𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Tuesday, November 30, 2021
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Generated Wed 1 Dec 02:41:49 GMT 2021
Created by Dr. Roy Schestowitz (𝚛𝚘𝚢 (at) 𝚜𝚌𝚑𝚎𝚜𝚝𝚘𝚠𝚒𝚝𝚣 (dot) 𝚌𝚘𝚖)
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Latest in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕 and older bulletins can be found at 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕-𝒂𝒓𝒄𝒉𝒊𝒗𝒆𝒔
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Gemini index for the day: gemini://gemini.techrights.org/2021/11/30/


╒═══════════════════ 𝐑𝐄𝐂𝐄𝐍𝐓 𝐁𝐔𝐋𝐋𝐄𝐓𝐈𝐍𝐒 ════════════════════════════════════╕
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╒═══════════════════ 𝐈𝐍𝐃𝐄𝐗 ═══════════════════════════════════════════════════╕

⦿ A Concise Manifesto For Freedom-Respecting Internet | Techrights

⦿ [Meme] EPO Administrative Council Believing EPO-Bribed ’Media’ (IAM Still Shilling and Lying for Cash) | Techrights

⦿ IRC Proceedings: Monday, November 29, 2021 | Techrights

⦿ Video: Making the Internet a Better Place for People, Not Megacorporations | Techrights

⦿ Freenode.net Becomes a ’Reddit Clone’ and Freenode IRC is Back to Old Configurations After Flushing Down Decades’ Worth of User/Channel Data and Locking/Shutting Out Longtime Users | Techrights

⦿ Jack Dorsey’s Decision is a Wake-up Call: Social Control Media is Just a Toxic Bubble | Techrights

⦿ The EPO’s Mythical “Gap” Has Been Found and It’s Bonuses for People Who Use Pure Fiction to Steal From Patent Examiners | Techrights

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
		http://techrights.org/2021/11/30/freedom-respecting-internet/#comments
		http://techrights.org/2021/11/30/iam-propaganda-mill-2021/#comments
		http://techrights.org/2021/11/30/irc-log-291121/#comments
		http://techrights.org/2021/11/30/making-the-internet-better/#comments
		http://techrights.org/2021/11/30/reddit-complex-freenode/#comments
		http://techrights.org/2021/11/30/social-control-media-bubble/#comments
		http://techrights.org/2021/11/30/stealing-from-patent-examiners-and-applicants/#comments

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
		http://techrights.org/2021/11/30/github-downtime/#comments
		http://techrights.org/2021/11/30/tux-paint-0-9-27/#comments

                    ䷩ 𝚕𝚒𝚗𝚎 66

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/11/30/freedom-respecting-internet/#comments
    Gemini version at gemini://gemini.techrights.org/2021/11/30/freedom-respecting-internet/

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Gemini_version_available_♊︎


✐ A_Concise_Manifesto_For_Freedom-Respecting_Internet⠀✐


Posted in Free/Libre_Software, Standard at 10:32 am by Dr. Roy Schestowitz


The NON-Manifesto Manifesto, or a number of key points to consider


                         🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇The Wall⦈
      No more paywalls, artificial obstructions, and planned obsolescence


Summary: An informal list of considerations to make when reshaping the Internet
to better serve people, not a few corporations that are mostly military
contractors subsidised by the American taxpayers


    * All protocols should be secure by design; back doors, however “well-
      meant”, invalidate them and forbid their use in any shape or form
    * The Internet should be divided into protocols, each of which excels at
      one single thing
    * Pages should be treated as pages, not an as assembly of computer programs
      (tying them together on a canvas)
    * Pages should be made accessible to all, including blind people
    * Protocols and implementations should be Free (libre) software
    * A protocol is admitted and accepted only if many parties implement and
      deploy instances of it
    * Centralisation disqualifies oneself (e.g. one site monopolising a
      protocol)
    * Monoculture disqualifies oneself (e.g. one application monopolising a
      protocol)
    * Protocols and implementations must conform to a “least complex” attitude/
      principle; simplicity is to be favoured over supposed power, for the
      betterment and advancement of a true technical diversity
    * Anonymous access (e.g. Tor or unlogged sessions) should be permitted; in
      some countries it’s a matter of life or death
    * DNS should be considered not mandatory; there’s a broad range of
      alternatives to it and they should be actively encouraged
    * Geo-blocking is not permitted; it facilitates racism, which has no room
      in society
    * Parties that implement DRM should be shunned and led to failure, setting
      an example for anyone else wishing to follow their lead
    * Participation in military (including spy agencies’) programs subjects
      oneself to greater scrutiny, suspicion, and even prejudiced rejection
    * File and transmission neutrality should be presumed benign and desirable;
      it’s a violation of human rights to presume any user is a law-breaker
    * Censorship, including bans, should be considered a “last resort” subject
      to very strict standards and regarded as a highly exceptional
      circumstance; there are ways to repel unwanted people/views without
      outright bans
    * Copyright law should be dealt with as a potential barrier to
      preservation; when a last remaining copy online is no longer available
      online, it should be perfectly lawful for a party with an offline copy to
      upload it somewhere
    * Throttling or traffic-shaping should be advisory only; people can be
      encouraged, not forced, to limit or change their usage/utility of the
      network; this should be done transparently, not covertly, and not by
      network operators with a financial stake in the outcome (or business
      partners with a stake)
    * Any expansion of existing protocols should be done with diligence and
      care, taking into account compatibility with old devices, environmental
      factors, and a balance between advancement and this planet’s natural
      limits
    * Standards bodies dominated by large corporations (vendor capture) can be
      ignored and disregarded
⠀⠀⠀⡀⣰⣤⣾⠿⣚⣤⡊⣿⢻⡿⢃⣭⣶⡇⣿⣿⣿⣿⣿⣿⡛⠃⠺⣿⣿⣿⣿⠸⢛⣩⣵⠀⣿⣿⡻⢟⣡⣶⣾⣻⣿⣿⣿⣿⣿⡇⢸⣿⠟⠛⢉⣠⣤⣶⠀⢸⣿⣇⣠⣼⣿⣿⣿⣿⣽⣿⣿⣿⣿⣾⣟⡂⡀⠀
⣀⣐⣵⣾⣿⢋⠅⣾⣿⣿⠑⣫⣱⣾⣿⣿⣿⢸⣿⣿⣿⡿⠟⠁⠁⠀⠀⠙⢛⣭⣶⣾⣿⣿⣿⢸⣿⣯⣶⣵⣿⣿⣿⣿⣏⣿⣿⡿⠟⢃⣨⣤⣴⡿⣿⣿⣯⣿⠀⠈⡻⣿⣿⡿⣿⢿⣿⣿⡿⠻⣿⢻⠽⠅⠓⠁⠀⠀
⣿⣿⣿⣿⡟⡟⠀⠛⣩⣶⣿⣇⣿⡿⢟⣫⡄⣿⣿⠋⠁⣀⣤⣾⠀⡀⠀⠀⠈⠻⣿⣿⣿⣿⠯⠨⢓⣿⣿⣿⣾⣿⣿⡿⠟⣋⣥⣶⣾⣿⣿⣿⣿⣿⠟⣻⣽⣿⠀⢈⣾⣿⣿⣿⣿⠿⠗⠋⠀⠀⠀⠀⠀⢀⣴⢖⡊⣀
⣿⣿⣿⣿⣪⣴⣞⣡⣿⡿⢟⣨⣵⢸⣿⣿⢱⣿⣿⣧⣿⣿⣿⡟⣸⣷⡀⠀⠀⠀⠼⠟⠋⠁⠲⠿⢿⣿⣿⡿⠟⣋⠁⣶⣿⣿⣿⣿⣿⣟⣿⡿⠋⣽⣿⣿⣿⣿⠀⠘⠛⠋⠉⢀⢀⣄⣴⣶⣿⠄⠀⢀⣰⣿⣤⢾⣷⠃
⣿⣿⣿⣿⣿⡼⢟⣨⡅⣾⣿⣿⡏⣿⠿⣛⣻⣭⣷⡇⣿⣿⣿⡇⢿⣿⣿⣷⡄⡰⢸⣿⣿⣿⣿⣿⣟⣋⣥⣶⣿⣿⠀⣿⡿⠋⠙⣿⠏⢀⠌⡀⠈⠉⠀⠀⢁⣠⣤⣴⣶⣿⣿⣿⣿⣿⣿⢤⣽⡆⠀⢼⢿⢫⣻⣧⣿⡧
⣿⣿⣟⣋⡅⣶⣿⡟⢹⡿⢟⣫⣵⣶⣧⣿⣿⣿⣿⡇⣿⣿⠿⠑⠸⢿⣿⣿⢡⡇⣿⣿⣿⣿⣿⡿⢿⣿⣿⣯⣿⡟⢰⡟⠀⣀⡴⡍⠀⢀⣸⣦⣦⣦⣶⣶⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣻⡆⠀⢸⢮⣿⠟⠗⡻⡃
⣿⣿⣿⣿⢩⡿⢟⣣⣵⣆⣿⣿⣿⣿⣸⢿⢟⢫⣽⡆⡉⠒⡛⠀⢐⠠⠙⢣⢿⠀⠽⠛⣋⡍⢠⣶⣿⣯⣿⣏⣽⣄⠸⠏⠀⣠⠿⢗⣒⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠽⡇⠀⠈⡷⢋⠁⠪⠙⠔
⣿⡿⣛⣩⣶⢶⢿⣿⣿⢸⡿⠟⣛⣥⣶⣾⣿⢨⣿⣿⠃⣼⡆⠀⠤⠂⣀⣨⣴⡶⡒⣿⣿⠃⣿⣾⣿⠋⠁⢈⣉⣥⣶⣾⣿⡇⠀⠈⠊⣿⣿⣟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠉⠇⠀⠀⠀⣀⠀⡠⠀⠀
⡽⢧⣿⣿⡟⡾⠿⣛⣭⣴⡞⣾⣿⣿⣿⣿⡟⢸⣿⣿⠀⠁⠀⠀⢈⣥⣿⣿⣿⡿⣾⣿⣿⢀⣿⣿⡍⠀⣰⣿⣿⣿⣿⣯⣴⣥⣦⣔⡾⢿⣿⣿⣿⣿⣿⣿⣿⣻⠟⠓⠛⠚⠛⠉⢉⡁⣠⡄⢴⣶⣾⣋⣠⣍⢀⡆⠀⠀
⡛⠼⠛⣫⣵⣶⢻⣿⣿⣿⢷⣿⡿⠿⢛⣋⡄⣾⣿⠇⣤⠀⠀⠀⣀⣽⣯⣿⣿⣿⣿⠿⠟⠘⢛⣻⣷⣿⣿⣿⣿⣽⣯⣿⣿⣿⣿⣷⡧⠀⣿⠿⠟⠛⠛⠉⢁⣀⡄⠀⡔⣶⣿⣍⣯⣿⣿⣾⣿⡧⣽⣿⣺⣕⠻⠂⡠⠠
⣶⣿⢸⣿⣿⡟⣿⠿⠟⣛⣬⣵⣶⢸⣿⠿⠀⣿⡿⢰⣿⡇⠀⢸⠿⠟⠛⢋⢉⣡⣤⣶⣾⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⠿⠟⠁⠀⣀⣀⣤⣠⣦⣶⣿⢿⣿⣿⡇⢰⣿⣾⣿⣹⣿⣿⣿⣿⢿⣿⡵⣩⣭⢉⣜⢀⠡⡄
⡿⠃⠟⢛⣩⣥⣶⢲⣿⣷⣿⣿⣿⡈⣿⡟⢀⠿⠁⣈⣩⠁⠀⣴⣶⣾⣿⡇⣸⣽⣟⣿⣿⣿⡟⣡⣿⣿⠿⠟⠛⠁⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣽⣷⣿⣿⣿⠃⢨⣿⣟⣼⣿⣿⡿⣯⣥⣿⣿⣯⡓⣋⡖⣄⢘⠀⡁
⣶⣖⡌⣼⣿⣿⡟⣾⣿⣿⡿⠟⢙⣃⣡⣴⣾⣿⣿⣿⢿⠀⠀⣿⣿⣿⣿⠇⣼⣿⣿⣿⣿⣿⣯⣷⠧⢀⣠⣶⣟⢸⣿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⠀⠈⣭⣿⣿⣿⣿⣯⠻⣿⡷⣫⡎⣚⠚⡃⠊⠀⠀⠊
⣾⢿⢣⠿⠿⢛⣃⣩⣅⣶⣶⢿⢸⣿⣿⡿⣏⢻⣻⠻⡟⠀⢸⣿⣿⣿⣿⢀⠿⠿⠿⠛⠛⣋⣩⣯⢶⣿⠿⣿⡇⢸⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣩⠀⠸⣿⣿⣿⡯⣿⠟⠶⠊⠁⠁⠐⠐⠃⠉⠁⠁⢀⣀
⢩⣄⣶⡆⣼⣿⣿⣾⢹⣾⣯⡇⣾⡸⡗⠹⠉⠰⡜⢠⡇⠀⠘⣋⣉⣭⣤⣴⣶⣶⣿⡇⣸⣿⣿⣷⣿⠁⢀⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡿⠟⠛⠟⠛⠀⠈⠉⣉⢁⡀⣀⣠⡀⢀⠐⠀⠀⢶⡶⢆⣿⣻⣿⡛
⣼⣿⣿⢢⣿⡿⣿⡏⣿⡾⠿⠁⡏⡇⠰⠈⡀⣃⡇⢸⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣼⠃⣿⣿⣿⣿⣿⣶⣿⣿⡇⣿⣿⠿⠟⠈⠛⠛⠋⢉⣉⣠⣤⣤⣤⣶⡶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣎⠛⠀⠃⢻⢛⢋⢛⡛⡛⢬
⠿⠟⢓⣈⣋⣨⣭⣴⣶⣶⡞⢸⢓⠁⠄⠀⠄⠐⠀⡟⠀⠀⣨⣿⣿⣿⣿⣿⡿⣿⣿⠀⣫⣿⠿⠿⠛⢛⣋⣉⣠⣤⣤⣶⣆⣠⣾⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠖⠂⠀⢹⣛⣟⣘⣅⣡⡭
⢂⣿⡿⣾⡆⣽⣷⣟⣿⣯⠁⠐⠐⠀⠀⠀⠀⠈⢠⡇⠀⢸⣿⣿⣿⣿⠿⠟⠀⠛⠛⠘⠛⢻⣷⣾⣿⣿⣿⣿⣿⢧⣾⣿⣿⣿⣿⣿⠁⠿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⡿⡄⠀⢸⣛⣋⡽⣋⣩⣡
⣸⣾⣻⣿⢀⣷⣿⣿⣿⣿⠀⡄⠀⠀⠂⠀⠀⠀⢸⠀⠀⣨⣥⣤⣤⠀⢠⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣴⣿⢿⣧⣾⣿⣾⣿⣿⣿⣿⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡿⡏⠀⣅⢸⣿⣿⣣⢿⢍⣭
⣚⡋⣉⣭⣬⣭⢠⣤⡦⠆⢠⢱⡄⣆⢡⠶⢸⠘⣾⠀⠀⠘⠉⢘⢿⡇⣾⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣸⣾⠀⠘⣛⣍⡻⢛⠭⠍
⣾⢸⢻⣹⣟⡃⣾⣿⡣⠀⠘⠆⠠⠉⠘⠀⠎⠂⡇⠀⠀⣿⣻⣿⣿⠀⣿⣿⣷⣾⣿⣿⣿⣻⣿⣿⡿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠿⠟⠙⠿⠿⠿⠿⠛⠛⠛⠛⠋⠀⠉⠉⠉⠉⢉⣉⣉⣁⣀⣘⣟⣫⣄⠬⠿⢟
⡏⣿⢟⣿⣿⢀⣿⡾⠀⠀⠇⠀⠀⠀⠀⠀⠀⢸⡇⠀⢠⣌⣻⣿⣿⠀⣿⣿⣿⠋⠉⢻⣿⣛⠛⠛⠀⢉⣉⡉⣉⣉⣁⣀⣀⣤⣤⠀⠀⢀⣤⣴⣶⣶⡶⠖⣲⡶⠀⢀⢘⡻⠿⣿⣿⣿⣿⡿⠂⠠⡀⠀⠀⠈⠀⠀⠀⠀
⣻⣈⣉⣩⡁⡈⡉⠁⡀⢠⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢠⣤⣤⣤⣤⣤⣤⣦⣤⢀⢠⣶⣼⣿⣿⣿⣿⣿⣿⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣻⠽⣿⣿⡇⠀⢀⡦⡶⣄⣊⢻⢿⣿⣿⣿⣷⣤⢄⡅⠀⠀⢄⠀⠀
⣫⣏⣸⣿⢻⡋⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢨⣿⣿⣿⣿⣿⣗⣿⣻⡇⣸⣿⣿⣿⣷⣿⣿⣟⡟⠀⣸⣿⡿⣿⣿⣿⣯⣻⣿⣯⣽⣵⢿⠊⡖⠶⡟⡇⠀⡴⠥⡏⠮⠂⡰⠀⠛⢉⠛⠻⣟⣿⠌⠀⠀⠌⠀⠀
⣷⡇⣷⣿⡷⠧⣀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⢺⣏⣽⣶⣿⢛⣿⣿⣻⠀⣻⣿⣿⣿⣿⣿⣿⣿⡏⢀⣿⢿⣛⣿⣿⣿⣿⡿⣿⣶⣛⢧⣟⠇⠗⠀⠈⡤⠀⠃⡵⡊⠀⠀⠢⠀⠀⠀⠀⠢⣀⢸⠟⠤⡭⠀⠀⠀
⣛⣙⡺⠿⠴⠾⠿⠁⣤⡀⢀⠀⠀⠀⠀⠀⣸⡀⠀⠀⣾⣿⣿⣿⣿⣿⢻⣽⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⣿⣿⢻⣿⣿⣿⣿⠷⣿⡟⡿⣧⣃⢆⠂⠨⡀⠀⠀⠀⠻⣡⢐⠀⠀⠀⠀⠀⠀⠀⠀⢨⠄⠄⡇⢀⠠⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣧⣤⣂⠀⠀⠀⣉⣙⣛⣛⣛⡋⡙⠛⠛⠘⠟⠿⠿⠿⠿⠿⠏⠀⠀⢸⠻⠿⢾⢿⣿⣿⣿⣿⣿⣾⣿⣿⣭⣜⣙⣥⣦⣄⠀⣄⣔⣯⣶⣾⡎⡀⢀⠀⠀⠀⠀⢠⣠⠈⠕⡾⡢⠆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠈⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣅⣀⣭⣉⣉⣉⣉⣉⣉⣉⠉⢉⢉⠈⠉⠉⠛⠓⠐⠋⠀
⠙⠛⠛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶

                    ䷩ 𝚕𝚒𝚗𝚎 175

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/11/30/iam-propaganda-mill-2021/#comments
    Gemini version at gemini://gemini.techrights.org/2021/11/30/iam-propaganda-mill-2021/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 11.30.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ [Meme]_EPO_Administrative_Council_Believing_EPO-Bribed_‘Media’_(IAM_Still
Shilling_and_Lying_for_Cash)⠀✐


Posted in Europe, Patents at 3:04 pm by Dr. Roy Schestowitz


Same as always:


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


And again yesterday:


                      🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇iam-epo-bribed⦈_


                🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇I_don't_see_nuthin'_wrong⦈_


Summary: IAM continues to do what brings money from EPO management and Team
UPC, never mind if it_is_being_disputed_by_the_patent_examiners_themselves


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

                    ䷩ 𝚕𝚒𝚗𝚎 1373

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/11/30/irc-log-291121/#comments
    Gemini version at gemini://gemini.techrights.org/2021/11/30/irc-log-291121/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 11.30.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ IRC_Proceedings:_Monday,_November_29,_2021⠀✐


Posted in IRC_Logs at 2:58 am by Needs Sunlight


Also available via the Gemini protocol at:


    * gemini://gemini.techrights.org/tr_text_version/irc-log-techrights-
      291121.txt
    * gemini://gemini.techrights.org/tr_text_version/irc-log-291121.txt
    * gemini://gemini.techrights.org/tr_text_version/irc-log-social-291121.txt
    * gemini://gemini.techrights.org/tr_text_version/irc-log-techbytes-
      291121.txt
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
 QmaGJdr37G9767BGsyuViScrJwt32GxCecUcuy9gSScs2j #boycottnovell  🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell
 QmQk9CiKvSUVUBrAWVo4UV5BeubBrmYbrwi9LYEzk27yGD (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
                                                 #boycottnovell-
 QmdscT3TBKJPCYUqWK9YKSpJgMKvr53kPmoiN5A14ckYMq social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell-
 QmdGvEQ4xTWdiuMaJaS9HS5pRih4WQZWKhL8HnMb2174Df social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 (full IRC log
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
 QmZ8K4pNazQFjMRXtQesHGDxSJBDrEuMCgLav9pEMPwbGn #techbytes      🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #techbytes
 QmScPRkZzWeUK5AgySWJrMNQxwcwWRc5rrnNnFZoejEdX4 (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
 QmSze77M3Q9Qgir95dBRvgsePJXPFexThnWqpPdXMQYpZ1 #techrights     🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #techrights
 QmeBWgVeaBqy5mD39aajcEPeF3MrajFUvtSnMmDEcoRQtf (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇IPFS logo⦈


§ Bulletin for Yesterday⠀➾


Local_copy | CID (IPFS): QmWxGDdEJSbvkgneVRR2pbXgmVk3pi5U6cgy64gq54Dsi7



                    ䷩ 𝚕𝚒𝚗𝚎 1502

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/11/30/making-the-internet-better/#comments
    Gemini version at gemini://gemini.techrights.org/2021/11/30/making-the-internet-better/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 11.30.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Video:_Making_the_Internet_a_Better_Place_for_People,_Not_Megacorporations⠀✐


Posted in Free/Libre_Software, Standard at 2:16 pm by Dr. Roy Schestowitz


Video_download_link | md5sum 9b3296013dc70bcae4b1413d80f71328


http://techrights.org/videos/freeing-the-internet.webm


Summary: Following that_earlier_list_of_suggested_improvements_for_a_freedom-
respecting_Internet, here’s a video and outline


THE Web_has_become_very_spammy because it was gradually taken over by the
marketing_industry. The news industry barely exists anymore. This afternoon in
Daily Links we showed how IAM had in effect become a mouthpiece of EPO
management, after bribes from Benoît_Battistelli. It never said anything
negative about António_Campinos as if it’s a taboo subject. But that’s not even
a technical issue but an editorial issue.


“We hope to put out there some pointers not just for us but also for others to
follow.”On the technical side, e.g. a lack of consistent experience and
accessibility for blind people, the Internet as a whole got worse. There was no
quality control, except by corporations which judged quality from their own
narrow (self-serving) perspective.


In the video above I go through the list posted earlier and I elaborate a bit
on the spot. It’s perfectly possible we’ll put it in the wiki and
collaboratively improve/expand it some time in the near future. We hope to put
out there some pointers not just for us but also for others to follow. █



                    ䷩ 𝚕𝚒𝚗𝚎 1553

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/11/30/reddit-complex-freenode/#comments
    Gemini version at gemini://gemini.techrights.org/2021/11/30/reddit-complex-freenode/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 11.30.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Freenode.net_Becomes_a_‘Reddit_Clone’_and_Freenode_IRC_is_Back_to_Old
Configurations_After_Flushing_Down_Decades’_Worth_of_User/Channel_Data_and
Locking/Shutting_Out_Longtime_Users⠀✐


Posted in Free/Libre_Software at 8:55 am by Dr. Roy Schestowitz


Video_download_link | md5sum 8c867b7e71ba4c385076f14ad8a10079


http://techrights.org/videos/freenode-social-control-media.webm


Video errata: At least a couple of times I said “last year” when referring to
earlier this year; that’s what happens when there’s a lack of preparation and
no scripting/editing.


Summary: Freenode is having another go; after “chits” and “jobs” (among many
other ideas) have clearly failed, and following the change of daemon (resulting
in massive loss of data and even security issues associated with impersonation)
as well as pointless rebrand as “Joseon”, the domain Freenode.net becomes
something completely different and the IRC network reopens to all


THE year 2021 has been craaaaaaazy for IRC. What a wild ride! IRC used to be
uneventful; for decades it was “just there” with barely anything changing…


Recently, as we noted here 10_days_ago, IRC grew in terms of the number of
known (to netsplit.de) networks, based on some threshold/criterion (apparently
about 50 simultaneous users). Based on this_page, things have improved since
then (89 or 90 new networks, not 88 as before), but Freenode remains unlisted
because it shut out anonymous connections/sessions.


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Freenode at netsplit.de⦈ See the image on the right. Andreas
of netsplit.de seems to have gotten fed up with Andrew Lee and cut off the
network (writing it off as “legacy”) some time around August or earlier.


Well, not many have noticed it, but last week Freenode became accessible to
everyone again. Also, aside from some server names here and there, the “Joseon”
branding got abandoned. For many like myself who forgot to change IRC
configurations it became apparent that Freenode had sprung back to life and
that connections could be made again unconditionally (except for limits like
connections per IP address). Many like myself left it in the background,
perhaps unaware, and therefore reconnected silently some time after 4:25PM on
some arbitrary day last week. Within half an hour CrystalMath announced this in
our IRC networks and over in my IRC client (XChat) I saw:


* VLIST=b WATCH=32 WHOX :are supported by this server
* There are 7 users and 2478 invisible on 16 servers
* 6 :operator(s) online
* 47 :unknown connections
* 6029 :channels formed
* I have 1023 clients and 1 servers
* Current local users: 1023  Max: 1023
* Current global users: 2485  Max: 2485
* *.freenode.net message of the day
*   Hello, World!
*
*   Welcome to the
[...]
So it had about 2,000 registered users (before opening up Freenode to everyone,
once again). Then there was an influx or returning IRC clients, such as mine,
perhaps oblivious to what had actually happened.


CrystalMath, who has long maintained contacts at/within the new Freenode, told
us that someone called “epony” had left. Apparently this person was advising
Andrew Lee to limit network access; once that influence was gone the network
reopened. I show some of the scrollback in the video above.


