𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Friday, November 26, 2021
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Generated Sat 27 Nov 02:40:00 GMT 2021
Created by Dr. Roy Schestowitz (𝚛𝚘𝚢 (at) 𝚜𝚌𝚑𝚎𝚜𝚝𝚘𝚠𝚒𝚝𝚣 (dot) 𝚌𝚘𝚖)
Full hyperlinks for navigation omitted but are fully available in the originals
The corresponding HTML versions are at 𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈
Latest in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕 and older bulletins can be found at 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕-𝒂𝒓𝒄𝒉𝒊𝒗𝒆𝒔
Full IPFS index in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔 and as plain text in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔/𝒕𝒙𝒕
Gemini index for the day: gemini://gemini.techrights.org/2021/11/26/


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

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QmdGDdRX8ZuGj76UZ5fvhjBZ81N9v4RyisduQDvtX5i4bQ
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╒═══════════════════ 𝐈𝐍𝐃𝐄𝐗 ═══════════════════════════════════════════════════╕

⦿ Improved Workflows: Achievement Unlocked | Techrights

⦿ 38+ Years of GNU and 19+ Years of FSF Associate Membership | Techrights

⦿ Gemini as a Platform for Gamers | Techrights

⦿ IRC Proceedings: Wednesday, November 24, 2021 | Techrights

⦿ IRC Proceedings: Thursday, November 25, 2021 | Techrights

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
		http://techrights.org/2021/11/26/achievement-unlocked/#comments
		http://techrights.org/2021/11/26/fsf-associate-membership-at-19/#comments
		http://techrights.org/2021/11/26/gemini-protocol-games/#comments
		http://techrights.org/2021/11/26/irc-log-241121/#comments
		http://techrights.org/2021/11/26/irc-log-251121/#comments

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
		http://techrights.org/2021/11/26/eurolinux-8-5/#comments
		http://techrights.org/2021/11/26/whonix-16-0-3-7/#comments

                    ䷩ 𝚕𝚒𝚗𝚎 60

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/11/26/achievement-unlocked/#comments
    Gemini version at gemini://gemini.techrights.org/2021/11/26/achievement-unlocked/

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Gemini_version_available_♊︎


✐ Improved_Workflows:_Achievement_Unlocked⠀✐


Posted in Site_News at 5:49 pm by Dr. Roy Schestowitz


Video_download_link | md5sum 70ae383a1ba706ca4e653b121c9f7f75


http://techrights.org/videos/more-automation.webm


Summary: Today we’ve completed a bunch of small projects that can make us more
efficient (e.g. more Daily Links per day, more articles); the above video was
recorded many hours ago to accompany the outline below


THE past few days were spent coding a bunch of improvements to site operations,
which mostly involve assessing, curating, and sharing news. In the process we
occasionally identify areas that merit more coverage if not rebuttal. We’re
unable to cover everything all the time, partly because we’re not experts in
every domain and partly because our time and resources are very limited. We’re
not sponsored by oligarchs and corporations; in over 15 years we’ve not sold
out or compromised our journalistic independence.


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Typing: Techrights loves weekends⦈ All the latest changes
(code) can be found in_Git and corresponding internal communication can be
found in IRC logs.


These past few days were fully utilised to carry out maintenance/system
updates, housekeeping chores, and of course coding some stuff that was well
overdue; we can only ever compete (the battle over narrative/information) with
the “Big Sites” if we’re very efficient and are capable of publishing very
rapidly (lately we’ve been posting Daily links thrice a day).


This coming weekend we’ll try to relax a bit (news cycles will be dry anyway)
and on Monday we’ll publish Microsoft GitHub Exposé — Part VIII, focusing on
Mr. Graveley’s notorious Tomboy project; of course he proceeded from attacking
GNU/Linux with Mono to working directly for Microsoft, spearheading the attack
on copyleft/GPL. Incidentally, the same people who mobbed Richard Stallman
earlier this year are coming to realise, as per today’s_press_statement, that
Microsoft is pure evil and Microsoft cannot be redeemed. Yes, even people in
the OSI’s Board can see it; will they can Microsoft employee who have entered
the Board? Because some have indeed resumed the entryism. █


