𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Tuesday, April 05, 2022
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Generated Wed 6 Apr 02:40:18 BST 2022
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 𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈
Latest in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕 and older bulletins can be found at 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕-𝒂𝒓𝒄𝒉𝒊𝒗𝒆𝒔
Full IPFS index in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔 and as plain text in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔/𝒕𝒙𝒕
Gemini index for the day: gemini://gemini.techrights.org/2022/04/05/


╒═══════════════════ 𝐑𝐄𝐂𝐄𝐍𝐓 𝐁𝐔𝐋𝐋𝐄𝐓𝐈𝐍𝐒 ════════════════════════════════════╕
  Previous bulletins in IPFS (past 21 days, in chronological order):

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QmUPqrHFRdqGwBx8p2FCLNocU3kbtbteb4MYP57ypavVZB
QmYvgv9zmTR2cBLvzpLNvAdsLo7iFFrWKJtu79JkWKTaRZ
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QmVmhebNywnTu6B8SmaNwvmpQrK5uGfyPHsAeM383HwKRx
QmbtCnKikT7Qr6XTD9CLjRmtU6T3bRTyVqgASiAa1S3VBY
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QmbZUGxupu36yFf72bxj4yCNrYAfeMKD4kf3TzSvrLqGkT
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QmRLV4LzQCcbGE4VJXvT8zja7a8Ehkc6z5ALTVvwBbNgA7
QmVsotEYMNPE1dyPEZpAQ81YQFtSrxNxJNRyba9tPacbNr
Qma6RvSv1ESUzDxUh7arsCZmoLXUaaSzK11P7gLczW1TKT
QmcKAXzUKRMGp3YdQETGwbF7nS2hNTSzE84u2fb9P3tEDf
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QmPA9baiheMyYvoirRpVxfonAnbATaW9SCDexu9yzCdwpR


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

⦿ [Video/Meme] Passengers Are Leaving Gulag Behind | Techrights

⦿ [Meme] Meanwhile at IP Kat | Techrights

⦿ IRC Proceedings: Monday, April 04, 2022 | Techrights

⦿ KDE Neon Added to the Workspace (or ’Battle Station’) | Techrights

⦿ Linux Foundation Starts Hiding What Software It Uses to Make Reports (But Readers Can Guess) | Techrights

⦿ Marleen Stikker, Author of ’The Internet is Broken’, on Research Institute Waag | Techrights

⦿ Linux Foundation Should Remove Linux From Its Name | Techrights

⦿ The EPO is Granting Loads of Software Patents in Order to Fake ’Growth’ | Techrights

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
		http://techrights.org/2022/04/05/gulag-is-dangerous/#comments
		http://techrights.org/2022/04/05/ip-kat-tumbleweed/#comments
		http://techrights.org/2022/04/05/irc-log-040422/#comments
		http://techrights.org/2022/04/05/kde-neon-feels-great/#comments
		http://techrights.org/2022/04/05/lf-hiding/#comments
		http://techrights.org/2022/04/05/libreplanet-keynote/#comments
		http://techrights.org/2022/04/05/not-so-linux-foundation/#comments
		http://techrights.org/2022/04/05/swpats-fake-growth/#comments

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
		http://techrights.org/2022/04/05/antitrust-day/#comments
		http://techrights.org/2022/04/05/lxd-5-0-lts/#comments

                    ䷩ 𝚕𝚒𝚗𝚎 69

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/04/05/gulag-is-dangerous/#comments
    Gemini version at gemini://gemini.techrights.org/2022/04/05/gulag-is-dangerous/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 04.05.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ [Video/Meme]_Passengers_Are_Leaving_Gulag_Behind⠀✐


Posted in Google, Videos at 12:12 pm by Dr. Roy Schestowitz


New_video


 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Are you a Linux user? No, I use Linux users for 'content'
                              and then ban them⦈
                 Who is Gulag trying to impress or appeal to?


Summary: Gulag’s (Google’s) exploitative relationship with GNU/Linux (the
software, its users, developers, creators) needs to be better understood


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣟⢿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠛⠛⠛⢿⢻⠋⡏⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⣿⣿⣿⡿⠟⠛⠛⠻⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣻⢿⡿⣿⡫⡿⢋⣤⣄⣘⡻⢿⣿⣤⡐⡇⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢻⢸⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡏⢸⣽⠃⢻⡅⢼⣻⣿⣿⣿⣷⡜⢿⣿⣆⠀⠀⠀⠀⡄⠀⠀⠀⣿⡇⠀⢸⡇⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⡞⠁⠀⣾⠀⢸⠻⣿⣿⣿⣿⣷⠸⣿⣿⣇⠀⠀⢀⣦⣤⣶⣶⣿⣷⣶⢸⡇⡇⠀⠀⠀⣸⣷⣶⣶⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣛⣛⣻⣿⣿⡿⠉⠉⠉⠉⠉⠹⣿⠁⠰⠀⠀⠀⣿⠀⣿⠈⠛⠻⣯⠀⢙⣧⣻⣿⡟⠀⠀⠀⠶⠴⠶⠶⡶⢶⠆⢸⠃⡇⠀⠠⢤⠤⣤⣤⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠉⠙⠻⢿⣿⣿⡿⠿⠿⠷⠂⠀⠀⠰⢶⣾⣿⠀⠀⠀⠀⠀⠈⢀⣿⠀⠀⠀⣿⣷⣿⣿⣾⣿⣷⠼⠻⣿⣿⣿⣿⠟⠛⠛⠛⠊⠀⠀⠐⠲⠿⠷⠶⠶⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣀⠶⣶⣶⣶⣶⣶⣴⣶⣶⡆⢶⣶⡆⣤⣼⠀⠀⠀⠀⠀⠀⠀⢺⠇⠘⠃⠀⠘⣿⣿⣿⣿⣿⣿⣶⣤⣤⣀⠀⠀⠀⠠⠤⣤⣴⣤⣴⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣶⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⡄⣷⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⢩⣿⣿⣿⣿⣟⠀⠀⢠⡄⠀⠀⠀⠀⠀⠙⠛⠛⠛⠿⠿⠿⠿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠿⠾⡀⠀⠀⢃⠠⣌⢂⠀⠀⠀⠀⠾⣟⣿⣿⣿⣿⡿⠿⠘⠷⠄⠠⠤⠴⡶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⣤⣤⠀⠀⠀⠀⠲⠿⠀
⠁⢀⣶⣶⣶⡆⠀⠀⠀⠀⠀⢀⣀⡀⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠹⣿⡆⠀⠀⣸⣴⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣠⣤⣶⡄⢺⡷⠶⠶⠠⠶⠀⠠⠶⠄⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡆⣿⡋⠉⠙⠁⠀⠉⠀⠉⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡄⡀⢸⡀⠈⠾⠁⠀⠀⢹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠦⣴⣶⣀⣤⣤⣤⣤⡀⣤⣤⢠⣤⣤⣄⢀⣴⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⣿⣿⡇⣾⣧⣄⣤⣤⣤⣤⣤⣶⡿⢿⣿⣿⣿⣿⣿⣿⣿⣸⣾⣷⣾⣦⣤⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡇⠀⢹⣿⣿⣿⣿⣯⣛⠃⣿⣧⡀⣿⣿⣿⠈⣉⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⢻⡇⣿⡟⣷⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠿⢿⣿⢹⣿⢠⡝⣿⡇⣿⣏⡀⣿⡇⣿⡄⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡷⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢻⣿⠀⣸⣿⣿⣿⣽⣽⣿⣦⢻⣿⣻⡟⣿⣷⠿⣿⣿⣿⡿⠟⠿⠀⠈⠛⠚⠋⠈⠛⠛⠁⠉⠉⠁⠉⠁⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠙⠋⠀⠀⠀⢀⣿⣿⣿⣿⣿⣹⣿⢿⣿⣿⣿⣿⣿⡇⠿⣿⣿⡿⠋⠛⢛⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢨⣴⣿⣿⡍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡖⣿⣿⣿⣿⡏⢡⣶⡗⠹⡆⢲⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣷⣶⣶⣶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⡿⠆⠀⣿⣿⠀⢷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢿⣿⣷⣸⣮⡏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣄⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠘⢻⣿⣿⣿⡇⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⡆⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠻⣿⣿⣧⠙⠃⠀⠀⠀⠈⠻⣿⣿⣷⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠙⣇⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣾⠟⠛⠛⠻⢿⣿⡿⠟⠉⠉⠈⠉⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠟⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⡀⠀⠀⠀⠸⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣷⠈⢀⠈⣠⣠⠄⠀⣤⡔⢤⣰⣶⣠⡴⣆⢸⣿⠟⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀
⣿⣿⣿⣿⣿⣿⣿⠏⣰⠟⠀⠀⠀⠀⠀⣴⠀⢀⣴⠇⠀⠀⠀⠘⣧⠀⠀⠀⠀⢸⣿⣦⡀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⢸⣿⡌⣷⣿⣿⣿⣭⣴⣿⣿⣶⣶⣶⣶⣿⣗⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠀⠋⠀⢠⠀⢿⡟⠋⠁⢠⣾⠋⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⣿⡟⠃⠀⠀⠀⣼⣷⣿⠀⠀⠀⠀⢀⣈⣿⣷⢹⣿⣿⣿⣿⣿⠿⡿⣟⣿⣿⣿⣿⡇⠛⠃⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⢈⣆⠈⠃⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠀⠀⠀⠀⣿⣿⣿⡇⠀⢀⣴⣿⣿⣿⣉⠈⢻⣿⠋⠩⠥⠶⣶⣶⣗⡁⢹⣿⣿⡀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠁⠀⢸⣦⢭⣄⣤⣤⡀⠀⢀⣀⠀⣀⣀⣀⢀⣀⢾⣿⣤⣤⣤⣤⣿⣿⣿⣧⣴⣾⣿⣿⣿⣿⣯⡘⠈⠻⠰⣷⣾⣛⣛⣻⣿⠟⠙⠋⠃⠘⠷⠀⠀⠒⠒⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣉⣩⣿⣿⣿⣯⣄⠀⠀⠀⠀⠀⠀⢸⣿⣿⢻⣿⣿⠇⠀⢸⡏⠀⣿⢻⡿⣿⣝⠋⣿⣛⣉⣿⣏⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⠉⢡⡄⣤⢠⣬⣍⣭⣿⢙⣁⡀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣀⡀⠘⠏⠿⠘⠷⠿⢰⠀⢸⡇⣄⣿⣾⡇⣾⣿⣿⣿⣉⣉⣿⣏⣿⣿⣿⣿⣿⣿⣿⣯⣿⣏⠀⣸⣧⣿⠸⣿⡍⣿⣯⢸⣯⡿⢸⣿⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣷⣶⣿⣿⣿⣿⣿⣿⣷⣾⣾⣿⡿⢿⣿⣿⡿⠿⢻⣿⣿⣛⣉⡛⠛⠘⠃⠛⠀⠙⠿⠋⠻⠾⠏⠿⢦⢸⣷⣿⢶⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⢾⣿⣿⢼⣿⣿⢹⣿⣿⣿⣿⣶⣶⣶⢰⡆⣤⣤⢠⡄⣤⠀⢠⣤⣀⢀⣀⡀⣀⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣸⡿⣿⣸⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠶⣼⣿⣿⠀⣼⣿⣟⣸⣿⡇⣿⣿⡇⠀⢹⡟⢹⣇⣿⢸⡟⠃⣶⣦⣶⡆⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠛⣋⣙⠛⣿⣿⣿⣿⠿⢿⣿⣛⣛⣃⣛⣒⣛⣸⡇⠀⠿⠿⠟⠿⢻⡇⣿⢿⡇⠀⢸⣇⣸⣏⣿⣸⣏⣱⣟⣿⣿⣁⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⡿⠁⠀⢿⣿⣿⣿⣆⠀⠻⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⢻⡿⠃⠀⠸⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠈⢠⠄⡿⠋⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⢀⡀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣠⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⠀⠀⠀⠀⠀⣀⣴⣶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠩⠁⢠⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠓⣿⣿⣿⠿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡟⠀⠀⠀⢠⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠼⠿⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⠀⠀⠾⠶⢖⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 150

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/04/05/ip-kat-tumbleweed/#comments
    Gemini version at gemini://gemini.techrights.org/2022/04/05/ip-kat-tumbleweed/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 04.05.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ [Meme]_Meanwhile_at_IP_Kat⠀✐


Posted in Deception, Europe, Patents at 10:57 am by Dr. Roy Schestowitz


    🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇I learned to stop worrying and ignore EPO scandals⦈
          The EPO’s aggression has ‘ousted’ the people behind Merpel


Summary: Over the past month or so IP Kat wrote just 2 posts about patents; it
has said nothing about EPO abuses since several years ago