Within a few days there were already 6,000 users online and now it’s over
10,000:


[11:36] [Users] There are 11 users and 10098 invisible on 16 servers
[11:36] [Users] 6 operator(s) online
[11:36] [Users] 33 unknown connections
[11:36] [Users] 13053 channels formed
[11:36] [Users] I have 4008 clients and 1 servers
[11:36] [Users] Current users on sunshine.freenode.net: 4008  Max: 4015.
[11:36] [Users] Current users on the network: 10109  Max: 10137


[11:37] [MOTD] Message of the day:
[11:37] [MOTD]   Hello, World!
[11:37] [MOTD]
[11:37] [MOTD]   Welcome to the
[11:37] [MOTD]           __                               _
[11:37] [MOTD]          / _|_ __ ___  ___ _ __   ___   __| | ___
[11:37] [MOTD]         | |_| '__/ _ \/ _ \ '_ \ / _ \ / _` |/ _ \
[11:37] [MOTD]         |  _| | |  __/  __/ | | | (_) | (_| |  __/
[11:37] [MOTD]         |_| |_|  \___|\___|_| |_|\___/ \__,_|\___|
[11:37] [MOTD]                                    AUTONOMOUS ZONE
[11:37] [MOTD]
[11:37] [MOTD]   Connect to us on:
[11:37] [MOTD]
[11:37] [MOTD]   Hostname: irc.freenode.net / chat.freenode.net
[11:37] [MOTD]   Plaintext: 6660-6669
[11:37] [MOTD]   TLS/SSL: 6697,7000,7070
[11:37] [MOTD]   Webchat: https://webchat.freenode.net
[11:37] [MOTD]
[11:37] [MOTD]   By connecting to freenode you indicate that you have read and
accept our
[11:37] [MOTD]   policies and guidelines as set out on https://freenode.net and
agree to
[11:37] [MOTD]   be scanned for an open proxy.
[11:37] [MOTD]
[11:37] [MOTD]   If you are looking for assistance, please try:
[11:37] [MOTD]
[11:37] [MOTD]   #help                    - Help with general IRC and Services.
[11:37] [MOTD]   #chanhelp                - Help with channels and channel
services.
[11:37] [MOTD]   #IRC                     - Help with the IRC.com by freenode
app.
[11:37] [MOTD]
[11:37] [MOTD]   Checkout some of our communities and services:
[11:37] [MOTD]
[11:37] [MOTD]   #freenode-bbs            - BBS [https://bbs.freenode.net/]
[11:37] [MOTD]   #freenode-bbs-discussion - BBS Discussion
[11:37] [MOTD]   #freenode-jobs           - Jobs [https://jobs.freenode.net/]
[11:37] [MOTD]   #freenode                - Chat about freenode.
[11:37] [MOTD]   #anonchan                - Chat anonymously.
[11:37] [MOTD]
[11:37] [MOTD]   Type /join #<channel>
[11:37] [MOTD]
[11:37] [MOTD]   Thank you for using freenode!
[11:37] [MOTD] End of message of the day
🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Freenode: We think we're Reddit⦈ But this is where it gets
really weird. About 10 minutes before recording the video someone brought up
(in IRC) the bizarre turn taken by the Freenode.net domain (for World Wide Web
or HTTPS). I spontaneously show the changes in the video above; it seems to be
in an experimental state, Lee is clearly involved in this (posting as “root”,
as usual), and it’s already going in a direction that’s guaranteed to alienate
most of the ordinary (traditional, old timers) tenants of the network. It’s not
about software, it’s already kind of edgy, and it’s not too clear what target
audience they have in mind.


Perhaps there’s a new “business plan”. Freenode becomes just a social control
network, which happens to have an IRC network ‘on the side’… with integration
to come. █


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

                    ䷩ 𝚕𝚒𝚗𝚎 2614

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/11/30/social-control-media-bubble/#comments
    Gemini version at gemini://gemini.techrights.org/2021/11/30/social-control-media-bubble/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 11.30.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Jack_Dorsey’s_Decision_is_a_Wake-up_Call:_Social_Control_Media_is_Just_a
Toxic_Bubble⠀✐


Posted in Deception at 7:45 am by Dr. Roy Schestowitz


Video_download_link | md5sum de4b7461663b0f628ad09b1e6e8d2c47)


http://techrights.org/videos/social-control-bubbles.webm


Summary: The state of the World Wide Web (reliability, preservation,
accessibility, compatibility etc.) was worsened a lot more_than_a_decade_ago;
with social control media that’s nowadays just a pile of JavaScript programs
we’re basically seeing the Web gradually turning into another Adobe Flash (but
this time they tell us it’s a “standard”), exacerbating an already-oversized
‘bubble economy’ where companies operate at a loss while claiming to be worth
hundreds of billions (USD) and generally serve imperialistic objectives by
means of manipulation like surveillance, selective curation, and censorship


THE traffic one gets in Twitter is rapidly decreasing, based not only on my_own
experience (as alluded to in the video above) but also the experiences of
friends whom I regularly speak to. Some of them only get about 10% the
“engagement” they got 5-10 years ago. Social control media is in general a bit
of a bubble; it was a thing back in the days, but people shift over to things
like TikTok at YouTube’s expense, looking for a new experience (under Alphabet
it became like television, there’s no “You” in YouTube) and Facebook keeps
buying companies in an effort to stay relevant. Jack Dorsey’s departure from
his leadership role isn’t due to some scandal; it is likely based on what he’s
seeing and not telling shareholders. It’s not often that we see founders
leaving their ‘baby’ (see “India-born_Parag_Agrawal_replaces_Jack_Dorsey_as
Twitter_CEO“; “Twitter’s_Jack_Dorsey_Steps_Down_From_C.E.O._Role“; “Twitter_co-
founder_Jack_Dorsey_to_leave_social_media_company“; “New_Twitter_CEO_Parag
Agrawal_is_central_to_Jack_Dorsey’s_plans_to_revamp_social_media“) unless that
baby has slim chances of surviving.


“The media rarely discusses those sorts of issues because it has a stake in the
status quo.”As we’ll note in the next batch of Daily Links (outline above),
Twitter’s founder and chief is stepping down. Most of Twitter’s history was
just endless losses and lawsuits, including a lawsuit from shareholders (over
Twitter faking its popularity). In recent years Twitter raised_money_from
criminals_in_exchange_for_reputation_laundering and it had actually made a bit
of money for a few years by giving a platform to extremists who spread hate and
misinformation.


Regardless of factors like audience size, we’re increasingly refocusing and
shifting emphasis to self-hosting (IRC, videos, textual publication etc.) while
adopting simpler protocols. Twitter became JavaScript-only about a year ago
(almost as bad as having a Flash site) and YouTube did the same around the same
time if not earlier. From Web pages they’ve moved to “web” “apps” and from
social they’ve moved to social control. This isn’t what the open Web was about
or what the World Wide Web was originally for (when a British scientist based
in Switzerland wanted to share his papers over the Internet).


The media rarely discusses those sorts of issues because it has a stake in the
status quo. Any shift or change is very expensive to those who are accustomed
to being the centre of attention. █



                    ䷩ 𝚕𝚒𝚗𝚎 2693

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/11/30/stealing-from-patent-examiners-and-applicants/#comments
    Gemini version at gemini://gemini.techrights.org/2021/11/30/stealing-from-patent-examiners-and-applicants/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 11.30.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ The_EPO’s_Mythical_“Gap”_Has_Been_Found_and_It’s_Bonuses_for_People_Who_Use
Pure_Fiction_to_Steal_From_Patent_Examiners⠀✐


Posted in Europe, Finance, Patents at 2:51 pm by Dr. Roy Schestowitz


Video_download_link | md5sum daa6c4b14f45f1292dcf04348028c109


http://techrights.org/videos/campinos-gap.webm


Summary: The phony president who has the audacity to claim there’s a budget gap
(see above) is issuing millions of euros for his enablers to enjoy; weeks ahead
of the next meeting of national delegates the Central Staff Committee (CSC)
tells them: “Events show that the delegations’ concerns about functional
allowances have materialised. The lack of transparency and inflation of the
budget envelope gives rise to the suspicion that high management is pursuing a
policy of self-service at the expense of EPO staff, which is difficult to
reconcile with the Office’s claimed cost-saving policy, and to the detriment of
the whole Organisation.”


The Central Staff Committee (CSC) of the EPO has sent António_Campinos a copy
of a letter about the same sort of thing we saw in the Benoît_Battistelli days.
The abusers take all the money, gamble with cash reserves illegally, and then
give themselves bonuses for these illegal acts.


Talking about spitting in your staff’s face…


The letter to the Chairman (of the Administrative Council) and heads of
national delegations is dated 4 days ago. EPO staff has been notified that “
[t]he Central Staff Committee (CSC) has sent this letter to the AC secretariat,
with a request to distribute it to the Heads of Delegations. Since 2015, the
budget envelope for functional allowances has inflated from 400.000€ to
2.370.000€.”


Remember similar things happened half a decade ago under Battistelli. We
covered that at the time. Campinos continues to prove he’s no better than
Battistelli and since both of them bribe and defang the media we no longer see
these issues aired in the media.


“The EPO is basically being robbed, exploiting the immunity by which managers
plunder everybody else with impunity.”The CSC continues: “While the number of
team managers and heads of department has increased in recent years, their
functional allowance remains frozen since 2018 at 360€ per month regardless of
grade. At the same time, from 2014 to 2021, the number of managers in the
Management Advisory Committee (MAC) increased from 8 to 30, and such members
are eligible for a functional allowance of up to two months’ salary per year at
the discretion of the President.”


“In addition to the financial aspects, functional allowances can also have a
deleterious effect on the functioning of the MAC and thus on the governance of
the Organisation. The MAC is the President’s advisory body and it advises him
on strategic or other important decisions. Most of its members (27 out of 30)
are however under the direct authority of the President and functional
allowances have accounted for a significant part of their remuneration since
2017. These circumstances can weaken the MAC as an advisory body, which is
expected to provide high-quality and objective advice in these areas of
strategic importance.


“Events show that the delegations’ concerns about functional allowances have
materialised. The lack of transparency and inflation of the budget envelope
gives rise to the suspicion that high management is pursuing a policy of self-
service at the expense of EPO staff, which is difficult to reconcile with the
Office’s claimed cost-saving policy, and to the detriment of the whole
Organisation.”


So there’s no lack of money, it’s just badly allocated. The EPO is wasting
money on stock market gambling (losing as much as 100 million euros per year in
past years) while insisting it cannot pay staff — i.e. people who do all the
work — as it did all along and as EPC standards generally demand (for talent
attraction and retention).


We’re reproducing the whole letter below as HTML:


     European Patent Office
     80298 Munich
     Germany


     Central Staff Committee
     Comité central du personnel
     Zentraler Personalausschuss


     centralSTCOM@epo.org


     Reference: sc21140cl


     Date: 26/11/2021


     To the Chairman and
     the Heads of Delegation of the
     Administrative Council of the
     European Patent Organisation


     OPEN LETTER


     Functional allowances at the EPO


     Dear Mr Chairman,
     Dear Heads of Delegation,


     After seven years of implementation, the New Career System (CA/D 10/
     14) is still a concern in terms of transparency for staff and proper
     consultation is still lacking. This year, for the first time, the
     budget for functional allowances was not even submitted to the
     General Consultative Committee (GCC) and the budget envelope was
     simply disclosed in an announcement published on the Intranet on 15
     October 2021. The details concerning the distribution and entitlement
     remain undisclosed. The Office also carried out a harmonisation
     reform without discussing it with the staff representation and
     without providing any details or basis for it. From the limited data
     available, the Central Staff Committee observes a trend towards less
     transparency and a continuous increase in the budget envelope.


     Back in 2014 when functional allowances were introduced, they were
     limited to a maximum of two steps1 per month of the relevant grade
     and applicable to employees in job groups 4, 5 and 6 called upon to
     perform additional duties or involving specific demands (Article 12
     (2) ServRegs)2. At the time, the Office explained3 that they would be
     used for rewarding managerial responsibilities not otherwise rewarded
     (e.g. heads of


     _________________
     1In 2014, the functional allowance of team leaders (e.g. for
     examiners) was set at 1,5 step in their grade per month, and thus
     below the maximum.
     2 CA/84/14, page 20/40, “New Career System”
     3 CA/84/14, par. 30


     =====================================================================
     department, team leaders), temporary extension of duties and specific
     constraints. Delegations expressed4 concerns about the lack of
     certainty on the entitlement5 and that a functional allowance would
     be difficult to withdraw even if the responsibilities end. They also
     saw a risk of inflation of the budget envelope. From 2015 to 2016,
     the budget envelope increased from 400.0006 € to 900.000 €7.


     In 2017, the Office proposed8 to extend functional allowances to job
     groups 1, 2 and 3 in order to open entitlement to managers9 and to
     increase the ceiling in view of a manager’s salary to two monthly
     basic salaries per year (namely around a 6-fold increase for higher
     grades). Delegations expressed10 concerns that this extension
     corresponds to 17% of yearly salary i.e. up to 35.000 € – 40.000 €
     for the higher job groups. The staff representation warned that a
     beneficiary could earn in practice a salary of an employee in a
     higher job group, i.e. one Principal Director becoming a Vice-
     President in terms of salary, under the exclusive authority and
     discretion of the President and without involvement of the Council.11
     From 2017 to 2021, the budget envelope continued to increase from
     1.400.000 €12 to 2.370.000 €13.


     While the number of team managers and heads of department has
     increased in recent years, their functional allowance remains frozen
     since 2018 at 360€ per month regardless of grade. At the same time,
     from 2014 to 2021, the number of managers holding the specific
     function of advising the President in the Management Advisory
     Committee (MAC) increased from 8 to 30, and such members are eligible
     for a functional allowance of up to two months’ salary per year at
     the discretion of the President.


     _____________
     4 CA/89/14 e, par. 17 & 22, “Draft minutes of the 110th meeting of
     the BFC” (20 November 2014)
     5 CA/96/14 e, par. 73, “Draft minutes of the 110th meeting of the
     BFC” (10/11 December 2014)
     6 GCC/DOC 12/2015
     7 GCC/DOC 16/2017
     8 CA/24/17 e, “Periodical review of the Service Regulations”
     9 CA/36/17 e, par. 102, “Draft minutes of the 151st meeting of the
     AC” (15/16 March 2017)
     10 CA/36/17 e, par. 103 and 105
     11 CA/36/17, par. 114
     12 GCC/DOC 16/2017
     13 Intranet announcement of 15 October 2021


     =====================================================================
     From a governance point of view, functional allowances can also have
     a deleterious effect on the functioning of the MAC. The President is
     assisted by the three Vice-Presidents14, who are appointed by the
     Administrative Council. On the other hand, the MAC is the President’s
     advisory body and it advises him on strategic or other important
     decisions15. Most of its members (27) are however under the direct
     authority of the President and functional allowances have accounted
     for a significant part of their remuneration since 2017. These
     circumstances can weaken the MAC as an advisory body, which is
     expected to provide high-quality and objective advice in these areas
     of strategic importance.


     Events show that the delegations’ concerns on functional allowances
     have materialised. The lack of transparency and inflation of the
     budget envelope gives rise to the suspicion that high management is
     pursuing a policy of self-service at the expense of EPO staff, which
     is difficult to reconcile with the Office’s claimed cost-saving
     policy, and to the detriment of the whole Organisation.


     The Central Staff Committee calls on the delegations to exercise
     their supervisory role over the Office to bring it to the proper
     standards of consultation and transparency.


     Yours sincerely,


     Alain Dumont
     Chairman of the Central Staff Committee


     cc.: President of the EPO
     _____________


     14Article 10(3) EPC
     15 See the Terms of Reference of the MAC


Maybe we’ll follow up on this soon, maybe as a video tomorrow. Either way, it
seems clear nothing is changing for the better. The EPO is basically being
robbed, exploiting the immunity by which managers plunder everybody else with
impunity. █



                    ䷩ 𝚕𝚒𝚗𝚎 2957

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 11.30.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_30/11/2021:_KDE_Plasma_5.23.4,_4MLinux_38.0,_Long_GitHub_Downtime,_and
Microsoft’s_CEO_Selling_Away_Shares⠀✐


Posted in News_Roundup at 12:30 pm by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


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


          o § Applications⠀➾


                # ⚓ Best_Torrent_Client_For_Linux_Based_Operating_Systems⠀⇛


                       The term “torrent” refers to file sharing through a
                       decentralized, peer-to-peer (P2P) sharing network.
                       Torrents are an excellent source to download large
                       files. P2P file-sharing protocols allow users to
                       exchange files without uploading them to the
                       server. They transform your PC into part of a host
                       where files are shared as it’s downloaded, so while
                       you’re downloading files from another host, you’re
                       likewise helping other people as they download the
                       part of the files that you have downloaded from
                       another host.


                       In this article, we are going to discuss or list
                       out the best torrent client for Linux-based
                       operating systems. So, if you are a Linux user and
                       looking for the best torrent client then you are at
                       the right place.


                # ⚓ What_is_Apache_Cassandra_|_Introduction_To_Cassandra⠀⇛


                       In this article, we are going to learn about NoSQL
                       concepts in high level as it’s family plays vital
                       role in the BigData market. We will also discuss
                       what is Cassandra which is the market leading NoSQL
                       DB, Cassandra architecture, key components and and
                       its use cases in detail.


                       In this article, we have gone through the overview
                       of NoSQL database concepts and basic architecture
                       of Cassandra. We will walk through the installation
                       of Cassandra in upcoming articles.


          o § Instructionals/Technical⠀➾


                # ⚓ How_to_install_Extreme_Tuxracer_on_a_Chromebook⠀⇛


                       Today we are looking at how to install Extreme
                       Tuxracer on a Chromebook. Please follow the video/
                       audio guide as a tutorial where we explain the
                       process step by step and use the commands below.


                # ⚓ How_To_Install_Google_Cloud_SDK_on_Linux_Mint_20_–_idroot⠀⇛


                       In this tutorial, we will show you how to install
                       Google Cloud SDK on Linux Mint 20. For those of you
                       who didn’t know, Google Cloud SDK (Software
                       Development Kit) provides a set of tools that are
                       used to manage resources hosted on Google Cloud
                       Platform (GCP). Good Cloud SDK presents a number of
                       important command-line tools such as gcloud, gsutil
                       and bq that enable effective management of
                       applications and other resources in the Google
                       Cloud


                       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 a Google Cloud SDK on a Linux Mint
                       20 (Ulyana).


                # ⚓ Shortcuts_for_adding_multiple_lines_of_text_to_files_on
                  Linux_|_Network_World⠀⇛


                       There are a number of ways to add text to files on
                       Linux systems without having to open an editor,
                       such as the echo and printf commands. On the other
                       hand, when you need to add A LOT of text, the
                       technique you use can make the job tedious or a
                       piece of cake.


                       This post describes some of the commands you can
                       use and the problems and benefits you can expect.


          o § Games⠀➾


                # ⚓ Party-based_RPG_Black_Geyser:_Couriers_of_Darkness_sees_a
                  huge_update⠀⇛


                       After entering Early Access in August, and then
                       releasing a Linux native version in October, Black
                       Geyser: Couriers of Darkness just got a nice big
                       upgrade for all players.


                       “Explore a land plagued by war, pestilence and
                       mysterious abductions, and uncover the hidden
                       legacy of your birth. Recruit powerful allies to
                       your cause; achieve your goals through sorcery,
                       stealth, a silver tongue or brute force; and
                       discover the truth of the Black Geyser.


                       Developed by a small indie team and inspired by
                       cRPG classics like Baldur’s Gate and Icewind Dale,
                       Black Geyser features challenging real time
                       tactical combat with pause, deep lore and memorable
                       companions, all set in a sprawling, unique fantasy
                       world.”


                # ⚓ Valve_puts_up_official_developer_FAQ_for_the_Steam_Deck_|
                  GamingOnLinux⠀⇛


                       With the Steamworks Virtual Conference: Steam Deck
                       over now, Valve has put up their own official set
                       of answers to various common questions.


                       Plenty of it we’ve already covered and explained in
                       previous articles like native versus Proton, and
                       expanded details on what we learned from the
                       conference. Still, it’s always good to have a few
                       reminders for people that missed it.


                # ⚓ Developing_A_Game_Engine_with_Perl_|_Shawn_
                  [blogs.perl.org]⠀⇛


                       To most in the know, coding a game engine with Perl
                       would be a surprise. I’ve certainly been asked,
                       “Why Perl?”. You see, unlike C++, C#, Java and
                       others, which are well established languages in
                       game engine design, Perl is not (well) known for
                       it’s role in the development of games. Especially
                       not as a game engine language. You are much more
                       likely to see Perl managing the network
                       infrastructure for the gaming industry then you are
                       to see it powering your favourite video games.


                # ⚓ NordicTrack_Patches_Out_‘God_Mode’_In_Treadmills_That
                  Allowed_Users_To_Watch_Anything_On_Its_Display⠀⇛


                       If you are a console gamer of a certain age, you
                       will remember the bullshit Sony pulled when it
                       patched its PS3 systems to remove useful features
                       it had used as selling points for the console to
                       begin with. Essentially, the PS3 had a feature that
                       allowed you to install another operating system on
                       it. This was used by hobbyists, companies, and the
                       US Military alike to creatively use PS3s for
                       purposes other than that for which they were built,
                       such as research supercomputers and creating
                       homebrew PS3 games. Sony later decided that those
                       features could also be used for piracy or other
                       nefarious actions and so patched it out. Sell the
                       console with a feature, remove it later after the
                       purchase… and then get sued in a class action, as
                       it turned out.


                # ⚓ GOG_to_go_through_some_reorganization_after_suffering
                  losses_|_GamingOnLinux⠀⇛


                       While Steam continues to do well with it being the
                       most popular games store, it seems CD PROJEKT
                       Group’s store GOG is really starting to struggle.


                       CD PROJEKT recently released their latest financial
                       results, along with a call with investors that went
                       over how the whole business is doing. It’s not all
                       bad news for them, since they saw overall 38% more
                       sales revenue compared to the third quarter of last
                       year. On the GOG side though, it posted increasing
                       losses and so it’s going to be restructured.


                # ⚓ GOverlay_for_editing_MangoHud_gets_a_new_Steam_Deck
                  friendly_UI_|_GamingOnLinux⠀⇛


                       GOverlay is an application that helps to manage
                       Linux gaming tools like the MangoHud performance
                       overlay, the Vulkan post-processing layer vkBasalt
                       and the video capture tool ReplaySorcery.


                       Over time GOverlay has supported an increasing
                       amount of options, and the UI ended up pretty
                       cluttered and confusing – not to mention it needing
                       a lot of monitor space. GOverlay release 0.7 goes a
                       long way towards fixing that, with a new tabbed
                       interface to spread things out a bit.


                # ⚓ Ubisoft_suggest_posting_on_their_forum_for_Proton_support
                  in_Rainbow_Six_Siege_|_GamingOnLinux⠀⇛


                       Now that getting games that use BattlEye for anti-
                       cheat working on Linux (either native or through
                       Proton) is much easier, an Ubisoft rep suggests
                       people post in their forum to show demand for it.


                       In response to a post on their official forum
                       asking about Ubisoft hooking it all up, the rep
                       mentioned they can pass the feedback onto
                       developers and that hopefully “other players will
                       reply here in favor of Proton support and the
                       development team may then look to implement it”.
                       It’s not exactly much and a pretty bog-standard
                       response but it’s a reply nonetheless and isn’t
                       being ignored.


          o § Desktop Environments/WMs⠀➾


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


                      # ⚓ KDE_developer_suggests_Plasma_needs_to_be_simpler_by
                        default⠀⇛


                             KDE developer Nate Graham, the same person
                             who recently said they may become the
                             “Windows or Android” of the FOSS world is
                             back again with more thoughts – this time
                             about keeping it simple.


                             The Plasma desktop is pretty darn powerful,
                             that’s for sure and it has a massive amount
                             of customization options for practically
                             every little thing. For many people this is
                             great, however it can also have a detrimental
                             affect on the experience by new users and
                             users less comfortable with computing. So
                             what’s the answer? Graham thinks they need to
                             keep things simpler out of the box.


                      # ⚓ Who_is_the_target_user?⠀⇛


                             As a teenager, I played a lot of Vampire the
                             Masquerade (VtM)–a tabletop role-playing
                             game. One of the skills in which your
                             character could become experienced was
                             Computers, with ability measured from 0 to 5
                             dots…


                             This little table has stayed with me over
                             time. As simple and crude as it is, I think
                             it provides a reasonable measurement scale
                             that can be used to guide software
                             development: you need to decide how many dots
                             in Computers a user must have before they can
                             use your software, which helps you organize
                             the user interface and prioritize features.


                             My sense is that currently most Linux-based
                             software targets people with three dots in
                             Computers or more, but is often usable for
                             people with two dots. My wife is a solidly
                             two-dot user who is happily using KDE Neon as
                             her distro.


                      # ⚓ A_Call_For_KDE_To_Fully_Embrace_Simplicity_By
                        Default,_Appeal_To_More_Novice_Users⠀⇛


                      # ⚓ KDE_Plasma_5.23.4,_Bugfix_Release_for_November⠀⇛


                             Tuesday, 30 November 2021. Today KDE releases
                             a bugfix update to KDE Plasma 5, versioned
                             5.23.4.


                             Plasma 5.23 was released in October 2021 with
                             many feature refinements and new modules to
                             complete the desktop experience.


                             This release adds three weeks’ worth of new
                             translations and fixes from KDE’s
                             contributors. The bugfixes are typically
                             small but important and include…


                      # ⚓ KDE_Plasma_5.23.4_Update_Brings_Back_the_Touchpad
                        Applet,_Fixes_More_Bugs⠀⇛


                             KDE Plasma 5.23.4 is here three weeks after
                             the KDE Plasma 5.23.3 update and it restores
                             the Touchpad applet that was previously
                             available in the Plasma 5.22 series. The
                             applet is now available as a read-only status
                             notifier that only shows when your laptop’s
                             touchpad has been disabled.


                             This point release also improves the Plasma
                             Wayland session to allow users to run
                             XWayland apps as a different user, improves
                             the Media Frame applet to display images from
                             folders that contain unusual characters like
                             backticks in their names, and improves the
                             notification about critical battery level to
                             automatically disappear when you connect your
                             laptop to its charger.


          o § Distributions⠀➾


                # ⚓ elementary_OS_6_Intros_a_Simpler_Alt_Tab_Experience⠀⇛


                       A recent update replaced the distro’s flashy (in
                       both senses of the word) alt + tab experience with
                       a simpler version. The new approach is more akin to
                       the sort of switchers found in other Linux desktop
                       environments and other desktop operating systems.


                       To better illustrate the change here’s a gif that
                       shows what window switching looked like in
                       elementary OS 6 previously…


                # § New Releases⠀➾


                      # ⚓ OSMC’s_November_update_is_here_with_Kodi_19.3_–
                        OSMC⠀⇛


                             At the end of the Summer, we released our
                             largest update ever delivering a new version
                             of Kodi, an improved video stack, support for
                             new Raspberry Pi models and a large number of
                             improvements and fixes.


                             Since then, we’ve been working hard to
                             deliver another significant update. This
                             update also features Kodi v19.3 which has a
                             number of bug fixes. One of the more
                             significant changes in Kodi v19.3 includes a
                             fix which improves the playback of videos
                             which have high-bitrate TrueHD tracks. This
                             would previously result in drop-outs when
                             playing back some titles with HD audio
                             passthrough enabled.


                      # ⚓ elementary_OS_6_Updates_for_November,_2021_⋅
                        elementary_Blog⠀⇛


                             This past week was Thanksgiving in the US,
                             which for my family means decorating for the
                             holidays is in full swing. In a similar vein,
                             we’ve spent some extra time over the past
                             month focusing on both visual and functional
                             polish to make sure elementary OS 6 looks as
                             good and works as well as it can—read on for
                             the details!


                      # ⚓ 4MLinux_38.0_Released_with_New_Apps,_Basic_Support
                        for_32-bit_Apps,_and_a_Games_Pack⠀⇛


                             Coming four months after 4MLinux 37.0, the
                             4MLinux 38.0 release is here to introduce
                             basic support for 32-bit apps, as well as a
                             new downloadable extension called 4MLinux
                             GamePack that includes a big collection of
                             classic Linux games, which you can download
                             from here.


                             It also comes with several new pre-installed
                             apps, including the Audacity audio editor,
                             Musique audio player, GQmpeg music player,
                             Minitube player for YouTube, wxCam webcam
                             app, xmp CLI module player, as well as the
                             GRUB2 bootloader.


