Tux Machines Bulletin for Saturday, March 21, 2026
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Generated Sun 22 Mar 02:49:51 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  -  Android 'Safeguards', RISC-V, and the War on Hardware Its Owner Can Control

⦿ Tux Machines  -  Application Releases: b4 v0.15.0, DeadBeef 1.10.2, and virtnbdbackup 2.46

⦿ Tux Machines  -  Applications: Common Picks, Simple Tools, and Tiagolr Sirial

⦿ Tux Machines  -  Best Free and Open Source Software, howtos and Installations

⦿ Tux Machines  -  BSD: FreeBSD and OpenBSD Updates (OpenZFS Also)

⦿ Tux Machines  -  Games: Godot 4.6.2 RC 2, Terra Nil, OpenTTD, and More

⦿ Tux Machines  -  GNOME: This Week in GNOME, GNOME Foundation Update, and Play a Video as Lock Screen Wallpaper in GNOME

⦿ Tux Machines  -  GNU/Linux, systemd trouble, and "Clown" Computing

⦿ Tux Machines  -  Huge Growth This Year

⦿ Tux Machines  -  IBM Red Hat Selling Slop, Microsoft and GAFAM Surveillance; Fedora Update (IBM-Run Faux Community)

⦿ Tux Machines  -  KDE: Krita Monthly Report and Marknote 1.5.1

⦿ Tux Machines  -  Linux Kernel Security: Slop, "an already-flawed CVE system", and more

⦿ Tux Machines  -  Mozilla and Firefox: Nightly, Emojis, and More

⦿ Tux Machines  -  Programming Leftovers

⦿ Tux Machines  -  Programming Leftovers

⦿ Tux Machines  -  Richard Stallman at Georgia Tech, and Some of My Thoughts about Free Software

⦿ Tux Machines  -  Security Leftovers

⦿ Tux Machines  -  Standards: Open Document Format (ODF) Mandatory in Germany, Messing With Apple’s Webloc Format

⦿ Tux Machines  -  SUSE/OpenSUSE: Tumbleweed Review, Planet News Roundup, and Agama 19 Released

⦿ Tux Machines  -  Systemd-Free antiX 26 Linux Distro Is Here Based on Debian 13 “Trixie”

⦿ Tux Machines  -  These 5 settings are making your Linux PC less secure

⦿ Tux Machines  -  The Value of a Human Does Not Exceed an Elephant's

⦿ Tux Machines  -  This Week in Plasma: Time Zone Offsets and Type-Ahead on the Desktop

⦿ Tux Machines  -  Today in Techrights

⦿ Tux Machines  -  today's howtos

⦿ Tux Machines  -  Videos/Shows About GNU/Linux

⦿ Tux Machines  -  Wayland set the Linux Desktop back by 10 years

⦿ Tux Machines  -  Wine 11.5

⦿ Tux Machines  -  Zentyal Server 8.1 Development Now Available

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
https://tuxmachines.org/n/2026/03/21/Android_Leftovers.shtml
https://tuxmachines.org/n/2026/03/21/Android_Safeguards_RISC_V_and_the_War_on_Hardware_Its_Owner_Can.shtml
https://tuxmachines.org/n/2026/03/21/Application_Releases_b4_v0_15_0_DeadBeef_1_10_2_and_virtnbdback.shtml
https://tuxmachines.org/n/2026/03/21/Applications_Common_Picks_Simple_Tools_and_Tiagolr_Sirial.shtml
https://tuxmachines.org/n/2026/03/21/Best_Free_and_Open_Source_Software_howtos_and_Installations.shtml
https://tuxmachines.org/n/2026/03/21/BSD_FreeBSD_and_OpenBSD_Updates_OpenZFS_Also.shtml
https://tuxmachines.org/n/2026/03/21/Games_Godot_4_6_2_RC_2_Terra_Nil_OpenTTD_and_More.shtml
https://tuxmachines.org/n/2026/03/21/GNOME_This_Week_in_GNOME_GNOME_Foundation_Update_and_Play_a_Vid.shtml
https://tuxmachines.org/n/2026/03/21/GNU_Linux_systemd_trouble_and_Clown_Computing.shtml
https://tuxmachines.org/n/2026/03/21/Huge_Growth_This_Year.shtml
https://tuxmachines.org/n/2026/03/21/IBM_Red_Hat_Selling_Slop_Microsoft_and_GAFAM_Surveillance_Fedor.shtml
https://tuxmachines.org/n/2026/03/21/KDE_Krita_Monthly_Report_and_Marknote_1_5_1.shtml
https://tuxmachines.org/n/2026/03/21/Linux_Kernel_Security_Slop_an_already_flawed_CVE_system_and_mor.shtml
https://tuxmachines.org/n/2026/03/21/Mozilla_and_Firefox_Nightly_Emojis_and_More.shtml
https://tuxmachines.org/n/2026/03/21/Programming_Leftovers.1.shtml
https://tuxmachines.org/n/2026/03/21/Programming_Leftovers.shtml
https://tuxmachines.org/n/2026/03/21/Richard_Stallman_at_Georgia_Tech_and_Some_of_My_Thoughts_about_.shtml
https://tuxmachines.org/n/2026/03/21/Security_Leftovers.shtml
https://tuxmachines.org/n/2026/03/21/Standards_Open_Document_Format_ODF_Mandatory_in_Germany_Messing.shtml
https://tuxmachines.org/n/2026/03/21/SUSE_OpenSUSE_Tumbleweed_Review_Planet_News_Roundup_and_Agama_1.shtml
https://tuxmachines.org/n/2026/03/21/Systemd_Free_antiX_26_Linux_Distro_Is_Here_Based_on_Debian_13_T.shtml
https://tuxmachines.org/n/2026/03/21/These_5_settings_are_making_your_Linux_PC_less_secure.shtml
https://tuxmachines.org/n/2026/03/21/The_Value_of_a_Human_Does_Not_Exceed_an_Elephant_s.shtml
https://tuxmachines.org/n/2026/03/21/This_Week_in_Plasma_Time_Zone_Offsets_and_Type_Ahead_on_the_Des.shtml
https://tuxmachines.org/n/2026/03/21/Today_in_Techrights.shtml
https://tuxmachines.org/n/2026/03/21/today_s_howtos.shtml
https://tuxmachines.org/n/2026/03/21/Videos_Shows_About_GNU_Linux.shtml
https://tuxmachines.org/n/2026/03/21/Wayland_set_the_Linux_Desktop_back_by_10_years.shtml
https://tuxmachines.org/n/2026/03/21/Wine_11_5.shtml
https://tuxmachines.org/n/2026/03/21/Zentyal_Server_8_1_Development_Now_Available.shtml


                    ䷩ 𝚕𝚒𝚗𝚎 103

╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/21/Android_Leftovers.shtml
    Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/21/Android_Leftovers.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Android
Leftovers⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Rianne Schestowitz on Mar 21, 2026


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇android_phone_UI_settings⦈_


    * ⚓ Google's_24-hour_delay_for_Android_sideloading_is_really_smart_-
      Android_Authority⠀⇛


    * ⚓ How_I_turned_my_Android_tablet_into_a_portable_monitor_for_cheap⠀⇛


    * ⚓ 7_things_Android_users_need_to_know_about_the_new_sideloading_rules⠀⇛


    * ⚓ This_Android_Update_Could_Make_Your_Phone_Faster_Than_Ever⠀⇛


    * ⚓ The_next_Android_update_may_finally_undo_some_of_Google's_worst
      decisions_|_Android_Central⠀⇛


    * ⚓ I_finally_trust_voice_typing_on_Android_—_and_it's_not_because_of
      Google⠀⇛


    * ⚓ Your_Android_16_phone_has_a_serious_VPN_bug_that_could_leave_you
      exposed_–_here's_how_to_fix_it_right_away_-_PhoneArena⠀⇛


    * ⚓ Android_17_will_Make_Using_SIM_PIN_Locks_Much_More_Convenient⠀⇛


    * ⚓ Google_Messages’_Live_Location_Sharing_Feature’s_Rollout_Begins_on
      Android⠀⇛


    * ⚓ Google’s_new_Android_sideloading_includes_a_mandatory_waiting_period_|
      The_Verge⠀⇛


    * ⚓ Google_just_dropped_a_new_Android_Canary_build_–_here's_everything_it
      reveals_about_your_phone's_future_-_PhoneArena⠀⇛


    * ⚓ Google_reverses_one_of_Android’s_most_annoying_UI_changes⠀⇛




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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣥⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⢀⣀⣀⢀⣀⣽⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿⠟⠛⠉⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⢀⣠⣤⣤⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 188

╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/21/Android_Safeguards_RISC_V_and_the_War_on_Hardware_Its_Owner_Can.shtml
    Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/21/Android_Safeguards_RISC_V_and_the_War_on_Hardware_Its_Owner_Can.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Android 'Safeguards', RISC-V, and the War
on Hardware Its Owner Can Control⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Mar 21, 2026


    * ⚓ CNX Software ☛ u-blox_JODY-W6_–_NXP_IW623/AW693_tri-band_Wi-Fi_6E_and
      Bluetooth_5.4_LE_audio_modules⠀⇛


           u-blox has expanded its JODY family of modules with the NXP
           IW623/AW693-based JODY-W6 series that adds tri-band Wi-Fi 6E
           and Bluetooth 5.4 (including LE Audio) in a single package.
           There are seven product variants across five main series
           models, mainly based on NXP’s IW623 chipset for professional
           use and the AW692/AW693 for automotive use.


    * ⚓ CNX Software ☛ Enabling_MediaTek_M7902_WiFi_and_Bluetooth_drivers_on
      Ubuntu_24.04_the_easy_way⠀⇛


           Last month, we noted that Mediatek MT7902 WiFi 6E and Bluetooth
           5.x chipset finally got drivers in mainline Linux, and should
           be part of the GNU/Linux 7.0 release. MT7902 wireless modules
           are used in many backdoored Windows laptops, but users have
           been asking for the GNU/Linux drivers for almost two years now.
           One method is to wait for the drivers to find their way into
           your distribution, but “hmtheyboy154” didn’t feel like waiting
           and backported the drivers to GNU/Linux 6.6 to 6.19.


    * ⚓ Hackaday ☛ User_Repair_Of_A_Not_User-Repairable_Victron_CCGX_Issue⠀⇛


           Power banks come in many sizes, and those that target
           construction sites are probably among the largest. The massive
           four ton unit based around lead-acid batteries which the [Buy
           it Fix it] YouTube channel got handed is a good example. Inside
           it are Victron CCGX inverters among a lot of other Victron
           electronics, with the control panel for the system throwing up
           an error that was deemed to be not user-serviceable. Naturally,
           this makes for a good challenge.


    * ⚓ Hackaday ☛ Conway’s_Game_Of_Life_With_Physical_Buttons⠀⇛


           Although there is no set size for the game board, [Michal] was
           constrained by his budget for the selected NKK JB15LPF-JF
           tactile buttons, resulting in a 17×17 matrix. That’s 289
           buttons, for those keeping score, which comes down to over
           $1,000 over at e.g. Digikey even with quantity-based pricing.
           Add to this the custom PCB and a Microchip AVR128DA64 squeezed
           in a corner of said PCB to run the whole show and it’s quite
           the investment.


    * ⚓ CNX Software ☛ Certified_Android_devices_won’t_let_users_sideload_APK
      app_files_anymore,_or_at_least_it_won’t_be_straightforward⠀⇛


           Google won’t allow people to (easily) sideload apps through APK
           files on certified Android devices starting in September 2026.
           It will still be possible, but either require “developer
           verification” and an “advanced flow” for power users.


    * ⚓ Security Week ☛ In_Other_News:_New_Android_Safeguards,_Operation_Alice,
      UK_Toughens_Cyber_Reporting⠀⇛


           Other noteworthy stories that might have slipped under the
           radar: vulnerabilities found in KVM devices, Claudy Day Claude
           vulnerabilities, The Gentlemen ransomware group.


    * ⚓ Unicorn Media ☛ AlmaLinux_Kitten_Gets_Its_Claws_Into_RISC-V⠀⇛


           This week, open met open. In this case, it was open source
           software, in the form of AlmaLinux Kitten, meeting open source
           hardware, in the form of the RISC-V instruction set
           architecture.





                    ䷩ 𝚕𝚒𝚗𝚎 285

╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/21/Application_Releases_b4_v0_15_0_DeadBeef_1_10_2_and_virtnbdback.shtml
    Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/21/Application_Releases_b4_v0_15_0_DeadBeef_1_10_2_and_virtnbdback.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Application Releases: b4 v0.15.0, DeadBeef
1.10.2, and virtnbdbackup 2.46⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Mar 21, 2026


    * ⚓ LWN ☛ b4_v0.15.0_released⠀⇛


           Version 0.15.0 of the b4 patch-management tool is out.
           Highlights in this


           release include the b4 review workflow manager for maintainers


           (covered briefly in this article), b4


           dig, which can find the original mailing-list submission behind
           a


           commit, three-way-merge support in b4 shazam, and more. See the
           release


           notes for details.


    * ⚓ Ubuntu Handbook ☛ DeadBeef_1.10.2_added_MPRIS_Plugin_for_Remote
      Playback_Control⠀⇛


           DeadBeef, the lightweight music player application for Linux,
           Windows, and macOS, released new 1.10.2 version few days ago.
           This free open-source music player released version 1.10.1 last
           week with new Lyrics Viewer plugin. User can enable “Design”
           mode and add Lyrics widget to show the lyrics for the song
           being played.


    * ⚓ Michael_Ablassmeier:_virtnbdbackup_2.46_-_bitlocker_recovery_keys⠀⇛


           I’ve released virtnbdbackup_2.46 which now attempts to extract
           the bitlocker recovery keys during backup. The windows domains
           need a working qemu agent installed during backup for this to
           work.


           Using the agent, it also extracts the available guestinfo
           (network config, OS version etc..) from the domain and stores
           it alongside with the backup.





                    ䷩ 𝚕𝚒𝚗𝚎 352

╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/21/Applications_Common_Picks_Simple_Tools_and_Tiagolr_Sirial.shtml
    Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/21/Applications_Common_Picks_Simple_Tools_and_Tiagolr_Sirial.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Applications: Common Picks, Simple Tools,
and Tiagolr Sirial⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Mar 21, 2026


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Nextcloud⦈_


    * ⚓ HowTo Geek ☛ Here_are_5_apps_I_always_install_when_I_set_up_a_Linux
      desktop⠀⇛


           If you use modern technology regularly, there are doubtless
           certain apps difficult to imagine going without. In the world
           of Linux distributions, there's no universal default set of
           apps, so you sort of have to forge your own path. After
           countless Linux desktop setups, here are my software
           essentials.


    * ⚓ XDA ☛ Linux_users_swear_by_simple_tools,_and_now_I_finally_understand
      why⠀⇛


           Back when I was a full-time Windows user, I didn't understand
           why Linux users relied so much on simple tools. Friends of mine
           who used Linux would rely on tools that looked like they came
           from the Windows XP era, and when I asked them why they kept
           using them, they said it was simple, reliable, and worked. I
           didn't understand it. I liked my modern-day flashy apps.


    * ⚓ Tiagolr_Sirial:_a_free,_open-source_rhythmic_delay_plugin_(mac,_Linux,
      Win)⠀⇛


           Tiagolr Sirial is a new free, open-source rhythmic delay plugin
           for macOS, Linux, and Windows inspired by the Soundtoys EchoBoy
           Tap mode.


           The market for open-source plugins has grown significantly in
           the last two years. A major player is the developer Tiagolr,
           who has been shaking up the free plugin market since last year.
           Among other things, he released the RipplerX synth, or the
           beautiful, lush QDelay.


           He’s just pulled another delay plugin out of his creative
           pocket. Tiagolr (or short Tilr) has released Sirial, a new
           versatile rhythmic delay plugin.




⢠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣉⡉⠉⠉⠉⠉⠉⠉⠉⢉⡉⠉⠉⠉⠉⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣤⣤⣤⣤⣴⡆⠀⢰⣴⣤⣤⣤⣤⣤⣦⠀⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠈⠈⠉⠉⠉⠉⠁⠉⠀⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣿⡇
⢸⣿⠀⡇⠀⠀⠀⠀⢀⣤⣤⣤⣄⠀⠀⠀⠀⣿⣿⣶⣶⣿⣶⣿⣶⣶⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⢸⣿⢀⣃⠀⠀⠀⢀⣿⠁⠀⠀⠹⣦⡀⠀⠀⣀⠀⠀⠀⡀⠀⠀⠀⡀⢀⠀⠀⠀⠀⡀⡀⢀⡀⠀⠀⡀⣀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⢸⣿⣿⡇
⢸⣿⠀⡇⠀⠀⢰⡟⠉⠀⠀⣠⣶⣾⣿⠀⠀⠿⡿⠿⠿⠿⠟⠿⠿⠿⠿⠿⣿⠹⠿⠿⠿⠻⠿⠿⠿⠟⠿⠿⠿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠇⢸⣿⣿⡇
⢸⣿⠀⡇⠀⠀⠈⠳⠶⠶⠶⣿⣿⣿⡿⠀⠀⣤⣤⣄⣤⣤⣤⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⢸⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⣾⣿⠀⡇⠀⣨⠄⠐⢲⠀⣶⡄⣴⣤⣤⣶⣤⢰⣦⣤⢠⣤⣦⣴⣤⣤⣤⣤⣶⣶⡆⣦⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⣿⣿⠀⡇⠀⢸⠀⠈⠉⠀⠉⠀⠁⠉⠉⠉⠉⠈⠈⠁⠈⠉⠉⠉⠉⠉⠉⠁⠉⠉⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⣿⣿⠀⡇⠀⢴⠂⢈⣹⠀⣿⠆⣾⣿⡿⣶⣶⣶⡖⣟⡷⣿⡿⢾⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⡇
⣿⣿⠀⡇⠀⢸⠀⢀⣀⠀⣀⡀⣀⡀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⣀⣀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⢿⣿⠀⡇⠀⢺⠁⠠⠼⠀⠻⠃⠿⠻⠿⠿⠿⠿⠻⠟⠿⠿⠻⠟⠟⠿⠸⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇
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⢸⣿⠀⡇⠀⢹⠀⠘⠛⠀⠙⠁⠋⠛⠙⠋⠛⠙⠋⠉⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇

                    ䷩ 𝚕𝚒𝚗𝚎 442

╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/21/Best_Free_and_Open_Source_Software_howtos_and_Installations.shtml
    Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/21/Best_Free_and_Open_Source_Software_howtos_and_Installations.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Best Free and Open Source Software, howtos
and Installations⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Rianne Schestowitz on Mar 21, 2026


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Pencil⦈_


    * ⚓ 9_Best_Free_and_Open_Source_Linux_Desktop_Wiki_GUI_Notes_Apps_-
      LinuxLinks⠀⇛


           Linux is well served with note taking software, and desktop
           wiki GUI applications fill an important niche. They combine the
           convenience of a graphical interface with the organisational
           strengths of a wiki, helping users capture information and then
           expand it over time into something more coherent and
           searchable. Some emphasise simplicity and lightweight text
           editing, while others provide richer formatting, attachments,
           plugins, and more advanced notebook features.


           In this article, we focus on the best free and open source
           desktop wiki GUI note applications for Linux. These programs
           make it easy to create, organise, and navigate interconnected
           notes, offering a practical way to keep everything from
           everyday thoughts to extensive reference material in one place.


           Here’s our verdict captured in a legendary LinuxLinks-style
           ratings chart. Only free and open source software is eligible
           for inclusion here.



    * ⚓ OctoSQL_-_query_databases_and_file_formats_-_LinuxLinks⠀⇛


           OctoSQL is a query tool that allows you to join, analyse and
           transform data from multiple databases and file formats using
           SQL.


           This is free and open source software.



    * ⚓ Dentry_-_keyboard-driven_file_manager_-_LinuxLinks⠀⇛


           Dentry is a minimal, keyboard-driven file manager for Linux
           built with Qt6.


           It is designed for tiling window managers and minimalist
           desktop environments, focusing on speed, clarity, and a
           consistent dark interface without unnecessary visual clutter.


           This is free and open source software.



    * ⚓ marina_-_dataset_manager_for_robotics_-_LinuxLinks⠀⇛


           marina is a dataset manager for robotics to organize, share,
           and discover datasets and bags across storage backends so we
           can finally stop emailing download links around.


           The focus lies primarily on ROS 2 bagfiles but plain folders
           are supported as well.


           Marina automatically compresses bags when pushing and restores
           them on pull. PointCloud2 messages are compressed with
           millimetre accuracy using the embedded cloudini library. This
           massively reduces network IO — a typical bottleneck for mobile
           robots.


           Marina extends the ros2 bag CLI directly when installing for
           ROS


           This is free and open source software.



    * ⚓ cecup_-_GUI_backup_tool_based_on_rsync_-_LinuxLinks⠀⇛


           cecup is a graphical backup and directory synchronisation tool
           built around rsync.


           It is designed as an incremental backup utility with a desktop
           frontend, making rsync-based copy and sync tasks more
           accessible for users who prefer a graphical interface over the
           command line.


           This is free and open source software.



    * ⚓ Exchange_-_convert_between_XML_and_Blueprint_-_LinuxLinks⠀⇛


           Exchange is a lightweight utility designed for developers
           working with GTK user interfaces. The application helps convert
           between different GTK UI definition formats, specifically XML
           and Blueprint. This is useful when migrating projects,
           experimenting with Blueprint-based workflows, or translating
           existing GTK interface files into another representation.


           Blueprint provides a more concise and human-friendly way to
           describe GTK interfaces, while XML is widely used in existing
           GTK projects. Exchange simplifies moving between these formats
           by automating the conversion process and detecting the format
           of input files automatically. This saves developers time and
           reduces the risk of manual conversion errors.


           This is free and open source software.



    * ⚓ Feedr_-_polished_Linux_terminal-based_RSS/Atom_feed_reader_-
      LinuxLinks⠀⇛


           Feedr is a decent terminal-based news aggregator. Feedr looks
           especially strong if you’re a Linux user who prefers the
           terminal and wants a feed reader that feels modern rather than
           spartan. Feedr rivals Newsboat in many respects as the finest
           terminal news aggregator for Linux. Newsboat is the mature,
           battle-tested option, while Feedr is the rising contender with
           a more polished TUI and a nicer user experience.


           Where Feedr looks better than many other feed readers,
           especially other terminal ones, is in the combination of polish
           and pragmatism. Many terminal-based feed readers offer the
           essential functionality including fetching feeds, marking read,
           and sometimes starring items.


           Feedr adds several quality-of-life features that are especially
           useful on Linux desktops and servers: per-domain rate limiting,
           background refresh, authenticated/private feed support, config
           editing from the CLI, compact mode for small terminals, and a
           proper “What’s New” summary view for articles added since the
           last session. That mix makes it feel more mature for everyday
           use than minimal readers that are only comfortable for hobby
           use.



    * ⚓ strace-tui_-_explore_strace_output_-_LinuxLinks⠀⇛


           strace-tui is a terminal user interface (TUI) for visualizing
           and exploring strace output.


           This is free and open source software.



    * ⚓ Icebg_-_Wayland_wallpaper_setter_-_LinuxLinks⠀⇛


           Icebg is a lightweight wallpaper setter for Wayland
           compositors.


           Written in Rust, it uses iced and the layer-shell protocol to
           display a wallpaper as a background surface, with support for
           hot-reloading configuration changes and targeting a specific
           monitor. The project is aimed at users who want a small,
           compositor-friendly wallpaper tool rather than a full wallpaper
           daemon.


           This is free and open source software.



    * ⚓ assh_-_make_your_ssh_client_smarter_-_LinuxLinks⠀⇛


           assh is a transparent wrapper for SSH that makes client
           configuration more powerful and easier to manage.


           It extends the standard SSH workflow with support for YAML-
           based configuration, aliases, regex host matching, gateway
           chaining, inheritance, variable expansion, JSON output, and
           Graphviz visualisation, while continuing to work seamlessly
           with tools such as ssh, scp, rsync, and git.


           This is free and open source software.




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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 682

╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/21/BSD_FreeBSD_and_OpenBSD_Updates_OpenZFS_Also.shtml
    Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/21/BSD_FreeBSD_and_OpenBSD_Updates_OpenZFS_Also.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ BSD: FreeBSD and OpenBSD Updates (OpenZFS
Also)⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Mar 21, 2026,
updated Mar 21, 2026


    * ⚓ MWL ☛ FreeBSD_security_report_on_successful_logins⠀⇛


           I don’t care about poorly-programmed password gropers fumbling
           at a service that doesn’t accept passwords. I don’t want to
           read pages of stupidity. Over the years I’ve trained myself to
           skip the stupidity, which is bad practice. If I get automated
           email it better contain only things I care about.


           I care about successful logins. The number of folks who log
           onto my hosts is minuscule. I want to skim a short list of
           logins, recognize them all, and move on with my day.


    * ⚓ Undeadly ☛ Pledge_changes_in_7.9-beta⠀⇛


           David Leadbeater (dgl@) posted to ports@ a message, entitled
           Pledge changes in 7.9-beta, which explains the consequences for
           porters of the recent pledge(2)/unveil(2) changes in -current
           (and, to some extent, 7.8). Whilst targeted at porters, it
           provides a good overview for anyone interested in the changes.


    * § Career/Education⠀➾


          o ⚓ MWL ☛ Talking_at_NYCBUG_1_April_2026⠀⇛


                 I’ll be presenting “What’s Changed Since The Last Time I
                 Came this Way – a talk that was supposed to be about
                 OpenZFS.”





                    ䷩ 𝚕𝚒𝚗𝚎 736

╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/21/Games_Godot_4_6_2_RC_2_Terra_Nil_OpenTTD_and_More.shtml
    Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/21/Games_Godot_4_6_2_RC_2_Terra_Nil_OpenTTD_and_More.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Games: Godot 4.6.2 RC 2, Terra Nil,
OpenTTD, and More⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Mar 21, 2026


    * ⚓ Godot Engine ☛ Release_candidate:_Godot_4.6.2_RC_2⠀⇛


           Once more for good measure!


    * ⚓ Pi My Life Up ☛ Cup_and_Counter_Dev_Blog_#2⠀⇛


           In this blog, we will explore some of the changes we have made
           to improve our coffee shop simulator over the last week. This
           particular week was very heavy on implementation and polishing.


           For example, the traffic light system that we showed off in the
           previous dev blog now actually functions. On top of this, there
           has been a lot of work to help improve the facades of our
           buildings.


    * ⚓ GamingOnLinux ☛ Environmental_strategy_game_Terra_Nil_gets_gamepad
      support_and_Steam_Deck_Verified_|_GamingOnLinux⠀⇛


           Terra Nil is an absolute joy, an environmental strategy game
           about bringing the wastes back to life and now it's Steam Deck
           Verified with gamepad support. The update just launched today,
           which is also the final update for the game as it's considered
           complete now.


    * ⚓ GamingOnLinux ☛ Get_some_quality_chess_games_and_female-fronted_games
      across_two_Humble_Bundles_|_GamingOnLinux⠀⇛


           Another couple of chances to grab some good games here, as
           Humble Bundle recently launched another two stacked bundles
           filled with goodies.


    * ⚓ GamingOnLinux ☛ RTS_fans_absolutely_need_to_check_out_D.O.R.F._Real-
      Time_Strategic_Conflict_|_GamingOnLinux⠀⇛


           Am I in love? I think I am. D.O.R.F. Real-Time Strategic
           Conflict is an upcoming retro-infused RTS game that looks
           absolutely incredible. First covered on GamingOnLinux by yours
           truly all the way back in 2023, I've been waiting what feels
           like a lifetime for more information on this one.


    * ⚓ GamingOnLinux ☛ Vampire_Crawlers:_The_Turbo_Wildcard_from_Vampire
      Survivors_arrives_April_21_|_GamingOnLinux⠀⇛


           Will lightning strike twice for developer poncle? We're going
           to find out when Vampire Crawlers: The Turbo Wildcard from
           Vampire Survivors releases April 21st.


    * ⚓ GamingOnLinux ☛ OpenTTD_devs_clarify_store_changes_with_Transport
      Tycoon_Deluxe_re-release_as_Atari_contribute_server_funding_|
      GamingOnLinux⠀⇛


           The OpenTTD developers have released a statement to clarify
           some confusion and misinformation on the Transport Tycoon
           Deluxe re-release from Atari. As covered recently on
           GamingOnLinux, if you want to grab OpenTTD from GOG or Steam
           now, you have to actually buy the classic Transport Tycoon
           Deluxe. This does not affecting grabbing it from their website
           directly.


    * ⚓ GamingOnLinux ☛ The_Darkside_Detective:_Backside_of_the_Moon_gets_a
      first_demo_|_GamingOnLinux⠀⇛


           Ready for some more investigating? The Darkside Detective:
           Backside of the Moon from Spooky Doorway has a first demo
           available with Linux support.


    * ⚓ GamingOnLinux ☛ Steam_Spring_Sale_2026_is_live_-_here's_some_indie_gems
      to_pick_up_|_GamingOnLinux⠀⇛


           Another big event is here with the Steam Spring Sale 2026 - and
           you know the drill, lots and lots of games have some pretty
           juicy discounts. You all probably have a big wishlist full of
           what you want already right? And a Steam Library filled with
           games you're still yet to even click play on I bet. I know it's
           not just me.


    * ⚓ GamingOnLinux ☛ SteamOS_3.8.0_Preview_brings_initial_Steam_Machine
      support,_and_improvements_for_many_handhelds_|_GamingOnLinux⠀⇛


           SteamOS 3.8.0 Preview is another big upgrade for Valve's Linux
           distribution, with lots of enhancements to hardware support
           across the board for handhelds. This also includes initial
           support for the Steam Machine, not that any of us actually has
           one yet but Valve are clearly working towards getting
           everything ready for it.


    * ⚓ GamingOnLinux ☛ New_Steam_Beta_can_run_the_Linux_client_inside_a
      container_with_64bit_|_GamingOnLinux⠀⇛


           Valve have been cooking! A new Steam Client Beta is available
           with something quite special for Linux gamers, as Valve work to
           continue improving Linux gaming.





                    ䷩ 𝚕𝚒𝚗𝚎 869

╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/21/GNOME_This_Week_in_GNOME_GNOME_Foundation_Update_and_Play_a_Vid.shtml
    Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/21/GNOME_This_Week_in_GNOME_GNOME_Foundation_Update_and_Play_a_Vid.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ GNOME: This Week in GNOME, GNOME Foundation
Update, and Play a Video as Lock Screen Wallpaper in
GNOME⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Mar 21, 2026


    * ⚓ This Week in GNOME ☛ This_Week_in_GNOME:_#241_Fifty!⠀⇛


           Update on what happened across the GNOME project in the week
           from March 13 to March 20.


           This week we released GNOME 50!


    * ⚓ GNOME ☛ Allan_Day:_GNOME_Foundation_Update,_2026-03-20⠀⇛


           Hello and welcome to another update on what’s been happening at
           the GNOME Foundation. It’s been two weeks since my last update,
           and there’s been plenty going on, so let’s dive straight in.


    * ⚓ Ubuntu Handbook ☛ Play_a_Video_as_Lock_Screen_Wallpaper_in_Ubuntu_
      (GNOME)⠀⇛


           Want to set a video as animated background for your lock
           screen? Here’s an extension to do the job for GNOME. For GNU/
           Linux desktop, there’s a free open-source python app to set
           video wallpaper. Now there’s a new app to do the job for the
           lock screen, though only for Gnome.





                    ䷩ 𝚕𝚒𝚗𝚎 916

╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/21/GNU_Linux_systemd_trouble_and_Clown_Computing.shtml
    Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/21/GNU_Linux_systemd_trouble_and_Clown_Computing.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ GNU/Linux, systemd trouble, and "Clown"
Computing⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Mar 21, 2026


    * ⚓ It's FOSS ☛ Systemd’s_New_Feature_Brings_Age_Verification_Option_to
      Linux⠀⇛


           The optional birthDate field gives other projects a
           standardized data source for age verification compliance.


           [...]


           systemd, the init system and service manager used by most major
           Linux distributions, has made a change tied to this whole
           situation, but it is probably not what you are imagining.


    * § Server⠀➾


          o ⚓ Kubernetes Blog ☛ Announcing_Ingress2Gateway_1.0:_Your_Path_to
            Gateway_API⠀⇛


                 With the Ingress-NGINX retirement scheduled for March
                 2026, the Kubernetes networking landscape is at a turning
                 point. For most organizations, the question isn't whether
                 to migrate to Gateway_API, but how to do so safely.


                 Migrating from Ingress to Gateway API is a fundamental
                 shift in API design. Gateway API provides a modular,
                 extensible API with strong support for Kubernetes-native
                 RBAC.


          o ⚓ Kubernetes Blog ☛ Running_Agents_on_Kubernetes_with_Agent
            Sandbox⠀⇛


                 The landscape of artificial intelligence is undergoing a
                 massive architectural shift. In the early days of
                 generative AI, interacting with a model was often treated
                 as a transient, stateless function call: a request that
                 spun up, executed for perhaps 50 milliseconds, and
                 terminated.


                 Today, the world is witnessing Hey Hi (AI) v2 eating Hey
                 Hi (AI) v1. The ecosystem is moving from short-lived,
                 isolated tasks to deploying multiple, coordinated Hey Hi
                 (AI) agents that run constantly. These autonomous agents
                 need to maintain context, use external tools, write and
                 execute code, and communicate with one another over
                 extended periods.


    * § Audiocasts/Shows⠀➾


          o ⚓ Hackaday ☛ Hackaday_Podcast_Episode_362:_Compression_Molding,
            IPv4x,_And_Wired_Headphones⠀⇛


                 To the hacks, and we have some good ones. An air hockey
                 robot might not seem like a challenge, but the
                 engineering which went into [BasementBuilds’] one proves
                 it’s not a job for the faint hearted. Then we look at
                 compression molding of recycled plastic using 3D-printed
                 molds, something that seems surprisingly accessible and
                 we’d like to try, too. We’ve got a new DOS, a 3D-printed
                 zipper repair, the IPv4 replacement we didn’t get, and
                 the mind-bending logic of ternary computing. It’s one of
                 those weeks where the quick hacks could all deserve their
                 own in-depth look, but perhaps the stand-outs are and
                 Arduino style compiler that includes the source code
                 compressed within the binary, and a beautifully-done
                 revival of a 1980s brick cellphone as a modern 5G unit.


    * § Distributions and Operating Systems⠀➾


          o § Debian Family⠀➾


                # ⚓ Raspberry Pi ☛ New:_Remote_updates_on_Raspberry_Pi
                  Connect⠀⇛


                       Now it’s time to take the next step in the
                       evolution of Raspberry Pi Connect. For the last six
                       months, we’ve been working away at a brand-new
                       capability: remote updates. The goal is simple
                       enough — to make updating the software on your
                       devices as straightforward and convenient as
                       possible.


          o § Canonical/Ubuntu Family⠀➾


                # ⚓ Ubuntu ☛ Introducing_MicroCloud_Cluster_Manager⠀⇛





                    ䷩ 𝚕𝚒𝚗𝚎 1037

╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/21/Huge_Growth_This_Year.shtml
    Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/21/Huge_Growth_This_Year.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Huge Growth This
Year⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Mar 21, 2026,
updated Mar 21, 2026


                      🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Plant_growing⦈_


Despite the LLM woes that are said to hurt many sites, this year we've managed
to publish a lot of original material, add many pages with links to legitimate,
human-composed articles (we_do_not_tolerate_slop), and also enjoy life with a
lot of time outdoors.


Yesterday our server served over 2 million requests and today (so far) it looks
like it'll exceed 3 million.


The more messy the Web becomes, the more people will need to rely on strict
curation services which cull the slop and cluster together the real news. Slop
online has only made us more relevant, more necessary to people fed up with so-
called 'AI'. █




