𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Saturday, March 26, 2022
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Generated Sun 27 Mar 02:40:19 BST 2022
Created by Dr. Roy Schestowitz (𝚛𝚘𝚢 (at) 𝚜𝚌𝚑𝚎𝚜𝚝𝚘𝚠𝚒𝚝𝚣 (dot) 𝚌𝚘𝚖)
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Gemini index for the day: gemini://gemini.techrights.org/2022/03/26/


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

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QmbZUGxupu36yFf72bxj4yCNrYAfeMKD4kf3TzSvrLqGkT


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

⦿ [Meme] Words That ’Offend’ Corporations | Techrights

⦿ Canonical is Becoming Softer (Pro-Microsoft and Against Free Speech) | Techrights

⦿ Links 26/03/2022: Capyloon and Status of Chrome OS, Fuchsia | Techrights

⦿ IRC Proceedings: Friday, March 25, 2022 | Techrights

⦿ Mike Gerwitz on the Ethics Void | Techrights

⦿ Moving On | Techrights

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
		http://techrights.org/2022/03/26/bribing-projects/#comments
		http://techrights.org/2022/03/26/canonical-self-censorship/#comments
		http://techrights.org/2022/03/26/fuchsia-woes/#comments
		http://techrights.org/2022/03/26/irc-log-250322/#comments
		http://techrights.org/2022/03/26/mike-gerwitz-ethics/#comments
		http://techrights.org/2022/03/26/moving-office/#comments

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
		http://techrights.org/2022/03/26/new-debian-releases/#comments

                    ䷩ 𝚕𝚒𝚗𝚎 62

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/03/26/bribing-projects/#comments
    Gemini version at gemini://gemini.techrights.org/2022/03/26/bribing-projects/

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Gemini_version_available_♊︎


✐ [Meme]_Words_That_‘Offend’_Corporations⠀✐


Posted in Deception, Microsoft at 2:09 am by Dr. Roy Schestowitz


  🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Microsoft is tied to hundreds of millions of dollars in
              foreign bribes, whistleblower alleges - The Verge⦈


 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Kylo Ren teaches Baby Yoda to speak: Say 'corruption', say
      'crime', Say 'Microsoft' [awkward silence] Windows 7 was my idea!⦈


Summary: What happens when criminals_from_Microsoft get to impose speech
restrictions on projects, by essentially bribing those projects to censor the
community (volunteers)?


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢶⣶⣶⣶⣶⡆⣶⢶⣶⣶⣶⣶⣤⣶⣆⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠸⠿⠏⠿⠿⠇⠘⠿⠸⠿⠻⠻⠞⠿⠟⠿⠆⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣏⡾⣿⣿⣿⣷⣱⢿⣿⣿⣿⣞⣎⡇⠀⣿⣿⣿⣿⣾⣿⣿⣿⣿⣶⣿⣿⣿⣿⣷⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣤⣀⠀⠀⠀⠀⠀⠀
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⠀⠀⣠⣤⣶⣦⣄⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⡟⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠈⢻⣿⣿⣿⣿⡎⠛⠙⠛⠋⠻⠿⢻⣿⣿⣿⣿⣦⠀⠀⣿⣿⣿⣿⢛⣿⣿⡿⣿⡟⣺⣿⣿⣿⣿⣓⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⠂⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡃
⠀⠀⠀⠹⣿⣿⣿⣧⠀⠀⠀⠀⢀⠀⠀⠉⠛⢻⣿⣿⡆⠀⠿⠿⠶⠿⠶⠾⠿⠷⠿⠷⠶⠿⠿⠾⠷⠶⠇⠀⠿⠿⠿⠷⠷⠿⠿⠿⠿⠾⠾⠿⠿⠿⠷⠷⠆⠀⠀⠀⢠⣿⣿⣿⡟⣿⣿⣿⡏⢩⣿⣿⣿⠉⣿⣷⢧⢰
⠀⠀⠀⠀⢽⣿⣿⣿⡆⠤⠤⣴⣿⣧⣀⣀⣀⣀⣽⣻⡇⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣴⣤⣤⣤⣤⣤⣤⣤⣶⣶⣦⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣷⣿⣿⣾⣾
⠀⠀⠀⠀⢸⣿⣿⣟⣛⣻⣧⡘⡎⣿⡽⣿⣿⣿⣿⣿⣧⠄⣿⣿⣿⣋⣓⣽⣿⣿⣟⣛⣺⣿⣿⣿⣛⣓⡇⣿⣿⣿⣿⣛⣛⣿⣿⣿⣟⣛⣻⣿⣿⣿⣾⣛⡀⣤⣤⣤⣾⣿⣿⣿⣿⣿⠿⡿⡿⠿⠿⢿⣿⠛⢻⣻⠉⡇
⣤⣤⣤⣄⣿⣿⣿⡿⣿⣿⣿⣷⡀⢿⣷⣿⣿⣿⣿⣿⡏⠀⣿⣿⣿⣶⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣾⣿⡇⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⣿⣿⢿⣿⣽⣿⠘⣿⣇⠀⣇⣧⠀⠀⢸⢸⠀⢸⣿⡄⢁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⢿⣿⣿⣿⣿⣿⣧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⠿⠿⠀⠛⠛⠁⢛⣛⣀⠀⠛⠚⠀⠈⢿⣇⣘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⢇⣼⣿⣿⣿⠉⣁⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢁⠉⢁⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤
⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⣾⡏⢡⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣠⣶⣿⣿⣿⣿⣇⣿⣿⣷⣿⣾⣷⣿⣿⣿⣻⣯⡿⣿⣿
⣠⣤⣄⣀⢀⣿⣸⣿⣿⣿⡿⠁⠊⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠟⠻⠃⢸⣿⣿⣿⣿⠿⠃⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⣿⠅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣠⠀⠀⠘⠋⣉⣁⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠃⣿⣿⠿⠿⠿⠿⠻⠿⠿⠿⠿⠛⠛⠿⠿⠟⠛⠃⣿⣿⠿⠿⠿⠟⠛⣿⡟⠛⠛⠛⣿⣿⠿⢿⣿⣿⣿⣿⣿
⢉⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⣿⣿⣧⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣴⣴⣼⣿⣧⠀⢀⠀⣿⣿⠀⡀⡄⢠⢠⣽⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⠏⢠⣿⣿⡟⣿⣿⣻⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣿⣿⣿⣿⣞⠷⡷⣾⣾⣿⣿
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠁⠉⠉⠉⠀⠉⠉⠉⠁⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠁⠉⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⠀⠀⠀⢠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣼⣿⣿⡟⢸⡇⡏⡟⣟⢸⡇⣏⢸⠁⢸⠸⡝⠀⣿⢸⢸⡁⣿⠀⢹⢹⢹⠀⣿⡇⣿⢸⣿⢸⣿⣿⡇⣏⢸⡇⢯⠃⢸⣿⣿⠁⢸⣼⣿⣿⡇⡇⣿⣾⡇⣧⡿⣟⠀⡏⡇⣏⠀⡏⡇⣿⢸⢸⡇⣿⢸⣹⢺⡃⠀⠀
⠀⠸⠏⠛⠛⠟⠸⠃⠳⠛⠞⠸⠇⠇⠘⠀⠸⠘⠟⠀⠛⠸⠸⠆⠟⠀⠸⠘⠞⠀⠛⠇⠿⠘⠹⠸⠟⠛⠇⠷⠸⠇⠻⠃⠘⠟⠛⠀⠸⠋⠛⠛⠇⠷⠛⠻⠃⠟⠛⠞⠀⠳⠃⠇⠀⠷⠃⠿⠸⠞⠇⠟⠺⠹⠺⠇⠀⠀
⠀⢸⢸⣿⠀⣏⢸⡇⣏⣿⣏⡇⣏⡃⣿⡇⢸⡷⣟⡇⡇⣿⢸⡁⢟⠂⠀⢧⣇⡇⣿⢸⠸⡓⢹⢹⠀⣏⣿⡇⡇⡏⡏⣿⣾⢸⡁⣿⠀⢸⡇⡇⡇⢸⡁⣟⢸⡁⢟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠸⠸⠿⠀⠇⠸⠇⠏⠾⠧⠇⠣⠇⠿⠇⠸⠟⠟⠇⠇⠿⠸⠄⠿⢳⠀⠸⠹⠁⠿⠸⠰⠟⠸⠸⠄⠧⠻⠇⠧⠣⠇⠟⠿⠸⠄⠿⠀⠾⠇⠧⠷⠸⠄⠿⠸⠄⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠑⠆⢶⠆⠒⠦⡄⠆⠦⠄⠆⠦⠈⠰⠀⠙⠘⠶⠶⠆⠀⠀⠀⠀⠐⢖⠶⠄⡀⠲⠄⠶⠀⠲⠆⠀⠲⠆⠐⠶⠆⢲⠲⠶⠀⠈⠚⠈⠃⠇⠰⠶⠰⠀⠆⠐⠶⠆⠘⠄⠄⠐⠲⠰⠄⠲⠀⠆⠢⠲⠆⠐⠆⠀⠀
⠀⠀⣠⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣠⣤⢀⢠⡀⣠⢄⡠⠀⣀⢠⢄⣤⠤⢠⢀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⣿⣿⣿⡿⠋⠁⠀⠈⣽⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣦⣤⣀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⢶⣶⣶⣄⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣷⣌⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⡉⠻⣿⡿⠆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⢠⣤⡆⠀⢹⣌⣹⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢰⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣷⣦⣤⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠈⣿⡏⠀⣸⣿⣿⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠐⡏⠀⣰⡏⢻⡇⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣀⢠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠃⢤⣤⣴⡿⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⣠⣤⣤⣼⣿⣿⣿⠿⠿⠿⣿⣿⣿⡿⣿⠟⠉⠟⠛⠉⠉⠉⠉⠛⠻⠆⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠂⣀⡀⠀⣠⠀⣀⢀⣀⣩⣏⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⡇⠀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣣⠶⠛⠀⠀⠈⡻⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣟⡛⢁⡀⡀⣀⢀⣈⢓⡐⢁⣚⢟⣛⢙⣿⢉⣛⣿⣿⣿⣿⣿⡿⣿⢿⡿⡿⣿⣿⣿⣿⣿⣿⠀⠘⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠁⠈⠉⢹⣿⠁⠀⠀⠀⠀⠀⠈⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡟⠁⣻⣍⣿⣧⢻⡇⠈⠉⣿⣛⣿⣿⢸⣿⣸⣿⣻⣿⣿⡿⠏⣿⢹⣿⣿⣿⣷⡇⣿⣾⣿⣿⣿⣿⠀⠸⣿⣟⣛⣋⡉⠁⠀⠀⠀⠀⢀⠀⠀⢸⣿⣄⡀⠀⠀⠀⣠⣿⠿⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡟⠀⠀⠙⠋⠛⠛⠘⠁⠀⠀⠙⠋⠙⠛⠘⠙⠙⠛⠋⠛⠙⠃⠀⢿⣼⣯⣿⣽⣯⣷⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣅⡀⠀⢠⣾⣿⣿⣦⣌⡙⠅⠀⠤⠒⠛⠫⣾⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⠿⠻⢿⣶⣶⣶⣶⣦⣤⣀⣀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣶⣶⡒⠛⠃
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠈⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠀⢀⠉⠉⠙⠛⠛⠉⠉⠿⠻⠟⠁⠀⠁⠀⠀⠀⠂⠙⠻⠿⠛⠋⠋⠁⠀⠀⠒⠚⠛⠉⠉⠉⠀⠁⠀⠀⠀⠀
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⠟⠓⠦⣄⠀⠀⠀⠀⢿⣿⣿⣿⡇⠿⢹⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⢠⣿⣿⡇⢻⣿⣸⣿⣇⣿⡇⣿⣧⣿⠏⣿⡇⣿⣿⢸⣿⢰⣿⣿⡇⢸⣿⢻⣷⢸⣿⣿⣿⡆⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⣀⣠⠄⠀⠀⠀⠀⠀⠘⡿⠊⠙⠠⠀⣼⣟⣿⣿⣿⣿⠀⠀⠁⢼⣿⢸⣿⢹⣷⢸⣿⣿⣿⣿⣿⠃⣿⣿⣿⠀⣿⣷⣿⣿⣿⣿⢸⣿⣻⣧⢸⣿⢿⣯⢸⣿⣿⣿⡇⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣰⣶⡀⠀⠀⢨⣾⣿⣿⣿⣿⠀⠀⠀⣸⣿⣾⣿⢻⣿⠘⣿⣿⢸⣿⣿⠀⣿⡏⣿⣇⢹⣿⡏⢿⣿⡇⣾⣿⢻⣿⢸⣿⢸⣿⢸⣿⣿⣿⠇⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠁⠀⠀⠀⠀⠀⠀⠀⠻⣿⠇⠀⣰⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣶⣶⣶⣿⡿⣿⡄⣿⡇⣿⣿⣤⣿⣿⣿⢸⣿⣸⣿⢰⣿⢻⣿⡆⣿⡿⢇⢻⣿⣀⣀⣀⣀⣀⣀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠀⢘⣿⣿⣿⣿⣿⠯⠻⢿⣦⡁⣿⡇⣿⣿⠋⣿⣿⠾⢸⣿⣿⣿⢸⣿⢈⣛⡃⣿⡷⠆⢸⣿⢻⣿⣿⣿⣿⡟
⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣦⣄⣀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡿⢿⣿⣿⢿⡞⣿⣧⣿⠇⣿⡇⣿⣿⣤⣿⣿⣤⢸⣿⢿⣿⠸⣿⣼⣿⠇⣿⣧⣤⣼⣿⢸⣿⣿⣿⡿⠇
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠈⠃⠛⠛⠛⠘⠓⠒⠉⠁⠀⠀⠐⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠁⠀
⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣀⣀⣀⣀⣀⣀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣿⣿⣿⣟⠉⠀⠀⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⡿⢷⣦⣤⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⣿⣿⣷⣦⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣦⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠄⠙⣿⢟⣃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣠⣄⣀⡀⡀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⢰⣶⣇⠀⢸⣦⣼⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⣼⣿⡿⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠈⡇⠀⠴⠆⣹⡇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢄⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠁⠲⣶⣾⠟⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⡿⠀⠀⠀⠀⣀⣴⣶⣶⣾⣿⣿⡿⠟⡛⠛⠿⢿⣿⡟⣿⠋⠀⠋⠉⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠁⢤⡄⠀⡴⣀⣤⣠⣤⣴⣧⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣇⣀⣤⣾⣿⣿⣿⡿⢿⣿⣿⣿⡵⠛⠋⠀⠀⠀⢝⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠉⠸⣦⣿⣿⣿⣾⡿⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢈⣿⣿⣿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣀⣼⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠟⠀⠀⠀⠀⢠⡶⣦⣰⣦⢰⣰⠆⢶⣾⣵⢾⣱⡶⡄⣶⢰⣏⣿⣿⡿⢽⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⣿⣯⣭⣥⣄⡀⠀⠀⠀⢀⣠⣀⠀⢸⡿⡦⠄⠀⠀⣀⣴⢿⡛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡏⠀⠀⠀⠀⠀⢠⣝⣷⣿⣿⠘⣿⠀⠀⠀⣿⣨⢼⡟⡇⣿⢸⢿⢿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣿⣿⣿⣿⣿⣦⣄⣀⣰⣿⣿⣿⣷⣦⣌⣀⠀⠒⠉⠉⠑⠿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⣿⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠈⠁⠁⠀⠀⠀⠈⠉⢈⠁⠁⠉⠈⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠸⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠟⠻⡿⠛⠙⠻⠿⣷⣾⣿⣷⣶⣤⡤⠀⠀⠀⢀⣠⣤⣤⣶⠶⡿⠿⠍⠉⠁
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠀⢠⣀⠀⠉⠉⠉⠀⠀⠿⠿⠿⠦⠄⠀⠀⠀⠀⠁⠸⠿⠛⠋⠃⠁⠀⠀⠈⠉⠉⠉⠀⠒⠂⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⠋⠉⠓⠦⠀⠀⠀⠀⢻⣿⢿⣿⠇⠛⢸⣿⣿⣿⣿⣿⠀⠸⡿⢹⣿⠁⣿⣿⡇⢻⣧⣾⣿⢸⣿⢹⣿⣸⡿⢹⣿⢸⣿⣦⣿⡇⣿⣿⡇⢸⣿⢻⣷⢸⣿⢻⣿⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣀⣴⠀⠀⠀⠀⠀⠀⠈⠟⠂⠈⠐⠀⢾⢯⣿⣿⣿⣿⠀⠀⠀⢸⣿⢸⣿⣹⣷⢸⣿⣿⣿⣿⣿⢸⣿⣿⣇⢸⣿⣿⣿⣿⣿⢠⣿⣹⣿⢸⣿⢿⣯⢸⣿⢸⣿⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣼⣿⡄⠀⠀⣰⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣼⣿⢻⣿⠸⣿⣿⢸⣿⡟⢸⣿⢸⣿⡀⣿⣿⠸⣿⣿⢸⣿⢻⣿⣸⣿⢸⣿⢸⣿⣾⡿⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠃⠀⣼⣿⣿⣿⣿⣿⣿⠀⢀⣀⣀⡀⠀⠀⠀⢀⣀⡀⠀⣀⡲⣚⡃⠀⣀⣀⡀⣀⠀⣀⡀⠀⣀⣀⠀⣀⣀⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀
⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣷⣿⡿⠿⢸⣿⡇⣿⡇⡆⣿⡟⡇⣿⣧⣿⡇⣿⡏⣿⡇⣿⣿⢛⢹⣿⣤⣤⣤⣤⣤⣤⣤
⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠀⢨⣿⣿⣿⣿⣿⣇⣙⣿⣷⣸⣿⡇⣿⡇⠃⣿⡟⠃⣿⣿⣿⡇⣿⡇⣭⡅⣿⣿⠋⢸⣿⢹⣿⣿⣿⣿⣿⡏
⢿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡟⣻⣿⣿⢻⡏⠿⣷⡿⠻⠿⠇⠿⠷⠆⠿⠷⠆⠿⠟⠿⠇⠻⣷⡿⠇⠿⠿⠶⠾⠿⢸⣿⣿⣿⣿⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠁⠉⠉⠉⠈⠉⠉⠀⠀⠁⠀⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀
⣠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣀⣀⣀⡀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣠⣤⣶⣾⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠽⢿⣿⣿⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠿⠊⠉⢠⠂⠀⣤⣴⣶⣿⣟⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⢈⡁⠀⢻⠃⢤⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠿⣿⣿⣿⣿⣿⣿⠿⠟⠉⠁⠀⠉⠓⠀⠂⠀⠁⠈⠉⠛⠿⠿⠟⠻⠿⠿⠿⣿⡻⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⡷⠀⢸⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠛⠛⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⢾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠠⡿⠃⢐⡚⣿⡏⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠇⠀⣘⣃⣼⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠃⢾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠐⢦⢀⢸⣿⡿⠇⣿⣿⡇⢿⣾⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢨⣽⢿⡆⣿⣽⣧⠘⣿⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠘⠛⠀⠛⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠃⣴⣴⣦⣶⡆⣶⣶⢰⣦⣠⡶⣦⣠⣶⣦⡄⣠⡶⣦⣀⣴⢶⡄⣭⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠈⠈⢹⣿⣿⣿⣿⢸⣿⣿⡇⠛⢻⣿⢾⡏⣿⡇⣿⡟⢿⣮⡅⣿⣿⣿⢸⣿⣾⣿⣿⢰⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠀⠀⠀⢸⣿⢻⣿⣿⢸⣿⢻⣧⣿⢻⣿⢸⣿⢻⣧⣿⠛⣿⣼⠇⢿⣿⡿⣸⣿⠈⢹⣿⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠑⠀⠀⠀⠀⠰⣿⡱⠾⢃⠀⢰⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣾⠁⠀⠀⠀⠀⠀⠀⢉⣀⠀⠈⠀⠻⣳⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⡄⣤⡄⣤⣤⣤⢠⣄⢤⡄⣤⣤⣄⢠⣤⣤⢠⣤⢠⣤⢠⡄⣤⣤⡄⠀⣤⣤⡄⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢿⣿⡆⠀⢠⣼⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣷⣿⣷⣿⢿⣿⢸⣿⣿⡇⣿⢸⣿⢸⡇⣿⡿⣿⣾⣿⣿⡏⢿⣮⡁⠀⠀⣿⠃⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⢠⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⣿⡟⣿⣿⢸⣿⢸⡏⣿⡇⣿⣼⡿⢸⣧⣿⠃⣿⣿⢻⣿⠃⣿⣼⡗⠀⢸⡿⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣀⢀⣀⢀⣀⢀⣀⡀⢀⣀⣀⠀⠀⣀⡀⣀⣀⣀⡀⣀⠀⢀⡀⣀⣀⡀⢀⣀⣀⢀⣀⡀⢀⣀⠀⠀
⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣾⣿⢸⣿⣧⢸⣯⡛⠀⠀⣿⣧⣿⣿⢹⣿⡟⠀⢸⡇⣿⡏⣿⢸⣿⣉⢸⣿⣧⢸⡏⠀⠀
⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢹⣿⣿⣿⡏⣾⣿⣿⢰⣟⣿⡆⠀⣿⣿⣿⣿⠈⣿⠁⠀⢸⡇⣿⣇⣿⢸⣿⣉⣿⣿⣿⢸⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠁⠉⠁⠉⠉⠉⠉⠀⠀⠉⠈⠉⠉⠀⠉⠀⠀⠈⠁⠉⠉⠉⠈⠉⠉⠉⠁⠉⠉⠁⠀⠀

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Gemini_version_available_♊︎


✐ Canonical_is_Becoming_Softer_(Pro-Microsoft_and_Against_Free_Speech)⠀✐


Posted in Free/Libre_Software, GNU/Linux, Microsoft, Ubuntu at 3:56 am by Dr.
Roy Schestowitz


Video_download_link | md5sum 803ce78aa023ddd2685a019f3aa941e6
Lessening Free Speech Is Not Ethics
Creative Commons Attribution-No Derivative Works 4.0


http://techrights.org/videos/canonical-ethics.webm


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇I'm trying to blacklist; I mean, killfile; I mean, denylist⦈
Summary: In the name of “protecting us” the folks_at_Microsoft_Canonical herald
a new era of censorship and self-censorship


THE INTERNET is becoming more oppressive a space over time. I’m not so old —
nor a “traditionalist” — but I think the way things are going is truly
Orwellian. It’s further magnified by centralised platforms such as social
control media and corporations that control Free software communities — to the
point of policing speech. Of course they call that “Open Source” and speak of
“conduct” (code word for control by those corporations).


Enter_Canonical. Yesterday it published “Inclusive Language and its Future at
Canonical” — a post that I wanted to respond to in video form. It’s harder to
take videos out of context.


“Are we mandating tolerance of corruption?”This issue isn’t a cross-
generational thing. It’s not even about age. It’s about corporate interests and
a divide-and-rule strategy, akin_to_trolling by the most_hypocritical_companies
out_there. A few months ago I turned 40 and my site has just turned_20 (I’m
hardly new to the Web; I’ve made sites since I was 15 and I’ve used IRC since I
was about 13; it was prior to that when I had practised some simple
programming). The actual technical progress made since then is nearly zero.
We’ve had technology turned against its users, using misleading doublespeak
like “smart” and “clown computing”. At the same time there was a watering down
of language — to the point where condemning a_criminal_company_like_Microsoft
is_considered_"hateful". You know we’ve gone too far when criminals are
protected from “offence”. Are we mandating tolerance of corruption? █


Note/clarification regarding meme: When you ban someone or ban whole groups
(e.g. IP addresses from China) there’s no “polite” term/way to put it. It’s a
never-ending or circular game of word-shuffle. It’ll appease nobody but
xenophobic corporations which abhor speech (except their own), and that
appeasement will only be temporary anyway. It’s a pretext or excuse for ‘agenda
creep’, governed_by_corporations,_not_communities.