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⣿⣟⣩⣥⣾⣿⠋⢉⣤⣾⣿⠟⣫⣼⣿⣿⣯⣤⣿⣿⣿⡿⠛⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠛⢧⣼⣷⣄⣀⣤⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠟⣛⣭⣶⣶⣿⣿⣿⣯⣶⣿⣿⣿⣿⣿⣿⣭⠿⣿⣿⣧⣀⠀⢀⣀⣀⣀⣶⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣀⣀⣀⡀⠀⠀⠀⣠⣿⣿⡿⠛⢶⣾⣿⡷⠀⠀⠀⠀⠤⠄⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⠆⠲⣶⠏⢶⠄⠸⠽⠿⠏⠀⠈⠉⠉⠉⠀⠀⠀⠉⠉⠉⠁⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢻⣿⣿⣷⡎⣖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠹⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⠟⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢀⣀⣤⣤⣀⣀⣈⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶
⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢻⣿⢳⡶⢦⣶⣮⢩⣅⣀⣀⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣍⣉⣉⡉⠉⠉⠉⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣸⡇⣼⣟⣹⣇⣛⣿⣿⡏⣿⣿⢷⣿⣴⢶⡆⣮⣭⣭⣙⣛⢿⠿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣶⣶⣶
⣿⣿⣿⣿⣿⣶⣷⣭⣭⣝⣛⣃⠿⠿⠿⣿⣿⣸⣧⣿⣶⣿⣿⣿⢣⣿⠹⣿⡿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡁⢰⠈⢡⠉⠙⢘⣛⣻⡸⠟⢸⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣛⢿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⡇⢠⠀⠸⠀⠀⣼⣿⣿⣿⣿⣷⣤⠒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣾⢿⣿⢳⣿⢆⣿⣭⢭⣭⣉⡉⣉⠉⠛⠛⠛⠛⡙⠙⠹⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡇⢸⠀⢰⠀⠀⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠿⢿⡿⣼⣏⣹⣟⢻⣿⡏⣾⣯⣼⣷⡿⣿⢿⣦⣶⣶⠁⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠇⠀⠀⢸⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣯⣭⣽⣟⣛⣻⠶⠿⣿⣷⣿⣿⢧⣿⣧⢨⠉⣭⢻⣿⣿⣿⣿⣿⡿⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠇⠀⠀⠘⠀⣀⣿⣿⣿⡏⣿⣿⡍⠀⠀⠀⠉⢿⣿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⠀⠁⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣥⢬⠙⠵⡿⣤⣿⣸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⠄⠀⠀⢰⣾⣟⠿⠿⠛⠁⢸⣿⠀⠀⠀⠀⠀⠀⠻⣤⡀⠀⢻⣿⣿⣿⡏⠉⠁⠀⠀⢀⣾⣿⠿⠿⠿⠿⠋⢹⣿⣿⣿⡟⠛⢿⣿⣿⣿⣿⣶⣷⣿⡿⠿⠛⠛⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⠀⠀⣠⣿⣿⣿⣇⡀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⣿⣿⣿⠗⠀⠀⠀⣴⡿⠛⠓⠀⠀⠀⠀⠀⠘⣿⣿⣿⣧⠠⢶⣿⡇⠀⠉⠉⠉⠀⠀⠠⠀⣾⣿⣿⣿⣿⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣶⡄⠀⠀⣽⡄⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣶⡶⠾⠿⠿⠿⠷⠼⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣋⣿⡇⠀⣦⣀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⠀⢸⡇⠀⠀⠀⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠘⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣱⣁⠴⠶⠶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢸⣿⠀⢸⣿⣿⣿⣿⣿⡀⠘⡇⠀⠀⠃⡯⠆⠀⠀
⢿⣿⣿⣿⢿⣿⣿⣿⡿⢿⣿⣷⣤⡿⣿⣿⣿⡿⣿⣿⣿⣿⣉⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠶⠶⠶⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⠉⠉⠁⠀⠁⠀⠀⠀⠑⠂⠻⣿
⣿⣿⣩⣵⣾⣿⠛⣉⣤⣾⣿⡟⣫⣼⣿⣿⣿⣤⣿⣿⣿⡿⠛⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄⢠⣤⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⢿⣛⣿⣶⣾⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣭⠿⣿⣿⣃⠀⠀⠀⣠⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢨⣿⡿⠛⢶⣾⣿⡿⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⠆⠲⣶⠏⢶⠄⠸⠽⠿⠏⠀⠉⠉⠉⠉⠀⠀⠀⠉⠉⠉⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠹⣿⣿⡁⠀⠀⢘⢫⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠹⣿⣷⣀⣤⣹⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⠟⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢀⣀⣤⣄⣀⣀⣀⡛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤
⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⢻⣿⢳⡶⢦⣶⣮⢩⣅⣀⣀⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣭⣭⣍⣉⣉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣸⡇⣼⣟⣹⣇⣛⣿⣿⡏⣿⣿⢷⣿⣴⢶⡆⣮⣭⣭⣙⣛⢛⠿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣶⣷⣭⣭⣜⣛⣃⠿⠿⠿⣿⣿⣸⣇⣿⣶⣿⣿⣿⢡⣿⠹⣿⡿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⡀⠰⠈⢡⠉⠙⢘⣛⣻⡸⠟⢸⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣛⢿⡿⠿⢿⣿⣿⣿⣿⣿⣟⣿⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡇⢠⠀⠸⠀⠀⣸⣿⣿⣿⣿⣶⣤⠐⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣷⣿⣾⢿⣿⢳⣷⢆⣾⣭⢭⣭⣉⡁⣉⠉⠛⠛⠙⠉⡉⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡇⠰⠀⢰⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⢿⢿⡿⣼⣏⣹⣟⢻⣿⡏⣾⣯⣼⣷⡿⣿⢿⣦⣶⣶⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠇⠀⠀⢸⠀⠀⣿⣿⣿⣿⣿⣿⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣶⣾⣯⣭⣽⣟⣛⣻⣶⠿⢿⣷⣿⣿⢣⣿⣧⢨⣉⣭⣻⣿⣿⣿⣿⣿⡿⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠇⠀⠀⠘⠀⣀⣿⣿⣿⣿⣶⣾⣿⡄⣠⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⡀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣥⣬⣽⣵⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⠀⠀⠀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢰⣿⠟⠻⢿⡟⠙⣿⣿⡿⣿⣿⣿⣿⣿⠛⠛⠻⣿⣿⣿⣿⣿⠛⠉⠉⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠀⠀⠀⠈⠛⠿⠟⠛⠧⠀⠀⡄⠀⠠⠀⣿⣿⣿⣿⡿⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⠀⢿⣿⣿⣿⣿⣿⣿⡿⠟⠈⢿⣿⡿⠟⠀⠙⣿⣯⣠⣿⣿⣿⠁⠀⠀⠀⢰⣆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣶⡶⠾⠿⠿⠿⠷⠬⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⢸⢀⣜⠛⠻⣿⡋⠈⠛⠃⠀⠀⠀⠹⠀⠀⠀⠀⠻⠟⠛⠻⠟⠋⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣋⣿⡇⠀⣦⣀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣼⣿⣉⡁⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⢸⣦⠀⢀⣤⣤⣤⣤⣤⣤⠀⢸⡇⠀⠀⠀⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣶⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠋⠀⣸⣿⡆⠘⢿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⡰⣁⠴⠶⠶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣮⠀⠀⠀⠀⢰⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⡀⠘⡇⠀⠀⠃⡯⠆⠀⠀
⢿⣿⣿⣿⢿⣿⣿⣿⡿⢿⣿⣿⣴⡿⣿⠿⠿⠿⣿⠿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠀⣠⣤⣴⣶⣶⣶⡶⠂⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠈⠉⠉⠁⠀⠁⠀⠀⠀⠑⠀⠻⣿
⣿⣟⣩⣵⣾⣿⠛⣉⣤⣾⣿⡟⣫⣼⣷⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣈⡙⠻⣧⣼⣿⡛⢻⣤⣽⣟⠁⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠿⣛⣯⣶⣾⣿⣿⣿⣯⣶⣿⣿⣿⣿⣿⣯⣤⠾⣿⣿⣷⣤⡾⢿⣿⣷⣤⣿⠿⢿⣿⣤⣾⣿⣿⣿⣦⣿⣿⣿⣿⣶⣿⣿⡟⠻⣶⣾⣿⡿⠛⢦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⠆⠲⣶⠏⢶⠄⠸⠽⠿⠇⠀⠈⠉⠉⠁⠀⠀⠀⠉⠉⠉⠁⠀⠈⠉⠉⠉⠁⠀⢀⣀⠀⠈⠉⠉⠉⠉⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠹⣿⣿⡁⠀⠀⠠⢉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠹⣿⣷⠀⢂⢰⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⠟⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⣷⣿⣿⣿⣿⣿⡏⢀⣀⣤⣄⣀⣀⣈⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤
⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⢻⣿⢳⡶⢦⡶⣮⢩⣅⣀⣀⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣍⡉⣉⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣸⡇⣼⣟⣹⣇⣛⣿⣿⡏⣿⣿⢷⣿⣴⢶⡆⣦⣭⣭⣙⣛⢻⠟⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣷⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣶⣷⣭⣭⣜⣛⣃⠿⠿⠿⣿⣿⣸⣇⣿⣶⣿⣿⣿⢡⣿⠹⣿⡿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⡀⠰⠈⢡⠉⠙⢘⣛⣻⡸⠟⢸⣿⡿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣛⢿⡿⠿⢿⣿⣿⣿⣿⣿⣟⣿⠛⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡇⢠⠀⠸⠀⠀⢸⣿⣿⣿⣿⣶⣤⠐⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣷⣿⣾⢿⣿⢳⣷⢆⣾⣭⢭⣥⣉⡀⣈⠉⠛⠉⠙⠉⡉⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡇⠰⠀⢰⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠿⢿⡿⣼⣏⣹⣟⢻⣿⡏⣾⣯⣼⣷⡿⣿⢿⣦⣶⣶⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠇⠀⠀⢸⠀⠀⣿⣿⣿⣿⣿⣿⣿⣠⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣶⣶⣮⣭⣩⣽⣟⣛⣻⠶⠿⢿⣷⣿⣿⢣⣿⣧⢨⠉⣭⢻⣿⣿⣿⣿⣿⡿⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠇⠀⠀⠈⢀⣤⣿⣿⣿⣿⣿⣿⣿⣷⣀⣈⣿⣹⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠡⢨⠙⠵⠿⠤⠿⣸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢷⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠁⠀⠀⢀⣾⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣤⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡆⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⡿⠀⠀⠹⣿⣿⣿⣿⣹⣿⣿⣿⡿⠿⠟⠋⠉⠉⠁⠀⣴⣿⣿⣿⡿⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⠀⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡏⠉⢻⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠻⠋⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠹⠿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡶⠾⠿⠿⠿⠷⠬⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣸⣾⣿⣿⣿⣿⣿⣿⣿⡏⠀⢻⣿⣿⡟⠁⠀⠀⠉⣍⣉⠛⠙⠿⠿⢿⠇⠀⠀⢰⣆⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⣿⡇⠀⣦⣀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠈⢿⣿⠁⠀⠀⠀⢸⣿⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⠀⢸⡇⠀⠀⠀⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠘⠃⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆⠘⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⡰⣁⠰⠶⠶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⢸⣿⣿⣿⣿⣿⡀⠘⡇⠀⠀⠃⡯⠆⠀⠀
⠿⣿⣿⣿⢿⣿⣿⣿⡿⢿⣿⣯⣼⡿⣿⣿⡿⠿⣿⡿⡛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣶⣶⣶⣶⠆⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠈⠉⠉⠁⠀⠁⠀⠀⠀⠑⠀⠻⣿
⣿⣟⣩⣵⣾⣿⠛⣉⣤⣾⣿⡟⣫⣴⠋⠁⠀⢀⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡈⢛⣤⣽⣟⠛⣠⣤⣤⣄⣠⣤⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠿⣛⣭⣶⣾⣿⣿⣿⣿⣶⣿⣿⣿⣶⣶⣆⡀⠀⣀⣀⣀⡀⠈⠀⣀⣀⣀⡀⠻⢿⣿⣤⣶⣿⣿⣿⣤⣿⣿⣿⣿⣶⣿⣿⡟⠻⣶⣾⣿⡿⠛⢶⣴⣶⠦⠀⠀⠐⠺⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⠆⠲⣶⠏⢶⠄⠸⠽⠿⠇⠀⠀⠉⠉⠁⠀⠀⠀⠉⠉⠉⠁⠀⠈⠉⠉⠉⠀⠀⢀⣀⠀⠈⠉⠉⠉⠉⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢻⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠹⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠿⠟⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣠⣤⣄⣀⣀⣈⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶
⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢻⣿⢳⡷⢦⣶⣮⢩⣅⣀⣀⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣍⣉⣉⣉⠉⠉⠉⠉⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣸⡇⣼⣟⣹⣇⣛⣿⣿⡏⣿⣿⢷⣿⣴⢶⡆⣮⣭⣭⣙⣛⢿⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣾⣶
⣿⣿⣿⣿⣿⣶⣷⣭⣭⣜⣛⣃⠿⠿⠿⣿⣿⣸⣧⣿⣶⣿⣿⣿⢣⣿⠹⣿⡿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡁⢰⠈⢡⠉⠙⢘⣛⣿⡸⠟⢸⣿⡿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣛⢿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⡇⢠⠀⠸⠀⠀⣾⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣾⢿⣿⣳⣿⢆⣿⣭⢭⣭⣉⡉⣉⠉⠿⣿⡿⠟⠻⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡇⢸⠀⢰⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⢿⢿⡿⣼⣏⣹⣟⢻⣿⣏⣾⣯⣼⣷⡿⣿⣿⣦⣶⣶⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠇⠀⠀⢸⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⠯⣷⣶⣶⣮⣭⣩⣽⡟⠛⠻⠶⠿⢿⣷⣿⣿⢧⣿⣧⣨⣩⣭⣿⣿⣿⣿⣿⣿⡿⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡇⠀⠀⠘⠀⣰⣿⣿⣿⣿⣿⣻⣿⣿⣿⡿⠋⠹⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡟⠀⠀⣴⡾⠀⠀⠀⠀⠡⣬⣽⣽⡿⠟⠋⠉⢈⣽⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⠄⠀⠀⢰⣾⡿⣿⣿⣿⡿⢿⣿⣿⡿⠋⠀⠀⠀⠸⡿⠟⠁⠹⣿⣿⣿⣿⣿⣷⣶⣶⣴⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠈⠀⠀⢠⣤⣴⡿⠟⠉⠁⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⠀⠀⣀⣿⣿⣿⣣⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢿⡟⠛⢻⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⡄⠀⠠⠁⣿⣿⣿⣿⣿⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⣀⣴⣿⡿⠿⠉⣏⢀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠁⠀⠀⠀⠀⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣶⡶⠾⠿⠿⠿⠷⠼⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣾⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣋⣿⡇⠀⣦⣀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⠀⢀⣤⣤⣤⣤⣤⣤⠀⢸⡇⠀⠀⠀⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⢠⣿⡄⠸⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⡱⣁⠴⠶⠶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣼⣿⡇⠀⢿⣿⣿⣿⣿⣿⡀⠘⡇⠀⠀⠃⡯⠆⠀⠀
⢿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣤⡿⣿⣿⣿⡿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⢶⣶⡶⠂⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠉⠉⠉⠁⠀⠁⠀⠀⠀⠑⠂⠻⣿
⣿⣿⣩⣵⣾⣿⠛⣉⣤⣾⣿⡟⣫⣼⣿⣿⣿⣤⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠿⢿⣛⣿⣶⣾⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣟⡉⠉⢉⣀⣠⣤⠾⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣦⣀⣀⣀⡀⠀⠀⠀⣤⣾⣿⡿⠛⢶⣶⣶⡶⠁⠐⠞⠿⠿⠧⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⠆⠲⣶⠏⢶⠄⠸⠿⠿⠏⠀⠈⠉⠉⠁⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢻⣿⣿⣷⡖⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠹⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⠿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⣀⣤⣄⣀⣀⣈⡛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶
⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢻⣿⢳⡶⢦⣶⣮⢩⣅⣀⣀⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣍⣉⣉⡉⠉⠉⠉⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣸⡇⣼⣟⣹⣇⣛⣿⣿⡏⣿⣿⢷⣿⣴⢶⡆⣮⣭⣭⣙⣛⢿⠿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣶⣶⣶
⣿⣿⣿⣿⣿⣶⣷⣭⣭⣝⣛⣃⠿⠿⠿⣿⣿⣸⣧⣿⣶⣿⣿⣿⢣⣿⠹⣿⡿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡁⢰⠈⢡⠉⠙⢘⣛⣻⡸⠟⢸⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣛⢿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⡇⢠⠀⠸⠀⠀⣼⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣾⢿⣿⣳⣿⢆⣿⣭⢭⣭⣉⡉⣉⠉⠛⠛⠛⠛⣛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡇⢸⠀⢰⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠿⢿⡿⣼⣏⣹⣟⢻⣿⣏⣾⣯⣼⣷⡿⣿⣿⣦⣶⣶⠹⠿⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠇⠀⠀⢸⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣯⣷⣶⣶⣮⣭⣩⣽⣟⣛⡻⠶⠿⢿⣷⣿⣿⢧⣿⣧⠀⠀⣌⢻⣿⣿⣿⣿⣿⡿⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡇⠀⠀⠘⠰⣿⣿⣿⣿⣯⣿⣿⡟⠁⠀⠀⠙⠋⠙⠛⠻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠁⠀⠀⠀⠉⣿⣿⣿⣹⣿⣿⣿⠋⠉⠉⠑⠲⠦⠁⢈⠙⠥⠾⢠⣿⣼⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⠄⠀⠀⣰⣾⠿⢿⣿⠉⠙⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡿⠁⠀⣶⡆⠀⠀⠀⠀⢸⣤⣷⣶⡿⠟⠛⠉⣠⣾⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⠀⠀⢀⣿⣿⣟⣂⢸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠟⠋⠁⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⡿⠁⠀⠴⣿⠁⣠⣦⣤⣾⡿⠟⠉⠁⠀⠀⠀⣿⣿⣿⣿⣿⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣀⣴⣿⣯⡉⣙⣁⣼⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠁⠀⠀⠀⠀⣰⣿⠿⠿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠙⠻⠟⠉⠀⠀⠀⠀⠀⣶⡶⠾⠿⠿⠿⠷⠼⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⣾⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡷⠀⠀⠀⢀⣿⡇⠀⠀⠀⢹⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣋⣿⡇⠀⣦⣀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠸⣿⡇⠀⠀⠀⠈⢿⣿⠿⠛⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⠀⢸⡇⠀⠀⠀⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⡱⣁⠴⠶⠶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡄⠀⣿⣿⣿⣿⣿⣿⡀⠘⡇⠀⠀⠃⡯⠆⠀⠀
