Tux Machines Bulletin for Monday, November 11, 2024
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Generated Tue 12 Nov 02:49:50 GMT 2024
Created by Dr. Roy Schestowitz (𝚛𝚘𝚢 (at) 𝚜𝚌𝚑𝚎𝚜𝚝𝚘𝚠𝚒𝚝𝚣 (dot) 𝚌𝚘𝚖)
Full hyperlinks for navigation omitted but are fully available in the originals
The corresponding HTML versions are at http://news.tuxmachines.org


╒═══════════════════ 𝐈𝐍𝐃𝐄𝐗 ═══════════════════════════════════════════════════╕

⦿ Tux Machines  -  5 Linux Features That Make It More Productive Than Windows or Mac

⦿ Tux Machines  -  9to5Linux Weekly Roundup: November 10th, 2024

⦿ Tux Machines  -  Android Leftovers

⦿ Tux Machines  -  Audiocasts/Shows: Open Source Security Podcast and This Week in Linux

⦿ Tux Machines  -  Auto-Match Ubuntu’s Accent Colour to Your Wallpaper

⦿ Tux Machines  -  DXVK 2.5 Improves Memory Management in God of War and Other Video Games

⦿ Tux Machines  -  Fedora Linux Elevates KDE to Edition Status

⦿ Tux Machines  -  Free, Libre, and Open Source Software Leftovers

⦿ Tux Machines  -  GNU/Linux Leftovers

⦿ Tux Machines  -  Habits to Keep Linux Resource Usage Low

⦿ Tux Machines  -  Linux 6.12-rc7

⦿ Tux Machines  -  Microsoft Windows at All-Time Lows

⦿ Tux Machines  -  Pop!_OS: One of the Best Linux Distros For Creators of All Types

⦿ Tux Machines  -  Programming Leftovers

⦿ Tux Machines  -  Putting Linux on a Tablet? 7 Distros to Try

⦿ Tux Machines  -  Radxa, Raspberry Pi, and More Hardware

⦿ Tux Machines  -  Review: Bazzite 40, Playtron OS Alpha 1, Tucana Linux 3.1

⦿ Tux Machines  -  Security Leftovers

⦿ Tux Machines  -  Streamlining openSUSE Translations Upstream

⦿ Tux Machines  -  This Week in KDE Apps: Adopt an App

⦿ Tux Machines  -  Today in Techrights

⦿ Tux Machines  -  today's howtos

⦿ Tux Machines  -  veraPDF – industry supported PDF/A validation

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
https://tuxmachines.org/n/2024/11/11/5_Linux_Features_That_Make_It_More_Productive_Than_Windows_or_M.shtml
https://tuxmachines.org/n/2024/11/11/9to5Linux_Weekly_Roundup_November_10th_2024.shtml
https://tuxmachines.org/n/2024/11/11/Android_Leftovers.shtml
https://tuxmachines.org/n/2024/11/11/Audiocasts_Shows_Open_Source_Security_Podcast_and_This_Week_in_.shtml
https://tuxmachines.org/n/2024/11/11/Auto_Match_Ubuntu_s_Accent_Colour_to_Your_Wallpaper.shtml
https://tuxmachines.org/n/2024/11/11/DXVK_2_5_Improves_Memory_Management_in_God_of_War_and_Other_Vid.shtml
https://tuxmachines.org/n/2024/11/11/Fedora_Linux_Elevates_KDE_to_Edition_Status.shtml
https://tuxmachines.org/n/2024/11/11/Free_Libre_and_Open_Source_Software_Leftovers.shtml
https://tuxmachines.org/n/2024/11/11/GNU_Linux_Leftovers.shtml
https://tuxmachines.org/n/2024/11/11/Habits_to_Keep_Linux_Resource_Usage_Low.shtml
https://tuxmachines.org/n/2024/11/11/Linux_6_12_rc7.shtml
https://tuxmachines.org/n/2024/11/11/Microsoft_Windows_at_All_Time_Lows.shtml
https://tuxmachines.org/n/2024/11/11/Pop_OS_One_of_the_Best_Linux_Distros_For_Creators_of_All_Types.shtml
https://tuxmachines.org/n/2024/11/11/Programming_Leftovers.shtml
https://tuxmachines.org/n/2024/11/11/Putting_Linux_on_a_Tablet_7_Distros_to_Try.shtml
https://tuxmachines.org/n/2024/11/11/Radxa_Raspberry_Pi_and_More_Hardware.shtml
https://tuxmachines.org/n/2024/11/11/Review_Bazzite_40_Playtron_OS_Alpha_1_Tucana_Linux_3_1.shtml
https://tuxmachines.org/n/2024/11/11/Security_Leftovers.shtml
https://tuxmachines.org/n/2024/11/11/Streamlining_openSUSE_Translations_Upstream.shtml
https://tuxmachines.org/n/2024/11/11/This_Week_in_KDE_Apps_Adopt_an_App.shtml
https://tuxmachines.org/n/2024/11/11/Today_in_Techrights.shtml
https://tuxmachines.org/n/2024/11/11/today_s_howtos.shtml
https://tuxmachines.org/n/2024/11/11/veraPDF_industry_supported_PDF_A_validation.shtml


                    ䷩ 𝚕𝚒𝚗𝚎 82

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

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2024/11/11/5_Linux_Features_That_Make_It_More_Productive_Than_Windows_or_M.shtml
    Gemini version at https://tuxmachines.org/n/2024/11/11/5_Linux_Features_That_Make_It_More_Productive_Than_Windows_or_M.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 5 Linux Features That Make It More
Productive Than Windows or Mac⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Rianne Schestowitz on Nov 11, 2024


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


Quoting: 5 Linux Features That Make It More Productive Than Windows or Mac —


     Most Linux operating systems, including popular ones like Ubuntu,
     offer a powerful implementation of virtual desktops unmatched by both
     Windows and macOS. For instance, Ubuntu and similar GNOME-based Linux
     OS, give you a powerful settings area to specify how many virtual
     desktops you want or even let the system generate them dynamically
     based on your needs. Like in Windows or macOS, you can drag and drop
     app windows into specific virtual desktops for better management. In
     addition to that, you can drag and drop applications from the dock
     onto a specific virtual desktop to launch them. This makes starting a
     new workflow extremely fast and efficient.


     You also get special tools to help you manage virtual desktops more
     easily. On Ubuntu, you can install the Workspace Indicator extension
     to switch between virtual desktops right from the panel—without
     needing to open the desktop overview. Likewise, KDE Plasma-based
     Linux OS like Kubuntu and Garuda Linux give you the Pager widget,
     which offers similar functionality.


Read_on




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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 154

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

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2024/11/11/9to5Linux_Weekly_Roundup_November_10th_2024.shtml
    Gemini version at https://tuxmachines.org/n/2024/11/11/9to5Linux_Weekly_Roundup_November_10th_2024.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 9to5Linux Weekly Roundup: November 10th,
2024⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Marius Nestor on Nov 11, 2024,
updated Nov 11, 2024


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇9to5Linux_Weekly_Roundup⦈_


Good news this week for KDE Plasma users as they got not one, not two, but
three great releases, including the KDE Plasma 6.2.3 desktop environment, as
well as KDE Gear 24.08.3 and KDE Frameworks 6.8 software suites. LXQt users
also got an awesome release with version 2.1, which finally brings a Wayland
session.


On top of that, this week brought us new Debian Bookworm, Steam Client,
CachyOS, and Ubuntu Touch releases to enjoy. Below you can check out this
week’s hottest news and access all the distro and package downloads released
this past week in the 9to5Linux weekly roundup for November 10th, 2024.


Read_on




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⣠⣴⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⣤⠀⠐⡆⢀⣀⠀⢀⡀⢰⠂⠀⢸⢀⠀⢀⠀⠀⣸⠊⢉⡆⣠⢤⠀⠀⠀⠀⣀⣀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠛⣿⠛⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⡰⠻⣄⢠⠃⣟⣊⠀⣗⣊⢸⠻⠅⢸⠸⣠⡎⠀⠀⣿⠶⣋⠀⣇⡼⢸⡠⢻⠰⠏⠸⡄⠯⣽⡄⣇⠜⡇⢺⣩⠇⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣠⣽⣿⣧⣄⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠏⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣈⡛⠿⠿⠿⢛⣁⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⠿⠿⠿⠟⠀⠙⠿⠿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 213

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

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2024/11/11/Android_Leftovers.shtml
    Gemini version at https://tuxmachines.org/n/2024/11/11/Android_Leftovers.gmi

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


posted by Rianne Schestowitz on Nov 11, 2024


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Wi-Fi⦈_


    * ⚓ When_will_Android_16_debut?_One_rumor_predicts_the_exact_day_we_could
      see_it_on_phones_|_Android_Central⠀⇛


    * ⚓ Android_15_adds_support_for_Wi-Fi_Ranging_to_improve_indoor
      navigation⠀⇛


    * ⚓ This_Android_update_might_just_give_public_Wi-Fi_login_pages_a_handy
      makeover⠀⇛


    * ⚓ Android_update_to_streamline_public_Wi-Fi_logins_-_Neowin⠀⇛


    * ⚓ I've_stopped_caring_about_OS_updates,_but_Android_skins_are_back_in
      fashion⠀⇛


    * ⚓ Gmail's_new_search_result_sorting_feature_is_now_live_on_Android⠀⇛


    * ⚓ Gmail_for_Android_is_picking_up_a_long-overdue_feature⠀⇛


    * ⚓ Gmail_feature_rolling_out_on_Android_takes_care_of_a_massive_pain_point
      -_PhoneArena⠀⇛


    * ⚓ Gmail_for_Android_is_picking_up_a_long-overdue_feature⠀⇛




⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠂⠂⠖⠄⠰⠦⠢⠂⠀⠦⠶⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢠⡆⠀⢠⣤⣀⣠⣄⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠈⠁⠀⠈⠀⠈⠈⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⣦⠀⢀⣤⣀⣀⣄⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠄⠀⢀⣀⣀⣀⡀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⠃⠀⠈⠈⠉⠉⠉⠉⠋⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠀⠈⠉⠉⠉⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠴⠀⠢⠲⠖⠢⠢⠶⠠⠦⠢⠄⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 287

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

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2024/11/11/Audiocasts_Shows_Open_Source_Security_Podcast_and_This_Week_in_.shtml
    Gemini version at https://tuxmachines.org/n/2024/11/11/Audiocasts_Shows_Open_Source_Security_Podcast_and_This_Week_in_.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Audiocasts/Shows: Open Source Security
Podcast and This Week in Linux⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Nov 11, 2024


    * ⚓ Open Source Security (Audio Show) ☛ Open_Source_Security_Podcast
      Episode_454_–_The_state_of_open_source_with_Brian_Fox_from_Sonatype_and
      Donald_Fischer_from_Tidelift [Ed: Sonatype and Tidelift are two Microsoft
      proxies/partners to a certain degree]⠀⇛


           Josh and Kurt talk to Brian Fox from Sonatype and Donald
           Fischer from Tidelift about their recent reports as well as
           open source. There are really interesting connections between
           the two reports. The overall theme seems to be open source is
           huge, everywhere, and needs help. But all is no lost! There’s
           some great ideas on what the future needs to look like.


    * ⚓ This_Week_in_Linux_285:_LXQt_desktop,_GIMP_3.0,_Manjaro_Data_Collection
      &_more_GNU/Linux_news⠀⇛


           This week in Linux, we've got a lot of good news with a new
           release of the LXQt desktop environment, a new accessory from
           Raspberry Pi. Valve has announced the official launch for the
           Steam game recording feature and GIMP 3.0 is finally at a point
           where we can just might have it at some point soon. We also
           have a bit of controversial news with Manjaro announcing a new
           data collection plan. We're gonna talk about all this and so
           much more on this week in Linux, the weekly news show that
           keeps you up to date with what's going on in the GNU/Linux and
           open source world. Now let's jump right into Your Source for
           GNU/Linux GNews.


    * ⚓ Tux Digital ☛ This_Week_in_Linux_285:_LXQt_desktop,_GIMP_3.0,_Manjaro
      Data_Collection_&_more_GNU/Linux_news⠀⇛


           This week in Linux, we’ve got a lot of good news with a new
           release of the LXQt desktop environment, a new accessory from
           Raspberry Pi.





                    ䷩ 𝚕𝚒𝚗𝚎 344

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

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2024/11/11/Auto_Match_Ubuntu_s_Accent_Colour_to_Your_Wallpaper.shtml
    Gemini version at https://tuxmachines.org/n/2024/11/11/Auto_Match_Ubuntu_s_Accent_Colour_to_Your_Wallpaper.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Auto-Match Ubuntu’s Accent Colour to Your
Wallpaper⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Rianne Schestowitz on Nov 11, 2024


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇GNOME_Extension⦈_


Quoting: Auto-Match Ubuntu's Accent Colour to Your Wallpaper - OMG! Ubuntu —


     Accent colours are a headline feature in GNOME 47, although not new
     to Ubuntu users since Ubuntu added its own approach to accent colours
     back in 2022.


     Now aligned with upstream, this new GNOME Shell extension is going to
     interest Ubuntu users who don’t wan the hassle of handpicking an
     accent colour to suit their wallpaper – instead, letting their
     wallpaper pick the accent colour!


Read_on




⠠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣴⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⠠⠀⠀⠤⣄⣤⡤⣄⣠⠤⢤⣤⣤⣤⠤⣤⣤⣦⣤⣤⣦⣤⠄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⡛⢻⣿⣿⣿⣿⢐⠀⠀⠈⠀⠉⠉⠀⠀⠉⠁⠈⠉⠉⠉⠉⠉⠉⢹⠿⣿⣭⠁⠀⠀⠀⠸⣶⣩⣽⣶⠀⠀⠀⠀⠀⠀⠀⠀
⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⣭⠭⠛⠀⠀⠀⠀⠘⣿⡿⢿⣿⡀⠂⠀⠀⠀⠀⠀⠀
⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠙⠋⠛⠃⠉⠿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠃⠀⠀⠀⠀⠀⠀⠐⢒⣠⡔⠐⠀⠀⠀⠀⠀⠀⠀
⠒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⠓⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⡿⠿⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⢿⣿⡿⠟⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣴⣾⣯⣿⠟⠋⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣦
⢒⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢐⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⢻⣿⣿⣿⣿
⠠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣒⣀⣀⣀⣀⣀⣀⠠⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢈⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠒⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣾⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⢸⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣧⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿

                    ䷩ 𝚕𝚒𝚗𝚎 403

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

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2024/11/11/DXVK_2_5_Improves_Memory_Management_in_God_of_War_and_Other_Vid.shtml
    Gemini version at https://tuxmachines.org/n/2024/11/11/DXVK_2_5_Improves_Memory_Management_in_God_of_War_and_Other_Vid.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ DXVK 2.5 Improves Memory Management in God
of War and Other Video Games⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Marius Nestor on Nov 11, 2024


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇DXVK_2.5⦈_


DXVK 2.5 is here one and a half months after DXVK 2.4.1 to improve memory
management for God of War and other video games by periodically performing
memory defragmentation to return some unused memory to the system. However,
this feature is currently disabled on Intel's ANV Vulkan driver.


It also enables strict float emulation by default on NVIDIA 565.57.01 beta and
newer graphics drivers to improve correctness, which may lead to a small
performance boost on some games, and improves support for Unreal Engine 3 games
by destroying unused Vulkan samplers on the fly and use the correct LOD bias.


Read_on




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⡀⠀⠀⢀⡀⠀⠀⠀⢀⡀⣀⡀⠀⠀⠀⠀⣀⡀⢀⡀⠀⠀⢀⣀⠀⠀⠀⠀⢀⣀⣄⣀⠀⠀⠀⠀⢀⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠉⠉⠻⣷⡀⠈⢿⣆⠀⣴⡟⠁⠹⣷⠀⠀⠀⢠⡿⠀⢸⡇⢀⣴⠿⠁⠀⠀⠀⠀⣾⠋⠉⢻⡇⠀⠀⠀⢸⣿⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢹⡇⠀⠀⣻⣿⡏⠀⠀⠀⠹⣧⠀⢠⡿⠁⠀⢸⣷⣿⣏⠀⠀⠀⠀⠀⠀⠁⠀⣠⡾⠃⠀⠀⠀⠘⠛⠛⠿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣠⣿⠃⢀⣴⠟⠉⢿⣆⠀⠀⠀⢻⣦⣾⠃⠀⠀⢸⡏⠈⠻⣦⡀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⢺⣇⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠟⠛⠁⠀⠺⠋⠀⠀⠀⠹⠇⠀⠀⠀⠻⠃⠀⠀⠀⠸⠇⠀⠀⠙⠗⠀⠀⠀⠀⠿⠿⠿⠿⠗⠐⠿⠂⠀⠛⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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                    ䷩ 𝚕𝚒𝚗𝚎 460

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

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2024/11/11/Fedora_Linux_Elevates_KDE_to_Edition_Status.shtml
    Gemini version at https://tuxmachines.org/n/2024/11/11/Fedora_Linux_Elevates_KDE_to_Edition_Status.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Fedora Linux Elevates KDE to Edition
Status⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Rianne Schestowitz on Nov 11, 2024,
updated Nov 11, 2024


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


Quoting: Fedora Linux Elevates KDE to Edition Status —


     There’s news, but then there’s the kind of news that can really shake
     things up—and this is definitely the latter.


     When Joshua Strobl, the creator and maintainer of Fedora Budgie Spin
     and Fedora Budgie Atomic, officially proposed on this year’s April
     Fool’s Day that the Plasma Spin should replace the current GNOME
     release as Fedora’s main edition, I have to admit I initially thought
     it was a not-so-original April Fool’s joke. Let me tell you why.


     Fedora is widely recognized as a project that enjoys substantial
     backing from Red Hat—financially, with infrastructure, and through a
     talented team of developers. This strong support is fantastic because
     it ensures Fedora maintains the high quality we’re all familiar with.


Read_on


It's FOSS News:


    * ⚓ The_Fedora_KDE_Spin_Confirmed_as_an_Alternative_Official_Edition_for
      Workstation_Users⠀⇛


           Fedora is a well-known Linux distribution that is recognized
           for its robustness and reliability, providing its users with a
           cutting-edge experience, but in a stable form and with
           effortless upgrades.


           It is available in many flagship Editions, such as Workstation,
           Server, CoreOS, etc., with many Spins offering different
           desktop environments (DE) options like Xfce, LxQt, Cinnamon,
           etc., and a line of Atomic Desktops.


           Since 2007, with the release of Fedora 7, GNOME has been the
           default desktop environment for Workstation. But, as things
           stand, the status quo is set to change with a new Edition
           joining Fedora Workstation.




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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣼⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 551

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

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2024/11/11/Free_Libre_and_Open_Source_Software_Leftovers.shtml
    Gemini version at https://tuxmachines.org/n/2024/11/11/Free_Libre_and_Open_Source_Software_Leftovers.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Free, Libre, and Open Source Software
Leftovers⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Nov 11, 2024


    * § Free, Libre, and Open Source Software⠀➾


          o ⚓ Terence Eden ☛ Introducing_ActivityBot_–_the_simplest_way_to
            build_Mastodon_Bots⠀⇛


                 Say… didn't I write my own ActivityPub server? Why, yes!
                 Yes I did!


                 I took the code and stripped it down to the bare
                 essentials. All you need to do is upload two files0 -
                 index.php and .htaccess - fill in your details, and
                 you're done.


          o ⚓ Lawrence Tratt ☛ pizauth:_HTTPS_redirects⠀⇛


                 I’ve just released pizauth-1.0.6 which introduces one
                 notable new feature: support for HTTPS redirects. New
                 features sound good, but what does this actually mean? My
                 experience is that the way OAuth2 works is sufficiently
                 counter-intuitive that people often struggle to make
                 sense of what it’s doing.


                 Here’s a very quick, simplified, summary of what OAuth2,
                 and pizauth do [1]. OAuth2 lets you obtain a time-limited
                 token which you can use to access a remote resource (e.g.
                 the ability to send email): pizauth’s job is to get you
                 such a token. If you ask pizauth for a token for a
                 resource and a token isn’t already available, pizauth
                 will create a URL which you then open in your local web
                 browser. That URL will take you to the remote resource
                 (e.g. your email provider) who will then ask you to
                 authenticate yourself (i.e. login). Once you’ve
                 successfully done so, the remote web page then needs to
                 tell pizauth that you’ve been successful: it does so by
                 redirecting you to an HTTP URL that’s actually pizauth
                 running on your local machine.


          o ⚓ Medevel ☛ Beyond_Strava:_Why_This_Free_Open-Source_Tracker_Became
            My_Go-To_for_Mountain_Biking_(Not_There_For_Equestrians_Yet)⠀⇛


                 As an avid mountain biker and occasional trail runner,
                 I've always struggled with activity tracking apps. They
                 either came with hefty subscription fees or bombarded me
                 with premium features I'd never use. That's when I
                 stumbled upon FitTrackee - a free, open-source activity
                 tracker...


          o ⚓ Medevel ☛ 14_Open-source_Free_Solution_to_Backup_your_Docker
            Container_and_Docker_Volume⠀⇛


                 As a web developer, Docker containers are my daily
                 companions - they've completely changed how I build and
                 ship applications. But here's the thing: I learned the
                 hard way that containers are temporary by design.


          o § SaaS/Back End/Databases⠀➾


                # ⚓ PostgreSQL ☛ PoWA_5_is_out!⠀⇛


                       PoWA (PostgreSQL Workload Analyzer) is a
                       performance tool, compatible with all supported
                       PostgreSQL versions. It allows to collect and
                       aggregate metrics gathered from multiple PostgreSQL
                       instances using various extensions covering all
                       parts of PostgreSQL and provides real-time charts
                       and graphs to help monitor and tune your servers.
                       It also suggest optimizations, like global or per-
                       query index suggestions, to easily improve
                       performances.


          o § Education⠀➾


                # ⚓ Uğur Erdem Seyfi ☛ Linux_Asceticism⠀⇛


                       When people argue for using Linux, they often focus
                       on either political or practical reasons. For
                       instance, they may choose Linux because it supports
                       the principles of software freedom and personal
                       control. They may also choose it for reasons such
                       as cost savings, customizability, flexibility to
                       meet specific needs, performance, tool
                       availability, and so on.


                       However, there’s another often-overlooked aspect
                       that can make using a minimal Linux distribution
                       worthwhile: using a minimal Linux distro on your
                       personal computer is a form of Askesis -disciplined
                       practices done for self-improvement. At first, it
                       will probably feel uncomfortable and overwhelming.
                       You’ll face many problems that you’ll need to
                       solve. But you’ll also come to realize and
                       understand better that many of the features you
                       take for granted in an OS with a preconfigured
                       desktop environment are actually separate
                       components that need to exist on your system for
                       you to have that functionality.


          o § Openness/Sharing/Collaboration⠀➾


                # § Open Data⠀➾


                      # ⚓ Simon Willison ☛ Visualizing_local_election_results
                        with_Datasette,_Observable_and_MapLibre_GL⠀⇛


                             Alex Garcia and myself hosted the first
                             Datasette Open Office Hours on Friday—a live-
                             streamed video session where we hacked on a
                             project together and took questions and tips
                             from community members on Discord.


                             We didn’t record this one (surprisingly not a
                             feature that Discord offers) but we hope to
                             do more of these and record them in the
                             future.


                             This post is a detailed write-up of what we
                             built during the session.





                    ䷩ 𝚕𝚒𝚗𝚎 710

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

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2024/11/11/GNU_Linux_Leftovers.shtml
    Gemini version at https://tuxmachines.org/n/2024/11/11/GNU_Linux_Leftovers.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ GNU/Linux
Leftovers⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Nov 11, 2024


    * § Games⠀➾


          o ⚓ GamingOnLinux ☛ GE-Proton_9-19_brings_fixes_for_Horizon_Zero_Dawn
            Remastered,_Monster_Hunter_Wilds_and_more⠀⇛


                 The latest upgrade for GE-Proton is now available with
                 GE-Proton 9-19 bringing an assortment of fixes for
                 specific games, along with updates to various components
                 that let it do its thing.


    * § Desktop Environments/WMs⠀➾


          o ⚓ Barry Kauler ☛ JWM_window_manager_2.4.7⠀⇛


                 I posted recently about a bug in the latest JWM:


          o Latest_JWM_has_wrong_colours — November 05, 2024
            Joe has fixed it, and Larry sent me an email that he tested it on
            EasyOS and the colours are now correct.


    * § Distributions and Operating Systems⠀➾


          o § Gentoo Family⠀➾


                # ⚓ Gentoo ☛ The_peculiar_world_of_Gentoo_package_testing⠀⇛


                       While discussing_uv_tests_with_Fedora_developers,
                       it occurred to me how different your average Gentoo
                       testing environment is — not only from these used
                       upstream, but also from these used by other GNU/
                       Linux distributions. This article will be dedicated
                       exactly to that: to pointing out how it’s
                       different, what does that imply and why I think
                       it’s not a bad thing.





                    ䷩ 𝚕𝚒𝚗𝚎 773

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

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2024/11/11/Habits_to_Keep_Linux_Resource_Usage_Low.shtml
    Gemini version at https://tuxmachines.org/n/2024/11/11/Habits_to_Keep_Linux_Resource_Usage_Low.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Habits to Keep Linux Resource Usage
Low⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Rianne Schestowitz on Nov 11, 2024


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


Quoting: Habits to Keep Linux Resource Usage Low —


     Linux is great at using your computer efficiently, but sometimes you
     might find yourself on a slower or older machine. How can you make
     Linux work better with lower performance?


Read_on




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⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣺⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣏⣍⠉⠛⠛⠟⠉⠉⢹⠟⠀⠀⢸⣶⣶⠖⣦⢤⣤⣄⣀⣤⣤
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠾⠿⣿⣿⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣉⣀⣀⠀⠀⠀⠀⠘⠄⢀⣠⣾⣿⣿⣭⣭⣼⣿⣿⣿⣿⣿
⣀⣀⣀⣤⣿⣿⣿⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠐⠂⣉⣉⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠋⠉⠉⠉⠙⠉⠉⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣭⣽⣿⣷⣦⣤⣦⣤⣄⣀⣀⠀⠄⠀⠚⠛⡿⠿⠿⣿⣿⣿⣿⣯⣭⠉⠛⠛⢛⣛⣿⣭⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⠒⠀⠀⠀⠀⠤⠤⠤⢺⣿⣿⣿⣿⣿⣿⣿⡿⠷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡿⢻⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢏⣛⣋⣉⠛⠻⣿⣿⣟⣿⣯⡛⠛⠛⣉⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⢟⣛⠻⠿⠷⠾⠶⠤⠤⠤⠤⠤⠤⠤⠥⠀⠀⠀⠛⣛⣡⣴⣾⣿⣿⣿⣿⣿⣿⣟⡻⠿⣿⣿⣿⣿⣾⡟⣴⣿⡿⣿⣿⡏⠒⠛⠻⠿⠃⠻⢿⣿⣿⣭⣭⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣟⣿⣿⣿⣿⣿⣿⣿⣯⣿⠏⠛⢷⣦⣝⠻⠿⠻⣿⣿⣿⣟⡟⢋⣀⣀⠀⠰⢷⣄⣺⣤⡀⠉⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣷⣦⣄⠹⣿⡇⠀⠀⠹⣿⣿⣿⣿⣿⣿⠿⣳⣄⠀⠙⠿⢿⣿⡶⠶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠉⠉⠈⠁⠀⠀⠀⠈⠻⣿⣿⣯⣤⠾⠿⠿⠛⠂⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 830

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

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2024/11/11/Linux_6_12_rc7.shtml
    Gemini version at https://tuxmachines.org/n/2024/11/11/Linux_6_12_rc7.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Linux 6.12-
rc7⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Nov 11, 2024


    * ⚓ Kernel_prepatch_6.12-rc7⠀⇛


           Linus has released 6.12-rc7 for testing. ""No big surprises,
           and I think everything is on track for a final 6.12 release
           next weekend.""


    *      No big surprises, and I think everything is on track for a
           final 6.12
           release next weekend.


           We've got the usual random driver updates (with gpu and
           networking
           dominating - no surprises there either). The arch updates are
           mostly
           devicetree fixes, and we have some filesystem fixes (bcachefs,
           btrfs,
           nfs,  smb).


           Some core mm changes, mostly around error handling corner
           cases.


           Please give this some final "kick the tires" love,


                          Linus




                    ䷩ 𝚕𝚒𝚗𝚎 878

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

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2024/11/11/Microsoft_Windows_at_All_Time_Lows.shtml
    Gemini version at https://tuxmachines.org/n/2024/11/11/Microsoft_Windows_at_All_Time_Lows.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Microsoft Windows at All-Time
Lows⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Nov 11, 2024,
updated Nov 11, 2024


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Remembrance_Day⦈_


                       🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇TM thumbs-up⦈


TODAY was a slow news day, as expected, but there's some good_news_regarding
Microsoft. The global_market_share_of_Windows has fallen to new lows of 25% and
it's almost below 12% in India.


The way things sway, Microsoft will just go deeper and deeper into debt. It's
already about_100,000,000,000_US_dollars_in_debt. █