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠿⠯⠀⠀⢀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣘⠁⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀
⠀⠀⠀⠀⠀⠀⠀⣶⢶⣴⣦⣶⡆⠰⣶⢶⣶⣦⢶⣴⢶⡆⣶⣴⣦⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣷⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⡇⠀⣿⢸⣿⣿⢸⣿⢸⡇⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉⠉⠁⠀⠉⠈⠉⠉⠈⠉⠈⠁⠉⠉⠉⠉⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣧⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣾⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢻⣿⢻⣿⣷⠀⣿⣿⢸⡇⢸⣿⣷⣿⠿⢸⣷⡏⣿⢸⣿⣿⣿⠟⣿⠃⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣧⠀⠀⠙⠛⣿⠿⠛⠁⠀⠀⠀⠀⠀⠠⠾⠋
⠀⠀⠀⠀⢸⣿⠸⣿⡿⠀⣿⣿⢿⣧⣿⢿⡿⣿⡿⢸⡿⣧⣿⣼⣿⢾⣿⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣍⣙⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡋⠁⣀⣀⣨⣽⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣤⣴⣦⣦⣶⣶⢶⠶⠶⠶⠶⢶⡦⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠰⠆⠀⠀⢀⠀⠀⠀⠀⣶⣶⡄⠀⠀
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣄⠀⠀⠀⠀⢲⣾⣿⣷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢸⡾⠃⠀⠾⣿⣿⡇⠀⢰
⠀⠀⢀⣠⣤⣿⡀⠀⢀⣤⣦⣤⣤⠀⠀⠀⢠⡆⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢻⣿⡏⠀⠀⠀⠀⣨⡟⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠀⠀⠀⠀⠀⢧⠸⠓⣾⣷⣿⣷⣄⠸
⣤⣴⣾⣿⣿⣿⢟⣴⣾⣿⣿⢙⣋⣀⣀⣀⣸⣧⠀⠀⠀⠀⠘⠛⠛⠛⠀⠀⠀⠙⠇⠀⣀⣤⣾⣿⣿⣿⣭⡠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠰⠆⢘⣿⡄⠐⣸⣿⡏⠁⣾
⠈⢻⣿⣿⠿⣿⠿⠟⠛⠛⠳⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣂⣿⣿⣿⣿⣿⡄⠙⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢀⠀⠈⡟⣇⠀⠘⢿⠃⠀⣽
⠀⠘⠛⠋⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡿⠛⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠈⠉⢿⣿⣿⣿⠏⠉⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠸
⠀⠂⠲⣶⠀⢶⣶⣶⣶⣶⣶⠀⣿⣿⡇⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢿⣿⣿⡀⠀⣸⠄⢠⡄⠀⡧⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢿⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠿⠯⠀⠀⢀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣘⠁⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀
⠀⠀⠀⠀⠀⠀⠀⣶⢶⣴⣦⣶⡆⠰⣶⢶⣶⣦⢶⣴⢶⡆⣶⣴⣤⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡷⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⡇⠀⣿⢸⣿⣿⢸⣿⢸⡇⣿⣿⣿⣷⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉⠉⠁⠀⠉⠈⠉⠉⠈⠉⠈⠁⠉⠉⠉⠉⢩⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣧⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣾⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢻⣿⢻⣿⣷⠀⣿⣿⢸⡇⢸⣿⣷⣿⠿⢸⣷⡏⣿⢸⣿⣿⣿⠟⣿⠃⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣧⠀⠀⠙⠛⢿⠿⠛⠁⠀⠀⠀⠀⠀⠠⠟⠋
⠀⠀⠀⠀⢸⣿⠸⣿⡿⠀⣿⣿⢿⣧⣿⢿⡿⣿⡿⢸⡿⣧⣿⣼⣿⢾⣿⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣍⣙⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡋⢁⣀⣀⣨⣽⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣴⣦⣦⣴⣶⣶⠶⠶⠶⠶⠶⢶⡦⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠰⠆⠀⠀⢀⠀⠀⠀⠀⣶⣶⡄⠀⠀
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣶⣄⠀⠀⠀⠀⢲⣾⣿⣷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠸⡿⠓⠀⠾⣿⣿⡇⠀⢰
⠀⠀⢀⣠⣤⣿⡀⠀⢀⣤⣦⣤⣤⠀⠀⠀⢠⡇⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢻⣿⡏⠀⠀⠀⠀⣨⡟⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠀⠀⠀⠀⠀⢥⣸⠓⣼⣷⣿⣷⣄⠸
⣤⣴⣾⣿⣿⣿⢟⣴⣾⣿⣿⢙⣋⣀⣀⣀⣸⣧⠀⠀⠀⠀⠘⠛⠛⠛⠀⠀⠀⠙⠇⠀⣀⣄⣞⣿⣿⣷⣭⡠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠐⠆⢸⣿⡀⠐⣰⣿⡟⠁⢺
⠈⢻⣿⣿⠿⣿⠿⠟⠛⠛⠳⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⢂⣾⣿⣿⣿⣟⡀⠉⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢨⠀⠈⣿⣇⠀⠘⠻⠅⠀⢺
⠀⠘⠛⠋⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡿⠛⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠌⡙⣿⣿⣿⣿⠇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠈⠀⠀⡀⢻⡄⠀⠀⠀⠀⠸
⠀⠂⠲⣶⠀⢶⣶⣶⣶⣶⣶⠀⣿⣿⡇⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡏⣻⣿⣿⡆⠀⢸⠀⢠⡄⠀⠆⡀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠿⠯⠀⠀⢀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣈⠁⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀
⠀⠀⠀⠀⠀⠀⠀⣶⢶⣴⣦⣶⡆⠰⣶⢶⣶⣦⢶⣴⢶⡆⣶⣴⣤⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣷⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⡇⠀⣿⢸⣿⣿⢸⣿⢸⡇⣿⣿⣿⣷⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉⠉⠁⠀⠉⠈⠉⠉⠈⠉⠈⠁⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣧⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣾⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢻⣿⢻⣿⣷⠀⣿⣿⢸⡇⢸⣿⣷⣿⠿⢸⣷⡏⣿⢸⣿⣿⣿⠟⣿⠃⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣧⠀⠀⠙⠛⣿⠿⠛⠁⠀⠀⠀⠀⠀⠠⠞⠋
⠀⠀⠀⠀⢸⣿⠸⣿⡿⠀⣿⣿⢿⣧⣿⢿⡿⣿⡿⢸⡿⣧⣿⣼⣿⢾⣿⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣍⣙⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡋⢁⣀⣀⣨⣽⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣤⣴⣦⣴⣶⡶⠶⡶⠶⠶⠶⢶⡦⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⠒⠀⠀⢀⠀⠀⠀⠀⣶⣶⡀⠀⠀
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣶⣄⠀⠀⠀⠀⢲⣾⣿⣷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢸⡿⠑⠀⠾⣿⣿⡇⠀⢰
⠀⠀⢀⣠⣤⣿⡀⠀⠀⣤⣦⣤⣤⠀⠀⠀⢠⡇⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢻⣿⡏⠀⠀⠀⠀⣨⡟⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠀⠀⠀⠀⠀⢤⣸⠓⣾⣷⣿⣷⣦⠸
⣤⣴⣾⣿⣿⣿⢟⣴⣾⣿⣿⢙⣋⣀⣀⣀⣸⣧⠀⠀⠀⠀⠘⠛⠛⠛⠀⠀⠀⠙⠇⠀⣀⣤⣾⣿⣿⣧⣭⡠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠰⠆⢸⣿⡀⠐⣨⣽⡟⠁⣿
⠈⢻⣿⣿⠿⣿⠿⠟⠛⠛⠓⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⢂⣼⣿⣿⣿⣿⡀⠙⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢸⠀⠀⣿⣇⠀⠘⠻⠇⠀⢽
⠀⠘⠛⠋⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡿⠛⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠌⡈⢿⣿⣿⣿⠏⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⢻⣆⠀⠀⠀⠀⠸
⠀⠂⠲⣶⠀⢶⣶⣶⣶⣶⣶⠀⣿⣿⡇⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⢻⣿⣿⡇⠀⢐⠀⢠⡀⠀⡆⡀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠿⠿⠀⠀⢀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣈⡁⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣶⢶⣴⣦⣶⡆⠰⣶⢶⣶⣦⢶⣴⢶⡆⣶⣴⣤⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⡇⠀⣿⢸⣿⣿⢸⣿⢸⡇⣿⣿⣿⣷⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉⠉⠁⠀⠉⠈⠉⠉⠈⠉⠈⠁⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢻⣿⢻⣿⣷⠀⣿⣿⢸⡇⢸⣿⣷⣿⠿⢸⣷⡏⣿⢸⣿⣿⣿⠟⣿⠃⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⡀⠀⠘⠻⣿⠿⠛⠁⠀⠀⠀⠀⠀⠰⠿⠉
⠀⠀⠀⠀⢸⣿⠸⣿⡿⠀⣿⣿⢿⣧⣿⢿⡿⣿⡿⢸⡿⣧⣿⣼⣿⢾⣿⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡟⢟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣏⣙⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡏⠁⠀⠀⣈⣹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠰⠆⠀⠀⢀⠀⠀⠀⢠⣶⣦⠀⠀⠀
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡄⠀⠀⠀⠐⢶⣾⣿⣷⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢸⡾⠂⠀⠾⣿⣿⡇⠀⢸
⠀⠀⢀⣠⣼⣇⠀⠀⢀⣤⣤⣠⣄⠀⠀⠀⢠⡂⠀⠀⠀⠀⢸⣿⣿⣷⠀⠀⢿⣿⡇⠀⠀⠀⠀⣸⡟⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣅⢰⠳⣶⣿⣿⣷⡤⠺
⣤⣶⣿⣿⣿⣿⢧⣴⣿⣿⣯⢛⣋⣀⣀⣀⣻⡇⠀⠀⠀⠀⠘⠛⠛⠛⠀⠀⠀⠻⠇⠀⣠⣴⣾⣻⣷⣷⣭⡠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢠⠀⢻⣧⠀⢻⢽⣿⡟⠀⣿
⠙⣿⣿⡿⢿⣿⠿⠟⠛⠛⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⢀⣀⣼⣿⣿⣿⣿⡀⠙⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢈⠀⢹⣿⠀⠈⠿⣿⠀⠀⢹
⠀⠛⠛⠁⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡟⠛⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⢈⡁⣿⣿⣿⣿⠏⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠈⠀⠀⠸
⠀⠀⠲⣶⠂⢶⣶⣶⣶⣶⡶⠸⣿⣿⠁⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢿⣿⣿⡇⠀⢸⠀⢀⡤⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢹⡆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠿⠿⠀⠀⢀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣈⡁⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣶⢶⣴⣦⣶⡆⠰⣶⢶⣶⣦⢶⣴⢶⡆⣶⣴⣤⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⡇⠀⣿⢸⣿⣿⢸⣿⢸⡇⣿⣿⣿⣷⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉⠉⠁⠀⠉⠈⠉⠉⠈⠉⠈⠁⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢻⣿⢻⣿⣷⠀⣿⣿⢸⡇⢸⣿⣷⣿⠿⢸⣷⡏⣿⢸⣿⣿⣿⠟⣿⠃⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⡀⠀⠘⠻⣿⠿⠛⠁⠀⠀⠀⠀⠀⠰⠿⠉
⠀⠀⠀⠀⢸⣿⠸⣿⡿⠀⣿⣿⢿⣧⣿⢿⡿⣿⡿⢸⡿⣧⣿⣼⣿⢾⣿⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡿⢟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣏⣙⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡏⠁⠀⠀⣈⣹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣴⣶⡶⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠆⠀⠀⢀⠀⠀⠀⢠⣶⣦⠀⠀⠀
⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡄⠀⠀⠀⠐⢶⣾⣿⣷⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢸⡿⠂⠀⠾⢿⣿⡇⠀⢸
⠀⠀⢀⣠⣼⣇⠀⠀⢀⣤⣤⣠⣄⠀⠀⠀⢰⡀⠀⠀⠀⠀⢰⣿⣿⣷⠀⠀⢿⣿⡇⠀⠀⠀⢀⣸⡟⣅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣅⢸⢷⣶⣿⣿⣷⡄⠺
⣤⣶⣿⣿⣿⣿⢧⣴⣿⣿⣿⢛⣋⣀⣀⣀⣿⡇⠀⠀⠀⠀⠘⠛⠛⠛⠀⠀⠀⠻⠇⠀⡠⣴⣾⣿⣿⣶⣭⡀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢠⠀⢻⣶⠀⢻⣻⣿⠟⠁⣿
⠙⣿⣿⣿⢿⣿⠿⠟⠛⠛⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⢠⣂⣸⣿⣿⣿⣿⡄⠙⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢈⠀⢸⣿⠀⠈⠿⣿⠀⠀⢸
⠀⠛⠛⠁⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡟⠛⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⢈⡉⣿⣿⣿⣿⠏⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠈⠀⠀⠸
⠀⠂⠲⣶⠀⢶⣶⣶⣶⣶⡶⠸⣿⣿⠁⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡏⢻⣿⣿⡇⠀⢸⠀⢠⡤⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢹⡆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠛⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣶⢴⣴⣆⣶⡆⠰⣶⢶⣶⣦⢶⣰⢶⡆⣶⣴⣤⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡄⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⢿⣿⡇⠀⣿⢸⣿⣿⠘⡟⢸⡇⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⠁⠀⠉⠈⠉⠉⠈⠁⠈⠁⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢻⣿⢻⣿⣷⠀⣿⣿⢸⡇⢸⣿⣶⣿⠿⢸⣷⡏⣿⢸⣿⢿⣿⠛⣿⠃⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣿⡗⠀⣿⣿⣋⣹⣛⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⡇⠀⠀⠘⠻⣿⠿⠛⠁⠀⠀⠀⠀⠀⠠⠞⠀
⠀⠀⠀⠀⢸⣿⠸⣿⡿⠀⣿⣿⢿⣧⣾⢿⡟⣿⡿⢸⡿⣧⣿⡼⣿⢾⣿⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢛⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡏⠛⢻⣥⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡟⠉⠉⠉⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣧⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣴⣶⣶⣦⣄⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⠀⠀
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣤⡀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠈⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⠀⠀⢰
⠀⠀⢀⣀⣸⠀⠀⠀⢀⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⡆⠀⠘⣿⣿⠃⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠀⠀⢾
⣤⣶⣿⣿⣿⣿⢢⣤⣿⣿⡏⠛⠃⠀⠀⠀⢠⠀⠀⠀⠀⠀⠛⠛⠛⠃⠀⠀⠈⠻⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⡀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠻⢿⣿⡿⣿⡿⠿⠛⠁⠛⢰⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠛⠁⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⠟⠋⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢰⠀⢶⣶⣴⣶⣶⡆⠸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠈⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠛⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣶⢴⣴⣆⣶⡆⠰⣶⢶⣶⣦⢶⣰⢶⡆⣶⣴⣤⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡄⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⢿⣿⡇⠀⣿⢸⣿⣿⢸⡟⢸⡇⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⠁⠀⠉⠈⠉⠉⠈⠁⠈⠁⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢻⣿⢻⣿⣷⠀⣿⣿⢸⡇⢸⣿⣶⣿⠿⢸⣷⡏⣿⢸⣿⢿⣿⠛⣿⠃⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⡗⠀⣿⣟⣋⣹⡛⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⡇⠀⠀⠘⠻⣿⠿⠛⠁⠀⠀⠀⠀⠀⠠⠞⠀
⠀⠀⠀⠀⢸⣿⠸⣿⡿⠀⣿⣿⢿⣧⣾⢿⡟⣿⡿⢸⡿⣧⣿⡼⣿⢾⣿⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⢛⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡏⠛⢿⣥⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡟⠉⠉⠉⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣧⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣠⣀⣤⣤⣤⣤⠤⢤⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣴⣶⣶⣦⣄⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣤⡀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠈⠙⠻⠿⢿⣿⣯⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠄⠀⠀⠾⣿⣿⠀⠀⢰
⠀⠀⢀⣀⣸⡀⠀⠀⢀⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⡆⠀⠘⣿⣿⠃⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⠀⢾
⣤⣶⣿⣿⣿⣿⢢⣤⣿⣿⡏⠛⠃⠀⠀⠀⢠⠀⠀⠀⠀⠀⠛⠛⠛⠃⠀⠀⠈⠻⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠻⢿⣿⡿⣿⡿⠿⠟⠑⠉⢰⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠛⠁⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢰⠀⢶⣶⣴⣶⣶⡆⠸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠈⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⠛⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣶⢴⣴⣆⣶⡆⠰⣶⢶⣶⣦⢶⣰⢶⡆⣶⣴⣤⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠚
⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⢿⣿⡇⠀⣿⢸⣿⣿⠸⡟⢸⡇⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡆⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⠁⠀⠉⠈⠉⠉⠈⠁⠈⠁⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢻⣿⢻⣿⣷⠀⣿⣿⢸⡇⢸⣿⣶⣿⠿⢸⣷⡏⣿⢸⣿⢿⣿⠛⣿⠃⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⣧⢸⣿⣛⣩⣍⢹⣿⣿⣿⣿⣟⣏⣩⣿⣿⣿⣿⣿⣿⡄⠀⠀⠸⠿⢿⣿⠿⠛⠁⠀⠀⠀⠀⠀⣰⠖⠀
⠀⠀⠀⠀⢸⣿⠸⣿⡿⠀⣿⣿⢿⣧⣾⢿⡟⣿⡿⢸⡿⣧⣿⡼⣿⢾⣿⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡙⠋⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠉⢛⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣧⣼⣧⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠋⠉⠉⠉⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣦⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣶⣾⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⠀⣴
⠀⠀⢀⣀⣸⠀⠀⠀⢀⣤⡀⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⣿
⣠⣴⣿⣿⣿⡿⣀⣤⣿⣿⡛⠛⠃⠀⠀⠀⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠂⠀⠀⠀
⠿⣿⣿⡿⣿⡾⠿⠟⠙⠋⣴⣿⣿⣿⣿⣿⣷⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠐⠿⠛⠀⠈⠀⠀⠀⠀⠀⠙⢿⣿⣿⠟⠛⠋⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢰⠀⢶⣦⣴⣶⣶⠆⢸⣿⡏⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣶⢴⣴⣆⣶⡆⠰⣶⢶⣶⣦⢶⣰⢶⡆⣶⣴⣤⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠒
⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⢿⣿⡇⠀⣿⢸⣿⣿⢸⡟⢸⡇⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡆⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⠁⠀⠉⠈⠉⠉⠈⠁⠈⠁⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢻⣿⢻⣿⣷⠀⣿⣿⢸⡇⢸⣿⣶⣿⠿⢸⣷⡏⣿⢸⣿⢿⣿⠛⣿⠃⠀⠀⠀⠀⠀⠀⠙⠛⠿⣿⣧⢸⣿⣟⣭⣍⢹⣿⣿⣿⣿⣟⣏⣩⣿⣿⣿⣿⣿⣿⡄⠀⠀⠸⠿⢿⣿⠿⠛⠁⠀⠀⠀⠀⠀⣰⠖⠀
⠀⠀⠀⠀⢸⣿⠸⣿⡿⠀⣿⣿⢿⣧⣾⢿⡟⣿⡿⢸⡿⣧⣿⡼⣿⢾⣿⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡙⠋⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠙⢻⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣧⣼⣧⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠋⠉⠉⠉⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣦⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣶⣾⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠄⠀⢠⣿⣿⣿⠀⠀⣴
⠀⠀⢀⣀⡾⠀⠀⠀⢀⣤⡀⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢀⣿⣿⣿⣿⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⣿
⣠⣴⣿⣿⣿⡷⣀⣤⣿⣿⡟⠛⠃⠀⠀⠀⡀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡀⠀⠀⠀
⠿⣿⣿⡿⣿⡶⠿⠟⠉⠋⣴⣿⣿⣿⣿⣿⣷⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠐⠿⠛⠀⠈⠀⠀⠀⠀⠀⠙⢿⣿⣿⠟⠛⠇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢰⠀⢴⣦⣴⣶⣶⠆⢸⣿⡏⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠿⠭⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣶⢴⣴⣆⣶⡆⠰⣶⢶⣶⣦⢶⣰⢶⡆⣶⣴⣤⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠒
⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⢿⣿⡇⠀⣿⢸⣿⣿⢘⡟⢸⡇⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡄⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⠁⠀⠉⠈⠉⠉⠈⠁⠈⠁⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢻⣿⢻⣿⣷⠀⣿⣿⢸⡇⢸⣿⣦⣿⠿⢸⣷⡏⣿⢸⣿⢿⣿⠚⣿⠃⠀⠀⠀⠀⠀⠈⠙⠻⠿⢰⢿⣋⣩⣍⣹⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⡆⠀⠀⠘⠿⠿⠿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⣠⠖⠀
⠀⠀⠀⠀⢸⣿⠸⣿⡿⠀⣿⣿⢿⣧⣼⢿⡟⣿⡿⢸⡿⣧⣿⡼⣿⢾⣿⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡉⣻⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣿⣧⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡟⠋⠉⣉⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣇⣀⣀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡇⠀⠀⢠⣤⣿⣧⠄⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣠⣿⣿⣇⠀⠀⣴
⠀⠀⠀⣀⡇⠀⠀⠀⢀⣀⣀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⡀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠙⠛⠟⠀⢀⣿
⣠⣼⣿⣿⣿⡗⣀⣰⣿⣿⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⢸⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⢿⣿⣿⢿⣿⣾⡿⠟⠛⠋⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠸⠿⠋⠀⠉⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢰⠀⢴⣤⣴⣴⣶⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠭⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣶⢴⣴⣆⣶⡆⠰⣶⢶⣶⣦⢶⣰⢶⡆⣶⣴⣤⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠒
⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⢿⣿⡇⠀⣿⢸⣿⣿⢸⡟⢸⡇⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡄⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⠁⠀⠉⠈⠉⠉⠀⠁⠈⠁⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢻⣿⢻⣿⣷⠀⣿⣿⢸⡇⢸⣿⣶⣿⠿⢸⣷⡏⣿⢸⣿⢿⣿⠚⣿⠃⠀⠀⠀⠀⠀⠈⠙⠻⠿⢰⠿⣋⣥⣍⣹⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⡄⠀⠀⠘⠿⠿⠿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⣠⠆⠀
⠀⠀⠀⠀⢸⣿⠸⣿⡿⠀⣿⣿⢿⣧⣾⢿⡟⢿⡿⢸⡿⣧⣿⡼⣿⢾⣿⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡉⣻⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣿⣧⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡟⠋⠉⣉⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣇⣀⣀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣠⣀⡀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡇⠀⠀⢠⣤⣿⣧⠄⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣠⣿⣿⡇⠀⠀⣴
⠀⠀⠀⣀⡇⠀⠀⠀⢀⣀⣀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⡀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠟⠀⢀⣿
⣠⣼⣿⣿⣿⡷⣀⣰⣿⣿⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⢸⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣿⣿⣿⢿⣿⣾⠿⠟⠛⠋⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠸⠿⠏⠀⠉⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢰⠀⣴⣤⣴⣴⣶⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣄⣀⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⠅⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣶⢴⣴⣆⣶⡆⠰⣶⢶⣶⣦⢶⣰⢶⡆⣶⣴⣤⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠒
⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⢿⣿⡇⠀⣿⢸⣿⣿⢸⡟⢸⡇⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⠁⠀⠉⠈⠉⠉⠈⠁⠈⠁⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢻⣿⢻⣿⣷⠀⣿⣿⢸⡇⢸⣿⣦⣿⠿⢸⣷⡏⣿⢸⣿⣿⣿⠚⣿⠃⠀⠀⠀⠀⠀⠈⠛⠇⢼⣟⣩⣭⣉⣿⣿⣿⣿⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⡀⠀⢀⠹⠿⠿⠿⠿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⣠⠆⠀
⠀⠀⠀⠀⢸⣿⠸⣿⡿⠀⣿⣿⢿⣧⣼⢿⡟⣿⡿⢸⡿⣧⣿⡼⣿⢾⣿⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⣉⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣛⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⢀⣀⣀⣠⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⢸⣿⣿⣿⣿⡄⠀⠀⠀⢠⣤⣿⡧⠀⠀⠀⠀⠀⠀⠀⠈⠉⠩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠉⡠⠀⠀⠀⣠⣿⣿⡇⠀⠀⣴
⠀⠀⠀⣀⡃⠀⠀⠀⢀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣦⢸⣿⣿⣿⣿⣧⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠍⢛⠻⠟⠀⢀⣿
⣠⣼⣿⣿⣿⡆⣀⣰⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠉
⣿⣿⣿⣿⣿⣾⡿⠟⠛⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⠀⠀⠀⠀
⠸⠿⠋⠀⠉⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢰⠀⣴⣤⣤⣤⣶⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠯⠅⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣶⢴⣴⣆⣶⡆⠰⣶⢶⣶⣦⢶⣰⢶⡆⣶⣴⣤⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠒
⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⢿⣿⡇⠀⣿⢸⣿⣿⠘⡟⢸⡇⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⠁⠀⠉⠈⠉⠉⠀⠁⠈⠁⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢻⣿⢻⣿⣷⠀⣿⣿⢸⡇⢸⣿⣦⣿⠿⢸⣷⡏⣿⢸⣿⢿⣿⠚⣿⠃⠀⠀⠀⠀⠀⠈⠙⠃⡾⣋⣥⣤⣌⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣷⡀⠀⣀⡹⠿⠿⠿⠿⢿⣿⠿⠛⠁⠀⠀⠀⠀⠀⣠⠆⠀
⠀⠀⠀⠀⢸⣿⠸⣿⡿⠀⣿⣿⢿⣧⣼⢿⡟⣿⡿⢸⡿⣧⣿⡼⣿⢾⣿⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢉⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣤⡀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣇⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣷⣶⡀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⣿⣧⣤⣄⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠈⢿⣿⣟⣩⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣧⡄⠀⠐⣿⣿⣿⣿⡄⢠⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣦⠀⢿⣿⣿⣿⠀⢼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⢿⣿⠟⠀⢸⣿⣿⣿⣿⡇⢀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣤⣄⢸⣿⣿⣿⣿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⣠⣿⣿⣧⠀⠀⣴
⠀⠀⠀⣀⡃⠀⠀⠀⢀⣀⡀⣀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠟⠀⢀⣿
⣠⣼⣿⣿⣿⡗⣀⣰⣿⣿⠙⠟⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⣿⣿⣿⢿⣿⣾⠿⠟⠻⠋⣶⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠸⠿⠋⠀⠉⠀⠀⠀⠀⠀⠻⣿⣿⣿⠟⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢰⠀⢴⣤⣴⣴⣶⠖⢿⣿⡇⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠅⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣶⢴⣴⣆⣶⡆⠰⣶⢶⣶⣦⢶⣰⢶⡆⣶⣴⣤⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠒
⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⢿⣿⡇⠀⣿⢸⣿⣿⠘⡟⢸⡇⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⠁⠀⠉⠈⠉⠉⠀⠁⠈⠁⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢻⣿⢻⣿⣷⠀⣿⣿⢸⡇⢸⣿⣶⣿⠿⢸⣷⡏⣿⢸⣿⢿⣿⠚⣿⠃⠀⠀⠀⠀⠀⠈⠙⠃⠾⣋⣥⣤⣌⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣷⡀⠀⣀⡹⠿⠿⠿⠿⢿⣿⠿⠛⠁⠀⠀⠀⠀⠀⣠⠆⠀
⠀⠀⠀⠀⢸⣿⠸⣿⡿⠀⣿⣿⢿⣧⣼⢿⡟⣿⡿⢸⡿⣧⣿⡼⣿⢾⣿⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢉⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣤⡀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣇⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣷⣶⡀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⣿⣧⣤⣄⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠈⢿⣿⣟⣩⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣷⡄⠀⠐⣿⣿⣿⣿⡄⢠⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣦⠀⢿⣿⣿⣿⠁⢼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⢿⣿⠟⠀⢸⣿⣿⣿⣿⡇⢀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⢸⣿⣿⣿⣿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠈⠉⠠⠀⠀⠀⣠⣿⣿⣧⠀⠀⣴
⠀⠀⠀⣀⡃⠀⠀⠀⢀⣀⡀⣀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠟⠀⠀⣿
⣠⣼⣿⣿⣿⡗⣀⣰⣿⣿⠛⠟⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⣿⣿⣿⢿⣿⣾⠿⠟⠻⠋⣶⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠸⠿⠋⠀⠉⠀⠀⠀⠀⠀⠻⣿⣿⣿⠟⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢰⠀⢴⣤⣴⣴⣶⠖⢿⣿⡏⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣄⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠙⠓⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣶⢴⣴⣆⣶⡆⠰⣶⢶⣶⣦⢶⣰⢶⡆⣶⣴⣤⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗
⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⢿⣿⡇⠀⣿⢸⣿⣿⠘⡟⢸⡇⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⠁⠀⠉⠈⠉⠉⠀⠁⠈⠁⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢻⣿⢻⣿⣷⠀⣿⣿⢸⡇⢸⣿⣦⣿⠿⢸⣷⡏⣿⢸⣿⢿⣿⠚⣿⠃⠀⠀⠀⠀⠀⠀⠙⠛⠰⣛⣥⣤⣤⣼⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣧⢀⢀⣀⠻⠿⠿⠿⢿⣿⡿⠛⠉⠀⠀⠀⠀⠀⢠⠖⠀
⠀⠀⠀⠀⢸⣿⠸⣿⡿⠀⣿⣿⢿⣧⣼⢿⡟⢿⡿⢸⡿⣷⣿⣾⣿⣾⣿⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢉⣨⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡿⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣄⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣩⣵⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣦⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡿⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⣴⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠉⠀⠄⠀⠀⣠⣾⣿⣿⠀⠀⢰
⠀⠀⠀⣀⡀⠀⠀⠀⢀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣽⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠀⠀⣿
⣠⣴⣿⣿⣿⡷⣀⣠⣿⣿⠛⠟⠃⠀⠀⠀⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⡀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢃⠀⠀⠀⠀⠉
⢿⣿⣿⢿⣿⡶⠿⠟⠋⠏⣶⣿⣿⣿⣿⣷⣷⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠐⠿⠟⠀⠈⠀⠀⠀⠀⠀⠙⢿⣿⣿⠟⠋⠋⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢰⠀⢴⣤⣴⣴⣶⠖⢺⣿⡏⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣄⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠙⠓⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣶⢴⣴⣆⣶⡆⠰⣶⢶⣶⣦⢶⣰⢶⡆⣶⣴⣤⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗
⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⢿⣿⡇⠀⣿⢸⣿⣿⠸⡟⢸⡇⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⠁⠀⠉⠈⠉⠉⠀⠁⠈⠁⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢻⣿⢻⣿⣷⠀⣿⣿⢸⡇⢸⣿⣶⣿⠿⢸⣷⡏⣿⢸⣿⢿⣿⠚⣿⠃⠀⠀⠀⠀⠀⠀⠙⠛⢰⣛⣥⣤⣤⣼⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣧⢀⢀⣀⠻⠿⠿⠿⢿⣿⡿⠛⠉⠀⠀⠀⠀⠀⢠⠖⠀
⠀⠀⠀⠀⢸⣿⠸⣿⡟⠀⣿⣿⢿⣧⣾⢿⡟⣿⡿⢸⡿⣷⣿⣾⣿⣾⣿⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢉⣨⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡿⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣄⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣩⣵⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣦⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡿⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⣴⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⣠⣾⣿⣿⠀⠀⢰
⠀⠀⠀⣀⣀⠀⠀⠀⢀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣽⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠛⠿⠀⠀⣿
⣠⣴⣿⣿⣿⡷⣀⣠⣿⣿⠛⠟⠃⠀⠀⠀⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠉
⢿⣿⣿⠿⣿⡶⠿⠟⠋⠏⣶⣿⣿⣿⣿⣷⣷⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀
⠐⠿⠟⠀⠈⠀⠀⠀⠀⠀⠙⢿⣿⣿⠟⠛⠋⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢠⠀⢴⣤⣴⣴⣶⠖⢺⣿⡏⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠙⠒⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣶⢴⣴⣆⣶⡆⠰⣶⢶⣶⣦⢶⣰⢶⡆⣶⣴⣤⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⢿⣿⡇⠀⣿⢸⣿⣿⠘⡟⢸⡇⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⠁⠀⠉⠈⠉⠉⠈⠁⠈⠁⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢻⣿⢻⣿⣷⠀⣿⣿⢸⡇⢸⣿⣶⣿⠿⢸⣷⡏⣿⢸⣿⢿⣿⠛⣿⠃⠀⠀⠀⠀⠀⠀⠉⠛⠰⣋⣥⣶⣤⣼⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣷⡀⣀⣀⡻⠿⠿⠿⠿⣿⡿⠛⠉⠀⠀⠀⠀⠀⢠⠖⠀
⠀⠀⠀⠀⢸⣿⠸⣿⡿⠀⣿⣿⢿⣧⣾⢿⡟⢿⡿⢸⡿⣧⣿⣼⣿⣾⣿⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢁⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡟⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣤⣤⣶⣶⣄⠀⠀⠀⠀⠀⣀⡀⠀⠸⣿⣿⣭⣵⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⣠⣿⣿⣿⡆⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣄⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⢠⣿⣿⣿⣿⡇⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢸⣿⣿⣿⣿⠃⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢠⣼⣿⣿⠀⠀⢠
⠀⠀⠀⣀⡀⠀⠀⠀⢀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠀⠀⣸
⣠⣤⣿⣿⣿⡷⢀⣠⣿⣿⠛⠟⠃⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⡀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⢿⣿⣿⡿⣿⡶⠿⠟⠛⠋⣶⣿⣿⣿⣿⣷⣿⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠐⠿⠟⠀⠈⠀⠀⠀⠀⠀⠙⢿⣿⣿⠟⠛⠉⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢠⠀⢴⣤⣴⣶⣶⠖⢸⣿⡟⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣶⣦⣤⣀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠙⠓⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣶⢴⣴⣆⣶⡆⠰⣶⢶⣶⣦⢶⣰⢶⡆⣶⣴⣤⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⢿⣿⡇⠀⣿⢸⣿⣿⢘⡟⢸⡇⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⠁⠀⠉⠈⠉⠉⠀⠁⠈⠁⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢻⣿⢻⣿⣷⠀⣿⣿⢸⡇⢸⣿⣶⣿⠿⢸⣷⡏⣿⢸⣿⢿⣿⠛⣿⠃⠀⠀⠀⠀⠀⠀⠉⠛⠰⣏⣥⣶⣤⣼⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣷⣀⣀⣀⡻⠿⠿⠿⠿⣿⡿⠛⠉⠀⠀⠀⠀⠀⢠⠖⠀
⠀⠀⠀⠀⢸⣿⠸⣿⡿⠀⣿⣿⢿⣧⣾⢿⡟⣿⡿⢸⡿⣧⣿⣼⣿⣾⣿⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢁⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡟⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣤⣤⣶⣶⣄⠀⠀⠀⠀⠀⣀⡀⠀⠸⣿⣿⣭⣵⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⣰⣿⣿⣿⡆⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⢠⣿⣿⣿⣿⡇⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢸⣿⣿⣿⣿⠃⠀⠀⠀⠈⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢠⣼⣿⣿⠀⠀⢰
⠀⠀⠀⣀⡀⠀⠀⠀⢀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠟⠿⠀⠀⣸
⣠⣤⣿⣿⣿⡷⢀⣠⣿⣿⠛⠿⠃⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⡀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⢿⣿⣿⡿⣿⡷⠿⠟⠛⠋⣴⣿⣿⣿⣿⣷⣿⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠐⠿⠟⠀⠈⠀⠀⠀⠀⠀⠘⢿⣿⣿⠟⠛⠋⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢠⠀⢴⣤⣴⣴⣶⠆⢸⣿⡟⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠂⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣶⢴⣴⣆⣶⡆⠰⣶⢦⣶⣦⢶⣰⢶⡆⣶⣴⣤⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⢿⣿⡇⠀⣿⢸⣿⣿⠸⡟⢸⡇⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⠁⠀⠉⠈⠉⠉⠀⠁⠈⠁⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢻⣿⢻⣿⣷⠀⣿⣿⢸⡇⢸⣿⣦⣿⠿⢸⣷⡏⣿⢸⣿⢿⣿⠚⣿⠃⠀⠀⠀⠀⠀⠀⠙⠃⠸⣫⣥⣤⣄⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣇⠀⣀⣀⡻⠿⠿⠿⠿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠴⠀
⠀⠀⠀⠀⢸⣿⠸⣿⡿⠀⣿⣿⢿⣧⣼⢿⡟⢿⡿⢸⡿⣧⣿⡼⣿⢾⣿⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⠟⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣤⣤⣶⣾⣿⣿⣿⣿⣿⣷⣤⡀⠀⢿⣿⣿⣋⣥⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣟⠛⢻⣿⣿⣿⡇⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢠⣼⣿⣿⠀⠀⢠
⠀⠀⠀⣀⡀⠀⠀⠀⢀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠟⠿⠀⠀⣸
⣠⣤⣿⣿⣿⡷⢀⣠⣿⣿⠛⠿⠃⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⢿⣿⣿⡿⣿⡶⠿⠟⠋⠋⣴⣿⣿⣿⣿⣷⣷⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠐⠿⠟⠀⠈⠀⠀⠀⠀⠀⠘⢿⣿⣿⠟⠛⠉⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢠⠀⢴⣤⣴⣶⣶⠆⢸⣿⡟⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣦⣤⣄⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣶⢴⣴⣆⣶⡆⠰⣶⢦⣶⣦⢶⣰⢶⡆⣶⣴⣤⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⢿⣿⡇⠀⣿⢸⣿⣿⠘⡟⢸⡇⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⠁⠀⠉⠈⠉⠉⠀⠁⠈⠁⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢻⣿⢻⣿⣷⠀⣿⣿⢸⡇⢸⣿⣦⣿⠿⢸⣷⡏⣿⢸⣿⢿⣿⠚⣿⠃⠀⠀⠀⠀⠀⠀⠉⢠⠟⣋⣥⣄⣹⣿⣿⣿⣿⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⣄⠀⣀⣈⠿⠿⠿⠿⢿⣿⡿⠟⠉⠀⠀⠀⠀⠀⢀⠴⠀
⠀⠀⠀⠀⢸⣿⠸⣿⡿⠀⣿⣿⢿⣧⣼⢿⡟⢿⡿⢸⡿⣧⣿⡼⣿⢾⣿⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡉⢙⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣤⣤⡀⢀⣀⣀⣀⣀⣠⣶⣶⡄⢸⣿⣿⡿⣛⣉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⢿⣿⣇⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠀⠀⠀⠙⠻⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⣼⣿⣿⠀⠀⢠
⠀⠀⠀⣀⡀⠀⠀⠀⢀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠀⠀⣸
⣠⣤⣿⣿⣿⣷⢀⣠⣾⣿⠛⠿⠃⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⢿⣿⣿⣿⣿⣷⡿⠟⠛⠋⣴⣿⣿⣿⣿⣶⣷⠀⠀⠸⣿⣿⣿⣿⣿⣿⣟⠀⠀⠻⣿⣿⡌⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠐⠿⠟⠀⠉⠀⠀⠀⠀⠀⠙⢿⣿⣿⠿⠛⠋⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣷⣦⣤⡈⢙⣵⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢠⠀⢴⣤⣴⣴⣶⠆⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣦⣤⣄⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣶⢴⣴⣆⣶⡆⠰⣶⢦⣶⣦⢶⣰⢶⡆⣶⣴⣤⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗
⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⢿⣿⡇⠀⣿⢸⣿⣿⠘⡟⢸⡇⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⠁⠀⠉⠈⠉⠉⠀⠁⠈⠁⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⣆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢻⣿⢻⣿⣷⠀⣿⣿⢸⡇⢸⣿⣦⣿⠿⢸⣷⡏⣿⢸⣿⢿⣿⠚⣿⠃⠀⠀⠀⠀⠀⠀⠉⠠⠟⣋⣥⣄⣹⣿⣿⣿⣿⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⡄⠀⣀⣈⠿⠿⠿⠿⢿⣿⡿⠟⠉⠀⠀⠀⠀⠀⢀⠤⠀
⠀⠀⠀⠀⢸⣿⠸⣿⡟⠀⣿⣿⢿⣧⣼⢿⡟⢿⡿⢸⡿⣧⣿⡼⣿⢾⣿⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡉⢙⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣤⣤⡀⢀⣀⣀⣀⣀⣠⣶⣶⡄⢸⣿⣿⡿⣛⣉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣇⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⣼⣿⣿⠀⠀⢠
⠀⠀⠀⣀⡀⠀⠀⠀⢀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠀⠀⣸
⣠⣤⣿⣿⣿⣷⢀⣠⣾⣿⠛⠿⠃⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⢿⣿⣿⣿⣿⣷⡿⠟⠋⠋⣴⣿⣿⣿⣿⣶⣿⠀⠀⠸⣿⣿⣿⣿⣿⣿⣟⠀⠀⠹⣿⣿⡌⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢳⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠐⠿⠟⠀⠉⠀⠀⠀⠀⠀⠹⢿⣿⣿⠿⠛⠋⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣷⣦⣤⣈⢙⣵⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢠⠀⢤⣤⣴⣤⣶⠆⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣶⣤⣤⣀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠂⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣶⢴⣴⣆⣶⡆⠰⣶⢦⣶⣦⢶⣰⢶⡆⣶⣴⣤⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗
⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⢿⣿⡇⠀⣿⢸⣿⣿⠘⡟⢸⡇⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⠁⠀⠉⠈⠉⠉⠀⠁⠈⠁⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢻⣿⢻⣿⣷⠀⣿⣿⢸⡇⢸⣿⣦⣿⠿⢸⣷⡏⣿⢸⣿⢿⣿⠚⣿⠃⠀⠀⠀⠀⠀⠀⠁⠸⢟⣉⣀⣈⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⣿⣧⠀⠀⣀⡘⠿⠿⠿⠿⠿⣿⡿⠟⠉⠀⠀⠀⠀⠀⢀⡤⠀
⠀⠀⠀⠀⢸⣿⠸⣿⡟⠀⣿⣿⢿⣧⣼⢿⡟⢿⡿⢸⡿⣧⣿⡼⣿⢾⣿⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⣫⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣾⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⠙⢻⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣤⣤⣀⣀⣀⣀⣄⣀⣴⣾⣶⡀⣿⣿⣿⠿⡋⠉⣉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⡀⣀⣀⢀⢀⣀⣀⣀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⢿⣿⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⡇⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠉⠉⢉⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⢀⣼⣿⣿⠀⠀⢠
⠀⠀⠀⢀⡀⠀⠀⠀⢀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠀⠀⣸
⣠⣤⣿⣿⣿⣷⢀⣠⣿⣿⠛⠿⠃⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⢿⣿⣿⣿⣿⣷⡿⠟⠉⠋⣴⣾⣿⣿⣿⣶⣶⠀⠀⢹⣿⣿⣿⣿⣿⣿⡄⠈⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠐⢶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠐⠿⠟⠀⠉⠀⠀⠀⠀⠀⠙⢿⣿⣿⠿⠛⠋⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣴⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢠⠀⢤⣤⣤⣤⣤⠆⢸⣿⡟⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣶⣤⣤⣀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠂⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣶⢴⣴⣆⣶⡆⠰⣶⢦⣶⣦⢶⣰⢶⡆⣶⣰⣤⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗
⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⢿⣿⡇⠀⣿⢸⣿⣿⠘⡟⢸⡇⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⠁⠀⠉⠈⠉⠉⠀⠁⠈⠁⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢻⣿⢻⣿⣷⠀⣿⣿⢸⡇⢸⣿⣶⣿⠿⢸⣷⡏⣿⢸⣿⢿⣿⠚⣿⠃⠀⠀⠀⠀⠀⠀⠁⠼⠟⣉⣀⡉⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⣿⣧⡀⢀⣀⡘⠿⠿⠿⠿⠿⣿⡿⠟⠉⠀⠀⠀⠀⠀⢀⡴⠀
⠀⠀⠀⠀⢸⣿⠸⣿⡟⠀⣿⣿⢿⣧⣼⢿⡟⢿⡿⢸⡿⣧⣿⡼⣿⢾⣿⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⢫⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣾⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣏⠙⢻⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣤⣤⣀⣀⣀⣀⣄⣀⣴⣾⣶⡀⣿⣿⣿⠿⡋⠉⣉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⢀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⢿⣿⡇⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⡇⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠈⠉⠉⢉⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⢀⣼⣿⣿⠀⠀⢠
⠀⠀⠀⢀⡀⠀⠀⠀⢀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠂⠀⣸
⣠⣤⣿⣿⣿⣷⢀⣠⣾⣿⠛⠿⠃⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⢿⣿⣿⣿⣿⣷⡿⠟⠉⠋⣴⣾⣿⣿⣿⣶⣷⠀⠀⢹⣿⣿⣿⣿⣿⣿⡄⠈⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠐⢶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠐⠿⠟⠀⠉⠀⠀⠀⠀⠀⠹⢿⣿⣿⠿⠛⠋⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣴⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢠⠀⢤⣤⣤⣤⣤⠆⢸⣿⡟⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣶⢴⣴⣆⣶⡆⠰⣶⢦⣶⣦⢶⣰⢶⡆⣶⣴⣤⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗
⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⢿⣿⡇⠀⣿⢸⣿⣿⠘⡟⢸⡇⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⠁⠀⠉⠈⠉⠉⠀⠁⠈⠁⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢻⣿⢻⣿⣷⠀⣿⣿⢸⡇⢸⣿⣦⣿⠿⢸⣷⡏⣿⢸⣿⢾⣿⠚⣿⠃⠀⠀⠀⠀⠀⠀⠀⠟⣋⣁⣀⣹⣿⣿⣿⣿⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⣆⠀⣀⣀⡻⠿⠿⠿⠿⠿⣿⡿⠟⠉⠀⠀⠀⠀⠀⢀⡤⠀
⠀⠀⠀⠀⢸⡿⠸⣿⡿⠀⣿⣿⢿⣧⣼⢿⡟⢿⡿⢸⡿⣧⣿⡼⣿⢾⣿⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⢋⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣴⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡉⠙⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣤⣤⣀⣤⣴⣶⣶⣶⣶⣶⣿⣿⣿⣿⡿⠏⠉⢁⣈⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⡀⢀⣀⠀⢀⣀⣀⣀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⣾⣿⣿⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⡇⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠉⠀⠀⢠⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⢀⣼⣿⣿⠀⠀⢠
⠀⠀⠀⢀⡀⠀⠀⠀⢀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⠀⠀⣸
⣠⣤⣿⣿⣿⣷⢀⣠⣾⣿⠛⠿⠃⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣟⠛⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⢿⣿⣿⣿⣿⣷⡿⠟⠋⠉⣴⣾⣿⣿⣿⣶⣶⠀⠀⢹⣿⣿⣿⣿⣿⣷⣄⠈⢿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠰⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠐⠿⠟⠀⠉⠀⠀⠀⠀⠀⠹⢿⣿⣿⠿⠛⠋⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣶⣥⣶⣾⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢠⠀⢤⣤⣤⣤⣴⠆⢸⣿⡟⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣶⢴⢰⣆⣶⡆⠰⣶⢦⡶⣦⢶⣰⢶⡆⣶⣰⢠⡶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠖
⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⢿⣿⡇⠀⣿⢸⡟⣿⠘⡟⢸⡇⣿⣿⣼⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠈⠉⠁⠀⠉⠈⠁⠉⠀⠁⠈⠁⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢻⣿⣿⣿⣷⢰⣿⣿⣾⣿⣿⣿⣿⣿⠿⢸⣿⣿⣿⠀⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠟⢋⣀⡀⢈⣿⣿⣿⣿⣿⣵⣤⣾⣿⣿⣿⣿⣿⣿⡄⠀⣀⣀⡻⠿⠿⠿⠿⠿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠄⠀
⠀⠀⠀⠀⢸⣿⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣾⢸⣿⣿⣿⡤⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢉⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⡿⣿⣿⣿⡇⣿⣿⣀⣸⣿⣾⣿⡇⣿⡟⣿⣿⢀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⠛⠃⠀⠘⠛⠃⠛⠛⠛⠃⠛⠛⠛⠛⠛⠀⠛⠓⠛⢃⡟⠛⢸⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠉⠙⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣀⡀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⠀⢀⣀⣀⡀⣤⣄⢠⣼⡇⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣧⣿⡇⢸⣿⠂⣿⡇⠀⣿⣿⠀⢸⣿⡟⠃⣿⣿⢸⣿⣿⣼⣿⣟⣯⣴⣶⣶⣶⣶⣶⣿⣷⣿⣿⡿⠋⠀⢁⣀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⡄⢸⣿⠀⣿⡇⠀⣿⣿⠀⢸⣿⡿⠇⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⠻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⡏⣿⣷⣸⣿⣄⣿⣷⣶⣿⣿⣶⢸⣿⡇⠀⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⢸⣿⣿⡄⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⣿⡇⠀⠙⠻⢿⣿⣿⣿⠿⠿⠛⢿⣟⣯⣽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⣼⣿⣷⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠀⠀⢸
⣀⣤⣿⣿⣿⡶⢀⣀⣾⣿⠛⠿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡍⠛⢿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⢿⣿⣿⢿⣿⣶⡿⠟⠈⠁⣰⣶⣿⣿⣿⣶⣦⠀⠀⠸⣿⣿⣿⣿⣿⣧⡄⠈⠻⡿⠘⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠰⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠿⠟⠀⠈⠀⠀⠀⠀⠀⠘⢿⣿⣿⠿⠛⠉⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣽⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⠀⢤⣤⣤⣤⣤⠂⢸⣿⡟⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢰⣿⡇⠀⢸⣿⣿⣆⣿⣿⡇⣿⣿⠿⠀⣿⣿⣿⠀⣿⣷⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⣋⣁⡀⢹⣿⣿⣿⣿⣿⣵⣤⣾⣿⣿⣿⣿⣿⣿⡄⠀⣀⣀⠿⠿⠿⠿⠿⠿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠄⠀
⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣤⢰⣿⣿⣿⡄⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢉⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⡿⣿⣿⣿⡇⣿⣿⣀⣸⣿⣿⣿⡇⣿⡟⣿⣿⢀⡀⢀⣶⣶⡄⠀⠀⠀⢰⣴⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⠛⠃⠀⠘⠛⠃⠛⠛⠛⠃⠛⠛⠛⠛⠛⠀⠛⠓⠛⢳⡟⠛⢸⣿⣿⣿⡿⠃⠀⠀⠀⢸⣿⣿⣿⠉⠛⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣀⡀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⠀⢀⣀⣀⡀⣤⣄⢠⣼⣧⢀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣧⣿⡏⢸⣿⠂⣿⡇⠀⣿⣿⠀⢸⣿⡟⠃⣿⣿⢸⣿⣿⣼⣿⣿⣿⣯⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⠟⠉⠉⠁⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⡄⢸⣿⠀⣿⡇⠀⣿⣿⠀⢸⣿⡿⠇⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⣼⣿⣿⣿⡿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⡏⣿⣷⣼⣿⣇⣿⣷⣶⣿⣿⣶⢸⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠙⢿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠉⠉⠉⠉⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⢀⣼⣿⣷⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠀⠀⢸