⢿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣤⡿⣿⣿⣿⡿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⢶⣶⠶⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠈⠉⠉⠁⠀⠁⠀⠀⠀⠁⠀⠻⠿
⣿⣿⣩⣵⣾⣿⠛⣉⣤⣾⣿⡟⣫⣼⣿⣿⣿⣤⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣼⣶⣄⣠⡤⣶⣆⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⢿⣛⣿⣷⣾⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⡉⠉⠁⣀⣀⣦⠄⠙⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⢀⣶⣤⣶⣦⣀⣠⣤⣤⣤⡞⢻⣶⣿⣿⡿⠛⢶⣿⣿⡶⠀⠐⠒⠛⠿⠧⠀⠘⠛⠛⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⠆⠲⣶⠏⢶⠄⠸⠽⠿⠏⠀⠉⠉⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠹⣿⣿⡥⠄⠈⢝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠹⣿⣷⣘⣜⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠿⠟⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡧⢀⣀⣤⣄⣀⣀⣈⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤
⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢻⣿⢳⡶⢦⣶⣮⢩⣅⣀⣀⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣭⣩⣉⣉⣉⠉⠉⠉⠉⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣸⡇⣼⣟⣹⣇⣛⣿⣿⡏⣿⣿⢷⣿⣴⢶⡆⣮⣭⣭⣙⣛⢿⠟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣶⣷⣭⣭⣜⣛⣃⠿⠿⠿⣿⣿⣸⣧⣿⣶⣿⣿⣿⢡⣿⠹⣿⡿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡀⢰⠈⢡⠉⠙⢘⣛⣻⡸⠟⢸⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣛⢿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⡇⢠⠀⠸⠀⠀⣼⣿⣿⣿⣿⣷⣦⠐⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣷⣿⣾⢿⣿⢳⣷⢆⣾⣭⢭⣭⣉⡉⣉⠉⠛⣛⣟⣛⡛⠛⠹⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡇⢘⠀⢰⠀⠀⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠿⢿⡿⣼⣏⣹⣟⢻⣿⡏⣾⣯⣼⣷⡿⣿⢿⣦⣶⣶⠁⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠇⠀⠀⢸⢀⣤⣿⣿⣿⣿⣿⣿⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠿⢿⣷⣶⣶⣬⣭⣭⣽⠛⠛⠻⠶⠿⢿⣷⣿⣿⢧⣿⣧⣼⣿⣿⠿⢻⣿⣿⣿⣿⡿⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠇⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⡿⠁⠀⠐⠆⠙⠛⠓⠀⣠⣵⣮⠝⠁⠛⠁⠀⣠⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢡⣶⣦⣼⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⢲⣶⣿⠿⠋⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣼⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⠙⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢻⡟⠋⠉⠙⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡄⠀⠠⠁⣿⣿⣿⣿⣿⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⠘⢿⣿⣏⡈⣿⣿⡿⠉⠈⣿⣿⣿⡿⠀⠹⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⣧⠀⠀⠀⠸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⣶⡶⠾⠿⠿⠿⠷⠼⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⢀⣼⣇⣹⣿⡟⠛⠀⠀⠀⢸⣿⠏⠀⠀⠀⠙⠉⠉⠉⠀⠈⠃⠀⠀⠀⠀⠈⠿⠆⠀⠀⠀⢹⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⣿⡇⠀⣦⣀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣼⣿⣿⣦⣄⣹⣷⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⣤⡄⠀⢀⣤⣤⣤⣤⣤⣤⠀⢸⡇⠀⠀⠀⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠘⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⡰⣁⠴⠶⠶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⡀⠘⡇⠀⠀⠃⡯⠆⠀⠀
⢿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣥⠿⣿⠿⢿⠿⣿⡿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⡶⣶⣶⣶⠂⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠁⠀⠀⠀⠑⠀⠻⠿
⣿⣟⣩⣵⣾⣿⠛⣉⣤⣾⣿⡟⣁⣀⠀⠈⠋⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⢸⡖⢀⣤⣴⣿⡛⢻⣤⣽⣿⠋⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠿⣛⣿⣶⣾⣿⣿⣿⣿⣶⣿⣿⣿⣿⣧⣤⣄⠀⣠⣤⣤⣤⡄⠀⣤⣤⣤⣿⠶⢶⣦⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡿⣻⣶⣾⣿⡿⠃⢤⣤⣤⠤⠀⠐⠚⠻⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠆⠲⣶⠏⢶⠄⠸⠽⠿⠏⠀⠈⠉⠉⠁⠀⠀⠀⠉⠉⠉⠀⠀⠈⠉⠉⠉⠁⠀⢀⣀⠉⠈⠉⠉⠉⠉⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠹⣿⣧⠀⠀⠀⠀⡀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠹⣿⣧⠀⠀⠈⠤⣔⣿⣿⣿⣿⣿⡿⠛⠿⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⣿⣦⣶⣶⣶⣶⣾⣿⣿⣿⣯⢀⣀⣤⣄⣀⣀⣈⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤
⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⣿⣿⣿⣿⣿⢻⣿⢳⡶⢦⣶⣮⢩⣅⣀⣀⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣉⡉⡉⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣸⡇⣼⣟⣹⣇⣛⣿⣿⡏⣿⣿⢷⣿⣴⢶⡆⣦⣭⣭⣙⣛⢟⠟⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣶⣷⣭⣭⣜⣛⣃⠿⠿⠿⣿⣿⣸⣧⣿⣶⢿⣿⣿⢡⣿⠹⣿⡿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⡀⢰⠈⢡⠉⠙⢘⣛⣻⡸⠟⢸⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣛⢿⡿⠿⢿⣿⣿⣿⣿⣿⡿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⡇⢠⠀⠸⠀⠀⢸⣿⣿⣿⣿⣶⣤⠐⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣷⣿⣾⢿⣿⢳⣷⢆⣾⣭⢭⣥⣉⡉⣁⠉⠛⠛⠛⠙⡋⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡇⠀⠀⢰⠀⠀⣾⣿⣿⣿⣿⣿⣿⠰⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⠿⢿⡿⣼⣏⣹⣟⢻⣿⡏⣾⣯⣼⣷⡿⣿⢿⣦⣶⣶⠁⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠇⠀⠀⢸⠀⠀⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⡿⠯⣷⣶⣶⣬⣭⢉⣽⣟⣛⣻⠶⠿⢿⣷⣿⣿⢣⣿⣧⢨⠈⣭⢹⣿⣿⣿⣿⣿⡿⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠇⠀⠀⠘⠀⢀⣿⣿⣟⠛⣿⣿⣿⣿⣿⣿⣿⡝⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣸⣿⣿⣿⣿⣿⣶⣦⣀⣀⣁⣬⠙⠥⠿⠠⠿⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢧⠀⣀⠀⢠⣼⣿⣿⣿⣟⣤⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡿⠿⠋⠙⢿⣿⣿⣿⡟⠛⠻⠿⠿⢿⣿⣿⡿⠟⠛⢻⡿⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢀⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠀⠉⠛⠉⠁⠀⠀⠀⠀⠀⣿⣿⣿⣷⣶⣾⠂⠀⠀⠁⠀⠀⠤⠾⠿⠷⠬⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⢿⣿⣿⣿⣿⠁⠘⣿⣿⡟⠁⠀⠀⠀⠀⠉⠉⠹⣿⠁⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠉⠀⠀⠀⢀⣴⡇⠀⣦⣀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⠀⢸⡇⠀⠀⠀⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠀⢸⡇⠀⠀⡰⣁⠴⠶⠶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢡⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠁⠀⢸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡀⠘⡇⠀⠀⠃⡯⠆⠀⠀
⠿⣿⣿⣿⢿⣿⣿⣿⡿⢿⣿⣧⠿⠿⣿⣿⣿⡿⣿⡿⠟⠃⠀⠀⠀⠈⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⣠⣤⣴⡶⣶⣶⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠁⠀⠀⠀⠑⠀⠻⠿
⣿⣟⣩⣵⣾⣿⠋⣉⣤⣾⡋⠀⣠⣴⣿⣿⠋⠀⠀⠀⠀⠀⢀⣯⡀⠀⠁⠀⠀⠀⠀⠀⣤⣤⣤⡄⠘⣧⣼⣿⡛⢻⣤⣽⣿⠛⣧⣤⣦⡄⢠⣤⣶⡄⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠿⣛⣽⣶⣶⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣷⣤⠾⣿⣿⣷⣤⡟⢁⣤⣤⣤⣤⠶⢿⣿⣮⣿⣿⣿⣿⣯⣿⣿⣿⣿⣦⣿⣿⡿⣻⣶⣾⣿⡿⠛⢴⣾⣷⡦⠀⠀⠀⠀⠈⠁⠀⠐⠒⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠆⠲⣶⠏⢶⠄⠸⠽⠿⠏⠀⠈⠉⠉⠁⠀⠀⠀⠉⠉⠉⠁⠀⠈⠉⠉⠉⠁⠀⢀⣀⠈⠈⠉⠉⠉⠉⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠹⣿⣧⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠹⣿⣇⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡿⠛⠿⠛⠛⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⢷⣦⣶⣶⣶⣶⣾⣿⣿⣿⡇⢀⣀⣤⣀⣀⣀⣈⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤
⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿
⣿⣿⣿⣿⣿⢻⣿⢳⡶⢦⡶⣮⢩⣅⣀⣀⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣍⣉⠉⡉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣸⡇⣼⣟⣹⣇⣛⣿⣿⡏⣿⣿⢷⣿⣴⢶⡆⣦⣭⣭⣉⣛⢛⠛⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣶⣶⣶⣴⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣶⣷⣭⣭⣜⣛⣃⠿⠿⠿⣿⣿⣸⣧⣿⣶⢿⣿⣿⢁⣿⠹⣿⡿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⡀⠰⠈⢡⠉⠙⢘⣛⣻⡸⠟⢸⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣛⢻⡿⠿⢿⣿⣿⣿⣿⣿⣿⡛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⡇⢠⠀⠸⠀⠀⢸⣿⣿⣿⣿⣶⣤⠐⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣷⣿⣾⢿⣿⢳⣷⢆⣾⣭⢭⣥⣀⡁⣀⠉⠛⠛⠛⠙⡋⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡇⠀⠀⢰⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⠿⢿⡿⣼⣏⣹⣟⢻⣿⡏⣾⣯⣼⣷⡿⣿⢿⣦⣶⣶⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠃⠀⠀⢸⠀⠀⢸⣿⣿⣿⡿⠿⠿⠴⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠿⣿⣿⣿⣷⣾⣭⣭⡝⠛⠛⠻⠶⠿⢿⣷⣿⣿⢣⣿⣧⣨⣬⣿⣿⣿⣿⣿⣿⣿⡿⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠆⠀⠀⠘⢀⣤⣿⣿⣿⣆⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⡟⠛⠋⣉⣿⠟⠀⠀⣠⠀⠀⠀⠀⠀⠀⢡⣨⣽⡥⠛⠉⠁⣼⣿⣿⣿⣿⣿⣿⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢧⠀⠀⠀⢰⣿⣿⣿⣿⣯⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⠀⠀⠁⠀⠀⠀⣸⣿⡇⠀⠀⠙⠋⠀⠀⠀⠁⠀⠀⣠⡀⣠⣼⠟⠛⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣀⣀⠀⠀⣠⣶⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠟⠛⠁⠀⠀⠀⠀⡄⠀⠠⠈⣿⣿⣿⣿⣿⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠈⣿⣿⣿⣿⣿⡿⠀⠀⠀⢿⣿⡷⠀⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡶⠾⠿⠿⠿⠷⠬⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠀⣿⡯⠁⠀⠀⠀⠀⠉⠁⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣦⣀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠙⣿⣿⣿⡇⠀⠀⠀⣆⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⠀⢸⡇⠀⠀⠀⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢻⣿⡿⠂⠀⠀⠀⡿⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠸⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⠰⣁⠰⠶⠶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠘⣿⡇⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⣿⣿⣿⣿⣿⣿⡀⠘⡇⠀⠀⠃⡯⠆⠀⠀
⠿⣿⣿⣿⢿⣿⣿⣿⡿⢿⣿⣷⣦⡤⣽⣿⣿⡿⣿⣿⣿⣇⠀⠀⠀⠀⠙⡆⠀⠀⠀⢸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⣦⣶⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠈⠉⠉⠁⠀⠁⠀⠀⠀⠑⠀⠻⠿
⣿⣟⣩⣥⣾⣿⠋⢉⣤⣾⣿⡟⣫⣼⣿⣿⣿⣤⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣟⠛⣧⣤⣤⡄⢠⣤⣤⡄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠿⣛⣯⣶⣶⣿⣿⣿⣯⣶⣿⣿⣿⣿⣿⠛⠉⠉⣩⣥⣤⣤⡾⠛⣀⣀⣀⣤⠀⢠⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⢠⣤⣴⣿⡿⠻⣶⣿⣿⡿⠛⢤⣾⣶⡦⠀⠀⠀⠀⠈⠁⠀⠐⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠆⠲⣶⠏⢶⠄⠸⠽⠿⠏⠀⠉⠉⠉⠀⠀⠀⠀⠉⠉⠉⠉⠀⠈⠉⠉⠉⠁⠀⠀⡉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠻⣿⣿⣷⣔⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠹⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⠛⠛⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣏⢀⣠⣤⣤⣀⣀⣬⡛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶
⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢻⣿⢳⡶⢦⣶⣮⢩⣅⣀⣀⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣉⣉⣉⣉⠉⠉⠉⠁⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣸⡇⣼⣟⣹⣇⣛⣿⣿⡏⣿⣿⢷⣿⣴⢶⡆⣮⣭⣭⣙⣛⢿⠟⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣷⣶⣶
⣿⣿⣿⣿⣿⣶⣷⣭⣭⣝⣛⣃⠿⠿⠿⣿⣿⣸⣧⣿⣶⣿⣿⣿⢣⣿⠹⣿⡿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡁⢰⠈⢡⠉⠙⢘⣛⣻⡸⠟⢸⣿⡿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣛⢿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⡇⢠⠀⠸⠀⠀⣸⣿⣿⣿⣿⣷⣦⣒⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣷⣿⣾⢿⣿⢳⣷⢆⣾⣭⢭⣭⣉⡉⣉⠉⠛⠛⠛⠛⡛⠛⠹⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡇⢸⠀⢰⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠿⢿⡿⣼⣏⣹⣟⢻⣿⣏⣾⣯⣼⣷⡿⣿⣿⣦⣶⣶⠁⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣧⣾⣷⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⠿⠿⠿⣶⣶⣾⣿⣭⣽⣟⣛⡻⠶⠿⢿⣷⣿⣿⢧⣿⣧⣨⠉⣭⣿⣿⣿⣿⣿⣿⡿⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣼⣿⠟⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠹⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣴⣿⣿⢿⣿⣿⣿⣿⣿⣿⣶⣄⣠⣄⣥⢨⣙⣥⣿⣾⣿⡿⠟⢛⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⠃⠀⠀⢠⣤⣽⣿⠟⠉⠉⠻⣿⠟⠋⠁⠀⠀⣿⣿⣿⡿⠿⠿⡷⠀⠀⠀⢁⣀⡀⠀⢀⣴⣿⣿⡿⠁⠀⢀⣽⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣤⣼⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⠀⠀⠀⣾⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠋⠀⠀⠀⣧⠀⠀⠀⣿⡿⠿⢷⣿⣿⣿⠋⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣔⡛⠙⢛⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠉⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠈⠉⣤⡤⠿⠿⠿⠿⠷⠼⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢰⣴⣿⣯⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢊⣿⡇⠀⣦⣀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡆⢀⣤⣤⣤⣤⣤⣤⠀⢸⡇⠀⠀⠀⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣽⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣰⣁⠴⠶⢶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠄⠀⠀⠀⠘⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⡀⠘⡇⠀⠀⠃⡯⠆⠀⠀
⢿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣧⡿⣿⣿⣿⡿⣿⠿⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⣶⣶⣶⡶⠒⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠙⣿⣿⣿⣷⠀⠀⠀⠈⠉⠉⠁⠀⠁⠀⠀⠀⠑⠀⠻⠿
⣿⣿⣩⣵⣾⣿⠛⣉⣤⣾⣿⡟⠋⠼⠛⠋⢁⣀⣤⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢻⣤⣽⣟⠃⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠈⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⢿⣛⣿⣷⣾⣿⣿⣿⣏⣀⣀⣤⣤⣶⣿⠛⠉⠉⠁⠀⣠⣤⠾⠛⠂⠀⠀⠀⠀⢺⣧⣀⣀⣀⣀⣀⣤⣾⣿⣿⣿⣦⣿⣿⡿⣿⣶⣾⣿⡿⠛⢶⣾⣿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠂⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠆⠲⣶⠏⢶⠄⠸⠽⠿⠏⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠉⠉⠉⠉⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠹⣿⣿⡅⠀⠀⢸⡩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠹⣿⣷⡐⣶⣽⣷⣿⣿⣿⣿⣿⣿⡿⠛⠻⠛⠛⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡇⢀⣀⣤⣤⣀⣀⣀⡛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤
⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⢻⣿⢳⡶⢦⣶⣮⢩⣅⣀⣀⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣯⣯⣭⣍⡉⣉⡉⠉⠁⠉⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣸⡇⣼⣟⣹⣇⣛⣿⣿⡏⣿⣿⢷⣿⣴⢶⡆⣦⣭⣭⣙⣛⢟⠟⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣶⣷⣭⣭⣜⣛⣃⠿⠿⠿⣿⣿⣸⣧⣿⣶⣿⣿⣿⢡⣿⠹⣿⡿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡀⢰⠈⢡⠉⠙⢘⣛⣻⡸⠟⢸⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣛⢻⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⡇⢠⠀⠸⠀⠀⢸⣿⣿⣿⣿⣶⣦⠐⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣷⣿⣾⢿⣿⢳⣷⢆⣾⣭⢭⣥⣁⡉⣉⠉⠛⠛⠛⠛⡛⠛⠹⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡇⠘⠀⢰⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⠿⢿⡿⣼⣏⣹⣟⢻⣿⡏⣾⣯⣼⣷⡿⣿⢿⣦⣶⣶⠁⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠇⠀⠀⣸⣀⣀⣼⣿⣿⣿⣿⣿⣿⡠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣶⣮⣭⣩⣽⣟⣛⣻⠶⠿⢿⣷⣿⣿⢣⣿⣧⢨⣉⣭⣿⣿⣿⣿⣿⣿⡿⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡇⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⣈⣹⡝⢿⣿⣿⣿⣿⡿⢿⣿⣿⣿⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⠵⢌⣉⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣧⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⣿⠃⠀⠀⠀⠁⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⡉⣡⣴⣶⣿⣿⠿⠛⠉⠁⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣹⣿⣿⣿⠟⠁⠈⢻⣿⣿⣿⣿⣿⣿⣏⣻⣿⣿⡆⠀⢰⣿⣷⣤⣴⣿⣿⡿⢿⣿⡿⠟⠁⠀⠀⠙⢿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⡄⠀⠠⠉⣿⣿⣿⣿⣿⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⢻⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⡿⠿⡿⠿⠿⠃⠀⢻⡟⠛⠙⠻⢿⠏⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠁⠀⣶⡶⠾⠿⠿⠿⠷⠬⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣠⣤⢼⣿⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣿⡇⠀⣦⣀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣬⣿⣷⣶⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⠀⢸⡇⠀⠀⠀⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⠀⠀⠸⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⡰⣁⠴⠶⢶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣱⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⡀⠘⡇⠀⠀⠃⡯⠆⠀⠀