⢀⡶⠄⢠⣼⢯⡵⢨⣧⣲⠌⠜⢙⣀⣠⠀⡉⠀⠀⠀⢳⣞⣓⠉⠉⠀⠀⠙⠂⢢⠈⡁⢿⡿⣆⠛⣿⠷⡏⠄⣽⣋⣉⣿⣿⣿⣶⣽⠿⢿⣿⣿⣹⣗⣿⣿⣿⡿⠗⠿⣷⡾⠟⠟⣝⡖⠀⣴⣶⡀⣠⣿⣿⣿⡉⠀⠀⠀
⣺⣥⠟⠂⠀⠞⠊⠸⠛⢏⠀⠤⠨⠀⢠⠀⠑⠐⡢⡀⠟⠿⠿⣶⡇⠀⢶⡾⠯⡏⠝⠧⢭⣝⡟⠂⠊⠋⢉⠊⠡⠀⣿⣿⠯⣼⣿⡿⡶⡍⠿⡿⡿⠧⡭⠋⠀⢤⢄⠀⠀⠀⠄⠠⠋⠀⠀⠾⠄⠈⠙⣷⠦⠙⣶⠺⠲⠶
⠀⠄⠀⠁⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠠⡷⠀⠀⠙⠁⠀⠀⣖⣿⠋⠘⠀⠀⠶⠉⠀⠄⢰⢠⡠⠀⠀⠒⠂⠀⠠⢀⠅⣠⣄⣈⠫⠀⠀⠁⠀⠀⠠⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡈⠁⢰
⣤⣤⣿⣿⣿⠀⢀⣠⣥⣤⢀⠀⠀⠀⠀⢁⡂⠂⠀⠀⠰⣿⡿⣿⡶⠃⠀⠀⠀⢀⠀⠀⢠⡼⠀⠀⠀⠀⢸⡅⠀⠰⣼⣿⣿⡏⠁⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣶⣦⡀⠀⠀⠀⠀⠈⠁⠀⠀⣢⣴⣿⠟
⠽⠟⠛⠙⠻⡇⠈⠛⠿⣿⣧⡀⠄⠀⠀⠈⠀⠀⠀⠀⠀⠔⣷⣶⣤⡗⠀⠀⠀⠈⠒⠀⠀⠀⠀⠁⠀⠀⠈⣁⠀⠘⠟⠛⠋⠀⠀⠀⠀⠀⣤⣄⣦⠀⠀⠀⠀⠀⢀⡤⢠⣬⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⣧⣿⢌
⢀⡂⠀⠀⠀⠀⠀⠁⡀⠱⡅⣀⠠⡆⠀⠀⠀⢀⣄⡀⢀⣤⣼⠇⠈⠉⠀⠠⠐⠀⠀⣤⣄⠀⠀⠶⠀⢥⣄⣀⢀⢄⠀⠀⠀⠠⠄⡀⣤⠐⣯⡉⠙⠀⠀⠀⢀⣤⣸⣤⣤⣥⡄⣀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠁⢈⣍⣼⠉
⢸⡄⠀⢠⣔⠀⠀⠀⡀⠀⣬⡀⢈⢿⣶⣤⡀⠀⠈⢰⣌⠝⢉⣼⣿⣇⣀⣶⣿⣧⣥⣍⠿⠀⠀⠀⠀⠁⠠⣾⠋⣤⣦⠀⢒⣴⣾⣶⠨⣈⣧⣷⣑⠶⣠⡄⢀⣛⡟⠛⠋⢹⢯⢾⡦⠀⠀⣈⠁⠀⠀⢴⣥⠾⢙⣟⠀⣀
⠿⢿⡆⠾⠏⡤⠀⠀⠑⠆⢉⡛⠺⡽⢮⣿⣿⣿⡔⠀⢁⣵⣾⣿⣿⡷⢠⣏⡙⣿⣻⠿⡤⣾⣾⢟⡌⣀⡀⠈⣍⡫⣐⣌⠘⠛⠿⣗⢡⣻⣾⣿⣅⣐⠂⠀⠪⠾⠷⣖⠐⡂⢀⣤⡌⣀⠸⣁⠀⠒⡶⣶⣶⣿⣿⡿⣯⣭
⣿⡿⡛⡯⠐⠀⠀⢄⢈⢈⣛⠩⣂⠙⢿⣉⠿⣷⣤⢈⣉⣿⣿⣿⣟⣿⣞⣙⣛⣟⣛⣿⠿⡿⣷⡎⣇⠙⢻⣧⠜⠘⡷⡍⡀⣺⣒⠀⢾⣷⣿⣿⢿⣟⠁⠀⠀⠀⠐⠮⠠⣵⣴⣶⠶⠿⣿⡭⠁⡜⠰⠈⣉⣛⣿⡲⢷⣾
⠈⠻⣾⣯⠀⢀⡘⠏⠁⣉⠀⠈⠁⠀⢆⣭⣙⣛⡻⠏⣸⣿⣿⠟⢿⣿⣿⡏⠐⢗⣛⠀⠀⠀⠿⡿⡼⣺⣿⣾⣷⠆⢠⠀⠀⠉⠁⢖⢘⠋⠀⠘⠈⣁⠀⠀⠀⠂⠲⣆⣀⣽⣸⣶⠶⡂⠲⢀⠀⠀⠀⡠⣉⢫⠷⣶⣾⣿
⣦⣿⠏⠙⣇⠀⠐⣀⢔⣿⡿⠁⢀⣠⣶⡟⠈⢩⡫⣐⠻⠟⠋⠘⠍⢻⣿⣾⠇⢸⡌⢴⣥⡄⠀⠀⠘⠙⢛⣯⣭⣧⡈⠙⠀⢠⠠⠈⡉⠀⠀⠀⢠⡷⠀⢐⢍⣵⣤⣛⣻⣿⣟⡻⢷⣮⢵⣬⣯⣅⢬⣿⡿⣭⢹⣷⣼⣧
⢛⠨⢷⠧⠭⢁⢙⠈⠛⣉⣁⠀⠀⠀⠀⠀⠀⠀⠌⢀⠛⣄⠀⠀⠀⠈⢢⣕⠢⢰⠬⣀⣉⡀⢀⣴⣦⡼⣿⣿⣿⣿⡿⠀⠸⠿⠿⢄⣠⣤⣰⣴⣆⣺⣆⣀⣶⣿⣿⠿⢿⢿⣧⣶⣾⣿⣿⣿⣞⣋⣽⢟⣀⡉⣶⡦⢝⣿
⡶⣶⠆⣤⣎⠿⠿⡄⠸⣿⢿⡸⣶⠄⡘⠑⣳⣻⣗⢲⣞⣺⣛⣳⣌⠁⠀⢉⣁⡀⠦⣬⣷⣆⠸⣿⣿⣿⣿⣿⡍⠉⠀⠀⠀⠀⠠⠶⠟⠛⠲⣞⠿⠯⣟⣲⣦⣻⣴⣮⠀⠤⠅⠩⢽⡋⠙⣿⣏⠛⢿⠟⢿⡿⡿⡿⡿⡿
⢺⣿⣶⣶⣾⢿⠴⠺⣧⡀⡀⣀⢰⡴⡀⠄⣠⣙⠻⢶⡾⡗⣞⣯⣽⣓⢦⣼⣿⠛⠂⠸⠯⣽⣿⣿⣿⠻⣿⣿⣧⠀⠈⢉⢑⡂⠀⠀⣃⣾⣖⠋⣭⡚⣿⣿⣿⣿⣷⠞⣇⣴⣵⣌⣴⣿⢋⣉⣻⣾⣿⣷⣶⣤⣌⡤⣥⣄
⢿⣿⣷⣤⣭⣓⢠⡀⠀⡑⣿⣻⣿⠗⠁⠹⣛⣘⣸⣜⡉⢾⣕⣽⣿⡿⢯⣎⢻⣦⡰⠆⡢⣿⣿⣿⣿⣿⣦⣿⡿⠀⣷⣶⣿⡿⠻⣦⡈⠉⣻⠁⣐⣘⣙⠛⣷⣟⣿⣿⡿⣿⣿⣿⣽⡾⣿⣿⠛⣻⣿⣿⣷⡿⢿⣿⢋⡲
⡂⢘⣟⡻⣿⡥⡧⠟⠀⣝⢍⡠⣤⣔⡶⡶⠑⠭⡨⠖⠙⠂⠘⠟⢛⣧⣬⣟⢾⠛⣻⣦⣄⢘⣿⣟⡟⣿⣿⣿⣿⣷⣝⣉⣤⣴⣆⣟⠿⣧⢿⢿⣿⣿⡿⡘⣿⣦⣿⣷⣿⣿⣾⣾⣯⢿⣿⣿⣦⣿⣿⣿⣿⣷⣿⣶⣿⣿
⡟⠀⠛⢿⣾⣇⠛⠃⠹⠡⢾⠾⢛⣛⢁⣨⠴⠶⢾⣿⠿⠄⡌⢷⡶⠠⣌⣹⣷⣷⣲⣯⣭⣿⣽⣯⣿⡿⢿⢿⠛⡋⠀⠹⠿⠟⠙⠋⠁⠙⣭⡷⢢⣵⡵⢖⣽⠿⠟⠡⣿⣻⣿⣷⡟⠻⠻⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⢀⠙⢛⡛⢃⣀⢔⣰⢷⡻⠿⠋⡆⠢⣿⣿⡍⣬⣅⣄⣹⢦⣸⣿⣿⣿⠛⢯⡭⢾⠻⠥⣷⣷⣯⣦⠀⠼⠻⡓⠒⢠⢷⣠⠶⢑⣾⢺⢾⣿⣷⣿⣻⣛⡳⣈⡒⢲⡦⠍⣸⣟⢷⠀⢀⣌⠛⢿⠹⢟⠩⠗⢐⠺⣋⠍
⠀⢩⢟⠾⡶⠠⣩⠤⣀⣽⣄⢩⣭⣼⣷⣮⡌⣷⣻⠻⣼⣟⣿⣿⣾⣻⠟⠥⣽⠻⣿⢻⡙⣶⣶⣶⠁⠛⣀⢖⡛⣿⣴⣾⣿⡙⣿⣿⣿⠟⠛⢀⣩⣃⡉⠩⢭⣷⣏⣿⣷⡋⠉⢁⣠⠀⣀⣝⣯⠂⠀⠉⣨⣾⡏⠀⣿⣿
⠻⠟⣯⣶⣦⢈⠿⣷⣁⠙⣿⠿⠛⣿⡿⢿⠟⠛⣏⣯⣑⣆⣭⣿⠿⣯⢿⠻⠷⠿⠋⢏⡏⠻⣬⣧⣦⣦⡼⠿⠆⢱⣟⣟⠿⢾⣿⣿⡿⠲⡞⣛⣿⣿⢯⢚⢛⣿⢮⣵⣿⣟⡯⣿⢥⢃⡞⣛⡾⣦⣈⣨⣿⢻⣤⡀⠿⢟
⠀⡀⢘⣿⣯⣽⡿⡛⠉⠉⢁⡀⣠⢈⡉⢷⣶⣤⣤⣺⣭⣥⣽⣿⣖⣿⣾⡻⡏⢱⣶⣖⠚⡵⢟⢻⣿⣻⡦⣴⣂⢉⡩⠑⢚⣿⣿⣿⣗⣤⣿⡿⡿⣿⣺⣼⡞⣿⣧⣿⣿⣿⣷⣻⣀⣤⣴⣻⣶⣴⣶⡿⠟⠂⣺⡵⠺⡽
⣯⣐⣭⡀⠉⠍⣀⠐⢲⣤⡯⢻⣿⣵⢁⣠⡋⣃⠠⣀⣬⢱⡿⠼⢟⡹⣯⣛⣽⣻⡮⣭⣡⡴⡼⣥⣿⣿⢯⣿⣾⣿⡿⠿⡄⢨⣿⣿⣿⣷⢿⠏⢜⣚⣿⣧⣯⣛⡛⠻⣿⣿⣿⡅⠿⠛⠲⡿⣿⡮⠻⠁⠀⠸⣿⣼⣆⡰
⣶⣟⠻⢯⣡⣤⠀⢀⣴⣿⡐⣆⢨⣽⣿⣽⣿⣷⣷⣶⣌⠸⢾⣐⠟⠿⣷⡏⡾⡿⣭⣯⣍⢹⠳⣇⠱⠛⢿⡏⠈⠻⠷⢯⣷⣆⣾⣿⣿⣿⣶⣟⠢⡸⠻⢿⣿⣿⣿⣿⣻⣿⣿⣿⣯⣿⣿⡾⠏⠀⠀⠀⠀⠀⠀⣴⣞⢏
⠠⢶⣾⢾⢿⣿⣦⢬⢿⡿⡯⣿⣿⡿⠻⣿⣾⣽⣿⣿⣿⡆⠀⠀⠳⠾⣿⣍⣿⣏⡟⢿⣴⡮⡉⢽⡂⠀⠈⢿⣎⢰⢶⣽⣿⣇⠈⡿⣿⣿⣭⣟⠂⣹⣿⣿⣿⣿⠿⢿⣿⣿⣿⣷⡍⢛⠙⢿⣧⣀⡀⠸⡈⠁⠀⠚⠁⢰
⢘⣾⣿⣬⣽⡏⢿⣌⠡⠙⢻⣿⣿⣑⣿⣿⠻⢿⠿⠋⠩⡁⠀⠀⠐⠹⣯⣿⣭⣷⣶⣎⣅⣿⣿⡚⠷⢓⣾⣭⣻⡄⡹⢘⡚⠷⢷⣜⣓⣤⠷⣡⣿⣿⣿⣿⣿⣽⣷⣿⣿⣿⣟⡻⣦⠀⠀⢂⣿⡿⣦⣤⣷⣀⣿⠷⣤⣾
⢀⢨⣉⢍⣯⡷⣿⡧⡭⠆⣻⣿⢿⣿⠛⠛⢀⣨⣦⠴⠀⡿⣆⣀⠠⣤⣾⢿⠿⣿⣿⣿⣏⢹⠟⡞⠳⠿⣟⣽⣿⣿⡁⣞⣹⣴⣘⣿⣿⢻⣿⣿⣿⣽⣟⢛⣿⣯⣿⣿⣿⣻⣿⣹⣩⣁⣘⣛⡻⢿⣿⡿⣿⣧⣽⣿⣿⣿
⢁⢻⣏⣛⣁⣠⠙⣃⣠⣌⣿⣟⡺⠿⢧⣬⡿⣿⣿⣿⣻⣿⣟⡊⣀⣽⡿⠖⢖⠛⠛⠋⡾⠀⢸⣷⣯⣶⡟⠛⢿⣷⣷⣶⣿⣭⣿⣿⣿⣿⣻⣯⣷⣿⣷⣾⣷⣶⣾⣿⣿⣾⣿⣿⣿⣿⣿⣯⣿⣷⣏⣿⣿⣿⣿⣿⠉⠉
⠘⠛⢿⣟⠟⢿⠛⢛⢻⣻⣯⣿⣿⣷⣶⣬⣟⠿⣿⣷⣷⠹⠻⠷⠔⣀⣠⣄⣾⠷⠠⡦⢠⣴⣴⣿⣶⣷⣿⣿⠨⣿⠯⢘⡍⠿⣿⣿⣿⣿⣽⣿⢿⣿⡿⣿⡿⣿⣿⣿⣧⣯⣍⡿⢿⠿⢿⣿⣿⣟⣏⡈⠛⠿⠿⢵⢫⣿
⢀⣶⡂⢠⣼⢯⡵⢨⣧⣶⠈⠜⢙⣀⣠⠀⡉⠀⠀⠀⢳⣞⣓⠉⠉⠀⠀⠙⠂⢠⠈⠁⢿⡿⣆⠛⣿⠷⡏⠄⣽⣋⣉⣿⣿⣿⣶⣽⠿⢿⣿⣿⣹⣗⣿⣿⣿⡿⠗⠿⣷⡾⠟⠟⣝⠖⠀⣴⣶⠀⣠⣿⣿⣿⡉⠀⠀⠀
⣺⣥⡟⠂⠀⠞⠊⠸⠛⢏⠀⠤⠨⠀⢀⠀⠁⠐⡢⡀⠟⠿⠿⣶⡇⠀⢶⡶⡯⡏⠝⠣⢭⣝⡟⠂⠊⠋⢉⠊⠡⠀⣿⣿⠟⣼⣿⡿⡶⣅⠿⡿⡿⠧⡭⠋⠀⢤⢄⠀⠀⠀⠤⠠⠋⠀⠀⠾⠄⠈⠙⣷⠦⠙⢷⠺⠲⠶
⠀⠄⠀⠁⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠠⡷⠀⠀⠙⠁⠀⠀⣖⣿⠋⠘⠀⠀⠺⠉⠀⠄⢰⢠⡠⠀⠀⠒⠃⠀⠠⢀⠅⣠⣄⣈⡻⠀⠀⠁⠀⠀⠠⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡈⠁⢠
⣤⣤⣿⣿⣿⠀⢀⣠⣤⣤⢀⠀⠀⠀⠀⣁⡀⠂⠀⠀⠰⣿⡿⣿⠶⠃⠀⠀⠀⢀⠀⠀⢠⡾⠀⠀⠀⠀⢸⡇⠀⠰⣾⣿⣿⡏⠁⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣶⣦⡀⠀⠀⠀⠀⠈⠁⠀⠀⣢⣴⣿⠟
⠽⠛⠛⠙⠻⡇⠈⠛⠿⣿⣧⡀⠄⠀⠀⠈⠀⠀⠀⠀⠀⠔⣷⣶⣤⡗⠀⠀⠀⠈⠒⠀⠀⠀⠀⠁⠀⠀⠈⣀⠀⠐⠟⠛⠋⠀⠀⠀⠀⠀⣤⣄⣦⠀⠀⠀⠀⠀⢀⡤⢠⣬⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢛⣧⣷⢄
⢀⡂⠀⠀⠀⠀⠀⠁⡁⠰⡇⣀⠠⡆⠀⠀⢀⢀⣄⡀⠀⣤⣼⠇⠈⠉⠀⠠⠒⠀⠀⣤⣄⠀⠀⠴⠀⢥⣄⣀⢀⢄⠀⠀⠀⠠⠄⡀⣤⠰⣯⡉⠙⠀⠀⠀⣀⣤⣸⣤⣤⣥⡄⣀⠀⠀⠀⠀⡀⠀⠠⠀⠐⠁⢈⣍⢼⠉
⠸⡀⠀⢠⣔⠀⠀⠀⡀⠀⣬⡀⢈⢿⣶⣤⡀⠀⠈⢠⡨⠝⢉⣼⣿⣇⣀⣶⣾⣦⣭⣍⠿⠀⠀⠀⠀⠁⠠⣾⡛⣤⣶⠀⢒⣴⣾⣶⠨⣈⣧⣧⣐⠶⣠⡄⢀⢛⡟⠛⠋⢹⢯⢷⡦⠀⠀⣈⠁⠀⠀⣰⣭⠾⢓⣟⠀⣀
⠿⢿⡆⠾⠏⡤⠀⠀⠑⠆⢉⡛⠻⣟⢮⣿⣿⣿⡔⠀⢁⣵⣾⣿⣿⡷⢠⣍⡙⣿⣻⠿⠤⣾⣾⢟⡌⣀⡀⠈⣍⡯⣐⣌⠘⠛⠿⢗⢡⣛⣾⣿⣅⣐⠀⠀⠪⠾⠷⣖⠐⡂⢀⢤⡌⢀⠘⣁⠀⠒⡶⣶⣶⣿⣿⡿⣯⣭
⣿⡿⡋⡯⠐⠀⠀⢄⠈⢈⣛⠩⣂⠉⢿⣋⠿⣷⣤⢈⣩⣿⣿⣿⣿⣿⣞⣙⣛⣟⣛⣿⠿⡿⣷⡎⣇⠙⢻⣧⠝⠘⡔⡍⡠⣺⣓⠀⢾⣷⣿⣿⢿⣟⠁⠀⠀⠀⠐⠮⠠⣵⣴⣶⠶⠿⣿⡭⠁⡜⠀⠨⣉⣻⣿⡲⢷⣾
⠈⠻⣾⣯⠀⢀⡘⠟⠁⢉⠀⢈⠀⠀⢆⣭⣑⣛⡻⠿⣼⣿⣿⠟⢻⣿⣯⡏⠐⢗⣛⠀⠀⠀⠟⡿⡾⣺⣿⣿⣷⠆⢠⠀⠀⠉⠉⢖⢘⠋⠀⠘⠊⣁⠀⠀⠀⠂⠲⣄⣂⣽⣸⣶⠦⡀⠴⢀⠀⠀⠀⡠⣉⢫⡗⣶⣾⣿
⣢⡿⠏⠙⣇⠀⠐⣀⢔⣿⡿⠁⠀⣤⣶⡏⠈⠩⡫⡐⠻⠟⠋⠘⠍⢻⣿⣾⠇⢘⡌⢴⣵⣄⠀⠀⠘⠙⢛⣯⣭⣧⡈⠑⠀⢠⠠⠈⡙⠀⠀⠀⢠⡷⠀⢐⢍⣵⣤⣛⣻⣿⣟⣻⢷⣮⢵⣬⣯⣁⢬⣿⡟⣯⠹⣷⣼⣧
⠛⠹⢿⠥⠭⢂⢙⠀⠛⣙⣁⠀⠀⠀⠀⠀⠀⠀⠌⢀⠚⣄⠀⠀⠀⠈⢢⣕⢢⢰⠬⣀⣉⡀⢀⣴⣤⡼⣿⣿⣿⣿⡿⠀⠸⠿⠿⢄⣠⣤⣰⣴⣆⣺⣆⣀⣴⣿⣿⠿⡿⢿⣧⣶⣾⣿⣿⣿⣞⣏⣽⢟⣀⡩⣶⡦⢙⣿
⡾⣶⠆⡤⡎⠿⠿⡀⠸⣿⢿⡸⣶⡄⠘⠑⣳⣻⣗⢳⣞⣺⣛⣳⣌⠁⠀⢉⣁⡀⢦⣬⣷⣆⠸⣿⣿⣿⣿⣯⡍⠉⠀⠀⢀⡀⠠⠶⠟⠛⠳⣊⡿⠯⡟⣓⣦⣻⣴⣮⠀⠤⠅⠩⢭⣏⠙⣯⣏⠛⢿⠟⢿⡿⡿⡿⡿⡿
⢺⣿⣶⣶⣾⢿⠴⠺⣧⡀⡀⣀⢴⡴⡀⠄⣰⣙⠛⢶⡾⡗⣞⣧⣿⣓⢦⣼⣿⠛⠂⠸⠯⣿⣿⣿⣿⠻⣿⣿⣧⠀⠈⢉⢑⡂⠀⠀⣃⣾⣖⠋⣭⡚⣾⣿⣿⣿⣷⠞⣇⣄⣵⣌⣴⣿⢋⣉⣻⣾⣿⣷⣶⣤⣄⡤⣥⣄
⢿⣿⣷⣤⣥⣓⢠⡀⠀⡑⣿⣻⣿⠗⠁⠹⣓⣘⣸⣜⡉⠿⣝⣿⣿⡿⢯⣎⢻⣤⣰⠆⡢⣿⣿⣿⣿⣾⣦⣿⡟⠀⣷⣶⣿⡿⠻⣦⡨⠉⣻⠁⢐⣘⣙⠹⣿⣿⣿⣿⡿⣿⣿⣻⣿⡞⣿⣿⠛⣻⣿⣿⣷⡿⢿⣿⢋⠲
⡂⢘⣟⡻⣿⡥⣥⠟⠀⣝⢏⡠⣤⣔⡶⡶⠑⠭⡩⠖⠙⠊⠘⠟⢛⣧⣬⣟⢾⠛⣿⣦⣄⢘⣿⣟⡛⣿⣿⣿⣿⣷⣝⣉⣤⣤⣦⣿⠿⣧⢿⢿⣿⣿⡿⡙⣿⣦⣿⣷⣿⣿⣾⣾⣯⢿⣿⣿⣦⣿⣷⣿⣿⣶⣿⣶⣿⣿
⡟⠀⠛⢻⣾⣇⠙⠃⠹⠡⢾⠶⢛⣛⢉⣨⠴⠶⢾⣿⠿⠄⡄⢷⡶⠠⣝⣹⣷⣷⣲⣿⣭⣿⣽⣿⣿⡿⢿⢿⠛⡋⠀⠹⠿⠟⠙⠋⠁⠙⣬⡷⢢⣵⣵⣖⣽⠿⠟⠡⣿⣻⣿⣿⡟⠻⠿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⢀⠙⢛⡛⢃⣐⢔⣰⢷⡹⠿⠉⡆⠢⣿⣿⡍⠭⣅⣄⣹⢦⢹⣻⣿⣿⠛⢯⡭⢾⠻⠥⣷⣷⣿⣦⠀⠴⠻⡓⠒⢠⢳⣠⠶⢑⣾⢺⢾⣿⣷⣿⣻⣛⡳⣈⡒⢲⡦⠍⣸⣿⢗⠀⢀⣌⠛⢿⠹⢟⠩⠷⢐⡺⣋⠝
⠀⢩⢟⠾⡶⠠⣩⠤⣀⣽⣄⢩⣥⣼⣷⣌⡜⣷⣿⠻⣸⣟⣿⣿⣾⣻⠛⠥⣽⠻⢿⢻⢙⣶⣶⣶⠁⠛⢀⢶⡛⣯⣴⣾⣿⡙⣿⣿⣿⠟⠛⢀⣩⣃⡉⠩⢭⣷⣏⣿⣷⡋⠙⠁⣀⡀⣀⣍⣯⠂⠀⠉⣨⣾⡏⠈⣿⣿
⠻⠟⣮⣶⣦⢈⢿⣯⣁⠙⣿⠿⠛⣿⡿⢿⠟⠛⣏⣯⣱⣆⣬⣿⠿⣿⠿⠻⠷⠿⠋⢏⡏⢫⣬⣷⣤⣦⡼⠿⠆⢱⣟⣿⠿⢾⣿⣿⣿⠲⡞⣛⣿⣿⣯⢚⢛⣿⢮⣵⣿⣟⡯⡿⠥⢃⡞⣛⡾⣦⣈⣨⣿⢿⣤⡀⠻⢟
⠀⡀⢘⣿⣿⣿⡟⡻⠉⠈⣁⡀⣰⢈⡉⢷⢶⣤⣤⣺⣭⣭⣽⣿⣞⣿⣿⣻⡗⢱⣶⣖⠚⡵⢛⢫⣿⣻⣶⣴⣀⢉⡡⠑⢚⣿⣿⣿⣷⢤⣿⡽⢿⣿⣺⣼⡞⣿⣧⣿⣿⣿⣧⣛⣀⣤⣴⣿⣶⣴⣾⡿⠟⠀⣾⡵⠺⡽
⣯⣐⣭⡀⠉⠍⣀⠐⣲⣤⡧⠻⣿⣑⢁⣰⡋⣋⠠⢀⣬⢱⡯⠽⢿⡹⣏⢛⣽⣻⡮⢍⡡⡵⡼⣡⣿⣿⢯⣿⣾⣿⡿⡿⡄⢨⣿⣿⣿⣿⢿⠏⢜⣛⣿⣧⣯⣛⡛⠿⣿⣿⣿⡁⠿⢙⠶⣿⣿⡮⠻⠁⠂⠸⣾⣽⣦⡰
⣶⣟⠻⣯⣡⣤⠀⢀⣴⣾⡀⣆⢨⣽⣿⣭⣿⣷⣷⣶⣌⠸⢾⣐⡟⠿⣷⣏⡾⡿⣭⣿⣍⠹⠳⣇⠰⠟⢿⡏⠈⠻⠷⢯⣷⣖⣿⣿⣿⣿⣶⣟⠢⡸⠻⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣾⠍⠀⠀⠄⠀⠀⠀⣴⣞⢏
⠠⢶⣾⢾⣿⣿⣆⢬⣿⡿⡯⣿⣿⡿⠻⣿⣮⣽⣿⣿⣿⡆⠀⠀⠳⠼⣿⣍⣿⣏⡟⢿⣶⡮⡭⢭⡂⠀⣈⢿⣎⢰⢶⣽⣿⣇⠈⡿⣿⣿⣭⣟⠂⣹⣿⣿⣿⣿⠿⢿⣿⣿⣿⣷⡍⢛⠙⢿⣧⣀⡀⠸⡈⠁⠀⠚⠁⢰
⢘⣞⣷⣬⣽⡏⢿⣌⠡⠙⢻⣿⣿⣑⣿⣿⠻⢿⠿⠋⠩⡀⠀⠀⠔⠹⣯⣿⣭⣷⣶⣮⣅⣿⣿⡞⠷⢓⣾⣽⣻⡄⡹⢀⡚⠷⢷⣘⣓⣤⠷⣡⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣟⡻⣦⠀⠀⢒⣿⡿⡦⣤⣷⣀⣿⡷⣤⣿
⢀⢨⣉⢏⣯⡷⣽⡧⡭⠆⢻⣿⢿⣿⠛⠛⢀⣨⣮⠴⠀⡿⣆⣀⢠⣤⣾⢿⡿⣿⣿⣿⣏⢭⠟⡞⠳⠿⣟⣽⣿⣿⡁⣞⣹⣴⡘⣿⣿⢻⣿⣿⣿⣽⣟⢛⣿⣯⣿⣿⣿⣻⣿⣛⣩⣁⣘⣛⡻⢿⣿⡿⣿⣯⣽⣿⣿⣿
⢁⢛⣏⣛⣁⣠⡙⣃⢠⣌⣿⣟⡺⠿⢧⣬⡿⣽⣿⣿⢻⣿⣟⡊⣀⣽⡿⠖⢖⠛⠛⠫⡾⠀⢸⣷⣿⣾⡟⠛⢿⣷⣿⣶⣿⣯⣿⣿⣿⣿⣻⣯⣷⣿⣿⡾⣿⣶⣺⣿⣿⣾⣿⣿⣿⣿⣿⣯⣿⣷⣏⣿⣿⣿⣿⣿⠉⠉
⠘⠛⢿⣟⠟⢿⠛⠛⢻⣿⣯⣿⣿⣷⣶⣬⣟⠿⣿⣿⣷⠹⠻⢷⠔⣀⣠⡤⣾⠷⠠⡦⢠⣶⣶⣿⣶⣷⣿⣿⠸⣿⠯⢙⡍⠿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⡿⣿⣿⣿⣷⣯⣍⡿⢿⠿⢿⣿⣿⣟⣯⡈⠛⠿⠿⢭⢫⣿
⢀⣶⡀⢠⣼⢯⡕⢨⣧⣶⠌⠔⢙⡀⣠⠀⡉⠀⠀⠀⢱⣞⣓⠉⠉⠀⠀⠙⠂⢠⢈⡁⢿⡿⣖⠛⣿⠗⠏⠀⣰⣋⣉⣿⣿⣿⣶⣝⠾⢾⣿⣿⢹⣇⣿⣿⣾⡷⠗⠾⢗⠾⠟⠏⣝⠖⠀⣤⣶⠀⢠⣿⣿⣿⡉⠀⠀⠀
⣺⣥⡟⡂⠀⠞⠊⠸⠛⢏⠀⡤⠨⠀⠀⠀⠁⠐⡢⡀⠟⠿⠿⣴⡇⠀⢶⡶⠯⡍⠙⠧⢭⣍⡟⠀⠊⠋⠁⠊⠡⠀⣿⣿⠟⣼⣿⡿⡶⣍⠿⡿⡿⠧⠭⠋⠀⢤⢄⠀⠀⠀⠄⠠⠃⠀⠀⠾⠀⠈⠙⣷⠦⠙⢷⠺⠲⠶
⠀⠄⠀⠁⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠠⡷⠀⠀⠙⠁⠀⠀⣲⣿⠃⠘⠀⠀⠾⠉⠄⠄⢰⢠⡠⠀⠀⠒⠂⠀⠠⢀⠅⣠⣄⣈⢻⠀⠀⠁⠀⠁⠠⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠃⢰
⣤⣤⣯⣿⣳⠀⢀⣠⣤⣤⢀⠀⠀⠀⠀⢁⡂⠂⠀⠀⠰⣿⡿⣿⡖⠃⠀⠀⠀⢀⠀⠀⢠⡾⠀⠀⠀⠀⢸⡅⠀⠰⣾⣿⣿⡏⠁⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⣶⣦⡀⠀⠀⠀⠀⠈⠁⠀⠀⢢⣴⣿⠋
⠹⠟⠛⠙⠻⡇⠈⠛⠿⣿⣧⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠔⣷⣶⣤⡓⠀⠀⠀⠈⠒⠀⠀⠀⠀⠁⠀⠀⠈⣁⠀⠐⠟⠛⠋⠀⠀⠀⠀⠀⣤⣄⣦⠀⠀⠀⠀⠀⢀⡤⢠⣼⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢛⣧⣿⢌
⢀⡂⠀⠀⠀⠀⠀⠀⡀⠲⡆⣀⠀⠆⠀⠀⢀⢀⣄⡀⢀⣤⣼⠇⠈⠉⠀⠠⠐⠀⠀⣤⣄⡀⠀⠴⠀⢥⣄⣀⢄⢄⠀⠀⠀⠠⠀⠀⣤⠐⣯⡉⠑⠀⠀⠀⢀⣄⣸⣤⣤⣥⡄⣀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠀⢈⣍⢼⠉
⢸⡀⠀⢠⣔⠀⠀⠀⡀⠀⣬⡀⢀⢿⣶⣤⡀⠀⠈⢰⡀⠝⢩⣼⣿⣇⡀⣴⣿⣦⣥⣍⠿⠀⠀⠀⠀⠁⠠⣾⠋⣠⢶⠂⢒⣤⣾⣶⠨⣀⣧⣧⣐⠶⣠⡄⢀⢛⣟⠛⠋⢹⢯⢷⡦⠀⠀⣈⠁⠀⠀⢤⣭⠾⠙⢝⠀⣀
⠿⢿⡆⠾⠏⠤⠀⠀⠑⠆⢈⡛⠺⣟⢮⣿⣿⣿⡔⠀⢁⣵⣾⣿⣿⡷⢠⣁⡙⣿⡻⠟⡤⣾⣾⢟⡈⣀⡀⠈⣍⡫⡐⣄⠘⠛⠿⣿⢡⣛⣾⣿⣅⣐⠀⠀⠨⠾⠿⢖⠐⡂⢀⣤⡌⢀⠸⣁⠀⠐⡶⣶⣶⣿⣿⡿⣯⣭
⣿⡿⠉⡯⠐⠀⠀⢄⠈⢈⡛⠩⣦⠛⢿⣛⠿⣗⣤⢈⣩⣿⣿⣿⣟⣿⣞⣙⣛⣟⣻⣿⠿⡿⣗⡎⣇⠙⢻⣧⠌⠘⡖⡍⠀⣺⣒⠀⢾⣷⣿⣿⢿⣟⠁⠀⠀⠀⠐⠮⠠⣽⣴⣶⠶⠾⣿⡍⠁⡜⠀⠈⣉⣻⣿⡲⢶⣿
⠀⠹⣿⣏⠀⢀⡘⠛⠁⢉⠈⠈⠀⠀⢆⣭⣑⣟⡿⠯⣸⣿⣿⠟⢿⣿⣯⡏⠐⢗⣛⠀⠀⠀⠿⠿⡾⣺⣿⣾⡷⠆⠠⠀⠀⠉⠉⢶⢘⠋⠀⠘⠈⣁⠀⠀⠀⠂⠲⣄⣂⣽⣺⣶⠢⡀⠲⢀⠀⠀⠀⠠⣉⢫⡗⣶⣷⣾
⣶⡿⠏⠹⣇⠀⠐⡀⢄⣿⡿⠁⠀⣰⣶⡟⠈⠩⠣⡐⠹⠙⠋⠘⠍⠻⣿⣾⠇⢘⡌⢴⣴⡄⠀⠀⠘⠙⣻⣿⣿⣷⣾⠘⠀⠠⠀⠈⡙⠁⠀⠀⢠⡷⠀⢰⣌⣵⣤⣙⣹⣿⡟⡻⢷⣮⢷⣬⣯⣅⢬⣿⡟⣿⢸⣷⣼⣧
⢛⢹⢷⠥⠭⣇⢙⠈⠛⢉⣁⠀⠀⠀⠠⠀⠀⠀⠄⣀⠚⣄⠀⠀⠀⠉⢢⣕⢢⢰⠬⢀⣉⡀⢀⣴⣤⣌⣹⣿⣿⣿⠟⠀⠠⠿⠿⢄⣠⣤⣰⣴⣂⣺⣆⣀⢴⣿⢿⠿⢿⢿⣧⣶⣾⢿⣽⣾⣞⣋⣵⢟⣀⠩⣴⡶⢽⣿
⡴⣶⠆⣤⡎⠽⠿⡄⠸⣿⢟⡸⡶⠄⠘⠑⣳⣻⣗⢲⣎⣚⣛⣳⣌⠁⠀⢉⣁⡀⠤⣨⣷⣄⠸⣿⣿⣿⣽⣦⡀⠀⠀⠀⠀⠀⠀⠶⠟⠛⠲⣊⠿⠯⡟⣲⣮⣻⣴⣮⠀⠤⠅⠉⢽⡋⠙⣿⣏⠛⢿⠛⢿⡿⡿⠿⠿⡿
⢺⣿⢶⣖⣾⢿⠔⠺⣧⡄⡀⣀⢴⣶⡁⠄⣠⣙⠛⢶⡶⠷⣞⣯⢿⣓⢦⣼⣿⠛⠂⠸⠯⣽⣿⣷⣿⢿⣿⣿⣿⠀⠀⢉⣁⡂⠀⠀⣃⣾⣶⠋⣥⡚⣻⣿⣿⣿⣷⠾⣆⣤⣴⣌⣴⣷⢋⣉⣻⣾⣿⣷⣴⣤⣀⡤⣥⣄
⢿⣿⣷⣤⣭⣓⢠⡀⠀⡑⣿⣛⣿⠗⠁⠹⣟⣘⣰⣾⡉⠻⣝⣿⣧⡿⢧⣏⢻⣦⣰⠖⣺⣿⣿⣿⣿⣴⣯⣿⡟⠀⣳⣶⣿⡿⠻⣤⡈⠉⡹⠁⢐⣘⣙⠩⣷⣿⣿⣯⡿⣿⣿⣻⣽⡞⣿⣿⠓⣻⣿⣿⢷⡻⢿⣿⠋⡳
⡂⢘⣟⡻⣿⡡⣧⠟⠀⣝⢍⡠⡤⢴⡶⡖⠑⠍⡩⠖⠙⠊⠘⠟⠛⣦⣬⣏⢾⠛⣻⣦⣄⢹⣿⣿⡛⣿⣽⣿⣿⣷⣙⣙⣤⣴⣦⣟⠿⣧⣿⢿⣿⣿⡿⡘⣿⣦⣿⣵⣿⣿⣿⣺⣯⢞⣿⣿⣶⣿⣷⣿⣿⣶⣿⣶⣻⣿
⡟⠀⠛⢻⣶⣇⠛⠂⠹⠡⢾⠾⢟⣛⢉⣠⠴⠶⢿⣿⠽⢄⣄⢷⡶⠤⣜⣹⣷⣷⣲⣯⣭⣿⣭⣭⣵⡟⢿⢿⠛⡋⠀⠹⠿⠟⠹⠋⠀⠙⣭⡷⢢⣵⡵⣐⣽⠿⠟⠡⣿⣻⣿⣷⡟⠻⠻⣷⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⢀⠙⢛⡛⠃⣀⢴⣸⢷⡻⠿⠉⡆⠢⣿⣿⠍⢸⣅⣀⡹⢦⢸⣿⣻⣿⠛⢯⡭⢞⠻⠥⣷⣷⣯⣆⠀⠴⠻⡒⠒⢢⢳⣠⠶⠑⣾⢺⢾⣿⣷⣿⣣⣛⡳⣈⡲⢲⣦⠍⣨⣟⢷⠀⢀⣈⠛⢿⠹⠟⢩⡷⢐⡺⢋⠝
⠀⢠⢟⢾⣦⠤⣩⠤⣀⣹⣄⢩⣵⣼⣷⣆⡙⣻⣿⠳⣸⣞⣿⣾⣾⣻⢛⠥⣼⠻⡿⢻⢙⣶⣶⣶⠁⠛⢀⢴⡛⡯⣔⣾⣿⡙⣿⣿⣿⠛⠛⢀⣩⣃⡩⠫⢭⣷⣏⣿⣶⡋⠉⢁⣀⠀⣀⣍⢧⠂⠀⠈⣨⣾⡏⠀⣿⣿
⠻⠟⣮⣦⣦⠈⠿⣧⡁⢙⣿⠿⠙⣿⡯⢿⠛⠛⣏⣿⣑⣆⣭⣿⠻⣿⠿⠻⠶⠿⠋⡏⡋⠉⣼⣷⣤⣦⡼⠿⠆⢰⣟⣿⠿⢾⣿⣿⣿⠲⡞⣛⣿⣿⣯⢚⢛⣯⢮⣥⣿⣟⡯⣿⣵⢃⡞⣛⡾⣦⣈⣨⣻⢻⣤⡀⠻⢟
⠀⡀⢘⣻⣿⣿⡟⡻⠉⠉⣁⡀⣠⢈⡉⢻⣶⣤⣤⣺⣨⡥⣽⣿⣟⡿⣶⡻⡗⢱⣶⣖⠚⡵⢛⢻⣿⣳⡲⣴⣂⣈⡡⠑⢚⣿⣿⣿⣗⢤⣿⡽⢿⣿⣶⣼⡞⣿⣧⣿⣿⣿⣧⣛⣈⣤⣴⣻⢂⣴⣾⡿⠟⠂⣸⡵⠼⡭
⣯⣐⣭⡀⠉⡍⣀⠐⢢⣤⡯⢻⣿⣹⢁⣤⡋⣋⢠⢀⣬⢰⣿⠽⢟⡹⣏⣙⣽⣻⡮⣍⢡⡵⡼⣥⣿⣿⢯⣿⣿⣿⡿⠿⡄⢨⣿⣿⣿⣿⢿⢏⢝⣛⣿⣥⣯⣙⡛⠻⣿⣿⣿⡁⠿⢉⠲⡿⣾⡬⠹⠁⠀⠸⣾⣤⣆⡰
⢶⣟⠻⣯⣡⣤⠀⢀⣴⣾⡐⢆⢨⣽⣿⣭⣿⣷⣷⡶⣍⣰⢿⣐⣿⠿⣿⣟⡾⡿⣭⣯⣏⠹⠳⣆⠰⠛⢿⡏⠈⠺⠷⢯⣷⡖⣾⣿⣟⣿⣶⣟⠀⡸⠻⣏⣿⣿⣿⣿⣻⣿⣿⣷⣿⣿⣿⣾⠏⠁⠀⠀⠀⠀⠀⣴⣮⢏
⢠⢶⣾⢺⣿⣿⣆⢬⢿⡶⡯⣿⡿⠿⠻⣿⣮⣽⣿⣿⣿⡆⠀⠀⠳⢾⣿⣍⣿⣏⡟⢿⣶⡮⡩⢭⡂⠀⠈⢿⣎⠰⣶⡽⣿⣇⠈⡿⣿⣭⣭⣟⠂⣹⣿⣿⣿⣷⠿⢟⣿⣿⣿⣷⡍⢋⠙⢿⣧⣀⡀⠸⡄⠀⠀⠘⠁⢰
⢘⣾⣿⣬⣽⡏⢷⣈⠡⠙⢻⣿⣿⣑⣿⣿⠻⢿⠿⠋⠹⠁⠀⠀⠐⠙⣯⣿⣼⣷⣶⣌⣄⣿⣿⡚⠖⢓⣾⣭⣻⡄⡹⠀⡚⠿⢷⣘⣓⣤⠷⣡⣾⣿⣿⣿⣿⣿⣳⣿⣿⣿⣟⡻⣦⠀⠀⢂⣿⡻⣦⣤⣷⣀⣓⠷⣤⣿
⢀⢨⣉⢍⣫⠇⣽⡧⡭⠦⣻⣿⢿⣿⠛⠛⢀⣈⣦⠰⠀⡿⣆⣀⠠⣤⣾⢽⡿⣿⣻⣽⣍⠩⠟⡖⠱⠟⡟⣽⣿⣿⡑⣞⣩⣴⣘⣿⣿⢻⣿⣿⣿⣽⣟⢛⣿⣿⣿⣿⣿⣫⣟⣙⣩⣁⣘⣛⡻⣿⣿⡿⣿⣯⣽⣻⣿⣿
⢁⢻⣏⣏⣉⣠⠉⢃⢠⣄⣿⣟⡿⠿⢧⣬⡿⣽⣿⣿⣻⣿⣿⡂⣀⣹⡿⠖⢖⠛⠛⠋⡾⠀⢸⣧⣭⣶⡟⠻⢿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣻⣯⣧⣿⣿⠾⣷⣶⣻⣿⣿⣾⣿⣿⣿⣿⣿⣯⡿⣷⣋⣻⣿⣿⣿⣿⠉⠙
⠘⠛⢻⣟⠟⢟⠛⢛⢻⣻⣯⣯⣿⣷⣶⣬⣟⠿⣿⣿⣷⠙⠻⢷⠔⣀⣠⣄⣾⠶⠠⠆⢠⣶⣴⣿⣾⣷⣿⣿⡸⣿⠯⢉⡍⢿⣿⣿⣿⣿⣽⣿⢿⣷⡿⣿⡿⣿⣿⡿⣷⣯⣍⡿⢿⢿⢿⣿⣿⣟⣫⡈⠛⠿⠿⢭⢽⣶
⢀⣶⡂⢠⣼⢯⣵⢨⣧⣷⠄⠜⢛⣀⣤⠀⡉⠀⠀⠀⢳⡞⣓⠉⠉⠀⠀⠙⠂⢢⢈⣁⢿⡿⣖⠛⣿⠷⠏⠄⣽⣋⣉⣿⣿⣷⣦⣝⠾⢿⣿⣿⢙⣟⣿⣿⣿⡷⠗⠿⢗⠾⠟⠏⣝⡖⠀⣤⣶⠀⢠⣿⣿⣿⡉⠀⠀⠀
⣾⣥⣟⡂⠀⠞⠊⠸⠛⢋⠀⡤⠨⠀⢀⠀⠑⠔⡢⡀⠿⠿⠿⣾⡧⠀⢶⡾⠯⡏⠙⠧⢭⣝⡟⠀⠊⠋⠁⠊⠡⠄⣿⣿⠫⣽⣿⡿⡶⣏⠿⡿⡿⠥⠭⠋⠀⢤⢄⠀⠀⠀⠄⠠⠋⠀⠀⠾⠄⠈⠘⣷⢦⠉⢵⠺⠲⢶
⠐⠄⠀⠁⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠠⡷⠀⠠⠙⠁⠀⠀⣒⣿⠋⠚⠀⠀⠾⠉⠀⠄⢰⢠⡠⠀⠀⠒⠃⠀⠠⢀⠅⣠⣄⣈⠻⠀⠀⠁⠀⠀⠠⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡈⠃⣰
⣤⣤⣿⣿⣻⠀⢀⣠⣤⣤⢀⠀⠀⠀⠀⢁⡂⠂⠀⠀⠰⣿⡿⣿⡶⠃⠀⠀⠀⢀⠀⠀⢠⡼⠀⠀⠀⠀⢸⡇⠀⠰⣼⣿⣿⡏⠁⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣶⣦⡀⠀⠀⠀⠀⠈⠁⠀⠀⢢⣴⣿⠋
⠽⡿⠛⠙⠿⠇⠈⠛⢿⣿⣧⡀⠄⠀⠀⠈⠀⠀⠀⠀⠀⠔⣷⣶⣤⡓⠀⠀⠀⠈⠂⠀⠀⠀⠀⠁⠀⠀⠈⣁⠀⠘⠟⠛⠋⠀⠀⠀⠀⠀⣤⣄⣦⠀⠀⠀⠀⠀⢀⡤⢠⣬⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢛⣧⣽⢍
⢀⡂⠀⠀⠀⠀⠀⠁⡐⠳⡇⣀⠡⢆⠀⠀⢀⢀⣄⡠⠀⣤⣾⠇⠈⠉⠀⠠⠐⠀⠀⣤⣄⡀⠀⠶⠀⢥⣄⣀⣄⢄⠀⠀⠀⠠⠀⡄⣤⠰⣯⡉⠑⠀⠀⠀⢀⣤⣸⣠⣤⣥⡄⣀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠁⢈⣍⢼⠉
⡸⡀⠀⢠⣔⠀⠀⠀⡀⠀⣬⡀⢘⢿⣶⣤⡀⠀⠈⢠⡈⠝⢉⣼⣿⣇⢀⣶⣿⣧⣥⣍⠿⠀⠀⠀⠀⠁⠠⣾⠛⣠⣶⠒⢒⣤⣾⣶⠨⣀⣷⣣⣑⠶⣠⡄⢀⣿⣿⠛⢋⢹⢯⢷⣦⠀⠀⢈⠁⠀⠀⣦⣽⡞⠛⢙⠀⣀
⠿⢿⠄⠾⠟⡤⠀⠀⠑⠆⢈⡛⠺⣿⢮⣿⣿⣿⡔⠀⢁⣵⣾⣿⣿⡷⢠⣇⡙⣿⣻⠿⢤⣾⣾⢟⡌⣀⡀⠨⣍⡯⣐⣌⠸⠛⠿⡗⢡⣛⣾⣿⣅⣐⠂⠀⠨⠾⠿⢖⠐⡂⢀⣤⡌⢀⠸⣁⠀⠒⡶⣶⣶⣯⣾⡿⣯⣭
⣿⣿⡉⡯⠀⠀⠀⢄⠈⢈⡛⠉⣦⠹⢿⣋⠯⣷⣬⢈⣉⣿⣿⣿⣟⣿⣞⣙⣛⡟⣻⣿⠿⡿⣟⡾⢇⠙⢻⣧⠌⠈⡔⡈⣀⣸⣒⠀⢾⣷⣿⣿⢿⣟⠁⠀⠀⠀⠐⠮⠠⣽⣤⣶⠶⠿⣿⡍⠁⡼⠀⠨⣉⣻⣿⡲⢶⣿
⠈⠻⣾⣯⠀⢀⡘⠟⠉⣉⠀⠀⠁⠀⢀⣭⢕⡟⡿⠿⣸⣿⣿⠟⢿⣿⣯⡏⠐⢗⣻⠀⠀⠀⠷⡶⡼⡺⣿⣼⡷⢆⠀⠀⠀⠉⠉⢖⢘⠋⠀⠘⠉⣁⠀⠀⠀⠂⠦⣔⣃⣽⣺⣶⠶⡀⠰⢠⠀⠀⠀⣠⣉⢫⡗⣶⣾⣾
⣶⢿⠏⠹⣇⠀⠐⡀⢄⣿⡿⠁⢀⣤⣶⡟⠈⢩⡣⣔⠻⠝⠋⠘⠍⠻⣿⣾⠇⢸⡌⢴⣴⣄⠀⠀⠘⠙⢻⣿⣿⣷⣿⡚⠀⠠⠀⠈⡉⠁⠀⠀⢠⡷⠀⢰⣍⣵⣤⣛⣛⣿⣟⡻⢷⣮⢿⣬⣯⣅⢬⣿⡝⣿⢹⣿⣾⣧
⢛⢹⢿⠤⠭⢁⢙⠈⠛⣙⣁⠀⠂⠀⡠⠀⠀⠀⠌⣀⠛⣄⡀⠀⠀⠉⢢⣕⠲⢰⠬⢀⣉⡀⢠⣴⣶⣜⣿⣿⣿⣿⠿⠃⠴⠹⠿⢄⣠⣤⣴⣴⣆⣚⣆⡀⣴⣿⢿⠿⢿⢿⣧⣶⣿⢿⡿⣾⣾⣏⣽⣟⣠⠩⣴⡶⢹⣿
⣴⣶⠆⣤⡎⠽⠿⣄⠸⣿⢿⡸⡶⡄⠘⠙⣳⣻⣕⢲⣞⣻⣛⣳⣌⠁⠀⢉⣁⡀⢦⣨⣷⣆⣿⣿⣿⣿⣥⣤⣀⠀⠀⠀⠀⡀⠐⠶⠟⠛⠲⣊⠿⠯⡟⣳⣮⣻⣴⣦⠀⠤⠅⠉⣽⡏⠙⣿⣏⠙⢿⠛⢿⡿⡿⡿⢿⡻
⢻⣿⣶⣖⣾⢿⠴⠺⣧⡀⡀⣀⢴⣴⡁⡀⣀⣙⠛⢲⡾⠷⣖⣯⣿⡓⢦⣸⣿⠛⠂⠸⢯⣿⣿⣶⣿⢾⣿⣿⣿⠀⠈⢁⢁⡂⢀⠀⣃⣾⣶⠫⣯⡚⣻⣿⣿⣿⣷⠾⣆⣀⣔⣌⣴⣷⢋⣉⣻⣾⣿⣷⣶⣤⣁⡤⣡⣄
⢿⣿⣷⣤⣥⣓⢀⡀⠀⣑⣿⣻⣿⠗⠁⠹⣓⣘⣸⣾⡉⢻⣝⣿⣧⡿⢧⣏⢻⣤⣰⢖⣿⣿⣿⣿⣿⣴⣭⣿⡿⠀⣷⣶⣿⡿⠻⣦⡌⠉⣹⡃⣐⣘⣙⠙⣷⣿⣿⣯⡿⣿⣿⣻⣭⡞⣿⣿⠛⣻⣿⣿⣷⣻⢿⣿⠋⡳
⡂⢘⣞⡻⣿⡹⡧⠟⠀⣝⣍⣠⣤⢰⣶⡖⠑⠌⡩⠗⠙⠊⠘⠟⠛⣧⣬⣍⢮⠙⣻⣦⣌⢻⣿⣿⡛⣿⣿⣿⣿⣷⣉⣉⣥⣤⣦⣿⠿⣥⣿⢿⣿⣿⡿⡙⣿⣦⣿⣱⣿⣿⣿⣺⣯⢞⣿⣿⣶⣿⣷⣿⣿⣶⣿⣖⣿⣿
⡿⠀⢛⢿⣾⣇⠙⠂⠙⠩⢾⠶⢟⣛⢉⣨⠴⠶⢿⣿⠽⢄⡌⢷⡶⠤⣝⣹⣷⣷⣲⣯⣽⣿⣽⣯⣵⡿⢿⢿⠻⡋⠀⠹⠿⠟⠹⠋⠉⠙⣬⡗⢢⣵⡵⣖⣩⠻⠟⠡⣿⣿⣿⣷⡿⠻⠿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⢀⠙⢛⡛⢃⣀⢴⣰⢷⡽⠿⠋⡆⠪⣿⣿⠍⣬⢥⣄⣹⣆⣰⣻⣻⣿⠛⢯⡭⣾⠻⠥⣣⣵⣯⣦⠀⠶⠻⡒⠒⢢⢷⣀⠶⢑⣾⢺⢾⣿⣿⣿⣻⣛⡳⣈⡲⢲⣦⠍⣸⣿⠷⠀⣀⣌⠛⢿⠹⢟⢩⠿⢐⢺⣋⡝
⠀⢡⣟⠾⡦⠠⣩⠤⣀⣹⣄⢡⣵⢼⣷⣎⡙⣻⣻⠻⣸⣞⣿⣾⣶⣻⠟⠧⣼⠿⣿⢻⢹⣶⣶⣦⠁⠛⣀⢶⡛⡿⣖⣾⣿⡘⣿⣿⣿⠟⠛⢀⣩⣃⡉⠫⢭⣷⣏⣯⣿⡋⠙⢁⣀⠀⣀⣍⣧⠂⠀⠉⣪⣾⡏⠈⣿⣿
⠻⠟⣯⣶⣦⠈⢿⣿⡁⢙⣿⠟⠛⢿⡿⢿⠛⠛⣎⣯⣑⣆⣭⣿⠿⣟⠿⠻⠷⠿⠋⠏⡋⠛⣼⣷⣤⣦⡼⠿⠆⣵⣟⣿⢿⢿⣿⣿⡿⠲⡞⣟⣿⣿⣯⢟⢛⣯⢯⣵⣿⣟⠯⡿⣵⢃⣞⣛⣾⣦⣈⣨⣻⢻⣤⡄⠻⢟
⠀⡀⢘⣻⣯⣿⡟⡛⠉⠉⣁⡀⣠⢈⡉⢛⣶⣤⣤⣺⣬⣥⣽⢿⣷⣿⢶⣻⡗⣱⣶⣆⠚⣵⢛⠻⣿⣳⡲⣴⣊⣉⡡⠑⢚⣿⣿⣿⣗⣤⣿⡽⠿⣿⣾⣼⡞⣿⣧⣿⣿⣿⣧⣛⣀⣤⣴⣿⢢⣴⣾⡿⠏⠂⣾⡵⠸⡽
⣏⣐⣥⡀⠉⡅⣀⠐⢲⣤⡯⢳⣿⣱⢁⣰⡋⣋⢠⣀⣬⢱⣿⠽⣟⡻⣯⣟⣭⣻⡮⢍⣡⡵⡼⣭⣿⣿⢯⣷⣮⣿⡿⢿⡌⢨⣿⣿⣿⣟⢿⠟⢝⣛⣿⣥⣯⣙⡛⠻⣿⣿⣿⡁⠿⠙⠲⡿⣾⡬⠹⠁⠀⠸⣾⣼⣦⡰
⣦⡟⠻⣯⣡⣤⠀⢀⣴⣿⡰⣆⢸⣽⣿⡭⣿⣷⣷⡶⣌⠸⢾⣕⠿⠿⣷⣿⡾⡿⣭⣿⣏⠹⠷⣅⠰⠟⢿⡏⠘⠻⠿⣯⣷⣖⣾⣿⣿⣿⣶⣟⠰⠸⠻⢏⣿⣿⣿⣿⣺⣿⣿⣷⣿⣿⣿⡾⡏⠁⠀⠀⢀⠀⠀⣴⣾⢏
⢠⣶⣾⢾⣿⣿⣆⢬⢿⡶⡯⣿⣿⠿⠻⣿⣮⣿⣿⣿⣿⡆⠀⠀⠳⢾⣿⣍⣿⣯⡟⢿⣴⡬⡩⢭⡂⠀⢈⣿⣆⠰⣶⡿⣿⣇⠂⡿⣿⣭⣭⣟⠂⣹⣿⣿⣿⣷⡿⢿⣿⣿⢿⣷⡍⢛⠙⢿⣧⣀⡀⠸⡄⠁⠀⠘⠁⣰
⢙⣟⣿⣬⣽⡏⢿⣌⠡⠝⢻⣿⣿⣑⣿⣿⠻⢿⠿⠋⢱⠁⠀⠀⠀⠙⣯⣿⣽⣷⣶⣌⣅⣿⣿⡚⠶⢓⣾⣯⣿⡄⡙⢀⡚⠿⢷⣘⣓⣤⠷⣡⣾⣿⣿⣿⣿⣽⣳⣿⣿⣿⣟⡻⣧⠀⠀⢂⣿⡻⡦⣤⣷⣀⣻⠷⣤⣿
⢀⢌⣉⢍⣯⠇⣽⡧⣭⠤⣿⣽⢿⣿⠛⠛⢀⣈⣦⠰⡀⡿⣆⣀⢠⣤⣾⢽⡿⣿⣻⣽⣏⢩⠟⡞⠳⠏⡟⣽⣿⣿⡱⣞⣩⣴⣘⣿⣿⠻⣿⣿⣿⣽⣟⢻⣿⣿⣽⣿⣿⣻⣟⣹⣩⣁⣘⣛⡻⣿⣷⡿⣿⣯⣽⣻⣿⣿
⢁⢻⡟⣏⣉⣠⠙⣃⣠⣄⣿⣟⡾⠿⢧⣬⡿⣽⣿⣿⣻⣿⣟⡊⣀⣽⡿⠶⢖⠛⠛⠋⡟⠈⢸⣧⣭⣾⡟⠛⢿⣿⡿⣶⣿⣯⣿⣿⣿⣿⣻⣯⣷⣿⣿⣾⣷⣶⣻⣿⣿⣾⣿⣿⣿⣿⣿⣯⡿⣷⣋⣻⣿⣿⣿⣿⠉⠑
⠘⠛⢻⣟⠟⢟⠛⢛⣻⣿⡯⣯⣿⣷⣶⣬⣟⠿⣿⣽⣷⠙⠻⠷⠔⣁⣡⡄⣾⣶⠠⣦⢠⣮⣴⣽⣾⣪⣿⣿⠺⣿⠯⢉⡭⠿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⡿⣿⣿⡿⣷⣯⣍⡽⢯⢿⢿⣿⣿⣟⣏⡈⠛⠿⠿⢭⢿⢷
⢀⣶⡂⢠⣼⢯⣵⢨⣧⣷⠌⠜⢛⡀⣤⠀⡉⠀⠀⠀⢳⡞⣓⠉⠉⠀⠀⠙⠂⢢⢈⣁⢿⡿⣖⠛⣿⠷⣇⠀⣼⣃⣉⣿⣿⣷⣦⣝⠾⢿⣿⣿⢙⣟⣿⣿⣿⡷⠗⠿⢗⠾⠟⠏⣝⡖⠀⣤⣶⠀⢠⣿⣿⣿⡉⠀⠀⠀
⣾⣥⣟⡂⠀⠖⠊⠸⠛⢃⠀⡤⠨⠀⠀⠀⠑⠔⡢⡀⠿⠿⠿⣶⡧⡀⢶⡶⡯⡏⠝⠧⢭⣝⡟⠀⠊⠋⠉⠋⠡⠄⣿⣿⠯⣽⣿⡿⡶⣍⡿⡿⡿⠧⡭⠋⠀⢤⢄⠀⠀⠀⠄⠠⠋⠀⠀⠾⠀⠈⠙⣷⢦⠉⢵⠺⠲⢶
⠐⠄⠀⠁⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠠⡷⠀⠀⠙⠁⠀⠀⣒⣿⠋⠚⠀⠀⠾⠉⠀⠄⢰⢠⡠⠀⠀⠒⠃⠀⠠⢀⠅⣠⣄⣀⣫⠀⠀⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡈⠃⣰
⣤⣤⣿⣿⣿⠀⢀⣠⣤⣤⢀⠀⠀⠀⠀⢁⡀⠂⠀⠀⠰⣿⡿⣿⡶⠃⠀⠀⠀⢀⠀⠀⢠⡼⠀⠀⠀⠀⢸⡇⠀⠰⣾⣿⣿⡏⠁⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣶⣦⡀⠀⠀⠀⠀⠈⠁⠀⠀⢦⣴⣿⡋
⠽⡿⠛⠙⠿⠇⠈⠛⠿⣿⣧⡀⠄⠀⠀⠈⠀⠀⠀⠀⠀⠔⣷⣶⣤⡓⠀⠀⠀⠈⠒⠀⠀⠀⠀⠁⠀⠀⠈⣁⠀⠘⠟⠛⠋⠀⠀⠀⠀⠀⣤⣄⣦⠀⠀⠀⠀⠀⢀⡤⢠⣼⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢛⣷⣷⢎
⢀⡂⠀⠀⠀⠀⠀⠁⡑⠳⡇⣀⠠⢆⠀⠀⢀⢀⣄⡠⠀⣤⣾⠇⠈⠉⠀⠠⠐⠀⠀⣤⣄⡀⠀⠶⠀⢥⣄⣀⣄⢄⠀⠀⠀⠠⠀⡄⣤⠰⣯⡉⠑⠀⠀⠀⢀⣄⣰⣤⣤⣥⡄⣀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠁⢈⣍⢼⠉
⣸⡀⠀⢠⣔⠀⠀⠀⡀⠀⣬⡀⢀⢿⡶⣤⡀⠀⠈⢰⡈⠝⢋⣼⣿⣇⢀⣶⣿⣧⣥⣍⠿⠀⠀⠀⠀⠁⠠⣾⠛⣠⣶⠒⢒⣤⣾⣶⠨⣄⣷⣷⣐⠶⣠⡄⢀⢻⣟⠛⢋⢹⢯⣿⣦⠀⠀⣈⠁⠀⠀⢲⣴⡾⠛⢝⠀⣀
⠿⢿⠄⠾⠟⠤⠀⠀⠑⠦⢉⡛⠺⣿⢮⣿⣿⣿⡔⠀⢁⣵⣾⣿⣿⡷⢠⣏⡙⣿⡻⠟⣤⣾⣾⢟⡌⣀⡀⠨⣍⡯⣐⣌⠸⠛⠻⡗⢡⣛⣾⣿⣇⣐⠂⠀⠨⠾⠻⢖⠐⡂⠀⣤⣌⢀⢸⣁⠀⠒⡶⣶⣶⣯⣽⡿⣯⣭
⣿⣿⡉⡯⠀⠀⠀⢄⠈⢈⡛⠉⣶⠝⢿⣋⠯⣷⣬⢈⣉⣿⣿⣿⣟⣿⣞⣙⣻⡟⣻⣿⠿⡿⣷⡾⢇⠙⢻⣧⠌⠈⡔⡌⡀⣼⣒⠀⢾⣷⣿⣿⢿⣟⠁⠀⠀⠀⠐⠮⠠⣽⣤⣶⠶⠿⣿⡍⠁⡜⠀⠈⣉⣛⣿⡲⢶⣿
⠈⠹⣿⣯⠀⢀⡘⠟⠉⢉⠀⠀⠀⠀⢆⣭⣕⡛⡿⠯⣸⣿⣿⠟⢿⣿⣯⡏⠐⢗⣛⠀⠀⠀⠷⡶⡼⡺⣿⣼⡷⢆⠀⠀⠀⠉⠉⢲⢘⠋⠀⠘⠉⣁⠀⠀⠀⠂⠦⣄⣃⣵⣺⣶⠢⡀⠲⢀⠀⠀⠀⣠⣉⢫⡗⣶⣶⣿
⣶⣿⠏⠹⣇⢀⠐⡀⢄⣿⡿⠁⢀⣤⣶⡟⠈⢩⡣⣐⠻⠝⠋⠘⠍⠻⣿⡾⠇⢸⡌⢴⣴⡄⠀⠀⠘⠙⣻⣿⣿⣷⣿⡓⠀⠠⠀⠈⡙⠁⠀⠀⢠⡷⠀⢰⣌⣵⣦⣙⣛⣿⣟⡻⢷⣯⢿⣬⣯⣅⢬⣿⡝⣿⢸⣿⣼⣧
⢛⢹⢿⠤⠭⢀⢙⠈⠛⣙⣁⠀⠂⠀⡠⠀⠀⠀⠄⣀⠛⣄⡀⠀⠀⠉⢣⣕⠲⢰⠬⢀⣉⡀⢠⣴⣶⣜⣻⣿⣿⣿⠿⠁⠴⠝⠿⠄⣠⣤⣴⣴⣆⣚⣆⣀⣴⣿⢿⠿⢿⢿⣧⣶⣿⣿⣿⣿⣾⣏⣽⣟⣠⠩⣴⡶⢹⣿
⣴⣶⠆⣤⡎⠽⠿⡄⠸⣿⢿⡸⣶⠄⡘⠙⣳⣻⣕⢲⣞⣚⣛⡳⣌⠁⠀⢉⣁⡀⢦⣸⣷⣆⣿⣿⣿⣿⣥⣤⣀⠀⠀⠀⠀⡀⠠⠶⠟⠛⠳⣊⠿⠯⣟⣓⣬⣻⣴⣦⠈⠤⠅⠉⣭⡋⠙⣿⣏⠛⢿⠟⢿⡿⡿⡿⠿⡻
⢻⣿⣶⣖⣾⢿⠴⠺⣧⡄⡀⣀⢴⣶⡁⡄⣀⣙⠛⢲⡶⡷⣖⣯⣿⣓⢦⣼⣿⠛⠂⠸⢯⣿⣿⣶⣿⢾⣿⣿⣿⠀⠈⢉⣑⡂⢀⠀⣃⣾⣶⠫⣧⡚⣻⣿⣿⣿⣷⠾⢎⣄⣵⣎⣴⣷⢋⣉⣻⣾⣿⣷⣶⣄⣁⡠⣅⣀
⢿⣿⣷⣤⣥⣓⢀⡀⠀⣑⣿⣹⣿⠗⠁⠹⣛⣘⣸⣾⡉⢻⣝⣿⣧⡿⢷⣏⢻⣤⡰⢖⣿⣿⣿⣿⣿⣴⣭⣿⡿⠀⣷⣶⣿⡿⠻⣦⡈⠉⣩⠁⣐⣘⡹⠉⣿⣿⣿⣯⡿⣿⣿⣻⣽⡞⣿⣿⠛⣻⣿⣿⣷⡻⢿⣿⠋⡳
⡂⢘⣞⡻⣿⡹⡥⠟⠀⣍⢍⣠⣠⢰⣶⡶⠑⠍⡩⠗⠙⠊⠘⠟⠛⣦⣬⣍⢮⠙⣻⣦⣌⢻⣿⣿⡛⣿⣿⣿⣿⣿⣙⣉⣥⣴⣦⣿⠿⣥⣿⢿⣿⣿⡿⡙⣿⣦⣿⣱⣿⣿⣿⣺⣯⢞⣿⣿⣦⣿⣷⣿⣿⣶⣿⣶⣿⣿
⡿⠀⢛⢿⣾⣇⠙⠂⠹⠡⢾⠾⠟⣛⢉⣨⠴⠶⢻⣿⠽⠄⡌⢷⡶⠤⣜⣻⣷⣷⣲⣯⣽⣿⣽⣭⣵⡿⢿⢿⠻⡋⠀⠹⠿⠟⠹⠋⠉⠙⣬⡗⢢⣵⡵⣗⣩⠻⠟⠡⣿⣻⣿⣷⡿⠻⠻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⢀⠙⢛⡛⢃⣀⢴⣰⢷⡽⠿⠋⡆⠺⣿⣿⠏⣨⢥⣀⡹⣆⢰⣿⣻⣿⠛⢯⡭⢾⠻⠥⣧⣵⣿⣮⠀⠴⠻⡒⠒⢢⢷⣀⠶⢑⣾⢺⢾⣿⣷⣿⣻⣛⡳⣈⡖⢶⣦⠍⣸⣿⠷⠀⣀⣌⠛⢿⠹⢟⢩⠷⢐⢺⣋⡝
⠀⢡⣟⢾⡦⠤⣩⠠⣀⣹⣄⢡⣵⢼⣷⣎⡝⣺⣿⠻⣸⣞⣿⣾⣶⣿⠟⢧⣼⠿⢿⢻⢹⣶⣶⣦⠉⠛⢀⢶⡛⠿⣔⣾⣿⡘⣿⣿⣿⠛⠛⢀⣩⣃⡉⠫⢭⣷⣏⣯⣿⡋⠙⢁⣀⠀⣀⣍⢧⠂⠀⠉⣪⣶⡇⠈⣿⣿
⠻⠿⣯⣶⣦⠘⢿⣿⡁⠙⣿⠟⠛⣿⡿⠿⠛⠛⣏⣭⣑⣆⣭⣿⠿⣿⠿⠻⠷⠿⠋⠏⡋⠛⣼⣷⣤⣦⡼⠿⠆⣵⣟⣿⢿⢿⣿⣿⣿⠲⡟⣟⣿⣿⣯⢿⢛⣿⢮⣥⣿⣟⡯⣿⣵⢃⣞⣛⣾⣦⣈⣨⣻⣻⣤⡄⠻⢟
⠀⡀⢘⣻⣯⣿⡟⡛⠉⠉⣡⡀⣰⢈⡉⢛⣶⣤⣤⣺⣬⣥⣽⢿⣼⡿⢶⡻⡗⣱⣶⣎⠚⡵⢛⠻⣿⣳⡲⣴⣎⣉⡡⠑⢚⣿⣿⣿⣗⢬⣿⡽⣿⣿⣾⣼⡞⣿⣧⣿⣿⣿⣧⣛⣁⣤⣴⣿⢲⣼⣾⡿⠏⠂⣺⡵⠸⡭
⣯⣐⣭⡀⠉⡅⣀⠐⢲⣤⡫⠳⣿⣱⢁⣠⡋⣋⢠⣀⣭⢱⣿⠽⣟⡻⣯⣟⣭⣻⡮⢍⣱⡵⡼⣥⣿⣿⢯⣷⣯⣿⡿⢿⡄⢨⣿⣿⣿⣷⢿⠟⢝⡚⣿⣥⣯⣛⡛⢻⣿⣽⣿⡅⠿⠙⠲⣿⣾⡭⠹⠁⠀⠸⣾⣼⣆⡰
⣧⡟⠻⣯⣡⣤⠀⢀⣼⣿⡸⣆⢨⣿⣿⣭⣿⣷⣷⡶⣌⠸⢿⣕⠿⠿⣷⣟⡾⡿⣭⡿⣏⠹⠷⣄⠱⠟⢿⡏⠘⠻⠿⣯⣷⣖⣾⣿⣟⣿⣶⣟⠲⠸⠻⢟⣿⣿⣿⣿⣺⣿⣿⣷⣯⣿⣿⡾⠏⠁⠀⠀⠀⢀⠀⣴⣾⢏
⢠⣶⣾⢺⣿⣯⣆⢬⢿⡶⡯⣿⣿⢿⠻⣿⣮⣿⣿⣿⣿⡆⠀⠈⠳⢾⣿⣍⣿⣯⡟⢿⣴⡬⡩⢭⡂⠀⣈⣿⣆⠰⢶⡿⣿⣇⠊⡿⣿⣽⣭⣟⠂⣹⣿⣿⣿⣷⡿⢟⣿⣿⢿⣷⡍⢋⠙⢿⣧⣀⡀⠸⡄⠀⠀⠘⠁⣰
⢚⣟⣿⣬⣽⡏⢿⣌⢡⠙⢻⣟⣿⣑⣿⣿⠻⢿⠿⠋⢹⠁⠀⠀⠔⠹⣯⣿⣽⣷⣶⣌⣅⣿⣿⡚⠖⣳⣾⣭⣿⡄⡹⢀⡚⠿⢷⣘⣓⡤⠷⣠⣿⣿⣿⣿⣿⣽⣳⣿⣿⣿⣟⡻⣧⠀⠀⢂⣿⡻⡦⣤⣷⣐⣻⠷⣤⣿
⢀⢬⣉⢍⣭⠇⣽⡧⣭⠄⣿⣽⢿⣿⠛⠛⢀⣈⣦⠰⡀⡿⣆⢀⢠⣤⣾⢽⡻⣿⣻⣿⣏⠙⠟⡞⠳⠿⡟⣽⣿⣿⡱⣞⣩⣤⡘⣿⣿⠻⣿⣿⣿⣽⣟⢛⣿⣿⣽⣿⣿⣻⣟⣹⣩⣁⣘⣛⡻⣿⣿⡿⣿⣯⣽⣻⣿⣿
⢁⢻⡟⣟⣉⣠⡙⣃⣠⣄⣻⣟⡾⠿⢧⣬⡿⣽⣿⣿⣻⣿⣟⡊⣀⣽⡿⠖⢖⠛⠟⠋⡟⠀⢸⣧⣭⣾⡟⠻⢿⣯⡿⣶⣿⣯⣿⣿⣿⣿⣻⣏⣧⣿⣿⢾⡷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⡿⣷⣏⣻⣿⣿⣿⣿⠉⠑
⠘⠛⢻⣟⠟⢟⠛⢛⣻⣿⡯⣯⣿⣷⣶⣬⣟⠿⣿⣽⣷⠛⠻⠷⠔⣀⣡⡄⣾⣶⠠⢦⢠⣮⣴⣿⣾⣮⣿⣿⠺⣿⠯⢩⡽⠿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⡿⣿⣿⡿⣧⣯⣍⡽⢯⢿⢿⣿⣿⣿⣏⡈⠛⠿⠿⢵⢿⢿
⢀⣶⠄⢠⣼⠏⡵⠨⣧⣶⡌⠘⢙⡂⣤⠀⣉⠀⠀⠀⢳⡞⣓⠛⠋⠀⠀⠙⠆⢰⢀⡁⢿⡿⢖⠛⢿⠇⠍⠄⣴⣃⣉⣿⣿⣿⣦⣝⠾⢿⣿⣿⣘⣟⡿⣿⣿⣷⠗⠿⢗⡶⠟⠟⣜⡖⠀⣤⣶⡀⢠⣿⣿⣿⡉⠀⠀⠀
⣺⣥⠟⡂⠈⠖⠊⠸⠛⢋⠀⠤⠨⠀⠠⠀⠑⠔⡢⡀⠿⠿⠿⣶⡧⡀⢶⡶⡧⡏⠝⠣⢭⣝⡟⠁⠊⠋⢉⠊⠡⠄⣿⣿⠋⣴⣿⡿⡶⣏⠿⡿⡿⠧⠭⠛⠀⢤⢆⠀⠈⠀⠄⠠⠊⠀⠀⠾⠀⠈⠙⣷⢦⠉⠴⠞⠲⠿
⠐⠤⠀⠉⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠠⡷⠀⠠⠙⠁⠀⠀⣖⣿⠋⠚⠀⠀⠸⠍⠄⠄⢰⢠⡠⠀⠀⠒⠂⠀⠠⢀⠄⣠⣄⣀⠫⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⢈⠁⢰
⣤⣴⣿⣿⣿⠀⢀⣠⣤⣤⢀⠀⠀⠀⠀⠁⡂⠂⠀⠀⠰⣿⡿⣿⠴⠃⠀⠀⠀⢀⠀⠀⢠⡾⠀⠀⠀⠀⢸⡇⠠⠰⣾⣿⣿⡏⠁⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣶⣦⡀⠀⠀⠀⠀⠈⠉⠀⠀⢃⣴⣿⠏
⠹⡟⠛⠙⠻⠇⠈⠛⠿⣿⣧⡀⠄⠀⠀⠈⠀⠀⠈⠀⠀⠄⣷⣶⣤⡃⠀⠀⠀⠈⠚⠀⠀⠀⠀⠁⠀⠀⠈⣀⠀⠐⠟⠛⠋⠀⠀⠀⠀⠀⣤⣄⣦⠀⠀⠀⠄⠀⠀⡤⢠⣼⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢚⣣⣷⣏
⢀⡂⠀⠀⠀⠀⠀⠁⡁⠲⡇⣀⠠⠆⠀⠀⢀⢀⣄⡠⠀⣤⣼⠇⠈⠉⠀⠠⠐⠀⠀⣤⣄⡀⠀⠴⠀⣥⣄⣈⢄⢄⠀⠀⠀⠠⠄⠠⢤⠐⣯⡉⠉⠀⠀⠀⢀⣤⣸⣠⣤⣭⡄⣀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⢈⣌⢴⠉
⣸⡀⠀⢠⣔⠀⠀⠀⡀⠠⣬⡀⢐⢿⣷⣤⡀⠀⠈⢠⣀⠝⢋⣼⣿⣇⡀⣶⣿⣶⢡⡍⠿⠀⠀⠀⠀⠁⠠⢾⠛⣀⣴⠒⠚⣤⣾⣶⠨⣄⣧⣣⣰⠲⣠⡄⢀⢙⣿⠛⠋⢫⠽⢷⣦⠀⠀⢈⠁⠀⠀⣠⣼⡶⠛⣝⠀⣀
⠿⢿⠆⠾⠏⡤⠀⠀⠑⠆⢈⡛⠺⣿⢮⣿⣿⣿⡔⠀⢁⣵⣾⣿⣿⣿⢠⣍⡉⣿⡻⠟⠠⣾⣾⢟⡌⣠⣀⠈⣍⣣⣘⣌⠸⠛⠻⢟⠠⣟⣾⣿⣥⢀⠂⠀⠨⠾⠳⢆⠐⠂⠀⣤⣌⢀⡸⣃⠀⠐⡶⣾⣶⣮⣽⡿⣯⣩
⣿⡿⡉⡯⠀⠀⠀⢄⠈⢈⣛⠩⣶⠝⢿⣋⠯⣷⣬⢈⣉⣿⣿⣿⣟⣿⣞⣙⣻⡟⣫⣿⠿⡿⣗⡊⢏⠙⢻⣧⠬⠐⡔⡌⡀⣸⣒⠀⢶⣷⡿⣿⢿⣟⠁⠀⠀⠀⠐⠦⡀⣽⣤⣶⠶⠿⣿⡏⠁⡰⠁⠨⣉⣛⣿⡲⢷⣿
⠈⠿⣾⣯⠀⢀⡘⠏⠁⣉⠀⠀⠁⠀⢌⣭⣕⣛⡻⠿⣸⣿⣿⠟⢻⣿⣿⡯⠐⢗⣛⠀⠀⠀⠷⡷⠼⡻⣾⣯⣷⠆⠀⠀⠀⠁⠉⢐⡘⠇⠈⠘⠃⣁⠀⠀⠀⠢⠴⣄⣂⣽⣺⣶⡦⡠⠰⢄⠀⠀⠀⡠⣉⢩⡕⣶⣶⣿
⣶⠿⠏⠙⣇⠀⠐⣀⢔⣿⡿⠁⠀⣤⣶⡟⠉⢭⡫⡔⠻⠟⠋⠑⠍⠻⣿⣾⡅⢸⡌⠴⣥⣄⠀⠀⠘⠹⢹⣿⣿⣿⣾⡍⠀⠠⠀⠈⡉⠁⠀⠀⢀⡿⠀⢐⣭⣵⣤⣝⣛⣿⣟⣛⢷⣮⢾⣤⣯⣩⢬⣿⡝⣯⠛⣿⣸⣷
⢛⢸⢿⠤⠭⣀⢙⠈⠛⣙⣁⠐⠀⠀⠠⠀⠀⠀⠄⣀⠜⣆⡀⠠⠀⠈⢢⣕⢢⢰⠮⢀⣉⣀⣴⣾⣶⣔⣹⡿⠿⢿⠿⠃⠠⠝⠿⠤⣀⣤⣰⣤⣆⣚⣦⣀⣴⣿⢿⠿⢿⢿⣷⣴⣾⣿⡿⢿⣞⣟⣽⣟⣁⡉⣴⡦⢹⣿
⡴⣴⠆⣠⣌⡽⠿⡄⠸⣿⢿⡸⣶⡄⡘⠙⣳⣻⣕⢲⣞⣚⣛⡳⣌⠑⠀⢈⣁⡀⢤⣨⣷⢞⢿⣿⢿⣿⣧⣤⣄⠀⠀⠀⠀⡀⠐⠶⠞⠛⠢⣂⡿⠮⣿⣓⣦⣻⣤⣬⡈⠠⠅⠙⢽⣛⠉⣿⣿⠙⢿⠟⢿⡿⡿⡷⠿⡻
⢺⣿⣶⣖⣾⢿⠔⠺⣧⡄⡀⢐⢴⣴⡁⠄⣀⣙⠻⢲⡶⡷⣖⣯⣿⣓⢦⣼⢿⠛⠂⠸⢏⣿⣷⣶⣿⢹⣿⣿⣿⡇⠂⢁⢁⡂⢀⠀⣓⣾⣶⠃⣧⡘⣻⣿⣿⣿⣷⠾⣏⣀⣔⣜⣴⣷⢛⣉⣹⣾⣿⣷⣶⣦⣈⡤⢈⣄
⢿⣿⣷⣤⣥⣓⢀⡀⠀⣙⣿⣻⣿⠟⠁⠹⣏⣐⣰⣮⡉⠻⣝⣿⣧⡿⢷⣎⢻⣦⣰⠦⣾⣿⣿⣿⣿⣴⣿⣿⣿⠂⢷⣶⣿⡿⠻⣦⣌⠉⡩⡁⣐⣘⣙⠹⣶⣿⣿⣿⣿⣿⣿⣿⣿⡶⣿⣿⠓⣻⣿⣿⣷⣻⢿⣿⡋⠱
⡂⢘⣞⡻⣿⡵⣥⠟⠀⣝⢍⡠⣠⢴⡶⡾⠑⠨⡩⠖⠙⠊⠘⠟⠛⣦⣬⣍⢮⡙⣿⣦⣌⢿⣿⣿⡛⣻⣽⣿⣿⣿⣉⣩⣥⣤⣶⣯⠿⣥⡾⢿⣿⣿⡿⡓⣿⣦⣯⡷⣿⣿⣿⣺⣯⠞⣿⣿⣦⣺⣷⣿⣿⣷⣿⣶⣾⣿
⡿⠀⠛⢿⣾⣇⠙⠂⠙⠡⢞⠾⢟⣛⢁⣨⣤⠶⢿⣿⡿⢄⡌⢷⡶⠤⣜⣹⣿⣷⣲⣯⣭⣿⣽⣯⣷⡿⢿⢿⠛⡋⠀⠻⠿⠟⠹⠋⠁⠙⣬⡟⢢⣴⣴⣝⣨⠻⠛⠃⢿⣿⣿⣷⣗⠛⠽⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⢄⠙⢛⡛⢓⣀⢴⣼⢷⡻⢿⠋⡆⠢⣿⣿⡍⢸⢅⣄⣹⣆⣰⣻⣿⣿⡟⢯⣭⢼⠻⠥⣷⣵⣮⣆⠀⠶⠻⡒⠒⢢⢷⣀⠶⠑⣾⢶⢾⣭⣷⣿⣭⣛⡻⣈⠒⢲⣦⠍⣠⣿⣷⠀⢀⣌⠛⠿⠉⠟⢉⠵⢀⣺⢋⡝
⠀⢡⢟⠺⡦⠥⣹⠤⣄⣽⣄⢹⣽⣼⣷⣎⡙⣻⣻⠻⣹⣟⣿⣾⣶⣻⠛⠯⣼⠿⠿⢹⢙⣶⣶⣦⠁⠛⢀⢶⡛⠧⣖⣾⣷⡛⣿⣿⣿⠟⠛⢀⣩⣋⡉⠹⢭⣿⣏⣯⣿⡋⠙⢁⣀⡀⣀⣍⢯⠆⠀⠉⣠⣶⡏⠀⣿⣿
⠻⠿⣮⣦⣦⠘⢟⣿⣁⠙⣿⡟⠙⢿⡿⢿⠛⠛⣎⣯⣱⣦⡩⣿⠿⢿⠿⡻⠷⠿⠋⡟⡛⠙⣌⣷⣤⣦⡬⠷⠆⢴⣞⣟⠿⢿⣿⣿⣿⠰⡞⣚⣿⣿⢯⢹⢛⣯⢮⣥⣿⣟⡯⡛⣥⠃⣞⡛⡾⣧⣈⣠⣻⢿⣥⡬⠻⢟
⠀⡀⢘⣻⣿⣽⡟⡛⠉⠈⣡⣀⣠⢊⡉⢻⣶⣤⣤⣚⣬⣭⣽⣟⡼⡿⢶⡛⡕⣡⣶⣞⠚⣧⢍⢻⣿⣳⡢⣴⣀⣉⣡⠑⢚⣿⣿⣿⢟⣤⣿⡿⢿⣿⣾⣶⡎⣿⣧⣽⣿⣯⣷⣛⣈⣤⣴⣿⢦⣾⣶⡿⠿⠀⣸⡵⠺⡭
⣷⣐⣭⡀⠉⣅⣀⠐⢢⣤⡫⢳⣿⣑⢅⣤⡋⣋⢠⣀⣬⠱⣿⠽⢟⡻⣯⣟⣭⣩⡮⢍⡑⡱⡼⣡⣿⢿⠯⣿⣾⣿⡿⠿⡄⢨⣿⣿⣿⣷⢿⢏⠝⡈⣿⣥⣿⣛⡛⠻⣿⣯⣿⡅⠿⠙⠲⣿⣿⣭⠙⠁⠀⠐⣾⣬⣦⡱
⢶⡟⠻⣯⣡⣤⠀⢀⣼⣿⡰⣆⣨⣽⣿⡭⣿⣵⣷⡴⣌⣸⢾⡕⣿⠿⣷⣟⡾⠿⣯⣿⣍⠹⠳⣄⠰⠞⢿⡏⠘⠻⠿⣯⣷⣦⣿⣿⣿⣿⣶⣟⠢⡸⠾⣏⣿⣿⣿⡿⣚⣿⣿⣷⣮⣿⣿⣶⡏⠁⠀⠠⠀⢀⠀⣠⣞⡏
⢠⢶⣾⢾⣿⣿⣆⢬⢿⡶⡯⣿⣿⢿⠻⣿⣾⣽⣿⣿⣿⡆⠀⠀⠳⠾⣿⣏⣿⣻⡟⢿⣴⡮⡩⢽⡂⠀⢈⣿⣆⠰⢶⡿⣿⣇⡐⡿⣿⣯⣭⣿⠂⢹⣿⣿⣿⣷⠿⢿⣿⣿⡿⣷⡍⠛⠙⢿⣧⢀⡀⠐⠄⠁⠀⠘⠁⣴
⢚⣿⣿⣬⣽⡏⢿⣌⠡⠙⢻⣿⣿⣑⣿⣿⠻⢿⠿⠋⢹⠁⠀⠀⠀⠻⣭⡿⣬⣷⣶⣌⢅⣿⣿⠖⠶⣓⣾⣿⣻⡄⡙⠀⡚⠷⢷⣈⣓⣤⠿⣠⣾⣿⣿⣿⣿⣽⣳⣿⣿⣿⣟⡻⣧⠀⠀⢒⣿⡟⡧⣤⣴⣐⣟⠷⣬⣿
⢀⢨⣉⢉⣫⡇⣽⡧⣭⠆⣿⣿⢿⣿⠛⠛⢀⣈⣦⠠⡀⡿⣆⣀⠠⣄⣾⢽⡿⣿⣻⣭⣇⢽⠟⡞⠓⠿⡟⣹⣿⣿⡑⣞⣩⣤⡘⣿⣿⠻⣿⣿⣿⣽⣟⠛⣿⣿⣿⣿⣿⣋⣟⣹⣯⣁⣘⣛⡻⣿⣿⡿⣿⣯⣭⣻⣿⣿
⢁⢻⡟⣗⣉⣠⡉⣃⣠⣌⣻⣟⡿⠿⣧⣬⡿⣿⣿⣿⢻⣿⣏⡂⣀⣽⡿⠞⢖⠛⠛⠋⡿⠈⢰⣱⣭⣶⡟⠻⢽⣯⠾⣶⣿⣯⣽⣾⣿⣾⣻⣯⣷⣽⣿⣾⣿⣶⣺⣿⣿⣿⣿⣿⣿⣿⣿⣯⡻⣷⣋⣻⣿⣿⣿⣿⡅⠑
⠘⠛⢻⣟⠟⢟⠛⢛⡻⣻⡯⣯⣾⣷⣶⣬⣟⠿⣿⣷⣷⠻⠻⢷⠔⣀⣀⣄⣾⠶⠠⢦⢠⣮⣰⣹⣿⣺⣿⣮⠺⣿⠯⢩⡅⠿⣿⣿⣿⣿⣽⣿⣿⣿⡿⣻⡿⣿⣿⡽⣧⣯⣍⡵⢿⠿⣿⣿⣿⣟⣋⡈⠛⠿⠿⢤⢿⢷
⢀⣶⡄⢠⣼⠯⡥⠨⣧⣶⡌⠜⢉⡂⣠⠀⣉⠀⠀⠀⢳⣞⣓⠋⠋⠀⠀⠙⠆⢰⣀⡁⢾⡿⢖⠛⣯⠷⡏⠄⣴⣋⣉⣿⣿⣿⣦⣌⠼⢿⣿⣿⢉⣟⡿⣿⣿⣷⠗⠾⢗⣶⠟⢟⣜⡖⠀⣤⣶⠀⢠⢿⣿⣿⡉⠀⠀⠀
⣼⣥⡟⡂⠈⠖⠋⠸⠛⢋⢀⠤⠨⡄⠠⠀⠕⠐⡢⡀⠿⠿⠿⣲⡧⠀⢶⡾⠯⡏⠝⠣⢬⣍⡟⠀⠊⠋⢉⠋⠡⠀⣷⣿⠏⣴⣿⡿⡶⣏⠿⡿⡿⠥⠭⠛⠀⢤⢆⠀⠈⠀⠄⠀⠊⠀⠀⠴⠀⠈⠙⣷⢦⠉⢽⠞⠶⢿
⠐⠤⠀⠉⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠠⣷⠀⠠⠙⠁⠀⠀⣔⣟⠋⠚⠀⠀⠰⠉⠄⠄⢰⢠⡠⠀⠀⠒⠂⠀⠠⢀⠄⣠⣄⣀⠫⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⣈⠃⢰
⣤⣴⣿⣿⣻⠀⢀⣠⣤⣤⢀⠀⠀⠀⠀⢁⡀⠂⠀⠀⠰⣿⡿⣿⠶⠣⠀⠀⠀⢀⠀⠀⢠⡼⠀⠀⠀⠀⢸⡇⠠⠰⣾⣿⣿⡏⠁⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣶⣦⡀⠀⠀⠀⠀⠈⠉⠀⠀⢳⣴⣿⠏
⠽⠟⠛⠝⠿⠇⠈⠛⢿⣿⣧⡀⠄⠀⠀⠈⠁⠀⠀⠀⠀⠄⣷⣶⢤⡃⠀⠀⠀⠈⠚⠀⠀⠀⠀⠀⠀⠀⠈⣀⠀⠐⠟⠛⠋⠀⠀⠀⠀⠀⣤⣄⣦⠀⠀⠀⠀⠀⠀⡤⢠⣼⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢚⣣⣷⣆
⢀⡂⠀⠀⠀⠀⠀⠁⡰⠰⡅⣀⠡⠆⠀⠀⢀⢀⣄⡠⠀⣤⣼⠃⠈⠉⠀⠠⠒⠀⠀⣤⣄⡀⠀⠴⠀⡥⣄⣈⢄⢄⠀⠀⢀⠠⠀⠠⢤⠐⣯⡉⠉⠀⠀⠀⢀⡤⣸⣠⣤⣭⡄⣀⠀⠀⠀⠀⡀⠀⠠⠀⠐⠁⢈⣌⢴⡉
⣸⡄⠀⢠⣜⠀⠀⠀⡀⠀⣬⡀⢐⢿⡶⣤⡀⠀⠈⢠⡈⠝⢉⣼⣿⣇⡀⣶⣿⣦⢥⣍⠿⠀⢀⠀⠀⠁⠠⢾⠛⣀⣴⠒⢚⣥⣾⣶⠨⣀⣧⣣⣱⠲⢠⣄⢀⣛⣿⠛⢋⢹⠯⢷⣦⠀⠀⢈⠁⠀⠀⣢⣬⠞⢛⢉⠀⣀
⠿⢿⠇⠾⠟⡤⠀⠀⠑⠆⢉⡘⠺⣿⢮⣿⣿⣿⡔⠀⢁⣵⣾⣿⣿⣿⢠⣍⡉⣿⡻⠟⠠⢾⣾⢛⡌⣠⣀⠈⣍⣧⡘⣌⠸⠛⠻⢟⠠⣟⣶⣿⣅⣀⠂⠀⠈⠾⠳⢖⠐⡂⠀⣤⡌⣀⡸⣃⠀⠐⡶⣶⣶⣮⣴⡿⣯⣩
⣿⣿⡋⡯⠐⠀⠀⢄⠨⢈⣛⠩⣶⠹⢷⣋⠯⣷⣬⢈⣩⣿⣿⣿⣟⣿⣞⣙⣻⡟⣻⣿⠿⡿⣗⡊⢇⠙⢻⣧⠬⠐⡔⡈⡀⡸⣒⠀⢶⣷⡿⣿⠿⣛⠁⠀⠄⠀⠐⠦⡀⣽⣤⣶⠶⠿⣿⡭⠁⡴⠀⠨⣉⣛⣿⡰⢷⣿
⠈⢻⣾⣯⠀⢀⣘⠏⠁⣉⠀⠀⠁⠀⢖⣭⣑⣛⡫⠯⣸⣿⣿⠟⢿⣿⣿⡏⠐⢗⣛⠀⠀⠀⠕⡷⠾⡱⣾⡭⣷⣆⡠⠀⠀⠁⠀⢖⡘⠃⠀⠘⠂⣁⠀⠀⠀⠢⠴⣔⣂⣴⣺⣶⡦⡤⠰⢄⠀⠀⠀⡠⣉⢩⡕⣶⣶⣾
⣲⢿⠏⠙⣃⡀⠐⣀⢔⣿⡿⠁⢁⣶⣶⡟⠈⢭⡫⡔⠹⠟⠋⠙⠍⠻⣿⣾⡇⢸⡎⠴⣥⣄⠀⠀⠘⠟⢻⣾⣿⣿⣿⣦⠀⠠⠀⠈⡉⡁⠀⠀⢠⡿⠀⢐⡭⣵⣦⣝⣙⣿⣟⢛⢷⣮⢾⣤⣯⣫⢬⣿⡝⣯⠑⣿⣨⣧
⢛⢸⢿⠥⠽⣀⠙⠈⠛⢉⣁⠀⠀⠀⢠⠀⠀⠀⢌⣀⠘⢆⡀⠠⠀⠉⠢⣕⢲⢰⠬⢀⣉⡀⣀⣴⣤⣄⣣⡿⠿⠿⠿⠃⠸⠍⠿⠅⣠⣤⣰⣴⣆⣚⣦⣀⣴⣿⢿⠿⢟⢿⣧⣴⣾⢿⡿⢿⣞⣎⣽⢟⣀⡉⣴⡦⢙⣿
⡔⣴⠆⣠⣮⡽⠿⡄⠸⣿⢟⡸⣲⡄⡘⠉⣱⣻⣕⢱⣞⣚⣛⡷⣌⠑⠀⢉⣃⡀⢤⣨⣷⢆⣿⣿⢿⣿⣷⣠⣀⠀⠀⠀⠀⡀⠀⠶⢟⠛⠢⣀⡿⠯⣟⢓⣦⣻⣴⣮⡈⠤⠥⢙⢭⡋⠉⣿⣿⠙⢿⠟⢿⡿⡿⠷⠿⡻
⢺⣿⢶⣖⣾⢿⠔⠺⣧⡀⡀⣀⢴⣴⡁⠄⣠⣙⠻⢶⡶⠷⢖⣧⢿⣑⠦⣸⣿⠚⠂⠸⢇⣿⣷⣶⣿⢡⣿⣿⣿⣿⡂⢁⢁⡂⢀⠀⣓⣶⣶⠃⣧⡚⣻⣿⣻⣿⣷⠾⣏⣀⣔⣜⣴⣷⢟⣉⣻⣾⣷⣷⣶⣦⣈⣤⢌⣤
⢻⣿⣷⣤⣥⣓⢠⡀⠀⡑⣿⣻⣿⠟⠁⠹⣛⣐⣸⣺⡫⠻⣝⣿⣧⡿⢷⣎⠻⣤⣠⢆⣿⣿⣿⣿⣿⣤⣿⣿⣿⠛⣷⣶⣿⡿⠻⣦⣌⠉⡩⠁⢐⣘⡙⠙⣶⡿⣿⣿⡿⣿⢿⣿⣯⡶⣿⣷⠓⣻⣿⣿⢷⡻⢿⣿⠋⠳
⡂⢘⣞⡻⣿⡵⡥⠟⠀⣝⢏⣡⣠⢔⡲⡾⠐⠉⡨⠞⠉⠊⠘⠟⠛⣦⣬⣅⢪⡉⣹⣦⣝⢿⣿⣿⠛⣻⣽⣿⣿⣶⣉⣽⣥⡤⣶⣏⠿⣥⡾⠿⣿⣿⡿⡃⣿⣦⣮⡡⣿⣿⣾⣺⣯⠞⣿⢿⣶⣺⣿⣿⣿⣷⣿⣶⣻⣿
⡟⠀⠛⢿⣶⣇⠙⠂⠙⠡⢞⠶⢟⣛⢁⣨⡤⠶⢿⣿⠽⠄⡌⢷⣦⢠⣜⣹⣷⣷⣲⣯⣽⣽⣽⣽⣷⡿⢿⠿⠛⡋⠀⠫⠿⠟⠙⠉⠁⠙⢬⡟⢢⣴⣴⣙⣩⠻⠟⠁⢿⣿⣿⣷⡟⠛⠽⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⢄⠙⢛⡛⢃⣀⢴⣺⢷⡹⢿⠉⡆⡢⣷⣿⡌⢸⣅⣄⣹⣆⢰⣻⣛⣿⡛⢯⡭⢾⠻⠥⣧⣵⣾⣦⠀⠽⠳⡒⠒⢠⢳⣀⠶⠑⣾⠶⢾⣯⣷⣿⣫⣛⡫⣈⠒⢖⣦⠍⣡⣿⢗⠀⢀⣈⠋⠿⠋⠟⡉⠥⢀⣺⢋⡝
⡀⢡⢟⠾⡦⠥⣹⠤⣀⣹⣄⢹⣵⢼⣷⣦⡜⣲⣻⠻⣸⣞⣿⣾⣾⣻⠛⠧⣽⠿⢿⢹⢙⣶⣶⣦⠁⠛⣀⢴⡛⠷⣔⣾⣾⡙⣿⣿⣿⠛⠛⢀⢩⣋⡋⠹⢭⣿⣏⣯⣽⡋⠙⢉⣀⡀⢀⣍⢯⠆⠀⠉⣢⣶⡏⠈⣿⣿
⠻⠟⣬⣶⣤⠘⢿⣭⣁⠙⣿⠟⠋⢿⡿⢿⠛⠛⣎⣯⣱⣆⡩⡽⠻⢏⠿⡻⠶⠿⠋⡏⡏⠻⣨⣳⣤⣦⡬⠿⠇⢴⣞⣟⠻⢿⣿⣿⣿⠲⡞⣚⣿⣿⢿⢽⢛⣯⢮⣥⣿⣟⡯⠛⣵⠂⡚⣛⡾⣧⣈⣠⣻⠿⣥⡤⠻⢟
⠀⡀⢘⣻⣿⣽⡟⡛⠉⠈⣡⡀⣠⢊⡉⢻⣶⣤⣄⣚⣭⡥⣽⣟⡜⡿⢶⡛⡕⢩⣶⣾⠛⣵⢍⢿⣿⣳⡢⣴⣄⣉⠡⠑⢚⣿⣿⣿⢟⣤⣿⡻⣿⣿⣶⣴⡎⣿⣧⣽⢟⣿⣧⣛⣉⣤⣴⣿⢢⣾⣶⡿⠿⠂⣸⡵⠪⡭
⣧⣒⣭⡀⠉⣅⣀⠑⢦⣤⡫⢳⣿⣒⢁⣠⡋⣋⢠⣄⣬⠱⣿⠼⢟⡹⣯⣟⣽⣹⡮⢍⡡⡱⡼⣡⣿⢿⠏⣯⡿⣿⡻⢿⡄⢩⣿⣿⡽⣖⢻⢏⠝⡘⣿⣇⣿⣙⡛⠻⣿⣯⣿⡁⠿⠉⠲⣿⣶⣮⠙⠁⠀⠐⣾⣬⣦⡰
⢧⡟⠻⣯⣡⣥⠀⢀⣼⣿⡰⢆⢨⣽⣿⡭⣿⣽⣷⠴⣌⠸⢿⣔⣿⠿⣷⡛⡾⡿⣯⣿⣏⠹⠳⣄⠰⠞⢿⡏⠙⠻⠿⣯⣷⣦⣽⣿⣿⣿⣶⣟⠂⡼⠾⢏⣾⣿⣿⣿⣚⣿⣿⣷⣮⣿⣿⣶⡏⠁⠀⠠⠀⠀⠀⣠⣞⡏
⢠⣶⡾⢾⣿⣯⣆⢬⣿⡵⡯⢿⣷⢿⠻⣿⢾⣽⣿⣿⢿⡆⠀⠀⠳⠾⣿⣏⣿⣋⡟⢿⣴⡮⡈⢭⡂⠀⢈⣿⣔⢴⢶⡽⣿⣇⠂⡿⣿⣭⣭⣟⠂⣹⣿⣿⣿⢷⠿⢿⣿⣿⡿⣷⡍⠛⠙⢿⣧⢀⡀⠘⠄⠀⠀⠘⢁⣴
⠸⣿⣿⣬⣽⡏⢿⣌⢡⠙⢻⣿⣿⣁⡻⣿⠻⢿⠿⠋⢱⠁⠀⠀⠀⠙⣭⡿⣬⣷⣶⣌⣁⣿⣿⠖⠶⢳⣾⣯⣻⡄⡙⢀⡒⠿⢷⣈⣓⣦⠿⣠⣾⣿⣿⣿⣿⣽⣳⣿⣿⣿⣟⡻⣧⠀⠀⢒⣿⡟⡧⣤⣴⣀⣗⠷⣼⣿
⢀⢭⣉⢍⣫⡇⣽⡧⣭⠦⣝⣽⢿⣿⠛⠛⢀⣨⣦⠠⡠⡿⣆⣀⠠⣄⣾⢽⡿⡿⣻⣭⣇⢽⠟⡞⠒⠿⡟⣽⣿⣿⡱⣞⣈⣤⡘⣿⡿⠿⣿⣿⣿⣽⣟⠛⣿⣿⣽⣿⣿⣋⣟⣹⣫⣁⣘⣛⡻⣿⣿⡿⢿⣧⣭⣻⣿⣿
⢁⢻⡟⣗⣉⣠⡉⣃⢠⣌⣻⣟⡿⠿⣧⣬⡿⣽⣿⣷⣻⣿⣏⡃⣀⣽⡿⠾⢖⠛⠛⠋⡞⠈⠰⣥⢭⣶⡟⠻⢽⣯⠾⣶⣿⣯⣿⣾⣿⣺⣻⣏⣥⣽⣿⣾⢿⣦⣺⣿⣿⣿⣿⣿⣿⣿⣿⣏⠷⣷⣫⢹⣿⣷⡿⢿⡍⠑
⠘⠛⢻⣟⠟⢟⢛⢛⡿⣿⣯⣯⣿⣷⣶⣬⣟⠿⣿⣷⣷⠛⠻⢷⠔⣀⣁⣄⣺⠶⠠⢦⢠⣬⣰⣹⣾⣶⣿⣮⡸⣿⠯⢉⡅⠿⣿⣿⣿⣿⣽⣿⢿⣿⡿⣻⣿⣿⣿⡿⣧⣯⣍⡵⢿⠿⣿⣿⣿⣟⣋⡈⠛⠿⠿⢵⢿⢷
⢀⣶⠄⢠⣼⠯⡥⠨⣧⣶⠄⠘⢙⡂⣤⠀⡉⠀⠀⠀⢱⡞⣓⠋⠋⠀⠀⠙⠂⢰⢈⡁⢾⡽⢖⠛⣯⠷⠏⠄⣴⣋⣉⣿⣿⣿⣦⣍⠼⢿⣿⣿⣉⣟⡿⣿⣿⣷⠗⠿⢗⣶⠟⢟⣜⡖⠀⣤⣶⠀⢠⣿⣿⣿⡉⠀⠀⠀
⣾⣵⠟⡂⠈⠼⠋⠸⠛⢃⢀⠤⠨⡀⢠⠀⠓⠔⡢⡀⠿⠿⠿⣶⡧⠀⢶⡶⡯⡍⠝⠣⢬⣍⡟⠀⠊⠋⢉⠊⠡⠀⣷⣿⠏⣴⣿⡿⡶⣏⠿⡿⡿⠥⠭⠛⠀⢤⢆⠀⠈⠀⠄⠠⠊⠀⠀⠼⠀⠈⠙⣷⢦⠉⢵⠞⠲⠿
⠐⠤⠀⠉⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠠⡷⠀⠠⠙⠁⠀⠀⣖⣟⠋⠚⠀⠀⠺⠍⠀⠄⢸⢠⡠⠀⠀⠒⠂⠀⠠⢀⠄⣠⣄⣀⠫⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⠈⠁⢰
⣤⣤⣿⣿⣿⠀⢀⣠⣤⣤⢀⠀⠀⠀⠀⢁⡠⠂⠀⠀⠰⣿⡿⣿⡴⠣⠀⠀⠀⢀⠀⠀⢠⡼⠀⠐⠀⠀⢸⡇⠀⠰⣼⣿⣿⡏⠁⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣶⣦⡀⠀⠀⠀⠀⠈⠉⠀⠀⢣⣴⣿⠏
⠽⠟⠛⠝⠿⠇⠈⠛⢿⣿⣧⡀⠄⠀⠀⠀⠀⠀⠈⠀⠀⠄⣷⣶⢤⡃⠀⠀⠀⠈⠒⠀⠀⠀⠀⠀⠀⠀⠈⣀⠀⠐⠟⠛⠋⠀⠀⠀⠀⠀⣤⣄⣦⠀⠀⠀⠀⠀⠀⡤⢠⣼⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢚⣣⣶⣄
⢀⡂⠀⠀⠀⠀⠀⠀⡱⠲⡇⣀⠡⠆⠀⠀⢀⢀⣄⡀⠀⣤⣼⠇⠈⠉⠀⠠⠒⠀⠀⣤⣄⡀⠀⠴⠀⣥⣄⣀⢀⢄⠀⠀⠀⠠⠀⠠⢤⠐⣯⡉⠙⠀⠀⠀⢀⡤⣰⣤⣤⣭⡄⣀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠁⢈⣍⢴⡉
⣸⡄⠀⢠⣜⠀⠀⠀⡀⠀⣬⡀⣐⣿⡶⣤⡀⠀⠈⢠⡈⠝⢉⣼⣿⣇⡀⣶⣿⣦⢥⣍⠿⠀⠀⠀⠀⠁⠠⢾⠛⣀⣴⠒⢒⣤⣾⣶⠨⣀⣧⣡⣰⠲⢠⡄⢀⣛⣿⠛⢋⢹⠿⢷⣦⠀⠀⢀⠁⠀⠀⣲⣬⠶⠛⢉⠀⣀
⠿⢿⠇⠾⠟⡤⠀⠀⠑⠆⠉⡚⠺⣿⢮⣿⣿⣿⡔⠀⢁⣵⣾⣿⣿⡿⢠⣍⡉⣿⡻⠿⠠⢾⣾⢟⡌⣀⣀⠈⣍⣧⡘⣌⠸⠛⠻⢟⠠⣛⣾⣿⣅⢐⠂⠀⠈⠾⠳⢖⠐⠂⠀⣤⡌⣀⡸⣃⠀⠐⡶⣶⣶⣮⣴⡿⣯⣩
⣿⡿⡉⡯⠐⠀⠀⢄⠈⢈⣛⠨⣦⠽⢷⣋⠯⣷⣬⢌⣩⣿⣿⣿⣟⣿⣞⣙⡻⡟⣫⣿⠿⡿⣗⡎⢇⠙⢻⣧⠌⠘⡔⡈⠀⡸⣒⠀⢶⣷⡿⣿⢿⣛⠁⠀⠀⠀⠐⠦⡀⣽⣤⣶⠶⠿⣿⡏⠉⡴⠁⠨⢉⣛⣿⡲⢷⣿
⢈⠻⣶⣯⠀⢀⡘⠏⠁⣉⠀⠀⠁⠀⢆⣭⢑⣛⡻⠯⣸⣿⣿⠟⢻⣿⣿⡏⠐⢗⣛⢀⠀⠀⠷⡷⠼⠱⣾⡽⣷⣄⡠⡀⠀⠁⠀⢖⡘⠃⠈⠘⠂⣁⠀⠀⠀⠢⠴⣔⣢⣼⣻⣶⡢⡠⠰⢄⠀⠀⠀⣠⣉⢩⡕⣶⣶⣾
⣶⢿⡏⠙⣅⠀⠐⣀⢔⣿⡿⠁⢀⣴⣶⡟⠉⢭⡫⡔⠹⠟⠋⠙⠍⠻⣿⣾⡇⢸⡝⠴⣧⣄⠀⠀⠘⠝⢻⣾⣿⣿⣿⣦⠀⠠⠀⠈⡉⠁⠀⠀⢠⡿⠀⢐⡭⣵⣦⣝⣛⣿⣟⣛⢷⣮⢿⣦⣯⣉⢬⣽⡝⣯⠓⣿⣸⣷
⢛⢸⢿⠤⠽⣀⠙⠈⠛⢉⣁⠀⠂⠀⡠⠀⠀⠀⢌⣀⠜⢆⡀⠠⠀⠉⠢⣕⢢⢰⠮⢀⣉⡀⣀⣴⣤⣄⣧⡿⠿⠿⠿⠋⠨⠉⠿⠄⣠⣤⣴⣤⣆⣚⣦⣀⣴⣿⣿⠿⢿⢿⣷⣴⣾⢿⡿⢿⣞⡏⣽⢟⣀⡉⣴⡦⢙⣿
⡴⣶⠆⣠⣎⡵⠿⣄⠸⣿⢿⡸⣶⡄⡘⠙⣳⣻⣗⢲⣾⣚⣛⡷⣌⠑⠀⠉⣁⡀⠤⣨⣷⢆⣿⣿⢿⣿⣷⣠⣀⠀⠀⠀⠀⡀⠀⠶⠟⠛⠢⣀⡿⠯⣟⢓⣤⣻⣴⣬⡈⠤⠥⠙⢭⡋⠉⣿⣿⠙⢿⠟⢿⡷⡿⠷⠿⡻
⢺⣿⣶⣶⣾⢿⠔⠺⣧⡀⡀⣁⢰⣴⡁⡄⣀⣙⠛⢷⡶⡯⢖⣧⣿⡑⢦⣸⢿⠛⠂⠸⢏⣿⣷⣶⣿⢡⣿⣿⣿⣷⡀⢁⠁⡂⢀⡀⣃⣾⣶⠃⣧⡘⣻⣿⣻⣿⣷⠾⣇⣀⣔⣜⣴⣷⢟⣉⣹⣾⣷⣷⣶⣢⣈⣤⢬⣄
⢿⣿⣷⣤⣭⣓⢠⡀⠀⡑⣿⣻⣿⠗⠁⠹⣛⣘⣲⣰⡩⢻⣕⣿⣧⡿⢷⣎⢻⣤⣰⢦⣿⣿⣿⣿⣿⣤⣿⣿⣿⠛⣷⣶⣿⡿⠻⣦⣌⠉⣩⠃⣐⣈⣙⠉⣷⡟⣿⣿⡿⣿⢿⣿⣭⡶⣻⣿⠓⣻⣿⣿⢷⣻⢿⣿⠋⠳
⡂⢸⣜⡻⣿⡵⡥⠟⠀⣝⢏⣡⣤⢴⣲⡶⠐⠩⡩⠖⠙⠊⠘⠟⠛⣦⣬⣅⢪⡉⣹⣶⣝⢿⣿⣿⡛⣫⣽⣿⣿⣷⣉⣉⣥⡤⣶⣏⠿⣥⡾⠿⣿⣿⡿⡀⣿⣦⣮⡵⣿⣿⣿⣺⣯⠞⣿⣿⣦⣺⣷⣿⣿⣷⣿⣶⣺⣿
⡿⠀⢛⢻⣶⣇⠙⠂⠙⠡⢞⠞⠟⣛⢁⣨⡤⠶⢿⣿⠿⢄⡌⢷⡦⢠⣝⣩⣷⣷⣲⣯⣽⣿⣽⣯⣷⡿⢿⢿⠛⡋⠀⠹⠿⠟⠙⠉⠑⠙⣭⣗⢢⣴⣴⣚⣩⠻⠟⠁⢿⣿⣿⣷⡿⠛⠽⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⡀⢄⠙⢛⡛⢃⣀⢴⣼⢷⡹⢿⠋⡆⠢⣷⣿⠭⢸⣅⣀⣹⡆⢰⣻⣛⣿⠛⢯⣭⢾⠻⠥⣧⣵⣮⣦⠀⠵⠳⠒⠒⢀⢳⡀⠶⢑⣾⢶⢾⣽⣷⣿⣥⣛⡩⣀⠒⠶⣦⠍⣠⣿⣗⠀⢀⣈⠛⠿⢋⠟⠉⠥⢀⣺⢋⡝
⠀⢡⢟⠾⡦⠥⣹⠠⣄⣹⣄⢹⣵⢼⣷⣦⡜⣲⣻⠻⣸⣟⣿⣾⣶⣻⠛⠧⣽⠿⠿⢻⢙⣶⣶⣦⠉⠛⢀⢴⡛⠷⣔⣾⣾⡙⣾⣿⣿⠟⠛⢀⢩⣋⡋⢸⢭⣿⣏⣯⣽⡋⠙⢉⣀⡀⢀⣍⢯⠆⠀⠈⣠⣶⡏⠀⣿⣿
⠻⠟⣬⣦⣤⠘⢿⣽⣁⠙⣿⠟⠉⢿⡿⢿⠛⠛⣎⣯⣑⣆⡩⡿⠻⢏⠿⡿⠷⠿⠋⠏⡏⠻⣨⣷⣤⣦⡬⠿⠆⢴⣞⣏⠿⢿⣿⣿⣿⠲⡞⣚⣿⣿⢯⢙⢛⣯⢮⣤⣿⣟⡯⡝⣵⠃⡚⣛⡾⣧⣈⣠⣛⢿⣥⡬⠻⢟
⠀⡀⢘⣿⣿⣽⡟⡛⠉⠘⢥⡀⣠⢈⡉⢻⣶⣤⣄⣚⣭⡭⣽⣿⡼⡿⢶⡻⡕⢩⣶⣖⠛⡵⢍⠻⣿⣳⣢⣴⣄⣉⡡⠑⢚⣿⣿⣿⢗⣤⣿⡿⣿⣿⣶⣴⡎⣿⣧⣿⣿⣿⣧⣛⣉⣤⣴⣿⢦⣾⣶⡿⠯⠂⣸⡵⠪⡭
⣧⣒⣭⡀⠙⣁⣀⠑⢶⣤⣻⢳⣿⣐⢁⣠⡋⣋⢠⢄⣬⠹⣿⠼⢟⡻⣯⣟⣽⣹⡮⢍⡁⡵⡼⣡⣿⢿⠯⣷⡾⣻⡿⠿⡄⢨⣿⣿⡿⣖⢿⢏⠝⣙⣿⣅⣿⣛⡛⠻⣿⣿⣿⡁⠿⠙⠲⣿⣶⣭⠙⠁⠀⠸⣿⣬⣦⡰
⢧⡟⠻⣯⣡⣥⠀⢀⣴⣾⡰⣆⢸⣽⣿⡭⣿⣿⣷⡴⣌⢸⢿⣕⡿⠿⣷⣝⡿⡿⣯⣿⣍⠹⠳⣄⠠⠞⢿⡏⠙⠻⠷⢯⣷⣦⣿⣿⣿⣿⣶⣟⠂⠼⠾⣏⣿⣿⣿⣿⣺⣿⣿⣷⣯⣿⣿⣷⡏⠁⠀⠠⠀⢀⠀⣠⣞⡏
⢠⢶⣾⢺⣿⣯⣆⢬⣿⡷⡯⢿⣿⢿⠻⣿⢮⣿⣿⣿⣿⡆⠀⠀⠳⠾⣿⣏⣿⣫⡟⢿⣴⡮⡉⢭⠂⠀⢈⣿⣦⢰⡶⠽⣿⣇⠀⡿⣿⣭⣭⡟⠂⢹⣿⣿⣿⢷⠿⢟⣿⣿⡿⣷⡍⠋⠙⠿⣦⢀⡀⠀⠄⠀⠀⠘⢁⣴
⠸⣿⣿⣬⣽⡏⢿⣌⢩⠙⢻⣿⣿⣑⡻⣿⠻⢿⠿⠋⢱⡁⠀⠀⠄⠙⣭⡿⣬⣷⣶⣌⢁⣿⣿⠖⠶⢿⣾⣯⣻⡄⡉⢀⡒⠷⢷⣈⣓⣦⠿⣠⣾⣿⣿⣿⣿⣽⣳⣿⣿⣿⣟⡻⣧⠀⠀⢒⣟⡿⡧⣤⣴⣀⣖⠧⣼⣿
⢀⢬⣉⢍⣫⡧⣽⡧⣭⠆⣝⣿⢿⣿⠛⠛⢀⣨⣦⠠⡢⡿⣆⢀⠠⣄⣾⢽⠿⣿⣻⣭⣅⢽⠟⡞⠓⠏⡟⣹⣯⣿⡑⣞⣨⣄⡘⣿⣭⠻⣿⣿⣿⣽⣟⠛⣿⣿⣝⣿⣿⣋⣟⣹⣩⣁⣘⣛⡻⣿⣿⡿⢿⣧⣭⣻⣿⣿
⢁⢻⡏⣗⣉⣠⡉⢃⣡⣌⣻⣟⡿⠿⣧⣬⡿⣽⣿⣷⣻⣿⣏⡃⣈⣽⡿⠾⢖⠛⠛⠋⡟⠈⠸⣵⢭⣶⡗⠻⢽⣯⢾⣶⣥⣯⢽⣾⣯⣻⣻⣯⣥⣽⣿⡾⢿⣦⣺⣿⣿⣿⣿⣿⣿⣿⣿⣏⠿⣷⣫⢻⣿⣿⡿⣟⡁⠙
⠘⠛⢻⣟⠟⢟⠛⢛⡿⣿⣯⣿⣿⣷⣶⣬⣟⠿⣿⣧⣷⠛⠻⢷⠔⣀⣀⣄⣺⠶⠠⢦⢡⣾⣰⣹⣷⣶⣿⣮⠸⣿⠯⢩⡅⠽⣿⣿⣿⣿⣽⣿⣿⣿⡿⣻⣿⣿⣿⡿⣧⣯⣍⡽⢿⠿⣿⣿⣿⣟⣏⡈⠛⠿⠿⢤⢿⢷
⢀⣶⠄⢠⣼⢏⡵⢨⣧⣶⠄⠘⢉⡀⣤⠀⣉⠀⠀⠀⢱⡞⣓⠋⠋⠀⠀⠙⠆⢰⢈⡁⢾⣿⣖⠙⣿⠷⣏⠄⣴⣋⣉⣿⣿⣿⣦⣝⠼⢿⣿⣿⣘⣟⡿⣿⣿⣷⠗⠿⢗⣶⠟⢟⣝⡖⠀⣤⣶⠀⢠⣿⣿⣿⡉⠀⠀⠀
⣾⣵⠟⡂⠈⠶⠋⠸⠛⢋⢀⠤⠠⠀⠠⠀⠑⠐⡢⡀⠟⠿⠿⣶⡧⠀⢶⡶⡧⡍⠝⠣⢬⣍⡟⠀⠊⠋⢉⠋⠡⠀⣿⣿⠋⣴⣿⡿⠶⡇⠿⡿⡿⠧⠭⠛⠀⢤⢆⠀⠈⠀⠄⠠⠊⠀⠀⠼⠀⠈⠙⣷⢦⠉⠴⠞⠲⢿
⠀⢤⠀⠉⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠠⡷⠀⠀⠙⠁⠀⠀⣖⣿⠋⠘⠀⠀⠰⠉⠄⠄⢸⢠⡠⠀⠀⠒⠂⠀⠠⢀⠄⣠⣄⣀⠫⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⡈⠁⢰
⣤⣴⣿⣿⢿⠀⢀⣠⣤⣤⢀⠀⠀⠀⠀⢃⡢⠂⠀⠀⠰⣿⡿⣿⠶⠣⠀⠀⠀⢀⠀⠀⢠⡼⠀⠀⠀⠀⢸⡃⠠⠰⣼⣿⣿⡏⠁⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣶⣦⡀⠀⠀⠀⠀⠈⠉⠀⠀⢃⣴⣿⠏
⠹⠟⠛⠝⠿⠇⠈⠛⠿⣿⣧⡀⠄⠀⠀⠈⠁⠀⠈⠀⠀⠄⣷⣶⢤⡓⠀⠀⠀⠈⠚⠀⠀⠀⠀⠁⠀⠀⠈⣁⠀⠐⠟⠛⠋⠀⠀⠀⠀⠀⣤⣄⣦⠀⠀⠀⠀⠀⠀⡤⢠⣼⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢚⣣⣷⣄
⢀⡂⠀⠀⠀⠀⠀⠁⡱⠲⡇⣀⠡⠆⠀⠀⢀⢀⣄⡠⠀⣤⣼⠇⠈⠉⠀⠠⠒⠀⠀⣤⣄⡀⠀⠴⠀⡥⣄⣈⢀⢄⠀⠀⠀⠠⠄⠠⢤⠐⣯⡉⠙⠀⠀⠀⢀⡄⣰⣠⣠⣭⡄⣀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠁⢈⣌⢴⡉
⢸⡀⠀⢠⣜⠀⠀⠀⡀⠀⣬⡀⣐⣿⡷⣤⡀⠀⠈⢠⡌⢙⢉⣼⣿⣇⡀⣶⣿⣦⢥⡍⠿⠀⠀⠀⠀⠁⠠⢾⠛⣁⣴⠐⢚⣥⣾⣶⠨⣀⣧⣡⣰⠲⢠⣄⢀⣟⣿⠛⢋⢹⠿⢷⣦⠀⠀⢀⠁⠀⠀⣠⣬⠾⠛⣉⠀⣀
⠿⢿⠇⠾⠟⡤⠀⠀⠁⠆⠉⡚⠺⣿⢮⣿⣿⣿⡔⠀⢁⣵⣾⣿⣿⡿⢠⣍⡙⣿⡻⠿⠠⣾⣾⢛⡌⣀⣀⠈⣍⣧⡘⣄⠸⠛⠻⢟⠠⣛⣾⣿⣅⢐⠂⠀⠼⠾⠳⢖⠐⡂⠀⣤⡌⣀⠰⣃⠀⠐⡶⣶⣶⣮⣴⡿⣯⣩
⣿⡿⡋⡯⠀⠀⠀⢄⠨⢈⣛⠩⣦⠝⢷⣉⠯⣷⣬⢌⣩⣿⣿⣿⣟⣿⣞⣙⣛⡟⣫⣿⠿⡿⣗⡎⢇⠙⢳⡧⠌⠈⡔⠈⠀⡸⣒⠀⢶⣷⡿⣿⠿⣝⠁⠀⠀⠀⠐⠦⡀⣽⣤⣶⠶⠾⣿⡍⠀⡴⠁⠨⢉⣻⣿⡲⢷⣿
⠈⠿⣶⣯⠀⢀⡘⠏⠁⣉⠀⠀⠁⠀⢖⣭⣕⣛⡫⠿⣼⣿⣿⠟⢿⣿⣿⡯⠐⢗⣛⠀⠀⠀⠗⡶⠴⠰⣸⣬⣷⣆⣀⡀⠀⠁⠀⢖⠘⠣⠀⠘⠂⣁⠀⠀⠀⠢⠴⣖⣢⣼⣺⣶⡢⡠⠰⢄⠀⠀⠀⡠⣉⢫⠕⣶⣶⣾
⣶⠿⠏⠙⣃⡀⠐⣀⢔⣿⡿⠁⢀⣶⣶⡟⠈⢩⡫⡔⠹⠟⠋⠙⠍⠻⣿⣾⡅⢸⡌⠴⣥⣄⠀⠀⠸⠩⠚⣿⣿⣿⣿⣷⠀⠠⠀⠈⡉⠁⠀⠀⢤⡿⠀⢐⡍⣵⣦⣝⣛⣿⣟⢛⢷⣮⢾⣦⣯⣉⢬⣽⡝⣯⠑⣿⣸⣷
⣛⢹⢿⠤⠽⣀⠙⠈⠛⣉⣁⠀⠀⠀⣠⠀⠀⠀⢌⣀⠚⢄⡀⠠⠀⠈⠢⣕⢲⢰⠮⢀⣉⡀⠀⢀⣀⣄⣧⠿⢿⠿⠿⠋⠀⠁⠚⠄⣠⣤⣠⣵⣆⣚⣆⣀⣴⣿⢿⠿⢿⢿⣷⣴⣾⢿⡿⢿⣞⣎⣽⣟⣀⡉⢴⡦⢙⣿
⣴⣶⠆⣠⣮⠽⠿⣄⠸⣿⢿⡸⣶⡄⡘⠙⣳⣛⣗⢲⣞⣚⣛⡳⣌⠑⠀⢉⣁⡀⢤⣨⣷⢆⣶⣿⣿⣿⣷⣄⣀⠀⠀⠀⠀⠀⠐⠶⠞⠛⠢⣂⡿⠯⣟⢓⣤⣹⣴⣬⡈⠤⠥⠙⢭⡋⠉⣿⣿⠙⢿⠟⢿⡿⡿⠷⠿⡻
⢺⣿⢶⣖⣺⢿⠔⠺⣧⡀⡀⣁⢴⣴⡁⡄⣀⣙⠛⢶⡶⡯⢖⣧⣿⡑⠦⣼⢿⠛⠂⢈⢯⣽⣿⣯⣿⠉⣿⣿⣿⣷⡄⢁⠁⡂⢀⡀⣓⣾⣦⠃⢥⡘⣻⣿⣿⣿⣷⠾⣇⣀⣔⣼⣴⣷⢛⣉⣻⣾⣷⣷⣶⣦⣈⣤⢌⣠
⢿⣿⣷⣤⣭⣓⢀⡀⠀⡑⣿⣻⣿⠗⠁⠹⣟⣘⣰⣚⡙⠻⣝⣿⣧⡿⢷⣏⢻⣦⣠⢦⣾⣿⣿⣿⣿⣤⣿⣿⣿⡿⣷⣶⣿⠿⠛⣦⣌⠉⡩⠁⣐⣈⡙⠹⣶⣟⣿⣿⡿⣿⣿⣿⣭⣶⣻⣷⠓⣻⣿⣿⢷⣻⢿⣿⠋⠳
⡂⢘⣞⡻⣿⡵⡥⠟⠀⣝⢏⡡⣠⢴⡲⡶⠑⠨⡨⠖⠉⠊⠘⠟⢛⣦⣬⣍⢮⡉⣿⣦⣝⢿⣿⣿⡛⣻⣽⣿⣿⣿⣉⣍⣥⡤⣶⣏⠿⣥⡿⠿⣿⣿⡿⡀⣿⣦⣮⡗⣿⣿⣾⣺⣯⠞⣿⢿⣦⣾⣷⣿⣿⣶⣿⣖⣺⣿
⡿⠀⢟⢿⣶⣇⠙⠂⠙⠩⢾⠾⠟⣛⢉⣨⡤⠶⢿⣿⠿⢄⡌⢷⡦⢠⣜⣹⣷⣷⣲⣯⣭⣽⣽⣭⣷⡿⢿⠿⠛⡋⠀⠻⠿⠟⠙⠉⠁⠙⣭⡗⢢⣴⣴⣓⣨⠻⠟⠁⢿⣻⣿⣷⡟⠛⠽⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠄⠙⢛⡛⢓⣐⢴⣺⢷⡹⢿⠋⡆⡲⣿⣿⠍⢸⢅⣀⣹⣦⢰⣻⣻⣿⡛⢯⣭⢾⠻⠥⣧⣵⣮⣆⠀⠴⠳⠒⠒⢀⢳⡀⠶⠑⣾⢶⢾⣭⣷⣿⣭⢛⡫⣀⠒⢶⣦⠍⣠⣟⣷⠀⢀⣌⠛⠿⠩⠟⡉⠵⢀⣺⢋⡝
⠀⢡⢞⠺⡦⠥⣩⠠⣄⣹⣄⢹⣵⢼⣷⣮⡜⣳⣿⠻⣸⣟⣿⣾⣶⣻⠟⠧⣽⠿⠿⢻⠹⣶⣶⣦⠁⠛⢀⢴⡛⠧⣔⣾⣷⣙⣾⣿⣿⠛⠛⢀⢩⣋⡋⢹⢭⣿⣏⣯⣽⡋⠙⢁⣀⡀⢀⣍⢯⠆⠀⠈⣠⣶⡇⠈⣿⣿
⠻⠟⣬⣶⣤⠘⢿⣭⣁⠙⣿⠟⠛⢿⡿⢿⠛⠛⣎⣯⣑⣆⡩⡿⠻⢯⠿⡿⠷⠿⠋⠏⡏⠹⣨⣳⣤⣦⡬⠵⠆⣴⣞⣏⠿⢿⣿⣿⣿⠰⡞⣚⣿⣿⢯⢹⢛⣯⢮⣤⣿⣟⡯⠿⣷⠃⡞⡛⣾⣧⣈⣠⣻⢿⣥⡬⠻⢟
⠀⡀⢘⣻⣿⣽⡟⡛⠉⠘⢡⡀⣠⢈⡉⢛⣶⣤⣄⣺⣭⣭⣽⣟⡜⡿⢶⡛⡕⢩⣶⣖⠛⣵⢍⠻⣿⣳⡂⣴⣄⢉⠡⠑⢚⣿⣿⣿⢗⢤⣟⡻⣿⣿⣶⣴⡎⣿⣦⣿⣿⣯⣧⣛⣉⣤⣴⣿⢢⣾⣶⡿⠭⠂⣺⡥⠲⡭
⣷⣐⣭⡀⠙⣁⣀⠑⢲⣤⣫⢳⣿⣐⢁⣠⡋⣋⢠⣄⣬⠱⣿⠼⢟⡻⣯⣟⣭⣹⡮⢍⡡⡵⡼⣥⣿⢿⠯⣧⡮⣻⡿⠿⡄⢩⣿⣿⡿⣖⢹⢏⠝⣋⣿⣇⣿⣙⡛⠻⣿⣿⣿⡁⠿⠙⠲⣿⣶⣭⠙⠁⠀⠀⣾⣬⣦⡰
⣧⡿⠻⢯⣡⣥⠀⢀⣼⣾⡐⢆⢸⣽⣿⡭⣽⣿⣷⡶⣌⢸⢷⣔⣿⠿⣷⣟⡾⡿⣯⣯⣍⠹⠳⣌⠱⠞⢿⡏⠉⠻⠷⣿⣷⣆⣽⣿⣟⣿⣶⣟⠂⠼⠾⢏⣿⣿⣿⣿⣚⣿⣿⣷⣯⣿⣿⣷⡏⠁⠀⠀⠀⢀⠀⣠⣞⡞
⢠⣶⡾⢺⣿⣿⣆⢬⣿⡵⡯⣿⣶⢿⠻⣿⢮⣿⣿⣿⣿⡆⠀⠀⠳⠾⣿⣏⣿⣫⡟⢿⣴⡮⡉⢭⠂⠀⢈⣿⣄⠰⡶⡿⣿⣇⠀⣿⣿⣭⣭⡟⠂⣹⣿⣿⣿⢷⠿⢟⣿⣿⡿⣿⡍⠛⠙⢿⣧⢀⡀⠈⠄⠀⠀⠘⠁⣴
⠸⣿⣿⣬⣽⡏⢿⣌⠩⠙⢻⣿⣿⣑⡻⣿⠻⢿⠿⠋⢱⠁⠀⠀⠐⠙⣭⡿⣬⣷⣶⣌⢁⣿⣿⠖⠶⣷⣾⣯⣻⡄⡊⢀⡒⠷⢷⣘⣓⣤⠿⣠⣾⣿⣿⣿⣿⣽⣳⣿⣿⣿⣟⡺⣧⠀⠀⢂⣿⡟⡧⣤⣴⣀⣖⠧⣼⣿
⢀⢬⣉⢍⣫⡇⣽⣧⣭⠆⣽⣿⢿⣿⠛⠛⢀⣈⣦⠠⡢⡿⣆⣀⢠⣄⣾⢽⠿⣿⣻⣭⣅⢽⠟⡞⠓⠏⡞⣹⣿⣿⡱⣞⣸⣄⡘⣿⣯⠻⣿⣿⣿⣽⣟⠛⣿⣿⣝⣿⣿⣋⣟⣹⣩⣁⣘⣛⡳⣿⣿⡿⢿⣧⣭⣻⣿⡿
⣁⢻⡟⣗⣉⣠⡉⣃⣠⣌⣻⣟⡿⠽⣧⣬⡿⣿⣿⣷⣻⣿⣏⡃⣀⣽⡿⠾⢖⠛⠛⠋⡟⠈⠰⣡⣭⣶⡗⠻⢿⣯⠾⣶⣭⣫⣽⣾⣿⣸⣻⣯⣥⣽⣿⡾⢿⣦⣺⣿⣿⣿⣿⣿⣿⣿⣿⣏⠲⣷⣫⢻⣿⣿⡿⣿⡁⠙
⠘⠛⢻⣟⠟⢟⠛⢛⣻⣻⡯⣿⣾⣷⣶⣬⣟⠿⣿⣿⣷⠛⠿⢷⠔⣀⣁⣄⣺⡶⠠⢦⢡⣼⣰⣹⣾⣶⣿⣮⠸⣿⠯⢩⡅⠿⣿⣿⢿⣽⣽⣿⣿⣿⡿⣻⡿⣿⣿⡿⣧⣯⣍⡵⢿⠿⣿⣿⣿⣟⣏⡈⠛⠿⠿⢥⢷⢷
⢀⣶⠄⢠⣼⠏⡥⢨⣧⣶⡌⠘⢉⡀⣤⠀⣉⠀⠀⠀⢳⡞⣓⠋⠋⠀⠀⠙⠆⢰⢈⡁⢿⡿⢖⠙⣟⠷⠇⠄⡰⣃⣉⣿⣿⣿⣦⣍⠾⣿⣿⣿⢘⡏⡿⣿⣿⣿⠗⠿⢗⣲⠿⠟⣜⡖⠀⣤⣶⠀⢠⣿⣿⣿⡉⠀⠀⠀
⣺⣥⠟⡂⠈⠖⠋⠸⠛⢃⢀⠤⠠⡄⢠⠀⠑⠐⡢⡀⠿⠿⠿⣶⡧⠐⢶⡾⡷⡏⠙⠣⢭⣍⡟⠀⠊⠋⢉⠊⠡⠄⣷⣿⠯⣴⣿⡿⠦⡏⠿⡿⡿⠥⠭⠛⠀⢤⠄⠀⠈⠠⠄⠢⠊⠀⠀⠾⠀⠀⠙⣷⢦⠩⠵⠞⠲⠿
⠐⠤⠀⠉⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠠⡷⠀⠠⠙⠁⠀⠀⣒⣟⠋⠘⠀⠀⠲⠉⠄⠄⢸⢠⡠⠀⠀⠒⠂⠀⠠⢀⠄⣠⣄⣀⠫⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⠈⠁⢰
⣤⣤⣮⣿⣳⠀⢀⣠⣤⣤⢀⠀⠀⠀⠀⢁⡂⠂⠀⠀⠰⣿⡿⣿⠶⠣⠀⠀⠀⢀⠀⠀⢠⡼⠀⠀⠀⠀⢸⡇⠀⠰⣼⣿⣿⡏⠁⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣶⣦⡀⠀⠀⠀⠀⠈⠁⠀⠀⢃⣴⣿⠏
⠹⠟⠛⠝⠻⠇⠈⠛⢿⣿⣧⡀⠄⠀⠀⠀⠀⠀⠀⡀⠀⠄⣷⣶⢤⡓⠀⠀⠀⠈⠒⠀⠀⠀⠀⠁⠀⠀⠈⣀⠀⠐⠟⠛⠋⠀⠀⠀⠀⠀⣤⣄⣦⠀⠀⠀⠀⠀⠀⡤⢠⣼⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢚⣣⣶⣆
⢀⡂⠀⠀⠀⠀⠀⠁⡑⠰⡇⣀⠠⠆⠀⠀⢀⢀⣄⡠⢀⣤⣼⠇⠈⠉⠀⠠⠒⠀⠀⣤⣄⡀⠀⠴⠀⣥⣄⣈⢀⢤⠀⠀⠀⠠⠄⠠⢤⠐⣯⡉⠙⠀⠀⠀⢀⡄⣸⣠⣠⣭⡄⣀⠀⠀⠀⠀⡀⠠⠠⠀⠐⠁⢈⣍⢼⠉
⢸⡀⠀⢠⣜⠀⠀⠀⡀⠀⣬⡀⢐⣿⡶⣤⡀⠀⠈⢠⡨⠙⠋⣼⣿⣇⡀⣶⣿⣦⢡⡍⠿⠀⠀⠀⠀⠁⠠⣾⠛⣁⣤⠒⠚⣤⣾⣶⠨⣀⣧⣣⣱⠲⢠⡄⢀⣟⣿⠛⢋⢹⡿⢷⣦⠀⠀⢈⠁⠀⠀⣢⣬⡶⠛⣉⠀⣀
⠿⢿⠇⠾⠟⠤⠀⠀⠉⠖⠉⡋⠻⣿⢬⣿⣿⣿⡔⠀⢁⣵⣾⣿⣿⡿⢠⣉⡉⣿⡻⠟⠠⢾⣾⢛⡈⣀⣀⠈⣍⡯⡘⡄⠘⠛⠻⠓⠠⣛⣾⣿⣅⢀⠂⠀⠨⠼⠳⢆⠐⡂⠀⣤⡌⣀⠰⣁⠀⠐⡶⣶⣶⣾⣴⡿⣯⢩
⣿⣟⡋⡯⠐⠀⠀⢄⠨⢈⣛⠩⣶⠽⢶⣋⠯⣷⣬⢌⣩⣿⣿⣿⣟⣿⣞⣙⣻⡟⣻⣿⠿⡿⣗⡊⢇⠙⢻⠇⠬⠐⡄⡈⡀⠸⣂⠀⢴⣿⡿⡿⢿⣛⠁⠀⠀⠀⠐⠤⡀⣽⣤⣶⠶⠿⣿⡍⠁⡼⠁⠨⣉⣻⣿⡰⢶⣿
⠈⢿⣶⣯⠀⢈⡘⠏⠁⢉⠀⠀⠁⠀⢖⣭⣑⣛⡻⠯⣹⣿⣿⠟⢻⣿⣿⡭⠐⢗⣛⠀⠀⠀⠗⠶⠴⠐⣸⣌⣷⣦⣄⡀⠀⠁⠀⢄⠘⠃⠀⠘⠂⣁⠀⠀⠀⠂⠴⣄⣢⣼⣪⣶⡶⡠⠰⢄⠀⠀⠀⡠⣉⢫⠗⣶⣶⣾
⣶⢿⠍⠹⣁⡀⠐⣀⢔⣿⡿⠁⢀⣴⣶⡟⠉⢩⡫⡔⠻⠟⠋⠙⠍⠹⣿⣾⡅⢸⡌⠴⣵⣄⠀⠀⠸⠱⠛⣿⣿⣿⣿⣿⠀⠢⠀⠈⡉⠁⠀⠀⢠⠷⠀⢀⡍⡵⣤⣙⣙⣿⡟⢻⢷⣬⢷⣬⣫⣉⢬⣽⡝⣯⠑⢿⣸⣯
⢛⢹⢿⠥⠽⣀⢙⠈⠛⢉⣁⠀⠀⠀⡠⠀⠀⠀⢌⢀⠘⢆⡀⠠⢀⠈⠣⣕⢲⢲⠬⢀⣉⡀⠀⠀⡀⢄⣷⠿⢟⠛⠛⠋⠠⠀⠘⠄⠠⣄⣠⣵⣂⣚⣂⣀⣴⣿⣿⠿⢿⢿⣷⣴⣾⢿⡿⢿⣞⣎⣽⣟⣁⡉⢴⡦⢙⣿
⡼⣴⠆⣤⣮⡽⠿⣄⠸⣿⢿⡸⣦⡄⡘⠁⣱⣛⣗⢳⣞⣚⣛⣳⣌⠑⠀⠉⡁⡀⢤⣸⣷⢆⣴⣾⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠐⠶⠞⠛⠢⣀⡿⠯⣿⢓⣢⢻⣥⣮⡈⠤⠥⠙⣭⡛⠉⣿⣿⠛⢿⠟⢿⡷⡿⠷⠿⡻
⢺⣿⢶⣖⣾⢿⠐⠺⣧⡀⡀⣀⢼⣴⡁⠄⣀⣙⠛⢲⡶⠷⢖⣧⢿⡑⢦⣸⢿⠚⠂⠘⠯⣿⣿⣯⣿⠋⣹⣿⣿⣷⡄⢀⢁⡂⠀⠀⣃⣶⣦⠃⣥⡘⣻⣿⣿⣿⣷⠾⢇⣀⣐⣜⣴⣷⢛⣉⣻⣾⣿⣷⣶⣢⣈⡤⢄⣤
⢿⣿⣷⣤⣭⣓⢀⡀⠀⣙⣿⣻⣿⠗⠁⠹⣛⣘⣲⣲⡫⢻⣝⣽⣧⡽⢶⣏⢻⣦⣰⠦⣾⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣴⣾⡿⠻⣆⡌⠉⣩⠁⢐⣈⣙⠩⣶⣟⢿⣿⡿⣿⢟⣿⣿⡶⣻⣷⠓⣻⣿⣿⢷⣻⢿⣿⠏⠲
⡂⢸⣞⡻⣿⡡⡧⠟⠀⣝⢏⡡⡤⢔⡲⡶⠑⠨⡩⠖⠉⠊⠘⠟⢛⣦⣬⣅⢪⡉⣻⣦⣝⣿⣿⣿⡟⣻⣽⣿⣿⣿⣈⣱⣥⠤⣴⣏⠿⣥⡿⠿⣿⣿⡿⡁⣿⣦⣯⡳⣿⣿⣾⣺⣯⠞⣿⣿⣄⣺⣷⣿⣿⣶⣿⣶⣺⣿
⡿⠀⢛⢻⣶⣇⠙⠂⠙⠩⢞⠖⠟⣛⢁⣨⣤⠶⢿⣿⠽⢄⡌⢷⡦⢠⣜⣹⣿⣷⣶⣯⣭⣽⣼⣭⣷⡿⢿⠿⠛⡃⠀⠫⠿⠟⠙⠉⠑⠙⣭⡗⢢⣴⣴⣗⣩⠻⠟⠡⢿⣻⣿⣷⡿⠛⠽⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠄⠙⢛⡛⢃⣐⢴⣸⢷⡻⢿⠋⡆⡲⣷⣿⠌⠨⢅⣀⣹⣆⣰⣳⣻⣿⠛⢯⡭⢾⠻⠥⣥⣵⣮⣆⠈⠤⠳⠒⠒⢀⢳⡀⠶⠑⣾⢲⢾⣭⣷⣿⣧⣛⡩⣀⠒⢖⣦⠍⣠⣟⠗⠀⢀⣌⠛⠿⠉⠟⡩⠥⢀⢺⢋⡝
⠀⢁⢞⠺⡦⠥⣹⠡⣀⣽⣄⢹⣥⢾⣷⣦⡘⣳⣿⠻⣸⣶⣿⣾⣶⣻⠟⠥⣼⠻⠿⢻⢙⣶⣶⣦⠁⠛⢂⠴⡚⠷⡄⣾⣾⣙⣿⣿⣿⠛⠛⢀⢩⢛⡉⠺⢭⣿⣍⣯⣿⡋⠙⢁⣀⡀⣀⣍⢯⠆⠀⠉⣠⣶⡏⠈⣿⣿