⣀⣤⣿⣿⣿⣶⢀⣠⣾⣿⠛⠿⠃⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⢿⣿⣿⣿⣿⣷⡿⠟⠉⠉⣰⣶⣿⣿⣿⣶⣶⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠠⣤⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠐⠿⠟⠀⠉⠀⠀⠀⠀⠀⠸⢿⣿⣿⠿⠛⠋⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢠⠀⢠⣤⣤⣤⣤⠆⢸⣿⡟⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢰⣿⡇⠀⢸⣿⣿⣆⣿⣿⡇⣿⣿⠿⠀⣿⣿⣿⠀⣿⣷⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⣋⣀⡀⢹⣿⣿⣿⣿⣿⣶⣤⣾⣿⣿⣿⣿⣿⣿⡄⠀⣀⣀⠿⠿⠿⠿⠿⠿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠄⠀
⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣦⢰⣿⣿⣿⡄⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢉⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⡿⣿⣿⣿⡇⣿⣿⣀⣸⣿⣿⣿⡇⣿⡟⣿⣿⢀⡀⢀⣴⣶⡆⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⠛⠃⠀⠘⠛⠃⠛⠛⠛⠃⠛⠛⠛⠛⠛⠀⠛⠓⠛⠃⡟⠛⢸⣿⣿⣿⡿⠃⠀⠀⠀⢸⣿⣿⣯⠉⢙⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣀⡀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⠀⢀⣀⣀⡀⣤⣄⢠⣼⣷⢀⣼⣿⣿⣿⠃⠀⠀⠀⠀⠈⢿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣧⣿⡏⢸⣿⠆⣿⡇⠀⣿⣿⠀⢸⣿⡟⠃⣿⣿⣸⣿⣿⣾⣿⣿⣿⣿⣷⣦⣄⠀⢀⣴⣿⣿⣿⡿⠋⠉⠀⠀⠉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⡄⢸⣿⠀⣿⡇⠀⣿⣿⠀⢸⣿⡿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⣾⣿⣿⣿⣿⣷⣴⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⡏⣿⣷⣼⣿⣇⣿⣷⣶⣿⣿⣶⣼⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⢉⣽⣿⣿⣿⣿⡆⠀⠀⣿⣿⣿⣿⡇⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣰⣿⣿⣿⣿⡇⠀⠀⠉⠛⠛⠛⠉⠁⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠃⠀⢸
⣀⣤⣿⣿⣿⣶⢀⣀⣾⣿⠛⠿⠃⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⢿⣿⣿⣿⣿⣷⡿⠟⠉⠁⢰⣶⣿⣿⣿⣶⣶⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠠⣄⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠿⠟⠀⠉⠀⠀⠀⠀⠀⠘⢿⣿⣿⠿⠛⠋⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⢠⠀⢠⣤⣤⣤⣤⠆⢸⣿⡟⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢰⣿⡇⠀⢸⣿⣿⣆⣿⣿⡇⣿⣿⠿⠀⣿⣿⣿⠀⣿⣷⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⣋⣀⡀⢹⣿⣿⣿⣿⣯⣶⣤⣾⣿⣿⣿⣿⣿⣿⡄⠀⣀⣀⠿⠿⠿⠿⠿⠿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠄⠀
⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣤⢰⣿⣿⣿⡀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢉⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⡿⣿⣿⣿⡇⣿⣿⣀⣸⣿⣿⣿⡇⣿⡟⣿⣿⢀⡀⢀⣴⣶⡆⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⠛⠃⠀⠘⠛⠃⠛⠛⠛⠃⠛⠛⠛⠛⠛⠀⠛⠓⠛⠃⡟⠛⢸⣿⣿⣿⡿⠃⠀⠀⠀⢸⣿⣿⣏⠉⢙⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣀⡀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⠀⢀⣀⣀⡀⣤⣄⢠⣼⣿⢀⣼⣿⣿⣿⠃⠀⠀⠀⠀⠈⢿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣧⣿⡇⢸⣿⠂⣿⡇⠀⣿⣿⠀⢸⣿⡟⠃⣿⣿⣸⣿⣿⣾⣿⣿⣿⣿⣷⣦⣀⠀⢀⣴⣿⣿⣿⡿⠋⠀⠀⠀⢉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⡄⢸⣿⠀⣿⡇⠀⣿⣿⠀⢸⣿⡿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣾⣿⣿⣿⣿⣷⣴⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⡏⣿⣷⣼⣿⣆⣿⣷⣶⣿⣿⣶⣼⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⢉⣽⣿⣿⣿⣿⡄⠀⠀⣿⣿⣿⣿⡇⠙⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣰⣿⣿⣿⣿⡇⠀⠀⠉⠙⠛⠛⠉⠁⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠃⠀⢸
⣀⣤⣿⣿⣿⣶⢀⣀⣾⣿⠛⠿⠃⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⢿⣿⣿⣿⣿⣷⡿⠟⠉⠁⢰⣶⣿⣿⣿⣶⣶⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠠⣄⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠿⠟⠀⠉⠀⠀⠀⠀⠀⠘⢿⣿⣿⠿⠛⠉⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⢠⠀⢠⣤⣤⣤⣤⠆⢸⣿⡟⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢰⣿⡇⠀⢸⣿⣿⣆⣿⣿⡇⣿⣿⠿⠀⣿⣿⣿⠀⣿⣷⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⢋⣀⡀⢸⣿⣿⣿⣿⣿⣵⣤⣾⣿⣿⣿⣿⣿⣿⣆⠀⣀⣀⡻⠿⠿⠿⠿⠿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠠⠀
⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣤⢰⣿⣿⣿⡀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠛⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⡿⣿⣿⣿⡇⣿⣿⣀⣸⣿⣾⣿⡇⣿⡟⣿⣿⢀⡀⠀⢀⣴⣶⡆⠀⠀⢠⣴⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⠛⠃⠀⠘⠛⠃⠛⠙⠛⠃⠛⠛⠛⠛⠛⠀⠛⠓⠛⠃⣿⠛⢸⢇⣴⣿⣿⣿⠃⠀⠀⢸⣿⣿⣯⠉⢙⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣀⡀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⠀⢀⣀⣀⡀⣤⣄⢠⣤⣿⢀⣠⣼⣿⣿⣿⣧⣄⠀⠀⠀⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣧⣿⡇⢸⣿⠂⣿⡗⠀⣿⣿⠀⢸⣿⡟⠃⣿⣿⣸⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣨⣿⣿⡟⠋⠀⠀⣀⣈⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⡄⢸⣿⠀⣿⡇⠀⣿⣿⠀⢸⣿⡿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢰⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⡏⣿⣷⣼⣿⣄⣿⣷⣶⣿⣿⣶⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠿⣿⣿⣿⣿⣇⣀⣭⣾⣿⣿⣿⣿⡄⠀⠀⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⣿⣿⣿⣿⡇⠀⠀⠉⠉⠉⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⣠⣿⣿⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠇⠀⢠
⣀⣤⣿⣿⣿⣶⠀⣀⣾⣿⠋⠿⠃⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣿⣿⡿⣿⣷⣾⠟⠉⠉⢰⣶⣿⣿⣿⣶⣶⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠾⠟⠁⠉⠁⠀⠀⠀⠀⠘⢿⣿⣿⡿⠛⠋⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⢠⠀⢠⣄⣤⣤⣤⠄⢸⣿⡿⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢰⣿⡇⠀⢸⣿⣿⣆⣿⣿⡇⣿⣿⠿⠀⣿⣿⣿⠀⣿⣷⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⢋⣀⡀⢸⣿⣿⣿⣿⣿⣵⣤⣾⣿⣿⣿⣿⣿⣿⣆⠀⣀⣀⡻⠿⠿⠿⠿⠿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⡠⠀
⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣤⢰⣿⣿⣿⡀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠛⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⡿⣿⣿⣿⡇⣿⣿⣀⣸⣿⣿⣿⡇⣿⡟⣿⣿⢀⡀⠀⢀⣴⣶⡆⠀⠀⢠⣴⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⠛⠃⠀⠘⠛⠃⠛⠙⠛⠃⠛⠛⠛⠛⠛⠀⠛⠓⠛⠃⣿⠛⢸⢇⣴⣿⣿⣿⠃⠀⠀⢸⣿⣿⣯⠉⢙⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣀⡀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⠀⢀⣀⣀⡀⣤⣄⢠⣤⣿⢀⣠⣼⣿⣿⣿⣧⣄⠀⠀⠀⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣧⣿⡇⢸⣿⠂⣿⡇⠀⣿⣿⠀⢸⣿⡟⠃⣿⣿⣸⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣨⣿⣿⡟⠋⠀⠀⣀⣀⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⡄⢸⣿⠀⣿⡇⠀⣿⣿⠀⢸⣿⡿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢰⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⡏⣿⣷⣼⣿⣆⣿⣷⣶⣿⣿⣶⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠿⣿⣿⣿⣿⣇⣀⣬⣿⣿⣿⣿⣿⡄⠀⠀⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⣿⣿⣿⣿⡇⠀⠀⠉⠉⠉⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⣠⣿⣿⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠇⠀⢠
⣀⣤⣿⣿⣿⣶⠀⣀⣾⣿⠋⠿⠃⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣿⣿⡿⣿⣷⣾⠟⠉⠉⢰⣶⣿⣿⣿⣶⣶⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⣤⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠾⠟⠁⠉⠁⠀⠀⠀⠀⠘⢿⣿⣿⡿⠛⠋⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⢠⠀⢠⣄⣤⣤⣤⠆⢸⣿⡿⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢰⣿⡇⠀⢸⣿⣿⣆⣿⣿⡇⣿⣿⠿⠀⣿⣿⣿⠀⣿⣷⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠛⣁⣀⠉⣿⣿⣿⣿⣿⣛⣛⣿⣿⣿⣿⣿⣿⣿⣧⠀⢀⣀⡘⠿⠿⠿⠿⠿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣤⢰⣿⣿⣿⡀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⡿⣿⣿⣿⡇⣿⣿⣀⣸⣿⣿⣿⡇⣿⡟⣿⣿⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⠛⠃⠀⠘⠛⠃⠛⠙⠛⠃⠛⠛⠛⠛⠛⠀⠛⠓⠛⠃⣿⠛⢸⠇⠀⠀⠀⢀⣤⣴⣾⣿⣿⣿⣿⡙⠛⢻⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣀⡀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⠀⢀⣀⣀⡀⣤⣄⢠⣤⣿⢀⣀⣀⣀⢀⣴⣿⣿⣿⡟⠋⢻⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣧⣿⡇⢸⣿⠂⣿⡗⠀⣿⣿⠀⢸⣿⡟⠃⣿⣿⢸⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣼⣿⣿⣿⣟⠋⠉⢉⣉⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⡄⢸⣿⠀⣿⡇⠀⣿⣿⠀⢸⣿⡿⠇⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⡏⣿⣷⣼⣿⣆⣿⣷⣶⣿⣿⣶⢸⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡃⣼⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⡇⠀⠉⠉⠉⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⣠⣿⣿⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠇⠀⠀
⣀⣤⣾⣿⣿⣷⠆⣀⣼⣿⠟⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣿⣿⣿⣿⣧⣾⠿⠋⠉⢠⣶⣾⣿⣶⣶⣶⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣤⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠾⠿⠃⠈⠁⠀⠀⠀⠀⠘⢿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⠀⢠⣄⣠⣤⣤⡆⠠⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢰⣿⡇⠀⢸⣿⣿⣆⣿⣿⡇⣿⣿⠿⠀⣿⣿⣿⠀⣿⣷⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠛⣁⣀⠈⣿⣿⣿⣿⣿⣛⣛⣿⣿⣿⣿⣿⣿⣿⣧⠀⢀⣀⡸⠿⠿⠿⠿⠿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣤⢰⣿⣿⣿⡀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⡿⣿⣿⣿⡇⣿⣿⣀⣸⣿⣾⣿⡇⣿⡟⣿⣿⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⠛⠃⠀⠘⠛⠃⠛⠛⠛⠃⠛⠛⠛⠛⠛⠀⠛⠓⠛⠃⣿⠛⢸⠇⠀⠀⠀⢀⣤⣴⣾⣿⣿⣿⣿⡙⠛⢻⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣀⡀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⠀⢀⣀⣀⡀⣤⣄⢠⣤⣿⢀⣀⣀⣀⢀⣴⣿⣿⣿⡟⠋⢻⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣧⣿⡇⢸⣿⠂⣿⡇⠀⣿⣿⠀⢸⣿⡟⠃⣿⣿⢸⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣼⣿⣿⣿⣿⠉⠉⢁⣉⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⡄⢸⣿⠀⣿⡇⠀⣿⣿⠀⢸⣿⡿⠇⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⡏⣿⣷⣼⣿⣆⣿⣷⣶⣿⣿⣶⢸⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡃⣼⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⡇⠀⠉⠉⠉⠉⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⣠⣿⣿⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠇⠀⠀
⣀⣤⣾⣿⣿⣷⠆⣀⣼⣿⠟⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣿⣿⣿⣿⣧⣾⠿⠋⠉⢠⣶⣶⣿⣶⣶⣶⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣤⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠾⠿⠃⠈⠁⠀⠀⠀⠀⠘⠿⣿⣿⡿⠟⠛⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⢠⠀⢠⣄⣠⣤⣤⡆⠠⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠅⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢰⣿⡇⠀⢰⣿⣿⡆⣿⣿⡇⣿⣿⠿⠀⣿⣿⣿⠀⣿⣷⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⠛⠛⠛⣿⣿⣿⣿⣿⠛⡛⣻⣿⣿⣿⣿⣿⣿⣧⠀⠀⣀⣘⠿⠿⠿⠿⠿⢿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣤⢰⣿⣿⣿⡀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣴⡶⢦⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⡿⣿⣿⣿⡇⣿⣿⣀⣸⣿⣾⣿⡇⣿⡟⣿⣿⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⠛⠃⠀⠘⠛⠃⠛⠛⠛⠃⠛⠛⠛⠛⠛⠀⠛⠓⠛⠃⣿⠛⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⣿⣿⢛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣀⡀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⠀⢀⣀⣀⡀⣠⣄⢠⣤⣿⣀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣆⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣧⣿⡇⢸⣿⠂⣿⡇⠀⣿⣿⠀⢸⣿⡟⠃⣿⣿⢸⣿⣿⣿⣿⣟⠋⢀⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⡄⢸⣿⠀⣿⡇⠀⣿⣿⠀⢸⣿⡿⠇⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣁⣾⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⡏⣿⣷⣸⣿⣄⣿⣷⣶⣿⣿⣶⢸⣿⡇⠀⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣧⣄⣽⣿⣿⣿⣿⣿⣿⠄⣾⣿⣿⣿⡏⠛⠛⠛⠋⠉⢁⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⢀⣾⣿⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠋⠙⠻⣿⣶⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠟⠀⠀
⣀⣠⣼⣿⣿⣷⡆⢀⣴⣿⠟⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠻⣿⣿⣿⣿⣿⣾⡿⠋⠉⢠⣶⣶⣿⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢀⣀⣠⣽⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠾⠿⠃⠈⠁⠀⠀⠀⠀⠈⠿⣿⣿⡿⠟⠛⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠀⢠⣄⣠⣤⣤⡆⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣄⣀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢰⣿⡇⠀⢸⣿⣿⣆⣿⣿⡇⣿⣿⠿⠀⣿⣿⣿⠀⣿⣷⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡿⠿⣿⣿⣿⣿⣿⣿⡛⠿⠿⣿⣿⣿⣿⣿⣿⣇⠀⠀⣀⣌⠿⠿⠿⠿⠿⢿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣤⢰⣿⣿⣿⡀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢁⣠⡀⠀⣿⣿⣿⣿⣿⣴⣷⣾⣿⣿⣿⣿⣿⣿⣿⣆⣾⣿⣿⡆⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⡿⣿⣿⣿⡇⣿⣿⣀⣸⣿⣿⣿⡇⣿⡟⣿⣿⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⠛⠃⠀⠘⠛⠃⠛⠙⠛⠃⠛⠛⠛⠛⠛⠀⠛⠓⠛⠃⢹⡟⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣀⡀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⠀⢀⣀⣀⡀⣠⣄⢠⣤⣼⣇⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠛⠿⣭⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣧⣿⡇⢸⣿⠆⣿⡇⠀⣿⣿⠀⢸⣿⡟⠃⣿⣿⢸⣿⣿⣿⣿⣟⠋⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⡄⢸⣿⠀⣿⡇⠀⣿⣿⠀⢸⣿⡿⠇⣿⣿⢸⣿⣿⣿⣿⣿⡇⠀⠀⣀⣠⣾⣿⣿⣿⠟⠛⣻⣿⣿⣉⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⡏⣿⣷⣸⣿⣄⣿⣷⣶⣿⣿⣶⢸⣿⡇⠀⣿⣿⢸⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⠿⠟⠛⣿⣿⣵⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⣼⣿⣧⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣼⣿⣿⣿⣿⣿⣯⣿⣿⡏⣿⣿⡟⠙⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠀⠀
⢀⣠⣴⣿⣿⣷⡆⠀⣠⣿⡿⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⣿⣿⣿⣿⣿⣿⣯⣍⣀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠻⣿⣿⣿⣿⣿⣴⡿⠏⠉⠁⣴⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣘⣻⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠰⠿⠏⠈⠉⠀⠀⠀⠀⠀⠻⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢲⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⢀⠀⠀⢄⣠⣤⣤⡆⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣄⣀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢰⣿⡇⠀⢰⣿⣿⣆⣿⣿⡇⣿⣿⠿⠀⣿⣿⣿⠀⣿⣷⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠿⣿⣿⣿⣿⣿⣿⡻⠿⠿⣿⣿⣿⣿⣿⣿⣇⠀⠀⣀⣌⠿⠿⠿⠿⠿⢿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣤⢰⣿⣿⣿⡀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢁⣠⡀⠀⣿⣿⣿⣿⣿⣴⣷⣾⣿⣿⣿⣿⣿⣿⣿⣇⣾⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⡿⣿⣿⣿⡇⣿⣿⣀⣸⣿⣾⣿⡇⣿⡟⣿⣿⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⠛⠃⠀⠘⠛⠃⠛⠙⠛⠃⠛⠛⠛⠛⠛⠀⠛⠓⠛⠃⢹⡟⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣀⡀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⠀⢀⣀⣀⡀⣠⣄⢠⣤⣼⣇⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡛⠛⠿⣭⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣧⣿⡇⢸⣿⠂⣿⡇⠀⣿⣿⠀⢸⣿⡟⠃⣿⣿⢸⣿⣿⣿⣿⣟⠋⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⡄⢸⣿⠀⣿⡇⠀⣿⣿⠀⢸⣿⡿⠇⣿⣿⢸⣿⣿⣿⣿⣿⡇⠀⠀⣀⣠⣾⣿⣿⣿⠟⠛⣻⣿⣿⣉⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⡏⣿⣷⣸⣿⣄⣿⣷⣶⣿⣿⣶⢸⣿⡇⠀⣿⣿⢸⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⡿⠿⠟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⣼⣿⣧⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣼⣿⣿⣿⣿⣿⣯⣿⣿⡏⣿⣿⡟⠙⢿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠀⠀
⢀⣠⣴⣿⣿⣷⡆⠀⣠⣿⡟⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⣿⣿⣿⣿⣿⣿⣯⣍⣀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠻⣿⣿⣿⣿⣿⣴⡿⠟⠉⠁⣴⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣈⣻⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠰⠿⠏⠈⠉⠀⠀⠀⠀⠀⠻⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢳⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⢀⠀⠀⢄⣠⣤⣤⡆⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢰⣿⡇⠀⢸⣿⣿⣆⣿⣿⡇⣿⣿⠿⠀⣿⣿⣿⠀⣿⣷⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⠿⠿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢀⣈⠿⠿⠿⠿⠿⠿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣤⢰⣿⣿⣿⡀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢉⣀⠀⠈⣿⣿⣿⣿⣿⣴⣦⣾⣿⣿⣿⣿⣿⣿⣿⣆⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⡿⣿⣿⣿⡇⣿⣿⣀⣸⣿⣾⣿⡇⣿⡟⣿⣿⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣰⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⠛⠃⠀⠘⠛⠃⠛⠙⠛⠃⠛⠛⠛⠛⠛⠀⠛⠓⠛⠃⢹⡟⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣀⡀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⠀⢀⣀⣀⡀⣠⣄⢠⣤⣸⣧⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⠿⣿⣋⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣧⣿⡇⢸⣿⠆⣿⡇⠀⣿⣿⠀⢸⣿⡟⠃⣿⣿⢸⣿⣿⣿⣿⣟⠋⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⡄⢸⣿⠀⣿⡇⠀⣿⣿⠀⢸⣿⡿⠇⣿⣿⢸⣿⣿⣿⣿⣿⡇⠀⣀⣤⣤⣶⣶⣿⣿⣿⣟⠛⣻⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⡏⣿⣷⣸⣿⣄⣿⣷⣶⣿⣿⣶⢸⣿⡇⠀⣿⣿⢸⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣯⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⣠⣿⣿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⡀⠸⣿⣿⣿⣿⣿⣿⡎⠛⠋⠹⣿⣿⣴⣾⣿⣿⡿⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠃⠀
⢀⣀⣤⣿⣿⣷⣶⠀⣠⣾⣿⠳⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠃⠀⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠹⣿⣿⣿⣿⣿⣵⣿⠟⠉⠁⣴⣶⣶⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠰⠿⠟⠀⠉⠀⠀⠀⠀⠀⠻⣿⣿⣿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⢰⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⢠⠀⠀⢄⣠⣤⣤⣆⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢰⣿⡇⠀⢸⣿⣿⣆⣿⣿⡇⣿⣿⠿⠀⣿⣿⣿⠀⣿⣷⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠿⠿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢀⣈⠿⠿⠿⠿⠿⠿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣦⢰⣿⣿⣿⡀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢉⣀⠀⠈⣿⣿⣿⣿⣿⣴⣦⣾⣿⣿⣿⣿⣿⣿⣿⣆⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⡿⣿⣿⣿⡇⣿⣿⣀⣸⣿⣾⣿⡇⣿⡟⣿⣿⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⣰⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⠛⠃⠀⠘⠛⠃⠛⠙⠛⠃⠛⠛⠛⠛⠛⠀⠛⠓⠛⠃⢹⡟⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣀⡀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⠀⢀⣀⣀⡀⣠⣄⢠⣤⣸⣧⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⣋⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣧⣿⡇⢸⣿⠂⣿⡇⠀⣿⣿⠀⢸⣿⡟⠃⣿⣿⢸⣿⣿⣿⣿⣟⠋⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⡄⢸⣿⠀⣿⡇⠀⣿⣿⠀⢸⣿⡿⠇⣿⣿⢸⣿⣿⣿⣿⣿⡇⠀⣀⣤⣤⣶⣶⣿⣿⣿⣟⢛⣻⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⡏⣿⣷⣸⣿⣄⣿⣷⣶⣿⣿⣶⢸⣿⡇⠀⣿⣿⢸⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⠻⢿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⣠⣿⣿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠸⣿⣿⣿⣿⣿⣿⡎⠛⠋⠻⣿⣿⣴⣾⣿⣿⡿⠀⠀⠀⠀⠀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠃⠀
⠀⣀⣴⣿⣿⣷⣶⠀⣀⣾⡿⠳⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠃⠀⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠹⣿⣿⣿⣿⣿⣵⣿⠟⠉⠉⣴⣶⣶⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢈⣻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠰⠿⠟⠀⠉⠀⠀⠀⠀⠀⠻⣿⣿⣿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⢠⠀⠀⢀⣠⣤⣤⣆⠀⢼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢰⣿⡇⠀⢸⣿⣿⣆⣿⣿⡇⣿⣿⠿⠀⣿⣿⣿⠀⣿⣷⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢀⣀⠿⠿⠿⠿⠿⠿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣦⢰⣿⣿⣿⡀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⠉⠉⠙⣿⣿⣿⣿⣿⣨⣤⣼⣿⣿⣿⣿⣿⣿⣿⣆⣴⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⡿⣿⣿⣿⡇⣿⣿⣀⣸⣿⣾⣿⡇⣿⡟⣿⣿⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⠛⠃⠀⠘⠛⠃⠛⠙⠛⠃⠛⠛⠛⠛⠛⠀⠛⠓⠛⠃⠙⡟⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣀⡀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⠀⢀⣀⣀⡀⣀⣄⢠⣤⣸⣷⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⣿⣿⠟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣧⣿⡇⢸⣿⠆⣿⡇⠀⣿⣿⠀⢸⣿⡟⠃⣿⣿⢸⣿⣿⣿⣿⣟⡋⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣧⣀⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⡄⢸⣿⠀⣿⡇⠀⣿⣿⠀⢸⣿⡿⠇⣿⣿⢸⣿⣿⣿⣿⣿⡗⠀⠀⠀⣠⣶⣶⣾⣷⣾⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⡏⣿⣷⣸⣿⣄⣿⣷⣶⣿⣿⣶⢸⣿⡇⠀⣿⣿⢸⣿⣿⣿⣿⣿⣷⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠁⣰⣿⣿⣿⣿⣧⡉⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣄⣠⣿⣿⣿⣿⣿⣿⡿⠋⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣯⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣠⣿⣿⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⣄⣀⣴⣾⣿⣿⡏⠉⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠇⠀
⠀⣀⣤⣾⣿⣿⣶⠀⣀⣾⣿⠓⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠃⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⢿⣿⣿⣿⣿⣧⣾⠟⠉⠉⢰⣶⣶⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠿⠿⠁⠉⠁⠀⠀⠀⠀⠸⢿⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⠀⠀⠀⣠⣤⣤⣆⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢰⣿⡇⠀⢸⣿⣿⣆⣿⣿⡇⣿⣿⠿⠀⣿⣿⣿⠀⣿⣷⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢀⣀⠿⠿⠿⠿⠿⠿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣦⢰⣿⣿⣿⡄⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⠉⠉⠙⣿⣿⣿⣿⣿⣨⣤⣴⣿⣿⣿⣿⣿⣿⣿⣆⣴⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⡿⣿⣿⣿⡇⣿⣿⣀⣸⣿⣾⣿⡇⣿⡟⣿⣿⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⠛⠃⠀⠘⠛⠃⠛⠛⠛⠃⠛⠛⠛⠛⠛⠀⠛⠓⠛⠃⠙⡟⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣀⡀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⠀⢀⣀⣀⡀⣀⣄⢠⣤⣸⣷⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⣿⣿⠟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣧⣿⡇⢸⣿⠂⣿⡗⠀⣿⣿⠀⢸⣿⡟⠃⣿⣿⢸⣿⣿⣿⣿⣟⡋⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣧⣀⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⡄⢸⣿⠀⣿⡇⠀⣿⣿⠀⢸⣿⡿⠇⣿⣿⢸⣿⣿⣿⣿⣿⡗⠀⠀⠀⣠⣶⣶⣾⣷⣾⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⡏⣿⣷⣸⣿⣄⣿⣷⣶⣿⣿⣶⢸⣿⡇⠀⣿⣿⢸⣿⣿⣿⣿⣿⣷⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠁⣰⣿⣿⣿⣿⣇⡉⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣄⣠⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣯⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣠⣿⣿⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⣄⣀⣴⣾⣿⣿⡏⠉⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠇⠀
⠀⣀⣤⣾⣿⣿⣶⠀⣀⣾⣿⠳⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠃⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⢿⣿⣿⣿⣿⣧⣾⠟⠉⠉⢰⣶⣶⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠿⠿⠁⠉⠁⠀⠀⠀⠀⠸⢿⣿⣿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⠀⠀⠀⣠⣤⣤⣆⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢰⣿⡇⠀⢸⣿⣿⣆⣿⣿⡇⣿⣿⠿⠀⣿⣿⣿⠀⣿⣷⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⣀⡻⠿⠿⠿⠿⠿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣦⢰⣿⣿⣿⡀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⠉⠉⠉⣿⣿⣿⣿⣿⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣆⣴⣿⣿⣧⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⡿⣿⣿⣿⡇⣿⣿⣀⣸⣿⣾⣿⡇⣿⡟⣿⣿⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢓⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⠛⠃⠀⠘⠛⠃⠛⠙⠛⠃⠛⠛⠛⠛⠛⠀⠛⠓⠛⠃⠙⣿⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣀⡀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⠀⢀⣀⣀⡀⣀⣄⢠⣤⣰⣿⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⣿⣿⠟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣧⣿⡇⢸⣿⠂⣿⡇⠀⣿⣿⠀⢸⣿⡟⠃⣿⣿⢸⣿⣿⣿⣿⣿⡋⠀⠀⠀⣀⣀⣀⣀⣸⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⡄⢸⣿⠀⣿⡇⠀⣿⣿⠀⢸⣿⡿⠇⣿⣿⢸⣿⣿⣿⣿⣿⣷⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⡏⣿⣷⣸⣿⣄⣿⣷⣶⣿⣿⣶⢸⣿⡇⠀⣿⣿⢸⣿⣿⣿⣿⣿⣷⢠⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠿⢃⣾⣿⣿⣿⣿⣶⣦⡍⠉⠉⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣤⣸⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣟⣻⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣠⣿⣿⡆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡄⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢨⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠇⠀
⠀⣀⣤⣾⣿⣿⣶⠀⣀⣼⣿⠛⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠇⠀⠀⠈⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⢿⣿⣿⣿⣿⣧⣾⠿⠉⠉⢰⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠿⠿⠁⠈⠁⠀⠀⠀⠀⠘⢿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⢠⠀⠀⠀⣠⣤⣤⣄⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢰⣿⡇⠀⢸⣿⣿⣆⣿⣿⡇⣿⣿⠿⠀⣿⣿⣿⠀⣿⣷⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⣿⣿⣿⣿⣿⣿⣛⠿⠿⢿⣿⣿⣿⣿⣿⣿⡀⠀⠀⣀⣘⠿⠿⠿⠿⠿⢿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣦⢰⣿⣿⣿⡀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢁⣀⡀⠀⣹⣿⣿⣿⣿⣧⣷⣶⣿⣿⣿⣿⣿⣿⣿⣷⣠⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⡿⣿⣿⣿⡇⣿⣿⣀⣸⣿⣾⣿⡇⣿⡟⣿⣿⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⠛⠃⠀⠘⠛⠃⠛⠙⠛⠃⠛⠛⠛⠛⠛⠀⠛⠓⠛⠃⠙⣿⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣀⡀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⠀⢀⣀⣀⡀⣀⣄⢠⣤⣀⣿⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣏⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡄⠀⠀⠀⢸⣿⣧⣿⡇⢸⣿⠆⣿⡇⠀⣿⣿⠀⢸⣿⡟⠃⣿⣿⢸⣿⣿⣿⣿⣿⡋⠀⣀⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⡄⢸⣿⠀⣿⡇⠀⣿⣿⠀⢸⣿⡿⠇⣿⣿⢸⣿⣿⣿⣿⣿⣿⢰⣿⣿⣿⣿⣿⣿⣻⠿⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⡏⣿⣷⣸⣿⣅⣿⣷⣶⣿⣿⣶⢸⣿⡇⠀⣿⣿⢸⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠿⠃⣾⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⣀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣰⣿⣿⣿⣿⠿⠿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣠⣼⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠀
⠀⣀⣤⣾⣿⣿⣷⠆⣀⣼⣿⠏⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠋⠀⠀⠈⠻⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⢿⣿⣿⣿⣿⣷⣾⠿⠉⠉⢠⣶⣶⣿⣿⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣙⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠾⠿⠃⠈⠁⠀⠀⠀⠀⠘⠿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⢀⠀⠀⠀⣠⣤⣴⣦⡀⠰⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢰⣿⡇⠀⢸⣿⣿⣆⣿⣿⡇⣿⣿⠿⠀⣿⣿⣿⠀⣿⣷⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⣿⣿⣿⣿⣿⣿⢛⠿⠿⢿⣿⣿⣿⣿⣿⣿⡀⠀⠀⣠⣘⠿⠿⠿⠿⠿⢿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣤⢰⣿⣿⣿⡀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢁⣀⡀⠀⣹⣿⣿⣿⣿⣧⣷⣶⣿⣿⣿⣿⣿⣿⣿⣷⣠⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⡿⣿⣿⣿⡇⣿⣿⣀⣸⣿⣾⣿⡇⣿⡟⣿⣿⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⠛⠃⠀⠘⠛⠃⠛⠛⠛⠃⠛⠛⠛⠛⠛⠀⠛⠓⠛⠃⠙⣿⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣀⡀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⠀⢀⣀⣀⡀⣀⣄⢠⣤⣀⣿⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣏⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠄⠀⠀⠀⢸⣿⣧⣿⡇⢸⣿⠆⣿⡗⠀⣿⣿⠀⢸⣿⡟⠃⣿⣿⢸⣿⣿⣿⣿⣿⡋⠀⣀⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⡄⢸⣿⠀⣿⡇⠀⣿⣿⠀⢸⣿⡿⠇⣿⣿⢸⣿⣿⣿⣿⣿⣿⢰⣿⣿⣿⣿⣿⡿⣻⠿⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⡏⣿⣷⣸⣿⣅⣿⣷⣶⣿⣿⣶⢸⣿⡇⠀⣿⣿⢸⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠿⠃⣾⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⣀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣰⣿⣿⣿⣿⠿⠿⠟⠛⠛⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣠⣾⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠃⠀
⠀⣀⣤⣾⣿⣿⣷⡆⣀⣼⣿⠏⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠋⠀⠀⠈⠻⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⢿⣿⣿⣿⣿⣷⣾⠿⠋⠉⢠⣶⣶⣿⣿⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣙⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠾⠿⠃⠈⠁⠀⠀⠀⠀⠘⠿⣿⣿⡿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⢠⠀⠀⠀⣠⣤⣤⣦⡀⠰⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀
⠀⠀⠀⠀⠀⢰⣿⡇⠀⢸⣿⣿⣆⣿⣿⡇⣿⣿⠿⠀⣿⣿⣿⠀⣿⣷⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠸⠿⠻⠿⢿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣤⢰⣿⣿⣿⡀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⢰⣿⣿⣿⣿⣿⣍⣛⣿⣿⣿⣿⣿⣿⣿⣿⣧⢀⣴⣶⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⡿⣿⣿⣿⡇⣿⣿⣀⣸⣿⣾⣿⡇⣿⡟⣿⣿⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠘⠛⠃⠀⠘⠛⠃⠛⠛⠛⠃⠛⠛⠛⠛⠛⠀⠛⠓⠛⠃⠙⣿⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣀⡀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⠀⢀⣀⣀⡀⣀⣀⢠⣤⡀⣿⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣯⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡆⠀⠀⠀⢸⣿⣧⣿⡇⢸⣿⠂⣿⡇⠀⣿⣿⠀⢸⣿⡟⠃⣿⣿⢸⣿⣷⣿⣿⣿⣏⠀⢀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠃⠀⠀⠀⢸⣿⣿⣿⡄⢸⣿⠀⣿⡇⠀⣿⣿⠀⢸⣿⡿⠇⣿⣿⢸⣿⣿⣿⣿⣿⣿⠀⣼⣿⣿⣿⣿⣿⠿⠿⠻⣿⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⡏⣿⣷⣸⣿⣆⣿⣷⣶⣿⣿⣶⢸⣿⡇⠀⣿⣿⢸⣿⣷⣿⣿⣿⣿⢰⣿⣿⣿⣿⣿⡷⠀⠀⢠⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⠿⠃⣸⣿⣿⣿⣿⣿⣦⡀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⣀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣀⣾⣿⣿⣿⠛⠛⠛⠛⠉⠉⣭⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⣼⣿⣧⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠀
⠀⣀⣠⣼⣿⣿⣷⡆⣀⣰⣿⡟⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠟⠛⠀⠀⠈⠻⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠻⣿⣿⣿⣿⣿⣾⡿⠋⠉⢀⣶⣶⣿⣿⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠺⠿⠋⠈⠁⠀⠀⠀⠀⠀⠿⣿⣿⡿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⢀⠀⠀⠀⣠⣤⣤⣤⡀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⢀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀
⠀⠀⠀⠀⠀⢰⣿⡇⠀⢸⣿⣿⣆⣿⣿⡇⣿⣿⠿⠀⣿⣿⣿⠀⣿⣷⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠸⠿⠿⠿⢿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣦⢰⣿⣿⣿⡀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⣰⣿⣿⣿⣿⣿⣍⣻⣿⣿⣿⣿⣿⣿⣿⣿⣧⢀⣴⣶⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⡿⣿⣿⣿⡇⣿⣿⣀⣸⣿⣾⣿⡇⣿⡟⣿⣿⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠘⠛⠃⠀⠘⠛⠃⠛⠙⠛⠃⠛⠛⠛⠛⠛⠀⠛⠓⠛⠃⠙⣿⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣀⡀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⠀⢀⣀⣀⡀⣀⣀⢠⣤⡀⣿⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣯⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡆⠀⠀⠀⢸⣿⣧⣿⡇⢸⣿⠂⣿⡇⠀⣿⣿⠀⢸⣿⡟⠃⣿⣿⢸⣿⣷⣿⣿⣿⣏⠀⢀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠃⠀⠀⠀⢸⣿⣿⣿⡄⢸⣿⠀⣿⡇⠀⣿⣿⠀⢸⣿⡿⠇⣿⣿⢸⣿⣿⣿⣿⣿⣿⠀⣼⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⡏⣿⣷⣸⣿⣄⣿⣷⣶⣿⣿⣶⢸⣿⡇⠀⣿⣿⢸⣿⣷⣿⣿⣿⣿⢰⣿⣿⣿⣿⣿⡷⠀⠀⢰⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠃⣸⣿⣿⣿⣿⣿⣦⡀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⣀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣀⣾⣿⣿⣿⠛⠛⠛⠛⠉⠉⣭⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⣼⣿⣧⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠀
⠀⣀⣠⣼⣿⣿⣷⡆⣀⣰⣿⡟⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠛⠀⠀⠈⠻⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠻⣿⣿⣿⣿⣿⣾⡿⠋⠉⢠⣶⣶⣿⣿⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠺⠿⠋⠈⠁⠀⠀⠀⠀⠀⠿⣿⣿⡿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⢀⠀⠀⠀⣠⣤⣤⣤⡀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣶⣶⣶⣦⣄⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⢀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀
⠀⠀⠀⠀⠀⢰⣿⡇⠀⢸⣿⣿⣆⣿⣿⡇⣿⣿⠿⠀⣿⣿⣿⠀⣿⣷⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠋⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠻⠿⠿⢿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣦⢰⣿⣿⣿⡀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⢇⣿⣿⣿⣿⣿⣷⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣴⣶⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⡿⣿⣿⣿⡇⣿⣿⣀⣸⣿⣾⣿⡇⣿⡟⣿⣿⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠘⠛⠃⠀⠘⠛⠃⠛⠛⠛⠃⠛⠛⠛⠛⠛⠀⠛⠓⠛⠃⠙⣿⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣀⡀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⠀⢀⣀⣀⡀⣀⣄⢠⣤⡀⣿⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣆⣩⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡆⠀⠀⠀⢸⣿⣧⣿⡇⢸⣿⠆⣿⡗⠀⣿⣿⠀⢸⣿⡟⠃⣿⣿⢸⣿⣧⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠇⠀⠀⠀⢸⣿⣿⣿⡄⢸⣿⡀⣿⡇⠀⣿⣿⠀⢸⣿⡿⠇⣿⣿⢼⣿⡿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⢸⣿⡏⣿⣷⣸⣿⣇⣿⣷⣶⣿⣿⣶⢸⣿⡇⠀⣿⣿⢸⣿⣷⣿⣿⣿⣿⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠃⠀⣴⣿⣿⣿⣿⣿⣏⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣠⣄⣀⣿⣿⣿⣿⣿⣿⡿⠃⠀⠘⢿⣿⣿⡿⠉⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⣼⣿⣷⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⠀⠀⢿⣿⡿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣴⣿⣿⡇⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠀
⠀⣀⣠⣼⣿⣿⣿⡆⣀⣰⣿⡟⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠛⠀⠀⠈⠻⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠻⣿⣿⣿⣿⣿⣶⡿⠋⠉⠁⣶⣶⣿⣿⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠺⠿⠏⠈⠁⠀⠀⠀⠀⠀⠻⣿⣿⡿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⢠⠀⠀⠀⣠⣤⣤⣦⡀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀
⠀⠀⠀⠀⠀⢰⣿⡇⠀⢸⣿⣿⣆⣿⣿⡇⣿⣿⠿⠀⣿⣿⣿⠀⣿⣷⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⠛⠛⠛⢿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣦⢰⣿⣿⣿⡀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⠉⠉⠉⢻⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣤⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⡿⣿⣿⣿⡇⣿⣿⣀⣸⣿⣾⣿⡇⣿⡟⣿⣿⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⢀⣾⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠘⠛⠃⠀⠘⠛⠃⠛⠛⠛⠃⠛⠛⠛⠛⠛⠀⠛⠓⠛⠃⠙⢻⢺⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⢀⣀⡀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⠀⢀⣀⣀⡀⣀⣄⢠⣤⡀⣾⣧⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡆⠀⠀⠀⢸⣿⣧⣿⡇⢸⣿⠆⣿⡗⠀⣿⣿⠀⢸⣿⡟⠃⣿⣿⢸⣿⡇⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣯⠙⢛⣥⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⢸⣿⣿⣿⡄⢸⣿⡇⣿⡇⠀⣿⣿⠀⢸⣿⡿⠇⣿⣿⢸⣿⡏⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⡏⣿⣷⣸⣿⣆⣿⣷⣶⣿⣿⣶⢸⣿⡇⠀⣿⣿⢸⣿⣷⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠿⠏⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⣄⡀⠀⠀⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⣼⣿⣷⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⠀⠀⢻⣿⡿⠀⠀⣿⣿⣿⣿⣿⣿⣆⠘⢿⠟⣿⣿⣿⣿⣿⠉⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠀
⠀⣀⣠⣼⣿⣿⣿⡆⣀⣰⣿⡟⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠟⠀⠀⠀⠹⠇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣶⣶⣬⣿⣿⣿⡏⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠻⣿⣿⣿⣿⣿⣶⡿⠏⠉⠁⣶⣶⣿⣿⣷⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⠿⠏⠀⠉⠀⠀⠀⠀⠀⠻⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢠⠀⠀⠀⢠⣤⣤⣦⡀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀
⠀⠀⠀⠀⠀⢰⣿⡇⠀⢸⣿⣿⣆⣿⣿⡇⣿⣿⠿⠀⣿⣿⣿⠀⣿⣷⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⠛⠛⠻⢿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣦⢰⣿⣿⣿⡀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⠉⠉⠉⢻⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣤⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⡿⣿⣿⣿⡇⣿⣿⣀⣸⣿⣿⣿⡇⣿⡟⣿⣿⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⢀⣾⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠘⠛⠃⠀⠘⠛⠃⠛⠛⠛⠃⠛⠛⠛⠛⠛⠀⠛⠓⠛⠃⠙⢻⢺⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⢀⣀⡀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⠀⢀⣀⣀⡀⣀⣄⢠⣤⡀⣿⣧⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡆⠀⠀⠀⢸⣿⣧⣿⡇⢸⣿⡆⣿⡷⠀⣿⣿⠀⢸⣿⡟⠃⣿⣿⢸⣿⡇⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣯⠙⢛⣧⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⢸⣿⣿⣿⡄⢸⣿⠇⣿⡇⠀⣿⣿⠀⢸⣿⡿⠇⣿⣿⢼⣿⡏⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⡏⣿⣷⣸⣿⣇⣿⣷⣶⣿⣿⣶⢸⣿⡇⠀⣿⣿⢸⣿⣷⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⠿⠏⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⣄⡀⠀⠀⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⣼⣿⣷⠀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⠀⠀⢻⣿⡿⠀⠀⢿⣿⣿⣿⣿⣿⣆⠘⢿⠟⣿⣿⣿⣿⣿⠋⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠀
⠀⣀⣠⣼⣿⣿⣿⡦⣀⣰⣿⡟⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠟⠀⠀⠀⠹⠇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣶⣶⣮⣿⣿⣿⡟⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠻⣿⣿⣿⣿⣿⣶⡿⠏⠉⠁⣶⣶⣿⣿⣷⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠸⠿⠟⠀⠉⠀⠀⠀⠀⠀⠻⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⣠⣾⣷⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢠⠀⠀⠀⣠⣤⣴⣦⡀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠈⠈⠀⠀⠀⠈⠉⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⣿⣆⣿⣿⡇⣿⣿⠿⠀⣿⣿⣿⠀⣿⣷⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠘⠟⠛⠛⠿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣶⢰⣿⣿⣿⡀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⡿⣿⣿⣿⡇⣿⣿⣀⣸⣿⣿⣿⡇⣿⡟⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠛⠋⠙⠛⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⠀⠀⠀⠀⠘⠛⠃⠀⠘⠛⠃⠛⠛⠛⠃⠛⠛⠛⠛⠛⠀⠛⠓⠛⠃⠙⢻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⣼⣿⣿⣿⣿⣦⣬⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⢀⣀⡀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⠀⢀⣀⣀⡀⣀⣀⢠⣤⡀⢸⣧⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⠀⠀⠀⢸⣿⣧⣿⡏⢸⣿⡆⣿⡷⠀⣿⣿⠀⢸⣿⡟⠃⣿⣿⢸⣿⡇⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⢸⣿⣿⣿⡄⢸⣿⡇⣿⣇⠀⣿⣿⠀⢸⣿⡿⠇⣿⣿⣸⣿⡇⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⣿⠿⣫⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⢸⣿⡏⣿⣷⣼⣿⣇⣿⣿⣶⣿⣿⣶⣸⣿⡇⠀⣿⣿⣼⣿⣷⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⠟⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⣤⣀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⢀⣴⣿⣿⡀
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⡄⠀⢸⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⣸⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠃
⠀⢀⣠⣴⣿⣿⣿⣶⢀⣠⣿⣟⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠻⠃⠀⠀⠙⠷⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣷⣭⣬⣿⣿⣶⣿⣿⡏⠉⠉⣰⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⢿⣿⣿⣿⣿⣷⣿⠟⠉⠉⣴⣶⣿⣿⣷⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⠿⠟⠀⠉⠀⠀⠀⠀⠀⠻⢿⣿⣿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢀⣹⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢠⠀⠀⠀⢠⣤⣤⣦⣄⠀⢾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⢶⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡃⠀⠀⠈⠈⠁⠀⠀⠈⠉⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⣿⣆⣿⣿⡇⣿⣿⠿⠀⣿⣿⣿⠀⣿⣷⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠘⠛⠛⠻⠿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣶⢰⣿⣿⣿⡀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⡿⣿⣿⣿⡇⣿⣿⣀⣸⣿⣿⣿⡇⣿⡟⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠛⠋⠙⠛⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⠀⠀⠀⠀⠘⠛⠃⠀⠘⠛⠃⠛⠛⠛⠃⠛⠛⠛⠛⠛⠀⠛⠓⠛⠃⠙⢻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⣼⣿⣿⣿⣿⣦⣬⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⢀⣀⡀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⠀⢀⣀⣀⡀⣀⣀⢠⣤⡀⣸⣧⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⠀⠀⠀⢸⣿⣧⣿⡇⢸⣿⡆⣿⡷⠀⣿⣿⠀⢸⣿⡟⠃⣿⣿⢸⣿⡇⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⢸⣿⣿⣿⡄⢸⣿⡇⣿⣿⠀⣿⣿⠀⢸⣿⡿⠇⣿⣿⣸⣿⡇⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⣿⠿⣻⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠃⠀⠀⠀⢸⣿⡏⣿⣷⣼⣿⣇⣿⣷⣶⣿⣿⣶⣸⣿⡇⠀⣿⣿⣽⣿⣷⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠟⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⣤⣀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⢀⣴⣿⣿⡄
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⡀⠀⢸⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⣸⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠃
⠀⢀⣠⣴⣿⣿⣿⣶⢀⣠⣾⣿⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠛⠃⠀⠀⠙⠿⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣷⣭⣼⣿⣿⣶⣿⣿⡏⠉⠉⣰⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⢿⣿⣿⣿⣿⣷⣿⠟⠋⠁⣶⣶⣿⣿⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⠿⠟⠀⠉⠀⠀⠀⠀⠀⠻⢿⣿⣿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢠⠀⠀⠄⢠⣤⣴⣦⣄⠀⢾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⡀⠀⠀⠈⠀⠋⠉⠀⠀⠀⠈⠉⠉⠛⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⣾⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⣿⣆⣿⣿⡇⣿⣿⠿⠀⣿⣿⣿⠀⣿⣷⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠘⠿⠿⠿⠿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣶⢰⣿⣿⣿⡀⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⡿⣿⣿⣿⡇⣿⣿⣀⣸⣿⣿⣿⡇⣿⡟⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠿⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣰⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⠀⠀⠀⠀⠘⠛⠃⠀⠘⠛⠃⠛⠛⠛⠃⠛⠛⠛⠛⠛⠀⠛⠓⠛⠃⠙⢻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⣌⣙⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⢀⣀⡀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⠀⢀⣀⣀⡀⣀⣀⢠⣤⡀⣸⣧⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⠀⠀⠀⢸⣿⣧⣿⡇⢸⣿⡆⣿⣷⠀⣿⣿⠀⢸⣿⡟⠃⣿⣿⢸⣿⡇⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠀⠀⠀⢸⣿⣿⣿⡄⢸⣿⡇⣿⣯⠀⣿⣿⠀⢸⣿⡿⠇⣿⣿⢸⣿⡇⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠃⠀⠀⠀⢸⣿⡏⣿⣷⣼⣿⣇⣿⣿⣶⣿⣿⣶⣸⣿⡇⠀⣿⣿⣾⣿⣷⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⣭⣿⣿⣷⣾⣭⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⠟⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⣤⣀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡏⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⢀⣴⣿⣿⡄
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⡄⠀⢸⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠃
⠀⢀⣠⣴⣿⣿⣿⣶⢀⣠⣾⣿⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠃⠀⠀⠙⠿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣮⣁⣿⣿⣧⣼⣿⣿⠛⠛⢋⣵⣾⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⢿⣿⣿⣿⣿⣷⣿⠟⠛⠁⣶⣾⣿⣿⣷⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⠿⠟⠀⠉⠀⠀⠀⠀⠀⠻⢿⣿⣿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢠⠀⠀⠀⢠⣤⣴⣦⣄⠀⢾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡂⠀⠀⠀⠀⠊⠉⠀⠀⠀⠈⠉⠉⠋⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⣾⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⣿⣆⣿⣿⡇⣿⣿⠿⠀⣿⣿⣿⠀⣿⣷⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠘⠿⠿⠿⠿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣶⢰⣿⣿⣿⡀⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⡿⣿⣿⣿⡇⣿⣿⣀⣸⣿⣿⣿⡇⣿⡟⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣰⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠘⠛⠃⠀⠘⠛⠃⠛⠛⠛⠃⠛⠛⠛⠛⠛⠀⠛⠓⠛⠃⠙⢻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⣌⣙⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⢀⣀⡀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⠀⢀⣀⣀⡀⣀⣀⢠⣤⡀⣸⣧⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⠀⠀⠀⢸⣿⣧⣿⡇⢸⣿⡆⣿⡷⠀⣿⣿⠀⢸⣿⡟⠃⣿⣿⢸⣿⡇⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠀⠀⠀⢸⣿⣿⣿⡄⢸⣿⡇⣿⣇⠀⣿⣿⠀⢸⣿⡿⠇⣿⣿⢸⣿⡇⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠃⠀⠀⠀⢸⣿⡏⣿⣷⣼⣿⣇⣿⣷⣶⣿⣿⣶⣸⣿⡇⠀⣿⣿⣸⣿⣷⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⣭⣿⣿⣷⣾⣭⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠟⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⣤⣀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡏⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣤⣿⣿⡄