⢱⣶⣶⣶⣶⣶⣶⠂⠀⠀⠠⣤⠀⢠⣤⢠⣤⣤⣤⣤⢠⣤⣤⣠⣤⢠⡄⣤⣤⣤⣤⣤⠒⣤⣤⣤⣤⣤⡄⠂⣤⣤⣤⣤⣤⣄⣤⣤⢠⣤⣤⠒⣤⣄⣤⣤⣤⣠⣤⡄⣤⣤⣄⣤⣤⣄⣤⢠⣤⣤⢠⣄⣤⢀⣤⣤⡀⠀
⢸⣿⣿⣿⣿⡟⠁⠀⠀⠀⠈⣿⠀⢸⣿⢸⣿⡆⣿⣿⣿⣿⣿⡇⣿⣿⡇⣿⣶⣿⣿⣿⠠⢸⣿⠀⣿⣿⣿⠀⠿⣮⡅⢸⡇⢸⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⡿⣿⣿⣿⣿⣿⣟⣿⣿⣟⢻⣿⢻⣿⢸⣿⣿⢸⣿⣿⡇⠀
⢸⣿⣿⣿⠏⠀⠀⠀⠀⢀⡸⠿⢀⠸⠿⠾⠿⠾⠿⠻⠿⠿⠿⠧⠿⠿⠇⠿⠶⠿⠿⠿⢠⡸⠿⠀⠿⣿⠏⡀⠿⣾⠟⠸⠇⠸⢿⡿⠻⠿⢰⣶⡸⠿⠿⠿⠇⠿⣿⠟⠿⠿⠿⠿⠿⠿⠸⠿⠸⠿⠸⠟⠿⠸⢿⠿⠇⠀
⢸⣿⣿⠃⠀⠀⠀⢠⣶⣿⣿⣾⣿⣿⣶⣿⣿⣿⣿⣷⣶⣾⣷⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠉⠐⠛⣷⣶⣞⡻⢶⡶⢾⡶⠶⠓⠶⠶⣶⣶⣿⣿⣷⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⢖⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡿⠁⠀⠀⢀⡐⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⢀⣠⣾⣿⣿⣿⣤⣤⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠟⣿⣿⣿⣽⣿⣿⣿⣟⣵⣴⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠁⠀⠀⠀⡚⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⢛⠠⣤⣿⣿⣿⣿⡿⠛⣩⠉⠱⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣶⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⣲⢇⡀⠐⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⢻⡀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠃⠘⠁⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠈⠀⠀⢨⢯⣶⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠑⢮⣦⣽⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣴⣿⣿⣿⣿⣿⣿⣿⣿⣯⡄⠀⠈⠛⠛⠛⣿⣿⣿⡟⠛⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣾⣟⠻⠿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠈⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣟⢿⡿⠿⣿⣿⣿⠿⠛⠿⠿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠸⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⡀⠀⠽⠇⠄⠝⠻⠁⠀⠀⠀⠠⣰⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠚⠮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣕⣿⢺⣕⠒⠲⣾⣿⠣⣾⣶⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢴⢻⣴⣄⡗⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⠦⢞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠿⣿⣯⣤⣼⣿⣫⡿⠛⢻⣿⣿⣿⣟⠷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢐⠄⡀⠉⠉⠛⠫⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡮⢀⠨⢿⣿⣿⣿⣷⣗⣷⢿⣿⣿⣿⠊⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠷⠶⣿⠿⢿⠷⠿⠾⠿⠿⠿⠿⠿⠿⠟⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠉⠉⠽⠿⠿⠥⠤⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣶⣶⣶⣶⣶⡖⠀⠀⠀⢠⣤⠀⢠⣤⢠⣤⣤⣤⣤⢢⣤⣤⣠⣤⢠⡄⣤⣤⣤⣤⣤⠒⣤⣤⣤⣤⣤⡄⠂⣤⣤⣤⣤⣤⣄⣤⣤⢠⣤⣤⠒⣤⣄⣤⣤⣤⣠⣤⡄⣤⣤⣄⣤⣤⣄⣤⢠⣤⣤⢠⣄⣤⢄⣤⣤⡀⠀
⢸⣿⣿⣿⣿⠏⠀⠀⠀⠀⢈⣿⠀⢸⣿⢸⣿⡆⣿⣿⣿⣿⣿⡇⣿⣿⡇⣿⣶⣿⣿⣿⠠⢸⣿⠀⣿⣿⣿⠀⠿⣮⡅⢸⡇⢸⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⡿⣿⣿⣿⣿⣿⣟⣿⣿⣟⢻⣿⢻⣿⢸⣿⣿⢸⣿⣿⡇⠀
⢸⣿⣿⡿⠃⠀⠀⠀⠀⣠⡸⠿⢀⠸⠿⠾⠿⠾⠿⠻⠿⠿⠿⠧⠿⠿⠇⠿⠶⠿⠿⠿⣰⡸⠿⠀⠿⣿⠏⡀⠿⣼⠟⠸⠇⠸⢿⡿⠻⠿⢰⣶⠸⠿⠿⠿⠇⠿⣿⠟⠿⠿⠿⠿⠿⠿⠸⠿⠸⠿⠸⠟⠿⠼⢿⠿⠇⠀
⢸⣿⡟⠁⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣶⣾⣿⣾⣿⣿⣿⣿⣿⣿⣶⡄⠀⠙⠒⠿⣶⣶⡾⠿⡶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣿⣿⣷⣶⣶⣶⣾⣷⣶⣾⣶⣶⣶⣶⣶⣶⣖⡴⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠏⠀⠀⠀⣠⠆⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⣀⣶⣿⣿⣿⣀⣸⠀⠈⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢻⣿⣿⣿⣿⣿⣿⣿⢇⣬⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⠋⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⡀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢨⣿⣿⣿⣿⣿⢟⡻⠛⢿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⡆⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢙⣏⠀⢹⡏⣷⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢿⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⡿⠀⠾⠃⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠘⠀⠀⢾⣿⡯⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠣⣵⣶⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣼⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣄⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⠋⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣡⣽⣿⣿⣿⣿⣿⣿⣿⣿⣁⠀⠈⠉⠉⠛⣿⣿⣿⣿⣿⠛⣿⣷⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⠐⠄⠀⠀⠀⠻⢿⢿⣿⣿⣿⠟⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⣿⣿⣿⣿⣿⡿⠛⠿⢿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⠀⠢⠴⠿⠅⠀⠹⠏⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢤⠭⢠⣥⣶⢊⡄⠐⣶⣾⣷⢢⡿⣷⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⢿⣑⣽⡠⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡠⠈⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡖⡿⣿⣯⣦⣾⣿⣙⣟⢛⣻⣿⣿⣿⣿⠣⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠂⠠⠀⠀⠑⠘⠽⡭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⡢⠠⢿⣿⣿⣿⣋⣼⣿⣿⣿⣿⣿⢟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠷⠶⣿⠿⢿⠷⠾⠿⠿⠿⠿⠿⠿⠿⠟⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠉⠁⠽⠿⠿⠄⠥⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣶⣶⣶⣶⣶⡶⠂⠀⠀⠀⣤⠀⢠⣤⢠⣤⣤⣤⣤⢠⣤⣤⡠⣤⢠⡄⣤⣤⣤⣤⣤⠒⣤⣤⣤⣤⣤⡄⠂⣤⣤⣤⣤⣤⣄⣤⣤⢠⣤⣤⠒⣤⣄⣤⣤⣤⣠⣤⡄⣤⣤⣄⣤⣤⣄⣤⢠⣤⣤⢠⣄⣤⢀⣤⣤⡀⠀
⢸⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⣿⠀⢸⣿⢸⣿⡆⣿⣿⣿⣿⣾⡇⣿⣿⡇⣿⣶⣿⣿⣿⠠⢸⣿⠀⣿⣿⣿⠀⠿⣮⡅⢸⡇⢸⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⡿⣿⣿⣿⣿⣿⣟⣿⣿⣟⢻⣿⢻⣿⢸⣿⣿⢸⣿⣿⡇⠀
⢸⣿⣿⣿⠏⠀⠀⠀⠀⣀⡸⠿⢀⠸⠿⠾⠿⠾⠿⠻⠿⠿⠿⠧⠿⠻⠇⠿⠶⠿⠿⠿⢠⡸⠿⠀⠿⣿⠏⡀⠿⣼⠟⠸⠇⠸⢿⡿⠻⠿⢰⣶⠸⠿⠿⠿⠇⠿⣿⠟⠿⠿⠿⠿⠿⠿⠸⠿⠸⠿⠸⠟⠿⠸⢿⠿⠇⠀
⢸⣿⡿⠃⠀⠀⠀⠠⣾⣿⣿⣶⣿⣿⣶⣿⣿⣿⣿⣷⣶⣶⣶⣾⣿⣿⣿⣷⣿⣿⣿⣦⡀⠉⠒⠻⢶⣶⣾⡿⣶⣶⣶⣶⣶⣷⣶⣶⣖⣶⣿⣿⣷⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣖⠒⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡟⠁⠀⠀⢀⠄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣠⣤⣿⣿⡟⢀⡀⠉⠋⠉⠉⠉⠉⣹⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣯⣿⣻⣿⣿⣿⠗⡠⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⠚⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠯⢀⣸⣿⣿⣿⣿⣿⠿⠗⠒⢤⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣇⣷⣾⣿⣯⣽⣿⠂⢢⡇⠀⢸⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣠⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡁⠸⡏⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⡿⢠⡿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣿⣿⣿⣿⣟⠁⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠘⢤⣂⣒⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣽⣷⣿⣿⣿⣿⣿⣿⣴⣤⣤⣴⣇⣀⣠⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣋⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣩⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠈⠉⠛⠙⠻⣿⣯⣽⣟⠻⣿⣥⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠐⠂⠄⠀⠀⠀⠈⠹⠿⠿⢞⠛⠛⡹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢐⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠟⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⠿⠿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠹⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡌⠀⠀⠠⠬⠀⠀⠙⠻⠁⠀⠀⠀⠀⢠⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⢟⡆⠤⠄⢤⡠⠀⢠⠀⠀⠠⠆⠐⢤⣶⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣷⣶⠒⠢⠿⣁⣀⡉⠀⠀⣮⣤⣴⡿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⠀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣦⣆⠠⢻⣷⣎⢄⣨⡆⢈⠙⠛⣻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⠀⠀⠈⠘⠁⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡮⠀⠀⢿⣿⣷⣿⣧⣅⣿⣿⣿⣿⣿⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠷⠶⣾⠿⢿⠷⠾⠿⠿⠿⠿⠿⠿⠿⠟⠛⠻⠿⠿⠿⠿⠿⠿⠿⠷⠀⠀⠠⠿⠽⠠⠀⠤⠴⠿⠿⠿⠿⠿⠿⠷⠶⠾⠿⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣶⣶⣶⣶⣶⡖⠀⠀⠀⠀⣤⠀⢠⣤⢠⣤⣤⣤⣤⢠⣤⣤⡠⣤⢠⡄⣤⣤⣤⣤⣤⠒⣤⣤⣤⣤⣤⡄⠂⣤⣤⣤⣤⣤⣄⣤⣤⢠⣤⣤⠒⣤⣄⣤⣤⣤⣠⣤⡄⣤⣤⣄⣤⣤⣄⣤⢠⣤⣤⢠⣄⣤⢀⣤⣤⡀⠀
⢸⣿⣿⣿⣿⠟⠀⠀⠀⠀⢀⣿⠀⢸⣿⢸⣿⡆⣿⣿⣿⣿⣾⡇⣿⣿⡇⣿⣶⣿⣿⣿⠠⢸⣿⠀⣿⣿⣿⠀⠿⣮⡅⢸⡇⢸⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⡿⣿⣿⣿⣿⣿⣟⣿⣿⣟⢻⣿⢻⣿⢸⣿⣿⢸⣿⣿⡇⠀
⢸⣿⣿⡿⠃⠀⠀⠀⠀⣠⡸⠿⢀⠸⠿⠾⠿⠾⠿⠻⠿⠿⠿⠇⠿⠻⠇⠿⠶⠿⠿⠿⠠⠸⠿⠀⠿⡿⠏⠀⠿⣼⠟⠸⠇⠸⢿⡿⠻⠿⢀⡆⠸⠿⠿⠿⠇⠿⣿⠟⠿⠿⠿⠿⠿⠿⠸⠿⠸⠿⠸⠟⠿⠼⢿⠿⠇⠀
⢸⣿⡟⠁⠀⠀⠀⠤⣾⣿⣿⣶⣿⣿⣶⣷⣿⣷⣾⣷⣶⣶⣶⣾⣿⣿⣿⣶⣶⣿⣿⣷⣄⠀⠐⠿⠶⣶⢦⣷⣴⣖⣶⣶⡤⢳⣶⣶⣖⣶⣿⣿⣦⣴⣶⣶⣾⣶⣦⣶⣶⣲⣶⣶⣶⣶⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠏⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣠⣸⣿⣷⠿⠋⠙⠛⠋⠙⠛⠛⠙⣿⣿⣿⣿⣿⣿⣿⡟⠊⠃⢐⢚⡃⢻⣿⣿⣿⠀⢠⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠂⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠻⣿⣿⣷⣶⣿⣿⣿⣿⣿⣶⣶⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡿⠃⣀⢈⣖⣛⣷⣞⡿⠿⠉⠐⢀⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⡀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡧⢐⣶⣾⣯⢙⣿⡟⠀⣴⡄⠀⢹⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⣠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣿⣏⠀⢿⠁⠈⠉⢻⣿⣿⣿⣿⣿⣿⣿⡇⣰⡆⠀⠀⣾⣿⣿⣿⣿⣿⣿⣫⣿⣟⣿⣿⣿⣿⣦⠀⠀⠀⠀⣸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⠢⣀⣤⣺⣿⣿⣿⣿⣿⡿⠋⠉⠉⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⣷⣿⣿⣿⡿⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣠⣬⣿⣾⣿⣿⣿⣿⣿⣇⣀⣀⣀⡴⠀⢀⣼⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣯⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢠⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣙⣻⣿⣿⣿⣿⣿⣿⣿⡟⠋⠛⠛⠿⠻⢿⣿⣿⣿⡟⢻⣂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠤⣀⠀⠀⠀⠈⠙⠻⠿⣧⣶⠝⠛⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡧⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢈⢣⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡏⠉⠁⠀⠀⠀⢀⠁⠀⠛⠋⠉⠀⠀⠀⠉⣩⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⡈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡿⡏⠀⠀⠄⠀⠠⠀⠀⠀⠀⠀⠠⠠⠀⢄⢠⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⠹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣽⣿⣧⣥⣠⣤⡂⠀⠰⠎⢀⠀⠀⠀⢀⣀⣡⠶⡛⢾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠠⠀⠘⣿⣿⡿⢻⣿⣯⣬⣿⣿⣿⠀⢿⣿⣿⣿⣿⣿⣽⣅⢀⢀⠀⢺⣗⢤⡄⣸⠀⠈⠓⠒⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠸⣿⣷⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣙⣧⣦⣇⠀⠈⣞⢿⣾⣧⣀⣀⣙⣻⠿⡿⢙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠷⠶⣾⠿⢿⠷⠾⠿⠿⠿⠿⠯⠫⠍⠋⠋⠻⠿⠭⠿⠿⠿⠿⠿⠗⠀⠀⠀⠄⠡⠀⠠⠀⠈⠮⠺⠿⠻⠿⠿⠯⠯⠦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣶⣶⣶⣶⣶⡶⠂⠀⠀⠀⣤⠀⢠⣤⢠⣤⣤⣤⣤⢠⣤⣤⡠⣤⢠⡄⣤⣤⣤⣤⣤⠒⣤⣤⣤⣤⣤⡄⠀⣤⣤⣤⣤⣤⣄⣤⣤⢠⣤⣤⠀⣤⣄⣤⣤⣤⣠⣤⡄⣤⣤⣄⣤⣤⣄⣤⢠⣤⣤⢠⣄⣤⢀⣤⣤⡀⠀
⢸⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⣿⠀⢸⣿⢸⣿⡆⣿⣿⣿⣿⣾⡇⣿⣿⡇⣿⣶⣿⣿⣿⠀⢸⣿⠀⣿⣾⣿⠀⠿⣮⡅⢸⡇⢸⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⡿⣿⣿⣿⣿⣿⣟⣿⣿⣟⢻⣿⢻⣿⢸⣿⣿⢸⣿⣿⡇⠀
⢸⣿⣿⣿⠃⠀⠀⠀⠀⣠⠰⠿⢀⠸⠿⠾⠿⠾⠿⠻⠿⠿⠾⠇⠿⠻⠇⠿⠶⠿⠿⠿⠀⠸⠿⠀⠿⡿⠏⠀⠿⣼⠟⠸⠇⠸⢿⡿⠻⠿⢠⡀⠸⠿⠿⠿⠇⠿⣿⠟⠿⠿⠿⠿⠿⠿⠸⠿⠸⠿⠸⠟⠿⠸⢿⠿⠇⠀
⢸⣿⡟⠁⠀⠀⠀⠠⢾⣿⣿⣶⣿⣷⣶⣶⣶⣷⣾⣷⣶⣶⣶⣾⣾⣷⣾⣶⣾⣾⣿⣿⣄⠀⠀⠚⠲⠦⠄⠂⣦⣤⡄⣖⣂⡐⠀⣠⣶⢶⣾⣿⣦⣄⣢⣶⣴⡲⣶⣶⣲⡲⡖⢦⡤⠴⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠏⠀⠀⠀⠀⠀⠐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⢀⣄⣴⣾⡶⠉⠉⠓⠀⠀⠐⠻⠜⢱⣾⣿⣿⣿⣿⣿⡏⠀⠉⠀⢈⠁⠉⣁⠉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠃⣰⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠛⠿⣯⣷⣶⣾⣿⣿⣿⣿⣷⣶⡆⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣟⡟⠀⠀⠀⡀⠈⣠⠜⠨⠢⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠀⠀⠀⠀⠻⣿⣿⣿⠿⣿⣧⡕⠀⣶⡦⠒⡛⢿⡀⠀⠰⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣠⣾⣯⡁⢸⡏⠀⠉⠙⣿⣿⣿⣿⣿⣿⣿⡟⢀⣶⠀⠀⢰⣾⠿⣿⣼⣿⣷⣑⣂⡴⠰⡾⢾⣿⣆⠀⠈⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠠⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣧⠀⠑⣔⣀⣜⣿⣿⣿⣿⣿⣿⠟⠉⠚⠁⠀⠀⠸⣿⣾⣛⣿⢿⣿⡿⠛⠁⠀⣾⠿⠿⣟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡀⣸⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣤⣽⣷⣿⣿⣿⣿⣿⣿⣀⣀⣀⣠⠆⠀⢠⣿⣿⡿⣾⣍⣘⣻⣿⣲⣾⠆⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣼⡟⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⡿⡟⣿⣟⣿⣿⣿⣿⠿⣟⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣻⣿⣿⣿⣿⣿⣿⣿⡿⠋⠛⠙⠦⠊⢋⢋⡋⠉⠁⠹⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⢀⠀⠀⠀⠀⠀⠀⠰⠇⠄⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢘⣿⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠉⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠅⢑⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢂⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⢿⢿⣉⡋⠉⠀⠀⠀⠀⢀⠁⠈⠻⠟⠉⠀⠀⠀⠉⢉⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣽⡿⠃⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⣿⢿⣿⣿⢿⣟⢫⣿⣬⣭⣹⣿⣥⣀⢀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠰⠂⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⠉⣿⣿⣿⣄⣜⣾⡿⠈⢺⣿⣿⣿⣿⣧⡉⠎⠀⠀⠀⠈⠔⠀⠀⣀⠀⠈⠀⠀⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⣿⣷⣽⣿⣿⣿⣿⣫⣦⣀⣼⣿⣿⣿⣟⡿⣿⡶⢑⠆⣀⠀⠀⠀⢺⢙⠠⢦⣀⠀⣈⢿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠶⠶⣾⠿⢷⠷⠾⠾⠿⠿⠿⠋⠙⠯⠙⠐⠸⠧⠥⠽⠾⠿⠿⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⠛⠚⠓⠙⠐⠶⠢⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣶⣶⣶⣶⣶⡶⠂⠀⠀⠀⣤⠀⢠⣤⢠⣤⣤⣤⣤⢠⣤⣤⡠⣤⢠⡄⣤⣤⣤⣤⣤⠀⣤⣤⣤⣤⣤⡄⠀⣤⣤⣤⣤⣤⣄⣤⣤⢠⣤⣤⠀⣤⣄⣤⣤⣤⣠⣤⡄⣤⣤⣄⣤⣤⣄⣤⢠⣤⣤⢠⣄⣤⢀⣤⣤⡀⠀
⢸⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⣿⠀⢸⣿⢸⣿⡆⣿⣿⣿⣿⣾⡇⣿⣿⡇⣿⣶⣿⣿⣿⢀⢸⣿⠀⣿⣾⣿⠀⠿⣮⡅⢸⡇⢸⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⡿⣿⣿⣿⣿⣿⣟⣿⣿⣟⢻⣿⢻⣿⢸⣿⣿⢸⣿⣿⡇⠀
⢸⣿⣿⡿⠃⠀⠀⠀⠀⣠⠠⠿⢀⠸⠿⠾⠿⠾⠿⠻⠿⠿⠼⠇⠿⠻⠇⠿⠶⠿⠿⠿⠀⠸⠿⠀⠿⡾⠏⡀⠿⣼⠏⠸⠇⠸⢿⡿⠻⠿⢀⠄⠸⠿⠿⠿⠇⠿⣿⠟⠿⠿⠿⠿⠿⠿⠸⠿⠸⠿⠸⠟⠿⠸⢿⠿⠇⠀
⢸⣿⡟⠁⠀⠀⠀⡠⢼⣿⣷⣶⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣦⡀⠀⠚⠒⠴⠠⢀⢦⡄⠂⠄⠀⠀⡀⠀⠀⠦⠘⣁⠶⢀⣀⣴⣐⢶⡦⣖⠢⡦⡂⠀⠀⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠏⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⣀⣠⣾⣶⠀⠙⠂⠀⠀⠀⠀⠄⠠⣤⣾⣾⣿⣿⣿⠓⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠂⣠⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠉⠹⠿⣽⣷⣾⣿⣿⣿⣿⣿⣦⣤⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡟⠛⠇⠀⠀⠀⠀⠈⠀⠐⠢⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣠⠀⠀⣼⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠚⣿⣿⣿⠯⢣⡀⠀⠀⠂⠀⠀⠰⠂⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⣴⣧⡀⠠⡏⠀⠍⠙⣿⣿⣿⣿⣿⣿⣿⣿⠀⣤⠄⠀⠠⣬⠿⠁⣤⣿⣦⠀⠀⠀⠀⠴⠶⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣭⣂⠐⣿⣿⣿⣷⠀⠑⢄⣀⣔⣿⣿⣿⣿⣿⣿⡿⠁⠚⠁⠀⠀⠸⡟⡶⠞⢿⣿⣿⡟⠚⠀⢀⣰⠢⠋⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣿⡺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣷⣿⣿⣿⣿⣦⣠⣠⣽⣷⣿⣿⣿⣿⣿⣿⢀⠀⠀⢀⡄⠀⠀⣿⣿⡾⠀⣉⡉⡠⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣰⠏⠍⣀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣾⡟⠻⢧⣢⣿⣿⣯⡜⠾⠿⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣛⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠒⠂⠀⠊⠉⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡏⢀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠑⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣾⢿⣋⣠⠼⠓⠹⠉⠉⠁⠀⠀⠀⠀⠉⠈⠛⠛⠉⠁⠈⠉⠛⢛⣿⣿⣿⣿⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢓⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⢺⣿⣥⡄⡼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠽⣿⣻⠛⢯⣽⠟⠉⠋⠋⠡⠀⠤⠀⢄⣀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡟⠁⠠⣿⣦⣄⡈⠷⠆⠀⢠⣶⣾⣿⣯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡒⣄⡿⣿⠛⠛⢀⠀⠀⢰⠒⠈⠁⠉⠙⢵⠀⠀⠀⠀⠀⠀⠀⢀⠈⠁⠀⠀⠀⠘⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠶⠶⣾⠿⢷⠷⠾⠾⠿⠿⠋⠀⠀⠁⠘⠀⠀⠤⠭⠥⠈⠀⠁⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣶⣶⣶⣶⣶⡶⠂⠀⠀⠀⣤⠀⢠⣤⢠⣤⣤⣤⣤⢠⣤⣤⡀⣤⢠⡄⣤⣤⣤⣤⣤⠀⣤⣤⣤⣤⣤⡄⠀⣤⣤⣤⣤⣤⣄⣤⣤⢠⣤⣤⠀⣤⣄⣤⣤⣤⣠⣤⡄⣤⣤⣄⣤⣤⣄⣤⢠⣤⣤⢠⣄⣤⢀⣤⣤⡀⠀
⢸⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⣿⠀⢸⣿⢸⣿⡆⣿⣿⣿⣿⣾⡇⣿⣿⡇⣿⣶⣿⣿⣿⠀⢸⣿⠀⣿⢸⣿⠀⠿⣮⡅⢸⡇⢸⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⡿⣿⣿⣿⣿⣿⣟⣿⣿⣟⢻⣿⢻⣿⢸⣿⣿⢸⣿⣿⡇⠀
⢸⣿⣿⣿⠃⠀⠀⠀⠀⢀⠠⠿⠀⠸⠿⠾⠿⠾⠿⠻⠿⠿⠼⠇⠿⠻⠇⠿⠶⠿⠿⠿⠀⠸⠿⠀⠿⡾⠏⠀⠿⣼⠏⠸⠇⠸⢿⡿⠻⠿⠀⠀⠸⠿⠿⠿⠇⠿⣿⠟⠿⠿⠿⠿⠿⠿⠸⠿⠸⠿⠸⠟⠿⠸⢿⠿⠇⠀
⢸⣿⡟⠁⠀⠀⠀⠠⢐⣿⣷⣶⣾⣷⣶⣶⣶⣶⣶⣶⡖⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣾⣷⡄⠀⠂⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠏⠀⠀⠀⠀⠀⠀⢸⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣇⡀⠀⠀⢀⣀⣤⣶⡄⠈⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠂⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠋⠈⠛⢫⣷⣶⣾⣿⣿⣿⣿⣧⣤⡀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠨⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠻⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢀⡄⠀⢠⣾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣴⡆⠀⠀⠀⠀⢿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡎⠙⣿⣿⡻⠿⠋⠀⠀⣠⣿⣆⠀⢸⠀⠨⠉⢻⣿⣿⣿⣿⣿⣿⣿⡇⢠⡄⠀⠀⢀⡉⠉⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠿⢏⣺⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡿⣿⣿⣿⣗⣀⣀⡀⠀⣰⣿⣿⣿⡄⠈⠢⣀⣤⣺⣿⣿⣿⣿⣿⣿⠟⠓⠞⠁⠀⠀⢿⠣⠀⠘⢹⣟⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡈⠸⠿⠟⢿⣿⣿⣯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣹⣿⣶⣾⣿⣿⣿⣧⣀⣠⣬⣿⣾⣿⣿⣿⣿⣿⠇⠀⠀⠠⣀⠀⠀⣸⣦⣤⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣴⣿⠉⠁⠀⢙⣁⡡⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢰⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⣿⣿⣿⣿⣿⣿⢿⢿⣿⣤⡀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠛⠿⣿⣿⣿⣦⣄⣸⣿⣿⣿⡿⢻⣟⡙⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣡⢀⡀⣁⠀⠀⠁⠀⠘⠉⠉⠉⠀⠀⠀⠈⠉⠈⠻⠛⠉⠉⠉⠉⠛⠛⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢽⣻⣿⣿⣿⣿⡿⣿⣿⠟⠻⠕⠐⡾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠟⠋⠛⠃⢀⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢤⣦⣭⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠛⠓⠀⠀⠀⠀⠀⠈⠀⠀⠉⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠶⠶⣶⠿⢷⠶⠶⠶⠶⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣶⣶⣶⣶⣶⣶⠂⠀⠀⠀⣤⠀⢠⣤⢠⣤⣤⣤⣤⢠⣤⣤⡀⣤⢠⡄⣤⣤⣤⣤⣤⠀⣤⣤⣤⣤⣤⡄⠀⣤⣤⣤⣤⣤⣄⣤⣤⢠⣤⣤⠀⣤⣄⣤⣤⣤⣠⣤⡄⣤⣤⣄⣤⣤⣄⣤⢠⣤⣤⢠⣄⣤⢀⣤⣤⡀⠀
⢸⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⣿⠀⢸⣿⢸⣿⡆⣿⣿⣿⣿⣾⡇⣿⣿⡇⣿⣶⣿⣿⣿⠀⢸⣿⠀⣿⢸⣿⠀⠿⣮⡅⢸⡇⢸⣿⣿⣿⣿⣿⠁⢸⣿⣿⣿⡿⣿⣿⣿⣿⣿⣟⣿⣿⣟⢻⣿⢻⣿⢸⣿⣿⢸⣿⣿⡇⠀
⢸⣿⣿⣿⠋⠀⠀⠀⠀⢀⠠⠿⠀⠸⠿⠾⠿⠾⠿⠻⠿⠿⠼⠇⠿⠻⠇⠿⠶⠿⠿⠿⣀⠸⠿⠀⠿⡾⠏⠀⠿⣼⠇⠸⠇⠸⢿⡿⠻⠿⠀⠀⠸⠿⠿⠿⠇⠿⣿⠟⠿⠿⠿⠿⠿⠿⠸⠿⠸⠿⠸⠟⠿⠸⢿⠿⠇⠀
⢸⣿⡿⠁⠀⠀⠀⠀⠀⢲⢖⢶⣾⣷⣶⣶⣶⣶⣶⣶⣆⢶⣶⣶⣶⣶⣶⣶⣶⣶⡖⢲⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠟⠀⠀⠀⠀⠀⠀⠠⣤⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣷⣀⠀⠀⠀⣀⣀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠐⠀⢀⣸⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠁⠀⠙⠛⣹⣶⣶⣶⣿⣿⣿⣿⣄⣀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⡀⠄⠀⣰⣟⣿⣯⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠰⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣶⣤⣄⠈⣽⡿⢛⠿⠟⠀⠀⢀⣾⣷⠀⠀⡏⠀⠍⠙⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⡀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠺⠛⣈⣿⣿⣿⣿⣿⣿⣿⣋⣙⠟⣿⣿⣿⣿⣿⣃⣀⣀⡀⠀⢠⣾⣿⣿⣧⠀⠑⣄⡀⠤⣿⣿⣿⣿⣿⣿⣿⠛⠴⠋⠀⠀⢠⡯⠀⠀⠓⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⣩⣭⣯⣶⣾⣿⣿⣿⣯⣄⣀⣨⣿⣭⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⡀⠀⠀⡇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣶⣾⡁⣀⣼⡇⠀⠀⠀⢃⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⠻⠿⢿⣷⡄⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠹⣿⣿⣿⣿⣆⡀⠀⣻⣿⣦⣤⣴⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠁⠀⠀⠏⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠹⣿⣿⡿⠻⠅⣀⣾⣶⡀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠘⠉⠉⠁⠀⠀⠀⠈⠉⠀⠛⠛⠋⠉⠉⠉⠛⠛⢿⣿⣿⣿⡟⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠙⣿⣴⣧⣿⠿⠿⠿⠿⠟⠍⠃⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠶⠶⣶⠿⢷⠶⠶⠶⠶⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣶⣶⣶⣶⣶⣶⠂⠀⠀⠀⣤⠀⢠⣤⢠⣤⣤⣤⣤⢠⣤⣤⡀⣤⢠⡄⣤⣤⣤⣤⣤⠀⣤⣤⣤⣤⣤⡄⠀⣤⣤⣤⣤⣤⣄⣤⣤⢠⣤⣤⠀⣤⣄⣤⣤⣤⣠⣤⡄⣤⣤⣄⣤⣤⣄⣤⢠⣤⣤⢠⣄⣤⢀⣤⣤⡀⠀
⢸⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⣿⠀⢸⣿⢸⣿⡆⣿⣿⣿⣿⣾⡇⣿⣿⡇⣿⣶⣿⣿⣿⠀⢸⣿⠀⣿⢸⣿⠀⠿⣮⡅⢸⡇⢸⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⡿⣿⣿⣿⣿⣿⣟⣿⣿⣟⢻⣿⢻⣿⢸⣿⣿⢸⣿⣿⡇⠀
⢸⣿⣿⣿⠏⠀⠀⠀⠀⢀⠀⠿⠀⠸⠿⠾⠿⠾⠿⠻⠿⠿⠼⠇⠿⠻⠇⠿⠶⠿⠿⠿⠀⡸⠿⠀⠿⡾⠏⡀⠿⣼⠇⠸⠇⠸⢿⡿⠻⠿⠀⠀⠸⠿⠿⠿⠇⠿⣿⠟⠿⠿⠿⠿⠿⠿⠸⠿⠸⠿⠸⠟⠿⠸⢿⠿⠇⠀
⢸⣿⡿⠁⠀⠀⠀⠀⠀⢲⡷⢶⣾⣷⣶⣶⣶⣶⣶⣶⡖⣲⣶⣶⣶⣶⣶⣶⣶⣶⡀⠐⢾⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡟⠀⠀⠀⠀⠀⠀⢠⣮⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⣿⣿⡀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣤⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣦⣀⣠⣤⣄⣀⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠁⠉⠈⠙⠛⣻⣴⣶⣶⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠛⠛⣽⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⣠⡴⠆⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⠀⠀⠀⠀⢀⣼⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡌⠉⣿⣿⣟⠿⡟⠀⠀⢀⣾⣿⣧⠀⢰⡏⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣁⣀⢀⢠⣾⣿⣿⣿⡄⠀⢂⡀⢀⡤⣿⣿⣿⣿⣿⣿⣿⣿⢠⠿⠀⠀⢠⡎⠀⠀⠈⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠿⣿⣿⣿⣿⠃⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣀⣀⣙⣟⣯⣿⣿⣿⣿⣿⡿⠁⠀⠈⠀⠀⠀⢸⣃⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠀⠙⠛⠻⠟⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣄⣠⡴⠀⠀⣼⠃⠀⠹⢣⠁⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣷⡀⠀⠀⢀⣄⡀⠀⠀⠀⣠⡀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣴⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣶⣾⣿⣿⣿⣷⣶⣿⣿⣷⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠦⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠸⣿⣿⢁⣩⣿⡿⣿⣿⣿⢿⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠀⠀⠀⠀⠉⣿⣿⡮⠈⠀⠀⠀⠀⠀⢙⡟⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠛⢟⠁⠀⢀⣤⣤⡀⡀⢂⣇⢀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠙⠋⠉⠻⠟⠛⠛⠙⠛⠻⠿⢿⣿⣿⣿⣿⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣤⣰⣿⡿⠿⣿⡿⠿⠟⠋⠀⠀⡄⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠋⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢠⠠⢬⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠂⠀⠀⠀⠀⠀⠉⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠶⠶⣶⠿⢷⠶⠶⠶⠶⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣶⣶⣶⣶⣶⡶⠂⠀⠀⠀⣤⠀⢠⣤⢠⣤⣤⣤⣤⢠⣤⣤⡀⣤⢠⡄⣤⣤⣤⣤⣤⠀⣤⣤⣤⣤⣤⡄⠀⣤⣤⣤⣤⣤⣄⣤⣤⢠⣤⣤⠀⣤⣄⣤⣤⣤⣠⣤⡄⣤⣤⣄⣤⣤⣄⣤⢠⣤⣤⢠⣄⣤⢀⣤⣤⡀⠀
⢸⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⣿⠀⢸⣿⢸⣿⡆⣿⣿⣿⣿⣾⡃⣿⣿⡇⣿⣶⣿⣿⣿⠀⢸⣿⠀⣿⢸⣿⠀⠿⣮⡅⢸⡇⢸⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⡿⣿⣿⣿⣿⣿⣟⣿⣿⣟⢻⣿⢻⣿⢸⣿⣿⢸⣿⣿⡇⠀
⢸⣿⣿⣿⡟⣀⠀⠀⠀⢀⠀⠿⠀⠸⠿⠾⠿⠾⠿⠻⠿⠿⠼⠇⠿⠻⠇⠿⠶⠿⠿⠿⠀⠸⠿⠀⠿⡾⠏⠀⠿⣼⠇⠸⠇⠸⢿⡿⠻⠿⠀⠀⠸⠿⠿⠿⠇⠿⣿⠟⠿⠿⠿⠿⠿⠿⠸⠿⠸⠿⠸⠟⠿⠸⢿⠿⠇⠀
⢸⣿⣿⣿⣿⣿⣿⣤⣶⣷⣦⣶⣾⣷⣶⣶⣶⣶⣶⣶⠒⣰⣐⣶⣶⣶⣶⣶⣶⣦⠀⠀⠐⣲⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣾⣿⣿⣧⣿⣿⣿⣿⣿⠿⠔⠶⢿⣿⣧⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠈⡀⠀⠙⢛⣥⣶⣴⣾⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⠸⠿⣾⣾⣷⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⠟⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⢯⣿⣿⣿⠃⠀⠀⢀⡴⡞⠋⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣀⣽⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠛⠛⠃⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠯⠝⠃⠀⠀⠀⣾⣿⣿⠀⠠⡏⠈⡙⠻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣾⣿⣿⣿⡆⠀⢣⡀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⠁⣴⠆⠀⠀⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣙⣛⣪⣿⣿⣿⣿⣿⣿⠏⠁⠈⠁⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⢀⣢⠄⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠄⣀⣤⣦⣄⡀⠀⠀⣀⣤⡂⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠐⠀⠻⣿⣿⣿⢿⣿⣿⣿⣿⣶⣀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣠⣬⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢙⠉⠈⠉⠘⢻⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣤⣾⣯⠁⡀⠈⠩⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠇⠈⠀⠀⠀⠀⠠⠛⠛⢻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⣀⣀⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁⠀⠀⠛⠋⠉⠻⠟⠛⠛⠛⠻⠿⡿⣿⣿⣿⣿⣿⠋⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⢀⣴⠿⠿⡿⡷⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠶⠶⣶⠿⢷⠶⠶⠶⠶⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣶⣶⣶⣶⣶⣶⠂⠀⠀⠀⣤⠀⢠⣤⢠⣤⣤⣤⣤⢠⣤⣤⡀⣤⢠⡄⣤⣤⣤⣤⣤⠀⣤⣤⣤⣤⣤⡄⠀⣤⣤⣤⣤⣤⣄⣤⣤⢠⣤⣤⠀⣤⣄⣤⣤⣤⣠⣤⡄⣤⣤⣄⣤⣤⣄⣤⢠⣤⣤⢠⣄⣤⢀⣤⣤⡀⠀
⢸⣿⣿⣿⣿⣿⣿⣷⣤⣄⠀⣿⠀⢸⣿⢸⣿⡆⣿⣿⣿⣿⣾⡃⣿⣿⡇⣿⣶⣿⣿⣿⠀⢸⣿⠀⣿⢸⣿⠀⠿⣮⡅⢸⡇⢸⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⡟⣿⣿⣿⣿⣿⣟⣿⣿⣟⢻⣿⢻⣿⢸⣿⣿⢸⣿⣿⡇⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡤⠿⠀⠸⠿⠾⠿⠾⠿⠻⠿⠿⠸⠇⠿⠻⠇⠿⠶⠿⠿⠿⠀⠸⠿⠀⠿⡾⠏⠀⠿⣼⠇⠸⠇⠸⢿⡿⠻⠿⠀⠀⠸⠿⠿⠿⠇⠿⣿⠟⠿⠿⠿⠿⠿⠿⠸⠿⠸⠿⠸⠟⠿⠸⢿⠿⠇⠀
⠸⢿⢿⠏⠀⠈⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⡒⣠⣒⣴⣶⣶⣲⣶⣶⣶⠂⠀⠀⢲⣼⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣿⣯⣿⣿⣿⣿⣿⣗⠦⢢⠟⣿⣿⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⢥⠆⠀⠙⣻⣴⣶⣶⣶⣿⣿⣿⠃⠀⠀⠀⠀⠀⠠⣼⣿⣋⣴⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠃⠀⠀⢀⣴⣲⠷⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣼⣿⣿⡇⠀⣶⠁⢉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠸⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣧⠀⠘⣄⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢀⣤⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⢀⣈⣻⣒⣺⣿⣿⣿⣿⣿⡿⠋⠉⠛⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣠⣤⣀⠀⠀⠀⠐⣚⠀⠀⠀⠩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⡀⠀⠠⣠⠀⠀⣧⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣶⣾⣿⣿⣷⣄⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠘⠌⠛⠿⣿⣿⣿⣿⣿⣷⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢁⣀⣽⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⣩⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⣠⣸⣋⠧⠀⠈⠉⠹⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠨⢿⣿⠗⠀⠀⠀⠀⠀⠀⠨⠋⠻⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⣀⣀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⠉⠻⠿⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⡏⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢐⣿⠿⠿⡟⠿⠏⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠶⠶⣶⠿⢷⠶⠶⠶⠶⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣰⣶⣶⣶⣶⣶⣶⠀⣤⠀⢠⣤⢠⣤⣤⣤⣤⢠⣤⣤⡀⣤⢠⡄⣤⣤⣤⣤⣤⠀⣤⣤⣤⣤⣤⡄⠀⣤⣤⣤⣤⣤⣄⣤⣤⢠⣤⣤⠀⣤⣄⣤⣤⣤⣠⣤⡄⣤⣤⣄⣤⣤⣄⣤⢠⣤⣤⢠⣄⣤⢀⣤⣤⡀⠀
⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣷⣿⠀⢸⣿⢸⣿⡆⣿⣿⣿⣿⣾⡃⣿⣿⡇⣿⣶⣿⣿⣿⠀⢸⣿⠀⣿⢸⣿⠀⠿⣮⡅⢸⡇⢸⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⡟⣿⣿⣿⣿⣿⣟⣿⣿⣟⢻⣿⢻⣿⢸⣿⣿⢸⣿⣿⡇⠀
⠀⠀⠀⠀⠚⢿⣿⣿⣿⣿⣿⠿⣰⡸⠿⠾⠿⠾⠿⠻⠿⠿⠸⠇⠿⠻⠇⠿⠶⠿⠿⠿⠀⠸⠿⢀⠿⡾⠏⠀⠿⣼⠇⠸⠇⠸⢿⡿⠻⠿⠀⠀⠸⠿⠿⠿⠇⠿⣿⠟⠿⠿⠿⠿⠿⠿⠸⠿⠸⠿⠸⠟⠿⠸⢿⠿⠇⠀
⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠂⠀⣀⣶⣶⣂⣲⣶⣶⠆⠀⠀⠀⠠⣴⣿⡆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣾⣿⣯⣌⣿⣿⣿⣿⠶⡀⠀⠀⠃⠛⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡋⢿⣿⣿⣿⣿⣿⣿⣩⣿⣿⣿⡿⠿⠓⠂⠀⠠⣶⣤⠀⠀⢉⣧⣶⣶⣶⣾⣿⣿⣾⠀⠀⠀⠀⠀⠀⢸⣧⣇⢂⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣇⢨⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⡁⠀⠀⢀⣶⡏⠀⠀⠀⢠⣿⣻⣿⣫⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⢉⣻⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⣼⣿⣿⣷⠀⠀⡏⠀⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢶⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠡⣀⠀⣠⢾⣿⣿⣿⣿⣿⣿⣿⡟⢠⡄⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠠⢌⡳⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⣀⣈⣛⣒⣿⣿⣿⣿⣿⣿⡿⠋⠑⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠀⣴⣄⣤⣆⡀⣤⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣯⠁⣀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠐⠈⣿⣿⣿⣿⣿⣿⣷⣀⠀⣀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣀⣈⣽⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⡰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠄⡘⠛⠛⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢺⡷⠢⠀⠀⠀⠀⠀⠀⠈⠛⠛⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠛⠙⠻⠟⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠉⠄⠒⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠶⠶⣶⠿⢷⠶⠶⠶⠶⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢰⣶⣶⣶⣶⣶⣶⣶⣦⠀⣤⢀⢠⣤⢠⣤⣤⣤⣤⢠⣤⣤⡀⣤⢠⡄⣤⣤⣤⣤⣤⠀⣤⣤⣤⣤⣤⡄⠀⣤⣤⣤⣤⣤⣄⣤⣤⢠⣤⣤⠀⣤⣄⣤⣤⣤⣠⣤⡄⣤⣤⣄⣤⣤⣄⣤⢠⣤⣤⢠⣄⣤⢀⣤⣤⡀⠀
⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⢸⢸⣿⢸⣿⡆⣿⣿⣿⣿⢾⡃⣿⣿⡇⣿⣶⣿⣿⣿⠀⢸⣿⠀⣿⢸⣿⠀⠿⣮⡅⢸⡇⢸⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⡟⣿⣿⣿⣿⣿⣟⣿⣿⣟⢻⣿⢻⣿⢸⣿⣿⢸⣿⣿⡇⠀
⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠿⣼⡸⠿⠾⠿⠾⠿⠻⠿⠿⠸⠇⠿⠻⠇⠿⠶⠿⠿⠿⠀⠸⠿⢀⠿⡾⠏⠀⠿⣼⠇⠸⠇⠸⢿⡿⠻⠿⠀⠀⠸⠿⠿⠿⠇⠿⣿⠟⠿⠿⠿⠿⠿⠿⠸⠿⠸⠿⠸⠟⠿⠸⢿⠿⠇⠀
⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠰⠀⠀⠠⡖⡀⠀⣲⣶⡆⠀⠀⠀⠠⣴⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⡿⠻⢿⣿⣿⣿⣿⣿⡔⢠⣿⣖⣀⣌⣳⣿⠓⢀⠀⠀⠀⠈⠚⠛⢿⣆⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⠚⠁⢀⣔⠖⠦⠀⠀⠀⣭⣴⣶⣶⣿⣿⣿⣷⣟⠀⠀⠀⠀⠐⢈⢭⡅⠈⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡆⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣾⣏⠀⠀⠀⠀⣾⣯⣿⣿⣽⣿⣿⣿⣿⣿⣶⡆⠀⠀⠀⠀⠉⠈⢉⣻⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣼⣿⣿⣿⡇⠀⢸⠁⠢⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠠⣶⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡇⠀⠀⢢⣀⠀⠴⣿⣿⣿⣿⣿⣿⣿⣿⡏⣠⡄⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣀⣙⣫⣭⣿⣿⣿⣿⣿⣿⠟⠉⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣷⣶⡏⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣀⣨⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⢸⣿⣿⢿⣿⡇⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠸⠊⠗⡺⢿⡖⠀⠽⠿⢩⠓⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠉⠉⠉⠉⠁⠀⠀⠈⠉⢿⡿⠿⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠶⠶⣶⠿⢷⠶⠴⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⢲⣶⢲⣤⣴⣤⣤⢠⣤⣤⡀⣤⢠⡄⣤⣤⣤⣤⣤⠀⣤⣤⣤⣤⣤⡄⠀⣤⣤⣤⣤⣤⣄⣤⣤⢠⣤⣤⠀⣤⣄⣤⣤⣤⣠⣤⡄⣤⣤⣄⣤⣤⣄⣤⢠⣤⣤⢠⣄⣤⢀⣤⣤⡀⠀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⣿⢸⣿⡆⣿⣿⣿⣿⢾⡃⣿⣿⡇⣿⣶⣿⣿⣿⠀⢸⣿⠀⣿⢸⣿⠀⠿⣮⡅⢸⡇⢸⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⡟⣿⣿⣿⣿⣿⣟⣿⣿⣟⢻⣿⢳⣿⢸⣿⣿⢸⣿⣿⡇⠀
⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡿⠿⣸⠸⠿⠾⠿⠾⠿⠻⠿⠿⠸⠇⠿⠻⠇⠿⠶⠿⠿⠿⠀⠸⠿⠀⠿⡾⠏⠀⠿⣼⠇⠸⠇⠸⢿⡿⠻⠿⠀⠀⠸⠿⠿⠿⠇⠿⣿⠟⠿⠿⠿⠿⠿⠿⠸⠿⠸⠿⠸⠟⠿⠸⢿⠿⠇⠀
⠀⠀⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣷⡆⠀⠀⡀⠄⠀⠀⢴⡶⠀⠀⠀⠀⠀⠀⢀⣾⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣤⣿⣯⡀⢀⣰⡾⠂⠀⠀⠀⠀⠀⠀⠀⠙⠻⠦⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣇⢑⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡋⠁⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣾⣿⣿⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⡂⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣼⣿⡄⢀⠀⠀⠀⠲⠿⢴⣿⣯⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠰⣶⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣇⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⡇⠀⠘⡇⠀⠄⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢠⣴⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠐⣄⡀⠤⢺⣿⣿⣿⣿⣿⣿⣿⣿⠇⣀⡀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀⣀⣨⣋⣭⣿⣿⣿⣿⣿⣿⣿⠟⠉⠱⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢀⣙⣿⣿⣿⣿⣿⣿⣶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣍⠙⠋⠡⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣽⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢧⣬⣿⣿⣿⣿⣿⠿⠟⠛⠛⠁⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠈⠙⠉⠙⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠶⠶⣶⠿⢷⠶⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣤⢶⢢⣴⢢⣤⣤⣤⣤⢠⣤⣤⡀⣤⢠⡄⣤⣤⣤⣤⣄⠀⣤⣤⣤⣤⣤⡄⠀⣤⣤⣤⣤⣤⣄⣤⣤⢠⣤⣤⠀⣤⣄⣤⣤⣤⣠⣤⡄⣤⣤⣄⣤⣤⣄⣤⢠⣤⣤⢠⣄⣤⢀⣤⣤⡀⠀
⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢸⢸⣿⢸⣿⡆⣿⣿⣿⣿⢾⡃⣿⣿⡇⣿⣶⣿⣿⣿⠀⢸⣿⠀⣿⢸⣿⠀⠿⣮⡅⢸⡇⢸⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⡟⣿⣿⣿⣿⣿⣟⣿⣿⣟⢻⣿⢳⣿⢸⣿⣿⢸⣿⣿⡇⠀
⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡁⠿⢸⠸⠿⠾⠿⠶⠿⠻⠧⠿⠸⠇⠿⠻⠇⠿⠶⠿⠿⠿⠀⠸⠿⠀⠿⡾⠏⠀⠿⣼⠇⠸⠇⠸⢿⡿⠻⠿⠀⠀⠸⠿⠿⠿⠇⠿⣿⠟⠿⠿⠿⠿⠿⠿⠸⠿⠸⠿⠸⠟⠿⠸⢿⠿⠇⠀
⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡀⠀⠀⠀⡀⠀⠀⠀⢐⡶⠀⠀⠀⠀⠀⠀⢠⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣧⣤⣠⣻⣷⡤⢀⣰⡞⠃⠀⠀⠀⠀⠀⠀⠀⠘⠻⢷⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⡇⠀⠀⠀⣴⠂⠀⠀⠀⠀⠀⢀⣴⣶⣶⣿⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⢗⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣼⣿⡄⢀⠀⠀⠀⠰⠿⢤⣿⣿⣼⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⣶⣶⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣧⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣼⣿⣿⣿⣿⡇⠀⠀⠏⠐⠤⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢀⣤⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣶⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠀⠀⠐⢄⡀⣀⠔⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀⣀⣈⣛⣃⣹⣿⣿⣿⣿⣿⣿⡿⠋⠣⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠉⠋⠻⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠙⢻⣿⣿⣿⣿⣿⣷⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣟⠛⠻⠏⣴⣶⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠙⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣘⣻⣿⣿⣿⣿⣿⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠉⠉⠙⠛⠛⠉⠀⠈⠉⠉⠉⠋⠋⠛⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢹⣿⣿⣿⠿⠻⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠶⠶⣶⠿⢷⠶⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣤⠒⢠⣤⢠⣤⣤⣤⣤⢠⣤⣤⡀⣤⢠⡄⣤⣤⣤⣤⣄⠀⣤⣤⣤⣤⣤⡄⠀⣤⣤⣤⣤⣤⣄⣤⣤⢠⣤⣤⠀⣤⣄⣤⣤⣤⣠⣤⡄⣤⣤⣄⣤⣤⣄⣤⢠⣤⣤⢠⣄⣤⢀⣤⣤⡀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠀⢸⣿⢸⣿⡆⣿⣿⣾⣿⢾⡃⣿⣿⡇⣿⣶⣿⣿⣿⠀⢸⣿⠀⣿⢸⣿⠀⠿⣮⡅⢸⡇⢸⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⡟⣿⣿⣿⣿⣿⣟⣿⣿⣟⢻⣿⢳⣿⢸⣿⣿⢸⣿⣿⡇⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠿⣸⡸⠿⠾⠿⠶⠿⠻⠧⠿⠸⠇⠿⠻⠇⠿⠶⠿⠿⠿⠀⠸⠿⠀⠿⡾⠏⠀⠿⣼⠇⠸⠇⠸⢿⡿⠻⠿⠀⠀⠸⠿⠿⠿⠇⠿⣿⠟⠿⠿⠿⠿⠿⠿⠸⠿⠸⠿⠸⠟⠿⠸⢿⠿⠇⠀
⠈⣿⣭⡿⠟⠿⢿⡽⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⠆⠀⠀⠀⠀⠀⠄⠀⠀⠐⡶⠀⠀⠀⠀⠀⠀⠀⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠉⣈⣅⠀⠀⢠⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣦⣤⣠⣾⣶⠄⠀⠐⡞⠁⠀⠀⠀⠀⠀⠀⠀⢉⠻⢶⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣶⣿⣿⣶⣶⢮⣡⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⠇⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣿⣿⣿⣿⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢃⣽⣿⣿⣿⣇⡉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⠀⠀⠀⣼⣿⡄⠀⠀⠀⠀⠀⡾⣭⣼⣿⣩⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⢰⣶⡾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⢿⣿⣿⣿⣿⣧⠛⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣀⣰⣿⣿⣿⣿⡇⠀⠀⢲⠠⢀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⢠⣴⡾⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣸⣿⣿⣿⣿⣿⣷⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠈⢄⠀⠀⣠⢾⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⡀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠻⠖⢒⣾⣿⣿⣿⣿⣿⣿⡿⠛⢃⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠑⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣄⣨⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠿⣿⣿⣿⣿⣿⣿⣤⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣿⡿⢿⣿⣿⠏⣤⣴⣶⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠈⢿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠿⠿⠛⠉⠈⠉⠉⠉⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⢻⣿⣿⣿⣿⣿⣿⠿⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⠿⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠶⠶⣶⠿⢷⠶⠴⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠰⣶⣶⣶⣶⣶⣶⣶⡀⠀⠀⣤⠀⢠⣤⢠⣤⡄⣤⣤⢠⣤⣤⡀⣤⢠⡄⣤⣤⣤⣤⣄⠀⣤⣤⣤⣠⣤⡄⠀⣤⣤⣤⣤⣤⣄⣤⣤⢠⣤⣤⠀⣤⣄⣤⣤⣤⣠⣤⡄⣤⣤⡄⣤⣤⣄⣤⢠⡤⣤⢠⣄⣤⢀⣤⣤⡀⠀
⠈⠟⢿⠿⣿⣿⣿⣿⣧⣀⠀⣿⠀⢸⣿⢸⣿⡆⣿⣿⡞⣿⢾⡃⣿⣿⡇⣿⣶⣿⣿⣿⠀⢰⣿⠀⣿⢸⣿⠀⠿⣮⡅⢸⡇⢸⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⡟⣿⣿⣿⣿⣿⣟⣿⣿⣟⢹⣿⢳⣿⢸⣿⣿⢸⣿⣿⡇⠀
⠀⠀⠀⠠⢹⣿⣿⣿⣿⣿⠀⠿⠀⠸⠿⠾⠿⠶⠿⠻⠧⠿⠸⠇⠿⠻⠇⠿⠶⠿⠿⠿⠀⠸⠿⠀⠿⡾⠏⠀⠿⡼⠇⠸⠇⠸⢿⡿⠻⠿⠀⠀⠸⠿⠿⠿⠇⠿⣿⠟⠿⠿⠿⠿⠿⠿⠸⠿⠸⠿⠸⠟⠿⠸⢿⠿⠇⠀
⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣶⣖⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣄⣠⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣤⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⡆⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣷⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣠⣶⣄⠀⠀⠀⢀⣼⣇⠀⠀⠀⠀⠀⠀⣾⣉⣹⣿⣉⣿⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⣶⡶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣀⣸⣿⣿⣶⣶⡀⠀⠀⢴⠀⢀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠀⠀⠀⢀⣤⡶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⠁⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣧⠀⠀⠐⡀⠀⠀⢀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠈⠳⠮⠭⢼⣿⣿⣿⣿⣿⣿⣿⠟⢃⡀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣷⣶⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣀⣐⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢐⢰⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣆⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⡿⢁⣀⣤⣼⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠈⣶⡄⡉⠉⠀⣿⣿⣿⣿⣿⣿⣿⡿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣶⣶⣦⣿⣿⣿⣿⣿⣿⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⠿⠟⠉⠛⠋⠈⠙⠙⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⠷⠶⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡶⢶⣶⣶⢖⠀⠀⠀⠀⠀⣤⠀⢠⣤⢠⣤⡄⣤⣤⢠⣤⣤⡀⣤⢠⡄⣤⣤⣤⣤⣄⠀⣤⣤⣤⣠⣤⡄⠀⣤⣤⣤⣤⣤⣄⣤⣤⢠⣤⣤⠀⣤⡄⣤⣤⣤⣠⣤⡄⣤⣤⡄⣤⣤⣄⣤⢠⡤⣤⢠⣄⣤⢀⣤⣤⡀⠀
⢀⣸⣿⣿⠿⠃⠀⠀⠀⠀⠀⣿⠀⢸⣿⢸⣿⡆⣿⢿⡆⣿⢾⡃⣿⣿⡇⣿⣶⣿⣿⣿⠀⢠⣿⠀⣿⢸⣷⠀⠿⣮⡅⢸⡇⢸⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⡟⣿⣿⣿⣿⣿⣟⣿⣿⣟⢹⣿⠳⣿⢸⣿⣿⢸⣿⣿⡇⠀
⠐⣻⣿⠟⠀⠀⠀⠀⠀⠀⠀⠿⠀⠸⠿⠾⠿⠶⠿⠻⠧⠿⠸⠇⠿⠻⠇⠿⠶⠿⠿⠿⠀⠸⠿⠀⠿⡾⠏⠀⠿⡼⠇⠸⠇⠸⢿⡿⠻⠿⠀⠀⠸⠿⠟⠿⠇⠿⣿⠟⠿⠿⠿⠿⠿⠿⠸⠿⠰⠿⠸⠟⠿⠸⢿⠿⠇⠀
⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢹⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢘⣶⣶⣶⣶⣷⣿⣿⣿⣶⣮⣬⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣷⣿⣿⣿⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣶⣷⣴⣰⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡅⠀⠀⠀⠀⠀⠀⣌⣉⣈⣿⣅⣽⣿⣿⣿⣿⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠒⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣠⣤⢤⣀⡀⠀⠀⠀⣸⣿⣿⣤⣤⠀⠀⠀⢠⠀⢀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⠀⠀⢀⣤⡶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣶⣾⣿⣿⣿⣿⠻⣧⠀⠀⠈⠀⠀⠀⠀⡐⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠈⠳⡦⠭⠄⣿⣿⣿⣿⣿⣿⣿⡿⠛⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢁⣀⣠⣽⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠈⠉⠉⠉⠛⠋⠡⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣠⣄⣿⣶⣦⣤⣽⣿⣿⣿⣿⣿⣿⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣎⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠙⠉⠁⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡿⠟⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⠶⠖⠰⠶⠶⠶⠀⠀⠀⠀⠙⠿⠿⠿⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⠿⠿⠿⠿⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣤⠀⢠⣤⢠⣤⡄⣤⣤⠀⣤⣤⡀⣤⢠⡄⣤⣤⣤⣤⣄⠀⣤⣤⣤⣠⣤⡄⠀⣤⣤⣤⣤⣤⣄⣤⣤⢠⣤⣤⠀⣤⡄⣤⣤⣤⣠⣤⡄⣤⣤⡄⣤⣤⣄⣤⢠⡤⣤⢠⡄⣤⢀⣤⣤⡀⠀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣿⠀⢸⣿⢸⣿⡆⣿⢿⡆⣿⢾⡃⣿⣿⡇⣿⣦⣿⣷⣿⠀⠀⣿⠀⣿⢸⣷⠀⠿⣮⡅⢸⡇⢸⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⡟⣿⣿⣿⣿⣿⣟⣿⣿⣟⢹⣿⠓⣿⢸⣿⣿⢸⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠸⠿⠾⠿⠶⠿⠻⠧⠿⠸⠇⠿⠻⠇⠿⠶⠿⠿⠿⠀⠀⠿⠀⠿⡾⠇⠀⠿⡼⠇⠸⠇⠸⢿⡿⠻⠿⠀⠀⠸⠿⠟⠿⠇⠿⡿⠏⠿⠿⠿⠿⠿⠿⠸⠿⠠⠿⠸⠟⠿⠸⢿⠿⠇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⡶⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⣿⣄⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠟⢀⠀⠀⠀⠀⠀⠈⠀⠀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣷⣦⣤⠓⠀⠀⠀⠈⠢⣤⡎⠁⢸⣿⣿⣿⣿⣿⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣀⠀⠀⠀⣀⣀⠀⢀⡀⠀⠀⠀⠀⢠⣠⣤⣴⣶⣤⣤⣤⣰⣴⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣀⣀⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣤⣤⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢀⣹⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣿⣿⣿⣿⣿⣿⣿⢃⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠍⠛⠿⣿⣿⣥⣬⣿⣿⣿⣿⣿⣿⣿⣿⣳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠷⠌⠀⠀⠀⠀⠨⡿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠁⠐⠈⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣫⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠑⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠟⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠲⣶⠏⠷⠔⠰⠶⠶⠿⠀⠉⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢠⣤⢠⣤⡄⣤⣤⠀⣤⣤⡀⣤⢠⡄⣤⣤⣤⣤⣄⠀⣤⣤⣤⣠⣤⡄⠀⣤⣤⣤⣤⣤⣄⣤⣤⢠⣤⣤⠀⣤⡄⣤⣤⣤⣠⣤⡄⣤⣤⡄⣤⣤⣄⣤⢠⡤⣤⢠⡄⣤⢀⣤⣤⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⢸⣿⡆⣿⢿⡆⣿⢾⡃⣿⣿⡇⣿⣦⣿⣧⣿⠀⠀⣿⠀⣿⢸⣧⠀⠿⣮⡅⢸⡇⢸⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⡟⣿⣿⣿⣿⣿⣟⣿⣿⣟⢹⣿⠓⣿⢸⣿⣿⢸⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠸⠿⠾⠿⠶⠿⠻⠧⠿⠸⠇⠿⠻⠇⠿⠶⠿⠿⠿⠀⠀⠿⠀⠿⡾⠇⠀⠿⡼⠇⠸⠇⠸⢿⠿⠻⠿⠀⠀⠸⠿⠟⠿⠇⠿⡿⠏⠿⠿⠿⠿⠿⠿⠸⠿⠀⠿⠸⠟⠿⠸⢿⠿⠇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣾⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣅⢸⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⣶⡆⠀⠀⠀⠘⠀⠀⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣅⡀⠠⠀⠀⠀⠀⠠⣀⣀⠚⠀⣿⣿⣿⣿⣿⣿⣿⡿⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⣀⣈⣉⣠⣴⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⣴⣶⣶⣶⣶⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣠⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣷⣶⣶⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠈⠉⣻⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⠇⣤⣶⣿⣿⣿⣿⣿⣿⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⠟⠿⣿⣿⣟⣋⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠉⠙⠻⢿⠿⢿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣌⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⢀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⢹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠪⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠉⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⠿⠿⢿⣿⡿⠃⠀⠀⠀⠀⠀
⠀⠖⠲⣶⠏⠷⠖⠰⠶⠶⠷⠀⠑⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠈⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣤⠀⢠⣤⢠⣤⡄⣤⣤⠀⣤⣤⡀⣤⢠⡄⣤⣤⣤⣤⣄⠀⣤⣤⣤⣠⣤⡄⠀⣤⣤⣤⣤⣤⣄⣤⣤⢠⣤⣤⠀⣤⡄⣤⣤⣤⣠⣤⡄⣤⣤⡄⣤⣤⣄⣤⢠⡤⣤⢠⡄⣤⢀⣤⣤⡀⠀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⢸⣿⡆⣿⢿⡆⣿⢾⡃⣿⣿⡇⣿⣦⣿⣿⣿⠀⠀⣿⠀⣿⢸⣷⠀⠿⣮⡅⢸⡇⢸⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⡟⣿⣿⣿⣿⣿⣟⣿⣿⣟⢹⣿⠓⣿⢸⣿⣿⢸⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠸⠿⠾⠿⠶⠿⠻⠧⠿⠸⠇⠿⠻⠇⠿⠶⠿⠿⠿⠀⠀⠿⠀⠿⡾⠇⠀⠿⡼⠇⠸⠇⠸⢿⡿⠻⠿⠀⠀⠸⠿⠟⠿⠇⠿⡿⠏⠿⠿⠿⠿⠿⠿⠸⠿⠠⠿⠸⠟⠿⠸⢿⠿⠇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⡏⢀⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⠺⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⣀⣤⠀⠀⠀⠀⠆⠀⠐⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠁⠀⡀⠀⠀⠀⠠⣀⡀⠠⠂⢹⣿⣿⣿⣿⣿⣿⣿⠟⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣷⣦⡁⠀⠀⠀⠀⠈⠛⣉⣠⣼⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⣤⣀⣀⣤⣤⣄⣀⣀⣀⡀⠀⠀⢀⣤⣶⣶⣷⣶⣶⣶⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣬⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠋⠉⠙⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⢁⣤⣴⣾⣿⣿⣿⣿⣿⣿⣍⣁⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠛⠻⠿⣿⣿⣿⡟⠋⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣷⡇
⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠉⠛⠛⠿⠿⣿⠿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠻⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠋⠉⠀⠀⠀⠀⠺⠿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠋⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠲⣶⠏⠶⠄⠰⠶⠶⠾⠀⠉⠙⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢠⣤⢠⣤⡄⣤⣤⠀⣤⣤⡀⣤⢠⡄⣤⣤⣤⣤⣄⠀⣤⣤⣤⣠⣤⡄⠀⣤⣤⣤⣤⣤⣄⣤⣤⢠⣤⣤⠀⣤⡄⣤⣤⣤⣠⣤⡄⣤⣤⡄⣤⣤⣄⣤⢠⡤⣤⢠⡄⣤⢀⣤⣤⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⢸⣿⡆⣿⢿⡆⣿⢾⡃⣿⣿⡇⣿⣦⣿⣿⣿⠀⠀⣿⠀⣿⢸⣷⠀⠿⣮⡅⢸⡇⢸⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⡟⣿⣿⣿⣿⣿⣟⣿⣿⣟⢹⣿⠓⣿⢸⣿⣿⢸⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠸⠿⠾⠿⠶⠿⠻⠧⠿⠸⠇⠿⠻⠇⠿⠶⠿⠿⠿⠀⠠⠿⠀⠿⡾⠇⠀⠿⡼⠇⠸⠇⠸⢿⡿⠻⠿⠀⠀⠸⠿⠟⠿⠇⠿⡿⠏⠿⠿⠿⠿⠿⠿⠸⠿⠠⠿⠸⠟⠿⠸⢿⠿⠇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⣿⣧⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣏⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⡀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠺⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣄⣀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⠃⠄⠀⠀⠀⠀⢀⡀⠀⠔⠈⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⣀⣀⣠⣄⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣶⣶⡈⠀⠀⠀⠀⠀⠙⢋⣀⣤⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣶⣷⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣦⣤⣥⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡟⠈⠉⢙⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⢀⣀⣀⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⡏⢠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠛⠻⢿⣿⡛⠛⠁⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠙⠛⠛⠿⠟⠻⠿⠛⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠋⠁⠀
⠀⠀⠀⠀⠀⠀⠡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠛⡻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠛⠟⠟⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠲⣶⠏⠶⠖⠰⠶⠶⠶⠀⠀⠀⠀⠉⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢠⣤⢠⣤⡄⣤⣤⠀⣤⣤⡀⣤⢠⡄⣤⣤⣤⣤⣄⠀⣤⣤⣤⣠⣤⡄⠀⣤⣤⣤⣤⣤⣄⣤⣤⢠⣤⣤⠀⣤⡄⣤⣤⣤⣠⣤⡄⣤⣤⡄⣤⣤⣄⣤⢠⡤⣤⢠⡄⣤⢀⣤⣤⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⢸⣿⡆⣿⢿⡆⣿⢾⡃⣿⣿⡇⣿⣦⣿⣷⣿⠀⠀⣿⠀⣿⢸⡧⠀⠿⣮⡅⢸⡇⢸⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⡟⣿⣿⣿⣿⣿⣟⣿⣿⣟⢹⣿⠓⣿⢸⣿⣿⢸⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠸⠿⠾⠿⠶⠿⠻⠧⠿⠸⠇⠿⠻⠇⠿⠶⠿⠿⠿⠀⠀⠿⠀⠿⡾⠇⠀⠿⡼⠇⠸⠇⠸⢿⠿⠻⠿⠀⠀⠸⠿⠟⠿⠇⠿⡿⠏⠿⠿⠿⠿⠿⠿⠸⠿⠀⠿⠸⠟⠿⠸⢿⠿⠇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⣿⣿⣿⣿⣿⣿⣦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣴⡆⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠇⠀⡀⠀⠀⠀⠠⣄⣀⡐⠁⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⣠⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⡀⠀⠀⢀⣀⣼⣿⣿⣷⣶⣆⠁⠀⠀⠀⢀⣀⣉⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣄⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣴⣶⡆
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣭⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⠃⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠈⠛⠛⢿⣯⣉⠁⢀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⣛⣻⣿⣿⡻⠿⠿⠁
⠀⠀⠀⠀⠀⠹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠈⠉⠁⡜⣹⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡩⠁⠀⠀⠋⠉⠈⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⠿⠟⠛⢿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠲⣶⠏⠶⠔⠰⠶⠶⠾⠀⠀⠀⠈⠈⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢠⣤⢠⣤⡄⣤⣤⠀⣤⣤⡀⣤⢠⡄⣤⣤⣤⣤⣄⠀⣤⣤⣤⣠⣤⡄⠀⣤⣤⣠⣤⣤⣄⣤⣤⢠⣤⣤⠀⣤⡄⣤⣤⣤⣠⣤⡄⣤⣤⡄⣤⣤⣄⣤⢠⡤⣤⢠⡄⣤⢀⣤⣤⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⢸⣿⡆⣿⢻⡆⣿⢾⡃⣿⣿⡇⣿⣦⣿⡇⣿⠀⠀⣿⠀⣿⢸⡇⠀⠿⣮⡅⢸⡇⢸⣿⣿⣿⣿⡿⠀⢸⣿⣿⣿⡟⣿⢹⣿⣿⣿⣟⣿⣿⣟⢹⣿⠃⣿⢸⣿⣿⢸⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠸⠿⠾⠿⠶⠿⠻⠧⠿⠸⠇⠿⠻⠇⠿⠶⠿⠷⠿⠀⠀⠿⠀⠿⡾⠇⠀⠿⡼⠇⠸⠇⠸⢿⠿⠻⠿⠀⠀⠸⠿⠟⠿⠇⠿⡾⠏⠿⠿⠿⠿⠿⠿⠸⠿⠀⠿⠸⠟⠿⠸⢿⠿⠇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣷⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠂⠀⠀⠀⠀⠀⠑⠲⠖⣀⣼⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣶⣦⣀⣀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣶⣶⣆⡀⢀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣶⡆
⢰⣶⣶⣤⣦⣤⣤⣄⣀⣀⣠⣤⣴⣿⣿⣿⣷⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⣄⣀⣀⣀⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠿⡿⠿⠟⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀
⠈⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠈⠙⠿⢿⣦⣶⢶⡮⠟⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠙⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠏⠷⠖⠰⠶⠶⠶⠀⠀⠀⠀⠸⠟⠿⠿⠻⠿⠿⠿⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢠⣤⢠⣤⡄⣤⣤⠀⣤⣤⡀⣤⢠⡄⣤⣤⣤⣤⣄⠀⣤⣤⣤⣠⣤⡄⠀⣤⣤⣠⣤⣤⣄⣤⣤⢠⣤⣤⠀⣤⡄⣤⣤⣤⣠⣤⡄⣤⣤⡄⣤⣤⣄⣤⢠⡤⣤⢠⡄⣤⢀⣤⣤⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⢸⣿⡆⣿⢻⡆⣿⢾⡃⣿⣿⡇⣿⣦⢿⡇⣿⠀⠀⣿⠀⣿⢸⡇⠀⠿⣮⡅⢸⡇⢸⣿⣿⣿⣿⡿⠀⢸⣿⣿⣿⡟⣿⢻⣿⣿⣿⣟⣿⣿⣟⢹⣿⠃⣿⢸⣿⣿⢸⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠸⠿⠾⠿⠶⠿⠻⠧⠿⠸⠇⠿⠻⠇⠿⠶⠿⠷⠿⠀⠀⠿⠀⠿⡾⠇⠀⠿⡼⠇⠸⠇⠸⢿⠿⠻⠿⠀⠀⠸⠿⠟⠿⠇⠿⡿⠏⠿⠿⠿⠿⠿⠿⠸⠿⠀⠿⠸⠟⠿⠸⢿⠿⠇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣷⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⠀⠀⠀⠀⠀⠀⠙⠛⣂⣠⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⣀⡀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣤⣀⣀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣠⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⢸⣿⣷⣿⣶⣶⣦⣤⣄⣠⣤⣴⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⠁⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣴⣶⣦⣀⣀⣤⣤⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣟⣟⡛⠋⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠙⠻⠿⠷⠾⠿⠖⠊⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠁⠀
⠀⠀⠀⠈⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠉⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠏⠶⠔⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠿⠏⠭⠿⠿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠉⠉⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢠⣤⢠⣤⡄⣤⣤⠀⣤⣤⡀⣤⢠⡄⣤⣤⣤⣤⣄⠀⣤⣤⣤⣠⣤⡄⠀⣤⣤⣠⣤⣤⣄⣤⣤⢠⣤⣤⠀⣤⡄⣤⣤⣤⣠⣤⡄⣤⣤⡄⣤⣤⡄⣤⢠⡤⣤⢠⡄⣤⢀⣤⣤⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⢸⣿⡆⣿⢻⡆⣿⢾⡃⣿⣿⡇⣿⣦⣿⡇⣿⠀⠀⣿⠀⣿⢸⡇⠀⠿⣮⡅⢸⡇⢸⣿⣿⣿⣿⡿⠀⢸⣿⣿⣿⡟⣿⣾⣿⣿⣿⣟⣿⣿⣟⢹⣿⠃⣿⢸⣿⣿⢸⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠸⠿⠾⠿⠶⠿⠻⠧⠿⠸⠇⠿⠻⠇⠿⠶⠿⠷⠿⠀⠀⠿⠀⠿⡾⠇⠀⠿⡼⠇⠸⠇⠸⢿⠿⠻⠿⠀⠀⠸⠿⠟⠿⠇⠿⡿⠏⠿⠿⠿⠿⠿⠿⠸⠿⠀⠿⠸⠟⠿⠸⢿⠿⠇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣾⣷⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠉⣉⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣤⣤⣤⣤⡀⠀⢀⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⣤⣀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⡀⢀⣄⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠉⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣶⣶⣶⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣶⣆⣀⡀⠀⠀⣀⣀⡀⠀⣀⣀⣀⣀⣀⣀⡀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣭⣭⣉⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠶⠀⠀⠀⠈⠛⠿⠿⠻⠟⠛⠉⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁
⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠉⠉⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠿⠏⠫⠿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⠶⠖⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⠿⠿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢠⣤⢠⣤⡄⣤⣤⠀⣤⣤⡀⣤⢠⡄⣤⣤⣤⣤⣄⠀⣤⣤⣤⣠⣤⡄⠀⣤⣤⣠⣤⣤⣄⣤⣤⢠⣤⣤⠀⣤⡄⣤⣠⣤⣠⣤⡄⣤⣤⡄⣤⣤⣄⣤⢠⡤⣤⢠⡄⣤⢀⣤⣤⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⢸⣿⡆⣿⢻⡆⣿⢾⡃⣿⣿⡇⣿⣦⢼⡇⣿⠀⠀⣿⠀⣿⢸⡇⠀⠿⣮⡅⢸⡇⢸⣿⣿⣿⣿⡿⠀⢸⣿⣿⣿⡟⣿⣿⣿⣿⣿⣟⣿⣿⣟⢹⣿⠃⣿⢸⣿⣿⢸⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠸⠿⠾⠿⠶⠿⠻⠧⠿⠸⠇⠿⠻⠇⠿⠶⠿⠷⠿⠀⠀⠿⠀⠿⡾⠇⠀⠿⡼⠇⠸⠇⠸⢿⠿⠻⠿⠀⠀⠸⠿⠟⠿⠇⠿⡿⠏⠿⠿⠿⠿⠿⠿⠸⠿⠀⠿⠸⠟⠿⠸⢿⠿⠇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣦⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠄⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣷⠀⠀⠀⠀⠀⠀⣈⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣷⣄⡀⢀⣾⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡀⣀⣀⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡃⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⣆⢀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⣀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠻⠿⣿⣭⣄⣀⣀⣈⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣷⡇
⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⠀⠀⠀⠀⠙⠻⠛⠛⠛⠋⠉⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠈⠙⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢟⠻⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⠀⠤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠈⠹⠻⢿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⠷⠶⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⡀⣶⣰⡆⣶⣶⣦⠀⢰⡆⣴⣶⣆⣶⡆⣶⢠⡶⣦⢰⣶⣶⣰⣶⠶⠀⣶⡶⢶⣶⣶⣠⣶⣶⡄⢠⣶⣶⡄⣴⢶⡄⣰⣶⡆⣶⣴⣶⣶⣶⣦⢰⣶⣆⢰⡦⢠⡶⣶⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⡇⣿⣿⣿⠀⢸⡇⣿⢯⣭⣿⣿⣿⢸⡇⣿⢸⣿⣿⣹⣿⠶⠀⣿⡷⢾⣿⠿⢻⣿⣿⡇⢈⣻⣶⣼⣿⢘⡃⣿⣹⡇⣿⣿⣿⣿⣿⣿⢸⣟⣿⢸⡿⢘⡻⣶⡐⠀⠐⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠹⠷⠿⠹⠇⠿⠿⠟⠀⠸⠇⠻⠿⠿⠿⠟⠿⠘⠷⠟⠸⠿⠿⠿⠿⠶⠀⠿⠷⠾⠿⠀⠘⠿⠿⠃⠈⠿⠾⠃⠿⠾⠣⠿⠹⠷⠿⠹⠿⠿⠿⠟⠿⠏⠿⠾⠿⠞⠷⠿⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣦⣴⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⢤⡤⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⣀⣀⣀⣀⡀⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⣠⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡍⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣶⣶⣶⣶⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠻⣶⣦⣤⣄⣀⣀⣈⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣴⣶⣦⣄⡀⢀⣀⠀⠀⠀⠀
⠘⠻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⠀⠀⠀⠀⠈⠛⠛⠛⠛⠋⠉⠉⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⡄
⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⢿⠟⠃
⠀⠀⠀⠀⠀⠈⠙⠛⠻⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠋⠁⠈⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠟⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠙⢿⣿⡛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠝⠻⠛⡄⠘⠳⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠟⠷⠶⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⡀⣶⣰⡆⣶⣶⣦⠀⢰⡆⣴⣶⣆⣶⡆⣶⢠⡶⣦⢰⣶⣶⣰⣶⠶⠀⣶⡶⢲⣶⣶⣠⣶⣶⡄⢠⣶⣶⣄⣴⢶⡄⣰⣶⡆⣶⣴⣶⣶⣶⣦⢰⣶⣆⢰⣦⢠⡶⣶⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⡇⣿⣿⣿⠀⢸⡇⣿⣯⣭⣿⣿⣿⢸⡇⣿⢸⣿⣿⣹⣿⠶⠀⣿⡷⢾⣿⠿⢻⣿⣿⡇⢈⣻⣶⣼⣿⢘⡃⣿⣹⡇⣿⣿⣿⣿⣿⣿⢸⣟⣿⢸⡿⢘⡿⣶⡐⠀⠐⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠹⠷⠿⠹⠇⠿⠿⠟⠀⠸⠇⠻⠿⠿⠿⠟⠿⠘⠷⠿⣸⣿⣿⣿⣿⠶⣀⡿⠷⠾⠿⠀⠘⠿⠿⠃⠈⠿⠾⠃⠿⠾⠣⠿⠹⠷⠿⠹⠿⠿⠿⠟⠿⠏⠿⠾⠿⠞⠿⠿⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠙⠛⣣⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⣦⣤⣤⣴⣄⠀⠀⠀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠁⠈⠉⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣠⣴⣤⣤⣤⣤⣶⣶⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣧⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣀⣠⣤⣤⣄⣀⣠⣄⣀⡀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣤⣤⣀⣀⣀⣈⣉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡦⠀⠀⠀⠈⠛⠿⠿⠻⠿⠿⠛⠙⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢟⠏⠇
⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠉⠀⠁⠀⠀⠀
⠀⠀⠈⠛⠻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣿⣿⣿⣿⣿⣿⣟⠝⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠻⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣯⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣿⣿⠉⠁⣠⣿⣿⠛⠙⢟⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠀⠀⠀⠛⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠶⠶⣶⠿⠷⠖⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⡀⣶⣰⡆⣶⣶⣦⠀⢰⡆⣴⣶⣆⣶⡆⣶⢠⡶⣦⢰⣶⣶⣰⣶⠶⠀⣶⡶⢴⣶⣶⣠⣶⣶⡄⢠⣶⣶⣄⣴⢶⡄⣰⣶⡆⣶⣴⣶⣶⣶⣦⢰⣶⣆⢰⣦⢠⡶⣶⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⡇⣿⣿⣿⠀⢸⡇⣿⣯⣭⣿⣿⣿⢸⡇⣿⢸⣿⣿⣹⣿⠶⠀⣿⡷⢾⣿⠿⢻⣿⣿⡇⢈⣻⣶⣼⣿⢘⡃⣿⣹⡇⣿⣿⣿⣿⣿⣿⢸⣟⣿⢸⡿⢘⡿⣶⡐⠀⠐⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠹⠷⠿⠹⠇⠿⠿⠟⠀⠸⠇⠻⠿⠿⠿⠟⠿⠘⠷⢿⣸⣿⣿⣿⣿⣶⣤⣿⠷⠾⠿⠀⠘⠿⠿⠃⠈⠿⠾⠃⠿⠾⠣⠿⠹⠷⠿⠹⠿⠿⠿⠟⠿⠏⠿⠾⠿⠞⠿⠿⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⣀⣀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠇⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣀⣀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣤⣴⣤⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣦⣤⣀⡀⢀⣀⣤⣤⣤⣤⣤⡄
⢀⣀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠃⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣷⣤⣤⣀⣀⣀⣀⣀⣀⣨⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣶⣧⡀⠀⠀⠀⠙⠛⠿⠿⠛⠟⠟⠋⠉⠁⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠙⠉⠀⠁
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠂⠀⠀⠀⠀⠀⠀⠀
⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣟⠻⣿⣿⣿⣿⣿⣿⣿⣿⡏⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠈⠙⠛⠻⠟⠛⢿⣿⣿⣧⣬⣿⣿⣿⡄⢸⣿⣿⣿⣹⣿⣿⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⡻⣿⣾⡉⠻⡿⠃⠀⣿⣿⠿⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡆⠀⠀⠀⠈⡿⠟⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠶⠶⣶⠿⠷⠶⠰⠶⠶⠶⠀⠀⠈⠀⠀⠀⠀⠀⠫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⡀⣶⣰⡆⣶⣶⣦⠀⢰⡆⣴⣶⣆⣶⡆⣶⢠⡶⣦⢰⣶⣶⣰⣶⠶⠀⣶⡶⢲⣶⣦⣠⣶⣶⡄⢠⣶⣶⣄⣴⢶⡄⣰⣶⡆⣶⣴⣶⣶⣶⣦⢰⣶⣆⢰⣦⢠⡶⣶⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⡇⣿⣿⣿⠀⢸⡇⣿⣯⣭⣿⣿⣿⢸⡇⣿⢸⣿⣿⣹⣿⢶⣄⣿⡷⢾⣿⠿⢻⣿⣿⡇⢈⣻⣶⣼⣿⢘⡃⣿⣹⡇⣿⣿⣿⣿⣿⣿⢸⣟⣿⢸⣿⢘⡿⣶⡐⠀⠐⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠹⠷⠿⠹⠇⠿⠿⠟⠀⠸⠇⠻⠿⠿⠿⠟⠿⠘⠷⠿⣸⣿⣿⣿⣿⣾⣿⣿⣷⣾⣿⣰⡘⠿⠿⠃⠈⠿⠾⠃⠿⠾⠣⠿⠹⠷⠿⠹⠿⠿⠿⠟⠿⠏⠿⠾⠿⠞⠿⠿⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣤⣤⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣸⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣲⣿⣿⣿⣯⣉⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢻⣶⣄⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣴⣶⣶⣿⡇
⠀⠀⢀⣤⣀⣀⣤⣤⣶⣦⣼⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠟⠋⠁⠀⠈⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡉⠁⠀⠀⠉⠙⠻⢿⠟⠛⠛⠛⠋⠁⠉⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠟⠃
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠉⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠿⠝⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣏⠙⣿⣿⣿⣿⠛⢟⣟⣛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠉⠛⠛⠙⠛⠹⣿⣿⣿⣆⣽⣿⣿⣿⡄⠈⣿⣿⠟⠀⣾⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⡧⠀⠉⠛⠁⠀⢹⡿⠀⠀⠊⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠶⠶⣶⠿⠷⠶⠴⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠺⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠿⠿⠿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⡀⣶⣰⡆⣶⣶⣦⠀⢰⡆⣴⣶⣆⣶⡆⣶⢠⡶⣦⢰⣶⣶⣰⣶⠶⡀⣶⡶⢶⣶⣶⣠⣶⣶⡄⢠⣶⣶⣄⣴⢶⡄⣰⣶⡆⣶⣴⣶⣶⣶⣦⢰⣶⣆⢰⣦⢠⡶⣶⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⡇⣿⣿⣿⠀⢸⡇⣿⣯⣭⣿⣿⣿⢸⡇⣿⢸⣿⣿⣹⣿⢾⣿⣿⡷⢾⣿⠿⢻⣿⣿⡇⢈⣻⣶⣼⣿⢘⡃⣿⣹⡇⣿⣿⣿⣿⣿⣿⢸⣟⣿⢸⣿⢘⡿⣶⡐⠀⠐⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠹⠷⠿⠹⠇⠿⠿⠟⠀⠸⠇⠻⠿⠿⠿⠟⠿⠘⠷⠿⣸⣿⣿⣿⣿⣾⣿⣿⣷⣾⣿⣾⡜⠿⠿⠃⠈⠿⠾⠃⠿⠾⠣⠿⠹⠷⠿⠹⠿⠿⠿⠟⠿⠏⠿⠾⠿⠞⠿⠿⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣩⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⡀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣃⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⠁⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣽⣿⣿⣿⣦⣤⣤⣤⣀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣤⡀⢰⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⡇
⠀⠀⠀⠀⠀⠀⡀⠀⣤⣀⣰⣾⣿⣶⣬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠋⠉⠀⠀⠀⠙⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣰⣿⣿⣶⣦⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣷⣶⣶⣶⣶⣦⣄⣀⣤⣤⣄⣀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠛⠋⠀⠀⠉⠙⠻⣿⣿⠟⠛⠛⠛⠋⠉⠉⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠃⠃
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣤⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠏⠋⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⣿⣿⣿⡍⠻⣿⣿⣿⡿⠿⢛⠹⠋⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠙⠿⠻⣿⣿⠛⢿⣿⣿⣿⣄⣿⣿⣿⣷⡀⠉⢿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⡋⠛⠻⢿⠧⠀⠘⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠶⠶⣶⠿⠷⠶⠰⠶⠶⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⡀⣶⣰⡆⣶⣶⣦⠀⢰⡆⣴⣶⣆⣶⡆⣶⢠⡶⣦⢰⣶⣶⣴⣶⢶⣶⣶⡶⢶⣶⣶⣤⣶⣶⡄⢠⣶⣶⣄⣴⢶⡄⣰⣶⡆⣶⣴⣶⣶⣶⣦⢰⣶⣆⢰⡦⢠⡶⣶⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⡇⣿⣿⣿⠀⢸⡇⣿⣯⣭⣿⣿⣿⢸⡇⣿⢸⣿⣿⣹⣿⢾⣿⣿⡷⢾⣿⠿⢻⣿⣿⡇⢈⣻⣶⣼⣿⢘⡃⣿⣹⡇⣿⣿⣿⣿⣿⣿⢸⣟⣿⢸⣿⢘⡿⣶⡐⠀⠐⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠹⠷⠿⠹⠇⠿⠿⠟⠀⠸⠇⠻⠿⠿⠿⠟⠿⠸⠷⠿⠸⢿⣿⣿⣿⣾⣿⣿⣷⣾⣿⣿⣞⠿⠿⠃⠈⠿⠿⠃⠿⠾⠣⠿⠹⠷⠿⠹⠿⠿⠿⠟⠿⠏⠿⠾⠿⠞⠿⠿⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⡤⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⣀⣠⣄⣀⣀⣀⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣯⣤⣤⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⢰⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⣤⣶⣄⣈⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠟⠋⠁⠀⠀⠛⠿⢿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢠⣶⣦⣤⡐⢷⣦⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣄⣀⡀⠀⠀⣀⡀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠁⠈⠛⠛⠿⣿⣿⣿⣿⣿⢿⠿⠿⠓⠛⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣄⡀⠀⠀⠀⠀⠀⠈⠉⠋⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠉⠉⠁
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⠻⡿⠿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⡟⢿⣿⣿⣿⡿⢿⠏⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢰⣿⣿⣿⣷⡀⠉⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠙⠋⠉⠙⢿⣿⣿⣿⣿⡿⣿⣿⣷⡀⠈⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠶⠶⣶⠿⠷⠶⠴⠶⠿⠿⠿⠻⠿⠀⠀⠈⠙⠁⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⡀⣶⣰⡆⣶⣶⣦⠀⢰⡆⣴⣶⣆⣶⡆⣶⢠⡶⣦⢰⣶⣶⣴⣶⢶⣶⣶⡶⢶⣶⣶⣦⣶⣶⡴⢢⣶⣶⣄⣴⢶⡄⣰⣶⡆⣶⣴⣶⣶⣶⣦⢰⣶⣆⢰⣦⢠⣶⣶⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⡇⣿⣿⣿⠀⢸⡇⣿⣯⣭⣿⣿⣿⢸⡇⣿⢸⣿⣿⣹⣿⢾⣿⣿⡷⢾⣿⢿⢻⣿⣿⡇⢈⣻⣶⣼⣿⢘⡃⣿⣻⡇⣿⣿⣿⣿⣿⣿⢸⣟⣿⢸⣿⢘⡿⣶⡐⠀⠐⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠹⠷⠿⠹⠇⠿⠿⠟⠀⠸⠇⠻⠿⠿⠿⠟⠿⠸⠷⠿⠸⠿⢿⣿⣿⣾⣿⣿⣷⣾⣿⣿⣿⡿⢿⣃⡘⠿⠿⠋⠿⠾⠣⠿⠹⠿⠿⠹⠯⠿⠿⠟⠾⠏⠿⠾⠿⠞⠿⠿⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣩⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣄⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⠉⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢨⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠃⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⡈⢿⣷⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠋⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣴⣶⣆⡀
⠀⠀⠀⣀⡀⠀⠀⢤⣄⢠⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡄⠀⠀⠀⢠⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣰⣿⣿⣿⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠉⠛⠛⢿⣿⣿⣿⣿⣷⣶⡶⣿⠟⠛⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠅⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠁⠀⣄⢀⣀⠀⡀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠟⠃
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡇⡘⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡺⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠿⣿⠟⡟⠙⠛⠈⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⠿⢿⠋⠂⠈⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⠿⣿⣿⣟⠀⠛⠛⠷⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠿⠿⣿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠅⠀⠸⠿⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⡀⣶⣰⡆⣶⣶⣦⠀⢰⡆⣴⣶⣆⣶⡆⣶⢠⡶⣦⢰⣶⣶⣴⣶⢶⣶⣶⡶⢶⣶⣶⣶⣶⣶⣴⢦⣶⣶⣄⣴⢶⡄⣰⣶⡆⣶⣴⣶⣶⣶⣦⢰⣶⣆⢰⣦⢠⣶⣶⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⡇⣿⣿⣿⠀⢸⡇⣿⣯⣭⣿⣿⣿⢸⡇⣿⢸⣿⣿⣹⣿⢾⣿⣿⡷⢾⣿⢿⢻⣿⣿⡿⣏⣻⣶⣼⣿⢘⡃⣿⣻⡇⣿⣿⣿⣿⣿⣿⢸⣟⣿⢸⣿⢘⡿⣶⡐⠀⠐⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠹⠷⠿⠹⠇⠿⠿⠟⠀⠸⠇⠻⠿⠿⠿⠟⠿⠸⠷⠿⠸⠿⠿⣿⣿⣾⣿⣿⣷⣾⣿⣿⣿⡿⢿⣻⣞⠿⠿⠋⠿⠾⠣⠿⠹⠿⠿⠹⠿⠿⠿⠟⠿⠏⠿⠾⠿⠞⠿⠿⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⢚⣡⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⠀⢶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠏⠁⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣶⣄⣀⡀⣀⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣤⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣋⡛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠉⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣠⣴⡆⠀
⠀⠀⠀⠀⢀⣄⣀⠀⠰⣦⣀⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣷⣦⣤⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡀⠀⣰⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠈⠉⠙⢿⣿⣿⣿⣿⣦⠂⠀⠴⠞⡦⠰⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠋⠁⠀⡀⢀⣄⣤⠀⠀⠀⢀⣠⣰⣿⣿⣿⣿⣿⣿⢿⡿⠿⣿⣿⣿⣿⣿⡿⣿⣿⡿⠟⠙⠋⠛⠍⠁
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⠿⠋⠝⠁⠨⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢸⣿⣿⣷⣴⣶⣷⣿⣿⣿⣿⣿⣿⣿⣧⢹⠀⠀⠈⠙⠈⠉⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⢿⣿⣾⠛⠛⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠸⠿⠿⣿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠈⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⡀⣶⣰⡆⣶⣶⣦⠀⢰⡆⣴⣶⣆⣶⡆⣶⢠⡶⣦⢰⣶⣶⣴⣶⢶⣶⣶⡶⢶⣶⣶⣶⣶⣶⣶⣦⣶⣶⣄⣴⢶⡄⣰⣶⡆⣶⣴⣖⣶⣶⣦⢰⣶⣆⢰⣦⢠⣶⣶⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⡇⣿⣿⣿⠀⢸⡇⣿⣯⣭⣿⣿⣿⢸⡇⣿⢸⣿⣿⣹⣿⢾⣿⣿⡷⢾⣿⢿⢻⣿⣿⣿⣏⣻⣶⣼⣿⢘⡃⣿⣻⡇⣿⣿⣿⣿⣿⣿⢸⣟⣿⢸⣿⢘⡿⣶⡐⠀⠐⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠹⠷⠿⠹⠇⠿⠿⠟⠀⠸⠇⠻⠿⠿⠿⠟⠿⠸⠷⠿⠸⠿⢿⣿⣿⣾⣿⣿⣷⣾⣿⣿⣿⣿⣿⣻⣟⠿⠿⠋⠿⠾⠣⠿⠹⠿⠿⠹⠿⠿⠿⠟⠿⠏⠿⠾⠿⠞⠿⠿⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠶⠶⣂⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠈⠀⠉⠉⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣤⣼⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣫⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡤⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣠⣾⣶⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠿⣿⣿⣿⣿⣷⣤⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣄⡄
⢀⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⠋⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⠤⠄⠠⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠤⠲⣸⣶⡄⣠⠀⠀⠀⠀⣠⣴⣶⣿⡿⠉⠋⠙⠋⠛⡻⠟⠿⠻⠿⠛⠿⠛⠉⠻⠋⠉⠋⠃
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⣿⣿⡿⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠳⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⡿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠸⠿⠿⣿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠉⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⡀⣶⣰⡆⣶⣶⣦⠀⢰⡆⣴⣶⣆⣶⡆⣶⢠⡶⣦⢰⣶⣶⣴⣶⢶⣶⣶⡶⢶⣶⣶⣶⣶⣶⣶⣦⣶⣶⣄⣴⢶⡄⣰⣶⡆⣶⣴⣶⣶⣶⣦⢰⣶⣆⢰⡦⢠⣶⣶⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⡇⣿⣿⣿⠀⢸⡇⣿⣯⣭⣿⣿⣿⢸⡇⣿⢸⣿⣿⣹⣿⢾⣿⣿⡷⢾⣿⢿⢻⣿⣿⣿⣏⣻⣶⣼⣿⢘⡃⣿⣻⡇⣿⣿⣗⣿⣿⣿⢸⣿⣿⢸⣿⢘⡿⣶⡐⠀⠐⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠹⠷⠿⠹⠇⠿⠿⠟⠀⠸⠇⠻⠿⠿⠿⠟⠿⠸⠷⠿⠸⢿⣿⣿⣿⣾⣿⣿⣷⣾⣿⣿⣿⣿⣿⣻⣟⠿⠿⠋⠿⠾⠣⠿⠹⠿⠿⠹⠿⠿⠿⠟⠿⠏⠿⠾⠿⠞⠿⠿⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣤⣶⣦⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠉⠉⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⣴⣦⣌⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⠟⠿⠟⠙⠣⣄⣽⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠻⢿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⠀⠀⠀⠀⠀
⢠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣿⣿⣧⠄⠀⣠⠖⠄⠀⠄⠀⢀⡀⣽⣍⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⠟⠻⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠁⠀⠀⠉⠡⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡿⠿⢿⠿⣿⣿⢿⡿⣿⢿⡟⠿⡏⠀⠀⠀
⠸⠿⠿⣿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠏⠀⠈⠉⠃⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠯⠍⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⡀⣶⣰⡆⣶⣶⣦⠀⢰⡆⣴⣶⣆⣶⡆⣶⢠⡶⣦⢰⣶⣶⣶⣶⢶⣶⣶⡶⢶⣶⣶⣶⣶⣶⣶⣦⣶⣶⣄⣴⢶⡄⣰⣶⡆⣶⣴⡶⣶⣶⣦⢰⣶⣆⢰⡦⢠⣶⣶⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⡇⣿⣿⣿⠀⢸⡇⣿⣯⣭⣿⣿⣿⢸⡇⣿⢸⣿⣿⣽⣿⢾⣿⣿⡷⢾⣿⢿⢻⣿⣿⣿⣏⣻⣶⣼⣿⢘⡃⣿⣻⡇⣿⣿⡿⣿⣿⣿⢸⣿⣿⢸⣿⢘⡿⣶⡐⠀⠐⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠹⠷⠿⠹⠇⠿⠿⠟⠀⠸⠇⠻⠿⠿⠿⠟⠿⠸⠷⠿⠸⢿⣿⣿⣿⣾⣿⣿⣷⣾⣿⣿⣿⡿⣿⣻⣟⠿⠿⠋⠿⠾⠣⠿⠹⠿⠿⠹⠿⠿⠿⠿⠿⠏⠿⠾⠿⠞⠿⠿⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠙⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠻⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣌⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠏⠀⠀⠀⠀⠀⠀⠋⠉⠙⣿⡏⠛⠉⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⣠⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣾⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣤⣶⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣷⣆⠀⢀⣀⣠⣀⠀⠀⠀⠠⣰⡖⡩⣽⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢿⣿⡿⠿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠁⠀⠀⠀⠹⣿⣿⣿⣤⣿⣾⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀
⠸⠿⠿⣿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠃⠀⠀⠉⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠭⠨⠿⠭⠷⠾⠿⠟⠿⠿⠿⠿⠿⠿⠭⠏⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⡀⣶⣰⡆⣶⣶⣦⠀⢴⡆⣴⣶⣆⣶⡆⣶⢠⡶⣦⢰⣶⣶⣶⣶⢶⣶⣶⡶⢶⣶⣶⣦⣶⣶⣶⣶⣶⣶⣄⣶⢶⡄⣰⣶⡆⣶⣴⣶⣶⣶⣦⢰⣶⣆⢰⣦⢠⣶⣶⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⡇⣿⣿⣿⠀⢸⡇⣿⣯⣯⣿⣿⣿⢸⡇⣿⢸⣿⣿⣽⣿⢾⣿⣿⡷⢾⣿⠿⢻⣿⣿⡿⣟⣻⣷⣼⣿⢘⡃⣿⣻⡇⣿⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⢘⣿⣶⡔⠀⠐⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠹⠷⠿⠻⠇⠿⠿⠟⠀⠼⠇⠻⠿⠿⠿⠟⠿⠸⠷⢿⣸⣿⣿⣿⣿⣾⣿⡿⠷⠾⠿⣸⡘⠿⠿⢣⡟⠿⠿⠋⠿⠾⠧⠿⠹⠿⠿⠹⠿⠿⠿⠿⠿⠏⠿⠾⠿⠞⠿⠿⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠛⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣥⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠰⠿⢿⣿⣿⣿⠟⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣽⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⡄⠀⠀⣀⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⣴⣶⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣠⣤⣄⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⢿⣿⣿⣿⢯⣿⡋⣷⠂⠀⠀⠀⠀⠈⠙⠛⠛⠛⠟⠳⠢⠤⣴⣶⣤⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⠀⠀⠀⠀
⠸⠿⠿⣿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠇⠀⠉⠙⠋⠈⠈⠙⠿⠀⠊⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠥⠤⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⡀⣶⣰⡆⣶⣶⣦⠀⣴⡆⣴⣶⣆⣶⡆⣶⢠⡶⣦⢰⣶⣶⣶⣶⢶⡶⣶⡶⢶⣶⣶⣤⣶⣶⡄⢠⣶⣶⣄⣶⢶⡄⣰⣶⡆⣶⣴⣶⣶⣶⣦⢰⣶⣆⢰⣶⢠⣶⣶⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇⣿⣿⡇⣿⣿⣿⠀⣿⡇⣿⣿⣯⣿⣿⣿⢸⡇⣿⢸⣿⣿⣽⣿⠶⡇⣿⡷⢾⣿⠿⢻⣿⣿⡇⢈⣻⣶⣼⣿⢘⡃⣿⣿⡇⣿⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⢘⣿⣶⡔⠆⠚⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠹⠷⠿⠻⠧⠿⠿⠟⠀⠿⢇⡿⢿⣿⣿⣿⣿⣼⣷⣿⣸⣿⣿⣿⠿⠾⡀⠿⠷⠾⠿⠀⠘⠿⠿⠃⠘⠿⠿⠋⠿⠾⠧⠿⠻⠿⠿⠹⠿⠿⠿⠿⠿⠏⠿⠾⠿⠞⠿⠿⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⣠⠤⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠯⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⡿⠋⠁⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⠟⠋⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠻⠛⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣧⠁⠀⠀⠀⣀⣠⣼⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣵⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣷⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣶⣾⣷⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠙⢿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠀⣀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠈⠛⠿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⡀⠀⠀⠀
⠸⠿⠿⣿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠷⠀⠀⠉⠻⠈⠈⠹⠿⠿⠛⠛⠛⠻⠟⠀⠀⠀⠀⠀⠀⠈⠁⠁⠋⠁⠀⠀⠀⠀⠠⠤⠤⠶⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠦⠤⠄
⢰⣶⣶⣶⣶⠆⠀⠀⠀⠀⠀⠀⣶⣶⡀⣶⣰⣶⣶⣶⣦⣶⣶⡖⣶⣶⣶⣶⣖⣶⣲⡶⣶⢲⣶⣶⣴⣶⠶⡂⣶⡶⢶⣶⣶⣤⣶⣶⡄⢠⣶⣶⣄⣴⢶⡄⣰⣶⡆⣶⣴⣶⣶⣶⣦⢰⣶⣆⢰⣶⢠⣶⣶⡄⠀⠀⠀⡆
⢸⣿⣿⠟⠁⠀⠀⢀⠄⢀⣀⢀⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⢸⡇⣿⢾⣿⣿⣿⣿⠶⡅⣿⡷⢾⣿⠿⢻⣿⣿⡇⢈⣻⣷⣼⣿⢘⣋⣿⣿⣇⣿⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⢘⣿⣶⡔⠗⠛⠇⠀
⢸⡿⠋⠀⠀⠀⠀⠀⠀⢻⣿⡸⠿⠹⠷⣿⣻⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣸⡷⣿⣸⢿⡿⠿⠿⠿⣁⠿⠷⠾⠿⠀⠘⠿⠿⠃⠘⠿⠿⠋⠿⠾⠧⠿⠻⠿⠿⠹⠿⠿⠿⠿⠿⠏⠿⠾⠿⠞⠿⠿⠃⠀⠀⠀⠀
⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣶⣶⣦⣄⣀⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇
⠀⠀⠀⠀⣈⣲⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⡟⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢀⣠⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠁⠋⠓⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠖⠻⠻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠟⠁⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⡁
⠀⠀⠀⠀⣴⣿⣿⣿⣿⡿⠃⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⣿⣿⣿⣿⣿⣿⠀
⠀⠀⢀⡀⣿⣿⣿⣿⣟⣧⣤⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢼⣿⣿⣿⣿⠿⠁⠀⠀
⢀⣴⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠁⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣷⣶⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣀⣄⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣀⠀⠀
⠸⠿⠿⣿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠉⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠆
⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣾⣿⣶⣶⣶⣶⣴⣶⣶⣶⣶⣿⣶⡆⣶⣶⣦⣶⣆⣶⢠⣶⣶⢰⣶⣶⣴⣶⠶⠀⣶⡶⢶⣶⣶⣤⣶⣶⡌⢠⣶⣶⣄⣶⢶⣄⣴⣶⡆⣶⣴⣶⣶⣶⣦⢰⣶⣆⢰⣶⢠⣶⣶⡌⠉⢹⣝⣾
⢸⣿⣿⠟⠁⠈⢹⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡇⣿⣿⣿⣿⣿⣿⢿⣿⣿⢾⣿⣿⣿⣿⠶⠀⣿⡷⢾⣿⠿⢻⣿⣿⡇⢈⣻⣷⣼⣿⢘⣋⣿⣿⣇⣿⣿⣿⣿⣿⣿⢸⣿⣿⢹⣿⢚⣿⣿⡕⠗⠿⠯⣿
⢸⡿⠋⡰⠀⠀⣺⣿⣿⣿⣿⣿⣿⣹⣿⣿⣻⣿⣿⠿⣿⣾⡿⠇⠿⠿⠿⠿⠿⠿⠸⠿⠿⠸⠿⠿⠿⠿⠿⠀⠿⠿⠾⠿⠀⠘⠿⠿⠃⠘⠿⠿⠋⠿⠾⠯⠿⠿⠿⠿⠹⠿⠿⠿⠿⠿⠏⠿⠿⠿⠞⠿⠿⠃⠀⠀⢐⣿
⠘⠁⠐⠐⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽
⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢨⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣟⠽⠛⠛⠿⣿⣿⠛⣻
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀⠀⠀⠀⢸
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⢨
⠸⠿⠿⣿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣴⣶⣴⣶⣶⣶⣦⠀⣶⡆⣴⣶⣦⣶⣆⣶⢠⣶⣦⢰⣶⣶⣴⣶⠶⠀⣶⡶⢶⣶⣶⣤⣶⣶⡌⢡⣶⣶⣄⣶⢶⣌⣴⣶⡆⣶⣴⣶⣶⣶⣦⢱⣶⣆⢰⣶⢠⣶⣶⡌⠉⠉⠁⠈
⢸⣿⣿⠟⢩⣿⣿⣿⣿⣿⣿⣏⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⣿⡇⣿⣿⣿⣿⣿⣿⢸⣿⣿⢾⣿⣿⣿⣿⠶⠀⣿⡷⢾⣿⠿⢻⣿⣿⡇⢈⣿⣷⣼⣿⢘⣋⣿⣿⣇⣿⣿⣿⣿⣿⣿⣸⣿⣿⢻⣿⢚⣿⣿⡕⠗⠛⠇⠈
⢸⡿⠃⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣹⠿⠿⡻⠿⠿⠿⠟⠀⠿⠇⠿⠿⠿⠿⠿⠿⠸⠿⠿⠸⠿⠿⠿⠿⠷⠀⠿⠷⠾⠿⠀⠘⠿⠿⠃⠘⠿⠿⠋⠿⠾⠿⠿⠿⠿⠿⠹⠿⠿⠿⠿⠿⠏⠿⠿⠿⠞⠿⠿⠃⠀⠀⠀⠀
⠘⠁⠜⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣶⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢘⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣼⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⣾⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⠛⡛⠛⢿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡇⠀⣠⠀⠀⠈⢩
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢸
⠸⠿⠿⣿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠤⢼

                    ䷩ 𝚕𝚒𝚗𝚎 1124

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/04/05/irc-log-040422/#comments
    Gemini version at gemini://gemini.techrights.org/2022/04/05/irc-log-040422/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 04.05.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ IRC_Proceedings:_Monday,_April_04,_2022⠀✐


Posted in IRC_Logs at 2:30 am by Needs Sunlight


Also available via the Gemini protocol at:


    * gemini://gemini.techrights.org/irc-gmi/irc-log-techrights-040422.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-040422.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-social-040422.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-techbytes-040422.gmi
Over HTTP:


                                      🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇H                                     🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇HTML5_logs⦈_


                                         #techrights_log_as_HTML5                                                                                  #boycottnovell_log_as_HTML5


                                      🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇H                                     🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇HTML5_logs⦈_


                                    #boycottnovell-social_log_as_HTML5                                                                               #techbytes_log_as_HTML5


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


                                          #techrights_log_as_text                                                                                   #boycottnovell_log_as_text


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


                                     #boycottnovell-social_log_as_text                                                                                #techbytes_log_as_text


                          Enter_the_IRC_channels_now


===============================================================================
§ IPFS Mirrors⠀➾


CID                                              Description     Object type


                                                 IRC log for
 QmY7m9ygVXBaTHYUgD68DWsoJQE2F5KBPW7SZ3S8fxyCPQ #boycottnovell  🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell
 QmYdwh4AurjRkbqTioTbpuF8CheRQGxb3YS2YrjgvTPZ9a (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
                                                 #boycottnovell-
 QmWuFGNzcg4T2JY8aS4E6wpRr46n6WdYxcAHA7kfDHbnxY social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell-
 QmfWZmr1BSJsZTWJ1oZu68Rxx1Gf69ZFL7qXL3ZhpwojLk social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 (full IRC log
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
 QmVUzBtivwrAobAt8FU71kSCJiJUV3EBC8MBq7dX9tdJxa #techbytes      🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #techbytes
 QmVNYevueLemdnSfHPMBvVYmFqeCrd6xheHa3nKw5PsDKn (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
 QmRGmCNqgXUWQ99wPqenPmCC7mcHUgHRJrKokPVSuER5KF #techrights     🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #techrights
 QmNZbbmJRGsYY4UeKj3ASAuFepcA6CxE1nybgGXk1VaSxJ (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇IPFS logo⦈


§ Bulletin for Yesterday⠀➾


Local_copy | CID (IPFS): QmPA9baiheMyYvoirRpVxfonAnbATaW9SCDexu9yzCdwpR



                    ䷩ 𝚕𝚒𝚗𝚎 1251

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/04/05/kde-neon-feels-great/#comments
    Gemini version at gemini://gemini.techrights.org/2022/04/05/kde-neon-feels-great/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 04.05.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ KDE_Neon_Added_to_the_Workspace_(or_‘Battle_Station’)⠀✐


Posted in GNU/Linux, KDE at 11:45 am by Dr. Roy Schestowitz


Video_download_link | md5sum 565a24e5141619e4c34e05504d36a29b
My New Workspace
Creative Commons Attribution-No Derivative Works 4.0


http://techrights.org/videos/nine-screen-setup.webm


Summary: A quick tour through the current setup and how tasks are split/spread
across different machines


TEN days ago I abandoned my previous_workspace as I needed more space and
access to a door (in case it gets too hot in summer). The video above explains
the way I use 6 machines in tandem and 9 screens in total, as some people have
asked how I manage them or utilise the equipment’s potential. There’s no
energy-hungry GPU and screens switch off while idle (or when I’m away), so
energy consumption isn’t as bad as it may seem.


In a later video I wish to show some of the very nice features of KDE_Neon”>KDE
Neon, which is what I installed on the new machine. It was needed due_to_SSD
problems. █



                    ䷩ 𝚕𝚒𝚗𝚎 1296

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/04/05/lf-hiding/#comments
    Gemini version at gemini://gemini.techrights.org/2022/04/05/lf-hiding/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 04.05.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Linux_Foundation_Starts_Hiding_What_Software_It_Uses_to_Make_Reports_(But
Readers_Can_Guess)⠀✐


Posted in Deception, GNU/Linux at 3:43 pm by Dr. Roy Schestowitz


Hours ago:


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


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


                        🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇LF_report⦈_
 The so-called ‘Linux’ Foundation (LF) went out of its way — yet again! (e.g.
forgery) — to hide its use of proprietary software for an “Open Source” report.
 Judging by the format, it’s the same as the last time/s. But people pointing
              out the hypocrisy is irksome to the LF’s spinners.


Summary: It would be nice to think that the Linux_Foundation quit using
proprietary_software_for_its_reports_on_"Open_Source"; but if that happened, it
would not hide the metadata (as shown above)


⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿
⣿⢹⣿⡇⣧⣻⣀⣥⣘⣇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣋⣰⣖⣲⣪⣒⣒⣒⣒⣚⣰⣘⣒⣚⣳⣀⣸⣿
⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠿⣿⠿⣿⣿⡿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠃⠆⢻⠀⣿⣿⡇⣏⣐⢸⣿⣿⢨⡌⠛⢑⣈⣧⢠⣧⢠⡝⢑⣈⡏⢨⣼⣿⡌⢇⠙⢸⠁⡇⢠⡇⢨⡌⣿⣿⠉⣦⢹⠁⣥⢹⠉⣂⣹⠈⡅⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣾⣿⣾⣶⣿⣿⣷⣷⣶⣾⣿⣿⣶⣶⣿⣶⣶⣿⣶⣾⣶⣾⣶⣶⣷⣾⣿⣿⣷⣾⣶⣿⣶⣿⣶⣷⣾⣷⣿⣿⣷⣶⣾⣀⣶⣾⣷⣶⣾⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠄⠒⡇⠶⢈⡇⠿⢸⡇⣶⡇⠶⢾⠀⠤⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⣀⠀⣀⡀⠀⡄⣠⢀⣀⡀⣠⣤⣀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⣁⣤⣥⢠⣌⣩⣩⢠⣬⢡⣍⣍⣭⡅⢌⡅⡁⢀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣿⣿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣥⣤⣤⣭⣭⣭⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣴⣶⡆⡟⣿⣟⢻⡟⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⡀⢀⡀⢀⡀⣀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣼⣹⡄⢸⠚⢸⡟⢸⡇⢻⠃⣿⢰⡞⠃⣸⢀⡯⣷⠀⡇⠀⠀⣧⢸⡟⣷⢘⡟⢠⡮⠷⠀⡇⢸⠀⡇⢰⠓⣷⢰⠯⠦⢸⡞⣷⢰⡞⠃⣶⠽⠆⠀⢀⡯⣷⠀⡗⢳⢠⡞⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠁⠀⠉⠈⠀⠈⠉⠈⠁⠉⠀⠉⠀⠉⠁⠉⠈⠉⠉⠈⠁⠀⠀⠉⠈⠁⠉⠀⠉⠁⠉⠉⠀⠁⠈⠀⠁⠨⠭⠏⠈⠉⠉⠈⠁⠉⠈⠉⠁⠈⠉⠁⠀⠈⠉⠉⠈⠁⠈⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣤⢤⡄⠀⣀⠀⢠⡄⠀⣀⠀⠀⠀⠤⠀⠀⡀⠀⠀⢀⡤⢤⡀⠀⢀⠀⠀⣀⠀⠀⢀⠀⠀⠀⡤⠤⠀⢀⡀⠀⠀⠀⠀⠀⢀⠀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣀⡿⢨⣚⣷⢸⣏⢨⣟⣷⠀⠀⣿⢸⡏⢹⠀⠀⢸⣄⣸⠇⣿⣉⡇⢾⣛⡃⣿⠉⡇⠀⠀⣙⣳⠄⣏⣹⠇⣿⣸⡇⣿⠉⢾⣉⡁⣟⣛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣛⠛⠛⢻⠀⠀⠀⣄⡄⢀⠠⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣤⡄⣼⠀⠁⠀⠁⠁⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣴⣶⠀⢀⡀⣀⢀⣄⡀⣚⡂⣰⣖⢐⡃⠀⣀⣀⢐⡃⢀⣀⣀⠀⣶⠀⠀⢰⡆⢀⣀⣀⡀⢀⣄⡀⢀⣀⡀⢰⡆⢰⡆⢘⡃⢀⣀⣀⡀⣀⣀⠀⢀⣀⣀⠀⢀⣀⡀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢰⣯⣼⣇⢸⡟⠉⢸⣏⠁⣿⡇⢹⡏⢸⡇⢸⡏⢉⢸⡇⢠⡷⣿⡇⣿⠀⠀⢸⡇⢸⡏⢹⡇⢸⡏⠁⣿⠷⠿⢸⡇⢸⡇⢸⡇⢻⠤⠟⢰⣿⠾⠇⢸⡏⢹⡇⣾⡉⠁⢾⡷⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 1423

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/04/05/libreplanet-keynote/#comments
    Gemini version at gemini://gemini.techrights.org/2022/04/05/libreplanet-keynote/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 04.05.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Marleen_Stikker,_Author_of_‘The_Internet_is_Broken’,_on_Research_Institute
Waag⠀✐


Posted in Free/Libre_Software at 11:05 am by Dr. Roy Schestowitz


Video_download_link


https://media.libreplanet.org/mgoblin_media/media_entries/2611/jupiter-
saturday-1215.webm


Summary: This keynote talk was uploaded a_week_ago. “Marleen is founder of
Waag, a social organization and research institute for creative technologies
and social innovation. The prolific advocate for free, honest, and inclusive
technology, and honorary PhD, is also founder of The Digital City (1993), a
group that provides free public access to the Internet in Amsterdam, and author
of the book “Het Internet is Stuk” (The Internet is Broken).”


Licence: CC_BY_SA_4.0



                    ䷩ 𝚕𝚒𝚗𝚎 1462

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/04/05/not-so-linux-foundation/#comments
    Gemini version at gemini://gemini.techrights.org/2022/04/05/not-so-linux-foundation/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 04.05.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Linux_Foundation_Should_Remove_Linux_From_Its_Name⠀✐


Posted in Deception, GNU/Linux, Kernel at 4:19 am by Dr. Roy Schestowitz


Video_download_link | md5sum f7acb3508ec52fa3019a3babba0acc44
LF has Abandoned Linux
Creative Commons Attribution-No Derivative Works 4.0


http://techrights.org/videos/linux-abandoned-by-lf.webm


Summary: Linus Torvalds seems to have gotten himself entrapped inside an
organisation (“Linux Foundation”; Linux only in name) that harms Linux and even
harms Git, the other famous project or Mr. Torvalds; in order to qualify for a
job at the “Linux Foundation” you need to neither know nor use Linux — an
absurd situation; Mr. Torvalds should_take_his_trademark_and_walk_away because
it keeps getting worse and his_employer_gets_more_secretive/shady


THE forces of proprietary software, or people who disagree with Software
Freedom and even “Open Source” (they just want openwashing slants for PR gain),
are making progress. They’ve infiltrated sites, institutions, events and so on.
We’ve provided very extensive evidence of this; there’s an ample body of
evidence, so let’s not get bogged down by that.


“This is a very profound issue and the damage extends way beyond the Linux
Foundation itself, as the above video explains.”So yesterday we saw an
announcement of interest. There’s a new “social control media” shill for
“content”. It seems to be one of those SEO types, who mistake JavaScript
frameworks for “the Web”. There was a similar post in the Linux_Foundation‘s
site last night (European time), which also included an image. The image may or
may not be the person in question (maybe decades-old photo; but more likely
stock photography). We_mentioned_it_at_the_time.


Is this the future of “Linux”? Some “content farming”? Microsoft GitHub?


What we’re generally seeing is that the Linux Foundation is departing from
Linux; it’s arguably trying to hurt Linux and its spokespeople come from
Microsoft. New hires have no experience with (or basic understanding of) Linux.
Those who do understand and promote GNU/Linux get ousted and fired. This is a
very profound issue and the damage extends way beyond the Linux Foundation
itself, as the above video explains.


I cover a number of other points in the video. For instance, Linux.com is
barely read by anybody (nothing of interest anymore) and it gives people a
rather poor impression of “Linux”. There’s no Varnish cache or CDN like
Clownflare to blame for the appallingly low (very poor) number of page views.
It’s like they’ve lost more than 95% of the traffic! █



                    ䷩ 𝚕𝚒𝚗𝚎 1533

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(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/04/05/swpats-fake-growth/#comments
    Gemini version at gemini://gemini.techrights.org/2022/04/05/swpats-fake-growth/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 04.05.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ The_EPO_is_Granting_Loads_of_Software_Patents_in_Order_to_Fake_‘Growth’⠀✐


Posted in Europe, Patents at 10:28 am by Dr. Roy Schestowitz


Video_download_link | md5sum f931ca2049b8412eab44b12a7fc3534f
The EPO Deception
Creative Commons Attribution-No Derivative Works 4.0


http://techrights.org/videos/epo-deceptive-numbers.webm


Summary: ‘Growth’ at the EPO is pretty much faked; the management crafted (e.g.
by legal_fudge) paperwork, conditions and unlawful guidelines by which to
routinely_crush_the_European_Patent_Convention_(EPC), calling software patents
“Hey Hi” (AI) or “MedTech” and all sorts of other novelty-sounding buzzwords


THE EPO‘s regime, a corrupt collective led by Benoît_Battistelli and his
friends (including António_Campinos, his friend who brought many of his own
friends from Alicante), is little but a propaganda operation at this stage. As
shown in the video above, perhaps most of the EPO’s patents are nowadays
European_software_patents. They’re faking ‘growth’ by granting lots of invalid
patents that don’t comply with the EPC.


“They’re faking ‘growth’ by granting lots of invalid patents that don’t comply
with the EPC.”To make matters worse, if one looks at this_year’s_‘news’_section
(lies section) (warning: epo.org link) of the EPO’s Web site, it is based not
on reality but on fiction. This latest_post (warning: epo.org link), dated
today, is entitled “[p]atent applications in Europe reach record level in 2021″
and it comes shortly after EPO staff shared figures showing a massive collapse
in the number of EPO grants, owing of course to industrial actions. The
collapse in patent quality is driving fake ‘demand’ and the EPO has just openly
admitted that about 80% of applications come from megacorporations, few of
which are actually European. So who or what is the EPO actually for? Whose
agenda is being advanced now that EPO management breaks laws, violates
constitutions, and trashes the EPC? The whole point of the EPC was to prevent
the agenda being warped so badly and granting authority being subjected to
perverse distortion/misinterpretation. As noted in yesterday’s comment (the
last one on the sole coverage of EPO strikes this past month, except our
coverage) :


     Assessment of « quality « which relies on revocation or nullification
     decisions seems logical when taking a legal approach. But it can only
     be based on a very small percentage of granted patents and takes
     place years, sometimes many years after the grant. In addition, the
     context in terms of the resources devoted by the parties and
     thoroughness of the review by the BOA or the court is quite different
     from the context of examination proceedings. This is why I do not
     think such an assessment can yield meaningful conclusions.
     I agree with your concern regarding the difference between T 1989/18
     and T 1024/18 over the requirement to adapt the description to the
     claim as granted. This is important practically speaking for
     applicants since it affects a great deal of applications. My personal
     view is that the adaptation is useless but entails additional costs
     and delays and opens up potential 123(2) issues.
     Another recent decision, T 0550/14 relating to a business method
     (Managing funding of catastrophe relief efforts), while it suggests
     an interesting approach to the assessment of what is « non-technical
     », does not seem to comply with the approach of the case law of the
     BOAs (2019, 1.4.1) which rejects the approach of the contribution to
     the prior art, and is at loggerheads with T 2101/12 (Vasco) over the
     definition of the skilled person and of the closest prior art. T
     2101/12 was issued by BOA 3.5.06, not by BOA 3.5.01 which has issued
     T 0550/14.


Ask the EPO’s own staff about patent quality. They know very well what’s going
on as examiners see it firsthand. Some of them are constantly bullied into
granting software patents against their well.


“The media is bribed and blackmailed to pretend all is well in EPOnia”See the
above for more information. There’s a_bunch_of_very_decent_comments_in_there
and the latest one, shown in the video, says the above (it’s the last comment
that can be posted due to time-limited posting periods).


We probably won’t be hearing about the EPO’s strike anymore. The media is
bribed and blackmailed to pretend all is well in EPOnia. The strike was_never_a
secret. █



                    ䷩ 𝚕𝚒𝚗𝚎 1634

╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 04.05.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_05/04/2022:_Antitrust_Day⠀✐


Posted in News_Roundup at 8:13 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Distributions
          o Devices/Embedded
    * Free_Software/Open_Source
    * Leftovers
    * § GNU/Linux⠀➾


          o § Applications⠀➾


                # ⚓ Lagrange_v1.12:_Export/Import,_Bottom_Bars,_Visual
                  Evolution⠀⇛


                       March was full steam ahead for Lagrange, and I
                       ended up addressing a bunch of long-standing
                       issues. The original idea of making page layout
                       more flexible didn’t really get worked on yet,
                       apart from one new style option. However, many of
                       the UI widgets underwent visual evolution.


                # ⚓ Announcing_Crabmail⠀⇛


                       I am happy to announce the first release of a
                       project I’ve been working on for a while, Crabmail.


                # ⚓ Top_6_apps_to_read_and_organize_comic_books_on_Linux⠀⇛


                       
                       Comic books have been an important part of popular
                       culture and media for many decades now. Be it the
                       depiction of web-slinging, superhuman strength, or
                       just someone doing extreme things simply through
                       their willpower, comic books have been an outlet of
                       beautiful human creativity and will continue to be
                       so.


                       With the digitization of everything else, comic
                       books have to become available to users in digital
                       formats. All you need is an application that can
                       read the format of the comic book, and you can
                       start your adventure.


          o § Instructionals/Technical⠀➾


                # ⚓ Ruben Schade ☛ Track_skipping_from_ripped_CDs⠀⇛


                       The title of this post sounds like someone from the
                       1990s observing VCR distortion, or a 1970s
                       audiophile worried about tape tension on their
                       reel-to-reel machine. How does a track skip? What’s
                       ripping a CD? How does doing the latter cause the
                       former?


                       There are people using streaming services today
                       who’ve never bought music, or ripped a CD, or
                       browsed an HVM, Tower Records, or Sembawang Music.
                       I’ve spilled enough electronic ink worrying about
                       why that’s a bad thing for artists, so in this case
                       I merely bring it up as a generational observation.
                       Ripping CDs must seem as foreign as faxing a
                       document, tuning in at a specific time on the TV,
                       or having digital privacy.


                       Wait, ouch.


                # ⚓ BSDly ☛ Spammers_in_the_Public_Cloud,_Protected_by_SPF;
                  Intensified_Password_Groping_Still_Ongoing;_Spamware_Hawked
                  to_Spamtraps⠀⇛


                       This past week was truly one for the blooper reel.
                       A public cloud service provider let the great
                       unwashed into the address ranges published as safe
                       mailers via their SPF records, with hilarious if
                       rather predictable results. Next up, we find an
                       intensive advertising campaign for spamware aimed
                       at our imaginary friends. And the password guessing
                       aimed at an ever-expanding dictionary of non-
                       existing users continues.


                # ⚓ Linux Capable ☛ How_to_Install_MariaDB_on_Arch_Linux⠀⇛


                       MariaDB is one of the most popular open-source
                       databases next to its originator MySQL. The
                       original creators of MySQL developed MariaDB in
                       response to fears that MySQL would suddenly become
                       a paid service due to Oracle acquiring it in 2010.
                       With its history of doing similar tactics, the
                       developers behind MariaDB have promised to keep it
                       open source and free from such fears as what has
                       happened to MySQL.


                       MariaDB has become just as popular as MySQL with
                       developers, with advanced clustering with Galera
                       Cluster 4, faster cache/indexes, storage engines,
                       and features/extensions that you won’t find in
                       MySQL.


                       In the following tutorial, you will learn how to
                       install MariaDB on Arch Linux. The tutorial will
                       install the database software using the Pacman
                       package manager using the command line and some
                       essential tips on securing MariaDB.


                # ⚓ 5_Keys_to_Optimizing_Application_Container_Testing⠀⇛


                       Developers are increasingly using application
                       containers, but how do you make sure they are safe
                       and properly tested for performance?


                # ⚓ Install_DBeaver_on_Debian_10/Debian_11_–_kifarunix.com⠀⇛


                       Follow through this tutorial to learn how to
                       install DBeaver on Debian 10/Debian 11. DBeaver is
                       free and open source universal database tool for
                       developers and database administrators.


                # ⚓ UNIX Cop ☛ How_to_install_Cockpit_on_Debian_11?_–_Unix_/
                  Linux_the_admins_Tutorials⠀⇛


                       Follow through this tutorial to learn how to
                       install DBeaver on Debian 10/Debian 11. DBeaver is
                       free and open source universal database tool for
                       developers


                # ⚓ How_To_Add_SSH_Key_To_Server_|_Itsubuntu.com⠀⇛


                       In this tutorial, we will show you the methods to
                       copy the public ssh key to the server. The public-
                       key authentication method requires you to copy your
                       public SSH key to the server’s authorized_keys
                       file. You might be wondering why we need to add the
                       SSH key to the server as the reason to add ssh key
                       to the server is to allow you to access a server
                       via SSH without a password. Here are two methods to
                       copy the public ssh key to the server.


                # ⚓ How_to_Use_Tags_in_Ansible_Playbook_(Examples)⠀⇛


                       Sometimes, you might want to run specific tasks
                       instead of running an entire playbook file. This
                       helps to reduce the total playbook execution time,
                       especially when dealing with a large playbook file.


          o § Games⠀➾


                # ⚓ Ted Unangst ☛ Fantasian⠀⇛


                       Fantasian is an Apple Arcade exclusive Final
                       Fantasy style RPG. I liked it.


                       I first found out about the game a year ago, seeing
                       some screenshots and reading articles about the art
                       style, which relies on real world dioramas. It
                       seemed intriguing, but it was Arcade exclusive, so
                       I swore I’d never get to play it, because why would
                       I ever sign up for that. Fast forward a few months,
                       I’m tired of my crap Roku, I buy an Apple TV, and
                       it includes a few months of free Arcade. Okay, I’ll
                       sign up.


                # ⚓ PC World ☛ 29_years_later,_classic_Doom_just_got_a_stunning
                  ray_tracing_mod⠀⇛


                       This isn’t the first time we’ve seen a
                       juxtaposition of high-tech lighting over low-tech
                       visuals. The famously blocky Minecraft has official
                       Nvidia-branded RTX support, and Nvidia rebuilt
                       Quake II to show off what full-blown path tracing
                       can look like. But the Doom mod is available for
                       free to every PC player. It’s also particularly
                       dramatic in Doom’s sci-fi setting, a Martian colony
                       infested with hoards of ravenous demons.
                       Realistically rendered shadows and reflections from
                       fireballs, plasma ammunition, and pools of lava
                       show off precisely how much good lighting can do,
                       even for Doom’s incredibly basic polygon
                       environments and sprite enemies.