                      # ⚓ 4MLinux_Releases:_4MLinux_38.0_STABLE_released.⠀⇛


                             The status of the 4MLinux 38.0 series has
                             been changed to STABLE. Edit your documents
                             with LibreOffice 7.2.3.2 and GNOME Office
                             (AbiWord 3.0.5, GIMP 2.10.28, Gnumeric
                             1.12.50), share your files using DropBox
                             133.4.4089, surf the Internet with Firefox
                             94.02 and Chromium 93.0.4577.82, send emails
                             via Thunderbird 91.3.2, enjoy your music
                             collection with Audacious 4.1, watch your
                             favorite videos with VLC 3.0.16 and mpv
                             0.33.1, play games powered by Mesa 21.1.6 and
                             Wine 6.19. You can also setup the 4MLinux
                             LAMP Server (Linux 5.10.79, Apache 2.4.51,
                             MariaDB 10.6.4, PHP 5.6.40 and PHP 7.4.25).
                             Perl 5.32.1, Python 2.7.18, and Python 3.9.4
                             are also available.


                # § Debian Family⠀➾


                      # ⚓ Linux_Mint_20.3_Arriving_Soon_with_a_Surprise_New
                        App⠀⇛


                             More updates available about what’s in store
                             for Linux Mint 20.3 “Una” with a gift from
                             the team – a new app.


                # § AWS⠀➾


                      # ⚓ Docker_Official_Images_Now_Available_on_Amazon
                        Elastic_Container_Registry_Public;_Completes
                        Integration_with_AWS_Graviton_Service⠀⇛


                             Docker extends confidence, security and
                             performance of trusted content and
                             architecture choice directly to AWS
                             developers


                      # ⚓ Canonical_Achieves_AWS_Graviton_Ready_Designation⠀⇛


                             Canonical, Publisher of Ubuntu, announced
                             today that it has achieved the AWS Graviton
                             Ready designation, part of the Amazon Web
                             Services, Inc. (AWS) Service Ready Program.
                             This designation recognizes that Canonical +
                             Ubuntu Server and Anbox Cloud Appliance has
                             demonstrated successful integration with AWS
                             Graviton Service.


          o § Devices/Embedded⠀➾


                # ⚓ AOI_System_Through_Workload_Consolidation_Brings_100X_Data
                  Transmission_Enhancement_–_EE_Times_Asia⠀⇛


                       When importing product inspections, a Linux-based
                       system with NVIDIA GPU runs inspection models for
                       image analysis. Because the two operating systems
                       are different, the company used two IPC systems to
                       conduct product quality inspections for the entire
                       AOI process.


                # § Mobile Systems/Mobile Applications⠀➾


                      # ⚓ The_Amazon_Appstore_is_broken_on_Android_12,_and
                        there’s_no_fix_in_sight⠀⇛


                      # ⚓ Samsung_One_UI_4.0_(Android_12)_update_tracker:
                        Eligible_devices_&_more⠀⇛


                      # ⚓ Samsung_One_UI_4.0_(Android_12)_update_bugs,_issues,
                        &_problems_tracker⠀⇛


                      # ⚓ TWRP_3.6_arrives_with_Android_11_support_and_faster
                        install_process⠀⇛


                      # ⚓ Which_Android_Root_App_is_Best?_|_Technology⠀⇛


                      # ⚓ Samsung_Galaxy_A71_gets_November_2021_Android
                        security_patch_–_Times_of_India⠀⇛


                      # ⚓ Nokia_T20_can_stop_the_budget_Android_tablet_market
                        from_drifting_aimlessly_–_Hindustan_Times⠀⇛


                      # ⚓ Fairphone_4_review:_The_most_repairable_Android
                        phone⠀⇛


                      # ⚓ YouTube_for_Android_TV_receives_a_new_playlist_UI⠀⇛


                      # ⚓ The_Realme_2_Pro_looks_just_like_one_of_our_favourite
                        Android_phones_ever⠀⇛


                      # ⚓ Wallpaper_Engine_is_now_available_for_Android_–
                        9to5Google⠀⇛


                      # ⚓ Android_Auto_starts_rolling_out_dual-SIM_support_–
                        9to5Google⠀⇛


                      # ⚓ Paranoid_Android_is_back_with_Android_12-based
                        Sapphire_builds⠀⇛


                      # ⚓ Google_offers_Lenovo_P12_Pro_discount_to_test_Android
                        12L_–_9to5Google⠀⇛


                      # ⚓ Vivo_Android_12_(Funtouch_OS_12/OriginOS/iQOO_UI_3.0)
                        update_tracker⠀⇛


                      # ⚓ Xiaomi_testing_MIUI_13_based_on_Android_11_and_12,
                        list_of_devices_in_tow_–_comments⠀⇛


                      # ⚓ How_to_Share_WiFi_on_Android_12_Using_Nearby_Share_–
                        TechPP⠀⇛


                      # ⚓ YouTube_TV_playlist_UI_added_to_smart_TV_app_–
                        9to5Google⠀⇛


                      # ⚓ Google_Voice_is_bringing_some_new_shortcuts_to_your
                        Android_home_screen⠀⇛


                      # ⚓ Android_Automotive_won’t_leave_you_hanging_next_time
                        you_need_to_voice-dial_for_help⠀⇛


                      # ⚓ Top_10_Best_Sports_Games_On_Android⠀⇛


                      # ⚓ Top_Android_Mobile_Casino_Games_2021⠀⇛


                      # ⚓ How_to_Choose_the_Best_Android_Spy_App_on_the
                        Market⠀⇛


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


                # ⚓ Raspberry_Pi_4_PLC_Industrial_controller_targets_IIoT
                  applications⠀⇛


                       I’ve just noticed Boot&Work Corp was now offering
                       an “Industrial Shields” branded PLC industrial
                       computer powered by Raspberry Pi 4 SBC. We
                       previously covered the company in 2017 at a time
                       when they provided Arduino-based PLC modules
                       optionally controlled with 10.1-inch panel PCs
                       based on ARM Linux SBCs such as Raspberry Pi or
                       Banana Pi.


                       The “Raspberry Pi PLC Industrial Controller” is
                       offered with either optoisolated outputs or relay
                       outputs, and optional GPRS connectivity. The Linux
                       PLC is equipped with up to 36 digital inputs, 16
                       analog inputs, 8 analog outputs, and 6 interrupts,
                       as well as communication interfaces such as CAN
                       bus, up to 2x Ethernet ports, dual RS-485, WiFi,
                       and Bluetooth.


                # § Programming/Development⠀➾


                      # ⚓ Responsively_App_Is_A_Browser_For_Fast_Responsive_Web
                        Development_(Free_And_Open_Source)⠀⇛


                             The application had its first public release
                             back in March 2020, and is already quite
                             popular, but I’ve only recently stumbled upon
                             it and thought I’d share it with you.


                             Main Responsively App features…


                             The application also includes a live CSS
                             editor, touch mode, design mode that allows
                             users to edit HTML directly without dev
                             tools, network speed emulation options, zoom,
                             disable SSL validation, and support for
                             various protocols (file://, ftp://, etc.),
                             and much, much more.


                             Using Responsively App, you also get network
                             proxy support, light and dark themes and
                             shortcut keys.


                      # ⚓ Musings_on_the_OWASP_Top_10⠀⇛


                             The recently released OWASP Top 10 – a
                             summary of the primary attack vectors used by
                             ne’er-do-wells has taken a somewhat different
                             approach than in previous years. As the
                             report states, “This instalment of the Top 10
                             is more data-driven than ever but not blindly
                             data-driven. We selected eight of the ten
                             categories from contributed data and two
                             categories from the Top 10 community survey
                             at a high level. We do this for a fundamental
                             reason, looking at the contributed data is
                             looking into the past. AppSec researchers
                             take time to find new vulnerabilities and new
                             ways to test for them. It takes time to
                             integrate these tests into tools and
                             processes. By the time we can reliably test a
                             weakness at scale, years have likely passed.
                             To balance that view, we use an community
                             survey to ask application security and
                             development experts on the front lines what
                             they see as essential weaknesses that the
                             data may not show yet.”


                      # ⚓ Spatial_AI_And_CV_Hack_Chat_|_Hackaday⠀⇛


                             A lot of what we take for granted these days
                             existed only in the realm of science fiction
                             not all that long ago. And perhaps nowhere is
                             this more true than in the field of machine
                             vision. The little bounding box that pops up
                             around everyone’s face when you go to take a
                             picture with your cell phone is a perfect
                             example; it seems so trivial now, but just
                             think about what’s involved in putting that
                             little yellow box on the screen, and how it
                             would not have been plausible just 20 years
                             ago.


    * § Leftovers⠀➾


          o ⚓ Giving_Josephine_Baker_a_Hero’s_Grave_Won’t_Bury_the_Truth…⠀⇛


                 As a student in Paris in the fall of 1990, my lodgings
                 were the envy of my peers—even if the means by which I
                 came about them were not. While fellow language students
                 from my university in Edinburgh were stuck in soulless
                 suburbs, I was ensconced in Rue des Fossés Saint-Jacques,
                 a short walk from the Jardin du Luxembourg and around the
                 corner from the Panthéon.1


          o § Hardware⠀➾


                # ⚓ Scrolling_Name_Badge_Is_Sure_To_Break_The_Ice_|_Hackaday⠀⇛


                       The badge runs on an ATtiny45 and uses three 8×8
                       ultra-bright LED matrices for scrolling [Madison]’s
                       name. It’s powered by a tiny LiPo battery that is
                       boosted to 5 V. This build really shows off a
                       number of skills, especially design. We love the
                       look of this badge, from the pink silkscreen to the
                       the typography. One of the hardest things about
                       design is finding fonts that work well together,
                       and we think [Madison] chose wisely. Be sure to
                       check it out in action after the break.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ Opinion_|_Omicron_Shows_Corporate_Media_Critics_of_China’s
                  Zero-Covid_Strategy_Are_Way_Off_the_Mark⠀⇛


                       As the new Omicron variant of Covid-19 threatens to
                       eviscerate the false sense of security that
                       political elites in many rich countries have felt
                       since vaccines were rolled out at the beginning of
                       the year, critics of China’s zero-Covid strategy
                       may want to carefully reflect on why they have been
                       so quick to dismiss Beijing’s stringent containment
                       measures.


                # ⚓ Opinion_|_Omicron:_Vaccine_Nationalism_Is_Prolonging_the
                  Pandemic⠀⇛


                       The United Kingdom and wealthy European nations are
                       in a panic. Unsurprisingly, hoarding huge swaths of
                       the global vaccine supply has enabled the emergence
                       of dangerous new variants of COVID-19. And once
                       again, rich countries are punishing the victims of
                       global vaccine inequality by slamming shut the
                       borders to anyone from southern African nations.


                # ⚓ WHO_Chief_Urges_Pandemic_Treaty_to_Avoid_Another_‘Crisis_of
                  Sharing_and_Solidarity’⠀⇛


                       As the World Health Organization warned of a “very
                       high” global risk posed by the Omicron variant of
                       Covid-19, representatives from the body’s 194
                       member states gathered in Geneva to forge a treaty
                       aimed at preparing the world for the next
                       pandemic—with public health officials warning that
                       the emergence of Omicron should push governments to
                       embrace global solidarity to avoid another
                       disastrous public health crisis.


                       “Vaccine equity is not charity; it’s in every
                       country’s best interests. No country can vaccinate
                       its way out of the Covid-19 pandemic alone.”


                # ⚓ Ireland’s_two-tier_health_insurance_system⠀⇛


                # ⚓ Unnecessary_and_Complicated_Transfers_Are_Spreading_COVID
                  in_Federal_Prisons⠀⇛


                # ⚓ Capitalism_Must_Not_Dictate_Our_Response_to_Omicron
                  Variant⠀⇛


                # ⚓ They_Knew_Industrial_Pollution_Was_Ruining_the
                  Neighborhood’s_Air._If_Only_Regulators_Had_Listened.⠀⇛


                       The white ranch house in Pascagoula, Mississippi,
                       was supposed to be Barbara Weckesser’s retirement
                       plan. In 2010, it was getting harder for the real
                       estate agent and her husband to climb the stairs of
                       their home on Dauphin Island, Alabama. She imagined
                       a quiet existence of gardening and puttering around
                       her porch. The Cherokee Forest subdivision seemed
                       like just the place to do it. Rabbits wandered the
                       lawns among the dozens of modest homes built in the
                       1960s and ’70s; families stayed put for decades.
                       The ranch was a fixer-upper, so the couple tackled
                       it together, installing drywall and hanging up new
                       doors and cabinets.


                # ⚓ Health_Justice_Advocates_Say_Vaccine_Equity,_Not_“Racist”
                  Travel_Bans,_Will_Stop_the_Omicron_Variant⠀⇛


                       We go to Cape Town, South Africa, to speak with a
                       leading health justice advocate about how
                       scientists in the country have identified a new
                       Omicron coronavirus variant, and the World Health
                       Organization warns it could be more transmissible
                       than previous variants. Against the advice of the
                       WHO, several countries have closed their borders to
                       foreign travelers. South African President Cyril
                       Ramaphosa criticized the travel bans and called on
                       wealthy nations to help poorer nations gain greater
                       access to COVID vaccines. The bans are “actually
                       quite racist,” says Fatima Hassan, founder and
                       director of Health Justice Initiative. “We need to
                       urgently … vaccinate as many people in Africa as
                       possible.”


                # ⚓ India’s_Farmers_Win_on_Many_Fronts,_Media_Fails_on_All⠀⇛


                # ⚓ Leonard_C._Goodman_lays_down_antivax_tropes_to_argue
                  against_vaccinating_children⠀⇛


                       I don’t know if I’ve mentioned this before, but I
                       spent three years at the University of Chicago in
                       the late 1990s, which is why I’m familiar with The
                       Chicago Reader. It’s one of those free alternative
                       weekly newspapers that most large cities have. (In
                       Detroit it’s the Metro Times.) Of course, things
                       change, and I haven’t lived in Chicago for over 20
                       years. I do, however, frequently visit because I
                       have family there and Chicago is a popular site for
                       medical meetings; so I have read the Reader from
                       time to time, although not recently. (Thanks to the
                       pandemic, I haven’t visited Chicago since the
                       summer of 2019, and I don’t often read the Reader
                       online.) Even so, I never would have expected what
                       a reader sent me, an article by a criminal defense
                       attorney named Leonard C. Goodman entitled Vaxxing
                       our kids. Let’s just say that if Mr. Goodman claims
                       not to be “antivax,” he sure does have a funny way
                       of showing it, given that he credulously parrots a
                       lot of COVID-19 antivaccine tropes, producing a
                       very high density of antivaccine misinformation for
                       a relatively short article.


                # ⚓ Dental_care_too_expensive_for_almost_half_of_the
                  population⠀⇛


                       Triinu Võlli would see all medical bills presented
                       to the Health Insurance Fund and not the patients.
                       While the benefits scheme has brought some clients
                       to visit the dentist, dentists have noticed that a
                       “some for all” approach still leaves some people
                       aside.


                # ⚓ South_Dakota’s_Governor_Succeeds_in_Blocking_Voter-Approved
                  Marijuana_Legalization⠀⇛


                       The court’s 4–1 decision does not affect Measure
                       26, which authorizes medical use of marijuana and
                       passed with support from 70 percent of voters last
                       November. But unless the state legislature
                       independently implements the policy embodied in
                       Amendment A, the ruling means supporters of broader
                       legalization will have to try again next year with
                       an initiative that addresses the court’s legal
                       objections.


          o § Integrity/Availability⠀➾


                # § Proprietary⠀➾


                      # ⚓ Microsoft’s_GitHub_back_online_after_two-hour
                        outage⠀⇛


                             Microsoft-owned open-source developer
                             platform GitHub is back online after
                             experiencing a more than two-hour-long
                             outage, affecting thousands or potentially
                             millions of developers that rely on its many
                             services.


                             GitHub started experiencing issues at around
                             3.45 p.m. ET on Saturday, with Git
                             operations, API requests, GitHub actions,
                             packages, pages, and pull requests all
                             affected, reports The Verge.


                      # § Security⠀➾


                            # § Privacy/Surveillance⠀➾


                                  # ⚓ Apple_Sues_NSO_Group_For_Targeting_IPhone
                                    Users_With_Powerful_Exploits⠀⇛


                                         NSO Group’s year from hell
                                         continues. Apple is now suing the
                                         Israeli exploit hawker for
                                         hacking its customers’ iPhones —
                                         customers who include not only
                                         the supposed terrorists and
                                         dangerous criminals NSO claims
                                         its customers target with
                                         malware, but also journalists,
                                         activists, lawyers, ex-wives,
                                         religious leaders, US citizens,
                                         and government officials NSO
                                         claims its customers don’t
                                         target.


                                  # ⚓ Yuval_Noah_Harari:_Lessons_from_a_year_of
                                    Covid⠀⇛


                                         Both Israel and the UK have
                                         subsequently been in the
                                         forefront of rolling out the
                                         vaccines, but their early
                                         misjudgments cost them dearly. In
                                         Britain, the pandemic has claimed
                                         the lives of 120,000 people,
                                         placing it sixth in the world in
                                         average mortality rates.
                                         Meanwhile, Israel has the seventh
                                         highest average confirmed case
                                         rate, and to counter the disaster
                                         it resorted to a “vaccines for
                                         data” deal with the American
                                         corporation Pfizer. Pfizer agreed
                                         to provide Israel with enough
                                         vaccines for the entire
                                         population, in exchange for huge
                                         amounts of valuable data, raising
                                         concerns about privacy and data
                                         monopoly, and demonstrating that
                                         citizens’ data is now one of the
                                         most valuable state assets.


                                  # ⚓ China’s_Twitter-like_Weibo_plans_$547
                                    million_Hong_Kong_listing⠀⇛


                                         US-listed Chinese microblogging
                                         platform Weibo is seeking to
                                         raise up to $547 million in a
                                         share offer in Hong Kong,
                                         documents showed Monday, the
                                         latest China tech company to list
                                         closer to home as tensions with
                                         the United States rise.


                                         Several US-listed Chinese tech
                                         firms such as Alibaba have held
                                         initial public offerings in Hong
                                         Kong over the past two years as
                                         the United States has stepped up
                                         scrutiny of Chinese companies.


                                  # ⚓ Is_“KAX17”_performing_de-anonymization
                                    Attacks_against_Tor_Users?⠀⇛


                                         As middle and exit relays are
                                         frequently changed the likelihood
                                         to use KAX17′s relays increases
                                         with tor usage over time. We have
                                         no evidence, that they are
                                         actually performing de-
                                         anonymization attacks, but they
                                         are in a position to do so and
                                         the fact that someone runs such a
                                         large network fraction of relays
                                         “doing things” that ordinary
                                         relays can not do (intentionally
                                         vague), is enough to ring all
                                         kinds of alarm bells.


          o § Defence/Aggression⠀➾


                # ⚓ The_NRA_Could_be_Winning_its_Long_Game_Even_as_it_Appears
                  to_be_in_Dire_Straits⠀⇛


                       On the one hand, more states are allowing Americans
                       to carry weapons in public without permits, and the
                       gun-rights movement could be on the verge of a
                       major Supreme Court victory. On the other, the
                       National Rifle Association, which advocates on
                       behalf of gun owners, faces an existential
                       crisisthat’s mostly due to the NRA’s own missteps.


                       As a political scientist who has studied gun
                       politics and policy for over 30 years, I’m
                       confident that there is no precedent for this
                       contradictory situation. Moreover, there’s no
                       reason to believe that the NRA’s problems will
                       influence how the courts treat gun-rights cases.


                # ⚓ ‘For_the_Sake_of_Peace,’_Anti-War_Groups_Demand_Biden
                  Return_to_Nuclear_Deal_With_Iran⠀⇛


                       As negotiations regarding Iran’s nuclear program
                       convened in Vienna on Monday, more than three years
                       after the U.S. walked away from an international
                       agreement, anti-war groups called on the Biden
                       administration “to choose the proven path of peace”
                       and re-enter the pact for the benefit of Iranians,
                       Americans, and the global population.


                       “We’ve delayed long enough,” said Sara Haghdoosti,
                       deputy director of the U.S.-based Win Without War.
                       “For the sake of peace, for the sake of prosperity,
                       for the security of people in Iran and the United
                       States alike, it’s time to put differences aside
                       and return to the Iran nuclear deal.”


                # ⚓ Lying_NYPD_Officers_Cost_Prosecutors_Sixty_More_Criminal
                  Convictions⠀⇛


                       Fighting crimes is easier when it’s not being done
                       by criminals. A bunch of cases are being tossed in
                       New York City because misbehaving NYPD officers
                       left their dirty handprints all over them.


                # ⚓ Iran_Says_US_Must_Lift_‘Tyrannical_and_Illegal’_Sanctions
                  to_Return_to_Nuclear_Deal⠀⇛


                       With Iran, China, European powers, and the U.S. set
                       to resume nuclear talks in Vienna on Monday,
                       Iranian negotiators made clear that the Biden
                       administration must lift crippling economic
                       sanctions if it hopes to return to the multilateral
                       deal that former President Donald Trump abandoned
                       in 2018.


                       “The Islamic Republic of Iran has entered the talks
                       with a strong will and elaborate preparations in
                       order to ensure the removal of unlawful and cruel
                       sanctions,” Ali Baqeri-Kani, Iranian deputy foreign
                       minister for political affairs and the nation’s
                       lead negotiator in Vienna, said Monday in an
                       interview with the IRIB News Agency.


                # ⚓ BLM_Co-Founder_Alicia_Garza:_Ahmaud_Arbery_Should_Still_Be
                  With_Us;_Biden_Must_Condemn_Vigilantes⠀⇛


                       After a Georgia jury reached a verdict of “guilty”
                       in the closely watched trial of three white men who
                       chased and fatally shot 25-year-old unarmed Black
                       man Ahmaud Arbery, many activists and racial
                       justice advocates following the case have expressed
                       some relief in hearing the conviction. We speak
                       with Black Lives Matter co-founder Alicia Garza,
                       who says while it might feel important that the
                       murders were held accountable for their actions,
                       “justice would be that Ahmaud Arbery would still be
                       with us today.” Garza also discusses the broader
                       context of other trials of white supremacists, like
                       Kyle Rittenhouse, and the role the federal
                       government can play. “Unfortunately, I think the
                       Biden-Harris administration could have been a lot
                       stronger in their condemnation of this kind of
                       behavior and activity,” says Garza. “But what we
                       saw was actually more of a milquetoast response,
                       which is especially concerning in this political
                       context of white nationalism and a rise in
                       vigilantism.”


                # ⚓ Placing_“Guardrails”_on_the_US-China_Nuclear_Competition⠀⇛


                       With the United States and China both speeding up
                       the acquisition of new nuclear weapons, some
                       analysts predicted that Presidents Joe Biden and Xi
                       Jinping would discuss limits on those munitions
                       during their virtual summit on November 15.
                       However, they barely touched on the matter,
                       agreeing only that both sides should take steps to
                       prevent the unintended escalation of future crises.
                       As Biden told Xi during their three-hour exchange,
                       the two sides need “commonsense guardrails to
                       ensure that competition does not veer into
                       conflict.” Yet no plans were made for negotiations
                       leading to the adoption of such measures, so the
                       US-China arms race will only gain further momentum.


                # ⚓ Mosul,_Destroyed_by_War,_Waits_to_be_Rebuilt_While_the_Hunt
                  for_Hidden_ISIS_Treasure_Goes_On⠀⇛


                       “A month ago, workers removing rubble from the
                       ruins near my house found black plastic bags full
                       of bank notes,” said Khalid, a 32-year-old resident
                       of west Mosul, where the destruction is at its
                       worst. “That is why reconstruction stopped
                       temporarily.” The two workers who found the cash
                       told him that the bags were splashed with mud and
                       scorched by fire, but that the bank notes inside
                       were undamaged.


                       Khalid says that six months earlier $1.6m (£1.2m),
                       along with gold and silver coins and ingots, were
                       found by building workers excavating a bombed-out
                       house. “Money and gold coins were found hidden in
                       barrels and plastic bags buried three metres
                       underground,” he said.


                # ⚓ Democrats_Push_to_Remove_Boebert_From_Committees_After
                  Islamophobic_Comments⠀⇛


                # ⚓ Omar_Hangs_Up_After_Boebert_Uses_Call_to_Double_Down_on
                  ‘Outright_Bigotry_and_Hate’⠀⇛


                       Congresswoman Ilhan Omar confirmed Monday that she
                       promptly ended a call with Rep. Lauren Boebert
                       because the Colorado Republican refused to publicly
                       apologize for her recent remarks about the
                       Minnesota Democrat and instead clung to her
                       Islamophobic rhetoric.


                       “Spewing this hate is as racist as it is
                       dangerous.”


                # ⚓ Where_the_Taliban_Rule⠀⇛


                       The Taliban’s own embrace of the media in recent
                       years — placing opinion pieces in The New York
                       Times and a cuddly representative in Doha during
                       talks with the U.S. government — while no more
                       self-serving than any other government’s, extends
                       as far as it can benefit the group’s cause but not
                       to independent outlets inside Afghanistan that
                       threaten to challenge it.


                # ⚓ British_F-35_crashed_into_sea_after_failing_to_take_off,
                  leaked_video_reveals⠀⇛


                       Given that the aircraft went down in about 1.24
                       miles of water, it is likely the search area on the
                       sea bed will be a circle of about four miles in
                       diameter. Royal Navy ships are remaining in the
                       area to deter anyone else trying to recover the
                       jet.


                       However, defence sources said while the jet would
                       have a locator device on board, the military would
                       not want to activate this amid concerns it could
                       alert rivals to its precise location.


                # ⚓ With_new_Omicron_variant_looming,_Republicans_are_now
                  bribing_people_to_avoid_vaccination⠀⇛


                       As Axios reported Monday morning, the concerted
                       efforts to keep shots from going in arms have
                       escalated in red states, with Republican
                       politicians now openly bribing constituents not to
                       get vaccinated. “Republican officials around the
                       country are testing a creative mechanism to build
                       loyalty with unvaccinated Americans while
                       undermining Biden administration mandates:
                       unemployment benefits,” the short piece explains.
                       “Florida, Iowa, Kansas and Tennessee have changed
                       their unemployment insurance rules to allow workers
                       who are fired or quit over vaccine mandates to
                       receive benefits.”


                # ⚓ GOP_courts_anti-vaxxers_with_jobless_aid⠀⇛


                       The backdrop: On Sept. 8, President Biden announced
                       a new rule requiring businesses with more than 100
                       employees to implement vaccine mandates, affecting
                       roughly 80 million private-sector workers, as well
                       as millions of federal workers and contractors.


                # ⚓ Taliban_and_9/11_Families_Fight_for_Billions_in_Frozen
                  Afghan_Funds_–_The_New_York_Times⠀⇛


                       Nearly 20 years ago, about 150 family members of
                       Sept. 11 victims sought a measure of justice for
                       their losses by suing a list of targets like Al
                       Qaeda and the Taliban. A decade later, a court
                       found the defendants liable by default and ordered
                       them to pay damages now worth about $7 billion.


                       But with no way to collect it, the judgment seemed
                       symbolic.


                       Today, however, the Taliban are back in control of
                       Afghanistan. The group’s leaders say their
                       country’s central bank account at the Federal
                       Reserve in New York, in which the former government
                       accumulated about $7 billion from foreign aid and
                       other sources, is rightfully theirs. And that in
                       turn has raised a question: If the money is the
                       Taliban’s, shouldn’t the plaintiffs in the Sept. 11
                       lawsuit be entitled to seize it?