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⣤⣄⣀⠀⠀⢀⣤⡤⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠐⠂⠀⠀⠀⠀⠀⠘⠡⠀⣺⣇⣀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠐⡄⠀⢀⠿⠙⢻⣿⣷⡄⠀⠈⢻⠁⠀⠘⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠐⢀⡂⠀⣾⣿⠋⠀⠀⠐⣦⠀⠈⠛⢿⣦⠀⠀⠀⠙⠀⠀⠀⠻⢿⡄⣀⡀⠸⡀⢠⣴⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠒⠀⢠⣶⠂⠀⡀⠁⠠⣿⠿⠆⠀⠀⠘⠋⠀⠛⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠶⠀⠉⢿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠈⠀⠀⢘⢠⡄⠀⠒⠀⠀⠀⠀⠀⠀⠈⣿⡖⠀⣠⣶⣀⣠⠤⢠⡤⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⢴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡄⠀⠈⠀⠀⠀⠀⢀⠀⠀⠀⢠⣖⡾⠋⡁⠠⠶⠀⢠⣾⡀⢰⣶⢀⣨⣳⣾⣿⡿⣫⣿⣶⣦⡀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢤⣠⣄⢀⣠⣶⣞⣇⠀⠘⠁⠖⢧⣶⡔⡿⠁⢒⣰⣮⣿⠗⢾⣿⣿⣿⣿⣿⣋⣴⣿⣿⣿⣿⣷⡔⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢠⣟⠈⢁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠘⠿⠿⠋⠁⢻⣷⣿⣿⣿⣿⣶⣺⣿⣁⣤⡆⣸⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣷⣿⣾⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠁⣀⢠⢀⣄⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡤⣶⠄⢀⣤⣤⢠⠞⠋⠢⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⣮⠋⡛⢿⣿⡆⠀⠀⠀⠀⠀⠄⠀⠀⠀⣄⠸⠿⣤⡋⠀⠙⣟⢹⣾⣷⡴⠴⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⣶⣾⠛⠀⠈⢁⠀⠀⠀⠀⠈⠀⠀⠀⠀⣿⠀⢘⡟⢡⣶⣶⣿⡿⣛⣩⣾⣿⣮⣋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠘⠛⢡⣤⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⡏⠰⣿⠁⡾⠉⣭⣤⣼⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢹⣾⣿⣿⣿⣿⠂
⠀⠀⠈⠒⢀⡉⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⢠⣾⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠠⢅⡐⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠰⠀⣘⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠭⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⣸⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠊⠀⠀⠸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⣿⠀
⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁⠃⣰⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⠀⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢈⣤⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠿⠟⠿⠘⢛⣛⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣷⣶⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠈⡻⣟⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠟⠀⣠⣽⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⠀
⠀⠙⠉⠹⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⣤⣾⠋⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠠⡤⢠⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠋⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⢀⣈⡃⠀⠹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠾⠋⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣯⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠄⠈⣀⣄⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣤⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⠛⠃⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⢼⣶⣶⣀⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⣿⣿⣿⣿⣟⣁⣦⣠⣴⣿⣿⣿⣿⣿⣿⣿⣦⣤⣴⣷⣤⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠠⢾⣤⠈⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣠⣿⡇⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢀⡦⠀⢀⣌⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣤⣬⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠈⣿⢂⠉⠿⣯⣃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⣟⣿⣾⣷⣾⡿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠙⣿⠾⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢉⣀⣀⣀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⣿⣧⣶⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠈⣷⣿⣿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣣⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⢿⣾⡟⣛⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⢻⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⢿⣿⠁
⠀⡈⠙⠓⠻⢿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣞⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣵⣮⣿⠀
⢈⣟⣷⣶⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠸⢿⣿⣿⣿⣿⣇⣾⣿⡇
⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠘⡇⠈⠻⣿⣿⠄⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡇
⠈⠙⠛⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡙⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣼⣧⣀⣠⣤⣤⣀⣀⡀⠀⣼⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⢘⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⠃⠀⠈⣿⡿⠿⢿⣿⣿⣿⢿⣿⠋⠙⠹⡿⢟⣿⠃⠀⠻⣿⣽⣿⠃⠉⠉⠀
⠀⠒⠒⠒⠖⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⢈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⢹⣿⣿⣿⡇⠀⣹⣿⣿⣿⣿⡟⠀⠀⠀⠈⠀⠀⠀⠀⠉⠈⠀⠋⠀⠀⠀⠋⠉⠉⠀⠀⠀⢸⣿⠟⠀⠀⠀⠀
⢰⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢀⣀⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣷⡆⠀⡀⢠⠀⠀⣤⠀⣆⠀⠀⣿⡇⠀⠠⠟⠙⠿⠿⠛⠀⠎⠿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠉⠉⠉⠉⠉⠉⠙⠉⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠏⠙⠏⠉⠉⠁⠠⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠦⡀⠀⣽⣿⣻⣷⠟⠂⠀⠀⠀⠀⠀⣠⠴⠺⠶⠖⠒⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠉⠀⠀⠀⣶⣴⠟⠃⠀⠀⠊⠉⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⢀⡀⠀⠀⣠⣼⠏⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠂⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢰⡖⣿⡆⠀⠀⠀⠁⠢⠤⠴⢏⠢⡀⢀⣸⠆⡄⠐⠒⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡗⠼⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡻⠉⠙⡛⢡⣄⡀⠚⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠀⠀⡴⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⡀⠀⢀⣀⠀⠀⡀⠀⣀⠀⠀⠀⢀⡀⠀⢀⡀⠀⢀⡀⢈⣉⠁⠀⠀⢀⡀⠀⣀⡀⠀⣀⠀⠀⣀⠀⢀⡀⠀⠀⠀⡀⠀⠀⠀⣀⡀⠀⠀⢀⠈⠁⢀⠀⠀⣀⠀⣀⡀⠀⢈⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⡿⠀⠀⣿⠀⠀⠀⠀⠙⣧⠀⠀⢸⡇⠀⢸⡇⢀⠀⠀⠀⠹⣆⠀⠀⢻⡇⠀⢸⡇⢀⡿⠀⠀⣿⠀⢨⡗⠀⠀⠀⢻⡄⠀⠀⠈⠻⣆⠀⠀⠀⣴⠃⠀⠀⠘⠀⢸⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠹⣆⠀⠀⣿⠈⠁⠀⠀⠀⠹⣇⠀⢸⡇⠀⢸⡇⠈⠀⠀⠀⠀⢻⣄⠀⢸⡇⠀⢸⡇⠀⢹⡆⠀⣿⠀⢻⡄⠀⠀⠀⠈⢷⡀⠀⠀⠀⠘⢷⡄⠀⢿⡄⠀⠀⠀⠀⢸⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠚⠃⠀⠙⠂⠐⠛⠂⠀⠚⠀⠃⠀⠉⠀⠘⠓⠀⠘⠛⠀⠀⠚⢐⣂⠀⢃⠀⠚⠃⠀⠚⠃⠀⠚⢁⣀⡛⠂⢀⡛⠀⠒⠀⠀⠘⠓⠀⠒⠀⠀⠀⠁⠀⠀⠙⠂⠀⠀⠀⠚⠓⠀⠐⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠙⣦⠀⠀⠀⢿⡀⠀⠀⠙⣧⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠈⣷⠀⠀⠀⠘⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠄⠀⠔⠋⠀⠦⠀⠀⠸⠧⠀⠀⠰⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⡉⠭⢉⠉⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠿⠏⣋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⢉⠉⠉⠉⢩⡍⠉⠉⠉⢉⠉⠉⠉⠉⠉⠉⠩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠍⠉⠭⠄⠀⡇⡇⢸⢸⢠⣌⠁⡻⣫⢋⢌⣼⣿⣿⡇⠈⠀⠿⢡⠋⢨⣿⡏⠸⢁⢁⠀⠀⢠⢊⠭⣭⣄⣀⠀⢸⠘⠀⢸⢸⠀⠀⠀⠀⡇⠀⠀⢸⢸⠀⠈⠡⠩⠅⠀⠀⠫⢍⡿⡿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣀⣤⡀⢀⣴⣶⣤⣧⣇⢸⢸⢸⣿⢗⡕⣁⢣⣿⣿⣿⣿⡇⠀⢈⠂⢡⢠⠈⣿⢃⠃⠂⡄⡄⠀⠠⢻⣿⣿⣿⠋⠀⢸⢀⠀⢨⢸⠀⠀⠀⠀⡇⡄⠀⢼⣼⣴⣶⣤⡀⠸⠀⠀⣨⡭⣉⣵⡏⣿⣿⣿⣿⣿
⠀⠀⢠⣼⣿⣿⣿⡇⣉⡙⣿⣿⣷⣔⣊⢜⣼⣋⣊⢜⣤⣝⣻⢿⣿⣿⣧⣀⡘⡀⣁⣘⡀⢏⣈⡬⠭⢁⣰⠀⠈⠙⣛⣓⡩⠊⠀⢘⣸⠀⣘⣸⠀⣀⡀⢀⣃⡇⠐⢪⣿⠿⣛⣁⣀⣀⡀⠀⠀⣒⡡⣣⡇⣿⣿⣿⣿⣿
⠀⠀⠸⠿⣿⣿⣿⣷⣶⣶⣿⣿⣷⣶⣶⡿⣷⣶⣶⣿⣿⣶⣶⣶⣿⣿⣷⣶⣶⣿⣷⣤⣴⣦⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⣸⣿⡇⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢹⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⡏⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠁⠀⠀⣀⣿⣿⣿⣟⣻⣿⣿⢈⣍⣉⣉⣉⣉⣭⣭⣭⣥⣤⠀⣴⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠐⠚⠿⠿⢿⡿⠁⡀⢸⣽⣿⣿⣿⠿⠿⠿⢿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢌⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⢹⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⠲⠆⠀⠉⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⣿⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠀⠀⠂⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⣾⣿⡇⠀⠀⠀⣿⠀⠿
⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣶⣿⣿⣿⡆⠀⠀⠀⠀⠀⢀⡇⠀⠀⣿⣿⡇⠀⠀⠀⢻⡆⠀
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣼⣿⣿⣿⣿⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣹⡆⠀⠀⠀⠀⠀⠤⠀⠄⠀⠟⠘⠛⠛⠛⠛⠛⣇⠀⠀⠀⠀⢀⣿⡇⠀⠀⣿⣿⠀⠀⠀⠀⢸⡁⠀
⠀⣾⠀⠀⠀⠀⠀⠀⢀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⠀⠀⢰⣿⣿⠀⠀⠀⠀⢘⡇⠀
⢸⡇⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⡟⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⡇⠀
⠘⠁⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢻⣿⠁⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠁⠀
⡇⠀⠀⢠⣴⣶⣦⣄⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⣿⠀⠀⢸⢸⣿⠃⠀⠀⠀⠐⠀⠀⠀
⠀⠀⠈⠉⣿⣿⣿⠟⡆⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣠⡀⠀⠀⠀⠹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠋⠀⠀⡿⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣈⣿⣿⣄⠥⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣟⢧⠿⣿⠳⠀⠀⠀⠀⠉⠳⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠒⠶⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠁⠿⠛⠻⣿⡟⢛⡟⠁⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣶⡻⠛⣿⡀⠀⠀⠀⠀⠀⠀⠉⠐⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢠⣄⣀⢴⡞⠃⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⡉⠭⢍⠩⠿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠿⠯⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⢉⠉⠉⠉⢩⡍⠉⠉⠉⢉⠉⠉⠉⠉⠉⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠍⠉⠭⠄⠀⡇⡇⢸⢸⢠⣈⠁⡻⣫⢋⢎⣼⣿⣿⡇⠈⠀⠿⢡⠋⢨⣿⡏⠸⢁⢑⠀⠀⢠⢊⠭⣭⣅⣀⠀⢸⠘⠀⢸⢸⠀⠀⠀⠀⡇⠀⠀⢸⢸⠀⠈⠩⠩⠥⠄⠀⠫⢍⡿⡿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣀⣤⣤⡀⢀⣴⣶⣤⣧⣇⢸⢸⢸⣿⢗⡕⣁⢣⣿⣿⣿⣿⡇⠀⢈⠒⢡⢠⠘⣿⢃⠃⠂⡌⡄⠀⠠⢻⣿⣿⣿⠋⠀⢸⢀⠀⢨⢸⠀⠀⠀⠀⡇⡄⠄⢼⣼⣴⣶⣤⡀⠸⠀⠀⣨⡭⣉⣵⡏⣿⣿⣿⣿⣿
⠀⠀⣠⣽⣿⣿⣿⡇⣉⡙⣿⣿⣷⣔⣊⢜⣾⣋⣊⢜⣬⣝⣻⢿⣿⣿⣧⣀⡘⡀⣁⣘⡀⢏⣈⡬⠭⢁⣰⠀⠈⠙⣛⣓⡩⠊⠀⢘⣸⠀⣘⣸⠀⣀⡀⢀⣃⡇⠐⢪⣿⠿⣛⣁⣀⣀⡀⠀⠀⣒⡡⣣⡇⣿⣿⣿⣿⣿
⠀⠀⠸⠿⣿⣿⣿⣷⣶⣶⣿⣿⣷⣶⣶⡿⣷⣶⣶⣿⣿⣶⣶⣾⣿⣿⣷⣶⣶⣿⣷⣤⣴⣦⣤⡴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⣸⣿⡇⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢩⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⡏⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠁⠀⠀⣀⣿⣿⣿⣧⢻⣿⣿⢈⣍⣉⣉⣉⣉⣩⣭⣭⣤⣤⠀⣤⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠐⠚⠿⠿⢿⡿⠃⡀⢸⣹⣿⣿⣿⠿⠿⠿⢿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣎⢼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣹⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⠒⠆⠀⠉⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠀⠀⠆⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣾⣿⡇⠀⠀⠀⣿⠀⠟
⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣿⣿⣿⡆⠀⠀⠀⠀⠀⢀⡇⠀⠀⣿⣿⡇⠀⠀⠀⣿⡆⠀
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⣿⣿⣿⣿⠃⠀⠀⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣻⡆⠀⠀⠀⠀⠀⠴⠠⠠⠀⠟⠘⠛⠛⠛⠛⠛⣇⠀⠀⠀⠀⢀⣿⡅⠀⠀⣿⣿⠀⠀⠀⠀⢸⡇⠀
⠀⣾⠀⠀⠀⠀⠀⠀⢀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⣿⠀⠀⠀⠀⢸⡇⠀
⢸⡇⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⡟⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⡇⠀
⠘⠁⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢻⣿⠅⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠁⠀
⡇⠀⠀⢠⣴⣶⣶⣄⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⣿⠀⠀⣸⢸⣿⠇⠀⠀⠀⠐⠀⠀⠀
⠀⠀⠈⠉⣿⣿⣿⡝⡆⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣀⡀⠀⠀⠀⠻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⠋⠀⠀⡿⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣈⣿⣿⣥⣥⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣟⢧⠿⣿⠳⠀⠀⠀⠀⠉⠳⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠇⠖⠶⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠑⠿⠛⠻⣿⡟⠛⡟⠁⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣶⡻⠛⣷⡠⠀⠀⠀⠀⠀⠀⠉⠐⢂⣀⣀⣀⡠⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢠⣄⣀⢤⡞⠃⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⡉⠭⢍⠩⠿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠿⠟⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⢉⠉⠉⠉⢩⡍⠉⠉⠉⢉⠉⠉⠉⠉⠉⠉⠩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠍⠉⠭⠄⠀⡇⡇⢸⢸⢠⣈⠁⡺⣫⢋⢌⣼⣿⣿⡇⠈⠀⠿⢣⠋⢸⣿⡏⠸⢁⢁⠀⠀⢠⢊⠭⣭⣄⣀⠀⢸⠘⠀⢸⢸⠀⠀⠀⠀⡇⠀⠀⢸⢸⠀⠈⠩⠩⠥⠄⠀⠫⢍⡿⡿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣄⣤⣤⡀⢀⣴⣶⣤⣧⣇⢸⢸⢸⣿⢗⡕⣁⢣⣿⣿⣿⣿⡇⠀⢈⠖⢡⢠⠘⣿⢃⠃⠂⡌⡄⠀⠠⢻⣿⣿⣿⠋⠀⢸⢀⠀⢨⢸⠀⠀⠀⠀⡇⡄⠀⢼⣼⣴⣶⣤⡀⠸⠀⠀⣨⡭⣉⣵⡏⣿⣿⣿⣿⣿
⠀⠀⡨⣼⣿⣿⣿⡇⣉⡙⣿⣿⣷⣔⣊⢜⣾⣋⣊⢜⣬⣝⣻⢿⣿⣿⣧⣀⡘⡀⡁⣘⡀⣇⣈⡬⠭⢁⣰⠀⠈⠙⣛⣓⡩⠊⠀⢘⣸⠀⣘⣸⠀⣀⡀⢀⣃⡇⠐⢪⣿⠿⣛⣁⣀⣀⡀⠀⠀⣒⡡⣣⡇⣿⣿⣿⣿⣿
⠀⠀⠙⠻⣿⣿⣿⣷⣶⣶⣿⣿⣷⣶⣶⡿⣷⣶⣶⣿⣿⣶⣶⣾⣿⣿⣷⣶⣶⣿⣷⣤⣴⣦⣤⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⣸⣿⡇⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢩⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⡏⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠁⠀⠀⣀⣿⣿⣿⣟⢿⣿⣿⢈⣍⣉⣉⣉⣭⣩⣭⣭⣤⣤⠀⣤⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠐⠚⠿⠿⢿⡿⠃⠀⢸⣽⣿⣿⣿⠿⠿⠿⢿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣪⣺⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣹⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⠒⠖⠀⠋⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠀⠀⠆⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡕⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣾⣿⡇⠀⠀⠀⣿⠀⠟
⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣿⣿⣿⡆⠀⠀⠀⠀⠀⢀⡇⠀⠀⣿⣿⡇⠀⠀⠀⢻⡆⠀
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⣿⣿⣿⣿⠃⠀⠀⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣹⡆⠀⠀⠀⠀⠀⠤⠠⠄⠀⠟⠚⠛⠛⠛⠛⠛⣇⠀⠀⠀⠀⢀⣿⡃⠀⠀⣿⣿⠀⠀⠀⠀⢸⡃⠀
⠀⣾⠀⠀⠀⠀⠀⠀⢀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⣿⠀⠀⠀⠀⢸⡇⠀
⢸⡇⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⡟⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⡇⠀
⠘⠁⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢻⣿⡁⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠁⠀
⡇⠀⠀⢠⣴⣶⣶⣄⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⣿⠀⠀⣸⢹⣿⠇⠀⠀⠀⠐⠀⠀⠀
⠀⠀⠈⠉⣿⣿⣿⣝⡆⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣠⡀⠀⠀⠀⠹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⠋⠀⠀⡿⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣈⣿⣿⣥⣵⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣟⢧⠿⣿⠳⠀⠀⠀⠀⠉⠳⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠖⠶⠀⠀⠨⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠑⠿⠛⠻⣿⡟⠛⡟⠁⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣶⡻⠛⣷⡠⠀⠀⠀⠀⠀⠀⠉⠐⢂⣀⣀⣀⡀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢠⣄⣀⢤⡞⠃⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⡩⠭⢍⠩⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣉⠉⢉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⢉⠉⠉⠉⢩⡍⠉⠉⠉⢉⠉⠉⠉⠉⠉⠉⠩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠍⠉⠩⠄⠀⡇⡇⢸⢸⢠⣌⠁⡻⣫⢋⢎⣼⣿⣿⡇⠈⠀⠿⢣⠋⢨⣿⡏⠸⢁⢑⠀⠀⢠⢊⠭⣭⣄⣀⠀⢸⠸⠀⢸⢸⠀⠀⠀⠀⡇⠀⠀⢸⢸⠀⠈⠩⠩⠥⠀⠀⠫⢍⡿⡿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣠⣴⣤⣶⡀⢀⣴⣶⣤⣧⣇⢸⢸⢸⣿⢗⡅⣁⢣⣿⣿⣿⣿⡇⠀⢈⠒⢡⢠⠐⣿⢃⠃⠂⡄⡄⠀⠠⢻⣿⣿⣿⠋⠄⢸⢀⠀⢨⢸⠀⠀⠀⠀⡇⡄⠀⢼⣼⣴⣶⣤⡀⠸⠀⠀⣨⡭⣉⣵⡏⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣿⣿⡇⣉⡙⣿⣿⣷⣔⣊⢜⣾⣋⣊⢜⣬⣙⣻⢿⣿⣿⣇⣀⡘⡀⣁⣘⡀⣏⣈⡬⠭⢁⣰⠀⠈⠙⣛⣓⡩⠊⠀⢘⣸⠀⣘⣸⠀⣀⡀⢀⣃⡇⠐⢪⣿⠿⣛⣁⣀⣀⡀⠀⠀⣒⡡⣣⡇⣿⣿⣿⣿⣿
⠀⠀⠹⢿⣿⣿⣿⣷⣶⣶⣿⣿⣷⣶⣶⡿⣷⣶⣶⣿⣿⣶⣶⣶⣿⣿⣷⣶⣶⣿⣷⣦⣴⣶⣤⣔⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⣸⣿⡇⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢹⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⣭⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⡏⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠀⠀⠀⣀⣿⣿⣿⣿⢿⣿⣿⠈⣍⣉⣉⣉⣉⣩⣭⣥⣤⣤⠀⣴⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠐⠚⠿⠿⢿⡿⠃⠀⢸⣽⣿⣿⣻⡿⠟⠿⢿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠮⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣹⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⡗⠲⠀⠙⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⣿⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠀⠀⠂⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡂⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⡇⠀⠀⣾⣿⡇⠀⠀⠀⣿⠀⠟
⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣼⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⡇⠀⠀⣿⣿⡇⠀⠀⠀⣿⡆⠀
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣴⣿⣿⣿⣿⡇⠀⠀⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣹⡆⠀⠀⠀⠀⠀⠤⠠⠄⠀⠿⠘⠛⠛⠛⠛⠛⣇⠀⠀⠀⠀⢀⣿⡇⠀⠀⣿⣿⠀⠀⠀⠀⢸⡇⠀
⠀⣾⠀⠀⠀⠀⠀⠀⢀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⣿⠀⠀⠀⠀⢸⡇⠀
⢸⡇⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⡟⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⡇⠀
⠘⠁⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢿⣿⠇⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠁⠀
⡇⠀⠀⢠⣤⣶⣶⣄⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⣿⠀⠀⣸⢸⣿⠃⠀⠀⠀⠐⠀⠀⠀
⠀⠀⠈⠉⣿⣿⣿⢞⡆⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣠⡀⠀⠀⠀⠹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠸⠋⠀⠀⡿⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣈⣿⣿⣥⣵⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣟⢧⠿⣿⠳⠀⠀⠀⠀⠉⠳⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠖⠶⠀⠀⠨⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠁⠿⠛⠻⣿⡟⠛⡟⠁⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣦⡻⠛⣷⡡⠀⠀⠀⠀⠀⠀⠋⠐⢂⣀⣀⣀⡠⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢠⣄⣀⢤⡞⠃⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⡍⠭⢍⠩⠿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠿⠿⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⢉⠉⠉⠉⢩⡍⠉⠉⠉⢉⠉⠉⠉⠉⠉⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠍⠉⠩⠄⠀⡇⡇⢸⢸⢠⣈⠁⡻⣫⢋⢎⣼⣿⣿⡇⠈⠀⠿⢣⠋⢨⣿⡏⠸⢁⢑⠀⠀⢠⢊⠭⣭⣄⣀⠀⢸⠘⠀⢸⢸⠀⠀⠀⠀⡇⠀⠀⢸⢸⠀⠈⠩⠩⠥⠀⠀⠫⢍⡿⡿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣀⣤⣴⣶⡀⢀⣴⣶⣤⣧⣇⢸⢸⢸⣿⢗⡕⣁⢣⣿⣿⣿⣿⡇⠀⢈⠐⢡⢠⠘⣿⢁⠃⠂⡌⡄⠀⠠⢻⣿⣿⣿⠋⠀⢸⢀⠀⢨⢸⠀⠀⠀⠀⡇⡄⠀⢼⣼⣴⣶⣤⡀⠸⠀⠀⣨⡭⣉⣵⡏⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣿⣿⡇⣉⡙⣿⣿⣷⣔⣊⢜⣾⣋⣊⢜⣬⣝⣻⢿⣿⣿⣧⣀⡘⡀⣁⣘⡀⣇⣈⡬⠭⢁⣰⠀⠈⠙⣛⣓⡩⠊⠀⢘⣸⠀⣘⣸⠀⣀⡀⢀⣃⡇⠐⢪⣿⠿⣛⣁⣀⣀⡀⠀⠀⣒⡡⣣⡇⣿⣿⣿⣿⣿
⠀⠀⠸⠿⣿⣿⣿⣷⣶⣶⣿⣿⣷⣶⣶⡿⣷⣶⣶⣿⣿⣶⣶⣾⣿⣿⣷⣶⣶⣿⣷⣤⣴⣶⣤⣴⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⣸⣿⡇⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢹⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⡏⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠀⠀⠀⣀⣿⣿⣿⣿⢿⣿⣿⠈⣍⣉⣉⣉⣉⣩⣭⣥⣤⣤⠀⣤⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠐⠚⠿⠿⢿⣿⠃⠀⢸⣽⣿⣿⣻⡿⠟⠿⢿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣮⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣹⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⡗⠲⠀⠙⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠂⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⡇⠀⠀⣾⣿⡇⠀⠀⠀⣿⠀⠟
⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⠇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣼⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⡇⠀⠀⣿⣿⡇⠀⠀⠀⢿⡆⠀
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣴⣿⣿⣿⣿⡇⠀⠀⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣻⡆⠀⠀⠀⠀⠀⠴⠠⠀⠠⠿⠘⠛⠛⠛⠛⠛⣇⠀⠀⠀⠀⢀⣿⡇⠀⠀⣿⣿⠀⠀⠀⠀⢸⡆⠀
⠀⣾⠀⠀⠀⠀⠀⠀⢀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⣿⠀⠀⠀⠀⢸⡇⠀
⢸⡇⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⡟⠀⠀⢸⣿⡟⠀⠀⠀⠀⠈⡇⠀
⠘⠁⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢻⣿⠇⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠁⠀
⡇⠀⠀⢠⣤⣶⣶⣄⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⣿⠀⠀⣸⢹⣿⠇⠀⠀⠀⠐⠀⠀⠀
⠀⠀⠈⠉⣿⣿⣿⠟⡆⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣀⡀⠀⠀⠀⠹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⠋⠀⠀⡿⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣈⣿⣿⣥⣵⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣟⢧⠿⣿⠳⠀⠀⠀⠀⠉⠳⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠖⠶⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠁⠿⠛⠻⣿⡟⠛⡟⠁⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣶⡻⠛⣿⡡⠀⠀⠀⠀⠀⠀⠋⠐⢂⣀⣀⣀⡠⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢠⣄⣀⢤⡞⠃⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⡩⠭⢭⠍⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⢉⠉⠉⠉⢩⡏⠉⠉⠉⢉⠉⠉⠉⠉⠉⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠍⠉⠭⠄⠀⡇⡇⢸⢸⢠⣌⠁⡺⣫⢋⢎⣼⣿⣿⡇⠈⠀⠿⢣⠋⢨⣿⡟⠸⢁⢁⠀⠀⢠⢊⠭⣭⣄⣀⠀⢸⠘⠀⢸⢸⠀⠀⠀⠀⡇⠀⠀⢸⢸⠀⠈⠩⠩⠥⠀⠀⠫⢍⡿⡿⣿⣿⣿⣿⣿⣿
⠀⠀⡄⣦⣶⣶⣴⡀⢀⣴⣶⣦⣧⣇⢸⢸⢸⣿⢗⡕⣁⢣⣿⣿⣿⣿⡇⠀⢈⠐⢡⢠⠘⣿⢃⠃⠂⡄⡄⠀⠠⢻⣿⣿⣿⠋⠀⢸⢀⠀⢨⢸⠀⠀⠀⠀⡇⡄⠄⢼⣼⣴⣶⣤⡀⠸⠀⠀⣸⡭⣉⣵⡏⣿⣿⣿⣿⣿
⠀⠀⣼⣿⣿⣿⣿⡇⣉⡙⣿⣿⣷⣔⣊⢜⣾⣋⣊⢜⣬⣙⣻⢿⣿⣿⣧⣀⡘⡀⣁⣘⡀⢏⣈⡬⠭⢁⣰⠀⠈⠙⣛⣓⡩⠊⠀⢘⣸⠀⣘⣸⠀⣀⡀⢀⣃⡇⠐⢪⣿⠿⣛⣁⣀⣀⡀⠀⠀⣚⡡⣣⡇⣿⣿⣿⣿⣿
⠀⠀⠹⣿⣿⣿⣿⣷⣶⣶⣿⣿⣷⣶⣶⡿⢷⣶⣶⣿⣿⣶⣶⣶⣿⣿⣷⣶⣶⣿⣷⣦⣴⣶⣤⣤⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⣸⣿⡇⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢈⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⡟⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠁⠀⠀⢀⣿⣿⣿⣿⢿⣿⣿⠀⣍⣉⣉⣉⣍⣉⣭⣥⣤⣤⠀⣤⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠐⠛⠿⠿⢿⣿⠃⠀⢨⣯⣿⣿⣻⡿⠿⠿⢿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣹⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⡷⠶⠐⠛⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⣿⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡏⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣾⣿⡇⠀⠀⠀⣿⠀⠟
⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⢇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣾⣶⣿⣿⣿⡆⠀⠀⠀⠀⠀⢀⡇⠀⠀⣿⣿⡇⠀⠀⠀⣿⡆⠀
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣦⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣻⣆⠀⠀⠀⠀⠀⠤⠠⠀⠀⠿⠘⠛⠛⠛⠛⠛⣇⠀⠀⠀⠀⢀⣿⡇⠀⠀⣿⣿⠀⠀⠀⠀⢸⡇⠀
⠀⣾⠀⠀⠀⠀⠀⠀⢀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⠀⠀⢰⣿⣿⠀⠀⠀⠀⢸⡇⠀
⢸⡇⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⡟⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⡇⠀
⠘⠁⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢿⣿⠇⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠃⠀
⡇⠀⠀⢠⣴⣶⡶⣄⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⣿⠀⠀⣸⢹⣿⠇⠀⠀⠀⠐⠀⠀⠀
⠀⠀⠈⠉⣿⣿⣿⢝⡆⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣀⡀⠀⠀⠀⠹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠸⠋⠀⠀⡟⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣈⣿⣿⣤⣵⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣟⢧⡻⣿⠳⠀⠀⠀⠀⠉⠳⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠖⠶⠀⠀⠨⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠁⠿⠛⠻⣿⡿⠻⡟⠁⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣮⡻⠻⣷⡁⡀⠀⠀⠀⠀⠀⠋⠐⢂⣀⣀⣀⡠⢀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢠⣄⣀⢴⡞⠃⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⡩⠭⢍⠽⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢿⣿⣟⡉⡍⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⢉⠉⠉⠉⢩⡍⠉⠉⠉⢉⠉⠉⠉⠉⠉⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠍⠉⠭⠄⠀⡇⡇⢸⢸⢠⣌⠁⡻⣫⢋⢌⣼⣿⣿⡏⠈⠀⠿⢣⠋⢨⣿⡟⠸⢁⢁⠀⠀⢠⢊⠭⣭⣄⣀⠀⢸⠘⠀⢸⢸⠀⠀⠀⠀⡇⠀⠀⢸⢸⠀⠈⠩⠩⠥⠀⠀⠫⢍⡿⡿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣠⣠⣴⣶⡄⢀⣴⣶⣦⣧⣇⢸⢸⢸⣿⢗⡕⣁⢣⣿⣿⣿⣿⣇⠀⢈⠔⢡⢠⠘⣿⢁⠃⠂⡌⡄⠀⠠⢻⣿⣿⣿⠋⠀⢸⢀⠀⢨⢸⠀⠀⠀⠀⡇⡄⠄⢼⣼⣴⣶⣤⡀⠸⠀⠀⣸⡭⣉⣵⡏⣿⣿⣿⣿⣿
⠀⡄⢼⣿⣿⣿⣿⡇⣉⡙⣿⣿⣷⣔⣊⢜⣾⣋⣊⢜⣬⣙⣻⢿⣿⣿⣧⣀⡘⡀⣁⣘⡀⣏⣈⡬⠭⢁⣰⠀⠈⠙⣛⣓⡩⠊⠀⢘⣸⠀⣘⣸⠀⣀⡀⢀⣃⡇⠀⢪⣿⠿⣛⣁⣀⣀⡀⠀⠀⣚⡡⣣⡇⣿⣿⣿⣿⣿
⠀⠀⠹⣿⣿⣿⣿⣷⣶⣶⣿⣿⣷⣶⣶⡿⢷⣶⣶⣿⣿⣶⣶⣶⣿⣿⣷⣶⣶⣿⣷⣤⣴⣶⣤⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⣸⣿⡇⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢈⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⡿⠀⠂⠀⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠃⠀⠀⢀⣿⣿⣿⣿⢹⣿⣿⡇⣉⣉⣉⣉⣭⣭⣭⣥⣤⣤⠀⣴⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠐⠚⠿⠿⠿⣿⠏⠐⠀⣿⣿⣿⣿⡿⠿⠿⢿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣹⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣷⠶⠄⠜⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⣿⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠃⠀⠐⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣾⣿⡇⠀⠀⠀⣿⠀⠟
⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡏⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⡇⠀⠀⣿⣿⡇⠀⠀⠀⢿⡆⠀
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣦⣿⣿⣿⣿⡇⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣹⣆⠀⠀⠀⠀⠀⠴⠠⠀⠀⠿⠘⠛⠛⠛⠛⠛⣇⠀⠀⠀⠀⢀⣿⡇⠀⠀⣿⣿⠀⠀⠀⠀⢸⡆⠀
⠀⣾⠀⠀⠀⠀⠀⠀⢀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⠀⠀⢰⣿⣿⠀⠀⠀⠀⢸⡇⠀
⢸⡇⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⡟⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⡇⠀
⠘⠁⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢻⣿⠇⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠁⠀
⡇⠀⠀⢠⣴⣶⡶⣄⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⣿⠁⠀⣸⢹⣿⠇⠀⠀⠀⠐⠀⠀⠀
⠁⠀⠈⠉⣿⣿⣿⡞⡆⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣀⡀⠀⠀⠀⠻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠘⠋⠀⠀⡟⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣈⣿⣿⣤⣵⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣟⢧⡳⣿⠳⠀⠀⠀⠀⠉⠳⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠆⠶⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠁⠿⠛⠻⣿⡿⠻⡟⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣮⡻⠛⣷⡁⡀⠀⠀⠀⠀⠀⠉⠐⢂⣀⣀⣀⡠⢀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢠⣄⣀⢴⡾⠃⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⡉⠭⢍⠝⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣋⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⢉⠉⠉⠉⢩⡍⠉⠉⠉⢉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠍⠉⠭⠄⠀⡇⡇⢸⢸⢠⣌⣁⡻⣫⢋⢎⣼⣿⣿⡇⠈⠀⠿⢣⠋⢨⣿⡏⠸⢁⢁⠀⠀⢠⢊⠭⣭⣅⣀⠀⢸⠘⠀⢸⢸⠀⠀⠀⠀⡇⠀⠀⢸⢸⠀⠈⠩⠩⠥⠀⠀⠫⢍⡿⡿⣿⣿⣿⣿⣿⣿
⠀⠀⠄⢠⣠⣔⣐⡄⢀⣴⣶⣤⣧⣇⢸⢸⢸⣿⢗⡕⣁⢣⣿⣿⣿⣿⡇⠀⢈⠔⢡⢠⠘⣿⢁⠃⠂⡌⡄⠀⠠⢻⣿⣿⣿⠋⠄⢸⢀⠀⢨⢸⠀⠀⠀⠀⡇⡄⠀⢼⣼⣴⣶⣤⡀⠸⠀⠀⣸⡭⣉⣵⡏⣿⣿⣿⣿⣿
⠀⠀⣲⣿⣿⣿⣿⡇⣉⡙⣿⣿⣷⣔⣊⢜⣾⣋⣊⢜⣬⣝⣻⢿⣿⣿⣧⣀⡘⡀⡁⣘⡀⣏⣈⡬⠭⢁⣰⠀⠈⠙⣛⣓⡩⠊⠀⢘⣸⠀⣘⣸⠀⣀⡀⢀⣃⡇⠐⢪⣿⠿⣛⣁⣀⣀⡀⠀⠀⣚⡡⣣⡇⣿⣿⣿⣿⣿
⠀⠀⠹⣿⣿⣿⣿⣷⣶⣶⣿⣿⣷⣶⣶⣿⠷⣶⣶⣿⣿⣶⣶⣾⣿⣿⣷⣶⣶⣿⣷⣤⣴⣦⣤⣴⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⣼⣿⡇⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠈⢹⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⠏⠐⠀⢀⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⠏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢈⣉⣉⣉⣍⣩⣭⣥⣥⣤⠀⣴⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠐⠚⠿⠿⠿⣿⡟⠀⠂⣺⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣹⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣷⣦⣤⡈⠙⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⣿⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⡇⠀⠀⣾⣿⡇⠀⠀⠀⣿⠀⠿
⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣾⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⡇⠀⠀⣿⣿⡇⠀⠀⠀⣿⡆⠀
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣤⣿⣿⣿⣿⡇⠀⠀⠐⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⢻⡆⠀⠀⠀⠀⠀⠦⠠⠀⠀⠿⠘⠛⠛⠛⠛⠛⣇⠀⠀⠀⠀⢀⣿⡇⠀⠀⣿⣿⠀⠀⠀⠀⢸⡄⠀
⠀⣾⠀⠀⠀⠀⠀⠀⢀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⠀⠀⢰⣿⣿⠀⠀⠀⠀⢸⡇⠀
⢸⡇⠀⠀⠀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⡟⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⡇⠀
⠘⠁⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢻⣿⠅⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠃⠀
⡇⠀⠀⢠⣴⣶⡶⣄⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⣿⠀⠀⣸⢹⣿⠃⠀⠀⠀⠐⠀⠀⠀
⠁⠀⠈⠉⢿⣿⣿⠿⡆⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣀⡀⠀⠀⠀⠻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⠋⠀⠀⡟⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣈⣿⣿⣦⣵⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣟⣧⡳⣿⠳⠀⠀⠀⠀⠉⢷⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠇⠆⠶⠀⠁⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠁⠿⠛⠻⣿⡿⠻⡟⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣮⡳⠿⣷⡀⡀⠀⠀⠀⠀⠀⠋⠐⢂⣀⣀⣀⡠⢀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢠⣄⣀⢤⡞⠃⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⡉⠭⢉⠙⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣏⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⢉⠉⠉⠉⢩⡍⠉⠉⠉⢉⠉⠉⠉⠉⠉⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠍⠉⠭⠄⠀⡇⡇⢸⢸⢠⣌⣁⡻⣫⢋⢎⣼⣿⣿⡇⠈⠀⠿⢣⠋⢨⣿⡏⠸⢁⢁⠁⠀⢠⢊⠭⣭⣅⣀⠀⢸⠘⠀⢸⢸⠀⠀⠀⠀⡇⠀⠀⢸⢸⠀⠈⠩⠩⠥⠀⠀⠫⢍⡿⡿⣿⣿⣿⣿⣿⣿
⠀⠠⠀⣠⣴⣔⣴⡄⢀⣴⣶⣦⣧⣇⢸⢸⢸⣿⢗⡕⣁⢣⣿⣿⣿⣿⡇⠀⢈⠐⢡⢠⠘⣿⢁⠃⠂⡌⡄⠀⠠⢻⣿⣿⣿⠋⠄⢸⢀⠀⢨⢸⠀⠀⠀⠀⡇⡄⠀⢼⣼⣴⣶⣤⡀⠸⠀⠀⣸⡭⣉⣵⡏⣿⣿⣿⣿⣿
⠀⠄⢴⣿⣿⣿⣿⡇⣉⡙⣿⣿⣷⣔⣊⢜⣾⣋⣊⢜⣬⣝⣻⢿⣿⣿⣷⣀⡘⡀⡁⣘⡀⣏⣈⡬⠭⢁⣰⠀⠈⠙⣛⣓⡩⠊⠀⢘⣸⠀⣘⣸⠀⣀⡀⢀⣃⡇⠐⢪⣿⠿⣛⣁⣀⣀⡀⠀⠀⣚⡡⣣⡇⣿⣿⣿⣿⣿
⠀⠀⠹⢿⣿⣿⣿⣷⣶⣶⣿⣿⣷⣶⣶⣿⠷⣶⣶⣿⣿⣶⣶⣾⣿⣿⣷⣶⣶⣿⣷⣤⣴⣦⣤⣴⣰⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⣸⣿⡇⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠈⢹⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⠏⠐⠀⢀⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⠏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢈⣉⣉⣉⣭⣩⣭⣥⣥⣤⠀⣴⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠐⠚⠿⠿⠿⣿⡟⠀⠂⣺⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣹⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠛⣿⣿⣿⣷⣦⣤⡈⠙⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⣿⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣾⣿⡇⠀⠀⠀⣿⠀⠿
⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⡇⠀⠀⣿⣿⡇⠀⠀⠀⣿⠄⠀
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣤⣿⣿⣿⣿⡇⠀⠀⠐⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣹⡆⠀⠀⠀⠀⠀⠤⠠⠀⠀⠿⠘⠛⠛⠛⠛⠛⣇⠀⠀⠀⠀⢀⣿⡇⠀⠀⣿⣿⠀⠀⠀⠀⢸⡄⠀
⠀⣾⠀⠀⠀⠀⠀⠀⢀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⠀⠀⢰⣿⣿⠀⠀⠀⠀⢸⡇⠀
⢸⡇⠀⠀⢀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⡟⠀⠀⢸⣿⡟⠀⠀⠀⠀⠈⡇⠀
⠘⠁⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢻⣿⠅⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠃⠀
⡇⠀⠀⢠⣤⣶⡶⣄⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⣿⠀⠀⣸⢹⣿⠇⠀⠀⠀⠐⠀⠀⠀
⠁⠀⠈⠉⣿⣿⣿⡞⡆⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣀⡀⠀⠀⠀⠻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠘⠋⠀⠠⡟⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣈⣿⣿⣤⣵⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣟⣧⡳⣿⠳⠀⠀⠀⠀⠉⢷⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠖⠶⠀⠀⢨⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠁⠿⠛⠻⣿⡿⠻⡟⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣮⡳⠿⣷⡀⡀⠀⠀⠀⠀⠀⠋⠐⢂⣀⣀⣀⡠⢀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢠⣄⣀⢴⡞⠃⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⡭⠭⢭⠹⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⢉⠉⠉⠉⢩⡍⠉⠉⠉⢉⠉⠉⠉⠉⠉⠉⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠍⠉⠩⠄⠀⡇⡇⢸⢸⢰⣌⣁⡻⣫⢋⢎⣼⣿⣿⡇⠈⠀⠽⢡⠋⢨⣿⡏⠸⢁⢑⠧⠀⢠⢊⠭⣭⣄⣀⠀⢸⠸⠀⢸⢸⠀⠀⠀⠀⡇⠀⠀⢸⢸⠀⠈⠩⠩⠥⠀⠀⠫⢍⡿⡿⣿⣿⣿⣿⣿⣿
⠀⠀⣀⣤⣼⣤⣤⡄⢀⣴⣾⣤⣧⣇⢸⢸⢸⣿⢗⡕⣁⢣⣿⣿⣿⣿⡇⠀⢈⠐⢡⢠⠘⣿⢃⠃⠂⡌⡄⠀⠠⢻⣿⣿⣿⠋⠄⢸⢀⠀⢨⢸⠀⠀⠀⠀⡇⡄⠄⢼⣼⣴⣶⣤⡀⠸⠀⠀⣨⡭⣉⣵⡏⣿⣿⣿⣿⣿
⠀⣀⣺⣿⣿⣿⣿⡇⣉⡙⣿⣿⣷⣔⣊⢜⣾⣋⣊⢜⣬⣝⣻⢿⣿⣿⣧⣀⡘⡀⣃⣘⡀⢏⣈⡬⠭⢁⣰⠀⠈⠙⣛⣓⡩⠊⠀⢘⣸⠀⣘⣸⠀⣀⡀⢀⣃⡇⠐⢪⣿⠿⣛⣁⣀⣀⡀⠀⠀⣚⡡⣣⡇⣿⣿⣿⣿⣿
⠀⠀⠸⢿⣿⣿⣿⣷⣶⣶⣿⣿⣷⣶⣶⣿⡷⢶⣶⣿⣿⣶⣶⣾⣿⣿⣷⣶⣶⣿⣷⣤⣴⣶⣤⣶⣷⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⣼⣿⡇⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⠏⠀⠂⠀⣾⣿⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢀⣉⣉⣉⣭⣩⣭⣭⣤⣤⠀⣴⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠁⠑⠛⠿⠿⢿⣿⡟⠀⠂⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣹⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠛⣿⣿⣿⣾⣦⣄⡈⠙⠛⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⣿⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣣⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣼⣿⡇⠀⠀⠀⣿⠀⡿
⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⡇⠀⠀⣿⣿⡇⠀⠀⠀⢿⡄⠀
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣤⣿⣿⣿⣿⡇⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣹⣆⠀⠀⠀⠀⠀⠤⠠⠄⠀⠿⠚⠛⠛⠛⠛⠛⣧⠀⠀⠀⠀⢀⣿⡃⠀⠀⣿⣿⠀⠀⠀⠀⢸⡇⠀
⠀⣾⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⣿⠀⠀⠀⠀⢸⡇⠀
⢸⡇⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⡟⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⡇⠀
⠘⠁⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢻⣿⠇⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠓⠀
⡗⠀⠀⢀⣴⣶⡶⣄⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⣿⠂⠀⣸⢹⣿⠇⠀⠀⠀⠐⠀⠀⠀
⠁⠀⠈⠉⢿⣿⣿⠞⡆⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣀⡀⠀⠀⠀⠻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠼⠋⠀⠀⡿⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣈⣿⣿⣧⣷⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣟⣧⡳⣾⠷⠀⠀⠀⠀⠉⢷⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⡇⠆⠶⠀⠁⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠁⠿⠛⠻⣿⣿⢛⡟⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣮⡳⠟⣷⡃⡀⠀⠀⠀⠀⠀⠋⠐⣂⣀⣀⣀⡠⢀⠀⢁⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢠⣄⣀⢤⡞⠃⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⡩⠭⢍⡉⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⠿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⢉⠉⠉⠉⢩⡍⠉⠉⠉⢉⠉⠉⠉⠉⠉⠉⠩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠍⠉⠭⠄⠀⡇⡇⢸⢸⢠⣌⡁⡻⣫⢋⢎⣼⣿⣿⡏⠈⠀⠽⢡⠋⢸⣿⡏⠸⢁⢑⠇⠀⢠⢊⠭⣭⣄⣀⠀⢸⠸⠀⢸⢸⠀⠀⠀⠀⡇⠀⠀⢸⢸⠀⠈⠩⠩⠥⠀⠀⠫⢍⡿⡿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣴⣼⣦⣤⡄⢀⣴⣾⣤⣧⣇⢸⢸⢸⣿⢗⡕⣁⢣⣿⣿⣿⣿⡇⠀⢈⠒⢡⢠⠘⣿⢃⠃⠂⡌⡤⠀⠠⢻⣿⣿⣿⠋⠄⢸⢀⠀⢨⢸⠀⠀⠀⠀⡇⡄⠄⢼⣼⣴⣶⣤⡀⠸⠀⠀⣨⡯⣉⣵⡏⣿⣿⣿⣿⣿
⠀⢰⣾⣿⣿⣿⣿⡇⣉⡙⣿⣿⣷⣔⣊⢜⣾⣋⣊⢜⣤⣝⣻⢿⣿⣿⣧⣀⡘⡀⣃⣘⡀⢏⣈⡬⠭⢁⣰⠀⠈⠙⣛⣓⡩⠊⠀⢘⣸⠀⣘⣸⠀⣀⡀⢀⣃⡇⠐⢪⣿⠿⣛⣁⣀⣀⡀⠀⠀⣚⡡⣣⡇⣿⣿⣿⣿⣿
⠀⠀⠸⠿⣿⣿⣿⣷⣶⣶⣿⣿⣷⣶⣶⣿⡷⣶⣶⣿⣿⣶⣶⣶⣿⣿⣷⣶⣶⣿⣷⣤⣴⣶⣤⣴⣥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⣼⣿⡇⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⠏⠐⠂⠀⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡟⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⢈⣉⣉⣩⣍⣩⣭⣭⣤⣤⠀⣴⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠉⠑⠛⠿⠿⠿⣿⡟⠀⠂⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠺⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣹⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠛⣿⣿⣿⣿⣶⢤⡄⠉⠋⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠲⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⣿⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣼⣿⡇⠀⠀⠀⣿⠀⡿
⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⡇⠀⠀⣿⣿⡇⠀⠀⠀⢿⡆⠀
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣤⣿⣿⣿⣿⡇⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣹⣆⠀⠀⠀⠀⠀⠴⠠⠀⠀⠿⠚⠛⠛⠛⠛⠛⣧⠀⠀⠀⠀⢀⣿⡃⠀⠀⣿⣿⠁⠀⠀⠀⢸⡇⠀
⠀⣾⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⣿⠀⠀⠀⠀⢸⡇⠀
⢸⡇⠀⠀⠀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⡟⠀⠀⢸⣿⡟⠀⠀⠀⠀⠈⡇⠀
⠘⠁⠀⠀⠀⠀⠈⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢿⣿⡇⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠱⠀
⡗⠀⠀⢠⣴⣶⡦⣄⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⣿⠂⠀⣸⢹⣿⠇⠀⠀⠀⠘⠀⠀⠀
⠁⠀⠈⠉⢿⣿⣿⠞⡆⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣀⡀⠀⠀⠀⠻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠼⠛⠀⠀⡿⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣈⣿⣿⣦⣷⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣟⢯⡳⣾⠷⠀⠀⠀⠀⠉⢷⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⠇⠆⠶⠀⠁⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠁⠿⠛⠻⣿⣿⠻⡟⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣮⡳⠟⣷⡂⡀⠀⠀⠀⠀⠀⠋⠐⢂⣀⣀⣀⡠⢄⠀⢁⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢠⣄⣀⢤⡞⠃⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⡩⠭⢍⠩⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠽⣋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⢉⠉⠉⠉⢩⡍⠉⠉⠉⢉⠉⠉⠉⠉⠉⠉⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣀⡀⠀⠀⠀⠍⠉⠩⠄⠀⡇⡇⢸⢸⢠⣌⠁⡻⣫⢋⢎⣼⣿⣿⡏⠈⠀⠿⢡⠋⢸⣿⡏⠸⢁⢑⠗⠀⢠⢊⠭⣭⣅⣀⠀⢸⠸⠀⢸⢸⠀⠀⠀⠀⡇⠀⠀⢸⢸⠀⠈⠩⠩⠥⠄⠀⠫⢍⡿⡿⣿⣿⣿⣿⣿⣿
⠀⠀⣀⣦⣦⣦⣴⡄⢀⣴⣶⣦⣧⣇⢸⢸⢸⣿⢗⡕⣁⢣⣿⣿⣿⣿⡇⠀⢈⠔⢡⢠⠘⣿⢃⠃⠂⡌⡼⠀⠠⢻⣿⣿⣿⠋⠀⢸⢀⠀⢨⢸⠀⠀⠀⠀⡇⡄⠄⢼⣼⣴⣶⣤⡀⠸⠀⠀⣨⡭⣉⣵⡏⣿⣿⣿⣿⣿
⠀⣼⣥⣿⣿⣿⣿⣇⣉⡙⣿⣿⣷⣔⣊⢜⣾⣏⣊⢜⣬⣝⣻⢿⣿⣿⣧⣀⡘⡀⣃⣘⡀⢏⣈⡬⠭⢁⣰⠀⠈⠙⣛⣓⡩⠊⠀⢘⣸⠀⣘⣸⠀⣀⡀⢀⣃⡇⠐⢪⣿⠿⣛⣁⣀⣀⡀⠀⠀⣒⡡⣣⡇⣿⣿⣿⣿⣿
⠀⠀⠸⢿⣿⣿⣿⣷⣶⣶⣿⣿⣷⣶⣶⣿⡷⣶⣶⣿⣿⣶⣶⣾⣿⣿⣷⣶⣶⣿⣷⣤⣴⣦⣤⣴⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⣼⣿⡇⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⠏⠀⠂⠀⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡟⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⢈⣍⣉⣉⣭⣭⣭⣥⣤⣤⠀⣴⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠐⠛⠿⠿⠿⣿⡟⠀⠂⣸⣿⣿⡿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣹⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠛⣿⣿⣿⣿⣶⢤⡀⠉⠋⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⣿⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣼⣿⡇⠀⠀⠀⣿⠀⡿
⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⢀⢰⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⡇⠀⠀⣿⣿⡇⠀⠀⠀⣿⡄⠀
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣤⣿⣿⣿⣿⡇⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣹⣆⠀⠀⠀⠀⠀⠴⠠⠄⠀⠿⠚⠛⠛⠛⠛⠛⣧⠀⠀⠀⠀⢀⣿⡃⠀⠀⣿⣿⠁⠀⠀⠀⢸⡇⠀
⠀⣾⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⠀⠀⢰⣿⣿⠀⠀⠀⠀⢸⡇⠀