⢿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣤⠿⣿⠿⣿⡿⣿⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⡶⠶⠶⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠁⠀⠀⠀⠑⠀⠻⠿
⣿⣟⣩⣵⣾⣿⠛⢉⣤⠞⠛⠉⣠⣤⣾⣿⠋⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⢠⣦⣀⠀⠀⠀⣀⣤⡄⠀⣀⣀⣿⠛⢻⣤⣤⣄⠀⣤⣼⣿⣇⢀⡀⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠿⣛⣿⣶⣾⣿⣷⣤⣤⣶⡿⠛⠉⠁⢀⣀⣠⠾⠛⠉⠀⠀⠀⠀⣴⣷⣬⣿⠿⢿⣿⣤⣿⣿⣿⣿⣭⣿⣿⣿⣿⣶⣿⣿⡿⣻⣦⣾⣿⡿⠛⢴⣤⣤⠄⠀⠀⠀⠛⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠆⠲⣶⠏⢶⠄⠸⠽⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⢀⣀⠉⠈⠉⠉⠉⠉⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠹⣿⣧⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠹⣿⣧⠀⠀⠀⢠⣸⣿⣿⣿⣿⣿⠟⠛⠻⠛⠋⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⣿⣶⣴⣶⣶⣶⣾⣿⣿⣿⡇⣀⣠⣤⣤⣀⣀⣈⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤
⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⣿⣿⣿⣿⣿⢻⣿⢳⡶⢦⣶⣮⢩⣅⣀⣀⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣉⣉⡉⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣸⡇⣼⣟⣹⣇⣛⣿⣿⡏⣿⣿⢷⣿⣴⢶⡆⣦⣭⣭⣙⣛⢛⠛⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣦⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣶⣷⣭⣭⣜⣛⣃⠿⠿⠿⣿⣿⣸⣇⣿⣶⢿⣿⣿⢡⣿⠹⣿⡿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⡀⢰⠈⢡⠉⠙⢘⣛⣻⡸⠟⢸⣿⡿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣛⢿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⡇⢠⠀⠸⠀⠀⢸⣿⣿⣿⣿⣶⣤⠐⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣷⣿⣾⢿⣿⢳⣷⢆⣾⣭⢭⣥⣀⡉⣁⠉⠛⠛⠛⠉⡋⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡇⠐⠀⢰⠀⠀⣸⣿⣿⣿⣿⣿⣿⠀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⠿⢿⡿⣼⣏⣹⣟⢻⣿⡏⣾⣯⣼⣷⡿⣿⢿⣦⣶⣶⠁⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠇⠀⠀⢸⠀⠀⣽⣿⣿⣿⡿⠿⠿⠷⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠿⣿⣷⣶⣶⣬⣭⢩⣽⣿⣛⣻⣶⠿⢿⣷⣿⣿⢧⣿⣧⢨⠉⣭⣿⣿⣿⣿⣿⣿⡿⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡇⠀⠀⠘⢀⣤⣿⣿⣿⣆⠀⢀⣄⣀⡀⠀⢹⠹⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠦⠅⢨⠙⣥⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣦⣧⣤⣤⣼⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⡟⠀⠀⠀⠀⠁⠀⠀⠀⣠⣶⣶⣦⣤⣾⣿⣿⡟⠉⠀⠀⠀⠉⠀⠀⣠⣴⣾⣿⡿⠛⠉⠁⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢠⣶⣦⣄⣼⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⣠⣶⣿⠿⠟⠉⠀⠀⡄⠀⠠⠉⣿⣿⣿⣿⡿⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⢁⣀⣀⣻⡿⠋⠀⣠⣦⠀⣼⣿⣿⣿⡟⠉⠙⠿⠿⣿⣿⣿⣿⣿⣄⠀⠀⣿⡿⡟⠟⠿⢿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⠁⠀⣶⡶⠾⠿⠿⠿⠧⠬⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣿⣿⣿⣿⣷⣄⠀⠉⠁⠀⣿⡿⠟⠛⠁⠀⠀⠀⠀⢻⣿⠋⠉⠉⠻⣿⣿⣿⣿⠀⠀⠀⠀⠙⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣿⡇⠀⣦⣀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣽⣿⣿⣿⣿⣿⣆⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠉⠇⠀⠀⠀⠀⢹⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⠀⢸⡇⠀⠀⠀⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣼⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠀⠀⠀⠀⣠⣄⠀⠀⠸⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⠰⣁⠰⠶⢶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⡀⠘⡇⠀⠀⠃⡯⠆⠀⠀
⠿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣤⡿⣿⣿⣿⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣤⣤⣤⡤⠤⠄⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠁⠀⠀⠀⠑⠀⠿⠿
⣿⣟⣩⣥⣾⣿⠋⢉⣤⣾⣿⡟⣫⣴⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠈⠉⠀⠴⡄⠀⣤⣴⣿⡟⢀⡀⠀⠀⠀⢀⠰⢶⡄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠿⣛⣿⣶⣶⣿⠿⠛⠋⠑⠛⠛⣉⣉⣁⣀⣠⠾⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣄⣀⣀⣀⣀⣄⣛⣿⣤⣴⣾⡿⣻⣤⣾⣿⡿⠛⢴⣾⣿⡿⠃⠘⠻⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠆⠲⣶⠏⢶⠄⠰⠴⠶⠆⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠉⠉⠉⠉⠉⠉⠁⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠹⣿⣿⡅⠀⠐⢼⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠹⣿⣷⢀⣥⣯⣿⣿⣿⣿⣿⣿⣿⠟⠛⠻⠛⠋⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣇⣀⣠⣤⣤⣄⣤⣌⠙⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦
⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⣿⣿⣿⣿⣿⢻⣿⢳⡶⢦⣶⣮⢩⣅⣀⣀⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⡉⢉⢉⠉⠉⠉⠉⠈⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣸⡇⣼⣟⣹⣇⣛⣿⣿⡏⣿⣿⢷⣿⣴⢶⡆⣮⣭⣭⣙⣛⢛⠛⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣶⣷⣭⣭⣜⣛⣃⠿⠿⠿⣿⣿⣸⣧⣿⣶⣿⣿⣿⢡⣿⠹⣿⡿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡀⢰⠈⢡⠉⠙⢘⣛⣻⡸⠟⢸⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣛⢿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⡇⢠⠀⠸⠀⠀⢸⣿⣿⣿⣿⣶⣤⠐⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣷⣿⣾⢿⣿⢳⣷⢆⣾⣭⢭⣭⣉⡉⣉⠉⠋⠙⠛⠛⡛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡇⠘⠀⢰⠀⠀⣸⣿⣿⣿⣿⣿⣿⠀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠿⢿⡿⣼⣏⣹⣟⢻⣿⡏⣾⣯⣼⣷⡿⣿⢿⣦⣶⣶⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠇⠀⠀⢸⠀⠀⣿⣿⣿⣿⣿⣿⣿⠴⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡿⠿⣿⣿⡶⠀⠈⢩⣉⣽⣟⣛⣻⠶⠿⢿⣷⣿⣿⢧⣿⣧⢨⣈⣥⣿⣿⣿⣿⣿⣿⡿⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡇⠀⠀⠘⠀⢀⣿⣿⣟⠋⠛⣦⡄⠀⠀⠀⢻⡙⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣷⣄⣀⣾⣿⣿⠃⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣥⣬⣽⣵⣿⣿⠿⠛⢉⣽⣿⣿⣿⣿⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢇⠀⠀⠀⢀⣴⣿⣿⠟⠋⠀⣀⣨⣷⣿⣿⣷⡌⠁⠘⣿⣿⣿⣿⠀⠀⠘⣿⠉⠀⠙⢻⣿⡿⠁⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣧⡀⣶⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⠀⠀⢀⣼⣯⣉⠁⠀⣠⣾⣿⣿⣿⣿⣿⣿⢿⣦⡀⠀⢻⣿⣧⠆⠀⠀⠘⡄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡇⠀⠐⠂⠈⠉⠉⠛⠛⠋⠙⠣⠉⣿⣿⣿⣿⡿⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⢹⣿⣦⢸⣿⣟⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣶⡶⠾⠿⠿⠿⠷⠬⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠈⢻⣿⣿⣿⢿⣷⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢃⣿⡇⠀⣦⣀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⢀⣮⣿⣾⣿⣿⣿⡿⠈⢸⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⢀⣤⣤⣤⣤⣤⣤⠀⢸⡇⠀⠀⠀⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡏⠀⠸⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⢰⣁⠴⠶⠶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣹⣿⣿⣿⣿⣿⣿⣷⣄⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⡀⠘⡇⠀⠀⠃⡯⠆⠀⠀
⢿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⠴⠿⣿⣿⣿⣿⡿⠋⠛⠋⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢠⣤⣴⣶⣶⡶⠒⠒⠂⠀⠀⠈⠁⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠁⠀⠀⠀⠑⠀⠿⣿
⣿⣟⣩⣥⣿⣿⠛⠉⠀⠀⣀⠀⣠⣴⣿⠛⠁⠀⠀⢀⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⣼⡟⠻⣦⣤⣾⡛⢻⣤⣽⡅⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠿⣛⣿⣶⣶⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣤⠾⣿⣿⣷⣤⡾⢿⣦⣄⣀⣄⠀⢰⣶⣬⣿⣿⣿⣿⣭⣿⣿⣿⣿⣶⣾⣷⡖⣲⣤⣾⣿⡿⠛⢶⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠆⠲⣶⠏⢶⠄⠸⠽⠿⠏⠀⠉⠉⠉⠁⠀⠀⠀⠉⠉⠉⠁⠀⠈⠉⠉⠉⠁⠀⢀⣉⠉⠉⠉⠉⠉⠉⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠹⣿⣿⡥⠂⠚⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠹⣿⣷⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠻⠛⠋⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣠⣤⣤⣄⣤⣬⠙⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤
⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⢻⣿⢳⡶⢦⣶⣮⢩⣅⣀⣀⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣭⣭⣍⣉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣸⡇⣼⣟⣹⣇⣛⣿⣿⡏⣿⣿⢷⣿⣴⢶⡆⣦⣭⣭⣙⣛⢻⠛⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣶⣷⣭⣭⣜⣛⣃⠿⠿⠿⣿⣿⣸⣧⣿⣶⣿⣿⣿⢣⣿⠹⣿⡿⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡀⢰⠈⢡⠉⠙⢘⣛⣻⡸⠟⢸⣿⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣛⢿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣶⣄⣸⠀⠀⣼⣿⣿⣿⣿⣷⣦⢒⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣷⣿⣾⢿⣿⢳⣷⢆⣾⣭⢭⣭⣉⡉⣉⠉⠛⠛⠛⠛⡛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣧⣀⠈⠙⢿⣿⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠿⢿⡿⣼⣏⣹⣟⢻⣿⡏⣾⣯⣼⣷⡿⣿⢿⣦⣶⣶⠁⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠟⢷⢄⡀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠷⣶⣶⣮⣭⣉⣽⣟⣛⣻⠶⠿⢿⣷⣿⣿⢧⣿⣧⢨⠉⣭⢻⣿⣿⣿⣿⣿⡿⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡇⠀⠀⠙⢠⣄⠈⢿⣿⣿⣿⣿⡏⢿⣿⣿⣿⣿⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠥⢬⠙⠵⠿⠠⠿⣸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣧⠁⠀⠀⣰⣿⣿⣷⠈⠻⣿⠟⠉⠀⠈⣿⣿⣿⣿⠀⠀⠀⠀⢺⠇⠀⠀⠀⠁⠀⠀⠀⠀⢀⣿⡿⠿⠿⢿⡿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⢀⣧⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⠀⠀⣠⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣿⣿⡿⠿⠀⠀⠀⠀⠀⠀⢀⣠⣴⣤⣀⠀⠀⣠⣾⡏⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⡿⠉⣿⣿⣿⣿⡿⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⣠⣾⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠙⢷⣾⣿⠟⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⠾⠿⠿⠿⠷⠼⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡿⠛⠁⠀⠉⠉⠉⠉⠉⠉⠉⣽⡇⠀⣦⣀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⠀⠀⢀⣤⣤⣤⣤⣤⣤⠀⢸⡇⠀⠀⠀⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣼⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⢰⣁⠴⠶⠶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡀⢀⣿⣿⣿⣿⣿⣿⡀⠘⡇⠀⠀⠃⡯⠆⠀⠀
⢿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣯⣤⡿⣿⣿⣿⡿⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠶⠶⠒⠒⢀⣤⣄⡀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣧⠀⠀⠀⠀⠉⠉⠉⠁⠀⠁⠀⠀⠀⠑⠀⠿⠿
⣿⣿⣩⣥⣿⣿⠛⢉⣤⣾⣿⡟⣫⣼⣿⣿⣿⣤⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⣦⣼⣿⡝⣣⣤⣤⠀⠀⠀⠀⠈⠛⠛⣻⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠿⣛⣿⣶⣶⣿⣿⣿⣿⣶⠿⠿⣟⣛⣋⣉⣁⠀⢠⣤⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⠈⠙⠛⢀⣿⣿⡿⠛⢴⣶⣶⡦⠀⠀⠀⠀⠉⠁⠀⠒⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠆⠲⣶⠏⢶⠄⠰⠴⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠹⣿⣿⡅⠀⠀⢘⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠹⣿⣷⣀⣉⣝⣽⣿⣿⣿⣿⣿⣿⠟⠛⠻⠛⠋⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣅⣀⣤⣤⣤⣀⣠⣌⠙⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦
⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⣿⣿⣿⣿⣿⢻⣿⢳⡶⢦⣶⣮⢩⣅⣀⣀⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣭⣭⣭⣍⣉⣉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣸⡇⣼⣟⣹⣇⣛⣿⣿⡏⣿⣿⢷⣿⣴⢶⡆⣦⣭⣭⣙⣛⢻⠛⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣶⣷⣭⣭⣜⣛⣃⠿⠿⠿⣿⣿⣸⣧⣿⣶⣿⣿⣿⢣⣿⠹⣿⡿⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡀⢰⠈⢡⠉⠙⢘⣛⣻⡸⠟⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣛⢿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣟⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⡇⠠⠀⠸⠀⠀⢸⣿⣿⣿⣿⣷⣤⠐⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣷⣿⣾⢿⣿⢳⣷⢆⣾⣭⢭⣭⣁⡉⣁⠉⠉⠙⠛⠛⡛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣧⣾⣤⣴⣀⡀⣸⣿⣿⣿⣿⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠿⢿⡿⣼⣏⣹⣟⢻⣿⡏⣾⣯⣼⣷⡿⣿⢿⣦⣶⣶⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠟⠷⣶⣶⣮⣭⣉⣽⣟⣛⣻⠶⠿⢿⣷⣿⣿⢣⣿⣧⣨⠈⣭⢻⣿⣿⣿⣿⣿⡿⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠏⠂⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⡀⠀⠀⠡⢬⠙⠥⣿⣴⣿⣾⣿⣿⣿⣿⣿⣿⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢧⠀⠀⠀⣠⣾⣿⣶⡄⠹⠿⠟⠋⠁⠀⢸⣿⣿⣿⣿⠏⠻⠟⠛⠉⠉⠟⠀⠁⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣤⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⠀⠀⠀⣿⣿⣶⣼⣿⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠀⠀⠀⠀⢀⡀⠀⣠⣄⣀⣴⣾⣿⡿⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠉⣿⣿⣿⣿⡿⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⠀⣠⣞⣋⠉⣻⣶⣿⣧⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠘⠁⢠⡿⠛⠛⠿⣿⡟⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣯⡀⠀⣶⡶⠾⠿⠿⠿⠷⠼⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢸⣶⣿⣯⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡁⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣦⣀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣾⣧⠀⠀⢀⣤⣬⣽⣿⣿⣿⠛⢻⡇⠀⠀⠀⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡆⠀⠸⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⢰⣁⠴⠶⠶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠀⠀⠀⣿⣿⣿⣿⡇⠀⢀⣿⣿⣿⣿⣿⣿⡀⠘⡇⠀⠀⠃⡯⠆⠀⠀
⢿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣥⡿⣿⣿⣿⡿⣿⣿⠟⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠶⠦⠄⠀⠀⠀⠀⠈⠉⠁⠀⠀⠈⢿⣿⣿⣿⡀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠁⠀⠀⠀⠱⠀⠻⢿
⣿⣟⣩⣥⣾⣿⠛⢉⣤⣾⣿⡟⣫⣼⣿⣿⡟⠀⠉⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠈⠻⣿⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠿⣛⣿⣶⣶⣿⠿⠛⠋⠐⠛⠋⣉⣉⣤⣀⣠⠾⠿⠟⠃⠀⠀⠀⣠⣦⣤⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣚⣿⣦⣾⣿⡿⠿⣤⣿⣿⡟⠛⢦⣤⣄⠀⠀⠀⠀⠐⠒⠀⠠⠖⠚⠳⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⠆⠲⣶⠏⢶⠄⠰⠴⠶⠆⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠹⣿⣧⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠹⣿⡇⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠟⠛⠛⠛⠋⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠙⣿⣶⣴⣶⣶⣶⣾⣿⣿⣿⣅⣀⣠⣤⣤⣀⣠⣌⠙⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤
⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⣿⣿⣿⣿⣿⢻⣿⢳⡶⢦⡶⣮⢩⣅⣀⣀⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣉⣉⡉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣸⡇⣼⣟⣹⣇⣛⣿⣿⡏⣿⣿⢷⣿⣴⢶⡆⣦⣭⣭⣙⣛⢛⠛⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣶⣷⣭⣭⣜⣛⣃⠿⠿⠿⣿⣿⣸⣇⣿⣶⣿⣿⣿⢡⣿⠹⣿⡿⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⡀⢰⠈⢡⠉⠙⢘⣛⣻⡸⠟⢸⣿⡿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣛⢻⡿⠿⢿⣿⣿⣿⣿⣿⣿⡛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⡇⠠⠀⠸⠀⠀⢸⣿⣿⣿⣿⣶⣤⠐⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣷⣿⣾⢿⣿⢳⣷⢆⣾⣭⢭⣥⣁⡈⣀⠉⠉⠙⠛⠉⡛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡇⠨⠀⢰⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⠿⢿⡿⣼⣏⣹⣟⢻⣿⡏⣾⣯⣼⣷⡿⣿⢿⣦⣶⣶⢁⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠇⠀⢀⣼⣿⣷⣿⣿⣿⣿⣿⣿⣿⠴⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠛⠷⢶⣶⣬⣭⢉⣽⣟⣛⣻⠶⠿⢿⣷⣿⣿⢧⣿⣧⢺⣿⣯⢻⣿⣿⣿⣿⣿⡿⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢹⠹⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣾⣿⣿⣿⣿⡿⠇⣀⣤⣴⣷⣮⣽⣥⠟⠛⠿⣼⣿⣿⣿⣿⣿⣿⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣜⣟⣤⣀⠹⠟⠻⣏⠁⠈⢿⣷⣾⣿⣿⣷⣜⢿⣿⣿⣿⠀⠀⠀⠀⠁⠀⢀⣀⣀⣀⣾⣿⣿⣿⣿⣿⣿⡿⠛⢋⣤⣾⣿⣿⣿⡿⢛⠉⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠻⢿⣿⣿⣿⣙⣷⠀⠀⠉⠀⠀⠈⠻⣿⣿⣿⣿⣿⣇⣻⣿⣧⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠿⠿⢰⣿⣿⣿⠟⠋⠁⠀⢨⠀⠁⡄⠀⠀⠁⣿⣿⣿⣿⡿⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡀⠘⠻⢿⡟⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⠿⢿⣿⡟⢀⣀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠉⠁⠀⠀⠈⠛⠛⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⣶⡶⠾⠿⠿⠿⠷⠬⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢰⠀⣼⡋⢰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠈⡿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣿⡇⠀⣦⣀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠸⣻⣋⣉⠉⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠀⠀⠀⠀⠈⠉⠀⠀⠀⠈⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⡄⠀⠀⢀⣤⣤⣤⣤⣤⣤⠀⢸⡇⠀⠀⠀⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣴⣾⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⠀⠀⠸⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⠰⣁⠰⠶⠶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠈⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠏⠈⠀⠀⣅⠀⠀⠀⠀⢾⣿⣿⣿⠀⠀⢀⣿⣿⣿⣿⣿⣿⡀⠘⡇⠀⠀⠃⡯⠆⠀⠀
⠿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡯⠾⣿⣿⣿⡿⣿⠿⠿⠛⠃⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠶⠶⠾⣟⣀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠁⠀⠀⠀⠑⠀⠻⠿
⣿⣟⣩⣥⣾⣿⠛⠉⠀⠈⠉⠀⣠⣼⣿⠟⠋⠀⠀⢀⣠⠞⠋⠀⠀⠀⠀⢻⣿⣤⣄⠀⣠⣤⣼⡟⠻⣧⣤⣤⡀⢀⣤⣤⣤⠻⠟⠀⠂⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠿⣛⣯⣶⣶⣿⣿⣿⣷⣶⣿⡿⣋⣁⠀⠀⣀⠞⠋⠁⠀⠀⠀⢠⣾⣷⣬⣿⠿⢿⣿⣬⣽⣿⣿⣿⣭⣿⣿⣿⣿⣤⣿⣿⡿⠻⣤⣾⣿⡿⠛⢤⣤⡄⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⠆⠲⣶⠏⢶⠄⠸⠽⠿⠏⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⢀⡉⠉⠉⠉⠉⠉⠉⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠹⣿⣿⠁⠀⠀⠈⠯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠹⣿⣷⠀⠐⠰⠠⣼⣿⣿⣿⣿⣿⠟⠛⠛⠛⠋⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⣿⣶⣾⣷⣾⣶⣾⣿⣿⣿⣅⣀⣠⣤⣤⣀⣠⣌⠙⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤
⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⣿⣿⣿⣿⣿⢻⣿⢳⡶⢦⣶⣮⢩⣅⣀⣀⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣉⡉⣉⠉⠉⠈⠁⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣸⡇⣼⣟⣹⣇⣛⣿⣿⡏⣿⣿⢷⣿⣴⢶⡆⣦⣭⣭⣙⣛⢛⠛⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣦⣶⣶⣦⣶
⣿⣿⣿⣿⣿⣶⣷⣭⣭⣜⣛⣃⠿⠿⠿⣿⣿⣸⣧⣿⣶⢿⣿⣿⢡⣿⠹⣿⡿⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⡀⢰⠈⢡⠉⠙⢘⣛⣻⡸⠟⢸⣿⡿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣛⢻⡿⠿⢿⣿⣿⣿⣿⣿⣿⡟⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⡇⠠⠀⠸⠀⠀⢸⣿⣿⣿⣿⣶⣤⠐⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣷⣿⣾⢿⣿⢳⣷⢆⣾⣭⢭⣭⣉⡉⣁⠉⠛⠛⠙⠙⡛⠋⠻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡇⠐⠀⢰⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⠿⢿⡿⣼⣏⣹⣟⢻⣿⡏⣾⣯⣼⣷⡿⣿⢿⣦⣶⣶⠁⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠇⠀⢀⣸⣤⣄⣸⣿⣿⣿⣿⣿⣿⠴⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⠿⠿⠏⠷⣶⣶⣾⣯⣭⣽⣿⣛⣻⡶⠿⢿⣷⣿⣿⢣⣿⣧⣼⣯⣭⢻⣿⣿⣿⣿⣿⡿⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡆⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠈⢻⠹⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⣄⣤⣵⣮⣝⠡⠟⠿⠿⣼⣿⣿⣿⣿⣿⣿⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣶⣦⠘⢿⣿⣿⣿⠀⠀⠀⠀⠁⠀⣠⣤⣤⣄⣴⣿⣿⠛⣿⣿⣿⣿⣏⣿⣿⣽⣿⣿⡿⠟⠛⠀⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠿⣿⣿⣿⣿⣿⣿⣧⢀⣺⣿⣧⣀⣀⠀⠀⢀⣼⣿⣿⣿⣿⣿⡟⠁⠀⢹⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⢀⢨⠀⠁⡄⠀⠀⠁⣿⣿⣿⣿⡿⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠘⣿⣿⣿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⠋⠀⠀⠀⠈⠿⠟⠋⠛⠛⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣶⡶⠾⠿⠿⠿⠷⠬⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⣛⣯⣽⡟⠿⠟⠋⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠉⠉⠉⠉⠉⠉⠀⠀⠈⠉⠹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣿⡇⠀⣦⣀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣪⣿⣶⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⠀⢸⡇⠀⠀⠀⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⣾⣿⣆⠀⠀⠸⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⠰⣁⠴⠶⠶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣹⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠀⠀⢀⣿⣿⣿⣿⣿⣿⡀⠘⡇⠀⠀⠃⡯⠆⠀⠀
⠿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⠴⠿⣿⣿⣿⠿⣿⠿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣤⠀⣀⣀⡠⠤⣶⣦⣄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠁⠀⠀⠀⠑⠀⠻⠿
⣿⣟⣩⣥⣾⣿⠛⠉⠀⠈⠁⠀⣠⣴⡿⠛⠉⠀⠀⣀⣤⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⣤⣤⡄⠀⣡⣤⣿⡛⢻⣤⣽⣟⠛⠀⠀⠀⠀⠀⡠⢶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀
⠿⠿⣛⣿⣶⣶⣿⣿⣿⣷⣶⠟⠉⣀⣀⣀⣀⠀⠀⢁⡀⠀⣠⡐⢾⣿⣷⣤⣾⠿⢿⣷⣤⣿⣿⣿⣿⣬⣿⣿⣿⣿⣦⣿⣿⡿⠻⣤⣾⣿⡿⠛⢶⣾⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⠆⠲⣶⠏⢶⠄⠸⠽⠿⠇⠀⠀⠀⠁⠀⠀⠀⠀⠈⠉⠈⠀⠀⠈⠉⠉⠉⠁⠀⢀⣈⠉⠉⠉⠉⠉⠉⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠹⣿⣧⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠹⣿⣧⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⠟⠛⠛⠛⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⣿⣶⣶⣶⣶⣶⣿⣿⣿⣿⣅⣀⣤⣤⣤⣤⣤⣬⠉⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤
⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⣿⣿⣿⣿⣿⢻⣿⢳⡶⢦⣶⣮⢩⣅⣀⣀⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣍⢉⣉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣸⡇⣼⣟⣹⣇⣛⣿⣿⡏⣿⣿⢷⣿⣴⢶⡆⣦⣭⣭⣙⣛⢛⠛⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⣴⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣶⣷⣭⣭⣜⣛⣃⠿⠿⠿⣿⣿⣸⣇⣿⣶⣿⣿⣿⢡⣿⠹⣿⡿⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡀⢰⠈⢡⠉⠙⢘⣛⣻⡸⠟⢸⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣛⢿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣛⠛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⡇⠠⠀⠸⠀⠀⢸⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣷⣿⣾⢿⣿⢳⣷⢆⣾⣭⢭⣥⣈⡉⣁⠉⠛⠉⠛⠉⡋⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡇⠐⠀⢰⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠿⢿⡿⣼⣏⣹⣟⢻⣿⡏⣾⣯⣼⣷⡿⣿⢿⣦⣶⣶⠁⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠇⠀⠀⢸⣤⣶⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⠿⠿⢯⣷⣶⣶⣮⣭⢉⣽⣟⣛⡻⠶⠿⢿⣷⣿⣿⢣⣿⣧⣨⠉⣭⢻⣿⣿⣿⣿⣿⡿⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣶⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⢺⣿⣿⣿⣿⣿⣦⠀⠀⠀⠁⢨⢉⣥⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⠀⠈⠛⠻⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠛⠛⠛⠉⠉⠉⠀⠀⠁⠀⠀⠀⣼⡟⠛⠛⠋⠉⠹⢿⣿⣿⣿⣿⣿⣟⡀⢀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢘⠓⠂⢀⣿⣿⣿⣿⣿⠃⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠩⠁⣿⣿⣿⣿⡿⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣴⣿⣿⣿⣿⣿⡿⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⠀⢰⣿⢿⣶⣤⣾⣿⠟⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⣶⡶⠾⠿⠿⠿⠷⠬⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢐⣿⣿⣛⣙⣿⣿⠋⠀⠀⠀⠀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⠛⠋⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠋⠉⠙⠻⠿⠛⠿⠿⠿⠓⠀⠋⣿⡇⠀⣦⣀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⠀⢸⡇⠀⠀⠀⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠸⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣀⣶⡀⠀⠘⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⢰⣁⠰⠶⠶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣰⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⡀⠘⡇⠀⠀⠃⡯⠆⠀⠀
⠿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣧⣿⡿⣿⣿⡿⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⠤⠤⢤⣤⠤⣤⣀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠉⠁⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠁⠀⠀⠀⠑⠀⠻⠿
⣿⣟⣩⣥⣾⣿⠛⢉⣤⣾⣿⡟⠋⠼⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢻⣤⣼⣟⠛⣧⣼⣿⡅⠀⠀⠀⠀⠈⠛⠛⠛⠀⠀⣀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠟⠛⠋⠁⠘⠛⢛⣋⣡⣤⣤⣤⣤⣶⡟⠃⠀⠀⠀⣀⣤⣤⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣲⣶⣤⣤⣤⣀⣩⣤⣿⣿⡿⠻⣤⣿⣿⡿⠛⢤⣤⠀⠀⠀⠀⠈⠻⠿⠇⠀⠐⠛⠷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠆⠲⣶⠇⢶⠄⠸⠿⠿⠏⠈⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠹⣿⣿⣵⡄⡀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠹⣿⣷⣼⣸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠻⠛⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣇⣀⣤⣤⣤⣤⣤⣤⡉⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤
⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⢻⣿⢳⡶⢦⣶⣮⢩⣅⣀⣀⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣉⣉⣉⠉⠉⠉⠉⠉⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣸⡇⣼⣟⣹⣇⣛⣿⣿⡏⣿⣿⢷⣿⣴⢶⡆⣮⣭⣭⣙⣛⢻⠛⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣶⣷⣭⣭⣜⣛⣃⠿⠿⠿⣿⣿⣸⣧⣿⣶⣿⣿⣿⢣⣿⠹⣿⡿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡁⢰⠈⢡⠉⠙⢘⣛⣻⡸⠟⢸⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣛⢿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⡇⠠⠀⠸⠀⠀⢸⣿⣿⣿⣿⣷⣦⢒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣷⣿⣾⢿⣿⢳⣷⢆⣾⣭⢭⣭⣉⡉⣉⠉⠛⠛⠛⠛⡛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡇⠸⠀⢰⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠿⢿⡿⣼⣏⣹⣟⢻⣿⡏⣾⣯⣼⣷⡿⣿⢿⣦⣶⣶⠁⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠇⠀⠀⢸⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣷⣶⣮⣭⢩⣽⣟⣛⣻⡶⠿⢿⣷⣿⣿⢧⣿⣧⢨⢉⣭⢻⣿⣿⣿⣿⣿⡿⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⢿⣿⣿⣿⣦⣘⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⡟⠋⠉⣉⣉⡻⢿⣿⣿⣿⣿⣿⡿⠟⠃⠀⣠⡤⠁⢈⠙⠵⠿⠠⠿⣼⣿⣿⣿⣿⣿⣿⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠈⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠘⣿⣿⣿⣿⣿⣇⠀⢱⣿⣿⣷⣤⣸⣿⣿⣿⣶⣿⣿⡿⠋⢁⣤⣤⡶⠾⠋⠀⠀⢸⠀⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢰⠛⠂⢀⣉⣿⣿⣿⣿⣿⠋⠉⢿⣿⣿⣿⣇⠀⠀⠀⠀⠈⠉⠀⠀⠀⠹⣷⣿⣿⠋⠉⠉⠛⢿⣿⣿⣿⣿⣿⡄⠾⠿⠛⣁⠀⠀⠀⠀⠀⢸⠉⠁⡆⠀⠠⠁⣿⣿⣿⣿⡿⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⠿⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⡇⠀⠀⠰⣿⠆⠀⠀⠀⠘⠀⠀⠀⠁⠀⣶⡶⠾⠿⠿⠿⠷⠼⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣰⣿⣟⣛⢛⣿⣿⠟⠁⠀⠀⠀⠀⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣋⣿⡇⠀⣦⣀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣷⣦⡀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⠀⢸⡇⠀⠀⠀⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⣿⣿⣿⡆⠀⠀⠸⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⢱⣁⠴⠶⢶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣰⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠘⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⡀⠘⡇⠀⠀⠃⡯⠆⠀⠀
⢿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣧⣿⡿⣿⣿⣿⠿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠁⠀⠀⠀⠑⠀⠿⣿
⣿⣟⣩⣥⣾⣿⠛⢉⣤⣾⣿⡟⣫⣼⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢻⣤⣿⣟⠛⣧⣼⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀
⠿⠿⠛⢫⣶⡶⠿⢟⣛⣉⣀⣀⣤⣤⣤⣶⡆⠀⠀⠀⠀⠀⣠⡄⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣤⣤⣤⣀⣠⣤⣿⣿⡿⢻⣤⣿⣿⡿⠃⠀⣀⡀⠀⠀⠀⠛⠿⠿⠇⠀⠚⠛⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠆⠲⣶⠇⢶⠄⠸⠿⠿⠏⠈⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠹⣿⣿⡁⠀⠀⠨⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠹⣿⣷⠀⢀⢸⣯⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣇⣀⣤⣤⣤⣤⣤⣬⠉⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤
⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⢻⣿⢳⡶⢦⣶⣮⢩⣅⣀⣀⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣉⣉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣸⡇⣼⣟⣹⣇⣛⣿⣿⡏⣿⣿⢷⣿⣴⢶⡆⣦⣭⣭⣙⣛⢛⠛⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣶⣷⣭⣭⣜⣛⣃⠿⠿⠿⣿⣿⣸⣇⣿⣶⣿⣿⣿⢡⣿⠹⣿⡿⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⡀⢰⠈⢡⠉⠙⢘⣛⣻⡸⠟⢸⣿⡿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣛⢿⡿⠿⢿⣿⣿⣿⣿⣿⡿⡿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣶⣷⣤⠀⠸⠀⠀⣾⣿⣿⣿⣿⣶⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣷⣿⣾⢿⣿⢳⣷⢆⣾⣭⢭⣭⣉⡉⣉⠉⠛⠉⠛⠉⡛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠙⠻⢿⣿⣦⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠿⢿⡿⣼⣏⣹⣟⢻⣿⡏⣾⣯⣼⣷⡿⣿⢿⣦⣶⣶⠁⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠙⠦⢀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠷⣶⣶⣮⣭⢉⣽⣟⣛⣻⠶⠿⢿⣷⣿⣿⢣⣿⣧⣨⠉⣭⢻⣿⣿⣿⣿⣿⡿⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠂⠀⠀⢰⣤⡌⠉⠻⣿⣿⡿⠿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣸⣿⣿⣿⣿⣿⣶⠀⠀⠀⠡⢨⠉⠥⠿⠠⠿⣼⣿⣿⣿⣿⣿⣿⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⠀⠀⠀⣼⣿⣧⠀⠀⠈⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⠙⠻⠿⠿⠿⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⡽⠁⠀⠀⠀⢸⠀⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠸⠀⠀⣰⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢻⣇⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢸⠉⠁⡆⠀⠀⠁⣿⣿⣿⣿⡿⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⣠⣾⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠻⣿⡿⠃⠀⠈⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣶⣶⣶⣶⣶⣦⣿⣿⣿⣿⣿⣦⣴⣄⡀⠈⠀⠀⠀⠁⣀⣶⣶⣾⣿⣿⠿⠷⠬⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣠⣾⣿⣿⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⢛⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠛⢿⣿⣿⣿⣿⡿⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢡⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠉⠉⠉⠙⣿⣿⣿⣟⠀⠀⠀⠀⠘⣿⣿⣿⣿⠇⠀⠀⣼⣿⣿⣿⣿⣿⠛⢹⡏⠀⠀⢰⣁⠰⠶⠶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⣿⣿⠋⠁⠀⠀⠀⠀⠀⠹⣿⣿⡛⡥⠀⢀⣿⣿⣿⣿⣿⣿⡀⠘⡇⠀⠀⠃⡯⠆⠀⠀
⢿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣤⣿⡿⣿⣿⣿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠾⠃⢀⣀⢻⣟⡀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣿⡆⠀⠀⠀⠀⠀⠉⠉⠁⠀⠁⠀⠀⠀⠑⠀⠻⡿
⣿⣟⣩⣥⣾⣿⠛⢉⣤⣾⣿⠟⣫⣼⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢻⣤⣼⣟⠛⠃⠿⡟⠀⠀⠀⢠⣍⠀⣀⠈⠛⠉⠙⠃⠲⠆⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠿⣛⣯⣶⣾⡿⠿⠛⠋⠐⠛⠛⣉⣉⣠⣤⣄⠴⠂⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⣿⣿⡿⠻⣶⣾⣿⣿⠛⢤⣿⣿⡿⠃⠐⠶⠶⠶⠄⠀⠘⠛⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠆⠲⣾⠏⢶⠄⠰⠴⠶⠆⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀

                    ䷩ 𝚕𝚒𝚗𝚎 583

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/11/26/fsf-associate-membership-at-19/#comments
    Gemini version at gemini://gemini.techrights.org/2021/11/26/fsf-associate-membership-at-19/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 11.26.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ 38+_Years_of_GNU_and_19+_Years_of_FSF_Associate_Membership⠀✐


Posted in Free/Libre_Software, FSF, GNU/Linux, Videos at 7:58 pm by Dr. Roy
Schestowitz


Association for Computing Machinery (ACM) Software System Award to Richard
Stallman


Video_download_link


http://techrights.org/wp-content/uploads/2021/11/rms-acm.webm


Summary: “On November 25, 2002,” Wikipedia_notes, “the FSF launched the FSF
Associate Membership program for individuals.” As the above video points_out,
it all started almost 40 years ago.



                    ䷩ 𝚕𝚒𝚗𝚎 619

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/11/26/gemini-protocol-games/#comments
    Gemini version at gemini://gemini.techrights.org/2021/11/26/gemini-protocol-games/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 11.26.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Gemini_as_a_Platform_for_Gamers⠀✐


Posted in Free/Libre_Software at 6:32 pm by Dr. Roy Schestowitz


Video_download_link | md5sum 3ad242d08f8e7076cd393246a6bb369c


http://techrights.org/videos/gemini-games.webm


Summary: Contrary to what people often assume (or are led to assume), even
without client-side scripting Gemini can accomplish a great deal; early
adopters, many of whom are technical, test the limits of the very_minimalistic_
(by_design_and_intention) specification


THE mailing lists of Gemini point_out some new games for Gemini Protocol; not
all Gemini clients (“browsers”) support these at the moment, not even an older
version of Lagrange and the widely-used Amfora (presented on the right hand
side at the start of the video above), but this comes to show how creative
spirits and server-side programming can accomplish a great deal. One can, in
theory, do banking in Gemini (certificates make sessions, which are are no less
secure than on the Web); many flight booking agencies used or still use
‘lesser’ UIs to do their job (like entering input, in a specialised querying
language, for the server to interpret and return results).


“The media will almost never mention Gemini, but that intentional snubbing —
due to a lack of financial incentive, e.g. spies and advertisers — does not
prevent Gemini’s growth.”The above video shows SpellBinding, which is new, and
then Wordtunneler. There are even online 'chat_clients' for Gemini. Don’t
discount it as primitive and useless; it’s actually vastly superior/cleaner
than other hypertext protocols/spaces when it comes to signal/noise ratio
because the_Web_became_a_spamfarm. That’s just the direction the Web has taken
and will continue to take.


The media will almost never mention Gemini, but that intentional snubbing — due
to a lack of financial incentive, e.g. spies and advertisers — does not prevent
Gemini’s growth. Earlier this week we reached 1,827 known (to_Lupa) capsules in
total. Just a couple of days after reaching_1,807. 2,000 by year’s end isn’t
insurmountable. █