                # ⚓ The Verge ☛ Valve_says_it’s_‘ramping_up’_Steam_Deck
                  shipments⠀⇛


                       It’s Monday, and Valve has sent its next weekly
                       batch of Steam Deck order emails to people who have
                       reserved one of the coveted handheld gaming PCs.
                       But if you are still eagerly waiting for your email
                       to come through, there’s good news: Valve says it’s
                       “ramping up” Steam Deck shipments, sending more
                       order emails every week, and “sometimes” plans to
                       send them twice per week.


                # ⚓ Ubuntu Pit ☛ 5_Best_Zombie_Games_for_Linux:_Play_To_Get_A
                  Thrilling_Experience⠀⇛


                       Among all the gaming genres, Zombie games always
                       have a separate fan base. It’s because most of the
                       zombie games are not just games with a lot of dead
                       zombies. But they are the perfect combination of
                       several genres like FPS, survival, horror games,
                       adventure games, and so on. Even also, horror games
                       lovers prioritize zombie games exceptionally.
                       However, there are lots of exciting zombie games
                       for Linux you can try. And today we will talk about
                       some of them.


                # ⚓ GamingOnLinux ☛ Wine_manager_‘Bottles’_improves_Steam
                  Proton_support,_adds_configurable_environments_|
                  GamingOnLinux⠀⇛


                       Bottles, a free and open source application for
                       Linux (that works well on the Steam Deck), has
                       another new release out bringing in major new
                       features.


                       Since a previous version, it came with support for
                       pre-configured environments (Gaming and
                       Applications), which has been massively extended in
                       version 2022.3.28. Now, you can setup your own
                       configuration and share these environments with
                       others, so in a way it’s sliding closer to some
                       capabilities of Lutris. These environments are
                       configured with a YAML file making them easy to
                       parse and read.


                       On top of that, there’s improved support for Steam
                       Play Proton directly. It’s under heavy development
                       and still experimental but Bottles can now read
                       Steam Launch Options for games installed via Proton
                       and deal with them in Bottles directly and
                       configure certain settings in Bottles. This
                       eventually might make it far easier than manually
                       editing Steam launch options.


                # ⚓ GamingOnLinux ☛ Project_Hospital_gets_big_Steam_Deck
                  improvements_in_Patch_39_|_GamingOnLinux⠀⇛


                       Project Hospital, a management sim from Oxymoron
                       Games was recently upgraded to make playing on
                       Steam Deck a better experience. Here’s what’s new.


                # ⚓ GamingOnLinux ☛ Return_to_Monkey_Island_announced_for
                  2022⠀⇛


                       Devolver Digital, Lucasfilm Games and Ron Gilbert
                       have announced something huge for adventure game
                       fans, with Return to Monkey Island on the way to
                       release in 2022. A series adored by many, with this
                       one taking place following on from Secret of Monkey
                       Island and Monkey Island 2: LeChuck’s Revenge.


                       Technically, this was announced on April 1 on
                       Gilbert’s official blog post that stated: “For 18
                       years the Grumpy Gamer blog has been April Fools’
                       day free because it’s a stupid tradition.


                # ⚓ GamingOnLinux ☛ Steam_Deck_Plugin_Loader_gets_upgraded,
                  easier_to_install_|_GamingOnLinux⠀⇛


                       Want to mod the Steam Deck? SteamOS Plugin Manager
                       (covered here previously) has been renamed to just
                       Plugin Loader and it’s had a bit of a Python
                       rewrite recently to make it better. As a result,
                       it’s now far easier to install too, along with
                       having its first proper initial release.


                # ⚓ GamingOnLinux ☛ dbrand_now_have_Steam_Deck_Skins_and_Wraps
                  |_GamingOnLinux⠀⇛


                       Want to customize your Steam Deck look to match
                       your style? Well, at least with dbrand now you can
                       and they have some nice looking choices to mix
                       together.


                       On their system you can order (each being separate
                       and costing extra): a front skin ($19.95), back
                       skin ($14.95), trackpad skins ($4.95) and tempered
                       glass screen protectors (two pack $24.95). There’s
                       28 different skin colours or patterns in total, so
                       you can really make something wild — or nice and
                       tame, whatever you want.


          o § Desktop Environments/WMs⠀➾


                # § K Desktop Environment/KDE SC/Qt⠀➾


                      # ⚓ Its FOSS ☛ Maui_Shell’s_First_Alpha_Release_Looks
                        Promising⠀⇛


                             
                             Even before its release, Maui shell has been
                             praised as the future of the Linux desktop
                             user interface.


                             And, for all the right reasons…


                             It attempts to bring convergence to the
                             mainstream, just like Canonical tried with
                             Unity. Regarding looks, you get modern
                             aesthetics inspired by various existing
                             desktop experiences.


                # § GNOME Desktop/GTK⠀➾


                      # ⚓ Its FOSS ☛ Here’s_What_Devs_Are_Planning_for_GNOME
                        43⠀⇛


                             
                             It hasn’t been that long since GNOME 42 was
                             released.


                             While it was an exciting upgrade over GNOME
                             41, you may not be able to find it on every
                             mainstream Linux distribution (except
                             OpenSUSE, Arch, and Clear Linux).


                             Fedora 36 and Ubuntu 22.04 should be the most
                             popular options featuring GNOME 42 with their
                             releases in the following weeks.


          o § Distributions⠀➾


                # ⚓ Unix Sheikh ☛ Linux_distribution_long_term_support_might
                  not_be_what_you_think_it_is⠀⇛


                       A Linux distribution cannot normally provide any
                       kind of long term support for any kind of third
                       party software if such software is no longer
                       supported by upstream.


                # § Gentoo Family⠀➾


                      # ⚓ Gentoo ☛ New_Gentoo_LiveGUI_ISO_and_artwork_/
                        branding_contest! [Ed: Now also in the main Gentoo
                        site]⠀⇛


                             After a long break, we now have again a
                             weekly LiveGUI ISO image for amd64 available!
                             The 4.7 GB download, suitable for DVD burning
                             or an USB stick, boots directly into KDE
                             Plasma and comes with a ton of up-to-date
                             software. This ranges from office
                             applicactions such as LibreOffice, Inkscape,
                             and Gimp all the way to many system
                             administrator tools.


                             Now, we need your help! Let’s make this the
                             coolest and most beautiful Linux live image
                             ever. We’re calling for submissions of
                             artwork, themes, actually anything from a
                             desktop background to a boot manager
                             animation, on the topic of Gentoo! The
                             winning entry will be added as default
                             setting to the official LiveGUI images, and
                             also be available for download and
                             installation.


                # § Canonical/Ubuntu Family⠀➾


                      # ⚓ Pop_OS_22.04_LTS_–_New_Features_and_Release_Updates⠀⇛


                             A summary of the new features and beta
                             download details of Pop OS 22.04 LTS from
                             System76.


                      # ⚓ The_Fridge:_Ubuntu_Weekly_Newsletter_Issue_729⠀⇛


                      # ⚓ Ubuntu_Fridge_|_Ubuntu_Weekly_Newsletter_Issue_729⠀⇛


                             Welcome to the Ubuntu Weekly Newsletter,
                             Issue 729 for the week of March 27 – April 2,
                             2022. The full version of this issue is
                             available here.


          o § Devices/Embedded⠀➾


                # ⚓ CNX Software ☛ Raspberry_Pi_Compute_Module_4S_SO-DIMM
                  module_is_powered_by_Broadcom_BCM2711_SoC⠀⇛


                       The Raspberry Pi Compute Module 4S is an upcoming
                       system-on-module based on the same Broadcom BCM2711
                       quad-core Cortex-A72 processor found in Raspberry
                       Pi Compute Module 4, but using the same SO-DIMM
                       connector as found in earlier Raspberry Pi Compute
                       Module boards, instead of the new board-to-board
                       connectors.


                       The Raspberry Pi Compute Module 4S is not launched
                       yet, but we discovered it will be used on
                       Revolution Pi S and SE series DIN-rail industrial
                       computers via a tweet from Jeff Geerling and his
                       post on Raspberry Pi forums.


                # § Open Hardware/Modding⠀➾


                      # ⚓ Raspberry Pi ☛ Exploring_cross-disciplinary_computing
                        education_in_our_new_seminar_series⠀⇛


                      # ⚓ Tom’s Hardware ☛ Pimoroni_Announces_Servo_2040_Servo
                        Motor_Controller⠀⇛


                             Although it’s slightly weird-looking, we’re
                             fairly sure that the image above is not an
                             April Fool prank. UK-based seller of useful
                             things Pimoroni has taken to Twitter to
                             announce the Servo 2040, an 18-channel servo
                             controller “for making things with lots of
                             moving parts”.


                             Servo 2040, as you might expect, is a
                             standalone servo controller making use of the
                             RP2040 microcontroller chip seen in the
                             Raspberry Pi Pico. There are enough pre-
                             soldered pin headers to connect up to 18
                             servos, current monitoring functionality to
                             keep an eye on power consumption, and six
                             addressable LEDs for visual feedback. You
                             also get pin headers for up to six analog
                             sensors for checking that you’re not applying
                             too much pressure to your test subject’s
                             head.


                      # ⚓ [Old] The_making_of_a_PCB:_Part_1⠀⇛


                             For some time now, we’ve wanted to have a
                             Printed Circuit Board (PCB) that we could use
                             to demonstrate Drogue Device and Drogue
                             Cloud. This is the first post in a series of
                             post telling the tale of this journey.


                      # ⚓ The_making_of_a_PCB:_Part_2⠀⇛


                             Throughout these two blog posts, we’ve seen
                             the steps we took starting from the initial
                             drawing to a potential large scale
                             manufacturing of a fully assembled PCB,
                             including additional equipment to program the
                             devices. A lot of trial and error is expected
                             when trying something new, but we got
                             something that worked in the end. With KiCad,
                             there is a lot of open hardware


                      # ⚓ Ken Shirriff ☛ Reverse-engineering_a_mysterious
                        Univac_computer_board⠀⇛


                             The IBM 1401 team at the Computer History
                             Museum accumulates a lot of mystery
                             components from donations and other sources.
                             While going through a box, we came across the
                             unusual circuit board below. At first, it
                             looked like an IBM SMS (Standard Modular
                             System) card, the building block of IBM’s
                             computers of the late 1950s and early 1960s.1
                             However, this board is larger, has double-
                             sided wiring, the connector is different, and
                             the labeling is different.2


                      # ⚓ Warner Losh ☛ DEC_Rainbow_100B_Power_Supply_Specs⠀⇛


                             Most ATX power supplies supply more 5V and
                             less 12V than is needed for the Rainbow to
                             power the system. However, the 12V supplies
                             are in large part for the older disk
                             technology in the Rainbow and if you are
                             using emulators you can get by with a little
                             less, though how much less is TBD.


                      # ⚓ Didier Stevens ☛ Power_Consumption_Of_A_Philips_Hue
                        lamp_In_Off_State⠀⇛


                             A Philips Hue lamp is a LED lamp that can be
                             controlled wirelessly. It always draws power
                             for its control circuitry, also when the LED
                             is turned off.


                             I wondered how much power it consumes in the
                             off state. Doing some research, I found a
                             couple of forums where people asked the same
                             question, and getting answers that is was
                             very little, varying from 0,01 A to 0,02 A.


                # § Mobile Systems/Mobile Applications⠀➾


                      # ⚓ Computer World ☛ Android_12_Upgrade_Report_Card:_What
                        a_weird_year_|_Computerworld⠀⇛


                      # ⚓ GSM Arena ☛ Samsung_Galaxy_M62_is_receiving_Android
                        12-based_One_UI_4.1_update_–_GSMArena.com_news⠀⇛


                      # ⚓ Indian Express ☛ How_to_back_up_the_photos_on_your
                        Android_phone_using_Google_Photos_or_Dropbox_|
                        Technology_News,The_Indian_Express⠀⇛


                      # ⚓ Android Central ☛ How_to_access_Google_Recorder_from
                        the_Android_Quick_Settings_menu_|_Android_Central⠀⇛


                      # ⚓ XDA ☛ Android_could_soon_start_warning_users_when
                        they_run_32-bit_apps⠀⇛


                      # ⚓ Android Police ☛ 8_best_simulation_games_for_Android
                        in_2022⠀⇛


                      # ⚓ The Verge ☛ Google’s_April_Android_12_update_is
                        rolling_out_for_Pixel_phones_–_The_Verge⠀⇛


                      # ⚓ The Verge ☛ Google_crackdown_means_you_won’t_be_able
                        to_buy_Barnes_&_Noble_ebooks_on_Android_–_The_Verge⠀⇛


                      # ⚓ Android_To_Soon_Allow_Users_To_Freely_Select_Text
                        Within_Tweets_/_Digital_Information_World⠀⇛


                      # ⚓ 9to5Google ☛ Rename_your_Bluetooth_devices_on_Android
                        –_Here’s_how_–_9to5Google⠀⇛


                      # ⚓ India Times ☛ android:_How_Google_may_be_planning_to
                        keep_your_old_Android_smartphones_safe_–_Times_of
                        India⠀⇛


                      # ⚓ India ☛ Realme_Pad_Mini_Android_Tablet_With_8.7-inch
                        Display_And_LTE_Support_Launched:_Price,
                        Specifications⠀⇛


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


                # § FSF⠀➾


                      # ⚓ FSF ☛ Antitrust_Day:_Tech_monopolies_shouldn’t_be
                        allowed_to_control_app_stores⠀⇛


                             Today is Antitrust Day, a day of action
                             organized by Fight for the Future, dedicated
                             to mobilizing support for two tech antitrust
                             bills currently on the US Senate floor: the
                             Open App Markets Act (OAMA), and the American
                             Innovation and Choice Online Act (AICOA).
                             Though these are two separate bills, their
                             general focus remains the same: preventing
                             large tech corporations from behaviors that
                             that take away people’s freedom. Chief among
                             these is the common practice of some devices
                             only allowing one specific app store, or
                             making it very hard to use any app store but
                             one. While much of the conversation around
                             these bills is focused on promoting
                             competition, that is not the key value for
                             us. The key value is freedom, and in this
                             case, the measures being targeted as anti-
                             competitive are also measures that take away
                             user freedom. Removing Apple’s ability to
                             block all app repositories but their own on
                             the devices they produce would allow freedom-
                             respecting ones to enter the scene, and
                             provide users of these devices with the first
                             step to their freedom.


                             We’ve written previously on the way “bad
                             apples” like Apple and Google take great
                             pains to restrict what users can and can’t do
                             with their devices. Platforms like these are
                             skilled at giving users the illusion of
                             autonomy and freedom. There’s an app for
                             every need, or so it seems, but there’s a
                             sinister reality behind the glossy finish.
                             It’s true that the overwhelming majority of
                             these apps are nonfree software, which is
                             overtly malware, but it’s less common that
                             users get to see the way corporations like
                             Apple are pulling the strings behind the
                             scenes, driving our use of technology further
                             and further away from being in our control.
                             Apple likes to present the gatekeeping they
                             do as a form of quality assurance. The exact
                             same quality assurance benefits could be had
                             in a world where users had the freedom to to
                             either stay with Apple or go to someone else
                             they trust more to provide the same services
                             without having to change their physical
                             device.


                      # § GNU Projects⠀➾


                            # ⚓ Joinup ☛ GNU_Health_declared_a_Digital_Public
                              Good_by_the_DPGA⠀⇛


                                   We are very proud to announce that the
                                   GNU Health project has been declared a
                                   Digital Public Good by the Digital
                                   Public Goods Alliance (DPGA). GNU
                                   Solidario received the announcement
                                   this Sunday, April 3rd 2022.


                                   The Digital Public Goods Alliance is a
                                   multi-stakeholder initiative endorsed
                                   by the United Nations Secretary-
                                   General, working to accelerate the
                                   attainment of the Sustainable
                                   Development Goals in low-and middle-
                                   income countries by facilitating the
                                   discovery, development, use of, and
                                   investment in digital public goods.


                            # ⚓ FSF ☛ March_GNU_Spotlight_with_Amin_Bandali:
                              Eleven_new_GNU_releases!⠀⇛


                                   Hello! I’m Amin Bandali, and starting
                                   this month I’m taking over the GNU
                                   Spotlight from my fellow GNU hacker and
                                   free software activist Mike Gerwitz.
                                   Mike, thank you so much for all your
                                   work over the past four years for
                                   curating and preparing the monthly GNU
                                   Spotlight, which is a personal favorite
                                   part of the Free Software Supporter for
                                   me. I will do my best to continue in
                                   your steps in bringing exciting news on
                                   new releases of GNU packages to our
                                   dear readers.


                      # § Licensing/Legal⠀➾


                            # ⚓ NCSNT ☛ New_security_requirements_introduced
                              for_medical_device_manufacturer⠀⇛


                                   In response, the Linux report showed
                                   that many hospitals are adding the SBOM
                                   requirements into their procurement
                                   contracts. However, many leaders don’t
                                   know how to examine an SBOM, the
                                   package manager listings, or open
                                   source licensing distribution lists to
                                   find risky elements.


                                   As such, even if the PATCH Act passes
                                   and the SOMB requirement is added, it’s
                                   unclear whether the legislation would
                                   also add needed educational elements to
                                   make SOMBs more user-friendly. As
                                   Abrahamson explained, “Only the
                                   manufacturer of the device will have
                                   the engineering knowledge of the device
                                   required to make this determination.”


                                   Despite these challenges, the FDA has
                                   advocated for continued transparency
                                   around device elements and risks
                                   through the SBOM. In its latest budget
                                   request, the agency asked for a $5
                                   million budget increase to develop “a
                                   more comprehensive cybersecurity
                                   program for medical devices,” including
                                   identifying and remediating device
                                   flaws that pose a national security
                                   risk.


                                   The proposed bills come on the heels of
                                   separate healthcare legislation
                                   introduced on Apr. 25, which would see
                                   the Department of Health and Human
                                   Services partnering with Cybersecurity
                                   Infrastructure Security Agency to
                                   improve the sector’s overall
                                   infrastructure.


                # § Openness/Sharing/Collaboration⠀➾


                      # § Open Access/Content⠀➾


                            # ⚓ Torrent Freak ☛ Sci-Hub_Only_Option_For
                              Academics_In_Russia_After_Major_Publishers_Pull
                              Out⠀⇛


                                   Fifteen major publishers, together
                                   representing an almost global monopoly
                                   on scientific papers, have announced a
                                   suspension of sales and services in
                                   Russia. The knowledge and information
                                   void left behind can still be filled by
                                   Sci-Hub but thanks to legal action by
                                   the publishers, not even that is
                                   straightforward.


                            # ⚓ Bjoern Brembs ☛ EU:_Academic_Publishers_Are
                              Monopolists⠀⇛


                                   The market power of academic publishers
                                   has been a concern for all those
                                   academic fields where publication in
                                   scholarly journals is the norm. For
                                   most non-economist researchers, the
                                   anti-trust aspects of academic
                                   publishing are likely confusing and
                                   opaque.


                                   For instance, libraries and consortia
                                   are exempted from organizing tenders
                                   for their publication needs as each
                                   article exists only in one journal with
                                   one publisher. This is called the
                                   single or sole source exemption from
                                   procurement law and essentially means
                                   that academic publishers have
                                   monopolies on each of their articles
                                   and hence each of their journals.


                                   At the same time, this conglomerate of
                                   monopolies is often referred to as the
                                   “publishing market“, where there is
                                   market consolidation or concentration,
                                   leading up to an “oligopoly“.


                                   So which is it now, a market with
                                   competing providers or a conglomerate
                                   of monopolists?


                # § Programming/Development⠀➾


                      # ⚓ Linux Links ☛ 6_Best_Free_and_Open_Source_Continuous
                        Delivery_Systems⠀⇛


                             
                             Continuous delivery (CD) is a software
                             engineering approach in which developers
                             produce software in short cycles, ensuring
                             that the software can be reliably released at
                             any time and, when releasing the software,
                             without doing so manually. It enables team to
                             get changes of all types such as new
                             features, configuration changes, bug fixes
                             and experiments—into production, or into the
                             hands of users, safely and quickly in a
                             reliable and consistent way.


                             Following the automation of builds and unit
                             and integration testing in CI, continuous
                             delivery automates the release of that
                             validated code to a repository. To have an
                             effective continuous delivery process, it’s
                             important that CI is already built into your
                             development pipeline. The goal of continuous
                             delivery is to have a codebase that is always
                             ready for deployment to a production
                             environment.


                      # ⚓ Frederic Cambus ☛ Toolchains_adventures_–_Q1_2022⠀⇛


                             This is the fourth post in my toolchains
                             adventures series. Please check the previous
                             posts in the toolchains category for more
                             context about this journey.


                      # ⚓ Brian Callahan ☛ I_wrote_a_simple,_explainable,
                        peephole_optimizer_(for_cproc_and_QBE),_part_2⠀⇛


                             It’s time to finish up our peephole
                             optimizer, O, that we started in the previous
                             post. This peephole optimizer, designed to be
                             plugged into cproc and used to fix up QBE
                             generated amd64 assembly, provides two
                             optimizations that we found reduced binary
                             size by between 2% and 3%: first, a one-line
                             optimization converting mov_ $0, %___ into
                             xor_ %___, %___ and a three-line optimization
                             removing a useless register-to-register self-
                             copy via a temporary register.


                      # ⚓ Ubuntu ☛ Design_patterns_and_the_software_operator_—
                        part_1⠀⇛


                             As writing software turned into a more and
                             more complex engineering effort, ideas
                             emerged to make writing software easier and
                             more stable: it was the idea of identifying
                             solution patterns when implementing commonly
                             experienced problems. Actually, many problems
                             in programming are raised over and over
                             again. As a consequence, communities emerged
                             to discuss such patterns in their meetings,
                             workshops and conferences. Descriptions about
                             design patterns were published as conference
                             proceedings.


                      # ⚓ Ubuntu ☛ The_software_operator_design_pattern_—_part
                        2⠀⇛


                             Over the years, the software development and
                             programming community developed a common
                             understanding of design patterns. A design
                             pattern is a general solution designed to
                             solve a repeatedly occurring problem when
                             writing — or better, designing — software.
                             This implies that if a design is new and has
                             not been proven to work in production
                             software, it cannot be a pattern. A pattern
                             is an abstract concept covering multiple
                             implemented solutions following that abstract
                             concept. If there are no solutions already in
                             place, such a pattern does not exist.


                      # § Rust⠀➾


                            # ⚓ Tor ☛ Arti_0.2.0_is_released:_Your_somewhat-
                              stable_API_is_here!⠀⇛


                                   Arti is our ongoing project to create a
                                   working embeddable Tor client in Rust.
                                   It’s not ready to replace the main Tor
                                   implementation in C, but we believe
                                   that it’s the future.


                                   Right now, our focus is on making Arti
                                   production-quality, by stress-testing
                                   the code, hunting for likely bugs and
                                   adding missing features that we know
                                   from experience that users will need.
                                   We’re going to try not to break
                                   backward compatibility too much, but
                                   we’ll do so when we think it’s a good
                                   idea.


          o § Standards/Consortia⠀➾


                # ⚓ Everything Smart Home ☛ Smart_Home_Protocols:_ZigBee
                  Explained!⠀⇛


                       ZigBee is also an open standard, which makes it low
                       cost compared to some other standards.


                # ⚓ Everything Smart Home ☛ Smart_Home_Protocols:_WiFi
                  Explained!⠀⇛


                       Welcome to the Smart Home Protocols Series, where
                       we are going to be deep diving on protocols that
                       our smart home devices use to communicate in our
                       smart homes and we’re going to be starting with
                       WIFI!


    * § Leftovers⠀➾


          o ⚓ New York Times ☛ The_Kids_Are_Right_About_Email,_Too⠀⇛


                 This generation missed the “You’ve Got Mail” era, that
                 brief, sunny time when email was still electronic mail:
                 long, thoughtful letters that got delivered,
                 miraculously, in a blink. Old-timers groused even then
                 that email could never adequately replace condolence
                 letters or thank-you notes, much less love letters, but
                 that was just tradition talking. In truth, “You’ve Got
                 Mail” was a movie about a 19th-century courtship
                 correspondence conducted via a 20th-century pony express.


                 My children never got the chance to know the pleasure of
                 a heartfelt exchange that traveled with the speed of a
                 text but nevertheless carried the soul of the sender. All
                 they have known is what email has devolved into: reply-
                 all responses to bulk messages, shipping notifications,
                 fund-raising pleas, systemwide reminders and, of course,
                 spam. Email is now just a way to be at the beck and call
                 of anyone, and any robot, with an internet connection.


          o § Education⠀➾


                # ⚓ Bjoern Brembs ☛ Scholarship_Has_No_Time_To_Waste⠀⇛


                       A second front was opened about ten years ago now
                       from an entirely different and mostly unanticipated
                       direction. More than just flush with funds, but
                       this time financed by academia herself, academic
                       publishers started (escalated?) their own attack on
                       science by gobbling up and developing digital
                       surveillance technologies. To expand the sources of
                       user data, these corporations bought digital tools
                       covering all aspects of academic life, from
                       literature search, data analysis, writing, citing
                       or outreach, all the way to citation analysis for
                       research assessment. These corporations formerly
                       known as publishers are using their expanded
                       digital surveillance network to accomplish two
                       separate goals. First, a copy of the data is
                       aggregated with private data from scholarly users
                       and sold, either to advertisers, to law enforcement
                       agencies not allowed to collect such intrusive data
                       themselves, or to any authoritarian government
                       interested in identifying potential opposition
                       intelligentsia. The second goal is to expand the
                       monopolies they enjoy on scholarly content, to a
                       monopoly on all scholarly services, i.e., the
                       mother of all vendor lock-ins. Packaging all the
                       different tools in a single bundle and selling it
                       to institutions akin to subscription “Big Deals”,
                       would make it impossible for any institution buying
                       such a package to ever switch to a different
                       provider again. An analogy outside of academia
                       would be a merger of Microsoft, SAP, Google and
                       Facebook. There are two corporations so far that
                       are standing ready to deploy such bundles, RELX
                       (parent of Elsevier) and Holtzbrinck
                       (SpringerNature, Digital Science). A related data
                       analytics corporation specializing on scholarly
                       data is Clarivate (Web of Science, ProQuest).


                       Both onslaughts aim to undermine independent
                       scholarship and subjugate it for special interests,
                       be it political or financial. To some extent, both
                       have been quite successful already. In fact, in the
                       use of journal rank and other citation metrics, the
                       political and financial fronts have closed ranks
                       and are cooperating. The worst outcome of
                       succumbing to these attacks would be the
                       destruction of publicly funded science. At best,
                       loosing on both fronts would entail academia
                       finding itself permanently strapped in neoliberal
                       purgatory, with a vast precariate, cut-throat
                       competition and results nobody can take seriously
                       any more, in other words: Idiocracy.


          o § Hardware⠀➾


                # ⚓ Hackaday ☛ ESP32:_Is_Two_Better_Than_One?⠀⇛


                       We’ve looked at the WROOM-DA module before. It’s an
                       ESP32 with two antennas, and [Andreas Spiess] says
                       it is the ugliest ESP32 he’s ever seen. But beauty
                       is only skin deep, after all. Did [Andreas] find
                       beauty in the twin antennas? Watch the video below
                       and see for yourself.


                # ⚓ Hackaday ☛ Detailed_Big_Screen_Multimeter_Review⠀⇛


                       It seems like large-screen cheap meters are really
                       catching on. [TheHWcave] does a very detailed
                       review of a KAIWEETS KM601, which is exactly the
                       same as a few dozen other Chinese brands you can
                       get from the usual sources. You can see the review
                       in the video below.


                # ⚓ Hackaday ☛ Rubber_Band_“Slide_Rule”_Doesn’t_Slide,_But
                  Rotates⠀⇛


                       Around here we mostly enjoy slide rules. We even
                       have our own collections including some cylindrical
                       and circular ones. But [Mathologer] discusses a
                       recent Reddit post that explains a circular slide
                       rule-like device using a wheel and a stretchable
                       rubber band. While it probably would be difficult
                       to build the actual device using a rubber band, it
                       can do wonders for your understanding of logarithms
                       which still show up in our lives when, for example,
                       you are calculating decibels. [Dimitri] did
                       simulate the rubber band for you in software.


                # ⚓ Hackaday ☛ Monitor_Space_Weather_And_The_Atmosphere_With
                  Your_Cellphone!⠀⇛


                       Above our heads, the atmosphere is a complex and
                       unpredictable soup of gasses and charged particles
                       subject to the influence of whatever the Sun throws
                       at it. Attempting to understand it is not for the
                       faint-hearted, so it has for centuries been the
                       object of considerable research. A new project from
                       the European Space Agency and ETH Zurich gives the
                       general public the chance to participate in that
                       research in a small way, by crowdsourcing
                       atmospheric data gathering to a mobile phone app.
                       How might a mobile phone observe the atmosphere?
                       The answer lies in their global positioning
                       receivers, which can track minute differences in
                       the received signals caused by atmospheric
                       conditions. By gathering as much of this data as
                       possible, the ESA scientists will gain valuable
                       insights into atmospheric conditions as they change
                       across the globe.


                # ⚓ Hackaday ☛ Levitate_The_NE555_Way⠀⇛


                       Ultrasonic levitation — the practice of creating a
                       standing wave between two ultrasonic sources and
                       positioning lightweight objects such that they can
                       float in the pressure minimums between them — has
                       been a source of fascination to more than one
                       experimenter. [Peter Lin] demonstrated this in the
                       video below the break, by creating an ultrasonic
                       levitation system using only the trusted chip of
                       all true experimenters, the NE555. (Video, embedded
                       below.)


                # ⚓ Hackaday ☛ Confessions_Of_A_Crimpoholic⠀⇛


                       Hi, my name is Dan and I’m a crimpoholic.


                # ⚓ Hackaday ☛ SAMD11_Provides_Two_Serial_Ports_For_Price_Of
                  One⠀⇛


                       While the average computer user likely hasn’t given
                       much thought to the lowly serial port in decades,
                       the same can’t be said for the hardware hacker.
                       Cheap serial-to-USB adapters are invaluable for
                       snooping debug ports or programming chips, and if
                       you ask us, you can never have too many laying
                       around the bench. [Quentin Bolsée] loves them so
                       much that he’s even figured out how to build a
                       dual-port adapter with a SAMD11C14 microcontroller.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ TruthOut ☛ Dwindling_Public_Concern_About_COVID_Is_Handing
                  Republicans_a_Gift⠀⇛


                # ⚓ TruthOut ☛ Watchdog_Finds_DeJoy_Invests_in_COVID_Test
                  Company,_Potentially_Breaking_the_Law⠀⇛


                # ⚓ TruthOut ☛ Poorest_US_Counties_Suffered_Twice_the_COVID
                  Deaths_of_the_Richest⠀⇛


                # ⚓ Common Dreams ☛ ‘A_Victory_for_the_Virus’:_Congress_Cuts
                  New_Global_Covid_Aid_to_$0⠀⇛


                       Republican and Democratic congressional negotiators
                       on Monday are reportedly set to announce a $10
                       billion coronavirus funding package that contains
                       no money to fight the pandemic globally, prompting
                       outrage from public health experts who say the
                       decision will prolong the Covid-19 crisis.


                       “Failing to fund the global fight against Covid-19
                       is a choice to extend the pandemic, to accept
                       preventable suffering and insecurity for all, and
                       to live with the knowledge that, deep in the time
                       of the world’s greatest need, the United States
                       gave up,” tweeted Peter Maybarduk, Access to
                       Medicines director at Public Citizen.


                # ⚓ Common Dreams ☛ ‘A_Poor_People’s_Pandemic’:_Poorest_US
                  Counties_Suffered_Twice_the_Covid_Deaths_of_Richest⠀⇛


                       A first-of-its-kind examination of the coronavirus
                       pandemic’s impact on low-income communities
                       published Monday shows that Covid-19 has been twice
                       as deadly in poor counties as in wealthy ones, a
                       finding seen as a damning indictment of the U.S.
                       government’s pandemic response.


                       “The neglect of poor and low-wealth people in this
                       country during a pandemic is immoral, shocking, and
                       unjust, especially in light of the trillions of
                       dollars that profit-driven entities received,” said
                       Rev. Dr. William Barber II, co-chair of the
                       national Poor People’s Campaign, which conducted
                       the new analysis alongside a team of economists and
                       other experts.


                # ⚓ Orac ☛ Bioethics_recycles_old_antivax_tropes_about_COVID
                  vaccines_for_children⠀⇛


                       Regular readers might be getting tired of my
                       pointing out how there’s nothing new under the
                       antivax sun in terms of deceptive arguments,
                       conspiracy theories, and tropes designed to argue
                       against vaccinating. However, the COVID-19 pandemic
                       introduced these talking points to a much large
                       audience than had ever seen them before so I
                       considered it my duty to educate our readers and to
                       point out that none of the antivaccine
                       misinformation that has hit us like a tsunami since
                       COVID-19 vaccines first entered large clinical
                       trials in the summer of 2020 is anything new. It
                       just seems new if you haven’t seen it before.
                       Examples include, of course, misinformation
                       claiming that the vaccine kills based on
                       misinterpretation of the VAERS database; that it
                       sterilizes our womenfolk; that it “sheds” and
                       endangers the unvaccinated; and that it causes
                       cancer, none of which are anything new. Even the
                       claim that it “permanently alters your DNA”,
                       although it might appear like a new talking point
                       based on the fact that Pfizer/BioNTech and Moderna
                       COVID-19 vaccines were the first successful
                       translations of mRNA technology into a clinical
                       product, if you look really hard, is not a new
                       claim. (Transhumanism, anyone?) As Charles
                       Pierce likes to say, history is so cool. In this
                       case, though, I’d add: It’s only cool and useful if
                       you know about it and can use it to counter the
                       pernicious misinformation about vaccines of the
                       sort published by, for example, The Wall Street
                       Journal and deconstructed by Jonathan Howard a week
                       ago. What I didn’t expect was to see common
                       antivaccine tropes weaponized in a bioethics
                       journal, but that’s exactly what I saw almost two
                       weeks ago.


                # ⚓ Common Dreams ☛ Opinion_|_Pain_at_the_Pumps_Originates_in
                  the_Paycheck⠀⇛


                       At the height of Covid, diaper banks across the US
                       upped their diaper contributions to communities by
                       86%, and we have no intention of scaling back,
                       because the need did not diminish alongside the
                       daily positivity rate. There are new stressors on
                       families, of course, like rising gas prices. But if
                       paying another 50 cents a gallon for gas means that
                       you can no longer afford diapers for your baby, the
                       price of gas is not the problem. Removing federal
                       and state taxes on gas might ease the pain
                       incrementally, but it won’t end the ongoing crisis
                       that is poverty.


          o § Integrity/Availability⠀➾


                # § Proprietary⠀➾


                      # § Pseudo-Open Source⠀➾


                            # § Privatisation/Privateering⠀➾


                                  # § Linux Foundation⠀➾


                                        # ⚓ Unicorn Media ☛ Free_Training_and
                                          Certification:_Linux_Foundation
                                          Taking_Submissions_for_LiFT
                                          Scholarships⠀⇛


                                               The Linux Foundation
                                               announced on Friday that
                                               it’s taking applications
                                               for LiFT (Linux Foundation
                                               Training) Scholarships
                                               through the end of the
                                               month. The scholarships,
                                               that cover the cost for the
                                               foundation’s online
                                               training courses and
                                               certification exams, have
                                               been handed out on a yearly
                                               bases under a program the
                                               foundation began in 2011.


                                               One of the best ways to
                                               jump start or improve a
                                               career in computer tech is
                                               through training and
                                               certifications. While there
                                               are plenty of venues
                                               offering certification
                                               programs, they’re not all
                                               created equal, and some are
                                               more valued by the people
                                               who make hiring decisions
                                               and hand out promotions
                                               than others, and
                                               certifications from the
                                               Linux Foundation are
                                               considered to be about as
                                               good as it gets.