⢸⡇⠀⠀⠀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⡟⠀⠀⢸⣿⡟⠀⠀⠀⠀⠈⡇⠀
⠘⠁⠀⠀⠀⠀⠈⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢿⣿⡇⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠁⠀
⡗⠀⠀⢠⣴⣶⡦⣄⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⣿⠂⠀⣸⢹⣿⠇⠀⠀⠀⠘⠀⠀⠀
⠁⠀⠈⠉⢿⣿⣿⠞⡆⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣀⡀⠀⠀⠀⠻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠼⠋⠀⠀⡿⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣈⣿⣿⣦⣷⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣟⢯⡳⣾⠷⠀⠀⠀⠀⠉⢷⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠖⠶⠀⠁⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠁⠿⠛⠻⣿⣟⠻⡟⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣮⡳⠟⣷⡂⡀⠀⠀⠀⠀⠀⠋⠐⢂⣀⣀⣀⡠⢄⠀⢁⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢠⣄⣀⢤⡞⠃⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⡩⠭⢭⠭⢿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠯⠭⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⢉⠉⠉⠉⠩⡍⠉⠉⠉⢉⠉⠉⠉⠉⠉⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠍⠉⠭⠄⠀⡇⡇⢸⢸⢠⣌⠁⡻⣫⢋⢎⣼⣿⣿⡇⠈⠀⠿⢣⠋⢸⣿⡏⠸⢁⢑⠅⠀⢠⢊⠭⣭⣄⣀⠀⢸⠸⠀⢸⢸⠀⠀⠀⠀⡇⠀⠀⢸⢸⠀⠈⠩⠩⠥⠄⠀⠫⢍⡿⡿⣿⣿⣿⣿⣿⣿
⠀⠀⢄⣄⣤⣤⣴⡀⢀⣴⣶⣤⣧⣇⢸⢸⢸⣿⢗⡕⣁⢣⣿⣿⣿⣿⡇⠀⢈⠖⢡⢠⠘⣿⢁⠃⠂⡌⡄⠀⠠⢻⣿⣿⣿⠋⠀⢸⢀⠀⢨⢸⠀⠀⠀⠀⡇⡄⠄⢼⣼⣴⣶⣤⡀⠸⠀⠀⣨⡭⣉⣵⡏⣿⣿⣿⣿⣿
⠀⣀⣼⣿⣿⣿⣿⡇⣉⡙⣿⣿⣷⣔⣊⢜⣾⣋⣊⢜⣬⣝⣻⢿⣿⣿⣧⣀⡘⡀⡃⣘⡀⢏⣈⡬⠭⢁⣰⠀⠈⠙⣛⣓⡩⠊⠀⢘⣸⠀⣘⣸⠀⣀⡀⢀⣃⡇⠀⢪⣿⠿⣛⣁⣀⣀⡀⠀⠀⣚⡡⣣⡇⣿⣿⣿⣿⣿
⠀⠀⠰⢿⣿⣿⣿⣷⣶⣶⣿⣿⣷⣶⣶⣿⠷⣶⣶⣿⣿⣶⣶⣾⣿⣿⣷⣶⣶⣿⣷⣦⣴⣶⣤⡴⡶⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⣼⣿⡇⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠈⣹⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⠏⠀⠀⢀⣿⣿⣿⣿⣿⣿⡷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠏⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⢈⣉⣉⣩⣭⣭⣭⣥⣤⣤⠀⣴⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠐⠛⠿⠿⢿⣿⡟⠀⠂⣸⣿⣿⡿⣿⣿⡿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⢽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣹⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⣿⣿⣿⣿⡶⠤⡄⠉⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡁⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⣿⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠃⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣼⣿⡇⠀⠀⠀⣿⠀⠿
⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣾⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⡇⠀⠀⣿⣿⡇⠀⠀⠀⢿⡆⠀
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣤⣿⣿⣿⣿⡇⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣹⣆⠀⠀⡀⠀⠀⢤⠠⠀⠀⠿⠚⠛⠛⠛⠛⠛⣧⠀⠀⠀⠀⢀⣿⡃⠀⠀⣿⣿⠁⠀⠀⠀⢸⡇⠀
⠀⣾⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⠀⠀⢰⣿⣿⠀⠀⠀⠀⢸⡇⠀
⢸⡇⠀⠀⠀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⡟⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⡇⠀
⠘⠁⠀⠀⠀⠀⠈⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢿⣿⠗⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⢃⠀
⡗⠀⠀⢀⣴⣶⣦⣄⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⣿⠀⠀⣸⢹⣿⠇⠀⠀⠀⠘⠀⠀⠀
⠁⠀⠈⠉⢿⣿⣿⠞⡆⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣀⡀⠀⠀⠀⠻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠼⠛⠀⠀⡿⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣈⣿⣿⣦⣷⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣟⢧⡳⣾⠳⠀⠀⠀⠀⠉⢷⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠘⠇⠖⠶⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠁⠿⠛⠻⣿⣟⠻⡟⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣮⡻⠟⣷⡂⡀⠀⠀⠀⠀⠀⠋⠐⢒⣀⣀⣀⡠⢄⠀⢁⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢠⣄⣀⢤⡞⠃⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⡩⠭⢍⠩⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠭⢭⡩⢍⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⢉⠉⠉⠉⠩⡍⠉⠉⠉⢉⠉⠉⠉⠉⠉⠉⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠍⠉⠭⠄⠀⡇⡇⢸⢸⢰⣌⠁⡺⣫⢋⢎⣼⣿⣿⡇⠈⠀⠿⢣⠋⢸⣿⡏⠸⢁⢁⠁⠀⢠⢊⠭⣭⣄⣀⠀⢸⠘⠀⢸⢸⠀⠀⠀⠀⡇⠀⠀⢸⢸⠀⠈⠩⠩⠥⠀⠀⠫⢍⡿⡿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣰⣶⣶⣶⡄⢀⣴⣾⣦⣥⣇⢸⢸⢸⣿⢗⡕⣁⢣⣿⣿⣿⣿⡇⠀⢈⠐⢡⢠⠘⣿⢃⠃⠂⡌⡄⠀⠠⢻⣿⣿⣿⠋⠀⢸⢀⠀⢨⢸⠀⠀⠀⠀⡇⡄⠀⢼⣼⣴⣶⣤⡀⠸⠀⠀⣸⡭⣉⣵⡏⣿⣿⣿⣿⣿
⠀⣄⣸⣿⣿⣿⣿⡇⣉⡙⣿⣿⣷⣔⣊⢜⣾⣋⣊⢜⣬⣝⣻⢿⣿⣿⣧⣀⡘⡀⣁⣘⡀⢏⣈⡬⠭⢁⣰⠀⠈⠙⣛⣓⡩⠊⠀⢘⣸⠀⣘⣸⠀⣀⡀⢀⣃⡇⠐⢪⣿⠿⣛⣁⣀⣀⡀⠀⠀⣒⡡⣣⡇⣿⣿⣿⣿⣿
⠀⠀⠸⢿⣿⣿⣿⣷⣶⣶⣿⣿⣷⣶⣶⡿⢷⣶⣶⣿⣿⣶⣶⣶⣿⣿⣷⣶⣶⣿⣷⣦⣶⣶⣤⣴⣒⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⣸⣿⡇⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠈⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⡿⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⠃⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⡇⣩⣉⣉⣉⣭⣩⣭⣭⣤⣤⠀⣴⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠁⠑⠛⠿⠿⢿⣿⠏⠘⢀⣯⣿⣿⣿⡿⠿⠿⢿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠪⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣹⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣷⠶⠀⠈⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⣿⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠁⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⡇⠀⠀⣼⣿⡇⠀⠀⠀⣿⠀⠟
⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡏⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣿⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⡇⠀⠀⣿⣿⡇⠀⠀⠀⣿⡆⠀
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣴⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣸⣆⠀⠀⠀⠀⠀⠴⠠⠀⠀⠿⠚⠛⠛⠛⠛⠛⣧⠀⠀⠀⠀⢀⣾⡇⠀⠀⣿⣿⠁⠀⠀⠀⢸⡇⠀
⠀⣾⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⠀⠀⢰⣿⣿⠀⠀⠀⠀⢸⡇⠀
⢸⡏⠀⠀⠀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⡟⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⡇⠀
⠘⠁⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢿⣿⠇⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠃⠀
⡇⠀⠀⠀⣤⣶⣦⣄⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣸⣿⠀⠀⣸⢹⣿⠇⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠈⠉⢿⣿⣿⡿⡆⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⣠⡀⠀⠀⠀⠙⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠜⠋⠀⠀⡿⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣈⣿⣿⣦⢷⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣟⢧⡿⣿⠹⠀⠀⠀⠀⠈⠱⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⡇⠆⠶⠀⠀⢨⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠁⠿⠛⠻⣿⣿⢻⡟⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣦⡻⠟⢷⡂⡀⠀⠀⠀⠀⠀⠉⠐⢒⣀⣀⣀⡠⢄⠀⢁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢠⣄⣀⢤⡞⠃⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⡉⠭⢩⠭⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠯⠭⣉⢉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⢉⠉⠉⠉⢩⡍⠉⠉⠉⢉⠉⠉⠉⠉⠉⠉⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠍⠉⠭⠄⠀⡇⡇⢸⢸⢰⣌⠁⡺⣫⢋⢌⣼⣿⣿⡏⠈⠀⠿⢣⠋⢨⣿⡏⠸⢁⢁⠄⠀⢠⢊⠭⣭⣄⣀⠀⢸⠘⠀⢸⢸⠀⠀⠀⠀⡇⠀⠀⢸⢸⠀⠈⠩⠩⠥⠀⠀⠫⢍⡿⡿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣼⣶⣦⣦⡄⢀⣴⣾⣦⣧⣇⢸⢸⢸⣿⠗⡅⣁⢣⣿⣿⣿⣿⣗⠀⢈⠔⢡⢠⠘⣿⢃⠃⠂⡌⡄⠀⠠⢻⣿⣿⣿⠋⠀⢸⢀⠀⢨⢸⠀⠀⠀⠀⡇⡄⠀⢼⣼⣴⣶⣤⡀⠸⠀⠀⡸⡭⣉⣵⡇⣿⣿⣿⣿⣿
⠀⣄⣲⣿⣿⣿⣿⡇⣉⡙⣿⣿⣷⣔⣊⢜⣾⣋⣊⢜⣬⣝⣻⢿⣿⣿⣧⣀⡘⡀⣃⣘⡀⣏⣈⡬⠭⢁⣰⠀⠈⠙⣛⣓⡩⠊⠀⢘⣸⠀⣘⣸⠀⣀⡀⢀⣃⡇⠐⢪⣿⠿⣛⣁⣀⣀⡀⠀⠀⣒⡡⣣⡇⣿⣿⣿⣿⣿
⠀⠀⠹⣿⣿⣿⣿⣷⣶⣶⣿⣿⣷⣶⣶⠿⢷⣶⣶⣿⣿⣶⣶⣶⣿⣿⣷⣶⣶⣿⣷⣦⣶⣦⣤⣴⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⣼⣿⡇⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢨⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⡏⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⡿⠀⠀⣀⣠⣿⣿⣿⣟⣿⣿⣿⠈⣉⣉⣉⣉⣭⣭⣭⣭⣤⣤⠀⣴⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠐⠛⠿⠿⢿⣿⠃⠈⢰⣿⣿⣿⣿⣟⡛⠛⠻⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣩⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡟⠛⣶⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣿⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⢰⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣼⣿⡇⠀⠀⠀⣿⡄⡟
⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡟⠀⠈⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⣿⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⡇⠀⠀⣿⣿⡇⠀⠀⠀⣿⡄⠀
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣸⣆⠀⠀⠀⠀⠀⠤⠰⠄⠀⠿⠚⠛⠛⠛⠛⠛⣇⠀⠀⠀⠀⢀⣾⠃⠀⠀⣿⣿⠀⠀⠀⠀⢸⡇⠀
⠀⣾⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⠀⠀⢰⣿⣿⠀⠀⠀⠀⢸⡇⠀
⢸⡏⠀⠀⠀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⡟⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⡇⠀
⠘⠁⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢿⣿⠇⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠃⠀
⡇⠀⠀⠀⣴⣶⣦⣄⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣸⣿⠀⠀⣸⢹⣿⠇⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠈⠁⢿⣿⣿⡾⡆⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⣠⡀⠀⠀⠀⠙⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠜⠋⠀⠀⡿⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣈⣿⣿⣧⢷⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣟⢧⡿⣿⡹⠀⠀⠀⠀⠈⠱⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠆⠶⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠁⠿⠛⠻⣿⣿⢻⡟⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣦⡻⠟⢷⡂⡀⠀⠀⠀⠀⠀⠉⠐⢒⣀⣀⣀⡠⢀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢠⣄⣀⢤⡞⠃⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⡩⠭⢭⠩⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠭⣍⠉⡉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⢉⠉⠉⠉⢩⡍⠉⠉⠉⢉⠉⠉⠉⠉⠉⠉⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠍⠉⠭⠄⠀⡇⡇⢸⢸⢰⣌⠁⡺⣫⢋⢎⣼⣿⣿⡇⠈⠀⠽⢣⠋⢸⣿⡏⠸⢁⢁⠄⠀⢠⢊⠭⣭⣄⣀⠀⢸⠘⠀⢸⢸⠀⠀⠀⠀⡇⠀⠀⢸⢸⠀⠈⠩⠩⠥⠀⠀⠫⢍⡿⡿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣴⣶⣦⣴⡄⢀⣴⣾⣤⣧⣇⢸⢸⢸⣿⢗⡕⣁⢣⣿⣿⣿⣿⡷⠀⢈⠔⢡⢠⠘⣿⢃⠃⠂⡌⡄⠀⠠⢻⣿⣿⣿⠋⠀⢸⢀⠀⢨⢸⠀⠀⠀⠀⡇⡄⠀⢼⣼⣴⣶⣤⡀⠸⠀⠀⣸⡭⣉⣵⡇⣿⣿⣿⣿⣿
⠀⣄⣳⣿⣿⣿⣿⡇⣉⡙⣿⣿⣷⣔⣊⢜⣾⣋⣊⢜⣬⣙⣻⢿⣿⣿⣧⣀⡘⡀⣃⣘⡀⣏⣈⡬⠭⢁⣰⠀⠈⠙⣛⣓⡩⠊⠀⢘⣸⠀⣘⣸⠀⣀⡀⢀⣃⡇⠐⢪⣿⠿⣛⣁⣀⣀⡀⠀⠀⣒⡡⣣⡇⣿⣿⣿⣿⣿
⠀⠀⠸⢿⣿⣿⣿⣷⣶⣶⣿⣿⣷⣶⣶⠿⢷⣶⣶⣿⣿⣶⣶⣶⣿⣿⣷⣶⣶⣿⣷⣦⣴⣶⣤⣴⠖⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⣸⣿⡇⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢨⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⡏⠀⠂⠀⣾⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⡿⠁⠀⣀⣠⣿⣿⣿⣟⣿⣿⣿⠈⣉⣉⣉⣩⣭⣭⣭⣭⣤⣤⠀⣴⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠁⠐⠛⠿⠿⢿⣿⠃⠈⢰⣿⣿⣿⣿⣟⡛⠛⠻⣿⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣩⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡟⠛⣶⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣿⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠠⢰⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣼⣿⡇⠀⠀⠀⣿⠄⡟
⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡟⠀⠈⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣾⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⡇⠀⠀⣿⣿⡇⠀⠀⠀⣿⡂⠀
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⢹⣆⠀⠀⠀⠀⠀⠤⠰⠀⠀⠿⠒⠛⠛⠛⠛⠛⣇⠀⠀⠀⠀⢀⣾⡃⠀⠀⣿⣿⠀⠀⠀⠀⢸⡇⠀
⠀⣾⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⠀⠀⢰⣿⣿⠀⠀⠀⠀⢸⡇⠀
⢸⡏⠀⠀⠀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⣟⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⡇⠀
⠘⠁⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢿⣿⠇⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠁⠀
⡇⠀⠀⠀⣴⣶⣦⣄⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⣿⠀⠀⣸⢹⣿⠇⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠈⠁⢿⣿⣿⡾⡆⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⣠⡀⠀⠀⠀⠙⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠜⠋⠀⠀⡿⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣈⣿⣿⣧⢷⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣟⢧⡿⣿⡹⠀⠀⠀⠀⠈⠱⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠇⠆⠶⠀⠀⢈⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠁⠿⠛⠻⣿⣿⢻⡟⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⡻⠟⢷⡂⡀⠀⠀⠀⠀⠀⠉⠐⢒⣀⣀⣀⡠⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢠⣄⣀⢴⡞⠃⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⡭⠉⢍⠙⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⢉⠉⠉⠉⠩⡍⠉⠉⠉⢉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡀⠀⠀⠀⠍⠉⠩⠄⠀⡇⡇⢸⢸⢰⣌⠁⡻⣫⢋⢎⣼⣿⣿⡇⠈⠀⠿⢣⠋⢸⣿⡏⠸⢁⢁⠀⠀⢠⢊⠭⣭⣄⣀⠀⢸⠘⠀⢸⢸⠀⠀⠀⠀⡇⠀⠀⢸⢸⠀⠈⠩⠩⠥⠀⠀⠫⢍⡿⡿⣿⣿⣿⣿⣿⣿
⠀⠀⢠⣷⣶⣴⣤⡄⢀⣴⣶⣦⣧⣇⢸⢸⢸⣿⢗⡕⣁⢣⣿⣿⣿⣿⡇⠀⢈⠔⢡⢠⠘⣿⢁⠃⠂⡌⡄⠀⠠⢻⣿⣿⣿⠋⠁⢸⢀⠀⢨⢸⠀⠀⠀⠀⡇⡄⠀⢼⣼⣴⣶⣤⡀⠸⠀⠀⣨⡭⣉⣵⡇⣿⣿⣿⣿⣿
⠀⣤⣿⣿⣿⣿⣿⡇⣉⡙⣿⣿⣷⣔⣊⢜⣾⣋⣊⢜⣬⣝⣻⢿⣿⣿⣧⣀⡘⡀⣃⣘⡀⣇⣈⡬⠭⢁⣰⠀⠈⠙⣛⣓⡩⠊⠀⢘⣸⠀⣘⣸⠀⣀⡀⢀⣃⡇⠐⢪⣿⠿⣛⣁⣀⣀⡀⠀⠀⣒⡡⣣⡇⣿⣿⣿⣿⣿
⠀⠀⠸⢿⣿⣿⣿⣷⣶⣶⣿⣿⣷⣶⣶⣿⣷⣶⣶⣿⣿⣶⣶⣶⣿⣿⣷⣶⣶⣿⣷⣦⣶⣦⣤⡴⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⣸⣿⡇⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠈⢉⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⡟⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠁⠀⠀⢀⣾⣿⣿⣟⣿⣿⣿⠈⣉⣉⣉⣉⣭⣍⣭⣭⣤⣄⠀⣴⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠁⠐⠛⠿⠿⢿⣿⠃⠀⢰⣿⣿⣿⣿⡿⠿⠿⠿⣿⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡺⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣹⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⡗⠶⣶⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⣿⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣧⢴⣿⠉⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⡇⠀⠀⣼⣿⡇⠀⠀⠀⣿⠀⡿
⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠁⠈⠉⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣾⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⡇⠀⠀⣿⣿⡇⠀⠀⠀⢿⡆⠀
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣤⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⢹⣆⠀⠀⠀⠀⠀⢤⠰⠀⠀⠿⠐⠛⠛⠛⠛⠛⣧⠀⠀⠀⠀⢀⣾⠇⠀⠀⣿⣿⠁⠀⠀⠀⢸⡇⠀
⢠⡿⠀⠀⠀⠀⠀⠀⢀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⣿⠀⠀⠀⠀⢸⡇⠀
⣼⡇⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⡟⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⡇⠀
⠛⠀⠀⠀⠀⠀⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢿⣿⡇⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠃⠀
⡇⠀⠀⢠⣤⣶⣦⣄⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⣿⠀⠀⢸⢹⣿⠇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠈⢿⣿⣿⡿⡄⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⣀⡀⠀⠀⠀⠻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠜⠋⠀⠀⡿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣈⣿⣿⣧⢷⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⡟⣥⢷⣿⠳⠀⠀⠀⠀⠈⠱⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠇⠆⠶⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠁⠿⠛⠻⣿⣿⠻⡟⠁⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣮⡻⠛⣷⡃⡀⠀⠀⠀⠀⠀⠉⠐⢒⣀⣀⣀⡠⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢠⣄⣀⢴⡞⠃⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⡩⠭⢭⡹⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠭⣍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⢉⠉⠉⠉⢩⡍⠉⠉⠉⢉⠉⠉⠉⠉⠉⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠍⠉⠭⠄⠀⡇⡇⢸⢸⢰⣌⠁⡺⣫⢋⢎⣼⣿⣿⡇⠈⠀⠿⢣⠋⢸⣿⡏⠸⢁⢁⠈⠀⢠⢊⠭⣭⣄⣀⠀⢸⠘⠀⢸⢸⠀⠀⠀⠀⡇⠀⠀⢸⢸⠀⠈⠩⠩⠥⠄⠀⠫⢍⡿⡿⣿⣿⣿⣿⣿⣿
⠀⢂⣸⣷⣶⣶⣶⡄⢀⣴⣾⣦⣥⣇⢸⢸⢸⣿⢗⡕⣁⢣⣿⣿⣿⣿⡇⠀⢈⠔⢡⢠⠘⣿⢃⠃⠂⡌⡄⠀⠠⢻⣿⣿⣿⠋⠀⢸⢀⠀⢨⢸⠀⠀⠀⠀⡇⡄⠀⢼⣼⣴⣶⣤⡀⠸⠀⠀⣸⡭⣉⣵⡇⣿⣿⣿⣿⣿
⠀⣼⣿⣿⣿⣿⣿⡇⣉⡙⣿⣿⣷⣔⣊⢜⣾⣋⣊⢜⣬⣝⣻⢿⣿⣿⣷⣀⡘⡀⣃⣘⡀⢏⣈⡬⠭⢁⣰⠀⠈⠙⣛⣓⡩⠊⠀⢘⣸⠀⣘⣸⠀⣀⡀⢀⣃⡇⠐⢪⣿⠿⣛⣁⣀⣀⡀⠀⠀⣚⡡⣣⡇⣿⣿⣿⣿⣿
⠀⠀⠹⢿⣿⣿⣿⣷⣶⣶⣿⣿⣷⣶⣶⣿⣷⣶⣶⣿⣿⣶⣶⣶⣿⣿⣷⣶⣶⣿⣷⣦⣴⣶⣤⣴⣶⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⣸⣿⡇⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠈⢩⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⡟⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠁⠀⠀⢀⣿⣿⣿⣟⣽⣿⣿⠈⣉⣉⣉⣉⣭⣉⣭⣭⣤⣄⠀⣴⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠉⠐⠛⠿⠿⢿⣿⠃⠀⢸⣿⣿⣿⣿⡿⠿⠿⢿⣿⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡺⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣹⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⡗⠶⣶⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⢢⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣿⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣵⢶⣿⠉⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡅⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⣼⣿⡇⠀⠀⠀⣿⡀⡿
⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠉⠈⠉⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⡇⠀⠀⣿⣿⡇⠀⠀⠀⢿⡆⠀
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⣤⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣹⣆⠀⠀⠀⠀⠀⢤⠰⠀⠀⠿⠚⠛⠛⠛⠛⠛⣇⠀⠀⠀⠀⢀⣾⠃⠀⠀⣿⣿⠀⠀⠀⠀⢸⡇⠀
⢠⡿⠀⠀⠀⠀⠀⠀⢀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⣿⠀⠀⠀⠀⠸⡇⠀
⣼⡇⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⡟⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⡇⠀
⠛⠀⠀⠀⠀⠀⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢿⣿⡇⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠃⠀
⡇⠀⠀⢠⣤⣶⣦⣄⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⣿⠀⠀⢸⢹⣿⠇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠈⢿⣿⣿⡿⡆⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⣀⡀⠀⠀⠀⠻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠘⠋⠀⠀⡿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣘⣿⣿⣧⢷⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⡟⣥⢷⣿⠳⠀⠀⠀⠀⠈⠱⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠇⠆⠶⠀⠀⢨⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠁⠿⠛⠻⣿⣿⠻⡟⠁⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣮⡻⠛⣷⡃⡀⠀⠀⠀⠀⠀⠉⠐⢒⣀⣀⣀⡠⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢠⣄⣀⢴⡞⠃⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⡩⠭⢍⠩⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠭⣫⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⢉⠉⠉⠉⢩⡍⠉⠉⠉⢉⠉⠉⠉⠉⠉⠉⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⡀⠀⠀⠀⠍⠉⠭⠄⠀⡇⡇⢸⢸⢰⣌⠁⡻⣫⢋⢎⣼⣿⣿⡇⠈⠀⠿⢣⠋⢸⣿⡏⠸⢁⢁⠀⠀⢠⢊⠭⣭⣄⣀⠀⢸⠸⠀⢸⢸⠀⠀⠀⠀⡇⠀⠀⢸⢸⠀⠈⠩⠩⠥⠀⠀⠫⢍⡿⡿⣿⣿⣿⣿⣿⣿
⠀⢀⣽⣿⣶⣶⣶⡄⢀⣴⣶⣦⣧⣇⢸⢸⢸⣿⢗⡕⣁⢣⣿⣿⣿⣿⡇⠀⢈⠔⢡⢠⠘⣿⢃⠃⠂⡌⡄⠀⠠⢻⣿⣿⣿⠋⠀⢸⢀⠀⢨⢸⠀⠀⠀⠀⡇⡄⠄⢼⣼⣴⣶⣤⡀⠸⠀⠀⣸⡭⣉⣵⡇⣿⣿⣿⣿⣿
⢀⣼⣿⣿⣿⣿⣿⡇⣉⡙⣿⣿⣷⣔⣊⢜⣾⣏⣊⢜⣬⣝⣻⢿⣿⣿⣧⣀⡘⡀⣃⣘⡀⢏⣈⡬⠭⢁⣰⠀⠈⠙⣛⣓⡩⠊⠀⢘⣸⠀⣘⣸⠀⣀⡀⢀⣃⡇⠐⢪⣿⠿⣛⣁⣀⣀⡀⠀⠀⣚⡡⣣⡇⣿⣿⣿⣿⣿
⠀⠀⠹⢿⣿⣿⣿⣷⣶⣶⣿⣿⣷⣶⣶⣿⣷⣶⣶⣿⣿⣶⣶⣶⣿⣿⣷⣶⣶⣿⣷⣦⣴⣶⣤⣴⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⣼⣿⡇⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⠏⠠⠀⢀⣿⣿⣿⣿⣿⣿⡟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠏⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡇⢈⣉⣉⣉⣭⣭⣭⣭⣤⣄⠀⣴⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠁⠐⠛⠿⠿⠿⣿⠟⠠⢀⣶⣶⣿⣿⣿⣯⣹⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡊⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣹⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠺⢿⣿⣯⣽⣟⠛⠛⠿⡿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣢⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣿⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠙⠓⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⡇⠀⠀⣼⣿⡇⠀⠀⠀⣿⠀⡿
⠀⠀⠀⠀⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠃⠀⠀⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⡇⠀⠀⣿⣿⡇⠀⠀⠀⣿⡄⠀
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣼⣿⣿⣿⣿⠀⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⢹⣆⠀⠀⠀⠀⠀⢤⠰⠀⠀⠿⠒⠛⠛⠛⠛⠛⣇⠀⠀⠀⠀⢀⣾⠃⠀⠀⣿⣿⠀⠀⠀⠀⢸⡇⠀
⢰⡇⠀⠀⠀⠀⠀⠀⠀⣀⣰⣿⣿⣿⣿⣿⣿⣿⡟⢘⡋⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⣿⠀⠀⠀⠀⠸⡇⠀
⣿⠁⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣤⡇⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⡟⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⡇⠀
⠛⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢿⣿⡇⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠁⠀
⠀⠀⠀⢠⣤⣶⣤⡀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣸⣿⠀⠀⢸⢹⣿⠇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠒⠘⣿⣿⣶⢿⡀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣄⠀⠀⠀⠀⠹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠘⠋⠀⠀⡿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣹⣿⣿⡴⣇⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⢿⣿⠣⠀⠀⠀⠀⠈⠱⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠇⠆⠶⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠁⠿⠛⢻⣿⡟⢻⡛⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⡻⠹⣷⡣⡀⠀⠀⠀⠀⠀⠉⠐⢂⣀⣀⣀⡠⢄⠀⢁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢠⣄⣀⢴⡞⠃⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⡩⠭⢍⠉⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠭⣍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⢉⠉⠉⠉⢩⡍⠉⠉⠉⢉⠉⠉⠉⠉⠉⠉⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⡀⠀⠀⠀⠍⠉⠭⠄⠀⡇⡇⢸⢸⢰⣌⠁⡻⣫⢋⢎⣼⣿⣿⡇⠈⠀⠿⢣⠋⢨⣿⡏⠸⢁⢁⠀⠀⢠⢊⠭⣭⣄⣀⠀⢸⠘⠀⢸⢸⠀⠀⠀⠀⡇⠀⠀⢸⢸⠀⠈⠩⠩⠥⠀⠀⠫⢍⡿⡿⣿⣿⣿⣿⣿⣿
⠀⢀⣸⣷⣶⣶⣴⡄⢀⣴⣶⣦⣧⣇⢸⢸⢸⣿⢗⡕⣁⢣⣿⣿⣿⣿⡇⠀⢈⠔⢡⢠⠘⣿⢃⠃⠂⡌⡄⠀⠠⢻⣿⣿⣿⠋⠁⢸⢀⠀⢨⢸⠀⠀⠀⠀⡇⡄⠀⢼⣼⣴⣶⣤⡀⠸⠀⠀⣸⡭⣉⣵⡏⣿⣿⣿⣿⣿
⢀⣼⣿⣿⣿⣿⣿⡇⣉⡙⣿⣿⣷⣔⣊⢜⣾⣋⣊⢜⣬⣝⣻⢿⣿⣿⣧⣀⡘⡀⣁⣘⡀⢏⣈⡬⠭⢁⣰⠀⠈⠙⣛⣓⡩⠊⠀⢘⣸⠀⣘⣸⠀⣀⡀⢀⣃⡇⠐⢪⣿⠿⣛⣁⣀⣀⡀⠀⠀⣚⡡⣣⡇⣿⣿⣿⣿⣿
⠀⠀⠸⢿⣿⣿⣿⣷⣶⣶⣿⣿⣷⣶⣶⣿⣷⣶⣶⣿⣿⣶⣶⣾⣿⣿⣷⣶⣶⣿⣷⣦⣴⣶⣤⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⣼⣿⡇⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⠏⠀⠀⢀⣿⣿⣿⣿⣿⣿⡟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⠏⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡇⢈⣉⣉⣉⣭⣭⣭⣭⣤⣄⠀⣴⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠐⠛⠿⠿⠿⣿⡟⠠⢀⣶⣶⣿⣿⣿⣿⣹⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡊⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣹⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠺⢿⣿⣯⣽⣟⠛⠛⠿⡿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠦⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣿⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠙⠓⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⡇⠀⠀⣼⣿⡇⠀⠀⠀⣿⠂⡿
⠀⠀⠀⠀⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⡇⠀⠀⣿⣿⡇⠀⠀⠀⣿⡆⠀
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣴⣿⣿⣿⣿⢀⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⢹⣆⠀⠀⠀⠀⠀⠤⠰⠀⠀⠿⠚⠛⠛⠛⠛⠛⣇⠀⠀⠀⠀⢀⣿⠇⠀⠀⣿⣿⠀⠀⠀⠀⢸⡆⠀
⢰⡇⠀⠀⠀⠀⠀⠀⠀⣀⣰⣿⣿⣿⣿⣿⣿⣿⡟⢘⡏⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⣿⠀⠀⠀⠀⢸⡇⠀
⣿⠁⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣤⡆⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⡟⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⡇⠀
⠛⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢿⣿⡏⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠁⠀
⠀⠀⠀⢠⣤⣶⣤⡀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⣿⠀⠀⢸⢹⣿⠇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠒⠘⣿⣿⣶⢿⡀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣄⠀⠀⠀⠀⠹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠘⠋⠀⠀⡿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣹⣿⣿⡤⣇⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⢿⣿⠣⠀⠀⠀⠀⠈⠱⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠇⠆⠶⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠁⠿⠛⢻⣿⡟⢻⡛⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⡻⠹⣷⡡⡀⠀⠀⠀⠀⠀⠉⠐⢂⣀⣀⣀⡠⢄⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢠⣄⣀⢴⡞⠃⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⡩⠭⢍⠭⢽⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠭⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⢉⠉⠉⠉⢩⡍⠉⠉⠉⢉⠉⠉⠉⠉⠉⠉⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⡀⠀⠀⠀⠍⠉⠭⠄⠀⡇⡇⢸⢸⢰⣌⠁⡻⣫⢋⢎⣼⣿⣿⡇⠈⠀⠿⢡⠋⢸⣿⡏⠸⢁⢁⠀⠀⢠⢊⠭⣭⣄⣀⠀⢸⠘⠀⢸⢸⠀⠀⠀⠀⡇⠀⠀⢸⢸⠀⠈⠩⠩⠥⠀⠀⠫⢍⡿⡿⣿⣿⣿⣿⣿⣿
⠀⢁⣸⣿⣵⣶⣦⡀⢀⣴⣶⣤⣧⣇⢸⢸⢸⣿⢗⡕⣁⢣⣿⣿⣿⣿⡇⠀⢈⠔⢡⢠⠘⣿⢃⠃⠂⡌⡄⠀⠠⢻⣿⣿⣿⠋⠀⢸⢀⠀⢨⢸⠀⠀⠀⠀⡇⡄⠀⢼⣼⣴⣶⣤⡀⠸⠀⠀⣨⡭⣉⣵⡇⣿⣿⣿⣿⣿
⢀⣼⣿⣿⣿⣿⣿⡇⣉⡙⣿⣿⣷⣔⣊⢜⣾⣋⣊⢜⣬⣝⣻⢿⣿⣿⣧⣀⡘⡀⣁⣘⡀⢏⣈⡬⠭⢁⣰⠀⠈⠙⣛⣓⡩⠊⠀⢘⣸⠀⣘⣸⠀⣀⡀⢀⣃⡇⠐⢪⣿⠿⣛⣁⣀⣀⡀⠀⠀⣚⡡⣣⡇⣿⣿⣿⣿⣿
⠀⠀⠸⢿⣿⣿⣿⣷⣶⣶⣿⣿⣷⣶⣶⣿⣷⣶⣶⣿⣿⣶⣶⣶⣿⣿⣷⣶⣴⣿⣷⣦⣶⣶⣤⣴⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⣼⣿⡇⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡦⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⠏⠀⠀⢀⣾⣿⣿⣿⣿⣿⡟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⠏⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡇⢈⣉⣉⣉⣭⣭⣭⣭⣤⣄⠀⣴⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠐⠛⠿⠿⠿⣿⡟⠠⢀⣶⣶⣿⣿⣿⣿⣻⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡊⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣹⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠺⢿⣿⣯⣽⣟⠛⠛⠿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠢⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣿⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠙⠃⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠀⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⡇⠀⠀⣼⣿⡇⠀⠀⠀⣿⠂⡟
⠀⠀⠀⠀⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠃⠀⠀⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣿⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⡇⠀⠀⣿⣿⡇⠀⠀⠀⣿⡆⠀
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣴⣿⣿⣿⣿⠀⣤⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⢹⣆⠀⠀⠀⠀⠀⠤⠠⠀⠀⠿⠚⠛⠛⠛⠛⠛⣧⠀⠀⠀⠀⢀⣿⠃⠀⠀⣿⣿⠀⠀⠀⠀⢸⡇⠀
⢰⡇⠀⠀⠀⠀⠀⠀⢀⣀⣰⣿⣿⣿⣿⣿⣿⣿⡟⢨⡏⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⣿⠀⠀⠀⠀⠸⡇⠀
⣿⠁⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣴⡆⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⡟⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⡇⠀
⠛⠀⠀⠀⠀⠈⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢿⣿⡇⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠁⠀
⠀⠀⠀⢠⣤⣤⣤⡀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⣿⠀⠀⢸⢹⣿⠇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠒⠙⣿⣿⣶⢳⡀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣄⠀⠀⠀⠀⠹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠜⠋⠀⠀⡿⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣹⣿⣿⡤⡇⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⢿⣿⢣⠀⠀⠀⠀⠈⠱⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⡇⠆⠶⠀⠀⢨⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠁⠿⠛⢻⣿⡟⢻⡛⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⡻⠹⣷⡡⡀⠀⠀⠀⠀⠀⠉⠐⢂⣀⣀⣀⠤⣄⠀⢁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢠⣄⣀⢴⡞⠃⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⡩⠭⢍⠉⣽⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠿⠍⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⢉⠉⠉⠉⠩⡍⠉⠉⠉⢉⠉⠉⠉⠉⠉⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡀⠀⠀⠀⠍⠉⠭⠄⠀⡇⡇⢸⢸⢰⣌⠁⡺⣫⢋⢎⣼⣿⣿⡇⠈⠀⠿⢣⠋⢸⣿⡏⠸⢁⢁⠀⠀⢠⢊⠭⣭⣄⣀⠀⢸⠘⠀⢸⢸⠀⠀⠀⠀⡇⠀⠀⢸⢸⠀⠈⠩⠩⠥⠀⠀⠫⢍⡿⡿⣿⣿⣿⣿⣿⣿
⠀⠀⢨⣤⣤⣤⣤⡄⢀⣴⣶⣦⣧⣇⢸⢸⢸⣿⢗⡕⣁⢣⣿⣿⣿⣿⡇⠀⢈⠐⢡⢠⠘⣿⢁⠃⠂⡌⡄⠀⠠⢻⣿⣿⣿⠋⠀⢸⢀⠀⢨⢸⠀⠀⠀⠀⡇⡄⠄⢼⣼⣴⣶⣤⡀⠸⠀⠀⣸⡭⣉⡵⡇⣿⣿⣿⣿⣿
⢀⣤⢶⣿⣿⣿⣿⡇⣉⡙⣿⣿⣷⣔⣊⢜⣾⣋⣊⢜⣬⣝⣻⢿⣿⣿⣧⣀⡘⡀⡁⣘⡀⣏⣈⡬⠭⢁⣰⠀⠈⠙⣛⣓⡩⠊⠀⢘⣸⠀⣘⣸⠀⣀⡀⢀⣃⡇⠐⢪⣿⠿⣛⣁⣀⣀⡀⠀⠀⣚⡡⣣⡇⣿⣿⣿⣿⣿
⠀⠀⠸⢿⣿⣿⣿⣷⣶⣶⣿⣿⣷⣶⣶⣿⡷⣶⣶⣿⣿⣶⣶⣾⣿⣿⣷⣶⣴⣿⣷⣦⣴⣦⣤⣴⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⣼⣿⡇⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⠏⠀⠀⢰⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠏⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡇⢈⣉⣉⣉⣭⣉⣭⣭⣥⣤⠀⣴⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠁⠐⠛⠿⠿⠿⣿⡟⠀⢠⣿⣿⣿⣿⣿⣿⣾⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣹⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢹⣿⣿⣿⣷⣤⣈⠉⠛⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣿⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠀⠀⠠⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠄⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⡇⠀⠀⣼⣿⡇⠀⠀⠀⣿⠀⡿
⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇⠀⠀⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣶⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⡇⠀⠀⣿⣿⡇⠀⠀⠀⣿⡆⠀
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⣿⣿⣿⣿⡅⠀⢠⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⢹⣆⠀⠀⠀⠀⠀⠤⠠⠀⠀⠿⠚⠛⠛⠛⠛⠛⣇⠀⠀⠀⠀⢀⣾⠃⠀⠀⣿⣿⠀⠀⠀⠀⢸⡇⠀
⢀⣿⠀⠀⠀⠀⠀⠀⢀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⠁⣮⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⣿⠀⠀⠀⠀⢸⡇⠀
⢸⡇⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡚⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⡟⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⡇⠀
⠛⠁⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢿⣿⡇⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠁⠀
⠃⠀⠀⣠⣄⡤⣤⡀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣸⣿⠀⠀⢸⢹⣿⠇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠚⠘⣿⣿⣶⢳⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⣄⠀⠀⠀⠀⠹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠜⠋⠀⠀⡿⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣹⣿⣿⡤⡇⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣭⢿⣯⠳⠀⠀⠀⠀⠈⠱⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠇⠆⠶⠀⠀⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠁⠿⠛⢻⣿⡟⢻⠛⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⠿⠻⣷⢂⠀⠀⠀⠀⠀⠀⠉⠐⢂⣀⣀⣀⠄⣄⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢠⣄⣀⢴⡞⠃⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⡩⠭⢍⠍⠽⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⠍⡩⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⢉⠉⠉⠉⠩⡍⠉⠉⠉⢉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⠀⠀⠀⠀⠍⠉⠭⠄⠀⡇⡇⢸⢸⢰⣌⠁⠻⣫⢋⢎⣼⣿⣿⡇⠈⠀⠿⢣⠋⢨⣿⡏⠸⢁⢁⠀⠀⢠⢊⠭⣭⣄⣀⠀⢸⠸⠀⢸⢸⠀⠀⠀⠀⡇⠀⠀⢸⢸⠀⠈⠩⠩⠥⠀⠀⠫⢍⡿⡿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣥⣤⣤⣶⡀⢀⣴⣶⣤⣥⣇⢸⢸⢸⣿⢗⡕⣁⢣⣿⣿⣿⣿⡇⠀⢈⠐⢡⢠⠘⣿⢁⠃⠂⡌⡄⠀⠠⢻⣿⣿⣿⠋⠀⢸⢀⠀⢨⢸⠀⠀⠀⠀⡇⡄⠀⢼⣼⣴⣶⣤⡀⠸⠀⠀⣸⡭⣉⡵⡇⣿⣿⣿⣿⣿
⠀⣤⣾⣿⣿⣿⣿⡇⣉⡙⣿⣿⣷⣔⣊⢜⣾⣋⣊⢜⣤⣝⣻⢿⣿⣿⣧⣀⡘⡀⣁⣘⡀⢏⣈⡬⠭⢁⣰⠀⠈⠙⣛⣓⡩⠊⠀⢘⣸⠀⣘⣸⠀⣀⡀⢀⣃⡇⠐⢪⣿⠿⣛⣁⣀⣀⡀⠀⠀⣚⡡⣣⡇⣿⣿⣿⣿⣿
⠀⠀⠻⢿⣿⣿⣿⣷⣶⣶⣿⣿⣷⣶⣶⣿⡷⣶⣶⣿⣿⣶⣶⣾⣿⣿⣷⣶⣶⣿⣷⣤⣴⣶⣤⣴⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⣼⣿⡇⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⡆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⠏⠀⠀⢠⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⠏⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡇⢈⣉⣉⣉⣭⣩⣭⣭⣤⣄⠀⣶⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠐⠛⠿⠿⠿⣿⡟⠀⢠⣿⣿⣿⣿⣿⣿⣾⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠪⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣹⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢹⣿⣿⣿⣷⣤⣈⠉⠛⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⣻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣿⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠀⠀⠠⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠂⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⡇⠀⠀⣼⣿⡇⠀⠀⠀⣿⡀⡿
⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇⠀⠀⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣾⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⡇⠀⠀⣿⣿⡇⠀⠀⠀⢿⡄⠀
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⣿⣿⣿⣿⡇⠀⠠⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⢹⣆⠀⠀⠀⠀⠀⠤⠠⠀⠀⠿⠚⠛⠛⠛⠛⠛⣇⠀⠀⠀⠀⢀⣾⠇⠀⠀⣿⣿⠀⠀⠀⠀⢸⡇⠀
⢀⣿⠀⠀⠀⠀⠀⠀⢀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⠀⠮⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⣿⠀⠀⠀⠀⢸⡇⠀
⢸⡇⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡚⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⡟⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⡇⠀
⠙⠁⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢿⣿⠇⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠃⠀
⠃⠀⠀⢠⣄⡤⣤⡀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⣿⠀⠀⣸⢹⣿⠇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠚⠘⣿⣿⣶⢳⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⣄⠀⠀⠀⠀⠹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠜⠋⠀⠀⡿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣹⣿⣿⡄⡇⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣭⢿⣯⠳⠀⠀⠀⠀⠈⠱⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠇⠆⠶⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠁⠿⠛⢻⣿⡟⢻⠛⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⠿⠻⣷⢂⠀⠀⠀⠀⠀⠀⠉⠐⣂⣀⣀⣀⠄⣄⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢠⣄⣀⢴⡞⠃⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⡭⠭⢍⠉⢽⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⢉⠉⠉⠉⠩⡍⠉⠉⠉⢉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠍⠉⠭⠄⠀⡇⡇⢸⢸⢰⣌⠁⠻⣫⢋⢎⣼⣿⣿⡇⠈⠀⠿⢣⠋⢨⣿⡏⠸⢁⢑⠀⠀⢠⢊⠭⣭⣄⣀⠀⢸⠸⠀⢸⢸⠀⠀⠀⠀⡇⠀⠀⢸⢸⠀⠈⠩⠩⠥⠀⠀⠫⢍⡿⡿⣿⣿⣿⣿⣿⣿
⠀⠀⢨⣤⣤⣤⣤⡄⢀⣴⣶⣤⣥⣇⢸⢸⢸⣿⢗⡕⣁⢣⣿⣿⣿⣿⡇⠀⢈⠒⢡⢠⠘⣿⢃⠃⠂⡌⡄⠀⠠⢻⣿⣿⣿⠋⠀⢸⢀⠀⢨⢸⠀⠀⠀⠀⡇⡄⠄⢼⣼⣴⣶⣤⡀⠸⠀⠀⣸⡭⣉⡵⡇⣿⣿⣿⣿⣿
⢀⣤⣬⣿⣿⣿⣿⣇⣉⡙⣿⣿⣷⣔⣊⢜⣾⣋⣊⢜⣬⣙⣻⢿⣿⣿⣧⣀⡘⡀⡁⣘⡀⢏⣈⡬⠭⢁⣰⠀⠈⠙⣛⣓⡩⠊⠀⢘⣸⠀⣘⣸⠀⣀⡀⢀⣃⡇⠐⢪⣿⠿⣛⣁⣀⣀⡀⠀⠀⣒⡡⣣⡇⣿⣿⣿⣿⣿
⠀⠀⠸⢿⣿⣿⣿⣷⣶⣶⣿⣿⣷⣶⣶⡿⠷⣶⣶⣿⣿⣶⣶⣶⣿⣿⣷⣶⣶⣿⣷⣦⣴⣶⣤⣴⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⣸⣿⡇⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣼⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣰⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⠃⠀⠀⢠⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⠇⠀⢀⣀⣼⣿⣿⣿⣿⣿⣿⡇⢈⣉⣉⣉⣭⣉⣭⣭⣥⣄⠀⣴⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠐⠛⠿⠿⢿⣿⡟⠀⠀⣿⣿⣿⣿⣿⣛⠛⠛⢿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠺⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣹⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿⠛⢃⣟⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⢻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⣿⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⡄⢼⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⡇⠀⠀⣼⣿⡇⠀⠀⠀⣿⠀⡟
⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡏⠀⢈⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣾⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⡇⠀⠀⣿⣿⡇⠀⠀⠀⢿⡁⠀
⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣾⣿⣿⣿⣿⡆⠀⠈⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⢹⣆⠀⠀⠀⠀⠀⠤⠠⠀⠀⠾⠚⠛⠛⠛⠛⠛⣧⠀⠀⠀⠀⢀⣿⠇⠀⠀⣿⣿⠁⠀⠀⠀⢸⡇⠀
⠀⣼⠃⠀⠀⠀⠀⠀⢀⣀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⠀⠀⢰⣿⣿⠀⠀⠀⠀⢸⡇⠀
⢠⣿⠀⠀⠀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⡟⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⡇⠀
⠈⠃⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢿⣿⡏⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠁⠀
⡟⠀⠀⠀⣤⣠⣤⣄⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⣿⠀⠀⣸⢱⣿⠇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⠊⢿⣿⣷⣿⡆⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⢀⡀⠀⠀⠀⠙⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⠋⠀⠀⡿⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣈⣿⣿⣥⣷⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡟⣏⡳⣾⡽⡄⠀⠀⠀⠈⠱⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠇⠆⠶⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠁⠿⠛⠻⣿⣿⢻⡛⠁⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣬⢳⠿⣷⠂⠀⠀⠀⠀⠀⠀⠉⠀⠂⣀⣀⣀⡠⢀⠀⢁⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢠⣄⣀⢴⡞⠃⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠩⡭⠭⢭⡩⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠭⡍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⢉⠉⠉⠉⢩⡍⠉⠉⠉⢉⠉⠉⠉⠉⠉⠉⠩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠍⠉⠭⠄⠀⡇⡇⢸⢸⢠⣌⠁⡻⣫⢋⢎⣼⣿⣿⡇⠈⠀⠿⢣⠋⢨⣿⡏⠸⢁⢁⠀⠀⢠⢊⠭⣭⣄⣀⠀⢸⠸⠀⢸⢸⠀⠀⠀⠀⡇⠀⠀⢸⢸⠀⠈⠩⠩⠥⠀⠀⠫⢍⡿⡿⣿⣿⣿⣿⣿⣿
⠀⠀⠐⣶⣶⣦⣤⡄⢀⣴⣶⣤⣧⣇⢸⢸⢸⣿⠆⡕⣁⢣⣿⣿⣿⣿⡇⠀⢈⠐⢡⢠⠘⣿⢃⠃⠂⡌⡄⠀⠠⢻⣿⣿⣿⠋⠀⢸⢀⠀⢨⢸⠀⠀⠀⠀⡇⡄⠄⢼⣼⣴⣶⣤⡀⠸⠀⠀⣨⡭⣉⣵⡇⣿⣿⣿⣿⣿
⢀⣧⣱⣿⣿⣿⣿⣇⣉⡙⣿⣿⣷⣔⣊⢜⣾⣋⣊⢜⣬⣝⣻⢿⣿⣿⣧⣀⡘⡀⣁⣘⡀⣏⣈⡬⠭⢁⣰⠀⠈⠙⣛⣓⡩⠊⠀⢘⣸⠀⣘⣸⠀⣀⡀⢀⣃⡇⠐⢪⣿⠿⣛⣁⣀⣀⡀⠀⠀⣚⡡⣣⡇⣿⣿⣿⣿⣿
⠀⠁⠺⢿⣿⣿⣿⣷⣶⣶⣿⣿⣷⣶⣶⡿⠷⣶⣶⣿⣿⣶⣶⣾⣿⣿⣷⣶⣶⣿⣷⣦⣶⣶⣤⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⣸⣿⡇⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣾⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡇⠀⢀⣀⣼⣿⣿⣿⣿⣿⣿⡇⢈⣉⣉⣩⣭⣭⣭⣭⣤⣤⠀⣴⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠸⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠁⠐⠛⠿⠿⠿⣿⡟⢀⠁⣿⣿⣿⣿⣿⣛⠛⠛⢿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⢾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣩⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠛⢃⣟⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⣿⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⡄⢼⡇⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⡇⠀⠀⣼⣿⡇⠀⠀⠀⣿⠂⡟
⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡇⠁⢈⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣾⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⡇⠀⠀⣿⣿⡇⠀⠀⠀⣿⡆⠀
⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣶⣾⣿⣿⣿⣿⡇⠀⠈⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣹⣆⠀⠀⠀⠀⠀⢴⠠⠀⠀⠿⠚⠛⠛⠛⠛⠛⣧⠀⠀⠀⠀⢀⣾⠇⠀⠀⣿⣿⠁⠀⠀⠀⢸⡇⠀
⠀⣼⠃⠀⠀⠀⠀⠀⢀⣀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⠀⠀⢰⣿⣿⠀⠀⠀⠀⢸⡇⠀
⢠⣿⠀⠀⠀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⡟⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⡇⠀