                       High-level officials in the Biden administration
                       are now debating the answer to that question, which
                       presents a complex knot of national security,
                       legal, diplomatic and political problems — the
                       latest example of how thorny issues stemming from
                       the terrorist attacks remain unresolved more than
                       two decades later.


          o § Transparency/Investigative Reporting⠀➾


                # ⚓ Washington_Post_Forgets_It_Fought_(And_Won)_Legal_Battle
                  Against_Mandatory_Transparency;_Now_Demands_Internet_Co’s
                  Face_The_Same⠀⇛


                       A few years ago the Washington Post (and a bunch of
                       other newspapers) fought and won a fairly important
                       1st Amendment lawsuit to strike down as
                       unconstitutional a Maryland law that required news
                       organizations to publicly post information about
                       the political ads they chose to carry. The district
                       court and then the appeals court found that the law
                       was pretty clearly unconstitutional:


          o § Environment⠀➾


                # ⚓ At_COP_26,_A_Bigger,_Stronger_Climate_Movement_Made_Its
                  Mark⠀⇛


                       This column is part of Covering Climate Now, a
                       global journalism collaboration cofounded by
                       Columbia Journalism Review and The Nation to
                       strengthen coverage of the climate story.


                # ⚓ Opinion_|_Rich_Nations’_COP26_Failures_Are_Modern
                  Colonialism_at_Its_Worst⠀⇛


                       The refusal of the United States and fellow rich
                       nations to compensate developing countries for the
                       devastation wrought by air pollution and climate
                       change smacks of a kind of modern colonialism at
                       its worst.


                # ⚓ Cyber_Monday_Report_Reveals_Climate-Wrecking_Supply_Chain
                  of_US_Retail_Giants⠀⇛


                       As shoppers scoured the internet for holiday deals
                       on Cyber Monday, a pair of environmental groups
                       published a report that exposes the planet-heating
                       maritime shipping practices of four major global
                       retailers: Amazon, IKEA, Target, and Walmart.


                       “Pandemic-fueled demand increases, record-breaking
                       profits, and the supply chain crisis reveal the
                       current maritime shipping system is ripe for
                       transformation.”


                # ⚓ New_Research_Finds_Climate_Emergency_the_‘Overwhelming
                  Factor’_Behind_Australian_Bushfires⠀⇛


                       New research finds “a robust and multi-evidence
                       link” between the climate crisis and Australia’s
                       trend of worsening wildfires.


                       “We need to be ready for more Black Summers—and
                       worse.”


                # ⚓ Shell_Slammed_for_Plan_to_Blast_South_African_Coastline_for
                  Oil_and_Gas_During_Whale_Season⠀⇛


                       Environmentalists responded with outrage to reports
                       that oil giant Shell plans to spend the next
                       several months conducting underwater explosions to
                       search for deep-sea oil and gas reserves off South
                       Africa’s coastline—a move that threatens to worsen
                       the fossil fuel-driven climate crisis, undermine
                       the livelihoods of fishers, and harm marine life.


                       “Shell’s project has been allowed by our
                       government, as if the threat of global heating from
                       burning more and more fossil fuels doesn’t exist.”


                # § Energy⠀➾


                      # ⚓ Is_the_new_crypto_bill_the_end_of_the_tunnel_for
                        crypto-trade_in_India?⠀⇛


                             After a long-drawn debate regarding
                             regulating cryptocurrency, the much-awaited
                             “Banning of Cryptocurrency & Regulation of
                             Official Digital Currency Bill, 2019″ draft
                             was introduced in the Indian Parliament on
                             24th November, 2021.


                             The legislation is a brief, a 17-pager draft
                             with a slightly concerning title – with it
                             being named “Banning of Cryptocurrency”, it,
                             needless to say, dismayed many experts and
                             crypto[currency]-enthusiasts.


                             What does this draft Bill say?


                      # ⚓ Work_set_to_begin_on_cross-border_Finland_to_Sweden
                        rail_line⠀⇛


                             The project will electrify the Laurila-
                             Tornio-Haparanda section of the network,
                             thereby opening up a cross-border rail
                             connection between Finland and Sweden.


                             Haparanda station reopened for passenger
                             trains in March this year after a 29-year
                             break, offering connections to long-distance
                             trains in the south of Sweden.


                # § Wildlife/Nature⠀➾


                      # ⚓ Behind_the_Science:_How_Do_We_Know_How_Many_Shark
                        Species_Are_at_Risk?⠀⇛


                      # ⚓ Sen._Tester’s_Wilderness_Act_Doesn’t_Go_Far_Enough⠀⇛


                             Paid pollsters with their surveys tell us it
                             is a good thing. Businessmen looking for
                             government handouts tell us the same fairy
                             tale.  Yard signs in the well-healed, “smart”
                             parts of university towns – “donor-class”
                             neighborhoods — reinforce this narrow-minded,
                             virtue-signaling, herd mentality. Tester’s
                             collaborators pontificate, regurgitate.  It
                             must be so. But is it so?


                             “Stakeholders” (vested financial interests)
                             proclaim their alleged “…love our mountains,
                             valleys, rivers, fish, wildlife, and
                             everything else available on our public
                             lands.”  The difference between “love” and
                             “available” is the difference between loving
                             one’s spouse infinitely and loving a young
                             beauty rented from an escort service for a
                             one-night stand. Or if it is love, it is the
                             kind that sentimentalizes desire and calls it
                             love, where love is reduced to pity and an
                             unconscious desire for exploitation.


                      # ⚓ Scientists_peered_into_an_octopus’_brain_—_and_were
                        astonished_at_what_they_saw⠀⇛


                             Among the smartest animals on Earth,
                             octopuses are unique for being utterly weird
                             in their evolutionary path to developing
                             those smarts. Philosopher Peter Godfrey-Smith
                             has called the octopus the closest thing to
                             an alien that we might encounter on Earth,
                             and their bizarre anatomy speaks to this: An
                             octopus’ mind isn’t concentrated in its head
                             but spread throughout its body. Their
                             tentacles are packed with neurons that endow
                             each one with a hyperaware sense of touch, as
                             well as the ability to smell and taste.
                             Marine biologists have remarked that each
                             tentacle sometimes seems like it has a mind
                             of its own. Every octopus is a tactile
                             thinker, constantly manipulating its
                             surroundings with a body so soft it almost
                             seems liquid.


          o § Finance⠀➾


                # ⚓ Majority_of_Likely_Voters_Support_Higher_Taxes_for
                  Billionaires,_Poll_Finds⠀⇛


                # ⚓ Republicans_Who_Backed_Trump_Tax_Cuts_Now_Accuse_Dems_of
                  Slashing_Taxes_for_Rich⠀⇛


                # ⚓ Win_for_Alabama_Workers_as_NLRB_Orders_New_Union_Vote_After
                  Amazon’s_Alleged_Misconduct⠀⇛


                       In a victory for employees at an Amazon warehouse
                       in Bessemer, Alabama, a federal labor official on
                       Monday formally directed a new union election
                       following allegations that the company engaged in
                       illegal misconduct leading up to an unsuccessful
                       vote in April.


                       “Amazon workers deserve to have a voice at work,
                       which can only come from a union.”


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ The_Political_Marriage_of_Todd_Gitlin_and_Bill_Kristol⠀⇛


                # ⚓ Opinion_|_These_So-Called_“Moderate_Centrists”_Are_Nothing
                  But_Corporate_Extremists⠀⇛


                       Long ago, in a United States that now seems far,
                       far away, the coming-to-America story of Saule
                       Omarova would be hailed as a stirring endorsement
                       of our nation as a beacon for democracy seekers.
                       Born in 1966 under the Communist dictatorship of
                       the USSR, and raised under her Kazakh grandmother
                       who’d lost the rest of her family to Stalinist
                       purges, she grew up with a passion for Pink Floyd
                       and political dissent that caused her to stay here
                       in the U.S. after the Soviet regime collapsed while
                       she was a grad student in Wisconsin.


                # ⚓ Paperwork_Keeps_People_Poor⠀⇛


                       Months of negotiations over the Democrats’ agenda
                       in Congress keep boiling down to one thing: What
                       will Joe Manchin agree to? Since his vote is
                       necessary to pass the party’s Build Back Better
                       package, which includes funding on climate change,
                       health care, housing, and caregiving, the
                       conservative West Virginia senator has been calling
                       many of the shots.


                # ⚓ ‘Triumph_for_Democracy’:_Socialist_Candidate_Takes
                  Commanding_Lead_in_Honduran_Election⠀⇛


                       Leftist presidential candidate Xiomara Castro took
                       a decisive lead in Honduras’ election on Sunday,
                       setting her up to defeat the right-wing incumbent
                       party’s candidate—though progressive observers
                       stressed the need to remain vigilant as ballots
                       continue to be counted and reactionary forces ramp
                       up misinformation following an apparently
                       unsuccessful attempt to suppress voting.


                       “Xiomara Castro’s likely victory is a testament to
                       the will of the Honduran people to have their
                       voices heard and their votes counted.”


                # ⚓ How_Steve_Bannon_Has_Exploited_Google_Ads_to_Monetize
                  Extremism⠀⇛


                       Almost a year ago, Google took a major step to
                       ensure that its ubiquitous online ad network didn’t
                       put money in the pocket of Steve Bannon, the
                       indicted former adviser to Donald Trump. The
                       company kicked Bannon off YouTube, which Google
                       owns, after he called for the beheading of Anthony
                       Fauci and urged Trump supporters to come to
                       Washington on Jan. 6 to try to overturn the
                       presidential election results.


                       Google also confirmed to ProPublica that it has at
                       times blocked ads from appearing on Bannon’s War
                       Room website alongside individual articles that
                       violate Google’s rules.


                # ⚓ Matthew_McConaughey_Says_He_Won’t_Run_for_Governor_of_Texas
                  Next_Year⠀⇛


                # ⚓ Trump_May_Win_in_2024_If_Democrats_Keep_Derailing_Their_Own
                  Agenda⠀⇛


                # ⚓ Facebook_(Again)_Tells_Law_Enforcement_That_Setting_Up_Fake
                  Accounts_Violates_Its_Terms_Of_Use⠀⇛


                       Law enforcement agencies routinely engage in
                       surveillance of social media accounts. Some of this
                       is accomplished with third-party tools that use
                       keywords and geofences to give cops info that may
                       be relevant to investigations. These tools also
                       give cops a lot of garbage data that law
                       enforcement is free to sift through for officers’
                       own entertainment or to bypass constitutional
                       protections surrounding speech and warrantless
                       searches.


                # ⚓ The_Republicans_Have_Become_the_Party_of_Organized
                  Violence⠀⇛


                       On November 12, while promoting his new book,
                       Betrayal, ABC News reporter Jonathan Karl released
                       an audio recording of a conversation with Donald
                       Trump. Responding to a question about the Capitol
                       rioters who’d chanted “Hang Mike Pence,” Trump said
                       those words were just “common sense,” given the
                       fraudulence of the 2020 election. Two days later,
                       Wyoming Republican Senator John Barrasso, who ran
                       as a moderate but has since swung to the right, was
                       asked by ABC’s George Stephanopoulos about Trump’s
                       comment. Despite repeated prodding, Barrasso kept
                       dodging the issue, emphasizing the need to move on
                       and suggesting that there had been voting
                       irregularities in the 2020 election that merited
                       further investigation.


                # ⚓ Now_He_Tells_Us:_David_Brooks_Suggests_That_the_Republican
                  Party_Has_Embraced_Fascism⠀⇛


                       These US Rightist “intellectuals” have in fact
                       manufactured a “Left” that they can hate. It has
                       almost nothing to do with any historical Left but
                       is a convenient label for their fascistic attacks.
                       It seems tailored to take advantage of some of the
                       more divisive ideas of the Democrats, especially
                       their “identity politics.” (More on this below).
                       David Brooks points none of this out.


                       Brooks’ focus is on the fact that these current
                       younger “conservatives” have abandoned any idea
                       that political differences can or should be worked
                       out with rational or practical assessment of
                       policies. What once might have been seen in our
                       two-party system as political disagreements about
                       how best to serve the American people, have been
                       turned into irreconcilable antagonisms that cannot
                       be compromised. Brooks quotes their spokesperson,
                       Rachel Bovard: “Woke elites – increasingly the
                       mainstream left of this country – do not want what
                       we want. What they want is to destroy us.” Who are
                       these “woke elites”? They are a “totalitarian cult
                       of billionaires and bureaucrats….” Thus, the
                       Right’s target is constructed for broad appeal to a
                       mass of generally poorly informed individuals.
                       Anyone who is concerned with racism and police
                       murder, and who might have considered the long
                       history of these tools of rule is “woke.”
                       Billionaires and bureaucrats – who doesn’t abhor
                       these people? Yet there is no mention that their
                       new leader, Donald Trump, is an authoritarian
                       billionaire who fits this bill, and has constructed
                       a cult around himself.


                # ⚓ Microsoft_CEO_Nadella_sells_off_nearly_$300_million_in
                  shares_of_the_company⠀⇛


                       Nadella disclosed the sale in an SEC filing.


                       “Satya sold approximately 840,000 shares of his
                       holdings of Microsoft stock for personal financial
                       planning and diversification reasons. He is
                       committed to the continued success of the company
                       and his holdings significantly exceed the holding
                       requirements set by the Microsoft Board of
                       Directors,” a Microsoft spokesman said in a written
                       statement to the Journal.


                # ⚓ Ex-Pentagon_chief_says_Defence_Department_censoring
                  ‘tumultuous’_details_of_Trump_presidency⠀⇛


                       The former head of the Pentagon has sued the
                       Department of Defence, accusing the government of
                       blocking the publication of a new book revealing
                       the “tumultuous” consequences of Donald Trump’s
                       presidency.


                       Mark Esper filed a lawsuit against his former
                       employer for allegedly blocking the release of
                       large swathes in his upcoming memoir, A Sacred
                       Oath.


                # ⚓ Digital_group_says_govt_troll_move_will_not_decrease_hate
                  online⠀⇛


                       The Australian arm of a global initiative working
                       to counter digital threats to democracy says the
                       Federal Government’s proposed new rules to expose
                       online trolls will not solve the problem on online
                       hate on social media.


                # ⚓ Govt_promises_new_rules_to_force_online_firms_to_unmask
                  trolls⠀⇛


                       The Federal Government will put in place new rules
                       to force technology companies to identify anonymous
                       online trolls, or be exposed to the risk of
                       defamation payouts.


                # ⚓ India-born_Parag_Agrawal_replaces_Jack_Dorsey_as_Twitter
                  CEO⠀⇛


                       Agrawal, an IIT-Bombay and Stanford University
                       alumnus, was the chief technology officer of
                       Twitter before the elevation that caught investors
                       by surprise. Twitter stock went up by as much as
                       10% with the news in opening trade. The two most
                       powerful people at Twitter will now be India-
                       born—the other being Vijaya Gadde, its policy and
                       safety lead director.


                # ⚓ Twitter’s_Jack_Dorsey_Steps_Down_From_C.E.O._Role⠀⇛


                       Jack Dorsey is stepping down as chief executive of
                       Twitter, the social media site he co-founded in
                       2006 and guided through the tumultuous years of the
                       Trump administration.


                       Twitter announced Mr. Dorsey’s departure on Monday.
                       He is being replaced by Parag Agrawal, the
                       company’s current chief technology officer. Mr.
                       Dorsey’s plans were first reported by CNBC. A
                       Twitter spokeswoman did not respond to a request
                       for comment.


                # ⚓ Twitter_co-founder_Jack_Dorsey_to_leave_social_media
                  company⠀⇛


                       Twitter co-founder Jack Dorsey is going to leave
                       the company and is stepping down as chief executive
                       office (CEO) of the social media platform, he
                       announced on Monday. He will be succeeded by
                       Twitter’s current chief technology officer (CTO),
                       Parag Agrawal.


                # ⚓ New_Twitter_CEO_Parag_Agrawal_is_central_to_Jack_Dorsey’s
                  plans_to_revamp_social_media⠀⇛


                       Agrawal has been Jack Dorsey’s closest partner in
                       thinking about the future of the Twitter platform
                       and decentralizing social media, a former company
                       executive told CNBC.


                # ⚓ The_dangers_of_anarchy_in_space⠀⇛


                       I can’t think of a more dramatic illustration of
                       how reckless actions in space put all at grave risk
                       than Russia’s recent anti-satellite (ASAT) test
                       blowing up one of its own defunct satellites and
                       creating a cloud of more than 1,500 pieces of space
                       debris.


                       Even small pieces of debris, when traveling at some
                       17,000 miles per hour, can cause horrific damage to
                       satellites, disrupting the space infrastructure
                       that is the nervous system of modern life. Moscow’s
                       test forced astronauts (including its own
                       cosmonauts) on board the International Space
                       Station (ISS) to take emergency safety measures for
                       fear of collision. Moscow’s test followed a
                       similarly dangerous Chinese ASAT test in 2007, and
                       a U.S. ASAT test (though designed to minimize
                       debris) in 2008.


          o § Censorship/Free Speech⠀➾


                # ⚓ Frances_Haugen_will_testify_before_Congress_again_this
                  week⠀⇛


                       House Democrats announced that Facebook
                       whistleblower Frances Haugen will testify before
                       Congress a second time on Wednesday to discuss
                       possible legislative changes to tech’s
                       controversial legal liability shield, Section 230.


                       The House Energy and Commerce subcommittee on
                       communications and technology will hold the
                       upcoming hearing to discuss what Democrats are
                       referring to as “targeted reforms” to Section 230.
                       Several committee members have already introduced
                       bills that would create carve-outs in the law that
                       would make big tech companies like Facebook and
                       Google legally liable for algorithms that amplify
                       content that leads to offline violence.


                # ⚓ Communist_Party_cancel_culture_targets_internet
                  celebrities⠀⇛


                       There appear to be two targets. The first is a
                       business model with 4.9trn ($767bn) of annual
                       revenues, the fan economy, that has sprung up
                       around internet celebrities, fan groups and
                       streaming platforms. In the most recent set of
                       rules, issued in late November, the Cyberspace
                       Administration of China (CAC) said that brand
                       campaigns featuring celebrities will be allowed to
                       show advertisements only in designated ad spaces.
                       And from now on, China’s huge fan groups, often
                       with millions of fans apiece, are to come under
                       close monitoring by the authorities.


                # ⚓ An_introduction_to_Parag_Agrawal,_Twitter’s_new_CEO⠀⇛


                       Agrawal isn’t the most well-known of names either
                       inside or outside of Twitter. He’s been with the
                       company for over a decade, though, working his way
                       up from an engineer to become its top executive
                       (and a close friend of Dorsey’s). Agrawal first
                       started at Twitter back in October 2011 with a
                       focus on ad products, and he became the first
                       recipient of the company’s “Distinguished Engineer”
                       title. He was later appointed chief technology
                       officer in October 2017, during which time he’s
                       jumped in to address high-profile problems (like a
                       large-scale password security issue) and take on
                       some of the company’s bolder initiatives (like
                       decentralization). But despite that long tenure,
                       Agrawal, who is 37, hasn’t spent much time in the
                       public eye — something that will immediately change
                       with his new role.


                # ⚓ ‘Could_offend_students’:_Canada_school_board_cancels_book
                  club_event_with_Yazidi_Nobel_laureate⠀⇛


                       The event was supposed to carry discussion on two
                       books in presence of their authors — Marie Henein’s
                       ‘Nothing But the Truth: A Memoir‘ and Nadia Murad’s
                       ‘The Last Girl: My Story of Captivity, and My Fight
                       Against the Islamic State‘.


                       The board said it has withdrawn support to hold the
                       October event with Henein, the daughter of Egyptian
                       immigrants and one of Canada’s most prominent
                       lawyers, because her book was “problematic” as she
                       “defended” former CBC host Jian Ghomeshi when he
                       was accused of sexual assault.


                       For Murad’s event, which was to be held in February
                       2022, the board said the book written by her could
                       “promote Islamophobia” and “offend” their Muslim
                       students.


                       Murad, a Yazidi human rights activist, was 19 when
                       she was taken as a sex slave in 2014 by the Islamic
                       State militants who invaded her village in northern
                       Iraq.


                # ⚓ Disney+_appears_to_censor_episode_of_The_Simpsons_in_Hong
                  Kong_referencing_Tiananmen_Massacre⠀⇛


                       Online video streaming service Disney+ appears to
                       have censored an episode of The Simpsons in Hong
                       Kong which references the 1989 Tiananmen Massacre.


                       The 12th episode of the 16th season was first
                       broadcast in 2005 and sees the family visit China,
                       where the cartoon family visits the mummified body
                       of ex-leader Mao Zedong. The newly-launched Disney+
                       platform skips from episode 11 to 13.


                # ⚓ Disney+_Drops_‘Simpsons’_Episode_in_Hong_Kong_Because_of
                  Tiananmen_Square_Joke⠀⇛


                       The 16th season of the iconic Fox animated show
                       jumps from episode 11 to 13 when viewers in the
                       city browse the flagship Disney streaming service.
                       The missing episode 12, first broadcast in 2005,
                       happens to be the one where Homer takes his family
                       to China, where they visit Tiananmen Square and
                       come across a placard that reads: “On this site, in
                       1989, nothing happened.”


                       It appears the episode has suffered precisely the
                       kind of the censorship it was written to ridicule.


                # ⚓ Disney+_Omits_‘The_Simpsons’_Tiananmen_Episode_in_Hong
                  Kong⠀⇛


                       In the missing episode, “Goo Goo Gai Pan,” the
                       cartoon family visits the Beijing square where a
                       character confronts a line of tanks — a reference
                       to the famous Tank Man photograph — and a sign
                       reads “Tien An Men Square: on this site, in 1989,
                       nothing happened.”


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


                # ⚓ When_The_FBI_Shows_Up_At_Your_Door_About_Your_Reporting,
                  That’s_Intimidation⠀⇛


                       Having the government show up at your door to ask
                       some questions about your reporting can be
                       extremely unnerving. Zack Whittaker, the top notch
                       cybersecurity reporter for TechCrunch got to
                       experience the fun of that when the FBI showed up
                       at his door over a year after he had published a
                       story about a hacker dumping thousands of Mexican
                       embassy documents from Guatemala after the Mexican
                       embassy left the data exposed online.


                # ⚓ China_surveillance_of_journalists_to_use_‘traffic-light’
                  system⠀⇛


                       Documents seen by BBC News describe a system that
                       classifies journalists into a “traffic-light”
                       system – green, amber and red.


                       Journalists in the “red” category would be “dealt
                       with accordingly”, they say.


                       The Henan Public Security Bureau has not responded
                       to a request for comment.


                       The documents, discovered by the surveillance
                       analyst firm IPVM, also outline plans to surveil
                       other “people of concern”, including foreign
                       students and migrant women.


                       Human Rights Watch said: “This is not a government
                       that needs more power to track more people…
                       especially those who might be trying to peacefully
                       hold it accountable.”


          o § Civil Rights/Policing⠀➾


                # ⚓ Calls_Grow_to_Drop_Murder_Charges_Against_Black_Teen
                  Chrystul_Kizer_in_Kenosha⠀⇛


                # ⚓ Off_to_the_Solomon_Islands:_Australia’s_Civilizers_Get
                  Busy⠀⇛


                       In the Solomon Islands, Australian interventionism
                       was originally cloaked in shining dress, justified
                       as humanitarian and utterly noble.  By the time
                       some 2,000 troops, police officers and support
                       personnel, mostly Australian, were deployed in
                       2003, the country had already mounted regional
                       interventions in Bougainville in Papua New Guinea
                       (1997) and East Timor, the latter as part of a UN-
                       mandated mission.


                       The Regional Assistance Mission to Solomon Islands
                       (RAMSI) was given a rhetorical flourish of
                       preventing a “failed state” while easing Australian
                       anxieties in a region marked by a supposed “arc of
                       instability”.  In a conscious nod to making sure
                       the mission would be seen benevolently, the PR pen
                       pushers came up with the pidgin named Operation
                       Helpem Fren.


                # ⚓ A_Place_of_Freedom⠀⇛


                       Upon its publication in 1975, Gayl Jones’s literary
                       debut, Corregidora, was met with great acclaim.
                       Jones’s mentor and teacher, the poet Michael
                       Harper, had introduced her work to his friend, the
                       editor and novelist Toni Morrison, who published
                       Corregidora and also Jones’s second novel, Eva’s
                       Man, the following year. Still in her mid-20s,
                       Jones was immediately heralded for her genius by
                       readers as diverse as James Baldwin and the New
                       York Times critic Raymond Sokolov. Part of what
                       drew them was what Sokolov referred to as her
                       “nonchalance” and “ease” of style, which served as
                       her fiction’s “consummate deception.” Writing with
                       a clarity and matter-of-factness that quietly
                       understated her work’s difficulty, Jones often
                       relayed moments of intense brutality with a kind of
                       quotidian ordinariness.


                # ⚓ In_An_Even_Marginally_Healthy_Society⠀⇛


                       He understood perfectly! All forms of encompassing,
                       emphatic, and egalitarian justice certainly are the
                       most reasonable things of all. And, as such, they
                       always have within themselves the possibility of
                       being understood and lived by people in just this
                       way. Yet, there are so many deeply sedimented
                       socio-historical, socio-economic, and socio-
                       existential structures that keep some people from
                       the exclamation of my nephew that day. A realized
                       egalitarian and equitable social formation that has
                       maximized justice and goodness to the fullest
                       extent possible by our very imperfect species that
                       will always be entwined with social antagonisms,
                       would truly be the most reasonable social formation
                       of all—civilizationally, historically, and
                       anthropologically.


                       I have, subsequent to the moment when my nephew
                       made his exclamation, taken pleasure in narrating
                       this episode because there was something special in
                       what he said and how he said it and it immediately
                       linked his statement with another extremely
                       resonant statement, the one in which Kwame Ture in
                       his book, Ready For Revolution: The Life And
                       Struggles Of Stokely Carmichael, described the
                       Freedom Rides of l961 (at 19 years of age
                       Ture—Stokely Carmichael at the time—was the
                       youngest of the Freedom Riders): “The plan,
                       however, was simplicity itself. In any sane, even
                       half-civilized society it would have been
                       completely innocuous, hardly worth a second thought
                       or meriting any comment at all. CORE would be
                       sending an integrated team–black and white
                       together–from the nation’s capital to New Orleans
                       on public transportation. That’s all. Except, of
                       course, that they would sit randomly on the buses
                       in integrated pairs and in the stations they would
                       use waiting room facilities casually, ignoring the
                       white/colored signs. What could be less harmless…in
                       any even marginally healthy society?”


                # ⚓ Europe’s_War_on_Woke⠀⇛


                       Paris—On my 32nd birthday, I agreed to appear on
                       Répliques, a popular show on the France Culture
                       radio channel hosted by the illustrious Alain
                       Finkielkraut. Now 72 and a household name in
                       France, Finkielkraut is a public intellectual of
                       the variety that exists only on the Left Bank: a
                       child of 1968 who now wears Loro Piana blazers and
                       rails against “la cancel culture.” The other guest
                       that day—January 9, less than 72 hours after the US
                       Capitol insurrection—was Pascal Bruckner, 72,
                       another well-known French writer who’d just
                       published “The Almost Perfect Culprit: The
                       Construction of the White Scapegoat,” his latest of
                       many essays on this theme. Happy birthday to me.1


                # ⚓ Self-Defense?_After_Rittenhouse,_Calls_to_Drop_Murder
                  Charges_Against_Black_Teen_Chrystul_Kizer⠀⇛


                       Since Kyle Rittenhouse was acquitted under claims
                       of self-defense for fatally shooting two people and
                       wounding a third during racial justice protests
                       last year in Kenosha, Wisconsin, another case in
                       the city is drawing new national attention. Human
                       rights advocates are calling for charges to be
                       dropped in the case of Chrystul Kizer, who faces
                       homicide and other charges for killing her white
                       sex trafficker in 2018 after he drugged her and
                       tried to rape her when she was just 17-years-old.
                       Court records show police knew Randall Volar had a
                       history of sexually abusing underage Black girls.
                       Although the court initially ruled Kizer could not
                       use a self-defense argument, an appellate court
                       reversed the decision and the Wisconsin Supreme
                       Court will now consider the ruling. “It has huge
                       ramifications for her, but it also has a huge
                       potential impact for other victims of trafficking,”
                       says reporter Anne Branigin. “We have a very clear
                       case where we are not receiving the same support,
                       the same outcry from folks who got behind Kyle
                       Rittenhouse to defend this young Black woman,” says
                       Wisconsin state representative David Bowen. “She
                       was trying to defend herself to get out of the sex
                       trafficking she was being abused with.”