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⡄⠀⢸⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡄⣿⣿⣻⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠃
⠀⢀⣠⣴⣿⣿⣿⣶⢀⣠⣾⣟⠻⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠟⠃⠀⠀⠙⠿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣮⣁⣻⣿⣧⣼⣿⣿⠛⠛⠋⣵⣾⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⢿⣿⣿⣿⣿⣷⣿⠟⠋⠁⣶⣾⣿⣿⣷⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⠿⠟⠀⠉⠀⠀⠀⠀⠀⠻⢿⣿⣿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢠⠀⠀⠄⢠⣤⣴⣦⣄⠀⢾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠘⠙⠋⠉⠀⠀⠒⠂⠉⠉⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠥⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠈⠿⠿⠿⠿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣠⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⢸⣿⣿⣿⣿⣭⣹⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣦⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡏⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢀⣠⣽⣿⣿⣿⣾⣭⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⠘⠉⠉⠉⠉⠉⠉⠁⠀⠉⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠟⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠐⠀⡀⠀⣀⡀⠀⠀⠀⠀⠀⣠⣀⠀
⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣦⣀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠐⠀⢘⣷⣤⣄⠀⢀⣼⣿⣿⡆
⠀⠀⠀⠀⠀⣀⣿⠀⠀⠀⢀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⣶⡄⠀⢸⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣔⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⠛⢿⡿⣷⣷⡿⠿⠿⣇
⠀⢀⣠⣴⣿⣿⣿⣷⣀⣴⣿⣿⡻⠿⠃⠀⠀⠀⡆⠀⠀⠀⠀⠀⠿⠿⠿⠃⠀⠀⠹⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣯⣁⣿⣿⣧⣾⣿⣿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⢿⠄⢘⡥⠐
⠀⠹⣿⣿⣿⣿⣿⣿⣿⠿⠻⠿⣶⣿⣿⣿⣿⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠙⠻⠊⠀
⠀⠀⠸⠿⠟⠁⠉⠀⠀⠀⠀⠀⠻⣿⣿⣿⠿⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠲⢲⠀⠰⠄⣰⣶⣶⣦⣄⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣷⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠛⠛⠛⠻⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢀⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⡄⠉⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡈⠛⠃⣠⣾⣿⣿⣿⣿⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⣀⣀⡀⣀⣀⡀⣀⣀⢀⣀⢀⣀⠀⠀⠀⠀⣿⣧⣤⣤⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⣿⡇⣿⣏⢱⣿⣿⣸⣿⣾⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠇⠀⠀⠀⠀⠀⢸⣿⢀⣸⣿⣿⣿⣇⣿⣏⣸⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⢿⣿⣿⣿⠃⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠉⠛⠀⠀⠀⠘⢿⣿⠟⠀⠀⠀⢀⣾⣿⣿⣿⣿⣷⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⣀⠀
⠀⠀⠀⠀⣿⣿⣷⢸⣿⠗⣿⡆⣿⢸⣧⣿⢸⣿⠀⣿⣰⣿⢿⡾⢿⣿⠇⠀⠈⢹⣤⣄⠀⠀⢸⣿⣿⣿⣿⣿⣿⡧⠀⠉⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠱⠄⠀⠀⢀⣴⣿⣿⡄
⠀⠀⠀⠀⣿⣿⣿⢸⣿⠃⣿⣿⣿⡈⣿⡇⢸⣿⢀⣿⣏⣻⣿⡆⣼⣿⣤⡄⠀⢸⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠈⠙⠛⠃
⠀⢀⣠⣴⣿⣿⣿⣿⣛⣻⣿⣿⠛⠿⠛⠃⠘⠛⡛⠛⠛⠻⠟⠃⠿⠿⠿⠃⠀⠀⠙⠿⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠉⠉⠉⣴⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⢿⣿⣿⣿⣿⣷⣿⠟⠛⠋⣶⣿⣿⣿⣿⣶⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⠿⠟⠀⠉⠀⠀⠀⠀⠀⠻⣿⣿⣿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢢⠀⠀⠄⣰⣴⣶⣦⣄⠀⢾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠛⠛⠛⠻⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢀⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣠⡄⠉⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡈⠛⠃⣠⣼⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⣀⣀⡀⣀⣀⡀⣀⣀⢀⣀⢀⣀⠀⠀⠀⠀⣿⣧⣤⣤⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⣿⡇⣿⣏⢱⣿⣿⣸⣿⣾⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠃⠀⠀⠀⠀⠀⢸⣿⢀⣸⣿⣿⣿⣧⣿⣏⣸⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⢿⣿⣿⣿⠃⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠉⠛⠀⠀⠀⠘⢿⣿⠟⠀⠀⠀⢀⣾⣿⣿⣿⣿⣷⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⣀⠀
⠀⠀⠀⠀⣿⣿⣷⢸⣿⠗⣿⡆⣿⢸⣧⣿⢸⣿⠀⣿⣴⣿⢿⡾⢿⣿⠇⠀⠈⢹⣤⣄⠀⠀⢸⣿⣿⣿⣿⣿⣿⡦⠀⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⢀⣴⣿⣿⡄
⠀⠀⠀⠀⣿⣿⣿⢸⣿⠃⣿⣿⣿⡈⣿⡇⢸⣿⠠⣿⣎⣻⣿⡆⣼⣿⣤⡄⠀⢸⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣟⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠈⠙⠛⠃
⠀⢀⣠⣴⣿⣿⣿⣿⣛⣻⣿⣿⠛⠿⠛⠃⠘⠛⠛⠛⠋⠻⠟⠃⠿⠿⠿⠃⠀⠀⠙⠿⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠉⠉⢉⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⢿⣿⣿⣿⣿⣷⣿⠟⠛⠋⣶⣿⣿⣿⣿⣶⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⠿⠟⠀⠉⠀⠀⠀⠀⠀⠻⣿⣿⣿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢢⠀⠠⠄⣰⣤⣴⣦⣄⠀⢿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣶⣾⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠘⠛⠛⠻⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⢉⠉⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠿⠆⢀⣸⣿⣿⣿⣿⣿⣛⣉⣻⣿⣿⣿⣿⣿⣿⣷⣰⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⣀⣀⡀⣀⣀⡀⣀⣀⢀⣀⢀⣀⠀⠀⠀⠀⣿⣧⣤⣤⠀⠀⠀⠀⢀⣠⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⣿⡇⣿⣏⢱⣿⣿⣸⣿⣾⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⢠⣶⣿⣿⣿⣿⡿⢿⣿⣿⣿⣯⠉⣫⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠃⠀⠀⠀⠀⠀⢸⣿⢀⣸⣿⣿⣿⣧⣿⣏⣸⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⢻⣿⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⡀⠀⠀⢻⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠉⠛⠀⠀⠀⠘⣿⣿⠟⠀⠀⢸⣿⣿⣿⣿⣿⣿⣄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⣠⣀⠀
⠀⠀⠀⠀⣿⣿⣷⢸⣿⠗⣿⡆⣿⢸⣧⣿⢸⣿⠀⣿⣴⣿⢿⡾⢿⣿⠇⠀⠈⢹⣤⣄⠀⠀⢻⣿⣿⣿⣿⣿⣿⣷⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⢀⣼⣿⣿⡄
⠀⠀⠀⠀⣿⣿⣿⢸⣿⠃⣿⣿⣿⡈⣿⡇⢸⣿⢠⣿⣏⣻⣿⡆⣾⣿⣶⡄⠀⢸⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⠙⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣽⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠉⠙⠛⠃
⠀⢀⣠⣴⣿⣿⣿⣿⣛⣻⣿⣿⠛⠿⠛⠃⠘⠛⠛⠛⠋⠻⠟⠃⠿⠿⠛⠃⠀⠀⠙⠿⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠙⢿⣿⣿⣿⣿⣷⡿⠟⠛⠉⣶⣿⣿⣿⣿⣶⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⠿⠟⠀⠉⠀⠀⠀⠀⠀⠻⣿⣿⣿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠲⢢⠀⠠⠄⢰⣤⣶⣦⣄⠀⢿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣶⣾⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠘⠛⠛⠻⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠉⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠿⠆⢀⣸⣿⣿⣿⣿⣿⣛⣉⣻⣿⣿⣿⣿⣿⣿⣷⣰⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⣀⣀⡀⣀⣀⡀⣀⣀⢀⣀⢀⣀⠀⠀⠀⠀⣿⣧⣤⣤⠀⠀⠀⠀⢀⣠⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⣿⡇⣿⣏⢱⣿⣿⣸⣿⣾⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⢠⣶⣿⣿⣿⣿⡿⢿⣿⣿⣿⣯⠉⣯⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠃⠀⠀⠀⠀⠀⢸⣿⢀⣸⣿⣿⣿⣧⣿⣏⣸⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⢻⣿⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⡀⠀⠀⢻⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠉⠛⠀⠀⠀⠸⣿⣿⠟⠀⠀⢸⣿⣿⣿⣿⣿⣿⣄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⣀⣀⠀
⠀⠀⠀⠀⣿⣿⣷⢸⣿⠗⣿⣆⣿⢸⣧⣿⢸⣿⠀⣿⣰⣿⢿⡾⢿⣿⠇⠀⠈⢹⣤⣄⠀⠀⢻⣿⣿⣿⣿⣿⣿⣷⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⢀⣼⣿⣿⡄
⠀⠀⠀⠀⣿⣿⣿⢸⣿⠃⣿⣿⣿⡈⣿⡇⢸⣿⢠⣿⣎⣻⣿⡆⣼⣿⣶⡄⠀⢸⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⠙⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣽⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠉⠙⠛⠃
⠀⢀⣠⣴⣿⣿⣿⣿⣛⣻⣿⣿⠛⠿⠛⠃⠘⠛⠛⠛⠛⠻⠟⠃⠿⠿⠛⠃⠀⠀⠙⠿⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠙⢿⣿⣿⣿⣿⣷⡿⠟⠛⠋⣶⣿⣿⣿⣿⣶⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⠿⠟⠀⠉⠀⠀⠀⠀⠀⠻⣿⣿⣿⠟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠲⢢⠀⠠⠄⣰⣤⣶⣦⣄⠀⢿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣴⣾⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣦⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠘⠛⠛⠻⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠋⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠶⠂⠀⣼⣿⣿⣿⣿⣟⣛⠛⢻⣿⣿⣿⣿⣿⣿⣿⡀⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⣀⣀⡀⣀⣀⡀⣀⣀⢀⣀⢀⣀⠀⠀⠀⠀⣿⣧⣤⣤⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⣿⡇⣿⣏⢱⣿⣿⣸⣿⣾⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡿⠉⠙⣯⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠇⠀⠀⠀⠀⠀⢸⣿⣀⣸⣿⣿⣿⣧⣿⣏⣸⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⢿⣿⣿⣿⠃⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡕⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠉⠛⠀⠀⠀⠸⣿⣿⠟⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⣠⣀⠀
⠀⠀⠀⠀⣿⣿⣷⢸⣿⠗⣿⣆⣿⢸⣧⣿⢸⣿⠀⣿⣶⣿⢿⡾⢿⣿⠇⠀⠈⢹⣦⣄⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠉⠣⠄⠀⠀⢀⣴⣿⣿⡆
⠀⠀⠀⠀⣿⣿⣿⢸⣿⠃⣿⣿⣿⣈⣿⡇⢸⣿⢰⣿⣏⣻⣿⡆⣾⣿⣶⡄⠀⢸⣿⣿⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⢀⠈⠙⠛⠛⠇
⠀⣀⣠⣴⣿⣿⣿⣿⣛⣿⣿⣿⠛⠟⠛⠃⠘⠛⡛⠛⠛⠻⠟⠃⠿⠿⠻⠃⠀⠀⠙⠿⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠙⢿⣿⣿⣿⣿⣿⡿⠟⠛⠟⣶⣿⣿⣿⣿⣷⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠸⠿⠟⠀⠉⠀⠀⠀⠀⠀⠻⣿⣿⣿⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠲⢲⠀⠠⠄⢰⣶⣶⣶⣄⠀⢿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣴⣾⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠘⠛⠛⠻⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠋⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠶⠂⠀⣼⣿⣿⣿⣿⣟⣛⠛⢻⣿⣿⣿⣿⣿⣿⣿⡀⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⣀⣀⡀⣀⣀⡀⣀⣀⢀⣀⢀⣀⠀⠀⠀⠀⣿⣧⣤⣤⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⣿⡇⣿⣏⢱⣿⣿⣸⣿⣾⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡿⠉⠛⣯⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠇⠀⠀⠀⠀⠀⢸⣿⣀⣸⣿⣿⣿⣧⣿⣏⣸⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⢿⣿⣿⣿⠃⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡽⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠉⠛⠀⠀⠀⠸⣿⣿⠟⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⣠⣀⠀
⠀⠀⠀⠀⣿⣿⣷⢸⣿⠗⣿⣆⣿⢸⣧⣿⢸⣿⢐⣿⣶⣿⢿⡾⢿⣿⠇⠀⠈⢹⣦⣄⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠉⠡⠄⠀⠀⢀⣴⣿⣿⡆
⠀⠀⠀⠀⣿⣿⣿⢸⣿⠃⣿⣿⣿⣈⣿⡇⢸⣿⢸⣿⣏⣻⣿⡆⣾⣿⣶⡄⠀⢸⣿⣿⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠉⠛⠻⠇
⠀⣀⣠⣴⣿⣿⣿⣿⣛⣿⣿⣿⠛⠟⠛⠃⠘⠛⡛⠛⠛⠻⠟⠃⠿⠻⠻⠃⠀⠀⠙⠿⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠁⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠙⢿⣿⣿⣿⣿⣿⡿⠟⠛⠛⣶⣿⣿⣿⣿⣷⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠸⠿⠟⠀⠉⠀⠀⠀⠀⠀⠻⣿⣿⣿⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠲⢲⠀⠰⠄⢰⣶⣶⣶⣄⠀⢿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣴⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠛⠛⠻⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡷⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣠⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⣴⣾⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⣴⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⣀⣀⡀⣀⣀⡀⣀⣀⢀⣀⢀⣀⠀⠀⠀⠀⣿⣧⣤⣤⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⣿⡇⣿⣏⢱⣿⣿⣸⣿⣾⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡟⠛⣫⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠃⠀⠀⠀⠀⠀⢸⣿⣀⣸⣿⣿⣿⣧⣿⣯⣼⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⢿⣿⣿⣿⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠉⠛⠀⠀⠀⠸⣿⣿⠟⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⣠⣀⠀
⠀⠀⠀⠀⣿⣿⣷⢸⣿⠗⣿⣆⣿⢸⣧⣿⢸⣿⠀⣿⣶⣿⢿⡾⢿⣿⠇⠀⠈⢹⣦⣄⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⢀⣴⣿⣿⡆
⠀⠀⠀⠀⣿⣿⣿⢸⣿⠃⣿⣿⣿⣀⣿⡇⢸⣿⢰⣿⣏⣻⣿⡆⣾⣿⣶⡄⠀⢸⣿⣿⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠙⠛⠛⠿⠇
⠀⣀⣠⣴⣿⣿⣿⣿⣛⣿⣿⣿⠛⠿⠛⠃⠘⠛⠛⠛⠛⠻⠟⠃⠿⠻⠿⠃⠀⠀⠙⠿⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠙⢿⣿⣿⣿⣿⣿⡿⠟⠛⠋⣾⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠸⠿⠟⠀⠉⠀⠀⠀⠀⠀⠻⣿⣿⣿⠟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣇⣦⣽⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢲⠀⠠⠄⣴⣶⣶⣶⣤⠀⢿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠫⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⣠⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⠛⠻⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠒⠀⠀⣿⣿⣿⣿⣿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣤⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣶⣿⣿⣿⣿⣿⣿⣷⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣆⣴⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⣀⣀⡀⣀⣀⡀⣀⣀⢀⣀⢀⣀⠀⠀⠀⠀⣿⣧⣤⣤⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⣿⡇⣿⣏⢱⣿⣿⣸⣿⣾⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡛⢛⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠃⠀⠀⠀⠀⠀⢸⣿⢀⣸⣿⣿⣿⣧⣿⣯⣼⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⢿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠉⠛⠀⠀⠀⠸⣿⣿⠟⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⣠⣄⠀
⠀⠀⠀⠀⣿⣿⣷⢸⣿⠗⣿⣆⣿⢸⣧⣿⢸⣿⠐⣿⣶⣿⢿⡾⢿⣿⠇⠀⠈⢹⣦⣄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⢀⣼⣿⣿⡆
⠀⠀⠀⠀⣿⣿⣿⢸⣿⠃⣿⣿⣿⣈⣿⡇⢸⣿⢘⣿⣏⣻⣿⡆⣾⣿⣶⡄⠀⢸⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠿⠇
⠀⣀⣠⣼⣿⣿⣿⣿⣛⣿⣿⣿⠛⠿⠛⠃⠘⠛⡛⠛⠋⠻⠟⠃⠟⠿⠿⠃⠀⠀⠙⠿⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠙⢿⣿⣿⣿⣿⣿⡿⠟⠛⠋⣾⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠸⠿⠟⠀⠉⠀⠀⠀⠀⠀⠻⣿⣿⣿⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣰⣬⣽⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠲⢲⠀⠠⠄⢴⣶⣶⣶⣄⠀⢿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠫⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣴⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⠛⠻⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠒⠀⠀⣿⣿⣿⣿⣟⠉⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣤⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣾⣿⣿⣿⣿⣿⣿⣷⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣆⣴⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⣀⣀⡀⣀⣀⡀⣀⣀⢀⣀⢀⣀⠀⠀⠀⠀⣿⣧⣦⣤⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⣿⡇⣿⣏⢱⣿⣿⣸⣿⣾⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡛⢛⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠃⠀⠀⠀⠀⠀⢸⣿⣀⣸⣿⣿⣿⣧⣿⣯⣸⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⢿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠉⠛⠀⠀⠀⠸⣿⣿⠟⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⣠⣀⠀
⠀⠀⠀⠀⣿⣿⣷⢸⣿⠗⣿⡆⣿⢸⣧⣿⢸⣿⠰⣿⣶⣿⢿⡾⢿⣿⠇⠀⠈⢹⣦⣄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠹⠅⠀⠀⠀⢀⣴⣿⣿⡆
⠀⠀⠀⠀⣿⣿⣿⢸⣿⠃⣿⣿⣿⣀⣿⡇⢸⣿⢰⣿⣏⣻⣿⣆⣾⣿⣶⡄⠀⢸⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠇
⠀⣀⣠⣼⣿⣿⣿⣿⣛⣿⣿⣿⠛⠟⠛⠃⠘⠛⡛⠛⠛⠻⠟⠃⠛⠛⠻⠃⠀⠀⠙⠿⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠙⣿⣿⣿⣿⣿⣿⡿⠟⠛⠋⣾⣿⣿⣿⣿⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠸⠿⠟⠀⠉⠀⠀⠀⠀⠀⠻⣿⣿⣿⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣤⡹⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢶⠀⠠⠄⣴⣶⣶⣦⣄⠀⢿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠓⠲⠒⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⢀⣀⣀⢀⣠⣴⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠛⠛⠻⣿⠿⠛⠁⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⠟⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣠⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⣤⣤⣴⣿⣿⣿⣿⣷⣤⣌⣉⣿⣿⣿⣿⣿⣿⣿⣿⡄⣰⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⣀⣀⡀⣀⣀⡀⣀⣀⢀⣀⢀⣀⠀⠀⠀⠀⣿⣧⣦⣤⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⣿⡇⣿⣏⢱⣿⣿⣸⣿⣾⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠇⠀⠀⠀⠀⠀⢸⣿⣀⣸⣿⣿⣿⣧⣿⣏⣸⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⢻⣿⣿⣿⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠈⠉⠛⠀⠀⠀⠘⣿⣿⠟⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⣠⣀⠀
⠀⠀⠀⠀⣿⣿⣷⢸⣿⠗⣿⡆⣿⢸⣧⣿⢸⣿⠀⣿⣶⣿⢿⡾⢿⣿⠇⠀⠈⢹⣦⣄⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠙⠅⠀⠀⠀⢀⣴⣿⣿⡆
⠀⠀⠀⠀⣿⣿⣿⢸⣿⠃⣿⣿⣿⣀⣿⡇⢸⣿⢠⣿⣏⣻⣿⡆⣾⣿⣶⡄⠀⢸⣿⣿⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠇
⠀⣀⣠⣼⣿⣿⣿⣿⣛⣿⣿⣿⠛⠟⠛⠃⠘⠛⠛⠛⠛⠻⠟⠃⠛⠛⠛⠃⠀⠀⠙⠿⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠙⢿⣿⣿⣿⣿⣿⡿⠟⠛⠃⣾⣿⣿⣿⣿⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠸⠿⠟⠀⠉⠀⠀⠀⠀⠀⠻⣿⣿⣿⠟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣌⠹⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢲⠀⠠⠄⣴⣶⣶⣦⣄⠀⢿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠿⠓⠲⠒⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⢀⣀⣀⢀⣠⣴⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠛⠛⠻⣿⠿⠛⠁⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠙⣿⣿⣿⣿⣿⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣠⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⣤⣤⣴⣿⣿⣿⣿⣷⣤⣌⣉⣿⣿⣿⣿⣿⣿⣿⣿⡄⣰⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⣀⣀⡀⣀⣀⡀⣀⣀⢀⣀⢀⣀⠀⠀⠀⠀⣿⣧⣦⣤⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⣿⡇⣿⣏⢱⣿⣿⣸⣿⣾⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠇⠀⠀⠀⠀⠀⢸⣿⣀⣸⣿⣿⣿⣧⣿⣏⣼⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⢿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠉⠛⠀⠀⠀⠘⣿⣿⠟⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⣠⣀⠀
⠀⠀⠀⠀⣿⣿⣷⢸⣿⠗⣿⣆⣿⢸⣧⣿⢸⣿⠀⣿⣶⣿⢿⡾⢿⣿⠇⠀⠈⢹⣦⣄⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠻⠅⠀⠀⠀⢀⣼⣿⣿⡆
⠀⠀⠀⠀⣿⣿⣿⢸⣿⠃⣿⣿⣿⣀⣿⡇⢸⣿⢠⣿⣏⣻⣿⣆⣾⣿⣶⡄⠀⢸⣿⣿⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠿⠿⠿⠇
⠀⣀⣠⣼⣿⣿⣿⣿⣛⣿⣿⣿⠛⠟⠛⠃⠘⠛⠛⠛⠋⠻⠟⠃⠛⠛⠛⠃⠀⠀⠙⠿⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀
⠀⠙⢿⣿⣿⣿⣿⣿⡿⠟⠛⠋⣾⣿⣿⣿⣿⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠸⠿⠟⠀⠉⠀⠀⠀⠀⠀⠻⣿⣿⣿⠟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣌⠻⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢢⠀⠠⠄⣴⣶⣶⣦⣄⠀⢿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⢏⠒⠒⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢀⣀⣀⣀⣠⣴⣶⣶⣷⣶⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠛⠛⠻⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⠛⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢀⣠⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣤⣤⣤⣿⣿⣿⣿⣷⣦⣄⣈⣻⣿⣿⣿⣿⣿⣿⣿⡆⣰⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⣀⣀⡀⣀⣀⡀⣀⣀⢀⣀⢀⣀⠀⠀⠀⠀⣿⣧⣦⣤⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡏⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⣿⡇⣿⣏⢱⣿⣿⣸⣿⣾⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠃⠀⠀⠀⠀⠀⢸⣿⣀⣸⣿⣿⣿⣧⣿⣏⣸⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⢻⣿⣿⣿⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠈⠉⠛⠀⠀⠀⠘⣿⣿⠟⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⣠⣀⠀
⠀⠀⠀⠀⣿⣿⣷⢸⣿⠗⣿⡆⣿⢸⣧⣿⢸⣿⠀⣿⢰⣿⢿⡾⢿⣿⠇⠀⠈⢹⣦⣄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠙⠥⠀⠀⠀⢀⣴⣿⣿⡆
⠀⠀⠀⠀⣿⣿⣿⢸⣿⠃⣿⣿⣿⣀⣿⡇⢸⣿⢠⣿⣏⣻⣿⣆⣾⣿⣶⡄⠀⢸⣿⡿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠇
⠀⣀⣠⣾⣿⣿⣿⣿⣛⣿⣿⣿⠛⠟⠛⠃⠘⠛⡛⠛⠋⠻⠟⠃⠛⠛⠛⠁⠀⠀⠙⠿⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠙⢿⣿⣿⣿⣿⡾⠿⠟⠛⠋⣾⣿⣿⣿⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠸⠿⠟⠀⠉⠀⠀⠀⠀⠀⠻⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠹⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢢⠀⠠⠄⣴⣶⣶⣶⣄⠀⢿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠒⠒⠂⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢀⣀⣀⣀⣠⣴⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠛⠛⠻⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣠⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣤⣤⣤⣿⣿⣿⣿⣷⣦⣄⣈⣻⣿⣿⣿⣿⣿⣿⣿⡆⣰⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⣀⣀⡀⣀⣀⡀⣀⣀⢀⣀⢀⣀⠀⠀⠀⠀⣿⣧⣦⣤⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡏⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⣿⡇⣿⣏⢱⣿⣿⣸⣿⣾⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡿⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠃⠀⠀⠀⠀⠀⢸⣿⣀⣸⣿⣿⣿⣧⣿⣏⣸⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⢿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠈⠉⠛⠀⠀⠀⠘⣿⣿⠟⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⣠⣀⠀
⠀⠀⠀⠀⣿⣿⣷⢸⣿⠗⣿⡆⣿⢸⣧⣿⢸⣿⠐⣿⣴⣿⢿⡾⢿⣿⠇⠀⠈⢹⣦⣄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⢀⣼⣿⣿⡆
⠀⠀⠀⠀⣿⣿⣿⢸⣿⠃⣿⣿⣿⣀⣿⡇⢸⣿⢠⣿⣏⣻⣿⣆⣾⣿⣶⡀⠀⢸⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠇
⠀⣀⣤⣾⣿⣿⣿⡿⣛⣿⣿⣿⠛⠟⠛⠃⠘⠛⠛⠛⠛⠻⠟⠋⠛⠛⠛⠃⠀⠀⠙⠿⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠙⢿⣿⣿⣿⣿⣿⠿⠟⠛⠋⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠸⠿⠟⠀⠉⠀⠀⠀⠀⠀⠻⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠹⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢢⠀⠠⠄⣴⣶⣶⣶⣄⠀⢿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠙⠛⠋⠙⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⢀⣤⣀⣀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠛⠛⠻⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⠟⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣠⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣤⣤⣤⣾⣿⣿⣿⣿⣶⣤⣄⣩⣿⣿⣿⣿⣿⣿⣿⣇⢠⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⣀⣀⡀⣀⣀⡀⣀⣀⢀⣀⢀⣀⠀⠀⠀⠀⣿⣷⣶⣦⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡟⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⣿⡇⣿⣏⢱⣿⣿⣸⣿⣾⣿⠀⠀⠀⠀⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠿⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠃⠀⠀⠀⠀⠀⢸⣿⣀⣸⣿⣿⣿⣧⣿⣯⣼⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⢿⣿⣿⣿⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠈⠉⠛⠀⠀⠀⠸⣿⣿⠋⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⣠⣄⠀
⠀⠀⠀⠀⣿⣿⣷⢸⣿⠗⣿⣆⣿⢸⣧⣿⢸⣿⠀⣿⣶⣿⢿⡾⢿⣿⠇⠀⠈⣽⣦⣄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⠙⠁⠀⠀⠀⢀⣼⣿⣿⡆
⠀⠀⠀⠀⣿⣿⣿⢸⣿⠃⣿⣿⣿⣀⣿⡏⢸⣿⢠⣿⣏⣻⣿⣦⣾⣿⣶⡄⠀⢻⣿⡿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠃
⠀⣀⣤⣾⣿⣿⣿⣿⣛⣿⣿⣿⠛⠟⠛⠃⠘⠛⡛⠛⠛⠻⠟⠋⠛⠛⠛⠁⠀⠀⠙⠗⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠙⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⣾⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠸⠿⠟⠀⠉⠀⠀⠀⠀⠀⠻⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡈⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢰⠀⠠⠄⣴⣶⣶⣶⣄⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠉⠁⠋⠙⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⣠⣄⣀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠛⠛⠻⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⡟⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣀⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⣤⣤⣼⣿⣿⣿⣿⣷⣤⣄⣈⣿⣿⣿⣿⣿⣿⣿⣿⢀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⣀⣀⡀⣀⣀⡀⣀⣀⢀⣀⢀⣀⠀⠀⠀⠀⣿⣷⣶⣦⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡏⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⣿⡇⣿⣏⢱⣿⣿⣸⣿⣾⣿⠀⠀⠀⠀⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⢸⣿⣀⣸⣿⣿⣿⣧⣿⣯⣼⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠈⠉⠛⠀⠀⠀⠸⣿⣿⠋⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⣠⣀⠀
⠀⠀⠀⠀⣿⣿⣷⢸⣿⠗⣿⣆⣿⢸⣧⣿⢸⣿⠀⣿⣰⣿⢿⡾⢿⣿⠇⠀⠈⣵⣦⣄⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠉⠡⠀⠀⠀⢀⣼⣿⣿⡆
⠀⠀⠀⠀⣿⣿⣿⢸⣿⠃⣿⣿⣿⣀⣿⡇⢸⣿⢀⣿⣏⣻⣿⣆⣾⣿⣶⡄⠀⢻⣿⡿⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠇
⠀⣀⣤⣾⣿⣿⣿⡿⣛⣿⣿⣿⠛⠛⠛⠃⠘⠛⡛⠛⠛⠻⠟⠋⠛⠛⠛⠁⠀⠀⠙⠇⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠙⢿⣿⣿⣿⣿⡿⠿⠟⠉⠉⣾⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠸⠿⠋⠀⠁⠀⠀⠀⠀⠀⠻⣿⣿⣿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡈⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢲⠀⠰⠄⣴⣶⣶⣶⣄⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠉⠉⠋⠉⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⣠⣄⣀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠚⠛⠻⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣿⣿⣿⣿⡟⠛⣛⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣀⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⣤⣤⣼⣿⣿⣿⣿⣷⣤⣆⣈⣽⣿⣿⣿⣿⣿⣿⣿⢀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⣀⣀⡀⣀⣀⡀⣀⣀⢀⣀⢀⣀⠀⠀⠀⠀⣿⣷⣶⣦⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡏⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⣿⡇⣿⣏⢱⣿⣿⣸⣿⣾⣿⠀⠀⠀⠀⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⢸⣿⣀⣸⣿⣿⣿⣧⣿⣯⣼⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠈⠉⠛⠀⠀⠀⠸⣿⣿⠋⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⣠⣀⠀
⠀⠀⠀⠀⣿⣿⣷⢸⣿⠗⣿⡆⣿⢸⣧⣿⢸⣿⠀⣿⣰⣿⢿⡾⢿⣿⠇⠀⠈⣵⣤⣄⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⢀⣼⣿⣿⡆
⠀⠀⠀⠀⣿⣿⣿⢸⣿⠃⣿⣿⣿⣀⣿⡇⢸⣿⠀⣿⣏⣻⣿⣆⣾⣿⣶⡄⠀⢻⣿⡿⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠇
⠀⣀⣤⣾⣿⣿⣿⡿⣛⣿⣿⣿⠛⠟⠛⠃⠘⠛⠛⠛⠛⠻⠟⠋⠛⠛⠛⠁⠀⠀⠙⠗⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠙⢿⣿⣿⣿⣿⡿⠿⠟⠙⠉⣾⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠸⠿⠋⠀⠁⠀⠀⠀⠀⠀⠻⣿⣿⣿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡈⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢲⠀⠰⠄⣴⣶⣶⣶⣄⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠋⠺⠉⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⣠⣄⣀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⠛⠻⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡟⠋⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣴⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣶⣶⣶⣶⣿⣿⣿⣿⣿⣶⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⣀⣀⡀⣀⣀⡀⣀⣀⢀⣀⢀⣀⠀⠀⠀⠀⣿⣷⣶⣦⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡏⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⣿⡇⣿⣏⢱⣿⣿⣸⣿⣾⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⢸⣿⣀⣸⣿⣿⣿⣧⣿⣯⣼⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⢿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠈⠉⠛⠀⠀⠀⠸⣿⣿⠋⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⣠⣄⠀
⠀⠀⠀⠀⣿⣿⣷⢸⣿⠗⣿⣆⣿⢸⣧⣿⢸⣿⠀⣿⣰⣿⢿⡾⢿⣿⠇⠀⠈⣵⣦⣄⠀⠀⠀⠀⠠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠈⠉⠥⠀⠀⠀⢀⣼⣿⣿⡆
⠀⠀⠀⠀⣿⣿⣿⢸⣿⠃⣿⣿⣿⣀⣿⡇⢸⣿⠀⣿⣏⣻⣿⣦⣾⣿⣶⡄⠀⢻⣿⡿⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠿⠇
⠀⣀⣤⣾⣿⣿⣿⡿⣻⣿⣿⣿⠛⠟⠛⠃⠘⠛⡛⠛⠋⠻⠟⠋⠛⠛⠛⠁⠀⠀⠙⠗⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠙⢿⣿⣿⣿⣿⡿⠿⠟⠛⢣⣾⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠘⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠸⠿⠋⠀⠁⠀⠀⠀⠀⠀⠻⣿⣿⣿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢢⠀⠰⠄⣴⣶⣶⣶⣄⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠋⠻⠉⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⣠⣄⣀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⠛⠻⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡟⠋⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣴⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣶⣶⣶⣶⣿⣿⣿⣿⣿⣶⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣀⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⣀⣀⡀⣀⣀⡀⣀⣀⢀⣀⢀⣀⠀⠀⠀⠀⣿⣷⣶⣦⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⣿⡇⣿⣏⢱⣿⣿⣸⣿⣾⣿⠀⠀⠀⠀⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⢸⣿⣀⣸⣿⣿⣿⣧⣿⣯⣼⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⢿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠈⠉⠛⠀⠀⠀⠸⣿⣿⠋⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⣠⣀⠀
⠀⠀⠀⠀⣿⣿⣷⢸⣿⠗⣿⡆⣿⢸⣧⣿⢸⣿⠀⣿⣴⣿⢿⡾⢿⣿⠇⠀⠈⣼⣦⣄⠀⠀⠀⠀⠠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠈⠙⠥⠀⠀⠀⢀⣼⣿⣿⡆
⠀⠀⠀⠀⣿⣿⣿⢸⣿⠃⣿⣿⣿⣀⣿⡇⢸⣿⠀⣿⣏⣻⣿⣦⣾⣿⣶⡄⠀⢻⣿⡿⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠛⠛⠿⠇
⠀⣠⣤⣾⣿⣿⣿⡿⣛⣿⣿⣿⠛⠟⠛⠃⠘⠛⡛⠛⠛⠻⠟⠋⠛⠛⠛⠁⠀⠀⠙⠗⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠹⣿⣿⣿⣿⣿⡿⠿⠟⠻⢣⣾⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠘⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠸⠿⠋⠀⠁⠀⠀⠀⠀⠀⠻⣿⣿⣿⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⢹⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢲⠀⠰⠄⣴⣶⣶⣶⣄⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠋⠚⠉⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⣠⣄⣀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⡃⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠛⠛⠻⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡿⠋⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⠀⠀⣠⣴⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣶⣶⣶⣶⣿⣿⣿⣿⣿⣶⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⣀⣀⡀⣀⣀⡀⣀⣀⢀⣀⢀⣀⠀⠀⠀⢠⣿⣷⣶⣦⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⣿⡇⣿⣏⢱⣿⣿⣸⣿⣾⣿⠀⠀⠀⠸⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⢸⣿⣀⣸⣿⣿⣿⣧⣿⣯⣼⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠈⠉⠛⠀⠀⠀⠸⣿⣿⠋⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⣤⣄⠀
⠀⠀⠀⠀⣿⣿⣷⢸⣿⠗⣿⣆⣿⢸⣧⣿⢸⣿⠀⣿⢰⣿⢿⡾⢿⣿⠇⠀⠈⣽⣦⣄⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠈⠙⠥⠀⠀⠀⢠⣼⣿⣿⡄
⠀⠀⠀⠀⣿⣿⣿⢸⣿⠃⣿⣿⣿⣀⣿⡇⢸⣿⠀⣿⣏⣻⣿⣦⣾⣿⣶⡄⠀⢻⣿⡿⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠇
⠀⣠⣤⣾⣿⣿⣿⣟⣛⣿⣿⣟⠛⠛⠛⠃⠘⠛⠛⠛⠛⠻⠟⠛⠛⠛⠛⠁⠀⠀⠙⠇⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠙⣿⣿⣿⣿⣿⡿⠿⠛⠛⢃⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠸⠿⠋⠀⠁⠀⠀⠀⠀⠀⠻⣿⣿⣿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡈⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢲⠀⠰⠄⣴⣶⣶⣶⣄⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠋⠚⠉⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⣠⣄⣀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡂⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠛⠛⠻⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡿⠋⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⣴⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣶⣶⣶⣶⣿⣿⣿⣿⣿⣶⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣀⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⣀⣀⡀⣀⣀⡀⣀⣀⢀⣀⢀⣀⠀⠀⠀⢠⣿⣷⣶⣦⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⣿⡇⣿⣏⢱⣿⣿⣸⣿⣾⣿⠀⠀⠀⠘⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⢸⣿⣀⣸⣿⣿⣿⣧⣿⣯⣼⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠈⠉⠛⠀⠀⠀⠸⣿⣿⠋⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⣤⣄⠀
⠀⠀⠀⠀⣿⣿⣷⢸⣿⠗⣿⣆⣿⢸⣧⣿⢸⣿⠀⣿⣰⣿⢿⡾⢿⣿⠇⠀⠈⣼⣦⣄⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠙⠡⠀⠀⠀⢠⣼⣿⣿⡆
⠀⠀⠀⠀⣿⣿⣿⢸⣿⠃⣿⣿⣿⣀⣿⡇⢸⣿⠀⣿⣏⣻⣿⣦⣾⣿⣶⡄⠀⢻⣿⡿⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠇
⠀⣠⣤⣾⣿⣿⣿⣟⣛⣿⣿⡟⠛⠛⠛⠃⠘⠛⡛⠛⠛⠻⠟⠛⠛⠛⠛⠁⠀⠀⠙⠇⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠙⢿⣿⣿⣿⣿⠿⠿⠛⠛⢣⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠨⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠸⠿⠋⠀⠁⠀⠀⠀⠀⠀⠻⣿⣿⡿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢢⠀⠰⠄⣴⣶⣶⣶⣄⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠉⠉⠉⠙⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⣤⣤⣀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠛⠛⠻⡿⠟⠋⠁⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⡟⠉⠉⠙⢻⢿⣿⣿⣿⣿⣿⡇⠀⠀⣠⣶⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣶⣶⣶⣾⣿⣿⣿⣿⣷⣶⣷⣾⣿⣾⣿⣿⣿⣿⣿⣿⣀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⣀⣀⡀⣀⣀⡀⣀⣀⢀⣀⢀⣀⠀⠀⠀⢸⣿⣷⣶⣦⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⣿⡇⣿⣏⢱⣿⣿⣸⣿⣾⣿⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣀⣸⣿⣿⣿⣧⣿⣯⣼⣿⣿⣿⣿⣿⣿⣀⠀⠀⠈⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠈⠉⠛⠀⠀⠀⠹⣿⡿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⢀⣠⣀⠀
⠀⠀⠀⠀⣿⣿⣷⢸⣿⠗⣿⣆⣿⢸⣧⣿⢸⣿⠀⣿⣰⣿⢿⡾⢿⣿⠇⠀⠀⣶⣤⡄⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢈⠙⠤⠀⠀⠀⢠⣼⣿⣿⡄
⠀⠀⠀⢀⣿⣿⣿⢸⣿⠃⣿⣿⣿⣀⣿⡇⢸⣿⠀⣿⣏⣻⣿⣦⣾⣿⣶⠀⠀⢿⣿⡟⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠿⠃
⠀⣠⣴⣾⣿⣿⣿⣟⣻⣿⣿⡟⠛⠛⠛⠃⠘⠛⠛⠛⠛⠻⠟⠛⠛⠛⠛⠀⠀⠀⠙⠇⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠻⣿⣿⣿⣿⣿⠿⠿⠛⠛⢳⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠺⠿⠋⠀⠁⠀⠀⠀⠀⠈⠻⣿⣿⡿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⢻⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢠⠀⠰⠄⣴⣶⣶⣶⡄⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠉⠉⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢀⣤⣄⣀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠛⠛⠻⡿⠟⠋⠁⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⡟⠉⠉⠙⢿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣤⣶⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣶⣶⣶⣾⣿⣿⣿⣿⣷⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣀⣾⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⣀⣀⡀⣀⣀⡀⣀⣀⢀⣀⢀⣀⠀⠀⠀⢸⣿⣷⣶⣦⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⣿⡇⣿⣏⢱⣿⣿⣸⣿⣾⣿⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣀⣸⣿⣿⣿⣧⣿⣯⣼⣿⣿⣿⣿⣿⣿⣀⠀⠀⠈⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠈⠉⠛⠀⠀⠀⠻⣿⡿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⢀⣤⣀⠀
⠀⠀⠀⠀⣿⣿⣷⢸⣿⠗⣿⣆⣿⢸⣧⣿⢹⣿⠀⣿⣴⣿⢿⡾⢿⣿⠇⠀⠀⣷⣤⡄⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠙⠄⠀⠀⠀⣠⣾⣿⣿⡀
⠀⠀⠀⢀⣿⣿⣿⢸⣿⠃⣿⣿⣿⡀⣿⡇⢸⣿⠀⣿⣏⣻⣿⣦⣾⣿⣶⠀⠀⢿⣿⡏⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠃
⢀⣤⣴⣿⣿⣿⣿⣟⣻⣿⣿⡟⠛⠛⠛⠃⠘⠛⠛⠛⠛⠻⠟⠛⠛⠛⠛⠀⠀⠀⠛⠇⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠻⣿⣿⣿⣿⣿⠿⠿⠛⠋⢱⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠻⠿⠋⠈⠁⠀⠀⠀⠀⠈⠻⣿⣿⡿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡈⢻⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢢⠀⠰⠄⣴⣶⣶⣶⡄⠸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠉⠉⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢀⣤⣤⣀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠛⠛⠻⡿⠟⠋⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⡟⠉⠉⠙⢻⣿⣿⣿⣿⣿⣿⡇⠀⢀⣤⣶⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣶⣶⣶⣾⣿⣿⣿⣿⣷⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣷⣀⣾⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⣀⣀⡀⣀⣀⠀⣀⣀⢀⣀⢀⣀⠀⠀⠀⢸⣿⣷⣶⣦⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⣿⡇⣿⣏⢱⣿⣿⣸⣿⣾⣿⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣀⣸⣿⣿⣿⣧⣿⣯⣼⣿⣿⣿⣿⣿⣿⣀⠀⠀⠈⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠈⠉⠛⠀⠀⠀⠹⣿⡿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⢀⣠⡀⠀
⠀⠀⠀⠀⣿⣿⣷⢸⣿⠗⣿⣆⣿⢸⣧⣿⢹⣿⠀⣿⣰⣿⢿⡾⢿⣿⠇⠀⠀⣶⣤⡄⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠙⠄⠀⠀⠀⣠⣾⣿⣿⡀
⠀⠀⠀⢀⣿⣿⣿⢸⣿⠃⣿⣿⣿⡀⣿⡇⢸⣿⠀⣿⣎⣻⣿⣦⣾⣿⣶⠀⠀⢿⣿⡏⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠃
⢀⣤⣴⣿⣿⣿⣿⢟⣻⣿⣿⡟⠛⠋⠛⠃⠘⠛⠛⠛⠛⠻⠟⠛⠛⠛⠛⠀⠀⠀⠙⠇⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠻⣿⣿⣿⣿⣿⠿⠿⠛⠙⢱⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠻⠿⠃⠈⠁⠀⠀⠀⠀⠈⠻⣿⣿⡿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⡈⢻⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢠⠀⠰⠄⣴⣶⣶⣶⡄⠐⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠉⠉⠉⠉⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢀⣤⣄⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠛⠛⠻⡿⠟⠋⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⡟⠉⠉⠙⢻⣿⣿⣿⣿⣿⣿⡇⠀⢀⣤⣶⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣶⣶⣶⣾⣿⣿⣿⣿⣷⣶⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣠⣾⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⣀⣀⡀⣀⣀⡀⣀⣀⢀⣀⢀⣀⠀⠀⠀⢸⣿⣷⣶⣦⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⣿⡇⣿⣏⢱⣿⣿⣸⣿⣾⣿⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣀⣸⣿⣿⣿⣧⣿⣯⣼⣿⣿⣿⣿⣿⣿⣀⠀⠀⠈⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠈⠉⠛⠀⠀⠀⠹⣿⡿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⢀⣤⣀⠀
⠀⠀⠀⠀⣿⣿⣷⢸⣿⠗⣿⣆⣿⢸⣧⣿⢹⣿⠀⣿⣶⣿⢿⡾⢿⣿⠇⠀⠀⣶⣤⡄⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠙⠄⠀⠀⠀⣠⣾⣿⣿⡀
⠀⠀⠀⢀⣿⣿⣿⢸⣿⠃⣿⣿⣿⡀⣿⡇⢸⣿⠀⣿⣏⣻⣿⣦⣾⣿⣶⠀⠀⢿⣿⡏⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠿⠁
⢀⣤⣴⣿⣿⣿⣿⢟⣻⣿⣿⡟⠛⠋⠛⠃⠘⠛⠛⠛⠋⠻⠟⠛⠛⠛⠛⠀⠀⠀⠙⠇⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠻⣿⣿⣿⣿⣿⠿⠿⠛⠋⢱⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠻⠿⠋⠀⠁⠀⠀⠀⠀⠈⠻⣿⣿⡿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡈⢻⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢠⠀⠰⠤⣴⣶⣶⣶⡄⠐⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢀⣤⣄⣀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠛⠛⠻⡿⠟⠋⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣿⣿⣿⣿⡟⠁⠉⠙⢻⣿⣿⣿⣿⣿⣿⡇⠀⢀⣤⣶⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣶⣶⣶⣾⣿⣿⣿⣿⣷⣶⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣠⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⣀⣀⡀⣀⣀⡀⣀⣀⢀⣀⢀⣀⠀⠀⠀⢸⣿⣷⣶⣤⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⣿⡇⣿⣏⢱⣿⣿⣸⣿⣾⣿⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣀⣸⣿⣿⣿⣧⣿⣯⣼⣿⣿⣿⣿⣿⣿⣀⠀⠀⠈⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠈⠉⠛⠀⠀⠀⠹⣿⡿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⢀⣠⣀⠀
⠀⠀⠀⠀⣿⣿⣷⢸⣿⠗⣿⣆⣿⢸⣧⣿⢸⣿⠀⣿⣰⣿⢿⡾⢿⣿⠇⠀⠀⣶⣤⡄⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠙⠄⠀⠀⠀⣠⣾⣿⣿⠀
⠀⠀⠀⢀⣿⣿⣿⢸⣿⠃⣿⣿⣿⡀⣿⡇⢸⣿⠀⣿⣏⣻⣿⣦⣾⣿⣶⠀⠀⢿⣿⡏⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠁
⢀⣤⣴⣿⣿⣿⣿⢟⣻⣿⣿⡟⠛⠋⠛⠃⠘⠛⠛⠛⠛⠻⠟⠛⠛⠛⠛⠀⠀⠀⠙⠇⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠻⣿⣿⣿⣿⣿⠿⠿⠛⠙⢱⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠻⠿⠃⠈⠁⠀⠀⠀⠀⠈⠻⣿⣿⡿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠈⣻⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢢⠀⠰⠤⣴⣶⣶⣶⡄⠐⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠉⠉⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢀⣤⣤⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠛⠛⠻⡿⠟⠋⠁⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⡏⠉⠉⠙⣻⣿⣿⣿⣿⣿⣿⡇⠀⢀⣤⣶⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣶⣶⣶⣾⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣠⣾⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⣀⣀⡀⣀⣀⡀⣀⣀⢀⣀⢀⣀⠀⠀⠀⢸⣿⣷⣶⣦⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⣿⡇⣿⣏⢱⣿⣿⣸⣿⣾⣿⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣀⣸⣿⣿⣿⣧⣿⣯⣼⣿⣿⣿⣿⣿⣿⣀⠀⠀⠈⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠈⠉⠛⠀⠀⠀⠻⣿⡿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⢀⣤⣀⠀
⠀⠀⠀⠀⣿⣿⣷⢸⣿⠗⣿⣆⣿⢸⣧⣿⢹⣿⠀⣿⣴⣿⢿⡾⢿⣿⠇⠀⠈⣷⣤⡄⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠙⠄⠀⠀⠀⣠⣾⣿⣿⡀
⠀⠀⠀⢀⣿⣿⣿⢸⣿⠃⣿⣿⣿⡀⣿⡇⢸⣿⠀⣿⣏⣻⣿⣦⣾⣿⣶⠀⠀⢿⣿⡏⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠿⠁
⢀⣤⣴⣿⣿⣿⣿⢟⣻⣿⣿⡟⠛⠋⠛⠃⠘⠛⠛⠛⠋⠻⠟⠛⠛⠛⠛⠀⠀⠀⠙⠇⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠻⣿⣿⣿⣿⣿⠿⠿⠛⠛⢱⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠻⠿⠋⠀⠁⠀⠀⠀⠀⠈⠻⣿⣿⡿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢠⠀⠰⠤⣴⣶⣶⣶⡄⠰⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠉⠉⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢀⣤⣄⣀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠛⠛⠻⡿⠟⠋⠁⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⡏⠉⠉⠙⣻⣿⣿⣿⣿⣿⣿⡇⠀⢀⣤⣶⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣶⣶⣶⣾⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣠⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⣀⣀⡀⣀⣀⡀⣀⣀⢀⣀⢀⣀⠀⠀⠀⢸⣿⣷⣶⣤⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⣿⡇⣿⣏⢱⣿⣿⣸⣿⣾⣿⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢿⠿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⢀⣸⣿⣿⣿⣧⣿⣯⣼⣿⣿⣿⣿⣿⣿⣀⠀⠀⠈⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠈⠉⠛⠀⠀⠀⠻⣿⡿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⢀⣠⣀⠀
⠀⠀⠀⠀⣿⣿⣷⢸⣿⠗⣿⣆⣿⢸⣧⣿⢹⣿⠀⣿⣶⣿⢿⡾⢿⣿⠇⠀⠀⣶⣤⡄⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⣠⣾⣿⣿⡀
⠀⠀⠀⢀⣿⣿⣿⢸⣿⠃⣿⣿⣿⡀⣿⡇⢸⣿⠀⣿⣏⣻⣿⣦⣾⣿⣶⠀⠀⢿⣿⡏⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠿⠁
⢀⣤⣴⣿⣿⣿⣿⢟⣻⣿⣿⡟⠛⠋⠛⠃⠘⠛⠛⠛⠋⠻⠟⠛⠛⠛⠛⠀⠀⠀⠹⠇⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠻⣿⣿⣿⣿⣿⠿⠿⠛⠛⢱⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠻⠿⠃⠈⠁⠀⠀⠀⠀⠈⠻⣿⣿⡿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⢿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢢⠀⠴⠤⣴⣶⣶⣶⡄⠰⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠉⠉⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢀⣤⣤⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠛⠛⠻⡿⠟⠋⠁⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⠏⠉⠉⠙⣻⣿⣿⣿⣿⣿⣿⡇⠀⢀⣤⣾⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣠⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⣀⣀⡀⣀⣀⡀⣀⣀⢀⣀⢀⣀⠀⠀⠀⢸⣿⣷⣶⣦⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠃⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⣿⡇⣿⣏⢱⣿⣿⣸⣿⣾⣿⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⢀⣸⣿⣿⣿⣧⣿⣯⣼⣿⣿⣿⣿⣿⣿⣀⠀⠀⠈⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠈⠉⠛⠀⠀⠀⠻⣿⡿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⢀⣤⣀⠀
⠀⠀⠀⠀⣿⣿⣷⢸⣿⠗⣿⣆⣿⢸⣧⣿⢹⣿⠀⣿⣴⣿⢿⡾⢿⣿⠇⠀⠀⣶⣤⡄⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⣠⣾⣿⣿⠀
⠀⠀⠀⢀⣿⣿⣿⢸⣿⠃⣿⣿⣿⡀⣿⡇⢸⣿⠀⣿⣏⣻⣿⣦⣾⣿⣶⠀⠀⢿⣿⡏⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠙⠛⠻⠿⠁
⢀⣤⣴⣿⣿⣿⣿⢟⣻⣿⣿⡟⠛⠛⠛⠃⠘⠛⠛⠛⠛⠻⠟⠛⠛⠛⠛⠀⠀⠀⠙⠇⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠻⣿⣿⣿⣿⣿⠿⠿⠛⠛⢱⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠻⠿⠃⠈⠁⠀⠀⠀⠀⠈⠻⣿⣿⡿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⢻⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢢⠀⠴⠤⣴⣶⣶⣶⡄⠸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 1870