                      # § Security⠀➾


                            # ⚓ Didier Stevens ☛ .ISO_Files_With_Office_Maldocs
                              &_Protected_View_in_Office_2019_and_2021 [iophk:
                              Windows TCO]⠀⇛


                                   But when an Office document is stored
                                   inside an ISO file, and that ISO has a
                                   ZoneIdentifier ADS, then Word will not
                                   open the document in Protected View.
                                   That is something I observed 5 years
                                   ago.


                            # ⚓ Computer World ☛ The_Russian_cyberattack_threat
                              might_force_a_new_IT_stance [iophk: Windows
                              TCO]⠀⇛


                                   Various US government agencies have
                                   warned of imminent attacks, but the
                                   very few specifics they have offered
                                   generally amount to, “Do what every
                                   enterprise CISO knows they should have
                                   done years ago.”


                            # ⚓ EFF ☛ Anatomy_of_an_Android_Malware_Dropper⠀⇛


                                   The sample we’ll be looking at was
                                   first seen on March 1st, 2022. This
                                   particular malware presents itself as
                                   the banking app for BAWAG, a prominent
                                   financial institution in Austria. Upon
                                   first run, the app prompts the user to
                                   give “accessibility services”
                                   permission to the app. The
                                   accessibility services permission
                                   grants an app broad access to read the
                                   screen and mimic user interaction. Upon
                                   granting the permission, the app
                                   backgrounds itself. Any attempt by the
                                   user to uninstall the app is prevented
                                   by the app interrupting and closing the
                                   uninstall dialogues. Attempting to open
                                   the app again also fails—nothing
                                   happens.


                                   The Android app manifest file contains
                                   a list of permissions, activities, and
                                   services that an app provides. If an
                                   activity is not listed in the app
                                   manifest, the app can’t launch that
                                   activity. Using an Android static
                                   analysis tool like jadx or apktool we
                                   can take a look at the manifest XML.
                                   The malware app’s manifest asks for a
                                   wide range of permissions, including
                                   the ability to read and send SMS
                                   messages (a common way for malware to
                                   propagate), request installation and
                                   deletion of packages, read contacts,
                                   initiate calls, and request the
                                   aforementioned accessibility service.
                                   In addition, a number of classes are
                                   referenced which are not defined
                                   anywhere in our jadx-reversed code:


                            # § Privacy/Surveillance⠀➾


                                  # ⚓ Techdirt ☛ Notorious_Human_Rights_Abuser
                                    Is_One_Of_NSO_Group’s_Main_Investors⠀⇛


                                         It’s more difficult to choose
                                         your investors than your
                                         customers. Maybe this isn’t
                                         entirely NSO’s fault, but it
                                         certainly helped make it easier
                                         to sell powerful zero-click
                                         exploits to the governments most
                                         likely to abuse them. Here’s Kaye
                                         Wiggins and Mehul Srivastava for
                                         the Financial Times.


                                  # ⚓ Techdirt ☛ Top_Court_In_Massachusetts
                                    Says_Cops_Unconstitutionally_Obtained_Cell
                                    Tower_Dumps_In_Homicide_Case⠀⇛


                                         The courts in Massachusetts
                                         continue to set the standard for
                                         privacy protections. They have
                                         handed down several rulings that
                                         have expanded residents’
                                         reasonable expectations beyond
                                         the baseline set by the Fourth
                                         Amendment and federal court
                                         rulings.


                                  # ⚓ EFF ☛ The_NDO_Fairness_Act_Is_an
                                    Important_Step_Towards_Transparency⠀⇛


                                         That’s why we recently sent a
                                         letter to the House Committee on
                                         the Judiciary in support of H.R.
                                         7072, the Nondisclosure Order 
                                         (NDO) Fairness Act. This bill
                                         takes important steps toward
                                         bringing transparency and
                                         accountability to the federal
                                         government’s use of sweeping gag
                                         orders accompanying requests for
                                         user data, and we appreciate
                                         Chair Nadler and the other co-
                                         sponsors for addressing these
                                         important issues.The legislation
                                         does away with indefinite gag
                                         orders, limiting the duration of
                                         nondisclosure orders to a maximum
                                         of 30 days and allowing the
                                         government to seek extensions
                                         only in 30-day increments. The
                                         NDO Fairness Act also requires
                                         courts to explain in writing why
                                         notice of the collection would be
                                         substantially likely to result in
                                         harm before issuing nondisclosure
                                         orders and to narrowly tailor
                                         orders to avoid complete bans on
                                         speech wherever possible. This is
                                         a much more demanding standard
                                         than the current requirement that
                                         courts find there be “reason to
                                         believe” that such harm “may”
                                         occur. And the legislation puts
                                         in place important measures to
                                         ensure greater transparency
                                         around the government’s use of
                                         these secretive orders, both for
                                         targeted individuals and the
                                         larger public, including by
                                         requiring the government to
                                         notify targets of surveillance
                                         that their communications were
                                         intercepted and to publish an
                                         annual report that provides
                                         information about the use of
                                         surveillance under Section 2703. 


                                         These reforms are a welcome step
                                         forward in reforming the secrecy
                                         surrounding electronic
                                         surveillance and bringing the
                                         Stored Communications Act closer
                                         in line with constitutional
                                         guarantees. The bill would be
                                         even stronger if it provided a
                                         more accessible path for
                                         individuals to seek remedies for
                                         government violations of this
                                         law, and we look forward to
                                         working with the Committee to
                                         enact these and other reforms.


                                  # ⚓ Techdirt ☛ Assholes_Are_Now_Forging
                                    ‘Emergency_Data_Requests’_To_Talk_Tech
                                    Companies_Out_Of_User_Data⠀⇛


                                         Never underestimate the ability
                                         of the baddies to exploit the
                                         good nature inherent to most
                                         people. That’s the takeaway from
                                         this latest depressing news that
                                         malicious people are abusing law
                                         enforcement tools to harvest
                                         personal information to exploit.
                                         Here’s William Turton, delivering
                                         the most recent bit of bad news
                                         for everyone everywhere.


                                  # ⚓ Site36 ☛ German_ANOM_investigations:_The
                                    mysterious_EU_third_state⠀⇛


                                         The FBI had a crypto-messenger
                                         programmed that was fully
                                         intercepted. For legal reasons,
                                         the US authority received the
                                         intercepted communication via
                                         detours. Because of „hearsay
                                         court orders“, its use in German
                                         criminal proceedings is
                                         questionable.


                                  # ⚓ PIA ☛ Clearview_AI_Fined_in_Italy,_Starts
                                    Scanning_Dead_Russian_Soldiers_in_Ukraine⠀⇛


                                         The Italian authority imposed a
                                         fine of 20 million euros on
                                         Clearview AI, and ordered the
                                         company to delete all the data
                                         that it held relating to
                                         individuals in Italy. It also
                                         banned any further collection and
                                         processing of similar data. Since
                                         Clearview AI says that it does
                                         not have a place of business in
                                         Italy (or the EU), and does not
                                         have customers in Italy, it’s not
                                         clear whether the company will
                                         comply with the latest order.


                                  # ⚓ CNET ☛ Your_Digital_Footprint:_It’s
                                    Bigger_Than_You_Realize⠀⇛


                                         A few years ago, Ken Crum started
                                         getting uncomfortable with how
                                         much of his life seemed to be
                                         online. The long-time computer
                                         programmer was particularly
                                         concerned by what companies
                                         appeared to know about him.


                                         The amount of personal
                                         information was mind-boggling to
                                         the 66-year-old Texan, who
                                         recently moved from Dallas to the
                                         small town of Weatherford. Data
                                         brokers were collecting his
                                         personal details. Social media
                                         was targeting ads at him. Then
                                         one day, after shopping at a
                                         local home improvement store, he
                                         got an email from the company
                                         asking how his visit was. While
                                         he can’t be absolutely certain,
                                         he’s pretty sure the company used
                                         location-tracking on his work
                                         phone to find him.


                                         He found it all unnerving.


                                  # ⚓ The Atlantic ☛ TikTok_Has_a_Problem⠀⇛


                                         That leads to problem No. 2: Once
                                         a TikTok video starts to get
                                         attention, there are no checks on
                                         its spread. This may seem true of
                                         all kinds of viral content on any
                                         social platform, but there are
                                         subtle differences. A viral tweet
                                         or Facebook post rarely gains its
                                         reach without assistance: Tweets
                                         may blow up only after they’ve
                                         been retweeted by accounts with
                                         big followings, or by tight-knit
                                         clusters of accounts (such as
                                         those belonging to MAGA Twitter
                                         or K-pop fans); Facebook posts
                                         may not catch fire until they’ve
                                         been shared to big pages or in
                                         super-active groups. On TikTok,
                                         you don’t need a middleman. You
                                         just need to perform well in
                                         front of the test audience you’re
                                         granted by default. As a result,
                                         whenever a potential villain
                                         starts to surface, a pile-on can
                                         form even faster than it might on
                                         other platforms.


                                  # ⚓ Techdirt ☛ Elon_Musk_Is_Now_Twitter’s
                                    Largest_Shareholder;_And_That’s_Probably
                                    Not_A_Good_Thing⠀⇛


                                         Elon Musk appears to have a
                                         childlike understanding of free
                                         speech, especially with regards
                                         to how content moderation and
                                         free speech work together. But
                                         after running a silly poll a few
                                         weeks ago, many people assumed
                                         that the reason Musk was
                                         agitating to see if people felt
                                         that Twitter “supported” free
                                         speech, was that he might try to
                                         buy the company. It turns out, he
                                         was already in the process of
                                         trying to do so. On Monday it was
                                         announced that Musk has
                                         accumulated nearly 10% of
                                         Twitter’s shares, via some pocket
                                         change, making him the single
                                         largest shareholder in the
                                         company.


                                  # ⚓ New York Times ☛ Elon_Musk_becomes
                                    Twitter’s_largest_shareholder.⠀⇛


                                         The purchase, equal to 9.2
                                         percent of the company, appears
                                         to make Mr. Musk Twitter’s
                                         largest shareholder. His holding
                                         is slightly larger than
                                         Vanguard’s 8.8 percent at the end
                                         of last year, and it dwarfs the
                                         2.3 percent stake of Jack Dorsey,
                                         Twitter’s former chief executive.
                                         The shares represent a fraction
                                         of Mr. Musk’s reported $270
                                         billion-plus net worth.


                                  # ⚓ CNN ☛ Elon_Musk_buys_9.2%_stake_in
                                    Twitter,_making_him_the_largest
                                    shareholder⠀⇛


                                         Elon Musk recently purchased 9.2%
                                         of Twitter stock, according to a
                                         filing Monday, making him the
                                         largest individual shareholder in
                                         the company.


                                         News of the purchase sent shares
                                         of Twitter (TWTR) soaring 20% in
                                         premarket trading. Musk did not
                                         disclose what he paid for the
                                         shares, but his stake was worth
                                         $2.9 billion as of the close of
                                         trading Friday, and $3.5 billion
                                         after the spike early Monday.


                                         Musk’s filing did not disclose
                                         the purpose of the purchase or
                                         any plans for the company. But he
                                         has been a high-profile critic of
                                         Twitter policies in the past.
                                         Last month he said he was giving
                                         “serious thought” to creating a
                                         new social media platfor


                                  # ⚓ Everything Smart Home ☛ 5_Reasons_Your
                                    Smart_Home_Should_Be_Local⠀⇛


                                         The final reason a local smart
                                         home is better is for security
                                         reasons. With cloud connected
                                         devices your data is being sent
                                         out to someone else’s servers
                                         which means that it’s up to them
                                         to protect and secure your data.
                                         Now these companies do have lots
                                         of resources at their disposal
                                         and you would like to think that
                                         they are doing everything
                                         possible to keep your data secure
                                         but, unfortunately, this also
                                         makes them more lucrative
                                         targets. Also, just being a big
                                         company doesn’t necessarily mean
                                         they are following good security
                                         practices – the lawsuit against
                                         Amazon’s Ring video products are
                                         a perfect example of that.


                                         Now, again, you may not care if
                                         someone can control your lights –
                                         although that could get pretty
                                         tedious quickly – but think about
                                         when it comes to security
                                         cameras; doorbells, baby monitors
                                         even. You probably don’t want
                                         anyone being able to view those
                                         whenever they want.


          o § Defence/Aggression⠀➾


                # ⚓ Craig Murray ☛ Striving_to_Make_Sense_of_the_Ukraine_War⠀⇛


                       No matter how hard we try to be dispassionate and
                       logical, our thinking is affected by our own
                       experiences, by the background knowledge we have
                       and by the assumptions they generate. In discussing
                       Ukraine – which arouses understandably high
                       passions – I want to explain to you some of the
                       experiences which affect my own thinking.


                # ⚓ Meduza ☛ ‘Suddenly,_these_outdated_ideas_are_being_used_to
                  justify_mass_murder’:_Why_Russia’s_war_against_Ukraine_is_the
                  logical_continuation_of_Russian_state_ideology.⠀⇛


                       For years, Russia’s official ideology has revolved
                       around the myth that the country is in danger and
                       its enemies are trying to destroy it. The war in
                       Ukraine is the logical continuation of this myth.
                       To learn how deep the historical foundations for
                       this conflict go, Meduza turned to Andrei Zorin, a
                       professor at the University of Oxford who studies
                       the history of Russian state ideology and the
                       cultural and political myths that support it.


                # ⚓ Meduza ☛ ‘Our_psyche_is_blown’:_Eyewitness_accounts_of_life
                  in_Bucha_under_Russian_occupation⠀⇛


                       For the third day in a row, international media
                       remains flooded with horrifying reports about
                       hundreds of civilians killed in Bucha, Ukraine.
                       Russian forces began occupying this and other
                       satellite cities of Kyiv in early March, but have
                       since retreated from the Kyiv region altogether. In
                       their wake, independent journalists have recorded
                       haunting scenes: in Bucha, the lifeless bodies of
                       civilians were left lying in the streets — some of
                       the victims had their hands tied behind their
                       backs. Predictably, the Russian Defense Ministry
                       claimed that the photos and videos emerging from
                       Bucha were “staged” by the authorities in Kyiv.
                       Meduza compiles eyewitness accounts of life in
                       Bucha under Russian occupation, as told to
                       journalists.


                # ⚓ Meduza ☛ ‘They_gave_their_rations_to_the_people_in_the
                  basement,_then_threw_down_a_grenade’:_Bucha_City_Council
                  Deputy_Kateryna_Ukraintseva_describes_life_under_Russian
                  occupation.⠀⇛


                       After the Russian army’s retreat from Ukraine’s
                       Kyiv region, dozens of civilians were found dead in
                       the city of Bucha, some of them with their arms
                       tied behind their backs. As of April 4, 410
                       civilian bodies have been removed from the recently
                       liberated towns. The Russian Defense Ministry said
                       that the images and videos from Bucha were “staged
                       by the Kyiv regime” — this is Russia’s standard
                       reaction to both statements from the Ukrainian
                       authorities and materials from independent
                       journalists reporting on the war. To learn what
                       life was like under Russian occupation, Meduza
                       spoke to Bucha City Council Deputy and Ukrainian
                       Territorial Defense Forces volunteer Kateryna
                       Ukraintseva.


                # ⚓ Meduza ☛ ‘Russia’s_culture_died_along_with_these
                  Ukrainians’:_The_world_reacts_to_evidence_of_Russian
                  atrocities_in_Bucha⠀⇛


                       On April 2, the Internet was flooded with photos
                       showing dozens of murdered civilians on the streets
                       of Bucha and other towns in Ukraine’s Kyiv region
                       that were recently freed from Russian occupation.
                       Since then, new eyewitness accounts and official
                       reports of the crimes committed in the occupied
                       territories have appeared; meanwhile, the Russian
                       authorities have declared the images and accounts
                       “fake” and a “provocation.” Meduza has compiled the
                       world’s reactions to the news so far.


                # ⚓ Counter Punch ☛ Save_the_Planet,_Behead_the_Military
                  Budget⠀⇛


                       Ouch!


                       Peter Isaacson, writing in Fair Observer, seems to
                       be saying . . . oh my God, democracy is a cliché, a
                       big sham. I stand up, put my hand on my heart,
                       pledge allegiance to the flag. This is America,
                       land of the empowered voter. Then I read about our
                       president’s latest budget proposal, which includes
                       $813 billion for “national defense” — pushing the
                       Pentagon budget’s already record-setting enormity
                       further into outer space — and I feel myself
                       collapse (yet again) into nothingness.


                # ⚓ Counter Punch ☛ Why_Biden_Can’t_Woo_the_Middle_East⠀⇛


                       Washington’s troubled relations with its Middle
                       Eastern allies have become particularly pronounced
                       since Russia began its invasion of Ukraine. Though
                       all the Middle Eastern countries that are American
                       allies—Saudi-led Gulf states, Israel, Egypt and
                       Turkey—condemned Russia at the UN Resolution in
                       March for starting a war with Ukraine, only Israel
                       has implemented sanctions, albeit minimally. The
                       reluctance to impose sanctions by the United
                       States’ allies in the Middle East reflects their
                       intention to avoid antagonizing Russia, which is
                       increasingly influential in the region, and also
                       reflects their dissatisfaction with Washington and
                       confirms the perception that its influence in the
                       region is waning.


                       U.S. relations with Saudi Arabia began to
                       deteriorate notably in 2015. The Iran nuclear deal
                       implemented by former President Barack Obama caused
                       considerable alarm in Riyadh, while Saudi Arabia’s
                       intervention in Yemen, which also began that year,
                       received only lukewarm U.S. support. Obama’s
                       successor, President Donald Trump, took a more pro-
                       Saudi approach upon entering the White House in
                       2017, traveling to Saudi Arabia on his first
                       foreign trip as president and increasing weapons
                       salesto the country.


                # ⚓ Counter Punch ☛ Afghan_Evacuees_Still_Lack_a_Clear_Path_for
                  Resettlement_in_the_U.S.,_7_Months_After_Taliban_Takeover⠀⇛


                       The United States said on March 24, 2022, that it
                       would welcome 100,000 Ukrainian refugees.


                       The Ukrainian refugee situation continues to
                       overshadow another refugee crisis. That crisis
                       stems from the U.S. military’s official withdrawal
                       from Afghanistan in August 2021.


                # ⚓ Counter Punch ☛ Ukraine_and_the_Global_Economic_War:_Is
                  This_Barbarism_or_Civilization?⠀⇛


                       The threat to the dollar hegemony is only one part
                       of the fallout. The complex supply chains, built on
                       the premise of a stable trading regime of the World
                       Trade Organization principles, are also threatening
                       to unravel. The United States is discovering that
                       Russia is not simply a petrostate as they thought
                       but that it also supplies many of the critical
                       materials that the U.S. needs for several
                       industries as well as its military. This is apart
                       from the fact that Russia is also a major supplier
                       of wheat and fertilizers.


                       Seizing Russia’s funds means that the faith in the
                       United States as the world’s banker and in the
                       dollar as the global reserve currency is in
                       question. Why should countries maintain any trade
                       surplus and bank it abroad if that surplus can be
                       seized at will through sanctions imposed by the
                       West? The promise of a dollar as the world’s
                       reserve currency was that all surpluses in dollars
                       were safe. With the seizure of the Afghan central
                       bank’s $9.5 billion, and allocating $7 billion out
                       of it, the United States has shown that it
                       considers the dollar reserves of another country,
                       held by the United States’ central bank, as its
                       money. It may be an economic asset in the books for
                       a country to maintain its currency reserves with
                       the U.S. central bank. But it is effectively a
                       political liability, as the U.S. government can
                       seize this asset at will. The United States has
                       earlier shown its capability of imposing sanctions
                       against countries such as Iraq, Libya and Venezuela
                       and seizing their assets that resulted in far-
                       reaching negative impacts for these countries. The
                       seizure of Russia’s foreign exchange reserves by a
                       handful of Western countries—ex-colonial and
                       settler-colonial states—shows that the so-called
                       rules-based order is now based on weaponizing the
                       dollar and the West’s control over the global
                       financial system.


                # ⚓ Common Dreams ☛ Biden_Demands_War_Crimes_Trial_for_Putin,
                  But_Will_US_End_Its_Opposition_to_ICC?⠀⇛


                       While U.S. President Joe Biden echoed human rights
                       defenders on Monday by calling Russian President
                       Vladimir Putin “a war criminal” in response to what
                       Ukrainian officials described as a “deliberate
                       massacre” in Bucha, the American leader’s remarks
                       also highlighted a refusal by his government to
                       acknowledge or face consequences for the United
                       States’ crimes abroad.


                       Recalling his remarks from mid-March, Biden told
                       reporters outside the White House on Monday that
                       “you may remember I got criticized for calling
                       Putin a war criminal. Well, the truth of the
                       matter—you saw what happened in Bucha… He is a war
                       criminal.”


                # ⚓ Common Dreams ☛ Opinion_|_Why_the_US_Must_Practice
                  Restraint⠀⇛


                       In Western military circles, it’s common to refer
                       to the “balance of forces”—the lineup of tanks,
                       planes, ships, missiles, and battle formations on
                       the opposing sides of any conflict. If one has
                       twice as many combat assets as its opponent and the
                       leadership abilities on each side are approximately
                       equal, it should win. Based on this reasoning, most
                       Western analysts assumed that the Russian army—with
                       a seemingly overwhelming advantage in numbers and
                       equipment—would quickly overpower Ukrainian forces.
                       Of course, things haven’t exactly turned out that
                       way. The Ukrainian military has, in fact, fought
                       the Russians to a near-standstill. The reasons for
                       that will undoubtedly be debated among military
                       theorists for years to come. When they do so, they
                       might begin with Moscow’s surprising failure to pay
                       attention to a different military equation—the
                       “correlation of forces”—originally developed in the
                       former Soviet Union.


                # ⚓ Common Dreams ☛ ‘Dark_Day_for_Democracy’_in_Hungary_as
                  Orbán_Wins_Dubious_Reelection⠀⇛


                       Democracy defenders on Monday warned of ominous
                       consequences as right-wing Hungarian President
                       Viktor Orbán was overwhelmingly elected to his
                       fourth term in a contest progressive observers said
                       was unfairly stacked against the opposition.


                       “Hungary seems to have reached a point of no
                       return.”


                # ⚓ Democracy Now ☛ Mass_Graves_in_Kyiv_Suburb_of_Bucha;
                  Amnesty_Int’l_Documents_Unlawful_Killing_of_Civilians_in
                  Ukraine⠀⇛


                       Ukrainian officials are accusing Russia of
                       committing war crimes for killing civilians.
                       Ukrainian President Volodymyr Zelensky and EU
                       leaders condemned images of dead civilians in the
                       Kyiv suburb of Bucha, where corpses were found
                       littering the streets after Russian troops withdrew
                       from the area, some with their hands bound behind
                       their backs. On Friday, Amnesty International also
                       published a report that independently verified
                       Russia has violated international law in using
                       banned cluster munitions and other weapons that
                       indiscriminately kill civilians. “What’s been going
                       on during the entire more than a month now of
                       conflict merits serious investigation and
                       accountability for the perpetrators,” says Joanne
                       Mariner, crisis response director at Amnesty
                       International, who co-authored the report. “Given
                       this relentless bombardment of civilian
                       neighborhoods and districts, we’re calling for the
                       establishment of safe humanitarian corridors to
                       allow civilians to escape.”


                # ⚓ The Nation ☛ Putin’s_Miscalculation_Should_Be_a_Lesson_to
                  the_US⠀⇛


                       In Western military circles, it’s common to refer
                       to the “balance of forces”—the lineup of tanks,
                       planes, ships, missiles, and battle formations on
                       the opposing sides of any conflict. If one has
                       twice as many combat assets as its opponent and the
                       leadership abilities on each side are approximately
                       equal, it should win. Based on this reasoning, most
                       Western analysts assumed that the Russian army—with
                       a seemingly overwhelming advantage in numbers and
                       equipment—would quickly overpower Ukrainian forces.
                       Of course, things haven’t exactly turned out that
                       way. The Ukrainian military has, in fact, fought
                       the Russians to a near-standstill. The reasons for
                       that will undoubtedly be debated among military
                       theorists for years to come. When they do so, they
                       might begin with Moscow’s surprising failure to pay
                       attention to a different military equation—the
                       “correlation of forces”—originally developed in the
                       former Soviet Union.


                # ⚓ The Nation ☛ “Mothers’_March_for_Ukrainian_Children”⠀⇛


                # ⚓ ABC ☛ Family_of_slain_journalist_testifies_about_ransom
                  demands⠀⇛


                       The Islamic State terrorists who kidnapped American
                       journalist James Foley never made serious attempts
                       to negotiate a ransom before brutally executing
                       him, family members testified Monday.


                       Foley’s brother and mother took the witness stand
                       at U.S. District Court in Alexandria at the terror
                       trial of El Shafee Elsheikh, a Briton accused of
                       played a leading role in a hostage-taking scheme
                       that resulted in the deaths of Foley and three
                       other Americans — Steven Sotloff, Peter Kassig and
                       Kayla Mueller.


          o § Environment⠀➾


                # ⚓ Common Dreams ☛ Campaigners_Say_IPCC_Report_Reveals_‘Bleak
                  and_Brutal_Truth’_About_Climate_Emergency⠀⇛


                       A United Nations report on the climate
                       emergency—released Monday after negotiations
                       spilled into overtime—sparked a fresh wave of calls
                       for bolder and scientifically informed action to
                       rapidly and dramatically reduce planet-heating
                       emissions for the sake of all life on Earth.


                       “This monumental climate report is distressing but
                       it is not surprising.”


                # ⚓ Common Dreams ☛ Opinion_|_The_Cost_of_Not_Acting_on
                  Climate?_US_Govt_Study_Says_$2_Trillion_Per_Year_by_2100⠀⇛


                       Journalist Timothy Gardner at Reuters has gotten an
                       advance look at a White House Office of Management
                       and Budget document that concludes that by the end
                       of this century, when Olivia Rodrigo would be 100
                       if she has the long life we wish for her, the
                       annual cost of the climate crisis we are causing
                       will amount to $2 trillion a year in today’s
                       dollars.


                # ⚓ Common Dreams ☛ ‘Climate_Revolution’:_Scientists_Launch
                  Global_Civil_Disobedience_Campaign⠀⇛


                       Scientists from around the world on Monday
                       mobilized to demand a “Climate Revolution,” holding
                       rallies and staging acts of civil disobedience with
                       the goal of making the planetary emergency
                       “impossible to ignore.”


                       With a kick-off timed to coincide with Monday’s
                       release of the latest report from the
                       Intergovernmental Panel on Climate Change (IPCC),
                       researchers across the globe this week will
                       participate in the Scientist Rebellion, staging
                       strikes and occupations at universities, research
                       institutes, and scientific journals to demand that
                       the community speak out forcefully against
                       continued fossil fuel emissions to highlight “the
                       urgency and injustice of the climate and ecological
                       crisis.”


                # ⚓ Common Dreams ☛ IPCC_Report_Release_Delayed_as_Rich_Nations
                  Sought_to_Weaken_Fossil_Fuel_Phaseout⠀⇛


                       The publication of the third and final part of the
                       United Nations’ latest comprehensive climate
                       assessment, originally scheduled for early Monday
                       morning, was postponed by several hours after a
                       contentious weekend of negotiations in which
                       wealthy governments attempted to weaken statements
                       about green financing for low-income nations and
                       fossil fuel-producing countries objected to
                       unequivocal language about the need to quickly
                       ditch coal, oil, and gas.


                       The landmark report by Working Group III of the
                       Intergovernmental Panel on Climate Change
                       (IPCC)—written by dozens of climate scientists from
                       around the world who synthesized the past eight
                       years of relevant research—is expected to call for
                       a rapid global phaseout of fossil fuels to avoid
                       the planetary emergency’s most dire consequences.


                # ⚓ Counter Punch ☛ Movement_Generation_Works_to_Usher_in_a
                  Sustainable_Just_Transition⠀⇛


                       “At that time, most of my peers in urban organizing
                       weren’t even discussing climate change,” says Nube.
                       “Once we started digging into it, we realized our
                       peers organizing in Miami might be underwater 50
                       years from now, and that climate change was a
                       symptom of a much deeper set of interlocking crises
                       rooted in industrial extractivism.”


                       In 2006, Nube and his colleagues co-founded the
                       Movement Generation Justice and Ecology Project to
                       create an analytical foundation for organizers
                       interested in the relationship between ecology and
                       social justice, and as a hub for strategic
                       organizing efforts through workshops, retreats and
                       campaign development.


                # ⚓ Counter Punch ☛ What_Those_Who_Feed_Us_Deserve⠀⇛


                # ⚓ Counter Punch ☛ ‘Oh,_That_House?_It’s_in_the_Sea_Now:”
                  India’s_Disappearing_Coastline⠀⇛


                # ⚓ Common Dreams ☛ Opinion_|_Big_Oil’s_Hypocrisy_Laid_Bare_by
                  Russia’s_War_on_Ukraine⠀⇛


                       CEOs of major oil and gas companies have been
                       called to testify before at least three
                       congressional committees about their record profits
                       as Russia wages an unjust war in Ukraine and gas
                       prices remain volatilely high, disproportionately
                       affecting low-income and fixed-income families. The
                       oil and gas industry has been in the spotlight for
                       its role in the humanitarian catastrophe whose
                       effects are rippling across the globe. It’s no
                       wonder these companies are spinning up a PR
                       campaign to promote their businesses as the answer
                       to our problems, publicly withdrawing from Russia,
                       and showing up at the White House to offer support
                       to the Biden administration’s efforts to end the
                       invasion and limit its economic fallout.


                # ⚓ Common Dreams ☛ UN_Chief:_Those_Expanding_Fossil_Fuels—Not
                  Climate_Activists—Are_the_‘Truly_Dangerous_Radicals’⠀⇛


                       Following the publication of a key United Nations
                       climate report on Monday, U.N. Secretary-General
                       António Guterres took aim at governments and
                       corporations—whom he accused “a litany of broken
                       climate promises”—while defending the activists
                       fighting for a future free from fossil fuels.


                       “The truly dangerous radicals are the countries
                       that are increasing the production of fossil fuels.
                       Investing in new fossil fuels infrastructure is
                       moral and economic madness.”


                # § Energy⠀➾


                      # ⚓ DeSmog ☛ Biden’s_Call_to_Increase_LNG_Export_Capacity
                        on_Gulf_Coast_is_Tantamount_To_Sarah_Palin’s_Call_to
                        ‘Drill_Baby_Drill’_According_to_Environmental
                        Advocates⠀⇛


                             Travis Dardar, an indigenous fisherman in
                             Cameron, Louisiana, has a front-row view of
                             the expansion of the liquified natural gas
                             (LNG) industry’s export capacity on the Gulf
                             Coast — and it isn’t pretty. “It disgusts me
                             what man is doing to the planet,” Dardar told
                             me as I photographed flares at the recently
                             built Venture Global Calcasieu Pass LNG
                             export facility from his boat out in the
                             Calcasieu Ship Channel, which empties into
                             the Gulf of Mexico.


                             I met Travis and his wife Nicole Dardar on
                             March 17, before attending an air quality
                             permit hearing held by the Louisiana
                             Department of Environmental Quality (LDEQ) in
                             Cameron for another proposed LNG export
                             project by Commonwealth LNG, a Texas-based
                             company.


                      # ⚓ Wired ☛ Europe’s_Biggest_Lithium_Mine_Is_Caught_in_a
                        Political_Maelstrom⠀⇛


                             Europe has big plans to phase out fossil-fuel
                             cars. In July, the European Union proposed a
                             ban on the sale of new petrol and diesel cars
                             by 2035. The bloc wants to replace those cars
                             with electric vehicles, built with locally
                             produced raw materials like lithium. The top
                             lithium producers are currently Australia,
                             Chile, and China. But Europe has ambitions to
                             produce more of the materials it needs for
                             electric cars at home. These materials “are
                             extremely expensive to ship and are
                             transported across the world several times
                             over,” says Emily Burlinghaus, a fellow at
                             the Institute for Advanced Sustainability
                             Studies in Germany. “So it’s much cheaper and
                             much safer to have these operations close to
                             battery manufacturing plants or auto
                             manufacturing plants.”


                             For Europeans it’s also a security issue. “We
                             cannot allow [the EU] to replace [its]
                             current reliance on fossil fuels with
                             dependency on critical raw materials,” said
                             Maroš Šefčovič, the commission vice president
                             for inter-institutional relations, in 2020.


                      # ⚓ The Nation ☛ The_Case_Against_Closing_Nuclear_Power
                        Plants⠀⇛


                             On a bright spring day in 1979, before
                             thousands who were propelled to Washington,
                             D.C., by the Three Mile Island reactor
                             meltdown, I pronounced nuclear power’s rapid
                             expansion disastrously unaffordable. My
                             remarks drew on years of work chronicling
                             reactors’ skyrocketing capital costs.


                # § Wildlife/Nature⠀➾


                      # ⚓ The Revelator ☛ Oil_Development_Is_Changing_the_Rules
                        of_the_Game_for_Wildlife⠀⇛


                # § Overpopulation⠀➾


                      # ⚓ New York Times ☛ I’m_a_Scientist_in_California.
                        Drought_Is_Worse_Than_We_Thought.⠀⇛


                             We are looking down the barrel of a loaded
                             gun with our water resources in the West.
                             Rather than investing in body armor, we’ve
                             been hoping that the trigger won’t be pulled.
                             The current water monitoring and modeling
                             strategies aren’t sufficient to support the
                             increasing number of people that need water.
                             I’m worried about the next week, month, year,
                             and about new problems that we’ll inevitably
                             face as climate change continues and water
                             becomes more unpredictable.


                      # ⚓ The Nation ☛ Can_Las_Vegas_Be_Made_Sustainable?⠀⇛


                             Las Vegas is all about light. Despite its
                             desert location and the sunsets that turn the
                             surrounding mountains and red-rock canyons
                             all colors of delicate pink, the lights for
                             which Las Vegas is most renowned are
                             electronic, the kind that blur the line
                             between night and day and leave visitors to
                             Las Vegas always feeling that they have,
                             somehow, stepped outside of normal time. Huge
                             television screens, some the size of 10-story
                             buildings, illuminate both the insides of
                             casinos and the edifices of their exterior.
                             Inside, gambling palaces are filled with
                             countless thousands of blinking slot
                             machines, alongside malls and food courts and
                             bars and theaters all flooded with a
                             fluorescent glow that creates an endless
                             afternoon.


          o § Finance⠀➾


                # ⚓ Common Dreams ☛ Opinion_|_The_Poor_People’s_Campaign_Gears
                  Up_for_Its_National_March_in_June⠀⇛


                       On March 28, the Poor People’s Campaign: A National
                       Call for Moral Revival brought together a diverse
                       coalition of participants in Madison, Wisconsin, to
                       march for the rights of poor and low-wage workers
                       across the United States. A parallel event took
                       place in Raleigh, North Carolina; both were part of
                       a buildup to a national march planned for June 18
                       in Washington, D.C.


                # ⚓ Common Dreams ☛ ‘Pick_Up_the_Pen,_Joe’:_DC_Protest_Calls_on
                  Biden_to_Cancel_Student_Debt⠀⇛


                       Hundreds of people converged in Washington, D.C. on
                       Monday for a national day of action to demand that
                       the Biden administration cancel all outstanding
                       federal student loan debt via executive order.


                       “All he needs to do is sign an executive order.
                       What is Biden waiting for?”