⡈⠁⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢿⣿⡏⠀⠀⣾⣿⡇⠀⠀⠀⠂⠀⠃⠀
⡟⠀⠀⠀⣤⣠⣤⣄⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣸⣿⠀⠀⢸⢹⣿⠇⠀⠀⠀⠂⠀⠀⠀
⠁⠀⠀⠂⢿⣿⣿⣿⡆⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⡀⠀⠀⠀⠙⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠸⠋⠀⠀⠿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣈⣿⣿⣧⣷⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡟⣏⣳⣾⡽⠀⠀⠀⠀⠉⠱⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠆⠶⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠁⠿⠛⠻⣿⣟⢻⡛⠁⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣬⢳⠿⣷⠀⠀⠀⠀⠀⠀⠀⠉⠀⢂⣀⣀⣀⡠⢀⠀⢁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢠⣄⣀⢴⡞⠃⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠭⡭⠭⢍⡉⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠯⠯⣍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⢉⠉⠉⠉⢩⡍⠉⠉⠉⢉⠉⠉⠉⠉⠉⠉⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⠀⠀⠀⠀⠍⠉⠭⠄⠀⡇⡇⢸⢸⢠⣌⠁⣺⣫⢋⢎⣼⣿⣿⣏⠉⠀⠿⢣⠋⢨⣿⡏⠸⢁⢁⠀⠀⢠⢊⠭⣭⣄⣀⠀⢸⠸⠀⢸⢸⠀⠀⠀⠀⡇⠀⠀⢸⢸⠀⠈⠩⠩⠥⠀⠀⠫⢍⡿⡿⣿⣿⣿⣿⣿⣿
⠀⠀⢠⣵⣶⣴⣤⡄⢀⣴⣾⣦⣧⣇⢸⢸⢸⣿⢗⡕⣁⢣⣿⣿⣿⣿⡿⠀⢈⠖⢡⢠⠘⣿⢃⠃⠂⡌⡄⠀⠠⢻⣿⣿⣿⠋⠄⢸⢀⠀⢨⢸⠀⠀⠀⠀⡇⡄⠀⢼⣼⣴⣶⣤⡀⠸⠀⠀⡨⡭⣉⣵⡏⣿⣿⣿⣿⣿
⠀⡅⣫⣿⣿⣿⣿⡇⣉⡙⣿⣿⣷⣔⣊⢜⣼⣋⣋⢜⣬⣝⣻⢿⣿⣿⣧⣀⡘⡂⣁⣘⡐⣏⣈⡬⠭⢁⣰⠀⠈⠙⣛⣓⡩⠊⠀⢘⣸⠀⣘⣸⠀⣀⡀⢀⣃⡇⠐⢪⣿⠿⣛⣁⣀⣀⡀⠀⠀⣚⡡⣣⡇⣿⣿⣿⣿⣿
⠀⠁⠼⣿⣿⣿⣿⣷⣶⣶⣿⣿⣷⣶⣶⣿⠷⢶⣶⣿⣿⣶⣶⣾⣿⣿⣷⣶⣶⣿⣷⣶⣶⣶⣤⣶⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⣸⣿⡇⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢨⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣥⣶⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⡟⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⠀⠀⠀⣀⣿⣿⣿⣟⣿⣿⣿⠀⣉⣉⣩⣭⣭⣭⣭⣥⣤⠀⣴⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠁⠐⠛⠿⠿⠿⣿⣿⠃⠀⣸⣽⣿⣿⣿⡿⠿⠿⢿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠮⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣩⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⡷⠶⠤⠛⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⣿⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠃⠀⡋⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⡇⠀⠀⣼⣿⡇⠀⠀⠀⣿⠂⡟
⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⡇⠀⠀⣿⣿⡇⠀⠀⠀⣿⡆⠀
⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣾⣿⣿⣿⣿⡇⠀⠀⠂⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣹⣦⠀⠀⠀⠀⠀⢴⠠⠄⠀⠿⠚⠛⠛⠛⠛⠛⣧⠀⠀⠀⠀⢀⣾⠇⠀⠀⣿⣿⠁⠀⠀⠀⢸⡇⠀
⠀⣾⠁⠀⠀⠀⠀⠀⠀⣀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⠀⠀⢰⣿⣿⠀⠀⠀⠀⢸⡇⠀
⢰⡿⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⣟⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⡇⠀
⠘⠁⠀⠀⠀⠀⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢿⣿⡏⠀⠀⣾⣿⡇⠀⠀⠀⡂⠀⠃⠀
⡿⠀⠀⠀⣤⣠⣤⣄⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣸⣿⠀⠀⢸⢹⣿⠇⠀⠀⠀⠃⠀⠀⠀
⠁⠀⠀⠂⢿⣿⣿⣿⡆⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠸⠋⠀⢀⡿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣈⣿⣿⣧⢷⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⡿⣏⢶⣿⢳⠀⠀⠀⠀⠉⢷⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠆⠶⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠁⠿⠛⠻⣿⣿⢻⡟⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣝⢷⠿⣦⠀⠀⠀⠀⠀⠀⠀⠋⠀⠂⣀⣀⣀⡠⢀⠀⢁⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢠⣄⣀⢴⡞⠃⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠭⡭⠭⢭⡉⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠯⣍⠍⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⢉⠉⠉⠉⢩⡍⠉⠉⠉⢉⠉⠉⠉⠉⠉⠉⠩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⡀⠀⠀⠀⠍⠉⠭⠄⠀⡇⡇⢸⢸⢰⣌⠁⣻⣫⢋⢎⣼⣿⣿⡏⠈⠈⠿⢣⠋⢸⣿⡏⠸⢁⢁⠆⠀⢠⢊⠭⣭⣄⣀⠀⢸⠸⠀⢸⢸⠀⠀⠀⠀⡇⠀⠀⢸⢸⠀⠈⠩⠩⠥⠀⠀⠫⢍⡿⡿⣿⣿⣿⣿⣿⣿
⠀⠀⢬⣷⣤⣤⣤⡀⢀⣴⣶⣦⣧⣇⢸⢸⢸⣿⢗⡕⣁⢣⣿⣿⣿⣿⣿⠀⢈⠒⢡⢠⠘⣿⢃⠃⠂⡌⡴⠀⠠⢻⣿⣿⣿⠋⠀⢸⢀⠀⢨⢸⠀⠀⠀⠀⡇⡄⠀⢼⣼⣴⣶⣤⡀⠸⠀⠀⡨⡭⣉⣵⡏⣿⣿⣿⣿⣿
⠀⣖⢸⣿⣿⣿⣿⡇⣉⡙⣿⣿⣷⣔⣊⢜⣼⣋⣊⢜⣬⣝⣻⢿⣿⣿⣷⣀⡘⡀⣁⣘⡐⣏⣈⡬⠭⢁⣰⠀⠈⠙⣛⣓⡩⠊⠀⢘⣸⠀⣘⣸⠀⣀⡀⢀⣃⡇⠐⢪⣿⠿⣛⣁⣀⣀⡀⠀⠀⣚⡡⣣⡇⣿⣿⣿⣿⣿
⠀⠁⠼⣿⣿⣿⣿⣷⣶⣶⣿⣿⣷⣶⣶⣿⠷⢶⣶⣿⣿⣶⣶⣾⣿⣿⣷⣶⣶⣿⣷⣶⣶⣶⣤⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⣸⣿⡇⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢨⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⡟⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⠀⠀⠀⣀⣿⣿⣿⣟⣿⣿⣿⠀⣉⣉⣩⣭⣭⣭⣭⣤⣤⠀⣴⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠸⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠁⠐⠚⠿⠿⠿⣿⣿⠃⠀⣸⣿⣿⣿⣿⡿⠿⠿⢿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠮⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣉⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⡷⠶⠤⠛⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⣿⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠃⠀⡋⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⡇⠀⠀⣼⣿⡇⠀⠀⠀⣿⠂⡟
⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⡇⠀⠀⣿⣿⡇⠀⠀⠀⣿⡆⠀
⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣿⣿⣿⣿⡇⠀⠀⠂⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣹⣦⠀⠀⠀⠀⠀⢴⠠⠄⠀⠿⠚⠛⠛⠛⠛⠛⣧⠀⠀⠀⠀⢀⣾⠇⠀⠀⣿⣿⠁⠀⠀⠀⢸⡇⠀
⠀⣾⠁⠀⠀⠀⠀⠀⠀⣀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⠀⠀⢰⣿⣿⠀⠀⠀⠀⢸⡇⠀
⢰⡿⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⡟⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⡇⠀
⠘⠁⠀⠀⠀⠀⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢿⣿⡇⠀⠀⣾⣿⡇⠀⠀⠀⡂⠀⠁⠀
⡿⠀⠀⠀⣤⣠⣤⣄⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣸⣿⠀⠀⢸⢹⣿⠇⠀⠀⠀⠃⠀⠀⠀
⠁⠀⠀⠂⢿⣿⣿⣿⡆⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠜⠋⠀⢀⠿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣈⣿⣿⣧⢷⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⡿⣏⢶⣾⢳⠀⠀⠀⠀⠉⢷⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠆⠶⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠁⠿⠛⠻⣿⣿⢻⡟⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣜⢷⠿⣦⠀⠀⠀⠀⠀⠀⠀⠉⠀⠂⣀⣀⣀⡠⢀⠀⢁⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢠⣄⣀⢴⡞⠃⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠭⡭⠭⢭⡽⣽⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠯⣭⡝⡍⠉⠍⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⢉⠉⠉⠉⢩⡍⠉⠉⠉⢉⠉⠉⠉⠉⠉⠉⠩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡄⠀⠀⠀⠍⠉⠭⠄⠀⡇⡇⢸⢸⢰⣌⠁⣻⣫⢋⢎⣼⣿⣿⡯⠈⠀⠿⢣⠋⢨⣿⡏⠸⢁⢁⠀⠀⢠⢊⠭⣭⣄⣀⠀⢸⠸⠀⢸⢸⠀⠀⠀⠀⡇⠀⠀⢸⢸⠀⠈⠩⠩⠥⠄⠀⠫⢍⡿⡿⣿⣿⣿⣿⣿⣿
⠀⠀⣨⣻⣴⣶⣦⡄⢀⣴⣾⣦⣧⣇⢸⢸⢸⣿⢗⡕⣁⢣⣿⣿⣿⣿⣏⠀⢈⠒⢡⢠⠘⣿⢃⠃⠂⡌⡄⠀⠠⢻⣿⣿⣿⠋⠄⢸⢀⠀⢨⢸⠀⠀⠀⠀⡇⡄⠄⢼⣼⣴⣶⣤⡀⠸⠀⠀⣩⡯⣉⣵⡏⣿⣿⣿⣿⣿
⠐⡖⣣⣿⣿⣿⣿⣇⣉⡙⣿⣿⣷⣔⣊⢜⣾⣋⣋⢜⣬⣝⣻⢿⣿⣿⣷⣀⡘⡀⣃⣘⡐⣏⣈⡬⠭⢁⣰⠀⠈⠙⣛⣓⡩⠊⠀⢘⣸⠀⣘⣸⠀⣀⡀⢀⣃⡇⠐⢪⣿⠿⣛⣁⣀⣀⡀⠀⠀⣚⡡⣣⡇⣿⣿⣿⣿⣿
⠀⠁⠼⣿⣿⣿⣿⣷⣶⣶⣿⣿⣷⣶⣶⣿⡷⢶⣶⣿⣿⣶⣶⣾⣿⣿⣷⣶⣶⣿⣷⣶⣶⣶⣤⣶⣶⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⣸⣿⡇⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢨⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⡟⠀⠂⠀⣼⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠇⣩⣉⣩⣭⣭⣭⣭⣥⣤⠀⣶⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠸⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠉⠐⠛⠿⠿⠿⣿⣿⠃⠀⣰⣿⣿⣿⢿⠿⠿⢿⣿⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣹⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⡶⠤⠀⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢢⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⣿⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⣼⣿⡇⠀⠀⠀⣿⠂⡟
⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⡇⠀⠀⣿⣿⡇⠀⠀⠀⣿⡄⠀
⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⣴⣿⣿⣿⣿⠇⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣹⣦⠀⠀⠀⠀⠀⢴⠠⠀⠀⠿⠚⠛⠛⠛⠛⠛⣧⠀⠀⠀⠀⢀⣾⡇⠀⠀⣿⣿⠁⠀⠀⠀⢹⡇⠀
⠀⣾⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⠀⠀⢰⣿⣿⠀⠀⠀⠀⢸⡇⠀
⢸⡏⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⣟⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⡇⠀
⠘⠁⠀⠀⠀⠀⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢿⣿⡇⠀⠀⣾⣿⡇⠀⠀⠀⡂⠀⠁⠀
⡗⠀⠀⠀⣤⣠⣤⣄⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣸⣿⠀⠀⢸⢹⣿⠇⠀⠀⠀⠇⠀⠀⠀
⠁⠀⠀⠂⢿⣿⣿⡿⡆⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠸⠋⠀⠀⡿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣈⣿⣿⣧⣷⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡿⣇⢶⣿⢷⠀⠀⠀⠀⠉⢷⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠇⠆⠶⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠁⠿⠛⠻⣿⣿⢻⡟⠁⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣷⣙⢿⢿⣦⠆⠀⠀⠀⠀⠀⠀⠉⠀⠂⣀⣀⣀⡠⢀⠀⢁⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢠⣄⣀⢴⡞⠃⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠩⠭⡭⠭⢭⡽⣽⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⠭⡍⠏⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⢉⠉⠉⠉⢩⡍⠉⠉⠉⢉⠉⠉⠉⠉⠉⠉⠩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡀⠀⠀⠀⠍⠉⠭⠄⠀⡇⡇⢸⢸⢠⣌⠁⣻⣫⢋⢎⣼⣿⣿⡇⠈⠀⠿⢣⠋⢨⣿⡟⠸⢁⢑⠄⠀⢠⢊⠭⣭⣄⣀⠀⢸⠸⠀⢸⢸⠀⠀⠀⠀⡇⠀⠀⢸⢸⠀⠈⠩⠩⠥⠀⠀⠫⢍⡿⡿⣿⣿⣿⣿⣿⣿
⠀⢀⢀⣃⣦⣦⣤⡄⢀⣴⣶⣤⣧⣇⢸⢸⢸⣿⢗⡕⣁⢣⣿⣿⣿⣿⣿⠀⢈⠖⢡⢠⠐⣿⢃⠃⠂⡌⡄⠀⠠⢻⣿⣿⣿⠋⠀⢸⢀⠀⢨⢸⠀⠀⠀⠀⡇⡄⠀⢼⣼⣴⣶⣤⡀⠸⠀⠀⣨⡭⣉⡵⡏⣿⣿⣿⣿⣿
⠀⡜⣸⣿⣿⣿⣿⡇⣉⡙⣿⣿⣷⣔⣊⢜⣾⣏⣊⢜⣬⣝⣻⢿⣿⣿⣿⣀⡘⡀⣃⣘⡀⣏⣈⡬⠭⢁⣰⠀⠈⠙⣛⣓⡩⠊⠀⢘⣸⠀⣘⣸⠀⣀⡀⢀⣃⡇⠐⢪⣿⠿⣛⣁⣀⣀⡀⠀⠀⣚⡡⣣⡇⣿⣿⣿⣿⣿
⠀⠁⠽⣿⣿⣿⣿⣷⣶⣶⣿⣿⣷⣶⣶⣿⡷⢶⣶⣿⣿⣶⣶⣶⣿⣿⣷⣶⣶⣿⣷⣶⣴⣶⣤⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⣸⣿⡇⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢉⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⣖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⡟⠁⠂⠀⣼⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⡿⠁⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡇⣉⣉⣩⣭⣭⣭⣭⣤⣤⠀⣴⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠉⠐⠛⠿⠿⠿⣿⣿⠃⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣹⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣶⠤⣄⠈⠛⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣿⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡏⠀⠀⠄⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⡇⠀⠀⣼⣿⡇⠀⠀⠀⣿⠇⡟
⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⡇⠀⠀⣿⣿⡇⠀⠀⠀⣿⡆⠀
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣤⣾⣿⣿⣿⣿⠀⠀⠠⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣹⣦⠀⠀⠀⠀⠀⢴⠠⠄⠀⠿⠚⠛⠛⠛⠛⠛⣧⠀⠀⠀⠀⢀⣾⠇⠀⠀⣿⣿⠁⠀⠀⠀⢸⡇⠀
⢀⣿⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⠀⠀⢰⣿⣿⠀⠀⠀⠀⢸⡇⠀
⢸⡇⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⡀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⣟⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⡇⠀
⠘⠁⠀⠀⠀⠈⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢿⣿⡏⠀⠀⣾⣿⡇⠀⠀⠀⡂⠀⠁⠀
⡇⠀⠀⢀⣤⣤⢤⡀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⣿⠀⠀⢸⢹⣿⠇⠀⠀⠀⠃⠀⠀⠀
⠁⠀⠐⠈⢿⣿⣷⣿⡆⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠸⠋⠀⠀⡿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣈⣿⣿⣧⣷⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣇⢶⣿⢷⠀⠀⠀⠀⠉⢷⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠇⠆⠶⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠁⠿⠛⠻⣿⣿⢻⡟⠁⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣷⣙⢾⢿⣦⠆⠀⠀⠀⠀⠀⠀⠋⠀⠂⣀⣀⣀⡠⢀⠀⢁⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢠⣄⣀⢴⡞⠃⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠭⡭⠭⢍⡽⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠭⣍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⢉⠉⠉⠉⢩⡍⠉⠉⠉⢉⠉⠉⠉⠉⠉⠉⠩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⠀⠀⠀⠀⠍⠉⠭⠄⠀⡇⡇⢸⢸⢰⣌⠁⣻⣫⢋⢎⣼⣿⣿⡏⠈⠈⠿⢣⠋⢨⣿⡟⠸⢁⢁⠀⠀⢠⢊⠭⣭⣄⣀⠀⢸⠸⠀⢸⢸⠀⠀⠀⠀⡇⠀⠀⢸⢸⠀⠈⠩⠩⠥⠄⠀⠫⢍⡿⡿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣷⣴⣶⣶⡄⢀⣴⣶⣤⣧⣇⢸⢸⢸⣿⢗⡕⣁⢣⣿⣿⣿⣿⣯⠀⢈⠖⢡⢠⠘⣿⢃⠃⠂⡌⡄⠀⠠⢻⣿⣿⣿⠋⠁⢸⢀⠀⢨⢸⠀⠀⠀⠀⡇⡄⠄⢼⣼⣴⣶⣤⡀⠸⠀⠀⣹⡭⣩⣵⡏⣿⣿⣿⣿⣿
⠀⡔⣺⣿⣿⣿⣿⡇⣉⡙⣿⣿⣷⣔⣊⢜⣾⣋⣊⢞⣬⣙⣻⢿⣿⣿⣷⣀⡘⡂⣁⣘⡐⣏⣈⡬⠭⢁⣰⠀⠈⠙⣛⣓⡩⠊⠀⣘⣸⠀⣘⣸⠀⣀⡀⢀⣃⡇⠐⢪⣿⠿⣛⣁⣀⣀⡀⠀⠀⣚⡡⣣⡇⣿⣿⣿⣿⣿
⠀⠁⠼⣿⣿⣿⣿⣷⣶⣶⣿⣿⣷⣶⣶⣿⡷⢶⣶⣿⣿⣶⣶⣾⣿⣿⣷⣶⣶⣿⣷⣦⣶⣶⣤⣴⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⣼⣿⡇⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢩⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⡿⠁⠂⠀⣼⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⠁⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡇⣉⣉⣩⣭⣭⣭⣭⣥⣤⠀⣴⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠸⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠉⠘⠛⠿⠿⢿⣿⣿⠃⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠮⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣹⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣶⣄⣀⠉⠛⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢂⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⣿⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡟⠀⠀⡀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⡇⠀⠀⣾⣿⡇⠀⠀⠀⣿⠂⡟
⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⡇⠀⠀⣿⣿⡇⠀⠀⠀⣿⡄⠀
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣤⣾⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣹⣦⠀⠀⠀⠀⠀⢴⠠⠄⠀⠿⠚⠛⠛⠛⠛⠛⣧⠀⠀⠀⠀⢀⣾⠇⠀⠀⣿⣿⠁⠀⠀⠀⢹⡇⠀
⢀⡿⠀⠀⠀⠀⠀⠀⠀⣀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⣿⠀⠀⠀⠀⢸⡇⠀
⢸⡇⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⣿⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⡇⠀
⠙⠁⠀⠀⠀⠈⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢿⣿⡏⠀⠀⣾⣿⡇⠀⠀⠀⠂⠀⠁⠀
⡇⠀⠀⠀⣤⣤⣤⡀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣸⣿⠀⠀⢸⢹⣿⠇⠀⠀⠀⠃⠀⠀⠀
⠀⠀⠐⠀⢿⣿⣷⣿⡄⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⣀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠸⠋⠀⠀⡿⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣈⣿⣿⣯⣧⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣗⢶⣿⢧⠀⠀⠀⠀⠉⢷⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠇⠆⠶⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠁⠿⠛⠻⣿⣿⢻⡛⠁⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣷⣙⢾⢿⣦⠆⠀⠀⠀⠀⠀⠀⠉⠀⠂⣀⣀⣀⡠⢀⠀⢁⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢠⣄⣀⢴⡞⠃⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠩⠭⡭⠭⢍⡹⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⡩⣉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⢉⠉⠉⠉⢩⡍⠉⠉⠉⢉⠉⠉⠉⠉⠉⠉⠩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠍⠉⠭⠄⠀⡇⡇⢸⢸⢠⣌⠁⡻⣫⢋⢎⣼⣿⣿⡏⠈⠈⠿⢣⠋⢨⣿⡟⠸⢁⢁⠀⠀⢠⢊⠭⣭⣄⣀⠀⢸⠸⠀⢸⢸⠀⠀⠀⠀⡇⠀⠀⢸⢸⠀⠈⠩⠩⠥⠀⠀⠫⢍⡿⡿⣿⣿⣿⣿⣿⣿
⠀⠀⢲⣷⣴⣶⣴⡄⢀⣴⣾⣦⣧⣇⢸⢸⢸⣿⢖⡕⣁⢣⣿⣿⣿⣿⣧⠀⢈⠒⢡⢠⠘⣿⢃⠃⠂⡌⡄⠀⠠⢻⣿⣿⣿⠋⠀⢸⢀⠀⢨⢸⠀⠀⠀⠀⡇⡄⠀⢼⣼⣴⣶⣤⡀⠸⠀⠀⡨⡭⣉⣵⡇⣿⣿⣿⣿⣿
⠀⡖⢺⣿⣿⣿⣿⣇⣉⡙⣿⣿⣷⣔⣊⢜⣾⣋⣋⢜⣬⣝⣻⢿⣿⣿⣧⣀⡘⡀⣃⣘⡈⣏⣈⡬⠭⢁⣰⠀⠈⠙⣛⣓⡩⠊⠀⢘⣸⠀⣘⣸⠀⣀⡀⢀⣃⡇⠐⢪⣿⠿⣛⣁⣀⣀⡀⠀⠀⣚⡡⣣⡇⣿⣿⣿⣿⣿
⠀⠁⠼⣿⣿⣿⣿⣷⣶⣶⣿⣿⣷⣶⣶⣿⡷⣶⣶⣿⣿⣶⣶⣾⣿⣿⣷⣶⣶⣿⣷⣦⣶⣶⣤⣴⣦⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⣼⣿⡇⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢹⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⡟⠁⠂⠀⣼⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⠁⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠀⣉⣉⣩⣭⣭⣭⣭⣤⣤⠀⣴⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠁⠐⠛⠿⠿⢿⣿⣿⠁⠀⣰⣷⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣹⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣶⢄⡈⠙⠋⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⣿⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠏⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⡇⠀⠀⣼⣿⡇⠀⠀⠀⣿⠆⡟
⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣿⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⡇⠀⠀⣿⣿⡇⠀⠀⠀⣿⡄⠀
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣤⣾⣿⣿⣿⣿⠀⠀⠠⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣹⣦⠀⠀⠀⠀⠀⢴⠠⠄⠀⠿⠚⠛⠛⠛⠛⠛⣧⠀⠀⠀⠀⢀⣾⠇⠀⠀⣿⣿⠀⠀⠀⠀⢹⡇⠀
⢀⡿⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⣿⠀⠀⠀⠀⢸⡇⠀
⢸⡇⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠐⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⣿⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⡇⠀
⠙⠀⠀⠀⠀⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢿⣿⡇⠀⠀⣾⣿⡇⠀⠀⠀⠂⠀⠃⠀
⡇⠀⠀⢀⣤⣤⣄⡀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣸⣿⠀⠀⢸⢹⣿⠇⠀⠀⠀⠃⠀⠀⠀
⠀⠀⠐⠀⣿⣿⣾⣷⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⣀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⠋⠀⠀⡿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣘⣿⣿⣭⡇⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣇⢶⣿⢧⠀⠀⠀⠀⠉⢷⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠆⠶⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠁⠿⠛⢻⣿⡟⢻⠛⠁⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣷⣙⢾⢿⣦⠆⠀⠀⠀⠀⠀⠀⠉⠀⠂⣀⣀⣀⡠⢀⠀⢁⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢠⣄⣀⢴⡞⠃⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠭⡭⠭⢉⠙⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⠩⡙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⢉⠉⠉⠉⢩⡍⠉⠉⠉⢉⠉⠉⠉⠉⠉⠉⠩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⡀⠀⠀⠀⠍⠉⠭⠄⠀⡇⡇⢸⢸⢰⣌⠁⡻⣫⢋⢎⣼⣿⣿⣏⠈⠀⠿⢣⠋⢸⣿⡏⠸⢁⢑⠅⠀⢠⢊⠭⣭⣄⣀⠀⢸⠸⠀⢸⢸⠀⠀⠀⠀⡇⠀⠀⢸⢸⠀⠈⠩⠩⠥⠄⠀⠫⢍⡿⡿⣿⣿⣿⣿⣿⣿
⠀⠀⣼⣷⣦⣶⣶⡄⢀⣴⣾⣦⣧⣇⢸⢸⢸⣿⢗⡕⣁⢣⣿⣿⣿⣿⡿⠀⢈⠒⢡⢠⠘⣿⢃⠃⠂⡌⡄⠀⠠⢻⣿⣿⣿⠋⠄⢸⢀⠀⢨⢸⠀⠀⠀⠀⡇⡄⠄⢼⣼⣴⣶⣤⡀⠸⠀⠀⣸⡭⣉⣵⡏⣿⣿⣿⣿⣿
⠀⡄⣷⣿⣿⣿⣿⣇⣉⡙⣿⣿⣷⣔⣊⢜⣾⣋⣊⢜⣬⣝⣻⢿⣿⣿⣷⣀⡘⡀⣃⣘⡐⣏⣈⡬⠭⢁⣰⠀⠈⠙⣛⣓⡩⠊⠀⢘⣸⠀⣘⣸⠀⣀⡀⢀⣃⡇⠐⢪⣿⠿⣛⣁⣀⣀⡀⠀⠀⣚⡡⣣⡇⣿⣿⣿⣿⣿
⠀⠀⠿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣷⣶⣶⣿⡷⣶⣶⣿⣿⣶⣶⣾⣿⣿⣿⣶⣶⣿⣷⣦⣴⣶⣤⣴⣦⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⣸⣿⡇⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⢹⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⡟⠀⠂⠀⣾⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⡟⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⢀⣩⣉⣩⣭⣭⣭⣭⣥⣤⠀⣴⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠐⠛⠿⠿⢿⣿⡿⠁⠂⣼⣿⣿⡿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣹⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣻⣿⣿⣿⣶⢤⡄⠉⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⣻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⣿⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠋⠀⠀⠁⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⡇⠀⠀⣼⣿⡇⠀⠀⠀⣿⠀⡟
⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣿⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⡇⠀⠀⣿⣿⡇⠀⠀⠀⣿⡄⠀
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣤⣾⣿⣿⣿⡟⠀⠀⠠⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣹⣦⠀⠀⣀⠀⠀⠥⠠⠄⠀⠿⠚⠛⠛⠛⠛⠛⣧⠀⠀⠀⠀⢀⣾⠇⠀⠀⣿⣿⠀⠀⠀⠀⢸⡇⠀
⢀⡿⠀⠀⠀⠀⠀⠀⠀⣀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⣿⠀⠀⠀⠀⢸⡇⠀
⣸⡇⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠐⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⣿⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⡇⠀
⠛⠀⠀⠀⠀⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢿⣿⡏⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠃⠀
⠇⠀⠀⢀⣠⣤⣄⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣸⣿⠀⠀⣸⢹⣿⠇⠀⠀⠀⠂⠀⠀⠀
⠀⠀⠐⠈⣿⣿⣿⣷⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠜⠋⠀⠀⡿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣘⣿⣿⣽⡆⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣓⢶⣿⢧⠀⠀⠀⠀⠙⣷⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⠇⠆⠶⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠁⠿⠛⢻⣿⡟⢿⠛⠁⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣧⣙⣾⢿⣦⠆⠀⠀⠀⠀⠈⠀⠋⠀⢂⣀⣀⣀⡀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢠⣄⣀⢴⡞⠃⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠭⡭⠭⢍⠙⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠩⣍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⢉⠉⠉⡉⢩⡍⠉⠉⠉⢉⠉⠉⠉⠉⠉⠉⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣀⡄⠀⠀⠀⠍⠉⠭⠄⠀⡇⡇⢸⢸⢰⣌⠁⣻⣫⢋⢎⣼⣿⣿⣏⠈⠀⠿⢣⠋⢸⣿⡏⠸⢁⢁⠁⠀⢠⢊⠭⣭⣄⣀⠀⢸⠸⠀⢸⢸⠀⠀⠀⠀⡇⠀⠀⢸⢸⠀⠈⠩⠩⠅⠀⠀⠫⢍⡿⡿⣿⣿⣿⣿⣿⣿
⠀⠀⣭⣷⣶⣤⣴⡀⢀⣴⣾⣦⣧⣇⢸⢸⢸⣿⢗⡕⣁⢣⣿⣿⣿⣿⡏⠀⢈⠒⢡⢠⠘⣿⢃⠃⠂⡌⡄⠀⠠⢻⣿⣿⣿⠋⠀⢸⢀⠀⢨⢸⠀⠀⠀⠀⡇⡄⠄⢼⣼⣴⣶⣤⡀⠸⠀⠀⡨⡭⣉⣵⡏⣿⣿⣿⣿⣿
⢀⡂⣷⣿⣿⣿⣿⣇⣉⡙⣿⣿⣷⣔⣊⢜⣾⣏⣋⢜⣬⣝⣻⢿⣿⣿⣧⣀⡘⡀⣁⣘⡀⣏⣈⡬⠭⢁⣰⠀⠈⠙⣛⣓⡩⠊⠀⢘⣸⠀⣘⣸⠀⣀⡀⢀⣃⡇⠐⢪⣿⠿⣛⣁⣀⣀⡀⠀⠀⣒⡡⣣⡇⣿⣿⣿⣿⣿
⠀⠀⠿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣷⣶⣶⣿⠷⣶⣶⣿⣿⣶⣶⣶⣿⣿⣷⣶⣶⣿⣷⣦⣶⣶⣤⣴⣔⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⣸⣿⡇⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢹⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣖⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⠏⠐⠀⢠⣿⣿⣿⣿⣿⣿⡷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡏⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⢈⣉⣉⣭⣭⣭⣭⣭⣤⣤⠀⣴⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠁⠐⠛⠿⠿⢿⣿⡟⠀⠃⣾⣿⣿⣿⣿⠿⠿⠿⣿⡗⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⢾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣹⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣷⠶⠄⠈⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⣿⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⡇⠀⠀⣾⣿⡇⠀⠀⠀⣿⠀⡟
⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣿⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⡇⠀⠀⣿⣿⡇⠀⠀⠀⣿⡄⠀
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣤⣾⣿⣿⣿⣿⠀⠀⠐⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣹⣆⠀⠀⠀⠀⠀⠤⠠⠄⠀⠿⠊⠛⠛⠛⠛⠛⣧⠀⠀⠀⠀⢀⣾⠇⠀⠀⣿⣿⠀⠀⠀⠀⢸⡇⠀
⢀⡿⠀⠀⠀⠀⠀⠀⠀⣀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⣿⠀⠀⠀⠀⢸⡇⠀
⢸⡇⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠐⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⣿⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⡇⠀
⠛⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢿⣿⡏⠀⠀⣾⣿⡇⠀⠀⠀⡀⠀⠁⠀
⡇⠀⠀⢀⣀⣤⣄⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⣿⠀⠀⣸⢹⣿⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⠈⣿⣿⣾⣷⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⣀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⠋⠀⠀⡿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣘⣿⣿⣽⡆⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣓⢶⣿⢧⠀⠀⠀⠀⠙⢷⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠆⠶⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠁⠿⠛⢻⣿⡟⢿⠛⠁⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣧⣙⢾⢿⣦⠆⠀⠀⠀⠀⠈⠀⠋⠀⢂⣀⣀⣀⡀⢀⠀⢁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢠⣄⣀⢴⡞⠃⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡭⣭⣭⡭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⡩⠯⠍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢩⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣀⣀⠀⠀⠀⠀⠀⢀⡠⣸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣚⣯⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⢿⣿⡇⣿⣿⣿⣿⣿
⠐⣤⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡟⢸⣿⡇⣿⣿⣿⣿⣿
⠀⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠁⣸⣿⡇⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⣹⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⠃⠘⠀⢠⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⡏⠀⢀⣀⣼⣿⣿⣿⣿⣿⣿⣿⢈⣉⣉⣭⣭⣭⣭⣭⣥⣤⠀⣶⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠸⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠁⠐⠛⠿⠿⢿⣿⡟⠀⠁⣾⣿⣿⣿⣿⠿⠿⠿⢿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣹⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⠲⠶⡜⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⢠⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⣿⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⢣⣰⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡡⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⣼⣿⡇⠀⠀⠀⣿⡇⡟
⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠁⠀⠈⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣇⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣿⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⡇⠀⠀⣿⣿⡇⠀⠀⠀⣿⡆⠀
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣾⣿⣿⣿⣿⠀⠀⠈⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣹⣆⠀⠀⡀⠀⠀⠴⠠⠄⠀⠿⠚⠛⠛⠛⠛⠛⣧⠀⠀⠀⠀⢀⣿⡇⠀⠀⣿⣿⠀⠀⠀⠀⢸⡇⠀
⢀⣿⠀⠀⠀⠀⠀⠀⠀⣀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⣿⠀⠀⠀⠀⢸⡇⠀
⢸⡇⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠐⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⣿⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⡇⠀
⠘⠁⠀⠀⠀⠈⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢿⣿⡏⠀⠀⣾⣿⡇⠀⠀⠀⡄⠀⠃⠀
⡇⠀⠀⢀⣤⣤⣤⡀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣸⣿⠀⠀⣸⢹⣿⠇⠀⠀⠀⠇⠀⠀⠀
⠀⠀⠐⠀⣿⣿⣿⣷⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠸⠋⠀⠀⡿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣘⣿⣿⡯⡇⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣇⢶⣿⢧⠀⠀⠀⠀⠙⢷⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⡇⠆⠶⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠁⠿⠛⢻⣿⡿⢿⠛⠁⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣷⣝⢾⢿⣦⠆⠀⠀⠀⠀⠈⠀⠋⠀⢂⣀⣀⣀⡠⢀⠀⢁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢠⣄⣀⢴⡞⠃⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠩⡭⢭⣭⣭⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡭⢩⠍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢩⡍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⣿⣯⣶⣶⣶⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⢊⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⢿⣿⡇⣿⣿⣿⣿⣿
⠐⡮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡟⢸⣿⡇⣿⣿⣿⣿⣿
⠀⠈⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⣸⣿⡇⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣹⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣵⣶⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⠃⠐⠀⢠⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡏⠀⢀⣀⣼⣿⣿⣿⣿⣿⣿⣿⢈⣉⣉⣭⣭⣭⣭⣭⣥⣤⠀⣴⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠸⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠁⠘⠛⠿⠿⢿⣿⡟⠀⠁⣾⣿⣿⣟⣻⡛⠛⠿⢿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣹⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⠳⠶⡶⠷⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⢪⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⣿⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⢷⣾⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡵⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⣼⣿⡇⠀⠀⠀⣿⠇⡿
⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠇⠀⠈⠁⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣇⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⡇⠀⠀⣿⣿⡇⠀⠀⠀⣿⡆⠀
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣾⣿⣿⣿⣿⠀⠀⠀⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣹⣦⠀⠀⡀⠀⠀⢴⠠⠄⠀⠿⠚⠛⠛⠛⠛⠛⣧⠀⠀⠀⠀⢀⣿⠇⠀⠀⣿⣿⠁⠀⠀⠀⢸⡇⠀
⢀⣿⠀⠀⠀⠀⠀⠀⠀⣀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⠀⠀⢰⣿⣿⠀⠀⠀⠀⢸⡇⠀
⢸⡇⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡄⠀⠐⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⣿⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⡇⠀
⠘⠁⠀⠀⠀⠈⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢿⣿⡏⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠃⠀
⡇⠀⠀⢀⣤⣤⣤⡀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣸⣿⠀⠀⣸⢹⣿⠇⠀⠀⠀⠄⠀⠀⠀
⠀⠀⠐⠀⣿⣿⣿⣿⡄⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠸⠋⠀⠀⡿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣈⣿⣿⡍⣇⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣇⢶⣿⢧⠀⠀⠀⠀⠙⣷⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⣠⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠘⡇⠆⠶⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠁⠿⠛⢻⣿⣿⢻⡛⠁⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣷⣝⢾⢿⣦⠆⠀⠀⠀⠀⠈⠀⠉⠀⠂⣀⣀⣀⡠⢀⠀⢁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢠⣄⣀⢴⡞⠃⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣭⢭⢭⢭⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⡍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢩⡍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⡀⢀⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡾⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠐⣿⣯⣷⣦⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣽⡕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿
⠀⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡟⢸⣿⡇⣿⣿⣿⣿⣿
⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⣸⣿⡇⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣹⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⣷⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⠃⠐⠀⢠⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡏⠀⢀⣀⣼⣿⣿⣿⣿⣿⣿⣿⢈⣍⣉⣭⣭⣭⣭⣭⣥⣤⠀⣴⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠁⠐⠛⠿⠿⢿⣿⡟⠀⠃⣾⣿⣿⣟⣻⡛⠛⠿⢿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣹⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⠳⠶⡶⠷⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢐⢢⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⣿⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⢷⣾⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡑⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⣼⣿⡇⠀⠀⠀⣿⠂⡿
⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠃⠀⠉⠁⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣇⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣿⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⡇⠀⠀⣿⣿⡇⠀⠀⠀⣿⡆⠀
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣾⣿⣿⣿⣿⠀⠀⠀⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣹⣆⠀⠀⡀⠀⠀⢴⠠⠄⠀⠿⠚⠛⠛⠛⠛⠛⣧⠀⠀⠀⠀⢀⣿⡇⠀⠀⣿⣿⠀⠀⠀⠀⢸⡇⠀
⢀⣿⠀⠀⠀⠀⠀⠀⠀⣀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⠀⠀⢰⣿⣿⠀⠀⠀⠀⢸⡇⠀
⢸⡇⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡄⠀⠐⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⣿⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⡇⠀
⠘⠁⠀⠀⠀⠈⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢿⣿⡏⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠃⠀
⡇⠀⠀⢀⣤⣤⣤⡀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣸⣿⠀⠀⣸⢹⣿⠇⠀⠀⠀⠆⠀⠀⠀
⠀⠀⠐⠀⣿⣿⣿⣿⡄⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠸⠋⠀⠀⡿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣘⣿⣿⡍⣇⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣗⢶⣿⢧⠀⠀⠀⠀⠙⣷⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠘⠇⠆⠶⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠁⠿⠛⢻⣿⣟⢻⡛⠁⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣷⣝⢾⢿⣦⠆⠀⠀⠀⠀⠈⠀⠉⠀⠂⣀⣀⣀⡠⢀⠀⢁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢠⣄⣀⢴⡞⠃⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⢩⣭⣭⣭⣭⣭⣭⣯⣭⣭⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣭⣽⣯⣭⣉⠉⠉⣭⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⡃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠉⠛⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⣰⣿⣿⠃⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣿⣤⣿⣿⣿⠃⠀⠀⠀⠀⠀⣾⣿⣿⣿⠁⠀⢸⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠁⠀⣿⣿⣿⠀⠈⠉⠉⠉⠉⠁⠀⣀⣀⣀⣀⣀⡀⠀⠀⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣾⣿⣿⣿⣿⡟⠀⠀⠀⠠⢠⣶⣾⣿⣿⣿⣧⣄⠀⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠿⠀⠀⠀⢀⣾⣾⣿⣿⣛⣛⠛⠛⠛⠺⠿⣿⣿⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⢨⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡆⠠⢀⠀⠀⠉⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣿⣶⣄⣄⣄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣷⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣤⣄⣀⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠄⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡄⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠀⠰⠄⠀
⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢨⣿⣿⣿⣿⣿⣿⠧⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠾⠃⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⣀⣀⣀⣠⠤⣀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣟⣛⣛⣻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠁⠼⠛⠻⢿⣿⣿⡟⢧⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢷⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⢉⣭⣭⣯⣽⣭⣯⣽⣿⣭⣭⣽⣭⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣽⣯⣭⢩⣉⢩⣭⡭⠉⢉⢉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠼⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣯⡅⠅⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠈⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⣾⣿⣿⣿⠅⠀⣾⣿⡟⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣤⣿⣿⣿⡟⠀⠀⠁⠀⠀⣴⣿⣿⣿⣿⡀⢀⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⢸⣿⣿⡇⠀⣉⠉⠉⠉⠉⢁⣀⣀⣀⣀⣀⡀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣶⣾⣿⣿⣿⣿⣿⠃⠀⠀⢠⠄⣴⣾⣿⣿⣿⣿⣅⠀⣺⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠿⠇⠀⠀⠀⣼⣿⣿⣿⣟⣛⡿⠿⠿⠤⢿⣿⣿⠇⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣿⣿⣿⣿⣿⣶⠀⢀⠀⠈⠉⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣿⣶⣤⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠨⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢈⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⣄⣀⣼⣿⣿⣿⣿⣿⠀⠀⠀⠀⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡆⢰⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠠⠀⠰⠄⠀
⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠧⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡿⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠐⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠃⠀⠀⠀⠀⠀⠉⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⣀⣀⠀⢤⣄⡀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣟⣛⣛⣻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠁⠼⠛⠻⢻⣿⣿⣿⡇⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⢿⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⢩⣭⣽⣿⣯⣭⣭⣭⣯⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣍⣩⣭⣍⡉⠉⠉⢉⠉⢉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⣻⣛⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠈⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣦⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⣾⣿⣿⣿⠏⠛⣾⣿⠏⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣤⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⣾⣿⣿⣿⡿⠀⢰⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⠀⢸⣿⣿⠀⠀⠉⠉⠉⠉⢀⣀⣀⣀⣀⣀⡀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣾⣿⣿⣿⣿⣿⡿⠁⠀⠀⢤⢠⣶⣾⣿⣿⣿⣿⣄⠀⣼⣿⡿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠿⠿⠁⠀⠀⣠⣿⣿⣿⣛⣛⡿⠿⠿⠿⣦⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣛⣿⣿⣿⣿⣷⣦⣄⠀⠈⠙⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣤⣤⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠉⠈⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⠀⠀⠀⠠⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢨⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣷⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⣄⣀⣰⣿⣿⣿⣿⣿⡇⠀⠀⢀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡄⢸⡄⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠤⠀⠰⠤⠀
⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠧⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡿⠀⠀⠀⠀⠀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠃⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⣀⡀⣀⣠⣀⡀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣛⣛⣻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠛⠁⠾⠛⠻⠻⣿⣿⣿⡁⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⢿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⢭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣍⣭⠉⡭⢉⠉⢩⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⢠⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⡎⡌⠸⠋⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠈⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣭⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⣼⣿⣿⣿⡿⢛⣿⣿⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣬⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⣼⣿⣿⣿⣿⠃⢰⣿⡏⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠀⣾⣿⡇⠀⠀⡈⠉⢉⣁⣀⣀⣀⣀⣀⡀⠀⢠⣤⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⣤⣶⣿⣿⣿⣿⣿⣇⠀⣿⣿⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠻⠿⠿⠟⠀⠀⠠⠬⣼⣿⣏⣙⣿⠿⢿⣿⣿⣾⣿⡟⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⣶⣤⡀⠈⠙⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣾⣦⣤⡠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠛⠛⠁⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⠀⠀⡇⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢨⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣷⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣄⡀⢠⣾⣿⣿⣿⣿⣿⠀⠀⡀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡆⢸⣄⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⡤⠀⠰⠾⠁
⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠁⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠧⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⠀⠀⠀⠀⠀⠠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠸⠇⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⣀⠀⣤⣶⣦⣄⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣛⣛⣻⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠃⠛⠁⠜⠛⠻⢻⣿⣿⣿⡇⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⢷⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⡍⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣍⣩⣉⠭⢩⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡛⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠁⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⣏⡹⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⢰⣿⣿⣿⣿⠏⢸⣿⡗⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠋⢲⠥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣟⠛⠁⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⢲⣿⣿⠃⠀⠀⠀⢉⣁⣀⣀⣀⣀⣀⡀⠀⢠⣤⣴⣾⢝⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⢀⣶⣶⣿⣿⣿⣿⣿⡟⣸⣿⡟⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⡗⠐⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠻⠿⠿⠿⠟⠅⠀⠀⢀⣼⣤⣍⣛⡿⠿⣿⣿⣿⣿⣿⠇⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⢸⣿⣯⣳⢄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⣿⣿⣿⣷⣦⣄⠘⠉⠉⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣷⣯⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⠀
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣄⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡆⢸⣄⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⣴⠀⠸⠾⠗
⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠈⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠧⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣼⡇⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⢢⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣿⠆⠀⠀⠀⠀⠐⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⡿⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⣀⠀⢶⣾⣷⣄⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠏⠛⠁⠜⠛⠻⢻⣿⣿⣿⠃⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⢉⣍⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣭⣽⣯⣍⣩⣭⡭⣩⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⠗⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠐⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠹⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⢿⢵⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢸⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⠋⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⢠⣤⣴⣮⣟⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠘⠓⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣟⣫⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⠿⢿⡟⠁⠀⠀⠲⣦⣤⣤⣙⡿⢿⣿⣿⠿⠏⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⣟⣐⡀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣼⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢸⠀
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⢀⣴⣿⣿⣿⣿⣿⣯⡀⣶⢶⡄⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇⢸⣄⠀⠀⠀⠀⠀⠀⠀⢀⡄⢀⠀⠀⠀⣶⠆⠸⠿⠏
⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣐⣻⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶⠄⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠧⠸⠏⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢠⣿⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣸⡿⠀⠀⠀⠀⠀⠘⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣹⡿⠿⠿⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣴⡄⠀⠀⠀⠀⠀⣀⣠⣀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡇⠀⠀⣐⠀⠀⢹⣿⣿⣧⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡟⠛⠁⠜⠛⠻⠃⢻⣿⣟⡿⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⡟⠛⠛⢻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠩⣽⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⣰⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠈⢻⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⡿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢸⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⠁⣀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⣀⣀⣀⣀⣀⡀⠀⢠⣦⣴⣿⣿⣿⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢀⡀⠈⠀⢸⣿⣿⣿⣿⣿⣿⢿⡿⠟⠉⠁⠀⢀⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠻⠿⠿⠿⣿⡿⠁⠀⠈⠁⢳⣦⣦⣬⣻⣿⣿⠛⠛⠉⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠃⠀⣀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰⣿⣟
⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⢀⣴⣿⣿⣿⡿⠷⢺⣿⠻⠿⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣸⣿⣿⣿⣿⣿⣿⡇⢸⣄⠀⠀⠀⠀⠀⠀⠀⢠⡄⢀⡀⠀⠀⣿⡆⠸⠿⠿
⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣽⣿⣷⣤⣿⣿⣿⣿⡿⠁⢠⣾⣿⣿⡗⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣻⣿⣿⣿⣿⣿⠷⠸⠏⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⠇⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⣾⣿⣿⠋⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣿⠃⠀⠀⠀⠀⠀⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣘⡛⠛⠛⣀⣠⣦⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣏⣩⣴⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣱⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣦⠀⠀⠀⠀⠀⢠⣤⣶⣤⡀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠟⢿⠻⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠀⠀⣀⠈⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢁⡀⠀⡿⣥⣄⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠛⠁⠜⠛⠻⠃⠛⣿⣿⣇⡇⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⢠⠼⢱⣶⣿⣿⣿⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠩⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣝⣉⡉⠉⣉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣀⣬⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⡍⠛⢿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⡏⠉⠸⢽⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⠟⠑⠒⠀⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⣀⣉⣉⣀⣠⣄⡀⢰⣶⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠒⠶⠾⢿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠲⢀⣀⣀⣙⢻⣿⣿⣿⣿⣿⣿⣿⡿⠋⢹⠃⢀⣾⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠿⠿⠿⠿⣿⡿⠃⠀⠀⠀⠘⣿⣿⣿⣿⣏⠉⠉⠛⠉⠀⠀⠀⠎⠀⣼⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⣠⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⢰⣿⣿⣿⠋⠉⠠⠄⠀⠀⠀⠀⢠⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠃⠀⠀⠀⠀⠀⠀⠠⠄⠈⠀⠀⢿⣿⡿⢛⣽⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⡇⠀⢀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⣿⣿⣿⣿⣿⣟⣸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⢀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡟⠀⠀⠼⢃⣀⡄⠀⠀⠀⢀⡄⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡿⠋⣿⣿⣿⣿⣿⣿⣁⠀⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡆⢿⣿⣿
⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣠⣿⣿⣿⣿⠋⠀⢀⣄⢀⣙⣻⡇⠀⠀⣤⠀⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡟⠉⣿⣿⣿⡏⢻⣄⠀⠁⠀⠀⠀⠀⠋⢸⣮⣿⣇⠀⢿⣿⡧⠾⠿⠿
⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣭⣿⣾⣿⣿⣿⡿⠁⠀⠠⣿⣿⣿⣿⡟⣠⣴⠋⣁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣦⣀⣼⣿⣿⡿⠾⠟⠀⠀⠈⠉⠁⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⠁⠀⢤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣷⣴⣴⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⠟⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣾⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⢫⣽⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣿⡄⠀⠀⠀⠀⠀⣴⣾⣿⣷⣦⡀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣏⣖⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⡇⠀⣀⠀⠚⠀⠸⣿⣿⣿⣿⣷⠒⠂⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⠋⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⠃⠝⠛⠻⠃⠛⠛⢿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠻⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣂⠁⠘⠃⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠩⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣝⣉⠉⠉⣉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠈⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣀⣬⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⡌⠛⢿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⡎⠉⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⠟⠑⠒⠂⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣀⣉⣉⣀⣠⣄⡀⢰⣶⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠒⠶⠾⢿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠲⠀⣀⣀⣙⢻⣿⣿⣿⣿⣿⣿⣿⠿⠋⢹⠃⢀⣾⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠿⠿⠿⠿⣿⡿⠃⠀⠀⠀⠘⣿⣿⣿⣿⣏⠉⠉⠛⠉⠀⠀⠀⠊⠀⣼⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⣠⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⢰⣿⣿⣿⠋⠋⠠⠄⠀⠀⠀⠀⢠⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠃⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⢻⣿⡿⢛⣽⣿⣿⣿⣇⢸⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⡏⠀⢀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣳⣿⣿⣿⣿⣿⣟⣸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⢀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠟⠀⠀⠸⢃⣀⡄⠀⠀⠀⢀⡄⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡿⠏⣿⣿⣿⣿⣿⣿⣁⠀⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡆⢿⣿⣿
⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣠⣾⣿⣿⣿⠋⠀⢀⣄⢀⣘⣻⠇⠀⠀⣤⠀⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡟⠉⣿⣿⣿⡏⢻⣄⠈⠁⠀⠀⠀⠀⠋⢸⣯⣿⣇⠀⢿⣿⡧⠾⠿⠿
⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣯⣿⣾⣿⣿⣿⡿⠃⠀⢠⣿⣻⣿⣿⡟⣠⣰⠋⣁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣦⣀⣼⣿⣿⡿⠿⠟⠀⠀⠈⠉⠁⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⠁⠀⢄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣷⣴⣶⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⠟⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣻⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⢫⣽⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣿⡄⠀⠀⠀⠀⠀⢴⣾⣿⣷⣦⡀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣏⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⡇⠀⣀⠀⠚⠀⠹⣿⣿⣿⣿⣷⠒⠂⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣿⣿⡿⠋⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⠃⠝⠛⠻⠃⠛⠛⢿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠻⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢂⠁⠈⠉⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣍⣝⡍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣟⣽⢍⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣠⣤⣬⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣜⣿⢿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢰⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡏⠉⠸⢹⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⠋⠉⠀⠰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⣀⣉⣉⣀⣠⣀⡀⢰⣶⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠒⠲⠿⢼⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠂⠀⢠⣤⣤⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⠇⠀⣼⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠿⠿⠿⠿⣿⣿⠏⠀⠀⠀⠀⣿⣿⣿⣧⣿⣄⠀⠀⠀⠀⠉⠍⠉⠀⢰⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⣠⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⠀⣸⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⡀⠀⠀⠀⢻⣿⠀⠹⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢠⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠹⢿⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⠀⠀⠀⠀⠰⣾⣾⣿⣿⣿⣻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⢀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠀⣀⣀⢀⢀⣬⣿⣿⣿⣿⣿⣿⡏⣉⣿⣿⣇⠀⢦⡄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⣠⣾⡆⢿⣿⣿
⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⢠⣿⣿⣿⡆⠈⠙⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⢻⣤⠈⠀⠀⠀⠀⠀⠋⢸⣶⣿⣆⠸⢼⣿⡧⠾⠿⠿
⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣬⣐⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣏⣛⣢⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠸⠟⠀⠀⠈⠉⠁⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣯⠿⠃⠀⠀⠛⠀⢀⣤⣴⣤⣴⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣿⠟⠀⠀⠀⠀⠀⠀⠀⠰⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣿⣿⡿⢿⠿⣿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣿⡀⠀⠀⠀⠀⠀⢀⣴⣦⣿⡟⢶⣄⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣸⣿⡇⠀⣀⠀⠀⠐⠀⢹⣿⣿⣿⣷⣿⣷⠂⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡿⠟⠛⠻⠃⠛⠛⠛⢿⣿⣿⣿⣏⡹⡇⠀⠀⠀⠙⣿⣿⣿⠟⠋⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡿⠟⠋⠁⠀⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⢉⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡯⠭⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢡⣀⢀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⢇⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢸⣿⣿⣿⣿⣿⣿⣿⣟⣛⠋⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣈⣉⣉⣀⣀⣀⣀⠀⢠⣶⣶⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠐⠢⠤⠤⣤⣶⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⢶⣶⣿⣿⢻⡏⠉⠉⠛⠻⢿⣿⣿⠁⠀⣸⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠻⠿⠿⠿⣿⡿⠁⠀⠀⠀⣸⣿⣿⣇⣿⠟⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⣝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠘⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢰⣿⣿⣿⡏⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠋⠀⣴⠂⠀⠀⠄⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⢸⣿⣿⣿⣿⣿⣄⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡄⢸⣿⣿
⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣰⣿⣿⣿⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢀⣀⣹⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠁⢰⣆⣤⡀⠀⢸⣿⡧⠼⠿⠿
⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣭⣾⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⠀⠀⣀⣠⣤⢶⣶⣶⠊⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⡿⠋⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢠⣤⣄⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣷⡀⠀⠀⠀⠀⠀⢀⣰⣾⣶⣿⡉⠻⣦⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⠋⠀⠉⣿⣿⣿⣿⢿⠥⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⡇⠀⣀⠀⠀⠀⠉⠁⢻⣿⣿⣿⣿⠋⣷⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⣼⣾⣯⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡟⠟⠛⠻⠃⠛⠛⠛⠋⢿⣿⣿⣿⣄⠸⡆⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠄⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⣉⠭⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠻⢏⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢍⣉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⢅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⡁⠀⢠⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢸⣿⣿⣿⣿⣿⣿⣿⣟⡛⠁⠀⠀⠀⠙⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢈⣉⣉⣀⣀⣀⣀⣀⠀⢠⣶⣶⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠐⠂⠤⠤⢤⣴⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠘⢳⣿⣿⣿⣿⣄⡀⠈⠉⠙⠻⠟⠁⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠁⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠻⠿⠿⠿⣿⡏⠀⠀⠀⠀⣼⣿⣿⣹⡿⠋⠁⠀⠀⠀⣄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠀⠀⠀⠀⢀⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡏⠹⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⠀⣸⡏⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⠿⠀⠀⣿⣿⣿⡿⡀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⢸⣿⣿
⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⣿⣿⣿⠇⠀⢠⡿⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢀⣿⣿⣿⡏⢻⣄⠀⠀⠀⠀⠀⠀⠀⢠⡄⣤⡀⠀⠸⣿⡇⠼⠿⠿
⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣮⣷⣿⣿⣿⣿⠄⠀⠸⠇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣼⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⡀⡀⢠⣤⣶⣿⣿⡏⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⣿⣿⣿⠛⠁⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡇⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣷⡀⠀⠀⠀⠀⠀⢀⡀⢺⣿⣶⣧⠙⣷⡄⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢀⠀⠀⢤⣤⣀⣀⣠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⡇⠀⣀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠁⢻⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢹⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠁⠉⠻⠿⠻⠓⠿⠋⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⡇⠝⠛⠻⠃⠛⠛⠛⠁⠸⣿⣿⣿⣀⡈⣇⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⣉⡍⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠻⢏⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣉⠍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠉⠰⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣟⠀⠀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢸⣿⣿⣿⣿⣿⣿⣿⣟⠋⠀⠀⠀⠈⢹⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⠀⠀⢈⣉⣉⣉⣁⣀⣀⣀⣀⠀⢠⣶⣶⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠐⠀⠤⠤⢤⣴⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠘⢻⣿⣿⣿⣿⣦⡀⣀⡀⠈⠉⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢸⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⠿⣿⡏⠀⠀⠀⠀⣾⣿⣿⣿⡟⠁⢘⣿⣿⡟⠃⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢞⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠀⠀⠀⠀⠀⣿⣿⣿⣿⠃⠀⠨⣿⣿⡿⢶⠂⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡏⠀⠀⠀⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛
⠀⠀⠀⠀⠀⠀⠀⠀⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⢻⡿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠇⠀⢠⡆⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣸⠁⢸⣿⣿⣿⣿⡀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡀⢸⣿⣿
⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣾⣿⣿⡿⠀⠀⣾⠇⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠀⢀⣿⣿⣿⡏⢻⣄⠀⠀⠀⠀⠀⠀⠁⢠⡄⣠⡀⠀⠰⣿⠆⠼⠿⠿
⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣮⣽⣺⣿⣿⣿⡿⠀⠀⠛⠀⠀⠀⢀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢸⣿⣿⣿⡷⠼⠟⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣼⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣄⣀⣠⣴⣶⣿⣿⠃⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠁⠀⠀⣀⣀⣤⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣷⣿⣿⠇⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⠿⢁⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣷⡀⠀⠀⠀⠀⠀⠀⣀⢺⣿⣶⣯⠙⣷⡄⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢀⠀⠀⠙⣿⣟⣵⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⡇⠀⣀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠉⢳⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢳⣆⠀⣸⣿⣧⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣟⣵⣿⡟⠉⠙⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⡗⠝⠛⠻⠃⠛⠛⠛⠁⠘⣿⣿⣿⣂⠘⡇⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠋⠀⠀⠀⠙⠛⠟⠋⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⢉⣉⣍⢭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠛⠫⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣭⡍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠉⠊⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⡃⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢸⣿⣿⣿⣿⣿⣿⣿⣟⠃⠀⠀⠀⠈⣹⣿⣿⡟⠛⠛⠿⠿⣿⣿⡇⠀⠀⣉⣉⣉⣉⣉⣀⣀⣀⣀⠀⢠⣶⣶⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠂⠤⠤⢤⣴⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⡟⠐⠀⠀⠙⢻⣿⣿⣿⣿⣶⣦⣤⣤⣀⡀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⠿⣿⡇⠀⠀⠀⠀⣾⣿⣿⣿⣿⠁⣿⣿⣿⣿⣯⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢞⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⣿⣿⣿⠇⠀⣿⣿⣿⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠄⠀⠸⢿⣿⠟⠉⠀⢠⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣻
⠀⠀⠀⠀⠀⠀⠀⠀⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠀⠀⠀⠈⠀⠄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡼⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠀⢀⠀⠀⠀⠀⠰⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡇⠈⣿⣿⣿⣿⣿⡀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡀⢸⣿⣿
⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢠⣿⣿⣿⡇⠀⠼⠁⠀⠀⠀⢸⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⠃⠀⣿⣿⣿⣿⡏⢻⣄⠀⠀⠀⠀⠀⠀⠁⢰⣄⣤⡀⠀⠰⣿⠆⠸⠿⠿
⠀⠀⢠⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣦⣽⣶⣿⣿⣿⡿⠗⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣿⣿⣿⣿⡷⠼⠟⠀⠀⠀⠈⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣥⣤⣀⣤⣤⣴⣦⣄⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⡏⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢀⣠⣴⣶⣶⣶⣶⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⠟⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣷⡀⠀⠀⠀⠀⠀⠀⣀⢺⣿⣶⣯⢙⣷⡀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⡀⠀⠀⠙⣿⣋⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⡇⠀⣀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⢏⣷⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣄⠀⣻⣿⣥⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣷⣿⠟⠙⠉⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡟⠟⠛⠻⠃⠛⠛⠛⠁⠘⣿⣿⣿⣆⢹⡄⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⠀⠀⠈⠛⠛⠛⠋⢤⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⢍⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠙⠟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⡭⢉⠉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢷⣌⣌⡌⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⠁⠀⢀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢸⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠈⠙⢻⣿⣿⣿⠿⠿⢿⣿⣿⣿⡁⠀⠈⣉⣉⣉⣉⣉⣀⣀⣠⣀⡀⢠⣶⣶⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠐⠒⠴⠤⣴⣶⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠲⣶⣿⣿⣿⣿⣦⣤⣤⣄⣈⠉⠁⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠻⠿⠿⠿⣿⡇⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣼⣿⣿⣿⣟⠉⢹⣿⣿⣿⣿⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⡟⠀⠀⠈⠉⣅⠇⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏⣰⡆⠀⠈⠀⢰⠇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠇⠀⣿⣿⣿⣿⣿⣿⣿⡄⠀⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡄⢸⣿⣿
⠀⠀⠀⢠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣾⣿⣿⣿⠁⣿⡇⠀⠀⠀⢸⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⢻⣄⠀⠀⠀⠀⠀⠀⠃⢸⣦⣶⡄⠀⢺⣿⡧⠼⠿⠿
⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣭⣿⣶⣾⣿⣿⣿⡿⠴⠿⠃⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠛⠛⠛⠻⢿⣿⣷⣾⠟⠀⠀⠀⠉⠁⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡁⢀⡀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⣀⣴⣾⣶⣶⣾⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⠂⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠃⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠈⢻⡿⣟⣥⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣿⡆⠀⠀⠀⠀⠀⢀⣄⣿⣿⣶⣯⣹⣶⡀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢶⣴⣇⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣟⠉⠛⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⡇⠀⣀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣗⠐⠂⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣹⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⠀⠀⢝⢟⣿⡁⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⡿⠟⠛⠻⠃⠛⠛⠛⠃⠹⣿⣿⣿⣇⢻⡀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠻⠿⠇⠀⠀⠀⠀⠀⠀⠩⠟⠊⠉⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⢭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣝⠉⠉⢉⢉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣟⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣀⣬⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣬⣟⢿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡏⠉⠹⢹⣿⣿⣿⣿⣿⣿⣿⣿⠛⠄⠀⠰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⣉⣉⣉⣉⣉⣁⣀⣠⣀⡀⢰⣶⣶⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠒⠲⠮⢭⣿⣷⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⡿⢀⠀⠀⣠⣀⣼⣿⣿⣿⣉⠉⠙⠛⠛⠿⠧⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠿⠿⠿⠿⣿⡇⠀⠀⠀⠈⢻⣿⣿⣿⣿⡿⣷⣷⣶⣶⣤⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⣠⢾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⡁⢸⣿⣿⣿⣾⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠉⠛⠛⣿⠀⢰⢸⣿⣿⣿⣿⣿⣿⣿⣿⢿⡇⢸⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢷⡇⠀⠀⠀⠀⡏⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠁⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣺⡇⠀⠀⠀⢸⠇⠀⠀⣿⣿⣿⣿⣿⣿⣿⠉⠉⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡅⠀⢶⡄⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⣀⣴⡆⢻⣿⣿
⠀⠀⠀⢠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠇⡿⠀⠀⠀⠀⢸⠀⢀⣼⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⢻⣤⠈⠁⠀⠀⠀⠀⠋⢸⣷⣷⣤⠐⢿⣿⣧⠾⠿⠿
⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣬⣽⣶⣀⣠⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠸⣶⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⢀⣀⣀⣀⣬⣿⣿⣿⣿⣾⠿⠆⠀⠈⠉⠁⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⡀⢠⠀⠀⠀⠀⠈⠻⣿⣿⣿⠿⢁⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢈⣻⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠛⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣿⡆⠀⠀⠀⠀⠀⢀⡠⣿⣿⣾⣯⣿⣆⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣧⠀⣘⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢹⣿⣿⣿⡷⢩⣾⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⡇⠀⣀⠀⠀⠀⠀⠁⢻⣿⣿⣿⣿⣿⡖⠒⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠁⠈⠙⣾⡋⢿⣿⣿⠷⠾⠿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⡿⠟⠛⠻⠃⠛⠛⠛⠃⢻⣿⣿⣿⣍⣷⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡿⠟⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠉⠉⠉⠁⠀⠀⠀⠀⠲⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣉⠉⢉⢉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠉⠻⣿⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣛⣿⣿⡶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⠀⠀⣀⣤⣬⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣿⣿⠿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⡏⠙⠲⢹⣿⣿⣿⣿⣿⣿⣿⣿⣻⠁⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢈⣉⣉⣉⣉⣁⣀⣠⣀⡀⢰⣶⣶⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠒⠲⠿⢭⣿⣷⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⠇⠆⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠿⠿⠿⢿⣿⣿⢀⠀⠀⢀⡀⢙⣿⣿⢻⠛⠛⠛⠛⠛⠿⠿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⣠⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡇⠀⠀⠀⠘⢻⣿⣿⡿⢸⣷⣤⠀⠀⠀⢀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⣿⣿⡇⣿⡇⠀⠀⠀⠀⠈⠀⠀⢠⣿⣿⣿⣿⣿⣹⡟⢿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣼⡧⠈⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣏⠀⠀⠀⢹⡇⢸⣿⣿⣿⣿⣿⣿⣿⣅⠀⢦⡄⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣠⣾⡆⢻⣿⣿
⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠀⠀⠀⠠⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠏⠀⠀⠀⠸⠇⠸⠿⢿⣿⣿⣿⣿⡟⢻⣄⠈⠁⠀⠀⠀⠀⠃⢸⣷⣶⡄⠘⣻⣿⣧⠾⠿⠿
⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⢠⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡏⠀⠀⠀⠀⣠⣤⣤⣴⣶⣿⣿⣿⣿⡿⠾⠟⠂⠀⠈⠉⠁⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣾⣷⣾⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠇⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣿⠟⠀⠀⠀⠀⠀⠀⠀⠐⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡿⢋⣠⣴⣾⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⠀⢀⣀⡀⠀⢀⣠⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣩⡿⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣿⡄⠀⠀⠀⠀⠀⠀⣴⣾⣯⣟⣳⣦⡀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣏⣹⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣉⣿⣿⣿⣿⣏⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⡇⠀⣀⠀⠀⠀⠙⠘⣿⣿⣿⣿⣿⣷⠂⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡯⠁⠀⠀⠸⣿⡏⣻⣿⠿⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡿⠟⠛⠻⠃⢛⠛⠛⠻⣿⣿⣿⣿⣿⡄⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡿⠟⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣡⠄⠀⠀⠀⠀⠀⢀⣐⡞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⢭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣍⡍⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠉⠻⣿⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⡯⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⠀⠀⣀⣤⣬⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⡏⠉⠰⢻⣿⣿⣿⣿⣿⣿⣿⣿⣻⠁⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢈⣉⣉⣉⣉⣈⣀⣠⣀⡀⢰⣶⣶⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠒⠲⠿⢿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠆⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠿⠿⠿⢿⣿⣿⢀⠀⠀⢀⡀⢙⣿⣿⢻⠛⠛⠛⠛⠛⠿⠿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⣠⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠇⠀⠀⠀⠘⢻⣿⣿⡿⢸⣷⣤⠀⠀⠀⢀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⣿⣿⠇⣿⡇⠀⠀⠀⠀⠈⠀⠀⢠⣿⣿⣿⣿⣿⣹⡟⢿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢸⣿⣿⣯⡿⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣼⡧⠈⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣏⠀⠀⠀⢹⡇⢸⣿⣿⣿⣿⣿⣿⣿⡅⠀⢶⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣠⣾⡆⢻⣿⣿
⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠀⠀⠀⠠⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠍⠀⠀⠀⠸⠇⠸⠿⢿⣿⣿⣿⣿⡟⢿⣄⠈⠁⠀⠀⠀⠀⠃⢰⣟⣴⣄⠼⢿⣿⡧⠾⠿⠿
⠈⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⢀⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡏⠀⠀⠀⠀⣠⣤⣤⣴⣶⣿⣿⣿⣿⠿⠾⠟⠆⠀⠈⠉⠁⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣾⣷⣾⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⠇⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣿⠟⠀⠀⠀⠀⠀⠀⠀⠐⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡿⢋⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⠀⢀⣀⡀⠀⢀⣠⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣩⠿⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣿⡄⠀⠀⠀⠀⠀⠀⣴⣾⣯⣿⡳⣦⡀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣏⣹⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣉⣿⣿⣿⣿⣏⣻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⡇⠀⣀⠀⠀⠀⠉⠘⣿⣿⣿⣿⣿⣷⠒⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡯⠁⠀⠀⠹⣿⡏⣻⣿⠿⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡿⠟⠛⠻⠃⢛⠛⠛⠻⣿⣿⣿⣿⣿⡄⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡿⠟⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣩⠄⠀⠀⠀⠀⠀⠀⣀⡞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡭⡭⢍⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠛⢻⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣛⣿⣻⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⢹⣶⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣤⣬⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠸⢾⣿⣿⣿⡏⠉⠱⢿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠁⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣉⣉⣉⣉⣉⣉⣀⣀⣀⡀⢰⣶⣶⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠒⠶⠿⢿⣿⣷⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⠣⠄⠀⢀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠿⠿⠿⢿⣿⡏⡀⠀⠀⠈⠛⢿⣿⡿⣿⢿⣿⡟⠛⠻⣿⣧⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⡠⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠉⠀⠀⠶⢦⣾⣿⡇⣶⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⣿⣧⣿⣅⠹⠙⠀⠀⠀⠀⠆⠀⠀⢸⣿⣿⣿⣿⣿⡿⣿⢿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠸⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡏⣿⡄⢻⡇⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣧⡏⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡍⠙⠁⠈⡇⢸⣿⣿⣿⣿⣿⣿⣿⣅⠀⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡆⢻⣿⣿
⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠇⠀⠀⠀⣠⡀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⢿⣄⠀⠀⠀⠀⠀⠀⠋⢸⣧⣴⡄⠘⢿⣿⡧⠼⠿⠿
⠀⠀⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣿⣿⣿⠋⠀⢀⣤⣆⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⢉⣉⣻⣿⣿⣿⣿⠾⠟⠂⠀⠈⠉⠁⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠀⠀⢸⣿⣷⠇⠀⠀⠘⢿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠰⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠻⠟⠋⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⠃⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⣻⣯⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣧⠀⠀⠀⠀⠀⠀⠀⣰⣾⣽⣟⢶⣄⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⢲⣶⣥⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣴⢟⣭⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⡆⠀⣀⠀⠀⠀⠛⠘⣿⣿⣿⣿⣿⣷⠦⠄⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠙⢫⣶⣿⣿⣿⣿⣷⣼⣿⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡟⠟⠛⠻⠃⠛⠛⠛⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣛⡯⠙⠋⠀⠀⠀⠈⣻⡿⠾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⢭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣍⣍⠉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠈⠙⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠙⢿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣓⣻⣷⡧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣤⣤⣝⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣭⣟⠿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠰⢿⣿⣿⣿⡇⠉⠱⢽⣿⣿⣿⣿⣿⣿⣿⣟⡋⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣉⣉⣉⣉⣉⣈⣀⣀⣀⡀⢰⣶⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠐⠲⠿⢿⣿⣷⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⡟⠠⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠿⠿⠿⠿⣿⠇⡀⠀⠀⠀⠙⣻⣿⠿⠟⠛⠻⠋⠛⠛⢿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⡠⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠛⣴⡿⣿⢠⣷⣤⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣿⣿⣿⡾⣿⠈⠀⠀⠀⠀⠁⠀⠀⣼⣿⣿⣿⣿⣿⡿⣿⢿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠸⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⡇⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡏⣽⡄⢻⡇⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡏⠙⠁⠈⡇⢸⣿⣿⣿⣿⣿⣿⣿⡅⠀⢦⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⣶⡆⢻⣿⣿
⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠀⠀⠀⠀⡰⠆⠀⠀⠀⣾⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⡀⢸⣿⣿⣿⣿⣿⣿⡟⢻⣄⠈⠁⠀⠀⠀⠀⠃⢰⣆⣴⡄⠀⢿⣿⡧⠼⠿⠿