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/03/26/fuchsia-woes/#comments
    Gemini version at gemini://gemini.techrights.org/2022/03/26/fuchsia-woes/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 03.26.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_26/03/2022:_Capyloon_and_Status_of_Chrome_OS,_Fuchsia⠀✐


Posted in Site_News at 4:33 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


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


          o § Kernel Space⠀➾


                # ⚓ OS News ☛ The_first_Asahi_Linux_Alpha_Release_is_here⠀⇛


                       This is an absolutely stunning effort and
                       achievement by the Asahi team, but as a mere user,
                       this whole thing does not exactly instill me with
                       the confidence needed to buy Apple hardware to run
                       Linux on it. There’s no denying M1 hardware is
                       amazing, but the idea of being entirely at the
                       mercy of whatever Apple decides to do with the
                       firmware and boot process seems like a terrible
                       place to be in. That being said, few people will
                       care about that possible issue, and for them, this
                       is great news.


                # ⚓ uni Toronto ☛ Some_notes_on_Linux’s_/proc/locks_listing_of
                  file_locks⠀⇛


                       As covered in the proc(5) manual page, /proc/locks
                       lists current flock(2) and fcntl(2) file locks (and
                       also lockf(3) locks, because those are actually
                       fcntl() locks). Unsurprisingly, this /proc file is
                       the fundamental source of information used by
                       lslocks(8), and so understanding what appears in /
                       proc/locks and what doesn’t can tell you something
                       about what lslocks can show you.


          o § Instructionals/Technical⠀➾


                # ⚓ Full_Circle_Magazine:_Full_Circle_Magazine_#179⠀⇛


                # ⚓ ID Root ☛ How_To_Install_Mirage_on_Ubuntu_20.04_LTS_–
                  idroot⠀⇛


                       In this tutorial, we will show you how to install
                       Mirage on Ubuntu 20.04 LTS. For those of you who
                       didn’t know, Mirage is an open-source application
                       that is used to view photos on Linux systems. The
                       graphical user interface enables the users to view
                       the images easily. The Mirage, you have many
                       options. Includes the ability to crop the image,
                       resize it or change the color saturation.
                       Furthermore, it automatically detects all the
                       images found in the directory and displays them in
                       the side panel.


                       This article assumes you have at least basic
                       knowledge of Linux, know how to use the shell, and
                       most importantly, you host your site on your own
                       VPS. The installation is quite simple and assumes
                       you are running in the root account, if not you may
                       need to add ‘sudo‘ to the commands to get root
                       privileges. I will show you the step-by-step
                       installation of the Mirage image viewer on Ubuntu
                       20.04 (Focal Fossa). You can follow the same
                       instructions for Ubuntu 18.04, 16.04, and any other
                       Debian-based distribution like Linux Mint.


                # ⚓ HowTo Forge ☛ How_to_Install_Chatwoot_Messaging_Platform_on
                  Debian_11⠀⇛


                       Chatwoot is a free, open-source, and real-time
                       messaging platform. It provides a simple and live
                       chat for your website and integrates it with other
                       apps. It helps your businesses to provide good
                       customer support to their clients via social media
                       channels. It can be easily integrated with social
                       media apps including, Facebook, WhatsApp, and
                       Twitter. It is a very good alternate solution to
                       other commercial software like Intercom, Zendesk,
                       etc.


                # ⚓ Finally⠀⇛


                       I gave up on WordPress for my personal blog,
                       because after all of that effort and time spent
                       yesterday, I have nothing to show for it. The site
                       still was not rendering correctly. On the upshot, I
                       discovered something called Hugo which generates a
                       static site and I found the perfect theme for me
                       called beautiful hugo. It is exactly the minimalist
                       approach I am looking for an does not require a
                       whole lot of resources to run. This is just a first
                       post to put something up. There will be more to
                       come soon.


                # ⚓ Vermaden ☛ ZFS_Compatibility⠀⇛


                       The best free filesystem on Earth – ZFS – also
                       often named OpenZFS recently – has also become very
                       portable in recent years of its development. The
                       OpenZFS Distributions page lists 6 (six) operating
                       systems already.


                       [...]


                       … but if you would like to create a ZFS pool
                       compatible with all of them … which options and ZFS
                       features should you choose? There is OpenZFS
                       Feature Flags page dedicated exactly to that topic.


                # ⚓ Heap_Overflow_in_OpenBSD’s_slaacd_via_Router
                  Advertisement⠀⇛


                       In this blog post we analyze a heap overflow
                       vulnerability we discovered in the IPv6 stack of
                       OpenBSD, more specifically in its slaacd daemon.
                       This issue, whose root cause can be found in the
                       mishandling of Router Advertisement messages
                       containing a DNSSL option with a malformed domain
                       label, was patched by OpenBSD on March 21, 2022. A
                       proof-of-concept to reproduce the vulnerability is
                       provided.


          o § Games⠀➾


                # ⚓ Techdirt ☛ More_Gaming_For_Good:_Charity_Bundles,_Fortnite
                  Team_Up_To_Raise_Millions_For_Ukraine⠀⇛


                       Once again, here comes the video game industry to
                       do good in the world. Despite being the easy
                       villain for many, including grandstanding
                       politicians, video games and their communities can
                       often be seen doing good for the world. A couple of
                       weeks back, we discussed how one itch.io game
                       bundle was offering thousands of dollars worth of
                       games in a bundle that had over 1,000 titles to
                       raise money for charities supporting Ukrainians.
                       Despite a minimum price of $10 in a “pay what you
                       want” format, that bundle had already raised $2
                       million from a $100k goal and was then aiming at $4
                       million instead.


          o § Distributions⠀➾


                # § Gentoo Family⠀➾


                      # ⚓ Make Use Of ☛ Is_Chrome_OS_Desktop_Linux?_8_Points_to
                        Consider⠀⇛


                             Do Chromebooks run Linux? This isn’t the way
                             they’re advertised, for sure. Google doesn’t
                             tell you Chromebooks come with Linux. They
                             run Chrome OS, Google’s take on what a
                             desktop operating system can be.


                             But despite how different Chrome OS looks and
                             feels, Chrome OS is based on Linux. So when
                             we talk about Linux, are we also talking
                             about Chrome OS? Here are eight points to
                             consider.


                      # ⚓ Extreme Tech ☛ Steam_Alpha_Has_Finally_Arrived_on
                        Chromebooks⠀⇛


          o § Devices/Embedded⠀➾


                # § Mobile Systems/Mobile Applications⠀➾


                      # ⚓ Forbes ☛ Android_Circuit:_Samsung_Galaxy’s_Surprising
                        Victory,_OnePlus_10_Pro_Goes_Global,_First_Look_At
                        Pixel_7_Pro⠀⇛


                      # ⚓ Android Police ☛ YouTube_Music_casting_to_Android_TV,
                        Chromecast,_and_Google_TV_is_broken⠀⇛


                      # ⚓ 9to5Google ☛ Wireless_Android_Auto;_How_to_use_it,_or
                        add_it_to_your_car_–_9to5Google⠀⇛


                      # ⚓ FOSSBytes ☛ Here’s_How_To_Mirror_Android_Phone_To
                        TV⠀⇛


                      # ⚓ Vivo_Just_Showed_Its_First-Ever_Android_Tablet⠀⇛


                      # ⚓ Android Police ☛ Google’s_tightening_key_security_on
                        Android_with_a_longer_(but_better)_chain_of_trust⠀⇛


                      # ⚓ Discord_app_crashing_on_Android_devices_after_every
                        few_minutes⠀⇛


                      # ⚓ Express ☛ Popular_Android_app_just_got_banned_by
                        Google_now_you_must_delete_it_|_Express.co.uk⠀⇛


                      # ⚓ CNX Software ☛ Capyloon_mobile_Web-based_OS_works_on
                        Pinephone_Pro,_Librem_5,_Pixel_3a⠀⇛


                             Capyloon is an experimental Web-based OS
                             leveraging b2gOS that served as the base for
                             the now-defunct Firefox OS. The developers’
                             goal is to provide an open-source OS
                             improving privacy and user control through
                             web technologies.


                             It’s still early stage, and some of the
                             technologies used include the IPFS protocol,
                             WebAssembly plugins, and the Tor network.
                             Capyloon is more like a new phone shell as it
                             replaces Phosh when installing it in a Linux
                             smartphone.


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


                # ⚓ Business Insider ☛ Open-source_developers_are_burning_out,
                  quitting,_and_even_sabotaging_their_own_projects_—_and_it’s
                  putting_the_entire_internet_at_risk [Ed: Rosalie Chan still
                  an_agent_of_FUD]⠀⇛


                # § FSF⠀➾


                      # ⚓ SDTimes ☛ Free_Software_Foundation_award_winners⠀⇛


                             The winners of Free Software Foundation’s
                             2021 Software Awards for achievements in the
                             field of free software, are SecuRepairs, Paul
                             Eggert, and Protesilaos Stavrou.


                             SecuRepairs was the winner of the Award for
                             Projects of Social Benefit, which is
                             presented to a project or team responsible
                             for applying free software, or the ideas of
                             the free software movement to benefit
                             society.


                             SecuRepairs helps to provide factual advice
                             on information security issues like data
                             privacy as they pertain to repairing devices
                             and software, and works to help combat the
                             anti-right-to-repair narrative spread by
                             certain large hardware manufacturers.


                # § Programming/Development⠀➾


                      # ⚓ Swapping_two_Numbers_without_Temporary_Variables⠀⇛


                             Please never use this in any production code.
                             The less we have to think about a piece of
                             code, the better it is. It’s a fun thought
                             experiment nevertheless!


          o § Standards/Consortia⠀➾


                # ⚓ Hackaday ☛ High_Noon_For_Daylight_Savings_Time⠀⇛


                       The US Senate has approved the “Sunshine Protection
                       Act”, a bill to make Daylight Saving time the
                       default time and do away with the annual time
                       changes. While I can get behind the latter half of
                       this motion, redefining Daylight Saving time as
                       Standard time is, in my opinion, nonsense.


                # ⚓ Patrick Breyer ☛ DMA:_European_Pirates_celebrate_success
                  with_interoperability_requirements_in_final_trilogue
                  results⠀⇛


                       The Pirates in the European Parliament welcome the
                       final trilogue outcome of the Digital Markets Act
                       (DMA) that was negotiated yesterday.
                       Representatives of the EU Parliament, the Council
                       and the Commission have agreed on including
                       interoperability requirements for messaging
                       services. According to Pirates, this will allow
                       more choice for users, who will no longer be forced
                       to use multiple platforms for private messenger
                       communication.


    * § Leftovers⠀➾


          o ⚓ Vice ☛ How_Is_There_Already_So_Much_‘Elden_Ring’_Porn?_We_Asked
            the_People_Who_Made_It⠀⇛


                 Elden Ring, one of the biggest games to launch this year,
                 about being a miserable wandering maidenless wretch of a
                 Tarnished on a Lord of the Rings type mission, is no
                 exception. The [Internet] is already filled with high
                 quality 3D Elden Ring porn. Who’s making it, and how are
                 they doing it so fast?


          o ⚓ The Register UK ☛ China’s_annual_parliament_gives_tech_industry
            much_to_ponder⠀⇛


                 China is this week staging its annual “Two Sessions”
                 meetings, which see its pair of top decision-making
                 bodies meet to set the agenda for the coming year. As
                 usual there is plenty of material that touches on tech.


                 The two bodies are the National People’s Congress – a
                 body of people installed by the Chinese Communist Party
                 that is technically a parliamentary body but never votes
                 against the Party’s wishes – and the National Committee
                 of the Chinese People’s Political Consultative
                 Conference. The latter is akin to the UK House of Lords
                 or US Senate in that it has an oversight role.


                 Premier Li Keqiang delivered the Two Sessions’ first big
                 set piece on Saturday, in the form of the “Report on the
                 work of the government”. Li emphasised increased adoption
                 of digital government services, more 5G, and many more
                 efforts to digitise many aspects of China’s society and
                 economy. The importance of improving China’s ability to
                 develop semiconductors, software, and AI was also
                 highlighted. Those plans have been aired before, but Li
                 this year said China’s government will “strengthen
                 overall planning” of digitization initiatives, suggesting
                 an acceleration.


          o § Education⠀➾


                # ⚓ The Nation ☛ What_I_Learned_About_Standardized_Testing⠀⇛


                       In June 2018, I heard that then-Mayor Bill de
                       Blasio wanted to do away with the Standardized High
                       School Admissions Test (SHSAT)—the exam New York
                       City students take to get into one of eight
                       specialized high schools. These specialized schools
                       are seen as huge stepping stones into elite
                       colleges.


                # ⚓ Daniel Miessler ☛ How_to_Disagree⠀⇛


                       Paul Graham has a great piece on how to disagree
                       with people in the best possible way.


                       He provides a hierarchy, with 7 being best: [...]


                # ⚓ Reuters ☛ Taliban_orders_girls’_high_schools_to_remain
                  closed,_leaving_students_in_tears⠀⇛


                       The last time the Taliban ruled Afghanistan, from
                       1996 to 2001, they banned female education and most
                       employment.


                # ⚓ India ☛ Hijab_Row:_TNTJ_Issues_Death_Threats_To_Karnataka
                  HC_Judges_Over_Case_Verdict⠀⇛


                       He also informed that Campus Front of India (CFI),
                       the student wing of Popular Front of India, said
                       that HC’s decision stands against the Constitution
                       and they will continue to fight against it.
                       Additionally, Amir-e-Shariat an Islamic
                       organisation gave a bandh call against the Court’s
                       verdict, Bhardwaj said.


                # ⚓ The Economist ☛ “A_library_is_more_powerful_than_Putin’s
                  aeroplanes”⠀⇛


                       The museum’s collection spans the 12th to the 20th
                       centuries, a period during which Lviv was part of
                       the Mongol empire, Poland, the Austro-Hungarian
                       empire, Imperial Russia, Poland again then, after
                       the second world war, the Soviet Union. The city’s
                       rich history is reflected in its architecture:
                       Renaissance palaces mingle with baroque churches
                       and neoclassical façades in ice-cream colours. The
                       city has a strong intellectual tradition. Over the
                       centuries it has been a hub for mathematicians,
                       scientists and philosophers.


          o § Hardware⠀➾


                # ⚓ Hackaday ☛ Polar_Planimeter_Quantifies_Area_By_Plotting
                  Perimeter⠀⇛


                       These days it’s hard to be carry the label “maker”
                       or “hacker” without also being proficient in some
                       kind of CAD- even if the C is for Cardboard. But
                       before there was CAD there was Drafting and its
                       associated arts, and one couldn’t just select a
                       shape and see its area in the square unit of your
                       choice. So how could an old school draftsman figure
                       out the area of complex shapes? [Chris Staecker]
                       introduces us to the polar planimeter, a measuring
                       tool created specifically for the purpose and
                       explained in full in the video below the break.


                # ⚓ Hackaday ☛ Get_GitHub_Tickets_IRL_With_A_Raspberry_Pi_And_A
                  Receipt_Printer⠀⇛


                       Thermal receipt printers are finding their way into
                       all sorts of projects that are well beyond the
                       point-of-sale environment that they normally
                       inhabit. And while we applaud all the creative and
                       artistic uses hackers have found for these little
                       gems, this GitHub physical ticket printer has to be
                       the best use for one yet.


                # ⚓ Hackaday ☛ DIY_Prony_Dyno_Properly_Displays_Power
                  Production⠀⇛


                       When hackers in the US think of a retailer called
                       Harbor Freight, we usually think of cheap tools,
                       workable but terrible DVM’s, zip ties, and tarps.
                       [Jimbo] over at [Robot Cantina] looked at the 212cc
                       “Predator” engine that they sell and thought “I bet
                       I could power my Honda Insight with that.” And he
                       did, successfully! How much power did the heavily
                       modified engine make? In the video below the break,
                       [Jimbo] takes us through the process of measuring
                       its output using a home built dyno.


                # ⚓ Hackaday ☛ DIY_SLS_3D_Printer_Getting_Ready_To_Print⠀⇛


                       Ten years ago the concept of having on our desks an
                       affordable 3D printer knocking out high quality
                       reproducible prints, with sub-mm accuracy, in a
                       wide range of colours and material properties would
                       be the would be just a dream. But now, it is
                       reality. The machines that are now so ubiquitous
                       for us hackers, are largely operating with the FDM
                       principle of shooting molten plastic out of a
                       moving nozzle, but they’re not the only game in
                       town. A technique that has also being around for
                       donkeys’ years is SLS or Selective Laser Sintering,
                       but machines of this type are big, heavy and
                       expensive. However, getting one of those in your
                       own ‘shop now is looking a little less like a dream
                       and more of a reality, with the SLS4All project by
                       [Tomas Starek] over on hackaday.io.


                # ⚓ Hackaday ☛ A_Robot_Game_To_Open_Your_Hackerspace⠀⇛


                       It’s always good to welcome a new hackerspace to
                       the fold, and thus we’re pleased to hear about the
                       upcoming opening of Hackerspace Drenthe, on the
                       north-eastern edge of the Netherlands. Starting a
                       new space during a global pandemic is something of
                       a feat. As part of their opening something is
                       required to demonstrate a robot for the curious
                       public, and what could be more accessible than a
                       robot arm playing tic-tac-toe!


                # ⚓ Hackaday ☛ Hackaday_Podcast_161:_Laser_Lithography,
                  Centurion_Hard_Drive,_And_Mad_BGA_Soldering⠀⇛


                       Join Hackaday Editor-in-Chief Elliot Williams and
                       Staff Writer Dan Maloney for an audio tour of the
                       week’s top stories and best hacks. We’ll look at
                       squeezing the most out of a coin cell, taking the
                       first steps towards DIY MEMS fabrication, and
                       seeing if there’s any chance that an 80’s-vintage
                       minicomputer might ride again. How small is too
                       small when it comes to chip packages? We’ll find
                       out, and discover the new spectator sport of
                       microsoldering while we’re at it. Find out what’s
                       involved in getting a real dead-tree book
                       published, and watch a hacker take revenge on a
                       proprietary memory format — and a continuous
                       glucose monitor, too.


                # ⚓ SparkFun Electronics ☛ Arm_Opens_Innovation_Lab_in_South
                  Africa⠀⇛


                       Arm is opening a new pilot innovation and
                       demonstration (E3)NGAGE lab in partnership with the
                       Cortex Hub, a regional technology incubator located
                       in East London, Eastern Cape, South Africa. The lab
                       will focus on engaging, educating and catalyzing
                       local technology ecosystems while making Arm the
                       computing foundation across the region.


                # ⚓ The Register UK ☛ Intel_axes_older_FPGA_cards,_moves
                  development_to_customers_•_The_Register⠀⇛


                       Intel is discontinuing its original lineup of
                       Programmable Acceleration Cards as it turns to an
                       “ecosystem first” strategy that helps customers
                       create their own FPGA-based products, including
                       SmartNICs.


                       The chipmaker issued an end-of-life notice
                       Wednesday for three products in its FPGA-powered
                       Programmable Acceleration Card lineup that debuted
                       in 2017: the Intel PAC with Intel Arria 10 GX FPGA,
                       the Intel FPGA PAC N3000, and the Intel FPGA PAC
                       D5005.


                       Intel is ending production of the cards “due to
                       product transition and declining demand,” and
                       customers have until July 11 to order them, the
                       notice said. The final shipments will go out March
                       10, 2023, though Intel warned it can’t guarantee
                       delivery for last-time orders “due to the
                       unprecedented global demand for and limited supply
                       of semiconductor components and substrates.”


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ Common Dreams ☛ Opinion_|_Will_Privatization_Force
                  Traditional_Medicare_Out_of_Business?⠀⇛


                       Five or ten years from now, seniors may wake up one
                       morning and discover that their beloved Medicare
                       program has been completely privatized. And it will
                       not be because that’s what seniors want; it will be
                       due to corporate influence and profiteering.
                       Medicare was not created as a private program. In
                       fact, it was enacted in 1965 as federal health
                       insurance for seniors because many private
                       insurers refused to cover them.  But over the past
                       three decades, insurance companies and private
                       investors have found a way to capture a growing
                       share of federal Medicare dollars—money that should
                       go toward patient care, not corporate profit. 


                # ⚓ TruthOut ☛ Senators_Call_for_Inquiry_Into_Low_Medicaid
                  COVID_Vaccination_Rates⠀⇛


                # ⚓ TruthOut ☛ Our_Governments_Have_Chosen_Capitalism_Over
                  Preparing_for_Next_COVID_Surge⠀⇛


                # ⚓ Orac ☛ Autopsies_for_everyone_will_end_vaccine
                  misinformation_immediately?⠀⇛


                       Although I had mentioned him before, first time I
                       dedicated a post to discussing Steve Kirsch, the
                       tech bro who started out the pandemic two years ago
                       as somewhat reasonable in his desire to fund
                       research into repurposed drugs to treat the COVID-
                       19 who later turned ivermectin zealot,
                       misinformation firehose, and outright antivaxxer,
                       it was about his “secret plan to end the vaccine
                       madness.” More recently, he’s been whining that no
                       one will “debate” him while harboring the apparent
                       delusion that a free-for-all five hour video debate
                       between him and his pseudoexperts versus real
                       experts will end vaccine hesitancy, while
                       complaining about “censorship.” (Of course, what he
                       views as censorship I view as quality control.)
                       Given Kirsch’s history of hare-brained schemes to
                       “end vaccine hesitancy” or “end COVID-19
                       misinformation,” I was somewhat amused at his
                       latest proposal; that is, until I realized that
                       some people might wonder why it’s not a good idea.
                       His proposal was published on his Substack earlier
                       this week under the title—yawn, again?—A simple way
                       to end vaccine misinformation immediately. The way?
                       Kirsch thinks that an autopsies will do the trick,
                       but not just any autopsies, rather:


                # ⚓ Counter Punch ☛ Two_Years_in_and_We_Still_Need_to_Learn_the
                  Lessons_of_This_Pandemic⠀⇛


                       A global pandemic had reached the United States and
                       changed each of our lives in ways we never
                       imagined. Millions of Americans would lose jobs,
                       friends, family, and even their lives to COVID-19,
                       while billionaires would see record increases in
                       their wealth.


                       While the country ground to a halt, and I googled
                       whether an imam would perform our marriage over
                       Zoom, there was a glimmer of hope at the back of my
                       mind. Surely, I thought, an event so monumental —
                       one that laid bare every inequity of our economic
                       system — would call for a change of equal measure.


                # ⚓ Pro Publica ☛ State_Launches_Cancer_Study_After_ProPublica
                  Identifies_Toxic_Air_Pollution_Hot_Spot⠀⇛


                       After learning from a ProPublica analysis that his
                       Missouri city is a hot spot of toxic air pollution,
                       Verona Mayor Joseph Heck demanded that government
                       officials look into the local cancer rate.


                       Three months later, the state health department
                       confirmed his fears: The rate of Non-Hodgkin
                       lymphoma in the Verona zip code is more than twice
                       as high as that of the surrounding county and
                       state, officials told him. Non-Hodgkin lymphoma, a
                       cancer that begins in the lymphatic system, can be
                       caused by exposure to ethylene oxide, a potent
                       carcinogen released by the BCP Ingredients plant in
                       Verona. ProPublica’s unique analysis of air
                       pollution data from the Environmental Protection
                       Agency found the facility’s ethylene oxide
                       emissions substantially increased local cancer
                       risk; in some areas, the estimated industrial
                       cancer risk was 27 times what the EPA considers
                       acceptable.


                # ⚓ Gannett ☛ How_Russia’s_war_against_Ukraine_could_make_our
                  food_prices_–_from_bread_to_beer_–_more_expensive⠀⇛


                       “The food supply chain is so integrated globally,
                       that it’s hard to imagine that something happening
                       half a world away is going to affect the price of
                       food here in the United States,” says Robb MacKie,
                       president and CEO of the American Bakers
                       Association, an advocate for the commercial baking
                       industry. “But it’s all intertwined.”


                # ⚓ RTL ☛ Scientists_find_microplastics_in_blood_for_first
                  time⠀⇛


                       A Dutch study published in the Environment
                       International journal on Thursday examined blood
                       samples from 22 anonymous, healthy volunteers and
                       found microplastics in nearly 80 percent of them.


                       Half of the blood samples showed traces of PET
                       plastic, widely used to make drink bottles, while
                       more than a third had polystyrene, used for
                       disposable food containers and many other products.


          o § Integrity/Availability⠀➾


                # § Proprietary⠀➾


                      # ⚓ The Verge ☛ Microsoft_is_tied_to_hundreds_of_millions
                        of_dollars_in_foreign_bribes,_whistleblower_alleges⠀⇛


                             In the two years that followed, Elabd says he
                             did everything in his power to stamp out
                             these quiet bribes — a fight that made him a
                             pariah among his colleagues and eventually
                             cost him his job. But looking back, he
                             believes Microsoft wasn’t interested in
                             stopping the payouts, preferring to let phony
                             contracts slip through and accept the
                             associated cash.


                             Elabd went public with his experiences in an
                             essay published Friday by the whistleblower
                             platform Lioness, alleging widespread bribery
                             through Microsoft’s foreign contract
                             business. Elabd estimates that more than $200
                             million each year is spent on bribes and
                             kickbacks linked to the company, often in
                             countries like Ghana, Nigeria, Zimbabwe,
                             Qatar and Saudi Arabia. For the regions he
                             worked in, he believes more than half of the
                             salespeople and managers took part. If true,
                             it’s a stunning look at the ongoing
                             corruption associated with international tech
                             contracting — and Microsoft’s ongoing
                             struggles to contain it.


                      # ⚓ Krebs On Security ☛ Estonian_Tied_to_13_Ransomware
                        Attacks_Gets_66_Months_in_Prison [iophk: Windows TCO]⠀⇛


                             Maksim Berezan, 37, is an Estonian national
                             who was arrested nearly two years ago in
                             Latvia. U.S. authorities alleged Berezan was
                             a longtime member of DirectConnection, a
                             closely-guarded Russian cybercriminal forum
                             that existed until 2015. Berezan’s indictment
                             (PDF) says he used his status at
                             DirectConnection to secure cashout jobs from
                             other vetted crooks on the exclusive crime
                             forum.


                             Berezan specialized in cashouts and “drops.”
                             Cashouts refer to using stolen payment card
                             data to make fraudulent purchases or to
                             withdraw money from bank accounts without
                             authorization. A drop is a location or
                             individual able to securely receive and
                             forward funds or goods obtained through
                             cashouts or other types of fraud. Drops
                             typically are used to make it harder for law
                             enforcement to trace fraudulent transactions
                             and to circumvent fraud detection measures
                             used by banks and credit card companies.


                      # ⚓ Macworld ☛ Apple_plots_hardware_subscription_service
                        for_iPhone_and_other_devices⠀⇛


                             According to Mark Gurman at Bloomberg, Apple
                             has been working on a new subscription
                             service for the iPhone and other hardware
                             products that will let customers subscribe to
                             Apple hardware with a monthly recurring
                             payment. According to Gurman’s sources, Apple
                             has been working on the subscription program
                             for several months and is expected to launch
                             it at the end of 2022.


                             Unfortunately, that’s all the detail we have
                             right now. We don’t know anything about
                             pricing, bundles, which Apple hardware would
                             be offered (other than the iPhone), or terms
                             for trade-ins and upgrades. Apple already
                             offers the iPhone Upgrade Program in the
                             U.S., U.K., and China, which lets users pay
                             for a new iPhone with AppleCare+ over 24
                             monthly payments with the option to upgrade
                             after 12 months.


                      # ⚓ The Verge ☛ Apple_will_reportedly_sell_the_iPhone_as
                        a_subscription_service⠀⇛


                             According to Bloomberg’s report, the monthly
                             charge wouldn’t simply be the price of the
                             device divided by 12 or 24 months, but rather
                             be a still-undecided monthly cost,
                             potentially with the option to upgrade to new
                             hardware as its released. And like Apple’s
                             other subscriptions, it would be tied to a
                             user’s existing Apple ID account, with the
                             possibility of bundling in AppleCare or Apple
                             One services as well.


                      # ⚓ MacRumors ☛ Apple_Developing_Hardware_Subscription
                        Service_for_iPhones_and_Other_Devices⠀⇛


                             Compared to the iPhone Upgrade Program, it
                             would differ because Apple would charge a
                             yet-to-be-determined monthly fee rather than
                             splitting the cost of a device across a 12 or
                             24 month period. It would also cover other
                             products while the iPhone Upgrade Program is
                             limited to the iPhone.


                      # ⚓ Mercury News ☛ Apple_is_working_on_a_subscription
                        service_for_iPhones_and_other_products⠀⇛


                             Adopting hardware subscriptions, akin to an
                             auto-leasing program, would be a major
                             strategy shift for a company that has
                             generally sold devices at full cost outright,
                             sometimes through installments or with
                             carrier subsidies. It could help Apple
                             generate more revenue and make it easier for
                             consumers to stomach spending thousands of
                             dollars on new devices.


                      # ⚓ Digital First Media ☛ Apple_is_working_on_a_hardware
                        subscription_service_for_iPhones⠀⇛


                             Apple Inc. is working on a subscription
                             service for the iPhone and other hardware
                             products, a move that could make device
                             ownership similar to paying a monthly app
                             fee, according to people with knowledge of
                             the matter.


                      # ⚓ IT Wire ☛ Australia_ranks_number_one_in_Asia_Pacific
                        for_most_ransomware_attacks [iophk: Windows TCO]⠀⇛


                             The research released from Unit 42 by global
                             cybersecurity leader. Palo Alto Networks also
                             found that ransomware payments hit new
                             records in 2021 as cybercriminals
                             increasingly turned to Dark Web “leak sites”
                             where they pressured victims to pay up by
                             threatening to release sensitive data.


                             In Australia the research also found that
                             2021 saw a 642% increase in dark web leaks on
                             the prior year and 38% of all attacks
                             targeted organisations in NSW; ACT the least
                             targeted geography.


                      # ⚓ Trail Of Bits ☛ Towards_Practical_Security
                        Optimizations_for_Binaries⠀⇛


                             This example is one of several well-
                             documented instances of a compiler
                             optimization inadvertently introducing a
                             security weakness into a program. Recently,
                             my colleagues at Georgia Tech and I published
                             an extensive study of how compiler design
                             choices impact another security property of
                             binaries: malicious code reusability. We
                             discovered that compiler code generation and
                             optimization behaviors generally do not
                             consider malicious reusability. As a result,
                             they produce binaries that are generally more
                             reusable by an attacker than is necessary.


                      # ⚓ BBC ☛ US_charges_four_Russians_over_[cracking]
                        campaign_on_energy_sector [iophk: Windows TCO]⠀⇛


                             They are accused of targeting hundreds of
                             companies and organisations in around 135
                             countries between 2012-2018.


                             Their activities are said to have caused two
                             separate emergency shutdowns at one facility
                             in Saudi Arabia.


                             The conspiracy then allegedly attempted to
                             [break into] the computers of a company that
                             managed similar critical infrastructure
                             entities in the US.


                      # § Security⠀➾


                            # ⚓ Bleeping Computer ☛ Western_Digital_My_Cloud_OS
                              update_fixes_critical_vulnerability⠀⇛


                                   The vulnerability, which has a CVSS v3
                                   severity score of 9.8, allows remote
                                   attackers to execute arbitrary code on
                                   the target device, in this case, WD
                                   PR4100 NAS, without requiring
                                   authentication.


                            # ⚓ TechRadar ☛ Western_Digital_customers_urged_to
                              update_to_latest_version_of_My_Cloud_OS⠀⇛


                                   Western Digital has pushed a new
                                   firmware update for its My Cloud OS,
                                   fixing a high- severity vulnerability
                                   that was discovered during a recent
                                   hacking contest.


                                   As reported by BleepingComputer,
                                   cybersecurity experts from the NCC
                                   Group exploited a flaw in Netatalk
                                   Service, an open-source implementation
                                   of the Apple Filing Protocol (AFP) that
                                   allows for Unix-like operating systems
                                   to serve as file servers for macOS
                                   clients.


                                   The flaw, now tracked as CVE-2022-
                                   23121, carries a severity score of 9.8/
                                   10, as it allows threat actors to run
                                   any code on the target endpoint,
                                   without authentication.


                            # ⚓ WD_My_Cloud_Users_Should_Update_to_Avoid_a
                              Dangerous_Vulnerability_–_Review_Geek [Ed: My
                              Cloud? My clown? Whose clown? Everyone gets
                              access...]⠀⇛


                                   Western Digital just rolled out a My
                                   Cloud OS update that resolves a
                                   dangerous remote access vulnerability.
                                   All My Cloud users should install the
                                   firmware update (version 5.19.117) to
                                   defend themselves from remote hacking
                                   attempts.