                # ⚓ Cornel_West_Moments_of_Interruption⠀⇛


                # ⚓ Digital_ID_expert_says_reducing_cyber_crime_will_need_new
                  thinking⠀⇛


                       H. Daniel Elbaum, chairman and joint chief
                       executive of VeroGuard, said the Joint Policing
                       Cybercrime Co-ordination Centre, announced by the
                       Federal Government on Monday, was a welcome
                       initiative.


                       But, he added, PwC modelling had estimated the
                       direct costs to business from cyber incidents to be
                       about $10.1 billion annually, with projections of a
                       total GDP loss of $114.9 billion by 2031.


                # ⚓ He_stole_a_rug_and_a_car._Why_did_he_spend_25_years
                  bouncing_between_prison_and_parole?⠀⇛


                       In America, a person under supervision – either as
                       an alternative to prison (probation) or a condition
                       of their release from one (parole) – can face as
                       many as 30 rules that range from vague to
                       “bizarrely specific”, according to a 2017 law-
                       review article by a lawyer at the American Civil
                       Liberties Union (ACLU). These provisions include
                       observing a curfew, refraining from being around
                       guns or anything that looks like a gun, disclosing
                       monthly bank-account statements, avoiding other
                       people with criminal records (including family
                       members), not having more than $100 cash in your
                       wallet, keeping a job, supporting one’s family,
                       getting approval to use knives at work from a
                       parole agent and carrying those knives only while
                       at work or travelling to and from work.


                       The net effect of these rules is a “nearly
                       impossible burden”, the ACLU lawyer wrote. People
                       have to navigate the narrow strait between “the
                       Scylla of failure to check in and the Charybdis of
                       unemployment”. More pointedly, as civil-rights
                       scholar Michelle Alexander wrote: “Today a criminal
                       freed from prison has scarcely more rights, and
                       arguably less respect, than a freed slave or a
                       black person living ‘free’ in Mississippi at the
                       height of Jim Crow.”


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ The_Law_Bytes_Podcast,_Episode_110:_Waiting_to_Connect_–
                  Karen_Barnes_and_Catherine_Middleton_on_the_CCA’s_Report_on
                  Internet_Access_in_Canadian_Rural,_Remote_and_Indigenous
                  Communities⠀⇛


                # ⚓ Cable_Giant_Spectrum_Endangered_Its_Employees_And_Screwed
                  Its_Technicians_During_COVID⠀⇛


                       Most broadband providers saw a major uptick in both
                       subscribers and revenue during the COVID crisis, as
                       working and schooling at home exploded. But at the
                       regional monopolies that dominate the U.S. telecom
                       sector, revenue most assuredly didn’t go to
                       employees at most of these major companies. In
                       fact, Gizmodo has a new report highlighting how
                       cable giant Charter (whose broadband and TV
                       services are sold under the Spectrum brand) doubled
                       its revenues last year thanks to COVID, yet found a
                       way to dramatically reduce pay for its field
                       technicians:


                # ⚓ Advocates_Call_for_Universal_Service_Fund_to_Include
                  Broadband_Revenues⠀⇛


                       A broad swath of organizations on Monday is calling
                       for policymakers in Washington to reform and
                       stabilize the Universal Service Fund by broadening
                       its funding base to include broadband revenues.


                       The Universal Service Fund, which supplies the
                       nation’s low-income and rural and remote
                       communities with basic telecommunications services,
                       currently relies on voice service revenues, which
                       has been a dwindling for years. Debate has emerged
                       about how the fund can be stabilized, with some
                       asking for the money to come from a congressional
                       budget item and others asking for it to come from
                       broadband revenues.


          o § Monopolies⠀➾


                # ⚓ What’s_at_Stake_at_WTO⠀⇛


                       One would think that every global institution, and
                       particularly one whose rules govern trade in
                       vaccines, medicines, and other medical products
                       necessary to end COVID-19, would be doing
                       everything in its power to contribute towards
                       ending this horrendous pandemic.


                       Unfortunately, we are talking about the WTO, where
                       the protection of billionaires’ intellectual
                       property monopolies, intended to reduce supply and
                       increase prices, are sacrosanct. Developing
                       countries introduced a proposal to waive certain
                       provisions of the WTO’s Agreement on Trade-Related
                       Intellectual Property Rights (TRIPS) in order to
                       ensure vaccines, treatments, diagnostics, and
                       medical products necessary for the treatment and
                       containment of the COVID-19 pandemic are accessible
                       to all. More than a year after its introduction,
                       members have still not agreed to start negotiations
                       on the waiver.


                # § Patents⠀➾


                      # ⚓ Africa:_patenting_against_the_clock [Ed: This fluff
                        from Inventa International mentions the PACE program of
                        EPO, which is likely illegal; after it was exposed_in
                        the_media the EPO engaged in creative revisionism to
                        make it seem acceptable, but it’s just more of the
                        usual corruption]⠀⇛


                             Considering this background, several patent
                             offices offer to the applicant legal
                             provisions that are configurated to provide a
                             faster prosecution of a patent application.
                             There are several embodiments of accelerated
                             examination procedures, wherein the simplest
                             ones comprise a mere request by an applicant
                             for an accelerated examination for a specific
                             patent application, as the PACE programme,
                             established by the European Patent Office
                             (EPO).


                      # ⚓ EPO_voted_best_for_patent_quality_once_more [Ed: IAM
                        will_continue_to_receive_bribes_from_the_EPO_as_long_as
                        it_helps_perpetuate_lies_like_these; it is a propaganda
                        mill/PR industry]⠀⇛


                      # ⚓ Strategic_patent_countries:_evidence_from_EPO
                        oppositions [Ed: Bad metrics which want us to assume
                        litigation is the goal, not science]⠀⇛


                             IP-savvy organisations not only file their
                             own patents but also keep close tabs on the
                             competition. Tony Afram and Gianluca
                             Tarasconi at ipQuants reveal exclusive
                             statistics on EPO oppositions, which provide
                             invaluable insight into which countries are
                             making the most of this data


                             Companies that file the the highest number of
                             patent applications are often singled out as
                             being exceptionally innovative. In fact, even
                             rankings that purport to classify countries
                             based on their innovation power usually
                             include the patent filing activity of
                             applicants originating from each country as a
                             proxy for innovative activity.


                             However, filing activity alone fails to tell
                             the full story. A true corporate patent
                             strategy needs not only to align with
                             business objectives, but also to monitor
                             patent activity and occasionally take action
                             against third-party patents.


                      # ⚓ Patents:_key_updates_and_developments_for_in-house
                        teams [Ed: Unable to make money, Lexology increasing
                        experiments with paywalls; EPO is now shamelessly
                        extending an illegal practice, which it rigged_courts
                        to_approve]⠀⇛


                             The German Patent Court rejects inventorship
                             for machines, the UK updates it guidance on
                             UK-China Cooperation on IP, and Brazil and
                             Japan renew the Patent Protection Highway –
                             plus other key updates.


                             [...]


                             On 24 November 2021, the European Patent
                             Office (EPO) announced that its pilot project
                             for conducting oral proceedings in opposition
                             by…


                      # ⚓ EPO:_Enlarged_Board_endorses_video_hearings_in_appeal
                        proceedings [Ed: Convenient revisionism “Sponsored by
                        By Jakob Pade Frederiksen”; this_was_an_astounding_act
                        of_EPO_corruption_and_court-rigging]⠀⇛


                             On October 28 2021, the Enlarged Board of
                             Appeal (EBA) issued its reasons for decision
                             G 1/21 on the legality of the conduct of oral
                             proceedings in the form of a videoconference
                             (ViCo). The decision lays down that during a
                             general emergency impairing the parties’
                             possibilities to attend in-person oral
                             proceedings at the EPO premises, the conduct
                             of oral proceedings before the boards of
                             appeal by way of ViCo is compatible with the
                             European Patent Convention even without the
                             consent of all parties to the proceedings.
                             The decision is specifically concerned with
                             oral proceedings at the appeal stage only and
                             is therefore not immediately applicable to
                             oral proceedings at the first instance.


                      # ⚓ EPO_revokes_key_Intellectual_Ventures_mobile_phone
                        patent [Ed: EPO admits it was granting fake patents to
                        Microsoft_patent_trolls]⠀⇛


                             After three days of hearings, the EPO
                             Opposition Division around chairman Thomas
                             Pieper revoked a patent owned by Intellectual
                             Ventures. At least one ground for opposition
                             was held as the company prejudicing the
                             maintenance of European patent EP 21 46 439,
                             after Art. 101(2) EPC.


                             Specifically, the patent specification
                             contained further elements not included in
                             the original application. In the past, the
                             EPO has applied this strictly as grounds for
                             revocation. Now this approach has brought
                             down the 20-year-old Intellectual Ventures
                             patent. The parties did not discuss novelty
                             and inventive step during the hearing.


                      # ⚓ Benchmarking_the_IP5 [Ed: IAM, bribed by the EPO,
                        once again spreads propaganda_about_EPO_patent
                        “quality”]⠀⇛


                             Once again, the EPO has taken the crown as
                             the patent office with the best reputation
                             for quality among IAM readers. More than a
                             quarter of respondents describe its output as
                             ‘excellent’ placing it well ahead of the pack
                             (the JPO comes closest with just 14%). Only a
                             miniscule percentage of survey takers told us
                             that EPO quality was ‘poor or adequate’.


                      # ⚓ Benefits_and_Considerations_for_Patent_Prosecution
                        under_Patent_Prosecution_Highway_in_the_U.S.,_Europe,
                        China,_and_Singapore [Ed: When litigation zealots'
                        agenda matters more than actual due process or
                        examination of patents]⠀⇛


                             Patent Prosecution Highway or PPH is a set of
                             initiatives promulgated by participating
                             patent offices around the world to accelerate
                             patent prosecution in countries of the
                             participating patent offices. PPH allows the
                             participating patent offices to share
                             information and to benefit from work
                             performed by other participating patent
                             offices, and thereby reducing examination
                             workload and improving quality of patents.


                             Under PPH, prosecution of a patent
                             application previously filed with a
                             participating patent office can be fast-
                             tracked in another participating patent
                             office if the patent application meets
                             certain requirements. This article provides a
                             brief overview of benefits of filing patent
                             applications under PPH and requirements by
                             which the patent applications must satisfy in
                             order to participate in PPH.


                      # ⚓ 2.5_Million_Nurses_Demand_UN_Probe_Into_Rich
                        Countries_Blocking_Patent_Waivers⠀⇛


                      # ⚓ ‘That’s_for_Them_to_Decide’:_UK_Secretary_Rebuked_for
                        Claiming_Vaccine_Patent_Waiver_Won’t_Be_‘Helpful’_to
                        Global_Poor⠀⇛


                             As 200 million workers on Monday demanded
                             rich nations drop their continued opposition
                             to a proposed waiver of intellectual property
                             protections on coronavirus vaccines at the
                             World Trade Organization, U.K. Health
                             Secretary Sajid Javid faced sharp criticism
                             for asserting that lifting such rules would
                             not “be helpful” because it would
                             disincentivize the industry from creating
                             life-saving medicines in the future.


                             “The health secretary can side with Big
                             Pharma billionaires or he can put public
                             health first, he can’t do both.”


                      # ⚓ 2.5_Million_Nurses_Demand_UN_Probe_Into_‘Covid-19
                        Criminals’_Blocking_Patent_Waiver⠀⇛


                             More than two million nurses from 28
                             countries across the globe filed a complaint
                             Monday calling on the United Nations to
                             investigate the rich countries that are
                             blocking a proposed patent waiver for
                             coronavirus vaccines, an appeal that came as
                             public health experts raced to understand the
                             newly detected Omicron variant.


                             “Continued opposition to the TRIPS waiver is
                             resulting in the violation of human rights of
                             peoples across the world.”


                      # ⚓ Our_Patent_Review_System_is_Ten_Years_Old._It’s_Time
                        to_Make_It_Stronger.⠀⇛


                             Thousands of patents get issued each year
                             that never should have been issued in the
                             first place. This is a particular problem in
                             software, which is a bad fit for the patent
                             system. That’s why it’s so critical that we
                             have a robust patent review system. It gives
                             companies that get threatened over patents
                             the opportunity to get a second, more in-
                             depth review of a patent—without spending the
                             millions of dollars that a jury trial can
                             cost. 


                             Our patent review system is ten years old
                             now, and unfortunately patent trolls and
                             other aggressive patent holders have learned
                             to game the system. Unfortunately, the USPTO
                             has let them get away with it. A recently
                             introduced bill, the Restoring the America
                             Invents Act (S. 2891) will close some of the
                             loopholes that patent owners have used to
                             dodge or weaken reviews. 


                             Congress recognized the need for such a
                             system when it passed the 2011 America
                             Invents Act, and created a review system
                             called “inter partes review,” or IPR. The IPR
                             process lets a particular department of the
                             patent office, the Patent Trial and Appeal
                             Board (PTAB), hold a quasi-judicial process
                             in which they take a second look to decide if
                             a patent really should have been granted in
                             the first place. 


                      # § Software Patents⠀➾


                            # ⚓ Software_Patent_Eligibility_Practice_At_The_EPO
                              [Ed: Software_patents_are_not_legal, but patent
                              litigation companies are celebrating criminals
                              who took over the EPO and now compel examiners to
                              grant such illegal patents, giving them tips in
                              how to dodge the law and get away with it]⠀⇛


                                   In common with many patent offices
                                   around the world, some inventions that
                                   are implemented in software may be
                                   patented before the EPO.


                                   In this chapter, we explore software
                                   patentability covering why only some
                                   software inventions are patentable
                                   before the EPO, the requirements for an
                                   invention to be patentable and how
                                   patent practice before the EPO with
                                   respect to software inventions may
                                   evolve in the future.


                                   [...]


                                   EPO tests


                                   At the EPO, every patent application is
                                   also examined with respect to novelty
                                   and inventive step, among other
                                   requirements. The EPO’s inventive step
                                   requirement corresponds to the USPTO’s
                                   requirement for non-obviousness.
                                   However, the inventive step requirement
                                   differs in some aspects from the non-
                                   obviousness requirement.


                                   The first hurdle to overcome before the
                                   EPO is also a form of eligibility test,
                                   but one with a relatively low bar, only
                                   excluding subject matter that is
                                   entirely devoid of any technical
                                   character. A claim that includes any
                                   technical means is said to clear the
                                   first hurdle to be considered as an
                                   invention. This test is often referred
                                   to as the ‘any hardware’ or ‘any
                                   technical means’ approach. This
                                   determination is made without reference
                                   to the prior art. Therefore, a first
                                   step to considering whether a claim is
                                   likely to be patentable before the EPO
                                   is to assess whether the claim recites
                                   a technical entity, particularly
                                   hardware. In practice it can be
                                   surprising how many claims,
                                   particularly method claims, can be
                                   found at the initial prosecution stage,
                                   which on close inspection do not
                                   actually refer to any hardware
                                   whatsoever. One relatively easy way of
                                   ensuring that the first hurdle is
                                   cleared can be to recite “a computer
                                   implemented method”. In other words, if
                                   any hardware (eg, a computer, storage
                                   or microprocessor, among other things)
                                   is mentioned in the claim, it will pass
                                   the first hurdle.


                                   At the second hurdle, the requirement
                                   for an inventive step over the prior
                                   art is examined. The examination for
                                   inventive step is simultaneously
                                   subject to a limitation that only
                                   aspects of the claimed invention that
                                   are technical can be considered. In
                                   other words, any matter in the claim
                                   that is not considered technical cannot
                                   give rise to an inventive step over the
                                   prior art. Therefore, at the EPO, the
                                   test whether the claimed subject matter
                                   fulfils the requirement of
                                   ‘technicality’ is assessed
                                   simultaneously with the evaluation of
                                   whether the subject matter of the
                                   patent application has an inventive
                                   step.


                                   Problem-solution approach


                                   The EPO has developed a special process
                                   for assessing inventive step, known as
                                   the ‘problem-solution approach. The
                                   problem-solution approach was modified
                                   by the EPO for assessing ‘computer
                                   implemented inventions’ (CIIs), which
                                   is the term used by the EPO for
                                   inventions that are usually realised by
                                   means of software and are colloquially
                                   called ‘software patents’.


                                   Under the modified problem-solution
                                   approach, features of the claim under
                                   examination are assessed as to whether
                                   they contribute to the solution of a
                                   technical problem. Only features of the
                                   claimed invention are considered that
                                   provide such a technical contribution.
                                   In some ‘mixed type’ inventions, being
                                   a mix of technical and non-technical
                                   claim elements, features can be
                                   considered that are non-technical, such
                                   as pure software steps, but only if
                                   they are said provide a contribution to
                                   the formulation of the technical
                                   problem solved by the invention.


                                   CII case law


                                   During its existence, the EPO has twice
                                   reviewed its case law relating to CIIs
                                   in the form of decisions of its
                                   Enlarged Board of Appeal. The first
                                   decision (G 03/08) from 2010 contains
                                   an overview of previous case law on
                                   CIIs, which confirmed the two-hurdle
                                   test and made no changes to the EPO’s
                                   approach going forward.


                                   The second decision of the Enlarged
                                   Board (G 01/19) was issued in 2021 and
                                   concerns the patenting of computer-
                                   aided simulations. On the one hand, the
                                   principles of the first decision were
                                   confirmed and, on the other hand,
                                   specific comments were made on the
                                   legal problems that arise when
                                   patenting computer-aided simulations.


                                   Computer-implemented simulations use a
                                   numerical model that is fed with input
                                   data and in turn produces data as an
                                   output indicative of the result of the
                                   simulation. Therefore, only data is
                                   processed without directly influencing
                                   the physical world. In this sense, a
                                   computer-implemented simulation could
                                   be considered a purely mathematical
                                   process. Mathematical methods as such
                                   are excluded from patentability and it
                                   could be concluded that computer-
                                   implemented simulations are, in
                                   principle, not patentable.


                                   In this decision, however, the Enlarged
                                   Board of Appeal came to a different
                                   conclusion and stated that computer-
                                   implemented simulations are not
                                   fundamentally excluded from
                                   patentability. Instead computer-
                                   implemented simulations can be patented
                                   if they relate to a technical invention
                                   according to the above principles.


                # § Copyrights⠀➾


                      # ⚓ MPA_Seeks_Person_to_Investigate_Online_Pirates_&
                        Their_Technical_Infrastructure⠀⇛


                             Whether they supply content, technical
                             infrastructure or even coding skills, those
                             involved with the online distribution of
                             pirated movies or TV shows can expect to get
                             noticed by the Motion Picture Association.
                             How the Hollywood group goes about its
                             investigations isn’t public knowledge but for
                             one talented individual, becoming a member of
                             the team is now on the horizon.


                      # ⚓ Cheat_Seller_AimJunkies_Accuses_Destiny_2_Creator
                        Bungie_of_“Sharp_Practices”⠀⇛


                             Earlier this year, game developer Bungie
                             filed a copyright infringement lawsuit
                             against AimJunkies.com, which offered a
                             popular ‘Destiny 2 Hacks’ suite. Soon after,
                             the parties began negotiating a potential
                             settlement deal. To AimJunkies’ surprise,
                             however, Bungie sneakily went ‘behind its
                             back’ by requesting the court to enter a
                             default.



                    ䷩ 𝚕𝚒𝚗𝚎 5710

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 11.30.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_1/12/2021:_Tux_Paint_0.9.27_and_WordPress_5.9_Beta⠀✐


Posted in News_Roundup at 8:48 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⠀➾


                # ⚓ Taking_Stock_of_Librem_14_–_Purism⠀⇛


                       Like many hardware companies, Purism has taken a
                       “Just In Time” manufacturing approach for our
                       products including the Librem laptop line. That
                       means that we make a bit more of a product than we
                       think we need, and schedule the next manufacturing
                       run so that the product arrives in our warehouse
                       “just in time” for us to deplete the previous
                       manufacturing run. In an ideal world that means we
                       never run out of stock, but also never have massive
                       inventories taking up space in our warehouse.


                       Also like many hardware companies the supply chain
                       woes of the last two years have caused us to
                       rethink this approach. Each time it seemed like we
                       had made enough Librem 14s to catch up to current
                       and projected orders, delays of one kind or another
                       created a new backlog as new orders continued to
                       come in. We’ve decided to scrap “Just in Time” in
                       favor of manufacturing far more Librem 14s than we
                       currently need, and will have our shelves full of
                       Librem 14 stock by the end of the year.


                # ⚓ HPi95LX_Puts_Linux_In_Your_Palm_|_Hackaday⠀⇛


                       A few decades ago, palmtop computers were mostly
                       based on MS-DOS, and while many users tried to
                       mimic the UNIX experience, the results were mixed.
                       Fast forward to the present and business-card-sized
                       Linux computers modules abound. Canadian tinkerer
                       [Rune Kyndal] decided to make his own Linux palmtop
                       by sacrificing an old HP-95LX and replacing the
                       guts with a Raspberry Pi Zero and a color LCD
                       screen. We’re impressed with the rich set of
                       features he has crammed into the limited volume of
                       the case:


                # ⚓ Linux_Fu:_The_Ultimate_Dual_Boot_Laptop?_|_Hackaday⠀⇛


                       I must confess, that I try not to run Windows any
                       more than absolutely necessary. But for many
                       reasons, it is occasionally necessary. In
                       particular, I have had several laptops that are
                       finicky with Linux. I still usually dual boot them,
                       but I often leave Windows on them for one reason or
                       another. I recently bought a new Dell Inspiron and
                       the process of dual booting it turned out to be
                       unusually effective but did bring up a few
                       challenges.


                       If you ever wanted a proper dual-booting laptop,
                       you’ll be interested in how this setup works. Sure,
                       you can always repartition the drive, but the
                       laptop has a relatively small drive and is set up
                       very specifically to work with the BIOS diagnostics
                       and recovery so it is always a pain to redo the
                       drive without upsetting the factory tools.


                       Since the laptop came with a 512 GB NVMe drive, I
                       wanted to upgrade the drive anyway. So one option
                       would have been to put a bigger drive in and then
                       go the normal route. That was actually my
                       intention, but I wound up going a different way.


                # ⚓ LXer:_Laptop_Dual_Boot_Project_Part_2⠀⇛


                       I know some of you are wondering why go through all
                       of this when I could just install a Linux distro
                       along side of windows and be done with it? One
                       reason was I had to pay it off. A financed $550
                       laptop takes a little while to pay off. I didn’t
                       want to change the machine any while I owed money
                       on it. And the idea of messing with a bone stock
                       laptop using Linux sounded fun. The good thing now
                       is that I have paid it off so it’s all mine to do
                       whatever I want with.


                       So, for me it came down to PCLOS, Mint, SUSE or
                       Ubuntu to install to my laptop. I tried them all
                       ‘live’ from USB drives and a couple of them using
                       VirtualBox. They are all good distros and there are
                       many articles on why one or the other is good or
                       better for you but for me, it came down to
                       PCLinuxOS or Mint. Having come from Windows
                       originally I am most comfortable with a “Windows
                       like” environment. I think both PCLOS and Mint are
                       two versions of that I like best. I like Mint mire
                       but what has drawn me to PCLOS is that it is the
                       only Linux I have tried in that the backlight on my
                       keyboard works. It may sound dumb but it makes it
                       easier for me being able to see the keys no matter
                       the lighting situation I’m in.


                       I tried to install PCLinuxOS onto my laptop and I
                       got a “can’t call method on first_usable_sector
                       unblessed reference” error at the very beginning of
                       the install process. I couldn’t get around it and
                       aborted the install. Time to do some research. Come
                       to find out I have a AHCI-RAID problem. I got into
                       the BIOS and changed the SATA configuration from
                       RAID to AHCI but in rebooting, it wouldn’t boot.


                       So I went back into my BIOS and wrote down the
                       configuration in the SATA settings. It says I am
                       running the “Intel RST Premium with Intel Optane
                       System Acceleration”. I have been looking that up
                       but haven’t found much…much I understand that is.
                       More Googling is required.


                       I got back into the boot menu and changed the SATA
                       config back to Intel’s RAID setting and it re-
                       booted just fine. It seems that for the moment I am
                       able to run Linux from USB ‘live’ and under
                       VirtualBox but I am unable to install it to the HD.
                       For those who don’t know the big difference AHCI
                       and Raid , it is how they store the data to the
                       hard drive.


                       I’ll use a sink with water filling it for the
                       metaphor. RAID 1 offers redundancy through
                       mirroring, i.e., data is written identically to two
                       drives. Think of two sinks with the same water in
                       them. RAID 0 offers no redundancy and instead uses
                       striping, i.e., data is split across all the
                       drives. think of two sinks with the water split
                       between them. Half of the data goes into one drive
                       and the other half into another drive. This means
                       RAID 0 offers no fault tolerance; if the drives
                       fails, the RAID unit fails.


                # ⚓ Apple_car_will_arrive_at_the_same_time_as_Linux_on_the
                  desktop [Ed: Nick Farrell is trolling or click-baiting GNU/
                  Linux users, as usual]⠀⇛


                       Years after big reveal, Tame Apple Press predicts


                       Apple is unlikely to get its car vapourware on the
                       road for at least another 20 years even if it has a
                       “big reveal” in five years, the Tame Apple Press
                       finally admits.


                       For years the TAPs has been running stories
                       insisting that an Apple car was a few years away,
                       even while its Project Titan was downsized and
                       talent left to go to real carmakers.


                # ⚓ Zoom_boosts_security_with_automatic_updates_for_Windows_and
                  macOS_—_but_Linux_users_miss_out [Ed: Microsoft's loyal
                  propagandist By Sofia Wyciślik-Wilson is trolling GNU/Linux
                  users again... Zoom itself is antithetical to security]⠀⇛


          o § ChromeOS⠀➾


                # ⚓ First_Look:_Chromebook_“extra_container_management”_in
                  Chrome_OS_98⠀⇛


                       Earlier this month, I covered down a new feature
                       that’s in the works for Chrome OS that will give
                       users a native user interface for managing Linux
                       containers. While still a work in progress, the
                       “extra container” management has finally made an
                       appearance in the Canary channel of Chrome OS and
                       we have our first look at how the feature is going
                       to play out. Getting the feature up and running
                       does require you to be in the very experimental
                       Canary channel, which I do not recommend visiting
                       unless you know what you’re doing and aren’t afraid
                       of possibly bricking your device.
                       In the Canary channel, the #crostini-multi-
                       container flag for the container management must
                       first be enabled, and then, the feature will appear
                       in the Developer section of the Chrome OS settings
                       menu. By default, users can see the “penguin”
                       container inside the Termina VM. This houses the
                       standard Debian framework that runs on Chrome OS
                       when you enable Linux applications. From the menu,
                       you can stop the default container and shut it down
                       but you can’t delete the container. To do this, you
                       would need to remove Linux from your system
                       entirely via the main Developer menu.