⠀⠀⢠⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⡀⠀⠀⠀⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢉⣉⣻⣿⣿⣿⣿⠾⠟⠀⠀⠀⠉⠁⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠀⠀⠰⠄⠄⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠰⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⠃⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠀⠀⠀⠀⠀⠀⠀⣛⣯⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢴⣧⠀⠀⠀⠀⠀⠀⠀⣴⣾⣽⣟⢷⣄⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⢶⣶⣧⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣤⢏⣱⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡆⠀⣀⠀⠀⠀⠋⠸⣿⣿⣿⣿⣿⡦⠦⠄⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠙⠫⣴⣿⣿⣿⣿⣷⣼⣿⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡗⠟⠛⠻⠃⠛⠛⠛⢻⣿⣿⣿⣿⣷⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⠟⠋⠀⠀⠀⠀⢻⡯⠼⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⢭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣭⢭⣍⣍⢉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠈⠙⠋⣍⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢏⣴⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣠⢌⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢽⢟⣿⣿⣷⣈⣻⠿⣿⣿⣿⣯⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⠃⠈⠰⢹⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢈⣉⣉⣉⣉⣁⣀⣀⣀⣄⠀⢰⣶⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠐⠲⠿⠿⣿⣶⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⡇⠒⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠿⠿⠿⠿⣿⠡⠄⠀⢀⣀⣨⣿⣿⢙⡉⠉⠉⠉⠉⠙⠛⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⣠⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠙⣿⣿⡟⢸⣿⠶⠀⠀⠀⢠⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣇⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡟⣿⢿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣃⣿⠀⢿⡇⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠋⠋⠀⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⡄⠀⢦⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣠⣾⡆⢻⣿⣿
⠀⠀⠀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠀⠀⠀⢠⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠙⠀⠀⠀⢸⡇⢸⣿⣿⣿⣿⣿⣿⡟⢻⣤⠀⠁⠀⠀⠀⠀⠃⢸⣇⣼⡄⠀⢺⣿⡧⠼⠿⠿
⠐⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⠀⠀⢀⣿⣿⣿⠇⠀⠀⠠⠀⠁⠀⠀⣠⣾⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣀⠀⣉⣉⣿⣿⣿⣿⣿⠾⠟⠀⠀⠀⠉⠁⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣷⣦⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠐⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⠁⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣙⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣷⠀⠀⠀⠀⠀⠀⠀⣴⣯⣽⣟⢷⣄⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⣶⣾⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣯⡼⣋⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⡇⠀⣀⠀⠀⠈⠁⠘⣿⣿⣿⣿⣿⡆⠦⠄⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣽⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠁⣄⡹⣿⣿⣿⣧⣼⣿⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡗⠟⠛⠻⠃⠛⠛⠛⢻⣿⣿⣿⣟⣷⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⣫⠤⠿⠛⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⢭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣯⣭⣍⣉⢉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠙⣳⣶⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣿⣻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⠀⠀⢠⣀⢌⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠼⠿⣿⣿⣷⣈⣛⠿⣿⣿⣿⣯⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⡁⠈⠰⢹⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢉⣉⣉⣉⣉⣉⣀⣀⣀⣀⠀⢰⣶⣶⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠐⠒⠿⢯⣽⣶⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⠁⠁⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠿⠿⠿⠿⣿⠐⠂⠀⢰⣤⣴⣿⡏⢸⣀⡀⠀⠀⠀⠉⠉⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣠⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⣼⡟⠉⠀⠀⠀⠲⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⡿⣷⠀⠀⠀⠀⢀⠀⠀⢰⣿⣿⣿⣿⣿⣿⢟⡿⢿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⡿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣸⣇⠈⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢺⠃⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠉⠁⠀⢹⡇⢸⣿⣿⣿⣿⣿⣿⣿⡄⠀⢦⡄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣠⣾⡆⢻⣿⣿
⠀⠀⠀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⢸⡇⢸⣿⣿⣿⣿⣿⣿⡏⢻⣄⠀⠁⠀⠀⠀⠀⠃⢰⣇⣾⡄⠈⢽⣿⡧⠼⠿⠿
⠐⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣀⠀⠀⢀⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠈⣁⢀⣉⣩⣿⣿⣿⣿⡿⠾⠟⠀⠀⠀⠉⠁⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⣠⣀⣀⠀⠀⠀⠀⠀⠈⢻⣿⣿⠟⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣩⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣷⡀⠀⠀⠀⠀⠀⠀⣴⣿⣽⣟⢷⣄⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⡿⠶⣷⣾⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⣧⠾⢉⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣸⣿⡇⠀⣀⠀⠀⠈⠁⠘⣿⣿⣿⣿⣿⡖⠂⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠉⠋⠀⣄⠿⣿⣿⣿⣶⣿⡯⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡟⠟⠛⠻⠃⠛⠛⠛⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⠛⠀⠀⠀⠀⠀⣩⠔⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠩⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣯⣭⣭⢉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠈⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠉⣴⣾⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣟⣾⡆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⠀⠀⠀⠀⣈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢼⢿⢿⣿⣗⣈⣛⢿⣿⣿⣿⣯⣿⣿⣿⣿⣿⠇⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⠇⠈⠰⢹⣿⣿⣿⣿⣿⣿⣿⡏⡀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣉⣉⣉⣉⣉⣁⣀⣀⣠⣀⠀⢠⣶⣶⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠐⠲⠿⠿⣿⣶⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠉⢻⣿⡿⠿⠿⠻⠿⠿⢿⣿⣷⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠿⠿⠿⠿⡟⠐⠀⠀⠸⢶⣿⣿⡇⢸⣤⡄⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⣠⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⣾⡇⠀⠀⠀⠀⠙⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣽⡏⡅⠀⠀⠀⠀⢸⠀⠀⢸⣿⣿⣿⣿⣿⣿⢻⡿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣧⡿⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣸⡇⠘⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢿⠇⠀⠀⠀⠠⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠉⠁⠀⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⡄⠀⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣶⡆⢺⣿⣿
⠀⠀⠀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠈⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡏⠋⠀⠀⠀⣸⡇⢸⣿⣿⣿⣿⣿⣿⡏⢻⣄⠀⠀⠀⠀⠀⠀⠁⢸⣇⣽⣄⠐⢿⣿⡧⠼⠿⠿
⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣠⡀⠀⢠⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⢈⣀⢀⣉⣩⣿⣿⣿⣿⡿⠾⠟⠀⠀⠀⠉⠁⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⣤⢄⣀⠀⠀⠀⠀⠀⠈⠻⣿⡿⠏⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢀⣩⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣷⡀⠀⠀⠀⠀⠀⠀⣴⣿⣽⣟⢷⣄⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⢶⣶⣧⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣧⠾⢍⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣸⣿⡇⠀⣀⠀⠀⠈⠁⠘⣿⣿⣿⣿⣿⡔⠂⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠙⠛⠤⣮⢿⣿⣿⣿⣤⣿⡯⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡟⠟⠛⠻⠃⠛⠛⠛⢻⣿⣿⣿⣻⡇⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⠿⠛⠀⠀⠀⠀⢀⣧⠔⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⣭⣭⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⢉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠩⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣩⣳⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⠀⠀⠀⣀⢬⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⢿⣿⣧⣈⡛⢿⣿⣿⣿⣯⣿⣿⣿⣿⣿⠃⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠇⠈⠰⢹⣿⣿⣿⣿⣿⣿⣿⡏⡀⠀⢀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⣉⣉⣉⣉⣉⣁⣀⣀⣀⣀⠀⢰⣶⣶⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠒⠲⠿⠿⣿⣶⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⣹⣿⣿⣿⠛⠛⠛⠿⠿⠿⠇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠿⠿⠿⠿⡟⠘⠀⠀⠘⢻⣿⣿⡧⣿⣶⣦⣀⣀⠠⣄⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⣠⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⣿⡇⠈⠻⠿⣿⣬⡄⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣽⡿⡃⠀⠀⠀⠈⢹⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣇⣧⠀⠀⠀⠀⠈⠀⠀⣼⣿⣿⣿⣿⣿⣿⣷⣿⠘⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⢿⡇⠀⠀⠀⠰⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⠟⠛⠀⢻⡇⢸⣿⣿⣿⣿⣿⣿⣿⡄⠀⢦⣄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⣾⡆⢸⣿⣿
⠀⠀⠀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠸⠁⠀⠠⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⢸⡇⢸⣿⣿⣿⣿⣿⣿⡏⢻⣄⠀⠁⠀⠀⠀⠀⠁⢰⣇⣽⣆⠙⢺⣿⡧⠼⠿⠿
⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣥⣀⡀⢀⣠⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢴⣾⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠘⠃⠘⠛⠛⣿⣿⣿⣿⡿⠾⠟⠀⠀⠈⠉⠁⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⠀⠀⠀⢀⣠⣶⣿⣶⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠚⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣒⣄⡠⠀⠀⠀⠀⠀⠈⠻⣿⣿⡟⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢙⣩⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣷⡀⠀⠀⠀⠀⠀⠀⢶⣯⣽⣝⢷⡄⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣦⣦⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣹⠟⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⡇⠀⣀⠀⠀⠈⠁⠘⣿⣿⣿⣿⣿⡒⠂⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣛⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠻⡿⢃⣰⣿⣿⣿⣿⣉⣿⣟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡟⠟⠛⠻⠃⠛⠛⠛⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠐⢏⣹⠿⠟⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣍⡍⢩⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠉⣾⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⣴⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣯⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢹⣿⣿⣿⣿⣿⣿⣿⡏⡀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢉⣉⣉⣉⣉⣉⣀⣀⣀⣀⠀⢠⣶⣶⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠐⠒⠦⠤⣤⣶⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⠀⠁⠀⠀⠉⢻⣿⣿⣿⠛⠛⠿⠿⠿⣿⠧⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠿⠿⠿⠿⡟⠐⠀⠀⠘⢿⣿⣿⣿⣿⣦⣤⠀⠀⠀⣀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⢾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⣼⠇⠀⠀⠠⢶⣈⡀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠐⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⣧⠀⠀⠀⠀⠸⠀⠀⢸⣿⣿⣿⣿⣿⣿⣇⣿⠙⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣷⡟⠀⠀⠀⠰⠆⠀⠀⣼⣿⣿⣿⣿⣿⣿⡿⠿⠀⢹⡇⢸⣿⣿⣿⣿⣿⣿⣿⡄⠀⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡆⢻⣿⣿
⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢸⠃⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⢻⠀⠀⠀⢸⡇⢸⣿⣿⣿⣿⣿⣿⡏⢻⣤⠀⠁⠀⠀⠀⠀⠁⢸⣇⣷⣄⠀⢸⣿⡧⠼⠿⠿
⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣔⣀⠀⠀⢀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⠃⠘⠿⠿⣿⣿⣿⣿⡿⠾⠿⠀⠀⠈⠉⠁⠀⠀⠈⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢀⣤⣶⣤⣴⣶⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠚⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⠤⠄⣀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠁⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠹⢛⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣷⡀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣟⣶⡄⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣤⣤⣀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⢻⠿⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⣿⡇⠀⣀⠀⠀⠈⠁⠸⣿⣿⣿⣿⣿⡒⠀⠄⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⣿⣯⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠟⠈⢽⣿⣿⣿⠛⣶⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡏⠟⠛⠻⠃⠛⠛⠛⢻⣿⣿⣿⣿⡇⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⡶⠘⣿⡿⠟⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠩⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡭⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠙⢻⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣷⡤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣯⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢹⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢈⣉⣉⣉⣉⣉⣀⣀⣀⣀⠀⢠⣶⣶⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠐⠒⠦⠤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠇⠒⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⢿⣿⠠⠀⠀⢀⣀⣈⣿⣿⢻⡏⠉⠉⠋⠙⠛⠟⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⣾⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⢾⣿⠶⠀⠀⠀⢠⠄⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⣼⣿⠀⠀⠀⠀⢀⡄⠀⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠰⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⣿⠀⠀⠀⠀⠸⠁⠀⢺⣿⣿⣿⣿⣿⣿⣿⣛⣿⢿⡇⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⡏⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠃⢸⣿⣿⣿⣿⣿⣿⣿⡄⠀⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡆⢻⣿⣿
⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠊⠀⠀⠀⡆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠀⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⡏⢻⣄⠀⠀⠀⠀⠀⠀⠁⢸⣇⣷⣄⠈⢸⣿⡧⠼⠿⠿
⠀⠀⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⣿⣿⣿⡟⠀⠀⠀⠈⠅⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡇⠁⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡿⠿⠟⠀⠀⠀⠉⠁⠀⠀⠈⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⣀⣀⣀⣠⣬⣷⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠲⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡇⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠹⡿⠛⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣷⠀⠀⠀⠀⠀⠀⠀⣴⣯⣽⡿⣦⡀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣀⣀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡆⠀⣀⠀⠀⠈⠁⠸⣿⣿⣿⣿⣿⠴⠄⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢹⣿⣿⣿⡴⢉⣽⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡇⠝⠛⠻⠃⠛⠛⠛⢿⣿⣿⣿⣻⡇⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠈⠀⢐⠸⣿⣿⣿⡷⢾⡿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡭⣉⠉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠹⢿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣶⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣿⣿⣯⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢈⣉⣉⣉⣉⣉⣀⣀⣀⣀⡀⢠⣶⣶⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠐⠒⠦⠤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠇⠒⠀⠀⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠻⠿⠿⢿⣿⠠⠀⠀⢀⣀⣈⣿⣿⢻⡏⠉⠉⠋⠙⠛⠟⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⣾⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⢾⣿⠶⠀⠀⠀⢠⠄⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣾⣿⠀⠀⠀⠀⢀⡄⠀⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠰⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⣿⠀⠀⠀⠀⠸⠁⠀⢺⣿⣿⣿⣿⣿⣿⣿⣛⣿⢿⡇⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⡏⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠃⢸⣿⣿⣿⣿⣿⣿⣿⣄⠀⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡄⢿⣿⣿
⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠊⠀⠀⢀⡆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠀⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⡏⢻⣄⠀⠀⠀⠀⠀⠀⠁⢰⣆⣶⣄⠈⢸⣿⡧⠼⠿⠿
⠀⠀⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⣿⣿⣿⡟⠀⠀⠀⠈⠅⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡇⠁⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡿⠾⠟⠀⠀⠀⠉⠁⠀⠀⠈⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⣀⣀⣀⣀⣬⣶⣾⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠲⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡇⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠹⡿⠛⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣷⠀⠀⠀⠀⠀⠀⠀⣶⣯⣽⡟⣦⡄⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣀⣀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡆⠀⣀⠀⠀⠈⠁⢸⣿⣿⣿⣿⣿⠤⠄⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢙⣿⣿⣿⡶⢩⣸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡇⠝⠛⠻⠃⠛⠛⠛⢿⣿⣿⣿⣻⡇⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠈⠀⢐⠸⣿⣿⣿⡷⢾⡿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⡭⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠉⠩⢿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣾⡶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣯⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢈⣉⣉⣉⣉⣉⣀⣀⣀⣀⠀⢠⣶⣶⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠒⠦⠤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠇⠐⠀⠀⢴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠻⠿⠿⠿⣿⢠⠀⠀⠀⣀⣈⣿⣿⠛⠏⠙⠛⠋⠉⠻⠿⠀⢀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⢾⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⢐⣶⣶⠀⠀⠀⢀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣸⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣇⣼⣿⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠰⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣟⣿⢿⡇⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠁⢸⣿⣿⣿⣿⣿⣿⣿⡄⠀⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡆⢻⣿⣿
⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠁⠀⠀⣠⡇⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡿⠀⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⡏⢻⣤⠀⠀⠀⠀⠀⠀⠁⢰⣇⣷⣄⠈⢺⣿⡧⠼⠿⠿
⠀⠀⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⣄⢀⠀⢀⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡇⠁⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡿⠾⠟⠀⠀⠀⠉⠁⠀⠀⠈⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣠⣄⣀⣠⣬⣶⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠚⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡇⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠹⠿⠛⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣷⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣟⢷⡄⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣀⣀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡇⠀⣀⠀⠀⠈⠁⢸⣿⣿⣿⣿⣿⡖⠦⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠹⣻⣿⣿⡾⢁⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡇⠟⠛⠻⠃⠛⠛⠛⢿⣿⣿⣿⣞⡇⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⣾⠟⣿⣿⡿⠶⠿⠿⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣩⣉⢉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠹⢯⣭⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣽⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣯⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢉⣉⣉⣉⣉⣉⣀⣀⣠⣀⠀⢠⣶⣶⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠐⠒⠤⠤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠉⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠻⠿⠿⠿⣿⠠⠄⠀⢠⣤⣤⣿⣿⠑⡀⠀⠈⠁⠈⠙⠋⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⢠⣿⠛⠀⠀⠀⠠⠀⠀⠆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⣸⣿⠀⠀⠀⠀⢠⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣏⣿⢻⡇⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠀⠁⢸⣿⣿⣿⣿⣿⣿⣿⣄⠀⢦⡄⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⢀⣾⡆⢹⣿⣿
⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠁⠀⠀⣠⡇⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡿⠀⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⢻⣄⠀⠁⠀⠀⠀⠀⠁⢰⣇⣾⡄⠀⢸⣿⡧⠼⠿⠿
⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣄⡀⣀⣠⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⡇⠁⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡿⠾⠟⠀⠀⠀⠉⠁⠀⠀⠈⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⢀⣠⣤⣠⣤⣬⣶⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⡇⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠙⠿⠋⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣷⡀⠀⠀⠀⠀⢀⡀⢾⣷⣿⣝⣳⣄⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⣀⡄⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⣿⡇⠀⣀⠀⠀⠈⠁⠸⣿⣿⣿⣿⣿⡖⠢⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢹⣿⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠋⢉⣿⣿⣿⡞⢡⣽⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡟⠟⠛⠻⠃⠛⠛⠛⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⣼⠛⣿⣿⡿⠶⠾⠿⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣍⢉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠘⢷⣶⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣯⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢸⣿⣿⣿⣿⣿⣿⣿⡏⡀⠀⠀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣉⣉⣉⣉⣉⣉⣀⣀⣠⣀⠀⢠⣶⣶⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠐⠲⠤⠤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠁⠁⠀⠀⠙⠻⣿⣿⣿⠿⠿⠿⠿⣿⣿⣧⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠿⠿⠿⠿⡿⠐⠂⠀⠰⢶⣾⣿⣿⠸⣄⣀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣏⣼⡯⠉⠀⠀⠀⢘⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣀⠀⠀⠀⠀⢸⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣏⣿⠻⡇⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣄⠀⢦⡄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢠⣾⡆⢺⣿⣿
⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠙⠀⠀⠀⠇⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣻⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡏⢻⣄⠀⠀⠀⠀⠀⠀⠁⢰⡇⣽⣄⠀⢸⣿⡧⠾⠿⠿
⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣄⣀⣰⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣏⠁⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡿⠾⠟⠀⠀⠀⠉⠁⠀⠀⠈⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⢀⣠⣤⣀⣤⣬⣶⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢠⣿⠟⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡿⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⣁⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣿⡀⠀⠀⠀⠀⢀⡀⣾⣷⣿⣝⣻⣆⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⣠⡄⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠟⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⣿⡇⠀⣀⠀⠀⠈⠁⢸⣿⣿⣿⣿⣿⡖⠒⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠹⣿⣯⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠏⢉⣻⣿⣿⡖⢡⣼⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡟⠝⠛⠻⠃⠛⠛⠛⢻⣿⣿⣿⣿⣧⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⣺⠑⣿⣿⣿⠷⠾⠿⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⣩⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣍⣉⣉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣯⣿⣿⣿⣿⣿⠁⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢸⣿⣿⣿⣿⣿⣿⣿⠇⡄⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⣉⣉⣉⣉⣉⣉⣀⣀⣀⣄⠀⢰⣶⣶⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠂⠤⠤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⣙⣿⣿⣿⠛⠛⠛⠛⠿⠿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠿⠿⠿⠿⡟⠈⠀⠀⠘⢻⣿⣿⣿⢸⡦⠶⠀⠀⠀⣠⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣾⠃⠀⠀⠻⣿⣷⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡀⠀⠀⠀⠀⣻⠀⠠⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⠇⢸⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⢀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⢿⡏⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⡄⠀⢦⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣾⡆⢸⣿⣿
⠀⠀⠀⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢸⠁⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠁⠉⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⢻⣄⠀⠁⠀⠀⠀⠀⠁⢰⡆⣶⡄⠀⢸⣿⡧⠾⠿⠿
⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣭⣶⣦⣀⣴⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢶⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡿⠾⠟⠀⠀⠀⠈⠁⠀⠀⠈⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⣀⣤⣀⣤⣤⣵⣾⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣔⣢⣤⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡿⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠿⠟⢁⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣿⡄⠀⠀⠀⠀⢀⡀⢺⣿⣿⣯⣻⣦⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣀⡄⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡟⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⡇⠀⣀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡇⠒⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠙⣿⣯⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⢻⣿⣿⡴⢋⣼⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡟⠝⠛⠻⠃⠛⠛⠛⢿⣿⣿⣿⣇⣷⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⢰⡖⢿⣿⣿⡷⠾⠿⠗⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⢩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣩⣭⣍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢉⣿⣿⣿⣿⣿⣿⣿⣿⠋⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣯⣿⣿⣿⣿⣿⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢹⣿⣿⣿⣿⣿⣿⣿⠃⠄⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠈⣉⣉⣉⣉⣉⣉⣀⣀⣀⣀⠀⢰⣶⣶⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠐⠲⠶⠤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢀⣀⣬⣿⣿⣿⡉⠉⠉⠙⠛⠛⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠿⠿⠿⠿⠇⠈⠀⠀⠈⢹⣿⣿⣿⣿⡿⣿⣿⣤⣶⡶⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⣿⠀⠀⠙⠛⠛⡿⠀⢠⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡄⠀⠀⠀⠀⡅⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡿⠇⢸⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡷⠀⠀⠀⠐⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣄⠀⢦⡄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⣶⡆⢸⣿⣿
⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⢸⠃⠀⠀⠀⠰⡇⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡏⠈⠁⠀⢸⣿⣿⣿⣿⣿⣿⡇⢻⣄⠀⠀⠀⠀⠀⠀⠁⢰⣆⣤⡀⠀⠠⣿⡧⠼⠿⠿
⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣭⣷⣦⣀⣼⣿⣿⣿⡇⢸⠀⠀⠀⠀⠐⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠸⠟⠀⠀⠀⠉⠁⠀⠀⠈⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠈⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣀⣀⣀⣀⣵⣶⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⠟⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣮⣥⢴⡂⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠈⢻⠿⠋⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣿⡄⠀⠀⠀⠀⢀⡀⢼⣿⣾⣯⣻⣦⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢀⣀⡤⠀⠀⣀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣻⡿⢟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⡇⠀⣀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡇⠂⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣍⣨⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠹⣿⣿⣧⠜⣩⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⡟⠝⠛⠻⠃⠛⠛⠛⢻⣿⣿⣿⣏⣿⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⠁⠐⡆⢳⣿⣿⣿⠴⣿⠿⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⢩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣭⡭⣍⠭⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣭⣿⣿⣿⣿⣿⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢹⣿⣿⣿⣿⣿⣿⣿⠇⡄⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠈⣉⣉⣉⣉⣉⣉⣀⣀⣀⣀⠀⢰⣶⣶⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠐⠒⠶⠤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣀⣨⣿⣿⣿⡏⠉⠉⠙⠛⠛⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠻⠿⠿⠿⡿⠈⠀⠀⠘⢹⣿⣿⣿⣿⣿⢿⣾⣿⣷⣶⠄⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⡇⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣟⣿⡁⠈⠻⣿⡿⣿⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡅⠀⠀⠀⠀⣿⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⠇⢸⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⣿⠀⠀⠀⠀⡟⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣄⠀⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡂⢸⣿⣿
⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⢇⡏⠀⠀⠀⠀⡇⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠋⠀⢸⣿⣿⣿⣿⣿⣿⡇⢻⣄⠀⠀⠀⠀⠀⠀⠁⢠⣆⣠⡀⠀⠨⣿⠧⠼⠿⠿
⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣭⣶⣦⣀⣠⣿⣿⣿⣿⢸⡇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠸⠟⠀⠀⠀⠉⠁⠀⠀⠈⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠈⠁⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠉⠉⠁⢀⣠⣤⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣶⣦⡤⡄⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡇⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠈⢿⣿⠿⠁⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣿⡄⠀⠀⠀⠀⠀⣀⢸⣿⣾⣿⢻⣦⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢀⠀⠀⠀⠀⣀⣥⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣸⣿⡇⠀⣀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⠒⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣝⠀⣻⣿⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⣿⣟⣠⠟⢫⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡟⠝⠛⠻⠃⠛⠛⠛⢻⣿⣿⣿⣏⣻⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠙⠉⣀⠠⣹⣿⣿⣃⠸⣿⣏⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣉⡉⡉⣍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣭⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢹⣿⣿⣿⣿⣿⣿⣿⡟⡀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⣉⣉⣉⣉⣉⣉⣀⣀⣀⣀⠀⢰⣶⣶⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠒⠂⠦⠤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠉⢙⣿⣿⣿⡟⠛⠛⠻⠿⠿⠇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠻⠿⠿⢿⣿⠐⠂⠀⠐⠻⣿⣿⣿⣿⣷⣶⣴⣦⣤⣤⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⣵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡏⠈⣿⣿⣿⣿⡆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢽⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡇⠀⠈⠛⠛⢿⠇⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇⠀⠀⠀⠀⣼⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣄⠀⢤⡄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⣶⡆⢸⣿⣿
⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⢇⡟⠀⠀⠀⠀⡇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠛⠀⠈⣿⣿⣿⣿⣿⣿⡇⢻⣄⠀⠀⠀⠀⠀⠀⠁⢠⡆⣤⡀⠀⠨⣿⡧⠼⠿⠿
⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣽⣶⣤⠀⣀⣿⣿⣿⣿⢸⡇⠀⠀⠀⠀⢷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⡷⠸⠟⠀⠀⠀⠈⠀⠀⠀⠈⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠘⠃⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⠷⠀⠀⠀⠀⠈⠉⠉⠀⠀⣀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣔⣂⣠⠄⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⠀⠀⠀⢀⣤⣶⣶⣶⣶⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡁⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⠃⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⡀⠀⠀⠀⠀⠀⣀⢸⣿⣿⣟⠳⣦⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⡀⠀⠀⠀⠀⣉⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⣿⡇⠀⣀⠀⠀⠀⠁⠸⣿⣿⣿⣿⣿⣇⠂⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡍⠀⣻⣿⣥⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⠋⡿⢟⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡇⠝⠛⠻⠃⠛⠛⠛⢻⣿⣿⣿⡏⢿⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠛⢁⢀⣺⣿⣿⡏⣰⣷⣟⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⢍⠉⡉⠍⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⠙⠿⣽⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠁⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣭⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢉⣉⣉⣉⣉⣉⣁⣀⣀⣀⠀⢰⣶⣶⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠐⠒⠤⠤⢤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠇⠘⠀⠀⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠿⠿⠿⢿⣿⠀⠄⠀⠀⣤⣤⣼⣿⡏⡏⠉⠉⠉⠉⠛⠋⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⡃⣿⠘⠂⠀⠀⠀⡆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣾⣿⠀⠀⠀⠀⢸⠇⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⣿⣿⠀⠀⠀⠀⠘⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡇⢸⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡏⠀⠀⠀⠀⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣟⣄⠀⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⢺⣿⣿
⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠋⠀⠀⠀⡂⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠛⠀⢸⣿⣿⣿⣿⣿⣿⡇⢻⣄⠀⠀⠀⠀⠀⠀⠁⢠⡆⣠⡀⠀⠠⣿⡇⠼⠿⠿
⠀⠀⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⣄⠀⠀⠀⣾⣿⣿⡿⠀⠀⢀⠀⠁⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡷⠼⠟⠀⠀⠀⠉⠁⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⡇⠀⠀⠈⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠷⠀⠀⠀⠀⠈⠉⠁⠈⠀⢀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡏⠀⠀⠀⢀⣠⣶⣶⣶⣶⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠃⠀⣀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣷⠀⠀⠀⠀⠀⠀⡀⢶⣿⣿⣟⢶⣄⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠘⣁⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡇⠀⣀⠀⠀⠈⠁⢸⣿⣿⣿⣿⣿⡆⠄⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠯⠐⢶⣾⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣿⣾⡿⠋⡿⢟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡇⠝⠛⠻⠃⠛⠛⠛⢻⣿⣿⣿⡏⣷⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠻⠛⠀⠀⣚⣿⣿⡟⢰⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣉⠩⠉⣉⣉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⠙⠿⣭⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡁⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣭⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢉⣉⣉⣉⣉⣉⣀⣀⣀⣀⠀⢰⣶⣶⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠐⠒⠤⠤⢤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠇⠘⠀⠀⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠻⠿⠿⢿⣿⠀⠄⠀⠀⣤⣤⣼⣿⡏⡏⠈⠉⠉⠉⠛⠛⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⠃⣿⠘⠂⠀⠀⠀⡆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣾⣿⠀⠀⠀⠀⢸⠇⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⣿⣿⠀⠀⠀⠀⠘⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡇⢸⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡏⠀⠀⠀⠀⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡟⣄⠀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀⢺⣿⣿
⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠋⠀⠀⠀⡂⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠛⠀⢸⣿⣿⣿⣿⣿⣿⡇⢻⣄⠀⠀⠀⠀⠀⠀⠁⢠⡄⣤⡀⠀⢠⣿⡧⠼⠿⠿
⠀⠀⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⣄⠀⠀⠀⣾⣿⣿⡿⠀⠀⢀⠀⠁⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡷⠼⠟⠀⠀⠀⠉⠁⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⡇⠀⠀⠈⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⠈⠉⠁⠈⠀⢀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡏⠀⠀⠀⢀⣠⣶⣶⣶⣶⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠃⠀⣀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣷⠀⠀⠀⠀⠀⠀⡀⢲⣿⣿⣟⢶⣄⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠘⣁⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡇⠀⣀⠀⠀⠈⠁⢸⣿⣿⣿⣿⣿⡆⠤⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠻⠐⢶⣾⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢿⣾⡿⠛⡿⢟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡇⠝⠛⠻⠃⠛⠛⠛⢻⣿⣿⣿⣋⣷⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣽⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠻⠓⠀⠀⣘⣿⣿⡟⢰⣿⠗⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 2403