⠻⠿⣬⣶⣤⠘⢿⣭⣁⠙⣿⡟⠙⢿⡿⠿⠛⠛⣎⣭⣱⣆⡨⡟⠻⢏⠿⡻⠶⠾⠋⠏⡏⠪⣨⣣⣤⣦⡬⠵⠆⣰⣞⣟⠻⢿⣿⣿⣿⠰⡖⣟⣿⣿⢯⢉⢛⣯⢮⣤⣿⣟⡯⠝⣥⢃⡜⡛⣺⣦⣈⣀⣛⢿⣥⡤⠿⢟
⠀⡀⢘⣻⣿⣽⡟⡛⠉⠙⢡⡄⢠⢊⡉⢛⣶⣤⣄⣺⣭⡥⣽⣟⡸⡿⢶⡛⡕⠩⣶⣞⠒⣷⢉⠛⣟⣻⡦⣴⣄⢉⠡⠑⢘⣽⣿⣿⢗⣤⣟⡹⢿⣿⣞⣴⡎⣿⣧⣿⣟⣯⣧⣛⣈⣤⣴⣿⢢⣾⣶⡿⠏⠀⣸⡥⠨⡭
⣧⣐⣭⡀⠉⣁⣀⠑⢦⣤⣫⢳⣿⣐⢁⣠⡋⢋⢠⢄⣬⠱⣿⠼⢟⡹⣯⣛⣭⣻⡮⢏⡁⠵⡼⣡⣿⢿⠯⣣⡬⣛⡻⠿⡄⢨⣿⣯⡿⣖⢹⢏⠝⣋⣿⣅⣿⣛⡛⠻⣿⣯⣿⡁⠿⠙⠲⣿⣶⣬⠛⠁⠀⠐⣾⣤⣆⡰
⣧⡟⠻⣯⣡⣥⠀⢀⣴⣞⡰⢆⢸⣽⣿⡭⣽⣽⣷⡶⣍⢸⢾⡅⡿⠿⣷⣟⡾⠿⣯⣫⣍⠹⠳⣄⠰⠞⢿⡎⠙⠺⠧⣿⣷⣆⣽⣿⣟⣟⣶⣿⠂⠌⠾⢏⣿⣿⣿⣾⣟⣿⣿⣷⣯⣿⣿⣶⡏⠁⠀⠀⢀⢀⠀⣠⣞⡟
⢠⣶⡾⢾⣿⣿⣆⢬⢿⡵⡿⣿⣿⢿⠻⣿⢾⣽⣿⣿⣿⡆⠀⠀⠳⠾⣿⣏⣿⣫⡟⢿⣴⡮⡈⢭⠂⠀⢈⣿⣄⢰⣶⡾⣿⣇⠀⠿⣿⣭⣭⡟⠂⢹⣿⣿⣿⣷⠿⢟⣿⣿⡿⣿⡍⠓⠙⢿⣮⢀⡀⠐⠄⠀⠀⠘⠁⣴
⠸⣿⣿⣬⣻⡏⢿⣌⢡⠙⢻⣿⣿⣑⡻⣿⠿⢿⠿⠋⢱⡁⠀⠀⠄⠻⣭⡿⣬⣧⣶⣌⢁⣿⣿⠒⠶⢓⣾⣯⣻⡄⡊⢀⡚⠷⢷⣈⣛⡤⠿⣠⣿⣿⣿⣿⣾⣽⣳⣿⣿⣿⣛⡺⣧⠀⠀⢂⣿⡞⡧⣤⣴⣀⣖⠧⣼⣿
⢀⢩⣉⢉⣫⡇⣽⡧⣭⠄⢝⣿⢟⣿⠛⠛⢀⣨⣦⠠⡀⡿⣎⣀⢠⣄⣾⢽⡿⣿⣻⣭⣅⢙⠟⡖⠒⠏⡟⣹⡯⣿⡱⣜⣨⣄⡘⣿⣭⠻⣿⣿⣿⣽⣟⠛⣿⣿⣝⣿⣿⣋⣿⣹⣩⣁⣘⣛⡳⣿⣿⡟⢿⣧⣭⣻⣿⡿
⢁⢻⡟⣗⣁⣠⡉⣃⣠⣔⣻⣟⡾⠿⢧⣬⡿⣿⣿⣷⣿⣿⣯⡃⣀⣹⡿⠶⢖⠛⠛⠋⡞⠈⢰⣡⢭⣶⡗⠻⢽⣧⠾⣶⣵⣫⣿⣾⣿⣸⣻⣿⣥⣽⡿⡾⠿⣦⣺⣿⣿⣾⣿⣿⣿⣿⣿⣏⠶⣷⣫⢻⣿⣷⡿⣿⠀⠑
⠘⠛⢻⣟⠟⢟⠛⢛⡻⣻⡯⣿⣾⣷⣶⣬⣟⠿⣿⣧⣷⠛⢿⢷⠔⣀⣁⣄⣺⠾⠠⢦⢠⣬⣰⣸⣾⣶⣿⣮⠸⣿⠯⢩⡅⠽⣿⡿⢿⣽⣽⣿⢿⣿⡿⣻⡿⣿⣿⡿⣧⣯⣍⡱⢿⠿⣿⣿⣿⣟⣏⡈⠛⢿⠿⢤⢟⢷
⢠⣶⡆⢠⣼⢏⣕⢨⣧⣷⡄⠜⢋⡀⣤⠀⣉⠀⠀⠀⢳⡟⣓⠋⠋⠀⠀⠙⠇⣰⢈⡁⢾⣿⡖⠛⣿⡷⢇⠄⣵⣃⣈⣿⣿⣿⣶⣍⠿⣿⣿⣿⢙⣏⡽⣿⣿⡷⠗⠿⢗⣶⠟⢟⣝⡖⠀⣤⣶⠀⢠⣿⣿⣿⡉⠀⠀⠀
⣾⣥⡟⡂⠈⠾⠊⠸⠛⢃⢀⠬⠨⠄⠠⠀⠓⠴⣠⡀⠟⠿⠿⣶⣧⠀⢶⡶⡷⡏⠝⠧⢬⣝⡟⠀⠊⠋⢋⠛⠡⠄⣷⣿⠿⣼⣿⡿⡶⡍⠿⡿⡿⠧⠭⠛⠀⢤⢄⠀⠈⠠⠄⠢⠊⠀⠀⠾⠀⠈⠙⣷⢦⠉⠴⠞⠶⢿
⠐⠦⠀⠉⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠠⡷⠀⠠⠙⠁⠀⠀⣶⣿⡋⠚⠀⠀⠴⠍⠀⠄⢸⢤⡠⠀⠀⠒⠂⠀⠠⢀⠅⣠⣄⣈⡫⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⣈⠁⣰
⣤⣤⣶⣿⣻⠀⢀⣠⣥⣤⢀⠀⠀⠀⠀⡁⡠⠂⠀⠀⠰⣿⡿⣿⠷⠣⠀⠀⠀⢀⠀⠀⢠⡾⠀⠀⠀⠀⢸⡇⠀⠰⣾⣿⣿⡏⠁⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣼⣶⣦⡀⠀⠀⠀⠂⠈⠁⠀⠀⣳⣴⣿⠯
⠽⡿⠛⠽⠻⡇⠈⠛⢿⣿⣧⡀⠄⠀⠀⠈⠀⠀⠀⠀⠀⠔⣷⣶⢤⡓⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠈⣃⠀⠘⠟⠛⠋⠀⠀⠀⠀⠀⣤⣄⣦⠀⠀⠀⠀⠀⠀⡤⢠⣼⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢚⣣⣷⡆
⢀⡂⠀⠀⠀⠀⠀⠁⡱⠲⣇⣀⢡⡆⠀⠀⢀⢀⣄⡠⠀⣤⣾⠇⠈⠉⠀⠠⠒⠀⠀⣤⣄⡀⠀⠴⠀⣥⣄⣈⢄⢤⠀⠀⠀⠠⠀⠠⢤⠐⣯⡉⠙⠀⠀⠀⢀⡤⣸⣠⣠⣭⡄⣀⠀⠀⠀⠀⡀⠠⠠⠀⠐⠁⢈⣝⢽⠉
⢸⡀⠀⣠⣟⠀⠀⠀⡀⠠⣮⣀⣐⣿⡷⣤⡀⠀⠈⢰⡨⠙⢋⣼⣿⣇⡀⣶⣿⣣⢡⣍⠿⠀⠀⠀⠁⠁⠠⣾⡻⣁⣴⠐⢒⣥⣾⣶⠨⣀⣧⣻⣱⠲⢢⡄⢀⣟⣿⠛⢋⢹⠿⢷⣦⠀⠀⢈⠁⠀⠀⣢⣬⡶⢛⣉⠀⣀
⠿⢿⠧⠾⠟⡤⠀⠀⠡⠆⢉⡛⠺⣿⢮⣿⣿⣿⡔⠈⢁⣵⣾⣿⣿⡿⢰⣍⡙⣿⡻⠟⠰⢾⣾⢛⡈⣠⡀⠈⣍⣫⡐⡄⠸⠛⠻⠟⠤⣛⣾⣿⣅⣀⠂⠀⠸⠾⠳⢖⠐⡂⢀⣤⡌⣀⡸⣁⠀⠐⡶⣶⣶⣮⣵⡿⣯⣩
⣿⣿⡋⡯⠐⠀⠀⢄⠨⢈⣛⠩⣦⡽⢿⣋⠯⣷⣬⢌⣫⣿⣿⣿⣟⣿⣞⣙⡛⡟⣻⣿⠿⣿⣗⡞⢏⠉⢻⡇⠬⠀⡔⡊⠀⡰⣒⠂⢼⣷⣿⣿⢿⣛⠁⠀⠄⠀⠐⠦⡀⣿⣤⣶⠶⠾⣿⡏⠁⡼⠀⠩⣉⣛⣿⡲⢶⣿
⠈⢿⣶⣯⠀⢘⣘⠟⠃⣉⠀⠀⠁⠀⢶⣭⣑⣛⡻⠏⣽⣿⣿⠟⢿⣿⣿⡯⠐⢗⣛⠀⠀⠀⠷⡷⠶⠐⣸⣬⣷⣶⣤⣄⠀⠁⠀⢒⠘⠣⠁⠘⠊⣁⠀⠀⠀⠢⠤⣔⣠⣾⣻⣶⡦⡤⠠⢕⠀⠀⠂⣠⣉⢻⠷⣶⣾⣾
⣶⢿⠍⠹⣁⠀⠐⣀⢔⣿⡿⠁⢁⣴⣶⡟⠉⢽⡯⣜⠻⠟⠋⠛⠍⠻⣿⣾⠇⢸⣝⠴⣥⣄⠀⠀⠸⠳⠽⣿⣿⣿⣿⣿⠀⠠⠀⠈⡉⠁⠀⠀⢠⡷⠀⢀⡭⣵⣦⣛⣻⣿⡟⣿⢷⣿⢵⣮⣯⣫⢬⣿⡟⣯⠙⣿⣸⣧
⢛⢹⢿⠤⠿⣀⠙⠈⠛⣙⣁⠂⠂⠀⣠⠀⠀⠀⢌⣀⠙⣄⠀⠠⠀⠉⢣⣕⢺⢲⠬⣀⣉⡀⠀⣀⣀⣜⣷⣿⣟⠛⠋⠁⠠⠀⠈⠄⠀⣄⣠⣴⣂⣚⣢⣀⣼⣿⢿⠿⢿⣿⣧⣴⣾⣿⡿⢿⣝⣏⣽⢟⣁⡉⣴⡶⢙⣿
⣕⣴⢆⣤⣮⡿⠿⡄⠸⣿⢿⡸⡦⣄⢸⠙⣱⣛⣕⢵⣾⣛⣻⡶⣌⠑⠀⠉⡃⡀⢤⣨⣿⣶⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠐⠴⠞⠛⠢⣀⡿⠯⡿⢳⣶⢻⣤⣬⡊⠤⠅⢙⣭⣛⠉⣿⣏⠛⢿⠛⢿⡿⡿⡷⠿⡻
⢻⣿⣶⣶⣾⣿⠴⠺⣧⣄⡀⣀⢼⣴⡁⣀⣀⣙⠿⢳⡾⠿⢖⣯⣿⣓⢦⣸⢿⠛⠂⡘⢯⣿⣿⣭⣿⠛⢙⣿⣿⣿⣶⡀⠀⡂⠀⠀⣓⣶⣦⠃⣥⡚⣻⣿⣿⣿⣷⠾⢏⣀⣐⣜⣼⣷⢛⣉⣻⣾⣷⣳⣴⣢⣈⣤⢅⣤
⢿⣿⣷⣤⣭⣒⢀⡀⠀⣙⣿⣻⣿⠗⠃⠹⣟⣘⣺⣺⣫⢿⣝⣿⣧⡿⢖⣏⢻⣤⣰⠦⣾⣿⣿⣿⣿⣤⣾⣿⣿⣿⣿⣷⣾⠿⠻⣄⡌⠉⣫⡁⣘⢘⣙⠋⣿⣿⣿⣿⣿⣻⢿⣿⣽⡶⣿⣷⠓⣻⣿⣿⣷⣻⣿⣿⠟⡲
⡂⢸⣟⡻⣿⡭⡥⠟⠀⣝⣏⡠⣠⢔⡲⡾⠑⠍⡩⠞⠉⠎⠘⠟⢛⣶⣬⣅⢾⡙⣿⣮⣿⣿⣿⣿⡟⣫⣽⣿⣿⣿⣿⣽⣥⡴⣰⣏⠿⣧⡿⢿⣿⣿⡿⡐⣿⣦⣮⡷⣷⣿⣿⣺⣯⠗⣿⣿⣆⣿⣿⣿⣿⣷⣿⣿⣻⣿
⡿⠀⢛⢻⣶⣇⠛⠂⠙⠩⢞⠶⠟⣛⢉⣨⣴⡴⢿⣿⠿⢄⡌⢷⣦⢤⣜⣹⣷⣿⣾⣯⣭⣿⣹⣭⣷⡿⢿⡿⠛⡃⠀⠻⠿⠟⠙⠉⠁⠙⣬⡗⢢⣬⣴⣗⣩⠻⠟⠡⣿⣻⣟⣷⣿⠛⠝⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠄⠙⢛⡛⢃⣐⢴⣺⢷⡻⢿⠋⡆⣲⣿⣿⡬⣸⢍⣀⣹⣖⣰⣳⣻⣿⠟⢯⡭⢾⠻⠭⣷⣵⣾⣧⠀⠤⠳⠒⠒⢀⢷⡀⠶⠑⣾⢲⢾⣽⣷⣿⣳⣛⡽⣈⠒⢖⣦⠍⣱⣿⠷⠀⢀⣈⠛⢿⠫⠟⣩⠥⢀⠾⢋⡽
⡀⢁⢟⢺⡦⠤⣹⠤⣄⣿⣄⢹⣥⢾⣷⣮⣘⣻⣿⠻⣹⣶⣿⣾⣶⢻⡟⡯⣽⠷⠾⢻⠹⣶⣶⣦⠉⠛⢂⠴⠚⠫⣖⣾⣿⢙⣿⣿⣿⠛⠛⠀⢨⠛⡉⢹⢭⣿⣍⣿⣿⡛⠙⢁⣀⡀⣈⣉⢣⠆⠀⠉⣢⣶⡏⠈⣿⣿
⠻⢿⣭⣦⣤⠸⢿⣽⣁⠙⣿⠿⠛⣿⡿⠿⠛⠛⣎⣭⣱⣆⡭⣟⠿⢏⠿⡻⠧⠿⠋⡟⡋⢫⣬⣧⣤⣦⡬⠽⠇⢰⣞⣷⠿⢽⣿⣿⣿⠰⡖⣟⣿⣿⢯⢹⢛⣯⢯⣥⣿⣟⡯⡹⣧⢃⡚⡛⣾⣦⣈⣠⣛⢿⣥⡬⠿⢟
⠀⡀⢘⣻⣯⣽⣟⡛⠉⠙⣡⡄⣠⢊⡍⢿⣶⣤⣤⣺⣭⣥⣽⣟⡜⡿⣶⡻⡕⣹⣶⣖⠓⡵⢉⢟⣟⣻⣦⣴⣀⠉⡡⠑⢚⣻⣿⣿⢗⣤⣟⡳⣿⣿⣶⣴⡎⣿⣧⣿⣟⣯⣷⣟⣉⣤⣴⣿⢤⣼⣶⡿⠏⠂⣸⡥⠲⡭
⣷⣰⣭⡀⠙⣑⣀⠑⢶⣤⣻⢳⣿⣐⢅⣰⡋⣎⢨⣂⣬⢱⣿⠼⢿⡻⣯⣟⣯⣫⡮⣏⡁⠵⡾⣡⣿⣿⢯⣫⡼⣻⡻⢿⡄⢨⣿⣿⡿⣖⢽⢏⢝⣋⣯⣅⣿⣛⡛⢛⣿⣭⣿⡁⠿⠉⠲⣿⣷⣬⠛⠁⠀⠘⣯⣴⣦⡰
⣷⡿⠻⣯⣡⣅⠀⢀⣵⣟⡸⣦⢹⣿⣿⣭⣿⣿⣷⣶⣍⢸⢶⣔⣿⠿⣷⣟⡾⠿⣯⣻⣍⠹⠳⣍⠱⠞⢿⡎⠙⠻⠾⣿⣷⣆⣿⣿⣿⣟⣴⣟⠒⡼⠾⢏⣾⣿⣿⡾⣿⣿⣿⣷⣾⣿⣿⣷⡏⠀⠀⠀⢀⢀⠀⣠⣞⡟
⢠⣶⡾⢾⣿⣿⣆⢬⣿⡾⡿⣿⣿⢟⠻⣿⢮⣿⣿⣿⣿⡆⠀⠀⠳⢾⣿⣏⣿⣻⡟⢿⣴⡬⡈⢽⡃⠀⣈⣿⣔⢰⢶⠿⣿⣇⢂⡿⣿⣭⣭⡟⠂⣹⣿⣿⣿⣷⠿⢿⣿⣿⠿⣿⡟⠓⠙⢿⣧⢀⡀⠐⠄⠁⠀⠘⠁⣴
⠸⣿⣿⣬⣿⡏⢿⣌⢫⠙⢻⣿⣿⣑⣻⣿⠻⢿⠿⠋⢱⡁⠀⠀⠐⠙⣭⡿⣬⣧⣾⣎⣅⣿⣿⠖⠶⢷⣮⣋⣻⡄⡒⢀⡚⠷⠷⣈⣛⡤⡿⣠⣾⣿⣟⣿⣿⣼⣳⣿⣿⣿⣟⡻⣧⠀⠀⢂⣿⡞⡦⢤⣴⣀⣒⠧⣼⣿
⣀⢭⣉⢍⣫⡷⣽⡇⣭⡄⣵⣿⢟⣿⠛⠟⢀⣨⣦⠠⣢⣿⣎⣀⢠⣄⣾⢽⠿⣿⣻⣽⣇⢍⠟⡖⠒⠟⡟⣹⣿⣿⡡⣞⢬⣀⡘⣿⣯⠿⣾⣿⡿⣽⣟⠛⣿⣿⣝⣻⣿⣛⣿⣻⣩⣁⣘⣛⡳⣿⣿⡿⢿⣧⣽⣻⣿⣿
⢃⢻⡟⣗⣉⣠⡙⣃⣠⣔⣿⣟⡿⠿⣧⣬⡿⣽⣿⣿⣿⣿⣿⡇⣀⣹⡿⠾⢖⠛⠟⡋⡞⠈⢰⣣⣭⣶⡗⠻⢿⣿⠴⣶⣵⣧⢿⣾⣿⣲⣻⣏⣥⣽⣿⣾⢿⣦⣿⣿⣿⢿⣿⣿⣿⣿⣿⣏⡷⣷⣯⢹⣿⣿⣿⣿⡍⠙
⠘⠛⢻⣟⠟⢟⢛⢛⣻⣿⣯⣿⣿⣷⣶⣭⣟⠿⣿⣯⣷⠻⢿⢷⠔⣈⣀⣄⣾⡾⠢⢦⢠⣮⣰⣹⣾⣾⣿⣮⠸⣿⠯⢩⡥⢿⣿⣿⢿⣿⣽⣿⣿⣿⡿⣹⡿⣿⣿⡿⣧⣯⣍⡵⢿⠿⣿⣿⣿⣟⣏⡈⠛⢿⠾⢽⢗⢷
⢠⣶⡄⢠⣼⢏⡵⢬⣧⣶⡄⠘⢊⣀⣤⠀⣉⠀⠀⠀⢳⡞⣓⠛⠋⠀⠀⠝⠆⢰⢈⡉⢿⡿⣖⠛⣿⠷⢗⠄⣴⣛⣉⣿⣿⣷⣶⣝⢟⢿⣿⣿⣘⣯⡿⣿⣿⣷⠿⠾⢗⡶⠿⠟⣝⡖⠀⣤⣶⠀⢠⣿⣿⣿⡉⠀⠀⠀
⣾⣧⠟⡂⠀⠶⠋⠸⠓⢋⢀⠬⠭⠄⠀⠀⠑⠴⣠⡀⠟⠿⠿⣾⣧⡀⢶⡶⡧⡍⠟⠣⢭⣕⡟⠈⠚⠋⠋⠊⠡⠄⣿⣿⠯⣴⣿⡿⡦⣇⡿⡿⡿⠧⠭⠛⠀⢠⢆⠀⠈⠀⠄⠢⠊⠀⠂⠾⠀⠘⠙⣷⢮⠩⢴⠞⠶⢿
⠀⠦⠀⠉⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠠⡷⠀⠠⠙⠁⠀⠀⣖⣿⡋⠘⠀⠀⠴⠉⠄⠄⢰⢠⡠⠀⠀⠒⠂⠀⠠⢀⠅⣠⣄⣈⢫⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣈⠃⢰
⣤⣤⣿⣿⣿⡀⢀⣠⣥⣤⢀⠀⠀⠀⠀⣁⡠⠂⠀⠀⠰⣿⡿⣿⡷⠇⠀⠀⠀⢀⠀⠀⢠⡼⠀⠀⠀⠀⢸⡅⠠⠰⣾⣿⣿⡏⠁⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⣬⣶⣦⡀⠀⠀⠀⠀⠈⠁⠀⠀⣳⣴⣿⠋
⠽⠟⠛⠝⠿⠇⠈⠛⢿⣿⣧⡀⠄⠀⠀⠈⠀⠀⠀⡀⠀⠴⣷⣶⢤⡓⠈⠀⠀⠈⠒⠀⠀⠀⠀⠀⠀⠀⠈⣂⠀⠘⠟⠛⠋⠀⠀⠀⠀⠀⣤⣄⣦⠀⠀⠀⠀⠀⠀⡤⢠⣬⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢚⣣⣽⡏
⢀⠂⠀⠀⠀⠀⠀⠁⡳⠰⣇⣀⢡⠆⠀⠀⠀⢀⣄⡁⠀⣤⣼⠇⠈⠉⠀⠠⠒⠀⠀⣤⣄⡀⠀⠴⠀⣥⣄⣈⢄⢤⠀⠀⠀⠠⠀⠠⢥⠰⣯⡉⠉⠀⠀⠀⢀⣅⣸⣀⣠⣭⡄⣀⠀⠀⠀⢀⠀⠠⠠⠀⠐⠁⢈⣝⢴⠉
⢸⡀⠀⣠⣞⠂⠀⠀⡀⠠⣌⣀⣘⢿⣶⣤⡀⠀⠈⢠⡠⠛⠋⣼⣿⣇⡀⣶⣿⣇⢡⣍⡿⠀⠁⠁⠁⠁⠠⣞⠞⣀⢤⡂⠒⣥⣾⣦⠨⣀⣧⣧⣡⠶⢠⡄⢀⣟⣿⠛⢋⢹⠿⣷⣦⠀⠀⢈⠁⠀⠀⣲⣽⡶⢛⣉⠀⣀
⠟⢻⠧⠿⠟⡤⠀⠀⠡⠆⢉⡛⠺⣿⢯⣿⣿⣿⡔⠀⢁⣵⣾⣿⣿⡿⢐⣏⡉⣿⣻⠿⠴⢾⣾⢟⡉⣀⡀⠠⢍⠣⡐⡀⠀⠛⠻⠛⠡⣛⣶⣿⣅⢐⠂⠀⠬⠾⠳⢆⠐⡂⢠⣤⡌⣀⡰⣁⠀⠔⡶⣶⣷⣾⣴⡿⣏⣭
⣿⣿⣉⡯⠀⠀⠀⣄⠨⢈⡛⠩⣦⠭⢷⣋⢯⣷⣌⢈⣩⣿⣿⣿⣟⣿⣞⣙⣛⡯⣻⣿⠿⡿⣗⡚⢇⠘⢺⣥⠬⠐⡄⠈⠀⠐⣒⠀⢼⣿⣿⣿⢿⢛⠉⠀⠄⠀⠐⠾⡀⣹⣤⣶⠶⠾⣿⡏⠁⡼⠁⠩⣉⣟⣿⡲⢶⣾
⠈⢿⣶⣯⠀⢈⡘⠟⠓⣉⠀⠀⠁⠀⢶⣭⣓⡛⡻⠏⢹⣿⣿⠟⢿⣿⣿⣏⠐⢗⣛⡀⠀⠀⠿⡗⠴⠀⣰⣨⣶⣶⣶⣤⠀⠁⠀⢄⠘⠃⠁⠘⠊⣁⠀⠀⠐⠢⢤⣄⣢⣵⣻⣶⡤⡤⠤⢅⠀⠀⠀⣠⣉⢫⠷⣾⣾⣿
⣦⣿⠏⠹⣅⡀⠐⡀⠔⣿⡿⠁⠁⣴⣯⡟⠉⢭⡫⡕⠻⠝⠋⠓⠍⠻⣿⣾⡇⢸⣌⢴⣥⡄⠀⠀⠹⠵⠼⣿⣿⣿⣿⣿⠁⠀⠀⠈⡉⠁⠀⠀⢤⠷⠀⢰⡍⣵⣦⡛⣻⣿⣟⣻⢷⣿⣷⣮⣯⣋⢬⣽⡝⣯⢛⣯⣼⣷
⢛⢹⠷⠤⠿⣀⠑⠈⠛⣙⣁⠂⠂⠀⣠⠀⠀⠀⠌⣀⠙⢄⡀⠠⠀⠘⢣⣕⢲⢲⠬⢀⣩⣶⣿⣿⣶⣞⣷⣿⣯⠙⠉⠑⠠⠀⠀⠀⠀⣄⣠⡴⣂⣚⣆⣀⢼⣿⣿⠿⢿⣿⣧⣴⣾⢿⡿⢿⣝⣟⣽⢿⣁⡉⣴⡮⢝⣿
⣖⣶⠆⣴⣮⠽⠿⣁⠸⣿⢿⡸⢦⡄⠘⠑⣳⣛⣑⢷⣿⣚⣿⡶⣌⠁⠀⠉⡃⡀⢤⣸⣿⣿⡿⢿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠐⠴⠂⠋⠂⣀⡿⡿⠿⠳⣠⣻⣤⣬⠂⠤⠥⢙⣭⡛⠙⣿⣟⠙⢿⠟⢿⡷⡿⡿⣿⡻
⢺⣿⣶⣶⣾⣽⠔⠺⣧⡀⣀⣑⢼⣴⡁⣀⣀⣙⠟⢲⡶⡿⢞⣯⣿⣓⢦⣸⢿⠚⠂⢸⢭⣻⣥⣬⣿⠛⠋⣿⣿⣿⣿⣦⡀⠀⠀⠀⣃⣶⡖⠇⣡⡚⣻⡿⣻⣿⣿⠾⢏⣀⣒⣜⣼⣷⢋⣉⣻⣼⣿⣳⣴⣧⣍⣤⢅⣄
⢿⣿⣷⣤⣥⣓⢀⡀⢀⣑⣿⣻⣿⠗⠃⠹⣟⢐⣰⣺⡫⢿⣝⣿⣧⡿⢖⣋⠻⣄⣰⠦⣾⣿⣿⣿⣿⣠⣤⣿⣿⣿⣿⣿⣿⡟⠻⣄⡬⠉⣩⡀⢈⢘⠛⠫⣿⣿⣿⣿⣿⣿⢟⣻⣽⡦⣻⣷⠗⣻⣿⣿⣷⣻⣿⣿⠟⢲
⡂⢸⣞⡻⣿⡩⡧⠟⠀⣝⣏⣠⣤⢜⣲⡾⠐⠉⣯⠇⠙⠎⠙⠟⠛⣶⣬⣍⢾⠙⣻⣮⡿⣿⣿⣿⠟⣻⣽⣿⣿⣿⣿⣿⣧⡴⣶⣏⠿⣥⡾⢿⣿⣿⡿⡐⣿⣦⣮⠳⣶⣿⣾⡾⣯⠞⣿⢷⣶⣮⣿⣿⣿⣷⣿⣾⣹⣿
⡿⠐⠿⢻⣾⣏⠛⠂⠙⠩⢟⠞⠿⣛⢁⣨⣴⠴⢿⣿⠿⣄⡌⢷⣾⢤⡜⣻⣷⣷⣶⣯⣭⣿⣸⣭⣵⡿⢿⠿⠛⡃⠀⢻⠿⠟⠙⠉⠑⠙⣭⡗⢢⣼⣲⣆⣹⠿⠛⠁⣿⣻⣟⣷⣿⠛⠽⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠄⠙⢛⡛⢛⣰⣴⣲⢷⡿⢿⠯⡖⣲⣿⣿⡍⢨⢅⣀⣻⣆⢰⣳⣻⣿⠛⢯⡭⢶⠻⠬⣧⣵⣾⣆⠀⠁⠳⡒⠖⢀⣷⡀⠶⠑⣾⢲⢾⣭⣷⣿⣣⣚⡯⣈⠒⢶⣦⠍⣱⣟⢷⠀⢠⣌⠻⢿⢹⠟⡉⠵⢐⢾⢏⡝
⡈⢡⢟⠺⣦⢅⣹⠠⣤⣽⣄⢹⣥⢾⣷⣮⣙⣻⣻⠻⣸⣟⣿⣾⣶⣻⠟⣧⣽⠷⠾⢹⢙⣶⣶⣦⠁⠛⠀⠴⠚⠣⣆⣾⣾⠙⣿⣿⣿⠛⠛⠀⢨⡛⡍⠻⢭⣷⣍⣯⣽⡋⠉⢉⣀⡀⣈⣉⢧⠆⠀⠉⣠⣶⡏⠈⣿⣿
⠻⢿⣭⣦⣦⡘⢿⣽⣁⢙⣿⠿⠙⢿⡿⣿⠛⠛⣏⣯⣱⣦⡭⡿⠻⢍⠿⡻⠧⠶⠋⠏⡏⢫⣬⣣⣤⣦⡬⠿⠆⢲⣞⣖⠿⢽⣿⣿⣿⠲⡾⣞⣿⣿⣯⢺⢟⣯⢮⣥⣿⣟⡯⡿⡧⢃⡚⡛⣾⣧⣈⣀⣻⢻⣥⡬⠿⢟
⠀⡀⢘⣿⣿⣽⣟⠹⠉⠙⣡⡂⣠⢊⡍⢷⣶⣤⣦⣻⣭⣭⣽⣿⡔⡿⣶⣻⡕⢹⣶⣮⠓⡥⢉⢿⣟⣻⣦⣴⣄⠈⠡⠑⢈⣻⣿⡿⢗⡤⣟⡳⣿⣿⣲⣴⡎⣿⣿⣿⢟⣯⣧⣿⣉⣥⣴⣿⢤⣾⣶⡿⠏⠂⣸⡅⠲⡭
⣷⣒⣭⡀⠙⡁⣀⠐⢶⣤⣻⢳⣿⣒⢁⣀⡋⣂⣨⣄⣭⢹⣯⠾⣝⡺⣯⣛⣯⣩⣯⣍⡁⠴⡾⣡⣿⢿⠟⣫⣬⣛⡿⢷⡄⢩⣿⣿⡿⣖⢿⢏⢝⡋⣿⣅⣿⣛⡛⠛⣿⣭⣿⡁⠿⠛⢲⣾⣶⣬⠛⠁⠀⠸⣾⣼⣆⡰
⣿⡿⠻⣯⣥⣥⠀⢀⣵⣟⣸⣆⣽⣽⣿⣭⣿⣿⣷⡶⣍⢱⢾⣔⣿⠿⣿⣛⡾⠿⣿⡿⣌⢹⠿⣍⠱⠞⢿⡏⠙⠻⠾⢿⣵⣆⣿⣿⣟⣿⡶⣟⠰⡞⠾⢯⣿⣿⣿⡾⣺⣿⣿⣷⣯⣿⣿⣷⡏⠁⠀⠀⢀⠀⠀⣴⣞⠿
⢤⣶⣾⢺⣿⣿⣆⢬⣿⡾⡿⣿⣿⢟⠻⣿⠮⣿⣿⣿⣿⡆⠁⠀⠳⢾⢿⡟⣿⣛⡟⢿⣴⡤⡈⢭⠃⠀⡈⣿⣴⢴⠶⢾⣿⣇⠂⠿⣿⣯⣭⡟⠂⣹⣿⣿⣿⣷⠿⢿⣿⡿⠿⣿⡝⢋⠙⢿⣯⢀⡀⠀⠀⠀⠀⠈⢁⣼
⠹⣿⣿⣬⣽⡏⢿⣌⢡⠝⢿⣿⣿⣑⣻⣿⠿⢿⠿⠛⠳⡁⠀⠀⠐⠛⣭⡿⣬⣧⣶⣎⣅⣿⣾⠞⠶⣷⣼⣋⣻⡄⡈⣈⡒⠿⢷⣈⢛⣤⡿⣨⣾⣿⣟⣿⣿⣽⣳⣿⣿⣿⣟⡹⣥⠀⠀⣂⣿⡞⡥⢤⣤⣐⣢⠦⣿⣿
⣀⢭⣉⢉⢫⡷⣽⡧⣥⠄⣽⣽⢿⣿⠛⠟⢀⣨⣢⠰⡀⣿⣖⣀⢠⣄⣾⢽⡿⣿⣻⣽⣍⢽⠟⡖⠒⠏⠟⣹⣿⣿⡁⣜⠜⣤⡘⣿⡏⠿⣾⣿⣿⣽⣟⢛⣿⣿⣝⣻⣿⣛⢻⣻⣩⣁⣘⣿⠻⣿⣿⡿⢿⣧⣽⣻⣿⡿
⢃⢻⡟⣖⣉⣠⡍⣃⣡⣔⣾⣟⡾⢿⣇⣬⡿⣽⣿⣷⣿⣿⣿⡃⣀⢹⡾⠾⣖⠛⠟⡃⡾⠈⠰⣣⣭⣶⡖⠻⢿⣧⠰⣶⣽⣭⣿⣺⣿⣳⣻⣏⣷⣽⡗⣾⠿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠶⣷⣯⢻⣿⣷⣿⣿⠌⠵
⠘⠛⢻⣟⠟⢟⠛⣛⣻⣿⣏⣿⣾⣷⣶⣽⣟⠿⣿⣯⣷⠻⣿⢷⠔⣁⣀⣄⣺⡾⠠⢦⢠⣬⣴⣹⣶⣪⣿⣦⠰⣿⠯⢩⡅⠽⣿⣿⢺⣽⣽⣿⢿⣿⡾⡻⡻⣿⣿⡿⣧⣯⣍⡵⡿⠿⣿⣿⣿⣟⣋⡈⠛⢿⠾⢭⣗⢷
⢠⣶⡄⢠⣼⢏⡷⢬⣧⣷⡄⠘⢊⣀⣤⠀⣉⠀⠀⠀⢳⡞⣓⠛⠋⠀⠀⠝⠇⢰⢈⡉⢿⡿⣖⠛⣿⠷⢗⠄⡴⣛⣩⣿⣿⣷⣶⣝⠟⢿⣿⣿⣘⣯⣿⣿⣿⣷⠿⠾⣗⡾⠿⠟⣝⡖⠀⣤⣶⠀⢠⣿⣿⣿⡉⠀⠀⠀
⣾⣧⡟⡂⠈⠶⠋⠸⠚⢋⢀⠬⠭⡄⠀⠀⠑⠴⣠⡀⠟⠿⠿⣾⣧⡀⢶⡶⡧⡍⠟⠣⢭⣗⡟⠈⠚⠋⠋⠊⠡⠀⣿⣿⠯⣴⣿⡿⡦⣇⡿⡿⡿⠧⠭⠛⠀⢠⢤⠀⠈⠠⠄⠢⠊⠀⠀⠾⠀⠈⠙⢷⢮⡩⢴⠞⠾⠿
⠀⠦⠀⠉⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠠⡷⠀⠠⠙⠁⠀⠀⣶⣿⡋⠘⠀⠀⠼⠍⠄⠄⢰⢠⡠⠀⠀⠒⠂⠀⠠⢀⠅⣠⣄⣈⢫⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣈⠃⣰
⣤⣤⣿⣿⡿⠀⢀⣠⣥⣤⢀⠀⠀⠀⠀⣁⡂⠂⠀⠀⠰⣿⡿⣟⡷⠇⠀⠀⠀⢀⠀⠀⢠⡼⠀⠀⠀⠀⢸⡅⠠⠰⣾⣿⣿⡏⠁⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⣶⣦⡀⠀⠀⠀⠀⠈⠁⠀⠀⣣⣴⣿⠋
⠽⠟⠛⠝⠿⠇⠈⠛⢿⣿⣧⡀⠄⠀⠀⠈⠀⠀⠀⡀⠀⠔⣷⣶⢤⡗⠀⠀⠀⠈⠒⠀⠀⠀⠀⠀⠀⠀⠈⣂⠀⠘⠟⠛⠋⠀⠀⠀⠀⠀⣤⣄⣦⠀⠀⠀⠀⠀⠀⡤⢠⣼⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢚⣣⣿⣎
⢀⠂⠀⠀⠀⠀⠀⠁⡳⠶⣇⣀⢠⠆⠀⠀⠀⢀⣄⡁⢀⣤⣼⠇⠈⠉⠀⠠⠒⠀⠀⣤⣄⡀⠀⡴⠀⣥⣄⣈⢄⢤⠀⠀⠀⠠⠀⠠⢤⠰⣯⡉⠉⠀⠀⠀⢀⡥⣸⣠⣠⣭⡄⣀⠀⠀⠀⠀⡀⠠⠠⠀⠐⠉⢈⣙⢴⠉
⢸⡀⠀⣠⣖⠂⠀⠀⡀⠠⣌⣀⣐⢿⣶⣦⡀⠀⠈⢠⡠⠛⢋⣼⣿⣇⡀⣶⣿⣆⢡⣍⡿⠀⠁⠁⠁⠁⠠⣞⠞⣠⢤⠒⠒⣥⣾⣦⠨⣀⣧⣣⣡⠶⢠⡄⢀⣟⣿⠛⢋⢹⠿⣷⣦⠀⠀⢈⠁⠀⠀⣲⣽⡶⢛⣙⠀⣀
⠟⢻⠧⠾⠟⡤⠀⠀⠩⠆⢉⡛⠺⣿⢯⣿⣿⣿⡔⠀⢁⣵⣾⣿⣿⡿⢠⣏⡉⣿⣻⠿⠰⣾⣾⢟⡈⣠⡀⠀⢍⠣⡘⠄⠈⠛⠻⠛⠡⣟⣾⣿⣅⣀⠂⠀⠬⠾⠻⢆⠐⡂⢀⣤⣜⣀⡰⣁⠀⠐⡶⣶⣷⣾⣴⡿⣏⣩
⣿⣿⣋⡯⠀⠀⠀⣄⠨⢨⡛⠡⣦⠭⢶⣋⢯⣷⣌⢈⣫⣿⣿⣿⣟⣿⣞⣙⡛⡿⣻⣿⠿⡿⣟⡚⢇⠘⠻⣥⠬⠐⡄⠈⠀⠐⣒⠀⢴⣿⣿⣿⢿⢛⠉⠀⠄⠀⠐⠼⡀⣻⣤⣶⠶⠾⣿⡏⠀⡼⠁⠩⣉⣟⣿⡲⢶⣾
⠈⢿⣶⣯⠀⢀⡘⠟⠋⣉⠀⠀⠁⢀⢾⣭⣓⡛⡻⠏⢹⣿⣿⠟⢿⣿⣿⡏⠐⢗⣛⠀⠀⠀⠿⡗⠴⠐⣰⣨⣶⣶⣶⣤⠀⠁⠀⢀⠘⠣⠁⠘⠊⣁⠀⠀⠐⠢⢤⣄⣠⣿⣺⣶⡤⡤⠤⢅⠀⠀⠆⣠⣉⢫⠷⣾⣾⣿
⣶⣿⠏⠹⣇⠀⠐⣀⠔⣿⡿⠁⠁⣴⣾⡟⠉⢭⡻⣜⠻⠝⠋⠓⠍⠻⣿⣾⡇⢸⣌⢴⣥⣄⠀⠀⠹⠿⠼⣿⣿⣿⣿⣿⠁⠀⠀⠈⡉⠁⠀⠀⢄⡷⠐⢰⡍⣵⣮⡛⣻⣿⣟⣻⢷⣿⢿⣮⣯⣋⢬⣽⡝⣯⢙⣯⣼⣷
⢛⢹⠷⠤⠿⣁⠑⠈⠛⣙⣁⠂⠂⠀⡠⠀⠀⠀⠌⣀⠙⢄⡀⠠⠀⠈⢣⣕⢲⢲⠮⢀⣩⣶⣿⣿⣶⣞⣷⣿⣿⠙⠉⠑⠠⠀⠀⠀⠀⣄⣤⡤⣂⣚⣦⣀⣴⣿⢿⠿⢿⣿⣧⣴⣾⢿⡽⢿⣝⣟⣽⢿⣁⠉⣴⡦⢝⣿
⣶⣶⠆⣴⣮⡽⠿⣁⠸⣿⢟⡸⡦⣄⠘⠑⣳⣚⣐⢷⣿⣛⣿⡶⣌⠁⠀⠉⣃⡀⢤⣸⣿⣿⡿⢿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠴⠂⠋⠂⣀⡿⡯⠿⠳⣠⣻⣤⣬⡀⠤⠥⢙⣭⡛⠉⣿⣟⠙⢿⠟⢿⡷⡿⡷⣿⡻
⢺⣿⣶⣶⣾⣽⠖⠺⣧⡀⡀⣑⢼⣴⡁⢀⣀⣙⠟⢲⡶⠿⣞⣯⣿⣓⢦⣸⢿⠚⠂⢈⢭⣿⣥⣬⣿⠛⠋⣿⣿⣿⣿⣦⠀⠀⠄⠀⣃⣶⡖⠇⣡⡚⣻⣿⣻⣿⣿⠾⣏⣀⣒⣜⣼⣷⢋⣉⣻⣾⣿⣳⣴⣦⣌⣤⢅⣄
⢿⣿⣷⣤⣬⣒⢀⡀⢀⣙⣿⣻⣿⠗⠁⠹⣟⢐⣰⣺⡫⢿⣝⣿⣇⡿⢖⣋⢻⣄⣰⠮⣾⣿⣿⣿⣿⣠⣤⣿⣿⣿⣿⣿⣿⡟⠻⣄⡬⠉⣩⡀⢈⢘⠛⠫⣿⣟⣿⣿⣿⣻⢟⣻⣽⡦⣻⣷⠟⣻⣿⣿⣷⣻⣿⣿⠟⠲
⡂⢸⣞⡻⣿⡩⡥⠟⠀⣝⣏⣠⣤⢜⡲⡶⠐⠌⣩⠆⠙⠎⠙⠿⠛⣶⣬⣍⢾⠉⣻⣮⡿⣿⣿⣿⠟⣻⣿⣿⣿⣿⣿⣿⣧⠴⣶⣏⠿⣧⡾⢿⣿⣿⡷⡐⣿⣦⣮⠳⣶⣿⣾⣺⣯⠞⣿⢷⣦⣾⣿⣿⣿⣷⣿⣶⣹⣿
⡿⠐⠿⢿⣶⣏⠻⠂⠙⠩⢟⠞⠿⣛⢁⣨⢴⡴⢿⣿⠿⣄⡌⢷⡮⢤⡜⣻⣷⣷⣶⣯⣽⣿⣸⣭⣥⡿⢿⠿⠛⡃⠀⢻⠿⠟⠙⠁⠑⠙⣬⡗⢢⣴⣲⣆⣹⠿⠛⠁⣿⣻⣟⣿⣿⠛⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠄⠙⢛⡛⢓⣲⢴⣺⢷⡿⢿⠯⡆⣲⣿⣿⠍⢨⢍⣄⢻⡆⢰⣳⣛⢿⠛⢯⡭⢾⠻⠬⣧⣵⣾⣆⠀⠁⠳⠒⠖⢀⣷⡀⠶⠑⣾⢶⢾⣯⣷⣿⣣⣛⡯⣈⠒⢶⣦⠍⣱⣟⠷⠄⣠⣜⠛⢿⣩⠟⡉⠥⢀⢾⢏⡝
⡈⢡⢟⠻⣦⠅⣹⠠⣤⣻⣄⢹⣥⢾⣷⣮⣙⣻⣻⠻⣸⣞⣿⣾⣾⣻⠟⣧⣽⠿⠾⢻⢙⢶⣶⣦⠁⠛⠀⠴⠚⠣⡆⣾⣾⠙⣿⣿⣿⠛⠛⠀⢩⠛⡍⠹⢭⣷⣍⣿⣽⡛⠉⢉⣀⡀⣈⣉⢣⠂⠀⠉⣠⣶⡏⠈⣿⣿
⠻⢾⣭⣦⣦⠘⢿⣽⣁⢙⣿⠿⠙⢿⡿⣿⠛⠛⣎⣯⣱⣦⡩⣿⠻⢭⠿⡻⠧⠶⠋⠟⡏⢫⣬⣣⣤⣦⡬⠿⠄⢲⣞⣖⠿⢽⣿⣿⣿⠲⡖⣟⣿⣿⣿⢺⢟⣯⢮⣥⣿⣟⠯⣿⡧⢃⡚⡛⣾⣧⣈⣀⣻⢻⣥⡤⠿⢟
⠀⡀⢘⣿⣿⣽⡟⠹⠉⠙⣡⡂⣠⢊⡍⣷⣶⣤⣤⣺⣭⣥⣼⣿⡖⡿⣶⣻⡕⣹⣶⣾⠓⡥⢉⢿⣟⣻⣦⣴⣄⠈⠁⠑⢈⣹⣿⣿⢇⡤⣟⡻⣿⣿⣶⣼⡎⣿⣿⣿⣟⣯⣧⣟⣉⣥⣴⣿⢠⣾⣶⡿⠏⠂⣸⡥⠲⡭
⣷⣒⣭⡀⠙⣁⣀⠐⢶⣤⣻⢳⣿⣐⢁⣀⡛⢂⣨⣄⣭⢹⣯⠾⣿⡻⣯⣛⣯⣩⡯⣍⡁⠴⡾⣡⣿⢿⠟⣯⣬⣛⡿⢷⡌⢨⣿⣯⡿⣖⢻⢏⢝⡋⣿⣇⣿⢛⡛⠛⣿⣭⣿⡁⠿⠙⢻⣿⣶⣭⠛⠁⠀⠘⣿⣴⣆⡰
⣿⡿⠻⣯⣡⣥⠀⢀⣵⣿⣸⣆⢽⣿⣿⣭⣿⣿⣷⡶⣍⢹⢶⣔⣿⠿⣿⣟⡾⠿⣿⡿⣄⢹⡣⣍⠱⠞⢿⡏⠙⠻⠾⢾⣳⣆⣿⣿⣟⣟⡶⣟⠰⡜⠾⢯⣿⣿⣿⡾⣾⣿⣿⣷⣯⣿⣿⣶⡏⠁⠀⠀⠀⠀⠀⣴⣾⠿
⢤⣶⣾⢺⣿⣿⣆⣬⣿⡾⡿⣿⣿⢟⢻⣿⠮⡿⣿⣿⣿⡆⠁⠀⠳⢾⢿⣏⣿⣻⡟⢿⣴⡬⡈⣭⡃⠀⡈⣿⣴⢴⠶⠾⣿⣇⠂⠿⣿⣭⣯⣟⠂⣹⣿⣿⣿⣗⡿⢟⣻⣿⠿⣽⡝⢋⠙⢿⣮⢀⡀⠀⠀⠀⠀⠈⢁⣼
⠹⣿⣿⣬⣽⡏⢿⣌⢡⠝⢿⣿⣿⣑⡻⣿⠿⢿⠿⠛⠳⡁⠀⠀⠐⠻⣭⡿⣬⣧⣾⣎⣅⣿⣾⠜⠶⣷⣼⣛⣻⡄⡊⡈⡚⠿⢷⣈⢛⣤⡿⣨⣾⣿⣿⣾⣿⣽⣳⣿⣿⣿⣟⡻⣥⠀⠀⣂⣿⡾⡥⢤⣤⣐⣲⠦⣿⣿
⣀⢭⣉⢍⢻⡷⣽⡧⣥⠄⣽⣽⢿⣿⠛⠟⢀⣨⣦⠰⡀⣿⣆⣀⢠⣄⣾⢽⡿⣿⣻⣽⣍⢙⠟⡖⠒⠏⡟⣽⣿⣿⡡⣜⢌⣤⡘⣿⣏⠿⣾⣿⣿⣽⣛⢛⣿⣿⣟⣻⣿⣛⢿⣻⣩⣁⣘⣿⠳⣿⣿⡿⢿⣧⣝⣻⣿⡿
⢃⢻⡟⣗⣋⣠⡍⣃⣡⣔⣺⣟⡾⠽⣇⣬⠿⣽⣿⣿⣿⣿⣿⡃⣈⢹⡾⠿⡖⠛⠟⡋⡿⠈⢸⣡⣭⣶⡖⠻⣿⣧⢰⣶⣿⢭⣿⣞⣿⣱⣻⣏⣧⣽⣿⣾⠿⣤⣺⣿⣿⣿⣿⣿⣿⣿⣿⣏⡶⣷⣯⢹⣿⣾⣿⣿⠄⠱
⠘⠛⢻⣟⠟⢟⢛⢛⣻⣿⣏⣿⣾⣷⣶⣽⣟⠿⣿⣯⣷⠛⢻⢷⠔⣁⣁⣄⣚⡾⠠⢦⢠⣮⣴⣹⣿⣪⣿⣮⠰⣿⠯⢨⡅⠽⣿⣿⠺⣽⣽⣿⣿⣿⡿⡻⡻⣿⣿⡿⢧⣯⣍⡵⠿⠿⣿⣿⣿⣟⣋⡈⠛⢿⠾⢭⢿⣷
⢠⣶⡄⢠⣼⢏⡕⢬⣧⣶⠀⠈⠊⡀⣤⠀⣉⠀⠀⠀⢳⡞⣓⠛⠋⠀⠀⠙⠇⣱⢈⡁⢶⡿⢖⠛⣿⠷⢗⠀⡰⣋⣉⣿⣿⣳⣶⣝⠞⢿⣿⣿⢙⣯⣿⣿⣿⣷⠗⠾⣗⡾⠿⠟⣝⡖⠀⣤⣶⠀⢠⣿⣿⣯⡉⠀⠀⠀
⣶⣥⡟⡂⠀⠶⠊⠸⠒⢋⠀⡬⠨⠀⠀⠀⠗⠴⡤⡀⠿⠿⠿⣼⣧⠀⢶⡶⡧⡍⠟⠣⢭⣅⡟⠈⠊⠋⠋⠊⠥⠄⣿⣿⢧⣼⣿⡿⠦⡎⠿⡿⡿⠥⠭⠛⠀⠠⢤⠀⠀⠀⠄⠢⠊⠀⠀⠾⠀⠈⠙⢷⢯⠉⠴⠾⠶⢿
⠀⢤⠀⠉⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠠⡧⠀⠠⠙⠁⠀⠀⣴⣟⡋⠚⠀⠀⠴⠉⠄⠄⢰⢠⡠⠀⠀⠒⠂⠀⠠⢀⠅⣠⣄⣈⢫⠀⠀⠁⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡈⠃⢰
⣠⣤⣿⣿⡿⡀⢀⣠⣥⣤⢀⠀⠀⠀⠀⣃⡀⠂⠀⠀⠰⣿⡿⣿⠴⠇⠀⠀⠀⢀⠀⠀⢠⡼⠀⠀⠀⠀⢸⡇⠀⠰⣾⣿⣿⡏⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⣶⣦⡀⠀⠀⠀⠀⠈⠁⠀⠀⣳⣴⣟⠋
⠽⡿⠛⠝⠻⠇⠈⠛⠿⣿⣧⡀⠄⠀⠀⠀⠀⠀⠀⡀⠀⠔⣷⣶⢤⡗⠀⠀⠀⠈⠂⠀⠀⠀⠀⠁⠀⠀⠈⣂⠀⠘⠟⠛⠋⠀⠀⠀⠀⠀⣤⣄⣤⠀⠀⠀⠀⠀⠀⡤⢠⣬⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠚⣧⣵⢍
⢀⡂⠀⠀⠀⠀⠀⠀⡳⠲⣇⣀⢡⠆⠀⠀⢀⢀⣌⡀⠀⣤⣾⠃⠈⠉⠀⠠⠒⠀⠀⣤⣄⡀⠀⠴⠀⣤⣄⣈⠀⢀⠀⠀⠀⠠⠀⠀⣄⠰⣯⡉⠉⠀⠀⠀⢀⣄⣸⣀⣠⣥⡄⣀⡀⠀⠀⠀⠀⠠⠠⠀⠐⠁⢀⣙⢼⠉
⢸⡀⠀⣠⣔⠂⠀⠀⡀⠠⣌⣀⢐⢿⣶⣦⡀⠀⠈⢠⡀⠛⢋⣼⣿⣇⡀⣶⣿⣆⢡⡍⡿⠀⠁⠀⠁⠁⠠⣞⠊⣀⣤⠂⠒⣥⣾⣶⠨⣀⣧⣣⣠⠶⢀⡄⢀⣟⣿⠛⢋⢹⠿⢷⣦⠀⠀⢈⠁⠀⠀⣲⣼⡶⢓⣉⠀⣀
⠿⢻⠧⠾⠟⠤⠀⠀⠡⠆⢙⡛⠺⡟⢯⣿⣿⣿⡔⠀⢁⣵⣾⣿⣿⡿⢀⣏⡉⣿⣻⠟⠰⢾⣾⢛⡈⣀⡀⠠⢍⠣⡐⠄⠈⠟⠻⠛⢠⣟⣶⣿⣅⢐⠂⠀⠬⠾⠻⢆⠐⡂⢀⣤⡌⣀⡰⣁⠀⠐⡶⣶⣷⣮⣴⡿⣏⣩
⣿⣿⡋⡯⠀⠀⠀⢄⠨⢸⡛⠩⣦⠭⢧⣋⢯⣷⣌⢈⣩⣿⣿⣿⣟⢿⣞⣙⡛⡟⣻⣿⠿⡿⣗⠈⠆⠈⠐⠅⠄⠀⡄⠈⠀⠐⣒⠀⢴⣾⣿⡿⢿⢛⠁⠀⠄⠀⠐⠬⡀⣹⣤⣶⠶⠶⣿⡏⠀⡼⠀⠨⣉⣛⣿⠰⢶⣾
⠈⢿⣶⣯⠀⢀⡘⠟⠁⣉⠀⠀⠁⠀⢖⣭⣐⡛⡻⠟⣹⣿⣿⠟⢻⣿⣿⣍⠐⢗⣛⠀⠀⠀⠵⠒⠴⠀⣐⣼⣾⣿⣷⣦⠀⠁⠀⢀⠘⠃⠀⠘⠊⣁⠀⠀⠀⠢⢤⢤⣢⣵⣺⣶⡤⡤⠤⢄⠀⠀⠂⣠⣉⢫⠷⣶⣾⣼
⣲⣿⠍⡹⣅⠀⠐⡀⠔⢿⡿⠁⢀⣴⣾⡟⠈⢍⡫⡔⠻⠝⠋⠓⠌⠻⣿⣾⡅⢸⡌⢴⣥⣤⣤⣀⠹⠱⠞⣿⣿⣿⣿⡿⠀⠀⠀⠈⡉⠁⠀⠀⢀⠧⠀⢀⠍⣵⣤⡛⣻⣿⡟⣿⢷⣿⢶⣮⣯⣋⢬⣿⡝⣯⢙⣿⣼⣧
⢛⢹⠷⢤⠿⣀⠑⠈⠛⣙⣁⠀⠂⢀⣠⠀⠀⠀⠌⣀⠑⢄⡀⠀⠀⠘⢣⣕⢲⢰⠬⣾⣿⣿⣿⣿⣇⣠⣾⣿⣅⠉⠁⠀⠠⠀⠈⠀⠀⣄⣀⡤⣂⣒⣆⣀⣼⣿⣿⠿⢟⣿⣧⣴⣾⢿⡿⢿⣜⣏⣽⣟⣀⠉⣴⡦⢝⣿
⣖⣶⠆⣤⣌⡽⠿⣁⠸⣿⢟⡹⣦⡄⠘⠁⣳⣛⣔⢷⡟⣛⣿⡢⣌⠁⠀⠙⡃⡀⢤⣸⣿⣿⠿⢻⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠄⠂⠉⠀⣀⡿⠯⡷⢣⣠⣻⣤⣤⠀⠤⠅⢙⣉⡋⠙⣿⣏⠛⢿⠟⢿⡷⡿⡷⡿⡻
⢻⣿⢶⣶⣾⣽⠴⠺⣧⡄⡀⢑⢰⣴⡁⢀⣀⣙⠿⢲⡶⠿⢖⣧⣯⡓⢦⣸⢿⠚⠂⠈⠭⣳⣥⣼⣿⠟⠋⣻⣷⣿⣿⣶⣄⠀⠄⠀⣂⣴⡖⠁⣅⡚⣻⣽⣻⣿⣿⠿⢏⣀⣒⣜⣴⣷⠋⣉⣻⣼⣷⣳⣴⣢⣄⡤⢁⣄
⢿⣿⣷⣤⣄⣒⢀⡀⢀⡙⣿⣻⣿⠗⠁⠹⣟⢐⣒⣺⡫⢿⣝⣿⣇⡿⢖⣛⢻⣄⣰⠦⣾⣿⣿⣿⣿⡠⣤⣿⣿⣿⣿⣿⣿⡞⠻⣄⡈⠉⡩⡀⢘⢘⠛⠋⣲⣿⣿⣾⡿⣿⢿⣺⣭⡶⣻⣧⠓⢻⣿⣿⢷⣻⣿⣿⠟⠲
⡂⢸⣞⠻⣾⡩⡥⠟⠀⣝⣏⡠⣤⢔⣲⡶⠐⠉⣩⠖⠑⠎⠘⠟⠛⣶⣬⣍⢮⠍⣻⣮⣿⣿⣿⣿⠟⣫⣿⣿⣿⣿⣿⣿⣿⠧⣰⣎⠿⣧⡾⢿⣿⣿⡿⡐⣿⣦⣮⠳⣶⣿⣾⡺⣯⠖⣿⢷⣶⣬⣿⣿⣽⣶⣿⣾⣾⣿
⡿⠀⠿⢻⣾⣏⠹⠂⠙⠩⢞⠖⠿⣛⢁⡨⢤⠶⢿⣿⠿⣄⡀⢷⡮⢬⡸⣙⣷⣷⣶⣯⣽⣿⣸⣭⣥⡿⢿⠿⠛⡃⠀⢫⠿⠟⠑⠉⠑⠉⣬⡗⢢⣽⣰⣖⣩⠿⠛⠁⣿⣻⣟⣿⣟⠛⠟⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⡀⠄⠙⢛⡛⢓⣴⢴⣺⢷⡿⢿⠩⡆⢲⣿⣿⡬⢨⢅⣀⢻⣆⢰⣳⣛⣿⠛⢯⡭⢾⠻⠬⣧⣵⣾⣆⠀⠀⠳⠒⠖⢀⢷⡀⠶⠑⣾⢶⢾⣭⣵⣿⣣⣛⡩⣈⠒⢶⣦⠅⣰⣟⢗⠀⢀⣈⠛⢿⡹⠟⣉⠥⢀⢾⢋⠽
⡀⢡⢟⠺⡦⠄⣹⠠⣤⣷⣄⢻⣥⢾⣷⣦⣙⣻⣿⠻⣸⣾⣿⣾⣾⢻⠟⠧⣽⠷⠷⢹⠙⢶⣶⣦⠁⠛⠀⠔⠚⠣⡆⣾⣾⢙⣿⣿⣿⠛⠛⠀⠨⠓⡉⢩⢭⣷⣍⣏⣽⡋⠙⢀⢀⠀⣀⣙⢣⠆⠀⠈⣬⣶⡆⠈⣿⣿
⠻⢾⣭⣦⣤⠘⢿⣽⡁⠙⣿⡿⠙⢿⡿⡿⠛⠛⣏⣯⣱⣆⡬⡿⠻⢍⠻⠻⠧⠶⠋⠞⡊⠋⣌⣣⣤⣦⡬⠽⠆⣴⣞⣖⠻⢬⣿⣿⣿⠢⡖⣟⣿⣾⣧⢶⢟⣿⢮⣥⣿⣟⡯⡿⡧⢆⡚⠛⣾⣦⣈⣈⡛⢻⣤⡄⠻⢟
⠀⡀⢘⣿⣿⣽⣟⠹⠉⠙⣡⡂⣠⢈⡉⣳⣶⣤⣦⣚⣭⣥⣼⣿⡖⡿⣶⡻⡕⢹⣴⣆⠓⠤⢉⠛⣟⣻⣆⣴⣄⠈⡡⠑⢀⣹⣿⡿⢗⡤⣟⡳⣿⣿⣶⣴⡌⣿⣮⣿⣟⣿⣧⣻⣉⣥⣴⣿⢀⣾⣶⡿⠇⠂⣸⡅⠰⡬
⣷⣐⣭⡀⠉⡁⣀⠐⢶⣤⣫⢳⣿⣐⢁⣀⡉⢂⣨⣀⣬⢹⡿⠼⢝⡺⣯⣛⣯⣩⡬⢍⡁⠰⡼⣡⣿⣿⠟⣫⡬⣛⡻⢷⡄⢈⢿⣧⡿⣖⢹⢏⢝⡉⣿⣅⣿⣛⡛⠻⣿⣭⣿⡁⠿⠙⠺⣾⣶⡬⠛⠁⠀⠘⣦⣤⣆⡰
⢿⡿⠿⣯⣡⣤⠀⢀⣵⣗⡸⣆⣽⣽⣿⣭⣿⣽⣷⡶⣌⢱⢖⢄⣿⠷⣷⣟⡾⠿⣯⡻⣄⢹⠣⣍⠱⠞⢿⡆⠉⠻⠶⢏⣱⣆⣾⣿⣛⣟⣴⣟⠐⠌⠾⢯⣿⣿⣿⡾⣺⣿⣿⣷⣯⣿⣿⡷⡋⠀⠀⠀⠀⢀⠀⣴⢞⡿
⢴⣶⡾⢺⢿⣿⣆⢬⣿⡶⡿⣿⣾⢟⠻⣿⠮⡿⣿⣿⣿⡆⠁⠀⠳⢾⢿⣟⣿⣛⡟⢿⣴⡬⡈⣽⡂⠀⠈⣿⣔⢰⠦⣴⣿⣇⠂⠿⣿⣭⣭⣟⠂⣹⣿⣿⣿⡷⠿⢟⣿⣿⠯⢵⡏⠋⠙⢿⣮⢀⠀⠀⠄⠀⠀⠈⣡⣾
⠹⣿⣿⣬⣽⡏⢿⣈⢡⠝⢿⣿⣿⣑⡻⣿⠻⢿⠿⠋⠱⡁⠄⠀⠐⠻⣭⣿⣼⣧⣶⣌⣅⣿⣷⠒⠶⢷⣮⣛⣻⡄⡈⢀⡚⠷⢷⣈⢛⣤⡾⣠⣾⣿⣟⣿⣿⣽⣲⣿⣿⣿⣟⡻⣥⠀⠀⣂⣿⡞⡦⢄⣤⣐⣢⢾⣿⣿
⣀⢭⣉⠍⢫⡧⣽⡧⣥⠄⣵⣽⢿⣿⠛⠛⢀⣨⣦⠠⡀⣿⣆⢀⢠⣄⣾⢽⠿⣿⣻⣽⣍⢝⠿⡖⠒⠍⡟⣹⣿⣷⡁⡖⠌⡠⡘⢻⡏⠻⣾⣿⣿⣽⣟⢛⣿⣿⣟⣻⣿⣛⢿⣻⣩⣁⣘⣟⠳⣷⣷⡿⢿⣧⣽⣻⣿⣟
⢃⢻⡟⣆⣋⣠⡍⢃⣠⣄⣺⣟⡾⢽⣇⣬⡿⣵⣿⣷⣿⣿⣟⡃⣀⢱⡾⠾⡖⠛⠟⡃⡾⠈⠘⣡⣽⣦⡖⠻⢾⣧⠰⣆⣝⢥⣷⣺⣟⣲⣻⣟⣥⣽⡗⣾⠷⣤⣻⣿⣿⣾⣿⣿⣿⣿⣿⣏⠶⣷⣏⢻⣿⣾⣿⣿⠌⠁
⠘⠛⢻⣟⠟⢟⠛⢛⣻⣿⣏⣿⣾⣷⣶⣭⣟⠿⣿⣯⣷⠹⠿⠷⠕⡀⣁⣄⣺⡶⠠⢦⢠⣬⣰⣹⣶⣪⣿⣦⠸⣿⠯⢩⡅⠽⣿⡯⢺⣽⣼⣿⢿⣿⡮⣻⡻⣿⣿⡿⢧⣯⣉⡵⢿⠿⣿⣿⢾⣟⣋⡈⠛⢿⠿⢭⢗⢶
⢠⣶⠀⢠⣼⢯⡥⠬⣧⣶⡀⠘⠈⣈⣤⠀⣉⠀⠀⠀⢳⡞⣓⠙⠋⢀⠀⠙⠆⢰⢈⡁⢷⡿⣖⠻⣿⠷⠗⠄⡰⣋⣉⣿⣿⣳⣶⣝⠜⢿⣿⣿⢘⣯⡿⣿⣾⣷⠷⠾⣗⡲⠿⣟⣝⡖⠀⣤⣶⠀⢠⣿⣿⣿⡉⠀⠀⠀
⣾⣥⠜⡂⠀⠶⠊⠸⠒⢋⠂⡬⠨⠀⠀⠀⠗⠼⡠⡀⠟⠿⠿⣼⡇⠀⢶⡶⣧⡍⠝⠣⢭⣅⡟⠈⠊⠋⠋⠊⠥⠄⣿⣿⠇⣼⣿⡿⡦⣄⠿⡿⡿⠥⠭⠛⠀⠠⠄⠀⠀⠀⠄⠂⠊⠀⠠⠾⠀⠈⠙⢷⢮⠩⠴⠟⠶⠿
⠀⠦⠀⠁⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠠⡧⠀⠠⠙⠀⠀⠀⣖⣟⠋⠘⠀⠀⠴⠍⠄⠄⢰⢠⡠⠀⠀⠒⠂⠀⠠⢀⠅⣠⣄⣈⣫⠀⠀⠁⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡈⠃⢰
⣤⣤⣾⣿⣳⠀⢀⣠⣥⣤⢀⠀⠀⠀⠀⣁⡄⠀⠀⠀⠰⣿⡿⣿⠵⠇⠀⠀⠀⢀⠀⠀⢠⡼⠀⠀⠀⠀⢹⡇⠀⠰⣾⣿⣿⡏⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣬⣶⣦⡀⠀⠀⠀⠀⠈⠁⠀⠀⣰⣴⣟⠛
⠽⠿⠛⠝⠿⠇⠈⠛⠿⣿⣧⡀⠄⠀⠀⠈⠀⠀⠀⡀⠀⠔⣷⣶⢤⡃⠀⠀⠀⠈⠂⠀⠀⠀⠀⠁⠀⠀⠈⣂⠀⠘⠟⠟⠋⠀⠀⠀⠁⠀⣤⣄⣦⠀⠀⠀⠀⠀⠀⡤⢠⣼⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠚⣣⣵⠌
⢀⡂⠀⠀⠀⠀⠀⠁⡳⠰⣇⣀⢡⠆⠀⠀⢀⢀⣄⡁⠀⣤⣾⠃⠈⠉⠀⠠⠒⠀⠀⣤⣄⠀⠀⠴⠀⣤⣄⣈⠀⢄⠀⠀⠀⠠⠀⠀⢄⠰⣯⡉⠉⠀⠀⠀⢀⣅⢸⣀⣠⣭⡄⣀⠀⠀⠀⠀⠀⠠⠠⠀⠐⠁⢀⣉⢼⠉
⢸⡀⠀⣠⣖⠀⠀⠀⡀⠠⣌⣀⢐⢿⣶⣤⡀⠀⠈⠠⡀⠛⠋⣼⣿⣇⣀⣶⣿⣇⢡⡍⠿⠀⠁⠀⠁⠁⠠⣞⠋⢀⢤⠂⠒⣥⣼⣶⠈⣀⣧⣣⣱⠶⢠⡄⢀⢟⣟⠛⠛⢻⠿⢵⣦⠀⠀⢘⠁⠀⠀⣲⣼⡶⢓⣉⠀⣀
⠿⢻⠅⠾⠛⠤⠀⠀⠩⠆⢙⡚⠺⣿⢯⣿⣿⣿⡔⠀⠁⣵⣾⣿⣿⡿⢀⣏⡉⣿⣻⠟⠠⢾⡶⢙⠈⣀⡀⠀⠉⠡⡐⠀⠀⠘⠛⠓⠠⣛⣢⣿⣅⢐⠂⠀⠨⠾⠻⢆⠐⡂⢀⣤⡌⣀⠰⣁⠀⠐⡶⣶⣷⣮⣴⡿⣏⢭
⣿⣟⡋⡯⠀⠀⠀⢄⠨⢘⡛⠩⣦⠭⢮⣉⠯⣷⣌⢈⣩⣿⣿⣿⣟⢿⣞⣙⡛⡟⣻⣿⠿⡿⣗⠈⠂⠈⠐⠄⢄⣀⡀⠈⠀⠐⣒⠀⢔⣾⣿⡿⢿⢛⠉⠀⠄⠀⠐⠼⡀⣹⣤⣶⠶⠶⣿⡍⠁⡼⠀⠩⣉⣛⣿⠲⢶⣾
⠈⢿⣶⣯⠀⢈⡘⠟⠂⢉⠀⠀⠁⠀⢶⣭⣐⡛⡻⠏⣹⣿⣿⠟⢿⣿⣿⡍⠐⢗⣛⠀⠀⠀⠕⠒⠰⠀⣀⣼⣿⣿⣿⣷⠀⠁⠀⢄⠘⠃⠀⢘⠈⣁⠀⠀⠐⠢⠤⣄⣠⣶⣺⣶⠠⠤⠤⢄⠀⠀⠀⣠⣉⢩⠗⣶⣶⣾
⣢⣿⠍⠹⣅⠀⠰⡀⠔⢿⡿⠁⠀⣰⣮⡝⠉⢍⡫⡜⠻⠟⠋⠒⠍⠹⣿⣾⡅⢸⡌⣴⣵⣤⣄⡀⠸⠱⠚⣿⣿⣿⣿⠟⠀⠀⠀⠈⠈⠁⠀⠀⢀⠧⠀⢠⡍⣵⣤⡛⣻⣿⡟⣿⢷⣯⢶⣮⣯⣋⢬⣿⡝⣮⢙⣯⣼⣧
⢛⢸⢷⡤⠽⣀⠑⠈⠛⣙⣁⠂⠂⠀⣠⡀⠀⠀⠌⣀⠑⢄⡀⠠⠀⠈⢣⣕⢲⢰⢼⣿⣿⣿⣿⣿⣆⣸⣾⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⡠⣂⣒⣆⢀⢴⣿⢿⠿⢿⣿⣧⣴⣾⢿⡽⢿⣜⣏⣽⣟⣀⠉⣴⡦⢝⣿
⣖⣶⠆⣴⣜⠽⠿⣀⠸⣿⢟⡹⢤⡄⠘⠀⣱⣚⣔⢳⡞⣛⣻⡢⣌⠁⠀⠙⡃⡀⢬⣻⣿⣿⠛⣹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠄⠀⠉⠀⡀⠿⠯⡗⢃⣀⢻⣴⣤⠂⠤⠅⢙⣉⡋⠙⣿⣏⢹⢿⠟⢿⡷⡿⠵⠿⡻
⣻⣿⢶⣶⣾⢿⠔⠺⣧⡀⡀⢑⠰⣴⡁⣀⣀⣙⠿⢲⡶⠷⢖⣯⣟⣓⢦⣸⢿⠛⠂⠘⠭⣻⣥⣽⣿⠿⠋⣽⣿⣶⣶⣦⣀⠀⠄⠀⣂⣴⡖⠁⣁⡘⣹⡝⣻⣿⣷⠾⢇⣀⣒⣜⣴⣷⢋⣉⣻⣼⣷⣳⣴⣆⣀⡤⢁⣀
⢿⣿⣷⣤⣬⣒⢀⡀⢀⡑⣿⣹⣿⠗⠁⠹⣝⢐⣐⣨⡫⢻⣝⣿⣇⡿⢖⣛⢻⣄⡰⠤⣾⣿⣿⣿⣿⡀⣤⣿⣿⣿⣿⣿⣿⣶⠚⣀⡈⠉⡩⡀⢘⣘⠙⠉⣳⣟⣿⣾⡿⣻⢿⣻⣩⡦⣻⣧⠛⣻⣿⣿⣷⣻⣿⣿⠟⠰
⡂⢸⣞⠻⣾⡩⡧⠟⠀⣝⣏⡠⣤⢔⡲⡦⠑⠉⣭⠖⠑⠎⠘⠟⠟⣦⣬⣍⢮⠉⣿⣮⡿⣿⣿⣿⠟⣋⣽⣿⣿⣿⣿⣿⣿⡿⣶⣏⠿⣥⡾⢿⣿⣿⡿⠐⣿⣦⣪⠱⣶⣿⣾⡺⣏⠖⣿⢷⣖⣬⣿⣿⣿⣶⣿⣶⣼⣷
⡿⠀⢿⢻⣾⣇⠻⠂⠙⠩⢞⠞⠿⣛⢁⣨⠤⠴⢿⣿⠿⣄⡀⢷⡮⢬⡬⣹⣷⣷⣶⣯⣽⣿⣨⣭⣥⡟⢿⠿⠛⡋⠉⢙⠿⠜⠑⠉⠑⠉⣬⡗⢢⣵⣰⣔⣩⠻⠛⠡⣿⣻⣟⣿⣿⠛⠽⣷⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿
⡄⠀⠄⠙⢛⡛⢓⣰⢵⣰⢷⡻⢿⠩⡆⢲⣿⣿⡬⢨⢅⣀⢻⡆⢰⣷⣛⢿⠟⢭⡭⢾⠻⠬⣧⣵⣾⣆⠀⠀⠳⡒⠂⠀⢳⡀⠶⠑⣾⢲⢾⣭⣵⡿⣡⣚⡩⣈⠒⢶⣦⠄⣰⣟⢗⠀⢀⣈⠻⢿⠩⠟⣉⠥⢀⢾⢋⠝
⡀⢱⠟⠺⡦⠀⣹⠠⣤⣻⣄⢿⣥⢾⣷⣮⣙⣻⣟⠳⣸⣾⣿⣾⣾⢺⠟⠧⣼⠷⠿⢹⠙⢶⣶⣦⠁⠛⠀⠴⠚⠣⡆⣾⣲⢙⣿⣿⣿⠟⠛⠀⢩⠓⡉⠩⢭⣷⣍⣅⣟⡋⠉⢁⣀⠀⣀⣙⢣⠆⠀⠈⢬⣶⡇⠀⣿⣿
⠻⢾⣭⣦⣤⠈⢿⣽⡁⠙⣿⠿⠙⢿⡿⡿⠛⠛⣎⣯⣑⣆⡨⡿⠻⢍⠻⠻⠧⠶⠊⢏⡋⠋⣌⣣⣤⣦⡬⠿⠒⢶⣞⣖⠻⢤⣿⣿⣿⠰⡖⣚⣿⣿⣧⢲⢛⣯⢮⣥⣿⣟⠫⡙⡥⢃⡚⠛⣾⣦⣈⣈⡛⢻⣤⠄⠻⠟
⠀⡀⢘⣿⣯⣽⡟⠹⠉⠙⣡⡀⣠⢊⡍⢳⣶⣤⣄⣚⣭⣥⣼⣿⠒⡿⣶⡳⡕⢹⣶⣆⠒⣥⢉⠟⣟⣻⡆⣴⣄⡈⠡⠑⢈⣻⣿⡿⢗⠠⣛⡳⣿⣿⣖⣴⡌⣽⣿⣽⢟⣯⣧⣻⣉⣠⣴⣿⢠⣼⣶⡻⠇⠀⡸⡅⠰⡭
⣷⣐⣭⡀⠉⡁⣀⠐⢶⣤⣫⢳⣿⣐⢁⣀⡋⣊⢨⣀⣬⢹⡯⠼⢟⡺⣯⣛⣯⣩⡭⢍⡁⠴⡼⣡⣿⣿⠟⣣⣬⣛⡻⢷⡄⢈⢿⣏⡿⣖⢹⢍⢝⡉⣯⣅⣿⣛⡛⠛⣿⣭⣿⡁⠟⠉⠹⣿⣶⡬⠛⠁⠀⠨⣦⣤⣆⡲
⢷⡿⠻⣿⣡⣤⠀⢀⣵⣟⡸⣆⢹⣽⣿⣭⣿⣽⣷⡶⣍⢱⢖⡄⡿⠿⣷⣟⡾⠿⣽⡻⣄⢹⠣⣍⠱⠞⢿⡆⠈⠹⠷⢏⣱⣆⣴⣿⣚⣟⣴⣟⠠⡜⠾⢯⣿⣿⣿⡾⣻⣿⣿⣷⡮⣿⣿⡿⡋⠀⠀⠀⠀⠀⠀⣰⣞⠟
⢠⣶⣾⢺⣿⣿⣆⣬⣿⡶⡿⣿⣿⢝⠻⣿⠮⡿⣿⣿⣿⡆⠁⠀⠳⢾⢿⣏⣿⣛⡟⢿⣴⡬⡈⢽⠂⠀⠈⣿⣔⢰⠦⡶⣽⣇⠂⠿⣿⣭⣭⣟⠂⣹⣿⣿⣿⣖⠿⢟⣻⣿⠟⢽⡏⠉⠙⢿⣦⢀⠀⠀⠌⠀⠀⢈⣵⣾
⠸⣟⣿⣭⣽⡏⢿⣌⢡⠝⢿⣿⣿⣁⡻⣟⠻⢿⠿⠋⠱⠁⠄⠀⠐⠹⣭⣿⣬⣧⣾⣌⣅⣿⣷⠒⠶⢷⣮⣛⣻⡄⡀⢀⡘⠷⢶⣈⢛⣤⡿⣠⣾⣿⣟⣿⣿⣼⣲⣿⣿⣿⣟⡻⣥⠀⠀⣂⣿⡜⡤⢀⣤⣀⣒⢿⣿⣿
⢀⢭⣉⠉⢫⡷⣽⡇⣥⠄⣕⣽⢿⣿⠛⠛⢀⣨⣦⠰⡀⣿⣆⣀⢠⣄⣾⢽⠿⣿⣻⣽⣍⢝⠟⡖⠒⠌⡟⣽⣿⣿⡀⡞⢜⣄⡘⢿⡏⠻⣾⣿⡿⣽⣟⢛⣿⣿⣟⣻⣿⣛⢟⣻⣩⣁⣘⣟⠳⣷⣷⡿⢿⣧⣩⣻⣿⣿
⢃⢻⡟⣆⣉⣠⡍⢃⢠⣄⣺⣟⡾⠽⣇⣬⡟⣿⣿⣿⣿⣿⣿⡃⡀⢱⡾⠾⡖⠛⠛⠃⠾⠈⠐⣡⣽⣦⡖⠻⢮⣧⠠⣦⣽⢕⣷⣪⣟⣐⣻⣟⣥⣽⡗⢼⠷⡄⣹⣿⣿⣾⣿⣿⣿⣿⣿⣏⠶⣷⣯⢻⣿⣾⣿⣿⠀⠰
⠘⠛⢻⡟⠟⢟⠛⢛⡻⣿⣏⣿⣾⣵⣶⣬⣟⠿⣿⣯⣷⠹⠿⢷⠕⣁⣀⣄⣚⠶⠠⢦⢠⣬⣐⣹⣶⢪⡿⢦⠰⣿⠏⢩⡅⠿⣿⡏⠒⣽⣼⣿⢿⣿⡮⣱⡻⣿⣿⡵⢧⣯⣍⡵⠿⠿⣿⣿⣿⣟⣋⡈⠛⢿⠾⢭⢃⢶
⢀⣤⡀⣠⣼⢏⣥⢬⣯⣶⠀⠚⢊⣈⣤⠀⣉⠀⠀⠀⢳⡞⣓⠛⠋⠀⠀⠽⠇⢩⠈⣡⢷⡿⣶⠻⣿⡷⢇⠀⡶⣋⣉⣿⣿⣷⣶⣽⢞⣿⣿⣿⢙⣯⢿⣿⣾⣷⣟⣾⣖⣷⠿⣟⣽⡔⠀⣰⣶⠀⢠⢿⣿⣿⡉⠀⠀⠀
⣲⣯⡖⡂⠐⠶⠊⠸⠚⢋⠀⠬⠨⡄⠀⠀⠳⠴⣤⡀⠿⠿⠿⣶⣇⡠⢶⡶⣧⡏⠟⠯⢭⣗⡟⠈⠊⠋⠋⠚⠥⠤⣿⣿⠯⣼⣿⡿⡶⣏⠿⡿⡿⠭⡭⠛⠁⢠⢄⠀⠀⠀⠀⠂⠊⠀⠂⠬⠁⠘⠹⢷⢯⠽⢱⠾⠶⢿
⠀⣤⠀⠉⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠠⡷⠀⠠⠙⠁⠀⠀⣲⣿⠋⠛⠀⠀⠴⠍⠄⠄⢰⣠⡠⠀⠀⠒⠆⠀⠠⢀⠅⣠⣄⡈⠫⡀⠀⠁⠀⠁⠠⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡈⠃⢰
⣀⣤⣷⣿⣿⠀⢀⣠⣥⣤⢀⠀⠀⠀⠀⢃⠆⠃⠀⠀⠰⣿⡿⣿⡶⠧⠀⠀⠀⢀⠀⠀⢠⡼⠀⠀⠀⠀⢸⡇⠠⠰⣾⣿⣿⡏⠁⠀⠀⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣀⣬⣶⣦⡀⠀⠀⠇⠀⠈⠁⠀⠀⣲⣴⣟⠛
⠽⠿⠛⠽⠿⠇⠈⠛⢿⣿⣧⡀⠄⠀⠀⠈⠀⠀⠀⡀⠀⠴⣷⣶⣤⡖⠀⠀⠀⠈⠂⠀⠈⠀⠀⠁⠀⠀⠈⣂⠀⠘⠟⠟⠋⠀⠀⠀⠀⠀⣤⣄⣤⠀⠀⠀⠀⠀⠀⡤⢠⣬⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢚⣣⣿⡍
⢀⡂⠀⠀⠀⠀⠀⠁⡳⠲⣇⣀⢡⠆⠀⠀⠀⢀⣈⡀⠀⣤⣾⠃⠈⠉⠀⠠⠒⠀⠀⣤⣄⡀⠀⠴⠀⣬⣄⣈⠄⢀⠀⠀⠀⠠⠀⠠⣤⠰⣯⠉⠉⠀⠀⠀⢀⡄⣘⣤⣀⣭⡄⣀⡀⠀⠀⢀⠀⠠⠠⠀⠐⠉⢈⣉⢼⠉
⢸⡀⠂⣠⣞⠂⠀⠀⡀⠠⣌⣀⣰⢿⣶⣄⡀⠀⠈⢠⡈⠛⢋⣼⣿⣇⢀⣶⣿⣏⢡⣍⠿⠀⠁⠀⠁⠁⠀⣞⠶⣨⢤⠂⠚⣥⣼⣶⠨⣀⣧⣣⣰⠶⣠⣄⢀⢟⣟⠛⢋⢻⠿⣷⣦⠀⠀⢘⠁⠀⢀⣲⣼⡶⢛⣙⠀⣀
⠿⢻⠧⠿⠛⡤⠀⠀⠡⠆⢉⡛⢾⣿⢯⣿⣿⣿⡔⠀⠁⣥⣾⣿⣿⡿⢰⣏⠙⣿⣿⡿⡀⣶⣞⢓⡈⡀⠀⠀⠉⠠⡐⡀⠈⠘⠻⠓⢠⣟⣾⣿⣅⣐⠂⠀⠼⠼⠻⢖⠐⡂⢀⣤⣜⣀⠸⢁⠀⠐⡶⣶⣷⣿⣴⡿⣏⣫
⣿⣟⣛⡯⠈⠀⠀⢤⠬⢘⡛⠩⣦⠽⢦⣋⢯⣷⣌⢈⣹⣿⣿⣿⣟⣿⣞⣙⣛⡿⣻⣿⡿⡿⡓⠈⠀⠈⠰⢂⣀⣀⣂⠈⠀⠐⡒⠀⢵⣾⣿⣿⢿⢛⠉⠀⠄⠀⠐⠬⡀⣻⣤⣶⠶⠾⣿⡍⠁⡼⠀⠩⣉⣛⣿⡰⢾⣾
⠈⢿⣶⣯⠂⢈⡘⠟⠋⢉⠀⠀⠁⠀⢶⣭⣑⡛⡿⠟⣹⣿⣿⠟⢿⣿⣿⡏⠐⢗⢛⡀⠀⠀⠵⠂⠴⠀⣠⣾⣿⣿⣿⣿⠀⠁⠀⢄⠘⠣⠀⢘⠊⣁⠀⠀⠐⠢⢤⣄⣣⣶⣸⣶⡤⠤⠬⢅⠀⠀⠀⣠⣉⣻⠳⣶⣷⣿
⣮⣿⠏⣻⣇⠀⠰⡀⠔⠿⡿⠃⢁⣴⣮⡟⠉⢍⣫⡔⠻⠟⠋⠓⠍⠻⣿⣾⡇⢨⣬⠴⣥⡄⠀⠀⠹⠱⢚⣿⡿⢿⠿⠛⠀⠀⠀⠈⠈⠁⠀⠀⢀⠧⠀⢠⡭⣵⣤⡟⣻⣿⣟⣿⢷⣿⣶⣮⣯⣃⢬⣿⡝⣾⢹⣧⣼⣧
⢛⢹⢷⢤⠿⣀⠑⠈⠛⢙⣁⠂⠂⢀⣠⠀⠀⠀⠌⣀⠑⣄⡀⠠⠀⠈⢣⣕⢲⢰⠮⢀⣽⣷⣶⣶⣦⣬⣾⣿⣷⣄⠀⠀⠠⠀⠀⠀⠀⣄⡀⡤⣂⣚⣆⣀⢴⣿⣿⠿⢿⣿⣧⣴⣾⢿⡽⢿⣝⣟⣽⢟⣀⠩⣴⡮⢽⣿
⣶⣶⠆⣴⣎⡿⡿⣄⢸⣿⣟⡸⢦⡤⠘⠑⣱⣚⣐⢷⡿⣻⣾⡶⣌⠁⠀⠙⣃⡀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠄⠂⠉⠀⡀⡻⠫⡗⢣⣵⢻⣴⣤⠂⠤⠅⢙⣙⡋⠙⣿⣏⠻⣿⠿⢿⡷⡿⡿⣿⡻
⢻⣿⣶⣲⣾⢽⠴⠺⣧⡀⣀⣑⢼⣴⡁⣀⣀⣙⠿⢶⡾⠷⢖⣯⣿⣓⢦⣸⢿⠛⠂⠘⠭⣻⣿⣿⣿⡟⠛⣿⣯⣥⣤⣄⠀⠀⠄⠀⣂⣴⡦⠁⣁⡚⣻⣟⣻⣿⣷⠾⣏⣀⣒⣘⣴⣷⢛⣉⣻⣼⣾⣳⣶⣤⣅⣤⢅⣄
⢿⣿⣷⣤⣬⣓⢀⡀⠀⡙⣿⣻⣿⠗⠁⠹⣟⣐⣰⣪⡫⢻⣝⣿⣧⡿⢶⣛⢻⣄⣰⠤⣾⣿⣿⣿⣿⡀⣤⣿⣿⣿⣿⣿⣿⣒⠺⣀⡈⠉⣩⡀⢘⢘⠙⠋⣾⣟⢿⣾⡿⣿⢿⣻⣽⡦⣻⣧⠛⣻⣿⣿⢿⣻⢿⣽⠟⠺
⡂⢸⣞⠻⣿⡩⡥⠟⡀⣝⣏⣡⣤⢜⣲⡾⠐⠍⡯⠖⠙⠌⠙⠟⢻⣦⣬⣍⢾⠋⣿⣦⣿⣿⣿⣿⡿⣫⣽⣿⣿⣿⣿⣿⣿⣷⣶⣎⠿⣥⡿⢿⣿⣿⡿⡐⣷⣦⣪⡳⣶⣿⣾⡾⣯⠖⣿⣷⣦⣯⣿⣿⣿⣶⣿⣧⣻⣿
⡿⠀⢻⢻⣾⣇⠻⠂⠙⠩⢞⠞⠿⣟⢉⣨⣴⡴⢿⣿⠿⣄⡈⢷⣮⣥⡼⣹⣷⣿⣶⣯⣭⣿⣹⣭⣥⡷⢿⠿⠻⡛⠿⢿⠿⠛⠑⠉⠓⠉⣭⡗⢢⣵⣶⣆⣩⠻⠛⠡⣿⣻⣟⣿⣟⠻⠽⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⡀⠄⠙⢛⡛⢓⣲⢵⣲⢷⡿⢿⠭⡆⣲⣿⣿⡬⢬⢍⣀⣻⣖⢰⣳⣛⣿⠛⢯⡭⢺⠻⠭⣧⣵⣿⣦⠀⠄⠳⠒⠆⢀⢷⡀⢶⠑⣾⢶⢾⣭⣷⡿⣥⣛⡭⣈⠒⢶⣦⠍⣰⣟⢗⠀⣀⣜⠻⢿⣩⠟⣉⠥⢠⣾⢏⡝
⡈⢁⢟⢺⣦⠄⣹⠠⣤⣿⣄⢿⣥⢿⣷⣯⣙⣻⣿⠻⣸⣿⣿⣾⣾⢻⠟⡧⣽⠷⠿⢹⠙⢶⣶⣧⠁⠛⠀⠼⠚⠷⡆⣾⣺⢙⣿⣿⣿⠋⠛⠀⠩⠛⡉⢻⢭⣷⣍⣍⣿⡋⠙⢁⣀⡀⣀⣙⢣⠆⠀⠉⣮⣶⡇⠈⣿⣿
⠻⠾⣭⣦⣦⠘⢿⣽⣁⠙⣿⠿⠛⢿⡿⣿⠛⠛⣏⣯⣱⣦⡨⣿⠻⢏⠿⠻⠧⠶⠋⠏⡋⢫⣌⣣⣤⣦⡬⠵⠖⣴⣞⣖⠻⢭⣿⣿⣿⠠⡖⣟⣿⣾⣧⢒⢟⣯⢮⣥⣿⣟⠫⡿⣧⢃⡚⠛⣾⣦⣈⣈⡻⣻⣤⠌⠻⠟
⠀⡀⢘⣿⣭⣽⡟⠻⠉⠙⣡⡒⣠⢊⡍⢳⣶⣤⣦⣛⣭⣥⣼⣿⡖⡿⣶⡻⡕⢹⣶⣆⠓⣥⢉⠿⣟⣻⣦⣴⣄⡉⡡⠑⢈⣻⣿⡿⢇⡤⣞⡳⣿⣿⣶⣴⡌⣽⣷⣿⣟⣯⣧⣿⣉⣥⣴⣿⢀⢼⣶⡿⠇⠁⣸⡅⠲⡭
⣷⣒⣭⡀⠉⡁⣀⠐⢶⣤⣫⢳⣿⣐⢁⣐⡋⣋⢨⣄⣬⢹⣯⠼⣟⡻⣯⣛⣯⣩⣯⣏⠁⢵⡼⣡⣿⣿⠟⣣⣬⣛⡻⢷⡄⢈⣿⣗⡿⣖⢹⢍⢝⣉⣯⣅⣿⢛⡛⠛⣿⣭⣿⡉⠟⠙⠻⣿⣶⡭⠛⠁⠀⠘⣮⣼⣆⡲
⢷⡿⠻⣿⣥⣥⠀⢀⣽⣿⡸⣆⣽⣽⣿⣭⣿⣿⣷⡶⣍⢱⢾⣄⣿⠿⣷⣝⡾⠿⣽⡻⣄⢹⡣⣏⢱⠞⢿⡆⠘⠻⠾⢿⣳⣆⣴⣿⣚⣟⣶⣟⠰⠜⠾⢯⣿⣿⣿⡾⣺⣿⣿⣷⣿⣿⣿⣷⡋⠁⠀⠀⠀⠀⠀⣴⣞⠳
⢤⣶⡾⢺⣿⣿⣆⣬⣿⡾⡿⣿⣾⢟⠻⣿⠮⡿⣿⣿⣿⡆⠁⠀⠳⢾⢿⣟⣿⣻⡟⢿⣴⡤⡈⣽⡂⠀⠈⣿⣴⢲⠦⡶⣿⣇⠂⠯⣿⣭⣭⣟⠂⣹⣿⣿⣿⣷⡿⢿⣻⣿⢿⢵⡟⢋⠙⢿⣦⢀⠀⠀⠀⠀⠀⢈⣵⣶
⠹⣟⣿⣬⣽⡏⢿⣌⢡⠝⢿⣿⣿⣑⡻⣿⠻⢿⠿⠋⠹⡁⠄⠀⠔⠻⣭⡿⣼⣧⣾⣌⣅⣿⣿⡖⠶⢷⣮⣛⣻⡄⡈⢀⡒⠷⢶⣈⢛⣤⡿⣠⣾⣿⣟⣿⣿⣽⣲⣿⣿⣿⣟⡿⣥⠀⠀⣂⣟⡞⡠⢤⣥⣀⣲⣿⣿⣿
⣀⢭⣍⢉⢫⡷⣽⡧⣥⠄⣗⣽⢿⣿⠛⠛⢀⣨⣦⠰⡀⣿⣖⣀⢠⣄⣾⢽⠿⣿⣻⣽⣍⣝⠿⡖⠒⠭⡟⣽⣿⣿⡡⡔⣜⣠⡘⢿⡯⠻⣾⣿⣿⣿⣝⢛⣿⣿⣟⣻⣿⣛⢿⢻⣧⣁⣘⣛⠳⣷⣷⡿⢿⣧⣩⣻⣿⣿
⢃⢻⡟⣟⣋⣠⡍⣃⣠⣔⣺⣟⡾⢿⣇⣬⡟⣿⣿⣿⣿⣿⣿⡇⣀⢹⡾⠾⡖⠛⠿⡋⡾⠈⠱⣡⣼⣦⡖⠻⢿⣧⠴⣶⣽⣉⢷⣮⣟⣰⣻⣟⣶⣽⡗⢼⠿⣤⣻⣿⣿⣾⣿⣿⣿⣿⣿⣏⠶⣷⣏⢻⣿⣿⠿⢿⠉⠱
⠘⠛⣻⣟⠟⢟⠛⢛⡻⣿⣏⣿⣾⣷⣶⣭⣟⠿⣿⣯⣷⠹⡿⢷⠕⣁⣉⣄⣺⡾⠠⢦⣠⣬⣰⣻⣵⣪⣿⢦⠸⣿⠏⢨⡅⢿⣿⡮⠹⣽⣼⣿⢿⣿⡮⡳⡻⣿⣿⡽⢧⣯⣍⡽⠿⠿⣿⣿⣾⣟⣋⡈⠛⢿⠮⢭⢢⢶
⢀⣤⡀⢠⣼⢯⡧⠭⣧⣷⡄⡚⠚⡈⣤⠀⠉⠀⠀⠀⢱⣖⣲⠻⠋⠀⠀⠽⠆⢩⠈⣁⣷⡿⡶⠻⣿⡷⢮⠀⡴⣏⣙⣿⣿⣷⣦⣝⢞⣿⣿⣿⢹⣯⣿⣿⣿⣷⣿⣾⣗⣶⠿⡿⣽⡔⠀⣴⣦⠀⢠⣿⣿⣯⠉⠁⠀⠀
⣶⣧⡖⡂⠐⠶⠚⠸⠛⢏⠀⠨⠬⠀⢀⠀⠷⠼⣄⡀⠿⠿⠿⣶⣧⠠⢶⡶⣯⡏⠟⠯⢭⡟⡞⠊⠋⠋⠋⠞⠥⠄⣿⣿⠯⣼⣿⡿⡦⣏⠿⡿⡿⠭⡽⠛⠁⢰⢄⠀⠀⠀⠀⠂⠊⠀⠂⠿⠁⠐⠹⢿⢯⠙⠴⡾⠾⣿
⠀⣤⠀⠉⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠠⡧⠀⠠⠙⡁⠀⠀⡴⣿⠛⠺⠀⠈⠼⠍⠄⠄⢰⢨⡠⠀⠀⠒⠆⠀⠠⢀⠅⣠⣄⡈⢫⡀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡈⠂⢰
⣀⣤⣶⣿⣿⠀⢀⣠⣥⣤⢀⠀⠀⠀⠀⣃⡄⠀⠀⠀⠠⣿⡿⣿⡶⠇⠀⠀⠀⢀⠀⠀⢨⡼⠐⠀⠀⠀⢸⡇⠠⠰⣾⣿⣿⡏⠁⠀⠀⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣠⣬⣶⣦⡀⠀⠀⠇⠄⠘⠁⠀⠀⣲⣴⣟⠛
⠽⠿⠛⠛⠿⠇⠈⠛⠿⣿⣧⡀⠄⠀⠀⠈⠀⠀⠁⡀⠀⠔⣷⣶⣤⡖⠀⠀⠀⠈⠂⠀⠈⠀⠀⠁⠀⠀⠈⣂⠀⠘⠟⠟⠋⠀⠀⠀⠀⠀⣤⣄⣤⠀⠀⠀⠀⠀⢀⡤⢠⣼⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢛⣧⣼⡍
⢀⡀⠀⠀⠀⠀⠀⠁⡺⠶⡇⣀⢡⠆⠀⠀⠀⢀⣈⡁⠀⣤⣾⠇⠈⠉⠀⠠⠒⠀⠀⢤⣄⡀⠀⠴⠀⡤⣄⣈⠀⢀⠀⠀⠀⠀⠀⠀⣄⠰⣿⡉⠩⢀⠀⠀⢀⣄⣘⣤⣠⣥⡀⣀⡀⠀⠀⢀⠀⠀⠤⠀⠐⠉⢀⡙⢼⠛
⣸⡄⠂⣠⣔⠂⠀⠀⠀⠠⣌⣀⣐⢿⣶⣄⡀⠀⠈⠠⡈⠟⢋⣼⣿⣇⡀⣶⣿⣏⣁⣍⠿⠀⠀⠀⠀⠁⠀⣞⠯⣠⢤⠀⠒⣤⣼⣦⠨⣀⣃⣣⣠⠴⣠⡄⢀⢟⣟⠛⡛⢻⠿⣷⣦⠀⠀⢘⠁⠀⢀⣶⣼⡶⢛⣻⠀⣀
⡟⣿⡧⠾⠛⣧⠀⠀⠫⠖⢙⡛⢿⣿⢯⣿⣿⣿⡆⠀⠁⣥⣼⣿⣿⡿⠐⣟⠙⣿⣿⡿⡰⣶⣎⢓⠈⣀⠀⠀⠉⠨⡐⠀⠀⠚⠻⠗⠀⣓⣬⣿⣅⣀⠂⠀⠼⢼⠻⢖⠐⡂⢄⣤⣜⣀⡸⢁⠀⠰⡶⣶⣷⣿⣶⡿⣎⢭
⣿⣟⡏⡯⠈⠀⠀⢤⠨⢘⡛⢩⣲⠽⣷⣋⢿⣷⣌⠀⣘⣿⣿⣿⣟⣷⣞⣙⣛⡟⣻⣿⡿⡿⡓⠈⠄⠈⠐⢄⣤⣴⣄⡈⠀⠐⡒⠀⢴⣾⣿⡿⣿⣛⠁⠀⠄⠀⠐⠼⡀⣳⣤⡶⠶⢾⣿⡏⠁⡼⠀⠩⣉⣟⣿⠲⢶⣾
⠈⢿⣶⣮⠆⢀⡘⡿⠊⢉⠁⠀⠉⠀⢶⣭⣘⡛⠿⠟⣹⣿⣿⠛⢿⣿⣿⡏⠐⢗⢛⡀⠀⠀⠕⠂⠴⠀⣠⣿⣿⣿⣿⣿⠀⠁⠁⢄⠘⠃⠀⢈⠈⣁⠀⠀⢐⠢⢠⣄⣢⣷⣹⣴⠤⡤⠬⢕⠀⠀⠂⣠⣉⢻⠳⣶⣶⣿
⣾⣿⡏⠻⣇⡀⠰⡀⠔⢿⡿⠂⢀⣰⣾⡟⠉⢏⡫⣼⠻⠟⠋⠚⠍⠻⣿⣾⡅⢨⡮⠶⣥⣄⠀⠀⠹⠳⢞⣿⡿⠿⠿⠋⠀⠀⠀⠀⠈⠀⠀⠀⢀⠧⠀⢠⡜⣷⣤⣟⣻⣿⣟⡻⢷⣟⣶⣮⣯⣃⣬⣿⡝⣾⢹⣧⣸⣧
⢛⢹⣷⣤⠿⣂⠙⠈⠛⢙⣁⠂⠂⢀⣠⡀⡀⠀⢌⣁⠕⣄⡀⠠⠀⠘⢣⣑⢶⢰⠬⢀⢉⣩⣤⣤⣄⣴⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⣄⠀⠠⣂⣚⣆⣀⢼⣿⣿⠿⢿⣾⣧⣴⣾⢿⡿⢿⣝⢏⢽⢟⣀⠩⣴⡮⢽⣿
⣾⣶⡆⣰⣮⡿⡿⣁⢸⣿⣿⡹⠦⡤⢘⠑⣳⣛⣖⢷⣾⣚⣿⡦⣌⠁⠀⠙⣃⡀⢤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠄⠀⠉⠀⡀⡹⠫⡷⢣⣴⣻⣥⣤⠂⠤⡅⢙⣙⡛⠙⣿⣟⠻⣿⠿⢿⡷⡿⡷⣿⡻
⢾⣿⣶⣦⣾⣿⠴⠺⣧⡀⣠⣐⢴⣴⡁⢀⣀⣹⠿⢶⡾⡿⢞⣯⡿⣓⢦⣸⢿⠛⠂⠙⠿⣛⣻⣿⣿⡿⠛⣿⣯⣥⣤⣄⠀⠀⠄⠀⢂⣴⡆⠁⣁⠘⣹⣿⣻⣽⣷⠿⣇⣐⣒⣘⣼⣷⢛⣉⣻⣸⣿⣳⣶⣅⣍⡠⢅⣄
⢿⣿⣷⣤⣭⣓⢀⡀⢀⡙⣿⣻⣿⠗⠃⠹⣟⢐⣲⣪⡫⢿⣝⣿⣇⡿⢖⣋⢻⣄⡐⠬⣾⣿⣿⣿⣿⡀⣤⣿⣿⣿⣿⣿⣿⣤⠺⡀⡈⠉⡉⠀⢘⢘⢉⠉⣳⣿⣿⣾⡿⣿⢿⣺⣭⡦⣻⣷⠛⣻⣿⣿⣟⣿⢿⣿⠟⢺
⡃⠸⣞⡻⣿⡩⡥⠿⡀⣝⣏⡡⣤⢞⣲⡾⠑⠍⡯⠖⠙⠎⠙⠟⢿⣦⣮⣍⢾⠋⣿⣦⣿⣿⣿⣿⡿⣛⣽⣿⣿⣿⣿⣿⣿⣿⣔⡏⠿⣥⡮⢿⣿⣿⡷⡐⣷⣦⣮⠳⣶⣿⣾⡾⣯⢶⣿⣷⣶⣭⣿⣿⣿⣶⣿⣿⣿⣿
⣿⠀⢿⢻⣾⣏⠻⠃⠙⠩⢞⠾⠿⣟⢉⡨⣴⠶⢿⣿⠱⣄⡄⢷⣮⣤⡬⣻⣷⣷⣶⣧⣭⣿⣹⣯⣥⡗⢿⠿⠻⡛⠿⣿⡿⡟⠛⠉⠑⠉⣭⡗⢢⣵⣶⣇⣩⠿⠟⠡⣿⡻⣟⣿⡟⠻⠟⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡄⠀⠄⠙⢛⡛⢷⣶⠵⣺⢿⡿⢿⠻⡆⣲⣿⣿⡬⢨⢍⣀⢻⡆⢰⣳⣛⢿⠛⢯⡭⢾⠻⠭⣧⣵⣯⣆⠀⡤⠲⠒⠆⢀⢷⡀⠦⠵⣾⠲⢾⣭⣵⣯⣣⢛⡭⣈⠲⢶⣦⠍⣰⣟⢗⠀⣀⣈⠻⢿⡹⠛⡩⠧⢀⡾⢋⡝
⡈⢩⢞⢻⣦⢄⣹⠠⣤⣿⣄⢟⣥⢾⣷⣮⣙⣻⣿⠻⣸⣶⣿⣾⣾⢺⠝⠯⣽⠷⠿⢹⠙⣶⣶⣧⠁⠛⠀⠔⠚⠳⡆⣾⣺⢘⣿⣿⣿⠋⠛⠀⠨⠋⡉⠺⠭⣿⣍⣭⣟⡋⠙⢈⣀⡀⣈⣙⢧⠆⠀⠉⣤⣶⡇⠀⣿⣿
⠻⢿⣭⣶⣦⠈⢿⣽⡁⠙⣿⠿⠛⢿⡿⣿⠻⠛⣏⣿⣑⣮⡭⣿⠻⢍⠿⠻⠧⠷⠊⠏⡊⢫⣌⣣⣤⣦⡬⠽⠓⢴⣞⣖⠻⢬⣿⣿⣿⠠⡒⣚⣿⣿⣧⢾⢟⣯⢯⣥⣿⣟⠫⣿⡥⢃⡚⠛⠾⣦⣈⣈⡻⣻⣠⠌⠻⠟
⠀⡀⢘⣿⣿⣿⡟⡹⠉⠙⣡⡐⣠⢊⡍⣳⣶⣤⣆⣺⣭⣥⣵⣿⠖⡿⣶⡻⡕⣹⣶⣆⠑⣤⢉⠟⣟⣫⡦⣴⣄⡉⢁⠑⢈⣹⣿⡿⢗⡠⣞⡳⢿⣿⣾⣰⡌⣽⣧⣿⣟⣯⣧⣿⣉⣥⣴⣻⢀⢼⣦⡿⠇⠉⡘⡅⠰⡬
⣷⣺⣭⣀⠋⡁⣀⠐⢶⣤⣫⢳⣿⣒⢁⣰⡋⣋⢨⣄⣭⢻⣿⠼⢟⡺⣯⣟⣯⣫⡯⣏⡁⠰⡼⣣⣿⢿⢟⣣⡭⣛⡻⢷⡌⢈⢿⣇⡿⣖⢹⠝⢝⣉⣯⣅⣿⢛⡛⢻⣿⣭⣿⡁⠿⠙⢻⣿⣶⡍⠛⠁⠀⠰⣮⣼⣆⡲
⢿⡿⠻⣿⣣⣤⠀⢀⣽⣿⣰⣦⢱⣽⣿⣭⣿⣽⣷⡶⣍⢱⢷⡄⣿⠿⣷⣟⡾⠿⣽⡳⣎⢹⠣⣏⢱⠞⢿⡇⠘⠹⠶⢎⣵⠆⣾⣿⣛⣟⣴⣟⠐⠜⠾⢯⣿⣿⣿⡾⣺⣿⣿⣵⣾⣿⣿⡷⡋⠁⠀⠀⠀⠀⠀⣴⢾⠷
⢰⣶⡾⢾⣿⣿⣦⢬⣿⡿⡿⣿⣿⢟⠻⣿⠮⣿⣿⣿⣿⡆⠁⠀⠳⢾⢿⡏⣿⣻⡟⢿⣴⡤⡈⣭⡂⠀⡈⣿⡴⢰⠦⡶⣽⣇⠂⠯⣿⣭⣭⡟⠂⣹⣿⣿⣿⣶⠿⢿⣻⣿⠿⢵⠏⢋⠙⢿⣦⢀⡀⠀⠈⠀⠀⢨⣵⣶
⠹⣟⣿⣬⣿⡟⢿⣌⢩⠝⢿⣿⣿⣁⡻⣿⠿⢿⠿⠋⠱⡁⠄⠀⠔⠻⣭⡿⣼⣯⣶⣌⣅⣾⣷⠒⠶⣷⣮⣻⣻⡄⡈⢀⡚⠶⢷⣈⢛⣤⡿⣠⣾⣿⣟⣿⣿⣽⣲⣿⣿⣿⣟⡻⣥⠀⠀⣂⣿⡼⡡⢀⣄⢐⡲⣿⣿⣿
⣀⣩⣍⢉⢫⡷⣽⡧⣵⠆⣵⣽⢿⣿⠟⠛⢀⣨⣦⢰⡂⣿⣖⣀⢠⣄⣾⢽⡿⣿⣻⣽⣍⢽⠿⡖⠒⠌⡿⣹⢿⣿⡠⡜⠜⣤⡘⢿⣎⠹⣾⣿⣿⣿⣝⢛⣿⣿⣟⣿⣿⣛⢟⢻⣡⣁⣚⣟⠳⣷⣧⡿⢿⣧⣙⣻⣿⣿
⢃⢻⡟⣟⣉⣠⡍⣃⣠⣔⣺⣟⡾⢿⣧⣬⠿⣿⣿⣿⣿⣿⣿⡇⣀⣹⡾⠾⣖⠛⠟⡋⠿⠈⠙⣡⢼⣦⡖⠻⣥⣧⠰⣶⣍⣑⢷⣌⣏⡰⣻⣟⣥⣽⡗⠼⠿⡬⣼⣿⣿⢾⣿⣿⣿⣿⣿⣏⠶⣷⣧⢻⣿⣾⣿⣿⠈⠹
⠘⠛⢻⣟⠟⢟⠛⣛⣻⣿⣏⣿⣿⣶⣶⣭⣿⠿⣿⣯⣷⠹⢿⢷⠕⣁⣁⣄⣞⡾⠠⢦⢠⣬⢐⣹⣶⣊⡿⣮⠰⣾⠏⢩⡅⢿⣿⡎⠰⣬⣼⣿⢿⣿⠯⡰⡳⣿⣿⠽⢧⣯⣉⡽⣿⠿⣿⣿⢾⣟⣏⡈⠛⢿⠯⢬⢡⢶
⢀⣤⡀⢠⣼⢏⡕⠭⣧⣶⡄⡘⠒⣈⣤⠀⡉⡀⠀⠀⢡⡾⡒⠛⠏⠀⠀⠝⠆⢩⠈⡁⣶⡿⡶⠻⣿⡷⠆⠀⡴⣋⣙⣿⣿⢷⣦⣝⢞⣿⣿⣿⢙⣯⢿⣿⣿⣷⡟⣾⣖⣶⠟⡏⣽⡔⠀⣰⣦⠀⢠⣿⣿⣿⠉⠀⠀⠀
⣲⣯⡖⡂⠐⠶⠚⠸⠚⢏⠀⠨⠭⠄⠀⠀⠡⠬⣄⡀⠿⠿⠿⣶⣇⡀⢶⡶⣯⡋⠟⠣⢭⡟⡞⠊⠏⠋⠋⠞⠥⠄⣿⣿⢏⣼⣿⡿⠤⣖⠿⡿⡿⠭⠽⠋⠀⢰⠄⠀⠀⠀⠀⠂⠊⠀⠂⠿⠁⠐⠹⢿⢯⠙⡰⡾⠮⡮
⠀⣴⠀⠉⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠠⡧⠀⠠⠝⠁⠀⠀⡔⣿⠋⠺⠀⠈⠜⠉⠄⠀⢰⢠⡠⠀⠀⠐⠆⠀⠠⢂⠅⣠⣄⣀⢫⠀⠀⠁⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⡈⠂⠰
⣀⣤⣶⣿⢿⠀⢀⣠⣤⣤⢀⠀⠀⠀⠀⣃⠄⠀⠀⠀⠠⣿⡿⣟⡷⠂⠀⠀⠀⢀⠀⠀⢨⡼⠀⠀⠀⠀⢰⡇⠀⠰⣼⣿⣿⡏⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⣶⣦⡀⠀⠀⠃⠄⠘⠁⠀⠀⣲⣴⣟⠛
⡽⠿⠛⠛⢿⠇⠈⠛⠿⣿⣧⡀⠄⠀⠀⠈⠀⠀⠀⡀⠀⠕⣷⣶⣄⡖⠀⠀⠀⠈⠂⠀⠈⠀⠀⠁⠀⠀⠈⣂⠀⠘⠟⠟⠋⠀⠀⠀⠀⠀⣤⣄⣤⠀⠀⠀⠀⠀⢀⡤⢠⣬⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢛⣧⣴⡈
⢀⡀⠀⠀⠀⠁⠀⠁⡱⠵⡇⣀⢡⠆⠀⠀⠀⢀⣈⡁⠀⣤⣾⠃⠈⠉⠀⠠⠐⠀⠀⢤⣄⠀⠀⠤⠀⡬⣄⠈⠀⢀⠀⠀⠀⠀⠀⠀⣅⠰⣿⠉⠉⠀⠀⠀⢀⣅⣘⣄⣀⣥⡀⣀⡀⠀⠀⢀⠀⠀⠤⠀⠐⠁⢀⡉⢼⠈
⠸⡕⠂⢠⣔⠂⠀⠀⠀⠠⣌⣀⢀⢿⡶⣄⡀⠀⠈⠠⡀⠟⢋⣼⣿⣇⣀⣶⣿⣏⢡⡍⠿⠀⠀⠀⠀⠁⠀⢚⠦⣠⢤⠀⠂⣤⣶⣦⠨⣀⣣⣣⣠⠴⢀⡄⢀⢿⡟⠛⠛⢻⠟⢷⣦⠀⠀⢘⠁⠀⢀⣲⣜⡶⢛⣙⠀⣀
⡟⣻⡥⠼⠛⣵⠄⠀⠋⠦⠙⡓⢻⣿⢯⣿⣿⣿⡄⠀⠁⣥⣼⣿⣿⡯⠰⣛⠙⣿⢻⡿⡐⢶⡮⢐⠈⣀⠀⠀⠈⠀⠂⠀⠀⠘⠻⠗⠀⢁⣠⣿⣅⢀⠀⠀⠬⢾⠿⢆⠐⠂⢄⣤⣌⣀⡸⢁⠀⠐⡶⣶⣷⣿⣴⡿⣌⠩
⣻⣟⡋⣯⠄⠀⠀⢄⠈⢘⡛⢩⣲⠽⣶⣋⠿⣵⣌⠀⣙⣿⣿⣿⣟⣻⣞⣙⡛⡟⣻⣿⡿⣿⡒⠈⠄⠈⠀⣠⣴⣶⣦⣄⠀⠐⡒⠀⢴⣶⡿⡿⢿⢚⠁⠀⠄⠀⠐⠬⠀⣳⣤⡶⠶⠾⣿⡍⠁⡼⠀⠈⣉⣛⣿⠰⢾⣾
⠈⢹⣶⣮⠅⠀⡙⠿⠓⢉⠀⠀⠁⠀⢖⣭⣐⡛⠿⠛⣹⣿⣿⠟⢻⣿⣯⡏⠐⢗⣛⠀⠀⠀⠅⠆⡠⠀⣰⣿⣿⣿⣿⣿⠀⠁⠀⠄⠘⠃⠀⠈⠈⣁⠀⠀⠐⠢⢠⣄⣠⣳⣹⣴⠤⡤⠬⢁⠀⠀⠀⡠⡉⢫⠳⣶⣾⣽
⣲⡿⡏⠻⣇⡀⠠⡀⠔⢿⡿⠂⠀⣠⣮⡍⠉⢍⡫⡜⠻⠟⠊⠐⠍⠻⣿⣶⡅⢨⣈⣤⣤⣤⣄⡀⠸⠳⢾⣿⣿⣛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠧⠀⢠⡌⣷⣤⡛⣻⣿⡟⡻⢷⣟⣴⣬⣯⣃⢬⣿⡝⣾⢸⣧⣸⣇
⢛⢹⣷⣤⠿⣂⠑⠈⠛⢙⣁⠀⠐⢀⢠⡀⠀⠀⠌⣁⠕⣄⡀⠀⠀⠘⢣⣙⢲⢸⣿⣿⣿⣿⣿⣿⣀⣠⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⡄⠀⠠⡂⣘⣆⣀⢴⣿⣿⠿⠿⣿⣧⣴⣾⢟⠽⢿⣜⢋⢽⢟⣀⡩⣴⡮⢽⣿
⣶⣶⡆⣰⣮⡿⡿⣅⢸⣿⣟⡹⠦⡄⢘⠑⣱⣚⣒⢷⣾⣛⣿⡢⣌⡑⠀⠙⡃⡈⠿⣿⣿⠿⢻⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠄⠀⠁⠀⠀⠙⠫⡖⢣⣠⣻⣥⣤⠂⠤⡅⠙⢙⡛⠙⣿⣏⠻⣿⠟⢿⡷⡿⠵⣿⣻
⢺⣿⣶⣶⣶⣿⠤⠺⣧⡀⣠⡀⠴⣴⣁⣀⣀⣙⠿⠶⡦⡷⢞⣧⡟⡓⢦⣸⠿⠛⠂⠘⠯⣍⣿⣿⣿⡿⠛⣹⣿⣭⣤⣥⣀⠀⠄⠀⣂⣴⡆⠀⣀⠘⣺⡿⣻⣿⣿⠿⡇⣀⣒⣘⣼⣷⠛⣉⣻⣸⣶⣳⣶⣄⣁⣤⢅⣀
⢽⣿⣷⣤⣬⣒⢀⡀⠀⣙⣿⣻⣿⠷⠃⠹⣏⢐⣰⣊⡩⢿⣝⣿⢇⡿⢖⣋⠻⣄⡰⠬⣸⣿⣿⣿⣿⡄⣤⣿⣿⣿⣿⣿⣿⣷⡞⠂⡈⠉⡉⠀⢈⢘⢉⠉⣺⡟⣿⣾⡿⣻⢻⣻⣽⡆⣻⣧⠛⣻⣿⣿⣟⣿⣽⣿⠋⢪
⡂⠸⣞⠻⣿⣩⡭⠿⡀⣍⣏⣡⡠⢜⣒⡶⠐⠈⡪⠑⠙⠌⠘⠟⢻⣦⣬⣍⢮⠋⣿⣦⣻⣿⣿⣿⡿⣛⣹⣿⣿⣿⣿⣿⣿⣿⣿⡌⠿⣥⡾⢿⣿⣿⡷⡐⣷⣦⣮⠳⣶⣿⣼⡾⣏⢴⣿⢷⣦⣯⣿⣿⣿⣶⣿⣏⣿⣷
⡿⠀⢿⢫⣶⣷⠙⠀⠙⠩⢞⠶⠿⣛⢉⣨⣵⡶⢻⣿⡷⣄⡌⢷⣮⣤⠬⣹⣷⣷⣶⣯⣽⣿⣩⣭⣥⡗⢿⠿⠛⡋⠻⢿⣿⡿⠿⠽⠑⠉⣭⡗⢢⣵⣶⢇⣩⠻⠛⠡⣿⡻⣟⣿⡿⠺⠝⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡄⢀⠄⠙⢛⡛⢳⣖⠵⣲⢷⡿⢿⡯⡆⣲⣿⣾⡭⠠⢅⣄⢻⣆⢰⣳⣛⢿⠛⢯⡭⢺⠿⠭⣧⣵⣮⣆⠀⡤⠲⠒⠒⢀⣂⡀⠦⠱⣿⢲⠾⣭⣵⣧⣡⢚⡭⣀⠲⢲⣦⠍⣰⣟⠷⠀⣀⣌⠻⢿⠹⠛⡉⠅⢀⠾⣋⠝
⡀⢉⠞⠻⣦⢄⣹⠠⣤⣹⣄⢿⣥⠾⣷⣊⣙⣻⣻⠺⣸⣷⣿⣾⣶⢺⠟⠎⣼⠿⢷⢹⠙⣶⣶⣤⠁⠛⠀⠄⠒⠢⡆⣞⣲⢘⣿⣿⣿⠋⠘⠀⠨⠋⡉⠨⠭⣿⣍⣭⣝⡋⠙⢀⣀⡀⣈⡙⢣⠂⠀⠉⣤⣶⡎⠀⣿⣿
⠻⠿⣭⣦⣤⠈⠿⣯⣁⠙⣿⡿⠋⢿⡿⢿⠻⠛⣎⣫⣑⣪⡩⡟⠻⢍⠻⡻⠧⠶⠋⠎⡊⢫⣌⣣⣤⣆⡌⠽⠓⢴⣚⣖⠻⢬⣿⣿⣿⠠⡖⣒⣿⣾⣧⢒⢟⣯⢯⣡⣿⣟⡫⡿⡧⢃⡚⠒⠾⣆⣀⣈⡻⡹⣠⠄⠻⠟
⠀⡀⢘⣿⣯⣽⣟⠙⠉⠙⣡⣐⢠⢊⡍⣳⠶⣤⣄⣚⣭⣥⣴⣿⠐⡿⣶⣻⡕⠹⣶⣆⠐⣤⢉⠛⣟⣫⡦⣴⣄⡈⢁⠑⠨⢹⣿⡿⢗⠠⣞⡱⢿⣿⣶⣰⡌⣿⣷⣿⢟⣯⣧⣿⣉⣤⣴⣿⢀⢼⣦⡿⠇⠀⡈⡅⠐⡨
⣿⣰⣭⡀⠋⣁⣂⠐⠶⣤⣾⠳⣿⣐⢅⣰⡋⣳⡨⣄⣬⢹⣿⠼⢝⡺⣯⣛⣭⣫⡭⣏⡁⠰⡼⣡⣿⢿⢟⢣⣬⣛⡻⢷⡄⢈⢿⣇⡿⣖⢙⠍⢕⣉⣿⣅⣿⢙⡛⢻⣿⣭⣿⠁⠟⠙⠻⣿⣶⡍⠛⠀⠀⠰⣦⣼⣆⡲
⢿⣿⠻⣿⣣⣤⠀⢀⣼⣿⣐⣆⣸⣽⣿⡭⣽⣵⣷⡶⣌⠑⢿⣄⣿⠿⣷⣟⡾⠿⣭⡲⣆⢹⡣⣌⢱⠞⢿⡇⠘⠚⠶⢆⣱⢆⣼⣿⣛⣟⣴⣕⠐⠜⠾⢯⣿⣿⣿⡾⣺⣿⣿⣵⣾⣿⣿⡶⡋⠀⠀⠀⠀⠀⠀⣴⢚⠑
⢰⣶⡾⢾⣿⣿⣦⢬⣿⡿⡿⣿⣷⢟⠻⣿⠮⣽⣿⣿⣿⡆⠁⠀⠳⢾⢿⡏⣿⣋⡟⢿⣴⡬⡈⢭⠂⠀⡈⣿⡐⠰⡦⡶⢽⣇⠀⠿⡾⣭⣭⡟⠂⣹⣿⡿⣿⣖⠿⢿⣿⣿⢿⢶⡏⢋⠛⢿⣆⢀⠀⠀⠀⠀⠀⣨⣴⣶
⠘⣟⣿⣬⣽⡏⢿⣌⢡⡝⢿⣿⣿⣑⡻⣿⡿⢿⠿⠋⠱⡁⠄⠀⠐⠹⣭⣻⣬⣧⣶⣌⣁⣾⣾⡐⠶⢳⣮⣻⣳⡄⡈⢀⡐⠔⢶⣈⢓⣤⡾⣠⣾⣿⣟⣿⡮⣼⣲⣿⣿⣿⣛⠻⣤⠀⠀⣂⣟⡸⠠⢀⣄⢐⢺⣿⣿⣿
⢀⢩⣍⠉⢫⡷⣼⣧⣯⠦⢵⣽⢿⣿⡟⠓⢀⢈⣦⢰⡂⣿⣖⣀⢠⣄⣾⢽⠻⣿⣻⣽⣍⢝⠟⡖⠒⠌⡿⣽⢿⣿⡀⡜⠜⣤⡘⢾⣎⠻⣾⣿⣿⣽⣝⠛⣺⣿⣟⣿⣿⣛⢟⢹⣡⣁⣘⣛⠣⣷⣧⡿⢟⣤⣉⡻⣿⡟
⢃⢻⣟⣒⣉⣠⡍⢃⣠⣌⣺⣟⡽⠽⣇⣬⠿⣿⣿⣷⣿⣿⣏⡇⡈⢹⡾⠾⡖⠛⠟⡋⠜⠈⠑⣡⢬⣦⡖⠻⢵⣧⠰⣶⣍⣑⢷⣌⠕⡰⣻⣟⣤⣽⡗⠼⠿⡬⣸⣿⣿⢾⣿⣿⣿⣿⣿⣏⠲⣷⣣⢹⣿⣿⠿⢿⠈⠐
⠘⠛⢻⣟⠟⢟⡛⢛⣻⣿⣯⣿⣿⣵⣶⣭⣟⠿⣿⣯⣷⠻⢿⢷⠔⣀⣁⣄⣚⡶⠠⢦⣠⡬⢐⣨⣷⣈⡿⢮⠰⣾⠏⢩⠅⠽⣿⡏⠠⣬⣽⣿⢿⣿⠎⡸⡳⡿⣿⠽⢧⣯⢉⡵⠿⠿⣿⣿⢾⣟⣏⡈⠛⢿⠮⢬⢫⢶
⢀⣤⡀⢠⣼⢯⣵⠭⣇⣦⡄⡖⠓⡊⣤⠀⡉⡀⠀⠀⢱⣾⡒⠛⠏⠀⠀⠽⠆⢩⡈⠁⣶⡿⡶⠻⣿⡷⢗⠀⣴⣋⣙⣿⣿⢷⣦⣽⢞⣿⣿⣿⢹⣯⢿⣿⣿⣷⣿⣾⣖⣶⠿⡏⣽⡴⠀⣰⣦⠀⢠⣿⣿⣯⠉⠀⠀⠀
⣲⣯⡖⡂⠐⠶⠛⠸⠛⢏⠀⠨⢬⠄⠀⠀⠥⠬⣤⡀⠿⠿⠿⣶⣧⡠⢶⡶⣯⡏⠟⠣⢭⡟⡗⠊⠋⠋⠋⠞⠥⠄⣿⣿⢏⣼⣿⡿⡦⣟⠿⡿⡿⠭⠽⠛⢁⢰⠄⠀⠀⠀⠀⠂⠊⠀⠂⠿⠁⠐⠹⢿⢯⠙⣵⡾⠮⡿
⠀⣴⠀⠉⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠠⡷⠀⠠⠝⡁⠀⠀⡔⣿⠋⠺⠀⠀⠔⠉⠄⠄⢰⢠⡠⠀⠀⠒⠆⠀⠠⢀⠅⣠⣄⣈⣫⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⡈⠂⢰
⣀⣤⣶⣿⠿⠀⢀⣠⣥⣤⢀⠀⠀⠀⠀⢃⡆⠀⠀⠀⠠⣿⣿⣿⡷⠆⠀⠀⠀⢀⠀⠀⢨⡼⠀⠈⠀⠀⢰⡇⠀⠰⣾⣿⣿⡏⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣬⣶⣦⡀⠀⠀⠃⠄⠘⠁⠀⠀⣲⣴⣟⠛
⡟⠿⠛⡋⢿⠇⠈⠛⠿⣿⣧⡀⠄⠀⠀⠈⠀⠀⠀⡀⠀⠥⣷⣶⣄⡖⠈⠀⠀⠈⠂⠀⠈⠀⠀⠁⠀⠀⠈⣂⠀⠘⠟⠟⠋⠀⠀⠀⠀⠀⣤⣄⣤⠀⠀⠀⠀⠀⠀⡤⢠⣬⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢛⣧⣼⡉
⢀⡀⠀⠀⠀⠁⠀⠁⣰⠷⡏⣀⠡⠆⠀⠀⠀⢀⣀⡁⠀⣤⣾⠃⠈⠉⠀⠠⠒⠀⠀⢠⣄⠀⠀⠴⠀⡤⣄⠈⠀⢀⠀⠀⠀⠀⠀⠀⣥⠰⣿⡉⠩⠀⠀⠀⢀⣄⣘⣤⣀⣥⡄⣀⡀⠀⠀⠀⠀⠀⠤⠀⠐⠉⢀⡉⢼⠊
⠸⣅⠂⢠⣔⠂⠀⠀⠀⠠⣬⣀⢰⢿⣶⣄⡀⠀⠈⢠⡀⠝⢋⣼⣿⣇⠀⣶⣿⣏⢡⡍⠿⠀⠀⠀⠀⠁⠀⣞⠾⣀⢤⠀⠂⣠⣼⣶⠨⣀⣣⣣⣠⢴⢀⡄⢀⢿⡟⠛⠛⢻⠟⢷⣦⠀⠀⢚⠁⠀⢀⣲⣜⡶⢛⢙⠈⣐
⡟⣿⣥⠽⠟⣵⠄⠀⠉⠶⠙⡚⢻⣿⢯⣿⣿⣶⡀⠀⠉⣥⣼⣿⣿⡯⠰⣏⠙⣿⣻⡿⡠⣶⣎⢐⠈⡀⠀⠀⠉⠀⡒⠀⠀⠘⠛⠗⠀⣟⣨⣿⣅⢀⠂⠀⠬⢾⠿⢖⠐⡂⢄⣤⣜⣀⠸⢁⠀⠐⡶⣶⣷⣿⣶⡿⣎⢩
⣻⣟⡛⣿⠄⠀⠀⣠⠬⢈⡛⢩⣲⠭⢷⣋⠿⣵⣌⠀⣘⣿⣿⣿⣟⢷⣞⣙⡛⡏⣻⣿⡿⠿⡒⠈⠀⠈⠀⣴⣾⣶⣶⣤⠀⠐⡒⠀⢴⣶⡿⡿⢿⢛⠁⠀⠀⠀⠐⠬⣀⣳⣤⡶⠶⠾⣿⡍⠁⡼⠀⠉⣉⣟⣿⠲⢾⣾
⠈⢹⣶⣮⠄⠀⡙⡿⠃⢉⠑⠀⠁⠀⢶⣭⣐⡛⠫⠟⢹⣿⣿⠛⢻⣿⣯⡏⠐⠗⣛⡀⠀⠀⠅⠂⠄⠀⣰⣿⣿⣿⣿⡿⠀⠁⠀⠀⠈⠁⠀⠈⠈⣁⠀⠀⠐⠢⢠⣤⣡⣳⣹⣴⠤⡤⠬⢑⠈⠀⠢⣠⡉⢫⠳⣶⣾⣽
⣶⣷⡏⠻⣇⡠⠰⡀⠰⢿⡿⠃⠁⣠⣮⡟⠈⢏⡫⡜⠹⠟⠊⠐⠍⠻⣿⣾⣷⣾⣿⣿⣿⣶⣆⠀⠸⠱⣻⣿⣿⣿⣏⠁⠀⠀⠀⠀⠈⠀⠀⠀⢀⠧⠀⢠⡜⣷⣤⡛⣻⣿⡟⡹⢷⣟⢴⣮⣯⣃⢬⣟⡝⣾⢸⣧⣸⣇
⢛⣹⣷⣤⠽⣂⠙⠊⠛⢉⣃⠂⠘⢁⡠⡀⠀⠀⢌⣁⠕⢄⡀⠠⠀⠘⢣⣙⢻⣿⣿⣿⣿⣿⣿⣤⣀⣤⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⡄⠀⠠⡂⣘⣆⡀⢼⣿⣿⠿⣿⣿⣧⣴⣾⠿⡿⢿⣞⢋⢽⢟⣀⠉⣴⡮⢹⢿
⣷⣶⡆⣰⣮⣿⡿⣅⠸⣿⣟⡹⠦⡄⠘⠁⣳⣚⣖⢶⣟⣛⣿⡢⣌⡑⠀⠙⣃⠙⣿⣿⣿⣟⣽⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠄⠀⠁⠀⠀⠘⠋⠖⠣⣔⣻⣥⣴⠂⠤⠅⢛⣙⡋⠙⣿⣏⠻⣿⠿⢿⡷⡿⠷⣿⡻
⢸⣿⣶⣶⣶⣿⡴⠺⣧⡀⣠⡘⠬⣵⡉⣀⣀⣙⠿⠷⣮⡿⢞⣯⡿⡓⢦⣼⠿⠚⠂⠸⠯⢹⣿⣿⣿⣿⠏⣩⣿⣦⣤⣷⣦⣄⡄⠀⡂⣴⡄⠀⡀⠘⣺⡿⣻⣽⣿⠿⡇⣐⣒⣘⣼⣷⢋⣉⣻⣼⣷⣳⣶⣥⣁⣠⢅⣀
⢼⣿⣷⣬⣭⣓⢀⡀⠀⣙⣿⣻⣿⠷⠋⠹⣯⣐⣲⣪⡫⢿⣝⣿⣇⡿⢖⣋⠻⣄⡐⠄⣰⣿⣿⣿⣿⡇⣀⣿⣿⣿⣿⣿⣿⣿⣿⣦⠈⠉⡁⠀⢘⢘⢉⠉⣺⣿⣿⣾⡾⣿⢿⣺⣭⡆⣻⣧⠛⣻⣿⣿⣟⣯⣿⣿⠋⢺
⡋⠸⣞⡻⣿⡭⡭⠿⠀⣍⣏⣡⡠⢔⣲⡶⠑⠈⡮⠑⠙⠎⠘⠟⠟⣦⣬⣍⢮⠟⣻⣶⣻⣿⣿⣿⣿⣏⣹⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⣥⡾⢿⣿⣿⡷⡐⣷⣦⣮⡵⣶⣿⣾⡾⣏⢶⣿⣷⣶⣯⣿⣿⣿⣴⣿⣯⣿⣷
⣿⠀⣽⢻⣶⣷⠹⠃⠙⠳⢼⠾⠿⢛⠉⣨⣴⡶⢺⣿⡝⢄⣤⢷⣮⣤⠌⣍⣷⣷⣶⣯⣭⣿⣩⣭⣥⡆⢿⠿⠻⡃⠉⠻⠿⠿⠿⠛⠛⠉⣭⡗⢢⣵⣶⣇⣩⠻⠟⠡⣿⣻⣟⣿⡿⠻⠝⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠆⢀⠄⠙⢛⡛⢳⣶⠴⣰⢷⡿⢿⡯⡆⣲⣿⣿⡬⠠⢅⣀⢹⡆⢰⣻⣋⣿⡟⢿⡭⢲⠻⠩⣧⣵⣾⣆⠀⡦⠲⠒⠂⢀⣶⡀⠦⠱⣿⢶⠾⣭⣷⣧⣣⢛⡭⣀⠲⢺⣤⠍⣸⣟⠷⠀⣀⡌⠻⢟⡹⠛⡩⠥⢀⠾⣏⠍
⡈⢁⣞⢻⣶⠡⣙⠠⣤⣹⣄⢻⣵⢾⣷⣎⣘⣻⣻⠺⣹⣷⣿⣾⣶⢺⡟⠧⣽⠷⠾⢹⠙⢶⣶⣦⠉⠛⠀⠴⡚⠳⡆⣞⣲⢙⣿⣿⣿⠋⠊⠀⢨⡋⡉⠨⠩⣿⣍⣭⣿⡋⠉⢀⣀⡀⣈⣙⢣⠂⠀⠉⣤⣶⡊⠀⣿⣿
⠻⠿⣭⣦⣴⠈⢿⣭⣁⠙⣻⠿⠋⢿⡿⢿⠻⠛⣏⣿⣑⣦⡩⣽⠻⢯⠻⠻⠦⠶⠋⠏⡊⠫⣈⣣⣤⣆⡌⠽⠗⢶⣚⣖⠻⢭⣿⣿⣿⠰⡲⣛⣿⣿⢧⢺⢟⣯⢯⣡⣿⣟⠫⡟⡧⢇⡞⠓⢾⣦⣀⣈⡻⣹⣠⠌⠿⠟
⠀⣀⢈⣿⣯⣿⣟⠙⠉⠘⣡⣐⢠⢊⡉⢳⡶⣤⣦⣚⣯⣭⣵⣿⡜⡿⣶⣓⡕⢙⣴⣎⠑⡤⢈⠛⣟⣻⡦⣴⣄⡉⢡⠑⢨⢽⣿⡿⢗⠤⣞⡹⣿⣿⣾⣰⡌⣿⣧⣽⣟⣯⣧⣿⣉⣥⣴⣾⢀⢸⣶⡾⠇⠁⣈⡅⠀⡨
⣿⣐⣭⣀⠋⣁⣂⠐⠶⣤⣺⠻⣿⣒⢅⣰⡋⣳⡠⣄⣬⡹⣿⠼⢟⡻⣯⣟⣿⣩⡧⣏⡁⠰⡼⣣⣿⢿⢟⣯⣬⣛⡻⢷⡄⢈⢿⣟⣿⣖⢹⠍⢝⣋⣯⣅⣯⢙⡛⢻⣿⣭⣿⠁⠿⠙⠽⣮⣶⡌⠫⠁⠀⠀⣮⣬⣎⠲
⢿⣿⠻⣯⣣⣥⠀⢀⣽⣿⣒⣧⣱⣽⣿⡭⣽⣵⣷⡆⣌⢙⢿⣇⣿⠿⣷⣟⡾⠿⣯⣳⣆⢹⠳⣆⢱⠞⢿⡏⠘⠺⠶⢎⣷⢆⣴⡿⣓⣟⣴⣟⠐⠜⠾⢯⣿⣿⣿⡾⣻⣿⣿⣷⣾⣿⣿⡷⡋⠀⠀⠀⠀⠀⠀⣴⣚⠁
⢤⣶⣾⢾⣿⣿⣷⢨⣿⡿⡿⣿⣷⢿⠻⣿⠾⣿⣿⣿⢿⡆⠈⠀⠳⠾⣿⡏⣿⣋⡟⢿⣴⡤⡈⣽⠂⠀⠈⣿⡔⢲⡦⠶⣽⣇⠀⠿⡿⣭⣭⣟⠂⣹⣿⣿⣿⣷⡿⢟⣻⣿⢯⢽⡍⢋⠛⢿⣆⢀⠀⠀⠀⠀⢀⣬⣷⣾
⠘⣿⣿⣬⣽⡟⢻⣌⢩⠝⢻⣿⣿⣁⡻⣿⡿⢿⠿⠛⠹⣁⠄⠀⠔⠹⣭⡿⣮⣧⣶⣌⣍⣾⣿⡚⠶⣷⣦⣛⣷⡄⡈⢀⡚⠔⠷⣈⢓⡤⡟⣠⣾⣿⣟⣾⣾⣼⣲⣿⣿⣿⢟⡳⣤⠀⠀⣂⣟⣸⡤⢀⣄⢐⣿⣿⣿⣿
⣀⣨⣍⠍⢫⡷⣼⣇⣭⡦⢽⣿⣻⣿⠿⠛⢀⣈⣦⢰⣆⡿⣖⣂⢠⣤⣼⢽⡿⣿⣻⣽⣍⢝⠟⡖⠒⠜⡿⣽⠯⣷⡀⡄⠜⣤⠘⢿⣍⠹⣾⣿⣿⣽⣝⢻⣻⣿⣝⣯⣿⣛⢟⢹⣬⣁⣘⣛⠳⣷⣷⡿⢟⣦⣉⡛⣿⡟
⣁⢘⣯⣳⣙⣠⡍⢃⣠⣜⣺⣿⡿⠽⢧⣬⡿⣿⣿⣿⣻⣿⣏⡇⣀⣩⡿⠾⢖⠛⠛⡋⠞⠈⠙⣡⢬⣦⡖⠻⢵⣇⠰⣶⣭⣣⢓⣬⣳⡰⣻⣟⣤⢽⡗⠼⠿⡔⣸⣿⣿⢾⣿⣿⣿⣿⣿⣏⠶⣷⣍⢻⣿⣾⠿⣿⠀⠐
⠘⠛⢻⣿⠿⢟⡛⢛⣻⣿⣯⣿⣿⣷⣶⣭⣿⠿⣿⣯⣷⠛⢿⠷⠜⣀⣁⣄⣸⡶⠢⢦⣠⡬⢐⣨⣷⣒⡿⣮⠠⢿⠇⢩⠥⢿⣿⡏⠐⣼⣼⣿⢿⡷⠎⣹⡻⣻⣿⠽⢇⣯⣉⡴⢿⠿⢿⣿⣿⣏⣍⡈⠛⢿⠯⢬⢧⢶
⢀⣤⡀⢠⣼⢯⣕⠭⣧⣶⡄⡒⠓⡊⣤⠀⡉⡀⠀⠀⢱⣾⡒⠛⠏⠀⠀⠽⠆⢩⠈⡁⣶⡿⡶⠻⣿⡷⢗⠀⣴⣏⣙⣿⣿⢷⣦⣽⢞⣿⣿⣿⢹⣯⢿⣿⣿⣷⣿⣾⣖⣶⠿⡏⣽⡴⠀⣰⣦⠀⢠⣿⣿⣯⠉⠀⠀⠀
⣲⣯⡖⡂⠐⠶⠚⠸⠟⢏⠀⠨⢭⠀⠀⠀⠵⠬⣤⡀⠿⠿⠿⣶⣧⡀⢶⡶⣯⡏⠽⠧⢭⡟⡞⠊⠏⠛⠋⠞⠥⠄⣿⣿⢯⣼⣿⡿⡦⣟⠿⡿⡿⠭⠽⠛⢁⢸⠄⠀⠀⠀⠀⠂⠋⠀⠂⠿⠁⠐⠹⢿⢯⠙⣰⡺⠮⡿
⠀⣤⠀⠉⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠠⡷⠀⠀⠝⡁⠀⠀⡴⣿⠋⠺⠀⠀⠔⠉⠄⠄⢰⢤⡠⠀⠀⠒⠆⠀⠠⢀⠅⣠⣄⣀⢫⠀⠀⠁⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⡈⠀⢰
⣀⣤⣶⣾⠿⠀⢀⣠⣤⣤⢀⠀⠀⠀⠀⢃⠄⠀⠀⠀⠠⣿⡿⣿⡷⠆⠀⠀⠀⢀⠀⠀⢨⡼⠐⠈⠀⠀⢰⡇⠠⠰⣾⣿⣿⡏⠁⠀⠀⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣀⣬⣶⣦⡀⠀⠀⠃⠄⠘⠁⠀⠀⣳⣴⣟⠛
⡿⠿⠛⡛⢿⠇⠈⠛⠿⣿⣧⡀⠄⠀⠀⠈⠀⠀⠀⡀⠀⠥⣷⣶⣄⡖⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠈⣂⠀⠘⠟⠟⠋⠀⠀⠀⠀⠀⣤⣄⣤⠀⠀⠀⠀⠀⠀⡤⢠⣬⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢛⣧⣼⣈
⢀⡀⠀⠀⠀⠁⠀⠁⡱⠷⡇⣀⡡⠆⠀⠀⠀⢀⣀⡁⠀⣤⣾⠃⠈⠉⠀⠠⠖⠀⠀⢤⣄⠀⠀⠴⠀⡤⣄⠀⡀⢀⠀⠀⠀⠠⠀⠀⣅⠰⣿⠉⠉⢀⠀⠀⢀⣄⣐⣤⣀⣥⡀⣀⡀⠀⠀⠀⠀⠀⠤⠀⠐⠁⢀⣉⢼⠋
⡸⣅⠂⣠⣴⠂⠀⠀⠀⠠⣬⣀⢰⢿⣶⣄⡀⠀⠈⢠⡀⠝⠋⣴⣿⣇⡀⣶⣿⣏⢡⣍⠿⠀⠀⠀⠀⠁⠀⣚⠶⣀⢤⢀⠊⣠⣼⣦⠨⣀⣃⣣⣠⢴⢀⡄⢀⢟⡟⠛⠛⢻⠟⢷⣦⠀⠀⢘⠁⠀⢀⣲⣜⡶⢛⢙⠈⣐
⡟⣿⣥⠼⠟⣵⠄⠀⠩⠶⠙⡚⠻⣿⢯⣿⣿⣾⡄⠀⠉⣥⣼⣿⣿⡿⢰⣟⠙⣿⣻⡿⡀⣶⣎⢐⠈⡀⠀⠀⠉⠀⡂⠀⠀⠘⠛⠗⠀⣗⣠⣿⣅⢀⠂⠀⠬⢾⠿⢖⠐⡂⢄⣤⡜⣀⠸⢁⠀⠐⡴⣶⣷⣿⣶⡿⣌⢩
⣻⣿⡟⣯⠄⠀⠀⣠⠬⢈⡛⢩⣲⠭⢿⣋⠿⣵⣌⠀⣚⣿⣿⣿⣟⣻⣞⣙⡛⡟⣻⣿⡿⠿⡒⠈⠀⠀⠀⣴⣾⣶⣶⣤⠀⠐⡒⠀⢴⣶⡿⡿⢿⢚⠁⠀⠀⠀⠐⠼⣀⣳⣤⣶⠶⠾⣿⡏⠁⡼⠀⠉⣉⣿⣿⠲⢾⣾
⠈⢹⣶⣮⠁⠀⡙⠿⠃⠉⠀⠀⠁⠀⢶⣭⣐⡛⠯⠛⢹⣿⣿⠛⢻⣿⣯⡏⠐⠗⣛⡀⠀⠀⠅⠂⠀⠀⣰⣿⣿⣿⣿⡿⠀⠁⠀⠄⠈⠁⠀⠈⠈⣁⠀⠀⠐⠢⢠⣄⣡⣳⣹⣴⠤⡤⠬⢑⠈⠀⠀⣠⡉⢫⢳⣶⣾⣽