                            # § Privacy/Surveillance⠀➾


                                  # ⚓ EFF ☛ Another_Tracker_Scanning_App
                                    Highlights_the_Need_for_a_Better_Way_to
                                    Protect_Victims_From_Digital_Stalking⠀⇛


                                  # ⚓ EFF ☛ EFF_Client_Erik_Johnson_and
                                    Proctorio_Settle_Lawsuit_Over_Bogus_DMCA
                                    Claims⠀⇛


                                         Johnson, who is also a security
                                         researcher, sued Proctorio a year
                                         ago after it misused the
                                         copyright takedown provisions of
                                         the DMCA to remove his posts.
                                         Proctorio had gone after a series
                                         of tweets Johnson published
                                         critiquing Proctorio that linked
                                         to short excerpts of its software
                                         code and a screenshot of a video
                                         illustrating how the software
                                         captures images of students’
                                         rooms that are accessible to
                                         teachers and potentially
                                         Proctorio’s agents. Johnson’s
                                         lawsuit asked the court to rule
                                         that his posts were protected by
                                         the fair use doctrine and hold
                                         Proctorio responsible for
                                         submitting takedown notices in
                                         bad faith.


                                         Under the settlement, Proctorio
                                         dropped its copyright claim and
                                         other claims it had filed blaming
                                         Johnson’s advocacy for damaging
                                         its reputation and interfering
                                         with its business. In return,
                                         Johnson dropped his claims
                                         against Proctorio. Johnson’s
                                         tweets, which were restored by
                                         Twitter through the DMCA’s
                                         counter-notice process, will
                                         remain up.


                                         Proctoring apps like Proctorio’s
                                         are privacy-invasive software
                                         that “watches” students using
                                         tools like face detection for
                                         supposed signs of cheating as
                                         they take tests or complete
                                         schoolwork. Their use skyrocketed
                                         during the pandemic, leading
                                         privacy advocates and students to
                                         protest this new kind of
                                         surveillance. Johnson, whose
                                         instructors use Proctorio, was
                                         concerned about how much private
                                         information the software could
                                         collect from students’ computers
                                         and used his skills as a security
                                         researcher to examine its
                                         functions.


                                  # ⚓ CSO ☛ US,_EU_reach_preliminary_data
                                    privacy_agreement⠀⇛


                                         The US and the European Union
                                         (EU) have a preliminary agreement
                                         over the storing of European data
                                         on US soil. It was announced by
                                         President Biden and EU President
                                         Ursula von der Leyen, speaking on
                                         Friday March 25. If successful,
                                         the data agreement would resolve
                                         a significant point of contention
                                         in US-EU relations since a
                                         previous deal regulating trans-
                                         Atlantic data flows—Privacy
                                         Shield—was deemed illegal by the
                                         EU’s top court in 2020. It ruled
                                         that the US did not provide EU
                                         citizens effective means to
                                         challenge US government
                                         surveillance of their data.


                                  # ⚓ India Times ☛ Twitter_expands_India_base
                                    for_global_boost⠀⇛


                                         Twitter has formed an in-region
                                         team in India with cross-
                                         functional expertise as part of a
                                         move to accelerate globally its
                                         growth momentum by 2023 end. The
                                         social networking site expects
                                         its revenue to more than double
                                         to $7.5 billion in 2023, from
                                         $3.7 billion in 2020. It also
                                         plans to reach 315 million
                                         monetisable daily active users by
                                         the end of 2023.


                                  # ⚓ NYOB ☛ “Privacy_Shield_2.0″?_–_First
                                    Reaction_by_Max_Schrems⠀⇛


                                         Today Commission President Ursula
                                         von der Leyen and President Biden
                                         have announced an “agreement in
                                         principle” on a new EU-US data
                                         sharing system.


                                         Some facts upfront: [...]


                                  # ⚓ EDRI ☛ Leaked_opinion_of_the_Commission
                                    sets_off_alarm_bells_for_mass_surveillance
                                    of_private_communications⠀⇛


                                         A newly-revealed Opinion of a
                                         European Commission review board
                                         about their own colleagues’
                                         upcoming proposal for a
                                         ‘Legislation to effectively
                                         tackle child sexual abuse’ shows
                                         strong concerns with the
                                         legislative proposal. Leaked by
                                         French media outlet Contexte
                                         yesterday (22 March), and dated
                                         15 February 2022, the Opinion
                                         confirms the fears EDRi and 39
                                         other civil society groups
                                         recently raised about the
                                         proposal which could destroy the
                                         integrity of private online
                                         communications across the EU, and
                                         set a dangerous precedent for the
                                         world.


                                  # ⚓ Pirate Party ☛ Chat_control:_Leaked
                                    Commission_paper_EU_mass_surveillance
                                    plans⠀⇛


                                         Moreover, the opinion indicates
                                         that the draft law would also
                                         require this generalised
                                         monitoring to be done not just
                                         for material that has been
                                         assessed by authorities to ensure
                                         that it is unlawful, but also to
                                         search for “unknown” images as
                                         well as so-called evidence of
                                         “grooming” using notoriously
                                         unreliable AI-based tools. We’ve
                                         all seen pictures being
                                         automatically flagged on social
                                         media because an AI tool wrongly
                                         thought that the picture
                                         contained nudity, and have all
                                         suffered the frustration of an
                                         important email automatically
                                         going into your spam folder.


                                  # ⚓ Google_said_to_be_working_on_a_new_Nest
                                    Hub_with_a_detachable_tablet⠀⇛


                                         This new Nest Hub will be a
                                         tablet that can be docked to a
                                         smart home device. There is not
                                         much about this, so we can
                                         speculate that the base might be
                                         used as a speaker that charges
                                         the device. This could be
                                         attribted to the work Google has
                                         done on Android 12L which has
                                         been made with tablets and
                                         foldables kept in mind. But we
                                         can’t be certain about the device
                                         running Android 12L.


                                  # ⚓ 9to5Google ☛ Chris_McKillop,_engineering
                                    director_of_Google’s_Fuchsia_project,
                                    leaves_the_company⠀⇛


                                         Google has been known to be
                                         developing Fuchsia as a from-
                                         scratch operating system since at
                                         least 2016. Fuchsia ultimately
                                         saw its first launch last year on
                                         the first-gen Nest Hub smart
                                         display. For much of that time,
                                         the Fuchsia project has been
                                         headed up by Director of
                                         Engineering Chris McKillop.


                                         With a successful launch now in
                                         the rearview and Fuchsia firmly
                                         on the path to greater things,
                                         McKillop has announced on Twitter
                                         that he has left Google after ten
                                         years with the company. During
                                         that time, in addition to
                                         starting the Fuchsia project,
                                         McKillop helped shape the Flutter
                                         team — which has long had close
                                         ties to Fuchsia — and was also
                                         briefly involved with the Android
                                         TV team.


          o § Defence/Aggression⠀➾


                # ⚓ Counter Punch ☛ Hulu’s_Catherine_the_Great:_Huzzah!⠀⇛


                       Among the reasons in play (at least, in my mind)
                       are Putin is a Napoleonic asshole; Biden’s covering
                       up his own corrupt doings in Ukraine by coaxing the
                       kitty to the catnip; Zelensky is a Jew and history
                       tells us that a kristallnacht can never be far
                       behind these unfortunate diasporic people; the MIC
                       needs something to do, now that the colossal waste
                       of US taxpayer money and time (20 years) in
                       Afghanistan is over; the American dollar, as global
                       reserve, is about to be usurped by Russian and
                       Chinese subversion, leading to the loss of pre-fab
                       ‘middle class American lifestyle’ exports by way
                       neo-liberal policies, and it’s now or never on the
                       global hegemony front for the US, meaning all-out
                       ‘limited’ war to save the PNACkers asses.


                       And from whom do we garner our information about
                       world events? The MSM that seems intent on
                       endlessly milking their cashbull Trump? Lefty
                       outrage rags? Personal history readings — from the
                       POV of the winners or the losers (i.e. the People)?
                       From facile, cynical, jaded wags like me, at the
                       event horizon’s edge looking to take minds with me,
                       oversupplied with the grist for lampoon? Who or
                       what informs us? It’s a Socratic question. How do
                       you know what you know? You’ll have to get off the
                       social media juice — get sober to answer that. You
                       need to get the fuck out of Plato’s Cave and away
                       from the shadow play of implied dark doings. Fawk!
                       This is supposed to be the Age of Aquarius, let’s
                       act like it.


                # ⚓ Common Dreams ☛ Russian_Activists_Pen_Open_Letter_Demanding
                  End_to_War_on_Ukraine⠀⇛


                       Several long-time Russian human rights advocates
                       plan to publish an open letter urging Moscow to end
                       its deadly assault on Ukraine, calling it “our
                       common duty” to “stop the war [and] protect the
                       lives, rights, and freedoms of all people, both
                       Ukrainians and Russians.”


                       As The Guardian, which obtained a draft statement,
                       reported Friday:


                # ⚓ Counter Punch ☛ Putin_Abandons_Mankind⠀⇛


                       A simple German monk, Martin Luther (1483-1546),
                       challenged the dominant Catholic Church of the
                       Middle Ages. When he nailed his 95 theses on the
                       door of the Castle church in Wittenberg in 1517, he
                       set off the beginning of the Protestant Reformation
                       and horrendous religious wars throughout Europe.
                       When he refused to compromise, declaring before the
                       authorities during his 1521 trial at Worms, “Here I
                       stand I can do no other,” he went against all
                       prevailing norms.


                       The English philosopher and political theorist
                       Michael Oakeshott describes Luther’s singularity as
                       an individual and his irresponsibility for
                       consequences as follows:


                # ⚓ Counter Punch ☛ The_United_States_is_Exceptional,_Just_Not
                  in_the_Ways_Any_of_Us_Should_Want⠀⇛


                       That, in a nutshell, was the postwar version of
                       U.S. exceptionalism and Washington was then
                       planning to manage the world in such a way as to
                       maintain that remarkably grotesque disparity. The
                       only obstacle Kennan saw was poor people demanding
                       a share of the wealth.


                       Today, as humanity confronts a looming climate
                       catastrophe, what’s needed is a new political-
                       economic project. Its aim would be to replace such
                       exceptionalism and the hoarding of the earth’s
                       resources with what’s been called “a good life for
                       all within planetary boundaries.”


                # ⚓ Counter Punch ☛ How_a_No-Fly_Zone_Could_Lead_to_Nuclear
                  War⠀⇛


                       What they’re actually proposing is that we launch a
                       war against nuclear-armed Russia.


                       Proponents say that while Ukrainians fight Russians
                       on the ground, the U.S. should tell Russia they’re
                       barred from Ukrainian skies. But what happens when
                       Russian planes fly over Ukraine anyway? Then our
                       planes must try to shoot them down.


                # ⚓ Common Dreams ☛ ‘Dangerous’:_Experts_Slam_Biden_for_Keeping
                  First-Use_Nuclear_Strike_on_the_Table⠀⇛


                       On the campaign trail, U.S. President Joe Biden
                       said the “sole purpose of the U.S. nuclear arsenal
                       should be deterring—and if necessary, retaliating
                       against—a nuclear attack” and vowed to “put that
                       belief into practice.”


                       But amid growing tensions with Russia as it wages a
                       deadly war on Ukraine, the president has reportedly
                       abandoned that campaign promise, opting instead to
                       leave in place a policy embraced by his
                       predecessors that allows for the use of nuclear
                       weapons in response to non-nuclear
                       warfare—including conventional, chemical,
                       biological, and cyber-related attacks.


                # ⚓ Meduza ☛ The_war_at_home:_Russia_is_de_facto_under_martial
                  law,_human_rights_experts_warn⠀⇛


                       Rights and freedoms in Russia have been restricted
                       to the point that the country is de facto under
                       martial law. This is the conclusion of a new report
                       authored by prominent human rights experts Pavel
                       Chikov, head of the rights group Agora, and Damir
                       Gainutdinov, head of the Net Freedoms Project.
                       Indeed, against the backdrop of Moscow’s month-long
                       invasion of Ukraine, the Russian authorities have
                       moved to impose serious restrictions on basic
                       constitutional rights and freedoms at home. As
                       Chikov and Gainutdinov write, these restrictions
                       have primarily affected freedoms of assembly,
                       speech, and movement, as well as private property
                       rights. Meduza summarizes the report’s main
                       findings here.


                # ⚓ Meduza ☛ ‘Nobody_understood_what_was_happening’:_Meduza
                  tells_the_story_of_Albert_Sakhibgareyev_—_a_Russian_contract
                  soldier_who_deserted_from_the_war_in_Ukraine⠀⇛


                       Five weeks ago, 25-year-old contract soldier Albert
                       Sakhibgareyev was in Russia’s Belgorod region,
                       several miles from the Ukrainian border, where his
                       brigade was “conducting training exercises.”
                       Sakhibgareyev says he and his fellow soldiers would
                       fire “wherever they were ordered to,” though what
                       exactly they were firing at was unclear. According
                       to him, he didn’t understand he was in a real war
                       until the Ukrainian side started firing back; soon
                       after that, he deserted. Meduza reports on how a
                       soldier from Bashkortostan decided enough was
                       enough.


                # ⚓ Meduza ☛ ‘We’ll_all_go_back_when_the_regime_falls’:_How
                  Tbilisi_become_a_hub_for_Russian_political_emigrants⠀⇛


                       In the first weeks after Vladimir Putin announced
                       his “special military operation” and invaded
                       Ukraine, tens of thousands of Russians flew to
                       Georgia, despite the fact that there are no direct
                       flights there from Russia. Many continued on to
                       other countries, but about 12,000 have stayed. For
                       Meduza, journalist Gleb Golod — who is among those
                       who moved to Georgia in recent weeks — reports on
                       the problems these new arrivals have faced and how
                       Georgians have responded to the Russian influx.


                # ⚓ The Nation ☛ Exclusive:_Ukraine’s_Defense_Intelligence
                  Chief_Warns_of_“Real_Hell”_for_Russians⠀⇛


                       In November last year, Brig. Gen. Kyrylo Budanov
                       sounded the alarm. Vladimir Putin, Budanov told the
                       Military Times, was using the massive Zapad 21
                       exercises in western Russia and Belarus as a screen
                       for a planned invasion of Ukraine. A day later,
                       Bloomberg reported that US intelligence sources
                       were saying that Russia was preparing for a
                       multipronged push into Ukraine.


                # ⚓ The Nation ☛ A_Last_Gift_of_Love:_One_Way_to_Switzerland,
                  Business_Class⠀⇛


                       On the night of February 6, my husband and I
                       boarded a plane from New York to Zurich,
                       Switzerland. It would be our last trip together and
                       the first trip we’d taken in many years. In many
                       ways, it felt like so many vacations we’d taken
                       over our 52 years together: making the plans,
                       booking the flight, finding a hotel—and a good
                       restaurant to eat our last meal. I even joked that
                       he had to be dying for us to fly business class. 
                       But this last trip was no joking matter. 


                # ⚓ The Nation ☛ We_Don’t_Need_to_Go_Back_to_Cold_War
                  Spending—We’re_Already_There⠀⇛


                       A growing chorus of pundits and policy-makers has
                       suggested that Russia’s invasion of Ukraine marks
                       the beginning of a new Cold War. If so, that means
                       trillions of additional dollars for the Pentagon in
                       the years to come coupled with a more aggressive
                       military posture in every corner of the world.


                # ⚓ Counter Punch ☛ Ending_the_War_in_Ukraine⠀⇛


                       Initially, he’d hoped to do so by seizing Kyiv,
                       replacing the government, and absorbing as much of
                       Ukrainian territory into Russia as he thought
                       feasible.


                       Now, after the resistance of the Ukrainians, he is
                       looking to eliminate their country by a different
                       method. He will bomb it into submission from the
                       air and depopulate the country by turning millions
                       of its citizens into refugees.


                # ⚓ Counter Punch ☛ Ukraine,_Russia_and_the_Sporting
                  McCarthyites⠀⇛


                       The main interest is never in the second answer,
                       but the first.  Putin must be condemned and
                       banished from your conscience, your mind and
                       history.  Ignore the fact that he is the elected
                       leader of a country – he remains a tyrant to be
                       condemned to liberal democratic execration.  Best
                       go about punishing people innocent of this fact.


                       Such a cringeworthy approach has seduced and
                       trapped some able minds over the years.  During the
                       Cold War, the division of camps and ideologies
                       demanded unthinking loyalty, not so much to truth
                       but a version of it long lost in political drag and
                       the hypocrisy of appearances.  On September 22,
                       1947, delegates from Communist parties across the
                       European spectrum heard the infantile ravings of
                       the main Soviet delegate Andrei Zhdanov, who
                       suggested with nether clenching tediousness that
                       the world was divided between the “imperialist and
                       democratic camp”.  The US, allied with Great
                       Britain and France, made up the former.  “The anti-
                       fascist forces comprise the second camp”, rooted in
                       the USSR and its various, anomalously named “new
                       democracies.”


                # ⚓ Counter Punch ☛ End_Times_Can_No_Longer_Be_Postponed⠀⇛


                       The forecast is for an accelerating whirlpool of
                       international violence that could possibly be
                       remembered, historically, as the Third World War.
                       The current situation involving Russia and Ukraine
                       is what congeals the storm clouds of this forecast.


                       In terms of geopolitical history, Russia has a
                       longstanding worry—three major invasions (one by
                       France, two by Germany) since the early nineteenth
                       century—and therefore wanting Ukraine as a Slavic
                       buffer against those encroaching, marauding
                       Europeans. Perfectly rational in the world of
                       geopolitics.


                # ⚓ Common Dreams ☛ Progressives_Demand_End_to_US_Involvement
                  on_7th_Anniversary_of_Saudi-Led_War_on_Yemen⠀⇛


                       On Friday, the seventh anniversary of the beginning
                       of the Saudi-led war on Yemen, four members of the
                       Congressional Progressive Caucus implored President
                       Joe Biden to immediately end U.S. military support
                       for the deadly assault—and vowed to pass a War
                       Powers Resolution to make it happen if the White
                       House refuses.


                       “With each passing day, the crisis in Yemen
                       intensifies.”


                # ⚓ FAIR ☛ ‘Just_Pay_Attention_to_What_Our_Own_Government_Is
                  Doing_in_Yemen’⠀⇛


                # ⚓ Counter Punch ☛ Imperialism_and_the_Struggle_Against_It
                  Begins_at_Home⠀⇛


                       Imperialism is born not in some abstract off-shore
                       political vacuum. At first blush, it speaks to
                       domestic expansion and repression… to the theft of
                       lands in a veracious rush to swell and secure one’s
                       base and the target of those who present a
                       different look, a different history, a different
                       aspiration. After-all, no imperial trek can hope to
                       accomplish anything but failure while domestic
                       dissent screams NOT. It was a costly lesson, one
                       belatedly understood by the Romanovs as they took
                       their well-deserved final royal stroll to the walls
                       of rebellion where they were met with a fuselage of
                       bullets and the bite of bayonets as their three-
                       hundred-year imperial dynasty faded into the
                       pathway of revolutionary history.


                       For historical purposes, it matters less who the
                       Romanovs were than what it is they represented… for
                       those who fail to recall the lessons of history are
                       doomed indeed to repeat its mistakes although, to
                       some today, these same “missteps” are easily white-
                       washed away as so much the unavoidable linchpin of
                       political necessity and group chant.


                # ⚓ Counter Punch ☛ Roaming_Charges:_Both_Ends_Burning⠀⇛


                       + In our identity-obsessed political culture,
                       Madeleine Albright finally proved that American
                       woman (the Israelis and Brits had demonstrated this
                       quality decades earlier) are fully capable of
                       supervising mass death without flinching or showing
                       the tiniest twinge of regret or remorse.


                       + It is the ultimate moral crime to target for
                       misery, pain and death those least responsible for
                       the offenses of their tyrannical rulers. Yet this
                       is the very policy Madeleine Albright made Standard
                       Operating Procedure for US diplomacy.


                # ⚓ Counter Punch ☛ Ukraine_Could_Turn_Into_Another_Endless
                  War,_Especially_if_NATO_Decides_More_Than_Just_Peace_is
                  Needed⠀⇛


                       But if we look at a larger map that includes not
                       only Europe but the Middle East and North Africa,
                       we get an entirely different impression because
                       Ukraine is no longer a blood-soaked exception in a
                       zone of peace. It is, on contrary, the new northern
                       extension of a giant zone of war that has extended
                       over the last twenty years east-west from
                       Afghanistan to north-east Nigeria and north-south
                       from Turkey to Somalia and Yemen.


                       Parallels are occasionally drawn between the
                       Ukrainian war and a dozen or so conventional and
                       guerrilla wars being fought out in this vast area
                       of conflict to the south of Ukraine. When
                       similarities between these conflicts are noted, it
                       is usually on the grounds that Russian shelling and
                       bombing of cities like Mariupol and Kharkiv is
                       similar to that of Damascus and Aleppo by Russian-
                       backed Syrian forces. This is true enough, but keep
                       in mind that the bombardment of Gaza by Israel and
                       Raqqa and Mosul by the Americans likewise led to
                       massive physical destruction and heavy civilian
                       loss of life.


                # ⚓ Counter Punch ☛ Putin_is_Not_Dealin’⠀⇛


                       Why Putin is running his dictatorship as a boy-in-
                       the-bubble is anyone’s guess. In recent weeks, from
                       varied sources, I have heard numerous diagnoses of
                       the president’s condition: he has pancreatic
                       cancer, is pumped up on steroids, lives in dread of
                       Coronavirus, fears assassination (especially by
                       poison—one of his own equalizers of choice), and
                       imagines plotters behind every curtain (which is
                       where the assassins of Tsar Paul I found him hiding
                       in his St. Petersburg bedchamber in 1801).


                       Putin’s self-imposed isolation can only mean that
                       he’s cut off from his commanders in the field, as
                       well as others in the Russian government, which
                       probably explains why no one other than the
                       president can make decisions about anything—be it a
                       matter of strategy, tactics, economics, war or
                       peace.


                # ⚓ Counter Punch ☛ A_Coward’s_War⠀⇛


                       In Book III of The Iliad, Paris shows up for battle
                       clad in a lion skin and brandishing a bow, a sword
                       and two bronze spears. His armor and weaponry are
                       replete – too replete. So, when he challenges the
                       bravest of the Achaeans to a duel, we know what to
                       expect. Menelaus, aggrieved husband of the abducted
                       Helen, springs from his chariot, Homer tells us,
                       “like a hungry lion that lights on the carcass of
                       some goat or horned stag and devours it then and
                       there.” But Menelaus doesn’t get to enjoy his meal.
                       Paris is a lover not a fighter, as J.L. David’s
                       painting shows, and he flees the battlefield for
                       the boudoir.


                       Reproached by Hector for his cowardice, Paris
                       finally agrees to the duel. Whoever wins, can claim
                       victory in the war, preventing further bloodshed.
                       Menelaus easily defeats Paris, but before he can
                       administer the coup de grace, Aphrodite spirits
                       away the vainglorious Trojan. The war resumes and
                       many more die in place of craven Paris – who
                       himself is finally killed.


                # ⚓ Counter Punch ☛ Immune_to_War_Fever,_Some_Countries_Stay
                  Neutral_to_Russia⠀⇛


                       For many of these countries, Moscow’s attack on
                       Ukraine does not look any different from
                       Washington’s 2003 attack on Iraq. They stayed out
                       of that and are staying out of this, despite the
                       wall-to-wall coverage, the comparisons to Pearl
                       Harbor and the media frenzy over this assault on a
                       country whose citizens are white (and therefore
                       apparently deserve more compassion than the
                       millions of non-European Afghans starved by U.S.
                       sanctions or the over 377,000 brown Yemenis
                       slaughtered with U.S. weapons), with breathless
                       claims that nothing like this has happened in
                       Europe since World War II. Our propaganda outlets
                       that call themselves media have apparently
                       forgotten NATO’s 1999 bombing of Yugoslavia. For
                       some unexplained reason, that didn’t count. Except
                       of course to the Serbs – another demonized ethnic
                       group, though I doubt their magnificent composers
                       were banned from the repertoires of western
                       orchestras, that their conductors and sopranos were
                       ordered to revile their country or be fired or that
                       their immortal novelists, like Dostoevsky, were
                       deleted, if temporarily, from curricula at the
                       University of Milan.


                       There’s nothing easier than denouncing a national
                       enemy. More arduous is attempting to regard
                       something objectively awful – the Russia/Ukraine
                       war – with clear eyes and without succumbing to the
                       required Two Minutes Hate. Few do that in the west.
                       Any western news report, any politician’s speech,
                       even casual conversation about this conflict zooms
                       quickly to Two Minutes Hate. Furious tirades
                       against Moscow and Putin explode everywhere, are
                       the norm, expected and those who don’t indulge thus
                       are suspect at the least and very likely considered
                       treasonous. Nothing nowadays comes more naturally
                       or facilely than this western and European hatred
                       of all things Russian. But that is not the case in
                       the Global South.


                # ⚓ Counter Punch ☛ The_Blowback_from_Sanctions_on_Russia⠀⇛


                       Michael Hudson Thank you for inviting me.


                       Ross Michael, sanctions, sanctions, sanctions is
                       all we hear now. We’re sanctioning people. The West
                       sanction people back to the Stone Age. What are the
                       unintended consequences of sanctions?


                # ⚓ Counter Punch ☛ Russian_Military_Adapting_in_Ukraine⠀⇛


                       The latest developments, including: – How Russian
                       tactics and strategy have changed since the war
                       began – What the shift means for the future of the
                       war – Impact to Russia from ban on semiconductor
                       sales from Taiwan – Can China fill the gap for
                       Russia? – What does the resignation and defection
                       of Chubais mean for the future of Putin’s
                       government? – Which of Putin’s top officials will
                       be next to flee?


                # ⚓ Counter Punch ☛ Thinking_About_the_Unthinkable⠀⇛


                       “One Minute to Midnight”


                       I doubt the people saying “stop worrying about
                       WWIII” have any idea how close the world came to
                       nuclear winter in October of 1962, when John
                       Fitzgerald Kennedy decided to turn Soviet missiles
                       sent to protect socialist Cuba from further U.S.
                       invasions into a game of nuclear chicken. On
                       October 27, 1962, Soviet submarine Second Captain
                       Vasily Arkhipov’s refusal to agree with his
                       Captain’s decision to assemble and launch a nuclear
                       torpedo at US destroyers in the Saragossa Sea may
                       well have saved humanity from annihilation. At the
                       time, one-third of the United States’ nuclear bomb-
                       carrying Air Force fleet was in the air at “Defcon
                       2,” the highest U.S. nuclear alert short of launch.
                       Each of the B-52s in the sky could have set off
                       terminal human catastrophe with or without
                       direction from US Strategic Air Command (SAC).


                # ⚓ Common Dreams ☛ ‘Ukrainian_Blood_on_Their_Hands’:_Analysis
                  Details_How_Big_Oil_Funded_Putin’s_War_Chest⠀⇛


                       Bolstering climate campaigners’ charges that fossil
                       fuels have funded Russia’s ongoing assault of
                       Ukraine, an analysis published Friday by three
                       green groups reveals top energy companies helped
                       build Russian President Vladimir Putin’s war chest
                       to the tune of nearly $100 billion since 2014.


                       “If we want to build a world based on equity,
                       peace, and stability then we must urgently
                       accelerate the move towards renewable energy.”


                # ⚓ Common Dreams ☛ Opinion_|_How_to_End_the_War_in_Ukraine⠀⇛


                       Vladimir Putin has a very clear strategy for ending
                       his war in Ukraine. He intends to wipe the country
                       off the map.


                # ⚓ Common Dreams ☛ Opinion_|_Before_Ukraine,_A_Massive_Refugee
                  Crisis_Ignored_and_Largely_Created_by_the_West⠀⇛


                       Since Russia’s invasion last month, nearly 6.5
                       million people have been forcibly displaced within
                       Ukraine and almost 3.4 million have fled across
                       international borders. 


                # ⚓ Common Dreams ☛ Ukraine_Officials_Say_300_Civilians_Were
                  Killed_by_Russian_Bombing_of_Mariupol_Theater⠀⇛


                       Officials in the besieged Ukrainian city of
                       Mariupol said Friday that they believe around 300
                       people were killed in a March 16 Russian airstrike
                       on a theater in which at least hundreds of
                       civilians were sheltering.


                       “We still do not want to believe in this horror. We
                       still want to believe that everyone managed to
                       escape.”


                # ⚓ The Gray Zone ☛ BBC_correspondent-fixer_shaping_Ukraine_war
                  coverage_is_PR_operative_involved_in_“war-messaging_tool”⠀⇛


                # ⚓ TruthOut ☛ US_Hawks_Are_Trying_to_Increase_Military_Budget
                  —_and_Use_Ukraine_as_Excuse⠀⇛


                # ⚓ TruthOut ☛ Progressives_Demand_Congress_Cut_Military
                  Support_for_War_on_Yemen⠀⇛


                # ⚓ Pro Publica ☛ These_Children_Fled_Afghanistan_Without_Their
                  Families._They’re_Stuck_in_U.S._Custody.⠀⇛


                       Seven months after the fall of Kabul, shelters in
                       the U.S. caring for children evacuated without
                       their parents are experiencing unprecedented
                       violence while workers at the facilities have
                       struggled to respond to the young Afghans’ trauma.


                       Some children have run away, punched employees and
                       stopped eating. Others have tried to kill
                       themselves. At one shelter, ProPublica has learned,
                       some children reported being hurt by employees and
                       sexually abused by other minors.


                # ⚓ Democracy Now ☛ Start_of_a_New_Cold_War?_U.S._Hawks_“Want
                  to_Jack_up_the_Military_Budget_and_Use_Ukraine_as_an
                  Excuse”⠀⇛


                       With NATO countries recommitting themselves to the
                       alliance and passing sweeping sanctions against
                       Russia as punishment for Vladimir Putin’s invasion
                       of Ukraine, is this the dawn of a new Cold War? We
                       speak with foreign policy expert William Hartung, a
                       senior research fellow at the Quincy Institute, who
                       warns that hawks in Washington are pushing for a
                       massive increase in the U.S. military budget, which
                       is already a record-high $800 billion a year.
                       “There’s a danger that not only will this be a war
                       in Ukraine, but the U.S. will use it as an excuse
                       for a more aggressive policy around the world,
                       arguing that it’s to counter Russia or China or
                       Iran, or whoever the enemy of the moment is.”
                       Hartung also speaks about the Saudi-led war in
                       Yemen, where U.S. support has allowed the conflict
                       to rage for years, killing about 400,000 people.
                       Unlike in Ukraine, where the U.S. has more limited
                       leverage, the Biden administration could “end that
                       killing tomorrow,” Hartung says.


                # ⚓ Democracy Now ☛ Yanis_Varoufakis:_The_West_Is_“Playing_with
                  Fire”_If_It_Pushes_Regime_Change_in_Nuclear-Armed_Russia⠀⇛


                       A month after the Russian invasion of Ukraine, more
                       than 3.6 million Ukrainians have left the country
                       as refugees, and the war risks becoming “an
                       Afghanistan-like quagmire,” warns Greek lawmaker
                       Yanis Varoufakis, founder of the Progressive
                       International with U.S. Senator Bernie Sanders. He
                       says the West’s sweeping sanctions on Russia and
                       bottomless military aid to Ukraine risk escalating
                       the conflict and foreclosing chances of a peaceful
                       resolution. “What is exactly the aim? Is it regime
                       change in Russia?” asks Varoufakis. “Well, whenever
                       the United States tried regime change, it didn’t
                       turn out very well and has never been tried with a
                       nuclear power. This is like playing with fire.”


                # ⚓ The Verge ☛ Russian_military_reportedly_[broke]_into
                  European_satellites_at_start_of_Ukraine_war⠀⇛


                       American government officials told The Washington
                       Post that the Russian military was responsible for
                       a cyberattack on a European satellite [Internet]
                       service that affected Ukrainian military
                       communications in late February.


                       The [break in] affected the KA-SAT satellite
                       broadband network, owned by Viasat, an American
                       satellite communications company. On February 24th,
                       the day the Russian invasion of Ukraine began, the
                       KA-SAT network was hit by outages that affected
                       Ukraine and surrounding regions in Europe. A few
                       days afterward, Viasat blamed outages on a “cyber
                       event,” but did not release further details.


                # ⚓ New Yorker ☛ Can_Anyone_Unseat_Marjorie_Taylor_Greene?⠀⇛


                       Greene is now facing another challenge, this one
                       legal rather than electoral. On Thursday morning, a
                       group of lawyers led by Ron Fein, the legal
                       director of a nonprofit called Free Speech For
                       People, is filing a lawsuit that, were it to be
                       successful, would prevent Greene from running for
                       office again. The suit argues that Greene’s
                       statements and activities related to the attack on
                       the Capitol on January 6th make the congresswoman
                       an insurrectionist. A clause of the Fourteenth
                       Amendment specifically prohibits those who have
                       “engaged in insurrection or rebellion” against the
                       United States from holding public office. The suit,
                       citing this clause, contends that Greene “is
                       constitutionally disqualified from congressional
                       office and, as such, ineligible to run as a
                       candidate under state and federal law.”


                # ⚓ ME Forum ☛ Todd_Bensman:_Jihadis_Infiltrate_Texas⠀⇛


                       Todd Bensman, Writing Fellow at the Middle East
                       Forum, Senior National Security Fellow at the
                       Center for Immigration Studies, and author of
                       America’s Covert Border War, spoke to participants
                       in a February 14 Middle East Forum Webinar (video)
                       to discuss the cases of unvetted migrants from
                       countries “associated with terrorist organization
                       activity” who are accompanying the mass migration
                       at the Southern border.


                # ⚓ Daily Post ☛ Go_after_bandits,_terrorists,_not_those
                  keeping_afro_–_Shehu_Sani_tells_Sharia_Police⠀⇛


                       “The need for them to reach out to rural
                       communities and educate our citizens on the need
                       for them not to join bandits and terrorists is also
                       very important. So apart from them to be enforcing
                       religious laws, there is need for them at this hour
                       to be very more present, active and agile in
                       finding a lasting solution to the problem of
                       bandits and terrorists that have been kidnapping
                       and killing our people,” Shehu Sani said.


                # ⚓ Medforth ☛ Employees_of_the_Koekelberg_Basilica_in_the
                  Muslim_stronghold_of_Brussels_fear_for_their_lives_–_pelted
                  daily_with_paving_stones⠀⇛


                       According to Martine Motteux-Abeloos, the church’s
                       deputy rector, the acts were committed by young
                       teenagers who had come on scooters or by adults
                       travelling by car. On Tuesday, a brick flew past
                       just 50 cm from her head while she was in her
                       office. “The situation is becoming untenable and
                       colleagues are starting to get seriously scared.
                       It’s crazy that there is so much senseless
                       vandalism that can injure or even kill. I never
                       thought that you have to fear for your life in the
                       Basilica,” she lamented on Facebook, adding photos
                       of the damage.


                # ⚓ VOA News ☛ Did_Taliban_Infiltrate_Afghan_Evacuees_to_the
                  US?⠀⇛


                       A report last month by the Department of Defense’s
                       inspector general concluded that “U.S. agencies did
                       not use all available data when vetting Afghan
                       evacuees” and that “the United States faces
                       potential security risks” if certain Afghans “are
                       allowed to stay in the country.”


          o § Environment⠀➾


                # ⚓ The Verge ☛ The_UN_plans_to_extend_weather_warning_systems
                  to_everyone_on_the_planet⠀⇛


                       The United Nations wants to make sure every person
                       on Earth can receive early warnings ahead of
                       disastrous weather events. It set a goal of hitting
                       that target within five years in an announcement
                       this week. Early warning systems are needed
                       urgently to save lives as climate change makes
                       extreme weather even worse, UN officials said.


                       Such systems include technology to forecast
                       dangerous weather systems and the ability to share
                       those forecasts with the public so that they can
                       take precautions ahead of storms, floods,
                       heatwaves, and droughts. One in three people in the
                       world still aren’t protected by early warning
                       systems, according to the World Meteorological
                       Organization (WMO).


                # ⚓ Futurism ☛ Scientist_Warns_That_a_Huge_Tanker_Is_Probably
                  Going_to_Spill_a_Million_Barrels_of_Oil_Into_the_Ocean⠀⇛


                       The tanker is filled with more than a million
                       barrels of crude oil, which makes it a major cause
                       of concern for scientists worried that any accident
                       involving the Safer could result in it spilling
                       into the ocean.


                # ⚓ CNN ☛ An_aging_oil_tanker_has_become_a_floating_time_bomb.
                  It’s_an_environmental_disaster_waiting_to_happen⠀⇛


                       An aging, decaying oil tanker, the FSO Safer, has
                       been anchored five miles off the coast of Yemen
                       since March 2015, when Houthi rebels took control
                       of the Red Sea coastline near the port city of Al-
                       Hudaydah.


                       International officials are working to stave off a
                       potential environmental and human catastrophe: The
                       362-meter (1,118-foot) Safer is filled with more
                       than a million barrels (40 million gallons) of
                       light, sweet crude oil — liquid cargo which could
                       lead to ecological disaster were the vessel to leak
                       oil or explode.


                # ⚓ Common Dreams ☛ ‘Wake-Up_Call’:_Antarctic_Ice_Shelf_the
                  Size_of_Los_Angeles_Has_Collapsed⠀⇛


                       Satellite imagery showing the recent “complete
                       collapse” of the Conger Ice Shelf in East
                       Antarctica sparked fresh alarm over the climate
                       emergency on Friday.


                       “While humans are killing humans, and governments
                       are spending on weaponry as if there is no
                       tomorrow, the environment is collapsing—so that
                       there will be no tomorrow,” said former Greek
                       finance minister and Progressive International co-
                       founder Yanis Varoufakis.


                # ⚓ Common Dreams ☛ Green_Groups_Decry_US_Energy_Panel’s
                  Reversal_on_Gas_Pipeline_Climate_Reviews⠀⇛


                       U.S. climate activists were outraged after a
                       federal regulatory agency on Thursday walked back
                       plans to consider the planet-heating emissions and
                       environmental justice impacts when weighing whether
                       to approve new fossil fuel infrastructure.


                       “Even the suggestion that the agency be more than
                       just a rubber-stamp for gas pipelines was a bridge
                       too far for industry and their politicians.”


                # ⚓ Counter Punch ☛ The_Truth_About_IPCC_Reports⠀⇛


                       That provocative depiction is examined in a recent
                       Nick Breeze ClimateGenn podcast interview:
                       Existential Risk Management with David Spratt,
                       research director of the Breakthrough National
                       Centre for Climate Restoration in Melbourne. Dr.
                       Spratt is highly regarded for solid research, which
                       is evidenced throughout his refreshingly
                       straightforward interview.


                       Spratt’s interview tackles: (1) failings of the
                       IPCC, (2) tipping points, and (3) a nearly out of
                       control global warming challenge that’s not
                       realistically understood, even as wobbly ecosystems
                       start to falter.


                # ⚓ Common Dreams ☛ Groups_Rip_‘Climate-Wrecking’_Biden_Plan_to
                  Boost_US_Gas_Exports_to_Europe⠀⇛


                       Global climate advocates on Friday panned as
                       “misguided and dangerous” the Biden
                       administration’s newly announced effort to ramp up
                       U.S. gas shipments to European Union countries as
                       they look to reduce their dependence on Russian
                       fossil fuels.


                       “If Europe truly wants to get off Russian gas, the
                       only real option it has is phasing out gas
                       altogether.”


                # ⚓ Common Dreams ☛ Locals_Warn_Biden’s_EU_Export_Plan_Would
                  Make_Gulf_Coast_‘Sacrifice_Zone’_for_Fracked_Gas⠀⇛


                       Frontline community activists on Friday joined
                       climate and environmental campaigners in denouncing
                       the Biden administration’s plan to ramp up U.S. gas
                       shipments to the European Union in response to
                       Russia’s invasion of Ukraine.


                       Elida Castillo, program director at Chispa Texas,
                       said in a statement that “our thoughts are with
                       those in Ukraine and Europe who are facing
                       humanitarian and energy crises, but we cannot
                       disregard the crises our communities are facing
                       every day.”


                # ⚓ Common Dreams ☛ Youth_Strikes_Worldwide_Demand_Climate
                  Action_That_Centers_‘People_Not_Profit’⠀⇛


                       From Dhaka, Bangladesh to Turin, Italy and beyond,
                       youth climate strikers took to the streets across
                       the globe Friday to demand that political leaders
                       stop ignoring the scientific community’s deafening
                       alarm bells and take action to slash carbon
                       emissions before it’s too late.


                       “The current system is widening the inequality
                       gap—it has no place in our society.”


                # ⚓ TruthOut ☛ Activists_Decry_“Climate-Wrecking”_Biden_Plan_to
                  Boost_US_Gas_Exports_to_Europe⠀⇛


                # ⚓ The Revelator ☛ The_Legacy_of_Lake_Pedder:_How_the_World’s
                  First_Green_Political_Party_Was_Born_in_Tasmania_50_Years
                  Ago⠀⇛


                # ⚓ Common Dreams ☛ Opinion_|_Navy_Decisions_on_Red_Hill_Jet
                  Fuel_Tanks_Very_Costly_to_Military_Families,_Taxpayers,_and
                  Hawaii’s_Environment⠀⇛


                       Total Congressional funding for all aspects of the
                       Navy’s Red Hill water contamination debacle is now
                       over $1.1 billion according to Hawai’i
                       Congressional representative Ed Case and billions
                       more are needed to complete clean-up, defueling and
                       closing of the massive leaking Red Hill jet fuel
                       storage facility.


                # § Energy⠀➾


                      # ⚓ Common Dreams ☛ Opinion_|_Largest_‘Built_All-At-Once’
                        Wind_Farm_Opens_in_Oklahoma,_Saves_Customers_$1
                        Billion⠀⇛


                             This week, American Electric Power (AEP),
                             which operates in several states, inaugurated
                             what it called the largest wind farm in the
                             US ever built all at once. That is, there are
                             larger wind facilities, but they were
                             actually a congeries of several projects
                             built over many years.


                      # ⚓ DeSmog ☛ Media_Repeats_Kremlin_Anti-Fracking_Claims_–
                        While_Ignoring_Russia’s_Promotion_of_Climate_Denial⠀⇛


                             In their latest attempt to use the Russian
                             invasion of Ukraine to argue for more fossil
                             fuel extraction, climate sceptics have
                             revived an old claim that anti-fracking
                             campaigns around the world have been
                             bankrolled by the Kremlin. 