                # ⚓ FAIR ☛ Corporate_Press_Scapegoats_Vulnerable_Homeless_for
                  Rise_in_Subway_Crime⠀⇛


                       A homeless man allegedly pushed 40-year-old
                       Michelle Go in front of an oncoming train at a New
                       York City subway station on January 15, killing
                       her. The high-profile attack received worldwide
                       coverage, with widespread reporting emphasizing
                       crimes committed by people without homes in New
                       York and around the country.


                # ⚓ Counter Punch ☛ Wages_Up_by_$1.2_Trillion_Since_Biden_Takes
                  Office,_$9,400_per_Household⠀⇛


                       This is worth noting, because the news media have
                       filled their pages and broadcasts with stories of
                       workers who are suffering because of the rise in
                       gas prices and inflation more generally. There are
                       undoubtedly many workers who are seriously
                       suffering, but this is always true. Since labor
                       income is higher today than it was before the
                       pandemic, we can reasonably infer that many more
                       workers were having trouble making ends meet in
                       2019 than today. If we hear more stories of
                       hardship now, it is because of the decision by the
                       media to give us more stories of hardship, not
                       because more stories exist in the world.


                       For those who want a picture of how labor income
                       growth since Biden took office compares with prior
                       years, here’s the picture since 2010.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ Counter Punch ☛ Putin_is_Being_Written_Off_as_an
                  Ineffectual_Monster,_but_a_Russian_Defeat_is_Far_From
                  Guaranteed⠀⇛


                       I was struck at the time by Putin’s cold smile and
                       athletic stride, both self-consciously geared to
                       conveying an impression of business-like authority.
                       I wondered what the man was really like, as did
                       many Russians curious about his public persona. One
                       joke in Moscow, adapted from a jibe often directed
                       at Soviet leaders in the past, asked: “Will there
                       ever be a Putin personality cult? No, because to
                       have such a cult you must first have a
                       personality.”


                       This put-down probably underestimated Putin. And in
                       any case, his control of the Russian media enabled
                       him to pose as a competent “tough-guy” national
                       leader. But for me he always remained an elusive
                       figure, expert in the mechanics of gaining and
                       keeping power in Russia while making a broad-brush
                       appeal to Russian nationalism.


                # ⚓ Counter Punch ☛ Is_Biden_Channeling_Tom_Paine_on_Taxes?⠀⇛


                # ⚓ Counter Punch ☛ Not_to_Rewrite_the_History_of_the
                  Dictatorship⠀⇛


                       Very well. But first, in order not to rewrite
                       history without contextualizing the time, one must
                       not rewrite the days of the calendar. For in the
                       coup propaganda, the first of April 1964 was always
                       brought forward to the 31st of March. Trying to
                       avoid the joke, the universal day of lies, they
                       lied in anticipation. They said that everything was
                       done on March 31. And the revolution was decreed.


                       In doubt, so as not to fall into historical
                       revisionism, look at the Brazilian newspapers of
                       April 2nd, 1964:


                # ⚓ TruthOut ☛ Watergate_Prosecutor_Calls_7-Hour_Gap_in_Trump
                  Phone_Records_“Suspicious”⠀⇛


                # ⚓ TruthOut ☛ How_the_World’s_Not-So-Great_Powers_Are
                  Miscalculating_on_Ukraine⠀⇛


                # ⚓ TruthOut ☛ Sanders_Announces_Budget_Committee_Hearing_on
                  Corporate_Greed_and_Profiteering⠀⇛


                # ⚓ TruthOut ☛ US_Charitable_Donations_Are_Funding_Displacement
                  of_Palestinians⠀⇛


                # ⚓ TruthOut ☛ January_6_Committee_Says_Criminal_Referral_on
                  Trump_to_DOJ_May_Be_Unnecessary⠀⇛


                # ⚓ TruthOut ☛ Betsy_DeVos_and_Her_Family_Are_Flooding_Florida
                  Gov._Ron_DeSantis_With_Cash⠀⇛


                # ⚓ Hungary ☛ If_Fidesz_won,_why_is_the_so-called_“child
                  protection”_referendum_invalid?⠀⇛


                       The so-called child protection referendum held on
                       Sunday, at the same time as the parliamentary
                       elections has been declared invalid. From the
                       appoximately 3.5 million valid answers which were
                       submitted, 3.2 million people voted “no”. But if so
                       many people gave the answer the government has been
                       pushing, and if the Fidesz-KDNP coalition won yet
                       another two-thirds majority, then how is it
                       possible that they were not able to get enough
                       valid votes that had four “no” answers to the
                       questions asked. The answer is simpler than one
                       might think.


                # ⚓ Hungary ☛ Viktor_Orbán’s_fourth_two-thirds_majority,_a
                  disaster_for_the_opposition_coalition_–_key_election
                  results⠀⇛


                       Now that the votes are almost all counted, we
                       present the key results of the 2022 parliamentary
                       elections. The bottom line: Viktor Orbán and
                       Fidesz-KDNP won by two-thirds for the fourth time,
                       the opposition coalition did much worse than
                       forecasted in all preliminary polls – winning
                       almost exclusively in Budapest’s constituencies.
                       Finally, Our Homeland Movement made it into
                       parliament. Translation by Dominic Spadacene


                # ⚓ Hungary ☛ President_of_Mi_Hazánk:_The_miracle_that_no_one
                  believed_in_has_happened⠀⇛


                       Well above the five percent threshold, with a list
                       vote share of 6.3 percent and over 310,000 list
                       votes, Mi Hazánk (Our Country) has entered
                       parliament as the third parliamentary force, if we
                       consider the opposition coalition as a bloc. After
                       the 2018 elections, the party of the more radical
                       MPs who broke away from the Jobbik party, can send
                       a total of 7 MPs to Parliament. Translation:
                       Dominic Spadacene


                # ⚓ NBC ☛ Elon_Musk_buys_9_percent_stake_in_Twitter⠀⇛


                       The stock-buying revelation comes as Musk emerges
                       as one of the loudest and most prominent critics of
                       Twitter’s moderation efforts, which in recent years
                       have cracked down on everything from harassment and
                       death threats to misinformation and conspiracy
                       theories.


                # ⚓ The Hill ☛ State_Department_formally_launches_new_cyber
                  bureau⠀⇛


                       The State Department launched its new Bureau of
                       Cyberspace and Digital Policy on Monday in what it
                       says is a modernization of the agency aimed at
                       emerging technology issues in diplomacy.


                       A statement issued by the department said the
                       bureau will address “the national security
                       challenges, economic opportunities, and
                       implications for U.S. values associated with
                       cyberspace, digital technologies, and digital
                       policy.”


                       It will consist of three policy units, including
                       international cyberspace security, international
                       information and communications policy, and digital
                       freedom.


                # ⚓ Helsinki Times ☛ Draft_of_Finland’s_digital_compass_sent
                  out_for_comments⠀⇛


                       Finland’s digital compass is based on the EU’s
                       Digital Compass, which was presented in spring
                       2021. Finland’s digital compass sets the level for
                       Finland’s national ambition with respect to the
                       objectives presented by the EU and sets national
                       objectives that go beyond those of the EU.


                       In line with the EU Digital Compass, Finland’s
                       digital compass revolves around four cardinal
                       points: skills, digital infrastructure, the digital
                       transformation of businesses, and digital of public
                       services. The compass includes prioritised national
                       objectives for each of these points up to 2030. The
                       compass also defines the measures required to reach
                       these objectives as well as progress indicators
                       that will be updated regularly.


                # ⚓ [Old] European Commission ☛ Europe’s_Digital_Decade:
                  digital_targets_for_2030⠀⇛


                       The Commission will provide an assessment of the
                       implementation of the digital principles in the
                       annual State of the Digital Decade report. The
                       Commission will also conduct an annual
                       Eurobarometer survey to monitor the follow-up
                       measures in the Member States. The Eurobarometer
                       will collect qualitative data, based on citizens’
                       perception of how the digital principles are put
                       into practice in various Member States. The
                       European Parliament and the Council of the European
                       Union will discuss the proposal before adoption.


          o § Misinformation/Disinformation⠀➾


                # ⚓ New York Times ☛ The_Latest_Covid_Misinformation_Star_Says
                  He_Invented_the_Vaccines⠀⇛


                       In spreading these exaggerations and unfounded
                       claims, Dr. Malone joins medical professionals and
                       scientists, like Dr. Joseph Mercola and Dr. Judy
                       Mikovits, whose profiles have grown during the
                       pandemic as they spread misinformation about mask-
                       wearing and convoluted conspiracy theories about
                       virus experts like Dr. Anthony Fauci


                # ⚓ Ofcom:_One_in_three_internet_users_cannot_spot_false
                  accounts_or_content⠀⇛


                       Some 30% of UK adults who use the internet – 14.5
                       million – are unsure about or do not even consider
                       the truthfulness of the information they see
                       online, the regulator’s annual survey found.


                       A further 6%, or about one in every 20 internet
                       users, believe everything they see online.


                       Both adults and children overestimate their ability
                       to spot misinformation, Ofcom found.


                # ⚓ Vox ☛ What_Chinese_media_is_saying_about_Russia’s_Ukraine
                  war⠀⇛


                       The close of the 2022 Beijing Olympics, on February
                       20, was a key moment in trying to decipher Russia’s
                       Ukraine invasion plans. Russian President Vladimir
                       Putin would wait until after the Games, the theory
                       went, so as not to distract from the Olympics and
                       to avoid jeopardizing any support Moscow would need
                       from Beijing.


                       Putin did wait, finally launching an invasion on
                       February 24. But China has not gone all-in on
                       Putin’s Ukraine war, despite Chinese President Xi
                       Jinping and Putin declaring there were “no limits”
                       to their friendship.


                       Instead, the Chinese government has tried to toe a
                       careful line. It has not condemned Russia’s
                       invasion. But though China has criticized Western
                       sanctions on Russia, it has not really moved to
                       help Russia evade them, and it looks like it’s
                       trying to avoid running afoul of the penalties. At
                       the same time, what it says and does outwardly may
                       be a lot different from what’s happening behind the
                       scenes.


          o § Censorship/Free Speech⠀➾


                # ⚓ TruthOut ☛ More_Book_Bans_Sought_in_2021_Than_Any_Other
                  Point_in_Past_20_Years,_Group_Says⠀⇛


                # ⚓ Censorship_in_Russia_and_its_impact_on_the_free_press_and
                  social_media⠀⇛


                # ⚓ CNX Software ☛ How_to_get_your_domain_suspended_in_five
                  easy_steps!_–_CNX_Software⠀⇛


                       Regular readers may have noticed CNX Software was
                       inaccessible for several days, and the reason was
                       that my domain was suspended. I’m a bit late for
                       April Fools’ day, but I’ll show how you can get
                       your domain suspended too in five easy steps! I’ll
                       also provide some background to what happened, and
                       several errors of judgment made along the way


                       What happened?


                       On March 28, as I woke up I noticed I could not
                       access the website and I had also received several
                       emails and mentions on social networks that the
                       website was down. I first tried to restart the LEMP
                       stack of the server nginx, mysql, php, but it did
                       not help. I quickly figured out there was a problem
                       with DNS, so I went to the Cloudflare dashboard
                       which is where I manage the DNS records, but I did
                       not see any problems there. Eventually, I saw the
                       domain name servers were changed to:
                       ns1.suspended.com and ns2.suspended.com, and I
                       could not change anything. So my domain was
                       suspended. CloudFlare is not managing the domain
                       registration, I only use it for the DNS records,
                       and they were not involved in this case at all.


                       Note that I did not receive any email or phone call
                       from the reseller where I purchased the domain in
                       2010. I first tried chat support but was told to
                       open a ticket, which was handled by the “billing”
                       department. I open the ticket on March 28th, 2022
                       (21:25) (some US timezone), and received an answer
                       on March 29th, 2022 (05:54) saying the domain was
                       suspended because of phishing. I know I’m not
                       running some phishing scam, so either the server
                       was hacked, or somebody had made a fake report to
                       take my domain down. I was not given the exact
                       reason yet, but a case was opened and was told I
                       would receive an email soon (to an email from my
                       suspended domain).


                       I replied I was probably the victim of fraud, and
                       so I had to refresh the ticket from time to time,
                       and on Tuesday, March 29th, 2022 (23:38), or 26
                       hours after opening the ticket I was given a
                       screenshot showing “definitive proof of my abusing
                       ways” (I make that up).


          o § Freedom of Information/Freedom of the Press⠀➾


                # ⚓ Don’t Extradite Assange ☛ Europe,_Justice_&_Press_Freedom:
                  The_Case_of_Julian_Assange_–_University_Lecture⠀⇛


          o § Civil Rights/Policing⠀➾


                # ⚓ Common Dreams ☛ Jackson’s_SCOTUS_Nomination_Clears
                  Deadlocked_Senate_Judiciary_Committee⠀⇛


                       Judge Ketanji Brown Jackson’s historic nomination
                       to the United States Supreme Court cleared a minor
                       hurdle Monday after the U.S. Senate overcame a
                       deadlocked Judiciary Committee via a procedural
                       vote in the upper chamber, where her confirmation
                       is all but guaranteed.


                       “I dream of a day where Black women don’t have to
                       be overqualified, jump through hoops, and face
                       misogynoir just to get to the jobs they already
                       deserve.”


                # ⚓ Techdirt ☛ New_Jersey_Town_Sues_82-Year-Old_Woman_For
                  Exercising_Her_Rights⠀⇛


                       It’s your right to request records from public
                       agencies. That fact cannot be disputed. The Freedom
                       of Information Act guarantees it in regards to
                       federal agencies and every state has their own laws
                       that guarantee access to public records.


                # ⚓ Techdirt ☛ Boulder_Councilwoman_Shared_Video_Claiming_That
                  5G_Is_An_‘Extinction_Level_Event’⠀⇛


                       Editor’s Note: After publication, we were alerted
                       the that key story about the councilwoman, was
                       actually from a few years ago, not recently. We
                       regret the mistake and will make efforts to avoid
                       such mistakes in the future. We’re leaving the
                       original article below.


                # ⚓ EFF ☛ Podcast_Episode:_Your_Tax_Dollars_At_Work⠀⇛


                # ⚓ Counter Punch ☛ Statement_of_Solidarity_&_Support_for
                  Walden_Bello_Amidst_Narco-Tagging_incident⠀⇛


                       In a recent statement released by Hugpong ng
                       Pagbabago (HNP or Alliance for Change), the
                       regional party founded by Sara Duterte, daughter of
                       Philippine President Rodrigo Duterte, activist-
                       scholar Professor Walden Bello was unfoundedly and
                       maliciously labeled as a “narco-politician.”


                       Prof. Bello is currently running for Vice President
                       under Laban ng Masa (Fight of the Masses), a left-
                       wing electoral coalition of democratic socialist
                       and progressive groups, against Sara Duterte and
                       several other candidates for the May 2022
                       Philippine National Elections. Last March 20, 2022,
                       in a televised debate, Prof. Bello called out the
                       issue of illicit drug trade in Davao City, dubbing
                       it the “Drug Center ” of Southern Philippines.
                       Prof. Bello questioned why the former aide of Sara
                       Duterte (Davao City’s incumbent Mayor) was
                       exonerated and freed despite clear involvement in a
                       recent drug bust in Davao. Prof. Bello also pointed
                       out that Sara Duterte’s refusal to attend the said
                       debate displayed a glaring lack of public
                       accountability in confronting the said issue,
                       against the backdrop of thousands killed in the
                       Duterte administration’s deadly “war on drugs”.


                # ⚓ Pro Publica ☛ Texas’_Border_Operation_Is_Meant_to_Deter
                  Cartels_and_Smugglers._More_Often,_It_Imprisons_Lone_Men_for
                  Trespassing.⠀⇛


                       For the past year, thousands of Texas National
                       Guard members and state troopers have been sweeping
                       through brush along the Rio Grande and cruising
                       border-town roadways. Their eyes scan the horizon
                       for the cartel operatives and smugglers whom Gov.
                       Greg Abbott vowed to hold at bay when he launched
                       his multibillion-dollar campaign to secure the
                       border.


                       But more often, the troopers arrest men like
                       Bartolo, a Mexican farmworker who came to the
                       United States looking for work, according to his
                       lawyers. They’ve also slapped cuffs on asylum-
                       seekers like Gastón, a human rights attorney who
                       said he fled Venezuela after being targeted by the
                       Maduro regime for defending political opponents.


                # ⚓ The Nation ☛ Black_Like_Me?_Bridgerton_and_the_Fantasy_of_a
                  Non-Racist_Past⠀⇛


                       When I first moved to the US from London, I asked
                       an American journalist what kind of reception I
                       might expect as a Black Briton. “Well, when they
                       hear an English accent, Americans usually add about
                       20 points to your IQ,” he said. “But when they see
                       a Black face, they usually don’t.” Recalling that
                       the authors of the book The Bell Curve had claimed
                       that Black people have an IQ 15 points lower than
                       whites, I figured that, at the very least, I would
                       still come out at least five points ahead.1


                # ⚓ The Nation ☛ Whose_Revolution?⠀⇛


                       To the surprise and consternation of scholars,
                       history has recently emerged as a battlefield in
                       the ongoing culture wars. Generally, historians
                       welcome public debate about the past. But new state
                       laws banning from classrooms any discussion of the
                       history of racism have been accompanied by so much
                       demagoguery and misinformation on the part of
                       legislators, school board officials, and agitated
                       parents that one is tempted to believe it would be
                       more edifying to ignore history altogether for the
                       time being.


                # ⚓ The Nation ☛ “F*ck_Leftist_Westsplaining!”⠀⇛


                       Berlin—This was once the fault line between East
                       and West in Europe. Almost 35 years after the
                       momentous change brought about by the fall of the
                       Wall, Germany still feels tied to two regions, two
                       histories. Russia’s invasion of Ukraine is viewed
                       and spoken about in a very different way here than
                       it is in the United States.


                # ⚓ Common Dreams ☛ Amazon_Union_Slams_Any_Attempt_to_‘Delay
                  Our_Hard-Won_Right_to_Bargain_Collectively’⠀⇛


                       In the wake of its historic victory in the election
                       to unionize Amazon’s JFK8 warehouse in Staten
                       Island, the Amazon Labor Union demanded over the
                       weekend that the company begin collective
                       bargaining negotiations in early May and
                       immediately halt any changes to employment policies
                       in the meantime.


                       “As you are aware, the Amazon Labor Union has
                       decisively won the union election,” Christian
                       Smalls, the president of ALU, wrote in a letter to
                       company management. “We are available to meet
                       anytime on May 2, 3, 4, or 5 of 2022 for collective
                       bargaining negotiations. Please provide your
                       available dates and times before close of business
                       on April 8, 2022.”


                # ⚓ Common Dreams ☛ Opinion_|_Amazon_Workers’_Historic_Win_and
                  Corporate_America’s_Ongoing_Greed⠀⇛


                # ⚓ Common Dreams ☛ ‘This_Seems_Totally_Illegal’:_Amazon_May
                  Ban_Union_Terms_in_Messaging_App⠀⇛


                       On the heels of a major organizing win for Amazon
                       workers in New York City last week, The Intercept
                       revealed Monday that the e-commerce giant is
                       considering a ban on various union-related terms
                       for a planned internal messaging application.


                       “In November 2021, Amazon convened a high-level
                       meeting in which top executives discussed plans to
                       create an internal social media program that would
                       let employees recognize co-workers’ performance
                       with posts called ‘Shout-Outs,’” according to
                       journalist Ken Klipperstein.


                # ⚓ The Hill ☛ Amazon_eyeing_plan_to_ban_words_such_as_‘union,’
                  ‘restrooms’_and_‘slave_labor’_from_internal_chat_app:
                  report⠀⇛


                       The “auto bad word monitor” reportedly blacklists
                       profanities and inappropriate terms but also
                       targets terms related to organized labor including
                       “union,” “grievance,” “pay raise,” “compensation”
                       and more.


                # ⚓ Democracy Now ☛ “We_Just_Unionized_Amazon”:_How_Two_Best
                  Friends_Beat_the_Retail_Giant’s_Union-Busting_Campaign⠀⇛


                       We speak with the two best friends who led a drive
                       to organize workers at Amazon’s warehouse in Staten
                       Island, New York, and made history Friday after a
                       majority voted to form the first Amazon union in
                       the U.S. We speak with Christian Smalls, interim
                       president of the new union and former Amazon
                       supervisor, about how he led the effort after
                       Amazon fired him at the height of the pandemic for
                       demanding better worker protections. “I think we
                       proved that it’s possible, no matter what industry
                       you work in, what corporation you work for,” says
                       Smalls. “We just unionized Amazon. If we can do
                       that, we can unionize anywhere.” We also speak with
                       Derrick Palmer, who works at the Amazon JFK8
                       warehouse in Staten Island and is the vice
                       president of the Amazon Labor Union, about
                       intimidation tactics the company used. Reporter
                       Josefa Velásquez covered the union drive for The
                       City and discusses what the victory means for the
                       broader labor movement.


                # ⚓ The Verge ☛ Amazon_union_workers_won_in_New_York_—_can_they
                  win_across_the_country?⠀⇛


                       The Amazon Labor Union (ALU) scored a historic
                       victory on April 1st when it became the first-ever
                       union to successfully organize Amazon employees.
                       Christian Smalls, a fired worker motivated by what
                       he viewed as poor treatment, rallied his co-workers
                       through the process and, in January 2022, got just
                       enough votes to qualify for a formal election. On
                       Friday, the workers of Amazon’s JFK8 warehouse
                       voted to unionize, 2,654 to 2,131.


                       It was a hard-won victory, coming after years of
                       work, and labor activists are already hoping to
                       apply the same tactics to the hundreds of thousands
                       of Amazon warehouse workers across the rest of the
                       country. After the RWDSU’s stumble in the Bessemer
                       election last year, the newly formed Amazon Labor
                       Union is pointing to a different path forward — and
                       forcing Amazon to take a hard second look at
                       working conditions in many of its fulfillment
                       centers.


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ Terry_Davis_Was_Right⠀⇛


                       In 2019, a pseudonymous hacker called Solderpunk
                       launched the Gemini network, a much simpler anti-
                       commercial alternative to the web. Gemini has less
                       than 1% of the complexity of the web, but can still
                       do the stuff that matters: delivering simple
                       hypertext documents. Further, it is designed
                       deliberately to never be able to do the things
                       enlightened users generally don’t want, like
                       tracking or complex scripting on what should just
                       be documents. The web itself has become so complex
                       that there may never be another web browser written
                       from scratch, but Gemini was designed to be simple
                       enough that any reasonably competent programmer
                       could write their own Gemini browser in a weekend,
                       so there are already dozens.
                       Gemini has exploded into a thriving scene of blogs
                       and social media, proving that it is possible for
                       any reasonably competent tech-prophet to overcome
                       the network effects of the metaverse borg with
                       their own niche alternative. It further
                       demonstrates an exemplary case of the higher
                       intentions of the software architect attempting to
                       structurally prevent later commercial adulteration.


          o § Monopolies⠀➾


                # ⚓ EFF ☛ Day_of_Action_for_Antitrust:_Our_Rights_Are_Tied_to
                  Having_Choices⠀⇛


                       We live in a world that increasingly requires us to
                       be online. The promise of all this technology was
                       that barriers would be lowered, allowing more
                       people to exercise their rights—especially rights
                       related to speech. For those who work in securing
                       rights for others, activists and journalists, for
                       example, this has been an invaluable change.


                # ⚓ Common Dreams ☛ Antitrust_Day_of_Action_Takes_Aim_at_Power
                  of_Tech_Giants⠀⇛


                       More than 100 advocacy groups were joined by some
                       of Silicon Valley’s smaller tech companies Monday
                       as they launched Antitrust Day, a day of action
                       aimed at pressuring federal lawmakers to pass
                       legislation that would rein in tech giants which
                       advocates say “pose an existential threat to
                       democracy” as they stifle competition and
                       disempower consumers.


                       Groups including Fight for the Future, Electronic
                       Frontier Foundation (EFF), and Demand Progress are
                       joining with Yelp, Patreon, DuckDuckGo, and other
                       internet companies to push for the passage of two
                       bills that would “increase competition, giving tech
                       users more control over their digital lives, and
                       reduce the monopoly power of Big Tech giants, which
                       has been abused as a choke point for censorship and
                       human rights violations,” according to organizers.


                # § Copyrights⠀➾


                      # ⚓ Creative Commons ☛ CC_publishes_policy_paper_titled
                        Towards_Better_Sharing_of_Cultural_Heritage_—_An_Agenda
                        for_Copyright_Reform⠀⇛


                      # ⚓ Torrent Freak ☛ Judge_Drops_Antitrust_Claims_From
                        YouTube_Piracy_Lawsuit⠀⇛


                             Florida federal Judge Darrin Gayles has
                             dismissed Content ID-related antitrust claims
                             against YouTube. The allegations were part of
                             a piracy lawsuit filed against the streaming
                             platform last year by movie tycoon Carlos
                             Vasallo. While the lawsuit has been slimmed
                             down, YouTube still has to defend itself
                             against copyright infringement claims.


                      # ⚓ Torrent Freak ☛ Pirate_IPTV:_Police_Organized_Crime
                        Unit_Arrests_Three_Men_in_UK⠀⇛


                             The North West Regional Organised Crime Unit
                             and Lancashire Police report that three men
                             have been arrested on suspicion of criminal
                             copyright infringement offenses. All from the
                             north of England, the men were arrested in
                             connection with the supply of pirate IPTV
                             services providing unlicensed access to
                             movies, TV shows and live sports.



                    ䷩ 𝚕𝚒𝚗𝚎 4811

╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 04.05.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_05/04/2022:_Firefox_99,_Q4OS_4.8,_and_LXD_5.0_LTS_Released⠀✐


Posted in News_Roundup at 4:58 pm by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Distributions
          o Devices/Embedded
    * Free_Software/Open_Source
    * Leftovers
    * § GNU/Linux⠀➾


          o § Server⠀➾


                # ⚓ Most_Reliable_Hosting_Company_Sites_in_March_2022 [Ed: GNU/
                  Linux dominant, as usual]⠀⇛


                       The most reliable hosting company site in March
                       2022 was Aruba, which has now topped the table for
                       four months in a row. Aruba provides hosting, cloud
                       and digital signature services, fibre optic
                       internet, digital preservation, and more. The
                       company has data centres across Europe, in the UK,
                       Germany, Czechia, Poland, Italy and France.


          o § Audiocasts/Shows⠀➾


                # ⚓ Video ☛ deepin_20.5_overview_|_Beautiful_and_Wonderful_–
                  Invidious⠀⇛


                       In this video, I am going to show an overview of
                       deepin 20.5 and some of the applications pre-
                       installed.


                # ⚓ 272:_Behind_The_Scenes_of_Destination_Linux_–_Destination
                  Linux⠀⇛


                       This week’s episode of Destination Linux, we’re
                       taking you on a behind the scenes tour of our
                       studio setups. All the equipment we use each week
                       to produce this show…DL which is quite unique being
                       that it’s a live video and audio podcast. We’re
                       also going to discuss the amazing open-source
                       software that powers it all. Then we’re going to
                       talk about the upcoming Thunderbird email client
                       release. Plus we’ve also got our famous tips,
                       tricks and software picks. All of this and so much
                       more this week on Destination Linux. So whether
                       you’re brand new to Linux and open source or a guru
                       of sudo. This is the podcast for you.


                # ⚓ LHS_Episode_#462:_Hamfest_and_LHS_Deep_Dive_|_Linux_in_the
                  Ham_Shack⠀⇛


                       Hello and welcome to Episode #462 of Linux in the
                       Ham Shack. In this episode, the hosts take on two
                       topics. The first is the art and science of the
                       hamfest, exploring what happens at hamfests, what
                       you can do, how you can participate and how you can
                       benefit. Then we discuss future changes to the
                       format and schedule of Linux in the Ham Shack to
                       keep everyone informed and explain how these
                       updates will make the show better. Thanks for
                       listening and have a great week.


                # ⚓ Late_Night_Linux_–_Episode_171_–_Late_Night_Linux⠀⇛


                       A varied selection of Discoveries including
                       Telegraf, writing tools, a book about networking,
                       and fixing a Mac. Plus your feedback about Matrix
                       bridges, virtualisation, Pocket alternatives, the
                       BBC, game development, and more.


                # ⚓ Jupiter Broadcasting ☛ Synapse_Collapse_|_LINUX_Unplugged
                  452⠀⇛


                       How we nearly crashed our Matrix server; what we
                       did wrong and how we’re fixing it.


                       Plus an update on elementary OS, GNOME’s next
                       chapter, and we kick off the NixOS Challenge.


                # ⚓ Headline_Hangout_w/Chris_|_Jupiter_Extras_85⠀⇛


                       Chris’s thoughts on Linux’s NVIDIA conundrum,
                       Elon’s takeover of Twitter, MailChimp’s insider
                       hack, and the Google Drones taking off in Texas.


          o § Applications⠀➾


                # ⚓ 9to5Linux ☛ Fwupd_1.7.7_Adds_Support_for_Logitech_M550,
                  M650_and_K650,_More_StarLite_Laptops⠀⇛


                       Coming one and a half months after fwupd 1.7.6,
                       which added support for Star Labs’ Star Lite Mk III
                       laptop, the fwupd 1.7.7 release is here with
                       support for even more of Star Labs’ StarLite Linux-
                       powered laptops, though no specific model is
                       mentioned in the release notes at this time, so if
                       it works with your device you’re in luck.


                # ⚓ LWN ☛ LXD_5.0_LTS_released⠀⇛


                       
                       The LXD team is proud to announce the release of
                       LXD 5.0 LTS!

                       LXD is a system container and virtual machine
                       manager which provides a
                       cloud-like user experience.
                       It can work on any regular Linux system from a
                       simple laptop all the
                       way to a large cluster of servers.

                       As a Long Term Support release, LXD 5.0 will be
                       getting upstream
                       bugfix and security support until June 2027.
                       The first two years will include frequent bugfix
                       releases and the
                       remaining three years will be limited to security
                       fixes.
                # ⚓ IT Pro Portal ☛ Best_remote_desktop_for_Linux_in_2022_|
                  ITProPortal⠀⇛


                       Choosing the best remote desktop for Linux will
                       enable you to access computers and mobile devices
                       remotely from your Linux computer. But there are
                       far fewer options available for Linux users than
                       for Windows or Mac owners, and these tend to be
                       much more difficult to use.


                       This can make it hard to select the right option,
                       particularly if you don’t want too steep of a
                       learning curve. Many Linux remote desktops are
                       open-source and versatile, but they also require
                       significant tech skills to install and use.


                       To help you find your way through the confusing
                       jargon surrounding Linux remote desktops and select
                       the right option for your business, we’ve put
                       together this guide. In it, we take a close look at
                       the leading Linux remote desktop programs available
                       today.


                # ⚓ GamingOnLinux ☛ A_new_tool_‘unsnap’_helps_you_move_from
                  Snaps_to_Flatpaks_|_GamingOnLinux⠀⇛


                       Want to migrate over from Snaps to Flatpaks on your
                       Linux machine? Well, unsnap is a new tool in the
                       early stages that will help you do just that.
                       Developed by Alan Pope, who previously worked for
                       Canonical and was an advocate for Snap packages,
                       it’s certainly an eyebrow raising move.


                       The idea is simple: to allow you to quickly and
                       easily migrate from Snap to Flatpak applications.
                       Done over a two-stage process, it allows you to
                       “view and/or edit the scripts prior to execution to
                       validate or tweak them”.


          o § Instructionals/Technical⠀➾


                # ⚓ TechRepublic ☛ How_to_switch_ChromeOS_to_use_Debian
                  Bullseye_|_TechRepublic⠀⇛


                       If you’ve added Linux support to your Chromebook,
                       chances are pretty good it’s not using the latest
                       version of Debian (which is version 11.3, aka
                       “Bullseye”). Given that there are several important
                       security and bug fixes to this release, you
                       shouldn’t think twice about upgrading it on your
                       Chromebook.


                # ⚓ Linux Journal ☛ How_to_Install_and_Uninstall_KernelCare_|
                  Linux_Journal⠀⇛


                       In my previous article, I described what KernelCare
                       is. In this article, I’m going to tell you how to
                       install, uninstall, clear the KernelCare cache, and
                       other important information regarding KernelCare.
                       In case you’re yet to know about the product,
                       here’s a short recap. KernelCare provides automated
                       security updates to the Linux kernel. It offers
                       patches and error fixes for various Linux kernels.


                       So, if you are looking for anything similar, you
                       have landed upon the right page. Let’s begin
                       without further ado.


                # ⚓ Ubuntu Handbook ☛ How_to_Get_Back_Previous_GNOME_Screenshot
                  Tool_in_Ubuntu_22.04_|_UbuntuHandbook⠀⇛


                       Ubuntu 22.04 has a new in-shell screenshot UI for
                       taking screenshots and recording desktop. The old
                       default screenshot app (GNOME Screenshot) is no
                       longer available out-of-the-box.


                       For those somehow sticking to the old screenshot
                       tool, here’s how to install it back and configure
                       keyboard shortcuts in Ubuntu 22.04.


                # ⚓ How_to_install_XFCE_desktop_on_Manjaro_Linux_|_FOSS_Linux⠀⇛


                       Manjaro is a Linux-based distro built upon the Arch
                       Linux OS with a core focus on convenience and an
                       easy UI experience. Like every other open-source
                       Linux-based distro, Manjaro is also free and comes
                       with great support from the community.


                       However, unlike popular options like Ubuntu,
                       Manjaro is developed in a rolling release method.
                       It is an excellent option for new Linux users as it
                       offers a flexible desktop experience and is
                       relatively user-friendly.


                       One of the best things about most Linux-based
                       distros is that they come with many different
                       editions, each boasting a separate GUI for various
                       users. Manjaro is no exception as it comes in three
                       different versions with other desktop environments,
                       namely KDE Plasma, Xfce and GNOME. You can check
                       them out from the official page by clicking here.


                # ⚓ How_to_install_Monitorix_on_Debian_11⠀⇛


                       One of the things I like most about Linux is that
                       we have many applications to do a task. And I like
                       this because each one has something to contribute.
                       An example of this are the monitoring tools. One
                       alternative to monitor a server is to install
                       Monitorix. Today, we will show you how to do it on
                       a Debian 11 system.


                # ⚓ Video ☛ How_to_get_WiFi_working_on_Linux_–_Invidious⠀⇛


                       It can be a bit frustrating when hardware doesn’t
                       work on your Linux install, especially WiFi.
                       Sometimes, WiFi works out of the box – and other
                       times, not so much. In this video, Jay from
                       LearnLinuxTV will let you know why this is
                       sometimes a problem, as well as some of the things
                       you can do about it.


                # ⚓ Linux Hint ☛ How_to_check_network_interface_status_in
                  CentOS8⠀⇛


                       Network Interface allows connecting your device
                       with some internet connection. In Linux, the
                       network interface can be either physical or
                       virtual. The physical network interface helps in
                       connecting with various computers or connecting
                       with the internet. On the other hand, the virtual
                       interface usually connects with one device.


                       The network interface must be enabled and
                       functioning properly to either connect with the
                       internet or locally. To have a functional network
                       interface, one must keep an eye on the status of
                       the network interface. This article provides the
                       possible ways to get the status of the network
                       interface on CentOS 8.


                # ⚓ Red Hat Official ☛ How_to_create_dynamic_inventory_files_in
                  Ansible_|_Enable_Sysadmin⠀⇛


                       Learn how to use the host_list and Nmap plugins to
                       build inventory files for your Ansible playbooks.


                # ⚓ HowTo Forge ☛ How_to_Install_and_Use_SFTP_on_Linux
                  Servers⠀⇛


                # ⚓ Linux Hint ☛ How_to_Install_GCC_for_Arch_Linux⠀⇛


                       GCC (GNU Compiler Collection) comprises compilers
                       for well-known programming languages such as C,
                       C++, Go, Fortran, Objective-C, and many more. The
                       GCC is completely free and provides cross-platform
                       support for Linux, Windows, and multiple BSD-based
                       systems.