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

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    Gemini version at https://tuxmachines.org/n/2024/11/11/Pop_OS_One_of_the_Best_Linux_Distros_For_Creators_of_All_Types.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Pop!_OS: One of the Best Linux Distros For
Creators of All Types⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Rianne Schestowitz on Nov 11, 2024


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Jack_Wallen’s_current_Pop!_OS_desktop⦈_


Quoting: Pop!_OS: One of the Best Linux Distros For Creators of All Types —


     I’ve been using Linux for nearly 30 years, and I’ve witnessed every
     type of distribution come and go. There have been distributions
     ranging from the very basic to the gimmicky and everything in
     between. I spent years “distro hopping,” which included the likes of
     Caldera OpenLinux, Corel Linux, Red Hat (way before Fedora/RHEL),
     Ubuntu, elementary OS, Bodhi Linux, Ubuntu Budgie, Deepin, Fedora,
     Zorin OS and more.


     But then, something interesting happened: I purchased my first
     System76 desktop computer. That first computer (a Leopard Extreme)
     shipped with Ubuntu Linux, and it worked like a charm. That was,
     hands down, the best desktop computer I’d had to date. So, naturally,
     when the Leopard Extreme showed signs of failing, I wanted to stick
     with System76. At the time, they were just announcing their new
     Thelio desktop computer, and I was all over it.


     I purchased my first Thelio, which shipped with the in-house Pop!_OS
     distribution, and I immediately loved it. Not only was it user-
     friendly and powerful, but it also worked seamlessly with System76
     hardware. In fact, the combination of the Thelio desktop and Pop!_OS
     created the finest computer experience I’d had to date.


Read_on




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⡀⠀⣀⣀⠀⢀⣀⣀⢀⣀⡀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⡀⢀⡀⣀⠀⠀⠀⠂⠀⠀⢀⣀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠿⠧⠀⢽⣿⣿⣹⣿⣦⡽⣾⣿⣿⣿⣿⣿⣿⡿⠗⠃⠀⠼⣿⣿⣶⠶⢾⠀⠀⠠⠀⠀⠻⠋⠀⠀⠀⠾⢿⣿⠿⣿⣿⣿⣿⣿⡇⠢⠒⠀⢠⣴⣻⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⢹
⣿⣿⣿⡍⠃⠈⠛⠻⠿⢿⣿⣋⡀⠀⠀⠀⢀⡄⢨⣿⣿⣿⠿⠏⠽⣛⣿⠛⠙⡟⠃⠄⠀⠈⠉⠉⠻⢿⣿⣦⠞⠃⠀⠄⠀⠄⠀⠀⠀⠀⠀⢄⠈⠐⢻⡶⠿⠿⠛⠀⠠⠀⠀⠉⠋⡛⠀⣠⠷⣿⠟⠛⢻⣋⣄⠁⠁⠘
⠈⠉⠉⠁⠀⠀⠀⣰⠖⠘⠋⠀⠀⠴⠆⢀⡄⠀⠛⠀⠉⠙⣦⣤⣤⣅⣥⣴⣿⣿⣷⣄⣴⣿⣶⡖⠀⢸⣿⡿⠀⠀⡂⢀⠀⠀⠀⢀⣆⡀⡄⣾⣶⣿⡽⠁⠀⣀⡀⠀⠀⠀⠀⠀⠘⠻⢷⡂⣰⡀⢀⣤⣘⣿⢟⠀⢶⣶
⠀⠀⢶⣾⣿⢿⠿⣿⣷⣤⣇⡄⣿⡀⣀⣘⢿⣶⡷⣤⣿⣯⣹⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢻⣿⣅⡀⢠⣤⠴⡷⣤⣄⣄⣀⠀⣠⠀⣸⣦⣷⣾⡟⠻⣷⡀⣥⣬⣿⣯⣗⣤⣀⠀⣴⡆⠀⣿⣿⣷⣿⣁⣿⣿⣁⠀⠈⠟
⠶⠀⠀⠀⠀⠻⣿⣿⣷⣬⣿⣿⣿⣿⣿⣷⣿⢽⣽⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⠿⠿⣿⣶⣾⣿⣇⡿⡿⠏⣨⣿⣿⣿⣿⡇⠀⡿⣿⡟⠛⠛⠻⣟⣉⠁⠈⠋⣼⠁⠸⢿⣿⣿⣿⣿⣿⣿⣿⣶⣶
⣶⡄⠈⠀⠀⠀⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡴⠋⠀⠙⠟⠋⠉⠛⣻⣿⣿⣿⡚⠉⠀⣹⣷⣿⣿⣿⣣⣀⣹⣿⠟⠙⠙⡗⣿⣷⣿⠿⠟⣿⣇⢀⣄⣹⣿⡇⠀⢸⡀⠀⠈⣾⡆⠀⡙⠦⠀⢸⣿⣿⣿⣿⡛⢿⣿⣿⣿
⣶⣶⣷⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣶⢦⡀⠀⣤⣅⣻⣿⣿⣿⣶⣤⣼⣻⣿⣿⣿⣿⢟⢏⠿⣤⡀⡀⣿⡆⠁⢸⣧⠀⣸⡟⠛⠅⠙⠟⢳⠶⣮⣥⠂⠈⠹⣷⣾⣿⣶⣿⣛⣿⣧⣼⣿⠅⢢⣿⣿⣿
⣿⢿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣡⣿⡷⢴⣿⣿⣿⣸⣿⣿⡏⠀⠀⣤⣿⣿⣿⣟⢿⣮⢵⡿⣤⡹⢦⣧⣴⡚⢿⣇⣽⣻⣾⣷⣶⣤⣦⣤⡶⠀⠲⠆⣁⣩⣤⣈⣿⣿⣼⣿⣿⣿⣷⣿⣿⣿⣿⣿
⢉⣿⡯⡝⣿⣾⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣾⠟⣿⣿⣿⣿⣿⣿⠿⣿⢿⣧⣤⣴⣿⣇⣕⣡⣿⢛⣡⣾⣿⣿⣿⠶⢿⡿⢳⣸⠿⣿⠟⠻⢿⡿⣿⣿⣿⣷⣼⣶⠷⣜⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠻⣿⣿
⠚⣿⢶⡉⠃⠉⢻⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⢺⣿⡂⠁⢳⣿⣟⢟⠊⢶⠿⠛⠿⣿⣿⣿⣾⣻⣵⣿⡿⠻⡳⣿⡞⠻⠿⢾⡏⣽⣿⣶⣶⣿⣽⣬⣷⣿⣷⡍⣻⣿⣝⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⢟
⣿⡿⠉⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣾⣯⣷⣦⣄⣿⣿⣿⡿⢿⣤⣠⣾⣿⣿⣿⣿⣿⡟⠳⣶⣿⣥⣼⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣏⠍⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣾
⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣋⣼⣿⣿⣿⣿⣿⣿⣿⣟⣉⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣽⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣹⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡽⣿⣷⢼⣶⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⠿⠻⢻⡝⣿⣽⡿⣿⣆⡝⠛⠷⣿⣛⣍⢶⣼⢿⣿⣿⠗⣄⣿⣿⣿⣿⣿⣿⣿⡿⢋⠝⠻⠟⣿⣿⣿⣽⡠⠯⠙⣟⠛⢻⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢽⣧⣿⣿⣿⢿⣿⢿⠿⣿⣿⣿⣿⣿⣿⠿⣿
⣦⣆⠈⠛⢸⣿⡆⠓⠛⡛⣋⣼⣶⡧⡆⢤⣟⢷⣯⢶⢀⡙⡘⠿⣸⣄⣼⡏⢰⣰⣠⡼⠿⢿⣿⣧⡄⠛⠤⡐⠿⠿⠟⠃⢠⣤⡙⣀⠸⠿⣿⣿⣿⡋⠘⢗⡨⢰⣾⢟⣻⡟⢏⢹⡟⠛⠍⠀⢠⠀⠈⣿⡟⣿⣭⡿⣼⣿
⠈⠁⢀⡘⠟⠈⠀⠆⠘⠻⢨⢿⡗⡇⣦⣈⣷⣧⢸⣜⣛⣧⡶⢸⣿⣿⡝⢷⣶⣿⡆⠘⠰⠆⡔⠰⠯⡦⢷⠟⠀⣀⡂⠀⠁⢈⢭⣉⣷⣵⡆⠿⢾⡿⠀⠘⠘⠛⡀⢾⣇⣻⣾⡔⣿⣆⣩⡄⠆⢰⢶⣴⠛⠛⣺⢺⠿⢼
⠠⠀⠶⠉⠐⠼⣆⡀⠈⣁⣿⠋⠀⡀⠆⠄⢙⡛⠙⢛⡏⢹⣏⠉⠽⠯⢅⠆⣥⣤⠂⠀⠈⠐⠑⢿⣠⠛⡃⠀⠁⢛⠃⠀⠺⡿⣿⣷⠛⣩⣿⠴⠇⠄⠁⠁⢠⡟⢡⡄⠭⠟⠛⠳⢴⣤⠉⢡⣸⣥⠚⢸⡆⣼⣿⣿⢦⣚
⢰⠆⠀⠀⠀⠀⢠⡠⠄⡿⠌⢡⣜⣶⣶⡌⠋⢀⠀⠉⠉⣼⠟⠀⠛⠀⠈⠷⠉⡀⠢⢤⡄⠺⠀⠠⠀⠀⠀⠂⣤⣈⠧⠀⠠⣄⡻⡷⢿⠙⠁⢀⠀⠉⠛⠁⠘⠀⠄⢚⠠⣄⠄⠃⠘⠭⣿⡄⢸⣄⡽⢿⠤⢙⡏⡁⢸⣾
⠟⠀⠛⠄⠀⢀⢀⣡⣦⠄⠛⠐⢨⣯⡉⡀⣶⣴⠄⣀⠀⠀⠀⠀⠀⠀⢠⡈⢛⠑⢂⣼⠀⠀⢨⡀⣤⡀⠀⠀⠀⠀⠀⠰⣦⣽⣿⢳⡾⠟⣴⠋⠀⠀⠀⠙⠀⠓⠀⠈⠀⠓⠂⢀⠀⠀⠛⠛⠃⣸⣟⠛⡀⣀⠶⣿⠃⠨
⠀⠆⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠞⠋⠁⠐⠙⠉⠘⠿⠿⣇⠀⠀⠀⠀⢀⡀⢴⠔⠶⡹⠁⠀⠘⠛⠉⠛⠀⠀⠀⠀⣀⡖⡙⠛⣿⢿⠧⣴⡧⠀⠀⢀⣀⡀⠙⠀⠀⢀⣠⣶⣤⣤⣤⠈⠉⠈⠀⠈⠃⠂⠛⣈⠁⢉⡀⣴
⠀⠀⠀⠀⠀⠀⠛⠀⠀⠘⠃⠁⠀⣀⠸⠂⢠⣆⡀⠀⠀⡀⠀⠀⠀⠰⠀⠐⠀⢠⣤⣄⠀⠂⠀⠀⠀⠀⠀⢰⠀⠀⡁⢀⠙⠈⠁⢄⠀⠈⡉⠀⠠⠉⠉⢠⣤⠀⠠⠈⠶⢾⠿⢿⠧⠀⡀⢻⠀⢠⠀⠀⠂⠉⠀⠈⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⠈⡉⣂⣹⡿⠧⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⠀⠈⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠦⠤⣰⣤⠀⠐⡇⠉⠀⠘⠒⠀⠉⠀⠀⠀⠀⢀
⠀⠀⢀⠀⠦⠀⠀⠀⠀⠘⠀⠀⠀⠀⠋⠈⠛⠩⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠄⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠐⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠿⠂⠀⠀⠀⠰⠀⠀⠿⠀⠸⠃⠀⠃⠀⠀⠀⠀⠀⠀⠰⠿⠀⠐⠂⠀⠶⠆⠀⠀⠀⠀⠀⠀⠉⠀⠸⠇⠀⠈⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 2483

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

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2024/11/11/Programming_Leftovers.shtml
    Gemini version at https://tuxmachines.org/n/2024/11/11/Programming_Leftovers.gmi

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


posted by Roy Schestowitz on Nov 11, 2024


    * ⚓ Paweł Świątkowski ☛ Booleans_Are_a_Trap⠀⇛


           As developers, we love our booleans. They map perfectly into
           how computers work at a low level and play nicely with if
           statements, our primary control-flow tool. They are simple to
           reason about. What's not to like?