                             This claim is being amplified by mainstream
                             conservative newspapers. “Did Putin plot with
                             eco-warriors to halt Britain’s fracking and
                             keep us all hooked on his gas?” asked Guy
                             Walters in the Daily Mail. Days later, coal
                             baron and climate sceptic Matt Ridley wrote
                             in The Sun: “FRACK NEWS: How lying Putin
                             spent millions spreading fake news about
                             fracking”. Similar allegations have appeared
                             in both The Telegraph and the Daily Express. 


                      # ⚓ The Nation ☛ Averting_Climate_Catastrophe⠀⇛


                      # ⚓ What_is_Earth_Hour_2022_and_how_does_the_event_help
                        the_planet?⠀⇛


                             Earth Hour 2022 is an event run by the World
                             Wildlife Fund (WWF) to raise awareness of the
                             climate crisis. The premise is pretty simple:
                             since 2007, people across the world have
                             turned out their lights for one hour on the
                             last Saturday in March. It’s a symbolic
                             gesture that aims to ‘increase awareness and
                             spark global conversations on protecting
                             nature’.


                      # ⚓ Lights_out_at_Helsinki_Expo_and_Convention_Centre_for
                        Earth_Hour_2022⠀⇛


                             Messukeskus Helsinki, Expo and Convention
                             Centre, takes part in the WWF’s Earth Hour by
                             switching off all its lights on Saturday 26
                             of March from 8.30 pm to 9.30 pm. All the
                             lights outdoors, in the exhibition halls,
                             meeting rooms, corridors, hallways and
                             billboards are switched off.


                      # ⚓ CNN ☛ These_fossil_fuel_companies_sent_more_than_$15B
                        in_taxes_to_Russia_since_it_annexed_Crimea,_NGOs_say⠀⇛


                             Nine European and US fossil fuel companies
                             have paid a collective $15.8 billion to
                             Russia in various forms of taxes and fees
                             since the country annexed Crimea from Ukraine
                             in 2014, a group of NGOs said Thursday.


                             The groups, Global Witness, Greenpeace USA
                             and Oil Change International, used data from
                             the Oslo-based Rystad Energy, an independent
                             energy research firm, to calculate how much
                             money oil and gas companies based in North
                             America and Europe had sent to the Russian
                             state. They looked only at companies with
                             exploration and production operations in
                             Russia.


                # § Wildlife/Nature⠀➾


                      # ⚓ CNN ☛ ‘I’ve_never_seen_a_snow_leopard_in_the_wild’_—
                        the_anthropologist_who_has_spent_two_decades_protecting
                        Pakistan’s_elusive_big_cats⠀⇛


                             Through his non-profit — the Baltistan
                             Wildlife Conservation & Development
                             Organization — Hussain tracks snow leopards
                             using camera traps and genetic testing, and
                             works with local communities in 26 villages
                             to resolve this conflict. With an estimated
                             30 to 50 snow leopards living in the region
                             around those villages, his mission is to find
                             ways for both humans and snow leopards to
                             survive and thrive.


                             CNN spoke to Hussain about his experiences
                             protecting these beautiful big cats and how
                             he’s found ways for them to live alongside
                             local communities.


          o § Finance⠀➾


                # ⚓ TruthOut ☛ Research_Finds_Investment_in_Permanent_Child_Tax
                  Credit_Would_Pay_Off_10-Fold⠀⇛


                # ⚓ Common Dreams ☛ Consumer_Rights_Groups_Applaud_EU_Passage
                  of_Law_to_Rein_in_Tech_Titans⠀⇛


                       Digital and consumer rights advocates on Friday
                       hailed a landmark European Union law aimed at
                       curbing Big Tech’s monopolistic behavior.


                       “This is a big moment for consumers and businesses
                       who have suffered from Big Tech’s harmful
                       practices.”


                # ⚓ Common Dreams ☛ Sanders_Intros_Revival_of_95%_Windfall
                  Profits_Tax_From_WWII_to_Curb_Corporate_Greed⠀⇛


                       U.S. Sen. Bernie Sanders on Friday unveiled the
                       Ending Corporate Greed Act, which aims to end
                       corporate price gouging in the midst of multiple
                       global crises by imposing a 95% tax on the windfall
                       profits of major companies.


                       “The working class cannot bear the brunt of this
                       economic crisis, while corporate CEOs, wealthy
                       shareholders, and the billionaire class make out
                       like bandits.”


                # ⚓ Eesti Rahvusringhääling ☛ Former_board_of_Swedbank_handed
                  suspicions_of_money_laundering⠀⇛


                       The Office of the Prosecutor General has brought
                       suspicions of facilitating money laundering against
                       Priit Perens (CEO of Swedbank Estonia in 2008-
                       2015), Robert Kitt (member of the board 2011-2019,
                       successor of Perens as CEO), Ulla Illison (member
                       of the board 2011-2017, head of customer service),
                       Heiki Raadik (member of the board 2011-2017), Vaiko
                       Tammeväli (member of the board 2011-2019, director
                       of corporate banking), Rait Pallo (member of the
                       board 2011-2017, head of credit and operational
                       risk), Kaie Metsla (member of the board 2015-2019,
                       director of private banking), Toomas Tuulin (former
                       head of the anti-money laundering department) and
                       Aleksei Averson (former account manager).


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ TruthOut ☛ Louisiana_Town_Passes_Texas-Style_Ordinance
                  Barring_Abortion_Outright⠀⇛


                # ⚓ TruthOut ☛ Fear-Based_“Parental_Bills_of_Rights”_Are_a
                  Right-Wing_Siege_on_Public_Education⠀⇛


                # ⚓ TruthOut ☛ Ilhan_Omar_Introduces_Bill_to_Guarantee_Housing
                  as_a_Human_Right⠀⇛


                # ⚓ TruthOut ☛ Wife_of_Supreme_Court_Justice_Texted_Trump’s
                  Chief_of_Staff_to_Overturn_Election⠀⇛


                # ⚓ Common Dreams ☛ Parkland_Survivors_Spell_‘Thoughts_and
                  Prayers’_With_Body_Bags_on_Capitol_Hill⠀⇛


                       Marking four years since the March for Our Lives
                       demonstration—and memorializing more than 170,000
                       people who have been killed in the United States by
                       gun violence since then—survivors of the 2018
                       Parkland, Florida school shooting used more than a
                       thousand body bags Thursday to spell out the words
                       “Thoughts and Prayers” on the ground outside the
                       U.S. Capitol building.


                       Each of the 1,100 body bags represented more than
                       150 deaths, according to organizers, who based the
                       numbers on data from the Gun Violence Archive. The
                       phrase “thoughts and prayers” has infuriated gun
                       control advocates in recent years, as the pro-gun
                       lobby and lawmakers across the political spectrum
                       have repeated the words after mass shootings, while
                       doing little to stop gun violence.


                # ⚓ Common Dreams ☛ Opinion_|_QAnon_Arrives_in_the_US_Senate⠀⇛


                       Specious claims of soft sentences in child
                       pornography cases were an unlikely theme for
                       Republicans to pursue in a confirmation hearing on
                       a U.S. Supreme Court nominee. Fact checkers had
                       thoroughly debunked the claims. Thoughtful
                       conservatives tried and failed to head them off.


                # ⚓ Common Dreams ☛ Jayapal_Rebukes_GOP_Over_‘Baseless_and
                  Frankly_Racist’_Attacks_on_Judge_Jackson⠀⇛


                       In the wake of this week’s Supreme
                       Court hearings—during which Judge Ketanji Brown
                       Jackson was forced to endure what critics
                       called “absolutely ridiculous” questions from
                       Senate Republicans—Rep. Pramila Jayapal on Friday
                       commended President Joe Biden’s nominee for
                       maintaining her composure and denounced GOP
                       lawmakers for engaging in “racist attacks.”


                       “The baseless and frankly racist attacks we have
                       seen in recent days demean the Senate Judiciary
                       Committee.”


                # ⚓ Counter Punch ☛ Brazil,_Amazon,_World:_Govern_By_Hate⠀⇛


                       The horrible paradox is that, though Bolsonaro’s
                       “Protector of Indigenous Communities” is a
                       grotesque taunt, his Merit Medal still performs
                       (the operative word) a very effective kind of
                       political communication or, better said,
                       propaganda. This kind of fake news provides a cover
                       of white noise that’s so stupefying it’s impossible
                       to see behind it. Nevertheless, if it’s difficult
                       to produce direct evidence that the Bolsonaro
                       government is committing a whole range of heinous
                       crimes, we can state that the militia gangs that
                       have been associated with the Bolsonaro family for
                       years are engaged in drug trafficking, arms deals,
                       and assassinations, creating a climate of fear
                       which, duly disseminated, is the perfect medium in
                       which such a regime can operate, especially with
                       help from the new “digital militia”.


                       Bolsonaro’s murderous antics are more than
                       diversionary tactics from the real business of his
                       shambles of a regime dominated by the interests of
                       the bullet-beef-and-bible lobby, which is all about
                       agribusiness (read: razing the Amazon), “family
                       values” (read: extreme homophobia and hatred of all
                       sexual and reproductive rights), and trigger-happy
                       paramilitaries (read: narco-militia), a foul mix of
                       drug traffickers, paramilitary forces, and neo-
                       Pentecostal churches waging a holy war, some under
                       an Israeli flag and with a copy of the Torah,
                       against rival criminal groups and Afro-Brazilian
                       religions. It’s not just about a bunch of Brazilian
                       fanatics. No corner of the Earth is free of the
                       politics of hate and fear which pervades almost all
                       aspects of social life. Everyone’s affected, one
                       way or another. In the case of Brazil, Bolsonaro
                       and his henchmen present themselves as patriotic
                       heroes when they’re blatantly committing lese-
                       patria at the service of local racketeers and
                       international corporations. This atrocious mix of
                       ecocide, genocide, religion justifying deadly
                       intolerance, and drug trafficking, all dressed up
                       as “government”, does one’s head in when trying to
                       understand the connections, the twists in the lies,
                       or how a man like Bolsonaro can get away with
                       political spectacles that as well as being morally
                       repugnant are insulting to the intelligence. At
                       this point we’d like to cite the whole of Guy
                       Debord’s prescient The Society of the Spectacle
                       (1967) but a few lines will have to suffice:


                # ⚓ Counter Punch ☛ To_the_Last_Ukrainian_or_All_of_Us?⠀⇛


                       Can anyone really believe that if Russia were again
                       to place nuclear capable missiles anywhere in the
                       Western hemisphere that Washington would not
                       envision a threat identical to that felt by Russia
                       today and act as aggressively and dangerously as it
                       did in 1962? Or imagine a scenario wherein Canada
                       aligned itself with China and invited Chinese
                       military advisers and their advanced weapons into
                       its territory.


                       Those of us of an age remember all too well the
                       first time our species faced self-extinction.
                       Understand too that the missiles of that time were
                       mere toys compared to the weapons that exist today.


                # ⚓ Counter Punch ☛ This_is_the_Time_to_Kick_Our_Oil
                  Addiction⠀⇛


                       News headlines link this sharp increase to Russia’s
                       war on Ukraine. But that assumes oil companies have
                       no control over the price of oil — that high prices
                       stem “naturally” from things like the war in
                       Ukraine, or the U.S. decision to halt oil and gas
                       imports from Russia.


                       Collin Rees, senior campaigner with Oil Change
                       International, told me in a recent interview that
                       there is “a complex interplay” of forces that
                       determine prices. Supply is only part of it.


                # ⚓ Counter Punch ☛ Stockholm_Syndrome_2022:_The_Faustian
                  Bargain_of_Left_Militarism_in_Ukraine⠀⇛


                       The Stockholm Syndrome has had a dramatic revival. 
                       Where?  No place other than in Stockholm, Sweden,
                       itself where the Left Party now embraces arms
                       shipments to Ukraine.  Who are the hostage takers? 
                       Not your average criminal, but rather the Swedish
                       military industrial complex comprised of defense
                       contractors, leaders of the armed forces, the
                       parliament, various parts of the media, and a small
                       army of “security experts.”  Who are the police who
                       have perceived not to have not cared for the
                       hostages’ safety?   The analogy here only partially
                       breaks down but relates to the supposedly
                       indifferent view of the peace movement, anti-
                       militarist intellectuals, and others opposed to the
                       militarist hostage takers.  So, you say, “it is
                       obvious that police oppose criminals!” So I say,
                       “it is obvious that anti-militarists oppose
                       militarism.”  We could end the story here, but the
                       devil is in the details.


                # ⚓ Hungary ☛ Telex’s_animated_informational_video_wins
                  prestigious_international_design_award⠀⇛


                # ⚓ Hungary ☛ Orbán_is_requesting_the_EU_loan:_after_four_big
                  blows,_Hungary_has_decided_that_cheap_money_is_better_than
                  expensive_money⠀⇛


                       The combination of Covid, the costs of the green
                       transition, inflation (especially of energy
                       prices), and the damage caused by the Russian
                       invasion of Ukraine have already brought Hungarian
                       economic policy to its knees. The disasters of
                       biblical proportions have finally made the
                       Hungarian political leadership realise that, even
                       at the cost of some political loss of face, it
                       needs the money from Brussels available in the form
                       of a loan. Translation by Andrea Horváth Kávai


                # ⚓ Hungary ☛ Zelensky_to_Orbán:_There_is_no_time_to_hesitate,
                  once_and_for_all,_you_must_decide_whose_side_you_are_on⠀⇛


                # ⚓ Counter Punch ☛ Cruelty_as_Border_Policy:_the_Biden
                  Version⠀⇛


                       This formula to measure the efficiency of the CDS
                       has been in use for more than a decade, but it is
                       being reupped by the Biden administration. Indeed,
                       the CBP guide was issued just as Biden was
                       declaring that he would create a fair, orderly, and
                       humane border and immigration system. While the
                       administration talked about rescinding Trump
                       initiatives such as the Migrant Protection Protocol
                       (now reinstated) and was hinting that Title 42
                       would be stopped (it’s still in effect), the CDS
                       and the more long-term deterrence strategies have
                       continued on without much comment. And its policies
                       and infrastructure of incarceration, which for
                       decades has led families to be arrested, detained,
                       and separated, lurks below the dominant rhetoric,
                       particularly that of the White House.


                       Behind closed doors, agents, like technocrats in a
                       Fortune 500 company, create color-coded graphics to
                       demonstrate the most “efficient” and “effective”
                       enforcement techniques. Even though the
                       effectiveness of deterrence has been questioned and
                       refuted, and even though the question of human
                       rights has not entered the equation at all, the
                       U.S. federal government seems to be plowing ahead
                       with this without any questions.


                # ⚓ Counter Punch ☛ Marxism_against_Marxism⠀⇛


                       It does so not least in light of the inevitable
                       construction of a strawmen to tear down for the
                       benefit of the party rank and file. It’s totally
                       fine to pick on Proudhon as if any anarchist is
                       wont (a) to quote him chapter and verse or (b)
                       identify as a Proudhonist.


                       Taking Stalin as representative of the entire
                       Marxist tradition, to cherrypick his authoritarian
                       excesses and ignore the Marxist critique of the
                       commodity form is, on the contrary, absolutely
                       opportunistic and disingenuous. No one with a shred
                       of honesty would go there.


                # ⚓ Counter Punch ☛ The_Billion_Dollar_Deal_that_Made_Google
                  and_Amazon_Partners_in_the_Israeli_Occupation_of_Palestine⠀⇛


                       In their letter, the signatories protested a $1.2
                       billion contract between Google, Amazon Web
                       Services (AWS) and the Israeli government which
                       provides cloud services for the Israeli military
                       and government that “allows for further
                       surveillance of and unlawful data collection on
                       Palestinians, and facilitates expansion of Israel’s
                       illegal settlements on Palestinian land”.


                       This is called Project Nimbus. The project was
                       announced in 2018 and went into effect in May 2021,
                       in the first week of the Israeli war on besieged
                       Gaza, which killed over 250 Palestinians and
                       wounded many more.


                # ⚓ Common Dreams ☛ Watchdogs_Say_If_Clarence_Thomas_Won’t
                  Resign,_‘Congress_Must_Move_to_Impeach’⠀⇛


                       Calls for Supreme Court Justice Clarence Thomas to
                       resign—or face impeachment proceedings—mounted late
                       Thursday after text messages revealed that his wife
                       urged former White House Chief of Staff Mark
                       Meadows to aggressively pursue efforts to overturn
                       the 2020 election results.


                       The Washington Post and CBS News obtained dozens of
                       texts that Ginni Thomas, a long-time far-right
                       activist who attended the January 6 rally that
                       preceded the Capitol assault, sent to Meadows in
                       the wake of Trump’s election loss, which she
                       characterized as fraudulent while her husband was
                       hearing election-related cases.


                # ⚓ Common Dreams ☛ Citing_New_Whiff_of_Corruption,_Wyden_Calls
                  on_Thomas_to_Recuse_From_All_Jan._6_Cases⠀⇛


                       Sen. Ron Wyden on Friday called on U.S. Supreme
                       Court Justice Clarence Thomas to recuse himself
                       from all cases related to the January 6, 2021
                       attack on the U.S. Capitol, after the justice’s
                       wife was found to have pushed for the overturning
                       of the presidential election.


                       “Justice Thomas’ conduct on the Supreme Court looks
                       increasingly corrupt.”


                # ⚓ The Nation ☛ The_Corruption_of_Clarence_and_Ginni_Thomas⠀⇛


                       It’s long been clear there is one set of rules for
                       liberal Democrats and another for conservative
                       Republicans. While Judge Ketanji Brown Jackson
                       promised this week to recuse herself from a case
                       involving Harvard University if she’s confirmed to
                       the Supreme Court (she’s on one of several Harvard
                       governing boards), Justice Clarence Thomas has for
                       months been ruling on issues relating to Donald
                       Trump’s efforts to overturn the 2020 election and
                       the January 6 coup attempt—even though it’s been
                       known that his wing nut wife was involved in
                       planning both.


                # ⚓ The Nation ☛ It’s_All_Connected⠀⇛


                # ⚓ Democracy Now ☛ Meet_Francia_Márquez,_the_Afro-Colombian
                  Land_Defender_Running_to_Be_Colombia’s_First_Black_VP⠀⇛


                # ⚓ Xe ☛ Book_Release:_Closed_Projects⠀⇛


                       Closed Projects is a retelling of a four-part
                       series on my blog where I process the events that
                       lead to the death of freenode, the largest IRC
                       network for peer-directed projects.


                       freenode was the reason that I managed to get into
                       tech. Without freenode I would be a vastly
                       different person today. The death of freenode last
                       year brought up many lingering memories and
                       emotions. I talk about my history with freenode,
                       the events that happened in the wake of its death
                       and how a new community took its place.


                # ⚓ NewYorkTimes ☛ Israel,_Fearing_Russian_Reaction,_Blocked
                  Spyware_for_Ukraine_and_Estonia⠀⇛


                       Israel feared that selling the cyberweapon to
                       adversaries of Russia would damage Israel’s
                       relationship with the Kremlin, they said.


          o § Misinformation/Disinformation⠀➾


                # ⚓ CNN ☛ Deepfakes_are_making_information_warfare_more_high
                  tech_and_worrisome_than_ever⠀⇛


                       Five years ago, nobody had even heard of deepfakes,
                       the persuasive-looking but false video and audio
                       files made with the help of artificial
                       intelligence. Now, they’re being used to impact the
                       course of a war. In addition to the fake Zelesnky
                       video, which went viral last week, there was
                       another widely circulated deepfake video depicting
                       Russian President Vladimir Putin supposedly
                       declaring peace in the Ukraine war.


                       Experts in disinformation and content
                       authentication have worried for years about the
                       potential to spread lies and chaos via deepfakes,
                       particularly as they become more and more realistic
                       looking. In general, deepfakes have improved
                       immensely in a relatively short period of time.
                       Viral videos of a faux Tom Cruise doing coin flips
                       and covering Dave Matthews Band songs last year,
                       for instance, showed how deepfakes can appear
                       convincingly real.


          o § Censorship/Free Speech⠀➾


                # ⚓ Techdirt ☛ Project_Veritas_Loses_Its_Defamation_Lawsuit
                  Against_CNN_Because_The_Truth_Is_Just_As_Damning_As_What_CNN
                  Said⠀⇛


                       Very serious laughably ridiculous buffoon stunt
                       journalists, Project Veritas, had its account
                       banned from Twitter a year ago, a couple months
                       before its founder James O’Keefe also had his own
                       account banned as well. O’Keefe vowed to sue CNN
                       and Twitter over the bans, and these plans seem to
                       be going about as well as a standard Project
                       Veritas special report: people too clueless to
                       understand reality think it means something, but it
                       falls apart under scrutiny. Just days after the
                       threat to sue, Project Veritas did, in fact, sue
                       CNN for defamation.


                # ⚓ FAIR ☛ New_York_Times’_Fear_of_Ordinary_People_Talking
                  Back⠀⇛


                       Samuel Freedman, author and long-time New York
                       Times writer, often told his journalism students
                       that they needed to keep in mind while writing copy
                       that they wouldn’t be able to literally stand
                       behind their reader at the newsstand. A writer must
                       make their copy as clean as possible, the lesson
                       was, because once it’s printed, they won’t be able
                       to clarify what they meant, or even have any kind
                       of dialogue with the reader.


                # ⚓ Techdirt ☛ Ted_Cruz,_Mike_Lee_Join_Dumb,_Baseless_GOP_Quest
                  To_Pretend_OAN_Was_Unfairly_Censored⠀⇛


                       So we’ve already noted how OAN was booted off of
                       the DirecTV lineup, severing a massive mainstream
                       distribution avenue for the conspiracy and fantasy
                       channel. DirecTV, recently spun off by AT&T, made
                       the decision because the channel, despite all the
                       attention, really wasn’t being watched very much.


                # ⚓ Techdirt ☛ On_Elon_Musk_And_Free_Speech⠀⇛


                       Let’s start this off by noting that I actually
                       think that Elon Musk sometimes receives both too
                       much criticism from some circles and too much
                       praise from others. I think he deserves tremendous
                       praise for taking visions that, at the time, seemed
                       nearly impossible, and then making them real. From
                       electric vehicles with Tesla, to space flight with
                       SpaceX, it’s unquestionable that he’s driven
                       tremendous innovation. And even in areas like
                       Starlink, which has been unfortunately overhyped,
                       he deserves kudos for actually building a working
                       (if somewhat limited) satellite internet service.
                       And that’s not even getting into his various
                       efforts with trying to create a hyperloop, or
                       trying to deal with transportation issues via The
                       Boring Company. Again, some of these have been
                       massively overhyped, but Musk, unlike many others,
                       gets a vision and then acts on it, and I find that
                       commendable — and helpful in driving innovation
                       forward.


                # ⚓ Project Censored ☛ THE_PROJECT_CENSORED_NEWSLETTER_–_March
                  2022_–_Censored_Notebook,_Newsletters⠀⇛


                       Independent News Stories We’re Tracking


                # ⚓ NPR ☛ Meet_the_Russians_who_are_fleeing_—_not_the_war,_but
                  their_own_government⠀⇛


                       Voloshinov flew first to Armenia, where he planned
                       to stay for a week or two. But after just a few
                       days, his father called him — the police were
                       looking for him in Moscow. Voloshinov is a
                       political journalist and has worked for opposition
                       publications. A new law introduced by Russian
                       President Vladimir Putin after the Russian invasion
                       of Ukraine means that Alexey could face up to 15
                       years in prison for even calling the war a war.


                       After he hung up the phone with his father, he
                       packed his bags again.


                       “That day, I decided to leave Armenia and move to
                       Georgia because there is no extradition from here,”
                       he remembers.


                # ⚓ Book Riot ☛ The_Censorship_Story_I_Can’t_Tell_You:_This
                  Week’s_Book_Censorship_News,_March_25,_2022⠀⇛


                       Despite the fact the job required library
                       experience and a library degree, Eledge was
                       approved by the Assembly without being qualified
                       for the role.


                       [...]


                       On Tuesday, February 8, I submitted a FOIA request
                       to the city of Anchorage. To do so requires sending
                       the request to department heads, meaning that to
                       FOIA information about the library, that request
                       goes to the library director. As Demboski has ceded
                       Eledge, this meant the FOIA request went to her.


                # ⚓ Patrick Breyer ☛ Chat_Control:_The_End_of_the_Privacy_of
                  Digital_Correspondence⠀⇛


                       A majority of the Members of the European
                       Parliament adopted the chatcontrol regulation on 6
                       July 2021 allowing providers to scan communications
                       voluntarily. So far only some unencrypted US
                       services such as GMail, Meta/Facebook Messenger and
                       X-Box apply chat control voluntarily. But this is
                       not the end of the story:


                       The European Commission announced that it will
                       propose follow-up legislation that will make the
                       use of chatcontrol mandatory for all e-mail and
                       messenger providers. This legislation will be
                       presented on 30 March 2022 and would also apply to
                       so far securely end-to-end encrypted communications
                       services. However, a public consultation by the
                       Commission demonstrated that the majority of
                       respondents, both citizens and stakeholders, were
                       opposed to an obligation to use chat control. Over
                       80% of respondents opposed its application to end-
                       to-end encrypted communications.


                # ⚓ The Epoch Times ☛ China_Cancels_Keanu_Reeves_Over_Support
                  for_Tibet⠀⇛


                       Reeves’s apparent offense had been appearing at a
                       March 3 virtual concert organized by Tibet House, a
                       New York-based nonprofit founded at the request of
                       Dalai Lama. The spiritual leader is exiled in India
                       where he established a shadow Tibetan government
                       that Beijing has labeled as being separatist.


                # ⚓ [Old] Linehan_shock_as_family_targeted_for_his_role_in_RTÉ
                  gender_debate⠀⇛


                       TV writer Graham Linehan has claimed that
                       opposition to his inclusion on an RTÉ programme
                       about transgender issues has resulted in him being
                       abused and his family targeted.


                # ⚓ It’s_not_Cancel_Culture,_it’s_Cancel_Technology⠀⇛


                       The really interesting question is whether
                       ostracism has changed in important and substantial
                       ways in the age of social media and the internet.
                       Even if human nature doesn’t change over time (and
                       I think the jury is still out on that one), the
                       tools we have access to do change, and that allows
                       society to reshape itself in new ways. (That’s what
                       I mean when I semi-ironically call myself a
                       “technological determinist”, by the way.)


                       What does the [Internet] do? Lots of stuff, but the
                       two things I want to focus on here are distribution
                       and memory. The [Internet]:


                       1. allows a very very large number of strangers to
                       see what you say and do, and


                       2. keeps a record of most of the things you say and
                       do online.


                # ⚓ Teacher_still_in_hiding_a_year_on_after_Prophet_Muhammed
                  Batley_Grammar_School_controversy⠀⇛


                       A teacher is still in hiding one year on from the
                       Prophet Muhammed Batley school row. The teacher had
                       shown a caricature of the founder of Islam, during
                       a religious studies lesson at Batley Grammar School
                       in March 2021.


                       The problem arose as the teacher claims he was
                       unaware of the sensitivities surrounding showing a
                       caricature. According to the BBC, there is no
                       mention in the Koran of a ban against using images
                       either drawn, carved or painted, of the Prophet
                       Muhammed or Allah.


                # ⚓ Yorkshire Live ☛ A_year_on_from_Prophet_Muhammad_Batley
                  school_row_and_teacher_still_in_hiding_as_family_‘at_risk’⠀⇛


                       Kim Leadbeater MP has said a teacher who showed an
                       image of the Prophet Muhammad during a lesson at a
                       Batley school faced “completely unacceptable”
                       backlash as she offered him her “full support” a
                       year on from the row.


                       The teacher was “forced into hiding” after showing
                       the caricature during a religious studies lesson at
                       Batley Grammar School in March, 2021. He was
                       suspended following heated protests outside the
                       school’s gates and was reportedly moved into police
                       protection after receiving death threats.


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


                # ⚓ VOA News ☛ ‘Press_Freedom_is_Dead_Already_in_Burma,’
                  Journalist_Says⠀⇛


                       All reporters in Myanmar are at risk of being
                       jailed just for doing their job, says a veteran
                       journalist now in exile.


                       The comments from Ye Wint Thu come after a
                       military-run court in Myanmar’s capital Naypyidaw
                       sentenced two more journalists to prison this week.


                # ⚓ RFERL ☛ ‘No_Room_For_Journalism’:_Russia’s_Independent
                  Regional_Press_Fights_To_Survive_Under_Wartime_Conditions⠀⇛


                       Kamalyagin and most of the newspaper’s long-
                       embattled staff have since left Russia. He hopes to
                       reassemble Pskovskaya Guberniya and renew
                       publication from outside the country in the near
                       future.


                       “It is hard getting information when you are
                       abroad, but we still have not only our own sources
                       but also our local stringers,” Kamalyagin told RFE/
                       RL’s North.Realities.


                # ⚓ Mexico News Daily ☛ Inter-American_rights_commission_urges
                  action_to_stop_violence_against_journalists⠀⇛


                       The Inter-American Commission on Human Rights
                       (IACHR) has urged Mexican authorities to implement
                       additional measures to prevent violence against
                       journalists and protect them from the threat of
                       physical attacks.


                       In a press release issued Thursday, the Office of
                       the Special Rapporteur for Freedom of Expression of
                       the IACHR said that in the first 10 weeks of 2022,
                       it received at least eight reports of murders of
                       journalists for reasons that could be related to
                       their work.


                       It warned of the “normalization and deepening of
                       violence” against journalists in Mexico.


                # ⚓ Craig Murray ☛ Free,_Enduring_Love⠀⇛


                       It was a cheap, white, trestle table, its thin top
                       slightly bowed down in the middle, of the type made
                       of a weetabix of sawdust and glue with a sheet of
                       plastic glued on top and plastic strips glued to
                       the sides, held up on four narrow, tubular, black
                       metal legs. On it was a register. In front of it
                       stood Stella Moris, looking beautiful and serene
                       with delight. She wore a stunning gown in a light
                       lilac, designed for her by Vivienne Westwood. It
                       had a mild satin shimmer, and appeared both
                       sumptuous and tightly tailored, with an expansively
                       lapeled jacket section diving in to a wasp waist,
                       that the apparently soft billows never intruded
                       upon, no matter how she moved.


          o § Civil Rights/Policing⠀➾


                # ⚓ Common Dreams ☛ Opinion_|_When_Jim_Crow_Greeted_Black
                  Veterans⠀⇛


                       I figured I’d better write this column while doing
                       so is still legal (at least I think it is), but I
                       don’t recommend reading it aloud in a third-grade
                       classroom.


                # ⚓ Counter Punch ☛ American_Democracy:_Alive_or_Dead?⠀⇛


                       To this point on November 22, 2021, the
                       International Institute for Democracy and Electoral
                       Assistance (IIDEA), based in Stockholm, Sweden,
                       released its 2021 Report on “The Global State of
                       Democracy.[1] The report’s introduction begins with
                       these chilling statements. “Democracy is at risk,”
                       “Its survival is endangered by a perfect storm of
                       threats, both from within and from a rising tide of
                       authoritarianism.” “The world is becoming more
                       authoritarian as nondemocratic regimes become even
                       more brazen in their repression, and many
                       democratic governments suffer from backsliding by
                       adopting their tactics of restricting free speech
                       and weakening the rule of law.”


                       Indeed, the annual report from Freedom House
                       reports that freedom around the world declined in
                       2021 for the 16th consecutive year, that China and
                       Russia are exporting authoritarianism, that
                       undemocratic regimes are growing more so, and that
                       even in established democracies, like the U.S.,
                       “internal forces have exploited the shortcomings of
                       their systems, distorting national politics to
                       promote hatred, violence and unbridled power.” Over
                       the past year, 60 countries became less free, while
                       only 25 improved.[2] 38% of the global population
                       live in countries that are not free (the highest
                       since 1997); 20% live in free countries; and 42%
                       live in “partly free” countries. Sadly, the United
                       States falls within this last category.[3]


                # ⚓ Counter Punch ☛ The_Shame_of_Santa_Rosa,_California:
                  Whiteness,_and_the_Culture_of_Lynching⠀⇛


                       From 1959 to this year, Lebaron penned thousands of
                       gossipy columns splashed with a bit of history,
                       attesting to the old-fashioned goodness of local
                       businesses, salt-of-the-earth ranchers, and police
                       and sheriff’s deputies who can do no wrong.


                       A ProQuest search of LeBaron’s columns in the Press
                       Democrat from 1994 to the present reveals hundreds
                       of stories glorifying white men wielding badges,
                       batons, guns, and in some instances, hanging
                       nooses. There is not a mention of the killing of
                       13-year-old Andy Lopez on Oct. 22, 2013 by Deputy
                       Sheriff Erick Gelhaus. LeBaron, 86, has also not
                       reported on killings by Sonoma County law
                       enforcers, a fact that she acknowledged in an
                       interview with the Bohemian last week.


                # ⚓ Counter Punch ☛ Want_to_Ensure_Marijuana_is_Safe?_Legalize
                  and_Regulate_It⠀⇛


                       A case in point: Police in Brattleboro, Vermont
                       recently generated headlines when they, along with
                       agents from the federal Drug Enforcement
                       Administration and Department of Homeland Security,
                       arrested multiple people on charges of distributing
                       fentanyl-tainted cannabis.


                       Days later, however, lab tests confirmed that no
                       fentanyl was present in any of the marijuana
                       samples that had been seized in the raid.


                # ⚓ Techdirt ☛ ICE’s_‘Fierce_Commitment’_To_Ensuring_Detainees
                  Are_Cared_For_Properly_Includes_Inadequate_Staffing,
                  Unsanitary_Facilities⠀⇛


                       ICE has never really cared about the people it
                       detains and processes for removal. It cared even
                       less when President Trump made it clear he believed
                       anyone less white and privileged than he is
                       deserved to be excluded from the “American dream.”


                # ⚓ Techdirt ☛ Arizona_Legislators_Want_To_Make_It_Illegal_For
                  People_To_Record_Cops_From_Whatever_Cops_Decide_Is_‘8_Feet
                  Away’⠀⇛


                       It’s pretty much understood that filming police is
                       protected by the First Amendment. Even in
                       jurisdictions where the highest courts have yet to
                       hand down a definitive decision, police departments
                       have made it clear to officers that filming cops
                       isn’t a crime. This has followed years of
                       jurisprudence and laws being repealed/rewritten to
                       reflect this position — something that has, years
                       after it became necessary, prevented police from
                       abusing wiretapping laws to arrest people for
                       “nonconsensual” recordings of officers performing
                       their public duties in public.


                # ⚓ Techdirt ☛ Ninth_Circuit_Says_Arresting_People_For_‘Fuck
                  The_Cops’_Chalk_Writing_Is_Unconstitutional_Retaliation⠀⇛


                       Cops and obscenities don’t mix.


                # ⚓ Counter Punch ☛ We_Must_End_Family_Separations_and_Here’s
                  How⠀⇛


                       I met him just five months after the Trump
                       administration took office and began an onslaught
                       of harsh immigration actions, including
                       prioritizing the deportation of all undocumented
                       immigrants. That included this 8-year-old citizen’s
                       parents, and he was terrified of losing them.


                       Despite the change in administration, our country
                       still has too many children living with the same
                       fear. With Congress failing again to create a
                       pathway to citizenship, over 5 million U.S.
                       children continue to face instability due to their
                       parents’ precarious immigration status.


                # ⚓ FAIR ☛ Carol_Anderson_on_History,_Race_and_Democracy⠀⇛


                # ⚓ The Nation ☛ California_Scrambles_to_Manage_Its_Housing
                  Crisis_and_Rising_Gas_Prices⠀⇛


                # ⚓ The Nation ☛ Kathy_Hochul_Is_About_to_Break_Ranks_With
                  Progressives⠀⇛


                       The Kathy Hochul honeymoon is coming to an end.
                       It’s New York, after all, and few politicians glide
                       above scrutiny or avoid agita. For many months, it
                       was good enough for Hochul to be not-Cuomo; smiling
                       and shaking hands, taking everyone’s phone calls,
                       and offering encouraging words.


                # ⚓ The Nation ☛ Why_Some_Ardent_Libertarians_Support_Judge
                  Ketanji_Brown_Jackson’s_Confirmation⠀⇛


                       Republicans on the Senate Judiciary Committee are
                       absolutely apoplectic about the fact that President
                       Biden’s Supreme Court nominee, Judge Ketanji Brown
                       Jackson, has been endorsed by progressive groups
                       that defend civil rights and civil liberties.
                       Senator Lindsey Graham got downright emotional on
                       the subject, declaring Jackson to be the choice of
                       “these left-wing radical groups that would destroy
                       the laws we know.” Graham told the nominee during
                       her confirmation hearing, “Every group that wants
                       to pack the court, that believes this court is a
                       bunch of right-wing nuts who are going to destroy
                       America, that consider the Constitution trash, all
                       wanted you picked.”


                # ⚓ Common Dreams ☛ Former_Amazon_Worker_Leads_Thousands_of
                  Warehouse_Employees_in_Historic_Union_Vote⠀⇛


                       Thousands of Amazon warehouse workers in Staten
                       Island, New York began voting Friday to whether or
                       not to join the Amazon Labor Union, an independent
                       group started by an employee who drew national
                       attention to working conditions at the company in
                       2020.


                       The union election could make the JFK8 warehouse
                       the first unionized Amazon facility in the country.
                       According to the Washington Post, the results of
                       the Staten Island vote and a union election being
                       held at an Amazon warehouse in Bessemer, Alabama
                       will both be announced in early April.


                # ⚓ NewYorkTimes ☛ Mandatory_Meetings_Reveal_Amazon’s_Approach
                  to_Resisting_Unions⠀⇛


                       On Staten Island, Amazon supervisors often refer to
                       them as “training.” At an Amazon warehouse in
                       Alabama, supervisors refer to them ambiguously as
                       “meetings.” Amazon says they’re officially “small
                       group meetings.”


                       Whatever Amazon calls them, the anti-union sessions
                       that the company has held for employees this year
                       have been part of an effort to fend off unions in
                       two contentious elections.


                # ⚓ RFA ☛ Officials_tell_Lao_Christians_to_remove_videos_of
                  attack_by_authorities,_villagers⠀⇛


                       When the family from Savannakhet province’s Dong
                       Savanh village took the body of their family
                       patriarch to the cemetery for burial on Dec. 6,
                       local authorities and residents angered by the
                       group’s practice of a “foreign religion” beat the
                       coffin with sticks and struck mourners and
                       pallbearers with clubs.


                       The family buried the man in their own rice field,
                       but authorities and residents continued to harass
                       them. Authorities expropriated their land in
                       February, and other villagers torched their home,
                       family members and other sources told RFA in an
                       earlier report.


                # ⚓ BBC ☛ Selling_sex_to_survive_in_Iran⠀⇛


                       Iran’s conservative religious establishment has
                       officially long denied the existence of sex workers
                       in the country. Instead, authorities allude to
                       prostitution there as a Western plot designed to
                       corrupt youth, or blame women for falling foul of
                       unscrupulous men.


                       Unofficial data also suggests Iran’s sex workers
                       are getting younger. Statistics from various NGOs
                       suggest that in 2016 girls as young as 12 were
                       involved in prostitution.


                       Aftab Society, an NGO dedicated to treatment of
                       drug-addicted women in Iran, said in 2019 that
                       there could be almost 10,000 female sex workers in
                       the capital, roughly 35% of whom were married.


                       According to Amir Mahmoud Harrichi, a professor of
                       social welfare at Tehran University, the figure for
                       the number of female sex workers in Tehran could be
                       twice as high.


                # ⚓ Morning Star News ☛ Family_Sprayed_with_Acid_for_Leaving
                  Islam⠀⇛


                       Upset over conversions to Christianity, hardline
                       Muslims in an area of eastern Uganda this month
                       sprayed a newly Christian family with acid and beat
                       a former mosque leader, sources said.


                       [...]


                       On March 9, while the three were receiving hospital
                       treatment in, their house was set ablaze, he said.


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ Running_the_ua.-top_level_domain_in_times_of_war⠀⇛


                       Dmitry Kohmanyuk has been working for the Ukrainian
                       ccTLD .ua since its foundation. In recent years he
                       worked as the national ccLTD’s strategist, working
                       on the monitoring and introduction of new
                       technology, like for example DNSSEC. Caught outside
                       of his country on February 24, Kohmanyuk cooperates
                       with his colleagues at home to keep the registry
                       for half a million .ua sites running.


                       The company is also operating the gov.ua TLD, a
                       much sought for and much attacked zone. Kohmanyuk
                       connects with international partners and he tries
                       to assure the .ua team dispersed over the Ukraine
                       and beyond. Being “like a mum” to those trapped in
                       Kiev felt strange and difficult, as he wanted to
                       cry himself, he said in a chat with heise online.
                       For now, the registry still has about 50 percent of
                       their infrastructure in the Ukraine. But the .ua
                       itself could become a refugee, operated from the
                       outside.


                # ⚓ Vice ☛ DIY_Volunteers_Are_Repairing_Ukraine’s_Destroyed
                  Internet_Infrastructure⠀⇛


                       Approximately 2,000 professional Ukrainian
                       operators are working to aid the effort to fix
                       broken [Internet] infrastructure and provide
                       communication services, and hundreds of civilians
                       have additionally volunteered to help repair and
                       rebuild the country’s [Internet] infrastructure,
                       according to Yurii Shchyhol, head of the State
                       Service of Special Communications and Information
                       Protection of Ukraine. This means reconnecting or
                       laying new fiber cables, restoring power, and
                       getting creative to keep people online. The agency
                       has referred to those doing this work as the
                       “invisible heroes” of the war effort—people risking
                       their lives to put back together fiber-optic cables
                       and mobile stations so that the nation can stay in
                       contact with the outside world.


