imagine our surprise when we got post (only a few hours ago) about Björn Ulvaeus from ABBA opening a vast new facility near us, which will include dining, cinemas, and several more things as_named_here. 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Mamma_Mia!_The_Party_at_Manchester_City’s_Etihad_Campus⦈_ There has been so much construction and development around us in recent years despite COVID-19 or even because of it (a boost in local investments in skyscrapers as well). I don't get it; do they reckon this venture will be profitable? The world isn't exactly booming. At the moment the UK is very distant from the world's wars, but there's no guarantee it'll stay that way in years to come. █ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⣴⠄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠀⣤⣤⣀⡈⢿⠏⠀⢸⣿⣟⠀⣤⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⠀⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣀⣿⡿⣿⠀⣾⢠⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣤⣴⣾⡇⠀⢀⡀ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣽⣾⣇⢸⣿⠇⣠⡀⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣛⣯⣥⡆⠈⠁⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⠀⠈⠉⠛⢛⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣄⣿⣿⢀⣶⡄⣤⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢸⠀⠿⣛⣛⠅⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⣾⣿⣿⣿⣷⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣸⠀⣿⣿⠿⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣿⣷⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢿⢊⣶⣿⡿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⠗⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⣾⠶⣿⠒⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⣿⣿⣴⣦⠄⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢸⣿⣶⣧⣰⣶⣿⣿⠟⠒⠒⠀⠀⠀⠀⠀⠘⣆⠀⠀⣿⣽⣏⣀⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣠⣀⢽⣿⣿⢿⣿⣿⣿⣿⣇⡘⠠⠀⠀⠀⠀⢀⠻⣄⠄⣿⣂⣫⢉⠉⠀⠀⠀⠀ ⠀⠀⢀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡍⢥⢴⡲⢦⣤⡸⠉⢿⣿⣿⣟⣕⣀⣀⡀⠀⠀⢀ ⠀⠀⠀⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⣤⣤⡄⠀⣽⣿⣿⣿⣿⣿⡟⣿⣿⣿⣏⣭⣯⣞⠱⠏⠀⠀⠀⢀⣹⣿⣿⣿⣿⣧⣤⡐⢀⠀ ⠀⠀⣀⡤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣰⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⣯⣴⣆⠀⣀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⢀⠀⡀⠀ ⠀⠈⢉⣈⡉⢉⠉⠙⠿⢿⣿⣿⣿⡧⡦⢶⣦⣾⣿⣷⣯⣿⣿⣶⣷⣾⣿⣿⣿⣶⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣻⣿⣦⠌⠓⠻ ⠀⠀⠀⠨⠀⠀⣠⣦⡤⢹⣿⠛⢺⣥⣽⣻⠞⠉⢿⣿⣿⣻⣿⣿⣿⣿⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠼⣿⣿⣿⣿⣿⣿⣿⣿⠿⠦⠄⣻⣿⠻⣿⠫⣿⣯⡄⢀⣈ ⠀⠀⠈⠛⠀⠴⡟⠛⠛⡌⡿⠀⣾⣿⣿⣿⣦⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢿⡷⡆⠀⠀⠀⢸⡏⣿⣭⣧⣭⣽⣿⡆⠀⠘⠐⢉⠤⠙⠀⠉⠁⠀⠈⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣿⣿⣿⣿⣿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠟⠛⠻⠿⠿⢯⣭⣿⣽⣛⣉⣉⣻⡿⠿⠿⠻⠿⢿⣷⣿⢷⠀⠀⠀⠀⠸⣷⣿⠛⠏⠭⠍⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⢴⡄⠀⠀⢹⣿⣿⣧⢠⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣭⣍⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠓⠒⠲⠾⠛⠋⠈⠛⡇⠀⠀⠁⠋⠙⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠁⠀⠀⢸⣿⣿⣿⠈⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠻⡟⠂⢴⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠻⠞⠓⠟⠻⠛⠚⠿⠻⠿⠺⠿⠿⠇⠓⠿⠿⡿⠿⢿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠈⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠈⠛⠘⠙⠟⠟⢫⠟⠛⠀⠀⠈⠛⠉⠁⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡛⡛⣛⣛⣻⢿⣿⡟⡛⢟⣻⠿⣿⠿⠟⣿⣿⡿⣹⣿⡿⣽⢿⣿⣿⡿⣿⣷⢾⣿⣿⠻⣿⣿⣿⠿⠿⡿⢿⢿⡿⣿⣿⣿⣿⣿⠿⠿⡽⣿⣿⢿⣿⢿⠿⢿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⣻⣿⣿⣿⣿ ⢮⢯⡽⣕⢎⠿⣚⣶⠹⢐⢵⣌⡖⢓⣂⠠⠒⠾⠲⣿⣖⡲⠴⠯⠯⠦⠋⠝⠅⡊⡁⠀⣙⢛⠩⠙⠿⠉⠯⠋⠘⠉⠈⠈⠛⡁⢢⠡⠐⢃⣅⠉⡐⠆⡦⣋⣭⢐⣂⠊⣋⢛⣻⡉⠍⠋⢩⠙⠞⠏⡙⡙⠃⠋⠽⠍⠀⠁ ⡀⢐⢊⠉⠅⠀⠁⠤⠴⠤⠂⠠⠴⠀⢥⠄⡔⠉⠱⠉⣃⠀⠐⠠⡏⣳⠍⠉⠓⢰⠙⠋⡦⠥⢦⡤⣂⡄⢀⠐⠠⠠⠰⣲⣠⣄⣄⣮⣤⣌⣴⣬⣤⣤⣬⣁⣘⣒⡠⠶⠧⠶⢷⠶⠒⠈⠤⠽⡋⣀⣈⠀⠀⠀⠋⠃⠂⠐ ⠋⠘⠛⢚⠚⠚⠛⠚⠟⠛⠑⠖⠂⡄⠖⠐⠀⠀⠔⠒⠂⠀⡀⠁⠈⠄⣂⣨⣠⣅⣤⣤⣵⣤⣬⣶⡬⠉⠷⣶⢾⠿⡿⢿⣻⡛⡈⠉⠉⠉⠉⠙⠛⠛⠛⠻⣿⣿⣿⣿⣷⣮⣄⣈⣅⣁⣀⡀⠀⠀⠐⠀⠜⠁⠀⠠⠢⠐ ⠀⠐⡂⠈⠀⡀⠩⣀⠀⢠⢀⢄⣔⣬⣉⣅⣤⣤⣀⡀⢀⣀⣀⠀⣄⣸⣻⡧⡀⠀⣀⣀⠠⠴⠴⠶⠶⢠⠄⢠⠤⡤⠠⠤⣨⠉⠉⠩⠉⢉⢹⠲⣶⣆⣔⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣻⠠⠀⢀⠡⣀⠀⠀⠀⠀⠂ ⠀⣄⡈⡠⢀⣐⣤⣤⣶⢲⠾⠏⠈⢉⠄⠀⠀⠌⠈⡍⢉⡉⠉⠉⠉⠉⠉⠉⣿⣿⣿⣟⡂⠀⠀⠀⠀⠘⠀⠀⠒⠒⠒⠛⠛⢻⣿⣷⣶⣾⣿⠀⠀⠈⣿⣿⣿⣿⣿⣿⠿⠟⢛⣭⣷⣿⣷⣿⣿⣥⣿⣥⠀⠀⠀⠢⠀⠦ ⠆⠀⢪⡻⠫⠚⠵⠚⠀⠀⠀⠀⠀⠀⡀⠀⠡⠄⠀⠀⠠⠃⢠⣤⣤⣤⣶⣤⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣭⣤⣿⣿⣿⣿⣿⠀⠀⠀⣟⠛⠋⢉⣁⣠⣴⣾⡉⠉⠭⠤⠿⢯⣍⠉⠉⠙⣏⣔⣀⡀⠀⠀ ⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⣀⡸⠀⠀⠂⠀⠀⠀⠨⠁⢸⡇⢤⣤⡤⣿⣿⣛⣁⣠⣤⣤⣤⣤⣤⣤⣤⡧⠤⣤⡂⣸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣺⣸⣿⣿⣭⡯⠋⠘⠃⠠⠶⠦⣤⣸⠐⢒⣢⣿⣿⣗⣶⠠⡉ ⣤⣤⣤⢤⣤⣤⣤⣴⣶⣾⠿⡿⡇⠈⠀⠀⠀⠀⠀⠀⠤⣤⢼⣏⣍⣉⣉⣿⢓⣻⠟⠛⠛⠛⢛⠛⠛⠿⠿⣷⠒⠛⠣⢼⣿⣿⣿⣿⣿⣿⢿⠤⠄⠀⣽⣐⡈⣀⣈⣉⣁⠀⠀⠀⠀⣀⣐⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⣯⡇⠀⠐⠐⠲⠆⠀⡀⠀⠀⠈⠉⢿⣿⡭⣭⠠⠈⠀⢘⣇⡀⠸⡄⡃⣀⠘⠛⠛⠿⠶⠾⠿⣿⡿⠿⣿⡏⡀⣤⡠⠄⣿⣹⣿⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⠉⠀⠠⠶⠶⠶⠶⠶⠶⠮⢶⣦⣤⣤⣤⣤⡀⠀⠠⡖⠛⠟⢇⣃⣌⣴⣏⢀⣀⣀⠀⠀⠀⠀⣧⣆⡀⣿⣲⣃⣍⣽⣿⠿⢃⢊⣰⣻⣯⣿⣶⣿⣿⣿⣿⣿⡇⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿ ⣿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠍⠁⠀⠠⠛⠂⠙⠛⠓⠒⠺⣵⣶⣶⠂⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⣩⣹⣻⣿⣿⠿⠛⠻⣛⠛⠁⠈⠻⣿⠟⡰⠁⠚⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢉⡰⣴⢾⣷⣯⡟⣻⣷⡿⠆⠍⠉⢉⠉⠀⠑⠁⠈⠉⡭⡍⠀⠀⠒⠉⠃⠀⠀⢀⡉⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠶⠟⠂⢉⠾⢾⠀⠀⢀⣠⡔⣹⡷⠯⢼⣖⣷⣼⠏⠀⠀⠙⢤⡀⠀⠀⡀⠀⠀⠀⠉⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠩⣡⠀⠀⠀⠁⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣀⣤⡶⠿⠛⠉⠀⠀⣄⣠⣥⣭⣨⢖⣴⢾⢫⡅⣷⣷⣾⣿⡿⠛⠁⠀⠀⠀⠀⢀⠉⠈⠃⠃⠐⠀⠀⠂⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀⠀⠀⠃⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠂⠀⠉⠘ ⣴⠾⠟⠋⠁⠀⠀⠀⠀⣄⠶⢶⣿⡿⣏⣾⢿⣝⣅⣿⢾⢷⣿⡟⡿⡃⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣀⡀⠀⠀⠀⠀⠀⣀⣄⣢⣤⣤⣤⣄⣀⣀⣀⡀⠖⠒⠀⠀⠀⠀⡤⠐⠈⠉⠂⠀⠂⢀⡀⠀⠀⠠⠀⠀ ⠀⠀⠀⢀⣠⣴⠶⠛⠊⣤⠶⢻⣲⣟⢉⣿⣾⢿⣮⡿⠋⡀⠔⣌⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣔⠒⠀⠀⠀⠀⠀⠀⠀⠛⠝⠀⠀⠀⠘⠂ ⢠⣴⡾⠛⠋⣀⣰⣊⡾⢼⢲⡽⣯⠿⣿⣹⡾⡛⢑⣌⢈⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀ ⣿⣷⣶⢶⣾⣷⣿⡿⣿⣿⣿⣿⣗⣾⡟⠫⠾⣞⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ䷩ 𝚕𝚒𝚗𝚎 3075 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/10/NVIDIA_580_142_Production_Ready_Linux_Graphics_Driver_Released_.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/10/NVIDIA_580_142_Production_Ready_Linux_Graphics_Driver_Released_.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ NVIDIA 580.142 Production-Ready Linux Graphics Driver Released with Bug Fixes⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Marius Nestor on Mar 10, 2026 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇NVIDIA⦈_ NVIDIA 580.142 is here as a small bugfix release that addresses a bug causing adaptive sync displays to go blank when connected with an active USB-C-to-HDMI adapter, and a bug that could cause Vulkan swapchains to stop presenting new frames on X11 sessions. Also fixed in this release is a regression introduced after the NVIDIA 470.xx graphics driver series, which could cause a setup with four 4K monitors, driven as separate X11 X screens on one NVIDIA GPU, to fail modeset. Read_on ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠉⢻⣷⠀⠀⢹⣿⣿⡿⠀⠀⣼⡇⠀⠀⣿⡇⠀⠀⠀⠀⠈⠉⠻⣿⣿⠀⠀⢹⣿⣿⣿⠇⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣆⠀⠀⣿⣇⠀⠈⣿⣿⠃⠀⢰⣿⡇⠀⠀⣿⡇⠀⠀⣿⣿⣷⡄⠀⢸⣿⠀⠀⢸⣿⣿⡏⠀⢠⣧⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⠀⠀⣿⣿⡄⠀⠸⡟⠀⢀⣿⣿⡇⠀⠀⣿⡇⠀⠀⣿⣿⣿⠇⠀⢸⣿⠀⠀⢸⣿⡟⠀⠀⠿⠿⠇⠀⠘⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⠀⠀⣿⣿⣷⠀⠀⠁⠀⣼⣿⣿⡇⠀⠀⣿⡇⠀⠀⠛⠋⠁⠀⢀⣼⣿⠀⠀⢸⡿⠁⠀⣤⣤⣤⣤⡄⠀⠘⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣶⣶⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣷⣶⣶⣿⣷⣶⣶⣶⣶⣶⣾⣿⣿⣿⣶⣶⣾⣷⣶⣾⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ䷩ 𝚕𝚒𝚗𝚎 3135 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/10/One_of_the_best_Arch_based_Linux_distros_out_there_just_got_eve.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/10/One_of_the_best_Arch_based_Linux_distros_out_there_just_got_eve.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ One of the best Arch-based Linux distros out there just got even easier to set up⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Rianne Schestowitz on Mar 10, 2026 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇CachyOS_Installer⦈_ Quoting: One of the best Arch-based Linux distros out there just got even easier to set up — One of the best parts of Arch Linux is that you don't have to install Arch Linux. I do recommend everyone give installing Arch Linux a shot one time (if only to get the FOSS scout badge saying you did), but when you just want to get a system up and running as quickly as possible, you have options like CachyOS. It sets up everything for you, which Arch veterans will scoff at, but it's the perfect way to get something set up using the Arch base. Read_on ⢶⠆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠤⠶⠤⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠀⠆ ⢠⣄⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠴⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠰⣦⣦⣤⣶⣴⣦⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣆⣾⣿⣿⣿⣶⣆⠀⢲⣶⣿⣿⣿⣿⣿⡶⠶⡶⣦⣤⣶⣶⣾⣿⣿⣿⡆⠐⢶⣶⣶⣶⣲⣾⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⢹⣿⣿⣿⣿⣿⣇⣠⡤⠛⢻⠧⣬⡿⣿⣿⣿⣿⢤⣤⢟⡿⡤⢿⣿⣿⣿⣿⡗⠁⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠐⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠻⠙⢹⣿⣿⣿⣿⠛⣿⣿⣿⣿⡇⠀⠻⠿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⣿⣇⠀⡸⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀ ⠈⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠸⣿⣿⣿⠟⠀⣿⣿⣿⣿⣿⡀⠀⣠⣄⠀⢸⣿⣒⣒⣒⣒⣒⣒⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣾⣿⠄⠀⢀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⢈⣉⣉⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⢉⣿⡇⠀⠀⢻⣿⣟⣛⡛⠂⢠⣿⣿⡄⠘⠋⠉⠩⠭⠭⠭⠉⠉⠉⠉⠭⠭⠉⠉⠉⠉⠩⠭⠍⠁⠀⣿⠀⠀⣰⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀ ⢠⣭⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠟⣠⣴⣦⣤⣤⣤⣼⣿⠿⡓⠀⠀⠸⣿⣿⠃⠀⠀⢀⣂⣛⣛⣒⣚⡀⣒⣛⣛⡃⣛⡃⢀⣘⣛⣛⡓⣃⠂⣿⡇⢸⣿⣿⣿⠉⣾⡆⠀⠀⠀⠀⠀⠀ ⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣍⣟⠃⢀⣠⡀⠀⠀⣩⡍⢁⠈⠀⠀⠉⠉⠁⠉⠁⠀⠁⢩⣭⠁⠁⠀⠘⠁⠀⠁⠛⢛⣼⣿⡇⠀⠀⠀⠀⠀⠀ ⠰⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠄⠄⠰⠶⠶⠀⠀⠐⠀⠀⠀⠀⠰⠶⠶⠀⠀⠀⠀⣿⡇⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠐⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠰⠦⠤⠤⠄⠀⠀⠀⠀⡤⡤⠀⠀⠀⠀⠀⠤⠤⠴⠄⣿⣿⠀⠀⣾⢿⣿⣿⠄⠀⠀⠀⠀⠀⠀ ⠈⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣶⡟⠁⠀⢠⢸⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⢈⣙⣉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣭⣅⣤⣆⢠⠻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⢠⣭⣩⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣝⣿⠀⠀⠀⠀⠀⠀⠀ ⠠⠤⠤⢤⠤⠤⣤⢤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀ ⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣛⢛⣿⣿⣿⣿⣟⣿⣻⣻⣟⣟⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀ ⠐⠲⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶⠶⠶⠴⠶⠶⠶⠶⠶⠰⠶⠶⠦⠶⠶⠶⠶⠶⠶⠶⠶⠶⠔⠶⠶⠦⠶⠶⠶⠶⠆⠶⠶⠶⠦⠶⠖⠶⠦⠰⠶⠆⠶⠶⠶⠶⠶⠶⠶⠦⠶⠶⠶⠰⠶⠶⠶⠀⠀ ⠘⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣭⣯⣭⣭⣭⣭⣭⣭⣭⣨⣭⣍⣭⣩⣭⢩⣭⣭⣭⣭⣍⣭⣩⣭⡉⠉⠉⠉⠙⠉⠉⠋⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠛⠋⠉⠙⠙⠉⠉⠉⠉⠉⠉⠋⠉⠉⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⠀⠀⠀⡀⣀⣀⠀⠀⠀⢀⡀⣀⣀⣀⠀ ⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⡀⡀⣀⡀⣀⣀⣀⡀⣉⢁⢀⣀⢀⣀⣈⣉⣀⡀⣀⠀⡁⣉⣈⣁⣀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢶⠆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠤⠶⠤⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠀⠆ ⢠⣄⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠴⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠰⣦⣦⣤⣶⣴⣦⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣆⣾⣿⣿⣿⣶⣆⠀⢲⣶⣿⣿⣿⣿⣿⡶⡶⡶⣦⣤⣶⣶⣾⣿⣿⣿⡆⠐⢶⣶⣶⣶⣲⣾⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⢹⣿⣿⣿⣿⣿⣇⣠⡤⠛⢻⠧⣬⡿⣿⣿⣿⣿⢤⣤⢟⡿⡤⢿⣿⣿⣿⣿⡗⠁⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠐⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠻⠙⢹⣿⣿⣿⣿⠛⣿⣿⣿⣿⡇⠀⠻⠿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⣿⣇⠀⡸⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀ ⠈⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠸⣿⣿⣿⠟⠀⣿⣿⣿⣿⣿⡀⠀⣠⣄⠀⢸⣿⣒⣒⣒⣒⣒⣒⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣾⣿⠄⠀⢀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⢈⣉⣉⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⢉⣿⡇⠀⠀⢻⣿⣟⣛⡛⠂⢠⣿⣿⡄⠘⠋⠉⠩⠭⠭⠭⠉⠉⠉⠉⠭⠭⠉⠉⠉⠉⠩⠭⠍⠁⠀⣿⠀⠀⣰⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀ ⢠⣭⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠟⣠⣴⣦⣤⣤⣤⣼⣿⠿⡓⠀⠀⠸⣿⣿⠃⠀⠀⢀⣂⣛⣛⣒⣚⡀⣒⣛⣛⡃⣛⡃⢀⣘⣛⣛⡓⣃⠂⣿⡇⢸⣿⣿⣿⠉⣾⡆⠀⠀⠀⠀⠀⠀ ⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣍⣟⠃⢀⣠⡀⠀⠀⣩⡍⢁⠈⠀⠀⠉⠉⠁⠉⠁⠀⠁⢩⣭⠁⠁⠀⠘⠁⠀⠁⠛⢛⣼⣿⡇⠀⠀⠀⠀⠀⠀ ⠰⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠄⠄⠰⠶⠶⠀⠀⠐⠀⠀⠀⠀⠰⠶⠶⠀⠀⠀⠀⣿⡇⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠐⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠰⠦⠤⠤⠄⠀⠀⠀⠀⡤⡤⠀⠀⠀⠀⠀⠤⠤⠴⠄⣿⣿⠀⠀⣾⢿⣿⣿⠄⠀⠀⠀⠀⠀⠀ ⠈⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣶⡟⠁⠀⢠⢸⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⢈⣙⣉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣭⣅⣤⣆⢠⠻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⢠⣭⣩⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣝⣿⠀⠀⠀⠀⠀⠀⠀ ⠠⠤⠤⢤⠤⠤⣤⢤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀ ⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣛⢛⣿⣿⣿⣿⣟⣿⣻⣻⣟⣟⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀ ⠐⠲⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶⠶⠶⠴⠶⠶⠶⠶⠶⠰⠶⠶⠦⠶⠶⠶⠶⠶⠶⠶⠶⠶⠔⠶⠶⠦⠶⠶⠶⠶⠆⠶⠶⠶⠦⠶⠖⠶⠦⠰⠶⠆⠶⠶⠶⠶⠶⠶⠶⠦⠶⠶⠶⠰⠶⠶⠶⠀⠀ ⠘⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣭⣯⣭⣭⣭⣭⣭⣭⣭⣨⣭⣍⣭⣩⣭⢩⣭⣭⣭⣭⣍⣭⣩⣭⡉⠉⠉⠉⠙⠉⠉⠋⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠛⠋⠉⠙⠙⠉⠉⠉⠉⠉⠉⠋⠉⠉⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⠀⠀⠀⡀⣀⣀⠀⠀⠀⢀⡀⣀⣀⣀⠀ ⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⡀⡀⣀⡀⣀⣀⣀⡀⣉⢁⢀⣀⢀⣀⣈⣉⣀⡀⣀⠀⡁⣉⣈⣁⣀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢶⠆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠤⠶⠤⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠀⠆ ⢠⣄⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠴⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠰⣦⣦⣤⣶⣴⣦⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣆⣾⣿⣿⣿⣶⣆⠀⢲⣶⣿⣿⣿⣿⣿⡶⡶⡶⣦⣤⣶⣶⣾⣿⣿⣿⡆⠐⢶⣶⣶⣶⣲⣾⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⢹⣿⣿⣿⣿⣿⣇⣠⡤⠛⢻⠧⣬⡿⣿⣿⣿⣿⢤⣤⢟⡿⡤⢿⣿⣿⣿⣿⡗⠁⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠐⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠻⠙⢹⣿⣿⣿⣿⠛⣿⣿⣿⣿⡇⠀⠻⠿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⣿⣇⠀⡸⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀ ⠈⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠸⣿⣿⣿⠟⠀⣿⣿⣿⣿⣿⡀⠀⣠⣄⠀⢸⣿⣒⣒⣒⣒⣒⣒⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣾⣿⠄⠀⢀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⢈⣉⣉⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⢉⣿⡇⠀⠀⢻⣿⣟⣛⡛⠂⢠⣿⣿⡄⠘⠋⠉⠩⠭⠭⠭⠉⠉⠉⠉⠭⠭⠉⠉⠉⠉⠩⠭⠍⠁⠀⣿⠀⠀⣰⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀ ⢠⣭⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠟⣠⣴⣦⣤⣤⣤⣼⣿⠿⡓⠀⠀⠸⣿⣿⠃⠀⠀⢀⣂⣛⣛⣒⣚⡀⣒⣛⣛⡃⣛⡃⢀⣘⣛⣛⡓⣃⠂⣿⡇⢸⣿⣿⣿⠉⣾⡆⠀⠀⠀⠀⠀⠀ ⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣍⣟⠃⢀⣠⡀⠀⠀⣩⡍⢁⠈⠀⠀⠉⠉⠁⠉⠁⠀⠁⢩⣭⠁⠁⠀⠘⠁⠀⠁⠛⢛⣼⣿⡇⠀⠀⠀⠀⠀⠀ ⠰⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠄⠄⠰⠶⠶⠀⠀⠐⠀⠀⠀⠀⠰⠶⠶⠀⠀⠀⠀⣿⡇⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠐⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠰⠦⠤⠤⠄⠀⠀⠀⠀⡤⡤⠀⠀⠀⠀⠀⠤⠤⠴⠄⣿⣿⠀⠀⣾⢿⣿⣿⠄⠀⠀⠀⠀⠀⠀ ⠈⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣶⡟⠁⠀⢠⢸⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⢈⣙⣉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣭⣅⣤⣆⢠⠻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⢠⣭⣩⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣝⣿⠀⠀⠀⠀⠀⠀⠀ ⠠⠤⠤⢤⠤⠤⣤⢤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀ ⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣛⢛⣿⣿⣿⣿⣟⣿⣻⣻⣟⣟⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀ ⠐⠲⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶⠶⠶⠴⠶⠶⠶⠶⠶⠰⠶⠶⠦⠶⠶⠶⠶⠶⠶⠶⠶⠶⠔⠶⠶⠦⠶⠶⠶⠶⠆⠶⠶⠶⠦⠶⠖⠶⠦⠰⠶⠆⠶⠶⠶⠶⠶⠶⠶⠦⠶⠶⠶⠰⠶⠶⠶⠀⠀ ⠘⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣭⣯⣭⣭⣭⣭⣭⣭⣭⣨⣭⣍⣭⣩⣭⢩⣭⣭⣭⣭⣍⣭⣩⣭⡉⠉⠉⠉⠙⠉⠉⠋⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠛⠋⠉⠙⠙⠉⠉⠉⠉⠉⠉⠋⠉⠉⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⠀⠀⠀⡀⣀⣀⠀⠀⠀⢀⡀⣀⣀⣀⠀ ⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⡀⡀⣀⡀⣀⣀⣀⡀⣉⢁⢀⣀⢀⣀⣈⣉⣀⡀⣀⠀⡁⣉⣈⣁⣀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢶⠆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠤⠶⠤⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠀⠆ ⢠⣄⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠴⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠰⣦⣦⣤⣶⣴⣦⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣆⣾⣿⣿⣿⣶⣆⠀⢲⣶⣿⣿⣿⣿⣿⡶⡶⡶⣦⣤⣶⣶⣾⣿⣿⣿⡆⠐⢶⣶⣶⣶⣲⣾⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⢹⣿⣿⣿⣿⣿⣇⣠⡤⠛⢻⠧⣬⡿⣿⣿⣿⣿⢤⣤⢟⡿⡤⢿⣿⣿⣿⣿⡗⠁⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠐⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠻⠙⢹⣿⣿⣿⣿⠛⣿⣿⣿⣿⡇⠀⠻⠿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⣿⣇⠀⡸⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀ ⠈⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠸⣿⣿⣿⠟⠀⣿⣿⣿⣿⣿⡀⠀⣠⣄⠀⢸⣿⣒⣒⣒⣒⣒⣒⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣾⣿⠄⠀⢀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⢈⣉⣉⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⢉⣿⡇⠀⠀⢻⣿⣟⣛⡛⠂⢠⣿⣿⡄⠘⠋⠉⠩⠭⠭⠭⠉⠉⠉⠉⠭⠭⠉⠉⠉⠉⠩⠭⠍⠁⠀⣿⠀⠀⣰⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀ ⢠⣭⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠟⣠⣴⣦⣤⣤⣤⣼⣿⠿⡓⠀⠀⠸⣿⣿⠃⠀⠀⢀⣂⣛⣛⣒⣚⡀⣒⣛⣛⡃⣛⡃⢀⣘⣛⣛⡓⣃⠂⣿⡇⢸⣿⣿⣿⠉⣾⡆⠀⠀⠀⠀⠀⠀ ⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣍⣟⠃⢀⣠⡀⠀⠀⣩⡍⢁⠈⠀⠀⠉⠉⠁⠉⠁⠀⠁⢩⣭⠁⠁⠀⠘⠁⠀⠁⠛⢛⣼⣿⡇⠀⠀⠀⠀⠀⠀ ⠰⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠄⠄⠰⠶⠶⠀⠀⠐⠀⠀⠀⠀⠰⠶⠶⠀⠀⠀⠀⣿⡇⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠐⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠰⠦⠤⠤⠄⠀⠀⠀⠀⡤⡤⠀⠀⠀⠀⠀⠤⠤⠴⠄⣿⣿⠀⠀⣾⢿⣿⣿⠄⠀⠀⠀⠀⠀⠀ ⠈⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣶⡟⠁⠀⢠⢸⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⢈⣙⣉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣭⣅⣤⣆⢠⠻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⢠⣭⣩⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣝⣿⠀⠀⠀⠀⠀⠀⠀ ⠠⠤⠤⢤⠤⠤⣤⢤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀ ⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣛⢛⣿⣿⣿⣿⣟⣿⣻⣻⣟⣟⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀ ⠐⠲⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶⠶⠶⠴⠶⠶⠶⠶⠶⠰⠶⠶⠦⠶⠶⠶⠶⠶⠶⠶⠶⠶⠔⠶⠶⠦⠶⠶⠶⠶⠆⠶⠶⠶⠦⠶⠖⠶⠦⠰⠶⠆⠶⠶⠶⠶⠶⠶⠶⠦⠶⠶⠶⠰⠶⠶⠶⠀⠀ ⠘⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣭⣯⣭⣭⣭⣭⣭⣭⣭⣨⣭⣍⣭⣩⣭⢩⣭⣭⣭⣭⣍⣭⣩⣭⡉⠉⠉⠉⠙⠉⠉⠋⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠛⠋⠉⠙⠙⠉⠉⠉⠉⠉⠉⠋⠉⠉⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⠀⠀⠀⡀⣀⣀⠀⠀⠀⢀⡀⣀⣀⣀⠀ ⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⡀⡀⣀⡀⣀⣀⣀⡀⣉⢁⢀⣀⢀⣀⣈⣉⣀⡀⣀⠀⡁⣉⣈⣁⣀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢶⠆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠤⠶⠤⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠀⠆ ⢠⣄⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠴⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠰⣦⣦⣤⣶⣴⣦⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣆⣾⣿⣿⣿⣶⣆⠀⢲⣶⣿⣿⣿⣿⣿⡶⡶⡶⣦⣤⣶⣶⣾⣿⣿⣿⡆⠐⢶⣶⣶⣶⣲⣾⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⢹⣿⣿⣿⣿⣿⣇⣠⡤⠛⢻⠧⣬⡿⣿⣿⣿⣿⢤⣤⢟⡿⡤⢿⣿⣿⣿⣿⡗⠁⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠐⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠻⠙⢹⣿⣿⣿⣿⠛⣿⣿⣿⣿⡇⠀⠻⠿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⣿⣇⠀⡸⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀ ⠈⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠸⣿⣿⣿⠟⠀⣿⣿⣿⣿⣿⡀⠀⣠⣄⠀⢸⣿⣒⣒⣒⣒⣒⣒⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣾⣿⠄⠀⢀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⢈⣉⣉⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⢉⣿⡇⠀⠀⢻⣿⣟⣛⡛⠂⢠⣿⣿⡄⠘⠋⠉⠩⠭⠭⠭⠉⠉⠉⠉⠭⠭⠉⠉⠉⠉⠩⠭⠍⠁⠀⣿⠀⠀⣰⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀ ⢠⣭⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠟⣠⣴⣦⣤⣤⣤⣼⣿⠿⡓⠀⠀⠸⣿⣿⠃⠀⠀⢀⣂⣛⣛⣒⣚⡀⣒⣛⣛⡃⣛⡃⢀⣘⣛⣛⡓⣃⠂⣿⡇⢸⣿⣿⣿⠉⣾⡆⠀⠀⠀⠀⠀⠀ ⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣍⣟⠃⢀⣠⡀⠀⠀⣩⡍⢁⠈⠀⠀⠉⠉⠁⠉⠁⠀⠁⢩⣭⠁⠁⠀⠘⠁⠀⠁⠛⢛⣼⣿⡇⠀⠀⠀⠀⠀⠀ ⠰⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠄⠄⠰⠶⠶⠀⠀⠐⠀⠀⠀⠀⠰⠶⠶⠀⠀⠀⠀⣿⡇⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠐⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠰⠦⠤⠤⠄⠀⠀⠀⠀⡤⡤⠀⠀⠀⠀⠀⠤⠤⠴⠄⣿⣿⠀⠀⣾⢿⣿⣿⠄⠀⠀⠀⠀⠀⠀ ⠈⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣶⡟⠁⠀⢠⢸⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⢈⣙⣉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣭⣅⣤⣆⢠⠻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⢠⣭⣩⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣝⣿⠀⠀⠀⠀⠀⠀⠀ ⠠⠤⠤⢤⠤⠤⣤⢤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀ ⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣛⢛⣿⣿⣿⣿⣟⣿⣻⣻⣟⣟⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀ ⠐⠲⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶⠶⠶⠴⠶⠶⠶⠶⠶⠰⠶⠶⠦⠶⠶⠶⠶⠶⠶⠶⠶⠶⠔⠶⠶⠦⠶⠶⠶⠶⠆⠶⠶⠶⠦⠶⠖⠶⠦⠰⠶⠆⠶⠶⠶⠶⠶⠶⠶⠦⠶⠶⠶⠰⠶⠶⠶⠀⠀ ⠘⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣭⣯⣭⣭⣭⣭⣭⣭⣭⣨⣭⣍⣭⣩⣭⢩⣭⣭⣭⣭⣍⣭⣩⣭⡉⠉⠉⠉⠙⠉⠉⠋⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠛⠋⠉⠙⠙⠉⠉⠉⠉⠉⠉⠋⠉⠉⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⠀⠀⠀⡀⣀⣀⠀⠀⠀⢀⡀⣀⣀⣀⠀ ⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⡀⡀⣀⡀⣀⣀⣀⡀⣉⢁⢀⣀⢀⣀⣈⣉⣀⡀⣀⠀⡁⣉⣈⣁⣀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢶⠆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠤⠶⠤⠴⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠀⠆ ⢠⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠤⠤⠴⠤⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣶⣶⣦⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣶⡖⣶⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣦⣶⣷⣾⣿⣿⣿⣶⠶⣶⣾⣿⣶⣶⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⢻⣿⣿⣿⣿⣿⣇⣠⣤⡿⣿⣯⣽⣿⣿⣿⣿⣿⣴⣤⣿⣿⣥⣿⣿⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠐⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠟⢿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣇⠈⠿⠿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⣿⣇⠀⣼⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀ ⠘⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⢸⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⡆⠀⣰⣌⠐⢸⣿⣒⣒⣒⣒⣒⣒⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣾⣿⡶⠊⢉⣹⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⢈⣉⣉⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠂⢹⣿⣿⠁⠀⢻⣿⣿⣿⣿⡇⢠⣿⣿⡆⠸⠏⠉⠩⠭⠯⠭⠉⠉⠉⠉⠭⠭⣉⣉⠉⠉⡩⢯⠍⠁⠈⣿⡁⢀⣰⣿⣿⣿⣿⢃⣀⠀⠀⠀⠀⢀ ⢨⣭⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣠⣾⣿⣯⣶⣶⣾⣿⣿⣿⡟⠀⣸⣿⣿⡇⠀⠀⣛⣛⣛⣛⣛⣛⣂⠋⠿⠷⠶⠶⠾⠿⠿⠿⠶⠶⣷⡷⣷⡶⠾⢿⣿⠟⠉⠉⠁⠉⠠⠡⠾⠶⠆ ⠠⠤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⣠⡄⣭⣭⣭⣭⣭⣭⡘⠀⢐⡆⠀⠟⠂⠀⠀⠀⠈⠁⠘⠛⠀⠀⠀⠀⠀⠘⠈⠉⠁⠐⠛⠓⠘⠘⠳ ⠰⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠰⠶⠶⠴⠶⠶⠶⠀⣼⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⣶⠶⢶⠶⠀⠀⠀⢻⣿⣿⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢈⣙⣉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣭⣩⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⡤⡤⢤⡤⠤⣤⢤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣖⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠰⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣓⠚⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠲⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠰⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠔⠶⠶⠦⠶⠶⠶⠶⠿⣿⡗⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⠘⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣭⣯⣭⣭⣭⣭⣭⣭⣭⣨⣭⣍⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣩⣭⡉⠉⠉⠉⠛⠉⠉⠋⠉⣿⣇⣀⣀⣀⣀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⣀⣀⣀⣀⣀⣸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⣿⣿⣿⣿⣿⠿⠟⢿⢿⣿⣿⠿⠿⠿⡿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠛ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣃⣀⣀⣀⣀⣈⣉⣀⣀⣀⣀⣁⣉⣈⣁⣀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢶⠆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠤⠶⠤⠴⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠀⠆ ⢠⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠤⠤⠴⠤⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣶⣶⣦⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣾⣿⣿⣿⣷⣶⡖⣶⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣦⣶⣷⣾⣿⣿⣿⣶⠲⣶⣾⣿⣶⣶⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⢻⣿⣿⣿⣿⣿⣇⣠⣤⡿⣿⣯⣼⣿⣿⣿⣿⣿⣴⣤⣿⣿⣥⣿⣿⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠐⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠟⢿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣇⠈⠻⠿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⣿⣇⠀⣼⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀ ⠘⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⢸⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⡦⠤⣰⣌⠐⢸⣿⣒⣒⣒⣒⣒⠀⠀⠀⠁⠈⠀⠀⠀⠉⠋⣿⣿⡦⠀⠀⠈⠉⠀⢨⠈⠉⠉⢹⡇⠀⠀⠀⠀⠀⠀ ⢈⣉⣉⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠂⢹⣿⣿⠁⠀⢻⣿⣿⣿⣿⡇⢠⣿⣿⡆⠸⠏⠉⠩⠭⠯⠭⠀⠀⠀⠀⠤⠤⣀⣀⠀⠀⡠⢦⠅⠀⠀⣶⡀⠀⣰⣶⣶⣶⣶⢃⣀⠀⠀⠀⠀⢀ ⢨⣭⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣠⣾⣿⣯⣶⣶⣾⣿⣿⣿⡟⠀⣸⣿⣿⡇⠀⠀⣛⣛⣛⢛⣿⡛⠂⠋⠿⠗⠲⠒⠾⠾⠿⠿⠖⠶⣷⡷⣷⡶⠾⠿⠿⠟⠉⠉⠁⠉⠠⠡⠾⠶⠆ ⠠⠤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⣠⣄⣥⣭⣭⣭⣭⣭⣼⠀⣰⣦⣤⢿⠆⠴⠶⠷⢷⣾⣼⣿⡀⠀⠀⠀⠀⠘⠈⠉⠁⠐⠛⠓⠘⠘⠳ ⠰⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠿⠿⠿⠿⠿⠿⠷⠀⣸⣷⣦⠤⠤⠤⠠⠤⠼⠿⠿⠿⠷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⠶⣶⠶⢶⠶⠀⠀⠀⢻⣷⣾⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢈⣙⣉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣭⣩⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⡤⡤⢤⡤⠤⣤⢤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣖⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠰⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣓⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠲⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠰⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠕⠶⠶⠦⠶⠶⠶⠶⠿⣿⡗⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⠘⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣭⣯⣭⣭⣭⣭⣭⣭⣭⣨⣭⣍⣭⣩⣭⣭⣭⣭⣭⣭⣭⣭⣩⣭⣩⠉⠉⠉⠛⠉⠉⠋⠉⣿⣇⣀⣀⣀⣀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⣀⣀⣀⣀⣀⣸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠒⠖⠶⠀⠀⠀⠀⠀⠛⠛⣿⣿⣿⣿⣿⠿⠟⢿⢿⣿⣿⢿⠿⠿⡿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠛ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣿⣀⠀⢀⠀⠶⣶⣦⣀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣉⠃⣸⣂⣀⣀⣈⣉⣀⣀⣀⣀⣁⣉⣈⣁⣀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢶⠆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠤⠶⠤⠴⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠀⠆ ⢠⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠤⠤⠴⠤⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣶⣶⣦⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣾⣿⣿⣿⣷⣶⡖⣶⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣦⣶⣷⣾⣿⣿⣿⣶⠲⣶⣾⣿⣶⣶⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⢻⣿⣿⣿⣿⣿⣇⣠⣤⡿⣿⣯⣼⣿⣿⣿⣿⣿⣴⣤⣿⣿⣥⣿⣿⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠐⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠟⢿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣇⠈⠻⠿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⣿⣇⠀⣼⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀ ⠘⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⢸⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⡦⠤⣰⣌⠐⢸⣿⣒⣒⣒⣒⣒⠀⠀⠀⠁⠈⠀⠀⠀⠉⠋⣿⣿⡦⠀⠀⠈⠉⠀⢨⠈⠉⠉⢹⡇⠀⠀⠀⠀⠀⠀ ⢈⣉⣉⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠂⢹⣿⣿⠁⠀⢻⣿⣿⣿⣿⡇⢠⣿⣿⡆⠸⠏⠉⠩⠭⠯⠭⠀⠀⠀⠀⠤⠤⣀⣀⠀⠀⡠⢦⠅⠀⠀⣶⡀⠀⣰⣶⣶⣶⣶⢃⣀⠀⠀⠀⠀⢀ ⢨⣭⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣠⣾⣿⣯⣶⣶⣾⣿⣿⣿⡟⠀⣸⣿⣿⡇⠀⠀⣛⣛⣛⢛⣿⡛⠂⠋⠿⠗⠲⠒⠾⠾⠿⠿⠖⠶⣷⡷⣷⡶⠾⠿⠿⠟⠉⠉⠁⠉⠠⠡⠾⠶⠆ ⠠⠤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⣠⣄⣥⣭⣭⣭⣭⣭⣼⠀⣰⣦⣤⢿⠆⠴⠶⠷⢷⣾⣼⣿⡀⠀⠀⠀⠀⠐⠾⠷⠀⠤⠐⠠⠤⠘⠳ ⠰⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠿⠿⠿⠿⠿⠿⠷⠀⣸⣷⣦⠤⠤⠤⠠⠤⠼⠿⠿⠿⠷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⠶⣶⠶⢶⠶⠀⠀⠀⢻⣷⣾⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢈⣙⣉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣭⣩⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⡤⡤⢤⡤⠤⣤⢤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣖⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠰⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣓⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠲⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠰⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠕⠶⠶⠦⠶⠶⠶⠶⠿⣿⡗⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⣔⣰⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⠘⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣭⣯⣭⣭⣭⣭⣭⣭⣭⣨⣭⣍⣭⣩⣭⣭⣭⣭⣭⣭⣭⣭⣩⣭⣩⠉⠉⠉⠛⠉⠉⠋⠉⣿⣇⣀⣀⣀⣀⠀⢀⣀⣀⣀⣀⣙⣙⣛⣚⣋⣀⣀⣀⠀⠀⣀⣀⣀⣀⣀⣸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠒⠖⠶⠀⠀⠀⠀⠀⠛⠛⣿⣿⣿⣿⣿⠿⠟⢿⢿⣿⣿⢿⠿⠿⡿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠛ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣿⣀⠀⢀⠀⠶⣶⣦⣀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣉⠃⣸⣂⣀⣀⣈⣉⣀⣀⣀⣀⣁⣉⣈⣁⣀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢶⠆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠤⠶⠤⠴⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠀⠆ ⢠⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠤⠤⠴⠤⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣶⣶⣦⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣶⡖⣶⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣦⣶⣷⣾⣿⣿⣿⣶⠶⣶⣾⣿⣶⣶⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⢻⣿⣿⣿⣿⣿⣇⣠⣤⡿⣿⣯⣽⣿⣿⣿⣿⣿⣴⣤⣿⣿⣥⣿⣿⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠐⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠟⢿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣇⠈⠿⠿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⣿⣇⠀⣼⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀ ⠘⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⢸⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⡦⠤⣰⣌⠐⢸⣿⣒⣒⣒⣒⣒⠀⠀⠀⠁⠈⠀⠀⠀⠉⠋⣿⣿⡦⠀⠀⠈⠉⠀⢨⠉⠉⠉⢹⡇⠀⠀⠀⠀⠀⠀ ⢈⣉⣉⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠂⢹⣿⣿⠁⠀⢻⣿⣿⣿⣿⡇⢠⣿⣿⡆⠸⠏⠉⠩⠭⠯⠭⠀⠀⠀⠀⠤⠤⣀⣀⠀⠀⡠⢧⠅⠀⠀⣶⡀⢀⣰⣶⣶⣶⣾⢃⣀⠀⠀⠀⠀⢀ ⢨⣭⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣠⣾⣿⣯⣶⣶⣾⣿⣿⣿⡟⠀⣸⣿⣿⡇⠀⠀⣛⣛⣛⢛⣿⡛⠂⠋⠿⠗⠲⠲⠾⠿⠿⠿⠶⠶⣷⡷⣷⡶⠾⢿⣿⡟⠉⠉⠁⠉⠠⠡⠾⠶⠆ ⠠⠤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⣠⣄⣥⣭⣭⣭⣭⣭⣼⠀⣰⣦⣤⣿⠦⠴⠶⠷⢷⣾⣼⣿⡄⠀⠀⠀⠀⠐⠾⠷⠄⠤⠐⠠⠤⠘⠳ ⠰⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠿⠿⠿⠿⠿⠿⠷⠀⣸⣷⣦⠤⠤⠤⠠⠤⠼⠿⠿⠿⠷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⠶⣶⠶⢶⠶⠀⠀⠀⢻⣷⣾⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢈⣙⣉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣭⣩⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⡤⡤⢤⡤⠤⣤⢤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣖⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠰⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣓⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠲⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠰⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠕⠶⠶⠦⠶⠶⠶⠶⠿⣿⡗⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⣔⣰⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⠘⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣭⣯⣭⣭⣭⣭⣭⣭⣭⣨⣭⣍⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣩⣭⣩⠉⠉⠉⠛⠉⠉⠋⠉⣿⣇⣀⣀⣀⣀⠀⢀⣀⣀⣀⣀⣙⣙⣛⣚⣋⣀⣀⣀⠀⠀⣀⣀⣀⣀⣀⣸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠖⠖⠶⠦⠀⠀⠀⠀⠛⠛⣿⣿⣿⣿⣿⠿⠟⢿⣿⣿⣿⢿⠿⠿⡿⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⠛ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣿⣀⠀⢀⠀⠶⣶⣦⣀⢀⣀⣀⣀⣀⣀⣀⣈⡀⠀⠀⣉⠃⣸⣂⣀⣐⣈⣉⣀⣀⣀⣀⣁⣉⣈⣁⣀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢶⠆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠤⠶⠤⠴⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠀⠆ ⢠⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠤⠤⠴⠤⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣶⣶⣦⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣾⣿⣿⣿⣷⣶⡖⣶⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣦⣶⣷⣾⣿⣿⣿⣶⠲⣶⣾⣿⣶⣶⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⢻⣿⣿⣿⣿⣿⣇⣠⣤⡿⣿⣯⣼⣿⣿⣿⣿⣿⣴⣤⣿⣿⣥⣿⣿⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠐⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠟⢿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣇⠈⠻⠿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⣿⣇⠀⣼⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀ ⠘⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⢸⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⡦⠤⣰⣌⠐⢸⣿⣒⣒⣒⣒⣒⠀⠀⠀⠁⠈⠀⠀⠀⠉⠋⣿⣿⡦⠀⠀⠈⠉⠀⢨⠈⠉⠉⢹⡇⠀⠀⠀⠀⠀⠀ ⢈⣉⣉⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠂⢹⣿⣿⠁⠀⢻⣿⣿⣿⣿⡇⢠⣿⣿⡆⠸⠏⠉⠩⠭⠯⠭⠀⠀⠀⠀⠤⠤⣀⣀⠀⠀⡠⢦⠅⠀⠀⣶⡀⠀⣰⣶⣶⣶⣶⢃⣀⠀⠀⠀⠀⢀ ⢨⣭⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣠⣾⣿⣯⣶⣶⣾⣿⣿⣿⡟⠀⣸⣿⣿⡇⠀⠀⣛⣛⣛⢛⣿⡛⠂⠋⠿⠗⠲⠒⠾⠾⠿⠿⠖⠶⣷⡷⣷⡶⠾⠿⠿⠟⠉⠉⠁⠉⠠⠡⠾⠶⠆ ⠠⠤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⣠⣄⣥⣭⣭⣭⣭⣭⣼⠀⣰⣦⣤⢿⠆⠴⠶⠷⢷⣾⣼⣿⡀⠀⠀⠀⠀⠐⠾⠷⠀⠤⠐⠠⠤⠘⠳ ⠰⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠿⠿⠿⠿⠿⠿⠷⠀⣸⣷⣦⠤⠤⠤⠠⠤⠼⠿⠿⠿⠷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⠶⣶⠶⢶⠶⠀⠀⠀⢻⣷⣾⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢈⣙⣉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣭⣩⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⡤⡤⢤⡤⠤⣤⢤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣖⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠰⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣓⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠲⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠰⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠕⠶⠶⠦⠶⠶⠶⠶⠿⣿⡗⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⣔⣰⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⠘⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣭⣯⣭⣭⣭⣭⣭⣭⣭⣨⣭⣍⣭⣩⣭⣭⣭⣭⣭⣭⣭⣭⣩⣭⣩⠉⠉⠉⠛⠉⠉⠋⠉⣿⣇⣀⣀⣀⣀⠀⢀⣀⣀⣀⣀⣙⣙⣛⣚⣋⣀⣀⣀⠀⠀⣀⣀⣀⣀⣀⣸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠒⠖⠶⠦⠀⠀⠀⠀⠛⠛⣿⣿⣿⣿⣿⠿⠟⢿⣿⣿⣿⢿⠿⠿⡿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⠛ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣿⣀⠀⢀⠐⠶⣶⣦⣀⢀⣀⣀⣀⣀⣀⣀⣈⡀⠀⠀⣉⠃⣸⣂⣀⣐⣘⣋⣆⣠⣀⣀⣁⣉⣈⣁⣀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢶⠆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠤⠶⠤⠴⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠀⠆ ⢠⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠤⠤⠴⠤⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣶⣶⣦⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣾⣿⣿⣿⣷⣶⡖⣶⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣦⣶⣷⣾⣿⣿⣿⣶⠲⣶⣾⣿⣶⣶⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⢻⣿⣿⣿⣿⣿⣇⣠⣤⡿⣿⣯⣼⣿⣿⣿⣿⣿⣴⣤⣿⣿⣥⣿⣿⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠐⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠟⢿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣇⠈⠻⠿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⣿⣇⠀⣼⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀ ⠘⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⢸⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⡦⠤⣰⣌⠐⢸⣿⣒⣒⣒⣒⣒⠀⠀⠀⠁⠈⠀⠀⠀⠉⠋⣿⣿⡦⠀⠀⠈⠉⠀⢨⠈⠉⠉⢹⡇⠀⠀⠀⠀⠀⠀ ⢈⣉⣉⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠂⢹⣿⣿⠁⠀⢻⣿⣿⣿⣿⡇⢠⣿⣿⡆⠸⠏⠉⠩⠭⠯⠭⠀⠀⠀⠀⠤⠤⣀⣀⠀⠀⡠⢦⠅⠀⠀⣶⡀⠀⣰⣶⣶⣶⣶⢃⣀⠀⠀⠀⠀⢀ ⢨⣭⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣠⣾⣿⣯⣶⣶⣾⣿⣿⣿⡟⠀⣸⣿⣿⡇⠀⠀⣛⣛⣛⢛⣿⡛⠂⠋⠿⠗⠲⠒⠾⠾⠿⠿⠖⠶⣷⡷⣷⡶⠾⠿⠿⠟⠉⠉⠁⠉⠠⠡⠾⠶⠆ ⠠⠤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⣠⣴⣥⣭⣭⣭⣭⣭⣼⠀⣰⣦⣤⢿⠆⠴⠶⠷⢷⣾⣼⣿⡀⠀⠀⠀⠀⠐⠾⠷⠀⠤⠐⠀⠀⠘⠳ ⠰⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠿⠿⠿⠿⠿⠿⠷⠀⣸⣷⣦⠤⠤⠤⠠⠤⠼⠿⠿⠿⠷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⠶⣶⠶⢶⠶⠀⠀⠀⢻⣷⣾⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢈⣙⣉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣭⣩⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⡤⡤⢤⡤⠤⣤⢤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣖⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠰⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣓⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠲⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠰⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠕⠶⠶⠦⠶⠶⠶⠶⠿⣿⡗⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⣔⣰⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⠘⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣭⣯⣭⣭⣭⣭⣭⣭⣭⣨⣭⣍⣭⣩⣭⣭⣭⣭⣭⣭⣭⣭⣩⣭⣩⠉⠉⠉⠛⠉⠉⠋⠉⣿⣇⣀⣀⣀⣀⠀⢀⣀⣀⣀⣀⣙⣙⣛⣚⣋⣀⣀⣀⠀⠀⣀⣀⣀⣀⣀⣸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠒⠖⠶⠦⠀⠀⠀⠀⠛⠛⣿⣿⣿⣿⣿⠿⠟⢿⣿⣿⣿⢿⠿⠿⡿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⠛ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣿⣀⠀⢀⠐⠶⣶⣦⣀⢀⣀⣀⣀⣀⣀⣀⣈⡀⠀⠀⣉⠃⣸⣂⣀⣐⣘⣋⣆⣠⣀⣀⣁⣉⣈⣁⣀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢶⠆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠤⠶⠤⠴⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠀⠆ ⢠⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠤⠤⠴⠤⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣶⣶⣦⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣾⣿⣿⣿⣷⣶⡖⣶⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣦⣶⣷⣾⣿⣿⣿⣶⠲⣶⣾⣿⣶⣶⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⢻⣿⣿⣿⣿⣿⣇⣠⣤⡿⣿⣯⣼⣿⣿⣿⣿⣿⣴⣤⣿⣿⣥⣿⣿⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠐⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠟⢿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣇⠈⠻⠿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⣿⣇⠀⣼⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀ ⠘⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⢸⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⡦⠤⣰⣌⠐⢸⣿⣒⣒⣒⣒⣒⠀⠀⠀⠁⠈⠀⠀⠀⠉⠋⣿⣿⡦⠀⠀⠈⠉⠀⢨⠈⠉⠉⢹⡇⠀⠀⠀⠀⠀⠀ ⢈⣉⣉⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠂⢹⣿⣿⠁⠀⢻⣿⣿⣿⣿⡇⢠⣿⣿⡆⠸⠏⠉⠩⠭⠯⠭⠀⠀⠀⠀⠤⠤⣀⣀⠀⠀⡠⢦⠅⠀⠀⣶⡀⠀⣰⣶⣶⣶⣶⢃⣀⠀⠀⠀⠀⢀ ⢨⣭⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣠⣾⣿⣯⣶⣶⣾⣿⣿⣿⡟⠀⣸⣿⣿⡇⠀⠀⣛⣛⣛⢛⣿⡛⠂⠋⠿⠗⠲⠒⠾⠾⠿⠿⠖⠶⣷⡷⣷⡶⠾⠿⠿⠟⠉⠉⠁⠉⠠⠡⠾⠶⠆ ⠠⠤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⣠⣴⣥⣭⣭⣭⣭⣭⣼⠀⣰⣦⣤⢿⠆⠴⠶⠷⢷⣾⣼⣿⡀⠀⠀⠀⠀⠐⠾⠷⠀⠤⠐⠀⠀⠘⠳ ⠰⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠿⠿⠿⠿⠿⠿⠷⠀⣸⣷⣦⠤⠤⠤⠠⠤⠼⠿⠿⠿⠷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⠶⣶⠶⢶⠶⠀⠀⠀⢻⣷⣾⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢈⣙⣉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀ ⢠⣭⣩⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⡤⡤⢤⡤⠤⣤⢤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣖⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠰⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣓⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠲⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠰⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠕⠶⠶⠦⠶⠶⠶⠶⠿⣿⡗⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⣔⣰⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⠘⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣭⣯⣭⣭⣭⣭⣭⣭⣭⣨⣭⣍⣭⣩⣭⣭⣭⣭⣭⣭⣭⣭⣩⣭⣩⠉⠉⠉⠛⠉⠉⠋⠉⣿⣇⣀⣀⣀⣀⠀⢀⣀⣀⣀⣀⣙⣙⣛⣚⣋⣀⣀⣀⠀⠀⣀⣀⣀⣀⣀⣸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠒⠖⠶⠦⠀⠀⠀⠀⠛⠛⣿⣿⣿⣿⣿⠿⠟⢿⣿⣿⣿⢿⠿⠿⡿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⠛ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣿⣀⠀⢀⠐⠶⣶⣦⣀⢀⣀⣀⣀⣀⣀⣀⣈⡀⠀⠀⣉⠃⣺⣂⣀⣐⣘⣋⣆⣠⣀⣀⣁⣉⣈⣁⣀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢶⠆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠤⠶⠤⠴⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠀⠆ ⢠⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠤⠤⠴⠤⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣶⣶⣦⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣾⣿⣿⣿⣷⣶⡖⣶⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣦⣶⣷⣾⣿⣿⣿⣶⠲⣶⣾⣿⣶⣶⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⢻⣿⣿⣿⣿⣿⣇⣠⣤⡿⣿⣯⣼⣿⣿⣿⣿⣿⣴⣤⣿⣿⣥⣿⣿⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠐⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠟⢿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣇⠈⠻⠿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⣿⣇⠀⣼⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀ ⠘⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⢸⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⡦⠤⣰⣌⠐⢸⣿⣒⣒⣒⣒⣒⠀⠀⠀⠁⠈⠀⠀⠀⠉⠋⣿⣿⡦⠀⠀⠈⠉⠀⢨⠈⠉⠉⢹⡇⠀⠀⠀⠀⠀⠀ ⢈⣉⣉⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠂⢹⣿⣿⠁⠀⢻⣿⣿⣿⣿⡇⢠⣿⣿⡆⠸⠏⠉⠩⠭⠯⠭⠀⠀⠀⠀⠤⠤⣀⣀⠀⠀⡠⢦⠅⠀⠀⣶⡀⠀⣰⣶⣶⣶⣶⢃⣀⠀⠀⠀⠀⢀ ⢨⣭⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣠⣾⣿⣯⣶⣶⣾⣿⣿⣿⡟⠀⣸⣿⣿⡇⠀⠀⣛⣛⣛⢛⣿⡛⠂⠋⠿⠗⠲⠒⠾⠾⠿⠿⠖⠶⣷⡷⣷⡶⠾⠿⠿⠟⠉⠉⠁⠉⠠⠡⠾⠶⠆ ⠠⠤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⣠⣴⣥⣭⣭⣭⣭⣭⣼⠀⣰⣦⣤⢿⠆⠴⠶⠷⢷⣾⣼⣿⡀⠀⠀⠀⠀⠐⠾⠷⠀⠤⠐⠀⠀⠘⠳ ⠰⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠿⠿⠿⠿⠿⠿⠷⠀⣸⣷⣦⠤⠤⠤⠠⠤⠼⠿⠿⠿⠷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⠶⣶⠶⢶⠶⠀⠀⠀⢻⣷⣾⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀ ⠘⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢈⣙⣉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀ ⢠⣭⣩⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⡤⡤⢤⡤⠤⣤⢤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣖⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠰⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣓⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠲⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠰⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠕⠶⠶⠦⠶⠶⠶⠶⠿⣿⡗⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⣔⣰⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⠘⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣭⣯⣭⣭⣭⣭⣭⣭⣭⣨⣭⣍⣭⣩⣭⣭⣭⣭⣭⣭⣭⣭⣩⣭⣩⠉⠉⠉⠛⠉⠉⠋⠉⣿⣇⣀⣀⣀⣀⠀⢀⣀⣀⣀⣀⣙⣙⣛⣚⣋⣀⣀⣀⠀⠀⣀⣀⣀⣀⣀⣸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠒⠖⠶⠦⠀⠀⠀⠀⠛⠛⣿⣿⣿⣿⣿⠿⠟⢿⣿⣿⣿⢿⠿⠿⡿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⠛ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣿⣀⠀⢀⠐⠶⣶⣦⣀⢀⣀⣀⣀⣀⣀⣀⣈⡀⠀⠀⣉⠃⣺⣂⣀⣐⣘⣋⣆⣠⣀⣀⣁⣉⣈⣁⣀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢶⠆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠤⠶⠤⠴⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠀⠆ ⢠⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠤⠤⠴⠤⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣶⣶⣦⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣾⣿⣿⣿⣷⣶⡖⣶⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣦⣶⣷⣾⣿⣿⣿⣶⠲⣶⣾⣿⣶⣶⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⢻⣿⣿⣿⣿⣿⣇⣠⣤⡿⣿⣯⣼⣿⣿⣿⣿⣿⣴⣤⣿⣿⣥⣿⣿⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠐⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠟⢿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣇⠈⠻⠿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⣿⣇⠀⣼⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀ ⠘⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⢸⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⡦⠤⣰⣌⠐⢸⣿⣒⣒⣒⣒⣒⠀⠀⠀⠁⠈⠀⠀⠀⠉⠋⣿⣿⡦⠀⠀⠈⠉⠀⢨⠈⠉⠉⢹⡇⠀⠀⠀⠀⠀⠀ ⢈⣉⣉⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠂⢹⣿⣿⠁⠀⢻⣿⣿⣿⣿⡇⢠⣿⣿⡆⠸⠏⠉⠩⠭⠯⠭⠀⠀⠀⠀⠤⠤⣀⣀⠀⠀⡠⢦⠅⠀⠀⣶⡀⠀⣰⣶⣶⣶⣶⢃⣀⠀⠀⠀⠀⢀ ⢨⣭⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣠⣾⣿⣯⣶⣶⣾⣿⣿⣿⡟⠀⣸⣿⣿⡇⠀⠀⣛⣛⣛⢛⣿⡛⠂⠋⠿⠗⠲⠒⠾⠾⠿⠿⠖⠶⣷⡷⣷⡶⠾⠿⠿⠟⠉⠉⠁⠉⠠⠡⠾⠶⠆ ⠠⠤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⣠⣴⣥⣭⣭⣭⣭⣭⣼⠀⣰⣦⣤⢿⠆⠴⠶⠷⢷⣾⣼⣿⡀⠀⠀⠀⠀⠐⠾⠷⠀⠤⠐⠀⠀⠘⠳ ⠰⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠿⠿⠿⠿⠿⠿⠷⠀⣸⣷⣦⠤⠤⠤⠠⠤⠼⠿⠿⠿⠷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⠶⣶⠶⢶⠶⠀⠀⠀⢻⣷⣾⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀ ⠘⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢈⣙⣉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀ ⢠⣭⣩⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⡤⡤⢤⡤⠤⣤⢤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣖⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠰⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣓⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠲⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠰⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠕⠶⠶⠦⠶⠶⠶⠶⠿⣿⡗⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⣔⣰⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⠘⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣭⣯⣭⣭⣭⣭⣭⣭⣭⣨⣭⣍⣭⣩⣭⣭⣭⣭⣭⣭⣭⣭⣩⣭⣩⠉⠉⠉⠛⠉⠉⠋⠉⣿⣇⣀⣀⣀⣀⠀⢀⣀⣀⣀⣀⣙⣙⣛⣚⣋⣀⣀⣀⠀⠀⣀⣀⣀⣀⣀⣸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠒⠖⠶⠦⠀⠀⠀⠀⠛⠛⣿⣿⣿⣿⣿⠿⠟⢿⣿⣿⣿⢿⠿⠿⡿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⠛ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣿⣀⠀⢀⠐⠶⣶⣦⣀⢀⣀⣀⣀⣀⣀⣀⣈⡀⠀⠀⣉⠃⣺⣂⣀⣐⣘⣋⣆⣠⣀⣀⣁⣉⣈⣁⣀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢶⠆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠤⠶⠤⠴⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠀⠆ ⢠⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠤⠤⠴⠤⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣶⣶⣦⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣾⣿⣿⣿⣷⣶⡖⣶⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣦⣶⣷⣾⣿⣿⣿⣶⠲⣶⣾⣿⣶⣶⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⢻⣿⣿⣿⣿⣿⣇⣠⣤⡿⣿⣯⣼⣿⣿⣿⣿⣿⣴⣤⣿⣿⣥⣿⣿⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠐⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠟⢿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣇⠈⠻⠿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⣿⣇⠀⣼⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀ ⠘⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⢸⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⡦⠤⣰⣌⠐⢸⣿⣒⣒⣒⣒⣒⠀⠀⠀⠁⠈⠀⠀⠀⠉⠋⣿⣿⡦⠀⠀⠈⠉⠀⢨⠈⠉⠉⢹⡇⠀⠀⠀⠀⠀⠀ ⢈⣉⣉⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠂⢹⣿⣿⠁⠀⢻⣿⣿⣿⣿⡇⢠⣿⣿⡆⠸⠏⠉⠩⠭⠯⠭⠀⠀⠀⠀⠤⠤⣀⣀⠀⠀⡠⢦⠅⠀⠀⣶⡀⠀⣰⣶⣶⣶⣶⢃⣀⠀⠀⠀⠀⢀ ⢨⣭⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣠⣾⣿⣯⣶⣶⣾⣿⣿⣿⡟⠀⣸⣿⣿⡇⠀⠀⣛⣛⣛⢛⣿⡛⠂⠋⠿⠗⠲⠒⠾⠾⠿⠿⠖⠶⣷⡷⣷⡶⠾⠿⠿⠟⠉⠉⠁⠉⠠⠡⠾⠶⠆ ⠠⠤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⣠⣴⣥⣭⣭⣭⣭⣭⣼⠀⣰⣦⣤⢿⠆⠴⠶⠷⢷⣾⣼⣿⡀⠀⠀⠀⠀⠐⠾⠷⠀⠤⠐⠀⠀⠘⠳ ⠰⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠿⠿⠿⠿⠿⠿⠷⠀⣸⣷⣦⠤⠤⠤⠠⠤⠼⠿⠿⠿⠷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⠶⣶⠶⢶⠶⠀⠀⠀⢻⣷⣾⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀ ⠘⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢈⣙⣉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀ ⢠⣭⣩⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⡤⡤⢤⡤⠤⣤⢤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣖⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠰⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣓⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠲⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠰⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠕⠶⠶⠦⠶⠶⠶⠶⠿⣿⡗⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⣔⣰⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⠘⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣭⣯⣭⣭⣭⣭⣭⣭⣭⣨⣭⣍⣭⣩⣭⣭⣭⣭⣭⣭⣭⣭⣩⣭⣩⠉⠉⠉⠛⠉⠉⠋⠉⣿⣇⣀⣀⣀⣀⠀⢀⣀⣀⣀⣀⣙⣙⣛⣚⣋⣀⣀⣀⠀⠀⣀⣀⣀⣀⣀⣸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠒⠖⠶⠦⠀⠀⠀⠀⠛⠛⣿⣿⣿⣿⣿⠿⠟⢿⣿⣿⣿⢿⠿⠿⡿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⠛ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣿⣀⠀⢀⠐⠶⣶⣦⣀⢀⣀⣀⣀⣀⣀⣀⣈⡀⠀⠀⣉⠃⣺⣂⣀⣐⣘⣋⣆⣠⣀⣀⣁⣉⣈⣁⣀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢶⠆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠤⠶⠤⠴⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠀⠆ ⢠⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠤⠤⠴⠤⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣶⣶⣦⣶⣶⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣾⣿⣿⣿⣷⣶⡖⣶⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣦⣶⣷⣾⣿⣿⣿⣶⠲⣶⣾⣿⣶⣶⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⢻⣿⣿⣿⣿⣿⣇⣠⣤⡿⣿⣯⣼⣿⣿⣿⣿⣿⣴⣤⣿⣿⣥⣿⣿⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠐⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠟⢿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣇⠈⠻⠿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⣿⣇⠀⣼⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀ ⠈⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⢸⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⡦⠤⣰⣌⠐⢸⣿⣒⣒⣒⣒⣒⠀⠀⠀⠁⠈⠀⠀⠀⠉⠋⣿⣿⡦⠀⠀⠈⠉⠀⢨⠈⠉⠉⢹⡇⠀⠀⠀⠀⠀⠀ ⢈⣉⣉⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠂⢹⣿⣿⠁⠀⢻⣿⣿⣿⣿⡇⢠⣿⣿⡆⠸⠏⠉⠩⠭⠯⠭⠀⠀⠀⠀⠤⠤⣀⣀⠀⠀⡠⢦⠅⠀⠀⣶⡀⠀⣰⣶⣶⣶⣶⢃⣀⠀⠀⠀⠀⢀ ⢨⣭⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣠⣾⣿⣯⣶⣶⣾⣿⣿⣿⡟⠀⣸⣿⣿⡇⠀⠀⣛⣛⣛⢛⣿⡛⠂⠋⠿⠗⠲⠒⠾⠾⠿⠿⠖⠶⣷⡷⣷⡶⠾⠿⠿⠟⠉⠉⠁⠉⠠⠡⠾⠶⠆ ⠠⠤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⣠⣴⣥⣭⣭⣭⣭⣭⣼⠀⣰⣦⣤⢿⠆⠴⠶⠷⢷⣾⣼⣿⡀⠀⠀⠀⠀⠐⠾⠷⠀⠤⠐⠀⠀⠘⠳ ⠰⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠿⠿⠿⠿⠿⠿⠷⠀⣸⣷⣦⠤⠤⠤⠠⠤⠼⠿⠿⠿⠷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⠶⣶⠶⢶⠶⠀⠀⠀⢻⣷⣾⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀ ⠘⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢈⣙⣉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀ ⢠⣭⣩⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣼⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⡤⡤⢤⡤⠤⣤⢤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣖⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠰⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣓⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠲⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠰⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠕⠶⠶⠦⠶⠶⠶⠶⠿⣿⡗⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⣔⣰⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⠘⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣭⣯⣭⣭⣭⣭⣭⣭⣭⣨⣭⣍⣭⣩⣭⣭⣭⣭⣭⣭⣭⣭⣩⣭⣩⠉⠉⠉⠛⠉⠉⠋⠉⣿⣇⣀⣀⣀⣀⠀⢀⣀⣀⣀⣀⣙⣙⣛⣚⣋⣀⣀⣀⠀⠀⣀⣀⣀⣀⣀⣸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠒⠖⠶⠦⠀⠀⠀⠀⠛⠛⣿⣿⣿⣿⣿⠿⠟⢿⣿⣿⣿⢿⠿⠿⡿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⠛ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣿⣀⠀⢀⠐⠶⡆⣦⣦⢀⣀⣀⣀⣀⣀⣀⣈⡀⠀⠀⣉⠃⣺⣂⣀⣐⣘⣋⣆⣠⣀⣀⣁⣉⣈⣁⣀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢶⠆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠤⠶⠤⠴⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠀⠆ ⢠⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠤⠤⠴⠤⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣶⣶⣦⣶⣶⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣾⣿⣿⣿⣷⣶⡖⣶⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣦⣶⣷⣾⣿⣿⣿⣶⠲⣶⣾⣿⣶⣶⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⢻⣿⣿⣿⣿⣿⣇⣠⣤⡿⣿⣯⣼⣿⣿⣿⣿⣿⣴⣤⣿⣿⣥⣿⣿⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠐⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠟⢿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣇⠈⠻⠿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⣿⣇⠀⣼⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀ ⠈⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⢸⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⡦⠤⣰⣌⠐⢸⣿⣒⣒⣒⣒⣒⠀⠀⠀⠁⠈⠀⠀⠀⠉⠋⣿⣿⡦⠀⠀⠈⠉⠀⢨⠈⠉⠉⢹⡇⠀⠀⠀⠀⠀⠀ ⢈⣉⣉⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠂⢹⣿⣿⠁⠀⢻⣿⣿⣿⣿⡇⢠⣿⣿⡆⠸⠏⠉⠩⠭⠯⠭⠀⠀⠀⠀⠤⠤⣀⣀⠀⠀⡠⢦⠅⠀⠀⣶⡀⠀⣰⣶⣶⣶⣶⢃⣀⠀⠀⠀⠀⢀ ⢨⣭⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣠⣾⣿⣯⣶⣶⣾⣿⣿⣿⡟⠀⣸⣿⣿⡇⠀⠀⣛⣛⣛⢛⣿⡛⠂⠋⠿⠗⠲⠒⠾⠾⠿⠿⠖⠶⣷⡷⣷⡶⠾⠿⠿⠟⠉⠉⠁⠉⠠⠡⠾⠶⠆ ⠠⠤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⣠⣴⣥⣭⣭⣭⣭⣭⣼⠀⣰⣦⣤⢿⠆⠴⠶⠷⢷⣾⣼⣿⡀⠀⠀⠀⠀⠐⠾⠿⠀⠤⠐⠀⠀⠘⠳ ⠰⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠿⠿⠿⠿⠿⠿⠷⠀⢸⣷⣦⠤⠤⠤⠠⠤⠼⠿⠿⠿⠷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⠶⣶⠶⢶⠶⠀⠀⠀⢻⣷⣾⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀ ⠘⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢈⣙⣉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀ ⢠⣭⣩⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣼⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⡤⡤⢤⡤⠤⣤⢤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣖⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠰⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣓⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠲⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠰⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠕⠶⠶⠦⠶⠶⠶⠶⠿⣿⡗⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⣔⣰⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⠘⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣭⣯⣭⣭⣭⣭⣭⣭⣭⣨⣭⣍⣭⣩⣭⣭⣭⣭⣭⣭⣭⣭⣩⣭⣩⠉⠉⠉⠛⠉⠉⠋⠉⣿⣇⣀⣀⣀⣀⠀⢀⣀⣀⣀⣀⣙⣙⣛⣚⣋⣀⣀⣀⠀⠀⣀⣀⣀⣀⣀⣸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠒⠖⠶⠦⠀⠀⠀⠀⠛⠛⣿⣿⣿⣿⣿⠿⠟⢿⣿⣿⣿⢿⠿⠿⡿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⠛ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣿⣀⠀⢀⠐⠶⡆⣦⣦⢀⣀⣀⣀⣀⣀⣀⣈⡀⠀⠀⣉⠃⣺⣂⣀⣐⣘⣋⣆⣠⣀⣀⣁⣉⣈⣁⣀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢶⠆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠤⠶⠤⠴⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠀⠆ ⢠⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠤⠤⠴⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠰⣶⣶⣦⣶⣶⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣾⣿⣿⣿⣷⣶⡖⣶⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣤⣶⣷⣾⣿⣿⣿⣶⠲⣶⣾⣾⣶⣶⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⢻⣿⣿⣿⣿⣿⣇⣠⣤⡿⣿⣯⣼⣿⣿⣿⣿⣿⣴⣤⣿⣿⣥⣿⣿⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠐⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠟⢿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣇⠈⠻⠿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⣿⣇⠀⣼⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀ ⠈⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⢸⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⡦⠤⣰⣄⠀⢸⣿⣒⣒⣒⣒⣒⠀⠀⠀⠁⠈⠀⠀⠀⠉⠉⣿⣿⡦⠀⠀⠈⠉⠀⢨⠈⠉⠉⢹⡇⠀⠀⠀⠀⠀⠀ ⢈⣉⣉⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠂⢹⣿⣿⠁⠀⢻⣿⣿⣿⣿⡇⢠⣿⣿⡆⠸⠏⠉⠩⠭⢯⣭⢀⣶⡂⠀⠠⠤⠀⡀⠀⠀⢠⣦⠅⠀⠀⣶⡀⠀⣰⣶⣶⣶⣶⣇⣀⠀⠀⢀⠀⣀ ⢨⣭⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣠⣶⣿⣭⣶⣶⣾⣿⣿⣿⡟⠀⣸⣿⣿⡇⠀⠀⣛⣛⣛⢛⣿⣿⣿⣷⣶⣶⣲⠶⠷⠾⠾⠷⠿⠷⠶⠶⡶⠶⠶⠶⠶⠦⠤⠀⣀⣀⣰⣶⣾⠀⠀ ⠠⠤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⣠⣤⣥⣭⣭⣭⣭⡍⣟⡛⠛⠛⠓⠀⠉⠁⠠⠤⢄⣈⣬⡄⡀⠀⠐⠀⠀⠀⠬⠥⠿⠿⠛⠛⠋⠩⠿ ⠰⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠿⠿⠿⠿⢷⠄⣿⣿⣧⠀⠀⠀⠀⠀⠠⠤⠼⠿⠿⠿⠷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀ ⠐⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⠶⣶⠶⢶⣾⠀⣿⣭⣭⣍⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉ ⠘⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉ ⢈⣙⣉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀ ⢠⣭⣩⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠛ ⠠⠤⡤⢤⡤⠤⣤⢤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣖⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠰⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣒⣀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶ ⠐⠲⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠰⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠕⠶⠶⠦⠶⠶⠾⣿⣿⣿⣿⣶⠃⢀⡀⠀⡀⠀⠀⠀⠀⣔⣰⣠⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⠘⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣭⣯⣭⣭⣭⣭⣭⣭⣭⣨⣭⣍⣭⣩⣭⣭⣭⣭⣭⣭⣭⣭⣩⣭⣩⠉⠉⠉⠛⠉⢹⣿⣾⣦⣤⣤⣦⣭⣭⡭⢭⣄⣠⣤⣤⣿⣻⣿⣾⣿⣶⣶⣶⣶⣶⣤⣄⣂⣶⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠒⠖⠶⠦⠀⠀⠀⠉⠛⠛⣿⣿⣿⣿⣿⠿⠟⢿⣿⣿⣿⢿⠿⠿⡿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⠛ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣿⣀⠀⢀⠐⠶⡆⣦⣦⢀⣀⣀⣀⣀⣀⣀⣈⡀⠀⠀⣉⠃⣺⣂⣀⣐⣘⣋⣆⣠⣀⣀⣁⣉⣈⣁⣀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢶⠆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠤⠶⠤⠴⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠀⠆ ⢠⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠤⠤⠴⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠰⣶⣶⣦⣶⣴⣦⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣾⣿⣿⣿⣷⣶⠖⣶⣿⣿⣿⣿⣿⣿⡶⣶⣶⣶⣤⣶⣶⣾⣿⣿⣿⣆⠲⣶⣾⣶⣶⣲⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⢻⣿⣿⣿⣿⣿⣇⣠⡤⡿⣿⣯⣼⡿⣿⣿⣿⣿⣴⣤⣿⣿⣥⣿⣿⣿⣿⣿⡿⠉⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠐⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠿⠟⢻⣿⣿⣿⣿⠟⣿⣿⣿⣿⣇⠀⠻⠿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⣿⣇⠀⣼⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀ ⠈⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⢸⣿⣿⣿⡟⠀⣿⣿⣿⣿⣿⡤⠤⣰⣄⠀⢸⣿⣒⣒⣒⣒⣒⠀⠀⠀⠁⠈⠀⢀⡀⠉⠉⣿⣿⡦⠀⠀⠈⠉⠀⢨⠈⠉⠉⢹⡇⠀⠀⠀⠀⠀⠀ ⢈⣉⣉⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠂⢹⣿⡏⠁⠀⢻⣿⣿⣿⡿⡇⢠⣿⣿⡆⠸⠏⠉⠩⠭⢯⣭⢀⣶⡂⠀⢠⣶⣾⣷⣷⣶⣾⣖⣀⠀⣀⣒⡀⢓⣒⣛⣷⣒⣲⣧⣀⣀⣀⣀⡀⣀ ⢨⣭⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣠⣴⣿⣥⣶⣶⣾⣿⣿⡟⠁⠀⣸⣿⣿⡇⠀⠀⣚⣚⣛⢛⣿⣿⣿⣷⣶⣾⣟⣿⣿⣿⣿⣿⣿⣉⣦⠅⢀⠀⣈⡁⠀⢍⠉⣉⣁⣉⣩⣭⣭⣉⢀ ⠠⠤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣀⣠⣤⣤⣭⣍⣭⣭⡅⣝⡛⠛⠁⠀⣿⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠤⠾⠿⠒⠓⠃⠨⠿ ⠰⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠿⠿⠿⠿⢷⠄⣿⣿⣧⠀⠀⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠐⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⠶⠶⠶⠶⣾⠀⣿⣭⣭⣧⣰⣿⣿⣿⡿⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈ ⠘⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⢈⣙⣉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠻⣿⣿⠿⢿⠤⠄⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠈⡉⠁⠈⠉⠁⠀⠀ ⢠⣭⣩⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠾⣿⣿⣿⡭⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛ ⠠⠤⠤⢤⡤⠤⣤⢤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣷⣶⣿⣿⣭⣭⡉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠰⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣒⣒⣈⣿⣿⣛⣿⣟⣳⡲⠁⢀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶ ⠐⠲⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠰⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠕⠶⠶⠦⠶⠶⠾⣿⣿⣻⣛⣿⣿⣾⣶⣶⣦⡤⣤⣭⣽⣿⣿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣿⣿ ⠘⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣭⣯⣭⣭⣭⣭⣭⣭⣭⣨⣭⣍⣭⣩⣭⣭⣭⣭⣭⣭⣭⣭⣩⣭⣉⠉⠉⠉⠙⠉⢹⣿⣾⣦⣤⣬⣯⣿⣿⡭⢭⣁⣩⣭⣭⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣭⣍⣉⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⣹⠒⠖⠶⠦⠀⠀⠀⠉⠛⠛⣿⣿⣿⣿⣿⠿⠟⢿⣿⣿⣿⢿⠿⠿⡿⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⠛ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⣿⣀⠀⢀⠐⠶⡆⣦⣦⢀⣀⣀⣀⣀⣀⣀⣈⡀⠀⠀⣉⠃⣺⣂⣀⣐⣘⣋⣆⣠⣀⣀⢁⣉⣈⣁⣀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿ ⢶⠆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠤⠶⠤⠴⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠀⠆ ⢠⣤⣤⡄⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠤⠤⠴⠤⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣶⣶⣦⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣶⡖⣶⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⣶⣿⣿⣿⣿⣿⣶⠶⣶⣾⣿⣷⣶⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⢻⣿⣿⣿⣿⣿⣇⣠⣤⣿⣿⣯⣽⣿⣿⣿⣿⣿⣴⣤⣿⣿⣥⣿⣿⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠐⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠿⢿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣇⠈⠿⠿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⣿⣇⠀⣼⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀ ⠘⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⢸⣿⣿⣿⡿⠂⣿⣿⣿⣿⣿⡦⠬⣴⣌⠐⢹⣿⣒⣒⣒⣒⣒⠀⠀⠀⠁⠈⠀⢀⡁⠉⠋⣿⣿⡦⠀⠀⠈⠉⠀⢨⠉⠉⠉⢹⡇⠀⠀⠀⠀⠀⠀ ⢈⣉⣉⣉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⢹⣿⣿⠁⠀⢿⣿⣿⣿⢿⣧⢠⣿⣿⡆⠸⠏⠉⠹⠯⣯⣭⢀⣶⡂⠀⢠⣶⣾⣷⣷⣶⣿⣟⣅⢀⣀⣒⡀⢓⣒⣻⣷⣖⣷⣧⣀⣀⣀⣀⣀⣀ ⢨⣭⣭⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣠⣾⣿⣿⣶⣶⣿⣿⣿⢳⣶⣿⣿⣿⣿⣟⣒⣲⣶⣶⣶⣶⣶⢿⣶⣶⣶⣶⣶⣶⣶⡖⠀⠀⠙⣉⣮⣏⣀⣀⣈⣁⣠⣭⣭⣍⣁⣍⣩⣭⣭⣉⣀ ⠠⠤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢸⣿⠿⠿⡇⠙⠃⣄⣠⣅⣉⣍⣩⣍⡆⣘⡛⠛⠹⠛⣻⣻⡷⣶⣶⡶⠀⠀⠀⠀⠀⠒⠂⠲⠄⠼⠤⠿⠿⠒⠓⠃⠨⠿ ⠰⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢰⣖⣂⠈⠅⠀⠀⣷⣿⠿⠿⠿⠿⢿⠆⣿⣿⣧⢤⠀⣿⣿⡇⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀ ⠐⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣸⣿⣾⡾⠀⠀⠀⣯⣿⠶⣶⠶⢶⣾⠀⣿⣭⣿⣿⣼⣿⣿⡇⠘⠿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉ ⠘⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠃⠀⠀⣼⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⡇⠸⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙ ⢈⣙⣉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢘⡂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⣻⠿⣿⣿⡿⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠈⡉⠁⠈⠉⠁⠀⢀ ⢨⣭⣩⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⠘⠕⠀⠀⣿⣿⣿⣿⣿⣯⣽⣶⣶⡶⠶⣿⣿⣿⡭⠄⢰⢶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠐⠛ ⠠⡤⡤⢤⡤⠤⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⡉⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣭⣭⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠰⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠛⠻⠇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣒⣈⣿⣿⣛⣿⡇⣠⣤⣌⣀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶ ⠐⠲⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠰⠶⠶⠶⠶⣿⣿⣛⣶⣒⡂⠀⠀⠕⠶⠶⠦⠶⠶⠾⣿⣿⣿⣿⣿⣿⣾⣶⣾⣿⣿⣿⣭⣽⣿⣿⣥⣤⣤⣤⣤⣤⣴⣴⣤⣶⣶⣶⣿⣿ ⠘⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣭⣯⣭⣭⣭⣭⣭⣭⣭⣨⣭⣍⣭⣭⣭⣭⣿⣿⣛⣛⣓⣰⣶⣶⠯⢉⣁⠉⠛⠉⠙⢟⣛⣂⣀⣚⣛⣟⣛⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣍⣋⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⠿⠻⠟⠻⠛⣻⠟⠟⠿⠿⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢿⠿⠿⡿⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⠛ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⣿⣀⠀⢀⢐⠶⡆⣶⣦⢀⣀⣀⣀⣀⣈⣀⣈⣀⠀⡈⣉⠃⣺⣂⣀⣐⣘⣋⣆⣠⣀⣀⣁⣉⣈⣁⣀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣶⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢶⠆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠴⠶⠤⠴⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠀⠆ ⠠⣤⣤⡤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠠⠤⠴⠤⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢤⣶⣶⣦⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣶⡖⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣶⣿⣿⣿⣿⣿⣶⠶⣾⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠸⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⢻⣿⣿⣿⣿⣿⣇⣠⣤⣿⣿⣯⣽⣿⣿⣿⣿⣿⣴⣴⣿⣿⣥⣿⣿⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠸⠿⢿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⣿⣷⠀⣼⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀ ⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⢸⣿⣿⣿⣿⠂⣿⣿⣿⣿⣿⡦⠬⣴⣜⠙⢻⣿⣒⣒⣒⣒⣒⠀⠀⠀⠁⠈⠀⢀⡁⠉⠋⣿⣿⡦⠀⠀⠉⠉⠀⢨⡍⠉⡉⣽⡇⠀⠀⠀⠀⢀⠀ ⢀⣉⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⢹⣿⣿⠅⠀⢿⣿⣷⣶⣿⣯⢹⣿⠿⡇⠸⠶⠾⠿⠷⢾⣭⢠⣲⣆⣀⣲⣶⣶⠑⢳⣶⣿⣿⣅⢀⣄⣒⡀⣓⣶⣿⣷⣶⣿⣧⣀⣄⣀⣀⣀⣀ ⢀⣭⣭⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣤⣾⣿⣿⣶⣶⣿⡅⠿⠟⣻⢿⠋⣭⣥⣍⣀⣠⣴⣤⣶⣶⣤⢬⣤⢨⣹⠽⣹⡙⠿⡗⠀⠀⠹⣩⣮⣏⣀⣁⣈⣁⣠⣭⣭⣍⣁⣍⣩⣭⣭⣉⣀ ⠀⠤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⣿⣿⣇⠿⠀⡇⠙⠃⣄⣠⣅⣉⣍⣩⣭⡆⣘⡛⠛⠽⠟⡃⠀⡷⣶⣶⡶⠀⠀⠀⠀⠀⠒⠂⠶⠄⠼⠴⠿⠿⠒⠓⠃⠨⠿ ⠀⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣿⣤⠀⠁⠀⠀⣷⣿⠿⠿⠿⠿⢿⠆⣿⣿⣧⣤⠀⡇⠀⡄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀ ⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣾⠀⠀⠀⠀⣯⣿⢶⣶⡶⣶⣾⠀⣿⣭⣿⣿⣼⣗⠀⠆⠘⠿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙ ⠀⡛⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣿⠀⠃⠀⠀⣼⣿⣿⣿⣿⣿⣯⣤⣿⣿⣿⣿⣿⡧⠰⠆⠸⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙ ⠀⣙⣉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠗⠀⡂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⣻⠿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠈⡉⠁⠈⠉⠁⠀⢀ ⢀⣭⣩⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣯⠀⠕⠀⠀⣿⣿⣿⣿⣿⣯⣽⣶⣶⣶⠶⣿⣿⣷⣶⣤⢰⢶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠐⠛ ⠀⡤⡤⢤⡤⠤⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡖⣀⣉⢀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣗⡶⢻⡟⠛⠀⣷⣾⣤⣬⣬⣷⣶⣾⣶⣶⣶⣶⣷⣾⣿⡟⣠⣤⣌⣀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶ ⠐⠲⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠲⠶⠶⠶⠶⣿⣿⣛⣷⣚⡂⠀⠀⠵⠶⠶⠦⠶⠶⢾⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣭⣽⣿⣿⣥⣤⣤⣤⣤⣤⣴⣴⣤⣶⣶⣶⣿⣿ ⠀⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣭⣯⣭⣭⣭⣭⣭⣭⣭⣨⣭⣭⣭⣭⣭⣭⣿⣿⣛⣛⣓⣰⣶⣶⣿⣉⣁⠉⠛⠉⠙⢟⣛⣂⣐⣚⣛⣟⣛⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣍⣋⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⠿⠻⠟⠻⠛⣻⠟⠟⠿⠿⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢿⠿⠿⡿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⠛ ⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⣿⣀⠀⢀⢐⠶⡆⣶⣦⢀⣀⣀⣀⣀⣈⣀⣈⣀⠀⡈⣉⠃⣺⣂⣀⣐⣘⣋⣆⣠⣀⣀⣁⣉⣈⣁⣀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣷⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢶⠆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠴⠶⠴⠴⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠀⠆ ⠠⣤⣤⡤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠠⠤⠴⠤⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢤⣶⣶⣦⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣶⡖⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣶⣿⣿⣿⣿⣿⣶⠶⣾⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠸⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠙⢻⣿⣿⣿⣿⣿⣇⣠⣤⣿⣿⣯⣽⣿⣿⣿⣿⣿⣴⣴⣿⣿⣥⣿⣿⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⡿⢿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⣿⣷⠀⣼⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀ ⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸⣷⡀⢸⣿⣿⣿⣿⠂⣿⣿⣿⣿⣿⡦⠭⣴⣜⠙⢻⣿⣒⣒⣒⣒⣒⠀⠀⠀⠁⠈⠀⢀⡁⠉⠋⣿⣿⡦⠀⠀⠉⠉⠀⢨⡍⠉⡉⣽⡇⠀⠀⠀⠀⢀⠀ ⠀⡁⣆⣀⠀⠀⠀⠀⠀⠀⠘⠗⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⢸⣿⣿⠇⣹⣿⣿⠇⠀⢿⣿⣷⣶⣿⣯⢹⣿⠿⡇⠸⠷⠾⠿⠷⢾⣭⢠⣲⣆⣀⣲⣶⣶⠑⢳⣶⣿⣿⣅⢀⣔⣒⡠⣓⣶⣿⣷⣶⣿⣧⣄⣄⣀⣀⣀⣄ ⢀⣥⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⣿⣿⣦⣾⣿⣿⣶⣶⣿⣇⣿⠟⣻⢿⠫⣭⣥⣍⣀⣠⣤⣤⣶⣶⣤⢬⣤⣨⣹⠽⣉⡙⠿⡗⠀⠀⠹⣩⣮⣏⣀⣁⣈⣁⣠⣭⣭⣍⣁⣍⣩⣭⣭⣉⣀ ⠀⢤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⣿⣿⣇⣿⣤⡇⠙⠃⣌⣩⣍⣉⣍⣩⣭⡦⣸⣿⣿⣽⣇⡃⠀⡷⣶⣶⡶⠀⠀⠀⠀⠀⠒⠂⠶⠄⠼⠴⠿⠿⠒⠓⠃⠨⠿ ⠀⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣷⣿⢡⠀⠁⠀⠀⣷⣿⠿⠿⠿⠿⢿⠎⣿⣿⣧⣤⠐⡇⠀⡄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀ ⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⢷⣺⠀⠀⠀⠀⣯⣿⢶⣶⡶⣶⣾⠀⣿⣭⣿⣿⡄⢓⠀⠆⠘⠿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⣙ ⠀⡛⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣽⢺⠀⠃⠀⠀⣼⣿⣿⣿⣿⣿⣯⣤⣿⣿⣿⣿⡏⡧⠰⡆⠸⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙ ⠀⣙⣉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠑⠀⡂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠿⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠈⡉⠅⠈⠉⠁⠀⢀ ⢀⣭⣩⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣩⠀⠕⠀⠀⣿⣿⣿⣿⣿⣯⣽⣶⣶⣶⠶⣿⡇⣷⣶⣤⢰⢶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠐⠛ ⠀⡤⣤⢤⡤⢤⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⠘⣀⣉⢀⠀⢻⣷⣾⣷⣿⣿⣿⣿⣿⣷⣶⣿⣗⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣗⡰⢻⡟⠛⠀⣷⣾⣤⣬⣬⣷⣶⣾⣶⣶⣶⣶⣗⣾⣿⡟⣠⣤⣌⣀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶ ⠐⠲⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠲⠶⠶⢿⣿⣿⣿⣛⣰⣚⡂⠀⠀⠵⠶⠶⠦⠶⠶⢾⣿⣿⣿⣿⣿⣞⣾⣿⣾⣿⣿⣿⣭⣽⣿⣿⣧⣤⣤⣤⣤⣤⣴⣴⣴⣶⣶⣶⣿⣿ ⠀⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣽⣯⣭⣭⣭⣭⣭⣭⣭⣨⣭⣭⣭⣭⣽⣿⣿⣿⣟⢚⣓⣰⣶⣶⣿⣉⣁⠉⠛⠉⠙⢟⣛⣂⣒⣚⣻⣿⣛⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣍⣋⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠛⠻⣿⢼⠿⠿⠿⠛⣻⠟⠟⠿⠿⠛⠛⠛⠛⠛⠛⣿⣯⣿⣿⣿⣿⣿⢿⣿⣿⣿⢿⠿⠿⡿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⠛ ⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀⣀⣀⣄⣰⣿⣀⠀⢀⣐⠶⡆⣶⣶⢀⣀⣀⣘⣀⣈⣀⣈⣀⠀⡈⣉⠃⣺⣂⣀⣐⣘⣋⣆⣠⣀⣀⣁⣉⣈⣁⣀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢶⠆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠴⠶⠴⠴⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠀⠆ ⠠⣤⣤⡤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠠⠤⠴⠤⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢤⣶⣶⣦⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣶⡖⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣶⣿⣿⣿⣿⣿⣶⠶⣾⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠸⢶⣶⣶⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠙⢻⣿⣿⣿⣿⣿⣇⣠⣤⣿⣿⣯⣽⣿⣿⣿⣿⣿⣴⣴⣿⣿⣥⣿⣿⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠰⠚⠛⠛⠀⠚⠈⠛⠤⣿⠕⠻⠛⠛⠻⠛⠃⠆⠀⠀⠀⠀⢸⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⡿⢿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⣿⣷⠀⣼⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀ ⠠⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⢸⣿⣿⣿⣿⠂⣿⣿⣿⣿⣿⡦⠭⣴⣜⠙⢻⣿⣒⣒⣒⣒⣒⠀⠀⠀⠁⠈⠀⢀⡁⠉⠋⣿⣿⡦⠀⠀⠉⠉⠀⢨⡍⠉⡉⣽⡇⠀⠀⠀⠀⢀⠀ ⠀⡁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢸⣿⣿⠇⣹⣿⣿⠇⠀⢿⣿⣷⣶⣿⣯⢹⣿⠿⡇⠸⠷⠾⠿⠷⢾⣭⢠⣲⣆⣀⣲⣶⣶⠑⢳⣶⣿⣿⣅⢀⣔⣒⡀⣓⣶⣿⣷⣶⣿⣧⣀⣄⣀⣀⣀⣀ ⢀⣥⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⣿⣿⣦⣾⣿⣿⣶⣶⣿⣇⣿⠟⣻⢿⠫⣭⣥⣍⣀⣠⣤⣤⣶⣶⣤⢬⣤⣨⣹⠽⣉⡙⠿⡗⠀⠀⠹⣩⣮⣏⣀⣁⣈⣁⣠⣭⣭⣍⣁⣍⣩⣭⣭⣉⣀ ⠀⢤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⣿⣿⣇⣿⣤⡇⠙⠃⣌⣩⣍⣉⣍⣩⣭⡦⣸⣿⣿⣽⣇⡃⠀⡷⣶⣶⡶⠀⠀⠀⠀⠀⠒⠂⠶⠄⠼⠴⠿⠿⠒⠓⠃⠨⠿ ⠀⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣷⣿⢡⠀⠁⠀⠀⣷⣿⠿⠿⠿⠿⢿⠎⣿⣿⣧⣤⠐⡇⠀⡄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀ ⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⢷⣺⠀⠀⠀⠀⣯⣿⢶⣶⡶⣶⣾⠀⣿⣭⣿⣿⡄⢓⠀⠆⠘⠿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⣙ ⠀⡛⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣽⢺⠀⠃⠀⠀⣼⣿⣿⣿⣿⣿⣯⣤⣿⣿⣿⣿⡏⡧⠰⡆⠸⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙ ⠀⣙⣉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠑⠀⡂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠿⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠈⡉⠅⠈⠉⠁⠂⢀ ⢀⣭⣩⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣩⠀⠕⠀⠀⣿⣿⣿⣿⣿⣯⣽⣶⣶⣶⠶⣿⡇⣷⣶⣤⢰⢶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠐⠛ ⠀⡤⡤⢤⡤⢤⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⠘⣀⣉⢀⠀⢻⣷⣾⣷⣿⣿⣿⣿⣿⣷⣶⣿⣗⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣗⡰⢻⡟⠛⠀⣷⣾⣤⣬⣬⣷⣶⣾⣶⣶⣶⣶⣗⣾⣿⡟⣠⣤⣌⣀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶ ⠐⠲⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠲⠶⠶⢿⣿⣿⣿⣛⣰⣚⡂⠀⠀⠵⠶⠶⠦⠶⠶⢾⣿⣿⣿⣿⣿⣞⣾⣿⣾⣿⣿⣿⣭⣽⣿⣿⣧⣤⣤⣤⣤⣤⣴⣴⣤⣶⣶⣶⣿⣿ ⠀⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣽⣯⣭⣭⣭⣭⣭⣭⣭⣨⣭⣭⣭⣭⣽⣿⣿⣿⣟⢚⣓⣰⣶⣶⣿⣉⣁⠉⠛⠉⠙⢟⣛⣂⣐⣚⣻⣿⣛⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣍⣋⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠛⠻⣿⢼⠿⠿⠿⠛⣻⠟⠟⠿⠿⠛⠛⠛⠛⠛⠛⣿⣯⣿⣿⣿⣿⣿⢿⣿⣿⣿⢿⠿⠿⡿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⠛ ⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀⣀⣀⣄⣰⣿⣀⠀⢀⣐⠶⡆⣶⣶⢀⣀⣀⣘⣀⣈⣀⣈⣀⠀⡈⣉⠃⣺⣂⣀⣐⣘⣋⣆⣠⣀⣀⣁⣉⣈⣁⣀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢶⠆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠴⠶⠴⠴⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠀⠆ ⠠⣤⣤⡤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠠⠤⠴⠤⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢤⣶⣶⣦⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣶⡖⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣶⣿⣿⣿⣿⣿⣶⠶⣾⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠸⢶⣶⣶⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠙⢻⣿⣿⣿⣿⣿⣇⣠⣤⣿⣿⣯⣽⣿⣿⣿⣿⣿⣴⣴⣿⣿⣥⣿⣿⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠰⠛⠛⠛⠀⠚⠈⠛⠤⣿⠕⠻⠛⠛⠻⠛⠃⠆⠀⠀⠀⠀⢸⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⡿⢿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⣿⣷⠀⣼⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀ ⠠⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⢸⣷⡀⢸⣿⣿⣿⣿⠂⣿⣿⣿⣿⣿⡦⠭⣴⣜⠙⢻⣿⣒⣒⣒⣒⣒⠀⠀⠀⠁⠈⠀⢀⡁⠉⠋⣿⣿⡦⠀⠀⠉⠉⠀⢨⡍⠉⡉⣽⡇⠀⠀⠀⠀⢀⠀ ⠀⡁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠀⠀⠀⠀⢸⣿⣿⠇⣹⣿⣿⠇⠀⢿⣿⣷⣶⣿⣯⢹⣿⠿⡇⠸⠷⠾⠿⠷⢾⣭⢠⣲⣆⣀⣲⣶⣶⠑⢳⣶⣿⣿⣅⢀⣔⣒⡠⣓⣶⣿⣷⣶⣿⣧⣄⣄⣀⣀⣀⣄ ⢀⣥⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⣿⣿⣦⣾⣿⣿⣶⣶⣿⣇⣿⠟⣻⢿⠫⣭⣥⣍⣀⣠⣤⣤⣶⣶⣤⢬⣤⣨⣹⠽⣉⡙⠿⡗⠀⠀⠹⣩⣮⣏⣀⣁⣈⣁⣠⣭⣭⣍⣁⣍⣩⣭⣭⣉⣀ ⠀⢤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⣿⣿⣇⣿⣤⡇⠙⠃⣌⣩⣍⣉⣍⣩⣭⡦⣸⣿⣿⣽⣇⡃⠀⡷⣶⣶⡶⠀⠀⠀⠀⠀⠒⠂⠶⠄⠼⠴⠿⠿⠒⠓⠃⠨⠿ ⠀⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣶⢡⠀⠁⠀⠀⣷⣿⠿⠿⠿⠿⢿⠎⣿⣿⣧⣤⠐⡇⠀⡄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀ ⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⢷⣺⠀⠀⠀⠀⣯⣿⢶⣶⡶⣶⣾⠀⣿⣭⣿⣿⡄⢓⠀⠆⠘⠿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⣙ ⠀⡛⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣽⢺⠀⠃⠀⠀⣼⣿⣿⣿⣿⣿⣯⣤⣿⣿⣿⣿⡏⡧⠰⡆⠸⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙ ⠀⣙⣉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠑⠀⡂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠿⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠈⡉⠅⠈⠉⠁⠂⢀ ⢀⣭⣩⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣩⠀⠕⠀⠀⣿⣿⣿⣿⣿⣯⣽⣶⣶⣶⠶⣿⡇⣷⣶⣤⢰⢶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠐⠛ ⠀⡤⣤⢤⡤⢤⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⠘⣀⣉⢀⠀⢻⣷⣾⣷⣿⣿⣿⣿⣿⣷⣶⣿⣗⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣗⡰⢻⡟⠛⠀⣷⣾⣤⣬⣬⣷⣶⣾⣶⣶⣶⣶⣗⣾⣿⡟⣠⣤⣌⣀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶ ⠐⠲⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠲⠶⠶⢿⣿⣿⣿⣛⣰⣚⡂⠀⠀⠵⠶⠤⠦⠶⠶⢾⣿⣿⣿⣿⣿⣞⣾⣿⣾⣿⣿⣿⣭⣽⣿⣿⣧⣤⣤⣤⣤⣤⣴⣴⣴⣶⣶⣶⣿⣿ ⠀⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣽⣯⣭⣭⣭⣭⣭⣭⣭⣨⣭⣭⣭⣭⣽⣿⣿⣿⣟⢚⣓⣰⣶⣶⣿⣉⣁⣉⠛⠉⠙⢟⣛⣂⣒⣚⣻⣿⣛⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣍⣋⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠛⠻⣿⢼⠿⠿⠿⠛⣻⠟⠟⠿⠿⠛⠛⠛⠛⠛⠛⣿⣯⣿⣿⣿⣿⣿⢿⣿⣿⣿⢿⠿⠿⡿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⠛ ⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀⣀⣀⣄⣰⣿⣈⠀⢀⣐⠶⡆⣶⣶⢀⣀⣀⣘⣀⣈⣀⣈⣀⠀⡈⣉⠃⣺⣂⣀⣐⣘⣋⣆⣠⣀⣀⣁⣉⣈⣁⣀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢶⠆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠴⠶⠴⠴⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠀⠆ ⠠⣤⣤⡤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠠⠤⠴⠤⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢤⣶⣶⣦⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣶⡖⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣶⣿⣿⣿⣿⣿⣶⠶⣾⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠸⢶⣶⣶⠀⠀⠀⠀⡀⠤⢤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠙⢻⣿⣿⣿⣿⣿⣇⣠⣤⣿⣿⣯⣽⣿⣿⣿⣿⣿⣴⣴⣿⣿⣥⣿⣿⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠰⠚⠛⠛⠀⠚⠈⠛⠿⣶⠄⠻⠛⠛⠻⠛⠃⠆⠀⠀⠀⠀⢸⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⡿⢿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⣿⣷⠀⣼⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀ ⠠⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢸⣷⡀⢸⣿⣿⣿⣿⠂⣿⣿⣿⣿⣿⡦⠭⣴⣜⠙⢻⣿⣒⣒⣒⣒⣒⠀⠀⠀⠁⠈⠀⢀⡁⠉⠋⣿⣿⡦⠀⠀⠉⠉⠀⢨⡍⠉⡉⣽⡇⠀⠀⠀⠀⢀⠀ ⠀⡁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢸⣿⣿⠇⣹⣿⣿⠇⠀⢿⣿⣷⣶⣿⣯⢹⣿⠿⡇⠸⠷⠾⠿⠷⢾⣭⢠⣲⣆⣀⣲⣶⣶⠑⢳⣶⣿⣿⣅⢀⣔⣒⡀⣓⣶⣿⣷⣶⣿⣧⣀⣄⣀⣀⣀⣀ ⢀⣥⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⣿⣿⣦⣾⣿⣿⣶⣶⣿⣇⣿⠟⣻⢿⠫⣭⣥⣍⣀⣠⣤⣤⣶⣶⣤⢬⣤⣨⣹⠽⣉⡙⠿⡗⠀⠀⠹⣩⣮⣏⣀⣁⣈⣁⣠⣭⣭⣍⣁⣍⣩⣭⣭⣉⣀ ⠀⢤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⣿⣿⣇⣿⣤⡇⠙⠃⣌⣩⣍⣉⣍⣩⣭⡦⣸⣿⣿⣽⣇⡃⠀⡷⣶⣶⡶⠀⠀⠀⠀⠀⠒⠂⠶⠄⠼⠴⠿⠿⠒⠓⠃⠨⠿ ⠀⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣶⢡⠀⠁⠀⠀⣷⣿⠿⠿⠿⠿⢿⠎⣿⣿⣧⣤⠐⡇⠀⡄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀ ⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⢷⣺⠀⠀⠀⠀⣯⣿⢶⣶⡶⣶⣾⠀⣿⣭⣿⣿⡄⢓⠀⠆⠘⠿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⣙ ⠀⡛⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣽⢺⠀⠃⠀⠀⣼⣿⣿⣿⣿⣿⣯⣤⣿⣿⣿⣿⡏⡧⠰⡆⠸⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙ ⠀⣙⣉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠑⠀⡂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠿⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠈⡉⠅⠈⠉⠁⠂⢀ ⢀⣭⣩⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣩⠀⠕⠀⠀⣿⣿⣿⣿⣿⣯⣽⣶⣶⣶⠶⣿⡇⣷⣶⣤⢰⢶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠐⠛ ⠀⡤⡤⢤⡤⢤⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⠘⣀⣉⢀⠀⢻⣷⣾⣷⣿⣿⣿⣿⣿⣷⣶⣿⣗⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣗⡰⢻⡟⠛⠀⣷⣾⣤⣬⣬⣷⣶⣾⣶⣶⣶⣶⣗⣾⣿⡟⣠⣤⣌⣀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶ ⠐⠲⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠲⠶⠶⢿⣿⣿⣿⣛⣰⣚⡂⠀⠀⠵⠶⠤⠦⠶⠶⢾⣿⣿⣿⣿⣿⣞⣾⣿⣾⣿⣿⣿⣭⣽⣿⣿⣧⣤⣤⣤⣤⣤⣴⣴⣤⣶⣶⣶⣿⣿ ⠀⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣽⣯⣭⣭⣭⣭⣭⣭⣭⣨⣭⣭⣭⣭⣽⣿⣿⣿⣟⢚⣓⣰⣶⣶⣿⣉⣁⣉⠛⠉⠙⢟⣛⣂⣐⣚⣻⣿⣛⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣍⣋⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠛⠻⣿⢼⠿⠿⠿⠛⣻⠟⠟⠿⠿⠛⠛⠛⠛⠛⠛⣿⣯⣿⣿⣿⣿⣿⢿⣿⣿⣿⢿⠿⠿⡿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⠛ ⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀⣀⣀⣄⣰⣿⣈⠀⢀⣐⠶⡆⣶⣶⢀⣀⣀⣘⣀⣈⣀⣈⣀⠀⡈⣉⠃⣺⣂⣀⣐⣘⣋⣆⣠⣀⣀⣁⣉⣈⣁⣀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢶⠆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠴⠶⠴⠴⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠀⠆ ⠠⣤⣤⡤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠠⠤⠴⠤⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢤⣶⣲⣆⣶⣰⢶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣶⡖⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣶⣿⣿⣿⣿⣿⣶⠶⣾⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠘⢻⣾⣷⠛⠤⠛⠓⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠙⢻⣿⣿⣿⣿⣿⣇⣠⣤⣿⣿⣯⣽⣿⣿⣿⣿⣿⣴⣴⣿⣿⣥⣿⣿⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠰⠛⠛⠛⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⢸⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⡿⢿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⣿⣷⠀⣼⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀ ⠠⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⢸⣷⡀⢸⣿⣿⣿⣿⠂⣿⣿⣿⣿⣿⡦⠭⣴⣜⠙⢻⣿⣒⣒⣒⣒⣒⠀⠀⠀⠁⠈⠀⢀⡁⠉⠋⣿⣿⡦⠀⠀⠉⠉⠀⢨⡍⠉⡉⣽⡇⠀⠀⠀⠀⢀⠀ ⠀⡁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠀⠀⠀⠀⢸⣿⣿⠇⣹⣿⣿⠇⠀⢿⣿⣷⣶⣿⣯⢹⣿⠿⡇⠸⠷⠾⠿⠷⢾⣭⢠⣲⣆⣀⣲⣶⣶⠑⢳⣶⣿⣿⣅⢀⣔⣒⡠⣓⣶⣿⣷⣶⣿⣧⣄⣄⣀⣀⣀⣄ ⢀⣥⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⣿⣿⣦⣾⣿⣿⣶⣶⣿⣇⣿⠟⣻⢿⠫⣭⣥⣍⣀⣠⣤⣤⣶⣶⣤⢬⣤⣨⣹⠽⣉⡙⠿⡗⠀⠀⠹⣩⣮⣏⣀⣁⣈⣁⣠⣭⣭⣍⣁⣍⣩⣭⣭⣉⣀ ⠀⢤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⣿⡟⠃⠻⣤⡇⠙⠃⣌⣩⣍⣉⣍⣩⣭⡦⣸⣿⣿⣽⣇⡃⠀⡷⣶⣶⡶⠀⠀⠀⠀⠀⠒⠂⠶⠄⠼⠴⠿⠿⠒⠓⠃⠨⠿ ⠀⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣶⢠⠀⠁⠀⠀⣷⣿⠿⠿⠿⠿⢿⠎⣿⣿⣧⣤⠐⡇⠀⡄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀ ⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⢷⣺⠀⠀⠀⠀⣯⣿⢶⣶⡶⣶⣾⠀⣿⣭⣿⣿⡄⢓⠀⠆⠘⠿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⣙ ⠀⡛⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣽⢺⠀⠃⠀⠀⣼⣿⣿⣿⣿⣿⣯⣤⣿⣿⣿⣿⡏⡧⠰⡆⠸⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙ ⠀⣙⣉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠑⠀⡂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠿⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠈⡉⠅⠈⠉⠁⠂⢀ ⢀⣭⣩⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣩⠀⠕⠀⠀⣿⣿⣿⣿⣿⣯⣽⣶⣶⣶⠶⣿⡇⣷⣶⣤⢰⢶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠐⠛ ⠀⡤⣤⢤⡤⢤⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⠘⣀⣉⢀⠀⢻⣷⣾⣷⣿⣿⣿⣿⣿⣷⣶⣿⣗⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣗⡰⢻⡟⠛⠀⣷⣾⣤⣬⣬⣷⣶⣾⣶⣶⣶⣶⣗⣾⣿⡟⣠⣤⣌⣀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶ ⠐⠲⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠲⠶⠶⢿⣿⣿⣿⣛⣰⣚⡂⠀⠀⠵⠶⠤⠦⠶⠶⢾⣿⣿⣿⣿⣿⣞⣾⣿⣾⣿⣿⣿⣭⣽⣿⣿⣧⣤⣤⣤⣤⣤⣴⣴⣴⣶⣶⣶⣿⣿ ⠀⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣽⣯⣭⣭⣭⣭⣭⣭⣭⣨⣭⣭⣭⣭⣽⣿⣿⣿⣟⢚⣓⣰⣶⣶⣿⣉⣁⣉⠛⠉⠙⢟⣛⣂⣒⣚⣻⣿⣛⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣍⣋⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠛⠻⣿⢼⠿⠿⠿⠛⣻⢟⠟⠿⠿⠛⠛⠛⠛⠛⠛⣿⣯⣿⣿⣿⣿⣿⢿⣿⣿⣿⢿⠿⠿⡿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⠛ ⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀⣀⣀⣄⣰⣿⣈⠀⢀⣐⠶⡆⣶⣶⢀⣀⣀⣘⣀⣈⣀⣈⣀⠀⡈⣉⠃⣺⣂⣀⣐⣘⣋⣆⣠⣀⣀⣁⣉⣈⣁⣀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠶⠄⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄ ⠀⣤⣤⡄⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣠⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⢐⠘⠛⠛⠒⠀⠘⠛⠛⠓⠒⠀⠀⠀⠒⠚⠛⠛⠛⠓⠀⠀⠀⠀⠀⡀⣒⡚⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠒⠒⠀⠚⠛⠛⠛⠀⡀⡀⠀⠀⠀⠀ ⢘⣛⣛⣓⣛⣛⣛⣓⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀ ⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡗⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀ ⠀⠫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢠⣿⠀⣿⣿⣦⡀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⢿⡿⠀⠀⠀⠀ ⠀⠁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢀⣺⣿⠀⣿⣿⣿⣿⣦⣄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⢀ ⠀⣄⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣷⣄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣧⠀⠀⠀⠠⠴⠾⠿⠿⠀⣻⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣀⣀⣀⣀⣀⣀⠀⠀⠁⠀⠭ ⠀⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀ ⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⢸⡟⠀⠀⢀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⠿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⣉⣉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⡇⠀⢠⡈⠉⠙⠛⠛⠛⢃⡿⢿⣿⣿⣿⡿⠋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢺⣿⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀ ⠀⣌⣩⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣦⡀⠀⠀⠀⠘⠀⠀⠙⠻⣿⡃⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠤⠤⠤⠤⠤⠤⠤⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣿⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⢢⣼⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⡿⠛⠛⠛⠛⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶ ⠀⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠆⠶⠶⠦⠐⣉⡃⠀⠘⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢧⢨⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⢀⣀⣤⣶⣶⣶⣿⣋⣀⣀⣀⣀⡀⠀⢠⣤⣾⣿ ⠀⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣁⣯⣍⣩⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠛ ⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠠⡞⠁⠀⠀⠀⠀⠀⢸⠸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢯⡷⠀⠀⠺⠾⠶⠶⠂⠀⠀⠷⠶⠷⠖⢀⣀⢰⣶⣔⢤⣀⣀⣀⣴⣰⣤⢤⣀⣀⣀⡒⣠⣤⣄⣀⣀⢤⡦⣄⣤⣄⣚⣭⣍⣩⣩⣏⣔⡄⣤⣤⣤⡠⣤⣤⣴⣀⣀⣦⣤⣀⢀⢀⣀⣠⣶⣦⡀⣀⣀⣀⡠⣠⣦⣀⣀ ⠶⠄⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄ ⠀⣤⣤⡄⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣠⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⢐⠘⠛⠛⠒⠀⠘⠛⠛⠓⠒⠀⠀⠀⠒⠚⠛⠛⠛⠓⠀⠀⠀⠀⠀⡀⣒⡚⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠒⠒⠀⠚⠛⠛⠛⠀⡀⡀⠀⠀⠀⠀ ⢘⣛⣛⣓⣛⣛⣛⣓⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀ ⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡗⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀ ⠀⠫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢠⣿⠀⣿⣿⣦⡀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⢿⡿⠀⠀⠀⠀ ⠀⠁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢀⣺⣿⠀⣿⣿⣿⣿⣦⣄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⢀ ⠀⣄⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣷⣄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣧⠀⠀⠀⠠⠴⠾⠿⠿⠀⣻⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣀⣀⣀⣀⣀⣀⠀⠀⠁⠀⠭ 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⠶⠄⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄ ⠀⣤⣤⡄⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣠⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⢐⠘⠛⠛⠒⠀⠘⠛⠛⠓⠒⠀⠀⠀⠒⠚⠛⠛⠛⠓⠀⠀⠀⠀⠀⡀⣒⡚⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠒⠒⠀⠚⠛⠛⠛⠀⡀⡀⠀⠀⠀⠀ ⢘⣛⣛⣓⣛⣛⣛⣓⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀ ⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡗⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀ ⠀⠫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢠⣿⠀⣿⣿⣦⡀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠀⠀⠀⠀⠈⢿⡿⠀⠀⠀⠀ ⠀⠁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢀⣺⣿⠀⣿⣿⣿⣿⣦⣄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⢀ ⠀⣄⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣷⣄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣧⠀⠀⠀⠠⠴⠾⠿⠿⠀⣻⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣀⣀⣀⣀⣀⣀⠀⠀⠁⠀⠭ ⠀⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀ ⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⢸⡟⠀⠀⢀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⠿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⣉⣉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⡇⠀⢠⡈⠉⠙⠛⠛⠛⢃⡿⢿⣿⣿⣿⣿⡋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢺⣿⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀ ⠀⣌⣩⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣦⡀⠀⠀⠀⠘⠀⠀⠙⠻⣿⡃⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀ ⠀⠤⠤⠤⠤⠤⠤⠤⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣿⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⢢⣼⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⡿⠛⠛⠛⠛⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶ ⠀⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠆⠶⠶⠦⠐⣉⡃⠀⠘⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢧⢨⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⢀⣀⣤⣶⣶⣶⣿⣋⣀⣀⣀⣀⡀⠀⢠⣤⣾⣿ ⠀⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣁⣯⣍⣩⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠛ ⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠠⡞⠁⠀⠀⠀⠀⠀⢸⠸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢯⡷⠀⠀⠺⠾⠶⠶⠂⠀⠀⠷⠶⠷⠖⢀⣀⢰⣶⣔⢤⣀⣀⣀⣴⣰⣤⢤⣀⣀⣀⡒⣠⣤⣄⣀⣀⢤⡦⣄⣤⣄⣚⣭⣍⣩⣩⣏⣔⡄⣤⣤⣤⡠⣤⣤⣴⣀⣀⣦⣤⣀⢀⢀⣀⣠⣶⣦⡀⣀⣀⣀⡠⣠⣦⣀⣀ ⠶⠄⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄ ⠀⣤⣤⡄⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣠⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⢐⠘⠛⠛⠒⠀⠘⠛⠛⠓⠒⠀⠀⠀⠒⠚⠛⠛⠛⠓⠀⠀⠀⠀⠀⡀⣒⡚⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠒⠒⠀⠚⠛⠛⠛⠀⡀⡀⠀⠀⠀⠀ ⢘⣛⣛⣓⣛⣛⣛⣓⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀ ⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡗⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀ ⠀⠫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢠⣿⠀⣿⣿⣦⡀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠀⠀⠀⠀⠈⢿⡿⠀⠀⠀⠀ ⠀⠁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢀⣺⣿⠀⣿⣿⣿⣿⣦⣄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⢀ ⠀⣄⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣷⣄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣧⠀⠀⠀⠠⠴⠾⠿⠿⠀⣻⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣀⣀⣀⣀⣀⣀⠀⠀⠁⠀⠭ ⠀⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀ ⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⢸⡟⠀⠀⢀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⠿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⣉⣉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⡇⠀⢠⡈⠉⠙⠛⠛⠛⢃⡿⢿⣿⣿⣿⣿⡋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢺⣿⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀ ⠀⣌⣩⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣦⡀⠀⠀⠀⠘⠀⠀⠙⠻⣿⡃⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀ ⠀⠤⠤⠤⠤⠤⠤⠤⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣿⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⢢⣼⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⡿⠛⠛⠛⠛⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶ ⠀⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠆⠶⠶⠦⠐⣉⡃⠀⠘⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢧⢨⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⢀⣀⣤⣶⣶⣶⣿⣋⣀⣀⣀⣀⡀⠀⢠⣤⣾⣿ ⠀⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣁⣯⣍⣩⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠛ ⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠠⡞⠁⠀⠀⠀⠀⠀⢸⠸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢯⡷⠀⠀⠺⠾⠶⠶⠂⠀⠀⠷⠶⠷⠖⢀⣀⢰⣶⣔⢤⣀⣀⣀⣴⣰⣤⢤⣀⣀⣀⡒⣠⣤⣄⣀⣀⢤⡦⣄⣤⣄⣚⣭⣍⣩⣩⣏⣔⡄⣤⣤⣤⡠⣤⣤⣴⣀⣀⣦⣤⣀⢀⢀⣀⣠⣶⣦⡀⣀⣀⣀⡠⣠⣦⣀⣀ ⠶⠄⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄ ⠀⣤⣤⡄⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣠⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⢐⠘⠛⠛⠒⠀⠘⠛⠛⠓⠒⠀⠀⠀⠒⠚⠛⠛⠛⠓⠀⠀⠀⠀⠀⡀⣒⡚⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠒⠒⠀⠚⠛⠛⠛⠀⡀⡀⠀⠀⠀⠀ ⢘⣛⣛⣓⣛⣛⣛⣓⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀ ⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡗⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀ ⠀⠫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢠⣿⠀⣿⣿⣦⡀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠀⠀⠀⠀⠈⢿⡿⠀⠀⠀⠀ ⠀⠁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢀⣺⣿⠀⣿⣿⣿⣿⣦⣄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⢀ ⠀⣄⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣷⣄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣧⠀⠀⠀⠠⠴⠾⠿⠿⠀⣻⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣀⣀⣀⣀⣀⣀⠀⠀⠁⠀⠭ ⠀⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀ ⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⢸⡟⠀⠀⢀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⠿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⣉⣉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⡇⠀⢠⡈⠉⠙⠛⠛⠛⢃⡿⢿⣿⣿⣿⣿⡋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢺⣿⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀ ⠀⣌⣩⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣦⡀⠀⠀⠀⠘⠀⠀⠙⠻⣿⡃⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀ ⠀⠤⠤⠤⠤⠤⠤⠤⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣿⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⢢⣼⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⡿⠛⠛⠛⠛⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶ ⠀⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠆⠶⠶⠦⠐⣉⡃⠀⠘⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢧⢨⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⢀⣀⣤⣶⣶⣶⣿⣋⣀⣀⣀⣀⡀⠀⢠⣤⣾⣿ ⠀⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣁⣯⣍⣩⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠛ ⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠠⡞⠁⠀⠀⠀⠀⠀⢸⠸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢯⡷⠀⠀⠺⠾⠶⠶⠂⠀⠀⠷⠶⠷⠖⢀⣀⢰⣶⣔⢤⣀⣀⣀⣴⣰⣤⢤⣀⣀⣀⡒⣠⣤⣄⣀⣀⢤⡦⣄⣤⣄⣚⣭⣍⣩⣩⣏⣔⡄⣤⣤⣤⡠⣤⣤⣴⣀⣀⣦⣤⣀⢀⢀⣀⣠⣶⣦⡀⣀⣀⣀⡠⣠⣦⣀⣀ ⠶⠄⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄ ⠀⣤⣤⡄⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣠⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⢐⠘⠛⠛⠒⠀⠘⠛⠛⠓⠒⠀⠀⠀⠒⠚⠛⠛⠛⠓⠀⠀⠀⠀⠀⡀⣒⡚⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠒⠒⠀⠚⠛⠛⠛⠀⡀⡀⠀⠀⠀⠀ ⢘⣛⣛⣓⣛⣛⣛⣓⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀ ⠸⠿⠿⠿⠿⠿⠿⠿⢿⣽⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡗⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀ ⠀⠫⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠂⠐⠂⠐⠂⠐⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢠⣿⠀⣿⣿⣦⡀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠀⠀⠀⠀⠈⢿⡿⠀⠀⠀⠀ ⠀⠁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢀⣺⣿⠀⣿⣿⣿⣿⣦⣄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⢀ ⠀⣄⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣷⣄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣧⠀⠀⠀⠠⠴⠾⠿⠿⠀⣻⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣀⣀⣀⣀⣀⣀⠀⠀⠁⠀⠭ 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⠶⠄⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄ ⠀⣤⣤⡄⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣠⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⢐⠘⠛⠛⠒⠀⠘⠛⠛⠓⠒⠀⠀⠀⠀⠚⠛⠛⠛⠃⠀⠀⠀⠀⠀⡀⣒⡚⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠒⠒⠀⠚⠛⠛⠛⠀⡀⡀⠀⠀⠀⠀ ⢘⣛⣛⣓⣛⣛⣛⣓⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣶⣶⣶⣶⣶⣶⣲⣶⣶⣶⣶⣶⣶⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣟⣋⣽⣿⣿⣿⣿⣿⣿⣀⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡗⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀ ⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠗⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢠⣷⠀⣿⣿⣦⡀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠀⠀⠀⠀⠈⢿⡿⠀⠀⠀⠀ ⠀⠶⣤⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢀⣺⣿⠀⣿⣿⣿⣿⣦⣄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⢀ ⠀⣄⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣷⣄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣧⠀⠀⠀⠠⠤⠾⠿⠿⠀⣻⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣀⣀⣀⣀⣀⣀⠀⠀⠁⠀⠭ ⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠃⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⢸⡟⠀⠀⢀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⠿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⣤⣀⡄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⡇⠀⢠⡈⠉⠙⠛⠛⠛⢃⡽⢿⣿⣿⣿⣿⡋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢺⣿⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀ ⠀⣍⣩⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣦⡀⠀⠀⠀⠘⠀⠀⠙⠻⣿⡃⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀ ⠀⠤⠤⠤⠤⠤⠤⠤⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢠⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣼⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⡿⠛⠛⠛⠛⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶ ⠀⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠆⠶⠶⠦⠐⣉⡃⠀⠘⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢧⢨⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⢀⣀⣤⣶⣶⣶⣿⣋⣀⣀⣀⣀⡀⠀⢠⣤⣾⣿ ⠀⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣁⣯⣍⣩⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠒⠂⠀⠂⠀⠀⠀⠀⠀⢸⣿⣿⠛ ⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠠⡞⠁⠀⠀⠀⠀⠀⢸⠸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢯⡷⠀⠀⠺⠾⠶⠶⠂⠀⠀⠶⠶⠷⠖⢀⣀⢰⣶⣔⢤⣀⡀⣀⣴⣠⣤⢤⣀⣀⣀⡒⣠⣤⣀⣀⣀⢤⡦⣄⣤⣄⣚⣭⣅⣩⣩⣏⣔⡄⣤⣤⣤⡠⣤⣤⣴⣀⣀⣦⣤⣀⢀⢀⣀⣠⣶⣦⡀⣀⣀⣀⡠⣠⣆⣀⣀ ⠶⠄⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄ ⠀⣤⣤⡄⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣠⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⢐⠘⠛⠛⠒⠀⠘⠛⠛⠓⠒⠀⠀⠀⠀⠚⠛⠛⠛⠃⠀⠀⠀⠀⠀⡀⣒⡚⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠂⠒⠀⠚⠛⠛⠛⠀⡀⡀⠀⠀⠀⠀ ⢘⣛⣛⣓⣛⣛⣛⣓⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣶⣶⣶⣶⣶⣶⣲⣶⣶⣶⣶⣶⣶⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣟⣋⣽⣿⣿⣿⣿⣿⣿⣀⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡗⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀ ⢈⣹⣿⣛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠓⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢠⣷⠀⣿⣿⣦⡀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠀⠀⠀⠀⠈⢿⡧⠀⠀⠀⠀ ⠈⠽⣭⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢀⣺⣿⠀⣿⣿⣿⣿⣦⣄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⢀ ⠀⣄⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣷⣄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣧⠀⠀⠀⠠⠤⠾⠿⠿⠀⣻⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣀⣀⣀⣀⣀⣀⠀⠀⠁⠀⠡ ⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⢀⣀⢀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⢸⡟⠀⠀⢀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⠿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠈⣭⣉⡅⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⡇⠀⢠⡈⠉⠙⠛⠛⠛⢃⡹⢿⣿⣿⣿⣿⡋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢺⣿⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀ ⠀⣍⣩⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣦⡀⠀⠀⠀⠘⠀⠀⠙⠻⣿⡃⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀ ⠀⠤⠤⠤⠤⠤⠤⠤⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢠⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣼⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⡿⠛⠛⠛⠛⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶ ⠀⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠆⠶⠶⠦⠀⣉⡃⠀⠘⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢧⢨⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⢀⣀⣤⣴⣶⣶⣿⣋⣀⣄⣀⣀⡀⠀⢠⣤⣾⣿ ⠀⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣁⣯⣍⣩⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠒⠂⠀⠂⠀⠀⠀⠀⠀⢸⣿⣿⠛ ⠘⠛⠟⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠠⡞⠁⠀⠀⠀⠀⠀⢸⠸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠰⠖⠶⠶⠶⠆⠷⠶⠶⠶⠂⠀⠀⠀⠀⠀⠀⢀⢰⣶⣔⢤⣀⡀⣀⣴⣠⣤⢤⣀⣀⣀⡒⣠⣤⣀⣀⣀⢤⡦⣄⣤⣄⣚⣭⣥⣩⣩⣏⣔⡄⣤⣠⣤⡠⣤⣤⣴⣀⣀⣦⣤⣀⢀⢀⣀⣠⣶⣦⡀⣀⣀⣀⡠⣠⣆⣀⣀ ⠶⠄⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄ ⠀⣤⣤⡄⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣠⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⢐⠐⠛⠛⠒⠀⠐⠛⠛⠓⠂⠀⠀⠀⠀⠚⠛⠛⠛⠃⠀⠀⠀⠀⠀⡀⢒⡐⠛⠛⠓⠂⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠂⠐⠀⠚⠛⠛⠛⠀⡀⡀⠀⠀⠀⠀ ⢘⣛⣛⣓⣛⣛⣛⣓⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣶⣶⣶⣶⣶⣶⣲⣶⣶⣶⣶⣶⣶⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣟⣋⣽⣿⣿⣿⣿⣿⣿⣀⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀ ⢈⣹⣿⣛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠓⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢠⣷⠀⣿⣿⣦⡀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠀⠀⠀⠀⠈⢿⡇⠀⠀⠀⠀ ⠈⠽⣭⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢀⣺⣿⠀⣿⣿⣿⣿⣦⣄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀ ⠀⣄⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣷⣄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣧⠀⠀⠀⠠⠤⠾⠿⠿⠀⣻⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣀⣀⣀⣀⣀⣀⠀⠀⠁⠀⠁ ⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⢀⣀⢀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠸⡟⠀⠀⢀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⠿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠈⣭⣉⡅⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⡇⠀⢠⡈⠉⠙⠛⠛⠛⢃⡹⢿⣿⣿⣿⣿⡋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⣿⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀ ⠀⣍⣩⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣦⡀⠀⠀⠀⠘⠀⠀⠙⠻⣿⡃⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣹⣿⣀⠀⠀⠂⠀⠀⠀⠀⠀⠀ ⠀⠤⠤⠤⠤⠤⠤⠤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢠⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣼⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⡿⠛⠛⠛⠛⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶ ⠀⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠆⠶⠶⠦⠀⣉⡃⠀⠘⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢇⢨⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⢀⣀⣤⣴⣶⣦⣿⣋⣀⣄⣀⣀⡀⠀⢀⣤⣾⣿ ⠀⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣁⣭⣍⣩⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠒⠂⠀⠂⠀⠀⠀⠀⠀⢸⣿⣿⠛ ⠘⠛⠟⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠠⡞⠁⠀⠀⠀⠀⠀⢸⠸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⣤⣤⣴⢤⠆⠷⠶⠶⠶⠂⠀⠀⠀⠀⠀⠀⢀⢰⣶⣔⢤⣀⡀⣀⣴⣠⣤⢤⣀⣀⣀⡒⣠⣤⣀⣀⣀⢤⡦⣄⣤⣄⣚⣬⣥⣉⣩⣏⣔⡄⣤⣠⣤⡠⣤⣤⣴⣀⣀⣦⣤⣀⢀⢀⣀⣠⣶⣦⡀⣀⣀⣀⡀⣠⣆⣀⣀ ⠶⠄⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄ ⠀⣤⣤⡄⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣠⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⢐⠐⠛⠛⠒⠀⠐⠛⠛⠓⠒⠀⠀⠀⠀⠚⠛⠛⠛⠃⠀⠀⠀⠀⠀⡀⢒⡐⠛⠛⠓⠂⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠂⠒⠀⠚⠛⠛⠛⠀⡀⡀⠀⠀⠀⠀ ⢘⣛⣛⣓⣛⣛⣛⣓⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣶⣶⣶⣶⣶⣶⣲⣶⣶⣶⣶⣶⣶⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣟⣋⣽⣿⣿⣿⣿⣿⣿⣀⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀ ⢈⣹⣿⣛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠓⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢠⣷⠀⣿⣿⣦⡀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠀⠀⠀⠀⠈⢿⡇⠀⠀⠀⠀ ⠈⠽⣭⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢀⣺⣿⠀⣿⣿⣿⣿⣦⣄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀ ⠀⣄⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣷⣄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣧⠀⠀⠀⠠⠤⠾⠿⠿⠀⣻⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣀⣀⣀⣀⣀⣀⠀⠀⠁⠀⠡ ⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⢀⣀⢀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⢸⡟⠀⠀⢀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⠿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠈⣭⣉⡅⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⡇⠀⢠⡈⠉⠙⠛⠛⠛⢃⡹⢿⣿⣿⣿⣿⡋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⣿⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀ ⠀⣍⣩⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣦⡀⠀⠀⠀⠘⠀⠀⠙⠻⣿⡃⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣹⣿⣀⠀⠀⠂⠀⠀⠀⠀⠀⠀ ⠀⠤⠤⠤⠤⠤⠤⠤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢠⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣼⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⡿⠛⠛⠛⠛⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶ ⠀⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠆⠶⠶⠦⠀⣉⡃⠀⠘⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢇⢨⣿⣿⣿⣿⣿⢿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⢀⣀⣤⣴⣶⣦⣿⣋⣀⣄⣀⣀⡀⠀⢀⣤⣾⣿ ⠀⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣁⣭⣍⣩⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠒⠂⠀⠂⠀⠀⠀⠀⠀⢸⣿⣿⠛ ⠘⠛⠟⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠠⡞⠁⠀⠀⠀⠀⠀⢸⠸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⣤⣤⣴⢤⠆⠷⠶⠶⠶⠂⠀⠀⠀⠀⠀⠀⢀⢰⣶⣔⢤⣀⡀⣀⣴⣠⣤⢤⣀⣀⣀⡒⣠⣤⣀⣀⣀⢤⡦⣄⣤⣄⣚⣬⣥⣉⣩⣏⣔⡄⣤⣠⣤⡠⣤⣤⣴⣀⣀⣦⣤⣀⢀⢀⣀⣠⣶⣦⡀⣀⣀⣀⡀⣠⣆⣀⣀ ⠶⠄⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄ ⠀⣤⣤⡄⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣠⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⢐⠐⠛⠛⠒⠀⠐⠛⠛⠓⠒⠀⠀⠀⠀⠚⠛⠛⠛⠃⠀⠀⠀⠀⠀⡀⢒⡐⠛⠛⠓⠂⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠂⠒⠀⠚⠛⠛⠛⠀⡀⡀⠀⠀⠀⠀ ⢘⣛⣛⣓⣛⣛⣛⣓⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣶⣶⣶⣶⣶⣶⣲⣶⣶⣶⣶⣶⣶⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣟⣋⣽⣿⣿⣿⣿⣿⣿⣀⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀ ⢈⣹⣿⣛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠓⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢠⣷⠀⣿⣿⣦⡀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠀⠀⠀⠀⠈⢿⡇⠀⠀⠀⠀ ⠈⠽⣭⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢀⣺⣿⠀⣿⣿⣿⣿⣦⣄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀ ⠀⣄⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣷⣄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣧⠀⠀⠀⠠⠤⠾⠿⠿⠀⣻⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣀⣀⣀⣀⣀⣀⠀⠀⠁⠀⠡ ⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⢀⣀⢀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⢸⡟⠀⠀⢀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⠿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠈⣭⣉⡅⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⡇⠀⢠⡈⠉⠙⠛⠛⠛⢃⡹⢿⣿⣿⣿⣿⡋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⣿⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀ ⠀⣍⣩⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣦⡀⠀⠀⠀⠘⠀⠀⠙⠻⣿⡃⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣹⣿⣀⠀⠀⠂⠀⠀⠀⠀⠀⠀ ⠀⠤⠤⠤⠤⠤⠤⠤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢠⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣼⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⡿⠛⠛⠛⠛⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶ ⠀⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠆⠶⠶⠦⠀⣉⡃⠀⠘⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢇⢨⣿⣿⣿⣿⣿⢿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⢀⣀⣤⣴⣶⣦⣿⣋⣀⣄⣀⣀⡀⠀⢀⣤⣾⣿ ⠀⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣁⣭⣍⣩⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠒⠂⠀⠂⠀⠀⠀⠀⠀⢸⣿⣿⠛ ⠘⠛⠟⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠠⡞⠁⠀⠀⠀⠀⠀⢸⠸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⣤⣤⣴⢤⠆⠷⠶⠶⠶⠂⠀⠀⠀⠀⠀⠀⢀⢰⣶⣔⢤⣀⡀⣀⣴⣠⣤⢤⣀⣀⣀⡒⣠⣤⣀⣀⣀⢤⡦⣄⣤⣄⣚⣬⣥⣉⣩⣏⣔⡄⣤⣠⣤⡠⣤⣤⣴⣀⣀⣦⣤⣀⢀⢀⣀⣠⣶⣦⡀⣀⣀⣀⡀⣠⣆⣀⣀ ⠶⠄⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄ ⠀⣤⣤⡄⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣠⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⢐⠐⠛⠛⠒⠀⠐⠛⠛⠓⠂⠀⠀⠀⠀⠚⠛⠛⠛⠃⠀⠀⠀⠀⠀⡀⢒⡐⠛⠛⠓⠂⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠂⠐⠀⠚⠛⠛⠛⠀⡀⡀⠀⠀⠀⠀ ⢘⣛⣛⣓⣛⣛⣛⣓⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣶⣶⣶⣶⣶⣶⣲⣶⣶⣶⣶⣶⣶⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣟⣋⣽⣿⣿⣿⣿⣿⣿⣀⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀ ⢈⣹⣿⣛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠓⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢠⣷⠀⣿⣿⣦⡀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠀⠀⠀⠀⠈⢿⡇⠀⠀⠀⠀ ⠈⠽⣭⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣸⣿⠀⣿⣿⣿⣿⣦⣄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀ ⠀⣄⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢨⣿⣿⠠⣿⣿⣿⣿⣿⣿⣷⣄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣧⠀⠀⠀⠠⠤⠾⠿⠿⠀⣻⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣀⣀⣀⣀⣀⣀⠀⠀⠁⠀⠁ ⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣸⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀ ⢀⣀⢀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠠⡟⠀⠀⠀⢀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⠿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠈⣭⣉⡅⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⡇⠀⢠⡀⠈⠉⠛⠛⠛⢃⡹⢿⣿⣿⣿⣿⡋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⣿⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀ ⠀⣍⣩⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣦⡀⠀⠀⠀⠘⠀⠀⠉⠻⣿⡃⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣹⣿⣀⠀⠀⠂⠀⠀⠀⠀⠀⠀ ⠀⠤⠤⠤⠤⠤⠤⠤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢠⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣼⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⡿⠛⢛⢻⣿⠟⣿⣿⠿⠛⠓⠀⠀⠀⠀⠀⢠⣶ ⠀⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠆⠲⠶⠦⠀⣉⡃⠀⠘⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢇⢨⣿⣿⣿⣿⣿⢿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⢀⣀⣼⣷⣶⣦⣿⣋⣀⣄⣀⣀⡀⠀⢀⣤⣾⣿ ⠀⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣁⣭⣍⣩⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠒⠂⠀⠂⠀⠀⠀⠀⠀⢸⣿⣿⠛ ⠘⠛⠟⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⡞⠁⠀⠀⠀⠀⠀⢸⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⣤⣤⣴⢤⠆⠷⠶⠶⠶⠂⠀⠀⠀⠀⠀⠀⢀⢰⣶⣔⢤⣀⡀⣀⣴⣠⣤⢤⣀⣀⣀⡒⣠⣤⣀⣀⣀⢤⡦⣄⣤⣄⣒⣬⣥⣉⣩⣏⣄⡄⣠⣠⣤⡠⣤⣤⣴⣀⣀⣦⣠⣀⢀⢀⣀⣠⣶⣦⡀⣀⣀⣀⡀⣠⣆⣀⣀ ⠶⠄⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄ ⠀⣤⣤⡄⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣠⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⢐⠐⠛⠛⠒⠀⠐⠛⠛⠓⠂⠀⠀⠀⠀⠚⠛⠛⠛⠃⠀⠀⠀⠀⠀⡀⢒⡐⠛⠛⠓⠂⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠂⠐⠀⠘⠛⠛⠛⠀⡀⡀⠀⠀⠀⠀ ⢘⣛⣛⣓⣛⣛⣛⣓⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣶⣶⣶⣶⣶⣶⣲⣶⣶⣶⣶⣶⣶⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣟⣋⣽⣿⣿⣿⣿⣿⣿⣀⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀ ⢈⣹⣿⣛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠓⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢠⣷⠀⣿⣿⣦⡀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠀⠀⠀⠀⠈⢿⡇⠀⠀⠀⠀ ⠈⠽⣭⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣸⣿⠀⣿⣿⣿⣿⣦⣄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀ ⠀⣄⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢨⣿⣿⠠⣿⣿⣿⣿⣿⣿⣷⣄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣧⠀⠀⠀⠠⠤⠾⠿⠿⠀⣻⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣀⣀⣀⣀⣀⣀⠀⠀⠁⠀⠁ ⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣸⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀ ⢀⣀⢀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠠⡟⠀⠀⠀⢀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⠿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠈⣭⣉⡅⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⡇⠀⢠⡀⠈⠉⠛⠛⠛⢃⡹⢿⣿⣿⣿⣿⡋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⣿⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀ ⠀⣍⣩⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣦⡀⠀⠀⠀⠘⠀⠀⠉⠻⣿⡃⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣹⣿⣀⠀⠀⠂⠀⠀⠀⠀⠀⠀ ⠀⠤⠤⠤⠤⠤⠤⠤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢠⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣼⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⡿⠛⢛⢻⣿⠟⣿⣿⠿⠛⠓⠀⠀⠀⠀⠀⢠⣶ ⠀⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠲⠶⠦⠀⣉⡃⠀⠘⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢇⢨⣿⣿⣿⣿⣿⢿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠘⢩⣄⣀⣼⣷⣶⣦⣿⣋⣀⣄⣀⣀⡀⠀⢀⣤⣾⣿ ⠀⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣁⣭⣍⣩⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠒⠂⠀⠂⠀⠀⠀⠀⠀⢸⣿⣿⠛ ⠘⠛⠟⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⡞⠁⠀⠀⠀⠀⠀⢸⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⣤⣤⣴⢤⠆⠷⠶⠶⠶⠂⠀⠀⠀⠀⠀⠀⢀⢰⣶⣔⢤⣀⡀⣀⣴⣠⣤⢤⣀⣀⣀⡒⣠⣤⣀⣀⣀⢤⡦⣄⣤⣄⣒⣬⣥⣉⣩⣏⣄⡄⣠⣠⣤⡠⣤⣤⣴⣀⣀⣦⣠⣀⢀⢀⣀⣠⣶⣦⡀⣀⣀⣀⡀⣠⣆⣀⣀ ⠶⠄⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄ ⠀⣤⣤⡄⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣠⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⢐⠐⠛⠛⠒⠀⠐⠛⠛⠓⠂⠀⠀⠀⠀⠚⠛⠛⠛⠃⠀⠀⠀⠀⠀⡀⢒⡐⠛⠛⠓⠂⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠂⠐⠀⠘⠛⠛⠛⠀⡀⡀⠀⠀⠀⠀ ⢘⣛⣛⣓⣛⣛⣛⣓⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣶⣶⣶⣶⣶⣶⣲⣶⣶⣶⣶⣶⣶⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣟⣋⣽⣿⣿⣿⣿⣿⣿⣀⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀ ⢈⣹⣿⣛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠓⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢠⣷⠀⣿⣿⣦⡀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠀⠀⠀⠀⠈⢿⡇⠀⠀⠀⠀ ⠈⠽⣭⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣸⣿⠀⣿⣿⣿⣿⣦⣄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀ ⠀⣄⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢨⣿⣿⠠⣿⣿⣿⣿⣿⣿⣷⣄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣧⠀⠀⠀⠠⠤⠾⠿⠿⠀⣻⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣀⣀⣀⣀⣀⣀⠀⠀⠁⠀⠁ 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⠶⠄⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄ ⠀⣤⣤⡄⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣠⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⢐⠐⠛⠛⠒⠀⠐⠛⠛⠓⠂⠀⠀⠀⠀⠚⠛⠛⠛⠃⠀⠀⠀⠀⠀⡀⢒⡐⠛⠛⠓⠂⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠂⠐⠀⠘⠛⠛⠛⠀⡀⡀⠀⠀⠀⠀ ⢘⣛⣛⣓⣛⣛⣛⣓⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣶⣶⣶⣶⣶⣶⣲⣶⣶⣶⣶⣶⣶⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣟⣋⣽⣿⣿⣿⣿⣿⣿⣀⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀ ⢈⣹⣿⣛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠓⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢠⣷⠀⣿⣿⣦⡀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠀⠀⠀⠀⠈⢿⡇⠀⠀⠀⠀ ⠈⠽⣭⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣸⣿⠀⣿⣿⣿⣿⣦⣄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀ ⠀⣄⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢨⣿⣿⠠⣿⣿⣿⣿⣿⣿⣷⣄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣧⠀⠀⠀⠠⠤⠾⠿⠿⠀⣻⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣀⣀⣀⣀⣀⣀⠀⠀⠁⠀⠁ ⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣸⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀ ⢀⣀⢀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠠⡟⠀⠀⠀⢀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⠿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠈⣭⣉⡅⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⡇⠀⢠⡀⠈⠉⠛⠛⠛⢃⡹⢿⣿⣿⣿⣿⡋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⣿⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀ ⠀⣍⣩⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣦⡀⠀⠀⠀⠘⠀⠀⠉⠻⣿⡃⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣹⣿⣀⠀⠀⠂⠀⠀⠀⠀⠀⠀ ⠀⠤⠤⠤⠤⠤⠤⠤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢠⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣼⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⡿⠛⢛⢻⣿⠟⣿⣿⠿⠛⠓⠀⠀⠀⠀⠀⢠⣶ ⠀⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠲⠶⠦⠀⣉⡃⠀⠘⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢇⢨⣿⣿⣿⣿⣿⢿⣿⡅⠀⠀⠀⠿⠀⠀⠀⠀⠘⢩⣄⣀⣼⣷⣶⣦⣿⣋⣀⣄⣀⣀⡀⠀⢀⣤⢾⣿ ⠀⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣁⣭⣍⣩⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠒⠂⠀⠂⠀⠀⠀⠀⠀⢸⣿⣿⠛ ⠘⠛⠟⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⡞⠁⠀⠀⠀⠀⠀⢸⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⣤⣤⣴⢤⠆⠷⠶⠶⠶⠂⠀⠀⠀⠀⠀⠀⢀⢰⣶⣔⢤⣀⡀⣀⣴⣠⣤⢤⣀⣀⣀⡒⣠⣤⣀⣀⣀⢤⡦⣄⣤⣄⣒⣬⣡⣉⣩⣏⣀⡄⣠⣠⣤⡠⣤⣤⣴⣀⣀⣦⣠⣀⢀⢀⣀⣠⣶⣦⡀⣀⣀⣀⡀⣠⣆⣀⣀ ⠶⠄⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄ ⠀⣤⣤⡄⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣠⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⢐⠐⠛⠛⠒⠀⠐⠛⠛⠓⠂⠀⠀⠀⠀⠚⠛⠛⠛⠃⠀⠀⠀⠀⠀⡀⢒⡐⠛⠛⠓⠂⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠂⠐⠀⠘⠛⠛⠛⠀⡀⡀⠀⠀⠀⠀ ⢘⣛⣛⣓⣛⣛⣛⣓⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣶⣶⣶⣶⣶⣶⣲⣶⣶⣶⣶⣶⣶⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣟⣋⣽⣿⣿⣿⣿⣿⣿⣀⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀ ⢈⣹⣿⣛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠓⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢠⣷⠀⣿⣿⣦⡀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠀⠀⠀⠀⠈⢿⡇⠀⠀⠀⠀ ⠈⠽⣭⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣸⣿⠀⣿⣿⣿⣿⣦⣄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀ ⠀⣄⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢨⣿⣿⠠⣿⣿⣿⣿⣿⣿⣷⣄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣧⠀⠀⠀⠠⠤⠾⠿⠿⠀⣻⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣀⣀⣀⣀⣀⣀⠀⠀⠁⠀⠁ ⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣸⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀ ⢀⣀⢀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠠⡟⠀⠀⠀⢀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⠿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠈⣭⣉⡅⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⡇⠀⢠⡀⠈⠉⠛⠛⠛⢃⡹⢿⣿⣿⣿⣿⡋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⣿⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀ ⠀⣍⣩⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣦⡀⠀⠀⠀⠘⠀⠀⠉⠻⣿⡃⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣹⣿⣀⠀⠀⠂⠀⠀⡀⠀⠀⠀ ⠀⠤⠤⠤⠤⠤⠤⠤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢠⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣼⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⡿⠛⢛⢻⣿⠟⣿⣿⠿⠛⠓⠀⠀⠀⠀⠀⢠⣶ ⠀⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠲⠶⠦⠀⣉⡃⠀⠘⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢇⢨⣿⣿⣿⣿⣿⢿⣿⡅⠀⠀⠀⠿⠀⠀⠀⠀⠘⢩⣄⣀⣼⣷⣶⣦⣿⣋⣀⣄⣀⣀⡀⠀⢀⣤⢾⢿ ⠀⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣁⣭⣍⣩⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⢴⣿⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠒⠂⠀⠂⠀⠀⠀⠀⠀⢸⣿⣿⠛ ⠘⠛⠟⠛⠂⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⡞⠁⠀⠀⠀⠀⠀⢸⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⣤⣤⣴⢤⠆⠦⠶⠶⠶⠂⠀⠀⠀⠀⠀⠀⢀⢰⣶⣔⢤⣀⡀⣀⣴⣠⣤⢤⣀⣀⣀⡒⣠⣤⣀⣀⣀⢤⡦⣄⣤⣄⣒⣬⣡⣉⣩⣏⣀⡄⣠⣠⣤⡠⣤⣤⣴⣀⣀⣦⣠⣀⢀⢀⣀⣠⣶⣦⡀⣀⣀⣀⡀⣠⣆⣀⣀ ⠶⠄⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄ ⠀⣤⣤⡄⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣠⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⢐⠐⠛⠛⠒⠀⠐⠛⠛⠓⠂⠀⠀⠀⠀⠚⠛⠛⠛⠃⠀⠀⠀⠀⠀⡀⢒⡐⠛⠛⠓⠂⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠂⠐⠀⠘⠛⠛⠛⠀⡀⡀⠀⠀⠀⠀ ⢘⣛⣛⣓⣛⣛⣛⣓⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣶⣶⣶⣶⣶⣶⣲⣶⣶⣶⣶⣶⣶⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣟⣋⣽⣿⣿⣿⣿⣿⣿⣀⡄⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀ ⢈⣹⣿⣛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠓⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢠⣷⠀⣿⣿⣦⡀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠀⠀⠀⠀⠈⢿⡇⠀⠀⠀⠀ ⠈⠽⣭⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣸⣿⠀⣿⣿⣿⣿⣦⣄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀ ⠀⣄⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢨⣿⣿⠠⣿⣿⣿⣿⣿⣿⣷⣄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣧⠀⠀⠀⠠⠤⠾⠿⠿⠀⣻⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣀⣀⣀⣀⣀⣀⠀⠀⠁⠀⠁ ⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣸⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀ ⢀⣀⢀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠠⡟⠀⠀⠀⢀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⠿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡀ ⠈⣭⣉⡅⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⡇⠀⢠⡀⠈⠉⠛⠛⠓⢃⡹⢿⣿⣿⣿⣿⡋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⣿⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀ ⠀⣍⣩⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣦⡀⠀⠀⠀⠘⠀⠀⠉⠻⣿⡃⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣹⣿⣀⠀⠀⠂⠀⠀⡀⠀⠀⠀ ⠀⠤⠤⠤⠤⠤⠤⠤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢠⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣼⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⡿⠛⢛⢻⣿⠟⣿⣿⠿⠛⠓⠀⠀⠀⠀⠀⢠⣶ ⠀⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠲⠶⠦⠀⣉⡃⠀⠘⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢇⢨⣿⣿⣿⣿⣿⢿⣿⡅⠀⠀⠀⠿⠀⠀⠀⠀⠘⢩⣄⣀⣼⣷⣶⣦⣿⣋⣀⣄⢀⣀⡀⠀⢀⣤⢾⢿ ⠀⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣁⣭⣍⣩⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⢴⣿⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠒⠂⠀⠂⠀⠀⠀⠀⠀⢸⣿⣿⠛ ⠘⠛⠟⠛⠂⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⡞⠁⠀⠀⠀⠀⠀⢸⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⣤⣤⣴⢤⠆⠦⠶⠶⠶⠂⠀⠀⠀⠀⠀⠀⢀⢰⣶⣔⢤⣀⡀⣀⣴⣠⣤⢤⣀⣀⣀⡒⣠⣤⣀⣀⣀⢤⡦⣄⣤⣄⣒⣬⣡⣉⣩⣏⣀⡄⣠⣠⣤⡠⣤⣤⣴⣀⣀⣦⣠⣀⢀⢀⣀⣠⣶⣦⡀⣀⣀⣀⡀⣠⣆⣀⣀ ⠶⠄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠦⠠⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄ ⠀⣄⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠠⠄⠀⠠⠠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⢐⠐⠛⠛⠒⠀⠐⠛⠛⠓⠀⠀⠀⠀⠀⠚⠛⠛⠛⠃⠀⠀⠀⠀⠂⡒⣤⡴⢿⠿⠳⠦⠤⠤⠤⠠⠠⠤⡜⠿⠿⠛⠂⠀⠀⠘⠛⠛⠛⠐⠀⡀⠀⠀⠀⠀ ⠸⢿⡷⡷⣟⣛⣛⣓⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣶⣾⣶⣶⣶⣲⣲⣶⣶⣶⣶⣶⣶⣰⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢘⣿⣿⣿⣿⣿⣿⣟⣃⣽⣿⣿⣿⣿⣿⣇⣀⡄⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡖⠒⠒⠒⠒⠒⠰⠚⠘⠻⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⢿⡟⠀⠀⠀⠀⠀⢐⣾⣿⠀⠀⠀⠀ ⠈⣹⣿⣛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠟⠓⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⡐⢠⡀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇⠐⠀⠀⠀⠀⠈⢨⡇⠀⠀⠀⠀ ⠀⠽⣭⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢠⣿⡂⠀⠀⠀⠀⠀⠀⣲⢀⢀⣿⣿⣿⣿⣦⣌⣄⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀ ⠀⣄⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡂⠀⠀⠀⠀⠀⢨⣫⢲⠩⣿⣿⣿⣿⣿⣿⣿⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣅⠀⠀⠀⠀⠤⠾⠿⠘⠀⣻⣿⣿⣿⣿⣿⣿⣿⢈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢀⣀⣀⣀⣀⠀⣀⠀⠀⠁⠀⠁ ⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠌⣸⣿⣿⣿⣿⣿⣿⢻⣿⣾⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣆⢩⠀⠀⠀⠀⠀ ⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢹⣨⠀⠀⢀⠀⠀⠀⠀⢠⢾⣿⣿⣿⣿⣿⣿⡞⣿⣲⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣫⣩⡿⢿⣿⣿⠟⢸⡆⠀⠀⠀⠀ ⢀⣀⢂⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⢐⣽⠘⢠⠀⠀⢀⣀⡀⢀⠈⢸⣿⣿⣿⣿⣿⣿⣿⠿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣽⣿⣿⣿⣑⣶⣿⡇⠀⠀⠀⡀ ⠀⣭⣉⡍⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣼⡄⢨⣠⡀⠀⠉⠛⠋⠐⠃⡹⢿⣿⣿⣿⣝⣇⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣟⣛⣻⣿⣿⣿⣿⣿⣿⣛⣼⣿⣥⣼⣿⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀ ⢀⣍⣩⣁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⣛⠃⠀⢺⣿⡆⠀⠀⠀⠀⠈⠀⠀⠈⢡⡩⡳⣅⢹⠿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣹⣿⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀ ⠀⠤⠤⠤⠤⠤⠥⠤⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡂⠀⢸⣿⣶⠃⠀⠀⠀⠀⠀⢀⠐⠉⠈⠻⣛⠀⠐⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢠⣼⣿⣿⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠨⢢⣼⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿⡿⠛⢛⠻⠿⠟⣿⣿⠿⠛⠓⠀⠀⠀⠀⠀⢠⣶ ⠀⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠲⠶⠦⠀⣉⡃⠀⠘⠻⣏⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣠⠀⢉⢨⣿⣿⣿⣿⣿⢿⣿⡅⠀⠀⠀⠛⠀⠀⠀⠀⠈⢩⣄⣀⣈⣧⡄⣢⣿⣋⣀⣄⢀⣀⡀⠀⢀⣤⢾⢿ ⠀⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣍⣅⣉⣍⣭⣉⡀⠈⢁⣬⡍⣤⣅⣀⠀⠀⠀⠀⠀⠁⣠⠞⠉⠈⢹⢸⣿⣿⣿⣿⣿⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠙⠛⠛⠛⠁⠉⠉⠉⠉⠉⠁⠉⠁⠈⢴⣿⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⡀⠀⠀⠒⠂⠀⡂⠀⠀⠀⠀⠀⢸⣿⣿⠛ ⠘⠛⠟⠛⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠁⠀⠀⠀⣀⣀⣸⣸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀ ⠰⣯⣷⣴⢤⠖⠶⠶⠶⠶⠂⠀⠐⠲⠒⠂⠀⢀⢰⣶⣖⢶⣂⡀⣀⣶⣲⣶⢶⣆⣀⣀⡒⣠⣤⣀⣀⣠⣿⣿⣿⣶⣶⣻⣬⣡⣻⣻⣯⣄⡀⣠⣠⣴⡲⣦⣤⣴⣀⣀⣶⣶⣶⢀⢀⣀⣠⣶⣶⡀⣀⣀⣀⡀⣰⣆⣀⣀ ⠶⠄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠦⠠⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄ ⠀⣄⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠠⠄⠀⠠⠠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⢐⠐⠛⠛⠒⠀⠐⠛⠛⠓⠀⠀⠀⠀⠀⠚⠛⠛⠛⠃⠀⠀⠀⠀⠂⡒⣤⡴⢿⠿⠳⠦⠤⠤⠤⠠⠠⠤⡜⠿⠿⠛⠂⠀⠀⠘⠛⠛⠛⠐⠀⡀⠀⠀⠀⠀ ⠸⢿⡷⡷⣟⣛⣛⣓⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣶⣾⣶⣶⣶⣲⣲⣶⣶⣶⣶⣶⣶⣰⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢘⣿⣿⣿⣿⣿⣿⣟⣃⣽⣿⣿⣿⣿⣿⣇⣀⡄⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠐⠒⠒⠒⠒⠰⠚⠘⠻⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⢿⡟⠀⠀⠀⠀⠀⢐⣾⣿⠀⠀⠀⠀ ⠈⣹⣿⣛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠟⠓⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⡐⢠⡀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇⠐⠀⠀⠀⠀⠈⢨⡇⠀⠀⠀⠀ ⠀⠽⣭⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢠⣿⡂⠀⠀⠀⠀⠀⠀⣲⢀⢀⣿⣿⣿⣿⣦⣌⣄⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀ ⠀⣄⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡂⠀⠀⠀⠀⠀⢨⣫⢲⠩⣿⣿⣿⣿⣿⣿⣿⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣅⠀⠀⠀⠀⠤⠾⠿⠘⠀⣻⣿⣿⣿⣿⣿⣿⣿⢈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢀⣀⣀⣈⣃⠀⣀⠀⠀⠁⠀⠁ ⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠌⣸⣿⣿⣿⣿⣿⣿⢻⣿⣾⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣆⢩⠀⠀⠀⠀⠀ ⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢹⣨⠀⠀⢀⠀⠀⠀⠀⢠⢾⣿⣿⣿⣿⣿⣿⡞⣿⣲⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣫⣩⡿⢿⣿⣿⠟⢸⡆⠀⠀⠀⠀ ⢀⣀⢂⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⢐⣽⠘⢠⠀⠀⢀⣀⡀⢀⠈⢸⣿⣿⣿⣿⣿⣿⣿⠿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣽⣿⣿⣿⣑⣶⣿⡇⠀⠀⠀⡀ ⠀⣭⣉⡍⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣼⡄⢨⣠⡀⠀⠉⠛⠋⠐⠃⡹⢿⣿⣿⣿⣝⣇⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣟⣛⣻⣿⣿⣿⣿⣿⣿⣛⣼⣿⣥⣼⣿⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀ ⢀⣍⣩⣁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⣛⠃⠀⢺⣿⡆⠀⠀⠀⠀⠈⠀⠀⠈⢡⡩⡳⣅⢹⠿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣹⣿⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀ ⠀⠤⠤⠤⠤⠤⠥⠤⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡂⠀⢸⣿⣶⠃⠀⠀⠀⠀⠀⢀⠐⠉⠈⠻⣛⠀⠐⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢠⣼⣿⣿⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠨⢢⣼⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿⡿⠛⢛⠻⠿⠟⣿⣿⠿⠛⠓⠀⠀⠀⠀⠀⢠⣶ ⠀⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠲⠶⠦⠀⣉⡃⠀⠘⠻⣏⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣠⠀⢉⢨⣿⣿⣿⣿⣿⢿⣿⡅⠀⠀⠀⠛⠀⠀⠀⠀⠈⢩⣄⣀⣈⣧⡄⣢⣿⣋⣀⣄⢀⣀⡀⠀⢀⣤⢾⢿ ⠀⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣍⣅⣉⣍⣭⣉⡀⠈⢁⣬⡍⣤⣅⣀⠀⠀⠀⠀⠀⠁⣠⠞⠉⠈⢹⢸⣿⣿⣿⣿⣿⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠙⠛⠛⠛⠁⠉⠉⠉⠉⠉⠁⠉⠁⠈⢴⣿⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⡀⠀⠀⠒⠂⠀⡂⠀⠀⠀⠀⠀⢸⣿⣿⠛ ⠘⠛⠟⠛⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠁⠀⠀⠀⣀⣀⣸⣸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀ ⠰⣯⣷⣴⢤⠖⠶⠶⠶⠶⠂⠀⠐⠲⠒⠂⠀⢀⢰⣶⣖⢶⣂⡀⣀⣶⣲⣶⢶⣆⣀⣀⡒⣠⣤⣀⣀⣠⣿⣿⣿⣶⣶⣻⣬⣡⣻⣻⣯⣄⡀⣠⣠⣴⡲⣦⣤⣴⣀⣀⣶⣶⣶⢀⢀⣀⣠⣶⣶⡀⣀⣀⣀⡀⣰⣆⣀⣀ ⠶⠄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠦⠠⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄ ⠀⣄⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠠⠄⠀⠠⠠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⢐⠐⠛⠛⠒⠀⠐⠛⠛⠓⠀⠀⠀⠀⠀⠚⠛⠛⠛⠃⠀⠀⠀⠀⠂⡒⣤⡴⢿⠿⠳⠦⠤⠤⠤⠠⠠⠤⡜⠿⠿⠛⠂⠀⠀⠘⠛⠛⠛⠐⠀⡀⠀⠀⠀⠀ ⠸⢿⡷⡷⣟⣛⣛⣓⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣶⣾⣶⣶⣶⣲⣲⣶⣶⣶⣶⣶⣶⣰⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢘⣿⣿⣿⣿⣿⣿⣟⣃⣽⣿⣿⣿⣿⣿⡇⣀⡄⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠐⠒⠒⠒⠒⠰⠚⠘⠻⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⢿⡟⠀⠀⠀⠀⠀⢐⣾⣿⠀⠀⠀⠀ ⠈⣹⣿⣛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠟⠓⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⡐⢠⡀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇⠐⠀⠀⠀⠀⠈⢨⡇⠀⠀⠀⠀ ⠀⠽⣭⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢠⣿⡂⠀⠀⠀⠀⠀⠀⣲⢀⢀⣿⣿⣿⣿⣦⣌⣄⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀ ⠀⣄⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡂⠀⠀⠀⠀⠀⢨⣫⢲⠩⣿⣿⣿⣿⣿⣿⣿⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣅⠀⠀⠀⠀⠤⠾⠿⠘⠀⣻⣿⣿⣿⣿⣿⣿⣿⢈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢀⣀⣀⣈⣃⡄⣀⠀⠀⠁⠀⠁ ⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠌⣸⣿⣿⣿⣿⣿⣿⢻⣿⣾⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣆⢩⠀⠀⠀⠀⠀ ⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢹⣨⠀⠀⢀⠀⠀⠀⠀⢠⢾⣿⣿⣿⣿⣿⣿⡞⣿⣲⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣫⣩⡿⢿⣿⣿⠟⢸⡆⠀⠀⠀⠀ ⢀⣀⢂⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⢐⣽⠘⢠⠀⠀⢀⣀⡀⢀⠈⢸⣿⣿⣿⣿⣿⣿⣿⠿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣽⣿⣿⣿⣑⣶⣿⡇⠀⠀⠀⡀ ⠀⣭⣉⡍⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣼⡄⢨⣠⡀⠀⠉⠛⠋⠐⠃⡹⢿⣿⣿⣿⣝⣇⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣟⣛⣻⣿⣿⣿⣿⣿⣿⣛⣼⣿⣥⣼⣿⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀ ⢀⣍⣩⣁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⣛⠃⠀⢺⣿⡆⠀⠀⠀⠀⠈⠀⠀⠈⢡⡩⡳⣅⢹⠿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣹⣿⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀ ⠀⠤⠤⠤⠤⠤⠥⠤⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡂⠀⢸⣿⣶⠃⠀⠀⠀⠀⠀⢀⠐⠉⠈⠻⣛⠀⠐⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢠⣼⣿⣿⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠨⢢⣼⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿⡿⠛⢛⠻⠿⠟⣿⣿⠿⠛⠓⠀⠀⠀⠀⠀⢠⣶ ⠀⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠲⠶⠦⠀⣉⡃⠀⠘⠻⣏⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣠⠀⢉⢨⣿⣿⣿⣿⣿⢿⣿⡅⠀⠀⠀⠛⠀⠀⠀⠀⠈⢩⣄⣀⣈⣧⡄⣢⣿⣋⣀⣄⢀⣀⡀⠀⢀⣤⢾⢿ ⠀⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣍⣅⣉⣍⣭⣉⡀⠈⢁⣬⡍⣤⣅⣀⠀⠀⠀⠀⠀⠁⣠⠞⠉⠈⢹⢸⣿⣿⣿⣿⣿⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠙⠛⠛⠛⠁⠉⠉⠉⠉⠉⠁⠉⠁⠈⢴⣿⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⡀⠀⠀⠒⠂⠀⡂⠀⠀⠀⠀⠀⢸⣿⣿⠛ ⠘⠛⠟⠛⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠁⠀⠀⠀⣀⣀⣸⣸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀ ⠰⣯⣷⣴⢤⠖⠶⠶⠶⠶⠂⠀⠐⠲⠒⠂⠀⢀⢰⣶⣖⢶⣂⡀⣀⣶⣲⣶⢶⣆⣀⣀⡒⣠⣤⣀⣀⣠⣿⣿⣿⣶⣶⣻⣬⣡⣻⣻⣯⣄⡀⣠⣠⣴⡲⣦⣤⣴⣀⣀⣶⣶⣶⢀⢀⣀⣠⣶⣶⡀⣀⣀⣀⡀⣰⣆⣀⣀ ⠶⠄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠦⠠⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄ ⠀⣄⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠠⠄⠀⠠⠠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⢐⠐⠛⠛⠒⠀⠐⠛⠛⠓⠀⠀⠀⠀⠀⠚⠛⠛⠛⠃⠀⠀⠀⠀⠂⡒⣤⡴⢿⠿⠳⠦⠤⠤⠤⠠⠠⠤⡜⠿⠿⠛⠂⠀⠀⠘⠛⠛⠛⠐⠀⡀⠀⠀⠀⠀ ⠸⢿⡷⡷⣟⣛⣛⣓⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣶⣾⣶⣶⣶⣲⣲⣶⣶⣶⣶⣶⣶⣰⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢘⣿⣿⣿⣿⣿⣿⣟⣃⣽⣿⣿⣿⣿⣿⡇⣀⡄⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠐⠒⠒⠒⠒⠰⠚⠘⠻⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⢿⡟⠀⠀⠀⠀⠀⢐⣾⣿⠀⠀⠀⠀ ⠈⣹⣿⣛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠟⠓⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⡐⢠⡀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇⠐⠀⠀⠀⠀⠈⢨⡇⠀⠀⠀⠀ ⠀⠽⣭⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢠⣿⡂⠀⠀⠀⠀⠀⠀⣲⢀⢀⣿⣿⣿⣿⣦⣌⣄⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀ ⠀⣄⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡂⠀⠀⠀⠀⠀⢨⣫⢲⠩⣿⣿⣿⣿⣿⣿⣿⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣅⠀⠀⠀⠀⠤⠾⠿⠘⠀⣻⣿⣿⣿⣿⣿⣿⣿⢈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢀⣀⣀⣈⣃⡄⣀⠀⠀⠁⠀⠁ ⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠌⣸⣿⣿⣿⣿⣿⣿⢻⣿⣾⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣆⢩⠀⠀⠀⠀⠀ ⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢹⣨⠀⠀⢀⠀⠀⠀⠀⢠⢾⣿⣿⣿⣿⣿⣿⡞⣿⣲⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣫⣩⡿⢿⣿⣿⠟⢸⡆⠀⠀⠀⠀ ⢀⣀⢂⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⢐⣽⠘⢠⠀⠀⢀⣀⡀⢀⠈⢸⣿⣿⣿⣿⣿⣿⣿⠿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣽⣿⣿⣿⣑⣶⣿⡇⠀⠀⠀⡀ ⠀⣭⣉⡍⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣼⡄⢨⣠⡀⠀⠉⠛⠋⠐⠃⡹⢿⣿⣿⣿⣝⣇⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣟⣛⣻⣿⣿⣿⣿⣿⣿⣛⣼⣿⣥⣼⣿⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀ ⢀⣍⣩⣁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⣛⠃⠀⢺⣿⡆⠀⠀⠀⠀⠈⠀⠀⠈⢡⡩⡳⣅⢹⠿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣹⣿⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀ ⠀⠤⠤⠤⠤⠤⠥⠤⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡂⠀⢸⣿⣶⠃⠀⠀⠀⠀⠀⢀⠐⠉⠈⠻⣛⠀⠐⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢠⣼⣿⣿⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠨⢢⣼⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿⡿⠛⢛⠻⠿⠟⣿⣿⠿⠛⠓⠀⠀⠀⠀⠀⢠⣶ ⠀⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠲⠶⠦⠀⣉⡃⠀⠘⠻⣏⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣠⠀⢉⢨⣿⣿⣿⣿⣿⢿⣿⡅⠀⠀⠀⠛⠀⠀⠀⠀⠈⢩⣄⣀⣈⣧⡄⣢⣿⣋⣀⣄⢀⣀⡀⠀⢀⣤⢾⢿ ⠀⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣍⣅⣉⣍⣭⣉⡀⠈⢁⣬⡍⣤⣅⣀⠀⠀⠀⠀⠀⠁⣠⠞⠉⠈⢹⢸⣿⣿⣿⣿⣿⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠙⠛⠛⠛⠁⠉⠉⠉⠉⠉⠁⠉⠁⠈⢴⣿⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⡀⠀⠀⠒⠂⠀⡂⠀⠀⠀⠀⠀⢸⣿⣿⠛ ⠘⠛⠟⠛⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠁⠀⠀⠀⣀⣀⣸⣸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀ ⠰⣯⣷⣴⢤⠖⠶⠶⠶⠶⠂⠀⠐⠲⠒⠂⠀⢀⢰⣶⣖⢶⣂⡀⣀⣶⣲⣶⢶⣆⣀⣀⡒⣠⣤⣀⣀⣠⣿⣿⣿⣶⣶⣻⣬⣡⣻⣻⣯⣄⡀⣠⣠⣴⡲⣦⣤⣴⣀⣀⣶⣶⣶⢀⢀⣀⣠⣶⣶⡀⣀⣀⣀⡀⣰⣆⣀⣀ ⠶⠄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠦⠠⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄ ⠀⣄⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠠⠄⠀⠠⠠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⢐⠐⠛⠛⠒⠀⠐⠛⠛⠓⠀⠀⠀⠀⠀⠚⠛⠛⠛⠃⠀⠀⠀⠀⠂⡒⣤⡴⢿⠿⠳⠦⠤⠤⠤⠠⠠⠤⡜⠿⠿⠛⠂⠀⠀⠘⠛⠛⠛⠐⠀⡀⠀⠀⠀⠀ ⠸⢿⡷⡷⣟⣛⣛⣓⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣶⣾⣶⣶⣶⣲⣲⣶⣶⣶⣶⣶⣶⣰⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢘⣿⣿⣿⣿⣿⣿⣟⣃⣽⣿⣿⣿⣿⣿⡇⣀⡄⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠐⠒⠒⠒⠒⠰⠚⠘⠻⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⢿⡟⠀⠀⠀⠀⠀⢐⣾⣿⠀⠀⠀⠀ ⠈⣹⣿⣛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠟⠓⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⡐⢠⡀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇⠐⠀⠀⠀⠀⠈⢨⡇⠀⠀⠀⠀ ⠀⠽⣭⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢠⣿⡂⠀⠀⠀⠀⠀⠀⣲⢀⢀⣿⣿⣿⣿⣦⣌⣄⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠃⠠⣤⠀⠀ ⠀⣄⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡂⠀⠀⠀⠀⠀⢨⣫⢲⠩⣿⣿⣿⣿⣿⣿⣿⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠈⠀⠀⢀⠀⠀⠀⠀⠀⠿⠀⠀ ⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣅⠀⠀⠀⠀⠤⠾⠿⠘⠀⣻⣿⣿⣿⣿⣿⣿⣿⢈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢀⣀⣀⣈⣃⡄⣀⠀⠀⠁⠀⠁ ⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠌⣸⣿⣿⣿⣿⣿⣿⢻⣿⣾⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣆⢩⠀⠀⠀⠀⠀ ⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢹⣨⠀⠀⢀⠀⠀⠀⠀⢠⢾⣿⣿⣿⣿⣿⣿⡞⣿⣲⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣫⣩⡿⢿⣿⣿⠟⢸⡆⠀⠀⠀⠀ ⢀⣀⢂⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⢐⣽⠘⢠⠀⠀⢀⣀⡀⢀⠈⢸⣿⣿⣿⣿⣿⣿⣿⠿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣽⣿⣿⣿⣑⣶⣿⡇⠀⠀⠀⡀ ⠀⣭⣉⡍⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣼⡄⢨⣠⡀⠀⠉⠛⠋⠐⠃⡹⢿⣿⣿⣿⣝⣇⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣟⣛⣻⣿⣿⣿⣿⣿⣿⣛⣼⣿⣥⣼⣿⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀ ⢀⣍⣩⣁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⣛⠃⠀⢺⣿⡆⠀⠀⠀⠀⠈⠀⠀⠈⢡⡩⡳⣅⢹⠿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣹⣿⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀ ⠀⠤⠤⠤⠤⠤⠥⠤⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡂⠀⢸⣿⣶⠃⠀⠀⠀⠀⠀⢀⠐⠉⠈⠻⣛⠀⠐⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢠⣼⣿⣿⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠨⢢⣼⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿⡿⠛⢛⠻⠿⠟⣿⣿⠿⠛⠓⠀⠀⠀⠀⠀⢠⣶ ⠀⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠲⠶⠦⠀⣉⡃⠀⠘⠻⣏⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣠⠀⢉⢨⣿⣿⣿⣿⣿⢿⣿⡅⠀⠀⠀⠛⠀⠀⠀⠀⠈⢩⣄⣀⣈⣧⡄⣢⣿⣋⣀⣄⢀⣀⡀⠀⢀⣤⢾⢿ ⠀⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣍⣅⣉⣍⣭⣉⡀⠈⢁⣬⡍⣤⣅⣀⠀⠀⠀⠀⠀⠁⣠⠞⠉⠈⢹⢸⣿⣿⣿⣿⣿⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠙⠛⠛⠛⠁⠉⠉⠉⠉⠉⠁⠉⠁⠈⢴⣿⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⡀⠀⠀⠒⠂⠀⡂⠀⠀⠀⠀⠀⢸⣿⣿⠛ ⠘⠛⠟⠛⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠁⠀⠀⠀⣀⣀⣸⣸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀ ⠰⣯⣷⣴⢤⠖⠶⠶⠶⠶⠂⠀⠐⠲⠒⠂⠀⢀⢰⣶⣖⢶⣂⡀⣀⣶⣲⣶⢶⣆⣀⣀⡒⣠⣤⣀⣀⣠⣿⣿⣿⣶⣶⣻⣬⣡⣻⣻⣯⣄⡀⣠⣠⣴⡲⣦⣤⣴⣀⣀⣶⣶⣶⢀⢀⣀⣠⣶⣶⡀⣀⣀⣀⡀⣰⣆⣀⣀ ⠶⠄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠦⠠⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄ ⠀⣄⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠠⠄⠀⠠⠠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⢐⠐⠛⠛⠒⠀⠐⠛⠛⠓⠀⠀⠀⠀⠀⠚⠛⠛⠛⠃⠀⠀⠀⠀⠂⡒⣤⡴⢿⠿⠳⠦⠤⠤⠤⠠⠠⠤⡜⠿⠿⠛⠂⠀⠀⠘⠛⠛⠛⠐⠀⡀⠀⠀⠀⠀ ⠸⢿⡷⡷⣟⣛⣛⣓⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣶⣾⣶⣶⣶⣲⣲⣶⣶⣶⣶⣶⣶⣰⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢘⣿⣿⣿⣿⣿⣿⣟⣃⣽⣿⣿⣿⣿⣿⡇⣀⡄⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠐⠒⠒⠒⠒⠰⠚⠘⠻⣟⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⢿⡟⠀⠀⠀⠀⠀⢐⣾⣿⠀⠀⠀⠀ ⠈⣹⣿⣛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠟⠓⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⡐⢠⡀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇⠐⠀⠀⠀⠀⠈⢨⡇⠀⠀⠀⠀ ⠀⠽⣭⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢠⣿⡂⠀⠀⠀⠀⠀⠀⣲⢀⢀⣿⣿⣿⣿⣦⣌⣄⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠃⠠⣤⠀⠀ ⠀⣄⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡂⠀⠀⠀⠀⠀⢨⣫⢲⠩⣿⣿⣿⣿⣿⣿⣿⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠈⠀⠀⢀⠀⠀⠀⠀⠀⠿⠀⠀ ⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣅⠀⠀⠀⠀⠤⠾⠿⠘⠀⣻⣿⣿⣿⣿⣿⣿⣿⢈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢀⣀⣀⣈⣃⡄⣀⠀⠀⠁⠀⠁ ⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠌⣸⣿⣿⣿⣿⣿⣿⢻⣿⣾⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣆⢩⠀⠀⠀⠀⠀ ⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢹⣨⠀⠀⢀⠀⠀⠀⠀⢠⢾⣿⣿⣿⣿⣿⣿⡞⣿⣲⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣫⣩⡿⢿⣿⣿⠟⢸⡆⠀⠀⠀⠀ ⢀⣀⢂⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⢐⣽⠘⢠⠀⠀⢀⣀⡀⢀⠈⢸⣿⣿⣿⣿⣿⣿⣿⠿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣽⣿⣿⣿⣑⣶⣿⡇⠀⠀⠀⡀ ⠀⣭⣉⡍⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣼⡄⢨⣠⡀⠀⠉⠛⠋⠐⠃⡹⢿⣿⣿⣿⣝⣇⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣟⣛⣻⣿⣿⣿⣿⣿⣿⣛⣼⣿⣥⣼⣿⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀ ⢀⣍⣩⣁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⣛⠃⠀⢺⣿⡆⠀⠀⠀⠀⠈⠀⠀⠈⢡⡩⡳⣅⢹⠿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣹⣿⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀ ⠀⠤⠤⠤⠤⠤⠥⠤⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡂⠀⢸⣿⣶⠃⠀⠀⠀⠀⠀⢀⠐⠉⠈⠻⣛⠀⠐⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢠⣼⣿⣿⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠨⢢⣼⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿⡿⠛⢛⠻⠿⠟⣿⣿⠿⠛⠓⠀⠀⠀⠀⠀⢠⣶ ⠀⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠲⠶⠦⠀⣉⡃⠀⠘⠻⣏⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣠⠀⢉⢨⣿⣿⣿⣿⣿⢿⣿⡅⠀⠀⠀⠛⠀⠀⠀⠀⠈⢩⣄⣀⣈⣧⡄⣢⣿⣋⣀⣄⢀⣀⡀⠀⢀⣤⢾⢿ ⠀⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣍⣅⣉⣍⣭⣉⡀⠈⢁⣬⡍⣤⣅⣀⠀⠀⠀⠀⠀⠁⣠⠞⠉⠈⢹⢸⣿⣿⣿⣿⣿⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠙⠛⠛⠛⠁⠉⠉⠉⠉⠉⠁⠉⠁⠈⢴⣿⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⡀⠀⠀⠒⠂⠀⡂⠀⠀⠀⠀⠀⢸⣿⣿⠛ ⠘⠛⠟⠛⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠁⠀⠀⠀⣀⣀⣸⣸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀ ⠰⣯⣷⣴⢤⠖⠶⠶⠶⠶⠂⠀⠐⠲⠒⠂⠀⢀⢰⣶⣖⢶⣂⡀⣀⣶⣲⣶⢶⣆⣀⣀⡒⣠⣤⣀⣀⣠⣿⣿⣿⣶⣶⣻⣬⣡⣻⣻⣯⣄⡀⣠⣠⣴⡲⣦⣤⣴⣀⣀⣶⣶⣶⢀⢀⣀⣠⣶⣶⡀⣀⣀⣀⡀⣰⣆⣀⣀ ⠴⠄⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠠⠠⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⣠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⠠⠄⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠄⠀⠠⠠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⢐⠐⠒⠒⠀⠀⠀⠛⠓⠂⠀⠀⠀⠀⠀⠐⠒⠂⠒⠂⠀⠀⠀⠀⠀⠂⠤⠴⠿⠿⠳⠤⠤⠤⠀⠠⠀⠤⠜⠛⠟⠓⠀⠀⠀⠐⠚⠛⠛⠀⠀⠀⠀⠀⠀⠀ ⠰⠷⠶⠶⠚⠚⠓⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠶⠶⣶⣶⣶⣒⠒⣶⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⡛⢛⠏⡃⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠐⠒⠒⠒⠒⠰⠒⠘⠳⠟⢻⣿⣿⣿⠛⢿⣿⣿⣿⣿⡿⢷⡆⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀ ⠀⠙⢛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣄⡀⠀⡀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣷⣾⡇⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀ ⠀⠽⢍⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡂⠀⠀⠀⠀⠀⠀⠐⠀⢀⣿⣿⣿⣿⣦⣀⢄⠀⢰⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀ ⠀⣀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡀⠀⠀⠀⠀⠀⠀⠀⢀⠈⣿⣿⣿⣿⣿⣿⣿⣄⢸⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣛⣿⣛⣉⣙⣁⣈⣀⣀⣀⣀⣀⣀⣀⣐⣻⣾⣶ ⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠠⠖⠘⠀⣻⣿⣿⣿⣿⣿⣿⣿⢈⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣉⣉⣭⣏⣽⣿⣿⣿⣿⣿⣋ ⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⢻⣿⡾⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠉⢹⣿⣿⣿⣿⡁⠉⠙⠛⠀⠀⠀ ⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⡞⣿⢲⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣋⢩⡟⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿ ⠀⡀⠂⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⣬⠘⢀⠀⠀⠀⠀⠀⢀⠀⢸⣿⣿⣿⣿⣿⣿⣯⠿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣔⣶⠀⠀⠀⠀⠉⠀ ⠀⣩⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄⠈⣀⡀⠀⠀⠈⠀⠀⠀⡹⢿⣿⣿⣿⣝⠅⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣟⣛⣛⣿⣟⣗⣿⣿⣿⣿⣾⣿⣿⣾⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶ ⠀⣈⣁⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⠁⠀⢚⠿⡀⠀⠀⠀⠀⠀⠀⠀⠈⠡⡡⠒⠅⢹⠟⢻⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠙⠋⠛⠛⠛⠛⠛ ⠀⠄⠤⠤⠤⠠⠥⠤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡂⠀⢸⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠻⡈⠀⠐⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⠀⠠⣾⣿⠿⠃⠀ ⠀⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢠⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⡿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠃⣿⡿⠓⢛⣿⣿⣿⣿⣿⠿⣿⡓⠀⠀⣰⣶⣦⡆⣘ ⠀⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠄⠠⠀⠉⠃⠀⠈⠻⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢁⢈⣿⣿⣿⣿⣿⢿⣿⡀⠀⠀⠀⠚⠀⠀⠀⠀⢀⣿⡟⢒⢚⢓⡛⡛⢻⣛⣓⡛⢛⣲⣶⣞⣓⣿⣿⣿ ⠀⠓⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣁⣉⣉⣉⢉⠀⠈⢁⣈⡁⣄⣁⢀⠀⠀⠀⠀⠀⠁⡠⠊⠁⠀⢹⢸⣿⣿⣿⣿⣭⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣽⣿⣿⣿⣿⣏⣉⣹⣿⣯⣭⣙⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⢸⠘⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣒⡒⢠⣴⣴⠆⠀⡂⣤⠀⠀⠀⠀⢠⣶⡿⠛ ⠈⠛⠚⠛⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⣀⣀⣘⣀⣿⣿⣿⣿⣟⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣗⠛⠒⡛⢛⣓⣒⣲⡚⠛⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠯⢷⠤⠤⠒⠶⠶⠶⠶⠀⠀⠀⠒⠒⠂⠀⢀⢐⣲⣒⢒⣂⡀⣀⣒⣒⣖⠖⣂⣀⣀⠒⣀⡀⣀⣀⣀⣿⣿⣿⣶⣶⣺⣀⣀⣰⡃⣏⢀⡀⣀⡠⣴⡒⣠⣄⣤⡀⣿⣷⣖⣶⣄⣀⣾⣿⣿⣿⣇⣀⣀⣀⣸⣷⣇⣀⣀ ⠴⠄⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠠⠠⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⣠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⠠⠄⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠄⠀⠠⠠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⢐⠐⠒⠒⠀⠀⠀⠛⠓⠂⠀⠀⠀⠀⠀⠐⠒⠂⠒⠂⠀⠀⠀⠀⠀⠂⠤⠴⠿⠿⠳⠤⠤⠤⠀⠠⠀⠤⠜⠛⠟⠓⠀⠀⠀⠐⠚⠛⠛⠀⠀⠀⠀⠀⠀⠀ ⠰⠷⠶⠶⠚⠚⠓⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠶⠶⣶⣶⣶⣒⠒⣶⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⡛⢛⠏⡃⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠐⠒⠒⠒⠒⠰⠒⠘⠳⠟⢻⣿⣿⣿⠛⢿⣿⣿⣿⣿⡿⢷⡆⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀ ⠀⠙⢛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣄⡀⠀⡀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣷⣾⡇⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀ ⠀⠽⢍⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡂⠀⠀⠀⠀⠀⠀⠐⠀⢀⣿⣿⣿⣿⣦⣀⢄⠀⢰⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀ ⠀⣀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡀⠀⠀⠀⠀⠀⠀⠀⢀⠈⣿⣿⣿⣿⣿⣿⣿⣄⢸⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣛⣿⣛⣉⣙⣁⣈⣀⣀⣀⣀⣀⣀⣀⣐⣻⣾⣶ ⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠠⠖⠘⠀⣻⣿⣿⣿⣿⣿⣿⣿⢈⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣉⣉⣭⣏⣽⣿⣿⣿⣿⣿⣋ ⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⢻⣿⡾⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠉⢹⣿⣿⣿⣿⡁⠉⠙⠛⠀⠀⠀ ⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⡞⣿⢲⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣋⢩⡟⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿ ⠀⡀⠂⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⣬⠘⢀⠀⠀⠀⠀⠀⢀⠀⢸⣿⣿⣿⣿⣿⣿⣯⠿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣔⣶⠀⠀⠀⠀⠉⠀ ⠀⣩⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄⠈⣀⡀⠀⠀⠈⠀⠀⠀⡹⢿⣿⣿⣿⣝⠅⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣟⣛⣛⣿⣟⣗⣿⣿⣿⣿⣾⣿⣿⣾⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶ ⠀⣈⣁⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⠁⠀⢚⠿⡀⠀⠀⠀⠀⠀⠀⠀⠈⠡⡡⠒⠅⢹⠟⢻⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠙⠋⠛⠛⠛⠛⠛ ⠀⠄⠤⠤⠤⠠⠥⠤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡂⠀⢸⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠻⡈⠀⠐⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⠀⠠⣾⣿⠿⠃⠀ ⠀⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢠⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⡿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠃⣿⡿⠓⢛⣿⣿⣿⣿⣿⠿⣿⡓⠀⠀⣰⣶⣦⡆⣘ ⠀⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠄⠠⠀⠉⠃⠀⠈⠻⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢁⢈⣿⣿⣿⣿⣿⢿⣿⡀⠀⠀⠀⠚⠀⠀⠀⠀⢀⣿⡟⢒⢚⢓⡛⡛⢻⣛⣓⡛⢛⣲⣶⣞⣓⣿⣿⣿ ⠀⠓⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣁⣉⣉⣉⢉⠀⠈⢁⣈⡁⣄⣁⢀⠀⠀⠀⠀⠀⠁⡠⠊⠁⠀⢹⢸⣿⣿⣿⣿⣭⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣽⣿⣿⣿⣿⣏⣉⣹⣿⣯⣭⣙⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⢸⠘⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣒⡒⢠⣴⣴⠆⠀⡂⣤⠀⠀⠀⠀⢠⣶⡿⠛ ⠈⠛⠚⠛⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⣀⣀⣘⣀⣿⣿⣿⣿⣟⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣗⠛⠒⡛⢛⣓⣒⣲⡚⠛⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠯⢷⠤⠤⠒⠶⠶⠶⠶⠀⠀⠀⠒⠒⠂⠀⢀⢐⣲⣒⢒⣂⡀⣀⣒⣒⣖⠖⣂⣀⣀⠒⣀⡀⣀⣀⣀⣿⣿⣿⣶⣶⣺⣀⣀⣰⡃⣏⢀⡀⣀⡠⣴⡒⣠⣄⣤⡀⣿⣷⣖⣶⣄⣀⣾⣿⣿⣿⣇⣀⣀⣀⣸⣷⣇⣀⣀ ⠐⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠄⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠒⠂⠀⠀⠀⠀⠠⠀⠤⠐⠒⠒⠒⠀⠀⠀⠀⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀ ⠀⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠀⠀⢶⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠐⠒⠒⠒⠒⠰⠒⠐⠲⠖⠛⠁⠐⠞⠓⢻⣿⣿⣿⣿⡿⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣶⣾⣿⣿⣿⣿⣷⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠁⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠂⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⣀⢠⣄⣦⣀⠄⠀⠀⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀ ⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣽⣿⣿⣿⣿⣷⡄⢠⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⠿⠙⠉⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣸⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠛⣿⠼⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⠿⠟⠻⠟⠛⠛⠓⠶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣽⣿⣿⣿⢿⣿⡞⣿⢲⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣻⣿⢊⣬⣽⣾⣿⣿⣿⣿⣿⣶⣾⣷⣿ ⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣮⡿⣿⣿⡯⠟⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣽⣿⣿⣿⠟⠛⠛⠛⠛⠛⠛⠛ ⠀⣈⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣯⠈⠁⠔⣾⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶ ⠀⣀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠘⠿⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡁⠀⠀⢨⠛⠺⣿⣿⣿⣿⣥⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠄⠤⠠⠤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡂⠀⠀⢳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠐⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⣀⣤⣶⣿⠿⠋⠀ ⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⡄⣯⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⡷⣿⡟⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⡟⠛⣻⣿⣿⣿⣿⣿⠿⠛⡓⢛⣙⣻⣿⣿⠆⠘ ⠀⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⣿⣿⣟⣙⣿⢏⣫⠀⠀⠀⠀⠚⠀⢸⣿⣿⣿⣿⣟⢿⣻⠿⣶⠖⢻⡛⠒⣟⢛⣿⣿⣿⣿⣷⣞⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⠀⣿⣿⣿⣽⣭⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣋⣉⣹⣿⣯⣭⣹⣿⣿⣿⣯⣽ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⢿⡿⢽⣿⣿⠼⠦⠾⣧⠬⠭⠭⠿⠽⠿⠭⠿ ⠀⠒⠚⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣙⡛⣟⣿⣟⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⠷⠶⣾⣿⣓⣒⣶⣶⠋⠀⠀⠀⠀⠀⠀⠀⢠ ⠀⠯⠤⠤⠤⠒⠖⠔⠲⠖⠀⠀⠀⠒⠒⠂⠀⢀⢀⠒⠒⢒⠂⠀⣀⡐⠒⠒⠒⠂⣀⠀⠐⠀⡀⠀⡀⠀⣯⣿⣿⣶⣶⣸⠀⠀⠐⠂⠂⠀⠀⠀⠠⠄⠒⠀⣿⣿⣿⣿⣿⣛⣯⣍⣉⣿⣿⣿⣿⣇⣀⣀⣀⣰⣷⣆⣀⣈ ⠐⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠄⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠒⠂⠀⠀⠀⠀⠠⠀⠤⠐⠒⠒⠒⠀⠀⠀⠀⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀ ⠀⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠀⠀⢶⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠐⠒⠒⠒⠒⠰⠒⠐⠲⠖⠛⠁⠐⠞⠓⢻⣿⣿⣿⣿⡿⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣶⣾⣿⣿⣿⣿⣷⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠁⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠂⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⣀⢠⣄⣦⣀⠄⠀⠀⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀ ⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣽⣿⣿⣿⣿⣷⡄⢠⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⠿⠙⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣸⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠛⣿⠼⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⣿⣿⡟⣿⣿⣿⣿⠿⢿⣿⣿⣿⠿⠟⠻⣿⣿⠟⠓⠶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣽⣿⣿⣿⢿⣿⡞⣿⢲⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣿⣻⣿⢊⣬⣽⣾⣿⣿⣿⣿⣿⣶⣾⣷⣿ ⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣮⡿⣿⣿⡯⠟⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣽⣿⣿⣿⠟⠛⠛⠛⠛⠛⠛⠛ ⠀⣈⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣯⠈⠁⠔⣾⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶ ⠀⣀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠘⠿⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡁⠀⠀⢨⠛⠺⣿⣿⣿⣿⣥⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠄⠤⠠⠤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡂⠀⠀⢳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠐⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⣀⣤⣶⣿⠿⠋⠀ ⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⡄⣯⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⡷⣿⡟⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⡟⠛⣻⣿⣿⣿⣿⣿⠿⠛⡓⢛⣙⣻⣿⣿⠆⠘ ⠀⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⣿⣿⣟⣙⣿⢏⣫⠀⠀⠀⠀⠚⠀⢸⣿⣿⣿⣿⣟⢿⣻⠿⣶⠖⢻⡛⠒⣟⢛⣿⣿⣿⣿⣷⣞⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⠀⣿⣿⣿⣽⣭⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣋⣉⣹⣿⣯⣭⣹⣿⣿⣿⣯⣽ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⢿⡿⢽⣿⣿⠼⠦⠾⣧⠬⠭⠭⠿⠽⠿⠭⠿ ⠀⠒⠚⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣙⡛⣟⣿⣟⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⠷⠶⣾⣿⣓⣒⣶⣶⠋⠀⠀⠀⠀⠀⠀⠀⢠ ⠀⠯⠤⠤⠤⠒⠖⠔⠲⠖⠀⠀⠀⠒⠒⠂⠀⢀⢀⠒⠒⢒⠂⠀⣀⡐⠒⠒⠒⠂⣀⠀⠐⠀⡀⠀⡀⠀⣯⣿⣿⣶⣶⣸⠀⠀⠐⠂⠂⠀⠀⠀⠠⠄⠒⠀⣿⣿⣿⣿⣿⣛⣯⣍⣉⣿⣿⣿⣿⣇⣀⣀⣀⣰⣷⣆⣀⣈ ⠐⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠀⠀⠀⠀⠀⠄⠐⠒⠒⠒⠀⠀⠀⠀⠐⠒⠒⠀⠀⠀⠀⠀⠀⠀ ⠀⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠂⠀⠀⢰⣶⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠓⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠐⠒⠒⠒⠒⠰⠒⠐⠲⠖⠛⠀⠐⠞⠒⢻⣿⣿⣿⣿⡿⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣶⣾⣿⣿⣿⣿⣷⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣤⣀⠀⠀⠀⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀ ⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣿⣿⣿⣿⣷⡀⢠⠆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡿⣿⣽⣿⣿⣿⣽⣬⣵⣤⣤⡤⢤⣤⣤⣤⣤⣤⢤⠭⢤⡤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠋⣿⠴⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣿⣿⣿⣿⡟⣿⣿⣿⣿⢿⣿⣿⣿⡿⠿⠟⠻⣿⣿⠟⡓⢶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣽⣿⣿⣿⢿⣿⡞⣿⢰⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣷⣿⣿⣻⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣮⡟⣿⣿⡯⠛⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⠟⠛⠛⠛⠛⠛⠛⠛ ⠀⣈⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣯⠈⠀⠔⣾⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠿⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠨⠛⠺⣿⣿⣿⣿⣥⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠄⠄⠠⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡂⠀⠀⢳⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠐⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡙⣛⣿⣷⣿⠿⠋⠀ ⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⢠⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡷⣿⡏⠉⠉⠉⠉⠋⢻⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⠿⠛⡛⣿⣛⣻⣿⣿⢆⠜ ⠀⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⣿⣿⣟⣉⣿⢏⣋⠀⠀⠀⠀⠚⠀⢸⣿⣿⣿⣿⣟⣿⣿⡿⣶⠖⢺⡟⠒⣟⣛⣿⣿⣿⣿⣷⣖⣻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣿⣾⣿⣽⣭⣿⣿⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣛⣉⣹⣯⣯⣭⣹⣿⣿⣿⣯⣭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡿⢿⡿⢽⣿⣿⡼⠦⠾⣧⠬⠥⠭⠿⠽⠿⠥⠾ ⠀⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣙⡛⡟⣿⣟⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⠶⣶⣾⣿⣛⣓⣶⣶⠋⠀⠀⠀⠀⠀⠀⠀⢠ ⠀⠯⠄⠠⠠⠒⠖⠐⠒⠖⠀⠀⠀⠒⠒⠂⠀⠀⢀⠒⠒⠒⠂⠀⠀⡐⠒⠒⠒⠀⢀⠀⠐⠀⠀⠀⠀⠀⣯⣿⣿⣶⣶⣸⠀⠀⠐⠂⠂⠀⠀⠀⠠⠄⠒⠀⣿⣿⣿⣿⣿⣛⣯⣍⣉⣿⣿⣿⣿⣇⣀⣀⣀⣰⣷⣆⣀⣈ ⠐⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠀⠀⠀⠀⠀⠄⠐⠒⠒⠒⠀⠀⠀⠀⠐⠒⠒⠀⠀⠀⠀⠀⠀⠀ ⠀⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠂⠀⠀⢰⣶⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠓⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠐⠒⠒⠒⠒⠰⠒⠐⠲⠖⠛⠀⠐⠞⠒⢻⣿⣿⣿⣿⡿⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣶⣾⣿⣿⣿⣿⣷⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣤⣀⠀⠀⠀⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀ ⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣿⣿⣿⣿⣷⡀⢠⠆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡿⣿⣽⣿⣿⣿⣽⣭⣽⣤⣤⡤⢤⣤⣤⣤⣤⣤⢤⠭⢤⡤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠋⣿⠴⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣿⣿⣿⣿⡟⣿⣿⣿⣿⢿⣿⣿⣿⡿⠿⠟⠻⣿⣿⠟⡓⢶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣽⣿⣿⣿⢿⣿⡞⣿⢰⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣷⣿⣿⣻⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣮⡟⣿⣿⡯⠛⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⠟⠛⠛⠛⠛⠛⠛⠛ ⠀⣈⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣯⠈⠀⠔⣾⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠿⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠨⠛⠺⣿⣿⣿⣿⣥⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠄⠄⠠⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡂⠀⠀⢳⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠐⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡙⣛⣿⣷⣿⠿⠋⠀ ⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⢠⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡷⣿⡏⠉⠉⠉⠉⠋⢻⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⠿⠛⡛⣿⣛⣻⣿⣿⢆⠜ ⠀⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⣿⣿⣟⣉⣿⢏⣋⠀⠀⠀⠀⠚⠀⢸⣿⣿⣿⣿⣟⣿⣿⡿⣶⠖⢺⡟⠒⣟⣛⣿⣿⣿⣿⣷⣖⣻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣿⣾⣿⣽⣭⣿⣿⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣛⣉⣹⣯⣯⣭⣹⣿⣿⣿⣯⣭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡿⢿⡿⢽⣿⣿⡼⠦⠾⣧⠬⠥⠭⠿⠽⠿⠥⠾ ⠀⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣙⡛⡟⣿⣟⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⠶⣶⣾⣿⣛⣓⣶⣶⠋⠀⠀⠀⠀⠀⠀⠀⢠ ⠀⠯⠄⠠⠠⠒⠖⠐⠒⠖⠀⠀⠀⠒⠒⠂⠀⠀⢀⠒⠒⠒⠂⠀⠀⡐⠒⠒⠒⠀⢀⠀⠐⠀⠀⠀⠀⠀⣯⣿⣿⣶⣶⣸⠀⠀⠐⠂⠂⠀⠀⠀⠀⠄⠒⠀⣾⣿⣿⣿⣿⣛⣯⣍⣉⣿⣿⣿⣿⣇⣀⣀⣀⣰⣷⣆⣀⣈ ⠐⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠀⠀⠀⠀⠀⠄⠐⠒⠒⠒⠀⠀⠀⠀⠐⠒⠒⠀⠀⠀⠀⠀⠀⠀ ⠀⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠂⠀⠀⢰⣶⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠓⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠐⠒⠒⠒⠒⠰⠒⠐⠲⠖⠛⠀⠐⠞⠒⢻⣿⣿⣿⣿⡿⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣶⣾⣿⣿⣿⣿⣷⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣤⣀⠀⠀⠀⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀ ⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣿⣿⣿⣿⣷⡀⢠⠆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡿⣿⣽⣿⣿⣿⣽⣭⣽⣤⣤⡤⢤⣤⣤⣤⣤⣤⢤⠭⢤⡤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠋⣿⠴⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣿⣿⣿⣿⡟⣿⣿⣿⣿⢿⣿⣿⣿⡿⠿⠟⠻⣿⣿⠟⡓⢶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣽⣿⣿⣿⢿⣿⡞⣿⢰⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣷⣿⣿⣻⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣮⡟⣿⣿⡯⠛⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⠟⠛⠛⠛⠛⠛⠛⠛ ⠀⣈⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣯⠈⠀⠔⣾⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠿⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠨⠛⠺⣿⣿⣿⣿⣥⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠄⠄⠠⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡂⠀⠀⢳⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠐⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡙⣛⣿⣷⣿⠿⠋⠀ ⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⢠⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡷⣿⡏⠉⠉⠉⠉⠋⢻⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⠿⠛⡛⣿⣛⣻⣿⣿⢆⠜ ⠀⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⣿⣿⣟⣉⣿⢏⣋⠀⠀⠀⠀⠚⠀⢸⣿⣿⣿⣿⣟⣿⣿⡿⣶⠖⢺⡟⠒⣟⣛⣿⣿⣿⣿⣷⣖⣻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣿⣾⣿⣽⣭⣿⣿⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣛⣉⣹⣯⣯⣭⣹⣿⣿⣿⣯⣭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡿⢿⡿⢽⣿⣿⡼⠦⠾⣧⠬⠥⠭⠿⠽⠿⠥⠾ ⠀⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣙⡛⡟⣆⣟⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⠶⣶⣾⣿⣛⣓⣶⣶⠋⠀⠀⠀⠀⠀⠀⠀⢠ ⠀⠯⠄⠠⠠⠒⠖⠐⠒⠖⠀⠀⠀⠒⠒⠂⠀⠀⢀⠒⠒⠒⠂⠀⠀⡐⠒⠒⠒⠀⢀⠀⠐⠀⠀⠀⠀⠀⣯⣿⣿⣶⣶⣸⠀⠀⠐⠂⠂⠂⠀⠀⠀⠄⠒⠀⣾⣿⣿⣿⣿⣛⣯⣍⣉⣿⣿⣿⣿⣇⣀⣀⣀⣰⣷⣆⣀⣈ ⠐⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠀⠀⠀⠀⠀⠄⠀⠒⠒⠒⠀⠀⠀⠀⠐⠒⠒⠀⠀⠀⠀⠀⠀⠀ ⠀⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠂⠀⠀⢰⣶⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠓⠛⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠐⠒⠒⠒⠒⠰⠒⠐⠲⠖⠓⠀⠐⠒⠒⠻⣿⣿⣿⣿⡷⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣴⣶⣶⣶⣶⣶⣿⣿⣶⣾⣿⣿⣿⣿⣷⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣤⣀⠀⠀⠀⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀ ⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣫⣿⣿⣿⣷⡀⢠⠆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡿⣿⣽⣿⣿⣿⣽⣭⣽⣤⣤⡤⢤⣤⣤⣤⣤⣤⢤⠭⢤⡤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠋⣿⠴⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣿⣿⡟⣿⡟⣿⣿⣿⣿⢿⣿⣿⣟⡿⠿⠟⠻⣿⣿⠟⡓⢶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣽⣿⣿⣿⢿⣿⡞⣿⢰⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣷⣿⣿⣻⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣮⡝⣿⣿⡯⠛⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⠟⠛⠛⠛⠛⠛⠛⠛ ⠀⣈⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣯⠈⠀⠔⣾⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠻⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠨⠓⠚⣿⣿⣿⣿⣥⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠄⠄⠠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡂⠀⠀⢳⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡙⣛⣿⣷⣿⠿⠋⠀ ⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⢠⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡷⣿⡏⠉⠉⠉⠉⠋⢻⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⠿⠛⡛⣿⣛⣻⣿⣿⢆⠜ ⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⣿⣿⣟⣉⣿⣯⣿⣦⣤⡄⣴⣾⣦⢸⣿⣿⣿⣿⣟⣿⣿⡿⣶⠖⢺⡟⠒⣟⣛⣿⣿⣿⢿⣷⣖⣻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣿⣾⣿⣽⣽⣿⣿⠛⠛⠛⠙⠻⠟⢺⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣛⣉⣹⣯⣯⣭⣹⣿⣿⣿⣯⣭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⡿⢿⠿⢽⣿⣿⡴⠦⠾⣧⠬⠥⠭⠿⠽⠿⠥⠾ ⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣙⡛⡟⣆⣟⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⠶⣶⣾⣿⣛⣓⣶⣶⠋⠀⠀⠀⠀⠀⠀⠀⢠ ⠀⠯⠄⠀⠠⠒⠖⠐⠒⠖⠀⠀⠀⠒⠒⠂⠀⠀⢀⠒⠒⠒⠂⠀⠀⠐⠒⠒⠒⠀⢀⠀⠐⠀⠀⠀⠀⠀⣯⣿⣿⣶⣶⣸⠀⠀⠐⠂⠂⠂⠀⠀⠀⠄⠒⠀⣾⣿⣿⣿⣿⣛⣯⣍⣉⣿⣿⣿⣿⣇⣀⣀⣀⣰⣷⣆⣀⣈ ⠐⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠀⠀⠀⠀⠀⠄⠀⠒⠒⠒⠀⠀⠀⠀⠐⠒⠒⠀⠀⠀⠀⠀⠀⠀ ⠀⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠒⠒⠀⠀⠀⢰⣶⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠓⠛⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠐⠒⠒⠒⠒⠰⠒⠐⠲⠖⠒⠀⠐⠒⠒⠻⣿⣿⣿⣿⡷⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣴⣶⣶⣶⣶⣶⣿⣿⣶⣾⣿⣿⣿⣿⣷⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣄⣀⠀⠀⠀⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀ ⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣩⣿⣿⣿⣷⡀⢠⠆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡿⣿⣽⣿⣿⣿⣽⣭⣽⣤⣤⡤⢤⣤⣤⣤⣤⣤⢤⠭⢤⡤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⣿⣿⣿⣷⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠋⣷⠴⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣿⣿⡟⣿⡟⣿⣿⣻⣿⢿⣿⣿⣟⠿⠿⠟⠻⣿⣿⠟⡓⢶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣝⡿⣿⣿⢿⣿⡞⣿⢰⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣷⣿⣿⣻⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣮⡝⣿⣿⡯⠛⣬⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⠟⠛⠛⠛⠛⠛⠛⠛ ⠀⣈⢉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣯⠀⠀⠔⣾⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠨⠓⠚⣿⣿⣿⣿⣥⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡂⠀⠀⢳⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡙⣛⣿⣷⣿⠿⠋⠀ ⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⢠⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣷⣿⡏⠉⠉⠉⠉⠉⢻⣿⣿⡏⣿⣿⡟⣿⣿⣿⣿⣿⣿⠿⠛⡛⣿⣛⣻⣿⣿⢆⠘ ⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠛⣿⣿⣿⣛⣿⣿⣿⣦⣤⡄⣴⣾⣦⢸⣿⣿⣷⣿⣟⣿⣿⡿⣶⠖⢺⡟⠒⣟⣓⣿⣿⣿⢷⣷⣖⣻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠈⣿⣿⣿⣿⣽⣿⣿⠛⠛⠛⠙⠛⠟⢺⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣛⣉⣹⣯⣯⣭⣹⣿⣿⣿⣯⣭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⡿⢿⠿⢽⣿⣿⡴⠦⠾⣧⠬⠥⠭⠿⠽⠿⠥⠾ ⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣐⣀⣘⡛⡟⣆⣟⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⠶⣶⣾⣿⣛⣓⣶⣶⠋⠀⠀⠀⠀⠀⠀⠀⢠ ⠀⠈⠁⠈⠈⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠂⠀⠀⠐⠒⠒⠒⠀⢀⠀⠐⠀⠀⠀⠀⠀⣯⣿⣿⣶⣶⣸⣀⠀⠐⠂⠂⠂⠀⠀⠠⠄⠒⠀⣾⣿⣿⣿⣿⣛⣯⣍⣉⣿⣿⣿⣿⣇⣀⣀⣀⣰⣷⣆⣀⣈ ⠐⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠀⠀⠀⠀⠀⠄⠀⠒⠒⠒⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠒⠒⠀⠀⠀⢰⣶⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠓⠛⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠐⠒⠒⠒⠒⠰⠒⠐⠲⠖⠒⠀⠐⠒⠒⠻⣿⣿⣿⣿⡷⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠛⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣴⣶⣶⣶⣶⣶⣿⣿⣶⣶⣿⣿⣿⣿⣷⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠂⠂⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⡿⢿⠿⢽⣿⣿⡴⠦⠾⣧⠬⠥⠭⠿⠽⠿⠥⠾ ⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣐⣀⣘⡛⡟⣆⣝⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⠶⣶⣾⣿⣛⣓⣶⣶⠋⠀⠀⠀⠀⠀⠀⠀⢠ ⠀⠈⠁⠈⠈⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠂⠀⠀⠐⠒⠒⠒⠀⠀⠀⠐⠀⠀⠀⠀⠀⣯⣿⣿⣶⣶⣸⣀⠀⠐⠂⠂⠂⠀⠀⠠⠄⠒⠀⣾⣿⣿⣿⣿⣛⣯⣍⣉⣿⣿⣿⣿⣇⣀⣀⣀⣰⣷⣆⣀⣈ ⠐⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠀⠀⠀⠀⠀⠄⠀⠒⠒⠒⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠒⠒⠀⠀⠀⢰⣶⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠓⠛⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠐⠒⠒⠒⠒⠰⠒⠐⠲⠖⠒⠀⠐⠒⠒⠻⣿⣿⣿⣿⡷⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠛⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣴⣶⣶⣤⣶⣶⣿⣿⣶⣾⣿⣿⣿⣿⣷⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣄⣀⠀⠀⠀⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀ ⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣩⣿⣿⣿⣷⡀⢠⠆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡿⣿⣽⣿⣿⣿⣽⣭⣽⣤⣤⡤⢤⣤⣤⣤⣤⣤⢤⠭⢤⡤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⣿⣿⣿⣷⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠋⣷⠴⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣿⣿⡟⣿⡟⣿⣿⣻⣿⢿⣿⣿⣟⠿⠿⠟⠻⣿⣿⠟⡓⢶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣝⡿⣿⣿⢿⣿⡞⣿⢰⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣷⣿⣿⣻⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣮⡝⣿⣿⡯⠛⣬⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⠟⠛⠛⠛⠛⠛⠛⠛ ⠀⣈⢉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣯⠀⠀⠄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠨⠓⠚⣿⣿⣿⣿⣥⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡙⣛⣿⣷⣿⠿⠋⠀ ⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣷⣿⡏⠉⠉⠉⠉⠉⢻⣿⣿⡏⣿⣿⡟⣿⣿⣿⣿⣿⣿⠿⠛⡛⣿⣛⣻⣿⣿⢆⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠛⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣴⣾⣦⢸⣿⣿⣷⣿⣟⣿⣿⡿⣶⠖⢺⡟⠒⣟⣓⣿⣿⣿⢷⣷⣖⣻ ⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠈⣿⣿⣿⣿⣿⣿⣿⠿⠻⠻⠛⠛⠟⢺⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣛⣉⣹⣯⣯⣭⣹⣿⣿⣿⣯⣭ ⠀⠂⠂⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⡿⢿⠿⢽⣿⣿⡴⠦⠾⣧⠬⠥⠭⠿⠽⠿⠥⠾ ⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣐⣀⣘⡛⡟⣆⣟⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⠶⣶⣾⣿⣛⣓⣶⣶⠋⠀⠀⠀⠀⠀⠀⠀⢠ ⠀⠈⠁⠈⠈⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠒⠂⠀⠀⠐⠒⠒⠒⠀⠀⠀⠐⠀⠀⠀⠀⠀⣯⣿⣿⣶⣶⣸⣀⠀⠐⠂⠂⠂⠀⠀⠠⠄⠒⠀⣾⣿⣿⣿⣿⣛⣯⣍⣉⣿⣿⣿⣿⣇⣀⣀⣀⣰⣷⣆⣀⣈ ⠐⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠖⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⢰⣶⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠓⠛⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠐⠒⠒⠒⠒⠰⠒⠐⠲⠖⠒⠀⠐⠒⠒⠻⣿⣿⣿⣿⡷⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠛⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣦⣶⣶⣴⣶⣶⣤⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣷⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣄⣀⠀⠀⠀⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀ ⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣈⣯⣿⣿⣧⡀⢠⠆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡿⣟⣙⣻⣿⣛⣽⣭⣽⣤⣤⡤⢤⣤⣤⣤⣤⣤⢤⠭⢤⡤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣾⣿⣿⣿⣿⣷⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠋⣷⠴⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣿⣿⡟⣿⡟⣿⣿⣻⣿⢿⣿⣿⣛⠿⠿⠟⠻⣿⣿⠟⡓⢶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣝⡿⣿⣿⢿⣿⡞⣿⢠⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣷⣿⣿⣻⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣮⡝⣿⣿⡯⠛⣬⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⠟⠛⠛⠛⠛⠛⠛⠛ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣷⣿⡏⠉⠉⠉⠉⠉⢻⣿⣿⡏⣿⣿⡟⣿⣿⣿⣿⣿⣿⠿⠛⠛⣿⣛⣻⣿⣿⢆⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠛⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣴⣾⣦⢸⣿⣿⣷⣿⣟⣿⣻⡿⣶⠖⢺⡟⠒⣟⣓⣿⣿⣿⢷⣗⣖⣺ ⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠈⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠛⠟⢺⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣛⣉⣹⣯⣯⣭⣹⣿⣿⣿⣯⣭ ⠀⠀⠂⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⢿⠿⢽⣿⣿⡴⠦⠾⣧⠬⠥⠭⠿⠽⠿⠥⠾ ⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣐⣀⣈⡙⡟⣆⣙⣿⣿⠀⠀⠀⣀⣀⣀⣀⣿⣿⣿⣿⣷⣶⣶⣾⣿⣛⣓⣶⣶⠋⠀⠀⠀⠀⠀⠀⠀⢠ ⠀⠀⠁⠈⠈⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠂⠀⠀⠐⠒⠒⠒⠀⠀⠀⠐⠀⠀⠀⠀⠀⣯⣿⣿⣶⣶⣸⣀⠀⠐⠂⠂⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⣰⣷⣆⣀⣈ ⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠖⠰⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠓⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠐⠒⠒⠒⠒⠰⠒⠐⠲⠖⠒⠀⠀⠒⠒⠚⠿⣿⣿⣿⡕⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠑⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣦⣶⣶⣴⣶⣶⣤⣶⣾⣷⣶⣶⣶⣾⣿⣿⣿⣷⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠀⠀⠀⢰⣤⣶⣦⣿⣿⣿⣿⣿⠿⠿⢽⣿⣿⣶⣶⡾⣧⠬⠥⠭⠿⠽⢿⣷⠾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠉⠂⠘⠿⠏⠀⠀⠀⣈⣉⣉⣉⣿⣿⣿⣿⣿⣷⣶⣾⣿⣛⣋⣽⣶⠋⠀⠀⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠂⠀⠀⠐⠒⠒⠒⠀⠀⠀⠐⠀⠀⠀⠀⠀⣯⣿⣿⣶⣶⡸⣀⠀⠐⠂⠀⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⣰⣖⣆⣀⣈ ⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠖⠰⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠓⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠐⠒⠒⠒⠒⠰⠒⠐⠲⠖⠒⠀⠀⠒⠒⠚⠿⣿⣿⣿⡕⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠑⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣦⣶⣶⣴⣶⣶⣤⣶⣾⣷⣶⣶⣶⣾⣿⣿⣿⣷⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⠀⠀⠀⠂⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣛⠶⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⢉⣿⣿⣦⡀⢠⠆⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⡟⡿⣿⣽⣻⣿⣛⣽⣭⣽⣼⣮⡤⢴⣦⣤⣤⣤⣤⠤⠭⢤⡤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣶⣿⣿⣿⡿⣷⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠃⣷⠴⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣟⣿⣿⣿⣟⣓⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣝⡿⣿⣿⢿⣿⡞⣿⢠⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣮⡝⣿⣿⡯⠙⣬⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⢿⣿⣿⣿⡛⡛ ⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⡧⠀⠀⠄⣺⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠹⠿⣿⣿⣿⣿⣿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⡛⣛⣿⣿⣿⣿⣿⣭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣷⣿⡏⠉⠉⠉⡛⣋⣻⣿⣿⡏⣿⣿⡟⣿⣿⣿⣿⣿⣿⠿⠛⢿⣿⣛⣻⣿⣿⣇⣉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣼⣿⣾⣿⣿⣿⣿⣿⣟⣿⣳⣿⣶⣟⣿⣟⣻⣟⣻⣿⣿⣿⣷⣿⣟⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠈⣿⣿⣿⣿⣿⣿⣿⠟⠉⠻⣟⣛⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣹⣿⣯⣿⣯⣽⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠀⠀⠒⢿⣯⣶⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣟⣛⣲⡾⣷⠎⠁⠉⠻⠽⢻⣛⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠉⠂⠘⠿⠏⠀⠀⠀⣈⣉⣉⣉⣿⣿⣿⣿⣿⣷⣶⣾⣿⣛⣋⣽⣶⠋⠀⠀⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠂⠀⠀⠐⠒⠒⠒⠀⠀⠀⠐⠀⠀⠀⠀⠀⣯⣿⣿⣶⣶⡸⣀⠀⠐⠂⠀⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⣰⣖⣆⣀⣈ ⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠖⠰⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠓⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠐⠒⠒⠒⠒⠰⠒⠐⠲⠖⠒⠀⠀⠒⠒⠚⠿⣿⣿⣿⡕⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠑⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣦⣶⣶⣴⣶⣶⣤⣶⣾⣷⣶⣶⣶⣾⣿⣿⣿⣷⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⠀⠀⠀⠂⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣛⠶⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⢉⣿⣿⣦⡀⢠⠆⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⡟⡿⣿⣽⣻⣿⣛⣽⣭⣽⣼⣮⡤⢴⣦⣤⣤⣤⣤⠤⠭⢤⡤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣶⣿⣿⣿⡿⣷⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠃⣷⠴⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣟⣿⣿⣿⣟⣓⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣝⡿⣿⣿⢿⣿⡞⣿⢠⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣮⡝⣿⣿⡯⠙⣬⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⢿⣿⣿⣿⡛⡛ ⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⡧⠀⠀⠄⣺⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠹⠿⣿⣿⣿⣿⣿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⡛⣛⣿⣿⣿⣿⣿⣭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣷⣿⡏⠉⠉⠉⡛⣋⣻⣿⣿⡏⣿⣿⡟⣿⣿⣿⣿⣿⣿⠿⠛⢿⣿⣛⣻⣿⣿⣇⣉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣼⣿⣾⣿⣿⣿⣿⣿⣟⣿⣳⣿⣶⣟⣿⣟⣻⣟⣻⣿⣿⣿⣷⣿⣟⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠈⣿⣿⣿⣿⣿⣿⣿⠟⠉⠻⣟⣛⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣹⣿⣯⣿⣯⣽⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠀⠀⠒⢿⣯⣶⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣟⣛⣲⡾⣷⠎⠁⠉⠻⠽⢻⣛⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠉⠂⠘⠿⠏⠀⠀⠀⣈⣉⣉⣉⣿⣿⣿⣿⣿⣷⣶⣾⣿⣛⣋⣽⣶⠋⠀⠀⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠂⠀⠀⠐⠒⠒⠒⠀⠀⠀⠐⠀⠀⠀⠀⠀⣯⣿⣿⣶⣶⡸⣀⠀⠐⠂⠀⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⣰⣖⣆⣀⣈ ⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣷⣿⡏⠉⠉⠉⡛⣋⣻⣿⣿⡏⣿⣿⡟⣿⣿⣿⣿⣿⣿⠿⠛⢿⣿⣛⣻⣿⣿⣇⣉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣼⣿⣾⣿⣿⣿⣿⣿⣟⣿⣳⣿⣶⣟⣿⣟⣻⣟⣻⣿⣿⣿⣷⣿⣟⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠈⣿⣿⣿⣿⣿⣿⣿⠟⠉⠻⣟⣛⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣹⣿⣯⣿⣯⣽⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠀⠀⠒⢿⣯⣶⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣟⣛⣲⡾⣷⠎⠁⠉⠻⠽⢻⣛⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠉⠂⠘⠿⠏⠀⠀⠀⣈⣉⣉⣉⣿⣿⣿⣿⣿⣷⣶⣾⣿⣛⣋⣽⣶⠋⠀⠀⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠂⠀⠀⠐⠒⠒⠒⠀⠀⠀⠐⠀⠀⠀⠀⠀⣯⣿⣿⣶⣶⡸⣀⠀⠐⠂⠀⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⣰⣖⣆⣀⣈ ⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠖⠰⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠓⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠐⠒⠒⠒⠒⠰⠒⠐⠲⠖⠒⠀⠀⠒⠒⠚⠿⣿⣿⣿⡕⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠑⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣦⣶⣶⣴⣶⣶⣤⣶⣾⣷⣶⣶⣶⣾⣿⣿⣿⣷⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠀⠀⠒⢿⣯⣶⣿⣿⣿⣿⣿⣿⢿⠿⢿⣿⣟⣛⣲⡾⣷⠎⠁⠉⠻⠽⢻⣛⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠉⠂⠘⠿⠏⠀⠀⠀⣈⣉⣉⣉⣿⣿⣿⣿⣿⣷⣶⣾⣿⣛⣋⣽⣶⠋⠀⠀⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠂⠀⠀⠐⠒⠒⠒⠀⠀⠀⠐⠀⠀⠀⠀⠀⣯⣿⣿⣶⣶⡸⣀⠀⠐⠂⠀⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⣰⣗⣆⣀⣈ ⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠖⠰⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠓⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠐⠒⠒⠒⠒⠰⠒⠐⠲⠖⠒⠀⠀⠒⠒⠚⠿⣿⣿⣿⡕⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠑⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣦⣶⣶⣴⣶⣶⣤⣶⣾⣷⣶⣶⣶⣾⣿⣿⣿⣷⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⠀⠀⠀⠂⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣛⣿⣛⠶⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⢉⣿⣿⣧⡀⢠⠆⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⡟⡿⣿⣽⣻⣿⣛⣽⣭⣽⣼⣮⡤⢴⣦⣤⣤⣤⣤⠤⠭⢤⡤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣶⣿⣿⣿⡿⣷⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠃⣷⠴⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣟⣿⣿⣿⣟⣓⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣝⡿⣿⣿⢿⣿⡞⣿⢠⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣮⡝⣿⣿⡯⠙⣬⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⢿⣿⣿⣿⡛⡛ ⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⡧⠀⠀⠄⣺⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠹⠿⣿⣿⣿⣿⣿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⡛⣛⣿⣿⣿⣿⣿⣭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣷⣿⡏⠉⠉⠉⡛⣋⣻⣿⣿⡏⣿⣿⡟⣿⣿⣿⣿⣿⣿⠿⠛⢿⣿⣛⣻⣿⣿⣇⣉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣼⣿⣾⣿⣿⣿⣿⣿⣟⣿⣳⣿⣶⣟⣿⣟⣻⣟⣻⣿⣿⣿⣷⣿⣟⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠈⣿⣿⣿⣿⣿⣿⣿⠟⠉⠻⣟⣛⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣹⣿⣯⣿⣯⣽⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠀⠀⠒⢿⣯⣶⣿⣿⣿⣿⣿⣿⢿⠿⢿⣿⣟⣛⣲⡾⣷⠎⠁⠉⠻⠽⢻⣛⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠉⠂⠘⠿⠏⠀⠀⠀⣈⣉⣉⣉⣿⣿⣿⣿⣿⣷⣶⣾⣿⣛⣋⣽⣶⠋⠀⠀⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠂⠀⠀⠐⠒⠒⠒⠀⠀⠀⠐⠀⠀⠀⠀⠀⣯⣿⣿⣶⣶⡸⣀⠀⠐⠂⠀⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⣰⣗⣆⣀⣈ ⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠖⠰⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠓⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠐⠒⠒⠒⠒⠰⠒⠐⠲⠖⠒⠀⠀⠒⠒⠚⠿⣿⣿⣿⡕⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠑⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣦⣶⣶⣴⣶⣶⣤⣶⣾⣷⣶⣶⣶⣾⣿⣿⣿⣷⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⠀⠀⠀⠂⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣛⣿⣛⠶⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⢉⣿⣿⣦⡀⢠⠆⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⡟⡿⣿⣽⣻⣿⣛⣽⣭⣽⣼⣮⡤⢴⣦⣤⣤⣤⣤⠤⠭⢤⡤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣶⣿⣿⣿⡿⣷⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠃⣷⠴⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣟⣿⣿⣿⣟⣓⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣝⡿⣿⣿⢿⣿⡞⣿⢠⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣮⡝⣿⣿⡯⠙⣬⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⢿⣿⣿⣿⡛⡛ ⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⡧⠀⠀⠄⣺⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠹⠿⣿⣿⣿⣿⣿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⡛⣛⣿⣿⣿⣿⣿⣭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣷⣿⡏⠉⠉⠉⡛⣋⣻⣿⣿⡏⣿⣿⡟⣿⣿⣿⣿⣿⣿⠿⠛⢿⣿⣛⣻⣿⣿⣇⣉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣼⣿⣾⣿⣿⣿⣿⣿⣟⣿⣳⣿⣶⣟⣿⣟⣻⣟⣻⣿⣿⣿⣷⣿⣟⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠈⣿⣿⣿⣿⣿⣿⣿⠟⠉⠻⣟⣛⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣹⣿⣯⣿⣯⣽⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠀⠀⠒⢿⣯⣶⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣟⣛⣲⡾⣷⠎⠁⠉⠻⠽⢻⣛⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠉⠂⠘⠿⠏⠀⠀⠀⣈⣉⣉⣉⣿⣿⣿⣿⣿⣿⣷⣿⣿⣛⣋⣽⣶⠋⠀⠀⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠂⠀⠀⠐⠒⠒⠒⠀⠀⠀⠐⠀⠀⠀⠀⠀⣯⣿⣿⣶⣶⡸⣀⠀⠐⠂⠀⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⣰⣖⣆⣀⣈ ⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣷⣿⡏⠉⠉⠉⡛⣋⣻⣿⣿⡏⣿⣿⡟⣿⣿⣿⣿⣿⣿⠿⠛⢿⣿⣛⣻⣿⣿⣇⣉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣼⣿⣾⣿⣿⣿⣿⣿⣟⣿⣻⣿⣶⣟⣿⣟⣻⣟⣻⣿⣿⣿⣷⣿⣟⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠈⣿⣿⣿⣿⣿⣿⣿⠟⠉⠻⣟⣛⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣹⣿⣯⣿⣯⣽⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠀⠀⠒⢿⣯⣶⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣟⣛⣲⡾⣷⠎⠁⠉⠻⠽⢻⣛⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠉⠂⠘⠿⠏⠀⠀⠀⣈⣉⣉⣉⣿⣿⣿⣿⣿⣿⣷⣿⣿⣛⣋⣽⣶⠋⠀⠀⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠂⠀⠀⠐⠒⠒⠒⠀⠀⠀⠐⠀⠀⠀⠀⠀⣯⣿⣿⣶⣶⡸⣀⠀⠐⠂⠀⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⣰⣖⣆⣀⣈ ⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠖⠰⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠓⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠐⠒⠒⠒⠒⠰⠒⠐⠲⠖⠒⠀⠀⠒⠒⠚⠿⣿⣿⣿⡕⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠑⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣦⣶⣶⣴⣶⣶⣤⣶⣾⣷⣶⣶⣶⣾⣿⣿⣿⣷⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠀⠀⠒⢿⣯⣶⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣟⣛⣲⡾⣷⠎⠁⠉⠻⠽⢻⣛⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠉⠂⠘⠿⠏⠀⠀⠀⣈⣉⣉⣉⣿⣿⣿⣿⣿⣿⣷⣿⣿⣛⣋⣽⣶⠋⠀⠀⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠂⠀⠀⠐⠒⠒⠒⠀⠀⠀⠐⠀⠀⠀⠀⠀⣯⣿⣿⣶⣶⡸⣀⠀⠐⠂⠀⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⣰⣖⣆⣀⣈ ⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠖⠰⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠓⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠐⠒⠒⠒⠒⠰⠒⠐⠲⠖⠒⠀⠀⠒⠒⠚⠿⣿⣿⣿⡕⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠑⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣦⣶⣶⣴⣶⣶⣤⣶⣾⣷⣶⣶⣶⣾⣿⣿⣿⣷⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⠀⠀⠀⠂⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣛⣿⣛⠶⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⢉⣿⣿⣦⡀⢠⠆⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⡟⡿⣿⣽⣻⣿⣛⣽⣭⣽⣼⣮⡤⢴⣦⣤⣤⣤⣤⠤⠭⢤⡤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣶⣿⣿⣿⡿⣷⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠃⣷⠴⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣟⣓⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣝⡿⣿⣿⢿⣿⡞⣿⢠⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣮⡝⣿⣿⡯⠙⣬⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⢿⣿⣿⣿⡛⡛ ⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⡧⠀⠀⠄⣺⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠹⠿⣿⣿⣿⣿⣿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⡛⣛⣿⣿⣿⣿⣿⣭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣷⣿⡏⠉⠉⠉⡛⣋⣻⣿⣿⡏⣿⣿⡟⣿⣿⣿⣿⣿⣿⠿⠛⢿⣿⣛⣻⣿⣿⣇⣉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣼⣿⣾⣿⣿⣿⣿⣿⣟⣿⣻⣿⣶⣟⣿⣟⣻⣟⣻⣿⣿⣿⣷⣿⣟⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠈⣿⣿⣿⣿⣿⣿⣿⠟⠉⠻⣟⣛⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣹⣿⣯⣿⣯⣽⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠀⠀⠒⢿⣯⣶⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣟⣛⣲⡾⣷⠎⠁⠉⠻⠽⢻⣛⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠉⠂⠘⠿⠏⠀⠀⠀⣈⣉⣉⣉⣿⣿⣿⣿⣿⣿⣷⣿⣿⣛⣋⣽⣶⠋⠀⠀⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠂⠀⠀⠐⠒⠒⠒⠀⠀⠀⠐⠀⠀⠀⠀⠀⣯⣿⣿⣶⣶⡸⣀⠀⠐⠂⠀⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⣰⣖⣆⣀⣈ ⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠖⠰⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠓⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠐⠒⠒⠒⠒⠰⠒⠐⠲⠖⠒⠀⠀⠒⠒⠚⠿⣿⣿⣿⡕⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠑⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣦⣶⣶⣴⣶⣶⣤⣶⣾⣷⣶⣶⣶⣾⣿⣿⣿⣷⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⠀⠀⠀⠂⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣛⣿⣛⠶⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⢉⣿⣿⣦⡀⢠⠆⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⡟⡿⣿⣽⣻⣿⣛⣽⣭⣽⣼⣮⡤⢴⣦⣤⣤⣤⣤⠤⠭⢤⡤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣶⣿⣿⣿⡿⣷⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠃⣷⠴⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣟⣓⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣝⡿⣿⣿⢿⣿⡞⣿⢠⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣮⡝⣿⣿⡯⠙⣬⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⢿⣿⣿⣿⡛⡛ ⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⡧⠀⠀⠄⣺⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠹⠿⣿⣿⣿⣿⣿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⡛⣛⣿⣿⣿⣿⣿⣭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣷⣿⡏⠉⠉⠉⡛⣋⣻⣿⣿⡏⣿⣿⡟⣿⣿⣿⣿⣿⣿⠿⠛⢿⣿⣛⣻⣿⣿⣇⣉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣼⣿⣾⣿⣿⣿⣿⣿⣟⣿⣻⣿⣶⣟⣿⣟⣻⣟⣻⣿⣿⣿⣷⣿⣟⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠈⣿⣿⣿⣿⣿⣿⣿⠟⠉⠻⣟⣛⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣹⣿⣯⣿⣯⣽⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠀⠀⠒⢿⣯⣶⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣟⣛⣲⡾⣷⠎⠁⠉⠻⠽⢻⣛⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠉⠂⠘⠿⠏⠀⠀⠀⣈⣉⣉⣉⣿⣿⣿⣿⣿⣿⣷⣿⣿⣛⣋⣽⣶⠋⠀⠀⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠂⠀⠀⠐⠒⠒⠒⠀⠀⠀⠐⠀⠀⠀⠀⠀⣯⣿⣿⣶⣶⡸⣀⠀⠐⠂⠀⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⣰⣖⣆⣀⣈ ⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣷⣿⡏⠉⠉⠉⡛⣋⣻⣿⣿⡏⣿⣿⡟⣿⣿⣿⣿⣿⣿⠿⠛⢿⣿⣛⣻⣿⣿⣇⣉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣼⣿⣾⣿⣿⣿⣿⣿⣟⣿⣻⣿⣶⣟⣿⣟⣻⣟⣻⣿⣿⣿⣷⣿⣟⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠈⣿⣿⣿⣿⣿⣿⣿⠟⠉⠻⣟⣛⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣹⣿⣯⣿⣯⣽⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠀⠀⠒⢿⣯⣶⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣟⣛⣲⡾⣷⠎⠁⠉⠻⠽⢻⣛⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠉⠂⠘⠿⠏⠀⠀⠀⣈⣉⣉⣉⣿⣿⣿⣿⣿⣿⣷⣿⣿⣛⣋⣽⣶⠋⠀⠀⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠂⠀⠀⠐⠒⠒⠒⠀⠀⠀⠐⠀⠀⠀⠀⠀⣯⣿⣿⣶⣶⡸⣀⠀⠐⠂⠀⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⣰⣖⣆⣀⣈ ⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠖⠰⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠓⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠐⠒⠒⠒⠒⠰⠒⠐⠲⠖⠒⠀⠀⠒⠒⠚⠿⣿⣿⣿⡕⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠑⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣦⣶⣶⣴⣶⣶⣤⣶⣾⣷⣶⣶⣶⣾⣿⣿⣿⣷⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠀⠀⠒⢿⣯⣶⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣟⣛⣲⡾⣷⠎⠁⠉⠻⠽⢻⣛⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠉⠂⠘⠿⠏⠀⠀⠀⣈⣉⣉⣉⣿⣿⣿⣿⣿⣿⣷⣿⣿⣛⣋⣽⣶⠋⠀⠀⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠂⠀⠀⠐⠒⠒⠒⠀⠀⠀⠐⠀⠀⠀⠀⠀⣯⣿⣿⣶⣶⡸⣀⠀⠐⠂⠀⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⣰⣖⣆⣀⣈ ⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠖⠰⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠓⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠐⠒⠒⠒⠒⠰⠒⠐⠲⠖⠒⠀⠀⠒⠒⠚⠿⣿⣿⣿⡕⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠑⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣦⣶⣶⣴⣶⣶⣤⣶⣾⣷⣶⣶⣶⣾⣿⣿⣿⣷⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⠀⠀⠀⠂⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣛⣿⣛⠶⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⢉⣿⣿⣦⡀⢠⠆⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⡟⡿⣿⣽⣻⣿⣛⣽⣭⣽⣼⣮⡤⢴⣦⣤⣤⣤⣤⠤⠭⢤⡤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣶⣿⣿⣿⡿⣷⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠃⣷⠴⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣟⣓⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣝⡿⣿⣿⢿⣿⡞⣿⢠⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣮⡝⣿⣿⡯⠙⣬⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠿⢿⣿⣿⣿⡟⡛ ⠀⢀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⡧⠀⠀⠄⣺⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠹⠿⣿⣿⣿⣿⣿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⡛⣛⣿⣿⣿⣿⣿⣭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣷⣿⡏⠉⠉⠉⡛⣋⣻⣿⣿⡏⣿⣿⡟⣿⣿⣿⣿⣿⣿⠿⠛⢿⣿⣛⣻⣿⣿⣇⣉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣼⣿⣾⣿⣿⣿⣿⣿⣟⣿⣻⣿⣶⣿⣿⣟⣻⣟⣻⣿⣿⣿⣷⣿⣟⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠈⣿⣿⣿⣿⣿⣿⣿⠟⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣹⣿⣯⣿⣯⣽⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠀⠀⠒⢿⣯⣶⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣟⣛⣲⡾⣷⠎⠁⠉⠻⣽⣻⣛⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠉⠂⠘⠿⠏⠀⠀⠀⣈⣉⣉⣉⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣽⣶⠋⠀⠀⠀⠈⠉⠉⠉⢱ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠂⠀⠀⠐⠒⠒⠒⠀⠀⠀⠐⠀⠀⠀⠀⠀⣯⣿⣿⣶⣶⡸⣀⠀⠐⠂⠀⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⣰⣖⣆⣀⣈ ⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠀⠀⠀⠐⠂⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠔⠐⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠓⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠐⠒⠒⠒⠒⠰⠒⠐⠲⠖⠒⠀⠀⠒⠒⠚⠻⣿⣿⣿⡕⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠑⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣦⣶⣶⣴⣶⣶⣤⣶⣾⣷⣶⣶⣶⣾⣿⣿⣿⣷⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⠀⠀⠀⠂⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣛⣿⣛⠶⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢉⣭⣿⣦⡀⢀⠆⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⡟⡿⣿⣽⣻⣿⣛⣽⣭⣼⣼⣮⡤⢴⣦⣤⣤⣤⣤⠤⠭⢤⡤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣐⣾⣿⣿⡿⣷⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠃⣵⠴⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣽⣟⣿⣿⣿⣿⣿⣿⣟⣓⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣝⡿⣿⣿⢿⣿⡞⣿⢠⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣮⡝⣿⣿⡯⠙⣬⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠿⢿⣿⣿⣿⡟⡛ ⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⡧⠀⠀⠄⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠹⠿⣿⣿⣿⣿⣿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⡛⣛⣿⣿⣿⣿⣿⣭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠿⣿⣛⣻⣿⣿⣇⣉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣼⣿⣾⣿⣿⣿⣿⣿⣟⣿⣻⣿⣶⣿⣿⣟⣻⣟⣻⣿⣿⣿⣷⣿⣟⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠈⣿⣿⣿⣿⣿⣿⣿⡟⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣹⣿⣯⣿⣯⣽⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣲⡾⣷⠎⠁⠉⠻⣽⣻⣛⣻ ⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡸⣿⣿⣿⣿⣿⠿⠿⠶⣾⣿⣏⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣶⠋⠀⠀⠀⠈⠉⠉⠉⢱ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠂⠀⠀⠐⠒⠒⠒⠀⠀⠀⠐⠀⠀⠀⠀⠀⣯⣾⣿⣶⡶⣘⣤⣤⢐⡂⣠⡂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣇⣀⣀⣀⣰⣖⣆⣀⣈ ⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠀⠀⠀⠐⠂⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠔⠐⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠓⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠐⠒⠒⠒⠒⠰⠒⠐⠲⠖⠒⠀⠀⠒⠒⠚⠻⣿⣿⣿⡕⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠑⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣦⣶⣶⣴⣶⣶⣤⣶⣾⣷⣶⣶⣶⣾⣿⣿⣿⣷⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⠀⠀⠀⠂⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣛⣿⣛⠶⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢉⣭⣿⣦⡀⢀⢆⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⡟⡿⣿⣽⣻⣿⣛⣽⣭⣼⣼⣮⡤⢴⣦⣤⣤⣤⣤⠤⠭⢤⡤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣾⣿⣿⡿⣷⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠁⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠃⣵⠴⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣽⣟⣿⣿⣿⣿⣿⣿⣟⣓⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣝⡿⣿⣿⢿⣿⡞⣿⢠⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣮⡝⣿⣿⡯⠙⣬⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠿⢿⣿⣿⣿⡟⡛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⡧⠀⠀⠄⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠹⠿⣿⣿⣿⣿⣿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⡛⣛⣿⣿⣿⣿⣿⣭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢿⣿⣛⣻⣿⣿⣇⣉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣼⣿⣾⣿⣿⣿⣿⣿⣟⣿⣻⣿⣶⣿⣿⣟⣻⣟⣻⣿⣿⣿⣷⣿⣟⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠈⣿⣿⣿⣿⣿⣿⣿⡟⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣹⣿⣯⣿⣯⣽⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣲⡾⣷⠎⠁⠉⠻⣽⣻⣛⣿ ⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡸⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣏⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣶⠋⠀⠀⠀⠈⠉⠉⠉⢱ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠂⠀⠀⠐⠒⠒⠒⠀⠀⠀⠐⠀⠀⠀⠀⠀⣯⣿⣿⣶⡶⣘⣤⣤⢐⡂⣠⡂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣇⣀⣀⣀⣰⣖⣆⣀⣈ ⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠀⠀⠀⠐⠂⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠔⠐⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠓⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠐⠒⠒⠒⠒⠰⠒⠐⠲⠖⠒⠀⠀⠒⠒⠚⠻⣿⣿⣿⡕⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠑⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣦⣶⣶⣴⣶⣶⣤⣶⣾⣷⣶⣶⣶⣾⣿⣿⣿⣷⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣲⡾⣷⠎⠁⠉⠻⣽⣻⣛⣿ ⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡸⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣏⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣶⠋⠀⠀⠀⠈⠉⠉⠉⢱ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠂⠀⠀⠐⠒⠒⠒⠀⠀⠀⠐⠀⠀⠀⠀⠀⣯⣿⣿⣶⡶⣘⣤⣤⢐⡂⣠⡂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣇⣀⣀⣀⣰⣖⣆⣀⣈ ⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠀⠀⠀⠐⠂⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠔⠐⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠓⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠐⠒⠒⠒⠒⠰⠒⠐⠲⠖⠒⠀⠀⠒⠒⠚⠻⣿⣿⣿⡕⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠑⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣦⣶⣶⣴⣶⣶⣤⣶⣾⣷⣶⣶⣶⣾⣿⣿⣿⣷⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⠀⠀⠀⠂⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣛⣿⣛⠶⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢉⣭⣿⣦⡀⢀⢆⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⡟⡿⣿⣽⣻⣿⣛⣽⣭⣼⣼⣮⡤⢴⣦⣤⣤⣤⣤⠤⠭⢤⡤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣾⣿⣿⡿⣷⠀⢸⣻⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠁⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠃⣵⠴⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣽⣟⣿⣿⣿⣿⣿⣿⣟⣓⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣝⡿⣿⣿⢿⣿⡞⣿⢠⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣮⡝⣿⣿⡯⠙⣬⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠿⢿⣿⣿⣿⡟⡛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⡧⠀⠀⠄⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠹⠿⣿⣿⣿⣿⣿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⡛⣛⣿⣿⣿⣿⣿⣭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢿⣿⣛⣻⣿⣿⣇⣉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣼⣿⣾⣿⣿⣿⣿⣿⣟⣿⣻⣿⣶⣿⣿⣟⣻⣟⣻⣿⣿⣿⣷⣿⣟⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠈⣿⣿⣿⣿⣿⣿⣿⡟⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣹⣿⣯⣿⣯⣽⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣲⡾⣷⠎⠁⠉⠻⣽⣻⣛⣿ ⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡸⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣏⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣶⠋⠀⠀⠀⠈⠉⠉⠉⢱ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠂⠀⠀⠐⠒⠒⠒⠀⠀⠀⠐⠀⠀⠀⠀⠀⣯⣿⣿⣶⡶⣘⣤⣤⢐⡂⣠⡂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣇⣀⣀⣀⣰⣖⣆⣀⣈ ⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠀⠀⠀⠐⠂⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠔⠐⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠓⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠐⠒⠒⠒⠒⠰⠒⠐⠲⠖⠒⠀⠀⠒⠒⠚⠻⣿⣿⣿⡕⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠑⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣦⣶⣶⣴⣶⣶⣤⣶⣾⣷⣶⣶⣶⣾⣿⣿⣿⣷⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⠀⠀⠀⠂⣿⣿⣿⣿⣻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣛⣿⣛⠶⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢉⣭⣿⣦⡀⢀⢆⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⡟⡿⣿⣽⣻⣿⣛⣽⣭⣼⣼⣮⡤⢴⣦⣤⣤⣤⣤⠤⠭⢤⡤ ⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣾⣿⣿⡿⣷⠀⢸⣻⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠁⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠃⣵⠴⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣽⣟⣿⣿⣿⣿⣿⣿⣟⣓⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣝⡿⣿⣿⢿⣿⡞⣿⢠⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣮⡝⣿⣿⡯⠙⣼⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠿⢿⣿⣿⣿⡟⡛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⡧⠀⠀⢤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠘⠻⠿⣿⣿⣿⣿⣿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⡛⣛⣿⣿⣿⣿⣿⣭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢿⣿⣛⣻⣿⣿⣇⣉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣼⣿⣾⣿⣿⣿⣿⣿⣟⣿⣻⣿⣶⣿⣿⣟⣻⣟⣻⣿⣿⣿⣷⣿⣟⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠈⣿⣿⣿⣿⣿⣿⣿⡟⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣹⣿⣯⣿⣯⣽⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣲⡾⣷⠎⠁⠉⠻⣽⣻⣛⣿ ⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡸⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣏⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣶⠋⠀⠀⠀⠈⠉⠉⠉⢱ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠂⠀⠀⠐⠒⠒⠒⠀⠀⠀⠐⠀⠀⠀⠀⠀⣯⣿⣿⣶⡶⣘⣤⣤⢐⡂⣠⡂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣇⣀⣀⣀⣰⣖⣆⣀⣈ ⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠀⠀⠀⠐⠂⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠔⠐⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠓⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠐⠒⠒⠒⠒⠰⠒⠐⠲⠖⠒⠀⠀⠒⠒⠚⠻⣿⣿⣿⡕⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠑⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣦⣶⣶⣴⣶⣶⣤⣶⣾⣷⣶⣶⣶⣾⣿⣿⣿⣷⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⠀⠀⠀⠂⣿⣿⣿⣿⣻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣛⣿⣛⠶⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢉⣭⣿⣦⡀⢀⢆⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⡟⡿⣿⣽⣻⣿⣛⣽⣭⣼⣼⣮⡤⢴⣦⣤⣤⣤⣤⠤⠭⢤⡤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣾⣿⣿⡿⣷⠀⢸⣻⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠁⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⣿⣿⣿⣿⠃⣵⠴⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣽⣟⣿⣿⣟⣿⣿⣿⣟⣓⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣝⡿⣿⣿⢿⣿⡞⡿⢠⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣮⡝⣿⣿⡯⠙⣼⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠿⢿⣿⣿⣿⡟⡛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⡧⠰⠄⢤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠘⠻⠿⣿⣿⣿⣿⣿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⡛⣛⣿⣿⣿⣿⣿⣭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢿⣿⣛⣻⣿⣿⣇⣉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣼⣿⣾⣿⣿⣿⣿⣿⣟⣿⣻⣿⣶⣿⣿⣟⣻⣟⣻⣿⣿⣿⣷⣿⣟⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠈⣿⣿⣿⣿⣿⣿⣿⡟⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣹⣿⣯⣿⣯⣽⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣲⡾⣷⠎⠁⠉⠻⣽⣻⣛⣿ ⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡸⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣏⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣶⠋⠀⠀⠀⠈⠉⠉⠉⢱ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠂⠀⠀⠐⠒⠒⠒⠀⠀⠀⠐⠀⠀⠀⠀⠀⣯⣿⣿⣶⡶⣘⣤⣤⢐⡂⣠⡂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣇⣀⣀⣀⣰⣖⣆⣀⣈ ⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠀⠀⠀⠐⠂⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠔⠐⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠓⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠐⠒⠒⠒⠒⠰⠒⠐⠲⠖⠒⠀⠀⠒⠒⠚⠻⣿⣿⣿⡕⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠑⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣦⣶⣶⣴⣶⣶⣤⣶⣾⣷⣶⣶⣶⣾⣿⣿⣿⣷⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣲⡾⣷⠎⠁⠉⠻⣽⣻⣛⣿ ⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡸⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣏⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣶⠋⠀⠀⠀⠈⠉⠉⠉⢱ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠂⠀⠀⠐⠒⠒⠒⠀⠀⠀⠐⠀⠀⠀⠀⠀⣯⣿⣿⣶⡶⣘⣤⣤⢐⡂⣠⡂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣇⣀⣀⣀⣰⣖⣆⣀⣈ ⢶⠄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠦⠤⠤⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄ ⠀⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢤⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠢⠄⠀⠢⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠐⠒⠂⠀⣀⠀⠀⡀⠠⣶⣦⣴⣶⣶⣶⣦⣴⣤⣦⣤⣶⣶⣤⣤⣤⣤⣶⣶⣶⣦⣤⣦⣤⣀⣀⣀⣶⣶⣖⠒⠒⠒⠒⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣶⣿⣆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⠸⣿⣿⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢿⣀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣷⣾⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⢻⣿⡟⠛⠛⠛⠛⠟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⠄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⡹⠿⠛⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠘⠟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⠟⢿⣿⣿⡇⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠠⣦⣤⣤⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡿⠿⢛⡃⠀⣴⣿⣿⣿⣶⣤⣶⣴⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⡇⠠⣴⡄⣠ ⢀⣀⡀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢡⣤⣼⣄⣴⣾⣿⣿⡇⠀⠒⣒⡒⠀⠀⠀⢀⣒⠀⠀⠀⠀⢐⣒⡀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢠⣼⢧⠿⢿⣾ ⠈⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡧⠀⠠⠤⠄⠀⠀⠀⠠⠤⠀⠀⠀⠀⠤⠤⠄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⠈⠚⠛⠛⠛⠛⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠃⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣐⠓⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠸⣿⣿⣟⣳⣿ ⠀⠒⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣯⣬⣭⣿⣿⣿⣿⣿⣿⣿⡇⣀⡀⠀⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣀⣀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⢠⣀⣂⡀⠀⠀⣠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢸⣿⣿⣿⣟⡻ ⠀⣁⣈⡉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⢀⣉⣉⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⠀⠽⢽⠋⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣷⠀⠀⠀⢸⣿⣿⣿⣿⣯ ⠠⠤⣄⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⡀⠘⠻⠋⠀⠀⠀⢘⣿⣿⣿⣿⣿ ⠀⠚⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠶⠶⠆⠀⣀⡀⠀⠀⠀⣀⠘⠿⠿⠿⠝⠿⠿⠿⠿⠿⠿⠿⠿⠿⠺⢗⡿⠿⠿⠿⡷⠿⡺⠿⠺⠟⠿⠇⠼⠿⠿⣿⡿⠿⠿⠏⡻⠿⡆⣀⢀⣀⣀⣀⣸⣿⣿⣿⣿⣿ ⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢶⡖⣻⣿⡟⢼⣟⢛⣯⣾⣍⡶⡷⡒⠒⢒⣒⠒⡚⠓⣶⡿⠻⣚⢻⣾⣿⣿⣿⣿⣿⣿⣿⡟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢁⡀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙⠉⠉⠉⠩⠉⠉⠉⠉⠈⠉⠉⠉⠋⣍⠉⠉⠉⡭⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⣿⠯⠭⠽⢿⣿⣿⣿⣿ ⠀⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠤⠿⠃⠀⠀⠀⣀⣀⣼⣸⣯⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠉⠉⠉⠉⢹ ⠨⣿⠋⠉⠉⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢀⣰⣶⣖⣖⣢⣀⣰⣶⣶⣶⢶⣦⣀⣀⡶⣤⣤⣄⣀⣸⣿⣿⣿⣶⣶⣿⣭⣭⣿⣿⣿⣷⡄⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣄⣀⣀⣸⣷⣧⣀⣈ ⢶⠄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠦⠤⠤⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄ ⠀⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢤⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠢⠄⠀⠢⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠐⠒⠂⠀⣀⠀⠀⡀⠠⣶⣦⣴⣶⣶⣶⣦⣴⣤⣦⣤⣶⣶⣤⣤⣤⣤⣶⣶⣶⣦⣤⣦⣤⣀⣀⣀⣶⣶⣖⠒⠒⠒⠒⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣶⣿⣆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⠸⣿⣿⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢿⣀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣷⣾⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⢻⣿⡟⠛⠛⠛⠛⠟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⠄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⡹⠿⠛⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠐⠟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⠟⢿⣿⣿⡇⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠠⣦⣤⣤⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡿⠿⢛⡃⠀⣴⣿⣿⣿⣶⣤⣶⣴⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⡇⠠⣴⡄⣠ ⢀⣀⡀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢡⣤⣼⣄⣴⣾⣿⣿⡇⠀⠒⣒⡒⠀⠀⠀⢀⣒⠀⠀⠀⠀⢐⣒⡀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢠⣼⢧⠿⢿⣾ ⠈⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡧⠀⠠⠤⠄⠀⠀⠀⠠⠤⠀⠀⠀⠀⠤⠤⠄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⠈⠚⠛⠛⠛⠛⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠃⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣐⠓⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠸⣿⣿⣟⣳⣿ ⠀⠒⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣯⣬⣭⣿⣿⣿⣿⣿⣿⣿⡇⣀⡀⠀⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣀⣀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⢠⣀⣂⡀⠀⠀⣠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢸⣿⣿⣿⣟⡻ ⠀⣁⣈⡉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⢀⣉⣉⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⠀⠽⢽⠋⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣷⠀⠀⠀⢸⣿⣿⣿⣿⣯ ⠠⠤⣄⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⡀⠘⠻⠋⠀⠀⠀⢘⣿⣿⣿⣿⣿ ⠀⠚⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠶⠶⠆⠀⣀⡀⠀⠀⠀⣀⠘⠿⠿⠿⠝⠿⠿⠿⠿⠿⠿⠿⠿⠿⠺⢗⡿⠿⠿⠿⡷⠿⡺⠿⠺⠟⠿⠇⠼⠿⠿⣿⡿⠿⠿⠏⡻⠿⡆⣀⢀⣀⣀⣀⣸⣿⣿⣿⣿⣿ ⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢶⡖⣻⣿⡟⢼⣟⢛⣯⣾⣍⡶⡷⡒⠒⢒⣒⠒⡚⠓⣶⡿⠻⣚⢻⣾⣿⣿⣿⣿⣿⣿⣿⡟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢁⡀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙⠉⠉⠉⠩⠉⠉⠉⠉⠈⠉⠉⠉⠋⣍⠉⠉⠉⡭⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⣿⠯⠭⠽⢿⣿⣿⣿⣿ ⠀⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠤⠿⠃⠀⠀⠀⣀⣀⣼⣸⣯⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠉⠉⠉⠉⢹ ⠨⣿⠋⠉⠉⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢀⣰⣶⣖⣖⣢⣀⣰⣶⣶⣶⢶⣦⣀⣀⡶⣤⣤⣄⣀⣸⣿⣿⣿⣶⣶⣿⣭⣭⣿⣿⣿⣷⡄⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣄⣀⣀⣸⣷⣧⣀⣈ ⢶⠄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠦⠤⠤⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄ ⠀⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢤⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠢⠄⠀⠢⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠐⠒⠂⠀⣀⠀⠀⡀⠠⣶⣦⣴⣶⣶⣶⣦⣴⣤⣦⣤⣶⣶⣤⣤⣤⣤⣶⣶⣶⣦⣤⣦⣤⣀⣀⣀⣶⣶⣖⠒⠒⠒⠒⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣶⣿⣆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⠸⣿⣿⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢿⣀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣷⣾⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⢻⣿⡟⠛⠛⠛⠛⠟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⠄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⡹⠿⠛⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠖⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⠟⢿⣿⣿⡇⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠠⣦⣤⣤⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡿⠿⢛⡃⠀⣴⣿⣿⣿⣶⣤⣶⣴⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⡇⠠⣴⡄⣠ ⢀⣀⡀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢡⣤⣼⣄⣴⣾⣿⣿⡇⠀⠒⣒⡒⠀⠀⠀⢀⣒⠀⠀⠀⠀⢐⣒⡀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢠⣼⢧⠿⢿⣾ ⠈⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡧⠀⠠⠤⠄⠀⠀⠀⠠⠤⠀⠀⠀⠀⠤⠤⠄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⠈⠚⠛⠛⠛⠛⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠃⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣐⠓⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠸⣿⣿⣟⣳⣿ ⠀⠒⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣯⣬⣭⣿⣿⣿⣿⣿⣿⣿⡇⣀⡀⠀⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣀⣀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⢠⣀⣂⡀⠀⠀⣠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢸⣿⣿⣿⣟⡻ ⠀⣁⣈⡉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⢀⣉⣉⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⠀⠽⢽⠋⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣷⠀⠀⠀⢸⣿⣿⣿⣿⣯ ⠠⠤⣄⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⡀⠘⠻⠋⠀⠀⠀⢘⣿⣿⣿⣿⣿ ⠀⠚⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠶⠶⠆⠀⣀⡀⠀⠀⠀⣀⠘⠿⠿⠿⠝⠿⠿⠿⠿⠿⠿⠿⠿⠿⠺⢗⡿⠿⠿⠿⡷⠿⡺⠿⠺⠟⠿⠇⠼⠿⠿⣿⡿⠿⠿⠏⡻⠿⡆⣀⢀⣀⣀⣀⣸⣿⣿⣿⣿⣿ ⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢶⡖⢻⣿⡟⢼⣟⢛⣯⣾⣍⡶⡷⡒⠒⢒⣒⠒⡚⠓⣶⡿⠻⣚⢻⣾⣿⣿⣿⣿⣿⣿⣿⡟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢁⡀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙⠉⠈⠉⠩⠉⠉⠉⠉⠈⠉⠉⠉⠋⣍⠉⠉⠉⡭⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⣿⠯⠭⠽⢿⣿⣿⣿⣿ ⠀⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠤⠿⠃⠀⠀⠀⣀⣀⣼⣸⣯⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠉⠉⠉⠉⢹ ⠨⣿⠋⠉⠉⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢀⢰⣶⣖⣖⣢⣀⣰⣶⣶⣶⢶⣦⣀⣀⡶⣤⣤⣄⣀⣸⣿⣿⣿⣶⣶⣿⣭⣭⣿⣿⣿⣷⡄⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣄⣀⣀⣸⣷⣧⣀⣈ ⢶⠄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠦⠤⠤⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄ ⠀⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢤⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠢⠄⠀⠢⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠐⠒⠂⠀⣀⠀⠀⡀⠠⣶⣦⣴⣶⣶⣶⣦⣴⣤⣦⣤⣶⣶⣤⣤⣤⣤⣶⣶⣶⣦⣤⣦⣤⣀⣀⣀⣶⣶⣖⠒⠒⠒⠒⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣶⣿⣆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⠸⣿⣿⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢿⣀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣷⣾⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⢻⣿⡟⠛⠛⠛⠛⠟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⠄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⡹⠿⠛⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠖⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⠟⢿⣿⣿⡇⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠠⣦⣤⣤⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡿⠿⢛⡃⠀⣴⣿⣿⣿⣶⣤⣶⣴⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⡇⠠⣴⡄⣠ ⢀⣀⡀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢡⣤⣼⣄⣴⣾⣿⣿⡇⠀⠒⣒⡒⠀⠀⠀⢀⣒⠀⠀⠀⠀⢐⣒⡀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢠⣼⢧⠿⢿⣾ ⠈⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡧⠀⠠⠤⠄⠀⠀⠀⠠⠤⠀⠀⠀⠀⠤⠤⠄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⠈⠚⠛⠛⠛⠛⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠃⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣐⠓⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠸⣿⣿⣟⣳⣿ ⠀⠒⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣯⣬⣭⣿⣿⣿⣿⣿⣿⣿⡇⣀⡀⠀⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣀⣀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⢠⣀⣂⡀⠀⠀⣠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢸⣿⣿⣿⣟⡻ ⠀⣁⣈⡉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⢀⣉⣉⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⠀⠽⢽⠋⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣷⠀⠀⠀⢸⣿⣿⣿⣿⣯ ⠠⠤⣄⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⡀⠘⠻⠋⠀⠀⠀⢘⣿⣿⣿⣿⣿ ⠀⠚⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠶⠆⠆⠀⣀⡀⠀⠀⠀⣀⠘⠿⠿⠿⠝⠿⠿⠿⠿⠿⠿⠿⠿⠿⠺⢗⡿⠿⠿⠿⡷⠿⡺⠿⠺⠟⠿⠇⠼⠿⠿⣿⡿⠿⠿⠏⡻⠿⡆⣀⢀⣀⣀⣀⣸⣿⣿⣿⣿⣿ ⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢶⡖⢻⣿⡟⢼⣟⢛⣯⣾⣍⡶⡷⡒⠒⢒⣒⠒⡚⠓⣶⡿⠻⣚⢻⣾⣿⣿⣿⣿⣿⣿⣿⡟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢁⡀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙⠉⠈⠉⠩⠉⠉⠉⠉⠈⠉⠉⠉⠋⣍⠉⠉⠉⡭⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⣿⠯⠭⠽⢿⣿⣿⣿⣿ ⠀⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠤⠿⠃⠀⠀⠀⣀⣀⣼⣸⣯⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠉⠉⠉⠉⢹ ⠨⣿⠋⠉⠉⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢀⢰⣶⣖⣖⣢⣀⣰⣶⣶⣶⢶⣦⣀⣀⡶⣤⣤⣄⣀⣸⣿⣿⣿⣶⣶⣿⣭⣭⣿⣿⣿⣷⡄⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣄⣀⣀⣸⣷⣧⣀⣈ ⢶⠄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠦⠤⠤⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄ ⠀⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢤⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠢⠄⠀⠢⠠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠐⠒⠂⠀⢀⠀⠀⡀⠠⣶⣦⣴⣶⣶⣶⣦⣤⣤⣤⣤⣶⣶⣤⣤⣤⣤⣶⣶⣦⣤⣤⣦⣤⣀⣀⣀⣶⣶⣖⠒⠒⠒⠒⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣶⣿⣆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀ ⠸⣿⣿⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠿⣀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣷⣾⣿⣿⡿⠛⠛⠛⠛⠛⠛⠛⢻⣿⡟⠛⠛⠛⠛⠟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣯⣦⣤⠄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣹⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢖⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⠟⢿⣿⣿⡇⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡿⠿⢛⡃⠀⣴⣿⣿⣿⣦⣤⣦⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⡇⠠⣴⡄⣠ ⢀⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢡⣤⣼⣄⣴⣾⣿⣿⡇⠀⠒⣒⡒⠀⠀⠀⢀⣒⠀⠀⠀⠀⢐⣒⡀⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢠⣬⢧⠿⢿⣾ ⠈⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡧⠀⠠⠤⠄⠀⠀⠀⠠⠤⠀⠀⠀⠀⠤⢴⠄⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⠈⠚⠛⠛⠛⠛⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠃⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣐⠋⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠸⣿⣿⣟⣳⣿ ⠀⠷⠾⠶⠆⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣯⣬⣭⣿⣿⣿⣿⣿⣿⣿⡇⣀⡀⠀⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣀⣀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⢀⣀⣂⡀⠀⠀⣠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢸⣿⣿⣿⣟⡻ ⠀⣁⣈⡉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⢀⣉⣉⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣽⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⠀⠽⢽⠋⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣷⠀⠀⠀⢸⣿⣿⣿⣿⣯ ⠠⠤⣄⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⡀⠈⠻⠋⠀⠀⠀⢘⣿⣿⣿⣿⣿ ⠀⠚⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠶⠆⠆⠀⣀⡀⠀⠀⠀⣀⠘⠿⠿⠿⠝⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⢗⡿⠿⠿⠿⡷⠿⡺⠿⠺⠟⠿⠇⠼⠿⠿⣿⡿⠿⠿⠏⡻⠿⡆⣀⢀⣀⣀⣀⣸⣿⣿⣿⣿⣿ ⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢶⡖⢲⣿⡟⢼⣟⢛⣯⣾⣍⡶⡷⡒⠒⢒⣒⠒⡚⠓⣶⡿⠻⣚⢻⣾⣿⣿⣿⣿⣿⣿⣿⡟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢁⡀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙⠉⠈⠉⠩⠉⠉⠉⠉⠈⠉⠉⠉⠉⣍⠉⠉⠉⡭⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⣿⠯⠭⠽⢿⣿⣿⣿⣿ ⠀⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠤⠿⠃⠀⠀⠀⣀⣀⣼⣸⣯⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠉⠉⠉⠉⢹ ⠨⣿⠋⠉⠉⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢀⢰⣶⣖⣖⣢⣀⣠⣶⣶⣶⢶⣦⣀⣀⡶⣤⣤⣄⣀⣸⣿⣿⣿⣶⣶⣻⣭⣭⣿⣿⣿⣷⡄⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣄⣀⣀⣸⣷⣧⣀⣈ ⢶⠄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠦⠤⠤⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄ ⠀⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢤⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠢⠄⠀⠢⠠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠐⠒⠂⠀⢀⠀⠀⡀⠠⣶⣦⣴⣶⣶⣶⣦⣤⣤⣤⣤⣶⣶⣤⣤⣤⣤⣶⣶⣦⣤⣤⣦⣤⣀⣀⣀⣶⣶⣖⠒⠒⠒⠒⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣶⣿⣆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀ ⠸⣿⣿⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠿⣀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣷⣾⣿⣿⡿⠛⠛⠛⠛⠛⠛⠛⢻⣿⡟⠛⠛⠛⠛⠟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣯⣦⣤⠄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣹⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢖⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⠟⢿⣿⣿⡇⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡿⠿⢛⡃⠀⣴⣿⣿⣿⣦⣤⣦⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⡇⠠⣴⡄⣠ ⢀⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢡⣤⣼⣄⣴⣾⣿⣿⡇⠀⠒⣒⡒⠀⠀⠀⢀⣒⠀⠀⠀⠀⢐⣒⡀⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢠⣬⢧⠿⢿⣾ ⠈⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡧⠀⠠⠤⠄⠀⠀⠀⠠⠤⠀⠀⠀⠀⠤⢴⠄⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⠀⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠃⣀⣀⠀⠀⠁⠀⠀⠀⠀⣀⣐⠋⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠸⣿⣿⣟⣳⣿ ⠀⠶⠾⠶⠆⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣯⣬⣭⣿⣿⣿⣿⣿⣿⣿⡇⣀⡀⠀⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣀⣀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⢀⣀⣂⡀⠀⠀⣠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢸⣿⣿⣿⣟⡻ ⠀⣁⣈⡉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣽⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⠰⠶⠶⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣷⠀⠀⠀⢸⣿⣿⣿⣿⣯ ⠠⠤⣄⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⡀⠈⠻⠋⠀⠀⠀⢘⣿⣿⣿⣿⣿ ⠀⠚⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠶⠆⠆⠀⣀⡀⠀⠀⠀⣀⠘⠿⠿⠿⠝⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⢗⡿⠿⠿⠿⡷⠿⡺⠿⠺⠟⠿⠇⠼⠿⠿⣿⡿⠿⠿⠏⡻⠿⡆⣀⢀⣀⣀⣀⣸⣿⣿⣿⣿⣿ ⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢶⡖⢲⣿⡟⢼⣟⢛⣯⣾⣍⡶⡷⡒⠒⢒⣒⠒⡚⠓⣶⡿⠻⣚⢻⣾⣿⣿⣿⣿⣿⣿⣿⡟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢁⡀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙⠉⠈⠉⠩⠉⠉⠉⠉⠈⠉⠉⠉⠉⣍⠉⠉⠉⡭⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⣿⠯⠭⠽⢿⣿⣿⣿⣿ ⠀⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠤⠿⠃⠀⠀⠀⣀⣀⣼⣸⣯⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠉⠉⠉⠉⢹ ⠨⣿⠋⠉⠉⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢀⢰⣶⣖⣖⣢⣀⣠⣶⣶⣶⢶⣦⣀⣀⡶⣤⣤⣄⣀⣸⣿⣿⣿⣶⣶⣻⣭⣭⣿⣿⣿⣷⡄⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣄⣀⣀⣸⣷⣧⣀⣈ ⢶⠄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠦⠤⠤⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄ ⠀⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢤⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠢⠄⠀⠢⠠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠐⠒⠂⠀⢀⠀⠀⡀⠠⣶⣦⣴⣶⣶⣶⣦⣤⣤⣤⣤⣶⣶⣤⣤⣤⣤⣶⣶⣦⣤⣤⣦⣤⣀⣀⣀⣶⣶⣖⠒⠒⠒⠒⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣶⣿⣆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀ ⠸⣿⣿⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠿⣀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣷⣾⣿⣿⡿⠛⠛⠛⠛⠛⠛⠛⢻⣿⡟⠛⠛⠛⠛⠟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣯⣦⣤⠄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣹⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢖⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⠟⢿⣿⣿⡇⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡿⠿⢛⡃⠀⣴⣿⣿⣿⣦⣤⣦⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⡇⠠⣴⡄⣠ ⢀⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢡⣤⣼⣄⣴⣾⣿⣿⡇⠀⠒⣒⡒⠀⠀⠀⢀⣒⠀⠀⠀⠀⢐⣒⡀⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢠⣬⢧⠿⢿⣾ ⠈⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡧⠀⠠⠤⠄⠀⠀⠀⠠⠤⠀⠀⠀⠀⠤⢴⠄⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⠀⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠃⣀⣀⠀⠀⠁⠀⠀⠀⠀⣀⣐⠋⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠸⣿⣿⣟⣳⣿ ⠀⠶⠾⠶⠆⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣯⣬⣭⣿⣿⣿⣿⣿⣿⣿⡇⣀⡀⠀⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣰⣀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⢀⣀⣂⡀⠀⠀⣠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢸⣿⣿⣿⣟⡻ ⠀⣁⣈⡉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣽⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⠰⠶⠶⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣷⠀⠀⠀⢸⣿⣿⣿⣿⣯ ⠠⠤⣄⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⡀⠈⠻⠋⠀⠀⠀⢘⣿⣿⣿⣿⣿ ⠀⠚⠿⠃⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠐⠆⠆⠀⣀⡀⠀⠀⠀⣀⠘⠿⠿⠿⠝⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⢗⡿⠿⠿⠿⡷⠿⡺⠿⠺⠟⠿⠇⠼⠿⠿⣿⡿⠿⠿⠏⡻⠿⡆⣀⢀⣀⣀⣀⣸⣿⣿⣿⣿⣿ ⠀⠉⠉⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⣄⠀⠀⢶⡖⠒⣿⡟⢼⣟⢛⣯⣾⣍⡶⡷⡒⠒⢒⣒⠒⡚⠓⣶⡿⠻⣚⢻⣾⣿⣿⣿⣿⣿⣿⣿⡟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢁⡀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙⠉⠈⠉⠩⠉⠉⠉⠉⠈⠉⠉⠉⠉⣍⠉⠉⠉⡭⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⣿⠯⠭⠽⢿⣿⣿⣿⣿ ⠀⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠤⠿⠃⠀⠀⠀⣀⣀⣼⣸⣯⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠉⠉⠉⠉⢹ ⠨⣿⠋⠉⠉⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢀⢰⣶⣖⣖⣢⣀⣠⣶⣶⣶⢶⣦⣀⣀⡶⣤⣤⣄⣀⣸⣿⣿⣿⣶⣶⣻⣭⣭⣿⣿⣿⣷⡄⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣄⣀⣀⣸⣷⣧⣀⣈ ⢶⠄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠦⠤⠤⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄ ⠀⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢤⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠢⠄⠀⠢⠠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠐⠒⠂⠀⢀⠀⠀⡀⠠⣶⣦⣴⣶⣶⣶⣦⣤⣤⣤⣤⣶⣶⣤⣤⣤⣤⣶⣶⣦⣤⣤⣦⣤⣀⣀⣀⣶⣶⣖⠒⠒⠒⠒⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣶⣿⣆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀ ⠸⣿⣿⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠿⣀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣷⣾⣿⣿⡿⠛⠛⠛⠛⠛⠛⠛⢻⣿⡟⠛⠛⠛⠛⠟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣯⣦⣤⠄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣹⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢖⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⠟⢿⣿⣿⡇⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡿⠿⢛⡃⠀⣴⣿⣿⣿⣦⣤⣦⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⡇⠠⣴⡄⣠ ⢀⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢡⣤⣼⣄⣴⣾⣿⣿⡇⠀⠒⣒⡒⠀⠀⠀⢀⣒⠀⠀⠀⠀⢐⣒⡀⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢠⣬⢧⠿⢿⣾ ⠈⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡧⠀⠠⠤⠄⠀⠀⠀⠠⠤⠀⠀⠀⠀⠤⢴⠄⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⠀⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠃⣀⣀⠀⠀⠁⠀⠀⠀⠀⣀⣐⠋⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠸⣿⣿⣟⣳⣿ ⠀⠶⠾⠶⠆⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣯⣬⣭⣿⣿⣿⣿⣿⣿⣿⡇⣀⡀⠀⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣰⣀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⢀⣀⣂⡀⠀⠀⣠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢸⣿⣿⣿⣟⡻ ⠀⣁⣈⡉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣽⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⠰⠶⠶⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣷⠀⠀⠀⢸⣿⣿⣿⣿⣯ ⠠⠤⣄⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⡀⠈⠻⠋⠀⠀⠀⢘⣿⣿⣿⣿⣿ ⠀⠚⠿⠃⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠐⠆⠆⠀⣀⡀⠀⠀⠀⣀⠘⠿⠿⠿⠝⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⢗⡿⠿⠿⠿⡷⠿⡺⠿⠺⠟⠿⠇⠼⠿⠿⣿⡿⠿⠿⠏⡻⠿⡆⣀⢀⣀⣀⣀⣸⣿⣿⣿⣿⣿ ⠀⠉⠉⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⣄⠀⠀⢶⡖⠒⣿⡟⢼⣟⢛⣯⣾⣍⡶⡷⡒⠒⢒⣒⠒⡚⠓⣶⡿⠻⣚⢻⣾⣿⣿⣿⣿⣿⣿⣿⡟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢁⡀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙⠉⠈⠉⠩⠉⠉⠉⠉⠈⠉⠉⠉⠉⣍⠉⠉⠉⡭⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⣿⠯⠭⠽⢿⣿⣿⣿⣿ ⠀⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠤⠿⠃⠀⠀⠀⣀⣀⣼⣸⣯⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠉⠉⠉⠉⢹ ⠨⣿⠋⠉⠉⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢀⢰⣶⣖⣖⣢⣀⣠⣶⣶⣶⢶⣦⣀⣀⡶⣤⣤⣄⣀⣸⣿⣿⣿⣶⣶⣻⣭⣭⣿⣿⣿⣷⡄⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣄⣀⣀⣸⣷⣧⣀⣈ ⢶⠄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠦⠤⠤⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄ ⠀⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢤⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠢⠄⠀⠢⠠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠐⠒⠂⠀⢀⠀⠀⡀⠠⣶⣦⣴⣶⣶⣶⣦⣤⣤⣤⣤⣶⣶⣤⣤⣤⣤⣶⣶⣦⣤⣤⣦⣤⣀⣀⣀⣶⣶⣖⠒⠒⠒⠒⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣶⣿⣆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀ ⠸⣿⣿⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠿⣀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣷⣾⣿⣿⡿⠛⠛⠛⠛⠛⠛⠛⢻⣿⡟⠛⠛⠛⠛⠟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣯⣦⣤⠄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣹⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢖⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⠟⢿⣿⣿⡇⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡿⠿⢛⡃⠀⣴⣿⣿⣿⣦⣤⣦⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⡇⠠⣴⡄⣠ ⢀⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢡⣤⣼⣄⣴⣾⣿⣿⡇⠀⠒⣒⡒⠀⠀⠀⢀⣒⠀⠀⠀⠀⢐⣒⡀⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢠⣬⢧⠿⢿⣾ ⠈⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡧⠀⠠⠤⠄⠀⠀⠀⠠⠤⠀⠀⠀⠀⠤⢴⠄⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⠀⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠃⣀⣀⠀⠀⠁⠀⠀⠀⠀⣀⣐⠋⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠸⣿⣿⣟⣳⣿ ⠀⠶⠾⠶⠆⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣯⣬⣭⣿⣿⣿⣿⣿⣿⣿⡇⣀⡀⠀⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣰⣀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⢀⣀⣂⡀⠀⠀⣠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢸⣿⣿⣿⣟⡻ ⠀⣁⣈⡉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣽⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⠰⠶⠶⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣷⠀⠀⠀⢸⣿⣿⣿⣿⣯ ⠠⠤⣄⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⡀⠈⠻⠋⠀⠀⠀⢘⣿⣿⣿⣿⣿ ⠀⠚⠿⠃⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠐⠆⠆⠀⣀⡀⠀⠀⠀⣀⠘⠿⠿⠿⠝⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⢗⡿⠿⠿⠿⡷⠿⡺⠿⠺⠟⠿⠇⠼⠿⠿⣿⡿⠿⠿⠏⡻⠿⡆⣀⢀⣀⣀⣀⣸⣿⣿⣿⣿⣿ ⠀⠉⠉⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⣄⠀⠀⢶⡖⠒⣿⡟⢼⣟⢛⣯⣾⣍⡶⡷⡒⠒⢒⣒⠒⡚⠓⣶⡿⠻⣚⢻⣾⣿⣿⣿⣿⣿⣿⣿⡟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢁⡀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙⠉⠈⠉⠩⠉⠉⠉⠉⠈⠉⠉⠉⠉⣍⠉⠉⠉⡭⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⣿⠯⠭⠽⢿⣿⣿⣿⣿ ⠀⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠤⠿⠃⠀⠀⠀⣀⣀⣼⣸⣯⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠉⠉⠉⠉⢹ ⠨⣿⠋⠉⠉⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢀⢰⣶⣖⣖⣢⣀⣠⣶⣶⣶⢶⣦⣀⣀⡶⣤⣤⣄⣀⣸⣿⣿⣿⣶⣶⣻⣭⣭⣿⣿⣿⣷⡄⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣄⣀⣀⣸⣷⣧⣀⣈ ⢶⠄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠦⠤⠤⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄ ⠀⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢤⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠢⠄⠀⠢⠠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠐⠒⠂⠀⢀⠀⠀⡀⠠⣶⣦⣴⣶⣶⣶⣦⣤⣤⣤⣤⣶⣶⣤⣤⣤⣤⣶⣶⣦⣤⣤⣦⣤⣀⣀⣀⣶⣶⣖⠒⠒⠒⠒⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣶⣿⣆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀ ⠸⣿⣿⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠿⣀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣷⣾⣿⣿⡿⠛⠛⠛⠛⠛⠛⠛⢻⣿⡟⠛⠛⠛⠛⠟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣯⣦⣤⠄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣹⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢖⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⠟⢿⣿⣿⡇⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⣿⡿⠿⢛⡃⠀⣴⣿⣿⣿⣦⣤⣦⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⡇⠠⣴⡄⣠ ⢀⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠈⢡⣤⣼⣄⣴⣾⣿⣿⡇⠀⠒⣒⡒⠀⠀⠀⢀⣒⠀⠀⠀⠀⢐⣒⡀⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢠⣬⢧⠿⢿⣾ ⠈⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡧⠀⠠⠤⠄⠀⠀⠀⠠⠤⠀⠀⠀⠀⠤⢴⠄⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⠀⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠃⣀⣀⠀⠀⠁⠀⠀⠀⠀⣀⣐⠋⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠸⣿⣿⣟⣳⣿ ⠀⠶⠾⠶⠆⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣯⣬⣭⣿⣿⣿⣿⣿⣿⣿⡇⣀⡀⠀⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣰⣀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⢀⣀⣂⡀⠀⠀⣠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢸⣿⣿⣿⣟⡻ ⠀⣁⣈⡉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣽⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⠰⠶⠶⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣷⠀⠀⠀⢸⣿⣿⣿⣿⣯ ⠠⠤⣄⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⡀⠈⠻⠋⠀⠀⠀⢘⣿⣿⣿⣿⣿ ⠀⠚⠿⠃⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠐⠆⠆⠀⣀⡀⠀⠀⠀⣀⠘⠿⠿⠿⠝⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⢗⡿⠿⠿⠿⡷⠿⡺⠿⠺⠟⠿⠇⠼⠿⠿⣿⡿⠿⠿⠏⡻⠿⡆⣀⢀⣀⣀⣀⣸⣿⣿⣿⣿⣿ ⠀⠉⠉⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⣄⠀⠀⢶⡖⠒⣿⡟⠼⣟⢛⣯⣾⣍⡶⡷⡒⠒⢒⣒⠒⡚⠓⣶⡿⠻⣚⢻⣾⣿⣿⣿⣿⣿⣿⣿⡟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢁⡀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙⠉⠈⠉⠩⠉⠉⠉⠉⠈⠉⠉⠉⠉⣍⠉⠉⠉⡭⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⣿⠯⠭⠽⢿⣿⣿⣿⣿ ⠀⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠤⠿⠃⠀⠀⠀⣀⣀⣼⣸⣯⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠉⠉⠉⠉⢹ ⠨⣿⠋⠉⠉⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢀⢰⣶⣖⣖⣢⣀⣠⣶⣶⣶⢶⣦⣀⣀⡶⣤⣤⣄⣀⣸⣿⣿⣿⣶⣶⣻⣭⣭⣿⣿⣿⣷⡄⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣄⣀⣀⣸⣷⣧⣀⣈ ⢶⠄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠦⠤⠤⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄ ⠀⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢤⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠢⠄⠀⠢⠠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠐⠒⠂⠀⢀⠀⠀⡀⠠⣶⣦⣴⣶⣶⣶⣦⣤⣤⣤⣤⣶⣶⣤⣤⣤⣤⣶⣶⣦⣤⣤⣦⣤⣀⣀⣀⣶⣶⣖⠒⠒⠒⠒⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣶⣿⣆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀ ⠸⣿⣿⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠿⣀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣷⣾⣿⣿⡿⠛⠛⠛⠛⠛⠛⠛⢻⣿⡟⠛⠛⠛⠛⠟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣯⣦⣤⠄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣹⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢖⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⠟⢿⣿⣿⡇⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⡀⠀⣀⠀⠀⠀⠀⠐⣿⡿⠿⢛⡃⠀⣴⣿⣿⣿⣦⣤⣦⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⡇⠠⣴⡄⣠ ⢀⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠀⠉⠀⠀⠀⠀⡀⠈⢡⣤⣼⣄⣴⣾⣿⣿⡇⠀⠒⣒⡒⠀⠀⠀⢀⣒⠀⠀⠀⠀⢐⣒⡀⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢠⣬⢧⠿⢿⣾ ⠈⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡧⠀⠠⠤⠄⠀⠀⠀⠠⠤⠀⠀⠀⠀⠤⢴⠄⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⠀⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠃⣀⣀⠀⠀⠁⠀⠀⠀⠀⣀⣐⠋⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠸⣿⣿⣟⣳⣿ ⠀⠶⠾⠶⠆⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣯⣬⣭⣿⣿⣿⣿⣿⣿⣿⡇⣀⡀⠀⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣰⣀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⢀⣀⣂⡀⠀⠀⣠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢸⣿⣿⣿⣟⡻ ⠀⣁⣈⡉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣿⣿⣿⣿⣿⣿⡻⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣽⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⠰⠶⠶⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣅⣷⠀⠀⠀⢸⣿⣿⣿⣿⣯ ⠠⠤⣄⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⡀⠈⠻⠋⠀⠀⠀⢘⣿⣿⣿⣿⣿ ⠀⠚⠿⠃⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠐⠆⠆⠀⣀⡀⠀⠀⠀⣀⠘⠿⠿⠿⠝⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⢗⡿⠿⠿⠿⡷⠿⡺⠿⠺⠟⠿⠇⠼⠿⠿⣿⡿⠿⠿⠏⡻⠿⡆⣀⢀⣀⣀⣀⣸⣿⣿⣿⣿⣿ ⠀⠉⠉⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⣄⠀⠀⢶⡖⠒⣿⡟⠼⣟⢛⣯⣾⣍⡶⡷⡒⠒⢒⣒⠒⡚⠓⣶⡿⠻⣚⢻⣾⣿⣿⣿⣿⣿⣿⣿⡟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢁⡀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙⠉⠈⠉⠩⠉⠉⠉⠉⠈⠉⠉⠉⠉⣍⠉⠉⠉⡭⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⣿⠯⠭⠽⢿⣿⣿⣿⣿ ⠀⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠤⠿⠃⠀⠀⠀⣀⣀⣼⣸⣯⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠉⠉⠉⠉⢹ ⠨⣿⠋⠉⠉⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢀⢰⣶⣖⣖⣢⣀⣠⣶⣶⣶⢶⣦⣀⣀⡶⣤⣤⣄⣀⣸⣿⣿⣿⣶⣶⣻⣭⣭⣿⣿⣿⣷⡄⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣄⣀⣀⣸⣷⣧⣀⣈ ⢶⠄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠦⠤⠤⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄ ⠀⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢤⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠢⠄⠀⠢⠠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠐⠒⠂⠀⢀⠀⠀⡀⠠⣶⣦⣴⣶⣶⣶⣦⣤⣤⣤⣤⣶⣶⣤⣤⣤⣤⣶⣶⣦⣤⣤⣦⣤⣀⣀⣀⣶⣶⣖⠒⠒⠒⠒⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣶⣿⣆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀ ⠸⣿⣿⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠿⣀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣷⣾⣿⣿⡿⠛⠛⠛⠛⠛⠛⠛⢻⣿⡟⠛⠛⠛⠛⠟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣯⣦⣤⠄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣹⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢖⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⠟⢿⣿⣿⡇⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⡀⠀⣀⠀⠀⠀⠀⠐⣿⡿⠿⢛⡃⠀⣴⣿⣿⣿⣦⣤⣦⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⡇⠠⣴⡄⣠ ⢀⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠈⠁⠀⠀⠁⠀⠉⠀⠀⠀⠀⡀⠈⢡⣤⣼⣄⣴⣾⣿⣿⡇⠀⠒⣒⡒⠀⠀⠀⢀⣒⠀⠀⠀⠀⢐⣒⡀⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢠⣬⢧⠿⢿⣾ ⠈⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡧⠀⠠⠤⠄⠀⠀⠀⠠⠤⠀⠀⠀⠀⠤⢴⠄⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⠀⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠃⣀⣀⠀⠀⠁⠀⠀⠀⠀⣀⣐⠋⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠸⣿⣿⣟⣳⣿ ⠀⠶⠾⠶⠆⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣯⣬⣭⣿⣿⣿⣿⣿⣿⣿⡇⣀⡀⠀⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣰⣀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⢀⣀⣂⡀⠀⠀⣠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢸⣿⣿⣿⣟⡻ ⠀⣁⣈⡉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣿⣿⣿⣿⣿⣿⡻⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣽⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⠰⠶⠶⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣅⣷⠀⠀⠀⢸⣿⣿⣿⣿⣯ ⠠⠤⣄⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⡀⠈⠻⠋⠀⠀⠀⢘⣿⣿⣿⣿⣿ ⠀⠚⠿⠃⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠐⠆⠆⠀⣀⡀⠀⠀⠀⣀⠘⠿⠿⠿⠝⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⢗⡿⠿⠷⠾⡷⠿⡺⠿⠺⠟⠿⠇⠼⠿⠿⣿⡿⠿⠿⠏⡻⠿⡆⣀⢀⣀⣀⣀⣸⣿⣿⣿⣿⣿ ⠀⠉⠉⠁⠀⠘⠋⠀⠀⠀⠀⠀⠀⣄⠀⠀⢶⡖⠒⣿⡟⠼⣟⢛⣯⣾⣍⡶⡷⡒⠒⢒⣒⠒⡚⠓⣶⡿⠻⣚⢻⣾⣿⣿⣿⣿⣿⣿⣿⡟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢁⡀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙⠉⠈⠉⠩⠉⠉⠉⠉⠈⠉⠉⠉⠉⣍⠉⠉⠉⡭⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⣿⠯⠭⠽⢿⣿⣿⣿⣿ ⠀⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠤⠿⠃⠀⠀⠀⣀⣀⣼⣸⣯⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠉⠉⠉⠉⢹ ⠨⣿⠋⠉⠉⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢀⢰⣶⣖⣖⣢⣀⣠⣶⣶⣶⢶⣦⣀⣀⡶⣤⣤⣄⣀⣸⣿⣿⣿⣶⣶⣻⣭⣭⣿⣿⣿⣷⡄⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣄⣀⣀⣸⣷⣧⣀⣈ ⢶⠄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠦⠤⠤⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄ ⠀⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢤⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠢⠄⠀⠢⠠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠐⠒⠂⠀⢀⠀⠀⡀⠠⣶⣦⣴⣶⣶⣶⣦⣤⣤⣤⣤⣶⣶⣤⣤⣤⣤⣶⣶⣦⣤⣤⣦⣤⣀⣀⣀⣶⣶⣖⠒⠒⠒⠒⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣶⣿⣆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀ ⠸⣿⣿⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠿⣀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣷⣾⣿⣿⡿⠛⠛⠛⠛⠛⠛⠛⢻⣿⡟⠛⠛⠛⠛⠟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣯⣦⣤⠄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣹⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢖⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⠟⢿⣿⣿⡇⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⡀⠀⣀⠀⠀⠀⠀⠐⣿⡿⠿⢛⡃⠀⣴⣿⣿⣿⣦⣤⣦⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⡇⠠⣴⡄⣠ ⢀⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠈⠉⠀⠀⠁⠀⠉⠀⠀⠀⠀⡀⠈⢡⣤⣼⣄⣴⣾⣿⣿⡇⠀⠒⣒⡒⠀⠀⠀⢀⣒⠀⠀⠀⠀⢐⣒⡀⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢠⣬⢧⠿⢿⣾ ⠈⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡧⠀⠠⠤⠄⠀⠀⠀⠠⠤⠀⠀⠀⠀⠤⢴⠄⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⠀⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠃⣀⣀⠀⠀⠁⠀⠀⠀⠀⣀⣐⠋⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠸⣿⣿⣟⣳⣿ ⠀⠶⠾⠶⠆⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣯⣬⣭⣿⣿⣿⣿⣿⣿⣿⡇⣀⡀⠀⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣰⣀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⢀⣀⣂⡀⠀⠀⣠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢸⣿⣿⣿⣟⡻ ⠀⣁⣈⡉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣿⣿⣿⣿⣿⣿⡻⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣽⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⠰⠶⠶⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣅⣷⠀⠀⠀⢸⣿⣿⣿⣿⣯ ⠠⠤⣄⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⢿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡆⡀⠈⠻⠋⠀⠀⠀⢘⣿⣿⣿⣿⣿ ⠀⠚⠿⠃⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠐⠆⠆⠀⣀⡀⠀⠀⠀⣀⠘⠿⠿⠿⠝⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⢗⡿⠿⠷⠾⡷⠿⡺⠿⠺⠟⠿⠇⠼⠿⠿⣿⡿⠿⠿⠏⡻⠿⡆⣀⢀⣀⣀⣀⣸⣿⣿⣿⣿⣿ ⠀⠉⠉⠁⠀⠘⠙⠁⠀⠀⠀⠀⠀⣄⠀⠀⢶⡖⠒⣿⡟⠼⣟⢛⣯⣾⣍⡶⡷⡒⠒⢒⣒⠒⡚⠓⣶⡿⠻⣚⢻⣾⣿⣿⣿⣿⣿⣿⣿⡟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢁⡀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙⠉⠈⠉⠩⠉⠉⠉⠉⠈⠉⠉⠉⠉⣍⠉⠉⠉⡭⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⣿⠯⠭⠽⢿⣿⣿⣿⣿ ⠀⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠤⠿⠃⠀⠀⠀⣀⣀⣼⣸⣯⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠉⠉⠉⠉⢹ ⠨⣿⠋⠉⠉⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢀⢰⣶⣖⣖⣢⣀⣠⣶⣶⣶⢶⣦⣀⣀⡶⣤⣤⣄⣀⣸⣿⣿⣿⣶⣶⣻⣭⣭⣿⣿⣿⣷⡄⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣄⣀⣀⣸⣷⣧⣀⣈ ⢶⠄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠦⠤⠤⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄ ⠀⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢤⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠢⠄⠀⠢⠠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠐⠒⠂⠀⢀⠀⠀⡀⠠⣶⣦⣴⣶⣶⣶⣦⣤⣤⣤⣤⣶⣶⣤⣤⣤⣤⣶⣶⣦⣤⣤⣦⣤⣀⣀⣀⣶⣶⣖⠒⠒⠒⠒⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣶⣿⣆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀ ⠸⣿⣿⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠿⣀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣷⣾⣿⣿⡿⠛⠛⠛⠛⠛⠛⠛⢻⣿⡟⠛⠛⠛⠛⠟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣯⣦⣤⠄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣹⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢖⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⠟⢿⣿⣿⡇⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⡀⠀⣀⠀⠀⠀⠀⠐⣿⡿⠿⢛⡃⠀⣴⣿⣿⣿⣦⣤⣦⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⡇⠠⣴⡄⣠ ⢀⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠈⠉⠀⠀⠁⠀⠉⠀⠀⠀⠀⡀⠈⢡⣤⣼⣄⣴⣾⣿⣿⡇⠀⠒⣒⡒⠀⠀⠀⢀⣒⠀⠀⠀⠀⢐⣒⡀⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢠⣬⢧⠿⢿⣾ ⠈⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡧⠀⠠⠤⠄⠀⠀⠀⠠⠤⠀⠀⠀⠀⠤⢴⠄⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⠀⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠃⣀⣀⠀⠀⠁⠀⠀⠀⠀⣀⣐⠋⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠸⣿⣿⣟⣳⣿ ⠀⠶⠾⠶⠆⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣯⣬⣭⣿⣿⣿⣿⣿⣿⣿⡇⣀⡀⠀⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣰⣀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⢀⣀⣂⡀⠀⠀⣠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢸⣿⣿⣿⣟⡻ ⠀⣁⣈⡉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣿⣿⣿⣿⣿⣿⡻⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣽⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⠰⠶⠶⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣅⣷⠀⠀⠀⢸⣿⣿⣿⣿⣯ ⠠⠤⣄⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣀⠀⢲⠶⠆⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡆⡀⠈⠻⠋⠀⠀⠀⢘⣿⣿⣿⣿⣿ ⠀⠚⠿⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠐⠆⠆⠀⣀⡀⠀⠀⠀⣀⠘⠿⠿⠿⠝⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⢗⡿⠿⠷⠾⡷⠿⡺⠿⠺⠟⠿⠇⠼⠿⠿⣿⡿⠿⠿⠏⡻⠿⡆⣀⢀⣀⣀⣀⣸⣿⣿⣿⣿⣿ ⠀⠉⠉⠁⠀⠈⠻⠀⠀⠀⠀⠀⠀⣄⠀⠀⢶⡖⠒⣿⡟⠼⣟⢛⣯⣾⣍⡶⡷⡒⠒⢒⣒⠒⡚⠓⣶⡿⠻⣚⢻⣾⣿⣿⣿⣿⣿⣿⣿⡟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢁⡀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙⠉⠈⠉⠩⠉⠉⠉⠉⠈⠉⠉⠉⠉⣍⠉⠉⠉⡭⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⣿⠯⠭⠽⢿⣿⣿⣿⣿ ⠀⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠤⠿⠃⠀⠀⠀⣀⣀⣼⣸⣯⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠉⠉⠉⠉⢹ ⠨⣿⠋⠉⠉⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢀⢰⣶⣖⣖⣢⣀⣠⣶⣶⣶⢶⣦⣀⣀⡶⣤⣤⣄⣀⣸⣿⣿⣿⣶⣶⣻⣭⣭⣿⣿⣿⣷⡄⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣄⣀⣀⣸⣷⣧⣀⣈ ⢶⠄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠶⠤⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠆ ⠀⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢤⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠢⠤⠀⠢⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⣠⠀⢀⡀⠠⣶⣦⣶⣶⣶⣶⣦⣶⣶⣶⣶⣶⣶⣶⣦⣤⣴⣶⣶⣶⣶⣦⣦⣤⣠⣴⣴⣶⣶⣖⠒⠒⠒⠒⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣠⣾⣿⣆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠤⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⠸⣿⣿⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢿⣀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⣿⣷⣾⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⢻⣿⡿⠛⠛⠛⠛⠿⠟⠟⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⠄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣹⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⢿⣿⣿⡇⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠐⣿⡿⠿⢛⡯⠀⣴⣿⣿⣿⣶⣬⣷⣼⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⡟⠠⣴⡄⣠ ⢈⣉⡉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⠁⠀⠉⠀⠀⠀⢀⣀⠈⢡⣤⣼⣦⣴⣾⣿⣿⣇⠀⢒⣒⡒⠀⠀⠀⢐⣒⠀⠀⠀⠀⢐⣒⡀⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣼⢧⠿⢿⣾ ⠈⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠉⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⡧⠀⠠⠤⠄⠀⠀⠀⠠⠤⠀⠀⠀⠀⠤⢴⠄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⠀⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠛⣀⣀⠀⠀⠃⠀⠀⠀⠀⣀⣘⠛⠀⠠⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠨⣿⣿⣟⣻⣿ ⠀⠶⠾⠶⠆⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣰⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣇⣀⡀⠀⣀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣰⣀⢀⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣽⣿⠦⢦⠶⢾⣿⣿⣿⣿⣿ ⢠⣀⣂⡀⠀⠀⣠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⣿⣿⣿⣿⣿⣿⡏⣿⣶⣒⡒⠀⣘⣿⣿⣿⣟⡻ ⠀⣁⣈⡉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣙⣙⣓⣒⢒⣙⣒⣚⡘⠛⣙⣛⣚⡂⢒⡂⢐⡒⢛⢈⣛⣛ ⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⣯⣿⣿⣍⣻⣙⣿⡿⡥⠤⠀⠀⠸⠿⢿⣿⣿⣿ ⠰⠶⠾⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠩⢿⠿⠿⠿⡿⠟⠿⣿⣷⣿⠶⠀⠀⠸⣿⠿⣿⠿⠯ ⠠⠤⣤⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣁⠉⢳⡶⡶⠀⠀⠀⠈⠛⢛⣤⣒⣶⣶⣀⠀⠐⠚⣛⡓⠒⠒⠀⠀⣛⣶⣲⣶⡟ ⠀⠛⠿⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⠖⠐⠆⠆⠂⣀⡀⠀⠀⢀⣀⡸⠿⠿⠿⠟⠿⠿⠿⠿⠿⢿⠿⠿⠿⠾⢷⡿⠿⠷⠿⡷⠿⡾⠿⠺⠿⠿⠧⠶⠶⠶⠾⠞⠿⠿⠿⡭⠿⡟⣛⢛⣛⣀⣀⣨⠿⠿⣿⣿⡶ ⠀⠉⠉⠁⠀⠈⠻⠀⠀⠀⠀⠀⠀⣄⠀⠠⢶⡖⠳⣿⣟⠼⣿⢛⣯⣾⣝⡶⣷⣒⠒⢒⣒⠒⡞⠓⣶⣿⠻⣚⢻⣾⣿⣿⣿⣿⣿⣿⣿⡟⠛⢻⣿⣿⣿⣯⣤⢤⣤⣥⠤⢤⣤⣼⣿⣿⡿⢿⣟⠷⢿⣿⣿⡤⣤⠬⢭⣤ ⠀⢁⡀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙⠉⠈⠉⠩⠉⠉⠉⠉⠈⠉⠉⠉⠫⣍⠉⠉⢉⡭⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀⣀⣛⣛⣛⣛⣙⣉⣙⣛⣺⡟⣋⠉⠉⠉⢛⣛⣛⣛⣉ ⠈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠠⠀⠘⠷⠤⠿⠋⠀⠀⢀⣀⣀⣼⣸⣯⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣻⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠉⠉⠉⠉⢹ ⠨⣿⠋⠉⠉⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣂⢰⣶⣖⣶⣦⣠⣴⣶⣶⣶⢶⣦⣀⣠⡶⣤⣤⣄⣀⣸⣿⣿⣿⣶⣿⣿⣭⣭⣿⣿⣿⣷⡄⣤⣿⣿⣿⣿⣼⣽⣿⣶⣼⣮⣿⣿⣿⣿⣯⣻⣾⣁⣄⣀⣀⣸⣷⣧⣍⣉ ⢶⠄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠶⠤⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠆ ⠤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢤⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠢⠤⠀⠢⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢠⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⣠⠀⢀⡀⠠⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣠⣴⣴⣶⣶⣖⠒⠒⠒⠚⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣤⣾⣿⣦⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠤⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⠸⣿⣿⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⣿⣿⣷⣾⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⢻⣿⡿⠛⠛⠛⠛⠿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⠄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣹⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⢿⣿⣿⡇⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠐⣿⡿⠿⢛⡯⠠⣴⣿⣿⣿⣶⣼⣷⣼⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⡟⠠⣴⡄⣠ ⢈⣉⡉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⠁⠀⠉⠀⠀⠀⢀⣀⠈⢡⣦⣼⣦⣴⣾⣿⣿⣇⠀⢒⣒⡒⠀⠀⠂⢘⣛⠉⠉⠉⠁⢙⣛⡀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣼⢧⢿⣿⣿ ⠈⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⢀⡉⢁⣤⣾⣿⣿⣿⣿⣿⣿⣿⡯⠀⠠⠤⠄⠀⠀⠀⠠⠤⢠⣤⣀⣬⣭⣽⢽⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⠀⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠛⣀⣀⢀⠀⠃⠀⠈⠛⠋⠋⠛⠛⢈⣛⠛⠛⠛⠙⠛⠛⡛⠛⣟⣿⣿⣿⡥⠁⠀⠀⠨⣿⣿⣟⣻⣿ ⠀⠶⠾⠶⠆⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣰⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣇⣀⡀⠀⣀⠀⠘⠀⢀⣀⡲⠆⠴⠆⠀⣰⣞⢧⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣽⣿⠦⢦⠶⢾⣿⣿⣿⣿⣿ ⢠⣄⣂⡀⠀⠀⣠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⣿⣿⣿⣿⣿⣿⡏⣿⣶⣒⡒⠀⣘⣿⣿⣿⣟⡻ ⠀⣁⣈⡉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣶⣾⣿⣿⣶⣟⣓⣒⣂⣒⣚⡒⡓⣘⡘⠛⣙⣛⣚⣂⢒⡒⣐⣒⢛⢈⣛⣛ ⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣷⣯⣍⣻⣙⣿⡿⡥⠤⠀⠀⠸⠿⢿⣿⣿⣿ ⠰⠶⠾⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠩⣿⠿⠿⠿⡿⠿⢿⣿⣷⣿⡶⠀⠀⠸⣿⠿⣿⠿⠯ ⠠⠤⣤⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡃⠀⣉⡉⢳⡶⡶⠁⠠⠤⠈⠛⢛⣤⣒⣖⣒⢀⠀⠐⠚⣛⡓⠒⠒⠀⠀⣛⣶⣲⣶⡟ ⠀⠛⠿⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⠖⠐⠆⠆⠂⣀⡀⠀⠀⢀⣀⡸⠿⠿⠿⠟⠿⠿⠿⠿⠿⢿⠿⠿⠿⠾⢷⡿⠿⠷⠿⡷⠿⡿⠿⠺⠿⠿⠧⠶⠶⠶⠿⠟⠿⠿⠿⡯⠿⡟⣛⢛⣛⣀⣀⣨⠿⠿⣿⣿⡶ ⠀⠉⠉⠁⠀⠈⠻⠀⠀⠀⠀⠀⠀⣄⠀⠨⢶⡶⡳⣿⣟⠼⣿⢛⣯⣾⣝⡶⣷⣒⠒⢒⣒⠒⡞⠓⣶⣿⠻⣚⢻⣾⣿⣿⣿⣿⣿⣿⣿⡟⠛⢻⣿⣿⣿⣯⣤⢤⣤⣥⠤⢤⣤⣼⣿⣿⡿⢿⣿⠷⢿⣿⣿⡤⣤⠬⢭⣤ ⠄⢁⣀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙⠉⠈⠉⠩⠉⠉⠉⠉⠈⠉⠉⠉⠫⣍⠉⠉⢉⡭⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀⣀⣛⣛⣛⣛⣛⣉⣙⣛⣺⡟⣋⠉⠉⠉⢛⣛⣛⣛⣉ ⡈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠠⠈⠘⠷⠤⠿⠋⠀⠀⢀⣀⣀⣼⣸⣯⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣻⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠉⠉⡉⠉⢹ ⠨⣿⠋⠉⠉⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⢴⣶⣖⣶⣦⣠⣴⣶⣶⣶⢶⣦⣀⣠⡶⣤⣤⣄⣀⣸⣿⣿⣿⣶⣿⣿⣭⣭⣿⣿⣿⣷⡄⣤⣿⣿⣿⣿⣼⣽⣿⣶⣾⣮⣿⣿⣿⣿⣯⣻⣾⣁⣄⣀⣄⣸⣷⣧⣭⣍ ⢶⠆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠶⠤⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠆ ⠤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢤⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠢⠤⠀⠢⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢠⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⣠⡀⢀⡀⠠⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣠⣴⣴⣶⣶⣶⠒⠚⠒⠚⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣤⣾⣿⣦⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠤⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⠸⣿⣿⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣷⣾⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⢻⣿⡿⠛⠛⠛⠛⠿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⠄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣹⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⢿⣿⣿⡇⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠐⣿⡿⡿⢛⡯⠠⣴⣿⣿⣿⣶⣼⣷⣾⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⡟⠠⣴⡄⣠ ⢈⣉⡉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⠁⣦⠉⠀⠀⠀⢀⣀⠈⢡⣦⣼⣦⣴⣾⣿⣿⣇⠀⢒⣒⡒⠀⠀⠂⢘⣛⠉⠉⠉⠁⢙⣛⡀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣼⢧⢿⣿⣿ ⠈⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⢀⡉⢁⣤⣾⣿⣿⣿⣿⣿⣿⣿⡯⠀⠠⠤⠄⠀⠀⠀⠠⠤⢠⣤⣀⣬⣭⣽⢽⡛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⠀⢸⣿⣿⣿⣿⣿ ⠀⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠛⣀⣀⢀⠀⠃⠀⠈⠛⠋⠋⠛⠛⢈⣓⠚⠛⠛⠙⠛⠛⡛⠛⡛⠛⠛⢛⣁⡁⠀⠀⠈⣿⣿⣟⣻⣿ ⠀⠶⠾⠶⠆⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣰⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣇⣀⡀⠀⣈⠀⠘⠀⢀⣀⡲⠆⠴⠆⠁⣰⣞⠧⠛⣛⣻⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠶⢾⣿⣿⣿⣿⣿ ⢠⣄⣂⡀⠀⠀⣠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⢉⠉⡉⠉⠉⠉⠉⠉⢉⡉⢉⣉⡉⠉⠀⢈⠉⠉⠩⢍⡉ ⠀⣁⣈⡉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣶⣾⣿⣿⣶⣟⣓⣒⣀⡀⢺⠶⡷⣞⡘⠛⣿⣿⣿⣶⢖⡒⣐⣲⣿⣾⢟⣉ ⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣿⢿⣿⣟⣉⣙⣿⡿⣿⠿⠂⠀⠨⠿⢿⣿⣿⣫ ⠰⠶⠾⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠛⠛⠭⠿⡿⠟⢿⣿⣟⣋⣿⡉⠀⠰⣿⠿⣟⠛⠋ ⠠⠤⣤⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡋⠀⣉⡉⢻⡶⡶⠁⠠⠤⠈⠛⢛⣄⣒⣖⣒⢀⠀⠐⠒⣛⣛⡛⠒⠀⠀⣚⣶⣲⣂⡙ ⠀⠛⠿⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢠⠖⠐⠆⠆⠂⣀⡀⠀⠀⢀⣀⡸⠿⠿⠿⠟⠿⠿⠿⠿⠿⢿⠿⠿⠿⠾⢷⡿⠿⠷⠿⡷⠿⡿⠿⠺⠿⠿⠧⠲⠶⠶⠯⠟⠿⠽⠭⡭⢭⡿⣛⢛⣛⣠⣤⣬⠿⠿⠿⣿⡴ ⠀⠉⠉⠁⠀⠈⠻⠀⠀⠀⠀⠀⠀⣄⠀⠨⢶⡶⡳⣿⣟⠼⣿⢛⣯⣾⣝⡾⣷⣒⠒⢒⣒⠒⡞⠓⣶⣿⠻⣚⢻⣾⣿⣿⣿⣿⣿⣿⣿⡟⠛⢻⣿⣿⣿⣯⣤⢤⣤⣥⠤⢤⣤⣴⣿⣿⡿⢿⣿⠷⢿⣿⣿⡤⣤⠤⢭⣤ ⠄⢁⣀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙⠉⠈⠉⠩⠉⠉⠉⠉⠉⠉⠉⠉⠫⣍⠉⠉⢉⡭⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣀⣛⣛⣛⣛⣛⣋⣙⣛⣊⢛⠉⠙⠉⠉⢛⣛⣛⣋⣉ ⡈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠠⠈⠘⠷⠤⠿⠋⠀⠀⢀⣀⣀⣼⣸⣯⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣻⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠉⠉⡉⠉⢹ ⠨⣿⠋⠉⠉⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⢶⣶⣖⣶⣦⣤⣴⣶⣶⣶⢶⣦⣀⣠⡶⣤⣤⣄⣀⣸⣿⣿⣿⣶⣿⣿⣭⣭⣿⣿⣿⣷⡄⣤⣿⣿⣿⣿⣼⣽⣿⣶⣾⣾⣿⣿⣿⣿⣯⣻⣾⣁⣄⣀⣄⣸⣷⣧⣭⣍ ⢶⠆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠶⠤⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠆ ⠤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢤⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠢⠤⠀⠢⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢠⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⣠⡀⢀⡀⠠⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣠⣴⣴⣶⣶⣶⠒⠚⠒⠚⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣤⣾⣿⣦⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠤⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⠸⣿⣿⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣷⣾⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⢻⣿⡿⠛⠛⠛⠛⠿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⠄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣹⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⢿⣿⣿⡇⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠐⣿⡿⡿⢛⡯⠠⣴⣿⣿⣿⣶⣼⣷⣾⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⡟⠠⣴⡄⣠ ⢈⣉⡉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⠁⣦⠉⠀⠀⠀⢀⣀⠈⢡⣦⣼⣦⣴⣾⣿⣿⣇⠀⢒⣒⡒⠀⠀⠂⢘⣛⠉⠉⠉⠁⢙⣛⡀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣼⢧⢿⣿⣿ ⠈⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⢀⡉⢁⣤⣾⣿⣿⣿⣿⣿⣿⣿⡯⠀⠠⠤⠄⠀⠀⠀⠠⠤⢠⣤⣀⣬⣭⣽⢽⡛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⠀⢸⣿⣿⣿⣿⣿ ⠀⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠛⣀⣀⢀⠀⠃⠀⠈⠛⠋⠋⠛⠛⢈⣓⠚⠛⠛⠙⠛⠛⡛⠛⡛⠛⠛⢛⣁⡁⠀⠀⠈⣿⣿⣟⣻⣿ ⠀⠶⠾⠶⠆⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣰⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣇⣀⡀⠀⣈⠀⠘⠀⢀⣀⡲⠆⠴⠆⠁⣰⣞⠧⠛⣛⣻⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠶⢾⣿⣿⣿⣿⣿ ⢠⣄⣂⡀⠀⠀⣠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⢉⠉⡉⠉⠉⠉⠉⠉⢉⡉⢉⣉⡉⠉⠀⢈⠉⠉⠩⢍⡉ ⠀⣁⣈⡉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣶⣾⣿⣿⣶⣟⣓⣒⣀⡀⢺⠶⡷⣞⡘⠛⣿⣿⣿⣶⢖⡒⣐⣲⣿⣾⢟⣉ ⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣿⢿⣿⣟⣉⣙⣿⡿⣿⠿⠂⠀⠨⠿⢿⣿⣿⣫ ⠰⠶⠾⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠛⠛⠭⠿⡿⠟⢿⣿⣟⣋⣿⡉⠀⠰⣿⠿⣟⠛⠋ ⠠⠤⣤⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡋⠀⣉⡉⢻⡶⡶⠁⠠⠤⠈⠛⢛⣄⣒⣖⣒⢀⠀⠐⠒⣛⣛⡛⠒⠀⠀⣚⣶⣲⣂⡙ ⠀⠛⠿⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢠⠖⠐⠆⠆⠂⣀⡀⠀⠀⢀⣀⡸⠿⠿⠿⠟⠿⠿⠿⠿⠿⢿⠿⠿⠿⠾⢷⡿⠿⠷⠿⡷⠿⡿⠫⠺⠿⠿⠧⠲⠶⠶⠯⠟⠿⠽⠭⡭⢭⡿⣛⢛⣛⣠⣤⣬⠿⠿⠿⣿⡴ ⠀⠉⠉⠁⠀⠈⠻⠀⠀⠀⠀⠀⠀⣄⠀⠨⢶⡶⡳⣿⣟⠼⣿⢛⣯⣾⣝⡾⣷⣒⠒⢒⣒⠒⡞⠓⣶⣿⠻⣚⢻⣾⣿⣿⣿⣿⣿⣿⣿⡟⣙⢻⣿⣿⣿⣯⣤⢤⣤⣥⠤⢤⣤⣴⣿⣿⡿⢿⣿⠷⢿⣿⣿⡤⣤⠤⢭⣤ ⠄⢁⣀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙⠉⠈⠉⠩⠉⠉⠉⠉⠉⠉⠉⠉⠫⣍⠉⠉⢉⡭⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣀⣛⣛⣛⣛⣛⣋⣙⣛⣊⢛⠉⠙⠉⠉⢛⣛⣛⣋⣉ ⡈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠠⠈⠘⠷⠤⠿⠋⠀⠀⢀⣀⣀⣼⣸⣯⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣻⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠉⠉⡉⠉⢹ ⠨⣿⠋⠉⠉⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⢶⣶⣖⣶⣦⣤⣴⣶⣶⣶⢶⣦⣀⣠⡶⣤⣤⣄⣀⣸⣿⣿⣿⣶⣿⣿⣭⣭⣿⣿⣿⣷⡄⣤⣿⣿⣿⣿⣼⣽⣿⣶⣾⣾⣿⣿⣿⣿⣯⣻⣾⣁⣄⣀⣄⣸⣷⣧⣭⣍ ⢶⠆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠶⠤⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠆ ⠤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢤⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠢⠤⠀⠢⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢠⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⣠⡀⢀⡀⠠⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣠⣴⣴⣶⣶⣶⠒⠚⠒⠚⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣤⣾⣿⣦⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠤⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⠸⣿⣿⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣷⣾⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⢻⣿⡿⠛⠛⠛⠛⠿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⠄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣹⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⢿⣿⣿⡇⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠐⣿⡿⡿⢛⡯⠠⣴⣿⣿⣿⣶⣼⣷⣾⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⡟⠠⣴⡄⣠ ⢈⣉⡉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⠁⣦⠉⠀⠀⠀⢀⣀⠈⢡⣦⣼⣦⣴⣾⣿⣿⣇⠀⢒⣒⡒⠀⠀⠂⢘⣛⠉⠉⠉⠁⢙⣛⡀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣼⢧⢿⣿⣿ ⠈⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⢀⡉⢁⣤⣾⣿⣿⣿⣿⣿⣿⣿⡯⠀⠠⠤⠄⠀⠀⠀⠠⠤⢠⣤⣀⣬⣭⣽⢽⡛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⠀⢸⣿⣿⣿⣿⣿ ⠀⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠛⣀⣀⢀⠀⠃⠀⠈⠛⠋⠋⠛⠛⢈⣓⠚⠛⠛⠙⠛⠛⡛⠛⡛⠛⠛⢛⣁⡁⠄⠀⠈⣿⣿⣟⣻⣿ ⠀⠶⠾⠶⠆⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣰⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣇⣀⡀⠀⣈⠀⠘⠀⢀⣀⡲⠆⠴⠆⠁⣰⣞⠧⠛⣛⣻⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠶⢾⣿⣿⣿⣿⣿ ⢠⣄⣂⡀⠀⠀⣠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡉⢉⠉⡉⠉⠉⠉⠉⠉⢉⡉⢉⣉⡉⠉⠀⢈⠉⠉⠩⢍⡉ ⠀⣁⣈⡉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣶⣾⣿⣿⣶⣟⣓⣒⣀⡀⢺⠶⡷⣞⡘⠛⣿⣿⣿⣶⢖⡒⣐⣲⣿⣾⢟⣉ ⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣿⢿⣿⣟⣉⣙⣿⡿⣿⠿⠂⠀⠨⠿⢿⣿⣿⣫ ⠰⠶⠾⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠛⠛⠭⠿⡿⠟⢿⣿⣟⣋⣿⡉⠀⠰⣿⠿⣟⠛⠋ ⠠⠤⣤⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡋⠀⣉⡉⢻⡶⡤⠁⠠⠤⠈⠛⢛⣄⣒⣖⣒⢀⠀⠐⠒⣛⣛⡛⠒⠀⠀⣚⣶⣲⣂⡙ ⠀⠛⠿⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢠⠖⠐⠆⠆⠂⣀⡀⠀⠀⢀⣀⡸⠿⠿⠿⠟⠿⠿⠿⠿⠿⢿⠿⠿⠿⠾⢷⡿⠿⠷⠿⡷⠿⡿⠫⠺⡿⠿⠧⠲⠶⠶⠯⠟⠿⠽⠭⡭⢭⡿⣛⢛⣛⣠⣤⣬⠿⠿⠿⣿⡴ ⠀⠉⠉⠁⠀⠈⠻⠀⠀⠀⠀⠀⠀⣄⠀⠨⢶⡶⡳⣿⣟⠼⣿⢛⣯⣾⣝⡾⣷⣒⠒⢒⣒⠒⡞⠓⣶⣿⠻⣚⢻⣾⣿⣿⣿⣿⣿⣿⣿⡟⣙⢻⣿⣿⣿⣯⣤⢤⣤⣥⠤⢤⣤⣴⣿⣿⡿⢿⣿⠷⢿⣿⣿⡤⣤⠤⢭⣤ ⠄⢁⣀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙⠉⠈⠉⠩⠉⠉⠉⠉⠉⠉⠉⠉⠫⣍⠉⠉⢉⡭⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣀⣛⣛⣛⣛⣛⣋⣙⣛⣊⢛⠉⠙⠉⠉⢛⣛⣛⣋⣉ ⡈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠠⠈⠘⠷⠤⠿⠋⠀⠀⢀⣀⣀⣼⣸⣯⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣻⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠉⠉⡉⠉⢹ ⠨⣿⠋⠉⠉⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⢶⣶⣖⣶⣦⣤⣴⣶⣶⣶⢶⣦⣀⣠⡶⣤⣤⣄⣀⣸⣿⣿⣿⣶⣿⣿⣭⣭⣿⣿⣿⣷⡄⣤⣿⣿⣿⣿⣼⣽⣿⣶⣾⣾⣿⣿⣿⣿⣯⣻⣾⣁⣄⣀⣄⣸⣷⣧⣭⣍ ⢶⠆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠶⠤⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠆ ⠤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢤⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠢⠤⠀⠢⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢠⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⣠⡀⢀⡀⠠⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣠⣴⣴⣶⣶⣶⠒⠚⠒⠚⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣤⣾⣿⣦⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠤⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⠸⣿⣿⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣷⣾⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⢻⣿⡿⠛⠛⠛⠛⠿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⠄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣹⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⢿⣿⣿⡇⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠐⣿⡿⡿⢛⡯⠠⣴⣿⣿⣿⣶⣼⣷⣾⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⡟⠠⣴⡄⣠ ⢈⣉⡉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⠁⣦⠉⠀⠀⠀⢀⣀⠈⢡⣦⣼⣦⣴⣾⣿⣿⣇⠀⢒⣒⡒⠀⠀⠂⢘⣛⠉⠉⠉⠁⢙⣛⡀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣼⢧⢿⣿⣿ ⠈⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⢀⡉⢁⣤⣾⣿⣿⣿⣿⣿⣿⣿⡯⠀⠠⠤⠄⠀⠀⠀⠠⠤⢠⣤⣀⣬⣭⣽⢽⡛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⠀⢸⣿⣿⣿⣿⣿ ⠀⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠛⣀⣀⢀⠀⠃⠀⠈⠛⠋⠋⠛⠛⢈⣓⠚⠛⠛⠙⠛⠛⡛⠛⡛⠛⠛⢛⣁⡁⠄⠀⠈⣿⣿⣟⣻⣿ ⠀⠶⠾⠶⠆⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣰⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣇⣀⡀⠀⣈⠀⠘⠀⢀⣀⡲⠆⠴⠆⠁⣰⣞⠧⠛⣛⣻⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠶⢾⣿⣿⣿⣿⣿ ⢠⣄⣂⡀⠀⠀⣠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡉⢉⠉⡉⠉⠉⠉⠉⠉⢉⡉⢉⣉⡉⠉⠀⢈⠉⠉⠩⢍⡉ ⠀⣁⣈⡉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣶⣾⣿⣿⣶⣟⣓⣒⣀⡀⢺⠶⡷⣞⡘⠛⣿⣿⣿⣶⢖⡒⣐⣲⣿⣾⢟⣉ ⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣿⢿⣿⣟⣉⣙⣿⡿⣿⠿⠂⠀⠨⠿⢿⣿⣿⣫ ⠰⠶⠾⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠛⠛⠭⠿⡿⠟⢿⣿⣟⣋⣿⡉⠀⠰⣿⠿⣟⠛⠋ ⠠⠤⣤⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡋⠀⣉⡉⢻⡶⡤⠁⠠⠤⠈⠛⢛⣄⣒⣖⣒⢀⠀⠐⠒⣛⣛⡛⠒⠀⠀⣚⣶⣲⣂⡙ ⠀⠛⠿⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢠⠖⠐⠆⠆⠂⣀⡀⠀⠀⢀⣀⡸⠿⠿⠿⠟⠿⠿⠿⠿⠿⢿⠿⠿⠿⠾⢷⡿⠿⠷⠿⡷⠿⡿⠫⠺⡿⠿⠧⠲⠶⠶⠯⠟⠿⠽⠭⡭⢭⡿⣛⢛⣛⣠⣤⣬⠿⠿⠿⣿⡴ ⠀⠉⠉⠁⠀⠈⠻⠀⠀⠀⠀⠀⠀⣄⠀⠨⢶⡶⡳⣿⣟⠼⣿⢛⣯⣾⣝⡾⣷⣒⠒⢒⣒⠒⡞⠓⣶⣿⠻⣚⢻⣾⣿⣿⣿⣿⣿⣿⣿⡟⣙⢻⣿⣿⣿⣯⣤⢤⣤⣥⠤⢤⣤⣴⣿⣿⡿⢿⣿⠷⢿⣿⣿⡤⣤⠤⢭⣤ ⠄⢁⣀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙⠉⠈⠉⠩⠉⠉⠉⠉⠉⠉⠉⠉⠫⣍⠉⠉⢉⡭⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣀⣛⣛⣛⣛⣛⣋⣙⣛⣊⢛⠉⠙⠉⠉⢛⣛⣛⣋⣉ ⡈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠠⠈⠘⠷⠤⠿⠋⠀⠀⢀⣀⣀⣼⣸⣯⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣻⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠉⠉⡉⠉⢹ ⠨⣿⠋⠉⠉⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⢶⣶⣖⣶⣦⣤⣴⣶⣶⣶⢶⣦⣀⣠⡶⣤⣤⣄⣀⣸⣿⣿⣿⣶⣿⣿⣭⣭⣿⣿⣿⣷⡄⣤⣿⣿⣿⣿⣼⣽⣿⣶⣾⣾⣿⣿⣿⣿⣯⣻⣾⣁⣄⣀⣄⣸⣷⣧⣭⣍ ⢶⠆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠶⠤⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠆ ⠤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢤⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠢⠤⠀⠢⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢠⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⣠⡀⢀⡀⠠⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣠⣴⣴⣶⣶⣶⠒⠚⠒⠚⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣤⣾⣿⣦⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠤⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⠸⣿⣿⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣷⣾⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⢻⣿⡿⠛⠛⠛⠛⠿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⠄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣹⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⢿⣿⣿⡇⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠐⣿⡿⡿⢛⡯⠠⣴⣿⣿⣿⣶⣼⣷⣾⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⡟⠠⣴⡄⣠ ⢈⣉⡉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⠁⣦⠉⠀⠀⠀⢀⣀⠈⢡⣦⣼⣦⣴⣾⣿⣿⣇⠀⢒⣒⡒⠀⠀⠂⢘⣛⠉⠉⠉⠁⢙⣛⡀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣼⢧⢿⣿⣿ ⠈⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⢀⡉⢁⣤⣾⣿⣿⣿⣿⣿⣿⣿⡯⠀⠠⠤⠄⠀⠀⠀⠠⠤⢠⣤⣀⣬⣭⣽⢽⡛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⠀⢸⣿⣿⣿⣿⣿ ⠀⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠛⣀⣀⢀⠀⠃⠀⠈⠛⠋⠋⠛⠛⢈⣓⠚⠛⠛⠙⠛⠛⣛⠛⡛⠛⠛⢛⣁⡁⠄⠀⠈⣿⣿⣟⣻⣿ ⠀⠶⠾⠶⠆⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣰⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣇⣀⡀⠀⣈⠀⠘⠀⢀⣀⡲⠆⠴⠆⠁⣰⣞⠧⠛⣛⣻⡛⣻⣿⢿⣿⣿⣿⣿⣿⣿⣶⣾⠶⢾⣿⣿⣿⣿⣿ ⢠⣄⣂⡀⠀⠀⣠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡉⢉⠉⡉⠉⠉⠘⠉⠉⢉⡉⢋⣙⡉⣉⠂⢈⠉⠉⠩⢍⡉ ⠀⣁⣈⡉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣶⣾⣿⣿⣶⣟⣓⣒⣀⡀⢺⠶⡷⣞⠘⠛⣿⣿⣿⣶⢖⡒⣐⣲⣿⣾⢟⣉ ⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣿⢿⣿⣟⣙⣛⣿⡿⣿⠿⠂⠀⠨⠿⢿⣿⣿⣫ ⠰⠶⠾⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠛⠛⠭⠿⡿⠟⠿⣿⣟⣋⣿⡉⠀⠰⣿⠿⣟⠛⠋ ⠠⠤⣤⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡋⠀⣉⡉⢻⡶⡤⠁⠠⠤⠘⠛⢛⣄⣒⣖⣒⢀⢀⠐⠒⣒⣛⡛⠒⠀⠀⣚⣶⣲⣂⡙ ⠀⠛⠿⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢠⠖⠐⠆⠆⠂⣀⡀⠀⠀⢀⣀⡸⠿⠿⠿⠟⠿⠿⠿⠿⠿⢿⠿⠿⠿⠾⢷⡿⠿⠷⠿⡷⠿⡿⠫⠺⡿⠿⠧⠲⠶⠶⠯⠟⠿⠽⠭⡯⢭⡿⣛⢛⣛⣠⣤⣬⠿⠿⠿⣿⡴ ⠀⠉⠉⠁⠀⠈⠻⠀⠀⠀⠀⠀⠀⣄⠀⠨⢶⡶⡳⣿⣟⠼⣿⢛⣯⣾⣝⡾⣷⣒⠒⢒⣒⠒⡞⠓⣶⣿⠻⣚⢻⣾⣿⣿⣿⣿⣿⣿⣿⡟⣙⢻⣿⣿⣿⣯⣤⢤⣤⣥⠤⢾⣧⣴⣿⣿⡿⢿⣿⠷⢿⣿⣿⡤⣤⠤⢭⣤ ⠄⢁⣀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙⠉⠈⠉⠩⠉⠉⠉⠉⠉⠉⠉⠉⠫⣍⠉⠉⢉⡭⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣀⣛⣛⣛⣛⣛⣋⣙⣛⣊⢛⠉⠙⠉⠩⢛⣛⣛⣋⣉ ⡈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠠⠈⠘⠷⠤⠿⠋⠀⠀⢀⣀⣀⣼⣸⣯⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣻⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠉⠉⡉⠉⢹ ⠨⣿⠋⠉⠉⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⢶⣶⣖⣶⣦⣠⣴⣶⣶⣶⢶⣦⣀⣠⡶⣤⣤⣄⣀⣸⣿⣿⣿⣶⣿⣿⣭⣭⣿⣿⣿⣷⡄⣤⣿⣿⣿⣿⣼⣽⣿⣶⣾⣾⣿⣿⣿⣿⣯⣻⣾⣁⣄⣀⣄⣸⣷⣧⣭⣍ ⢶⠆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠶⠤⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠆ ⠤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢤⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠢⠤⠀⠢⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢠⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⣠⡀⢀⡀⠠⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣠⣴⣴⣶⣶⣶⠒⠚⠒⠚⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣤⣾⣿⣦⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠤⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⠸⣿⣿⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣷⣾⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⢻⣿⡿⠛⠛⠛⠛⠿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⠄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣹⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⢿⣿⣿⡇⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠐⣿⡿⡿⢛⡯⠠⣴⣿⣿⣿⣶⣼⣷⣾⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⡟⠠⣴⡄⣠ ⢈⣉⡉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⠁⣦⠉⠀⠀⠀⢀⣀⠈⢡⣦⣼⣦⣴⣾⣿⣿⣇⠀⢒⣒⡒⠀⠀⠂⢘⣛⠉⠉⠉⠁⢙⣛⡀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣼⢧⢿⣿⣿ ⠈⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⢀⡉⢁⣤⣾⣿⣿⣿⣿⣿⣿⣿⡯⠀⠠⠤⠄⠀⠀⠀⠠⠤⢠⣤⣀⣬⣭⣽⢽⡛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⠀⢸⣿⣿⣿⣿⣿ ⠀⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠛⣀⣀⢀⠀⠃⠀⠈⠛⠋⠋⠛⠛⢈⣓⠚⠛⠛⠙⠛⠛⣛⠛⡛⠛⠛⢛⣁⡁⠄⠀⠈⣿⣿⣟⣻⣿ ⠀⠶⠾⠶⠆⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣰⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣇⣀⡀⠀⣈⠀⠘⠀⢀⣀⡲⠆⠴⠆⠁⣰⣞⠧⠛⣛⣻⡛⣻⣿⢿⣿⣿⣿⣿⢿⣿⣶⣾⠶⢾⣿⣿⣿⣿⣿ ⢠⣄⣂⡀⠀⠀⣠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡉⢉⠉⡉⠉⠋⠘⠉⠉⢉⡉⢋⣙⡉⣉⠂⢈⠉⠉⠩⢍⡉ ⠀⣁⣈⡉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣶⣾⣿⣿⣶⣟⣓⣒⣀⡀⢺⠶⡷⣖⠘⠛⣿⣿⣿⣶⢖⡒⣐⣲⣿⣾⢟⣉ ⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣿⢿⣿⣟⣙⣛⣿⡿⣿⠿⠂⠀⠨⠿⢿⣿⣿⣫ ⠰⠶⠾⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠛⠛⠭⠿⡿⠟⠿⣿⣟⣋⣿⡉⠀⠰⣿⠿⣟⠛⠋ ⠠⠤⣤⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡋⠀⣉⡉⢻⡶⡤⠁⠠⠤⠘⠛⢛⣄⣒⣖⣒⢀⢀⠐⠒⣒⣓⡚⠒⠀⠀⣚⣶⣲⣂⡙ ⠀⠛⠿⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢠⠖⠐⠆⠆⠂⣀⡀⠀⠀⢀⣀⡸⠿⠿⠿⠟⠿⠿⠿⠿⠿⢿⠿⠿⠿⠾⢷⡿⠿⠷⠿⡷⠿⡿⠫⠺⡿⠿⠧⠲⠶⠶⠯⠟⠿⠽⠭⡯⢭⡿⣛⢛⣛⣠⣤⣬⠿⠿⠿⣿⡴ ⠀⠉⠉⠁⠀⠈⠻⠀⠀⠀⠀⠀⠀⣄⠀⠨⢶⡶⡳⣿⣟⠼⣿⢛⣯⣾⣝⡾⣷⣒⠒⢒⣒⠒⡞⠓⣶⣿⠻⣚⢻⣾⣿⣿⣿⣿⣿⣿⣿⡟⣙⢻⣿⣿⣿⣯⣤⢤⣤⣥⠤⢾⣧⣴⣿⣿⡿⢿⣿⠷⢿⣿⣿⡤⣤⠤⢭⣤ ⠄⢁⣀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙⠉⠈⠉⠩⠉⠉⠉⠉⠉⠉⠉⠉⠫⣍⠉⠉⢉⡭⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣀⣛⣛⣛⣛⣻⣋⣙⣛⣊⢛⠉⠙⠉⠩⢛⣛⣛⣋⣉ ⡈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠠⠈⠘⠷⠤⠿⠋⠀⠀⢀⣀⣀⣼⣸⣯⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣻⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠉⠉⡉⠉⢹ ⠨⣿⠋⠉⠉⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⢶⣶⣖⣶⣦⣠⣴⣶⣶⣶⢶⣦⣀⣠⡶⣤⣤⣄⣀⣸⣿⣿⣿⣶⣿⣿⣭⣭⣿⣿⣿⣷⡄⣤⣿⣿⣿⣿⣼⣽⣿⣶⣾⣾⣿⣿⣿⣿⣯⣻⣾⣁⣄⣀⣄⣸⣷⣧⣭⣍ ⢶⠆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠶⠤⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠆ ⠤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢤⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠢⠤⠀⠢⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢠⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⣠⡀⢀⡀⠠⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣠⣴⣴⣶⣶⣶⠒⠚⠒⠚⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣤⣾⣿⣦⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠤⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⠸⣿⣿⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣷⣾⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⢻⣿⡿⠛⠛⠛⠛⠿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⠄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣹⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⢿⣿⣿⡇⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠐⣿⡿⡿⢛⡯⠠⣴⣿⣿⣿⣶⣼⣷⣾⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⡟⠠⣴⡄⣠ ⢈⣉⡉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⠁⣦⠉⠀⠀⠀⢀⣀⠈⢡⣦⣼⣦⣴⣾⣿⣿⣇⠀⢒⣒⡒⠀⠀⠂⢘⣛⠉⠉⠉⠁⢙⣛⡀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣼⢧⢿⣿⣿ ⠈⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⢀⡉⢁⣤⣾⣿⣿⣿⣿⣿⣿⣿⡯⠀⠠⠤⠄⠀⠀⠀⠠⠤⢠⣤⣀⣬⣭⣽⢽⡛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⠀⢸⣿⣿⣿⣿⣿ ⠀⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠛⣀⣀⢀⠀⠃⠀⠈⠛⠋⠋⠛⠛⢈⣓⠚⠛⠛⠙⠛⠛⣛⠛⡛⠛⠛⢛⣁⡁⠄⠀⠈⣿⣿⣟⣻⣿ ⠀⠶⠾⠶⠆⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣰⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣇⣀⡀⠀⣈⠀⠘⠀⢀⣀⡲⠆⠴⠆⠁⣰⣞⠧⠛⣛⣻⡛⣻⣿⢿⣿⣿⣿⣿⢿⣿⣶⣾⠶⢾⣿⣿⣿⣿⣿ ⢠⣄⣂⡀⠀⠀⣠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡉⢉⠉⡉⠉⠋⠘⠉⠉⢉⡉⢋⣙⡉⣉⠂⢈⠉⠉⠩⢍⡉ ⠀⣁⣈⡉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣶⣾⣿⣿⣶⣟⣓⣒⣀⡀⢺⠶⡷⣖⠘⠛⣿⣿⣿⣶⢖⡒⣐⣲⣿⣾⢟⣉ ⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣿⢿⣿⣟⣙⣛⣿⡿⣿⠿⠂⠀⠨⠿⢿⣿⣿⣫ ⠰⠶⠾⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠛⠛⠭⠿⡿⠟⠿⣿⣟⣋⣿⡉⠀⠰⣿⠿⣟⠛⠋ ⠠⠤⣤⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡋⠀⣉⡉⢻⡶⡤⠁⠠⠤⠘⠛⢛⣄⣒⣖⣒⢀⢀⠐⠒⣒⣓⡚⠒⠀⠀⣚⣶⣲⣂⡙ ⠀⠛⠿⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢠⠖⠐⠆⠆⠂⣀⡀⠀⠀⢀⣀⡸⠿⠿⠿⠟⠿⠿⠿⠿⠿⢿⠿⠿⠿⠾⢷⡿⠿⠷⠿⡷⠿⡿⠫⠺⡿⠿⠧⠲⠶⠶⠯⠟⠿⠽⠭⡯⢭⡿⣛⢛⣛⣠⣤⣬⠿⠿⠿⣿⡴ ⠀⠉⠉⠁⠀⠈⠻⠀⠀⠀⠀⠀⠀⣄⠀⠨⢶⡶⡳⣿⣟⠼⣿⢛⣯⣾⣝⡾⣷⣒⠒⢒⣒⠒⡞⠓⣶⣿⠻⣚⢻⣾⣿⣿⣿⣿⣿⣿⣿⡟⣙⢻⣿⣿⣿⣯⣤⢤⣤⣥⠤⢾⣧⣴⣿⣿⡿⢿⣿⠷⢿⣿⣿⡤⣤⠤⢭⣤ ⠄⢁⣀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙⠉⠈⠉⠩⠉⠉⠉⠉⠉⠉⠉⠉⠫⣍⠉⠉⢉⡭⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣀⣛⣛⣛⣛⣻⣋⣙⣛⣊⢛⠉⠙⠉⠩⢛⣛⣛⣋⣉ ⡈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠠⠈⠘⠷⠤⠿⠋⠀⠀⢀⣀⣀⣼⣸⣯⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣻⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠉⠉⡉⠉⢹ ⠨⣿⠋⠉⠉⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⢶⣶⣖⣶⣦⣠⣴⣶⣶⣶⢶⣦⣀⣠⡶⣤⣤⣄⣀⣸⣿⣿⣿⣶⣿⣿⣭⣭⣽⣿⣿⣷⡄⣤⣿⣿⣿⣿⣼⣽⣿⣶⣾⣾⣿⣿⣿⣿⣯⣻⣾⣁⣄⣀⣄⣸⣷⣧⣭⣍ ⢶⠆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠶⠤⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠆ ⠤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢤⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠢⠤⠀⠢⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢠⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⣠⡀⢀⡀⠠⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣠⣴⣴⣶⣶⣶⠒⠚⠒⠚⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣤⣾⣿⣦⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠤⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⠸⣿⣿⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣷⣾⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⢻⣿⡿⠛⠛⠛⠛⠿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⠄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣹⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⢿⣿⣿⡇⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠐⣿⡿⡿⢛⡯⠠⣴⣿⣿⣿⣶⣼⣷⣾⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⡟⠠⣴⡄⣠ ⢈⣉⡉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⠁⣦⠉⠀⠀⠀⢀⣀⠈⢡⣦⣼⣦⣴⣾⣿⣿⣇⠀⢒⣒⡒⠀⠀⠂⢘⣛⠉⠉⠉⠁⢙⣛⡀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣼⢧⢿⣿⣿ ⠈⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⢀⡉⢁⣤⣾⣿⣿⣿⣿⣿⣿⣿⡯⠀⠠⠤⠄⠀⠀⠀⠠⠤⢠⣤⣀⣬⣭⣽⢽⡛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⠀⢸⣿⣿⣿⣿⣿ ⠀⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠛⣀⣀⢀⠀⠃⠀⠈⠛⠋⠋⠛⠛⢈⣓⠚⠛⠛⠙⠛⠛⣛⠛⡛⠛⠛⢛⣁⡁⠄⠀⠈⣿⣿⣟⣻⣿ ⠀⠶⠾⠶⠆⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣰⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣇⣀⡀⠀⣈⠀⠘⠀⢀⣀⡲⠆⠴⠆⠁⣰⣞⠧⠛⣛⣻⡛⣻⣿⢿⣿⣿⣿⣿⢿⣿⣶⣾⠶⢾⣿⣿⣿⣿⣿ ⢠⣄⣂⡀⠀⠀⣠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡉⢉⠉⡉⠉⠋⠘⠉⠉⢉⡉⢋⣙⡉⣉⠂⢈⠉⠉⠩⢍⡉ ⠀⣁⣈⡉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣶⣾⣿⣿⣶⣟⣓⣒⣀⡀⢺⠶⡷⣖⠘⠛⣿⣿⣿⣶⢖⡒⣐⣲⣿⣾⢟⣉ ⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣿⢿⣿⣟⣙⣛⣿⡿⣿⠿⠂⠀⠨⠿⢿⣿⣿⣫ ⠰⠶⠾⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠛⠛⠭⠿⡿⠟⠿⣿⣟⣋⣿⡉⠀⠰⣿⠿⣟⠛⠋ ⠠⠤⣤⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡋⠀⣉⡉⢻⡶⡤⠁⠠⠤⠘⠛⢛⣄⣒⣖⣒⢀⢀⠐⠒⣒⣓⡚⠒⠀⠀⣚⣶⣲⣂⡙ ⠀⠛⠿⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢠⠖⠐⠆⠆⠂⣀⡀⠀⠀⢀⣀⡸⠿⠿⠿⠟⠿⠿⠿⠿⠿⢿⠿⠿⠿⠾⢷⡿⠿⠷⠿⡷⠿⡿⠫⠺⡿⠿⠧⠲⠶⠶⠯⠟⠿⠽⠭⡯⢭⡿⣛⢛⣛⣠⣤⣬⠿⠿⠿⣿⡴ ⠀⠉⠉⠁⠀⠈⠻⠀⠀⠀⠀⠀⠀⣄⠀⠨⢶⡶⡳⣿⣟⠼⣿⢛⣯⣾⣝⡾⣷⣒⠒⢒⣒⠒⡞⠓⣶⣿⠻⣚⢻⣾⣿⣿⣿⣿⣿⣿⣿⡟⣙⢻⣿⣿⣿⣯⣤⢤⣤⣥⠤⢾⣧⣴⣿⣿⡿⢿⣿⠷⢿⣿⣿⡤⣤⠤⢭⣤ ⠄⢁⣀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙⠉⠈⠉⠩⠉⠉⠉⠉⠉⠉⠉⠉⠫⣍⠉⠉⢉⡭⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣀⣛⣛⣛⣛⣻⣋⣙⣛⣊⢛⠉⠙⠉⠩⢛⣛⣛⣋⣉ ⡈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠠⠈⠘⠷⠤⠿⠋⠀⠀⢀⣀⣀⣼⣸⣯⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣻⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠉⠉⡉⠉⢹ ⠨⣿⠋⠉⠉⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⢶⣶⣖⣶⣦⣠⣴⣶⣶⣶⢶⣦⣀⣠⡶⣤⣤⣄⣀⣸⣿⣿⣿⣶⣿⣿⣭⣭⣽⣿⣿⣷⡄⣤⣿⣿⣿⣿⣼⣽⣿⣶⣾⣾⣿⣿⣿⣿⣯⣻⣾⣁⣄⣀⣄⣸⣷⣧⣭⣍ ⢶⠆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠶⠤⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠆ ⠤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢤⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠢⠤⠀⠢⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢠⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⣠⡀⢀⡀⠠⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣠⣴⣴⣶⣶⣶⠒⠚⠒⠚⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣤⣾⣿⣦⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠤⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⠸⣿⣿⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣷⣾⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⢻⣿⡿⠛⠛⠛⠛⠿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⠄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣹⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⢿⣿⣿⡇⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠐⣿⡿⡿⢛⡯⠠⣴⣿⣿⣿⣶⣼⣷⣾⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⡟⠠⣴⡄⣠ ⢈⣉⡉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⠁⣦⠉⠀⠀⠀⢀⣀⠈⢡⣦⣼⣦⣴⣾⣿⣿⣇⠀⢒⣒⡒⠀⠀⠂⢘⣛⠉⠉⠉⠁⢙⣛⡀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣼⢧⢿⣿⣿ ⠈⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⢀⡉⢁⣤⣾⣿⣿⣿⣿⣿⣿⣿⡯⠀⠠⠤⠄⠀⠀⠀⠠⠤⢠⣤⣀⣬⣭⣽⢽⡛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⠀⢸⣿⣿⣿⣿⣿ ⠀⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠛⣀⣀⢀⠀⠃⠀⠈⠛⠋⠋⠛⠛⢈⣓⠚⠛⠛⠙⠛⠛⣛⠛⡛⠛⠛⢛⣁⡁⠄⠀⠈⣿⣿⣟⣻⣿ ⠀⠶⠾⠶⠆⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣰⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣇⣀⡀⠀⣈⠀⠘⠀⢀⣀⡲⠆⠴⠆⠁⣰⣞⠧⠛⣛⣻⡛⣻⣿⢿⣿⣿⣿⣿⢿⣿⣶⣾⠶⢾⣿⣿⣿⣿⣿ ⢠⣄⣂⡀⠀⠀⣠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡉⢉⠉⡉⠉⠋⠘⠉⠉⢉⡉⢋⣙⡉⣉⠂⢈⠉⠉⠩⢍⡉ ⠀⣁⣈⡉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣶⣾⣿⣿⣶⣟⣓⣒⣀⡀⢺⠶⡷⣖⠘⠛⣿⣿⣿⣶⢖⡒⣐⣲⣿⣾⢟⣉ ⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣿⢿⣿⣟⣙⣛⣿⡿⣿⠿⠂⠀⠨⠿⢿⣿⣿⣫ ⠰⠶⠾⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠛⠛⠭⠿⡿⠟⠿⣿⣟⣋⣿⡉⠀⠰⣿⠿⣟⠛⠋ ⠠⠤⣤⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡋⠀⣉⡉⢻⡶⡤⠁⠠⠤⠘⠛⢛⣄⣒⣖⣒⢀⢀⠐⠒⣒⣓⡚⠒⠀⠀⣚⣶⣲⣂⡙ ⠀⠛⠿⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢠⠖⠐⠆⠆⠂⣀⡀⠀⠀⢀⣀⡸⠿⠿⠿⠟⠿⠿⠿⠿⠿⢿⠿⠿⠿⠾⢷⡿⠿⠷⠿⡷⠿⡿⠫⠺⡿⠿⠧⠲⠶⠶⠯⠟⠿⠽⠭⡯⢭⡿⣛⢛⣛⣠⣤⣬⠿⠿⠿⣿⡴ ⠀⠉⠉⠁⠀⠈⠻⠀⠀⠀⠀⠀⠀⣄⠀⠨⢶⡶⡳⣿⣟⠼⣿⢛⣯⣾⣝⡾⣷⣒⠒⢒⣒⠒⡞⠓⣶⣿⠻⣚⢻⣾⣿⣿⣿⣿⣿⣿⣿⡟⣙⢻⣿⣿⣿⣯⣤⢤⣤⣥⠤⢾⣧⣴⣿⣿⡿⢿⣿⠷⢿⣿⣿⡤⣤⠤⢭⣤ ⠄⢁⣀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙⠉⠈⠉⠩⠉⠉⠉⠉⠉⠉⠉⠉⠫⣍⠉⠉⢉⡭⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣀⣛⣛⣛⣛⣻⣋⣙⣛⣊⢛⠉⠙⠉⠩⢛⣛⣛⣋⣉ ⡈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠠⠈⠘⠷⠤⠿⠋⠀⠀⢀⣀⣀⣼⣸⣯⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣻⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠉⠉⡉⠉⢹ ⠨⣿⠋⠉⠉⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⢶⣶⣖⣶⣦⣠⣴⣶⣶⣶⢶⣦⣀⣠⡶⣤⣤⣄⣀⣸⣿⣿⣿⣶⣿⣿⣭⣭⣽⣿⣿⣷⡄⣤⣿⣿⣿⣿⣼⣽⣿⣶⣾⣾⣿⣿⣿⣿⣯⣻⣾⣁⣄⣀⣄⣸⣷⣧⣭⣍ ⢶⠆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠶⠤⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠆ ⠤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢤⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠢⠤⠀⠢⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢠⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⣠⡀⢀⡀⠠⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣠⣴⣴⣶⣶⣶⠒⠚⠒⠚⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣤⣾⣿⣦⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠤⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⠸⣿⣿⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣷⣾⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⢻⣿⡿⠛⠛⠛⠛⠿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⠄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣹⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⢿⣿⣿⡇⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠐⣿⡿⡿⢛⡯⠠⣴⣿⣿⣿⣶⣼⣷⣾⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⡟⠠⣴⡄⣠ ⢈⣉⡉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⠁⣦⠉⠀⠀⠀⢀⣀⠈⢡⣦⣼⣦⣴⣾⣿⣿⣇⠀⢒⣒⡒⠀⠀⠂⢘⣛⠉⠉⠉⠁⢙⣛⡀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣼⢧⢿⣿⣿ ⠈⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⢀⡉⢁⣤⣾⣿⣿⣿⣿⣿⣿⣿⡯⠀⠠⠤⠄⠀⠀⠀⠠⠤⢠⣤⣀⣬⣭⣽⢽⡛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⠀⢸⣿⣿⣿⣿⣿ ⠀⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠛⣀⣀⢀⠀⠃⠀⠈⠛⠋⠋⠛⠛⢈⣓⠚⠛⠛⠙⠛⠛⣛⠛⡛⠛⠛⢛⣁⡁⠄⠀⠈⣿⣿⣟⣻⣿ ⠀⠶⠾⠶⠆⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣰⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣇⣀⡀⠀⣈⠀⠘⠀⢀⣀⡲⠆⠴⠆⠁⣰⣞⠧⠛⣛⣻⡛⣻⣿⢿⣿⣿⣿⣿⢿⣿⣶⣾⠶⢾⣿⣿⣿⣿⣿ ⢠⣄⣂⡀⠀⠀⣠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡉⢉⠉⡉⠉⠋⠘⠉⠉⢉⡉⢋⣙⡉⣉⠂⢈⠉⠉⠩⢍⡉ ⠀⣁⣈⡉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣶⣾⣿⣿⣶⣟⣓⣒⣀⡀⢺⠶⡷⣖⠘⠛⣿⣿⣿⣶⢖⡒⣐⣲⣿⣾⢟⣉ ⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣿⢿⣿⣟⣙⣛⣿⡿⣿⠿⠂⠀⠨⠿⢿⣿⣿⣫ ⠰⠶⠾⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠛⠛⠭⠿⡿⠟⠿⣿⣟⣋⣿⡉⠀⠰⣿⠿⣟⠛⠋ ⠠⠤⣤⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡋⠀⣉⡉⢻⡶⡤⠁⠠⠤⠘⠛⢛⣄⣒⣖⣒⢀⢀⠐⠒⣒⣓⡚⠒⠀⠀⣚⣶⣲⣂⡙ ⠀⠛⠿⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢠⠖⠐⠆⠆⠂⣀⡀⠀⠀⢀⣀⡸⠿⠿⠿⠟⠿⠿⠿⠿⠿⢿⠿⠿⠿⠾⢷⡿⠿⠷⠿⡷⠿⡿⠫⠺⡿⠿⠧⠲⠶⠶⠯⠟⠿⠽⠭⡯⢭⡿⣛⢛⣛⣠⣤⣬⠿⠿⠿⣿⡴ ⠀⠉⠉⠁⠀⠈⠻⠀⠀⠀⠀⠀⠀⣄⠀⠨⢶⡶⡳⣿⣟⠼⣿⢛⣯⣾⣝⡾⣷⣒⠒⢒⣒⠒⡞⠓⣶⣿⠻⣚⢻⣾⣿⣿⣿⣿⣿⣿⣿⡟⣙⢻⣿⣿⣿⣯⣤⢤⣤⣥⠤⢾⣧⣴⣿⣿⡿⢿⣿⠷⢿⣿⣿⡤⣤⠤⢭⣤ ⠄⢁⣀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙⠉⠈⠉⠩⠉⠉⠉⠉⠉⠉⠉⠉⠫⣍⠉⠉⢉⡭⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣀⣛⣛⣛⣛⣻⣋⣙⣛⣊⢛⠉⠙⠉⠩⢛⣛⣛⣋⣉ ⡈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠠⠈⠘⠷⠤⠿⠋⠀⠀⢀⣀⣀⣼⣸⣯⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣻⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠉⠉⡉⠉⢹ ⠨⣿⠋⠉⠉⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⢶⣶⣖⣶⣦⣠⣴⣶⣶⣶⢶⣦⣀⣠⡶⣤⣤⣄⣀⣸⣿⣿⣿⣶⣿⣿⣭⣭⣽⣿⣿⣷⡄⣤⣿⣿⣿⣿⣼⣽⣿⣶⣾⣾⣿⣿⣿⣿⣯⣻⣾⣁⣄⣀⣄⣸⣷⣧⣭⣍ ⢶⠆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠶⠤⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠆ ⠤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢤⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠢⠤⠀⠢⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢠⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⣠⡀⢀⡀⠠⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣠⣴⣴⣶⣶⣶⠓⠚⠒⠚⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣤⣾⣿⣦⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠤⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⠸⣿⣿⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣷⣾⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⢻⣿⡿⠛⠛⠛⠛⠿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⠄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣹⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⢿⣿⣿⡇⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠐⣿⡿⡿⢛⡯⠠⣴⣿⣿⣿⣶⣼⣷⣾⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⡟⠠⣴⡄⣠ ⢈⣉⡉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⠁⣦⠉⠀⠀⠀⢀⣀⠈⢡⣦⣼⣦⣴⣾⣿⣿⣇⠀⢒⣒⡒⠀⠀⠂⢘⣛⠉⠉⠉⠁⢙⣛⡀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣼⢧⢿⣿⣿ ⠈⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⢀⡉⢁⣤⣾⣿⣿⣿⣿⣿⣿⣿⡯⠀⠠⠤⠄⠀⠀⠀⠠⠤⢠⣤⣀⣬⣭⣽⢽⡛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⠀⢸⣿⣿⣿⣿⣿ ⠀⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠛⣀⣀⢀⠀⠃⠀⠈⠛⠋⠋⠛⠛⢈⣓⠚⠛⠛⠙⠛⠛⣛⠛⡛⠛⠛⢛⣁⡁⠄⠀⠈⣿⣿⣟⣻⣿ ⠀⠶⠾⠶⠆⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣰⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣇⣀⡀⠀⣈⠀⠘⠀⢀⣀⡲⠆⠴⠆⠁⣰⣞⠧⠛⣛⣻⡛⣻⣿⢿⣿⣿⣿⣿⢿⣿⣶⣾⠶⢾⣿⣿⣿⣿⣿ ⢠⣄⣂⡀⠀⠀⣠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡉⢉⠉⡉⠉⠋⠘⠉⠉⢉⡉⢋⣙⡉⣉⠂⢈⠉⠉⠩⢍⡉ ⠀⣁⣈⡉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣶⣾⣿⣿⣶⣟⣓⣒⣀⡀⢺⠶⡷⣖⠘⠛⣿⣿⣿⣶⢖⡒⣐⣲⣿⣾⢟⣉ ⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣿⢿⣿⣟⣙⣛⣿⡿⣿⠿⠂⠀⠨⠿⢿⣿⣿⣫ ⠰⠶⠾⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠛⠛⠭⠿⡿⠟⠿⣿⣟⣋⣿⡉⠁⠰⣿⠿⣟⠛⠋ ⠠⠤⣤⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡋⠀⣉⡉⢻⡶⡤⠁⠠⠤⠘⠛⢛⣄⣒⣖⣒⢀⢀⠐⠒⣒⣓⡚⠒⠀⠀⣚⣶⣲⣂⡙ ⠀⠛⠿⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢠⠖⠐⠆⠆⠂⣀⡀⠀⠀⢀⣀⡸⠿⠿⠿⠟⠿⠿⠿⠿⠿⢿⠿⠿⠿⠾⢷⡿⠿⠷⠿⡷⠿⡿⠫⠺⡿⠿⠧⠲⠶⠶⠯⠟⠿⠽⠭⡯⢭⡿⣛⢛⣛⣠⣤⣬⠿⠿⠿⣿⡴ ⠀⠉⠉⠁⠀⠈⠻⠀⠀⠀⠀⠀⠀⣄⠀⠨⢶⡶⡳⣿⣟⠼⣿⢛⣯⣾⣝⡾⣷⣒⠒⢒⣒⠒⡞⠓⣶⣿⠻⣚⢻⣾⣿⣿⣿⣿⣿⣿⣿⡟⣙⢻⣿⣿⣿⣯⣤⢤⣤⣥⠤⢾⣧⣴⣿⣿⡿⢿⣿⠷⢿⣿⣿⡤⣤⠤⢭⣤ ⠄⢁⣀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙⠉⠈⠉⠩⠉⠉⠉⠉⠉⠉⠉⠉⠫⣍⠉⠉⢉⡭⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣀⣛⣛⣛⣛⣻⣋⣙⣛⣊⢛⠉⠙⠉⠩⢛⣛⣛⣋⣉ ⡈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠠⠈⠘⠷⠤⠿⠋⠀⠀⢀⣀⣀⣼⣸⣯⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣻⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠉⠉⡉⠉⢹ ⠨⣿⠋⠉⠉⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⢶⣶⣖⣶⣦⣠⣴⣶⣶⣶⢶⣦⣀⣠⡶⣤⣤⣄⣀⣸⣿⣿⣿⣶⣿⣿⣭⣭⣽⣿⣿⣷⡄⣤⣿⣿⣿⣿⣼⣽⣿⣶⣾⣾⣿⣿⣿⣿⣯⣿⣾⣁⣄⣀⣄⣸⣷⣧⣭⣍ ⢶⠆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠶⠤⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠆ ⠤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢤⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠢⠤⠀⠢⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢠⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⣠⡀⢀⡀⠠⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣠⣴⣴⣶⣶⣶⠓⠚⠒⠚⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣤⣾⣿⣦⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠤⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⠸⣿⣿⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣷⣾⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⢻⣿⡿⠛⠛⠛⠛⠿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⠄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣹⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⢿⣿⣿⡇⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠐⣿⡿⡿⢛⡯⠠⣴⣿⣿⣿⣶⣼⣷⣾⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⡟⠠⣴⡄⣠ ⢈⣉⡉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⠁⣦⠉⠀⠀⠀⢀⣀⠈⢡⣦⣼⣦⣴⣾⣿⣿⣇⠀⢒⣒⡒⠀⠀⠂⢘⣛⠉⠉⠉⠁⢙⣛⡀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣼⢧⢿⣿⣿ ⠈⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⢀⡉⢁⣤⣾⣿⣿⣿⣿⣿⣿⣿⡯⠀⠠⠤⠄⠀⠀⠀⠠⠤⢠⣤⣀⣬⣭⣽⢽⡛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⠀⢸⣿⣿⣿⣿⣿ ⠀⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠛⣀⣀⢀⠀⠃⠀⠈⠛⠋⠋⠛⠛⢈⣓⠚⠛⠛⠙⠛⠛⣛⠛⡛⠛⠛⢛⣁⡁⠄⠀⠈⣿⣿⣟⣻⣿ ⠀⠶⠾⠶⠆⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣰⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣇⣀⡀⠀⣈⠀⠘⠀⢀⣀⡲⠆⠴⠆⠁⣰⣞⠧⠛⣛⣻⡛⣻⣿⢿⣿⣿⣿⣿⢿⣿⣶⣾⠶⢾⣿⣿⣿⣿⣿ ⢠⣄⣂⡀⠀⠀⣠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡉⢉⠉⡉⠉⠋⠘⠉⠉⢉⡉⢋⣙⡉⣉⠂⢈⠉⠉⠩⢍⡉ ⠀⠁⠈⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣶⣾⣿⣿⣶⣟⣓⣒⣀⡀⢺⠶⡷⣖⠘⠛⣿⣿⣿⣶⢖⡒⣐⣲⣿⣾⢟⣉ ⠐⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣿⢿⣿⣟⣙⣛⣿⡿⣿⠿⠂⠀⠨⠿⢿⣿⣿⣫ ⠐⠟⠻⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠛⠛⠭⠿⡿⠟⠿⣿⣟⣋⣿⡉⠁⠰⣿⠿⣟⠛⠋ ⠠⠤⣤⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡋⠀⣉⡉⢻⡶⡤⠁⠠⠤⠘⠛⢛⣄⣒⣖⣒⢀⢀⠐⠒⣒⣓⡚⠒⠀⠀⣚⣶⣲⣂⡙ ⠀⠛⠿⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢠⠖⠐⠆⠆⠂⣀⡀⠀⠀⢀⣀⡸⠿⠿⠿⠟⠿⠿⠿⠿⠿⢿⠿⠿⠿⠾⢷⡿⠿⠷⠿⡷⠿⡿⠫⠺⡿⠿⠧⠲⠶⠶⠯⠟⠿⠽⠭⡯⢭⡿⣛⢛⣛⣠⣤⣬⠿⠿⠿⣿⡴ ⠀⠉⠉⠁⠀⠈⠻⠀⠀⠀⠀⠀⠀⣄⠀⠨⢶⡶⡳⣿⣟⠼⣿⢛⣯⣾⣝⡾⣷⣒⠒⢒⣒⠒⡞⠓⣶⣿⠻⣚⢻⣾⣿⣿⣿⣿⣿⣿⣿⡟⣙⢻⣿⣿⣿⣯⣤⢤⣤⣥⠤⢾⣧⣴⣿⣿⡿⢿⣿⠷⢿⣿⣿⡤⣤⠤⢭⣤ ⠄⢁⣀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙⠉⠈⠉⠩⠉⠉⠉⠉⠉⠉⠉⠉⠫⣍⠉⠉⢉⡭⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣀⣛⣛⣛⣛⣻⣋⣙⣛⣊⢛⠉⠙⠉⠩⢛⣛⣛⣋⣉ ⡈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠠⠈⠘⠷⠤⠿⠋⠀⠀⢀⣀⣀⣼⣸⣯⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣻⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠉⠉⡉⠉⢹ ⠨⣿⠋⠉⠉⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⢶⣶⣖⣶⣦⣠⣴⣶⣶⣶⢶⣦⣀⣠⡶⣤⣤⣄⣀⣸⣿⣿⣿⣶⣿⣿⣭⣭⣽⣿⣿⣷⡦⣤⣿⣿⣿⣿⣼⣽⣿⣶⣾⣾⣿⣿⣿⣿⣯⣿⣾⣁⣄⣀⣄⣸⣷⣧⣭⣍ ⢶⠆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠶⠤⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠆ ⠤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢤⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠢⠤⠀⠢⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢠⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⣠⡀⢀⡀⠠⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣠⣴⣴⣶⣶⣶⠓⠚⠒⠚⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣤⣾⣿⣦⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠤⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⠸⣿⣿⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣷⣾⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⢻⣿⡿⠛⠛⠛⠛⠿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⠄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣹⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⢿⣿⣿⡇⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠐⣿⡿⡿⢛⡯⠠⣴⣿⣿⣿⣶⣼⣷⣾⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⡟⠠⣴⡄⣠ ⢈⣉⡉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⠁⣦⠉⠀⠀⠀⢀⣀⠈⢡⣦⣼⣦⣴⣾⣿⣿⣇⠀⢒⣒⡒⠀⠀⠂⢘⣛⠉⠉⠉⠁⢙⣛⡀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣼⢧⢿⣿⣿ ⠈⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⢀⡉⢁⣤⣾⣿⣿⣿⣿⣿⣿⣿⡯⠀⠠⠤⠄⠀⠀⠀⠠⠤⢠⣤⣀⣬⣭⣽⢽⡛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⠀⢸⣿⣿⣿⣿⣿ ⠀⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠛⣀⣀⢀⠀⠃⠀⠈⠛⠋⠋⠛⠛⢈⣓⠚⠛⠛⠙⠛⠛⣛⠛⡛⠛⠛⢛⣁⡁⠄⠀⠈⣿⣿⣟⣻⣿ ⠀⠶⠾⠶⠆⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣰⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣇⣀⡀⠀⣈⠀⠘⠀⢀⣀⡲⠆⠴⠆⠁⣰⣞⠧⠛⣛⣻⡛⣻⣿⢿⣿⣿⣿⣿⢿⣿⣶⣾⠶⢾⣿⣿⣿⣿⣿ ⢠⣄⣂⡀⠀⠀⣠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡉⢉⠉⡉⠉⠋⠘⠉⠉⢉⡉⢋⣙⡉⣉⠂⢈⠉⠉⠩⢍⡉ ⠀⠁⠈⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣶⣾⣿⣿⣶⣟⣓⣒⣀⡀⢺⠶⡷⣖⠘⠛⣿⣿⣿⣶⢖⡒⣐⣲⣿⣾⢟⣉ ⠐⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣿⢿⣿⣟⣙⣛⣿⡿⣿⠿⠂⠀⠨⠿⢿⣿⣿⣫ ⠐⠟⠻⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠛⠛⠭⠿⡿⠟⠿⣿⣟⣋⣿⡉⠁⠰⣿⠿⣟⠛⠋ ⠠⠤⣤⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡋⠀⣉⡉⢻⡶⡤⠁⠠⠤⠘⠛⢛⣄⣒⣖⣒⢀⢀⠐⠒⣒⣓⡚⠒⠀⠀⣚⣶⣲⣂⡙ ⠀⠛⠿⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢠⠖⠐⠆⠆⠂⣀⡀⠀⠀⢀⣀⡸⠿⠿⠿⠟⠿⠿⠿⠿⠿⢿⠿⠿⠿⠾⢷⡿⠿⠷⠿⡷⠿⡿⠫⠺⡿⠿⠧⠲⠶⠶⠯⠟⠿⠽⠭⡯⢭⡿⣛⢛⣛⣠⣤⣬⠿⠿⠿⣿⡴ ⠀⠉⠉⠁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣄⠀⠨⢶⡶⡳⣿⣟⠼⣿⢛⣯⣾⣝⡾⣷⣒⠒⢒⣒⠒⡞⠓⣶⣿⠻⣚⢻⣾⣿⣿⣿⣿⣿⣿⣿⡟⣙⢻⣿⣿⣿⣯⣤⢤⣤⣥⠤⢾⣧⣴⣿⣿⡿⢿⣿⠷⢿⣿⣿⡤⣤⠤⢭⣤ ⠄⢁⣀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙⠉⠈⠉⠩⠉⠉⠉⠉⠉⠉⠉⠉⠫⣍⠉⠉⢉⡭⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣀⣛⣛⣛⣛⣻⣋⣙⣛⣊⢛⠉⠙⠉⠩⢛⣛⣛⣋⣉ ⡈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠠⠈⠘⠷⠤⠿⠋⠀⠀⢀⣀⣀⣼⣸⣯⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣻⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠉⠉⡉⠉⢹ ⠨⣿⠋⠉⠉⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⢶⣶⣖⣶⣦⣠⣴⣶⣶⣶⢶⣦⣀⣠⡶⣤⣤⣄⣀⣸⣿⣿⣿⣶⣿⣿⣭⣭⣽⣿⣿⣷⡦⣤⣿⣿⣿⣿⣼⣽⣿⣶⣾⣾⣿⣿⣿⣿⣯⣿⣾⣁⣄⣀⣄⣸⣷⣧⣭⣍ ⢶⠆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠶⠤⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠆ ⠤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢤⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠢⠤⠀⠢⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢠⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⣠⡀⢀⡀⠠⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣠⣴⣴⣶⣶⣶⠓⠚⠒⠚⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣤⣾⣿⣦⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠤⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⠸⣿⣿⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣷⣾⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⢻⣿⡿⠛⠛⠛⠛⠿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⠄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣹⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⢿⣿⣿⡇⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠐⣿⡿⡿⢛⡯⠠⣴⣿⣿⣿⣶⣼⣷⣾⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⡟⠠⣴⡄⣠ ⢈⣉⡉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⠁⣦⠉⠀⠀⠀⢀⣀⠈⢡⣦⣼⣦⣴⣾⣿⣿⣇⠀⢒⣒⡒⠀⠀⠂⢘⣛⠉⠉⠉⠁⢙⣛⡀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣼⢧⢿⣿⣿ ⠈⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⢀⡉⢁⣤⣾⣿⣿⣿⣿⣿⣿⣿⡯⠀⠠⠤⠄⠀⠀⠀⠠⠤⢠⣤⣀⣬⣭⣽⢽⡛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⠀⢸⣿⣿⣿⣿⣿ ⠀⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠛⣀⣀⢀⠀⠃⠀⠈⠛⠋⠋⠛⠛⢈⣓⠚⠛⠛⠙⠛⠛⣛⠛⡛⠛⠛⢛⣁⡁⠄⠀⠈⣿⣿⣟⣻⣿ ⠀⠶⠾⠶⠆⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣰⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣇⣀⡀⠀⣈⠀⠘⠀⢀⣀⡲⠆⠴⠆⠁⣰⣞⠧⠛⣛⣻⡛⣻⣿⢿⣿⣿⣿⣿⢿⣿⣶⣾⠶⢾⣿⣿⣿⣿⣿ ⢠⣄⣂⡀⠀⠀⣠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡉⢉⠉⡉⠉⠋⠘⠉⠉⢉⡉⢋⣙⡉⣉⠂⢈⠉⠉⠩⢍⡉ ⠀⠁⠈⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣶⣾⣿⣿⣶⣟⣓⣒⣀⡀⢺⠶⡷⣖⠘⠛⣿⣿⣿⣶⢖⡒⣐⣲⣿⣾⢟⣉ ⠐⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣿⢿⣿⣟⣙⣛⣿⡿⣿⠿⠂⠀⠨⠿⢿⣿⣿⣫ ⠐⠟⠻⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠛⠛⠭⠿⡿⠟⠿⣿⣟⣋⣿⡉⠁⠰⣿⠿⣟⠛⠋ ⠠⠤⣤⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡋⠀⣉⡉⢻⡶⡤⠁⠠⠤⠘⠛⢛⣄⣒⣖⣒⢀⢀⠐⠒⣒⣓⡚⠒⠀⠀⣚⣶⣲⣂⡙ ⠀⠛⠿⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢠⠖⠐⠆⠆⠂⣀⡀⠀⠀⢀⣀⡸⠿⠿⠿⠟⠿⠿⠿⠿⠿⢿⠿⠿⠿⠾⢷⡿⠿⠷⠿⡷⠿⡿⠫⠺⡿⠿⠧⠲⠶⠶⠯⠟⠿⠽⠭⡯⢭⡿⣛⢛⣛⣠⣤⣬⠿⠿⠿⣿⡴ ⠀⠉⠉⠁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣄⠀⠨⢶⡶⡳⣿⣟⠼⣿⢛⣯⣾⣝⡾⣷⣒⠒⢒⣒⠒⡞⠓⣶⣿⠻⣚⢻⣾⣿⣿⣿⣿⣿⣿⣿⡟⣙⢻⣿⣿⣿⣯⣤⢤⣤⣥⠤⢾⣧⣴⣿⣿⡿⢿⣿⠷⢿⣿⣿⡤⣤⠤⢭⣤ ⠄⢁⣀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙⠉⠈⠉⠩⠉⠉⠉⠉⠉⠉⠉⠉⠫⣍⠉⠉⢉⡭⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣀⣛⣛⣛⣛⣻⣋⣙⣛⣊⢛⠉⠙⠉⠩⢛⣛⣛⣋⣉ ⡈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠠⠈⠘⠷⠤⠿⠋⠀⠀⢀⣀⣀⣼⣸⣯⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣻⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠉⠉⡉⠉⢹ ⠨⣿⠋⠉⠉⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⢶⣶⣖⣶⣦⣠⣴⣶⣶⣶⢶⣦⣀⣠⡶⣤⣤⣄⣀⣸⣿⣿⣿⣶⣿⣿⣭⣭⣽⣿⣿⣷⡦⣤⣿⣿⣿⣿⣼⣽⣿⣶⣾⣾⣿⣿⣿⣿⣯⣿⣾⣁⣄⣀⣄⣸⣷⣧⣭⣍ ⢶⠆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠶⠤⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠆ ⠤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢤⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠢⠤⠀⠢⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢠⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⣠⡀⢀⡀⠠⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣠⣴⣴⣶⣶⣶⠓⠚⠒⠚⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣤⣾⣿⣦⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠤⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⠸⣿⣿⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣷⣾⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⢻⣿⡿⠛⠛⠛⠛⠿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⠄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣹⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⢿⣿⣿⡇⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠐⣿⡿⡿⢛⡯⠠⣴⣿⣿⣿⣶⣼⣷⣾⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⡟⠠⣴⡄⣠ ⢈⣉⡉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⠁⣦⠉⠀⠀⠀⢀⣀⠈⢡⣦⣼⣦⣴⣾⣿⣿⣇⠀⢒⣒⡒⠀⠀⠂⢘⣛⠉⠉⠉⠁⢙⣛⡀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣼⢧⢿⣿⣿ ⠈⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⢀⡉⢁⣤⣾⣿⣿⣿⣿⣿⣿⣿⡯⠀⠠⠤⠄⠀⠀⠀⠠⠤⢠⣤⣀⣬⣭⣽⢽⡛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⠀⢸⣿⣿⣿⣿⣿ ⠀⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠛⣀⣀⢀⠀⠃⠀⠈⠛⠋⠋⠛⠛⢈⣓⠚⠛⠛⠙⠛⠛⣛⠛⡛⠛⠛⢛⣁⡁⠄⠀⠈⣿⣿⣟⣻⣿ ⠀⠶⠾⠶⠆⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣰⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣇⣀⡀⠀⣈⠀⠘⠀⢀⣀⡲⠆⠴⠆⠁⣰⣞⠧⠛⣛⣻⡛⣻⣿⢿⣿⣿⣿⣿⢿⣿⣶⣾⠶⢾⣿⣿⣿⣿⣿ ⢠⣄⣂⡀⠀⠀⣠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡉⢉⠉⡉⠉⠋⠘⠉⠉⢉⡉⢋⣙⡉⣉⠂⢈⠉⠉⠩⢍⡉ ⠀⠁⠈⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣶⣾⣿⣿⣶⣟⣓⣒⣀⡀⢺⠶⡷⣖⠘⠛⣿⣿⣿⣶⢖⡒⣐⣲⣿⣾⢟⣉ ⠐⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣿⢿⣿⣟⣙⣛⣿⡿⣿⠿⠂⠀⠨⠿⢿⣿⣿⣫ ⠐⠟⠻⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠛⠛⠭⠿⡿⠟⠿⣿⣟⣋⣿⡉⠁⠰⣿⠿⣟⠛⠋ ⠠⠤⣤⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡋⠀⣉⡉⢻⡶⡤⠁⠠⠤⠘⠛⢛⣄⣒⣖⣒⢀⢀⠐⠒⣒⣓⡚⠒⠀⠀⣚⣶⣲⣂⡙ ⠀⠛⠿⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢠⠖⠐⠆⠆⠂⣀⡀⠀⠀⢀⣀⡸⠿⠿⠿⠟⠿⠿⠿⠿⠿⢿⠿⠿⠿⠾⢷⡿⠿⠷⠿⡷⠿⡿⠫⠺⡿⠿⠧⠲⠶⠶⠯⠟⠿⠽⠭⡯⢭⡿⣛⢛⣛⣠⣤⣬⠿⠿⠿⣿⡴ ⠀⠉⠉⠁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣄⠀⠨⢶⡶⡳⣿⣟⠼⣿⢛⣯⣾⣝⡾⣷⣒⠒⢒⣒⠒⡞⠓⣶⣿⠻⣚⢻⣾⣿⣿⣿⣿⣿⣿⣿⡟⣙⢻⣿⣿⣿⣯⣤⢤⣤⣥⠤⢾⣧⣴⣿⣿⡿⢿⣿⠷⢿⣿⣿⡤⣤⠤⢭⣤ ⠄⢁⣀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙⠉⠈⠉⠩⠉⠉⠉⠉⠉⠉⠉⠉⠫⣍⠉⠉⢉⡭⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣀⣛⣛⣛⣛⣻⣋⣙⣛⣊⢛⠉⠙⠉⠩⢛⣛⣛⣋⣉ ⡈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠠⠈⠘⠷⠤⠿⠋⠀⠀⢀⣀⣀⣼⣸⣯⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣻⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠉⠉⡉⠉⢹ ⠨⣿⠋⠉⠉⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⢶⣶⣖⣶⣦⣠⣴⣶⣶⣶⢶⣦⣀⣠⡶⣤⣤⣄⣀⣸⣿⣿⣿⣶⣿⣿⣭⣭⣽⣿⣿⣷⡦⣤⣿⣿⣿⣿⣼⣽⣿⣶⣾⣾⣿⣿⣿⣿⣯⣿⣾⣁⣄⣀⣄⣸⣷⣧⣭⣍ ⢶⠆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠶⠤⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠆ ⠤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢤⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠢⠤⠀⠢⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢠⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⣠⡀⢀⡀⠠⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣠⣴⣴⣶⣶⣶⠓⠚⠒⠚⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣤⣾⣿⣦⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠤⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⠸⣿⣿⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣷⣾⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⢻⣿⡿⠛⠛⠛⠛⠿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⠄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣹⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⢿⣿⣿⡇⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠐⣿⡿⡿⢛⡯⠠⣴⣿⣿⣿⣶⣼⣷⣾⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⡟⠠⣴⡄⣠ ⢈⣉⡉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⠁⣦⠉⠀⠀⠀⢀⣀⠈⢡⣦⣼⣦⣴⣾⣿⣿⣇⠀⢒⣒⡒⠀⠀⠂⢘⣛⠉⠉⠉⠁⢙⣛⡀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣼⢧⢿⣿⣿ ⠈⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⢀⡉⢁⣤⣾⣿⣿⣿⣿⣿⣿⣿⡯⠀⠠⠤⠄⠀⠀⠀⠠⠤⢠⣤⣀⣬⣭⣽⢽⡛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⠀⢸⣿⣿⣿⣿⣿ ⠀⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠛⣀⣀⢀⠀⠃⠀⠈⠛⠋⠋⠛⠛⢈⣓⠚⠛⠛⠙⠛⠛⣛⠛⡛⠛⠛⢛⣁⡁⠄⠀⠈⣿⣿⣟⣻⣿ ⠀⠶⠾⠶⠆⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣰⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣇⣀⡀⠀⣈⠀⠘⠀⢀⣀⡲⠆⠴⠆⠁⣰⣞⠧⠛⣛⣻⡛⣻⣿⢿⣿⣿⣿⣿⢿⣿⣶⣾⠶⢾⣿⣿⣿⣿⣿ ⢠⣄⣂⡀⠀⠀⣠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡉⢉⠉⡉⠉⠋⠘⠉⠉⢉⡉⢋⣙⡉⣉⠂⢈⠉⠉⠩⢍⡉ ⠀⠁⠈⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣶⣾⣿⣿⣶⣟⣓⣒⣀⡀⢺⠶⡷⣖⠘⠛⣿⣿⣿⣶⢖⡒⣐⣲⣿⣾⢟⣉ ⠐⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣿⢿⣿⣟⣙⣛⣿⡿⣿⠿⠂⠀⠨⠿⢿⣿⣿⣫ ⠐⠟⠻⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠛⠛⠭⠿⡿⠟⠿⣿⣟⣋⣿⡉⠁⠰⣿⠿⣟⠛⠋ ⠠⠤⣤⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡋⠀⣉⡉⢻⡶⡤⠁⠠⠤⠘⠛⢛⣄⣒⣖⣒⢀⢀⠐⠒⣒⣓⡚⠒⠀⠀⣚⣶⣲⣂⡙ ⠀⠛⠿⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢠⠖⠐⠆⠆⠂⣀⡀⠀⠀⢀⣀⡸⠿⠿⠿⠟⠿⠿⠿⠿⠿⢿⠿⠿⠿⠾⢷⡿⠿⠷⠿⡷⠿⡿⠫⠺⡿⠿⠧⠲⠶⠶⠯⠟⠿⠽⠭⡯⢭⡿⣛⢛⣛⣠⣤⣬⠿⠿⠿⣿⡴ ⠀⠉⠉⠁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣄⠀⠨⢶⡶⡳⣿⣟⠼⣿⢛⣯⣾⣝⡾⣷⣒⠒⢒⣒⠒⡞⠓⣶⣿⠻⣚⢻⣾⣿⣿⣿⣿⣿⣿⣿⡟⣙⢻⣿⣿⣿⣯⣤⢤⣤⣥⠤⢾⣧⣴⣿⣿⡿⢿⣿⠷⢿⣿⣿⡤⣤⠤⢭⣤ ⠄⢁⣀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙⠉⠈⠉⠩⠉⠉⠉⠉⠉⠉⠉⠉⠫⣍⠉⠉⢉⡭⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣀⣛⣛⣛⣛⣻⣋⣙⣛⣊⢛⠉⠙⠉⠩⢛⣛⣛⣋⣉ ⡈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠠⠈⠘⠷⠤⠿⠋⠀⠀⢀⣀⣀⣼⣸⣯⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣻⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠉⠉⡉⠉⢹ ⠨⣿⠋⠉⠉⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⢶⣶⣖⣶⣦⣠⣴⣶⣶⣶⢶⣦⣀⣠⡶⣤⣤⣄⣀⣸⣿⣿⣿⣶⣿⣿⣭⣭⣽⣿⣿⣷⡦⣤⣿⣿⣿⣿⣼⣽⣿⣶⣾⣾⣿⣿⣿⣿⣯⣿⣾⣁⣄⣀⣄⣸⣷⣧⣭⣍ ⢶⠆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠶⠤⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠆ ⠤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢤⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠢⠤⠀⠢⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢠⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⣠⡀⢀⡀⠠⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣠⣴⣴⣶⣶⣶⠓⠚⠒⠚⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣤⣾⣿⣦⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠤⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⠸⣿⣿⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣷⣾⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⢻⣿⡿⠛⠛⠛⠛⠿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⠄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣹⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⢿⣿⣿⡇⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠐⣿⡿⡿⢛⡯⠠⣴⣿⣿⣿⣶⣼⣷⣾⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⡟⠠⣴⡄⣠ ⢈⣉⡉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⠁⣦⠉⠀⠀⠀⢀⣀⠈⢡⣦⣼⣦⣴⣾⣿⣿⣇⠀⢒⣒⡒⠀⠀⠂⢘⣛⠉⠉⠉⠁⢙⣛⡀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣼⢧⢿⣿⣿ ⠈⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⢀⡉⢁⣤⣾⣿⣿⣿⣿⣿⣿⣿⡯⠀⠠⠤⠄⠀⠀⠀⠠⠤⢠⣤⣀⣬⣭⣽⢽⡛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⠀⢸⣿⣿⣿⣿⣿ ⠀⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠛⣀⣀⢀⠀⠃⠀⠈⠛⠋⠋⠛⠛⢈⣓⠚⠛⠛⠙⠛⠛⣛⠛⡛⠛⠛⢛⣁⡁⠄⠀⠈⣿⣿⣟⣻⣿ ⠀⠶⠾⠶⠆⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣰⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣇⣀⡀⠀⣈⠀⠘⠀⢀⣀⡲⠆⠴⠆⠁⣰⣞⠧⠛⣛⣻⡛⣻⣿⢿⣿⣿⣿⣿⢿⣿⣶⣾⠶⢾⣿⣿⣿⣿⣿ ⢠⣄⣂⡀⠀⠀⣠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡉⢉⠉⡉⠉⠋⠘⠉⠉⢉⡉⢋⣙⡉⣉⠂⢈⠉⠉⠩⢍⡉ ⠀⠁⠈⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣶⣾⣿⣿⣶⣟⣓⣒⣀⡀⢺⠶⡷⣖⠘⠛⣿⣿⣿⣶⢖⡒⣐⣲⣿⣾⢟⣉ ⠐⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣿⢿⣿⣟⣙⣛⣿⡿⣿⠿⠂⠀⠨⠿⢿⣿⣿⣫ ⠐⠟⠻⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠛⠛⠭⠿⡿⠟⠿⣿⣟⣋⣿⡉⠁⠰⣿⠿⣟⠛⠋ ⠠⠤⣤⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡋⠀⣉⡉⢻⡶⡤⠁⠠⠤⠘⠛⢛⣄⣒⣖⣒⢀⢀⠐⠒⣒⣓⡚⠒⠀⠀⣚⣶⣲⣂⡙ ⠀⠛⠿⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢠⠖⠐⠆⠆⠂⣀⡀⠀⠀⢀⣀⡸⠿⠿⠿⠟⠿⠿⠿⠿⠿⢿⠿⠿⠿⠾⢷⡿⠿⠷⠿⡷⠿⡿⠫⠺⡿⠿⠧⠲⠶⠶⠯⠟⠿⠽⠭⡯⢭⡿⣛⢛⣛⣠⣤⣬⠿⠿⠿⣿⡴ ⠀⠉⠉⠁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣄⠀⠨⢶⡶⡳⣿⣟⠼⣿⢛⣯⣾⣝⡾⣷⣒⠒⢒⣒⠒⡞⠓⣶⣿⠻⣚⢻⣾⣿⣿⣿⣿⣿⣿⣿⡟⣙⢻⣿⣿⣿⣯⣤⢤⣤⣥⠤⢾⣧⣴⣿⣿⡿⢿⣿⠷⢿⣿⣿⡤⣤⠤⢭⣤ ⠄⢁⣀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙⠉⠈⠉⠩⠉⠉⠉⠉⠉⠉⠉⠉⠫⣍⠉⠉⢉⡭⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣀⣛⣛⣛⣛⣻⣋⣙⣛⣊⢛⠉⠙⠉⠩⢛⣛⣛⣋⣉ ⡈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠠⠈⠘⠷⠤⠿⠋⠀⠀⢀⣀⣀⣼⣸⣯⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣻⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠉⠉⡉⠉⢹ ⠨⣿⠋⠉⠉⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⢶⣶⣖⣶⣦⣠⣴⣶⣶⣶⢶⣦⣀⣠⡶⣤⣤⣄⣀⣸⣿⣿⣿⣶⣿⣿⣭⣭⣽⣿⣿⣷⡦⣤⣿⣿⣿⣿⣼⣽⣿⣶⣾⣾⣿⣿⣿⣿⣯⣿⣾⣁⣄⣀⣄⣸⣷⣧⣭⣍ ⢶⠆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠶⠤⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠆ ⠤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢤⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠢⠤⠀⠢⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢠⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⣠⡀⢀⡀⠠⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣠⣴⣴⣶⣶⣶⠓⠚⠒⠚⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣤⣾⣿⣦⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠤⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⠸⣿⣿⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣷⣾⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⢻⣿⡿⠛⠛⠛⠛⠿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⠄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣹⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⢿⣿⣿⡇⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠐⣿⡿⡿⢛⡯⠠⣴⣿⣿⣿⣶⣼⣷⣾⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⡟⠠⣴⡄⣠ ⢈⣉⡉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⠁⣦⠉⠀⠀⠀⢀⣀⠈⢡⣦⣼⣦⣴⣾⣿⣿⣇⠀⢒⣒⡒⠀⠀⠂⢘⣛⠉⠉⠉⠁⢙⣛⡀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣼⢧⢿⣿⣿ ⠈⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⢀⡉⢁⣤⣾⣿⣿⣿⣿⣿⣿⣿⡯⠀⠠⠤⠄⠀⠀⠀⠠⠤⢠⣤⣀⣬⣭⣽⢽⡛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⠀⢸⣿⣿⣿⣿⣿ ⠀⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠛⣀⣀⢀⠀⠃⠀⠈⠛⠋⠋⠛⠛⢈⣓⠚⠛⠛⠙⠛⠛⣛⠛⡛⠛⠛⢛⣁⡁⠄⠀⠈⣿⣿⣟⣻⣿ ⠀⠶⠾⠶⠆⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣰⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣇⣀⡀⠀⣈⠀⠘⠀⢀⣀⡲⠆⠴⠆⠁⣰⣞⠧⠛⣛⣻⡛⣻⣿⢿⣿⣿⣿⣿⢿⣿⣶⣾⠶⢾⣿⣿⣿⣿⣿ ⢠⣄⣂⡀⠀⠀⣠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡉⢉⠉⡉⠉⠋⠘⠉⠉⢉⡉⢋⣙⡉⣉⠂⢈⠉⠉⠩⢍⡉ ⠀⠁⠈⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣶⣾⣿⣿⣶⣟⣓⣒⣀⡀⢺⠶⡷⣖⠘⠛⣿⣿⣿⣶⢖⡒⣐⣲⣿⣾⢟⣉ ⠐⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣿⢿⣿⣟⣙⣛⣿⡿⣿⠿⠂⠀⠨⠿⢿⣿⣿⣫ ⠐⠟⠻⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠛⠛⠭⠿⡿⠟⠿⣿⣟⣏⣿⡉⠁⠰⣿⠿⣟⠛⠋ ⠠⠤⣤⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡋⠀⣉⡉⢻⡶⡤⠁⠠⠤⠘⠛⢛⣄⣒⣖⣒⢀⢀⠐⠒⠒⣓⡚⠒⠀⠀⣚⣶⣲⣂⡙ ⠀⠛⠿⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢠⠖⠐⠆⠆⠂⣀⡀⠀⠀⢀⣀⡸⠿⠿⠿⠟⠿⠿⠿⠿⠿⢿⠿⠿⠿⠾⢷⡿⠿⠷⠿⡷⠿⡿⠫⠺⡿⠿⠧⠲⠶⠶⠯⠟⠿⠽⠭⡯⢭⡿⣛⢛⣛⣠⣤⣬⠿⠿⠿⣿⡴ ⠀⠉⠉⠁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣄⠀⠨⢶⡶⡳⣿⣟⠼⣿⢛⣯⣾⣝⡾⣷⣒⠒⢒⣒⠒⡞⠓⣶⣿⠻⣚⢻⣾⣿⣿⣿⣿⣿⣿⣿⡟⣙⢻⣿⣿⣿⣯⣤⢤⣤⣥⠤⢾⣧⣴⣿⣿⡿⢿⣿⠷⢿⣿⣿⡤⣤⠤⢭⣤ ⠄⢁⣀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙⠉⠈⠉⠩⠉⠉⠉⠉⠉⠉⠉⠉⠫⣍⠉⠉⢉⡭⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣀⣛⣛⣛⣛⣻⣋⣙⣛⣊⢛⠉⠙⠉⠩⢛⣛⣛⣋⣉ ⡈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠠⠈⠘⠷⠤⠿⠋⠀⠀⢀⣀⣀⣼⣸⣯⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣻⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠉⠉⡉⠉⢹ ⠨⣿⠋⠉⠉⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⢶⣶⣖⣶⣦⣠⣴⣶⣶⣶⢶⣦⣀⣠⡶⣤⣤⣄⣀⣸⣿⣿⣿⣶⣿⣿⣭⣭⣽⣿⣿⣷⡦⣤⣿⣿⣿⣿⣼⣽⣿⣶⣾⣾⣿⣿⣿⣿⣯⣿⣾⣁⣄⣀⣄⣸⣷⣧⣭⣍ ⢶⠆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠶⠤⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠆ ⠤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢤⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠢⠤⠀⠢⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢠⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⣠⡀⢀⡀⠠⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣠⣴⣴⣶⣶⣶⠓⠚⠒⠚⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣤⣾⣿⣦⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠤⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⠸⣿⣿⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣷⣾⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⢻⣿⡿⠛⠛⠛⠛⠿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⠄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣹⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⢿⣿⣿⡇⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠐⣿⡿⡿⢛⡯⠠⣴⣿⣿⣿⣶⣼⣷⣾⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⡟⠠⣴⡄⣠ ⢈⣉⡉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⠁⣦⠉⠀⠀⠀⢀⣀⠈⢡⣦⣼⣦⣴⣾⣿⣿⣇⠀⢒⣒⡒⠀⠀⠂⢘⣛⠉⠉⠉⠁⢙⣛⡀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣼⢧⢿⣿⣿ ⠈⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⢀⡉⢁⣤⣾⣿⣿⣿⣿⣿⣿⣿⡯⠀⠠⠤⠄⠀⠀⠀⠠⠤⢠⣤⣀⣬⣭⣽⢽⡛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⠀⢸⣿⣿⣿⣿⣿ ⠀⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠛⣀⣀⢀⠀⠃⠀⠈⠛⠋⠋⠛⠛⢈⣓⠚⠛⠛⠙⠛⠛⣛⠛⡛⠛⠛⢛⣁⡁⠄⠀⠈⣿⣿⣟⣻⣿ ⠀⠶⠾⠶⠆⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣰⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣇⣀⡀⠀⣈⠀⠘⠀⢀⣀⡲⠆⠴⠆⠁⣰⣞⠧⠛⣛⣻⡛⣻⣿⢿⣿⣿⣿⣿⢿⣿⣶⣾⠶⢾⣿⣿⣿⣿⣿ ⢠⣄⣂⡀⠀⠀⣠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡉⢉⠉⡉⠉⠋⠘⠉⠉⢉⡉⢋⣙⡉⣉⠂⢈⠉⠉⠩⢍⡉ ⠀⠁⠈⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣶⣾⣿⣿⣶⣟⣓⣒⣀⡀⢺⠶⡷⣖⠘⠛⣿⣿⣿⣶⢖⡒⣐⣲⣿⣾⢟⣉ ⠐⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣿⢿⣿⣟⣙⣛⣿⡿⣿⠿⠂⠀⠨⠿⢿⣿⣿⣫ ⠐⠟⠻⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠛⠛⠭⠿⡿⠟⠿⣿⣟⣏⣿⡉⠁⠰⣿⠿⣟⠛⠋ ⠠⠤⣤⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡋⠀⣉⡉⢻⡶⡤⠁⠠⠤⠘⠛⢛⣄⣒⣖⣒⢀⢀⠐⠒⠒⣓⡚⠒⠀⠀⣚⣶⣲⣂⡙ ⠀⠛⠿⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢠⠖⠐⠆⠆⠂⣀⡀⠀⠀⢀⣀⡸⠿⠿⠿⠟⠿⠿⠿⠿⠿⢿⠿⠿⠿⠾⢷⡿⠿⠷⠿⡷⠿⡿⠫⠺⡿⠿⠧⠲⠶⠶⠯⠟⠿⠽⠭⡯⢭⡿⣛⢛⣛⣠⣤⣬⠿⠿⠿⣿⡴ ⠀⠉⠉⠁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣄⠀⠨⢶⡶⡳⣿⣟⠼⣿⢛⣯⣾⣝⡾⣷⣒⠒⢒⣒⠒⡞⠓⣶⣿⠻⣚⢻⣾⣿⣿⣿⣿⣿⣿⣿⡟⣙⢻⣿⣿⣿⣯⣤⢤⣤⣥⠤⢾⣧⣴⣿⣿⡿⢿⣿⠷⢿⣿⣿⡤⣤⠤⢭⣤ ⠄⢁⣀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙⠉⠈⠉⠩⠉⠉⠉⠉⠉⠉⠉⠉⠫⣍⠉⠉⢉⡭⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣀⣛⣛⣛⣛⣻⣋⣙⣛⣊⢛⠉⠙⠉⠩⢛⣛⣛⣋⣉ ⡈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠠⠈⠘⠷⠤⠿⠋⠀⠀⢀⣀⣀⣼⣸⣯⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣻⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠉⠉⡉⠉⢹ ⠨⣿⠋⠉⠉⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⢶⣶⣖⣶⣦⣠⣴⣶⣶⣶⢶⣦⣀⣠⡶⣤⣤⣄⣀⣸⣿⣿⣿⣶⣿⣿⣭⣭⣽⣿⣿⣷⡦⣤⣿⣿⣿⣿⣼⣽⣿⣶⣾⣾⣿⣿⣿⣿⣯⣿⣾⣁⣄⣀⣄⣸⣷⣧⣭⣍ ⢶⠆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠶⠤⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠆ ⠤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢤⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠢⠤⠀⠢⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢠⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⣠⡀⢀⡀⠠⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣠⣴⣴⣶⣶⣶⠓⠚⠒⠚⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣤⣾⣿⣦⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠤⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⠸⣿⣿⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣷⣾⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⢻⣿⡿⠛⠛⠛⠛⠿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⠄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣹⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⢿⣿⣿⡇⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠐⣿⡿⡿⢛⡯⠠⣴⣿⣿⣿⣶⣼⣷⣾⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⡟⠠⣴⡄⣠ ⢈⣉⡉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⠁⣦⠉⠀⠀⠀⢀⣀⠈⢡⣦⣼⣦⣴⣾⣿⣿⣇⠀⢒⣒⡒⠀⠀⠂⢘⣛⠉⠉⠉⠁⢙⣛⡀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣼⢧⢿⣿⣿ ⠈⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⢀⡉⢁⣤⣾⣿⣿⣿⣿⣿⣿⣿⡯⠀⠠⠤⠄⠀⠀⠀⠠⠤⢠⣤⣀⣬⣭⣽⢽⡛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⠀⢸⣿⣿⣿⣿⣿ ⠀⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠛⣀⣀⢀⠀⠃⠀⠈⠛⠋⠋⠛⠛⢈⣓⠚⠛⠛⠙⠛⠛⣛⠛⡛⠛⠛⢛⣁⡁⠄⠀⠈⣿⣿⣟⣻⣿ ⠀⠶⠾⠶⠆⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣰⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣇⣀⡀⠀⣈⠀⠘⠀⢀⣀⡲⠆⠴⠆⠁⣰⣞⠧⠛⣛⣻⡛⣻⣿⢿⣿⣿⣿⣿⢿⣿⣶⣾⠶⢾⣿⣿⣿⣿⣿ ⢠⣄⣂⡀⠀⠀⣠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡉⢉⠉⡉⠉⠋⠘⠉⠉⢉⡉⢋⣙⡉⣉⠂⢈⠉⠉⠩⢍⡉ ⠀⠁⠈⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣶⣾⣿⣿⣶⣟⣓⣒⣀⡀⢺⠶⡷⣖⠘⠛⣿⣿⣿⣶⢖⡒⣐⣲⣿⣾⢟⣉ ⠐⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣿⢿⣿⣟⣙⣛⣿⡿⣿⠿⠂⠀⠨⠿⢿⣿⣿⣫ ⠐⠟⠻⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠛⠛⠭⠿⡿⠟⠿⣿⣟⣏⣿⡉⠁⠰⣿⠿⣟⠛⠋ ⠠⠤⣤⡀⠀⠀⢀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡋⠀⣉⡉⢻⡶⡤⠁⠠⠤⠘⠛⢛⣄⣒⣖⣒⢀⢀⠐⠒⠒⣓⡚⠒⠀⠀⣚⣶⣲⣂⡙ ⠀⠛⠿⠃⠀⢀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠰⢠⠖⠐⠆⠆⠂⣀⡀⠀⠀⢀⣀⡸⠿⠿⠿⠟⠿⠿⠿⠿⠿⢿⠿⠿⠿⠾⢷⡿⠿⠷⠿⡷⠿⡿⠫⠺⡿⠿⠧⠲⠶⠶⠯⠟⠿⠽⠭⡯⢭⡿⣛⢛⣛⣠⣤⣬⠿⠿⠿⣿⡴ ⠀⠉⠉⠁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣄⠀⠨⢶⡶⡳⣿⣟⠼⣿⢛⣯⣾⣝⡾⣷⣒⠒⢒⣒⠒⡞⠓⣶⣿⠻⣚⢻⣾⣿⣿⣿⣿⣿⣿⣿⡟⣙⢻⣿⣿⣿⣯⣤⢤⣤⣥⠤⢾⣧⣴⣿⣿⡿⢿⣿⠷⢿⣿⣿⡤⣤⠤⢭⣤ ⠄⢁⣀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙⠉⠈⠉⠩⠉⠉⠉⠉⠉⠉⠉⠉⠫⣍⠉⠉⢉⡭⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣀⣛⣛⣛⣛⣻⣋⣙⣛⣊⢛⠉⠙⠉⠩⢛⣛⣛⣋⣉ ⡈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠠⠈⠘⠷⠤⠿⠋⠀⠀⢀⣀⣀⣼⣸⣯⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣻⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠉⠉⡉⠉⢹ ⠨⣿⠋⠉⠉⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⢶⣶⣖⣶⣦⣠⣴⣶⣶⣶⢶⣦⣀⣠⡶⣤⣤⣄⣀⣸⣿⣿⣿⣶⣿⣿⣭⣭⣽⣿⣿⣷⡦⣤⣿⣿⣿⣿⣼⣽⣿⣶⣾⣾⣿⣿⣿⣿⣯⣿⣾⣁⣄⣀⣄⣸⣷⣧⣭⣍ ⢶⠆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠶⠤⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠆ ⠤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢤⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠢⠤⠀⠢⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢠⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⣠⡀⢀⡀⠠⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣠⣴⣴⣶⣶⣶⠓⠚⠒⠚⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣤⣾⣿⣦⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠤⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⠸⣿⣿⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣷⣾⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⢻⣿⡿⠛⠛⠛⠛⠿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⠄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣹⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⢿⣿⣿⡇⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠐⣿⡿⡿⢛⡯⠠⣴⣿⣿⣿⣶⣼⣷⣾⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⡟⠠⣴⡄⣠ ⢈⣉⡉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⠁⣦⠉⠀⠀⠀⢀⣀⠈⢡⣦⣼⣦⣴⣾⣿⣿⣇⠀⢒⣒⡒⠀⠀⠂⢘⣛⠉⠉⠉⠁⢙⣛⡀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣼⢧⢿⣿⣿ ⠈⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⢀⡉⢁⣤⣾⣿⣿⣿⣿⣿⣿⣿⡯⠀⠠⠤⠄⠀⠀⠀⠠⠤⢠⣤⣀⣬⣭⣽⢽⡛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⠀⢸⣿⣿⣿⣿⣿ ⠀⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠛⣀⣀⢀⠀⠃⠀⠈⠛⠋⠋⠛⠛⢈⣓⠚⠛⠛⠙⠛⠛⣛⠛⡛⠛⠛⢛⣁⡁⠄⠀⠈⣿⣿⣟⣻⣿ ⠀⠶⠾⠶⠆⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣰⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣇⣀⡀⠀⣈⠀⠘⠀⢀⣀⡲⠆⠴⠆⠁⣰⣞⠧⠛⣛⣻⡛⣻⣿⢿⣿⣿⣿⣿⢿⣿⣶⣾⠶⢾⣿⣿⣿⣿⣿ ⢠⣄⣂⡀⠀⠀⣠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡉⢉⠉⡉⠉⠋⠘⠉⠉⢉⡉⢋⣙⡉⣉⠂⢈⠉⠉⠩⢍⡉ ⠀⠁⠈⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣶⣾⣿⣿⣶⣟⣓⣒⣀⡀⢺⠶⡷⣖⠘⠛⣿⣿⣿⣶⢖⡒⣐⣲⣿⣾⢟⣉ ⠐⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣿⢿⣿⣟⣙⡛⣿⡷⣿⠿⠂⠀⠨⠿⢿⣿⣿⣫ ⠐⠟⠻⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠛⠛⠭⠿⡿⠟⠿⣿⣟⣏⣿⡉⠁⠰⣿⠿⣟⠛⠋ ⠠⠤⣤⡀⠀⠀⢀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡋⠀⣉⡉⢻⡶⡤⠁⠠⠤⠘⠛⢛⣄⣒⣖⣒⢀⢀⠐⠒⠒⣓⡚⠒⠀⠀⣚⣶⣲⣂⡙ ⠀⠛⠿⠃⠀⢀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠰⢠⠖⠐⠆⠆⠂⣀⡀⠀⠀⢀⣀⡸⠿⠿⠿⠟⠿⠿⠿⠿⠿⢿⠿⠿⠿⠾⢷⡿⠿⠷⠿⡷⠿⡿⠫⠺⡿⠿⠧⠲⠶⠶⠯⠟⠿⠽⠭⡯⢭⡿⣛⢛⣛⣠⣤⣬⠿⠿⠿⣿⡴ ⠀⠉⠉⠁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣄⠀⠨⢶⡶⡳⣿⣟⠼⣿⢛⣯⣾⣝⡾⣷⣒⠒⢒⣒⠒⡞⠓⣶⣿⠻⣚⢻⣾⣿⣿⣿⣿⣿⣿⣿⡟⣙⢻⣿⣿⣿⣯⣤⢤⣤⣥⠤⢾⣧⣴⣿⣿⡿⢿⣿⠷⢿⣿⣿⡤⣤⠤⢭⣤ ⠄⢁⣀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙⠉⠈⠉⠩⠉⠉⠈⠉⠉⠉⠉⠉⠫⣍⠉⠉⢉⡭⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣀⣛⣛⣛⣛⣻⣋⣙⣛⣊⢛⠉⠙⠉⠩⢛⣛⣛⣋⣉ ⡈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠠⠈⠘⠷⠤⠿⠋⠀⠀⢀⣀⣀⣼⣸⣯⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣻⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠉⠉⡉⠉⢹ ⠨⣿⠋⠉⠉⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⢶⣶⣖⣶⣦⢠⣴⣶⣶⣶⢶⣦⣀⣠⡶⣤⣤⣄⣀⣸⣿⣿⣿⣶⣿⣿⣭⣭⣽⣿⣿⣷⡦⣤⣿⣿⣿⣿⣼⣽⣿⣶⣾⣾⣿⣿⣿⣿⣯⣿⣾⣁⣄⣀⣄⣸⣷⣧⣭⣍ ⢶⠆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠶⠤⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠆ ⠤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢤⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠢⠤⠀⠢⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢠⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⣠⡀⢀⡀⠠⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣠⣴⣴⣶⣶⣶⠓⠚⠒⠚⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣤⣾⣿⣦⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠤⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⠸⣿⣿⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣷⣾⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⢻⣿⡿⠛⠛⠛⠛⠿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⠄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣹⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⢿⣿⣿⡇⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠐⣿⡿⡿⢛⡯⠠⣴⣿⣿⣿⣶⣼⣷⣾⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⡟⠠⣴⡄⣠ ⢈⣉⡉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⠁⣦⠉⠀⠀⠀⢀⣀⠈⢡⣦⣼⣦⣴⣾⣿⣿⣇⠀⢒⣒⡒⠀⠀⠂⢘⣛⠉⠉⠉⠁⢙⣛⡀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣼⢧⢿⣿⣿ ⠈⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⢀⡉⢁⣤⣾⣿⣿⣿⣿⣿⣿⣿⡯⠀⠠⠤⠄⠀⠀⠀⠠⠤⢠⣤⣀⣬⣭⣽⢽⡛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⠀⢸⣿⣿⣿⣿⣿ ⠀⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠛⣀⣀⢀⠀⠃⠀⠈⠛⠋⠋⠛⠛⢈⣓⠚⠛⠛⠙⠛⠛⣛⠛⡛⠛⠛⢛⣁⡁⠄⠀⠈⣿⣿⣟⣻⣿ ⠀⠶⠾⠶⠆⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣰⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣇⣀⡀⠀⣈⠀⠘⠀⢀⣀⡲⠆⠴⠆⠁⣰⣞⠧⠛⣛⣻⡛⣻⣿⢿⣿⣿⣿⣿⢿⣿⣶⣾⠶⢾⣿⣿⣿⣿⣿ ⢠⣄⣂⡀⠀⠀⣠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡉⢉⠉⡉⠉⠋⠘⠉⢉⣉⡉⢋⣙⡉⣉⠂⢈⠉⠉⠩⢍⡉ ⠀⠁⠈⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣶⣾⣿⣿⣶⣟⣓⣒⣀⡀⢺⠶⡷⣖⠘⠛⣿⣿⣿⣶⢖⡒⣐⣲⣿⣾⢟⣉ ⠐⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣿⢿⣿⣟⣙⡛⣿⡷⣿⠿⠂⠀⠨⠿⢿⣿⣿⣫ ⠐⠟⠻⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠛⠛⠭⠿⡿⠟⠿⣿⣟⣏⣿⡉⠁⠰⣿⠿⣟⠛⠋ ⠠⠤⣤⡀⠀⠀⢀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡋⠀⣉⡉⢻⡶⡤⠁⠠⠤⠘⠛⢛⣄⣒⣖⣒⢀⢀⠐⠒⠒⣓⡚⠒⠀⠀⣚⣶⣲⣂⡙ ⠀⠛⠿⠃⠀⢀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠰⢠⠖⠐⠆⠆⠂⣀⡀⠀⠀⢀⣀⡸⠿⠿⠿⠟⠿⠿⠿⠿⠿⢿⠿⠿⠿⠾⢷⡿⠿⠷⠿⡷⠿⡿⠫⠺⡿⠿⠧⠲⠶⠶⠯⠟⠿⠽⠭⡯⢭⡿⣛⢛⣛⣠⣤⣬⠿⠿⠿⣿⡴ ⠀⠉⠉⠁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣄⠀⠨⢶⡶⡳⣿⣟⠼⣿⢛⣯⣾⣝⡾⣷⣒⠒⢒⣒⠒⡞⠓⣶⣿⠻⣚⢻⣾⣿⣿⣿⣿⣿⣿⣿⡟⣙⢻⣿⣿⣿⣯⣤⢤⣤⣥⠤⢾⣧⣴⣿⣿⡿⢿⣿⠷⢿⣿⣿⡤⣤⠤⢭⣤ ⠄⢁⣀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙⠉⠈⠉⠩⠉⠉⠈⠉⠉⠉⠉⠉⠫⣍⠉⠉⢉⡭⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣀⣛⣛⣛⣛⣻⣋⣙⣛⣊⢛⠉⠙⠉⠩⢛⣛⣛⣋⣉ ⡈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠠⠈⠘⠷⠤⠿⠋⠀⠀⢀⣀⣀⣼⣸⣯⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣻⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠉⠉⡉⠉⢹ ⠨⣿⠋⠉⠉⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⢶⣶⣖⣶⣦⢠⣴⣶⣶⣶⢶⣦⣀⣠⡶⣤⣤⣄⣀⣸⣿⣿⣿⣶⣿⣿⣭⣭⣽⣿⣿⣷⡦⣤⣿⣿⣿⣿⣼⣽⣿⣶⣾⣾⣿⣿⣿⣿⣯⣿⣾⣁⣄⣀⣄⣸⣷⣧⣭⣍ ⢶⠆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠶⠤⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠆ ⠤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢤⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠢⠤⠀⠢⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢠⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⣠⡀⢀⡀⠠⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣠⣴⣴⣶⣶⣶⠓⠚⠒⠚⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣤⣾⣿⣦⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠤⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⠸⣿⣿⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣷⣾⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⢻⣿⡿⠛⠛⠛⠛⠿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⠄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣹⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⢿⣿⣿⡇⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠐⣿⡿⡿⢛⡯⠠⣴⣿⣿⣿⣶⣼⣷⣾⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⡟⠠⣴⡄⣠ ⢈⣉⡉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⠁⣦⠉⠀⠀⠀⢀⣀⠈⢡⣦⣼⣦⣴⣾⣿⣿⣇⠀⢒⣒⡒⠀⠀⠂⢘⣛⠉⠉⠉⠁⢙⣛⡀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣼⢧⢿⣿⣿ ⠈⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⢀⡉⢁⣤⣾⣿⣿⣿⣿⣿⣿⣿⡯⠀⠠⠤⠄⠀⠀⠀⠠⠤⢠⣤⣀⣬⣭⣽⢽⡛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⠀⢸⣿⣿⣿⣿⣿ ⠀⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠛⣀⣀⢀⠀⠃⠀⠈⠛⠋⠋⠛⠻⢈⣓⠚⠛⠛⠙⠛⠛⣛⠛⡛⠛⠛⢛⣁⡁⠄⠀⠈⣿⣿⣟⣻⣿ ⠀⠶⠾⠶⠆⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣰⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣇⣀⡀⠀⣈⠀⠘⠀⢀⣀⡲⠆⠴⠆⠁⣰⣞⠧⠛⣛⣻⡛⣻⣿⢿⣿⣿⣿⣿⢿⣿⣶⣾⠶⢾⣿⣿⣿⣿⣿ ⢠⣄⣂⡀⠀⠀⣠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⢿⣿⡉⢉⠉⡉⠉⠋⠘⠉⢉⣉⡉⢋⣙⡉⣉⠂⢈⠉⠉⠩⢍⡉ ⠀⠁⠈⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣶⣾⣿⣿⣶⣟⣓⣒⣀⡀⢺⠶⡷⣖⠘⠛⣿⣿⣿⣶⢖⡒⣐⣲⣿⣾⢟⣉ ⠐⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣿⢿⣿⣟⣙⡛⣿⡷⣿⠿⠂⠀⠨⠿⢿⣿⣿⣫ ⠐⠟⠻⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠛⠛⠭⠿⡿⠟⠿⣿⣟⣏⣿⡉⠁⠰⣿⠿⣟⠛⠋ ⠠⠤⣤⡀⠀⠀⢀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡋⠀⣉⡉⢻⡶⡤⠁⠠⠤⠘⠛⢛⣄⣒⣖⣒⢀⢀⠐⠒⠒⣓⡚⠒⠀⢀⣚⣶⣲⣂⡙ ⠀⠛⠿⠃⠀⢀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠰⢠⠖⠐⠆⠆⠂⣀⡀⠀⠀⢀⣀⡸⠿⠿⠿⠟⠿⠿⠿⠿⠿⢿⠿⠿⠿⠾⢷⡿⠿⠷⠿⡷⠿⡿⠫⠺⡿⠿⡧⠲⠶⠶⠯⠟⠿⠽⠭⡯⢭⡿⣛⢛⣛⣠⣤⣭⠿⠿⠿⣿⡴ ⠀⠉⠉⠁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣄⠀⠨⢶⡶⡳⣿⣟⠼⣿⢛⣯⣾⣝⡾⣷⣒⠒⢒⣒⠒⡞⠓⣶⣿⠻⣚⢻⣾⣿⣿⣿⣿⣿⣿⣿⡟⣙⢻⣿⣿⣿⣯⣤⢤⣤⣥⠤⢾⣧⣴⣿⣿⡿⢿⣿⠷⢿⣿⣿⡤⣤⠤⢭⣤ ⠄⢁⣀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙⠉⠈⠉⠩⠉⠉⠈⠉⠉⠉⠉⠉⠫⣍⠉⠉⢉⡭⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣀⣛⣛⣛⣛⣻⣋⣙⣛⣊⢛⠉⠙⠉⠩⢛⣛⣛⣋⣉ ⡈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠠⠈⠘⠷⠤⠿⠋⠀⠀⢀⣀⣀⣼⣸⣯⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣻⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠉⠉⡉⠉⢹ ⠨⣿⠋⠉⠉⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⢶⣶⣖⣶⣦⢠⣴⣶⣶⣶⢶⣦⣀⣠⡶⣤⣤⣄⣀⣸⣿⣿⣿⣶⣿⣿⣭⣭⣽⣿⣿⣷⡦⣤⣿⣿⣿⣿⣼⣽⣿⣶⣾⣾⣿⣿⣿⣿⣯⣿⣾⣁⣄⣀⣄⣸⣷⣧⣭⣍ ⢶⠆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠶⠤⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠆ ⠤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢤⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠢⠤⠀⠢⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢠⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⣠⡀⢀⡀⠠⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣠⣴⣴⣶⣶⣶⠓⠚⠒⠚⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣤⣾⣿⣦⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠤⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⠸⣿⣿⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣷⣾⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⢻⣿⡿⠛⠛⠛⠛⠿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⠄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣹⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⢿⣿⣿⡇⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠐⣿⡿⡿⢛⡯⠠⣴⣿⣿⣿⣶⣼⣷⣾⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⡟⠠⣴⡄⣠ ⢈⣉⡉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⠁⣦⠉⠀⠀⠀⢀⣀⠈⢡⣦⣼⣦⣴⣾⣿⣿⣇⠀⢒⣒⡒⠀⠀⠂⢘⣛⠉⠉⠉⠁⢙⣛⡀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣼⢧⢿⣿⣿ ⠈⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⢀⡉⢁⣤⣾⣿⣿⣿⣿⣿⣿⣿⡯⠀⠠⠤⠄⠀⠀⠀⠠⠤⢠⣤⣀⣬⣭⣽⢽⡛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⠀⢸⣿⣿⣿⣿⣿ ⠀⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠛⣀⣀⢀⠀⠃⠀⠈⠛⠋⠋⠛⠻⢈⣓⠚⠛⠛⠙⠹⠛⣛⠛⡻⡟⠛⢛⣁⡁⠄⠀⠈⣿⣿⣟⣻⣿ ⠀⠶⠾⠶⠆⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣰⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣇⣀⡀⠀⣈⠀⠘⠀⢀⣀⡲⠆⠴⠆⠁⣰⣞⠧⠛⣛⣻⡛⣻⣿⢿⣿⣿⣿⣿⢿⣿⣶⣾⠶⢾⣿⣿⣿⣿⣿ ⢠⣄⣂⡀⠀⠀⣠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⢿⣿⡉⢉⠉⡉⠉⠋⠘⠉⢉⣉⡉⢋⣙⡉⣉⠂⢈⠉⠉⠩⢍⡉ ⠀⠁⠈⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣶⣾⣿⣿⣶⣟⣓⣒⣀⡀⢺⠶⡷⣖⠘⠛⣿⣿⣿⣶⢖⡒⣐⣲⣿⣾⢟⣉ ⠐⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣿⢿⣿⣟⣙⡛⣿⡷⣿⠿⠂⠀⠨⠿⢿⣿⣿⣫ ⠐⠟⠻⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠛⠛⠭⠿⡿⠟⠿⣿⣟⣏⣿⡉⠁⠰⣿⠿⣟⠛⠋ ⠠⠤⣤⡀⠀⠀⢀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡋⠀⣉⡉⢻⡶⡤⠁⠠⠤⠘⠛⢛⣄⣒⣖⣒⢀⢀⠐⠒⠒⣓⡚⠒⠀⢀⣚⣶⣲⣂⡙ ⠀⠛⠿⠃⠀⢀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠰⢠⠖⠐⠆⠆⠂⣀⡀⠀⠀⢀⣀⡸⠿⠿⠿⠟⠿⠿⠿⠿⠿⢿⠿⠿⠿⠾⢷⡿⠿⠷⠿⡷⠿⡿⠫⠺⡿⠿⡧⠲⠶⠶⠯⠟⠿⠽⠭⡯⢭⡿⣛⢛⣛⣠⣤⣭⠿⠿⠿⣿⡴ ⠀⠉⠉⠁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣄⠀⠨⢶⡶⡳⣿⣟⠼⣿⢛⣯⣾⣝⡾⣷⣒⠒⢒⣒⠒⡞⠓⣶⣿⠻⣚⢻⣾⣿⣿⣿⣿⣿⣿⣿⡟⣙⢻⣿⣿⣿⣯⣤⢤⣤⣥⠤⢾⣧⣴⣿⣿⡿⢿⣿⠷⢿⣿⣿⡤⣤⠤⢭⣤ ⠄⢁⣀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙⠉⠈⠉⠩⠉⠉⠈⠉⠉⠉⠉⠉⠫⣍⠉⠉⢉⡭⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣀⣛⣛⣛⣛⣻⣋⣙⣛⣊⢛⠉⠙⠉⠩⢛⣛⣛⣋⣉ ⡈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠠⠈⠘⠷⠤⠿⠋⠀⠀⢀⣀⣀⣼⣸⣯⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣻⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠉⠉⡉⠉⢹ ⠨⣿⠋⠉⠉⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⢶⣶⣖⣶⣦⢠⣴⣶⣶⣶⢶⣦⣀⣠⡶⣤⣤⣄⣀⣸⣿⣿⣿⣶⣿⣿⣭⣭⣽⣿⣿⣷⡦⣤⣿⣿⣿⣿⣼⣽⣿⣶⣾⣾⣿⣿⣿⣿⣯⣿⣾⣁⣄⣀⣄⣸⣷⣧⣭⣍ ⢶⠆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠶⠤⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠆ ⠤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢤⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠢⠤⠀⠢⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢠⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⣠⡀⢀⡀⠠⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣠⣴⣴⣶⣶⣶⠓⠚⠒⠚⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣤⣾⣿⣦⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠤⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⠸⣿⣿⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣷⣾⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⢻⣿⡿⠛⠛⠛⠛⠿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⠄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣹⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⢿⣿⣿⡇⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠐⣿⡿⡿⢛⡯⠠⣴⣿⣿⣿⣶⣼⣷⣾⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⡟⠠⣴⡄⣠ ⢈⣉⡉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⠁⣦⠉⠀⠀⠀⢀⣀⠈⢡⣦⣼⣦⣴⣾⣿⣿⣇⠀⢒⣒⡒⠀⠀⠂⢘⣛⠉⠉⠉⠁⢙⣛⡀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣼⢧⢿⣿⣿ ⠈⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⢀⡉⢁⣤⣾⣿⣿⣿⣿⣿⣿⣿⡯⠀⠠⠤⠄⠀⠀⠀⠠⠤⢠⣤⣀⣬⣭⣽⢽⡛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⠀⢸⣿⣿⣿⣿⣿ ⠀⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠛⣀⣀⢀⠀⠃⠀⠈⠛⠋⠋⠛⠻⢈⣓⠚⠛⠛⠙⠙⠛⣛⠛⡻⡟⠛⢛⣃⡁⠄⠀⠈⣿⣿⣟⣻⣿ ⠀⠶⠾⠶⠆⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣰⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣇⣀⡀⠀⣈⠀⠘⠀⢀⣀⡲⠆⠴⠆⠁⣰⣞⠧⠛⣛⣻⡛⣻⣿⢿⣿⣿⣿⣿⢿⣿⣶⣾⠶⢾⣿⣿⣿⣿⣿ ⢠⣄⣂⡀⠀⠀⣠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⢿⣿⡉⢉⠉⡉⠉⠋⠘⠉⢉⣉⡉⢋⣙⡉⣉⠂⢈⠉⠉⠩⢍⡉ ⠀⠁⠈⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣶⣾⣿⣿⣶⣟⣓⣒⣀⡀⢺⠶⡷⣖⠘⠛⣿⣿⣿⣶⢖⡒⣐⣲⣿⣾⢟⣉ ⠐⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣿⢿⣿⣟⣙⡛⣿⡷⣿⠿⠂⠀⠨⠿⢿⣿⣿⣫ ⠐⠟⠻⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠛⠛⠭⠿⡿⠟⠿⣿⣟⣏⣿⡉⠁⠰⣿⠿⣟⠛⠋ ⠠⠤⣤⡀⠀⠀⢀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡋⠀⣉⡉⢻⡶⡤⠁⠠⠤⠘⠛⢛⣄⣒⣖⣒⢀⢀⠐⠒⠒⣓⡚⠒⠀⢀⣚⣶⣲⣂⡙ ⠀⠛⠿⠃⠀⢀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠰⢠⠖⠐⠆⠆⠂⣀⡀⠀⠀⢀⣀⡸⠿⠿⠿⠟⠿⠿⠿⠿⠿⢿⠿⠿⠿⠾⢷⡿⠿⠷⠿⡷⠿⡿⠫⠺⡿⠿⡧⠲⠶⠶⠯⠟⠿⠽⠭⡯⢭⡿⣛⢛⣛⣠⣤⣭⠿⠿⠿⣿⡴ ⠀⠉⠉⠁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣄⠀⠨⢶⡶⡳⣿⣟⠼⣿⢛⣯⣾⣝⡾⣷⣒⠒⢒⣒⠒⡞⠓⣶⣿⠻⣚⢻⣾⣿⣿⣿⣿⣿⣿⣿⡟⣙⢻⣿⣿⣿⣯⣤⢤⣤⣥⠤⢾⣧⣴⣿⣿⡿⢿⣿⠷⢿⣿⣿⡤⣤⠤⢭⣤ ⠄⢁⣀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙⠉⠈⠉⠩⠉⠉⠈⠉⠉⠉⠉⠉⠫⣍⠉⠉⢉⡭⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣀⣛⣛⣛⣛⣻⣋⣙⣛⣊⢛⠉⠙⠉⠩⢛⣛⣛⣋⣋ ⡈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠠⠈⠘⠷⠤⠿⠋⠀⠀⢀⣀⣀⣼⣸⣯⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣻⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠉⠉⡉⠉⢹ ⠨⣿⠋⠉⠉⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⢶⣶⣖⣶⣦⢠⣴⣶⣶⣶⢶⣦⣀⣠⡶⣤⣤⣄⣀⣸⣿⣿⣿⣶⣿⣿⣭⣭⣽⣿⣿⣷⡦⣤⣿⣿⣿⣿⣼⣽⣿⣶⣾⣾⣿⣿⣿⣿⣯⣿⣾⣁⣄⣀⣄⣸⣷⣧⣭⣍ ⢶⠆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠶⠤⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠆ ⠤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢤⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠢⠤⠀⠢⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢠⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⣠⡀⢀⡀⠠⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣠⣴⣴⣶⣶⣶⠓⠚⠒⠚⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣤⣾⣿⣦⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠤⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⠸⣿⣿⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣷⣾⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⢻⣿⡿⠛⠛⠛⠛⠿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⠄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣹⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⢿⣿⣿⡇⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠐⣿⡿⡿⢛⡯⠠⣴⣿⣿⣿⣶⣼⣷⣾⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⡟⠠⣴⡄⣠ ⢈⣉⡉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⠁⣦⠉⠀⠀⠀⢀⣀⠈⢡⣦⣼⣦⣴⣾⣿⣿⣇⠀⢒⣒⡒⠀⠀⠂⢘⣛⠉⠉⠉⠁⢙⣛⡀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣼⢧⢿⣿⣿ ⠈⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⢀⡉⢁⣤⣾⣿⣿⣿⣿⣿⣿⣿⡯⠀⠠⠤⠄⠀⠀⠀⠠⠤⢠⣤⣀⣬⣭⣽⢽⡛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⠀⢸⣿⣿⣿⣿⣿ ⠀⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠛⣀⣀⢀⠀⠃⠀⠈⠛⠋⠋⠛⠻⢈⣓⠚⠛⠛⠙⠙⠛⣛⠛⡻⡟⠛⢛⣃⡁⠄⠀⠈⣿⣿⣟⣻⣿ ⠀⠶⠾⠶⠆⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣰⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣇⣀⡀⠀⣈⠀⠘⠀⢀⣀⡲⠆⠴⠆⠁⣰⣞⠧⠛⣛⣻⡛⣻⣿⢿⣿⣿⣯⣿⢿⣿⣶⣾⠶⢾⣿⣿⣿⣿⣿ ⢠⣄⣂⡀⠀⠀⣠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⢿⣿⡉⢉⠉⡉⠉⠋⠘⠉⢉⣉⡉⢋⣙⡉⣉⠂⢈⠉⠉⠩⢍⡉ ⠀⠁⠈⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣶⣾⣿⣿⣶⣟⣓⣒⣀⡀⢺⠶⡷⣖⠘⠛⣿⣿⣿⣶⢖⡒⣐⣲⣿⣾⢟⣉ ⠐⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣿⢿⣿⣟⣙⡛⣿⡷⣿⠿⠂⠀⠨⠿⢿⣿⣿⣫ ⠐⠟⠻⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠛⠛⠭⠿⡿⠟⠿⣿⣟⣏⣿⡉⠁⠰⣿⠿⣟⠛⠋ ⠠⠤⣤⡀⠀⠀⢀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡋⠀⣉⡉⢻⡶⡤⠁⠠⠤⠘⠛⢛⣄⣒⣖⣒⢀⢀⠐⠒⠒⣓⡚⠒⠀⢀⣚⣶⣲⣂⡙ ⠀⠛⠿⠃⠀⢀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠰⢠⠖⠐⠆⠆⠂⣀⡀⠀⠀⢀⣀⡸⠿⠿⠿⠟⠿⠿⠿⠿⠿⢿⠿⠿⠿⠾⢷⡿⠿⠷⠿⡷⠿⡿⠫⠺⡿⠿⡧⠲⠶⠶⠯⠟⠿⠽⠭⡯⢭⡿⣛⢛⣛⣠⣤⣭⠿⠿⠿⣿⡴ ⠀⠉⠉⠁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣄⠀⠨⢶⡶⡳⣿⣟⠼⣿⢛⣯⣾⣝⡾⣷⣒⠒⢒⣒⠒⡞⠓⣶⣿⠻⣚⢻⣾⣿⣿⣿⣿⣿⣿⣿⡟⣙⢻⣿⣿⣿⣯⣤⢤⣤⣥⠤⢾⣧⣴⣿⣿⡿⢿⣿⠷⢿⣿⣿⡤⣤⠤⢭⣤ ⠄⢁⣀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙⠉⠈⠉⠩⠉⠉⠈⠉⠉⠉⠉⠉⠫⣍⠉⠉⢉⡭⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣀⣛⣛⣛⣛⣻⣋⣙⣛⣊⢛⠉⠙⠉⠩⢛⣛⣛⣋⣋ ⡈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠠⠈⠘⠷⠤⠿⠋⠀⠀⢀⣀⣀⣼⣸⣯⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣻⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠉⠉⡉⠉⢹ ⠨⣿⠋⠉⠉⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⢶⣶⣖⣶⣦⢠⣴⣶⣶⣶⢶⣦⣀⣠⡶⣤⣤⣄⣀⣸⣿⣿⣿⣶⣿⣿⣭⣭⣽⣿⣿⣷⡦⣤⣿⣿⣿⣿⣼⣽⣿⣶⣾⣾⣿⣿⣿⣿⣯⣿⣾⣁⣄⣀⣄⣸⣷⣧⣭⣍ ⢶⠄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠶⠤⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠆ ⠤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⢤⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠢⠤⠀⠢⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢐⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⣠⠀⢀⡀⠰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣠⣴⣴⣶⣶⣶⠒⠒⠒⠚⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣤⣾⣿⣦⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠤⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⣿⣿⣿⣾⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡿⠿⡻⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣔⠄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣻⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢦⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⢿⣿⣿⣿⠂⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠐⣿⡿⠿⢛⡿⠠⣴⣿⣿⣿⣶⣼⣗⣾⣶⣦⣤⣤⣶⣤⣦⣴⣤⣤⣤⣤⠤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⡟⠠⣴⡄⣠ ⢈⣉⡉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠀⠈⠁⣦⠉⠀⠀⠀⢀⣀⠈⢡⣦⣼⣧⣴⣾⣿⣿⡿⠀⢒⣒⡒⠀⠀⠂⢘⣛⠉⠉⠉⠁⢙⣛⡀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣼⢧⢿⣿⣿ ⠈⣍⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⢀⡉⢁⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠠⠤⠄⠸⠁⠀⠠⢤⣥⣦⣀⣬⣭⣽⢽⡛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⠀⢸⣿⣿⣿⣿⣿ ⠀⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠛⣀⣀⣀⠀⠃⠤⠈⠛⡋⠋⠛⠻⢈⣓⢺⡟⠛⣹⠛⣛⣿⡻⣻⡟⠟⢛⣃⡁⠄⠀⠈⣿⣿⣟⣻⣿ ⠀⠶⠶⠶⠆⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢈⣰⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⠀⣀⠈⠙⠁⢀⣀⡲⠆⠴⠆⠀⣰⣞⠧⠛⣛⣿⡛⣻⣿⢿⣿⣿⣯⣿⣿⣿⣶⣾⠶⢾⣿⣿⣿⣿⣿ ⢠⣆⣦⡀⠀⠢⣠⠀⠁⠀⠀⠀⠀⠀⠀⢰⠀⢠⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣶⣷⣿⣿⣿⣿⣿⣷⣶⣶⣿⣶⣿⢶⣿⡟⢋⠉⡉⠛⠋⠘⠍⢙⣏⡉⢋⣙⡉⣉⠂⢈⠉⠉⠩⢍⡉ ⠀⠁⠈⠙⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣶⣟⣓⣒⣀⡀⢺⠶⡷⣖⠚⢿⣿⣿⣿⣶⢖⡒⣐⣲⢿⢾⢏⣉ ⠐⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣟⣙⣻⣿⡷⣿⠿⠂⠀⠨⠿⢿⣿⣿⣫ ⠀⠟⠻⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠛⠛⠭⠿⡿⠟⠿⣿⣟⣏⣿⡉⠁⠰⣿⠿⣟⠛⠋ ⠠⢤⣤⡀⠀⠀⢀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣳⠎⣉⡉⢳⡶⡤⠁⠠⠤⠘⠛⢛⣄⣒⣖⣒⢀⢀⠐⠒⠒⣓⡚⠒⠀⢀⣚⣶⣲⣂⡙ ⠀⠛⠿⠃⠀⢀⡈⠀⠀⠀⠀⠀⠀⠀⠀⢨⢠⠖⠐⠆⠆⠂⣀⡀⠀⠀⢀⣀⡸⠿⠿⠿⠟⠿⠿⠿⠿⢿⣿⢿⡿⢿⣿⣿⣿⣿⣷⢿⡷⢿⡽⣿⣺⣿⣿⡧⢰⢶⠶⠯⠟⠿⢽⠭⡯⢭⡟⣛⢛⣛⣠⣤⣭⠿⠿⠿⣿⡴ ⠀⠉⠉⠁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣄⠀⠸⢶⣶⡳⣿⣟⠼⣿⢛⣯⣾⣝⡶⣷⣖⠒⢖⣲⠒⡟⠓⣴⣿⠻⣚⢾⣾⣿⣿⣷⣿⣿⣿⣶⡿⣘⢺⣿⣿⣿⡯⣤⢤⣬⣭⠥⢾⣯⣴⣿⣿⡿⢿⣿⢷⢿⣿⣿⡤⣤⠤⢭⣤ ⠄⢥⣤⡥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠤⠤⠙⠛⠊⠉⠹⠉⠉⠊⠉⠈⠙⠋⠉⠫⣍⠉⠋⢉⡯⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣷⠀⠐⣀⣛⣓⣛⣛⣻⣉⣙⣛⣊⢛⠉⠉⠉⠹⢛⣛⣛⣛⣋ ⡈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠠⠈⠘⠷⠤⠿⠋⠀⠀⢀⣀⣀⣼⣸⣯⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣻⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠉⠉⡉⠉⢹ ⠨⣿⡏⠉⠉⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⢴⣶⣖⣶⣦⢠⣴⣶⣶⣶⢶⣦⣀⣠⡶⣤⣤⣄⣀⣸⣿⣿⣿⣶⣿⣿⣭⣭⣽⣿⣿⣷⡦⣤⣿⣿⣿⣿⣼⣽⣿⣶⣾⣮⣿⣿⣿⣿⣯⣿⣾⣁⣄⣀⣄⣸⣷⣧⣭⣍ ⢶⠄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠶⠤⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠆ ⠤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⢤⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠢⠤⠀⠢⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢐⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⣠⠀⢀⡀⠰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣠⣴⣴⣶⣶⣶⠒⠒⠒⠚⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣤⣾⣿⣦⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠤⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⣿⣿⣿⣾⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡿⠿⡻⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣔⠄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣻⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢦⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⢿⣿⣿⣿⠂⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠐⣿⡿⠿⢛⡿⠠⣴⣿⣿⣿⣶⣼⣗⣾⣶⣦⣤⣤⣶⣤⣦⣴⣤⣤⣤⣤⠤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⡟⠠⣴⡄⣠ ⢈⣉⡉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠀⠈⠁⣦⠉⠀⠀⠀⢀⣀⠈⢡⣦⣼⣧⣴⣾⣿⣿⡿⠀⢒⣒⡒⠀⠀⠂⢘⣛⠉⠉⠉⠁⢙⣛⡀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣼⢧⢿⣿⣿ ⠈⣍⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⢀⡉⢁⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠠⠤⠄⠸⠥⠀⠠⢤⣥⣦⣀⣬⣭⣽⢽⡛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⠀⢸⣿⣿⣿⣿⣿ ⠀⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠛⣀⣀⣀⠀⠃⠤⠈⠛⡋⠋⠛⠻⢈⣓⢺⡟⠛⣹⠛⣛⣿⡻⣻⡟⠟⢛⣃⡁⠄⠀⠈⣿⣿⣟⣻⣿ ⠀⠶⠶⠶⠆⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢈⣰⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⠀⣀⠈⠙⠁⢀⣀⡲⠆⠴⠆⠀⣰⣞⠧⠛⣛⣿⡛⣻⣿⢿⣿⣿⣯⣿⣿⣿⣶⣾⠶⢾⣿⣿⣿⣿⣿ ⢠⣆⣦⡀⠀⠢⣠⠀⠁⠀⠀⠀⠀⠀⠀⢠⡄⢠⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣶⣷⣿⣿⣿⣿⣿⣷⣶⣶⣿⣶⣿⢶⣿⡟⢋⠉⡉⠛⠋⠘⠍⢙⣏⡉⢋⣙⡉⣉⠂⢈⠉⠉⠩⢍⡉ ⠀⠁⠈⠙⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣶⣟⣓⣒⣀⡀⢺⠶⡷⣖⠚⢿⣿⣿⣿⣶⢖⡒⣐⣲⢿⢾⢏⣉ ⠐⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣟⣙⣻⣿⡷⣿⠿⠂⠀⠨⠿⢿⣿⣿⣫ ⠀⠟⠻⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠛⠛⠭⠿⡿⠟⠿⣿⣟⣏⣿⡉⠁⠰⣿⠿⣟⠛⠋ ⠠⢤⣤⡀⠀⠀⢀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣳⠎⣉⡉⢳⡶⡤⠁⠠⠤⠘⠛⢛⣄⣒⣖⣒⢀⢀⠐⠒⠒⣓⡚⠒⠀⢀⣚⣶⣲⣂⡙ ⠀⠛⠿⠃⠀⢀⡈⠀⠀⠀⠀⠀⠀⠀⠀⢨⢠⠖⠐⠆⠆⠂⣀⡀⠀⠀⢀⣀⡸⠿⠿⠿⠟⠿⠿⠿⠿⢿⣿⢿⡿⢿⣿⣿⣿⣿⣷⢿⡷⢿⡽⣿⣺⣿⣿⡧⢰⢶⠶⠯⠟⠿⢽⠭⡯⢭⡟⣛⢛⣛⣠⣤⣭⠿⠿⠿⣿⡴ ⠀⠉⠉⠁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣄⠀⠸⢶⣶⡳⣿⣟⠼⣿⢛⣯⣾⣝⡶⣷⣖⠒⢖⣲⠒⡟⠓⣴⣿⠻⣚⢾⣾⣿⣿⣷⣿⣿⣿⣶⡿⣘⢺⣿⣿⣿⡯⣤⢤⣬⣭⠥⢾⣯⣴⣿⣿⡿⢿⣿⢷⢿⣿⣿⡤⣤⠤⢭⣤ ⠄⢥⣤⡥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠤⠤⠙⠛⠊⠉⠹⠉⠉⠊⠉⠈⠙⠋⠉⠫⣍⠉⠋⢉⡯⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣷⠀⠐⣀⣛⣓⣛⣛⣻⣉⣙⣛⣊⢛⠉⠉⠉⠹⢛⣛⣛⣛⣋ ⡈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠠⠈⠘⠷⠤⠿⠋⠀⠀⢀⣀⣀⣼⣸⣯⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣻⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠉⠉⡉⠉⢹ ⠨⣿⡏⠉⠉⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⢴⣶⣖⣶⣦⢠⣴⣶⣶⣶⢶⣦⣀⣠⡶⣤⣤⣄⣀⣸⣿⣿⣿⣶⣿⣿⣭⣭⣽⣿⣿⣷⡦⣤⣿⣿⣿⣿⣼⣽⣿⣶⣾⣮⣿⣿⣿⣿⣯⣿⣾⣁⣄⣀⣄⣸⣷⣧⣭⣍ ⢶⠄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠶⠤⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠆ ⠤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⢤⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠢⠤⠀⠢⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢐⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⣠⠀⢀⡀⠰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣠⣴⣴⣶⣶⣶⠒⠒⠒⠚⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣤⣾⣿⣦⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠤⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⣿⣿⣿⣾⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡿⠿⡻⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣔⠄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣻⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢦⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⢿⣿⣿⣿⠂⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠐⣿⡿⠿⢛⡿⠠⣴⣿⣿⣿⣶⣼⣗⣾⣶⣦⣤⣤⣶⣤⣦⣴⣤⣤⣤⣤⠤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⡟⠠⣴⡄⣠ ⢈⣉⡉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠀⠈⠁⣦⠉⠀⠀⠀⢀⣀⠈⢡⣦⣼⣧⣴⣾⣿⣿⡿⠀⢒⣒⡒⠀⠀⠂⢘⣛⠉⠉⠉⠁⢙⣛⡀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣼⢧⢿⣿⣿ ⠈⣍⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⢀⡉⢁⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠠⠤⠄⠸⠥⠀⠠⢤⣥⣦⣀⣬⣭⣽⢽⡛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⠀⢸⣿⣿⣿⣿⣿ ⠀⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠛⣀⣀⣀⠀⠃⠤⠈⠛⡋⠋⠛⠻⢈⣓⢺⡟⠛⣹⠛⣛⣿⡻⣻⡟⠟⢛⣃⡁⠄⠀⠈⣿⣿⣟⣻⣿ ⠀⠶⠶⠶⠆⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢈⣰⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⠀⣀⠈⠙⠁⢀⣀⡲⠆⠴⠆⠀⣰⣞⠧⠛⣛⣿⡛⣻⣿⢿⣿⣿⣯⣿⣿⣿⣶⣾⠶⢾⣿⣿⣿⣿⣿ ⢠⣆⣦⡀⠀⠢⣠⠀⠁⠀⠀⠀⠀⠀⠀⢠⡄⢠⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣶⣷⣿⣿⣿⣿⣿⣷⣶⣶⣿⣶⣿⢶⣿⡟⢋⠉⡉⠛⠋⠘⠍⢙⣏⡉⢋⣙⡉⣉⠂⢈⠉⠉⠩⢍⡉ ⠀⠁⠈⠙⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣶⣟⣓⣒⣀⡀⢺⠶⡷⣖⠚⢿⣿⣿⣿⣶⢖⡒⣐⣲⢿⢾⢏⣉ ⠐⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣟⣙⣻⣿⡷⣿⠿⠂⠀⠨⠿⢿⣿⣿⣫ ⠀⠟⠻⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠛⠛⠭⠿⡿⠟⠿⣿⣟⣏⣿⡉⠁⠰⣿⠿⣟⠛⠋ ⠠⢤⣤⡀⠀⠀⢀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣳⠎⣉⡉⢳⡶⡤⠁⠠⠤⠘⠛⢛⣄⣒⣖⣒⢀⢀⠐⠒⠒⣓⡚⠒⠀⢀⣚⣶⣲⣂⡙ ⠀⠛⠿⠃⠀⢀⡈⠀⠀⠀⠀⠀⠀⠀⠀⢨⢠⠖⠐⠆⠆⠂⣀⡀⠀⠀⢀⣀⡸⠿⠿⠿⠟⠿⠿⠿⠿⢿⣿⢿⡿⢿⣿⣿⣿⣿⣷⢿⡷⢿⡽⣿⣺⣿⣿⡧⢰⢶⠶⠯⠟⠿⢽⠭⡯⢭⡟⣛⢛⣛⣠⣤⣭⠿⠿⠿⣿⡴ ⠀⠉⠉⠁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣄⠀⠸⢶⣶⡳⣿⣟⠼⣿⢛⣯⣾⣝⡶⣷⣖⠒⢖⣲⠒⡟⠓⣴⣿⠻⣚⢾⣾⣿⣿⣷⣿⣿⣿⣶⡿⣘⢺⣿⣿⣿⡯⣤⢤⣬⣭⠥⢾⣯⣴⣿⣿⡿⢿⣿⢷⢿⣿⣿⡤⣤⠤⢭⣤ ⠄⢥⣤⡥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠤⠤⠙⠛⠊⠉⠹⠉⠉⠊⠉⠈⠙⠋⠉⠫⣍⠉⠋⢉⡯⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣷⠀⠐⣀⣛⣓⣛⣛⣻⣉⣙⣛⣊⢛⠉⠉⠉⠹⢛⣛⣛⣛⣋ ⡈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⠀⠀⠀⠀⠀⠠⠈⠘⠷⠤⠿⠋⠀⠀⢀⣀⣀⣼⣸⣯⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣻⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠉⠉⡉⠉⢹ ⠨⣿⡏⠉⠉⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⢴⣶⣖⣶⡸⢠⣴⣶⣶⣶⢶⣦⣀⣠⡶⣤⣤⣄⣀⣸⣿⣿⣿⣶⣿⣿⣭⣭⣽⣿⣿⣷⡦⣤⣿⣿⣿⣿⣼⣽⣿⣶⣾⣮⣿⣿⣿⣿⣯⣿⣾⣁⣄⣀⣄⣸⣷⣧⣭⣍ ⢶⠄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠶⠤⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠆ ⠤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⢤⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠢⠤⠀⠢⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢐⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⣠⠀⢀⡀⠰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣠⣴⣴⣶⣶⣶⠒⠒⠒⠚⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣤⣾⣿⣦⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠤⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⣿⣿⣿⣾⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡿⠿⡻⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣔⠄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣻⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢦⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⢿⣿⣿⣿⠂⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠐⣿⡿⠿⢛⡿⠠⣴⣿⣿⣿⣶⣼⣗⣾⣶⣦⣤⣤⣶⣤⣦⣴⣤⣤⣤⣤⠤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⡟⠠⣴⡄⣠ ⢈⣉⡉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠀⠈⠁⣦⠉⠀⠀⠀⢀⣀⠈⢡⣦⣼⣧⣴⣾⣿⣿⡿⠀⢒⣒⡒⠀⠀⠂⢘⣛⠉⠉⠉⠁⢙⣛⡀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣼⢧⢿⣿⣿ ⠈⣍⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⢀⡉⢁⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠠⠤⠄⠸⠥⠀⠠⢤⣥⣦⣀⣬⣭⣽⢽⡛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⠀⢸⣿⣿⣿⣿⣿ ⠀⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠛⣀⣀⣀⠀⠃⠤⠈⠛⡋⠋⠛⠻⢈⣓⢺⡟⠛⣹⠛⣛⣿⡻⣻⡟⠟⢛⣃⡁⠄⠀⠈⣿⣿⣟⣻⣿ ⠀⠶⠶⠶⠆⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢈⣰⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⠀⣀⠈⠙⠁⢀⣀⡲⠆⠴⠆⠀⣰⣞⠧⠛⣛⣿⡛⣻⣿⢿⣿⣿⣯⣿⣿⣿⣶⣾⠶⢾⣿⣿⣿⣿⣿ ⢠⣆⣦⡀⠀⠢⣠⠀⠁⠀⠀⠀⠀⠀⠀⢠⡄⢠⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣶⣷⣿⣿⣿⣿⣿⣷⣶⣶⣿⣶⣿⢶⣿⡟⢋⠉⡉⠛⠋⠘⠍⢙⣏⡉⢋⣙⡉⣉⠂⢈⠉⠉⠩⢍⡉ ⠀⠁⠈⠙⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣶⣟⣓⣒⣀⡀⢺⠶⡷⣖⠚⢿⣿⣿⣿⣶⢖⡒⣐⣲⢿⢾⢏⣉ ⠐⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣟⣙⣻⣿⡷⣿⠿⠂⠀⠨⠿⢿⣿⣿⣫ ⠀⠟⠻⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠛⠛⠭⠿⡿⠟⠿⣿⣟⣏⣿⡉⠁⠰⣿⠿⣟⠛⠋ ⠠⢤⣤⡀⠀⠀⢀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣳⠎⣉⡉⢳⡶⡤⠁⠠⠤⠘⠛⢛⣄⣒⣖⣒⢀⢀⠐⠒⠒⣓⡚⠒⠀⢀⣚⣶⣲⣂⡙ ⠀⠛⠿⠃⠀⢀⡈⠀⠀⠀⠀⠀⠀⠀⠀⢨⢠⠖⠐⠆⠆⠂⣀⡀⠀⠀⢀⣀⡸⠿⠿⠿⠟⠿⠿⠿⠿⢿⣿⢿⡿⢿⣿⣿⣿⣿⣷⢿⡷⢿⡽⣿⣺⣿⣿⡧⢰⢶⠶⠯⠟⠿⢽⠭⡯⢭⡟⣛⢛⣛⣠⣤⣭⠿⠿⠿⣿⡴ ⠀⠉⠉⠁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣄⠀⠸⢶⣶⡳⣿⣟⠼⣿⢛⣯⣾⣝⡶⣷⣖⠒⢖⣲⠒⡟⠓⣴⣿⠻⣚⢾⣾⣿⣿⣷⣿⣿⣿⣶⡿⣘⢺⣿⣿⣿⡯⣤⢤⣬⣭⠥⢾⣯⣴⣿⣿⡿⢿⣿⢷⢿⣿⣿⡤⣤⠤⢭⣤ ⠄⢥⣤⡥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠤⠤⠙⠛⠊⠉⠹⠉⠉⠊⠉⠈⠙⠋⠉⠫⣍⠉⠋⢉⡯⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣷⠀⠐⣀⣛⣓⣛⣛⣻⣉⣙⣛⣊⢛⠉⠉⠉⠹⢛⣛⣛⣛⣋ ⡈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⠀⠀⠀⠀⠀⠠⠈⠘⠷⠤⠿⠋⠀⠀⢀⣀⣀⣼⣸⣯⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣻⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠉⠉⡉⠉⢹ ⠨⣿⡏⠉⠉⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⢴⣶⣖⣶⡸⢠⣴⣶⣶⣶⢶⣦⣀⣠⡶⣤⣤⣄⣀⣸⣿⣿⣿⣶⣿⣿⣭⣭⣽⣿⣿⣷⡦⣤⣿⣿⣿⣿⣼⣽⣿⣶⣾⣮⣿⣿⣿⣿⣯⣿⣾⣁⣄⣀⣄⣸⣷⣧⣭⣍ ⢶⠄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠶⠤⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠆ ⠤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⢤⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠢⠤⠀⠢⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢐⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⣠⠀⢀⡀⠰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣠⣴⣴⣶⣶⣶⠒⠒⠒⠚⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣤⣾⣿⣦⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠤⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⣿⣿⣿⣾⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡿⠿⡻⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣔⠄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣻⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢦⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⢿⣿⣿⣿⠂⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠐⣿⡿⠿⢛⡿⠠⣴⣿⣿⣿⣶⣼⣗⣾⣶⣦⣤⣤⣶⣤⣦⣴⣤⣤⣤⣤⠤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⡟⠠⣴⡄⣠ ⢈⣉⡉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠀⠈⠁⣦⠉⠀⠀⠀⢀⣀⠈⢡⣦⣼⣧⣴⣾⣿⣿⡿⠀⢒⣒⡒⠀⠀⠂⢘⣛⠉⠉⠉⠁⢙⣛⡀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣼⢧⢿⣿⣿ ⠈⣍⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⢀⡉⢁⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠠⠤⠄⠸⠥⠀⠠⢤⣥⣦⣀⣬⣭⣽⢽⡛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⠀⢸⣿⣿⣿⣿⣿ ⠀⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠛⣀⣀⣀⠀⠃⠤⠈⠛⡋⠋⠛⠻⢈⣓⢺⡟⠛⣹⠛⣛⣿⡻⣻⡟⠟⢛⣃⡁⠄⠀⠈⣿⣿⣟⣻⣿ ⠀⠶⠶⠶⠆⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢈⣰⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⠀⣀⠈⠙⠁⢀⣀⡲⠆⠴⠆⠀⣰⣞⠧⠛⣛⣿⡛⣻⣿⢿⣿⣿⣯⣿⣿⣿⣶⣾⠶⢾⣿⣿⣿⣿⣿ ⢠⣆⣦⡀⠀⠢⣠⠀⠁⠀⠀⠀⠀⠀⠀⢠⡄⢠⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣶⣷⣿⣿⣿⣿⣿⣷⣶⣶⣿⣶⣿⢶⣿⡟⢋⠉⡉⠛⠋⠘⠍⢙⣏⡉⢋⣙⡉⣉⠂⢈⠉⠉⠩⢍⡉ ⠀⠁⠈⠙⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣶⣟⣓⣒⣀⡀⢺⠶⡷⣖⠚⢿⣿⣿⣿⣶⢖⡒⣐⣲⢿⢾⢏⣉ ⠐⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣟⣙⣻⣿⡷⣿⠿⠂⠀⠨⠿⢿⣿⣿⣫ ⠀⠟⠻⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠛⠛⠭⠿⡿⠟⠿⣿⣟⣏⣿⡉⠁⠰⣿⠿⣟⠛⠋ ⠠⢤⣤⡀⠀⠀⢀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣳⠎⣉⡉⢳⡶⡤⠁⠠⠤⠘⠛⢛⣄⣒⣖⣒⢀⢀⠐⠒⠒⣓⡚⠒⠀⢀⣚⣶⣲⣂⡙ ⠀⠛⠿⠃⠀⢀⡈⠀⠀⠀⠀⠀⠀⠀⠀⢨⢠⠖⠐⠆⠆⠂⣀⡀⠀⠀⢀⣀⡸⠿⠿⠿⠟⠿⠿⠿⠿⢿⣿⢿⡿⢿⣿⣿⣿⣿⣷⢿⡷⢿⡽⣿⣺⣿⣿⡧⢰⢶⠶⠯⠟⠿⢽⡭⡯⢭⡟⣛⢛⣛⣠⣤⣭⠿⠿⠿⣿⡴ ⠀⠉⠉⠁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣄⠀⠸⢶⣶⡳⣿⣟⠼⣿⢛⣯⣾⣝⡶⣷⣖⠒⢖⣲⠒⡟⠓⣴⣿⠻⣚⢾⣾⣿⣿⣷⣿⣿⣿⣶⡿⣘⢺⣿⣿⣿⡯⣤⢤⣬⣭⠥⢾⣯⣴⣿⣿⡿⢿⣿⢷⢿⣿⣿⡤⣤⠤⢭⣤ ⠄⢥⣤⡥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠤⠤⠙⠛⠊⠉⠹⠉⠉⠊⠉⠈⠙⠋⠉⠫⣍⠉⠋⢉⡯⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣷⠀⠐⣀⣛⣓⣛⣛⣻⣉⣙⣛⣊⢛⠉⠉⠉⠹⢛⣛⣛⣛⣋ ⡈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⠀⠀⠀⠀⠀⠠⠈⠘⠷⠤⠿⠋⠀⠀⢀⣀⣀⣼⣸⣯⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣻⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠉⠉⡉⠉⢹ ⠨⣿⡏⠉⠉⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⢴⣶⣖⣶⡸⢠⣴⣶⣶⣶⢶⣦⣀⣠⡶⣤⣤⣄⣀⣸⣿⣿⣿⣶⣿⣿⣭⣭⣽⣿⣿⣷⡦⣤⣿⣿⣿⣿⣼⣽⣿⣶⣾⣮⣿⣿⣿⣿⣯⣿⣾⣁⣄⣀⣄⣸⣷⣧⣭⣍ ⢶⠄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠶⠤⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠆ ⠤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⢤⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠢⠤⠀⠢⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢐⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⣠⠀⢀⡀⠰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣠⣴⣴⣶⣶⣶⠒⠒⠒⠚⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣤⣾⣿⣦⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠤⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⣿⣿⣿⣾⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡿⠿⡻⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣔⠄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣻⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢦⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⢿⣿⣿⣿⠂⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠐⣿⡿⠿⢛⡿⠠⣴⣿⣿⣿⣶⣼⣗⣾⣶⣦⣤⣤⣶⣤⣦⣴⣤⣤⣤⣤⠤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⡟⠠⣴⡄⣠ ⢈⣉⡉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠀⠈⠁⣦⠉⠀⠀⠀⢀⣀⠈⢡⣦⣼⣧⣴⣾⣿⣿⡿⠀⢒⣒⡒⠀⠀⠂⢘⣛⠉⠉⠉⠁⢙⣛⡀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣼⢧⢿⣿⣿ ⠈⣍⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⢀⡉⢁⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠠⠤⠄⠸⠥⠀⠠⢤⣥⣦⣀⣬⣭⣽⢽⡛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⠀⢸⣿⣿⣿⣿⣿ ⠀⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠛⣀⣀⣀⠀⠃⠤⠈⠛⡋⠋⠛⠻⢈⣓⢺⡟⠛⣹⠛⣛⣿⡻⣻⡟⠟⢛⣃⡁⠄⠀⠈⣿⣿⣟⣻⣿ ⠀⠶⠶⠶⠆⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢈⣰⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⠀⣀⠈⠙⠁⢀⣀⡲⠆⠴⠆⠀⣰⣞⠧⠛⣛⣿⡛⣻⣿⢿⣿⣿⣯⣿⣿⣿⣶⣾⠶⢾⣿⣿⣿⣿⣿ ⢠⣆⣦⡀⠀⠢⣠⠀⠁⠀⠀⠀⠀⠀⠀⢠⡄⢠⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣶⣷⣿⣿⣿⣿⣿⣷⣶⣶⣿⣶⣿⢶⣿⡟⢋⠉⡉⠛⠋⠘⠍⢙⣏⡉⢋⣙⡉⣉⠂⢈⠉⠉⠩⢍⡉ ⠀⠁⠈⠙⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣶⣟⣓⣒⣀⡀⢺⠶⡷⣖⠚⢿⣿⣿⣿⣶⢖⡒⣐⣲⢿⢾⢏⣉ ⠐⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣟⣙⣻⣿⡷⣿⠿⠂⠀⠨⠿⢿⣿⣿⣫ ⠀⠟⠻⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠛⠛⠭⠿⡿⠟⠿⣿⣟⣏⣿⡉⠁⠰⣿⠿⣟⠛⠋ ⠠⢤⣤⡀⠀⠀⢀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣳⠎⣉⡉⢳⡶⡤⠁⠠⠤⠘⠛⢛⣄⣒⣖⣒⢀⢀⠐⠒⠒⣓⡚⠒⠀⢀⣚⣶⣲⣂⡙ ⠀⠛⠿⠃⠀⢀⡈⠀⠀⠀⠀⠀⠀⠀⠀⢨⢠⠖⠐⠆⠆⠂⣀⡀⠀⠀⢀⣀⡸⠿⠿⠿⠟⠿⠿⠿⠿⢿⣿⢿⡿⢿⣿⣿⣿⣿⣷⢿⡷⢿⡽⣿⣺⣿⣿⡧⢰⢶⠶⠯⠟⠿⢽⡿⡯⢭⡟⣛⢛⣛⣠⣤⣭⠿⠿⠿⣿⡴ ⠀⠉⠉⠁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣄⠀⠸⢶⣶⡳⣿⣟⠼⣿⢛⣯⣾⣝⡶⣷⣖⠒⢖⣲⠒⡟⠓⣴⣿⠻⣚⢾⣾⣿⣿⣷⣿⣿⣿⣶⡿⣘⢺⣿⣿⣿⡯⣤⢤⣬⣭⠥⢾⣯⣴⣿⣿⡿⢿⣿⢷⢿⣿⣿⡤⣤⠤⢭⣤ ⠄⢥⣤⡥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠤⠤⠙⠛⠊⠉⠹⠉⠉⠊⠉⠈⠙⠋⠉⠫⣍⠉⠋⢉⡯⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣷⠀⠐⣀⣛⣓⣛⣛⣣⣋⣙⣛⣊⢛⠉⠉⠉⠹⢛⣛⣛⣛⣋ ⡈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⠀⠀⠀⠀⠀⠠⠈⠘⠷⠤⠿⠋⠀⠀⢀⣀⣀⣼⣸⣯⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣻⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠉⠉⡉⠉⢹ ⠨⣿⡏⠉⠉⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⢴⣶⣖⣶⡸⢠⣴⣶⣶⣶⢶⣦⣀⣠⡶⣤⣤⣄⣀⣸⣿⣿⣿⣶⣿⣿⣭⣭⣽⣿⣿⣷⡦⣤⣿⣿⣿⣿⣼⣽⣿⣶⣾⣮⣿⣿⣿⣿⣯⣿⣾⣁⣄⣀⣄⣸⣷⣧⣭⣍ ⢶⠄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠶⠤⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠆ ⠤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⢤⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠢⠤⠀⠢⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢐⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⣠⠀⢀⡀⠰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣠⣴⣴⣶⣶⣶⠒⠒⠒⠚⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣤⣾⣿⣦⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠤⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⣿⣿⣿⣾⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡿⠿⡻⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣔⠄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣻⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢦⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⢿⣿⣿⣿⠂⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠐⣿⡿⠿⢛⡿⠠⣴⣿⣿⣿⣶⣼⣗⣾⣶⣦⣤⣤⣶⣤⣦⣴⣤⣤⣤⣤⠤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⡟⠠⣴⡄⣠ ⢈⣉⡉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠀⠈⠁⣦⠉⠀⠀⠀⢀⣀⠈⢡⣦⣼⣧⣴⣾⣿⣿⡿⠀⢒⣒⡒⠀⠀⠂⢘⣛⠉⠉⠉⠁⢙⣛⡀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣼⢧⢿⣿⣿ ⠈⣍⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⢀⡉⢁⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠠⠤⠄⠸⠥⠀⠠⢤⣥⣦⣀⣬⣭⣽⢽⡛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⠀⢸⣿⣿⣿⣿⣿ ⠀⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠛⣀⣀⣀⠀⠃⠤⠈⠛⡋⠋⠛⠻⢈⣓⢺⡟⠛⣹⠛⣛⣿⡻⣻⡟⠟⢛⣃⡁⠄⠀⠈⣿⣿⣟⣻⣿ ⠀⠶⠶⠶⠆⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢈⣰⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⠀⣀⠈⠙⠁⢀⣀⡲⠆⠴⠆⠀⣰⣞⠧⠛⣛⣿⡛⣻⣿⢿⣿⣿⣯⣿⣿⣿⣶⣾⠶⢾⣿⣿⣿⣿⣿ ⢠⣆⣦⡀⠀⠢⣠⠀⠁⠀⠀⠀⠀⠀⠀⢠⡄⢠⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣶⣷⣿⣿⣿⣿⣿⣷⣶⣶⣿⣶⣿⢶⣿⡟⢋⠉⡉⠛⠋⠘⠍⢙⣏⡉⢋⣙⡉⣉⠂⢈⠉⠉⠩⢍⡉ ⠀⠁⠈⠙⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣶⣟⣓⣒⣀⡀⢺⠶⡷⣖⠚⢿⣿⣿⣿⣶⢖⡒⣐⣲⢿⢾⢏⣉ ⠐⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣟⣙⣻⣿⡷⣿⠿⠂⠀⠨⠿⢿⣿⣿⣫ ⠀⠟⠻⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠛⠛⠭⠿⡿⠟⠿⣿⣟⣏⣿⡉⠁⠰⣿⠿⣟⠛⠋ ⠠⢤⣤⡀⠀⠀⢀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣳⠎⣉⡉⢳⡶⡤⠁⠠⠤⠘⠛⢛⣄⣒⣖⣒⢀⢀⠐⠒⠒⣓⡚⠒⠀⢀⣚⣶⣲⣂⡙ ⠀⠛⠿⠃⠀⢀⡈⠀⠀⠀⠀⠀⠀⠀⠀⢨⢠⠖⠐⠆⠆⠂⣀⡀⠀⠀⢀⣀⡸⠿⠿⠿⠟⠿⠿⠿⠿⢿⣿⢿⡿⢿⣿⣿⣿⣿⣷⢿⡷⢿⡽⣿⣺⣿⣿⡧⢰⢶⠶⠯⠟⠿⢽⡿⡯⢭⡟⣛⢛⣛⣠⣤⣭⠿⠿⠿⣿⡴ ⠀⠉⠉⠁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣄⠀⠸⢶⣶⡳⣿⣟⠼⣿⢛⣯⣾⣝⡶⣷⣖⠒⢖⣲⠒⡟⠓⣴⣿⠻⣚⢾⣾⣿⣿⣷⣿⣿⣿⣶⡿⣘⢺⣿⣿⣿⡯⣤⢤⣬⣭⠥⢾⣯⣴⣿⣿⡿⢿⣿⢷⢿⣿⣿⡤⣤⠤⢭⣤ ⠄⢥⣤⡥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠤⠤⠙⠛⠊⠉⠹⠉⠉⠊⠉⠈⠙⠋⠉⠫⣍⠉⠋⢉⡯⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣷⠀⠐⣀⣛⣓⣛⣛⣣⣈⣙⣛⣊⢛⠉⠉⠉⠹⢛⣛⣛⣛⣋ ⡈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⠀⠀⠀⠀⠀⠠⠈⠘⠷⠤⠿⠋⠀⠀⢀⣀⣀⣼⣸⣯⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣻⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠉⠉⡉⠉⢹ ⠨⣿⡏⠉⠉⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⢴⣶⣖⣶⡸⢠⣴⣶⣶⣶⢶⣦⣀⣠⡶⣤⣤⣄⣀⣸⣿⣿⣿⣶⣿⣿⣭⣭⣽⣿⣿⣷⡦⣤⣿⣿⣿⣿⣼⣽⣿⣶⣾⣮⣿⣿⣿⣿⣯⣿⣾⣁⣄⣀⣄⣸⣷⣧⣭⣍ ⢶⠄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠶⠤⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠆ ⠤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⢤⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠢⠤⠀⠢⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢐⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⣠⠀⢀⡀⠰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣠⣴⣴⣶⣶⣶⠒⠒⠒⠚⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣤⣾⣿⣦⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠤⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⣿⣿⣿⣾⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡿⠿⡻⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣔⠄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣻⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢦⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⢿⣿⣿⣿⠂⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠐⣿⡿⠿⢛⡿⠠⣴⣿⣿⣿⣶⣼⣗⣾⣶⣦⣤⣤⣶⣤⣦⣴⣤⣤⣤⣤⠤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⡟⠠⣴⡄⣠ ⢈⣉⡉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠀⠈⠁⣦⠉⠀⠀⠀⢀⣀⠈⢡⣦⣼⣧⣴⣾⣿⣿⡿⠀⢒⣒⡒⠀⠀⠂⢘⣛⠉⠉⠉⠁⢙⣛⡀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣼⢧⢿⣿⣿ ⠈⣍⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⢀⡉⢁⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠠⠤⠄⠸⠥⠀⠠⢤⣥⣦⣀⣬⣭⣽⢽⡛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⠀⢸⣿⣿⣿⣿⣿ ⠀⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠛⣀⣀⣀⠀⠃⠤⠈⠛⡋⠋⠛⠻⢈⣓⢺⡟⠛⣹⠛⣛⣿⡻⣻⡟⠟⢛⣃⡁⠄⠀⠈⣿⣿⣟⣻⣿ ⠀⠶⠶⠶⠆⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢈⣰⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⠀⣀⠈⠙⠁⢀⣀⡲⠆⠴⠆⠀⣰⣞⠧⠛⣛⣿⡛⣻⣿⢿⣿⣿⣯⣿⣿⣿⣶⣾⠶⢾⣿⣿⣿⣿⣿ ⢠⣆⣦⡀⠀⠢⣠⠀⠁⠀⠀⠀⠀⠀⠀⢠⡄⢠⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣶⣷⣿⣿⣿⣿⣿⣷⣶⣶⣿⣶⣿⢶⣿⡟⢋⠉⡉⠛⠋⠘⠍⢙⣏⡉⢋⣙⡉⣉⠂⢈⠉⠉⠩⢍⡉ ⠀⠁⠈⠙⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣶⣟⣓⣒⣀⡀⢺⠶⡷⣖⠚⢿⣿⣿⣿⣶⢖⡒⣐⣲⢿⢾⢏⣉ ⠐⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣟⣙⣻⣿⡷⣿⠿⠂⠀⠨⠿⢿⣿⣿⣫ ⠀⠟⠻⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠛⠛⠭⠿⡿⠟⠿⣿⣟⣏⣿⡉⠁⠰⣿⠿⣟⠛⠋ ⠠⢤⣤⡀⠀⠀⢀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣳⠎⣉⡉⢳⡶⡤⠁⠠⠤⠘⠛⢛⣄⣒⣖⣒⢀⢀⠐⠒⠒⣓⡚⠒⠀⢀⣚⣶⣲⣂⡙ ⠀⠛⠿⠃⠀⢀⡈⠀⠀⠀⠀⠀⠀⠀⠀⢨⢠⠖⠐⠆⠆⠂⣀⡀⠀⠀⢀⣀⡸⠿⠿⠿⠟⠿⠿⠿⠿⢿⣿⢿⡿⢿⣿⣿⣿⣿⣷⢿⡷⢿⡽⣿⣺⣿⣿⡧⢰⢶⠶⠯⠟⠿⢽⡿⡯⢭⡟⣛⢛⣛⣠⣤⣭⠿⠿⠿⣿⡴ ⠀⠉⠉⠁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣄⠀⠸⢶⣶⡳⣿⣟⠼⣿⢛⣯⣾⣝⡶⣷⣖⠒⢖⣲⠒⡟⠓⣴⣿⠻⣚⢾⣾⣿⣿⣷⣿⣿⣿⣶⡿⣘⢺⣿⣿⣿⡯⣤⢤⣬⣭⠥⢾⣯⣴⣿⣿⡿⢿⣿⢷⢿⣿⣿⡤⣤⠤⢭⣤ ⠄⢥⣤⡥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠤⠤⠙⠛⠊⠉⠹⠉⠉⠊⠉⠈⠙⠋⠉⠫⣍⠉⠋⢉⡯⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣷⠀⠐⣀⣛⣓⣛⣛⣣⣈⣙⣛⣊⢛⠉⠉⠉⠹⢛⣛⣛⣛⣋ ⡈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⠀⠀⠀⠀⠀⠠⠈⠘⠷⠤⠿⠋⠀⠀⢀⣀⣀⣼⣸⣯⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣻⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠉⠉⡉⠉⢹ ⠨⣿⡏⠉⠉⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⢴⣶⣖⣶⡸⢠⣴⣶⣶⣶⢶⣦⣀⣠⡶⣤⣤⣄⣀⣸⣿⣿⣿⣶⣿⣿⣭⣭⣽⣿⣿⣷⡦⣤⣿⣿⣿⣿⣼⣽⣿⣶⣾⣮⣿⣿⣿⣿⣯⣿⣾⣁⣄⣀⣄⣸⣷⣧⣭⣍ ⢶⠄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠶⠤⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠆ ⠤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⢤⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠢⠤⠀⠢⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢐⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⣠⠀⢀⡀⠰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣠⣴⣴⣶⣶⣶⠒⠒⠒⠚⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣤⣾⣿⣦⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠤⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⣿⣿⣿⣾⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡿⠿⡻⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣔⠄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣻⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢦⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⢿⣿⣿⣿⠂⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠐⣿⡿⠿⢛⡿⠠⣴⣿⣿⣿⣶⣼⣗⣾⣶⣦⣤⣤⣶⣤⣦⣴⣤⣤⣤⣤⠤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⡟⠠⣴⡄⣠ ⢈⣉⡉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠀⠈⠁⣦⠉⠀⠀⠀⢀⣀⠈⢡⣦⣼⣧⣴⣾⣿⣿⡿⠀⢒⣒⡒⠀⠀⠂⢘⣛⠉⠉⠉⠁⢙⣛⡀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣼⢧⢿⣿⣿ ⠈⣍⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⢀⡉⢁⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠠⠤⠄⠸⠥⠀⠠⢤⣥⣦⣀⣬⣭⣽⢽⡛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⠀⢸⣿⣿⣿⣿⣿ ⠀⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠛⣀⣀⣀⠀⠃⠤⠈⠛⡋⠋⠛⠻⢈⣓⢺⡟⠛⣹⠛⣛⣿⡻⣻⡟⠟⢛⣃⡁⠄⠀⠈⣿⣿⣟⣻⣿ ⠀⠶⠶⠶⠆⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢈⣰⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⠀⣀⠈⠙⠁⢀⣀⡲⠆⠴⠆⠀⣰⣞⠧⠛⣛⣿⡛⣻⣿⢿⣿⣿⣯⣿⣿⣿⣶⣾⠶⢾⣿⣿⣿⣿⣿ ⢠⣆⣦⡀⠀⠢⣠⠀⠁⠀⠀⠀⠀⠀⠀⢠⡄⢠⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣶⣷⣿⣿⣿⣿⣿⣷⣶⣶⣿⣶⣿⢶⣿⡟⢋⠉⡉⠛⠋⠘⠍⢙⣏⡉⢋⣙⡉⣉⠂⢈⠉⠉⠩⢍⡉ ⠀⠁⠈⠙⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣶⣟⣓⣒⣀⡀⢺⠶⡷⣖⠚⢿⣿⣿⣿⣶⢖⡒⣐⣲⢿⢾⢏⣉ ⠐⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣟⣙⣻⣿⡷⣿⠿⠂⠀⠨⠿⢿⣿⣿⣫ ⠀⠟⠻⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠛⠛⠭⠿⡿⠟⠿⣿⣟⣏⣿⡉⠁⠰⣿⠿⣟⠛⠋ ⠠⢤⣤⡀⠀⠀⢀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣳⠎⣉⡉⢳⡶⡤⠁⠠⠤⠘⠛⢛⣄⣒⣖⣒⢀⢀⠐⠒⠒⣓⡚⠒⠀⢀⣚⣶⣲⣂⡙ ⠀⠛⠿⠃⠀⢀⡈⠀⠀⠀⠀⠀⠀⠀⠀⢨⢠⠖⠐⠆⠆⠂⣀⡀⠀⠀⢀⣀⡸⠿⠿⠿⠟⠿⠿⠿⠿⢿⣿⢿⡿⢿⣿⣿⣿⣿⣷⢿⡷⢿⡽⣿⣺⣿⣿⡧⢰⢶⠶⠯⠟⠿⢽⡿⡯⢭⡟⣛⢛⣛⣠⣤⣭⠿⠿⠿⣿⡴ ⠀⠉⠉⠁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣄⠀⠸⢶⣶⡳⣿⣟⠼⣿⢛⣯⣾⣝⡶⣷⣖⠒⢖⣲⠒⡟⠓⣴⣿⠻⣚⢾⣾⣿⣿⣷⣿⣿⣿⣶⡿⣘⢺⣿⣿⣿⡯⣤⢤⣬⣭⠥⢾⣯⣴⣿⣿⡿⢿⣿⢷⢿⣿⣿⡤⣤⠤⢭⣤ ⠄⢥⣤⡥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠤⠤⠙⠛⠊⠉⠹⠉⠉⠊⠉⠈⠙⠋⠉⠫⣍⠉⠋⢉⡯⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣷⠀⠐⣀⣛⣓⣛⣛⣣⣈⣙⣛⣊⢛⠉⠉⠉⠹⢛⣛⣛⣛⣋ ⡈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⠀⠀⠀⠀⠀⠠⠈⠘⠷⠤⠿⠋⠀⠀⢀⣀⣀⣼⣸⣯⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣻⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠉⠉⡉⠉⢹ ⠨⣿⡏⠉⠉⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⢴⣶⣖⣶⡸⢠⣴⣶⣶⣶⢶⣦⣀⣠⡶⣤⣤⣄⣀⣸⣿⣿⣿⣶⣿⣿⣭⣭⣽⣿⣿⣷⡦⣤⣿⣿⣿⣿⣼⣽⣿⣶⣾⣮⣿⣿⣿⣿⣯⣿⣾⣁⣄⣀⣄⣸⣷⣧⣭⣍ ⢶⠄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠶⠤⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠆ ⠤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⢤⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠢⠤⠀⠢⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢐⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⣠⠀⢀⡀⠰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣠⣴⣴⣶⣶⣶⠒⠒⠒⠚⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣤⣾⣿⣦⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠤⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⣿⣿⣿⣾⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡿⠿⡻⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣔⠄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣻⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢦⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⢿⣿⣿⣿⠂⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠐⣿⡿⠿⢛⡿⠠⣴⣿⣿⣿⣶⣼⣗⣾⣶⣦⣤⣤⣶⣤⣦⣴⣤⣤⣤⣤⠤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⡟⠠⣴⡄⣠ ⢈⣉⡉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠀⠈⠁⣦⠉⠀⠀⠀⢀⣀⠈⢡⣦⣼⣧⣴⣾⣿⣿⡿⠀⢒⣒⡒⠀⠀⠂⢘⣛⠉⠉⠉⠁⢙⣛⡀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣼⢧⢿⣿⣿ ⠈⣍⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⢀⡉⢁⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠠⠤⠄⠸⠥⠀⠠⢤⣥⣦⣀⣬⣭⣽⢽⡛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⠀⢸⣿⣿⣿⣿⣿ ⠀⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠛⣀⣀⣀⠀⠃⠤⠈⠛⡋⠋⠛⠻⢈⣓⢺⡟⠛⣹⠛⣛⣿⡻⣻⡟⠟⢛⣃⡁⠄⠀⠈⣿⣿⣟⣻⣿ ⠀⠶⠶⠶⠆⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢈⣰⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⠀⣀⠈⠙⠁⢀⣀⡲⠆⠴⠆⠀⣰⣞⠧⠛⣛⣿⡛⣻⣿⢿⣿⣿⣯⣿⣿⣿⣶⣾⠶⢾⣿⣿⣿⣿⣿ ⢠⣆⣦⡀⠀⠢⣠⠀⠁⠀⠀⠀⠀⠀⠀⢠⡄⢠⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣶⣷⣿⣿⣿⣿⣿⣷⣶⣶⣿⣶⣿⢶⣿⡟⢋⠉⡉⠛⠋⠘⠍⢙⣏⡉⢋⣙⡉⣉⠂⢈⠉⠉⠩⢍⡉ ⠀⠁⠈⠙⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣶⣟⣓⣒⣀⡀⢺⠶⡷⣖⠚⢿⣿⣿⣿⣶⢖⡒⣐⣲⢿⢾⢏⣉ ⠐⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣟⣙⣻⣿⡷⣿⠿⠂⠀⠨⠿⢿⣿⣿⣫ ⠀⠟⠻⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠛⠛⠭⠿⡿⠟⠿⣿⣟⣏⣿⡉⠁⠰⣿⠿⣟⠛⠋ ⠠⢤⣤⡀⠀⠀⢀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣳⠎⣉⡉⢳⡶⡤⠁⠠⠤⠘⠛⢛⣄⣒⣖⣒⢀⢀⠐⠒⠒⣓⡚⠒⠀⢀⣚⣶⣲⣂⡙ ⠀⠛⠿⠃⠀⢀⡈⠀⠀⠀⠀⠀⠀⠀⠀⢨⢠⠖⠐⠆⠆⠂⣀⡀⠀⠀⢀⣀⡸⠿⠿⠿⠟⠿⠿⠿⠿⢿⣿⢿⡿⢿⣿⣿⣿⣿⣷⢿⡷⢿⡽⣿⣺⣿⣿⡧⢰⢶⠶⠯⠟⠿⢽⡿⡯⢭⡟⣛⢛⣛⣠⣤⣭⠿⠿⠿⣿⡴ ⠀⠉⠉⠁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣄⠀⠸⢶⣶⡳⣿⣟⠼⣿⢛⣯⣾⣝⡶⣷⣖⠒⢖⣲⠒⡟⠓⣴⣿⠻⣚⢾⣾⣿⣿⣷⣿⣿⣿⣶⡿⣘⢺⣿⣿⣿⡯⣤⢤⣬⣭⠥⢾⣯⣴⣿⣿⡿⢿⣿⢷⢿⣿⣿⡤⣤⠤⢭⣤ ⠄⢥⣤⡥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠤⠤⠙⠛⠊⠉⠹⠉⠉⠊⠉⠈⠙⠋⠉⠫⣍⠉⠋⢉⡯⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣷⠀⠐⣀⣛⣓⣛⣛⣣⣈⣙⣛⣊⢛⠉⠉⠉⠹⢛⣛⣛⣛⣋ ⡈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⠀⠀⠀⠀⠀⠠⠈⠘⠷⠤⠿⠋⠀⠀⢀⣀⣀⣼⣸⣯⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣻⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠉⠉⡉⠉⢹ ⠨⣿⡏⠉⠉⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⢴⣶⣖⣶⡸⢠⣴⣶⣶⣶⢶⣦⣀⣠⡶⣤⣤⣄⣀⣸⣿⣿⣿⣶⣿⣿⣭⣭⣽⣿⣿⣷⡦⣤⣿⣿⣿⣿⣼⣽⣿⣶⣾⣮⣿⣿⣿⣿⣯⣿⣾⣁⣄⣀⣄⣸⣷⣧⣭⣍ ⢶⠄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠶⠤⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠆ ⠤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⢤⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠢⠤⠀⠢⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢐⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⣠⠀⢀⡀⠰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣠⣴⣴⣶⣶⣶⠒⠒⠒⠚⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣤⣾⣿⣦⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠤⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⣿⣿⣿⣾⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡿⠿⡻⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣔⠄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣻⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢦⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⢿⣿⣿⣿⠂⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠐⣿⡿⠿⢛⡿⠠⣴⣿⣿⣿⣶⣼⣗⣾⣶⣦⣤⣤⣶⣤⣦⣴⣤⣤⣤⣤⠤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⡟⠠⣴⡄⣠ ⢈⣉⡉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠀⠈⠁⣦⠉⠀⠀⠀⢀⣀⠈⢡⣦⣼⣧⣴⣾⣿⣿⡿⠀⢒⣒⡒⠀⠀⠂⢘⣛⠉⠉⠉⠁⢙⣛⡀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣼⢧⢿⣿⣿ ⠈⣍⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⢀⡉⢁⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠠⠤⠄⠸⠥⠀⠠⢤⣥⣦⣀⣬⣭⣽⢽⡛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⠀⢸⣿⣿⣿⣿⣿ ⠀⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠛⣀⣀⣀⠀⠃⠤⠈⠛⡋⠋⠛⠻⢈⣓⢺⡟⠛⣹⠛⣛⣿⡻⣻⡟⠟⢛⣃⡁⠄⠀⠈⣿⣿⣟⣻⣿ ⠀⠶⠶⠶⠆⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢈⣰⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⠀⣀⠈⠙⠁⢀⣀⡲⠆⠴⠆⠀⣰⣞⠧⠛⣛⣿⡛⣻⣿⢿⣿⣿⣯⣿⣿⣿⣶⣾⠶⢾⣿⣿⣿⣿⣿ ⢠⣆⣦⡀⠀⠢⣠⠀⠁⠀⠀⠀⠀⠀⠀⢠⡄⢠⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣶⣷⣿⣿⣿⣿⣿⣷⣶⣶⣿⣶⣿⢶⣿⡟⢋⠉⡉⠛⠋⠘⠍⢙⣏⡉⢋⣙⡉⣉⠂⢈⠉⠉⠩⢍⡉ ⠀⠁⠈⠙⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣶⣟⣓⣒⣀⡀⢺⠶⡷⣖⠚⢿⣿⣿⣿⣶⢖⡒⣐⣲⢿⢾⢏⣉ ⠐⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣟⣙⣻⣿⡷⣿⠿⠂⠀⠨⠿⢿⣿⣿⣫ ⠀⠟⠻⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠛⠛⠭⠿⡿⠟⠿⣿⣟⣏⣿⡉⠁⠰⣿⠿⣟⠛⠋ ⠠⢤⣤⡀⠀⠀⢀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣳⠎⣉⡉⢳⡶⡤⠁⠠⠤⠘⠛⢛⣄⣒⣖⣒⢀⢀⠐⠒⠒⣓⡚⠒⠀⢀⣚⣶⣲⣂⡙ ⠀⠛⠿⠃⠀⢀⡈⠀⠀⠀⠀⠀⠀⠀⠀⢨⢠⠖⠐⠆⠆⠂⣀⡀⠀⠀⢀⣀⡸⠿⠿⠿⠟⠿⠿⠿⠿⢿⣿⢿⡿⢿⣿⣿⣿⣿⣷⢿⡷⢿⡽⣿⣺⣿⣿⡧⢰⢶⠶⠯⠟⠿⢽⡿⡯⢭⡟⣛⢛⣛⣠⣤⣭⠿⠿⠿⣿⡴ ⠀⠉⠉⠁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣄⠀⠸⢶⣶⡳⣿⣟⠼⣿⢛⣯⣾⣝⡶⣷⣖⠒⢖⣲⠒⡟⠓⣴⣿⠻⣚⢾⣾⣿⣿⣷⣿⣿⣿⣶⡿⣘⢺⣿⣿⣿⡯⣤⢤⣬⣭⠥⢾⣯⣴⣿⣿⡿⢿⣿⢷⢿⣿⣿⡤⣤⠤⢭⣤ ⠄⢥⣤⡥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠤⠤⠙⠛⠊⠉⠹⠉⠉⠊⠉⠈⠙⠋⠉⠫⣍⠉⠋⢉⡯⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣷⠀⠐⣀⣛⣓⣛⣛⣣⣈⣙⣛⣊⢛⠉⠉⠉⠹⢛⣛⣛⣛⣋ ⡈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⠀⠀⠀⠀⠀⠠⠈⠘⠷⠤⠿⠋⠀⠀⢀⣀⣀⣼⣸⣯⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣻⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠉⠉⡉⠉⢹ ⠨⣿⡏⠉⠉⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⢴⣶⣖⣶⡸⢠⣴⣶⣶⣶⢶⣦⣀⣠⡶⣤⣤⣄⣀⣸⣿⣿⣿⣶⣿⣿⣭⣭⣽⣿⣿⣷⡦⣤⣿⣿⣿⣿⣼⣽⣿⣶⣾⣮⣿⣿⣿⣿⣯⣿⣾⣁⣄⣀⣄⣸⣷⣧⣭⣍ ⢶⠄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠶⠤⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠆ ⠤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⢤⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠢⠤⠀⠢⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢐⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⣠⠀⢀⡀⠰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣠⣴⣴⣶⣶⣶⠒⠒⠒⠚⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣤⣾⣿⣦⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠤⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⣿⣿⣿⣾⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡿⠿⡻⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣔⠄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣻⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢦⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⢿⣿⣿⣿⠂⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠐⣿⡿⠿⢛⡿⠠⣴⣿⣿⣿⣶⣼⣗⣾⣶⣦⣤⣤⣶⣤⣦⣴⣤⣤⣤⣤⠤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⡟⠠⣴⡄⣠ ⢈⣉⡉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠀⠈⠁⣦⠉⠀⠀⠀⢀⣀⠈⢡⣦⣼⣧⣴⣾⣿⣿⡿⠀⢒⣒⡒⠀⠀⠂⢘⣛⠉⠉⠉⠁⢙⣛⡀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣼⢧⢿⣿⣿ ⠈⣍⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⢀⡉⢁⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠠⠤⠄⠸⠥⠀⠠⢤⣥⣦⣀⣬⣭⣽⢽⡛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⠀⢸⣿⣿⣿⣿⣿ ⠀⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠛⣀⣀⣀⠀⠃⠤⠈⠛⡋⠋⠛⠻⢈⣓⢺⡟⠛⣹⠛⣛⣿⡻⣻⡟⠟⢛⣃⡁⠄⠀⠈⣿⣿⣟⣻⣿ ⠀⠶⠶⠶⠆⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢈⣰⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⠀⣀⠈⠙⠁⢀⣀⡲⠆⠴⠆⠀⣰⣞⠧⠛⣛⣿⡛⣻⣿⢿⣿⣿⣯⣿⣿⣿⣶⣾⠶⢾⣿⣿⣿⣿⣿ ⢠⣆⣦⡀⠀⠢⣠⠀⠁⠀⠀⠀⠀⠀⠀⢠⡄⢠⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣶⣷⣿⣿⣿⣿⣿⣷⣶⣶⣿⣶⣿⢶⣿⡟⢋⠉⡉⠛⠋⠘⠍⢙⣏⡉⢋⣙⡉⣉⠂⢈⠉⠉⠩⢍⡉ ⠀⠁⠈⠙⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣶⣟⣓⣒⣀⡀⢺⠶⡷⣖⠚⢿⣿⣿⣿⣶⢖⡒⣐⣲⢿⢾⢏⣉ ⠐⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣟⣙⣻⣿⡷⣿⠿⠂⠀⠨⠿⢿⣿⣿⣫ ⠀⠟⠻⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠛⠛⠭⠿⡿⠟⠿⣿⣟⣏⣿⡉⠁⠰⣿⠿⣟⠛⠋ ⠠⢤⣤⡀⠀⠀⢀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣳⠎⣉⡉⢳⡶⡤⠁⠠⠤⠘⠛⢛⣄⣒⣖⣒⢀⢀⠐⠒⠒⣓⡚⠒⠀⢀⣚⣶⣲⣂⡙ ⠀⠛⠿⠃⠀⢀⡈⠀⠀⠀⠀⠀⠀⠀⠀⢨⢠⠖⠐⠆⠆⠂⣀⡀⠀⠀⢀⣀⡸⠿⠿⠿⠟⠿⠿⠿⠿⢿⣿⢿⡿⢿⣿⣿⣿⣿⣷⢿⡷⢿⡽⣿⣺⣿⣿⡧⢰⢶⠶⠯⠟⠿⢽⡿⡯⢭⡟⣛⢛⣛⣠⣤⣭⠿⠿⠿⣿⡴ ⠀⠉⠉⠁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣄⠀⠸⢶⣶⡳⣿⣟⠼⣿⢛⣯⣾⣝⡶⣷⣖⠒⢖⣲⠒⡟⠓⣴⣿⠻⣚⢾⣾⣿⣿⣷⣿⣿⣿⣶⡿⣘⢺⣿⣿⣿⡯⣤⢤⣬⣭⠥⢾⣯⣴⣿⣿⡿⢿⣿⢷⢿⣿⣿⡤⣤⠤⢭⣤ ⠄⢥⣤⡥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠤⠤⠙⠛⠊⠉⠹⠉⠉⠊⠉⠈⠙⠋⠉⠫⣍⠉⠋⢉⡯⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣷⠀⠐⣀⣛⣓⣛⣛⣣⣈⣙⣛⣊⢛⠉⠉⠉⠹⢛⣛⣛⣛⣋ ⡈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⠀⠀⠀⠀⠀⠠⠈⠘⠷⠤⠿⠋⠀⠀⢀⣀⣀⣼⣸⣯⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣻⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠉⠉⡉⠉⢹ ⠨⣿⡏⠉⠉⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⢴⣶⣖⣶⡸⢠⣴⣶⣶⣶⢶⣦⣀⣠⡶⣤⣤⣄⣀⣸⣿⣿⣿⣶⣿⣿⣭⣭⣽⣿⣿⣷⡦⣤⣿⣿⣿⣿⣼⣽⣿⣶⣾⣮⣿⣿⣿⣿⣯⣿⣾⣁⣄⣀⣄⣸⣷⣧⣭⣍ ⢶⠄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠶⠤⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠆ ⠤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⢤⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠢⠤⠀⠢⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢐⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⣠⠀⢀⡀⠰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣠⣴⣴⣶⣶⣶⠒⠒⠒⠚⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣤⣾⣿⣦⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠤⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⣿⣿⣿⣾⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡿⠿⡻⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣔⠄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣻⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢦⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⢿⣿⣿⣿⠂⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠐⣿⡿⠿⢛⡿⠠⣴⣿⣿⣿⣶⣼⣗⣾⣶⣦⣤⣤⣶⣤⣦⣴⣤⣤⣤⣤⠤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⡟⠠⣴⡄⣠ ⢈⣉⡉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠀⠈⠁⣦⠉⠀⠀⠀⢀⣀⠈⢡⣦⣼⣧⣴⣾⣿⣿⡿⠀⢒⣒⡒⠀⠀⠂⢘⣛⠉⠉⠉⠁⢙⣛⡀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣼⢧⢿⣿⣿ ⠈⣍⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⢀⡉⢁⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠠⠤⠄⠸⠥⠀⠠⢤⣥⣦⣀⣬⣭⣽⢽⡛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⠀⢸⣿⣿⣿⣿⣿ ⠀⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠛⣀⣀⣀⠀⠃⠤⠈⠛⡋⠋⠛⠻⢈⣓⢺⡟⠛⣹⠛⣛⣿⡻⣻⡟⠟⢛⣃⡁⠄⠀⠈⣿⣿⣟⣻⣿ ⠀⠶⠶⠶⠆⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢈⣰⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⠀⣀⠈⠙⠁⢀⣀⡲⠆⠴⠆⠀⣰⣞⠧⠛⣛⣿⡛⣻⣿⢿⣿⣿⣯⣿⣿⣿⣶⣾⠶⢾⣿⣿⣿⣿⣿ ⢠⣆⣦⡀⠀⠢⣠⠀⠁⠀⠀⠀⠀⠀⠀⢠⡄⢠⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣶⣷⣿⣿⣿⣿⣿⣷⣶⣶⣿⣶⣿⢶⣿⡟⢋⠉⡉⠛⠋⠘⠍⢙⣏⡉⢋⣙⡉⣉⠂⢈⠉⠉⠩⢍⡉ ⠀⠁⠈⠙⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣶⣟⣓⣒⣀⡀⢺⠶⡷⣖⠚⢿⣿⣿⣿⣶⢖⡒⣐⣲⢿⢾⢏⣉ ⠐⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣟⣙⣻⣿⡷⣿⠿⠂⠀⠨⠿⢿⣿⣿⣫ ⠀⠟⠻⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠛⠛⠭⠿⡿⠟⠿⣿⣟⣏⣿⡉⠁⠰⣿⠿⣟⠛⠋ ⠠⢤⣤⡀⠀⠀⢀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣳⠎⣉⡉⢳⡶⡤⠁⠠⠤⠘⠛⢛⣄⣒⣖⣒⢀⢀⠐⠒⠒⣓⡚⠒⠀⢀⣚⣶⣲⣂⡙ ⠀⠛⠿⠃⠀⢀⡈⠀⠀⠀⠀⠀⠀⠀⠀⢨⢠⠖⠐⠆⠆⠂⣀⡀⠀⠀⢀⣀⡸⠿⠿⠿⠟⠿⠿⠿⠿⢿⣿⢿⡿⢿⣿⣿⣿⣿⣷⢿⡷⢿⡽⣿⣺⣿⣿⡧⢰⢶⠶⠯⠟⠿⢽⡿⡯⢭⡟⣛⢛⣛⣠⣤⣭⠿⠿⠿⣿⡴ ⠀⠉⠉⠁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣄⠀⠸⢶⣶⡳⣿⣟⠼⣸⢛⣯⣾⣝⡶⣷⣖⠒⢖⣲⠒⡟⠓⣴⣿⠻⣚⢾⣾⣿⣿⣷⣿⣿⣿⣶⡿⣘⢺⣿⣿⣿⡯⣤⢤⣬⣭⠥⢾⣯⣴⣿⣿⡿⢿⣿⢷⢿⣿⣿⡤⣤⠤⢭⣤ ⠄⢥⣤⡥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠤⠤⠙⠛⠊⠉⠹⠉⠈⠊⠉⠈⠙⠋⠉⠫⣍⠉⠋⢉⡯⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣷⠀⠐⣀⣛⣓⣛⣛⣣⣈⣙⣛⣊⢛⠉⠉⠉⠹⢛⣛⣛⣛⣋ ⡈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⠀⠀⠀⠀⠀⠠⠈⠘⠷⠤⠿⠋⠀⠀⢀⣀⣀⣼⣸⣯⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣻⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠉⠉⡉⠉⢹ ⠨⣿⡏⠉⠉⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⢴⣶⣖⣶⡸⢠⣴⣶⣶⣶⢶⣦⣀⣠⡶⣤⣤⣄⣀⣸⣿⣿⣿⣶⣿⣿⣭⣭⣽⣿⣿⣷⡦⣤⣿⣿⣿⣿⣼⣽⣿⣶⣾⣮⣿⣿⣿⣿⣯⣿⣾⣁⣄⣀⣄⣸⣷⣧⣭⣍ ⢶⠄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠶⠤⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠆ ⠤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⢤⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠢⠤⠀⠢⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢐⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⣠⠀⢀⡀⠰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣠⣴⣴⣶⣶⣶⠒⠒⠒⠚⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣤⣾⣿⣦⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠤⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⣿⣿⣿⣾⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡿⠿⡻⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣔⠄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣻⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢦⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⢿⣿⣿⣿⠂⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠐⣿⡿⠿⢛⡿⠠⣴⣿⣿⣿⣶⣼⣗⣾⣶⣦⣤⣤⣶⣤⣦⣴⣤⣤⣤⣤⠤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⡟⠠⣴⡄⣠ ⢈⣉⡉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠀⠈⠁⣦⠉⠀⠀⠀⢀⣀⠈⢡⣦⣼⣧⣴⣾⣿⣿⡿⠀⢒⣒⡒⠀⠀⠂⢘⣛⠉⠉⠉⠁⢙⣛⡀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣼⢧⢿⣿⣿ ⠈⣍⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⢀⡉⢁⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠠⠤⠄⠸⠥⠀⠠⢤⣥⣦⣀⣬⣭⣽⢽⡛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⠀⢸⣿⣿⣿⣿⣿ ⠀⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠛⣀⣀⣀⠀⠃⠤⠈⠛⡋⠋⠛⠻⢈⣓⢺⡟⠛⣹⠛⣛⣿⡻⣻⡟⠟⢛⣃⡁⠄⠀⠈⣿⣿⣟⣻⣿ ⠀⠶⠶⠶⠆⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢈⣰⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⠀⣀⠈⠙⠁⢀⣀⡲⠆⠴⠆⠀⣰⣞⠧⠛⣛⣿⡛⣻⣿⢿⣿⣿⣯⣿⣿⣿⣶⣾⠶⢾⣿⣿⣿⣿⣿ ⢠⣆⣦⡀⠀⠢⣠⠀⠁⠀⠀⠀⠀⠀⠀⢠⡄⢠⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣶⣷⣿⣿⣿⣿⣿⣷⣶⣶⣿⣶⣿⢶⣿⡟⢋⠉⡉⠛⠋⠘⠍⢙⣏⡉⢋⣙⡉⣉⠂⢈⠉⠉⠩⢍⡉ ⠀⠁⠈⠙⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣶⣟⣓⣒⣀⡀⢺⠶⡷⣖⠚⢿⣿⣿⣿⣶⢖⡒⣐⣲⢿⢾⢏⣉ ⠐⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣟⣙⣻⣿⡷⣿⠿⠂⠀⠨⠿⢿⣿⣿⣫ ⠀⠟⠻⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠛⠛⠭⠿⡿⠟⠿⣿⣟⣏⣿⡉⠁⠰⣿⠿⣟⠛⠋ ⠠⢤⣤⡀⠀⠀⢀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣳⠎⣉⡉⢳⡶⡤⠁⠠⠤⠘⠛⢛⣄⣒⣖⣒⢀⢀⠐⠒⠒⣓⡚⠒⠀⢀⣚⣶⣲⣂⡙ ⠀⠛⠿⠃⠀⢀⡈⠀⠀⠀⠀⠀⠀⠀⠀⢨⢠⠖⠐⠆⠆⠂⣀⡀⠀⠀⢀⣀⡸⠿⠿⠿⠟⠿⠿⠿⠿⢿⣿⢿⡿⢿⣿⣿⣿⣿⣷⢿⡷⢿⡽⣿⣺⣿⣿⡧⢰⢶⠶⠯⠟⠿⢽⡿⠫⢭⡟⣛⢛⣛⣠⣤⣭⠿⠿⠿⣿⡴ ⠀⠉⠉⠁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣄⠀⠸⢶⣶⡳⣿⣟⠼⣸⢛⣯⣾⣝⡶⣷⣖⠒⢖⣲⠒⡟⠓⣴⣿⠻⣚⢾⣾⣿⣿⣷⣿⣿⣿⣶⡿⣘⢺⣿⣿⣿⡯⣤⢤⣬⣭⠥⢾⣯⣴⣿⣿⡿⢿⣿⢷⢿⣿⣿⡤⣤⠤⢭⣤ ⠄⢥⣤⡥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠤⠤⠙⠛⠊⠉⠹⠁⡎⠊⠉⠈⠙⠋⠉⠫⣍⠉⠋⢉⡯⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣷⠀⠐⣀⣛⣓⣛⣛⣣⣈⣙⣛⣊⢛⠉⠉⠉⠹⢛⣛⣛⣛⣋ ⡈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢃⠀⠀⠀⠀⠀⠠⠈⠘⠷⠤⠿⠋⠀⠀⢀⣀⣀⣼⣸⣯⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣻⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠉⠉⡉⠉⢹ ⠨⣿⡏⠉⠉⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⢴⣶⣖⣶⡸⢠⣴⣶⣶⣶⢶⣦⣀⣠⡶⣤⣤⣄⣀⣸⣿⣿⣿⣶⣿⣿⣭⣭⣽⣿⣿⣷⡦⣤⣿⣿⣿⣿⣼⣽⣿⣶⣾⣮⣿⣿⣿⣿⣯⣿⣾⣁⣄⣀⣄⣸⣷⣧⣭⣍ ⢶⠄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠶⠤⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠆ ⠤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⢤⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠢⠤⠀⠢⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢐⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⣠⠀⢀⡀⠰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣠⣴⣴⣶⣶⣶⠒⠒⠒⠚⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣤⣾⣿⣦⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠤⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⣿⣿⣿⣾⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡿⠿⡻⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣔⠄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣻⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢦⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⢿⣿⣿⣿⠂⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠐⣿⡿⠿⢛⡿⠠⣴⣿⣿⣿⣶⣼⣗⣾⣶⣦⣤⣤⣶⣤⣦⣴⣤⣤⣤⣤⠤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⡟⠠⣴⡄⣠ ⢈⣉⡉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠀⠈⠁⣦⠉⠀⠀⠀⢀⣀⠈⢡⣦⣼⣧⣴⣾⣿⣿⡿⠀⢒⣒⡒⠀⠀⠂⢘⣛⠉⠉⠉⠁⢙⣛⡀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣼⢧⢿⣿⣿ ⠈⣍⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⢀⡉⢁⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠠⠤⠄⠸⠥⠀⠠⢤⣥⣦⣀⣬⣭⣽⢽⡛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⠀⢸⣿⣿⣿⣿⣿ ⠀⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠛⣀⣀⣀⠀⠃⠤⠈⠛⡋⠋⠛⠻⢈⣓⢺⡟⠛⣹⠛⣛⣿⡻⣻⡟⠟⢛⣃⡁⠄⠀⠈⣿⣿⣟⣻⣿ ⠀⠶⠶⠶⠆⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢈⣰⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⠀⣀⠈⠙⠁⢀⣀⡲⠆⠴⠆⠀⣰⣞⠧⠛⣛⣿⡛⣻⣿⢿⣿⣿⣯⣿⣿⣿⣶⣾⠶⢾⣿⣿⣿⣿⣿ ⢠⣆⣦⡀⠀⠢⣠⠀⠁⠀⠀⠀⠀⠀⠀⢠⡄⢠⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣶⣷⣿⣿⣿⣿⣿⣷⣶⣶⣿⣶⣿⢶⣿⡟⢋⠉⡉⠛⠋⠘⠍⢙⣏⡉⢋⣙⡉⣉⠂⢈⠉⠉⠩⢍⡉ ⠀⠁⠈⠙⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣶⣟⣓⣒⣀⡀⢺⠶⡷⣖⠚⢿⣿⣿⣿⣶⢖⡒⣐⣲⢿⢾⢏⣉ ⠐⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣟⣙⣻⣿⡷⣿⠿⠂⠀⠨⠿⢿⣿⣿⣫ ⠀⠟⠻⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠛⠛⠭⠿⡿⠟⠿⣿⣟⣏⣿⡉⠁⠰⣿⠿⣟⠛⠋ ⠠⢤⣤⡀⠀⠀⢀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣳⠎⣉⡉⢳⡶⡤⠁⠠⠤⠘⠛⢛⣄⣒⣖⣒⢀⢀⠐⠒⠒⣓⡚⠒⠀⢀⣚⣶⣲⣂⡙ ⠀⠛⠿⠃⠀⢀⡈⠀⠀⠀⠀⠀⠀⠀⠀⢨⢠⠖⠐⠆⠆⠂⣀⡀⠀⠀⢀⣀⡸⠿⠿⠿⠟⠿⠿⠿⠿⢿⣿⢿⡿⢿⣿⣿⣿⣿⣷⢿⡷⢿⡽⣿⣺⣿⣿⡧⢰⢶⠶⠯⠟⠿⢽⡿⠫⢭⡟⣛⢛⣛⣠⣤⣭⠿⠿⠿⣿⡴ ⠀⠉⠉⠁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣄⠀⠸⢶⣶⡳⣿⣟⠼⣸⢛⣯⣾⣝⡶⣷⣖⠒⢖⣲⠒⡟⠓⣴⣿⠻⣚⢾⣾⣿⣿⣷⣿⣿⣿⣶⡿⣘⢺⣿⣿⣿⡯⣤⢤⣬⣭⠥⢾⣯⣴⣿⣿⡿⢿⣿⢷⢿⣿⣿⡤⣤⠤⢭⣤ ⠄⢥⣤⡥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠤⠤⠙⠛⠊⠉⠹⠁⢺⠊⠉⠈⠙⠋⠉⠫⣍⠉⠋⢉⡯⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣷⠀⠐⣀⣛⣓⣛⣛⣣⣬⣙⣛⣊⢛⠉⠉⠉⠹⢛⣛⣛⣛⣋ ⡈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢊⠀⠀⠀⠀⠀⠠⠈⠘⠷⠤⠿⠋⠀⠀⢀⣀⣀⣼⣸⣯⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣻⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠉⠉⡉⠉⢹ ⠨⣿⡏⠉⠉⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⢴⣶⣖⣶⡸⢠⣴⣶⣶⣶⢶⣦⣀⣠⡶⣤⣤⣄⣀⣸⣿⣿⣿⣶⣿⣿⣭⣭⣽⣿⣿⣷⡦⣤⣿⣿⣿⣿⣼⣽⣿⣶⣾⣮⣿⣿⣿⣿⣯⣿⣾⣁⣄⣀⣄⣸⣷⣧⣭⣍ ⢶⠄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠶⠤⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠆ ⠤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⢤⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠢⠤⠀⠢⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢐⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⣠⠀⢀⡀⠰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣠⣴⣴⣶⣶⣶⠒⠒⠒⠚⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣤⣾⣿⣦⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠤⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⣿⣿⣿⣾⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡿⠿⡻⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣔⠄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣻⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢦⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⢿⣿⣿⣿⠂⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠐⣿⡿⠿⢛⡿⠠⣴⣿⣿⣿⣶⣼⣗⣾⣶⣦⣤⣤⣶⣤⣦⣴⣤⣤⣤⣤⠤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⡟⠠⣴⡄⣠ ⢈⣉⡉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠀⠈⠁⣦⠉⠀⠀⠀⢀⣀⠈⢡⣦⣼⣧⣴⣾⣿⣿⡿⠀⢒⣒⡒⠀⠀⠂⢘⣛⠉⠉⠉⠁⢙⣛⡀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣼⢧⢿⣿⣿ ⠈⣍⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⢀⡉⢁⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠠⠤⠄⠸⠥⠀⠠⢤⣥⣦⣀⣬⣭⣽⢽⡛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⠀⢸⣿⣿⣿⣿⣿ ⠀⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠛⣀⣀⣀⠀⠃⠤⠈⠛⡋⠋⠛⠻⢈⣓⢺⡟⠛⣹⠛⣛⣿⡻⣻⡟⠟⢛⣃⡁⠄⠀⠈⣿⣿⣟⣻⣿ ⠀⠶⠶⠶⠆⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢈⣰⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⠀⣀⠈⠙⠁⢀⣀⡲⠆⠴⠆⠀⣰⣞⠧⠛⣛⣿⡛⣻⣿⢿⣿⣿⣯⣿⣿⣿⣶⣾⠶⢾⣿⣿⣿⣿⣿ ⢠⣆⣦⡀⠀⠢⣠⠀⠁⠀⠀⠀⠀⠀⠀⢠⡄⢠⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣶⣷⣿⣿⣿⣿⣿⣷⣶⣶⣿⣶⣿⢶⣿⡟⢋⠉⡉⠛⠋⠘⠍⢙⣏⡉⢋⣙⡉⣉⠂⢈⠉⠉⠩⢍⡉ ⠀⠁⠈⠙⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣶⣟⣓⣒⣀⡀⢺⠶⡷⣖⠚⢿⣿⣿⣿⣶⢖⡒⣐⣲⢿⢾⢏⣉ ⠐⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣟⣙⣻⣿⡷⣿⠿⠂⠀⠨⠿⢿⣿⣿⣫ ⠀⠟⠻⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠛⠛⠭⠿⡿⠟⠿⣿⣟⣏⣿⡉⠁⠰⣿⠿⣟⠛⠋ ⠠⢤⣤⡀⠀⠀⢀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣳⠎⣉⡉⢳⡶⡤⠁⠠⠤⠘⠛⢛⣄⣒⣖⣒⢀⢀⠐⠒⠒⣓⡚⠒⠀⢀⣚⣶⣲⣂⡙ ⠀⠛⠿⠃⠀⢀⡈⠀⠀⠀⠀⠀⠀⠀⠀⢨⢠⠖⠐⠆⠆⠂⣀⡀⠀⠀⢀⣀⡸⠿⠿⠿⠟⠿⠿⠿⠿⢿⣿⢿⡿⢿⣿⣿⣿⣿⣷⢿⡷⢿⡽⣿⣺⣿⣿⡧⢰⢶⠶⠯⠟⠿⢽⡿⠫⢭⡟⣛⢛⣛⣠⣤⣭⠿⠿⠿⣿⡴ ⠀⠉⠉⠁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣄⠀⠸⢶⣶⡳⣿⣟⠼⣸⢛⣯⣾⣝⡶⣷⣖⠒⢖⣲⠒⡟⠓⣴⣿⠻⣚⢾⣾⣿⣿⣷⣿⣿⣿⣶⡿⣘⢺⣿⣿⣿⡯⣤⢤⣬⣭⠥⢾⣯⣴⣿⣿⡿⢿⣿⢷⢿⣿⣿⡤⣤⠤⢭⣤ ⠄⢥⣤⡥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠤⠤⠙⠛⠊⠉⠹⠁⢺⠊⠉⠈⠙⠋⠉⠫⣍⠉⠋⢉⡯⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣷⠀⠐⣀⣛⣓⣛⣛⣣⣬⣙⣛⣊⢛⠉⠉⠉⠹⢛⣛⣛⣛⣋ ⡈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢈⠀⠀⠀⠀⠀⠠⠈⠘⠷⠤⠿⠋⠀⠀⢀⣀⣀⣼⣸⣯⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣻⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠉⠉⡉⠉⢹ ⠨⣿⡏⠉⠉⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⢴⣶⣖⣶⡸⢠⣴⣶⣶⣶⢶⣦⣀⣠⡶⣤⣤⣄⣀⣸⣿⣿⣿⣶⣿⣿⣭⣭⣽⣿⣿⣷⡦⣤⣿⣿⣿⣿⣼⣽⣿⣶⣾⣮⣿⣿⣿⣿⣯⣿⣾⣁⣄⣀⣄⣸⣷⣧⣭⣍ ⢶⠄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠶⠤⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠆ ⠤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⢤⣤⣤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠢⠤⠀⠢⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢐⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⣠⠀⢀⡀⠰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣠⣴⣴⣶⣶⣶⠒⠒⠒⠚⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣤⣾⣿⣦⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠤⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⣿⣿⣿⣾⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡿⠿⡻⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣔⠄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣻⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢦⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⢿⣿⣿⣿⠂⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠐⣿⡿⠿⢛⡿⠠⣴⣿⣿⣿⣶⣼⣗⣾⣶⣦⣤⣤⣶⣤⣦⣴⣤⣤⣤⣤⠤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⡟⠠⣴⡄⣠ ⢈⣉⡉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠀⠈⠁⣦⠉⠀⠀⠀⢀⣀⠈⢡⣦⣼⣧⣴⣾⣿⣿⡿⠀⢒⣒⡒⠀⠀⠂⢘⣛⠉⠉⠉⠁⢙⣛⡀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣼⢧⢿⣿⣿ ⠈⣍⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⢀⡉⢁⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠠⠤⠄⠸⠥⠀⠠⢤⣥⣦⣀⣬⣭⣽⢽⡛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⠀⢸⣿⣿⣿⣿⣿ ⠀⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠛⣀⣀⣀⠀⠃⠤⠈⠛⡋⠋⠛⠻⢈⣓⢺⡟⠛⣹⠛⣛⣿⡻⣻⡟⠟⢛⣃⡁⠄⠀⠈⣿⣿⣟⣻⣿ ⠀⠶⠶⠶⠆⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢈⣰⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⠀⣀⠈⠙⠁⢀⣀⡲⠆⠴⠆⠀⣰⣞⠧⠛⣛⣿⡛⣻⣿⢿⣿⣿⣯⣿⣿⣿⣶⣾⠶⢾⣿⣿⣿⣿⣿ ⢠⣆⣦⡀⠀⠢⣠⠀⠁⠀⠀⠀⠀⠀⠀⢠⡄⢠⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣶⣷⣿⣿⣿⣿⣿⣷⣶⣶⣿⣶⣿⢶⣿⡟⢋⠉⡉⠛⠋⠘⠍⢙⣏⡉⢋⣙⡉⣉⠂⢈⠉⠉⠩⢍⡉ ⠀⠁⠈⠙⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣶⣟⣓⣒⣀⡀⢺⠶⡷⣖⠚⢿⣿⣿⣿⣶⢖⡒⣐⣲⢿⢾⢏⣉ ⠐⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣟⣙⣻⣿⡷⣿⠿⠂⠀⠨⠿⢿⣿⣿⣫ ⠀⠟⠻⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠛⠛⠭⠿⡿⠟⠿⣿⣟⣏⣿⡉⠁⠰⣿⠿⣟⠛⠋ ⠠⢤⣤⡀⠀⠀⢀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣳⠎⣉⡉⢳⡶⡤⠁⠠⠤⠘⠛⢛⣄⣒⣖⣒⢀⢀⠐⠒⠒⣓⡚⠒⠀⢀⣚⣶⣲⣂⡙ ⠀⠛⠿⠃⠀⢀⡈⠀⠀⠀⠀⠀⠀⠀⠀⢨⢠⠖⠐⠆⠆⠂⣇⡀⠀⠀⢀⣀⡸⠿⠿⠿⠟⠿⠿⠿⠿⢿⣿⢿⡿⢿⣿⣿⣿⣿⣷⢿⡷⢿⡽⣿⣺⣿⣿⡧⢰⢶⠶⠯⠟⠿⢽⡿⠫⢭⡟⣛⢛⣛⣠⣤⣭⠿⠿⠿⣿⡴ ⠀⠉⠉⠁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣄⠀⠸⢶⣶⡳⣿⣟⠤⣸⢛⣯⣾⣝⡶⣷⣖⠒⢖⣲⠒⡟⠓⣴⣿⠻⣚⢾⣾⣿⣿⣷⣿⣿⣿⣶⡿⣘⢺⣿⣿⣿⡯⣤⢤⣬⣭⠥⢾⣯⣴⣿⣿⡿⢿⣿⢷⢿⣿⣿⡤⣤⠤⢭⣤ ⠄⢥⣤⡥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠤⠤⠙⠛⠊⠉⠹⠁⢺⠊⠉⠈⠙⠋⠉⠫⣍⠉⠋⢉⡯⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣷⠀⠐⣀⣛⣓⣛⣛⣣⣬⣙⣛⣊⢛⠉⠉⠉⠹⢛⣛⣛⣛⣋ ⡈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢈⠀⠀⠀⠀⠀⠠⠈⠘⠷⠤⠿⠋⠀⠀⢀⣀⣀⣼⣸⣯⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣻⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠉⠉⡉⠉⢹ ⠨⣿⡏⠉⠉⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⢴⣶⣖⣶⡸⢠⣴⣶⣶⣶⢶⣦⣀⣠⡶⣤⣤⣄⣀⣸⣿⣿⣿⣶⣿⣿⣭⣭⣽⣿⣿⣷⡦⣤⣿⣿⣿⣿⣼⣽⣿⣶⣾⣮⣿⣿⣿⣿⣯⣿⣾⣁⣄⣀⣄⣸⣷⣧⣭⣍ ⢶⡆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠤⠶⠤⠤⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠀⠆ ⡦⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢤⢤⣤⣴⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⢦⠤⠀⠲⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢸⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠚⠒⠒⣲⡒⢖⡶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠷⠖⠛⠛⠓⠀⠀⠀⡀⠀⠀⠀⠀ ⡠⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣴⣾⣿⣷⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠿⣿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡏⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣻⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⠂⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣿⣤⣬⣤⣤ ⠘⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠸⣿⡿⡿⢿⡿⠠⣴⣿⣿⣿⣿⣿⣗⣿⣿⣦⣤⣤⣶⣤⣾⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡉⢉⠉⠉⣟⢩⣽⣽⣫ ⢈⣉⡉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢙⠉⠉⠉⠀⠈⠁⣶⠉⠀⠀⠀⢀⣀⠘⣡⣷⣽⣧⣴⣿⣿⣿⣿⢀⣒⣒⣒⡀⠀⣂⣙⣛⠋⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠨⣍⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⢈⣋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠠⠤⠥⠬⠼⠥⠤⠤⢴⣧⡎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢪⣦⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠛⣀⣑⣀⡄⠣⠤⠌⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠶⠾⠶⠆⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢈⣾⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⣀⣈⠉⠙⠁⢀⣒⡶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿ ⢠⣆⣦⡀⠀⠢⣠⠀⠁⠀⠀⠀⠀⠀⠀⢠⡄⢸⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠠⠁⠈⠙⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠘⠛⢋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿ ⠘⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠟⠿⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠠⢤⣤⡀⠀⠀⣀⠀⠀⠘⠃⠀⠀⠀⠀⢠⠀⠐⠀⠀⠀⠀⡆⠀⠀⠀⠁⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⠞⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠂⠛⠿⠃⠀⢀⡈⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⡶⠒⠆⠆⠂⣇⡀⠀⠀⣀⣀⡻⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⢿⡿⣿⣿⣿⣿⣿⣷⢿⡷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠋⠙⠁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣤⠀⢸⢶⣾⡳⣿⣿⡦⣸⢟⣿⣿⣽⣾⣷⣖⠒⢖⣲⠒⡟⢓⣶⣿⠻⣚⢾⣾⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠄⣷⣶⡷⠶⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠮⠙⠛⠊⠉⠹⠁⢺⠊⠋⠉⠙⠻⢽⣿⣍⠉⠋⢉⡿⡿⠋⠉⠋⠉⢹⢻⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⡻⣛⣿⣿⣿⣟⣿⣿⣿⣻⣿⢟⡿⠛⠻⠿⢿⣿⣿⣟⣛ ⡈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠐⢘⢀⢀⡀⣀⣀⣩⣿⣿⣷⣴⣿⣛⣁⣀⣀⣀⣀⣼⣸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣻⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠉⠉⣉⠉⢹ ⠨⣿⡏⠉⠉⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⣶⣶⣖⣶⣸⢠⣴⣶⣶⣶⣶⣦⣀⣠⡶⣬⣭⣤⣀⣾⣿⣿⣿⣷⣿⣿⣭⣭⣽⣿⣿⣷⣦⣤⣿⣿⣿⣿⣾⣽⣿⣶⣾⣾⣿⣿⣿⣿⣯⣿⣿⣁⣄⣤⣄⣸⣷⣧⣭⣍ ⢶⡆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠤⠶⠤⠤⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠀⠆ ⡦⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢤⢤⣤⣴⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⢦⠤⠀⠲⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢸⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠚⠒⠒⣲⡒⢖⡶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⠷⠖⠛⠛⠛⠀⠀⠀⡀⠀⠀⠀⠀ ⡰⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣴⣿⣿⣷⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠿⣿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡟⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣻⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⠂⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣤⣤⣿⣤⣬⣤⣤ ⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠸⣿⡿⣿⢿⡿⠠⣴⣿⣿⣿⣿⣿⣗⣿⣿⣦⣤⣤⣷⣤⣾⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡉⢉⠉⠉⣿⢩⣽⣽⣫ ⢈⣉⡉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⠉⠉⠉⠀⠈⠁⣶⠉⠀⠀⠀⢀⣀⠘⣡⣷⣽⣧⣴⣿⣿⣿⣿⢀⣒⣒⣒⡀⠂⣂⣙⣛⠋⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠨⣍⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⢈⣋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠠⠤⠥⠬⠼⠥⠤⠤⢴⣯⡎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢪⣦⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠛⣀⣑⣀⡄⡣⠤⠌⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠶⠾⠶⠆⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢈⣾⣿⣿⣯⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⣀⣈⠉⠙⠁⢀⣒⡶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿ ⢠⣆⣦⡀⠀⠢⣠⠀⠁⠀⠀⠀⠀⠀⠀⢠⡄⢸⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠠⠁⠈⠙⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠘⠛⢋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿ ⠘⠛⠛⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠟⠿⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠠⢤⣤⡀⠀⠀⣀⠀⠀⠘⠃⠀⠀⠀⠀⢠⠀⠐⠀⠀⠀⠀⡆⠀⠀⠀⠁⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⠞⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠂⠛⠿⠃⠀⢀⡈⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⡶⠒⠆⠆⠂⣇⡀⠀⠀⣀⣀⡻⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⢿⡿⣿⣿⣿⣿⣿⣷⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠋⠙⠁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣤⠀⢸⢶⣾⡳⣿⣿⡆⣹⢿⣿⣿⣽⣾⣷⣖⠒⢖⣲⠒⡟⢓⣶⣿⠻⣚⢾⣾⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠄⣷⣶⡷⠶⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠮⠙⠛⠊⠉⠹⠁⢺⠊⠋⠉⠙⠻⢽⣿⣍⠉⠋⢉⡿⡿⠋⠉⠋⠉⢹⢻⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⡻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿ ⡈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠐⢘⢀⢀⡀⣀⣀⣭⣿⣿⣷⣴⣿⣛⣁⣀⣀⣀⣀⣼⣸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣻⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠛⠁⡀⠀⠉⠉⣉⠉⢹ ⠨⣿⡏⠉⠉⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⣶⣶⣖⣶⣸⢠⣴⣶⣶⣶⣶⣦⣀⣠⡶⣬⣭⣤⣀⣾⣿⣿⣿⣷⣿⣿⣭⣭⣿⣿⣿⣷⣦⣤⣿⣿⣿⣿⣾⣽⣿⣶⣾⣾⣿⣿⣿⣿⣯⣿⣿⣁⣄⣤⣄⣸⣷⣧⣭⣍ ⢶⡆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠤⠶⠤⠤⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠀⠆ ⡦⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢤⢤⣤⣴⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⢦⠤⠀⠲⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢸⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠚⠒⠒⣲⡒⢖⡶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⠷⠖⠛⠛⠛⠀⠀⠀⡀⠀⠀⠀⠀ ⡰⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣴⣿⣿⣷⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠿⣿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡟⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣻⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⠂⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣤⣤⣿⣤⣬⣤⣤ ⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠸⣿⡿⣿⢿⡿⠠⣴⣿⣿⣿⣿⣿⣗⣿⣿⣦⣤⣤⣷⣤⣾⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡉⢉⠉⠉⣿⢩⣽⣽⣫ ⢈⣉⡉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⠉⠉⠉⠀⠈⠁⣶⠉⠀⠀⠀⢀⣀⠘⣡⣷⣽⣧⣴⣿⣿⣿⣿⢀⣒⣒⣒⡀⠂⣂⣙⣛⠋⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠨⣍⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⢈⣋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠠⠤⠥⠬⠼⠥⠤⠤⢽⣯⡮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢪⣦⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠛⣀⣑⣀⡄⡣⠤⠌⠿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠶⠾⠶⠆⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢈⣾⣿⣿⣯⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⣀⣈⠉⠙⠁⢀⣒⡶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿ ⢠⣆⣦⡀⠀⠢⣠⠀⠁⠀⠀⠀⠀⠀⠀⢠⡄⢸⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠠⠁⠈⠙⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠘⠛⢋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿ ⠘⠛⠛⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠟⠿⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠠⢤⣤⡀⠀⠀⣀⠀⠀⠘⠃⠀⠀⠀⠀⢠⠀⠐⠀⠀⠀⠀⡆⠀⠀⠀⠁⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⠞⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠂⠛⠿⠃⠀⢀⡈⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⡶⠒⠆⠆⠂⡇⡀⠀⠀⣀⣀⡻⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⢿⡿⣿⣿⣿⣿⣿⣷⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠋⠙⠁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣤⠀⢸⢶⣾⡳⣿⣿⡆⣹⢿⣿⣿⣽⣾⣷⣖⠒⢖⣲⠒⡟⢓⣶⣿⠻⣚⢾⣾⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠄⣷⣶⡷⠶⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠮⠙⠛⠊⠉⠹⠁⢺⠊⠋⠉⠙⠻⢽⣿⣍⠉⠋⢉⡿⡿⠋⠉⠋⠉⢹⢻⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⡻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⢿⣿⣿⣿⣿⣿ ⡈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠐⢘⢀⢀⡀⣀⣀⣭⣿⣿⣷⣴⣿⣛⣁⣀⣀⣀⣀⣼⣸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣻⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣷⡂⠐⠍⠉⣉⠉⢹ ⠨⣿⡏⠉⠉⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⣶⣶⣖⣶⣸⢠⣴⣶⣶⣶⣶⣦⣀⣠⡶⣬⣭⣤⣀⣾⣿⣿⣿⣷⣿⣿⣭⣭⣿⣿⣿⣷⣦⣤⣿⣿⣿⣿⣾⣽⣿⣶⣾⣾⣿⣿⣿⣿⣯⣿⣿⣉⣌⣤⣄⣸⣷⣧⣭⣍ ⢶⡆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠤⠶⠤⠤⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠀⠆ ⡦⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢤⢤⣤⣴⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⢦⠤⠀⠲⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢸⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠚⠒⠒⣲⡒⢖⡶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⠷⠖⠛⠛⠛⠀⠀⠀⡀⠀⠀⠀⠀ ⡰⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣴⣿⣿⣷⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠿⣿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡟⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣻⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⠂⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣤⣤⣿⣤⣬⣤⣤ ⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠸⣿⡿⣿⢿⡿⠠⣴⣿⣿⣿⣿⣿⣗⣿⣿⣦⣤⣤⣷⣤⣾⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡉⢉⠉⠉⣿⢩⣽⣽⣫ ⢈⣉⡉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⠉⠉⠉⠀⠈⠁⣶⠉⠀⠀⠀⢀⣀⠘⣡⣷⣽⣧⣴⣿⣿⣿⣿⢀⣒⣒⣒⡀⠂⣂⣙⣛⠋⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠨⣍⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⢈⣋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠠⠤⠥⠬⠼⠥⠤⠤⢽⣯⡮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢪⣦⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠛⣀⣑⣀⡄⡣⠤⠌⠿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠶⠾⠶⠆⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢈⣾⣿⣿⣯⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⣀⣈⠉⠙⠁⢀⣒⡶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿ ⢠⣆⣦⡀⠀⠢⣠⠀⠁⠀⠀⠀⠀⠀⠀⢠⡄⢸⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠠⠁⠈⠙⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠘⠛⢋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿ ⠘⠛⠛⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠟⠿⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠠⢤⣤⡀⠀⠀⣀⠀⠀⠘⠃⠀⠀⠀⠀⢠⠀⠐⠀⠀⠀⠀⡆⠀⠀⠀⠁⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⠞⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠂⠛⠿⠃⠀⢀⡈⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⡶⠒⠆⠆⠂⢹⡀⠀⠀⣀⣀⡻⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⢿⡿⣿⣿⣿⣿⣿⣷⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠋⠙⠁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣤⠀⢸⢶⣾⡳⣿⣿⡆⣹⢿⣿⣿⣽⣾⣷⣖⠒⢖⣲⠒⡟⢓⣶⣿⠻⣚⢾⣾⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠄⣷⣶⡷⠶⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠮⠙⠛⠊⠉⠹⠁⢺⠊⠋⠉⠙⠻⢽⣿⣍⠉⠋⢉⡿⡿⠋⠉⠋⠉⢹⢻⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⡻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⢿⣿⣿⣿⣿⣿ ⡈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠐⢘⢀⢀⡀⣀⣀⣭⣿⣿⣷⣴⣿⣛⣁⣀⣀⣀⣀⣼⣸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣻⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣷⡂⠐⠍⠉⣉⠉⢹ ⠨⣿⡏⠉⠉⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⣶⣶⣖⣶⣸⢠⣴⣶⣶⣶⣶⣦⣀⣠⡶⣬⣭⣤⣀⣾⣿⣿⣿⣷⣿⣿⣭⣭⣿⣿⣿⣷⣦⣤⣿⣿⣿⣿⣿⣽⣿⣶⣾⣾⣿⣿⣿⣿⣯⣿⣿⣉⣌⣤⣄⣸⣷⣧⣭⣍ ⢶⡆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠤⠶⠤⠤⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠀⠆ ⡦⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢤⢤⣤⣴⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⢦⠤⠀⠲⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢸⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠚⠒⠒⣲⡒⢖⡶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⠷⠖⠛⠛⠛⠀⠀⠀⡀⠀⠀⠀⠀ ⡰⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣴⣿⣿⣷⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠿⣿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡟⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣻⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⠂⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣤⣤⣿⣤⣬⣤⣤ ⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠸⣿⡿⣿⢿⡿⠠⣴⣿⣿⣿⣿⣿⣗⣿⣿⣦⣤⣤⣷⣤⣾⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡉⢉⠉⠉⣿⢩⣽⣽⣫ ⢈⣉⡉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⠉⠉⠉⠀⠈⠁⣶⠉⠀⠀⠀⢀⣀⠘⣡⣷⣽⣧⣴⣿⣿⣿⣿⢀⣒⣒⣒⡀⠂⣂⣙⣛⠋⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠨⣍⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⢈⣋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠠⠤⠥⠬⠼⠥⠤⠤⢽⣯⡮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢪⣦⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠛⣀⣑⣀⡄⡣⠤⠌⠿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠶⠾⠶⠆⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢈⣾⣿⣿⣯⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⣀⣈⠉⠙⠁⢀⣒⡶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿ ⢠⣆⣦⡀⠀⠢⣠⠀⠁⠀⠀⠀⠀⠀⠀⢠⡄⢸⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠠⠁⠈⠙⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠘⠛⢋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿ ⠘⠛⠛⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠟⠿⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠠⢤⣤⡀⠀⠀⣀⠀⠀⠘⠃⠀⠀⠀⠀⢠⠀⠐⠀⠀⠀⠀⡆⠀⠀⠀⠁⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⠞⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠂⠛⠿⠃⠀⢀⡈⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⡶⠒⠆⠆⠂⢸⡀⠀⠀⣀⣀⡻⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⢿⡿⣿⣿⣿⣿⣿⣷⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠋⠙⠁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣤⠀⢸⢶⣾⡳⣿⣿⡆⣸⢿⣿⣿⣽⣾⣷⣖⠒⢖⣲⠒⡟⢓⣶⣿⠻⣚⢾⣾⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠄⣷⣶⡷⠶⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠮⠙⠛⠊⠉⠹⠁⢺⠊⠋⠉⠙⠻⢽⣿⣍⠉⠋⢉⡿⡿⠋⠉⠋⠉⢹⢻⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⡻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⢿⣿⣿⣿⣿⣿ ⡈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠐⢘⢀⢀⡀⣀⣀⣭⣿⣿⣷⣴⣿⣛⣁⣀⣀⣀⣀⣼⣸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣻⡿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣷⡂⠐⠍⠉⣉⠉⢹ ⠨⣿⡏⠉⠉⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⣶⣶⣖⣶⣸⢠⣴⣶⣶⣶⣶⣦⣀⣠⡶⣬⣭⣤⣀⣾⣿⣿⣿⣷⣿⣿⣭⣭⣿⣿⣿⣷⣦⣤⣿⣿⣿⣿⣿⣽⣿⣶⣾⣾⣿⣿⣿⣿⣯⣿⣿⣉⣌⣤⣄⣸⣷⣧⣭⣍ ⢶⡆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠤⠶⠤⠤⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠀⠆ ⡦⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢤⢤⣤⣴⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⢦⠤⠀⠲⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢸⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠚⠒⠒⣲⡒⢖⡶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⠷⠖⠛⠛⠛⠀⠀⠀⡀⠀⠀⠀⠀ ⡠⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣴⣿⣿⣷⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠿⣿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡟⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣻⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⠂⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣤⣤⣿⣤⣬⣤⣤ ⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠸⣿⡿⡿⢿⡿⠠⣴⣿⣿⣿⣿⣿⣗⣿⣿⣦⣤⣤⣷⣤⣾⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡉⢉⠉⠉⣟⢩⣽⣽⣫ ⢈⣉⡉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⠉⠉⠉⠀⠈⠁⣶⠉⠀⠀⠀⢀⣀⠘⣡⣷⣿⣧⣴⣿⣿⣿⣿⢀⣒⣒⣒⡀⠀⣂⣙⣛⠋⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠨⣍⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⢈⣋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠠⠤⠥⠬⠼⠥⠤⠤⢽⣯⡮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢪⣦⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠛⣀⣑⣀⡄⠣⠤⠌⠿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠶⠾⠶⠆⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢈⣾⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⣀⣈⠉⠙⠁⢀⣒⡶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿ ⢠⣆⣦⡀⠀⠢⣠⠀⠁⠀⠀⠀⠀⠀⠀⢠⡄⢸⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠠⠁⠈⠙⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠘⠛⢋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿ ⠘⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠟⠿⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠠⢤⣤⡀⠀⠀⣀⠀⠀⠘⠃⠀⠀⠀⠀⢠⠀⠐⠀⠀⠀⠀⡆⠀⠀⠀⠁⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⠞⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠂⠛⠿⠃⠀⢀⡈⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⡶⠒⠆⠆⠂⢸⡀⠀⠀⣀⣀⡻⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⢿⡿⣿⣿⣿⣿⣿⣷⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠋⠙⠁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣤⠀⢸⢶⣾⡳⣿⣿⡆⣸⢿⣿⣿⣽⣾⣷⣖⠒⢖⣲⠒⡟⢓⣶⣿⠻⣚⢾⣾⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠄⣷⣶⡷⠶⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠮⠙⠛⠊⠉⠹⠁⢺⠊⠋⠉⠙⠻⢽⣿⣍⠉⠋⢉⡿⡿⠋⠉⠋⠉⢹⢻⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⡻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⢿⣿⣿⣿⣿⣿ ⡈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠐⢘⢀⢀⡀⣀⣀⣭⣿⣿⣷⣴⣿⣛⣁⣀⣀⣀⣀⣼⣸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣻⡿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣷⡂⠐⠍⠉⣉⠉⢹ ⠨⣿⡏⠉⠉⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⣶⣶⣖⡆⢸⢠⣴⣶⣶⣶⣶⣦⣀⣠⡶⣬⣭⣤⣀⣾⣿⣿⣿⣷⣿⣿⣭⣭⣿⣿⣿⣷⣦⣤⣿⣿⣿⣿⣿⣽⣿⣶⣾⣮⣿⣿⣿⣿⣯⣿⣿⣉⣌⣤⣄⣸⣷⣧⣭⣍ ⢶⡆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠤⠶⠤⠤⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠀⠆ ⡦⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢤⢤⣤⣴⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⢦⠤⠀⠲⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢸⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠚⠒⠒⣲⡒⢖⡶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠷⠖⠛⠛⠓⠀⠀⠀⡀⠀⠀⠀⠀ ⡠⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣴⣾⣿⣷⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠿⣿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡏⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣻⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⠂⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣿⣤⣬⣤⣤ ⠘⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠸⣿⡿⡿⢿⡿⠠⣴⣿⣿⣿⣿⣿⣗⣿⣿⣦⣤⣤⣶⣤⣾⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡉⢉⠉⠉⣟⢩⣽⣽⣫ ⢈⣉⡉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢙⠉⠉⠉⠀⠈⠁⣶⠉⠀⠀⠀⢀⣀⠘⣡⣷⣽⣧⣴⣿⣿⣿⣿⢀⣒⣒⣒⡀⠀⣂⣙⣛⠋⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠨⣍⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⢈⣋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠠⠤⠥⠬⠼⠥⠤⠤⢽⣯⡮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢪⣦⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠛⣀⣑⣀⡄⠣⠤⠌⠿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠶⠾⠶⠆⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢈⣾⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⣀⣈⠉⠙⠁⢀⣒⡶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿ ⢠⣆⣦⡀⠀⠢⣠⠀⠁⠀⠀⠀⠀⠀⠀⢠⡄⢸⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠠⠁⠈⠙⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠘⠛⢋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿ ⠘⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠟⠿⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠠⢤⣤⡀⠀⠀⣀⠀⠀⠘⠃⠀⠀⠀⠀⢠⠀⠐⠀⠀⠀⠀⡆⠀⠀⠀⠁⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⠞⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠂⠛⠿⠃⠀⢀⡈⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⡶⠒⠆⠆⠂⢸⡀⠀⠀⣀⣀⡻⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⢿⡿⣿⣿⣿⣿⣿⣷⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠋⠙⠁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣤⠀⢸⢶⣾⡳⣿⣿⡆⣸⢟⣿⣿⣽⣾⣷⣖⠒⢖⣲⠒⡟⢓⣶⣿⠻⣚⢾⣾⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠄⣷⣶⡷⠶⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠮⠙⠛⠊⠉⠹⠁⢺⠊⠋⠉⠙⠻⢽⣿⣍⠉⠋⢉⡿⡿⠋⠉⠋⠉⢹⢻⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⡻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⢿⣿⣿⣿⣿⣿ ⡈⠛⠛⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠐⢘⢀⢀⡀⣀⣀⣭⣿⣿⣷⣴⣿⣛⣁⣀⣀⣀⣀⣼⣸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣻⡿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣷⡂⠐⠍⠉⣉⠉⢹ ⠨⣿⡏⠉⠉⠸⠇⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⣾⣶⣖⡆⢸⢠⣴⣶⣶⣶⣶⣦⣀⣠⡶⣬⣭⣤⣀⣾⣿⣿⣿⣷⣿⣿⣭⣭⣿⣿⣿⣷⣦⣤⣿⣿⣿⣿⣿⣽⣿⣶⣾⣮⣿⣿⣿⣿⣯⣿⣿⣉⣌⣤⣄⣸⣷⣧⣭⣍ ⢶⡆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠤⠶⠤⠤⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠀⠆ ⡦⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢤⢤⣤⣴⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⠦⠤⠀⠲⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢰⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠒⠒⠀⣲⡒⢒⡶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣶⣶⣶⣶⠷⠒⠚⠛⠓⠀⠀⠀⡀⠀⠀⠀⠀ ⠠⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣴⣾⣿⣷⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣾⣿⣿⣿⠿⢿⠿⠿⣿⠿⣿⣿⣿⣿⣿⡿⠿⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⡏⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣻⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⠿⢿⣿⣿⣿⠢⣄⣤⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣿⣤⣬⣤⣤ ⠘⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠘⣿⡿⡿⢻⡿⠠⣴⣿⣿⣿⣿⣿⣗⣾⣷⣦⣤⣤⣶⣤⣾⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⡉⢁⠉⠉⣟⢩⣽⣽⣫ ⢈⣉⡉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠉⠉⠉⠀⠈⠁⣦⠉⠀⠀⠀⢀⣀⠘⢡⣶⣼⣧⣴⣿⣿⣿⣿⠀⣒⣒⣒⡀⠀⣂⢙⣛⠋⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠨⣍⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⢈⣋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠠⠠⠥⠬⠼⠥⠤⠤⢼⣧⡮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢪⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠛⣀⣀⣀⡄⠃⠤⠌⠿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠶⠾⠶⠆⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢈⣴⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⢀⣈⠉⠙⠁⢀⣒⡶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣯⣿⣿⣿⣿⣿⣿ ⠠⠆⠆⠀⠀⠢⠠⠀⠁⠀⠀⠀⠀⠀⠀⠠⠄⢸⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣶⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠘⠻⠖⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⠛⢉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣯⣿⣿ ⠠⠶⡾⠃⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⡖⠶⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢀⣀⣀⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⠎⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠊⠉⠉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡴⠐⠆⠆⠂⢸⡀⠀⠀⣀⣀⡻⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⢿⡿⣿⣿⣿⣿⣿⣷⢿⡷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣟⣿⣿⣿⣿⣿⣿⢿ ⠀⠋⠙⠁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣤⠀⢸⢶⣾⡳⣿⣟⠄⣸⢟⣿⣾⣝⣾⣷⣖⠒⢖⣲⠒⡟⢓⣶⣿⠻⣚⢾⣾⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠄⢷⣶⡷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠶⠮⠙⠛⠊⠉⠹⠁⢺⠊⠉⠉⠙⠻⠙⣿⣍⠉⠋⢉⡯⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⡻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⢿⣿⣿⣿⣿⣿ ⡈⠛⠛⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠐⢈⢀⢀⡀⣀⣀⣨⣘⣟⣷⣴⣿⣋⣁⣀⣀⣀⣀⣼⣸⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣻⡿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣷⡂⠐⠍⠉⣉⠉⢹ ⠨⣿⡏⠉⠉⠸⠇⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⣾⣶⣖⡆⢸⢠⣴⣶⣶⣶⣶⣦⣀⣠⡶⣬⣬⣤⣀⣺⣿⣿⣿⣷⣿⣿⣭⣭⣽⣿⣿⣷⣦⣤⣿⣿⣿⣿⣽⣽⣿⣶⣾⣮⣿⣿⣿⣿⣯⣿⣿⣉⣌⣠⣄⣸⣷⣧⣭⣍ ⢶⡆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠤⠶⠤⠤⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠀⠆ ⡦⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢤⢤⣤⣴⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⠦⠤⠀⠲⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢰⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠒⠒⠀⣲⡒⢒⡶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣶⣶⣶⣶⠷⠒⠚⠛⠓⠀⠀⠀⡀⠀⠀⠀⠀ ⠠⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣴⣾⣿⣷⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣾⣿⣿⣿⠿⢿⠿⠿⣿⠿⣿⣿⣿⣿⣿⡿⠿⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⡏⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣻⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⠿⢿⣿⣿⣿⠢⣄⣤⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣿⣤⣬⣤⣤ ⠘⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠘⣿⡿⡿⢻⡿⠠⣴⣿⣿⣿⣿⣿⣗⣾⣷⣦⣤⣤⣶⣤⣾⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⡉⢁⠉⠉⣟⢩⣽⣽⣫ ⢈⣭⣭⣥⣬⣍⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⠁⣦⠉⠀⠀⠀⢀⣀⠘⢡⣶⣼⣧⣴⣿⣿⣿⣿⠀⣒⣒⣒⡀⠀⣂⢙⣛⠋⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠠⣅⣁⠁⠈⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⢈⣋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠠⠠⠥⠬⠼⠥⠤⠤⢼⣧⡮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢪⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠛⣀⣀⣀⡄⠃⠤⠌⠿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠒⠚⠒⠂⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢈⣴⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⢀⣈⠉⠙⠁⢀⣒⡶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣯⣿⣿⣿⣿⣿⣿ ⠈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣶⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠛⠛⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⠛⢉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣯⣿⣿ ⠠⠶⡾⠃⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⡖⠶⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢀⣀⣀⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⠎⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠊⠉⠉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡴⠐⠆⠆⠂⢸⡀⠀⠀⣀⣀⡻⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⢿⡿⣿⣿⣿⣿⣿⣷⢿⡷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣟⣿⣿⣿⣿⣿⣿⢿ ⠀⠋⠙⠁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣤⠀⢸⢶⣾⡳⣿⣟⠄⣸⢟⣿⣾⣝⣾⣷⣖⠒⢖⣲⠒⡟⢓⣶⣿⠻⣚⢾⣾⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠄⢷⣶⡷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠶⠮⠙⠛⠊⠉⠹⠁⢺⠊⠉⠉⠙⠻⠙⣿⣍⠉⠋⢉⡯⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⡻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⢿⣿⣿⣿⣿⣿ ⡈⠛⠛⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠐⢈⢀⢀⡀⣀⣀⣨⣘⣟⣷⣴⣿⣋⣁⣀⣀⣀⣀⣼⣸⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣻⡿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣷⡂⠐⠍⠉⣉⠉⢹ ⠨⣿⡏⠉⠉⠸⠇⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⣾⣶⣖⡆⢸⢠⣴⣶⣶⣶⣶⣦⣀⣠⡶⣬⣬⣤⣀⣺⣿⣿⣿⣷⣿⣿⣭⣭⣽⣿⣿⣷⣦⣤⣿⣿⣿⣿⣽⣽⣿⣶⣾⣮⣿⣿⣿⣿⣯⣿⣿⣉⣌⣠⣄⣸⣷⣧⣭⣍ ⢶⡆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠤⠶⠤⠤⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠀⠆ ⡦⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢤⢤⣤⣴⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⠦⠤⠀⠲⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢰⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠒⠒⠀⣲⡒⢒⡶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣶⣶⣶⣶⠷⠒⠚⠛⠓⠀⠀⠀⡀⠀⠀⠀⠀ ⠠⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣴⣾⣿⣷⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣾⣿⣿⣿⠿⢿⠿⠿⣿⠿⣿⣿⣿⣿⣿⡿⠿⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⡏⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣻⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⠿⢿⣿⣿⣿⠢⣄⣤⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣿⣤⣬⣤⣤ ⠘⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠘⣿⡿⡿⢻⡿⠠⣴⣿⣿⣿⣿⣿⣗⣾⣷⣦⣤⣤⣶⣤⣾⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⡉⢁⠉⠉⣟⢩⣽⣽⣫ ⠈⠛⠛⠓⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠀⠈⠁⣦⠉⠀⠀⠀⢀⣀⠘⢡⣶⣼⣧⣴⣿⣿⣿⣿⠀⣒⣒⣒⡀⠀⣂⢙⣛⠋⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠘⠛⠃⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⢈⣋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠠⠠⠥⠬⠼⠥⠤⠤⢼⣧⡮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠢⠶⠶⡶⠶⠶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠛⣀⣀⣀⡄⠃⠤⠌⠿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠒⠒⠒⠂⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣴⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⢀⣈⠉⠙⠁⢀⣒⡶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣯⣿⣿⣿⣿⣿⣿ ⠈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣶⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠛⠛⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⠛⢉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣯⣿⣿ ⠠⠶⡾⠃⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⡖⠶⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢀⣀⣀⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⠎⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠊⠉⠉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡴⠐⠆⠆⠂⢸⡀⠀⠀⣀⣀⡻⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⢿⡿⣿⣿⣿⣿⣿⣷⢿⡷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣟⣿⣿⣿⣿⣿⣿⢿ ⠀⠋⠙⠁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣤⠀⢸⢶⣾⡳⣿⣟⠄⣸⢟⣿⣾⣝⣾⣷⣖⠒⢖⣲⠒⡟⢓⣶⣿⠻⣚⢾⣾⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠄⢷⣶⡷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠶⠮⠙⠛⠊⠉⠹⠁⢺⠊⠉⠉⠙⠻⠙⣿⣍⠉⠋⢉⡯⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⡻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⢿⣿⣿⣿⣿⣿ ⡈⠛⠛⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠐⢈⢀⢀⡀⣀⣀⣨⣘⣟⣷⣴⣿⣋⣁⣀⣀⣀⣀⣼⣸⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣻⡿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣷⡂⠐⠍⠉⣉⠉⢹ ⠨⣿⡏⠉⠉⠸⠇⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⣾⣶⣖⡆⢸⢠⣴⣶⣶⣶⣶⣦⣀⣠⡶⣬⣬⣤⣀⣺⣿⣿⣿⣷⣿⣿⣭⣭⣽⣿⣿⣷⣦⣤⣿⣿⣿⣿⣽⣽⣿⣶⣾⣮⣿⣿⣿⣿⣯⣿⣿⣉⣌⣠⣄⣸⣷⣧⣭⣍ ⢶⡆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠤⠶⠤⠤⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠀⠆ ⡦⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢤⢤⣤⣴⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⢦⠤⠀⠲⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢸⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠚⠒⠒⣲⡒⢖⡶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠷⠖⠛⠛⠓⠀⠀⠀⡀⠀⠀⠀⠀ ⡠⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣴⣿⣿⣷⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠿⣿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡏⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣻⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⠢⣄⣤⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣿⣤⣬⣤⣤ ⠘⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠸⣿⡿⡿⢿⡿⠠⣴⣿⣿⣿⣿⣿⣗⣿⣿⣦⣤⣤⣶⣤⣾⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡉⢉⠉⠉⣟⢩⣽⣽⣫ ⠈⠛⠛⠓⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠀⠈⠁⣶⠉⠀⠀⠀⢀⣀⠘⣡⣷⣽⣧⣴⣿⣿⣿⣿⢀⣒⣒⣒⡀⠀⣂⣙⣛⠋⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠘⠛⠃⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⢈⣋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠠⠠⠥⠬⠼⠥⠤⠤⢽⣧⡮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠢⠶⠶⡶⠶⠆⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠛⣀⣁⣀⡄⠣⠤⠌⠿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠒⠒⠒⠂⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣾⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⣀⣈⠉⠙⠁⢀⣒⡶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿ ⠈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠛⠛⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠘⠛⢋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿ ⠰⡶⡾⠃⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⡖⠶⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢀⣀⣀⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⡆⠀⠀⠀⠁⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⠞⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠊⠉⠉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡶⠒⠆⠆⠂⢸⡀⠀⠀⣀⣀⡻⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⢿⡿⣿⣿⣿⣿⣿⣷⢿⡷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠋⠙⠁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣤⠀⢸⢶⣾⡳⣿⣿⡆⣸⢿⣿⣿⣽⣾⣷⣖⠒⢖⣲⠒⡟⢓⣶⣿⠻⣚⢾⣾⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠄⣷⣶⡷⠶⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠮⠙⠛⠺⠉⠹⠁⢺⠊⠋⠉⠙⠻⢽⣿⣍⠉⠋⢉⡯⡿⠋⠉⠋⠉⢹⢻⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⢿⣿⣿⣿⣿⣿ ⡈⠛⠛⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠐⢘⢀⢀⡀⣀⣀⣩⣿⣿⣷⣴⣿⣛⣁⣀⣀⣀⣀⣼⣸⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣷⡂⠐⠍⠉⣉⠉⢹ ⠨⣿⡏⠉⠉⠸⠇⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⣾⣶⣖⡆⢸⢠⣴⣶⣶⣶⣶⣦⣀⣠⡶⣬⣭⣤⣀⣾⣿⣿⣿⣷⣿⣿⣭⣭⣽⣿⣿⣷⣦⣾⣿⣿⣿⣿⣿⣽⣿⣶⣾⣿⣿⣿⣿⣿⣯⣿⣿⣯⣏⣤⣄⣸⣷⣧⣭⣍ ⢶⡆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠤⠶⠤⠤⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠀⠆ ⡦⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢤⢤⣤⣴⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⢦⠤⠀⠲⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢸⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠚⠒⠒⣲⡒⢖⡶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠷⠖⠛⠛⠓⠀⠀⠀⡀⠀⠀⠀⠀ ⡠⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣴⣿⣿⣷⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠿⣿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡏⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣻⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⠢⣄⣤⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣿⣤⣬⣤⣤ ⠘⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠸⣿⡿⡿⢿⡿⠠⣴⣿⣿⣿⣿⣿⣗⣿⣿⣦⣤⣤⣶⣤⣾⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡉⢉⠉⠉⣟⢩⣽⣽⣫ ⠈⠛⠛⠓⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠀⠈⠁⣶⠉⠀⠀⠀⢀⣀⠘⣡⣷⣽⣧⣴⣿⣿⣿⣿⢀⣒⣒⣒⡀⠀⣂⣙⣛⠋⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠘⠛⠃⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⢈⣋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠠⠠⠥⠬⠼⠥⠤⠤⢽⣧⡮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠢⠶⠶⡶⠶⠆⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠛⣀⣁⣀⡄⠣⠤⠌⠿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠒⠒⠒⠂⠀⢢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣾⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⣀⣈⠉⠙⠁⢀⣒⡶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿ ⠈⠛⠛⠃⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠛⠛⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠘⠛⢋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿ ⠰⡶⡾⠃⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⡖⠶⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢀⣀⣀⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⡆⠀⠀⠀⠁⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⠞⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠊⠉⠉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡶⠒⠆⠆⠂⢸⡀⠀⠀⣀⣀⡻⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⢿⡿⣿⣿⣿⣿⣿⣷⢿⡷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠋⠙⠁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣤⠀⢸⢶⣾⡳⣿⣿⡆⣸⢿⣿⣿⣽⣾⣷⣖⠒⢖⣲⠒⡟⢓⣶⣿⠻⣚⢾⣾⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠄⣷⣶⡷⠶⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠮⠙⠛⠺⠉⠹⠁⢺⠊⠋⠉⠙⠻⢽⣿⣍⠉⠋⢉⡯⡿⠋⠉⠋⠉⢹⢻⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⢿⣿⣿⣿⣿⣿ ⡈⠛⠛⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠐⢘⢀⢀⡀⣀⣀⣩⣿⣿⣷⣴⣿⣛⣁⣀⣀⣀⣀⣼⣸⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣷⡂⠐⠍⠉⣉⠉⢹ ⠨⣿⡏⠉⠉⠸⠇⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⣾⣶⣖⡆⢸⢠⣴⣶⣶⣶⣶⣦⣀⣠⡶⣬⣭⣤⣀⣾⣿⣿⣿⣷⣿⣿⣭⣭⣽⣿⣿⣷⣦⣾⣿⣿⣿⣿⣿⣽⣿⣶⣾⣿⣿⣿⣿⣿⣯⣿⣿⣯⣏⣤⣄⣸⣷⣧⣭⣍ ⢶⡆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠤⠶⠤⠤⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠀⠆ ⡦⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢤⢤⣤⣴⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⢦⠤⠀⠲⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢸⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠚⠒⠒⣲⡒⢖⡶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠷⠖⠛⠛⠓⠀⠀⠀⡀⠀⠀⠀⠀ ⡠⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣴⣿⣿⣷⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠿⣿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡏⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣻⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⠢⣄⣤⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣿⣤⣬⣤⣤ ⠘⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠸⣿⡿⡿⢿⡿⠠⣴⣿⣿⣿⣿⣿⣗⣿⣿⣦⣤⣤⣶⣤⣾⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡉⢉⠉⠉⣟⢩⣽⣽⣫ ⠈⠛⠛⠓⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠀⠈⠁⣶⠉⠀⠀⠀⢀⣀⠘⣡⣷⣽⣧⣴⣿⣿⣿⣿⢀⣒⣒⣒⡀⠀⣂⣙⣛⠋⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠘⠛⠃⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⢈⣋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠠⠠⠥⠬⠼⠥⠤⠤⢽⣧⡮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠢⠶⠶⡶⠶⠆⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠛⣀⣁⣀⡄⠣⠤⠌⠿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠒⠒⠒⠂⠀⢢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣾⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⣀⣈⠉⠙⠁⢀⣒⡶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿ ⠈⠛⠛⠃⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠛⠛⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠘⠛⢋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿ ⠰⡶⡾⠃⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⡖⠶⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢀⣀⣀⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⡆⠀⠀⠀⠁⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⠞⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠊⠉⠉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡶⠒⠆⠆⠂⢸⡀⠀⠀⣀⣀⡻⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⢿⡿⣿⣿⣿⣿⣿⣷⢿⡷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠋⠙⠁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣤⠀⢸⢶⣾⡳⣿⣿⡆⣸⢿⣿⣿⣽⣾⣷⣖⠒⢖⣲⠒⡟⢓⣶⣿⠻⣚⢾⣾⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠄⣷⣶⡷⠶⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠮⠙⠛⠺⠉⠹⠁⢺⠊⠋⠉⠙⠻⢽⣿⣍⠉⠋⢉⡯⡿⠋⠉⠋⠉⢹⢻⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⢿⣿⣿⣿⣿⣿ ⡈⠛⠛⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠐⢘⢀⢀⡀⣀⣀⣩⣿⣿⣷⣴⣿⣛⣁⣀⣀⣀⣀⣼⣸⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣷⡂⠐⠍⠉⣉⠉⢹ ⠨⣿⡏⠉⠉⠸⠇⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⣾⣶⣖⡆⢸⢠⣴⣶⣶⣶⣶⣦⣀⣠⡶⣬⣭⣤⣀⣾⣿⣿⣿⣷⣿⣿⣭⣭⣽⣿⣿⣷⣦⣾⣿⣿⣿⣿⣿⣽⣿⣶⣾⣿⣿⣿⣿⣿⣯⣿⣿⣯⣏⣤⣄⣸⣷⣧⣭⣍ ⢶⡆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠤⠶⠤⠤⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠀⠆ ⡦⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢤⢤⣤⣴⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⢦⠤⠀⠲⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢸⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠚⠒⠒⣲⡒⢖⡶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠷⠖⠛⠛⠓⠀⠀⠀⡀⠀⠀⠀⠀ ⡠⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣴⣿⣿⣷⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠿⣿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡏⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣻⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⠢⣄⣤⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣿⣤⣬⣤⣤ ⠘⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠸⣿⡿⡿⢿⡿⠠⣴⣿⣿⣿⣿⣿⣗⣿⣿⣦⣤⣤⣶⣤⣾⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡉⢉⠉⠉⣟⢩⣽⣽⣫ ⠈⠛⠛⠓⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠀⠈⠁⣶⠉⠀⠀⠀⢀⣀⠘⣡⣷⣽⣧⣴⣿⣿⣿⣿⢀⣒⣒⣒⡀⠀⣂⣙⣛⠋⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠘⠛⠃⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⢈⣋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠠⠠⠥⠬⠼⠥⠤⠤⢽⣧⡮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠢⠶⠶⡶⠶⠆⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠛⣀⣁⣀⡄⠣⠤⠌⠿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠒⠒⠒⠂⠀⢢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣾⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⣀⣈⠉⠙⠁⢀⣒⡶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿ ⠈⠛⠛⠃⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠛⠛⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠘⠛⢋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿ ⠰⡶⡾⠃⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⡖⠶⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢀⣀⣀⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⡆⠀⠀⠀⠁⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⠞⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠊⠉⠉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡶⠒⠆⠆⠂⢸⡀⠀⠀⣀⣀⡻⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⢿⡿⣿⣿⣿⣿⣿⣷⢿⡷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠋⠙⠁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣤⠀⢸⢶⣾⡳⣿⣿⡆⣸⢿⣿⣿⣽⣾⣷⣖⠒⢖⣲⠒⡟⢓⣶⣿⠻⣚⢾⣾⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠄⣷⣶⡷⠶⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠮⠙⠛⠺⠉⠹⠁⢺⠊⠋⠉⠙⠻⢽⣿⣍⠉⠋⢉⡯⡿⠋⠉⠋⠉⢹⢻⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⢿⣿⣿⣿⣿⣿ ⡈⠛⠛⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠐⢘⢀⢀⡀⣀⣀⣩⣿⣿⣷⣴⣿⣛⣁⣀⣀⣀⣀⣼⣸⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣷⡂⠐⠍⠉⣉⠉⢹ ⠨⣿⡏⠉⠉⠸⠇⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⣾⣶⣖⡆⢸⢠⣴⣶⣶⣶⣶⣦⣀⣠⡶⣬⣭⣤⣀⣾⣿⣿⣿⣷⣿⣿⣭⣭⣽⣿⣿⣷⣦⣾⣿⣿⣿⣿⣿⣽⣿⣶⣾⣿⣿⣿⣿⣿⣯⣿⣿⣯⣏⣤⣄⣸⣷⣧⣭⣍ ⢶⡆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠤⠶⠤⠤⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠀⠆ ⡦⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢤⢤⣤⣴⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⢦⠤⠀⠲⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢸⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠚⠒⠒⣲⡒⢖⡶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠷⠖⠛⠛⠓⠀⠀⠀⡀⠀⠀⠀⠀ ⡠⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣴⣿⣿⣷⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠿⣿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡏⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣻⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⠢⣄⣤⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣿⣤⣬⣤⣤ ⠘⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠸⣿⡿⡿⢿⡿⠠⣴⣿⣿⣿⣿⣿⣗⣿⣿⣦⣤⣤⣶⣤⣾⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡉⢉⠉⠉⣟⢩⣽⣽⣫ ⠈⠛⠛⠓⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠀⠈⠁⣶⠉⠀⠀⠀⢀⣀⠘⣡⣷⣽⣧⣴⣿⣿⣿⣿⢀⣒⣒⣒⡀⠀⣂⣙⣛⠋⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠘⠛⠃⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⢈⣋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠠⠠⠥⠬⠼⠥⠤⠤⢽⣧⡮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠢⠶⠶⡶⠶⠆⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠛⣀⣁⣀⡄⠣⠤⠌⠿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠒⠒⠒⠂⠀⢢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣾⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⣀⣈⠉⠙⠁⢀⣒⡶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿ ⠈⠛⠛⠃⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠛⠛⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠘⠛⢋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿ ⠰⡶⡾⠃⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⡖⠶⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢀⣀⣀⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⡆⠀⠀⠀⠁⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⠞⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠊⠉⠉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡶⠒⠆⠆⠂⢸⡀⠀⠀⣀⣀⡻⠿⠹⡿⠿⠿⠿⠿⠿⢿⣿⢿⡿⣿⣿⣿⣿⣿⣷⢿⡷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠋⠙⠁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣤⠀⢸⢶⣾⡳⣿⣿⡆⣸⢿⣿⣿⣽⣾⣷⣖⠒⢖⣲⠒⡟⢓⣶⣿⠻⣚⢾⣾⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠄⣷⣶⡷⠶⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠮⠙⠛⠺⠉⠹⠁⢺⠊⠋⠉⠙⠻⢽⣿⡍⠉⠋⢉⡯⡿⠋⠉⠋⠉⢹⢻⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⢿⣿⣿⣿⣿⣿ ⡈⠛⠛⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠐⢘⢀⢀⡀⣀⣀⣩⣿⣷⣷⣴⣿⣛⣁⣀⣀⣀⣀⣼⣸⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣷⡂⠐⠍⠉⣉⠉⢹ ⠨⣿⡏⠉⠉⠸⠇⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⣾⣶⣖⡆⢸⢠⣴⣶⣶⣶⣶⣦⣀⣠⡶⣬⣭⣤⣀⣾⣿⣿⣿⣷⣿⣿⣭⣭⣽⣿⣿⣷⣦⣾⣿⣿⣿⣿⣿⣽⣿⣶⣾⣿⣿⣿⣿⣿⣯⣿⣿⣯⣏⣤⣄⣸⣷⣧⣭⣍ ⢶⡆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠤⠶⠤⠤⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠀⠆ ⡦⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢤⢤⣤⣴⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⢦⠤⠀⠲⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢸⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠚⠒⠒⣲⡒⢖⡶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠷⠖⠛⠛⠓⠀⠀⠀⡀⠀⠀⠀⠀ ⡠⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣴⣿⣿⣷⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠿⣿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡏⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣻⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⠢⣄⣤⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣿⣤⣬⣤⣤ ⠘⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠸⣿⡿⡿⢿⡿⠠⣴⣿⣿⣿⣿⣿⣗⣿⣿⣦⣤⣤⣶⣤⣾⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡉⢉⠉⠉⣟⢩⣽⣽⣫ ⠈⠛⠛⠓⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠀⠈⠁⣶⠉⠀⠀⠀⢀⣀⠘⣡⣷⣽⣧⣴⣿⣿⣿⣿⢀⣒⣒⣒⡀⠀⣂⣙⣛⠋⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠘⠛⠃⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⢈⣋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠠⠠⠥⠬⠼⠥⠤⠤⢽⣧⡮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠢⠶⠶⡶⠶⠆⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠛⣀⣁⣀⡄⠣⠤⠌⠿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠒⠒⠒⠂⠀⢢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣾⣿⣯⣬⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⣀⣈⠉⠙⠁⢀⣒⡶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿ ⠈⠛⠛⠃⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠛⠛⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠘⠛⢋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿ ⠰⡶⡾⠃⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⡖⠶⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢀⣀⣀⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⡆⠀⠀⠀⠁⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⠞⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠊⠉⠉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡶⠒⠆⠆⠂⢸⡀⠀⠀⣀⣀⡻⠿⠹⡿⠿⠿⠿⠿⠿⢿⣿⢿⡿⣿⣿⣿⣿⣿⣷⢿⡷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠋⠙⠁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣤⠀⢸⢶⣾⡳⣿⣿⡆⣸⢿⣿⣿⣽⣾⣷⣖⠒⢖⣲⠒⡟⢓⣶⣿⠻⣚⢾⣾⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠄⣷⣶⡷⠶⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠮⠙⠛⠺⠉⠹⠁⢺⠊⠋⠉⠙⠻⢽⣿⡍⠉⠋⢉⡯⡿⠋⠉⠋⠉⢹⢻⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⢿⣿⣿⣿⣿⣿ ⡈⠛⠛⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠐⢘⢀⢀⡀⣀⣀⣩⣿⣷⣷⣴⣿⣛⣁⣀⣀⣀⣀⣼⣸⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣷⡂⠐⠍⠉⣉⠉⢹ ⠨⣿⡏⠉⠉⠸⠇⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⣾⣶⣖⡆⢸⢠⣴⣶⣶⣶⣶⣦⣀⣠⡶⣬⣭⣤⣀⣾⣿⣿⣿⣷⣿⣿⣭⣭⣽⣿⣿⣷⣦⣾⣿⣿⣿⣿⣿⣽⣿⣶⣾⣿⣿⣿⣿⣿⣯⣿⣿⣯⣏⣤⣄⣸⣷⣧⣭⣍ ⢶⡆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠤⠶⠤⠤⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠀⠆ ⡦⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢤⢤⣤⣴⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⢦⠤⠀⠲⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢸⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠚⠒⠒⣲⡒⢖⡶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠷⠖⠛⠛⠓⠀⠀⠀⡀⠀⠀⠀⠀ ⡠⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣴⣿⣿⣷⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠿⣿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡏⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣻⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⠢⣄⣤⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣿⣤⣬⣤⣤ ⠘⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠸⣿⡿⡿⢿⡿⠠⣴⣿⣿⣿⣿⣿⣗⣿⣿⣦⣤⣤⣶⣤⣾⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡉⢉⠉⠉⣟⢩⣽⣽⣫ ⠈⠛⠛⠓⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠀⠈⠁⣶⠉⠀⠀⠀⢀⣀⠘⣡⣷⣽⣧⣴⣿⣿⣿⣿⢀⣒⣒⣒⡀⠀⣂⣙⣛⠋⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠘⠛⠃⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠂⢈⣋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠠⠠⠥⠬⠼⠥⠤⠤⢽⣧⡮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠢⠶⠶⡶⠶⠆⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠛⣀⣁⣀⡄⠣⠤⠌⠿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠒⠒⠒⠂⠀⢢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣾⣿⣯⣬⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⣀⣈⠉⠙⠁⢀⣒⡶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿ ⠈⠛⠛⠃⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠛⠛⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠘⠛⢋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿ ⠰⡶⡾⠃⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⡖⠶⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢀⣀⣀⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⡆⠀⠀⠀⠁⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⠞⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠊⠉⠉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡶⠒⠆⠆⠂⢸⡀⠀⠀⣀⣀⡻⠿⠹⡿⠿⠿⠿⠿⠿⢿⣿⢿⡿⣿⣿⣿⣿⣿⣷⢿⡷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠋⠙⠁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣤⠀⢸⢶⣾⡳⣿⣿⡆⣸⢿⣿⣿⣽⣾⣷⣖⠒⢖⣲⠒⡟⢓⣶⣿⠻⣚⢾⣾⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠄⣷⣶⡷⠶⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠮⠙⠛⠺⠉⠹⠁⢺⠊⠋⠉⠙⠻⢽⣿⡍⠉⠋⢉⡯⡿⠋⠉⠋⠉⢹⢻⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⢿⣿⣿⣿⣿⣿ ⡈⠛⠛⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠐⢘⢀⢀⡀⣀⣀⣩⣿⣷⣷⣴⣿⣛⣁⣀⣀⣀⣀⣼⣸⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣷⡂⠐⠍⠉⣉⠉⢹ ⠨⣿⡏⠉⠉⠸⠇⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⣾⣶⣖⡆⢸⢠⣴⣶⣶⣶⣶⣦⣀⣠⡶⣬⣭⣤⣀⣾⣿⣿⣿⣷⣿⣿⣭⣭⣽⣿⣿⣷⣦⣾⣿⣿⣿⣿⣿⣽⣿⣶⣾⣿⣿⣿⣿⣿⣯⣿⣿⣯⣏⣤⣄⣸⣷⣧⣭⣍ ⢶⡆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠤⠶⠤⠤⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠀⠆ ⡦⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢤⢤⣤⣴⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠦⠤⠀⠲⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢰⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠒⠒⠀⣲⡒⢒⡶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣶⣶⣶⣶⠷⠒⠚⠛⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠠⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣴⣾⣿⣷⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡦⡄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣾⣿⣿⣿⠿⢿⠿⠿⡿⠿⣿⢿⣿⡿⡿⡿⠿⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣻⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⠿⢿⣿⣿⣿⠢⣄⣤⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣿⣤⣬⣤⣤ ⠘⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠘⣿⡿⡿⢻⡿⠠⣴⣿⣿⣿⣿⣿⣗⣾⣷⣦⣤⣤⣶⣤⣾⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣟⣞⠉⢁⠉⠉⣟⢩⣽⣽⣫ ⠈⠛⠛⠓⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠀⠈⠁⣦⠉⠀⠀⠀⢀⣀⠘⢡⣶⣼⣧⣴⣿⣿⣿⣿⠀⣒⣒⣒⡀⠀⣂⢙⣛⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠘⠛⠃⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠂⢈⣉⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠠⠠⠥⠬⠸⠥⠤⠤⢼⣧⡮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣯⣿⣿⣿⣿⣿⣿⣿ ⠢⠶⠶⡶⠶⠆⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠛⣀⣀⣀⡄⠃⠤⠌⠿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠒⠒⠒⠂⠀⢢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣴⣿⣯⣬⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⢀⣈⠉⠙⠁⢀⣒⡶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣿⣿⣿⣿⣿⣿ ⠈⠛⠛⠃⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣶⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿ ⠀⠛⠛⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⠛⢉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣯⣿⣿ ⠠⠶⡾⠃⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⡖⠶⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽ ⢀⣀⣀⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⠞⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⠊⠉⠉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡴⠐⠆⠆⠂⢸⡀⠀⠀⣀⣀⡻⠿⠹⡿⠿⠿⠿⠿⠿⢿⣿⢿⡿⣿⣿⣿⣿⣿⣷⢿⡷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣻⣟⣿⣿⣿⣿⣿⣿⢿ ⠀⠉⠙⠁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣤⠀⢸⢶⣾⡳⣿⣟⠄⣸⢟⣿⣾⣝⣾⣷⣖⠒⢖⣲⠒⡟⢓⣴⣿⠻⣚⢾⣾⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣽⣽⣿⣿⣿⣿⣭⣽ ⠄⢷⣶⡷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠶⠮⠙⠛⠺⠉⠹⠁⢺⠊⠉⠉⠙⠻⠙⣿⡍⠉⠋⢉⡯⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⢿⢿⣿⣿⣿⣿ ⡈⠛⠛⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠐⢈⢀⢀⡀⣀⣀⣨⣘⣗⣷⣴⣿⣋⣁⣀⣀⣀⣀⣼⣸⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣷⡂⠐⠍⠉⣉⠉⢹ ⠨⣿⡏⠉⠉⠸⠇⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⣾⣶⣖⡆⢸⢠⣴⣶⣶⣶⣶⣦⣀⣠⡶⣬⣬⣄⣀⣺⣿⣿⣿⣷⣿⣿⣭⣭⣽⣿⣿⣷⣦⣾⣿⣿⣿⣿⣿⣽⣿⣶⣾⣿⣿⣿⣿⣿⣯⣿⣿⣯⣏⣠⣄⣸⣷⣧⣭⣍ ⢶⡆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠤⠶⠤⠤⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠀⠆ ⡦⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢤⢤⣤⣴⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠦⠤⠀⠲⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢰⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠒⠒⠀⣲⡒⢒⡶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣶⣶⣶⣶⠷⠒⠚⠛⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠠⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣴⣾⣿⣷⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡦⡄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣾⣿⣿⣿⠿⢿⠿⠿⡿⠿⣿⢿⣿⡿⡿⡿⠿⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣻⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⠿⢿⣿⣿⣿⠢⣄⣤⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣿⣤⣬⣤⣤ ⠘⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠘⣿⡿⡿⢻⡿⠠⣴⣿⣿⣿⣿⣿⣗⣾⣷⣦⣤⣤⣶⣤⣾⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣟⣞⠉⢁⠉⠉⣟⢩⣽⣽⣫ ⠈⠛⠛⠓⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠀⠈⠁⣦⠉⠀⠀⠀⢀⣀⠘⢡⣶⣼⣧⣴⣿⣿⣿⣿⠀⣒⣒⣒⡀⠀⣂⢙⣛⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠘⠛⠃⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠂⢈⣉⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠠⠠⠥⠬⠸⠥⠤⠤⢼⣧⡮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣯⣿⣿⣿⣿⣿⣿⣿ ⠢⠶⠶⡶⠶⠆⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠛⣀⣀⣀⡄⠃⠤⠌⠿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠒⠒⠒⠂⠀⢢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣴⣿⣯⣬⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⢀⣈⠉⠙⠁⢀⣒⡶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣿⣿⣿⣿⣿⣿ ⠈⠛⠛⠃⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣶⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿ ⠀⠛⠛⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⠛⢉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣯⣿⣿ ⠠⠶⡾⠃⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⡖⠶⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽ ⢀⣀⣀⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⠞⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⠊⠉⠉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡴⠐⠆⠆⠂⢸⡀⠀⠀⣀⣀⡻⠿⠹⡿⠿⠿⠿⠿⠿⢿⣿⢿⡿⣿⣿⣿⣿⣿⣷⢿⡷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣻⣟⣿⣿⣿⣿⣿⣿⢿ ⠀⠉⠙⠁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣤⠀⢸⢶⣾⡳⣿⣟⠄⣸⢟⣿⣾⣝⣾⣷⣖⠒⢖⣲⠒⡟⢓⣴⣿⠻⣚⢾⣾⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣽⣽⣿⣿⣿⣿⣭⣽ ⠄⢷⣶⡷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠶⠮⠙⠛⠺⠉⠹⠁⢺⠊⠉⠉⠙⠻⠙⣿⡍⠉⠋⢉⡯⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⢿⢿⣿⣿⣿⣿ ⡈⠛⠛⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠐⢈⢀⢀⡀⣀⣀⣨⣘⣗⣷⣴⣿⣋⣁⣀⣀⣀⣀⣼⣸⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣷⡂⠐⠍⠉⣉⠉⢹ ⠨⣿⡏⠉⠉⠸⠇⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⣾⣶⣖⡆⢸⢠⣴⣶⣶⣶⣶⣦⣀⣠⡶⣬⣬⣄⣀⣺⣿⣿⣿⣷⣿⣿⣭⣭⣽⣿⣿⣷⣦⣾⣿⣿⣿⣿⣿⣽⣿⣶⣾⣿⣿⣿⣿⣿⣯⣿⣿⣯⣏⣠⣄⣸⣷⣧⣭⣍ ⢶⡆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠤⠶⠤⠤⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠀⠆ ⡦⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢤⢤⣤⣴⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠦⠤⠀⠲⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢰⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠒⠒⠀⣲⡒⢒⡶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣶⣶⣶⣶⠷⠒⠚⠛⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠠⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣴⣾⣿⣷⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡦⡄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣾⣿⣿⣿⠿⢿⠿⠿⡿⠿⣿⢿⣿⡿⡿⡿⠿⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣻⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⠿⢿⣿⣿⣿⠢⣄⣤⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣿⣤⣬⣤⣤ ⠘⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠘⣿⡿⡿⢻⡿⠠⣴⣿⣿⣿⣿⣿⣗⣾⣷⣦⣤⣤⣶⣤⣾⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣟⣞⠉⢁⠉⠉⣟⢩⣽⣽⣫ ⠈⠛⠛⠓⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠀⠈⠁⣦⠉⠀⠀⠀⢀⣀⠘⢡⣶⣼⣧⣴⣿⣿⣿⣿⠀⣒⣒⣒⡀⠀⣂⢙⣛⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠘⠛⠃⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠂⢈⣉⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠠⠠⠥⠬⠸⠥⠤⠤⢼⣧⡮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣯⣿⣿⣿⣿⣿⣿⣿ ⠢⠶⠶⡶⠶⠆⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠛⣀⣀⣀⡄⠃⠤⠌⠿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠒⠒⠒⠂⠀⢢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣴⣿⣯⣬⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⢀⣈⠉⠙⠁⢀⣒⡶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣿⣿⣿⣿⣿⣿ ⠈⠛⠛⠃⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣶⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿ ⠀⠛⠛⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⠛⢉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣯⣿⣿ ⠠⠶⡾⠃⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⡖⠶⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽ ⢀⣀⣀⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⠞⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⠊⠉⠉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡴⠐⠆⠆⠂⢸⡀⠀⠀⣀⣀⡻⠿⠹⡿⠿⠿⠿⠿⠿⢿⣿⢿⡿⣿⣿⣿⣿⣿⣷⢿⡷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣻⣟⣿⣿⣿⣿⣿⣿⢿ ⠀⠉⠙⠁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣤⠀⢸⢶⣾⡳⣿⣟⠄⣸⢟⣿⣾⣝⣾⣷⣖⠒⢖⣲⠒⡟⢓⣴⣿⠻⣚⢾⣾⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣽⣽⣿⣿⣿⣿⣭⣽ ⠄⢷⣶⡷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠶⠮⠙⠛⠺⠉⠹⠁⢺⠊⠉⠉⠙⠻⠙⣿⡍⠉⠋⢉⡯⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⢿⢿⣿⣿⣿⣿ ⡈⠛⠛⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠐⢈⢀⢀⡀⣀⣀⣨⣘⣗⣷⣴⣿⣋⣁⣀⣀⣀⣀⣼⣸⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣷⡂⠐⠍⠉⣉⠉⢹ ⠨⣿⡏⠉⠉⠸⠇⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⣾⣶⣖⡆⢸⢠⣴⣶⣶⣶⣶⣦⣀⣠⡶⣬⣬⣄⣀⣺⣿⣿⣿⣷⣿⣿⣭⣭⣽⣿⣿⣷⣦⣾⣿⣿⣿⣿⣿⣽⣿⣶⣾⣿⣿⣿⣿⣿⣯⣿⣿⣯⣏⣠⣄⣸⣷⣧⣭⣍ ⢶⡆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠤⠶⠤⠤⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠀⠆ ⡦⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢤⢤⣤⣴⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠦⠤⠀⠲⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢰⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠒⠒⠀⣲⡒⢒⡶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣶⣶⣶⣶⠷⠒⠚⠛⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠠⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣴⣾⣿⣷⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡦⡄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣾⣿⣿⣿⠿⢿⠿⠿⡿⠿⣿⢿⣿⡿⡿⡿⠿⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣻⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⠿⢿⣿⣿⣿⠢⣄⣤⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣿⣤⣬⣤⣤ ⠘⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠘⣿⡿⡿⢻⡿⠠⣴⣿⣿⣿⣿⣿⣗⣾⣷⣦⣤⣤⣶⣤⣾⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣟⣞⠉⢁⠉⠉⣟⢩⣽⣽⣫ ⠈⠛⠛⠓⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠀⠈⠁⣦⠉⠀⠀⠀⢀⣀⠘⢡⣶⣼⣧⣴⣿⣿⣿⣿⠀⣒⣒⣒⡀⠀⣂⢙⣛⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠘⠛⠃⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠂⢈⣉⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠠⠠⠥⠬⠸⠥⠤⠤⢼⣧⡮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣯⣿⣿⣿⣿⣿⣿⣿ ⠢⠶⠶⡶⠶⠆⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠛⣀⣀⣀⡄⠃⠤⠌⠿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠒⠒⠒⠂⠀⢢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣴⣿⣯⣬⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⢀⣈⠉⠙⠁⢀⣒⡶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣿⣿⣿⣿⣿⣿ ⠈⠛⠛⠃⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣶⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿ ⠀⠛⠛⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⠛⢉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣯⣿⣿ ⠠⠶⡾⠃⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⡖⠶⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽ ⢀⣀⣀⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⠞⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⠊⠉⠉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡴⠐⠆⠆⠂⢸⡀⠀⠀⣀⣀⡻⠿⠹⡿⠿⠿⠿⠿⠿⢿⣿⢿⡿⣿⣿⣿⣿⣿⣷⢿⡷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣻⣟⣿⣿⣿⣿⣿⣿⢿ ⠀⠉⠙⠁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣤⠀⢸⢶⣾⡳⣿⣟⠄⣸⢟⣿⣾⣝⣾⣷⣖⠒⢖⣲⠒⡟⢓⣴⣿⠻⣚⢾⣾⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣽⣽⣿⣿⣿⣿⣭⣽ ⠄⢷⣶⡷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠶⠮⠙⠛⠺⠉⠹⠁⢺⠊⠉⠉⠙⠻⠙⣿⡍⠉⠋⢉⡯⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⢿⢿⣿⣿⣿⣿ ⡈⠛⠛⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠐⢈⢀⢀⡀⣀⣀⣨⣘⣗⣷⣴⣿⣋⣁⣀⣀⣀⣀⣼⣸⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣷⡂⠐⠍⠉⣉⠉⢹ ⠨⣿⡏⠉⠉⠸⠇⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⣾⣶⣖⡆⢸⢠⣴⣶⣶⣶⣶⣦⣀⣠⡶⣬⣬⣄⣀⣺⣿⣿⣿⣷⣿⣿⣭⣭⣽⣿⣿⣷⣦⣾⣿⣿⣿⣿⣿⣽⣿⣶⣾⣿⣿⣿⣿⣿⣯⣿⣿⣯⣏⣠⣄⣸⣷⣧⣭⣍ ⢶⡆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠤⠶⠤⠤⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠀⠆ ⡦⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢤⢤⣤⣴⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠦⠤⠀⠲⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢰⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠒⠒⠀⣲⡒⢒⡶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣶⣶⣶⣶⠷⠒⠚⠛⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠠⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣴⣾⣿⣷⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡦⡄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣾⣿⣿⣿⠿⢿⠿⠿⡿⠿⣿⢿⣿⡿⡿⡿⠿⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣻⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⠿⢿⣿⣿⣿⠢⣄⣤⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣿⣤⣬⣤⣤ ⠘⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠘⣿⡿⡿⢻⡿⠠⣴⣿⣿⣿⣿⣿⣗⣾⣷⣦⣤⣤⣶⣤⣾⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣟⣞⠉⢁⠉⠉⣟⢩⣽⣽⣫ ⠈⠛⠛⠓⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠀⠈⠁⣦⠉⠀⠀⠀⢀⣀⠘⢡⣶⣼⣧⣴⣿⣿⣿⣿⠀⣒⣒⣒⡀⠀⣂⢙⣛⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠘⠛⠃⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠂⢈⣉⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠠⠠⠥⠬⠸⠥⠤⠤⢼⣧⡮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣯⣿⣿⣿⣿⣿⣿⣿ ⠢⠶⠶⡶⠶⠆⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠛⣀⣀⣀⡄⠃⠤⠌⠿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠒⠒⠒⠂⠀⢢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣴⣿⣯⣬⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⢀⣈⠉⠙⠁⢀⣒⡶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣿⣿⣿⣿⣿⣿ ⠈⠛⠛⠃⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣶⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿ ⠀⠛⠛⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⠛⢉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣯⣿⣿ ⠠⠶⡾⠃⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⡖⠶⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽ ⢀⣀⣀⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⠞⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⠊⠉⠉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡴⠐⠆⠆⠂⢸⡀⠀⠀⣀⣀⡻⠿⠹⡿⠿⠿⠿⠿⠿⢿⣿⢿⡿⣿⣿⣿⣿⣿⣷⢿⡷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣻⣟⣿⣿⣿⣿⣿⣿⢿ ⠀⠉⠙⠁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣤⠀⢸⢶⣾⡳⣿⣟⠄⣸⢟⣿⣾⣝⣾⣷⣖⠒⢖⣲⠒⡟⢓⣴⣿⠻⣚⢾⣾⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣽⣽⣿⣿⣿⣿⣭⣽ ⠄⢷⣶⡷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠶⠮⠙⠛⠺⠉⠹⠁⢺⠊⠉⠉⠙⠻⠙⣿⡍⠉⠋⢉⡯⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⢿⢿⣿⣿⣿⣿ ⡈⠛⠛⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠐⢈⢀⢀⡀⣀⣀⣨⣘⣗⣷⣴⣿⣋⣁⣀⣀⣀⣀⣼⣸⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣷⡂⠐⠍⠉⣉⠉⢹ ⠨⣿⡏⠉⠉⠸⠇⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⣾⣶⣖⡆⢸⢠⣴⣶⣶⣶⣶⣦⣀⣠⡶⣬⣬⣄⣀⣺⣿⣿⣿⣷⣿⣿⣭⣭⣽⣿⣿⣷⣦⣾⣿⣿⣿⣿⣿⣽⣿⣶⣾⣿⣿⣿⣿⣿⣯⣿⣿⣯⣏⣠⣄⣸⣷⣧⣭⣍ ⢶⠆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠤⠶⠤⠤⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠀⠆ ⡤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢤⢤⣤⣴⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠦⠤⠀⠲⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢰⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠒⠒⠀⣲⡒⢒⡶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣶⣶⣶⣶⠷⠒⠚⠛⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠠⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣴⣾⣿⣷⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡤⡄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣾⣿⣿⣿⠿⢿⠿⠿⡿⠿⣿⢿⣿⡿⡿⡿⠿⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣻⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⢟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⠿⢿⣿⣿⣿⠢⣄⣤⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣿⣤⣬⣤⣤ ⠘⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠘⣿⡿⡿⢻⡿⠠⣴⣿⣿⣿⣿⣿⣗⣾⣷⣦⣤⣤⣶⣤⣾⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣶⣟⣞⠈⢁⠉⠉⣟⢩⣽⣽⣫ ⠈⠛⠛⠓⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠀⠈⠁⣦⠉⠀⠀⠀⢀⣀⠘⢡⣶⣼⣧⣴⣿⣿⣿⣿⠀⣒⣒⣒⡀⠀⣂⢙⣛⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠘⠛⠃⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠂⢈⣉⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠠⠠⠥⠬⠸⠥⠤⠤⢼⣧⡮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣯⣿⣿⣿⣿⣿⣿⣿ ⠢⠶⠶⠶⠶⠆⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠛⣀⣀⣀⡄⠃⠤⠌⠿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠒⠒⠒⠂⠀⢢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣴⣿⣯⣬⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⢀⣈⠉⠙⠁⢀⣒⡶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣿⣿⣿⣿⣿⣿ ⠈⠛⠛⠃⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣶⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿ ⠀⠛⠛⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⠛⢉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣯⣿⣿⣯⣿⣿ ⠠⠶⡾⠃⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⡖⠶⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽ ⢀⣀⣀⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⠞⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⠊⠉⠉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡴⠐⠆⠆⠂⢸⡀⠀⠀⣀⣀⡻⠿⠹⡿⠿⠿⠿⠿⠿⢿⣿⢿⡿⣿⣿⣿⣿⣿⣷⢿⡷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣻⣟⣿⣿⣿⣿⣿⣿⢿ ⠀⠉⠙⠁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣤⠀⢸⢶⣾⡳⣿⣟⠄⣸⢟⣿⣾⣝⣾⣷⣖⠒⢖⣲⠒⡟⢓⣴⣿⠻⣚⢾⣾⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣽⣽⣿⣿⣿⣿⣭⣽ ⠄⢷⣶⡷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠶⠮⠙⠛⠺⠉⠹⠁⢺⠊⠉⠉⠙⠻⠙⣿⡍⠉⠋⢉⡯⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⢿⢿⣿⣿⣿⣿ ⡈⠛⠛⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠐⢈⢀⢀⡀⣀⣀⣨⣘⣗⣷⣴⣿⣋⣁⣀⣀⣀⣀⣼⣸⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣷⡂⠐⠍⠉⣉⠉⢹ ⠨⣿⡏⠉⠉⠸⠇⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⣾⣶⣖⡆⢸⢠⣴⣶⣶⣶⣶⣦⣀⣠⡶⣬⣬⣄⣀⣺⣿⣿⣿⣷⣿⣿⣭⣭⣽⣿⣿⣷⣦⣾⣿⣿⣿⣿⣿⣽⣿⣶⣾⣿⣿⣿⣿⣿⣯⣿⣿⣯⣏⣠⣄⣸⣷⣧⣭⣍ ⢶⠆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠤⠶⠤⠤⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠀⠆ ⡤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢤⢤⣤⣴⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠦⠤⠀⠲⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢰⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠒⠒⠀⣲⡒⢒⡶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣶⣶⣶⣶⠷⠒⠚⠛⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠠⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣴⣾⣿⣷⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡤⡄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣾⣿⣿⣿⠿⢿⠿⠿⡿⠿⣿⢿⣿⡿⡿⡿⠿⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣻⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⢟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⠿⢿⣿⣿⣿⠢⣄⣤⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣿⣤⣬⣤⣤ ⠘⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠘⣿⡿⡿⢻⡿⠠⣴⣿⣿⣿⣿⣿⣗⣾⣷⣦⣤⣤⣶⣤⣾⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣶⣟⣞⠈⢁⠉⠉⣟⢩⣽⣽⣫ ⠈⠛⠛⠓⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠀⠈⠁⣦⠉⠀⠀⠀⢀⣀⠘⢡⣶⣼⣧⣴⣿⣿⣿⣿⠀⣒⣒⣒⡀⠀⣂⢙⣛⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠘⠛⠃⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠂⢈⣉⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠠⠠⠥⠬⠸⠥⠤⠤⢼⣧⡮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣯⣿⣿⣿⣿⣿⣿⣿ ⠢⠶⠶⠶⠶⠆⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠛⣀⣀⣀⡄⠃⠤⠌⠿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠒⠒⠒⠂⠀⢢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣴⣿⣯⣬⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⢀⣈⠉⠙⠁⢀⣒⡶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣿⣿⣿⣿⣿⣿ ⠈⠛⠛⠃⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣶⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿ ⠀⠛⠛⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⠛⢉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣯⣿⣿⣯⣿⣿ ⠠⠶⡾⠃⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⡖⠶⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽ ⢀⣀⣀⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⠞⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⠊⠉⠉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡴⠐⠆⠆⠂⢸⡀⠀⠀⣀⣀⡻⠿⠹⡿⠿⠿⠿⠿⠿⢿⣿⢿⡿⣿⣿⣿⣿⣿⣷⢿⡷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣻⣟⣿⣿⣿⣿⣿⣿⢿ ⠀⠉⠙⠁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣤⠀⢸⢶⣾⡳⣿⣟⠄⣸⢟⣿⣾⣝⣾⣷⣖⠒⢖⣲⠒⡟⢓⣴⣿⠻⣚⢾⣾⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣽⣽⣿⣿⣿⣿⣭⣽ ⠄⢷⣶⡷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠶⠮⠙⠛⠺⠉⠹⠁⢺⠊⠉⠉⠙⠻⠙⣿⡍⠉⠋⢉⡯⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⢿⢿⣿⣿⣿⣿ ⡈⠛⠛⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠐⢈⢀⢀⡀⣀⣀⣨⣘⣗⣷⣴⣿⣋⣁⣀⣀⣀⣀⣼⣸⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣷⡂⠐⠍⠉⣉⠉⢹ ⠨⣿⡏⠉⠉⠸⠇⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⣾⣶⣖⡆⢸⢠⣴⣶⣶⣶⣶⣦⣀⣠⡶⣬⣬⣄⣀⣺⣿⣿⣿⣷⣿⣿⣭⣭⣽⣿⣿⣷⣦⣾⣿⣿⣿⣿⣿⣽⣿⣶⣾⣿⣿⣿⣿⣿⣯⣿⣿⣯⣏⣠⣄⣸⣷⣧⣭⣍ ⢶⠆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠤⠶⠤⠤⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠀⠆ ⡤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢤⢤⣤⣴⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠦⠤⠀⠲⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢰⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠒⠒⠀⣲⡒⢒⡶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣶⣶⣶⣶⠷⠒⠚⠛⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠠⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣴⣾⣿⣷⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡤⡄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣾⣿⣿⣿⠿⢿⠿⠿⡿⠿⣿⢿⣿⡿⡿⡿⠿⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣻⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⢟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⠿⢿⣿⣿⣿⠢⣄⣤⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣿⣤⣬⣤⣤ ⠘⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠘⣿⡿⡿⢻⡿⠠⣴⣿⣿⣿⣿⣿⣗⣾⣷⣦⣤⣤⣶⣤⣾⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣶⣟⣞⠈⢁⠉⠉⣟⢩⣽⣽⣫ ⠈⠛⠛⠓⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠀⠈⠁⣦⠉⠀⠀⠀⢀⣀⠘⢡⣶⣼⣧⣴⣿⣿⣿⣿⠀⣒⣒⣒⡀⠀⣂⢙⣛⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠘⠛⠃⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠂⢈⣉⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠠⠠⠥⠬⠸⠥⠤⠤⢼⣧⡮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣯⣿⣿⣿⣿⣿⣿⣿ ⠢⠶⠶⠶⠶⠆⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠛⣀⣀⣀⡄⠃⠤⠌⠿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠒⠒⠒⠂⠀⢢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣴⣿⣯⣬⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⢀⣈⠉⠙⠁⢀⣒⡶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣿⣿⣿⣿⣿⣿ ⠈⠛⠛⠃⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣶⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿ ⠀⠛⠛⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⠛⢉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣯⣿⣿⣯⣿⣿ ⠠⠶⡾⠃⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⡖⠶⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽ ⢀⣀⣀⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⠞⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⠊⠉⠉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡴⠐⠆⠆⠂⢸⡀⠀⠀⣀⣀⡻⠿⠹⡿⠿⠿⠿⠿⠿⢿⣿⢿⡿⣿⣿⣿⣿⣿⣷⢿⡷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣻⣟⣿⣿⣿⣿⣿⣿⢿ ⠀⠉⠙⠁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣤⠀⢸⢶⣾⡳⣿⣟⠄⣸⢟⣿⣾⣝⣾⣷⣖⠒⢖⣲⠒⡟⢓⣴⣿⠻⣚⢾⣾⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣽⣽⣿⣿⣿⣿⣭⣽ ⠄⢷⣶⡷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠶⠮⠙⠛⠺⠉⠹⠁⢺⠊⠉⠉⠙⠻⠙⣿⡍⠉⠋⢉⡯⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⢿⢿⣿⣿⣿⣿ ⡈⠛⠛⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠐⢈⢀⢀⡀⣀⣀⣨⣘⣗⣷⣴⣿⣋⣁⣀⣀⣀⣀⣼⣸⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣷⡂⠐⠍⠉⣉⠉⢹ ⠨⣿⡏⠉⠉⠸⠇⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⣾⣶⣖⡆⢸⢠⣴⣶⣶⣶⣶⣦⣀⣠⡶⣬⣬⣄⣀⣺⣿⣿⣿⣷⣿⣿⣭⣭⣽⣿⣿⣷⣦⣾⣿⣿⣿⣿⣿⣽⣿⣶⣾⣿⣿⣿⣿⣿⣯⣿⣿⣯⣏⣠⣄⣸⣷⣧⣭⣍ ⢶⠆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠤⠶⠤⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠀⠆ ⡤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⢤⣤⣴⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠦⠤⠀⠲⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢐⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠒⠒⠀⣠⡐⢀⡶⠲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣴⣶⣶⣶⠷⠒⠓⠛⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣴⣾⣿⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠤⡄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⡸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣾⣿⣿⣿⠿⠿⠿⠿⠿⠿⣿⣿⣿⡿⠿⡻⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⠅⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣻⡿⡛⣯⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⣿⢟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠿⣿⣿⣿⣿⠢⣄⣭⠐⠋⣭⣭⣭⣭⣭⣭⣭⣿⣿⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣿⣤⣤⣤⣤ ⠈⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠘⣿⡿⡿⢻⡿⠠⣼⣿⣿⣿⣷⣿⣗⣾⣷⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣾⣿⣶⡕⣞⠈⠀⠉⠉⣗⠩⠽⣭⣫ ⠈⠛⠛⠓⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠀⠈⠁⣦⠉⠀⠀⠀⢀⣀⠈⢡⣦⣼⣧⣴⣾⣿⣿⣿⣀⢒⣒⣲⣿⣿⣖⣙⣛⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣻⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿ ⠘⡛⡃⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠂⢈⡉⢁⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠁⠠⠤⠴⢻⠥⠁⠤⢬⣡⡮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢿⣯⢿⣟⣿⣿⣟⣿⣟ ⠠⠶⠶⠶⠶⠆⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠛⣀⣄⣀⠄⠃⠤⠈⠻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿ ⠀⠒⠒⠒⠂⠀⢢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣴⣿⣯⣬⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⠀⣈⣍⠙⠁⢀⣐⡲⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣧⣿⣿⣿⣿⣿⣧ ⠘⠛⠛⠃⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣶⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣽⣿⣿⣿⣿⣽⠷ ⠀⠛⠛⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣯⣽⣿⣯⡿⣿ ⠠⠶⡾⠃⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⣿⣿⣿⣽⣿⣿⣹⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠖⠶⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣭ ⢀⣀⣀⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⠎⣛⣻⣿⣿⣿⣻⣟⣟⣿⣿⣿⣿⢛⣟⣛⣿⣟⣻⢿⣿⣿⣻⢿⢿⣿⣿⣿⣿⣿⢷ ⠈⠉⠉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡴⠐⠆⠆⠂⢸⡀⠀⠀⣀⣀⡻⠿⠹⡿⠟⠿⠿⠿⠿⢿⠿⢿⠿⢿⣿⣿⢿⣿⡿⢿⠿⢿⡿⢿⠿⣿⣿⣿⡿⣿⣿⣿⣺⣿⣿⣿⣿⢿⣷⢿⣷⣻⣜⣶⣿⣿⣿⣿⣿⢿ ⠀⠉⠉⠁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣤⠀⢸⢶⣾⠳⣿⣟⠄⣸⢛⣯⣾⣝⣾⣷⣖⠒⢖⣲⠒⡟⢓⣴⣿⠻⣚⢾⣾⣿⢿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣽⣿⣿⣿⣿⣯⣹ ⠄⢷⣶⡷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠶⠮⠙⠛⠻⠉⠹⠁⢺⠊⠉⠉⠙⠫⠉⣻⡍⠉⠋⢉⡯⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣷⣾⣿⣿⣿⣾⣟⣟⣿⣿⠟⢻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣛⠿⢿⢿⢿⣿⣿⣿⣿ ⡈⠛⠛⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠐⢈⢀⢀⡀⣀⣀⣨⣈⣗⣷⣴⣿⣋⣀⣀⣀⣀⣀⣼⣸⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣷⡂⠐⠍⠉⣉⠉⢹ ⠨⣿⡏⠉⠉⠸⠇⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⣦⣶⣖⡆⢸⢠⣴⣶⣶⣶⣶⣦⣀⣠⡶⣤⣤⣄⣀⣺⣿⣿⣿⣿⣿⣿⣭⣭⣽⣿⣿⣷⡦⣾⣿⣿⣿⣿⣿⣽⣿⣶⣾⣿⣿⣿⣿⣿⣯⣿⣿⣏⣏⣠⣄⣸⣷⣧⣭⣍ ⢶⠆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠤⠶⠤⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠀⠆ ⡤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⢤⣤⣴⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠦⠤⠀⠲⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢐⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠒⠒⠀⣰⡐⢒⡶⠲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣶⣴⣶⣶⣶⣶⠷⠒⠓⠛⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣴⣾⣿⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡤⡄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⡸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣾⣿⣿⣿⠿⠿⠿⠿⡿⠿⣿⣿⣿⡿⠿⡿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⠅⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣻⡿⡛⣯⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⣿⢟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠿⣿⣿⣿⣿⠢⣄⣭⠐⠋⣭⣭⣭⣭⣭⣭⣭⣿⣿⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣿⣤⣤⣤⣤ ⠈⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠘⣿⡿⡿⢻⡿⠠⣼⣿⣿⣿⣷⣿⣗⣾⣷⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣶⣟⣞⠈⢁⠉⠉⣗⠩⢽⣽⣫ ⠈⠛⠛⠓⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠀⠈⠁⣦⠉⠀⠀⠀⢀⣀⠘⢡⣦⣼⣧⣴⣾⣿⣿⣿⣀⢒⣒⣲⣿⣿⣖⣙⣛⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠘⡛⡃⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠂⢈⡉⣁⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠁⠠⠤⠴⢻⠥⠁⠤⢬⣡⡮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢿⣯⣿⣿⣿⣿⣟⣿⣟ ⠠⠶⠶⠶⠶⠆⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠛⣀⣄⣀⠄⠃⠤⠌⠻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿ ⠀⠒⠒⠒⠂⠀⢢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣴⣿⣯⣬⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⠀⣈⣍⠙⠁⢀⣐⡲⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣿⣿⣿⣿⣿⣧ ⠘⠛⠛⠃⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣶⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⢿ ⠀⠛⠛⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣯⣿⣿⣯⡿⣿ ⠠⠶⡾⠃⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⣿⣿⣿⣽⣿⣿⣽⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠖⠶⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽ ⢀⣀⣀⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⠞⣛⣻⣿⣿⣿⣻⣿⣟⣿⣿⣿⣿⣛⣟⣛⣿⣟⣻⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣷ ⠊⠉⠉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡴⠐⠆⠂⠂⢸⡀⠀⠀⣀⣀⡻⠿⠹⡿⠟⠿⠿⠿⠿⢿⠿⢿⠿⢿⣿⣿⢿⣿⡿⢿⠿⢿⡿⢿⠿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⣷⣻⣜⣾⣿⣿⣿⣿⣿⢿ ⠀⠉⠉⠁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣤⠀⢸⢶⣾⠳⣿⣞⠄⣸⢛⣿⣾⣝⣾⣷⣖⠒⢖⣲⠒⡟⢓⣴⣿⠻⣚⢾⣾⣿⢿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣽⣿⣿⣿⣿⣯⣽ ⠄⢷⣶⡷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠶⠮⠙⠛⠻⠉⠹⠁⢺⠊⠉⠉⠙⠫⠉⣻⡍⠉⠋⢉⡯⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣷⣾⣿⣿⣿⣾⣿⣿⣿⣿⠟⢻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⠿⢿⢿⢿⣿⣿⣿⣿ ⡈⠛⠛⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠐⢈⢀⢀⡀⣀⣀⣨⣈⣗⣷⣴⣿⣋⣀⣀⣀⣀⣀⣼⣸⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣷⡂⠐⠍⠉⣉⠉⢹ ⠨⣿⡏⠉⠉⠸⠇⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⣦⣶⣖⡆⢸⢠⣴⣶⣶⣶⣶⣦⣀⣠⡶⣤⣤⣄⣀⣺⣿⣿⣿⣿⣿⣿⣭⣭⣽⣿⣿⣷⣦⣾⣿⣿⣿⣿⣿⣽⣿⣶⣾⣿⣿⣿⣿⣿⣯⣿⣿⣏⣏⣠⣄⣸⣷⣧⣭⣍ ⢶⠆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠤⠶⠤⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠀⠆ ⡤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⢤⣤⣴⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠦⠤⠀⠲⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢐⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠒⠒⠀⣰⡐⢒⡶⠲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣶⣴⣶⣶⣶⣶⢷⡒⠓⠛⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣴⣾⣿⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡥⡄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⡸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣾⣿⣿⣿⠿⠿⠿⠿⡿⠿⣿⣿⣿⡿⠿⡿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⠅⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣻⡿⡛⣯⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⣿⢟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠿⣿⣿⣿⣿⠢⣄⣭⠐⠋⣭⣭⣭⣭⣭⣭⣭⣿⣿⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣿⣤⣤⣤⣤ ⠈⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠘⣿⡿⡿⢻⡿⠠⣼⣿⣿⣿⣷⣿⣗⣾⣷⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣶⣟⣞⠈⢁⠉⠉⣗⠩⢽⣽⣫ ⠈⠛⠛⠓⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠀⠈⠁⣆⠉⠀⠀⠀⢀⣀⠘⢡⣦⣼⣧⣴⣾⣿⣿⣿⣀⢒⣒⣲⣿⣿⣖⣙⣛⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠘⡛⡃⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠂⢈⡉⣁⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠁⠠⠤⠴⢻⠥⠁⠤⢬⣡⡮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢿⣯⣿⣿⣿⣿⣟⣿⣟ ⠠⠶⠶⠶⠶⠆⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠛⣀⣄⣀⠄⠃⠤⠌⠻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿ ⠀⠒⠒⠒⠂⠀⢢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣴⣿⣯⣬⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⠀⣈⣍⠙⠁⢀⣐⡲⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣿⣿⣿⣿⣿⣧ ⠘⠛⠛⠃⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣶⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⢿ ⠀⠛⠛⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣯⣿⣿⣯⡿⣿ ⠠⠶⡾⠃⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⣿⣿⣿⣽⣿⣿⣽⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠖⠶⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽ ⢀⣀⣀⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⠞⣛⣻⣿⣿⣿⣻⣿⣟⣿⣿⣿⣿⣛⣟⣛⣿⣟⣻⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣷ ⠊⠉⠉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡴⠐⠆⠂⠂⢸⡀⠀⠀⣀⣀⡻⠿⠹⡿⠟⠿⠿⠿⠿⢿⠿⢿⠿⢿⣿⣿⢿⣿⡿⢿⠿⢿⡿⢿⠿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⣷⣻⣜⣾⣿⣿⣿⣿⣿⢿ ⠀⠉⠉⠁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣤⠀⢸⢶⣾⠳⣿⣞⠄⣸⢛⣿⣾⣝⣾⣷⣖⠒⢖⣲⠒⡟⢓⣴⣿⠻⣚⢾⣾⣿⢿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣽⣿⣿⣿⣿⣯⣽ ⠄⢷⣶⡷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠶⠮⠙⠛⠻⠉⠹⠁⢪⠊⠉⠉⠙⠫⠉⣻⡍⠉⠋⢉⡯⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣷⣾⣿⣿⣿⣾⣿⣿⣿⣿⠟⢻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⠿⢿⢿⢿⣿⣿⣿⣿ ⡈⠛⠛⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠐⠈⢀⢀⡀⣀⣀⣨⣈⣗⣷⣴⣿⣋⣀⣀⣀⣀⣀⣼⣸⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣷⡂⠐⠍⠉⣉⠉⢹ ⠨⣿⡏⠉⠉⠸⠇⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⣦⣶⣖⡆⢰⢠⣴⣶⣶⣶⣶⣦⣀⣠⡶⣤⣤⣄⣀⣺⣿⣿⣿⣿⣿⣿⣭⣭⣽⣿⣿⣷⣦⣾⣿⣿⣿⣿⣿⣽⣿⣶⣾⣿⣿⣿⣿⣿⣯⣿⣿⣏⣏⣠⣄⣸⣷⣧⣭⣍ ⢶⠆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠤⠶⠤⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠀⠆ ⡤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⢤⣤⣴⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠦⠤⠀⠲⠠⠤⡠⠀⠀⠀⠀⠀⠀⠀⢐⠈⠉⠉⠉⠀⠀⠀⠀⠐⠒⠒⠒⠒⠀⣰⡐⢒⡶⠲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣶⣴⣶⣶⣶⣶⢷⡒⠓⠛⠒⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣴⣾⣿⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡥⡄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⡸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣾⣿⣿⣿⠿⠿⠿⠿⡿⠿⣿⣿⣿⡿⠿⡿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⠅⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠘⣻⡿⡛⣯⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⣿⢟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠿⣿⣿⣿⣿⠢⣄⣭⠐⠋⣭⣭⣭⣭⣭⣭⣭⣿⣿⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣿⣤⣤⣤⣤ ⠈⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣇⠀⢀⡀⠀⣀⠀⠀⠀⠀⠘⣿⡿⡿⢻⡿⠠⣼⣿⣿⣿⣷⣿⣗⣾⣷⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣶⣟⣞⠈⢁⠉⠉⣗⠩⢽⣽⣫ ⠈⠛⠛⠓⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠉⠀⠈⠁⣆⠉⠀⠀⠀⢀⣀⠘⢡⣦⣼⣧⣴⣾⣿⣿⣿⣀⢒⣒⣲⣿⣿⣖⣙⣛⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠘⡛⡃⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠂⢈⡉⣁⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠁⠠⠤⠴⢻⠥⠁⠤⢬⣡⡮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢿⣯⣿⣿⣿⣿⣟⣿⣟ ⠠⠶⠶⠶⠶⠆⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠛⣀⣄⣀⠄⠃⠤⠌⠻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿ ⠀⠒⠒⠒⠂⠀⢢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣴⣿⣯⣬⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⠀⣈⣍⠙⠁⢀⣐⡲⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣿⣿⣿⣿⣿⣧ ⠘⠛⠛⠃⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣶⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⢿ ⠀⠛⠛⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣯⣿⣿⣯⡿⣿ ⠠⠶⡾⠃⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⣿⣿⣿⣽⣿⣿⣽⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠖⠶⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽ ⢀⣀⣀⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⠞⣛⣻⣿⣿⣿⣻⣿⣟⣿⣿⣿⣿⣛⣟⣛⣿⣟⣻⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣷ ⠊⠉⠉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡴⠐⠆⠂⠂⢸⡀⠀⠀⣀⣀⡻⠿⠹⡿⠟⠿⠿⠿⠿⢿⠿⢿⠿⢿⣿⣿⢿⣿⡿⢿⠿⢿⡿⢿⠿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⣷⣻⣜⣾⣿⣿⣿⣿⣿⢿ ⠀⠉⠉⠁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣤⠀⢸⢶⣿⠳⣿⣞⠄⣸⢛⣿⣾⣝⣾⣷⣖⠒⢖⣲⠒⡟⢓⣴⣿⠻⣚⢾⣾⣿⢿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣽⣿⣿⣿⣿⣯⣽ ⠄⢷⣶⡷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠶⠮⠙⠟⠻⠉⠹⠁⢪⠊⠉⠉⠙⠫⠉⣻⡍⠉⠋⢉⡯⡿⠋⠉⠉⠉⢹⢻⣿⣿⣿⣿⣷⣾⣿⣿⣿⣾⣿⣿⣿⣿⠟⢻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⠿⢿⢿⢿⣿⣿⣿⣿ ⡈⠛⠛⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠐⠈⢀⢀⡀⣀⣀⣨⣈⣗⣷⣴⣿⣋⣀⣀⣀⣀⣀⣼⣸⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣷⡂⠐⠍⠉⣉⠉⢹ ⠨⣿⡏⠉⠉⠸⠇⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣆⣦⣶⣖⡆⢰⢠⣴⣶⣶⣶⣶⣦⣀⣠⡶⣤⣤⣄⣀⣺⣿⣿⣿⣿⣿⣿⣭⣭⣽⣿⣿⣷⣦⣾⣿⣿⣿⣿⣿⣽⣿⣶⣾⣿⣿⣿⣿⣿⣯⣿⣿⣏⣏⣠⣄⣸⣷⣧⣭⣍ ⣶⡦⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣶⢶⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠦⠰⠆ ⣾⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢻⣶⣶⠶⢴⡦⠦⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠿⣿⣿⡳⢶⡶⠓⠚⠺⠶⠶⠶⠾⢿⡍⣿⠉⠏⠁⠀⠀⣤⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⣀⡀⠀⠀⠀ ⣿⣶⣶⣶⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⢾⠀⡀⠀⠀⠀⠉⣫⣭⣭⣭⢍⣭⣭⣥⣶⣤⣤⣴⣤⣤⣬⣬⣤⣤⣤⣤⣤⣬⣭⣭⡍⣬⣤⣬⣤⣤⣭⣥⣤⣬⣥⣴⣤⣬⣬⣥⣥⣬⣭⣭⣥⣤⣭⡅⠰⣶⡆⠀⠀⠠ ⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣷⣾⡀⠂⠀⠁⠀⢙⠿⠻⢿⢿⠛⡿⠽⠿⠟⠛⠞⠹⠿⠿⠿⠿⠿⠿⠿⠿⠻⠿⠻⠿⠟⠻⠿⠛⠙⠛⠀⠽⠭⠤⠃⠹⠋⠈⠉⠘⠛⠛⠃⠃⠋⠁⠹⠀⢰⣿⡇⠀⠀⠀ ⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⡃⠀⠇⡁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣷⣮⣧⣴ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡠⢆⣅⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣛⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠈⢫⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣿⡿⣿⠿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⠆⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠁⢻⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣷⣶⣶⣶⣶⡞⠛⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⢹⣀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣗⣒⠒⡒⠒⠒⢲⣖⠒⠒⠒⠒⠒⠒⠒⠚⠲⢾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⡿⠻⣛⣃⡀⠀⠘⢋⣀⣀⣀⢀⣀⣀⣀⣐⡀⢸⡇⡄⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⡝⠛⠿⣻⣿⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⡇⠀⠀⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⡀⠀⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣷⣶⣿⣇⣀⣿⣃⣀⣀⣀⣀⣀⣀⣀⣀⣘⣀⣻⠇⠁⠀⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⣄⠹⣿⣿⣿⣿⣿⣿⠀⠀⢀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣷⣶⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣷⣬⣛⡋⠛⠿⠿⣠⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣏⣙⣙⡙⠛⠙⠉⠙⠛⠙⠛⠛⠛⠋⠛⠚⠛⣿⠁⠀⠀⠠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣏⣛⣛⢃⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣨⣠⣿⠟⢶⢿⣦⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⡿⠿⠿⠿⠿⠿⣿⠾⠿⠿⠿⠿⠟⣿⠿⢿⣿⣿⣿⣿⣿⣧⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣟⣿⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠟⣿⠻⠉⡻⣵⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣤⣠⡽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠍⠩⣛⣿⣻ ⡿⣿⡿⠿⠿⠿⣿⠿⠿⠿⣿⡿⠿⠿⠿⠿⢉⣅⣬⣤⣈⣧⣬⣀⣀⣄⣠⣀⣄⣠⣠⣠⣀⣠⣀⣀⣀⣀⣀⣀⣠⣤⣤⡀⣠⣀⣀⣠⣄⣄⣄⣄⣤⣀⣠⣠⣤⣠⣄⣠⣀⣄⣤⣠⣀⣄⣤⣠⣀⣀⣀⣀⣄⣬⣥⣬⣭⣍ ⣶⡦⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣶⢶⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠦⠰⠆ ⣾⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢻⣶⣶⠶⢴⡦⠦⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠿⣿⣿⡳⢶⡶⠓⠚⠺⠶⠶⠶⠾⢿⡍⣿⠉⠏⠁⠀⠀⣤⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⣀⡀⠀⠀⠀ ⣿⣶⣶⣶⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⢾⠀⡀⠀⠀⠀⠉⣫⣭⣭⣭⢍⣭⣭⣥⣶⣤⣤⣴⣤⣤⣬⣬⣤⣤⣤⣤⣤⣬⣭⣭⡍⣬⣤⣬⣤⣤⣭⣥⣤⣬⣥⣴⣤⣬⣬⣥⣥⣬⣭⣭⣥⣤⣭⡅⠰⣶⡆⠀⠀⠠ ⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣷⣾⡀⠂⠀⠁⠀⢙⠿⠻⢿⢿⠛⡿⠽⠿⠟⠛⠞⠹⠿⠿⠿⠿⠿⠿⠿⠿⠻⠿⠻⠿⠟⠻⠿⠛⠙⠛⠀⠽⠭⠤⠃⠹⠋⠈⠉⠘⠛⠛⠃⠃⠋⠁⠹⠀⢰⣿⡇⠀⠀⠀ ⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⡃⠀⠇⡅⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣷⣮⣧⣴ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡠⢆⣅⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣛⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠈⢫⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣿⡿⣿⠿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⠆⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠁⢻⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣷⣶⣶⣶⣶⡞⠛⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⢹⣀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣗⣒⠒⡒⠒⠒⢲⣖⠒⠒⠒⠒⠒⠒⠒⠚⠲⢾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⡿⠻⣛⣃⡀⠀⠘⢋⣀⣀⣀⢀⣀⣀⣀⣐⡀⢸⡇⡄⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⡝⠛⠿⣻⣿⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⡇⠀⠀⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⡀⠀⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⣛⣿⣿ ⣷⣶⣿⣇⣀⣿⣃⣀⣀⣀⣀⣀⣀⣀⣀⣘⣀⣻⠇⠁⠀⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⣄⠹⣿⣿⣿⣿⣿⣿⠀⢀⢀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣷⣶⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣷⣬⣛⡋⠛⠿⠿⣠⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣏⣙⣙⡙⠛⠙⠉⠙⠛⠙⠛⠛⠛⠋⠛⠚⠛⣿⠁⠀⠀⠠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠟⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣏⣛⣛⢃⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣨⣠⣿⠟⢶⢿⣦⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⡿⠿⠿⠿⠿⠿⣿⠾⠿⠿⠿⠿⠟⣿⠿⢿⣿⣿⣿⣿⣿⣧⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣟⣿⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠟⣿⠻⠉⡻⣵⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣤⣠⡽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠍⠩⣛⣿⣻ ⡿⣿⡿⠿⠿⠿⣿⠿⠿⠿⣿⡿⠿⠿⠿⠿⢉⣅⣬⣤⣈⣧⣬⣀⣀⣄⣠⣀⣄⣠⣠⣠⣀⣠⣀⣀⣀⣀⣀⣀⣠⣤⣤⡀⣠⣀⣀⣠⣄⣄⣄⣄⣤⣀⣠⣠⣤⣠⣄⣠⣀⣄⣤⣠⣀⣄⣤⣠⣀⣀⣀⣀⣄⣬⣥⣬⣭⣍ ⣶⡦⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣶⢶⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠦⠰⠆ ⣾⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢻⣶⣶⠶⢴⡦⠦⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠿⣿⣿⡳⢶⡶⠓⠚⠺⠶⠶⠶⠾⢿⡍⣿⠉⠏⠁⠀⠀⣤⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⣀⡀⠀⠀⠀ ⣿⣶⣶⣶⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⢾⠀⡀⠀⠀⠀⠉⣫⣭⣭⣭⢍⣭⣭⣥⣶⣤⣤⣴⣤⣤⣬⣬⣤⣤⣤⣤⣤⣬⣭⣭⡍⣬⣤⣬⣤⣤⣭⣥⣤⣬⣥⣴⣤⣬⣬⣥⣥⣬⣭⣭⣥⣤⣭⡅⠰⣶⡆⠀⠀⠠ ⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣷⣾⡀⠂⠀⠁⠀⢙⠿⠻⢿⢿⠛⡿⠽⠿⠟⠛⠞⠹⠿⠿⠿⠿⠿⠿⠿⠿⠻⠿⠻⠿⠟⠻⠿⠛⠙⠛⠀⠽⠭⠤⠃⠹⠋⠈⠉⠘⠛⠛⠃⠃⠋⠁⠹⠀⢰⣿⡇⠀⠀⠀ ⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⡃⠀⠇⡅⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣷⣮⣧⣴ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡠⢆⣅⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣛⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠈⢫⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣿⡿⣿⠿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⠆⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠁⢻⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣷⣶⣶⣶⣶⡞⠛⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⢹⣀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣗⣒⠒⡒⠒⠒⢲⣖⠒⠒⠒⠒⠒⠒⠒⠚⠲⢾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⡿⠻⣛⣃⡀⠀⠘⢋⣀⣀⣀⢀⣀⣀⣀⣐⡀⢸⡇⡄⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⡝⠛⠿⣻⣿⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⡇⠀⠀⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⡀⠀⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⣛⣿⣿ ⣷⣶⣿⣇⣀⣿⣃⣀⣀⣀⣀⣀⣀⣀⣀⣘⣀⣻⠇⠁⠀⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⣄⠹⣿⣿⣿⣿⣿⣿⠀⢀⢀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣷⣶⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣷⣬⣛⡋⠛⠿⠿⣠⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣏⣙⣙⡙⠛⠙⠉⠙⠛⠙⠛⠛⠛⠋⠛⠚⠛⣿⠁⠀⠀⠠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠟⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣏⣛⣛⢃⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣨⣠⣿⠟⢶⢿⣦⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⡿⠿⠿⠿⠿⠿⣿⠾⠿⠿⠿⠿⠟⣿⠿⢿⣿⣿⣿⣿⣿⣧⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣟⣿⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠟⣿⠻⠉⡻⣵⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣤⣠⡽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠍⠩⣛⣿⣻ ⡿⣿⡿⠿⠿⠿⣿⠿⠿⠿⣿⡿⠿⠿⠿⠿⢉⣅⣬⣤⣈⣧⣬⣀⣀⣄⣠⣀⣄⣠⣠⣠⣀⣠⣀⣀⣀⣀⣀⣀⣠⣤⣤⡀⣠⣀⣀⣠⣄⣄⣄⣄⣤⣀⣠⣠⣤⣠⣄⣠⣀⣄⣤⣠⣀⣄⣤⣠⣀⣀⣀⣀⣄⣬⣥⣬⣭⣍ ⣶⡦⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣶⢶⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠦⠰⠆ ⣾⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢻⣶⣶⠶⢴⡦⠦⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠿⣿⣿⡳⢶⡶⠓⠚⠺⠶⠶⠶⠾⢿⡍⣿⠉⠏⠁⠀⠀⣤⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⣀⡀⠀⠀⠀ ⣿⣶⣶⣶⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⢾⠀⡀⠀⠀⠀⠉⣫⣭⣭⣭⢍⣭⣭⣥⣶⣤⣤⣴⣤⣤⣬⣬⣤⣤⣤⣤⣤⣬⣭⣭⡍⣬⣤⣬⣤⣤⣭⣥⣤⣬⣥⣴⣤⣬⣬⣥⣥⣬⣭⣭⣥⣤⣭⡅⠰⣶⡆⠀⠀⠠ ⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣷⣾⡀⠂⠀⠁⠀⢙⠿⠻⢿⢿⠛⡿⠽⠿⠟⠛⠞⠹⠿⠿⠿⠿⠿⠿⠿⠿⠻⠿⠻⠿⠟⠻⠿⠛⠙⠛⠀⠽⠭⠤⠃⠹⠋⠈⠉⠘⠛⠛⠃⠃⠋⠁⠹⠀⢰⣿⡇⠀⠀⠀ ⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⡃⠀⠇⡅⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣷⣮⣧⣴ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡠⢆⣅⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣛⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠈⢫⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣿⡿⣿⠿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⠆⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠁⢻⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣷⣶⣶⣶⣶⡞⠛⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⢹⣀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣗⣒⠒⡒⠒⠒⢲⣖⠒⠒⠒⠒⠒⠒⠒⠚⠲⢾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⡿⠻⣛⣃⡀⠀⠘⢋⣀⣀⣀⢀⣀⣀⣀⣐⡀⢸⡇⡄⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⡝⠛⠿⣻⣿⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⡇⠀⠀⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⡀⠀⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⣛⣿⣿ ⣷⣶⣿⣇⣀⣿⣃⣀⣀⣀⣀⣀⣀⣀⣀⣘⣀⣻⠇⠁⠀⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⣄⠹⣿⣿⣿⣿⣿⣿⠀⢀⢀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣷⣶⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣷⣬⣛⡋⠛⠿⠿⣠⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣏⣙⣙⡙⠛⠙⠉⠙⠛⠙⠛⠛⠛⠋⠛⠚⠛⣿⠁⠀⠀⠠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠟⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣏⣛⣛⢃⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣨⣠⣿⠟⢶⢿⣦⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⡿⠿⠿⠿⠿⠿⣿⠾⠿⠿⠿⠿⠟⣿⠿⢿⣿⣿⣿⣿⣿⣧⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣟⣿⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠟⣿⠻⠉⡻⣵⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣤⣠⡽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠍⠩⣛⣿⣻ ⡿⣿⡿⠿⠿⠿⣿⠿⠿⠿⣿⡿⠿⠿⠿⠿⢉⣅⣬⣤⣈⣧⣬⣀⣀⣄⣠⣀⣄⣠⣠⣠⣀⣠⣀⣀⣀⣀⣀⣀⣠⣤⣤⡀⣠⣀⣀⣠⣄⣄⣄⣄⣤⣀⣠⣠⣤⣠⣄⣠⣀⣄⣤⣠⣀⣄⣤⣠⣀⣀⣀⣀⣄⣬⣥⣬⣭⣍ ⣶⡦⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣶⢶⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠦⠰⠆ ⣾⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢻⣶⣶⠶⢴⡦⠦⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠿⣿⣿⡳⢶⡶⠓⠚⠺⠶⠶⠶⠾⢿⡍⣿⠉⠏⠁⠀⠀⣤⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⣀⡀⠀⠀⠀ ⣿⣶⣶⣶⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⢾⠀⡀⠀⠀⠀⠉⣫⣭⣭⣭⢍⣭⣭⣥⣶⣤⣤⣴⣤⣤⣬⣬⣤⣤⣤⣤⣤⣬⣭⣭⡍⣬⣤⣬⣤⣤⣭⣥⣤⣬⣥⣴⣤⣬⣬⣥⣥⣬⣭⣭⣥⣤⣭⡅⠰⣶⡆⠀⠀⠠ ⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣷⣾⡀⠂⠀⠁⠀⢙⠿⠻⢿⢿⠛⡿⠽⠿⠟⠛⠞⠹⠿⠿⠿⠿⠿⠿⠿⠿⠻⠿⠻⠿⠟⠻⠿⠛⠙⠛⠀⠽⠭⠤⠃⠹⠋⠈⠉⠘⠛⠛⠃⠃⠋⠁⠹⠀⢰⣿⡇⠀⠀⠀ ⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⡃⠀⠇⡅⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣷⣮⣧⣴ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡠⢆⣅⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣛⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠈⢫⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣿⡿⣿⠿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⠆⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠁⢻⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣷⣶⣶⣶⣶⡞⠛⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⢹⣀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣗⣒⠒⡒⠒⠒⢲⣖⠒⠒⠒⠒⠒⠒⠒⠚⠲⢾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⡿⠻⣛⣃⡀⠀⠘⢋⣀⣀⣀⢀⣀⣀⣀⣐⡀⢸⡇⡄⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⡝⠛⠿⣻⣿⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⡇⠀⠀⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⡀⠀⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⣛⣿⣿ ⣷⣶⣿⣇⣀⣿⣃⣀⣀⣀⣀⣀⣀⣀⣀⣘⣀⣻⠇⠁⠀⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⣄⠹⣿⣿⣿⣿⣿⣿⠀⢀⢀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣷⣶⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣷⣬⣛⡋⠛⠿⠿⣠⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣏⣙⣙⡙⠛⠙⠉⠙⠛⠙⠛⠛⠛⠋⠛⠚⠛⣿⠁⠀⠀⠠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠟⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣏⣛⣛⢃⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣨⣠⣿⠟⢶⢿⣦⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⡿⠿⠿⠿⠿⠿⣿⠾⠿⠿⠿⠿⠟⣿⠿⢿⣿⣿⣿⣿⣿⣧⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣟⣿⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠟⣿⠻⠉⡻⣵⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣤⣠⡽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠍⠩⣛⣿⣻ ⡿⣿⡿⠿⠿⠿⣿⠿⠿⠿⣿⡿⠿⠿⠿⠿⢉⣅⣬⣤⣈⣧⣬⣀⣀⣄⣠⣀⣄⣠⣠⣠⣀⣠⣀⣀⣀⣀⣀⣀⣠⣤⣤⡀⣠⣀⣀⣠⣄⣄⣄⣄⣤⣀⣠⣠⣤⣠⣄⣠⣀⣄⣤⣠⣀⣄⣤⣠⣀⣀⣀⣀⣄⣬⣥⣬⣭⣍ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⣶⣶⠶⠶⣶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠦⠰⠆ ⣶⣶⣷⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢲⣶⣦⠴⢴⡤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡷⢶⠶⠆⣶⠳⢴⡶⠒⠒⠒⠶⠶⠶⠲⢺⡈⣽⠉⠎⠁⠀⠀⣤⣿⣿⣿⣾⣷⣾⣿⣿⣷⡻⡿⢿⠿⠿⠿⠿⢾⣿⢿⠿⣿⢿⣿⣷⣿⠾⠿⠷⢿⠿⡿⢿⢿⡿⡿⢿⡿⠿⡿⠿⡿⣿⣿⣿⣿⣿⣤⡄⠀⣀⡀⠀⠀⠀ ⣷⢶⣶⣶⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣧⢾⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⣶⡀⠀⠀⠠ ⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⣮⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀ ⣿⣛⣛⣟⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⠃⠀⠇⡅⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣷⣬⣥⣴ ⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢀⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣙⣿⣿⣿⣿⣿ ⣾⣿⣿⠿⢾⠿⠿⣿⠿⠿⠿⠿⠿⡿⠿⣿⢿⠻⠉⠁⠈⢡⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣿⡟⣻⠈⠁⢰⡆⠷⠾⠎⠀⠀⠸⠇⠀⠶⠀⠹⠆⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠁⢻⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⣀⣤⣴⣶⣴⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⡷⣶⡶⣶⣾⡟⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⡟⠙⠐⠀⠒⠞⠉⠍⠉⢯⠒⠠⠆⠆⠒⠂⠒⠒⠒⠒⠂⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⢖⣒⠒⡒⠒⠐⢲⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⡇⣁⣀⣀⡐⣂⠀⠀⠉⠀⠀⠀⠈⠍⠀⠀⢀⡀⠁⠀⡠⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⡿⠛⢛⡃⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠐⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣶⣾⣿⣿⡿⢀⠀⠀⠀⢀⡀⠀⠀⢀⡀⠀⠀⠀⠤⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠙⠛⠛⠃⠀⣀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢸⠐⣠⠀⠀⠀⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠁⠈⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣟⣙⣿⣿ ⣶⣶⣾⠇⠀⢻⡃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣸⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⡄⠸⣿⢛⣻⣿⣿⣿⡇⢀⢀⣾⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣗⡶⠶⠇⠀⠘⠏⠀⠀⠀⠁⠀⠀⠀⠀⠹⠇⢿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣷⣌⡙⣿⣿⣿⣿⢡⣴⣿⠫⣿⣿⣹⣿⣭⣿⡏⠆⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣇⣁⣁⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠘⠉⣾⠁⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⢸⣿⣿⣿⣿⡿⠟⠁⠀⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣏⠋⠛⢁⣀⣠⣀⢀⣀⣀⣀⣀⣀⣀⣀⣈⣠⣿⠖⠆⢶⡆⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⢸⣿⣿⣿⣿⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⡟⠛⠛⠃⠋⠹⣷⠞⠙⠛⠋⠛⠊⣯⠛⢻⣿⣿⣻⣿⣿⣧⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡆⠀⠀⠸⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿ ⣞⣿⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡿⠻⠉⡻⠑⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣧⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡵⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⠀⠀⢠⣤⢸⣿⣿⣿⣿⡿⠀⠀⠀⠀⢠⡄⠀⠀⠀⠰⠍⠉⣉⣉⣹ ⡿⣿⡟⠛⠙⠹⠇⠀⠀⠀⣴⡄⠀⠀⠀⠀⢈⣅⣬⣠⣈⣇⣀⣀⣀⣄⣠⣀⣄⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⡀⣠⣀⣀⣠⣿⣿⣿⣿⣿⣶⣠⣠⣩⣈⣽⣿⣿⣿⣷⣀⣀⣀⣤⣿⣁⣀⣀⣀⣄⣌⣥⣬⣭⣍ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⣶⣶⠶⠶⣶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠰⠆ ⣶⣶⣷⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡷⢶⠶⠆⣶⠳⢤⡶⠒⠒⠒⠶⠶⠶⠲⢺⡈⣽⠉⠎⠀⠀⠀⣠⣿⣿⣿⣾⣷⣾⣿⣟⣷⡻⡿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⢿⣿⣷⣿⠾⠿⠷⢿⠿⡿⢿⢿⠿⡿⠿⡿⠿⡿⠿⡿⣿⣿⣿⣿⣿⣤⡄⠀⣀⡀⠀⠀⠀ ⣷⢶⣶⣶⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣧⢾⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⣶⡀⠀⠀⠠ ⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⣮⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⡃⠀⠀⠀ ⣿⣛⣛⣟⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⠃⠀⠇⡅⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣷⣬⣥⣴ ⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢀⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣙⣿⣻⣿⣿⣿ ⣾⣿⣿⠿⠾⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⣿⢿⠻⠉⠁⠈⢡⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣿⡛⣻⠈⠱⢶⡆⠶⠾⠿⠀⠀⠸⠆⠀⠶⠀⠹⠆⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠁⢻⣿⣿⣿⣿⣿⣦⣦⣐⣻⣿⣿⣯⣭⣿⣵⣤⣤⣄⣀⣤⣄⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⡷⣶⡶⣶⣾⡟⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⢸⣿⡿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣉⣏⣻⣿⣿⣿⠐⠒⠂⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⢖⣒⠒⡒⠒⠐⢲⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⢿⠏⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠄⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⡿⠛⢛⡃⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠐⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⡷⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠙⠛⠛⠃⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⣠⠀⠀⠀⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⡀⠀⠂⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⣿⣿⣏⣙⣿⣿ ⣶⣶⣾⠇⠀⢻⡃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣸⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠋⠛⠛⠋⠛⠻⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣗⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⢿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣯⣭⣤⣤⣤⣤⣤⣤⣤⣿⠀⠈⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣇⣁⣁⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠘⠉⣾⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠘⣿⣿⣿⣿⣷⣿⣿⡇⡀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣏⠋⠛⢁⣀⣠⣀⢀⣀⣀⣀⣀⣀⣀⣀⣈⣠⣿⠖⠆⢶⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣿⣿⣿⠿⣿⡿⠿⢿⣿⣷⠶⢶⠷⠶⠶⢶⡶⠶⡶⠶⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⡟⠛⠛⠃⠋⠹⣷⠞⠙⠛⠋⠛⠊⣯⠛⢻⢿⣿⣻⣿⣿⣧⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡛⢿⣿⣷⣾⣿⡅⠀⢀⠀⠀⠈⡀⠀⠀⣀⠐⣿⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿ ⣞⣿⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡿⠻⠉⡻⠑⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣻⣿⣿⣟⣿⣟⣿⣿⣟⣿⣛⠻⠿⠛⠿⠛⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡵⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣤⣴⣤⣿⠀⢠⡄⠀⠀⠀⠰⠍⠉⣉⣉⣹ ⡿⣿⡟⠛⠙⠹⠇⠀⠀⠀⣴⡄⠀⠀⠀⠀⢈⣅⣬⣠⣈⣇⣀⣀⣀⣄⣠⣀⣄⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⡀⣠⣀⡀⣿⣯⣿⣿⣿⣉⣩⣉⣉⣉⣈⣉⣉⣙⣉⡉⠉⠉⣿⢰⣿⣁⣀⣀⣀⣄⣌⣥⣬⣩⣍ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⣶⣶⠶⠶⢶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠰⠆ ⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡷⢶⠶⠆⣶⠳⢤⡶⠒⠒⠒⠶⠶⠶⠲⢺⡈⣽⠉⠎⠀⠀⠀⣠⣻⣿⣿⣾⣷⣾⣿⣟⣷⡛⠿⠿⠿⠿⠿⠿⠾⠷⠿⠿⠿⢿⣿⣷⣿⠾⠿⠷⠿⠿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣤⡄⠀⣀⡀⠀⠀⠀ ⣷⢶⣶⣶⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣧⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣶⡀⠀⠀⠠ ⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⣮⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⡃⠀⠀⠀ ⣿⣛⣛⣛⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⠃⠀⠃⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣷⣬⣤⣴ ⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣙⣿⣻⣿⣿⣯ ⣾⣿⣿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠉⠁⠈⠡⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣿⡛⣻⠀⠰⢴⡆⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠰⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠁⢻⣿⣿⣿⣿⣿⣦⣆⣐⣛⣿⣿⣯⣭⣿⣵⣤⣤⣄⣀⣤⣄⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⡷⣶⡶⣶⣾⡏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⢸⣿⡿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣉⣭⣟⣿⣿⣿⠐⠒⠂⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⢖⣒⠒⡒⠒⠐⢲⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⢻⠏⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⣾⣿⣿⣿⠀⠄⠀⠠⠤⢴⣿⣿⣿⣿⣿⣿ ⡿⠛⢛⡃⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠐⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⡷⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣫⣀⣤⣤⣼⣿⣿⣿⣿⣿⣿ ⠙⠛⠛⠃⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣠⠀⠀⠀⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⡀⠀⠂⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⠿⠏⠀⢰⣿⣿⣽⣿⣿⣿ ⣶⣶⣾⠇⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣸⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⡄⠀⣿⣿⣟⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⡛⠉⠉⢉⡉⠉⠹⣿⠀⣅⠀⢀⠀⢸⣿⣿⣿⣿⣿⣿ ⣗⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢽⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣤⣯⣷⣤⣴⣾⣿⣿⣿⣿⣿⣿ ⣇⣁⣁⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠘⠀⣾⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠘⣿⣿⣿⣿⣷⣾⣷⡇⡟⠀⠀⠈⢀⣉⣙⣫⡹⠃⡞⣙⣛⡛⠉⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿ ⣏⠋⠛⠁⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣠⣿⠖⠆⠖⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣿⣿⣿⠿⢿⡿⠿⢿⣿⡶⠶⣿⡿⣿⣿⣿⡿⠟⠛⠛⣛⠛⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⡟⠛⠛⠃⠀⠸⣷⠆⠀⠀⠀⠀⠀⣦⠀⢸⢿⣿⣻⣿⣿⣧⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡛⢿⣿⡗⣦⣽⠁⢀⣴⣂⣀⣀⣚⡆⠀⡀⠀⣿⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿ ⣞⣿⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡟⠻⠉⡻⠑⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣩⣫⣿⣷⣟⣿⣛⣿⣿⣿⣿⣿⡿⠟⠛⠻⠛⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣪⣤⣴⣄⣿⠀⢠⡄⠀⠀⠀⠰⠍⠉⣉⣉⣹ ⡯⣿⡟⠛⠙⠹⠇⠀⠀⠀⣴⡄⠀⠀⠀⠀⢈⣅⣬⣠⣈⣇⣀⢀⣀⣄⣠⣀⣄⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⡀⣠⣀⡀⣿⣭⣿⣿⣿⣁⣿⣏⣉⣻⣫⣿⣿⣽⣭⣭⠉⠈⣿⢰⣿⣁⣀⣀⣀⣄⣌⣥⣬⣩⣍ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⣶⣶⠶⠶⢶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠰⠆ ⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡷⢶⠶⠆⣶⠳⢤⡶⠒⠒⠒⠶⠶⠶⠲⢺⡈⣽⠉⠎⠀⠀⠀⣠⣻⣿⣿⣾⣷⣾⣿⣟⣷⡛⠿⠿⠿⠿⠿⠿⠾⠷⠿⠿⠿⢿⣿⣷⣿⠾⠿⠷⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣤⡄⠀⣀⡀⠀⠀⠀ ⣷⢶⣶⣶⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣧⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣶⡀⠀⠀⠠ ⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⣮⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⡃⠀⠀⠀ ⣿⣛⣛⣛⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⠃⠀⠃⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣷⣬⣤⣴ ⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣙⣿⣻⣿⣿⣯ ⣞⣿⣿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠉⠱⠈⠡⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣿⡛⣻⠀⠰⢴⡆⠀⠀⠿⡀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠰⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠁⢻⣿⣿⣿⣿⣿⣆⣄⣐⣛⣿⣿⣯⣿⣿⣵⣤⣤⣄⣀⣀⣄⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⡷⣶⡶⣶⣾⡏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⢸⣿⡿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣉⣭⣟⣿⣿⣿⠐⠒⠂⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⢖⣒⠒⡒⠒⠀⢲⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⢻⠏⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⣾⣿⣿⣿⠀⠄⠀⠠⠤⢴⣿⣿⣿⣿⣿⣿ ⡿⠛⢛⡃⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠐⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⡷⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣫⣀⣤⣤⣼⣿⣿⣿⣿⣿⣿ ⠙⠛⠛⠃⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣠⠀⠀⠀⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⡀⠀⠂⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⠿⠏⠀⢰⣿⣿⣽⣿⣿⣿ ⣶⣶⣾⠇⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣸⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⡄⠀⣿⣿⣟⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⡛⠉⠉⢉⡉⠩⠹⣿⠀⣅⠀⢀⠀⢸⣿⣿⣿⣿⣿⣿ ⣗⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢽⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣤⣯⣷⣤⣴⣾⣿⣿⣿⣿⣿⣿ ⣇⣁⣁⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠘⠀⣾⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠘⣿⣿⣿⣿⣷⣾⣷⡇⡟⠀⠀⠈⢀⣭⣙⣫⡹⠃⡞⣙⣛⡛⠉⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿ ⣏⠋⠛⠁⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣠⣿⠖⠆⠖⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣿⣿⣿⠿⢿⡿⠿⢿⣿⡶⠶⣿⡿⣿⣿⣿⡿⠟⠛⠛⣛⠛⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⡇⠛⠛⠃⠀⠸⣷⠆⠀⠀⠀⠀⠀⣦⠀⢸⢿⣿⣻⣿⣿⣧⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡛⢿⣿⡗⣮⣽⠁⢀⣔⣂⣀⣀⣚⡆⠀⡀⠀⣿⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿ ⣞⣿⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡟⠻⠉⡻⠑⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣩⣫⣿⣷⣟⣿⣛⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣢⣤⣴⣄⣿⠀⢠⡄⠀⠀⠀⠰⠍⠉⣉⣉⣹ ⡯⣿⡟⠛⠙⠹⠇⠀⠀⠀⣴⡄⠀⠀⠀⠀⢈⣅⣬⣠⣈⣇⣀⢀⣀⣄⣠⣀⣄⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⡀⣠⣀⡀⣿⣭⣿⣿⣿⣁⣿⣏⣉⣻⣫⣿⣿⣽⣽⣿⠉⠈⣿⢰⣿⣁⣀⣀⣀⣄⣌⣥⣬⣩⣍ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⣶⣶⠶⠶⢶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠰⠆ ⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡷⢶⠶⠆⣶⠳⢤⡶⠒⠒⠒⠶⠶⠶⠲⢺⡈⣽⠉⠎⠀⠀⠀⣠⣻⣿⣿⣾⣷⣾⣿⣟⣷⡛⠿⠿⠿⠿⠿⠿⠾⠷⠿⠿⠿⢿⣿⣷⣿⠾⠿⠷⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣤⡄⠀⣀⡀⠀⠀⠀ ⣷⢶⣶⣶⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣧⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣶⡀⠀⠀⠠ ⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⣮⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⡃⠀⠀⠀ ⣿⣛⣛⣛⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⠃⠀⠃⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣷⣬⣤⣴ ⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢀⡄⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣙⣿⣻⣿⣿⣯ ⣞⣿⣿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠉⠱⠈⠡⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣿⡛⣻⠀⠰⢴⡆⠀⠀⠿⡀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠰⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠁⢻⣿⣿⣿⣿⣿⣆⣄⣐⣛⣿⣿⣯⣿⣿⣵⣤⣤⣄⣀⣀⣄⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⡷⣶⡶⣶⣾⡏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⢸⣿⡿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣉⣭⣟⣿⣿⣿⠐⠒⠂⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⢖⣒⠒⡒⠒⠀⢲⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⢻⠏⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⣾⣿⣿⣿⠀⠄⡄⠠⠤⢴⣿⣿⣿⣿⣿⣿ ⡿⠛⢛⡃⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠐⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⡷⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣫⣀⣤⣤⣼⣿⣿⣿⣿⣿⣿ ⠙⠛⠛⠃⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣠⠀⠀⠀⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⡀⠀⠂⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⠿⠏⠀⢰⣿⣿⣽⣿⣿⣿ ⣶⣶⣾⠇⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣸⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⡄⠀⣿⣿⣟⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⡛⠉⠉⢉⡉⠩⠹⣿⠀⣅⠀⢀⠀⢸⣿⣿⣿⣿⣿⣿ ⣗⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢽⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣤⣯⣷⣤⣴⣾⣿⣿⣿⣿⣿⣿ ⣇⣁⣁⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠘⠀⣾⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠘⣿⣿⣿⣿⣷⣾⣷⡇⡟⠀⠀⠈⢀⣭⣙⣫⡹⠃⡞⣙⣛⡛⠉⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿ ⣏⠋⠛⠁⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣠⣿⠖⠆⠖⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣿⣿⣿⠿⢿⡿⠿⢿⣿⡶⠶⣿⡿⣿⣿⣿⡿⠟⠛⠛⣛⠛⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⡇⠛⠛⠃⠀⠸⣷⠆⠀⠀⠀⠀⠀⣦⠀⢸⢿⣿⣻⣿⣿⣧⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡛⢿⣿⡗⣮⣽⠁⢀⣔⣂⣀⣀⣚⡆⠀⡀⠀⣿⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿ ⣞⣿⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡟⠻⠉⡻⠑⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣩⣫⣿⣷⣟⣿⣛⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣢⣤⣴⣄⣿⠀⢠⡄⠀⠀⠀⠰⠍⠉⣉⣉⣹ ⡯⣿⡟⠛⠙⠹⠇⠀⠀⠀⣴⡄⠀⠀⠀⠀⢈⣅⣬⣠⣈⣇⣀⢀⣀⣄⣠⣀⣄⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⡀⣠⣀⡀⣿⣭⣿⣿⣿⣁⣿⣏⣉⣻⣫⣿⣿⣽⣽⣿⠉⠈⣿⢰⣿⣁⣀⣀⣀⣄⣌⣥⣬⣩⣍ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⣶⣶⠶⠶⢶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠰⠆ ⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡷⢶⠶⠆⣶⠳⢤⡶⠒⠒⠒⠶⠶⠶⠲⢺⡈⣽⠉⠎⠀⠀⠀⣠⣻⣿⣿⣾⣷⣾⣿⣟⣷⡛⠿⠿⠿⠿⠿⠿⠾⠷⠿⠿⠿⢿⣿⣷⣿⠾⠿⠷⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣤⡄⠀⣀⡀⠀⠀⠀ ⣷⢶⣶⣶⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣧⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣶⡀⠀⠀⠠ ⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⣮⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⡃⠀⠀⠀ ⣿⣛⣛⣛⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⠃⠀⠃⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣷⣬⣤⣴ ⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢀⡄⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣙⣿⣻⣿⣿⣯ ⣞⣿⣿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠉⠱⠈⠡⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣿⡿⣻⠀⠰⢴⡆⠀⠀⠿⡀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠰⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠁⢻⣿⣿⣿⣿⣿⣆⣄⣐⣛⣿⣿⣯⣿⣿⣵⣤⣤⣄⣀⣀⣄⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⡷⣶⡶⣶⣾⡏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⢸⣿⡿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣏⣭⣟⣿⣿⣿⠐⠒⠂⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⢖⣒⠒⡒⠒⠀⢲⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⢻⠏⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⣾⣿⣿⣿⠀⠄⡄⠠⠤⢴⣿⣿⣿⣿⣿⣿ ⡿⠛⢛⡃⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠐⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⡷⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣫⣀⣤⣤⣼⣿⣿⣿⣿⣿⣿ ⠙⠛⠛⠃⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣠⠀⠀⠀⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⡀⠀⠂⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⠿⠏⠀⢰⣿⣿⣽⣿⣿⣿ ⣶⣶⣾⠇⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣸⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⡄⠀⣿⣿⣟⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⡛⠉⢉⢉⡉⠩⠹⣿⠀⣅⠀⢀⠀⢸⣿⣿⣿⣿⣿⣿ ⣗⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢽⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣉⣩⣽⣿⣿⣿⣿⣿⣼⣿⣧⣴⣿⣤⣯⣷⣤⣴⣾⣿⣿⣿⣿⣿⣿ ⣇⣁⣁⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠘⠀⣾⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠘⣿⣿⣿⣿⣷⣾⣷⡇⡟⠀⠀⠈⢀⣭⣙⣫⡹⠃⡞⣙⣛⡛⠉⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿ ⣏⠋⠛⠁⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣠⣿⠖⠆⠖⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣿⣿⣿⠿⢿⡿⠿⢿⣿⡶⠶⣿⡿⣿⣿⣿⡿⠟⠛⠛⣛⠛⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⡇⠛⠛⠃⠀⠸⣷⠆⠀⠀⠀⠀⠀⣦⠀⢸⢿⣿⣻⣿⣿⣧⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡛⢿⣿⡗⣮⣽⠁⢀⣔⣂⣀⣀⣚⡆⠀⠀⠀⣿⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿ ⣞⣿⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡟⠻⠉⡻⠑⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣉⣫⣿⣷⣟⣿⣛⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣢⣤⣴⣄⣿⠀⢠⡄⠀⠀⠀⠰⠍⠉⣉⣉⣹ ⡯⣿⡟⠛⠙⠹⠇⠀⠀⠀⣴⡄⠀⠀⠀⠀⢈⣅⣬⣠⣈⣇⣀⢀⣀⣄⣠⣀⣄⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⡀⣠⣀⡀⣿⣭⣿⣿⣿⣁⣿⣏⣉⣻⣫⣿⣿⣽⣽⣿⠉⠈⣿⢰⣿⣁⣀⣀⣀⣄⣌⣥⣬⣩⣍ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⣶⣶⠶⠶⢶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠰⠆ ⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡷⢶⠶⠆⣶⠳⢤⡶⠒⠒⠒⠶⠶⠶⠲⢺⡈⣽⠉⠎⠀⠀⠀⣠⣻⣿⣿⣾⣷⣾⣿⣟⣷⡛⠿⠿⠿⠿⠿⠿⠾⠷⠿⠿⠿⢿⣿⣷⣿⠾⠿⠷⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣤⡄⠀⣀⡀⠀⠀⠀ ⣷⢶⣶⣶⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣧⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣶⡀⠀⠀⠠ ⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⣮⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⡃⠀⠀⠀ ⣿⣛⣛⣛⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⠃⠀⠃⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣷⣬⣤⣴ ⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢀⡄⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣙⣿⣻⣿⣿⣯ ⣞⣿⣿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠉⠱⠈⠡⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣿⡿⣻⠀⠰⢴⡆⠀⠀⠿⡀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠰⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠁⢻⣿⣿⣿⣿⣿⣆⣄⣐⣛⣿⣿⣯⣿⣿⣵⣤⣤⣄⣀⣀⣄⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⡷⣶⡶⣶⣾⡏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⢸⣿⡿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣏⣭⣟⣿⣿⣿⠐⠒⠂⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⢖⣒⠒⡒⠒⠀⢲⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⢻⠏⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⣾⣿⣿⣿⠀⠄⡄⠠⠤⢴⣿⣿⣿⣿⣿⣿ ⡿⠛⢛⡃⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠐⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⡷⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣫⣀⣤⣤⣼⣿⣿⣿⣿⣿⣿ ⠙⠛⠛⠃⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣠⠀⠀⠀⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⡀⠀⠂⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⠿⠏⠀⢰⣿⣿⣽⣿⣿⣿ ⣶⣶⣾⠇⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣸⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⡄⠀⣿⣿⣟⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⡛⠉⢉⢉⡉⠩⠹⣿⠀⣅⠀⢀⠀⢸⣿⣿⣿⣿⣿⣿ ⣗⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢽⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣉⣩⣽⣿⣿⣿⣿⣿⣼⣿⣧⣴⣿⣤⣯⣷⣤⣴⣾⣿⣿⣿⣿⣿⣿ ⣇⣁⣁⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠘⠀⣾⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠘⣿⣿⣿⣿⣷⣾⣷⡇⡟⠀⠀⠈⢀⣭⣙⣫⡹⠃⡞⣙⣛⡛⠉⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿ ⣏⠋⠛⠁⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣠⣿⠖⠆⠖⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣿⣿⣿⠿⢿⡿⠿⢿⣿⡶⠶⣿⡿⣿⣿⣿⡿⠟⠛⠛⣛⠛⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⡇⠛⠛⠃⠀⠸⣷⠆⠀⠀⠀⠀⠀⣦⠀⢸⢿⣿⣻⣿⣿⣧⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡛⢿⣿⡗⣮⣽⠁⢀⣔⣂⣀⣀⣚⡆⠀⠀⠀⣿⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿ ⣞⣿⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡟⠻⠉⡻⠑⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣉⣫⣿⣷⣟⣿⣛⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣢⣤⣴⣄⣿⠀⢠⡄⠀⠀⠀⠰⠍⠉⣉⣉⣹ ⡯⣿⡟⠛⠙⠹⠇⠀⠀⠀⣴⡄⠀⠀⠀⠀⢈⣅⣬⣠⣈⣇⣀⢀⣀⣄⣠⣀⣄⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⡀⣠⣀⡀⣿⣭⣿⣿⣿⣁⣿⣏⣉⣻⣫⣿⣿⣽⣽⣿⠉⠈⣿⢰⣿⣁⣀⣀⣀⣄⣌⣥⣬⣩⣍ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⣶⣶⠶⠶⢶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠰⠆ ⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡷⢶⠶⠆⣶⠳⢤⡶⠒⠒⠒⠶⠶⠶⠲⢺⡈⣽⠉⠎⠀⠀⠀⣠⣻⣿⣿⣾⣷⣾⣿⣟⣷⡛⠿⠿⠿⠿⠿⠿⠾⠷⠿⠿⠿⢿⣿⣷⣿⠾⠿⠷⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣤⡄⠀⣀⡀⠀⠀⠀ ⣷⢶⣶⣶⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣧⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣶⡀⠀⠀⠠ ⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⣮⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⡃⠀⠀⠀ ⣿⣛⣛⣛⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⠃⠀⠃⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣷⣬⣤⣴ ⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢀⡄⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣙⣿⣻⣿⣿⣯ ⣞⣿⣿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠉⠱⠈⠡⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣿⡿⣻⠀⠰⢴⡆⠀⠀⠿⡀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠰⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠁⢻⣿⣿⣿⣿⣿⣆⣄⣐⣛⣿⣿⣯⣿⣿⣵⣤⣤⣄⣀⣀⣄⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⡷⣶⡶⣶⣾⡏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⢸⣿⡿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣏⣭⣟⣿⣿⣿⠐⠒⠂⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⢖⣒⠒⡒⠒⠀⢲⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⢻⠏⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⣾⣿⣿⣿⠀⠄⡄⠠⠤⢴⣿⣿⣿⣿⣿⣿ ⡿⠛⢛⡃⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠐⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⡷⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣫⣀⣤⣤⣼⣿⣿⣿⣿⣿⣿ ⠙⠛⠛⠃⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣠⠀⠀⠀⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⡀⠀⠂⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⠿⠏⠀⢰⣿⣿⣽⣿⣿⣿ ⣶⣶⣾⠇⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣸⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⡄⠀⣿⣿⣟⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⡛⠉⢉⢉⡉⠩⠹⣿⠀⣅⠀⢀⠀⢸⣿⣿⣿⣿⣿⣿ ⣗⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢽⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣉⣩⣽⣿⣿⣿⣿⣿⣼⣿⣧⣴⣿⣤⣯⣷⣤⣴⣾⣿⣿⣿⣿⣿⣿ ⣇⣁⣁⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠘⠀⣾⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠘⣿⣿⣿⣿⣷⣾⣷⡇⡟⠀⠀⠈⢀⣭⣙⣫⡹⠃⡞⣙⣛⡛⠉⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿ ⣏⠋⠛⠁⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣠⣿⠖⠆⠖⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣿⣿⣿⠿⢿⡿⠿⢿⡿⠶⠶⣿⡿⣿⣿⣿⡿⠟⠛⠛⣛⠛⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⡇⠛⠛⠃⠀⠸⣷⠆⠀⠀⠀⠀⠀⣦⠀⢸⢿⣿⣻⣿⣿⣧⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡛⢿⣿⡗⣮⣽⠀⢀⣔⣂⣀⣀⣚⡆⠀⠀⠀⣿⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿ ⣞⣿⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡟⠻⠉⡻⠑⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣉⣫⣿⣷⣟⣿⣛⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣢⣤⣴⣄⣿⠀⢠⡄⠀⠀⠀⠰⠍⠉⣉⣉⣹ ⡯⣿⡟⠛⠙⠹⠇⠀⠀⠀⣴⡄⠀⠀⠀⠀⢈⣅⣬⣠⣈⣇⣀⢀⣀⣄⣠⣀⣄⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⡀⣠⣀⡀⣿⣭⣿⣿⣿⣁⣿⣏⣉⣻⣫⣿⣿⣽⣽⣿⠉⠈⣿⢰⣿⣁⣀⣀⣀⣄⣌⣥⣬⣩⣍ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⣶⣶⠶⠶⣶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠦⠰⠆ ⣶⣷⣷⣶⣶⣷⠶⠶⠷⠶⠶⠶⠶⠶⠶⢲⣶⣦⠴⢴⡤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡷⢶⠶⠶⣶⠳⢶⡶⠒⠒⠒⠶⠶⠶⠲⢺⡈⣽⠉⠎⠁⠀⠀⣤⣿⣿⣿⣾⣷⣾⣿⣿⣷⡻⣿⣿⣿⣿⣿⣿⣾⣿⣿⢿⣿⣿⣿⣿⣿⣾⣿⣷⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡄⠀⣀⡀⠀⠀⠀ ⣷⢶⣶⣶⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣯⢾⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⣶⠀⠀⠀⠠ ⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⣮⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⡄⠀⠀⠀ ⣿⣛⣛⣟⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣸⣿⣿⠃⠀⠇⡅⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣷⣬⣥⣴ ⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢀⡄⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠂⠉⢁⣴⣶⣿⠿⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣙⣿⣿⣿⣿⣿ ⣾⣿⣿⢿⣾⠿⢿⣿⡿⠿⠿⠿⠿⡿⠿⣿⢿⠻⠉⠱⠈⢡⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠇⢀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣿⡿⣻⠈⠿⢶⣆⠿⠿⠿⡀⠀⠸⠷⠀⠶⠀⠹⠆⠀⠀⠰⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠏⢠⣿⣿⣿⠃⠸⣿⣶⣿⣿⣿⣶⣿⡟⠀⠀⠀⠀⠀⢀⣀⣤⣄⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣷⣶⡶⣶⣾⡟⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⢀⣿⣿⣿⡏⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢐⠒⠂⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⢗⣒⠒⡒⠒⠐⢲⣄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⣿⣿⣿⡇⠀⠀⠹⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠰⣾⣿⣿⣿⠀⢾⡯⠠⠤⢴⣿⣿⣿⣿⣿⣿ ⡿⠛⢛⡃⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠐⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⣿⣿⣿⡇⠀⠀⣼⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣹⣫⣀⣤⣤⣼⣿⣿⣿⣿⣿⣿ ⠙⠛⠛⠃⠀⣀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢸⠐⣰⠀⠀⠀⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⠸⣿⣿⣿⣿⡀⠀⢸⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢀⡄⢀⡻⣿⣿⡋⠙⠿⠟⠀⢰⣿⣿⣿⣿⣿⣿ ⣶⣶⣾⠇⠀⢻⡃⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⣸⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡄⢻⣿⣿⣿⣷⣄⠈⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣠⡾⠁⡸⢻⣿⣿⠀⣅⠀⢀⠀⢸⣿⣿⣿⣿⣿⣿ ⣷⡶⠶⠇⠀⠘⠏⠀⠀⠀⠁⠀⠀⠀⠀⠹⠇⢿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣇⠻⣿⣿⣿⣿⣷⣬⣙⠿⠛⠿⠿⠿⢀⣤⣾⡿⠁⢸⣿⣿⣿⣿⣤⣯⣷⣤⣴⣾⣿⣿⣿⣿⣿⣿ ⣇⣁⣁⡀⠀⠀⠀⠁⠀⠘⠃⠀⠀⠀⠀⠘⠉⣾⠁⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⡿⠋⠀⠀⢰⠿⣿⣿⣿⡛⠉⠈⠀⠙⢻⣿⣿⣿⣿⣿⣿ ⣏⠋⠛⢁⣀⣠⣀⢀⣀⣀⣀⣀⣀⣀⣀⣈⣠⣿⠖⠆⢶⡆⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠿⠿⠟⠋⠁⠀⠀⠀⠀⠸⠟⣿⣟⣛⠛⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⡟⠛⠛⠃⠛⠹⣷⠞⠙⠛⠋⠛⠊⣯⠛⢻⣿⣿⣻⣿⣿⣧⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⣀⣠⣤⡀⣤⣤⣀⣀⣀⣀⣀⣀⣀⢸⠿⢿⣿⣿⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿ ⣞⣿⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡿⠻⠉⡻⠑⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣻⣿⣿⣷⣟⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⠀⡵⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣽⣼⣿⠀⢠⡄⠀⠀⠀⠰⠍⠉⣉⣉⣹ ⡿⣿⡟⠛⠙⠹⠇⠀⠀⠀⣴⡄⠀⠀⠀⠀⢈⣅⣬⣠⣈⣇⣠⣀⣀⣄⣠⣀⣄⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⡀⣠⣀⡀⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣯⣿⣿⣿⣽⣿⢏⣿⣿⢰⣿⣁⣀⣀⣀⣄⣌⣥⣬⣭⣍ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⣶⣶⠶⠶⣶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠦⠰⠆ ⣶⣷⣷⣶⣶⣷⠶⠶⠷⠶⠶⠶⠶⠶⠶⢲⣶⣦⠴⢴⡤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡷⢶⠶⠶⣶⠳⢶⡶⠒⠒⠒⠶⠶⠶⠲⢺⡈⣽⠉⠎⠁⠀⠀⣤⣿⣿⣿⣾⣷⣾⣿⣿⣷⡻⣿⣿⣿⣿⣿⣿⣾⣿⣿⢿⣿⣿⣿⣿⣿⣾⣿⣷⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡄⠀⣀⡀⠀⠀⠀ ⣷⢶⣶⣶⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣯⢾⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⣶⠀⠀⠀⠠ ⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⣮⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⡄⠀⠀⠀ ⣿⣛⣛⣟⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣸⣿⣿⠃⠀⠇⡅⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣷⣬⣥⣴ ⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢀⡄⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠂⠉⢁⣴⣶⣿⠿⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣙⣿⣿⣿⣿⣿ ⣾⣿⣿⢿⣾⠿⢿⣿⡿⠿⠿⠿⠿⡿⠿⣿⢿⠻⠉⠱⠈⢡⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠇⢀⣴⣿⣿⠟⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣿⡿⣻⠈⠿⢶⣆⠿⠿⠿⡀⠀⠸⠷⠀⠶⠀⠹⠆⠀⠀⠰⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠏⢠⣿⣿⣿⠃⠸⣿⣶⣿⣿⣿⣶⣾⡟⠀⠀⠀⠀⠀⢀⣀⣤⣄⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣷⣶⡶⣶⣾⡟⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⢀⣿⣿⣿⡏⠀⢀⣿⣿⣿⣿⣿⣿⣿⠀⠀⡀⠐⠀⠈⢸⣿⣿⣿⣿⢐⠒⠂⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⢗⣒⠒⡒⠒⠐⢲⣄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⣿⣿⣿⡇⠀⠘⠽⣿⣿⣿⣿⣿⣟⢆⡀⠖⢀⣀⠀⠰⣾⣾⣿⣿⠀⢾⡯⠠⠤⢴⣿⣿⣿⣿⣿⣿ ⡿⠛⢛⡃⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠐⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⣿⣿⣿⡇⠀⠀⣼⣿⣿⣿⣿⣿⣿⡟⣁⠀⠉⠀⠀⠀⢞⣿⣿⣿⣹⣫⣀⣤⣤⣼⣿⣿⣿⣿⣿⣿ ⠙⠛⠛⠃⠀⣀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢸⠐⣰⠀⠀⠀⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⠸⣿⣿⣿⣿⡀⢰⢽⣿⣿⣿⣿⣿⣿⣷⠋⠀⠀⠀⢀⡄⢀⡻⣿⣿⡋⠙⠿⠟⠀⢰⣿⣿⣿⣿⣿⣿ ⣶⣶⣾⠇⠀⢻⡃⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⣸⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡄⢻⣿⣿⣿⣿⣿⡜⢿⣿⣿⣿⣿⣿⣿⠛⠀⠀⣠⡾⠁⡸⢻⣿⣿⠀⣅⠀⢀⠀⢸⣿⣿⣿⣿⣿⣿ ⣷⡶⠶⠇⠀⠘⠏⠀⠀⠀⠁⠀⠀⠀⠀⠹⠇⢿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣇⠻⣿⣿⣿⣿⣿⣬⣙⠷⠛⠿⠿⠿⣄⣤⣾⣿⣅⢸⣿⣿⣿⣿⢤⣯⣷⢤⣴⣾⣿⣿⣿⣭⣿⣿ ⣇⣁⣁⡀⠀⠀⠀⠁⠀⠘⠃⠀⠀⠀⠀⠘⠉⣾⠁⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⡿⠋⠉⠀⢰⠿⣿⣛⣿⣻⠍⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿ ⣏⠋⠛⢁⣀⣠⣀⢀⣀⣀⣀⣀⣀⣀⣀⣈⣠⣿⠖⠆⢶⡆⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⢿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠸⠟⣿⣟⣛⠛⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⡟⠛⠛⠃⠛⠹⣷⠞⠙⠛⠋⠛⠊⣯⠛⢻⣿⣿⣻⣿⣿⣧⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⣀⣠⣤⡀⣤⣤⣀⣀⣀⣀⣀⣀⣀⢸⠿⢿⠟⢿⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿ ⣞⣿⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡿⠻⠉⡻⠑⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣻⣿⣿⣷⣟⣿⣟⣻⣻⣿⣿⣿⡿⢟⠛⣫⣠⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⠀⡵⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣻⣿⣿⣷⣿⣿⣿⣿⣿⣿⣾⣿⣽⣼⣿⠀⢠⡄⠀⠀⠀⠰⠍⠉⣉⣉⣹ ⡿⣿⡟⠛⠙⠹⠇⠀⠀⠀⣴⡄⠀⠀⠀⠀⢈⣅⣬⣠⣈⣇⣠⣀⣀⣄⣠⣀⣄⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⡀⣠⣀⡀⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣯⣿⣿⣿⣽⣿⢏⣿⣿⢰⣿⣁⣀⣀⣀⣄⣌⣥⣬⣭⣍ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⣶⣶⠶⠶⣶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠦⠰⠆ ⣶⣷⣷⣶⣶⣷⠶⠶⠷⠶⠶⠶⠶⠶⠶⢲⣶⣦⠴⢴⡤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡷⢶⠶⠶⣶⠳⢶⡶⠒⠒⠒⠶⠶⠶⠲⢺⡈⣽⠉⠎⠁⠀⠀⣤⣿⣿⣿⣾⣷⣾⣿⣿⣷⡻⣿⣿⣿⣿⣿⣿⣾⣿⣿⢿⣿⣿⣿⣿⣿⣾⣿⣷⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡄⠀⣀⡀⠀⠀⠀ ⣷⢶⣶⣶⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣯⢾⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⣶⠀⠀⠀⠠ ⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⣮⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⡄⠀⠀⠀ ⣿⣛⣛⣟⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣸⣿⣿⠃⠀⠇⡅⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣷⣬⣥⣴ ⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢀⡄⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠂⠉⢁⣴⣶⣿⠿⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣙⣿⣿⣿⣿⣿ ⣾⣿⣿⢿⣾⠿⢿⣿⡿⠿⠿⠿⠿⡿⠿⣿⢿⠻⠉⠱⠈⢡⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠇⢀⣴⣿⣿⠟⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣿⡿⣻⠈⠿⢶⣆⠿⠿⠿⡀⠀⠸⠷⠀⠶⠀⠹⠆⠀⠀⠰⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠏⢠⣿⣿⣿⠃⠸⣿⣶⣿⣿⣿⣶⣾⡟⠀⠀⠀⠀⠀⢀⣀⣤⣄⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣷⣶⡶⣶⣾⡟⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⢀⣿⣿⣿⡏⠀⢀⣿⣿⣿⣿⣿⣿⣿⠀⠀⡀⠐⠀⠈⢸⣿⣿⣿⣿⢐⠒⠂⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⢗⣒⠒⡒⠒⠐⢲⣄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⣿⣿⣿⡇⠀⠘⠽⣿⣿⣿⣿⣿⣟⢆⡀⠖⢀⣀⠀⠰⣾⣾⣿⣿⠀⢾⡯⠠⠤⢴⣿⣿⣿⣿⣿⣿ ⡿⠛⢛⡃⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠐⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⣿⣿⣿⡇⠀⠀⣼⣿⣿⣿⣿⣿⣿⡟⣁⠀⠉⠀⠀⠀⢞⣿⣿⣿⣹⣫⣀⣤⣤⣼⣿⣿⣿⣿⣿⣿ ⠙⠛⠛⠃⠀⣀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢸⠐⣰⠀⠀⠀⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⠸⣿⣿⣿⣿⡀⢰⢽⣿⣿⣿⣿⣿⣿⣷⠋⠀⠀⠀⢀⡄⢀⡻⣿⣿⡋⠙⠿⠟⠀⢰⣿⣿⣿⣿⣿⣿ ⣶⣶⣾⠇⠀⢻⡃⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⣸⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡄⢻⣿⣿⣿⣿⣿⡜⢿⣿⣿⣿⣿⣿⣿⠛⠀⠀⣠⡾⠁⡸⢻⣿⣿⠀⣅⠀⢀⠀⢸⣿⣿⣿⣿⣿⣿ ⣷⡶⠶⠇⠀⠘⠏⠀⠀⠀⠁⠀⠀⠀⠀⠹⠇⢿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣇⠻⣿⣿⣿⣿⣿⣬⣙⠷⠛⠿⠿⠿⣄⣤⣾⣿⣅⢸⣿⣿⣿⣿⢤⣯⣷⢤⣴⣾⣿⣿⣿⣭⣿⣿ ⣇⣁⣁⡀⠀⠀⠀⠁⠀⠘⠃⠀⠀⠀⠀⠘⠉⣾⠁⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⡿⠋⠉⠀⢰⠿⣿⣛⣿⣻⠍⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿ ⣏⠋⠛⢁⣀⣠⣀⢀⣀⣀⣀⣀⣀⣀⣀⣈⣠⣿⠖⠆⢶⡆⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⢿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠸⠟⣿⣟⣛⠛⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⡟⠛⠛⠃⠛⠹⣷⠞⠙⠛⠋⠛⠊⣯⠛⢻⣿⣿⣻⣿⣿⣧⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⣀⣠⣤⡀⣤⣤⣀⣀⣀⣀⣀⣀⣀⢸⠿⢿⠟⢿⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿ ⣞⣿⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡿⠻⠉⡻⠑⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣻⣿⣿⣷⣟⣿⣟⣻⣻⣿⣿⣿⡿⢟⠛⣫⣠⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⠀⡵⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣻⣿⣿⣷⣿⣿⣿⣿⣿⣿⣾⣿⣽⣼⣿⠀⢠⡄⠀⠀⠀⠰⠍⠉⣉⣉⣹ ⡿⣿⡟⠛⠙⠹⠇⠀⠀⠀⣴⡄⠀⠀⠀⠀⢈⣅⣬⣠⣈⣇⣠⣀⣀⣄⣠⣀⣄⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⡀⣠⣀⡀⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣯⣿⣿⣿⣽⣿⢏⣿⣿⢰⣿⣁⣀⣀⣀⣄⣌⣥⣬⣭⣌ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⣶⣶⠶⠶⣶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠦⠰⠆ ⣶⣶⣷⣶⣶⣷⠶⠶⠷⠶⠶⠶⠶⠶⠶⢲⣶⣦⠴⢴⡤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡷⢶⠶⠶⣶⠳⢴⡶⠒⠒⠒⠶⠶⠶⠲⢺⡈⣽⠉⠎⠁⠀⠀⣤⣿⣿⣿⣾⣷⣾⣿⣿⣷⡻⣿⣿⣿⣿⣿⣿⣾⣿⣿⢿⣿⣿⣿⣷⣿⣾⣿⣷⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡄⠀⣀⡀⠀⠀⠀ ⣷⢶⣶⣶⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣧⢾⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⣶⠀⠀⠀⠠ ⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⣮⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⡄⠀⠀⠀ ⣿⣛⣛⣟⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣸⣿⣿⠃⠀⠇⡅⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣷⣬⣥⣴ ⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢀⡄⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠂⠉⢁⣴⣶⣿⠿⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣙⣿⣿⣿⣿⣿ ⣾⣿⣿⢿⣾⠿⢿⣿⠿⠿⠿⠿⠿⡿⠿⣿⢿⠻⠉⠱⠈⢡⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠇⢀⣴⣿⣿⠟⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣿⡿⣻⠈⠿⢶⣆⠿⠿⠿⡀⠀⠸⠷⠀⠶⠀⠹⠆⠀⠀⠰⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠏⢠⣿⣿⣿⠃⠸⣿⣶⣿⣿⣿⣶⣾⡟⠀⠀⠀⠀⠀⢀⣀⣤⣄⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⡷⣶⡶⣶⣾⡟⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⢀⣿⣿⣿⡏⠀⢀⣿⣿⣿⣿⣿⣿⣿⠀⠀⡀⠐⠀⠈⢸⣿⣿⣿⣿⠐⠒⠂⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⢖⣒⠒⡒⠒⠐⢲⣄⠀⠀⠀⠀⢀⡠⢀⡈⠀⠸⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⣿⣿⣿⡇⠀⠘⠽⣿⣿⣿⣿⣿⣟⢆⡀⠖⠀⣀⠀⠰⣾⣾⣿⣿⠀⠆⡤⠠⠤⢴⣿⣿⣿⣿⣿⣿ ⡿⠛⢛⡃⠀⠀⠘⠋⠀⠀⠀⠀⠘⠃⠘⠓⠀⢸⡏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⣿⣿⣿⡇⠀⠀⣼⣿⣿⣿⣿⣿⣿⡟⣁⠀⠉⠀⠀⠀⢞⣿⣿⣿⣹⣫⣀⣤⣤⣼⣿⣿⣿⣿⣿⣿ ⠙⠛⠛⠃⠀⣀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢸⠐⣰⠀⠀⠀⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⠸⣿⣿⣿⣿⡀⢰⢽⣿⣿⣿⣿⣿⣿⣷⠋⠀⠀⠀⢀⡄⢀⡻⣿⣿⡋⠙⠿⠟⠀⢰⣿⣿⣽⣿⣿⣿ ⣶⣶⣾⠇⠀⢻⡃⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⣸⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡄⢻⣿⣿⣿⣿⣿⡜⢿⣿⣿⣿⣿⣿⣿⠛⠀⠀⣠⡾⠁⡸⢻⣿⣿⠀⣅⠀⢀⠀⢸⣿⣿⣿⣿⣿⣿ ⣗⡶⠶⠇⠀⠘⠏⠀⠀⠀⠁⠀⠀⠀⠀⠹⠇⢿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣇⠻⣿⣿⣿⣿⣿⣬⣙⠷⠛⠿⠿⠿⣄⣤⣾⣿⣅⢸⣿⣿⣿⣿⢤⣯⣷⢤⣴⣾⣿⣿⣿⣭⣿⣿ ⣇⣁⣁⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠘⠉⣾⠁⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⡿⠋⠉⠀⢰⠿⣿⣛⣿⣻⠍⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿ ⣏⠋⠛⢁⣀⣠⣀⢀⣀⣀⣀⣀⣀⣀⣀⣈⣠⣿⠖⠆⢶⡆⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⢿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠸⠟⣟⠛⣛⠛⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⡟⠛⠛⠃⠋⠹⣷⠞⠙⠛⠋⠛⠊⣯⠛⢻⣿⣿⣻⣿⣿⣧⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⣀⣠⣤⡀⣤⣤⣀⣀⣀⣀⣀⣀⣀⢈⠿⢟⠟⢿⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿ ⣞⣿⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡿⠻⠉⡻⠑⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣻⣿⣿⣷⣟⣿⣟⣻⣻⣿⣿⣿⡿⢟⠛⣫⣠⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⠀⡵⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣻⣿⣿⣷⣿⣿⣿⣿⣿⣿⣾⣿⣽⣼⣿⠀⢠⡄⠀⠀⠀⠰⠍⠉⣉⣉⣹ ⡿⣿⡟⠛⠙⠹⠇⠀⠀⠀⣴⡄⠀⠀⠀⠀⢈⣅⣬⣠⣈⣇⣀⣀⣀⣄⣠⣀⣄⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⡀⣠⣀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣽⣿⢏⣿⣿⢰⣿⣁⣀⣀⣀⣄⣌⣥⣬⣭⣌ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⣶⣶⠶⠶⣶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠦⠰⠆ ⣶⣶⣷⣶⣶⣷⠶⠶⠷⠶⠶⠶⠶⠶⠶⢲⣶⣦⠴⢴⡤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡷⢶⠶⠶⣶⠳⢴⡶⠒⠒⠒⠶⠶⠶⠲⢺⡈⣽⠉⠎⠁⠀⠀⣤⣿⣿⣿⣾⣷⣾⣿⣿⣷⡻⣿⣿⣿⣿⣿⣿⣾⣿⣿⢿⣿⣿⣿⣷⣿⣾⣿⣷⣿⣿⣿⣿⣿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡄⠀⣀⡀⠀⠀⠀ ⣷⢶⣶⣶⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣧⢾⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⣶⠀⠀⠀⠠ ⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⣮⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⡀⠀⠀⠀ ⣿⣛⣛⣟⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣸⣿⣿⠃⠀⠇⡅⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣷⣬⣥⣴ ⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢀⡄⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠂⠉⢁⣴⣶⣿⠿⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣙⣿⣿⣿⣿⣿ ⣾⣿⣿⢿⣾⠿⢿⣿⠿⠿⠿⠿⠿⡿⠿⣿⢿⠻⠉⠱⠈⢡⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠇⢀⣴⣿⣿⠟⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣿⡿⣻⠈⠿⢶⡆⠿⠿⠿⡀⠀⠸⠷⠀⠶⠀⠹⠆⠀⠀⠰⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠏⢠⣿⣿⣿⠃⠸⣿⣶⣿⣿⣿⣶⣾⡟⠀⠀⠀⠀⠀⢀⣀⣤⣄⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⡷⣶⡶⣶⣾⡟⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⢀⣿⣿⣿⡏⠀⢀⣿⣿⣿⣿⣿⣿⣿⠀⠀⡀⠐⠀⠈⢸⣿⣿⣿⣿⠐⠒⠂⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⢖⣒⠒⡒⠒⠐⢲⡄⠀⠀⠀⠀⢀⡠⢀⡈⠀⠸⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⣿⣿⣿⡇⠀⠘⠽⣿⣿⣿⣿⣿⣟⢆⡀⠖⠀⣀⠀⠰⣾⣾⣿⣿⠀⠆⡤⠠⠤⢴⣿⣿⣿⣿⣿⣿ ⡿⠛⢛⡃⠀⠀⠘⠋⠀⠀⠀⠀⠘⠃⠘⠓⠀⢸⡏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⣿⣿⣿⡇⠀⠀⣼⣿⣿⣿⣿⣿⣿⡟⣁⠀⠉⠀⠀⠀⢞⣿⣿⣿⣹⣫⣀⣤⣤⣼⣿⣿⣿⣿⣿⣿ ⠙⠛⠛⠃⠀⣀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢸⠐⣠⠀⠀⠀⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⠸⣿⣿⣿⣿⡀⢰⢽⣿⣿⣿⣿⣿⣿⣷⠋⠀⠀⠀⢀⡄⢀⡻⣿⣿⡋⠙⠿⠟⠀⢰⣿⣿⣽⣿⣿⣿ ⣶⣶⣾⠇⠀⢻⡃⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⣸⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡄⢻⣿⣿⣿⣿⣿⡜⢿⣿⣿⣿⣿⣿⣿⠛⠀⠀⣠⡾⠁⡸⢻⣿⣿⠀⣅⠀⢀⠀⢸⣿⣿⣿⣿⣿⣿ ⣗⡶⠶⠇⠀⠘⠏⠀⠀⠀⠁⠀⠀⠀⠀⠹⠇⢿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣇⠻⣿⣿⣿⣿⣿⣬⣙⠷⠙⠿⠿⠿⣄⣤⣾⣿⣅⢸⣿⣿⣿⣿⢤⣯⣷⢤⣴⣾⣿⣿⣿⣭⣿⣿ ⣇⣁⣁⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠘⠉⣾⠁⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⡿⠋⠉⠀⢰⠿⣿⣛⣿⣻⠍⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿ ⣏⠋⠛⢁⣀⣠⣀⢀⣀⣀⣀⣀⣀⣀⣀⣈⣠⣿⠖⠆⢶⡆⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⢿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠸⠟⣟⠛⣛⠛⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⡟⠛⠛⠃⠋⠹⣷⠞⠙⠛⠋⠛⠊⣯⠛⢻⣿⣿⣻⣿⣿⣧⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⣀⣠⣤⡀⣤⣤⣀⣀⣀⣀⣀⣀⣀⢈⠿⢟⠟⢿⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿ ⣞⣿⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡿⠻⠉⡻⠑⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣻⣿⣿⣷⣟⣿⣟⣻⣻⣿⣿⣿⡿⢟⠛⣫⣠⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⠀⡵⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣻⣿⣿⣷⣿⣿⣿⣿⣿⣿⣾⣿⣽⣼⣿⠀⢠⡄⠀⠀⠀⠰⠍⠉⣉⣉⣹ ⡿⣿⡟⠛⠙⠹⠇⠀⠀⠀⣴⡄⠀⠀⠀⠀⢈⣅⣬⣠⣈⣇⣀⣀⣀⣄⣠⣀⣄⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⡀⣠⣀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣽⣿⢏⣿⣿⢰⣿⣁⣀⣀⣀⣄⣌⣥⣬⣭⣌ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⣶⣶⠶⠶⣶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠦⠰⠆ ⣶⣶⣷⣶⣶⣷⠶⠶⠷⠶⠶⠶⠶⠶⠶⢲⣶⣦⠴⢴⡤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡷⢶⠶⠶⣶⠳⢴⡶⠒⠒⠒⠶⠶⠶⠲⢺⡈⣽⠉⠎⠁⠀⠀⣤⣿⣿⣿⣾⣷⣾⣿⣿⣷⡻⣿⣿⣿⣿⣿⣿⣾⣿⣿⢿⣿⣿⣿⣷⣿⣾⣿⣷⣿⣿⣿⣿⣿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡄⠀⣀⡀⠀⠀⠀ ⣷⢶⣶⣶⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣧⢾⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⣶⠀⠀⠀⠠ ⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⣮⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⡀⠀⠀⠀ ⣿⣛⣛⣟⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣸⣿⣿⠃⠀⠇⡅⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣷⣬⣥⣴ ⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢀⡄⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠂⠉⢁⣴⣶⣿⠿⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣙⣿⣿⣿⣿⣿ ⣾⣿⣿⢿⣾⠿⢿⣿⠿⠿⠿⠿⠿⡿⠿⣿⢿⠻⠉⠱⠈⢡⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠇⢀⣴⣿⣿⠟⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣿⡿⣻⠈⠿⢶⡆⠿⠿⠿⡀⠀⠸⠷⠀⠶⠀⠹⠆⠀⠀⠰⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠏⢠⣿⣿⣿⠃⠸⣿⣶⣿⣿⣿⣶⣾⡟⠀⠀⠀⠀⠀⢀⣀⣤⣄⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⡷⣶⡶⣶⣾⡟⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⢀⣿⣿⣿⡏⠀⢀⣿⣿⣿⣿⣿⣿⣿⠀⠀⡀⠐⠀⠈⢸⣿⣿⣿⣿⠐⠒⠂⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⢖⣒⠒⡒⠒⠐⢲⡄⠀⠀⠀⠀⢀⡠⢀⡈⠀⠸⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⣿⣿⣿⡇⠀⠘⠽⣿⣿⣿⣿⣿⣟⢆⡀⠖⠀⣀⠀⠰⣾⣾⣿⣿⠀⠆⡤⠠⠤⢴⣿⣿⣿⣿⣿⣿ ⡿⠛⢛⣣⡤⠄⠘⠋⠠⠀⠀⠀⠜⠃⠜⠓⠠⢸⡏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⣿⣿⣿⡇⠀⠀⣼⣿⣿⣿⣿⣿⣿⡟⣁⠀⠉⠀⠀⠀⢞⣿⣿⣿⣹⣫⣀⣤⣤⣼⣿⣿⣿⣿⣿⣿ ⠙⠛⠛⠛⠛⣀⠀⠀⠒⠂⠀⠀⠀⠀⠀⢸⠐⣠⠀⠀⠀⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⠸⣿⣿⣿⣿⡀⢰⢽⣿⣿⣿⣿⣿⣿⣷⠋⠀⠀⠀⢀⡄⢀⡻⣿⣿⡋⠙⠿⠟⠀⢰⣿⣿⣽⣿⣿⣿ ⣶⣶⣾⠇⠀⢻⡃⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⣸⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡄⢻⣿⣿⣿⣿⣿⡜⢿⣿⣿⣿⣿⣿⣿⠛⠀⠀⣠⡾⠁⡸⢻⣿⣿⠀⣅⠀⢀⠀⢸⣿⣿⣿⣿⣿⣿ ⣗⡶⠶⠇⠀⠘⠏⠀⠀⠀⠁⠀⠀⠀⠀⠹⠇⢿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣇⠻⣿⣿⣿⣿⣿⣬⣙⠷⠙⠿⠿⠿⣄⣤⣾⣿⣅⢸⣿⣿⣿⣿⢤⣯⣷⢤⣴⣾⣿⣿⣿⣭⣿⣿ ⣇⣁⣁⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠘⠉⣾⠁⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⡿⠋⠉⠀⢰⠿⣿⣛⣿⣻⠍⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿ ⣏⠋⠛⢁⣀⣠⣀⢀⣀⣀⣀⣀⣀⣀⣀⣈⣠⣿⠖⠆⢶⡆⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⢿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠸⠟⣟⠛⣛⠛⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⡟⠛⠛⠃⠋⠹⣷⠞⠙⠛⠋⠛⠊⣯⠛⢻⣿⣿⣻⣿⣿⣧⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⣀⣠⣤⡀⣤⣤⣀⣀⣀⣀⣀⣀⣀⢈⠿⢟⠟⢿⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿ ⣞⣿⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡿⠻⠉⡻⠑⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣻⣿⣿⣷⣟⣿⣟⣻⣻⣿⣿⣿⡿⢟⠛⣫⣠⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⠀⡵⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣻⣿⣿⣷⣿⣿⣿⣿⣿⣿⣾⣿⣽⣼⣿⠀⢠⡄⠀⠀⠀⠰⠍⠉⣉⣉⣹ ⡿⣿⡟⠛⠙⠹⠇⠀⠀⠀⣴⡄⠀⠀⠀⠀⢈⣅⣬⣠⣈⣇⣀⣀⣀⣄⣠⣀⣄⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⡀⣠⣀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣽⣿⢏⣿⣿⢰⣿⣁⣀⣀⣀⣄⣌⣥⣬⣭⣌ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⣶⣶⠶⠶⣶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠦⠰⠆ ⣶⣶⣷⣶⣶⣷⠶⠶⠷⠶⠶⠶⠶⠶⠶⢲⣶⣦⠴⢴⡤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡷⢶⠶⠶⣶⠳⢴⡶⠒⠒⠒⠶⠶⠶⠲⢺⡈⣽⠉⠎⠁⠀⠀⣤⣿⣿⣿⣾⣷⣾⣿⣿⣷⡻⣿⣿⣿⣿⣿⣿⣾⣿⣿⢿⣿⣿⣿⣷⣿⣾⣿⣷⣿⣿⣿⣿⣿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡄⠀⣀⡀⠀⠀⠀ ⣷⢶⣶⣶⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣧⢾⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⣶⠀⠀⠀⠠ ⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⣮⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⡀⠀⠀⠀ ⣿⣛⣛⣟⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣸⣿⣿⠃⠀⠇⡅⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣷⣬⣥⣴ ⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢀⡄⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠂⠉⢁⣴⣶⣿⠿⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣙⣿⣿⣿⣿⣿ ⣾⣿⣿⢿⣾⠿⢿⣿⠿⠿⠿⠿⠿⡿⠿⣿⢿⠻⠉⠱⠈⢡⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠇⢀⣴⣿⣿⠟⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣿⡿⣻⠈⠿⢶⡆⠿⠿⠿⡀⠀⠸⠷⠀⠶⠀⠹⠆⠀⠀⠰⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠏⢠⣿⣿⣿⠃⠸⣿⣶⣿⣿⣿⣶⣾⡟⠀⠀⠀⠀⠀⢀⣀⣤⣄⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⡷⣶⡶⣶⣾⡟⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⢀⣿⣿⣿⡏⠀⢀⣿⣿⣿⣿⣿⣿⣿⠀⠀⡀⠐⠀⠈⢸⣿⣿⣿⣿⠐⠒⠂⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⢖⣒⠒⡒⠒⠐⢲⡄⠀⠀⠀⠀⢀⡠⢀⡈⠀⠸⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⣿⣿⣿⡇⠀⠘⠽⣿⣿⣿⣿⣿⣟⢆⡀⠖⠀⣀⠀⠰⣾⣾⣿⣿⠀⠆⡤⠠⠤⢴⣿⣿⣿⣿⣿⣿ ⡿⠛⢛⣣⡤⠄⠘⠋⠠⠀⠀⠀⠜⠃⠜⠓⠠⢸⡏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⣿⣿⣿⡇⠀⠀⣼⣿⣿⣿⣿⣿⣿⡟⣁⠀⠉⠀⠀⠀⢞⣿⣿⣿⣹⣫⣀⣤⣤⣼⣿⣿⣿⣿⣿⣿ ⠙⠛⠛⠛⠛⣀⠀⠀⠒⠂⠀⠀⠀⠀⠀⢸⠐⣠⠀⠀⠀⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⠸⣿⣿⣿⣿⡀⢰⢽⣿⣿⣿⣿⣿⣿⣷⠋⠀⠀⠀⢀⡄⢀⡻⣿⣿⡋⠙⠿⠟⠀⢰⣿⣿⣽⣿⣿⣿ ⣶⣶⣾⠇⠀⢻⡃⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⣸⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡄⢻⣿⣿⣿⣿⣿⡜⢿⣿⣿⣿⣿⣿⣿⠛⠀⠀⣠⡾⠁⡸⢻⣿⣯⠀⣅⠀⢀⠀⢸⣿⣿⣿⣿⣿⣿ ⣗⡶⠶⠇⠀⠘⠏⠀⠀⠀⠁⠀⠀⠀⠀⠹⠇⢿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣇⠻⣿⣿⣿⣿⣿⣬⣙⠷⠙⠿⠿⠿⣄⣤⣾⣿⣅⢸⣿⣿⣿⣿⢤⣯⣷⢤⣴⣾⣿⣿⣿⣭⣿⣿ ⣇⣁⣁⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠘⠉⣾⠁⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⡿⠋⠉⠀⢰⠿⣿⣛⣿⣻⠍⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿ ⣏⠋⠛⢁⣀⣠⣀⢀⣀⣀⣀⣀⣀⣀⣀⣈⣠⣿⠖⠆⢶⡆⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⢿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠸⠟⣟⠛⣛⠛⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⡟⠛⠛⠃⠋⠹⣷⠞⠙⠛⠋⠛⠊⣯⠛⢻⣿⣿⣻⣿⣿⣧⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⣀⣠⣤⡀⣤⣤⣀⣀⣀⣀⣀⣀⣀⢈⠿⢟⠟⢿⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿ ⣞⣿⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡿⠻⠉⡻⠑⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣻⣿⣿⣷⣟⣿⣟⣻⣻⣿⣿⣿⡿⢟⠛⣫⣠⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⠀⡵⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣻⣿⣿⣷⣿⣿⣿⣿⣿⣿⣾⣿⣽⣼⣿⠀⢠⡄⠀⠀⠀⠰⠍⠉⣉⣉⣹ ⡿⣿⡟⠛⠙⠹⠇⠀⠀⠀⣴⡄⠀⠀⠀⠀⢈⣅⣬⣠⣈⣇⣀⣀⣀⣄⣠⣀⣄⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⡀⣠⣀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣽⣿⢏⣿⣿⢰⣿⣁⣀⣀⣀⣄⣌⣥⣬⣭⣌ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⣶⣶⠶⠶⣶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠦⠰⠆ ⣶⣶⣷⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢲⣶⣦⠴⢴⡤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡷⢶⠶⠖⣶⠳⢴⡶⠒⠒⠒⠶⠶⠶⠲⢺⡈⣽⠉⠎⠁⠀⠀⣤⣿⣿⣿⣾⣷⣾⣿⣿⣷⡻⣿⣿⣿⣿⣿⣿⣾⣿⣿⢿⣿⣿⣿⣷⣿⣾⣿⣷⣿⣿⣿⣿⣿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡄⠀⣀⡀⠀⠀⠀ ⣷⢶⣶⣶⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣧⢾⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⣶⠀⠀⠀⠠ ⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⣮⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⡀⠀⠀⠀ ⣿⣛⣛⣟⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣸⣿⣿⠃⠀⠇⡅⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣷⣬⣥⣴ ⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢀⡄⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠂⠉⢁⣴⣶⣿⠿⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣙⣿⣿⣿⣿⣿ ⣾⣿⣿⢿⣾⠿⢿⣿⠿⠿⠿⠿⠿⡿⠿⣿⢿⠻⠉⠱⠈⢡⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠇⢀⣴⣿⣿⠟⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣿⡿⣻⠈⠻⢶⡆⠿⠿⠿⡀⠀⠸⠷⠀⠶⠀⠹⠆⠀⠀⠰⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠏⢠⣿⣿⣿⠃⠸⣿⣶⣿⣿⣿⣶⣾⡟⠀⠀⠀⠀⠉⢉⣀⣤⣄⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⡷⣶⡶⣶⣾⡟⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⢀⣿⣿⣿⡏⠀⢀⣿⣿⣿⣿⣿⣿⣿⠀⠀⡀⠐⠀⠀⢸⣿⣿⣿⣿⠐⠒⠂⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⢖⣒⠒⡒⠒⠐⢲⡄⠀⠀⠀⠀⢀⡠⢀⡈⠀⠸⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⣿⣿⣿⡇⠀⠘⠽⣿⣿⣿⣿⣿⣟⢆⡀⠖⠀⣀⠀⠰⣾⣬⣽⣹⠀⠄⡤⠠⠤⢴⣿⣿⣿⣿⣿⣿ ⡿⠛⢛⣣⡤⠄⠘⠋⠠⠀⠀⠀⠜⠃⠜⠓⠠⢸⡏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⣿⣿⣿⡇⠀⠀⣼⣿⣿⣿⣿⣿⣿⡟⣁⠀⠉⠀⠀⠀⢞⣿⣿⣿⣹⣫⣀⣤⣤⣼⣿⣿⣿⣿⣿⣿ ⠙⠛⠛⠛⠛⣀⠀⠀⠒⠂⠀⠀⠀⠀⠀⢸⠐⣠⠀⠀⠀⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⠸⣿⣿⣿⣿⡀⢰⢽⣿⣿⣿⣿⣿⣿⣷⠋⠀⠀⠀⢀⡄⢀⡻⣿⣿⡋⠙⠿⠟⠀⢰⣿⣿⣽⣿⣿⣿ ⣶⣶⣾⠇⠀⢻⡃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣸⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡄⢻⣿⣿⣿⣿⣿⡜⢿⣿⣿⣿⣿⣿⣿⠛⠀⠀⣠⡾⠁⡸⢻⣿⣯⠀⣅⠀⢀⠀⢸⣿⣿⣿⣿⣿⣿ ⣗⡶⠶⠇⠀⠘⠏⠀⠀⠀⠁⠀⠀⠀⠀⠹⠇⢿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣇⠻⣿⣿⣿⣿⣿⣬⣙⠷⠙⠿⠿⠿⣄⣤⣾⣿⣅⢸⣿⣿⣰⣿⢤⣯⣷⢤⣴⣾⣿⣿⣿⣭⣿⣿ ⣇⣁⣁⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠘⠉⣾⠁⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣾⣶⣶⣾⡿⠋⠉⠀⢰⠿⣯⣚⣿⣻⠍⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿ ⣏⠋⠛⢁⣀⣠⣀⢀⣀⣀⣀⣀⣀⣀⣀⣈⣠⣿⠖⠆⢶⡆⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠛⠿⠿⢿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠸⠟⣟⠛⢛⠛⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⡟⠛⠛⠃⠋⠹⣷⠞⠙⠛⠋⠛⠊⣯⠛⢻⣿⣿⣻⣿⣿⣧⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⣀⣠⣤⡀⣤⣤⣀⣀⣀⣀⣀⣀⣀⢈⠿⢛⠟⢿⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿ ⣞⣿⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡿⠻⠉⡻⠑⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣻⣿⣿⣷⣟⣿⣟⣻⣻⣿⣿⣿⡿⢟⠛⣯⡀⢸⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡵⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣻⣿⣿⣷⣿⣿⣿⣿⣿⣿⣾⣿⣽⣤⣾⠀⣠⡄⠀⠀⠀⠰⠍⠉⣉⣉⣹ ⡿⣿⡟⠛⠙⠹⠇⠀⠀⠀⣴⡄⠀⠀⠀⠀⢈⣅⣬⣠⣈⣇⣀⣀⣀⣄⣠⣀⣄⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⡀⣠⣀⡀⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣯⣿⣿⣷⣽⣏⢏⣿⣿⢾⣿⡁⢀⣀⣀⣄⣌⣥⣬⣭⣌ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⣶⡶⠶⠶⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠠⠆ ⣶⣶⣴⣤⣶⣶⠶⠶⠶⠶⠦⠶⠶⠶⠶⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⢶⠶⠆⢲⠲⢤⡶⠒⠒⠒⠶⠶⠶⠲⢸⡈⡍⠉⠎⠀⠀⠀⣠⣻⣿⣿⣾⣷⣾⣿⣟⢓⠛⠿⠿⠿⣿⣿⣷⠾⠷⠿⠿⠿⢿⣿⣷⣿⠾⠿⠷⠿⠿⡿⠿⠿⠿⠛⠛⠻⠿⠿⠿⠿⢿⣿⣿⣿⣿⣤⡄⠀⣀⠀⠀⠀⠀ ⣷⢶⣶⣶⣆⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⢸⡧⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣬⣯⣿⣯⣤⣤⣤⣤⣤⣤⣬⣤⣤⣤⣤⣤⣤⣭⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣤⠀⠀⠀⠠ ⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⣮⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⡿⢿⡿⣿⣿⣿⣿⠿⠿⠿⠿⢿⢿⡿⢿⠿⠿⠿⢿⡿⡿⣿⡿⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⡀⠀⠀⠀ ⣟⣛⣛⣛⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⠃⠀⠃⡄⠀⠀⠀⠀⠀⣿⠀⢽⣿⡷⣿⣹⣿⣛⣛⣾⣏⣷⣓⣚⣋⣞⣏⣚⣚⣾⣷⡶⠲⡞⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣷⣬⣤⣴ ⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢀⡄⠀⠆⠀⠀⠀⣿⣀⣚⣛⣛⣛⣿⣷⣿⣛⣿⣿⣿⡛⣿⣿⣿⣻⠛⢻⣯⡿⡇⣰⣼⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⣿⣹⣿⣿⣯ ⣎⣟⣿⠓⠚⠿⠻⠿⠿⠟⠛⠛⠛⠛⠿⠻⠿⠻⠉⠱⠈⠁⣆⠀⠀⠀⠀⣿⣭⣽⣿⣿⣿⣿⣭⣯⣯⣧⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣯⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣿⡿⣻⠀⠰⢴⡆⠀⠀⠷⡀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠰⠛⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣛⣛⣟⡛⢿⣟⣿⣟⣿⢛⢛⣟⣿⣿⠟⠀⠀⠀⠀⠉⢉⢀⣀⣀⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⡷⣶⡶⡶⣾⡏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢨⠀⠀⠀⠀⠆⠀⠀⠀⠀⣿⠀⡶⠶⠶⠶⠶⠶⠀⠀⣾⣷⣿⠶⠶⣎⣦⢷⠾⣭⡏⠳⠶⠶⢯⣿⣿⣿⠐⠀⡀⠐⠀⠀⢨⣝⣿⣿⣿⠀⠒⠂⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠆⢒⠒⠒⠂⠀⢲⡄⠀⠀⠀⠀⢀⡠⢀⡈⠀⠈⣤⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡀⠖⠀⣀⠀⠰⣮⣬⣭⣹⠀⠄⠄⠠⠤⢰⣿⣿⣿⣿⣿⣿ ⡿⠛⢛⣣⡤⠄⠘⠃⠠⠀⠀⠀⠜⠃⠜⠓⠀⢸⡏⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣿⣿⣿⣾⣾⣿⣿⣿⣾⣾⣷⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣁⠀⠉⠀⠀⠀⢞⣿⣿⣿⣹⣫⣀⣤⣤⣼⣿⣿⣿⣿⣿⣿ ⠙⠛⠛⠛⠃⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠀⣠⠀⠀⠀⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⢻⣿⣻⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠋⠁⠀⠀⢀⡄⢀⡻⣿⣾⠉⠉⠻⠏⠀⢰⣿⣿⣽⣿⣿⣿ ⡶⡶⣾⠇⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣘⠀⠁⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⡿⣿⡿⡿⡿⠿⢿⠿⢯⢿⢿⣿⠷⠿⣿⢼⣿⣿⣿⢿⡿⣿⢿⢿⣿⣿⠛⠀⠀⣠⡾⠁⡈⠡⠩⣯⠀⣅⠀⢀⠀⢸⣿⣿⣿⣿⣿⣿ ⣗⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢩⠀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣄⣤⣾⣿⣅⢸⣻⣧⣰⣿⢤⣯⣷⢤⣴⣾⣿⣿⣿⣭⣿⣿ ⣇⣁⣁⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠈⠀⡾⠀⠀⠀⠀⡆⠀⠀⠀⠀⣿⠋⠛⠛⠉⠝⠛⠁⠊⠁⠑⠐⠛⠑⠛⠛⠊⠛⠼⣿⣟⣟⣿⡟⠷⣿⢟⣿⣶⣾⡿⠋⠉⠀⠐⠳⣎⣘⣛⣩⠍⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿ ⡏⠉⠉⠁⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣠⣿⠒⠆⠆⡆⢸⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡟⣿⢿⣿⢿⢻⣿⣿⠋⠁⠀⢀⠀⠰⠾⠟⣟⠛⢛⠛⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⡇⠛⠛⠃⠀⠸⡷⠂⠀⠀⠀⠀⠀⣤⠀⢸⢿⣿⣳⣿⣿⣇⣹⠀⠀⠀⠀⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⡿⠻⣇⠡⢽⣿⠀⣀⣀⣀⣀⣀⠀⠀⠘⠟⢿⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿ ⣎⣷⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡟⠻⠉⡻⠑⢻⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠘⠹⣿⢛⣻⣿⣿⣿⡟⠝⠚⣭⠀⢸⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⢨⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣾⣿⣷⣿⣿⣠⣄⣉⣀⣼⠀⣠⡄⠀⠀⠀⠰⠍⠉⣉⣉⣹ ⠯⣿⡏⠛⠙⠹⠇⠀⠀⠀⢴⡄⠀⠀⠀⠀⢈⣅⣬⣠⣈⣇⣀⢀⣀⣄⣀⣿⠆⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣈⣹⣩⣿⣿⣤⣤⣄⠀⠀⣿⢾⣿⡁⢀⣀⣀⣄⣌⣥⣬⣩⣌ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⣶⠶⠶⠴⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠠⠆ ⡶⣶⣤⣤⣶⣶⠴⠶⠶⠶⠦⠶⠶⠶⠶⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⢶⠶⠆⢲⠲⢤⡲⠒⠒⠒⠶⠶⠶⠲⢸⡈⠍⠉⠎⠀⠀⠀⣠⣻⣿⣷⣾⣗⣾⣿⣟⠒⠓⠲⠿⢿⡿⢿⡷⠾⢷⣾⠿⠿⠿⣿⣷⣷⠾⠛⠳⠿⠷⡷⠿⠿⠟⠛⠛⠛⠛⠛⠟⠻⢿⣷⣿⣿⣿⣠⡄⠀⣀⠀⠀⠀⠀ ⣷⠶⣶⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣭⣭⣤⣤⣤⣤⣭⣯⣿⣿⣿⣻⣿⣥⣤⣤⣬⣤⣤⣤⣤⣤⣤⣬⣟⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣤⠀⠀⠀⠀ ⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⣎⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⡿⠿⡿⢿⣿⣿⡿⠿⠿⠿⠿⢿⢿⠿⢿⠿⠿⠿⢿⠿⡿⣿⡿⠿⢿⣿⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⡀⠀⠀⠀ ⣟⣛⣛⣛⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⠃⠀⠃⡄⠀⠀⠀⠀⠀⣿⠀⢹⣿⡷⢾⣹⡿⣛⣚⣺⣀⣇⣓⣚⣋⣘⣉⣘⣚⣾⣶⡶⠠⠖⢾⣿⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣷⣬⣤⣴ ⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢀⡄⠀⠆⠀⠀⠀⣿⣀⣚⣛⣛⣛⣻⣧⣟⣛⣻⣿⣟⡛⣿⣿⣿⣛⠛⢻⣿⡿⡇⣀⣼⣾⣿⣿⠀⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⣿⣹⣿⣿⣯ ⣎⣛⡛⠓⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠟⠹⠉⠱⠈⠁⣆⠀⠀⠀⠀⣿⣍⣿⣿⣯⣿⣿⣯⣭⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣷⣿⣿⣯⣴⣿⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣿⡿⣻⠀⠰⢴⡆⠀⠀⠷⡀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠛⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠻⣿⣿⣿⡿⢿⢿⣟⡻⣿⠟⢺⡀⠀⠀⠉⢉⢀⣀⣀⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⡷⣶⡶⡶⢾⡏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢨⠀⠀⠀⠀⠆⠀⠀⠀⠀⣿⣉⠲⠶⣶⡶⡶⠶⠶⠀⢴⣶⡷⠶⠶⢾⣶⠷⠦⣭⡏⠳⠶⠶⣿⣿⣿⣿⠐⢸⡉⠐⠀⠀⢨⣜⣿⣿⣿⠀⠒⠂⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠆⢒⠒⠒⠂⠀⢲⡄⠀⠀⠀⠀⢀⡀⢀⡈⠀⠈⢠⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣸⡗⠀⣀⠀⠰⣮⣬⣭⣹⠀⠀⠄⠠⠤⢰⣿⣿⣿⣿⣿⣿ ⡿⠛⢛⢣⡤⠄⠘⠃⠠⠀⠀⠀⠜⠃⠜⠓⠀⢸⡏⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣾⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣹⠯⠉⠀⠀⠀⠞⣿⣿⣿⣹⣫⣀⣤⣤⣼⣿⣿⣿⣿⣿⣿ ⠙⠛⠛⠛⠃⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠀⣠⠀⠀⠀⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⢻⣿⣻⣿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⠇⠀⠀⢀⡄⢀⡻⣿⣾⠉⠉⠻⠏⠀⢰⣿⣿⣽⣿⣿⣿ ⡶⡶⣾⠇⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣐⠀⠁⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⡿⣿⡿⠿⡿⠿⢿⠿⢯⠿⢿⣿⠶⠿⠿⠼⣿⣿⣿⢿⡿⣿⢿⢿⣿⣿⢹⠀⠀⣠⡾⠁⡈⠡⠩⣯⠀⣅⠀⢀⠀⢸⣿⣿⣿⣿⣿⣿ ⣗⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⡀⠀⠀⠀⠀⠀⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣼⣤⣾⣿⣅⢸⣻⣧⣰⣿⢤⣯⣷⢤⣴⣼⣿⣿⣿⣭⣿⣿ ⣆⣁⣁⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠈⠀⡾⠀⠀⠀⠀⡆⠀⠀⠀⠀⣿⠊⠚⠊⠀⠝⠋⠁⠈⠉⠉⠐⠋⠐⠓⠚⠈⠚⠈⣾⣛⣛⣿⡟⠾⣾⢟⣿⣶⣾⡿⠋⠉⠀⠐⠓⣊⣘⣛⣩⠍⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿ ⡏⠉⠉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣠⣿⠒⠆⠆⡆⢸⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡞⢻⢿⡿⢿⢻⣿⣿⠋⢹⠀⢀⠀⠰⠾⠟⣟⠛⢛⠛⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⡇⠛⠛⠃⠀⠸⡷⠂⠀⠀⠀⠀⠀⣤⠀⢸⢿⣿⣳⣿⣿⣇⣹⠀⠀⠀⠀⣿⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⠷⠃⠃⠁⢽⣿⠀⣸⣀⣀⣀⣀⠀⠀⠘⠏⢹⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿ ⠎⣷⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡟⠻⠉⡻⠑⢻⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠹⣿⠋⣻⣿⣿⣿⡟⠙⠚⣭⠀⢸⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⢨⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣾⣿⣷⣾⣿⣀⣀⣉⣀⣼⠀⣠⡄⠀⠀⠀⠰⠍⠉⣉⡉⢹ ⠯⣿⡏⠛⠙⠹⠇⠀⠀⠀⢴⡀⠀⠀⠀⠀⢈⣄⣬⣠⣈⣇⣀⢀⣀⣀⣀⣿⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⢹⣨⣿⣿⣤⣤⣄⠀⠀⣿⢾⣿⡁⢀⣀⣀⣀⣌⣥⣌⣩⣌ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⣶⠶⠶⠴⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠠⠆ ⡶⣶⣤⣤⣶⣶⠴⠶⠶⠶⠦⠶⠶⠶⠶⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⢶⠶⠆⢲⠲⢤⡲⠒⠒⠒⠶⠶⠶⠲⢸⡈⠍⠉⠎⠀⠀⠀⣠⣻⣿⣷⣾⣗⣾⣿⣟⠒⠓⠲⠿⢿⡿⢿⡷⠾⢷⣾⠿⠿⠿⣿⣷⣷⠾⠛⠳⠿⠷⡷⠿⠿⠟⠛⠛⠛⠛⠛⠟⠻⢿⣷⣿⣿⣿⣠⡄⠀⣀⠀⠀⠀⢀ ⣷⠶⣶⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣭⣭⣤⣤⣤⣤⣭⣯⣿⣿⣿⣻⣿⣥⣤⣤⣬⣤⣤⣤⣤⣤⣤⣬⣟⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣤⠀⠀⠀⠀ ⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⣎⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⡿⠿⡿⢿⣿⣿⡿⠿⠿⠿⠿⢿⢿⠿⢿⠿⠿⠿⢿⠿⡿⣿⡿⠿⢿⣿⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⡀⠀⠀⠀ ⣟⣛⣛⣛⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⠃⠀⠃⡄⠀⠀⠀⠀⠀⣿⠀⢹⣿⡷⢾⣹⡿⣛⣚⣺⣀⣇⣓⣚⣋⣘⣉⣘⣚⣾⣶⡶⠠⠖⢾⣿⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣷⣬⣤⣴ ⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢀⡄⠀⠆⠀⠀⠀⣿⣀⣚⣛⣛⣛⣻⣧⣟⣛⣻⣿⣟⡛⣿⣿⣿⣛⠛⢻⣿⡿⡇⣀⣼⣾⣿⣿⠀⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⣿⣹⣿⣿⣯ ⣎⣛⡛⠓⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠟⠹⠉⠱⠈⠁⣆⠀⠀⠀⠀⣿⣍⣿⣿⣯⣿⣿⣯⣭⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣷⣿⣿⣯⣴⣿⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣿⡿⣻⠀⠰⢴⡆⠀⠀⠷⡀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠛⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠻⣿⣿⣿⡿⢿⢿⣿⡻⣿⠟⢺⡀⠀⠀⠉⢉⢀⣀⣀⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⡷⣶⡶⡶⢾⡏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢨⠀⠀⠀⠀⠆⠀⠀⠀⠀⣿⣉⠲⠶⣶⡶⡶⠶⠶⠀⢴⣶⡷⠶⠶⢾⣶⠷⠦⣭⡏⠳⠶⠶⣿⣿⣿⣿⠐⢸⡉⠐⠀⠀⢨⣜⣿⣿⣿⠀⠒⠂⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠆⢒⠒⠒⠂⠀⢲⡄⠀⠀⠀⠀⢀⡀⢀⡈⠀⠈⢠⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣸⡗⠀⣀⠀⠰⣮⣬⣭⣹⠀⠀⠄⠠⠤⢰⣿⣿⣿⣿⣿⣿ ⡿⠛⢛⢣⡤⠄⠘⠃⠠⠀⠀⠀⠜⠃⠜⠓⠀⢸⡏⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣾⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣹⠯⠉⠀⠀⠀⠞⣿⣿⣿⣹⣫⣀⣤⣤⣼⣿⣿⣿⣿⣿⣿ ⠙⠛⠛⠛⠃⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠀⣠⠀⠀⠀⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⢻⣿⣻⣿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⠇⠀⠀⢀⡄⢀⡻⣿⣾⠉⠉⠻⠏⠀⢰⣿⣿⣽⣿⣿⣿ ⡶⡶⣾⠇⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣐⠀⠁⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⡿⣿⡿⠿⡿⠿⢿⠿⢯⠿⢿⣿⠶⠿⠿⠼⣿⣿⣿⢿⡿⣿⢿⢿⣿⣿⢹⠀⠀⣠⡾⠁⡈⠡⠩⣯⠀⣅⠀⢀⠀⢸⣿⣿⣿⣿⣿⣿ ⣗⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⡀⠀⠀⠀⠀⠀⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣼⣤⣾⣿⣅⢸⣻⣧⣰⣿⢤⣯⣷⢤⣴⣼⣿⣿⣿⣭⣿⣿ ⣆⣁⣁⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠈⠀⡾⠀⠀⠀⠀⡆⠀⠀⠀⠀⣿⠊⠚⠊⠀⠝⠋⠁⠈⠉⠉⠐⠋⠐⠓⠚⠈⠚⠈⣾⣛⣛⣿⡟⠾⣾⢟⣿⣶⣾⡿⠋⠉⠀⠐⠓⣊⣘⣛⣩⠍⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿ ⡏⠉⠉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣠⣿⠒⠆⠆⡆⢸⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡞⢻⢿⡿⢿⢻⣿⣿⠋⢹⠀⢀⠀⠰⠾⠟⣟⠛⢛⠛⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⡇⠛⠛⠃⠀⠸⡷⠂⠀⠀⠀⠀⠀⣤⠀⢸⢿⣿⣳⣿⣿⣇⣹⠀⠀⠀⠀⣿⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⠷⠃⠃⠁⢽⣿⠀⣸⣀⣀⣀⣀⠀⠀⠘⠏⢹⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿ ⠎⣷⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡟⠻⠉⡻⠑⢻⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠹⣿⠋⣻⣿⣿⣽⡟⠙⠚⣭⠀⢸⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⢨⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣾⣿⣷⣾⣿⣀⣀⣉⣀⣼⠀⣠⡄⠀⠀⠀⠰⠍⠉⣉⡉⢹ ⠯⣿⡏⠛⠙⠹⠇⠀⠀⠀⢴⡀⠀⠀⠀⠀⢈⣄⣬⣠⣈⣇⣀⢀⣀⣀⣀⣿⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⢹⣨⣿⣿⣤⣤⣄⠀⠀⣿⢾⣿⡁⢀⣀⣀⣀⣌⣥⣌⣩⣌ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⣶⠶⠶⠴⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠠⠆ ⡶⣶⣤⣤⣶⣶⠴⠶⠶⠶⠦⠶⠶⠶⠶⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⢶⠶⠆⢲⠲⢤⡲⠒⠒⠒⠶⠶⠶⠲⢸⡈⠍⠉⠎⠀⠀⠀⣠⣻⣿⣷⣾⣗⣾⣿⣟⠒⠓⠲⠿⢿⡿⢿⡷⠾⢷⣾⠿⠿⠿⣿⣷⣷⠾⠛⠳⠿⠷⡷⠿⠿⠟⠛⠛⠛⠛⠛⠟⠻⢿⣷⣿⣿⣿⣠⡄⠀⣀⠀⠀⠀⢀ ⣷⠶⣶⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣭⣭⣤⣤⣤⣤⣭⣯⣿⣿⣿⣻⣿⣥⣤⣤⣬⣤⣤⣤⣤⣤⣤⣬⣟⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣤⠀⠀⠀⠀ ⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⣎⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⡿⠿⡿⢿⣿⣿⡿⠿⠿⠿⠿⢿⢿⠿⢿⠿⠿⠿⢿⠿⡿⣿⡿⠿⢿⣿⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⡀⠀⠀⠀ ⣟⣛⣛⣛⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⠃⠀⠃⡄⠀⠀⠀⠀⠀⣿⠀⢹⣿⡷⢾⣹⡿⣛⣚⣺⣀⣇⣓⣚⣋⣘⣉⣘⣚⣾⣶⡶⠠⠖⢾⣿⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣷⣬⣤⣴ ⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢀⡄⠀⠆⠀⠀⠀⣿⣀⣚⣛⣛⣛⣻⣧⣟⣛⣻⣿⣟⡛⣿⣿⣿⣛⠛⢻⣿⡿⡇⣀⣼⣾⣿⣿⠀⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⣿⣹⣿⣿⣯ ⣎⣛⡛⠓⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠟⠹⠉⠱⠈⠁⣆⠀⠀⠀⠀⣿⣍⣿⣿⣯⣿⣿⣯⣭⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣷⣿⣿⣯⣴⣿⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣿⡿⣻⠀⠰⢴⡆⠀⠀⠷⡀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠛⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠻⣿⣿⣿⡿⢿⢿⣿⡻⣿⠟⢺⡠⠀⠀⠉⢉⢀⣀⣀⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⡷⣶⡶⡶⢾⡏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢨⠀⠀⠀⠀⠆⠀⠀⠀⠀⣿⣉⠲⠶⣶⡶⡶⠶⠶⠀⢴⣶⡷⠶⠶⢾⣶⠷⠦⣭⡏⠳⠶⠶⣿⣿⣿⣿⠐⢸⡉⠐⠀⠀⢨⣜⣿⣿⣿⠀⠒⠂⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠆⢒⠒⠒⠂⠀⢲⡄⠀⠀⠀⠀⢀⡀⢀⡈⠀⠈⢠⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣸⡗⠀⣀⠀⠰⣮⣬⣭⣹⠀⠀⠄⠠⠤⢰⣿⣿⣿⣿⣿⣿ ⡿⠛⢛⢣⡤⠄⠘⠃⠠⠀⠀⠀⠜⠃⠜⠓⠀⢸⡏⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣾⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣹⠯⠉⠀⠀⠀⠞⣿⣿⣿⣹⣫⣀⣤⣤⣼⣿⣿⣿⣿⣿⣿ ⠙⠛⠛⠛⠃⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠀⣠⠀⠀⠀⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⢻⣿⣻⣿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⠇⠀⠀⣄⡄⢀⡻⣿⣾⠉⠉⠻⠏⠀⢰⣿⣿⣽⣿⣿⣿ ⡶⡶⣾⠇⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣐⠀⠁⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⡿⣿⡿⠿⡿⠿⢿⠿⢯⠿⢿⣿⠶⠿⠿⠼⣿⣿⣿⢿⡿⣿⢿⢿⣿⣿⢹⠀⠀⣠⡾⠁⡈⠡⠩⣯⠀⣅⠀⢀⠀⢸⣿⣿⣿⣿⣿⣿ ⣗⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⡀⠀⠀⠀⠀⠀⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣼⣤⣾⣿⣅⢸⣻⣧⣰⣿⢤⣯⣷⢤⣴⣼⣿⣿⣿⣭⣿⣿ ⣆⣁⣁⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠈⠀⡾⠀⠀⠀⠀⡆⠀⠀⠀⠀⣿⠊⠚⠊⠀⠝⠋⠁⠈⠉⠉⠐⠋⠐⠓⠚⠈⠚⠨⣾⣿⣟⣿⡟⠾⣾⢟⣿⣶⣾⡿⠋⠉⠄⠐⠓⣊⣘⣛⣩⠍⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿ ⡏⠉⠉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣠⣿⠒⠆⠆⡆⢸⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡞⢻⢿⡿⢿⢻⣿⣿⠋⢹⠀⢀⠀⠰⠾⠟⣟⠛⢛⠛⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⡇⠛⠛⠃⠀⠸⡷⠂⠀⠀⠀⠀⠀⣤⠀⢸⢿⣿⣳⣿⣿⣇⣹⠀⠀⠀⠀⣿⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⠷⠃⠃⠁⢽⣿⠀⣸⢀⣀⣀⣀⠀⠀⠘⠏⢹⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿ ⠎⣷⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡟⠻⠉⡻⠑⢻⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠹⣿⠋⣻⣿⣿⣽⡟⠙⠚⣭⠀⢸⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⢨⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣾⣿⣷⣾⣿⣀⣀⣉⣀⣼⠀⣠⡄⠀⠀⠀⠰⠍⠉⣉⡉⢹ ⠯⣿⡏⠛⠙⠹⠇⠀⠀⠀⢴⡀⠀⠀⠀⠀⢈⣄⣬⣠⣈⣇⣀⢀⣀⣀⣀⣿⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⢹⣨⣿⣿⣤⣤⣄⠀⠀⣿⢾⣿⡁⢀⣀⣀⣀⣌⣥⣌⣩⣌ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⣶⠶⠶⠴⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠠⠆ ⡶⣶⣤⣤⣶⣶⠴⠶⠶⠶⠦⠶⠶⠶⠶⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⢶⠶⠆⢲⠲⢤⡲⠒⠒⠒⠶⠶⠶⠲⢸⡈⠍⠉⠎⠀⠀⠀⣠⣻⣿⣷⣾⣗⣾⣿⣟⠒⠓⠲⠿⢿⡿⢿⡷⠾⢷⣾⠿⠿⠿⣿⣷⣷⠾⠛⠳⠿⠷⡷⠿⠿⠟⠛⠛⠛⠛⠛⠟⠻⢿⣷⣿⣿⣿⣠⡄⠀⣀⠀⠀⠀⢀ ⣷⠶⣶⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣭⣭⣤⣤⣤⣤⣭⣯⣿⣿⣿⣻⣿⣥⣤⣤⣬⣤⣤⣤⣤⣤⣤⣬⣟⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣤⠀⠀⠀⠀ ⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⣎⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⡿⠿⡿⢿⣿⣿⡿⠿⠿⠿⠿⢿⢿⠿⢿⠿⠿⠿⢿⠿⡿⣿⡿⠿⢿⣿⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⡀⠀⠀⠀ ⣟⣛⣛⣛⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⠃⠀⠃⡄⠀⠀⠀⠀⠀⣿⠀⢹⣿⡷⢾⣹⡿⣛⣚⣺⣀⣇⣓⣚⣋⣘⣉⣘⣚⣾⣶⡶⠠⠖⢾⣿⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣷⣬⣤⣴ ⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢀⡄⠀⠆⠀⠀⠀⣿⣀⣚⣛⣛⣛⣻⣧⣟⣛⣻⣿⣟⡛⣿⣿⣿⣻⡟⢻⣿⡿⡇⣀⣼⣾⣿⣿⠀⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⣿⣹⣿⣿⣯ ⣎⣛⡛⠓⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠟⠹⠉⠱⠈⠁⣆⠀⠀⠀⠀⣿⣍⣿⣿⣯⣿⣿⣯⣭⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣷⣿⣿⣯⣴⣿⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣿⡿⣻⠀⠰⢴⡆⠀⠀⠷⡀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠛⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠻⣿⣿⣿⡿⢿⢿⣿⡻⣿⠟⢺⡠⠀⠀⠉⢉⢀⣀⣀⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⡷⣶⡶⡶⢾⡏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢨⠀⠀⠀⠀⠆⠀⠀⠀⠀⣿⣉⠲⠶⣶⡶⡶⠶⠶⠀⢴⣶⡷⠶⠶⢾⣶⠷⠦⣭⡏⠳⠶⠶⣿⣿⣿⣿⠐⢸⡉⠐⠀⠀⢨⣜⣿⣿⣿⠀⠒⠂⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠆⢒⠒⠒⠂⠀⢲⡄⠀⠀⠀⠀⢀⡀⢀⡈⠀⠈⢠⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣸⡗⠀⣀⠀⠰⣮⣬⣭⣹⠀⠀⠄⠠⠤⢰⣿⣿⣿⣿⣿⣿ ⡿⠛⢛⢣⡤⠄⠘⠃⠠⠀⠀⠀⠜⠃⠜⠓⠀⢸⡏⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣾⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣹⠯⠉⠀⠀⠀⠞⣿⣿⣿⣹⣫⣀⣤⣤⣼⣿⣿⣿⣿⣿⣿ ⠙⠛⠛⠛⠃⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠀⣠⠀⠀⠀⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⢻⣿⣻⣿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⠇⠀⠀⣄⡄⢀⡻⣿⣾⠉⠉⠻⠏⠀⢰⣿⣿⣽⣿⣿⣿ ⡶⡶⣾⠇⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣐⠀⠁⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⡿⣿⡿⠿⡿⠿⢿⠿⢯⠿⢿⣿⠶⠿⠿⠼⣿⣿⣿⢿⡿⣿⢿⢿⣿⣿⢹⠀⠀⣠⡾⠁⡈⠡⠩⣯⠀⣅⠀⢀⠀⢸⣿⣿⣿⣿⣿⣿ ⣗⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⡀⠀⠀⠀⠀⠀⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣼⣤⣾⣿⣅⢸⣻⣧⣰⣿⢤⣯⣷⢤⣴⣼⣿⣿⣿⣭⣿⣿ ⣆⣁⣁⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠈⠀⡾⠀⠀⠀⠀⡆⠀⠀⠀⠀⣿⠊⠚⠊⠀⠝⠋⠁⠈⠉⠉⠐⠋⠐⠓⠚⠈⠚⠨⣾⣿⣟⣿⡟⠾⣾⢟⣿⣶⣾⡿⠋⠉⠄⠐⠓⣊⣘⣛⣩⠍⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿ ⡏⠉⠉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣠⣿⠒⠆⠆⠆⢸⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡞⢻⢿⡿⢿⢻⣿⣿⠋⢹⠀⢀⠀⠰⠾⠟⣟⠛⢛⠛⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⡇⠛⠛⠃⠀⠸⡷⠂⠀⠀⠀⠀⠀⣤⠀⢸⢿⣿⣳⣿⣿⣇⣹⠀⠀⠀⠀⣿⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⠷⠃⠃⠁⢽⣿⠀⣸⢀⣀⣀⣀⠀⠀⠘⠏⢹⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿ ⠎⣷⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡟⠻⠉⡻⠑⢻⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠹⣿⠋⣻⣿⣿⣽⡟⠙⠚⣭⠀⢸⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⢨⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣾⣿⣷⣾⣿⣀⣀⣉⣀⣼⠀⣠⡄⠀⠀⠀⠰⠍⠉⣉⡉⢹ ⠯⣿⡏⠛⠙⠹⠇⠀⠀⠀⢴⡀⠀⠀⠀⠀⢈⣄⣬⣠⣈⣇⣀⢀⣀⣀⣀⣿⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⢹⣨⣿⣿⣤⣤⣄⠀⠀⣹⢾⣿⡁⢀⣀⣀⣀⣌⣥⣌⣩⣌ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⣶⠶⠶⠴⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠠⠆ ⡶⣶⣤⣤⣶⣶⠴⠶⠶⠶⠦⠶⠶⠶⠶⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⢶⠶⠆⢲⠲⢤⡲⠒⠒⠒⠶⠶⠶⠲⢸⡈⠍⠉⠎⠀⠀⠀⣠⣻⣿⣷⣾⣗⣾⣿⣟⠒⠓⠲⠿⢿⡿⢿⡷⠾⢷⣾⠿⠿⠿⣿⣷⣷⠾⠛⠳⠿⠷⡷⠿⠿⠟⠛⠛⠛⠛⠛⠟⠻⢿⣷⣿⣿⣿⣠⡄⠀⣀⠀⠀⠀⢀ ⣷⠶⣶⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣭⣭⣤⣤⣤⣤⣭⣯⣿⣿⣿⣻⣿⣥⣤⣤⣬⣤⣤⣤⣤⣤⣤⣬⣟⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣤⠀⠀⠀⠀ ⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⣎⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⡿⠿⡿⢿⣿⣿⡿⠿⠿⠿⠿⢿⢿⠿⢿⠿⠿⠿⢿⠿⡿⣿⡿⠿⢿⣿⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⡀⠀⠀⠀ ⣟⣛⣛⣛⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⠃⠀⠃⡄⠀⠀⠀⠀⠀⣿⠀⢹⣿⡷⢾⣹⡿⣛⣚⣺⣀⣇⣓⣚⣋⣘⣉⣘⣚⣾⣶⡶⠠⠖⢾⣿⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣷⣬⣤⣴ ⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢀⡄⠀⠆⠀⠀⠀⣿⣀⣚⣛⣛⣛⣻⣧⣟⣛⣻⣿⣟⡛⣿⣿⣿⣻⡟⢻⣿⡿⡇⣀⣼⣾⣿⣿⠀⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⣿⣹⣿⣿⣯ ⣎⣛⡛⠓⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠟⠹⠉⠱⠈⠁⣆⠀⠀⠀⠀⣿⣍⣿⣿⣯⣿⣿⣯⣭⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣷⣿⣿⣯⣴⣿⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣿⡿⣻⠀⠰⢴⡆⠀⠀⠷⡀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠛⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠻⣿⣿⣿⡿⢿⢿⣿⡻⣿⠟⢺⡠⠀⠀⠉⢉⢀⣀⣀⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⡷⣶⡶⡶⢾⡏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢨⠀⠀⠀⠀⠆⠀⠀⠀⠀⣿⣉⠲⠶⣶⡶⡶⠶⠶⠀⢴⣶⡷⠶⠶⢾⣶⠷⠦⣭⡏⠳⠶⠶⣿⣿⣿⣿⠐⢸⡉⠐⠀⠀⢨⣜⣿⣿⣿⠀⠒⠂⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠆⢒⠒⠒⠂⠀⢲⡄⠀⠀⠀⠀⢀⡀⢀⡈⠀⠈⢠⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣸⡗⠀⣀⠀⠰⣮⣬⣭⣹⠀⠀⠄⠠⠤⢰⣿⣿⣿⣿⣿⣿ ⡿⠛⢛⢣⡤⠄⠘⠃⠠⠀⠀⠀⠜⠃⠜⠓⠀⢸⡏⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣾⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣹⠯⠉⠀⠀⠀⠞⣿⣿⣿⣹⣫⣀⣤⣤⣼⣿⣿⣿⣿⣿⣿ ⠙⠛⠛⠛⠃⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠀⣠⠀⠀⠀⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⢻⣿⣻⣿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⠇⠀⠀⣄⡄⢀⡻⣿⣾⠉⠉⠻⠏⠀⢰⣿⣿⣽⣿⣿⣿ ⡶⡶⣾⠇⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣐⠀⠁⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⡿⣿⡿⠿⡿⠿⢿⠿⢯⠿⢿⣿⠶⠿⠿⠼⣿⣿⣿⢿⡿⣿⢿⢿⣿⣿⢹⠀⠀⣠⡾⠁⡈⠡⠩⣯⠀⣅⠀⢀⠀⢸⣿⣿⣿⣿⣿⣿ ⣗⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⡀⠀⠀⠀⠀⠀⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣼⣤⣾⣿⣅⢸⣻⣧⣰⣿⢤⣯⣷⢤⣴⣼⣿⣿⣿⣭⣿⣿ ⣆⣁⣁⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠈⠀⡾⠀⠀⠀⠀⡆⠀⠀⠀⠀⣿⠊⠚⠊⠀⠝⠋⠁⠈⠉⠉⠐⠋⠐⠓⠚⠈⠚⠨⣾⣿⣟⣿⡟⠾⣾⢟⣿⣶⣾⡿⠋⠉⠄⠐⠓⣊⣘⣛⣩⠍⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿ ⡏⠉⠉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣠⣿⠒⠆⠆⠆⢸⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡞⢻⢿⡿⢿⢻⣿⣿⠋⢹⠀⢀⠀⠰⠾⠟⣟⠛⢛⠛⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⡇⠛⠛⠃⠀⠸⡷⠂⠀⠀⠀⠀⠀⣤⠀⢸⢿⣿⣳⣿⣿⣇⣹⠀⠀⠀⠀⣿⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⠷⠃⠃⠁⢽⣿⠀⣸⢀⣀⣀⣀⠀⠀⠘⠏⢹⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿ ⠎⣷⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡟⠻⠉⡻⠑⢻⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠹⣿⠋⣻⣿⣿⣽⡟⠙⠚⣭⠀⢸⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⢨⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣾⣿⣷⣾⣿⣀⣀⣉⣀⣼⠀⣠⡄⠀⠀⠀⠰⠍⠉⣉⡉⢹ ⠯⣿⡏⠛⠙⠹⠇⠀⠀⠀⢴⡀⠀⠀⠀⠀⢈⣄⣬⣠⣈⣇⣀⢀⣀⣀⣀⣿⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⢹⣨⣿⣿⣤⣤⣄⠀⠀⣹⢾⣿⡁⢀⣀⣀⣀⣌⣥⣌⣩⣌ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⣶⠶⠶⠴⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠠⠆ ⡶⣶⣤⣤⣶⣦⠴⠶⠶⠶⠦⠶⠶⠶⠶⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⢶⠶⠆⢲⠲⢤⡲⠒⠒⠒⠶⠶⠶⠲⢸⡈⠍⠉⠎⠀⠀⠀⣠⣻⣿⣷⣾⣗⣾⣿⣟⠒⠓⠲⠿⢿⡿⢿⡷⠾⢷⣾⠿⠿⠻⣿⣷⣷⠾⠛⠳⠿⠷⡷⠿⠿⠟⠛⠛⠛⠛⠛⠟⠻⢿⣷⣿⣿⣿⣠⡄⠀⣀⠀⠀⠀⢀ ⣷⠶⣶⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣭⣭⣤⣤⣤⣤⣭⣯⣿⣿⣿⣻⣿⣥⣤⣤⣬⣤⣤⣤⣤⣤⣤⣬⣟⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣤⠀⠀⠀⠀ ⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⣎⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⡿⠿⡿⢿⣿⣿⡿⠿⠿⠿⠿⢿⢿⠿⢿⠿⠿⠿⢿⠿⡿⣿⡿⠿⢿⣿⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⡀⠀⠀⠀ ⣟⣛⣛⣛⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⠃⠀⠃⡄⠀⠀⠀⠀⠀⣿⠀⢹⣿⡷⢾⣹⡿⣛⣚⣺⣀⣇⣓⣚⣋⣘⣉⣘⣚⣾⣶⡶⠠⠖⢾⣿⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣷⣬⣤⣴ ⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢀⡄⠀⠆⠀⠀⠀⣿⣀⣚⣛⣛⣛⣻⣧⣟⣛⣻⣿⣟⡛⣿⣿⣿⣻⡟⢻⣿⡿⡇⣀⣼⣾⣿⣿⠀⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⣿⣹⣿⣿⣯ ⣎⣛⡛⠓⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠟⠹⠉⠱⠈⠁⣆⠀⠀⠀⠀⣿⣍⣿⣿⣯⣿⣿⣯⣭⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣷⣿⣿⣯⣴⣿⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣿⡿⣻⠀⠰⢴⡆⠀⠀⠷⡀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠛⠀⠀⠀⢀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠻⣿⣿⣿⡿⢿⢿⣿⡻⣿⠟⢺⡠⠀⠀⠉⢉⢀⣀⣀⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⡷⣶⡶⡶⢾⡏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢈⠀⠀⠀⠀⠆⠀⠀⠀⠀⣿⣉⠲⠶⣶⡶⡶⠶⠶⠀⢴⣶⡷⠶⠶⢾⣶⠷⠦⣭⡏⠳⠶⠶⣿⣿⣿⣿⠐⢸⡉⠐⠀⠀⢨⣜⣿⣿⣿⠀⠒⠂⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠆⢒⠒⠒⠂⠀⢲⡄⠀⠀⠀⠀⢀⡀⢀⡈⠀⠈⢠⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣸⡗⠀⣀⠀⠰⣮⣬⣭⣹⠀⠀⠄⠠⠤⢰⣿⣿⣿⣿⣿⣿ ⡿⠛⢛⢣⡤⠄⠘⠃⠠⠀⠀⠀⠜⠃⠜⠓⠀⢸⡏⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣾⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣹⠯⠉⠀⠀⠀⠞⣿⣿⣿⣹⣫⣀⣤⣤⣼⣿⣿⣿⣿⣿⣿ ⠙⠛⠛⠛⠃⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠀⣠⠀⠀⠀⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⢻⣿⣻⣿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⠇⠀⠀⣄⡄⢀⡻⣿⣾⠉⠉⠻⠏⠀⢰⣿⣿⣽⣿⣿⣿ ⡶⡶⣾⠇⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣐⠀⠁⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⡿⣿⡿⠿⡿⠿⢿⠿⢯⠿⢿⣿⠶⠿⠿⠼⣿⣿⣿⢿⡿⣿⢿⢿⣿⣿⢹⠀⠀⣠⡾⠁⡈⠡⠩⣯⠀⣅⠀⢀⠀⢸⣿⣿⣿⣿⣿⣿ ⣗⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⡀⠀⠀⠀⠀⠀⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣼⣤⣾⣿⣅⢸⣻⣧⣰⣿⢤⣯⣷⢤⣴⣼⣿⣿⣿⣭⣿⣿ ⣆⣁⣁⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠈⠀⡾⠀⠀⠀⠀⡆⠀⠀⠀⠀⣿⠊⠚⠊⠀⠍⠋⠁⠈⠉⠉⠐⠋⠐⠓⠚⠈⠚⠨⣾⣿⣟⣿⡟⠾⣾⢟⣿⣶⣿⡿⠋⠉⠄⠐⠓⣊⣘⣛⣩⠍⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿ ⡏⠉⠉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣠⣿⠒⠆⠆⠆⢸⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡞⢻⢿⡿⢿⢻⣿⣿⠋⢹⠀⢀⠀⠰⠾⠟⣟⠛⢛⠛⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⡇⠛⠛⠃⠀⠸⡷⠂⠀⠀⠀⠀⠀⣤⠀⢸⢿⣿⣳⣿⣿⣇⣹⠀⠀⠀⠀⣿⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⠷⠃⠃⠁⢽⣿⠀⣸⢀⣀⣀⣀⠀⠀⠘⠏⢹⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿ ⠎⣷⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡟⠻⠉⡻⠑⢻⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠹⣿⠋⣻⣿⣿⣽⡟⠙⠒⣭⠀⢸⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⢨⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣾⣿⣷⣾⣿⣀⣀⣉⣀⣼⠀⣠⡄⠀⠀⠀⠰⠍⠉⣉⡉⢹ ⠯⣿⡏⠛⠙⠹⠇⠀⠀⠀⢴⡀⠀⠀⠀⠀⢈⣄⣬⣠⣈⣇⣀⢀⣀⣀⣀⣿⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⢹⣨⣿⣿⣤⣤⣄⠀⠀⣹⢾⣿⡁⢀⣀⣀⣀⣌⣥⣌⣩⣌ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⣶⣶⠶⠶⢶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠰⠆ ⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠷⢶⠶⠆⢶⠲⢤⡶⠒⠒⠒⠶⠶⠶⠲⢺⡈⣽⠉⠎⠀⠀⠀⣠⣻⣿⣿⣾⣷⣾⣿⣟⣗⡛⠿⢿⢿⡿⣿⣿⠾⣷⣿⡿⠿⢿⣿⣷⣿⠾⠿⠷⣿⠿⡿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣤⡄⠀⣀⡀⠀⠀⢀ ⣷⢶⣶⣶⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢸⣧⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠭⠭⠤⠤⠤⠾⠛⠻⠛⠛⠛⠻⠻⠥⠤⠤⠬⠤⠤⠤⠤⠼⠿⠟⣻⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀⣦⣀⣀⣀⣠ ⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⣮⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠏⠙⠸⣿⡿⣿⢿⠿⠿⣿⣿⢿⣿⣿⠿⠏⠿ ⣟⣛⣛⣛⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⠃⠀⠃⡄⠀⠀⠀⠀⠀⣿⣐⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣻⣟⣟⣛⣟⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⡇⠀⣤⣤⡄⠀⠀⣤⣤⡀⠀⢀⣤⣽⠂⠀⢠⣤ ⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢀⡄⠀⠆⠀⠀⠀⣿⣐⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⡇⠀⢿⣿⡇⠀⠀⣿⣿⠇⠀⠸⣿⣿⠀⠀⠸⣿ ⣞⣿⣿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠉⠱⠈⠡⣆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⡇⠀⢙⣛⠃⠀⠈⣛⢛⠋⠀⢙⣛⠛⠃⠀⢀⡛ ⣿⡿⣻⠀⠰⢴⡆⠀⠀⠿⡀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠰⠛⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⢿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⡇⠀⠀⣿⣿⡇⠀⢸⣿⣿⠀⠀⢸⣿ ⡷⣶⡶⣶⣾⡏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠆⠀⠀⠀⠀⣿⣙⡷⣶⣶⣶⡶⠾⣿⣿⣿⣿⣿⣶⣶⣿⣾⣿⣿⣿⣿⣿⡿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡇⠀⠸⠿⠇⠀⠀⠾⠿⠆⠀⠰⠿⠿⠀⠀⠐⠿ ⠖⣒⠒⡒⠂⠀⢲⡄⠀⠀⠀⠀⢀⡠⢀⡈⠀⠈⣤⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣾⣿⡆⠀⠀⣿⣿⡆⠀⢰⣿⣿⠀⠀⠀⠀ ⡿⠛⢛⣣⡤⠄⠘⠃⠠⠀⠀⠀⠜⠃⠜⠓⠀⢸⡏⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢹⣿⠃⠀⠠⣿⣿⡅⠀⠈⣿⣿⠀⠀⠀⠀ ⠙⠛⠛⠛⠃⣀⠀⠀⠒⠀⠀⠀⠀⠀⠀⢸⠀⣠⠀⠀⠀⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⡶⣾⠇⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣸⠀⠁⠀⠀⠈⠀⠀⠀⠀⣿⣿⣿⡿⣿⡿⡿⣿⡿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣽⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣗⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢽⠀⡀⠀⠀⠀⠀⠀⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀ ⣇⣁⣁⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠈⠀⣾⠀⠀⠀⠀⡆⠀⠀⠀⠀⣿⡿⠿⠿⠛⠿⠿⢷⠛⣿⠟⠛⠟⠛⠻⠛⠟⠛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣏⠉⠙⠁⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣠⣿⠖⠆⠆⡆⢸⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⢽⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠛⠛⠃⠀⠸⣷⠂⠀⠀⠀⠀⠀⣤⠀⢸⢿⣿⣳⣿⣿⣧⣹⠀⠀⠀⠀⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣞⣿⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡟⠻⠉⡻⠑⢻⠀⠀⠀⠀⣿⡷⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⢸⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡯⣿⡟⠛⠙⠹⠇⠀⠀⠀⢴⡄⠀⠀⠀⠀⢈⣅⣬⣠⣈⣇⣀⢀⣀⣄⡀⣿⣇⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⣶⡶⠶⠶⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠠⠆ ⣶⣶⣴⣤⣶⣶⠶⠶⠶⠶⠦⠶⠶⠶⠶⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⢶⠶⠆⢲⠲⢤⡶⠒⠒⠒⠶⠶⠶⠲⢸⡈⠍⠉⠎⠀⠀⠀⣠⣻⣿⣿⣾⣷⣾⣿⣟⠓⠓⠶⠿⢿⡿⢿⡷⠾⢷⣿⠿⠿⢿⣿⣷⣿⠾⠿⠷⣿⣿⡷⠿⠿⠿⠛⠛⠻⠿⠿⠿⠿⢿⣿⣿⣿⣿⣤⡄⠀⣀⠀⠀⠀⢀ ⣷⢶⣶⣶⣆⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⢸⡧⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠭⠭⠤⠤⠥⠶⠛⠛⠛⠛⠀⠻⠻⠥⠤⠤⠬⠤⠤⠤⠤⠬⠿⠟⡻⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀⣤⣀⣀⣀⣡ ⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⣮⡀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠗⣼⣽⣷⣿⣞⣾⡿⠶⣯⢿⢿⣿⣿⣿⣯⣯⣷⣿⣾⣳⣻⣽⣿⣿⣿⡷⣿⣿⣿⣿⣿⡿⠏⠙⠰⢶⡿⠿⢿⠿⠿⡿⢿⠿⢿⠿⠿⢏⠿ ⣟⣛⣛⣛⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⠃⠀⠃⡄⠀⠀⠀⠀⠀⣿⠀⢱⣿⡷⣿⣹⡿⣛⣒⣺⣏⣶⣓⣒⣊⣞⣉⣘⣚⣿⣿⡿⠱⠞⢿⢸⣿⣿⣿⣿⣿⣿⡇⠈⣠⣤⣤⣤⠀⣤⣤⣤⣤⢀⣤⣽⣤⡄⢠⣤ ⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢀⡄⠀⠆⠀⠀⠀⣿⣀⣚⣛⣛⣛⣿⣷⣿⣛⣿⣿⣿⡛⣿⣿⣿⣻⡟⢻⣿⡿⡇⣰⣼⣾⣼⣿⣿⣿⣿⣿⣿⡇⠀⢿⣿⣿⣷⠀⣿⣿⣿⡿⠸⣿⣿⣿⡶⠸⣿ ⣎⣟⣿⠛⠚⠿⠻⠿⠿⠟⠛⠛⠛⠛⠿⠻⠿⠻⠉⠱⠈⠁⣆⠀⠀⠀⠀⣿⣭⣿⣿⣿⣿⣿⣯⣯⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣯⢸⣿⣿⣿⣿⣿⣿⡇⠀⢙⣛⣛⣛⡈⣛⢛⡛⠛⢙⣛⢛⡛⠛⢀⡛ ⣿⡿⣻⠀⠰⢴⡆⠀⠀⠷⡀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠰⠛⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⢿⣿⣿⣿⣿⢿⢿⣿⢸⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣻⣿⢸⣿ ⡷⣶⡶⡶⣾⡏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢨⠀⠀⠀⠀⠆⠀⠀⠀⠀⣿⣉⠶⠶⣶⣶⡶⠶⡶⠀⣶⣷⣿⠶⠶⣾⣶⢷⠾⣭⡏⠳⠶⠶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡇⠀⠘⠿⠿⠿⠿⠺⠿⠿⠟⠐⠻⠿⠿⠇⠐⠿ ⠆⢒⠒⠒⠂⠀⢲⡄⠀⠀⠀⠀⢀⡠⢀⡈⠀⠈⣤⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣼⣷⣿⢶⠄⣿⣿⣷⠶⢰⣿⣿⣻⣶⠀⠀ ⡿⠛⢛⣣⡤⠄⠘⠃⠠⠀⠀⠀⠜⠃⠜⠓⠀⢸⡏⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣾⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢹⣿⣟⡈⠀⣿⣿⣍⣿⡈⣿⣿⣟⣛⠀⠀ ⠙⠛⠛⠛⠃⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠀⣠⠀⠀⠀⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⢻⣿⣻⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡶⡶⣾⠇⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣘⠀⠁⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⡿⣿⡿⡿⡿⠿⢿⠿⢯⢿⢿⣿⠷⠿⠿⢼⣿⣿⣿⢿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣗⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢩⠀⡀⠀⠀⠀⠀⠀⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣇⣁⣁⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠈⠀⡾⠀⠀⠀⠀⡆⠀⠀⠀⠀⣿⠋⠛⠛⠉⠝⠛⠁⠊⠉⠙⠐⠛⠑⠓⠛⠋⠛⠼⣿⣿⣿⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡏⠉⠉⠁⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣠⣿⠒⠆⠆⡆⢸⠀⠀⠀⠀⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡟⣿⢿⣿⢿⢻⢽⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠛⠛⠃⠀⠸⡷⠂⠀⠀⠀⠀⠀⣤⠀⢸⢿⣿⣳⣿⣿⣇⣹⠀⠀⠀⠀⣿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠻⣇⠡⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣎⣷⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡟⠻⠉⡻⠑⢻⠀⠀⠀⠀⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠈⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⢨⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠯⣿⡏⠛⠙⠹⠇⠀⠀⠀⢴⡄⠀⠀⠀⠀⢈⣅⣬⣠⣈⣇⣀⢀⣀⣄⡀⣿⠄⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⣶⠶⠶⠶⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠠⠆ ⣶⣶⣤⣤⣶⣶⠶⠶⠶⠶⠦⠶⠶⠶⠶⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⢶⠶⠆⢲⠲⢤⡶⠒⠒⠒⠶⠶⠶⠲⢸⡈⠍⠉⠎⠀⠀⠀⣠⣻⣿⣿⣾⣷⣾⣿⣟⠓⠓⠶⠿⢿⡿⢿⡷⠾⢷⣾⠿⠿⢿⣿⣷⣿⠾⠿⠷⣿⣿⡷⠿⠿⠿⠛⠛⠛⠛⠿⠿⠿⢿⣿⣿⣿⣿⣤⡄⠀⣀⠀⠀⠀⢀ ⣷⢶⣶⣶⣆⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⢸⡧⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠭⠭⠤⠤⠥⠶⠛⠻⠛⠛⠀⠛⠻⠥⠤⠤⠬⠤⠤⠤⠤⠬⠿⠟⡻⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀⣤⣂⣀⣀⣡ ⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⣮⡀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠗⣼⣽⣷⣿⣞⣾⡿⠦⣯⢿⢿⣿⣿⣿⣯⣯⣷⣽⣮⣳⣻⣽⣿⣿⣿⡷⣿⣿⣿⣿⣿⡿⠏⠙⠸⢶⡿⠿⢿⠿⠿⡿⢿⠿⢿⠿⠿⢏⠿ ⣟⣛⣛⣛⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⠃⠀⠃⡄⠀⠀⠀⠀⠀⣿⠀⢱⣿⡷⣿⣹⡿⣛⣒⣺⣏⣶⣓⣒⣊⣞⣉⣘⣚⣿⣿⡿⠱⠞⢿⢸⣿⣿⣿⣿⣿⣿⡇⣈⣠⣤⣤⣤⠀⣤⣤⣤⣤⢀⣤⣽⣤⡄⢠⣤ ⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢀⡄⠀⠆⠀⠀⠀⣿⣀⣚⣛⣛⣛⣿⣷⣿⣛⣿⣿⣿⡛⣿⣿⣿⣻⡟⢻⣿⡿⡇⣠⣼⣾⣼⣿⣿⣿⣿⣿⣿⡇⠛⢿⣿⣿⣿⠀⣿⣿⣿⡿⠸⣿⣿⣿⡶⠸⣿ ⣎⣟⣛⠛⠚⢿⡿⠟⠻⠛⠛⠛⠛⠛⠿⠻⠿⠻⠉⠱⠈⠁⣆⠀⠀⠀⠀⣿⣭⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣯⢸⣿⣿⣿⣿⣿⣿⡇⠀⢙⣛⣛⣛⡈⣛⢛⡛⠛⢙⣛⢛⡛⠛⢀⡛ ⣿⡿⣻⠀⠰⢴⡆⠀⠀⠷⡀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠰⠛⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⢿⣿⣿⣿⣿⢿⢿⣿⢸⣿⣿⣿⣿⣿⣿⡧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣻⣿⢸⣿ ⡷⣶⡶⡶⢾⡏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢨⠀⠀⠀⠀⠆⠀⠀⠀⠀⣿⣉⠶⠶⣶⣶⡶⠶⠶⠀⣶⣷⣿⠶⠶⣾⣶⢷⠾⣭⡏⠳⠶⠶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡇⠀⠘⠿⠿⠿⠿⠺⠿⠿⠟⠐⠻⠿⠿⠇⠐⠿ ⠆⢒⠒⠒⠂⠀⢲⡄⠀⠀⠀⠀⢀⡠⢀⡈⠀⠈⣤⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣼⣷⣿⢶⢤⣿⣿⢳⠶⢰⣿⣿⣻⣶⠀⠀ ⡿⠛⢛⣣⡤⠄⠘⠃⠠⠀⠀⠀⠜⠃⠜⠓⠀⢸⡏⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣾⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠞⢻⣿⣟⡈⠉⣿⣿⣌⣻⡊⣿⣿⣟⣛⠀⠀ ⠙⠛⠛⠛⠃⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠀⣠⠀⠀⠀⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⢻⣿⣻⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡶⡶⣾⠇⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣘⠀⠁⠀⠀⠀⠀⠀⠀⠄⣿⢿⣿⡿⣿⡿⡿⡿⠿⢿⠿⢯⢿⢿⣿⠷⠿⠿⢼⣿⣿⣿⢿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣗⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢩⠀⡀⠀⠀⠀⠀⠀⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣇⣁⣁⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠈⠀⡾⠀⠀⠀⠀⡆⠀⠀⠀⠀⣿⠋⠛⠛⠁⠝⠋⠁⠊⠉⠙⠐⠛⠐⠓⠛⠋⠛⠼⣿⣿⣿⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⡏⠉⠉⠁⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣠⣿⠒⠆⠆⡆⢸⠀⠀⠀⠀⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡟⣿⢿⣿⢿⢻⢽⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠛⠛⠃⠀⠸⡷⠂⠀⠀⠀⠀⠀⣤⠀⢸⢿⣿⣳⣿⣿⣇⣹⠀⠀⠀⠀⣿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠻⣇⠡⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣎⣷⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡟⠻⠉⡻⠑⢻⠀⠀⠀⠀⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠈⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⢨⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠯⣿⡏⠛⠙⠹⠇⠀⠀⠀⢴⡀⠀⠀⠀⠀⢈⣅⣬⣠⣈⣇⣀⢀⣀⣀⡀⣿⠄⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⣶⠶⠶⠶⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠠⠆ ⣶⣶⣤⣤⣶⣶⠶⠶⠶⠶⠦⠶⠶⠶⠶⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⢶⠶⠆⢲⠲⢤⡶⠒⠒⠒⠶⠶⠶⠲⢸⡈⠍⠉⠎⠀⠀⠀⣠⣻⣿⣷⣾⣷⣾⣿⣟⠓⠓⠶⠿⢿⡿⢿⡷⠾⢷⣾⠿⠿⢿⣿⣷⣿⠾⠿⠷⣿⣿⡷⠿⠿⠿⠛⠛⠛⠛⠿⠿⠿⢿⣿⣿⣿⣿⣤⡄⠀⣀⠀⠀⠀⢀ ⣷⢶⣶⣶⣆⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⢸⡧⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠭⠭⠤⠤⠥⠶⠛⠻⠛⠛⠀⠛⠻⠥⠤⠤⠬⠤⠤⠤⠤⠬⠿⠟⡻⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀⣤⣂⣀⣀⣡ ⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⣮⡀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠗⣼⣽⣷⣿⣞⣾⡿⠦⣯⢿⢿⣿⣿⣿⣯⣯⣷⣽⣮⣳⣻⣽⣿⣿⣿⠷⣿⣿⣿⣿⣿⡿⠏⠙⠸⢶⡿⠿⢿⠿⠿⡿⢿⠿⢿⠿⠿⢏⠿ ⣟⣛⣛⣛⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⠃⠀⠃⡄⠀⠀⠀⠀⠀⣿⠀⢱⣿⡷⣿⣹⡿⣛⣒⣺⣏⣶⣓⣒⣊⣞⣉⣘⣚⣿⣿⡿⠱⠞⢿⢸⣿⣿⣿⣿⣿⣿⡇⣈⣠⣤⣤⣤⠀⣤⣤⣤⣤⢀⣤⣽⣤⡄⢠⣤ ⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢀⡄⠀⠆⠀⠀⠀⣿⣀⣚⣛⣛⣛⣿⣷⣿⣛⣿⣿⣿⡛⣿⣿⣿⣻⡟⢻⣿⡿⡇⣠⣼⣾⣼⣿⣿⣿⣿⣿⣿⡇⠛⢿⣿⣿⣿⠀⣿⣿⣿⡿⠸⣿⣿⣿⡶⠸⣿ ⣎⣟⣛⠛⠚⣿⣿⠟⠻⠛⠛⠛⠛⠛⠿⠻⠿⠻⠉⠱⠈⠁⣆⠀⠀⠀⠀⣿⣭⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣯⢸⣿⣿⣿⣿⣿⣿⡇⠀⢙⣛⣛⣛⡈⣛⢛⡛⠛⢙⣛⢛⡛⠛⢀⡛ ⣿⡿⣻⠀⠰⢭⡏⠀⠀⠷⡀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠰⠛⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⢿⣿⣿⣿⣿⢿⢿⣿⢸⣿⣿⣿⣿⣿⣿⡧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣻⣿⢸⣿ ⡷⣶⡶⡶⢾⡏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢨⠀⠀⠀⠀⠆⠀⠀⠀⠀⣿⣉⠲⠶⣶⣶⡶⠶⠶⠀⣶⣷⣿⠶⠶⣾⣶⢷⠾⣭⡏⠳⠶⠶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡇⠀⠘⠿⠿⠿⠿⠺⠿⠿⠟⠐⠻⠿⠿⠇⠐⠿ ⠆⢒⠒⠒⠂⠀⢲⡄⠀⠀⠀⠀⢀⡠⢀⡈⠀⠈⣤⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣼⣷⣿⢶⢤⣿⣿⢳⠶⢰⣿⣿⣻⣶⠀⠀ ⡿⠛⢛⣣⡤⠄⠘⠃⠠⠀⠀⠀⠜⠃⠜⠓⠀⢸⡏⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣾⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠞⢻⣿⣟⡈⠉⣿⣿⣌⣻⡊⣿⣿⣟⣛⠀⠀ ⠙⠛⠛⠛⠃⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠀⣠⠀⠀⠀⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⢻⣿⣻⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡶⡶⣾⠇⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣘⠀⠁⠀⠀⠀⠀⠀⠀⠄⣿⢿⣿⡿⣿⡿⡿⡿⠿⢿⠿⢯⢿⢿⣿⠷⠿⠿⢼⣿⣿⣿⢿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣗⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢩⠀⡀⠀⠀⠀⠀⠀⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣇⣁⣁⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠈⠀⡾⠀⠀⠀⠀⡆⠀⠀⠀⠀⣿⠋⠛⠛⠁⠝⠋⠁⠊⠉⠙⠐⠛⠐⠓⠛⠋⠛⠼⣿⣿⣿⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⡏⠉⠉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣠⣿⠒⠆⠆⡆⢸⠀⠀⠀⠀⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡟⣿⢿⣿⢿⢻⢽⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠛⠛⠃⠀⠸⡷⠂⠀⠀⠀⠀⠀⣤⠀⢸⢿⣿⣳⣿⣿⣇⣹⠀⠀⠀⠀⣿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠻⣇⠡⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣎⣷⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡟⠻⠉⡻⠑⢻⠀⠀⠀⠀⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠈⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⢨⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠯⣿⡏⠛⠙⠹⠇⠀⠀⠀⢴⡀⠀⠀⠀⠀⢈⣅⣬⣠⣈⣇⣀⢀⣀⣀⡀⣿⠄⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⣶⠶⠶⠶⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠠⠆ ⣶⣶⣤⣤⣶⣶⠶⠶⠶⠶⠦⠶⠶⠶⠶⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⢶⠶⠆⢲⠲⢤⡶⠒⠒⠒⠶⠶⠶⠲⢸⡈⠍⠉⠎⠀⠀⠀⣠⣻⣿⣷⣾⣷⣾⣿⣟⠓⠓⠶⠿⢿⡿⢿⡷⠾⢷⣾⠿⠿⢿⣿⣷⣿⠾⠿⠷⣿⣿⡷⠿⠿⠿⠛⠛⠛⠛⠿⠿⠿⢿⣿⣿⣿⣿⣤⡄⠀⣀⠀⠀⠀⢀ ⣷⢶⣶⣶⣆⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⢸⡧⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠭⠭⠤⠤⠥⠶⠛⠻⠛⠛⠀⠛⠻⠥⠤⠤⠬⠤⠤⠤⠤⠬⠿⠟⡻⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀⣤⣂⣀⣀⣡ ⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⣮⡀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠗⣼⣽⣷⣿⣞⣾⡿⠦⣯⢿⢿⣿⣿⣿⣯⣯⣷⣽⣮⣳⣻⣽⣿⣿⣿⠷⣿⣿⣿⣿⣿⡿⠏⠙⠸⢶⡿⠿⢿⠿⠿⡿⢿⠿⢿⠿⠿⢏⠿ ⣟⣛⣛⣛⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⠃⠀⠃⡄⠀⠀⠀⠀⠀⣿⠀⢱⣿⡷⣿⣹⡿⣛⣒⣺⣏⣶⣓⣒⣊⣞⣉⣘⣚⣿⣿⡿⠱⠞⢿⢸⣿⣿⣿⣿⣿⣿⡇⣈⣠⣤⣤⣤⠀⣤⣤⣤⣤⢀⣤⣽⣤⡄⢠⣤ ⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢀⡄⠀⠆⠀⠀⠀⣿⣀⣚⣛⣛⣛⣿⣷⣿⣛⣿⣿⣿⡛⣿⣿⣿⣻⡟⢻⣿⡿⡇⣠⣼⣾⣼⣿⣿⣿⣿⣿⣿⡇⠛⢿⣿⣿⣿⠀⣿⣿⣿⡿⠸⣿⣿⣿⡶⠸⣿ ⣎⣟⣛⠛⠚⣿⣿⠟⠻⠛⠛⠛⠛⠛⠿⠻⠿⠻⠉⠱⠈⠁⣆⠀⠀⠀⠀⣿⣭⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣯⢸⣿⣿⣿⣿⣿⣿⡇⠀⢙⣛⣛⣛⡈⣛⢛⡛⠛⢙⣛⢛⡛⠛⢀⡛ ⣿⡿⣻⠀⠰⢭⡏⠀⠀⠷⡀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠰⠛⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⢿⣿⣿⣿⣿⢿⢿⣿⢸⣿⣿⣿⣿⣿⣿⡧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣻⣿⢸⣿ ⡷⣶⡶⡶⢾⡏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢨⠀⠀⠀⠀⠆⠀⠀⠀⠀⣿⣉⠲⠶⣶⣶⡶⠶⠶⠀⣶⣷⣿⠶⠶⣾⣶⢷⠾⣭⡏⠳⠶⠶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡇⠀⠘⠿⠿⠿⠿⠺⠿⠿⠟⠐⠻⠿⠿⠇⠐⠿ ⠆⢒⠒⠒⠂⠀⢲⡄⠀⠀⠀⠀⢀⡠⢀⡈⠀⠈⣤⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣼⣷⣿⢶⢤⣿⣿⢳⠶⢰⣿⣿⣻⣶⠀⠀ ⡿⠛⢛⣣⡤⠄⠘⠃⠠⠀⠀⠀⠜⠃⠜⠓⠀⢸⡏⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣾⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠞⢻⣿⣟⡈⠉⣿⣿⣌⣻⡊⣿⣿⣟⣛⠀⠀ ⠙⠛⠛⠛⠃⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠀⣠⠀⠀⠀⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⢻⣿⣻⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡶⡶⣾⠇⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣘⠀⠁⠀⠀⠀⠀⠀⠀⠄⣿⢿⣿⡿⣿⡿⡿⡿⠿⢿⠿⢯⢿⢿⣿⠷⠿⠿⢼⣿⣿⣿⢿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣗⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢩⠀⡀⠀⠀⠀⠀⠀⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣇⣁⣁⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠈⠀⡾⠀⠀⠀⠀⡆⠀⠀⠀⠀⣿⠋⠛⠛⠁⠝⠋⠁⠊⠉⠙⠐⠛⠐⠓⠛⠋⠛⠼⣿⣿⣿⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⡏⠉⠉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣠⣿⠒⠆⠆⡆⢸⠀⠀⠀⠀⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡟⣿⢿⣿⢿⢻⢽⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠛⠛⠃⠀⠸⡷⠂⠀⠀⠀⠀⠀⣤⠀⢸⢿⣿⣳⣿⣿⣇⣹⠀⠀⠀⠀⣿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠻⣇⠡⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣎⣷⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡟⠻⠉⡻⠑⢻⠀⠀⠀⠀⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠈⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⢨⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠯⣿⡏⠛⠙⠹⠇⠀⠀⠀⢴⡀⠀⠀⠀⠀⢈⣅⣬⣠⣈⣇⣀⢀⣀⣀⡀⣿⠄⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⣶⠶⠶⠶⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠠⠆ ⣶⣶⣤⣤⣶⣶⠶⠶⠶⠶⠦⠶⠶⠶⠶⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⢶⠶⠆⢲⠲⢤⡶⠒⠒⠒⠶⠶⠶⠲⢸⡈⠍⠉⠎⠀⠀⠀⣠⣻⣿⣷⣾⣷⣾⣿⣟⠓⠓⠶⠿⢿⡿⢿⡷⠾⢷⣾⠿⠿⢿⣿⣷⣿⠾⠿⠷⣿⣿⡷⠿⠿⠿⠛⠛⠛⠛⠿⠿⠿⢿⣿⣿⣿⣿⣤⡄⠀⣀⠀⠀⠀⢀ ⣷⢶⣶⣶⣆⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⢸⡧⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠭⠭⠤⠤⠥⠶⠛⠻⠛⠛⠀⠛⠻⠥⠤⠤⠬⠤⠤⠤⠤⠬⠿⠟⡻⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀⣤⣂⣀⣀⣡ ⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⣮⡀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠗⣼⣽⣷⣿⣞⣾⡿⠦⣯⢿⢿⣿⣿⣿⣯⣯⣷⣽⣮⣳⣻⣽⣿⣿⣿⠷⣿⣿⣿⣿⣿⡿⠏⠙⠸⢶⡿⠿⢿⠿⠿⡿⢿⠿⢿⠿⠿⢏⠿ ⣟⣛⣛⣛⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⠃⠀⠃⡄⠀⠀⠀⠀⠀⣿⠀⢱⣿⡷⣿⣹⡿⣛⣒⣺⣏⣶⣓⣒⣊⣞⣉⣘⣚⣿⣿⡿⠱⠞⢿⢸⣿⣿⣿⣿⣿⣿⡇⣈⣠⣤⣤⣤⠀⣤⣤⣤⣤⢀⣤⣽⣤⡄⢠⣤ ⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢀⡄⠀⠆⠀⠀⠀⣿⣀⣚⣛⣛⣛⣿⣷⣿⣛⣿⣿⣿⡛⣿⣿⣿⣻⡟⢻⣿⡿⡇⣠⣼⣾⣼⣿⣿⣿⣿⣿⣿⡇⠛⢿⣿⣿⣿⠀⣿⣿⣿⡿⠸⣿⣿⣿⡶⠸⣿ ⣎⣟⣛⠛⠚⣿⣿⠟⠻⠛⠛⠛⠛⠛⠿⠻⠿⠻⠉⠱⠈⠁⣆⠀⠀⠀⠀⣿⣭⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣯⢸⣿⣿⣿⣿⣿⣿⡇⠀⢙⣛⣛⣛⡈⣛⢛⡛⠛⢙⣛⢛⡛⠛⢀⡛ ⣿⡿⣻⠀⠰⢭⡏⠀⠀⠷⡀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠰⠛⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⢿⣿⣿⣿⣿⢿⢿⣿⢸⣿⣿⣿⣿⣿⣿⡧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣻⣿⢸⣿ ⡷⣶⡶⡶⢾⡏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢨⠀⠀⠀⠀⠆⠀⠀⠀⠀⣿⣉⠲⠶⣶⣶⡶⠶⠶⠀⣶⣷⣿⠶⠶⣾⣶⢷⠾⣭⡏⠳⠶⠶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡇⠀⠘⠿⠿⠿⠿⠺⠿⠿⠟⠐⠻⠿⠿⠇⠐⠿ ⠆⢒⠒⠒⠂⠀⢲⡄⠀⠀⠀⠀⢀⡠⢀⡈⠀⠈⣤⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣼⣷⣿⢶⢤⣿⣿⢳⠶⢰⣿⣿⣻⣶⠀⠀ ⡿⠛⢛⣣⡤⠄⠘⠃⠠⠀⠀⠀⠜⠃⠜⠓⠀⢸⡏⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣾⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠞⢻⣿⣟⡈⠉⣿⣿⣌⣻⡊⣿⣿⣟⣛⠀⠀ ⠙⠛⠛⠛⠃⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠀⣠⠀⠀⠀⠃⠀⠀⠀⠀⠀⣿⣟⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⢻⣿⣻⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡶⡶⣾⠇⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣘⠀⠁⠀⠀⠀⠀⠀⠀⠄⣿⢿⣿⡿⣿⡿⡿⡿⠿⢿⠿⢯⢿⢿⣿⠷⠿⠿⢼⣿⣿⣿⢿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣗⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢩⠀⡀⠀⠀⠀⠀⠀⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣇⣁⣁⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠈⠀⡾⠀⠀⠀⠀⡆⠀⠀⠀⠀⣿⠋⠛⠛⠁⠝⠋⠁⠊⠉⠙⠐⠛⠐⠓⠛⠋⠛⠼⣿⣿⣿⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⡏⠉⠉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣠⣿⠒⠆⠆⡆⢸⠀⠀⠀⠀⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡟⣿⢿⣿⢿⢻⢽⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠛⠛⠃⠀⠸⡷⠂⠀⠀⠀⠀⠀⣤⠀⢸⢿⣿⣳⣿⣿⣇⣹⠀⠀⠀⠀⣿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠻⣇⠡⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣎⣷⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡟⠻⠉⡻⠑⢻⠀⠀⠀⠀⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠈⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⢨⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠯⣿⡏⠛⠙⠹⠇⠀⠀⠀⢴⡀⠀⠀⠀⠀⢈⣅⣬⣠⣈⣇⣀⢀⣀⣀⡀⣿⠄⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⣶⠶⠶⠶⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠠⠆ ⣶⣶⣤⣤⣶⣶⠶⠶⠶⠶⠦⠶⠶⠶⠶⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⢶⠶⠆⢲⠲⢤⡶⠒⠒⠒⠶⠶⠶⠲⢸⡈⠍⠉⠎⠀⠀⠀⣠⣻⣿⣿⣾⣷⣾⣿⣟⠓⠓⠶⠿⢿⡿⢿⡷⠾⢷⣾⠿⠿⢿⣿⣷⣿⠾⠿⠷⣿⣿⡷⠿⠿⠿⠛⠛⠛⠛⠿⠿⠿⢿⣿⣿⣿⣿⣤⡄⠀⣀⠀⠀⠀⢀ ⣷⢶⣶⣶⣆⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⢸⡧⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠭⠭⠤⠤⠥⠶⠛⠻⠛⠛⠀⠛⠻⠥⠤⠤⠬⠤⠤⠤⠤⠬⠿⠟⡻⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀⣤⣂⣀⣀⣡ ⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⣮⡀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠗⣼⣽⣷⣿⣞⣾⡿⠦⣯⢿⢿⣿⣿⣿⣯⣯⣷⣽⣮⣳⣻⣽⣿⣿⣿⠷⣿⣿⣿⣿⣿⡿⠏⠙⠸⢶⡿⠿⢿⠿⠿⡿⢿⠿⢿⠿⠿⢏⠿ ⣟⣛⣛⣛⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⠃⠀⠃⡄⠀⠀⠀⠀⠀⣿⠀⢱⣿⡷⣿⣹⡿⣛⣒⣺⣏⣶⣓⣒⣊⣞⣉⣘⣚⣿⣿⡿⠱⠞⢿⢸⣿⣿⣿⣿⣿⣿⡇⣈⣠⣤⣤⣤⠀⣤⣤⣤⣤⢀⣤⣽⣤⡄⢠⣤ ⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢀⡄⠀⠆⠀⠀⠀⣿⣀⣚⣛⣛⣛⣿⣷⣿⣛⣿⣿⣿⡛⣿⣿⣿⣻⡟⢻⣿⡿⡇⣠⣼⣾⣼⣿⣿⣿⣿⣿⣿⡇⠛⢿⣿⣿⣿⠀⣿⣿⣿⡿⠸⣿⣿⣿⡶⠸⣿ ⣎⣟⣛⠛⠚⣿⣿⠟⠻⠛⠛⠛⠛⠛⠿⠻⠿⠻⠉⠱⠈⠁⣆⠀⠀⠀⠀⣿⣭⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣯⢸⣿⣿⣿⣿⣿⣿⡇⠀⢙⣛⣛⣛⡈⣛⢛⡛⠛⢙⣛⢛⡛⠛⢀⡛ ⣿⡿⣻⠀⠰⢭⡏⠀⠀⠷⡀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠰⠛⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⢿⣿⣿⣿⣿⢿⢿⣿⢸⣿⣿⣿⣿⣿⣿⡧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣻⣿⢸⣿ ⡷⣶⡶⡶⢾⡏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢨⠀⠀⠀⠀⠆⠀⠀⠀⠀⣿⣉⠶⠶⣶⣶⡶⠶⠶⠀⣶⣷⣿⠶⠶⣾⣶⢷⠾⣭⡏⠳⠶⠶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡇⠀⠘⠿⠿⠿⠿⠺⠿⠿⠟⠐⠻⠿⠿⠇⠐⠿ ⠆⢒⠒⠒⠂⣺⣶⡄⠀⠀⠀⠀⢀⡠⢀⡈⠀⠈⣤⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣼⣷⣿⢶⢤⣿⣿⢳⠶⢰⣿⣿⣻⣶⠀⠀ ⡿⠛⢛⣣⡤⠌⠙⠃⠠⠀⠀⠀⠜⠃⠜⠓⠀⢸⡏⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣾⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠞⢻⣿⣟⡈⠉⣿⣿⣌⣻⡊⣿⣿⣟⣛⠀⠀ ⠙⠛⠛⠛⠃⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠀⣠⠀⠀⠀⠃⠀⠀⠀⠀⠀⣿⣟⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⢻⣿⣻⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡶⡶⣾⠇⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣘⠀⠁⠀⠀⠀⠀⠀⠀⠄⣿⢿⣿⡿⣿⡿⡿⡿⠿⢿⠿⢯⢿⢿⣿⠷⠿⠿⢼⣿⣿⣿⢿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣗⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢩⠀⡀⠀⠀⠀⠀⠀⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣇⣁⣁⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠈⠀⡾⠀⠀⠀⠀⡆⠀⠀⠀⠀⣿⠋⠛⠛⠁⠝⠋⠁⠊⠉⠙⠐⠛⠐⠓⠛⠋⠛⠼⣿⣿⣿⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⡏⠉⠉⠁⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣠⣿⠒⠆⠆⡆⢸⠀⠀⠀⠀⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡟⣿⢿⣿⢿⢻⢽⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠛⠛⠃⠀⠸⡷⠂⠀⠀⠀⠀⠀⣤⠀⢸⢿⣿⣳⣿⣿⣇⣹⠀⠀⠀⠀⣿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠻⣇⠡⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣎⣷⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡟⠻⠉⡻⠑⢻⠀⠀⠀⠀⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠈⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⢨⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠯⣿⡏⠛⠙⠹⠇⠀⠀⠀⢴⡀⠀⠀⠀⠀⢈⣅⣬⣠⣈⣇⣀⢀⣀⣀⡀⣿⠄⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⣶⠶⠶⠶⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠠⠆ ⣶⣶⣤⣤⣶⣶⠶⠶⠶⠶⠦⠶⠶⠶⠶⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⢶⠶⠆⢲⠲⢤⡶⠒⠒⠒⠶⠶⠶⠲⢸⡈⠍⠉⠎⠀⠀⠀⣠⣻⣿⣿⣾⣷⣾⣿⣟⠓⠓⠶⠿⢿⡿⢿⡷⠾⢷⣾⠿⠿⢿⣿⣷⣿⠾⠿⠷⣿⣿⡷⠿⠿⠿⠛⠛⠛⠛⠿⠿⠿⢿⣿⣿⣿⣿⣤⡄⠀⣀⠀⠀⠀⢀ ⣷⢶⣶⣶⣆⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⢸⡧⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠭⠭⠤⠤⠥⠶⠛⠻⠛⠛⠀⠛⠻⠥⠤⠤⠬⠤⠤⠤⠤⠬⠿⠟⡻⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀⣤⣂⣀⣀⣡ ⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⣮⡀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠗⣼⣽⣷⣿⣞⣾⡿⠦⣯⢿⢿⣿⣿⣿⣯⣯⣷⣽⣮⣳⣻⣽⣿⣿⣿⠷⣿⣿⣿⣿⣿⡿⠏⠙⠸⢶⡿⠿⢿⠿⠿⡿⢿⠿⢿⠿⠿⢏⠿ ⣟⣛⣛⣛⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⠃⠀⠃⡄⠀⠀⠀⠀⠀⣿⠀⢱⣿⡷⣿⣹⡿⣛⣒⣺⣏⣶⣓⣒⣊⣞⣉⣘⣚⣿⣿⡿⠱⠞⢿⢸⣿⣿⣿⣿⣿⣿⡇⣈⣠⣤⣤⣤⠀⣤⣤⣤⣤⢀⣤⣽⣤⡄⢠⣤ ⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢀⡄⠀⠆⠀⠀⠀⣿⣀⣚⣛⣛⣛⣿⣷⣿⣛⣿⣿⣿⡛⣿⣿⣿⣻⡟⢻⣿⡿⡇⣠⣼⣾⣼⣿⣿⣿⣿⣿⣿⡇⠛⢿⣿⣿⣿⠀⣿⣿⣿⡿⠸⣿⣿⣿⡶⠸⣿ ⣎⣟⣛⠛⠚⣿⣿⠟⠻⠛⠛⠛⠛⠛⠿⠻⠿⠻⠉⠱⠈⠁⣆⠀⠀⠀⠀⣿⣭⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣯⢸⣿⣿⣿⣿⣿⣿⡇⠀⢙⣛⣛⣛⡈⣛⢛⡛⠛⢙⣛⢛⡛⠛⢀⡛ ⣿⡿⣻⠀⠰⢭⡏⠀⠀⠷⡀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠰⠛⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⢿⣿⣿⣿⣿⢿⢿⣿⢸⣿⣿⣿⣿⣿⣿⡧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣻⣿⢸⣿ ⡷⣶⡶⡶⢾⡏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢨⠀⠀⠀⠀⠆⠀⠀⠀⠀⣿⣉⠶⠶⣶⣶⡶⠶⠶⠀⣶⣷⣿⠶⠶⣾⣶⢷⠾⣭⡏⠳⠶⠶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡇⠀⠘⠿⠿⠿⠿⠺⠿⠿⠟⠐⠻⠿⠿⠇⠐⠿ ⠆⢒⠒⠒⠂⣺⣶⡄⠀⠀⠀⠀⢀⡠⢀⡈⠀⠈⣤⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣼⣷⣿⢶⢤⣿⣿⢳⠶⢰⣿⣿⣻⣶⠀⠀ ⡿⠛⢛⣣⡤⠌⠙⠃⠠⠀⠀⠀⠜⠃⠜⠓⠀⢸⡏⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣾⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠞⢻⣿⣟⡈⠉⣿⣿⣌⣻⡊⣿⣿⣟⣛⠀⠀ ⠙⠛⠛⠛⠃⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠀⣠⠀⠀⠀⠃⠀⠀⠀⠀⠀⣿⣟⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⢻⣿⣻⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡶⡶⣾⠇⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣘⠀⠁⠀⠀⠀⠀⠀⠀⠄⣿⢿⣿⡿⣿⡿⡿⡿⠿⢿⠿⢯⢿⢿⣿⠷⠿⠿⢼⣿⣿⣿⢿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣗⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢩⠀⡀⠀⠀⠀⠀⠀⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣇⣁⣁⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠈⠀⡾⠀⠀⠀⠀⡆⠀⠀⠀⠀⣿⠋⠛⠛⠁⠝⠋⠁⠊⠉⠙⠐⠛⠐⠓⠛⠋⠛⠼⣿⣿⣿⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⡏⠉⠉⠁⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣠⣿⠒⠆⠆⡆⢸⠀⠀⠀⠀⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡟⣿⢿⣿⢿⢻⢽⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠛⠛⠃⠀⠸⡷⠂⠀⠀⠀⠀⠀⣤⠀⢸⢿⣿⣳⣿⣿⣇⣹⠀⠀⠀⠀⣿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠻⣇⠡⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣎⣷⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡟⠻⠉⡻⠑⢻⠀⠀⠀⠀⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠈⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⢨⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠯⣿⡏⠛⠙⠹⠇⠀⠀⠀⢴⡀⠀⠀⠀⠀⢈⣅⣬⣠⣈⣇⣀⢀⣀⣀⡀⣿⠄⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⣶⠶⠶⠶⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠠⠆ ⣶⣶⣤⣤⣶⣶⠶⠶⠶⠶⠦⠶⠶⠶⠶⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⢶⠶⠆⢲⠲⢤⡶⠒⠒⠒⠶⠶⠶⠲⢸⡈⠍⠉⠎⠀⠀⠀⣠⣻⣿⣿⣾⣷⣾⣿⣟⠓⠓⠶⠿⢿⡿⢿⡷⠾⢷⣾⠿⠿⢿⣿⣷⣿⠾⠿⠷⣿⣿⡷⠿⠿⠿⠛⠛⠛⠛⠿⠿⠿⢿⣿⣿⣿⣿⣤⡄⠀⣀⠀⠀⠀⢀ ⣷⢶⣶⣶⣆⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⢸⡧⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠭⠭⠤⠤⠥⠶⠛⠻⠛⠛⠀⠛⠻⠥⠤⠤⠬⠤⠤⠤⠤⠬⠿⠟⡻⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀⣤⣂⣀⣀⣡ ⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⣮⡀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠗⣼⣽⣷⣿⣞⣾⡿⠦⣯⢿⢿⣿⣿⣿⣯⣯⣷⣽⣮⣳⣻⣽⣿⣿⣿⠷⣿⣿⣿⣿⣿⡿⠏⠙⠸⢶⡿⠿⢿⠿⠿⡿⢿⠿⢿⠿⠿⢏⠿ ⣟⣛⣛⣛⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⠃⠀⠃⡄⠀⠀⠀⠀⠀⣿⠀⢱⣿⡷⣿⣹⡿⣛⣒⣺⣏⣶⣓⣒⣊⣞⣉⣘⣚⣿⣿⡿⠱⠞⢿⢸⣿⣿⣿⣿⣿⣿⡇⣈⣠⣤⣤⣤⠀⣤⣤⣤⣤⢀⣤⣽⣤⡄⢠⣤ ⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢀⡄⠀⠆⠀⠀⠀⣿⣀⣚⣛⣛⣛⣿⣷⣿⣛⣿⣿⣿⡛⣿⣿⣿⣻⡟⢻⣿⡿⡇⣠⣼⣾⣼⣿⣿⣿⣿⣿⣿⡇⠛⢿⣿⣿⣿⠀⣿⣿⣿⡿⠸⣿⣿⣿⡶⠸⣿ ⣎⣟⣛⠛⠚⣿⣿⠟⠻⠛⠛⠛⠛⠛⠿⠻⠿⠻⠉⠱⠈⠁⣆⠀⠀⠀⠀⣿⣭⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣯⢸⣿⣿⣿⣿⣿⣿⡇⠀⢙⣛⣛⣛⡈⣛⢛⡛⠛⢙⣛⢛⡛⠛⢀⡛ ⣿⡿⣻⠀⠰⢭⡏⠀⠀⠷⡀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠰⠛⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⢿⣿⣿⣿⣿⢿⢿⣿⢸⣿⣿⣿⣿⣿⣿⡧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣻⣿⢸⣿ ⡷⣶⡶⡶⢾⡏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢨⠀⠀⠀⠀⠆⠀⠀⠀⠀⣿⣉⠶⠶⣶⣶⡶⠶⠶⠀⣶⣷⣿⠶⠶⣾⣶⢷⠾⣭⡏⠳⠶⠶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡇⠀⠘⠿⠿⠿⠿⠺⠿⠿⠟⠐⠻⠿⠿⠇⠐⠿ ⠆⢒⠒⠒⠂⣺⣶⡄⠀⠀⠀⠀⢀⡠⢀⡈⠀⠈⣤⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣼⣷⣿⢶⢤⣿⣿⢳⠶⢰⣿⣿⣻⣶⠀⠀ ⡿⠛⢛⣣⡤⠌⠙⠃⠠⠀⠀⠀⠜⠃⠜⠓⠀⢸⡏⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣾⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠞⢻⣿⣟⡈⠉⣿⣿⣌⣻⡊⣿⣿⣟⣛⠀⠀ ⠙⠛⠛⠛⠃⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠀⣠⠀⠀⠀⠃⠀⠀⠀⠀⠀⣿⣟⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⢻⣿⣻⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡶⡶⣾⠇⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣘⠀⠁⠀⠀⠀⠀⠀⠀⠄⣿⢿⣿⡿⣿⡿⡿⡿⠿⢿⠿⢯⢿⢿⣿⠷⠿⠿⢼⣿⣿⣿⢿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣗⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢩⠀⡀⠀⠀⠀⠀⠀⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣇⣁⣁⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠈⠀⡾⠀⠀⠀⠀⡆⠀⠀⠀⠀⣿⠋⠛⠛⠁⠝⠋⠁⠊⠉⠙⠐⠛⠐⠓⠛⠋⠛⠼⣿⣿⣿⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⡏⠉⠉⠁⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣠⣿⠒⠆⠆⡆⢸⠀⠀⠀⠀⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡟⣿⢿⣿⢿⢻⢽⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠛⠛⠃⠀⠸⡷⠂⠀⠀⠀⠀⠀⣤⠀⢸⢿⣿⣳⣿⣿⣇⣹⠀⠀⠀⠀⣿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠻⣇⠡⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣎⣷⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡟⠻⠉⡻⠑⢻⠀⠀⠀⠀⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠈⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⢨⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠯⣿⡏⠛⠙⠹⠇⠀⠀⠀⢴⡀⠀⠀⠀⠀⢈⣅⣬⣠⣈⣇⣀⢀⣀⣀⡀⣿⠄⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⡴⠶⠴⠴⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠠⠆ ⡶⣦⣤⣤⣤⣤⠤⠤⠤⠤⠤⠤⠤⠤⠔⢲⣴⣤⠴⢴⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⢦⠶⠆⢲⠲⢤⡲⠒⠒⠒⠴⠶⠖⠲⢸⡈⠍⠉⠎⠀⠀⠀⢰⠺⢿⡶⢾⠗⣾⣿⣏⠶⠷⠒⠲⠗⠿⢿⠶⠾⠗⠒⠒⠓⠓⡶⣶⣷⣺⣒⣓⣷⣒⣒⣓⣒⣚⣒⣒⣚⣛⣛⣛⣻⣿⣷⡿⣿⡿⣦⡆⠀⣀⠀⠀⠀⢀ ⡶⡶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠭⠭⠤⠼⠿⠿⠛⠚⠛⠛⠀⠛⠻⠥⠤⠦⠬⢼⡿⠭⠷⠧⠿⠏⡻⣋⣟⣛⣟⣉⣉⣉⣉⣉⣉⣙⣃⣒⣂⣂⣚⡇⣀⣤⣂⣀⣀⣡ ⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⣎⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⣄⣤⣤⣤⣄⡀⣤⣶⣻⡿⠿⠿⠧⠀⠀⠀⢺⣿⣬⢠⡴⠷⠲⠶⣿⣿⣿⣿⣿⣿⡏⠐⣸⣶⡿⠿⢿⣿⣿⡿⡇⠿⢿⠿⠿⢏⠶ ⣿⣿⣟⣛⣡⣦⣉⣉⣉⣿⣉⣏⣉⣉⣉⣹⣿⣿⠃⠀⠁⡄⠀⠀⠄⠠⠀⣷⠀⠀⠀⠭⠍⠉⠉⣉⣉⣁⣀⣊⣀⣀⣀⣀⣀⣀⣀⣻⣖⣳⣶⠃⠀⢸⣿⣿⣿⣿⣿⣿⡛⣊⣠⣾⣿⣧⠀⣬⣭⣥⣤⡇⣤⣽⣤⡄⢠⣄ ⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢀⡄⠀⠆⣑⣌⠢⣿⣠⣀⣈⣖⣐⣒⣖⣛⣻⡟⠻⠿⠿⠿⠿⠿⣿⡿⠟⢻⣿⢤⡏⢀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠟⢻⢿⣿⣇⠀⢿⣿⣿⡿⡟⣿⣿⣿⡶⠸⣿ ⡇⣛⠛⠛⠚⣿⣟⠛⠛⠛⠛⠛⠛⠛⠛⠻⠟⠹⠉⠱⠈⠁⣆⠀⠀⠀⠂⣿⣟⣿⣭⣯⣽⣫⣯⣫⣻⣿⣛⣠⣤⣄⣶⣶⣤⣤⣄⣿⣄⣤⣤⣤⣤⢸⣿⣿⣿⣿⣿⣿⣯⡀⢙⣻⣭⡙⡈⣛⢋⡋⠛⡇⣛⢛⡛⠛⢀⡙ ⡿⡿⣻⠀⠰⢭⡏⠀⠀⠷⡀⠀⠀⠀⠀⢘⠀⠰⠆⠀⠀⠀⠛⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠻⠻⠻⠿⣿⡿⠟⢿⠿⠿⢸⣿⣿⣿⣿⣿⣿⣿⡃⣽⣿⣿⣿⡁⣿⣿⣿⣿⡗⣿⣿⣻⣿⢸⣿ ⠇⡶⠶⡶⢾⠏⠛⠀⠀⠘⠁⠀⠀⠀⠀⢸⠀⠈⠀⠀⠀⠀⠆⠀⠂⠀⠂⣷⣁⠰⠶⡶⡶⡶⠶⠶⠂⠀⠀⠰⠶⠶⣶⢶⡶⠀⠀⣿⡷⠶⠶⣶⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⠋⠿⠿⠊⠺⠿⠿⠟⡇⠺⠿⠿⠇⠐⠿ ⠆⢒⠒⠒⠂⣺⣶⡄⠀⠀⠀⠀⢀⡀⢀⣸⠀⠈⢠⡄⠀⠀⠀⠀⠁⠐⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡇⠀⣼⣷⣿⢶⢠⣿⣿⢳⠖⡇⣿⣾⣳⣦⠀⠀ ⡉⠛⠛⢣⡤⠌⠙⠃⠠⠀⠀⠀⠜⠃⠜⢻⠀⢸⡏⠃⠀⠀⠀⠀⠀⠀⠀⣿⣶⣿⣿⣿⣿⣿⣷⣿⣿⣿⣶⣶⣾⣿⣾⣾⣶⣶⣾⣿⣷⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡇⠚⢻⣿⣏⡈⠉⣿⣿⣌⣻⡇⣿⣿⣟⡛⠀⠀ ⡉⠛⠛⠛⠃⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠀⡠⠀⠀⠀⠃⠀⠀⠀⠀⠀⣿⣏⣹⣛⣛⣻⣛⣛⣛⡛⠛⠛⠛⠛⠛⠛⠛⠛⢛⣻⢿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠗⡶⣾⠃⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⡎⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢡⠀⡀⠀⠀⠀⠀⠀⠀⠀⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠅⣀⣈⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢸⠀⡾⠀⠀⠀⠀⡆⠀⠀⠀⠀⣿⠀⠀⠀⠀⠄⠁⠀⠀⠈⠉⠀⠀⠀⠀⠈⠀⠀⠠⠄⣿⡯⠉⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠ ⣎⠉⠉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⣿⠒⠆⠆⠂⢸⠀⠀⣀⠀⣿⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢹⡇⠀⠀⢀⠀⢽⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀ ⣯⠋⠛⠃⠀⠸⡷⠂⠀⠀⠀⠀⠀⣤⠀⢸⢿⣿⣳⣿⣿⣇⣹⠀⠈⠉⠉⣿⠤⠀⠁⠀⠀⠀⠙⠛⠃⠀⠀⠀⠀⠀⠁⠈⠉⠉⠁⠰⠶⠶⠶⠶⠶⣾⣿⣿⣯⣭⣽⣿⡷⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠃⠀⠀⠀⠀⠀⠀ ⠎⣷⣷⡷⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡟⠻⠙⠻⠓⢻⠒⠒⠒⠂⣿⠒⠐⠒⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡚⠛⠛⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⠨⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠯⣿⡏⠛⠙⠹⠇⠀⠀⠀⢴⡀⠀⠀⠀⠀⢀⣄⣬⣠⣈⣇⣀⢀⣀⣀⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡇⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⡴⠶⠴⠴⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠠⠆ ⡶⣦⣤⣤⣤⣤⠤⠤⠤⠤⠤⠤⠤⠤⠔⢲⣴⣤⠴⢴⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⢦⠶⠆⢲⠲⢤⡲⠒⠒⠒⠴⠶⠖⠲⢸⡈⠍⠉⠎⠀⠀⠀⢰⠺⢿⡶⢾⠗⣾⣿⡟⠶⠷⠒⠲⠷⠿⢿⠶⠾⠗⠒⠒⠓⠓⡾⣶⣷⣺⣒⣓⣷⣒⣒⣓⣒⣚⣒⣒⣚⣛⣛⣛⣻⣿⣷⡿⣿⡿⣦⡆⠀⣀⠀⠀⠀⢀ ⡶⡶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠭⠭⠤⠼⠿⠿⠛⠚⠛⠛⠀⠛⠻⠥⠤⠦⠬⢼⡿⠭⠿⠿⠿⠟⡻⣋⣟⣛⣟⣉⣉⣉⣉⣉⣉⣙⣃⣒⣂⣂⣚⡇⣀⣤⣂⣀⣀⣡ ⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⣎⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⣄⣤⣤⣤⣄⡀⣤⣶⣻⡿⠿⠿⠧⠀⠀⠀⢺⣿⣬⢠⡴⠷⠲⠶⣿⣿⣿⣿⣿⣿⡏⠐⣸⣶⡿⠿⢿⣿⣿⡿⡇⠿⢿⠿⠿⢏⠶ ⣿⣿⣿⣛⣣⣦⣉⣉⣉⣿⣉⣏⣉⣉⣉⣹⣿⣿⠃⠀⠁⡄⠀⠀⠄⠠⠀⣷⠀⠀⠀⠭⠍⠉⠉⣉⣉⣁⣀⣊⣀⣀⣀⣀⣀⣀⣀⣻⣖⣻⣶⠃⠀⢸⣿⣿⣿⣿⣿⣿⡛⣊⣠⣾⣿⣧⠀⣬⣭⣥⣤⡇⣤⣽⣤⡄⢠⣄ ⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢀⡄⠀⠆⣑⣌⠣⣿⣠⣀⣈⣖⣐⣒⣖⣛⣻⡟⠻⠿⠿⠿⠿⠿⣿⡿⠟⢻⣿⢤⡯⢀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠟⢻⢿⣿⣇⠀⢿⣿⣿⡿⡟⣿⣿⣷⡶⠸⣿ ⡇⣛⠛⠛⠚⣿⣟⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠹⠉⠱⠈⠁⣆⠀⠀⠀⠂⣿⣟⣿⣭⣯⣽⣫⣯⣫⣻⣿⣛⣠⣤⣤⣶⣶⣤⣤⣄⣿⣆⣤⣤⣤⣤⢸⣿⣿⣿⣿⣿⣿⣯⡀⢙⣻⣭⡙⡈⣛⢋⡋⠛⡇⣛⢛⡛⠛⢀⡙ ⡿⡿⣻⠀⠰⢭⡏⠀⠀⠷⡀⠀⠀⠀⠀⢘⠀⠰⠆⠀⠀⠀⠛⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠻⠻⠿⣿⡿⠿⢿⠿⠿⢸⣿⣿⣿⣿⣿⣿⣿⡃⣽⣿⣿⣿⡁⣿⣿⣿⣿⡗⣿⣿⣻⣿⢸⣿ ⢇⡶⠶⡶⢾⠏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⠈⠀⠀⠀⠀⠆⠀⠂⠀⠂⣷⣁⠰⠶⡶⡶⡶⠶⠶⠂⠀⠀⠰⠶⠶⣶⢶⡶⠀⠀⣿⡷⠶⠶⣶⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⠋⠿⠿⠊⠺⠿⠿⠟⡇⠺⠿⠿⠇⠐⠿ ⠆⢒⠒⠒⠂⣺⣶⡄⠀⠀⠀⠀⢀⡀⢀⣸⠀⠈⢠⡄⠀⠀⠀⠀⠁⠐⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡇⠀⣼⣷⣿⢶⢠⣿⣿⢳⠶⡇⣿⣾⣳⣦⠀⠀ ⡉⠛⠛⢣⡤⠌⠙⠃⠠⠀⠀⠀⠜⠃⠜⢻⠀⢸⡏⠃⠀⠀⠀⠀⠀⠀⠀⣿⣶⣿⣿⣿⣿⣿⣷⣿⣿⣿⣶⣶⣾⣿⣾⣾⣶⣶⣾⣿⣷⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡇⠚⢻⣿⣏⡈⠉⣿⣿⣌⣻⡇⣿⣿⣟⡛⠀⠀ ⡉⠛⠛⠛⠃⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠀⡠⠀⠀⠀⠃⠀⠀⠀⠀⠀⣿⣏⣻⣛⣛⣻⣛⣛⣛⡛⠛⠛⠛⠛⠛⠛⠛⠛⢛⣻⢿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠗⡶⣾⠃⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⡎⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢡⠀⡀⠀⠀⠀⠀⠀⠀⠀⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⡅⣀⣈⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢸⠀⡾⠀⠀⠀⠀⡆⠀⠀⠀⠀⣿⠀⠀⠀⠀⠄⠁⠀⠀⠈⠉⠀⠀⠀⠀⠈⠀⠀⠠⠄⣿⡯⠉⠁⠄⠈⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠ ⣎⠉⠉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⣿⠒⠆⠆⠂⢸⠀⠀⣀⠀⣿⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢹⡇⠀⠀⢀⠀⢽⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀ ⣯⠋⠛⠃⠀⠸⡷⠂⠀⠀⠀⠀⠀⣤⠀⢸⢿⣿⣳⣿⣿⣇⣹⠀⠈⠉⠉⣿⠤⠀⠁⠀⠀⠀⠙⠛⠃⠀⠀⠀⠀⠀⠁⠈⠉⠉⠁⠰⠶⠶⠶⠶⠶⣾⣿⣿⣯⣭⣽⣿⡷⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠃⠀⠀⠀⠀⠀⠀ ⠎⣷⣷⡷⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡟⠻⠙⠻⠓⢻⠒⠒⠒⠂⣿⠒⠐⠒⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡚⠛⠛⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⠨⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠯⣿⡏⠛⠙⠹⠇⠀⠀⠀⢴⡀⠀⠀⠀⠀⢀⣄⣬⣠⣈⣇⣀⢀⣀⣀⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡇⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⣶⣶⠶⠶⣶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠦⠰⠆ ⣶⣶⣷⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡷⢶⠶⠖⣶⠳⢤⡶⠒⠒⠒⠶⠶⠶⠲⢺⡈⣽⠉⠎⠀⠀⠀⣴⣿⢿⡿⠾⠷⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣾⣶⣿⣾⣿⣷⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠟⠿⠿⠿⠿⠿⠿⠦⠆⠀⠀⠀⠀⠀⠀ ⣷⣶⣶⣶⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣧⢾⠀⠀⠀⠀⠀⠀⠁⠉⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠐⠉⠂⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠚⠒⠒⢻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠂⠀⠀ ⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⣮⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣷⠀⠀⣼⣿⣷⠀⠀⣿⣿⡆⠀⢰⣿⣷⡄⢸⣯⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣻⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⣿⣿⣿⣟⣣⣧⣙⣉⣹⣿⣿⣿⣿⣩⣝⣿⣿⣿⠃⠀⠇⡅⢀⠀⠆⠠⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⣸⣿⣿⡀⠀⢾⡿⠷⠀⠰⣿⡿⠷⠀⠈⣹⡏⠀⢸⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢀⡄⠈⠆⣓⣌⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⢻⣿⡿⠀⠀⣿⣿⡇⠀⠸⣿⣿⠆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀ ⡏⣿⣿⠿⢾⣿⣿⣿⠿⠿⠿⠿⠿⡿⠿⣿⢿⠻⠉⠱⠈⢡⣦⠀⠁⠐⠂⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠘⢫⣿⣛⠛⠀⣹⣟⣃⠀⠀⣽⣟⡃⠀⠀⠙⠋⠀⢸⣿⣷⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡀⠀⠀ ⣿⡿⣻⠈⠱⢭⡏⠯⠼⠿⡀⠀⠸⠇⠀⢾⠁⠹⠆⠀⠀⠰⠛⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠸⣿⡿⠀⠀⣹⣿⣟⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⣷⣶⡶⣶⣾⡟⠛⠐⠀⠙⠁⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠆⠀⠂⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠀⠀⠀⠈⠉⠉⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀ ⢗⣒⠒⡒⠒⣺⣶⡄⠀⠀⠀⠀⢀⡠⢀⣸⠂⠸⣤⡄⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀ ⡏⠛⢛⣣⡤⠌⠙⠋⠠⠀⠀⠀⠜⠃⠜⢻⠀⢸⡏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⡛⠛⠛⠛⠃⣀⠀⠀⠒⠂⠀⠀⠀⠀⠀⢸⠒⣠⠀⠀⠀⠃⢀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⡷⣶⣾⠇⠀⢻⡃⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣸⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⣟⡶⠶⠇⠀⠘⠏⠀⠀⠀⠁⠀⠀⠀⠀⢹⡇⢿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢲⣄⣀⣀⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⣇⣁⣉⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢸⠉⣾⠁⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⣏⠋⠛⢁⣀⣠⣀⢀⣀⣀⣀⣀⣀⣀⣀⣸⣠⣿⠖⠆⢶⡆⣸⠀⠀⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡌⠠⠀⠀⠀⠀⠀⠀⣙⣿⡻⣛⡻⠿⠛⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣽⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠀⠀⠀ ⣿⠋⠛⠃⠋⠹⣷⠞⠙⠛⠋⠛⠊⣯⠛⢻⣿⣿⣻⣿⣿⣧⣹⠀⠈⠉⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣥⣤⣀⣤⣤⣤⣠⣭⣿⣁⣤⣄⣥⣄⣠⣤⣤⣤⣤⣼⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠿⠿⠿⠿⠿⠃⠀⠀ ⣞⣿⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠹⡿⠻⠛⡻⠓⢻⠒⠒⠒⠂⣿⡷⠐⠿⠆⠖⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠷⠶⠾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡵⢸⠀⠀⠀⠀⣿⡿⠀⠁⠀⠀⠀⠀⠤⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⣿⡟⠛⠙⠹⠇⠀⠀⠀⣴⡄⠀⠀⠀⠀⢈⣅⣬⣠⣈⣇⣀⣀⣀⣄⡀⣿⣿⣄⣠⣀⣀⣀⣀⣀⡀⢂⢰⠀⠀⠀⣤⣀⣀⠈⠂⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⣶⡶⠶⠶⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠠⠆ ⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⢶⠶⠆⢶⠲⢤⡶⠒⠒⠒⠶⠶⠶⠲⢸⡈⣍⠉⠎⠀⠀⠀⢴⣻⢿⡿⠾⠷⣾⣿⣟⣷⣿⣿⣻⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣾⣶⣿⣾⣟⣷⣿⣿⣿⣿⣿⠿⠟⠛⠻⠟⠻⠟⠿⠿⠿⠿⠿⠿⠦⠆⠀⠀⠀⠀⣤⠀ ⣷⣶⣶⣶⣆⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⢸⡧⢾⠀⠀⠀⠀⠀⠀⠀⠈⠁⢰⣿⣿⣿⣿⣿⣿⡟⠟⠿⢿⣷⣶⣿⣿⣿⠿⠿⠿⠿⠿⣿⢽⣯⡯⡟⣴⣷⠤⢴⣥⣿⣾⣿⣿⣿⢿⣷⣶⣾⣿⣾⣻⣶⣟⣞⣿⣿⢢⣦⣤ ⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⣮⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡆⠀⣤⣤⡰⠻⢶⣤⣤⠸⠻⢢⣤⣄⡞⠷⣦⣤⣰⠿⣿⣿⣿⣯⣯⣿⣿⣿⣿⣿⣿⣿⣽⣯⣻⣿⣿⣿⣧⣿⣿⢰⣾⣾ ⣿⣿⣿⣛⣣⣦⣙⣉⣹⣿⣿⣟⣟⣩⣝⣿⣿⣿⠃⠀⠃⡄⠀⠀⠆⠠⠀⢸⣿⣿⣿⣿⣿⣿⡃⠀⣿⣿⡇⠀⣸⣿⣿⡖⠀⣸⣿⣿⠆⠀⠿⣿⠇⡀⣿⣿⣿⡿⣿⠽⡿⠿⢿⡿⢿⣿⢿⡿⡿⣿⠿⡿⡿⣿⢿⢸⣷⣿ ⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢀⡄⠀⠆⣑⣌⠁⢸⣿⣿⣿⣿⣿⣿⠇⣠⣯⣭⣽⠒⢪⣭⣭⠱⠒⢻⣭⣍⠒⠒⣦⣥⡼⠓⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣿⣿ ⡇⣟⣿⠟⠚⣿⣿⠿⠿⠿⠛⠛⠛⠟⠿⠻⠿⠻⠉⠱⠈⠁⣆⠀⠀⠀⠂⢸⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⢫⠀⢘⣿⣿⠈⠀⣸⣿⣟⡀⠀⣿⣿⡇⠀⣿⢿⢿⣿⠿⣿⣿⣿⣿⣿⢿⣿⢿⣿⣿⢿⣿⢿⣟⣿⣿⠻⣻⣿ ⣿⡿⣻⠀⠰⢭⡏⠀⠀⠷⡀⠀⠀⠀⠀⢘⠁⠰⠆⠀⠀⠰⠛⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⣿⣭⡜⠒⢲⣯⣭⣘⠛⣻⣯⣥⠟⠛⠋⠉⠀⠀⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿ ⣗⣶⡶⡶⣾⡏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢠⠀⠀⠀⠀⠆⠀⠂⠀⠀⢸⣿⣿⣿⣿⣿⣿⠅⠀⢛⣛⠃⠀⢘⣛⣛⡀⠀⢙⣟⡛⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠆⢒⠒⠒⠂⣺⣶⡄⠀⠀⠀⠀⢀⡠⢀⣸⠀⠈⣤⡄⠀⠀⠀⠀⠁⠐⠀⢸⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿ ⡏⠛⢛⣣⡤⠌⠙⠃⠠⠀⠀⠀⠜⠃⠜⢻⠀⢸⡏⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⡋⠛⠛⠛⠃⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠀⣠⠀⠀⠀⠃⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡅⠀⠀⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣾⣿⣷⣿⣷⣻⣯⣷⣿⣿⣾⣿⣿⣿⣿⣾⣿⣿ ⡗⡶⣾⠇⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣸⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠿⢿⣿⣿⣿⢿⠷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣟⣿⣿⣻⣿⠙⣿⣻ ⡏⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢩⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢢⣀⡀⡀⢀⠀⠀⣿⣻⣿⣗⣿⣿⣿⣽⣿⣿⣿⣿⡯⢿⣿⣿⣿⣿⢿⣿⣿⠀⣿⣿ ⣇⣁⣉⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢸⠁⡾⠀⠀⠀⠀⡆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡃⠀⠀⠙⠒⠟⠛⠻⠛⠛⠛⣾⣿⣿⣿⣿⣿⠏⠀⠀⣿⣿⣿⣟⣿⣾⣿⣿⣿⢿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⠀⢿⣿ ⣏⠉⠉⠁⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⣿⠒⠆⠆⡆⢸⠀⠀⣀⠀⢸⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠻⣛⠻⠿⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⢽⣿⣿⢿⣿⣿⣿⣯⣿⣟⣿⡿⣿⠰⣿⣿ ⣯⠋⠛⠃⠀⠸⣷⠂⠀⠀⠀⠀⠀⣤⠀⢸⢿⣿⣳⣿⣿⣇⣹⠀⠈⠉⠀⢸⣿⣿⣿⣿⣿⣿⠇⠀⠀⣀⣀⣀⣀⣀⣀⣀⣉⣋⣁⣀⣀⣀⣀⣀⣀⣀⣿⣻⣿⠿⠿⠿⠛⠿⠾⠟⠿⠿⠻⠻⠶⠟⠻⠛⠻⠻⠿⠀⣿⣿ ⣎⣷⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡿⠻⠛⡻⠓⢻⠒⠒⠒⠂⣿⣿⣿⣿⠆⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⣿⣿⣿⣿⣿⣿⣿⡇⢀⢀⡀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣰⣳⣿ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⢨⠀⠀⠀⠀⣿⡿⠿⠿⠆⠀⠀⠴⠶⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡀⢼⣟⣛⣛⣻⣿⣿⡇⠙⠉⠁⠛⠛⠃⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠙ ⡯⣿⡏⠛⠙⠹⠇⠀⠀⠀⢴⡄⠀⠀⠀⠀⢈⣅⣬⣠⣈⣇⣀⢀⣀⣄⡀⣿⣇⣀⣀⣀⣀⣀⣀⣀⠀⠀⠰⠀⠀⠀⠀⢀⣀⠀⠂⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⣶⠶⠶⠴⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠠⠆ ⡶⣶⣤⣤⣶⣦⠴⠶⠶⠶⠦⠶⠶⠶⠶⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⢶⠶⠆⢲⠲⢤⡲⠒⠒⠒⠶⠶⠶⠲⢸⡈⠍⠉⠎⠀⠀⠀⢴⢻⢿⡷⠾⠷⣾⣿⣟⣶⣷⣲⣺⣿⣿⣿⣷⣾⣷⣾⣿⣿⣛⣾⣶⣷⣾⣛⣳⣿⣗⣶⣷⣛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠷⠿⠿⠿⠦⠆⠀⠀⠀⠀⣤⠀ ⣷⡶⢶⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⢦⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣿⣿⣿⣿⣿⠛⠛⠟⣿⣿⣶⣶⣿⣿⣿⠿⠿⠿⢿⣿⣿⢭⣭⢫⣶⠀⠂⠀⠀⠁⠁⠈⠛⠛⠛⠛⣷⣶⣦⣤⡄⠀⠀⠀⠔⠓⠚⠂⣦⣤ ⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⣎⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⢠⣄⣀⠀⠰⣻⣶⡄⢀⠸⣷⣂⡀⢀⣾⣶⣆⠀⣸⠃⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣛⣣⣦⣉⣉⣹⣿⣿⣟⣟⣩⣝⣻⣿⣿⠃⠀⠃⡄⠀⠀⠄⠠⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⡿⠀⣃⣿⣿⣇⠘⣖⣿⣿⡇⢐⠾⢿⠿⢀⢿⡄⣀⠀⠀⠀⠉⠉⠙⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠆⢀⠀⠀⠀⠀ ⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢀⡄⠀⠆⣑⣌⣿⣿⣿⣿⣿⣿⣿⢀⣬⣭⣭⡀⠈⣭⣍⡩⢤⠹⣿⣟⡥⢄⢲⣽⣣⠤⣸⢘⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣤⣠ ⡇⣛⡛⠛⠚⣿⣟⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠹⠉⠱⠈⠁⣆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⠄⠀⣿⣿⡇⠘⠀⣿⣿⠇⢘⡸⣿⡿⢀⢻⡸⠿⠿⠿⠿⠿⠿⠿⢿⢿⢿⠿⠛⠛⠛⠛⢻⠿⢿⠟⠛⠛⠛⠛⠛ ⡿⡿⣻⠀⠰⢭⡏⠀⠀⠷⡀⠀⠀⠀⠀⢘⠀⠰⠆⠀⠀⠀⠛⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⢩⣭⣍⠡⡔⣿⣿⡇⢠⣘⣿⣿⡀⠤⠛⠛⠃⠀⢸⣇⣈⣿⣿⣿⡿⢿⣿⣿⣿⣿⣭⣿⣿⡿⣿⣿⣿⢿⢯⡽⢿⣿⣇⣀ ⣗⣶⡶⡶⢾⡏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢀⠀⠀⠀⠀⠆⠀⠂⠀⣿⣿⣿⣿⣿⣿⣿⠀⠸⣿⡿⣀⠃⣻⣿⣇⣘⡀⣿⣿⣇⡐⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠆⢒⠒⠒⠂⣺⣶⡄⠀⠀⠀⠀⢀⡀⢀⣸⠀⠈⢠⡄⠀⠀⠀⠀⠁⠐⣿⣿⣿⣿⣿⣿⣿⠀⠀⠉⠁⠀⠀⠉⠉⠉⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⠿⢿⠿⠆⢸⡿⡟⠻⠿⠿⢿⣿⣿⣿⡿⣿⣿⣿⣿⠿⠿⢿ ⡏⠛⢛⢣⡤⠌⠙⠃⠠⠀⠀⠀⠜⠃⠜⢻⠀⢸⡏⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⣿⣷⣿⣿⣿⣿⢸⣿⣿⣿⣿⠀⠀⠈⢹⣿⣿⣿⣷⣿⣿⣿ ⡋⠛⠛⠛⠃⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠀⣠⠀⠀⠀⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣿⣿⣷⣦⣶⣤⣬⣽⣶⡖⣶⣶⢠⣴⣤⣤⣤⣤⣤⣤⣴⣶⣶⣾ ⡗⡶⣾⠃⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⠀⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠉⠉⠁⠁⠀⠀⠀⠀⠀⠛⠛⠈⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙ ⡏⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢡⠀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⡷⢸⣿⣿⣿⣿⣶⢠⣀⡀⠀⢀⢸⡄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣇⣁⣈⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢸⠀⡾⠀⠀⠀⠀⡆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠉⠀⠈⠀⠀⠈⠈⠈⠨⠄⣿⡯⠉⠉⠌⢸⡇⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣏⠉⠉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⡿⠒⠆⠆⠆⢸⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠻⠃⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣯⠋⠛⠃⠀⠸⡷⠂⠀⠀⠀⠀⠀⣤⠀⢸⢿⣷⣳⣿⣿⣇⣹⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣁⣀⣀⣀⣀⣀⣸⠀⡀⠀⠀⠀⠀⠀⠐⠾⠾⠗⠀⠀⠀⠀⠀⠛⠛⠛⠛⠻⠿⠀⠀⠀ ⠎⣷⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡟⠻⠙⡻⠓⢻⠒⠒⠒⣿⣿⣿⣿⣿⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⢀⣫⣦⣤⣾⣿⣿⣇⡀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⢨⠀⠀⠀⣿⣿⡿⠿⠿⠆⠀⣀⠴⠴⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠸⢟⣛⣛⣻⣿⣿⡿⠇⠀⠀⠉⠿⠿⠗⠀⠀⠀⠀⠀⠘⠛⠛⠛⠻ ⠯⣿⡏⠛⠙⠹⠇⠀⠀⠀⢴⡀⠀⠀⠀⠀⢈⣄⣬⣠⣈⣇⣀⢀⣀⣀⡀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⡇⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⡶⠶⠴⠴⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠠⠆ ⡶⣦⣤⣤⣤⣤⠤⠤⠤⠤⠤⠤⠤⠤⠴⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⢦⠶⠆⢲⠲⢤⡲⠒⠒⠒⠴⠶⠶⠲⢸⡈⠍⠉⠎⠀⠀⠀⢴⠻⢿⡷⠾⠷⣾⣿⣟⣶⣷⣲⣲⣷⣿⣷⣷⣾⣷⣒⣒⣓⣛⣾⣶⣷⣾⣛⣓⣷⣗⣶⣷⣒⠚⠛⠓⠚⠛⠛⠛⠻⠿⠷⠿⠿⠿⠦⠆⠀⠀⠀⠀⣤⠀ ⣶⡶⢶⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⢆⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣿⣿⣿⣿⣿⠛⠛⠟⣿⣿⣶⣶⣿⣿⣿⠿⠿⠿⢿⣟⣿⣭⡭⣫⣶⡆⠀⠀⠀⠁⠁⠈⠛⠛⠛⠛⣷⣶⣦⣤⡤⠀⠀⠀⠐⠓⠚⠀⣤⣤ ⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⣎⡀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⠄⢠⣤⣀⡀⠰⣻⣶⣀⢀⠸⣷⣂⡀⢀⣾⣶⣆⡀⡘⡇⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣛⣣⣦⣉⣉⣹⣿⣿⣟⣟⣩⣝⣻⣿⣿⠃⠀⠁⡄⠀⠀⠄⠠⢹⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⠃⣃⢿⣿⣿⠘⣒⣿⣿⣇⢐⠾⢿⡿⠇⢏⣧⣀⠀⠀⠀⠉⠉⠙⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀ ⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢀⡄⠀⠆⣑⣌⢹⣿⣿⣿⣿⣿⣿⢀⠈⣭⣭⡀⠈⣭⣭⣩⢥⠹⣿⣏⡭⢄⢲⣽⣣⡤⣸⡇⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣄⣠ ⡇⣛⡛⠛⠚⣿⣟⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠹⠉⠱⠈⠁⣆⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⠃⠀⣿⣿⣿⠘⠀⣿⣿⡇⢘⡸⣿⣿⢇⢻⣇⠿⠿⠿⠿⠿⠿⠿⢿⢿⢿⠿⠟⠛⠛⠛⠻⠿⢿⠟⠛⠛⠛⠛⠛ ⡿⡿⣻⠀⠰⢭⡏⠀⠀⠷⡀⠀⠀⠀⠀⢘⠀⠰⠆⠀⠀⠀⠛⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢠⣭⣭⡠⡔⣿⣿⣯⢠⣘⣿⣿⡅⠤⠛⠛⠋⠀⢸⣿⣈⣿⣿⣿⡿⢿⣿⣿⣿⣯⣭⣿⣿⡿⢿⣿⠿⢿⢯⡽⢿⣿⣛⣀ ⢇⡶⠶⡶⢾⠏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢀⠀⠀⠀⠀⠆⠀⠂⠀⣼⣿⣿⣿⣿⣿⣿⠀⠸⣿⡿⣃⠃⣻⣿⣟⣘⡀⣿⣿⣃⡐⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠆⢒⠒⠒⠂⣺⣶⡄⠀⠀⠀⠀⢀⡀⢀⣸⠀⠈⢠⡄⠀⠀⠀⠀⠁⠐⢾⣿⣿⣿⣿⣿⣿⠀⠀⠉⠁⠀⠀⠉⠉⠉⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⠿⢿⠿⠖⢸⡿⡟⠻⠿⠿⠿⣿⣿⣿⡿⣿⣿⣿⣿⠿⠿⢿ ⡏⠛⠛⢣⡤⠌⠙⠃⠠⠀⠀⠀⠜⠃⠜⢻⠀⢸⡏⠃⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣿⣿⣿⣿⣾⣿⣿⣿⣿⠀⠀⠈⢹⣿⣿⣿⣷⣿⣿⣿ ⡉⠛⠛⠛⠃⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠀⡠⠀⠀⠀⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣷⣦⣶⣤⣬⣽⣶⡖⣶⣶⢠⣴⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶ ⠗⡶⣾⠃⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⠀⠁⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣟⠉⠉⠁⠁⠀⠀⠀⠀⠀⠙⠛⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙ ⡎⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢡⠀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣶⢠⣀⡀⠀⠀⢸⣧⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣇⣁⣈⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢸⠀⡾⠀⠀⠀⠀⡆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠈⠀⠠⠄⣿⡯⠉⠁⠌⢸⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣏⠉⠉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⡿⠒⠆⠆⠂⢸⠀⠀⣀⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠻⠃⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣯⠋⠛⠃⠀⠸⡷⠂⠀⠀⠀⠀⠀⣤⠀⢸⢿⣷⣳⣿⣿⣇⣹⠀⠈⠉⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣁⣀⣀⣀⣀⣀⣸⡇⡀⠀⠀⠀⠀⠀⠐⠾⠾⠗⠀⠀⠀⠀⠀⠛⠛⠛⠛⠻⠿⠀⠀⠀ ⠎⣷⣷⡷⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡟⠻⠙⡻⠓⢻⠒⠒⠒⢸⣿⣿⣿⣿⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⣇⣫⣤⣤⣼⣿⣿⣇⡀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤ ⡛⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⠨⠀⠀⠀⣾⣿⠿⠿⠿⠆⠀⣀⠤⠴⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠟⢟⣛⣛⣻⣿⣿⡿⠇⠀⠀⠉⠿⠿⠟⠀⠀⠀⠀⠀⠘⠛⠛⠛⠻ ⠯⣿⡏⠛⠙⠹⠇⠀⠀⠀⢴⡀⠀⠀⠀⠀⢀⣄⣬⣠⣈⣇⣀⢀⣀⣀⡀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⡇⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⡶⠶⠴⠴⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠠⠆ ⡶⣦⣤⣤⣤⣤⠤⠤⠤⠤⠤⠤⠤⠤⠴⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⢦⠶⠆⢲⠲⢤⡲⠒⠒⠒⠴⠶⠖⠲⢸⡈⠍⠉⠎⠀⠀⠀⢴⠻⢿⡷⠾⠷⣾⣿⣟⣶⣷⣲⣲⣷⣿⣷⣷⣾⣷⣒⣒⣓⣛⣾⣶⣷⣾⣛⣓⣷⣗⣶⣷⣒⠚⠛⠓⠚⠛⠛⠛⠻⠿⠷⠿⠿⠿⠦⠆⠀⠀⠀⠀⣤⠀ ⣶⡶⢶⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⢆⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣿⣿⣿⣿⣿⠛⠛⠟⣿⣿⣶⣶⣿⣿⣿⠿⠿⠿⢿⣟⣿⣭⡭⣫⣶⡆⠀⠀⠀⠁⠁⠈⠛⠛⠛⠛⣷⣶⣦⣤⡤⠀⠀⠀⠐⠓⠚⠀⣦⣤ ⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⣎⡀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⠄⢠⣤⣀⡀⠰⣻⣶⣀⢀⠸⣷⣂⡀⢀⣾⣶⣆⡀⡘⡇⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣛⣣⣦⣉⣉⣹⣿⣿⣟⣟⣩⣝⣻⣿⣿⠃⠀⠁⡄⠀⠀⠄⠠⢹⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⠃⣃⢿⣿⣿⠘⣒⣿⣿⣇⢐⠾⢿⡿⠇⢏⣧⣀⠀⠀⠀⠉⠉⠙⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀ ⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢀⡄⠀⠆⣑⣌⢹⣿⣿⣿⣿⣿⣿⢀⠈⣭⣭⡀⠈⣭⣽⣯⢥⠹⣿⣏⡭⢄⢲⣽⣣⡤⣸⡇⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣄⣠ ⡇⣛⡛⠛⠚⣿⣟⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠹⠉⠱⠈⠁⣆⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⠃⠀⣿⣿⣿⠘⠀⣿⣿⡇⢘⡸⣿⣿⢇⢻⣇⠿⠿⠿⠿⠿⠿⠿⢿⢿⢿⠿⠟⠛⠛⠛⠻⠿⢿⠟⠛⠛⠛⠛⠛ ⡿⡿⣻⠀⠰⢭⡏⠀⠀⠷⡀⠀⠀⠀⠀⢘⠀⠰⠆⠀⠀⠀⠛⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢠⣭⣭⡠⡔⣿⣿⣯⢠⣘⣿⣿⡅⠤⠛⠛⠫⠀⢸⣿⣈⣿⣿⣿⡿⢿⣿⣿⣿⣯⣭⣿⣿⡿⢿⣿⠿⢿⢯⡽⢿⣿⣛⣀ ⢇⡶⠶⡶⢾⠏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢀⠀⠀⠀⠀⠆⠀⠂⠀⣼⣿⣿⣿⣿⣿⣿⠀⠸⣿⡿⣃⠃⣻⣿⣟⣘⡀⣿⣿⣃⡐⠀⠀⠂⠀⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠆⢒⠒⠒⠂⣺⣶⡄⠀⠀⠀⠀⢀⡀⢀⣸⠀⠈⢠⡄⠀⠀⠀⠀⠁⠐⢾⣿⣿⣿⣿⣿⣿⠀⠀⠉⠁⠀⠀⢹⠉⠩⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⠿⢿⠿⠖⢸⡿⡟⠻⠿⠿⠿⣿⣿⣿⡿⣿⣿⣿⣿⠿⠿⢿ ⡏⠛⠛⢣⡤⠌⠙⠃⠠⠀⠀⠀⠜⠃⠜⢻⠀⢸⡏⠃⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣿⣿⣿⣿⣾⣿⣿⣿⣿⠀⠀⠈⢹⣿⣿⣿⣷⣿⣿⣿ ⡉⠛⠛⠛⠃⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠀⡠⠀⠀⠀⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣷⣦⣶⣤⣬⣽⣶⡖⣶⣶⢠⣴⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶ ⠗⡶⣾⠃⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⠀⠁⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣟⠉⠉⠁⠁⠀⠀⠀⠀⠀⠙⠛⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙ ⡎⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢡⠀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣶⢠⣀⡀⠀⠀⢸⣧⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣇⣁⣈⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢸⠀⡾⠀⠀⠀⠀⡆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠈⠀⠠⠄⣿⡯⠉⠁⠌⢸⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣏⠉⠉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⡿⠒⠆⠆⠂⢸⠀⠀⣀⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠻⠃⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣯⠋⠛⠃⠀⠸⡷⠂⠀⠀⠀⠀⠀⣤⠀⢸⢿⣷⣳⣿⣿⣇⣹⠀⠈⠉⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣁⣀⣀⣀⣀⣀⣸⡇⡀⠀⠀⠀⠀⠀⠐⠾⠾⠗⠀⠀⠀⠀⠀⠛⠛⠛⠛⠻⠿⠀⠀⠀ ⠎⣷⣷⡷⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡟⠻⠙⡻⠓⢻⠒⠒⠒⢸⣿⣿⣿⣿⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣫⣤⣤⣼⣿⣿⣇⡀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤ ⡛⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⠨⠀⠀⠀⣾⣿⠿⠿⠿⠆⠀⣀⠤⠴⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠟⢟⣛⣛⣻⣿⣿⡿⠇⠀⠀⠉⠿⠿⠟⠀⠀⠀⠀⠀⠘⠛⠛⠛⠻ ⠯⣿⡏⠛⠙⠹⠇⠀⠀⠀⢴⡀⠀⠀⠀⠀⢀⣄⣬⣠⣈⣇⣀⢀⣀⣀⡀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⡇⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⡶⠶⠴⠴⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠠⠆ ⡶⣦⣤⣤⣤⣤⠤⠤⠤⠤⠤⠤⠤⠤⠴⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⢦⠶⠆⢲⠲⢤⡲⠒⠒⠒⠴⠶⠖⠲⢸⡈⠍⠉⠎⠀⠀⠀⢴⠻⢿⡷⠾⠷⣾⣿⣟⣶⣷⣲⣲⣷⣿⣷⣷⣾⣷⣒⣒⣓⣛⣾⣶⣷⣾⣛⣓⣷⣗⣶⣷⣒⠚⠛⠓⠚⠛⠛⠛⠻⠿⠷⠿⠿⠿⠦⠆⠀⠀⠀⠀⣤⠀ ⣶⡶⢶⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⢆⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣿⣿⣿⣿⣿⠛⠛⠟⣿⣿⣶⣶⣿⣿⣿⠿⠿⠿⢿⣟⣿⣭⡭⣫⣶⡆⠀⠀⠀⠁⠁⠈⠛⠛⠛⠛⣷⣶⣦⣤⡤⠀⠀⠀⠐⠓⠚⠀⣦⣤ ⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⣎⡀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⠄⢠⣤⣀⡀⡰⣻⣶⣀⢀⠸⣷⣂⡀⢀⣾⣶⣆⡀⡘⡇⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣛⣣⣦⣉⣉⣹⣿⣿⣟⣟⣩⣝⣻⣿⣿⠃⠀⠁⡄⠀⠀⠄⠠⢹⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⠃⣃⢿⣿⣿⠘⣒⣿⣿⣇⢐⠾⢿⡿⠇⢏⣧⣀⠀⠀⠀⠉⠉⠙⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀ ⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢀⡄⠀⠆⣑⣌⢹⣿⣿⣿⣿⣿⣿⢀⠈⣭⣭⡀⠈⣭⣽⣯⢥⠹⣿⣏⡭⢄⢲⣽⣣⡤⣸⡇⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣄⣠ ⡇⣛⡛⠛⠚⣿⣟⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠹⠉⠱⠈⠁⣆⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⠃⠀⣿⣿⣿⠘⠀⣿⣿⡇⢘⡸⣿⣿⢇⢻⣇⠿⠿⠿⠿⠿⠿⠿⢿⢿⢿⠿⠟⠛⠛⠛⠻⠿⢿⠟⠛⠛⠛⠛⠛ ⡿⡿⣻⠀⠰⢭⡏⠀⠀⠷⡀⠀⠀⠀⠀⢘⠀⠰⠆⠀⠀⠀⠛⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢠⣭⣭⡠⡔⣿⣿⣯⢠⣘⣿⣿⡅⠤⠛⠛⠫⠀⢸⣿⣈⣿⣿⣿⡿⢿⣿⣿⣿⣯⣭⣿⣿⡿⢿⣿⠿⢿⢯⡽⢿⣿⣛⣀ ⢇⡶⠶⡶⢾⠏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢀⠀⠀⠀⠀⠆⠀⠂⠀⣼⣿⣿⣿⣿⣿⣿⠀⠸⣿⡿⣃⠃⣻⣿⣟⣘⡀⣿⣿⣃⡐⠀⠀⠂⠀⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠆⢒⠒⠒⠂⣺⣶⡄⠀⠀⠀⠀⢀⡀⢀⣸⠀⠈⢠⡄⠀⠀⠀⠀⠁⠐⢾⣿⣿⣿⣿⣿⣿⠀⠀⠉⠁⠀⠀⢹⠉⠩⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⠿⢿⠿⠖⢸⡿⡟⠻⠿⠿⠿⣿⣿⣿⡿⣿⣿⣿⣿⠿⠿⢿ ⡏⠛⠛⢣⡤⠌⠙⠃⠠⠀⠀⠀⠜⠃⠜⢻⠀⢸⠋⠃⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣿⣿⣿⣿⣾⣿⣿⣿⣿⠀⠀⠈⢹⣿⣿⣿⣷⣿⣿⣿ ⡉⠛⠛⠛⠃⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠀⡠⠀⠀⠀⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣷⣦⣶⣤⣬⣽⣶⡖⣶⣶⢠⣴⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶ ⠗⡶⣾⠃⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⠀⠁⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣟⠉⠉⠁⠁⠀⠀⠀⠀⠀⠙⠛⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙ ⡎⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢡⠀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣶⢠⣀⡀⠀⠀⢸⣧⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣇⣁⣈⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢸⠀⡾⠀⠀⠀⠀⡆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠈⠀⠠⠄⣿⡯⠉⠁⠌⢸⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣏⠉⠉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⡿⠒⠆⠆⠂⢸⠀⠀⣀⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠻⠃⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣯⠋⠛⠃⠀⠸⡷⠂⠀⠀⠀⠀⠀⣤⠀⢸⢿⣷⣳⣿⣿⣇⣹⠀⠈⠉⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣁⣀⣀⣀⣀⣀⣸⡇⡀⠀⠀⠀⠀⠀⠐⠾⠾⠗⠀⠀⠀⠀⠀⠛⠛⠛⠛⠻⠿⠀⠀⠀ ⠎⣷⣷⡷⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡟⠻⠙⡻⠓⢻⠒⠒⠒⢸⣿⣿⣿⣿⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣫⣤⣤⣼⣿⣿⣇⡀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤ ⡛⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⠨⠀⠀⠀⣾⣿⠿⠿⠿⠆⠀⣀⠤⠴⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠟⢟⣛⣛⣻⣿⣿⡿⠇⠀⠀⠉⠿⠿⠟⠀⠀⠀⠀⠀⠘⠛⠛⠛⠻ ⠯⣿⡏⠛⠙⠹⠇⠀⠀⠀⢴⡀⠀⠀⠀⠀⢀⣄⣬⣠⣈⣇⣀⢀⣀⣀⡀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⡇⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⡶⠶⠴⠴⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠠⠆ ⡶⣦⣤⣤⣤⣤⠤⠤⠤⠤⠤⠤⠤⠤⠴⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⢦⠶⠆⢲⠲⢤⡲⠒⠒⠒⠴⠶⠖⠲⢸⡈⠍⠉⠎⠀⠀⠀⢴⠻⢿⡷⠾⠷⣾⣿⣟⣶⣷⣲⣲⣷⣿⣷⣷⣾⣷⣒⣒⣓⣛⣾⣶⣷⣾⣛⣓⣷⣗⣶⣷⣒⠚⠛⠓⠚⠛⠛⠛⠻⠿⠷⠿⠿⠿⠦⠆⠀⠀⠀⠀⣤⠀ ⣶⡶⢶⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⢆⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣿⣿⣿⣿⣿⠛⠛⠟⣿⣿⣶⣶⣿⣿⣿⠿⠿⠿⢿⣟⣿⣭⡭⣫⣶⡆⠀⠀⠀⠁⠁⠈⠛⠛⠛⠛⣷⣶⣦⣤⡤⠀⠀⠀⠐⠓⠚⠀⣦⣤ ⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⣎⡀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⠄⢠⣤⣀⡀⡰⣻⣶⣀⢀⠸⣷⣂⡀⢀⣾⣶⣆⡀⡘⡇⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣛⣣⣦⣉⣉⣹⣿⣿⣟⣟⣩⣝⣻⣿⣿⠃⠀⠁⡄⠀⠀⠄⠠⢹⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⠃⣃⢿⣿⣿⠘⣒⣿⣿⣇⢐⠾⢿⡿⠇⢏⣧⣀⠀⠀⠀⠉⠉⠙⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀ ⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢀⡄⠀⠆⣑⣌⢹⣿⣿⣿⣿⣿⣿⢀⠈⣭⣭⡀⠈⣭⣽⣯⢥⠹⣿⣏⡭⢄⢲⣽⣣⡤⣸⡇⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣄⣠ ⡇⣛⡛⠛⠚⣿⣟⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠹⠉⠱⠈⠁⣆⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⠃⠀⣿⣿⣿⠘⠀⣿⣿⡇⢘⡸⣿⣿⢇⢻⣇⠿⠿⠿⠿⠿⠿⠿⢿⢿⢿⠿⠟⠛⠛⠛⠻⠿⢿⠟⠛⠛⠛⠛⠛ ⡿⡿⣻⠀⠰⢭⡏⠀⠀⠷⡀⠀⠀⠀⠀⢘⠀⠰⠆⠀⠀⠀⠛⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢠⣭⣭⡠⡔⣿⣿⣯⢠⣘⣿⣿⡅⠤⠛⠛⠫⠀⢸⣿⣈⣿⣿⣿⡿⢿⣿⣿⣿⣯⣭⣿⣿⡿⢿⣿⠿⢿⢯⡽⢿⣿⣛⣀ ⢇⡶⠶⡶⢾⠏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢀⠀⠀⠀⠀⠆⠀⠂⠀⣼⣿⣿⣿⣿⣿⣿⠀⠸⣿⡿⣃⠃⣻⣿⣟⣘⡀⣿⣿⣃⡐⠀⠀⠂⠀⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠆⢒⠒⠒⠂⣺⣶⡄⠀⠀⠀⠀⢀⡀⢀⣸⠀⠈⢠⡄⠀⠀⠀⠀⠁⠐⢾⣿⣿⣿⣿⣿⣿⠀⠀⠉⠁⠀⠀⢹⠉⠩⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⠿⢿⠿⠖⢸⡿⡟⠻⠿⠿⠿⣿⣿⣿⡿⣿⣿⣿⣿⠿⠿⢿ ⡏⠛⠛⢣⡤⠌⠙⠃⠠⠀⠀⠀⠜⠃⠜⢻⠀⢸⠋⠃⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣿⣿⣿⣿⣾⣿⣿⣿⣿⠀⠀⠈⢹⣿⣿⣿⣷⣿⣿⣿ ⡉⠛⠛⠛⠃⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠀⡠⠀⠀⠀⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣷⣦⣶⣤⣬⣽⣶⡖⣶⣶⢠⣴⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶ ⠗⡶⣾⠃⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⠀⠁⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣟⠉⠉⠁⠁⠀⠀⠀⠀⠀⠙⠛⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙ ⡎⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢡⠀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣶⢠⣀⡀⠀⠀⢸⣧⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣇⣁⣈⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢸⠀⡾⠀⠀⠀⠀⡆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠈⠀⠠⠄⣿⡯⠉⠁⠌⢸⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣏⠉⠉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⡿⠒⠆⠆⠂⢸⠀⠀⣀⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠻⠃⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣯⠋⠛⠃⠀⠸⡷⠂⠀⠀⠀⠀⠀⣤⠀⢸⢿⣷⣳⣿⣿⣇⣹⠀⠈⠉⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣁⣀⣀⣀⣀⣀⣸⡇⡀⠀⠀⠀⠀⠀⠐⠾⠾⠗⠀⠀⠀⠀⠀⠛⠛⠛⠛⠻⠿⠀⠀⠀ ⠎⣷⣷⡷⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡟⠻⠙⡻⠓⢻⠒⠒⠒⢸⣿⣿⣿⣿⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣫⣤⣤⣼⣿⣿⣇⡀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤ ⡛⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⠨⠀⠀⠀⣾⣿⠿⠿⠿⠎⠀⣀⠤⠴⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠟⢟⣛⣛⣻⣿⣿⡿⠇⠀⠀⠉⠿⠿⠟⠀⠀⠀⠀⠀⠘⠛⠛⠛⠻ ⠯⣿⡏⠛⠙⠹⠇⠀⠀⠀⢴⡀⠀⠀⠀⠀⢀⣄⣬⣠⣈⣇⣀⢀⣀⣀⡀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⡇⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⡶⠶⠴⠴⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠠⠆ ⡶⣦⣤⣤⣤⣤⠤⠤⠤⠤⠤⠤⠤⠤⠴⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⢦⠶⠆⢲⠲⢤⡲⠒⠒⠒⠴⠶⠖⠲⢸⡈⠍⠉⠎⠀⠀⠀⢴⠻⢿⡷⠾⠷⣾⣿⣟⣶⣷⣲⣲⣷⣿⣷⣷⣾⣷⣒⣒⣓⣛⣾⣶⣷⣾⣛⣓⣷⣗⣶⣷⣒⠚⠛⠓⠚⠛⠛⠛⠻⠿⠷⠿⠿⠿⠦⠆⠀⠀⠀⠀⣤⠀ ⣶⡶⢶⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⢆⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣿⣿⣿⣿⣿⠛⠛⠟⣿⣿⣶⣶⣿⣿⣿⠿⠿⠿⢿⣟⣿⣭⡭⣫⣶⡆⠀⠀⠀⠁⠁⠈⠛⠛⠛⠛⣷⣶⣦⣤⡤⠀⠀⠀⠐⠓⠚⠀⣦⣤ ⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⣎⡀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⠄⢠⣤⣀⡀⡰⣻⣶⣀⢀⠸⣷⣂⡀⢀⣾⣶⣆⡀⡘⡇⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣛⣣⣦⣉⣉⣹⣿⣿⣟⣟⣩⣝⣻⣿⣿⠃⠀⠁⡄⠀⠀⠄⠠⢹⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⠃⣃⢿⣿⣿⠘⣒⣿⣿⣇⢐⠾⢿⡿⠇⢏⣧⣀⠀⠀⠀⠉⠉⠙⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀ ⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢀⡄⠀⠆⣑⣌⢹⣿⣿⣿⣿⣿⣿⢀⠈⣭⣭⡀⠈⣭⣽⣯⢥⠹⣿⣯⡭⢄⢲⣽⣣⡤⣸⡇⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣄⣠ ⡇⣛⡛⠛⠚⣿⣟⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠹⠉⠱⠈⠁⣆⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⠃⠀⣿⣿⣿⠘⠀⣿⣿⡇⢘⡘⣿⣿⢇⢻⣇⠿⠿⠿⠿⠿⠿⠿⢿⢿⢿⠿⠟⠛⠛⠛⠻⠿⢿⠟⠛⠛⠛⠛⠛ ⡿⡿⣻⠀⠰⢭⡏⠀⠀⠷⡀⠀⠀⠀⠀⢘⠀⠰⠆⠀⠀⠀⠛⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢠⣭⣭⡠⡔⣿⣿⣯⢠⣘⣿⣿⡅⠤⠛⠛⠫⠀⢸⣿⣈⣿⣿⣿⡿⢿⣿⣿⣿⣯⣭⣿⣿⡿⢿⣿⠿⢿⢯⡽⢿⣿⣛⣀ ⢇⡶⠶⡶⢾⠏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢀⠀⠀⠀⠀⠆⠀⠂⠀⣼⣿⣿⣿⣿⣿⣿⠀⠸⣿⡿⣃⠃⣻⣿⣟⣘⡀⣿⣿⣃⡐⠀⠀⠂⠀⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠆⢒⠒⠒⠂⣺⣶⡄⠀⠀⠀⠀⢀⡀⢀⣸⠀⠈⢠⡄⠀⠀⠀⠀⠁⠐⢾⣿⣿⣿⣿⣿⣿⠀⠀⠉⠁⠀⠀⢹⠉⠩⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⠿⢿⠿⠖⢸⡿⡟⠻⠿⠿⠿⣿⣿⣿⡿⣿⣿⣿⣿⠿⠿⢿ ⡏⠛⠛⢣⡤⠌⠙⠃⠠⠀⠀⠀⠜⠃⠜⢻⠀⢸⠋⠃⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣿⣿⣿⣿⣾⣿⣿⣿⣿⠀⠀⠈⢹⣿⣿⣿⣷⣿⣿⣿ ⡉⠛⠛⠛⠃⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠀⡠⠀⠀⠀⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣷⣦⣶⣤⣬⣽⣶⡖⣶⣶⢠⣴⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶ ⠗⡶⣾⠃⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⠀⠁⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣟⠉⠉⠁⠁⠀⠀⠀⠀⠀⠙⠛⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙ ⡎⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢡⠀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣶⢠⣀⡀⠀⠀⢸⣧⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣇⣁⣈⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢸⠀⡾⠀⠀⠀⠀⡆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠈⠀⠠⠄⣿⡯⠉⠁⠌⢸⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣏⠉⠉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⡿⠒⠆⠆⠂⢸⠀⠀⣀⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠻⠃⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣯⠋⠛⠃⠀⠸⡷⠂⠀⠀⠀⠀⠀⣤⠀⢸⢿⣷⣳⣿⣿⣇⣹⠀⠈⠉⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣁⣀⣀⣀⣀⣀⣸⡇⡀⠀⠀⠀⠀⠀⠐⠾⠾⠗⠀⠀⠀⠀⠀⠛⠛⠛⠛⠻⠿⠀⠀⠀ ⠎⣷⣷⡷⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡟⠻⠙⡻⠓⢻⠒⠒⠒⢸⣿⣿⣿⣿⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣫⣤⣤⣼⣿⣿⣇⡀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤ ⡛⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⠨⠀⠀⠀⣾⣿⠿⠿⠿⠎⠀⣀⠤⠴⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠟⢟⣛⣛⣻⣿⣿⡿⠇⠀⠀⠉⠿⠿⠟⠀⠀⠀⠀⠀⠘⠛⠛⠛⠻ ⠯⣿⡏⠛⠙⠹⠇⠀⠀⠀⢴⡀⠀⠀⠀⠀⢀⣄⣬⣠⣈⣇⣀⢀⣀⣀⡀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⡇⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⡶⠶⠴⠴⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠠⠆ ⡶⣦⣤⣤⣤⣤⠤⠤⠤⠤⠤⠤⠤⠤⠴⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⢦⠶⠆⢲⠲⢤⡲⠒⠒⠒⠴⠶⠖⠲⢸⡈⠍⠉⠎⠀⠀⠀⢴⠻⢿⡷⠾⠷⣾⣿⣟⣶⣷⣲⣲⣷⣿⣷⣷⣾⣷⣒⣒⣓⣛⣾⣶⣷⣾⣛⣓⣷⣗⣶⣷⣒⠚⠛⠓⠚⠛⠛⠛⠻⠿⠷⠿⠿⠿⠦⠆⠀⠀⠀⠀⣤⠀ ⣶⡶⢶⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⢆⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣿⣿⣿⣿⣿⠛⠛⠟⣿⣿⣶⣶⣿⣿⣿⠿⠿⠿⢿⣟⣿⣭⡭⣫⣶⡆⠀⠀⠀⠁⠁⠈⠛⠛⠛⠛⣷⣶⣦⣤⡤⠀⠀⠀⠐⠓⠚⠀⣦⣤ ⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⣎⡀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⠄⢠⣤⣀⡀⡰⣻⣶⣀⢀⠸⣷⣂⡀⢀⣾⣶⣆⡀⡘⡇⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣛⣣⣦⣉⣉⣹⣿⣿⣟⣟⣩⣝⣻⣿⣿⠃⠀⠁⡄⠀⠀⠄⠠⢹⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⠃⣃⢿⣿⣿⠘⣒⣿⣿⣇⢐⠾⢿⡿⠇⢏⣧⣀⠀⠀⠀⠉⠉⠙⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀ ⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢀⡄⠀⠆⣑⣌⢹⣿⣿⣿⣿⣿⣿⢀⠈⣭⣭⡀⠈⣭⣽⣯⢥⠹⣿⣯⡭⢄⢲⣽⣣⡤⣸⡇⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣄⣠ ⡇⣛⡛⠛⠚⣿⣟⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠹⠉⠱⠈⠁⣆⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⠃⠀⣿⣿⣿⠘⠀⣿⣿⡇⢘⡘⣿⣿⢇⢻⣇⠿⠿⠿⠿⠿⠿⠿⢿⢿⢿⠿⠟⠛⠛⠛⠻⠿⢿⠟⠛⠛⠛⠛⠛ ⡿⡿⣻⠀⠰⢭⡏⠀⠀⠷⡀⠀⠀⠀⠀⢘⠀⠰⠆⠀⠀⠀⠛⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢠⣭⣭⡠⡔⣿⣿⣯⢠⣘⣿⣿⡅⠤⠛⠛⠫⠀⢸⣿⣈⣿⣿⣿⡿⢿⣿⣿⣿⣯⣭⣿⣿⡿⢿⣿⠿⢿⢯⡽⢿⣿⣛⣀ ⢇⡶⠶⡶⢾⠏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢀⠀⠀⠀⠀⠆⠀⠂⠀⣼⣿⣿⣿⣿⣿⣿⠀⠸⣿⡿⣃⠃⣻⣿⣟⣘⡀⣿⣿⣃⡐⠀⠀⠂⠀⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠆⢒⠒⠒⠂⣺⣶⡄⠀⠀⠀⠀⢀⡀⢀⣸⠀⠈⢠⡄⠀⠀⠀⠀⠁⠐⢾⣿⣿⣿⣿⣿⣿⠀⠀⠉⠁⠀⠀⢹⠉⠩⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⠿⢿⠿⠖⢸⡿⡟⠻⠿⠿⠿⣿⣿⣿⡿⣿⣿⣿⣿⠿⠿⢿ ⡏⠛⠛⢣⡤⠌⠙⠃⠠⠀⠀⠀⠜⠃⠜⢻⠀⢸⠋⠃⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣿⣿⣿⣿⣾⣿⣿⣿⣿⠀⠀⠈⢹⣿⣿⣿⣷⣿⣿⣿ ⡉⠛⠛⠛⠃⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠀⡠⠀⠀⠀⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣷⣦⣶⣤⣬⣽⣶⡖⣶⣶⢠⣴⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶ ⠗⡶⣾⠃⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⠀⠁⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣟⠉⠉⠁⠁⠀⠀⠀⠀⠀⠙⠛⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙ ⡎⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢡⠀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣶⢠⣀⡀⠀⠀⢸⣧⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣇⣁⣈⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢸⠀⡾⠀⠀⠀⠀⡆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠈⠀⠠⠄⣿⡯⠉⠁⠌⢸⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣏⠉⠉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⡿⠒⠆⠆⠂⢸⠀⠀⣀⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠻⠃⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣯⠋⠛⠃⠀⠸⡷⠂⠀⠀⠀⠀⠀⣤⠀⢸⢿⣷⣳⣿⣿⣇⣹⠀⠈⠉⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣁⣀⣀⣀⣀⣀⣸⡇⡀⠀⠀⠀⠀⠀⠐⠾⠾⠗⠀⠀⠀⠀⠀⠛⠛⠛⠛⠻⠿⠀⠀⠀ ⠎⣷⣷⡷⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡟⠻⠙⡻⠓⢻⠒⠒⠒⢸⣿⣿⣿⣿⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣫⣤⣤⣼⣿⣿⣇⡀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤ ⡛⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⠨⠀⠀⠀⣾⣿⠿⠿⠿⠎⠀⣀⠤⠴⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠟⢟⣛⣛⣻⣿⣿⡿⠇⠀⠀⠉⠿⠿⠟⠀⠀⠀⠀⠀⠘⠛⠛⠛⠻ ⠯⣿⡏⠛⠙⠹⠇⠀⠀⠀⢴⡀⠀⠀⠀⠀⢀⣄⣬⣠⣈⣇⣀⢀⣀⣀⡀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⡇⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⡶⠶⠴⠴⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠠⠆ ⡶⣦⣤⣤⣤⣤⠤⠤⠤⠤⠤⠤⠤⠤⠴⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⢦⠶⠆⢲⠲⢤⡲⠒⠒⠒⠴⠶⠖⠲⢸⡈⠍⠉⠎⠀⠀⠀⢴⠻⢿⡷⠾⠷⣾⣿⣟⣶⣷⣲⣲⣷⣿⣷⣷⣾⣷⣒⣒⣓⣛⣾⣶⣷⣾⣛⣓⣷⣗⣶⣷⣒⠚⠛⠓⠚⠛⠛⠛⠻⠿⠷⠿⠿⠿⠦⠆⠀⠀⠀⠀⣤⠀ ⣶⡶⢶⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⢆⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣿⣿⣿⣿⣿⠛⠛⠟⣿⣿⣶⣶⣿⣿⣿⠿⠿⠿⢿⣟⣿⣭⡭⣫⣶⡆⠀⠀⠀⠁⠁⠈⠛⠛⠛⠛⣷⣶⣦⣤⡤⠀⠀⠀⠐⠓⠚⠀⣦⣤ ⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⣎⡀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⠄⢠⣤⣀⡀⡰⣻⣶⣀⢀⠸⣷⣂⡀⢀⣾⣶⣆⡀⡘⡇⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣛⣣⣦⣉⣉⣹⣿⣿⣟⣟⣩⣝⣻⣿⣿⠃⠀⠁⡄⠀⠀⠄⠠⢹⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⠃⣃⢿⣿⣿⠘⣒⣿⣿⣇⢐⠾⢿⡿⠇⢏⣧⣀⠀⠀⠀⠉⠉⠙⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀ ⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢀⡄⠀⠆⣑⣌⢹⣿⣿⣿⣿⣿⣿⢀⠈⣭⣭⡀⠈⣭⣽⣯⢥⠹⣿⣯⡭⢄⢲⣽⣣⡤⣸⡇⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣄⣠ ⡇⣛⡛⠛⠚⣿⣟⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠹⠉⠱⠈⠁⣆⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⠃⠀⣿⣿⣿⠘⠀⣿⣿⡇⢘⡘⣿⣿⢇⢻⣇⠿⠿⠿⠿⠿⠿⠿⢿⢿⢿⠿⠟⠛⠛⠛⠻⠿⢿⠟⠛⠛⠛⠛⠛ ⡿⡿⣻⠀⠰⢭⡏⠀⠀⠷⡀⠀⠀⠀⠀⢘⠀⠰⠆⠀⠀⠀⠛⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢠⣭⣭⡠⡔⣿⣿⣯⢠⣘⣿⣿⡅⠤⠛⠛⠫⠀⢸⣿⣈⣿⣿⣿⡿⢿⣿⣿⣿⣯⣭⣿⣿⡿⢿⣿⠿⢿⢯⡽⢿⣿⣛⣀ ⢇⡶⠶⡶⢾⠏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢀⠀⠀⠀⠀⠆⠀⠂⠀⣼⣿⣿⣿⣿⣿⣿⠀⠸⣿⡿⣃⠃⣻⣿⣟⣘⡀⣿⣿⣃⡐⠀⠀⠂⠀⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠆⢒⠒⠒⠂⣺⣶⡄⠀⠀⠀⠀⢀⡀⢀⣸⠀⠈⢠⡄⠀⠀⠀⠀⠁⠐⢾⣿⣿⣿⣿⣿⣿⠀⠀⠉⠁⠀⠀⢹⠉⠩⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⠿⢿⠿⠖⢸⡿⡟⠻⠿⠿⠿⣿⣿⣿⡿⣿⣿⣿⣿⠿⠿⢿ ⡏⠛⠛⢣⡤⠌⠙⠃⠠⠀⠀⠀⠜⠃⠜⢻⠀⢸⠋⠃⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣿⣿⣿⣿⣾⣿⣿⣿⣿⠀⠀⠈⢹⣿⣿⣿⣷⣿⣿⣿ ⡉⠛⠛⠛⠃⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠀⡠⠀⠀⠀⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣷⣦⣶⣤⣬⣽⣶⡖⣶⣶⢠⣴⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶ ⠗⡶⣾⠃⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⠀⠁⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣟⠉⠉⠁⠁⠀⠀⠀⠀⠀⠙⠛⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙ ⡎⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢡⠀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣶⢠⣀⡀⠀⠀⢸⣧⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣇⣁⣈⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢸⠀⡾⠀⠀⠀⠀⡆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠈⠀⠠⠄⣿⡯⠉⠁⠌⢸⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣏⠉⠉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⡿⠒⠆⠆⠂⢸⠀⠀⣀⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠻⠃⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣯⠋⠛⠃⠀⠸⡷⠂⠀⠀⠀⠀⠀⣤⠀⢸⢿⣷⣳⣿⣿⣇⣹⠀⠈⠉⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣁⣀⣀⣀⣀⣀⣸⡇⡀⠀⠀⠀⠀⠀⠐⠾⠾⠗⠀⠀⠀⠀⠀⠛⠛⠛⠛⠻⠿⠀⠀⠀ ⠎⣷⣷⡷⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡟⠻⠙⡻⠓⢻⠒⠒⠒⢸⣿⣿⣿⣿⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣫⣤⣤⣼⣿⣿⣇⡀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤ ⡛⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⠨⠀⠀⠀⣾⣿⠿⠿⠿⠎⠀⣀⠤⠴⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠟⢟⣛⣛⣻⣿⣿⡿⠇⠀⠀⠉⠿⠿⠟⠀⠀⠀⠀⠀⠘⠛⠛⠛⠻ ⠯⣿⡏⠛⠙⠹⠇⠀⠀⠀⢴⡀⠀⠀⠀⠀⢀⣄⣬⣠⣈⣇⣀⢀⣀⣀⡀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⡇⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⡶⠶⠴⠴⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠠⠆ ⡶⣦⣤⣤⣤⣤⠤⠤⠤⠤⠤⠤⠤⠤⠴⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⢦⠶⠆⢲⠲⢤⡲⠒⠒⠒⠴⠶⠖⠲⢸⡈⠍⠉⠎⠀⠀⠀⢴⠻⢿⡷⠾⠷⣾⣿⣟⣶⣷⣲⣲⣷⣿⣷⣷⣾⣷⣒⣒⣓⣛⣾⣶⣷⣾⣛⣓⣷⣗⣶⣷⣒⠚⠛⠓⠚⠛⠛⠛⠻⠿⠷⠿⠿⠿⠦⠆⠀⠀⠀⠀⣤⠀ ⣶⡶⢶⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⢆⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣿⣿⣿⣿⣿⠛⠛⠟⣿⣿⣶⣶⣿⣿⣿⠿⠿⠿⢿⣟⣿⣭⡭⣫⣶⡆⠀⠀⠀⠁⠁⠈⠛⠛⠛⠛⣷⣶⣦⣤⡤⠀⠀⠀⠐⠓⠚⠀⣦⣤ ⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⣎⡀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⠄⢠⣤⣀⡀⡰⣻⣶⣀⢀⠸⣷⣂⡀⢀⣾⣶⣆⡀⡘⡇⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣛⣣⣦⣉⣉⣹⣿⣿⣟⣟⣩⣝⣻⣿⣿⠃⠀⠁⡄⠀⠀⠄⠠⢹⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⠃⣃⢿⣿⣿⠘⣒⣿⣿⣇⢐⠾⢿⡿⠇⢏⣧⣀⠀⠀⠀⠉⠉⠙⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀ ⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢀⡄⠀⠆⣑⣌⢹⣿⣿⣿⣿⣿⣿⢀⠈⣭⣭⡀⠈⣭⣽⣯⢥⠹⣿⣯⡭⢄⢲⣽⣣⡤⣸⡏⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣄⣠ ⡇⣛⡛⠛⠚⣿⣟⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠹⠉⠱⠈⠁⣆⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⠃⠀⣿⣿⣿⠘⠀⣿⣿⡇⢘⡘⣿⣿⢇⢻⣇⠿⠿⠿⠿⠿⠿⠿⢿⢿⢿⠿⠟⠛⠛⠛⠻⠿⢿⠟⠛⠛⠛⠛⠛ ⡿⡿⣻⠀⠰⢭⡏⠀⠀⠷⡀⠀⠀⠀⠀⢘⠀⠰⠆⠀⠀⠀⠛⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢠⣭⣭⡠⡔⣿⣿⣯⢠⣘⣿⣿⡅⠤⠛⠛⠫⠀⢸⣿⣈⣿⣿⣿⡿⢿⣿⣿⣿⣯⣭⣿⣿⡿⢿⣿⠿⢿⢯⡽⢿⣿⣛⣀ ⢇⡶⠶⡶⢾⠏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢀⠀⠀⠀⠀⠆⠀⠂⠀⣼⣿⣿⣿⣿⣿⣿⠀⠸⣿⡿⣃⠃⣻⣿⣟⣘⡀⣿⣿⣃⡐⠀⠀⠂⠀⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠆⢒⠒⠒⠂⣺⣶⡄⠀⠀⠀⠀⢀⡀⢀⣸⠀⠈⢠⡄⠀⠀⠀⠀⠁⠐⢾⣿⣿⣿⣿⣿⣿⠀⠀⠉⠁⠀⠀⢹⠉⠩⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⠿⢿⠿⠖⢸⡿⡟⠻⠿⠿⠿⣿⣿⣿⡿⣿⣿⣿⣿⠿⠿⢿ ⡏⠛⠛⢣⡤⠌⠙⠃⠠⠀⠀⠀⠜⠃⠜⢻⠀⢸⠋⠃⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣿⣿⣿⣿⣾⣿⣿⣿⣿⠀⠀⠈⢹⣿⣿⣿⣷⣿⣿⣿ ⡉⠛⠛⠛⠃⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠀⡠⠀⠀⠀⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣷⣦⣶⣤⣬⣽⣶⡖⣶⣶⢠⣴⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶ ⠗⡶⣾⠃⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⠀⠁⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣟⠉⠉⠁⠁⠀⠀⠀⠀⠀⠙⠛⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙ ⡎⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢡⠀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣶⢠⣀⡀⠀⠀⢸⣧⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣇⣁⣈⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢸⠀⡾⠀⠀⠀⠀⡆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠈⠀⠠⠄⣿⡯⠉⠁⠌⢸⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣏⠉⠉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⡿⠒⠆⠆⠂⢸⠀⠀⣀⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠻⠃⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣯⠋⠛⠃⠀⠸⡷⠂⠀⠀⠀⠀⠀⣤⠀⢸⢿⣷⣳⣿⣿⣇⣹⠀⠈⠉⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣁⣀⣀⣀⣀⣀⣸⡇⡀⠀⠀⠀⠀⠀⠐⠾⠾⠗⠀⠀⠀⠀⠀⠛⠛⠛⠛⠻⠿⠀⠀⠀ ⠎⣷⣷⡷⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡟⠻⠙⡻⠓⢻⠒⠒⠒⢸⣿⣿⣿⣿⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣫⣤⣤⣼⣿⣿⣇⡀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤ ⡛⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⠨⠀⠀⠀⣾⣿⠿⠿⠿⠎⠀⣀⠤⠴⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠟⢟⣛⣛⣻⣿⣿⡿⠇⠀⠀⠉⠿⠿⠟⠀⠀⠀⠀⠀⠘⠛⠛⠛⠻ ⠯⣿⡏⠛⠙⠹⠇⠀⠀⠀⢴⡀⠀⠀⠀⠀⢀⣄⣬⣠⣈⣇⣀⢀⣀⣀⡀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⡇⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⡶⠶⠴⠴⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠠⠆ ⡶⣦⣤⣤⣤⣤⠤⠤⠤⠤⠤⠤⠤⠤⠴⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⢦⠶⠆⢲⠲⢤⡲⠒⠒⠒⠴⠶⠖⠲⢸⡈⠍⠉⠎⠀⠀⠀⢴⠻⢿⡷⠾⠷⣾⣿⣟⣶⣷⣲⣲⣷⣿⣷⣷⣾⣷⣒⣒⣓⣛⣾⣶⣷⣾⣛⣓⣷⣗⣶⣷⣒⠚⠛⠓⠚⠛⠛⠛⠻⠿⠷⠿⠿⠿⠦⠆⠀⠀⠀⠀⣤⠀ ⣶⡶⢶⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⢆⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣿⣿⣿⣿⣿⠛⠛⠟⣿⣿⣶⣶⣿⣿⣿⠿⠿⠿⢿⣟⣿⣭⡭⣫⣶⡆⠀⠀⠀⠁⠁⠈⠛⠛⠛⠛⣷⣶⣦⣤⡤⠀⠀⠀⠐⠓⠚⠀⣦⣤ ⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⣎⡀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⠄⢠⣤⣀⡀⡰⣻⣶⣀⢀⠸⣷⣂⡀⢀⣾⣶⣆⡀⡘⡇⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣛⣣⣦⣉⣉⣹⣿⣿⣟⣟⣩⣝⣻⣿⣿⠃⠀⠁⡄⠀⠀⠄⠠⢹⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⠃⣃⢿⣿⣿⠘⣒⣿⣿⣇⢐⠾⢿⡿⠇⢏⣧⣀⠀⠀⠀⠉⠉⠙⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀ ⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢀⡄⠀⠆⣑⣌⢹⣿⣿⣿⣿⣿⣿⢀⠈⣭⣭⡀⠈⣭⣽⣯⢥⠹⣿⣯⡭⢄⢲⣽⣣⡤⣸⡏⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣄⣠ ⡇⣛⡛⠛⠚⣿⣟⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠹⠉⠱⠈⠁⣆⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⠃⠀⣿⣿⣿⠘⠀⣿⣿⡇⢘⡘⣿⣿⢇⢻⣇⠿⠿⠿⠿⠿⠿⠿⢿⢿⢿⠿⠟⠛⠛⠛⠻⠿⢿⠟⠛⠛⠛⠛⠛ ⡿⡿⣻⠀⠰⢭⡏⠀⠀⠷⡀⠀⠀⠀⠀⢘⠀⠰⠆⠀⠀⠀⠛⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢠⣭⣭⡠⡔⣿⣿⣯⢠⣘⣿⣿⡅⠤⠛⠛⠫⠀⢸⣿⣈⣿⣿⣿⡿⢿⣿⣿⣿⣯⣭⣿⣿⡿⢿⣿⠿⢿⢯⡽⢿⣿⣛⣀ ⢇⡶⠶⡶⢾⠏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢀⠀⠀⠀⠀⠆⠀⠂⠀⣼⣿⣿⣿⣿⣿⣿⠀⠸⣿⡿⣃⠃⣻⣿⣟⣘⡀⣿⣿⣃⡐⠀⠀⠂⠀⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠆⢒⠒⠒⠂⣺⣶⡄⠀⠀⠀⠀⢀⡀⢀⣸⠀⠈⢠⡄⠀⠀⠀⠀⠁⠐⢾⣿⣿⣿⣿⣿⣿⠀⠀⠉⠁⠀⠀⢽⠏⠩⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⠿⢿⠿⠖⢸⡿⡟⠻⠿⠿⠿⣿⣿⣿⡿⣿⣿⣿⣿⠿⠿⢿ ⡏⠛⠛⢣⡤⠌⠙⠃⠠⠀⠀⠀⠜⠃⠜⢻⠀⢰⠋⠃⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣿⣿⣿⣿⣾⣿⣿⣿⣿⠀⠀⠈⢹⣿⣿⣿⣷⣿⣿⣿ ⡉⠛⠛⠛⠃⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠀⡠⠀⠀⠀⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣷⣦⣶⣤⣬⣽⣶⡖⣶⣶⢠⣴⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶ ⠗⡶⣾⠃⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣘⠀⠁⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣟⠉⠉⠁⠁⠀⠀⠀⠀⠀⠙⠛⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙ ⡎⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢡⠀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣶⢠⣀⡀⠀⠀⢸⣧⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣇⣁⣈⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢸⠀⡾⠀⠀⠀⠀⡆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠈⠀⠠⠄⣿⡯⠉⠁⠌⢸⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣏⠉⠉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⡿⠒⠆⠆⠂⢸⠀⠀⣀⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠻⠃⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣯⠋⠛⠃⠀⠸⡷⠂⠀⠀⠀⠀⠀⣤⠀⢸⢿⣷⣳⣿⣿⣇⣹⠀⠈⠉⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣁⣀⣀⣀⣀⣀⣸⡇⡀⠀⠀⠀⠀⠀⠐⠾⠾⠗⠀⠀⠀⠀⠀⠛⠛⠛⠛⠻⠿⠀⠀⠀ ⠎⣷⣷⡷⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡟⠻⠙⡻⠓⢻⠒⠒⠒⢸⣿⣿⣿⣿⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣫⣤⣤⣼⣿⣿⣇⡀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤ ⡛⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⠨⠀⠀⠀⣾⣿⠿⠿⠿⠎⠀⣀⠤⠴⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠟⢟⣛⣛⣻⣿⣿⡿⠇⠀⠀⠉⠿⠿⠟⠀⠀⠀⠀⠀⠘⠛⠛⠛⠻ ⠯⣿⡏⠛⠙⠹⠇⠀⠀⠀⢴⡀⠀⠀⠀⠀⢀⣄⣬⣠⣈⣇⣀⢀⣀⣀⡀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡇⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⡶⠶⠴⠴⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠠⠆ ⡶⣦⣤⣤⣤⣤⠤⠤⠤⠤⠤⠤⠤⠤⠴⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⢦⠶⠆⢲⠲⢤⡲⠒⠒⠒⠴⠶⠖⠲⢸⡈⠍⠉⠎⠀⠀⠀⢴⠻⢿⡷⠾⠷⣾⣿⣟⣶⣷⣲⣲⣷⣿⣷⣷⣾⣷⣒⣒⣓⣛⣾⣶⣷⣾⣛⣓⣷⣗⣶⣷⣒⠚⠛⠓⠚⠛⠛⠛⠻⠿⠷⠿⠿⠿⠦⠆⠀⠀⠀⠀⣤⠀ ⣶⡶⢶⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⢆⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣿⣿⣿⣿⣿⠛⠛⠟⣿⣿⣶⣶⣿⣿⣿⠿⠿⠿⢿⣟⣿⣭⡭⣫⣶⡆⠀⠀⠀⠁⠁⠈⠛⠛⠛⠛⣷⣦⣦⣤⡤⠀⠀⠀⠐⠓⠚⠀⣦⣤ ⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⣎⡀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⠄⢠⣤⣀⡀⡰⣻⣶⣀⢀⠸⣷⣂⡀⢀⣾⣶⣆⡀⡘⡇⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣛⣣⣦⣉⣉⣹⣿⣿⣟⣟⣩⣝⣻⣿⣿⠃⠀⠁⡄⠀⠀⠄⠠⢹⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⠃⣃⢿⣿⣿⠘⣒⣿⣿⣇⢐⠾⢿⡿⠇⢏⣧⣀⠀⠀⠀⠉⠉⠙⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀ ⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢀⡄⠀⠆⣑⣌⢹⣿⣿⣿⣿⣿⣿⢀⠈⣭⣭⡀⠈⣭⣽⣯⢥⠹⣿⣯⡭⢄⢲⣽⣣⡤⣸⡏⣛⣛⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣄⣠ ⡇⣛⡛⠛⠚⣿⣟⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠹⠉⠱⠈⠁⣆⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⠃⠀⣿⣿⣿⠘⠀⣿⣿⡇⢘⡘⣿⣿⢇⢻⣇⠿⠿⠿⠿⠿⠿⠿⢿⢿⢿⠿⠟⠛⠛⠛⠻⠿⢿⠟⠛⠛⠛⠛⠛ ⡿⡿⣻⠀⠰⢭⡏⠀⠀⠷⡀⠀⠀⠀⠀⢘⠀⠰⠆⠀⠀⠀⠛⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢠⣭⣭⡠⡔⣿⣿⣯⢠⣘⣿⣿⡅⠤⠛⠛⠫⠀⢸⣿⣈⣿⣿⣿⡿⢿⣿⣿⣿⣯⣭⣿⣿⡿⢿⣿⠿⢿⢯⡽⢿⣿⣛⣀ ⢇⡶⠶⡶⢾⠏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢀⠀⠀⠀⠀⠆⠀⠂⠀⣼⣿⣿⣿⣿⣿⣿⠀⠸⣿⡿⣃⠃⣻⣿⣟⣘⡀⣿⣿⣃⡐⠀⠀⠂⠀⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠆⢒⠒⠒⠂⣺⣶⡄⠀⠀⠀⠀⢀⡀⢀⣸⠀⠈⢠⡄⠀⠀⠀⠀⠁⠐⢾⣿⣿⣿⣿⣿⣿⠀⠀⠉⠁⠀⠀⢽⠏⠩⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢼⣿⣿⠿⠿⢿⠿⠖⢸⡿⡟⠻⠿⠿⠿⣿⣿⣿⡿⣿⣿⣿⣿⠿⠿⢿ ⡏⠛⠛⢣⡤⠌⠙⠃⠠⠀⠀⠀⠜⠃⠜⢻⠀⢰⠋⠃⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣿⣿⣿⣿⣾⣿⣿⣿⣿⠀⠀⠈⢹⣿⣿⣿⣷⣿⣿⣿ ⡉⠛⠛⠛⠃⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠀⡠⠀⠀⠀⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⣿⣿⣷⣷⣦⣶⣤⣬⣽⣶⡖⣶⣶⢠⣴⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶ ⠗⡶⣾⠃⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣘⠀⠁⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⡿⣟⠉⠉⠁⠁⠀⠀⠀⠀⠀⠙⠛⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙ ⡎⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢡⠀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣶⢠⣀⡀⠀⠀⢸⣧⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣇⣁⣈⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢸⠀⡾⠀⠀⠀⠀⡆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠈⠀⠠⠄⣿⡯⠉⠁⠌⢸⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣏⠉⠉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⡿⠒⠆⠆⠂⢸⠀⠀⣀⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠻⠃⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣯⠋⠛⠃⠀⠸⡷⠂⠀⠀⠀⠀⠀⣤⠀⢸⢿⣷⣳⣿⣿⣇⣹⠀⠈⠉⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣁⣀⣀⣀⣀⣀⣸⡇⡀⠀⠀⠀⠀⠀⠐⠾⠾⠗⠀⠀⠀⠀⠀⠛⠛⠛⠛⠻⠿⠀⠀⠀ ⠎⣷⣷⡷⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡟⠻⠙⡻⠓⢻⠒⠒⠒⢸⣿⣿⣿⣿⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣫⣤⣤⣼⣿⣿⣇⡀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤ ⡛⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⠨⠀⠀⠀⣾⣿⠿⠿⠿⠎⠀⣀⠤⠴⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠟⢟⣛⣛⣻⣿⣿⡿⠇⠀⠀⠉⠿⠿⠟⠀⠀⠀⠀⠀⠘⠛⠛⠛⠻ ⠯⣿⡏⠛⠙⠹⠇⠀⠀⠀⢴⡀⠀⠀⠀⠀⢀⣄⣬⣠⣈⣇⣀⢀⣀⣀⡀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡇⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⡶⠶⠴⠴⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠠⠆ ⡶⣦⣤⣤⣤⣤⠤⠤⠤⠤⠤⠤⠤⠤⠴⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⢦⠶⠆⢲⠲⢤⡲⠒⠒⠒⠴⠶⠖⠲⢸⡈⠍⠉⠎⠀⠀⠀⢴⠻⢿⡷⠾⠷⣾⣿⣟⣶⣷⣲⣲⣷⣿⣷⣷⣾⣷⣒⣒⣓⣛⣾⣶⣷⣾⣛⣓⣷⣗⣶⣷⣒⠚⠛⠓⠚⠛⠛⠛⠻⠿⠷⠿⠿⠿⠦⠆⠀⠀⠀⠀⣤⠀ ⣶⡶⢶⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⢆⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣿⣿⣿⣿⣿⠛⠛⠟⣿⣿⣶⣶⣿⣿⣿⠿⠿⠿⢿⣟⣿⣭⡭⣫⣶⡆⠀⠀⠀⠁⠁⠈⠛⠛⠛⠛⣷⣦⣦⣤⡤⠀⠀⠀⠐⠓⠚⠀⣦⣤ ⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⣎⡀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⠄⢠⣤⣀⡀⡰⣻⣶⣀⢀⠸⣷⣂⡀⢀⣾⣶⣆⡀⡘⡇⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣛⣣⣦⣉⣉⣹⣿⣿⣟⣟⣩⣝⣻⣿⣿⠃⠀⠁⡄⠀⠀⠄⠠⢹⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⠃⣃⢿⣿⣿⠘⣒⣿⣿⣇⢐⠾⢿⡿⠇⢏⣧⣀⠀⠀⠀⠉⠉⠙⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀ ⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢀⡄⠀⠆⣑⣌⢹⣿⣿⣿⣿⣿⣿⢀⠈⣭⣭⡀⠈⣭⣽⣯⢥⠹⣿⣯⡭⢄⢲⣽⣣⡤⣸⡏⣛⣛⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣄⣠ ⡇⣛⡛⠛⠚⣿⣟⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠹⠉⠱⠈⠁⣆⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⠃⠀⣿⣿⣿⠘⠀⣿⣿⡇⢘⡘⣿⣿⢇⢻⣇⠿⠿⠿⠿⠿⠿⠿⢿⢿⢿⠿⠟⠛⠛⠛⠻⠿⢿⠟⠛⠛⠛⠛⠛ ⡿⡿⣻⠀⠰⢭⡏⠀⠀⠷⡀⠀⠀⠀⠀⢘⠀⠰⠆⠀⠀⠀⠛⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢠⣭⣭⡠⡔⣿⣿⣯⢠⣘⣿⣿⡅⠤⠛⠛⠫⠀⢸⣿⣈⣿⣿⣿⡿⢿⣿⣿⣿⣯⣭⣿⣿⡿⢿⣿⠿⢿⢯⡽⢿⣿⣛⣀ ⢇⡶⠶⡶⢾⠏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢀⠀⠀⠀⠀⠆⠀⠂⠀⣼⣿⣿⣿⣿⣿⣿⠀⠸⣿⡿⣃⠃⣻⣿⣟⣘⡀⣿⣿⣃⡐⠀⠀⠂⠀⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠆⢒⠒⠒⠂⣺⣶⡄⠀⠀⠀⠀⢀⡀⢀⣸⠀⠈⢠⡄⠀⠀⠀⠀⠁⠐⢾⣿⣿⣿⣿⣿⣿⠀⠀⠉⠁⠀⠀⢽⠏⠩⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢼⣿⣿⠿⠿⢿⠿⠖⢸⡿⡟⠻⠿⠿⠿⣿⣿⣿⡿⣿⣿⣿⣿⠿⠿⢿ ⡏⠛⠻⢧⡤⠌⠙⠃⠠⠀⠀⠀⠜⠃⠜⢻⠀⢰⠋⠃⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣿⣿⣿⣿⣾⣿⣿⣿⣿⠀⠀⠈⢹⣿⣿⣿⣷⣿⣿⣿ ⡉⠛⠛⠛⠃⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠀⡠⠀⠀⠀⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⣿⣿⣷⣷⣦⣶⣤⣬⣽⣶⡖⣶⣶⢠⣴⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶ ⠗⡶⣾⠃⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣘⠀⠁⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⡿⣟⠉⠉⠁⠁⠀⠀⠀⠀⠀⠙⠛⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙ ⡎⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢡⠀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣶⢠⣀⡀⠀⠀⢸⣧⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣇⣁⣈⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢸⠀⡾⠀⠀⠀⠀⡆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠈⠀⠠⠄⣿⡯⠉⠁⠌⢸⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣏⠉⠉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⡿⠒⠆⠆⠂⢸⠀⠀⣀⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠻⠃⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣯⠋⠛⠃⠀⠸⡷⠂⠀⠀⠀⠀⠀⣤⠀⢸⢿⣷⣳⣿⣿⣇⣹⠀⠈⠉⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣁⣀⣀⣀⣀⣀⣸⡇⡀⠀⠀⠀⠀⠀⠐⠾⠾⠗⠀⠀⠀⠀⠀⠛⠛⠛⠛⠻⠿⠀⠀⠀ ⠎⣷⣷⡷⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡟⠻⠙⡻⠓⢻⠒⠒⠒⢸⣿⣿⣿⣿⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣫⣤⣤⣼⣿⣿⣇⡀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤ ⡛⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⠨⠀⠀⠀⣾⣿⠿⠿⠿⠎⠀⣀⠤⠴⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠟⢟⣛⣛⣻⣿⣿⡿⠇⠀⠀⠉⠿⠿⠟⠀⠀⠀⠀⠀⠘⠛⠛⠛⠻ ⠯⣿⡏⠛⠙⠹⠇⠀⠀⠀⢴⡀⠀⠀⠀⠀⢀⣄⣬⣠⣈⣇⣀⢀⣀⣀⡀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡇⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⡶⠶⠴⠴⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠠⠆ ⡶⣦⣤⣤⣤⣤⠤⠤⠤⠤⠤⠤⠤⠤⠴⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⢦⠶⠆⢲⠲⢤⡲⠒⠒⠒⠴⠶⠖⠲⢸⡈⠍⠉⠎⠀⠀⠀⢴⠻⢿⡷⠾⠷⣾⣿⣟⣶⣷⣲⣲⣷⣿⣷⣷⣾⣷⣒⣒⣓⣛⣾⣶⣷⣾⣛⣓⣷⣗⣶⣷⣒⠚⠛⠓⠚⠛⠛⠛⠻⠿⠷⠿⠿⠿⠦⠆⠀⠀⠀⠀⣤⠀ ⣶⡶⢶⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⢆⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣿⣿⣿⣿⣿⠛⠛⠟⣿⣿⣶⣶⣿⣿⣿⠿⠿⠿⢿⣟⣿⣭⡭⣫⣶⡆⠀⠀⠀⠁⠁⠈⠛⠛⠛⠛⣷⣦⣦⣤⡤⠀⠀⠀⠐⠓⠚⠀⣦⣤ ⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⣎⡀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⠄⢠⣤⣀⡀⡰⣻⣶⣀⢀⠸⣷⣂⡀⢀⣾⣶⣆⡀⡘⡇⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣛⣣⣦⣉⣉⣹⣿⣿⣟⣟⣩⣝⣻⣿⣿⠃⠀⠁⡄⠀⠀⠄⠠⢹⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⠃⣃⢿⣿⣿⠘⣒⣿⣿⣇⢐⠾⢿⡿⠇⢏⣧⣀⠀⠀⠀⠉⠉⠙⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀ ⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢀⡄⠀⠆⣑⣌⢹⣿⣿⣿⣿⣿⣿⢀⠈⣭⣭⡀⠈⣭⣽⣯⢥⠹⣿⣯⡭⢄⢲⣽⣣⡤⣸⡏⣛⣛⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣄⣠ ⡇⣛⡛⠛⠚⣿⣟⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠹⠉⠱⠈⠁⣆⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⠃⠀⣿⣿⣿⠘⠀⣿⣿⡇⢘⡘⣿⣿⢇⢻⣇⠿⠿⠿⠿⠿⠿⠿⢿⢿⢿⠿⠟⠛⠛⠛⠻⠿⢿⠟⠛⠛⠛⠛⠛ ⡿⡿⣻⠀⠰⢭⡏⠀⠀⠷⡀⠀⠀⠀⠀⢘⠀⠰⠆⠀⠀⠀⠛⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢠⣭⣭⡠⡔⣿⣿⣯⢠⣘⣿⣿⡅⠤⠛⠛⠫⠀⢸⣿⣈⣿⣿⣿⡿⢿⣿⣿⣿⣯⣭⣿⣿⡿⢿⣿⠿⢿⢯⡽⢿⣿⣛⣀ ⢇⡶⠶⡶⢾⠏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢀⠀⠀⠀⠀⠆⠀⠂⠀⣼⣿⣿⣿⣿⣿⣿⠀⠸⣿⡿⣃⠃⣻⣿⣟⣘⡀⣿⣿⣃⡐⠀⠀⠂⠀⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠆⢒⠒⠒⠃⣺⣶⡄⠀⠀⠀⠀⢀⡀⢀⣸⠀⠈⢠⡄⠀⠀⠀⠀⠁⠐⢾⣿⣿⣿⣿⣿⣿⠀⠀⠉⠁⠀⠀⢽⠏⠩⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢼⣿⣿⠿⠿⢿⠿⠖⢸⡿⡟⠻⠿⠿⠿⣿⣿⣿⡿⣿⣿⣿⣿⠿⠿⢿ ⡏⠛⠻⢧⡤⠌⠙⠃⠠⠀⠀⠀⠜⠃⠜⢻⠀⢰⠋⠃⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣿⣿⣿⣿⣾⣿⣿⣿⣿⠀⠀⠈⢹⣿⣿⣿⣷⣿⣿⣿ ⡉⠛⠛⠛⠃⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠀⡠⠀⠀⠀⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⣿⣿⣷⣷⣦⣶⣤⣬⣽⣶⡖⣶⣶⢠⣴⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶ ⠗⡶⣾⠃⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣘⠀⠁⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⡿⣟⠉⠉⠁⠁⠀⠀⠀⠀⠀⠙⠛⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙ ⡎⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢡⠀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣶⢠⣀⡀⠀⠀⢸⣧⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣇⣁⣈⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢸⠀⡾⠀⠀⠀⠀⣶⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠈⠀⠠⠄⣿⡯⠉⠁⠌⢸⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣏⠉⠉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⡿⠒⠆⠆⠂⢸⠀⠀⣀⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠻⠃⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣯⠋⠛⠃⠀⠸⡷⠂⠀⠀⠀⠀⠀⣤⠀⢸⢿⣷⣳⣿⣿⣇⣹⠀⠈⠉⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣁⣀⣀⣀⣀⣀⣸⡇⡀⠀⠀⠀⠀⠀⠐⠾⠾⠗⠀⠀⠀⠀⠀⠛⠛⠛⠛⠻⠿⠀⠀⠀ ⠎⣷⣷⡷⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡟⠻⠙⡻⠓⢻⠒⠒⠒⢸⣿⣿⣿⣿⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣫⣤⣤⣼⣿⣿⣇⡀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤ ⡛⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⠨⠀⠀⠀⣾⣿⠿⠿⠿⠎⠀⣀⠤⠴⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠟⢟⣛⣛⣻⣿⣿⡿⠇⠀⠀⠉⠿⠿⠟⠀⠀⠀⠀⠀⠘⠛⠛⠛⠻ ⠯⣿⡏⠛⠙⠹⠇⠀⠀⠀⢴⡀⠀⠀⠀⠀⢀⣄⣬⣠⣈⣇⣀⢀⣀⣀⡀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡇⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⣶⡶⠶⠶⢶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠰⠆ ⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡷⢶⠶⠆⣶⠳⢤⡶⠒⠒⠒⠶⠶⠶⠲⢺⡈⣽⠉⠎⠀⠀⠀⢴⣿⢿⡿⠾⠷⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣾⣶⣿⣾⣟⣷⣿⣿⣿⣿⣿⠿⠿⠿⠿⠟⠿⠟⠿⠿⠿⠿⠿⠿⠦⠆⠀⠀⠀⠀⣤⠀ ⣷⣶⣶⣶⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣧⢾⠀⠀⠀⠀⠀⠀⠁⠈⡿⠷⠿⠿⠿⠿⠿⠛⠛⠟⠿⠿⠷⠾⠿⠿⠿⠿⠿⠿⠿⠟⠿⠿⠿⠻⠿⡗⢷⡤⣴⣥⣿⣾⣿⣿⣿⢿⣿⣮⣾⣿⣾⣿⣾⣿⣾⣿⣿⢲⣦⣤ ⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⣮⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠄⢠⣤⣾⡿⡿⣿⣿⣏⢩⠿⣿⣏⡹⢇⣿⣷⣆⡰⡆⢼⠟⣛⡛⠫⢿⠟⠻⡿⣻⡿⣋⠙⠉⠉⢙⣟⣻⣻⣿⣿⣿⢙⣿⣙ ⣿⣿⣿⣛⣣⣧⣙⣉⣹⣿⣿⣿⣿⣩⣝⣿⣿⣿⠃⠀⠃⡄⢀⠀⠆⠠⢸⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⠇⣃⣿⣿⣿⠘⣖⣿⣿⣇⢐⠾⢿⡿⠇⠏⢸⣤⣿⣷⣾⣿⡿⡚⢿⣿⡯⢿⣿⣾⣿⣿⣿⣿⡿⣿⣿⢿⢹⣷⣿ ⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢀⡄⠀⠆⣑⣌⢹⣿⣿⣿⣿⣿⣿⢠⠊⣭⣭⡁⠉⣭⣽⣯⢥⠻⣿⣿⡭⢌⢲⣽⣧⡤⣴⣼⠈⠘⣿⣿⣿⣿⣿⣥⣤⣤⣤⣤⣥⣀⣤⣅⣤⣤⣼⣿⣿⣟⣿⣿ ⡏⣿⣿⠿⠿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠉⠱⠈⠡⣆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢸⠀⣿⣿⠃⠀⣿⣿⣿⠘⠉⣿⣿⡇⢘⡘⣿⣿⢇⡇⢸⠤⣤⣩⢍⠭⣙⠭⣍⡉⢿⢿⣿⢿⣟⣟⢻⣿⣿⣟⣟⣿⢻⣿⣿ ⣿⡿⣻⠀⠰⢭⡏⠈⠀⠿⡀⠀⠀⠀⠀⢘⠁⠸⠆⠀⠀⠰⠛⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠈⢠⣽⣭⡤⡔⣿⣿⣯⢠⣙⣿⣿⡅⠤⠟⠛⠫⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠉⠀⡀⡀⢀⣐⠖⠇⠞⠗⠿⣿⣿⣷ ⣷⣶⡶⣶⣾⡏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢰⠀⠀⠀⠀⠆⠀⠂⠀⢸⣿⣿⣿⣿⣿⣿⠀⠸⣿⣿⣃⠃⣻⣿⣟⣼⡀⣿⣿⣇⡐⠀⠀⠂⠀⢸⣾⣶⣶⡶⠀⠔⠐⢶⣶⣶⣷⣾⡿⠛⠿⣿⣿⣿⣗⣉⣛⣿⣿⢻⣟ ⠖⣒⠒⡲⠓⣺⣶⡄⠀⠀⠀⠀⢀⡠⢀⣸⠂⠘⣤⡄⠀⠀⠀⠀⠁⠐⢸⣿⣿⣿⣿⣿⣿⠀⠀⠉⠁⠀⠀⢽⢯⠭⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⠐⠀⠂⠈⠉⠉⠉⠉⠀⠂⡀⠉⠻⣿⣿⣯⣀⣿⡿⣯⢝ ⡏⠛⢻⣧⡤⠌⠙⠃⠠⠀⠀⠀⠜⠃⠜⢻⠀⢰⠋⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠀⠀⢨⣿⢸⣽⣯⣿⣯⣿⣿ ⡋⠛⠛⠛⠃⣀⠀⠀⠒⠀⠀⠀⠀⠀⠀⢸⠀⣠⠀⠀⠀⠃⢀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⢀⡀⢸⣿⣿⣯⠀⠈⠀⠀⠠⠀⠀⠀⠀⠡⠀⠀⠀⢀⡳⠫⢿⣿⣿⢟⣋⣿ ⡷⣶⣾⠇⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣸⠀⠁⠀⠀⠈⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢻⣿⣿⣿⣿⢿⣷⣄⠀⠀⠀⠀⠀⠈⠁⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⢸⣟⣇⡺⣧⣄⣀⢻⡛ ⡟⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢽⠀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢢⣀⣀⣀⣀⢸⣿⣿⣿⣇⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠚⢿⣿⣿⣷⣾⣵⡿⣷ ⣇⣁⣉⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢸⠁⣾⠀⠀⠀⠀⣶⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠿⠟⠟⠛⠿⠻⠿⠛⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣷⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠙⠊⠁⠈⠙⠛⠋⠛ ⣏⠋⠙⠁⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⣿⠖⠆⠆⡆⢸⠀⠀⣀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣉⣿⠻⣛⡻⠿⠛⢨⢿⡻⢿⡿⠀⣀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⣀⣿⣟⣶⡿⣿⢌⣿⣿ ⣯⠋⠛⠃⠀⠸⣷⠆⠀⠀⠀⠀⠀⣦⠀⢸⢿⣿⣻⣿⣿⣧⣹⠀⠈⠉⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣠⣀⣀⣀⣀⣀⣀⣉⣋⣁⣀⣀⣀⣀⣀⣸⣾⣶⣾⣷⣤⡿⠏⠀⠀⠀⠀⠀⠠⠀⠁⠀⠟⠿⠿⠿⠻⠿⠳⣿⣿ ⣞⣿⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡿⠻⠛⡻⠓⢻⠒⠒⠒⢸⣿⣿⣿⣿⠆⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⢾⣿⣿⣿⣟⡏⠁⠄⠐⠀⠀⠀⠀⢀⡄⠀⠂⠀⠀⠀⣀⣀⣀⣸⣿⣿ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⢸⠀⠀⠀⢸⣿⡿⠿⠿⠎⠀⣀⠴⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡀⢹⠉⠉⠉⢁⠀⠀⠀⠠⣀⠀⢀⠀⢠⠀⠀⠀⠁⠀⠀⠙⠛⠛⠛⠻ ⡯⣿⡟⠛⠙⠹⠇⠀⠀⠀⢴⡄⠀⠀⠀⠀⢈⣅⣬⣠⣈⣇⣀⢀⣀⣄⠐⣷⣇⣀⣀⣀⣀⣀⣀⣀⡀⠀⠰⠀⠀⠀⣀⣀⣀⠀⠂⠀⠀⠀⠀⠀⠀⢸⠀⠀⠁⠀⠀⠀⠀⠁⢒⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⣶⣶⠶⠶⢶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠰⠆ ⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡷⢶⠶⠆⣶⠳⢤⡶⠒⠒⠒⠶⠶⠶⠲⢺⡈⣽⠉⠎⠀⠀⠀⢴⣿⢿⡿⠾⠷⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⣾⣷⣿⣿⣿⣿⣾⣶⣿⣾⣟⣗⣿⣿⣿⣿⣿⠿⠿⠿⠿⠟⠿⠟⠿⠿⠿⠿⠿⠿⠦⠆⠀⠀⠀⠀⣤⠀ ⣷⣶⣶⣶⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣧⢾⠀⠀⠀⠀⠀⠀⠁⠈⡿⠷⠿⠿⠿⠿⠿⠛⠛⠟⠽⠯⠻⣥⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠿⣿⣿⣥⣴⣥⣿⣾⣿⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⣾⣿⣿⣶⣦⣤ ⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⣮⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠄⢠⣤⣿⡿⡿⣿⣿⣿⢿⠿⣿⣏⡹⢟⣿⣿⣟⡸⡆⣿⠜⣻⡛⠯⢿⠟⠻⡿⣻⡿⣋⠙⠋⠉⢙⣿⣻⣻⣿⣿⣿⢹⣯⣙ ⣿⣿⣿⣟⣣⣧⣙⣉⣹⣿⣿⣿⣿⣩⣝⣿⣿⣿⠃⠀⠃⡄⢀⠀⠆⠠⢸⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⠇⣃⣿⣿⣿⠘⣖⣿⣿⣇⢰⠾⢿⡿⠇⠏⣿⣤⣿⣷⣾⣿⡿⡚⢿⣿⣯⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⢿⢹⣷⣿ ⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢀⡄⠈⠆⣓⣌⢹⣿⣿⣿⣿⣿⣿⢠⠊⣭⣭⡁⠉⣭⣽⣯⢥⠻⣿⣿⡭⢌⢲⣽⣧⡤⣴⣿⠈⠘⣿⣿⣿⣿⣿⣥⣤⣤⣤⣤⣥⣀⣤⣅⣤⣤⣼⣿⣿⣟⣷⣶ ⡏⣿⣿⠿⠿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⢿⠿⠻⠉⠱⠈⠡⣆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢸⠀⣿⣿⠃⠀⣿⣿⣿⠘⠉⣿⣿⡇⢘⡘⣿⣿⢇⡇⣿⠤⣤⣩⢍⢭⣙⡭⢍⡋⢿⢿⣿⣿⣟⣟⢻⣿⣿⣿⣿⣿⢻⣿⣷ ⣿⡿⣻⠀⠰⢭⡏⠈⠀⠿⡀⠀⠀⠀⠀⢘⠁⠸⠆⠀⠀⠰⠛⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠈⢠⣽⣭⡤⡔⣿⣿⣯⢤⣙⣿⣿⡅⠤⠟⠛⠫⠀⢀⣿⠃⠀⡀⠀⠀⠀⡀⠁⢢⣄⠉⠀⡀⣀⢀⣰⠚⠇⠞⡟⢿⣿⣿⣷ ⣷⣶⡶⣶⣾⡏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢰⠀⠀⠀⠀⠆⠀⠂⠀⢸⣿⣿⣿⣿⣿⣿⠀⠸⣿⣿⣃⠃⣻⣿⣟⣼⡀⣿⣿⣇⡐⠀⠀⠂⠀⢸⣿⠀⠀⡰⠀⠄⠖⢶⣶⣶⣷⣾⡿⠟⠿⣿⣿⣿⣧⣉⣛⣻⣟⢻⣟ ⠗⣒⠒⡲⠓⣺⣶⡄⠀⠀⠀⠀⢀⡠⢀⣸⠂⠘⣤⡄⠀⠀⠀⠀⠁⠐⢸⣿⣿⣿⣿⣿⣿⠀⠀⠉⠁⠀⠀⢽⢯⠭⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠁⠐⠀⠂⠈⠉⠉⠉⠉⠀⠂⡀⠉⠻⣿⣿⣯⣀⣻⡿⣯⢝ ⡏⠛⢻⣧⡤⠌⠙⠃⠠⠀⠀⠀⠜⠃⠜⢻⠀⢰⠋⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⢸⣿⠀⣤⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠀⠀⢨⣭⢼⠿⠯⢿⣯⣿⣿ ⡋⠛⠛⠛⠃⣀⠀⠀⠒⠀⠀⠀⠀⠀⠀⢸⠀⣠⠀⠀⠀⠃⢀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⢀⡀⢸⣿⠀⠀⠀⠈⠀⠀⠠⠀⠀⠀⠀⠡⠀⠀⠀⢀⣳⠻⢿⣿⣿⢟⣋⣿ ⡷⣶⣾⠇⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣸⠀⠁⠀⠀⠈⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢻⣿⣿⣿⣿⢿⣷⣄⠀⠀⠀⠀⠀⠈⠁⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⢸⣟⣗⡾⣦⣄⣀⢿⡛ ⡟⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢽⠀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢢⣄⣀⣀⣀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠚⢿⣿⣿⣿⣚⣑⣛⣷ ⣇⣁⣉⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢸⠁⣾⠀⠀⠀⠀⣶⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠿⠿⠟⠛⠿⠻⠿⠛⣿⣿⣿⣿⣿⣿⡿⢸⣿⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠙⠊⠁⠈⠙⠛⠛⠛ ⣏⠋⠛⠁⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⣿⠖⠆⠆⡆⢸⠀⠀⣀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣉⣿⠻⣛⡻⠿⠛⢨⣿⠲⠶⠶⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⣀⣿⣟⣿⡿⣿⢌⣿⣿ ⣯⠋⠛⠃⠀⠸⣷⠆⠀⠀⠀⠀⠀⣦⠀⢸⢿⣿⣻⣿⣿⣧⣹⠀⠈⠉⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣠⣀⣀⣀⣀⣀⣠⣉⣋⣁⣀⣀⣀⣀⣀⣸⣷⠀⠀⢀⣡⡾⠏⠀⠀⠀⠀⠀⠠⠀⠁⠀⠟⠿⠿⠿⠻⠿⠳⣿⣿ ⣞⣿⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡿⠻⠛⡻⠓⢻⠒⠒⠒⢸⣿⣿⣿⣿⠆⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠾⣿⣶⣶⣟⡏⠁⠄⠐⠀⠀⠀⠀⢀⡄⠀⠂⠀⠀⠀⣀⣀⣀⣸⣿⣿ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⢸⠀⠀⠀⢸⣿⡿⠿⠿⠎⠀⣀⠴⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡀⣿⠉⠉⠉⢁⠀⠀⠀⠠⣀⠀⢀⠀⢠⠀⠀⠀⠁⠀⠀⠙⠛⠛⠛⠻ ⡯⣿⡟⠛⠙⠹⠇⠀⠀⠀⣴⡄⠀⠀⠀⠀⢈⣅⣬⣠⣈⣇⣀⢀⣀⣄⠐⣷⣇⣀⣀⣀⣀⣀⣀⣀⡀⠀⠰⠀⠀⠀⣀⣀⣀⠀⠂⠀⠀⠀⠀⠀⠀⣿⠀⠀⠁⠀⠀⠀⠀⠁⢒⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⣶⡶⠶⠶⢶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠰⠆ ⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡷⢶⠶⠆⣶⠳⢤⡶⠒⠒⠒⠶⠶⠶⠲⢺⡈⣽⠉⠎⠀⠀⠀⢴⣿⢿⡿⠾⠷⣾⣿⣿⣷⣿⣿⣻⣿⡿⣿⠿⣾⣷⣿⣿⣿⣿⣾⣶⣿⣾⣟⣗⣿⣿⣿⣿⣿⠿⠿⠿⠿⠟⠿⠟⠿⠿⠿⠿⠿⠿⠦⠆⠀⠀⠀⠀⣤⠀ ⣷⣶⣶⣶⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣧⢾⠀⠀⠀⠀⠀⠀⠁⠈⡿⠷⠿⠿⠿⠿⠿⠛⠛⠟⡽⠯⠀⣠⣿⣛⣿⣿⣟⣻⡿⠟⠿⠿⠿⠻⠿⣿⣿⣥⣴⣥⣿⣾⣿⣿⣾⣿⣿⣮⣮⣭⣾⣿⣾⣿⣾⣿⣿⣶⣦⣤ ⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⣮⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠄⢠⣤⣿⡿⡿⣿⣿⣿⢿⠿⣿⣟⡿⢟⣿⣿⣟⡸⡆⣿⡿⢿⣯⠿⣯⡿⠿⡭⡿⠿⣽⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⢙⣏⣙ ⣿⣿⣿⣛⣣⣧⣙⣉⣹⣿⣿⣿⣿⣩⣝⣿⣿⣿⠃⠀⠃⡄⢀⠀⠆⠠⢸⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⠇⣃⣿⣿⣿⠘⣖⣿⣿⣇⢐⠾⢿⡿⠇⠏⣿⡄⣿⣷⣾⣿⡿⡚⢿⣿⡯⢿⣿⣾⣿⣿⣿⣿⡿⣿⣿⢿⢹⣷⣿ ⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢀⡄⠀⠆⣑⣌⢹⣿⣿⣿⣿⣿⣿⢠⠊⣭⣭⡁⠉⣭⣽⣯⢥⠻⣿⣿⡭⢌⢲⣽⣧⡤⣴⣿⠋⠘⣿⣿⣿⣿⣿⣥⣤⣤⣤⣤⣥⣀⣤⣅⣤⣤⣼⣿⣿⣟⣷⣶ ⡏⣿⣿⠿⠿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠉⠱⠈⠡⣆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢸⠀⣿⣿⠃⠀⣿⣿⣿⠘⠉⣿⣿⡇⢘⡘⣿⣿⢇⡇⣿⠤⣤⣩⢍⠭⣙⠭⢍⡉⢿⢿⣿⢿⣟⣟⢻⣿⣿⣟⣟⣿⢻⣿⣷ ⣿⡿⣻⠀⠰⢭⡏⠈⠀⠿⡀⠀⠀⠀⠀⢘⠁⠸⠆⠀⠀⠰⠛⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠈⢠⣽⣭⡤⡔⣿⣿⣯⢠⣙⣿⣿⡅⠤⠟⠛⠫⠀⠀⣿⠂⠀⠀⠀⠀⠀⠀⠁⢠⣄⠉⠀⡀⡀⢀⣰⠒⠇⠞⠟⠿⣿⣿⣷ ⣷⣶⡶⣶⣾⡏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢰⠀⠀⠀⠀⠆⠀⠂⠀⢸⣿⣿⣿⣿⣿⣿⠀⠸⣿⣿⣃⠃⣻⣿⣟⣼⡀⣿⣿⣇⡐⠀⠀⠂⠀⢸⣿⠀⠀⡰⠀⠄⠒⢶⣶⣶⣷⣾⡿⠛⠿⣿⣿⣿⣧⣉⣛⣻⣟⢻⣟ ⠖⣒⠒⡲⠓⣺⣶⡄⠀⠀⠀⠀⢀⡠⢀⣸⠂⠘⣤⡄⠀⠀⠀⠀⠁⠐⢸⣿⣿⣿⣿⣿⣿⠀⠀⠉⠁⠀⠀⢽⢯⠭⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠁⠐⠀⠂⠈⠉⠉⠉⠉⠀⠂⡀⠉⠻⣿⣿⣯⣀⣻⡿⣯⢝ ⡏⠛⢻⣧⡤⠌⠙⠃⠠⠀⠀⠀⠜⠃⠜⢻⠀⢰⠋⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⢸⣿⠀⢠⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠀⠀⢨⣭⢸⠿⠯⢿⣯⣿⣿ ⡋⠛⠛⠛⠃⣀⠀⠀⠒⠀⠀⠀⠀⠀⠀⢸⠀⣠⠀⠀⠀⠃⢀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⢀⡀⢸⣿⠀⠀⠀⠈⠀⠀⠠⠀⠀⠀⠀⠡⠀⠀⠀⢀⡳⠫⢿⣿⣿⢟⣋⣿ ⡷⣶⣾⠇⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣸⠀⠁⠀⠀⠈⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢻⣿⣿⣿⣿⢿⣷⣄⠀⠀⠀⠀⠀⠈⠁⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⢸⣟⣇⡪⣦⣄⣀⢻⡛ ⡟⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢽⠀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢢⣀⣀⣀⣀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠚⢿⣿⣿⣷⣚⣑⡛⣷ ⣇⣁⣉⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢸⠁⣾⠀⠀⠀⠀⣶⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠿⠟⠟⠛⠿⠻⠿⠛⣿⣿⣿⣿⣿⣿⡿⢸⣿⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠂⠙⠊⠁⠈⠙⠛⠋⠛ ⣏⠋⠙⠁⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⣿⠖⠆⠆⡆⢸⠀⠀⣀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣉⣿⠻⣛⡻⠿⠛⢨⣿⠲⠶⠶⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⣀⣿⣟⣿⡿⣿⢌⣿⣿ ⣯⠋⠛⠃⠀⠸⣷⠆⠀⠀⠀⠀⠀⣦⠀⢸⢿⣿⣻⣿⣿⣧⣹⠀⠈⠉⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣠⣀⣀⣀⣀⣀⣀⣉⣋⣁⣀⣀⣀⣀⣀⣸⣷⠀⠀⢀⣡⡾⠏⠀⠀⠀⠀⠀⠠⠀⠁⠀⠟⠿⠿⠿⠻⠿⠳⣿⣿ ⣞⣿⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡿⠻⠛⡻⠓⢻⠒⠒⠒⢸⣿⣿⣿⣿⠆⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠾⣿⣶⣶⣟⡏⠁⠄⠐⠀⠀⠀⠀⢀⡄⠀⠂⠀⠀⠀⣀⣀⣀⣸⣿⣿ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⢸⠀⠀⠀⢸⣿⡿⠿⠿⠎⠀⣀⠴⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡀⣿⠉⠉⠉⢁⠀⠀⠀⠠⣀⠀⢀⠀⢠⠀⠀⠀⠁⠀⠀⠙⠛⠛⠛⠻ ⡯⣿⡟⠛⠙⠹⠇⠀⠀⠀⢴⡄⠀⠀⠀⠀⢈⣅⣬⣠⣈⣇⣀⢀⣀⣄⠐⣷⣇⣀⣀⣀⣀⣀⣀⣀⡀⠀⠰⠀⠀⠀⣀⣀⣀⠀⠂⠀⠀⠀⠀⠀⠀⣿⠀⠀⠁⠀⠀⠀⠀⠁⢒⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⣶⡶⠶⠶⢶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠰⠆ ⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡷⢶⠶⠆⣶⠳⢤⡶⠒⠒⠒⠶⠶⠶⠲⢺⡈⣽⠉⠎⠀⠀⠀⢴⣿⢿⡿⠾⠷⣾⣿⣿⣷⣿⣿⣻⣿⣿⣿⠿⣾⣷⣿⣿⣿⣿⣾⣶⣿⣾⣟⣗⣿⣿⣿⣿⣿⠿⠿⠿⠿⠟⠿⠟⠿⠿⠿⠿⠿⠿⠦⠆⠀⠀⠀⠀⣤⠀ ⣷⣶⣶⣶⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣧⢾⠀⠀⠀⠀⠀⠀⠁⠈⡿⠷⠿⠿⠿⠿⠿⠛⠛⠟⡽⠿⠃⣠⣿⣛⣿⣿⣟⣻⡿⠟⠿⠿⠿⠻⠿⣿⣿⣥⣴⣥⣿⣾⣿⣿⣾⣟⣿⣮⣮⣭⣾⣿⣾⣿⣾⣿⣿⣶⣦⣤ ⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⣮⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠄⢠⣤⣿⡿⡿⣿⣿⣿⢿⠿⣿⣟⡿⢟⣿⣿⣞⡸⡆⣿⡿⢿⣯⠿⣯⡿⠿⡭⡿⠿⣽⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⢙⣏⣙ ⣿⣿⣿⣛⣣⣧⣙⣉⣹⣿⣿⣿⣿⣩⣝⣿⣿⣿⠃⠀⠃⡄⢀⠀⠆⠠⢸⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⠇⣃⣿⣿⣿⠘⣖⣿⣿⣇⢐⠾⢿⡿⠇⠏⣿⡄⣿⣷⣾⣿⡿⡚⢿⣿⡯⢿⣿⣾⣿⣿⣿⣿⡿⣿⣿⢿⢹⣷⣿ ⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢀⡄⠀⠆⣑⣌⢹⣿⣿⣿⣿⣿⣿⢠⠊⣭⣭⡁⠉⣭⣽⣯⢥⠻⣿⣿⡭⢌⢲⣽⣧⡤⣴⣿⠋⠘⣿⣿⣿⣿⣿⣥⣤⣤⣤⣤⣥⣀⣤⣅⣤⣤⣼⣿⣿⣟⣷⣶ ⡏⣿⣿⠿⠿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠉⠱⠈⠡⣆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢸⠀⣿⣿⠃⠀⣿⣿⣿⠘⠉⣿⣿⡇⢘⡘⣿⣿⢇⡇⣿⠤⣤⣩⢍⠭⣙⠭⢍⡉⢿⢿⣿⢿⣟⣟⢻⣿⣿⣟⣟⣿⢻⣿⣷ ⣿⡿⣻⠀⠰⢭⡏⠈⠀⠿⡀⠀⠀⠀⠀⢘⠁⠸⠆⠀⠀⠰⠛⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠈⢠⣽⣭⡤⡔⣿⣿⣯⢠⣙⣿⣿⡅⠤⠟⠛⠫⠀⠀⣿⠂⠀⠀⠀⠀⠀⠀⠁⢠⣄⠉⠀⡀⡀⢀⣰⠒⠇⠞⠟⠿⣿⣿⣷ ⣷⣶⡶⣶⣾⡏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢰⠀⠀⠀⠀⠆⠀⠂⠀⢸⣿⣿⣿⣿⣿⣿⠀⠸⣿⣿⣃⠃⣻⣿⣟⣼⡀⣿⣿⣇⡐⠀⠀⠂⠀⢸⣿⠀⠀⡰⠀⠄⠒⢶⣶⣶⣷⣾⡿⠛⠿⣿⣿⣿⣧⣉⣛⣻⣟⢻⣟ ⠖⣒⠒⡲⠓⣺⣶⡄⠀⠀⠀⠀⢀⡠⢀⣸⠂⠘⣤⡄⠀⠀⠀⠀⠁⠐⢸⣿⣿⣿⣿⣿⣿⠀⠀⠉⠁⠀⠀⢽⢯⠭⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠁⠐⠀⠂⠈⠉⠉⠉⠉⠀⠂⡀⠉⠻⣿⣿⣯⣀⣻⡿⣯⢝ ⡏⠛⢻⣧⡤⠌⠙⠃⠠⠀⠀⠀⠜⠃⠜⢻⠀⢰⠋⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⢸⣿⠀⢠⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠀⠀⢨⣭⢸⠿⠯⢿⣯⣿⣿ ⡋⠛⠛⠛⠃⣀⠀⠀⠒⠀⠀⠀⠀⠀⠀⢸⠀⣠⠀⠀⠀⠃⢀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⢀⡀⢸⣿⠀⠀⠀⠈⠀⠀⠠⠀⠀⠀⠀⠡⠀⠀⠀⢀⡳⠫⢿⣿⣿⢟⣋⣿ ⡷⣶⣾⠇⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣸⠀⠁⠀⠀⠈⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢻⣿⣿⣿⣿⢿⣷⣄⠀⠀⠀⠀⠀⠈⠁⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⢸⣟⣇⡪⣦⣄⣀⢻⡛ ⡟⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢽⠀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢢⣀⣀⣀⣀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠚⢿⣿⣿⣷⣚⣑⡛⣷ ⣇⣁⣉⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢸⠁⣾⠀⠀⠀⠀⣶⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠿⠟⠟⠛⠿⠻⠿⠛⣿⣿⣿⣿⣿⣿⡿⢸⣿⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠂⠙⠊⠁⠈⠙⠛⠋⠛ ⣏⠋⠙⠁⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⣿⠖⠆⠆⡆⢸⠀⠀⣀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣉⣿⠻⣛⡻⠿⠛⢨⣿⠲⠶⠶⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⣀⣿⣟⣾⡿⣿⢌⣿⣿ ⣯⠋⠛⠃⠀⠸⣷⠆⠀⠀⠀⠀⠀⣦⠀⢸⢿⣿⣻⣿⣿⣧⣹⠀⠈⠉⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣠⣀⣀⣀⣀⣀⣀⣉⣋⣁⣀⣀⣀⣀⣀⣸⣷⠀⠀⢀⣡⡾⠏⠀⠀⠀⠀⠀⠠⠀⠁⠀⠟⠿⠿⠿⠻⠿⠳⣿⣿ ⣞⣿⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡿⠻⠛⡻⠓⢻⠒⠒⠒⢸⣿⣿⣿⣿⠆⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠾⣿⣶⣶⣟⡏⠁⠄⠐⠀⠀⠀⠀⢀⡄⠀⠂⠀⠀⠀⣀⣀⣀⣸⣿⣿ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⢸⠀⠀⠀⢸⣿⡿⠿⠿⠎⠀⣀⠴⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡀⣿⠉⠉⠉⢁⠀⠀⠀⠠⣀⠀⢀⠀⢠⠀⠀⠀⠁⠀⠀⠙⠛⠛⠛⠻ ⡯⣿⡟⠛⠙⠹⠇⠀⠀⠀⢴⡄⠀⠀⠀⠀⢈⣅⣬⣠⣈⣇⣀⢀⣀⣄⠐⣷⣇⣀⣀⣀⣀⣀⣀⣀⡀⠀⠰⠀⠀⠀⣀⣀⣀⠀⠂⠀⠀⠀⠀⠀⠀⣿⠀⠀⠁⠀⠀⠀⠀⠁⢒⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⣶⡶⠶⠶⢶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠰⠆ ⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡷⢶⠶⠆⣶⠳⢤⡶⠒⠒⠒⠶⠶⠶⠲⢺⡈⣽⠉⠎⠀⠀⠀⢴⣿⢿⡿⠾⠷⣾⣿⣿⣷⣿⣿⣻⣿⣿⣿⠿⣾⣷⣿⣿⣿⣿⣾⣶⣿⣾⣟⣗⣿⣿⣿⣿⣿⠿⠿⠿⠿⠟⠿⠟⠿⠿⠿⠿⠿⠿⠦⠆⠀⠀⠀⠀⣤⠀ ⣷⣶⣶⣶⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣧⢾⠀⠀⠀⠀⠀⠀⠁⠈⡿⠷⠿⠿⠿⠿⠿⠛⠛⠟⡽⠿⠃⣠⣿⣛⣿⣿⣟⣻⡿⠟⠿⠿⠿⠻⠿⣿⣿⣥⣴⣥⣿⣾⣿⣿⣾⣟⣿⣮⣮⣭⣾⣿⣾⣿⣾⣿⣿⣶⣦⣤ ⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⣮⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠄⢠⣤⣿⡿⡿⣿⣿⣿⢿⠿⣿⣟⡿⢟⣿⣿⣞⡸⡆⣿⡿⢿⣯⠿⣯⡿⠿⡭⡿⠿⣽⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⢙⣏⣛ ⣿⣿⣿⣛⣣⣧⣙⣉⣹⣿⣿⣿⣿⣩⣝⣿⣿⣿⠃⠀⠃⡄⢀⠀⠆⠠⢸⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⠇⣃⣿⣿⣿⠘⣖⣿⣿⣇⢐⠾⢿⡿⠇⠏⣿⡄⣿⣷⣾⣿⡿⡚⢿⣿⡯⢿⣿⣾⣿⣿⣿⣿⡿⣿⣿⢿⢹⣷⣿ ⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢀⡄⠀⠆⣑⣌⢹⣿⣿⣿⣿⣿⣿⢠⠊⣭⣭⡁⠉⣭⣽⣯⢥⠻⣿⣿⡭⢌⢲⣽⣧⡤⣴⣿⠋⠘⣿⣿⣿⣿⣿⣥⣤⣤⣤⣤⣥⣀⣤⣅⣤⣤⣼⣿⣿⣟⣷⣶ ⡏⣿⣿⠿⠿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠉⠱⠈⠡⣆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢸⠀⣿⣿⠃⠀⣿⣿⣿⠘⠉⣿⣿⡇⢘⡘⣿⣿⢇⡇⣿⠤⣤⣩⢍⠭⣙⠭⢍⡉⢿⢿⣿⢿⣟⣟⢻⣿⣿⣟⣟⣿⢻⣿⣷ ⣿⡿⣻⠀⠰⢭⡏⠈⠀⠿⡀⠀⠀⠀⠀⢘⠁⠸⠆⠀⠀⠰⠛⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠈⢠⣽⣭⡤⡔⣿⣿⣯⢠⣙⣿⣿⡅⠤⠟⠛⠫⠀⠀⣿⠂⠀⠀⠀⠀⠀⠀⠁⢠⣄⠉⠀⣶⡀⢀⣰⠒⠇⠞⠟⠿⣿⣿⣷ ⣷⣶⡶⣶⣾⡏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢰⠀⠀⠀⠀⠆⠀⠂⠀⢸⣿⣿⣿⣿⣿⣿⠀⠸⣿⣿⣃⠃⣻⣿⣟⣼⡀⣿⣿⣇⡐⠀⠀⠂⠀⢸⣿⠀⠀⡰⠀⠄⠒⢶⣶⣶⣷⣾⡿⠓⠿⣿⣿⣿⣧⣉⣛⣻⣟⢻⣟ ⠖⣒⠒⡲⠓⣺⣶⡄⠀⠀⠀⠀⢀⡠⢀⣸⠂⠘⣤⡄⠀⠀⠀⠀⠁⠐⢸⣿⣿⣿⣿⣿⣿⠀⠀⠉⠁⠀⠀⢽⢯⠭⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠁⠐⠀⠂⠈⠉⠉⠉⠉⠀⠂⡀⠉⠻⣿⣿⣯⣀⣻⡿⣯⢝ ⡏⠛⢻⣧⡤⠌⠙⠃⠠⠀⠀⠀⠜⠃⠜⢻⠀⢰⠋⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⢸⣿⠀⢠⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠀⠀⢨⣭⢸⠿⠯⢿⣯⣿⣿ ⡋⠛⠛⠛⠃⣀⠀⠀⠒⠀⠀⠀⠀⠀⠀⢸⠀⣠⠀⠀⠀⠃⢀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⢀⡀⢸⣿⠀⠀⠀⠈⠀⠀⠠⠀⠀⠀⠀⠡⠀⠀⠀⢀⡳⠫⢿⣿⣿⢟⣋⣿ ⡷⣶⣾⠇⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣸⠀⠁⠀⠀⠈⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢻⣿⣿⣿⣿⢿⣷⣄⠀⠀⠀⠀⠀⠈⠁⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⢸⣟⣇⡪⣦⣄⣀⢻⡛ ⡟⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢽⠀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢢⣀⣀⣀⣀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠚⢿⣿⣿⣷⣚⣑⡛⣷ ⣇⣁⣉⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢸⠁⣾⠀⠀⠀⠀⣶⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠿⠟⠟⠛⠿⠻⠿⠛⣿⣿⣿⣿⣿⣿⡿⢸⣿⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠂⠙⠊⠁⠈⠙⠛⠋⠛ ⣏⠋⠙⠁⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⣿⠖⠆⠆⡆⢸⠀⠀⣀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣉⣿⠻⣛⡻⠿⠛⢨⣿⠲⠶⠶⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⣀⣿⣟⣾⡿⣿⢌⣿⣿ ⣯⠋⠛⠃⠀⠸⣷⠆⠀⠀⠀⠀⠀⣦⠀⢸⢿⣿⣻⣿⣿⣧⣹⠀⠈⠉⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣠⣀⣀⣀⣀⣀⣀⣉⣋⣁⣀⣀⣀⣀⣀⣸⣷⠀⠀⢀⣡⡾⠏⠀⠀⠀⠀⠀⠠⠀⠁⠀⠟⠿⠿⠿⠻⠿⠳⣿⣿ ⣞⣿⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡿⠻⠛⡻⠓⢻⠒⠒⠒⢸⣿⣿⣿⣿⠆⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠾⣿⣶⣶⣟⡏⠁⠄⠐⠀⠀⠀⠀⢀⡄⠀⠂⠀⠀⠀⣀⣀⣀⣸⣿⣿ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⢸⠀⠀⠀⢸⣿⡿⠿⠿⠎⠀⣀⠴⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡀⣿⠉⠉⠉⢁⠀⠀⠀⠠⣀⠀⢀⠀⢠⠀⠀⠀⠁⠀⠀⠙⠛⠛⠛⠻ ⡯⣿⡟⠛⠙⠹⠇⠀⠀⠀⢴⡄⠀⠀⠀⠀⢈⣅⣬⣠⣈⣇⣀⢀⣀⣄⠐⣷⣇⣀⣀⣀⣀⣀⣀⣀⡀⠀⠰⠀⠀⠀⣀⣀⣀⠀⠂⠀⠀⠀⠀⠀⠀⣿⠀⠀⠁⠀⠀⠀⠀⠁⢒⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⣶⣶⠶⠶⢶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠰⠆ ⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡷⢶⠶⠆⣶⠳⢤⡶⠒⠒⠒⠶⠶⠶⠲⢺⡈⣽⠉⠎⠀⠀⠀⢴⣿⢿⡿⠾⠷⣾⣿⣿⣷⣿⣿⣻⣿⣿⣿⠿⣾⣷⣿⣿⣿⣿⣾⣶⣿⣾⣟⣗⣿⣿⣿⣿⣿⠿⠿⠿⠿⠟⠿⠟⠿⠿⠿⠿⠿⠿⠦⠆⠀⠀⠀⠀⣤⠀ ⣷⣶⣶⣶⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣧⢾⠀⠀⠀⠀⠀⠀⠁⠈⡿⠷⠿⠿⠿⠿⠿⠛⠛⠟⡽⠿⠃⣠⣿⣛⣿⣿⣟⣻⡿⠟⠿⠿⠿⠻⠿⣿⣿⣥⣴⣥⣿⣾⣿⣿⣾⣟⣿⣮⣮⣭⣾⣿⣾⣿⣾⣿⣿⣶⣦⣤ ⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⣮⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠄⢠⣤⣿⡿⡿⣿⣿⣿⢿⠿⣿⣟⡿⢟⣿⣿⣞⡸⡇⣿⡿⢿⣯⠿⣯⡿⠿⡭⡿⠿⣽⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⢙⣏⣛ ⡿⠿⠿⠛⠃⠇⠙⠉⠹⠿⠿⠟⠟⠉⠙⠻⠿⣿⠃⠀⠃⡄⢀⠀⠆⠠⢸⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⠇⣃⣿⣿⣿⠘⣖⣿⣿⣇⢐⠾⢿⡿⠇⠏⣿⡄⣿⣷⣾⣿⡿⡚⢿⣿⡯⢿⣿⣾⣿⣿⣿⣿⡿⣿⣿⢿⢹⣷⣿ ⠿⠷⠷⡿⠆⠀⡀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⣿⣧⡀⢀⡄⠀⠆⣓⣌⢹⣿⣿⣿⣿⣿⣿⢠⠊⣭⣭⡁⠉⣭⣽⣯⢥⠻⣿⣿⡭⢌⢲⣽⣧⡤⣴⣿⠋⠘⣿⣿⣿⣿⣿⣥⣤⣤⣤⣤⣥⣀⣤⣅⣤⣤⣼⣿⣿⣟⣷⣶ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠱⠈⠡⣆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢸⠀⣿⣿⠃⠀⣿⣿⣿⠘⠉⣿⣿⡇⢘⡘⣿⣿⢇⡇⣿⠤⣤⣩⢍⠭⣙⡭⢍⡉⢿⢿⣿⢿⣟⣟⢻⣿⣿⣿⣟⣿⢻⣿⣷ ⣯⡯⣩⠉⠹⢯⡏⠉⠉⠿⡉⠉⠉⠉⠉⢙⠉⠹⠆⠀⠀⠰⠛⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠈⢠⣽⣭⡤⡔⣿⣿⣯⢤⣙⣿⣿⡅⠤⠟⠛⠫⠀⢀⣿⠂⠀⡀⠀⠀⠀⠀⠁⢠⣄⠉⠀⣶⡀⢀⣰⠚⠇⠖⠟⢿⣿⣿⣷ ⣷⣶⡶⣶⣾⡏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢰⠀⠀⠀⠀⠆⠀⠂⠀⢸⣿⣿⣿⣿⣿⣿⠀⠸⣿⣿⣃⠃⣻⣿⣟⣼⡀⣿⣿⣇⡐⠀⠀⠂⠀⢸⣿⠀⠀⡰⠀⠄⠒⢶⣶⣶⣷⣾⡿⠓⠿⣿⣿⣿⣧⣉⣛⣻⣟⢻⣟ ⠗⣒⠒⡲⠓⣺⣶⡄⠀⠀⠀⠀⢀⡠⢀⣸⠂⠘⣤⡄⠀⠀⠀⠀⠁⠐⢸⣿⣿⣿⣿⣿⣿⠀⠀⠉⠁⠀⠀⢽⢯⠭⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠁⠐⠀⠂⠈⠉⠉⠉⠉⠀⠂⡀⠉⠻⣿⣿⣯⣀⣻⡿⣯⢝ ⡏⠛⢻⣧⡤⠌⠙⠃⠠⠀⠀⠀⠜⠃⠜⢻⠀⢰⠋⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⢸⣿⠀⢠⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠀⠀⢨⣭⢼⠿⠯⢿⣯⣿⣿ ⡋⠛⠛⠛⠃⣀⠀⠀⠒⠀⠀⠀⠀⠀⠀⢸⠀⣠⠀⠀⠀⠃⢀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⢀⡀⢸⣿⠀⠀⠀⠈⠀⠀⠠⠀⠀⠀⠀⠡⠀⠀⠀⢀⣳⠫⢿⣿⣿⢟⣋⣿ ⡷⣶⣾⠇⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣸⠀⠁⠀⠀⠈⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢻⣿⣿⣿⣿⢿⣷⣄⠀⠀⠀⠀⠀⠈⠁⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⢸⣟⣇⡮⣦⣄⣀⢿⡛ ⡟⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢽⠀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢢⣄⣀⣀⣀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠚⢿⣿⣿⣿⣚⣑⣛⣷ ⣇⣁⣉⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢸⠁⣾⠀⠀⠀⠀⣶⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠿⠟⠟⠛⠿⠻⠿⠛⣿⣿⣿⣿⣿⣿⡿⢸⣿⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠂⠙⠊⠁⠈⠙⠛⠋⠛ ⣏⠋⠛⠁⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⣿⠖⠆⠆⡆⢸⠀⠀⣀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣉⣿⠻⣛⡻⠿⠛⢨⣿⠲⠶⠶⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⣀⣿⣟⣾⡿⣿⢌⣿⣿ ⣯⠋⠛⠃⠀⠸⣷⠆⠀⠀⠀⠀⠀⣦⠀⢸⢿⣿⣻⣿⣿⣧⣹⠀⠈⠉⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣠⣀⣀⣀⣀⣀⣀⣉⣋⣁⣀⣀⣀⣀⣀⣸⣷⠀⠀⢀⣡⡾⠏⠀⠀⠀⠀⠀⠠⠀⠁⠀⠟⠿⠿⠿⠻⠿⠳⣿⣿ ⣞⣿⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡿⠻⠛⡻⠓⢻⠒⠒⠒⢸⣿⣿⣿⣿⠆⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠾⣿⣶⣶⣟⡏⠁⠄⠐⠀⠀⠀⠀⢀⡄⠀⠂⠀⠀⠀⣀⣀⣀⣸⣿⣿ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⢸⠀⠀⠀⢸⣿⡿⠿⠿⠎⠀⣀⠴⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡀⣿⠉⠉⠉⢁⠀⠀⠀⠠⣀⠀⢀⠀⢠⠀⠀⠀⠁⠀⠀⠙⠛⠛⠛⠻ ⡯⣿⡟⠛⠙⠹⠇⠀⠀⠀⣴⡄⠀⠀⠀⠀⢈⣅⣬⣠⣈⣇⣀⢀⣀⣄⠐⣷⣇⣀⣀⣀⣀⣀⣀⣀⡀⠀⠰⠀⠀⠀⣀⣀⣀⠀⠂⠀⠀⠀⠀⠀⠀⣿⠀⠀⠁⠀⠀⠀⠀⠁⢒⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⣶⡶⠶⠶⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠠⠆ ⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⢶⠶⠆⢶⠲⢤⡶⠒⠒⠒⠶⠶⠶⠲⢺⡈⣍⠉⠎⠀⠀⠀⢴⣻⢿⡿⠾⠷⣾⣿⣟⣷⣿⣿⣻⣿⡿⣿⠿⣾⣷⣿⣿⣿⣿⣾⣶⣿⣾⣟⣗⣿⣿⣿⢿⣿⠿⠛⠛⠻⠟⠻⠟⠿⠿⠿⠿⠿⠿⠦⠆⠀⠀⠀⠀⣤⠀ ⣷⣶⣶⣶⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢸⡧⢾⠀⠀⠀⠀⠀⠀⠀⠀⡿⠷⠿⠿⠿⠿⠿⠛⠛⠛⡿⠟⠃⣠⣿⣛⣿⣿⣟⣻⡿⠛⠿⠽⠿⠿⢿⣯⣮⣥⣴⣥⣿⣾⣿⣿⣾⣟⣷⣦⣮⣭⣾⣿⣶⣿⣾⣿⣿⣦⣦⣤ ⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⣮⡀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠆⢠⣌⣿⡿⡿⣿⣿⣿⢿⠿⣿⣏⡿⢗⣿⣿⣞⡾⡟⣿⣿⢿⡭⠽⣭⣯⣿⡿⠯⠭⣽⠿⠽⠿⢯⣿⣿⣿⣛⣟⡛⢙⣋⣛ ⡿⠿⠿⠛⠃⠆⠙⠉⠹⠿⠿⠟⠛⠉⠙⠻⠻⣿⠃⠀⠃⡄⠀⠀⠆⠠⣿⣿⣿⣿⣿⣿⣿⠀⣸⣿⣿⠇⣃⣿⣿⣿⠘⣖⣿⣿⣇⢐⢾⣿⡿⠇⡏⣿⠀⣿⣶⡮⣿⠷⡙⠿⢿⡯⢿⣿⣾⣿⡿⣿⠿⡿⡿⣿⢿⢹⡷⠿ ⠿⠷⠶⠿⠆⢀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⡀⢀⡄⠀⠆⣑⡌⢾⣿⣿⣿⣿⣿⣿⢀⠘⣭⣭⡁⠉⣽⣿⣯⢥⠹⣿⣿⡭⢌⢺⣽⣧⣤⣶⣷⠋⠘⣿⣿⣿⣿⣿⣥⣤⣤⣤⣤⣤⣀⣤⣄⣀⣤⣼⣿⣿⣞⣷⣦ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠱⠈⠁⣆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠠⠀⣿⣿⠃⠀⣿⣿⣿⠘⠈⣿⣿⡇⢘⡘⣿⣿⠇⣇⣿⠠⣄⡩⠍⠭⡉⠭⢍⠉⢿⢿⣿⢛⡛⢟⢻⣿⢿⢟⣟⣿⠻⢻⣗ ⣯⡯⣩⠉⠹⢭⡍⠉⠉⠿⡉⠉⠉⠉⠉⢙⠉⠱⠆⠀⠀⠰⠛⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⠀⢶⣿⣭⡤⡔⣿⣿⣯⢠⣸⣿⣿⡅⠤⠟⠟⠫⠀⠛⡟⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠉⠀⣴⠀⠀⠀⠒⠇⠒⠇⠫⣉⣁⣠ ⣷⣶⡶⡶⣾⡏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢰⠀⠀⠀⠀⠆⠀⠂⠀⣻⣿⣿⣿⣿⣿⣿⠀⠸⣿⡿⣃⠃⣻⣿⣟⣘⡀⣿⣿⣇⡐⠐⠀⠂⠀⢸⡗⠀⠀⡀⠀⠀⠂⢶⣶⣶⣷⣾⠟⠓⠻⣿⣿⣿⣇⣈⣛⢻⣟⢻⣟ ⠖⢒⠒⠲⠃⣺⣶⡄⠀⠀⠀⠀⢀⡠⢀⣸⠀⠈⣤⡄⠀⠀⠀⠀⠁⠐⢸⣿⣿⣿⣿⣿⣿⠀⣘⠛⠃⠀⠀⢽⠯⠭⠀⢠⣭⠉⠀⠀⠀⠀⠀⠀⣾⡯⠀⠀⠁⠀⠀⠀⠈⠉⠈⠉⠉⠀⠀⠀⠉⠛⢟⡻⠃⣀⣛⡻⢎⠙ ⡏⠛⢻⣧⡤⠌⠙⠃⠠⠀⠀⠀⠜⠃⠜⢻⠀⢰⠋⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡇⠀⠀⠀⠀⠀⢠⣾⣿⠀⢠⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⣭⠰⠿⠭⢿⣦⣵⣯ ⡋⠛⠛⠛⠃⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠀⣠⠀⠀⠀⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⢀⡀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⠋⢻⣒⢟⠒⣃⣓ ⡷⡶⣾⠇⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣸⠀⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠻⢯⢿⢿⣿⠷⠷⣀⠀⠀⠀⠀⠀⠈⠁⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⡇⠊⣤⢄⣀⢻⠋ ⡟⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢩⠀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢢⣀⡀⡀⢀⢸⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⣿⣶⣒⣀⡛⣳ ⣇⣁⣉⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢸⠁⡾⠀⠀⠀⠀⣶⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠙⠐⠟⠓⠻⠛⠛⠛⠾⣿⣿⣿⣿⣟⠏⢸⣿⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠈⠙⠛⠋⠙ ⣏⠉⠉⠁⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⡿⠒⠆⠆⡆⢸⠀⠀⣀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠻⣛⠻⠿⠃⢨⡿⠒⠶⠶⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⣀⣿⣗⣾⡿⣿⠀⢯⣯ ⣯⠋⠛⠃⠀⠸⣷⠂⠀⠀⠀⠀⠀⣤⠀⢸⢿⣷⣳⣿⣿⣇⣹⠀⠈⠉⢽⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣉⣋⣁⣀⣀⣀⣀⣀⣸⡇⠀⠀⠀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠻⠛⠻⠻⠿⠀⣿⣿ ⣎⣷⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡿⠻⠛⡻⠓⢻⠒⠒⠒⢸⣿⣿⣿⣿⠆⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠸⡇⣶⣶⣛⡏⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣰⣳⣷ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⢨⠀⠀⠀⢸⣿⡿⠿⠿⠎⠀⣀⠴⠶⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡧⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠻ ⡯⣿⡏⠛⠙⠹⠇⠀⠀⠀⢴⡄⠀⠀⠀⠀⢈⣅⣬⣠⣈⣇⣀⢀⣀⣄⠀⣷⠆⠀⠀⠀⡀⣀⣀⣀⠀⠀⠰⠀⠀⠀⠀⢀⣀⠀⠂⠀⠀⠀⠀⠀⠀⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⣶⡶⠶⠶⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠠⠆ ⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⢶⠶⠆⢶⠲⢤⡶⠒⠒⠒⠶⠶⠶⠲⢺⡈⣍⠉⠎⠀⠀⠀⢴⣻⢿⡿⠾⠷⣾⣿⣟⣷⣿⣿⣻⣿⡿⣿⠿⣾⣷⣿⣿⣿⣿⣾⣶⣿⣾⣟⣗⣿⣿⣿⢿⣿⠿⠛⠛⠻⠟⠻⠟⠿⠿⠿⠿⠿⠿⠦⠆⠀⠀⠀⠀⣤⠀ ⣷⣶⣶⣶⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢸⡧⢾⠀⠀⠀⠀⠀⠀⠀⠀⡿⠷⠿⠿⠿⠿⠿⠛⠛⠛⡿⠟⠃⣠⣿⣛⣿⣿⣟⣻⡿⠛⠿⠽⠿⠿⢿⣯⣮⣥⣴⣥⣿⣾⣿⣿⣿⣟⣷⣦⣮⣭⣾⣿⣶⣿⣾⣿⣿⣦⣦⣤ ⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⣮⡀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠆⢠⣌⣿⡿⡿⣿⣿⣿⢿⠿⣿⣏⡿⢗⣿⣿⣞⡾⡟⣿⣿⢿⡭⠽⣭⣯⣿⡿⠯⠭⣽⠿⠽⠿⢯⣿⣿⣿⣛⣟⡛⢙⣋⣛ ⡿⠿⠿⠛⠃⠆⠙⠉⠹⠿⠿⠟⠛⠉⠙⠻⠻⣿⠃⠀⠃⡄⠀⠀⠆⠠⣿⣿⣿⣿⣿⣿⣿⠀⣸⣿⣿⠇⣃⣿⣿⣿⠘⣖⣿⣿⣇⢐⢾⣿⡿⠇⡏⣿⠀⣿⣶⡮⣿⠷⡙⠿⢿⡯⢿⣿⣾⣿⡿⣿⠿⡿⡿⣿⢿⢹⡷⠿ ⠿⠷⠶⠿⠆⢀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⡀⢀⣄⠀⠆⣑⡌⢾⣿⣿⣿⣿⣿⣿⢀⠘⣭⣭⡁⠉⣽⣿⣯⢥⠹⣿⣿⡭⢌⢺⣽⣧⣤⣶⣷⠋⠘⣿⣿⣿⣿⣿⣥⣤⣤⣤⣤⣤⣀⣤⣄⣀⣤⣼⣿⣿⣞⣷⣦ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠱⠈⠙⣆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣟⠠⠀⣿⣿⠃⠀⣿⣿⣿⠘⠈⣿⣿⡇⢘⡘⣿⣿⠇⣇⣿⠠⣄⡩⠍⠭⡉⠭⢍⠉⢿⢿⣿⢛⡛⢟⣻⣿⢿⢟⣟⣿⠻⢻⣗ ⣯⡯⣩⠉⠹⢭⡍⠉⠉⠿⡉⠉⠉⠉⠉⢙⠉⠱⠆⠀⠀⠰⠛⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⠀⢶⣿⣭⡤⡔⣿⣿⣯⢠⣸⣿⣿⡅⠤⠟⠟⠫⠀⠛⡟⠀⢀⡀⠀⠀⠀⠀⠀⠠⣄⠉⠀⣴⠀⠀⠀⠒⠇⠒⠇⠫⣉⣁⣠ ⣷⣶⡶⡶⣾⡏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢰⠀⠀⠀⠀⠆⠀⠂⠀⣻⣿⣿⣿⣿⣿⣿⠀⠸⣿⡿⣃⠃⣻⣿⣟⣘⡀⣿⣿⣇⡐⠐⠀⠂⠀⢸⡗⠀⠀⡁⠀⠀⠂⢶⣶⣶⣷⣾⠟⠓⠻⣿⣿⣿⣇⣈⣛⢻⣟⢻⣟ ⠖⢒⠒⠲⠃⣺⣶⡄⠀⠀⠀⠀⢀⡠⢀⣸⠀⠈⣤⡄⠀⠀⠀⠀⠁⠐⢸⣿⣿⣿⣿⣿⣿⠀⣘⠛⠃⠀⠀⢽⠯⠭⠀⢠⣭⠉⠀⠀⠀⠀⠀⠀⣾⡯⢠⡄⠁⠀⠀⠀⠈⠉⠈⠉⠉⣀⠀⠀⠉⠛⢟⡻⠃⣀⣛⡻⢎⠙ ⡏⠛⢻⣧⡤⠌⠙⠃⠠⠀⠀⠀⠜⠃⠜⢻⠀⢰⠋⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡇⠀⠀⠀⠀⠀⢠⣾⣿⠈⢠⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⣭⠰⠿⠭⢿⣦⣵⣯ ⡋⠛⠛⠛⠃⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠀⣠⠀⠀⠀⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⢀⡀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⠋⢻⣒⢟⠒⣃⣓ ⡷⡶⣾⠇⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣸⠀⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠻⢯⢿⢿⣿⠷⠷⣀⠀⠀⠀⠀⠀⠈⠁⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⡇⠊⣤⢄⣀⢻⠋ ⡟⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢩⠀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢢⣀⡀⡀⢀⢸⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⣿⣶⣒⣀⡛⣳ ⣇⣁⣉⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢸⠁⡾⠀⠀⠀⠀⣶⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠙⠐⠟⠓⠻⠛⠛⠛⠾⣿⣿⣿⣿⣟⠏⢸⣿⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠈⠙⠛⠋⠙ ⣏⠉⠉⠁⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⡿⠒⠆⠆⡆⢸⠀⠀⣀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠻⣛⠻⠿⠃⢨⡿⠒⠶⠶⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⣀⣿⣗⣾⡿⣿⠀⢯⣯ ⣯⠋⠛⠃⠀⠸⣷⠂⠀⠀⠀⠀⠀⣤⠀⢸⢿⣷⣳⣿⣿⣇⣹⠀⠈⠉⢽⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣉⣋⣁⣀⣀⣀⣀⣀⣸⡇⠀⠀⠀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠻⠛⠻⠻⠿⠀⣿⣿ ⣎⣷⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡿⠻⠛⡻⠓⢻⠒⠒⠒⢸⣿⣿⣿⣿⠆⠒⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠸⡇⣶⣶⣛⡏⠀⠀⠀⠀⠀⠀⠀⠛⡀⠀⠀⠀⠀⠀⣀⣀⣀⣰⣳⣷ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⢨⠀⠀⠀⢸⣿⡿⠿⠿⠎⠀⣀⠴⠶⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡧⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠻ ⡯⣿⡏⠛⠙⠹⠇⠀⠀⠀⢴⡄⠀⠀⠀⠀⢈⣅⣬⣠⣈⣇⣀⢀⣀⣄⠀⣷⠆⠀⠀⠀⡀⣀⣀⣀⠀⠀⠰⠀⠀⠀⠀⢀⣀⠀⠂⠀⠀⠀⠀⠀⠀⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⣶⡶⠶⠶⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠠⠆ ⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⢶⠶⠆⢶⠲⢤⡶⠒⠒⠒⠶⠶⠶⠲⢸⡈⣍⠉⠎⠀⠀⠀⢴⣻⢿⡿⠾⠷⣾⣿⣟⣷⣿⣿⣻⣿⡿⣿⠷⣾⣷⣿⣿⣿⣿⣾⣶⣿⣾⣟⣗⣿⣿⣿⢿⣿⠿⠛⠛⠻⠟⠻⠟⠿⠿⠿⠿⠿⠿⠦⠆⠀⠀⠀⠀⣤⠀ ⣷⣶⣶⣶⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢸⡧⢾⠀⠀⠀⠀⠀⠀⠀⠀⡿⠷⠿⠿⠿⠿⠿⠛⠛⠛⡿⠟⠃⣠⣿⣛⣿⣿⣟⣻⡿⠛⠿⠽⠿⠿⢿⣯⣮⣥⣴⣥⣿⣾⣿⣿⣿⣟⣷⣦⣮⣭⣾⣿⣶⣿⣾⣿⣿⣦⣦⣤ ⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⣮⡀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠆⢠⣌⣿⡿⡿⣿⣿⣿⢿⠿⣿⣏⡿⢗⣿⣿⣞⡾⡟⣿⣿⢿⡭⠽⣭⣯⣿⡿⠯⠭⣽⠿⠽⠿⢯⣿⣿⣿⣛⣟⡛⢙⣋⣛ ⡿⠿⠿⠛⠃⠆⠙⠉⠹⠿⠿⠟⠛⠉⠙⠻⠻⣿⠃⠀⠃⡄⠀⠀⠆⠠⣿⣿⣿⣿⣿⣿⣿⠀⣸⣿⣿⠇⣃⣿⣿⣿⠘⣖⣿⣿⣇⢐⢾⣿⡿⠇⡏⣿⠀⣿⣶⡮⣿⠷⡙⠿⢿⡯⢿⣿⣾⣿⡿⣿⠿⡿⡿⣿⢿⢉⡷⠿ ⠿⠷⠶⠿⠆⢀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⡀⢀⣄⠀⠆⣑⡌⢾⣿⣿⣿⣿⣿⣿⢀⠘⣭⣭⡁⠩⣽⣿⣯⢥⠹⣿⣿⡭⢌⢺⣽⣧⣤⣶⣷⠋⠘⣿⣿⣿⣿⣿⣥⣤⣤⣤⣤⣤⣀⣤⣄⣀⣤⣼⣿⣿⣞⣷⣦ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠱⠈⠙⣆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣟⠠⠀⣿⣿⠃⠀⣿⣿⣿⠘⠈⣿⣿⡇⢘⡘⣿⣿⠇⣇⣿⠠⣄⡩⠍⠭⡉⠭⢍⠉⢿⢿⣿⢛⡛⢟⣻⣿⢿⢟⣟⣿⠻⢻⣗ ⣯⡯⣩⠉⠹⢭⡍⠉⠉⠿⡉⠉⠉⠉⠉⢙⠉⠱⠆⠀⠀⠰⠛⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⠀⢶⣿⣭⡤⡔⣿⣿⣯⢠⣸⣿⣿⡅⠤⠟⠟⠫⠀⠛⡟⠀⢀⡀⠀⠀⠀⠀⠀⠠⣄⠉⠀⣴⠀⠀⠀⠒⠇⠒⠇⠫⣉⣁⣠ ⣷⣶⡶⡶⣾⡏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢠⠀⠀⠀⠀⠆⠀⠂⠀⣻⣿⣿⣿⣿⣿⣿⠀⠸⣿⡿⣃⠃⣻⣿⣟⣘⡀⣿⣿⣇⡐⠐⠀⠂⠀⢸⡗⠀⠀⡁⠀⠀⠂⢶⣶⣶⣷⣾⠟⠓⠻⣿⣿⣿⣇⣈⣛⢻⣟⢻⣟ ⠖⢒⠒⠲⠃⣺⣶⡄⠀⠀⠀⠀⢀⡠⢀⣸⠀⠈⣤⡄⠀⠀⠀⠀⠁⠐⢸⣿⣿⣿⣿⣿⣿⠀⣘⠛⠃⠀⠀⢽⠯⠭⠀⢠⣭⠉⠀⠀⠀⠀⠀⠀⣾⡯⢠⡄⠁⠀⠀⠀⠈⠉⠈⠉⠉⣀⠀⠀⠉⠛⢟⡻⠃⣀⣛⡻⢎⠙ ⡏⠛⢻⣧⡤⠌⠙⠃⠠⠀⠀⠀⠜⠃⠜⢻⠀⢰⠋⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡇⠀⠀⠀⠀⠀⢠⣾⣿⠈⢠⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⣭⠰⠿⠭⢿⣦⣵⣯ ⡋⠛⠛⠛⠃⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠀⣠⠀⠀⠀⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⢀⡀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⠋⢻⣒⢟⠒⣃⣓ ⡷⡶⣾⠇⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣸⠀⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠻⢯⢿⢿⣿⠷⠷⣀⠀⠀⠀⠀⠀⠈⠁⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⡇⠊⣤⢄⣀⢻⠋ ⡟⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢩⠀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢢⣀⡀⡀⢀⢸⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⣿⣶⣒⣀⡛⣳ ⣇⣁⣉⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢸⠁⡾⠀⠀⠀⠀⣶⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠙⠐⠟⠓⠻⠛⠛⠛⠾⣿⣿⣿⣿⣟⠏⢸⣷⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠈⠙⠛⠋⠙ ⣏⠉⠉⠁⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⡿⠒⠆⠆⡆⢸⠀⠀⣀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠻⣛⠻⠿⠃⢨⡿⠒⠶⠶⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⣀⣿⣗⣾⡿⣿⠀⢯⣯ ⣯⠋⠛⠃⠀⠸⣷⠂⠀⠀⠀⠀⠀⣤⠀⢸⢿⣷⣳⣿⣿⣇⣹⠀⠈⠉⢽⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣉⣋⣁⣀⣀⣀⣀⣀⣸⡇⠀⠀⠀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠻⠛⠻⠻⠿⠀⣿⣿ ⣎⣷⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡿⠻⠛⡻⠓⢻⠒⠒⠒⢸⣿⣿⣿⣿⠆⠒⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠸⡇⣶⣶⣛⡏⠀⠀⠀⠀⠀⠀⠀⠛⡀⠀⠀⠀⠀⠀⣀⣀⣀⣰⣳⣷ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⢨⠀⠀⠀⢸⣿⡿⠿⠿⠎⠀⣀⠴⠶⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡇⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠻ ⡯⣿⡏⠛⠙⠹⠇⠀⠀⠀⢴⡄⠀⠀⠀⠀⢈⣅⣬⣠⣈⣇⣀⢀⣀⣄⠀⣷⠆⠀⠀⠀⡀⣀⣀⣀⠀⠀⠰⠀⠀⠀⠀⢀⣀⠀⠂⠀⠀⠀⠀⠀⠀⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⣶⡶⠶⠶⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠠⠆ ⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⢶⠶⠆⢶⠲⢤⡶⠒⠒⠒⠶⠶⠶⠲⢸⡈⣍⠉⠎⠀⠀⠀⢴⣻⢿⡿⠾⠷⣾⣿⣟⣷⣿⣿⣻⣿⡿⣿⠷⣾⣷⣿⣿⣿⣿⣾⣶⣿⣾⣟⣗⣿⣿⣿⢿⣿⠿⠛⠛⠻⠟⠻⠟⠿⠿⠿⠿⠿⠿⠦⠆⠀⠀⠀⠀⣤⠀ ⣷⣶⣶⣶⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢸⡧⢾⠀⠀⠀⠀⠀⠀⠀⠀⡿⠷⠿⠿⠿⠿⠿⠛⠛⠛⡿⠟⠃⣠⣿⣛⣿⣿⣟⣻⡿⠛⠿⠽⠿⠿⢿⣯⣮⣥⣴⣥⣿⣾⣿⣿⣿⣟⣷⣦⣮⣭⣾⣿⣶⣿⣾⣿⣿⣦⣦⣤ ⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⣮⡀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠆⢠⣌⣿⡿⡿⣿⣿⣿⢿⠿⣿⣏⡿⢗⣿⣿⣞⡾⡟⣿⣿⢿⡭⠽⣭⣯⣿⡿⠯⠭⣽⠿⠽⠿⢯⣿⣿⣿⣛⣟⡛⢙⣋⣻ ⡿⠿⠿⠛⠃⠆⠙⠉⠹⠿⠿⠟⠛⠉⠙⠻⠻⣿⠃⠀⠃⡄⠀⠀⠆⠠⣿⣿⣿⣿⣿⣿⣿⠀⣸⣿⣿⠇⣃⣿⣿⣿⠘⣖⣿⣿⣇⢐⢾⣿⡿⠇⡏⣿⠀⣿⣶⡮⣿⠷⡙⠿⢿⡯⢿⣿⣾⣿⡿⣿⠿⡿⡿⣿⢿⢉⡷⠿ ⠿⠷⠶⠿⠆⢀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⡀⢀⣄⠀⠆⣑⡌⢾⣿⣿⣿⣿⣿⣿⢀⠘⣭⣭⡁⠩⣽⣿⣯⢥⠹⣿⣿⡭⢌⢺⣽⣧⣤⣶⣷⠋⠘⣿⣿⣿⣿⣿⣥⣤⣤⣤⣤⣤⣀⣤⣄⣀⣤⣼⣿⣿⣞⣷⣦ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠱⠈⠙⣆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣟⠠⠀⣿⣿⠃⠀⣿⣿⣿⠘⠈⣿⣿⡇⢘⡘⣿⣿⠇⣇⣿⠠⣄⡩⠍⠭⡉⠭⢍⠉⢿⢿⣿⢛⡛⢟⣻⣿⢿⢟⣟⣿⠻⢻⣗ ⣯⡯⣩⠉⠹⢭⡍⠉⠉⠿⡉⠉⠉⠉⠉⢙⠉⠱⠆⠀⠀⠰⠛⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⠀⢶⣿⣭⡤⡐⣿⣿⣯⢠⣸⣿⣿⡅⠤⠟⠟⠫⠀⠛⡟⠀⢀⡀⠀⠀⠀⠀⠀⠠⣄⠉⠀⣴⠀⠀⠀⠒⠇⠒⠇⠫⣉⣁⣠ ⣷⣶⡶⡶⣾⡏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢠⠀⠀⠀⠀⠆⠀⠂⠀⣻⣿⣿⣿⣿⣿⣿⠀⠸⣿⡿⣃⠃⣻⣿⣟⣘⡀⣿⣿⣇⡐⠐⠀⠂⠀⢸⡗⠀⠀⡁⠀⠀⠂⢶⣶⣶⣷⣾⠟⠓⠻⣿⣿⣿⣇⣈⣛⢻⣟⢻⣟ ⠖⢒⠒⠲⠃⣺⣶⡄⠀⠀⠀⠀⢀⡠⢀⣸⠀⠈⣤⡄⠀⠀⠀⠀⠁⠐⢸⣿⣿⣿⣿⣿⣿⠀⣘⠛⠃⠀⠀⢽⠯⠭⠀⢠⣭⠉⠀⠀⠀⠀⠀⠀⣾⡯⢠⡄⠁⠀⠀⠀⠈⠉⠈⠉⠉⣀⠀⠀⠉⠛⢟⡻⠃⣀⣛⡻⢎⠙ ⡏⠛⢻⣧⡤⠌⠙⠃⠠⠀⠀⠀⠜⠃⠜⢻⠀⢰⠋⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡇⠀⠀⠀⠀⠀⢠⣾⣿⠈⢠⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⣭⠰⠿⠭⢿⣦⣵⣯ ⡋⠛⠛⠛⠃⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠀⣠⠀⠀⠀⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⢀⡀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⠋⢻⣒⢟⠒⣃⣓ ⡷⡶⣾⠇⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣸⠀⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠻⢯⢿⢿⣿⠷⠷⣀⠀⠀⠀⠀⠀⠈⠁⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⡇⠊⣤⢄⣀⢻⠋ ⡟⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢩⠀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢢⣀⡀⡀⢀⢸⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⣿⣶⣒⣀⡛⣳ ⣇⣁⣉⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢸⠁⡾⠀⠀⠀⠀⣶⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠙⠐⠟⠓⠻⠛⠛⠛⠾⣿⣿⣿⣿⣟⠏⢸⣷⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠈⠙⠛⠋⠙ ⣏⠉⠉⠁⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⡿⠒⠆⠆⡆⢸⠀⠀⣀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠻⣛⠻⠿⠃⢨⡿⠒⠶⠶⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⣀⣿⣗⣾⡿⣿⠀⢯⣯ ⣯⠋⠛⠃⠀⠸⣷⠂⠀⠀⠀⠀⠀⣤⠀⢸⢿⣷⣳⣿⣿⣇⣹⠀⠈⠉⢽⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣉⣋⣁⣀⣀⣀⣀⣀⣸⡇⠀⠀⠀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠻⠛⠻⠻⠿⠀⣿⣿ ⣎⣷⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡿⠻⠛⡻⠓⢻⠒⠒⠒⢸⣿⣿⣿⣿⠆⠒⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠸⡇⣶⣶⣛⡏⠀⠀⠀⠀⠀⠀⠀⠛⡀⠀⠀⠀⠀⠀⣀⣀⣀⣰⣳⣷ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⢨⠀⠀⠀⢸⣿⡿⠿⠿⠎⠀⣀⠴⠶⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡇⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠻ ⡯⣿⡏⠛⠙⠹⠇⠀⠀⠀⢴⡄⠀⠀⠀⠀⢈⣅⣬⣠⣈⣇⣀⢀⣀⣄⠀⣷⠆⠀⠀⠀⡀⣀⣀⣀⠀⠀⠰⠀⠀⠀⠀⢀⣀⠀⠂⠀⠀⠀⠀⠀⠀⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⣶⡶⠶⠶⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠠⠆ ⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⢶⠶⠆⢶⠲⢤⡶⠒⠒⠒⠶⠶⠶⠲⢺⡈⣍⠉⠎⠀⠀⠀⢴⣻⢿⡿⠾⠷⣾⣿⣟⣷⣿⣿⣻⣿⡿⣿⠿⣾⣷⣿⣿⣿⣿⣾⣶⣿⣾⣟⣗⣿⣿⣿⢿⣿⠿⠛⠛⠻⠟⠻⠟⠿⠿⠿⠿⠿⠿⠦⠆⠀⠀⠀⠀⣤⠀ ⣷⣶⣶⣶⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢸⡧⢾⠀⠀⠀⠀⠀⠀⠀⠀⡿⠷⠿⠿⠿⠿⠿⠛⠛⠛⡿⠟⠃⣠⣿⣛⣿⣿⣟⣻⡿⠛⠿⠽⠿⠿⢿⣯⣮⣥⣴⣥⣿⣾⣿⣿⣿⣟⣷⣦⣮⣭⣾⣿⣶⣿⣾⣿⣿⣦⣦⣤ ⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⣮⡀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠆⢠⣌⣿⡿⡿⣿⣿⣿⢿⠿⣿⣏⡿⢗⣿⣿⣞⡾⡟⣿⣿⢿⡭⠽⢉⣯⣿⡿⠯⠭⣽⠿⠽⠿⢯⣿⣿⣿⣛⣟⡛⢙⣋⣻ ⡿⠿⠿⠛⠃⠆⠙⠉⠹⠿⠿⠟⠛⠉⠙⠻⠻⣿⠃⠀⠃⡄⠀⠀⠆⠠⣿⣿⣿⣿⣿⣿⣿⠀⣸⣿⣿⠇⣃⣿⣿⣿⠘⣖⣿⣿⣇⢐⢾⣿⡿⠇⡏⣿⠀⣿⣶⡮⣿⠷⡙⠿⢿⡯⢿⣿⣾⣿⡿⣿⠿⡿⡿⣿⢿⢉⡷⠿ ⠿⠷⠶⠿⠆⢀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⡀⢀⣄⠀⠆⣑⡌⢾⣿⣿⣿⣿⣿⣿⢀⠘⣭⣭⡁⠩⣽⣿⣯⢥⠹⣿⣿⡭⢌⢺⣽⣧⣤⣶⣷⠋⠘⣿⣿⣿⣿⣿⣥⣤⣤⣤⣤⣤⣀⣤⣄⣀⣤⣼⣿⣿⣞⣷⣦ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠱⠈⠙⣆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣟⠠⠀⣿⣿⠃⠀⣿⣿⣿⠘⠈⣿⣿⡇⢘⡘⣿⣿⠇⣇⣿⠠⣄⡩⠍⠭⡉⠭⢍⠉⢿⢿⣿⢛⡛⢟⣻⣿⢿⢟⣟⣿⠻⢻⣗ ⣯⡯⣩⠉⠹⢭⡍⠉⠉⠿⡉⠉⠉⠉⠉⢙⠉⠱⠆⠀⠀⠰⠛⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⠀⢶⣿⣭⡤⡐⣿⣿⣯⢠⣸⣿⣿⡅⠤⠟⠟⠫⠀⠛⡟⠀⢀⡀⠀⠀⠀⠀⠀⠠⣄⠉⠀⣴⠀⠀⠀⠒⠇⠒⠇⠫⣉⣁⣠ ⣷⣶⡶⡶⣾⡏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢰⠀⠀⠀⠀⠆⠀⠂⠀⣻⣿⣿⣿⣿⣿⣿⠀⠸⣿⡿⣃⠃⣻⣿⣟⣘⡀⣿⣿⣇⡐⠐⠀⠂⠀⢸⡗⠀⠀⡁⠀⠀⠂⢶⣶⣶⣷⣾⠟⠓⠻⣿⣿⣿⣇⣈⣛⢻⣟⢻⣟ ⠖⢒⠒⠲⠃⣺⣶⡄⠀⠀⠀⠀⢀⡠⢀⣸⠀⠈⣤⡄⠀⠀⠀⠀⠁⠐⢸⣿⣿⣿⣿⣿⣿⠀⣘⠛⠃⠀⠀⢽⠯⠭⠀⢠⣭⠉⠀⠀⠀⠀⠀⠀⣾⡯⢠⡄⠁⠀⠀⠀⠈⠁⠈⠉⠉⣀⠀⠀⠉⠛⢟⡻⠃⣀⣛⡻⢎⠙ ⡏⠛⢻⣧⡤⠌⠙⠃⠠⠀⠀⠀⠜⠃⠜⢻⠀⢰⠋⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡇⠀⠀⠀⠀⠀⢠⣾⣿⠈⢠⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⣭⠰⠿⠭⢿⣦⣵⣯ ⡋⠛⠛⠛⠃⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠀⣠⠀⠀⠀⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⢀⡀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⠋⢻⣒⢟⠒⣃⣓ ⡷⡶⣾⠇⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣸⠀⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠻⢯⢿⢿⣿⠷⠷⣀⠀⠀⠀⠀⠀⠈⠁⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⡇⠊⣤⢄⣀⢻⠋ ⡟⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢩⠀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢢⣀⡀⡀⢀⢸⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⣿⣶⣒⣀⡛⣳ ⣇⣁⣉⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢸⠁⡾⠀⠀⠀⠀⣶⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠙⠐⠟⠓⠻⠛⠛⠛⠾⣿⣿⣿⣿⣟⠏⢸⣿⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠈⠙⠛⠋⠙ ⣏⠉⠉⠁⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⡿⠒⠆⠆⡆⢸⠀⠀⣀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠻⣛⠻⠿⠃⢨⡿⠒⠶⠶⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⣀⣿⣗⣾⡿⣿⠀⢯⣯ ⣯⠋⠛⠃⠀⠸⣷⠂⠀⠀⠀⠀⠀⣤⠀⢸⢿⣷⣳⣿⣿⣇⣹⠀⠈⠉⢽⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣉⣋⣁⣀⣀⣀⣀⣀⣸⡇⠀⠀⠀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠻⠛⠻⠻⠿⠀⣿⣿ ⣎⣷⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡿⠻⠛⡻⠓⢻⠒⠒⠒⢸⣿⣿⣿⣿⠆⠒⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠸⡇⣶⣶⣛⡏⠀⠀⠀⠀⠀⠀⠀⠛⡀⠀⠀⠀⠀⠀⣀⣀⣀⣰⣳⣷ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⢨⠀⠀⠀⢸⣿⡿⠿⠿⠎⠀⣀⠴⠶⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡧⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠻ ⡯⣿⡏⠛⠙⠹⠇⠀⠀⠀⢴⡄⠀⠀⠀⠀⢈⣅⣬⣠⣈⣇⣀⢀⣀⣄⠀⣷⠆⠀⠀⠀⡀⣀⣀⣀⠀⠀⠰⠀⠀⠀⠀⢀⣀⠀⠂⠀⠀⠀⠀⠀⠀⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⣶⡶⠶⠶⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠠⠆ ⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⢶⠶⠆⢶⠲⢤⡶⠒⠒⠒⠶⠶⠶⠲⢺⡈⣍⠉⠎⠀⠀⠀⢴⣻⢿⡿⠾⠷⣾⣿⣟⣷⣿⣿⣻⣿⡿⣿⠿⣾⣷⣿⣿⣿⣿⣾⣶⣿⣾⣟⣗⣿⣿⣿⢿⣿⠿⠛⠛⠻⠟⠻⠟⠿⠿⠿⠿⠿⠿⠦⠆⠀⠀⠀⠀⣤⠀ ⣷⣶⣶⣶⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢸⡧⢾⠀⠀⠀⠀⠀⠀⠀⠀⡿⠷⠿⠿⠿⠿⠿⠛⠛⠛⡿⠟⠃⣠⣿⣛⣿⣿⣟⣻⡿⠛⠿⠽⠿⠿⢿⣯⣮⣥⣴⣥⣿⣾⣿⣿⣿⣟⣷⣦⣮⣭⣾⣿⣶⣿⣾⣿⣿⣦⣦⣤ ⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⣮⡀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠆⢠⣌⣿⡿⡿⣿⣿⣿⢿⠿⣿⣏⡿⢗⣿⣿⣞⡾⡟⣿⣿⢿⡭⠽⢉⣯⣿⡿⠯⠭⣽⠿⠽⠿⢯⣿⣿⣿⣛⣟⡛⢙⣋⣻ ⡿⠿⠿⠛⠃⠆⠙⠉⠹⠿⠿⠟⠛⠉⠙⠻⠻⣿⠃⠀⠃⡄⠀⠀⠆⠠⣿⣿⣿⣿⣿⣿⣿⠀⣸⣿⣿⠇⣃⣿⣿⣿⠘⣖⣿⣿⣇⢐⢾⣿⡿⠇⡏⣿⠀⣿⣶⡮⣿⠷⡙⠿⢿⡯⢿⣿⣾⣿⡿⣿⠿⡿⡿⣿⢿⢉⡷⠿ ⠿⠷⠶⠿⠆⢀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⡀⢀⣄⠀⠆⣑⡌⢾⣿⣿⣿⣿⣿⣿⢀⠘⣭⣭⡁⠩⣽⣿⣯⢥⠹⣿⣿⡭⢌⢺⣽⣧⣤⣶⣷⠋⠘⣿⣿⣿⣿⣿⣥⣤⣤⣤⣤⣤⣀⣤⣄⣀⣤⣼⣿⣿⣞⣷⣦ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠱⠈⠙⣆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣟⠠⠀⣿⣿⠃⠀⣿⣿⣿⠘⠈⣿⣿⡇⢘⡘⣿⣿⠇⣇⣿⠠⣄⡩⠍⠭⡉⠭⢍⠉⢿⢿⣿⢛⡛⢟⣻⣿⢿⢟⣟⣿⠻⢻⣗ ⣯⡯⣩⠉⠹⢭⡍⠉⠉⠿⡉⠉⠉⠉⠉⢙⠉⠱⠆⠀⠀⠰⠛⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⠀⢶⣿⣭⡤⡐⣿⣿⣯⢠⣸⣿⣿⡅⠤⠟⠟⠫⠀⠛⡟⠀⢀⡀⠀⠀⠀⠀⠀⠠⣄⠉⠀⣴⠀⠀⠀⠒⠇⠒⠇⠫⣉⣁⣠ ⣷⣶⡶⡶⣾⡏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢰⠀⠀⠀⠀⠆⠀⠂⠀⣻⣿⣿⣿⣿⣿⣿⠀⠸⣿⡿⣃⠃⣻⣿⣟⣘⡀⣿⣿⣇⡐⠐⠀⠂⠀⢸⡗⠀⠀⡁⠀⠀⠂⢶⣶⣶⣷⣾⠟⠓⠻⣿⣿⣿⣇⣈⣛⢻⣟⢻⣟ ⠖⢒⠒⠲⠃⣺⣶⡄⠀⠀⠀⠀⢀⡠⢀⣸⠀⠈⣤⡄⠀⠀⠀⠀⠁⠐⢸⣿⣿⣿⣿⣿⣿⠀⣘⠛⠃⠀⠀⢽⠯⠭⠀⢠⣭⠉⠀⠀⠀⠀⠀⠀⣾⡯⢠⡄⠁⠀⠀⠀⠈⠁⠈⠉⠉⣀⠀⠀⠉⠛⢟⡻⠃⣀⣛⡻⢎⠙ ⡏⠛⢻⣧⡤⠌⠙⠃⠠⠀⠀⠀⠜⠃⠜⢻⠀⢰⠋⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡇⠀⠀⠀⠀⠀⢠⣾⣿⠈⢠⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⣭⠰⠿⠭⢿⣦⣵⣯ ⡋⠛⠛⠛⠃⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠀⣠⠀⠀⠀⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⢀⡀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⠋⢻⣒⢟⠒⣃⣓ ⡷⡶⣾⠇⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣸⠀⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠻⢯⢿⢿⣿⠷⠷⣀⠀⠀⠀⠀⠀⠈⠁⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⡇⠊⣤⢄⣀⢻⠋ ⡟⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢩⠀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢢⣀⡀⡀⢀⢸⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⣿⣶⣒⣀⡛⣳ ⣇⣁⣉⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢸⠁⡾⠀⠀⠀⠀⣶⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠙⠐⠟⠓⠻⠛⠛⠛⠾⣿⣿⣿⣿⣟⠏⢸⣿⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠈⠙⠛⠋⠙ ⣏⠉⠉⠁⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⡿⠒⠆⠆⡆⢸⠀⠀⣀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠻⣛⠻⠿⠃⢨⡿⠒⠶⠶⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⣀⣿⣗⣾⡿⣿⠀⢯⣯ ⣯⠋⠛⠃⠀⠸⣷⠂⠀⠀⠀⠀⠀⣤⠀⢸⢿⣷⣳⣿⣿⣇⣹⠀⠈⠉⢽⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣉⣋⣁⣀⣀⣀⣀⣀⣸⡇⠀⠀⠀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠻⠛⠻⠻⠿⠀⣿⣿ ⣎⣷⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡿⠻⠛⡻⠓⢻⠒⠒⠒⢸⣿⣿⣿⣿⠆⠒⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠸⡇⣶⣶⣛⡏⠀⠀⠀⠀⠀⠀⠀⠛⡀⠀⠀⠀⠀⠀⣀⣀⣀⣰⣳⣷ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⢨⠀⠀⠀⢸⣿⡿⠿⠿⠎⠀⣀⠴⠶⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡧⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠻ ⡯⣿⡏⠛⠙⠹⠇⠀⠀⠀⢴⡄⠀⠀⠀⠀⢈⣅⣬⣠⣈⣇⣀⢀⣀⣄⠀⣷⠆⠀⠀⠀⡀⣀⣀⣀⠀⠀⠰⠀⠀⠀⠀⢀⣀⠀⠂⠀⠀⠀⠀⠀⠀⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⣶⡶⠶⠶⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠠⠆ ⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⢶⠶⠆⢶⠲⢤⡶⠒⠒⠒⠶⠶⠶⠲⢺⡈⣽⠉⠎⠀⠀⠀⢴⣿⢿⡿⠾⠷⣾⣿⣟⣷⣿⣿⣻⣿⡿⣿⠿⣾⣷⣿⣿⣿⣿⣾⣶⣿⣾⣟⣗⣿⣿⣿⢿⣿⠿⠟⠛⠿⠟⠻⠟⠿⠿⠿⠿⠿⠿⠦⠆⠀⠀⠀⠀⣤⠀ ⣷⣶⣶⣶⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢸⡧⢾⠀⠀⠀⠀⠀⠀⠀⢸⡿⠷⠿⠿⠇⠀⠘⠻⠿⠿⡿⠿⠇⣠⣿⣛⣿⣿⣷⣷⡸⠟⠿⠟⣿⣿⣿⣿⣿⣷⣶⣷⣿⣶⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣽⣾⣿⣿⣦⣦⣤ ⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⣮⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⣾⣶⡄⠈⢻⣿⣿⠉⠉⣿⣿⣿⠉⢉⣿⣿⡟⠉⣿⣄⠈⠽⣿⢿⣭⠽⢉⣯⣿⡿⡿⠯⣽⠿⠿⠿⢯⣿⣿⣧⣚⣟⡛⢙⣋⣻ ⡿⠿⠿⠛⠃⠆⠙⠉⠹⠿⠿⠟⠛⠉⠙⠻⠻⣿⠃⠀⠃⡄⠀⠀⠆⢸⣿⣿⣿⣿⡇⠀⣿⣿⣇⣀⣾⣿⣿⣄⣀⣼⣿⣯⣀⣀⣿⣿⢷⣀⣿⠙⠀⣳⠄⣿⣷⡮⣿⡷⡙⠿⣿⡯⢿⣿⣾⣿⡿⣿⠿⡿⡿⣿⢿⢉⡷⠿ ⠿⠷⠶⠿⠆⢠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⡀⢀⣄⠀⠆⣑⢜⣿⣿⣿⣿⡇⠀⣾⣶⡎⠉⢹⣷⣿⠈⠉⢹⣷⣧⠈⢩⣿⣾⡎⠉⣿⠀⠀⣳⠋⠘⣿⣿⣿⣿⣿⣥⣤⣤⣤⣤⣥⣀⣤⣄⣤⣤⣼⣿⣿⣞⣷⣦ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠱⠈⠙⣆⠀⠀⢸⣹⣿⣿⣿⡇⠀⠹⠿⠁⢀⣻⠿⠿⣠⣴⣿⠿⠏⣠⣸⡿⢿⡁⣀⣿⠀⠂⣻⠠⣄⡩⠍⠭⡙⠭⢍⠉⢿⢿⣿⢻⡟⣟⣻⣿⢿⢟⣟⣿⠻⢿⣷ ⣯⡯⣩⠉⠹⢭⡍⠉⠉⠿⡉⠉⠉⠉⠉⢙⠉⠱⠆⠀⠀⠰⠛⠀⠀⢸⣼⣿⣿⣿⡇⠀⣿⣿⡇⠈⢹⣿⣿⠀⢀⣹⣿⣷⠀⢸⡅⠤⠟⠟⣿⠀⠂⣿⠂⢀⡀⠀⠀⠀⠀⠁⠠⣄⠉⠀⣶⠀⠀⠀⠒⠇⠒⠇⠯⣉⣁⣡ ⣷⣶⡶⣶⣾⡏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢰⠀⠀⠀⠀⠆⠀⠂⢸⣻⣿⣿⣿⡇⠀⢸⠛⠠⣽⡿⣛⠓⣫⣭⣝⣛⡃⣬⣽⣇⡐⠐⠀⣿⠈⡀⣟⠀⠈⡡⠀⠀⠂⢶⣶⣶⣷⣾⡟⠓⠿⣿⣿⣿⣇⣈⣛⣻⣟⢻⣟ ⠖⢒⠒⡲⠃⣺⣶⡄⠀⠀⠀⠀⢀⡠⢀⣸⠀⠈⣤⡄⠀⠀⠀⠀⠁⢸⢸⣿⣿⣿⡇⠀⢸⠀⣘⠛⠃⠀⠀⢽⠯⠭⠀⢠⣭⠉⠀⠀⠀⠀⣿⠀⠀⣯⢠⡄⠁⠀⠀⠀⠈⠁⠈⠉⠉⣀⠀⠀⠉⠛⢟⡿⠇⣀⣻⡻⢏⠙ ⡏⠛⢻⣧⡤⠌⠙⠃⠠⠀⠀⠀⠜⠃⠜⢻⠀⢰⠋⠃⠀⠀⠀⠀⠀⢸⣺⣿⣿⣿⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡇⠀⠀⠀⠀⣿⠀⠁⣿⠈⢠⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⣭⢰⠿⠭⢿⣦⣽⣯ ⡋⠛⠛⠛⠃⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠀⣠⠀⠀⠀⠃⠀⠀⠀⠸⢿⣿⣿⣿⡇⠀⢸⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⠋⢿⣒⢟⠛⣋⣓ ⡷⡶⣾⠇⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣸⠀⠁⠀⠀⠈⠀⠀⢸⢿⣿⣿⣿⡇⠀⢸⠀⠀⠀⠀⢻⢿⣿⣿⣿⢿⡷⣀⠀⠀⠀⠀⠀⣿⠀⢀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⡇⡊⣦⣄⣀⢻⡋ ⡟⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢩⠀⡀⠀⠀⠀⠀⠀⢸⢾⣿⣿⣿⡇⠀⢸⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢢⣀⣀⣿⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠘⢿⡿⣿⣷⣚⣁⡛⣷ ⣇⣁⣉⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢸⠁⡾⠀⠀⠀⠀⣶⠀⠀⢸⢼⣿⣿⣿⡇⠀⢸⠀⠀⠀⠀⠙⠒⠟⠛⠻⠛⠛⠛⣾⣿⣿⣿⡿⢻⠠⢠⣿⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠈⠙⠛⠋⠙ ⣏⠉⠉⠁⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⣿⠒⠆⠆⡆⢸⠀⠀⣸⢹⣿⣿⣿⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠻⣛⠃⢸⠀⠀⣿⠒⠶⠶⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⣀⣿⣗⣾⡿⣿⠀⣿⣿ ⣯⠋⠛⠃⠀⠸⣷⠂⠀⠀⠀⠀⠀⣤⠀⢸⢿⣷⣳⣿⣿⣇⣹⠀⠈⢙⢾⣿⣿⣿⡇⠀⢸⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣉⣋⣁⣀⣀⣀⢸⠢⠀⣷⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠻⠛⠻⠻⠿⠀⣿⣿ ⣞⣿⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡿⠻⠛⡻⠓⢻⠒⠒⠚⢸⣿⣿⣿⣃⠀⠐⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠦⣿⣶⣶⣛⡌⠀⠀⠀⠀⠀⠀⠀⠛⡀⠀⠀⠀⠀⠀⣀⣀⣀⣰⣳⣿ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⢸⠀⠀⠀⢸⣿⡿⠿⠿⠎⠀⣀⠴⠶⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡀⣿⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⠛⠛⠛⠻ ⡯⣿⡏⠛⠙⠹⠇⠀⠀⠀⢴⡄⠀⠀⠀⠀⢈⣅⣬⣠⣈⣇⣀⢀⣀⣄⠐⣷⣆⣀⣀⣀⣀⣀⣀⣀⠀⠀⠰⠀⠀⠀⢀⢀⣀⠀⠂⠀⠀⠀⠀⠀⠀⣿⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⣶⡶⠶⠶⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠠⠆ ⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⢶⠶⠆⢶⠲⢤⡶⠒⠒⠒⠶⠶⠶⠲⢺⡈⣽⠉⠎⠀⠀⠀⢴⣿⢿⡿⠾⠷⣾⣿⣟⣷⣿⣿⣻⣿⡿⣿⠿⣾⣷⣿⣿⣿⣿⣾⣶⣿⣾⣟⣗⣿⣿⣿⢿⣿⠿⠟⠛⠿⠟⠻⠟⠿⠿⠿⠿⠿⠿⠦⠆⠀⠀⠀⠀⣤⠀ ⣷⣶⣶⣶⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢸⡧⢾⠀⠀⠀⠀⠀⠀⠀⢸⡿⢷⢿⣿⡇⠀⠘⢻⣿⣯⣿⢿⣧⣠⣿⣛⣿⣿⣷⣷⡬⡟⢿⠟⣻⣿⣿⣿⣿⣷⣶⣷⣿⣶⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣼⣿⣿⠶⣦⣤ ⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⣮⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⢰⣶⣄⠈⠻⣿⣿⣍⠉⠿⣿⣿⣍⠉⠿⣷⣿⣍⠿⠀⣿⠉⠋⢯⣭⠽⢉⣯⣿⡿⡯⠯⣽⠿⠽⠭⢯⣿⣯⣭⣛⣟⡋⢘⣋⣻ ⡿⠿⠿⠛⠃⠆⣽⣯⠹⠿⠿⠟⠛⠉⠙⠻⠻⣿⠃⠀⠃⡄⠀⠀⠆⢸⣿⣿⣿⣿⡇⠀⢸⣿⣿⠀⠠⣿⣿⣿⡀⠀⣿⣿⣿⡀⠀⣽⢿⣿⣀⠀⣿⠻⠀⣀⣳⡮⣿⡷⡙⠿⣿⡯⢿⣿⣾⣿⡿⣿⠿⡿⡿⣿⢿⢉⡷⠿ ⠿⠷⠶⠿⠆⢠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⡀⢀⣄⠀⠆⣑⢜⣿⣾⣿⣿⡇⠀⢸⣿⣏⠀⠰⣿⣿⣍⠁⠰⣿⣯⣍⠁⠶⣾⣯⣍⠒⢸⣿⠀⠀⠘⣿⣿⣿⣿⣿⣥⣤⣤⣤⣤⣥⣀⣤⣄⣤⣤⣼⣿⣿⣞⣷⣦ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠱⠈⠙⣆⠀⠀⢸⣹⣿⣿⣿⡇⠀⢸⣿⡿⠀⠀⢿⣿⣿⠀⠀⢿⣿⣿⠀⠀⢿⣿⣿⠀⢀⣿⠀⠀⣄⡩⠍⠭⡙⠭⢍⠉⢿⢿⣿⢻⡟⣟⣻⣿⢿⢟⣟⣿⠻⢿⣷ ⣯⡯⣩⠉⠹⢭⡍⠉⠉⠿⡉⠉⠉⠉⠉⢙⠉⠱⠆⠀⠀⠰⠛⠀⠀⢸⣼⣿⣿⣿⡇⠀⢸⣿⣇⠀⠸⣿⣿⣭⠀⠸⣿⣿⣭⠐⠀⠤⠟⠟⣷⠘⣿⠀⠀⢀⡀⠀⠀⠀⠀⠁⠠⣄⠉⠀⣶⠀⠀⠀⠒⠇⠒⠇⠯⣉⣁⣡ ⣷⣶⡶⣶⣾⡏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢰⠀⠀⠀⠀⠆⠀⠂⢸⣻⣿⣿⣿⡇⠀⠸⣿⡿⢀⠀⣻⣿⣿⡀⣀⣻⣿⣿⠀⣀⡐⠐⠀⣿⠀⣿⠀⠁⠈⡡⠀⠀⠂⢶⣶⣶⣷⣾⡟⠓⠿⣿⣿⣿⣇⣈⣛⣻⣟⢻⣟ ⠖⢒⠒⡲⠃⣺⣶⡄⠀⠀⠀⠀⢀⡠⢀⣸⠀⠈⣤⡄⠀⠀⠀⠀⠁⢸⢸⣿⣿⣿⡇⠀⠀⠉⣙⠛⠂⠈⠉⢽⠧⠤⠀⢩⣭⠀⠀⠀⠀⠀⣿⠀⣿⠠⢡⡄⠀⡀⠀⠀⠈⠁⠈⠉⠉⣀⠀⠀⠉⠛⢟⡿⠇⣀⣻⡻⢏⠙ ⡏⠛⢻⣧⡤⠌⠙⠃⠠⠀⠀⠀⠜⠃⠜⢻⠀⢰⠋⠃⠀⠀⠀⠀⠀⢸⣺⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡇⠀⠀⠀⠀⣿⠀⣿⢀⠀⢠⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⣭⢰⠿⠭⢿⣦⣽⣯ ⡋⠛⠛⠛⠃⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠀⣠⠀⠀⠀⠃⠀⠀⠀⠸⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⠋⢿⣒⢟⠛⣋⣓ ⡷⡶⣾⠇⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣸⠀⠁⠀⠀⠈⠀⠀⢸⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢻⢿⣿⣿⣿⢿⡷⣀⠀⠀⠀⠀⠀⣿⢠⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⡇⡊⣦⣄⣀⢻⡋ ⡟⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢩⠀⡀⠀⠀⠀⠀⠀⢸⢾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢢⣀⣀⣿⢸⣿⠀⠄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠘⢿⡿⣿⣷⣚⣁⡛⣷ ⣇⣁⣉⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢸⠁⡾⠀⠀⠀⠀⣶⠀⠀⢸⢼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠙⠒⠟⠛⠻⠛⠛⠛⣾⣿⣿⣿⡿⢻⠸⣿⠠⠁⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠈⠙⠛⠋⠙ ⣏⠉⠉⠁⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⣿⠒⠆⠆⡆⢸⠀⠀⣸⢹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠻⣛⠃⢸⠀⣿⠀⠀⠶⠶⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⣀⣿⣗⣾⡿⣿⠀⣿⣿ ⣯⠋⠛⠃⠀⠸⣷⠂⠀⠀⠀⠀⠀⣤⠀⢸⢿⣷⣳⣿⣿⣇⣹⠀⠈⢙⢾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣉⣋⣁⣀⣀⣀⢸⠀⣽⢦⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠻⠛⠻⠻⠿⠀⣿⣿ ⣞⣿⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡿⠻⠛⡻⠓⢻⠒⠒⠚⢸⣿⣿⣿⡃⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⢸⠌⢀⣶⣛⡌⠀⠀⠀⠀⠀⠀⠀⠛⡀⠀⠀⠀⠀⠀⣀⣀⣀⣰⣳⣿ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⢸⠀⠀⠀⢸⣿⡿⠿⠇⠀⠀⣀⠴⠶⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⢸⣠⣠⡍⠉⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⠛⠛⠛⠻ ⡯⣿⡏⠛⠙⠹⠇⠀⠀⠀⢴⡄⠀⠀⠀⠀⢈⣅⣬⣠⣈⣇⣀⢀⣀⣄⠐⣷⣆⣀⣀⣀⣀⣀⣀⣀⠀⠀⠰⠀⠀⠀⢀⢀⣀⠀⠂⠀⠀⠀⠀⠀⠀⣿⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⣶⡶⠶⠶⢶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠰⠆ ⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡷⢶⠶⠆⢶⠲⢤⡶⠒⠒⠒⠶⠶⠶⠲⢺⡈⣽⠉⠎⠀⠀⠀⢴⣿⢿⡿⠾⠷⣾⣿⣟⣷⣿⣿⣻⣿⣿⣿⠿⣾⣷⣿⣿⣿⣿⣾⣶⣿⣾⣟⣗⣿⣿⣿⣿⣿⠿⠿⠿⠿⠟⠻⠟⠿⠿⠿⠿⠿⠿⠦⠆⠀⠀⠀⠀⣤⠀ ⣷⣶⣶⣶⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢸⣧⢾⠀⠀⠀⠀⠀⠀⠁⢸⡿⢷⣿⡇⠁⢀⢸⣿⣿⣿⣿⢿⣧⣠⣿⣛⣿⣿⣷⣡⣬⣟⡿⣿⣻⣿⣿⣿⣿⣷⣶⣗⣿⣾⣿⣿⣿⣿⣶⣾⣶⣿⣿⣿⣿⠫⠾⠿⠓⠲⣦⣤ ⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⣮⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣀⣐⡛⢌⠉⣻⣿⡻⢍⠉⣿⣿⡿⢍⠉⣿⣷⡿⢍⢿⡟⢛⡛⠛⢿⣯⠿⢛⣿⣿⡿⡿⠯⣿⠿⠽⠿⢿⣟⣭⣭⣠⣆⡈⢘⣏⣻ ⡿⠿⠿⠛⠃⠇⣽⣿⠹⠿⠿⠟⠛⠉⠙⠻⠿⣿⠃⠀⠃⡄⠀⠀⠆⢸⣿⣿⣿⡇⠀⣿⣿⣿⣀⠀⣿⣿⡗⠸⡀⣿⣿⡟⠀⡀⣿⣿⡇⣈⣸⡷⠇⠘⠀⣠⣷⣮⣿⡿⡛⢿⣿⡯⢿⣿⣾⣿⡿⣿⣿⡿⡿⣽⢿⢉⡷⠿ ⠿⠷⠶⡿⠆⢠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⡀⢀⣄⠀⠆⣑⢼⣿⣾⣿⡇⠀⣛⣛⡟⣆⠈⣻⣿⣿⣄⠈⣟⣿⣻⣄⠀⣾⣿⣠⣍⣼⡇⠀⠂⠀⠘⣿⣿⣿⣿⣿⣥⣤⣤⣤⣤⣥⣀⣤⣅⣤⣤⣼⣿⣿⣞⣷⣶ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠱⠈⠹⣆⠀⠀⢸⣹⣿⣿⡇⠀⠿⠿⠯⠀⠀⠿⠿⠇⢸⠀⠿⠿⠇⢀⠀⢿⢿⠇⢀⢿⡇⣠⠀⠀⣄⡩⠍⠭⣙⠭⢍⡉⢿⢿⣿⢻⣟⣟⣻⣿⢿⣟⣟⣿⢻⣿⣷ ⣯⡯⣩⠉⠹⢯⡏⠉⠉⠿⡉⠉⠉⠉⠉⢙⠉⠹⠆⠀⠀⠰⠛⠀⠀⢸⣼⣿⣿⡇⠀⣨⣙⡓⢆⠀⣹⣿⡷⠬⠀⣹⣿⡳⢬⠐⠈⠭⠗⠟⣼⡇⠀⠐⠀⢀⡀⠀⠀⠀⠀⠁⠠⣄⠉⠀⣶⡀⢀⠀⠒⠇⠖⠇⠿⣽⣹⣧ ⣷⣶⡶⣶⣾⡏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢰⠀⠀⠀⠀⠆⠀⠂⢸⣻⣿⣿⡇⠀⢿⣿⣿⡀⢀⣿⣿⡇⣀⡀⢿⣿⡗⣀⠀⣄⡐⠐⠀⣿⡇⠀⠀⠁⠈⡱⠀⠄⠂⢶⣶⣶⣷⣾⡟⠓⠿⣿⣿⣿⣧⣈⣛⣻⣟⢻⣟ ⠖⣒⠒⡲⠃⣺⣶⡄⠀⠀⠀⠀⢀⡠⢀⣸⠀⠘⣤⡄⠀⠀⠀⠀⠁⢸⢸⣿⣿⡇⠀⠈⠛⠀⣘⠛⠛⠛⠋⢴⢧⠼⠛⢡⣬⠀⠀⠀⠀⠀⣿⡇⠀⠰⢡⡄⠀⡀⠀⠀⠈⠁⠉⠉⠉⣀⠀⠀⠉⠛⢿⣿⢇⣀⣻⡻⢯⢙ ⡏⠛⢻⣧⡤⠌⠙⠃⠠⠀⠀⠀⠜⠃⠜⢻⠀⢰⠋⠃⠀⠀⠀⠀⠀⢸⣺⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡇⠀⠀⠀⠀⡻⡇⠀⢀⠀⢤⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⣭⢸⠿⠯⢿⣯⣽⣯ ⡋⠛⠛⠛⠃⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠀⣠⠀⠀⠀⠃⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⢱⣇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡓⠋⢿⣓⢿⠟⣋⣗ ⡷⡶⣾⠇⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣸⠀⠁⠀⠀⠈⠀⠀⢸⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⢿⣷⣄⠀⠀⠀⠀⠠⣿⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣇⡪⣦⣄⣀⢻⡛ ⡟⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢽⠀⡀⠀⠀⠀⠀⠀⢸⢾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢢⣀⣀⣿⡇⠸⠀⠄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠘⢿⡿⣿⣷⣚⣁⡛⣷ ⣇⣁⣉⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢸⠁⣾⠀⠀⠀⠀⣶⠀⠀⢸⢼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⠛⠟⠛⠻⠛⠛⠛⣾⣿⣿⣿⡿⢿⡇⠀⠡⠁⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊⠁⠈⠙⠛⠋⠛ ⣏⠉⠙⠁⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⣿⠖⠆⠆⡆⢸⠀⠀⣸⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⠻⣛⠃⠈⡏⢠⠈⡀⠶⠶⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⣀⣿⣟⣾⡿⣿⢀⣿⣿ ⣯⠋⠛⠃⠀⠸⣷⠂⠀⠀⠀⠀⠀⣤⠀⢸⢿⣿⣳⣿⣿⣇⣹⠀⠈⢹⢾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⣀⣀⣀⣀⣉⣋⣁⣀⣀⣀⠀⡇⠀⢦⠀⠀⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠻⠿⠿⠻⠿⠀⣿⣿ ⣞⣿⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡿⠻⠛⡻⠓⢻⠒⠒⠚⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⠀⢌⢀⣶⣟⡌⠁⠀⠐⠀⠀⠀⠀⢛⡀⠀⠀⠀⠀⠀⣀⣀⣀⣸⣳⣿ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⢸⠀⠀⠀⢸⣿⡿⠇⠀⠀⠀⣀⠴⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⢠⣠⣄⡉⠉⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠙⠛⠛⠛⠻ ⡯⣿⡟⠛⠙⠹⠇⠀⠀⠀⢴⡄⠀⠀⠀⠀⢈⣅⣬⣠⣈⣇⣀⢀⣀⣄⠐⣷⣆⣀⣀⣀⣀⣀⣀⣀⡀⠀⠰⠀⠀⠀⣀⣀⣀⠀⠂⠀⠀⠀⠀⠉⠉⣿⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⣶⡶⠶⠶⢶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠰⠆ ⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠷⢶⠶⠆⢶⠲⢤⡶⠒⠒⠒⠶⠶⠶⠲⢺⡈⣽⠉⠎⠀⠀⠀⢴⣿⢿⡿⠾⠷⣾⣿⣟⣷⣿⣿⣻⣿⣿⣿⠿⣾⣷⣿⣿⣿⣿⣾⣶⣿⣾⣟⣗⣿⣿⣿⢿⣿⠿⠿⠿⠿⠟⠻⠟⠿⠿⠿⠿⠿⠿⠦⠆⠀⠀⠀⠀⣤⠀ ⣷⣶⣶⣶⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢸⣧⢾⠀⠀⠀⠀⠀⠀⠁⢸⡿⠓⠻⡇⢡⣤⣼⣿⣿⣿⣿⢿⣧⣠⣿⣛⡟⣟⢳⣡⡬⣟⢿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣿⣾⣿⣿⣿⣿⣶⣾⣶⣿⣿⡛⣿⠫⠾⠟⠓⠲⣦⣤ ⡿⠿⠿⠿⠿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⣮⡀⠀⠀⠀⠀⠀⠀⢸⣿⠃⢸⣇⣈⡉⢙⡛⣌⣉⠻⢿⡻⣉⣉⠿⢿⡿⣄⣉⠿⢷⣿⠛⠛⠛⢛⣛⠛⢿⣿⠿⢋⣿⣿⡿⡿⠿⣿⠿⠿⠿⢵⣟⣭⣬⣠⣆⡈⢈⣏⣻ ⡿⠿⠿⠛⠃⠇⣽⣯⠹⠿⠿⠟⠛⠉⠙⠻⠿⣿⠃⠀⠃⡄⠀⠀⠆⢸⣿⠀⢘⣿⣿⡇⢀⣿⣿⣿⡇⠀⠓⣿⣿⡇⢸⡿⣿⣿⠇⢸⢻⠿⢀⡱⠇⠘⠀⣠⣷⣮⣿⡷⡙⢿⣿⡯⢿⣿⣾⣿⡿⣿⡿⡿⡿⣽⢿⢉⡷⠿ ⠿⠷⠶⡿⠆⢠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⡀⢀⣄⠀⠆⣑⢜⣿⡂⠸⣟⣛⡃⣀⡟⣟⣛⡻⠶⣾⣛⣛⣓⣶⣻⣜⣃⠶⠿⣸⢠⢻⡇⠀⠀⠀⠘⣿⣿⣿⣿⣿⣥⣤⣤⣤⣤⣥⣀⣤⣅⣤⣤⣼⣿⣿⣞⣷⣶ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠱⠈⠙⣆⠀⠀⢸⣹⠅⢀⣿⣿⠇⠀⠯⣿⣿⠇⠀⠇⣿⣿⠇⠸⠇⣿⣿⠇⢘⣿⠐⢸⡇⣠⠀⠀⣄⡩⠍⠭⣉⠭⢍⠉⢿⢿⣿⢻⣟⣟⣻⣿⢿⢟⣟⣿⢻⣿⣷ ⣯⡯⣩⠉⠹⢯⡏⠉⠉⠿⡉⠉⠉⠉⠉⢙⠉⠱⠆⠀⠀⠰⠛⠀⠀⢸⣼⡇⢸⣿⣉⡀⢘⡓⣏⣉⡱⠾⡿⣍⣙⡱⢾⡳⢽⠛⠀⢼⣿⠀⢐⡆⠀⠐⠀⢀⡀⠀⠀⠀⠀⠁⠠⣄⠉⠀⣶⡀⠀⠀⠒⠇⠖⠇⠿⣙⣹⣧ ⣷⣶⡶⣶⣾⡏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢰⠀⠀⠀⠀⠆⠀⠂⢸⣻⠇⢀⣿⣿⡇⢀⣿⣿⣿⡇⢀⡇⣿⣿⠇⢸⡗⣀⠀⣄⡸⢿⠀⢸⡇⠀⠀⠁⠈⡱⠀⠄⠂⢶⣶⣶⣷⣾⡟⠓⠿⣿⣿⣿⣇⣈⣛⣻⣟⢻⣟ ⠖⢒⠒⡲⠃⣺⣶⡄⠀⠀⠀⠀⢀⡠⢀⣸⠀⠈⣤⡄⠀⠀⠀⠀⠁⢸⢸⡇⢸⡟⠛⠀⠘⠈⣛⠛⠃⠀⠋⢽⢿⠤⠈⢡⣬⠀⠀⠀⢸⠀⢸⡇⠀⠰⢡⡄⠀⡀⠀⠀⠈⠁⠉⠉⠉⣀⠀⠀⠉⠛⢟⣿⢇⣀⣻⡻⢯⢙ ⡏⠛⢻⣧⡤⠌⠙⠃⠠⠀⠀⠀⠜⠃⠜⢻⠀⢰⠋⠃⠀⠀⠀⠀⠀⢸⣺⡇⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡇⠀⢠⣾⠀⢘⡇⠀⢀⠀⢤⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⣭⢸⠿⠯⢿⣯⣽⣯ ⡋⠛⠛⠛⠃⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠀⣠⠀⠀⠀⠃⠀⠀⠀⢸⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⢸⣿⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡓⠋⢿⣓⢟⠟⣋⣗ ⡷⡶⣾⠇⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣸⠀⠁⠀⠀⠈⠀⠀⢸⢿⡅⢸⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⢿⡷⣄⠀⠀⢸⣿⠀⢸⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣇⡪⣦⣄⣀⢻⡛ ⡟⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢹⠀⡀⠀⠀⠀⠀⠀⢸⢾⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢺⣿⢀⢸⡇⠸⠀⠄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠘⢿⡿⣿⣷⣚⣁⡛⣷ ⣇⣁⣉⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢸⠁⣾⠀⠀⠀⠀⣶⠀⠀⢸⢼⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠙⠓⠟⠛⠻⠛⠛⠛⣾⣿⣿⢻⠀⢼⡇⠀⠡⠁⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠁⠈⠙⠛⠋⠛ ⣏⠉⠉⠁⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⣿⠖⠆⠆⡆⢸⠀⠀⣸⢹⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⠻⢸⠀⡈⡏⢠⠀⡂⠶⠶⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⣀⣿⣟⣾⡿⣿⢀⣿⣿ ⣯⠋⠛⠃⠀⠸⣷⠂⠀⠀⠀⠀⠀⣤⠀⢸⢿⣿⣳⣿⣿⣇⣹⠀⠈⢙⢾⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⣀⣀⣀⣀⣉⣋⣁⣀⢸⠀⢠⡅⠀⢦⠀⠀⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠻⠻⠻⠻⠿⠀⣿⣿ ⣞⣿⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡿⠻⠛⡻⠓⢻⠒⠒⠚⢸⠄⢸⡇⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠠⣗⠀⠌⢀⣶⣟⡌⠁⠀⠐⠀⠀⠀⠀⢛⡀⠀⠀⠀⠀⠀⣀⣀⣀⣸⣳⣿ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⢸⠀⠀⠀⢸⡆⠸⠇⠀⠀⠀⣀⠴⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠐⡗⢠⣠⣄⡉⠉⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⠛⠛⠛⠻ ⡯⣿⡟⠛⠙⠹⠇⠀⠀⠀⢴⡄⠀⠀⠀⠀⢈⣅⣬⣠⣈⣇⣀⢀⣀⣄⠐⣷⣆⣀⣀⣀⣀⣀⣀⣀⡀⠀⠰⠀⠀⠀⣀⣀⣀⠀⠂⠀⠈⠉⠉⠉⠉⣿⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⣶⣶⠶⠶⢶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠰⠆ ⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡷⢶⠶⠆⣶⠳⢤⡶⠒⠒⠒⠶⠶⠶⠲⢺⡈⣽⠉⠎⠀⠀⠀⢴⣿⢿⡿⠾⠷⣾⣿⣿⣷⣿⣿⣻⣿⣿⣿⠿⣾⣷⣿⣿⣿⣿⣾⣶⣿⣾⣟⣗⣿⣿⣿⣿⣿⠿⠿⠿⠿⠟⠿⠟⠿⠿⠿⠿⠿⠿⠦⠆⠀⠀⠀⠀⣤⠀ ⣗⣒⣒⣒⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⣾⠀⠀⠀⠀⠀⠀⠁⣼⣿⣷⣿⡧⣥⣤⣼⣿⣿⣿⢩⡯⡧⣤⣿⢻⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣿⣾⡻⠿⠿⠻⣾⣾⣶⣿⣿⡛⣿⠻⠾⠟⠓⠲⣦⣤ ⣟⣋⣛⣛⠋⠀⠸⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡀⠀⠀⠀⠀⠀⠀⣸⣿⠃⣼⣇⣈⡉⢹⣿⣌⣉⠻⣿⣿⣉⡙⢹⡟⠋⠛⢛⠿⠿⣿⠛⠛⠛⢛⣛⠛⢽⣿⠯⢋⣧⣼⡭⡴⠿⣿⠿⠿⠿⢷⣟⣭⣬⣤⣦⣬⢘⣏⣿ ⡯⠉⠉⠍⠁⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠃⡄⢀⠀⠆⣿⣿⢀⣿⣿⣿⡇⢸⣿⣿⣿⡆⠿⣿⣿⣿⢸⠿⠀⠀⢈⠁⢸⢻⠿⢀⡱⠇⠘⠠⣠⣷⣾⣿⡿⡛⢿⣿⡯⢿⣿⣾⣿⣿⣿⣿⡿⣿⣽⢿⢉⣷⣿ ⠿⠷⠷⡿⠆⢠⣶⡄⡀⠀⡀⠀⠀⠀⠀⠀⠀⣿⣧⡀⢀⣄⠀⠆⣑⣿⣿⠋⣽⣟⣛⡂⢩⣿⣟⣛⡒⣾⣿⡛⣛⢻⣧⡄⠀⢀⣶⠿⣸⢨⢻⡇⠀⠂⠀⠘⣿⣿⣿⣿⣿⣥⣤⣤⣤⣤⣥⣀⣤⣅⣤⣤⣼⣿⣿⣟⣷⣶ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠱⠈⠹⣆⠀⠀⢿⣹⠀⣿⣿⣿⠇⢸⡿⣿⣿⠇⢿⣿⣿⣿⢸⠷⠀⠀⣿⠇⢸⣿⠐⢸⡗⠂⠀⠀⣤⣩⢍⢭⣉⠭⢍⡉⢿⢿⣿⢿⣟⣟⣻⣿⣿⣿⣟⣿⢻⣿⣷ ⣯⡯⣩⠉⠹⢯⡏⠉⠉⠿⡉⠉⠉⠉⠉⢙⠉⠹⠆⠀⠀⠰⠛⠀⠀⣠⣼⡇⣽⣿⣉⡀⢸⣿⣯⣛⠱⠾⡿⣍⣛⢸⠒⠀⠀⠙⠀⢼⣿⠀⢲⡆⠀⠐⠀⢀⡀⠀⠈⠀⠀⠁⢠⣄⠉⠀⣶⡀⢀⣰⠒⠇⠖⠟⠿⣿⣹⣷ ⣷⣶⡶⣶⣾⡏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢰⠀⠀⠀⠀⠆⠀⠂⢿⣻⢀⣿⣿⣿⡇⢸⣿⣿⣿⠆⢠⡤⣿⣿⣿⡄⠀⠀⠀⣄⡸⢿⠀⢸⡇⠀⠀⠁⠈⡱⠀⠄⠒⢶⣶⣶⣷⣾⡿⠓⠿⣿⣿⣿⣧⣉⣛⣻⣟⢻⣟ ⠗⣒⠒⡲⠓⣺⣶⡄⠀⠀⠀⠀⢀⡠⢀⣸⠂⠘⣤⡄⠀⠀⠀⠀⠁⢸⢸⡏⢹⡟⠛⠀⠈⠉⣛⠛⠃⠀⠋⢽⢿⣿⠀⠀⠀⠀⠀⠀⢸⠀⢸⡏⠀⠰⢡⡄⠀⡐⠀⠂⠈⠉⠉⠉⠉⣀⠂⡀⠉⠻⣿⣿⣯⣀⣻⡿⣯⢝ ⡏⠛⢻⣧⡤⠌⠙⠃⠠⠀⠀⠀⠜⠃⠜⢻⠀⢰⠋⠃⠀⠀⠀⠀⠀⢸⣺⡇⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠂⠀⠀⠀⠀⢠⣾⠀⢸⡇⠀⢀⠀⢤⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠀⠀⢨⣭⢸⠿⠯⢿⣯⣿⣯ ⡋⠛⠛⠛⠃⣀⠀⠀⠒⠀⠀⠀⠀⠀⠀⢸⠀⣠⠀⠀⠀⠃⢀⠀⠀⢸⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⢻⡀⠀⠀⠀⠀⠸⣿⠄⢹⣏⠀⢁⠂⠀⠀⠈⠀⠀⠠⠀⠀⠀⠀⠡⠀⠀⠀⢀⡳⠫⢿⣿⣿⢟⣋⣷ ⡷⣶⣾⠇⠀⢻⡃⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣸⠀⠁⠀⠀⠈⠀⠀⢸⢿⡅⢸⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⢸⠀⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⢸⣟⣇⡪⣦⣄⣀⢻⡛ ⡟⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢽⠀⡀⠀⠀⠀⠀⠀⢸⢾⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢸⣅⣶⠀⢸⣶⢺⣿⢀⢸⡇⠸⠀⠄⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠚⢿⣿⣿⣷⣚⣑⣛⣷ ⣇⣁⣉⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢸⠁⣾⠀⠀⠀⠀⣶⠀⠀⢸⢼⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠿⠟⠟⠛⢸⠻⠠⠀⢸⣿⣿⢻⠀⢼⡇⠀⠡⠁⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠂⠙⠊⠁⠈⠙⠛⠋⠛ ⣏⠋⠙⠁⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⣿⠖⠆⠆⡆⢸⠀⠀⣸⢹⠃⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢸⡀⠀⠀⣈⣿⠻⢸⠀⡈⣏⢤⠀⡂⠶⠶⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⣀⣿⣟⣾⡿⣿⢌⣿⣿ ⣯⠋⠛⠃⠀⠸⣷⠆⠀⠀⠀⠀⠀⣦⠀⢸⢿⣿⣻⣿⣿⣧⣹⠀⠈⢹⢾⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⣀⢸⣀⣀⠀⢉⣁⣀⢸⠀⢨⡅⠀⢦⠀⠀⢀⣡⡾⠏⠀⠀⠀⠀⠀⠠⠀⠁⠀⠟⠿⠿⠿⠻⠿⠱⣿⣿ ⣞⣿⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡿⠻⠛⡻⠓⢻⠒⠒⠈⢸⠄⢸⡇⠀⠀⠀⠀⠀⡀⡀⠀⠀⡀⠀⢸⠀⠠⠐⠀⠀⠀⢸⠀⠠⣗⠄⢜⢀⣶⣟⡌⠁⠄⠐⠀⠀⠀⠀⢛⡄⠀⠂⠀⠀⠀⣀⣀⣀⣸⣿⣿ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⢸⠀⠀⠀⢸⡆⠸⠇⠀⠀⠀⣀⠴⠶⠶⠀⠀⠀⠀⢸⣀⣄⣀⡀⠀⠀⢸⠈⡐⡷⢤⣠⣄⣉⡉⢁⠀⠀⢀⡠⣀⠀⢀⠀⢠⠀⠀⠀⠁⠀⠀⠙⣛⡛⠛⠻ ⡯⣿⡟⠛⠙⠹⠇⠀⠀⠀⢴⡄⠀⠀⠀⠀⢈⣅⣬⣠⣈⣇⣀⢀⣀⣄⠐⣷⣆⣀⣀⣀⣀⣀⣀⣀⡀⠀⠰⠀⠀⠈⣉⣉⣉⠉⠂⠀⠈⠉⠉⠉⠉⣿⠀⠈⠁⠀⠀⠀⠀⠁⢒⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠁⡀⠀ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⣶⡶⠶⠶⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠠⠆ ⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠷⢶⠶⠆⢶⠲⢤⡶⠒⠒⠒⠶⠶⠶⠲⢺⡈⣽⠉⠎⠀⠀⠀⢴⣿⢿⡿⠾⠷⣾⣿⣟⣷⣿⣿⣻⣿⡿⣿⠿⣾⣷⣿⣿⣿⣿⣮⣶⣿⣾⣟⣗⣿⣿⣿⢿⣿⠿⠟⠛⠿⠟⠻⠟⠿⠿⠿⠿⠿⠿⠦⠆⠀⠀⠀⠀⣤⠀ ⣗⣒⣒⣒⣂⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠘⠃⣾⠀⠀⠀⠀⠀⠀⠁⣼⣿⣷⣿⣧⣥⣤⣼⣿⣿⣯⢩⡯⡇⡄⣿⢻⣿⣿⣿⢳⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣿⣶⣿⣿⣿⣿⣶⣶⡖⠛⢿⠛⣿⠋⠼⠟⠓⠲⣦⣤ ⣏⣋⣛⣛⠋⠀⠸⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⣯⡀⠀⠀⠀⠀⠀⠀⣸⣿⠃⢼⣇⣈⣭⣙⣻⣌⣉⣿⣿⣻⣉⡉⣼⣯⡋⠛⢹⣿⠿⣿⠛⠙⠛⢛⢛⠛⢽⣿⠯⢋⣯⣽⡭⡽⠿⣿⠿⠽⠿⢤⣟⣥⣤⣀⣆⡀⢈⣋⣿ ⡯⠉⠉⠉⠁⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠃⡄⠀⠀⠆⣿⣿⠀⢼⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⣿⣿⢿⡿⠇⠀⢸⡿⢏⢹⠿⢀⡱⠆⠘⠀⣀⣳⡮⣿⡷⡙⠿⣿⡯⢿⣿⣮⣻⡿⣿⡿⡿⡿⣽⢿⢉⡷⠿ ⠿⠷⠶⠿⠆⢠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⡀⢀⣄⠀⠆⣑⣟⣿⠉⢹⣟⣛⣯⣭⣟⣟⣛⣯⣯⣿⡛⣛⣽⣭⡄⠀⢸⣷⠟⣸⠀⢹⡇⠀⠀⠀⠘⣿⣿⣿⣿⣿⣥⣤⣤⣤⣤⣥⣀⣤⣄⣤⣤⣼⣿⣿⣞⣷⣦ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠱⠈⠙⣆⠀⠀⢿⣹⠈⣸⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢸⡇⢘⣿⠐⢸⡇⠀⠀⠀⣄⡩⠍⠭⣉⠭⢍⠉⢿⢿⣿⢻⡟⣟⣻⣿⢿⢿⣟⣿⢻⣿⣷ ⣯⡯⣩⠉⠹⢯⡏⠉⠉⠿⡉⠉⠉⠉⠉⢙⠉⠱⠆⠀⠀⠰⠛⠀⠀⣠⣼⡇⢽⣿⣉⣭⣽⣛⣏⣉⣭⣿⡿⣍⣙⢹⠛⠀⠀⢸⡇⢼⣿⠀⢐⡆⠀⠀⠀⢀⡀⠀⠈⠀⠀⠁⠠⣄⠉⠀⣶⠀⠀⠀⠒⠇⠖⠇⠯⣉⣁⣡ ⣷⣶⡶⣶⣾⡏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢰⠀⠀⠀⠀⠆⠀⠂⢿⣻⢀⣼⣿⣿⣿⣿⡿⣿⣿⣿⣿⡇⣿⣿⣿⠄⠀⠀⢸⡇⡘⢿⠀⢸⡇⠀⠀⠁⠈⡡⠀⠄⠂⢶⣶⣶⣷⣾⡟⠓⠿⣿⣿⣿⣇⣈⣛⣻⣟⢻⣟ ⠖⢒⠒⡲⠃⣺⣶⡄⠀⠀⠀⠀⢀⡠⢀⣸⠀⠈⣤⡄⠀⠀⠀⠀⠁⢘⢸⡇⢹⡟⠛⠉⠉⠁⣛⠛⠋⠉⠋⢽⢿⣿⠀⠀⠀⢸⡇⠀⢸⠀⢸⡇⠀⠰⢡⡄⠀⡀⠀⠀⠈⠁⠉⠉⠉⣀⠀⠀⠉⠛⢟⣿⠇⣀⣻⡻⢏⠙ ⡏⠛⢻⣧⡤⠌⠙⠃⠠⠀⠀⠀⠜⠃⠜⢻⠀⢰⠋⠃⠀⠀⠀⠀⠀⢸⣺⡇⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡧⢠⣾⠀⢘⡇⠀⢀⠀⢠⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⣭⢰⠿⠭⢿⣦⣽⣯ ⡋⠛⠛⠛⠃⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠀⣠⠀⠀⠀⠃⠀⠀⠀⢸⢿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⡤⢻⠀⠀⠀⢸⡇⠸⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⠋⢿⣓⢟⠛⣋⣗ ⡷⡶⣾⠇⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣸⠀⠁⠀⠀⠈⠀⠀⢸⢿⡅⢸⡇⠀⠀⠀⠀⠀⠀⠀⢻⢿⣿⡇⢸⠀⠀⠀⠘⡇⢸⣿⠀⢸⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⡇⡊⣦⣄⣀⢻⡋ ⡟⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢩⠀⡀⠀⠀⠀⠀⠀⢸⢾⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⢸⣁⣴⠀⠀⣇⢸⣿⢀⢸⡇⠸⠀⠄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠘⢿⡿⣷⣶⣒⣁⡛⣷ ⣇⣁⣉⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢸⠁⡾⠀⠀⠀⠀⣶⠀⠀⢸⢼⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠙⠒⠟⠋⢸⠛⠀⠀⠀⡇⣿⢻⠀⢼⡇⠀⠠⠁⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠈⠙⠛⠋⠛ ⣏⠉⠉⠁⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⣿⠒⠆⠆⡆⢸⠀⠀⣸⢹⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⡇⠈⢸⠀⡈⡏⢠⠀⠂⠶⠶⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⣀⣿⣗⣾⡿⣿⠀⣿⣿ ⣯⠋⠛⠃⠀⠸⣷⠂⠀⠀⠀⠀⠀⣤⠀⢸⢿⣷⣳⣿⣿⣇⣹⠀⠈⢙⢾⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⣀⢸⣀⣀⠀⠀⣇⣀⢸⠀⢠⡅⠀⢦⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠻⠻⠻⠻⠿⠀⣿⣿ ⣞⣿⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡿⠻⠛⡻⠓⢻⠒⠒⠈⢸⠄⢸⡇⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⢸⠀⠀⠀⠀⡇⠀⢸⠀⠠⣗⠀⠌⢀⣶⣛⡌⠀⠀⠀⠀⠀⠀⠀⠛⡀⠀⠀⠀⠀⠀⣀⣀⣀⣰⣳⣿ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⢸⠀⠀⠀⢸⡆⠸⠇⠀⠀⠀⣀⠴⠶⠶⠀⠀⠀⠀⢸⣀⣀⣀⡀⣇⡀⢸⠀⠐⡗⢠⣠⣀⣉⡉⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⣛⡛⠛⢻ ⡯⣿⡟⠛⠙⠹⠇⠀⠀⠀⢴⡄⠀⠀⠀⠀⢈⣅⣬⣠⣈⣇⣀⢀⣀⣄⠐⣷⣆⣀⣀⣀⣀⣀⣀⣀⠀⠀⠰⠀⠀⠈⢉⢉⣉⠁⠂⠀⠈⠉⠉⠉⠉⣿⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠁⡀⠀ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⣶⡶⠶⠶⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠠⠆ ⣶⣶⣴⣤⣶⣶⠶⠶⠶⠶⠦⠶⠶⠶⠶⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⢶⠶⠆⢲⠲⢤⡶⠒⠒⠒⠶⠶⠶⠲⢸⡈⠍⠉⠎⠀⠀⠀⢴⢻⢿⡷⠾⠷⣾⣿⣟⣷⣷⣶⣻⣿⡿⣿⠷⣾⣷⣾⣿⣿⣿⣮⣶⣿⣾⣛⣗⣿⣟⣷⣿⣿⢿⡛⠛⠛⠛⠻⠟⠿⠿⠿⠿⠿⠿⠦⠆⠀⠀⠀⠀⣤⠀ ⣗⣒⣒⣒⣂⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠘⠃⣶⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣿⣧⣥⣤⣬⣿⣿⣯⢩⠯⡇⡄⣯⢻⣿⣿⣿⣳⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣷⣶⣿⣿⣿⣷⣶⣶⠖⠛⢻⠛⣿⠃⣴⠟⠓⠲⡦⣤ ⣏⣋⢛⣙⠃⠀⠘⠿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣯⡀⠀⠀⠀⠀⠀⠀⣸⣿⠛⢻⣟⣈⣭⣙⣛⣌⣉⣿⣿⣻⣙⡋⣿⣯⡙⠋⣿⣿⠿⣿⡿⡽⠿⢿⠿⠿⢿⢿⠿⢯⣿⣿⡯⠿⠿⣿⠿⠭⠿⠤⣟⣥⣄⢀⠀⡀⠀⣈⣯ ⡯⠉⠉⠉⠁⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠣⠀⠃⡄⠀⠀⠆⣿⣿⠀⢼⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠇⠀⣿⣼⢏⢹⠾⢀⡱⠆⠘⠀⣀⡰⠆⣿⠑⡘⠿⢿⡆⢿⣿⠎⣻⡿⠿⠿⠿⠿⣵⠿⠉⡱⠿ ⠿⠷⠶⠾⠆⢀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⡀⢀⣄⠀⠆⣑⣟⣿⠀⢹⣟⣛⣯⣻⣟⣟⣛⣿⣻⣿⡛⡛⣿⣿⡄⠀⣿⣿⠟⣸⠀⢸⡇⠀⠀⠀⠘⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣀⣤⣀⣀⣤⣼⣿⣿⣆⣷⣦ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠱⠈⠙⣆⠀⠀⢿⣹⠀⣸⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠇⠀⣿⡇⢐⣿⠐⢸⡇⠀⠀⠀⠄⡩⠍⠭⠉⠭⢍⠉⢿⢿⣟⠛⠛⠟⠻⠿⢿⠟⢟⣿⠛⠻⠗ ⣯⡯⣩⠉⠹⢭⡍⠉⠉⠿⡉⠉⠉⠉⠉⢙⠉⠱⠆⠀⠀⠰⠛⠀⠀⣀⣼⡅⢽⣿⣹⣿⣿⣙⣏⣹⣯⣿⡿⣉⣹⢿⠿⠀⠀⣿⡇⢼⣿⠀⢀⡆⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠠⣄⠈⠀⣴⠀⠀⠀⠐⠁⠒⠅⠩⣉⣁⣠ ⣗⣶⡶⡶⣾⡏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢠⠀⠀⠀⠀⠆⠀⠂⢿⣻⠀⣼⣿⣿⣿⣿⡿⣿⣿⣿⣿⡇⣿⣿⣿⠋⠀⠀⣿⡇⡘⢿⠀⢸⡇⠀⠀⠀⠀⡁⠀⠀⠂⢶⣶⣶⣷⣶⠟⠓⠻⣿⣿⣿⢇⣈⣛⢻⣟⢻⣟ ⠆⢒⠒⠲⠃⣺⣶⡄⠀⠀⠀⠀⢀⡠⢀⣸⠀⠈⣤⡄⠀⠀⠀⠀⠁⢐⢸⠄⢹⡟⢻⣿⣿⠁⣛⢹⠿⣿⠉⢽⢿⣿⠀⠀⠀⣿⡆⠀⢸⠀⢸⡇⠀⠀⠡⡄⠀⠀⠀⠀⠈⠀⠈⠀⠀⣀⠀⠀⠉⠛⢟⡻⠃⢀⣛⡻⠊⠙ ⡏⠛⢻⣧⡤⠌⠙⠃⠠⠀⠀⠀⠜⠃⠜⢻⠀⢰⠋⠃⠀⠀⠀⠀⠀⢸⣺⠁⢨⡇⠲⠶⠶⠀⠀⠘⠶⠞⠀⠀⠀⣿⠀⠀⠀⣿⡇⢠⣾⠀⢘⡇⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣍⠰⠶⠭⢯⢤⣥⣯ ⡋⠛⠛⠛⠃⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠀⣠⠀⠀⠀⠃⠀⠀⠀⠸⢿⡂⢸⡇⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡤⢻⠀⠀⠀⣿⡇⠘⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠃⢲⣒⢚⠂⣃⣃ ⡗⡶⣾⠇⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣘⠀⠁⠀⠀⠀⠀⠀⢸⢿⠅⢸⡇⠀⠀⠀⠀⠀⠀⠀⠸⢯⢿⠇⢸⠀⠀⠀⣿⡇⢸⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠇⠂⣤⠄⣀⠫⠉ ⡏⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢩⠀⡀⠀⠀⠀⠀⠀⢰⢾⠃⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⢸⣀⢴⠀⣿⣅⢸⣿⢀⢸⡇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡷⢶⠶⣀⠀⠁⠱ ⣇⣁⣉⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢸⠁⡾⠀⠀⠀⠀⣶⠀⠀⠘⢼⠆⢸⡇⠀⠀⠀⠀⠀⠀⠀⠙⠐⠛⠀⢸⠛⠀⠀⣿⡃⣿⢻⠀⢼⡇⠀⠠⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠋⠋⠑ ⣏⠉⠉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⡿⠒⠆⠆⡆⢸⠀⠀⣠⢹⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⡀⠈⢸⠀⠈⡇⢠⠀⠂⠶⠶⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣇⣦⡿⡿⠀⢯⣯ ⣯⠋⠛⠃⠀⠸⡷⠂⠀⠀⠀⠀⠀⣤⠀⢸⢿⣷⣳⣿⣿⣇⣹⠀⠈⢙⢾⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⢸⣀⣀⠀⣿⣄⣀⢸⠀⢠⡅⠀⠆⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⠛⠻⠻⠿⠀⡿⣾ ⣎⣷⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡿⠻⠙⡻⠓⢻⠒⠒⠈⢸⠀⢸⡇⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⢸⠀⠀⠀⣿⡇⠀⢸⠀⠠⣇⠀⠀⢀⣶⣛⡌⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣳⣷ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⢨⠀⠀⠀⢸⡄⠸⠇⠀⠀⠀⣀⠴⠶⠴⠀⠀⠀⠀⢸⣀⣀⣀⣿⣇⡀⣼⠀⠐⡇⢠⣠⣀⣉⡉⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⡛⠛⢻ ⠯⣿⡏⠛⠙⠹⠇⠀⠀⠀⢴⡀⠀⠀⠀⠀⢈⣅⣬⣠⣈⣇⣀⢀⣀⣀⠀⣷⠄⠀⠀⠀⠀⣀⣀⣀⠀⠀⠰⠀⠀⠈⠉⢉⡉⣿⠀⠀⠈⠉⠉⠉⠉⡇⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⡀⠀ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⣶⡶⠶⠶⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠠⠆ ⣶⣶⣴⣤⣶⣶⠶⠶⠶⠶⠦⠶⠶⠶⠶⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⢶⠶⠆⢲⠲⢤⡶⠒⠒⠒⠶⠶⠶⠲⢸⡈⠍⠉⠎⠀⠀⠀⢴⢻⢿⡷⠾⠷⣾⣿⣟⣷⣷⣶⣻⣿⡿⣿⠷⣾⣷⣾⣿⣿⣿⣮⣶⣿⣾⣛⣗⣿⣟⣷⣿⣿⢿⡛⠛⠛⠛⠻⠟⠿⠿⠿⠿⠿⠿⠦⠆⠀⠀⠀⠀⣤⠀ ⣗⣒⣒⣒⣂⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠘⠃⣶⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣿⣧⣥⣤⣬⣿⣿⣯⢩⠯⡇⡄⣯⢻⣿⣿⣿⣳⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣷⣶⣿⣿⣿⣷⣶⣶⠖⠛⢻⠛⣿⠃⣴⠟⠓⠲⡦⣤ ⣏⣋⢛⣙⠃⠀⠘⠿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣯⡀⠀⠀⠀⠀⠀⠀⣸⣿⠛⢻⣟⣈⣭⣙⣛⣌⣉⣿⣿⣻⣙⡋⣿⣯⡙⠋⣿⣿⠿⣿⡿⡽⠿⢿⠿⠿⢿⢿⠿⢯⣿⣿⡯⣿⠿⣿⠿⠭⠿⠤⣟⣥⣄⢀⠀⡘⠀⣈⣯ ⡯⠉⠉⠉⠁⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠣⠀⠃⡄⡆⠀⠆⣿⣿⠀⢼⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠇⠀⣿⣼⢏⢹⠾⢀⡱⠆⠘⠀⣀⡰⠆⣿⠑⡘⠿⢿⡆⢿⣿⠎⣻⡿⠿⠿⠿⠿⣵⠿⠉⡱⠿ ⠿⠷⠶⠾⠆⢀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⡀⢀⣄⠁⠆⣑⣟⣿⠀⢹⣟⣛⣯⣻⣟⣟⣛⣿⣻⣿⡛⡛⣿⣿⡅⠀⣿⣿⠟⣸⠀⢸⡇⠀⡀⠀⠘⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣀⣤⣀⣀⣤⣼⣿⣿⣆⣷⣦ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠱⠈⠙⣆⠀⠀⢿⣹⠀⣸⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠇⠀⣿⡇⢐⣿⠐⢸⡇⠀⠧⠀⠄⡩⠍⠭⠉⠭⢍⠉⢿⢿⣟⠛⠛⠟⠻⠿⢿⠟⢟⣿⠛⠻⠗ ⣯⡯⣩⠉⠹⢭⡍⠉⠉⠿⡉⠉⠉⠉⠉⢙⠉⠱⠆⠀⠀⠰⠛⠀⠀⣀⣼⡅⢽⣿⣹⣿⣿⣙⣏⣹⣯⣿⡿⣉⣹⢿⠿⠀⠀⣿⡇⢼⣿⠄⢀⡆⠀⡆⠀⢀⡀⠀⠀⠀⠀⠀⠠⣄⠈⠀⣴⠀⠀⠀⠐⠁⠒⠅⠩⣉⣁⣠ ⣗⣶⡶⡶⣾⡏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢠⠀⠀⠀⠀⠆⠀⠂⢿⣻⠀⣼⣿⣿⣿⣿⡿⣿⣿⣿⣿⡇⣿⣿⣿⠋⠀⠀⣿⡇⡘⢿⠀⢸⡇⠀⠃⠀⠀⡁⠀⠀⠂⢶⣶⣶⣷⣶⠟⠓⠻⣿⣿⣿⢇⣈⣛⢻⣟⢻⣟ ⠆⢒⠒⠲⠃⣺⣶⡄⠀⠀⠀⠀⢀⡠⢀⣸⠀⠈⣤⡄⠀⠀⠀⠀⠁⢐⢸⠄⢹⡟⢻⣿⣿⠁⣛⢹⠿⣿⠉⢽⢿⣿⠀⠀⠀⣿⡆⠀⢸⠀⢸⡇⠀⠀⠡⡄⠀⠀⠀⠀⠈⠀⠈⠀⠀⣀⠀⠀⠉⠛⢟⡻⠃⢀⣛⡻⠊⠙ ⡏⠛⢻⣧⡤⠌⠙⠃⠠⠀⠀⠀⠜⠃⠜⢻⠀⢰⠋⠃⠀⠀⠀⠀⠀⢸⣺⠁⢨⡇⠲⠶⠶⠀⠀⠘⠶⠞⠀⠀⠀⣿⠀⠀⠀⣿⡇⢠⣾⠀⢘⡇⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣍⠰⠶⠭⢯⢤⣥⣯ ⡋⠛⠛⠛⠃⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠀⣠⠀⠀⠀⠃⠀⠀⠀⠸⢿⡂⢸⡇⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡤⢻⠀⠀⠀⣿⡇⠘⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠃⢲⣒⢚⠂⣃⣃ ⡗⡶⣾⠇⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣘⠀⠁⠀⠀⠀⠀⠀⢸⢿⠅⢸⡇⠀⠀⠀⠀⠀⠀⠀⠸⢯⢿⠇⢸⠀⠀⠀⣿⡇⢸⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠇⠂⣤⠄⣀⠫⠉ ⡏⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢩⠀⡀⠀⠀⠀⠀⠀⢰⢾⠃⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⢸⣀⢴⠀⣿⣅⢸⣿⢀⢸⡇⠸⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡷⢶⠶⣀⠀⠁⠱ ⣇⣁⣉⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢸⠁⡾⠀⠀⠀⠀⣶⠀⠀⠘⢼⠆⢸⡇⠀⠀⠀⠀⠀⠀⠀⠙⠐⠛⠀⢸⠛⠀⠀⣿⡃⣿⢻⠀⢼⡇⠀⠠⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠋⠋⠑ ⣏⠉⠉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⡿⠒⠆⠆⡆⢸⠀⠀⣠⢹⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⡀⠈⢸⠀⠈⡇⢠⠀⠂⠶⠶⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣇⣦⡿⡿⠀⢯⣯ ⣯⠋⠛⠃⠀⠸⡷⠂⠀⠀⠀⠀⠀⣤⠀⢸⢿⣷⣳⣿⣿⣇⣹⠀⠈⢙⢾⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⢸⣀⣀⠀⣿⣄⣀⢸⠀⢠⡅⠀⠆⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⠛⠻⠻⠿⠀⡿⣾ ⣎⣷⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡿⠻⠙⡻⠓⢻⠒⠒⠈⢸⠀⢸⡇⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⢸⠀⠀⠀⣿⡇⠀⢸⠀⠠⣇⠀⠀⢀⣶⣛⡌⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣳⣷ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⢨⠀⠀⠀⢸⡄⠸⠇⠀⠀⠀⣀⠴⠶⠴⠀⠀⠀⠀⢸⣀⣀⣀⣿⣇⡀⣼⠀⠐⡇⢠⣀⣀⣉⡉⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⡛⠛⢻ ⠯⣿⡏⠛⠙⠹⠇⠀⠀⠀⢴⡀⠀⠀⠀⠀⢈⣅⣬⣠⣈⣇⣀⢀⣀⣀⠀⣷⠄⠀⠀⠀⠀⣀⣀⣀⠀⠀⠰⠀⠀⠈⠉⢉⡉⣿⠀⠀⠈⠉⠉⠉⠉⡇⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⡀⠀ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⣶⡶⠶⠶⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠠⠆ ⣶⣶⣴⣤⣶⣶⠶⠶⠶⠶⠦⠶⠶⠶⠶⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⢶⠶⠆⢲⠲⢤⡶⠒⠒⠒⠶⠶⠶⠲⢸⡈⠍⠉⠎⠀⠀⠀⢴⢻⢿⡷⠾⠷⣾⣿⣟⣷⣷⣶⣻⣿⡿⣿⠷⣾⣷⣾⣿⣿⣿⣮⣶⣿⣾⣛⣗⣿⣟⣷⣿⣿⢿⡛⠛⠛⠛⠻⠟⠿⠿⠿⠿⠿⠿⠦⠆⠀⠀⠀⠀⣤⠀ ⣗⣒⣒⣒⣂⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠘⠃⣶⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣿⣧⣥⣤⣬⣿⣿⣯⢩⠯⡇⡄⣯⢻⣿⣿⣿⣳⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣷⣶⣿⣿⣿⣷⣶⣶⠖⠛⢻⠛⣿⠃⣴⠟⠓⠲⡦⣤ ⣏⣋⢛⣙⠃⠀⠘⠿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣯⡀⠀⠀⠀⠀⠀⠀⣸⣿⠛⢻⣟⣈⣭⣙⣛⣌⣉⣿⣿⣻⣙⡋⣿⣯⡙⠋⣿⣿⠿⣿⡿⡽⠿⢿⠿⠿⢿⢿⠿⢯⣿⣿⡯⣿⠿⣿⠿⠭⠿⠤⣟⣥⣄⢀⠀⡘⠀⣈⣯ ⡯⠉⠉⠉⠁⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠣⠀⠃⡄⡆⠀⠆⣿⣿⠀⢼⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠇⠀⣿⣼⢏⢹⠾⢀⡱⠆⠘⠀⣀⡰⠆⣿⠑⡘⠿⢿⡆⢿⣿⠎⣻⡿⠿⠿⠿⠿⣵⠿⠉⡱⠿ ⠿⠷⠶⠾⠆⢀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⡀⢀⣄⠁⠆⣑⣟⣿⠀⢹⣟⣛⣯⣻⣟⣟⣛⣿⣻⣿⡛⡛⣿⣿⡅⠀⣿⣿⠟⣸⠀⢸⡇⠀⡀⠀⠘⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣀⣤⣀⣀⣤⣼⣿⣿⣆⣷⣦ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠱⠈⠙⣆⠀⠀⢿⣹⠀⣸⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠇⠀⣿⡇⢐⣿⠐⢸⡇⠀⠧⠀⠄⡩⠍⠭⠉⠭⢍⠉⢿⢿⣟⠛⠛⠟⠻⠿⢿⠟⢟⣿⠛⠻⠗ ⣯⡯⣩⠉⠹⢭⡍⠉⠉⠿⡉⠉⠉⠉⠉⢙⠉⠱⠆⠀⠀⠰⠛⠀⠀⣀⣼⡅⢽⣿⣹⣿⣿⣙⣏⣹⣯⣿⡿⣉⣹⢿⠿⠀⠀⣿⡇⢼⣿⠄⢀⡆⠀⡆⠀⢀⡀⠀⠀⠀⠀⠀⠠⣄⠈⠀⣴⠀⠀⠀⠐⠁⠒⠅⠩⡉⣁⣠ ⣗⣶⡶⡶⣾⡏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢠⠀⠀⠀⠀⠆⠀⠂⢿⣻⠀⣼⣿⣿⣿⣿⡿⣿⣿⣿⣿⡇⣿⣿⣿⠋⠀⠀⣿⡇⡘⢿⠀⢸⡇⠀⠃⠀⠀⡁⠀⠀⠂⢶⣶⣶⣷⣶⠟⠓⠻⣿⣿⣿⢇⣀⣛⢻⣟⢻⣟ ⠆⢒⠒⠲⠃⣺⣶⡄⠀⠀⠀⠀⢀⡠⢀⣸⠀⠈⣤⡄⠀⠀⠀⠀⠁⢐⢸⠄⢹⡟⢻⣿⣿⠁⣛⢹⠿⣿⠉⢽⢿⣿⠀⠀⠀⣿⡆⠀⢸⠀⢸⡇⠀⠀⠡⡄⠀⠀⠀⠀⠈⠀⠈⠀⠀⣀⠀⠀⠉⠛⢟⡻⠃⢀⣛⡻⠊⠙ ⡏⠛⢻⣧⡤⠌⠙⠃⠠⠀⠀⠀⠜⠃⠜⢻⠀⢰⠋⠃⠀⠀⠀⠀⠀⢸⣺⠁⢨⡇⠲⠶⠶⠀⠀⠘⠶⠞⠀⠀⠀⣿⠀⠀⠀⣿⡇⢠⣾⠀⢘⡇⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣍⠰⠶⠭⢯⢤⣥⣯ ⡋⠛⠛⠛⠃⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠀⣠⠀⠀⠀⠃⠀⠀⠀⠸⢿⡂⢸⡇⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡤⢻⠀⠀⠀⣿⡇⠘⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠃⢲⣒⢚⠂⣃⣃ ⡗⡶⣾⠇⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣘⠀⠁⠀⠀⠀⠀⠀⢸⢿⠅⢸⡇⠀⠀⠀⠀⠀⠀⠀⠸⢯⢿⠇⢸⠀⠀⠀⣿⡇⢸⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠇⠂⣤⠄⣀⠫⠉ ⡏⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢩⠀⡀⠀⠀⠀⠀⠀⢰⢾⠃⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⢸⣀⢴⠀⣿⣅⢸⣿⢀⢸⡇⠸⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡷⢶⠶⣀⠀⠁⠱ ⣇⣁⣉⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢸⠁⡾⠀⠀⠀⠀⣶⠀⠀⠘⢼⠆⢸⡇⠀⠀⠀⠀⠀⠀⠀⠙⠐⠛⠀⢸⠛⠀⠀⣿⡃⣿⢻⠀⢼⡇⠀⠠⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠋⠋⠑ ⣏⠉⠉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⡿⠒⠆⠆⡆⢸⠀⠀⣠⢹⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⡀⠈⢸⠀⠈⡇⢠⠀⠂⠶⠶⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣇⣦⡿⡿⠀⢯⣯ ⣯⠋⠛⠃⠀⠸⡷⠂⠀⠀⠀⠀⠀⣤⠀⢸⢿⣷⣳⣿⣿⣇⣹⠀⠈⢙⢾⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⢸⣀⣀⠀⣿⣄⣀⢸⠀⢠⡅⠀⠆⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⠛⠻⠻⠿⠀⡿⣾ ⣎⣷⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡿⠻⠙⡻⠓⢻⠒⠒⠈⢸⠀⢸⡇⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⢸⠀⠀⠀⣿⡇⠀⢸⠀⠠⣇⠀⠀⢀⣶⣛⡌⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣳⣷ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⢨⠀⠀⠀⢸⡄⠸⠇⠀⠀⠀⣀⠴⠶⠴⠀⠀⠀⠀⢸⣀⣀⣀⣿⣇⡀⣼⠀⠐⡇⢠⣀⣀⣉⡉⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⡛⠛⢻ ⠯⣿⡏⠛⠙⠹⠇⠀⠀⠀⢴⡀⠀⠀⠀⠀⢈⣅⣬⣠⣈⣇⣀⢀⣀⣀⠀⣷⠄⠀⠀⠀⠀⣀⣀⣀⠀⠀⠰⠀⠀⠈⠉⢉⡉⣿⠀⠀⠈⠉⠉⠉⠉⡇⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⡀⠀ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⣶⡶⠶⠶⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠠⠆ ⣶⣶⣴⣤⣶⣶⠶⠶⠶⠶⠦⠶⠶⠶⠶⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⢶⠶⠆⢲⠲⢤⡶⠒⠒⠒⠶⠶⠶⠲⢸⡈⠍⠉⠎⠀⠀⠀⢴⢻⢿⡷⠾⠷⣾⣿⣟⣷⣷⣶⣻⣿⡿⣿⠷⣾⣷⣾⣿⣿⣿⣮⣶⣿⣾⣛⣗⣿⣟⣷⣿⠿⢿⡛⠛⠛⠛⠻⠟⠿⠿⠿⠿⠿⠿⠦⠆⠀⠀⠀⠀⣤⠀ ⣗⣒⣒⣒⣂⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠘⠃⣶⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣿⣧⣥⣤⣬⣿⣿⣯⢩⠯⡇⡄⣯⢻⣿⣿⣿⣳⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣷⣶⣿⣿⣿⣷⣶⣶⠖⠛⢻⠛⣿⠃⣴⠟⠓⠲⡦⣤ ⣏⣋⢛⣙⠃⠀⠘⠿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣯⡀⠀⠀⠀⠀⠀⠀⣸⣿⠛⢻⣟⣈⣭⣙⣛⣌⣉⣿⣿⣻⣙⡋⣿⣯⡙⠋⣿⣿⠿⣿⡿⡽⠿⢿⢿⠿⢿⢿⠿⢯⣿⣿⡯⣿⠿⣿⠿⠭⠿⠤⣟⣥⣄⢀⠀⡘⠀⣈⣯ ⡯⠉⠉⠉⠁⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠣⠀⠃⡄⡆⠀⠆⣿⣿⠀⢼⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠇⠀⣿⣼⢏⢹⠾⢀⡱⠆⠘⠀⣀⡰⠆⣿⠑⡘⠿⢿⡆⢿⣿⠎⣻⡿⠿⠿⠿⠿⣵⠿⠉⡱⠿ ⠿⠷⠶⠿⠆⢀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⡀⢀⣄⠁⠆⣑⣟⣿⠀⢹⣟⣛⣯⣻⣟⣟⣛⣿⣻⣿⡛⡛⣿⣿⡅⠀⣿⣿⠟⣸⠀⢸⡇⠀⡀⠀⠘⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣀⣤⣀⣀⣤⣼⣿⣿⣆⣷⣦ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠱⠈⠙⣆⠀⠀⢿⣹⠀⣸⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠇⠀⣿⡇⢘⣿⠐⢸⡇⠀⠧⠀⠄⡩⠍⠭⠉⠭⢍⠉⢿⢿⣟⠛⠛⠟⠻⠿⢿⠟⢟⣿⠛⠻⠗ ⣯⡯⣩⠉⠹⢭⡍⠉⠉⠿⡉⠉⠉⠉⠉⢙⠉⠱⠆⠀⠀⠰⠛⠀⠀⣀⣼⡅⢽⣿⣹⣿⣿⣙⣏⣹⣯⣿⡿⣉⣹⢿⠿⠀⠀⣿⡇⢼⣿⠄⢀⡆⠀⡆⠀⢀⡀⠀⠀⠀⠀⠀⠠⣄⠈⠀⣴⠀⠀⠀⠐⠁⠒⠅⠩⡉⣁⣠ ⣗⣶⡶⡶⣾⡏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢠⠀⠀⠀⠀⠆⠀⠂⢿⣻⠀⣼⣿⣿⣿⣿⡿⣿⣿⣿⣿⡇⣿⣿⣿⠋⠀⠀⣿⡇⡘⢿⠀⢸⡇⠀⠃⠀⠀⡁⠀⠀⠂⢶⣶⣶⣷⣶⠟⠓⠻⣿⣿⣿⢇⣀⣛⢻⣟⢻⣟ ⠆⢒⠒⠲⠃⣺⣶⡄⠀⠀⠀⠀⢀⡠⢀⣸⠀⠈⣤⡄⠀⠀⠀⠀⠁⢐⢸⠄⢹⡟⢻⣿⣿⠁⣛⢹⠿⣿⠉⢽⢿⣿⠀⠀⠀⣿⡆⠀⢸⠀⢸⡇⠀⠀⠡⡄⠀⠀⠀⠀⠈⠀⠈⠀⠀⣀⠀⠀⠉⠛⢟⡻⠃⢀⣛⡻⠊⠙ ⡏⠛⢻⣧⡤⠌⠙⠃⠠⠀⠀⠀⠜⠃⠜⢻⠀⢰⠋⠃⠀⠀⠀⠀⠀⢸⣺⠁⢨⡇⠲⠶⠶⠀⠀⠘⠶⠞⠀⠀⠀⣿⠀⠀⠀⣿⡇⢠⣾⠀⢘⡇⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣍⠰⠶⠭⢯⢦⣥⣯ ⡋⠛⠛⠛⠃⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠀⣠⠀⠀⠀⠃⠀⠀⠀⠸⢿⡂⢸⡇⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡤⢻⠀⠀⠀⣿⡇⠘⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠃⢲⣒⢚⠂⣃⣃ ⡗⡶⣾⠇⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣘⠀⠁⠀⠀⠀⠀⠀⢸⢿⠅⢸⡇⠀⠀⠀⠀⠀⠀⠀⠸⢯⢿⠇⢸⠀⠀⠀⣿⡇⢸⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠇⠂⣤⠄⣀⠫⠉ ⡏⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢩⠀⡀⠀⠀⠀⠀⠀⢰⢾⠃⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⢸⣀⢴⠀⣿⣅⢸⣿⢀⢸⡇⠸⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡷⢶⠶⣀⠀⠁⠱ ⣇⣁⣉⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢸⠁⡾⠀⠀⠀⠀⣶⠀⠀⠘⢼⠆⢸⡇⠀⠀⠀⠀⠀⠀⠀⠙⠐⠛⠀⢸⠛⠀⠀⣿⡃⣿⢻⠀⢼⡇⠀⠠⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠋⠋⠑ ⣏⠉⠉⠁⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⡿⠒⠆⠆⡆⢸⠀⠀⣠⢹⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⡀⠈⢸⠀⠈⡇⢠⠀⠂⠶⠶⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣇⣾⡿⡿⠀⢯⣯ ⣯⠋⠛⠃⠀⠸⡷⠂⠀⠀⠀⠀⠀⣤⠀⢸⢿⣷⣳⣿⣿⣇⣹⠀⠈⢙⢾⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⢸⣀⣀⠀⣿⣄⣀⢸⠀⢠⡅⠀⠆⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⠛⠻⠻⠿⠀⡿⣾ ⣎⣷⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡿⠻⠙⡻⠓⢻⠒⠒⠈⢸⠀⢸⡇⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⢸⠀⠀⠀⣿⡇⠀⢸⠀⠠⣇⠀⠀⢀⣶⣛⡌⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣳⣷ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⢨⠀⠀⠀⢸⡄⠸⠇⠀⠀⠀⣀⠴⠶⠴⠀⠀⠀⠀⢸⣀⣀⣀⣿⣇⡀⣼⠀⠐⡇⢠⣀⢀⣉⡉⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⡛⠛⢻ ⠯⣿⡏⠛⠙⠹⠇⠀⠀⠀⢴⡀⠀⠀⠀⠀⢈⣅⣬⣠⣈⣇⣀⢀⣀⣀⠀⣷⠄⠀⠀⠀⠀⣀⣀⣀⠀⠀⠰⠀⠀⠈⠉⢉⡉⣿⠀⠀⠈⠉⠉⠉⠉⡇⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⡀⠀ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⡶⠶⠴⠴⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠠⠆ ⡶⣦⣤⣤⣤⣤⠤⠤⠤⠤⠤⠤⠤⠤⠴⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⢦⠶⠆⢲⠲⢤⡲⠒⠒⠒⠴⠶⠶⠲⢸⡈⠍⠉⠎⠀⠀⠀⢴⠻⢿⡷⠾⠷⣾⣿⣟⣶⣷⣲⢺⣷⡿⢷⠷⣾⣷⣒⣒⣓⣛⣮⣶⣷⣾⣛⣓⣿⣗⣶⣷⠒⢚⡛⠛⠚⠛⠛⠛⠻⠿⠷⠿⠿⠿⠦⠆⠀⠀⠀⠀⣤⠀ ⣒⣒⣒⣒⡂⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠘⠃⣆⠀⠀⠀⠀⠀⠀⠀⣬⣿⣷⣿⣧⣤⣤⣨⣿⣶⣯⢩⣫⣥⣤⣯⢻⣟⣿⣿⣳⣾⣿⣿⣿⣿⣿⣿⢿⣿⣷⣶⣷⣷⣶⣿⣿⣿⣷⣶⣶⣶⣷⣿⣿⣿⣤⣴⢿⣶⣶⣦⣤ ⣏⣋⢉⣉⠃⠀⠘⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣏⡀⠀⠀⠀⠀⠀⠀⣸⣿⠚⢻⣏⣈⣭⣘⣛⣌⣈⣾⣾⣻⣙⡋⣿⣏⡉⠋⣿⣯⠿⣿⡽⢽⠿⢯⠽⠯⣯⡿⡿⢯⣿⣯⣿⢿⠿⣼⠿⠿⠽⠿⣌⠿⠟⠛⠛⠛⠛⠃⠿ ⡯⠉⠉⠉⠁⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠣⠀⠁⡄⡆⠀⠄⢿⣿⠀⢼⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⣿⣿⣿⣿⢿⡇⣿⣔⠏⣿⢿⣿⠷⠆⠐⠘⣿⠉⣿⠉⠀⠈⣿⢻⠀⠿⠿⠎⠻⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀ ⠿⠷⠶⠾⠆⠀⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⡀⢀⣄⠁⠆⣑⣝⣿⠀⢹⣟⣛⣯⣻⣟⣟⣛⣿⣻⣿⡛⡛⣿⣻⡟⠛⣿⣿⠟⣻⣛⣻⡇⠀⡀⠀⣘⣻⣿⣾⣿⡟⣷⣤⣄⣄⣄⣀⣀⣀⣀⣀⣤⣸⣿⣿⣆⣄⣠ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠱⠈⠉⣆⠀⠀⠿⣹⠀⣸⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢿⡇⣿⡇⠀⣿⠙⢻⠇⠀⠧⠘⣿⠿⣿⠭⠉⠅⣿⠉⢿⠿⠟⠛⠛⠛⠻⠿⢿⠟⠛⠛⠛⠛⠓ ⡯⡭⣩⠉⠩⢭⡍⠉⠉⠿⡉⠉⠉⠉⠉⢙⠉⠱⠆⠀⠀⠀⠛⠀⠀⣀⣼⠄⢽⣟⣹⣿⣿⣙⣏⣹⣯⣿⡿⣉⣹⢿⣿⣛⠃⣿⡇⠼⣿⣟⣛⡇⠀⡆⠀⢛⡛⠃⠀⠀⠀⣿⠀⣄⠈⠀⣴⠀⠀⠀⠀⠀⠒⠀⠈⡁⣀⣀ ⢇⡶⠶⡶⢾⠏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢀⠀⠀⠀⠀⠆⠀⠂⠿⣻⠀⣼⣿⣿⣿⣿⡻⣿⣿⣿⣿⡇⣿⣿⣿⡿⢻⡇⣿⡇⡐⣿⣿⣿⡇⠀⠃⠀⠀⠁⠀⠀⠀⠆⣟⣶⡷⣶⠟⠓⠻⣿⣿⣿⢇⡀⡛⢛⣛⢻⣟ ⠆⢒⠒⠒⠃⣺⣶⡄⠀⠀⠀⠀⢀⡀⢀⣸⠀⠈⢠⡄⠀⠀⠀⠀⠁⠀⢸⠀⢹⡍⢻⡿⢿⠁⣛⢹⠿⢿⠉⢽⢿⣿⠛⠛⠃⣿⡆⠀⢸⠛⢻⡇⠀⠀⠀⡄⠀⠀⠀⠀⠀⣿⠀⠀⠀⣀⠀⠀⠉⠛⢛⠛⠃⢀⠘⠛⠊⠙ ⡏⠛⠻⢧⡤⠌⠙⠃⠠⠀⠀⠀⠜⠃⠜⢻⠀⢰⠋⠃⠀⠀⠀⠀⠀⢀⣺⠀⢠⡇⠲⠶⠶⠀⠀⠘⠶⠞⠀⠀⠀⣿⠀⠀⠀⣿⡇⠀⣾⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⠬⠧⢤⣥⣤ ⡉⠛⠛⠛⠃⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠀⡠⠀⠀⠀⠃⠀⠀⠀⠨⢿⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⣿⡇⠘⣿⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⡁⠂⢒⣒⢒⠀⣂⣁ ⠗⡶⣾⠃⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣘⠀⠁⠀⠀⠀⠀⠀⠈⢿⠄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⡇⢸⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠩⠉ ⡎⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢡⠀⡀⠀⠀⠀⠀⠀⠐⢾⠂⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢸⢀⢴⠀⣿⣅⢸⣿⠀⢸⡇⠸⠗⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀ ⣇⣁⣈⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢸⠀⡾⠀⠀⠀⠀⣶⠀⠀⠐⢼⠄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢸⠈⠀⠀⣿⡃⢻⢻⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠉⠉⠀ ⣏⠉⠉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⡿⠒⠆⠆⠂⢸⠀⠀⡀⢹⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⡀⠈⢸⠀⠈⡇⢠⠀⠀⠶⠖⠀⠀⢀⡄⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣯⠋⠛⠃⠀⠸⡷⠂⠀⠀⠀⠀⠀⣤⠀⢸⢿⣷⣳⣿⣿⣇⣹⠀⠈⠉⢾⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⢸⣀⣀⠀⣿⣄⣀⢸⠀⢠⡅⠀⠆⠀⠀⠀⣀⡴⠋⠀⣿⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠻⠿⠀⠀⠀ ⠎⣷⣿⡷⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡟⠻⠙⡻⠓⢻⠒⠒⠈⢸⠀⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⠀⠀⠀⣿⡇⠀⢸⠀⠠⡇⠀⠀⠀⣶⣛⡌⠀⠀⠀⣿⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤ ⡛⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⠨⠀⠀⠀⢸⡄⠸⠇⠀⠀⠀⣀⠤⠴⠴⠀⠀⠀⠀⢸⣀⣀⣀⣿⣇⡀⣸⠀⠐⡇⢠⣀⢀⣉⡉⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⡛⠛⢻ ⠯⣿⡏⠛⠙⠹⠇⠀⠀⠀⢴⡀⠀⠀⠀⠀⢀⣄⣬⣠⣈⣇⣀⢀⣀⣀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠉⠉⠉⣿⠀⠀⠈⠉⠉⠉⠉⡇⠀⠈⠁⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⡀⠀ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⣶⣶⠶⠶⢶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠰⠆ ⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡷⢶⠶⠆⣶⠳⢤⡶⠒⠒⠒⠶⠶⠶⠲⢺⡈⣽⠉⠎⠀⠀⠀⢴⣿⢿⡿⠾⠷⣾⣿⣿⣷⣿⣿⣻⣿⣿⣿⠿⣾⣷⣿⣿⣿⣿⣾⣶⣿⣾⣟⣗⣿⣿⣿⣿⢿⢿⡿⠿⠿⠟⠿⠟⠿⠿⠿⠿⠿⠿⠦⠆⠀⠠⠄⠀⣤⠀ ⣗⣒⣒⣒⣂⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠘⠓⣾⠀⠀⠀⠀⠀⠀⠁⣼⣿⣷⣿⣧⣥⣤⣼⣿⣿⣿⢩⢯⡇⢰⡟⣙⢛⣟⢫⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣿⣾⣿⣿⣿⣿⣾⣾⣶⣿⣿⣿⣿⣿⣾⣿⣷⣶⢦⣤ ⣟⣋⣛⣛⠋⠀⠸⠿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣯⡀⠀⠀⠀⠀⠀⠀⣸⣿⠛⢿⣟⣈⣭⣙⣻⣌⣉⣿⣿⣿⣝⣛⡟⠋⠛⢻⣟⠟⠏⢛⠻⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⠿⣿⠿⠿⠿⢿⣟⣽⣿⣇⣽⡯⢃⣍⣿ ⡯⠉⠉⠍⠁⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠣⠀⠃⡄⣆⠀⠆⣿⣿⠀⢾⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢐⣿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡹⢿⣿⣮⣿⣿⣿⣿⡿⣿⣽⢿⢉⣥⣿ ⠿⠷⠷⡿⠆⢠⣾⡄⡀⠀⡀⠀⠀⠀⠀⠀⠀⣿⣧⡀⢀⣄⠉⠆⣑⣿⣿⠃⢹⣟⣛⣯⣻⣿⣟⣛⣿⣿⣿⣟⣛⡴⠰⠄⢀⡷⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠁⠀⠀⠀⢀⣤⣤⣤⣤⣥⣀⣤⣅⣤⣤⣼⣿⣿⣟⣷⣶ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠱⠈⠹⣆⠀⠀⢿⣹⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠀⠀⠐⡧⠀⠀⠂⠀⠀⠀⠀⠆⠀⠀⠀⠀⠄⠀⠀⠀⡉⢿⢿⣿⣿⣟⣟⣻⣿⣿⣿⣿⣿⢻⣿⣷ ⣯⡯⣩⠉⠹⢯⡏⠉⠉⠿⡉⠉⠉⠉⠉⢙⠉⠹⠆⠀⠀⠰⠛⠀⠀⣠⣼⡇⢽⣿⣹⣿⣿⣙⣯⣻⣯⣿⡿⣍⣹⠷⠶⠒⠂⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢠⣄⠉⠀⣶⡀⢠⣰⠒⠇⠖⢟⢿⣿⣹⣷ ⣷⣶⡶⣶⣾⡏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢰⠀⠀⠀⠀⠆⠀⠂⢿⣻⠀⣽⣿⣿⣿⣿⡿⣿⣿⣿⣿⡇⣿⣿⡃⠀⠀⠀⡟⠃⠀⠂⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠠⣶⣷⣾⡿⠓⠿⣿⣿⣿⣧⣉⣛⣻⣟⢻⣟ ⠗⣒⠒⡲⠓⣺⣶⡄⠀⠀⠀⠀⢀⡠⢀⣸⠂⠘⣤⡄⠀⠀⠀⠀⠁⢸⢸⡇⢹⡟⢻⣿⣿⠁⣛⢹⢿⣿⠋⢽⢿⣿⠐⠒⠂⣗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠉⠉⣀⠂⡀⠉⠻⣿⣿⣯⣀⣻⡿⣯⢝ ⡏⠛⢻⣧⡤⠌⠙⠃⠠⠀⠀⠀⠜⠃⠜⢻⠀⢰⠋⠃⠀⠀⠀⠀⠀⢸⣺⡇⢨⡇⠶⠶⠶⠀⠀⠘⠶⠾⠀⠀⠈⣿⠂⠀⠀⣧⠀⠄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢨⣭⢸⠿⠯⢿⣯⣿⣯ ⡛⠛⠛⠛⠃⣀⠀⠀⠒⠀⠀⠀⠀⠀⠀⢸⠀⣠⠀⠀⠀⠃⢀⠀⠀⢸⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⢻⡀⠀⠀⣏⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⢀⣳⠫⢿⣿⣿⢟⣋⣷ ⡷⣶⣾⠇⠀⢻⡃⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣸⠀⠁⠀⠀⠈⠀⠀⢸⢿⡅⢸⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠒⠀⠀⠀⠀⠀⢸⣟⣇⡺⣦⣄⣀⢻⡛ ⡟⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢽⠀⡀⠀⠀⠀⠀⠀⢸⢾⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢸⣅⣶⠀⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠚⢿⣿⣿⣿⣒⣑⣛⣷ ⣇⣁⣉⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢸⠁⣾⠀⠀⠀⠀⣶⠀⠀⢸⢼⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠿⠿⠟⠛⢸⠻⠠⠀⣏⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠂⠙⠊⠁⠈⠙⠛⠋⠛ ⣏⠋⠛⠁⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⣿⠖⠆⠆⡆⢸⠀⠀⣸⢹⠃⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢸⡀⠀⠀⣧⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣟⣾⡿⣿⢌⣿⣿ ⣯⠋⠛⠃⠀⠸⣷⠆⠀⠀⠀⠀⠀⣦⠀⢸⢿⣿⣻⣿⣿⣧⣹⠀⠈⢹⢾⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⣀⢸⣀⣀⠀⡿⠀⠐⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠠⠀⠁⠀⠟⠿⠿⠿⠻⠿⠳⣿⣿ ⣞⣿⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡿⠻⠛⡻⠓⢻⠒⠒⠈⢸⠄⢸⡇⠀⠀⠀⠀⠀⡀⡀⠀⠀⡀⠀⢸⠀⠠⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣄⠈⠀⠀⠀⠀⠀⠀⠀⢛⡄⠀⠂⠀⠀⠀⣀⣀⣀⣸⣿⣿ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⢸⠀⠀⠀⢸⡆⠸⠇⠀⠀⠀⣀⠴⠶⠶⠀⠀⠀⠀⢸⣀⣄⠀⣧⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀⣀⠀⢀⠀⢠⠀⠀⠀⠁⠀⠀⠙⣛⡛⠛⢻ ⡯⣿⡟⠛⠙⠹⠇⠀⠀⠀⣴⡄⠀⠀⠀⠀⢈⣅⣬⣠⣈⣇⣀⢀⣀⣄⠐⣷⣆⣀⣀⣀⣀⣀⣀⣀⡀⠀⠰⠀⠀⠈⣉⣉⡁⣾⠉⠉⠉⠉⠉⠉⠉⣿⡉⠉⠉⠉⠉⠉⠉⠙⢛⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠁⡀⠀ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⣶⣶⠶⠶⣶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠰⠆ ⣶⣶⣷⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡷⢶⠶⠦⣶⠳⢤⡶⠒⠒⠒⠶⠶⠶⠲⢺⡈⣽⠉⠎⠀⠀⠀⣴⣿⢿⡿⠾⠷⣾⣿⣿⣷⣿⣿⣻⣿⣿⣿⡿⣾⣿⣿⣿⣿⣿⣾⣶⣿⣾⣿⣗⣿⣿⣿⣿⢿⢿⡿⠿⠿⠟⠿⠟⠿⠿⠿⠿⠿⠿⠦⠆⠀⠠⠄⠀⣤⠀ ⣷⣶⣲⣶⣂⣤⡄⣠⣄⢀⡀⢀⣀⣠⢀⣜⣳⣾⠀⠀⠀⠀⠀⠀⠁⣽⣿⣷⣿⣧⣥⣤⣼⣿⣿⣿⢹⢯⣇⣱⣛⣟⣛⣿⣫⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣶⣶⣶ ⣟⣋⣛⣛⠋⠛⠸⠿⡏⠛⠛⠛⠛⠛⠋⠓⠛⣯⡀⠀⠀⠁⠀⠀⠀⣸⣿⠛⢿⣟⣈⣭⣽⣿⣌⣉⣿⣡⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠻⢓⡚⠋⠛⢉⠛⠙⠋⠍⠍ ⡯⠉⠉⠍⠁⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠣⠀⠇⡅⣆⠀⠦⣿⣿⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⠉⠉⠿⠋⡉⠉⠿⠏⠉⠉⠉⠉⠉⠉⠉⠁⠉⠁⠉⠁⠉⠋⢙⣹⣿⣼⣮⣿⣿⣿⣿⣿⣿⣿⣾⣿⣵⣾ ⠿⡿⣿⣿⡇⣠⣾⡅⣐⠀⡉⠁⠐⠀⡁⠀⠀⣿⣧⡀⢀⣄⠉⠆⣓⣿⣿⠃⢹⣟⣿⣯⣻⣿⣟⣛⣿⣻⣸⣿⣷⠀⠈⠄⠀⠐⠀⢀⠀⠀⠠⠀⠀⠅⠅⠀⠀⠁⠆⠀⠀⢠⣦⣤⣤⣤⣧⣄⣤⣅⣤⣤⣼⣿⣿⣿⣷⣶ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠱⠈⢹⣦⠀⠁⢿⣹⠌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⠐⠐⠛⠀⠀⠀⠀⠀⠀⠂⢀⠀⠈⠀⠆⠀⠀⠀⠀⠄⠂⠀⠀⡫⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣷ ⣿⡯⣩⠉⠹⢯⡏⠯⠽⠿⡉⠉⠹⠏⠉⢿⠉⠹⠆⠀⠀⠰⠛⠀⠀⣨⣼⡇⢽⣿⣹⣿⣿⣙⣯⣻⣯⣽⢸⠰⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠠⠀⠀⢢⣄⠉⢉⣶⣀⣱⣴⢚⠿⠶⣿⣿⣿⣽⣷ ⣷⣶⡶⣶⣾⡟⠛⠐⠀⠙⠁⠀⠀⠀⠀⢸⠀⢰⠀⠀⠀⠀⠆⠀⠂⢿⣻⣄⣿⣿⣿⣿⣿⡿⣿⣿⣿⢯⢸⠂⠀⠀⠀⠀⠀⠘⡣⠀⠂⡀⠀⠀⢀⠂⡀⠀⠀⠀⠀⠠⠀⢠⣾⣿⣾⡿⠗⠿⣿⣿⣿⣯⣋⣛⣿⣟⢿⣟ ⢗⣒⠒⡲⠓⣺⣶⡄⠀⠀⠀⠀⢀⡠⢀⣸⠂⠸⣤⡄⠀⠀⠀⠀⠁⢸⢸⡇⢹⡟⢻⣿⣿⠁⣛⢹⢿⠿⢸⠀⢠⣖⠀⡀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠃⠀⠀⠘⠋⠉⠉⣁⠂⡀⠭⠻⣿⣿⣯⣐⣿⡿⣯⣝ ⡏⠛⢻⣧⡤⠌⠙⠃⠠⠀⠀⠀⠜⠃⠜⢻⠀⢰⠋⠃⠀⠀⠀⠀⠀⢸⣺⡇⢨⡇⠶⠶⠶⠀⠀⠘⠶⠲⢸⡒⠀⡁⠀⠀⠀⠀⠀⠄⠁⠠⠀⠀⠄⠁⠅⠊⠄⠤⠁⠄⠄⠠⠈⠀⠀⠄⢄⡀⠀⢺⣽⢾⠿⠯⢿⣿⣿⣿ ⡛⠛⠛⠛⠃⣀⠀⠀⠒⠂⠀⠀⠀⠀⠀⢸⠒⣠⠀⠀⠀⠃⢀⠀⠀⢸⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⡄⢸⡫⠀⠇⠀⡀⠠⢀⡀⠀⠁⠀⠀⠀⠀⡁⠀⠀⠀⠀⠁⠀⠀⠀⠀⣀⠀⠹⠄⠄⠀⢨⣳⠻⢿⣿⣿⢟⣛⣿ ⡷⣶⣾⠇⠀⢻⡃⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣸⠀⠁⠀⠀⠈⠀⠀⢸⢿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠃⢸⢡⠀⠀⠀⠂⠐⠀⠅⠈⡂⠠⠀⠀⠈⡤⢔⢀⠀⠈⡤⠀⠁⠄⠀⡒⡀⠂⠐⠀⠀⢸⣿⣷⣾⣦⣄⣠⣿⣟ ⡟⡶⠶⠇⠀⠘⠏⠀⠀⠀⠁⠀⠀⠀⠀⢹⡇⢿⠀⡀⠀⠀⠀⠀⠀⢸⢾⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⣶⢸⠀⠀⡆⠀⠀⠀⠀⠉⠀⠄⠀⠀⠐⠀⠀⠀⡀⠀⠂⠀⠀⠀⡐⡤⠀⠀⠁⠀⠀⠀⠚⣿⣿⣿⣿⣟⣙⣛⣷ ⣇⣁⣉⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢸⠉⣾⠀⠀⠀⠀⣶⠀⠀⢸⢼⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠇⢸⠜⠀⠁⠄⠀⠀⢀⠹⢄⠁⠀⠀⠀⡂⠀⠀⠀⠀⠁⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀⠀⠂⠙⡋⠉⢘⡛⠛⠛⠛ ⣏⠋⠛⢁⣀⣠⣀⢀⣀⣀⣀⣀⣀⣀⣀⣸⣠⣿⠖⠆⢶⡆⣸⠀⠀⣸⢹⠃⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⢸⠞⠂⡇⡀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⡿⣿⢎⣿⣿ ⣿⠋⠛⠃⠋⠹⣷⠞⠙⠛⠋⠛⠊⣯⠛⢻⣿⣿⣻⣿⣿⣧⣹⠀⠈⢹⢾⠂⢰⡇⠀⠀⠀⠀⠀⠀⠀⣀⢸⠟⠀⡇⠀⠂⠀⠘⠀⢐⠀⠀⠀⠀⠀⠁⠊⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠠⢁⡁⠀⠟⠿⠿⠿⠻⠿⠻⣿⣿ ⣞⣿⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠹⡿⠻⠛⡻⠓⢻⠒⠒⠘⢸⠇⢸⡇⠀⠀⠀⠀⠀⡀⡀⠀⢸⠀⠀⠀⠀⠀⠀⢘⠀⠐⠀⠀⠀⠀⠀⠀⠐⢲⣀⠈⠀⠀⠀⠐⠁⠀⠀⢛⡄⢌⠇⠀⡀⠀⣀⣀⣀⣸⣿⣿ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡵⢸⠀⠀⠀⢸⡆⠸⠇⠀⠀⠀⣀⠴⠶⠶⠀⢸⠸⠃⠀⠀⠀⠀⠀⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⡄⢀⣀⣠⣀⠠⢀⠄⢠⠁⠀⠈⠁⠀⠒⠙⣛⡛⠛⢿ ⡿⣿⡟⠛⠙⠹⠇⠀⠀⠀⣴⡄⠀⠀⠀⠀⢈⣅⣬⣠⣈⣇⣀⣀⣀⣄⢰⣷⣆⣄⣠⣀⣀⣀⣀⣀⡀⠀⢸⠸⠇⠀⠁⠀⠀⢀⠍⠉⠉⠉⠉⠉⠉⣿⡉⠉⠉⠉⠩⡩⢍⠙⢛⡍⠀⠀⣠⠀⠠⠀⠀⠀⠀⠀⠉⠁⡀⠀ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⣶⡶⠶⠶⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠠⠆ ⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⢶⠶⠆⢶⠲⢤⡶⠒⠒⠒⠶⠶⠶⠲⢸⡈⣍⠉⠎⠀⠀⠀⣶⣿⢿⣾⣾⣗⣾⣿⣟⣶⣾⣿⣻⣿⣿⣿⣿⣾⣷⣿⣿⣓⣿⣶⣶⣿⣺⣛⣓⣿⣿⣿⣿⣿⣿⣟⢛⣻⣟⣻⡟⡿⢟⣿⣿⣻⣻⡶⠆⠀⠠⠄⠀⣤⠀ ⣷⣶⣶⣶⣆⠀⢲⢠⡀⠀⠀⠀⠀⠀⠀⢼⠃⣾⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⢿⣿⣟⣋⣐⣒⣒⣢⣶⣾⣾⣷⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣾⣖⣶⣶⣶⣶⡾⣟⣺⣿⣷⣿⣽⣾⣿⣷⣶⣆⣤ ⡗⠋⠛⠟⠋⠀⠘⠿⡏⠀⠀⠀⠀⠀⠀⢸⠀⣯⡀⠀⠀⠀⠀⣿⡄⣸⣿⠛⢿⣟⣈⣭⣙⣻⣌⣉⣿⣡⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡿⣿⣿⣿⣿⣿⠻⠉⠙⠀⠊⣿⠙⢀⠋⠉⠁⠉⠁ ⣿⣿⣯⣭⡅⣀⣤⣄⣀⣀⣀⣀⣀⣀⡀⣿⠀⣿⠣⠀⠃⡄⡆⣿⠄⣿⣿⠀⢼⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡉⠉⠉⠉⠉⠈⠉⠿⠏⠉⠉⠉⠉⠉⠉⠈⠁⠈⠀⠈⠁⠉⠉⠉⠩⢷⣸⡮⣻⡿⣿⣿⠿⡿⣴⢶⢁⡤⠶ ⠟⠷⠶⠿⠆⢀⣶⡄⠀⠀⠀⠀⠀⠀⠀⢸⠀⢿⣇⡀⢀⣄⠁⣿⣑⣟⣿⠀⢹⣟⣛⣯⣻⣟⣟⣛⣿⣻⢸⠶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠰⠀⠁⠀⠀⠀⢀⣤⣄⣤⣤⣤⣁⣤⣀⣿⣠⣼⣿⣿⣞⣷⣦ ⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠱⠈⠙⣆⣿⠀⢿⣹⠀⣸⣿⣿⣿⣿⡿⣿⣿⣿⣿⢺⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⢿⣿⢛⡛⢟⣻⣿⢿⢟⣟⣿⠻⢻⣷ ⣧⡯⣩⠉⠹⢭⡍⠉⠉⠿⡉⠉⠉⠉⠉⢹⠉⠱⠆⠀⠀⠰⠛⣿⠀⣀⣼⡅⢽⣿⣹⣿⣿⣙⣏⣹⣯⣽⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠉⠀⣴⢀⠀⠀⣿⠇⠒⠇⠫⡉⣁⣠ ⣷⣶⡶⡶⣾⡏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢰⠀⠀⠀⠀⠆⣿⠂⢻⣻⠀⣼⣿⣿⣿⣿⡿⣿⣿⣿⢫⢸⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡷⣾⠟⠓⠻⣿⣿⣿⣇⣈⣛⢻⣟⢻⣟ ⠶⢒⠒⠲⠃⣺⣶⡄⠀⠀⠀⠀⢀⡠⢀⣸⠀⠈⣤⡄⠀⠀⠀⣿⠁⢘⢸⠆⢹⡟⢻⣿⣿⠁⣛⢹⠿⠾⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣀⠀⠀⠉⠛⣿⡻⠃⣀⣛⡻⢎⠙ ⡏⠛⢻⣧⡤⠌⠙⠃⠠⠀⠀⠀⠜⠃⠜⢻⠀⢰⠋⠃⠀⠀⠀⣿⠀⢸⣺⡇⢨⡇⠲⠶⠶⠀⠀⠘⠶⠒⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠰⠿⠭⢯⣦⣽⣯ ⡋⠛⠛⠛⠃⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠀⣠⠀⠀⠀⠃⠀⣿⠀⠸⢿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⢻⣒⢟⠒⣃⣓ ⡷⡶⣾⠇⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣸⠀⠁⠀⠀⠀⣿⠀⢸⢿⡅⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡯⠇⠊⣤⢄⣀⢻⠋ ⡟⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢩⠀⡀⠀⠀⠀⣿⠀⢸⢾⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⣶⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡷⠺⣷⣶⣒⣁⡛⣳ ⣇⣁⣉⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢸⠁⡾⠀⠀⠀⠀⡆⣿⠀⢸⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠁⢸⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠈⠁⠈⠙⠛⠋⠙ ⣏⠉⣉⠁⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⡿⠒⠆⠆⡆⠀⣿⠀⣨⢹⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⢗⣾⡿⣿⠀⣯⣿ ⣯⠋⠻⢃⠀⠸⣷⠂⠀⠀⠀⠀⠀⣤⠀⢸⢿⣷⣳⣿⣿⣇⣱⠙⠬⢿⢾⠶⢶⡷⠶⠶⠶⠴⠶⠦⠶⣶⢼⠶⠶⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠶⠶⠶⠶⠶⠦⠶⠶⠶⠿⠧⠛⠻⠻⠿⠀⣿⣿ ⣎⣷⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠙⡿⠻⠙⡻⠓⢻⠒⠒⠈⢸⠄⢺⡇⠀⠀⠀⠀⠀⠀⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣀⠈⠀⠀⠀⠀⠀⠀⠀⠛⡀⠀⠀⠀⠀⠀⣀⣀⣀⣰⣳⣷ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⢨⠀⠀⠀⢸⡆⠸⠇⠀⠀⠀⣀⠴⠶⠴⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⣀⠀⣀⡀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⡛⠛⢻ ⡯⣿⡏⠛⠙⠹⠇⠀⠀⠀⢴⡄⠀⠀⠀⠀⢈⣅⣬⣠⣈⣇⣀⢀⣀⣄⠀⣷⡆⡀⠀⠀⣀⣀⣀⣀⠐⠀⢼⡒⠒⠒⠒⠒⠀⠀⡉⢉⠉⡉⠉⠉⠉⡏⠉⠉⠉⠉⠉⠉⠉⢙⣋⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠁⡀⠀ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⣶⡶⠶⠶⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠠⠆ ⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⢶⠶⠆⢲⠲⢤⡶⠒⠒⠒⠶⠶⠶⠲⢸⡈⣍⠉⠎⠀⠀⠀⣶⣿⣿⣾⣾⣗⣾⣿⣟⣶⣾⣶⣻⣿⣿⣿⣷⣾⣷⣿⣿⣓⣿⣶⣶⣿⣺⣛⣓⣿⣟⣷⣿⣿⣿⣛⢛⣻⣟⣻⡟⡿⢟⣿⣿⣻⣻⡶⠆⠀⠠⠄⠀⣤⠀ ⣷⣶⣶⣶⣆⠀⢲⢠⡀⠀⠀⠀⠀⠀⠀⢸⢳⣾⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⣒⣒⣢⣶⣾⣾⣷⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣾⣖⣶⣶⣶⣶⡾⣟⣺⣿⣷⣿⣵⣶⣿⣷⣶⣆⣤ ⡗⠋⠛⠟⠃⠀⠘⠿⡏⠀⠀⠀⠀⠀⠀⢸⢸⣯⡀⠀⠀⠀⠀⣿⣾⣾⣿⠛⢻⣟⣈⣭⣙⣻⣌⣉⣿⣠⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡿⣿⣿⣿⣿⣿⠻⠉⠙⠀⠊⣿⠉⠀⠋⠉⠁⠉⠁ ⣿⣿⣯⣭⡅⣀⣤⣄⣀⣀⣀⣀⣀⣀⡀⣿⠈⣿⠣⠀⠃⡄⡆⣿⢾⣿⣿⠀⢼⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡉⠉⠉⠉⠉⠈⠉⠿⠏⠉⠈⠉⠉⠉⠉⠈⠁⠈⠀⠈⠁⠉⠉⠉⠩⢷⣸⡮⣻⡿⢿⣿⠿⠿⣴⢶⠁⡠⠶ ⠟⠷⠶⠿⠆⢀⣶⡄⠀⠀⠀⠀⠀⠀⠀⢸⠀⢿⣇⡀⢀⣄⠁⣿⢹⣙⣿⠀⢹⣟⣛⣯⣻⣟⣟⣛⣿⣻⢸⠶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠰⠀⠁⠀⠀⠀⢀⣤⣄⣤⣤⣤⣁⣤⣀⣿⣠⣼⣿⣿⣆⣷⣦ ⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠱⠈⠙⣆⣿⢸⢿⣹⠀⣸⣿⣿⣿⣿⡿⣿⣿⣿⣿⢺⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⢿⣟⠛⡛⠟⠻⣿⢿⠟⣟⣿⠛⢻⡗ ⣧⡯⣩⠉⠹⢭⡍⠉⠉⠿⡉⠉⠉⠉⠉⢹⠉⠱⠆⠀⠀⠰⠛⣿⢸⣀⣼⡅⢽⣿⣹⣿⣿⣙⣏⣹⣯⣽⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠉⠀⣴⠀⠀⠀⣿⠅⠒⠅⠫⡉⣁⣠ ⣷⣶⡶⡶⣾⡏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢠⠀⠀⠀⠀⠆⣿⢺⢻⣻⠀⣼⣾⣿⣿⣿⡿⣿⣿⣿⢫⢸⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡷⣾⠟⠓⠻⣿⣿⣿⣇⣈⣛⢻⣟⢻⣟ ⠶⢒⠒⠲⠃⣺⣶⡄⠀⠀⠀⠀⢀⡠⢀⣸⠐⠈⣤⡄⠀⠀⠀⣿⢹⢘⢸⠆⢹⡟⢻⣿⣿⠁⣛⢹⠿⠾⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⠀⠀⠉⠛⣿⡻⠃⣀⣛⡻⠎⠙ ⡏⠛⢻⣧⡤⠌⠙⠃⠠⠀⠀⠀⠜⠃⠜⢻⠠⢰⠋⠃⠀⠀⠀⣿⢸⢸⣺⡇⢨⡇⠲⠶⠶⠀⠀⠘⠶⠒⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠰⠷⠭⢯⣦⣭⣯ ⡋⠛⠛⠛⠃⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠀⣠⠀⠀⠀⠃⠀⣿⢸⠸⢿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⢻⣒⢟⠂⣃⣓ ⡗⡶⣾⠇⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣸⠀⠁⠀⠀⠀⣿⢸⢸⢿⡅⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡯⠇⠂⣤⢄⣀⠻⠉ ⡟⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢩⠀⡀⠀⠀⠀⣿⢸⢱⢾⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⣶⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠺⢷⠶⣂⢀⠉⠱ ⣇⣁⣉⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢸⠁⡾⠀⠀⠀⠀⡆⣿⢸⠘⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠁⢸⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠈⠁⠀⠉⠋⠋⠑ ⣏⠉⣉⠁⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⡿⠒⠆⠆⡆⠀⣿⢸⣠⢹⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⢇⣾⡿⡿⠀⢯⣯ ⣯⠋⠻⢃⠀⠸⡷⠂⠀⠀⠀⠀⠀⣤⠀⢸⢿⣷⣳⣿⣿⣇⣱⠙⢺⣿⢾⠶⢶⡷⠶⠶⠶⠤⠶⠦⠶⣶⢼⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠦⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠦⠶⠶⠶⠿⠧⠛⠻⠻⠿⠀⡿⣾ ⣎⣷⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠹⡿⠻⠙⡻⠓⢻⠒⠒⠈⢸⠄⢺⡇⠀⠀⠀⠀⠀⠀⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣀⠈⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣳⣷ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⢨⠀⠀⠀⢸⡆⠸⠇⠀⠀⠀⣀⠴⠶⠴⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⣀⠀⣀⡀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⡛⠛⢻ ⡯⣿⡏⠛⠙⠹⠇⠀⠀⠀⢴⡄⠀⠀⠀⠀⢈⣅⣬⣠⣈⣇⣀⢀⣀⣄⠀⣷⠄⠀⠀⠀⠀⣀⣀⣀⠐⠀⢼⡒⠒⠒⠒⠒⠀⠀⡉⢉⠉⡉⠉⠉⠉⡏⠉⠉⠉⠉⠉⠉⠉⢙⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⡀⠀ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⣶⡶⠶⠶⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠠⠆ ⣶⣶⣴⣤⣶⣶⠶⠶⠶⠶⠦⠶⠶⠶⠶⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⢶⠶⠆⢶⠲⢤⡶⠒⠒⠒⠶⠶⠶⠲⢸⡈⣍⠉⠎⠀⠀⠀⣶⣿⣿⣾⣾⣗⣾⣿⣟⣶⣾⣿⣻⣿⣿⣿⣷⣾⣷⣿⣿⣓⣿⣶⣶⣿⣺⣛⣓⣿⣟⣿⣿⣿⣿⣛⢛⣻⣟⣻⡟⡿⢟⣿⣿⣻⣻⡶⠆⠀⠠⠄⠀⣠⠀ ⣷⣶⣶⣶⣆⠀⢲⢠⡀⠀⠀⠀⠀⠀⠀⢸⢳⣾⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⣞⣛⣢⣶⣾⣾⣷⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣾⣖⣶⣶⣶⣶⡾⣟⣺⣿⣷⣿⣽⣾⣿⣷⣶⣆⣤ ⡗⠋⠛⠟⠃⠀⠘⠿⡏⠀⠀⠀⠀⠀⠀⢸⢸⣯⡀⠀⠀⠀⠀⣿⣾⣾⣿⠛⢻⣟⣈⣭⣙⣻⣌⣉⣿⣥⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠻⠉⠙⠀⠊⣿⠙⢀⠋⠉⠁⠉⠁ ⣿⣿⣯⣭⡅⣀⣤⣄⣀⣀⣀⣀⣀⣀⡀⣿⠈⣿⠣⠀⠃⡄⡆⣿⢾⣿⣿⠀⢼⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡉⠉⠉⠉⠉⠈⠉⠿⠏⠉⠈⠉⠉⠉⠉⠈⠁⠈⠀⠈⠁⠉⠉⠉⠩⢷⣸⡮⣻⡿⣿⣿⠿⡿⣴⢶⠁⡤⠶ ⠟⠷⠶⠿⠆⢀⣶⡄⠀⠀⠀⠀⠀⠀⠀⢸⠀⢿⣇⡀⢀⣄⠁⣿⢹⣙⣿⠀⢹⣟⣛⣯⣻⣟⣟⣛⡏⣻⠺⠶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠰⠀⠁⠀⠀⠀⢀⣤⣄⣤⣤⣤⣁⣤⣀⣿⣠⣼⣿⣿⣖⣷⣦ ⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠱⠈⠙⣆⣿⢸⢿⣹⠀⣸⣿⣿⣿⣿⡿⣿⣿⣿⣹⢺⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⢿⣿⢛⡛⢟⣻⣿⢿⢟⣟⣿⠛⢻⣗ ⣧⡯⣩⠉⠹⢭⡍⠉⠉⠿⡉⠉⠉⠉⠉⢹⠉⠱⠆⠀⠀⠰⠛⣿⢸⣀⣼⡅⢽⣿⣹⣿⣿⣙⣏⣹⣯⣽⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠉⠀⣴⠀⠀⠀⣿⠇⠒⠇⠫⡉⣁⣠ ⣷⣶⡶⡶⣾⡏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢠⠀⠀⠀⠀⠆⣿⢺⢻⣻⠀⣼⣾⣿⣿⣿⡿⣿⣿⣿⢫⢸⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡷⣾⠟⠓⠻⣿⣿⣿⣇⣈⣛⢻⣟⢻⣟ ⠶⢒⠒⠲⠃⣺⣶⡄⠀⠀⠀⠀⢀⡠⢀⣸⠐⠈⣤⡄⠀⠀⠀⣿⢹⢘⢸⠆⢹⡟⢻⣿⣿⠁⣛⢹⠯⠾⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣀⠀⠀⠉⠛⣿⡻⠃⣀⣛⡻⢎⠙ ⡏⠛⢻⣧⡤⠌⠙⠃⠠⠀⠀⠀⠜⠃⠜⢻⠠⢰⠋⠃⠀⠀⠀⣿⢸⢸⣺⡇⢨⡇⠲⠶⠶⠀⠀⠘⠶⢰⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠰⠿⠭⢯⣦⣭⣯ ⡋⠛⠛⠛⠃⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠀⣠⠀⠀⠀⠃⠀⣿⢸⠸⢿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⢻⣒⢟⠒⣃⣓ ⡗⡶⣾⠇⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣸⠀⠁⠀⠀⠀⣿⢸⢸⢿⡅⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡯⠇⠊⣤⢄⣀⠻⠋ ⡟⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢩⠀⡀⠀⠀⠀⣿⢸⢱⢾⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⣰⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡷⠺⣷⡶⣒⣀⡛⢳ ⣇⣁⣉⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢸⠁⡾⠀⠀⠀⠀⡆⣿⢸⠘⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠁⢸⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠈⠁⠈⠙⠋⠋⠑ ⣏⠉⣉⠁⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⡿⠒⠆⠆⡆⠀⣿⢸⣠⢹⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⢇⣾⡿⡿⠀⢯⣯ ⣯⠋⠻⢃⠀⠸⡷⠂⠀⠀⠀⠀⠀⣤⠀⢸⢿⣷⣳⣿⣿⣇⣱⠙⢺⣿⢾⠶⢶⡷⠶⠶⠶⠴⠶⠦⠶⣶⢘⠶⠶⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠶⠶⠶⠶⠶⠦⠶⠶⠶⠿⠧⠛⠻⠻⠿⠀⣿⣿ ⣎⣷⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠹⡿⠻⠙⡻⠓⢻⠒⠒⠈⢸⠄⢺⡇⠀⠀⠀⠀⠀⠀⡀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣀⠈⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣳⣷ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⢨⠀⠀⠀⢸⡆⠸⠇⠀⠀⠀⣀⠴⠶⠤⣰⢿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⣀⠀⣀⡀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⡛⠛⢻ ⡯⣿⡏⠛⠙⠹⠇⠀⠀⠀⢴⡄⠀⠀⠀⠀⢈⣅⣬⣠⣈⣇⣀⢀⣀⣄⠀⣷⠆⠀⠀⠀⡀⣀⣀⣀⠐⢨⣾⡒⠒⠒⠒⠒⠀⠀⡉⢉⠉⡉⠉⠉⠉⡏⠉⠉⠉⠉⠉⠉⠉⢙⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⡀⠀ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⣶⡶⠶⠶⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠠⠆ ⣶⣶⣴⣤⣶⣶⠶⠶⠶⠶⠦⠶⠶⠶⠶⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⢶⠶⠆⢶⠲⢤⡶⠒⠒⠒⠶⠶⠶⠲⢸⡈⣍⠉⠎⠀⠀⠀⣶⣿⣿⣾⣾⣗⣾⣿⣟⣶⣾⣿⣻⣿⣿⣿⣷⣾⣷⣿⣿⣓⣿⣶⣶⣿⣺⣛⣓⣿⣟⣿⣿⣿⣿⣛⢛⣻⣟⣻⡟⡿⢟⣿⣿⣻⣻⡶⠆⠀⠠⠄⠀⣠⠀ ⣷⣶⣶⣶⣆⠀⢲⢠⡀⠀⠀⠀⠀⠀⠀⢸⢳⣾⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⣞⣛⣢⣶⣾⣿⣷⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣾⣖⣶⣶⣶⣶⡾⣟⣺⣿⣷⣿⣽⣾⣿⣿⣶⣆⣤ ⡗⠋⠛⠟⠃⠀⠘⠿⡏⠀⠀⠀⠀⠀⠀⢸⢸⣯⡀⠀⠀⠀⠀⣿⣾⣾⣿⠛⢻⣟⣈⣭⣙⣻⣌⣉⣿⣥⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠻⠉⠙⠀⠊⣿⠙⢀⠋⠉⠁⠉⠁ ⣿⣿⣯⣭⡅⣀⣤⣄⣀⣀⣀⣀⣀⣀⡀⣿⠈⣿⠣⠀⠃⡄⡆⣿⢾⣿⣿⠀⢼⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡉⠉⠉⠉⠉⠈⠉⠿⠏⠉⠈⠉⠉⠉⠉⠈⠁⠈⠀⠈⠁⠉⠉⠉⠩⢷⣸⡮⣻⡿⣿⣿⠿⡿⣴⢶⠁⡤⠶ ⠟⠷⠶⠿⠆⢀⣶⡄⠀⠀⠀⠀⠀⠀⠀⢸⠀⢿⣇⡀⢀⣄⠁⣿⢹⣙⣿⠀⢹⣟⣛⣯⣻⣟⣟⣛⡏⣻⠺⠶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠰⠀⠁⠀⠀⠀⢠⣤⣄⣤⣤⣤⣁⣤⣀⣿⣠⣼⣿⣿⣖⣷⣦ ⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠱⠈⠙⣆⣿⢸⢿⣹⠀⣸⣿⣿⣿⣿⡿⣿⣿⣿⣹⢺⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⢿⣿⢛⡛⢟⣻⣿⢿⢟⣟⣿⠛⢻⣗ ⣧⡯⣩⠉⠹⢭⡍⠉⠉⠿⡉⠉⠉⠉⠉⢹⠉⠱⠆⠀⠀⠰⠛⣿⢸⣀⣼⡅⢽⣿⣹⣿⣿⣙⣏⣹⣯⣽⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠉⠀⣴⠀⠀⠀⣿⠇⠒⠇⠫⡉⣁⣠ ⣷⣶⡶⡶⣾⡏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢠⠀⠀⠀⠀⠆⣿⢺⢻⣻⠀⣼⣾⣿⣿⣿⡿⣿⣿⣿⢫⢸⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡷⣾⠟⠓⠻⣿⣿⣿⣇⣈⣛⢻⣟⢻⣟ ⠶⢒⠒⠲⠃⣺⣶⡄⠀⠀⠀⠀⢀⡠⢀⣸⠐⠈⣤⡄⠀⠀⠀⣿⢹⢘⢸⠆⢹⡟⢻⣿⣿⠁⣛⢹⠯⠾⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣀⠀⠀⠉⠛⣿⡻⠃⣀⣛⡻⢎⠙ ⡏⠛⢻⣧⡤⠌⠙⠃⠠⠀⠀⠀⠜⠃⠜⢻⠠⢰⠋⠃⠀⠀⠀⣿⢸⢸⣺⡇⢨⡇⠲⠶⠶⠀⠀⠘⠶⢰⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠰⠿⠭⢯⣦⣭⣯ ⡋⠛⠛⠛⠃⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠀⣠⠀⠀⠀⠃⠀⣿⢸⠸⢿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⢻⣒⢟⠒⣃⣓ ⡗⡶⣾⠇⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣸⠀⠁⠀⠀⠀⣿⢸⢸⢿⡅⢸⡇⠀⠀⠀⠀⠀⠀⠀⠲⣘⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡯⠇⠊⣤⢄⣀⠻⠋ ⡟⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢩⠀⡀⠀⠀⠀⣿⢸⢱⢾⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⣰⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡷⠺⣷⡶⣒⣀⡛⢳ ⣇⣁⣉⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢸⠁⡾⠀⠀⠀⠀⡆⣿⢸⠘⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠁⢸⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠈⠁⠈⠙⠋⠋⠑ ⣏⠉⣉⠁⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⡿⠒⠆⠆⡆⠀⣿⢸⣠⢹⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⢇⣾⡿⡿⠀⢯⣯ ⣯⠋⠻⢃⠀⠸⡷⠂⠀⠀⠀⠀⠀⣤⠀⢸⢿⣷⣳⣿⣿⣇⣱⠙⢺⣿⢾⠶⢶⡷⠶⠶⠶⠴⠶⠦⠶⣶⢘⠶⠶⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠶⠶⠶⠶⠶⠦⠶⠶⠶⠿⠧⠛⠻⠻⠿⠀⣿⣿ ⣎⣷⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠹⡿⠻⠙⡻⠓⢻⠒⠒⠈⢸⠄⢺⡇⠀⠀⠀⠀⠀⠀⡀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣀⠈⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣳⣷ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⢨⠀⠀⠀⢸⡆⠸⠇⠀⠀⠀⣀⠴⠶⠤⣰⢿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⣀⠀⣀⡀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⡛⠛⢻ ⡯⣿⡏⠛⠙⠹⠇⠀⠀⠀⢴⡄⠀⠀⠀⠀⢈⣅⣬⣠⣈⣇⣀⢀⣀⣄⠀⣷⠆⠀⠀⠀⡀⣀⣀⣀⠐⢨⣾⡒⠒⠒⠒⠒⠀⠀⡉⢉⠉⡉⠉⠉⠉⡏⠉⠉⠉⠉⠉⠉⠉⢙⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⡀⠀ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⣶⡶⠶⠶⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠠⠆ ⣶⣶⣴⣤⣶⣶⠶⠶⠶⠶⠦⠶⠶⠶⠶⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⢶⠶⠆⢶⠲⢤⡶⠒⠒⠒⠶⠶⠶⠲⢸⡈⣍⠉⠎⠀⠀⠀⣶⣿⣿⣾⣾⣗⣾⣿⣟⣶⣾⣿⣻⣿⣿⣿⣷⣾⣷⣿⣿⣓⣿⣶⣶⣿⣺⣛⣓⣿⣟⣿⣿⣿⣿⣛⢛⣻⣟⣻⡟⡿⢟⣿⣿⣻⣻⡶⠆⠀⠠⠄⠀⣠⠀ ⣷⣶⣶⣶⣆⠀⢲⢠⡀⠀⠀⠀⠀⠀⠀⢸⢳⣾⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⣞⣛⣢⣶⣾⣿⣷⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣾⣖⣶⣶⣶⣶⡾⣟⣺⣿⣷⣿⣽⣾⣿⣿⣶⣆⣤ ⡗⠋⠛⠟⠃⠀⠘⠿⡏⠀⠀⠀⠀⠀⠀⢸⢸⣯⡀⠀⠀⠀⠀⣿⣾⣾⣿⠛⢻⣟⣈⣭⣙⣻⣌⣉⣿⣥⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠻⠉⠙⠀⠊⣿⠙⢀⠋⠉⠁⠉⠁ ⣿⣿⣯⣭⡅⣀⣤⣄⣀⣀⣀⣀⣀⣀⡀⣿⠈⣿⠣⠀⠃⡄⡆⣿⢾⣿⣿⠀⢼⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡉⠉⠉⠉⠉⠈⠉⠿⠏⠉⠈⠉⠉⠉⠉⠈⠁⠈⠀⠈⠁⠉⠉⠉⠩⢷⣸⡮⣻⡿⣿⣿⠿⡿⣴⢶⠁⡤⠶ ⠟⠷⠶⠿⠆⢀⣶⡄⠀⠀⠀⠀⠀⠀⠀⢸⠀⢿⣇⡀⢀⣄⠁⣿⢹⣙⣿⠀⢹⣟⣛⣯⣻⣟⣟⣛⡏⣻⠺⠶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠰⠀⠁⠀⠀⠀⢠⣤⣄⣤⣤⣤⣁⣤⣀⣿⣠⣼⣿⣿⣖⣷⣦ ⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠱⠈⠙⣆⣿⢸⢿⣹⠀⣸⣿⣿⣿⣿⡿⣿⣿⣿⣹⢺⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⢿⣿⢛⡛⢟⣻⣿⢿⢟⣟⣿⠛⢻⣗ ⣧⡯⣩⠉⠹⢭⡍⠉⠉⠿⡉⠉⠉⠉⠉⢹⠉⠱⠆⠀⠀⠰⠛⣿⢸⣀⣼⡅⢽⣿⣹⣿⣿⣙⣏⣹⣯⣽⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠉⠀⣴⠀⠀⠀⣿⠇⠒⠇⠫⡉⣁⣠ ⣷⣶⡶⡶⣾⡏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢠⠀⠀⠀⠀⠆⣿⢺⢻⣻⠀⣼⣾⣿⣿⣿⡿⣿⣿⣿⢫⢸⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡷⣾⠟⠓⠻⣿⣿⣿⣇⣈⣛⢻⣟⢻⣟ ⠶⢒⠒⠲⠃⣺⣶⡄⠀⠀⠀⠀⢀⡠⢀⣸⠐⠈⣤⡄⠀⠀⠀⣿⢹⢘⢸⠆⢹⡟⢻⣿⣿⠁⣛⢹⠯⠾⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣀⠀⠀⠉⠛⣿⡻⠃⣀⣛⡻⢎⠙ ⡏⠛⢻⣧⡤⠌⠙⠃⠠⠀⠀⠀⠜⠃⠜⢻⠠⢰⠋⠃⠀⠀⠀⣿⢸⢸⣺⡇⢨⡇⠲⠶⠶⠀⠀⠘⠶⢰⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠰⠿⠭⢯⣦⣭⣯ ⡋⠛⠛⠛⠃⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠀⣠⠀⠀⠀⠃⠀⣿⢸⠸⢿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⢻⣒⢟⠒⣃⣓ ⡗⡶⣾⠇⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣸⠀⠁⠀⠀⠀⣿⢸⢸⢿⡅⢸⡇⠀⠀⠀⠶⠀⠀⠀⠲⣘⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡯⠇⠊⣤⢄⣀⠻⠋ ⡟⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢩⠀⡀⠀⠀⠀⣿⢸⢱⢾⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⣰⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡷⠺⣷⡶⣒⣀⡛⢳ ⣇⣁⣉⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢸⠁⡾⠀⠀⠀⠀⡆⣿⢸⠘⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠁⢸⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠈⠁⠈⠙⠋⠋⠑ ⣏⠉⣉⠁⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⡿⠒⠆⠆⡆⠀⣿⢸⣠⢹⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⢇⣾⡿⡿⠀⢯⣯ ⣯⠋⠻⢃⠀⠸⡷⠂⠀⠀⠀⠀⠀⣤⠀⢸⢿⣷⣳⣿⣿⣇⣱⠙⢺⣿⢾⠶⢶⡷⠶⠶⠶⠴⠶⠦⠶⣶⢘⠶⠶⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠶⠶⠶⠶⠶⠦⠶⠶⠶⠿⠧⠛⠻⠻⠿⠀⣿⣿ ⣎⣷⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠹⡿⠻⠙⡻⠓⢻⠒⠒⠈⢸⠄⢺⡇⠀⠀⠀⠀⠀⠀⡀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣀⠈⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣳⣷ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⢨⠀⠀⠀⢸⡆⠸⠇⠀⠀⠀⣀⠴⠶⠤⣰⢿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⣀⠀⣀⡀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⡛⠛⢻ ⡯⣿⡏⠛⠙⠹⠇⠀⠀⠀⢴⡄⠀⠀⠀⠀⢈⣅⣬⣠⣈⣇⣀⢀⣀⣄⠀⣷⠆⠀⠀⠀⡀⣀⣀⣀⠐⢨⣾⡒⠒⠒⠒⠒⠀⠀⡉⢉⠉⡉⠉⠉⠉⡏⠉⠉⠉⠉⠉⠉⠉⢙⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⡀⠀ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⣶⡶⠶⠶⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠠⠆ ⣶⣶⣴⣤⣶⣶⠶⠶⠶⠶⠦⠶⠶⠶⠶⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⢶⠶⠆⢶⠲⢤⡶⠒⠒⠒⠶⠶⠶⠲⢸⡈⣍⠉⠎⠀⠀⠀⣶⣿⣿⣾⣾⣗⣾⣿⣟⣶⣾⣿⣻⣿⣿⣿⣷⣾⣷⣿⣿⣓⣿⣶⣶⣿⣺⣛⣓⣿⣟⣿⣿⣿⣿⣛⢛⣻⣟⣻⡟⡿⢟⣿⣿⣻⣻⡶⠆⠀⠠⠄⠀⣠⠀ ⣷⣶⣶⣶⣆⠀⢲⢠⡀⠀⠀⠀⠀⠀⠀⢸⢳⣾⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⣞⣛⣢⣶⣾⣿⣷⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣾⣖⣶⣶⣶⣶⡾⣟⣺⣿⣷⣿⣽⣾⣿⣿⣶⣆⣤ ⡗⠋⠛⠟⠃⠀⠘⠿⡏⠀⠀⠀⠀⠀⠀⢸⢸⣯⡀⠀⠀⠀⠀⣿⣾⣾⣿⠛⢻⣟⣈⣭⣙⣻⣌⣉⣿⣥⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠻⠉⠙⠀⠊⣿⠙⢀⠋⠉⠁⠉⠁ ⣿⣿⣯⣭⡅⣀⣤⣄⣀⣀⣀⣀⣀⣀⡀⣿⠈⣿⠣⠀⠃⡄⡆⣿⢾⣿⣿⠀⢼⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡉⠉⠉⠉⠉⠈⠉⠿⠏⠉⠈⠉⠉⠉⠉⠈⠁⠈⠀⠈⠁⠉⠉⠉⠩⢷⣸⡮⣻⡿⣿⣿⠿⡿⣴⢶⠁⡤⠶ ⠟⠷⠶⠿⠆⢀⣶⡄⠀⠀⠀⠀⠀⠀⠀⢸⠀⢿⣇⡀⢀⣄⠁⣿⢹⣙⣿⠀⢹⣟⣛⣯⣻⣟⣟⣛⡏⣻⠺⠶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠰⠀⠁⠀⠀⠀⢠⣤⣄⣤⣤⣤⣁⣤⣀⣿⣠⣼⣿⣿⣖⣷⣦ ⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠱⠈⠙⣆⣿⢸⢿⣹⠀⣸⣿⣿⣿⣿⡿⣿⣿⣿⣹⢺⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⢿⣿⢛⡛⢟⣻⣿⢿⢟⣟⣿⠛⢻⣗ ⣧⡯⣩⠉⠹⢭⡍⠉⠉⠿⡉⠉⠉⠉⠉⢹⠉⠱⠆⠀⠀⠰⠛⣿⢸⣀⣼⡅⢽⣿⣹⣿⣿⣙⣏⣹⣯⣽⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠉⠀⣴⠀⠀⠀⣿⠇⠒⠇⠫⡉⣁⣠ ⣷⣶⡶⡶⣾⡏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢠⠀⠀⠀⠀⠆⣿⢺⢻⣻⠀⣼⣾⣿⣿⣿⡿⣿⣿⣿⢫⢸⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡷⣾⠟⠓⠻⣿⣿⣿⣇⣈⣛⢻⣟⢻⣟ ⠶⢒⠒⠲⠃⣺⣶⡄⠀⠀⠀⠀⢀⡠⢀⣸⠐⠈⣤⡄⠀⠀⠀⣿⢹⢘⢸⠆⢹⡟⢻⣿⣿⠁⣛⢹⠯⠾⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣀⠀⠀⠉⠛⣿⡻⠃⣀⣛⡻⢎⠙ ⡏⠛⢻⣧⡤⠌⠙⠃⠠⠀⠀⠀⠜⠃⠜⢻⠠⢰⠋⠃⠀⠀⠀⣿⢸⢸⣺⡇⢨⡇⠲⠶⠶⠀⠀⠘⠶⢰⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠰⠿⠭⢯⣦⣭⣯ ⡋⠛⠛⠛⠃⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠀⣠⠀⠀⠀⠃⠀⣿⢸⠸⢿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⢻⣒⢟⠒⣃⣓ ⡗⡶⣾⠇⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣸⠀⠁⠀⠀⠀⣿⢸⢸⢿⡅⢸⡇⠀⠀⠀⠶⠀⠀⠀⠲⣘⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡯⠇⠊⣤⢄⣀⠻⠋ ⡟⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢩⠀⡀⠀⠀⠀⣿⢸⢱⢾⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⣰⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡷⠺⣷⡶⣒⣀⡛⢳ ⣇⣁⣉⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢸⠁⡾⠀⠀⠀⠀⡆⣿⢸⠘⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠁⢸⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠈⠁⠈⠙⠋⠋⠑ ⣏⠉⣉⠁⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⡿⠒⠆⠆⡆⠀⣿⢸⣠⢹⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⢇⣾⡿⡿⠀⢯⣯ ⣯⠋⠻⢃⠀⠸⡷⠂⠀⠀⠀⠀⠀⣤⠀⢸⢿⣷⣳⣿⣿⣇⣱⠙⢺⣿⢾⠶⢶⡷⠶⠶⠶⠴⠶⠦⠶⣶⢘⠶⠶⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠶⠶⠶⠶⠶⠦⠶⠶⠶⠿⠧⠛⠻⠻⠿⠀⣿⣿ ⣎⣷⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠹⡿⠻⠙⡻⠓⢻⠒⠒⠈⢸⠄⢺⡇⠀⠀⠀⠀⠀⠀⡀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣀⠈⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣳⣷ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⢨⠀⠀⠀⢸⡆⠸⠇⠀⠀⠀⣀⠴⠶⠤⣰⢿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⣀⠀⣀⡀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⡛⠛⢻ ⡯⣿⡏⠛⠙⠹⠇⠀⠀⠀⢴⡄⠀⠀⠀⠀⢈⣅⣬⣠⣈⣇⣀⢀⣀⣄⠀⣷⠆⠀⠀⠀⡀⣀⣀⣀⠐⢨⣾⡒⠒⠒⠒⠒⠀⠀⡉⢉⠉⡉⠉⠉⠉⡏⠈⠉⠉⠉⠉⠉⠉⢙⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⡀⠀ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⣶⡶⠶⠶⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠠⠆ ⣶⣶⣴⣤⣶⣶⠶⠶⠶⠶⠦⠶⠶⠶⠶⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⢶⠶⠆⢶⠲⢤⡶⠒⠒⠒⠶⠶⠶⠲⢸⡈⣍⠉⠎⠀⠀⠀⣶⣿⣿⣾⣾⣗⣾⣿⣟⣶⣾⣿⣻⣿⣿⣿⣷⣾⣷⣿⣿⣓⣿⣶⣶⣿⣺⣛⣓⣿⣟⣿⣿⣿⣿⣛⢛⣻⣟⣻⡟⡿⢟⣿⣿⣻⣻⡶⠆⠀⠠⠄⠀⣠⠀ ⣷⣶⣶⣶⣆⠀⢲⢠⡀⠀⠀⠀⠀⠀⠀⢸⢳⣾⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⣞⣛⣢⣶⣾⣿⣷⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣾⣖⣶⣶⣶⣶⡾⣟⣺⣿⣷⣿⣽⣾⣿⣿⣶⣆⣤ ⡗⠋⠛⠟⠃⠀⠘⠿⡏⠀⠀⠀⠀⠀⠀⢸⢸⣯⡀⠀⠀⠀⠀⣿⣾⣾⣿⠛⢿⣟⣈⣭⣙⣻⣌⣉⣿⣥⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠻⠉⠙⠀⠊⣿⠙⢀⠋⠉⠁⠉⠁ ⣿⣿⣯⣭⡅⣀⣤⣄⣀⣀⣀⣀⣀⣀⡀⣿⠈⣿⠣⠀⠃⡄⡆⣿⢾⣿⣿⠀⢼⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡉⠉⠉⠉⠉⠈⠉⠿⠏⠉⠈⠉⠉⠉⠉⠈⠁⠈⠀⠈⠁⠉⠉⠉⠩⢷⣸⡮⣻⡿⣿⣿⠿⡿⣴⢶⢁⡤⠶ ⠟⠷⠶⠿⠆⢀⣶⡄⠀⠀⠀⠀⠀⠀⠀⢸⠀⢿⣇⡀⢀⣄⠁⣿⢹⣙⣿⠀⢹⣟⣛⣯⣻⣟⣟⣛⡏⣻⠺⠶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠰⠀⠁⠀⠀⠀⢠⣤⣄⣤⣤⣤⣁⣤⣀⣿⣠⣼⣿⣿⣞⣷⣦ ⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠱⠈⠙⣆⣿⢸⢿⣹⠀⣸⣿⣿⣿⣿⡿⣿⣿⣿⣹⢺⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⢿⣿⢛⡛⢟⣻⣿⢿⢟⣟⣿⠛⢻⣗ ⣧⡯⣩⠉⠹⢭⡍⠉⠉⠿⡉⠉⠉⠉⠉⢹⠉⠱⠆⠀⠀⠰⠛⣿⢸⣀⣼⡅⢽⣿⣹⣿⣿⣙⣏⣹⣯⣽⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠉⠀⣴⠀⠀⠀⣿⠇⠒⠇⠫⡉⣁⣠ ⣷⣶⡶⡶⣾⡏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢰⠀⠀⠀⠀⠆⣿⢺⢻⣻⠀⣼⣾⣿⣿⣿⡿⣿⣿⣿⢫⢸⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡷⣾⠟⠓⠻⣿⣿⣿⣇⣈⣛⢻⣟⢻⣟ ⠶⢒⠒⠲⠃⣺⣶⡄⠀⠀⠀⠀⢀⡠⢀⣸⠐⠈⣤⡄⠀⠀⠀⣿⢹⢘⢸⠆⢹⡟⢻⣿⣿⠁⣛⢹⠯⠾⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣀⠀⠀⠉⠛⣿⡻⠃⣀⣛⡻⢎⠙ ⡏⠛⢻⣧⡤⠌⠙⠃⠠⠀⠀⠀⠜⠃⠜⢻⠠⢰⠋⠃⠀⠀⠀⣿⢸⢸⣺⡇⢨⡇⠲⠶⠶⠀⠀⠘⠶⢰⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠰⠿⠭⢯⣦⣽⣯ ⡋⠛⠛⠛⠃⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠀⣠⠀⠀⠀⠃⠀⣿⢸⠸⢿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⢻⣒⢟⠒⣃⣓ ⡗⡶⣾⠇⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣸⠀⠁⠀⠀⠀⣿⢸⣸⢿⡅⢸⡇⠀⠀⠀⠶⡀⠀⠀⠲⣘⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡯⠇⠊⣤⢄⣀⢻⠋ ⡟⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢩⠀⡀⠀⠀⠀⣿⢸⢱⢾⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⣰⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡷⠺⣷⣶⣒⣁⡛⣳ ⣇⣁⣉⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢸⠁⡾⠀⠀⠀⠀⡆⣿⢸⠘⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠁⢸⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠈⠁⠈⠙⠛⠋⠙ ⣏⠉⣉⠁⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⡿⠒⠆⠆⡆⠀⣿⢸⣠⢹⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⢗⣾⡿⣿⠀⢯⣯ ⣯⠋⠻⢃⠀⠸⡷⠂⠀⠀⠀⠀⠀⣤⠀⢸⢿⣷⣳⣿⣿⣇⣱⠙⢺⣿⢾⠶⢶⡷⠶⠶⠶⠴⠶⠦⠶⣶⢘⠶⠶⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠦⠶⠶⠶⠶⠾⠶⠶⠶⠶⠶⠦⠶⠶⠶⠿⠧⠛⠻⠻⠿⠀⣿⣿ ⣎⣷⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠹⡿⠻⠙⡻⠓⢻⠒⠒⠈⢸⠄⢺⡇⠀⠀⠀⠀⠀⠀⡀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣀⠈⠀⠀⠀⠀⠀⠀⠀⠛⡀⠀⠀⠀⠀⠀⣀⣀⣀⣰⣳⣷ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⢨⠀⠀⠀⢸⡆⠸⠇⠀⠀⠀⣀⠴⠶⠤⣰⢿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⣀⠀⣀⡀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⡛⠛⢻ ⡯⣿⡏⠛⠙⠹⠇⠀⠀⠀⢴⡄⠀⠀⠀⠀⢈⣅⣬⣠⣈⣇⣀⢀⣀⣄⠀⣷⠆⠀⠀⠀⡀⣀⣀⣀⠐⢨⣾⡒⠒⠒⠒⠒⠀⠀⡉⢉⠉⡉⠉⠉⠉⡏⠈⠉⠉⠉⠉⠉⠉⢙⣋⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠁⡀⠀ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⣶⡶⠶⠶⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠠⠆ ⣶⣶⣴⣤⣶⣶⠶⠶⠶⠶⠦⠶⠶⠶⠶⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⢶⠶⠆⢶⠲⢤⡶⠒⠒⠒⠶⠶⠶⠲⢸⡈⣍⠉⠎⠀⠀⠀⣶⣿⣿⣾⣾⣗⣾⣿⣟⣶⣾⣿⣻⣿⣿⣿⣷⣾⣷⣿⣿⣓⣿⣶⣶⣿⣺⣛⣓⣿⣟⣿⣿⣿⣿⣛⢛⣻⣟⣻⡟⡿⢟⣿⣿⣻⣻⡶⠆⠀⠠⠄⠀⣠⠀ ⣷⣶⣶⣶⣆⠀⢲⢠⡀⠀⠀⠀⠀⠀⠀⢸⢳⣾⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⣞⣛⣢⣶⣾⣿⣷⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣾⣖⣶⣶⣶⣶⡾⣟⣺⣿⣷⣿⣽⣾⣿⣿⣶⣆⣤ ⡗⠋⠛⠟⠃⠀⠘⠿⡏⠀⠀⠀⠀⠀⠀⢸⢸⣯⡀⠀⠀⠀⠀⣿⣾⣾⣿⠛⢻⣟⣈⣭⣙⣻⣌⣉⣿⣥⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠻⠉⠙⠀⠊⣿⠙⢀⠋⠉⠁⠉⠁ ⣿⣿⣯⣭⡅⣀⣤⣄⣀⣀⣀⣀⣀⣀⡀⣿⠈⣿⠣⠀⠃⡄⡆⣿⢾⣿⣿⠀⢼⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡉⠉⠉⠉⠉⠈⠉⠿⠏⠉⠈⠉⠉⠉⠉⠈⠁⠈⠀⠈⠁⠉⠉⠉⠩⢷⣸⡮⣻⡿⣿⣿⠿⡿⣴⢶⠀⡤⠶ ⠟⠷⠶⠿⠆⢀⣶⡄⠀⠀⠀⠀⠀⠀⠀⢸⠀⢿⣇⡀⢀⣄⠁⣿⢹⣙⣿⠀⢹⣟⣛⣯⣻⣟⣟⣛⡏⣻⠺⠶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠰⠀⠁⠀⠀⠀⢠⣤⣄⣤⣤⣤⣁⣤⣀⣿⣠⣼⣿⣿⣖⣷⣦ ⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠱⠈⠙⣆⣿⢸⢿⣹⠀⣸⣿⣿⣿⣿⡿⣿⣿⣿⣹⢺⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⢿⣿⢛⡛⢟⣻⣿⢿⢟⣟⣿⠛⢻⣗ ⣧⡯⣩⠉⠹⢭⡍⠉⠉⠿⡉⠉⠉⠉⠉⢹⠉⠱⠆⠀⠀⠰⠛⣿⢸⣀⣼⡅⢽⣿⣹⣿⣿⣙⣏⣹⣯⣽⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠉⠀⣴⠀⠀⠀⣿⠇⠒⠇⠿⡋⣁⣠ ⣷⣶⡶⡶⣾⡏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢠⠀⠀⠀⠀⠆⣿⢺⢻⣻⠀⣼⣾⣿⣿⣿⡿⣿⣿⣿⢫⢸⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡷⣾⠟⠓⠻⣿⣿⣿⣇⣈⣛⢻⣟⢻⣟ ⠶⢒⠒⠲⠃⣺⣶⡄⠀⠀⠀⠀⢀⡠⢀⣸⠐⠈⣤⡄⠀⠀⠀⣿⢹⢘⢸⠆⢹⡟⢻⣿⣿⠁⣛⢹⠯⠾⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣀⠀⠀⠉⠛⣿⡻⠃⣀⣛⡻⢎⠙ ⡏⠛⢻⣧⡤⠌⠙⠃⠠⠀⠀⠀⠜⠃⠜⢻⠠⢰⠋⠃⠀⠀⠀⣿⢸⢸⣺⡇⢨⡇⠲⠶⠶⠀⠀⠘⠶⢰⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠰⠿⠭⢯⣦⣭⣯ ⡋⠛⠛⠛⠃⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠀⣠⠀⠀⠀⠃⠀⣿⢸⠸⢿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⢻⣒⢟⠒⣃⣓ ⡗⡶⣾⠇⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣸⠀⠁⠀⠀⠀⣿⢸⢸⢿⡅⢸⡇⠀⠀⠀⠶⠀⠀⠀⠲⣘⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡯⠇⠊⣤⢄⣀⠻⠋ ⡟⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢩⠀⡀⠀⠀⠀⣿⢸⢱⢾⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⣰⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡿⠺⣷⡶⣒⣀⡛⢳ ⣇⣁⣉⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢸⠁⡾⠀⠀⠀⠀⡆⣿⢸⠘⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠁⢸⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠈⠁⠈⠙⠋⠋⠑ ⣏⠉⣉⠁⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⡿⠒⠆⠆⡆⠀⣿⢸⣠⢹⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⢇⣾⡿⡿⠀⢯⣯ ⣯⠋⠻⢃⠀⠸⡷⠂⠀⠀⠀⠀⠀⣤⠀⢸⢿⣷⣳⣿⣿⣇⣱⠙⢺⣿⢾⠶⢶⡷⠶⠶⠶⠴⠶⠦⠶⣶⢘⠶⠶⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠦⠶⠶⠶⠶⠾⠶⠶⠶⠶⠶⠦⠶⠶⠶⠿⠧⠛⠻⠻⠿⠀⣿⣿ ⣎⣷⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠹⡿⠻⠙⡻⠓⢻⠒⠒⠈⢸⠄⢺⡇⠀⠀⠀⠀⠀⠀⡀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣀⠈⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣳⣷ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⢨⠀⠀⠀⢸⡆⠸⠇⠀⠀⠀⣀⠴⠶⠤⣰⢿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⣀⠀⣀⡀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⡛⠛⢻ ⡯⣿⡏⠛⠙⠹⠇⠀⠀⠀⢴⡄⠀⠀⠀⠀⢈⣅⣬⣠⣈⣇⣀⢀⣀⣄⠀⣷⠆⠀⠀⠀⡀⣀⣀⣀⠐⢨⣾⡒⠒⠒⠒⠒⠀⠀⡉⢉⠉⡉⠉⠉⠉⡏⠈⠉⠉⠉⠉⠉⠉⢙⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⡀⠀ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⣶⡶⠶⠶⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠠⠆ ⣶⣶⣴⣤⣶⣶⠶⠶⠶⠶⠦⠶⠶⠶⠶⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⢶⠶⠆⢶⠲⢤⡶⠒⠒⠒⠶⠶⠶⠲⢸⡈⣍⠉⠎⠀⠀⠀⣶⣿⣿⣾⣾⣗⣾⣿⣟⣶⣾⣿⣻⣿⣿⣿⣷⣾⣷⣿⣿⣓⣿⣶⣶⣿⣺⣛⣓⣿⣟⣿⣿⣿⣿⣛⢛⣻⣟⣻⡟⡿⢟⣿⣿⣻⣻⡶⠆⠀⠠⠄⠀⣠⠀ ⣷⣶⣶⣶⣆⠀⢲⢠⡀⠀⠀⠀⠀⠀⠀⢸⢳⣾⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⣞⣛⣢⣶⣾⣿⣷⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣾⣖⣶⣶⣶⣶⡾⣟⣺⣿⣷⣿⣽⣾⣿⣿⣶⣆⣤ ⡗⠋⠛⠟⠃⠀⠘⠿⡏⠀⠀⠀⠀⠀⠀⢸⢸⣯⡀⠀⠀⠀⠀⣿⣾⣾⣿⠛⢻⣟⣈⣭⣙⣻⣌⣉⣿⣥⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠻⠉⠙⠀⠊⣿⠙⢀⠋⠉⠁⠉⠁ ⣿⣿⣯⣭⡅⣀⣤⣄⣀⣀⣀⣀⣀⣀⡀⣿⠈⣿⠣⠀⠃⡄⡆⣿⢾⣿⣿⠀⢼⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡉⠉⠉⠉⡉⠈⠉⠿⠏⠉⠈⠉⠉⠉⠉⠈⠁⠈⠀⠈⠁⠉⠉⠉⠩⢷⣸⡮⣻⡿⣿⣿⠿⡿⣴⢶⠀⡤⠶ ⠟⠷⠶⠿⠆⢀⣶⡄⠀⠀⠀⠀⠀⠀⠀⢸⠀⢿⣇⡀⢀⣄⠁⣿⢹⣙⣿⠀⢹⣟⣛⣯⣻⣟⣟⣛⡏⣻⠺⠶⠇⠀⠀⠛⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠰⠀⠁⠀⠀⠀⢠⣤⣄⣤⣤⣤⣁⣤⣀⣿⣠⣼⣿⣿⣖⣷⣦ ⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠱⠈⠙⣆⣿⢸⢿⣹⠀⣸⣿⣿⣿⣿⡿⣿⣿⣿⣹⢺⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⢿⣿⢛⡛⢟⣻⣿⢿⢟⣟⣿⠛⢻⣗ ⣧⡯⣩⠉⠹⢭⡍⠉⠉⠿⡉⠉⠉⠉⠉⢹⠉⠱⠆⠀⠀⠰⠛⣿⢸⣀⣼⡅⢽⣿⣹⣿⣿⣙⣏⣹⣯⣽⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠉⠀⣴⠀⠀⠀⣿⠇⠒⠇⠿⡋⣁⣠ ⣷⣶⡶⡶⣾⡏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢠⠀⠀⠀⠀⠆⣿⢺⢻⣻⠀⣼⣾⣿⣿⣿⡿⣿⣿⣿⢫⢸⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡷⣾⠟⠓⠻⣿⣿⣿⣇⣈⣛⢻⣟⢻⣟ ⠶⢒⠒⠲⠃⣺⣶⡄⠀⠀⠀⠀⢀⡠⢀⣸⠐⠈⣤⡄⠀⠀⠀⣿⢹⢘⢸⠆⢹⡟⢻⣿⣿⠁⣛⢹⠯⠾⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣀⠀⠀⠉⠛⣿⡻⠃⣀⣛⡻⢎⠙ ⡏⠛⢻⣧⡤⠌⠙⠃⠠⠀⠀⠀⠜⠃⠜⢻⠠⢰⠋⠃⠀⠀⠀⣿⢸⢸⣺⡇⢨⡇⠲⠶⠶⠀⠀⠘⠶⢰⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠰⠿⠭⢯⣦⣭⣯ ⡋⠛⠛⠛⠃⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠀⣠⠀⠀⠀⠃⠀⣿⢸⠸⢿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⢻⣒⢟⠒⣃⣓ ⡗⡶⣾⠇⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣸⠀⠁⠀⠀⠀⣿⢸⢸⢿⡅⢸⡇⠀⠀⠀⠶⠀⠀⠀⠲⣘⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡯⠇⠊⣤⢄⣀⠻⠋ ⡟⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢩⠀⡀⠀⠀⠀⣿⢸⢱⢾⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⣰⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡿⠺⣷⡶⣒⣀⡛⢳ ⣇⣁⣉⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢸⠁⡾⠀⠀⠀⠀⡆⣿⢸⠘⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠁⢸⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠈⠁⠈⠙⠋⠋⠑ ⣏⠉⣉⠁⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⡿⠒⠆⠆⡆⠀⣿⢸⣠⢹⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⢇⣾⡿⡿⠀⢯⣯ ⣯⠋⠻⢃⠀⠸⡷⠂⠀⠀⠀⠀⠀⣤⠀⢸⢿⣷⣳⣿⣿⣇⣱⠙⢺⣿⢾⠶⢶⡷⠶⠶⠶⠴⠶⠦⠶⣶⢘⠶⠶⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠦⠶⠶⠶⠶⠾⠶⠶⠶⠶⠶⠦⠶⠶⠶⠿⠧⠛⠻⠻⠿⠀⣿⣿ ⣎⣷⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠹⡿⠻⠙⡻⠓⢻⠒⠒⠈⢸⠄⢺⡇⠀⠀⠀⠀⠀⠀⡀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣀⠈⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣳⣷ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⢨⠀⠀⠀⢸⡆⠸⠇⠀⠀⠀⣀⠴⠶⠤⣰⢿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⣀⠀⣀⡀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⡛⠛⢻ ⡯⣿⡏⠛⠙⠹⠇⠀⠀⠀⢴⡄⠀⠀⠀⠀⢈⣅⣬⣠⣈⣇⣀⢀⣀⣄⠀⣷⠆⠀⠀⠀⡀⣀⣀⣀⠐⢨⣾⡒⠒⠒⠒⠒⠀⠀⡉⢉⠉⡉⠉⠉⠉⡏⠈⠉⠉⠉⠉⠉⠉⢙⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⡀⠀ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⣶⡶⠶⠶⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠠⠆ ⣶⣶⣴⣤⣶⣶⠶⠶⠶⠶⠦⠶⠶⠶⠶⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⢶⠶⠆⢶⠲⢤⡶⠒⠒⠒⠶⠶⠶⠲⢸⡈⣍⠉⠎⠀⠀⠀⣶⣿⣿⣾⣾⣗⣾⣿⣟⣶⣾⣿⣻⣿⣿⣿⣷⣾⣷⣿⣿⣓⣿⣶⣶⣿⣺⣛⣓⣿⣟⣿⣿⣿⣿⣛⢛⣻⣟⣻⡟⡿⢟⣿⣿⣻⣻⡶⠆⠀⠠⠄⠀⣠⠀ ⣷⣶⣶⣶⣆⠀⢲⢠⡀⠀⠀⠀⠀⠀⠀⢸⢳⣾⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⣞⣛⣢⣶⣾⣿⣷⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣾⣖⣶⣶⣶⣶⡾⣟⣺⣿⣷⣿⣽⣾⣿⣿⣶⣆⣤ ⡗⠋⠛⠟⠃⠀⠘⠿⣏⠀⠀⠀⠀⠀⠀⢸⢸⣯⡀⠀⠀⠀⠀⣿⣾⣾⣿⠛⢻⣟⣈⣭⣙⣻⣌⣉⣿⣥⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠻⠉⠙⠀⠊⣿⠙⢀⠋⠉⠁⠉⠁ ⣿⣿⣯⣭⡅⣀⣤⣌⣋⣀⣀⣀⣀⣀⡀⣿⠈⣿⠣⠀⠃⡄⡆⣿⢾⣿⣿⠀⢼⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡉⠉⠉⠉⡉⠈⠉⠿⠏⠉⠈⠉⠉⠉⠉⠈⠁⠈⠀⠈⠁⠉⠉⠉⠩⢷⣸⡮⣻⡿⣿⣿⠿⡿⣴⢶⠀⡤⠶ ⠟⠷⠶⠿⠆⢀⣶⡄⠀⠀⠀⠀⠀⠀⠀⢸⠀⢿⣇⡀⢀⣄⠁⣿⢹⣙⣿⠀⢹⣟⣛⣯⣻⣟⣟⣛⡏⣻⠺⠶⠇⠀⠀⠛⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠰⠀⠁⠀⠀⠀⢠⣤⣄⣤⣤⣤⣁⣤⣀⣿⣠⣼⣿⣿⣖⣷⣦ ⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠱⠈⠙⣆⣿⢸⢿⣹⠀⣸⣿⣿⣿⣿⡿⣿⣿⣿⣹⢺⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⢿⣿⢛⡛⢟⣻⣿⢿⢟⣟⣿⠛⢻⣗ ⣧⡯⣩⠉⠹⢭⡍⠉⠉⠿⡉⠉⠉⠉⠉⢹⠉⠱⠆⠀⠀⠰⠛⣿⢸⣀⣼⡅⢽⣿⣹⣿⣿⣙⣏⣹⣯⣽⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠉⠀⣴⠀⠀⠀⣿⠇⠒⠇⠿⡋⣁⣠ ⣷⣶⡶⡶⣾⡏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢠⠀⠀⠀⠀⠆⣿⢺⢻⣻⠀⣼⣾⣿⣿⣿⡿⣿⣿⣿⢫⢸⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡷⣾⠟⠓⠻⣿⣿⣿⣇⣈⣛⢻⣟⢻⣟ ⠶⢒⠒⠲⠃⣺⣶⡄⠀⠀⠀⠀⢀⡠⢀⣸⠐⠈⣤⡄⠀⠀⠀⣿⢹⢘⢸⠆⢹⡟⢻⣿⣿⠁⣛⢹⠯⠾⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣀⠀⠀⠉⠛⣿⡻⠃⣀⣛⡻⢎⠙ ⡏⠛⢻⣧⡤⠌⠙⠃⠠⠀⠀⠀⠜⠃⠜⢻⠠⢰⠋⠃⠀⠀⠀⣿⢸⢸⣺⡇⢨⡇⠲⠶⠶⠀⠀⠘⠶⢰⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠰⠿⠭⢯⣦⣭⣯ ⡋⠛⠛⠛⠃⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠀⣠⠀⠀⠀⠃⠀⣿⢸⠸⢿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⢻⣒⢟⠒⣃⣓ ⡗⡶⣾⠇⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣸⠀⠁⠀⠀⠀⣿⢸⢸⢿⡅⢸⡇⠀⠀⠀⠶⠀⠀⠀⠲⣘⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡯⠇⠊⣤⢄⣀⠻⠋ ⡟⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢩⠀⡀⠀⠀⠀⣿⢸⢱⢾⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⣰⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡿⠺⣷⡶⣒⣀⡛⢳ ⣇⣁⣉⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢸⠁⡾⠀⠀⠀⠀⡆⣿⢸⠘⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠁⢸⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠈⠁⠈⠙⠋⠋⠑ ⣏⠉⣉⠁⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⡿⠒⠆⠆⡆⠀⣿⢸⣠⢹⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⢇⣾⡿⡿⠀⢯⣯ ⣯⠋⠻⢃⠀⠸⡷⠂⠀⠀⠀⠀⠀⣤⠀⢸⢿⣷⣳⣿⣿⣇⣱⠙⢺⣿⢾⠶⢶⡷⠶⠶⠶⠴⠶⠦⠶⣶⢘⠶⠶⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠦⠶⠶⠶⠶⠾⠶⠶⠶⠶⠶⠦⠶⠶⠶⠿⠧⠛⠻⠻⠿⠀⣿⣿ ⣎⣷⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠹⡿⠻⠙⡻⠓⢻⠒⠒⠈⢸⠄⢺⡇⠀⠀⠀⠀⠀⠀⡀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣀⠈⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣳⣷ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⢨⠀⠀⠀⢸⡆⠸⠇⠀⠀⠀⣀⠴⠶⠤⣰⢿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⣀⠀⣀⡀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⡛⠛⢻ ⡯⣿⡏⠛⠙⠹⠇⠀⠀⠀⢴⡄⠀⠀⠀⠀⢈⣅⣬⣠⣈⣇⣀⢀⣀⣄⠀⣷⠆⠀⠀⠀⡀⣀⣀⣀⠐⢨⣾⡒⠒⠒⠒⠒⠀⠀⡉⢉⠉⡉⠉⠉⠉⡏⠈⠉⠉⠉⠉⠉⠉⢙⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⡀⠀ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⣶⡶⠶⠶⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠠⠆ ⣶⣶⣴⣤⣶⣶⠶⠶⠶⠶⠦⠶⠶⠶⠶⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠶⠶⠆⠶⠲⠄⠶⠒⠒⠒⠶⠶⠶⠲⠸⠈⡍⠉⠎⠀⠀⠀⣶⣿⣿⣾⣾⣗⣾⣿⣟⣶⣾⣿⣻⣿⣿⣿⣷⣾⣷⣿⣿⣓⣿⣶⣶⣿⣺⣛⣓⣿⣟⣿⣿⣿⣿⣛⢛⣻⣟⣻⡟⡿⢟⣿⣿⣻⣻⡶⠆⠀⠠⠄⠀⣠⠀ ⡿⠻⠿⠿⠿⠿⠿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⣞⣛⣢⣶⣾⣿⣷⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣾⣖⣶⣶⣶⣶⡾⣟⣺⣿⣷⣿⣽⣾⣿⣿⣶⣆⣤ ⡷⠷⠾⠿⠇⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⣿⣾⣾⣿⠛⢻⣟⣈⣭⣙⣻⣞⣉⣿⣥⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠻⠉⠙⠀⠊⣿⠙⢀⠋⠉⠁⠉⠁ ⣿⣿⣯⣭⡄⣀⣤⣌⣃⣀⣀⣀⣀⣀⡀⣿⠀⣿⠣⠀⠃⡄⡆⣿⢾⣿⣿⠀⢼⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡉⠉⠉⠉⡉⠈⠉⠿⠏⠉⠈⠉⠉⠉⠉⠈⠁⠈⠀⠈⠁⠉⠉⠉⠩⢷⣸⡮⣻⡿⣿⣿⠿⡿⣴⢶⠀⡤⠶ ⠟⠷⠶⠿⠆⢀⣶⡄⠀⠀⠀⠀⠀⠀⠀⢸⠀⢿⣇⡀⢀⣄⠁⣿⢹⣙⣿⠀⢹⣟⣛⣯⣻⣟⣟⣛⡏⣻⠺⠶⠇⠀⠀⠛⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠰⠀⠁⠀⠀⠀⢠⣤⣄⣤⣤⣤⣁⣤⣀⣿⣠⣼⣿⣿⣖⣷⣦ ⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠱⠈⠙⣆⣿⢸⢿⣹⠀⣸⣿⣿⣿⣿⡿⣿⣿⣿⣹⢺⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⢿⣿⢛⡛⢟⣻⣿⢿⢟⣟⣿⠛⢻⣗ ⣧⡯⣩⠉⠹⢭⡍⠉⠉⠿⡉⠉⠉⠉⠉⢹⠉⠱⠆⠀⠀⠰⠛⣿⢸⣀⣼⡅⢽⣿⣹⣿⣿⣙⣏⣹⣯⣽⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠉⠀⣴⠀⠀⠀⣿⠇⠒⠇⠿⡋⣁⣠ ⣷⣶⡶⡶⣾⡏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢠⠀⠀⠀⠀⠆⣿⢺⢻⣻⠀⣼⣾⣿⣿⣿⡿⣿⣿⣿⢫⢸⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡷⣾⠟⠓⠻⣿⣿⣿⣇⣈⣛⢻⣟⢻⣟ ⠶⢒⠒⠲⠃⣺⣶⡄⠀⠀⠀⠀⢀⡠⢀⣸⠐⠈⣤⡄⠀⠀⠀⣿⢹⢘⢸⠆⢹⡟⢻⣿⣿⠁⣛⢹⠯⠾⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣀⠀⠀⠉⠛⣿⡻⠃⣀⣛⡻⢎⠙ ⡏⠛⢻⣧⡤⠌⠙⠃⠠⠀⠀⠀⠜⠃⠜⢻⠠⢰⠋⠃⠀⠀⠀⣿⢸⢸⣺⡇⢨⡇⠲⠶⠶⠀⠀⠘⠶⢰⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠰⠿⠭⢯⣦⣭⣯ ⡋⠛⠛⠛⠃⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠀⣠⠀⠀⠀⠃⠀⣿⢸⠸⢿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⢻⣒⢟⠒⣃⣓ ⡗⡶⣾⠇⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣸⠀⠁⠀⠀⠀⣿⢸⢸⢿⡅⢸⡇⠀⠀⠀⠶⠀⠀⠀⠲⣘⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡯⠇⠊⣤⢄⣀⠻⠋ ⡟⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢩⠀⡀⠀⠀⠀⣿⢸⢱⢾⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⣰⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡿⠺⣷⡶⣒⣀⡛⢳ ⣇⣁⣉⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢸⠁⡾⠀⠀⠀⠀⡆⣿⢸⠘⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠁⢸⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠈⠁⠈⠙⠋⠋⠑ ⣏⠉⣉⠁⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⡿⠒⠆⠆⡆⠀⣿⢸⣠⢹⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⢇⣾⡿⡿⠀⢯⣯ ⣯⠋⠻⢃⠀⠸⡷⠂⠀⠀⠀⠀⠀⣤⠀⢸⢿⣷⣳⣿⣿⣇⣱⠙⢺⣿⢾⠶⢶⡷⠶⠶⠶⠴⠶⠦⠶⣶⢘⠶⠶⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠦⠶⠶⠶⠶⠾⠶⠶⠶⠶⠶⠦⠶⠶⠶⠿⠧⠛⠻⠻⠿⠀⣿⣿ ⣎⣷⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠹⡿⠻⠙⡻⠓⢻⠒⠒⠈⢸⠄⢺⡇⠀⠀⠀⠀⠀⠀⡀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣀⠈⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣳⣷ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⢨⠀⠀⠀⢸⡆⠸⠇⠀⠀⠀⣀⠴⠶⠤⣰⢿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⣀⠀⣀⡀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⡛⠛⢻ ⡯⣿⡏⠛⠙⠹⠇⠀⠀⠀⢴⡄⠀⠀⠀⠀⢈⣅⣬⣠⣈⣇⣀⢀⣀⣄⠀⣷⠆⠀⠀⠀⡀⣀⣀⣀⠐⢨⣾⡒⠒⠒⠒⠒⠀⠀⡉⢉⠉⡉⠉⠉⠉⡏⠈⠉⠉⠉⠉⠉⠉⢙⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⡀⠀ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⣶⡶⠶⠶⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠠⠆ ⣶⣶⣴⣤⣶⣶⠶⠶⠶⠶⠦⠶⠶⠶⠶⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠶⠶⠆⠶⠲⠄⠶⠒⠒⠒⠶⠶⠶⠲⠸⠨⡍⠉⠎⠀⠀⠀⣶⣿⣿⣾⣾⣗⣾⣿⣟⣶⣾⣿⣻⣿⣿⣿⣷⣾⣷⣿⣿⣓⣿⣶⣶⣿⣺⣛⣓⣿⣟⣿⣿⣿⣿⣛⢛⣻⣟⣻⡟⡿⢟⣿⣿⣻⣻⡶⠆⠀⠠⠄⠀⣠⠀ ⡿⠻⣿⠿⡿⠿⠿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠺⢻⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⣞⣛⣢⣶⣾⣿⣷⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣾⣖⣶⣶⣶⣶⡾⣟⣺⣿⣷⣿⣽⣾⣿⣿⣶⣆⣤ ⡷⠷⠾⠿⠇⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⣿⣾⣾⣿⠛⢻⣟⣈⣭⣙⣻⣞⣉⣿⣥⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠻⠉⠙⠀⠊⣿⠙⢀⠋⠉⠁⠉⠁ ⣿⣿⣯⣭⡄⣀⣤⣌⣃⣀⣀⣀⣀⣀⡀⣿⠀⣿⠣⠀⠃⡄⡆⣿⢾⣿⣿⠀⢼⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡉⠉⠉⠉⡉⠈⠉⠿⠏⠉⠈⠉⠉⠉⠉⠈⠁⠈⠀⠈⠁⠉⠉⠉⠩⢷⣸⡮⣻⡿⣿⣿⠿⡿⣴⢶⠀⡤⠶ ⠟⠷⠶⠿⠆⢀⣶⡄⠀⠀⠀⠀⠀⠀⠀⢸⠀⢿⣇⡀⢀⣄⠁⣿⢹⣙⣿⠀⢹⣟⣛⣯⣻⣟⣟⣛⡏⣻⠺⠶⠇⠀⠀⠛⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠰⠀⠁⠀⠀⠀⢠⣤⣄⣤⣤⣤⣁⣤⣀⣿⣠⣼⣿⣿⣖⣷⣦ ⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠱⠈⠙⣆⣿⢸⢿⣹⠀⣸⣿⣿⣿⣿⡿⣿⣿⣿⣹⢺⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⢿⣿⢛⡛⢟⣻⣿⢿⢟⣟⣿⠛⢻⣗ ⣧⡯⣩⠉⠹⢭⡍⠉⠉⠿⡉⠉⠉⠉⠉⢹⠉⠱⠆⠀⠀⠰⠛⣿⢸⣀⣼⡅⢽⣿⣹⣿⣿⣙⣏⣹⣯⣽⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠉⠀⣴⠀⠀⠀⣿⠇⠒⠇⠿⡋⣁⣠ ⣷⣶⡶⡶⣾⡏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢠⠀⠀⠀⠀⠆⣿⢺⢻⣻⠀⣼⣾⣿⣿⣿⡿⣿⣿⣿⢫⢸⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡷⣾⠟⠓⠻⣿⣿⣿⣇⣈⣛⢻⣟⢻⣟ ⠶⢒⠒⠲⠃⣺⣶⡄⠀⠀⠀⠀⢀⡠⢀⣸⠐⠈⣤⡄⠀⠀⠀⣿⢹⢘⢸⠆⢹⡟⢻⣿⣿⠁⣛⢹⠯⠾⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣀⠀⠀⠉⠛⣿⡻⠃⣀⣛⡻⢎⠙ ⡏⠛⢻⣧⡤⠌⠙⠃⠠⠀⠀⠀⠜⠃⠜⢻⠠⢰⠋⠃⠀⠀⠀⣿⢸⢸⣺⡇⢨⡇⠲⠶⠶⠀⠀⠘⠶⢰⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠰⠿⠭⢯⣦⣭⣯ ⡋⠛⠛⠛⠃⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠀⣠⠀⠀⠀⠃⠀⣿⢸⠸⢿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⢻⣒⢟⠒⣃⣓ ⡗⡶⣾⠇⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣸⠀⠁⠀⠀⠀⣿⢸⢸⢿⡅⢸⡇⠀⠀⠀⠶⠀⠀⠀⠲⣘⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡯⠇⠊⣤⢄⣀⠻⠋ ⡟⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢩⠀⡀⠀⠀⠀⣿⢸⢱⢾⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⣰⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡿⠺⣷⡶⣒⣀⡛⢳ ⣇⣁⣉⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢸⠁⡾⠀⠀⠀⠀⡆⣿⢸⠘⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠁⢸⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠈⠁⠈⠙⠋⠋⠑ ⣏⠉⣉⠁⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⡿⠒⠆⠆⡆⠀⣿⢸⣠⢹⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⢇⣾⡿⡿⠀⢯⣯ ⣯⠋⠻⢃⠀⠸⡷⠂⠀⠀⠀⠀⠀⣤⠀⢸⢿⣷⣳⣿⣿⣇⣱⠙⢺⣿⢾⠶⢶⡷⠶⠶⠶⠴⠶⠦⠶⣶⢘⠶⠶⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠦⠶⠶⠶⠶⠾⠶⠶⠶⠶⠶⠦⠶⠶⠶⠿⠧⠛⠻⠻⠿⠀⣿⣿ ⣎⣷⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠹⡿⠻⠙⡻⠓⢻⠒⠒⠈⢸⠄⢺⡇⠀⠀⠀⠀⠀⠀⡀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣀⠈⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣳⣷ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⢨⠀⠀⠀⢸⡆⠸⠇⠀⠀⠀⣀⠴⠶⠤⣰⢿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⣀⠀⣀⡀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⡛⠛⢻ ⡯⣿⡏⠛⠙⠹⠇⠀⠀⠀⢴⡄⠀⠀⠀⠀⢈⣅⣬⣠⣈⣇⣀⢀⣀⣄⠀⣷⠆⠀⠀⠀⡀⣀⣀⣀⠐⢨⣾⡒⠒⠒⠒⠒⠀⠀⡉⢉⠉⡉⠉⠉⠉⡏⠈⠉⠉⠉⠉⠉⠉⢙⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⡀⠀ ⢶⡦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⣶⡶⠶⠶⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠠⠆ ⣶⣶⣴⣤⣶⣶⠶⠶⠶⠶⠦⠶⠶⠶⠶⢲⣶⣦⠴⢴⠤⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠶⠶⠆⠶⠲⠄⠶⠒⠒⠒⠶⠶⠶⠲⠸⠨⡍⠉⠎⠀⠀⠀⣶⣿⣿⣾⣾⣗⣾⣿⣟⣶⣾⣿⣻⣿⣿⣿⣷⣾⣷⣿⣿⣓⣿⣶⣶⣿⣺⣛⣓⣿⣟⣿⣿⣿⣿⣛⢛⣻⣟⣻⡟⡿⢟⣿⣿⣻⣻⡶⠆⠀⠠⠄⠀⣠⠀ ⡿⠻⣿⠿⡿⠿⠿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠺⢻⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣖⣞⣛⣢⣶⣾⣿⣷⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣾⣖⣶⣶⣶⣶⡾⣟⣺⣿⣷⣿⣽⣾⣿⣿⣶⣆⣤ ⡷⠷⠾⠿⠇⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⣿⣾⣾⣿⠛⢻⣟⣈⣭⣙⣻⣞⣉⣿⣥⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠻⠉⠙⠀⠊⣿⠙⢀⠋⠉⠁⠉⠁ ⣿⣿⣯⣭⡄⣀⣤⣌⣃⣀⣀⣀⣀⣀⡀⣿⠀⣿⠣⠀⠃⡄⡆⣿⢾⣿⣿⠀⢼⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡉⠉⠉⠉⡉⠈⠉⠿⠏⠉⠈⠉⠉⠉⠉⠈⠁⠈⠀⠈⠁⠉⠉⠉⠩⢷⣸⡮⣻⡿⣿⣿⠿⡿⣴⢶⠀⡤⠶ ⠟⠷⠶⠿⠆⢀⣶⡄⠀⠀⠀⠀⠀⠀⠀⢸⠀⢿⣇⡀⢀⣄⠁⣿⢹⣙⣿⠀⢹⣟⣛⣯⣻⣟⣟⣛⡏⣻⠺⠶⠇⠀⠀⠛⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠰⠀⠁⠀⠀⠀⢠⣤⣄⣤⣤⣤⣁⣤⣀⣿⣠⣼⣿⣿⣖⣷⣦ ⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠱⠈⠙⣆⣿⢸⢿⣹⠀⣸⣿⣿⣿⣿⡿⣿⣿⣿⣹⢺⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⢿⣿⢛⡛⢟⣻⣿⢿⢟⣟⣿⠛⢻⣗ ⣧⡯⣩⠉⠹⢭⡍⠉⠉⠿⡉⠉⠉⠉⠉⢹⠉⠱⠆⠀⠀⠰⠛⣿⢸⣀⣼⡅⢽⣿⣹⣿⣿⣙⣏⣹⣯⣽⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠉⠀⣴⠀⠀⠀⣿⠇⠒⠇⠿⡋⣁⣠ ⣷⣶⡶⡶⣾⡏⠛⠀⠀⠙⠁⠀⠀⠀⠀⢸⠀⢠⠀⠀⠀⠀⠆⣿⢺⢻⣻⠀⣼⣾⣿⣿⣿⡿⣿⣿⣿⢫⢸⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡷⣾⠟⠓⠻⣿⣿⣿⣇⣈⣛⢻⣟⢻⣟ ⠶⢒⠒⠲⠃⣺⣶⡄⠀⠀⠀⠀⢀⡠⢀⣸⠐⠈⣤⡄⠀⠀⠀⣿⢹⢘⢸⠆⢹⡟⢻⣿⣿⠁⣛⢹⠯⠾⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣀⠀⠀⠉⠛⣿⡻⠃⣀⣛⡻⢎⠙ ⡏⠛⢻⣧⡤⠌⠙⠃⠠⠀⠀⠀⠜⠃⠜⢻⠠⢰⠋⠃⠀⠀⠀⣿⢸⢸⣺⡇⢨⡇⠲⠶⠶⠀⠀⠘⠶⢰⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠰⠿⠭⢯⣦⣭⣯ ⡋⠛⠛⠛⠃⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠀⣠⠀⠀⠀⠃⠀⣿⢸⠸⢿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⢻⣒⢟⠒⣃⣓ ⡗⡶⣾⠇⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣸⠀⠁⠀⠀⠀⣿⢸⢸⢿⡅⢸⡇⠀⠀⠀⠶⠀⠀⠀⠲⣘⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡯⠇⠊⣤⢄⣀⠻⠋ ⡟⡶⠶⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢩⠀⡀⠀⠀⠀⣿⢸⢱⢾⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⣰⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡿⠺⣷⡶⣒⣀⡛⢳ ⣇⣁⣉⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢸⠁⡾⠀⠀⠀⠀⡆⣿⢸⠘⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠁⢸⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠈⠁⠈⠙⠋⠋⠑ ⣏⠉⣉⠁⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⡿⠒⠆⠆⡆⠀⣿⢸⣠⢹⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⢇⣾⡿⡿⠀⢯⣯ ⣯⠋⠻⢃⠀⠸⡷⠂⠀⠀⠀⠀⠀⣤⠀⢸⢿⣷⣳⣿⣿⣇⣱⠙⢺⣿⢾⠶⢶⡷⠶⠶⠶⠴⠶⠦⠶⣶⢘⠶⠶⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠦⠶⠶⠶⠶⠾⠶⠶⠶⠶⠶⠦⠶⠶⠶⠿⠧⠛⠻⠻⠿⠀⣿⣿ ⣎⣷⣿⡿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠹⡿⠻⠙⡻⠓⢻⠒⠒⠈⢸⠄⢺⡇⠀⠀⠀⠀⠀⠀⡀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣀⠈⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣳⣷ ⡟⠛⠛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⢨⠀⠀⠀⢸⡆⠸⠇⠀⠀⠀⣀⠴⠶⠤⣰⢿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⣀⠀⣀⡀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⡛⠛⢻ ⡯⣿⡏⠛⠙⠹⠇⠀⠀⠀⢴⡄⠀⠀⠀⠀⢈⣅⣬⣠⣈⣇⣀⢀⣀⣄⠀⣷⠆⠀⠀⠀⡀⣀⣀⣀⠐⢨⣾⡒⠒⠒⠒⠒⠀⠀⡉⢉⠉⡉⠉⠉⠉⡏⠈⠉⠉⠉⠉⠉⠉⢙⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⡀⠀ ⢶⠄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠶⠤⠤⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄ ⠀⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣂⣀⣀⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠈⠉⠉⠉⠉⠉⠉⣵⣴⣶⣴⣆⠀⣰⣦⣤⣄⣶⠀⠀⢐⣰⣦⣤⣴⣦⣤⣀⣀⣶⡒⠀⢀⣀⣀⣤⣴⣦⣀⠀⣀⣀⣀⣀⡀⣀⣴⣶⣶⣶⣆⣒⣂⣦⣦⣦⣤⠠⠄⠀⣠⠀ ⠸⠿⣿⠿⡿⠿⠿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣥⡀⠘⢿⣿⣿⣿⣿⣿⡏⠉⠉⣱⣶⣎⢟⣿⣿⣿⣿⣿⡀⠈⢹⣿⣿⢡⣿⣿⣿⣿⣿⡿⠋⢿⣿⣿⣿⣿⠚⠒⢂⣄⣀ ⠐⠶⠶⠶⠆⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⢀⣿⣿⣿⣿⣿⡆⠀⣾⣿⣿⣾⣿⣿⣿⣿⣿⠄⠀⣺⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠿⠿⠭⠭⠀⠀⠠⠄⠁⠀⠀⠀⠀⠀⠀⠶⠀⠚⠃⠀⠀⠀⠀⠘⠁⠀⣿⣿⣿⣿⡏⠁⣿⣿⣿⣿⡄⠀⠋⠙⠙⠛⠻⣿⣶⣀⡿⠿⠿⢾⣿⣿⢿⣿⣿⣧⠀⠿⠿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢺⢿⡿⣿⣿⠀⠀⠀⠀⠀ ⠐⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⡀⠀⣷⡄⠀⢹⣿⣿⣿⠇⠀⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠈⠉⠈⠁⠲⠶⠖⠀⠀⠈⠉⠉⠇⠐⠀⠂⠘⠛⣮⣍⣻⣿⣿⡇⠀⠀⠈⢸⣿⣿⣰⣿⣀⣀⣀ ⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⡏⠉⠀⠀⠁⡆⣿⣷⡀⠈⠙⠉⠉⠀⠀⠻⣿⣻⣿⡿⠂⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⣀⣄⣀⣤⡀⠀⠀⠀⠀⠀⠀⡄⠀⠙⣻⣿⣿⡇⠀⠀⢀⣶⣾⣿⣿⠘⠛⠛⠛⠓ ⠀⡭⣉⠉⠩⢩⡍⠉⠉⠛⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢻⣿⠁⠀⠀⠀⠀⠀⠀⠐⠦⠌⠀⠀⠀⠠⠤⠤⠤⠤⠤⠄⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣷⠀⢠⣿⣿⣿⣯⠀⢠⣿⣿⣿⠛⢻⠀⠸⠀⠀⠀ ⢠⠶⠶⠶⠾⠆⠛⠀⠀⠈⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠄⠹⠋⠀⣠⣶⣶⣤⣶⣦⡀⠀⠀⠀⠀⠀⢰⠶⠷⠷⠷⠶⠶⠶⠷⠶⠾⠷⠾⠶⠶⠿⠶⠿⠿⠞⠃⠀⠀⣾⢿⣿⣻⣿⠀⠸⢿⣿⡿⢀⣾⠘⠛⠛⠛⠓ ⠀⠒⠒⠒⠂⢸⣦⡄⠀⠀⠀⠀⢀⡀⢀⣠⠀⠀⢀⡀⠀⠀⠀⣶⣷⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣶⣦⠈⠀⠉⣉⡉⠁⠀⠀⠀⢈⣉⠁⠀⠀⠀⠀⣈⣉⡀⠀⠀⠀⠀⢈⠳⠬⠭⠞⠀⠀⠀⠒⠀⣾⣿⠀⠐⠒⠊⠉ ⠀⠛⠛⠇⡤⠌⠈⠃⠠⠀⠀⠀⠘⠃⠜⠻⠀⠀⠈⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣉⣁⠀⠀⠀⠀⢀⣉⠀⠀⠀⠀⠀⣈⣉⡁⠀⠀⠀⠀⠀⠑⢂⣾⣷⠀⠀⠀⠀⣼⣿⣿⠠⠤⢤⠠⠤ ⠀⠚⠛⠉⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⠀⠀⣸⡿⣿⣿⢀⠀⠀⠀⠀ ⠀⠶⡾⠃⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⣷⣤⡀⠀⢟⠿⠿⠇⠀⠀⡉⢻⣮⡿⠀⠀⠀⠀⠁ ⠀⠒⠒⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⣿⣿⠀⠑⠉⠁⠀⠀⠀⠘⣆⣙⡿⠀⠀⠀⠀⠀ ⠀⣀⣈⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣉⣁⣀⣈⣤⣤⣤⣤⣼⣿⣧⣤⣤⣀⣠⣬⣭⣭⣬⣤⣿⣿⣿⣷⣄⣀⣀⣀⡀⠀⠀⠈⠛⠳⠀⠀⠀⠀⠀ ⢈⠉⢉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡄⠐⠆⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠉⠀⠀⠀⠀⠀⠀ ⠀⠉⠩⢁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣄⠀⢸⢶⣖⠳⣿⣞⠄⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠘⠛⠀⠀⠀ ⠀⢥⡤⡥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠤⠜⠙⠟⠋⠙⠻⠓⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣀⣀⣀⣀ ⠀⠛⠛⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⠿⠿⠿⡿⢿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠯⠽⠿⠿⠩⠭⠉⢽⣿⣿⣿⣯⣽⡍⠉⠉⠏⠿⠿⠿⠿⠿⠿⠿⠿⠈⠉⠙⠛⠙ ⠨⣿⡏⠉⠉⠘⠇⠀⠀⠀⢠⡀⠀⠀⠀⠀⠰⠦⢴⣦⣶⠤⠦⠤⠴⠶⠤⠤⠦⠦⢤⠤⠤⠤⠴⠤⠶⠤⠴⠤⡤⠤⠄⠦⠤⠦⠤⠴⠦⠤⠦⠤⠤⠤⡤⠤⠤⠰⠦⠤⠤⠤⠤⠤⠤⠤⠴⠤⠦⠤⠤⠤⢦⠴⠽⠥⡶⠤ ⢶⠄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠶⠤⠤⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄ ⠀⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣂⣀⣀⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠈⠉⠉⠉⠉⠉⠉⣵⣴⣶⣴⣆⠀⣰⣦⣤⣄⣶⠀⠀⢐⣰⣦⣤⣴⣦⣤⣀⣀⣶⡒⠀⢀⣀⣀⣤⣴⣦⣀⠀⣀⣀⣀⣀⡀⣀⣴⣶⣶⣶⣆⣒⣂⣦⣦⣦⣤⠠⠄⠀⣠⠀ ⠸⠿⣿⠿⡿⠿⠿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣥⡀⠘⢿⣿⣿⣿⣿⣿⡏⠉⠉⣱⣶⣎⢟⣿⣿⣿⣿⣿⡀⠈⢹⣿⣿⢡⣿⣿⣿⣿⣿⡿⠋⢿⣿⣿⣿⣿⠚⠒⢂⣄⣀ ⠐⠶⠶⠶⠆⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⢀⣿⣿⣿⣿⣿⡆⠀⣾⣿⣿⣾⣿⣿⣿⣿⣿⠄⠀⣺⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠿⠿⠭⠭⠀⠀⠠⠄⠁⠀⠀⠀⠀⠀⠀⠶⠀⠚⠃⠀⠀⠀⠀⠘⠁⠀⣿⣿⣿⣿⡏⠁⣿⣿⣿⣿⡄⠀⠋⠙⠙⠛⠻⣿⣶⣀⡿⠿⠿⢾⣿⣿⢿⣿⣿⣧⠀⠿⠿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢺⢿⡿⣿⣿⠀⠀⠀⠀⠀ ⠐⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⡀⠀⣷⡄⠀⢹⣿⣿⣿⠇⠀⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠈⠉⠈⠁⠲⠶⠖⠀⠀⠈⠉⠉⠇⠐⠀⠂⠘⠛⣮⣍⣻⣿⣿⡇⠀⠀⠈⢸⣿⣿⣰⣿⣀⣀⣀ ⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⡏⠉⠀⠀⠁⡆⣿⣷⡀⠈⠙⠉⠉⠀⠀⠻⣿⣻⣿⡿⠂⠀⠀⠀⠀⠀⠀⢀⣤⣈⣀⣀⣄⣀⣤⡀⠀⠀⠀⠀⠀⠀⡄⠀⠙⣻⣿⣿⡇⠀⠀⢀⣶⣾⣿⣿⠘⠛⠛⠛⠓ ⠀⡭⣉⠉⠩⢩⡍⠉⠉⠛⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢻⣿⠁⠀⠀⠀⠀⠀⠀⠐⠦⠌⠀⠀⠀⠠⠤⠤⠤⠤⠤⠄⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣷⠀⢠⣿⣿⣿⣯⠀⢠⣿⣿⣿⠛⢻⠀⠸⠀⠀⠀ ⢠⠶⠶⠶⠾⠆⠛⠀⠀⠈⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠄⠹⠋⠀⣠⣶⣶⣤⣶⣦⡀⠀⠀⠀⠀⠀⢰⠶⠷⠷⠷⠶⠶⠶⠷⠶⠾⠷⠾⠶⠶⠿⠶⠿⠿⠞⠃⠀⠀⣾⢿⣿⣻⣿⠀⠸⢿⣿⡿⢀⣾⠘⠛⠛⠛⠓ ⠀⠒⠒⠒⠂⢸⣦⡄⠀⠀⠀⠀⢀⡀⢀⣠⠀⠀⢀⡀⠀⠀⠀⣶⣷⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣶⣦⠈⠀⠉⣉⡉⠁⠀⠀⠀⢈⣉⠁⠀⠀⠀⠀⣈⣉⡀⠀⠀⠀⠀⢈⠳⠬⠭⠞⠀⠀⠀⠒⠀⣾⣿⠀⠐⠒⠊⠉ ⠀⠛⠛⠇⡤⠌⠈⠃⠠⠀⠀⠀⠘⠃⠜⠻⠀⠀⠈⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣉⣁⠀⠀⠀⠀⢀⣉⠀⠀⠀⠀⠀⣈⣉⡁⠀⠀⠀⠀⠀⠑⢀⣾⣷⠀⠀⠀⠀⣼⣿⣿⠠⠤⢤⠠⠤ ⠀⠚⠛⠉⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⠀⠀⣸⡿⣿⣿⢀⠀⠀⠀⠀ ⠀⠶⡾⠃⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⣷⣤⡀⠀⢟⠿⠿⠇⠀⠀⡉⢻⣮⡿⠀⠀⠀⠀⠁ ⠀⠒⠒⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⣿⣿⠀⠑⠉⠁⠀⠀⠀⠘⣆⣙⡿⠀⠀⠀⠀⠀ ⠀⣀⣈⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣉⣁⣀⣈⣤⣤⣤⣤⣼⣿⣧⣤⣤⣀⣠⣬⣭⣭⣬⣤⣿⣿⣿⣷⣄⣀⣀⣀⡀⠀⠀⠈⠛⠳⠀⠀⠀⠀⠀ ⢈⠉⢉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡄⠐⠆⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠉⠀⠀⠀⠀⠀⠀ ⠀⠉⠩⢁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣄⠀⢸⢶⣖⠳⣿⣞⠄⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠘⠛⠀⠀⠀ ⠀⢥⡤⡥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠤⠜⠙⠟⠋⠙⠻⠓⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣀⣀⣀⣀ ⠀⠛⠛⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⠿⠿⠿⡿⢿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠯⠽⠿⠿⠩⠭⠉⢽⣿⣿⣿⣯⣽⡍⠉⠉⠏⠿⠿⠿⠿⠿⠿⠿⠿⠈⠉⠙⠛⠙ ⠨⣿⡏⠉⠉⠘⠇⠀⠀⠀⢠⡀⠀⠀⠀⠀⠰⠦⢴⣦⣶⠤⠦⠤⠴⠶⠤⠤⠦⠦⢤⠤⠤⠤⠴⠤⠶⠤⠴⠤⡤⠤⠄⠦⠤⠦⠤⠴⠦⠤⠦⠤⠤⠤⡤⠤⠤⠰⠦⠤⠤⠤⠤⠤⠤⠤⠴⠤⠦⠤⠤⠤⢦⠴⠽⠥⡶⠤ ⢶⠄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠶⠤⠤⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄ ⠀⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣂⣀⣀⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠈⠉⠉⠉⠉⠉⠉⣵⣴⣶⣴⣆⠐⣰⣦⣤⣄⣶⠀⠀⣐⣰⣦⣤⣶⣦⣤⣀⣀⣶⡒⠀⢀⣀⣀⣤⣴⣦⣀⠀⣀⣀⣀⣀⣀⣀⣴⣶⣶⣶⣆⣒⣂⣦⣦⣦⣤⠠⠄⠀⣠⠀ ⠸⠿⣿⠿⡿⠿⠿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣥⡀⠸⢿⣿⣿⣿⣿⣿⡏⠙⠙⣳⣿⣮⢟⣿⣿⣿⣿⣿⡀⠈⢻⣿⣿⢡⣿⣿⣿⣿⣿⡿⠛⢿⣿⣿⣿⣿⠚⠒⢂⣄⣀ ⠐⠶⠶⠶⠆⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠘⣿⣿⣿⣿⣿⡧⠀⠀⣿⣿⣿⢀⣿⣿⣿⣿⣿⡆⠀⣾⣿⣿⣾⣿⣿⣿⣿⣿⠇⠀⣺⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⡿⠿⠭⠭⠀⠀⠠⠄⠁⠀⠀⠀⠀⠀⠀⠶⠀⠚⠃⠀⠀⠀⠂⠸⠡⠉⣿⣿⣿⣿⡏⠁⣿⣿⣿⣿⡄⠀⠋⠝⠛⠻⠻⣿⣶⣀⡿⠿⠿⢾⣿⣿⢿⣿⣿⣧⠀⠿⠿⣿⣿⣿⣿⣿⣿⣿⢇⢀⣺⢿⡿⣿⣿⠀⠀⠀⠀⠀ ⠐⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢀⡀⠀⣷⡄⠀⢹⣿⣿⣿⠇⠀⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢈⡿⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⣴⣦⣤⠈⠉⠈⣙⣻⣭⣙⡛⡛⢛⢊⠈⠻⠿⢴⣿⣀⣀⣀ ⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⡏⠉⠀⠈⠁⡆⣿⣷⡀⠈⠙⠉⠉⠀⠀⢿⣿⣻⣿⡿⠂⠀⠀⠀⠀⠀⢸⠅⠀⠀⠀⣀⣄⣄⣤⡀⠁⠀⠀⠉⠉⠉⡄⠀⠈⣩⣿⣯⡄⠀⠀⢀⣤⡄⠀⠀⠘⠛⠛⠛⠓ ⠀⡭⣉⠉⠩⢩⡍⠉⠉⠟⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢿⣿⠁⠀⠀⠀⠀⠀⠀⠐⠦⠌⠀⠀⠀⠠⠤⠤⠤⠤⠤⠀⠀⠀⠀⠉⠉⠉⠉⠰⠶⠶⠶⠶⠶⠶⣿⠶⢶⣋⡛⢙⣯⠀⢠⣿⣿⡇⢠⣿⣷⠸⠀⠀⠀ ⢠⠶⠶⠶⠾⠆⠛⠀⠀⠈⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠄⠹⠏⠀⣠⣶⣶⣶⣶⣦⡀⠀⠀⠀⠀⠀⢰⠶⠿⠷⠷⠖⠀⣓⣒⣲⣶⣗⣲⣺⣥⣭⣠⣝⣿⣞⣃⣀⣀⣾⣿⣟⣻⣿⣀⣸⣿⣻⢰⣿⣿⡿⠛⠛⠛⠓ ⠀⠒⠒⠒⠂⢸⣦⡄⠀⠀⠀⠀⢀⡀⢀⣸⠀⠀⢀⡀⠀⠀⠀⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣶⣦⠈⠀⠉⣉⡉⠁⠀⠛⠙⣛⣛⣋⣓⠛⠛⠛⣙⡛⢛⣛⡛⠛⠛⢋⠻⠽⠯⣛⣙⠛⠁⠀⠀⠁⠉⠁⠐⠒⠊⠉ ⠀⠛⠛⢇⡤⠌⠈⠃⠠⠀⠀⠀⠘⠃⠜⠻⠀⠀⠈⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣉⣁⢰⡆⠀⠀⢈⣭⣭⠀⠀⠀⠀⣈⡉⢩⣭⠁⠀⠀⠀⠁⢀⣾⣿⣥⡄⠀⠀⠀⠀⠀⠀⠤⢤⠠⠤ ⠀⠚⠛⠉⠃⢀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣀⠀⢽⡇⠀⠄⢠⣤⣤⠀⠀⠀⠀⢀⣀⣠⣤⡀⠀⠀⠀⠀⣴⣿⣦⣤⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠶⡾⠃⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⠀⠀⣠⣼⡇⠀⠀⠀⢤⡀⠀⠀⢠⠀⠀⠀⠀⠀⠀⣶⣦⡀⠀⠒⠂⣤⡄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠁ ⠀⠒⠒⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⣄⣄⡄⠀⠀⠀⠀⠀⠀⣉⠛⣽⢠⣴⣄⠀⠀⠀⠀⠐⢀⣴⣿⣿⠀⠀⠀⠀ ⠀⣀⣈⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠈⠀⠄⠀⠀⠀⠀⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣉⣁⣀⣈⣿⡇⠀⠀⠠⠶⠦⠤⣤⡀⠠⣤⣤⣤⣤⣤⣶⣦⣴⣦⣄⣀⣀⣀⡀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀ ⢈⠉⢉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡄⠐⠆⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣈⣛⣻⣛⣉⣛⣃⣀⣀⣸⣿⣻⣺⣟⣉⣁⣹⣿⣿⡻⠿⣿⣿⣘⣃⣸⣿⣿⣿⠀⠀⠀⠀ ⠀⠉⠩⢁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣄⠀⢸⢶⣖⠳⣿⣞⠄⡐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠛⢙⠛⠀⠀⠀ ⠀⢥⡤⡥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠤⠜⠙⠟⠋⠙⠻⠓⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣀⣀⣀⣀ ⠀⠛⠛⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⢿⡿⣿⣿⣿⡿⠿⠿⠿⠿⢿⠿⣿⠿⢿⡿⠿⠿⠿⠿⠿⣿⣿⡿⠿⠿⠽⠿⠿⠩⠭⠉⢽⣿⣿⣿⣿⣽⡍⠉⠉⠏⠿⠿⠿⠿⠿⠿⠿⠿⠈⠉⠙⠛⢙ ⠨⣿⡏⠉⠉⠘⠇⠀⠀⠀⢠⡀⠀⠀⠀⠀⠰⠦⢴⣦⣶⠤⠦⠤⠴⠶⠤⠤⠦⠦⢤⠤⠤⠤⠴⠤⠶⠤⠴⠤⡤⠤⠄⠦⠤⠦⠤⠴⠦⠤⠦⠤⠤⠤⡤⠤⠤⠰⠦⠤⠤⠤⠤⠤⠤⠤⠴⠤⠦⠤⠤⠤⢦⠴⠽⠥⡶⠤ ⢶⠄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠶⠤⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠆ ⠀⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣆⣀⣀⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⠈⠉⠉⠉⠉⠉⠉⣵⣴⣶⣴⣆⠐⣰⣦⣤⣤⣶⠀⠀⣰⣴⣦⣤⣶⣦⣤⣀⣀⣶⡒⠀⢀⣀⣠⣤⣶⣦⣀⠀⣀⣀⣀⣀⣀⣀⣴⣶⣶⣶⣦⣗⣆⣦⣦⣦⣤⠠⠄⠀⣠⠀ ⠸⠿⣿⠿⡿⠿⠿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣥⡀⢸⣿⣿⣿⣿⣿⣿⡟⠙⠛⣳⣿⣮⢿⣿⣿⣿⣿⣿⡀⠙⢻⣿⣿⢣⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⠚⠒⢂⣄⣀ ⠐⠶⠶⠶⠆⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢸⣿⣿⣿⣿⣿⣧⠀⠀⣿⣿⣿⢀⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣾⣿⣿⣿⣿⣿⠇⠀⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⡿⠿⠭⠭⠀⠀⠠⠄⠁⠀⠀⠀⠀⠀⠀⠶⠀⠚⠃⠀⠀⠀⠂⠸⠹⠋⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⡄⠀⠻⠟⠻⡻⠿⣿⣶⣀⡿⠿⡿⢿⣿⣿⣿⣿⣿⣧⠀⠿⢿⣿⣿⣿⣿⣿⣿⣿⣇⢀⣻⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠐⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢀⡀⠀⣷⡄⠀⢹⣿⣿⣿⡇⠀⣿⣿⣿⣿⣷⠀⠀⠀⠀⢀⣀⣈⡿⠀⢀⠀⠈⠀⠀⠀⠈⡙⠻⠛⣴⣦⣤⠉⠉⠉⣙⣻⣽⣿⡛⣛⢛⢊⠉⠿⢿⣾⣿⣀⣀⣀ ⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⡏⠉⠀⠈⠁⡆⣿⣿⡀⠈⠙⡉⠋⠀⠀⢿⣿⣿⣿⡿⠂⠀⠀⠀⣿⠛⠛⡃⠀⠀⠀⣌⣄⣤⣬⡄⣿⣿⣦⠛⠉⠉⡄⠀⠉⣩⣭⡽⡛⣻⣿⣇⠀⠀⠀⠀⠘⠛⠛⠛⠓ ⠠⡭⣉⠉⠩⢩⡍⠉⠉⠟⠉⠉⠉⠉⠉⢉⠉⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠐⠦⠬⠠⠀⠀⠠⠤⠤⡏⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠭⠭⠭⠤⠄⠠⣭⠤⠬⣉⡉⣉⣯⠀⣿⣿⠂⠄⢠⣿⣷⠸⠀⠀⠀ ⢠⠶⠶⠶⠾⠆⠛⠀⠀⠈⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠄⠹⠏⠀⣴⣶⣶⣶⣶⣶⡀⠁⠀⠀⠀⠀⢰⠶⠿⡁⠀⠀⠀⣓⣒⣲⣷⣷⣿⣾⣧⣤⣥⣿⣿⣾⣷⠀⠀⣺⣿⣿⣿⣿⣀⣿⣿⡃⢰⣿⣿⡿⠛⠛⠛⠛ ⠀⠒⠒⠒⠂⢸⣦⡄⠀⠀⠀⠀⢀⡀⢀⣸⠀⠀⢀⡀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣶⣦⠈⠀⠉⠀⠤⠤⠤⠯⠿⠿⠿⠏⠓⠛⠛⠚⣛⡛⢛⣛⡛⠛⠚⢋⠻⠽⠯⣛⣉⣻⣿⣧⠀⠁⠉⠁⠐⠒⠊⠉ ⠀⠛⠛⢇⡤⠌⠈⠃⠠⠀⠀⠀⠘⠃⠜⢻⠀⠀⠈⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⠀⣶⣶⣶⣶⣶⣾⣿⣿⣶⣶⣶⣶⣾⣿⣿⣿⣶⣶⣶⣶⣷⣶⣶⠛⠓⠛⣻⣿⠁⠀⠀⠀⠤⢤⠠⠤ ⠀⠛⠛⠉⠃⢀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡶⠶⠶⠶⣀⠀⠀⠀⠀⠰⢶⣆⣀⣀⡀⠀⠀⠰⠶⣖⡋⢂⡄⠛⠛⣹⠀⠀⠀⠀⠀⠀⡀⡀ ⠀⠶⡾⠃⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⢠⡇⠀⠀⠀⠶⠶⠀⠀⠀⠀⠀⠠⠰⠦⠀⠀⠀⠀⠶⠆⠰⠶⠶⠂⠀⠀⠸⣟⡁⠀⠀⠀⣀⠀⠀⠀⠁ ⠀⠖⠲⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡀⢰⡇⠀⠀⠠⣤⣤⠄⠀⢀⢀⣄⡄⣤⣤⠀⠀⠀⠀⣉⠩⣭⣤⡥⠀⠀⠀⠐⠚⠀⢀⣴⣿⣿⠀⠀⠀⠀ ⠀⣀⣈⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢘⠀⠔⠀⠀⠀⠀⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣉⣩⡇⠀⠀⡀⣀⡀⠠⠒⠦⠀⠀⢀⠠⣤⣤⣤⣤⣤⠂⠂⣠⣀⡄⠀⢀⣀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀ ⢈⠉⢉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢀⡄⠐⠆⠂⠂⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⣈⣉⣰⣛⣉⣒⣂⣀⡀⠸⣛⠛⣚⣓⣀⣀⣉⣻⣿⡸⠷⠗⠀⠀⢀⣼⣿⣿⣿⠀⠀⠀⠀ ⠀⠉⠩⢁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣄⠀⢸⢶⣗⠳⣿⣞⠄⡐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣤⣭⣭⣍⣩⣥⣤⣬⣽⣧⣤⣭⣥⣭⣭⣭⣭⣭⣤⣤⣭⣭⣤⣾⣿⣿⣿⡛⠛⢙⠛⠀⠀⠀ ⠀⢥⡤⡥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠤⠜⠙⠟⠻⠙⠻⠓⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠠⣶⣾⡟⢳⣿⠋⠉⠙⣿⣟⣻⣻⡟⠛⢛⣿⣿⣿⣿⣿⣿⣿⢿⠙⣿⣿⣿⣿⣿⣿⢀⣐⣀⣀⣀ ⡈⠛⠛⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⢿⣿⣿⣿⣿⣿⣿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣶⣶⣶⣶⣶⣶⣶⠤⢤⣿⡾⠶⠶⢶⣶⣶⣶⣷⣾⣿⣿⢭⣵⢿⢷⣿⣿⣿⡿⠿⠿⠈⠉⠙⠛⢙ ⠨⣿⡏⠉⠉⠸⠇⠀⠀⠀⢠⡀⠀⠀⠀⠀⠰⠶⢴⣦⣶⠤⠦⠤⠴⠶⠤⠤⠦⠦⢤⠤⠤⠤⠴⠤⠶⠤⠴⠤⣤⠤⠴⠦⠤⠦⠤⠼⠧⠤⠦⠤⠥⠤⡤⠤⠤⠸⠿⠿⠷⣴⣥⠬⠥⠤⠴⠬⠦⢤⠤⠤⢦⠴⠽⠥⡶⠦ ⢶⠄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠶⠤⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄ ⠀⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣂⣀⣀⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⠈⠉⠉⠉⠉⠉⠉⣵⣴⣶⣴⣆⠐⣰⣦⣤⣤⣶⠀⠀⣰⣴⣦⣤⣶⣦⣤⣀⣀⣶⡒⠀⢀⣀⣠⣤⣶⣦⣀⠀⣀⣀⣀⣀⣀⣀⣴⣶⣶⣶⣦⣗⣂⣦⣦⣦⣤⠠⠄⠀⣠⠀ ⠸⠿⣿⠿⡿⠿⠿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣥⡀⢸⣿⣿⣿⣿⣿⣿⡟⠙⠛⣳⣿⣮⢿⣿⣿⣿⣿⣿⡀⠙⢻⣿⣿⢣⣿⣿⣿⣿⣿⡿⠟⣿⣿⣿⣿⣿⠚⠒⢂⣄⣀ ⠐⠶⠶⠶⠆⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢸⣿⣿⣿⣿⣿⣧⠀⠀⣿⣿⣿⣀⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣾⣿⣿⣿⣿⣿⠇⠀⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⡿⠿⠭⠭⠀⠀⠠⠄⠁⠀⠀⠀⠀⠀⠀⠶⠀⠚⠃⠀⠀⠀⠂⠸⠹⠋⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⡄⠀⠻⠟⠻⡻⠿⣿⣶⣀⡿⠿⡿⢿⣿⣿⣿⣿⣿⣧⠀⠿⢿⣿⣿⣿⣿⣿⣿⣿⣇⢀⣻⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠐⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢀⡀⠀⣷⡄⠀⢹⣿⣿⣿⡇⠀⣿⣿⣿⣿⣷⠀⢀⢀⣤⣤⣤⣬⡟⠀⠀⢤⣬⣤⣄⣀⣬⡝⠛⠛⢰⣦⣤⣭⠍⣩⣽⣿⣽⣻⡛⣛⢛⢊⠉⠿⢿⣾⣿⣀⣀⣀ ⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⡏⠉⠀⠈⠁⡆⣿⣿⡀⠈⠙⡉⠋⠀⠀⢿⣿⣿⣿⡿⠂⠀⠈⠉⠉⠉⠉⠁⠀⠀⢠⠀⢰⣶⣶⡦⠀⠀⠀⠀⠉⠉⢭⠠⠌⠍⠍⢿⣿⣿⣿⣇⠀⠀⠀⠀⠘⠛⠛⠛⠓ ⠠⡭⣉⠉⠩⢩⡍⠉⠉⠟⠉⠉⠉⠉⠉⢉⠉⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠐⠦⠬⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠂⠄⢠⣿⣷⠸⠀⠀⠀ ⢠⠶⠶⠶⠾⠆⠛⠀⠀⠈⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠄⠹⠏⠀⣴⣶⣶⣶⣶⣶⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⢲⣶⣷⣶⣿⣮⣷⣶⣷⣿⣹⣾⣷⠀⠀⣠⣿⣽⣿⣿⣿⣿⣿⡃⢰⣿⣿⡿⠛⠛⠛⠛ ⠀⠒⠒⠒⠂⢸⣦⡄⠀⠀⠀⠀⢀⡀⢀⣸⠀⠀⢀⡀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣶⡆⠠⠤⠤⠤⠤⠤⠤⠭⠾⠿⠿⠇⠀⠀⠀⠀⣀⡀⢀⣀⡀⠘⠒⢋⠻⠝⣿⣿⣿⣿⣿⣧⠀⠅⠉⠁⠐⠒⠊⠉ ⠀⠛⠛⢇⡤⠌⠈⠃⠠⠀⠀⠀⠘⠃⠜⢻⠀⠀⠈⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢐⣖⣶⣶⣶⣶⣖⣶⣶⣾⣿⣿⣶⣶⣶⣲⣾⣿⣟⣿⣖⣖⣶⣶⣗⡆⢻⣿⣿⣿⣿⣿⠁⠀⠀⠀⠤⢤⠠⠤ ⠀⠛⠛⠉⠃⢀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠠⣤⣤⣤⡤⠀⠀⠀⠀⠀⢤⣤⠄⠀⠀⣀⠀⢀⠠⣤⡄⠀⠂⠀⣤⣉⣛⣛⣛⣹⠀⠀⠀⠀⠀⠀⡀⡀ ⠀⠶⡾⠃⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⢠⣤⣤⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⣤⣤⣤⠀⠀⠀⣈⠛⠻⠿⢟⡁⠀⠀⠀⣀⠀⠀⠀⠁ ⠀⠖⠲⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣀⣀⠠⣄⣀⠀⠀⢀⣀⣄⡀⣤⢀⠀⠀⢀⣀⣀⣀⣤⣀⡀⠙⠿⠿⠶⠟⠀⢀⣴⣿⣿⠀⠀⠀⠀ ⠀⣀⣈⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢘⠀⠔⠀⠀⠀⠀⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⣀⣀⣉⠉⠉⠀⠀⠀⠰⠶⠶⡶⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀ ⢈⠉⢉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢀⡄⠐⠆⠂⠂⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠂⠛⠀⠀⠈⠉⠰⠒⠀⢂⡀⣀⡀⠰⣊⠁⣀⣙⠛⠂⠈⠉⠁⠀⠠⠠⠀⠀⢀⣼⣿⣿⣿⠀⠀⠀⠀ ⠀⠉⠩⢁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣄⠀⢸⢶⣗⠳⣿⣞⠄⡐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠠⠶⠷⠌⠉⠀⠀⠠⠄⠀⠀⣀⠀⠶⠶⠦⠉⠀⠁⠀⢠⠘⠒⠒⠀⢸⣿⣿⡛⠛⢙⠛⠀⠀⠀ ⠀⢥⡤⡥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠤⠜⠙⠟⠻⠙⠻⠓⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⢀⢀⣻⡀⠀⢀⣀⣀⣀⣀⡀⠀⣴⣦⣤⣤⣿⣿⣿⣿⣿⢀⣐⣀⣀⣀ ⠈⠛⠛⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⢿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⡿⣿⣿⢿⡇⠘⠛⠃⠀⠘⠃⣒⣶⣀⣢⣤⠾⣾⣾⣄⣶⣶⣆⣶⡶⠟⢿⣿⠛⣤⣿⣿⣿⣿⣿⣿⡿⠿⠿⠈⠉⠙⠛⢙ ⠨⣿⡏⠉⠉⠸⠇⠀⠀⠀⢠⡀⠀⠀⠀⠀⠰⠶⢴⣦⣶⠤⠦⠤⠴⠶⠤⠤⠦⠦⢤⠤⠤⠤⠴⠤⠶⠤⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣮⣿⣿⣿⣿⣿⣿⠧⢤⠤⠤⢦⠴⠽⠥⡶⠤ ⢶⠆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠶⠤⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠆ ⠤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣆⣀⣀⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⠈⠉⠉⠉⠉⠉⠉⣵⣴⣶⣴⣖⡐⣲⣦⣤⣤⣶⠀⠀⣲⣴⣦⣤⣶⣦⣤⣂⣀⣷⡒⠀⢀⣀⣠⣤⣶⣦⣀⠀⣀⣀⣀⣀⣀⣀⣴⣶⣶⣷⣦⣗⣆⣦⣦⣦⣤⠠⠄⠀⣠⠀ ⠹⠿⣿⠿⡿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣧⡀⢹⣿⣿⣿⣿⣿⣿⡟⠙⠛⣷⣿⣾⢿⣿⣿⣿⣿⣿⡀⠙⢻⣿⣿⢯⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠟⠒⢂⣄⣀ ⠐⠶⠶⠶⠆⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢹⣿⣿⣿⣿⣿⣧⠀⠀⣿⣿⣿⣀⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣾⣿⣿⣿⣿⣿⠇⠀⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀ ⡿⠿⠭⠭⠀⠀⠠⠄⠁⠀⠀⠀⠀⠀⠀⠶⠀⠚⠃⠀⠀⠀⠂⠸⠹⠋⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⡆⠈⠻⠟⠿⡿⡿⣿⣶⣀⡿⠿⡿⢿⣿⣿⣿⣿⣿⣧⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⣻⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢀⡀⠀⣷⡄⠀⢻⣿⣿⣿⡯⠀⣿⣿⣿⣿⣷⠀⢀⢠⣤⣤⣤⣬⡟⠐⠀⣤⣬⣤⣄⣁⣬⣿⣿⣿⣾⣦⠀⠉⠙⠻⠿⠿⠿⠿⠿⠿⠿⢾⠿⠙⠙⠘⠻⣶⣶⣶ ⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⡏⠉⠀⠈⠁⡆⣿⣿⡀⠈⠙⡛⠏⠁⠀⢿⣿⣿⣿⣿⠖⠀⠈⠉⠉⠉⠉⠁⠉⠀⢢⠂⣰⣶⣶⣾⣿⠀⣺⠇⢀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠾⢿⣿⣿⣿⡷⠀⠀⠂⠀⠈ ⠠⡭⣉⠉⠩⢩⡍⠉⠉⠟⠉⠉⠉⠉⠉⢉⠉⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠐⠮⠭⠥⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀ ⢠⠶⠶⠶⠾⠆⠛⠀⠀⠈⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠄⠻⡏⠀⣴⣶⣶⣶⣶⣶⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⢲⣾⣷⣶⠀⠀⣿⡏⣴⣿⣹⣾⣶⠀⠀⣠⣿⣽⣿⣷⣾⣭⣿⣤⣶⣿⣿⣿⣿⣾⣿⠓ ⠂⠒⠒⠒⠂⢺⣦⡄⠀⠀⠀⠀⢀⡀⢀⣸⠀⠀⢀⡀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⡆⠠⠤⠤⠤⠤⠤⠤⠭⠾⠿⠿⠏⠀⠀⣿⠇⣤⣭⣤⣤⣤⣼⣾⣥⣤⣄⢉⠉⠉⣉⣁⠁⠀⠁⠀⠀⠘⠓⠊⠉ ⠀⠛⠛⢇⡤⠌⠈⠃⠠⠀⠀⠀⠘⠃⠜⢻⠀⢀⠈⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢐⣖⣶⣶⣶⣶⣖⣶⣶⣾⣿⡇⠀⠀⠻⠃⢶⣴⣿⣾⣶⣶⣦⣤⣦⣤⣽⣯⣿⣿⣿⣾⣥⣤⣤⣤⣤⣤⣤⣤ ⡀⠛⠛⠉⠃⢀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠠⣤⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠁⠀⠙⠛⠋⣉⣛⣙⣋⣉⠛⠉⠛⠋⠋⠉⠛⢙⣛⣋⠉⠉⠙⠉⠉⠛ ⠀⠶⡾⠃⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡐⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢠⣤⣤⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠛⠫⠽⠭⠋⠀⠀⠀⠂⠲⠲⠒⠈⠉⠉⠀⠀⠀⠀⠀⠀ ⠀⠖⠲⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣀⣀⡠⣄⣀⠀⠀⣸⣿⣷⣄⠀⠀⠀⠀⠀⠛⠛⠛⠀⠀⠀⠀⠂⠀⠀⠀⠛⠛⠃⠀⠀⠀⠀⠀⠀ ⢀⣀⣈⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢘⠀⠖⠀⠀⠀⠀⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠉⠈⠀⠀⠀⠀⢻⣿⣿⣿⡇⠀⠀⠀⠠⣦⣤⣴⡄⠀⠀⠀⠔⠖⠀⠀⣴⣶⡶⠚⠓⠀⠄⠀⠀ ⢈⠉⢉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢀⡄⠐⠆⠂⠂⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⠂⠛⠀⠀⠈⠉⠰⠒⢺⣿⣿⣿⣷⠀⠀⠀⣀⣀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠉⠩⢁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣄⠀⢸⢶⣷⠳⣿⣞⠄⡐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠄⠰⠶⠷⠌⠉⠈⢿⣿⣿⣿⣷⠀⠀⠀⠀⠈⠉⠀⠀⠀⢠⠀⠓⠖⠀⢸⣿⣿⠛⠛⠉⠙⠀⠀⠂ ⠄⢥⣤⡥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠤⠞⠙⠟⠻⠙⠻⠓⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠰⠶⠶⠶⠆⠀⠀⣀⠀⠀⠓⠄⠀⠀⠀⠀⠀⠰ ⡈⠛⠛⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡇⠘⠛⠃⡀⠘⠓⣒⣶⣀⣢⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⣀⣀⣀⣿⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀ ⠨⣿⡏⠉⠉⠸⠇⠀⠀⠀⢠⡀⠀⠀⠀⠀⠰⠶⣴⣦⣶⠤⠦⠤⠶⠶⠤⠤⠦⠦⢤⠤⠴⠤⠴⠤⠶⠴⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠺⠿⠣⠀⠀⠘⠿⠄⡻⣿⣿⣿⣿⠷⢰⡦⣶⢢⠴⠽⠤⠶⠦ ⢶⠆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠶⠤⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠆ ⠤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣆⣀⣀⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⠈⠉⠉⠉⠉⠉⠉⣵⣴⣶⣴⣆⡐⣰⣦⣤⣤⣶⠀⠀⣲⣴⣦⣤⣶⣦⣤⣀⣀⣷⡒⠀⢀⣀⣠⣤⣶⣦⣀⠀⣀⣀⣀⣀⣀⣀⣴⣶⣶⣶⣦⣗⣆⣦⣦⣦⣤⠠⠄⠀⣠⠀ ⠹⠿⣿⠿⡿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣥⣀⢹⣿⣿⣿⣿⣿⣿⣟⣙⣛⣷⣿⡾⢿⣿⣿⣿⣿⣿⣠⣙⣿⣿⣿⠯⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⠚⠒⢂⣄⣀ ⠐⠶⠶⠶⠆⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣏⠉⢻⣿⣿⡟⠋⠉⠁⠀⣀⣈⣛⣛⣃⣠⣿⣿⡟⠛⡛⠁⠀⠀⠽⠻⠡⢨⢿⠂⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⡿⠿⠭⠭⠀⠀⠠⠄⠁⠀⠀⠀⠀⠀⠀⠶⠀⠚⠃⠀⠀⠀⠂⠸⠹⠋⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⡄⠈⠻⢿⡇⣤⣀⡤⠤⡤⢤⣤⣤⣤⣴⣶⣤⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⢸⢀⣻⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢀⡀⠀⣷⡄⠀⢻⣿⣿⣿⡏⠀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢀⡀⣈⣀⣀⣀⣀⣀⣈⣉⣭⣿⣿⣿⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⢠⡿⠿⠾⠽⠙⠙⠘⠻⣶⣶⣶ ⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⡏⠉⠀⠈⠁⡆⣿⣿⡀⠈⠙⡋⠏⠁⠀⢿⣿⣿⡿⣿⣿⡿⢿⠀⠀⣿⣿⠷⠿⠶⠶⠶⠶⠶⠶⠾⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠒⠀⠮⢹⣿⣾⣿⡷⠀⠀⠀⠀⠈ ⠠⡭⣉⠉⠩⢩⡍⠉⠉⠟⠉⠉⠉⠉⠉⢉⠉⠀⠀⠀⠀⠀⠀⣿⣿⠅⠀⠀⠀⠀⠀⠀⠐⠦⠬⡓⠲⠄⠀⠀⠀⢰⣿⡟⠀⠀⠛⣛⡛⠃⠀⠀⠴⠗⣚⡛⠀⠀⠀⠀⠀⣘⣛⡃⠀⠀⢰⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀ ⢠⠶⠶⠶⠾⠆⠛⠀⠀⠈⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠄⠹⠏⠀⣴⣶⣶⣶⣶⣶⡄⠁⠀⡈⠀⠀⠀⠀⢀⡀⠿⠇⠀⠀⣘⣉⣁⠐⠁⠀⠈⠃⣈⣑⠉⠂⠀⠀⠀⣉⣉⡉⠀⠀⢸⣬⣿⣤⣶⣽⣿⣿⣿⣾⣿⠓ ⠂⠒⠒⠒⠂⢸⣦⡄⠀⠀⠀⠀⢀⡀⢀⣸⠀⠀⢀⡀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣶⣾⣿⣅⠀⠀⠀⠈⠈⣉⠉⠁⠀⠀⣈⠀⣭⣭⣤⣄⠀⠀⠀⢉⣉⠁⠀⠀⢈⣉⣁⠁⠀⠁⠀⠀⠘⠒⠊⠉ ⠀⠛⠛⢇⡤⠌⠈⠃⠠⠀⠀⠀⠘⠃⠜⢻⠀⢀⠈⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣒⣒⡒⢳⣒⣢⣄⠀⠀⠀⢠⠄⠀⠀⠀⣀⣀⣄⠁⠀⠀⠀⠀⣿⣿⣾⣥⣤⣤⣤⣤⣤⣤⣤ ⡀⠛⠛⠉⠃⢀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠛⢙⣙⣋⠉⠉⠉⠉⠉⠛ ⠀⠶⡾⠃⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣭⣥⣀⣨⣤⣤⣤⣤⣤⣿⣿⣤⣭⣄⣄⣄⣈⣭⣭⣍⣁⡠⠲⠒⠈⠉⠉⠀⠀⠀⠀⠀⠀ ⠀⠖⠲⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠟⢛⣛⣛⡻⣿⣻⢟⣟⣿⣿⣿⣟⠛⠛⠛⠛⠛⠛⠛⠛⠀⠈⠉⠀⠂⠀⠀⠀⠛⠛⠃⠀⠀⠀⠀⠀⠀ ⠀⣀⣈⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢘⠀⠔⠀⠀⠀⠀⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠉⠈⠀⠀⠘⠟⢻⣿⣿⣿⡇⠀⠀⠀⠠⣦⣤⣴⡄⠀⠀⠀⠐⠖⠀⠀⣴⣶⡶⠚⠓⠀⠀⠀⠀ ⢈⠉⢉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢀⡄⠐⠆⠂⠂⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⠂⠛⠀⠀⠈⠉⠰⠒⢺⣿⣿⣿⡷⠀⠀⠀⣀⣀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠩⢁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣄⠀⢸⢶⣷⠳⣿⣞⠄⡐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠠⠶⠷⠌⠉⠈⢿⣿⣿⣿⣷⠀⠀⠀⠀⠈⠉⠀⠀⠀⢠⠀⠓⠖⠀⢸⣿⣿⠛⠛⠈⠙⠀⠀⠂ ⠄⢥⣤⡥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠤⠜⠙⠟⠻⠙⠻⠓⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠰⠶⠶⠶⠆⠀⠀⣀⠀⠀⠓⠄⠀⠀⠀⠀⠀⠰ ⡈⠛⠛⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡇⠘⠛⠃⠀⠘⠓⣒⣶⣀⣢⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⣀⣀⣀⣿⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀ ⠨⣿⡏⠉⠉⠸⠇⠀⠀⠀⢠⡀⠀⠀⠀⠀⠰⠶⣴⣦⣶⠤⠦⠤⠴⠶⠤⠤⠦⠦⢤⠤⠤⠤⠴⠤⠶⠴⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠺⠿⠣⠀⠀⠐⠷⠀⡻⣿⣿⣿⣿⠷⢰⠦⣶⢢⠴⠽⠤⠶⠦ ⢶⠄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠶⠤⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄ ⠀⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣂⣀⣀⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠈⠉⠉⠉⠉⠉⠉⣵⣴⣶⣴⣆⠐⣰⣦⣤⣤⣶⠀⠀⣰⣴⣦⣤⣶⣦⣤⣀⣀⣶⡒⠀⢀⣀⣠⣤⣶⣦⣀⠀⣀⣀⣀⣀⣀⣀⣴⣶⣶⣶⣦⣓⣂⣦⣦⣦⣤⠠⠄⠀⣠⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣅⣀⢸⣿⣿⣿⣿⣿⣿⣟⣙⣛⣳⣿⡮⢿⣿⣿⣿⣿⣿⣠⣙⣿⣿⣿⠣⣿⣿⣿⣿⣿⡿⠟⢿⣿⣿⣿⣿⠚⠒⢂⣄⣀ ⠐⠿⠿⠿⠧⠿⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣏⠉⢻⣿⣿⡟⠉⠉⠁⠀⣀⢈⣙⣋⣃⣠⣿⣿⡟⠉⠛⠁⠀⠀⠭⠩⠡⠨⢿⠂⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⡧⣶⣶⣶⡆⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠂⠸⠩⠋⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⡄⠈⠻⠿⣥⣾⣿⡀⠀⡀⢀⣻⣾⣦⣀⠨⢼⣶⣬⣿⠄⠀⠀⠠⠼⠄⠀⠼⠿⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠐⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢀⡀⠀⣷⡄⠀⢹⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢀⣾⣿⡇⣀⣤⣠⣤⣄⣉⣉⣿⣦⣼⣿⣛⠋⠁⠀⠀⠀⠀⠙⠈⠘⠈⢼⠾⠝⠙⠙⠐⠻⣶⣶⣶ ⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⡏⠉⠀⠈⠁⡆⣿⣷⡀⠈⠙⡉⠋⠀⠀⢿⣿⣻⡿⣿⣿⡿⠿⠀⠀⣿⣿⣽⠄⠶⠶⠶⠶⠶⠖⠚⣿⣶⣖⣶⣒⣒⣲⣶⡶⠶⠶⠖⠒⠀⠀⢸⣿⣾⣶⡗⠀⠀⠀⠀⠀ ⠀⡭⣉⠉⠩⢩⡍⠉⠉⠟⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢿⣿⠁⠀⠀⠀⠀⠀⠀⠐⠦⠌⠓⠒⠀⠀⠀⠀⢰⣿⡇⠀⠀⣛⢛⢛⠃⡀⣀⡴⠍⢉⡋⠉⠉⠉⠙⠉⢙⣛⡂⠀⠀⠀⠀⢈⠀⠀⠀⠀⡀⠀⠀⠀⠀ ⢠⠶⠶⠶⠾⠆⠛⠀⠀⠈⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠄⠹⠏⠀⣠⣶⣶⣴⣶⣦⡀⠁⠀⡈⠀⠀⠀⠀⠀⡀⠿⣿⡄⠀⣙⣉⣉⣉⣉⣉⣉⣃⣈⣑⣈⣂⣀⣀⣀⣉⣉⣉⣀⣀⣈⣀⣸⣥⣶⣽⣿⣿⣿⣾⣿⠓ ⠀⠒⠒⠒⠂⢸⣦⡄⠀⠀⠀⠀⢀⡀⢀⣸⠀⠀⢀⡀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣷⣶⣶⣶⣿⣄⠀⣿⣧⠀⠛⠙⣛⣋⣙⡛⣛⠛⠉⠛⣻⣟⠃⠛⠉⢋⠉⢙⣋⡙⠃⠀⢸⠅⠀⠁⠀⠀⠘⠒⠊⠉ ⠀⠛⠛⢇⡤⠌⠈⠃⠠⠀⠀⠀⠘⠃⠜⠻⠀⠀⠈⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠒⠐⢛⣋⣉⠁⠀⠀⠠⠄⣉⡉⠀⢀⡀⣀⠀⣈⣉⡁⠀⠀⢸⣿⣥⣤⣤⣤⣤⣤⣤⣤ ⠀⠚⠛⠉⠃⢀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠏⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠉⣁⠀⠀⠀⠀⠀⠈⠉⡁⠀⠀⢨⢙⣉⣋⠉⠉⠉⠉⠉⠛ ⠀⠶⡾⠃⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⣤⣀⡘⣿⣧⣤⣄⣤⣭⣴⣿⣟⣄⣀⣀⣀⣤⣟⣛⣃⠀⠀⢠⠈⠉⠉⠀⠀⠀⠀⠀⠀ ⠀⠒⠒⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠟⣟⣛⣣⣤⡄⢻⢏⣙⢾⣶⡏⠀⠘⠛⠛⠛⠛⠛⠃⠀⠀⠈⠸⠶⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀ ⠀⣀⣈⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠈⠀⠔⠀⠀⠀⠀⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⣽⣿⡇⠀⠈⠟⢈⢾⣿⣿⡇⠀⠀⠀⠠⣦⣤⠐⢠⣤⣤⠀⠀⠀⠀⠀⣴⣶⡶⠚⠐⠀⠀⠀⠀ ⢈⠉⢉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢀⡄⠐⠆⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠛⢿⣿⣿⠁⠰⠒⢺⠷⢿⣷⡇⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠩⢁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣄⠀⢸⢶⣖⠳⣿⣞⠄⡐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢺⣿⣏⠐⠺⠂⠻⠰⠘⠿⠷⠀⠀⠶⠶⠈⠉⠀⠀⠀⠐⠒⠒⠒⠃⠀⣿⣟⠛⠛⠈⠘⠀⠀⠀ ⠀⢥⡤⡥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠤⠜⠙⠟⠻⠙⠻⠓⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠐⠛⠛⢈⡁⢪⣽⣿⣿⣿⡟⠋⠙⠉⠉⠛⠀⠙⠿⠿⠿⠛⠐⠒⣀⠀⠀⠓⠄⠀⠀⠀⠀⠀⠰ ⠀⠛⠛⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⢿⣿⢿⣿⢿⡿⠿⠿⠿⠿⢿⠿⣿⠿⢿⡇⠘⠛⠂⠀⠈⠃⣒⣾⣀⣢⣿⣿⣿⣿⣧⠀⢄⡀⠀⠀⠀⡄⠀⠀⢀⣀⣀⣀⣿⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀ ⠨⣿⡏⠉⠉⠘⠇⠀⠀⠀⢠⡀⠀⠀⠀⠀⠰⠦⢴⣦⣶⠤⠦⠤⠴⠶⠤⠤⠦⠦⢤⠤⠤⠤⠴⠤⠶⠤⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠻⠿⠧⠀⠀⠀⠃⠀⡻⣿⣿⣿⣿⠧⢰⠦⡶⢢⠴⠽⠤⠶⠤ ⢶⠄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠶⠤⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄ ⠀⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣂⣀⣀⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠈⠉⠉⠉⠉⠉⠉⣵⣴⣶⣴⣆⠐⣰⣦⣤⣤⣶⠀⠀⣰⣴⣦⣤⣶⣦⣤⣀⣀⣶⡒⠀⢀⣀⣠⣤⣶⣦⣀⠀⣀⣀⣀⣀⣀⣀⣴⣶⣶⣶⣦⣓⣂⣦⣦⣦⣤⠠⠄⠀⣠⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣻⣄⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣅⣀⢸⣿⣿⣿⣿⣿⣿⣟⣙⣛⣳⣿⡮⢿⣿⣿⣿⣿⣿⣠⣙⣿⣿⣿⠣⣿⣿⣿⣿⣿⡿⠟⢿⣿⣿⣿⣿⠚⠒⢂⣄⣀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣏⠉⢻⣿⣿⡟⠉⠉⠁⠀⣀⣈⣙⣛⣃⣠⣿⣿⡟⢉⡻⠁⠀⠀⠭⠫⠡⠨⢿⢢⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⣧⣶⣴⣶⡄⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠂⠸⠩⠋⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⡄⠈⠻⠿⣥⣾⣿⣿⡄⡀⠀⠙⣛⣛⣀⠘⠛⠛⢻⣿⣿⡀⠀⠘⠛⠋⠀⣛⢛⢛⢛⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠴⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢀⡀⠀⣷⡄⠀⢹⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢀⣾⣿⣿⣿⠁⣀⣀⣀⣉⣉⣉⣀⣘⣀⣈⠋⠉⠀⠀⠀⠀⠈⠀⠁⠀⠈⠀⢿⠙⠙⠐⠻⣶⣶⣶ ⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⡏⠉⠀⠈⠁⡆⣿⣷⡀⠈⠙⡉⠋⠀⠀⢿⣿⣿⡿⣿⣿⡿⠿⠀⠀⣿⣿⣽⠯⣿⡷⠶⠶⠶⠖⠚⠿⢶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠖⠒⠀⠀⠀⠀⢸⣶⡗⠀⠀⠀⠀⠀ ⠀⡭⣉⠉⠩⢩⡍⠉⠉⠟⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠐⠦⠌⠓⠒⠀⠀⠀⠀⢰⣿⡇⠀⠀⢸⣿⣛⣃⣀⣀⣴⣄⣀⡉⠉⠉⠈⠈⠉⢙⣛⡃⠀⠀⠀⠀⠀⠀⣈⠀⠀⡀⠀⠀⠀⠀ ⢠⠶⠶⠶⠾⠆⠛⠀⠀⠈⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠄⠹⠏⠀⣤⣶⣶⣴⣶⣦⡀⠁⠀⡈⠀⠀⠀⠀⠀⡀⠿⣿⡄⠀⢸⡧⣤⣤⣤⣤⣬⣧⣤⣵⣬⣦⣤⣤⡤⣭⣭⣭⣤⣤⣬⣤⡤⠤⣿⣽⣿⣿⣿⣾⣿⠓ ⠀⠒⠒⠒⠂⢸⣦⡄⠀⠀⠀⠀⢀⡀⢀⣸⠀⠀⢀⡀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣶⣶⣿⣅⠀⣿⣧⠀⠸⠃⠉⢩⣭⣭⣭⠉⠉⠉⠩⠍⣭⣭⠉⢉⠉⠉⠉⢩⣭⠉⠁⠀⣿⠁⠀⠀⠘⠒⠊⠉ ⠀⠛⠛⢇⡤⠌⠈⠃⠠⠀⠀⠀⠘⠃⠜⠻⠀⠀⠈⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠐⢀⣀⣀⣠⡀⠀⠀⠀⠀⠀⣄⣀⣀⣀⠀⡀⠀⣄⣠⡀⠀⠀⢻⣦⣤⣤⣤⣤⣤⣤ ⠀⠚⠛⠉⠃⢀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠏⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢙⣋⠉⠉⠉⠉⠉⠛ ⠀⠶⡾⠃⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢀⠀⠁⢉⠉⠉⠀⠉⣀⣉⣉⣉⣁⣀⣀⣀⠉⠉⣉⠉⠁⠀⠀⢈⠉⠀⠀⠀⠀⠀⠀ ⠀⠒⠒⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠟⣟⣛⣣⣤⣤⣶⠀⠐⠒⠚⠓⠀⠀⠀⠚⠛⠛⠛⠃⠀⠀⠀⠐⠒⠚⠛⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀ ⠀⣀⣈⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢘⠀⠔⠀⠀⠀⠀⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⣽⣿⣿⣿⡎⠁⠈⠶⠖⠶⠶⠦⠀⠀⠠⠆⠤⠐⠀⠤⠴⠶⠆⠀⠀⠀⠀⣿⡷⠚⠐⠀⠀⠀⠀ ⢈⠉⢉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢀⡄⠐⠆⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠛⢿⣿⣿⣿⡇⠒⠲⠶⠶⠶⠆⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀ ⠀⠉⠩⢁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣄⠀⢸⢶⣖⠳⣿⣞⠄⡐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢿⣿⣿⣿⣇⣚⠛⢀⠀⠈⠀⠀⠀⠀⠀⠟⠿⠀⠀⠀⠀⠀⠈⠉⠉⠘⠃⣹⠛⠛⠈⠘⠀⠀⠀ ⠀⢥⡤⡥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠤⠜⠙⠟⠻⠙⠻⠓⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠐⠛⠻⢿⣷⢿⣛⣿⣿⣿⡿⠿⠿⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⣀⠀⠐⠒⠄⠀⠀⠀⠀⠀⠰ ⠀⠛⠛⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⢿⣿⣿⣿⣿⡿⠿⠿⠿⠿⢿⠿⣿⠿⢿⡇⠘⠛⠃⠀⠈⠋⣒⣾⣰⣪⣿⣿⣿⣿⣧⠀⢄⡀⠀⠀⠀⡄⠀⠀⢀⣀⣀⣀⣿⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀ ⠨⣿⡏⠉⠉⠘⠇⠀⠀⠀⢠⡀⠀⠀⠀⠀⠰⠦⢴⣦⣶⠤⠦⠤⠴⠶⠤⠤⠦⠦⢤⠤⠤⠤⠴⠤⠶⠤⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠻⠿⠧⠀⠀⠀⠃⠀⡻⣿⣿⣿⣿⠧⢰⠦⡶⢢⠴⠽⠤⠶⠤ ⢶⠄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠶⠤⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄ ⠀⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣂⣀⣀⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠈⠉⠉⠉⠉⠉⠉⣵⣴⣶⣴⣆⠐⣰⣦⣤⣤⣶⠀⠀⣰⣴⣦⣤⣶⣦⣤⣀⣀⣶⡒⠀⢀⣀⣠⣤⣶⣦⣀⠀⣀⣀⣀⣀⣀⣀⣴⣶⣶⣶⣦⣓⣂⣦⣦⣦⣤⠠⠄⠀⣠⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣻⣄⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣅⣀⢸⣿⣿⣿⣿⣿⣿⣟⣙⣛⣳⣿⡮⢿⣿⣿⣿⣿⣿⣠⣙⣿⣿⣿⠣⣿⣿⣿⣿⣿⡿⠟⢿⣿⣿⣿⣿⠚⠒⢂⣄⣀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣏⠉⢻⣿⣿⡟⠉⠉⠁⠀⣀⣈⣙⣛⣃⣠⣿⣿⡟⢉⡻⠁⠀⠀⠭⠫⠡⠨⢿⢢⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⣧⣶⣴⣶⡄⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠂⠸⠩⠋⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⡄⠈⠻⠿⣥⣾⣿⣿⡄⡀⠀⠙⣛⣛⣀⠘⠛⠛⢻⣿⣿⡀⠀⠘⠛⠋⠀⣛⢛⢛⢛⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠴⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢀⡀⠀⣷⡄⠀⢹⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢀⣾⣿⣿⣿⠁⣀⣀⣀⣉⣉⣉⣀⣘⣀⣈⠋⠉⠀⠀⠀⠀⠈⠀⠁⠀⠈⠀⢿⠙⠙⠐⠻⣶⣶⣶ ⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⡏⠉⠀⠈⠁⡆⣿⣷⡀⠈⠙⡉⠋⠀⠀⢿⣿⣿⡿⣿⣿⡿⠿⠀⠀⣿⣿⣽⠯⣿⡷⠶⠶⠶⠖⠚⠿⢶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠖⠒⠀⠀⠀⠀⢸⣶⡗⠀⠀⠀⠀⠀ ⠀⡭⣉⠉⠩⢩⡍⠉⠉⠟⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠐⠦⠌⠓⠒⠀⠀⠀⠀⢰⣿⡇⠀⠀⢸⣿⣛⣃⣀⣀⣴⣄⣀⡉⠉⠉⠈⠈⠉⢙⣛⡃⠀⠀⠀⠀⠀⠀⣈⠀⠀⡀⠀⠀⠀⠀ ⢠⠶⠶⠶⠾⠆⠛⠀⠀⠈⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠄⠹⠏⠀⣤⣶⣶⣴⣶⣦⡀⠁⠀⡈⠀⠀⠀⠀⠀⡀⠿⣿⡄⠀⢸⡧⣤⣤⣤⣤⣬⣧⣤⣵⣬⣦⣤⣤⡤⣭⣭⣭⣤⣤⣬⣤⡤⠤⣿⣽⣿⣿⣿⡾⣿⠓ ⠀⠒⠒⠒⠂⢸⣦⡄⠀⠀⠀⠀⢀⡀⢀⣸⠀⠀⢀⡀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣶⣶⣿⣅⠀⣿⣧⠀⠸⠃⠉⢩⣭⣭⣭⠉⠉⠉⠩⠍⣭⣭⠉⢉⠉⠉⠉⢩⣭⠉⠁⠀⣿⠁⠀⠀⠘⠒⠊⠉ ⠀⠛⠛⢇⡤⠌⠈⠃⠠⠀⠀⠀⠘⠃⠜⠻⠀⠀⠈⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠐⢀⣀⣀⣠⡀⠀⠀⠀⠀⠀⣄⣀⣀⣀⠀⡀⠀⣄⣠⡀⠀⠀⢻⣦⣤⣤⣤⣤⣤⣤ ⠀⠚⠛⠉⠃⢀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠏⠀⠀⠀⢀⡀⣀⣀⡀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢙⣋⠉⠉⠉⠉⠉⠛ ⠀⠶⡾⠃⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢀⠀⠁⢉⠉⠉⠀⠉⣀⣉⣉⣉⣁⣀⣀⣀⠉⠉⣉⠉⠁⠀⠀⢈⠉⠀⠀⠀⠀⠀⠀ ⠀⠒⠒⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠟⣟⣛⣣⣤⣤⣶⠀⠐⠒⠚⠓⠀⠀⠀⠚⠛⠛⠛⠃⠀⠀⠀⠐⠒⠚⠛⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀ ⠀⣀⣈⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢘⠀⠔⠀⠀⠀⠀⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⣽⣿⣿⣿⡎⠁⠈⠶⠖⠶⠶⠦⠀⠀⠠⠆⠤⠐⠀⠤⠴⠶⠆⠀⠀⠀⠀⣿⡷⠚⠐⠀⠀⠀⠀ ⢈⠉⢉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢀⡄⠐⠆⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠛⢿⣿⣿⣿⡇⠒⠲⠶⠶⠶⠆⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀ ⠀⠉⠩⢁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣄⠀⢸⢶⣖⠳⣿⣞⠄⡐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢿⣿⣿⣿⣇⣚⠛⢀⠀⠈⠀⠀⠀⠀⠀⠟⠿⠀⠀⠀⠀⠀⠈⠉⠉⠘⠃⣹⠛⠛⠈⠘⠀⠀⠀ ⠀⢥⡤⡥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠤⠜⠙⠟⠻⠙⠻⠓⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠐⠛⠻⢿⣷⢿⣛⣿⣿⣿⡿⠿⠿⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⣀⠀⠐⠒⠄⠀⠀⠀⠀⠀⠰ ⠀⠛⠛⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⢿⣿⣿⣿⣿⡿⠿⠿⠿⠿⢿⠿⣿⠿⢿⡇⠘⠛⠃⠀⠈⠋⣒⣾⣰⣪⣿⣿⣿⣿⣧⠀⢤⡀⠀⠀⠀⡄⠀⠀⢀⣀⣀⣀⣿⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀ ⠨⣿⡏⠉⠉⠘⠇⠀⠀⠀⢠⡀⠀⠀⠀⠀⠰⠦⢴⣦⣶⠤⠦⠤⠴⠶⠤⠤⠦⠦⢤⠤⠤⠤⠴⠤⠶⠤⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠻⠿⠧⠀⠀⠀⠃⠀⡻⣿⣿⣿⣿⠧⢰⠦⡶⢢⠴⠽⠤⠶⠬ ⢶⠄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠶⠤⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄ ⠀⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣂⣀⣀⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠈⠉⠉⠉⠉⠉⠉⣵⣴⣶⣴⣆⠐⣰⣦⣤⣤⣶⠀⠀⣰⣴⣦⣤⣶⣦⣤⣀⣀⣶⡒⠀⢀⣀⣠⣤⣶⣦⣀⠀⣀⣀⣀⣀⣀⣀⣴⣶⣶⣶⣦⣗⣂⣦⣦⣦⣤⠠⠄⠀⣠⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣻⣄⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣥⣀⢸⣿⣿⣿⣿⣿⣿⣟⣙⣛⣷⣿⡮⢿⣿⣿⣿⣿⣿⣠⣙⣿⣿⣿⠣⣿⣿⣿⣿⣿⡿⠟⢿⣿⣿⣿⣿⠚⠒⢂⣄⣀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣏⠉⢻⣿⣿⡟⠉⠉⠁⠀⣀⣈⣙⣛⣃⣠⣿⣿⡟⢉⡻⠁⠀⠀⠭⠫⠡⠨⢿⢢⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⣧⣶⣴⣶⡄⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠁⠀⠀⠂⠸⠩⠋⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⡄⠈⠻⠿⣥⣾⣿⣿⡄⡀⠀⠙⣛⣛⣀⠘⠛⠛⢻⣿⣿⡀⠀⠘⠛⠋⠀⣛⢛⢛⢛⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠴⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢀⡀⠀⣷⡄⠀⢹⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢀⣾⣿⣿⣿⠁⣀⣀⣀⣉⣉⣉⣀⣘⣀⣈⠋⠉⠀⠀⠀⠀⠈⠀⠁⠀⠈⠀⢿⠙⠙⠐⠻⣶⣶⣶ ⠀⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⡏⠉⠀⠈⠁⡆⣿⣷⡀⠈⠙⡉⠋⠀⠀⢿⣿⣿⡿⣿⣿⡿⠿⠀⠀⣿⣿⣽⠯⣿⡷⠶⠶⠶⠖⠚⠿⢶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠖⠒⠀⠀⠀⠀⢸⣶⡗⠀⠀⠀⠀⠀ ⠀⡭⣉⠉⠩⢩⡍⠉⠉⠟⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠐⠦⠌⠓⠒⠀⠀⠀⠀⢰⣿⡇⠀⠀⢸⣿⣛⣃⣀⣀⣴⣄⣀⡉⠉⠈⠈⠈⠁⢙⣛⡃⠀⠀⠀⠀⠀⠀⣈⠀⠀⡀⠀⠀⠀⠀ ⢠⠶⠶⠶⠾⠆⠛⠀⠀⠈⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠄⠹⠏⠀⣤⣶⣶⣴⣶⣦⡀⠁⠀⡈⠀⠀⠀⠀⠀⡀⠿⣿⡄⠀⢸⡧⣤⣤⣤⣤⣬⣧⣤⣵⣬⣦⣤⣤⡤⣭⣭⣭⣤⣤⣬⣤⡤⠤⣿⣽⣿⣿⣿⡾⣿⠓ ⠀⠒⠒⠒⠂⢸⣦⡄⠀⠀⠀⠀⢀⡀⢀⣸⠀⠀⢀⡀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣶⣶⣿⣅⠀⣿⣧⠀⠸⠃⠉⢩⣭⣭⣭⠉⠉⠉⠩⠍⣭⣭⠉⢋⠉⠉⠉⢩⣭⠉⠁⠀⣿⠁⠀⠀⠘⠒⠊⠉ ⠀⠛⠛⢇⡤⠌⠈⠃⠠⠀⠀⠀⠘⠃⠜⠻⠀⠀⠈⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠐⢀⣀⣀⣠⡀⠀⠀⠀⠀⠀⣄⣀⣀⣀⠀⡀⠀⣄⣠⡀⠀⠀⢻⣦⣤⣤⣤⣤⣤⣤ ⠀⠚⠛⠉⠃⢀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠏⠀⠀⠀⢀⡀⣀⣀⡀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢙⣋⠩⠋⠉⠉⠉⠛ ⠀⠶⡾⠃⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢀⠀⠁⢉⠋⠉⠀⠉⣀⣉⣉⣉⣁⣀⣀⣀⠉⠉⣉⠉⠁⠀⠀⢈⠉⠀⠀⠀⠀⠀⠀ ⠀⠒⠒⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠟⣟⣛⣣⣤⣤⣶⠀⠐⠒⠚⠓⠀⠀⠀⠚⠛⠛⠛⠃⠀⠀⠀⠐⠒⠚⠛⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀ ⠀⣀⣈⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢘⠀⠔⠀⠀⠀⠀⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⣽⣿⣿⣿⡎⠁⠎⠶⠖⠶⠶⠦⠀⠀⠠⠆⠤⠐⠀⠤⠴⠶⠆⠀⠀⠀⠀⢿⡷⠚⠐⠀⠀⠀⠀ ⢈⠉⢉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢀⡄⠐⠆⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠛⢿⣿⣿⣿⡇⠒⠲⠶⠶⠶⠆⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀ ⠀⠉⠩⢁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣄⠀⢸⢶⣖⠳⣿⣞⠄⡐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢿⣿⣿⣿⣇⣚⠛⢀⠀⠈⠀⠀⠀⠀⠀⠟⠿⠀⠀⠀⠀⠀⠈⠉⠉⠙⠃⣹⠛⠛⠈⠘⠀⠀⠀ ⠀⢥⡤⡥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠤⠜⠙⠟⠻⠙⠻⠓⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠐⠛⠻⢿⣷⢿⣛⣿⣿⣿⡿⠿⠿⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⣀⠀⠐⠒⠄⠀⠀⠀⠀⠀⠰ ⠈⠛⠛⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⢿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⠿⣿⠿⢿⡇⠘⠛⠃⠀⠈⠋⣒⣾⣰⣪⣿⣿⣿⣿⣧⠀⢤⡀⠀⠀⠀⡄⠀⠀⢀⣀⣀⣀⣿⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀ ⠨⣿⡏⠉⠉⠘⠇⠀⠀⠀⢠⡀⠀⠀⠀⠀⠰⠦⢴⣦⣶⠤⠦⠤⠴⠶⠤⠤⠦⠦⢤⠤⠤⠤⠴⠤⠶⠤⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠻⠿⠧⠀⠀⠀⠃⠀⡻⣿⣿⣿⣿⠧⢰⠦⡶⢢⠴⠽⠤⠶⠬ ⢶⠄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠶⠤⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄ ⠀⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣂⣀⣀⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠈⠉⠉⠉⠉⠉⠉⣵⣴⣶⣴⣆⠐⣰⣦⣤⣤⣶⠀⠀⣰⣴⣦⣤⣶⣦⣤⣀⣀⣶⡒⠀⢀⣀⣠⣤⣶⣦⣀⠀⣀⣀⣀⣀⣀⣀⣴⣶⣶⣶⣦⣗⣂⣦⣦⣦⣤⠠⠄⠀⣠⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣻⣄⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣥⣀⢸⣿⣿⣿⣿⣿⣿⣟⣙⣛⣷⣿⡮⢿⣿⣿⣿⣿⣿⣠⣙⣿⣿⣿⠣⣿⣿⣿⣿⣿⡿⠟⢿⣿⣿⣿⣿⠚⠒⢂⣄⣀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣏⠉⢻⣿⣿⡟⠉⠉⠁⠀⣀⣈⣙⣛⣃⣠⣿⣿⡟⢉⡻⠁⠀⠀⠭⠫⠡⠨⢿⢢⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⣧⣶⣴⣶⡄⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠁⠀⠀⠂⠿⠩⠋⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⡄⠈⠻⠿⣥⣾⣿⣿⡄⡀⠀⠙⣛⣛⣀⠘⠛⠛⢻⣿⣿⡀⠀⠘⠛⠋⠀⣛⢛⢛⢛⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠴⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢀⡀⠀⣷⡄⠀⢹⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢀⣾⣿⣿⣿⠁⣀⣀⣀⣉⣉⣉⣀⣘⣀⣈⠋⠉⠀⠀⠀⠀⠈⠀⠁⠀⠈⠀⢿⠙⠙⠐⠻⣶⣶⣶ ⠀⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⡏⠉⠀⠈⠁⡆⣿⣷⡀⠈⠙⡉⠋⠀⠀⢿⣿⣿⡿⣿⣿⡿⠿⠀⠀⣿⣿⣽⠯⣿⡷⠶⠶⠶⠖⠚⠿⢶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠖⠒⠀⠀⠀⠀⢸⣶⡗⠀⠀⠀⠀⠀ ⠀⡭⣉⠉⠩⢩⡍⠉⠉⠟⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠐⠦⠌⠓⠒⠀⠀⠀⠀⢰⣿⡇⠀⠀⢸⣿⣛⣃⣀⣀⣴⣄⣀⡉⠉⠈⠈⠈⠁⢙⣛⡃⠀⠀⠀⠀⠀⠀⣈⠀⠀⡀⠀⠀⠀⠀ ⢠⠶⠶⠶⠾⠆⠛⠀⠀⠈⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠄⠹⠏⠀⣤⣶⣶⣴⣶⣦⡀⠁⠀⡈⠀⠀⠀⠀⠀⡀⠿⣿⡄⠀⢸⡧⣤⣤⣤⣤⣬⣧⣤⣵⣬⣦⣤⣤⡤⣭⣭⣭⣤⣤⣬⣤⡤⠤⣿⣽⣿⣿⣿⡾⣿⠓ ⠀⠒⠒⠒⠂⢸⣦⡄⠀⠀⠀⠀⢀⡀⢀⣸⠀⠀⢀⡀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣶⣶⣿⣅⠀⣿⣧⠀⠸⠃⠉⢩⣭⣭⣭⠉⠉⠉⠩⠍⣭⣭⠉⢋⠉⠉⠋⢩⣭⠉⠁⠀⣿⠁⠀⠀⠘⠒⠊⠉ ⠀⠛⠛⢇⡤⠌⠈⠃⠠⠀⠀⠀⠘⠃⠜⠻⠀⠀⠈⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠐⢀⣀⣀⣠⡀⠀⠀⠀⠀⠀⣄⣀⣀⣀⠀⡀⠀⣄⣠⡀⠀⠀⢻⣦⣤⣤⣤⣤⣤⣤ ⠀⠚⠛⠉⠃⢀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠏⠀⠀⠀⢀⡀⣀⣀⡀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢙⣋⠩⠋⠉⠉⠉⠛ ⠀⠶⡾⠃⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢀⠀⠁⢉⠋⠉⠀⠉⣀⣉⣉⣉⣁⣀⣀⣀⠉⠉⣉⠉⠁⠀⠀⢈⠉⠀⠀⠀⠀⠀⠀ ⠀⠒⠒⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠟⣟⣛⣣⣤⣤⣶⠀⠐⠒⠚⠓⠀⠀⠀⠚⠛⠛⠛⠃⠀⠀⠀⠐⠒⠚⠛⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀ ⠀⣀⣈⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢘⠀⠔⠀⠀⠀⠀⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⣽⣿⣿⣿⡎⠁⠎⠶⠖⠶⠶⠦⠀⠀⠠⠆⠤⠐⠆⠤⠴⠶⠆⠀⠀⠀⠀⢿⡷⠚⠐⠀⠀⠀⠀ ⢈⠉⢉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢀⡄⠐⠆⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠛⢿⣿⣿⣿⡇⠒⠲⠶⠶⠶⠆⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀ ⠀⠉⠩⢁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣄⠀⢸⢶⣖⠳⣿⣞⠄⡐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢿⣿⣿⣿⣇⣚⠛⢀⠀⠈⠀⠀⠀⠀⠈⠛⠿⠀⠀⠀⠀⠀⠈⠉⠉⠙⠃⣹⠛⠛⠈⠘⠀⠀⠀ ⠀⢥⡤⡥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠤⠜⠙⠟⠻⠙⠻⠓⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠐⠛⠻⢿⣷⢿⣛⣿⣿⣿⡿⠿⠿⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⣀⠀⠐⠒⠄⠀⠀⠀⠀⠀⠰ ⠈⠛⠛⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⢿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⠿⣿⠿⢿⡇⠘⠛⠃⠀⠈⠋⣒⣾⣰⣪⣿⣿⣿⣿⣧⠀⢤⡀⠀⠀⠀⡄⠀⠀⢀⣀⣀⣀⣿⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀ ⠨⣿⡏⠉⠉⠘⠇⠀⠀⠀⢠⡀⠀⠀⠀⠀⠰⠦⢴⣦⣶⠤⠦⠤⠴⠶⠤⠤⠦⠦⢤⠤⠤⠤⠴⠤⠶⠤⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠻⠿⠧⠀⠀⠀⠃⠀⡻⣿⣿⣿⣿⠧⢰⠦⡶⢢⠴⠽⠤⠶⠬ ⢶⠄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠶⠤⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄ ⠀⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣂⣀⣀⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠈⠉⠉⠉⠉⠉⠉⣵⣴⣶⣴⣆⠐⣰⣦⣤⣤⣶⠀⠀⣰⣴⣦⣤⣶⣦⣤⣀⣀⣶⡒⠀⢀⣀⣠⣤⣶⣦⣀⠀⣀⣀⣀⣀⣀⣀⣴⣶⣶⣶⣦⣗⣂⣦⣦⣦⣤⠠⠄⠀⣠⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣻⣄⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣥⣀⢸⣿⣿⣿⣿⣿⣿⣟⣙⣛⣷⣿⡮⢿⣿⣿⣿⣿⣿⣠⣙⣿⣿⣿⠣⣿⣿⣿⣿⣿⡿⠟⢿⣿⣿⣿⣿⠚⠒⢂⣄⣀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣏⠉⢻⣿⣿⡟⠉⠉⠁⠀⣀⣈⣙⣛⣃⣠⣿⣿⡟⢉⡻⠁⠀⠀⠭⠫⠡⠨⢿⢢⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⣧⣶⣴⣶⡄⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠁⠀⠀⠂⡿⠩⠋⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⡄⠈⠻⠿⣥⣾⣿⣿⡄⡀⠀⠙⣛⣛⣀⠘⠛⠛⢻⣿⣿⡀⠀⠘⠛⠋⠀⣛⢛⢛⢛⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠴⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢀⡀⠀⣷⡄⠀⢹⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢀⣾⣿⣿⣿⠁⣀⣀⣀⣉⣉⣉⣀⣘⣀⣈⠋⠉⠀⠀⠀⠀⠈⠀⠁⠀⠈⠀⢿⠙⠙⠐⠻⣶⣶⣶ ⠀⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⡏⠉⠀⠈⠁⡆⣿⣷⡀⠈⠙⡉⠋⠀⠀⢿⣿⣿⡿⣿⣿⡿⠿⠀⠀⣿⣿⣽⠯⣿⡷⠶⠶⠶⠖⠚⠿⢶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠖⠒⠀⠀⠀⠀⢸⣶⡗⠀⠀⠀⠀⠀ ⠀⡭⣉⠉⠩⢩⡍⠉⠉⠟⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠐⠦⠌⠓⠒⠀⠀⠀⠀⢰⣿⡇⠀⠀⢸⣿⣛⣃⣀⣀⣴⣄⣀⡉⠉⠈⠈⠈⠁⢙⣛⡃⠀⠀⠀⠀⠀⠀⣈⠀⠀⡀⠀⠀⠀⠀ ⢠⠶⠶⠶⠾⠆⠛⠀⠀⠈⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠄⠹⠏⠀⣤⣶⣶⣴⣶⣦⡀⠁⠀⡈⠀⠀⠀⠀⠀⡀⠿⣿⡄⠀⢸⡧⣤⣤⣤⣤⣬⣧⣤⣵⣬⣦⣤⣤⡤⣭⣭⣭⣤⣤⣬⣤⡤⠤⣿⣽⣿⣿⣿⡾⣿⠓ ⠀⠒⠒⠒⠂⢸⣦⡄⠀⠀⠀⠀⢀⡀⢀⣸⠀⠀⢀⡀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣶⣶⣿⣅⠀⣿⣧⠀⠸⠃⠉⢩⣭⣭⣭⠉⠉⠉⠩⠍⣭⣭⠉⢋⠉⠉⠋⢩⣭⠉⠁⠀⣿⠁⠀⠀⠘⠒⠊⠉ ⠀⠛⠛⢇⡤⠌⠈⠃⠠⠀⠀⠀⠘⠃⠜⠻⠀⠀⠈⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠐⢀⣀⣀⣠⡀⠀⠀⠀⠀⠀⣄⣀⣀⣀⠀⡀⠀⣄⣠⡀⠀⠀⢻⣦⣤⣤⣤⣤⣤⣤ ⠀⠚⠛⠉⠃⢀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠏⠀⠀⠀⢀⡀⣀⣀⡀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢙⣋⠩⠋⠉⠉⠉⠛ ⠀⠶⡾⠃⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢀⠀⠁⢉⠋⠉⠀⠉⣀⣉⣉⣉⣁⣀⣀⣀⠉⠉⣉⠉⠁⠀⠀⢈⠉⠀⠀⠀⠀⠀⠀ ⠀⠒⠒⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠟⣟⣛⣣⣤⣤⣶⠀⠐⠒⠚⠓⠀⠀⠀⠚⠛⠛⠛⠃⠀⠀⠀⠐⠒⠚⠛⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀ ⠀⣀⣈⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢘⠀⠔⠀⠀⠀⠀⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⣽⣿⣿⣿⡎⠁⠎⠶⠖⠶⠶⠦⠀⠀⠠⠆⠤⠐⠆⠤⠴⠶⠆⠀⠀⠀⠀⢿⡷⠚⠐⠀⠀⠀⠀ ⢈⠉⢉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢀⡄⠐⠆⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠛⢿⣿⣿⣿⡇⠒⠲⠶⠶⠶⠆⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀ ⠀⠉⠩⢁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣄⠀⢸⢶⣖⠳⣿⣞⠄⡐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢿⣿⣿⣿⣇⣚⠛⢀⠀⠈⠀⠀⠀⠀⠈⠛⠿⠀⠀⠀⠀⠀⠈⠉⠉⠙⠃⣹⠛⠛⠈⠘⠀⠀⠀ ⠀⢥⡤⡥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠤⠜⠙⠟⠻⠙⠻⠓⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠐⠛⠻⢿⣷⢿⣛⣿⣿⣿⡿⠿⠿⣿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠷⣀⠀⠐⠒⠄⠀⠀⠀⠀⠀⠰ ⠈⠛⠛⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⢿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⠿⣿⠿⢿⡇⠘⠛⠃⠀⠈⠋⣒⣾⣰⣪⣿⣿⣿⣿⣧⠀⢤⡉⠀⠀⠀⡄⠀⠀⢀⣀⣀⣀⣿⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀ ⠨⣿⡏⠉⠉⠘⠇⠀⠀⠀⢠⡀⠀⠀⠀⠀⠰⠦⢴⣦⣶⠤⠦⠤⠴⠶⠤⠤⠦⠦⢤⠤⠤⠤⠴⠤⠶⠤⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠻⠿⠧⠀⠀⠀⠃⠀⡻⣿⣿⣿⣿⠧⢰⠦⡶⢢⠴⠽⠤⠶⠬ ⢶⠄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠶⠤⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄ ⠀⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣂⣀⣀⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠈⠉⠉⠉⠉⠉⠉⣵⣴⣶⣴⣆⠐⣰⣦⣤⣤⣶⠀⠀⣰⣴⣦⣤⣶⣦⣤⣀⣀⣶⡒⠀⢀⣀⣠⣤⣶⣦⣀⠀⣀⣀⣀⣀⣀⣀⣴⣶⣶⣶⣦⣗⣂⣦⣦⣦⣤⠠⠄⠀⣠⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣻⣄⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣥⣀⢸⣿⣿⣿⣿⣿⣿⣟⣙⣛⣷⣿⡮⢿⣿⣿⣿⣿⣿⣠⣙⣿⣿⣿⠣⣿⣿⣿⣿⣿⡿⠟⢿⣿⣿⣿⣿⠚⠒⢂⣄⣀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣏⠉⢻⣿⣿⡟⠉⠉⠁⠀⣀⣈⣙⣛⣃⣠⣿⣿⡟⢉⡻⠁⠀⠀⠭⠫⠡⠨⢿⢢⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⣧⣶⣴⣶⡄⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠁⠀⠀⠂⡿⠩⠋⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⡄⠈⠻⠿⣥⣾⣿⣿⡄⡀⠀⠙⣛⣛⣀⠘⠛⠛⢻⣿⣿⡀⠀⠘⠛⠋⠀⣛⢛⢛⢛⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠴⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢀⡀⠀⣷⡄⠀⢹⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢀⣾⣿⣿⣿⠁⣀⣀⣀⣉⣉⣉⣀⣘⣀⣈⠋⠉⠀⠀⠀⠀⠈⠀⠁⠀⠈⠀⢿⠙⠙⠐⠻⣶⣶⣶ ⠀⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⡏⠉⠀⠈⠁⡆⣿⣷⡀⠈⠙⡉⠋⠀⠀⢿⣿⣿⡿⣿⣿⡿⠿⠀⠀⣿⣿⣽⠯⣿⡷⠶⠶⠶⠖⠚⠿⢶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠖⠒⠀⠀⠀⠀⢸⣶⡗⠀⠀⠀⠀⠀ ⠀⡭⣉⠉⠩⢩⡍⠉⠉⠟⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠐⠦⠌⠓⠒⠀⠀⠀⠀⢰⣿⡇⠀⠀⢸⣿⣛⣃⣀⣀⣴⣄⣀⡉⠉⠈⠈⠈⠁⢙⣛⡃⠀⠀⠀⠀⠀⠀⣈⠀⠀⡀⠀⠀⠀⠀ ⢠⠶⠶⠶⠾⠆⠛⠀⠀⠈⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠄⠹⠏⠀⣤⣶⣶⣴⣶⣦⡀⠁⠀⡈⠀⠀⠀⠀⠀⡀⠿⣿⡄⠀⢸⡧⣤⣤⣤⣤⣬⣧⣤⣵⣬⣦⣤⣤⡤⣭⣭⣭⣤⣤⣬⣤⡤⠤⣿⣽⣿⣿⣿⡾⣿⠓ ⠀⠒⠒⠒⠂⢸⣦⡄⠀⠀⠀⠀⢀⡀⢀⣸⠀⠀⢀⡀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣶⣶⣿⣅⠀⣿⣧⠀⠸⠃⠉⢩⣭⣭⣭⠉⠉⠉⠩⠍⣭⣭⠉⢋⠉⠉⠋⢩⣭⠉⠁⠀⣿⠁⠀⠀⠘⠒⠊⠉ ⠀⠛⠛⢇⡤⠌⠈⠃⠠⠀⠀⠀⠘⠃⠜⠻⠀⠀⠈⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠐⢀⣀⣀⣠⡀⠀⠀⠀⠀⠀⣄⣀⣀⣀⠀⡀⠀⣄⣠⡀⠀⠀⢻⣦⣤⣤⣤⣤⣤⣤ ⠀⠚⠛⠉⠃⢀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠏⠀⠀⠀⢀⡀⣀⣀⡀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢙⣋⠩⠋⠉⠉⠉⠛ ⠀⠶⡾⠃⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢀⠀⠁⢉⠋⠉⠀⠉⣀⣉⣉⣉⣁⣀⣀⣀⠉⠉⣉⠉⠁⠀⠀⢈⠉⠀⠀⠀⠀⠀⠀ ⠀⠒⠒⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠟⣟⣛⣣⣤⣤⣶⠀⠐⠒⠚⠓⠀⠀⠀⠚⠛⠛⠛⠃⠀⠀⠀⠐⠒⠚⠛⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀ ⠀⣀⣈⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢘⠀⠔⠀⠀⠀⠀⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⣽⣿⣿⣿⡎⠁⠎⠶⠖⠶⠶⠦⠀⠀⠠⠆⠤⠐⠆⠤⠴⠶⠆⠀⠀⠀⠀⢿⡷⠚⠐⠀⠀⠀⠀ ⢈⠉⢉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢀⡄⠐⠆⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠛⢿⣿⣿⣿⡇⠒⠲⠶⠶⠶⠆⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀ ⠀⠉⠩⢁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣄⠀⢸⢶⣖⠳⣿⣞⠄⡐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢿⣿⣿⣿⣇⣚⠛⢀⠀⠈⠀⠀⠀⠀⠈⠛⠿⠀⠀⠀⠀⠀⠈⠉⠉⠙⠃⣹⠛⠛⠈⠘⠀⠀⠀ ⠀⢥⡤⡥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠤⠜⠙⠟⠻⠙⠻⠓⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠐⠛⠻⢿⣷⢿⣛⣿⣿⣿⡿⠿⠿⣿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠷⣀⠀⠐⠒⠄⠀⠀⠀⠀⠀⠰ ⠈⠛⠛⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⢿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⠿⣿⠿⢿⡇⠘⠛⠃⠀⠈⠋⣒⣾⣰⣪⣿⣿⣿⣿⣧⠀⢤⡉⠀⠀⠀⡄⠀⠀⢀⣀⣀⣀⣿⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀ ⠨⣿⡏⠉⠉⠘⠇⠀⠀⠀⢠⡀⠀⠀⠀⠀⠰⠦⢴⣦⣶⠤⠦⠤⠴⠶⠤⠤⠦⠦⢤⠤⠤⠤⠴⠤⠶⠤⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠻⠿⠧⠀⠀⠀⠃⠀⡻⣿⣿⣿⣿⠧⢰⠦⡶⢢⠴⠽⠤⠶⠬ ⢶⠄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠶⠤⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄ ⠀⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣂⣀⣀⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠈⠉⠉⠉⠉⠉⠉⣵⣴⣶⣴⣆⠐⣰⣦⣤⣤⣶⠀⠀⣰⣴⣦⣤⣶⣦⣤⣀⣀⣶⡒⠀⢀⣀⣠⣤⣶⣦⣀⠀⣀⣀⣀⣀⣀⣀⣴⣶⣶⣶⣦⣗⣂⣦⣦⣦⣤⠠⠄⠀⣠⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣻⣄⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣥⣀⢸⣿⣿⣿⣿⣿⣿⣟⣙⣛⣷⣿⡮⢿⣿⣿⣿⣿⣿⣠⣙⣿⣿⣿⠣⣿⣿⣿⣿⣿⡿⠟⢿⣿⣿⣿⣿⠚⠒⢂⣄⣀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣏⠉⢻⣿⣿⡟⠉⠉⠁⠀⣀⣈⣙⣛⣃⣠⣿⣿⡟⢉⡻⠁⠀⠀⠭⠫⠡⠨⢿⢢⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⣧⣶⣴⣶⡄⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠁⠀⠀⠂⡿⠩⠋⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⡄⠈⠻⠿⣥⣾⣿⣿⡄⡀⠀⠙⣛⣛⣀⠘⠛⠛⢻⣿⣿⡀⠀⠘⠛⠋⠀⣛⢛⢛⢛⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠴⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢀⡀⠀⣷⡄⠀⢹⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢀⣾⣿⣿⣿⠁⣀⣀⣀⣉⣉⣉⣀⣘⣀⣈⠋⠉⠀⠀⠀⠀⠈⠀⠁⠀⠈⠀⢿⠙⠙⠐⠻⣶⣶⣶ ⠀⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⡏⠉⠀⠈⠁⡆⣿⣷⡀⠈⠙⡉⠋⠀⠀⢿⣿⣿⡿⣿⣿⡿⠿⠀⠀⣿⣿⣽⠯⣿⡷⠶⠶⠶⠖⠚⠿⢶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠖⠒⠀⠀⠀⠀⢸⣶⡗⠀⠀⠀⠀⠀ ⠀⡭⣉⠉⠩⢩⡍⠉⠉⠟⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠐⠦⠌⠓⠒⠀⠀⠀⠀⢰⣿⡇⠀⠀⢸⣿⣛⣃⣀⣀⣴⣄⣀⡉⠉⠈⠈⠈⠁⢙⣛⡃⠀⠀⠀⠀⠀⠀⣈⠀⠀⡀⠀⠀⠀⠀ ⢠⠶⠶⠶⠾⠆⠛⠀⠀⠈⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠄⠹⠏⠀⣤⣶⣶⣴⣶⣦⡀⠁⠀⡈⠀⠀⠀⠀⠀⡀⠿⣿⡄⠀⢸⡧⣤⣤⣤⣤⣬⣧⣤⣵⣬⣦⣤⣤⡤⣭⣭⣭⣤⣤⣬⣤⡤⠤⣿⣽⣿⣿⣿⡾⣿⠓ ⠀⠒⠒⠒⠂⢸⣦⡄⠀⠀⠀⠀⢀⡀⢀⣸⠀⠀⢀⡀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣶⣶⣿⣅⠀⣿⣧⠀⠸⠃⠉⢩⣭⣭⣭⠉⠉⠉⠩⠍⣭⣭⠉⢋⠉⠉⠋⢩⣭⠉⠁⠀⣿⠁⠀⠀⠘⠒⠊⠉ ⠀⠛⠛⢇⡤⠌⠈⠃⠠⠀⠀⠀⠘⠃⠜⠻⠀⠀⠈⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠐⢀⣀⣀⣠⡀⠀⠀⠀⠀⠀⣄⣀⣄⣀⠀⡀⠀⣄⣠⡀⠀⠀⢻⣦⣤⣤⣤⣤⣤⣤ ⠀⠚⠛⠉⠃⢀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠏⠀⠀⠀⢀⡀⣀⣀⡀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢙⣋⠩⠋⠉⠉⠉⠛ ⠀⠶⡾⠃⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢀⠀⠁⢉⠋⠉⠀⠉⣀⣉⣉⣉⣁⣀⣀⣀⠉⠉⣉⠉⠁⠀⠀⢈⠉⠀⠀⠀⠀⠀⠀ ⠀⠒⠒⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠟⣟⣛⣣⣤⣤⣶⠀⠐⠒⠚⣳⡄⠀⡀⠚⠛⠛⠛⠃⠀⠀⠀⠐⠒⠚⠛⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀ ⠀⣀⣈⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢘⠀⠔⠀⠀⠀⠀⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⣽⣿⣿⣿⡎⠁⠎⠶⠖⠶⠶⠦⠀⠀⠠⠆⠤⠐⠆⠤⠴⠶⠆⠀⠀⠀⠀⢿⡷⠚⠐⠀⠀⠀⠀ ⢈⠉⢉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢀⡄⠐⠆⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠛⢿⣿⣿⣿⡇⠒⠲⠶⠶⠶⠆⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀ ⠀⠉⠩⢁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣄⠀⢸⢶⣖⠳⣿⣞⠄⡐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢿⣿⣿⣿⣇⣚⠛⢀⠀⠈⠀⠀⠀⠀⠈⠛⠿⠀⠀⠀⠀⠀⠈⠉⠉⠙⠃⣹⠛⠛⠈⠘⠀⠀⠀ ⠀⢥⡤⡥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠤⠜⠙⠟⠻⠙⠻⠓⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠐⠛⠻⢿⣷⢿⣛⣿⣿⣿⡿⠿⠿⣿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠷⣀⠀⠐⠒⠄⠀⠀⠀⠀⠀⠰ ⠈⠛⠛⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⢿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⠿⣿⠿⢿⡇⠘⠛⠃⠀⠈⠋⣒⣾⣰⣪⣿⣿⣿⣿⣧⠀⢤⡉⠀⠀⠀⡄⠀⠀⢀⣀⣀⣀⣿⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀ ⠨⣿⡏⠉⠉⠘⠇⠀⠀⠀⢠⡀⠀⠀⠀⠀⠰⠦⢴⣦⣶⠤⠦⠤⠴⠶⠤⠤⠦⠦⢤⠤⠤⠤⠴⠤⠶⠤⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠻⠿⠧⠀⠀⠀⠃⠀⡻⣿⣿⣿⣿⠧⢰⠦⡶⢢⠴⠽⠤⠶⠬ ⢶⠄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠶⠤⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄ ⠀⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣂⣀⣀⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠈⠉⠉⠉⠉⠉⠉⣵⣴⣶⣴⣆⠐⣰⣦⣤⣤⣶⠀⠀⣰⣴⣦⣤⣶⣦⣤⣀⣀⣶⡒⠀⢀⣀⣠⣤⣶⣦⣀⠀⣀⣀⣀⣀⣀⣀⣴⣶⣶⣶⣦⣗⣂⣦⣦⣦⣤⠠⠄⠀⣠⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣻⣄⡄⠀⠀⠀⠀⡀⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣥⣀⢸⣿⣿⣿⣿⣿⣿⣟⣙⣛⣷⣿⡮⢿⣿⣿⣿⣿⣿⣠⣙⣿⣿⣿⠣⣿⣿⣿⣿⣿⡿⠟⢿⣿⣿⣿⣿⠚⠒⢂⣄⣀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣏⠉⢻⣿⣿⡟⠉⠉⠁⠀⣀⣈⣙⣛⣃⣠⣿⣿⡟⢉⡻⠁⠀⠀⠭⠫⠡⠨⢿⢢⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⣧⣶⣴⣶⡄⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠁⠀⠀⠂⡿⠩⠋⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⡄⠈⠻⠿⣥⣾⣿⣿⡄⡀⠀⠙⣛⣛⣀⠘⠛⠛⢻⣿⣿⡀⠀⠘⠛⠋⠀⣛⢛⢛⢛⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠴⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢀⡀⠀⣷⡄⠀⢹⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢀⣾⣿⣿⣿⠁⣀⣀⣀⣉⣉⣉⣀⣘⣀⣈⠋⠉⠀⠀⠀⠀⠈⠀⠁⠀⠈⠀⢿⠙⠙⠐⠻⣶⣶⣶ ⠀⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⡏⠉⠀⠈⠁⡆⣿⣷⡀⠈⠙⡉⠋⠀⠀⢿⣿⣿⡿⣿⣿⡿⠿⠀⠀⣿⣿⣽⠯⣿⡷⠶⠶⠶⠖⠚⠿⢶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠖⠒⠀⠀⠀⠀⢸⣶⡗⠀⠀⠀⠀⠀ ⠀⡭⣉⠉⠩⢩⡍⠉⠉⠟⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠐⠦⠌⠓⠒⠀⠀⠀⠀⢰⣿⡇⠀⠀⢸⣿⣛⣃⣀⣀⣴⣄⣀⡉⠉⠈⠈⠈⠁⢙⣛⡃⠀⠀⠀⠀⠀⠀⣈⠀⠀⡀⠀⠀⠀⠀ ⢠⠶⠶⠶⠾⠆⠛⠀⠀⠈⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠄⠹⠏⠀⣤⣶⣶⣴⣶⣦⡀⠁⠀⡈⠀⠀⠀⠀⠀⡀⠿⣿⡄⠀⢸⡧⣤⣤⣤⣤⣬⣧⣤⣵⣬⣦⣤⣤⡤⣭⣭⣭⣤⣤⣬⣤⡤⠤⣿⣽⣿⣿⣿⡾⣿⠓ ⠀⠒⠒⠒⠂⢸⣦⡄⠀⠀⠀⠀⢀⡀⢀⣸⠀⠀⢀⡀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣶⣶⣿⣅⠀⣿⣧⠀⠸⠃⠉⢩⣭⣭⣭⠉⠉⠉⠩⠍⣭⣭⠉⢋⠉⠉⠋⢩⣭⠉⠁⠀⣿⠁⠀⠀⠘⠒⠊⠉ ⠀⠛⠛⢇⡤⠌⠈⠃⠠⠀⠀⠀⠘⠃⠜⠻⠀⠀⠈⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠐⢀⣀⣀⣠⡀⠀⠀⠀⠀⠀⣄⣀⣄⣀⠀⡀⠀⣄⣠⡀⠀⠀⢻⣦⣤⣤⣤⣤⣤⣤ ⠀⠚⠛⠉⠃⢀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠏⠀⠀⠀⢀⡀⣀⣀⡀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢙⣋⠩⠋⠉⠉⠉⠛ ⠀⠶⡾⠃⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢀⠀⠁⢉⠋⠉⠀⠉⣀⣉⣉⣉⣁⣀⣀⣀⠉⠉⣉⠉⠁⠀⠀⢈⠉⠀⠀⠀⠀⠀⠀ ⠀⠒⠒⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠟⣟⣛⣣⣤⣤⣶⠀⢰⣶⠚⣳⡄⠀⡀⠚⠛⠛⠛⠃⠀⠀⠀⠐⠒⠚⠛⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀ ⠀⣀⣈⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢘⠀⠔⠀⠀⠀⠀⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⣽⣿⣿⣿⡎⠁⠎⠶⠖⠶⠶⠦⠀⠀⠠⠆⠤⠐⠆⠤⠴⠶⠆⠀⠀⠀⠀⢿⡷⠚⠐⠀⠀⠀⠀ ⢈⠉⢉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢀⡄⠐⠆⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠛⢿⣿⣿⣿⡇⠒⠲⠶⠶⠶⠆⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀ ⠀⠉⠩⢁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣄⠀⢸⢶⣖⠳⣿⣞⠄⡐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢿⣿⣿⣿⣇⣚⠛⢀⠀⠈⠀⠀⠀⠀⠈⠛⠿⠀⠀⠀⠀⠀⠈⠉⠉⠙⠃⣹⠛⠛⠈⠘⠀⠀⠀ ⠀⢥⡤⡥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠤⠜⠙⠟⠻⠙⠻⠓⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠐⠛⠻⢿⣷⢿⣛⣿⣿⣿⡿⠿⠿⣿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠷⣀⠀⠐⠒⠄⠀⠀⠀⠀⠀⠰ ⠈⠛⠛⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⢿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⠿⣿⠿⢿⡇⠘⠛⠃⠀⠈⠋⣒⣾⣰⣪⣿⣿⣿⣿⣧⠀⢤⡉⠀⠀⠀⡄⠀⠀⢀⣀⣀⣀⣿⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀ ⠨⣿⡏⠉⠉⠘⠇⠀⠀⠀⢠⡀⠀⠀⠀⠀⠰⠦⢴⣦⣶⠤⠦⠤⠴⠶⠤⠤⠦⠦⢤⠤⠤⠤⠴⠤⠶⠤⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠻⠿⠧⠀⠀⠀⠃⠀⡻⣿⣿⣿⣿⠧⢰⠦⡶⢢⠴⠽⠤⠶⠬ ⢶⠄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠶⠤⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄ ⠀⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣂⣀⣀⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠈⠉⠉⠉⠉⠉⠉⣵⣴⣶⣴⣆⠐⣰⣦⣤⣤⣶⠀⠀⣰⣴⣦⣤⣶⣦⣤⣀⣀⣶⡒⠀⢀⣀⣠⣤⣶⣦⣀⠀⣀⣀⣀⣀⣀⣀⣴⣶⣶⣶⣦⣗⣂⣦⣦⣦⣤⠠⠄⠀⣠⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣻⣄⡄⠀⠀⠀⠀⡀⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣥⣀⢸⣿⣿⣿⣿⣿⣿⣟⣙⣛⣷⣿⡮⢿⣿⣿⣿⣿⣿⣠⣙⣿⣿⣿⠣⣿⣿⣿⣿⣿⡿⠟⢿⣿⣿⣿⣿⠚⠒⢂⣄⣀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣏⠉⢻⣿⣿⡟⠉⠉⠁⠀⣀⣈⣙⣛⣃⣠⣿⣿⡟⢉⡻⠁⠀⠀⠭⠫⠡⠨⢿⢢⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⣧⣶⣴⣶⡄⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠁⠀⠀⠂⡿⠩⠋⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⡄⠈⠻⠿⣥⣾⣿⣿⡄⡀⠀⠙⣛⣛⣀⠘⠛⠛⢻⣿⣿⡀⠀⠘⠛⠋⠀⣛⢛⢛⢛⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠴⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢀⡀⠀⣷⡄⠀⢹⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢀⣾⣿⣿⣿⠁⣀⣀⣀⣉⣉⣉⣀⣘⣀⣈⠋⠉⠀⠀⠀⠀⠈⠀⠁⠀⠈⠀⢿⠙⠙⠐⠻⣶⣶⣶ ⠀⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⡏⠉⠀⠈⠁⡆⣿⣷⡀⠈⠙⡉⠋⠀⠀⢿⣿⣿⡿⣿⣿⡿⠿⠀⠀⣿⣿⣽⠯⣿⡷⠶⠶⠶⠖⠚⠿⢶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠖⠒⠀⠀⠀⠀⢸⣶⡗⠀⠀⠀⠀⠀ ⠀⡭⣉⠉⠩⢩⡍⠉⠉⠟⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠐⠦⠌⠓⠒⠀⠀⠀⠀⢰⣿⡇⠀⠀⢸⣿⣛⣃⣀⣀⣴⣄⣀⡉⠉⠈⠈⠈⠁⢙⣛⡃⠀⠀⠀⠀⠀⠀⣈⠀⠀⡀⠀⠀⠀⠀ ⢠⠶⠶⠶⠾⠆⠛⠀⠀⠈⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠄⠹⠏⠀⣤⣶⣶⣴⣶⣦⡀⠁⠀⡈⠀⠀⠀⠀⠀⡀⠿⣿⡄⠀⢸⡧⣤⣤⣤⣤⣬⣧⣤⣵⣬⣦⣤⣤⡤⣭⣭⣭⣤⣤⣬⣤⡤⠤⣿⣽⣿⣿⣿⡾⣿⠓ ⠀⠒⠒⠒⠂⢸⣦⡄⠀⠀⠀⠀⢀⡀⢀⣸⠀⠀⢀⡀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣶⣶⣿⣅⠀⣿⣧⠀⠸⠃⠉⢩⣭⣭⣭⠉⠉⠉⠩⠍⣭⣭⠉⢋⠉⠉⠋⢩⣭⠉⠁⠀⣿⠁⠀⠀⠘⠒⠊⠉ ⠀⠛⠛⢇⡤⠌⠈⠃⠠⠀⠀⠀⠘⠃⠜⠻⠀⠀⠈⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠐⢀⣀⣀⣠⡀⠀⠀⠀⠀⠀⣄⣀⣄⣀⠀⡀⠀⣄⣠⡀⠀⠀⢻⣦⣤⣤⣤⣤⣤⣤ ⠀⠚⠛⠉⠃⢀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠏⠀⠀⠀⢀⡀⣀⣀⡀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢙⣋⠩⠋⠉⠉⠉⠛ ⠀⠶⡾⠃⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢀⠀⠁⢉⠋⠉⠀⠉⣀⣉⣉⣉⣁⣀⣀⣀⠉⠉⣉⠉⠁⠀⠀⢈⠉⠀⠀⠀⠀⠀⠀ ⠀⠒⠒⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠟⣟⣛⣣⣤⣤⣶⠀⢰⣶⠚⣳⡄⠀⡀⠚⠛⠛⠛⠃⠀⠀⠀⠐⠒⠚⠛⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀ ⠀⣀⣈⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢘⠀⠔⠀⠀⠀⠀⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⣽⣿⣿⣿⡎⠁⠎⠶⠖⠶⠶⠦⠀⠀⠠⠆⠤⠐⠆⠤⠴⠶⠆⠀⠀⠀⠀⢿⡷⠚⠐⠀⠀⠀⠀ ⢈⠉⢉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢀⡄⠐⠆⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠛⢿⣿⣿⣿⡇⠒⠲⠶⠶⠶⠆⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀ ⠀⠉⠩⢁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣄⠀⢸⢶⣖⠳⣿⣞⠄⡐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢿⣿⣿⣿⣇⣚⠛⢀⠀⠈⠀⠀⠀⠀⠈⠛⠿⠀⠀⠀⠀⠀⠈⠉⠉⠙⠃⣹⠛⠛⠈⠘⠀⠀⠀ ⠀⢥⡤⡥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠤⠜⠙⠟⠻⠙⠻⠓⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠶⠛⠻⢿⣷⢿⣛⣿⣿⣿⡿⠿⠿⣿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠷⣄⠀⠐⠒⠄⠀⠀⠀⠀⠀⠰ ⠈⠛⠛⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⢿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⠿⣿⠿⢿⡇⠘⠛⠃⠀⠈⠋⣒⣾⣰⣪⣿⣿⣿⣿⣧⠀⢤⡉⠀⠀⠀⡄⠀⠀⢀⣀⣀⣀⣿⣀⣀⡀⠀⠀⠀⠀⠀⠀⣐ ⠨⣿⡏⠉⠉⠘⠇⠀⠀⠀⢠⡀⠀⠀⠀⠀⠰⠦⢴⣦⣶⠤⠦⠤⠴⠶⠤⠤⠦⠦⢤⠤⠤⠤⠴⠤⠶⠤⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠻⠿⠧⠀⠀⠀⠃⠀⡻⣿⣿⣿⣿⠧⢰⠦⡶⢢⠴⠽⠤⠶⠬ ⢶⠄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠶⠤⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄ ⠀⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣂⣀⣀⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠈⠉⠉⠉⠉⠉⠉⣵⣴⣶⣴⣆⠐⣰⣦⣤⣤⣶⠀⠀⣰⣴⣦⣤⣶⣦⣤⣀⣀⣶⡒⠀⢀⣀⣠⣤⣶⣦⣀⠀⣀⣀⣀⣀⣀⣀⣴⣶⣶⣶⣦⣗⣂⣦⣦⣦⣤⠠⠄⠀⣠⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣻⣄⡄⠀⠀⠀⠀⡀⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣥⣀⢸⣿⣿⣿⣿⣿⣿⣟⣙⣛⣷⣿⡮⢿⣿⣿⣿⣿⣿⣠⣙⣿⣿⣿⠣⣿⣿⣿⣿⣿⡿⠟⢿⣿⣿⣿⣿⠚⠒⢂⣄⣀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣏⠉⢻⣿⣿⡟⠉⠉⠁⠀⣀⣈⣙⣛⣃⣠⣿⣿⡟⢉⡻⠁⠀⠀⠭⠫⠡⠨⢿⢢⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⣧⣶⣴⣶⡄⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠁⠀⠀⠂⡿⠩⠋⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⡄⠈⠻⠿⣥⣾⣿⣿⡄⡀⠀⠙⣛⣛⣀⠘⠛⠛⢻⣿⣿⡀⠀⠘⠛⠋⠀⣛⢛⢛⢛⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠴⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢀⡀⠀⣷⡄⠀⢹⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢀⣾⣿⣿⣿⠁⣀⣀⣀⣉⣉⣉⣀⣘⣀⣈⠋⠉⠀⠀⠀⠀⠈⠀⠁⠀⠈⠀⢿⠙⠙⠐⠻⣶⣶⣶ ⠀⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⡏⠉⠀⠈⠁⡆⣿⣷⡀⠈⠙⡉⠋⠀⠀⢿⣿⣿⡿⣿⣿⡿⠿⠀⠀⣿⣿⣽⠯⣿⡷⠶⠶⠶⠖⠚⠿⢶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠖⠒⠀⠀⠀⠀⢸⣶⡗⠀⠀⠀⠀⠀ ⠀⡭⣉⠉⠩⢩⡍⠉⠉⠟⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠐⠦⠌⠓⠒⠀⠀⠀⠀⢰⣿⡇⠀⠀⢸⣿⣛⣃⣀⣀⣴⣄⣀⡉⠉⠈⠈⠈⠁⢙⣛⡃⠀⠀⠀⠀⠀⠀⣈⠀⠀⡀⠀⠀⠀⠀ ⢠⠶⠶⠶⠾⠆⠛⠀⠀⠈⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠄⠹⠏⠀⣤⣶⣶⣴⣶⣦⡀⠁⠀⡈⠀⠀⠀⠀⠀⡀⠿⣿⡄⠀⢸⡧⣤⣤⣤⣤⣬⣧⣤⣵⣬⣦⣤⣤⡤⣭⣭⣭⣤⣤⣬⣤⡤⠤⣿⣽⣿⣿⣿⡾⣿⠓ ⠀⠒⠒⠒⠂⢸⣦⡄⠀⠀⠀⠀⢀⡀⢀⣸⠀⠀⢀⡀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣶⣶⣿⣅⠀⣿⣧⠀⠸⠃⠉⢩⣭⣭⣭⠉⠉⠉⠩⠍⣭⣭⠉⢋⠉⠉⠋⢩⣭⠉⠁⠀⣿⠁⠀⠀⠘⠒⠊⠉ ⠀⠛⠛⢇⡤⠌⠈⠃⠠⠀⠀⠀⠘⠃⠜⠻⠀⠀⠈⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠐⢀⣀⣀⣠⡀⠀⠀⠀⠀⠀⣄⣀⣄⣀⠀⡀⠀⣄⣠⡀⠀⠀⢻⣦⣤⣤⣤⣤⣤⣤ ⠀⠚⠛⠉⠃⢀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠏⠀⠀⠀⢀⡀⣀⣀⡀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢙⣋⠩⠋⠉⠉⠉⠛ ⠀⠶⡾⠃⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢀⠀⠁⢉⠋⠉⠀⠉⣀⣉⣉⣉⣁⣀⣀⣀⠉⠉⣉⠉⠁⠀⠀⢈⠉⠀⠀⠀⠀⠀⠀ ⠀⠒⠒⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠟⣟⣛⣣⣤⣤⣶⠀⢰⣶⠚⣳⡄⠀⡀⠚⠛⠛⠛⠃⠀⠀⠀⠐⠒⠚⠛⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀ ⠀⣀⣈⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢘⠀⠔⠀⠀⠀⠀⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⣽⣿⣿⣿⡎⠁⠎⠶⠖⠶⠶⠦⠀⠀⠠⠆⠤⠐⠆⠤⠴⠶⠆⠀⠀⠀⠀⢿⡷⠚⠐⠀⠀⠀⠀ ⢈⠉⢉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢀⡄⠐⠆⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠛⢿⣿⣿⣿⡇⠒⠲⠶⠶⠶⠆⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀ ⠀⠉⠩⢁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣄⠀⢸⢶⣖⠳⣿⣞⠄⡐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢿⣿⣿⣿⣇⣚⠛⢀⠀⠈⠀⠀⠀⠀⠈⠛⠿⠀⠀⠀⠀⠀⠈⠉⠉⠙⠃⣹⠛⠛⠈⠘⠀⠀⠀ ⠀⢥⡤⡥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠤⠜⠙⠟⠻⠙⠻⠓⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣶⠛⠻⢿⣷⢿⣛⣿⣿⣿⡿⠿⠿⣿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠷⣄⠀⠐⠒⠄⠀⠀⠀⠀⠀⠰ ⠈⠛⠛⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⢿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⠿⣿⠿⢿⡇⠘⠛⠃⠀⠉⠋⣒⣾⣰⣪⣿⣿⣿⣿⣧⠀⢤⡉⠀⠀⠀⡄⠀⠀⢀⣀⣀⣀⣿⣀⣀⡀⠀⠀⠀⠀⠀⠀⣐ ⠨⣿⡏⠉⠉⠘⠇⠀⠀⠀⢠⡀⠀⠀⠀⠀⠰⠦⢴⣦⣶⠤⠦⠤⠴⠶⠤⠤⠦⠦⢤⠤⠤⠤⠴⠤⠶⠤⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠻⠿⠧⠀⠀⠀⠃⠀⡻⣿⣿⣿⣿⠧⢰⠦⡶⢢⠴⠽⠤⠶⠬ ⢶⠄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠦⠤⠤⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄ ⠀⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣂⣀⣀⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠈⠉⠉⠉⠉⠉⠉⣵⣴⣶⣴⣆⠀⣰⣦⣤⣤⣖⠀⠀⢰⣰⣦⣤⣴⣦⣤⣀⣀⣶⡒⠀⢀⣀⣠⣤⣴⣦⣀⠀⣀⣀⣀⣀⣀⣀⣴⣶⣶⣶⣦⣒⣂⣦⣦⣦⣤⠠⠄⠀⣠⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣻⣄⡄⠀⠀⠀⢀⡀⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣅⢀⡸⢿⣿⣿⣿⣿⣿⣏⣙⣙⣳⣿⡮⢿⣿⣿⣿⣿⣿⣠⣈⣿⣿⣿⠡⣿⣿⣿⣿⣿⡿⠏⢿⣿⣿⣿⣿⠚⠒⢂⣀⣀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣶⣾⣏⠉⠻⣿⣿⡟⠉⠉⠁⠀⢀⢈⣉⣋⣃⣠⣿⣿⡏⠉⡩⠁⠀⠀⠭⠩⠡⠨⢿⢢⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠧⣶⣴⣶⡄⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠁⠀⠀⠀⡿⠁⠋⣿⣿⣿⣿⡟⠉⣿⣿⣿⣿⣿⣿⣿⡄⠀⠹⠿⣥⣾⣿⣿⠄⠀⠀⠙⣛⣛⣀⠘⠛⠛⢻⣿⣿⡀⠀⠘⠛⠋⠀⣛⢛⠛⢛⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠴⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⡀⠀⣷⡄⠀⢹⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢀⣾⣿⣿⣿⠀⣀⣀⣀⣉⣉⣉⣀⣈⣀⣈⠉⠉⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⢿⠙⠙⠐⠻⣶⣶⣶ ⠀⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⡏⠉⠀⠀⠁⡆⣿⣷⡀⠈⠙⠉⠉⠀⠀⠿⣿⣻⡿⣿⣿⡿⠿⠀⠀⣿⡿⢽⠯⠿⡷⠶⠶⠶⠖⠚⠿⢶⣶⣶⢶⣶⣶⣶⣶⣶⠶⠖⠒⠀⠀⠀⠀⢸⣶⡗⠀⠀⠀⠀⠰ ⠀⡭⣉⠉⠩⢩⡍⠉⠉⠛⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢿⣿⠁⠀⠀⠀⠀⠀⠀⠐⠦⠈⠓⠂⠀⠀⠀⠀⢰⣿⡇⠀⠀⢸⣿⣛⣃⣀⣀⣴⣄⣀⡉⠉⠈⠈⠈⠁⢙⣛⡃⠀⠀⠀⠀⠀⠀⣈⠀⠀⡀⠀⠀⠀⠀ ⢠⠶⠶⠶⠾⠆⠛⠀⠀⠈⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠄⠹⠋⠀⣠⣶⣴⣤⣶⣦⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠿⣿⡄⠀⢸⡧⣤⣤⣤⣤⣬⣧⣤⣵⣬⣦⣤⣤⡤⣭⣭⣭⣤⣤⣬⣤⡤⠤⣿⣽⣿⣿⣿⡾⣿⠓ ⠀⠒⠒⠒⠂⢸⣦⡄⠀⠀⠀⠀⢀⡀⢀⣸⠀⠀⢀⡀⠀⠀⠀⣶⣷⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣶⣶⣶⣶⣿⣄⠀⣿⣧⠀⠸⠃⠉⢩⣭⣭⣭⠉⠉⠉⠉⠍⣭⣭⠉⢋⠉⠉⠋⢩⣭⠉⠁⠀⣿⠀⠀⠀⠘⠒⠊⠉ ⠀⠛⠛⠇⡤⠌⠈⠃⠠⠀⠀⠀⠘⠃⠜⠻⠀⠀⠈⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⠀⠀⠐⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣄⣀⠀⠀⠀⣀⣠⡀⠀⠀⢻⣦⣤⣤⣤⣤⣤⣤ ⠀⠚⠛⠉⠁⢀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠏⠀⠀⠀⢀⡀⣀⣀⡀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢙⣋⠩⠋⠉⠉⠉⠛ ⠀⠶⡾⠂⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢀⠀⠁⢉⠉⠉⠀⠉⣀⣉⣉⣉⣁⣀⣀⣀⠀⠉⣉⠉⠁⠀⠀⢈⠉⠀⠀⠀⠀⠀⠀ ⠀⠒⠒⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠟⣟⣛⣣⣤⣤⣶⠀⢰⡶⠒⣳⡄⠀⡀⠚⠛⠛⠛⠃⠀⠀⠀⠐⠒⠚⠛⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀ ⠀⣀⣈⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⣽⣿⣿⣿⡎⠁⠆⠶⠖⠶⠶⠆⠀⠀⠠⠄⠤⠐⠆⠤⠴⠶⠆⠀⠀⠀⠀⢿⡷⠚⠐⠀⠀⠀⠀ ⢈⠉⢉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡄⠐⠆⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠛⢿⣿⣿⣿⡇⠒⠲⠶⠖⠶⠆⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀ ⠀⠉⠩⢁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣄⠀⢸⢶⣖⠲⣿⡞⠄⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢻⣿⣿⣿⣇⡚⠛⠀⠀⠈⠀⠀⠀⠀⠈⠛⠿⠀⠀⠀⠀⠀⠈⠉⠉⠘⠃⣸⠛⠛⠈⠘⠀⠀⠀ ⠀⢥⡤⡥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠤⠜⠙⠟⠋⠙⠻⠓⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣶⠛⠻⢿⣷⢿⣛⣿⣿⣿⣿⠿⠿⣿⠿⠾⠿⠿⠿⠿⠿⠿⠷⠶⣀⠀⠐⠒⠄⠀⠀⠀⠀⠀⠰ ⠀⠛⠛⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⠿⠿⠿⡿⢿⡿⠿⠿⠿⠿⠿⠿⡿⠿⢿⡇⠘⠛⠀⠀⠉⠉⣒⣾⣰⣪⣿⣿⣿⣿⣿⠀⢤⠉⠀⠀⠀⡄⠀⠀⢀⣀⣀⣀⣿⣀⣀⡀⠀⠀⠀⠀⠀⠀⡐ ⠈⣿⡏⠉⠉⠘⠇⠀⠀⠀⢠⡀⠀⠀⠀⠀⠰⠦⢴⣦⣶⠤⠦⠤⠴⠶⠤⠤⠦⠦⢤⠤⠤⠤⠴⠤⠶⠤⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠛⠿⠧⠀⠀⠀⠃⠈⡻⣿⣿⣿⣿⠧⢰⠦⡷⢢⠾⠽⠤⠶⠬ ⢶⠄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠦⠤⠤⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄ ⠀⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣂⣀⣀⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠈⠉⠉⠉⠉⠉⠉⣵⣴⣶⣴⣆⠀⣰⣦⠤⣤⣖⠀⠀⢰⣰⣦⣤⣴⣦⣤⣀⣀⣶⡒⠀⢀⣀⣠⣤⣴⣦⣀⠀⣀⣀⣀⣀⣀⣀⣴⣶⣶⣶⣦⣒⣂⣦⣦⣦⣤⠠⠄⠀⣠⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣻⣄⡄⠀⠀⠀⢀⡀⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣅⢀⡸⢿⣿⣿⣿⣿⣿⣏⣙⣙⣳⣿⡮⢿⣿⣿⣿⣿⣿⣠⣈⣿⣿⣿⠡⣿⣿⣿⣿⣿⡿⠏⢿⣿⣿⣿⣿⠚⠒⢂⣀⣀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣶⣾⣏⠉⠻⣿⣿⡟⠉⠉⠁⠀⢀⢈⣉⣋⣃⣠⣿⣿⡏⠉⡩⠁⠀⠀⠭⠩⠡⠨⢿⢢⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠧⣶⣴⣶⡄⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠁⠀⠀⠀⡿⠁⠋⣿⣿⣿⣿⡟⠁⣾⣿⣿⣿⣿⣿⣿⡄⠀⠹⠿⣥⣾⣿⣿⠄⠀⠀⠙⣛⣛⣀⠘⠛⠛⢻⣿⣿⡀⠀⠘⠛⠋⠀⣛⢛⠛⢛⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠴⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⡀⠀⣷⡄⠀⢹⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢀⣾⣿⣿⣿⠀⣀⣀⣀⣉⣉⣉⣀⣈⣀⣈⠉⠉⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⢿⠙⠙⠐⠻⣶⣶⣶ ⠀⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⡏⠉⠀⠀⠁⡆⣿⣷⡀⠈⠙⠉⠉⠀⠀⠿⣿⣻⡿⣿⣿⡿⠿⠀⠀⣿⡿⢽⠯⠿⡷⠶⠶⠶⠖⠚⠿⢶⣶⣶⢶⣶⣶⣶⣶⣶⠶⠖⠒⠀⠀⠀⠀⢸⣶⡗⠀⠀⠀⠀⠰ ⠀⡭⣉⠉⠩⢩⡍⠉⠉⠛⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢿⣿⠁⠀⠀⠀⠀⠀⠀⠐⠦⠈⠓⠂⠀⠀⠀⠀⢰⣿⡇⠀⠀⢸⣿⣛⣃⣀⣀⣴⣄⣀⡉⠉⠈⠈⠈⠁⢙⣛⡃⠀⠀⠀⠀⠀⠀⣈⠀⠀⡀⠀⠀⠀⠀ ⢠⠶⠶⠶⠾⠆⠛⠀⠀⠈⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠄⠹⠋⠀⣠⣶⣴⣤⣶⣦⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠿⣿⡄⠀⢸⡧⣤⣤⣤⣤⣬⣧⣤⣵⣬⣦⣤⣤⡤⣭⣭⣭⣤⣤⣬⣤⡤⠤⣿⣽⣿⣿⣿⡾⣿⠓ ⠀⠒⠒⠒⠂⢸⣦⡄⠀⠀⠀⠀⢀⡀⢀⣸⠀⠀⢀⡀⠀⠀⠀⣶⣷⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣶⣶⣶⣶⣿⣄⠀⣿⣧⠀⠸⠃⠉⢩⣭⣭⣭⠉⠉⠉⠉⠍⣭⣭⠉⢋⠉⠉⠋⢩⣭⠉⠁⠀⣿⠀⠀⠀⠘⠒⠊⠉ ⠀⠛⠛⠇⡤⠌⠈⠃⠠⠀⠀⠀⠘⠃⠜⠻⠀⠀⠈⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⠀⠀⠐⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣄⣀⠀⠀⠀⣀⣠⡀⠀⠀⢻⣦⣤⣤⣤⣤⣤⣤ ⠀⠚⠛⠉⠁⢀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠏⠀⠀⠀⢀⡀⣀⣀⡀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢙⣋⠩⠋⠉⠙⠉⠛ ⠀⠶⡾⠂⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢀⠀⠁⢉⠉⠉⠀⠉⣀⣉⣉⣉⣁⣀⣀⣀⠀⠉⣉⠉⠁⠀⠀⢈⠉⠀⠀⠀⠀⠀⠀ ⠀⠒⠒⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠟⣟⣛⣣⣤⣤⣶⠀⢰⡶⠒⣳⡄⠀⡀⠚⠛⠛⠛⠃⠀⠀⠀⠐⠒⠚⠛⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀ ⠀⣀⣈⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡀⠀⠈⠉⣽⣿⣿⣿⡎⠁⠆⠶⠖⠶⠶⠆⠀⠀⠠⠄⠤⠐⠆⠤⠴⠶⠆⠀⠀⠀⠀⢿⡷⠚⠐⠀⠀⠀⠀ ⢈⠉⢉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡄⠐⠆⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠛⢿⣿⣿⣿⡇⠒⠲⠶⠖⠶⠆⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀ ⠀⠉⠩⢁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣄⠀⢸⢶⣖⠲⣿⡞⠄⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢻⣿⣿⣿⣇⡚⠛⠀⠀⠈⠀⠀⠀⠀⠈⠛⠿⠀⠀⠀⠀⠀⠈⠉⠉⠘⠃⣸⠛⠛⠈⠘⠀⠀⠀ ⠀⢥⡤⡥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠤⠜⠙⠟⠋⠙⠻⠓⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣶⠛⠻⢿⣷⢿⣛⣿⣿⣿⣿⠿⠿⣿⠿⠾⠿⠿⠿⠿⠿⠿⠷⠶⣀⠀⠐⠒⠄⠀⠀⠀⠀⠀⠰ ⠀⠛⠛⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⠿⠿⠿⡿⢿⡿⠿⠿⠿⠿⠿⠿⡿⠿⢿⡇⠘⠛⠀⠀⠉⠉⣒⣾⣰⣪⣿⣿⣿⣿⣿⠀⢤⠉⠀⠀⠀⡄⠀⠀⢀⣀⣀⣀⣿⣀⣀⡀⠀⠀⠀⠀⠀⠀⡐ ⠈⣿⡏⠉⠉⠘⠇⠀⠀⠀⢠⡀⠀⠀⠀⠀⠰⠦⢴⣦⣶⠤⠦⠤⠴⠶⠤⠤⠦⠦⢤⠤⠤⠤⠴⠤⠶⠤⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠛⠿⠧⠀⠀⠀⠃⠈⡻⣿⣿⣿⣿⠧⢰⠦⡷⢢⠾⠽⠤⠶⠬ ⢶⠄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠦⠤⠤⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄ ⠀⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣂⣀⣀⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠈⠉⠉⠉⠉⠉⠉⣵⣴⣶⣴⣆⠀⣰⣦⠤⣤⣖⠀⠀⢰⣰⣦⣤⣴⣦⣤⣀⣀⣶⡒⠀⢀⣀⣠⣤⣴⣦⣀⠀⣀⣀⣀⣀⣀⣀⣴⣶⣶⣶⣦⣒⣂⣦⣦⣦⣤⠠⠄⠀⣠⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣻⣄⡄⠀⠀⠀⢀⡀⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣅⢀⡸⢿⣿⣿⣿⣿⣿⣏⣙⣙⣳⣿⡮⢿⣿⣿⣿⣿⣿⣠⣈⣿⣿⣿⠡⣿⣿⣿⣿⣿⡿⠏⢿⣿⣿⣿⣿⠚⠒⢂⣀⣀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣶⣾⣏⠉⠻⣿⣿⡟⠉⠉⠛⠀⢀⢈⣉⣋⣃⣠⣿⣿⡏⠉⡩⠁⠀⠀⠩⠩⠡⠨⢿⢢⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠧⣶⣴⣶⡄⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠁⠀⠀⠀⡿⠁⠋⣿⣿⣿⣿⡟⠁⣾⣿⣿⣿⣿⣿⣿⡄⠀⠹⠿⣥⣾⣿⣿⠄⠀⠀⠙⣛⣛⣀⠘⠛⠛⢻⣿⣿⡀⠀⠘⠛⠋⠀⣛⢛⠛⢛⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠴⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⡀⠀⣷⡄⠀⢹⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢀⣾⣿⣿⣿⠀⣀⣀⣀⣉⣉⣉⣀⣈⣀⣈⠉⠉⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⢿⠙⠙⠐⠺⣶⣶⣶ ⠀⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⡏⠉⠀⠀⠁⡆⣿⣷⡀⠈⠙⠉⠉⠀⠀⠿⣿⣻⡿⣿⣿⡿⠿⠀⠀⣿⡿⢽⠯⠿⡷⠶⠶⠶⠖⠚⠿⢶⣶⣶⢶⣶⣶⣶⣶⣶⠶⠖⠒⠀⠀⠀⠀⢸⣶⡗⠀⠀⠀⠀⠰ ⠀⡭⣉⠉⠩⢩⡍⠉⠉⠛⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢿⣿⠁⠀⠀⠀⠀⠀⠀⠐⠦⠈⠓⠂⠀⠀⠀⠀⢰⣿⡇⠀⠀⢸⣿⣛⣃⣀⣀⣴⣄⣀⡉⠉⠈⠈⠈⠁⢙⣛⡃⠀⠀⠀⠀⠀⠀⣈⠀⠀⡀⠀⠀⠀⠀ ⢠⠶⠶⠶⠾⠆⠛⠀⠀⠈⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠄⠹⠋⠀⣠⣶⣴⣤⣶⣦⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠿⣿⡄⠀⢸⡧⣤⣤⣤⣤⣬⣧⣤⣵⣬⣦⣤⣤⡤⣭⣭⣭⣤⣤⣬⣤⡤⠤⣿⣽⣿⣿⣿⡾⣿⠓ ⠀⠒⠒⠒⠂⢸⣦⡄⠀⠀⠀⠀⢀⡀⢀⣸⠀⠀⢀⡀⠀⠀⠀⣶⣷⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣶⣶⣶⣶⣿⣄⠀⣿⣧⠀⠸⠃⠉⢩⣭⣭⣭⠉⠉⠉⠉⠍⣭⣭⠉⢋⠉⠉⠋⢩⣭⠉⠁⠀⣿⠀⠀⠀⠘⠒⠊⠉ ⠀⠛⠛⠇⡤⠌⠈⠃⠠⠀⠀⠀⠘⠃⠜⠻⠀⠀⠈⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⠀⠀⠐⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣄⣀⠀⠀⠀⣀⣠⡀⠀⠀⢻⣦⣤⣤⣤⣤⣤⣤ ⠀⠚⠛⠉⠁⢀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠏⠀⠀⠀⢀⡀⣀⣀⡀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢙⣋⠩⠋⠉⠙⠉⠛ ⠀⠶⡾⠂⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠰⢀⠀⠁⢉⠉⠉⠀⠉⣀⣉⣉⣉⣁⣀⣀⣀⠀⠉⣉⠉⠁⠀⠀⢈⠉⠀⠀⠀⠀⠀⠀ ⠀⠒⠒⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠟⣟⣛⣣⣤⣤⣶⠀⢰⡶⠒⣳⡄⠀⡀⠚⠛⠛⠛⠃⠀⠀⠀⠐⠒⠚⠛⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀ ⠀⣀⣈⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡀⠀⠈⠉⣽⣿⣿⣿⡎⠁⠆⠶⠖⠶⠶⠆⠀⠀⠠⠄⠤⠐⠆⠤⠴⠶⠆⠀⠀⠀⠀⢿⡷⠚⠐⠀⠀⠀⠀ ⢈⠉⢉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡄⠐⠆⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠛⢿⣿⣿⣿⡇⠒⠲⠶⠖⠶⠆⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀ ⠀⠉⠩⢁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣄⠀⢸⢶⣖⠲⣿⡞⠄⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠘⠁⠀⠀⢻⣿⣿⣿⣇⡚⠛⠀⠀⠈⠀⠀⠀⠀⠈⠛⠿⠀⠀⠀⠀⠀⠈⠉⠉⠘⠃⣸⠛⠛⠈⠘⠀⠀⠀ ⠀⢥⡤⡥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠤⠜⠙⠟⠋⠙⠻⠓⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣶⠛⠻⢿⣷⢿⣛⣿⣿⣿⣿⠿⠿⣿⠿⠾⠿⠿⠿⠿⠿⠿⠷⠶⣀⠀⠐⠒⠄⠀⠀⠀⠀⠀⠰ ⠀⠛⠛⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⠿⠿⠿⡿⢿⡿⠿⠿⠿⠿⠿⠿⡿⠿⢿⡇⠘⠛⠀⠀⠉⠉⣒⣾⣰⣪⣿⣿⣿⣿⣿⠀⢤⠉⠀⠀⠀⡄⠀⠀⢀⣀⣀⣀⣿⣀⣀⡀⠀⠀⠀⠀⠀⠀⡐ ⠈⣿⡏⠉⠉⠘⠇⠀⠀⠀⢠⡀⠀⠀⠀⠀⠰⠦⢴⣦⣶⠤⠦⠤⠴⠶⠤⠤⠦⠦⢤⠤⠤⠤⠴⠤⠶⠤⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠛⠿⠧⠀⠀⠀⠃⠈⡻⣿⣿⣿⣿⠧⢰⠦⡷⢢⠾⠽⠤⠶⠬ ⢶⠄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠦⠤⠤⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄ ⠀⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣂⣀⣀⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠈⠉⠉⠉⠉⠉⠉⣵⣴⣶⣴⣆⠀⣰⣦⠤⣄⣖⠀⠀⢰⣰⣦⣤⣴⣦⣤⣀⣀⣶⡒⠀⢀⣀⣠⣤⣴⣦⣀⠀⣀⣀⣀⣀⣀⣀⣴⣶⣶⣶⣆⣒⣀⣦⣦⣦⣤⠠⠄⠀⣠⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣻⣄⡄⠀⠀⠀⢀⡀⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣅⢀⡸⢿⣿⣿⣿⣿⣿⣏⣙⣙⣳⣿⡮⢿⣿⣿⣿⣿⣿⣠⣈⣿⣿⣿⠡⣿⣿⣿⣿⣿⡿⠏⢿⣿⣿⣿⣿⠚⠒⢂⣄⣀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣶⣾⣏⠉⠻⣿⣿⡟⠉⠉⠛⠀⢀⢈⣉⣉⣃⣠⣿⣿⡏⠉⡩⠁⠀⠀⠩⠩⠡⠨⢿⢢⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠧⣶⣴⣶⡄⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠁⠀⠀⠀⡿⠁⠋⣿⣿⣿⣿⡟⠁⣾⣿⣿⣿⣿⣿⣿⡄⠀⠹⠿⣥⣾⣿⣿⠄⠀⠀⠙⣛⣛⣀⠘⠛⠛⢻⣿⣿⡀⠀⠘⠛⠋⠀⣛⢛⠛⢛⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠴⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⡀⠀⣷⡄⠀⢹⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢀⣾⣿⣿⣿⠀⣀⣀⣀⣉⣉⣉⣀⣈⣀⣈⠉⠉⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⢿⠙⠙⠐⠺⣶⣶⣶ ⠀⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⡏⠉⠀⠀⠁⡆⣿⣷⡀⠈⠙⠉⠉⠀⠀⠿⣿⣻⡿⣿⣿⡿⠿⠀⠀⣿⡿⢽⠯⠿⡷⠶⠶⠶⠖⠚⠿⢶⣶⣶⢶⣶⣶⣶⣶⣶⠶⠖⠒⠀⠀⠀⠀⢸⣶⡗⠀⠀⠀⠀⠰ ⠀⡭⣉⠉⠩⢩⡍⠉⠉⠛⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢿⡿⠁⠀⠀⠀⠀⠀⠀⠐⠤⠈⠒⠂⠀⠀⠀⠀⢰⣿⡇⠀⠀⢸⣿⣛⣃⣀⣀⣴⣄⣀⡉⠉⠈⠈⠈⠁⢙⣛⡃⠀⠀⠀⠀⠀⠀⣈⠀⠀⡀⠀⠀⠀⠀ ⢠⠶⠶⠶⠾⠆⠛⠀⠀⠈⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠄⠹⠋⠀⣠⣶⣴⣤⣶⣦⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠿⣿⡄⠀⢸⡧⣤⣤⣤⣤⣬⣧⣤⣵⣬⣦⣤⣤⡤⣭⣭⣭⣤⣤⣬⣤⡤⠤⣿⣽⣿⣿⣿⡾⣿⠓ ⠀⠒⠒⠒⠂⢸⣦⡄⠀⠀⠀⠀⢀⡀⢀⣠⠀⠀⢀⡀⠀⠀⠀⣶⣷⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣶⣶⣶⣶⣿⣄⠀⣿⣧⠀⠸⠃⠉⢩⣭⣭⣭⠉⠉⠉⠉⠍⣭⣭⠉⢋⠉⠉⠋⢩⣭⠉⠁⠀⣿⠀⠀⠀⠘⠒⠊⠉ ⠀⠛⠛⠇⡤⠌⠈⠃⠠⠀⠀⠀⠘⠃⠜⠻⠀⠀⠈⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⠀⠀⠐⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣄⣀⠀⠀⠀⣀⣠⡀⠀⠀⢻⣦⣤⣤⣤⣤⣤⣤ ⠀⠚⠛⠉⠁⢀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠏⠀⠀⠀⢀⡀⣀⣀⡀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢙⣋⠩⠋⠉⠙⠉⠛ ⠀⠶⡾⠂⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠰⢀⠀⠁⢉⠉⠉⠀⠉⣀⣉⣉⣉⣁⣀⣀⣀⠀⠉⣉⠉⠁⠀⠀⢈⠉⠀⠀⠀⠀⠀⠀ ⠀⠒⠒⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠟⣟⣛⣣⣤⣤⣶⠀⢰⡶⠒⣳⡄⠀⡀⠚⠛⠛⠛⠃⠀⠀⠀⠐⠒⠚⠛⠀⠀⠀⣠⠃⠀⠠⠀⠀⠀⠀ ⠀⣀⣈⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡀⠀⠈⠉⣽⣿⣿⣿⡎⠁⠆⠶⠖⠶⠶⠆⠀⠀⠠⠄⠤⠐⠆⠤⠴⠶⠆⠀⠀⠀⠀⢿⡷⠚⠐⠀⠀⠀⠀ ⢈⠉⢉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡄⠐⠆⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠛⢿⣿⣿⣿⡇⠒⠲⠶⠖⠶⠆⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀ ⠀⠉⠩⢁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣄⠀⢸⢶⣖⠲⣿⡞⠄⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠘⠁⠀⠀⢻⣿⣿⣿⣇⡚⠛⠀⠀⠈⠀⠀⠀⠀⠈⠛⠿⠀⠀⠀⠀⠀⠈⠉⠉⠘⠃⣸⠛⠛⠈⠘⠀⠀⠀ ⠀⢥⡤⡥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠤⠜⠙⠟⠋⠙⠻⠓⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣶⠛⠻⢿⣷⢿⣛⣿⣿⣿⣿⠿⠿⣿⠿⠾⠿⠿⠿⠿⠿⠿⠷⠶⣀⠀⠐⠒⠄⠀⠀⠀⠀⠀⠰ ⠀⠛⠛⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⠿⠿⠿⡿⢿⡿⠿⠿⠿⠿⠿⠿⡿⠿⣿⡇⠘⠛⠀⠀⠉⠉⣒⣾⣰⣪⣿⣿⣿⣿⣿⠀⢤⠉⠀⠀⠀⡄⠀⠀⢀⣀⣀⣀⣿⣀⣀⡀⠀⠀⠀⠀⠀⠀⡐ ⠈⣿⡏⠉⠉⠘⠇⠀⠀⠀⢠⡀⠀⠀⠀⠀⠰⠦⢴⣦⣶⠤⠦⠤⠴⠶⠤⠤⠦⠦⢤⠤⠤⠤⠴⠤⠶⠽⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠛⠿⠧⠀⠀⠀⠃⠈⡻⣿⣿⣿⣿⠧⢰⠦⡷⢢⠾⠽⠤⠶⠬ ⢶⠄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠦⠤⠤⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄ ⠀⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣂⣀⣀⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠈⠉⠉⠉⠉⠉⠉⣵⣴⣶⣴⣆⠀⣰⣦⠤⣄⣖⠀⠀⢰⣰⣦⣤⣴⣦⣤⣀⣀⣶⡒⠀⢀⣀⣠⣤⣴⣦⣀⠀⣀⣀⣀⣀⣀⣀⣴⣶⣶⣶⣆⣒⣀⣦⣦⣦⣤⠠⠄⠀⣠⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣻⣄⡄⠀⠀⠀⢀⡀⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣅⢀⡸⢿⣿⣿⣿⣿⣿⣏⣙⣙⣳⣿⡮⢿⣿⣿⣿⣿⣿⣠⣈⣿⣿⣿⠡⣿⣿⣿⣿⣿⡿⠏⢿⣿⣿⣿⣿⠚⠒⢂⣄⣀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣶⣾⣏⠉⠻⣿⣿⡟⠉⠉⠛⠀⢀⢈⣉⣉⣃⣠⣿⣿⡏⠉⡩⠁⠀⠀⠩⠩⠡⠨⢿⢢⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠧⣶⣴⣶⡄⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠁⠀⠀⠀⡿⠁⠋⣿⣿⣿⣿⡟⠁⣾⣿⣿⣿⣿⣿⣿⡄⠀⠹⠿⣥⣾⣿⣿⠄⠀⠀⠙⣛⣛⣀⠘⠛⠛⢻⣿⣿⡀⠀⠘⠛⠋⠀⣛⢛⠛⢛⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠴⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⡀⠀⣷⡄⠀⢹⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢀⣾⣿⣿⣿⠀⣀⣀⣀⣉⣉⣉⣀⣈⣀⣈⠉⠉⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⢿⠙⠙⠐⠺⣶⣶⣶ ⠀⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⡏⠉⠀⠀⠁⡆⣿⣷⡀⠈⠙⠉⠉⠀⠀⠿⣿⣻⡿⣿⣿⡿⠿⠀⠀⣿⡿⢽⠯⠿⡷⠶⠶⠶⠖⠚⠿⢶⣶⣶⢶⣶⣶⣶⣶⣶⠴⠖⠒⠀⠀⠀⠀⢸⣶⡗⠀⠀⠀⠀⠰ ⠀⡭⣉⠉⠩⢩⡍⠉⠉⠛⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢿⡿⠁⠀⠀⠀⠀⠀⠀⠐⠤⠈⠒⠂⠀⠀⠀⠀⢰⣿⡇⠀⠀⢸⣿⣛⣃⣀⣀⣴⣄⣀⡉⠉⠈⠈⠈⠁⢙⣛⡃⠀⠀⠀⠀⠀⠀⣈⠀⠀⡀⠀⠀⠀⠀ ⢠⠶⠶⠶⠾⠆⠛⠀⠀⠈⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠄⠹⠋⠀⣠⣶⣴⣤⣶⣦⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠿⣿⡄⠀⢸⡧⣤⣤⣤⣤⣬⣧⣤⣵⣬⣦⣤⣤⡤⣭⣭⣭⣤⣤⣬⣤⡤⠤⣿⣽⣿⣿⣿⡾⣿⠓ ⠀⠒⠒⠒⠂⢸⣦⡄⠀⠀⠀⠀⢀⡀⢀⣠⠀⠀⢀⡀⠀⠀⠀⣶⣷⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣶⣶⣶⣶⣿⣄⠀⣿⣧⠀⠸⠃⠉⢩⣭⣭⣭⠉⠉⠉⠉⠍⣭⣭⠉⢋⠉⠉⠋⢩⣭⠉⠁⠀⣿⠀⠀⠀⠘⠒⠊⠉ ⠀⠛⠛⠇⡤⠌⠈⠃⠠⠀⠀⠀⠘⠃⠜⠻⠀⠀⠈⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⠀⠀⠐⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣄⣀⠀⠀⠀⣀⣠⡀⠀⠀⢻⣦⣤⣤⣤⣤⣤⣤ ⠀⠚⠛⠉⠁⢀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠏⠀⠀⠀⢀⡀⣀⣀⡀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢙⣋⠩⠋⠉⠙⠉⠛ ⠀⠶⡾⠂⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢰⣀⠀⠁⢉⠉⠉⠀⠉⣀⣉⣉⣉⣁⣀⣀⣀⠀⠉⣉⠉⠁⠀⠀⢈⠉⠀⠀⠀⠀⠀⠀ ⠀⠒⠒⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠟⣟⣛⣣⣤⣤⣶⠁⢰⡶⠒⣳⡄⠀⡀⠚⠛⠛⠛⠃⠀⠀⠀⠐⠒⠚⠛⠀⠀⠀⣠⠃⠀⠠⠀⠀⠀⠀ ⠀⣀⣈⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡀⠀⠈⠉⣽⣿⣿⣿⡎⠁⠆⠶⠖⠶⠶⠆⠀⠀⠠⠄⠤⠐⠆⠤⠴⠶⠆⠀⠀⠀⠀⢿⡷⠚⠐⠀⠀⠀⠀ ⢈⠉⢉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡄⠐⠆⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠛⢿⣿⣿⣿⡇⠒⠲⠶⠖⠶⠆⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀ ⠀⠉⠩⢁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣄⠀⢸⢶⣖⠲⣿⡞⠄⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠘⠁⠀⠀⢻⣿⣿⣿⣇⡚⠛⠀⠀⠈⠀⠀⠀⠀⠈⠛⠿⠀⠀⠀⠀⠀⠈⠉⠉⠘⠃⣸⠛⠛⠈⠘⠀⠀⠀ ⠀⢥⡤⡥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠤⠜⠙⠟⠋⠙⠻⠓⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣶⠛⠻⢿⣷⢿⣛⣿⣿⣿⣿⠿⠿⣿⠿⠾⠿⠿⠿⠿⠿⠿⠷⠶⣀⠀⠐⠒⠄⠀⠀⠀⠀⠀⠰ ⠀⠛⠛⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⠿⠿⠿⡿⢿⡿⠿⠿⠿⠿⠿⠿⡿⠿⣿⡇⠘⠛⠀⠀⠉⠉⣒⣾⣰⣪⣿⣿⣿⣿⣿⠀⢤⠉⠀⠀⠀⡄⠀⠀⢀⣀⣀⣀⣿⣀⣀⡀⠀⠀⠀⠀⠀⠀⡐ ⠈⣿⡏⠉⠉⠘⠇⠀⠀⠀⢠⡀⠀⠀⠀⠀⠰⠦⢴⣦⣶⠤⠦⠤⠴⠶⠤⠤⠦⠦⢤⠤⠤⠤⠴⠤⠶⠽⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠛⠿⠧⠀⠀⠀⠃⠈⡻⣿⣿⣿⣿⠧⢰⠦⡷⢢⠾⠽⠤⠶⠬ ⢶⠄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠦⠤⠤⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄ ⠀⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣂⣀⣀⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠈⠉⠉⠉⠉⠉⠉⣵⣴⣶⣴⣆⠀⣰⣦⠤⣄⣖⠀⠀⢰⣰⣦⣤⣴⣦⣤⣀⣀⣶⡒⠀⢀⣀⣠⣤⣴⣦⣀⠀⣀⣀⣀⣀⣀⣀⣴⣶⣶⣶⣆⣒⣀⣦⣦⣦⣤⠠⠄⠀⣠⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣻⣄⡄⠀⠀⠀⢀⡀⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣅⢀⡸⢿⣿⣿⣿⣿⣿⣏⣙⣙⣳⣿⡮⢿⣿⣿⣿⣿⣿⣠⣈⣿⣿⣿⠡⣿⣿⣿⣿⣿⡿⠏⢿⣿⣿⣿⣿⠚⠒⢂⣄⣀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣶⣾⣏⠉⠻⣿⣿⡟⠉⠉⠛⠀⢀⢈⣉⣉⣃⣠⣿⣿⡏⠉⡩⠁⠀⠀⠩⠩⠡⠨⢿⢢⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠧⣶⣴⣶⡄⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠁⠀⠀⠀⡿⠁⠋⣿⣿⣿⣿⡟⠁⣾⣿⣿⣿⣿⣿⣿⡄⠀⠹⠿⣥⣾⣿⣿⠄⠀⠀⠙⣛⣛⣀⠘⠛⠛⢻⣿⣿⡀⠀⠘⠛⠋⠀⣛⢛⠛⢛⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠴⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⡀⠀⣷⡄⠀⢹⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢀⣾⣿⣿⣿⠀⣀⣀⣀⣉⣉⣉⣀⣈⣀⣈⠉⠉⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⢿⠙⠙⠐⠺⣶⣶⣶ ⠀⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⡏⠉⠀⠀⠁⡆⣿⣷⡀⠈⠙⠉⠉⠀⠀⠿⣿⣻⡿⣿⣿⡿⠿⠀⠀⣿⡿⢽⠯⠿⡷⠶⠶⠶⠖⠚⠿⢶⣶⣶⢶⣶⣶⣶⣶⣶⠴⠖⠒⠀⠀⠀⠀⢸⣶⡗⠀⠀⠀⠀⠰ ⠀⡭⣉⠉⠩⢩⡍⠉⠉⠛⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢿⡿⠁⠀⠀⠀⠀⠀⠀⠐⠤⠈⠒⠂⠀⠀⠀⠀⢰⣿⡇⠀⠀⢸⣿⣛⣃⣀⣀⣴⣄⣀⡉⠉⠈⠈⠈⠁⢙⣛⡃⠀⠀⠀⠀⠀⠀⣈⠀⠀⡀⠀⠀⠀⠀ ⢠⠶⠶⠶⠾⠆⠛⠀⠀⠈⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠄⠹⠋⠀⣠⣶⣴⣤⣶⣦⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠿⣿⡄⠀⢸⡧⣤⣤⣤⣤⣬⣧⣤⣵⣬⣦⣤⣤⡤⣭⣭⣭⣤⣤⣬⣤⡤⠤⣿⣽⣿⣿⣿⡾⣿⠓ ⠀⠒⠒⠒⠂⢸⣦⡄⠀⠀⠀⠀⢀⡀⢀⣠⠀⠀⢀⡀⠀⠀⠀⣶⣷⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣶⣶⣶⣶⣿⣄⠀⣿⣧⠀⠸⠃⠉⢩⣭⣭⣭⠉⠉⠉⠉⠍⣭⣭⠉⢋⠉⠉⠋⢩⣭⠉⠁⠀⣿⠀⠀⠀⠘⠒⠊⠉ ⠀⠛⠛⠇⡤⠌⠈⠃⠠⠀⠀⠀⠘⠃⠜⠻⠀⠀⠈⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⠀⠀⠐⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣄⣀⠀⠀⠀⣀⣠⡀⠀⠀⢻⣦⣤⣤⣤⣤⣤⣤ ⠀⠚⠛⠉⠁⢀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠏⠀⠀⠀⢀⡀⣀⣀⡀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢙⣋⠩⠋⠉⠙⠉⠛ ⠀⠶⡾⠂⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢰⣀⠀⠁⢉⠉⠉⠀⠉⣀⣉⣉⣉⣁⣀⣀⣀⠀⠉⣉⠉⠁⠀⠀⢈⠉⠀⠀⠀⠀⠀⠀ ⠀⠒⠒⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠟⣟⣛⣣⣤⣤⣶⠁⢰⡶⠒⣳⡄⠀⡀⠚⠛⠛⠛⠃⠀⠀⠀⠐⠒⠚⠛⠀⠀⠀⣠⠃⠀⠠⠀⠀⠀⠀ ⠀⣀⣈⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡀⠀⠈⠉⣽⣿⣿⣿⡎⠁⠆⠶⠖⠶⠶⠆⠀⠀⠠⠄⠤⠐⠆⠤⠴⠶⠆⠀⠀⠀⠀⢿⡷⠚⠐⠀⠀⠀⠀ ⢈⠉⢉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡄⠐⠆⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠛⢿⣿⣿⣿⡇⠒⠲⠶⠖⠶⠆⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀ ⠀⠉⠩⢁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣄⠀⢸⢶⣖⠲⣿⡞⠄⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠘⠁⠀⠀⢻⣿⣿⣿⣇⡚⠛⠀⠀⠈⠀⠀⠀⠀⠈⠛⠿⠀⠀⠀⠀⠀⠈⠉⠉⠘⠃⣸⠛⠛⠈⠘⠀⠀⠀ ⠀⢥⡤⡥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠤⠜⠙⠟⠋⠙⠻⠓⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣶⠛⠻⢿⣷⢿⣛⣿⣿⣿⣿⠿⠿⣿⠿⠾⠿⠿⠿⠿⠿⠿⠷⠶⣀⠀⠐⠒⠄⠀⠀⠀⠀⠀⠰ ⠀⠛⠛⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⠿⠿⠿⡿⢿⡿⠿⠿⠿⠿⠿⠿⡿⠿⣿⡇⠘⠛⠀⠀⠉⠉⣒⣾⣰⣪⣿⣿⣿⣿⣿⠀⢤⠉⠀⠀⠀⡄⠀⠀⢀⣀⣀⣀⣿⣀⣀⡀⠀⠀⠀⠀⠀⠀⡐ ⠈⣿⡏⠉⠉⠘⠇⠀⠀⠀⢠⡀⠀⠀⠀⠀⠰⠦⢴⣦⣶⠤⠦⠤⠴⠶⠤⠤⠦⠦⢤⠤⠤⠤⠴⠤⠶⠽⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠛⠿⠧⠀⠀⠀⠃⠈⡻⣿⣿⣿⣿⠧⢰⠦⡷⢢⠾⠽⠤⠶⠬ ⢶⠄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠦⠤⠤⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄ ⠀⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣂⣀⣀⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠈⠉⠉⠉⠉⠉⠉⣵⣴⣶⣴⣆⠀⣰⣦⠤⣄⣖⠀⠀⢰⣰⣦⣤⣴⣦⣤⣀⣀⣶⡒⠀⢀⣀⣠⣤⣴⣦⣀⠀⣀⣀⣀⣀⣀⣀⣴⣶⣶⣶⣆⣒⣀⣦⣦⣦⣤⠠⠄⠀⣠⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣻⣄⡄⠀⠀⠀⢀⡀⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣅⢀⡸⢿⣿⣿⣿⣿⣿⣏⣙⣙⣳⣿⡮⢿⣿⣿⣿⣿⣿⣠⣈⣿⣿⣿⠡⣿⣿⣿⣿⣿⡿⠏⢿⣿⣿⣿⣿⠚⠒⢂⣄⣀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣶⣾⣏⠉⠻⣿⣿⡟⠉⠉⠛⠀⢀⢈⣉⣉⣃⣠⣿⣿⡏⠉⡩⠁⠀⠀⠩⠩⠡⠨⢿⢢⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠧⣶⣴⣶⡄⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠁⠀⠀⠀⡿⠁⠋⣿⣿⣿⣿⡟⠁⣾⣿⣿⣿⣿⣿⣿⡄⠀⠹⠿⣥⣾⣿⣿⠄⠀⠀⠙⣛⣛⣀⠘⠛⠛⢻⣿⣿⡀⠀⠘⠛⠋⠀⣛⢛⠛⢛⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠴⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⡀⠀⣷⡄⠀⢹⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢀⣾⣿⣿⣿⠀⣀⣀⣀⣉⣉⣉⣀⣈⣀⣈⠉⠉⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⢿⠙⠙⠐⠺⣶⣶⣶ ⠀⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⡏⠉⠀⠀⠁⡆⣿⣷⡀⠈⠙⠉⠉⠀⠀⠿⣿⣻⡿⣿⣿⡿⠿⠀⠀⣿⡿⢽⠯⠿⡷⠶⠶⠶⠖⠚⠿⢶⣶⣶⢶⣶⣶⣶⣶⣶⠴⠖⠒⠀⠀⠀⠀⢸⣶⡗⠀⠀⠀⠀⠰ ⠀⡭⣉⠉⠩⢩⡍⠉⠉⠛⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢿⡿⠁⠀⠀⠀⠀⠀⠀⠐⠤⠈⠒⠂⠀⠀⠀⠀⢰⣿⡇⠀⠀⢸⣿⣛⣃⣀⣀⣴⣄⣀⡉⠉⠈⠈⠈⠁⢙⣛⡃⠀⠀⠀⠀⠀⠀⣈⠀⠀⡀⠀⠀⠀⠀ ⢠⠶⠶⠶⠾⠆⠛⠀⠀⠈⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠄⠹⠋⠀⣠⣶⣴⣤⣶⣦⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠿⣿⡄⠀⢸⡧⣤⣤⣤⣤⣬⣧⣤⣵⣬⣦⣤⣤⡤⣭⣭⣭⣤⣤⣬⣤⡤⠤⣿⣽⣿⣿⣿⡾⣿⠓ ⠀⠒⠒⠒⠂⢸⣦⡄⠀⠀⠀⠀⢀⡀⢀⣠⠀⠀⢀⡀⠀⠀⠀⣶⣷⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣶⣶⣶⣶⣿⣄⠀⣿⣧⠀⠸⠃⠉⢩⣭⣭⣭⠉⠉⠉⠉⠍⣭⣭⠉⢋⠉⠉⠋⢩⣭⠉⠁⠀⣿⠀⠀⠀⠘⠒⠊⠉ ⠀⠛⠛⠇⡤⠌⠈⠃⠠⠀⠀⠀⠘⠃⠜⠻⠀⠀⠈⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⠀⠀⠐⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣄⣀⠀⠀⠀⣀⣠⡀⠀⠀⢻⣦⣤⣤⣤⣤⣤⣤ ⠀⠚⠛⠉⠁⢀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠏⠀⠀⠀⢀⡀⣀⣀⡀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢙⣋⠩⠋⠉⠙⠉⠛ ⠀⠶⡾⠂⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢰⣀⠀⠁⢉⠉⠉⠀⠉⣀⣉⣉⣉⣁⣀⣀⣀⠀⠉⣉⠉⠁⠀⠀⢈⠉⠀⠀⠀⠀⠀⠀ ⠀⠒⠒⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠟⣟⣛⣣⣤⣤⣶⠁⢰⡶⠒⣳⡄⠀⡀⠚⠛⠛⠛⠃⠀⠀⠀⠐⠒⠚⠛⠀⠀⠀⣠⠃⠀⠠⠀⠀⠀⠀ ⠀⣀⣈⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡀⠀⠈⠉⣽⣿⣿⣿⡎⠁⠆⠶⠖⠶⠶⠆⠀⠀⠠⠄⠤⠐⠆⠤⠴⠶⠆⠀⠀⠀⠀⢿⡷⠚⠐⠀⠀⠀⠀ ⢈⠉⢉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡄⠐⠆⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠛⢿⣿⣿⣿⡇⠒⠲⠶⠖⠶⠆⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀ ⠀⠉⠩⢁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣄⠀⢸⢶⣖⠲⣿⡞⠄⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠘⠁⠀⠀⢻⣿⣿⣿⣇⡚⠛⠀⠀⠈⠀⠀⠀⠀⠈⠛⠿⠀⠀⠀⠀⠀⠈⠉⠉⠘⠃⣸⠛⠛⠈⠘⠀⠀⠀ ⠀⢥⡤⡥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠤⠜⠙⠟⠋⠙⠻⠓⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣶⠛⠻⢿⣷⢿⣛⣿⣿⣿⣿⠿⠿⣿⠿⠾⠿⠿⠿⠿⠿⠿⠷⠶⣀⠀⠐⠒⠄⠀⠀⠀⠀⠀⠰ ⠀⠛⠛⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⠿⠿⠿⡿⢿⡿⠿⠿⠿⠿⠿⠿⡿⠿⣿⡇⠘⠛⠀⠀⠉⠉⣒⣾⣰⣪⣿⣿⣿⣿⣿⠀⢤⠉⠀⠀⠀⡄⠀⠀⢀⣀⣀⣀⣿⣀⣀⡀⠀⠀⠀⠀⠀⠀⡐ ⠈⣿⡏⠉⠉⠘⠇⠀⠀⠀⢠⡀⠀⠀⠀⠀⠰⠦⢴⣦⣶⠤⠦⠤⠴⠶⠤⠤⠦⠦⢤⠤⠤⠤⠴⠤⠶⠽⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠛⠿⠧⠀⠀⠀⠃⠈⡻⣿⣿⣿⣿⠧⢰⠦⡷⢢⠾⠽⠤⠶⠬ ⢶⠄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠦⠤⠤⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄ ⠀⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣂⣀⣀⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠈⠉⠉⠉⠉⠉⠉⣵⣴⣶⣴⣆⠀⣰⣦⠤⣄⣖⠀⠀⢰⣰⣦⣤⣴⣦⣤⣀⣀⣶⡒⠀⢀⣀⣠⣤⣴⣦⣀⠀⣀⣀⣀⣀⣀⣀⣴⣶⣶⣶⣆⣒⣀⣦⣦⣦⣤⠠⠄⠀⣠⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣻⣄⡄⠀⠀⠀⢀⡀⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣅⢀⡸⢿⣿⣿⣿⣿⣿⣏⣙⣙⣳⣿⡮⢿⣿⣿⣿⣿⣿⣠⣈⣿⣿⣿⠡⣿⣿⣿⣿⣿⡿⠏⢿⣿⣿⣿⣿⠚⠒⢂⣄⣀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣶⣾⣏⠉⠻⣿⣿⡟⠉⠉⠛⠀⢀⢈⣉⣉⣃⣠⣿⣿⡏⠉⡩⠁⠀⠀⠩⠩⠡⠨⢿⢢⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠧⣶⣴⣶⡄⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠁⠀⠀⠀⡿⠁⠋⣿⣿⣿⣿⡟⠁⣾⣿⣿⣿⣿⣿⣿⡄⠀⠹⠿⣥⣾⣿⣿⠄⠀⠀⠙⣛⣛⣀⠘⠛⠛⢻⣿⣿⡀⠀⠘⠛⠋⠀⣛⢛⠛⢛⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠴⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⡀⠀⣷⡄⠀⢹⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢀⣾⣿⣿⣿⠀⣀⣀⣀⣉⣉⣉⣀⣈⣀⣈⠉⠉⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⢿⠙⠙⠐⠺⣶⣶⣶ ⠀⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⡏⠉⠀⠀⠁⡆⣿⣷⡀⠈⠙⠉⠉⠀⠀⠿⣿⣻⡿⣿⣿⡿⠿⠀⠀⣿⡿⢽⠯⠿⡷⠶⠶⠶⠖⠚⠿⢶⣶⣶⢶⣶⣶⣶⣶⣶⠴⠖⠒⠀⠀⠀⠀⢸⣶⡗⠀⠀⠀⠀⠰ ⠀⡭⣉⠉⠩⢩⡍⠉⠉⠛⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢿⡿⠁⠀⠀⠀⠀⠀⠀⠐⠤⠈⠒⠂⠀⠀⠀⠀⢰⣿⡇⠀⠀⢸⣿⣛⣃⣀⣀⣴⣄⣀⡉⠉⠈⠈⠈⠁⢙⣛⡃⠀⠀⠀⠀⠀⠀⣈⠀⠀⡀⠀⠀⠀⠀ ⢠⠶⠶⠶⠾⠆⠛⠀⠀⠈⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠄⠹⠋⠀⣠⣶⣴⣤⣶⣦⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠿⣿⡄⠀⢸⡧⣤⣤⣤⣤⣬⣧⣤⣵⣬⣦⣤⣤⡤⣭⣭⣭⣤⣤⣬⣤⡤⠤⣿⣽⣿⣿⣿⡾⣿⠓ ⠀⠒⠒⠒⠂⢸⣦⡄⠀⠀⠀⠀⢀⡀⢀⣠⠀⠀⢀⡀⠀⠀⠀⣶⣷⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣶⣶⣶⣶⣿⣄⠀⣿⣧⠀⠸⠃⠉⢩⣭⣭⣭⠉⠉⠉⠉⠍⣭⣭⠉⢋⠉⠉⠋⢩⣭⠉⠁⠀⣿⠀⠀⠀⠘⠒⠊⠉ ⠀⠛⠛⠇⡤⠌⠈⠃⠠⠀⠀⠀⠘⠃⠜⠻⠀⠀⠈⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⠀⠀⠐⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣄⣀⠀⠀⠀⣀⣠⡀⠀⠀⢻⣦⣤⣤⣤⣤⣤⣤ ⠀⠚⠛⠉⠁⢀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠏⠀⠀⠀⢀⡀⣀⣀⡀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢙⣋⠩⠋⠉⠙⠉⠛ ⠀⠶⡾⠂⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢰⣀⠀⠁⢉⠉⠉⠀⠉⣀⣉⣉⣉⣁⣀⣀⣀⠀⠉⣉⠉⠁⠀⠀⢈⠉⠀⠀⠀⠀⠀⠀ ⠀⠒⠒⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠟⣟⣛⣣⣤⣤⣶⠁⢰⡶⠒⣳⡄⠀⡀⠚⠛⠛⠛⠃⠀⠀⠀⠐⠒⠚⠛⠀⠀⠀⣠⠃⠀⠠⠀⠀⠀⠀ ⠀⣀⣈⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡀⠀⠈⠉⣽⣿⣿⣿⡎⠁⠆⠶⠖⠶⠶⠆⠀⠀⠠⠄⠤⠐⠆⠤⠴⠶⠆⠀⠀⠀⠀⢿⡷⠚⠐⠀⠀⠀⠀ ⢈⠉⢉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡄⠐⠆⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠛⢿⣿⣿⣿⡇⠒⠲⠶⠖⠶⠆⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀ ⠀⠉⠩⢁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣄⠀⢸⢶⣖⠲⣿⡞⠄⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠘⠁⠀⠀⢻⣿⣿⣿⣇⡚⠛⠀⠀⠈⠀⠀⠀⠀⠈⠛⠿⠀⠀⠀⠀⠀⠈⠉⠉⠘⠃⣸⠛⠛⠈⠘⠀⠀⠀ ⠀⢥⡤⡥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠤⠜⠙⠟⠋⠙⠻⠓⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣶⠛⠻⢿⣷⢿⣛⣿⣿⣿⣿⠿⠿⣿⠿⠾⠿⠿⠿⠿⠿⠿⠷⠶⣀⠀⠐⠒⠄⠀⠀⠀⠀⠀⠰ ⠀⠛⠛⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⠿⠿⠿⡿⢿⡿⠿⠿⠿⠿⠿⠿⡿⠿⣿⡇⠘⠛⠀⠀⠉⠉⣒⣾⣰⣪⣿⣿⣿⣿⣿⠀⢤⠉⠀⠀⠀⡄⠀⠀⢀⣀⣀⣀⣿⣀⣀⡀⠀⠀⠀⠀⠀⠀⡐ ⠈⣿⡏⠉⠉⠘⠇⠀⠀⠀⢠⡀⠀⠀⠀⠀⠰⠦⢴⣦⣶⠤⠦⠤⠴⠶⠤⠤⠦⠦⢤⠤⠤⠤⠴⠤⠶⠽⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠛⠿⠧⠀⠀⠀⠃⠈⡻⣿⣿⣿⣿⠧⢰⠦⡷⢢⠾⠽⠤⠶⠬ ⢶⠄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠦⠤⠤⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄ ⠀⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣂⣀⣀⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠈⠉⠉⠉⠉⠉⠉⣵⣴⣶⣴⣆⠀⣰⣦⠤⣄⣖⠀⠀⢰⣰⣦⣤⣴⣦⣤⣀⣀⣶⡒⠀⢀⣀⣠⣤⣴⣦⣀⠀⣀⣀⣀⣀⣀⣀⣴⣶⣶⣶⣆⣒⣀⣦⣦⣦⣤⠠⠄⠀⣠⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣻⣄⡄⠀⠀⠀⢀⡀⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣅⢀⡸⢿⣿⣿⣿⣿⣿⣏⣙⣙⣳⣿⡮⢿⣿⣿⣿⣿⣿⣠⣈⣿⣿⣿⠡⣿⣿⣿⣿⣿⡿⠏⢿⣿⣿⣿⣿⠚⠒⢂⣄⣀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣶⣾⣏⠉⠻⣿⣿⡟⠉⠉⠛⠀⢀⢈⣉⣉⣃⣠⣿⣿⡏⠉⡩⠁⠀⠀⠩⠩⠡⠨⢿⢢⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠧⣶⣴⣶⡄⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠁⠀⠀⠀⡿⠁⠋⣿⣿⣿⣿⡟⠁⣾⣿⣿⣿⣿⣿⣿⡄⠀⠹⠿⣥⣾⣿⣿⠄⠀⠀⠙⣛⣛⣀⠘⠛⠛⢻⣿⣿⡀⠀⠘⠛⠋⠀⣛⢛⠛⢛⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠴⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⡀⠀⣷⡄⠀⢹⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢀⣾⣿⣿⣿⠀⣀⣀⣀⣉⣉⣉⣀⣈⣀⣈⠉⠉⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⢿⠙⠙⠐⠺⣶⣶⣶ ⠀⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⡏⠉⠀⠀⠁⡆⣿⣷⡀⠈⠙⠉⠉⠀⠀⠿⣿⣻⡿⣿⣿⡿⠿⠀⠀⣿⡿⢽⠯⠿⡷⠶⠶⠶⠖⠚⠿⢶⣶⣶⢶⣶⣶⣶⣶⣶⠴⠖⠒⠀⠀⠀⠀⢸⣶⡗⠀⠀⠀⠀⠰ ⠀⡭⣉⠉⠩⢩⡍⠉⠉⠛⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢿⡿⠁⠀⠀⠀⠀⠀⠀⠐⠤⠈⠒⠂⠀⠀⠀⠀⢰⣿⡇⠀⠀⢸⣿⣛⣃⣀⣀⣴⣄⣀⡉⠉⠈⠈⠈⠁⢙⣛⡃⠀⠀⠀⠀⠀⠀⣈⠀⠀⡀⠀⠀⠀⠀ ⢠⠶⠶⠶⠾⠆⠛⠀⠀⠈⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠄⠹⠋⠀⣠⣶⣴⣤⣶⣦⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠿⣿⡄⠀⢸⡧⣤⣤⣤⣤⣬⣧⣤⣵⣬⣦⣤⣤⡤⣭⣭⣭⣤⣤⣬⣤⡤⠤⣿⣽⣿⣿⣿⡾⣿⠓ ⠀⠒⠒⠒⠂⢸⣦⡄⠀⠀⠀⠀⢀⡀⢀⣠⠀⠀⢀⡀⠀⠀⠀⣶⣷⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣶⣶⣶⣶⣿⣄⠀⣿⣧⠀⠸⠃⠉⢩⣭⣭⣭⠉⠉⠉⠉⠍⣭⣭⠉⢋⠉⠉⠋⢩⣭⠉⠁⠀⣿⠀⠀⠀⠘⠒⠊⠉ ⠀⠛⠛⠇⡤⠌⠈⠃⠠⠀⠀⠀⠘⠃⠜⠻⠀⠀⠈⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⠀⠀⠐⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣄⣀⠀⠀⠀⣀⣠⡀⠀⠀⢻⣦⣤⣤⣤⣤⣤⣤ ⠀⠚⠛⠉⠁⢀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠏⠀⠀⠀⢀⡀⣀⣀⡀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢙⣋⠩⠋⠉⠙⠉⠛ ⠀⠶⡾⠂⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢰⣀⠀⠁⢉⠉⠉⠀⠉⣀⣉⣉⣉⣁⣀⣀⣀⠀⠉⣉⠉⠁⠀⠀⢈⠉⠀⠀⠀⠀⠀⠀ ⠀⠒⠒⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠟⣟⣛⣣⣤⣤⣶⠁⢰⡶⠒⣳⡄⠀⡀⠚⠛⠛⠛⠃⠀⠀⠀⠐⠒⠚⠛⠀⠀⠀⣠⠃⠀⠠⠀⠀⠀⠀ ⠀⣀⣈⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡀⠀⠈⠉⣽⣿⣿⣿⡎⠁⠆⠶⠖⠶⠶⠆⠀⠀⠠⠄⠤⠐⠆⠤⠴⠶⠆⠀⠀⠀⠀⢿⡷⠚⠐⠀⠀⠀⠀ ⢈⠉⢉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡄⠐⠆⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠛⢿⣿⣿⣿⡇⠒⠲⠶⠖⠶⠆⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀ ⠀⠉⠩⢁⠀⠘⡶⠀⠀⠀⠀⠀⠀⣄⠀⢸⢶⣖⠲⣿⡞⠄⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠘⠁⠀⠀⢻⣿⣿⣿⣇⡚⠛⠀⠀⠈⠀⠀⠀⠀⠈⠛⠿⠀⠀⠀⠀⠀⠈⠉⠉⠘⠃⣸⠛⠛⠈⠘⠀⠀⠀ ⠀⢥⡤⡥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠤⠜⠙⠟⠋⠙⠻⠓⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣶⠛⠻⢿⣷⢿⣛⣿⣿⣿⣿⠿⠿⣿⠿⠾⠿⠿⠿⠿⠿⠿⠷⠶⣀⠀⠐⠒⠄⠀⠀⠀⠀⠀⠰ ⠀⠛⠛⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⠿⠿⠿⡿⢿⡿⠿⠿⠿⠿⠿⠿⡿⠿⣿⡇⠘⠛⠀⠀⠉⠉⣒⣾⣰⣪⣿⣿⣿⣿⣿⠀⢤⠉⠀⠀⠀⡄⠀⠀⢀⣀⣀⣀⣿⣀⣀⡀⠀⠀⠀⠀⠀⠀⡐ ⠈⣿⡏⠉⠉⠘⠇⠀⠀⠀⢠⡀⠀⠀⠀⠀⠰⠦⢴⣦⣶⠤⠦⠤⠴⠶⠤⠤⠦⠦⢤⠤⠤⠤⠴⠤⠶⠽⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠛⠿⠧⠀⠀⠀⠃⠈⡻⣿⣿⣿⣿⠧⢰⠦⡷⢢⠾⠽⠤⠶⠬ ䷩ 𝚕𝚒𝚗𝚎 9261 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/10/Open_Hardware_Modding_Raspberry_Pi_Arduino_and_More.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/10/Open_Hardware_Modding_Raspberry_Pi_Arduino_and_More.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Open Hardware/Modding: Raspberry Pi, Arduino, and More⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Mar 10, 2026 * ⚓ Linux Gizmos ☛ Arduino_expands_lineup_with_Ventuno_Q_board_pairing Dragonwing_IQ8_and_STM32H5⠀⇛ Arduino has introduced the Ventuno Q, a development board designed for robotics, embedded computing, and edge inference workloads. The platform combines a high-performance application processor with a real-time microcontroller in a dual-processor architecture intended for systems that process data and control physical hardware simultaneously. * ⚓ Raspberry_Pi_Weekly_Issue_#526_-_Pico_projects,_Cornell_experiments, and_marine_conservation_robots⠀⇛ Click on the orange book at the bottom of this week’s issue to unlock a special discount from Raspberry Pi Press Howdy, This Maker Monday, we inspired you with a selection of the best Raspberry Pi Pico projects around, courtesy of the latest issue of Raspberry Pi Official Magazine. * ⚓ Bunnie Huang ☛ Baochip-1x:_A_Mostly-Open,_22nm_SoC_for_High_Assurance Applications⠀⇛ One of my latest projects is the Baochip-1x, a mostly-open, full-custom silicon chip fabricated in TSMC 22nm, targeted at high assurance applications. It’s a security chip, but far more open than any other security chip; it’s also a general purpose microcontroller that fills a gap in between the Raspberry Pi RP2350 [...] * ⚓ Arduino ☛ Introducing_Arduino®_VENTUNO™_Q:_your_new_AI,_robotics,_and actuation_platform!⠀⇛ We’ve been dropping hints about a new, revolutionary product we’ve been working on, and now we can finally tell you all about it! Ahead of Embedded World our team has announced the upcoming VENTUNO Q, a single-board computer purpose-built for AI, robotics, and actuation.  * ⚓ CNX Software ☛ Makerfabs_CM0IQ_–_An_ultra-compact_(42x36mm)_Raspberry Pi_CM0_Lite_board⠀⇛ The CM0IQ is an ultra-compact board based on the Raspberry Pi CM0 Lite Compute Module. It measures just 42 × 36 mm and squeezes multiple interfaces into a 15.1 cm² footprint, making it suitable for space-constrained applications such as robotics, IoT devices, and custom hardware integrations. Despite being smaller than a Raspberry Pi Zero 2 W (19.5 cm²), the CM0IQ manages to include a full-sized USB-A port, a Micro HDMI port, and 4-lane MIPI CSI and DSI connectors. To fit everything into this small footprint, the designer also relied on a 1.27 mm 40-pin GPIO header rather than the standard 2.54 mm header. * ⚓ CNX Software ☛ STMicro_STM32C5_entry-level,_144_MHz_Cortex-M33_MCU features_up_to_1MB_flash,_256KB_SRAM,_Ethernet,_CAN_Bus⠀⇛ Not to be confused with the just-released STM32U3B5/C5 ultra- low-power MCUs, the entry-level STM32C5 Arm Cortex-M33 MCU family is designed for industrial sensors, smart home devices, electronic locks, thermostats, wearables, robotic actuators, and computer peripherals. The MCUs are manufactured using ST’s 40 nm flash process, clocked at up to 144 MHz, and feature 128 KB to 1 MB of flash and up to 256 KB of SRAM, with a dynamic power consumption of <80 µA/MHz. * ⚓ I_Built_a_5″_Portable_Raspberry_Pi_Homelab⠀⇛ What if you could take your entire homelab with you when you travel? In this project, I designed a portable Pi homelab by shrinking my original 10″ Lab Rax down to a 5″ rack that can still run a router, NAS and Docker server using Raspberry Pi hardware. ䷩ 𝚕𝚒𝚗𝚎 9365 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/10/OpenSSL_4_0_Promises_Support_for_Encrypted_Client_Hello_SNMP_KD.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/10/OpenSSL_4_0_Promises_Support_for_Encrypted_Client_Hello_SNMP_KD.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ OpenSSL 4.0 Promises Support for Encrypted Client Hello, SNMP KDF, and SRTP KDF⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Marius Nestor on Mar 10, 2026 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇OpenSSL⦈_ OpenSSL 4.0 promises support for Encrypted Client Hello (ECH, RFC 9849), support for RFC 8998, support for signature algorithm sm2sig_sm3, key exchange group curveSM2 support, support for [tls-hybrid-sm2-mlkem] post-quantum group curveSM2MLKEM768, and support for SNMP KDF and SRTP KDF. It also promises cSHAKE function support as per the SP 800-185 specification, support for the “ML-DSA-MU” digest algorithm, support for using either static or dynamic VC runtime linkage on Windows systems, and support for negotiated FFDHE key exchange in TLS 1.2 in accordance with RFC 7919. Read_on ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⡿⠿⠿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣴⣾⣷⣦⠹⣿⢿⡿⠿⢿⣿⣿⡿⠿⢿⣿⣿⢿⠿⠿⣿⣿⠁⣴⣶⣄⣈⣿⠁⢠⣶⣦⣈⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⡆⢻⡏⠶⠿⠦⢹⣿⢰⣿⣷⢸⣿⣤⣈⣉⠉⠛⣿⣦⣄⣉⡉⠛⢿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⠿⣿⣿⠟⣡⣿⠀⢿⣿⠇⣼⣇⢿⣿⠟⣻⣿⢸⣿⣿⢸⣯⠉⠻⠿⠟⢀⣿⡉⠹⠿⠿⠀⣸⡇⠀⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⠀⣷⣶⣾⣿⣿⣷⣶⣾⣿⣿⣾⣿⣿⣾⣿⣿⣶⣶⣶⣿⣿⣿⣶⣶⣶⣾⣿⣷⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ䷩ 𝚕𝚒𝚗𝚎 9422 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/10/Programming_Leftovers.1.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/10/Programming_Leftovers.1.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Programming Leftovers⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Mar 10, 2026 * ⚓ HowTo Geek ? Ruby_is_still_the_easiest_programming_language_to learn?here's_the_proof⠀⇛ When faced with the prospect of learning to code, aspiring programmers are hit with the complexity, the arcane symbols, and the fear that they simply aren't technical enough to learn code. The initial choice of a first programming language feels like a high-stakes decision, one that can determine whether the journey ends in frustration or flows into lasting success. Ruby is a great starter language, and one that will make you feel like coding is just a little harder than writing. If you believe that a coding language should read like plain English, handle complex logistics automatically, and guide you effortlessly into the core concepts of modern software architecture, then you will love Ruby. * § Python⠀➾ o ⚓ HowTo Geek ? 8_Python_mistakes_even_senior_devs_make⠀⇛ Even the most seasoned senior developers, armed with years of experience, routinely stumble over traps in Python. It's not hard and doesn't stem from a lack of technical skill, but from an ingrained reliance on programming intuitions that simply do not hold true in the Python ecosystem. o § Canonical/Ubuntu Family⠀➾ # ⚓ HowTo Geek ? Why_27_lines_of_Python_is_all_you_need_for_an inspiring_Linux_Mint_desktop⠀⇛ Desklets are my favorite Linux Mint customization feature because they make adding desktop widgets super easy, which you'll appreciate if you want a Windows-like widget experience after switching to Mint. Although Mint's desklets experience is solid, it's not as complete as I'd like. For starters, the 'Download Desklets' tab doesn't have many options; at the time of writing this, I counted approximately 67 downloadable desklets. Second, although some desklets are highly customizable, others are not, especially if you have unique desktop widget needs, which I do. Let me give you an example. If you've read any of my articles about automatically changing or updating the wallpaper, you know I like having an inspiring desktop look. I usually achieve that look by using tools like Shotwell, Variety, or an infinite desktop wallpaper script that cycles through a collection of inspiring quote wallpapers I've downloaded. It's not the most elegant solution, but it works. * § Shell/Bash/Zsh/Ksh⠀➾ o ⚓ HowTo Geek ? 4_simple_habits_that_instantly_transform_Bash scripts_into_cleaner,_more_readable_code⠀⇛ Whether you're a beginner or a hardened Bash-writing veteran, there's always room for picking up new tips. Some of the best ones take only moments to learn but are so transformative that they change your entire approach. I have four that will unscramble your Bash spaghetti into a well-formatted work of art. A pipeline is a sequence of commands joined by the "|" character. Each command processes the output of the previous. * § Rust⠀➾ o ⚓ HowTo Geek ? Why_Rust_is_the_secret_ingredient_behind_the_next generation_of_Linux⠀⇛ So, you're getting into software development, and one elemental name keeps coming up: Rust. After experiencing that myself, I looked into the increasingly popular programming language. Here's what I learned about it, plus the steps it took to start writing Rust programs myself. § Rust is a fast, safe programming language First created in 2006 by a Mozilla employee, Rust is a programming language that emphasizes speed and safety. I didn't know what that meant at first, so I'll explain. ䷩ 𝚕𝚒𝚗𝚎 9551 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/10/Programming_Leftovers.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/10/Programming_Leftovers.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Programming Leftovers⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Mar 10, 2026 * ⚓ Bozhidar Batsov ☛ Emacs_and_Vim_in_the_Age_of_AI⠀⇛ I’ve been an Emacs fanatic for over 20 years. I’ve built and maintained some of the most popular Emacs packages, contributed to Emacs itself, and spent countless hours tweaking my configuration. Emacs isn’t just my editor – it’s my passion, and my happy place. Over the past year, I’ve also been spending a lot of time with Vim and Neovim, relearning them from scratch and having a blast contrasting how the two communities approach similar problems. It’s been a fun and refreshing experience.1 * ⚓ Austin White ☛ Please_Can_We_Address_This⠀⇛ Trust me, if you can collect the information from your users faster and with less hassle, they will understand and be happy. * ⚓ Isoken_Ibizugbe:_Starting_Out_in_Outreachy⠀⇛ So you want to join Outreachy but you don’t understand it, you’re scared, or you don’t know what open source is about. § What is FOSS anyway?  Free and Open Source Software (FOSS) refers to software that anyone can use, modify, and share freely. Think of it as a community garden; instead of one company owning the “food,” people from all over the world contribute, improve, and maintain it so everyone can benefit for free. You can read more here on what it means to contribute to open source. Outreachy provides paid internships to anyone from any background who faces underrepresentation, systemic bias, or discrimination in the technical industry where they live. Their goal is to increase diversity in open source. Read their website for more. I spent a good amount of time reading all the guides listed, including the applicant guide and the how-to- apply guide.  * ⚓ Ken Kantzer ☛ Let’s_be_honest_about_Hey_Hi_(AI)_Coding⠀⇛ Ken’s early 2026 thoughts on the state of Hey Hi (AI) coding, Claude, Kernigan’s Law, and what technology has worked thus far * ⚓ Godot Engine ☛ Release_candidate:_Godot_4.6.2_RC_1⠀⇛ Maintenance of maintenance? Is such a thing even possible!? * ⚓ Juan J Martínez ☛ Another_Tomato⠀⇛ How did it go? First of all, I’ve got much further, faster, writing OCaml than when I started with Haskell. Which may not mean anything, because I’m learning OCaml knowing some Haskell already, and that changes things quite a bit. * § Python⠀➾ o ⚓ Kushal_Das:_In_the_land_of_XML⠀⇛ One of the major thing at work is XML, due to all things identity. Yes, XML and SAML are very much alive. SWAMID is the identity fedeation for research and higher education in Sweden and edusgain which is the global identify federation around the world connected 80+ pariticipaaant federations connecting over 10k identify and service providers. And these are based on SAML. In the last few weeks I released two libraries in Rust and then python bindings for the same using pyo3. uppsala is the zero dependency XML library and pyuppsala is the python binding. * § R / R-Script⠀➾ o ⚓ Rlang ☛ Get_Better:_loading_multiple_csv_files_in_R⠀⇛ In the test dataset from the previous post we have a single folder of 80 csv files. 4 experiments, 2 conditions, 10 files from each. And each file has 20 rows of data. See below for other scenarios. The goal is to load of the data into R and assemble into a single data frame. There are many ways to do this, I’ll show three of the most popular. o ⚓ Rlang ☛ Learning_PK/PD_Simulation:_A_Beginner’s_Monte_Carlo Analysis_With_mrgsolve_in_R⠀⇛ Population pharmacokinetics (popPK) is a statistical approach that describes how medications behave in the body across groups of people, accounting for variability between individuals. Instead of studying one person intensively, popPK analyzes sparse data from many patients to understand typical medication behavior and why people differ in their medication exposure. o ⚓ Dirk Eddelbuettel ☛ Dirk_Eddelbuettel:_nanotime_0.3.13_on_CRAN: Maintenance⠀⇛ This release, the first in eleven months, rounds out a few internal corners and helps Rcpp with the transition away from Rf_error to only using Rcpp::stop which deals more gracefully with error conditions and unwinding. We also updated how the vignette is made, its references, updated the continuous integration as one does, altered how the documentation site is built, gladly took a PR from Michael polishing another small aspect, and tweaked how the compilation standard is set. ䷩ 𝚕𝚒𝚗𝚎 9706 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/10/Red_Hat_RHEL_Libvirt_Slop_Hype_and_AlmaLinux.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/10/Red_Hat_RHEL_Libvirt_Slop_Hype_and_AlmaLinux.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Red Hat/RHEL: Libvirt, Slop Hype, and AlmaLinux⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Mar 10, 2026, updated Mar 10, 2026 * ⚓ Red Hat ☛ Effortless_Red_Bait_Enterprise_GNU/Linux_virtual_machines with_Libvirt_and_Kickstart⠀⇛ From time to time, as a developer you need to do something on a full-fledged virtual machine (VM). Maybe you need to reproduce an issue or perform integration tests in an environment configured as close as possible to the production environment, including kernel, system services, firewall settings, authentication policies, and anything not easily reproduced in a container. In this article, I demonstrate a quick and easy way to create such a VM using the standard libvirt found in any GNU/Linux distribution, and Kickstart scripts supported by Red Bait Enterprise GNU/Linux (RHEL). * ⚓ Red Hat ☛ 5_steps_to_triage_vLLM_performance [Ed: Red Hat is sick. IBM makes it promote slop all the time.]⠀⇛ As enterprises move large language models (LLMs) from pilot to production, maintaining consistent inference performance becomes a primary operational challenge. While vLLM is efficient out of the box, users often encounter performance that differs from their expectations once they move beyond simple benchmarks. vLLM provides a comprehensive set of metrics that offer a window into the server's internal state, which can help determine the root cause of performance issues. This article provides a diagnostic workflow to help you improve the performance of your vLLM deployments. * ⚓ Red Hat ☛ Automate_Hey_Hi_(AI)_agents_with_the_Responses_API_in_Llama Stack⠀⇛ Building reliable Hey Hi (AI) agents requires a careful balance between automated orchestration and precise control over conversation flow. By adopting the Responses API within the Llama Stack ecosystem, we automated complex tool calling while using LangGraph to maintain granular control over our agent’s state. This is the fourth post in a series covering what we learned while developing the it-self-service-agent Hey Hi (AI) quickstart: [...] * ⚓ Unicorn Media ☛ AlmaLinux_Gets_CUDA_Parity_With_Ubuntu,_RHEL,_and_RLC⠀⇛ AlmaLinux users no longer have to juggle Nvidia workarounds: CUDA and GPU drivers are moving into the distro’s normal package workflow. FOSS Force: * ⚓ AlmaLinux_Gets_CUDA_Parity_With_Ubuntu,_RHEL,_and_RLC_-_FOSS_Force⠀⇛ Nvidia has added official CUDA support for Linux distributions that are compatible with Red Hat Enterprise Linux. Benefiting most from this will be AlmaLinux, whose biggest competitor in the RHEL-clone arena, Rocky Linux, already offers direct CUDA availability to users of its subscription-based Rocky Linux from CIQ variations. This should help tighten the gap that has been developing between the two, as CIQ has lately been busy increasing the number of supported use-case-based variations of Rocky Linux it offers. This is important for enterprises running — or planning to run — AI workloads on Nvidia GPUs, since CUDA is Nvidia’s go-to accelerated computing platform and programming model. It includes optimized libraries and development tools for developing and deploying accelerated workloads for Nvidia GPUs. While CUDA’s not the AI superhero that Nvidia would have you think it is, it’s at least somewhat essential for developers, ML engineers, researchers, and the like who are looking to get the most bang for their Nvidia hardware bucks. Its use generally outperforms generic CPU or OpenCL in typical real- world implementations. ䷩ 𝚕𝚒𝚗𝚎 9816 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/10/Security_and_Standards_NTP_Security_New_Attack_Against_Wi_Fi_Ai.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/10/Security_and_Standards_NTP_Security_New_Attack_Against_Wi_Fi_Ai.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Security and Standards: NTP Security, New Attack Against Wi-Fi, AirSnitch, and More⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Mar 10, 2026 * ⚓ LWN ☛ Security_updates_for_Monday⠀⇛ Security updates have been issued by AlmaLinux (delve, git-lfs, and postgresql16), Fedora (cef, chezmoi, chromium, coturn, erlang-hex_core, firefox, gh, gimp, k9s, keylime, keylime- agent-rust, libsixel, microcode_ctl, nextcloud, nss, perl- Crypt-URandom, pgadmin4, php-zumba-json-serializer, postgresql16-anonymizer, prometheus, python-asyncmy, python3.10, python3.11, python3.9, staticcheck, valkey, and vim), SUSE (chromedriver, chromium, coredns, expat, freetype2- devel, gitea-tea, go1.24-openssl, go1.25-openssl, grpc, gstreamer-rtsp-server, gstreamer-plugins-ugly,, helm, jetty- annotations, kubeshark-cli, libaec, libblkid-devel, libsoup, libxml2, libxslt, NetworkManager-applet-strongswan, podman, python-joserfc, python-Markdown, python-pypdf2, python-tornado, python-uv, python311-Django, python311-joserfc, python311-nltk, roundcubemail, and valkey), and Ubuntu (python3.4, python3.5, python3.6, python3.7, python3.8, python3.9, python3.10, python3.11, python3.12, python3.13, python3.14). ⚓ Securing_NTP⠀⇛ On 31 December 2016, the world’s clocks briefly hiccupped as Coordinated Universal Time (UTC) inserted an extra second into the final minute of the year. Such adjustments are not unusual; it was the 27th leap second added to the UTC timescale. ⚓ Bruce Schneier ☛ New_Attack_Against_Wi-Fi_-_Schneier_on_Security⠀⇛ ⚓ Internet Society ☛ AirSnitch:_Demystifying_and_Breaking_Client_Isolation_in Wi-Fi_Networks_-_NDSS_Symposium⠀⇛ In this paper, we undertake a structured security analysis of Wi-Fi client isolation and uncover new classes of attacks that bypass this protection. We identify several root causes behind these weaknesses. First, Wi-Fi keys that protect broadcast frames are improperly managed and can be abused to bypass client isolation. Second, isolation is often only enforced at the MAC or IP layer, but not both. Third, weak synchronization of a client's identity across the network stack allows one to bypass Wi-Fi client isolation at the network layer instead, enabling the interception of uplink and downlink traffic of other clients as well as internal backend devices. Every tested router and network was vulnerable to at least one attack. More broadly, the lack of standardization leads to inconsistent, ad hoc, and often incomplete implementations of isolation across vendors. ⚓ [Old] Peter Hofmann ☛ Why_octal_notation_should_be_used_for_UTF-8_(and Unicode)⠀⇛ Disclaimer: I read about this topic in another blog first, but I just can't find that posting anymore. If you, the "original author", happen to read this, drop me a note and I'll add a link to your posting. Now. It's 2016 and I finally took the time to write a very basic UTF- 8 encoder and decoder. This is an important thing that, IMHO, anyone should do to get a better understanding of what's going on. ䷩ 𝚕𝚒𝚗𝚎 9902 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/10/Security_Leftovers.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/10/Security_Leftovers.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Security Leftovers⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Mar 10, 2026 * ⚓ OpenSSF (Linux Foundation) ☛ Introducing_the_Gemara_Model⠀⇛ * ⚓ Cyble Inc ☛ ClipXDaemon_Malware,_a_Stealthy_Cryptocurrency_Clipboard Hijacker_on_Linux⠀⇛ Security researchers have identified a new Linux malware strain called ClipXDaemon, a stealthy threat designed to target cryptocurrency users by manipulating copied wallet addresses. Cyble’s Research & Intelligence Labs (CRIL) found the malware delivered through a loader structure previously associated with ShadowHS activity. Despite that structural overlap, researchers say there is no evidence that ClipXDaemon and ShadowHS share the same operators or malware authors. Instead, both threats appear to rely on bincrypter, an open- source shell-script encryption framework hosted on GitHub. * ⚓ Federal News Network ☛ CISA_delays_cyber_incident_reporting_town_halls due_to_shutdown⠀⇛ CISA had been planning to hold the town halls starting on Monday. The shutdown is "likely" to also delay issuance of the final cyber incident reporting rule. * ⚓ Federal News Network ☛ U.S._organizations_should_prepare_for_cyber retaliation_as_conflict_with_Iran_escalates⠀⇛ "[T]his is about making sure that you are ready for it because it's not a question of if, it's a question when," said James Turgal. ䷩ 𝚕𝚒𝚗𝚎 9960 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/10/Servers_Slop_Promoted_by_Kubernetes_Hetzner_Prices_Soar_After_S.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/10/Servers_Slop_Promoted_by_Kubernetes_Hetzner_Prices_Soar_After_S.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Servers: Slop Promoted by Kubernetes, Hetzner Prices Soar After Slop Grifting (Hoarding Hardware)⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Mar 10, 2026 * ⚓ Kubernetes Blog ☛ Announcing_the_Hey_Hi_(AI)_Gateway_Working_Group⠀⇛ The community around Kubernetes includes a number of Special Interest Groups (SIGs) and Working Groups (WGs) facilitating discussions on important topics between interested contributors. Today, we're excited to announce the formation of the AI_Gateway_Working_Group, a new initiative focused on developing standards and best practices for networking infrastructure that supports Hey Hi (AI) workloads in Kubernetes environments. § What is an Hey Hi (AI) Gateway? In a Kubernetes context, an AI Gateway refers to network gateway infrastructure (including proxy servers, load- balancers, etc.) that generally implements the Gateway_API specification with enhanced capabilities for Hey Hi (AI) workloads. Rather than defining a distinct product category, Hey Hi (AI) Gateways describe infrastructure designed to enforce policy on Hey Hi (AI) traffic, including: [...] * ⚓ Michael Tsai ☛ Hetzner_Price_Hikes⠀⇛ Here’s the table of pricing changes, which seem to vary from single-digit to triple-digit increases. * ⚓ Jeremy Cherfas ☛ My_new_host,_three_months_on⠀⇛ The great thing about a server on Hetzner is that you can have SSH access, which allows you to do maximum damage with minimum effort and also enables reasonably simple day-to-day maintenance when required. It is also very easy to create S3 compatible buckets, so I could move my backups and podcast audio files away from Amazon S3. Without SSH, however, things like updating a file or creating an off-site backup or deleting a directory are much more tedious. ䷩ 𝚕𝚒𝚗𝚎 10023 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/10/Today_in_Techrights.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/10/Today_in_Techrights.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Today in Techrights⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Mar 10, 2026 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_Civil_War_Sketches_of_Adolph_Metzner_(1861–64)⦈_ ⚓ Updated This Past Day⠀⇛ 1. ⚓ Attacks_on_Techrights_Make_Techrights_Stronger_and_Attract_More Whistleblowers_to_Techrights⠀⇛ The harder they attack us, the more productive we become 2. ⚓ An_American_War_on_GNU/Linux,_Software_Freedom,_and_British Investigative,_Science-Based_Reporting_-_Part_III_-_Very_Strong_Legal Basis_for_an_Appeal⠀⇛ The case is now being escalated to a Foreign Secretary and former Deputy Prime Minister 3. ⚓ No_Slop_Found_in_RSS_Feeds,_Only_in_Google_News⠀⇛ No slopfarm will survive for very long, certainly it'll go bust as soon as readers (if it had any) know what it is 4. ⚓ What_the_Solicitors_Regulation_Authority_(SRA)_and_Action_Fraud_UK_Have in_Common⠀⇛ Don't let London become the world's "crime capital" 5. ⚓ Dr._Andy_Farnell_on_How_GAFAM,_NVIDIA_and_Others_Lie_to_People_Via_the Sponsored_Media_to_Prop_Up_Lies_Under_the_Guise_of_"AI"⠀⇛ Lots of key aspects are covered ⚓ New⠀⇛ 6. ⚓ The_Register_MS_Has_Just_Taken_Money_From_Google_(Where_the_Former Chief_Editor_Now_Works)_for_Femmewashing_and_Ponzi_Scheme_Promotion⠀⇛ now The Register MS not only promotes a Ponzi scheme but also bags money to pretend Google respects women 7. ⚓ People_at_IBM_Are_Still_Smart_Enough_to_Understand_What's_Really_Going on⠀⇛ "I would never refer someone to work at IBM that I liked! I hope all of you have reviewed IBM on Glassdoor." 8. ⚓ European_Patent_Office_(EPO)_to_"Eventually_Eliminate_the_Tasks Performed_by_Formalities_Officers";_EPO_Run_by_People_Without_Experience in_Patents⠀⇛ full paper 9. ⚓ RMS_is_73_Next_Week⠀⇛ Richard Matthew Stallman (RMS) turns 73 exactly 7 days from now 10. ⚓ Iran_&_FSFE:_blackmailing_women,_from_football_to_the_French Government_(CNIL)⠀⇛ Reprinted with permission from Daniel Pocock 11. ⚓ Police_investigations,_lawsuits_&_Debian_leader_election_candidate shortage⠀⇛ Reprinted with permission from Daniel Pocock 12. ⚓ Richard_Stallman_(RMS)_Has_Defeated_Cancel_Culture,_a_Mostly_American Phenomenon⠀⇛ RMS is talking now 13. ⚓ Links_09/03/2026:_Many_Security_Breaches_and_a_Pandemic_of_Censorship⠀⇛ Links for the day 14. ⚓ People_Who_Work_or_Worked_at_IBM_Hate_It⠀⇛ bluewashing is only the first step 15. ⚓ Richard_Stallman_(RMS)_Talks_in_30_Minutes,_Next_Stop_Bern_(Last Stop)⠀⇛ We assume he'll travel back to Boston after that 16. ⚓ IBM's_Fedora_as_a_Booster_of_Slop_Disguised_as_Code_or_Computer Programs⠀⇛ Maybe we should also stop seeing a doctor and instead ask chatbots about symptoms? 17. ⚓ Richard_Stallman_(RMS)_Talk_Five_Hours_From_Now⠀⇛ there is growing recognition for what he really did for everybody 18. ⚓ EPO_Strike_10_Days_From_Now,_Planning_Assembly_Tomorrow,_Last_Couple_of Strikes_Had_High_Participation_Rates_(1,500-1,600_Staff_Went_on_Strike)⠀⇛ The next strike is in 10 days' time and then there will be another strike 19. ⚓ Links_09/03/2026:_GAFAM_Outsourcing,_"MAGA_Political_Meddling"_in_EU, Indonesia_Bans_Social_Control_Media_for_Children_Under_16⠀⇛ Links for the day 20. ⚓ Using_Slop_(and_Slop_in_Articles)_to_Attack_Copyleft_'on_Budget'⠀⇛ This article is pure BS from an anti-GPL and anti-RMS 'activist' 21. ⚓ Why_The_Register_MS_Sold_Out_to_Microsoft:_They're_Losing_Lots_of Money,_The_Register_MS_is_Bleeding_to_Death,_Based_on_Its_Own_Financial Records⠀⇛ With over 6 million pounds in debt (nearly 10 million US dollars) we guess it's likely some other company will take over the site (if it deems it worthwhile) 22. ⚓ Microsofters'_SLAPP_Censorship_-_Part_7_Out_of_200:_Like_With_the Serial_Strangler_From_Microsoft,_Misuse_of_UK-GDPR_to_Try_to_Hide Embarrassing_Facts⠀⇛ They do and say really bad things, then allege it's a "privacy violation" to mention those things 23. ⚓ Over_at_Tux_Machines...⠀⇛ GNU/Linux news for the past day 24. ⚓ IRC_Proceedings:_Sunday,_March_08,_2026⠀⇛ IRC logs for Sunday, March 08, 2026 25. ⚓ Gemini_Links_09/03/2026:_Exponentials_and_Tailscale⠀⇛ Links for the day 26. ⚓ Sloppyleft⠀⇛ Article by Alexandre Oliva ========================================================================= The corresponding text-only bulletin for Monday contains all the text. 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⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣻⣿⣶⣿⣿⣿⣿⡿⠟⠋⢉⣠⣴⣾⣿⡿⣿⣿⣿⢟⣻⣿⢓⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣾⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣋⣡⣴⣾⣿⣿⣿⣿⣿⣿⣿⣽⣾⣿⡟⠋⠀⠀⠊⠀⠀⠀⠀⢠⣠⣤⡠⠀⠀⢀⠀⠀⣀⣀⣀⡀⠀⠀⢀⡀⠀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⣄⣰⣀⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣛⣡⣤⣤⣤⣤⣤⣶⣶⣼⣿⣿⣭⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ䷩ 𝚕𝚒𝚗𝚎 10547 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/10/today_s_howtos.1.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/10/today_s_howtos.1.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ today's howtos⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Mar 10, 2026 * § Kernel Space / File Systems / Virtualization⠀➾ o ⚓ 7_Types_of_Files_in_GNU/Linux_-_Every_User_Should_Know⠀⇛ GNU/Linux recognizes 7 types of files: Regular files (-), Directory files (d), Character device files (c), Block device files (b) [...] * § Instructionals/Technical⠀➾ o ⚓ HowTo Geek ☛ Stop_using_these_5_deprecated_Linux_commands_(and what_to_use_instead)⠀⇛ Linux has hundreds of available commands, and unless you're keeping up with the latest news, changes to the default tools may slip under your radar. While it's true that Linux is very stable, and tool deprecations are rare, some of our much-beloved and well-known utilities changed years ago, and nobody informed us. I have five deprecated Linux commands and their replacements. o ⚓ HowTo Geek ☛ 10_tricks_you_can_do_with_FFmpeg_on_Linux⠀⇛ Want to do more with the Linux terminal? You might not instinctively put videos and the command line together, but with FFmpeg you can actually do a lot with a video file just by typing a simple command in your terminal. Whether you want to quickly play a video, retrieve some information, or perform cool video-editing tricks, FFmpeg has got you covered. Here are some useful things you can do with FFmpeg on your Linux machine. ䷩ 𝚕𝚒𝚗𝚎 10606 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/10/today_s_howtos.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/10/today_s_howtos.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ today's howtos⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Mar 10, 2026 * ⚓ Linuxize ☛ ping_Cheatsheet⠀⇛ Quick reference for testing network reachability and latency with ping in Linux * ⚓ LinuxConfig ☛ How_to_Change_SSH_Port_on_Ubuntu_26.04⠀⇛ * ⚓ LinuxConfig ☛ How_to_Check_NTP_on_Ubuntu_26.04⠀⇛ * ⚓ Linux Capable ☛ How_to_Install_Homebrew_on_Fedora_Linux⠀⇛ Some developer tools move faster than Fedora’s repositories, and Homebrew gives GNU/Linux a separate package manager for command-line tools, language runtimes, and utilities in that gap. * § idroot⠀➾ o ⚓ ID Root ☛ How_To_Install_XRDP_on_Fedora_43⠀⇛ Remote access to a GNU/Linux machine shouldn’t require you to be physically present. If you manage a Fedora 43 server or workstation, setting up XRDP gives you full graphical desktop access from any Windows, macOS, or GNU/ Linux machine — using the familiar Remote Desktop Protocol. o ⚓ ID Root ☛ How_To_Install_OpenClaw_on_Linux_Mint_22⠀⇛ If you’ve been looking for a powerful, self-hosted Hey Hi (AI) automation assistant that runs quietly in the background and integrates with your messaging apps, OpenClaw is the answer. Installing it on Linux Mint 22 is straightforward — but only if you follow the right steps from the start. o ⚓ ID Root ☛ How_To_Install_Borgmatic_on_Debian_13⠀⇛ Backing up data is crucial for system administrators and GNU/Linux users who value their information. Borgmatic provides an elegant solution for automated, encrypted backups on Debian 13 systems. This comprehensive guide walks through every step of installing and configuring Borgmatic, from initial setup to automated backup scheduling. o ⚓ ID Root ☛ How_To_Install_SeaMonkey_on_AlmaLinux_10⠀⇛ If you need a powerful, all-in-one internet suite on your AlmaLinux 10 system, SeaMonkey is one of the best options available. o ⚓ ID Root ☛ How_To_Install_HandBrake_on_Fedora_43⠀⇛ If you work with video files on Linux, at some point you will run into one problem: Fedora 43 does not ship HandBrake out of the box. HandBrake — the gold standard open-source video transcoder — is not in Fedora’s default repositories, which means you need a third-party source to install HandBrake on Fedora 43. o ⚓ ID Root ☛ How_To_Install_Astro_on_Ubuntu_24.04_LTS⠀⇛ If you build content-heavy websites — blogs, documentation portals, marketing pages — you already know the frustration of bloated JavaScript frameworks slowing your site to a crawl. Astro solves that problem by shipping zero JavaScript to the browser by default, letting you build blazing-fast websites with the tools you already know. o ⚓ ID Root ☛ How_To_Install_Gatsby_on_AlmaLinux_10⠀⇛ If you’re a developer or sysadmin looking to build blazing-fast, modern websites on a reliable GNU/Linux server, Gatsby is one of the best tools in your stack. Built on React and powered by Node.js, Gatsby produces statically generated sites that are fast, secure, and SEO-ready out of the box. ䷩ 𝚕𝚒𝚗𝚎 10724 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/10/today_s_leftovers.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/10/today_s_leftovers.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ today's leftovers⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Mar 10, 2026 * § Audiocasts/Shows⠀➾ o ⚓ The Cyber Show ☛ Cybershow:_Mad_Times_|_Banter⠀⇛ We're talking about our mad times, mad leaders, culture and ever more insane technology * § Desktop Environments (DE)/Window Managers (WM)⠀➾ o ⚓ XDA ☛ COSMIC_feels_like_the_first_Linux_desktop_designed_for normal_people⠀⇛ The world of Linux is chock-full of options users can choose from. Whether it's entirely different distros, desktops, or other customization options, there's a ton you can do to make your system work for you. But even with the overabundance of options, there's always room for a new one, and recently, we got just that in the form of COSMIC. COSMIC is a new desktop environment from System76, which develops the Pop! OS Linux distro and also makes some hardware running Linux out of the box. COSMIC is heavily inspired by GNOME, which was previously used for Pop! OS, but the changes it makes make this feel like the first Linux desktop that really feels designed for everyday, regular users. Let me explain. * § Free, Libre, and Open Source Software⠀➾ o § FSF / Software Freedom⠀➾ # ⚓ FSF ☛ Job_opportunity:_Engineering_and_Certification Manager_at_the_Free_Software_Foundation⠀⇛ The Free Software Foundation (FSF), a Massachusetts 501(c)(3) charity with a worldwide mission to promote computer user freedom, seeks a motivated and talented individual to be our new Engineering and Certification Manager. This position is ideally full-time and US-based, but exceptions can be made for a qualified candidate. The Engineering and Certification Manager reports to the executive director and takes a leadership role in managing and growing the FSF’s Respects Your Freedom (RYF) program. This role will work in close collaboration with FSF management and the technology and licensing teams. The Engineering and Certification Manager serves as a senior technical authority for the organization and is responsible for evaluating, certifying, and guiding hardware product submissions under the RYF certification requirements and other free hardware design initiatives. o § So-called 'FSFE'⠀➾ # ⚓ FSFE ☛ 2026-03-05_[Older]_22_events,_one_message: Maintainers_Matter_and_we_love_Free_Software⠀⇛ ䷩ 𝚕𝚒𝚗𝚎 10816 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/10/Using_the_Terminal_in_GNU_Linux_Coding_Scripting_Studying_Logs.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/10/Using_the_Terminal_in_GNU_Linux_Coding_Scripting_Studying_Logs.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Using the Terminal in GNU/Linux: Coding, Scripting, Studying Logs⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Mar 10, 2026 * ⚓ HowTo Geek ☛ If_you_use_the_Linux_command_line,_you’re_already programming⠀⇛ If you use Linux, chances are you're familiar with the command line. The shell is a powerful command-line interface, but you can think of running commands as a kind of programming. Here's why. * ⚓ HowTo Geek ☛ Stop_copy-pasting_commands:_How_to_make_scripts_you actually_reuse⠀⇛ Shell scripts are great, for many reasons, but one of the most tangible benefits is simple: you can stop running the same lengthy, obscure commands again and again. You might have a text file of commands you copy and paste, or you might find yourself on Stack Overflow looking up the same thing every day. Overcome these bad habits, learn how to script your shell, and reclaim some valuable time. * ⚓ HowTo Geek ☛ Stop_reading_raw_logs:_Use_these_terminal_tools_to visualize_your_data_instead⠀⇛ If you spend significant time debugging systems, analyzing servers, or reviewing application behavior, you know that logs are the most valuable and most exhausting part of your workflow. They are detailed, precise, and completely chaotic depending on your system’s temperament that day. I have stared at hundreds of GB of logs in a single session, watching lines scroll past like a waterfall. Over time, I have come across a small set of terminal tools that shift the experience from constant friction to something manageable, and at times, genuinely enjoyable. ䷩ 𝚕𝚒𝚗𝚎 10876 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/10/Web_Browsers_Curl_Blocking_HTTP1_1_and_Mozilla_Peddling_Slop_vi.shtml Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/10/Web_Browsers_Curl_Blocking_HTTP1_1_and_Mozilla_Peddling_Slop_vi.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Web Browsers: Curl, Blocking HTTP1.1, and Mozilla Peddling Slop via Firefox⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Mar 10, 2026 * ⚓ Daniel Stenberg ☛ 10K_curl_downloads_per_year⠀⇛ I held back so I never blogged and taunted OpenSSF for their scorecard attempts that were always lame and misguided. This Insights thing looks like their next attempt to “grade” and “rate” Open Source. It is so flawed and full of questionable details that I decided there is no point in me listing them all in a blog post – it would just be too long and boring. Instead I will just focus on a single metric. The one that made me laugh out load when I saw it. * ⚓ Andrew Stephens ☛ Blocking_HTTP1.1_-_Some_Results⠀⇛ I should mention that I went into this experiment with impression that almost all maintained software would be at least using the newish HTTP2.0 standard to make requests - it is officially over 10 years old as of 2026 and is widely implemented in libraries and frameworks. It turns out this assumption is very wrong. The main problems are listed below but, cutting to the chase, the relevant section of my Caddyfile now looks like this: [...] o § Mozilla⠀➾ # ⚓ Firefox_Nightly:_Hey_Hi_(AI)_Controls_–_These_Weeks_in Firefox:_Issue_196⠀⇛ ╘══════════════════════════════════════════════════════════════════════════════╛ ¶ Lines in total: 10928 ➮ Generation completed at 02:51, i.e. 78 seconds to (re)generate ⟲