                       Apart from this, one can suggest or make
                       enhancements to GCC and you can utilize the
                       enhancements done by other developers/users as
                       well. Moreover, the GCC can be used to make
                       executable files for other systems which makes it
                       the best choice for embedded systems (as they don’t
                       have any compiler).


                       Keeping in view the importance of GCC, this guide
                       demonstrates the step-by-step procedure to install
                       GCC on Arch Linux.


                # ⚓ Linux Hint ☛ How_to_Use_Rc.local_on_CentOS_8⠀⇛


                       The RC stands for “run commands” and usually the rc
                       phenomenon is practiced by system administrators to
                       run a command at system boot. The “rc.local” is a
                       script that contains the commands to be exercised
                       at system startup.


                       In Linux, the system administrators may wish to
                       conduct a system test before startup. In such a
                       situation, the admin must put the relevant commands
                       inside the rc.local file to make their execution
                       possible at system startup.


                       If you are curious about using the rc-local file on
                       CentOS 8; you are in the right place.


                # ⚓ Installation_and_Review_of_Q4OS_Linux_[Lightweight
                  Distro]⠀⇛


                       Q4OS is a new Linux distribution that’s based on
                       Debian; a common base that’s shared with other
                       distributions like Ubuntu and Linux Mint.


                       It’s aimed at users who just want a simple, stable,
                       easy to use Linux operating system that they can
                       conveniently run on an aging computer so they may
                       surf the web, check emails, watch videos, and even
                       play games while offering them a good level of
                       security and privacy.


                # ⚓ Linux Shell Tips ☛ How_to_Download_Files_with_Curl_Command
                  in_Linux⠀⇛


                       Curl, short for Client URL, is a handy and flexible
                       command-line tool used to transfer data between
                       client systems. It supports a myriad of protocols
                       such as FTP, FTPS, HTTP, HTTP, LDAP, POP3, and SCP
                       just to mention a few.


                # ⚓ How_To_Access_Proxmox_Virtual_Machine_With_SPICE_Client⠀⇛


                       By default, Proxmox uses noVNC client to access the
                       console of a Virtual machine. The noVNC client is
                       just enough if you want to connect to a Proxmox VM
                       without any additional tools. However, a few things
                       don’t seem to work well with noVNC.


                       One of the major problem is I can’t hear any sound
                       from the VM. Also, when I play a YouTube video, it
                       is lagging and stuttering and out of sync with the
                       audio.


                       After searching through Proxmox forums, many users
                       have suggested that SPICE client helped them to
                       solved such issues. So I gave it a try. To my
                       surprise, SPICE works great.


          o § Games⠀➾


                # ⚓ Unreal_Engine_5_is_now_available!_–_Unreal_Engine⠀⇛


                       UE5 will empower you to realize next-generation
                       real-time 3D content and experiences with greater
                       freedom, fidelity, and flexibility than ever
                       before.


                # ⚓ Phoronix ☛ Unreal_Engine_5_Officially_Released⠀⇛


                # ⚓ GamingOnLinux ☛ Unreal_Engine_5_has_officially_launched,
                  lots_of_Linux_and_Vulkan_improvements_|_GamingOnLinux⠀⇛


                       After being available in Early Access since May
                       2021 and Preview since February 2022, Epic Games
                       has today released Unreal Engine 5 which will no
                       doubt go on to power some of the biggest upcoming
                       releases.


                       “With this release, we aim to empower both large
                       and small teams to really push the boundaries of
                       what’s possible, visually and interactively. UE5
                       will enable you to realize next-generation real-
                       time 3D content and experiences with greater
                       freedom, fidelity, and flexibility than ever
                       before.” — Epic Games.


                       Epic say that developers will be able to continue
                       using “workflows supported in UE 4.27″ but get
                       access to the redesigned Unreal Editor, better
                       performance, improved path tracing and the list
                       goes on.


                # ⚓ GamingOnLinux ☛ The_Steam_Deck_hit_me_over_the_head_with
                  feelings_of_nostalgia_|_GamingOnLinux⠀⇛


                       Something happened to me recently while playing the
                       Steam Deck that I felt the need to share with you.


                       The Steam Deck may be a modern device but it’s been
                       giving me a very heavy dose of nostalgia recently.
                       No, it’s not because it’s a great machine for
                       emulation, which I’ve done very little of so far
                       because so many amazing modern games work but for
                       something totally different.


                       Here’s something it reminds me of: I grew up with
                       the likes of the Game Boy. In fact, I originally
                       had the Game Boy Pocket, the one you could see
                       through the case and get a look at the insides. I
                       used to stay up far too late playing Pokémon
                       Yellow, with one of those terrible bulky light and
                       magnifier attachments which had quite a bit of
                       weight to it with the batteries inside. To me, the
                       Steam Deck is bringing back memories of that. As
                       weird as it might be to say from a modern device,
                       the injection of nostalgia I’ve been getting has
                       been quite wonderful.


          o § Desktop Environments/WMs⠀➾


                # ⚓ Its FOSS ☛ Xfce_Terminal_1.0.0_is_a_Feature-Packed_Major
                  Upgrade_After_a_Year⠀⇛


                       
                       The popular terminal emulator found on almost all
                       Xfce-powered distributions, Xfce Terminal has just
                       released its first major upgrade under a new
                       maintainer (and a new versioning scheme).


                       Let us take a look at some highlights of the
                       release.


                       Igor Zakharov was leading the development from 2016
                       until 2020. Unfortunately, it was left unmaintained
                       in 2021 when the new maintainer, Sergios Anestis
                       Kefalidis (also a developer of Thunar file
                       manager), took over the responsibility.


                # § K Desktop Environment/KDE SC/Qt⠀➾


                      # ⚓ Liliputing ☛ Maui_Shell_Alpha_released_(convergent
                        desktop_environment_for_Linux_phones_and_PCs)⠀⇛


                             The developers of the Linux-based NitruxOS
                             (NXOS) have been working on a slick new
                             convergent desktop environment called Maui
                             Shell designed to look good and function well
                             on just about any device no matter the screen
                             size, which makes it an interesting option
                             for phones, tablets, laptops, and desktop
                             computers – or devices that are designed to
                             work as one or more of those, like a phone
                             that can be used as a desktop when an
                             external display is connected.


          o § Distributions⠀➾


                # § New Releases⠀➾


                      # ⚓ Q4OS_4.8_Gemini,_stable⠀⇛


                             An update to Q4OS 4 Gemini LTS has been
                             released. The new 4.8 series receives the
                             recent Debian Bullseye 11.3 update, updated
                             Debian stable kernel and important security
                             and bug fixes. This update brings along
                             significant Q4OS specific improvements, fixes
                             and a cumulative upgrade covering all the
                             changes from the previous stable Gemini
                             release. Among other improvements,
                             localization and languages support API
                             library for the Desktop profiler as well as
                             for other Q4OS tools has been rewritten and
                             vastly improved, Setup tool gets polished and
                             installation process has been more secured.


                             We welcome everyone to download installation
                             media images from the Downloads section of
                             the Q4OS website. We are currently pushing
                             all the changes mentioned above into the Q4OS
                             repositories, automatic update process will
                             take care about to update computers for
                             current users.


                # § SUSE/OpenSUSE⠀➾


                      # ⚓ Leap_Micro_Beta_Available_for_Testers⠀⇛


                             
                             People browsing through openSUSE’s websites
                             may spot something new on get.opensuse.org.


                             Leap Micro, which is currently showing the
                             5.2 beta version, is for containerized and
                             virtualized workloads. It is immutable and
                             ideal for host-containers and described as an
                             ultra-reliable, lightweight operating system
                             that experts can use for compute deployments.
                             The community version of Leap Micro is based
                             on SUSE Linux Enterprise Micro and leverages
                             the enterprise hardened security of twins
                             SUSE Linux Enterprise and openSUSE Leap,
                             which merges this to a modern, immutable,
                             developer-friendly OS platform.


                             Leap Micro has several use cases for edge,
                             embedded/IoT deployments and more. Leap Micro
                             is well suited for decentralized computing
                             environments, microservices, distributed
                             computing projects and more. The release will
                             help developers and IT professionals to build
                             and scale systems for uses in aerospace,
                             telecommunications, automotive, defense,
                             healthcare, robotics, blockchain and more.
                             Leap Micro provides automated administration
                             and patching.


                # § IBM/Red Hat/Fedora⠀➾


                      # ⚓ Fedora ☛ Anaconda_is_getting_a_new_suit_and_a_wizard
                        –_Fedora_Community_Blog⠀⇛


                             In January, we published “Anaconda is getting
                             a new suit” to let you know that we’re
                             looking to modernize and improve Anaconda’s
                             user experience. Before starting the redesign
                             work for the Anaconda installer, the team
                             reviewed user feedback and usability study
                             data that we’ve gathered over the years.


                             [...]


                             We sorted the feedback into high-level
                             groupings. One of the larger groupings
                             focused on the current installer navigation
                             model, often referred to as “hub and spoke.”
                             In a “hub and spoke” model, the summary
                             screen, known as a “hub”, is the central
                             point. Individual configuration screens are
                             known as “spokes”. The phrase is commonly
                             used today for airport connections because
                             passengers often have to change flights at a
                             central airport—or hub—instead of flying
                             directly between two airports.


                # § Debian Family⠀➾


                      # ⚓ 9to5Linux ☛ Tails_5.0_Enters_Beta_Testing_as_First
                        Release_Based_on_Debian_GNU/Linux_11_“Bullseye”⠀⇛


                             Due out next month, Tails 5.0 will be a major
                             update to this GNU/Linux distribution for
                             anonymous surfing of the Internet and the
                             first version to be based on the latest
                             Debian GNU/Linux 11 “Bullseye” operating
                             system series.


                      # ⚓ Tails ☛ Call_for_testing:_5.0~beta1⠀⇛


                             We plan to release Tails 5.0 on May 3 or May
                             31. It will be the first version of Tails
                             based on Debian 11 (Bullseye). It brings new
                             versions of most of the software included in
                             Tails and some important usability
                             improvements.


                # § Canonical/Ubuntu Family⠀➾


                      # ⚓ Make Use Of ☛ Ubuntu_MATE_22.04_Hits_Beta,_and_“Jammy
                        Jellyfish”_Is_Looking_Good_So_Far⠀⇛


                             The 22.04 beta release allows Ubuntu Mate
                             users to test the system with added features
                             but a reduced installation image size.


                      # ⚓ ZDNet ☛ Ubuntu_22.04_beta_has_arrived_and_it’s_one_of
                        the_best_releases_from_Canonical_yet⠀⇛


                             Linux on the desktop continues to grow in
                             popularity. Although it doesn’t enjoy the
                             consumer market share of Android, Windows,
                             iOS, or macOS, the open-source operating
                             system on the server end is massively popular
                             within enterprise businesses. But little by
                             little, Linux continues climbing up the
                             market share ladder. One reason for this is
                             Ubuntu.


                             For those that don’t know, Ubuntu has been,
                             for years, one of the top 10 most popular
                             Linux desktop distributions on the market.
                             One of the many reasons for this is due to
                             remarkable user-friendliness. Ubuntu is
                             simple to install, use, and maintain,
                             supports a wide range of hardware, just
                             works, and (of course) is free to anyone.


                      # ⚓ Yahoo News ☛ SteelCloud_Software_Automates_eMASS_and
                        Splunk_Data_Integration⠀⇛


                      # ⚓ Ubuntu ☛ Standing_with_Ukraine [Ed: The company whose
                        founder flew with Russia to space took 1.5 months to
                        post this]⠀⇛


                             In response to the Russian invasion and acts
                             of war in Ukraine, Canonical has sent notice
                             of termination of support, professional
                             services, and channel partnerships with
                             Russian enterprises. We will not resume such
                             engagements while broad and democratically
                             instituted sanctions on Russia remain in
                             place.


                             We will not restrict access to security
                             patches for Ubuntu users in Russia – free
                             software platforms like Ubuntu, VPN
                             technologies, and Tor, are important for
                             those who seek news and dialogue outside
                             state control. We will direct any Russian
                             subscription income for such maintenance to
                             Ukrainian humanitarian causes.


          o § Devices/Embedded⠀➾


                # § Mobile Systems/Mobile Applications⠀➾


                      # ⚓ India Times ☛ android:_Explained:_Know_all_about_the
                        Emoji_Kitchen_on_Android_–_Times_of_India⠀⇛


                      # ⚓ Top_4_Ways_to_Improve_Location_Accuracy_on_Android_–
                        Guiding_Tech⠀⇛


                      # ⚓ SamMobile ☛ Best_cheap_Android_phones_in_2022_for_the
                        US_are_made_by_Samsung_–_SamMobile⠀⇛


                      # ⚓ Android Central ☛ Twitter_for_Android_may_soon_pick
                        up_this_long-overdue_feature_|_Android_Central⠀⇛


                      # ⚓ Informa PLC ☛ Orange_Belgium_taps_CommScope_for
                        Android_TV_streamer⠀⇛


                      # ⚓ Giz China ☛ Over_170_million_Android_manufacturers
                        smartphone_orders_are_cut_off⠀⇛


                      # ⚓ Digital Trends ☛ Android_13_will_enable_two_carrier
                        lines_on_a_single_eSIM_|_Digital_Trends⠀⇛


                      # ⚓ HowTo Geek ☛ It’s_Time_to_Ditch_Your_Old_Android
                        Phone⠀⇛


                      # ⚓ Mashable ☛ OnePlus_10_Pro_review:_The_best_Android
                        competitor_to_Pixel_6_Pro_yet⠀⇛


                      # ⚓ /e/OS_&_Murena_websites_–_Gaël_Duval_(blog,_mandrake,
                        /e/_my_data_is_my_data…)⠀⇛


                             Last week, we discovered that our two main
                             websites had been supressed from the Google
                             search engine for more than one year.
                             Although this doesn’t seem to hurt us a lot
                             (we get thousands links from external
                             websites), and although it’s quite fun to
                             extend our “geGooglisation” to being totally
                             out from Google Search, we realize that,
                             besides the misconfiguration of some of our
                             web servers, we have to care about our “SEO”
                             (Search Engine Optimization) at some point.


                             What is also important is to be transparent
                             about our websites URLs, so that people can
                             put the correct links to them. This is really
                             the most helpful practise that brings new
                             users and let them discover what we do.


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


                # ⚓ Open Source Initiative ☛ Google_OSPO:_Why_we_support_the
                  OSI [Ed: Distracting from the fact so much of the OSI's
                  resources go to Microsoft, which attacks the mission?]⠀⇛


                       This week, we’re pleased to spotlight another OSI
                       sponsor, Google, and learn why open source is
                       important to their organization.


                # § Web Browsers⠀➾


                      # § Mozilla⠀➾


                            # ⚓ The_Theological_Problem_Behind_Firefox_in
                              Ubuntu_22.04⠀⇛


                                   Warning to all Ubuntu users. Starting
                                   with Ubuntu 22.04, Firefox users will
                                   be forced to migrate to the “Snap”
                                   version of Firefox. This will be done
                                   automatically. Ubuntu doesn’t provide a
                                   native Firefox anymore. You had
                                   probably been warned with Ubuntu 21.10.


                                   You may observe that Firefox is slower
                                   to start, that it doesn’t follow your
                                   theme anymore and other problems. But
                                   the main issue is that Snap Firefox is,
                                   by design, unable to speak to other
                                   software. In Belgium, this breaks the
                                   official Belgian id authentication.


                                   It should be highlighted that Belgian
                                   officials are doing a really good job
                                   at providing the official electronic ID
                                   tool for Linux (they have a Debian/
                                   Ubuntu repository) and they are well
                                   aware of the issue.


                            # ⚓ LWN ☛ Firefox_99.0_released⠀⇛


                            # ⚓ 99.0_Firefox_Release⠀⇛


                            # ⚓ OMG Ubuntu ☛ Firefox_99_Released_with_GTK
                              Overlay_Scrollbar_Support,_Fixes⠀⇛


                                   


                                   What’s new? Well, a lots of folks,
                                   including Mozilla are hyped about
                                   Firefox 99’s support for GTK overlay
                                   scrollbars. These slimmer page sliders
                                   hide when not in use but appear on
                                   scroll and increase in size when you
                                   interact with them.


                                   Thing is they aren’t enabled by default
                                   in the stable version, just the beta
                                   and nightly builds. So to enjoy GTK
                                   overlay scrollbars in Firefox 99 on
                                   your system you need to dive into the
                                   browser’s about:config page and set the
                                   widget.gtk.overlay-scrollbars.enabled
                                   setting to true…


                            # ⚓ Video ☛ Firefox_DYING_is_TERRIBLE_for_the_Web_–
                              Invidious⠀⇛


                # § FSF⠀➾


                      # § GNU Projects⠀➾


                            # ⚓ GNU_Health_declared_Digital_Public_Good⠀⇛


                                   We are very proud to announce that the
                                   GNU Health project has been declared a
                                   Digital Public Good by the Digital
                                   Public Goods Alliance (DPGA). GNU
                                   Solidario received the announcement
                                   this Sunday, April 3rd 2022.


                                   The Digital Public Goods Alliance is a
                                   multi-stakeholder initiative endorsed
                                   by the United Nations Secretary-
                                   General, working to accelerate the
                                   attainment of the Sustainable
                                   Development Goals in low-and middle-
                                   income countries by facilitating the
                                   discovery, development, use of, and
                                   investment in digital public goods.


                # § Programming/Development⠀➾


                      # ⚓ OpenSource.com ☛ What_Git_aliases_are_in_your
                        .bashrc?_|_Opensource.com⠀⇛


                             Many open source users love a good Bash alias
                             and are usually happy to show off a
                             particularly robust .bashrc file when given
                             the chance. If you’re a frequent user of Git,
                             you might benefit from a few Git aliases
                             mixed in with your other Bash aliases.
                             Alternately, you can create aliases specific
                             to Git with this git config command. This
                             example sets the git co command to git
                             checkout.


                      # ⚓ Cython_is_20!_|_Stefans_Welt⠀⇛


                             Today, Cython celebrates its 20th
                             anniversary!


                             On April 4th, 2002, Greg Ewing published the
                             first release of Pyrex 0.1.


                             Already at the time, it was invented and
                             designed as a compiler that extended the
                             Python language with C data types to build
                             extension modules for CPython. A design that
                             survived the last 20 years, and that made
                             Pyrex, and then Cython, a major corner stone
                             of the Python data ecosystem. And way beyond
                             that.


                             Now, on April 4th, 2022, its heir Cython is
                             still very much alive and serves easily
                             hundreds of thousands of developers
                             worldwide, day to day.


                             I’m very grateful for Greg’s ingenious
                             invention at the time. Let’s look back at how
                             we got to where we are today.


                      # ⚓ LWN ☛ Behnel:_Cython_is_20!_[LWN.net]⠀⇛


                             On his blog, Stefan Behnel writes about the
                             20th anniversary of Cython, which is a
                             compiler for Python extensions written in C,
                             for wrapping C libraries in order to provide
                             Python bindings for them, and for embedding
                             Python into other applications. It is used by
                             NumPy, scikit-learn (and other scikit-
                             * extensions), pandas, and more.


                      # ⚓ Dirk Eddelbuettel ☛ Dirk_Eddelbuettel:_RcppSpdlog
                        0.0.8_on_CRAN:_Upstream_Update⠀⇛


                             A new version 0.0.8 of RcppSpdlog is now on
                             CRAN. RcppSpdlog bundles spdlog, a wonderful
                             header-only C++ logging library with all the
                             bells and whistles you would want that was
                             written by Gabi Melman, and also includes fmt
                             by Victor Zverovich.


                      # ⚓ Dirk Eddelbuettel ☛ Dirk_Eddelbuettel:_RcppArmadillo
                        0.11.0.0.0_on_CRAN:_Upstream_Updates⠀⇛


                             Armadillo is a powerful and expressive C++
                             template library for linear algebra aiming
                             towards a good balance between speed and ease
                             of use with a syntax deliberately close to a
                             Matlab. RcppArmadillo integrates this library
                             with the R environment and language–and is
                             widely used by (currently) 972 other packages
                             on CRAN, downloaded over 24 million times
                             (per the partial logs from the cloud mirrors
                             of CRAN), and the CSDA paper (preprint /
                             vignette) by Conrad and myself has been cited
                             465 times according to Google Scholar.


                      # ⚓ Dirk Eddelbuettel ☛ RInside_0.2.17⠀⇛


                             A new release 0.2.17 of RInside arrived on
                             CRAN and in Debian today. This is the first
                             release in two years since the 0.2.16
                             release. RInside provides a set of
                             convenience classes which facilitate
                             embedding of R inside of C++ applications and
                             programs, using the classes and functions
                             provided by Rcpp.


                      # § Rust⠀➾


                            # ⚓ Rust_Lang_Roadmap_for_2024⠀⇛


                                   Rust 1.0 was released in 2015. Since
                                   that time, we’ve seen Rust grow from a
                                   small language used for a handful of
                                   prominent projects into a mainstay in
                                   use at virtually every major tech
                                   company.


                                   As we work towards Rust 2024, it’s
                                   natural to ask what’s next for the
                                   language. This roadmap provides insight
                                   into that question by describing what
                                   we, as members of the lang team with
                                   input from other Rust teams, would like
                                   to prioritize.


    * § Leftovers⠀➾


          o § Hardware⠀➾


                # ⚓ Peter ‘CzP’ Czanik ☛ The_cult_of_Amiga_and_SGI,_or_why
                  workstations_matter_|_Random_thoughts_of_Peter_‘CzP’_Czanik⠀⇛


                       I’m considered to be a server guy. I had access to
                       some really awesome server machines. Still, when
                       computers come up in discussions, we are almost
                       exclusively talk about workstations. Even if
                       servers are an important part of my life, that’s
                       “just” work. I loved the SGI workstations I had
                       access to during my university years. Many of my
                       friends still occasionally boot their 30 years old
                       Amiga boxes.


                       [...]


                       I started my IT life with x86: an XT then 286, 486,
                       and so on. I used some really powerful RS/6000
                       machines remotely at Dartmouth College. I learned
                       basics of scripting on them, how to exit from vi,
                       and few more things. But it was just a bit of
                       curiosity, not any kind of attachment. I also had
                       access to Macs there, but I never really liked it,
                       as MacOS felt a kind of dumb, and does so ever
                       since.


                       Fast forward a few years. Soon after I started
                       university I became part of the student team at the
                       faculty IT department. When a couple of SGI
                       workstations arrived there, I got user access, and
                       soon admin access as well. This is where I first
                       used Netscape Navigator, ran Java applications, and
                       enjoyed running a GUI on a UNIX machine.


          o § Integrity/Availability⠀➾


                # § Proprietary⠀➾


                      # § Pseudo-Open Source⠀➾


                            # § Privatisation/Privateering⠀➾


                                  # § Linux Foundation⠀➾


                                        # ⚓ FSFE ☛ European_Parliament
                                          recognises_Free_Software_as_key_for
                                          fair_AI⠀⇛


                                               The Special Committee on
                                               Artificial Intelligence in
                                               a Digital Age (AIDA) of the
                                               European Parliament voted
                                               on its resolution on
                                               Artificial Intelligence in
                                               a Digital Age on March
                                               22nd, and underlined the
                                               importance of Free Software
                                               for AI with a broad
                                               majority. We now ask EU co-
                                               legislators to take this
                                               position into account and
                                               to include provisions and
                                               guidelines on Free Software
                                               in the upcoming
                                               legislation.


                                               Public authorities using AI
                                               systems should make them
                                               publicly available. Public
                                               research inventing AI
                                               systems should make them
                                               publicly available.
                                               Transparency in AI
                                               technologies is necessary
                                               to test them, evaluate
                                               their results, and improve
                                               them. The FSFE is following
                                               closely the legislative
                                               process and analysed how AI
                                               can remain verifiable and
                                               trustworthy as well as lead
                                               to further innovation with
                                               Free Software.


                                        # ⚓ Linux Foundation’s Site/Blog ☛ AI
                                          is_better_with_open_source [Ed:
                                          Produced_using_proprietary
                                          software]⠀⇛


                                               Open Source Software (OSS)
                                               is a proven model that
                                               delivers tangible benefits
                                               to businesses, including
                                               improved time-to-market,
                                               reduced costs, and
                                               increased flexibility. OSS
                                               is pervasive in the
                                               technology landscape and
                                               beyond it, with adoption
                                               across multiple industries.
                                               In a 2022 survey by Red
                                               Hat, 95 percent of IT
                                               leaders said they are using
                                               open source in their IT
                                               infrastructure, which will
                                               only increase.


                                        # ⚓ I Programmer ☛ Applications_Open
                                          For_LiFT_Scholarships [Ed: Lots of
                                          this paid-for webspam]⠀⇛


                      # § Security⠀➾


                            # ⚓ LWN ☛ Security_updates_for_Tuesday_[LWN.net]⠀⇛


                                   Security updates have been issued by
                                   Arch Linux (polkit, postgresql, and
                                   zlib), openSUSE (389-ds and opera), Red
                                   Hat (kpatch-patch), SUSE (389-ds and
                                   util-linux), and Ubuntu (waitress).


                            # ⚓ security_things_in_Linux_v5.10_«_codeblog⠀⇛


                                   Linux v5.10 was released in December,
                                   2020. Here’s my summary of various
                                   security things that I found
                                   interesting:


                                   seccomp user_notif file descriptor
                                   injection
                                   Sargun Dhillon added the ability for
                                   SECCOMP_RET_USER_NOTIF filters to
                                   inject file descriptors into the target
                                   process using
                                   SECCOMP_IOCTL_NOTIF_ADDFD. This lets
                                   container managers fully emulate
                                   syscalls like open() and connect(),
                                   where an actual file descriptor is
                                   expected to be available after a
                                   successful syscall. In the process I
                                   fixed a couple bugs and refactored the
                                   file descriptor receiving code.


                            # ⚓ LWN ☛ Cook:_Security_things_in_Linux_v5.10_
                              [LWN.net]⠀⇛


                                   Kees Cook catches up with the security-
                                   related changes in the 5.10 kernel,
                                   released at the end of 2020.


                            # ⚓ Matthew Garrett ☛ mjg59_|_Bearer_tokens_are
                              just_awful⠀⇛


                                   As I mentioned last time, bearer tokens
                                   are not super compatible with a model
                                   in which every access is verified to
                                   ensure it’s coming from a trusted
                                   device. Let’s talk about that in a bit
                                   more detail.


                            # ⚓ CISA ☛ CISA_Adds_Four_Known_Exploited
                              Vulnerabilities_to_Catalog⠀⇛


                            # § Privacy/Surveillance⠀➾


                                  # ⚓ Bruce Schneier ☛ Hackers_Using_Fake
                                    Police_Data_Requests_against_Tech_Companies
                                    –_Schneier_on_Security⠀⇛


                                         Brian Krebs has a detailed post
                                         about hackers using fake police
                                         data requests to trick companies
                                         into handing over data.


                                         [...]


                                         The “credentials” are even more
                                         insecure than we could have
                                         imagined: access to an email
                                         address. And the data, of course,
                                         isn’t very secure. But imagine
                                         how this kind of thing could be
                                         abused with a law enforcement
                                         encryption backdoor.


                                  # ⚓ MakeTech Easier ☛ 4_Ways_Google_Tracks
                                    You_and_How_to_Stop_it⠀⇛


                                         From Gmail and Google Photos to
                                         Google searches and other online
                                         activities, the tech giant tracks
                                         all your movements. Almost
                                         anything connected with Google
                                         (hardware and software) gathers
                                         your personal information.
                                         However, the tech giant insists
                                         it doesn’t spy on you with
                                         malicious intent. Instead, your
                                         collected details are used to
                                         enhance the performance of its
                                         services and tools.


                                  # ⚓ AccessNow ☛ Facing_the_consequences:
                                    Access_Now_welcomes_legal_action_against
                                    NSO_Group_–_Access_Now⠀⇛


                                         Access Now welcomes the new
                                         lawsuit filed today, April 5, in
                                         France against the Israeli
                                         spyware company NSO Group for
                                         facilitating the unlawful
                                         surveillance of French-
                                         Palestinian human rights
                                         defender, Salah Hammouri, through
                                         the use of its spyware Pegasus.


                                         The legal action was submitted
                                         jointly by the International
                                         Federation of Human Rights
                                         (FIDH), the Human Rights League
                                         (LDH), and Salah Hammouri.


                                         [...]


                                         “Litigation remains an important
                                         tool in the fight against spyware
                                         abuses,” said Natalia Krapiva,
                                         Tech-Legal Counsel at Access Now.
                                         “Spyware companies like NSO Group
                                         and states that use their
                                         technologies should know: you
                                         will be held accountable.”


                                         Access Now reiterates its call to
                                         the European Union to urgently
                                         sanction NSO Group and take all
                                         appropriate action to prohibit
                                         the sale, transfer, and use of
                                         NSO Group’s surveillance
                                         technologies until adequate human
                                         rights safeguards are in place.


                                  # ⚓ Citizen Lab ☛ Peace_through_Pegasus:
                                    Jordanian_Human_Rights_Defenders_and
                                    Journalists_[cr]acked_with_Pegasus_Spyware
                                    –_The_Citizen_Lab⠀⇛


                                         Jordanian human rights defenders
                                         (HRDs) work in a generally
                                         hostile environment. Since the
                                         Arab Spring in 2011, grassroots
                                         protests have emerged, reflecting
                                         growing discontent with
                                         government corruption and wealth
                                         inequality, among other issues.
                                         In response, authorities have
                                         often arrested activists and
                                         curtailed freedoms.


                                         Jordan saw a wave of protests in
                                         2011, as part of the Arab Spring.
                                         Protests were driven partly by
                                         the Hirak, groups of youth
                                         activists not connected with
                                         traditional centres of political
                                         power in Jordan. Protests flared
                                         up again in June 2018, galvanised
                                         by a government plan to increase
                                         taxes and reduce subsidies, as
                                         required by the International
                                         Monetary Fund (IMF). More than 30
                                         trade unions called a general
                                         strike, and protesters occupied
                                         the Fourth Circle area of Amman
                                         near the Prime Minister’s office.
                                         In response, the government
                                         temporarily withdrew the bill,
                                         and re-introduced it in September
                                         2018 with minor changes. When the
                                         bill’s final text was published
                                         in the Official Gazette in
                                         December 2018, activists once
                                         again held protests in the Fourth
                                         Circle that persisted into 2019.
                                         In March 2019, Jordanian
                                         authorities began a wave of
                                         arrests against Hirak members,
                                         charging them with “insulting the
                                         King” and “undermining the
                                         political regime.”


                                  # ⚓ Authoritarians_love_smart_cities._Russia
                                    is_no_exception⠀⇛


                                         Authoritarians love smart cities
                                         projects.


                                         Vladimir Putin is no exception.
                                         Moscow has been on a mission to
                                         become a smart city for the last
                                         decade. Russia’s capital has
                                         around 200,000 surveillance
                                         cameras. That’s more cameras per
                                         square mile than in Beijing or
                                         New York. In October 2021, the
                                         Moscow Metro launched a facial
                                         recognition payment system.
                                         Branded as a quick, contactless
                                         way of paying ride fares, it was
                                         also used for surveillance. Since
                                         September 2020, almost 3,000
                                         criminals have been caught in the
                                         Moscow Metro because of the
                                         system, according to city
                                         authorities. But the extreme
                                         crackdown on dissent triggered by
                                         the war in Ukraine makes Moscow’s
                                         technological advances terrifying
                                         for anyone who opposes the
                                         government.


                                         Since the start of war in
                                         Ukraine, speaking out against the
                                         government has become incredibly
                                         risky for the Russians. Over
                                         15,000 people have been detained
                                         for protesting and anyone who
                                         does as little as sharing a
                                         social media post that
                                         contradicts the official position
                                         risks a 15-year prison sentence.


    * § Defence/Aggression⠀➾


          o ⚓ How_to_document_war_crimes_in_the_digital_age⠀⇛


                 The stories coming out of Bucha, a small city near Kyiv
                 that was under Russian occupation since early March, are
                 horrific. Witnesses have described scenes of torture,
                 summary executions and mass graves. Journalists who
                 accompanied Ukrainian troops moving into the city have
                 reported seeing civilian corpses along the road, some
                 with their hands tied behind their backs, others with a
                 gun blow to the head.


                 This adds to the growing pile of evidence that Russian
                 troops have perpetrated war crimes in Ukraine. On April
                 4, President Biden called for Russian President Vladimir
                 Putin to be brought to trial. The European Union created
                 a Joint Investigation Team with Ukraine that will collect
                 and process evidence that can be brought before the
                 International Criminal Court.


          o ⚓ The Washington Post ☛ 4,000_letters_and_four_hours_of_sleep:
            Ukrainian_leader_wages_digital_war⠀⇛


          o ⚓ Politico ☛ Ukraine_minister_pleads_to_expand_‘digital_blockade’
            on_Russia⠀⇛


    * § Internet Policy/Net Neutrality⠀➾


          o ⚓ I_Answer_Questions,_Part_III⠀⇛


                 In the last couple of years I’ve mostly seen talk about
                 how the Internet hasn’t fulfilled its promise of making
                 the world better. Centralised social media, algorithmic
                 amplification, the control of military drones or state
                 surveillance, proof or work cryptocurrencies.


          o ⚓ Ukraine’s_Internet_System_Is_A_Hidden_Weapon_In_The_War_(VIDEO)⠀⇛


                 Ukraine’s ability to keep its internet up and running has
                 allowed its citizens to stay connected to the world
                 despite Russia’s invasion.


                 Since the beginning of the invasion of Ukraine, Russia
                 has launched cyberattacks and missiles that have knocked
                 out large portions of the country’s internet, but it’s
                 failed to push Ukrainians completely offline thanks to a
                 robust telecommunications system.


                 “Unlike a much smaller country that may rely on just a
                 couple of connections out to the outside world, there is
                 a rich fiber optic backbone connecting the cities of
                 Ukraine,” said Doug Madory, director of internet analysis
                 at Kentik. “If one line gets cut, there’s other paths to
                 get around it.”


                 “We haven’t seen very long-term outages for the larger
                 providers,” said Amanda Meng, research scientist at
                 Georgia Tech. “For some smaller operators, we do see
                 disconnections that we’ve seen for weeks.”


          o ⚓ Politico ☛ The_West’s_plan_to_keep_global_data_flows_alive⠀⇛


                 U.S. President Joe Biden and European Commission
                 President Ursula von der Leyen just secured a political
                 agreement to keep data flowing between the European Union
                 and the United States.


                 But with EU and U.S. negotiators still hammering out
                 details on the new transatlantic data pact — and legal
                 challenges expected once the deal is completed —
                 policymakers are already scrambling to shore up the free
                 flow of data across the Western world.


                 The Organization for Economic Cooperation and
                 Development, a Paris-based group of mostly rich
                 countries, may have an answer.


    * § Digital Restrictions (DRM)⠀➾


          o ⚓ Mashable ☛ How_to_stop_Spotify_from_sharing_your_data,_and_why
            you_should⠀⇛


                 It sounds like the setup to a bad joke, but the wildly
                 popular music streaming service in fact collects, stores,
                 and shares reams of seemingly mundane user data, adding
                 up to an intrusion that’s much more than just the sum of
                 its parts. While Spotify customers are busy rocking out,
                 the company has its metaphorical hands full profiting off
                 the data that rocking generates.
                 And it generates a surprising amount. What Spotify does
                 with that data, and why that should concern you, are
                 complex questions involving third-party advertisers,
                 densely written terms of service, and inferences drawn
                 from every piece of music or podcast you’ve ever listened
                 to on the streaming platform.
                 But according to privacy experts, one aspect of this
                 digital mess is absolutely straightforward: Spotify users
                 should pay attention to how their data is used, and take
                 the available steps to limit that use whenever possible.


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