           We actually like them so much that we use them for domain
           modeling. And that's where things get problematic. I would like
           to show you some examples of a mess we land in because of using
           booleans and to offer a better approach.


    * ⚓ Dirk Eddelbuettel ☛ Dirk_Eddelbuettel:_inline_0.3.20:_Mostly
      Maintenance⠀⇛


           A new release of the inline package got to CRAN today marking
           the first release in three and half years. inline facilitates
           writing code in-line in simple string expressions or short
           files. The package was used quite extensively by Rcpp in the
           very early days before Rcpp_Attributes arrived on the scene
           providing an even better alternative for its use cases. inline
           is still used by rstan and a number of other packages.


          o § Python⠀➾


                # ⚓ Rlang ☛ Build_a_Python_CLI_with_Click+Cookiecutter_
                  (repost)⠀⇛


                       In the spirit of Learning in Public, I wanted an
                       excuse to explore (1) click for creating command
                       line interfaces, (2) Cookiecutter project
                       templates, and (3) modern tools in the Python
                       packaging ecosystem. If you’re primarily an R
                       developer like me, I recently wrote about resources
                       for getting better at Python for R users.





                    ䷩ 𝚕𝚒𝚗𝚎 2544

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

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2024/11/11/Putting_Linux_on_a_Tablet_7_Distros_to_Try.shtml
    Gemini version at https://tuxmachines.org/n/2024/11/11/Putting_Linux_on_a_Tablet_7_Distros_to_Try.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Putting Linux on a Tablet? 7 Distros to
Try⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Rianne Schestowitz on Nov 11, 2024


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Penguin_waving⦈_


Quoting: Putting Linux on a Tablet? 7 Distros to Try —


     Choosing the right Linux distro for your tablet depends on your
     hardware and personal preferences. Whether you're after something
     user-friendly like Ubuntu or Pop!OS or prefer more advanced options
     like NixOS or Arch, there's something here for everyone.


     Once you're ready to get started, learn how to install Linux on an
     Android tablet.


Read_on




⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢁⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⠇⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡻⠃⠀⠀⠀⠀⠀⠀⢰⣶⣶⣿⣿⣶⣶⣤⣤⣤⣄⣀⣀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠀⠀⠀⣬⠁⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⠀⠀⣸⣷⠀⠀⠀⠀⠀⡀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣴⣾⣯⣭⣽⣶⣷⣶⣤⠀⣤⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠠⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⣀⢠⣄⠀⣼⡮⣭⠉⠀⣄⢠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣧⣤⣿⣿⣿⣿⠃⠠⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣤⡀⠀⠀⣞⣿⣿⣿⣧⣼⣿⣧⣤⣸⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠐⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠌⠀⠀⡀⢦⡖⠀⠀⠀⢸⡿⠫⣝⣿⡀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢠⣬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⡐⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⣇⠀⠀⣿⡇⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠠⠁⠀⠀⠀⢐⠄⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣦⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠉⠉⢉⣿⣿⠃⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⢟⢁⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣤⣦⣤⣌⣉⡙⠛⠿⠿⣿⣷⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢛⣿⣿⡜⣿⣇⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣸⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡙⠛⠛⠿⢿⣿⣶⣶⣤⣄⣀⡀⠀⠉⠙⠛⠿⠿⠋⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣜⢿⡀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣈⡉⠉⠛⠛⠟⢿⠶⣶⣦⣤⣀⣠⣾⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡡⡀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⡀⠀⠉⠉⠋⠿⢿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠹⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢡⠀⠀⠀⠀⠈⠙⣿⣿⡆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠹⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⣀⣤⣬⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣿⣶⣾⣿⣿⣷⣿⣿⣿⡟⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢀⣀⣰⡟⠉⠉⡅⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣾⣯⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣧⡈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⣄⠀⣸⣿
⣿⣿⣿⣿⣿⣿⣿⡏⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠡⠀⠈⢹⡿⠿⠆⠒⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢻⣿⣆⡈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢰⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 2606

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

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2024/11/11/Radxa_Raspberry_Pi_and_More_Hardware.shtml
    Gemini version at https://tuxmachines.org/n/2024/11/11/Radxa_Raspberry_Pi_and_More_Hardware.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Radxa, Raspberry Pi, and More
Hardware⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Nov 11, 2024


    * § Devices/Embedded⠀➾


          o ⚓ Linux Gizmos ☛ Radxa_Introduces_the_Palmshell_SLiM_X4L_with_Intel
            N100_Processor_and_2.5GbE_RJ45_Port⠀⇛


                 The Radxa X4L, also known as the Palmshell SLiM X4L, is a
                 compact device powered by Intel’s quad-core N100
                 processor. With features like a 2.5GbE LAN port, Wi-Fi
                 6E, and dual 4K@30Hz display support, it’s well-suited
                 for multimedia and general-purpose use.


          o ⚓ Linux Gizmos ☛ Radxa_Enhances_Compact_RK3582-Based_Networking
            Device_with_Dual_2.5GbE_Ports⠀⇛


                 Radxa recently introduced a compact networking device
                 powered by the hexacore Rockchip RK3582 System-on-Chip.
                 This new model builds on the design of the previous Radxa
                 E20C but features dual 2.5GbE RJ45 ports, enhancing its
                 networking capabilities.


    * § Open Hardware/Modding⠀➾


          o ⚓ James Stanley ☛ My_diaphragm_piston_air_engine_with_rotary
            valve⠀⇛


                 Compared to making my Wig-Wag, this engine was a lot less
                 work, despite the unconventional design. I went from the
                 idea in my head to a working engine in a single day
                 thanks to the power of 3d printing. And that includes
                 several iterations of some parts when my first attempt
                 didn't work.


          o ⚓ Tom's Hardware ☛ Super_tiny_Raspberry_Pi_RP2040_RGB_LED_matrix
            display_hits_Kickstarter⠀⇛


                 Vcc Labs has created a Raspberry Pi RP2040-powered RGB
                 LED matrix that's super small and powered via USB Type-C.





                    ䷩ 𝚕𝚒𝚗𝚎 2671

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

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2024/11/11/Review_Bazzite_40_Playtron_OS_Alpha_1_Tucana_Linux_3_1.shtml
    Gemini version at https://tuxmachines.org/n/2024/11/11/Review_Bazzite_40_Playtron_OS_Alpha_1_Tucana_Linux_3_1.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Review: Bazzite 40, Playtron OS Alpha 1,
Tucana Linux 3.1⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Rianne Schestowitz on Nov 11, 2024


Quoting: DistroWatch.com: Put the fun back into computing. Use Linux, BSD. —


     I usually like small projects which are trying to keep things simple
     and clean. These sorts of projects usually bring improved efficiency
     and speed at the cost of modern features. However, Tucana manages to
     do the opposite. Its install process and package manager are slower,
     by far, compared to most modern systems and there doesn't appear to
     be any reduction in resource consumption (the live environment used
     830MB of RAM to run Plasma). Which means we are missing out on
     thousands of packages and convenient features for a slower and
     similar sized operating system, when compared to most mainstream
     Linux distributions.


     Maybe Tucana will improve in future releases, or make more use of its
     custom package manager. For now, it's not bringing anything helpful
     to the experience.


     I also want to note that one frustration I experienced twice this
     week was live systems providing working graphical interfaces, while
     the installed system did not. One of the reasons people use live
     desktop media is to test to confirm an operating system will work
     properly with their hardware before they install it. Using an install
     process which installs alternative packages or configurations which
     provide a different experience largely nullifies the benefits of
     having live media. I hope other up and coming projects keep this in
     mind so that their installed software works (or doesn't) the same as
     the live media.


Read_on





                    ䷩ 𝚕𝚒𝚗𝚎 2723

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

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2024/11/11/Security_Leftovers.shtml
    Gemini version at https://tuxmachines.org/n/2024/11/11/Security_Leftovers.gmi

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


posted by Roy Schestowitz on Nov 11, 2024


    * § Security⠀➾


          o ⚓ Reproducible_Builds:_Reproducible_Builds_in_October_2024⠀⇛


                 Welcome to the October 2024 report from the Reproducible
                 Builds project.


                 Jens Dietrich, Tim White, of Victoria University of
                 Wellington, New Zealand along with Behnaz Hassanshahi and
                 Paddy Krishnan of Oracle Labs Australia published a paper
                 entitled “Levels_of_Binary_Equivalence_for_the_Comparison
                 of_Binaries_from_Alternative_Builds”:


                 The availability of multiple binaries built from the same
                 sources creates new challenges and opportunities, and
                 raises questions such as: “Does build A confirm the
                 integrity of build B?” or “Can build A reveal a
                 compromised build B?”. To answer such questions requires
                 a notion of equivalence between binaries. We demonstrate
                 that the obvious approach based on bitwise equality has
                 significant shortcomings in practice, and that there is
                 value in opting for alternative notions. We conceptualise
                 this by introducing levels of equivalence, inspired by
                 clone detection types.


          o § Integrity/Availability/Authenticity⠀➾


                # ⚓ Nigerian_national_gets_10-year_sentence_for_stealing_$20
                  million_through_business_email_compromise_scams⠀⇛


                       Through the phishing emails, the hackers gained
                       access to employee login information, which they
                       used to monitor email accounts for messages
                       indicating a buyer was preparing to make a payment.
                       Ayeni and his co-conspirators would then contact
                       the buyer from the compromised email address and
                       provide wire information linking to their financial
                       accounts.


                # ⚓ If_you_want_to_ask_me_security_questions,_I_might_want_to
                  ask_you_security_questions⠀⇛


                       What annoys me, more and more often when these
                       calls crop up, is that the callers - or more
                       accurately, their employers - haven’t stopped to
                       think that maybe they should confirm their identity
                       with me too.


                       The point of confirming my identity is that the
                       calling company wants to be certain that it’s
                       getting accurate information from the right person.
                       It’s reasonable for that person to want to be
                       certain that they are giving accurate information
                       to the right company. Just because you call me,
                       doesn’t make you legit from my perspective. After
                       all, almost half the calls I get these days are
                       spams, scams or timewasters of some sort.





                    ䷩ 𝚕𝚒𝚗𝚎 2809

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

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2024/11/11/Streamlining_openSUSE_Translations_Upstream.shtml
    Gemini version at https://tuxmachines.org/n/2024/11/11/Streamlining_openSUSE_Translations_Upstream.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Streamlining openSUSE Translations
Upstream⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Rianne Schestowitz on Nov 11, 2024


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


Quoting: Streamlining openSUSE Translations Upstream - openSUSE News —


     Managing localization of desktop menus and applications takes a
     specific tool and approach that fills a gap but leaves inconsistent
     upstream translations.


     Open-source translation standards have advanced over the years and
     the downstream-only model being used has proven to become
     inefficient, which is why Update-Desktop-Files Deprecation efforts
     are developing.


     Over the past two decades, SUSE’s translation system has grown to
     cover more than 5,747 packages, with a total of about 380,000
     translated strings. These efforts are labor-intensive and often
     redundant since many translations upstream already exist. The update-
     desktop-files tool contradicts an upstream-first policy. The SUSE-
     specific translations override upstream versions, causing
     inconsistencies and duplicating translation work. It also limits
     package maintainers’ control as translations are often integrated
     during runtime, which then appear different from what package
     maintainers expect. The tool adds complexity and requires SUSE-
     specific infrastructure (e.g., SUSE intranet and OpenQA VPN) that
     complicates maintenance and makes it challenging to align with
     certain open-source practices.


Read_on




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                    ䷩ 𝚕𝚒𝚗𝚎 2880

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

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2024/11/11/This_Week_in_KDE_Apps_Adopt_an_App.shtml
    Gemini version at https://tuxmachines.org/n/2024/11/11/This_Week_in_KDE_Apps_Adopt_an_App.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ This Week in KDE Apps: Adopt an
App⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Rianne Schestowitz on Nov 11, 2024


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇KDE_Itinery⦈_


Quoting: This Week in KDE Apps: Adopt an App - KDE Blogs —


     This week, we released KDE Gear 24.08.3 and we are preparing the
     24.12.0 release with the beta planned for next week. The final
     release will happen on December 12th, but, meanwhile, and as part of
     the 2024 end-of-year fundraiser, you can "Adopt an App" in a symbolic
     effort to support your favorite KDE app.


     This week, we are particularly grateful to
     @petejones@hcommons.social, @DaisyLee@mastodon.social and Karcsesz
     for showing their support for Tokodon; manchicken for Merkuro and
     fat_malama, Alexandru Traistaru and Neeko iko for KDE Connect.


     Any monetary contribution, however small, will help us cover
     operational costs, salaries, travel expenses for contributors and in
     general just keep KDE bringing Free Software to the world. So
     consider donating today!


     Getting back to all that's new in the KDE App scene, let's dig in!


Read_on




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⠀⠀⠀⠀⠀⢠⠀⢠⠄⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠄⠠⠠⠠⠤⠤⠤⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⣤⢤⣤⠤⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣾⣿⣾⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣇⣠⣿⣿⣼⣿⣆⣁⣀⣤⣀⣤⣀⣯⣧⣄⣠⣄⣹⣽⣄⣀⣤⣐⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⢡⣼⣟⣛⣊⠁⠀⠀⠉⣥⣁⣭⠀⠉⠀⠉⠉⠉⠁⠉⠈⠁⠈⠉⠉⠉⠉⠉⢁⣀⣀⠀⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢈⣉⣉⣁⣉⣉⣁⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⠿⠿⠿⠷⠀⡀⣠⠌⠉⠀⠀⣀⣀⣾⣆⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⣿⣿⣿⠿⠿⠻⢿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⡛⠛⡛⣺⣿⢟⣀⣠⣤⣬⣭⣭⣭⣍⣄⠀⠀⣀⣤⣤⣶⣾⣿⢸⣿⣿⡉⠉⡉⡁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⣿⣷⣶⣴⣶⣾⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⡀⣶⣾⣿⣿⣿⣿⣿⣾⣷⣤⣦⣤⣶⣴⣦⣶⣬⡀⣹⣿⣿⣿⣿⣿⣿⣧⣿⣿⣟⣛⣻⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣤⣼⣾⣿⣯⣉⣉⣉⣉⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⡀⣠⡈⣉⣭⣿⣿⣿⣛⠛⠓⠁⠛⢛⠛⣿⣿⣿⣿⣿⣿⢿⡟⠿⠇⠽⠿⠿⣿⣿⣿⣿⡋⠛⠋⠛⠛⠛⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠟⡛⠛⠛⠛⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠸⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⠿⠿⠷⠶⢢⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢨⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠟⠛⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⣠⣿⣿⣿⡯⢽⣿⣤⣭⣥⣭⣭⣭⣬⣥⣼⠟⠛⠋⢉⣉⣈⣁⡀⠀⠰⣶⣷⣭⣿⣿⣿⢿⣠⣉⡉⣉⣁⣽⣿⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⢀⣄⣉⣀⣉⣤⣋⣭⡁⣼⣿⣿⣿⣿⣿⣿⣿⡟⠉⣁⣠⣶⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⠋⢙⣿⣿⣿⣿⣙⣉⡉⣉⣉⣻⠛⠀⠀⠀⠀⠀⠀⠀⣠⣻⣿⣿⣿⣿⣿⣩⣭⣶⣿⣿⣿⣿⣿⣿⣿⡮⠟⠀⣧⠤⢄⣠⣤⣤⣤⢄⡸⣿⣿⣿⣿⡇⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣾⡆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣷⣤⡄⠀⠀⠀⠀⣠⣸⡿⢟⣩⣭⣝⡿⢀⡀⣉⡉⣌⣈⣩⣸⣿⣿⠝⠋⠀⠠⠿⠿⠿⠿⠿⡿⢿⣿⣿⣯⣿⣯⣿⣷⡎⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠁⣤⣤⣶⢿⣿⣿⣟⢙⠛⠙⢛⢙⠃⢵⣿⣿⣿⣿⠟⢿⠛⠾⠦⡆⠀⣆⣶⣶⣶⣶⣶⣶⣾⣿⠛⠿⠿⠟⠏⠙⢃⡙⠿⣿⠛⠛⠛⠛⠛⠛⣿⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⣬⣤⣤⣦⣋⠙⢋⡛⢛⠛⠛⢛⣇⠻⠿⣻⣿⡶⠤⢤⠤⠤⠄⠀⣭⣿⣿⣿⣟⠿⢫⣿⠿⠖⣡⣴⣶⣶⣺⣽⣿⣷⣦⡍⣽⡿⢿⣿⣿⣿⣭⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣶⠀⠓⠙⠛⢛⡛⡍⣶⣿⣿⣿⣗⠲⡆⠀⣀⣠⣶⣿⣿⣷⣿⣾⣿⣷⡠⢿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⣡⢇⣆⡸⠿⣾⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⡻⠇⠛⠎⣿⣛⢩⣶⣾⣿⠿⡯⣯⣽⠏⠙⢙⡉⠙⢙⡋⣯⢸⣿⣿⣿⣽⣿⣿⣐⣉⣉⣉⣹⣿⢿⣷⣾⣿⣿⡧⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⣷⣷⣶⣦⣤⣶⣿⣿⣿⣿⡟⠻⠟⠿⣿⣿⣿⠿⠿⠋⠉⠉⠉⠀⠀⠉⠙⠊⢿⣿⠿⣷⣾⣿⣿⣷⢿⣿⣷⣿⣿⣿⣿⣧⣝⠻⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣶⢿⣿⣿⢃⡰⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢂⣀⡀⠀⠀⠀⠀⠐⠐⠒⠒⢒⠛⠻⠿⠿⠶⠂⢀⣼⣿⣻⣿⣿⡿⣿⣿⣧⣬⣩⣭⣽⣿⣷⣌⠻⣿⡿⢃⣴⣬⣟⣿⣛⠿⣛⣛⡵⣿⠡⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣷⡎⠒⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣤⣤⣬⣤⣤⣬⣤⣄⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⡿⣟⣶⣤⣤⣤⡟⣿⣿⣤⡀⢩⡡⣦⣿⣷⣿⣄⠂⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⡿⠿⢿⣿⣿⣾⣿⣿⣝⣿⣿⣿⣻⣿⡿⣿⣿⣸⣿⣿⢿⣿⣿⣿⣿⣿⠛⠛⠛⠚⠛⠛⢻⡸⣟⢿⣿⣿⡿⣿⡿⣿⣿⣶⣾⣧⣩⡻⣿⣿⣿⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠻⣿⣿⣿⣿⣿⠛⣻⠗⠛⢻⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿⠛⠗⢉⢩⣥⣤⣐⠈⢉⡑⠟⣛⡻⢛⣩⣭⣴⣤⣀⣧⣀⣠⣤⣤⣤⣠⣤⣤⢵⢄⣶⣿⣿⣾⣿⣾⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣽⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⠴⣦⣤⡤⠄⢤⣤⣤⣘⢿⠾⣿⡿⠿⣿⣛⢻⣟⣿⣿⣟⠛⣻⣿⡻⢿⣻⣿⠙⣸⣿⣇⣁⣋⡉⣉⡁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣼⣤⣤⣤⣤⣼⣿⣭⣿⣿⣿⣿⣿⣿⣿⡟⡥⠤⢤⣤⡤⠤⣄⣤⣤⠤⣤⡄⣀⣶⣷⣿⣿⣿⣦⣉⣚⣛⠛⠿⢿⠿⢃⣀⣠⣤⡦⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⣈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣀⣴⣇⢽⣿⣧⢄⣤⠀⠅⣰⣥⣦⣽⣿⣿⣿⠿⣻⣯⣿⣿⣯⠘⠛⠛⠒⠛⠛⠟⣥⣶⣿⣮⡻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣈⣉⣅⣬⣈⣉⣭⣋⣯⣍⣉⣉⣉⣏⣩⣭⣥⣨⣩⣩⣍⣻⣿⣻⣿⣛⣿⣿⣿⣏⣴⣶⣶⣾⣏⣀⣀⣛⣛⣻⣿⣍⣙⣴⣿⣿⣿⣿⣟⣛⣈⣻⣿⣿⣿⣏⣥⣿⣿⣿⣿⣷⣶⣭⣭⣭⡆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⣿⣿⣿⣿⣿⣿⡟⠟⣿⣿⣿⣿⣿⣿⣿⣿⣀⣈⣿⣿⣿⣿⣿⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠿⠾⠟⠿⣿⣿⣿⡿⠻⠿⢿⠿⠿⣿⣿⣿⣿⣤⣭⣭⣭⣥⣽⣿⣿⢿⠿⠿⠷⢶⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠶⠶⠶⠶⠾⠿⠿⠿⠿⠿⠾⠿⠿⠾⠿⠿⠿⠿⠶⠤⠠⠤⠤⠼⠿⠿⠿⠾⠿⠿⠿⠿⠿⠷⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 2962

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

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posted by Roy Schestowitz on Nov 11, 2024


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


⚓  Updated This Past Day⠀⇛


   1. ⚓ The_'Other'_Bruce..._on_Openwashing_at_OSI_(and_Not_Bruce_Perens,_the
      OSI's_Co-founder)⠀⇛


           Openwashing people (connected to Microsoft) already do "open
           weights"


   2. ⚓ Gemini_Links_10/11/2024:_A_Writer's_Block,_VIM_Tips_and_Tricks⠀⇛


           Links for the day


      ⚓  New⠀⇛


   3. ⚓ Gemini_Links_10/11/2024:_Taking_Jokes_and_Writing_Dense_Assembly⠀⇛


           Links for the day


   4. ⚓ Links_10/11/2024:_Meaning_of_Life_and_iPhone_‘Inactivity_Reboot’⠀⇛


           Links for the day


   5. ⚓ Links_10/11/2024:_Microsoft_Adds_Surveillance_to_Notepad_and_Paint,
      TikTok_Shutdown_Order⠀⇛


           Links for the day


   6. ⚓ Gemini_Links_10/11/2024:_Scrawlspace_and_California⠀⇛


           Links for the day


   7. ⚓ Links_10/11/2024:_Politics,_Economics,_and_Ticketmaster_Issues⠀⇛


           Links for the day


   8. ⚓ Linux_Foundation:_We've_Shut_Down_the_Mailing_Lists_and_Fired_Everyone
      at_Linux.com_So_We_Can_Spend_Money_Buying_Puff_Pieces_and_Paying
      Clickfraud/Spammers⠀⇛


           deeply rogue


   9. ⚓ Over_at_Tux_Machines...⠀⇛


           GNU/Linux news for the past day


  10. ⚓ IRC_Proceedings:_Saturday,_November_09,_2024⠀⇛


           IRC logs for Saturday, November 09, 2024


  11. ⚓ [Meme]_Linux_Foundation_Cuts⠀⇛


           money is spent by the million on highly dubious things


  12. ⚓ Politics_Becoming_Way_Too_'Toxic'⠀⇛


           'Toxic' political discourse ought to be covered, but reducing
           the toxicity of coverage itself (e.g. inaccurately covering
           things to incite "the left" and "the right") is still
           challenging


  13. ⚓ "Paperless_Office"_(Incompatible_With_the_Law)_as_a_Threat_to_Workers'
      Health_at_the_EPO,_Europe's_Second-Largest_Institution_and_Largest_Patent
      Office⠀⇛


           "Software Ergonomics need to be brought back to the agenda at a
           high level!"


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


                          Span from 2024-11-04 to 2024-11-10
      1726 /n/2024/11/04/GNU_Linux_Users_Are_Not_Cheaters.shtml


      1482 /n/2024/11/07/
           Microsoft_Connected_Publishers_Want_Us_to_Think_That_Linux_is_S.shtml


      1307 /n/2024/11/09/
           Linux_Foundation_is_a_Scam_Like_Crypto_So_is_the_Company_of_Jim.shtml


      1236 /n/2024/11/04/Shout_out_to_Christine_From_FOSSForce.shtml


      925  /n/2024/11/09/
           Joel_Espy_Klecker_unpaid_terminally_ill_youth_labor_Debian_knew.shtml


      793  /n/2024/11/04/
           Saving_the_Planet_With_Honesty_Transparency_and_Sharing_Not_Onl.shtml


      779  /n/2024/11/06/
           Mass_Layoffs_at_Mozilla_Announced_During_US_Elections.shtml


      688  /n/2024/11/04/
           Apple_s_MacOS_Shows_Us_the_Vision_of_Computing_That_GAFAM_Has_f.shtml


      647  /n/2024/11/05/Halloween_All_Saints_Day_Swiss_citizenship.shtml


      641  /n/2024/10/25/
           Links_25_10_2024_Erosion_of_Trust_Online_and_Disability_Rights.shtml


      640  /n/2024/11/06/Would_You_Trust_a_Liar.shtml


      639  /n/2024/11/08/
           Donald_Trump_as_Censor_in_Chief_Can_Now_Leverage_Censorship_Com.shtml


      574  /n/2024/11/05/
           Links_05_11_2024_Criminal_Referrals_Regarding_Patent_Trolls_and.shtml


      523  /n/2024/11/04/
           Active_as_in_One_URL_One_Emoji_and_4_Words_in_One_Week.shtml


      515  /n/2024/11/06/Sanctions_Cause_Fragmentation_in_Software.shtml


      509  /n/2024/11/07/
           Anti_Linux_FUD_Now_in_LLM_Form_Thanks_to_Brittany_Day.shtml


      507  /n/2024/11/06/
           Computer_Generator_Crap_Flooding_the_Web_the_Latest_Example_Abo.shtml


      506  /n/2024/11/07/Today_We_Got_an_Early_Birthday_Gift.shtml


      505  /n/2024/11/05/Oppose_the_Fascist.shtml


      504  /n/2024/11/09/
           Linux_Foundation_is_Rebuilding_the_Berlin_Wall_to_Keep_Russians.shtml


      502  /n/2024/11/07/Who_Next_on_the_Linux_Foundation_s_Kill_List.shtml




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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣶⡀⠀⠀⣠⣄⣀⣰⣦⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠀⣀⣨⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣧⡀⢰⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢻⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⠟⣤⣌⡈⠛⣋⠻⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡆⠀⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⣻⣶⡟⠻⣿⣿⣿⣶⣿⠛⢁⣼⢿⣶⣿⠄⢀⣴⣾⣿⣿⣿⣷⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣶⠂⣀⣀⠀⣀⣤⣤⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡁⢡⡏⡼⠙⠋⢹⢁⣾⡿⠛⠛⠏⠻⠟⢿⣷⠂⣹⣬⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠴⠿⠿⢿⣿⣿⣿⠿⠿⣿⣿⡟⣡⡊⠀⠀⣴⣯⣽⣟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⣠⣿⣷⣾⣿⣷⣶⣾⣿⢠⣤⣤⣀⠀⠀⠀⠁⣼⣿⣿⣿⣾⣿⣿⣿⢿⡿⠟⠋⠀⢸⠿⠿⠻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣠⣴⣿⢟⣯⣤⣤⣴⡾⣫⣾⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣙⣻⣿⣷⣶⣦⡀⠹⣿⣿⣿⣿⣯⡠⡙⠢⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢽⣿⣿⣿⣿⣷⡟⢤⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⡄⠀⠳⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠈⢯⡻⣾⣿⣿⣧⡥⢹⡁⠹⡆⢀⠀⠀⠀⠀⠀⠀⠘⣿⣿⢿⢧⣀⣀⣼
⣿⣿⣿⣿⣿⡿⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠛⢮⣻⣿⠿⢤⣀⠳⣤⣿⣦⣡⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣯⣄
⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢻⡿⠿⠛⢋⣽⣾⡄⢙⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠀⠀⢀⣠⣤⣤⣀⡀⠘⣾⣇⣤⣙⠋⢀⣿⣿⣿⣿⣧⣤⣤⣤⣭⣭⣿⣿⣿⣿⣷⣿⣟
⡿⢟⣭⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠐⠂⣼⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⠛⠻⣆⠀⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣹⣯⣫⣿⣿
⣶⣿⣿⣿⣿⣿⣿⣿⠁⠘⢛⡉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠙⢹⣿⡿⠋⠙⠿⡟⠁⠈⠀⠀⠀⠀⣠⣾⣿⣿⡿⠋⠀⠀⠀⣰⣿⠆⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠯⠋⡄
⣿⣿⡿⠟⠛⠉⠁⠀⠀⠀⠸⣿⠗⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠘⠋⠁⠀⢀⣠⣶⣶⣶⣶⣶⡶⣾⣿⠿⠟⠉⠀⠀⣠⣴⠿⠛⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀
⠁⠀⠀⠀⣀⣀⣤⣴⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⢠⡄⠁⠉⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠂⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⠿⢿⣿⣿⠟⠁⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠿⠻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⠛⠻⠿⣿⠿⠟⠀⠀⠀⠀⠉⠀⠀⠀⠀⣄⢀⠀
⣻⣿⣿⣿⣿⣷⣷⣾⣷⣷⣶⣾⣤⣤⣤⣶⣼⡇⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣼⣿⣿⣶⣄⣀⢀⣀⡀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣴⣶⣶⣿⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣶⣶⣷⣶⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠰⣶⣦⣤⣄⡀⢀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠿⣿⣷⡀⠹⣿⣿⣿⣿⣿⣷⣴⣾⣿⣿⣷⢷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣾⣿⣷⡀⠹⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠙⠛⣿⣿⣿⣿⣿⠻⠍⠛⠱

                    ䷩ 𝚕𝚒𝚗𝚎 3186

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

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howtos⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Nov 11, 2024


    * ⚓ Medium ☛ Proving_Grounds_-Nibbles_(Intermediate)_Linux_Box_-Walkthrough
      —_A_Journey_to_Offensive_Security⠀⇛


           In this blog post, we will explore the walkthrough of the
           “Nibbles” intermediate-level Linux box from the Proving
           Grounds. We will walk through the process of exploiting a
           PostgreSQL vulnerability to gain initial access on a target
           machine, followed by privilege escalation techniques to achieve
           root access. Starting with default credentials in PostgreSQL,
           we’ll leverage a known exploit to obtain a foothold, then
           uncover and utilize an SUID binary — /usr/bin/find—as our path
           to escalate privileges. By referencing GTFOBins, we’ll
           demonstrate how to use this binary to elevate permissions and
           ultimately gain full root control over the system.


    * ⚓ Ubuntubuzz ☛ How_To_Install_Kubuntu_24.04_LTS_with_Dualboot_+_UEFI_+
      External_Disk_Methods⠀⇛


           This tutorial will help you install Kubuntu 24.04 LTS "Noble
           Numbat" to your computer or laptop. Kubuntu is an operating
           system powered by KDE and Qt technologies, one Official Flavor
           among many from the Ubuntu GNU/Linux family. Different to
           previous OS versions, this version features a newly designed
           installer and despite that affects some points in the
           installation process, it is still as easy as ever for Kubuntu.
           As always, we wish you safe and successful installation!


    * ⚓ SANS ☛ zipdump_&_PKZIP_Records⠀⇛


           In yesterday's diary entry "zipdump & Evasive ZIP
           Concatenation" I showed how one can inspect the PKZIP records
           that make up a ZIP file.


           My tool zipdump.py can also inspect the data of PKZIP file
           records, and decompress it (not decrypt it).


    * § idroot⠀➾


          o ⚓ ID Root ☛ How_To_Install_Gufw_on_Ubuntu_24.04_LTS⠀⇛


                 In today’s digital landscape, ensuring the security of
                 your computer system is paramount. For Ubuntu users, GUFW
                 (Graphical Uncomplicated Firewall) serves as a user-
                 friendly interface for managing the UFW (Uncomplicated
                 Firewall).


          o ⚓ ID Root ☛ How_To_Install_Figma_on_Ubuntu_24.04_LTS⠀⇛


                 Figma is a powerful web-based design tool that has gained
                 immense popularity among UI/UX designers for its
                 collaborative features and versatility. While Figma
                 primarily operates in a browser, many users prefer to
                 have a dedicated desktop application for improved
                 performance and offline access.


          o ⚓ ID Root ☛ How_To_Install_Draw.io_Desktop_App_on_Ubuntu_24.04
            LTS⠀⇛


                 Draw.io, now known as diagrams.net, is a powerful and
                 versatile diagramming tool that allows users to create
                 flowcharts, UML diagrams, network diagrams, and much
                 more. With its intuitive interface and extensive
                 features, it has become a favorite among developers,
                 project managers, and students alike.


          o ⚓ ID Root ☛ How_To_Install_Jupyter_Notebook_on_Ubuntu_24.04_LTS⠀⇛


                 Jupyter Notebook is a powerful tool that has become a
                 staple in the world of data science, machine learning,
                 and scientific computing. It allows users to create and
                 share documents that contain live code, equations,
                 visualizations, and narrative text. Installing Jupyter
                 Notebook on Ubuntu 24.04 LTS can enhance your
                 productivity and streamline your workflow.


          o ⚓ ID Root ☛ How_To_Install_Jupyter_Notebook_on_Fedora_41⠀⇛


                 Jupyter Notebook is an open-source web application that
                 allows you to create and share documents containing live
                 code, equations, visualizations, and narrative text. It
                 is widely used in data science, machine learning, and
                 scientific computing.


    * ⚓ Installing_KDE_Plasma_on_AlmaLinux_9_or_Rocky_Linux-_Step_by_Step⠀⇛


           KDE Plasma on GNU/Linux offers an eye-catching graphical user
           interface to users who want the most visually appealing and
           highly customizable desktop environments.


    * ⚓ Ubuntu Handbook ☛ How_to_Downgrade_Flatpak_App_Package_in_Ubuntu
      Linux⠀⇛


           This tutorial shows how to downgrade and lock (prevent
           automatic & manual update) Flatpak app packages in Ubuntu and
           other Linux. Flatpak is an universal GNU/Linux package format
           that runs in sandbox environment.


    * ⚓ Real Linux User ☛ How_to_add_and_use_GNOME_Shell_extensions_in_Zorin
      OS⠀⇛


           Zorin OS is in my opinion a fantastic GNU/Linux distribution
           for both novice GNU/Linux users and experienced GNU/Linux
           users...


    * ⚓ How_to_Install_and_Configure_Wine_on_AlmaLinux_9_or_Rocky_Linux⠀⇛


           Wine (Wine Is Not an Emulator) is mainly used on GNU/Linux
           desktops such as Ubuntu. However, users of server GNU/Linux
           distros such as Almalinux, Rocky Linux, Redhat, Fedora, and
           Oracle GNU/Linux can also use this open-source compatibility
           layer.





                    ䷩ 𝚕𝚒𝚗𝚎 3341

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

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2024/11/11/veraPDF_industry_supported_PDF_A_validation.shtml
    Gemini version at https://tuxmachines.org/n/2024/11/11/veraPDF_industry_supported_PDF_A_validation.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ veraPDF – industry supported PDF/
A validation⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Rianne Schestowitz on Nov 11, 2024


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇PDF⦈_


Quoting: veraPDF - industry supported PDF/A validation - LinuxLinks —


     veraPDF is a purpose-built, open source, file-format validator
     covering all PDF/A and PDF/UA parts and conformance levels.


     veraPDF is designed to meet the needs of digital preservationists and
     is supported by the PDF software developer community.


     This is free and open source software.


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