⣲⡷⡏⠛⣇⡀⠠⡀⠰⢿⡿⠂⠀⣠⣾⡿⠈⢏⡫⡜⠻⠟⠊⠒⠍⠿⣿⣶⣷⣾⣿⣿⣿⣶⣆⠀⠸⠱⣺⣿⣿⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠧⠀⢠⡌⣷⣤⡛⣻⣿⣟⡹⢷⣟⢴⣬⣯⣃⢮⣿⣍⣾⢸⣧⣸⣇
⢛⣹⣷⣤⠽⣂⠑⠊⠛⢉⣃⠀⠈⢀⣠⡀⠀⠀⢌⣁⠕⢄⡀⠠⠀⠘⢣⣙⢻⣿⣿⣿⣿⣿⣿⣤⣄⣨⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⡄⠀⠠⡂⣘⣆⣀⢼⣿⣿⠿⢿⣿⣧⣴⣾⠟⠽⢿⣞⢛⢽⢟⣀⠉⣴⡮⢽⣿
⣷⣶⡎⣰⣮⣿⡿⣁⠸⣿⣟⡹⠦⡄⢘⠁⣳⣚⣖⢷⣟⣛⣿⡢⣌⡑⠀⢙⣃⡙⢿⣿⣿⣟⣽⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠄⠀⠁⠀⠀⠘⠋⡖⢣⣐⣻⣥⣴⠂⠤⡅⠛⣙⡛⠙⣿⣏⠻⣿⠿⢿⡷⡿⡵⣿⡻
⢸⣿⣶⣶⣾⣿⡶⠺⣧⡀⣀⣘⠼⣷⡉⣀⣀⢙⠿⢷⡮⡿⢞⣧⡿⡓⢦⣼⠿⠚⠂⠸⠯⢹⣿⣿⣿⣿⠟⣩⣿⣦⣤⣷⣦⣄⡄⠀⡂⣴⡄⠀⣀⠘⣺⡿⣻⣽⣿⠿⡇⣐⣒⣘⣼⣷⢛⣉⣻⣼⣶⣳⣶⣅⣁⣠⢁⣀
⢽⣿⣷⣬⣭⣒⢀⡀⠀⡙⣿⣻⣿⠷⠛⠹⣿⢐⣰⣺⡫⢿⣝⣿⣇⡿⢖⣋⠻⣄⣰⠄⣰⣿⣿⣿⣿⡇⣀⣿⣿⣿⣿⣿⣿⣿⣿⣦⠈⠉⡁⠀⢈⢘⢋⠋⣺⡟⣿⣾⡿⣿⢿⣻⣩⡆⣛⣯⠛⣻⣿⣿⣟⣯⣽⣿⠋⢺
⡊⠸⣞⠻⣿⡭⡭⠿⠀⣌⢏⣡⡠⢖⣒⡾⠐⠈⡮⠐⠙⠎⠘⠗⢟⣆⣬⣍⢮⠟⣿⣦⣻⣿⣿⣿⣿⣇⣹⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⣥⡮⢿⣿⡿⡷⠐⣷⣦⣮⠵⣶⣿⣾⡾⣏⠶⣿⣷⣤⣯⣿⣿⣿⣶⣿⣯⣿⣷
⣿⠀⢽⢫⣶⣷⠹⠃⠙⠱⢼⠶⠿⢛⠉⣨⡴⡶⢺⣿⡝⢄⡌⢷⣮⣤⠌⣝⣷⣷⣶⣏⣭⣿⣭⣭⣥⡖⢿⠿⠻⡃⠉⠻⠿⠿⠿⡛⠛⠉⣭⡗⢢⣵⡶⣇⣩⠿⠟⠡⣿⣻⣟⣿⡿⠻⠟⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠆⢀⠄⠙⢛⡛⢳⣷⠴⣰⢷⡿⢿⡯⡆⣲⣿⣿⡭⠠⢅⣀⢹⡆⢰⣻⣛⣿⠟⢿⡍⢶⠺⠨⣥⣵⣾⣆⠀⡆⠲⠒⠂⢀⢶⡀⠦⠱⣿⢶⠾⣭⣵⣧⣣⢛⡭⣀⠲⢲⣦⠍⣸⣟⠗⠀⣀⣌⠻⢟⡹⠛⡩⠅⢐⠾⣋⠽
⡈⢠⢞⠻⡦⢥⣙⠠⣤⣹⣄⢛⣵⢾⣷⣎⣘⣻⣿⠺⣹⣷⣿⣾⣶⢻⠙⠦⣽⠷⠾⢹⠙⢶⣶⣦⠁⠛⠀⠴⡚⠱⡆⣞⣲⢙⣿⣿⣿⠋⠈⠀⠨⠋⡉⢨⠩⣿⣍⣭⣟⡋⠙⢀⣀⡀⣈⣙⠣⠂⠀⠉⣤⣶⡂⠀⣿⣿
⠻⢿⣿⣦⣴⡈⠿⣭⣁⠙⣿⠿⠋⢿⡿⢿⠻⠛⣏⣯⣑⣦⡩⣽⠻⢯⠻⠻⠧⠶⠋⠏⡊⢋⣈⣣⣤⣆⡌⠽⠗⣶⣞⣖⠻⢬⣿⣿⣿⠰⡒⣛⣿⣾⢧⢲⢟⣯⢯⣡⣿⣟⠫⡟⡥⢃⡞⠓⢾⣄⣀⣈⡻⣻⣠⠄⠿⠟
⠀⣀⢈⣿⣭⣿⣟⠙⠉⠘⣡⣐⢠⢊⡉⣳⡶⣤⣦⣚⣯⣭⣵⣿⡜⡿⣶⣳⡕⠙⣴⣆⠑⡤⢈⠛⣟⣻⡦⣴⣄⡉⢁⠐⢈⢿⣿⡿⢗⠤⣛⡹⣿⣿⣶⣰⡌⣿⣧⣿⢟⣯⣧⣻⣉⣤⣴⣿⢀⢸⣶⡾⠇⠀⣈⡅⠀⡨
⣿⣰⣭⣀⠋⣁⢀⠐⠶⣤⣻⠻⣿⣒⢅⣠⡋⣻⡠⣄⣬⡹⣿⠽⢟⡺⣯⣝⣯⣡⡧⣍⡁⡰⡼⣡⣿⢿⢟⣫⣬⣛⡻⢷⡄⢈⣿⣗⡿⣖⢙⠍⢝⣋⣯⣅⣿⢙⡛⢻⣿⣭⣿⠁⠿⠉⠿⣮⣶⡌⠻⠁⠀⠀⣮⣼⣆⠲
⢿⣿⠻⣿⣳⣤⠀⢀⣵⣿⡐⣧⢰⣽⣿⡭⣽⣵⣷⡆⣌⣐⢿⡅⢿⠿⢷⣟⡾⠿⣭⣳⣆⠹⠳⣆⢱⠞⢿⡇⠘⠚⠶⢄⣷⢆⣴⡿⣟⣟⣴⣟⠐⡜⠾⢯⣿⣿⣿⡾⣺⣿⣿⣷⣾⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⣴⡒⠁
⢰⣶⣾⢾⣿⣿⣷⢨⣿⡷⡿⣿⣷⣿⠻⣿⠾⣿⣿⣿⢿⡆⠈⠀⠳⠾⣿⡏⣿⣛⡟⢿⣴⡬⡈⢭⠂⠀⡈⣿⡔⢲⡦⣶⣽⣇⠂⠿⣾⣭⣭⣟⠂⣹⣿⣿⣿⣖⡿⢟⣻⣿⢿⢼⡍⠋⠙⢿⣦⢀⠀⠀⠀⠀⢀⣬⣷⣶
⢘⣿⣿⣬⣽⡟⢿⣌⢩⠝⢻⣿⣿⣉⡻⣿⡿⢿⠿⠛⠹⣁⠄⠀⠔⠹⣭⡿⣾⣧⣶⣌⢌⣾⣿⡒⠶⢿⣦⣛⣷⡄⡈⢀⡘⠕⢷⣈⢓⡤⡿⣠⣾⣿⣟⣾⣶⣼⣲⣿⣿⣿⣟⡲⣤⠀⠀⣂⣿⣺⡤⢀⣄⢐⣿⣿⣿⣿
⢀⣩⣍⠍⢻⡷⣼⣗⣭⡦⢼⣿⣻⣿⡿⠓⢀⣈⣦⢠⡢⡿⣆⣂⠠⣤⣼⢽⡿⣿⣻⣽⣍⢽⠟⡖⠒⠜⣿⣽⢿⣷⡀⡔⠜⣤⠘⢿⣍⠻⣾⣿⡿⣽⣟⢛⣺⣿⣝⣿⣿⣛⢿⢹⣭⣁⣘⣛⠳⣷⣷⡿⢞⣤⣉⡛⣿⡿
⣃⢘⣿⣲⣙⣠⡍⢃⣠⣌⣾⣿⡿⠽⢯⣬⡿⣿⣿⣷⣻⣿⣏⡇⣀⣹⡿⠾⢖⠛⠛⡋⠞⠈⠙⣥⣬⣦⡖⠻⢵⣧⠴⣶⣭⣣⢷⣌⣳⡰⣻⣟⣤⣽⡓⠼⠿⡼⣸⣿⣿⢾⣿⣿⣿⣿⣿⣏⠶⣷⣍⢻⣿⣿⠿⣿⠀⠐
⠘⠛⢻⣟⠟⢟⡛⣛⣻⣿⣯⣿⣿⣷⣶⣭⣿⠿⣿⣿⣷⠋⢿⢷⠔⣀⣀⣄⣸⣺⠢⢦⣠⡤⢐⣸⣷⣀⣿⣮⠠⢾⠇⢩⠥⢿⣿⡯⠐⣼⣼⣿⢿⣷⠎⣹⡻⣻⣿⠽⢧⡯⣉⡵⢿⠿⠿⣿⣿⣏⣏⠈⠛⢿⠯⢬⢥⢶
⢀⣤⡄⢠⣼⢯⣵⠽⣷⣢⡄⡒⠃⡂⣠⡀⠉⠁⠀⠀⢱⣾⡲⠛⠏⠀⠀⠽⠆⢩⠈⣁⣷⡿⡶⠻⣿⡵⠿⡀⣴⣟⣙⢿⣿⢷⣦⣝⢞⣿⣿⣿⢹⣯⢿⣷⣿⣿⣟⣾⣗⣾⡿⡿⣽⡔⠀⣰⣦⠀⢠⣿⣿⣿⠉⠁⠀⠀
⣲⣿⡗⡆⠐⠶⠟⠸⠟⢟⠀⠠⠍⠁⠀⡀⠗⠬⣅⡀⠿⠿⠿⣶⣇⡀⢶⡶⣧⡏⠿⠷⢭⡗⡖⠊⠏⠛⠛⠞⠧⠄⣿⣿⢯⣽⣿⡿⡦⡟⡿⡿⡿⠭⠽⠛⢁⢹⠄⠀⠀⠀⠀⠢⠋⠀⠂⠽⠁⠐⠹⣾⢯⠉⣵⣶⠮⣮
⠁⣴⠀⠉⠀⠀⠀⠀⠀⠨⠀⠀⠀⠁⠠⣶⠀⠠⠜⡁⠀⠀⡔⣿⡛⠻⠀⠀⠴⠉⠄⠀⢰⢤⡠⠀⠀⠒⠆⠀⠠⢂⠅⣠⣄⣈⢫⠀⠀⠁⠀⠁⠠⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⢁⠈⠂⢢
⣀⣤⣷⣾⣿⠀⢀⣠⣥⣤⢀⠀⠀⠀⠀⡣⠤⠀⠀⠀⠠⣿⣿⣿⡷⠦⠀⠀⠀⢀⠀⠀⢨⡼⠀⠈⠀⠀⢰⡇⠀⠰⣾⣿⣿⡏⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⣶⣦⡀⠀⠀⠃⠄⠘⠁⠀⠀⣲⣷⣞⠛
⡟⠿⠿⡫⠿⠇⠈⠛⢿⣿⣧⡀⠄⠀⠀⠀⠀⠀⠈⡀⠀⠵⣷⣶⣤⡖⠀⠀⠀⠈⠂⠀⠈⠀⠀⠁⠀⠀⠈⣂⠀⠐⠟⠛⠋⠀⠀⠀⠀⠀⣤⣄⣤⠀⠀⠀⠀⠀⢀⡤⢠⣬⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢛⣯⣼⢉
⢀⡤⠀⠀⠀⠁⠀⠁⣲⠷⡯⣀⡁⠶⡀⠀⠀⢀⣀⡁⠀⣤⣾⠇⠈⠉⠀⠠⠖⠀⠀⢠⣄⡀⠀⠴⠀⠤⣄⠈⡀⢀⠀⠀⠀⠀⠀⠠⣄⠰⣿⠉⠉⠀⠀⠀⢀⣀⣘⣤⣡⣥⡀⣄⡀⠀⠀⢀⠀⠀⠤⠀⠐⠉⢀⡉⣼⠛
⣸⣕⠂⣠⣴⠂⠀⠀⠀⠠⣌⣀⣰⢾⡶⢄⡀⠀⠈⠠⣀⠝⠋⣴⣿⣧⡀⣶⣿⣏⢁⡍⠷⠁⠀⠀⠀⠀⠀⢒⠖⢀⢤⠀⠂⣠⣴⣦⠨⣈⣣⣣⣠⠴⣀⡄⢀⢻⡟⠛⠛⢻⠾⣷⣄⠀⠀⢘⠀⠀⢀⣲⣜⣾⢛⣙⠀⣐
⡿⣿⣵⠼⠿⣥⠄⠀⠩⠶⠙⡘⠺⣿⢯⣿⣿⣺⡄⠀⠉⣥⣼⣿⣿⡿⠐⣏⠙⣿⣺⠿⡀⢴⡄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠘⠛⠇⠀⢑⣨⣿⣅⡀⠀⠀⠬⢾⠷⢆⠐⡂⢄⣤⡜⣀⡰⢁⠀⠰⡶⣶⣷⣿⣶⡿⣌⠩
⣿⣟⡛⣯⠄⠀⠀⠀⡬⢸⣛⠩⣲⠭⢿⣋⠹⣧⣌⠀⣚⣿⣿⣿⣟⢷⣞⣙⡛⡏⣻⣷⠿⡶⠀⠀⠀⠀⢀⣶⣿⣿⣷⣦⠀⠐⡒⠀⢄⣶⡽⡯⠟⢛⠁⠀⠀⠀⠔⠜⣀⣷⣤⣶⠶⢶⣿⡍⠁⠼⠀⠉⣉⣛⣿⠶⢾⣾
⠄⢹⣶⣶⠅⠀⡙⠻⠓⠉⠁⠀⠁⠁⢴⣭⣑⡛⠫⠻⣹⣿⣾⠛⠻⣿⣯⣏⣵⣷⣯⣤⣀⡀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡟⠀⠀⠀⠀⠈⠁⠀⠈⠈⣁⠀⠀⠐⠢⢠⣄⣢⣗⣹⣴⠤⡤⠬⢁⠈⠀⠢⢠⡉⣻⢳⣶⣶⣯
⣶⣷⣏⠹⣇⡀⠀⣀⠰⢿⡿⠂⠈⣠⣾⡭⠉⢩⣫⡜⠹⠟⠊⠐⠍⠿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠸⠳⣿⣿⣿⣿⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⢠⠌⣵⣬⠟⣻⣿⡿⡻⢷⣟⣶⣬⣯⣃⢬⣿⣟⣾⢺⡧⣴⣇
⢛⣹⣷⣄⠼⣃⠉⠋⠛⢋⣃⠠⠈⠀⡠⡀⢀⠀⡬⣁⠙⢆⡀⠀⢀⠘⢣⣙⢿⣿⣿⣿⣿⣿⣷⣤⣤⣼⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⡄⠀⠀⠀⣈⣄⣀⢼⣿⣿⠿⠻⣿⣧⣴⣾⠟⡿⢿⣟⢏⢽⢟⣀⠩⣴⡦⢽⢿
⣿⣶⡆⣰⣮⣿⡿⢇⠸⣿⣿⡻⠦⣤⠘⠁⣳⣚⣷⢶⣾⣛⣿⡳⣌⡑⠀⠈⣃⡉⢿⣻⣿⢇⣾⣿⣿⣿⣿⣿⣿⠿⠿⢛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠖⢁⣐⣻⣥⣤⠀⠬⡅⢋⣙⡋⠹⣿⡏⠻⣿⠟⢿⡾⣿⡽⢟⡻
⢸⣿⣷⣶⣾⣿⡰⠺⣧⡀⣀⡘⠸⡷⡈⠀⣀⣘⠿⠷⡶⡿⢞⣿⣿⡟⢦⣼⢿⠘⠂⠸⠏⢿⣿⣿⣿⣿⠛⣩⣿⣷⣶⣷⣿⣷⣦⣀⠂⣤⡄⠀⠀⠘⣸⡽⣫⣿⣷⠞⣇⣀⣒⣀⣴⣷⢛⣉⣻⣸⣶⣳⣶⣅⣁⡤⢇⣄
⢹⣿⣷⣭⣭⣐⣀⡀⠀⣑⢿⣿⣿⠿⠋⠩⣿⢰⣲⣂⣋⢿⣝⣿⢇⣿⢆⣋⠻⣤⣀⠀⢰⣿⣿⣿⣿⣇⣀⣿⣿⢸⣿⣿⣿⣿⣿⣿⣯⠉⠁⠀⢀⢘⢉⠉⣾⡟⣿⣾⡞⣿⢻⣚⡹⡆⣻⣿⠟⣻⣟⣿⣿⣻⢿⣿⠉⢎
⡚⠙⣟⡛⣿⣯⣯⠽⠀⣌⢏⣡⡬⢔⣔⡦⠘⠨⣪⠓⠉⠊⠉⠟⢛⡧⣬⣍⢺⠙⣿⣦⣸⣿⣿⣿⣿⣟⣹⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣧⡪⢿⣿⣿⡷⡘⣷⣴⣮⠱⣶⣷⣼⡾⣏⢸⣿⣷⣆⣯⣿⣿⣿⣴⣿⣏⣿⣿
⣿⠀⣽⢿⣶⣷⠙⠃⠙⠫⢼⠶⠿⣛⠋⣨⣥⡶⢺⣿⡞⢄⣄⢳⣾⢠⡨⣩⣷⣷⣶⣦⣭⣿⣭⣽⣥⡖⢿⢿⠻⡃⠁⠙⠿⠿⠿⠛⠛⣬⣭⠗⢢⢭⡖⣃⣩⠻⠟⠡⣿⣻⣿⣿⡟⠻⠟⣶⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿
⢇⢄⢄⠙⢛⡛⢻⣗⠔⣴⢷⡿⢿⡯⡆⣲⣿⣿⡍⠠⢅⣀⢹⡆⢱⣻⣙⣿⡟⢯⡉⢶⠺⠬⣥⣵⣮⣇⠀⡄⠲⢂⠀⠀⢳⡀⠦⠑⣿⠴⠿⣭⣵⣧⣣⢛⡩⣀⠰⢺⣤⠍⣸⣟⠗⠀⣀⣈⠻⢟⡹⠛⡩⡄⢀⠞⣉⠝
⣀⢨⣾⡻⡶⠤⣙⠀⣄⣹⣆⢑⣽⣼⣷⣎⣈⣻⣿⡺⣸⣷⣿⣾⣴⢚⠟⡧⡽⢿⠶⢸⠙⣶⣶⣦⠁⠛⢀⠴⡚⠥⡆⣖⣲⠙⣿⣿⣿⠉⠈⠀⢩⡋⡁⠩⠭⣷⣍⣯⣝⡋⠙⢀⣀⠀⣈⡙⠧⠂⠀⠉⣠⣶⡀⠀⣿⣿
⠻⠿⣯⣶⣶⣈⠿⣯⣉⠙⣿⠿⠋⢿⡿⠿⠻⠛⣯⣫⣅⣦⡩⣽⠛⢯⠻⡻⠇⠾⠋⠏⡊⠻⢈⣣⣤⣆⡌⠹⠃⢴⣞⢖⠹⢽⣿⣿⣿⠰⡲⣛⣿⣿⢧⢒⢞⣯⢮⣡⣿⣟⠫⡿⡥⢇⡞⠓⠾⣄⣀⣀⡛⠩⣠⠀⠻⠟
⠀⣀⢀⣿⣿⣿⣿⠙⠍⠈⢩⣲⢠⢊⡅⢿⢶⣤⣤⣚⣯⣭⣵⢿⣜⡿⣷⣓⡵⠱⣖⣦⠐⡤⢈⠋⣿⣣⡢⣴⣄⣈⢡⠑⠨⢹⣿⡿⢗⠄⣛⡹⣻⣿⣲⣴⡌⣿⣦⣿⣟⣿⣧⣻⣉⣦⣴⣺⢀⣰⣦⡾⠇⠀⣨⡀⠀⡬
⣿⣐⣯⣀⠋⡅⢀⡘⢒⣤⣚⠻⣿⣗⣅⣰⣊⣳⡠⣄⣬⣹⣿⠽⢟⡹⣏⣝⣩⣡⡤⠏⠁⡰⡼⣡⣿⢿⠍⢣⣬⣙⡛⠿⡄⢈⢾⣛⡹⣶⢹⠍⢕⣉⣯⣅⣯⣙⡛⢫⣿⣭⣿⡁⠿⠙⠶⣟⣶⡌⠙⠁⠀⠐⡦⢤⣄⠐
⢷⣿⠿⢯⣫⣧⠀⢈⣼⣿⡊⣧⢐⣿⣿⡭⣽⣵⣷⡖⣬⣱⢿⣅⣿⠿⢷⣛⡿⠿⣭⣻⣄⠹⠳⣆⢰⠚⢿⡆⠈⠘⠦⢭⣵⢆⢴⣿⣓⡟⣴⣗⠐⠜⠿⢯⣿⣿⣿⡾⣺⣿⣿⣷⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⣴⡂⠈
⢤⣴⣾⢾⣿⣿⣷⢨⣿⣿⡿⣿⣷⠯⡻⣿⢟⣽⣿⣿⣿⡆⠀⠀⠻⠾⢿⡏⣿⣋⡟⢿⣴⡤⡈⣭⠃⠀⠈⣿⡄⠶⡦⡶⣿⣇⠂⠻⡾⣭⣬⠟⠂⢹⡿⣿⣿⣶⠿⣏⣯⢿⣿⢔⠉⠃⠛⢿⣧⣀⠀⠀⠀⠀⢠⣼⣶⣶
⢘⣻⣿⣬⣭⣟⢻⣄⣡⠝⢻⣿⣿⣉⡻⣿⡿⢿⠿⠋⠹⢁⠄⠀⠀⠙⣯⣿⣾⣧⣶⣌⢈⣿⣿⡒⠶⠻⣮⣿⢿⡄⢀⢀⡘⠖⠳⣈⢑⡤⠿⣠⣾⣿⣏⣾⣶⣜⣲⣿⣿⣿⣛⡲⣦⠀⠀⣂⣿⣼⡄⠀⣄⠀⣿⣿⣿⣿
⢀⡨⣭⡍⢻⡷⣼⣷⣭⡦⢽⣿⣻⣿⡿⠛⣠⣈⣦⡠⣆⡿⣆⣂⢠⣤⣶⢽⡿⣿⣻⣽⣥⢸⠙⡖⠂⠎⡿⣽⣫⣿⡀⣌⠄⣤⡘⢻⣅⠛⣾⣿⡿⣽⣟⢚⣺⣯⣝⣿⣿⣛⣈⢝⣤⣁⣘⣛⠳⢷⣧⠟⢞⣤⣌⡛⢿⠿
⣁⢘⣿⢓⣙⢠⡌⢛⣨⣔⣼⣿⡿⠽⢧⣬⡾⣿⣿⣷⣻⣿⣿⡇⣈⣹⡿⠾⢖⠛⠛⠋⠈⠀⠘⣣⣭⣦⡔⠛⢷⣧⡴⣖⣿⣋⢟⣨⡿⡰⣻⣏⣄⢽⡗⠼⠷⡔⡼⣿⡿⢾⣿⣿⣿⣿⣿⣏⠾⣗⣍⢺⣯⣾⠽⣻⠀⠐
⡞⠛⢻⣟⡟⢿⣛⣛⣻⣿⣯⣻⣿⣷⣶⣭⣟⠿⣿⣯⣷⠛⢻⢿⠜⣄⣀⣄⣘⡿⠠⢦⢀⡼⢰⢰⣶⢐⣟⣷⠈⢿⠯⢨⡅⢹⣿⡏⠀⣴⣽⡿⢿⡷⠎⡶⠓⣿⣿⠍⢃⡯⢍⡿⠿⠿⢿⣿⣿⣟⣍⡈⠛⠿⠿⠬⢪⣿
⢀⣤⣄⢢⣼⢯⣵⠩⣷⣢⡄⣚⢒⡊⣠⠀⠈⠁⠀⠀⢱⣾⡲⠛⠏⠀⠀⠽⠆⢩⠉⣁⣷⡿⡶⠿⣿⡦⢟⡀⣶⣟⣙⣿⣿⣿⣦⣱⢞⣾⣿⣿⢹⣯⣿⣷⣿⣷⣿⣾⣗⣿⡿⡿⣽⡴⢀⣰⣆⠀⢠⣿⣿⣿⠋⠁⠀⠀
⣲⣿⡗⡆⠐⠶⠟⠸⠟⢟⠄⠠⢍⠁⠀⡀⠧⠬⣔⡀⠿⢿⠿⣶⣷⡠⢶⡶⣯⡏⠿⠷⢭⡗⡖⠊⠏⠛⠷⠞⠧⠄⣿⣿⢯⣽⣿⣿⠦⡟⡿⡿⡿⠭⠽⠛⢁⢹⠄⠀⠀⠀⠀⠲⠋⠀⠂⠭⠁⠘⠹⣿⢯⠭⡵⡳⠮⣯
⠁⣴⠄⠋⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠠⣶⠀⠀⠝⡁⠀⠀⡴⣿⡟⠲⠀⠀⠌⠉⠀⠀⢰⢭⡀⠀⠀⠐⠆⠀⠠⢂⠅⣠⣄⣈⣫⠁⠀⠁⠀⠁⠠⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⠠⠀⠀⠀⣁⡈⠂⢢
⣀⣤⣶⣾⣿⠀⢀⣠⣥⣤⢀⠀⠀⠀⠀⡫⠤⠀⠀⠀⠠⣿⣿⣿⡷⠦⠀⠀⠀⢀⠀⠀⢨⡼⠀⠈⠀⠀⢰⡃⠠⠰⣼⣿⣿⡏⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣶⣦⡀⠀⠀⠁⠄⠘⠁⠀⠀⣢⣾⣿⠛
⡟⠿⠿⡻⠿⠇⠈⠛⡿⣿⣧⡀⠄⠀⠀⠈⠀⠀⠈⡀⠀⠽⣷⣴⣄⡶⠀⠀⠀⠈⠒⠀⠈⠀⠀⠀⠀⠀⠈⣃⠀⠐⠟⠟⠋⠀⠀⠀⠀⠀⣤⣄⣤⠀⠀⠀⠀⠀⢀⡤⢠⣼⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⣾⢈
⢀⡤⠀⠀⠀⠁⠀⠁⢷⠷⣯⣀⡁⠖⠀⠀⠀⢀⣈⡁⠀⣤⣾⡏⠈⠉⠄⠠⠶⠀⠀⢠⣄⡀⠀⠴⠀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠰⣿⡉⠉⠀⠀⠀⢀⣀⣐⣄⣀⣭⡀⣄⠀⠀⠀⢀⠀⠠⠤⠀⠐⠁⢁⡉⣼⠚
⣼⣕⠀⢰⣜⢂⠀⠀⠀⠠⣬⣀⣰⢿⣶⢄⡀⠀⠈⠠⣀⠝⢋⣴⣿⣧⡀⣴⣿⣯⢁⣍⠷⠁⠀⠀⠀⠀⠀⢚⠖⢀⢤⠀⠀⣠⣴⣦⠨⡀⣫⣡⣠⠤⣀⡄⢀⢻⡟⠛⠛⢻⠾⣷⣄⠀⠐⢚⠀⠀⠀⣲⣔⠾⢚⣛⠀⣐
⡟⣿⣷⠼⠿⣧⠄⠀⠩⠶⠘⡘⠺⣿⣯⣿⣿⣲⡆⠀⠉⣭⣼⣿⣿⡿⢠⣏⠙⣿⣸⠿⡀⢠⠄⠀⠀⠀⠀⠀⣉⣀⠂⠀⠀⠘⠻⠏⠀⠁⢠⣿⣅⠀⠀⠀⠼⢾⠷⢆⠐⡂⢤⣤⣜⣀⠸⢁⠀⢴⣷⣶⣷⣿⣶⡿⣍⠯
⣿⣟⣟⣯⠄⠀⠀⢀⡬⢨⣛⢉⣲⡭⢿⣛⠽⣬⣌⠀⣊⣿⣿⣿⣟⣷⣞⣛⣛⡿⣻⣷⠷⠶⠀⠀⠀⠀⢰⣿⣿⣿⣿⡆⠀⠐⡒⠀⠄⣔⡿⡯⠏⠚⠁⠀⠀⠀⠔⠌⣀⣷⣤⡶⠶⢶⣿⡍⠁⡜⠀⠍⣉⣿⣿⠶⢮⣾
⠂⢹⣶⣾⠇⠀⡙⠻⠓⢉⠁⠀⠋⠀⢰⣯⣠⡛⠯⠫⣹⣿⣿⠟⢻⣿⣿⣯⣷⣷⣿⣤⣄⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠈⠁⠀⠈⠈⣁⠀⠀⠐⠢⢠⣄⣤⣷⣹⣴⠦⠄⠬⢥⠈⠀⠲⢀⡙⣻⢳⣶⣷⣭
⣶⣷⣏⢻⣗⡠⠀⣀⠰⢿⡿⠓⠈⣰⣾⡽⠉⢻⣫⣜⠻⠟⠊⠘⠍⠿⣹⣿⣿⣿⣿⣿⣿⣧⠀⠀⠘⢳⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢠⠌⣷⣮⣛⣻⣿⣿⡹⢷⣟⣶⣍⣏⣋⢬⣿⣟⣾⢺⣧⣵⣇
⢛⣹⣿⣥⠼⣆⡙⠋⠛⢛⣃⠠⠘⠀⠠⡀⣀⠀⡌⣁⠙⢄⡀⠀⢀⠈⢫⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣼⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⡄⠀⠀⠀⡀⣄⡀⣾⣿⣿⠿⠿⣿⣧⣴⣾⠟⡿⠿⣟⢫⢽⢟⣀⠙⣴⡾⢽⢯
⣷⣶⡶⣰⣮⣿⡿⢇⠸⣿⣟⡹⠦⣤⠘⠇⣓⣚⣗⢴⣮⣻⣿⡳⣌⡑⠀⠙⡃⡉⢿⣹⣯⣦⣾⣿⣿⣿⣿⣿⣿⡻⠛⡋⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁⠖⠡⣐⣻⣥⣤⠀⠤⠅⢉⣙⡋⠙⣿⡟⠻⣿⠻⢿⡟⡿⡿⢿⡻
⢸⣿⣷⣴⣾⣿⡠⠺⣷⡄⣀⡘⠸⡶⡨⠀⣠⣙⠿⢷⣦⠻⢞⣿⣿⡟⣦⣼⢿⠘⠂⠸⠭⣿⣿⣿⣿⣿⠛⣩⣽⢿⣶⣾⣿⣿⣶⣄⢂⣴⡄⠀⠀⠘⣺⠿⣯⣿⣷⠿⣇⣀⣒⣐⣴⣷⢓⣉⣻⣾⣶⣳⣶⣅⣅⡤⢅⣄
⢸⣿⣿⣩⣭⣚⣀⡀⠀⣑⢿⣟⣿⠷⠓⠙⢻⢘⣲⣦⡋⢽⣿⣿⣧⡿⢆⣫⠻⣦⣰⠄⢠⣿⣿⣿⣿⣏⣄⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡉⠁⢠⣀⢘⢉⠉⣿⣟⣿⣾⡾⣿⢻⣛⡝⡆⣻⣿⠛⣻⣿⣿⢿⣿⣿⣿⠛⢞
⣓⠹⣟⡛⣿⣯⣯⠼⠀⣌⢏⣡⡤⢼⣔⡶⠐⠬⣪⠛⠈⠊⠙⠟⢛⣅⣬⣝⢾⠙⣿⣦⣼⣿⣿⣿⣿⣟⣹⣿⣿⣾⢿⣿⣿⣿⣿⣿⣿⣧⡾⣿⣿⣿⡷⡘⣷⣶⣮⠴⣷⣷⣾⡿⣏⢺⣿⣷⣆⣿⣿⣿⣿⣴⣿⣿⣿⣿
⣿⠀⣽⢯⣶⣷⠙⠃⠙⠛⢔⠷⠿⢛⢋⣨⡵⡶⢻⣿⡟⢄⣄⢳⣾⢬⢬⣹⣷⣷⣶⣿⣽⣿⣫⣽⣥⡖⢿⢿⠻⠁⠁⢹⠿⠿⠿⠿⠛⠋⣬⡗⢢⣥⡕⢇⣹⠻⠛⠱⣿⣻⣿⣿⡟⠻⠿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠇⠀⢄⠙⢛⡛⢳⣾⢔⣴⣷⡿⠿⡫⡆⣲⣿⣿⡭⠠⣁⣀⢹⡎⣰⣻⣋⣿⡟⢿⡉⢶⠻⠼⣧⣵⣮⣇⠀⣄⠲⠂⠆⠀⢲⡀⠦⠐⣾⠲⢿⣭⣷⡧⣣⢛⡹⣀⠰⣶⣤⠌⣸⣟⢷⠀⣀⣌⠻⢟⠹⠛⡉⡅⢀⠞⣋⠝
⣀⢨⢾⡻⣶⣰⣙⠤⣤⣹⣤⢻⣽⣾⣷⣮⣙⣻⣿⡺⣩⣷⣿⣾⣴⢛⡟⡯⡼⢿⢷⢺⢳⢶⣶⣢⠁⠛⢀⠜⠚⠱⡆⣞⣷⠙⣿⣿⣿⠁⠈⠀⢩⡑⡁⠩⢩⣿⣍⣭⣟⡋⠉⢁⡀⠀⣈⡙⢃⠂⠀⠉⣠⣶⡀⠀⣿⣷
⠻⠿⣿⣶⣶⣈⠿⣯⣉⡙⣿⠟⠛⢿⣿⢿⠻⠛⣇⣫⣁⣲⡩⣽⠻⢯⠻⠻⠗⠾⠏⠏⡊⠫⣉⣧⣤⣆⡬⠹⠅⢴⣞⢗⠻⢬⣿⣿⣿⠰⡖⣟⣿⣿⢧⢸⢯⣿⢮⣡⣿⣟⠫⣿⡵⢇⡞⠓⠾⣆⣀⣈⡻⢫⣠⠀⠻⠟
⠀⣀⢀⣿⣿⣿⣿⠛⠍⠉⢠⣤⢠⢊⠁⢿⣶⢦⣤⣸⣭⣭⣵⣿⡼⡿⣷⣓⣗⠳⣤⣆⠑⠦⢘⠋⣯⣡⣠⣴⣄⣉⢡⡑⠨⣺⣿⡿⢗⠤⣚⡹⢿⣿⣲⣴⡌⣽⣦⣽⣟⣿⣧⣻⣉⣦⣴⣻⢤⣴⣦⡺⠅⠀⣪⡀⠀⡬
⣿⣲⣭⣀⠋⡅⢂⡘⢲⣤⣎⠻⣿⣳⣇⣨⣊⣳⡨⣄⣤⣹⣿⠽⢟⡹⣏⢝⣫⣡⡄⠯⣁⡴⡼⣣⣿⢿⢽⢧⣬⣛⡻⢿⡄⢈⠿⣷⣹⣶⢙⠍⢜⣉⣯⣄⣏⣙⡛⢿⣿⣭⣿⠁⢿⠛⢶⣿⣶⡌⠛⠁⠀⠐⠤⡤⡌⠀
⢷⣿⠿⢿⣫⣧⡀⢈⣽⣿⡏⣧⡘⣿⣿⡯⣽⣷⣷⣄⣬⣹⢿⣅⣿⠷⣿⡛⡿⠿⣭⣚⣎⠹⡳⣆⠰⠞⢿⡂⠀⠚⠶⢥⣷⢄⣷⣿⣞⣟⣴⣟⠐⠘⠻⢏⣾⣿⣿⡾⣺⣿⢿⣷⣿⣿⣿⡾⡋⠀⠀⠀⠀⢀⠀⣴⡀⠀
⢴⣼⣾⢾⣿⣿⣷⢨⢿⡿⡿⣿⣷⡿⣻⣿⢞⣽⣿⣿⣿⡦⠀⠀⢻⠾⣿⡏⣿⣋⡟⢿⣴⡦⡈⣭⠃⠀⠈⣿⡄⠲⡦⢶⣿⣇⠄⠻⣿⣯⣬⠟⠂⢹⡿⣿⡿⣷⠿⣻⣯⡿⢿⢼⠉⠋⠛⢿⣮⣀⠀⠀⠀⠀⣠⣾⣶⣶
⢘⣽⣿⣬⣭⣟⢻⡄⣡⠝⢻⣿⣿⣉⡻⣿⡿⢿⠿⠛⠹⢁⠀⠀⠔⠻⣿⡿⣮⣧⣾⣌⢨⣿⣿⡖⠶⠻⣦⣧⣿⡄⠀⢀⡚⠞⠷⣈⢹⡤⡿⣠⣾⣿⣿⣾⣾⣽⣶⣿⣿⣿⣟⡲⣦⠀⠀⣂⣞⣼⡄⢄⣄⠀⣿⣿⣿⣿
⢀⠨⣍⠭⢻⡿⣼⣧⣯⡦⣽⣿⣻⣿⡿⠛⣠⣨⣢⣤⣆⡿⣗⣂⠠⣤⣶⢝⡿⣿⣻⣽⣧⢽⠛⡔⠂⠎⡿⣽⣫⣿⡀⣌⡜⣔⠘⣿⣄⠛⣾⣿⡿⣽⣟⢚⣺⣯⣝⣿⣿⣛⡪⢙⣥⣁⣚⣙⠻⣷⣧⠿⢚⣤⣌⣛⣿⠟
⣁⢘⣯⢳⣑⢀⡍⢋⣨⣜⣾⣿⡿⠽⢯⣬⣾⣿⣿⣗⣻⣿⣯⡇⣈⢹⣿⡾⢖⠛⠛⠋⠊⠀⠘⣣⢭⣦⡔⠻⢵⣷⣼⣶⣧⣛⣟⣈⣿⠐⣻⣟⣴⢿⡓⠾⠷⡶⠼⣿⣿⢾⣿⣿⣿⣿⣿⣏⢾⣇⣇⢾⣿⣾⢿⣟⠀⠀
⡞⢛⢻⣟⡟⢿⣛⣛⣻⣿⣯⣻⣿⣷⣶⣥⣿⠿⣿⣯⣷⠛⢿⢿⢔⡉⣠⢄⣚⡿⢢⢦⢀⡴⢐⣰⣶⣂⣟⢷⠘⢿⠏⢈⡅⢽⣿⡯⠨⣬⣽⡿⢿⡷⠎⡶⠛⣏⣿⡝⢇⡯⢍⡾⠿⠿⢿⣿⣿⣿⣍⡈⠛⠿⠿⢭⠡⣿
⠀⣦⣄⢀⣼⢯⣵⠭⣿⣺⡄⣒⠒⡊⣠⠀⠈⡁⠀⠀⢱⣾⡲⠛⠏⠀⠀⠽⡇⢩⠉⣡⣷⡿⡶⠿⣿⡦⡾⡀⣼⡟⣙⣿⣿⣿⣦⣱⢞⣾⣿⣿⢹⣯⣿⣷⣿⣷⣿⣾⣗⣿⡿⠿⣽⡔⢀⣰⣦⠀⢠⣿⣿⣿⠉⠁⠀⠀
⣲⣿⡗⡆⠐⠶⠟⠨⠟⢟⠤⠨⢍⠁⢀⡀⠥⠬⣔⡀⠿⢿⠿⣶⣷⡠⢶⡶⣯⡏⠿⠷⢭⡗⡖⠚⠏⠛⠷⠞⠥⠄⣿⣿⢯⣽⣿⡿⠦⡟⡿⡿⡿⠭⠽⠛⢁⢹⠄⠀⠀⠀⠀⠒⠋⠀⠢⠭⠁⠐⠹⣾⢯⠽⣥⡳⠬⣯
⠁⣴⠄⠋⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠠⣶⠀⠀⠝⡁⠀⠀⡴⣿⠛⠺⠀⠀⠌⠉⠄⠀⢰⢭⡀⠀⠀⠐⠆⠀⠠⢂⠅⣠⣄⣈⢫⠁⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⠠⠀⠀⠀⣁⡈⠂⢢
⣀⣤⣶⣾⡿⡀⢀⣠⣥⣤⢀⠀⠀⠀⠀⡫⠄⠀⠀⠀⠠⣿⣿⣿⡷⠦⠀⠀⠀⢀⠀⠀⢨⡼⠀⠈⠀⠀⢰⡇⠠⠰⣼⣿⣿⡏⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣶⣦⡀⠀⠀⠁⠄⠘⠁⠀⠀⣲⣶⣿⠛
⡟⠿⠿⡻⢿⠇⠈⠛⡿⣿⣧⡀⠄⠀⠀⠈⠀⠀⠈⠀⠀⠝⣷⣴⣄⡖⠀⠀⠀⠈⠂⠀⠈⠀⠀⠁⠀⠀⠈⣃⠀⠐⠟⠛⠋⠀⠀⠀⠀⠀⣤⣄⣤⠀⠀⠀⠀⠀⢀⡤⢠⣼⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⣵⠉
⢀⡄⠀⠀⠀⠁⠀⠁⢣⠷⣯⣀⡁⠶⡀⠀⠀⢀⣈⡁⠀⣤⢾⠇⠈⠉⠄⠠⠶⠀⠀⢠⣄⡀⠀⠴⠀⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠰⣿⡉⠉⠀⠀⠀⢀⣁⣘⣄⣠⣥⡀⣀⠀⠀⠀⢀⠀⠀⠤⠀⠐⠁⢁⡋⣼⠚
⣼⣕⠂⢠⣜⢂⠀⠀⠀⠠⣬⣀⣰⢿⣶⢄⡀⠀⠈⠠⣀⠝⢋⣴⣿⣧⡀⣶⣿⣯⢅⡍⠷⠁⠀⠀⠀⠀⠀⢚⠒⠈⢠⠀⠀⣤⣴⣦⠈⡀⣫⣡⣀⠄⣀⡄⢀⢻⡿⠛⠛⢻⠾⣷⣄⠀⠀⢚⠀⠀⢀⣲⣔⡾⢚⣛⠀⣐
⡟⣿⣷⠼⠟⣧⠄⠀⢩⠶⠘⡘⠺⣿⣯⣿⣿⣺⡄⠀⠉⣭⣼⣿⣿⡿⢀⣏⠙⣿⣸⠿⡀⢰⠄⠀⠀⠀⠀⣀⣬⣀⡂⠀⠀⠘⠛⠇⠀⠁⢠⣿⣅⡀⠀⠀⠼⢾⠷⢆⠐⡂⢤⣤⣜⣀⠰⢁⠀⢰⣷⣶⣷⣿⣶⡿⣌⠯
⣿⣟⣟⣯⠄⠁⠀⢀⡨⢨⣛⠉⣲⡭⢿⣛⠽⣧⣌⠀⣘⣿⣿⣿⣟⢳⣞⣙⡛⡿⣻⣷⠿⠶⠀⠀⠀⠀⣼⣿⣿⣿⣿⡆⠀⠐⡒⠀⠄⣔⡭⡭⠟⠚⠁⠀⠀⠀⠐⠌⣀⣷⣤⡶⠶⠾⣿⡍⠁⡜⠀⠍⣉⣿⣿⠶⢾⣾
⠂⢹⣶⣾⠇⠐⡙⠻⠃⢉⠁⠀⠋⠀⠰⣭⣠⡛⠫⠫⣹⣿⣿⠝⠻⣿⣿⣫⣵⣷⣯⣤⣀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⠃⠀⠀⠀⠀⠈⠁⠀⠈⠈⣁⠀⠀⠐⠢⢠⣄⣤⣳⣹⣴⠤⠄⠬⢅⠈⠀⠂⢀⡙⣻⢳⣶⣷⣏
⣶⣷⣏⠻⣇⡠⠤⣀⠰⢾⡿⠚⠈⣰⣾⡽⠉⢹⣯⣜⠻⠟⠊⠘⠌⠿⣹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠘⢹⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢠⠎⣷⣮⣛⣻⣿⣿⡹⢷⣟⣶⣼⣯⣃⢮⣿⣟⣾⢺⣧⣴⡇
⢛⣹⣿⣤⠼⣆⡙⠋⠛⢏⣃⠠⠘⠀⡠⡀⢀⠀⡌⣁⠹⣄⡀⠀⢀⠘⢫⣿⣿⣿⣿⣿⣿⣿⢶⣶⣤⣼⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⡄⠀⠀⠀⡐⣀⡀⢼⣿⣿⠿⢿⣿⣧⣴⣾⠟⡿⢿⣟⢛⢽⢟⣀⠙⣴⡾⢽⢯
⣿⣶⡶⣰⣮⡻⡿⢇⠸⣿⣟⡹⠦⣤⠘⠃⣳⣛⣗⢴⣿⣻⣿⡳⣌⡑⠀⠘⣃⡉⢯⣹⣿⣶⣿⣿⣿⣿⣿⣿⣿⡛⠛⠉⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁⠖⠡⣐⣻⣥⣤⠀⠤⠅⢉⣙⡋⠙⣿⡞⠻⣿⠻⢿⡿⢿⡿⢿⡻
⢸⣿⣷⣶⣾⣿⡢⠾⣷⣂⣀⡈⠼⡶⡨⠀⣀⣙⠿⢷⡶⡻⢞⣿⣿⡟⣶⣼⢿⠚⠂⡸⣿⣿⣿⣿⣿⣿⠛⣯⣝⢿⣶⣾⣿⣿⣦⡀⢀⣴⡄⠀⠀⠈⣸⡿⣯⣿⣷⠟⣃⣀⣒⣀⣴⣷⢃⣉⣻⣼⣷⣳⣶⣅⣅⡤⢁⣀
⢹⣿⣿⣩⣭⣙⣀⡀⠀⣑⣿⣟⣿⡿⠃⠙⣟⢘⣲⣢⡫⢿⣽⣿⣧⡿⢆⣫⠻⣤⣰⠐⢸⣿⣿⣿⣿⣯⣄⣿⣿⢸⣿⣿⣿⣿⣿⣿⣎⠉⠁⠀⣀⢘⠩⠋⣿⣟⣿⣾⠟⣿⢻⣚⡹⡆⣛⣿⠛⣻⣿⣿⢿⣿⣿⣿⠋⢏
⣓⠹⣟⡛⣿⣯⣯⠼⠀⣍⢏⣡⡠⢜⣔⡆⠙⠬⣪⠛⠉⠊⠉⠟⢛⣇⣬⣝⢾⡛⣿⣦⣜⣿⣿⣿⣿⣿⣽⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣧⠼⣿⣿⣿⡷⡘⣷⣴⣮⠵⣷⣷⣾⡿⣏⢺⣿⣷⣄⣿⣿⣿⣿⣴⣿⣟⣿⣿
⣿⠂⣼⣯⣶⣷⠙⠃⠙⠫⢴⠶⠿⣛⠋⣨⡥⡶⢻⣿⡞⢄⣄⢳⣼⠬⠬⣹⣷⣿⣶⣿⣭⣿⣯⣭⣥⡖⢿⢿⠻⠁⠘⠻⢿⣿⣿⡿⠿⠋⣬⡗⢢⣭⡅⣇⣹⠻⠛⠡⣿⣻⣟⣿⡟⠻⠿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠆⢄⢄⠙⢛⡛⢳⣟⠼⣴⣷⡿⢿⡯⡆⣲⣿⣿⡭⠠⣅⣄⣹⡆⣰⣻⣉⣿⡟⢿⡩⢖⠻⠬⣡⣵⣮⣏⠀⢄⠲⠒⠄⠂⢒⡀⠦⠑⣾⠺⢿⣭⣴⡧⣣⢛⡱⣀⠲⣲⣤⠈⣸⣟⠷⠀⣠⣈⠻⢟⠹⠛⡉⡄⢀⠞⣉⠝
⣀⢨⣿⡻⣷⢰⣙⠤⣤⣽⣤⢱⣽⣾⣷⣮⣙⣻⣿⡺⣩⣷⣷⣾⣼⢛⡛⡧⡽⢿⢾⢸⢑⢶⣶⡦⠁⠛⠀⠔⡚⠡⡆⣞⣷⠙⣿⣿⣿⠁⠊⠀⢈⡁⡡⠩⠩⣿⣍⣧⣟⡋⠉⢁⡀⠀⣈⡙⠃⠂⠀⠁⣠⣶⠀⠀⣿⣶
⠻⠿⣿⣶⣶⣌⠿⣿⣉⡙⣿⠿⠋⢿⣿⢿⠻⠛⣏⣫⣅⡶⡩⣽⠻⢫⠻⠻⠗⠾⠎⠟⡊⠫⢉⣣⣤⣦⡬⠹⠇⢴⣞⢖⠻⢬⣿⣿⣿⠰⡖⣟⣿⣿⣧⢚⢯⣿⢮⣡⣿⣟⠫⣿⡵⢇⠚⠒⠺⣄⣀⣈⡻⠩⣠⠀⠻⠟
⠀⣀⢀⣿⣿⣿⣿⠙⠍⠈⢨⣄⢠⢎⠅⢿⣶⢦⣤⣸⣭⣭⣵⣿⡾⡾⣷⣓⣷⠱⣶⣦⠓⡠⢈⠛⣿⣳⣂⢴⣄⣉⢡⠑⢊⣸⣿⡿⢗⠄⣚⡹⢻⣿⣾⣴⡌⣿⣦⣿⣿⣿⣧⣻⣉⢦⣴⢪⢤⣴⣦⠺⠅⠀⡊⡀⠀⠤
⣿⣰⣩⣀⡋⡅⢂⡈⢲⣤⣎⠻⣿⣿⣇⣨⣉⣳⡠⣔⣤⣹⣿⠽⢟⡹⣯⢝⣻⣡⡄⠯⢁⡴⡴⣣⣿⢿⢽⢥⣬⣉⡻⠿⡄⢈⢿⣿⣽⣶⢙⠍⢝⣙⣯⣀⣟⣙⡋⢹⣿⣭⣿⠁⢿⡙⠲⣿⣶⡌⠉⠁⠀⠀⠤⡄⠀⠀
⢷⡿⠿⢯⣯⣧⡀⢀⣽⣟⡞⢷⠘⣿⣿⡯⣽⣷⣷⣖⣬⣹⢿⣄⣿⠿⣷⡛⡿⢿⣭⣛⣎⠹⠣⣆⠰⠞⢿⡆⠀⠘⠶⢭⣵⣖⣶⣿⣕⡟⣴⣟⠒⠘⠻⢏⣾⣿⣿⡾⣺⣿⢿⣷⣿⣿⣿⡶⡏⠀⠀⠀⠀⠀⠀⣴⡀⠀
⢴⣼⣾⢿⣿⣿⣷⢨⣻⡿⡿⢿⣷⡿⡻⢿⠶⣽⣿⣿⣿⡦⠀⠀⠻⠾⣿⣏⣿⣋⡟⢿⣴⡦⠈⢭⠀⠀⠈⣿⡄⠲⡦⢶⣿⣇⠀⠳⡾⣿⣬⡟⠂⢹⡿⣿⡿⣷⠿⣻⣯⡿⢿⣼⠉⠋⠛⢿⣮⣀⠀⠀⠀⠀⣠⣾⣶⣶
⢘⣽⣿⣤⣭⣏⢻⣄⣡⠜⢻⣿⣿⣁⡻⣿⡿⢿⠿⠛⠹⢁⠀⠀⠔⠹⣿⡿⣾⣧⣶⣎⢠⣾⢿⡒⠶⢻⣮⣦⣿⡄⠈⣀⡘⠞⠳⣈⢑⡤⠿⣠⣾⣿⣿⣾⣶⣜⣲⣿⣿⣿⣛⡲⣤⠀⠀⣚⣞⣸⠀⢄⣄⠀⣿⣿⣿⣿
⢀⠨⣭⣭⢻⡿⣼⣷⢯⠦⢽⣿⣻⣿⡿⠛⣡⣀⣲⡦⡦⡿⣗⣀⠀⣤⣾⢝⡿⣿⣻⣽⣧⢼⠻⡞⠀⠊⡿⣽⣫⡿⡀⢌⠜⣐⠘⢿⢄⠙⣾⣿⡿⣽⣟⢚⣚⣯⣝⣯⣿⣻⢢⢙⣡⣁⣘⣙⠻⢷⡧⠿⣚⣤⣌⣛⣿⠿
⣁⢘⣯⢿⣑⢀⡭⢃⣩⣬⣼⢿⡿⠽⠧⣬⣿⣿⣿⣷⣻⣿⣯⡇⣈⣹⣿⠾⢖⠛⠛⠋⠊⠈⠘⣣⢬⣶⡖⠛⢵⣧⣴⣶⣧⣛⣷⣨⣷⡰⣻⣯⣴⢿⡓⠾⠷⡴⠼⣿⣿⣾⣿⣿⣿⣿⣿⣏⢾⣇⣅⢾⣿⣾⢿⣛⠀⠐
⡞⢛⢻⣟⡿⢿⣛⣛⣻⣿⣯⣿⣿⣿⣶⣥⣿⠿⣿⣿⣿⠛⢿⢿⠬⣈⣤⢤⣘⡿⠠⢦⢀⡴⢐⢰⣶⣒⣿⣧⠐⣟⠯⢉⡍⠻⣿⠏⠨⣤⣽⡿⢟⡿⠆⣖⠓⣏⣿⡕⢇⡯⢍⡶⡿⠿⢿⣿⣿⣽⣍⡈⠛⠿⠿⠯⢠⣿
⠀⣤⣄⢀⣼⢯⣽⠭⣿⣨⡄⡒⠒⡂⣠⡄⡈⡁⠀⠀⢱⣾⡶⠛⠟⠀⠀⠽⠇⢉⠈⣁⣷⡿⡖⠻⣿⡤⡟⡀⣾⣟⣙⣿⣿⣷⣦⣑⢞⣾⣿⣿⢹⣯⣿⣿⣿⣷⡟⣮⡗⣶⡿⠟⣽⡴⢀⣰⣆⠀⢠⣿⣿⣿⠋⠁⠀⠀
⣲⣷⣗⠆⠐⠢⠞⠨⠎⢟⠅⠠⢍⠁⠀⡀⠷⠬⣔⡀⠿⢿⠿⣔⣧⡠⢶⡶⣧⡏⠟⠿⢭⡗⡖⠊⠏⠛⠟⠞⠥⠄⣿⣿⢯⣽⣿⡿⠦⡟⡿⡿⡿⠭⠽⠛⢁⢹⢄⠀⠀⠀⠀⠂⠋⠀⠂⠭⠁⠘⠹⣿⢭⠩⡵⡲⠬⣯
⠁⣼⠄⠃⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠠⣶⠀⠀⠝⡁⠀⠀⡴⣿⠛⠢⠀⠀⠌⠉⠄⠀⢰⢭⡀⠀⠀⠐⠎⠀⠠⢀⠅⣠⣄⣈⣫⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⠠⠀⠀⠀⣀⠈⠂⢢
⣀⣤⣶⣾⡿⠀⢀⣠⣤⣤⢀⠀⠀⠀⠀⡫⠄⠀⠀⠀⠠⣾⣿⣿⡷⠦⠀⠀⠀⢀⠀⠀⢨⡼⠐⠈⠀⠀⢰⠃⠀⠰⣼⣿⣿⡏⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣶⣦⡀⠀⠀⠀⠄⠘⠀⠀⠀⣢⣶⣞⠛
⡟⠿⠿⡻⢿⠇⠈⠛⠿⣿⣧⡀⠄⠀⠀⠀⠀⠀⠈⠀⠀⠽⣷⣴⣄⡖⠈⠀⠀⠈⠂⠀⠈⠀⠀⠀⠀⠀⠈⣃⠀⠐⠟⠟⠋⠀⠀⠀⠀⠀⣤⣄⣤⠀⠀⠀⠀⠀⢀⡤⢠⣼⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢛⣯⣴⢈
⠀⡤⠀⠀⠀⠁⠀⠁⢸⠷⡫⣀⡁⠴⡀⠀⠀⢀⣈⡀⠀⣤⢾⠋⠈⠉⠄⠠⠶⠀⠀⢠⣄⡀⠀⠴⠀⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠰⣿⡉⠉⠀⠀⠀⢀⣀⣘⣄⣡⣥⡀⣄⠀⠀⠀⢀⠀⠀⠤⠀⠐⠁⢀⡋⣼⠚
⢐⣅⠀⢠⣬⢂⠄⠀⠀⠠⣬⣀⣠⢾⣶⢄⡀⠀⠈⠠⣀⠝⢋⣴⣿⣧⡀⣴⣶⣿⢁⡍⠿⠁⠀⠀⠀⠀⠀⢒⠀⠀⢠⠀⠀⣠⣰⣦⠈⡀⣉⣡⣀⠤⢠⡄⢀⣻⡟⠛⠛⢻⠟⣶⣄⠀⠀⢚⠀⠀⢀⣲⣔⠾⢛⣙⠀⣐
⡿⣻⣵⠼⠿⣷⠄⠀⠉⠶⠘⠘⠺⣿⢯⣿⣿⣲⡀⠀⠉⣭⣼⣿⣿⡿⠀⣏⠙⣿⣸⠷⠀⠲⠄⠀⠀⠀⢀⣤⣤⣄⡂⠀⠀⠘⠛⠃⠀⠁⢠⣿⣅⠀⠀⠀⠬⢾⠳⢦⠐⠂⢤⣤⣜⣀⠸⢁⠀⢴⣷⣶⣷⣽⣶⣿⣌⡭
⣿⣿⣛⣯⠄⠁⠀⠀⡌⠁⣛⠉⣲⡭⢿⣛⠝⣦⣌⠀⣈⣿⣻⣿⣿⢳⣞⣙⡻⡭⣳⣷⠷⠶⠀⠀⠀⠀⣿⣿⣿⣿⣿⡀⠀⠐⡒⠀⠄⡔⡤⡭⠏⠚⠁⠀⠀⠀⠐⠌⣀⣷⣤⡶⠶⢶⣿⡉⠁⡜⠀⠉⣉⣿⣿⠶⢾⣾
⠆⠹⣷⣶⠇⠐⡉⠻⠃⢉⠁⠀⠃⠀⠠⣯⣀⡛⠫⠫⣹⣿⣿⠟⠻⣿⣿⣯⠑⣗⣛⣄⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣟⡀⠀⠀⠀⠀⠈⠁⠀⠈⠀⣀⠀⠀⠐⠢⢠⣄⣠⣳⣹⣤⠦⠄⠬⢡⠈⠀⠂⢀⡉⣻⢳⣶⣷⣍
⣶⣷⡯⠻⣗⡀⠀⣄⠠⢺⡿⠖⠈⣰⣮⡽⠉⢻⡫⡌⠻⠟⠊⠘⠌⠿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠸⠱⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⠌⣵⣤⣛⣻⣿⣟⡹⢷⣟⢶⣬⣏⣁⢮⣿⢟⣾⢺⣧⣴⣄
⢛⣑⡷⣦⠼⣆⡉⠋⠙⢏⣃⠰⠘⢀⠠⡀⣀⠀⣌⣁⠙⢆⡀⠀⢀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣼⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⡄⠀⠀⠂⡀⣄⠀⢼⣿⡿⠿⢻⣾⣧⣴⣾⢿⠿⢿⣞⢛⢽⢏⣀⠙⣴⡎⢽⢯
⣿⣶⡶⣰⣮⡻⡿⢇⠸⣿⣟⡻⠦⣤⠘⠃⡓⣚⣗⣴⣯⣻⣿⡷⣌⡑⠀⢈⣛⠛⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⠋⠀⠀⠀⠀⠁⠀⠀⠈⠁⠖⠁⣐⣻⣥⣤⠀⠤⡍⠋⣉⡋⠹⣿⡏⠻⣿⠛⢿⡟⣿⡿⢿⡻
⢸⣿⣷⣴⣶⣿⡠⠺⣷⡂⣁⡈⠸⡴⡨⣀⣀⣘⠿⢷⡶⡻⢞⣿⣿⡛⣶⣼⣿⠚⢂⢹⣿⣿⣿⣿⣿⡟⠻⣿⣽⢿⣶⣶⣿⣷⣦⡀⢂⣴⡄⠀⠀⠈⣸⠹⣯⣿⣷⠿⣇⣐⣐⣀⣼⣷⢓⣉⣻⣺⣶⣳⣶⣇⣁⡠⢃⣄
⢸⣿⣿⣣⣭⣙⣠⡀⠀⣑⢽⣟⣿⠷⠋⠈⢿⢘⣲⣢⡋⢿⣝⣿⢇⡿⢆⣋⠻⣦⣐⠚⢿⣿⣿⣿⣿⣧⣀⣿⣿⢸⣿⣿⣿⣿⣿⣿⣌⠉⠁⠀⣀⢘⠉⠉⣾⡟⣿⣾⡾⣿⢻⣛⡍⡆⣛⣿⠉⣻⣟⣿⢝⣻⢿⣿⠋⢋
⣚⠙⣿⡛⣿⡯⣭⠼⠀⣌⢏⣡⡨⣞⣖⡶⠀⠬⣪⠻⠉⠊⠉⠟⢛⡇⣬⣇⢾⡙⣿⣦⣄⢿⣿⣿⣿⣿⣻⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣧⡸⢿⣿⣿⡿⠘⣷⣦⣮⠱⣶⣷⣾⡾⣍⢴⣿⣷⣄⣽⣿⣿⣾⣴⣿⣟⣿⣿
⣿⠂⣼⢿⣶⣷⠙⠁⠙⠯⢼⠾⠿⣛⠋⣨⡥⡶⢺⣿⡞⢄⣄⢳⣶⠨⢈⣩⣽⣷⣶⣮⣭⣿⣯⡭⣩⡒⢿⠟⠛⡃⠙⢿⣿⣿⣿⣿⣿⠏⣬⡗⢢⢤⡕⣇⣩⠻⠛⠠⣿⣻⣟⣷⡟⠻⠽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠆⠄⢄⠙⠛⣛⢓⣟⠘⣴⣷⡿⣿⡫⡇⣲⣿⣿⡭⠰⣅⣄⣹⡆⣰⢲⣍⡿⡟⢿⡩⢰⠻⠤⣡⣵⣮⣏⠀⡄⠲⠒⠆⢂⢊⣉⠭⢑⣿⢺⢺⣭⣰⡧⣣⢛⡱⣀⠰⣲⡤⠉⣸⣟⢷⠀⣠⣈⠻⢟⠹⠛⡩⡄⢀⠞⡉⠝
⣀⢠⣿⡻⣷⢤⣙⠤⣤⣹⣦⢳⣽⣾⣷⡦⣜⣳⣿⡻⣨⣷⣷⣾⣴⢞⠛⡧⡼⠿⢾⢸⢓⢶⣶⣦⠁⠛⢀⠔⡚⠩⡆⣞⣲⠙⣿⣿⣿⠁⠊⠀⢩⡁⡁⠩⢭⣷⣍⣥⣟⡋⠉⢁⢀⠀⣈⡙⠃⠂⠀⠉⣠⣶⠀⠀⣿⣿
⠻⡟⣯⣶⣶⣄⠿⣿⣉⡙⣿⡿⠋⢿⡿⢾⠻⠛⢟⣫⣅⡲⡩⣽⠟⢫⠻⡻⠦⠾⠊⠇⡎⠫⣉⣣⣤⣦⡌⠹⠃⢴⣞⢖⠹⢬⣿⣿⣿⠰⡖⣛⣿⣿⢧⢚⢎⣿⢮⣡⣿⣟⠫⡛⡵⢅⡒⢒⠺⣄⣀⣈⡻⠩⣠⠀⠻⠟
⡀⣀⢀⣿⣿⣿⣿⠙⠍⠈⢠⣬⢠⠊⡁⢿⣶⢦⣤⣻⣭⣭⣵⣿⡜⡾⣷⣓⡳⠑⣤⣆⠓⡠⢈⠛⣿⣳⣂⢼⣀⣈⢡⡐⢂⢸⣿⡿⢗⠄⣚⡹⢿⣿⣺⣴⡌⣽⣦⣽⣿⣿⣧⣻⣉⢢⣴⣺⢄⣴⣦⠺⠅⠀⣊⡀⠀⠤
⣿⣰⢢⣁⡋⣍⢀⡈⢲⣥⣞⠚⣿⣛⣇⣠⣈⢳⡠⣄⢤⡹⣿⠭⢟⡙⢏⢝⣻⣡⡤⡯⣁⡴⡔⣥⣽⢿⣭⢫⣬⣉⡻⠿⡄⢈⢿⢿⣹⣖⢙⠍⢍⣙⣭⣅⣏⣙⡛⢹⣿⣭⣿⠁⢿⠉⢮⣿⣷⡌⠉⠁⠀⠀⠤⠤⠌⠀
⢳⣿⡽⢿⣯⣧⡀⢈⣼⣿⡂⢧⡘⣿⣿⡭⣽⣵⣷⣖⣬⣰⢿⣄⣻⠿⣿⣛⡷⢿⣭⣻⣎⠹⠳⣆⠰⠜⢿⡆⠀⠛⠦⢥⣿⣖⣴⡿⣟⣟⣶⣟⠒⠘⠻⢇⣾⣿⣿⡿⣺⣿⢿⣷⡿⣿⣿⡷⡋⠀⠀⠀⠀⠀⠀⣴⠀⠀
⢴⣶⣾⢾⣿⣿⣷⢨⣿⣿⣿⢿⣷⡯⡻⢿⡷⣽⣿⣿⣿⡆⠀⠀⠻⠾⣿⣏⣿⣋⡟⢿⣴⡦⠈⢭⠃⠀⠈⣿⡄⠶⡦⣶⣽⣇⠀⠳⡾⡽⣬⡟⠂⢹⡿⣿⡿⣶⠿⣛⣯⡿⡿⢔⠉⠋⠙⢿⣮⣀⠀⠀⠀⠀⣠⣾⣶⣶
⢘⣟⣿⣤⣭⣯⢻⣄⣣⠜⢻⣿⣿⣉⡻⣿⡿⢿⠿⠝⠹⣁⠄⠀⠔⠛⣯⣽⣾⣧⣾⣌⢈⣿⣾⡒⠶⠿⣮⣧⢿⡄⠀⢀⡚⠟⠳⣈⢑⡴⠾⣠⣾⣿⣏⣾⣶⣜⣲⣿⣿⣿⢛⡲⣦⠀⠀⣂⣞⣩⠀⠄⣄⠘⣿⣿⣿⣿
⣀⠨⣭⣍⢛⡿⣼⣷⢭⠦⢽⣿⣻⣿⡻⢛⣡⣀⣦⡠⡆⡝⣇⣂⠀⣤⣶⢝⡿⣿⣻⣽⣅⢸⠟⡞⠀⠎⡟⣿⣫⣿⡀⣈⡕⣌⠘⣻⣆⡙⣾⣿⡿⣿⣟⢚⣺⣯⣝⣯⣿⣛⢠⢹⣨⣀⣚⣙⠻⢿⣧⠿⣚⣤⣌⡛⣿⠿
⣁⢘⣿⢳⣑⢀⡬⢛⣈⣬⣽⢿⣿⡽⠯⣬⣾⣯⣿⣷⣿⣿⣿⡇⣈⣭⡿⡾⢖⠛⠛⠋⠈⠀⠐⣣⢽⣶⣗⠛⢧⣧⣤⣖⣧⣙⣟⣨⣿⡰⣻⣍⣄⢽⡗⠾⠽⡴⢼⣿⡿⣾⣾⣿⣿⣿⣿⣏⢺⣇⣅⢾⣿⣼⠝⣛⠀⠐
⡞⠛⢻⣟⡿⢿⣛⡛⣻⣟⣯⣿⣿⡿⣾⣥⣿⠻⣿⣯⣿⠛⢿⢿⠠⣄⣠⢄⣸⡳⠠⢦⠀⡴⣰⢴⣦⣂⣟⣷⠐⢿⠏⢉⡅⠻⣿⠏⠘⢤⣽⡿⢿⡷⠆⡶⠛⣇⣻⠕⢇⡯⢍⡾⠿⠿⢿⣿⣿⣿⣍⡈⠛⠿⠿⢬⠠⣾
⠀⣤⣄⢀⣼⢯⣽⠭⣿⣪⡄⣓⠒⡂⣠⡄⠈⡁⠀⠀⢡⣾⡲⠛⠟⠀⠀⠽⠇⢩⠀⣁⣷⡿⡖⠻⣿⡴⠿⡀⣾⣏⣙⣿⣿⣷⣦⣑⢞⣾⣿⣿⢹⣯⣿⣿⣿⣷⡗⣾⡗⣶⡿⡗⣹⡔⠀⣰⣆⠀⢠⣿⣿⡿⠋⠁⠀⠀
⣲⣿⣗⠆⠐⠲⠞⠨⠎⢟⠅⠠⢍⠁⠀⠁⠇⠬⣔⡀⠿⢿⠿⣖⣧⡠⢶⡶⣧⡋⠟⠻⢭⡗⡖⠊⠏⠛⠓⠞⠥⠄⣿⣿⢯⣽⣿⡿⠦⣟⡿⡿⡿⠭⠽⠋⢁⢸⠄⠀⠀⠀⠀⠂⠋⠀⠂⠭⠁⠘⠹⣿⢍⠉⡵⡲⠬⣯
⠁⣼⠄⠃⠀⠀⠀⠀⠀⠨⠀⠀⠀⠁⠠⣶⠄⠀⠝⡁⠀⠀⡴⣿⡓⠢⠀⠀⠜⠉⠄⠀⢰⢭⡀⠀⠀⠐⠆⠀⠠⢀⠅⣠⣄⣈⣫⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⠠⠀⠀⠀⣀⡈⠂⢢
⣀⣤⣶⣾⡿⠀⢀⣠⣤⣤⢀⠀⠀⠀⠀⡫⠄⠀⠀⠀⠠⣾⣿⣿⡷⠆⠀⠀⠀⢀⠀⠀⢨⡼⠐⠈⠀⠀⢰⠂⠀⠰⣼⣿⣿⡏⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣶⣦⡀⠀⠀⠁⠄⠘⠁⠀⠀⣲⣶⣞⠛
⡟⠿⠷⠋⠿⠇⠈⠛⠿⣿⣧⡀⠄⠀⠀⠀⠀⠀⠈⠀⠀⠽⣷⣴⣄⡖⠀⠀⠀⠈⠂⠀⠈⠀⠀⠀⠀⠀⠈⢂⠀⠐⠟⠟⠋⠀⠀⠀⠀⠀⣤⣄⣤⠀⠀⠀⠀⠀⢀⡤⢠⣼⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢛⣷⣵⢉
⡀⡠⠀⠀⠀⠁⠀⠁⢒⠷⣣⣀⡁⠔⡀⠀⠀⢀⣈⡀⠀⣤⢾⠋⠈⠉⠄⠠⠶⠀⠀⢠⡄⡀⠀⠴⠀⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠰⣿⡉⠉⠀⠀⠀⢀⣀⣘⣄⣡⣥⡀⣄⠀⠀⠀⢀⠀⠀⠤⠀⠐⠁⢁⡉⣼⠊
⢴⣅⠀⢠⣬⢂⠀⠀⠀⠠⣬⣀⣐⢾⡶⢄⡀⠀⠈⠠⣀⠝⢋⣴⣿⣧⡀⣶⣶⣯⢁⡍⠿⠁⠀⠀⠀⠀⠀⠒⠀⠀⢀⠀⠀⣠⣴⣦⠈⡀⣃⣡⢀⠤⢠⡄⢈⢻⡟⠛⠛⢻⠿⣶⣄⠀⠀⢘⠀⠀⢀⣲⣔⠾⢛⣙⠈⣐
⡿⣛⣵⠼⠟⣧⠄⠀⠉⠶⠘⠘⠺⣿⢧⣿⣿⣶⡀⠀⠉⣭⣼⣿⣿⡿⠀⠏⠙⣿⢸⠷⠀⠰⡀⠀⠀⠀⢀⣤⣤⣀⡂⠀⠀⠘⠛⠃⠀⠁⢀⣿⣅⠀⠀⠀⠬⢺⠳⢆⠐⠂⢤⣤⣜⣀⠸⢁⠀⢴⣷⣶⣷⣿⣼⣿⣌⠩
⣿⣿⣏⣯⠆⠁⠀⠀⠬⠁⣛⠉⣲⡭⢿⣛⠽⣦⣌⠀⣘⣿⣿⣿⣿⢳⣞⣙⡛⡯⣳⣷⠷⠶⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠐⡒⠀⠄⡔⠬⡩⠟⠚⠁⠀⠀⠀⠐⠌⣀⣷⣤⣶⠶⠾⣿⡏⠁⠜⠀⠍⣉⣿⣿⠶⢮⣾
⠆⠹⣶⣶⠇⠀⡉⠻⠃⢉⠁⠀⠃⠀⠢⣯⣀⡛⠫⠫⣹⣿⣿⠛⠻⣿⣿⣯⠑⣗⣛⣀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣟⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣀⠀⠀⠐⠢⢠⣄⡠⣳⣹⣤⠤⡄⠬⢡⠈⠀⠂⣠⡉⡻⢱⣶⣷⣍
⣶⡷⡯⠻⢗⡀⠠⣄⠰⢾⡿⠖⠈⣠⣮⡭⠉⢫⡫⡜⠹⠟⠊⠐⠍⠿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠸⠱⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢠⠈⣵⣦⣛⣻⣿⣟⡹⢷⣏⢶⣌⣏⣃⢮⣿⢽⣾⢺⣧⣴⡅
⢛⣑⡷⣦⠼⣖⡉⠋⠙⢏⣃⠰⠘⠀⡠⠀⢀⠀⡌⣁⠙⢆⡀⠀⢀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣼⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⡄⠀⠀⠀⣀⡀⠀⢼⣿⡿⠿⢻⣿⣧⣴⣾⢿⡿⢿⣝⢋⢽⢏⣀⠉⣴⡎⢝⢏
⣿⣶⡶⣰⣮⡺⡿⢇⠸⣿⣟⡻⠦⡤⠘⠃⡓⣚⣗⣴⣾⣻⣿⡣⣌⡑⠀⢈⣛⠛⢻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⠋⠀⠀⠀⠀⠁⠀⠀⠈⠁⠖⠁⣐⣻⣥⣥⠀⠤⠍⠋⢉⡋⠹⣿⡏⠻⣿⠛⢿⡟⣿⡿⢟⡻
⢸⣿⣷⣴⣾⣿⡢⠲⣷⣂⣀⡈⠨⡴⡨⡀⣀⣘⠿⢷⡶⠿⢞⣿⣿⡟⣶⣼⢿⠚⠂⢹⣿⣿⣿⣿⣿⡟⠻⣿⣽⢿⣶⣶⣿⣷⣦⡀⢂⣴⡄⠀⠀⠈⣸⠹⣯⣿⣷⠿⣇⣐⣐⣀⣼⣶⢃⣉⣻⣺⣶⣳⣶⣅⣅⡤⢃⣄
⢸⣿⣿⣠⣭⣙⣠⡀⠀⣑⢽⣟⣿⡿⠛⠈⢻⢘⣲⣢⡋⢿⣝⣿⢇⡽⢆⣋⠻⣤⣰⠘⢿⣿⣿⣿⣿⣧⣀⣿⣿⢸⣿⣿⣿⣿⣿⣿⣌⠉⠁⠀⢀⢘⠉⠉⣾⣟⣿⣾⠾⣿⢻⡚⡬⡆⣛⣿⠋⣻⣟⣿⢿⣫⢿⣿⠉⢊
⣚⠙⣷⡛⢿⡯⣭⠼⠀⣌⢏⣡⡨⢞⣶⡖⠐⠨⣪⠛⠉⠊⠉⠟⢛⡇⣬⣅⢾⡙⣿⣦⣄⢿⣿⣿⣿⣿⣻⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣦⡸⢿⣿⣿⡿⡘⣷⣤⣦⠱⣷⣷⣾⡿⣏⢶⣿⣷⣄⣿⣿⣿⣿⣴⣿⣟⣿⣿
⣿⠀⣼⢿⣷⣷⠙⠃⠉⠯⢜⠷⠿⢛⠋⣨⡥⡶⢺⣿⡞⠄⣄⢳⣼⠨⢈⣱⣿⣷⣶⣿⣭⣿⣯⡭⣍⡒⢿⢿⠛⠁⠙⢿⣿⣿⣿⣿⣿⠋⣬⡗⢢⢤⡕⣇⣩⠻⠛⠠⣿⣻⣟⣷⡟⠻⠿⡶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠆⢀⢄⡙⠛⣛⢓⣞⡰⣴⣷⡿⣿⣋⡆⣲⣿⣿⡭⠠⣅⣀⣹⡆⣰⢳⣭⡿⠟⢿⡩⢲⠺⠤⣡⣵⣮⣇⠀⠆⠲⠒⠂⠂⢂⣉⠭⢑⣿⠺⢟⣥⣰⡧⣣⢛⡱⣀⠲⣲⡤⠀⣸⣟⠗⠀⣠⣈⠻⢟⠹⠛⡩⡄⢀⠞⡉⠝
⣀⠠⣿⠻⣷⢠⣉⠌⣤⣹⣆⢻⣽⣾⣷⣦⣽⣳⣿⡻⣨⣷⣿⣾⣴⢚⠟⡧⡽⢿⢾⢸⢓⢶⣶⣢⠁⠚⢀⡔⡚⠲⡆⣞⣲⠙⣿⣿⣿⠁⠈⠀⢈⡑⡁⠨⣭⣷⣍⣥⣝⡋⠉⢁⢀⠀⣈⡙⠃⠂⠀⠉⣠⣶⠀⠀⣿⣿
⠛⡿⣿⣴⣴⣄⠿⣿⣉⡙⣿⠟⠋⢿⡿⢿⠻⠛⢗⣫⣅⣲⣩⣽⠛⢋⠻⡻⠧⠾⠋⠇⡈⠫⣉⣣⣦⣦⡬⠹⠃⢴⣞⢖⠹⢼⣿⣿⣿⠰⡒⣛⣿⣿⢧⢐⢎⣿⢮⣡⣿⣟⠫⡹⡥⢅⡒⢒⠺⣄⣁⣈⡻⠩⣠⠀⠻⠟
⡀⣀⢀⣿⣿⣿⣿⢙⠍⠈⢠⣤⢠⢊⢁⢿⣶⢦⣤⣸⣯⣭⣵⣿⡼⡾⣷⣓⣳⠑⣤⣂⠑⡤⢈⠛⣿⣳⣢⣼⣄⣈⢡⡐⢂⢸⣿⡿⢗⠤⣚⡹⢿⣿⣚⣴⡌⣽⣦⣽⣟⣿⣥⣛⣉⢢⣴⢺⢄⣴⣆⠺⠅⠀⣊⡀⠀⠬
⣿⣐⣠⣁⡉⡍⢀⡈⢲⣤⣞⠚⣿⣿⣇⣰⣊⣓⡠⣄⢤⡹⣿⠽⢟⡙⢏⢝⣻⣡⡤⠯⢁⡰⡔⣅⣽⢿⣍⣯⣬⣉⡻⠿⡄⢈⢿⣷⣹⣶⢝⠍⢍⣙⣭⣄⣏⣙⡋⢹⣿⣭⣿⠁⠿⠉⢪⣿⣶⡌⠉⠁⠀⠀⠤⡄⢄⠀
⢳⣿⡽⢿⣯⣧⡀⢈⣽⣿⡂⢧⠐⣿⣿⡭⣽⣵⣷⣶⣬⣱⢿⣄⣻⠿⣿⡛⡷⢿⣭⣛⣌⠹⠳⣆⠰⠞⢿⡎⠀⠘⠦⢭⡷⣖⣶⡿⣖⣟⡴⣟⠒⠜⠻⢏⣾⣿⣿⡿⣺⣿⢿⣷⡿⣿⣿⡷⡋⠀⠀⠀⠀⠀⠀⣴⠀⠀
⠴⣾⣾⢾⣿⣿⣷⢠⣿⡿⣿⣿⣷⠯⡻⢿⣗⣽⣿⣿⣿⡆⠀⠀⠻⠼⢿⣏⣿⣋⣟⢿⣴⡦⠈⢭⠂⠀⠈⣿⡌⠲⡦⣶⣿⣇⠄⠳⡾⡽⣬⠟⠂⢹⡿⣿⡿⣶⠿⢛⣯⡿⣿⢔⠉⠋⠙⢿⣮⣀⠀⠀⠀⠀⣠⣾⣶⣶
⠐⣝⣿⣤⣭⣏⢻⣄⣣⠜⢻⣿⣿⣉⡺⣿⡿⢿⠿⠉⠹⣁⠄⠀⠐⠙⣯⣾⡾⣧⣶⣌⢈⣿⣾⠒⠶⢿⣮⣦⣿⡄⠀⢀⡚⠟⠷⣈⢱⡴⡿⣠⣾⣿⣏⣾⣶⣝⣲⣿⣿⣿⢛⡲⣦⠀⠀⣂⡞⣸⠀⠀⣄⠘⣿⣿⣿⣿
⢀⠨⣭⣭⢫⡾⣼⣷⢭⠦⢼⣿⣻⣿⡻⢛⣡⣀⣦⡤⡦⡽⣇⣂⢀⣤⣶⢝⡿⣿⣻⣽⣍⢼⠟⡞⠀⠈⡟⣽⣫⡿⡀⣌⠝⣠⠘⢿⣄⡛⣾⣿⡟⣿⣟⢚⣺⣯⣝⣯⣿⣛⢂⢹⣬⣁⣘⣉⠻⢷⣧⠟⣪⣤⣌⡛⢿⠿
⣁⢸⣯⢳⣓⢀⡬⢛⣈⣬⣿⢿⡿⠽⠯⣮⣾⣯⣿⣷⣻⣿⣿⡇⣈⡭⡿⡾⢖⠛⠛⠃⠈⠀⠘⣣⣬⣶⡖⠙⢵⣧⣰⣶⣷⣉⣛⣉⡷⠐⡻⣏⣄⢽⡓⠾⠵⡴⠾⣿⡿⣾⣿⣿⣿⣿⣿⣏⢚⣇⣅⢾⣯⣼⢝⣟⠀⠐
⡞⠛⢻⣟⡿⢿⡛⡛⣻⣟⣧⣿⣿⣿⣾⣥⣿⠻⣿⣯⣿⠛⢿⢿⠤⡈⣤⠄⣘⡿⠠⢧⢀⣴⣰⢴⣶⣐⣟⣷⠐⢿⠯⢩⡅⢻⣿⡏⠘⢤⣽⡿⠟⠷⠎⡼⠛⡏⣻⡕⢇⡯⢍⡿⠿⠿⢿⣿⣿⣽⣍⡈⠛⠿⠷⢬⠠⣾
⠀⣤⣄⢠⣼⢯⣽⠽⣗⣨⡄⣓⠒⡂⣠⡄⠈⡁⠀⠀⢡⣶⡖⠟⠟⠁⠀⠽⠇⢩⠀⣁⣷⣿⡦⠻⣿⡴⡟⡀⣾⣟⣙⣿⣿⣷⣦⣑⢞⣿⣿⣿⢹⡯⣿⣿⣿⣷⣏⣾⡗⣾⡿⡞⣽⡔⢀⣰⣆⠀⢠⣿⣿⣿⠉⠁⠀⠀
⣲⣿⣕⠆⠐⠂⠞⠸⠎⢟⠍⠠⢍⠅⠀⡀⠁⠬⣴⡀⠿⢿⠿⣶⣧⡠⢶⡶⣧⡋⠟⠳⢭⡗⡖⠊⠏⠛⠗⠖⠥⠄⣿⣿⠯⣽⣿⡿⠦⡟⠿⡿⡿⠭⠽⠛⢁⢹⠄⠀⠀⠀⠀⠂⠋⠀⠂⠭⠉⠘⠹⣾⢍⠍⣤⡲⠼⣯
⠁⣤⠀⠋⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠠⣶⠀⠀⠝⡁⠀⠀⡴⣿⠛⠲⠀⠀⠜⠉⠄⠀⢰⢭⡀⠀⠀⠐⠆⠀⠠⢀⠅⣠⣄⡈⢫⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⠠⠀⠀⠀⣁⠈⠂⢠
⣀⣤⣷⣾⡿⠀⢀⣤⣤⣤⢀⠀⠀⠀⠀⡫⠄⠀⠀⠀⠠⣾⣿⣿⡷⠦⠀⠀⠀⢀⠀⠀⢨⡜⠀⠈⠀⠀⢰⠃⠠⠰⣼⣿⣿⡏⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣬⣶⣦⡀⠀⠀⠁⠄⠘⠁⠀⠀⣂⣶⣞⠛
⡞⠿⠿⠫⠿⠇⠈⠛⡿⣿⣧⡀⠄⠀⠀⠀⠀⠀⠈⠀⠀⠽⣷⣴⣤⡖⠀⠀⠀⠈⠂⠀⠈⠀⠀⠀⠀⠀⠈⢂⠀⠐⠟⠟⠋⠀⠀⠀⠀⠀⣤⣄⣤⠀⠀⠀⠀⠀⠀⡤⢠⣼⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢛⣯⣼⠉
⡀⡤⠀⠀⠀⠁⠀⠁⢲⡷⣯⣀⡁⠶⠀⠀⠀⢀⣈⡀⠀⣤⣾⠏⠈⠉⠄⠠⠶⠀⠀⢠⡄⡀⠀⠰⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠰⣟⠉⠉⠀⠀⠀⢀⣀⣐⣄⣠⣥⡀⣄⠀⠀⠀⢀⠀⠀⠄⠀⠐⠉⢁⡋⣼⠊
⢴⣅⠂⢠⣼⢂⠄⠀⠀⠠⣬⣀⣰⢾⣶⢄⡀⠀⠈⠀⣀⠝⢋⣴⣿⣧⡀⣴⣿⣯⢁⡍⠇⠀⠀⠀⠀⠀⠀⢒⠆⠀⢠⠀⠀⣠⣴⣦⠈⠀⣁⣡⢀⠤⢀⠄⢀⢻⡿⠛⠛⢻⠞⣴⣄⠀⠀⢚⠀⠀⢀⣲⣔⢾⢋⣉⠀⣐
⡿⣛⣵⠼⠿⣷⡄⠀⠉⠶⠘⠐⠺⣿⢯⣿⣟⣲⡀⠀⠉⣭⣼⣿⣿⡿⠠⠏⠙⣿⠸⠿⠀⠀⠀⠀⠀⠀⣠⣶⣦⣤⡂⠀⠀⠘⠛⠃⠀⠁⢀⢿⣀⠀⠀⠀⠼⢾⠳⣆⠀⠂⢤⣤⣜⣀⠸⢁⠀⢴⣷⣶⣷⣽⣾⡿⣌⠭
⣿⣿⣏⣿⠆⠁⠀⢀⡌⠁⣛⢉⣲⡭⢿⣋⠙⣦⣌⠀⣘⣿⣿⣿⣟⢳⣞⣙⡻⡭⣳⣳⠷⠶⠀⠀⠀⢰⣿⣿⣿⣿⣧⣤⣄⣐⠒⠀⠀⣔⡬⡭⠟⠚⠀⠀⠀⠀⠔⠌⣀⣷⣤⡶⠶⢾⣿⡉⠁⠜⠀⠉⣉⣿⣷⠶⢾⣾
⠆⠹⣶⣶⠇⠐⡉⠻⠓⠉⠁⠀⠉⠀⠰⣭⣀⡛⠫⠫⣹⣿⣿⠙⢻⣿⣿⣿⣶⣷⣿⣤⡀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠁⠀⠈⠀⣀⠀⠀⠐⠢⢠⣄⣤⣳⣹⣤⠦⡄⠬⢡⠈⠠⠢⣀⡙⡻⢱⣶⣦⣅
⣖⣷⡏⠙⣗⡠⠀⣀⠰⢿⡿⠖⠈⣰⣾⡭⠉⢩⣫⠜⠻⠟⠊⠐⠌⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠘⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠃⠀⢠⠈⣵⣦⢛⣻⣻⣟⡽⢷⡏⢶⣜⣏⣁⢮⣿⢿⣾⢸⣧⣱⡅
⢛⣑⣷⣦⡼⣇⡉⠃⠙⢏⣃⠰⠐⠀⡠⡀⢀⠀⣌⣁⠸⢆⠀⠀⢀⠙⣿⣿⣿⣿⣿⣿⣿⢿⠶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⡄⠀⠀⠀⡀⣀⠀⣼⣿⡿⠿⢻⣼⣧⣴⣾⠟⡿⠿⣟⢋⢽⢟⣀⠋⣴⡎⢝⢏
⣿⣶⡶⣰⣮⣻⡿⢇⠸⣿⣟⡻⠦⣤⠘⠃⣓⣚⣗⣶⣿⣛⣿⡣⣌⡑⠀⢙⡛⣛⢿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠖⠁⣐⣳⣤⣤⠀⠠⠅⢋⣙⡋⠹⣿⡏⠻⣿⠻⢿⡟⢿⡵⢟⡻
⢸⣿⣷⣴⣶⣿⡠⠲⣷⡂⣀⡈⠰⡷⡠⣀⣀⣘⠿⢷⣶⡛⢞⣿⡽⡟⢶⣼⣿⠚⢢⣿⣿⣿⣿⣿⣿⡟⠿⣿⣿⢻⣷⣷⣤⣶⣦⣄⢀⣴⠄⠀⠀⠈⣸⠹⠮⣽⣶⠻⣃⣀⡐⣀⣴⣷⢓⣉⣻⣸⣷⣳⣶⣄⣅⡤⢃⣀
⠸⣿⣿⣡⣭⣐⣠⡀⠀⣑⢽⣟⣿⡷⠛⠨⢿⢘⣲⣢⡋⢹⣭⣿⢇⡾⢖⣋⡻⣦⣻⣿⣿⣿⣿⣿⣿⣷⣄⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣍⠁⠀⠀⠐⠁⠉⣶⡟⣿⣾⠖⡯⢳⡛⡬⡆⣛⣿⠋⣻⣟⣿⢯⡻⢿⣿⠉⣏
⣞⠙⣿⡛⣿⣯⣭⠼⠀⣎⢏⣡⡸⢜⣖⡖⠐⠮⣪⠚⠉⠊⠈⠟⢛⡥⣬⣅⢾⡋⣻⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⢯⣿⣿⡷⠘⣷⣤⣦⠱⣴⣷⣾⡿⣏⢲⣽⣷⢤⣭⣿⣿⣿⣴⢿⣷⣿⣿
⣿⠀⣜⢯⣷⣷⡙⠃⠉⠯⢼⠷⠿⣛⠋⣨⡥⡖⢸⣿⡞⠄⣄⠳⣶⠠⢈⣩⣵⣿⣶⣦⣭⣿⣯⡽⣭⡓⢶⢿⠛⠁⠘⢿⣿⣿⣿⣿⣿⣿⢏⠗⢢⣴⡕⢃⣹⠻⠛⠡⣿⣻⢟⣗⡛⠻⠝⡶⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿
⢆⢀⢄⠘⠛⡛⢛⣟⡔⣔⣷⡹⠿⣯⡆⣲⣿⣿⡭⠠⣅⣀⣹⡆⣰⢻⣏⡿⠟⢷⡠⢐⠻⠬⣡⣵⣮⣃⠀⡄⠲⠒⠆⢂⢊⡙⠛⠛⣿⢻⢚⣥⣴⡧⣣⢛⡱⡀⠒⢲⣤⠀⣸⣟⠗⠀⣠⣈⠙⠛⡹⠋⡩⡄⠀⠎⡉⠝
⣀⠨⢾⠻⣷⢤⣙⠠⣠⣹⣦⣹⣭⣾⣿⡦⣌⣲⣿⡸⣈⣷⣷⣾⣶⣛⠟⡇⡼⢿⢾⢸⢛⢶⣶⡦⠁⠚⠀⡔⠒⠡⡆⣞⣶⠙⣿⣿⣿⠁⠚⠀⢩⡁⡁⠩⢭⣻⣍⣥⣝⡋⠉⢁⣀⠀⣈⡙⠃⠂⠀⠁⣠⣴⠀⠀⣿⣿
⠛⠟⢻⣴⣶⣌⠿⣽⣋⡈⣿⡿⠋⢿⣿⠿⠻⠛⢃⣫⣥⡢⣈⣽⠛⢉⠩⡻⠆⠺⠊⠇⡈⠉⣙⣧⣤⣆⡬⠹⠃⢰⣞⢖⠹⢤⣿⣿⣿⠰⡖⣓⣷⣿⣧⢲⢎⣿⢎⣠⣿⣟⠫⢝⡥⢇⠒⠒⠺⡄⢀⡈⠹⠩⣠⠀⠻⠛
⠀⣀⢀⣿⣿⣽⣿⢙⠍⠈⢠⣬⢠⠎⣁⢿⢶⢦⣤⣹⣭⣭⣵⣿⡼⡾⣷⣓⡳⠑⣴⣂⠑⡠⢈⠋⣿⣱⣂⢴⣄⣀⢡⡑⢂⣸⣿⡿⢗⠄⣚⡹⢹⣿⣶⣴⡌⣽⣦⣿⢟⣿⣧⣛⣉⢢⣴⢺⢄⣴⣦⠺⠅⠀⡊⡀⠀⠤
⣿⣐⣣⣁⠉⡉⢀⡈⢒⣧⣎⠚⣿⣟⣇⣨⣊⣳⡀⣥⢦⡹⣿⠭⢟⡙⢯⢜⣻⣡⡄⠯⢁⡴⡄⣥⣿⢿⢌⢣⣬⣉⡛⠿⡄⢈⢿⢷⣹⣶⠝⠍⢝⣙⣯⣀⣏⣙⡛⢹⣿⣭⣿⠁⢿⡙⢲⣿⣷⡌⠉⠀⠀⠀⠤⠤⣀⠀
⢳⡽⡽⢿⣯⣧⡀⢈⣽⣿⡂⣷⠀⣿⣿⡽⢽⣴⣷⣆⣬⣹⢿⣎⣿⠿⢿⣛⡿⠿⣭⣉⣎⠹⡳⢄⠰⠞⢿⡃⠀⠘⠦⢭⣵⣆⣶⡿⣖⡟⡴⣿⠒⠊⠻⢏⣾⢿⣿⡿⣺⣿⣟⣵⡿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⣤⠀⠀
⡔⣾⣾⢷⣿⣿⣷⢠⣻⡾⡿⢿⣷⡯⡻⢿⡗⣽⣿⣿⣿⡧⠀⠀⠻⠾⢿⣏⣿⣋⣟⢾⣴⡦⠈⢭⠓⡀⠀⣿⡄⠲⡦⠶⣻⣇⠀⠳⡾⠭⣌⠏⠂⢹⡷⣿⠿⢔⠝⢛⣾⡛⣿⢄⠉⠋⠙⢿⣦⣀⠀⠀⠀⠀⣤⣶⣶⣦
⢘⣾⣿⣤⣭⡟⢻⣄⣣⠼⢻⣿⣿⣉⣺⣿⡟⢿⡿⠉⠹⣀⠀⠀⠐⠙⣯⣽⡮⣧⣼⣮⢀⣾⣿⡖⠶⠻⣮⣧⣿⡄⠀⢀⡚⠝⠳⢈⢱⡤⠞⣠⣾⣿⣯⣼⣶⣜⡲⣿⣿⣿⣛⡲⣦⠀⠀⣺⣞⢹⠀⠄⡄⠘⣿⣿⣿⣿
⢀⠨⣍⡍⢻⡿⣼⣷⢭⠦⢽⣿⣻⣿⡻⢛⣡⣀⡶⡬⡆⢝⣖⣂⠀⣤⣶⢽⡿⣿⣻⣽⣇⢬⠟⡞⠃⠈⡟⣿⣯⡿⡀⣈⡜⣰⠐⢻⢄⡑⣿⣿⡿⣿⣛⢚⣘⣭⡝⣽⣿⡫⢢⢙⣩⣁⣚⣛⠻⢿⣧⠗⠊⣄⣉⠛⠿⠿
⣉⠈⣏⢳⣑⢀⡬⢉⣈⣌⣼⣿⡷⠽⠯⣬⣾⣯⣿⢗⣻⣿⣯⡇⣈⣬⣿⠿⢖⠛⠛⠃⠊⠀⠐⣣⢽⣶⡖⠛⢵⣧⣤⣖⣧⣋⣗⣨⡟⠰⢻⣍⣔⢽⡓⠼⠡⡔⠸⣿⡿⢾⣿⣿⣿⣿⣿⣏⢚⣇⣅⢸⣮⣼⠉⢈⠀⠀
⡟⠛⢻⣟⡿⢿⣛⣛⣻⣟⣧⣿⣿⣿⣾⣭⣿⡻⣿⣿⣿⠛⢿⢿⠀⣈⣤⢄⣘⡿⠠⢧⢀⡴⣐⢴⣶⢀⡟⢷⠘⠻⠯⢉⡅⠻⣿⡏⠀⢠⣼⡿⠎⠷⠎⣔⠓⠃⢻⠅⢇⠇⢉⡾⠿⠿⢿⣻⢿⣽⣍⡈⠛⠿⠷⠤⠠⣶
⠀⣤⣄⢀⣼⢏⣽⡽⣗⣨⡄⣓⢒⡂⣠⠄⠈⡁⠀⠀⢡⣾⡶⠟⠟⠀⠀⠽⠇⢩⠀⣁⣷⡿⡶⠻⣿⡤⣟⡀⣾⣟⣙⣿⣿⣷⣦⣑⢞⣾⣿⣿⢙⡯⣿⣷⣿⣷⣏⣾⡗⣾⡿⡞⣽⡔⢀⣰⣆⠀⢠⣿⣿⣿⠋⠁⠀⠀
⣲⣿⡕⡆⠐⠢⠟⠨⠎⢟⠄⠠⢍⠅⠀⡀⠅⠬⣴⡀⠿⢿⠿⣶⣧⡠⢶⡶⣧⡋⠟⠻⢭⡗⡖⠂⠏⠛⢗⠖⠥⠄⣿⣿⠯⣽⣿⡿⠧⡟⠿⡿⡿⠭⠽⠛⢁⢹⠄⠀⠀⠀⠀⠂⠋⠀⠂⠭⠁⠘⠹⣾⢍⢍⣵⡲⠬⣮
⠀⣼⠀⠋⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠠⣶⠄⠀⠝⡁⠀⠀⡴⣿⠛⠪⠀⠀⠌⠉⠄⠀⢰⢭⡀⠀⠀⠐⠆⠀⠠⢀⠅⣠⣄⣈⢫⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⠠⠀⠀⠀⣁⡘⠂⢠
⣀⣤⣷⣾⡿⠀⢀⣠⣤⣤⢀⠀⠀⠀⠀⡫⠄⠀⠀⠀⠠⣾⣿⣿⡵⠦⠀⠀⠀⢀⠀⠀⢨⡜⠀⠈⠀⠀⢰⠃⠠⠰⣼⣿⣿⡏⠁⠀⠀⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣠⣬⣶⣦⡀⠀⠀⠁⠄⠘⠀⠀⠠⣂⣶⣞⠛
⡟⠿⠷⠋⠿⠇⠈⠛⡿⣿⣧⡀⠄⠀⠀⠀⠀⠀⠈⠀⠀⠽⣷⣴⣤⡖⠈⠀⠀⠈⠂⠀⠈⠀⠀⠀⠀⠀⠈⢂⠀⠐⠟⠟⠋⠀⠀⠀⠀⠀⣤⣄⣤⠀⠀⠀⠀⠀⠀⡤⢠⣼⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢛⣯⣼⢉
⣀⡤⠀⠀⠀⠁⠀⠁⢖⠷⣯⣀⡁⠴⡀⠀⠀⢀⣀⡀⠀⣤⢾⠇⠈⠉⠄⠠⠶⠀⠀⢠⡄⡀⠀⠰⠀⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠰⣿⡉⠉⠀⠀⠀⢀⡀⣐⣄⣡⣥⡀⣀⠀⠀⠀⢀⠀⠀⠤⠀⠐⠉⢁⡋⣼⠊
⢴⣅⠀⢠⣼⢂⠀⠀⠀⠠⣬⣀⢰⢾⣶⢄⡀⠀⠈⠠⣀⠝⢋⣴⣿⣧⡀⣴⣿⢏⢁⡍⠇⠁⠀⠀⠀⠀⠀⢒⠂⠀⢠⠀⠀⣠⣴⣦⠈⠀⣁⣡⢀⠄⢀⠄⢀⢻⡟⠛⠛⢻⠾⣷⣄⠀⠀⢚⠀⠀⢀⣲⣔⠞⢋⣙⠀⣐
⡿⣛⣵⠽⠿⣧⠄⠀⠉⠶⠘⠐⠺⣿⢯⣿⣟⣲⡀⠀⠉⣭⣼⣿⣿⡿⠀⠏⠙⡿⠸⠿⠀⠀⠀⠀⠀⠀⣠⣶⣤⣤⡂⠀⠀⠘⠛⠃⠀⠁⢀⣿⣀⠀⠀⠀⠼⢾⠳⠄⠐⠂⢤⣤⣜⣀⠸⢁⠀⢴⣵⣶⣷⣽⣾⡿⣌⠯
⣿⣿⣟⣿⠄⠁⠀⢀⡌⠁⣛⢉⣲⡭⢿⡋⠙⣥⣌⠀⣚⣿⣿⣿⣿⢳⣞⣙⡛⡍⣳⣳⠿⠶⠀⠀⠀⢠⣿⣿⣿⣿⣷⣤⣄⣐⠒⠀⠄⣔⡌⡭⠏⠘⠀⠀⠀⠀⠐⠌⣀⣷⣤⡶⠶⢾⣿⡉⠁⡜⠀⠉⣉⣻⣷⣶⢾⣼
⠆⠹⣶⣶⠅⠐⡉⠻⠓⠉⠁⠀⠉⠀⠰⣭⣀⡛⠫⠫⣹⣿⣿⠙⢻⣿⣿⣿⣶⣷⣷⣤⡀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠁⠀⠀⠀⣀⠀⠀⠐⠢⢠⣄⡤⣳⣹⣴⠤⡄⠬⢁⠈⠠⠦⣀⡙⣻⢰⣶⣦⣇
⣖⡷⡏⠙⣗⡀⠀⣄⠰⢿⡿⠖⠈⣠⣾⡭⠉⢩⣫⡌⠻⠟⠊⠐⠌⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠘⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠃⠀⢠⠈⣷⣦⢛⣻⣹⣟⡹⢷⡏⢶⣌⣏⣁⢾⣿⢟⣾⢸⣧⣵⡅
⢓⣑⣷⣧⡼⣇⡉⠃⠙⢏⣃⠰⠘⠀⡠⡀⢀⠀⣌⣁⠸⢆⠀⠀⢀⠙⣿⣿⣿⣿⣿⣿⣿⢿⠶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⡄⠀⠀⠀⡀⣀⠀⢼⣿⡿⠿⢻⣽⣧⣴⣾⢟⡿⠿⣝⢋⢽⢟⣀⠩⣴⡎⢽⢏
⣿⣶⡶⣠⣮⣻⡿⢇⠸⣿⣟⡻⠦⣤⠈⠃⡓⣚⣗⢴⣿⣛⣿⡣⣌⡑⠀⢉⣛⣛⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠖⠁⣐⣳⣤⣤⠀⠠⠅⢉⣙⡋⠹⣿⡏⠻⣿⠛⢿⡿⢿⡵⢟⡻
⢸⣿⣷⣶⣶⣿⡠⠲⣷⡂⣀⠈⠰⡷⡠⡀⣀⣘⠿⢳⣶⠻⢞⣿⡽⡟⣦⣼⣿⠚⢢⣿⣿⣿⣿⣿⣿⡟⠿⣿⣿⢻⣷⣥⣤⣶⣦⣄⢀⣤⠄⠀⠀⠈⣸⠹⠮⣿⣲⠿⣃⣀⣐⣀⣴⣷⢓⣉⣻⣸⣷⣷⣶⣅⣉⡤⢃⣀
⢸⣿⣿⣥⣭⣐⣠⡀⠀⣑⢽⣟⣿⡷⠚⠉⢿⢘⣲⣂⡋⠹⣭⣿⢇⡼⠆⣋⡻⣦⣻⣿⣿⣿⣿⣿⣿⣷⣄⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣍⠁⠀⠀⠐⠁⠉⣶⡟⢿⣶⠶⡻⢳⡛⡬⡆⣛⣿⠋⣻⣟⣿⢯⡫⢿⣿⠙⣎
⣞⠙⣿⡛⣿⣯⣯⠼⠀⣎⢏⣡⡼⢜⣶⡖⠐⠮⣢⠚⠈⠊⠉⠟⠛⡧⣬⣅⢾⡛⣻⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣦⠭⣻⣿⡷⠘⣷⣦⣦⠱⣴⣷⣼⡾⣏⢰⣝⣷⣄⣭⣿⣿⣿⣴⣿⣷⣿⣿
⣿⠀⣜⢯⣷⣷⡙⠁⠉⠯⢜⠷⠿⣛⠋⣨⡥⡖⢸⣿⡞⢄⣄⠳⣴⠨⢈⣩⣵⣿⣶⣦⣭⣽⣮⡭⣭⡓⢶⢿⠻⠃⠘⢿⣿⣿⣿⣿⣿⣿⢏⠗⢢⣬⡑⣃⣩⠻⠛⠡⣯⣻⢟⣷⡛⠻⠽⡶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢆⢀⢄⠘⠛⡛⢛⣟⠘⣔⣷⡿⢿⡯⡆⣲⣿⣷⡭⠠⣅⣀⣹⣆⢰⢻⣋⡿⡟⢷⡠⢐⠺⠤⣡⣵⣮⣏⠀⠄⠲⠒⠂⠂⢊⡙⠟⠛⣿⢻⢚⣥⣰⡧⣣⢛⡱⡀⠲⣶⣤⠈⣸⣟⠗⠀⣠⣈⠙⢛⠹⠋⡩⡄⠀⠊⡉⠍
⣀⠨⣿⠻⣷⠤⣙⠄⣠⣹⣦⣹⣽⣾⡿⡦⣝⣳⣿⡸⣉⣷⣿⣾⣴⢛⠟⡇⡽⢿⢾⢸⢳⢶⣶⣢⠁⠚⢀⡔⠚⠹⡆⣎⣶⠙⣿⣿⣿⠁⠊⠀⢨⡁⡁⠩⢭⣻⣍⣥⣝⡋⠉⢁⣀⠀⣈⡙⠃⠂⠀⠁⣠⣴⠀⠀⣿⣷
⠛⠿⢿⣴⣶⣌⠿⣿⣋⡈⣻⡿⠋⢿⣿⠿⠻⠛⢳⣫⣅⡢⡉⣽⠛⢩⠩⡻⠆⠾⠊⠇⡉⠩⢙⣧⣦⣦⡬⠽⠃⢴⣞⢔⠹⢤⣿⣿⣿⠰⡖⣛⣷⣷⢧⢲⢞⣯⢊⣠⣿⣟⠫⢿⡥⢁⠒⠒⠪⡄⢁⡨⡙⠩⣠⠀⠻⠏
⡀⣀⢀⣿⣿⣽⣿⠙⠍⠈⢠⢪⢠⠊⣁⢿⣶⣦⣤⣹⣯⣭⣵⣿⣼⡾⣷⣓⡳⠰⣴⣂⠑⡠⢈⠛⣾⣨⣢⢼⣀⣈⢡⠑⢀⢸⣿⡿⢗⠄⣚⡹⢿⣿⣒⣴⡌⣽⣦⣽⣟⣿⣧⣛⣉⢢⣴⢪⢄⣴⣦⠺⠅⠀⡊⡀⠀⠄
⣿⣐⣣⣁⡉⡍⢂⡈⢒⣥⣎⠘⣿⣟⣇⣸⣊⣳⡀⣤⢢⡹⣿⠭⢟⡙⢯⢝⣻⣡⡤⠯⢁⡰⡔⣥⣽⢿⢍⢣⣬⣉⡛⠿⡄⢉⢿⢳⣹⣶⢈⠍⢍⣉⣭⣀⣏⣙⡛⢹⣿⣭⣿⠁⢿⡙⢶⣿⣶⡌⠋⠀⠀⠀⠤⠄⣀⠀
⣳⣿⡽⢿⣯⣧⡀⢈⣽⣿⡂⢷⠈⣿⣿⡿⢽⣴⣷⣆⣬⣉⢿⣎⣻⠷⣿⣛⡿⠿⣭⣛⣎⠹⣳⢆⠰⠜⢿⡋⠀⠘⠦⢭⣷⢆⣶⡿⣐⡟⡴⣿⠒⠚⠻⢏⣾⠿⣿⡿⣺⣿⣿⣷⡽⣿⣿⣾⡋⠀⠀⠀⠀⠀⠀⣄⠀⠀
⡔⣾⣾⢷⣿⣿⣷⢠⣽⡾⡿⢿⣷⠯⡻⢿⠗⣽⣿⣿⣿⡇⠀⠀⠻⠾⢿⣏⣿⣋⣟⢾⣴⡦⠈⢭⠃⠀⠈⣿⡄⠲⡦⢴⣹⣇⠄⠳⡾⡭⣌⠟⠂⢹⡷⣿⡿⢖⠝⢛⣮⡻⣏⢤⠉⠋⠙⢿⣧⣀⠀⠀⠀⠀⣤⣾⣶⣦
⢘⣸⣿⣤⣭⣏⢻⣄⣣⠜⢻⣿⣿⣉⡺⣿⡿⢿⡿⠉⠩⣁⠄⠀⠐⠛⣯⣽⡮⣧⣾⣬⢈⣿⣿⡐⠶⢻⣮⣥⣿⡄⠀⣀⡚⠗⠳⢈⢱⡤⠾⣠⣾⣿⣯⣾⣶⣼⡲⣿⣿⣿⢛⡲⣦⠀⠀⣪⣞⣹⠀⠀⠄⠸⣿⣿⣿⣿
⢀⠨⣍⣭⢻⡿⣼⣷⢭⠦⢽⣿⣻⣿⡻⠛⣡⣀⡶⡬⡆⢝⣖⣂⠀⣤⣶⢽⡿⣿⣻⣽⣇⢨⠛⡞⠂⠈⠿⣿⣯⡿⡀⣈⡕⣰⠐⢺⣄⠓⣿⣿⡟⣿⣋⢚⣺⣭⡝⣽⣿⡫⠠⢙⣠⣀⣚⣛⠻⢷⡧⠗⠊⣀⡉⠛⠿⠿
⣉⠈⣏⢱⣑⢀⡬⢋⣈⣌⣼⢿⡷⡽⠿⣬⣾⣯⣿⣷⣻⣿⣯⡇⣈⣬⡽⠿⢖⠛⠛⠃⠊⠀⠐⣣⢭⣶⡇⠛⢷⣧⣰⣖⣧⣫⣿⣨⣟⠐⡻⣍⣄⢽⠑⠾⠥⠔⠸⣿⡿⢾⣿⣿⣿⣿⣿⣏⢚⣇⣅⢺⣯⣴⠉⢈⠀⠀
⡟⠛⢻⣟⡿⢿⡛⣛⣻⣟⣧⣿⣿⣿⣾⣥⣿⡻⣿⣿⣿⠛⢿⢿⠈⣌⣄⢄⣘⡿⠠⢦⢀⣴⣐⣴⣶⢐⡟⣿⠀⠟⠯⢉⡄⠹⣿⠏⠀⢤⣼⡿⠎⠷⠆⡔⠓⠁⢻⠄⢃⠇⢉⡿⠿⠿⢿⣻⣿⣽⣍⡈⠛⠿⠷⠤⠠⣶
⠀⣤⣄⣀⣼⢯⣿⡽⣷⣨⡄⣓⢒⡂⣡⡄⠈⡁⠀⠀⢡⣾⡶⠟⠟⠀⠀⠽⠇⢩⠀⣁⣿⣿⡆⠻⣿⡤⠟⡀⣵⣟⣙⣿⣿⣷⣦⣕⢞⣾⣿⣿⢹⣯⣿⣿⣿⣿⡟⣾⡷⣾⡿⡟⣽⡕⢀⣰⣆⠀⢠⣿⣿⣿⠉⠁⠀⠀
⣦⣿⡵⡆⠐⠢⠟⠨⠏⢟⠍⠠⢍⠅⠀⡀⠙⠬⣴⡀⠾⢿⠿⣖⣧⡠⢶⡶⣧⡏⠟⠳⢭⡗⡖⠊⠏⠛⠗⠖⠥⠄⣿⣿⢯⣽⣿⣿⠦⡟⠿⡿⡿⠭⠽⠛⢁⢹⠄⠀⠀⠀⠀⠂⠋⠀⠢⠭⠁⠘⠹⣾⢍⠍⣵⡲⠤⣮
⠁⣼⡄⠋⠀⠀⠀⠀⠀⠨⠀⠀⠀⠁⠠⣶⠄⠀⠝⡁⠀⠀⡴⣿⠛⠒⠀⠀⠼⠉⠄⠀⢰⢭⡀⠀⠀⠐⠆⠀⠠⢂⠅⣠⣄⣈⣻⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⠠⠀⠀⠀⣁⡘⠂⢠
⣀⣤⣷⣾⡿⠄⢀⣠⣤⣤⢀⠀⠀⠀⠀⡫⠄⠀⠀⠀⠠⣾⣿⣿⡷⠦⠀⠀⠀⢀⠀⠀⢨⡜⠀⠈⠀⠀⢰⠃⠠⠰⣼⣿⣿⡏⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⣶⣦⡀⠀⠀⠁⠄⠘⠁⠀⠠⣑⣶⣟⠛
⡞⠿⠷⡫⠿⠇⠈⠛⢿⣿⣧⡀⠄⠀⠀⠀⠀⠀⠈⠀⠀⠽⣷⣶⣤⡖⠀⠀⠀⠈⠂⠀⠈⠀⠀⠀⠀⠀⠈⢂⠀⠐⠟⠋⠋⠀⠀⠀⠀⠀⣤⣄⣤⠀⠀⠀⠀⠀⠀⡤⢠⣼⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⣶⢉
⣀⡤⠀⠀⠀⠁⠀⠀⢭⠷⣯⣀⡁⡴⡀⠀⠀⢀⣈⡀⠀⣤⢾⠏⠈⠉⠄⠠⠖⠀⠀⢠⡄⠀⠀⠠⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠰⣟⠉⠉⠀⠀⠀⢀⡁⣐⣄⣤⣥⡀⣄⡀⠀⠀⢀⠀⠀⠄⠀⠀⠈⢁⡉⣞⠊
⣴⣅⠀⢠⣬⢂⠀⠀⠀⠀⣬⣀⣐⢾⣶⢄⡀⠀⠈⠀⣀⠝⢋⣴⣿⣧⡀⣶⣿⢏⢁⡌⠅⠀⠀⠀⠀⠀⠀⠐⠀⠀⢠⠀⠀⣠⣴⣦⠈⠀⣁⢡⢀⠄⢀⠄⢀⢿⡟⠛⠛⢻⠾⣷⣄⠀⠐⢚⠀⠀⠀⣰⣔⡾⢛⣙⠀⣐
⡿⡻⣵⠼⠿⣿⡄⠀⠉⠶⠘⡙⠺⣿⢯⣿⣷⣲⡀⠀⠉⢭⣼⣿⣿⣿⢠⡏⠙⡿⣸⠷⠀⠀⠀⠀⠀⠀⣤⣶⣦⣤⡂⠀⠀⠘⠻⠃⠀⠀⢀⣹⡀⠀⠀⠀⠬⢺⠳⢄⠀⡂⢤⣤⣜⣀⠸⢁⠀⢴⣷⣶⣷⣽⣾⡿⣌⠭
⣿⣿⣟⣯⠆⠁⠀⢀⡌⠁⣛⢉⣲⡭⢿⡋⠙⣧⣄⠀⣚⣿⣿⣿⣟⢳⣞⣙⡛⡭⣓⠳⠦⠆⠀⠀⠀⢸⣿⣿⣿⣿⣷⣾⣿⣶⣦⣄⠀⡐⠄⠤⠋⠚⠀⠀⠀⠀⠀⠜⣀⣷⣤⡶⠶⢾⣿⡉⠁⠜⠀⠍⣉⣿⣷⠶⢾⣾
⠂⠹⣷⣶⠅⠀⣙⠻⠃⠉⠁⠀⠁⢀⠰⣬⣁⡛⠫⠋⢹⣿⣿⠙⣻⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠁⠀⠀⠀⣀⠀⠀⠐⠢⢠⣤⡤⣳⣹⣴⠤⡄⠬⢡⠈⠀⠂⣀⡙⣿⢱⣶⣦⣇
⣶⡿⡏⠙⢷⣀⠀⣄⠰⢿⡿⠖⠈⣠⣾⡬⠁⢩⣫⠌⠹⠟⠊⠐⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⢰⣴⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠇⠀⢀⢈⣵⣦⠛⣛⣻⣟⡹⢷⣇⢶⣌⣏⣁⢬⣿⢽⣶⢸⣧⣰⡅
⢙⡉⡷⣧⡼⣗⡉⠋⠙⢏⣃⠰⠘⠀⡀⡀⢀⠀⣨⣁⠸⢆⡀⠀⢘⠿⣿⣿⣿⣿⣿⣿⢿⠿⠶⢶⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⠿⠟⠀⡄⠀⠀⠀⡈⠀⠀⢼⣿⣿⠿⢻⣼⣧⣴⣾⢟⡿⠿⣟⢛⢽⢟⣀⠉⣴⡎⢝⢏
⣿⣶⡶⣠⣮⣻⡿⢇⠰⣿⡿⡻⠶⡤⡈⠇⣓⣚⣓⣴⣾⣓⣿⣳⣌⡑⠈⠉⡙⢋⢭⣼⣿⣿⣿⣷⣿⣿⣿⣿⣿⣇⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠖⠁⡐⣳⣥⣤⠀⠠⠅⠉⢉⡋⠹⣿⡟⠻⣿⠻⢿⡟⢻⡷⢟⠻
⢸⣿⣷⣶⣶⣷⡧⠲⣷⡂⣅⡈⡠⡷⡨⡀⣀⣘⡿⢷⡦⡛⢞⣿⣽⣟⠦⣴⣿⠘⣾⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⠿⣿⣔⣠⣤⣤⣄⣀⣴⠄⠀⠀⠀⣐⠘⢯⣟⣶⠗⢃⣀⡐⢀⣴⣶⢃⣉⣻⣸⣷⣳⣶⣁⣁⠤⢃⣀
⠸⣿⣿⣧⣭⣙⡠⡀⠀⣘⢽⣟⣿⡿⠊⠈⢻⢘⣲⣢⣋⠹⣭⢻⢇⡸⢇⣋⡻⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⣾⣿⠀⢿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠐⠉⠈⣶⡟⢿⣾⠶⡫⢳⡛⡌⡆⣉⣿⠋⣻⣟⣿⢿⡯⢿⣿⠙⣋
⣚⠙⣿⣛⢿⣯⣭⠼⠁⣌⣏⡡⡌⢜⣴⡖⠐⠬⣢⠚⠈⠊⠈⠟⢙⡆⣬⣅⢺⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⡴⡉⣿⡷⠘⣷⣦⣦⠱⣴⣧⣾⡿⣏⢰⣝⣷⣄⣿⣿⣿⣿⣴⢿⣟⣿⣿
⣿⠂⣜⢯⣷⣿⡙⠃⠉⠏⢜⠺⠿⢛⠋⣨⡥⠴⢚⣿⡞⢄⣄⠳⣾⢠⢈⣩⣵⣻⣒⡦⣭⣿⡭⡭⡭⡃⢶⢿⠛⠁⠘⢿⣿⣿⣿⣿⣿⣿⣿⡷⢢⢠⡀⢃⣭⠻⠛⠠⣯⡻⢟⣷⡛⠻⠿⡶⣿⣿⣿⣿⣿⣿⣻⡿⣿⣿
⠆⢀⠤⠘⢛⡛⢻⣷⡰⣶⡷⡿⢿⡏⡇⣲⣿⣷⡯⠠⣅⣀⡹⣆⢰⢻⣍⡿⡟⢻⡁⢴⠻⠤⣡⣴⣮⣇⠁⠆⠲⠒⠂⠀⢛⠟⠿⢿⣿⠿⢛⣭⣰⡧⣣⢛⡱⡀⠲⡲⣤⠈⣸⣟⠖⠀⣠⡈⠙⠋⠸⠋⡩⡄⠀⠎⡉⠝
⣀⢨⢿⡻⣷⢴⣙⠀⣠⣹⣦⣙⣭⣾⡿⡦⣌⣲⣾⡼⣬⣷⣷⣾⣴⣓⠟⡇⡼⠿⢾⢼⢑⢶⣶⡢⠁⠚⢀⣖⡚⠡⡆⣎⣶⠑⣿⣿⣿⠁⠘⠀⢩⡁⡁⠩⢩⣳⣍⣥⣟⡋⠉⢀⣀⠀⣈⡙⠃⠂⠀⠁⣠⣰⠀⠀⣻⣿
⠻⠿⣿⣴⣶⣤⠿⣿⣉⡘⣿⠿⠃⢻⣿⠾⡻⠛⢇⣫⣥⡦⣁⣽⠛⢫⠹⡻⠧⠺⠋⠇⠌⠉⢙⣣⣤⣆⡬⠽⠃⢤⣞⢖⠺⢤⣿⣿⣿⠰⡒⣓⣷⣿⣧⢐⢆⣿⢊⣠⣿⣓⠫⠽⡡⢀⠒⢒⠪⡄⢁⡈⠙⠩⣠⠀⠻⠋
⠀⣀⢀⣿⣿⣿⣿⢙⠍⠈⢠⣪⢠⢎⣁⢿⣶⢶⣤⣵⣭⣭⣴⣿⣌⣾⣷⣓⡓⠰⣤⣂⠙⠄⢈⠋⣾⣱⣐⣼⣀⣀⣡⡑⢂⢸⣿⡿⢇⠄⣛⡹⢿⣿⣒⡴⣌⣼⣦⣿⢟⣿⣥⣛⣀⢢⣶⣪⢀⣴⣆⠢⠄⠀⡊⠀⠀⠀
⣿⣐⣣⣁⡋⡍⢀⡈⠓⣥⡜⠘⣿⣋⡧⣨⣊⣹⡄⣤⢢⡹⢿⠯⢟⡙⢏⢜⣹⣱⡤⠭⠁⡴⡌⢁⡿⢿⣌⢣⣌⣉⡛⠿⡄⠈⠿⢷⡹⣶⢈⠍⠌⣙⣭⣄⣏⣙⡋⢹⣿⣽⣿⠁⢾⠑⠢⣝⣶⡌⠉⠀⠀⠀⠠⠄⠀⠀
⣳⡽⡽⢿⣍⣧⡀⢈⣥⣿⡂⢧⠀⣿⡿⡿⢽⣴⣷⣶⣬⣨⢿⣇⣻⠿⢿⣛⡿⣿⣯⣉⢋⠹⣳⣦⠠⠘⢿⡏⠀⠘⠦⢭⣷⣆⣴⡿⣸⡟⡴⣿⠐⠞⠻⢯⣾⠿⣿⡿⣺⣿⢿⣵⡽⣿⣿⡿⡋⠀⠀⠀⠀⠀⠀⣄⠀⠀
⡔⣶⣾⢻⣿⣿⣷⡠⣽⣶⣿⣿⣷⠯⡛⢿⢗⣿⣿⣿⣿⡇⠀⠀⠻⠾⢿⣏⣿⣋⣛⢺⣴⡆⠀⠭⠃⡀⠀⣿⡄⠲⡶⠶⣽⡇⠀⣳⡾⡍⣌⡟⠂⢹⡷⣿⡿⢶⠟⣋⣾⠛⣏⢄⠈⠋⠙⢿⣮⣀⠀⠀⠀⢀⣴⣶⣶⣶
⢘⣾⣿⣤⣭⣯⢹⣆⣱⠼⢻⣿⣿⣉⣺⣿⡟⢿⡿⠍⠹⣀⠀⠀⠐⠙⣯⣾⡦⣧⣼⣮⢀⣾⣿⡒⠶⢻⣮⣿⣽⡆⠀⣠⡚⠟⠓⢈⢱⡤⠹⣠⣿⣿⣿⣾⣶⣼⣲⣿⣿⣿⢛⡲⣦⠀⠀⣪⣖⢹⠀⠄⠄⠘⣿⣿⣿⣿
⢀⠨⣭⣍⣉⡿⣼⣧⢭⠦⢽⣿⣻⣿⡻⢛⣡⣀⡶⡠⡆⢝⣗⣂⢀⣦⣶⢝⠿⣿⣿⣿⣆⢌⠟⡞⠃⠈⠟⣽⣫⡿⡀⣈⣔⣐⡀⢹⣆⠑⣿⣿⡿⣽⣟⢘⣈⣭⡝⣭⢿⡋⠠⢙⣠⣁⣘⣙⢣⠷⣧⠗⡊⢀⡈⡛⠿⣿
⣁⠈⣿⢹⣘⢀⠬⢙⣈⣴⣾⣿⡳⡽⠯⣼⣾⣿⣿⣷⣻⣿⣿⡇⣈⣌⡝⡟⢖⠚⠛⠋⠈⠀⠘⣣⣽⣷⡆⠛⢷⣧⣸⣶⣷⣫⣿⣠⢷⡼⠻⣝⣄⠿⠁⠾⠡⠔⠸⣿⡿⢶⣾⣿⣿⣿⣿⣏⢚⣇⣅⢸⣦⣤⠈⢐⠀⠉
⡟⠛⢻⣟⡿⢿⣛⣛⣻⣟⣧⣿⣿⡿⣾⣥⣿⡻⣿⣿⣿⠛⢿⢿⢈⣌⣤⠄⣘⠿⠐⢧⢀⡴⣘⣴⣶⢀⡟⡿⠀⠚⠯⢩⡔⠹⢿⠯⠀⢀⣼⡿⠈⠳⠂⡄⠓⠂⢳⠀⢃⠇⣈⡿⠿⠻⢿⣻⣿⣿⣍⡈⠛⠿⠇⠠⠀⣿
⠀⣤⣄⢠⣼⢯⣿⡽⣷⣩⡌⣓⢒⡂⣡⡄⠈⡁⠀⠀⢡⣶⡶⠟⠟⠁⠂⠽⠇⢩⠀⣁⣾⣿⡦⠻⣟⡦⣟⡀⣶⡟⣙⣿⣿⣷⣦⣱⣞⣿⣿⣿⢹⣯⣿⣷⣿⣿⣿⢾⡗⣾⡿⠟⣿⡕⢀⣰⣦⠀⢠⣿⣿⣿⠉⠁⠀⠈
⣢⣿⡕⡆⠐⠢⠟⠨⠏⢿⠉⠤⢍⠅⠀⡁⠍⠬⣵⡀⠿⢿⠿⣶⣷⡠⢶⡶⣧⡛⠿⠷⢬⡗⡖⠂⠏⠛⠟⠞⠥⠄⣿⣿⢯⣽⣿⣿⠦⡟⠿⡿⡿⡯⠽⠛⢁⢸⠄⠀⠀⠀⠀⠂⠋⠀⠂⠭⠉⠘⠹⢾⢍⠏⡷⡳⠬⣮
⠁⣼⡄⠃⠀⠀⠀⠀⠀⠨⠀⠀⠀⠁⠀⣶⠄⠀⠝⡁⠀⠀⡴⣿⠛⠢⠀⠀⠔⠉⠌⠀⢸⢭⡀⠀⠀⠐⠎⠀⠠⢂⠅⣠⣄⣈⢻⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⠠⠀⠀⠀⣁⡘⠀⢢
⢀⣤⣷⣾⡿⠄⢀⣠⣤⣤⢀⠀⠀⠀⠀⢫⠄⢀⠀⠀⠠⣾⡿⣿⡷⠶⠀⠀⠀⠀⠀⠀⢈⡜⠀⠈⠀⠀⢰⠂⠠⠰⣾⣿⣿⡏⠁⠀⠀⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣠⣬⣶⣦⡀⠀⠀⠁⠄⠘⠁⠀⠠⣠⣾⣿⠛
⡞⠿⠿⠋⠻⠇⠈⠛⣿⣿⣧⡀⠄⠀⠀⠀⠀⠀⠈⠀⠀⠽⣷⣴⣤⡶⠀⠀⠀⠈⠂⠀⠈⠀⠀⠀⠀⠀⠈⢂⠀⠐⠟⠋⠋⠀⠀⠀⠀⠀⣤⣄⣤⠀⠀⠀⠀⠀⠀⡤⢠⣼⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣛⣧⣴⢉