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


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠷⠦⢄⠀⢹⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⣀⣀⣠⣄⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠀⡆⢸⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣄⠀⠀⣾⣿⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣧⡀⣿⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣦⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠀⠙⢿⣿⣿⣿⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣶⣿⣿⠿⠋⠀⠀⢸⣿⣿⣧⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠀⠀⠀⠻⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠉⠉⣿⣿⣿⣿⣿⣯⣭⣽⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣠⣼⣿⣿⣿⣿⣿⣿
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡇⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⠛⠉⣉⣿⣿⣿⠃⠀⣸⣿⣿⣏⣉⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⣀⣀⣀⣀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡆⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⡃⢹⣿⣿⣭⣿⣿⡁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠃⠀⢠⠀⠀⠀⠀⢈⣿⣿⣿⡿⢿⣿⡿⠉⣽⣿⢿⣿⡄⠀⣿⣿⣷⣾⣿⡋⠈⣿⣿⢿⣛⣛⡃⢠⣿⣿⣹⣿⣿⡟⠀⠀⠀⢸⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣮⠆⠀⠀⠀⠀⠀⠰⠶⣦⣀⡈⠀⠀⠐⣾⣿⣿⣿⣿⣀⣠⣶⡦⣾⣿⣿⣾⣿⣿⡄⣿⣿⣀⣻⣿⣿⣤⣿⣿⣿⠿⠿⠟⠒⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛
⣿⡏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣶⣄⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣽⡟⠛⠋⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡤⠶⠦⣤⠶⠦⡤⠦⣤⠶⢶⠶⡶⠶⡴⢶⠶⢿⡛⢠⡴⠾⠿⡿⠿⠿⡿⠿⢿⡿⠿⠿⣶⠶⡶⢶⣤⠤⠦⢤⠶⠶⣶⠶⠶⢤⡀⡤⠶⠦⡤⠶⠦⢤⠴⢤⠶⢤⠴⠦⡴⠶⢦⣠⠶⠶⢶⠶⢦⠶⢦⠶⠦⡴⠶⢤⡀
⢻⡇⢸⠤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣿⡇⠰⠀⡽⠀⠶⡇⢠⠘⡇⠀⡆⢸⡄⠃⣼⣿⠀⠰⡆⠀⡆⢸⠀⠐⢀⡗⡇⠀⠂⡀⠀⠆⣸⠀⢸⠀⠘⠀⠀⡇⠰⢾⠙⡆⠀⣾⠀⣻⠀⠘⠀⠀⡇⠰⢾⡟
⠸⡇⠸⠀⢸⠀⠶⡇⢰⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⢹⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⣿⣿⠀⢰⡇⠀⠇⢸⠀⢰⠀⣷⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⠀⡇⠀⣿⠀⢻⠀⡄⠀⠀⡇⠰⢾⡅
⠀⠛⠲⢷⠚⠲⣶⢳⡾⠖⠗⠚⠒⠓⠒⣷⣾⣶⣾⠒⠋⠓⠚⢲⣷⣶⣶⡖⠚⢲⣶⣶⣶⣿⣷⣶⣿⣿⣶⣾⡟⠲⠶⠿⠒⠚⠒⠁⠓⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠒⠒⠓⠒⠚⠀⠑⠒⠛⠒⠚⠒⠓⠓⠒⠓⠒⠚⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡪⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠦⢄⠀⢹⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⣀⣀⣠⣄⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠀⡆⢸⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣄⠀⠀⣼⣿⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣧⡀⣿⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠀⠙⢿⣿⣿⣿⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣶⣿⣿⠿⠋⠀⠀⢸⣿⣿⣷⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣦⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠀⠀⠀⠻⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⠈⠉⠉⣿⣿⣿⣿⣿⣯⣭⣽⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡤⣿⣿⣿⣿⣿⣿
⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠈⣽⣿⣿⠛⠉⢉⣿⣿⣿⠃⠀⣸⣿⣿⣏⣉⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⣀⠀⠀⣠⣤⣴⣦⣴⣞⣷⣿⣶⣿⣿⣿⣿⣿⣿⣿
⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⢿⣿⣿⡃⢹⣿⣯⣭⣿⣿⡁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠸⠰⠃⠀⢠⠀⠀⠀⠀⠈⣿⣿⣿⣿⢿⣿⡿⠉⣽⣿⢿⣿⡄⠀⣿⣿⣷⣾⣿⡋⠈⣿⣿⢟⣛⣛⡃⢠⣽⣯⣩⣿⣿⠟⠀⠀⠀⠘⣿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣿⣆⡀⠀⠠⠀⠀⠠⠶⣦⣀⣈⠀⠀⡐⣤⣿⣿⣿⣿⣀⣠⣶⡶⣾⣿⣿⣾⣿⣿⡄⣿⣿⣈⣻⣿⣿⣤⣿⣿⡿⠿⠿⠛⠒⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛
⣿⡿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣦⣢⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⡟⠛⠋⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡥⠶⠦⣤⠶⠦⡤⠦⣤⠶⢶⠶⣶⠶⡴⢶⠶⢿⡛⢠⡶⠾⠿⣿⠿⠿⡿⠿⢿⡿⠿⠿⣶⠶⡶⢦⣤⠴⠶⢦⠶⠶⣦⠶⠶⢤⡀⡤⠶⠦⡤⠶⠦⢤⠶⢤⠴⢦⠴⠦⡴⠶⢦⣠⠴⠶⢶⠶⢤⠶⢦⠴⠦⡴⠶⢤⣰
⢻⡇⢸⠤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣿⡇⠰⠀⣽⠀⠶⡇⢠⠘⡇⠀⡆⢸⡄⠃⣼⣿⠀⠰⡆⠀⡆⢸⠀⠐⢀⡇⡇⠀⠆⡀⠀⠆⣸⠀⢸⠀⠘⠀⠀⡇⠰⢾⠙⡆⠀⣾⠀⢸⠀⠘⠀⠀⡇⠰⢾⣿
⠸⡇⠸⠀⢸⠀⠶⡇⢸⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⠹⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⣿⣿⠀⢰⡇⠀⠇⢸⠀⢰⠀⣷⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⡀⡇⠀⣿⠀⢹⠀⡄⠀⠀⡇⠰⢾⣿
⠀⠛⠲⢷⠚⠶⢶⠳⡾⠖⠗⠚⠒⠓⠒⣷⣾⣶⣾⠒⠋⠓⠚⠲⣷⣶⣶⠖⠚⢶⣶⣶⣶⣿⣷⣶⣿⣿⣶⣾⠙⠲⠶⠛⠒⠒⠒⠁⠓⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠒⠒⠓⠒⠚⠀⠑⠒⠛⠒⠚⠒⠓⠓⠒⠓⠒⠚⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠦⢄⠀⢹⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠀⡆⢸⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣄⠀⠀⣾⣿⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⡀⣿⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣷⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠀⠙⢿⣿⣿⣿⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣶⣿⣿⠿⠋⠀⠀⢸⣿⣿⣷⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡧⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠻⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣀⣸⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠉⠁⣿⣿⣿⣿⣿⣭⣭⣽⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⡤⣬⣿⣿⣿⣿⣿⣿
⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠈⣽⣿⣿⠛⠉⢉⣿⣿⣿⠃⠀⢸⣿⣿⣏⣉⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠀⢀⢀⡄⣀⣦⣴⣦⣤⣾⣷⣶⣷⣶⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠘⠀⠀⠀⠀⠀⠀⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⢿⣿⣟⠃⢸⣿⣯⣭⣿⣿⡁⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣥⣀⡀⠀⠀⠀⠀⠀⠀⠰⠰⠃⠀⢠⡀⠀⠀⠀⣀⢻⣿⣿⣿⢿⣿⣿⠉⣽⣿⢿⣿⡄⠀⣿⣿⣷⣾⣿⡋⢘⣿⣿⢟⣛⣛⡁⢤⣽⣯⣩⣿⣿⠟⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣞⡃⡄⠀⠀⠀⠀⠶⣦⣄⣈⠀⠀⣤⣶⣿⣿⣿⣿⣁⣀⣶⡶⣶⣿⣿⣾⣿⣿⡄⣿⣿⣈⣻⣿⣿⣼⣿⣿⠿⠿⠟⠓⠂⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠿⢿⣏
⣿⣿⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣾⣯⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⡿⠛⠋⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⣿⡧⠶⠦⣤⠴⠶⡤⠦⣤⠶⢶⠶⡶⠶⡴⢶⠶⢿⡛⢠⡴⠾⠿⡿⠿⠿⡿⠿⢿⡿⠿⠿⣶⠶⡶⢦⣠⠴⠶⢶⠶⠶⣤⠶⠶⢤⡀⡤⠶⠦⡤⠶⠶⢤⠴⢤⠶⢦⠴⠦⡴⠶⢤⣠⠴⠶⢶⠶⢶⠶⢦⠴⠦⡴⠶⢴⣿
⢻⡇⢸⠤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣿⡇⠰⠀⣽⠀⠶⡇⢠⠘⡇⠀⡆⢸⡄⠃⣼⣿⠀⠰⡆⠀⡆⢸⠀⠐⢀⡇⡇⠀⠆⡀⠀⠆⣸⠀⢸⠀⠘⠀⠀⡇⠰⢾⠙⡆⠀⣾⠀⢸⠀⠸⠀⠀⡇⠰⢾⣿
⠸⡇⠸⠀⢸⠀⠶⡇⢸⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⢹⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⣿⣿⠀⢰⡇⠀⠇⢸⠀⠰⠀⣷⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⠀⡇⠀⣿⠀⢹⠀⡄⠀⠀⡇⠰⢾⣿
⠀⠛⠲⢷⠚⠶⢶⠷⣾⠖⠗⠚⠒⠓⠒⣷⣾⣶⣾⠒⠋⠓⠚⠲⣷⣶⣶⠖⠚⢶⣶⣶⣶⣿⣷⣶⣿⣿⣶⠚⠙⠶⠶⠛⠒⠒⠒⠁⠑⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠒⠒⠓⠒⠚⠀⠑⠒⠛⠒⠚⠲⠓⠓⠒⠓⠒⢾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠬⠶⠦⢄⠀⢹⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠀⡆⢸⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣄⠀⠀⣾⣿⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⣿⣿⣿⣿⡟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣧⡀⣿⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣷⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡳⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠙⢿⣿⣿⣿⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣶⣿⣿⠿⠋⠀⠀⢸⣿⣿⣷⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣄⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠻⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⡇⠀⠀⠀⠀⣀⣸⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿
⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠉⠁⣿⣿⣿⣿⣿⣭⣭⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⢸⣿⣿⣿⣿⣿⣿
⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⠛⠋⢉⣿⣿⣿⠃⠀⢸⣿⣿⣏⣉⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠀⢀⠀⠀⣀⢠⣀⣴⣶⣶⣾⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢸⠀⠀⠀⠀⠀⠀⣠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⢿⣿⣟⠃⢸⣿⣯⣭⣿⣿⡁⠀⠀⠀⠈⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⡄⠀⠀⠀⠀⣛⣿⣿⣿⢿⣿⣿⠉⣹⣿⢿⣿⡄⠀⣿⣿⣷⣾⣿⡋⢸⣿⣿⢟⣛⣛⡀⢤⣽⣯⣩⣿⣿⠇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣀⡀⠠⠀⠀⠀⠶⣦⣄⣀⠀⠀⠤⣢⣾⣿⣿⣿⡁⣀⣶⣦⣴⣿⣿⣾⣿⣿⡄⣿⣿⣈⣻⣿⣿⣼⣿⠿⠿⠿⠛⠓⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠻⠿⣿⣿⣝
⣿⣿⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⣦⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡿⠛⠋⣙⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿
⣿⡧⠶⠦⣤⠶⠶⡴⠶⣤⠶⢶⠶⣶⠶⡴⢶⠶⢿⡛⢠⡶⠾⠿⣿⠿⠿⡿⠿⢿⡿⠿⠿⣶⠶⡶⢤⣠⠴⠶⢶⠶⠶⣤⠶⠶⢤⡀⡤⠶⠦⡤⠶⠦⢤⠴⢦⠶⢤⠴⠦⡴⠶⢤⣤⠶⠶⢶⠶⢤⠶⢦⠴⠦⡤⠶⢿⣿
⢻⡇⢸⠤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣿⡇⠰⠀⣽⠀⠶⡇⢠⠈⡇⠀⡆⢸⡄⠃⣼⣿⠀⠰⡆⠀⡆⢸⠀⠐⢀⡇⡇⠀⠆⡀⠀⠆⣸⠀⢸⠀⠘⠀⠀⡇⠰⢾⠙⡆⠀⣾⠀⢺⠀⠘⠀⠀⡇⠰⢾⣿
⠸⡇⠸⠀⢸⠀⠶⡇⢸⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⢱⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⣿⣿⠀⢰⡇⠀⠇⢸⠀⠰⠀⣇⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⡀⡇⠀⣿⠀⢺⠀⡄⠀⠀⡇⠰⢾⣿
⠀⠛⠲⢷⠚⠶⢶⡷⣾⠖⠗⠚⠒⠓⠒⣷⣾⣶⣾⠒⠋⠓⠚⢲⣷⣶⣶⠖⠚⢲⣶⣶⣶⣿⣷⣶⣿⣿⡖⠚⠙⠶⠖⠛⠒⠒⠒⠁⠑⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠒⠒⠓⠒⠚⠀⠓⠒⠛⠒⠚⠒⠓⠓⠒⠳⣶⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠦⢄⠁⢹⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠀⡆⢸⣿⣿⣿⣿⣤⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠃⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣄⠀⠀⣾⣿⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⣿⣿⣿⣿⡟⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⡀⣿⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣷⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣷⣄⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡾⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠙⢿⣿⣿⣿⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣶⣿⣿⠿⠋⠀⠀⢸⣿⣿⣷⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡄⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠀⠀⠀⠻⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿
⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⡇⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡃⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⠈⠉⠁⣿⣿⣿⣿⣿⣭⣭⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣿⣿⣿⣿⣿
⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠇⠀⠀⠀⠀⠀⠈⣹⣿⣿⠟⠋⢉⣿⣿⣿⠃⠀⢸⣿⣿⣏⣉⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⣀⣀⣄⢴⣿⣦⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠀⠀⠀⠀⠀⠀⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣟⠃⢹⣿⣯⣭⣿⣯⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⢲⡟⠀⠀⡄⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⠉⣹⣿⢿⣿⡄⠀⣿⣿⣷⣾⣿⡋⢸⣿⣿⢟⣛⣛⡀⢤⣿⣯⣭⣿⣿⠇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠶⣦⣄⣀⡁⠀⠀⢠⣾⣿⣿⣿⡁⢀⣶⣦⣴⣿⣿⣾⣿⣿⡄⣿⣿⣈⣻⣿⣿⣼⣿⠿⠿⠟⠛⠓⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠿⢿⣿⣿⣯⣛
⣿⣿⡏⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣤⣰⣽⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣿⣿⣿⣿⠿⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡟⣻
⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢺⡿⠛⠋⣙⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿
⣿⡿⠶⠦⣤⠴⠦⡤⠶⣤⠶⢶⠶⡶⠶⡴⢶⠶⢾⡛⢠⡶⠾⠿⣿⠿⠿⡿⠿⢿⡿⠿⠿⣶⠶⡤⢤⣠⠶⠶⢶⠶⠶⣤⠶⠶⢤⡀⡤⠶⠦⡤⠶⠦⢤⠴⢤⠶⢤⠴⠦⡴⠶⢦⣤⠶⠶⢶⠶⢤⠶⢤⠴⠤⡴⠿⢿⣿
⢿⡇⢸⠤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣿⡇⠰⠀⡽⠀⠶⡇⢠⠈⡇⠀⡆⢸⡄⠃⣼⣿⠀⠰⡆⠀⡆⢸⠀⠐⢀⡇⡇⠀⠂⡀⠀⠆⣸⠀⢸⠀⠘⠀⠀⡇⠰⢾⠙⡆⠀⣾⠀⢸⠀⠘⠀⠀⡇⠰⢾⣿
⠸⡇⠸⠀⢸⠀⠶⡇⢰⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⠹⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⣿⣿⠀⢰⡇⠀⠇⢸⠀⠰⠀⡗⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⡀⡇⠀⣿⠀⢿⠀⡄⠀⠀⡇⠰⢾⣿
⠀⠛⠲⢷⠚⠲⢶⡷⣾⠖⠗⠚⠒⠓⠒⣷⣾⣶⣾⠒⠋⠓⠚⠲⣷⣶⣶⠖⠚⢶⣶⣶⣶⣿⣷⣶⣿⡟⠒⠚⠛⠲⠒⠛⠒⠒⠒⠁⠑⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠒⠒⠓⠒⠚⠁⠑⠒⠛⠒⠚⠒⠓⠓⠒⣷⣶⡾⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠦⢄⠀⢹⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠀⠆⢸⣿⣿⣿⣿⣀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣄⠀⠀⣾⣿⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⣿⣿⣿⣿⡟⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣦⡀⣿⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣶⠀⢸⣿⣿⣿⣿⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣾⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣷⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠙⢿⣿⣿⣿⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣶⣿⣿⠿⠋⠀⠀⢸⣿⣿⣷⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡋⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠀⠀⠀⠻⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣯⣷
⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⠈⠉⠉⣿⣿⣿⣿⣿⣭⣭⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿
⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠈⣹⣿⣿⠟⠋⢉⣿⣿⣿⠃⠀⢸⣿⣿⣏⣉⣻⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⡀⠀⢀⠀⣤⣶⣤⣬⣶⣴⣶⣽⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢁⠀⠀⠀⠀⠀⠀⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣟⠃⢿⣿⣯⣽⣿⣯⡀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⢒⡞⠀⠀⡄⠀⠀⠀⢀⠻⣿⣿⣿⣿⣿⣿⠉⣹⣿⢿⣿⡄⠀⣿⣿⣷⣾⣿⡋⢸⣿⣿⢛⣛⣛⡀⢤⣿⣯⣭⣿⣿⠇⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣖⠀⠀⠀⠀⠀⠴⣦⣄⣀⠁⠀⢠⣬⣿⣿⣿⣿⡇⢀⣶⣤⣰⣿⣿⣾⣿⣿⡄⣿⣿⣈⣻⣿⣷⣼⡿⠿⠿⠛⠛⠃⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠛⠛⠿⢿⣿⣿⣿⣭⣻
⣿⣿⡟⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⡬⣪⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣿⣿⣿⣿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣟⣻
⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢳⣯⠛⠋⢙⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿
⣿⡿⠶⠦⣤⠴⠦⡤⠶⡤⠶⢶⠶⣶⠶⡴⢶⠶⢾⡛⢡⡴⠾⠿⡿⠿⠿⡿⠿⢿⡿⠿⠷⣶⠦⡤⢤⣠⠶⠶⢦⠶⠶⣤⠴⠶⢤⡀⡤⠶⠦⡤⠶⠦⢤⠴⢤⠶⢦⠴⠦⡴⠶⢦⣠⠶⠶⢶⠶⢤⠶⢤⠤⠶⡿⠿⢿⣿
⢿⡇⢸⠤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣿⡇⠰⠀⣟⠀⠶⡇⢠⠈⡇⠀⡆⢸⡄⠃⣼⣿⠀⠰⡆⠀⡆⢸⠀⠐⢀⡇⡇⠀⠂⡀⠀⠆⣸⠀⢸⠀⠘⠀⠀⡇⠰⢾⠙⡆⠀⣾⠀⢸⠀⠘⠀⠀⡇⠰⢾⣿
⠸⡇⠸⠀⢸⠀⠶⡇⢰⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⣿⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⣿⣿⠀⢰⡇⠀⠇⢸⠀⠰⠀⣧⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⡀⡇⠀⣿⠀⢸⠀⡄⠀⠀⡇⠰⢾⣿