                # ⚓ The Economist ☛ The_degrading_treatment_of_Ukraine’s
                  internet⠀⇛


                       DEGRADING AND ideally destroying your opponents’
                       ability to communicate are elementary military
                       tactics. And, in its war on Ukraine, Russia has
                       certainly attempted to do this. These days, closing
                       down communications focuses on the enemy’s internet
                       capabilities. So it is not surprising that analyses
                       by NetBlocks, a firm in London that monitors
                       [Internet] activity, suggest that the number of
                       devices connected to Ukraine’s internet has fallen
                       by nearly a quarter since Russia’s onslaught began.
                       Alp Toker, NetBlocks’ founder, describes that loss
                       as striking. But it could be a lot worse, for it
                       means that most Ukrainians are still online. What
                       is going on?


          o § Monopolies⠀➾


                # ⚓ Hollywood Reporter ☛ MGM’s_Amazon_Era_Begins_With_Big,
                  Unanswered_Questions⠀⇛


                       So MGM acquired UA, and its films, for some $380
                       million ($1.2 billion adjusted for inflation), with
                       Frank Rosenfelt, MGM’s chairman, telling The
                       Washington Post at the time that UA’s library would
                       be critical as Hollywood transitioned “from the
                       movie business to the entertainment software
                       business.”


                # § Patents⠀➾


                      # ⚓ [Old] Cutting_Back_Patent_Over-Enforcement_–_How_to
                        Address_Abusive_Practices_Within_the_EU_Enforcement
                        Framework⠀⇛


                             The debate over the degree of flexibility at
                             the disposal of national courts in Europe to
                             grant, deny, or tailor, injunctive relief in
                             patent litigation seems to be a never-ending
                             story. In most jurisdictions, absent
                             exceptional circumstances, findings of
                             infringement lead national courts to grant,
                             quasi-automatically, an injunction. However,
                             some scholars as well as industry players,
                             have argued that in light of recent changes
                             in litigation behaviour as well as technology
                             developments, a general principle of
                             proportionality should play a more prominent
                             role vis-à-vis injunctive relief. It is in
                             particular with reference to Art. 3(2) of the
                             Enforcement Directive that such claims have
                             been made. If UK courts have been inclined to
                             consider that, under certain circumstances, a
                             balance of interests may take place before
                             granting a permanent injunction, German
                             courts on the other hand have firmly stood on
                             the ground that the principle of
                             proportionality should not interfere with the
                             right of patent holders to obtain such
                             remedy. However, most recently, the German
                             Ministry of Justice published a draft
                             amendment to the German Patent Act providing
                             some guidance on the role of proportionality
                             vis-à-vis the rules of injunctive relief. The
                             issue of flexibility and injunctive relief is
                             symptomatic of a broader debate regarding
                             potential over-enforcement practices by right
                             holders and the means to overcome or reduce
                             the negative effects of these practices.
                             Overall, this article examines how the
                             origins and justifications of the Enforcement
                             Directive, which focus on fighting piracy and
                             counterfeiting, may affect the applicability
                             of the principle of proportionality in the
                             ever-changing context of patent law. How
                             national courts have (or have not) relied on
                             different mechanisms to infuse more
                             flexibility in case of over-enforcement
                             practices by right holders. And finally, how
                             the principle of proportionality as well as
                             the principle of the prohibition of abuse of
                             rights may serve national courts in this
                             endeavour of limiting excesses in patent
                             litigation.


                      # ⚓ EFF ☛ Defend_Innovation⠀⇛


                             The result is Defend Innovation: How to Fix
                             Our Broken Patent System, a whitepaper
                             providing a comprehensive view of the issues
                             plaguing the patent system today, as well as
                             a series of solutions that Congress, the
                             Patent Office, the courts, and companies can
                             implement.


                # § Copyrights⠀➾


                      # ⚓ Torrent Freak ☛ Court:_Null-Routing_is_Not_a
                        Practical_Anti-Piracy_Measure⠀⇛


                             A federal court in Florida maintains that
                             there is no reason to believe that hosting
                             company Quadranet is liable for the pirating
                             activities of its VPN customers. A group of
                             filmmakers suggests that the provider could
                             have null-routed IP-addresses, but the court
                             doesn’t see this as a practical or effective
                             measure.


                      # ⚓ Torrent Freak ☛ Pirate_IPTV_Services_Disrupted_By
                        Dozens_of_Rightsholders_On_Multiple_Fronts⠀⇛


                             Rightsholder measures against pirate IPTV
                             providers, sellers and resellers are nothing
                             new but in the last week alone, numerous
                             actions have come to fruition in a number of
                             regions. Whether in Canada, the Netherlands,
                             France or the UK, life is getting just that
                             little bit harder for those in the pirate TV
                             business.



                    ䷩ 𝚕𝚒𝚗𝚎 5462

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/03/26/irc-log-250322/#comments
    Gemini version at gemini://gemini.techrights.org/2022/03/26/irc-log-250322/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 03.26.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ IRC_Proceedings:_Friday,_March_25,_2022⠀✐


Posted in IRC_Logs at 2:13 am by Needs Sunlight


Also available via the Gemini protocol at:


    * gemini://gemini.techrights.org/irc-gmi/irc-log-techrights-250322.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-250322.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-social-250322.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-techbytes-250322.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
 QmPHKVsv9hbgpz7BfnfC351SPtY6Tf27hBf5ZdoMEreFUk #boycottnovell  🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell
 QmPbyqnJvrPDRUB9t7rCP3h1o3SRxG4XPbxWgNp8kTvPnU (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
                                                 #boycottnovell-
 Qmc3BrXv8Tp3HLJHjG2eXuydqu9iQF7PXCmvGGPU9Drdqf social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell-
 QmatjUCz5TvUdioJvZyMo2QicdLYHuybchMHJGKTm1524o social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 (full IRC log
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
 QmbZPTVzGD5z8cnEAFcorV4TkpptAfPNeDykypVZqCMgyU #techbytes      🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #techbytes
 QmT5Mn6o7cP9XDdi3C9u7sLgpUurJMfGgtgK2LWx4qBpH7 (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
 QmUbknkZ9K3NQGcoZqiv8tGKUxEYnhZEwXyLxeoRwKexRE #techrights     🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #techrights
 QmXwvnw9MDf1YtTkT11VQRA45EAtCy3xSyCF8BwSYEa5Wd (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇IPFS logo⦈


§ Bulletin for Yesterday⠀➾


Local_copy | CID (IPFS): QmbZUGxupu36yFf72bxj4yCNrYAfeMKD4kf3TzSvrLqGkT



                    ䷩ 𝚕𝚒𝚗𝚎 5589

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/03/26/mike-gerwitz-ethics/#comments
    Gemini version at gemini://gemini.techrights.org/2022/03/26/mike-gerwitz-ethics/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 03.26.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Mike_Gerwitz_on_the_Ethics_Void⠀✐


Posted in Free/Libre_Software, FSF at 12:09 am by Dr. Roy Schestowitz


Video_download_link


https://media.libreplanet.org/mgoblin_media/media_entries/2039/stream-
101_20180325__11-34-46.webm


Summary: From the_official_talk‘s description: “Many communities have widely
adopted codes of ethics governing the moral conduct of their members and
professionals. Some of these codes may even be enshrined in law, and for good
reason—certain conduct can have enormous consequences on the lives of others.”


Licence: CC_BY_SA_4.0



                    ䷩ 𝚕𝚒𝚗𝚎 5625

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/03/26/moving-office/#comments
    Gemini version at gemini://gemini.techrights.org/2022/03/26/moving-office/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 03.26.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Moving_On⠀✐


Posted in Free/Libre_Software, GNU/Linux at 4:42 pm by Dr. Roy Schestowitz


Video_download_link | md5sum c583b13f70142fbc89e83abe030e0dd6
Adding Space
Creative Commons Attribution-No Derivative Works 4.0


http://techrights.org/videos/office-move.webm


Summary: Today I moved to a more spacious desk and added a bunch of equipment
to compensate for a failing SSD


TODAY was a very unusual day. None of this was planned, but a solution for the
failing SSD was long overdue. I took precautionary measures to avoid
catastrophic data loss, but short of literally replacing the storage nothing
would work properly. Postponing and procrastinating was a disaster waiting to
happen. I also needed quite a lot of storage, so I ended up buying a low-budget
machine, cobbling together all the machines from noon till evening time, taking
the opportunity to also turn the dining room into an office, which is generally
a lot safer as there’s no carpeting. There will be several practical benefits
in the long run and at the moment I control 9 screens and 6 computers with one
mouse and one illuminated (external) keyboard that I’m accustomed to. It is
mechanical. Tomorrow will be a very busy day because of data migration, so I
don’t anticipate much output. Today was a long-term investment that can pay off
for months to come.


Incidentally, today I finally became a KDE Neon user. I was always intrigued by
and curious about this distro, now I can warmly recommend it to KDE lovers. I
also really liked Linux Mint Debian Edition, which is only days old. Shame on
Mozilla for turning Firefox into adware; I hadn’t imagined it would get this
bad. I think several distros should consider making Falkon or LibreWolf the
default Web browser. █



                    ䷩ 𝚕𝚒𝚗𝚎 5680

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 03.26.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_26/03/2022:_New_Debian_Releases⠀✐


Posted in News_Roundup at 4:27 pm by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


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


          o § Desktop/Laptop⠀➾


                # ⚓ Unix Men ☛ How_Businesses_Can_Benefit_from_Using_Linux⠀⇛


                       Many businesses spend a lot of time weighing up the
                       benefits of cloud automation and orchestration,
                       without spending too much time considering
                       operating systems. Historically, Microsoft Windows
                       has been the OS of choice. However, when it comes
                       to hosting services, Linux is definitely the better
                       option.


          o § Audiocasts/Shows⠀➾


                # ⚓ Video ☛ ProtonDB_Has_A_New_Linux_Game_Ranking_System_–
                  Invidious⠀⇛


                       ProtonDB is an incredible website to check the
                       state of Linux gaming but recently it received a
                       massive change and ruined the site but now it has
                       been redesigned and in many ways is better than
                       ever


                # ⚓ Video ☛ I_Need_More_Audio_Jacks_On_My_Computer_–
                  Invidious⠀⇛


                       I’ve got a problem. I’ve got multiple sets of
                       speakers and headphones that I switch between, and
                       I’m tired of having to constantly plug/unplug stuff
                       into the one 3.5mm jack on the back of my computer.


                # ⚓ Video ☛ My_New_Linux_Desktop_–_Material_Shell_–_Invidious⠀⇛


                       This is an absolutely amazing desktop experience.
                       By far one of my favorites, because we revisit one
                       of my favorite layouts and developers of modern UI
                       interfaces.


          o § Kernel Space⠀➾


                # ⚓ Asahi_Linux_Is_Reverse-Engineering_Support_For_Apple
                  Silicon,_Including_M1_Ultra⠀⇛


                       For months, a small group of volunteers has worked
                       to get this Arch Linux-based distribution up and
                       running on Apple Silicon Macs, adapting existing
                       drivers and (in the case of the GPU) painstakingly
                       writing their own. And that work is paying off —
                       last week, the team released its first alpha
                       installer to the general public, and as of
                       yesterday, the software supports the new M1 Ultra
                       in the Mac Studio. In the current alpha, an
                       impressive list of hardware already works,
                       including Wi-Fi, USB 2.0 over the Thunderbolt ports
                       (USB 3.0 only works on Macs with USB-A ports, but
                       USB 3.0 over Thunderbolt is “coming soon”), and the
                       built-in display. But there are still big features
                       missing, including DisplayPort and Thunderbolt, the
                       webcam, Bluetooth, sleep mode, and GPU
                       acceleration. That said, regarding GPU
                       acceleration, the developers say that the M1 is
                       fast enough that a software-rendered Linux desktop
                       feels faster on the M1 than a GPU-accelerated
                       desktop feels on many other ARM chips.


          o § Applications⠀➾


                # ⚓ Make Use Of ☛ Why_Run_Windows_Apps_on_Linux?_Here_Are_15
                  Linux_Alternatives⠀⇛


                       As you might have noticed, more and more people are
                       switching to Linux these days. However, it is still
                       pretty common for Linux users to look for apps they
                       are used to using on Windows.


                       If you want to enjoy the Linux experience to the
                       fullest, we recommend switching to Linux apps to
                       perform your day-to-day tasks. That’s how your
                       journey will come full circle.


                       So, to aid you in this process, here is a list of
                       Linux alternatives to popular Windows apps that you
                       can download and use for free.


          o § Instructionals/Technical⠀➾


                # ⚓ DT ☛ Upgrade_PostgreSQL_Database_(Cluster)_from_one_Major
                  Version_to_Another⠀⇛


                       I’m in the process of finally upgrading my Debian
                       install from oldstable (buster) to stable
                       (bullseye). My DAViCal installation uses PostgreSQL
                       for its database backend. Strangely, I have two
                       versions of PostgreSQL (9.6 and 11) and I purged
                       the older one (without deleting the databases,
                       thankfully).


                # ⚓ ID Root ☛ How_To_Install_ExifTool_on_Ubuntu_20.04_LTS_–
                  idroot⠀⇛


                       In this tutorial, we will show you how to install
                       ExifTool on Ubuntu 20.04 LTS, as well as some extra
                       required packages by ExifTool


                # ⚓ Streaming_the_Steam_Deck_to_OBS⠀⇛


                       Valve was kind enough to send Steam Deck devkits to
                       Arch Linux maintainers and developers which gave us
                       an opportunity to mess around with the device.


                       Personally I find it a bit fun to mess around with
                       video streaming, thus one of the first things I
                       wanted to try figure out was how I could stream the
                       gamemode on the Steam Deck. Installing the OBS
                       flatpak and adding it to the menu doesn’t actually
                       work so we sadly have to be a bit more clever.


                # ⚓ Ubuntu_22.04_Chromium_Browser_installation⠀⇛


                       The purpose of this tutorial is to show how to
                       install the Chromium web browser on Ubuntu 22.04
                       Jammy Jellyfish. Chromium is an open source browser
                       maintained by Google. Along with the Chromium
                       browser itself, Google Chrome, Microsoft Edge,
                       Opera, Vivaldi, and a slew of other notable web
                       browsers are all based on the Chromium source code.
                       It’s safe to say that Chromium plays a huge role in
                       the way that many users view the web today.


                # ⚓ How_to_set_browser_environment_variable_on_Linux⠀⇛


                       The purpose of this tutorial is to show how to set
                       the web browser environment variable on Linux.
                       Setting environment variables is usually how users
                       can set the default applications and programs used
                       on their Linux system. Therefore, the browser
                       environment variable should point to the user’s
                       desired default web browser.


                       In the case of a default web browser, this setting
                       is best configured by the GUI itself. Simply
                       setting the $BROWSER variable is not going to give
                       you the the result you are expecting. Manually
                       setting the web browser environment variable
                       through other means is possible, but the process
                       for doing so will vary across distributions and
                       desktop environments.


                # ⚓ How_to_set_or_change_boot_partition_flag_on_Linux⠀⇛


                       The boot partition flag is used to indicate that an
                       MBR partition is bootable. Although MBR has been
                       superseded by GUID Partition Table in recent years,
                       MBR is still very prevalent across many systems.
                       The boot loader resides on a bootable partition and
                       is what tells your system where to look for the
                       operating system.


                       In this tutorial, you will find the step by step
                       instructions to set or change the boot partition
                       flag on a Linux system via command line and GUI.


                # ⚓ Install_Couchbase_Server_on_Debian_11/Debian_10_–
                  kifarunix.com⠀⇛


                       In this tutorial, you will learn how to install
                       Couchbase Server on Debian 11/Debian 10. According
                       to the documentation, Couchbase Server is an open
                       source, distributed, JSON document database. It
                       exposes a scale-out, key-value store with managed
                       cache for sub-millisecond data operations, purpose-
                       built indexers for efficient queries, and a
                       powerful query engine for executing SQL-like
                       queries.


                # ⚓ ByteXD ☛ How_to_Install_KDE_Plasma_or_Kubuntu_in_Ubuntu
                  22.04_or_20.04_–_ByteXD⠀⇛


                       The KDE desktop environment is called KDE Plasma,
                       and also referred to as Plasma Desktop.


                       It’s one of the most popular desktop environments,
                       is very intuitive and easy to use, is available in
                       many languages, and provides a consistent user
                       experience across a wide range of devices.


                       The KDE Plasma is also one of the most feature rich
                       and customizable desktop environments, and it has a
                       very modern look and feel.


                # ⚓ MakeTech Easier ☛ How_to_Use_WhatsApp_Web_on_Desktop_and
                  Chrome_–_Make_Tech_Easier⠀⇛


                       If you have particularly chatty people on your
                       WhatsApp list, you’ll know how annoying it can be
                       to converse with them using a mobile keyboard. You
                       can’t really get the gossip grapevine (or more
                       important messages) going at a measly 20 words-per-
                       minute. Thankfully, there is a way to use WhatsApp
                       on your PC, so you can type with your hardware
                       keyboard and really express yourself.


                # ⚓ How_to_customize_i3status_on_Linux⠀⇛


                       I3 is one of the most used tiling window managers
                       on Linux. A tiling window manager arranges windows
                       in a non-overlapping way: this allows us to use
                       screen space efficiently, but can require a little
                       bit of time to get used to.


                       The i3 window manager on Linux is usually installed
                       together with the i3status utility, which can be
                       used to populate supported status bars with
                       information such as memory or CPU usage. In this
                       tutorial we see how to customize i3status and use
                       some of its modules.


                # ⚓ How_to_set_alarm_on_Linux⠀⇛


                       Setting an alarm on Linux can be helpful to remind
                       you of something or act as a timer. It might also
                       come in handy if you take a little snooze at your
                       desk. In this tutorial, we will show you how to set
                       an alarm on Linux via command line and GUI.


                # ⚓ How_To_Install_and_Run_Linux_on_Android_(With/Without_Root)
                  –_DekiSoft⠀⇛


                       Technology is moving at such a pace that users
                       prefer smaller handhelds as their preferred choice
                       of hardware. Phones have become smaller in size and
                       more powerful in terms of computing power. They are
                       more than enough capable of running a full-sized
                       operating system.


                # ⚓ The New Stack ☛ How_to_Deploy_Kubernetes_with_Kubeadm_and
                  containerd_–_The_New_Stack⠀⇛


                       There’s no easy way to say this, but Kubernetes is
                       challenging. And although at one time it was
                       actually fairly simple to deploy a Kubernetes
                       cluster to bare metal (thanks, in part, to Docker),
                       it’s not quite as simple as it once was. To
                       complicate matters even further, there’s an almost
                       endless amount of paths to getting the platform up
                       and running.


                # ⚓ H2S Media ☛ How_to_Install_PowerShell_on_Ubuntu_22.04_LTS
                  [Ed: Microsoft junk, but some people use this to migrate away
                  from Windows]⠀⇛


                # ⚓ H2S Media ☛ Install_PowerShell_on_Debian_11_Bullseye
                  Linux⠀⇛


                # ⚓ How_To_Install_OpenRGB_On_Ubuntu_22.04_|_20.04_LTS_|
                  Itsubuntu.com⠀⇛


                       How to install OpenRGB tools on Ubuntu 22.04 LTS
                       Jammy JellyFish or Ubuntu 20.04 LTS Focal Fossa.


                # ⚓ Install_Couchbase_Server_on_Ubuntu_22.04/Ubuntu_20.04_–
                  kifarunix.com⠀⇛


                       In this tutorial, you will learn how to install
                       Couchbase Server on Ubuntu 22.04/Ubuntu 20.04.
                       According to the documentation, Couchbase Server is
                       an open source, distributed, JSON document
                       database. It exposes a scale-out, key-value store
                       with managed cache for sub-millisecond data
                       operations, purpose-built indexers for efficient
                       queries, and a powerful query engine for executing
                       SQL-like queries.


                # ⚓ AddictiveTips ☛ How_to_back_up_and_restore_your_website_on
                  Linux⠀⇛


                       If you run a website on a Linux server, you should
                       be keeping regular backups. We’ve got you covered
                       if you’re new to Linux server administration.
                       Here’s how to back up and restore websites on
                       Linux.


                # ⚓ ID Root ☛ How_To_Install_Passbolt_on_AlmaLinux_8_–_idroot⠀⇛


                       In this tutorial, we will show you how to install
                       Passbolt on AlmaLinux 8. For those of you who
                       didn’t know, Passbolt is a free and open-source
                       password manager based on PHP, MySQL, and OpenPGP
                       which allows you to securely store and share login
                       credentials of website, router password, Wi-Fi
                       password, etc. It is self-hosted and available in
                       both community and subscription-based editions.


                       This article assumes you have at least basic
                       knowledge of Linux, know how to use the shell, and
                       most importantly, you host your site on your own
                       VPS. The installation is quite simple and assumes
                       you are running in the root account, if not you may
                       need to add ‘sudo‘ to the commands to get root
                       privileges. I will show you through the step-by-
                       step installation of the Passbolt password manager
                       on an AlmaLinux 8. You can follow the same
                       instructions for Fedora, RHEL, CentOS, and Rocky
                       Linux distributions.


                # ⚓ AddictiveTips ☛ How_to_set_up_a_LAMP_server_on_Debian_11⠀⇛


                       While many people think of Debian as a rock-solid
                       workstation operating system, that’s not all it can
                       be used for. Debian is also one of the most used
                       Linux-based server operating systems.


                       There are a lot of server applications for Debian.
                       However, one of the most popular things users set
                       up is LAMP. LAMP is Linux, Apache, MySQL, and PHP,
                       and it is essential for hosting web apps. Here’s
                       how you can set up a LAMP server on Debian 11.


          o § Wine or Emulation⠀➾


                # ⚓ 9to5Linux ☛ DXVK_1.10.1_Adds_Initial_Support_for_Shared
                  Resources,_Fixes_God_of_War_and_GTA:_San_Andreas⠀⇛


                       DXVK 1.10.1 is the first point release in the DXVK
                       1.10 stable series and it’s here to implement
                       initial support for shared resources in an attempt
                       to fix video playback for several Koei Tecmo games,
                       including the Atelier series and Nioh 2, as well as
                       the D3D11-based UI in the Windows version of Black
                       Mesa.


                       However, “initial” means that this feature is
                       considered experimental as it hasn’t been
                       thoroughly tested against all graphics drivers.
                       According to the release notes, only basic 2D
                       texture sharing between the D3D9 and D3D11
                       implementations is supported when using DXVK for
                       both APIs.


                # ⚓ GamingOnLinux ☛ DXVK_1.10.1_is_out_with_initial_support_for
                  shared_resources_|_GamingOnLinux⠀⇛


                       DXVK is the free and open source project that
                       translates Direct3D 9 / 10 / 11 to Vulkan for use
                       with the Wine and Proton Windows translation
                       layers. One of the major parts of Steam Play Proton
                       that helps games run well on Linux desktops and
                       Steam Deck.


                       Version 1.10.1 brings on initial support for shared
                       resources, fixing video playback in a number of
                       Koei Tecmo games (Atelier series, Nioh 2), as well
                       as the D3D11-based UI in the Windows version of
                       Black Mesa. It’s still quite experimental now and
                       needs more testing across various drivers.


          o § Games⠀➾


                # ⚓ Boiling Steam ☛ Steam_Starts_Collecting_Feedback_From_Users
                  on_Steam_Deck_Verified_titles_–_Boiling_Steam⠀⇛


                       Valve has just announced through the Steam
                       community news that they are adding a new feature
                       to collect feedback from end users about the Steam
                       Deck Verified games they try out. In practice it
                       will first ask you to opt-in to be part of the
                       feedback service, and afterwards it will ask you
                       questions about the titles you have just played on
                       the Steam Deck to confirm if it matches your
                       experience:


                # ⚓ GamingOnLinux ☛ Syncthing_is_a_great_way_to_transfer_files
                  from_PC_to_Steam_Deck_|_GamingOnLinux⠀⇛


                       Recently I did a guide using the Warpinator tool to
                       transfer files from PC to Steam Deck, here’s
                       another way using the wonderful tool Syncthing that
                       you might prefer. that you might prefer.


                       A lot of people seemed to like the previous guide
                       and video, however a few people couldn’t get
                       Warpinator to work although most did. So as a
                       bonus, I checked out Syncthing to see how that
                       works. It’s just as easy to get going too.


                # ⚓ GamingOnLinux ☛ Valve_actually_announced_Steam_for_Chrome
                  OS_now_too_|_GamingOnLinux⠀⇛


                       After a bit of a false start with an announcement
                       made too early, Google has now announced Steam for
                       Chrome OS and Chromebooks and now Valve has done
                       their own brief announcement. So it’s all
                       officially official now.


          o § Desktop Environments/WMs⠀➾


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


                      # ⚓ Wikidata_Data_Reuse_Days_2022_Recap⠀⇛


                             Over the past two weeks I attended a number
                             of sessions of the Wikidata Data Reuse Days
                             2022 and presented KDE’s use of Wikidata in
                             our travel apps there. Here are some of the
                             things I found particularly interesting from
                             a KDE perspective.


          o § Distributions⠀➾


                # § IBM/Red Hat/Fedora⠀➾


                      # ⚓ Fedora ☛ Nest_with_Fedora_&_Fedora_Hatch:_Announcing
                        dates_&_call_for_volunteers⠀⇛


                             Hi Fedora Friends! We made it through another
                             year of living with COVID-19, with plenty of
                             other challenges added on top. To everyone
                             who make up Fedora – thank you for your
                             presence, contributions, and efforts during
                             this trying time. Because we have yet to see
                             an end to living with COVID-19, I opened a
                             discussion with the community about what we
                             should do for this year’s contributor
                             conference.


                             Based on that feedback, I am pleased to
                             announce that we will be holding the third
                             edition of Nest with Fedora on August 4th,
                             5th, & 6th. I will be publishing info on the
                             CfP in the upcoming months. We will also be
                             funding local in person meetups that we have
                             titled Fedora Hatch. If you want to
                             participate in an in person meetup, make sure
                             to read on and suggest your ideas on the
                             Flock pagure!


                # § Debian Family⠀➾


                      # ⚓ Linuxiac ☛ Parrot_5.0_Released_with_Cloud_and
                        Customizability_in_Mind⠀⇛


                             From release 5.0, Parrot is also available
                             for Raspberry Pi 4. Without a desktop
                             environment, you can install whatever you
                             like.


                             Penetration testing and ethical hacking have
                             risen in popularity and industry needs over a
                             previous couple of decades. From learning
                             about the dangers of the internet to
                             protecting data from hackers, the software
                             industry has become increasingly aware of the
                             millions of dollars that could be lost in a
                             breach.


                             Similar to Kali Linux, Parrot Security OS was
                             created as an operating system for ethical
                             hackers to raise awareness even further. It
                             is a free and open-source Linux distribution
                             based on Debian.


                      # ⚓ Debian_—_News_—_Updated_Debian_11:_11.3_released⠀⇛


                             The Debian project is pleased to announce the
                             third update of its stable distribution
                             Debian 11 (codename bullseye). This point
                             release mainly adds corrections for security
                             issues, along with a few adjustments for
                             serious problems. Security advisories have
                             already been published separately and are
                             referenced where available.


                             Please note that the point release does not
                             constitute a new version of Debian 11 but
                             only updates some of the packages included.
                             There is no need to throw away old bullseye
                             media. After installation, packages can be
                             upgraded to the current versions using an up-
                             to-date Debian mirror.


                      # ⚓ Debian_—_News_—_Updated_Debian_10:_10.12_released⠀⇛


                             The Debian project is pleased to announce the
                             twelfth update of its oldstable distribution
                             Debian 10 (codename buster). This point
                             release mainly adds corrections for security
                             issues, along with a few adjustments for
                             serious problems. Security advisories have
                             already been published separately and are
                             referenced where available.


                             Please note that the point release does not
                             constitute a new version of Debian 10 but
                             only updates some of the packages included.
                             There is no need to throw away old buster
                             media. After installation, packages can be
                             upgraded to the current versions using an up-
                             to-date Debian mirror.


                      # ⚓ FLOSSLinux:_Debian_media_team_–_testing_and_releasing
                        Debian_11.3_–_20220326_1243UTC⠀⇛


                             And back to relative normality : the usual
                             suspects are in Cambridge. It’s a glorious
                             day across the UK and we’re spending it
                             indoors with laptops 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇:)⦈


                             We’ll also be releasing a point release of
                             Buster as a wrap up of recent changes.


                             Debian 10 should move from full support to
                             LTS on July 14th – one year after the release
                             of Debian 11.


                             All seems to be behaving itself well.


                      # ⚓ Still_testing_Debian_media_images_20220326_2026UTC-
                        almost_finished_11.3_–_Buster_starting_soon⠀⇛


                      # ⚓ FLOSSLinux:_Part_way_through_testing_Debian_media
                        images_20220326_1555UTC_–_Found_a_new_useful_utility⠀⇛


                             For various obscure reasons, I have a mirror
                             of Debian in one room and the main laptop and
                             so on I use in another. The mirror is
                             connected to a fast Internet line – and has a
                             1Gb Ethernet cable into the back directly
                             from the router, the laptop and everything
                             else – not so much, everything is wired, but
                             depends on a WiFi link across the property.
                             One end is fast – one end runs like a snail.


          o § Devices/Embedded⠀➾


                # ⚓ Piwigo_and_Raspberry_PI:_a_Private_Open_Source_Photo
                  Management_Platform⠀⇛


                       Keeping your pictures and videos in smartphones can
                       suddenly drain your storage space. Piwigo with
                       Raspberry PI can save your space and give you more
                       features to manage them privately


                       In this tutorial, I’m going to show you how to
                       install Piwigo on your Raspberry PI computer board.
                       It can also be considered a great Google Photo
                       alternative, as the Google service requires a paid
                       subscription once you require more space. An
                       important thing is, after the Piwigo installation,
                       to use the official users manual to keep our files
                       secure from any outage with periodic backups.


                # ⚓ Wind_River_Studio_Addresses_Challenges_of_Managing_Secure
                  Linux-Based_Intelligent_Systems⠀⇛


                # ⚓ Linux On Mobile ☛ Weekly_Update_(12/2022):_GNOME_42,_Phosh
                  0.17.0,_Phoc_0.13.0,_Mepo_0.4_and_Capyloon_on_Linux_Phones!⠀⇛


                       A new PinePhone Modem Firmware release, updates on
                       Nemo Mobile and GNUnet Messenger progress, Calls on
                       the Poco F1, and a bunch of gaming centric
                       PinePhone videos! And do try Capyloon on your
                       Mobian-running Librem 5 or PinePhone Pro!


                # § Open Hardware/Modding⠀➾


                      # ⚓ New_Toy:_Hello_Precursor!⠀⇛


                             Those of you with a Spock-like mind will not
                             be surprised to hear that a new toy has made
                             it to my desk: the Precursor by the most
                             respected Andrew “bunnie” Huang and his gang.


                      # ⚓ Bye_bye,_openmoko!⠀⇛


                             Someone has responded to my message, that I
                             would give away my trusty openmoko neo — I
                             have changed technology for the last duty it
                             had until recently. And I am happy that
                             someone else is interested to keep it for a
                             little longer.


                      # ⚓ Arduino ☛ Top_Three_Arduino_Cloud_Games_Projects
                        Revealed_|_Arduino_Blog⠀⇛


                             The Arduino Cloud Games was first hinted at
                             just after Christmas, 2021. That’s how long
                             these amazing members of the Arduino
                             community have been toiling on some genuinely
                             incredible projects.


                             The top three were just announced live on the
                             community day at Arduino Week 2022, so we
                             thought we’d give you a closer look at what
                             they built. Firstly though, even if it’s
                             something of a cliche, we’ve got to say that
                             picking them was insanely difficult. The
                             quality, imagination and skills we’ve seen
                             throughout the Arduino Cloud Games has been
                             staggering. Seriously, there are very few
                             people who work at Arduino that could build
                             such amazing things.


                             So if you didn’t make it into the top three,
                             despair not! You were up against some of the
                             toughest creative competition in the maker
                             world. You all blew our minds with every new
                             project that arrived on Project Hub, so you
                             should be incredibly proud that you made it
                             into the finals. Keep on building!


                # § Mobile Systems/Mobile Applications⠀➾


                      # ⚓ Phone Arena ☛ Google_releases_Android_12_QPR3_beta
                        1.1_for_Pixel_6_and_Pixel_6_Pro_only_–_PhoneArena⠀⇛


                      # ⚓ Samsung_One_UI_4.0_(Android_12)_update_roll_out
                        tracker_[Cont._updated]⠀⇛


                      # ⚓ Google_Maps_search_throwing_“No_results_found”_error
                        on_Android_for_some⠀⇛


                      # ⚓ The_Best_New_Games_for_Android_This_Week_–_Cat
                        Museum,_Critical_Slash_and_More_–_Droid_Gamers⠀⇛


                      # ⚓ Android Authority ☛ 5_Android_apps_you_shouldn’t_miss
                        this_week_–_Android_Apps_Weekly⠀⇛


                      # ⚓ Android Central ☛ How_to_control_Chromecast_volume
                        with_your_Android_phone_|_Android_Central⠀⇛


                      # ⚓ HowTo Geek ☛ Why_Doesn’t_My_Android_Phone_Have_a_WPS
                        Button?⠀⇛


                      # ⚓ The Verge ☛ Global_science_project_links_Android
                        phones_with_satellites_to_improve_weather_forecasts_–
                        The_Verge⠀⇛


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


                # ⚓ Projects_for_the_benefit_of_others⠀⇛


                       I recently saw @vidak@zoinks.one thinking about
                       setting up a server where people could host Gemini
                       or Gopher content, and how nobody really joined
                       their previous effort of building something for the
                       benefit of others, a tilde server. It felt like a
                       very familiar problem.


                # ⚓ Linux Links ☛ Best_Free_and_Open_Source_Alternatives_to
                  Apple_Boot_Camp⠀⇛


                       Apple, Microsoft, Alphabet (Google’s parent),
                       Amazon and Facebook dominate the tech landscape.
                       Their dominance is so broad they account for more
                       than 20% of the S&P 500.


                       There are many things to admire about Apple’s
                       hardware and software. Apple make great looking
                       (albeit expensive) hardware. Over the years key
                       successes include the iPhone, iPad, iPod, and the
                       MacBook Air. The company designs its own hardware
                       and software. This gives them the power to make an
                       operating system and suite of apps that are tailor-
                       made and optimized for their hardware. Apple also
                       operates the Apple Music and Apple TV media
                       distribution platforms.


                       Mac OS X is Apple’s proprietary operating system
                       for its line of Macintosh computers. Its interface,
                       known as Aqua, is highly polished and built on top
                       of a BSD derivative (Darwin). There’s a whole raft
                       of proprietary applications that are developed by
                       Apple for their operating software. This software
                       is not available for Linux and there’s no prospect
                       of that position changing.


                       In 2020, Apple began the Apple silicon transition,
                       using self-designed, 64-bit ARM-based Apple M1
                       processors on new Mac computers. Maybe it’s the
                       perfect time to move away from the proprietary
                       world of Apple, and embrace the open source Linux
                       scene.


                # § Programming/Development⠀➾


                      # ⚓ Linux Links ☛ 3_Top_Free_and_Open_Source_Ruby_Web
                        Frameworks_–_LinuxLinks⠀⇛


                             One of the types of software that’s important
                             for a web developer is the web framework. A
                             framework “is a code library that makes a
                             developer’s life easier when building
                             reliable, scalable, and maintainable web
                             applications” by providing reusable code or
                             extensions for common operations. By saving
                             development time, developers can concentrate
                             on application logic rather than mundane
                             elements.


                             A web framework offers the developer a choice
                             about how to solve a specific problem. By
                             using a framework, a developer lets the
                             framework control portions of their
                             application. While it’s perfectly possible to
                             code a web application without using a
                             framework, it’s more practical to use one.


                             Ruby is a general purpose, scripting,
                             structured, flexible, fully object-oriented
                             programming language with a focus on
                             simplicity and productivity. Ruby is a very
                             conservative language. It’s equipped with
                             very carefully chosen features that have been
                             fully tested.


                             When it comes to web development, there are a
                             fairly small range of Ruby frameworks to
                             choose. The choice depends on finding the
                             right tool for the job at hand. Here’s our
                             pick of the finest Ruby web frameworks.


                      # ⚓ GCC ☛ LoongArch_port_accepted_and_maintainers
                        appointed⠀⇛


                             I am pleased to announce that the GCC
                             Steering Committee has accepted
                             the LoongArch port for inclusion in GCC and
                             appointed Chenghua Xu and
                             Lulu Cheng as maintainers.

                             Please work with Richard Sandiford on the
                             final technical review and
                             approval of the patches.  Please coordinate
                             with the GCC Release
                             Managers for merging the port into the
                             development tree, hopefully for
                             inclusion in GCC 12 release.

                             Please join me in congratulating Chenghua and
                             Lulu on their new roles.
                             Please update your listing in the MAINTAINERS
                             file.

                             Happy hacking!
                             David
    * § Leftovers⠀➾


          o § Education⠀➾


                # ⚓ The_Rhodes_Scholars_Guiding_Biden’s_Presidency⠀⇛


                       The recent, pandemic-ridden years have involved a
                       steep and often traumatic learning curve for many
                       citizens across the Trans Atlantic. One
                       particularly shocking revelation that has ripped
                       virally across the internet in recent days revolves
                       around the revelations that the World Economic
                       Forum’s ‘Young Global Leaders’ have been positioned
                       across western governments and powerful private
                       institutions over the past three decades.


                       Videos of Klaus Schwab bragging that Young Leaders
                       have been positioned across the governments of
                       Canada, Argentina, Europe and beyond are now being
                       posted across social media platforms on a daily
                       basis, confirming the suspicions of many that the
                       World Economic Forum is not a benign business
                       networking operation, as it has tried to project
                       for the credulous. Rather, it is something much
                       darker and insidious.


                       Set up in 1993 as the Global Leaders of Tomorrow
                       and renamed WEF Young Leaders Forum in 2004 (fueled
                       with funds from such benevolent institutions as JP
                       Morgan Chase and the Bill and Melinda Gates
                       Foundation), over 1400 young leaders (under the age
                       of 38) from both public and private sectors have
                       been processed through the program. For those
                       tapped to become members of this elitist clique,
                       they agree to attend six years of regular WEF
                       conferences featuring seminars, focus groups and
                       other special experiences both at Davos and at
                       regional WEF events, at which point they graduate
                       and become “alumni” who, in turn, become capable of
                       nominating future young leaders.


                       Just a tiny sampling of the prominent figures who
                       have been processed and installed into positions of
                       influence to advance the WEF globalist agenda over
                       the past 30 years include Angela Merkel, Nicholas
                       Sarkozy, Emmanuel Macron, Tony Blair, Mark
                       Zuckerberg, José Manuel Barroso, Bill Gates,
                       Chrystia Freeland, Pete Buttigieg, Jacinda Arden
                       (PM New Zealand), Jack Ma (Ali Baba founder), Larry
                       Fink (Blackrock CEO), Larry Page (Google founder),
                       Lynn Forrester de Rothschild (Council for Inclusive
                       Capitalism founder), Jimmy Wales (Wikipedia
                       founder), Peter Thiel (Paypal founder), Leonardo Di
                       Caprio (tool), Richard Branson (Virgin Records
                       CEO), Jeff Bezos (Amazon founder), Stephan Bancel
                       (Moderna CEO), Pierre Omidyar (Ebay co-founder),
                       Alizia Garza (co-founder BLM), Jonathan Soros (son
                       of sociopath) and, according the Schwab, himself
                       “half the Canadian Cabinet” under Prime Minister
                       Justin Trudeau.


          o § Integrity/Availability⠀➾


                # § Proprietary⠀➾


                      # ⚓ Business Standard ☛ Microsoft_paying_hundreds_of
                        millions_in_bribes,_claims_whistleblower⠀⇛


                      # ⚓ International Business Times ☛ Whistleblower_Says_He
                        Lost_Job_At_Microsoft_For_Exposing_$200_Million_Foreign
                        Bribe_Scandal⠀⇛


                      # ⚓ Paul Thurrott ☛ Microsoft_Accused_of_Violating_the
                        Foreign_Corrupt_Practices_Act_Again [Ed: More on this,
                        even from Microsoft boosters]⠀⇛


                      # § Pseudo-Open Source⠀➾


                            # § Entrapment (Microsoft GitHub)⠀➾


                                  # ⚓ The Register UK ☛ GitHub_explains_outage
                                    string_in_incidents_update [Ed: The liars
                                    from Microsoft blame Free software for
                                    their proprietary software failing]⠀⇛


                                         Still, it’s not as if GitHub also
                                         chose this time to alienate large
                                         chunks of its customer base with
                                         an unpopular social-media-like
                                         algorithmic feed.


                      # § Security⠀➾


                            # ⚓ The Register UK ☛ How_AI_can_help_reverse-
                              engineer_malware:_Predicting_function_names_of
                              code⠀⇛


                                   Disassembling and analyzing malware to
                                   see how it works, what it’s designed to
                                   do and how to protect against it, is
                                   mostly a long, manual task that
                                   requires a strong understanding of
                                   assembly code and programming,
                                   techniques and exploits used by
                                   miscreants, and other skills that are
                                   hard to come by.


                                   What with the rise of deep learning and
                                   other AI research, infosec folks are
                                   investigating ways machine learning can
                                   be used to bring greater speed,
                                   efficiency, and automation to this
                                   process. These automated systems must
                                   cope with devilishly obfuscated
                                   malicious code that’s designed to evade
                                   detection. One key aim is to have AI
                                   systems take on more routine work,
                                   freeing up reverse engineers to focus
                                   on more important tasks.


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ The_Change_Game:_MeitY_Resorts_To_Quick_Fixes_To_Silence
                  Experts⠀⇛


                       On February 21, 2022, the Ministry for Electronics
                       & Information Technology (MeitY) published the
                       Draft India Data Accessibility & Use Policy, 2022.
                       Immediately, civil society experts pointed out
                       several flaws concerning data privacy and security
                       rights of citizens. To our shock, on March 6, 2022,
                       we noticed MeitY had made substantial changes to
                       the Draft India Data Accessibility & Use Policy,
                       2022, during the consultation period, without any
                       public acknowledgement. Effectively this resulted
                       in multiple versions of it, contracted the
                       consultation timeline, and confused stakeholders.
                       Responding to this, IFF wrote to MeitY indicating
                       the need for a fresh consultation process as these
                       actions have completely vitiated the ongoing
                       consultation process and led to an erosion of
                       public trust.


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