⠀⡴⠀⠀⠀⠁⠀⠁⢻⠷⣯⢀⡁⠴⡀⠀⠀⢀⣀⡀⠀⣤⢾⠏⠈⠉⠄⠠⠶⠀⠀⠠⡄⠀⠀⠠⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠰⣟⠉⠉⠀⠀⠀⢀⡀⣘⣄⣀⣥⡀⣄⠀⠀⠀⢀⠀⠀⠤⠀⠀⠉⢁⡋⣼⠊
⢴⣝⠂⢠⣴⢂⠄⠀⠀⠠⣭⣀⣐⣾⣶⢆⡀⠀⠈⠀⣀⠝⠋⣴⣿⣧⡀⣶⣾⢋⢁⡌⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⣠⣴⣦⠈⠀⡁⢡⢀⠀⢀⠄⢀⢚⡟⠛⠛⢻⠾⣷⡄⠀⠐⢚⠀⠀⢀⣶⣴⢾⢉⣉⠈⣘
⣿⣻⣷⡼⠿⣿⡄⠀⠉⠶⠘⡙⠺⣿⢯⣿⣿⣲⡀⠀⠉⣭⣼⣿⣿⣿⠐⠏⠉⠿⠼⠖⠀⠀⠀⠀⠀⢀⣴⣶⣦⣤⠂⠀⠀⠙⠛⠏⠀⠁⢀⢼⡀⠀⠀⠀⠬⢾⠱⡆⠐⡂⢤⣤⡘⣀⠸⢁⠀⢴⣷⣶⣷⣽⣼⡿⣌⠯
⣿⣿⣟⣻⡆⠅⠀⠀⡬⠅⣛⠋⣲⡽⢿⡋⠙⣦⣌⠀⣘⣿⣿⣿⣟⢳⣞⣙⣛⡍⣓⠲⠦⠆⠀⠀⠀⢸⣿⣿⣿⣿⣧⣴⣶⣶⣦⣄⡀⣔⠄⡠⠍⠚⠀⠀⠀⠀⠔⠌⣀⣷⣤⡶⠶⢾⣿⡉⠁⠜⠐⠍⣉⣿⣷⠶⢾⡼
⠆⠹⣷⣶⠅⠐⡉⠻⠓⢉⠁⠀⠃⢀⠰⣭⣀⡛⠫⠩⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠈⠀⣀⠀⠀⠐⠢⢠⣤⡤⣳⣹⣴⠦⡄⠬⢱⠈⠀⠢⠀⡙⣻⢰⣶⣦⣍
⣶⣿⣯⠹⣗⡀⠀⣄⠠⢻⡿⠖⠈⣰⣾⡭⠁⠩⡫⡌⠻⠟⠊⢿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⢰⣴⣿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠁⠀⢠⠉⣷⣦⣛⣻⣿⣟⡹⢷⣇⢶⣜⣏⣁⢬⣿⢝⣾⢺⣧⣷⡇
⢟⣙⡷⣧⡼⢗⡉⠃⠙⢏⣃⠰⠘⠀⡀⡀⢀⡀⡨⣁⡸⢆⡀⠈⢻⣿⣿⣿⣿⣿⣿⣿⡿⠿⠷⢶⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠿⡅⠀⠀⠀⡈⠀⠀⢼⣿⡿⠿⢻⣽⣧⣴⣾⢟⡿⠿⣞⢛⢽⢏⣀⠩⣴⡎⢽⢏
⣿⣶⡶⣠⣦⣻⡿⢇⠰⣿⡿⡟⠶⣤⡌⠇⣓⣚⣓⣴⣆⣓⣿⡓⣌⡙⠉⠉⡉⣉⢷⣬⣽⣴⣦⣤⣾⣿⣿⣿⣿⣷⡀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠁⠖⠀⣐⣳⣤⣤⠀⠠⠅⠉⢉⡋⠹⣿⡏⠻⣿⠻⠟⡟⣿⡽⢟⠻
⢸⣿⣷⣶⣶⣿⡷⠲⣷⣆⣅⡈⠠⡷⡨⡀⣀⣘⡟⢷⡦⠏⢞⣽⡍⡟⠶⣴⣿⢸⣾⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣷⣤⣀⣀⣀⣀⣀⣤⠄⠀⠀⠀⣐⠸⠬⢝⡢⠿⢂⣀⡐⣀⣴⣷⢃⣉⣻⣸⣷⣷⣶⣇⣅⡤⢁⣀
⠸⣿⣿⣯⣭⣙⡠⡀⠀⣘⢿⣟⣿⡿⠊⠉⣿⢰⣲⣢⣋⠵⣯⣿⢧⡸⠅⣋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⣽⣿⠀⢹⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠐⠁⠈⣶⡟⣽⡾⠶⡺⢻⡛⡌⡆⣙⣿⠋⣻⣟⣿⢯⡻⠿⣿⢉⣊
⣞⠙⣷⡻⢿⣯⣭⡼⠀⣬⣏⡡⡼⣜⣴⡶⠔⠮⣢⠚⠈⠊⠈⠟⢙⡧⣬⣥⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣺⣿⣿⣿⣿⣿⣿⣿⣿⣆⡉⢿⡷⡘⣷⣦⣦⠰⣤⣧⣾⡻⣏⢰⣝⣷⢤⣿⣿⣿⣾⣴⢿⣷⣿⣿
⣿⠀⣞⣯⣷⣷⡙⠃⠙⠏⢼⠷⠿⣛⠏⡨⡥⠶⢘⣿⡞⠄⣤⠳⣾⠨⢌⣩⣽⣻⣛⡿⢿⣿⡍⡭⡭⡗⢶⠿⠛⠁⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣨⡁⢃⣭⠻⠛⠡⣿⣻⢛⣗⡛⠻⠿⡶⣿⡿⣿⣿⣿⣿⣿⣷⣾⣿
⢆⢀⠄⠈⠛⡛⢻⣿⡐⣖⡷⡻⠿⣯⡶⣲⣿⣿⡮⠤⣅⣄⣹⠆⣠⣺⣏⡿⠟⢿⡥⢶⠻⠤⢡⣴⣮⠫⠁⡆⠒⠒⠒⢀⢹⡻⢿⣿⣿⣿⢿⣯⣰⡧⣣⢚⡱⡀⠒⠖⣤⠀⣸⣟⠶⠀⣠⡈⠙⠋⠸⠋⡩⡄⠀⠊⡉⠍
⣀⠨⣿⡻⣷⢤⣉⠤⣠⣸⣦⣸⣭⣾⣷⣦⣬⣺⣾⡽⢬⣿⣧⣾⣔⣟⠟⡧⡼⠿⢾⢰⢳⢶⣶⣢⠁⠚⢀⣖⡊⠲⡖⣆⣲⠙⣿⣿⣿⠂⠊⠀⢩⡁⡁⠩⢭⣻⣍⣥⣝⡋⠉⢀⣀⠀⣈⡙⠃⠂⠀⠁⣠⣰⠀⠀⣯⡷
⠛⠿⢿⣵⣶⣄⡿⣿⣍⡈⣿⠿⠏⢻⣿⢿⡫⠛⢷⣯⣅⡶⣈⣽⠛⢫⠺⡻⠧⠺⠋⠏⡌⠉⢙⣷⢦⣦⡬⠽⠃⠤⣞⢗⠸⢴⣿⣿⣿⠰⡞⣛⣷⣿⢧⢐⢎⣧⢎⣤⣿⡓⠯⠿⡥⢁⠒⠒⠠⢄⣀⠈⠙⠨⣠⠀⠻⠋
⢀⢀⣀⣿⣿⣽⣿⢛⠍⠈⢡⢪⢠⡎⢁⢿⣶⢶⣤⣱⣭⣭⣷⣿⣬⣞⢷⣓⣣⠘⣴⣚⠙⠰⢈⠋⣾⣰⣲⣼⣄⣀⣡⡑⢢⢹⣿⡿⢗⠄⣛⡹⠽⣿⣚⣴⣌⣬⣦⣿⣟⣿⣤⣛⣈⢢⣶⣪⢄⣴⡆⠨⠀⠀⡈⡀⠀⠄
⣿⣐⣣⣁⡋⡍⢀⡈⢗⣥⡼⡘⣿⣻⡧⣸⣚⣻⡄⣤⢦⡹⢿⠯⣏⡙⢯⢝⣹⣵⣤⠬⠁⡴⡌⢁⡿⢿⣌⣥⣎⣩⡛⠿⡄⢉⢿⣽⣹⣶⢘⡍⠌⣙⣭⣄⣏⣙⡋⢹⣿⣽⣿⠁⢿⡙⠠⣬⣷⡌⠉⠀⠀⠀⠤⠄⠀⠀
⢳⡽⡽⢿⣯⣧⡀⢈⣯⣾⣃⣷⠈⣿⣿⣿⢽⣾⣿⣶⣬⣌⢿⣎⣻⠿⢿⣛⣷⢿⣭⣩⢎⠹⣳⣤⠰⠎⢽⡋⠀⠜⠮⠭⣷⢇⣴⡿⡥⡟⡰⣿⠒⡊⠻⢧⣾⠿⣟⡿⣺⣿⣿⣵⡿⣿⣿⡿⡁⠀⠀⠀⠀⠀⠀⢀⠀⠀
⠄⣶⣾⢷⣿⣿⣷⡠⣽⣶⣿⣿⣿⠿⡛⢿⣗⣿⣿⣿⣿⡇⠈⠀⢻⠶⢿⣏⣿⣏⣙⢺⣶⡆⠀⢭⠂⡀⢀⣿⡔⠲⡶⢶⢟⣇⠄⡳⣾⠭⣤⠏⠃⢹⡷⣿⡿⢶⠟⣛⣮⡟⣏⢄⠈⠋⠙⢿⣆⣀⠀⠀⠀⢀⣴⣾⣶⣶
⢘⣾⣿⣤⣭⡯⢹⣆⣱⠼⢻⣿⣿⣍⡘⣿⡝⢟⡿⠉⡩⣀⠀⠀⠔⠙⣯⣼⡮⣧⣼⣮⢈⣿⣯⡐⠾⢿⣮⣷⣿⡄⠀⣠⠚⠟⠓⢈⢱⣬⢛⣤⣿⣿⣎⣾⣶⣜⡳⣿⡿⣿⠛⡲⣦⠀⠀⣪⣞⣹⠀⠀⠄⠘⣿⣿⣿⣿
⣀⠨⣭⣍⣉⡿⣼⣷⢭⠦⢽⣿⣻⣿⡻⢛⣡⣄⣦⡭⡦⢽⣗⣂⠀⣦⣶⣝⡿⣿⣳⣭⣆⠬⠛⡞⠃⠈⠟⣿⢫⡿⡀⣊⣅⣼⠐⢻⣅⡛⣿⣿⡻⣽⣟⠘⣊⢩⡝⡭⣿⠫⠠⢙⣠⣅⣘⣉⠳⠳⡇⠓⠈⢀⡈⠹⣿⣿
⣁⠨⡿⢹⣐⢀⡬⢛⣨⣴⣼⣿⡷⡽⠿⣤⣿⣿⣿⣗⢹⣿⣿⣟⣈⢘⡽⠟⢖⠚⠛⠃⠈⠀⢘⣁⣬⣷⡆⠙⢷⣯⣴⣶⣷⣫⣿⣨⣿⡾⠻⣅⣄⠼⠁⠼⠠⠄⠨⡿⡿⣾⢺⣿⣿⣿⣿⣏⢛⣇⣅⢸⣢⡈⠉⢀⠈⠛
⡟⠛⢻⣟⡿⢿⣛⣛⣻⣟⣧⣿⣿⣿⣾⣭⣿⡻⣿⣿⣿⣛⢿⢟⢈⣈⣤⠄⣘⠿⡂⢧⡀⡴⣰⣴⣶⢀⡟⡳⠘⠿⠯⢨⡄⠹⢿⠯⠈⢀⣼⡿⠈⠷⠂⡄⠓⠂⠚⠐⠃⠇⠈⠾⠿⠻⢿⣻⣿⣿⣄⡈⠛⠿⠅⠀⠠⣷
⠀⣤⣄⣠⣼⢯⣽⠭⣿⣩⡄⣓⢒⡢⣡⡄⠈⡁⠀⠀⢡⣶⡶⠟⠟⠁⠂⠽⠧⢩⡀⣁⣾⣿⡦⠻⣿⡦⡟⡀⡿⣟⣙⣿⣿⣷⣦⣵⣞⣾⣿⣿⢹⣯⣿⣷⣿⣿⡿⢾⡗⣾⡿⠟⣿⡕⢀⣰⣦⠀⢠⣷⣿⣿⠉⠁⠀⠀
⣢⣿⡵⠆⠀⠲⠞⠨⠏⢟⠭⠤⢍⠅⠀⡁⠍⠬⣴⡀⠾⢿⠿⣶⣷⡠⢶⡶⣧⡟⠿⠷⢭⡗⡖⠂⠏⠺⠟⠞⠱⠄⣿⣿⢯⣽⣿⡿⠦⡟⠿⡿⡿⡭⠽⠛⢁⢸⠄⠀⠀⠀⠀⠒⠋⠀⠂⠯⠁⠐⠹⢮⢭⠍⣷⡲⠬⣮
⠁⣬⡄⠃⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⣶⠄⠀⠝⡁⠀⠀⡴⣿⠟⠚⠀⠀⠔⠉⠌⠀⢰⢭⡀⠀⠀⠐⠆⠀⠠⢂⠅⣠⣄⣈⣻⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⠠⠀⠀⠀⣁⡙⠀⢢
⣀⣤⣶⣾⡿⠂⢀⣠⣥⣤⢀⠀⠀⠀⠀⣫⠄⠀⠀⠐⠠⣾⣿⣿⡷⠶⠀⠀⠀⢀⠀⠀⢠⡜⠀⠈⠀⠀⢐⠂⠀⠰⣼⣿⣿⡏⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣬⣶⣦⡀⠀⠀⠁⠄⠘⠁⠀⠀⣠⣞⣟⠛
⡞⠿⠿⠋⠻⠇⠈⠛⢿⣿⣧⡀⠄⠀⠀⠀⠀⠀⠈⠀⠀⠽⣷⣴⣄⡒⠀⠀⠀⠈⠂⠀⠈⠀⠀⠀⠀⠀⠈⢂⠀⠐⠟⠋⠋⠀⠀⠀⠀⠀⣤⣄⣤⠀⠀⠀⠀⠀⠀⡤⢠⣼⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⣧⣴⢈
⡠⡴⠀⠀⠀⠁⠀⠀⢻⠷⢯⣀⡁⠴⡀⠀⠀⠀⣀⡀⠀⣤⢾⠇⠈⠉⠄⠠⠶⠀⠀⠀⡄⠀⠀⠠⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠰⣟⠉⠉⠀⠀⠀⢀⡀⢐⣄⣠⣥⡀⣄⠀⠀⠀⢀⠀⠀⠄⠀⠀⠉⢁⡋⣼⠚
⢴⣅⠂⢠⣴⣂⠀⠀⠀⠠⣬⣀⢀⣿⣶⢄⡀⠀⠈⠀⣀⠝⢋⣴⣿⣧⡀⣴⣿⢋⢁⡌⠅⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣠⣰⣦⠈⠀⣁⢡⢀⠀⠀⠄⢀⢚⡟⠛⠛⢻⠾⢷⡄⠀⠐⢚⠀⠀⢀⣶⣴⠾⢛⣙⠈⣘
⣿⡻⣷⠼⠿⣿⡄⠀⠉⠶⠘⡙⠺⣿⢯⣿⣿⣲⠀⠀⠈⣭⣼⣿⣿⣿⠀⠏⠉⠿⠰⠔⠀⠀⠀⠀⠀⢀⣴⣶⣦⣤⡂⠀⠀⠘⠛⠋⠀⠁⢀⢺⡀⠀⠀⠀⠬⢨⠑⠄⠐⡆⢤⣤⡜⣀⠸⢁⠀⢴⣷⣶⣷⣽⣾⣿⣜⠯
⣿⣿⣿⣻⡆⠁⠀⠀⠤⠅⣛⠉⣲⡭⢿⣋⠙⣧⣌⠀⣚⣿⣿⣿⣟⢻⣞⣙⠛⣅⣐⢱⠆⠂⠀⠀⠀⢸⣿⣿⣿⣿⣧⣤⣴⣶⣶⣦⣄⣐⠄⠠⠍⠚⠀⠀⠀⠀⠐⠌⣀⣷⣤⡶⠶⢾⣿⡉⠁⠜⠀⠍⣉⣿⣷⠲⢾⡼
⠂⠹⣷⣶⠅⠀⡁⠻⠓⢉⠁⠀⠃⢀⠠⣭⠀⡋⠫⠃⣹⣿⣿⣽⣿⣿⣿⣿⣿⣿⣮⡄⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⠀⣀⠀⠀⠐⠢⢢⢤⣤⣳⣹⣴⠦⡤⠬⢱⠈⠀⠢⠀⡙⣻⢰⣶⣦⣏
⣶⣿⣯⢙⢟⡀⠄⣄⠰⢹⡿⠖⠈⣠⣦⡬⠁⢩⡫⡌⠹⠏⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⢘⣴⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠁⠀⢠⠈⣷⣮⣛⣻⣻⣟⡹⢷⡇⢶⣌⣏⣁⢬⣿⢽⣾⣺⣧⣴⡅
⢟⣛⡷⣦⡼⣗⡉⠃⠛⢏⣃⠰⠈⠀⡀⡀⢀⡀⠨⣁⠸⢆⡀⠘⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠶⢶⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⡀⠀⠀⢼⣿⣿⠿⠻⣽⣧⣴⣾⠟⡿⠿⣾⢻⢽⢏⣀⠩⣴⡎⢏⢏
⣿⣶⡶⣠⣦⣻⡿⢇⠰⣿⡿⡛⢶⣤⡄⠇⠓⣚⣓⣴⣶⢃⣿⡓⣄⡙⠉⠙⡉⢉⢧⣨⣯⣤⣤⣤⣼⣿⣿⣿⣿⣿⡆⠈⠉⠋⠉⠉⠀⠀⠀⠀⠈⠁⠖⠀⡐⣱⣤⣤⠀⠨⠅⠉⢉⡋⠙⣿⡏⠻⣿⠻⢿⡟⢻⡽⢞⡻
⢸⣿⣷⣶⣶⣿⡳⠱⣷⡆⣅⠈⡠⡷⡠⡀⣠⣘⠿⢷⣶⠋⢒⣯⡭⡛⠶⣼⣿⣸⣾⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣷⣄⡀⢀⣀⣀⣀⣤⠄⠀⠀⠀⠘⠘⠮⢝⡢⠙⢂⣀⠐⢀⣴⣶⢃⣉⣻⣸⣷⣷⣶⣇⣅⡄⢃⣀
⠸⣿⣿⣣⣬⣙⡠⡀⠀⣘⢿⣋⣿⡿⠚⠈⣻⢐⣲⣢⣃⠱⣭⢿⢧⡸⠇⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⣿⣿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠐⠡⠉⣶⡟⣿⡿⠶⡻⢻⡛⡍⡆⣙⣷⠋⣻⣟⣿⢭⡯⢿⣿⢉⣎
⣞⠙⣿⣻⢿⣯⢿⠼⠀⢬⣇⡡⡼⢜⣴⡖⠄⠮⣠⠺⠈⠊⠈⠟⢙⡧⣬⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⢒⣿⣿⣿⣿⣿⣿⣿⣿⣆⡈⢿⡷⡘⣷⣦⣦⠠⣄⣧⣾⡻⣏⢰⣝⣷⣦⣿⢿⣿⣿⡴⢷⣷⣿⣿
⣿⠀⢞⢯⣷⣷⡙⠃⠉⠍⢜⠲⠿⣛⠋⣨⡥⠶⢘⣿⡎⠦⣤⠳⣾⠠⢌⣩⡽⣿⣿⣿⣿⣿⡏⡽⡩⡓⢶⢿⠋⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⣤⡁⣃⣽⠻⠛⠠⣯⣻⣛⣗⡛⠛⠿⡶⣿⡿⣿⣿⣿⣿⣻⣿⣿⣿
⢇⢄⠤⠈⠛⣛⢻⣿⡖⣖⣗⡹⢿⣏⡦⣲⣿⣷⡯⠠⣅⣀⣸⠆⣰⣻⣝⣿⠝⢿⡁⢕⠻⠤⢱⣴⣮⣋⠁⠂⠒⠒⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣱⣧⣣⢚⡱⡀⠒⠒⡤⠀⣸⣟⠒⠀⣠⡈⠉⠋⠸⠋⡩⡄⠀⠊⡉⠝
⣀⠨⣿⡻⣷⢤⣍⡬⣠⣸⣦⣹⣭⣾⣶⣦⣌⣳⣾⡽⢩⣿⣧⣾⣔⣓⠟⡇⡼⠿⢿⢴⢶⢶⣶⡦⠁⠚⢀⣖⡊⠰⡗⣄⣶⠂⣿⣿⣿⠋⠉⠀⢩⣁⡡⠩⢉⣹⣏⣥⣜⡋⠉⢀⣀⠀⣈⡙⠃⠂⠀⠁⣠⣰⠀⠀⣧⣷
⠛⠿⢿⣷⣶⣄⡿⣿⣍⡈⣿⠿⠏⢻⣿⢿⠫⠛⢧⣯⣅⡶⣉⣭⠙⢡⠻⡻⠧⠺⠋⠇⠍⠉⢩⣧⣦⣦⡬⠽⠃⡄⣞⢖⠸⢬⣿⣿⣿⠰⡖⣛⣿⣾⣧⢐⢦⣯⢂⣠⣿⣖⠫⠟⡥⢁⠚⠚⠨⠄⢀⠈⠙⠨⣀⠀⠻⠋
⢀⢀⢀⣿⣿⣽⣿⠛⠍⠈⢢⢢⢠⡎⢁⢿⣶⢶⣦⣼⣭⣭⣶⣿⣎⣾⢷⣃⣳⠘⡴⣊⠛⠰⢈⠋⣾⣶⣒⢼⣠⣀⣡⡑⢂⢹⣿⡿⢇⠄⣛⡹⠽⣿⣺⣴⡌⣽⣦⣿⢟⣿⣵⣛⣀⢢⣴⣪⢄⣴⡆⠠⠀⠀⡊⡀⠀⠀
⣿⣐⣳⣁⡋⡏⢀⡈⢓⣥⡼⡘⣿⣻⡧⣨⣚⣹⡄⣤⢦⡹⢿⠭⢟⡙⢯⢝⣹⣵⣤⠬⠁⡰⡎⢅⡿⢿⣬⢥⣬⣉⡛⠿⡄⠈⢿⢵⣹⣶⠘⠍⠌⣘⣭⣄⣇⣙⡋⢩⣿⣽⣿⠁⢦⡙⠠⡌⣷⡌⠀⠀⠀⠀⠤⠄⠀⠀
⢲⡽⡽⢿⣯⣧⡀⢈⣭⣾⡇⣷⠀⣿⡿⣿⢽⣾⣷⣶⣬⣌⢽⣌⣻⠿⢿⣛⣿⢿⣭⣉⢊⠹⣳⣦⠀⠘⢻⡏⠀⡘⠢⢭⣵⣧⣶⡿⡨⡟⡰⣿⠒⡚⠻⢯⣾⡿⣿⡿⢘⣿⣯⣵⡽⣿⣿⡪⡃⠀⠀⠀⠀⠀⠀⢀⠀⠀
⠄⣶⣾⢳⣿⣿⣷⡠⣹⣾⣾⣿⣿⠯⡛⢿⢗⣿⢿⣿⣿⡇⠌⠀⠻⠶⢾⣏⣿⣏⡉⢺⣶⡆⠀⠭⠂⡀⢀⣿⡄⠲⡶⣶⣻⣇⠄⣳⡾⠍⣤⣏⠂⢹⠷⣿⡿⢆⠕⣛⣮⡛⣇⢄⠀⠏⠙⢿⣆⣀⠀⠀⠀⢀⣴⣾⣶⣦
⢘⣺⣿⣤⣭⣯⢹⣄⣳⠜⢻⣿⣿⣍⣺⣿⡝⢟⡿⠉⡩⣉⠀⠀⠐⠙⢯⣼⡮⣧⣼⣮⢈⣿⡯⡐⠾⢿⣮⣿⢿⡄⠀⣤⠚⠟⠳⢈⢱⡬⠿⣤⣾⣿⣯⣾⣦⣜⡣⣿⣿⣿⠛⡲⣦⠀⠀⣪⣞⡹⠀⠀⠄⠈⣿⣿⣿⣿
⣀⠨⣭⣏⢉⡿⣼⣷⢬⠦⢽⣿⣻⣿⡫⢙⣡⣀⣶⡥⡦⣽⣗⡂⠀⣦⣾⠝⠻⣿⣳⣮⣆⠬⠟⡞⠃⠈⠟⣿⢫⡿⡀⢈⡕⣲⡔⢻⣄⡛⣿⣿⡟⣽⢛⠚⣪⢩⡝⡭⣟⠁⠠⢙⣠⣄⣚⣙⠳⣳⡇⠓⠊⢀⠈⣽⣿⣿
⣂⠨⡟⢹⣘⢀⡬⢛⣀⣴⣼⣿⡗⡽⠿⣶⣾⣿⣿⣗⠹⣿⣿⣇⣈⢜⡽⠟⢖⠚⠛⠋⠂⠀⢘⣁⣭⣷⡆⠙⢷⣧⣰⣖⣷⣫⣿⣨⣿⡘⠻⣡⣄⠾⠑⠼⠠⠖⠠⢿⡟⢾⣸⣿⣿⣿⣿⣯⢋⢇⣅⢰⣦⡈⠉⠘⠻⠿
⡟⠛⠻⣟⡿⢿⣛⣛⣻⣟⣯⣿⣿⡿⣿⣭⣿⡻⣿⣿⣿⣛⣿⢿⢊⣁⣤⠤⣘⠿⠂⢧⠀⡴⣲⣴⣤⢀⡟⡳⠘⠟⠯⢬⡔⠻⢿⠯⠀⢀⣼⡿⠊⠻⠂⡄⠓⠃⠓⠐⢃⠃⠈⠶⠿⠻⢟⣻⣿⣿⣄⡀⠙⠿⠱⠀⠠⣿
⠀⣤⣄⢀⣼⢿⣽⠭⣿⣹⡅⣓⢒⡢⣡⡄⠈⡁⠀⠀⢱⣶⡶⠟⠟⠀⡀⠽⠇⢩⡁⣉⣾⡿⡄⠻⣟⡦⢿⣀⣼⣟⣙⣿⣿⣿⣦⣵⣞⣿⣿⣿⢹⣯⣿⣿⣿⣿⣷⣮⡷⣾⡿⡟⣽⡕⢀⣰⣦⠀⠠⢿⣿⣿⠋⠁⡀⠀
⣶⣿⣵⡆⠀⠲⠞⠨⠇⢟⠩⠠⠍⠅⠀⡨⠝⠬⣵⡀⠿⢿⠿⣶⣧⡀⢶⡶⣧⡟⠟⠿⢭⡗⠒⠎⠍⠋⠿⠞⠥⠤⣿⣿⢯⣽⣿⡿⠦⡏⠿⡿⡿⡯⠽⠛⢁⢹⢆⠀⠀⠀⠀⠒⠋⠀⠢⠭⠉⠐⠹⢾⢭⠍⢴⣷⠬⣯
⠈⣼⡅⠃⠀⠀⠀⠀⠀⠨⠀⠀⠀⠁⠀⣶⠄⠀⠝⡁⠀⠀⡴⣿⡟⠢⢀⠀⠔⠉⠄⠀⢸⢬⡀⠄⠀⠐⠎⠀⠠⢂⠅⣠⣄⣈⡫⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⠠⠀⠀⠀⣀⡘⠀⢢
⢀⣤⣶⣾⡿⠂⢀⣠⣴⣤⢀⠀⠀⠀⠀⢫⠄⠀⠀⠐⠠⣾⡿⣿⡵⠦⠀⠀⠀⢀⠀⠀⢀⡜⠀⠈⠀⠀⢐⠂⠀⠰⣾⣿⣿⡏⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣶⣦⡀⠀⠀⠁⠄⠘⠀⠀⠀⣀⣾⣞⠛
⡟⠿⠿⠋⠻⠇⠈⠛⢿⣿⣧⡀⠄⠀⠀⠀⠀⠀⠈⠀⠀⠽⣷⣴⣄⡖⠈⠀⠀⠈⠂⠀⠈⠀⠀⠀⠀⠀⠈⢀⠀⠐⠟⠋⠋⠀⠀⠀⠀⠀⣄⣄⣤⠀⠀⠀⠀⠀⠀⡤⢠⣼⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⡛⣯⣼⢈
⡠⡰⠀⠀⠀⠁⠀⠁⢹⠿⡯⡀⡁⢴⡀⠀⠀⠀⣈⡀⠀⣤⢾⠏⠈⠉⠄⠠⠔⠀⠀⠀⡄⠀⠀⠠⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠰⢍⠉⠉⠀⠀⠀⢀⣀⠀⣄⣀⣥⡀⣄⠀⠀⠀⢀⠀⠀⠄⠀⠐⠀⢀⡋⣎⠚
⢠⣅⠂⢠⣴⣂⠆⠀⠀⠠⢬⣀⠀⣾⣶⢄⡀⠀⠈⠀⣀⠽⢋⣼⣿⣧⡀⣴⣶⣋⢀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣤⣼⣦⠈⠀⢁⢡⢀⠀⠀⠀⠀⢚⡟⠛⠛⢻⠿⢷⣄⠀⠐⢚⠀⠀⠀⣶⣴⠾⢋⣉⠀⣘
⣿⣻⣷⡼⠿⢻⡄⠀⠙⠦⠘⡑⠺⣿⢧⣝⣿⣲⠀⠀⠈⣬⣼⣿⣿⡿⢠⡇⠁⠿⠰⠶⠀⠀⠀⠀⠀⢀⣴⣶⣦⣤⡂⠀⣀⣼⣿⣭⣀⡀⢠⣈⡀⠀⠀⠀⠠⠨⠁⠄⠀⠂⢠⣤⣜⣀⠸⢁⠀⢰⣷⣾⣷⣽⣶⣿⣜⡭
⣿⣿⣟⣻⡇⠁⠀⠀⡄⠅⣛⠉⣲⡭⢷⡋⠙⣤⣄⠀⣘⣽⣿⣿⣿⣳⣞⣙⠛⡌⣁⠲⠆⠂⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠉⠚⠀⠀⠀⠀⠄⠌⣀⣷⣤⡶⠶⢾⣿⡉⢁⠜⠀⠍⣉⣿⣷⠶⢾⡮
⡇⠹⣷⣶⠕⠀⠉⠻⠛⠉⠁⠀⠋⠀⠐⣡⡀⠛⠫⠡⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡀⠀⠀⠀⠀⠀⠈⢿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⡀⠀⠀⠀⠂⠠⣆⡠⡺⡹⣤⠤⠄⠤⢡⠈⠀⠂⡀⡉⣻⢲⡶⣴⣅
⣶⣷⣯⢙⢿⡀⠀⣄⠠⢸⡻⠗⠀⣠⣶⡍⠉⢩⣫⣌⠺⠍⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⣸⣥⣿⣇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠁⠀⢠⠌⣵⣦⡛⡻⣻⣯⡹⢷⡇⢴⣌⣋⣁⢪⣽⢔⣼⢺⣧⣴⡅
⠛⡋⣷⣷⡽⢧⡉⠂⠛⢏⣃⠰⠘⠀⡀⡀⢀⠀⢬⣁⡘⢆⡀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠶⢾⣿⣿⣿⣿⣿⡟⠻⠿⢿⣿⣿⣿⠿⡟⠁⠀⠀⠀⠀⠀⢴⣿⣿⠿⢩⣬⣧⣴⣾⠟⡿⠿⣟⢫⣽⢏⣀⠩⣴⡞⢋⣇
⣷⣷⡶⣠⣦⣺⡿⢧⠰⣿⡿⣻⢶⣤⠈⠇⡃⣞⣇⣲⣦⢓⣿⢱⣌⡉⠛⠛⣛⢉⢧⣨⣿⣦⣄⣠⣼⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⢀⣱⣤⢤⠀⠨⠅⠉⢉⡋⠹⣿⡏⠻⢿⠻⢿⡿⠿⡿⢏⠻
⢸⣿⣷⣶⣾⡿⡣⠲⣷⡂⣧⠈⡪⡷⡨⣀⣀⣘⠿⠳⡲⠯⢔⣩⡭⡙⠶⣬⣿⢸⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢀⣀⣀⣀⣤⠄⠀⠀⠀⠐⠀⠨⢜⡰⠲⢂⢀⠀⢀⣴⣶⢃⣉⣻⣸⣷⣷⣶⣅⣁⠤⣁⣠
⠸⣿⣿⣧⣭⣙⣀⣀⠀⣘⢿⣏⣿⡿⠊⠉⣻⢐⣒⣠⣃⢕⣭⣻⢧⡸⠇⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠡⠈⣲⡟⣿⡾⠖⡋⢳⡺⡌⡆⣙⡾⠋⡻⣟⡿⢬⡿⢿⣾⢙⣂
⣞⠙⣿⣻⢿⣯⢿⡼⠂⢮⣯⣡⡠⢜⣶⡶⠅⡮⣩⠺⠈⠊⠈⠟⢙⣧⡬⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣒⣾⣿⣿⣿⣿⣿⣿⣿⣧⠈⣿⡷⠐⢷⣦⣦⠠⣄⣧⣾⡻⣏⠰⣵⢷⣄⣿⣿⣿⣾⣴⢷⣵⣿⣿
⣿⠃⡞⣿⣷⣿⡙⠃⠙⠯⢜⠲⠿⣻⠋⣨⡥⠶⢘⣿⡎⠦⣤⠳⣶⠠⢌⣡⣿⣿⣿⣿⣿⣿⣏⡽⡻⡃⢶⢿⠛⠁⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡦⡄⡀⢁⣽⠻⠛⠡⣯⣻⣛⣗⡛⠛⠟⡶⢿⣿⣿⣿⣿⣿⣻⢿⣿⣿
⢆⢄⠤⡈⠛⣛⢻⣿⠒⣖⠷⡻⠿⣏⡆⢲⣿⣷⡯⢤⣅⣀⠸⠆⢠⣻⣏⡿⠝⢿⡩⢕⠿⠄⢱⣴⣾⣋⠁⠄⠒⠲⠆⢈⣻⣿⣿⣿⣿⣿⣿⣿⣳⣧⣓⢊⡱⡀⠐⠲⣤⠄⣸⣏⠖⠀⣠⡈⠙⠋⠸⠋⡩⡆⠀⠊⠉⠝
⣀⠨⣿⡻⣷⢴⣍⡄⣠⣸⣦⣙⣭⣾⣶⣦⣬⣳⣾⡜⢩⣿⣧⣾⣔⣓⠟⡏⡼⠻⢾⢴⠷⢶⣾⠂⠁⠚⢀⣖⡊⠲⡖⢆⣿⠋⣿⣿⣿⠛⠋⠁⠈⣁⡡⠩⢩⣸⢍⣥⣜⠋⠉⢁⡀⠀⣀⡉⠃⠂⠀⠁⣠⣰⠀⠀⣱⡶
⠛⠿⢿⣷⣶⣤⠿⣿⣍⡈⢿⠿⠋⢻⣿⠿⠻⠛⠧⣭⣅⡶⡉⣭⠛⢣⠨⡫⠃⠘⠏⠋⠈⠉⢩⣿⣦⣦⡬⠽⠃⢄⣞⢅⠪⢬⣿⣿⣿⠰⡗⣓⣟⣾⡧⠸⢬⣣⢢⣠⣿⡒⠣⠟⡤⢄⠂⠐⠪⠄⢀⠀⠙⠨⣠⠀⠻⠋
⣀⢀⣀⣿⣿⣽⣿⢛⠍⠈⢢⢮⢠⣎⣁⢹⣷⢶⣤⣰⣭⣯⣿⣿⣨⣞⢷⣓⣻⠠⣔⣚⠙⠤⢌⠛⣾⣱⣰⢼⣠⣀⣡⡑⢂⣹⣿⠿⢇⠄⣹⡹⢿⣿⣻⡴⡆⣮⣶⣿⢟⣿⣤⣛⣀⠢⣶⢾⢄⣴⡆⠀⠄⠀⡈⡀⠀⠀
⣿⣑⢳⣅⡉⡏⢠⡈⢓⣷⡼⡚⣿⣿⣧⣠⣚⢹⡔⣥⢦⡽⢿⠬⢏⡙⢯⢝⣹⣵⡤⠄⠁⡴⡎⠅⡿⠻⢎⣭⣬⣉⡙⠿⡄⠉⠿⣵⡽⣮⠸⠌⠬⣉⣭⣄⣏⣙⡋⠹⣿⣽⣟⠁⢮⡝⠠⡬⣶⡄⠀⠀⠀⠀⠄⠀⠀⠀
⢳⣼⡝⢿⣏⣯⡀⢈⣭⣿⡧⢳⡐⣿⡿⣷⣽⣾⣿⣤⣬⣄⠹⣈⣻⠿⢿⣙⣿⣿⣯⣰⠢⠹⣳⣤⠀⠐⢽⡋⠀⡈⠢⢮⣵⢢⣴⡿⡨⡟⡱⣿⠐⣚⠻⢧⣾⡿⣽⡿⢘⣿⣿⣴⡿⣿⣿⡮⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀
⠀⣶⣾⢷⣿⣿⣷⡠⣹⣷⣾⣿⣿⠾⡻⢿⣗⣿⢿⣿⣯⣇⠀⠀⢛⠺⢾⣏⣿⣏⣉⢺⣖⡆⠄⠭⠂⡀⢀⣿⡄⠰⣶⢾⣻⣧⣀⣳⣺⠍⣴⠟⠂⢹⠷⣿⠟⢖⠕⣛⣮⡛⡃⣄⠀⠋⠙⢿⣆⣀⠀⠀⠀⢀⣴⣿⣶⣶
⢉⣺⣿⣦⣭⣯⢹⣇⡱⠜⢻⣿⣿⣍⡘⣿⡝⢟⡟⠍⡉⣄⠀⠀⠐⠓⢾⣾⡦⣧⣼⣮⣨⣾⡯⡰⠾⢿⣬⣿⢿⡄⠈⣄⠞⠟⠳⢈⢡⡸⠻⣤⣾⣿⣯⣾⣤⣜⡳⣿⣿⣻⠙⡲⢦⠀⢀⣺⣜⡰⠀⠀⠀⠈⢿⣿⣿⣿
⣀⠠⣬⣍⢉⡿⣼⣷⢨⠦⢽⣿⣻⣿⡫⠙⣡⣄⡶⡧⡧⢽⣷⡂⠀⣦⣶⠋⠻⢟⣷⣾⡆⠬⠟⡞⠃⠈⠿⢿⢩⡿⡀⢈⡽⣼⡄⢿⣇⡋⣿⣿⡋⣽⣟⠚⣊⢭⠝⡭⢟⠡⠠⢈⣨⣄⣚⣉⠳⠻⠇⠓⠈⢀⣼⣿⣿⣿
⣊⠨⣻⢹⣎⢀⡬⢙⣠⣤⣾⣿⣟⡽⠿⣤⣾⣿⣿⣷⡻⣿⡿⡟⣀⢈⡽⠟⢖⠚⠛⠋⠄⠀⠘⣁⢌⢵⡂⠙⢶⡧⣴⣶⣯⣫⣿⣪⣿⡎⢹⣯⣄⠬⡑⠌⠀⠀⠠⣿⡿⢶⠸⣿⣿⣿⣿⣏⢉⢆⣅⢰⣦⡄⠘⢿⣿⣿
⡟⠛⠻⣟⡿⢿⣟⣛⣻⣿⣧⣿⣿⣿⣿⣦⣿⡻⣿⣿⣿⣋⣿⢟⣎⣠⣤⠤⣘⠿⡤⢷⡀⡴⣲⢶⣤⢀⡾⠣⠐⠛⠏⠼⠀⠛⢿⠯⠈⠀⣼⡿⠊⠷⠂⠄⠀⠀⠀⠀⠃⠅⢀⠶⠯⠛⢛⣻⣿⣯⣄⡀⠙⠿⠃⠀⠀⣿
⠀⣤⣄⢀⣼⢿⣿⠭⣿⣹⡅⣓⢒⡢⣡⡄⠈⡁⠀⠀⢡⣶⡶⠟⠟⠀⡀⠽⠧⢩⠁⣉⣾⡿⡄⠻⣟⡦⣟⡀⣼⣟⣙⣿⣿⣷⣦⣵⣞⣿⣿⣿⢹⣯⢿⣿⣿⣿⡷⣮⡷⣾⡿⡟⣽⡵⠀⣰⣦⠀⠠⢿⣿⣿⠋⠁⡀⠀
⣶⣿⣵⠆⠀⠲⠟⠨⠗⢟⠩⠠⠍⠅⠀⡡⠝⠬⣵⡀⠾⢿⠿⣷⣧⡠⢶⡶⣷⡟⠟⠿⢭⡗⠒⠊⠏⠛⠟⠖⠥⠄⣿⣿⢯⣼⣿⡿⠶⡟⠿⡿⡿⠯⠽⠋⢁⢸⠄⠀⠀⠀⢀⠢⠋⠀⠢⠭⠉⠐⠹⢾⢭⠏⣴⣷⠼⣮
⠈⣼⡅⠃⠀⠀⠀⠀⠀⠸⠀⠀⠀⠁⠀⣶⠄⠀⠙⡁⠀⠀⡴⣿⡟⠢⠀⠀⠄⠉⠄⠀⢸⣬⡀⠀⠀⠐⠎⠀⠠⢂⠅⣠⣄⣈⡻⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⠠⠀⠀⠀⣀⠘⠀⢢
⢀⣤⣶⣾⡿⠂⢀⣠⣴⣤⢀⠀⠀⠀⠀⢋⠄⠀⠀⠀⠠⣾⣿⣿⡵⠦⠈⠀⠀⠀⠀⠀⢀⡜⠀⠈⠀⠀⢐⠂⠀⠰⣾⣿⣿⡏⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣶⣦⡀⠀⠀⠁⠄⠘⠀⠀⠀⣲⣾⣟⡙
⡟⠿⠗⠋⠻⠇⠈⠛⢿⣿⣧⡀⠄⠀⠀⠀⠀⠀⠈⠀⠀⠽⣷⣴⣤⡖⠀⠀⠀⠈⠂⠀⠈⠀⠀⠀⠀⠀⠈⢂⠀⠐⠟⠋⠋⠀⠀⠀⠀⠀⣤⣄⣤⠀⠀⠀⠀⠀⠀⡤⢠⣼⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⡛⣯⣼⢀
⡠⡰⠀⠀⠀⠁⠀⠀⢸⠿⣮⢀⣁⠴⡀⠀⠀⠀⣈⡀⠀⣤⢾⠏⠈⠉⠄⠠⠄⠀⠀⢀⡄⠀⠀⠠⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠰⢟⠉⠉⠀⠀⠀⠀⣀⢐⣄⣀⣥⡀⣄⠀⠀⠀⢀⠀⠀⠤⠀⠐⠀⢁⡋⣎⠚
⢠⣅⠂⢠⣴⣂⠄⠀⠀⠠⣭⣀⡀⣾⡶⢄⡀⠀⠈⠀⣀⠽⢋⣼⣿⣧⡀⣴⣶⣏⢀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⠀⠀⣤⣴⣦⠈⡀⢁⢡⢀⠀⢀⠄⠀⢚⡟⠛⠛⢻⠿⢷⣄⠀⠐⢚⠀⠀⢀⣶⣔⢾⢋⣉⠀⣘
⣿⣻⣷⠼⠿⢻⡄⠀⠙⠦⠘⡑⠺⣿⢯⣟⡷⣲⠀⠀⠈⣬⣼⣿⣿⡿⢠⡃⠁⠿⠰⠶⠀⠀⠀⠀⠀⢀⣴⣶⣦⣤⡂⠀⣀⣼⣿⣭⣀⡀⢀⢈⡀⠀⠀⠀⠠⠨⠁⠄⠐⡂⢠⣤⣜⣀⠸⢁⠀⢰⣷⣶⣷⣽⣾⣿⣌⡫
⣿⣿⣟⣻⡇⠁⠀⠠⠄⠅⣛⢋⣲⡽⢷⡉⠙⣤⣄⠀⣘⣿⣿⣿⣟⣳⣞⣙⠛⡌⣁⠰⠆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠁⠞⠀⠀⠀⠀⠄⠌⣀⣷⣤⡶⠶⢾⣿⡉⢁⠜⠀⠝⣩⣿⣷⠶⢞⡼
⡎⠹⣷⣶⠗⠀⢉⠳⠛⠉⠁⠀⠋⠀⠐⡥⡀⠛⠫⠡⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡀⠀⠀⠀⠀⠀⠈⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⡀⠀⠀⠀⢂⢠⣆⡠⡳⡹⣤⠤⠄⠬⢡⠈⠀⠢⠀⡉⣻⢰⡶⣴⣅
⣖⣷⣯⢙⢿⡀⠀⣄⠰⢺⡻⠗⠀⣠⣾⡍⠉⢩⡫⣌⠺⠍⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⣸⣥⣿⣇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠁⠀⢠⠌⣵⣦⡛⣻⣻⣿⡹⢷⡇⢴⣜⣋⣁⢨⣽⢅⣼⢺⣇⣴⡇
⠟⡋⣿⣷⡼⢇⡉⠊⠙⢏⣃⠰⠘⠀⡀⡀⢀⠀⣬⣁⡸⢆⡀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠶⢾⣿⣿⣿⣿⣿⡟⠻⡿⢿⣿⣿⡿⠿⡟⠃⠀⠀⠀⠀⠀⢼⣿⣿⠿⢩⣼⣧⣶⣾⠟⡿⠿⣟⢯⣵⢏⣀⠩⣴⡎⢩⢅
⣷⣷⡶⣠⣾⣻⡿⢧⠰⣿⡿⣻⢶⣤⠀⠇⡃⣾⣇⣲⣦⢓⣿⢳⣌⡉⠛⠛⣛⢉⢧⣨⣿⣦⣄⣠⣼⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⢐⣱⣤⠤⠀⠨⠅⠉⢉⡋⠹⣿⡏⠻⣿⠻⢿⡿⠿⡿⢏⠻
⢸⣿⣷⣾⣾⡿⡣⠒⣷⡂⣅⠈⡢⡷⡨⣀⣀⣘⠟⠳⡲⠫⢖⣩⡽⡛⠶⣤⣿⢸⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢀⣀⣀⣀⣴⠄⠀⠀⠀⠐⠀⠨⢜⡰⠂⢂⢀⠀⢀⣴⣶⢓⣉⣻⣽⣷⣷⣶⣅⣁⠤⣀⣠
⠸⣿⣿⣫⣭⣙⡀⣀⠀⣘⢿⣏⣿⡿⠊⠉⣻⢐⣒⣠⣃⢵⣭⣻⢧⡸⠇⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠁⠈⣲⡟⣿⡾⠖⡫⢳⡚⡌⢆⣹⡾⠋⡻⣟⣯⢬⡯⢿⣾⢙⣆
⣚⠙⣿⣛⢿⣯⢿⡼⠂⢮⢥⣡⡤⢜⣶⡶⠕⠮⣩⠘⠈⠊⠈⠟⢙⣥⡬⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣒⣾⣿⣿⣿⣿⣿⣿⣿⣧⡈⣿⡷⠘⣷⣶⣦⠠⣄⣧⣾⡻⣇⠰⣵⢷⣦⣿⣿⣿⣾⣴⢷⣵⣿⣿
⣿⠃⡟⣿⣷⣿⡙⠃⠙⠯⢜⠲⠿⣻⠋⡠⠥⠶⢘⣿⠎⠆⣤⠳⣶⠠⢌⣩⣿⣿⣿⣿⣿⣿⣏⡽⣻⡋⢶⣿⠛⠁⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡆⡰⡀⣁⣽⠻⠛⠡⣯⣻⣛⣗⡛⠻⠟⡶⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿
⢆⢄⠤⡈⠛⣛⢻⣿⠶⣖⡷⡻⠿⣏⡢⢰⣽⣷⡮⢤⢅⣀⠸⠆⢰⣻⣍⡿⠝⢿⠩⢵⠿⠄⢱⣴⡾⣋⠉⠅⠐⠲⠆⢈⢿⣿⣿⣿⣿⣿⣿⣿⣷⣧⣃⢊⡱⡀⠐⠒⣤⠀⣸⣏⠒⠂⣤⡈⠙⠉⠸⠋⡩⡄⠀⠊⡉⠍
⣀⠨⣿⡻⣷⢴⣝⠌⣠⣼⣦⣹⣭⣾⣶⣦⣌⣳⣾⡜⢩⣿⣧⣾⣄⣑⠟⡏⡼⠻⢾⠴⢷⢶⣾⡦⠁⠚⢀⣖⡊⠺⡖⣆⣺⠋⣿⣿⣿⠛⠛⠁⢈⣁⡠⠩⢉⣱⢍⣥⣜⠋⡉⢁⡀⠀⣈⡙⠁⠂⠀⠁⣠⣰⠀⠀⣱⡶
⠛⠿⢿⣷⣶⣤⠿⣿⣍⡈⣿⠿⠋⢻⣿⠿⠻⠛⠧⣭⣅⡶⡉⣭⠛⢫⠨⡫⠧⠚⠏⠃⠈⠉⢩⣯⣦⣦⡬⠽⠒⠄⣞⢕⠨⢬⣿⣿⣿⠰⡗⣛⣟⣾⡧⠘⢨⣡⢢⣠⣿⡒⠣⠟⡄⢂⠂⠐⠨⠄⢀⡈⠙⠸⣀⠀⠻⠋
⣀⢀⣀⣿⣿⣿⣿⢛⠍⠈⢠⢮⢠⡎⢁⢹⣷⢶⣤⣘⣭⣯⣷⢿⣈⣞⢷⣓⣺⠹⣔⣚⠙⠡⢄⠛⣿⣱⣶⢼⣠⣀⣡⡑⢂⣹⣿⠿⢇⠌⣹⣹⢿⣿⣻⡴⡆⣮⣮⣿⢟⣿⣦⣛⣀⠢⣶⢿⢄⣴⡆⠀⠄⠀⡀⡀⠀⠀
⣿⣑⢳⣇⡉⡏⢠⡈⢓⣧⡾⡘⣿⣿⣧⣠⣘⣹⡔⣥⢬⡽⢿⡭⢟⡙⢯⢍⣹⣵⣤⠬⠁⡴⡎⠇⣿⢿⢌⣝⢬⣉⡙⠿⡄⠉⠿⣷⣽⣮⠘⠌⠬⣙⣭⣄⢯⣙⡋⠹⣿⣭⣟⠅⢾⡍⠠⠬⣶⠄⠀⠀⠀⠀⠄⠄⠄⠀
⢳⣼⡽⠿⣯⣯⡄⢀⣭⣿⡧⢳⡐⣿⡿⣷⣽⣾⣿⣶⣭⣄⠹⣎⣻⠷⢿⣛⣿⣿⣯⣙⠊⠹⣳⣤⠀⠘⢽⡋⠀⡈⠻⢯⣵⣢⣶⣿⡠⡟⡱⣿⠂⢚⠻⢧⣾⡿⡽⠿⢸⣿⣿⣰⡿⣿⣿⡢⠁⠀⠀⠀⠀⢀⠀⢀⠀⠀
⠀⣶⣾⢳⣿⣿⣿⡠⣹⣶⣾⣿⣿⠾⡻⢿⣗⣿⣿⣿⣯⡇⠀⠀⠛⠲⢾⣏⣿⣏⣋⢺⣖⡆⠄⠭⠂⡀⢀⣿⡄⠰⡶⠾⣻⣧⣀⣳⡿⡍⣴⣝⠃⢹⡷⣿⠟⢆⠕⣚⣮⡛⣇⣔⠀⠋⠙⢿⣆⣀⠀⠀⠀⢀⣶⣿⣶⣶
⢉⣺⣿⣦⣭⣿⢹⣇⣱⠜⢻⣿⣿⣍⡘⣿⡝⢟⡿⠍⡩⣄⠀⠀⠐⠛⢾⣿⡦⣧⣼⣮⣨⣾⣧⡰⠾⢿⣌⣿⣿⡄⠈⢄⠚⠞⠓⢈⢱⡼⠹⣤⣾⣿⣿⢾⣤⣜⡳⣿⣿⣻⠋⡲⢦⠀⢀⣺⣜⡨⠀⠀⠀⠈⢿⣿⣿⣿
⣀⠠⣬⣍⢉⡿⣼⣷⢨⠦⢽⣿⣻⣿⡫⠙⣡⣄⡶⡧⡦⢽⢷⡂⠀⣦⣾⡉⡿⢿⣗⣾⡇⠬⠟⡞⠃⠈⠿⣿⢋⡿⡀⢈⣿⣜⡐⢻⣇⡋⣿⣿⡋⣽⣏⠘⣀⢭⠕⡭⢿⠡⠠⢈⣠⣄⣘⣉⠳⡿⠇⠓⠈⢀⣼⣿⣿⣿
⣊⠨⣻⢻⣊⢀⡬⢙⣀⣴⣾⣿⣟⡽⠿⣴⣾⣿⣿⣷⡹⣿⡿⡏⣀⢈⣽⠟⢖⠚⠛⠋⠄⠀⠘⣁⢌⢵⣂⠙⢶⠧⣰⣲⣿⣫⣿⣪⣿⡊⢻⣧⣄⢬⠑⠌⠀⠀⠠⣾⡿⢶⠸⣿⣿⣿⣿⣏⢚⢇⣅⢸⣦⡐⠘⢿⣿⣿
⡟⠛⠻⣟⡿⢿⣟⣛⣻⣿⣧⣿⣿⣿⣾⣧⣿⡻⣿⣿⣿⢋⣿⢟⣎⢤⣤⠤⣘⠿⠠⢷⠀⡷⣲⣴⢆⡀⡾⠣⠘⠟⠯⠕⠄⠛⢿⠯⠈⢀⣼⡿⠊⠳⠂⠄⠀⠀⠀⠀⠃⠁⢀⠶⠯⠻⢛⣻⣿⣏⣄⡀⠙⠿⠃⠠⠀⣿
⠀⣤⣄⢀⣼⢿⣽⠭⣿⣨⣄⣒⠒⡢⣡⡄⠈⡁⠀⠀⢡⣶⡲⠟⠟⠀⠀⠽⠥⢩⡈⣉⣶⡿⡄⠻⣟⡤⣟⡀⣼⣏⣙⣾⣿⣿⣦⣵⣞⣾⣿⣿⢹⣯⣿⣿⣿⣿⡷⣮⡗⣾⡿⡟⣽⠕⢀⣰⣆⠀⢠⣿⣿⣿⠉⠁⡀⠈
⣶⣿⡴⡆⠀⠲⠟⠈⠗⢟⠉⠠⠍⠅⠀⡀⠍⠬⡕⡀⠾⠿⠿⣷⣧⡀⢶⡶⣧⡍⠟⠿⢭⡗⡒⠂⠍⠚⠟⠞⠥⠄⣿⣿⠯⣼⣿⣿⠦⡟⠿⡿⡿⠭⠽⠛⢁⢹⠄⠀⠀⠀⠀⠂⠋⠀⠂⠭⠉⠘⠹⢮⢭⠉⢤⣲⠤⣮
⠈⣤⠀⠃⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⣶⠄⠀⠝⠁⠀⠀⡴⣿⠗⠂⠀⠀⠴⠁⠄⠀⢸⢬⡀⠀⠀⠐⠆⠀⠠⢀⠅⣠⣄⡈⡻⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⠠⠀⠀⠀⣀⡘⠀⢢
⢀⣤⣶⣾⡿⠂⢀⣠⣴⣤⢀⠀⠀⠀⠀⡫⠄⠀⠀⠐⠠⣾⡿⣿⡷⠦⠀⠀⠀⠀⠀⠀⢀⡜⠀⠈⠀⠀⢐⠂⠀⠰⣾⣿⣿⡏⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣶⣦⡀⠀⠀⠀⠄⠘⠀⠀⠀⣀⣾⣞⠛
⡞⠿⠿⠋⠻⠇⠈⠛⠿⣿⣧⡀⠄⠀⠀⠀⠀⠀⠈⠀⠀⠽⣷⣴⣄⡖⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠐⠟⠋⠋⠀⠀⠀⠀⠀⣄⣄⣤⠀⠀⠀⠀⠀⠀⡤⢠⣼⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⣯⣼⢀
⡠⡰⠀⠀⠀⠁⠀⠀⢙⠷⡯⠀⡁⠴⡀⠀⠀⠀⣈⡀⠀⣤⢾⠋⠈⠉⠀⠠⠄⠀⠀⢀⡄⠀⠀⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⢏⠉⠉⠀⠀⠀⢀⣀⢐⣄⣀⣥⡀⣄⠀⠀⠀⢀⠀⠀⠤⠀⠀⠀⢀⡃⣬⠚
⢠⣅⠀⢀⣴⣂⠀⠀⠀⠀⢬⣀⠀⣾⡶⢄⠀⠀⠈⠀⣀⠝⠋⣴⣿⣧⡀⣤⣶⢋⢀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣠⣴⣶⣶⣾⣶⣦⣥⠀⠀⢀⠄⠀⢚⡟⠛⠛⢻⠟⢷⣄⠀⠐⢘⠀⠀⠀⣶⣔⢾⢉⣉⠀⣘
⣿⣛⣷⠼⠿⢻⡄⠀⠙⠆⠘⡙⠲⣿⢧⣟⡷⣲⠀⠀⠈⣬⣸⣿⣿⣿⠠⡃⠉⠿⠔⠴⠀⠀⠀⠀⠀⢀⣴⣶⣦⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠠⠈⠑⠄⠀⠂⢠⣤⣜⣀⠸⢁⠀⢰⣷⣶⣷⣽⣾⣿⣌⡭
⣿⣿⣟⣻⡆⠀⠀⠀⠀⡁⣛⠋⣲⡽⢷⡋⠙⣤⣀⠀⣈⣿⣿⣿⣟⣳⣼⣝⣙⡈⡁⠲⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠌⠀⠀⠀⠀⠀⠄⣀⣷⣤⡶⠶⢾⣿⡉⠁⠜⠀⠍⣉⣻⣷⠲⢌⡌
⡆⠹⣷⣶⠅⠀⡉⠻⠓⠁⠁⠀⠁⠀⠐⣡⠀⠛⠪⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢻⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⡀⠀⠀⠀⠂⠠⢄⡠⡳⡱⣴⠤⡄⠤⢡⠈⠀⠆⡀⡉⣹⢰⡶⣴⢅
⣶⣿⣯⢙⢟⡀⠀⣄⠰⢸⡯⠖⠈⣠⣪⠌⠁⠩⡫⡌⠸⠝⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⢀⣼⣾⣿⣯⣠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠁⠀⠀⠈⣵⣤⠛⣛⣻⡟⡹⢷⡇⢴⣄⣉⣀⢌⣽⢥⣼⢘⠇⣴⡆
⢛⡃⡿⣶⠼⢄⡉⠂⠙⢋⣃⠰⠈⠀⡀⡀⢀⠀⡬⣀⠘⢆⣀⠻⣿⣿⣿⣿⣿⣿⣿⢿⡿⠿⠿⢾⣿⣿⣿⣿⣟⣛⠉⠙⠉⠉⠙⠋⠁⡀⠀⠀⠀⠀⠀⠀⢴⡿⡿⠿⠩⣬⣧⣴⣾⢟⠿⠿⣝⢋⢽⢏⣀⠉⣴⡎⠉⢇
⣷⣷⡶⣠⣦⣻⡿⢇⠠⣿⡿⣻⢶⣤⠀⠇⠒⣪⣁⣀⣦⣃⢻⠑⣄⡉⠉⠛⣋⢉⠷⣤⣉⡀⠀⣀⣼⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠀⠀⣱⡤⢤⠀⠠⠅⠉⢉⡋⠙⢿⡏⠻⢿⠻⢟⡾⠿⡽⢖⠻
⢸⣿⣷⣶⣾⡿⡣⠐⣷⡀⢅⠈⡠⡷⡀⣀⣀⣘⡟⠳⡲⠋⢐⣩⡍⡙⠶⣤⣿⣬⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⣀⣀⣤⠄⠀⠀⠀⠀⠀⠠⢘⡰⠒⢃⢀⠐⢀⣴⣶⢃⣁⣻⣸⣷⣷⣶⣅⣅⠄⣁⣀
⠸⣿⣿⣧⣬⣙⣀⡀⠀⣘⢽⣋⣿⡿⠊⠉⢻⢀⣒⣀⣁⠑⣍⢪⢧⡼⣢⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠁⠈⣲⡞⢹⡾⠖⡻⢳⡛⡌⡆⣹⡶⠊⡻⣛⡯⢬⡯⢿⣾⢑⣂
⣒⠙⣿⣛⢿⣯⢿⡼⠀⢬⢯⡡⡄⠜⣶⡶⠄⠪⢡⠘⠈⠂⠈⠟⠙⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣼⣿⣿⣿⣿⣿⣿⣿⣿⡌⣷⡷⠐⢷⣤⣦⠠⣄⣧⡼⡿⣏⠰⣽⢷⣄⣼⣿⣿⣾⡴⢿⣱⣿⣿
⣿⠁⠞⣿⣷⣿⡘⠃⠉⠏⠜⠲⠿⣻⠃⡠⠥⠴⢘⣿⠎⠆⣤⠳⣴⡸⣿⣿⣿⣿⣿⣿⣿⣟⣏⡽⣫⡃⢶⣾⠛⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⡀⢁⣭⠛⠛⠠⣯⢻⢛⣗⡛⠛⠟⡶⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿
⢆⠄⠄⡈⠛⣛⢛⣾⠲⣖⠷⡻⠿⢏⡒⢰⣿⣷⡮⢤⣄⣀⠸⠆⢰⣻⣍⣿⠟⢻⠋⢵⠖⠄⢵⣴⣮⣃⠁⠀⠐⠲⠆⢀⣻⣿⣿⣿⣿⣿⣿⣿⣿⢧⣃⢊⡱⡀⠐⠒⡤⠀⣸⣟⠔⠀⣤⣈⠉⠉⠸⠋⡩⡄⠀⠊⡉⠍
⣀⠨⣾⡳⣷⢴⣍⠄⣀⣸⣦⣙⣭⣾⣾⢦⣄⣱⣾⡜⢬⣿⣧⣾⣄⣑⠟⠇⡼⠿⢾⠄⢷⢵⣾⡦⠁⠚⢀⢖⡚⠰⡗⢄⣸⠋⣿⣿⣿⠿⠟⠛⠉⣁⡠⠨⢍⣵⢄⣥⣜⡋⡉⢁⡀⠀⣀⡉⠁⠂⠀⠁⣠⣰⠀⠀⣥⡶
⠛⠿⢿⣷⣶⣤⠿⣿⣌⡈⢿⡿⠋⢻⣿⠷⠫⠛⠧⢭⣅⡶⡈⣭⠛⢣⠨⡫⠣⠘⠟⠃⠈⠉⢩⣧⣦⡆⡬⠹⠓⠀⣞⢗⠨⢬⣿⣿⣿⠰⡞⣓⣿⣖⡇⠸⢌⣡⠂⣠⣿⠒⠣⠟⡄⢀⠀⠐⠠⠄⢀⠀⠙⠨⣀⠀⠻⠋
⠀⢀⣀⣿⣿⣭⣿⢛⠅⠈⢠⢬⢠⡆⢀⢹⣶⢶⣤⣘⣭⣭⣷⣿⣨⣞⢷⣓⣋⠰⣄⣊⠙⠀⢀⠙⣾⣡⣲⡸⣀⣀⡡⡑⢂⣩⣿⠿⢇⠌⣹⡻⠿⣿⣶⡴⡄⣾⣦⣿⢝⣶⣤⣙⣀⠢⢶⢾⠄⣴⡆⠀⠄⠀⡀⡀⠀⠀
⣿⣓⢳⣅⡉⠍⢠⡈⢓⣧⡼⡘⣿⣿⡦⣠⣆⣹⡄⣤⢢⡽⢿⠥⢏⡙⢫⢉⣹⣵⡤⠈⠁⡠⡎⠁⡿⠻⢎⣭⢬⣉⡙⠿⡄⠉⢿⣵⠹⣮⠘⡄⠬⣉⣯⡀⣏⣙⡋⢹⣿⣭⣟⠁⣦⡙⠠⠌⣶⠄⠀⠀⠀⠀⠀⠄⠀⠀
⠳⣼⡝⠿⣍⣯⡄⢈⣭⣿⡃⢳⡀⣿⡿⡵⢽⣶⣷⣤⢬⣀⠹⣀⣻⠷⢿⣙⢿⣟⡭⣉⠊⠩⣳⣤⠀⠀⢹⡋⠀⡌⠢⢯⣷⣦⣴⢿⡡⡯⡰⣾⠒⠚⠻⢧⣾⡿⣽⠿⢘⣿⣯⣴⡿⣿⣿⡂⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀
⠀⣶⣾⢓⣿⣿⣷⡠⣹⡾⣶⣿⣿⠾⡳⢿⣗⣿⣿⣿⣯⡁⠀⠀⢙⠰⢾⣏⣿⣎⣋⢺⣖⡆⠄⠬⠂⡀⢀⣿⡄⠰⠶⠾⣻⣇⣠⣳⡿⠍⣴⠙⠂⢹⠷⣿⠟⢆⠕⣚⣶⡛⡃⢀⠀⠋⠙⢷⡆⢀⠀⠀⠀⢀⣴⣿⣷⣶
⢈⣾⣿⣦⣭⣭⢹⣇⣰⠜⢻⣿⣿⣍⡚⣿⡟⢽⡟⠉⡉⣄⠀⠀⠐⠛⢾⣼⡦⣧⣼⣮⣨⣺⣯⡰⠾⢿⣈⣷⢿⣆⠀⣄⠐⠞⠓⢈⢱⡨⠹⣤⣾⣿⣎⢾⣆⣜⡳⣿⡿⣻⠉⡲⠦⠀⠀⣚⡀⡀⠀⠀⠀⢈⣿⣿⣿⣿
⣀⠠⣬⣉⢩⡿⣼⣷⢨⠦⢽⣿⣻⣿⡫⠙⡁⣄⡦⡥⠦⢽⣗⡂⠀⣦⣼⠋⠻⢟⣷⣾⡆⠈⡛⡖⠃⠈⠟⢿⢩⡿⡀⢘⡝⣜⡀⢛⣆⡃⣿⣿⡋⣽⢋⠚⣈⢩⠕⡭⠟⠡⠀⢉⣠⣄⣘⣉⠳⣸⠅⠑⠀⣾⣿⣿⣿⣿
⣂⠨⣻⢹⣈⢀⡬⢙⣀⣴⣾⣿⡗⡿⠿⣴⣾⣿⣿⣗⡹⣿⡏⡇⣀⢈⡽⠟⢖⠚⠛⠋⠄⠀⠈⣃⢬⢅⡂⠙⢶⠧⢱⣖⡯⣺⣹⣪⡻⠀⢻⣥⣄⠬⡓⠚⠀⠀⠀⠾⡟⢰⠸⣿⣿⣿⣿⣏⢋⢆⣅⢰⣠⡹⣿⣿⣿⣿
⡟⠛⠻⣟⡿⢿⣟⡛⣻⣿⣧⣿⣿⣿⣾⣮⣿⡛⣿⣿⣿⢋⣻⢟⣎⣠⣤⠤⣘⠻⠠⢷⡀⡵⣲⢴⢦⢀⡜⠣⠐⠛⠯⠤⠄⠛⢿⠿⠀⢀⣼⡿⠈⠳⠂⠄⠀⠀⠀⠀⠁⠁⢀⠶⠫⠻⢙⣻⣿⣇⣄⠀⠙⠟⠁⠉⠉⣻
⠀⣤⣄⢀⣬⢿⣽⠭⣿⣸⣄⣒⠒⡂⣡⡄⠈⡁⠀⠀⢡⣶⡶⠟⠟⠀⡀⠽⠧⢩⠀⢉⣶⡿⡄⠻⣟⡤⡿⣀⣴⣏⣙⣿⣿⣷⣦⣵⣞⣿⣿⣿⢹⣯⣽⣿⣿⣵⡇⢮⡖⣶⠟⡟⣽⡕⢀⣰⣆⠀⠠⣿⣿⣿⠉⠁⠀⠀
⣶⣿⣔⡆⠀⠲⠞⠈⠗⢟⠉⠤⠍⠅⠀⠀⠉⠬⡕⡀⠾⢿⠿⣷⣧⡀⢶⡶⣧⡙⠝⠷⢭⡗⡒⠂⠍⠊⠟⠖⠡⠄⣿⣿⢏⣼⣿⡿⠥⡏⠿⡿⡿⠭⠽⠋⠁⢸⠄⠀⠀⠀⠀⠂⠋⠀⠂⠭⠁⠘⠹⢮⠍⠉⢵⣲⠌⣮
⠀⢴⠄⠃⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⣶⠄⠀⠝⠁⠀⠀⠴⣿⡗⠢⠀⠀⠸⠉⠄⠀⢰⢬⡀⠀⠀⠐⠆⠀⠠⢀⠅⣠⣄⡈⠫⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⠠⠀⠀⠀⣀⡘⠀⠢
⢀⣠⣶⣾⡿⠂⢀⣠⣴⣤⢀⠀⠀⠀⠀⡋⠄⠀⠀⠐⠠⣾⡿⣿⡵⠦⠀⠀⠀⠀⠀⠀⢀⡌⠀⠈⠀⠀⢐⠂⠀⠰⣾⣿⣿⡋⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣶⣦⡀⠀⠀⠀⠄⠘⠀⠀⠀⣲⣖⡞⠙
⡟⠿⠗⠋⠹⠇⠈⠛⠿⣿⣧⡀⠄⠀⠀⠀⠀⠀⠈⠀⠀⠽⣷⣴⣄⡒⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠋⠋⠀⠀⠀⠀⠀⢄⣄⣤⠀⠀⠀⠀⠀⠀⡤⢠⣼⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠚⣯⣴⢈
⢠⡰⠀⠀⠀⠁⠀⠀⢙⠿⠪⠀⡀⠴⠀⠀⠀⠀⣈⡀⠀⣤⢾⠃⠈⠉⠀⠠⠄⠀⠀⠀⡄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣬⣶⣿⣭⣍⠀⠀⠀⠀⣀⢐⣄⣀⣡⡀⣄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⡋⣌⠊
⢰⣅⠂⢀⣤⣂⠀⠀⠀⠠⣬⣀⣀⣾⡶⢄⠀⠀⠈⠀⣀⠙⢋⣴⣿⣧⡀⣤⣶⢊⢀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢀⠄⠀⢚⡟⠛⠛⢹⠟⢵⣄⠀⠐⢚⠀⠀⠀⣶⣴⢾⢉⣉⠀⣐
⣿⡛⣷⠼⠿⢫⡄⠀⠉⠒⠘⡘⠺⣿⢯⣟⡥⣲⠀⠀⠈⣬⣸⣿⣿⣿⠀⡃⠁⠯⠐⠴⠀⠀⠀⠀⠀⢀⣴⣶⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠠⠨⠑⠄⠐⠂⢠⣤⣄⣀⠸⠁⠀⢰⣷⣶⣷⣽⣶⣿⣌⡭
⣿⣿⣟⣻⡇⠀⠀⠀⡀⠅⣛⠋⣲⡭⢷⡋⠙⣤⣀⠀⣈⢽⣿⣿⣟⣿⣼⣝⣈⡄⡀⠰⠄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠄⣀⣷⣤⡶⠶⢶⣿⡉⢁⠜⠀⠉⣉⣻⣷⠲⠼⡌
⡆⠹⣷⣶⠅⠀⠉⠻⠓⠁⠁⠀⠃⠀⠐⡡⠀⠐⠪⠃⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⢀⠀⢻⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⡀⠀⠀⠀⠂⠠⢄⡠⡳⡱⣤⠤⡄⠤⢡⠈⠀⠢⠀⡉⣩⢰⡶⣴⣅
⣶⣷⣯⢙⢇⡀⠀⣄⠠⢸⡫⠖⠀⣀⣦⠬⠁⠩⡋⡌⠨⠝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⢠⣾⣿⣿⣿⣦⣾⣿⠿⠿⠿⠿⠿⠿⠛⠁⠀⠀⠁⠀⠀⠈⣵⣤⠛⣛⣹⡛⡹⢷⡇⢰⣄⣉⣀⢈⢭⢥⣴⠘⠇⣤⡄
⢛⡁⡿⣷⠽⢥⡉⠃⠙⢏⣃⠐⠈⠀⡀⡀⢀⠀⠤⣀⠘⢆⡘⠿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠿⠷⣿⣿⣿⣿⣿⣟⡉⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢴⡿⡿⠿⠉⣨⣦⣴⣾⠟⠽⠿⣝⢋⣽⢏⣀⠉⣴⡎⠉⡇
⣷⣷⡶⣠⣦⣺⡿⢇⠰⣿⡿⡋⢶⣤⠀⠃⠒⣂⣁⣀⣦⣂⣻⠀⣌⡙⠛⠛⣋⢉⠠⡀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣱⡄⢤⠀⠠⠅⠉⢉⡉⠙⢿⡎⠻⢾⠻⢟⡞⠻⡽⢆⠻
⢸⣿⣷⣶⣶⡿⡡⠐⣷⡂⣅⠈⡢⡷⡨⡀⢀⡘⠟⠓⠲⠉⢔⣩⡽⡙⠶⣤⣿⣾⣶⣾⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢀⣤⠄⠀⠀⠀⠐⠀⠠⠈⡠⠐⢁⢀⠀⢀⣴⣶⢃⣉⣻⣸⣶⣳⣶⣅⣅⡤⣀⣀
⠸⣿⣿⣧⡬⣙⡀⣀⠀⣈⢾⣋⣿⡿⠊⠈⢓⠀⣒⣀⣀⠑⣍⢢⠧⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠁⠈⣲⡞⢱⡞⠖⡊⢲⡻⡌⠆⣁⡲⠊⡻⣛⡯⢬⡯⢽⣾⢑⣂
⣒⠙⣿⣛⢿⣏⢿⡼⠂⢬⢭⡡⡔⡜⣦⡖⠄⠪⢨⠘⠈⠂⠈⠏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡷⠀⢷⣤⣤⠀⢄⣧⡾⡿⣏⠰⣵⢧⢄⣤⢷⣿⣼⡤⣿⣡⣿⣿
⣿⠃⡞⣻⣷⣿⡙⠃⠉⠇⠜⠲⠿⢻⠋⣠⡥⠶⠘⣿⠎⠄⣤⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡏⡿⣻⡃⢶⣾⠛⠁⠀⠋⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢃⣬⠻⠛⠠⣮⠻⢛⣗⡛⠛⠟⠶⣾⡽⣿⡿⣿⣯⣳⢽⣿⣿
⢆⢀⠄⡈⠛⣛⢛⣟⠲⣾⠷⡻⠿⢏⡲⢠⣿⣷⡦⢤⣀⣀⠘⠆⢘⣻⣿⣿⠟⢿⠝⢕⠒⠄⢱⣴⣮⣃⠀⠄⠐⠒⠐⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⢗⢈⡱⡀⠐⠲⡤⠀⣸⣗⠐⠀⣀⣈⠉⠉⠸⠋⡩⡄⠀⠂⡉⠍
⣀⠨⣾⡳⣷⢔⣍⠄⣀⣸⣦⣙⣭⣼⣾⢦⣄⣰⣾⡜⢬⣿⣧⣾⣄⣓⠟⠏⡼⠻⢾⠄⢷⢵⣶⣦⠀⠚⢀⣖⡊⠰⠗⢆⣲⠋⣿⣿⣿⠿⠿⠟⠋⣉⡁⠨⢍⣱⢀⣥⣜⠋⡉⢀⡀⠀⣀⡉⠁⠂⠀⠁⣠⡰⠀⠀⣥⡲
⠛⠿⢿⣷⣶⡤⠿⣯⣍⡈⢻⠿⠃⢻⣿⠾⠫⠋⠧⢭⣥⡦⡀⣭⠛⢣⠨⡫⠣⠚⠎⠃⠈⠉⢩⣧⢦⣆⡤⠽⠓⠀⣞⢠⠨⢤⣿⣿⣿⠐⡖⣓⣓⣖⡧⠘⢠⣡⢢⣠⣿⠒⠣⠞⠄⢀⠀⠐⠠⠄⢀⠀⠙⠨⣠⠀⠻⠃
⠀⢀⣀⣿⣿⣽⣿⠛⠅⠈⢠⢬⢠⡆⢀⢹⣶⢶⣤⣘⣥⣥⣾⣿⣈⣞⢷⣓⣂⠐⢄⣊⠙⠄⠀⠙⢿⡠⣖⢴⣠⣁⣡⡑⢂⣩⣿⠿⢇⠌⣹⡹⢽⣿⣲⣴⡆⣾⣦⣿⢝⣶⣤⣙⣀⠢⢶⢾⠄⣴⡆⠀⠄⠀⡀⡀⠀⠀
⣿⣒⢲⣅⡉⠉⢠⡈⢓⣧⡼⡘⣯⢻⣦⣠⣆⣹⡄⢥⢪⡼⢿⠥⢋⡘⢫⢙⣹⣵⡤⠍⠁⡤⡎⢁⣿⠻⢌⣍⢬⣉⡙⠿⡄⠉⠟⣕⡹⣯⠘⠄⠬⣈⣯⣀⣇⣙⡋⠹⣿⣭⣟⠁⢦⡉⠠⠍⣶⠄⠀⠀⠀⠀⠀⠄⠀⠀
⠳⣽⡽⠿⣍⣮⡄⢈⣭⣿⡇⢳⠐⣿⡿⡴⢽⣶⣷⣦⢬⣀⠹⣀⣻⠧⢽⣉⠟⣞⠏⣉⠊⠩⣳⡤⠀⠂⢽⡋⠀⡌⠢⢭⣷⣢⡶⢿⡠⡿⡰⣾⠒⣚⠻⢇⣾⡿⡽⠾⢘⢿⡋⣰⡻⣿⣿⡢⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀
⠀⣶⣾⢓⣿⣿⣷⡠⣹⡶⢶⣿⣿⠾⠳⢿⣗⣿⢿⣿⣯⡁⠀⠀⠙⠰⢿⣇⣿⣎⣉⢺⠖⡆⠀⠨⠂⡀⢀⣿⡄⠰⡶⢞⣻⣯⡄⣳⣾⠍⣤⢙⠂⠹⠷⣿⠟⢆⠕⢘⣦⠙⠃⢄⠀⠊⠙⢷⡆⣀⠀⠀⠀⠀⣴⣿⣷⣶
⢈⣺⣽⣦⣭⣭⢹⣇⡰⠜⢻⣿⣿⣉⡘⣿⡏⢽⡟⠍⡩⣄⠀⠀⠰⠓⢾⣾⡦⣧⣼⣮⣨⣺⡯⡰⠾⢿⣈⣵⢿⣆⠀⢄⠘⠞⠓⢈⢡⡸⠻⣠⣾⣿⣎⠜⣂⣐⡠⣿⡿⠻⠉⠲⢦⠀⠀⣚⡀⠀⠀⠀⠀⢈⣿⣿⣿⣿
⣀⠠⣬⣉⢉⡿⢼⣷⢨⠦⢽⣿⣻⣿⡫⠙⡁⣄⡦⡤⠆⢝⢗⡂⠀⣦⣔⠋⠻⢟⣗⣾⡆⠌⠛⡞⠃⠈⠿⢿⢩⡿⠀⢈⡅⡘⡀⢛⣆⡂⣽⣿⡋⣽⢃⠘⠀⠡⠐⠨⠘⠁⠀⢈⣠⣄⣘⣉⠓⠨⠄⠓⢀⣿⣿⣿⣿⣿
⣂⠨⣻⢹⣊⢀⡬⢙⣈⣴⣾⣿⡗⠽⠿⣴⣾⢿⣿⣷⡹⣿⡟⣗⣀⠈⡽⠟⢶⠈⠛⠋⠄⠀⠐⣓⢈⢕⡂⠙⢶⠥⢰⣖⡭⢋⣭⣢⡿⡂⢹⢥⣄⠬⠁⠈⠀⠀⠀⠾⡟⢴⠸⣿⣿⣿⣿⣏⠋⢆⣅⢴⣸⣿⣿⣿⣿⣿
⡟⠛⠻⢟⡿⢿⣟⡛⣻⣿⣧⣽⣿⣿⣾⣮⣿⡻⣿⣿⣿⢋⣻⢟⢊⢠⣤⠤⣘⠻⠠⢷⡀⡖⣲⣴⢦⢀⠞⠃⠀⠃⠇⠄⠄⠛⢿⡿⠈⣄⣼⣿⣬⣷⡂⠀⠀⠀⠀⠀⠁⠁⡀⠶⠫⠛⢛⣻⡿⣏⣄⠀⠙⠿⠛⠛⠛⣿
⠀⣤⣄⢀⣬⢿⣽⠭⣿⣸⣄⡂⠒⡢⣡⡄⠈⡁⠀⠀⢱⣶⡶⠟⠏⠀⡀⠽⠧⢩⠀⣉⣶⡿⡄⠻⡟⡄⡟⠀⣵⣏⣘⣾⣿⣷⣦⣕⣞⣾⣿⣿⢹⣯⢿⣾⣿⣷⡗⣮⡖⣶⠿⠟⣽⠕⢀⣰⣆⠀⠠⣿⣿⣿⠋⠁⠀⠀
⣦⣿⡕⡆⠀⠲⠞⠈⠏⢟⠉⠤⠍⠅⠀⠀⠉⠬⣕⡀⠾⢿⠿⣵⣦⡀⢶⠶⣧⡍⠝⠷⢭⡓⠖⠂⠏⠋⠟⠖⠡⠄⣿⣿⠏⣼⣿⡿⠥⡏⠿⡿⡻⠭⠽⠋⠁⢸⠄⠀⠀⠀⠀⠢⠋⠀⠂⠭⠁⠘⠹⢮⢍⠉⢥⣲⠬⣮
⠈⢴⡄⠁⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⣶⠄⠀⠝⡁⠀⠀⠴⣿⠓⠂⠀⠀⠐⠁⠄⠀⢰⢬⡀⠀⠀⠐⠆⠀⠠⢀⠅⣀⣄⡈⠻⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⣀⠘⠀⢠
⢀⣤⣶⣾⡿⠀⢀⣠⣴⣤⢀⠀⠀⠀⠀⡋⠄⠀⠀⠐⠠⣾⡿⣿⡵⠦⠀⠀⠀⠀⠀⠀⢀⡈⠀⠈⠀⠀⠐⠂⠀⠰⣾⣿⣿⡋⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣶⣦⡀⠀⠀⠀⠄⠘⠀⠀⠀⣀⣶⡞⠛
⡟⠿⠗⠋⠻⠇⠈⠛⠿⣿⣧⡀⠄⠀⠀⠀⠀⠀⠈⠀⠀⠽⣷⣴⣄⡖⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠋⠋⠀⠀⠀⠀⠀⢄⣄⣤⠀⠀⠀⠀⠀⠀⡤⢠⣼⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠚⣯⣼⢀
⣠⡠⠀⠀⠀⠁⠀⠀⢙⠷⢮⠀⡁⠴⠀⠀⠀⠀⣈⡀⠀⡤⢾⠋⠈⠉⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣠⣍⣉⠉⠀⠀⠀⠀⠀⢀⣀⣀⣡⡀⣄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⡋⣌⠈
⢰⣅⠂⢀⣤⣂⠀⠀⠀⠠⣬⡀⠀⣾⡶⢄⠀⠀⠈⠀⣀⠙⠋⣴⣿⣧⡀⣤⣶⢃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣦⠀⠄⠀⢚⡟⠛⠛⢹⠟⢵⡄⠀⠐⢚⠀⠀⠀⣶⣔⠾⢉⣉⠀⣐
⣿⡛⡷⡼⠿⢯⡄⠀⠉⠆⠈⡐⠲⣿⢧⣟⡧⣲⠀⠀⠈⢬⣸⣿⣿⣻⠀⡂⠁⠯⠀⠔⠀⠀⠀⠀⠀⢀⣤⣶⣦⣤⣢⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠠⠈⠑⠄⠐⠂⢠⣤⡜⣀⠸⠁⠀⢰⣷⣶⣷⣽⣶⣿⣄⡭
⣿⣿⣞⢻⡅⠀⠀⠀⠀⠁⣛⠋⣲⡽⢵⠉⠙⡤⢀⠀⣈⣽⣿⣿⣿⣿⣾⣽⣤⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠄⣀⣷⣤⡶⠶⢶⣿⡉⢁⠜⠀⠉⣉⣻⣷⠲⠔⡤
⡃⠹⣷⣶⠅⠀⠉⠳⠓⠁⠁⠀⠃⠀⠐⡠⠀⠈⠊⠁⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢀⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠂⠠⢄⡠⡳⡱⣴⠤⡄⠬⢡⠈⠀⠢⠀⡉⡹⢰⡶⣴⣅
⣶⣷⣯⢙⢏⡀⠀⢄⠠⢸⡻⠖⠀⣀⣦⡌⠁⠩⡋⡌⠨⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡀⠀⣠⣾⣿⣿⣿⣦⣾⡿⠿⠻⠿⠿⠿⠿⠿⠟⠁⠀⠁⠀⠀⠈⣥⣤⠛⡛⣹⣟⡹⢷⡇⢴⣌⣉⣀⢈⢽⢍⣬⠘⡇⣤⡄
⠛⡃⡿⣧⡼⢥⡉⠂⠙⢍⣃⠐⠈⠀⡀⡀⠀⠀⠬⢀⠘⢄⡙⢿⣿⣿⣿⣿⣿⣿⡿⢿⠿⠿⠷⣿⣿⣿⣿⣿⣿⡉⠀⠈⠁⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢴⡿⡿⠟⠉⠨⣦⣴⡿⠟⠽⠿⣘⣋⢽⢏⣀⠉⣴⡎⠉⢅
⣷⣶⡶⣠⣦⠨⡿⢇⠠⣿⡿⡋⢶⣤⠀⠃⡀⣂⣁⣀⣦⢂⢹⠁⢍⡉⠙⠛⣉⢁⠠⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠀⠀⣰⡄⠠⠀⠠⠅⠉⢉⡉⠙⢿⡎⠻⢾⠻⠟⡟⠻⠹⢎⠛
⢸⣿⣷⣶⣶⡳⡡⠐⣷⡆⣅⠈⠢⡷⡀⠀⢀⡘⠟⠓⠢⠉⢀⣩⡽⡛⠶⣄⣿⣦⣴⣶⣦⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣤⠄⠀⠀⠀⠀⠀⠠⠈⡠⠀⠀⢀⠀⢀⣰⣶⢃⣁⣻⣸⣖⣳⣶⣁⢁⠄⣀⣀
⠸⣿⣿⣧⡬⣙⡀⣀⠀⣈⢼⣋⣿⡿⠊⠈⠓⠀⣒⡀⢀⠑⣍⢂⢣⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣷⣦⣄⠀⠀⠀⢲⡎⢁⡮⠆⡪⢲⣚⡈⠆⣁⡒⠊⡫⣛⡯⢬⡧⢽⣾⢁⣂
⣒⠙⣿⣛⢿⣏⢯⡼⠀⢬⠁⡡⡀⣜⣶⡖⠀⠪⢠⠐⠈⠂⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡤⠀⢷⣤⣤⠀⢄⣦⣾⡻⣇⠰⣵⢧⢀⣤⢶⣵⣬⡤⢷⣡⣿⣿
⣿⠃⡞⣿⣷⣿⡘⠓⠉⠇⢜⠳⠿⣛⠃⣠⡥⠶⠘⣿⠎⠄⣔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡏⡿⡻⠋⢴⠾⠛⠁⠀⠋⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢁⣭⠛⠛⠠⣯⣻⢛⣗⡛⠛⠟⠦⢹⡿⣿⡿⣿⡧⣲⠽⣿⡟
⢆⢄⠤⡈⠛⣛⢛⣞⠒⣖⠗⡻⠿⠏⡲⢠⣿⣷⡦⢥⢁⣀⡙⠟⢿⢿⣿⣿⢿⢿⠛⢕⠓⠄⠱⣴⡮⡃⠀⠄⠐⠂⠂⢀⣉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢈⡑⡀⠐⠒⡤⠀⣨⣏⠐⠀⣠⡈⠉⠉⠸⠋⡩⠄⠀⠈⠉⠅
⣀⠈⣾⡳⣷⢔⣍⠀⣀⣸⣦⣘⣭⣮⣶⢦⣄⣰⣾⡜⢬⣷⢧⣾⡄⣓⠟⡅⡼⠻⢾⠄⠷⢵⣶⡢⠀⠚⢀⢒⡊⠠⠗⢄⣲⠉⣿⣿⣿⢿⣿⡿⠿⢛⡉⠨⢉⣥⢀⣥⣜⠋⠉⢀⡀⠀⣀⡉⠃⠂⠀⠁⢠⠰⠀⠀⣡⡂
⠛⠿⢿⣵⣶⣤⠿⣿⣅⡈⢻⠟⠃⢻⣿⠾⡫⠋⠧⢩⣅⡶⡈⣭⠙⢣⠨⡫⠣⠚⠎⠃⠈⠉⢩⣷⢦⣆⡤⠹⠃⠄⡞⠠⠨⢤⣿⣿⣿⠐⡞⣓⣗⣖⡇⠐⢀⡡⢂⣠⣿⠒⠣⠜⠀⢀⠂⠐⠠⠄⠀⠀⠘⠨⣀⠀⠻⠋
⠀⢀⣀⣿⣿⣽⡿⠋⠅⠈⢠⢦⢠⠆⢀⢹⣷⢶⣤⣘⣭⣥⣶⣿⣀⣜⢷⣃⣒⠀⢄⣊⠙⠀⢀⠙⢿⣰⣲⢸⣀⣁⡡⡑⢂⣩⣿⠿⢇⠌⢹⡹⢭⣿⣢⡰⡀⣮⣢⣽⢙⣶⣤⣑⣀⠢⢤⢢⠄⣴⡆⠀⠄⠀⡀⡀⠀⠀
⣿⣒⢳⣅⡉⠅⢠⡈⢓⣧⡼⡐⢮⣻⣦⣠⣈⣹⡀⣤⢪⡸⢿⠤⢏⡙⢫⢉⣹⣵⡤⠌⠁⡴⡆⠁⡏⠺⠄⣅⢬⣉⡙⠿⡄⠉⠟⡑⡹⣿⠈⠄⠬⣈⣩⣄⣏⣙⡃⠹⢷⣬⣟⠁⢦⡉⠠⠌⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀
⠳⣽⡝⠿⣍⣮⡄⢈⣤⣿⡃⢳⠐⣿⡿⣵⢽⣾⣷⣤⢬⣀⠹⣈⡻⠷⢹⣙⠗⣞⠏⣘⠊⠩⣳⣤⠀⠀⢽⡋⠀⡈⠣⢬⣶⣦⡴⢿⡠⡟⡰⣾⠒⡚⠛⢇⣾⠿⡝⠯⢘⢻⠋⣰⡽⣿⣯⠂⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀
⠀⣶⣾⢓⣿⣿⣷⠠⣹⣶⣶⡿⣿⠮⠻⠿⣗⣯⢿⣿⣯⡅⠀⠀⠙⠰⢾⣏⣿⣎⣋⢸⡖⡆⠄⠬⠀⣀⢀⣿⡄⠰⡶⠞⣻⣇⡄⣳⢾⠅⣴⠙⠃⠹⠷⣽⠜⢆⠔⢈⣤⠘⠁⢀⠀⠈⠙⢷⡆⣀⠀⠀⠀⠀⣴⣿⣿⣶
⠈⣺⣿⣦⣭⢭⢹⣇⣠⠜⢛⣿⣿⣅⡸⣿⡍⢿⡟⠍⠩⣀⠀⠀⠐⠓⢾⣾⡦⣧⣼⣮⣨⣸⡯⠐⠖⢿⣈⣵⢿⡆⠀⢀⠘⠞⠓⢀⢡⡠⠻⣠⣾⣿⣊⠐⢂⣀⡀⣹⠟⠡⠉⠲⠦⠀⠀⣂⡈⠠⠀⠀⠀⠀⢻⣿⣿⣿
⣀⠠⣬⣍⢉⡿⢼⣷⢨⠦⢽⣿⣻⣿⡫⠙⡡⣄⡶⡤⠦⢝⢷⡂⠀⣦⣼⠉⠻⢚⣳⣾⡆⠌⢛⡆⠃⠈⠟⢿⢀⠟⠀⢈⡀⠘⡀⢛⣇⡂⣿⣿⡋⣼⢂⠘⠀⠀⠀⠀⠘⠀⠀⢈⣠⣄⣘⣉⠃⠠⠀⠑⠀⢀⣾⣿⣿⣿
⣂⠨⣫⢹⣊⢀⡬⢙⣈⣤⣾⣿⡕⠹⠿⣴⣾⣻⣿⣷⡻⣿⡟⣗⣀⠈⡽⠞⢶⠈⠛⠋⠄⠀⠐⡑⢨⢵⡆⠙⢆⠤⠰⠀⠡⢂⢭⣢⣿⡌⠻⣡⣄⡬⠁⠀⠀⠀⠀⠴⡟⢰⠸⣾⣿⣿⣿⣏⠉⢆⡅⢠⣀⣾⣿⣿⣿⣿
⡟⠛⠻⣟⡿⢿⣛⡛⣻⣿⣧⣽⣿⣿⣿⣦⣿⡛⣿⣿⣿⢋⣻⠟⢊⣠⣤⠤⣘⠿⠀⢿⡀⡐⣂⣴⣦⠀⡞⠃⠀⠃⠂⠀⠀⠙⠻⡷⣠⣶⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠁⠁⢀⠶⠫⠛⢛⣻⡾⣆⣄⠀⠙⠻⣿⣿⣿⣿
⠀⣤⣄⢀⣬⢿⣽⠭⣿⣨⡄⡒⠒⡢⣡⡀⠈⡁⠀⠀⢱⣴⡶⠟⠟⠀⡀⠽⠵⢩⡀⣁⣶⡿⡆⠻⡟⡄⡛⡀⡵⣏⢘⣾⣿⡷⣦⣕⣞⣾⣿⣿⢙⣯⢽⣶⣿⣵⡇⢪⡖⣶⠟⠟⣽⠕⠀⣰⣆⠀⢠⣿⣿⡿⠉⠁⠀⠀
⣦⣟⡕⡆⠀⠲⠞⠈⠇⢟⠉⠤⠍⠅⠀⠀⠉⠬⡕⡀⠾⢿⠿⣔⣦⡀⢶⡶⣧⡉⠝⠷⢨⡑⠖⠂⠍⠋⠋⠖⠡⠄⣿⣿⠏⣼⣿⡿⠤⡏⠿⡿⡾⠭⠱⠋⠁⢰⠄⠀⠀⠀⠀⠀⠋⠀⠂⠭⠁⠘⠹⢮⢍⠉⢤⣲⠬⣬
⠈⢴⡄⠁⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⣶⠄⠀⠝⠁⠀⠀⠴⣟⠟⠂⠀⠀⠰⠁⠄⠀⢰⢤⡀⠀⠀⠐⠆⠀⠀⢀⠅⣀⣄⡈⠻⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⠠⠀⠀⠀⢀⠘⠀⢢
⢀⣤⣶⣾⡿⠂⢀⣠⣴⣤⢀⠀⠀⠀⠀⠋⠄⠀⠀⠐⠠⣾⡿⣿⡵⠦⠀⠀⠀⠀⠀⠀⢀⡌⠀⠈⠀⠀⠐⠂⠀⠰⣾⣿⣿⡋⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣶⣦⡀⠀⠀⠀⠄⠘⠀⠀⠀⣀⣶⡞⠛
⡞⠿⠗⠋⠻⠇⠈⠛⢿⣿⣧⡀⠄⠀⠀⠀⠀⠀⠈⠀⠀⠽⣷⣴⣄⡒⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠉⠋⠀⠀⠀⠀⠀⢄⣄⣤⠀⠀⠀⠀⠀⠀⡠⢠⣼⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠚⠧⣴⢀
⠠⡠⠀⠀⠀⠁⠀⠀⢙⠷⠮⠀⡁⠴⠀⠀⠀⠀⣈⡀⠀⣤⢾⠃⠈⠉⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠰⢍⠉⠉⠀⠀⠀⠀⠀⠀⢀⣀⣡⡀⣄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⡋⣌⠚
⢰⣅⠀⢀⣤⣂⠂⠀⠀⠀⢬⣀⣀⣾⡶⢄⡀⠀⠈⠀⣀⠙⠋⣴⣿⣧⡀⣤⡶⢂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣶⣦⡀⠀⠀⢚⠟⠛⠛⢹⠟⢵⣄⠀⠀⢘⠀⠀⠀⣶⣔⠾⠉⣉⠀⣐
⣿⢛⡷⠼⠿⢻⡄⠀⠉⠆⠘⡐⠲⣿⢪⣕⡥⣲⠀⠀⠈⣬⣸⣿⣿⣻⠀⠂⠁⠯⠀⠔⠀⠀⠀⠀⠀⢀⣤⣶⣦⣤⡀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠠⠨⠁⠄⠀⠂⢠⣤⡜⣀⠸⠁⠀⢰⣷⣶⣷⣵⣶⡿⣄⠭
⣟⣿⣾⢻⡆⠀⠀⠀⠀⠁⣛⠋⣒⡽⢵⡃⠙⣤⢀⠀⣈⣽⣿⣿⣿⣿⣾⣽⣄⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠄⣀⣷⣤⡶⠶⢾⣿⡉⠁⠜⠀⠉⣉⣻⣷⠲⠔⡼
⠃⠹⣷⣶⠅⠀⠉⠳⠓⠀⠁⠀⠃⠀⠐⡠⠀⠁⠊⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⣀⣻⣿⠿⠟⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠐⠂⠠⢄⡠⡳⡹⣤⠤⠄⠤⢡⠈⠀⠂⠀⡉⣻⢰⡶⢔⣅
⣖⣿⣯⠙⢏⡀⠀⢀⠠⢸⡫⠔⠀⣀⣢⠌⠁⠩⣋⢌⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⣴⣿⣿⣿⣿⣧⣶⣿⠿⠿⠿⠿⠿⣿⣿⣿⠿⠋⠁⠀⠀⠈⣥⣤⠟⣛⣹⣟⡹⢷⡅⢰⡌⣉⣀⢈⣼⢤⣬⠘⠇⣴⡄
⠛⡃⡷⣶⠬⢅⡉⠂⠙⢉⣁⠐⠈⠀⡀⠀⠀⠀⠠⢀⠸⢎⠿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⠿⠷⣿⣿⣿⣿⣿⣿⣍⠀⠀⠁⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢴⡿⠿⠟⠉⠨⣦⣴⣾⠟⠽⠿⣜⢋⢽⢏⣀⠉⣴⡎⠉⢇
⣷⣷⡶⣠⣦⠨⡿⢇⠠⣿⡿⡋⢶⡤⡀⠃⠀⣂⣁⣀⢆⠂⠱⠁⢍⡛⠛⠛⣉⠁⠠⢀⡄⠀⠀⠈⣹⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠁⠀⠀⠈⠁⠐⠀⠀⢰⡄⠠⠀⠠⠅⠉⢉⡉⠙⢷⡎⠻⢾⠻⢿⡞⠻⡴⢆⠻
⢸⣿⡷⣶⣶⡳⡡⠐⣷⡂⢅⠀⡢⡲⡈⠀⠀⠘⠟⠓⠲⠈⢀⣩⠍⡙⠶⣄⣿⢀⣀⣬⣤⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢀⣤⠄⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⣰⢶⠃⣁⣻⣸⣶⣳⣶⣁⢁⠄⣀⣀
⠸⣿⣿⣇⡬⣙⡀⣀⠀⣈⢺⣊⣿⡷⠊⠈⠀⠀⣒⡀⢀⠑⣍⠀⠇⣀⢀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣿⣿⣿⣿⣿⣿⣿⣷⣾⣾⣿⣿⣷⣦⣀⠁⠀⢢⡆⢁⡍⠆⡊⢳⣚⡌⠆⣁⡐⠈⠻⡛⡯⢌⡣⠽⣿⢁⣊
⣘⠙⣿⣛⠿⣏⢽⡼⠀⢬⠁⡡⡀⠜⣴⠖⠄⠢⢠⠀⠈⠀⠈⠧⢚⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢳⣤⣠⠀⢀⣦⣼⡿⣇⠰⡕⢧⢀⢤⢶⣴⡴⣤⢿⣱⣿⣿
⣿⠃⡞⣻⣷⣿⡘⠃⠉⠏⠜⠲⠿⣛⠃⡠⠅⠐⠘⡿⡎⠆⣤⢻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡿⣻⡋⠴⠾⠋⠀⠈⠋⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⠙⠛⠀⣮⣻⢛⣗⡛⠛⠟⡦⢹⠿⣿⡿⣿⡦⣲⠜⣺⡿
⢇⢀⠤⡈⠛⣛⢛⣟⠒⡦⠗⡻⠿⠏⡦⢰⣽⡷⡢⢠⣀⣀⢘⠎⣿⣿⣿⣿⣿⣿⣿⣿⠟⠄⠱⡴⠮⠋⠀⠀⠐⠂⠀⢀⢁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡑⡀⠐⠒⡤⠀⣸⣏⠐⠀⣠⡈⠉⠉⠰⠋⡩⡄⠀⠈⠉⠁
⣀⠈⣾⡳⣷⢐⣍⠄⣀⣨⣦⣐⣭⣦⣴⢆⣄⣰⣾⡘⢤⣷⣣⣄⣜⣻⣿⣿⠿⠟⢿⠄⠶⢴⣶⡢⠀⠒⢀⢒⡊⠠⠗⢄⣲⠋⣿⣿⣿⣿⣿⣿⣿⣿⡟⠫⢨⢥⢀⣥⣔⠋⠉⢀⡀⠀⣀⡉⠀⠂⠀⠁⡠⠰⠀⠀⣡⡒
⠛⠿⢿⣵⣶⡤⡿⣿⣀⡈⢻⠟⠃⢻⣿⠾⠯⠉⠧⢭⣅⡶⡀⣬⠛⢣⠨⡉⠢⠚⠏⠁⠈⠉⢩⣯⢢⣆⡤⠭⠃⠄⡞⠠⠨⢼⣿⣿⣿⠐⡼⣛⣟⣖⠇⠐⢀⡠⢂⣠⣿⠒⠣⠟⠄⢀⠀⠐⠠⠀⢀⠀⠘⠠⣀⠀⠻⠋
⠀⢀⣀⣻⣿⣽⣿⠋⠍⠈⢠⢦⢠⡆⢀⢙⣶⢶⣤⣔⣥⣥⣶⣻⡤⡜⢷⣃⣐⠀⠄⣊⠙⠠⠀⠙⢯⣰⣤⠰⣠⣁⡡⡑⢀⢹⣿⠿⢇⠌⢹⡙⢽⣿⣢⠰⠀⣮⣢⣿⢙⣶⣤⣉⢀⠢⢤⢺⠄⣴⡆⠀⠀⠀⠀⡀⠀⠀
⣿⣐⢳⣄⡉⠍⢠⡈⢓⣧⡼⠘⣮⢋⣦⣠⣔⣹⡀⣄⢨⡸⢿⠮⢋⡙⢫⢉⣹⣕⣤⠈⠁⡠⡆⠁⡏⠚⠌⣥⢬⣉⡓⠿⡄⠈⠟⡑⣹⢯⠈⠄⠬⣈⣫⠈⢇⣙⡃⠹⣳⣬⣝⠁⢦⡁⠠⠌⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀
⠳⣼⡽⢿⣍⣮⡄⢈⣭⣾⡇⢣⠐⣿⡿⡵⢽⣾⣷⣤⣬⣀⠱⢀⣻⠯⢹⣛⠗⠞⡍⣉⠉⠩⣳⣤⠀⠐⢹⡋⠀⡈⠲⢮⣶⣦⣶⣿⡤⡟⡰⣿⠒⠚⠛⢇⠼⡫⡝⠈⢘⢻⠋⠠⡹⢿⣯⡂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀
⠀⣶⣾⠓⣿⣿⣷⡠⣹⣶⣶⣿⣿⠯⠳⢿⣕⣯⢿⣿⣯⣅⠀⠀⠙⠰⢾⢏⣿⣎⣋⠸⡆⡄⠄⠤⠂⣀⢀⣿⡄⠰⡶⠾⣻⣏⡄⣓⣾⠏⢴⠙⠀⠹⠷⡼⠜⢆⠄⢈⣤⠐⠁⠀⠀⠈⠙⢷⡄⡀⠀⠀⠀⠀⣴⣿⣿⣶
⠀⣺⣹⣦⣭⣭⢹⣇⣀⠜⠛⣿⣿⣍⡘⣿⡏⢟⡟⠉⠩⣈⠀⠀⠀⠓⢾⣼⡧⣧⣼⣮⢈⣸⡦⠐⠶⢿⣈⣵⢿⡆⠀⢀⠘⠞⠓⢈⢁⡨⠫⣤⣾⣿⣊⠀⢀⣀⡀⣹⠟⠠⠉⠰⠂⠀⠀⣂⡀⠠⠀⠀⠀⠀⢻⣿⣿⣿
⣀⠀⣬⣉⢉⡾⢼⣷⢨⠦⠽⣿⣻⣿⡫⠙⡁⣄⡴⡤⠇⢹⢶⡂⠀⣦⣴⠋⠻⠙⣲⣾⣆⠌⢛⡔⠁⠈⠟⢻⢀⠟⠀⢈⡀⠊⡄⢹⢆⡂⣿⣿⡋⣼⢂⠐⠀⠀⠀⠀⠀⠀⠀⢈⣠⣀⣈⣉⠃⠠⠀⠐⠀⠀⣼⣿⣿⣿
⢂⠈⣋⢹⣊⢀⠬⢙⣀⣼⣼⣿⡝⢹⠿⣴⣾⣻⣿⢗⡩⣿⡟⣇⣀⠈⡽⠟⢖⠈⠙⠃⠄⠀⠐⣐⣠⢅⡂⠙⢦⠀⠠⠀⠡⢂⢭⣢⡿⡊⠹⣠⣄⡬⠁⠀⠀⠀⠀⠴⡟⢐⠐⣾⣿⣿⣿⣅⠈⠂⠅⢰⣀⣰⣿⣿⣿⣿
⡟⠛⠻⣟⡿⢿⣟⡛⣻⣟⣧⣽⣿⣿⣿⣦⣿⡛⣿⣿⣿⢋⣹⠟⢊⣀⣤⠄⣘⠿⠠⢾⡀⡔⣒⣴⣦⠀⡌⠃⠀⠂⠃⠀⠀⠉⠣⣶⣬⣾⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠁⠁⢀⠶⠫⠙⢛⣻⡶⣆⣄⠀⠙⢿⣿⣿⣿⣿
⠀⣤⣄⢀⣬⢿⣵⠭⣽⣸⡄⣒⠒⡢⣡⡄⠈⡁⠀⠀⢡⣶⡶⠟⠟⠀⡀⠽⠧⢩⡀⣁⣶⡿⡆⠻⣟⡦⠟⣀⣸⣏⢘⣾⣿⣷⣦⣕⣞⣾⣿⣿⢙⡯⢽⣾⣿⣵⡇⢪⡖⣶⠟⠟⣽⠕⠀⣰⣆⠀⢠⢿⣿⡿⠉⠁⠀⠀
⣦⣟⣕⠆⠀⠢⠞⠈⠗⢟⠉⠤⠍⠅⠀⠀⠉⠬⠕⡀⠾⢿⠿⣴⣦⡀⢶⡶⣧⡍⠝⠷⢭⡗⠒⠂⠍⠋⠟⠖⠡⠄⣿⣿⠏⣽⣿⡿⠤⡏⠿⡿⡿⠯⠵⠋⠁⢰⠄⠀⠀⠀⠀⠀⠋⠀⠂⠭⠁⠘⠹⢮⢍⠉⢥⡲⠬⣬
⠈⢴⠄⠁⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⣶⠄⠀⠝⠁⠀⠀⠴⣟⠗⠂⠀⠀⠰⠁⠄⠀⢰⢤⡀⠀⠀⠐⠆⠀⠠⢀⠅⣠⣄⡈⠻⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⠠⠀⠀⠀⣀⠘⠀⢢
⢀⣤⣶⣾⡿⠂⢀⣠⣴⣤⢀⠀⠀⠀⠀⠋⠄⠀⠀⠐⠠⣾⡿⣿⡵⠦⠀⠀⠀⠀⠀⠀⢀⠈⠀⠈⠀⠀⠐⠂⠀⠰⣾⣿⣿⡋⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣶⣦⡀⠀⠀⠁⠄⠘⠀⠀⠀⣀⡶⡞⠙
⡞⠿⠗⠋⠳⠇⠈⠛⠿⣿⣧⡀⠄⠀⠀⠀⠀⠀⠈⠀⠀⠽⣷⣴⣄⡒⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠉⠋⠀⠀⠀⠀⠀⢄⣀⣤⠀⠀⠀⠀⠀⠀⡠⢠⣼⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠚⡯⣴⢀
⠠⡰⠀⠀⠀⠁⠀⠀⢙⠿⠮⠀⡁⠴⠀⠀⠀⠀⣀⡀⠀⣤⢾⠃⠈⠉⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⢍⠉⠉⠀⠀⠀⠀⠀⠀⢀⣀⣡⡀⣄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⡋⣌⠚