                # ⚓ Chrome_OS_98_adds_management_of_multiple_Chromebook_Linux
                  containers⠀⇛


                       Earlier this month I reported that Chrome OS was
                       adding multiple container management to Chromebook.
                       The last Dev Channel update has finally brought the
                       first iteration of that feature and I do have it
                       working. At the moment, however, I’ve only been
                       able to add a second Linux container for Debian.
                       Regardless, here’s how Chrome OS 98 adds management
                       of multiple Chromebook Linux containers.


                       For starters, I had to enable the following
                       experimental flag in Chrome OS 98: chrome://
                       flags#crostini-multi-container and restart my
                       browser. After that, I saw the new “manage extra
                       containers” option in my Linux settings:


                       Chrome OS 98 multiple Chromebook Linux containers
                       management
                       Choosing this option brought me to the following
                       screen, which initially had a single container, as
                       expected. Here I could change the color of each
                       one. I clicked the Create button, added a second
                       Debian container, and left it the default color.
                       The three-dot option offers ways to stop or delete
                       a container.


          o § Audiocasts/Shows⠀➾


                # ⚓ Is_Deepin_Linux_The_Windows_Killer?_(Deepin_20.3_First
                  Look)_–_Invidious⠀⇛


                       Deepin is a Debian-based Linux distro that is
                       devoted to providing a beautiful, easy-to-use,
                       safe, and reliable operating system. The Deepin
                       Desktop Environment is absolutely gorgeous, and it
                       comes with a suite of custom applications.


                # ⚓ Free_Software_Doesn’t_Mean_Better_Privacy?_–_Invidious⠀⇛


                       Most free software advocates can agree that you
                       can’t really trust proprietary software with
                       privacy but does that mean that Free Software is
                       always more private, well not always.


                # ⚓ Live_–_Building_a_New_Linux_Experience_–_The_Complete
                  Interface_–_Invidious⠀⇛


                       Back to the code… building out the experience and
                       testing.


                # ⚓ Give_Your_Cinnamon_Desktop_Fresh_And_Elegant_Look_With
                  Orchis_GTK_Theme_–_Invidious⠀⇛


                # ⚓ Make_Your_First_KDE_Patch:_How_To_Improve_System_Settings!
                  –_Kockatoo_Tube⠀⇛


                # ⚓ How_to_install_Inkscape_on_Elementary_OS_6.0_–_Invidious⠀⇛


                       In this video, we are looking at how to install
                       Inkscape on Elementary OS 6.0. Enjoy!


                # ⚓ Linux_overview_|_Ubuntu_MATE_21.10_–_Invidious⠀⇛


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


          o § Kernel Space⠀➾


                # ⚓ IO_uring_Network_Zero-Copy_Send_Is_Boasting_Mighty_Speed-
                  Ups_–_Phoronix⠀⇛


                       Early patches providing for IO_uring zero-copy send
                       support for the Linux kernel’s networking subsystem
                       is looking extremely promising for greater
                       throughput.


                       Developer Pavel Begunkov posted the set of twelve
                       patches today working on this zero-copy send
                       support for IO_uring with the networking subsystem.
                       These initial patches are marked as a “request for
                       comments” as some items are still being sorted out
                       with the code.


                # ⚓ AMD-Pstate_Driver_Updated_A_5th_Time_For_Improving_Ryzen
                  Power_Efficiency_On_Linux_–_Phoronix⠀⇛


                       Sent out today was the fifth revision to AMD’s new
                       “amd-pstate” kernel driver focused on providing
                       enhanced CPU frequency controls for Linux systems.


                       AMD’s P-State driver remains under active
                       development for improving the Linux power
                       efficiency for Ryzen (and EPYC) processors. AMD P-
                       State makes use of ACPI CPPC for more informed and
                       finer-grained frequency controls on modern (Zen 2
                       and newer) processors compared to what is afforded
                       by the existing ACPI CPUFreq frequency scaling
                       driver currently used by AMD Linux systems.


                # ⚓ Intel_Posts_Linux_Patches_Bringing_Up_Alder_Lake_N_Graphics
                  –_Phoronix⠀⇛


                       With the graphics driver support for Alder Lake S-
                       series in good shape with Linux 5.16 and the Alder
                       Lake P-series support also coming together for
                       upcoming ADL-based laptops, next up is the Alder
                       Lake N enablement happening for Linux.


                       Alder Lake N for low-end, low-power hardware is now
                       coming together. Though over the existing ADL-S and
                       ADL-P Linux support, it’s basically adding in new
                       PCI IDs for ADL-N.


                # ⚓  Analog_Devices_Expands_Linux_Distribution_with_Over_1000
                  Device_Drivers_to_Support_the_Development_of_High-Performance
                  Solutions_|_Business_Wire⠀⇛


                       As the Linux open-source operating system marks its
                       30th anniversary, Analog Devices, Inc. (ADI)
                       announces the expansion of its Linux distribution
                       by recognizing over 1000 ADI peripherals supported
                       by in kernel Linux device drivers. Designed to
                       enable the rapid development of embedded solutions,
                       these open-source device drivers streamline the
                       software development process for ADI’s customers,
                       providing access to tested, high-quality software
                       to create innovative solutions across a range of
                       industries, including telecom, industrial,
                       military, aerospace, medical, automotive, security,
                       Internet of Things (IoT), consumer, and more. This
                       portfolio includes products from Maxim Integrated
                       Products, Inc., now part of Analog Devices.


                # § Graphics/Zink⠀➾


                      # ⚓ Zink_Is_Ending_2021_In_Fantastic_Shape_For_OpenGL
                        Over_Vulkan⠀⇛


                             For those wondering about the state today for
                             Zink with mainline Mesa, here are some fresh
                             benchmarks. My last time testing Zink was in
                             August and since then Blumenkrantz has worked
                             on fixes for the various games reported to
                             have issues and even more performance
                             optimizations, making this round of testing
                             now quite interesting.


                             Using Mesa 22.0-devel as of 26 November
                             (using the Oibaf PPA for easy
                             reproducibility), I ran benchmarks of various
                             OpenGL Linux games using the native OpenGL
                             driver (RadeonSI in this case) and then again
                             when using Zink running atop the RADV Vulkan
                             driver. This testing was done on an AMD Ryzen
                             9 5950X system with AMD Radeon RX 6700 XT
                             graphics card. The focus is on seeing how
                             Zink compares to using RadeonSI OpenGL across
                             a variety of Linux games.


                             


                      # ⚓ Haiku_OS_Managing_To_Run_Zink_OpenGL_Atop_Radeon
                        Vulkan_Driver_For_3D_Acceleration_–_Phoronix⠀⇛


                             Last month we reported on progress for
                             porting the Mesa Radeon Vulkan driver to
                             Haiku, the BeOS-inspired open-source
                             operating system. Now in ending out November
                             they not only have RADV running but also
                             working with Gallium3D’s Zink for offering
                             OpenGL acceleration over Vulkan.


                             Haiku developer “X512″ has been the one
                             devoted to this recent effort for getting the
                             open-source AMD Radeon Vulkan driver running
                             on this platform. With some modifications he
                             has been successful in enabling the RADV
                             driver to work on Haiku for 3D hardware
                             acceleration.


          o § Applications⠀➾


                # ⚓ Announcing_Tux_Paint_version_0.9.27⠀⇛


                       The Tux Paint development team is proud to announce
                       version 0.9.27 of Tux Paint, which adds many new
                       features to the popular children’s drawing program.


                # ⚓ Tux_Paint_0.9.27_Release_Adds_New_Magic_Tools_to_Make
                  Drawing_Easier_Than_Ever_–_It’s_FOSS_News⠀⇛


                       Known for its simplicity and ease of use, Tux Paint
                       is a drawing app primarily aimed at kids.


                       Tux Paint has come a long way since its initial
                       release in 2002 on Linux and is now available on
                       many other platforms.


                       The latest release of Tux Paint 0.9.27 comes just
                       after four months of its previous release. Just
                       like the previous one, this release is feature-rich
                       but includes new additions and improvements.


                # ⚓ OpenPrinting_Releases_CUPS_2.4_With_AirPrint,_OAuth_2.0
                  Support_–_Phoronix⠀⇛


                       Earlier this year OpenPrinting took over
                       development of the CUPS print server with Apple no
                       longer interested in handling the future
                       development of this open-source Linux/macOS/Unix/
                       Solaris print server. Out this week is CUPS 2.4 as
                       the first major release under the guidance of
                       OpenPrinting.


                       Apple’s work on CUPS ceased pretty much when CUPS
                       founder Michael Sweet left Apple originally
                       acquiring it back in 2007. Apple is no longer
                       actively developing CUPS but has even contracted
                       Sweet to backport important OpenPrinting CUPS fixes
                       back to Apple’s CUPS code-base.


                # ⚓ CUPS_2.4.0_Printing_System_Released,_Check_Out_What’s_New⠀⇛


                       OpenPrinting project has just released CUPS 2.4.0
                       formed without Apple’s participation, which has
                       since 2007.


                       The Common UNIX Printing System (CUPS) is a cross-
                       platform printing solution used on many different
                       Linux distros. Its use is very widespread, as it
                       has become the standard print manager on the
                       majority of popular Linux distros.


                       CUPS acts as a print spooler, scheduler, print job
                       manager, and can store information for numerous
                       local or network printers. It is based on the
                       Internet Printing Protocol and provides complete
                       printing services to most PostScript and raster
                       printers.


                       At the end of 2019, Michael Sweet, the lead
                       developer of CUPS left Apple after he joined Apple
                       and the company purchased the source code a decade
                       prior for this long-standing open-source printing
                       system. As a result, Apple’s public CUPS
                       development effectively ended and Apple now is
                       basically interested in just maintaining CUPS 2.3
                       and not really developing it further.


                       Therefore, OpenPrinting now controls the CUPS
                       project moving forward with Michael Sweet being
                       involved in the effort, and the results were not
                       late.
                       Now CUPS 2.4.0 is finally here in its production-
                       ready state, bringing numerous security and
                       performance improvements to make the widely used
                       printing system more reliable and stable than ever.


                # ⚓ Best_Torrent_Client_For_Linux_Based_Operating_Systems_|
                  Itsubuntu.com⠀⇛


                       The term “torrent” refers to file sharing through a
                       decentralized, peer-to-peer (P2P) sharing network.
                       Torrents are an excellent source to download large
                       files. P2P file-sharing protocols allow users to
                       exchange files without uploading them to the
                       server. They transform your PC into part of a host
                       where files are shared as it’s downloaded, so while
                       you’re downloading files from another host, you’re
                       likewise helping other people as they download the
                       part of the files that you have downloaded from
                       another host.


                       In this article, we are going to discuss or list
                       out the best torrent client for Linux-based
                       operating systems. So, if you are a Linux user and
                       looking for the best torrent client then you are at
                       the right place.


          o § Instructionals/Technical⠀➾


                # ⚓ Collaborate_on_a_file_using_Linux_diff_and_patch⠀⇛


                       I edit a lot of text files. Sometimes it’s code.
                       Other times it’s the written word for role-playing
                       games (RPGs), programming books, or general
                       correspondence. Sometimes it’s nice to make a
                       change, but for my collaborator to compare my
                       change with what they originally had written. Many
                       people default to office suites, like LibreOffice,
                       using comments or change tracking features.
                       Sometimes a simpler tool makes more sense, though,
                       and for that, you can look at programming history
                       for tools like diff and patch, which provide
                       standardized formatting for tracking and applying
                       changes to shared files.


                # ⚓ Best_ways_to_destroy_Microsoft_Windows_–_blackMORE_Ops⠀⇛


                       OK, like seriously don’t do it unless you’re doing
                       it in a practice Virtual machine or have permission
                       to do so.. I take no responsibility for these
                       collection of best ways to destroy Microsoft
                       Windows!


                # ⚓ Quickemu-_Run_Windows_11_on_Ubuntu_20.04_LTS_Linux_in_few
                  clicks⠀⇛


                       o you want to install Windows 10 or 11 on your
                       Ubuntu 20.04 or 22.04 LTS Linux using QEMU-KVM
                       virtual machine? Then here is a tutorial to do that
                       using the command terminal and Quickemu + Quickgui.


                       Although we all have a simple solution that is a
                       virtual box to run Windows 11 virtual machine, what
                       about KVM? Some will say it is not easy to operate
                       because of the command line but no there are few
                       open-source GUI programs to give KVM an easy
                       interface. However, another thing is downloading
                       ISO images of various operating systems including
                       Windows 10 or 11 to use with Virtualbox can be a
                       headache. Hence, to solve all of this, there is a
                       project called QuickEMU with a GUI interface known
                       as QuickGUI. QickEMU uses QEMU_KVM on Linux
                       operating system to run a virtual machine and can
                       easily download all popular operating system Images
                       to install including macOS. Whereas it can be
                       operated via CLI but for ease of usage users can
                       install QuickGUI to download, create, and manage
                       operating systems virtual machines.


                # ⚓ Steinar_H._Gunderson:_Commitcoin⠀⇛


                       How do you get a git commit with an interesting
                       commit ID (or “SHA”)? Of course, interesting is in
                       the eye of the beholder, but let’s define it as
                       having many repeated hex nibbles, e.g. “000” in the
                       commit would be somewhat interesting and
                       “8888888888888888888888888” would be very
                       interesting. This is pretty similar to the dreaded
                       cryptocoin mining; we have no simple way of forcing
                       a given SHA-1 hash unless someone manages a
                       complete second-preimage break, so we must brute-
                       force. (And hopefully without boiling the planet in
                       the process; we’d have to settle for a bit shorter
                       runs than in the example above.)


                       Git commit IDs are SHA-1 checksums of what they
                       contain; the tree object (“what does the commit
                       contain”), the parents, the commit message and some
                       dates. Of those, let’s use the author date as the
                       nonce (I chose to keep the committer date truthful,
                       so as to not be accused of forging history too
                       much). We can set up a shell script to commit with
                       –amend, sweeping GIT_AUTHOR_DATE over the course of
                       a day or so and having EDITOR=true in order not to
                       have to close the editor all the time.


                # ⚓ How_to_Install_Kuma_on_Ubuntu_20.04_|_LinuxHostSupport⠀⇛


                       Kuma is an open source monitoring tool like “Uptime
                       Robot” written in Nodejs. In this article, we’ll
                       learn how to install it on Ubuntu 20.04 so we can
                       self-host our Uptime Bot. We’ll also set up a
                       reverse proxy on Apache with a Let’s Encrypt SSL to
                       secure our website.


                       Kuma is easy to use and upgrade, and is powerful
                       for traffic control, observability, service
                       discovery, etc.


                # ⚓ How_to_Install_SuiteCRM_with_Apache_and_free_Let’s_Encrypt
                  SSL_on_Debian_11⠀⇛


                       SuiteCTM is an open-source Customer Relationship
                       Management solution written in PHP. It is a fully-
                       featured and highly-extensible CRM application that
                       runs on any operating system. It became popular
                       when SugarCRM decided to stop the development of
                       its community edition. It is used for creating
                       business strategies, actions, and decisions. It is
                       an alternate CRM solution for other commercial CRM
                       such as SugarCRM, Salesforce, and Microsoft.


                       In this post, we will show you how to install
                       SuiteCRM with Apache and Let’s Encrypt SSL on
                       Debian 11.


                # ⚓ How_to_Install_Rudder_System_Configuration_and_Auditing
                  Tool_on_Ubuntu_20.04_–_VITUX⠀⇛


                       Rudder is an open-source and user-friendly web-
                       based system configuration and audit tool. It helps
                       you to manage your IT infrastructure by automating
                       system configurations while ensuring visibility and
                       control of your infrastructure. Two main components
                       of Rudder are: Root server and node. Root server
                       defines the configurations for the systems it
                       manages. The systems managed by Rudder are known as
                       nodes. Rudder manages the nodes using the Rudder
                       agent which is installed on these systems.


                       In today’s post, we will install the Rudder root
                       server and agent on Ubuntu 20.04 LTS. We will use
                       two Ubuntu machines: one as the Rudder root server
                       and the other one as the Rudder node.


                       Note: You must be a root user or have sudo
                       privileges on both machines in order to install the
                       Rudder server and agent.


                # ⚓ How_to_check_if_packages_in_RHEL-based_Linux_distributions
                  have_been_patched_for_specific_CVEs_–_TechRepublic⠀⇛


                       CVEs (Common Vulnerabilities and Exposures) are
                       constantly being discovered and patched. When
                       discovered, it means a new security flaw exists in
                       either an operating system or a piece of software
                       and should be patched as soon as possible. Fixing
                       the vulnerabilities, of course, is up to the
                       developers. Patching those vulnerabilities,
                       however, is up to the admin (or user). Thing is,
                       you might not know if you’re using a piece of
                       software that includes one or more CVEs.


                       How do you uncover this information? Do you have to
                       spend hours researching? Not really. In fact, all
                       you need to know is the CVE you’re looking for and
                       the piece of software it affects. With those two
                       bits of information in hand, you can quickly
                       discover if what’s installed on your Red Hat
                       Enterprise Linux-based distribution contains that
                       vulnerability.


                       I’m going to show you how to do just that.


                # ⚓ How_to_Install_and_Configure_Nginx_on_Ubuntu⠀⇛


                       Web applications have gained wide popularity over
                       the past few years as a means of providing services
                       to different clients. With a web application, you
                       can reach out to a wider audience regardless of the
                       device or operating system they are using.


                       Being able to install and configure a web server is
                       a valuable skill to have both as a web developer
                       and software engineer. A web server is a program
                       responsible for delivering your web content to
                       clients over the internet or a network.


                       Let’s take a look at how to install and configure
                       the Nginx web server on Ubuntu.


                # ⚓ How_to_install_Sublime_Merge_on_a_Chromebook⠀⇛


                       Today we are looking at how to install Sublime
                       Merge on a Chromebook. Please follow the video/
                       audio guide as a tutorial where we explain the
                       process step by step and use the commands below.


                # ⚓ How_to_Install_OpenEMR_on_Ubuntu_20.04_With_LAMP_Stack⠀⇛


                       OpenEMR is a popular open-source software for the
                       healthcare industry. It offers electronic health
                       records and medical practice management solutions.
                       OpenEMR provides a fully integrated Workflow
                       Management inside healthcare facilities. Any
                       healthcare facility would be able to capture and
                       control patient data using the following features
                       in OpenEMR.


                # ⚓ Add_current_user_to_all_groups_on_the_system_except
                  “nobody/nogroup”⠀⇛


                # ⚓ How_To_Install_Hyperbola_KDE_on_a_Virtual_Machine⠀⇛


                       This tutorial explains how to install Hyperbola
                       computer operating system with KDE Plasma Desktop
                       on a virtual machine. Let’s start!


                # ⚓ How_To_Install_Java_on_Fedora_35_–_idroot⠀⇛


                       In this tutorial, we will show you how to install
                       Java on Fedora 35. For those of you who didn’t
                       know, Java is a secure, stable, and well-known,
                       general-purpose programming language and computing
                       technology platform with many interconnected
                       capabilities. If you want to use a Java-based tool
                       or program in Java, you’ll need to have Java on
                       your system.


                       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 Java on a Fedora 35.


                # ⚓ How_To_Install_Nginx_with_Let’s_Encrypt_SSL_on_Fedora_35_–
                  idroot⠀⇛


                       In this tutorial, we will show you how to install
                       Nginx with Let’s Encrypt SSL on Fedora 35. For
                       those of you who didn’t know, Let’s Encrypt is a
                       non-profit Certificate Authority (CA) managed by
                       the Internet Security Research Group. It provides
                       free SSL certificates for your domains to secure
                       data on the transport layer. The certificate is
                       valid for 90 days, during which renewal can take
                       place at any time. The offer is accompanied by an
                       automated process designed to overcome manual
                       creation, validation, signing, installation, and
                       renewal of certificates for secure websites.


                       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 Nginx with Let’s Encrypt
                       SSL on a Fedora 35.


                # ⚓ How_to_Check_Supported_TLS_and_SSL_Ciphers_(version)_on
                  Linux⠀⇛


                       OpenSSL is a toolkit and a cryptography library
                       that support the Secure Sockets Layer (SSL)) and
                       Transport Layer Security (TLS) protocol on Linux.


                       It provides cryptographic protocols to varies
                       applications running on Linux such as ssh, Apache
                       (httpd), Nginx, etc.


                       TLS is a cryptographic protocol used to secure
                       network communications between the devices.


                       OpenSSL configuration file is located at /etc/pki/
                       tls/openssl.cnf, referred to as the master
                       configuration file, which is read by the OpenSSL
                       library.


                       In this guide, we will show you how to check
                       supported TLS and SSL ciphers (version) on opneSUSE
                       system. The same procedure is applicable for other
                       distribution as well.


                # ⚓ How_to_Compile_and_Run_your_First_Java_Program⠀⇛


                       Java is one of the most powerful and popular
                       programming languages. Even with several niche
                       languages available now, Java has retained its
                       leading position among developers.


                       If you have decided to learn Java, it’s definitely
                       a good choice to enter the world of programming,
                       but the question is, how to create your first piece
                       of code?


                       Let’s go through six steps of creating a Java
                       program. We’ve also prepared bonus advice on where
                       you can learn and practice Java.


                # ⚓ How_to_Enable_SSH_on_Debian_11_Bullseye_Linux_–_Linux
                  Shout⠀⇛


                       Tutorial to learn the steps to install and enable
                       SSH server in Debian 11 Bullseye Linux using
                       command line terminal. SSH is a network protocol
                       originally developed in 1995 by Finn Tatu Ylönen
                       for encrypted access to other computers in an IP
                       network.


                       [...]


                       SSH is the abbreviation for Secure Shell. With the
                       help of this protocol, the user can securely
                       establish connections with other devices, for
                       example from a PC to a web server. SSH enables
                       mutual authentication and encrypted data
                       transmission so that sensitive data such as
                       passwords or user names cannot be hacked or seen by
                       unauthorized persons. Secure Shell offers a high
                       level of security. It provides functions for
                       logging in, transmitting and executing text-based
                       commands, and for copying data. In addition to
                       encryption, SSH offers reliable mutual
                       authentication using certificates and public and
                       private key procedures. A popular area of
                       ​​application for Secure Shell is the remote
                       maintenance of servers.


                # ⚓ How_to_Install_Brew_on_Ubuntu_and_Other_Linux⠀⇛


                       Homebrew, also known as Brew, is a command line
                       package manager primarily created for macOS.


                       Homebrew grew quite popular among macOS users as
                       more developers created command line tools that
                       could be easily installed with Homebrew.


                       This popularity resulted in the creation of
                       Linuxbrew, a Linux port for Homebrew. Since it is
                       primarily Git and Ruby, and Linux and macOS are
                       both Unix-like systems, Brew works good on both
                       kind of operating systems.


                       Linuxbrew project eventually merged with Homebrew
                       project and now you just have one Brew project
                       called Homebrew.


                       Why am I calling it brew, instead of Homebrew?
                       Because the command starts with brew. You’ll see it
                       in detail in a later section.


                # ⚓ How_to_Install_Lazarus_IDE_in_Ubuntu_20.04,_18.04,_21.10_|
                  UbuntuHandbook⠀⇛


                       This is a step by step guide shows how to install
                       the Lazarus IDE in Ubuntu 18.04, Ubuntu 20.04,
                       Ubuntu 21.10 and their derivatives, e.g., Linux
                       Mint, Elementary OS and more.


                       Lazarus is a free Delphi compatible cross-platform
                       IDE for rapid application development using the
                       Free Pascal compiler. User may install the project
                       either from Ubuntu repository or by using the
                       official DEB packages.


                # ⚓ How_to_Install_Lazarus_IDE_in_Ubuntu_20.04,_18.04,_21.10_|
                  UbuntuHandbook⠀⇛


                       The most popular Javascript runtime is Node.js,
                       which uses the V8 engine to perform useful tasks
                       such as interacting with local storage. Node.js has
                       boosted the popularity of Javascript, which was
                       already well-known. Previously, Javascript was only
                       used in web browsers to create interactive web
                       applications; however, with Node.js, we can now use
                       Javascript to create command-line applications, as
                       well as web applications that are designed and even
                       backed by Javascript.


                       In this article, we will not go into greater detail
                       about Node.js and its functionality. In this
                       article, we will learn how to install Node.js on
                       Ubuntu Linux.


                # ⚓ How_to_Install_PuTTY_on_Debian_11_Bullseye_–_Linux_Shout⠀⇛


                       Here we learn the steps to install PuTTy on Debian
                       11 Bullseye using the command terminal to establish
                       an SSH connection using the graphical user
                       interface.


                       Using PuTTY free Telnet and SSH client application
                       on Windows, Linux, and macOS – the user can
                       establish a connection with remote computers and
                       systems in the network via SSH. Encrypted or
                       unencrypted protocols can be used. Although this is
                       a common application to use in Windows, yet still
                       it somebody is interested the can be easily
                       installed on Linux as well for remote system
                       administration.


                       Apart from the SSH client, PuTTy comes with a few
                       additional command-line tools such as Plink, PSFTP,
                       and PSCP. With the help of Plink, PuTTY can be
                       controlled via the shell. Shell scripts can also be
                       used. The SCP client PSCP can also be used to
                       transfer encrypted data – PSFTP, on the other hand,
                       is an SFTP client and thus an encrypted FTP
                       alternative.


                # ⚓ How_to_list_all_running_&_stopped_Docker_containers_–_Linux
                  Shout⠀⇛


                       Docker is the popular platform to run container
                       virtual machines using the pre-built app images.
                       The installation and its usage are pretty simple,
                       yet, if you are new to it and want to know how to
                       list all the created or stopped Docker containers
                       to delete or manage them easily. Then here are the
                       commands to follow.


                # ⚓ How_to_modify_the_Proxmox_repositories_–_Unixcop_the_Unix_/
                  Linux_the_admins_deams⠀⇛


                       Hello friends. When we refresh the Proxmox
                       repositories we get an error stating that our IP
                       address is not authorized to access a repository.
                       Well, this repository gives us access to enterprise
                       packages and to use it you must have a valid
                       license. In this post, I will show you how to
                       modify the Proxmox repositories to avoid this
                       annoying error. We will also add another free one
                       and have more tools available.


                       So let’s get to work.


                # ⚓ How_to_play_Dead_Cells_on_Linux⠀⇛


                       Dead Cells is a roguelike video game inspired by
                       Metroid and Castlevania. It was developed and
                       published by Motion Twin. Here’s how you can play
                       Dead Cells on your Linux PC.


                # ⚓ How_to_reset_Ubuntu_password_–_LinuxH2O⠀⇛


                       In this article, you will learn how to reset your
                       Ubuntu password if you have forgotten it. The guide
                       work on various Ubuntu versions such as Ubuntu
                       18.04, 20.04, 21.04, and the newer versions.


                       There are times when you forget the password for
                       your Ubuntu system, maybe not you, it could be your
                       family member, friend, or colleague. Not just
                       password, people sometimes also forget the username
                       of their system. In any of these cases, you have to
                       show off your Linux skills and resolve the issue.
                       So in this guide, you will basically learn all the
                       steps to reset the Ubuntu password and also
                       identify the username.


                       So let’s start.


          o § Wine or Emulation⠀➾


                # ⚓ CrossOver_21.1.0_Release_Adds_GTA_V_Support_on_Linux_Among
                  Other_Enhancements_–_It’s_FOSS_News⠀⇛


                       CrossOver is a paid tool that lets you run
                       Microsoft Windows software on Linux and Mac. In
                       case you did not know, it is built on top of Wine
                       and other open-source software along with their
                       proprietary tools that make it easy to run Windows-
                       only software.


                       With the latest release, i.e., CrossOver 21.1.0,
                       there are some significant additions for Linux and
                       macOS users.


                       Here, let me highlight the key changes in this
                       release.


          o § Games⠀➾


                # ⚓ Valve_Posts_Updated_Steam_Deck_FAQs_To_Address_More
                  Community_Questions_–_Phoronix⠀⇛


                       Valve has provided an updated developer-focused
                       “frequently asked questions” area stemming from
                       community questions during the recent Steam Deck
                       developer event.


                       While the Steam Deck shipping date slipped into Q1
                       due to hardware supply chain issues, Valve
                       continues making great progress on the software
                       front and readying the ecosystem and developer
                       partners for their much anticipated Arch Linux
                       powered gaming handheld console.


          o § Desktop Environments/WMs⠀➾


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


                      # ⚓ More_about_those_zero-dot_users_–_Adventures_in_Linux
                        and_KDE⠀⇛


                             Yesterday’s article about KDE’s target users
                             generated some interesting discussions about
                             the zero-dot users. One of the most
                             insightful comments I read was that nobody
                             can really target zero-dot users because they
                             operate based on memorization and habit,
                             learning a series of cause-effect
                             relationships: “I click/touch this picture/
                             button, then something useful happens”–even
                             with their smartphones! So even if GNOME and
                             ElementaryOS might be simpler, that doesn’t
                             really matter because it’s not much harder to
                             memorize a random-seeming sequence of clicks
                             or taps in a poor user interface than it is
                             in a good one.


                             I think there’s a lot of truth to this
                             perspective. We have all known zero-dot users
                             who became quite proficient at specific
                             tasks; maybe they learned how to to
                             everything they needed in MS Office, Outlook,
                             or even Photoshop.


                             The key detail is that these folks rely on
                             the visual appearance and structure of the
                             software remaining the same. When the
                             software’s user interface changes–even for
                             the better–they lose critical visual cues and
                             reference points and they can’t find anything
                             anymore.


                      # ⚓ KDE_Plasma_Desktop_Update_»_PCLinuxOS⠀⇛


                             The KDE Plasma Desktop packages have been
                             updated to 5.23.4. This is a service release
                             update.


                      # ⚓ TSDgeos’_blog:_Okular_PDF_digital_signature
                        improvements_coming_“soon”_thanks_to_NLnet⠀⇛


                             Starting on January I will be working on a
                             project named “Improve Okular digital
                             signature support” that has received a grant
                             from the NLnet foundation as part of the NGI
                             Assure fund.


                             This will allow me to work part time on
                             Okular (in case it’s not clear I work on
                             Okular on a “when I have time-hobby” basis
                             right now), the planned improvements are:


                             1. Support for signing unsigned signatures. I
                             know it sounds confusing, think about it like
                             something like the old “sign here” boxes on
                             printed paper forms.


          o § Distributions⠀➾


                # ⚓ 2021_hardcore_list_of_linux_distributions_without_elogind
                  and_other_systemd_parts⠀⇛


                       This list is going to be short and there may be a
                       sublist of distros with a medium strict standard.
                       We shall explain what the object is, below the
                       short list (which we hope the community will assist
                       in making longer as we have not been able to
                       currently review the work of every distro and fork.


                # § BSD⠀➾


                      # ⚓ What_Is_OpenBSD?_Everything_You_Need_to_Know⠀⇛


                             OpenBSD is no doubt one of the most secure
                             operating systems on the internet. Here’s
                             what you need to know about it.


                             Linux fans love to tout their system’s
                             security, but for one group of BSD
                             developers, it doesn’t go far enough. One
                             version of BSD, OpenBSD, claims to be one of
                             the most secure operating systems around.
                             Does it live up to the hype? Let’s find out.


                # § IBM/Red Hat/Fedora⠀➾


                      # ⚓ Fugaku_Retains_Official_#1_Spot_on_TOP500⠀⇛


                             Summit, which is an IBM-built system
                             installed at the Oak Ridge National
                             Laboratory (ORNL) in Tennessee, remains the
                             fastest system in the United States.


                      # ⚓ Modernizing_Enterprise_Java:_A_cloud_native_guide_for
                        developers⠀⇛


                             Looking for a quick guide to migrating and
                             modernizing your organization’s Java-based
                             applications? Modernizing Enterprise Java
                             walks you through the journey. Download the
                             free e-book today.


                             Java has been one of the most popular
                             programming language choices for developers
                             since its release 25 years ago. It is backed
                             by an open source ecosystem of contributors
                             and a growing number of companies who rely on
                             Java for their core business workloads.


                      # ⚓ Build_lightweight_and_secure_container_images_using
                        RHEL_UBI⠀⇛


                             Deploying applications in lightweight
                             container images has practical benefits
                             because container images pack all of the
                             dependencies required for your application to
                             function properly. However, you could lose
                             the benefits of containerization if the
                             container images are too large, and thus take
                             several minutes to boot up the application.
                             In this article, I guide you through how to
                             use Red Hat Universal Base Images (UBI) as
                             the foundation to build lightweight and
                             secure container images for your
                             applications.


                      # ⚓ Automate_dependency_analytics_with_GitHub_Actions
                        [Ed: IBM's Red Hat boosting Microsoft's proprietary
                        software and vendor lock-in]⠀⇛


                      # ⚓ 20_Years_of_Red_Hat_Product_Security:_From_inception
                        to_customer_experience_(Part_1)⠀⇛


                             From its inception in 2001, the Product
                             Security team has been focused on providing
                             Red Hat’s customers value in the form of
                             hardened and streamlined security updates and
                             testing across the entire product line,
                             including managed services and, most
                             recently, our own open source software supply
                             chain.


                             But more than that, they’ve also been
                             essential members of the wider open source
                             security community, helping ensure the
                             openness and transparency of security
                             vulnerability information, aiding in the
                             fight against open source fear, uncertainty,
                             and doubt (FUD), and being key contributors
                             in the response to a wide array of high
                             profile security incidents and
                             vulnerabilities.


                             So, let’s take a look at how Product Security
                             has evolved at Red Hat over the past 20
                             years, and at what the future might look
                             like.


                      # ⚓ Skills_gap_proves_a_growing_barrier_for_digital
                        transformation_initiatives⠀⇛


                             In this year’s Red Hat 2022 Global Tech
                             Outlook report, skill-set or talent gaps
                             emerged as the top barrier organizations
                             believe will prevent them from achieving
                             their digital transformation goals. This was
                             also reflected in organizations’ non-IT
                             funding priorities for the next 12 months.


                             Red Hat develops a Global Tech Outlook report
                             every year, and from June through August
                             2021, we surveyed 1,341 information
                             technology (IT) leaders and decision makers
                             to learn about their digital transformation
                             journeys, their IT and non-IT funding
                             priorities for the coming year, and the types
                             of infrastructure they’re using to run their
                             applications.


                      # ⚓ U.S._Government_issues_directive_to_prioritize_fixing
                        exploited_CVEs:_How_Red_Hat_Insights_can_help⠀⇛


                             In November 2021, the U.S. federal government
                             published a Cybersecurity and Infrastructure
                             Security Agency’s Binding Operational
                             Directive. This Department of Homeland
                             Security (DHS) directive mandates federal
                             agencies within the U.S. act to protect
                             themselves from “…increasingly sophisticated
                             malicious cyber campaigns that threaten the
                             public sector, private sector, and ultimately
                             the American people’s security and privacy.”


                             The directive requires United States federal
                             agencies to patch known, “publicly exploited”
                             vulnerabilities. The list of these
                             vulnerabilities is cataloged and updated by
                             the Cybersecurity & Infrastructure Security
                             Agency (CISA) (on their website)
                             periodically.


                      # ⚓ Digital_transformation:_How_to_beat_the_challenges_of
                        a_federated_organization_|_The_Enterprisers_Project⠀⇛


                             In early 2019, I started my role as business
                             transformation executive for the Federal
                             Reserve System, responsible for leading the
                             digital transformation of finance, human
                             resources, and procurement.


                             As the central bank of the United States, the
                             Federal Reserve is a federated organization
                             made up of 22,000 employees across the 12
                             Reserve banks. Each bank is its own separate
                             legal entity with its own board of directors,
                             CEO, CFO, CIO, and senior HR and procurement
                             officers.


                             Over the years, technology was consolidated
                             while processes and capabilities remained
                             disparate, and it became increasingly
                             challenging to deliver even basic
                             capabilities. With over 40 disjointed, mostly
                             homegrown legacy applications and a high
                             degree of customization supporting
                             proprietary business processes, the system
                             was costly and challenging to maintain. New
                             employees were frustrated by the poor user
                             experience and difficulty accessing data, and
                             collaboration and innovation were hampered.


                      # ⚓ Digital_transformation:_4_questions_CIOs_should_ask
                        now_|_The_Enterprisers_Project⠀⇛


                             One of the things CIOs have learned during
                             the past eighteen months is that when you
                             have the business behind you, the momentum
                             for transformation is turbocharged. Top CIOs
                             are capitalizing on this lesson to further
                             integrate technology strategy with business
                             strategy. And the first place they’re
                             starting is with the people.


                             How well are you doing on the people front of
                             digital transformation? Here are four
                             questions to ask yourself, based on my recent
                             conversations with the CIOs of CarMax, Dow,
                             and Johnson & Johnson.


                      # ⚓ Virtual_Machine_Secure_Boot_Database_Updates_Made
                        Easy_with_Oracle_Linux⠀⇛


                      # ⚓ IBM_applauds_Knative’s_application_to_join_the_Cloud
                        Native_Computing_Foundation⠀⇛


                             Today, Knative applied to become an
                             incubating project at the Cloud Native
                             Computing Foundation. Today’s news is a major
                             step in the right direction for the future of
                             Knative.


                             Knative adds the necessary components that
                             enable Kubernetes users to more quickly
                             deploy and manage their workloads on
                             Kubernetes — but without the need to become
                             Kubernetes experts. Additionally, Knative
                             adds “serverless” runtime semantics, allowing
                             users to reap the benefit of features such as
                             quick load-based scaling and scaling to zero
                             when idle.


                      # ⚓ 3_ways_to_optimize_Ansible_Automation_Platform_for
                        scale_and_performance_|_Enable_Sysadmin⠀⇛


                             Try these settings to optimize performance
                             with Ansible Automation Platform on a massive
                             scale.


                      # ⚓ Introduction_to_Ansible_prompts_and_runtime
                        variables⠀⇛


                             This tutorial is part of a series we
                             dedicated to Ansible. Previously we talked
                             about the Ansible basics, then we focused on
                             some Ansible modules we can use to perform
                             some very common administration tasks, and we
                             also talked about Ansible loops. In this
                             article, instead, we learn how to create
                             interactive prompts we can use to ask for
                             user input and how to pass variables at
                             runtime.


                      # ⚓ MIXAL_on_Fedora_|_Adam_Young’s_Web_Log⠀⇛


                             The examples in The Art of Computer
                             Programming (TAOCP) are in the MIXAL
                             programming language. In order to see these
                             examples run, I want to install the tools on
                             my Fedora box. They are packaged as RPMS, so
                             this is trivial. Here are the steps to run
                             and debug a sample program in MIXAL.


                      # ⚓ Fedora_Contributor_Annual_Survey_Data_Set_Available_–
                        Fedora_Community_Blog⠀⇛


                             Over the summer of 2021, the Fedora Council
                             held the first annual Contributor Survey. The
                             survey received 800 complete responses, which
                             exceeded the goal of 500. We have processed
                             the data, which are available for download.


                             Coordination of the survey was a wonderful
                             community effort. Fedora Council member
                             Aleksandra Fedorova proposed and led the
                             survey effort with support from Marie Nordin
                             (FCAIC). Many teams across the Fedora Project
                             contributed, including: the Mindshare
                             Committee, the Outreach Revamp Team, the
                             Design Team, the Websites & Apps Team, and
                             the Community Platform Engineering Team.
                             Aleksandra and Marie presented a session at
                             Nest with Fedora which goes further into the
                             process and outcomes.


                             Over the last couple months, the work of
                             cleaning up the dataset has been underway.
                             This has been a slow process as there are
                             just a couple of people working on that
                             regularly. An example of “cleaning” would be
                             folks who chose “Other”, filled in “idk”,
                             when the option “I don’t know” existed. Those
                             answers need to be integrated in order to
                             have a more accurate dataset. We removed
                             fill-in answers due to the fact that some
                             people identified themselves, intentionally
                             or not. As we process the data, we are noting
                             feedback to improve the survey for 2022.


                # § Canonical/Ubuntu Family⠀➾


                      # ⚓ Linux_Mint_Monthly_News_–_November_2021⠀⇛


                             Many thanks to all the people who support our
                             project. Thank you very much to all of you
                             for your help and your generous donations.


                             All of our focus is on the BETA for Linux
                             Mint 20.3. We’re planning to release it early
                             this December. We’re finalizing translations,
                             artwork and still making fixes and
                             adjustments but for the most part it’s almost
                             ready to enter QA.


                             Some of the new features in 20.3 haven’t been
                             revealed yet, but we’re so close to release,
                             I’m not sure there’s much point in giving you
                             a preview


                             MATE 1.26 and Flatpak 1.12 were backported.


                             In the XApps, the PDF reader received proper
                             manga support (hitting the left arrow key in
                             manga mode now goes forward in the document),
                             the image viewer received the ability to
                             quickly fit to the width or the height of the
                             displayed picture, and many of the apps
                             received improvements for small display
                             resolutions (hiding the menubar, not showing
                             the toolbar in fullscreen…etc), and dark-mode
                             support.


                      # ⚓ Compact_edge_AI_boxes_offer_choice_of_Jetson_Nano,
                        TX2_NX,_and_Xavier_NX⠀⇛


                             All three systems ship with the Ubuntu 18.04
                             with Nvidia JetPack 4.5.1. They also support
                             Advantech’s Edge AI Suite and FaceView
                             applications, which are available on its
                             earlier AIR systems.


                      # ⚓ Ubuntu_Blog:_Embedded_systems:_the_advent_of_the
                        Internet_of_Things_–_Part_II⠀⇛


                             This is the second part of the two-part blog
                             series covering embedded Linux systems and
                             the challenges brought about by the
                             proliferation of Internet of Things (IoT)
                             devices. In Part I, we surveyed the embedded
                             ecosystem and the role Linux plays within
                             that space. This blog takes you on the next
                             step in the journey, where we explore the
                             most demanding challenges facing
                             manufacturers of tightly embedded IoT
                             devices.


                      # ⚓ CyberDog:_a_four_legged_robot_revolution_with
                        Ubuntu⠀⇛


                             Late this year, Chinese tech giant Xiaomi
                             unveiled CyberDog: a quadrupedal,
                             experimental, open-source robot that the firm
                             claims will improve the robot development
                             environment and promote the development of
                             the robot industry. Today, Canonical dives
                             into the specifications of this four legged
                             robot and discover how Ubuntu is helping the
                             device become an open source technological
                             platform.


                             Xiaomi has a clear vision for its product. As
                             Huang Changjiang, PM at Xiaomi, explains,
                             “CyberDog is developers’ technological
                             partner from the future. It equips inhouse-
                             made high-performance servo motors, high
                             computing ability, with built-in AI for
                             visual detection system and voice interaction
                             system, supporting a variety of bionic motion
                             gestures.”


                      # ⚓ ZeroDown®_Software_Targets_Open_Source_with_New
                        Canonical_Partnership⠀⇛


                             As businesses around the world and in every
                             major industry define and accelerate their
                             cloud strategies, the lack of open, flexible
                             and complete high availability has become a
                             major concern. The ZeroDown platform, built
                             upon Canonical’s industry-leading operating
                             system, Ubuntu, aims at integrating into
                             Canonical’s broader Charmed OpenStack
                             platform with its ZeroDown Ultra High-
                             Availability TM Software, eliminating
                             downtime and data loss for its customers,
                             running seamlessly through planned or
                             unplanned downtime events.


                      # ⚓ Data_centre_networking:_what_is_OVS?_|_Ubuntu⠀⇛


                             In one of our preceding blogs, we spoke about
                             Software-Defined Networking (SDN) and the key
                             drivers behind it. Virtualisation is one of
                             the fundamental aspects that characterises
                             SDN, and has influenced the architecture of
                             network switching in the data centre. OVS
                             (Open vSwitch) is a fundamental component of
                             modern and open data centre SDNs, where it
                             aggregates all the virtual machines at the
                             server hypervisor layer. It represents the
                             ingress point for all the traffic exiting
                             VMs, and can be used to forward traffic
                             between multiple virtual network functions in
                             the form of service chains. Let’s take a
                             closer look in order to understand what OVS
                             is.


          o § Devices/Embedded⠀➾


                # ⚓ FPGA_SoC_modules_gain_networking_carrier_and_new_PolarFire
                  SoC_model⠀⇛


                       Enclustra’s “Mercury+ PE3” carrier for its FPGA/SoC
                       Mercury/Mercury+ modules can act as an SBC or plug
                       into a PC via PCIe x8. It offers QSFP+, 4x SFP+,
                       FireFly, and 2x GbE. We also examine a new
                       “Mercury+ MP1” module based on the RISC-V based
                       PolarFire SoC.


                       In May, Switzerland based Enclustra announced a
                       Mercury+ ST1 baseboard for its FPGA/SoC powered
                       Mercury and Mercury+ compute modules. These include
                       a Xilinx Zynq UltraScale+ MPSoC based Mercury+ XU6
                       module that was announced at the same time. Now the
                       company has unveiled a more feature-rich Mercury+
                       PE3 board for the Mercury/Mercury+ product line.


                       Farther below, we report on a similarly “in
                       development” Mercury+ MP1 module based on
                       Microchip’s based PolarFire SoC, which includes
                       RISC-V based CPU cores and Microchip’s PolarFire
                       FPGA.


                # ⚓ We’ve_scaled_Fairtrade_gold_–_Fairphone⠀⇛


                       We have paved the way to source more Fairtrade
                       gold! Together with Fairtrade, we have partnered
                       with Hirose Electric Co., Ltd. in Japan in order to
                       integrate more Fairtrade gold into our supply
                       chain. Our relationship with Hirose and Fairtrade
                       continues our support of ASM gold projects and
                       miners. This is an incredible stepping stone for
                       the larger vision of a Fairtrade and Fairphone
                       partnership to scale responsible gold in the
                       electronics sector.


                # § Open Hardware/Modding⠀➾


                      # ⚓ Buy_A_Piece_Of_The_Pi?_|_Hackaday⠀⇛


                             The various companies and organisations that
                             supply our community have achieved differing
                             levels of success, with some staying as
                             kitchen-table operations and others reaching
                             the giddy heights of multinational commerce.
                             Perhaps none has risen so far as Raspberry Pi
                             though, as there are reports that the
                             developer of single board computers might be
                             seeking a £400m listing on the London Stock
                             Exchange some time next year. The news is
                             that they have sought the advice of
                             investment bankers over the possibility of a
                             float, seeking to secure further investment
                             to further develop their product portfolio.


                             We’re not investment advisers here at
                             Hackaday so we’re not going to suggest
                             whether or not to bet your shirt on Pi
                             shares, instead our interest lies in what
                             this might mean for their family of products.
                             It’s an inevitable process for any start-up
                             that achieves major success that it will over
                             time progress from being directed by vision
                             to being directed by commerce, and perhaps a
                             listing could be the culmination of this
                             process. It’s fair to say that we tinkerers
                             probably represent less of a market than
                             education or industry to the Pi folks, so how
                             might we win or lose when the suits take the
                             helm?


                      # ⚓ What’s_The_Deal_With_UEFI?⠀⇛


                             The Linux community, generally speaking, is
                             agnostic at best and antagonistic at worst
                             towards UEFI. The BIOS interface is pushing
                             45 years as of the time of writing and is
                             considered legacy in every sense


                      # ⚓ Open-Source_FPGA-Based_RISC-V_GPGPU_That_Supports
                        OpenCL_1.2_–_Phoronix⠀⇛


                             While there was the Libre RISC-V GPU effort
                             aiming to provide an open-source GPU
                             accelerator based on RISC-V, it ultimately
                             turned into Libre-SOC with a focus now on the
                             POWER ISA. Meanwhile Vortex is continuing to
                             mature as an open-source, FPGA-based RISC-
                             V GPGPU processor.


                             Vortex is a RISC-V GPGPU currently for FPGA-
                             based implementation with either the Intel
                             Arria 10 or Intel Stratix 10 working. This
                             general purpose GPU makes use of the RISV-
                             V RV32IMF 32-bit ISA and can yield up to 1024
                             threads at 250MHz.


                # § Mobile Systems/Mobile Applications⠀➾


                      # ⚓ How_to_Split-Screen_and_Multitask_on_Android_–
                        Dignited⠀⇛


                      # ⚓ How_To_Wipe_Your_Android_Device_&_Restore_It_To
                        Factory_Settings⠀⇛


                      # ⚓ Samsung_Android_12_update:_These_devices_have_One_UI
                        4.0_–_9to5Google⠀⇛


                      # ⚓ Android_12_should_make_these_changes_in_future
                        updates_–_9to5Google⠀⇛


                      # ⚓ Want_Android_11_on_Your_Nokia_9?_Nokia_Says_Buy_a_New
                        Phone_|_Digital_Trends⠀⇛


                      # ⚓ Millions_of_Android_phones_need_to_be_fixed_NOW_over
                        ‘eavesdropping’_scare⠀⇛


                      # ⚓ 25_best_free-to-play_Android_games_in_2021⠀⇛


                      # ⚓ Amazon_Appstore_Is_Crashing_on_Android_12_Even_After
                        a_Month_of_Its_Public_Release:_Reports_|_Technology
                        News⠀⇛


                      # ⚓ Xiaomi_testing_MIUI_13_based_on_Android_11_and_12,
                        list_of_devices_in_tow_–_comments⠀⇛


                      # ⚓ Android_12_gets_home_controls,_wallet_in_power_menu
                        w/_app_–_9to5Google⠀⇛


                      # ⚓ Nokia_9_PureView_won’t_get_Android_11,_here_is_why_–
                        PhoneArena⠀⇛


                      # ⚓ Nokia_9_Android_11_upgrade_canceled_permanently_–
                        Android_Authority⠀⇛


                      # ⚓ YouTube_for_Android_is_trying_out_a_new_Material_You
                        look⠀⇛


                      # ⚓ How_to_Control_Your_Android_Phone_With_Facial
                        Gestures⠀⇛


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


                # ⚓ Best_3_Open-source,_privacy-aware,_ads-free_Diabetes
                  Managers_for_Android⠀⇛


                       Diabetes is a long-lasting (chronic) health
                       condition, that occurs when blood sugar is too
                       high. It is a life-altering disease, as it changes
                       eating habits and exercises routine.


                       Diabetes management apps are many, and they come as
                       web-based services, standalone mobile apps, and
                       desktop apps. However, most of them are not free,
                       open-source, or respect patient privacy much.
                       Therefore, we write this article.


                       Diabetes management and assistant apps are
                       classified under a PHR “Personal Health Records”
                       apps, where the patient logs and keeps all of his
                       private records for future analysis and use.


                # ⚓ Penpot:_an_open-source_Prototyping_and_design_platform_for
                  teams⠀⇛


                       Penpot is a free, open-source web-based design and
                       prototyping application for teams. It works with
                       open web standards as it uses SVG (Scalable Vector
                       Graphics) format.


                       Penpot can be installed on a remote server or the
                       local machine with help of Docker and Docker
                       Compose.


                       With Penpot, you can quickly design a web or mobile
                       prototype in no time.


                # ⚓ FreeScout_is_an_open-source_helpdesk_for_teams⠀⇛


                       FreeScout is a free, open-source web-based support
                       and ticketing system. It is written in PHP using
                       the Laravel framework.


                       FreeScout features a responsive user interface that
                       works on small mobile screens and tablets.


                       It is an ideal solution for team, technical
                       support, and customer support for small and medium-
                       sized companies as well as enterprise.


                       FreeScout is battle tested with hundreds of
                       satisfied companies, it is also supported with a
                       large community of advanced users and
                       professionals.


                       [...]


                       FreeScout is released under GNU Affero General
                       Public License v3.0.


                       The GNU Affero General Public License v3.0 permits
                       commercial use, system modification, distribution,
                       patent use, and private use. However, it comes with
                       a limitation for liability and warranty, and
                       several conditions.


                # ⚓ UMLet:_Open-source_multi-platform_UML_tool⠀⇛


                       UMLet is a free, open-source UML modeling tool for
                       developers that allows them to draw UML diagrams
                       quickly and export them to many formats.


                       The program is released as an open-source under
                       GPL-3.0 License.


                # ⚓ JetUML:_Open-source_UML_diagramming_tool_for_Windows,
                  Linux,_and_macOS⠀⇛


                       JetUML is a free, lightweight desktop app for
                       building and editing UML diagrams.


                       JetUML is built with Java which comes also in a
                       small .jar package.


                # ⚓ The_OpenNMS_Group_Releases_OpenNMS_Minion_Appliance_–_the
                  Next_Evolution_of_Distributed_Monitoring⠀⇛


                # ⚓ Monica_is_your_own_persona_CRM/_Assistant_solution⠀⇛


                       Monica is a free, open-source self-hosted personal
                       CRM solution to help you keep tracking all of your
                       social events, activities, work information and
                       strengthen your interaction with your family
                       members.


                       [...]


                       Monica is released under Affero General Public
                       License (AGPL) v3.0.


                # ⚓ Watch_Blender_Plugin_Make_Animated_PCB_Traces_(and_More)_|
                  Hackaday⠀⇛


                       The idea is that one begins with an image texture
                       with a structure showing a bunch of paths (like a
                       maze, or traces on a PCB), and that gets used as an
                       input. The plugin then uses a path finding
                       algorithm to determine how these paths could grow
                       from an origin point, and stores the relevant data
                       in the color channels of an output image. That
                       output is further used within Blender as the
                       parameters with which to generate the actual
                       animation, resulting in the neat self-creating PCB
                       seen above. That PCB isn’t just for show, by the
                       way. It’s the PCB for [Staacks]’s smart doorbell
                       project.


                       Blender is an amazingly comprehensive tool for
                       modeling and animation, and while we’ve covered
                       using it to create high-quality KiCad renders, this
                       kind of animation is really something else.


                # ⚓ Weekly-ish_recap_—_30_November_2021⠀⇛


                       This is more of a monthly recap, for my sins!
                       Highlights: new releases of BlenderBIM and
                       IfcOpenShell, Natron, LibrePCB, Shotcut, VCV Rack,
                       Blender 3.0 is coming later this week, Krita and
                       darktable are prepping up for a major update.


                       [...]


                       The most recent release of Shotcut arrived with
                       support for markers (at long, long last). Dan has
                       been expanding this feature ever since. There’s now
                       a Markers dock where you can add, edit/rename, and
                       remove markers. UX for marker color selection has
                       been improved too, and you can now seek to previous
                       and next markers. Also, you can now export markers
                       as chapters. You can expect all that (and more) in
                       the next release.


                # § Web Browsers⠀➾


                      # § Mozilla⠀➾


                            # ⚓ Mozilla_Performance_Blog:_Updates_to_Warm_Page
                              Load_Tests⠀⇛


                                   We have recently begun the process of
                                   updating our warm page load tests to be
                                   more representative of real user
                                   behavior.