⢐⣅⠀⢀⣤⢂⠂⠀⠀⠀⢬⣀⣀⣾⡶⢄⡀⠀⠈⠀⣀⠙⠋⣴⣿⣧⡀⣄⣶⢂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣶⣦⡀⠀⢀⢚⠟⠛⠛⢹⠟⢵⣄⠀⠀⢘⠀⠀⠀⣲⣔⠾⠉⢉⠀⣐
⣿⣻⡷⠼⠿⢫⡄⠀⠙⠆⠘⡐⠲⣿⢪⣗⡥⣲⠀⠀⠈⣬⣸⣿⣿⣻⠀⡂⠁⠯⠀⠔⠀⠀⠀⠀⠀⢀⣤⣶⣦⣤⡀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠠⠈⠁⠄⠀⠂⢠⣤⡌⣀⠸⠁⠀⢰⣷⣶⣷⣵⣶⡿⣄⠭
⣿⣿⣮⣻⡄⠀⠀⠀⠀⠁⣛⠋⣲⡭⢵⡃⠙⣤⢀⠀⣈⣿⣿⣿⣿⣿⣾⣽⣄⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠄⠌⣀⣷⣤⡶⠶⢾⣿⡉⠁⠜⠀⠉⣉⣻⣷⠶⠄⡤
⡃⠹⣷⣶⠅⠀⠉⠣⠂⠀⠁⠀⠃⠀⠐⡠⠀⠀⠊⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⣀⣻⣿⠿⠟⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠂⠠⢄⡠⡻⡹⣤⠤⠄⠤⢡⠈⠀⠂⠀⡉⣹⢰⡶⢴⣅
⣶⣷⣯⢙⢇⡀⠀⢄⠠⢸⡫⠔⠈⣀⣢⠌⠁⠩⡋⣌⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⣴⣿⣿⣿⣿⣧⣶⣿⠿⠿⠿⠿⠿⣿⣿⣿⡿⠋⠁⠀⠀⠈⣥⣤⠟⣛⣹⣏⡹⢷⡅⢰⣌⣉⣀⢈⣬⢅⣦⠘⠇⣴⡄
⠛⡃⡷⣶⠼⢄⡉⠂⠑⢉⣁⠀⠈⠀⡀⡀⠀⠀⠠⢀⠸⢌⠿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⠿⠷⣿⣿⣿⣿⣿⣿⣍⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢴⡿⠿⠟⠉⠨⣦⣴⡾⠟⠽⠿⣜⢋⢽⢏⣀⠉⣴⡎⠉⠅
⣷⣶⡶⣠⣦⠨⡿⢇⠠⣿⡿⡋⠶⣤⡀⠁⠀⣂⣁⣀⢆⠂⠱⠁⣍⡛⠛⠛⣉⠀⠠⢀⡄⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠁⠀⠀⠈⠀⠐⠀⠀⣱⡄⠠⠀⠠⠅⠉⢉⡉⠙⢿⡎⠻⢞⠻⠟⡿⠻⠼⢄⠻
⢸⣿⡷⣶⣶⡷⡡⠐⣷⡂⢅⠀⡢⡲⡀⠀⠀⠘⠟⠓⠢⠉⢀⣩⠭⡙⠶⣄⣿⠀⣀⣬⣤⣀⣴⣾⣿⣿⢿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢀⣤⠄⠀⠀⠀⠀⠀⠠⠈⡀⠀⠂⠀⠀⢀⣰⣶⢃⣁⢻⣸⣶⣳⣶⡁⢁⠄⣀⣀
⠸⣿⣿⣇⡬⣙⡀⣀⠀⣈⢼⣋⣿⡷⠊⠈⠀⠀⣒⡀⣀⠁⣍⢀⠇⣠⢀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣿⣿⣿⣿⣿⣿⣿⣷⣾⣾⣿⣿⣷⣦⣀⠀⠀⢢⡄⢁⡎⠆⡨⢳⣚⡈⠆⣁⡰⠈⠫⡛⡯⢈⡣⢽⣿⢁⣊
⣚⠙⣯⣛⠿⣏⢯⡼⠀⢬⠡⡡⡀⢜⣴⠖⠄⠪⢀⠀⠈⠀⠈⠯⢘⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢳⣤⣠⠀⢀⣦⣼⡿⣃⠰⡕⢡⢀⢤⢔⣴⣴⡤⢷⣱⣿⣿
⣿⠃⡞⣻⣷⣿⡘⠓⠉⠏⠜⠓⠟⣻⠋⢠⠥⠐⠘⣿⡎⠆⣤⢻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡿⣻⡋⠴⠾⠋⠀⠀⠋⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⠛⠛⠀⣮⡹⢛⣗⡛⠛⠟⠦⠙⠿⣿⡿⣿⡦⣲⠜⣾⡟
⢆⠀⠤⡈⠛⣛⢛⣟⠒⡆⠗⡻⠿⠏⡲⢠⣽⡵⡢⢡⣁⣀⠘⠆⣿⣿⣿⣿⣿⣿⣿⣿⠟⠄⠰⡴⡾⠋⠀⠀⠐⠂⠀⢀⢁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡡⡀⠐⠒⡤⠀⣨⣏⠀⠀⣠⡈⠉⠉⠸⠋⡩⡄⠀⠈⠉⠁
⣀⠈⣾⡳⣷⢔⣍⡄⣀⣸⣦⡘⣭⣦⣶⢦⣌⣰⣾⡘⢤⣷⣣⣤⣜⣻⠿⣿⡿⠟⢿⠄⢶⢴⣶⠢⠀⠒⢀⢐⡊⠠⠇⢄⣲⠋⣿⣿⣿⣿⣿⣿⣿⣿⡟⠫⢨⣥⢀⣥⣜⠋⠉⢀⡀⠀⣀⡉⠁⠂⠀⠁⡠⠐⠀⠀⣡⡒
⠛⠿⢿⣵⣶⡤⡟⣯⣄⡈⢻⠟⠃⢻⣿⠾⠯⠉⠧⢭⡅⡶⠀⣭⠙⢣⠨⡋⠡⠚⠏⠃⠈⠉⢩⣧⢂⣦⡤⠩⠃⠄⡞⠁⠨⢤⣿⣿⣿⠐⡼⣛⣛⡖⠇⠐⢀⡀⠂⣠⣿⠒⠃⠜⠀⢀⠀⠐⠠⠀⢀⠀⠘⠠⣀⠀⠻⠋
⢀⢀⣀⣿⣿⣽⣿⠋⠍⠈⢠⢦⢠⠄⢀⢘⣷⢶⣤⣜⣥⣥⣾⣿⠠⡜⢷⣃⣒⠀⠄⣊⠙⠀⠀⡙⢿⣐⣢⠰⣀⣁⡡⡑⢀⢰⣿⡿⢇⠌⢹⡙⢽⣿⣢⠠⡀⣬⣢⣿⢙⣶⣤⣑⢀⠢⢠⢺⠄⣴⡆⠀⠀⠀⠀⡀⠀⠀
⣿⣖⢷⣅⡉⠍⠀⡈⢓⣧⡼⡘⢯⢻⣧⣠⣐⣹⡀⣤⠠⡘⢿⠮⢏⡙⢫⢉⣹⣥⡤⠈⠁⡠⡌⠁⡏⠚⠄⣥⢎⣉⡑⠿⡄⠉⢟⣑⡸⣷⠈⠄⠨⣈⣫⢈⢇⣙⡃⠩⣧⣭⣝⠁⢦⡁⠠⠌⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀
⠲⣼⡝⠿⣍⣮⡄⢈⢭⣷⣇⢳⠐⣿⡿⣵⢭⣶⣷⣦⢬⣀⠑⣀⣻⠯⢻⣙⠗⠞⣭⣉⠊⠩⣳⡤⠀⠀⢹⡋⠀⡈⠳⢎⣴⣢⡶⡿⡠⠟⡰⣾⠒⠊⠛⢇⠾⠫⡝⠈⢘⢻⠋⡀⠹⢿⣏⠂⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀
⠀⣶⣾⠓⣿⣿⣷⡠⣹⡶⣶⡿⣿⠯⠳⢿⣗⣯⢿⣷⣯⡅⠀⠀⠙⠰⢾⢏⣿⢎⣉⢸⡆⡆⠀⠤⠂⣀⢀⣿⡄⠰⡦⠞⣻⣇⡄⣓⣾⠍⢴⠝⠂⠹⠷⣬⠘⢀⠄⢈⣤⠐⠁⠀⠀⠈⠙⢷⡄⣀⠀⠀⠀⠀⣴⣿⣿⣶
⠀⣺⣹⣦⣭⡭⢹⣇⡀⠜⠟⣿⣿⣍⡘⣿⡍⢽⡟⠉⡩⣀⠀⠀⠀⠓⢾⣼⡧⣧⣼⣮⢨⣸⡧⠰⠖⢿⣈⣵⢿⣄⠀⢀⠘⠞⠓⢈⢡⡨⠫⣠⣾⣿⣊⠀⢀⣀⡀⣹⠟⠡⠉⠰⠂⠀⠀⣂⠈⠠⠀⠀⠀⠀⢻⣿⣿⣿
⣀⠠⣬⣍⢉⡾⢼⣷⢨⠦⠽⣿⣻⣿⡫⠙⡃⣄⡶⡤⠇⢹⢷⡂⠀⣦⣴⠋⠻⠟⣲⣾⣆⠌⢚⡐⠁⠈⠟⢿⢀⠟⠀⢈⡀⠘⡄⢻⣂⡂⣽⣿⡋⣼⢃⠐⠀⠀⠀⠀⠀⠀⠀⢈⣠⣄⣘⣉⠁⠠⠀⠐⠀⠀⣼⣿⣿⣿
⢂⠈⣋⢹⣊⢀⡬⢙⣠⣼⣼⣿⡕⡹⠿⣴⣾⣿⣿⢗⡩⣿⡟⣇⣀⠈⡽⠟⢖⠈⠋⠋⠄⠀⠐⣐⢠⢅⡂⠙⢦⠀⠠⠀⠥⢂⢩⣢⣿⠜⠻⣠⣄⣼⠁⠀⠀⠀⠀⠴⡟⢐⠐⣾⣿⣿⣿⣅⠈⠂⠀⢐⣀⣰⣿⣿⣿⣿
⡟⠛⠻⣟⡿⠿⣟⡛⣛⣟⣧⣽⣿⣿⣿⣦⣿⡛⣿⣿⣿⢋⣹⢟⢊⢀⣤⠤⣘⠽⠀⢾⡀⡐⣒⣴⣂⠀⡎⠃⠀⠀⠂⠀⠀⠉⠣⣾⣬⣶⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠁⠁⢀⠶⠫⠛⢛⣻⡾⣆⣄⠀⠙⢿⣿⣿⣿⣿
⠀⣤⣄⢀⣬⢿⣵⠭⣷⣸⡅⣒⠒⡢⣡⡀⠘⡁⠀⠀⠡⣼⡶⠟⠟⠀⡀⠽⠥⢩⡀⣁⣲⡿⡆⠻⡟⡄⠟⣀⣼⣏⣘⣾⣿⣷⣦⣕⣞⣿⣿⣿⠙⡯⢽⣾⣿⣵⡇⢪⡖⣶⠟⠗⢹⡕⠀⣰⣆⠀⠠⢷⣯⡿⠉⠁⠀⠀
⣦⣷⣵⡆⠀⠢⠖⠈⠇⢟⠉⠤⠍⠅⠀⠈⠑⠬⠕⡀⠾⢿⠿⣶⣦⡀⢶⡶⣧⡉⠝⠧⢬⡁⠒⠂⠍⠊⠏⠖⠡⠀⣿⣿⠯⣼⣿⡿⠤⡏⠿⠿⡻⠭⠱⠋⠁⠰⠄⠀⠀⠀⠀⠢⠋⠀⠂⠍⠁⠐⠹⢮⢍⠍⢤⡲⠌⣬
⠉⢤⡄⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣶⠄⠀⠙⡀⠀⠀⡴⣿⠗⠂⠀⠀⠐⠁⠄⠀⢰⢤⡀⠀⠀⠐⠆⠀⠠⢀⠅⣀⣄⡈⠋⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⢀⡘⠀⢠
⢀⣠⣶⣾⡿⠀⢀⣠⣴⣤⢀⠀⠀⠀⠀⠉⠄⠀⠀⠀⠠⣾⡿⣿⡥⠦⠀⠀⠀⠀⠀⠀⢀⠈⠀⠈⠀⠀⠐⠀⠀⠰⣼⣿⣿⡋⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣶⣦⡀⠀⠀⠀⠄⠘⠀⠀⠀⣀⣖⣞⠙
⡞⠿⠗⠋⠓⠇⠈⠛⢿⣿⣧⡀⠄⠀⠀⠀⠀⠀⠈⠀⠀⠽⣷⣴⣄⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠉⠋⠀⠀⠀⠀⠀⢄⣄⣤⠀⠀⠀⠀⠀⠀⡠⢠⣬⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠚⡯⣼⠀
⢠⡰⠀⠀⠀⠀⠀⠀⢐⠿⢮⠀⡁⠴⠀⠀⠀⠀⣀⡀⠀⣠⢾⠃⠈⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣰⣭⣭⣭⣀⡀⠀⠀⠀⠀⢀⣀⣡⡀⣄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⡉⣌⠊
⢐⣅⠀⢀⣴⣂⠆⠀⠀⠀⢬⡀⠀⣾⡶⢄⠀⠀⠈⠀⣀⠝⠋⣴⡿⣧⡀⣤⡖⢂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⢘⠛⠛⠛⢩⠞⢴⡄⠀⠀⢘⠀⠀⠀⣲⣔⠾⠋⢉⠀⣐
⣿⠛⡷⠼⠾⢫⡄⠀⠙⠖⠈⡀⠲⣿⢣⣕⠥⣲⠀⠀⠈⣬⣸⣿⣿⣳⠀⠂⠁⠯⠀⠔⠀⠀⠀⠀⠀⢀⣤⣶⣦⣤⡂⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⠡⠄⠐⠂⢠⣤⡜⣀⠸⢁⠀⢰⠷⣶⣷⣴⣶⣿⣀⠩
⣿⣿⣞⢻⡆⠀⠀⠀⠀⠅⣛⠋⣒⡭⢵⡋⠙⣤⢀⠀⣈⣽⣼⣿⣿⣿⣾⣿⣄⡀⠀⠀⠀⠐⠀⠀⠀⢸⣿⣿⣿⣿⡇⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠄⣀⣷⣤⡶⠶⢶⣿⡉⠁⠜⠀⠉⣉⣻⣷⠰⢄⡤
⡇⠹⣷⣶⠅⠀⠉⠣⠃⠀⠁⠀⠃⠀⠐⡠⠀⠀⠈⠋⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢀⣤⣴⣿⣿⣿⠛⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢠⢄⡠⡳⡹⣤⠤⡄⠤⢡⠈⠀⠂⠀⡉⣹⢰⡶⢄⢅
⣶⣿⣯⠙⢗⡀⠀⢄⠠⠰⡪⠔⠈⣀⣢⠌⠁⠩⡋⡄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⠀⢰⣿⣿⣿⣿⣿⣷⣴⣾⡿⠿⠟⠿⠛⠿⠿⠿⠿⠟⠉⠀⠀⠊⡡⣤⠟⣻⣹⡍⡹⢷⡅⢰⣌⣉⣀⢈⣬⢄⣮⠘⠇⣴⡄
⠛⡃⡷⢧⠬⢅⠉⠂⠑⢉⣀⠐⠈⠀⡀⠀⠀⠀⠠⣀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢴⡿⠿⠟⠉⠈⣧⣴⣾⠟⠽⠿⣜⢋⢽⢏⣀⠉⣴⡆⠉⢀
⣷⣶⡶⢠⣦⡨⠿⢇⠠⣿⡿⡋⠶⢤⡀⠃⠀⢂⣁⣀⣦⠂⢹⠙⢟⡛⠛⠛⣉⠀⠠⣠⡄⠀⠀⠉⢻⣿⡿⣿⣿⣿⣶⣶⣤⣀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠀⠀⢀⡄⠀⠀⠀⠅⠉⢉⡉⠙⠷⡎⠹⢞⠻⢟⡞⠻⡵⢄⠫
⢸⣿⡷⣶⣶⡷⡅⠐⣷⡆⢅⠈⠂⡶⡈⠀⠀⠘⡟⠓⠲⠈⢀⣡⡭⡙⠶⣤⣿⠀⠀⣀⣅⣀⣀⣴⣿⣿⠁⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⣴⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣰⣶⠃⣀⣻⣸⣖⣳⣲⣁⢁⠄⢀⣀
⠸⣿⣿⣇⡬⣙⡀⣀⠀⢀⠺⣊⢿⡷⠊⠈⠀⠀⣒⡀⢀⠁⣍⠂⢇⡰⠀⣈⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣷⣦⡈⢠⡄⢀⡄⠀⡀⢱⣛⡄⠆⡀⡐⠈⠻⡉⣭⢘⡣⠿⣿⢉⣊
⣐⠉⣻⣛⢿⣏⢯⡼⠂⢠⠡⡁⡀⠜⣤⡖⠄⠪⢀⠀⠈⠀⠈⠟⢚⢦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣠⠀⠀⢂⡼⡿⣏⠰⡕⢣⢀⢤⢴⣽⣼⣄⢷⣱⣿⣿
⣿⠃⠜⢿⣷⣿⡙⠃⠉⠇⠝⠓⠻⣛⠋⣠⠅⠔⠊⣷⠎⠆⣤⠻⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡿⡻⡉⢴⠾⠋⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠀⣯⡹⢛⣗⡛⠛⠝⠆⡿⠿⣿⡿⣿⡦⣢⠼⣻⡟
⢆⠀⠠⡈⠛⣛⢛⣞⠒⡶⠗⣫⠟⠏⡳⢠⣿⣵⡦⢥⢀⣀⡘⠆⣿⣿⣿⣿⣿⣿⣿⣿⡿⠄⢹⡸⡮⠋⠀⠀⠐⠒⠂⠀⢁⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠒⡤⠀⣨⡏⠀⠀⣠⡀⠉⠉⠸⠃⡩⡄⠀⠈⠉⠁
⣀⡀⣼⡳⣷⠔⣍⡀⣀⣨⣦⡘⣩⣤⡶⢆⣄⣰⣾⡘⢠⣷⣧⣤⣿⣿⣿⣿⣿⣿⣿⡯⢷⢵⣶⡢⠀⠚⢀⠒⡊⠰⠗⠄⣲⡀⣿⣿⣿⢿⣿⣿⣿⣿⣿⡿⢟⣩⣀⣥⣜⠃⠉⢀⡀⠀⣀⡉⠀⠂⠀⠁⡠⠰⠀⠀⣡⡀
⠛⠿⢷⣵⣶⡄⠿⢿⣄⡈⢻⠿⠃⢻⣿⠲⠯⠋⠧⢭⣅⡶⠈⣬⠙⢫⠙⡛⠡⠞⠎⠋⠈⠉⠩⣯⢂⣆⠤⠭⠃⠀⡞⠁⠈⢤⣿⣿⣿⠰⡼⣟⣿⣿⡇⠰⢀⡡⢀⣠⣿⠒⠀⠝⠁⢀⠀⠐⠀⠀⠀⠀⠘⠨⣀⠀⠻⠃
⠀⢀⣀⣿⣿⣬⡿⠋⠄⠀⢠⢦⢠⡄⢀⢸⣶⢦⣤⡴⣥⣭⣾⢿⡠⡜⠷⣒⣐⠐⠤⣂⠙⠀⢀⡙⢯⣀⣢⠰⣐⣁⡡⡑⢂⢠⣿⠿⢇⠌⣻⣹⢽⣿⣳⠠⡂⣬⣢⣽⠉⣶⣤⣐⣀⠢⢠⢶⠄⣴⠆⠀⠀⠀⠀⠀⠀⠀
⣿⣗⢶⣅⡉⠉⠀⡈⢓⣧⡼⠈⢯⠟⣢⣠⣔⡙⡀⢤⢸⡘⢿⠧⠋⡙⢫⢉⢹⣥⡤⠈⠁⡴⡆⠇⢏⠚⠈⣅⢜⣉⡑⠿⡄⠈⠟⣵⣹⣵⠈⠄⠬⣈⢯⢨⢇⣉⡃⠉⣮⣭⠍⠀⢄⡀⠀⠌⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀
⠲⣼⠝⠿⣍⣮⡄⢈⠭⣷⣃⢳⡀⣧⡿⣿⣭⣷⣶⣄⢬⡁⠘⢄⣻⠷⢼⣙⢇⡞⢏⣉⠊⠩⣓⡤⠀⠀⢹⡋⠀⡈⠳⢯⣶⣶⣶⠿⡰⡟⡰⣶⠒⠚⠛⢇⠼⠃⡅⠈⠘⠛⠁⠀⠸⢷⡏⠂⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀
⠀⢶⣶⠛⣿⣿⣷⡠⣡⣶⢶⣿⣿⠾⠷⠿⣗⣫⣿⣿⣯⣁⠀⠀⠙⠰⢾⢏⣿⣎⣋⢺⠆⡆⠄⠠⠂⣀⢀⣿⡄⠰⡦⢔⣻⣇⡀⠳⢿⠅⢴⡝⠂⠹⠷⣤⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠙⢦⠄⣀⠀⠀⠀⠀⣴⣿⣿⣷
⠁⣲⣹⣧⣭⣭⢹⣇⣠⠄⠛⢿⣿⣩⡘⣯⡏⠟⡟⠋⡉⣄⡀⠀⠐⠓⢾⣜⣧⣧⣼⣎⢨⣸⡧⠐⠾⢿⣈⣿⢽⡆⠀⢀⠘⠞⠓⠈⠁⡠⠫⣠⣾⣷⣊⠀⢀⢀⠀⡙⠇⠀⠁⠐⠀⠀⠀⠂⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿
⣀⠠⢬⣍⢉⡾⢠⣿⢨⠷⠽⣿⣛⣿⡫⠙⣃⣄⡴⠤⢧⢹⢷⡂⠀⣦⣴⡈⠻⠛⣳⣶⣆⠌⢚⡂⠁⠈⠟⠿⢈⡟⠀⢈⡀⠀⠀⢙⠆⡂⣙⠿⡋⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⣁⠀⠠⢀⣾⣿⣿⣿⣿⣿⣿
⣊⠀⣟⢱⣎⢀⡨⢙⣀⣴⣼⣿⡕⢶⠿⣴⣾⣹⣿⢗⡉⢟⡏⣗⣠⢈⡭⠟⠶⠀⠋⠋⠄⠀⠐⣀⣨⢅⡆⠙⢶⠀⢠⠀⠤⠂⢡⢠⣟⠸⣱⣬⣤⣼⣄⣀⠀⠀⠀⠰⡂⠐⠀⢶⣦⣿⣿⡀⠈⢂⣾⣿⣿⣿⣿⣿⣿⣿
⡟⠛⠻⣟⡿⠟⣟⡛⣛⣟⣧⣽⣿⣿⢿⣦⣿⡛⣿⣿⣾⣋⣙⠟⢊⣤⣤⠄⢘⠽⡀⢾⡀⡐⣠⣴⣤⠀⡎⠃⠀⠀⠀⠀⠀⠀⢰⣿⣴⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠁⠁⣀⠴⠩⠉⢛⣸⡶⣎⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣤⣄⢀⣬⢿⣵⠭⣗⣸⡅⡒⠒⡢⣡⡀⠈⡁⠀⠀⠡⣴⡖⠟⠏⠀⡀⠽⠥⢩⠀⢁⢲⡿⠆⠻⡟⡄⠟⣀⣼⣏⢐⣾⣿⣷⣦⣕⣖⣿⣿⣿⢙⡯⢽⣶⡿⣵⡇⢪⡖⣰⠟⠇⠹⡕⠀⣠⣆⠀⠠⢷⣿⣿⠉⠁⠀⠀
⣦⣟⣵⠆⠀⠢⠖⠀⠇⢟⠉⠤⠍⠁⠀⠁⠁⠬⠕⡀⠾⢿⠿⣴⣦⡀⠶⠶⣦⡉⠝⠇⢬⡁⠒⠂⠍⠊⠋⠔⠡⠀⣿⣿⠯⣼⣿⡿⠤⡏⠿⠿⡺⠭⠵⠋⠁⠰⠀⠀⠀⠀⠀⠀⠉⠀⠂⠭⠁⠐⠹⢬⠍⠉⢤⡲⠌⣬
⠉⢤⠄⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣶⠄⠀⠘⡁⠀⠀⠴⣟⠓⠂⠀⠀⠠⠁⠀⠀⢰⢤⡀⠀⠀⠐⠆⠀⠠⢀⠄⣀⣄⡈⠋⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⠘⠀⠠
⢀⣠⣴⣾⡿⠂⢀⣠⣴⣤⢀⠀⠀⠀⠀⠉⠄⠀⠀⠀⠠⣾⡿⣟⡥⠦⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠐⠀⠀⠰⣼⣿⣿⡋⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣶⣦⡀⠀⠀⠀⠄⠘⠀⠀⠀⣀⠖⡞⠙
⡎⠿⠗⠋⠱⠇⠈⠛⠿⢿⣧⡀⠄⠀⠀⠀⠀⠀⠈⠀⠀⠽⣷⣴⣄⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠉⠋⠀⠀⠀⠀⠀⢄⣄⣤⠀⠀⠀⠀⠀⠀⡠⢠⣼⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠚⠯⣴⠀
⠠⡠⠀⠀⠀⠀⠀⠀⢐⠷⠮⠀⡁⠴⠀⠀⠀⠀⣀⡀⠀⣠⢼⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣰⣭⣭⣭⣀⡀⠀⠀⠀⠀⢀⣀⣡⡀⣄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⡁⢌⠊
⢀⣅⠀⢀⣤⢂⠀⠀⠀⠀⢤⡀⠀⣾⡴⢄⠀⠀⠈⠀⣀⠙⠋⣴⡿⣧⡀⣄⡖⢂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠘⡟⠛⠋⢩⠞⢤⡄⠀⠀⢘⠀⠀⠀⣰⣔⠾⠈⢁⠀⣐
⣿⠛⡷⠼⠿⢫⡄⠀⠉⠂⠈⠀⠲⣿⢣⣕⡥⣲⠀⠀⠈⢨⣸⣿⣿⣳⠀⠀⠁⠯⠀⠔⠀⠀⠀⠀⠀⢀⣤⣶⣦⣤⡂⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⠁⠀⠀⠀⠠⣤⡜⣀⠸⠁⠀⠰⡷⣶⣷⣴⣶⡿⣀⠩
⣿⣿⣞⢻⠄⠀⠀⠀⠀⠁⣛⠋⣒⡭⢵⠃⠙⡤⠀⠀⣈⣿⣼⣿⣿⣿⣾⣽⣄⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠄⣀⣷⣤⡶⠶⢶⣿⡉⢁⠜⠀⠉⡉⣻⢷⠲⢄⡤
⡆⠩⣷⣶⠅⠀⠉⠣⠁⠀⠁⠀⠁⠀⠐⡠⠀⠀⠈⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢀⣤⣴⣿⣿⣿⠛⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⢄⡠⡳⡰⣴⠤⠄⠤⢁⠈⠀⠂⠀⡉⡩⢰⡶⢄⢅
⣴⣿⣯⢙⢇⡀⠀⢄⠠⠰⠠⠔⠀⣀⣦⠌⠁⠩⡋⡄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⠀⢰⣿⣿⣿⣿⣿⣷⣴⣾⡿⠿⠛⠿⠛⠿⠿⠿⠿⠟⠉⠀⠀⠈⣡⣤⠝⡊⣹⣏⡹⢷⡅⢠⡌⣉⡀⢈⢜⢄⣤⠘⠆⣴⡄
⠃⡃⡷⢦⠌⢅⠉⠂⠑⢉⣀⠀⠈⠀⡀⠀⠀⠀⠠⣀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢴⡿⠿⠟⠁⠈⣦⣴⡾⠟⠽⠿⣔⢋⢽⢏⣀⠉⣴⡎⠉⠀
⣷⣶⡶⢠⣦⠨⡿⢇⠠⣿⡿⡉⠶⢤⠀⠃⠀⢂⣀⣀⢆⠂⠹⠙⢟⡛⠛⠛⡉⠀⠠⢠⡄⠀⠀⠉⢻⣿⡿⣿⣿⣿⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡄⠀⠀⠀⠄⠁⢈⡉⠙⠷⡎⠱⢞⠻⢟⡞⠛⠰⢄⠋
⢸⣿⡷⣴⣶⡳⡁⠐⣷⡂⢅⠀⠢⡒⡀⠀⠀⠘⠟⠑⠲⠈⢀⣡⡭⡙⠶⣄⢻⠀⠀⣀⣁⣀⣀⣴⣿⣿⠓⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢖⠃⣀⣻⣸⣖⣳⣲⡁⢁⠄⢀⣀
⠸⣿⣿⣇⡬⣙⡀⣀⠀⢀⢸⣎⢿⡷⠊⠈⠀⠀⣒⡀⢀⠁⣍⠂⠇⡰⠀⣈⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣆⣻⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣷⣦⡀⢠⠄⠀⡄⠀⠀⢠⣊⡀⠆⡀⡀⠈⠫⠍⡥⢈⡣⠭⣟⢉⢊
⣐⠉⣳⣛⠷⣏⢮⡼⠂⢠⠁⡁⠀⠜⣤⡖⠄⠢⠀⠀⠈⠀⠈⠟⢚⢦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣠⠀⢀⠀⡼⡻⣇⠐⡕⢣⢀⣤⢴⣴⡤⡀⠷⣡⣿⣿
⣿⠃⠜⣻⣷⣿⡙⠃⠁⠇⠜⠒⠛⢛⠃⡠⡅⠔⠈⡷⠌⠆⣤⠱⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⡿⡻⡋⠴⠾⠋⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⣮⠱⢛⣗⡛⠛⠝⠦⠻⠿⣿⡿⣿⡦⣒⠼⣺⡟
⢆⠀⠀⡈⠛⣛⢛⣞⠒⡆⠝⣫⠟⢏⠳⢠⣽⡵⡦⢡⢀⣀⡘⠆⣿⣿⣿⣿⣿⣿⣿⣿⡿⠈⢱⡨⡮⠃⠁⠀⠐⠒⠂⠀⢁⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠒⡤⠀⣨⣏⠀⠀⣀⡀⠁⠉⠰⠋⡩⡄⠀⠈⠁⠁
⣀⠀⣼⡳⣷⢐⣍⡀⣀⣨⣦⡘⣩⢬⡴⢆⣄⣰⣾⡘⢠⣷⢃⣤⣿⣿⣿⣿⣿⡿⣿⡭⠕⢵⣶⡂⠀⠐⢀⠒⡂⠰⠗⠄⣲⡀⣿⣿⣿⢿⣿⣿⣿⣿⣿⡿⢟⣩⣀⣅⣔⠋⠉⢀⡀⠀⣀⠉⠁⠂⠀⠁⡠⠰⠀⠀⣡⡀
⠛⠿⢷⣵⣶⡄⠻⢿⣄⡈⢻⠟⠃⢻⣿⠲⠫⠉⠧⢭⡅⡒⠈⣬⠙⢫⠙⡙⠡⠐⠎⠃⠈⠉⠉⣧⢂⣆⡄⠭⠃⠀⡞⠁⠈⢤⣿⣿⣿⠰⡾⢛⣿⣿⡇⠐⢀⡀⠀⣠⣿⠒⠣⠘⠁⢀⠀⠐⠀⠀⢀⠀⠘⠀⡀⠀⠻⠃
⠀⢀⣀⣿⣿⣬⡿⠋⠄⠀⢠⢦⢀⡆⢀⠸⣶⢶⣤⡔⣥⣥⣾⢻⡠⡜⠷⣂⣐⠐⠄⣂⠑⠀⢀⡙⢮⣀⣦⠰⣀⣁⡁⡑⢀⢠⣿⠿⢇⠈⢹⡙⢽⣿⣓⠠⠀⣬⠢⣜⠘⣶⣤⣐⢀⠢⢠⢲⢄⣴⠆⠀⠀⠀⠀⠀⠀⠀
⣿⣖⢦⣅⡈⠉⠀⡈⢓⣧⡜⠀⢮⠟⣢⣠⣐⡙⡀⢄⢪⡈⠿⠥⠋⡙⢫⠉⣹⣥⡤⠈⠁⡄⡆⠁⢏⠚⠌⣅⢎⣉⡑⠿⡄⠈⠞⠴⡹⠵⠈⠄⠠⣈⢹⠀⢆⣉⡃⠁⢚⣬⢍⠀⢄⠀⠀⠄⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀
⠲⣼⠝⠿⣍⣮⡄⢈⠭⣷⣇⢣⡀⣯⡿⣧⢭⣷⣶⣄⢬⡀⠀⢀⣹⠷⢼⣉⢇⡞⢍⢉⠂⠉⣓⡤⠀⠀⢹⡋⠀⡈⠣⢎⣶⣦⡶⠿⡰⡟⡐⣷⠒⠒⠛⢇⠼⠂⡅⠈⠈⠛⠁⠀⠨⢷⡍⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀
⠀⢴⣶⠓⣿⣿⣷⡠⡡⣶⢶⣻⣿⠾⠳⠿⣕⣫⣿⣿⣯⣁⠀⠀⠘⠰⢾⢏⣟⣎⣉⠺⡖⡆⠀⠠⠂⣀⢀⣿⡄⠰⡆⠔⣹⣇⡀⠓⡻⠅⣤⣝⠂⠹⠷⡤⠈⢀⠀⢀⣠⠀⠀⠀⠀⠀⠙⠢⠀⡀⠀⠀⠀⠀⣴⣿⣿⣷
⠁⣲⣹⣧⣭⣭⠹⣇⡀⠄⠛⢿⣿⣉⡘⣯⡏⠟⡟⠋⡩⣄⡀⠀⠐⠑⢶⣜⡧⣦⣼⣎⢨⣸⠇⠐⠾⢿⣈⣿⢽⡆⠀⠀⠘⠚⠓⠀⢡⡠⠩⣠⣾⣷⣊⠀⠀⢀⠀⡙⠃⠀⠁⠐⠀⠀⠀⠂⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿
⣀⠠⢬⣍⢉⡿⢰⣷⢨⠶⠭⣿⣛⣿⡫⠛⣁⣄⡴⠠⢧⢙⢶⡀⠀⣦⡴⡌⠳⠙⢲⣾⣆⠌⢚⡀⠀⠈⠟⠿⠉⡟⠀⢀⠀⠀⡀⢰⠀⡂⣘⡿⡋⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣁⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿
⢊⠀⣛⢹⣎⠀⠨⢙⣀⣤⣼⣿⡕⠺⠿⢴⣾⢹⣿⢗⡉⢟⡞⢗⣠⠈⡭⠞⠖⠀⠁⠋⠄⠀⠐⣐⣠⢅⡂⠙⠂⠀⠠⠀⠄⠀⠡⢠⡳⠸⣡⣠⣦⣴⣀⣀⠀⠀⠀⠰⡒⠀⠀⢦⣦⣽⣿⡀⠈⢂⣾⣿⣿⣿⣿⣿⣿⣿
⡟⠛⠻⢟⡿⠟⣟⡛⣛⣟⣧⣽⣿⣿⢿⣶⣿⡙⣿⣽⣾⣋⣙⠟⢊⢠⣤⠄⢘⠽⡀⢾⡀⡐⣠⣴⣤⠀⡞⠃⠀⠀⠀⠀⠀⠐⠡⣿⣴⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠁⠁⢀⠴⠫⠙⢘⢸⡾⣎⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣤⣄⠀⣨⢿⣥⠨⣕⣸⡌⢃⠂⡂⣡⡄⠈⠁⠀⠀⠁⣴⡖⠛⠏⠀⡀⠹⠡⢉⠀⠁⢰⡺⡄⠻⡟⡀⠖⠀⡰⢋⢐⡺⣾⡶⣦⡑⢖⣿⣿⣿⢉⡏⢽⣶⡿⣴⡇⢠⡔⣰⠖⠆⡽⠔⠀⣀⣆⠀⠠⢧⣿⡿⠉⠁⠀⠀
⣆⣗⣵⠆⠀⠂⠖⠀⠇⢾⠈⠠⠄⠅⠀⠀⠁⠬⢔⡀⠾⠿⠿⣅⣆⠀⠶⡶⣧⡉⠙⠇⢈⡀⠐⠀⠈⠊⠋⠀⠡⠀⣿⣿⠯⣸⣿⡯⠄⡋⠿⠿⡺⠭⠑⠋⠁⠰⠀⠀⠀⠀⠀⠀⠋⠀⠂⠉⠁⠐⠹⠬⠍⠉⢤⡲⠀⡬
⠈⢤⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣶⠄⠀⠘⠀⠀⠀⠤⣟⠓⠂⠀⠀⠀⠁⠄⠀⢰⢠⡀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣄⡈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⠀⠀⠀
⢀⣠⣶⣾⡿⠀⢀⣠⣴⣤⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⣾⡿⣟⠥⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠀⠀⠰⢼⣿⣿⡋⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⣶⣦⡀⠀⠀⠀⠀⠘⠀⠀⠀⢀⠂⡞⠛
⡌⠿⠗⠋⠑⠃⠈⠛⠿⢿⣧⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠼⣷⣴⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠉⠋⠀⠀⠀⠀⢀⣀⢄⣤⡄⠀⣀⠀⠀⠀⡀⢠⣬⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠚⠫⣴⠀
⠀⡰⠀⠀⠀⠀⠀⠀⢀⠵⠢⠀⡁⠴⠀⠀⠀⠀⣀⡀⠀⠠⢼⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣬⣾⣿⣭⣿⣧⣭⣾⣧⣄⠀⢀⣀⣁⡀⣄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⡁⢄⠈
⢀⣅⠀⢐⣤⢂⠀⠀⠀⠀⢤⡀⠀⡾⡴⢀⠀⠀⠀⠀⣀⠙⠋⣴⡿⣧⡀⣀⡐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠋⢩⠞⢤⡄⠀⠀⢘⠀⠀⠀⣠⢔⠼⠈⢉⠀⢐
⢿⢛⡧⠼⠾⢫⡅⠀⠉⠂⠀⠀⠐⣿⢣⣕⠅⡲⠀⠀⠀⣨⣰⣿⣿⡣⠀⠀⠀⠭⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⣤⡀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠠⣤⡀⣀⠰⠁⠀⠐⡷⡶⣇⣤⣲⡿⣀⠩
⢾⣿⣖⢸⠄⠀⠀⠀⠀⠁⣛⠋⣒⠭⢵⠃⠙⡤⠀⠀⣠⣿⣿⣿⣿⣿⣾⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠄⢀⣷⣤⡶⠶⢶⣿⡉⠁⠜⠀⠉⡈⣻⢷⠰⠀⡠
⠂⠨⣷⣶⠅⠀⠀⠓⠀⠀⠁⠀⠀⠀⠀⡠⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⠛⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠄⡀⠳⠸⣤⠠⠀⠤⢁⠈⠀⠂⠀⡀⠩⢰⡶⠀⠀
⣔⣶⠏⠉⢇⠀⠀⠀⠀⠰⠀⠀⠀⢀⡠⠌⠀⠉⡑⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠀⣿⣿⣿⣿⣿⣿⣿⣴⣿⠿⠟⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠈⡡⣤⢟⡈⣱⡅⡹⢷⡅⢠⡄⡉⠀⢀⣍⢄⣤⠘⠆⣠⡄
⠚⡃⡷⢆⠀⠀⠈⠀⠁⢉⣀⠀⠈⠀⠀⠀⠀⠀⠠⢀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢴⡿⠿⠎⠁⠀⢤⣴⡾⠛⠽⠾⣔⠋⢽⠏⣀⠉⣴⡆⠈⠀
⣷⣦⡶⢠⣤⠨⠿⢅⠠⣿⡿⡈⠢⠤⠀⠁⠀⢀⣀⣀⢆⠀⠹⠉⢟⡛⠛⠋⡁⠀⠠⠀⠀⠀⠀⠙⣻⣿⣿⣿⣿⣿⣧⣤⣄⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⡈⠙⠷⡎⠡⢄⠻⠟⡞⠛⠰⢄⠋
⠐⣿⡗⣶⣀⠢⠀⠐⢷⡀⢅⠈⠀⡒⡀⠀⠀⠈⠟⠑⠢⠈⢀⣠⠌⡙⠲⣄⢽⠀⠀⠀⠀⠀⣠⣾⣿⣿⠃⣹⣿⣿⣿⣿⣿⣿⣷⣄⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠃⡀⣻⢨⢒⣣⣒⡁⢀⠀⢀⠀
⠰⣿⣿⣁⡬⣙⡀⣀⠀⢀⠸⡊⢿⠷⠂⠀⠀⠀⢂⡀⠀⠀⣅⠀⢃⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿⣷⣦⣄⢠⡆⠀⡀⠀⠀⢠⣈⠀⠂⠀⡀⠈⠫⠙⠥⠈⠣⠬⣶⢁⢊
⣐⠀⣣⣚⠷⣏⠭⠼⠂⢠⠁⠀⠀⠔⣄⠆⠀⠀⠀⠀⠈⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⡸⠻⣃⠀⡑⢁⢀⢤⢐⡤⠄⡄⠷⣠⣻⣿
⣿⠃⠘⣛⣷⣿⡈⠃⠀⠅⠌⡓⠛⣛⠃⠠⠅⠐⠈⠿⢬⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⡍⡟⡛⡋⠵⠞⠋⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠙⠁⡮⠱⠛⡖⠉⠛⠙⠆⠈⠼⣷⡿⢶⡦⠂⠬⣮⡙
⢂⠀⠠⠈⠛⣛⢛⣞⠐⣆⠕⡨⠝⢋⠐⠀⣽⡔⡂⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢻⠂⠀⠱⠤⡮⠋⠀⠀⠀⠐⠀⠈⢙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠒⠤⠀⣨⠇⠀⠀⢀⡈⠁⠉⠰⠂⠉⠀⠀⠀⠀⠁
⣀⠀⣼⡣⣷⠐⣌⠀⣀⣨⣦⡀⡩⢤⡴⢂⣄⣰⣞⡐⢻⣿⣿⣿⣿⣿⡿⠿⠟⠛⢾⠤⠶⢾⣶⡆⠀⠘⢀⠐⡀⠠⠗⠀⣲⠀⣾⣿⣿⠿⣿⣿⣿⣿⣿⣿⡿⠯⣄⣅⣀⠁⠉⢀⡀⠀⡀⠉⠀⠂⠀⠁⠠⠀⠀⠀⣠⡀
⠛⠿⢳⣵⣶⣄⠟⢫⡄⡈⢻⠟⠂⢹⣿⠰⠫⠃⠡⢩⡅⡴⠀⣬⠛⢂⠀⡁⠀⠈⠟⠁⠈⠉⠉⣇⣆⣆⠤⠉⠀⠀⡆⠁⠈⠤⣿⣿⣿⠐⠼⢋⣛⣿⠏⠁⢠⡀⠀⠠⢻⠂⠁⠈⠀⠀⠀⠐⠀⠀⠀⠀⠘⠈⡀⠀⠻⠃
⠀⠀⡀⣻⣿⣬⡿⠋⠀⠀⠠⢦⢠⠆⢀⠘⣶⢶⣤⡔⣠⣭⣶⢿⡀⡘⠳⣀⣀⠀⠄⠀⠀⠀⢀⠉⢮⢀⢀⡂⢀⣀⡀⡁⢀⢠⣿⠿⢇⠈⢩⡸⢹⣿⣓⠀⠀⣬⡠⣄⠀⢲⣤⡀⢀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀
⣿⣐⢢⣄⡈⠁⠀⡈⢓⣇⡜⠀⢮⠎⡂⣠⣐⡙⡀⠀⠪⡘⠿⠤⠋⠈⢫⠉⠹⣅⡤⠀⠁⡀⠆⠀⠍⠚⠀⢅⢎⣉⠁⠿⠄⠀⠘⡵⠰⡦⠀⠀⠈⣈⠁⠀⢃⢉⡃⠀⢀⢀⠍⠀⠀⠀⠀⠀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀
⠲⢸⠝⠿⣍⣮⡄⢀⠥⣖⣃⢡⠀⣧⡿⣧⢭⣶⣞⣄⢤⡀⠈⢀⣹⠢⢼⣉⠇⡚⠇⠀⠀⠈⣓⡄⠀⠀⢩⡃⠀⡈⠣⢍⣶⢲⡶⠿⡰⡊⠈⣴⠀⠂⠛⢇⠸⠂⠅⠀⠀⠉⠀⠀⠐⠦⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢴⣶⠓⣿⣿⣴⡠⣁⣶⢶⡿⣿⠪⠓⠿⢕⣫⣿⣷⣮⣁⠀⠀⠘⠠⠾⢏⣙⢀⣉⢠⠆⡄⠀⠠⠂⣀⢀⣿⡄⠐⠦⠐⢹⣇⠀⠓⠰⠄⢆⠉⠀⠸⠵⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣷
⠀⣲⣹⣧⣬⡭⠙⣄⡀⠤⠛⢿⣿⣁⡘⣯⡏⠟⡟⠉⡉⣄⠀⠀⠐⠁⢦⣜⡧⡦⣴⣦⠠⢸⠆⠀⠾⢻⣈⣵⢿⡆⠀⠀⠈⠘⠓⠀⠁⡠⠑⣠⣾⣶⡂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿
⢀⠀⢬⣉⠉⡶⢠⣷⠨⠶⠥⣿⣙⣿⡢⠙⠁⣄⡴⠠⠧⢽⢶⡀⠀⡦⣴⡈⠓⠙⠒⡆⡆⠀⠈⠀⠀⠀⠟⠻⠀⠟⠀⢀⠀⠀⡀⢀⠀⡀⢈⠿⡋⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿
⢂⠀⡛⢱⣌⠀⠨⢉⣀⣤⣬⣯⡕⠻⠿⢴⣾⢱⣿⢗⠉⢟⡊⠗⣀⠀⡼⠒⠒⠀⠀⠡⠄⠀⠀⠀⠀⢄⠂⠙⠂⠀⢀⠀⠀⠀⠡⣂⡁⣀⣤⣶⣶⣶⣶⣤⣀⠀⠀⠰⡂⠀⠀⢤⣤⣽⣿⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠛⠻⢟⡿⠟⡟⡛⣻⣟⣧⣽⣿⣿⠾⣦⣿⡙⡿⣽⢾⢊⢙⠟⢊⢠⣤⠀⢈⠘⠀⢾⡀⡀⣠⣴⡄⠀⠈⠃⠀⠀⠀⠀⠀⠀⠰⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠁⠀⢀⠔⠉⠉⢐⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻
⠀⣤⣄⠀⣠⢿⣅⠬⣵⣨⡄⢂⠒⡂⣁⡀⠈⠁⠀⠀⠁⣴⠖⠚⠏⠀⠀⠹⠥⢀⠀⠀⢰⡚⠄⠻⡏⡀⠐⠀⡠⢋⢐⡺⣾⡷⣦⣑⢔⣾⣿⣿⢉⡏⢽⣶⣽⣤⡇⠀⠄⣰⠕⠆⠹⠐⠀⣀⣄⠀⠀⢣⣯⡽⠉⠁⠀⠀
⣆⣗⣵⠆⠀⠒⠖⠀⠇⠿⠀⠠⠄⠅⠀⠀⠁⠤⡕⡀⠾⢿⠿⣅⣆⡀⠶⠶⣆⡉⠚⠃⢈⡁⠐⠀⠈⠂⠋⠀⠀⠀⣿⣯⠏⣸⣿⠯⠠⡊⠽⠿⡚⠭⠑⠋⠁⠘⠀⠀⠀⠀⠀⠀⠋⠀⠂⠨⠁⠐⠹⠬⠌⠉⢤⡰⠀⠌
⠀⢠⠄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣶⠄⠀⠘⠁⠀⠀⠄⢟⠗⠂⠀⠀⠀⠁⠀⠀⢐⢀⡀⠀⠀⠀⠀⠀⠀⢀⠄⣀⣄⡈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀
⢀⣠⣤⢶⡿⠄⢀⣠⣴⣤⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⣾⡿⣟⡥⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢺⣿⣿⠋⠁⠀⠀⡀⠀⠀⣀⡄⡀⣀⡀⠀⠀⠀⠀⣀⣬⣶⣦⡀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠂⠞⠛
⡌⠿⠟⠋⠁⠂⠈⠙⢿⢿⣧⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣴⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠉⠋⠀⠀⢀⢄⣴⣶⢇⣿⡇⢇⣿⡇⠀⠀⠀⢠⣼⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⡤⠀
⠀⡠⠀⠀⠀⠀⠀⠀⢀⠱⢊⠀⡀⠰⠀⠀⠀⠀⣀⡀⠀⠠⠼⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣭⣾⣿⣭⣿⣷⣭⣿⣯⣭⡄⢀⣀⣡⡀⣀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⡁⢄⠈
⢀⣇⠀⢐⣤⠂⠀⠀⠀⠀⢤⡀⠀⡼⠥⢀⠀⠀⠀⠀⣀⠙⠋⣴⡾⣧⡀⢀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠋⢩⠜⢤⡄⠀⠀⠘⠀⠀⠀⡠⢔⠞⠈⠁⠀⢀
⢾⢛⡧⡼⠾⢭⡅⠀⠈⠂⠀⠀⠐⣿⠧⣕⡄⡒⠀⠀⠀⢨⣠⣿⣿⣢⠀⠀⠀⠬⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣦⣤⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⣠⡀⣀⠰⠁⠀⠀⠴⡶⣇⣠⣴⡿⣀⠡
⢿⣿⣒⢱⠄⠀⠀⠀⠀⠁⢛⠋⢀⠭⠱⠂⠙⡠⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⢀⣤⣼⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠄⢀⣷⡤⡶⠶⢶⣿⡉⠁⠌⠀⠉⡁⣻⠗⠐⠀⡀
⡆⠩⣷⣶⠅⠀⠀⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⠛⢁⣴⣿⣿⣿⣿⠿⠿⠿⠿⠟⠋⠁⠀⠀⠀⠀⠄⡀⠓⠱⣄⠀⠀⠤⢁⠀⠀⠀⠀⠀⠸⢰⡶⠀⠀
⡕⡼⢏⠉⢃⠀⠀⢀⠀⠠⠀⠀⠀⢀⣠⠈⠀⠉⡁⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⣸⣿⣿⣿⣿⣿⣿⣿⣶⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⣤⠝⡢⢁⣁⡙⢧⡄⢠⣄⡈⠀⢀⢀⠄⡤⠐⠄⣠⡄
⠂⡀⠶⢆⠀⢀⠈⠀⠀⠉⣀⠀⠀⠀⡀⠀⠀⠀⠠⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢴⠿⠿⠎⠁⠀⣤⣴⡾⠛⠩⠿⣔⠋⢵⠏⣀⠉⣴⡆⠈⠁
⣷⢲⡶⢀⣤⠠⠿⢃⠠⢿⡿⡀⠢⢄⠀⠁⠀⢀⣀⣀⢄⠀⠹⠉⢝⡛⠛⠉⠁⠀⠀⠀⠀⠀⠈⠛⣻⣿⣿⣿⣿⣿⣿⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡉⠉⠦⡎⠡⢄⠻⠟⡖⠛⠰⢀⠋
⠀⣿⡗⣔⣀⠀⠀⠐⢷⡀⢅⠀⠀⡀⠀⠀⠀⠈⠛⠑⠢⠈⠀⡠⠄⠉⠢⣄⠸⠀⠀⠀⠀⢀⣤⣾⣿⣿⠛⢹⣿⣿⣿⣿⣿⣷⣦⣄⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠃⡀⢻⢨⢢⡰⣒⡁⠀⠀⢀⠀
⠰⣿⣿⣀⡤⣑⡀⣀⠀⢀⠈⠂⢾⡷⠀⠀⠀⠀⢂⡀⣠⣥⣬⣶⣾⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣆⣸⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣴⣶⣶⣶⣦⣄⡠⠄⠀⡀⠀⠀⢠⣀⡀⠀⠀⡀⠈⠫⠉⠀⠈⠣⠌⡂⠉⠈
⣐⠁⣣⡛⠷⣏⠬⠼⠂⢀⠀⠀⠀⠀⣀⠆⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⠽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⠀⠀⠀⠸⠿⣇⠀⡐⠃⢀⢠⠀⡐⠄⡀⠧⠀⣻⣿
⣿⠃⠘⢛⣷⣾⡈⠃⠀⠅⠀⡂⠛⢛⠃⠀⡅⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢀⡜⡍⠟⢛⡋⠴⠖⠋⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝⠀⢌⠐⠛⠒⠀⠃⠉⠆⠐⠯⣿⡿⢾⡦⠀⠨⣾⡟
⢂⠀⠠⡈⠛⡛⢛⣟⠄⠆⠐⠊⠝⠋⢀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠫⠉⢁⠒⠀⠡⠠⡮⠃⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠤⠀⣰⡇⠀⠀⢠⡀⠁⠉⠐⠂⠁⠀⠀⠈⠁⠀
⣀⠀⡼⡣⣗⠐⣌⠀⣀⣨⣦⡀⡩⣦⣤⢂⢄⢐⣮⡙⢿⣿⣿⣿⣟⣛⠛⠏⠀⠓⢶⠤⠶⢴⣦⡂⠀⠐⢀⠐⡂⠀⠇⠀⢰⠈⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣃⡤⣀⠁⠉⢀⠀⠀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠛⠟⢿⣵⣶⣄⠛⢁⡀⡈⠻⠿⠂⢹⣯⠸⠯⠁⠠⢩⡍⡀⠀⡬⠙⢡⠈⡈⠀⠀⠛⠁⠈⠉⠉⣇⣂⣦⠄⠅⠀⠀⡎⠠⠈⠠⣿⣿⣿⠀⠼⢽⣿⡿⠟⠛⢉⡀⠀⠠⠓⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃
⠀⠀⡀⣻⢷⣬⡿⠊⠀⠀⠠⢦⢠⡆⠀⠈⣷⢦⢤⡐⣁⣽⣴⠷⠀⡈⠷⣀⡀⠁⠠⠀⠀⠀⠀⡉⢣⡀⠀⡂⢀⡁⠀⡀⢀⢠⣿⠿⠇⠈⢹⡸⠽⣿⣃⠀⠀⣄⠀⡄⠀⢰⣠⡀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀
⣿⣀⢢⣄⡈⠀⠁⡈⠓⣃⡬⠀⢮⠎⡆⡠⣀⣉⡀⠀⠈⡘⠿⠤⠃⠐⢋⠈⠩⡥⡤⠈⠉⡀⠀⠀⢌⠒⠀⢁⢌⣉⠁⠿⠄⠀⠘⣠⠲⢦⠀⠀⠀⣈⢁⠀⢃⢙⡁⠀⢀⠀⠉⠀⠀⠀⠀⠀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀
⠲⡨⠌⠿⣍⣬⡄⢀⠤⣖⣃⠩⠀⣧⡿⣦⢭⣶⣞⣄⢠⠁⠀⠀⠰⠲⢼⣈⠇⠒⢊⠀⠀⠈⣑⡄⠀⠀⢨⣊⠀⡈⠂⠍⣴⠖⡶⠷⠰⡎⠀⢼⠀⠀⠙⢇⠨⠀⠀⠀⠀⠁⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢶⣶⠓⣿⣿⣴⠀⣁⣶⢶⣻⣿⠮⠑⠿⢕⣫⣿⣷⣯⣁⠀⠀⠐⠀⢺⢏⣙⣀⣈⠠⠄⠄⠀⠠⠢⣀⢀⠹⡄⠐⠆⠐⢹⣇⠀⠓⢰⠡⠔⠉⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣿⣿⣷
⠀⣢⣸⣧⣬⠭⠙⣄⣀⠄⠝⢿⣿⣅⡈⣯⡭⠟⡿⠉⠉⣀⠀⠀⠀⠁⢶⣜⠃⣦⣼⣄⠠⢐⠄⠐⠖⢻⣨⣵⢿⡆⠀⠀⠘⠈⠃⠀⠁⡀⠁⣠⣾⣶⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿
⢀⠀⢤⣍⠁⡶⢠⣷⠨⠥⠠⣳⣛⣿⡂⠙⠁⣄⠀⠀⣧⢜⢷⡀⠀⡦⡴⡈⠒⠄⠢⣎⡃⠀⠈⠄⠀⠀⠟⠋⠀⠝⠀⢀⠀⠀⠀⢁⢀⣦⣾⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢂⠀⡛⢡⣀⠀⠨⠉⣀⣤⣬⣻⡕⠲⠿⠤⣾⢳⣿⢓⠉⢿⡊⠗⢀⠀⡸⠒⠂⠀⠀⠁⠀⠀⠀⡀⡀⢄⡂⠉⠐⠀⠀⠀⠀⠀⠡⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⡂⠀⠀⢤⣤⣼⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⡟⠛⠻⢟⡿⠟⠛⠛⣻⣟⣧⣽⣿⣟⡾⣦⣿⡙⣿⣿⢾⢊⢙⢟⢣⢠⣤⠀⠈⠐⠀⢮⡀⠀⣀⢴⡄⠀⠈⠃⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠁⠀⢀⠀⠉⠁⢹⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⢰
⠀⣤⣄⠀⣀⢿⣁⠨⢵⣨⡄⢂⠀⡂⣁⡀⠈⠁⠀⠀⠀⣰⠖⠚⠏⠀⠀⠹⠥⢀⠀⠀⠰⡚⠄⠻⠏⡀⠐⠀⠠⠈⢐⠺⣾⡶⢦⣐⢔⣾⣿⣿⠈⡍⢥⢖⡡⣄⡇⠀⠀⢰⠐⠆⠰⠐⠀⣀⣄⠀⠀⢡⣯⡝⠉⠁⠀⠀
⣀⣖⡴⠆⠀⠂⠔⠀⠇⠾⠀⠠⠄⠅⠀⠀⠁⠤⡔⡀⠾⠿⠿⣁⣆⠀⠶⠶⡦⡉⠘⠃⢀⡀⠀⠀⠈⠂⠃⠀⠀⠀⣺⣯⠭⣠⢿⠯⠠⡀⠽⠯⠚⠅⠐⠉⠁⠐⠀⠀⠀⠀⠀⠀⠋⠀⠂⠈⠁⠐⠹⠬⠄⠈⠤⡰⠀⠄
⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠄⠀⠘⠀⠀⠀⠄⢟⠃⠀⠀⠀⠀⠁⠀⠀⢐⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣄⡀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣠⣤⢶⡿⠄⢀⣠⣴⣤⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⣾⠿⡟⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢸⣿⣿⠋⠁⠀⠀⡀⠀⡀⣤⡄⡄⣄⡀⠀⠀⠀⠀⣀⣬⣶⣦⡀⠀⠀⠀⠀⠘⠀⠀⠀⢀⠀⠚⠛
⠌⠻⠗⠋⠁⠂⠈⠙⠿⢿⣧⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠨⣷⣤⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠉⠋⠀⢀⣀⢆⣷⣶⢇⣿⡇⢅⣿⡇⠀⡄⡀⢠⣬⡿⠻⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⡤⠀
⠀⡀⠀⠀⠀⠀⠀⠀⢀⠰⠂⠀⡀⠰⠀⠀⠀⠀⣀⡀⠀⠠⠼⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣭⣾⣿⣭⣿⣿⣭⣾⣯⣭⣾⢀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⡀⢀⠈
⠀⣅⠀⢀⣠⠂⠀⠀⠀⠀⢤⡀⠀⠼⠤⢀⠀⠀⠀⠀⣀⠘⠋⣰⡎⣧⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⢩⠜⢤⡄⠀⠀⠘⠀⠀⠀⡠⢄⠴⠈⠁⠀⢀
⢿⢛⡥⡼⠮⢩⡅⠀⠈⠂⠀⠀⠐⣿⠢⡅⠅⡒⠀⠀⠀⢨⢠⣿⣯⠢⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⣠⡄⣀⠠⠁⠀⠀⠔⡶⣂⣠⣰⡿⡀⠠
⢹⣿⣒⢰⠄⠀⠀⠀⠀⠀⣛⠉⢐⠍⠱⠂⠈⡀⠀⠀⣠⣼⣼⣿⣿⣶⣤⣅⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣿⣿⣿⡇⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠄⢀⣷⡤⡶⠶⠶⣿⡉⠁⠌⠀⠈⡀⣹⠗⠐⠀⡀
⡂⠨⣷⣲⠄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⠛⢁⣴⣿⣿⠿⠿⠿⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠄⠀⠒⠠⣄⠀⠀⠤⢁⠀⠀⠀⠀⠀⠠⢰⡶⠀⠀
⠔⡴⢏⠉⢃⠀⠀⢀⠀⠀⠀⠀⠀⢀⡀⠈⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣼⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣤⠝⡠⢡⡁⠙⢇⡄⢠⡄⡈⠀⢀⢀⠀⡤⠐⠀⣠⡄
⠂⠀⡗⢆⠀⠀⠈⠀⠀⠈⣀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠿⠿⠎⠁⠀⣤⣴⡾⠛⠡⠪⣐⠋⢴⠋⣀⠉⣴⡆⠀⠁
⡷⢢⡶⢀⣤⠀⠿⢁⠠⢿⠟⡀⠢⠄⠀⠃⠀⢀⣀⡀⠄⠉⠛⠿⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠉⠉⠴⡌⠁⠄⠺⠟⡖⠛⠰⠀⠊
⠀⣿⡇⡄⠀⠀⠀⠐⢷⡀⢁⠀⠀⡀⠀⠀⠀⠈⠛⠑⠂⠀⢀⣀⣀⣀⣀⣀⠰⠀⠀⠀⣀⣠⣴⣿⢿⣿⠟⢻⣿⣿⣿⣿⣷⣦⣀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⢣⠨⢢⡠⢒⡁⠀⠀⠀⠀
⠰⣿⣿⣀⡀⣐⡀⣀⠀⢀⠀⠀⢾⠷⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⢿⣿⣿⣿⣿⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣠⣴⣶⣶⣶⣤⣠⠀⠀⡀⠀⠀⢀⣀⡀⠀⠀⡀⠈⠣⠁⠀⠀⠣⠌⡀⠀⠀
⣐⠀⢣⡚⠧⣏⠤⠼⠂⢀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⢸⣿⣿⣿⣿⡿⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠸⠿⡇⠀⡀⠁⠀⠠⠀⡀⠀⠀⠧⠀⣻⣿
⣿⠃⠘⠛⣷⣾⡈⠃⠀⠁⠀⠃⠚⢛⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣁⠀⠀⡀⡍⠛⠛⡋⠰⠔⠋⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢌⠀⠙⠒⠁⠃⠁⠆⠈⠼⣷⡷⢶⡦⠀⠁⢊⡙
⢂⠀⠀⠈⠛⡛⢛⣟⠀⠂⠀⠈⠝⠂⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠅⠳⠀⢁⠂⠀⠀⠠⠮⠃⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠠⠀⣨⠅⠀⠀⢀⡀⠀⠁⠐⠂⠀⠀⠀⠀⠀⠁
⣀⠀⠼⡣⡖⠀⢌⠀⣀⣈⣤⡀⠨⢤⣠⠀⠀⢰⡾⠙⢻⢿⡫⢫⡍⠁⠚⠃⠀⠙⢲⠤⠆⢼⣆⡀⠀⠐⢀⠐⠀⠀⠀⠈⢛⠻⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠤⢀⠁⠁⢀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠋⠟⠷⣵⣴⣄⠛⢁⡀⡈⠻⠻⠂⢹⣧⠰⠫⠁⠠⢩⣅⡠⠀⡬⠘⢠⠀⡀⠀⠀⠛⠁⠈⠉⠉⣇⢂⣆⠄⠅⠀⠀⡆⠀⠀⠠⣿⣿⣿⠀⠬⢿⣿⡿⠿⠟⢻⠁⠀⠠⠓⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃
⠀⠀⡀⣻⢷⣬⡿⠊⠀⠀⠠⢢⢀⠄⠀⠈⣶⠦⢤⡔⢀⣥⣴⠶⠀⡈⠳⣀⡀⠀⠄⠀⠀⠀⠀⠁⢣⠀⠐⡀⢀⠀⠀⡀⢀⢠⣿⠿⠇⠈⢩⡈⢵⡯⣂⠀⠀⡄⠀⡄⠀⠰⢠⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣀⢢⣀⡈⠀⠀⡀⠓⣆⡌⠀⢮⠈⡀⡠⣀⣉⡀⠀⠈⡘⠿⠄⠉⠀⢃⠈⠩⡅⡰⠈⠉⡀⠀⠀⠈⠂⠀⠀⠈⡈⠁⠿⠄⠀⠘⠰⠰⠦⠀⠀⠀⢈⠁⠀⢂⠉⠁⠀⢀⠀⠉⠀⠀⠀⠀⠀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀
⠲⠨⠈⠿⡍⣬⠄⠀⢠⣖⣁⠡⠀⣧⡿⣦⢬⣶⣞⣄⢠⠀⠀⠀⠰⠰⢼⣀⠇⡚⢂⠀⠀⠈⢐⠄⠀⠀⢠⣁⠀⠀⠂⠈⣔⠒⡖⠷⠰⠈⠀⢬⠀⠀⠙⢇⠈⠀⠀⠀⠀⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠴⣶⠓⣿⣿⣴⠀⣀⣶⢶⣹⣿⠪⠑⠿⢕⣪⣿⣷⣮⣁⠀⠀⠐⠀⠺⢏⣙⢀⣈⠠⠄⠄⠀⠠⠀⣀⢀⠹⡄⠐⠂⠀⢙⣁⠀⠒⠠⠡⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣿⣿⣿
⠀⢢⣸⣦⣬⠭⠙⣄⡀⠄⠝⢿⣿⣁⡈⣭⡭⠏⡿⠉⠉⣀⠀⠀⠀⠀⢢⣜⠇⠦⢴⣄⠠⢰⠄⠀⠞⢻⣈⣵⠹⡄⠀⠀⠈⠈⠁⠀⠁⡀⠁⣠⣾⣶⣦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿
⢀⠀⢤⣉⠈⡶⢠⣷⠨⠤⠠⣳⡙⣿⡂⠙⠁⣄⠀⠀⠧⢜⢷⡀⠀⡦⡴⠘⠒⠀⠂⢎⡃⠀⡀⠀⠀⠀⠟⠋⠀⠍⠀⠀⠀⠀⠀⢀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢂⠀⡋⢡⣄⠀⠨⠉⣀⣤⣬⣻⡕⠲⠿⠤⣾⢳⣿⢓⠉⢿⠊⠗⢀⠀⡘⠐⠂⠀⠀⠁⠄⠀⠀⡀⡀⢄⡂⠁⠀⠀⠀⠀⠀⠀⠁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠂⠀⠀⠤⣤⣼⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⡟⠛⠻⢟⡻⠟⠛⠛⣛⣟⣧⣽⣟⣟⠶⣤⢿⡙⣿⡯⢾⢊⠙⠟⢂⢀⡤⠀⠈⠐⠀⠮⠀⠀⣀⢴⡄⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⠀⠉⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢲
⠀⣤⣄⠀⣠⢿⣁⠨⢵⣨⡄⢂⠂⡂⣁⡀⠈⠁⠀⠀⠀⣴⠖⠚⠏⠀⡀⠹⠁⢀⠀⠀⢰⡚⠄⠻⡎⡀⠐⠀⠠⠈⠐⠺⣾⡷⣆⡐⢔⣾⣿⣿⠁⡏⢥⣖⠱⣄⡇⠀⠀⣰⠐⠆⠰⠐⠀⣀⣄⠀⠀⢡⣫⡙⠉⠁⠀⠀
⣆⢖⡴⠆⠀⠒⠔⠀⠆⠾⠈⠠⠄⠁⠀⠀⠁⠤⡕⡀⠾⠿⠿⣅⣆⠀⠶⠶⡆⡉⠘⠃⢀⡁⠀⠀⠈⠂⠃⠀⠀⠀⣻⣯⠏⣨⣿⠇⠀⡂⠹⠿⠚⠥⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠂⠈⠁⠐⠹⠬⠌⠈⠤⠰⠀⠄
⠀⢤⠄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢶⠄⠀⠘⠁⠀⠀⠤⢟⠇⠀⠀⠀⠀⠁⠀⠀⢐⢀⡀⠀⠀⠀⠀⠀⠀⢀⠄⣀⣄⡀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣠⣤⢶⡿⠄⢀⣠⣴⣤⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⣾⠿⣟⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢸⣿⣿⠋⠁⠀⠀⡀⠀⡀⣴⡆⡆⣤⡄⠀⠀⠀⠀⣀⣬⣶⣦⡀⠀⠀⠀⠀⠘⠀⠀⠀⢀⠀⠚⠛
⠌⠻⠗⠋⠀⠀⠈⠙⠿⢿⣧⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣴⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠉⠋⠀⢀⣄⠆⣷⣦⢇⣿⡇⢅⣿⡇⠀⣷⡄⢠⣬⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⡤⠀
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠱⠂⠀⡀⠰⠀⠀⠀⠀⣀⡀⠀⠠⠜⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣯⣭⣾⣿⣭⣿⣷⣭⣾⣧⣭⣾⣧⣀⣁⡀⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⡁⢄⠈
⢀⣅⠀⢐⣠⠀⠀⠀⠀⠀⢤⡀⠀⠼⠤⢀⠀⠀⠀⠀⣀⠘⠋⣰⡞⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⢩⠞⢤⡄⠀⠀⠘⠀⠀⠀⣠⢔⠴⠈⠁⠀⢀
⢾⢛⡥⠼⠾⢩⡅⠀⠈⠂⠀⠀⠐⣿⠢⡅⡄⠲⠀⠀⠀⢨⢠⣿⣧⠢⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⣠⡀⣀⠠⠁⠀⠀⠴⡶⡃⣠⣰⠿⡀⠠
⢸⣿⣒⢰⠄⠀⠀⠀⠀⠁⢛⠉⢀⠭⠱⠂⠙⠀⠀⠀⢐⣸⣼⣿⣯⣥⣄⡁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠄⢀⣷⣤⡶⠶⢶⣿⡉⠁⠌⠀⠉⡀⣹⠇⠒⠀⡠
⡂⠨⣷⣰⠄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⠟⠁⣴⣿⣿⡿⠿⠟⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠄⡀⠃⠠⣄⠀⠀⠤⢁⠀⠀⠀⠀⡀⠨⢰⡶⠀⠀
⠔⡴⠏⠉⢃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⣤⢝⡠⢡⡅⡹⢇⡄⢠⡌⡈⠀⢀⢈⠀⡠⠐⠀⣠⡄
⠂⡀⠶⠆⠀⠀⠈⠀⠀⠈⣀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢴⠿⠿⠍⠁⠀⣤⣴⡾⠛⠩⠋⣐⠋⠴⠋⣀⠉⣴⡆⠁⠁
⡧⢢⡶⢀⢤⠀⠿⢁⠠⢿⡟⡀⠢⠄⠀⠃⠀⢀⣀⡀⠙⠻⠿⢿⣿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠈⢙⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠉⠉⠤⡎⠡⢄⠺⢟⡖⠛⠰⠀⠊
⠀⣿⠇⡄⠀⠀⠀⠐⢷⡀⢁⠀⠀⠀⠀⠀⠀⠈⠛⠑⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣀⣤⣶⡿⣿⣿⠿⣿⣿⣿⣿⣿⣶⣤⡄⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⢣⠨⢂⠠⢒⡁⢀⠀⠀⠀
⠐⣿⣿⣀⡀⣐⡀⣀⠀⢀⠀⠀⢾⠷⠀⠀⠀⢀⣠⣤⣴⣶⣾⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⢿⣿⣿⣿⣿⣆⣸⣿⣿⣿⣿⣿⣿⣿⣶⣄⣀⣀⣠⣤⣴⣤⣤⣠⠄⠀⡀⠀⠀⢠⣤⡀⠀⠀⠀⠈⠣⠁⠀⠀⠣⠈⡀⠁⠈
⣐⠀⢣⡚⠷⣏⠤⠼⠂⢀⠠⠀⠀⠀⣀⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣄⢸⣿⣿⣿⣿⣿⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠸⠿⡇⠀⡐⠁⠀⠠⠀⠀⠀⡀⠇⢀⢻⣿
⣿⠃⠘⠛⣷⣾⡈⠃⠀⠅⠄⠃⠚⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣀⠀⠀⠈⡍⠛⠛⡋⠰⠔⠋⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠄⠀⠛⠐⠀⠃⠑⠆⠀⠮⠷⠷⢶⡆⠀⠀⢺⡚
⠂⠀⠠⡈⠛⣙⢛⣟⠂⠆⠐⠊⠝⠂⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠲⠀⢀⠂⠀⠁⠠⠮⠃⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠠⠀⣨⠇⠀⠀⢀⡀⠀⠁⠐⠂⠀⠀⠀⠀⠀⠀
⣀⠀⠼⡣⡗⠀⢌⠀⣀⣨⣦⡀⠩⣦⡈⠛⢿⣿⣿⣿⣿⣿⡿⣿⣿⠛⠛⠉⠀⠙⢲⠤⠦⢼⣆⠢⠀⠐⢀⠐⠀⠠⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⠁⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠛⠟⢷⣵⣶⣄⠛⢃⡄⡈⠻⠛⠂⢹⣧⠰⠫⠉⠠⢨⣅⡠⠀⡬⠙⢠⠨⡀⠀⠀⠛⠁⠈⠉⠉⡇⣂⣦⠄⠥⠀⠀⡆⠀⠈⠀⣿⣿⣿⠛⠻⢛⣿⣿⣿⣿⠿⠟⠋⠠⠓⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃
⠀⠀⡀⣻⢿⣬⡿⠊⠀⠀⠠⢤⢀⠄⠀⠈⣶⠦⢤⡔⠀⣵⣴⠷⠀⡌⠳⣀⡀⠀⠀⠀⠀⠀⠀⠉⢣⠀⠐⠀⢀⡀⠀⡀⢀⢠⣿⠿⠇⠈⢹⡨⠹⣯⢃⠀⠀⠀⠀⡄⠀⠠⢠⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀
⠿⣀⢢⣄⡈⠀⠀⡈⢓⣂⡌⠀⢮⠊⡂⡀⣀⣉⡀⠀⠊⡈⠿⠤⠃⡈⢋⠈⠩⣅⡰⠈⠉⡀⠄⠀⠄⠒⠀⠁⠈⣈⠁⠿⠄⠀⠉⢠⠲⠆⠈⠀⠈⣈⠁⠀⢂⠉⠁⠀⢀⠀⠁⠀⠀⠀⠀⠀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀
⠲⠈⠉⠿⡍⣬⡄⠀⠥⣖⣃⠡⠀⣧⡿⣦⢬⣶⣞⢄⢠⠁⠀⠀⠰⠲⢼⣈⠕⡚⠃⠀⠀⠈⢑⠄⠀⠀⢠⣁⠀⠈⠂⠉⣴⠐⡶⠷⠰⠌⠀⢭⠀⠀⠙⢁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀
⠀⠴⣶⠓⣿⣿⣴⠀⣁⣶⠶⡻⣿⠪⠑⠿⢕⣪⣿⣷⣮⣁⠀⠀⠐⠀⠞⢏⣙⣀⣈⠠⠴⠄⠀⠠⠢⣀⢀⠹⡄⠐⠂⠈⢙⡅⠀⠂⠰⠁⠔⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣼⣿⣿⣿
⠀⠢⣸⡦⣬⠥⠙⣄⡀⠄⠘⢿⣿⣅⡈⣯⡭⠋⡿⠉⠉⣀⠀⠀⠀⠁⢲⣌⠇⡧⢼⣄⠀⢐⠀⠀⠞⢻⣀⣵⢻⡄⠀⠀⠐⠈⠁⠀⠁⠀⠁⢠⣾⣶⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿
⣀⠀⢤⡍⠉⡶⢠⣧⠨⠦⠠⣷⡙⣿⡂⠙⠁⣄⡀⠀⠧⢜⢷⡀⠀⠤⡰⠈⠓⠀⡀⡌⡂⠀⡀⠄⠀⠀⠟⠋⠀⠍⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿
⢂⠀⡛⢡⣄⠀⠨⠉⣀⣤⣬⣻⡕⠲⠿⢴⢾⢑⣻⢓⠉⢿⡊⠒⢀⠀⡘⠔⠂⠀⠀⠁⠀⠀⠀⡀⡀⠄⡂⠑⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠤⣤⣼⠿⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠛⠻⢟⡛⠟⠛⠛⣛⣟⣧⣽⣟⣟⠶⣤⢿⡙⣿⣯⢾⢊⢙⢟⢠⢀⣤⠀⠈⠐⠀⢾⡀⡀⣀⢴⡄⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⠀⠈⠁⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣤⣄⠀⣠⢿⣁⠨⢵⣨⡄⢂⠀⡂⣁⡀⠘⠁⠀⠀⠀⣴⠖⠚⠏⠀⠀⠹⠡⢀⠀⠀⢰⡚⠄⠻⠎⡀⠐⠀⡠⠈⢐⠺⣾⡷⣆⡐⢔⣾⣿⣿⠁⡍⢥⢖⠱⣄⡇⠀⠀⣰⠐⠆⠱⠐⠀⣀⣄⠀⠀⢡⣯⡙⠉⠁⠀⠀
⠂⣖⡴⠆⠀⠂⠐⠀⠆⠾⠈⠠⠄⠁⠀⠀⠁⠤⡕⡀⠾⠿⠿⢁⣆⠀⠴⠶⡆⡉⠘⠃⢀⠁⠀⠀⠈⠂⠃⠀⠀⠀⣺⣯⠎⣸⢿⠏⠀⡂⠙⠯⡚⠅⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠂⠈⠁⠐⠹⠌⠄⠀⠄⡠⠀⠄
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢶⠄⠀⠘⠀⠀⠀⠤⢟⠗⠂⠀⠀⠀⠁⠀⠀⢐⢀⡀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣄⡀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣠⣤⢶⡿⠄⢀⣠⣴⣤⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⣾⠿⣟⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢸⣿⣿⠋⠁⠀⠀⡀⠀⡀⣴⡆⡆⣤⡄⠀⠀⠀⠀⣀⣬⣶⣦⡀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠐⠚⠛