                                   Cold page load is defined as the first
                                   page load, just after the initial
                                   startup of the browser. Warm page load
                                   is any load of a page after the first
                                   page load, and the cache has been
                                   populated with some data for the page,
                                   i.e. the cache is “warmed up”.


                # § SaaS/Back End/Databases⠀➾


                      # ⚓ PostgreSQL:_PGConf_NYC_2021_starts_Thursday!⠀⇛


                             That means registration is closing since the
                             conference will be starting!


                             The first community PostgreSQL conference in
                             North America in many months is in New York
                             City this Thursday and Friday! PGConf NYC is
                             a non-profit, community-run and PostgreSQL
                             community recognized conference being run by
                             the United States PostgreSQL Association
                             (PgUS).


                             Don’t wait any longer to register for this
                             great event happening right in downtown New
                             York City!


                             PGConf NYC delivers two days packed with
                             presentations about PostgreSQL and related
                             technologies, as well as the usual hallway
                             and social track. PGConf NYC is being held
                             December 2nd and 3rd, 2021 in New York City.


                      # ⚓ Publication_of_the_“Transition_guide_to_PostgreSQL”⠀⇛


                             We’re pleased to announce an English version
                             of the “Transition guide to PostgreSQL”. This
                             aims to answer questions from project owners
                             and management about implementing PostgreSQL
                             in place of a commercial solution.


                # § Content Management Systems (CMS)⠀➾


                      # ⚓ WordPress_5.9_Beta_1⠀⇛


                             WordPress 5.9 Beta 1 is now available for
                             testing!


                             This version of the WordPress software is
                             under development. You don’t want to run this
                             version on a production site. Instead, it is
                             recommended that you run this on a test site.
                             This will allow you to test out the new
                             version.


                      # ⚓ People_of_WordPress:_Devin_Maeztri⠀⇛


                             In this series, we share some of the
                             inspiring stories of how WordPress and its
                             global network of contributors can change
                             people’s lives for the better. This month we
                             feature a translator and campaigner who uses
                             WordPress to highlight good causes and helps
                             people in her area benefit from the open
                             source platform.


                # § FSF⠀➾


                      # ⚓ Help_the_FSF_tech_team_maintain_email_services_in
                        freedom⠀⇛


                             The Free Software Foundation’s (FSF) tech
                             team is a small but dedicated team of three
                             staff. With your support, and with the help
                             of volunteers and interns, we run hundreds of
                             services on a few dozen physical machines in
                             four data centers.


                             We are very excited about some of the
                             initiatives we are working on, like deploying
                             our upcoming forge site and other new
                             systems, expanding our physical server
                             deployments, and a further refresh of
                             fsf.org. In parallel, the tech team is always
                             working to better maintain, understand, and
                             document our existing systems. Mastering
                             those keeps vital systems running smoothly
                             and lays the groundwork for future
                             improvements.


                             Email is a key service we provide. Besides it
                             being one of the FSF campaigns and licensing
                             teams’ most important ways of communicating,
                             we also support thousands of mailing lists
                             for other free software projects, which send
                             millions of emails per year. Free software is
                             extremely capable in all aspects of email,
                             and there continue to be innovative
                             advancements in free software email programs
                             that we are excited to explore and adopt.


                      # § Licensing/Legal⠀➾


                            # ⚓ First_Update_on_the_Vizio_lawsuit_–_Conservancy
                              Blog_–_Software_Freedom_Conservancy⠀⇛


                                   Yesterday, we received from Vizio their
                                   first official response in our pending
                                   litigation against Vizio for their
                                   copyleft license violations. So, what
                                   was their response?


                                   Did Vizio release the source code — as
                                   the GPL and LGPL require — for the
                                   modified versions of Linux, alsa-utils,
                                   GNU bash, GNU awk, BusyBox, dmesg,
                                   findutils, dmsetup, GNU tar, mount and
                                   selinux found in their TV’s firmwares?
                                   No.


                                   Did Vizio propose a CCS candidate for
                                   us to review, provide them with
                                   additional feedback, so that we could
                                   help them get consumers who bought
                                   their TVs the source code they deserve?
                                   Nope.


                                   Did Vizio argue that we had erred, and
                                   in fact, none of those programs we list
                                   above appear in their firmware? Not
                                   that either. (Unlikely though — after
                                   all, they surely know those programs
                                   are in their firmware!)


                # § Public Services/Government⠀➾


                      # ⚓ German_coalition_treaty_endorses_“Public_Money,
                        Public_Code”_principle_–_The_Document_Foundation_Blog⠀⇛


                             A quick news update from Germany: the
                             upcoming coalition government endorses free
                             and open source software. In the coalition
                             agreement (German), there are some key
                             sentences on this topic, for instance…


                      # ⚓ Nextcloud_Forms_European_Coalition_—_Begins_Antitrust
                        Actions_Against_Microsoft⠀⇛


                             A European coalition formed by Nextcloud is
                             taking antitrust action against Microsoft
                             like it’s 1999.


                             The Germany-based company behind the on-
                             premises content collaboration platform that
                             shares its name, has put together a coalition
                             of 30 organizations to fight Microsoft on
                             antitrust grounds.


                             “The 90s have just called and they see that
                             nothing has changed,” Stefane Fermigier,
                             founder and CEO of open source software
                             vendor Abilian — a part of the coalition —
                             said in a statement. “Microsoft’s anti-
                             competitive practices remain a major concern
                             for the competitiveness of the European
                             software and cloud industry. As it has done
                             in the past in similar cases, the European
                             Commission must put an end to these
                             practices.”


                # § Programming/Development⠀➾


                      # ⚓ Daniel_Aleksandersen:_Closing_the_open_redirect_in
                        the_Libravatar_ecosystem⠀⇛


                             Libravatar is a decentralized open-source
                             alternative to Gravatar – the avatar image
                             service. Last week, I noticed an URL
                             Redirection to Untrusted Site (‘Open
                             Redirect’) vulnerability (CWE-601) in the
                             Libravatar application programming interface
                             (API) specification.


                             [...]


                             An attacker can use the redirect to leech off
                             the reputation of a Libravatar server’s
                             domain. An open redirect can be used to
                             obscure a link’s true destination, or help a
                             spam or phishing message to sneak past
                             filters.


                             An open redirect is a common vulnerability,
                             but the security community tries to shut them
                             down whenever they’re discovered. What’s
                             making this one noteworthy is that you can
                             auto-discover Libravatar servers using DNS
                             service discovery (DNS-SD) by querying
                             domains for the DNS SRV records.


                             I DNS-SD queried the web’s top 5,1 million
                             domains (Tranco list #44KX) to see how many
                             Libravatar instances and open redirects I
                             could find. In total, I discovered 18
                             instances (unique IP addresses) on 23
                             distinct domain names. 11 instances were
                             vulnerable (13 domain names).


                             Notably, the servers operated by academic
                             institutions were not vulnerable. These
                             institutions are likely running custom
                             software solutions on top of their staff and
                             student databases to generate the avatars.


                      # ⚓ Hacks_Decoded:_Seyi_Akiwowo,_Founder_of_Glitch⠀⇛


                             I’m not, I don’t think I want to “keep going”
                             anymore. I grew my organization by 50% in
                             terms of income and more in terms of staff
                             and diversified our income streams before we
                             hit the two-year mark — during a pandemic!
                             I’m ready to rest, I’m ready to sleep more,
                             I’m ready to do work that is still great with
                             minimum viable effort. That’s the sweet spot
                             I’m looking for.


                      # ⚓ A_Super_Speedy_Lightweight_Lossless_Compression
                        Algorithm_|_Hackaday⠀⇛


                             [Dominic Szablewski] was tinkering around
                             with compressing RGB images, when he stumbled
                             upon idea of how to make a simple lossless
                             compression algorithm, resulting in the Quite
                             OK Image Format, which seems to offer
                             comparable file sizes to the PNG format but
                             is so simple it runs up to 50 times faster
                             for compression and up to four times faster
                             for decompression. Implementation can be
                             achieved with a miniscule 300 lines of C.
                             Need a bit more detail on the real-world
                             performance? Well [Dominic] has that covered
                             too, with a complete set of benchmarks for
                             your perusal.


                      # ⚓ HLK-W801_board_features_Alibaba_Xuantie_XT804_based
                        MCU_with_WiFi_4,_Bluetooth_LE_4.2_–_CNX_Software⠀⇛


                             But the company has a nearly identical
                             WinnerMicro W801 microcontroller that bumps
                             the internal flash to 2MB, and more
                             importantly adds a 2.4 GHz radio with WiFi 4
                             and Bluetooth LE 4.2 connectivity, and HiLink
                             also released the HLK-W801 board that’s
                             nearly identical to HLK-W806, except for some
                             extra LEDs, a USB-C port instead of a Micro
                             USB port, and a longer form factor to make
                             space for the PCB antenna.


                      # ⚓ Running_the_MIXAL_Insertion_Sort_|_Adam_Young’s_Web
                        Log⠀⇛


                             With the information gained in last posts
                             investigations, I now know how to turn the
                             smaple code of the insertion sort out of
                             TAOCP into runnable code.


                             The key insight I had was that the
                             Accumulator was operating on the whole value
                             it would fetch or store, and the I# registers
                             were just used for counters. Thus, the buffer
                             needed to be of word length elements. For MIX
                             that means 5 characters long.


                      # ⚓ Russell_Coker:_Your_Device_Has_Been_Improved⠀⇛


                             By “stability improved” they mean “fixed some
                             bugs that made it unstable” and no technical
                             person would imagine that after a certain
                             number of such updates the number of bugs
                             will ever reach zero and the tablet will be
                             perfectly reliable. In fact if you should
                             consider yourself lucky if they fix more bugs
                             than they add. It’s not THAT uncommon for
                             phones and tablets to be bricked (rendered
                             unusable by software) by an update. In the
                             past I got a Huawei Mate9 as a warranty
                             replacement for a Nexus 6P because an update
                             caused so many Nexus 6P phones to fail that
                             they couldn’t be replaced with an identical
                             phone [1].


                             By “security improved” they usually mean
                             “fixed some security flaws that were recently
                             discovered to make it almost as secure as it
                             was designed to be”. Note that I deliberately
                             say “almost as secure” because it’s sometimes
                             impossible to fix a security flaw without
                             making significant changes to interfaces
                             which requires more work than desired for an
                             old product and also gives a higher
                             probability of things going wrong. So it’s
                             sometimes better to aim for almost as secure
                             or alternatively just as secure but with some
                             features disabled.


                      # ⚓ All_change_at_JetBrains:_Remote_development,_new_IDE
                        preview_•_The_Register⠀⇛


                             JetBrains has introduced remote development
                             for its range of IDEs as well as previewing a
                             new IDE called Fleet, which will form the
                             basis for fresh tools covering all major
                             programming languages.


                             JetBrains has a core IDE used for the
                             IntelliJ IDEA Java tool as well other IDEs
                             such as Android Studio, the official
                             programming environment for Google Android,
                             PyCharm for Python, Rider for C#, and so on.
                             The IDEs run on the Java virtual machine
                             (JVM) and are coded using Java and Kotlin,
                             the latter being primarily a JVM language but
                             with options for compiling to JavaScript or
                             native code.


                      # ⚓ PHP_Foundation_Looks_to_Fund_Open_Source_Language
                        Development⠀⇛


                             The PHP Foundation is gearing up as a new
                             organization to help fund and support the
                             continued development of the open source PHP
                             programming language.


                      # § Perl/Raku⠀➾


                            # ⚓ MONKEY-SEE-NO-CROSSPRODUCT_|_Playing_Perl
                              6␛b6xA_Raku⠀⇛


                                   The challenge of the week is screaming:
                                   “Nest all the loops!”. I don’t like
                                   being yelled at, so I refuse to use any
                                   nested for/while/loop. The rules don’t
                                   require to put the two sub-challenges
                                   into separate files, so I won’t.


                            # ⚓ Excellent_Free_Tutorials_to_Learn_Raku_–
                              LinuxLinks⠀⇛


                                   Raku is a member of the Perl family of
                                   programming languages. Formerly known
                                   as Perl 6, it was renamed in October
                                   2019. Raku introduces elements of many
                                   modern and historical languages.
                                   Compatibility with Perl was not a goal,
                                   though a compatibility mode is part of
                                   the specification.


                            # ⚓ It’s_that_time_of_the_year…_again_–_Raku_Advent
                              Calendar⠀⇛


                                   And we’re still around and kicking new
                                   advent posts with the best, the nicest
                                   and the merely possible in the Raku
                                   realm.


                                   Also the 13th year in a row for this
                                   calendar, and also 6th year since what
                                   was then called Perl 6 was released.
                                   Raku is now faster, it’s already in
                                   production in a number of places, and
                                   it’s got a healthy ecosystem with lots
                                   of useful modules. Who would wish for
                                   more? Well, we wish for a dozen and a
                                   again (possibly) baker’s dozen of
                                   articles for everyone to enjoy.


                      # § Shell/Bash/Zsh/Ksh⠀➾


                            # ⚓ Combinations_from_2_lists:_speed_trials⠀⇛


                                   This post was inspired by a recently
                                   published scientific paper describing
                                   how Python was used to build a list of
                                   a million scientific names. Each name
                                   was composed of parts taken from a
                                   list, and combinations of those parts
                                   were generated.


                                   The result was something like a
                                   Cartesian product, about which I’ve
                                   blogged before. This time I was
                                   interested in performance: how does the
                                   time required to get a result vary with
                                   the number of combinations to be built?


                      # § Rust⠀➾


                            # ⚓ 1.57.0_pre-release_testing⠀⇛


                                   The 1.57.0 pre-release is ready for
                                   testing. The release is scheduled for
                                   this Thursday, December 2nd. Release
                                   notes can be found here.


    * § Leftovers⠀➾


          o ⚓ Recycled_Parts_Round_Out_Soap_Shaped_Electric_Car⠀⇛


                 Hong Kong based [Handy Geng] has a knack for fitting his
                 creations with a large percentage of recycled material.
                 And as is exemplified by the video below the break, he
                 also loves to mix the practical with the whimsical.


                 Using parts salvaged from motor scooters, trash heaps,
                 and likely many other sources, [Handy] has put together a
                 small vehicle that he himself describes as looking like a
                 bar of soap as it slips across the floor. You’ll agree
                 when you see the independent front and rear steering at
                 work, allowing the car’s front and rear to be driven and
                 steered on their own. Crabbing sideways, driving
                 diagonally, and we’re guessing spinning in place are
                 possible.


          o § Hardware⠀➾


                # ⚓ Two-Stage_Dust_Collector_Recycles_Blasting_Media_|
                  Hackaday⠀⇛


                       A critical element of a good blasting cabinet setup
                       is a vacuum system that can suck out the dust,
                       blasting media, and bits of removed material faster
                       than it collects inside the chamber. A cyclone
                       separator can get the job done, but since it dumps
                       all the waste from the cabinet into one bucket, it
                       can make reusing the blasting material a dirty job.
                       But as [Daniel Bauen] explains in the latest
                       Engineerable video, his two-stage dust collector is
                       able to keep the cabinet clear while separating the
                       used blasting material into its own container.


                # ⚓ Giving_Flip_Dots_The_Oil_Treatment_To_Shut_Them_Up_|
                  Hackaday⠀⇛


                       Flip dot displays are awesome — too bad it’s so
                       hard to find large panels to play around with, but
                       that’s for another article. [Pierre Muth] has been
                       working to find different and interesting things to
                       do with these flip dots, and he recently explored
                       how you can flip them very very gently.


                       Now you likely remember [Pierre’s] work from
                       earlier this year where he was pushing the speed of
                       the displays as high as possible. Using a capacitor
                       discharge trick he made it to 30 fps, which
                       absolutely stunning work. This time around he
                       attempted to do something equally impressive by
                       micro-stepping the dots. It’s a bonkers idea and
                       unfortunately didn’t work. It seems the dots are
                       engineered for two steady states and you just can’t
                       get very good performance with the in-between
                       states.


                # ⚓ Amazon_Announces_C7g_AWS_Instances_Coming_Powered_By
                  Graviton3_–_Phoronix⠀⇛


                       Amazon Web Services today shared that C7g instances
                       are coming powered by Graviton3, their next-gen in-
                       house AArch64 processors.


          o § Integrity/Availability⠀➾


                # § Proprietary⠀➾


                      # § Pseudo-Open Source⠀➾


                            # § Privatisation/Privateering⠀➾


                                  # § Linux Foundation⠀➾


                                        # ⚓ New_Linux_Foundation_Project
                                          Accelerates_Collaboration_on
                                          Container_Systems_Between_Enterprise
                                          and_HPC_Environments⠀⇛


                                               The Linux Foundation, the
                                               nonprofit organization
                                               enabling mass innovation
                                               through open source, today
                                               announced it will host the
                                               Apptainer project. Formerly
                                               the Singularity project,
                                               Apptainer is the most
                                               widely used container
                                               system for High-Performance
                                               (HPC) computing and is one
                                               of the container systems
                                               uniquely suited for both
                                               enterprise and HPC use
                                               cases. It is designed to
                                               execute applications at
                                               bare-metal performance
                                               while being secure,
                                               portable and completely
                                               reproducible.


                                        # ⚓ New_Linux_Foundation_Project
                                          Accelerates_Collaboration_on
                                          Container_Systems_Between_Enterprise
                                          and_High-Performance_Computing
                                          Environments⠀⇛


                                               The Linux Foundation, the
                                               nonprofit organization
                                               enabling mass innovation
                                               through open source, today
                                               announced it will host the
                                               Apptainer project. Formerly
                                               the Singularity project,
                                               Apptainer is the most
                                               widely used container
                                               system for High-Performance
                                               (HPC) computing and is one
                                               of the container systems
                                               uniquely suited for both
                                               enterprise and HPC use
                                               cases. It is designed to
                                               execute applications at
                                               bare-metal performance
                                               while being secure,
                                               portable and completely
                                               reproducible.


                                               “The Apptainer project has
                                               had massive growth and
                                               needs a neutral home with
                                               proven open source
                                               governance to support its
                                               next development and
                                               adoption phase,” said
                                               Gregory Kurtzer, CEO of CIQ
                                               and Founder and Project
                                               Lead of Singularity/
                                               Apptainer. “The Linux
                                               Foundation is the natural
                                               host for Apptainer, where
                                               it can also collaborate
                                               with the Cloud Native
                                               Computing Foundation, Open
                                               Container Initiative,
                                               OpenHPC and other projects
                                               to expand its ecosystem.”


                                        # ⚓ New_Quantum_Intermediate
                                          Representation_Alliance_Serves_as
                                          Common_Interface_for_Quantum
                                          Computing_Development [Ed: 'Linux'
                                          'Foundation' letting Microsoft become
                                          its forefront speaker]⠀⇛


                                               he Linux Foundation, the
                                               nonprofit organization
                                               enabling mass innovation
                                               through open source, today
                                               announced the new QIR
                                               Alliance, a joint effort to
                                               establish an intermediate
                                               representation with the
                                               goal to facilitate
                                               interoperability within the
                                               quantum ecosystem and
                                               provide a representation
                                               suitable for current and
                                               future heterogenous quantum
                                               processors. Founding
                                               members include Honeywell,
                                               Microsoft, Oak Ridge
                                               National Laboratory,
                                               Quantum Circuits Inc. and
                                               Rigetti Computing.


                                        # ⚓ Linux_Foundation_launches_quantum
                                          computing_alliance_to_drive
                                          interoperability [Ed: Microsoft
                                          employees speak for the ‘Linux’
                                          Foundation now; it’s sold, it is
                                          compromised]⠀⇛


                                               The Linux Foundation has
                                               announced a new joint
                                               effort to help facilitate
                                               interoperability within the
                                               quantum computing
                                               ecosystem.


                                               Dubbed Quantum Intermediate
                                               Representation (QIR), the
                                               alliance is part of the
                                               Linux Foundation’s efforts
                                               to promote the development
                                               and use of open standards.


                                        # ⚓ Linux_Foundation:_Defending_the
                                          Global_Software_Supply_Chain_from
                                          Cyberattacks_in_2021 [Ed: With
                                          partners like these, as show, it can
                                          be presumed also a selective back
                                          doors_alliance with NSA_ties]⠀⇛


                                               Attackers are increasingly
                                               targeting software supply
                                               chains (the processes,
                                               repositories, and
                                               toolchains used for
                                               developing and delivering
                                               software). The European
                                               Union Agency for
                                               Cybersecurity, ENISA,
                                               estimated in “Threat
                                               Landscape for Supply Chain
                                               Attacks” that there would
                                               be four times as many
                                               software supply chain
                                               attacks in 2021 as compared
                                               to 2020. The report states
                                               due to “…more robust
                                               security protection that
                                               [many] organizations have
                                               put in place [today],
                                               attackers successfully
                                               shifted towards suppliers.”


                                               Governments around the
                                               world have noted and
                                               responded to this growing
                                               risk to the software supply
                                               chain. In May 2021, the US
                                               released an Executive Order
                                               on Improving the Nation’s
                                               Cybersecurity to enhance
                                               software supply chain
                                               security, including
                                               providing software
                                               purchasers with a Software
                                               Bill of Materials (SBOM).
                                               Similar efforts are
                                               underway around the world.


                                               In 2021, our communities
                                               rose to the challenge of
                                               providing tools and best
                                               practices for the security
                                               hardening of the global
                                               software supply chains. Our
                                               efforts included launching
                                               Open Source Security
                                               Foundation (OpenSSF) as a
                                               funded project, expanding
                                               Let’s Encrypt — the world’s
                                               largest certificate
                                               authority, ensuring the ISO
                                               standardization of SPDX as
                                               the SBOM standard,
                                               directing funds to identify
                                               and fix vulnerabilities in
                                               critical open source
                                               software, and building new
                                               training curriculum to
                                               improve secure coding
                                               practices.


                                        # ⚓ Linux_Foundation_Launches_New
                                          Quantum_Intermediate_Representation
                                          Alliance [Ed: In Spamnil's site (LF-
                                          funded fluff)]⠀⇛


                                               The Linux Foundation has
                                               announced the new QIR
                                               Alliance, a joint effort to
                                               establish an intermediate
                                               representation with the
                                               goal to facilitate
                                               interoperability within the
                                               quantum ecosystem and
                                               provide a representation
                                               suitable for current and
                                               future heterogenous quantum
                                               processors.


                      # § Security⠀➾


                            # ⚓ New_HP_MFP_vulnerabilities_show_why_you_should
                              update_and_isolate_printers_|_CSO_Online⠀⇛


                                   Security researchers have published
                                   details about two serious
                                   vulnerabilities that impact over 150
                                   different HP multifunction printer
                                   models with FutureSmart firmware going
                                   back at least nine years. The attack
                                   vectors associated with the flaws and
                                   their impact serve as a reminder that
                                   printers can pose significant security
                                   risks to enterprise networks if not
                                   properly secured, updated and
                                   segmented.


                                   “For one, the vulnerabilities date back
                                   to at least 2013 and affect a large
                                   number of HP products released,”
                                   researchers from security firm F-
                                   Secure, who found the flaws, said in
                                   their report. “HP is a large company
                                   that sells products all over the world.
                                   Many companies are likely using these
                                   vulnerable devices. To make matters
                                   worse, many organizations don’t treat
                                   printers like other types of endpoints.
                                   That means IT and security teams forget
                                   about these devices’ basic security
                                   hygiene, such as installing updates.”


                                   Exploiting one of the vulnerabilities
                                   requires physical access and can be
                                   done through physical ports that are
                                   exposed on its communications board. A
                                   skilled attacker with physical access
                                   to a vulnerable MFP would need around
                                   five minutes to perform the attack and
                                   deploy a stealthy implant that could
                                   take full control of the device and
                                   exfiltrate potentially sensitive
                                   information.


                                   The second vulnerability is even more
                                   dangerous because it’s located in the
                                   firmware’s font parsing code and
                                   essentially allows anyone who can print
                                   a specifically crafted file to execute
                                   malicious code on the vulnerable MFPs.
                                   The vulnerability is wormable and
                                   exploitation can be achieved in seconds
                                   through multiple remote attack vectors,
                                   including by users visiting malicious
                                   websites.


                            # ⚓ Security_updates_for_Tuesday_[LWN.net]⠀⇛


                                   Security updates have been issued by
                                   Debian (samba), Fedora (kernel),
                                   openSUSE (netcdf and tor), SUSE (netcdf
                                   and python-Pygments), and Ubuntu
                                   (imagemagick).


                            # ⚓ Nasty_Windows_10_vulnerability_gets_a_patch,
                              but_not_from_Microsoft⠀⇛


                                   Cybersecurity researchers have released
                                   an unofficial patch for a bug in
                                   Windows 10, originally reported to
                                   Microsoft in October 2020, which later
                                   research revealed could take the form
                                   of a local privilege vulnerability as
                                   well.


                            # ⚓ RedHat:_RHSA-2021-4848:07_Moderate:_Migration
                              Toolkit_for_Containers_(MTC)⠀⇛


                            # ⚓ Inside_Intel’s_Secret_Warehouse_in_Costa_Rica⠀⇛


                                   Chip maker is stockpiling legacy
                                   technology for security research, plans
                                   to expand facility to house 6,000
                                   pieces of equipment


          o § Civil Rights/Policing⠀➾


                # ⚓ Over_100_civil_society_groups_call_for_changes_to_EU_AI
                  Act⠀⇛


                       A total of 114 civil society organisations have
                       signed an open letter calling on European
                       institutions to amend the forthcoming Artificial
                       Intelligence Act (AIA) so that it properly protects
                       fundamental human rights and addresses the
                       structural impacts of artificial intelligence (AI).


                       The European Commission’s proposed AIA was
                       published in April 2021 and sought to create a
                       risk-based, market-led approach to regulating AI by
                       establishing self-assessments, transparency
                       procedures and various technical standards.


                       Digital civil rights experts and organisations have
                       previously told Computer Weekly that although the
                       regulation is a step in the right direction, it
                       will ultimately fail to protect people’s
                       fundamental rights and mitigate the technology’s
                       worst abuses because it does not address the
                       fundamental power imbalances between tech firms and
                       those who are subject to their systems.


                # ⚓ The_EU_needs_an_Artificial_Intelligence_Act_that_protects
                  fundamental_rights⠀⇛


                       Access Now and over 110 civil society organisations
                       have laid out proposals to make sure the European
                       Union’s Artificial Intelligence Act addresses the
                       real-world impacts of the use of artificial
                       intelligence (AI), places fundamental rights
                       protection front-and-centre, and maintains a broad
                       definition of AI systems.


                       “Access Now’s priority is not to have an EU law on
                       AI, but to have one that is an effective instrument
                       to protect people’s rights,” said Fanny Hidvégi,
                       Europe Policy Manager at Access Now. “We’ve laid
                       out the steps needed to boost the proposed
                       regulation’s human rights standards, and are
                       looking forward to working with the Council and
                       Parliament to guarantee they are achieved.”


                       Access Now and AlgorithmWatch rang the alarm bell
                       last week when information leaked suggesting the
                       European Council is planning on drastically
                       narrowing the definition of AI systems, potentially
                       excluding many technologies that impact human
                       rights. The AI Act needs to be amended, but those
                       amendments must increase protections for
                       fundamental rights, not water them down.


          o § Monopolies⠀➾


                # § Copyrights⠀➾


                      # ⚓ *Clavis_Artis*_by_“Zoroaster”_–_The_Public_Domain
                        Review⠀⇛


                             Alchemical images from a 17th- or 18th-
                             century manuscript that claims to be much
                             older: a direct translation from Zoroaster
                             himself.


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