⠌⠻⠗⠋⠀⠀⠈⠛⠿⢿⣧⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣴⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠉⠋⠀⢀⣄⠆⣷⣦⢇⣿⡇⢅⣿⡇⠀⢷⡄⢠⣬⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⣤⠀
⠀⡠⠀⠀⠀⠀⠀⠀⢀⠱⢂⠀⡀⠰⠀⠀⠀⠀⣀⡀⠀⠠⠼⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣯⣭⣾⣿⣭⣿⣷⣭⣾⣧⣭⣾⣇⣀⣁⡀⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⡁⢄⠈
⢀⣅⠀⢀⣠⠀⠀⠀⠀⠀⢤⡀⠀⠜⠤⢀⠀⠀⠀⠀⣀⠘⠋⣰⡎⣧⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⢩⠜⢤⡄⠀⠀⠘⠀⠀⠀⢠⢔⠴⠈⠁⠀⢀
⢾⢛⡥⠸⠾⢩⡅⠀⠈⠂⠀⠀⠀⣿⠢⡅⠅⡲⠀⠀⠀⢨⢠⣿⣯⠢⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⣠⡀⣀⠠⠀⠀⠀⠔⡶⡃⣠⣰⠿⣀⠠
⢸⣿⣒⢰⠄⠀⠀⠀⠀⠁⢛⠉⢐⠭⠱⠂⠙⡀⠀⠀⢐⣺⣼⣿⣯⣥⣄⡁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠄⢀⣷⡤⡶⠶⢶⣿⡉⠁⠌⠀⠉⡀⣹⠇⠐⠀⡠
⡂⠨⣷⣰⠄⠀⠀⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⠟⠁⣴⣿⣿⡿⠿⠟⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠄⡀⠓⠠⣄⠀⠀⠤⢁⠀⠀⠀⠀⡀⠡⢰⡶⠀⠀
⠄⡴⠏⠉⢃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠌⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⣤⢝⡠⢁⡅⡹⢇⡄⠠⡄⡈⠀⢀⢀⠄⡠⠐⠀⣠⡄
⠂⡁⠖⠆⠀⠀⠈⠀⠀⠈⣀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢴⠿⠿⠎⠁⠀⣤⣴⡾⠛⠠⠚⣐⠋⠴⠋⣀⠉⣴⡆⠀⠁
⣷⢢⡶⢀⢦⠀⠾⢁⠠⢿⡟⡀⠂⠄⠀⠃⠀⢀⣀⡀⠙⠻⠿⣿⣿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠈⢙⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠙⠦⡎⠡⠄⠪⠟⡖⠛⠰⠀⠋
⠀⣿⠇⡄⠀⠀⠀⠐⢷⡀⢁⠀⠀⠀⠀⠀⠀⠈⠛⠑⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⣀⣤⣶⣿⣿⣿⠿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⢣⠨⢂⠠⢒⡁⠀⠀⠀⠀
⠐⣿⣿⣄⡠⣐⡀⣀⠀⢀⠀⠀⢾⠷⠀⠀⠀⢀⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⢿⣿⣿⣿⣿⣆⢸⣿⣿⣿⣿⣿⣿⣿⣶⣄⣀⣀⣠⣤⣴⣤⣤⣠⠄⠀⡀⠀⠀⢠⣤⡀⠀⠀⠀⠈⠢⠁⠀⠀⠣⠈⡀⠀⢀
⣐⠀⢣⡊⠣⣏⠤⠼⠂⢀⠀⠀⠀⠀⣀⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣄⢸⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠸⠿⣇⠀⡀⠁⠀⠠⠀⠀⠀⠀⠇⢀⢻⣿
⣿⠃⠘⠛⣷⣾⡈⠃⠀⠅⠄⠃⠚⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣀⠀⠀⠈⡍⠛⠛⡋⠠⠔⠋⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠄⠀⠙⠀⠀⠃⠙⠆⠉⠮⠷⠷⢶⡄⠀⠀⢮⡚
⠂⠀⠠⡈⠛⣙⢛⣟⠆⠆⠐⠊⠍⠂⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠳⠀⢀⠂⠀⠀⠠⠮⠃⠀⠀⠀⠐⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠠⠀⣠⠄⠀⠀⢀⡀⠀⠁⠐⠂⠀⠀⠀⠀⠀⠁
⣀⠀⠼⡣⣗⠀⢌⠀⣀⣨⣦⡀⠩⣤⡈⠛⢿⣿⣿⣿⣿⣿⡿⣿⣿⢛⠛⠉⠀⠙⢲⠤⠦⢼⣦⡂⠀⠀⢀⠒⠀⠠⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⠁⠉⢀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠛⠟⠷⣵⣶⣄⠛⢁⡀⡈⠻⠛⠂⢹⣧⠰⠫⠉⠰⢨⣅⡠⠀⣬⠙⢠⠨⡁⠀⠀⠚⠁⠀⠉⠩⣏⣂⣦⠄⠡⠀⠀⡆⠁⠈⠀⣿⣿⣿⠛⡻⢛⣿⣿⣿⣿⠿⠟⠉⠠⠓⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃
⠀⠀⡀⣻⢿⣬⡿⠊⠀⠀⠠⢦⢀⡄⠀⠈⣶⠦⢤⡐⠅⣽⣶⠷⠀⡌⠳⣀⡀⠀⠄⠀⠀⠀⠀⠉⢣⠀⠂⠀⢀⠀⠀⡀⢀⢠⣿⠿⠇⠈⢹⡸⠹⣯⣃⠀⠀⠀⠀⡄⠀⠠⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣀⢢⣄⡈⠀⠀⡈⠓⣂⡌⠀⢮⠆⡂⡀⣀⠉⡀⢀⠊⡈⠿⠄⠃⡈⢫⠈⠩⣅⡴⠀⠉⡀⠄⠀⢌⠐⠀⠀⠈⡈⠁⠻⠄⠀⠈⣠⠰⠆⠈⠀⠈⢈⠁⠀⢂⠉⠁⠀⢀⠀⠁⠀⠀⠀⠀⠀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀
⠲⠈⠌⠿⡍⣬⠄⠀⠥⣖⣃⠡⠀⣧⡿⣦⢬⣶⢞⢄⢠⠁⠀⠀⠸⠲⢼⣈⠕⡚⠃⠀⠀⠈⢑⠄⠀⠀⢠⣁⠀⡈⠂⠙⣤⠐⡶⠷⠰⠌⠀⢭⠀⠀⠙⢁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀
⠀⠴⣾⠓⣿⣿⣴⠀⡁⣶⠶⡛⣿⠪⠑⠿⢑⣪⣿⣷⣮⣁⠀⠀⠐⠀⠚⢏⣙⣀⣈⠠⠖⠄⠀⠠⠢⣀⢀⠹⡄⠐⠂⠈⢙⡇⠀⠒⠰⠁⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣼⣿⣿⣿
⠀⠢⣸⡦⣬⠥⠙⣄⠀⠄⠜⢿⣿⣁⡈⣯⡭⠋⡿⠉⠉⣀⠀⠀⠀⠁⢦⣌⠗⡧⢼⣤⡀⠐⠀⠐⠞⢻⣨⣵⢹⡄⠀⠀⠐⠈⠁⠀⠁⠀⠁⢠⣾⣶⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿
⢀⠀⢤⡍⠉⡶⢠⣧⠨⠦⠠⣳⣙⣿⡢⠙⠁⣄⡄⠀⠧⢘⢷⡀⠀⡠⡰⠈⠓⠀⠀⣈⡃⠀⡀⢄⠀⠀⠟⠋⠀⠍⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿
⢂⠀⡛⢡⣄⠀⠨⠉⣀⣤⣬⣹⡕⠲⠿⢴⢾⢹⣻⢓⠉⢿⡊⠒⢀⠀⡨⠐⠂⠀⠀⠉⠀⠀⠀⡀⡀⢄⡂⠙⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠤⣤⣼⠿⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠛⠻⢟⡻⠟⠛⠛⣛⣟⣧⣽⣿⣟⠶⣤⢿⡙⣿⣯⢾⢊⢙⠟⢠⢀⣤⠀⠀⠐⠀⢾⡀⡀⣀⢴⡄⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⠀⠈⠁⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠠⠀⠀⢀⢏⠀⠈⢄⢠⡄⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⡐⠒⠈⠋⠀⠀⠈⠁⢀⠀⠀⠐⠀⠀⠙⠌⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄⠀⢐⣼⣾⡶⠀⡀⠀⠀⠀⠄⠃⠀⠀⢀⠀⠀⠰⠀⠀⣀⣄⠀⠀⠀⢋⠉⠉⠀⠀⠀
⠀⢐⡐⠂⠀⠂⠐⠀⠂⠖⠀⠀⠀⠁⠀⠀⠀⠀⠄⡀⠼⠿⠿⠀⡆⠀⠴⠶⠀⡈⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⢢⠈⠀⡠⠦⠀⠀⠀⠁⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠸⠀⠀⠀⠀⠠⠀⠀
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠀⠈⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⡀⠀⣴⡇⠀⣼⡇⢐⢤⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣠⣤⢰⡿⠄⠀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡾⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠋⠁⠀⣀⡈⠁⠀⣽⡇⠄⣹⡇⠘⠹⣻⠄⣀⣠⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙
⠈⠛⠗⠋⠀⠀⠈⠙⠿⢿⣧⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠉⠉⠀⣰⣇⠃⣵⣦⠇⢿⡇⠀⢿⡇⠀⢸⣾⢡⣤⠮⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⡤⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⣤⣾⣯⣭⣾⣧⣭⣾⣧⣭⣾⣿⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⡀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⠈⠃⢠⡊⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⢩⠀⢠⡄⠀⠀⠘⠀⠀⠀⠀⢀⠀⠀⠁⠀⢀
⠠⠊⠀⠀⠄⠉⡁⠀⠈⠀⠀⠀⠀⢹⠀⠅⠀⠂⠀⠀⠀⢨⢀⡛⡅⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣶⣶⣦⣴⣦⣤⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢠⡐⠿⠀⠀
⢸⣿⠀⠀⠄⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠈⠀⣀⣤⣶⣾⣾⣿⣶⣶⣤⡀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣾⣿⣿⣿⣿⣿⠿⠿⠿⠛⠋⠁⠀⠀⠀⢀⣣⡤⠴⠶⠖⣿⠉⠀⠀⠀⠀⠀⠘⠃⠐⠀⠀
⠂⠀⢔⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢀⣴⣿⡿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⡄⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠰⡶⠀⠀
⠄⠠⠊⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣭⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠙⡀⠁⡁⠘⢂⡀⠀⡀⠀⠀⠀⢀⠀⡀⠀⠀⢠⡄
⠀⠀⠔⠄⠀⠀⠈⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠳⠌⠀⠀⢤⠴⠾⠃⠀⠂⢀⠉⠄⠃⣀⠀⣴⠀⠀⠀
⠦⢠⡶⠀⠀⠀⠾⠁⠀⢿⠏⠀⠀⠄⠀⠀⠀⢀⣀⠈⠙⠻⠿⠿⢿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠈⢉⣹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⡌⠀⠀⠀⠁⠄⠊⠐⠀⠂
⠀⠿⠇⠀⠀⠀⠀⠐⢦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠁⠢⣀⠸⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢁⠀⠀⠀⠐⠀⠀⠀⠀⠀
⠀⢿⢓⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⠗⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⣑⣤⣤⣴⣿⣿⣿⣿⣿⣿⡟⢹⡟⣿⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⣀⣤⣤⣤⣤⡀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡐⠀⢂⡀⠀⡍⠄⠰⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡋⢸⣿⣿⣿⣿⡿⠘⠣⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠉⠙⠛⣻⣿⣿⣦⡀⠀⠀⠀⠻⠂⠀⠀⠀⠀⠠⠀⠀⠀⠀⠃⠀⢹⣰
⣿⠀⠀⠋⣴⣴⡀⠀⠀⠀⠀⠂⠘⠋⠁⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠉⠛⠛⠋⠠⠐⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣰⣿⣿⣿⣿⣷⡄⠀⠈⠀⠀⠀⠀⠀⠀⠈⠷⠥⠤⠀⠀⠀⠀⡈
⠂⠀⠀⠀⠙⡉⠛⢐⠀⠀⠀⠈⠁⠂⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠂⠀⠀⠠⠎⠂⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠀⠐⠃⠖⠀⢈⠀⣀⣈⣄⠀⠈⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠐⠄⠀⠐⣂⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀
⠁⠛⠣⣤⣤⡀⠘⢀⠀⠈⠋⠓⠂⠸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠉⠀⠀⠀⠈⠁⠀⠀⠈⠃⢀⣆⠄⠀⠀⠀⡀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃
⠀⠀⠀⡛⢑⢠⠱⠀⠀⠀⠀⢠⢀⠄⠀⠈⠻⠿⠿⠿⠻⣿⡽⠋⠀⠀⠳⢀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠋⠙⠻⠛⠛⠙⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠷⠀⠀⣀⡈⠀⠀⡀⠐⢀⠄⠀⢪⠈⠀⠀⠀⠈⠀⠀⠈⠈⠭⠀⠁⠀⠀⠈⠉⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠈⠳⡌⢤⠀⠀⠀⠄⠀⠁⠀⣅⠋⠀⢈⢤⠜⠀⢠⠀⠀⠀⠐⠠⢈⣀⠄⠀⠀⠀⠀⠈⢀⠄⠀⠀⢀⡀⠀⠀⠀⠀⡄⠀⠆⠀⠀⠀⠀⢀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢰
⠀⠐⠶⠃⣎⣻⡰⠀⠀⡰⠀⠐⣕⠊⠑⠾⠁⠠⢵⢖⡀⠀⠀⠀⠀⠀⠘⢃⠈⠀⡀⠀⠀⠀⠀⠀⠀⣀⠀⠹⡄⠐⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣼⣿⣿⣿
⠀⠠⢘⡠⣤⠄⠘⢀⠀⠄⠘⢿⡬⣁⡀⠬⡍⠉⡛⠈⠈⣀⠀⠀⠀⠀⢠⣈⠂⠀⢠⢄⠀⠐⠀⠀⠞⠻⣀⢁⠹⡄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⠀⠀⡶⠠⢢⠠⠠⠀⡂⡁⡏⡂⠑⠀⣄⠀⠀⠧⠈⢂⡀⠀⠠⠐⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⠀⠈⢁⣀⠀⠀⠉⢀⢤⣠⠨⠁⠂⠷⠤⢞⢁⠰⠀⠀⢘⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠤⡄⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠟⠙⠻⠟⡙⠟⠙⠛⠛⢛⣣⣜⡟⠖⠆⡄⢮⠙⠻⠄⠜⠈⠉⠓⠀⠀⠠⠀⠀⠀⠀⠠⠀⠀⠀⢤⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢠
⠀⠠⠀⠀⣀⠏⠁⠈⢀⢨⡄⠀⠀⠀⢀⠀⠈⠁⠀⠀⠀⡐⠒⠈⠋⠀⠀⠈⠁⢀⠀⠀⠐⡀⠀⠙⠌⠀⠀⠀⠀⠀⠀⠂⠀⠀⠄⠀⢐⣼⣾⡶⠀⡀⠀⠀⠀⢄⠃⠀⠀⢀⠀⠀⠰⠀⠀⣀⣄⠀⠀⠁⣉⠉⠉⠀⠀⠀
⠀⢐⡐⠂⠀⠂⠐⠀⠂⠖⠀⠠⠀⠁⠀⠀⠀⠠⠄⡀⠾⠿⠿⠀⡆⠀⠴⠖⡀⡈⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⢢⠨⠀⡠⠦⠄⠀⠀⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠀⠈⠀⠀⠀⠄⠔⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⡀⠀⣴⡏⡄⣼⡇⢐⢤⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣠⣤⢰⡿⠀⠀⣠⣤⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡾⠿⠟⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠋⠁⠀⡀⡈⠁⠀⣿⡇⠇⣻⡇⠘⢹⣺⠄⣀⣤⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛
⠌⠛⠗⠋⠀⠀⠈⠙⠿⢿⣧⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠉⠉⠀⣰⣇⠇⣷⣦⠇⣿⣇⠀⣿⡇⠀⢹⣾⢡⣤⠾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⡤⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣯⣤⣼⣯⣭⣿⣧⣭⣾⣧⣥⣾⣿⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⡀⢀⠀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠊⢠⡊⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⢩⠀⢠⡄⠀⠀⠘⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀
⠠⠊⠀⠀⠄⠉⡅⠀⠈⠀⠀⠀⠀⢹⠀⠅⠀⠒⠀⠀⠀⢨⢀⡛⠅⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣦⣴⣦⣤⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠂⠀⢠⡰⠿⠀⠀
⢸⣿⠀⠠⠄⠀⠀⠀⠀⠀⠒⠀⢀⠀⠀⠀⠈⠀⣀⣤⣶⣾⣾⣿⣶⣶⣤⡀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣾⣿⣿⣿⣿⣿⠿⠿⠿⠛⠋⠁⠀⠀⠄⢀⣳⡤⠴⠶⠖⣿⠁⠀⠄⠀⠀⠀⠘⠃⠐⠀⠀
⠀⠀⢖⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢀⣴⣿⡿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⡄⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠰⡶⠀⠀
⠄⠠⠊⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣭⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠘⡀⢁⡁⠉⢂⡀⠀⡄⠀⠀⠀⢀⠀⡀⠀⠀⢠⡄
⠀⠀⠔⠆⠀⠀⠈⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠱⠌⠀⠀⢤⠴⠾⠃⠀⠊⢀⠉⠤⠃⣀⠁⣴⠀⠀⠀
⠦⢠⡶⠀⠀⠀⠾⠁⠠⢿⠏⠀⠀⠄⠀⠀⠀⢀⣀⡈⠙⠻⠿⠿⢿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⢉⣻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⡌⠀⠀⠀⠁⠔⠋⠐⠀⠂
⠀⠿⠅⠀⠀⠀⠀⠐⢦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠁⠢⣀⠸⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⢁⠀⠀⠀⠐⠀⠀⠀⠀⠀
⠀⣿⢓⠀⠀⠀⠀⡀⠀⠀⠀⠀⢼⠗⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⣑⣄⣠⣴⣿⣿⣿⣿⣿⣿⡟⢹⡟⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⣀⣤⣤⣤⣤⡀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡐⠀⢂⡀⠢⡌⠄⠴⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡋⢸⣿⣿⣿⣿⡿⠘⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠏⠙⠛⣛⣿⣿⣦⡀⠀⠀⠀⠻⠂⠀⠀⠀⠀⠠⠀⠀⠀⠀⠇⠀⢹⣴
⣿⠀⠀⠋⣴⣴⡀⠀⠀⠀⠀⠂⠘⠋⠁⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠉⠛⠛⠋⠠⠐⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣸⣿⣿⣿⣿⣷⡄⠀⠈⠀⠀⠀⠀⠀⠀⠈⠷⠦⠤⠀⠀⠀⠀⡈
⠂⠀⠀⠀⠙⡉⠛⢐⠀⠀⠀⠈⠁⠂⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠂⠀⠀⠠⠎⠂⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣀⠀⠀⠀⢀⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀
⢀⠀⠘⡃⠖⠀⢌⠀⢀⣈⣤⡀⠨⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠁⠰⠀⠀⠰⣂⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀
⠁⠛⠣⣤⣤⡀⠘⢀⠀⠈⠋⠓⠀⠸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠉⠀⠀⠀⠈⠁⠀⠀⠈⠃⢀⣆⠀⠀⠀⠀⡀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃
⠀⠀⠀⡛⢑⢠⠵⠀⠀⠀⠀⢠⠀⠄⠀⠈⠹⠿⠿⠿⠻⣿⡿⠛⠀⠈⠓⢀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠋⠛⠻⠛⠛⠙⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠷⠀⠀⣀⡈⠀⠀⡀⠐⢀⠄⠀⢪⠈⠀⠀⠀⠉⠀⠀⠈⡈⠯⠄⠁⠀⠀⠈⠉⠁⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠈⠳⡍⢤⠀⠀⠀⠄⠁⠁⠀⣥⠋⠀⠈⢤⠔⠀⢠⠀⠀⠀⠐⠠⢈⣀⠄⠂⠂⠀⠀⠈⢀⠄⠀⠀⢀⡀⠀⠀⠀⠀⡄⠀⠂⠀⠀⠀⠀⢀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢰
⠀⠐⠶⠓⣎⣷⠐⠀⠀⡰⠀⠐⣕⠊⠑⠶⠁⠨⢱⢖⡂⠀⠀⠀⠀⠀⠘⢋⢉⠀⡀⠀⠀⠀⠀⠀⠀⣀⠀⠹⡄⠐⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣼⣿⣿⣿
⠀⠠⢘⡠⣤⠄⠙⢀⠀⠄⠘⢿⡬⣁⡀⡬⡍⠉⡏⠈⠈⣀⠀⠀⠀⠀⢠⣌⠂⠂⢬⢄⠀⠐⠀⠀⠞⠋⣀⡥⠹⡄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⠀⠀⡶⠠⢢⠠⠤⠀⣢⡁⡽⡂⠑⠁⣄⠀⠀⠧⠘⢂⡀⠀⠠⠐⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠌⠁⠀⠄⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢂⠀⠀⢁⣀⠀⠀⠈⢀⢤⣠⠨⠁⠐⠵⠤⢞⢁⠰⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠤⡄⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠟⠙⠻⠟⠙⠟⠛⠛⠛⢛⣣⡔⡟⠖⠆⡄⢮⡘⠷⠤⠞⠀⠉⠓⠀⠀⡤⠀⠀⠀⠀⠤⠀⠀⠀⢤⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⣠
⠀⠀⠀⠀⠀⢂⠀⠈⢀⠠⡄⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⡀⠒⠈⠋⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣶⡶⠀⡀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⠐⠀⠀⠀⣄⠀⠀⠀⠉⠉⠉⠀⠀⠀
⠀⢐⡐⠂⠀⠀⠀⠀⠄⠔⠀⠀⠀⠁⠀⠀⠀⠀⠄⡀⠸⠳⠟⠀⠀⠀⠴⠔⠀⡈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢠⠀⠀⠠⠄⠀⠀⠀⠁⣀⣤⣶⣶⢶⣶⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠠⡆⠁⢹⡏⡀⣸⡏⢐⢽⣿⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣠⣤⢰⡿⠀⠀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⣿⠋⠁⡄⡀⡉⠁⠀⣾⡇⠀⣿⡇⠘⢹⣺⠀⣀⣠⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛
⠈⠛⠗⠋⠀⠀⠈⠙⠿⢽⣧⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠉⠉⠀⣰⡇⠃⣵⣦⢃⣿⡇⠀⢸⡇⠀⢸⣾⢡⣤⠦⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡠⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣤⣼⣧⣬⣿⣧⣥⣾⣧⣭⣾⣿⣃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠀⢀⠂⡀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠋⢩⠀⢀⡄⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀
⠠⠀⠀⠀⠄⠀⡀⠀⠈⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⢀⣀⡁⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⡐⠷⠀⠀
⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣾⣿⣿⡿⠿⠿⠛⠋⠉⠉⠀⠀⠀⠀⠀⢀⣡⡤⠴⠶⠒⣿⠁⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀
⠀⠀⢄⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⢀⣴⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠠⡶⠀⠀
⠄⠠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣿⣷⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠀⠁⡁⠈⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠑⠌⠀⠀⠠⠴⠾⠂⠀⠀⠀⠈⠀⠃⡀⠀⣠⠀⠀⠀
⠄⢠⡶⠀⠀⠀⠦⠁⠀⢿⠏⠀⠀⠄⠀⠀⠀⢀⣀⠈⠙⠻⠿⠿⢿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡌⠀⠀⠀⠁⠀⠂⠐⠀⠀
⠀⠿⠅⠀⠀⠀⠀⠐⢦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠁⠀⢀⠨⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠺⢑⠀⠀⠀⠀⡀⠀⠀⠀⠀⠸⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡿⣿⣿⣿⣿⡿⢿⡇⢿⣿⣿⣿⣿⣷⣄⣀⠀⠀⠀⢀⣀⣠⣤⣤⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡐⠀⠀⡀⠀⡀⠄⠰⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡋⢸⣿⣿⣿⣿⡷⠘⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⡟⠛⠻⢿⣿⣿⣷⡄⠀⠀⠀⠻⠂⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠉⢀
⡷⠀⠀⠋⣴⣤⡀⠀⠀⠀⠀⠀⠘⠊⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠙⠻⠟⠋⠠⠐⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⣀⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠠⠄⠀⠀⠀⠀⠀
⠂⠀⠀⠀⠙⡉⠛⢀⠀⠀⠀⠈⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠠⠆⠂⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⠃⠆⠀⢈⠀⠀⣈⣤⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠐⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀
⠁⠛⠃⣤⣄⡀⠐⢀⠀⠈⠋⠃⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠉⠀⠀⠀⠈⠁⠀⠀⠈⠁⢀⣀⠀⠀⠀⠀⡀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁
⠀⠀⠀⡛⢑⢠⠱⠀⠀⠀⠀⢀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠟⠻⠿⣿⣿⣿⣿⠿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠆⠀⠀⣀⠀⠀⠀⠀⠐⠀⠀⠀⢪⠈⠀⠀⠀⠈⠀⠀⠈⠈⠭⠀⠀⠀⠀⠈⠉⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠄⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠈⠈⠱⠌⢤⠀⠀⠀⠀⠀⠀⠀⣁⠊⠀⠈⠄⠄⠀⢠⠀⠀⠀⠐⠠⢀⣀⠀⠀⠀⠀⠀⠈⢀⠄⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠐⠦⠂⢌⢻⠐⠀⠀⠰⠀⠀⣕⠈⠑⠲⠁⠀⠰⢆⠀⠀⠀⠀⠀⠀⠘⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠹⡄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣄⣀⣤⣄⣹
⠀⠀⢈⡠⣤⠄⠈⠀⠀⠄⠈⢻⡬⣁⡀⠤⠍⠉⠊⠈⠀⡀⠀⠀⠀⠀⢠⣈⠂⠀⠠⢄⠀⠐⠀⠀⠞⠋⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣷⣶⣦⣄⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠰⠠⠢⠠⠀⠀⠀⡁⡍⡂⠑⠀⣀⠀⠀⠧⠈⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⢀⠀⠀⢁⣀⠀⠀⠁⢀⢤⣠⠨⠁⠀⠷⠤⢞⠁⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀
⠟⠙⠻⠟⠙⠟⠘⠛⠚⠛⡣⡄⡞⠆⠂⡀⠮⠘⠳⠄⠘⠀⠀⠑⠀⠀⠠⠀⠀⠀⠀⠠⠀⠀⠀⠤⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠒⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣴⡶⣠⣤⣴⣶⣶⣤⣅⡀⠀⠀⠀⠀⠐⠀⠀⠀⡀⠀⠀⠀⠉⠉⠁⠀⠀⠀
⠀⠐⠐⠂⠀⠀⠀⠀⠀⠔⠀⠀⠀⠁⠀⠀⠀⠀⠄⡀⠘⠰⠟⠀⠀⠀⠴⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢠⣷⣿⣿⣿⣿⢿⣿⣿⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⡀⠀⢹⡇⠀⢸⡏⠀⣼⡏⢐⢽⣻⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣠⣤⢰⡿⠀⠀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠾⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣹⣿⠋⠱⡇⡀⡉⠁⠀⢸⡇⠀⢸⡇⠘⠹⣺⠀⣀⡠⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠈⠛⠗⠋⠀⠀⠈⠙⠿⢴⣦⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠉⠈⠀⣰⡇⠁⣴⣆⢀⣿⡇⠀⢸⡇⠀⢸⣮⢁⣤⠦⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡠⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣤⣼⣷⣥⣼⣧⣬⣼⣧⣤⡼⢋⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠁⢩⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀
⠀⠀⠀⠀⠄⠀⡀⠀⠈⠀⠀⠀⠀⠸⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠁⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠖⠀⠀
⠘⠿⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣠⣿⣿⡿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⠤⠴⠶⠒⢯⠁⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀
⠀⠀⢀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⢀⣴⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀
⠄⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣇⣴⣿⣿⣷⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠰⠞⠀⠀⠀⠀⠀⠴⠖⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀
⠀⢀⡶⠀⠀⠀⠤⠁⠀⢿⠇⠀⠀⠄⠀⠀⠀⢀⣀⠀⠈⠛⠛⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡈⠀⠀⠀⠁⠀⠀⠀⠀⠀
⠀⠮⠅⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠺⠑⠀⠀⠀⠀⡀⠀⠀⠀⠀⠨⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⡿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣾⣝⣷⣤⡀⠀⠀⠀⣀⣤⣤⣶⣦⣤⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⡀⠀⠀⠄⠐⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡁⢸⣿⣿⣿⣿⡿⠘⠃⠘⣿⣿⣿⣿⣿⣿⣿⣿⣦⠾⠻⣿⣿⣿⣻⣿⣿⣷⡀⠀⠀⠻⠂⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠉⢀
⡧⠀⠀⠁⣴⣄⡀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠙⠻⠛⠋⠀⠐⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠉⡉⠛⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠠⠆⠂⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⠃⠆⠀⠈⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠐⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀
⠁⠊⠀⣤⢄⡀⠐⠀⠀⠀⠋⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⢀⣤⠀⠀⠀⠀⡀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁
⠀⠀⠀⡛⠀⠠⠱⠀⠀⠀⠀⢀⠉⠛⠿⠿⡿⢿⠿⠿⠿⢿⠙⠃⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠿⢿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾
⠆⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠭⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠄⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠈⠀⠱⠀⠤⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⢀⠄⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠠⠂⠌⢣⠀⠀⠀⠠⠀⠀⢁⠀⠁⠢⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠘⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣀⣠⣠⣤⣼
⠀⠀⢈⡠⢤⠄⠈⠀⠀⠀⠈⢉⡈⢁⡀⠠⠌⠁⠀⠈⠀⡀⠀⠀⠀⠀⢠⣈⠂⠀⠠⠄⠀⠐⠀⠀⠖⠋⠀⠀⠨⠄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠠⠀⠠⠠⠀⠀⠀⡁⡈⡂⠐⠀⣀⠀⠀⠇⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉
⢀⠀⠀⢁⣀⠀⠀⠀⢀⢤⡀⠠⠀⠀⠥⠤⢞⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀
⠟⠙⠻⠟⠙⠗⠘⠛⠚⠛⡣⡄⡞⠄⠀⡀⠄⠈⠡⠀⠈⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠒⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣴⣶⣶⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠠⠀⠀⠀⡀⠀⠀⠀⠉⠉⠁⠀⠀⠀
⠀⠐⠐⠂⠀⠀⠀⠀⠀⠄⠀⠀⠀⠁⠀⠀⠀⠀⠄⠀⠘⠰⠟⠀⠀⠀⠴⠄⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⢿⣿⣿⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⢀⡄⠀⠉⡏⠀⢸⡏⠀⢼⡏⢐⢽⣿⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣠⣤⢰⡿⠀⠀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠾⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣹⣿⠋⠱⡇⠀⡉⠁⠀⣸⡇⠂⢸⡇⠘⠉⣺⠀⣀⡠⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠈⠛⠗⠋⠀⠀⠈⠙⠿⢵⣦⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠉⠈⠀⣰⡇⠀⣴⣦⢀⢿⡇⠀⢸⡇⠀⢸⣮⢠⣤⠦⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢰⣿⣤⣤⣴⣤⣤⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣤⣼⣧⣤⣼⣧⣤⣼⣧⣤⣼⠏⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⢉⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀
⠀⠀⠀⠀⠄⠀⡀⠀⠈⠀⠀⠀⠀⠙⠀⠀⢀⣤⣶⣾⣿⣿⣶⣶⣤⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⡀⠀⠀⢠⣿⣿⣿⣿⣿⡿⠿⠛⠛⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡐⠖⠀⠀
⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣠⣿⣿⠿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠤⠤⠶⠒⢏⠁⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀
⠄⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣠⣴⣿⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠈⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠰⠞⠀⠈⠀⠀⠀⠴⠞⠂⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀
⠀⢀⡶⠀⠀⠀⠤⠁⠀⢿⠇⠀⠀⠄⠀⠀⠀⢀⣀⠀⠈⠙⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠦⠅⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠢⠑⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⢀⣀⣤⣴⣾⣿⠿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣷⣆⠉⠻⢶⣄⣀⡀⢀⣠⣴⣶⣿⣿⣷⣶⣄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⡀⠀⠀⠄⠐⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠯⡅⢸⣿⣿⣿⣿⡿⠛⠃⡈⣿⣿⣿⣿⣦⣄⡈⠙⢿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣷⣄⠀⠸⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠉⠀
⠃⠀⠀⠉⣰⣄⡀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠙⠻⠟⠋⠀⠐⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣶⡍⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠉⡉⠛⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠠⠄⠂⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⠃⠆⠀⠈⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠐⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀
⠁⠊⠀⣤⢄⡀⠐⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⢀⢄⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣵
⠀⠀⠀⡙⠀⠠⠱⠀⠀⠀⠈⠛⠿⠿⣿⣿⣿⣿⠿⠿⠟⢻⡵⠂⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⠆⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠍⠀⠀⠀⠀⠈⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠈⠀⠱⠀⠤⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⢀⠄⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿
⠀⠀⠠⠂⡌⢣⠀⠀⠀⠠⠀⠀⠅⠈⠀⠢⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠘⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⣀⠀⢀⣀⣠⣤
⠀⠀⢈⡠⢤⠄⠈⠀⠀⠀⠈⢈⡈⢁⡀⠠⠍⠁⠀⠈⠀⡀⠀⠀⠀⠀⢀⡈⠂⠀⠠⢄⠀⠐⠀⠀⠖⠋⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠠⠠⠀⠠⠀⠀⠀⡁⡌⡂⠐⠀⣀⠀⠀⠧⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⢁⣀⠀⠀⠀⢀⢤⢀⠠⠀⠀⠥⠤⢞⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀
⠟⠙⠻⠟⠙⠗⠘⠛⠚⠛⡣⡄⡜⠄⠀⡀⠄⠈⠡⠄⠈⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢠
⠀⠀⠀⠀⠀⢂⠀⠈⠀⠀⡄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣴⣶⣤⣶⣿⣿⣿⣿⣿⣶⣦⡀⠀⠀⠠⠀⠀⠀⡀⠀⠀⠀⠉⠉⠁⠀⠀⠀
⠀⠀⠀⠂⠀⠀⠀⠀⠄⠄⠀⠀⠀⠁⠀⠀⠀⠀⠄⠀⠘⠰⠞⠀⠀⠀⠤⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⢿⣿⣿⢿⣿⢿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠙⡏⠁⢸⡏⠀⣼⡏⢐⢽⣿⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣀⣄⢰⡿⠀⠀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠾⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣹⣿⠋⠁⡆⠀⡈⠁⠀⢹⡇⠀⢻⡇⠘⠩⣺⠀⣀⡼⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠈⠛⠗⠋⠀⠀⠈⠙⠿⢵⣦⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠉⠈⠀⢠⡇⠀⣤⣆⠀⣾⡇⠀⢸⡇⠀⢸⣾⢡⣴⠦⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡠⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣤⣾⣿⣥⣤⣤⣤⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⣼⣧⣤⣼⣧⣥⣼⣧⣥⣾⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⢉⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀
⠠⠀⠀⠀⠄⠀⡁⠀⠈⠀⠀⠀⠀⠙⠀⠀⣠⣶⣾⣿⣿⣿⣿⣷⣦⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣤⣤⣤⡀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠿⠿⠛⠛⠋⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡐⠆⠀⠀
⢸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⣾⣿⡿⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣃⡤⠤⠶⠖⣏⠁⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⢀⣴⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀
⠄⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣈⡛⣿⣿⣿⣿⣿⣿⣿⣿⣀⣶⣿⣿⣿⣿⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠰⠞⠀⠈⠁⠀⠀⠴⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀
⠂⢀⡶⠀⠀⠀⠤⠁⠀⢿⠇⠀⠀⠀⠀⠀⠀⢀⣀⠀⠈⠉⠙⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠮⠄⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠢⠐⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷⣀⠉⠛⠷⣤⣄⣀⣀⣀⣴⣶⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡀⠀⠀⠄⠀⠀⠀⠀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⠟⠯⡅⢸⣿⣿⣿⣿⡿⠟⠃⠈⣿⣿⣿⣦⣄⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣷⣄⠀⠘⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠁⠀
⠃⠀⠀⠃⣰⣄⡀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠙⠿⠟⠋⠁⠐⠀⠀⢹⣿⣿⣿⣿⣷⣦⣄⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠉⡈⢛⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⠃⠆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠐⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠
⠁⠚⠂⣤⣄⡀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⢀⣤⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⠀⠀⠀⡙⠀⠠⠡⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡵⠃⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿
⠆⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠩⠙⠉⠉⠉⠉⠀⠀⠀⠈⠭⠀⠀⠀⠀⠈⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠈⠀⠱⠄⢤⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⢁⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿
⠀⠀⠠⠀⠌⢣⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⠀⠀⠠⠄⡀⠀⠀⠀⠀⠀⠘⢃⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⣛⣯⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣤
⠀⠀⢈⡠⡤⠄⠈⠀⠀⠀⠈⢨⡈⢁⡀⠠⠍⠁⠀⠈⠀⡀⠀⠀⠀⠀⢀⡈⠀⠀⠠⢄⠀⠐⠀⠀⠞⠋⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⣠⣶⣶⣶⣷⣶⣦⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⡁⡄⡂⠐⠀⣀⠀⠀⠣⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠐⠀⠀⢁⣀⠀⠀⠀⢀⢤⡀⠠⠀⠀⠥⠤⢞⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀
⠛⠙⠻⠟⠙⠗⠘⠛⠚⠛⡣⣄⡞⠄⠀⠀⠀⠈⠡⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⢀

                    ䷩ 𝚕𝚒𝚗𝚎 2474

╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/21/IBM_Red_Hat_Selling_Slop_Microsoft_and_GAFAM_Surveillance_Fedor.shtml
    Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/21/IBM_Red_Hat_Selling_Slop_Microsoft_and_GAFAM_Surveillance_Fedor.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ IBM Red Hat Selling Slop, Microsoft and
GAFAM Surveillance; Fedora Update (IBM-Run Faux
Community)⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Mar 21, 2026


 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Get_the_most_out_of_Red_Hat_Enterprise_Linux_for_Microsoft
                                    Azure⦈_


    * ⚓ Red Hat Official ☛ Beyond_the_move:_Introducing_the_Virtualization
      Migration_Assessment_Expanded⠀⇛


           For a long time, organizations treated their infrastructure’s
           virtualization layer as steady and predictable. You built on it
           and you trusted it. Lately, that stability has been disrupted
           by complex shifts, including rising licensing costs and the
           urgent requirement to get ready for Hey Hi (AI) by adding more
           compute, storage, and other hardware resources.


    * ⚓ Red Hat Official ☛ Shift_gears:_10_stories_redefining_enterprise_IT⠀⇛


           We’ve long moved past the era where open source was just a
           collection of parts; today, it’s the factory itself. Whether
           you are building Hey Hi (AI) agents with MCP or migrating
           legacy virtual machines (VMs) to a unified platform, the value
           isn't just in the code—it’s in the 'golden path' that gets that
           code into production safely.


    * ⚓ Red Hat Official ☛ Solve_multi-controller_contention_with_Red_Bait
      OpenShift_networking⠀⇛


           As your organization scales its Red Bait OpenShift platform to
           support mission-critical workloads, your networking
           requirements often extend beyond a single load balancing
           solution. Many environments adopt a hybrid approach: Use
           software-defined load balancers (such as MetalLB) for internal,
           east-west traffic, and rely on enterprise-grade appliances like
           F5 BIG-IP to handle public-facing ingress at the network edge.


    * ⚓ Red Hat Official ☛ Get_the_most_out_of_Red_Bait_Enterprise_GNU/Linux
      for_AWS⠀⇛


           Running Red Bait Enterprise GNU/Linux (RHEL) for Amazon Web
           Services (AWS) offers several benefits, including enhanced
           scalability, flexibility, cost-efficiency, and access to a wide
           range of managed services.


    * ⚓ Red Hat Official ☛ Get_the_most_out_of_Red_Bait_Enterprise_GNU/Linux
      for_Abusive_Monopolist_Microsoft_Azure [Ed: IBM as Microsoft reseller]⠀⇛


           Running Red Bait Enterprise GNU/Linux for Abusive Monopolist
           Microsoft Microsoft trap Azure offers several benefits,
           including increased scalability, flexibility, cost-efficiency,
           and access to a wide range of managed services. By using
           Abusive Monopolist Microsoft Azure's global infrastructure, you
           can scale your Red Bait Enterprise GNU/Linux workloads to meet
           changing demands, reduce capital expenditure, and take
           advantage of various purchase models.


    * ⚓ Fedora Project ☛ Fedora_Community_Blog:_Community_Update_–_Week_12
      2026⠀⇛


           This is a report created by CLE_Team, which is a team
           containing community members working in various Fedora groups
           for example Infrastructure, Release Engineering, Quality etc.
           This team is also moving forward some initiatives inside Fedora
           project.


           Week: 16 – 20 March 2026




⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⡟⠋⠻⣿⠿⠿⢿⠿⢿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣀⣀⣽⣴⣤⣤⣥⣴⣤⣼⣼⣿⣿⣷⣽⣷⣿⣿⣿⣴⣶⣤⣤⣼⣼⣤⣤⣿⣾⣿⣿⣷⣶⣼⣤⣦⣤⣿⣾⣿⣿⣿⣷⣤⣦⣼⣼⣷⣿⣿⣿⣬⣤⣵⣾⣷⣿⣿⣿⣴⣤⣦⣤⣴⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⡟⠻⠿⢻⠟⠿⢻⠛⠻⠿⢿⣿⣿⠛⢿⠿⠿⠟⡿⠟⡿⢿⣿⣿⠛⢿⠻⠿⠻⢿⢿⣿⣿⡟⠻⠟⠿⠿⠻⡿⢿⣿⣿⡿⠻⠿⢿⠿⠿⠿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣾⣷⣶⣾⣶⣶⣶⣾⣿⣿⣶⣾⣶⣷⣶⣶⣶⣿⣿⣿⣿⣶⣾⣶⣶⣶⣾⣿⣿⣿⣿⣷⣶⣶⣶⣶⣿⣿⣿⣿⣿⣶⣿⣾⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣶⡼⠛⠛⠈⣿⠉⡇⡟⠛⠟⣿⢻⢛⠛⢛⡛⠻⢻⢸⡟⣻⠛⢻⢻⢸⡟⣻⢻⢰⣿⢰⢊⠻⠻⢻⠀⡇⢘⡃⠟⠛⠉⣿⢐⣲⠛⡛⡇⠟⠟⠟⡟⣟⠛⣻⠚⠟⠛⠛⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣾⣮⣽⣦⣿⣦⣥⣧⣦⣵⣿⣼⣼⣦⣮⣴⣮⣾⣬⣷⣬⣾⣬⣼⣬⣷⣬⣾⣼⣿⣼⣦⣮⣼⣮⣤⣷⣼⣧⣮⣥⣦⣿⣬⣭⣴⣧⣧⣵⣥⣧⣇⣥⣦⣿⣤⣵⣦⣽⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⡏⢛⡻⢻⠛⠻⢻⡏⠐⣛⠛⢛⡏⠙⠏⠉⠙⣛⠛⡛⡛⠟⣛⢛⡻⢁⡋⣻⡿⡉⢟⡛⡛⡟⡟⡛⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣭⣥⣼⣧⣬⣤⣵⣽⣧⣴⣭⣤⣼⣧⣴⣼⣤⣤⣭⣤⣧⣥⣦⣤⣬⣥⣼⣧⣽⣥⣶⣬⣬⣥⣥⣧⣧⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠙⠛⠋⢻⠍⠝⠯⠉⠩⠉⢻⡇⣿⠿⠙⠛⠙⠛⢻⠟⠛⠛⠟⢻⣿⣿⡏⢙⠛⠋⠛⢿⠛⡟⠛⠛⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 2588

╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/21/KDE_Krita_Monthly_Report_and_Marknote_1_5_1.shtml
    Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/21/KDE_Krita_Monthly_Report_and_Marknote_1_5_1.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ KDE: Krita Monthly Report and Marknote
1.5.1⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Mar 21, 2026


    * ⚓ Krita ☛ Krita_Monthly_Report_-_March_2026⠀⇛


           The second and third betas for Krita 5.3.0/6.0.0 have been
           released, with the final release drawing near. There was also a
           hotfix stable release, 5.2.16, to fix a regression causing
           problems with HEIF files.


    * ⚓ KDE ☛ Marknote_1.5.1⠀⇛


           Last week we released version 1.5 of Marknote, a fast and free
           alternative to existing slow and pay-walled note-taking apps.
           Today we announce a release that fixes some issues and improves
           a few things across the app.


           So here is a list of the most notable changes and improvements:
           [...]





                    ䷩ 𝚕𝚒𝚗𝚎 2627

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(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/21/Linux_Kernel_Security_Slop_an_already_flawed_CVE_system_and_mor.shtml
    Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/21/Linux_Kernel_Security_Slop_an_already_flawed_CVE_system_and_mor.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Linux Kernel Security: Slop, "an already-
flawed CVE system", and more⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Mar 21, 2026


    * ⚓ The Register UK ☛ Sashiko:_AI_code_review_system_for_the_Linux_kernel
      spots_bugs_humans_miss⠀⇛


           AI is coming to the Linux kernel in the form of a code review
           system - not code submissions.


           Announced on LinkedIn by Roman Gushchin, a Linux kernel
           engineer at Google, Sashiko is a tool written in Rust for
           spotting bugs and screening code.


           Gushchin said: "In my measurement, Sashiko was able to find 53
           percent of bugs based on a completely unfiltered set of 1,000
           recent upstream issues based on 'Fixes:' tags (using Gemini 3.1
           Pro). Some might say that 53 percent is not that impressive,
           but 100 percent of these issues were missed by human
           reviewers."


    * ⚓ Hackaday ☛ This_Week_In_Security:_Linux_Flaws,_Python_Ownage,_And_A
      Botnet_Shutdown⠀⇛


           The ides of security March are upon us — Qualys reports the
           discovery by their threat research unit of vulnerabilities in
           the Linux AppArmor system used by SUSE, Debian, Ubuntu, and
           Kubernetes as an additional security mechanism and application
           firewall.


    * ⚓ The New Stack ☛ Linux_kernel_scale_is_swamping_an_already-flawed_CVE
      system⠀⇛


           Linux kernel developers operate under constraints that very few
           other open source community maintainers experience. Evolving
           the capabilities of the world’s most popular operating system
           is just one side of the coin. The other is that you can “never
           break userspace,” and you must maintain backward compatibility
           and stability for the millions of devices and users running on
           Linux.





                    ䷩ 𝚕𝚒𝚗𝚎 2689

╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/21/Mozilla_and_Firefox_Nightly_Emojis_and_More.shtml
    Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/21/Mozilla_and_Firefox_Nightly_Emojis_and_More.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Mozilla and Firefox: Nightly, Emojis, and
More⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Mar 21, 2026


    * ⚓ Martin Stransky ☛ Firefox_hacking_in_Fedora:_Firefox_&_Gtk_Emoji
      picker⠀⇛


           After nearly three years of development (it takes time to make
           up one’s mind) Firefox for GNU/Linux users can now enjoy
           seamless emoji insertion using the native GTK emoji chooser.
           This long-requested feature, implemented in
           Firefox 150 (recent Beta), brings a more integrated experience
           for GNU/Linux users who want to add emojis to their web
           content.


    * ⚓ Mozilla ☛ Mozilla_Addons_Blog:_How_Your_Feedback_Shapes_the_Firefox
      Add-ons_Experience⠀⇛


           Hey everyone! I’m Christos Bacharakis, and I’ve recently joined
           Mozilla as the new Add-ons Senior Developer Relations Engineer.
           I’m here to help developers overcome technical challenges so
           your extension visions may become reality.


           My goal is to keep things moving smoothly so you can focus on
           what you do best: building awesome add-ons.


    * ⚓ Firefox_Tooling_Announcements:_Firefox_Profiler_Deployment_(March_20,
      2026)⠀⇛


           The latest version of the Firefox_Profiler is now live! Check
           out the full changelog below to see what’s changed.


    * ⚓ Firefox_Nightly:_Extension_Theming_Improvements_and_More_–_These_Weeks
      in_Firefox:_Issue_198⠀⇛


    * ⚓ Martin Stransky ☛ Firefox_&_Gtk_Emoji_picker⠀⇛


           It also needs to be correctly positioned to show the
           GtkEmojiChooser in the right location, and connected to other
           signals like ‘insert_text’ to retrieve the selected emoji.


           After nearly three years of development (it takes time to make
           up one’s mind) Firefox for Linux users can now enjoy seamless
           emoji insertion using the native GTK emoji chooser. This long-
           requested feature, implemented in Firefox 150 (recent Beta),
           brings a more integrated experience for Linux users who want to
           add emojis to their web content.





                    ䷩ 𝚕𝚒𝚗𝚎 2761

╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/21/Programming_Leftovers.1.shtml
    Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/21/Programming_Leftovers.1.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Programming
Leftovers⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Mar 21, 2026


    * ⚓ Rlang ☛ Bayesian_Neural_Networks_in_{tidymodels}_with_{kindling}⠀⇛


           This post was written in collaboration with Joshua Marie.


    * ⚓ Dirk Eddelbuettel ☛ Dirk_Eddelbuettel:_RcppSpdlog_0.0.28_on_CRAN:
      Micro-Maintenance⠀⇛


           Version 0.0.28 of RcppSpdlog arrived on CRAN today, has been
           uploaded to Debian and built for r2u.


    * ⚓ Rust Blog ☛ The_Rust_Programming_Language_Blog:_What_we_heard_about
      Rust's_challenges,_and_how_we_can_address_them⠀⇛


           When we set out to understand Rust's challenges, we expected to
           hear about the borrow checker learning curve and maybe some
           ecosystem gaps. Of course, we did. A lot. But, of course, it's
           more nuanced.


           The conventional wisdom is that Rust has a steep learning
           curve, but once you "get it," smooth sailing awaits. We found
           that while some challenges disappear with experience, they are
           replaced with others. Beginners struggle with ownership
           concepts, experts face domain-specific challenges: async
           complexity for network developers, certification gaps for
           safety-critical teams, ecosystem maturity issues for embedded
           developers.


    * ⚓ Adam_Young:_tags_for_rust⠀⇛


           I use tags to navigate source code in vim. Here is how I set
           things up for generating tags for rust.





                    ䷩ 𝚕𝚒𝚗𝚎 2819

╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/21/Programming_Leftovers.shtml
    Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/21/Programming_Leftovers.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Programming
Leftovers⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Mar 21, 2026


    * ⚓ Andrew Nesbitt ☛ Package_Manager_Mirroring⠀⇛


           Mike Fiedler from PyPI asked me recently: which package
           ecosystems have mirroring tools and what protocols do they use?
           Here’s what I found.


           This post primarily covers mirroring: tools and protocols for
           creating and maintaining copies of package registries. It
           doesn’t cover private registries, artifact storage, or
           dependency proxying except where those tools also support
           mirroring.


    * ⚓ Niel Madden ☛ Maybe_version_ranges_are_a_good_idea_after_all?⠀⇛


           There’s clearly a problem, but what would a solution look like?
           I have some ideas, but this is a complex problem where it is
           easy to introduce unintended side-effects. So take these
           suggestions as just that: suggestions. To provoke discussion,
           not as a perfect fully-baked solution. There are lots of
           competing factors to balance here, and I’m not going to claim
           that I’ve considered them all.


    * ⚓ Martin Chang ☛ Benchmarking_ET-SoC-1_Naive_Matrix_Multiplication
      Performance⠀⇛


           I am currently working on the GGML backend for the ET-SoC-1. To
           answer the question of "how well does this chip actually
           perform?", I decided to benchmark the most basic FP32 matrix
           multiplication implementation using the matrix engine. The plan
           is the same as in my previous RK3588 matmul benchmarking
           attempt: gather a large amount of data first, then extract
           useful conclusions afterward. See the previous post: [...]


    * ⚓ Balthazar Rouberol ☛ Pushing_to_multiple_git_remotes_at_once⠀⇛


           I recently learned that you can configured multiple URLs when
           pushing to a remote, which means that git push origin master
           would push to all remotes.


    * ⚓ [Old] James Hague ☛ Do_You_Really_Want_to_be_Doing_This_When_You're
      50?⠀⇛


           I still like to build things, and if there's no one else to do
           it, then I'll do it myself. I keep improving the the tiny Perl
           script that puts together this site, because that tiny Perl
           script is unobtrusive and reliable and lets me focus on
           writing. I have a handy little image compositing tool that's
           less than 28 kilobytes of C and Erlang source. I know how it
           works inside and out, and I can make changes to it in less time
           than than it takes to coax what I want out of ImageMagick.





                    ䷩ 𝚕𝚒𝚗𝚎 2898

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(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/21/Richard_Stallman_at_Georgia_Tech_and_Some_of_My_Thoughts_about_.shtml
    Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/21/Richard_Stallman_at_Georgia_Tech_and_Some_of_My_Thoughts_about_.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Richard Stallman at Georgia Tech, and Some
of My Thoughts about Free Software⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Mar 21, 2026


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Man_out_of_Florida⦈_


I barely know that world myself. I have memories of my parents making doctors
appointments by phone, of buying train tickets in cash, of having to wait at
the airport without the ability to call and text the person picking you up. But
I never did any of that myself. I grew up in a world where computers were
already everywhere. I was required to use a computer in first grade in 2007,
for “Accelerated Reader” tests, and my school district and school had websites
that we would have to look at to learn information about the school year.


As a consequence of being raised by people very resistant to change who were
employed by an entity very resistant to change (a university), I lived in a
world where people weren’t expected to have a computer on them at all times
longer than most other people my age. My experience of that life (and the
knowledge of people who try to live similarly) makes it much easier to choose
to live that life even if it alienates me from others. But telling a freshman
in the audience that has no knowledge of that life first-hand that they should
live like that is like telling your average American to become Buddhist monk.
It’s not like they can’t do so, physically, but it’s so foreign to them and to
those around them that they would have to make major sacrifices for a life that
they is just not as clear to them as it is to me (or Stallman).


Of course, I don’t live like Stallman, even though I live closer to that life
than most people. I use non-free Javascript to order airplane tickets and make
doctors appointments, even if I refuse to use Discord or WhatsApp. I have a
smartphone (running PostmarketOS with a mostly mainline-Linux kernel) even if I
almost never use it.


So how should we feel about the ability for people to control their digital
lives in the future? One student approached Stallman after the talk and asked
him what made him optimistic about the future of free software. Stallman’s
reply (paraphrasing) was “Oh no, I’m not optimistic. But while I’m still alive,
I might as well keep on fighting. If you give up, then you just lose.”


Read_on




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴
⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⡿⠿⢿⠛⠟⢿⠿⠿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣻⢯⣶⡔⣇⡇⣇⣿⣧⣻⢨⡞⣭⢻⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣎⣢⠧⣋⣅⢀⠄⠒⠲⣷⣾⣭⣅⠣⣖⣱⣄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢴⡛⢮⢛⣵⣿⣯⠀⠈⠁⠈⠃⣺⡿⣿⠗⠂⠀⠙⣔⡳⠄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⢰⣛⠏⣡⣿⡅⣽⣿⣗⢀⡀⢀⣼⣿⣿⣿⣶⣶⣄⣀⣀⢶⠿⡦⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⢐⣿⣶⢣⣾⣿⣦⢀⠿⣿⣿⡇⣿⣿⣿⡏⣽⣿⣿⠿⠋⠉⠐⣓⣹⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱⠖⡲⠀⠈⠛⠏⡂⠢⣍⠉⡇⣿⣿⣿⡇⣼⡟⡷⢲⠶⠾⠧⣨⠬⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⠟⢷⠀⠶⠶⠀⠀⠀⠘⠖⠃⢀⡶⢤⣤⣭⡴⣬⣷⡤⣤⡖⠑⣔⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⢙⣍⡑⡀⠀⠒⠀⠀⠀⢶⣟⣯⣿⠟⢿⣿⠏⠁⠀⠛⠿⣿⣏⠤⢒⠂⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠽⣛⣵⡠⣬⠀⠀⢠⣬⠍⠩⠥⠄⠈⠈⠁⠀⠀⠀⠀⢍⣬⣽⠇⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⢙⢯⣿⣌⠉⣀⣄⡀⠠⢤⣄⠀⠀⠀⠀⠀⠀⠀⣠⣾⡽⠛⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⣼⢱⣭⣄⠲⠿⢿⡏⡀⠀⠀⠀⣀⣴⡚⣜⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣽⡪⡯⣋⡹⣶⠒⣖⢺⣯⣯⣸⢜⣫⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣾⣯⣯⣽⣭⣯⣽⣶⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿
⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 2983

╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/21/Security_Leftovers.shtml
    Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/21/Security_Leftovers.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Security
Leftovers⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Mar 21, 2026


    * ⚓ LWN ☛ Security_updates_for_Friday⠀⇛


           Security updates have been issued by AlmaLinux (capstone,
           glibc, grub2, kernel, libarchive, libpng, mysql, and
           python3.11), Debian (evolution-data-server, imagemagick, and
           snapd), Fedora (bpfman, chromium, cpp-httplib, dotnet10.0,
           openssh, polkit, and vim), Mageia (graphicsmagick, imagemagick,
           openssh, and perl-YAML-Syck), Oracle (capstone, grub2, kernel,
           mysql, and python-pyasn1), Red Hat (container-tools:rhel8, rhc,
           yggdrasil, and yggdrasil-worker-package-manager), SUSE
           (cargo1.92, cargo1.93, chromedriver, coturn, curl, freerdp, jq,
           kernel, libssh, php-composer2, python311-uv, python312, qemu,
           tomcat, util-linux, vim, and virtiofsd), and Ubuntu (exiv2,
           freerdp3, glance, linux, linux-aws, linux-aws-hwe, linux-gcp,
           linux-gcp-4.15, linux-hwe, linux-kvm, linux-oracle, and linux-
           aws-fips, linux-fips, linux-gcp-fips).


    * ⚓ Security Week ☛ Aisuru_and_Kimwolf_DDoS_Botnets_Disrupted_in
      International_Operation⠀⇛


           The lesser-known JackSkid and Mossad botnets have also been
           targeted in the operation.


    * ⚓ Security Week ☛ Thousands_of_Magento_Sites_Hit_in_Ongoing_Defacement
      Campaign⠀⇛


           The attacks started on February 27 and have targeted e-commerce
           platforms, global brands, and government services.


    * ⚓ Diffoscope ☛ Reproducible_Builds_(diffoscope):_diffoscope_315
      released⠀⇛


           The diffoscope maintainers are pleased to announce the release
           of diffoscope version 315. This version includes the following
           changes:


           * Adjust PGP file detection regex.


    * ⚓ Security Week ☛ Navia_Data_Breach_Impacts_2.7_Million⠀⇛


           Between late December 2025 and mid-January 2026, hackers stole
           personal and health plan information from Navia’s environment.


    * ⚓ Security Week ☛ Critical_Langflow_Vulnerability_Exploited_Hours_After
      Public_Disclosure⠀⇛


           Because attacker-supplied flow data is used in public flows,
           the bug leads to unauthenticated remote code execution.


    * ⚓ SANS ☛ GSocket_Backdoor_Delivered_Through_Bash_Script,_(Fri,_Mar
      20th)⠀⇛


           Yesterday, I discovered a malicious Bash script that installs a
           GSocket backdoor on the victim's computer. I don't know the
           source of the script not how it is delivered to the victim.





                    ䷩ 𝚕𝚒𝚗𝚎 3071

╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/21/Standards_Open_Document_Format_ODF_Mandatory_in_Germany_Messing.shtml
    Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/21/Standards_Open_Document_Format_ODF_Mandatory_in_Germany_Messing.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Standards: Open Document Format (ODF)
Mandatory in Germany, Messing With Apple’s Webloc
Format⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Mar 21, 2026


    * ⚓ Document Foundation ☛ BIG_NEWS:_Germany_has_just_made_the_standard_Open
      Document_Format_(ODF)_mandatory⠀⇛


           The German federal government has quietly taken an extremely
           significant step: hidden amongst the technical specifications
           of the Deutschland-Stack – the rules that will govern the
           sovereign digital infrastructure supporting public
           administration at all levels of government, from federal
           ministries to local council offices [...]


    * ⚓ Ruben Schade ☛ Extracting_URLs_from_Apple’s_webloc_format⠀⇛


           Moving stuff off my personal machine to my new ThinkPad (and
           clearing up a bunch of state while I’m at it) lead me to a
           folder of webloc files I must have dragged to my desktop at
           some point.


           Turns out, they’re just regular Fashion Company Apple plist
           files in XML: [...]





                    ䷩ 𝚕𝚒𝚗𝚎 3114

╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/21/SUSE_OpenSUSE_Tumbleweed_Review_Planet_News_Roundup_and_Agama_1.shtml
    Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/21/SUSE_OpenSUSE_Tumbleweed_Review_Planet_News_Roundup_and_Agama_1.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ SUSE/OpenSUSE: Tumbleweed Review, Planet
News Roundup, and Agama 19 Released⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Mar 21, 2026


    * ⚓ Dominique Leuenberger ☛ Tumbleweed_–_Review_of_the_week_2026/12⠀⇛


           Dear Tumbleweed users and hackers,


           Tumbleweed is rolling full steam ahead with 7 snapshots in 7
           days (0312 through 0318). No major issues have shown up in
           openQA – everything was detected and fixed in the staging
           areas.


           Without further ado, let’s look at what those snapshots brought
           you this week: [...]


    * ⚓ OpenSUSE ☛ Planet_News_Roundup⠀⇛


           This is a roundup of articles from the openSUSE community
           listed on planet.opensuse.org. The community blog feed
           aggregator lists the featured highlights below from March 13 to
           March 19.


    * ⚓ Agama_19_-_A_New_Beginning⠀⇛


           In our previous_post from November 2025 we already told you to
           expect a temporal slow down in this blog activity. And here we
           are, more than four months later, to finally break that hiatus
           by announcing a new Agama version. But, why did it take so long
           to go from Agama 18 to Agama 19?


    * ⚓ LWN ☛ Agama_19_released⠀⇛


           Version_19 of the Agama installer for openSUSE and SUSE has
           been released. This release includes major changes in Agama's
           architectural design, organization of the web interface, and
           more.





                    ䷩ 𝚕𝚒𝚗𝚎 3175

╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/21/Systemd_Free_antiX_26_Linux_Distro_Is_Here_Based_on_Debian_13_T.shtml
    Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/21/Systemd_Free_antiX_26_Linux_Distro_Is_Here_Based_on_Debian_13_T.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Systemd-Free antiX 26 Linux Distro Is Here
Based on Debian 13 “Trixie”⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Marius Nestor on Mar 21, 2026


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇antiX_26⦈_


Based on the latest and greatest Debian 13 “Trixie” operating system series,
antiX 26 is powered by the long-term supported Linux 6.6 LTS kernel series and
features the IceWM (default), Fluxbox, JWM, and herbstluftwm window managers,
and the runit (default), SysVinit, dinit, s6-rc, and s6-66 init systems.


In the tradition of the antiX and MX Linux distributions, this release doesn’t
ship with the systemd init system, nor the libsystemd0 library, and it doesn’t
support Flatpak (elogind) or Snap (systemd) apps. It ships with eudev instead
of systemd-udev for better compatibility with the OpenRC init system.


Read_on




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀
⠸⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⢧⠀⠀⠀
⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢠⡍⠙⠚⠺⠦⢥⡄
⠈⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠛⢦⡀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⢸⣟⠀⠁⠀⠀⣹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠈⠁⠂⠀⢀⣦⡿⡇
⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣒⣦⠶⠿⠯⠅⠲⡇
⢰⣤⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣀⡤⠶⠛⠭⠤⠄⠀⠀⠀⠤⡇
⠐⠒⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⣿⣿⣿⣿⡏⠙⢻⣿⣿⣿⢿⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⠀⠀⠀⢀⣀⣀⡀⠀⠀⣀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠸⣿⣿⣿⣿⡇⠀⠈⠻⢿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⣿⡟⢹⡇⠀⠀⠀⠠⢨⢸⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠿⠿⠛⠛⢿⣿⣿⣿⣿⣧⣤⣼⣦⣤⣶⣶⣶⣦⣶⡦⠀⢐⣻⣑⣿⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢿⡇⠘⠛⠀⠀⠀⠀⢸⢸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⣿⡟⠛⠻⠋⠉⠙⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⢸⣇⠀⡀⠀⠀⠀⠀⢀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢨⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣛⣛⣻⣿⣿⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣷⣶⣼⡀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣾⣿⣿⣿⣀⣀⣀⣀⠀⠤⠼⢿⣿⣟⣺⣛⣻⣛⣛⣺⣻⣻⣿⣿⣼⣤⣤⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠉⠉⠉⠁⣹⣷⣶⣾⡿⠶⠶⠶⠶⣦⣤⣤⣤⣴⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣿⣿⣿⣿⡟⠛⠛⠁⠀⢿⣿⣿⣿⣿⣿
⣿⣿⣛⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⡿⣿⣯⣿⣿⣿⣿⣽⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⢿⣿⣿⣿⣿⣶⣦⣄⣀⠈⠛⠻⠿⣿⣿
⣿⣷⣶⣶⣿⣿⣵⣷⣾⣶⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣛⣛⣛⣛⣛⣋⡉⠉⠉⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀
⡿⣯⣿⣿⣿⣿⣾⣿⣿⠿⠿⢽⣿⣿⣿⣿⣿⣻⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀
⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⠙⠻⣿⣿⣿⣿⣿⣿⣷⣤⡀
⣿⡿⠿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⠿⣯⡽⠿⣿⢿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿
⣿⣯⣭⣭⣿⣿⣮⣿⣿⣿⣷⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣛⣿⣟⣿⣿⣿⣿⣿⣟⣿⣻⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣤⣤⡄⠀⠒⢲⣶

                    ䷩ 𝚕𝚒𝚗𝚎 3232

╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/21/These_5_settings_are_making_your_Linux_PC_less_secure.shtml
    Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/21/These_5_settings_are_making_your_Linux_PC_less_secure.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ These 5 settings are making your Linux PC
less secure⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Rianne Schestowitz on Mar 21, 2026


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇penguin,_laptop_and_security_logo⦈_


Quoting: 5 settings making your Linux PC less secure —


     Think your Linux PC is secure just because it’s Linux? Well, I hate
     to break it to you, but Linux—while it might be more secure than
     Windows—is not invulnerable. The architecture is solid, the open-
     source model helps, and yes, the threat landscape is smaller. But
     none of that matters if you've left the wrong settings unchecked.
     Here’s a quick look at five common settings that people leave enabled
     (or disabled) that are making their Linux PCs less secure.


Read_on




⣉⣛⣉⣉⣋⣉⣛⣋⣛⣋⣙⣋⣙⣛⣋⣙⣉⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣈⣛⣉⣛⣋⣉⣋⣉⣋⣉⣛⣋⣙⣋⣙⣉⣙⣙
⣙⣛⣙⣛⣉⣋⣏⣋⣛⣋⣛⣋⣙⣻⣙⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⣛⣉⣛⣋⣉⣋⣉⣋⣙⣛⣋⣙⣋⣙⣋⣙⣛
⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠁⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣛⣛⣛⣛⣛⣛⣛⣛⣋⣛⣛⣛⣛⣛⣛
⣛⣿⣟⣛⣟⣛⣟⣟⣻⣟⣟⣛⣻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⠿⠟⠋⠉⠀⠀⣦⣬⣙⡛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣟⣛⣿⣟⣛⣻⣻⣛⣻⣻
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠹⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠿⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠘⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠀⠀⢀⣸⣿⣶⣦⣄⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡇⠀⢱⠉⠻⣿⠀⣠⣤⡀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢠⡀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⡟⠛⢻⣿⠀⣾⢠⣿⣿⣿⣆⠀⠻⢿⣿⣿⡿⠿⠿⠿⠛⠋⠀⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣷⣀⣾⣿⢰⡏⣸⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 3289

╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/21/The_Value_of_a_Human_Does_Not_Exceed_an_Elephant_s.shtml
    Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/21/The_Value_of_a_Human_Does_Not_Exceed_an_Elephant_s.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ The Value of a Human Does Not Exceed an
Elephant's⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Mar 21, 2026


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Behemoth⦈_


Last year Rianne published a couple of articles about Limpopo [1, 2] and then
contacted several NGOs about what happened to Limpopo (she was put down despite
being healthy).


The charity which raised Limpopo (and which we supported for years) has since
then mentioned Limpopo and efforts to learn from failures/misunderstandings. It
is now reaching out to supporters several times per week.


It looks like Limpopo's death (killing rather) was a self-inflicted wound. The
lesson to learn here (from Limpopo) is clear. We'll carry on pursuing justice
for as long as necessary. █


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Image source: Behemoth


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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⢿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⣿⣿⣿⡿⠃⣉⣠⣤⣶⣶⢶⢾⣅⠀⠀⠀⠀⣀⣜⣵⣶⣬⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠑⠌⠳⣬⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠟⣯⣆⠀⠀⠁⢀⠀⣸⣿⣿⡰⡿⡟⣽⡿⣿⡏⢿⠀⠀⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠈⠪⡂⠈⠛⠁⠀⠀⠀⣠⢤⢶⡿⠏⣿⣿⣯⣾⣻⢏⢀⣽⣿⣿⣼⣿⣿⣿⡻⠁⢁⣿⡇⡟⠃⠀⠀⠀⢿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠙⠢⣀⢀⣢⣝⢷⣽⠯⡹⡖⠯⠛⠹⣽⣿⣿⣿⣷⣶⣿⣿⣿⣿⡟⠋⠀⠀⢸⠏⠃⠀⠐⠀⠀⠀⢸⣧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠧⠀⠀⠀⠈⠓⠦⣅⣒⠼⠚⠃⠀⠀⠆⣪⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠅⠁⠠⣠⣶⡿⠢⠀⠀⠀⠉⠛⠿⢶⣦⡄⠠⣾⡏⡿⣿⣿⣿⡟⢿⠉⠀⠀⠀⠀⠘⡸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠉⠀⣨⡾⣏⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠈⠐⠲⠿⠓⠛⠉⠀⠀⠀⢚⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠝⠀⢔⣿⠻⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠒⠠⣱⣟⠯⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣦⣤⠀⠀⠀⠈⠡⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢀⣰⡿⠎⠁⠀⢀⣴⠀⠀⠀⠀⠀⣩⣽⣿⣿⣿⣿⣿⣧⠀⢤⣴⡲⢮⣼⣷⣳⣖⡀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⢰⡟⣼⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⢴⣯⠁⠀⠀⢠⣾⣿⡆⠀⠀⠀⠐⢹⣿⣿⣿⣿⣿⣿⣿⡄⠀⣎⣿⣿⣿⣿⣿⣟⣁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡞⢰⣿⣽⡧⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠐⡚⠂⠀⠀⢠⣻⣿⣿⣧⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣷⣤⡰⣤⣼⣿⣿⡛⠛⠋⠁⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⢰⣀⡈⠀⠀⢤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢐⠀⠀⢀⡮⣾⣿⣿⣿⡀⠀⠀⠀⠰⠾⣿⣿⣿⣿⣿⣿⣿⣷⡼⡉⠂⠁⠀⠀⠀⠲⠾⠓⠀⠉⣀⠸⣧⡀⠀⢀⡏⠬⣁⠀⠀⠀⠙⣻⣿⠝⢿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣼⣪⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⢤⠶⠟⢻⣗⣚⣢⠘⠷⠀⠊⠼⠗⠂⠛⠂⠀⠀⠀⠀⠀⠀⠰⣶⡎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⡻⣺⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠉⢛⣿⣿⣿⣿⣿⣿⣿⣿⣣⣄⣤⣴⣶⣿⠿⠿⠻⠓⠂⢢⣴⣿⣷⣶⣶⣬⣽⣿⣶⣶⣤⡐⠄⠀⠰⣿⡏⢱⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢨⣪⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣔⠲⠶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣷⠀⢠⣿⠇⢸⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠸⢝⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣛⢿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣯⠀⣫⠁⠀⣾⡏⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⢵⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠈⠋⣐⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⠄⣠⠏⣴⡟⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣟⣷⠀⠀⠀⠀⢐⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⠁⠀⡾⣰⣽⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡀⡀⠀⢿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠩⠶⡀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⡇⢀⠀⠀⠀⠛⣏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣿⣿⣧⣒⡗⣰⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣻⣿⣿⠇⣐⡶⠠⢰⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢀⡶⠰⣾⣿⠀⡀⠀⠀⠀⠀⠈⣧⡉⠘⢿⣿⣦⣙⢿⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⠿⠷⣾⣿⣿⣧⡐⢊⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠏⣐⠮⡁⢠⡭⠽⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠁⢈⠉⢑⡺⢮⡩⢔⠪⡠⠄⠀⠀⠀⠹⢷⣄⠀⠀⠈⠛⢻⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⠀⠀⢨⣯⣿⣿⠃⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠋⣤⣔⡾⠁⣰⣿⣿⣛⣾⣿⣿⣿⠋⠀⠀⠀⠀⠀⠠⠤⢒⠮⣿⣆⠉⠧⠐⠁⠂⠢⠠⣀⣀⣀⣈⠻⢊⣰⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣴⢈⣫⣾⡿⠀⢘⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣇⣠⣄⠀⣨⣾⣿⣿⣿⣿⣿⣟⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⠩⡁⣈⠉⣽⣦⣐⠮⠍⡲⠀⠈⠀⠁⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣳⣿⣟⢗⣷⠁⢀⣿⣿⣟⣛⣻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣯⣭⣿⣿⣿⣿⠋⠄⢀⣠⡄⠀⠀⠀⠂⠲⢈⣉⣙⣟⠋⠀⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡉⢙⠿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠟⠟⢽⣿⣿⣿⠋⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣛⣩⣩⣭⡅⠀⠀⠀⠀⠄⢄⢽⣾⣿⡳⣦⡤⣦⡄⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠕⢟⠜⡻⠋⠈⠕⠁⠀⠀⠠⠶⢗⠏⠁⣰⣿⡿⠿⠷⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣭⣯⣽⢽⣿⣯⣽⣿⣿⣿⣿⣿⡏⠂⠀⠀⠀⢀⠀⣨⣧⢿⣿⣿⣿⣷⣿⣾⣿⠿⠤⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠕⠐⡚⠒⠒⠛⢿⣿⣿⣿⡿⡃⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿⣟⡿⣷⣫⣾⡉⠒⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣽⡂⠀⠀⠀⠀⠀⠀⠀⠙⠛⠟⠀⠀⠀⠀⠀⠀⠀⠀⠬⠛⡟⣋⠿⡟⢿⠫⠝⠀⠀⠰⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢘⢷⡹⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠁⠈⢀⣴⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠘⢉⡉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⠩⠹⠛⡟⠿⣿⣿⣆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠉⠈⠚⠚⠣⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡠⢄⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠂⢉⠟⠛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣍⡿⠟⢽⣿⡿⣻⣒⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣭⡀⢚⣥⡘⠞⣡⡀⢀⡀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⢔⠔⢂⡴⣂⣀⠀⢲⡆⡷⢯⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣟⣟⣿⣿⡿⣿⣿⣭⡻⣿⣿⣿⣶⣶⣤⣤⣤⣀⡀⠀⠈⠻⠃⠸⠿⠃⠠⣿⠟⠸⠧⢸⣿⣿⣿⣿⣶⣶⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠉⠿⡆⠐⢃⣁⣴⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣶⣶⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣴⣶⣿⣿⣿⣿⣯⣿⣾⣼⣿⣿⣿⣽⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 3374

╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/21/This_Week_in_Plasma_Time_Zone_Offsets_and_Type_Ahead_on_the_Des.shtml
    Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/21/This_Week_in_Plasma_Time_Zone_Offsets_and_Type_Ahead_on_the_Des.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ This Week in Plasma: Time Zone Offsets and
Type-Ahead on the Desktop⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Rianne Schestowitz on Mar 21, 2026


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Digital_Clock_widge⦈_


Quoting: This Week in Plasma: Time Zone Offsets and Type-Ahead on the Desktop -
KDE Blogs —


     This week several new features landed, in addition to a number of
     user interface improvements and some nice performance improvements
     and bug fixes. Check ‘em out...


Read_on




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠐⠒⠒⠒⠒⠒⠂⠀⣤⠤⣤⣤⣤⣤⣤⡤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⣤⡤⢤⣤⠤⡤⣤⢤⡤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠁⠀⠉⠉⠈⠀⠁⠉⠉⡇⠈⠀⠀⠁⠁⠀⠉⡆⡐⠷⠂⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠁⠉⠉⠉⠁⠈⢿⣿⣿⣿⣿⣿⣿
⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿
⡇⣤⣤⣤⣤⣤⣤⡄⢰⡟⠛⠿⠿⠿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿
⡇⣿⣿⣿⣿⣿⣿⡇⢸⣧⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣄⣠⣼⣿⣿⣿⣿⣿⣿
⠃⣿⣿⣿⣿⣿⣿⡇⢨⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭
⠀⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿⠿⠿⣿⣿⣿⠛⠟⠿⠿⠿⣿
⠀⣿⣿⠟⠛⠿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣿⣿⣿⣤⣤⣤⣤⣤⣿
⠀⣿⣿⠀⠀⢸⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠙⢿⡿⠋⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣤⣤⣼⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⣿⣿⣿⡿⡿⢿⣿⣿
⠀⣿⡟⠁⣾⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣑⣃⣿⣿⣿⣿⣿⣏⣚⣸⣿⣿
⠀⣿⣷⣄⣈⣭⣠⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⠟⠛⠻⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣧⣀⠀⢠⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣩⡀⣀⣀⢀⣀⣀⣀⣘⣆⣀⣀⣰⣇⣀⣀⣀⣀⡀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿
⠀⣿⣿⠿⠿⢿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿
⠀⣿⣿⠀⠀⢸⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣤⣤⣼⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢻⣿⣿⣿⣿⣿⡟⠛⢿⣿⣿
⠀⣿⣟⠍⠉⠝⣿⡇⠀⣷⢀⠈⠉⠉⢹⠀⠈⠉⠉⠉⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⡁⠀⠉⠀⠁⠈⠛⢻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿
⠀⣿⣿⣇⣀⣾⣿⡇⢀⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣒⣚⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣟⢿⣿⣿⡇⢸⡏⠋⠛⠛⠛⠙⠋⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠙⠋⠉⠏⠋⠋⣛⡏⡏⠛⠛⠛⠛⠛⠛⠙⠛⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⢿⠿⣿⣿⣿⣿⣿⡿⡿⢿⣿⣿
⠀⣿⣿⡿⢃⣽⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣰⣀⣽⣿⣿⣿⣿⣇⣄⣠⣿⣿
⠀⣿⠿⡷⠿⠿⢿⠇⢸⡏⠛⠛⠻⠙⠛⠛⠛⠙⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⠉⠉⠋⡉⠋⣟⡏⡏⠛⠛⢻⠛⠛⠋⠛⢻⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⠤⠦⠴⠦⢼⠀⢸⣿⣾⣿⣿⣿⣿⣶⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⡒⡖⠒⠒⢺⠀⢸⡏⠉⠙⠉⠛⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠋⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡷⠀⠂⢽⣿⣿⣿⣿⠆⠄⢈⣿⣿
⠀⡿⢿⢶⣶⢾⠿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣏⣐⣠⣢⣀⣀⡇⢸⡏⠛⠛⠙⠉⠛⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⠉⠉⠋⡉⠉⣛⡏⡏⠛⠛⠛⠋⠛⠙⢛⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣏⣉⣉⣹⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣯⠉⠉⢻⣿⣿⣿⣿⡍⠉⠙⣿⣿
⠀⣿⡿⠿⠿⠿⢿⡇⢸⡏⠉⠛⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠙⠉⠉⡋⡉⠉⣛⠉⡏⠛⠛⠛⢋⠛⠙⢛⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿
⠀⣿⡇⡟⠉⡇⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣧⣀⣀⣁⣼⡇⢸⡏⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠏⠉⠉⡏⠙⠋⠉⠉⠙⢛⣫⡉⠉⠉⢉⠉⠉⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠛⠛⠛⠛⠛⠛⠃⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

                    ䷩ 𝚕𝚒𝚗𝚎 3439

╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/21/Today_in_Techrights.shtml
    Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/21/Today_in_Techrights.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Today in
Techrights⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Mar 21, 2026


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇View_form_the_table_at_a_restaurant⦈_


⚓  Updated This Past Day⠀⇛


   1. ⚓ SLAPP_Censorship_-_Part_17_Out_of_200:_A_Long_Track_Record_of_Online
      Abuse,_Then_Choosing_a_Low-Cost_Law_Firm_to_Muzzle_People_Who_Have
      Illuminated_This_Abuse_for_Over_a_Decade⠀⇛


           Censorship by targeting ISPs and webhosts isn't unprecedented


   2. ⚓ Symptom_of_Publishers_Dying:_They_Move_to_Adopt_Slop._Symptom_of
      Software_Companies_Dying:_They_Move_to_Adopt_Slop_('Vibe').⠀⇛


           It'll always fail. It's hype. It's a bubble.


   3. ⚓ Under_IBM,_Red_Hat_Replaces_Code_With_LLM_Slop,_Fedora_is_Slopware⠀⇛


           Not even hiding it, those things are in plain sight


   4. ⚓ "systemd_is_essentially_a_corporate_IBM/Redhat_project_and_corporations
      of_course_will_comply"⠀⇛


           Microsoft and IBM care about users' freedom like Cheeto Lump
           cares about the US Constitution


   5. ⚓ Gemini_Links_20/03/2026:_Digital_Identity_Bifurcation_and_a_"Return_to
      Gemini"⠀⇛


           Links for the day


      ⚓  New⠀⇛


   6. ⚓ Plagiarism_in_"Linux"_Clothing_(LLM_Slop_in_linuxiac.com,
      LinuxTeck.com,_and_linuxsecurity.com)⠀⇛


           The net effect of those slopfarms is very negative


   7. ⚓ Links_20/03/2026:_Facebook_Weaponised_Politically,_Openwashing_by_LF
      and_NVIDIA,_Encyclopedia_Britannica_Sues_Microsoft_Proxy_for_Plagiarism⠀⇛


           Links for the day


   8. ⚓ The_EPO's_Local_Staff_Committee_Munich_(LSCMN)_Explains_to_the
      Administrative_Council_(AC)_How_Bad_Things_Have_Become_at_Europe's
      Second-Largest_Institution,_Biggest_Patent_Office,_and_Corruption/Cocaine
      Hub_(Jobs_Sold_to_Friends)⠀⇛


           We'll say a bit more tomorrow


   9. ⚓ IBM's_Red_Hat_Diversity:_Only_3_Women_(Out_of_11_Leaders)⠀⇛


           For comparison's sake, the FSF is about 50% female


  10. ⚓ Gemini_Links_20/03/2026:_Depictions_of_Culture_and_The_Social_Smolnet⠀⇛


           Links for the day


  11. ⚓ SimilarWeb_Was_Never_a_Reliable_Yardstick_for_Traffic⠀⇛


           5RB may need some "house-cleaning"


  12. ⚓ Strangulation,_suffocation,_Jonathan_Carter_&_Debian_toxic_culture
      confirmed⠀⇛


           Reprinted with permission from Daniel Pocock


  13. ⚓ Reports_or_Hearsay_Suggest_Ogilvy_Broke_Up_With_IBM_and_Insiders_Report
      Mass_Layoffs_in_"Infrastructure"_(Might_Impact_Red_Hat_Entrants)⠀⇛


           hearsay in Social Control Media


  14. ⚓ Scheduled_Server_Maintenance_Tomorrow_Night⠀⇛


           Starting 9PM


  15. ⚓ None_of_the_Above_(NotA)_&_Debian_snubbing_Sruthi_Chandran⠀⇛


           Reprinted with permission from Daniel Pocock


  16. ⚓ Links_20/03/2026:_Cryptography_Pioneers_Win_Turing_Award_and_BMG_Sues
      Anthropic_for_Copyright_Infringement⠀⇛


           Links for the day


  17. ⚓ Even_Uganda_Understands_That_Journalists_Never_Belong_in_Prison⠀⇛


           "Ugandan authorities must respect the spirit of this ruling and
           abandon any measures that seek to jail Ugandans for the free
           flow of ideas."


  18. ⚓ Inaction_Helps_Your_Enemies⠀⇛


           Without freedom, there's nothing else left


  19. ⚓ Windows_Down_From_99%_to_~50%_in_Republic_of_Seychelles_(République_des
      Seychelles)⠀⇛


           Windows fell by a lot


  20. ⚓ Confluent_Insiders:_IBM_Laid_Over_Over_800_at_Confluent,_Not_Just_800⠀⇛


           For the record, the layoffs at Confluent won't be over. After
           the bluewashing there will be "IBM RAs" impacting Confluent
           folks, aside from PIPs


  21. ⚓ The_Layoffs_at_IBM_Carry_on_(Shades_of_Enron)⠀⇛


           Is IBM another Enron?


  22. ⚓ "IBM_boss_Arvind_Krishna..._financial_package_valued_at_$38_million_in
      calendar_2025_-_equivalent_to_the_average_collective_pay_of_765_Big_Blue
      workers."⠀⇛


           continues to ruin the company to enrich himself while
           pretending he has a strategy


  23. ⚓ Over_at_Tux_Machines...⠀⇛


           GNU/Linux news for the past day


  24. ⚓ IRC_Proceedings:_Thursday,_March_19,_2026⠀⇛


           IRC logs for Thursday, March 19, 2026


      =========================================================================
      The corresponding text-only bulletin for Friday contains all the text.
      Top-read articles (excluding bot/crawler visits):


                          Span from 2026-03-14 to 2026-03-20
      3762 /about.shtml


      2496 /n/2026/03/14/
           Links_14_03_2026_Mass_Layoffs_at_Facebook_Meta_and_Sweeping_Lay.shtml


      2020 /n/2026/03/15/
           Links_15_03_2026_Slop_Bubble_Driving_Interest_in_Chip_Alternati.shtml


      1921 /n/2026/03/14/
           Links_14_03_2026_Adoption_of_Slop_Has_Killed_BuzzFeed_Russia_Se.shtml


      1766 /index.shtml


      1639 /n/2026/03/15/software_in_the_public_domain.shtml


      1620 /n/2026/03/18/
           IBM_Thrashing_Confluent_Upon_Arrival_Based_on_Rumours.shtml


      1490 /n/2026/03/15/
           Sruthi_Chandran_Debian_Diversity_Favoritism_Hidden_Conflicts_of.shtml


      1330 /n/2026/03/14/IRC_Proceedings_Friday_March_13_2026.shtml


      1167 /n/2026/03/17/
           Hector_Oron_Martinez_Debian_shadow_candidate_pressure_on_Sruthi.shtml


      1054 /n/2026/03/16/2026_Microsoft_Layoff_Rumours.shtml


      1026 /n/2026/03/13/
           Reminder_Microsoft_silent_Layoffs_by_RTO_Commute_Time_and_Lack_.shtml


      1015 /n/2026/03/16/
           Today_s_Discussions_About_How_IBM_Pushes_Workers_Out.shtml


      1004 /irc.shtml


      957  /n/2026/03/17/
           Sophie_Brun_Raphel_Hertzog_Debian_sexual_conflicts_of_interest.shtml


      915  /n/2026/03/13/Founder_of_IBM_Ventures_Has_Just_Quit_IBM.shtml


      898  /n/2026/03/14/
           Reporting_New_and_Suppressed_Information_is_What_Journalism_is_.shtml


      896  /n/2026/03/17/
           British_Justice_Minister_Sarah_Sackman_Blasts_Solicitors_Regula.shtml


      890  /n/2026/03/20/
           Confluent_Insiders_IBM_Laid_Over_Over_800_at_Confluent_Not_Just.shtml


      883  /browse/latest.shtml


      864  /n/2026/03/14/
           Microsofters_SLAPP_Censorship_Part_12_Out_of_200_Months_Ahead_o.shtml


      864  /n/2026/03/16/
           Links_16_03_2026_Moscow_Experiencing_Cellphone_Internet_Outages.shtml


      854  /n/2026/03/19/
           IBM_Effect_at_Confluent_Mass_Layoffs_and_IBM_s_Business_Conduct.shtml


      825  /n/2026/03/13/
           Alternative_to_Microsoft_Office_Must_Use_Free_Open_Standards_Fo.shtml


      798  /n/2026/03/18/
           New_Post_Has_Just_Explained_How_IBM_Gets_Robbed_by_the_People_W.shtml


      779  /n/2026/03/14/
           commandlinux_com_linuxteck_com_linuxiac_com_and_linuxsecurity_c.shtml


      761  /n/2026/03/14/Universities_Became_Bad_Places_for_Work.shtml


      747  /n/2026/03/14/
           Facebook_Layoffs_Due_to_Enormous_Debt_Nothing_to_Do_With_Hey_Hi.shtml


      743  /n/2026/03/14/
           The_Limits_of_Speech_and_the_Rationale_of_Limitations.shtml


      740  /n/2026/03/16/
           Debian_is_Dying_for_Some_of_the_Same_Reasons_IBM_s_Fedora_is_Ra.shtml


      701  /n/2026/03/16/
           Pirate_Praveen_Arimbrathodiyil_Debian_denouncing_volunteers_hid.shtml


      697  /n/2026/03/15/IRC_Proceedings_Saturday_March_14_2026.shtml


      689  /n/2026/03/16/EPO_Strike_This_Week.shtml


      686  /n/2026/03/16/At_Least_Six_EPO_Strikes_Next_Month_Yes_Six.shtml


      685  /n/2026/03/14/
           The_Good_IBM_Managers_Have_Flown_Away_All_That_s_Left_is_the_Bo.shtml


      685  /n/2026/03/15/A_Happy_Birthday_to_Richard_Stallman.shtml


      677  /n/2026/03/14/
           Change_of_Address_at_the_Hired_Guns_Address_Removed.shtml


      676  /n/2026/03/17/
           The_European_Patent_Office_EPO_Holds_a_Public_Demonstration_Tom.shtml


      676  /browse/index.shtml


      658  /n/2026/03/17/
           Links_17_03_2026_American_Fentanylware_TikTok_Investors_Implica.shtml


      653  /n/2026/03/16/
           EPO_Cocaine_Communication_Manager_Part_VII_Cult_Mentality_Mobbi.shtml


      647  /n/2026/03/18/
           EPO_Demonstration_Happening_Right_Now_Later_This_Week_Things_Wi.shtml


      644  /n/2026/03/18/
           A_Step_Close_to_Shutting_Down_the_European_Patent_Office_EPO.shtml


      637  /n/2026/03/14/Wrong_Time_Wrong_Place_Digg.shtml


      625  /n/2026/03/18/EPO_Staff_Demonstration_Today.shtml


      614  /n/2026/03/17/
           For_Third_Time_in_a_Week_The_Register_MS_Runs_Google_SPAM_That_.shtml


      611  /n/2026/03/14/Crime_Comes_in_Many_Forms.shtml


      608  /n/2026/03/18/
           Estimates_That_IBM_to_Lay_Off_Close_to_10_000_Workers_in_2026_N.shtml


      606  /n/2026/03/16/
           Microsofters_SLAPP_Censorship_Part_14_Out_of_200_The_Abusive_Ca.shtml


      605  /n/2026/03/15/
           Microsofters_SLAPP_Censorship_Part_13_Out_of_200_Abuse_of_Proce.shtml


      598  /n/2026/03/17/Over_at_Tux_Machines.shtml


      595  /n/2026/03/15/
           What_Puts_the_Brakes_on_GNU_Linux_Adoption_on_Laptops_and_Deskt.shtml




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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄⠀⠘⢺⣿⣻⢮⠈⠈⢙⢹⣿⢻⣿⣿⡇⠀⠄⠀⣿⠉⠉⣽⣿⣿⣿⣿⣿⣿⠤⠬⢭⣉⣛⣛⣛⣿⠿⠿⣿⣿⣿⣿⠀⢸⣿⡿⠀⠀⣿⣿⣿⣿
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣦⠀⠀⡀⣿⡄⣄⠀⠀⣸⡄⣿⣿⡇⠀⠀⠀⠘⡃⢽⠀⢀⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣻⢛⠀⠄⣿⢿⡿⣠⡄⠀⡛⡟⡿⠁⠀⠀⠀⠠⡇⢸⠀⢸⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⣿⣿⠀⢰⠷⠦⠒⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⢸⠀⡖⠆⠘⣦⡀⣀⢰⠀⣡⡇⠀⠀⠀⠀⠀⡇⢸⡆⢼⣿⣿⢿⣿⡿⣿⣿⡇⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡛⡞⠿⢿⡶⢶⣿⣦⣶⣿⡥⣿⡇⡄⠠⠀⠀⠀⢠⢠⠋⣼⣿⠏⣾⡿⢰⣿⣿⠃⡀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠑⠂⠀⠀⠉⠉⠉⠀⠰⣿⣾⣿⣟⣀⣤⣄⣸⠃⢠⡿⠏⢘⢛⠃⠾⠛⠃⢠⡃⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡂⠀⠀⠀⣠⣴⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠢⢭⣥⡄⠀⡰⠃⢀⢀⠜⠀⢈⠄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⠆⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢇⠀⠈⠀⡴⠁⠀⢀⠞⠀⢚⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠛⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⠀⠀⠀⠀⠀⠀⠀⢀⣾⠄⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⣿⣿⣿⣶⣿⠀⣴⡿⠃⢀⡠⠀⠀⢀⡄⣼⢏⡄⣴⡇⣠⡀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣴⣷⣾⣿⣿⣿⣿⣿⢴⣿⣷⣶⣯⣤⣾⣿⠋⣠⣿⣿⢣⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⡿⠋⡉⠀⠀⡞⣯⣿⣭⡷⠟⢁⣶⣾⠿⢷⣿⣿⣿⣿⡿⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿
⠀⠠⣤⣠⣤⣴⣾⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣶⣾⣷⣷⣿⣿⣦⣴⣾⣯⣤⣿⣿⠿⠿⠟⠋⢀⡁⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⠋⠉
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠈⠻⣷⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⣿⣷⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠘⠁⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠿⠿⠛⢉⣤⣾⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣦⡀
⣿⡿⠿⠛⠉⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣷
⠁⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇

                    ䷩ 𝚕𝚒𝚗𝚎 3856

╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/21/today_s_howtos.shtml
    Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/21/today_s_howtos.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ today's
howtos⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Mar 21, 2026


    * ⚓ C.J._Adams-Collier:_The_WWW::Mechanize::Chrome_Saga:_A_Comprehensive
      Narrative_of_PR_#104⠀⇛


    * ⚓ Barry Kauler ☛ PKGget_fix_bug_when_uninstall_PET⠀⇛


           Caramel found a bug when uninstalling a PET package:


           https://forum.puppylinux.com/viewtopic.php?p=166938#p166938


           Yes, the problem is in /usr/local/petget/removepreview.sh
           script. It thinks that the PET is actually a Devuan DEB
           package, then tries to use 'apt' to uninstall. Fixed.


    * ⚓ Linuxize ☛ git_clone:_Clone_a_Repository⠀⇛


           How to use git clone to copy a remote or local repository,
           clone a specific branch, and create shallow clones, with
           examples for HTTPS and SSH.


    * ⚓ Linuxize ☛ df_Cheatsheet⠀⇛


           Quick reference for the df command: check disk space, display
           formats, filesystem filtering, inodes, and custom output fields


    * § idroot⠀➾


          o ⚓ ID Root ☛ How_To_Install_Obsidian_on_Linux_Mint_22⠀⇛


                 If you want a powerful, offline-first note-taking app
                 that stores your data as plain Markdown files, Obsidian
                 is one of the best tools available for GNU/Linux users
                 today. Getting it running on Linux Mint 22 “Wilma” is
                 straightforward, but the process differs depending on
                 which packaging format you choose.


          o ⚓ ID Root ☛ How_To_Install_OpenShot_on_Fedora_43⠀⇛


                 If you run Fedora 43 and need a capable, free, open-
                 source video editor without switching distros or paying
                 for proprietary software, OpenShot Video Editor is one of
                 the strongest options available on GNU/Linux today.


          o ⚓ ID Root ☛ How_To_Install_UNetbootin_on_Fedora_43⠀⇛


                 If you work with GNU/Linux regularly, you already know
                 how often you need to flash an ISO to a USB drive.
                 Whether you are testing a new distribution, setting up a
                 recovery environment, or deploying a fresh OS on a
                 server, having a reliable USB creation tool matters.


          o ⚓ ID Root ☛ How_To_Install_Spicetify_on_GNU/Linux_Mint_22⠀⇛


                 If you use Spotify on GNU/Linux Mint 22, you already know
                 the default client is a locked-down, visually static
                 experience with zero customization options. Spicetify is
                 the open-source CLI tool that fixes that, letting you
                 install themes, block ads, hide podcasts, and manage
                 extensions through a built-in Marketplace.


    * ⚓ Linux Capable ☛ How_to_Install_Python_on_Fedora_Linux⠀⇛


           Fedora already tracks CPython closely, and current Fedora
           releases expose far more than a single default interpreter.


    * ⚓ dwaves.de ☛ GNU_GNU/Linux_Debian_13_(vm)_how_to_install_airllm,
      openclaw.ai_what_is_picoclaw.io_?_the_cyber_security_implications_of_Hey
      Hi_(AI)_(AI_and_the_privacy_problem:_1984_calling?)⠀⇛





                    ䷩ 𝚕𝚒𝚗𝚎 3962

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(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/21/Videos_Shows_About_GNU_Linux.shtml
    Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/21/Videos_Shows_About_GNU_Linux.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Videos/Shows About GNU/
Linux⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Mar 21, 2026,
updated Mar 21, 2026


    * ⚓ Invidious ☛ 2026-03-16_[Older]_The_Big_Pop!_OS_Upgrade_is_HERE!_GNOME
      Out_-_COSMIC_In_(Why_This_is_Actually_Huge?)⠀⇛


    * ⚓ Invidious ☛ 2026-03-16_[Older]_'tail'_-_print_the_ending_of_files_-
      Video_Man_Pages⠀⇛


    * ⚓ Invidious ☛ 2026-03-16_[Older]_A_Whole_New_Challenge_For_Open_Source
      Licenses⠀⇛


    * ⚓ Invidious ☛ 2026-03-15_[Older]_Fedora_44_First_Look!_GNOME_50,_NTSync,
      and_Whisper_AI_(678%_FPS_Is_Real)⠀⇛


    * ⚓ Invidious ☛ 2026-03-15_[Older]_'head'-_print_the_beginning_of_files_-
      Video_Man_Pages⠀⇛


    * ⚓ Invidious ☛ 2026-03-15_[Older]_The_Linux_Uptime_Obsession_(Stop
      Bragging_About_This)⠀⇛


    * ⚓ Invidious ☛ 2026-03-15_[Older]_Linux_Weekly_News:_AI_invades_Kwin,
      Lutris_&_AMD_drivers,_SUSE_could_be_sold⠀⇛


    * ⚓ Invidious ☛ 2026-03-15_[Older]_Nitrux_6.0_RELEASED!_9_Changes_That
      Actually_Matter_(Upgrade_or_Skip?)⠀⇛


    * ⚓ Invidious ☛ 2026-03-15_[Older]_Why_C++_Never_Got_Into_The_Linux
      Kernel⠀⇛


    * ⚓ Invidious ☛ 2026-03-14_[Older]_Ageless_Linux_Thinks_It's_Exempt_From
      Age_Verification⠀⇛


    * ⚓ Invidious ☛ 2026-03-13_[Older]_Students_learning_programming_should_not
      miss_this.⠀⇛


    * ⚓ Invidious ☛ 2026-03-13_[Older]_Age_Verification_On_Linux_Is_Worse_Than
      We_Thought⠀⇛


    * ⚓ Invidious ☛ 2026-03-13_[Older]_Did_Linus_Seriously_Break_PopOS_Again_|
      Linux_Nerd_Reacts⠀⇛


    * ⚓ Invidious ☛ 2026-03-13_[Older]_15_Essential_Keyboard_Shortcuts_for
      Linux_Mint_Users⠀⇛


    * ⚓ Invidious ☛ 2026-03-12_[Older]_Origami_Linux_Is_Both_Elegant_And
      Opinionated_(And_I_Like_It!)⠀⇛


    * ⚓ Invidious ☛ 2026-03-12_[Older]_Open_Source_has_a_UX_problem._Here's_how
      we_can_fix_it.⠀⇛


    * ⚓ Invidious ☛ 2026-03-11_[Older]_How_to_run_most_Windows_apps_on_Linux,
      and_why_it_won't_really_help⠀⇛


    * ⚓ Invidious ☛ 2026-03-11_[Older]_SPICY_Opinions_About_Switching_To_Linux
      |_Featuring_Ed_Crisler_of_Sapphire_Tech⠀⇛


    * ⚓ Invidious ☛ 2026-03-10_[Older]_Become_a_pro_Ubuntu_user_with_this
      handbook_🔥⠀⇛


    * ⚓ Invidious ☛ 2026-03-10_[Older]_My_Xonsh_Shell_Experiment_Failed!_
      (...Kind_Of)⠀⇛





                    ䷩ 𝚕𝚒𝚗𝚎 4060

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(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/21/Wayland_set_the_Linux_Desktop_back_by_10_years.shtml
    Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/21/Wayland_set_the_Linux_Desktop_back_by_10_years.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Wayland set the Linux Desktop back by 10
years⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Mar 21, 2026


Wayland has been a broad misdirection and misallocation of time and developer
resources at the expense of users. With more migration from other operating
systems, the pressure to fix fundamental problems has become more prominent.
After 17 years of development, now is a good time to reflect on some of the
larger promises that have been made around the development of Wayland as a
replacement for the X11 display protocol.


If you're not in this space, hopefully it will still be interesting as an
engineering post-mortem on taking on new greenfield projects. Namely: What are
the issues with what exists, why can they not be fixed, what do we hope to
achieve with a new project, and how long do we expect it to take?


Read_on





                    ䷩ 𝚕𝚒𝚗𝚎 4094

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(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/21/Wine_11_5.shtml
    Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/21/Wine_11_5.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Wine 11.5⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█
⌧


posted by Roy Schestowitz on Mar 21, 2026


§ Release notes


The Wine development release 11.5 is now available.


What's new in this release:


    * C++ support in the build system.
    * Bundled ICU libraries.
    * Support for Syscall User Dispatch on Linux.
    * A number of VBScript compatibility fixes.
    * Various bug fixes.
The source is available at https://dl.winehq.org/wine/source/11.x/wine-
11.5.tar.xz


Binary packages for various distributions will be available from the respective
download_sites.


You will find documentation here.


Wine is available thanks to the work of many people. See the file AUTHORS for
the complete list.


Read_on





                    ䷩ 𝚕𝚒𝚗𝚎 4143

╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2026/03/21/Zentyal_Server_8_1_Development_Now_Available.shtml
    Gemini version at gemini://gemini.tuxmachines.org/n/2026/03/21/Zentyal_Server_8_1_Development_Now_Available.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Zentyal Server 8.1 Development Now
Available⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Mar 21, 2026


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Zentyal_Linux_Server⦈_


Zentyal Development Team today announced the availability of Zentyal Server
Development Edition 8.1.


Zentyal Server 8.1 is based on Ubuntu Server 24.04 LTS and comes with the
latest versions of all integrated software. This release focuses on improving
overall performance, security hardening, and system stability, and includes a
large number of internal improvements and bug fixes across the platform.


[...]


Zentyal Server provides an easy-to-use Linux alternative to Windows Server®.
Thanks to the integration of Samba, Zentyal provides native compatibility with
the Microsoft Active Directory® and allows transparent management of Windows®
clients. It is used by companies and public administrations mainly as a domain
and directory server and a file server. The graphical user inferface that
Zentyal offers helps to make Linux server management easier for all and
specially for new Linux users.


Read_on




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡿⢿⢽⡿⢿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣊⡯⣏⣿⡗⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣵⣿⠺⣺⣼⣿⣿⣿⣿⡿⢠⠄⠀⠀⠀⠀⠀⠀⢰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⢹⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠏⠀⢸⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⠀⢸⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠀⠀⠀⣾⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⠀⠀⢰⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⢾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⢤⡄⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣟⡅⢀⣸⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⢣⣺⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣗⢘⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣦⣤⣤⣀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣤⣤⣶⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣾⣿⣶⣶⣦⣤⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀
⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀
⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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