⠀⠛⠲⢷⠚⠶⢶⡷⣾⠖⠗⠚⠒⠓⠒⣷⣾⣶⣾⠒⠋⠓⠚⢲⣷⣶⣶⠖⠚⢲⣶⣶⣶⣿⣷⣶⣿⠙⠲⠞⠙⠒⠒⠛⠒⠒⠒⠁⠑⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠒⠒⠓⠒⠚⠁⠑⠒⠛⠒⠚⠒⠓⠓⢲⣷⣶⡾⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣨⠤⠶⠦⢄⠀⢹⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠀⡆⢸⣿⣿⣿⣿⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⡄⠀⠀⣿⣿⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⣿⣿⣿⣿⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣦⡀⣿⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⣿⣿⣿⡿⠀⢹⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡂⠀⠀⠀⠀⠀⣼⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⣿⣿⡿⠃⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣦⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⠆⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠙⢿⣿⣿⣿⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣶⣿⣿⠿⠋⠀⠀⢸⣿⣿⣷⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣧⠃⠢
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠻⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣷⡌
⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣷
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠉⠉⣿⣿⣿⣿⣯⣭⣽⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿
⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡗⠀⠀⠀⠀⠀⠈⢹⣿⣿⠟⠛⠛⣿⣿⣿⠇⠀⢸⣿⣿⣏⣉⣻⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⠂⠀⠀⠀⠀⠀⠀⣀⣶⣆⣴⣶⣶⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡆⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⡇⠀⠀⠀⠀⠀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣟⠁⢿⣿⣯⣽⣿⣍⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠐⣾⠁⠀⢀⡀⠀⠀⠀⢛⣿⣿⣿⣿⣿⣿⠋⣹⣿⢿⣿⡄⠀⣿⣿⣷⣾⣿⡋⢸⣿⣿⢟⣛⣛⡀⣤⣿⣯⣭⣿⡿⠃⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⢂⠀⡀⠀⠀⢰⣶⣤⣀⣀⠐⢐⣲⣿⣿⣿⣿⡇⢀⣴⣥⣰⣿⣿⣾⣿⣿⡄⣿⣿⣈⣻⣿⣷⡼⠿⠿⠟⠛⠛⠃⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣝⣧
⣿⣿⣿⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣶⣞⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣿⣿⣿⡿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣛⣿
⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⠟⠛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿
⣿⡿⠷⠦⣤⠴⠦⡤⠶⣤⠶⢶⠶⡶⠶⡴⢶⠶⢾⡛⢣⡶⠾⠿⡿⠿⠿⡿⠿⢿⡿⠿⠷⣤⠤⡤⢶⣤⠶⠶⢦⠶⠶⣤⠴⠶⢤⡀⡤⠶⠦⡤⠶⠦⢤⠴⢦⠶⢤⠴⠶⡴⠶⢶⣤⠶⠶⢶⠶⢤⠤⢤⠾⠿⡿⠿⢿⣿
⢿⡇⢸⠤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⡽⠀⠶⡇⢠⠘⡇⠀⡆⢸⡄⠃⣼⢿⠀⠰⡆⠀⡆⢸⠀⠐⢀⡗⡇⠀⠆⡀⠀⠆⣸⠀⢸⠀⠘⠀⠀⡇⠰⢾⡟⡆⠀⣾⠀⢿⠀⠘⠀⠀⡇⠰⢾⣿
⠸⡇⠸⠀⢸⠀⠶⡇⢰⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⠹⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡏⢸⠀⢰⡇⠀⠇⢸⠀⢰⠀⣷⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⡇⡇⠀⣿⠀⢸⠀⡄⠀⠀⡇⠰⢾⣿
⠀⠛⠲⢷⠚⠶⠖⡷⢾⠖⠗⠚⠒⠓⠒⢷⣾⣶⣾⠒⠋⠓⠚⠲⣷⣶⣶⠖⠚⢲⣶⣶⣶⣿⣷⣶⠃⠘⠶⠚⠙⠒⠒⠛⠒⠒⠒⠁⠑⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠒⠒⠓⠒⠚⢣⠑⠒⠛⠒⠚⠒⣷⣷⣶⣷⣶⢾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠬⠿⠯⢄⠁⢹⣿⣿⣷⡄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠀⡆⢸⣿⣿⣿⣷⠀⠀⣰⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠃⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⡄⠀⠀⣿⣿⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⣿⣿⣿⣿⠀⢰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣦⡀⣿⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⣿⣿⣿⡿⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⣿⣿⡿⠃⠀⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣆⠀⠀⠀
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠙⢿⣿⣿⣿⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣶⣿⣿⠿⠋⠀⠀⢸⣿⣿⣷⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣆⡐⠀
⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠈⠻⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣌⡀
⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠉⠈⣿⣿⣿⣿⣿⣭⣽⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠐⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⡀⠀⠀⠀⠀⠈⢹⣿⣿⡟⠛⠛⣻⣿⣿⠇⠀⢸⣿⣿⣏⣙⣻⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠂⠀⠀⠀⠀⣀⣠⣠⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡎⠀⠀⠀⠀⠀⣀⣸⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣟⠁⢿⣿⣯⣽⣿⣍⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠐⣶⠃⠁⢀⡀⣀⣀⡀⣟⣿⣿⣿⣿⣿⣿⠛⣹⣿⢿⣿⡄⠀⣿⣿⣷⣾⣿⠃⢸⣿⣿⢛⣛⣛⡀⣤⣿⣯⣭⣿⡿⠃⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡗⠀⣀⠀⠀⢠⣶⣤⣀⡈⡁⣸⣿⣿⣿⣿⣿⡇⢀⣽⣧⣰⣿⣿⣾⣿⣿⡄⣿⣿⣈⣻⣿⣷⡼⠿⠿⠟⠛⠛⠃⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣧
⣿⣿⣿⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣥⣷⣽⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣿⣿⣿⣿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣻⣷
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⠟⠟⢛⣛⣛⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⣿
⣿⡿⠷⠦⣤⠶⠦⡤⠶⣤⠶⢶⠶⣶⠶⡶⢶⠶⢶⡛⢣⡶⠶⠿⡿⠿⠿⡿⠿⢿⡿⠿⠦⣤⠤⡴⢶⣴⠶⠶⢤⠴⠶⣤⠴⠶⢤⡀⡤⠶⠦⡤⠶⠦⢤⠴⢤⠶⢶⠶⠦⡴⠶⢦⣠⠶⠶⢶⠶⢤⠤⢾⠿⠿⡿⠿⢿⣿
⢿⡇⢸⠤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠛⣾⡇⠰⠀⡽⠀⠶⡇⢠⠘⡇⠀⡆⢸⡄⠃⣼⣿⠀⠰⡆⠀⡆⢸⠀⠐⢀⡗⡇⠀⠆⡀⠀⠆⣸⠀⢸⠀⠘⠀⠀⡇⠰⢾⠙⡆⠀⣾⠀⣸⠀⠘⠀⠀⡇⠰⢾⣿
⠸⡇⠸⠀⢸⠀⠶⡇⢰⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⢱⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡏⣿⠀⢰⡇⠀⠇⢸⠀⠰⠀⣷⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⡀⡇⠀⣿⠀⢾⠀⡄⠀⠀⡇⠰⢾⣿
⠀⠙⠲⢷⠚⠶⠖⣷⢾⠖⠗⠚⠒⠓⠒⢷⣾⣶⣾⠒⠋⠓⠚⠲⣷⣶⣶⠖⠚⢲⣶⣶⣶⣿⣷⡖⠃⠘⠒⠚⠙⠒⠒⠛⠒⠒⠒⠁⠑⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠒⠒⠓⠒⡞⠀⠑⠒⠛⠒⠚⢲⣷⣷⣶⣷⣶⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠬⠶⠦⢄⠀⢹⣿⣿⣷⡀⠀⠀⠀⠀⣰⡄⠀⠀⠀⠀⠀⢹⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡎⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠀⡆⢸⣿⣿⣿⣷⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⡀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣷⡄⠀⠀⣿⣿⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⣿⣿⣿⣿⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣦⡀⣿⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⣿⣿⣿⡟⠀⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢺⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⣿⣿⡿⠁⠀⠀⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀
⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⣾⣿⣿⣿⠁⠙⢿⣿⣿⣿⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣶⣿⣿⠿⠋⠀⠀⢸⣿⣿⣶⣶⣶⡆⠘⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣧⠀⠀⠀
⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠻⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣾⠀⡀
⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢀⣿⣿⣿⣿⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣵⣥
⢺⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠉⢸⣿⣿⣿⣿⣿⣭⣽⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿
⠝⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡂⠀⠀⠀⠀⠈⢙⣿⣿⡿⠛⠛⣻⣿⣿⠇⠀⢸⣿⣿⣏⣙⣻⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⠀⠀⠀⠀⠀⣀⣄⣠⣄⣶⣶⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢸⠀⠀⠀⠀⠀⣀⣘⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣟⠀⢿⣿⣯⣽⣿⣍⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣦⣿⣿⣿⣿⣄⣄⠀⠀⠀⠀⠀⢀⢠⠇⠀⢀⣁⣀⣀⡀⠛⣿⣿⣿⣿⣿⣿⠛⢹⣿⣿⣿⡄⠀⣿⣿⣽⣿⣿⠃⢸⣿⣿⢛⣛⣛⡀⣤⣿⣭⣽⣿⡿⠁⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣠⣀⠀⠀⠀⣶⣦⣀⣈⡈⣙⣽⣷⣾⣿⣿⡏⠀⣬⣥⢰⣿⣿⣾⣿⣿⡄⣿⣿⣈⣻⣿⣷⠼⠿⠿⠟⠛⠛⠓⠚⠛⠛⠛⠋⠋⠉⠁⠀⠀⠀⠀⠘⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣴
⣿⣿⣿⡟⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠉⠙⢿⣽⣿⣟⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣿⣿⣿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣟⣷⣾
⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⠿⠟⢛⣛⣛⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⣿
⣿⡿⠿⠦⣤⠶⠦⡤⠶⣤⠶⢶⠶⣶⠶⡶⢦⠶⢦⡛⢳⡶⠾⠿⡿⠿⠿⡿⠿⢿⡿⠷⠦⣤⠶⡶⢶⣤⠶⠶⢤⠴⠶⣤⠴⠶⢤⡀⡴⠶⠦⡤⠶⠦⢤⠴⢦⠶⢦⠶⠶⡶⠶⢦⣤⠶⠶⢤⠤⢾⠿⢿⠿⠿⡿⠿⢿⣿
⢿⡇⢸⠤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⣵⠀⠶⡇⢠⠘⡇⠀⡆⢸⡄⠃⣼⢻⠀⠰⡆⠀⡆⢸⠀⠐⢀⡇⡇⠀⠆⡀⠀⠆⣸⠀⢸⠀⠘⠀⠀⡇⠰⢾⠙⡆⠀⣾⠀⢾⠀⠘⠀⠀⡇⠰⢾⣿
⠸⡇⠸⠀⢸⠀⠶⡇⢰⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⢹⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⣿⢸⠀⢰⡇⠀⠇⢸⠀⢰⠀⣧⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⡀⡇⠀⣿⠀⢸⠀⡄⠀⠀⡇⠰⢾⡿
⠀⠙⠲⢷⠚⠲⠖⣷⢾⡖⠗⠚⠒⠓⠒⢷⣾⣶⣾⠒⠋⠓⠚⠲⣷⣶⣶⠖⠚⢲⣶⣶⣶⣿⠓⠲⠃⠘⠒⠊⠉⠒⠒⠛⠒⠚⠒⠁⠑⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠒⠖⠓⠒⠚⠀⠑⠒⠛⠒⠚⣶⣷⣷⣶⣷⡶⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠧⢄⠀⢹⣿⣿⣧⡀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠈⢻⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠔⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢰⣾⣿⣿⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠀⡆⢸⣿⣿⣿⣷⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠸⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡆⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⡄⠀⠀⢸⣿⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⣿⣿⣿⣿⠀⠀⠀⢰⣿⡧⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣦⡀⣿⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⣿⣿⣿⡏⠀⠀⢀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀
⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⣿⣿⡟⠁⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⣼⣿⣿⣿⠇⠙⢿⣿⣿⣿⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣶⣿⣿⠿⠋⠀⠀⢸⣿⣿⣶⣶⣶⡀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡆⠀⠀⠀
⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠈⠻⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠷⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡄⠀⠀
⠙⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣷⣦⢀
⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⠉⢸⣿⣿⣿⣿⣯⣭⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠹⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠈⢛⣿⣿⡿⠛⠛⣻⣿⣿⠇⠀⢸⣿⣿⣏⣙⣻⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⠀⠀⠀⠀⠀⣂⣀⣀⣤⣶⣴⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⠅⠀⠀⠀⠀⢀⣘⣿⣿⣷⣶⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣛⠀⣿⣿⣯⣽⣯⣅⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣠⣤⣾⣿⣿⣷⣄⣀⠀⠀⠀⠀⠀⣤⡾⠈⠀⣀⣠⣤⣄⣘⣿⣿⣿⣿⣿⣿⠛⢻⣿⣿⣿⡄⠀⣿⣿⣽⣿⣿⠃⢸⣿⣿⢛⣛⣛⠀⣴⣿⣭⣽⣿⡿⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠀⠀⠀⣴⣦⣄⡀⢓⣿⣿⣿⣿⣿⣿⡏⠀⣼⣥⢰⣿⣿⣾⣿⣿⡀⣿⣿⣈⣻⣿⣷⠼⠿⠿⠿⠿⠛⠓⠚⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣥⣾
⣿⣿⣿⣿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⠿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣿⣿⣿⣿⣟⣻⣶⣿
⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⠿⠿⢛⣛⣛⣻⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿
⣿⡿⠿⠧⣤⠶⠶⡤⠶⣤⠶⢶⠶⣶⠶⡴⢶⠶⢦⡚⢳⡶⠾⠿⡿⠿⠿⡿⠿⢿⡷⠶⠤⣴⠶⡶⢶⣤⠴⠶⢤⠴⠶⣤⠴⠶⢤⡀⡤⠶⠦⡤⠶⠦⢤⠶⢤⠶⢦⠴⠦⡴⠶⢦⣠⠴⠴⢶⠿⢿⠿⢿⠿⠿⡿⠿⢿⣿
⢿⡇⢸⠤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⣽⠀⠶⡇⢠⠘⡇⠀⡆⢸⡄⠃⣼⢹⠀⠰⡆⠀⡆⢸⠀⠐⢀⡯⡇⠀⠆⡀⠀⠆⣸⠀⢸⠀⠘⠀⠀⡇⠰⢾⠙⡆⠀⣾⠀⣸⠀⠘⠀⠀⡇⠰⢾⣿
⠸⡇⠸⠀⢸⠀⠶⡇⢸⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⢹⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡇⢸⠀⢰⡇⠀⠇⢸⠀⢰⠀⣷⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⠀⡇⠀⣿⠀⢻⠀⡄⠀⠀⡇⠰⢾⡿
⠀⠙⠲⢷⠚⠶⠖⢳⢾⡶⠗⠚⠒⠓⠒⢷⣾⣶⣾⡒⠋⠓⠚⠲⣷⣶⣶⠖⠚⢲⣶⣶⣶⡏⠓⠖⠃⠈⠒⠊⠉⠒⠒⠛⠒⠒⠒⠁⠓⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠖⠒⠓⠒⠚⠀⠑⠒⠙⠒⢺⣶⣷⣷⣶⣷⣶⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣺⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠘⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠦⢄⠀⢹⣿⣿⣦⡀⠀⠀⠀⠀⠀⢠⣾⡇⠀⠀⠻⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀
⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢰⣾⣿⣿⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠀⡆⢸⣿⣿⣿⣧⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⢻⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡍⠀⠀⠀⠀⠀⣶⣿⣿⣿⣷⡄⠀⠀⢸⣿⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀
⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠇⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣦⡀⣾⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⣿⣿⣿⡇⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀
⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠅⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⣿⣿⡟⠀⠀⠀⢠⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀
⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠙⢿⣿⣿⣿⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣶⣿⣿⠿⠋⠀⠀⢸⣿⣿⣶⣶⣶⡀⠀⢿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀
⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⣾⣿⣿⣿⠁⠀⠈⠻⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠧⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣧⠀⠀⠀
⠈⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⣿⣿⣿⣿⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣦⣄⠀
⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⡇⠈⠉⢹⣿⣿⣿⣿⣿⣽⣿⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⢻⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠈⠛⣿⣿⡿⠛⠛⣻⣿⣿⠏⠀⢸⣿⣿⣏⣙⣻⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⠗⠀⠀⠀⠀⠀⢰⣤⣦⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢈⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢠⡇⡇⢀⠀⠀⠀⢀⣘⣿⣿⣷⣶⣾⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⡿⣿⣿⡟⠀⣿⣿⣭⣿⣯⣅⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣠⣴⣿⣿⣿⣷⣄⣀⠀⠀⠀⠀⠀⡼⠀⠁⣀⣠⣶⣦⣘⣿⣿⣿⣿⣿⣿⠛⢻⣿⣿⣿⡄⠀⣿⣿⣽⣿⣿⠃⢸⣿⣿⢛⣛⣃⠠⣼⣿⣭⣽⣿⡟⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⢰⣤⣄⣀⢙⣿⣿⣿⣿⣿⣿⣟⠀⣩⣥⢤⣿⣿⣾⣿⣿⡀⣿⣿⣈⣻⣿⣷⡼⠿⠿⠿⠿⠿⠶⠾⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣴⣿
⣿⣿⣿⣿⠟⠛⠛⠉⠉⠉⠀⠀⠀⠀⠈⠙⠻⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡿⠿⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣷⣾⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢿⡿⠿⢻⣟⣟⣻⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣷
⣿⡿⠿⠿⣤⠶⠶⡤⠶⣤⠴⢶⠶⣶⠶⡶⢶⠶⢦⡘⢓⡶⠶⠿⡿⠿⠿⡿⠿⢷⡤⠴⠶⣴⠶⡶⢦⣠⠴⠶⢤⠴⠶⣤⠴⠶⢤⡀⡤⠶⠦⡤⠶⠦⢤⠴⢦⠶⢦⠴⠦⡴⠶⢤⣠⠴⠾⢿⠿⢿⠿⢿⠿⠿⡿⠿⢿⣿
⢿⡇⢸⠤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⡵⠀⠶⡇⢠⠘⡇⠀⡆⢸⡄⠃⣼⢹⠀⠰⡆⠀⡆⢸⠀⠐⢀⡇⡇⠀⠆⡀⠀⠆⣸⠀⢸⠀⠘⠀⠀⡇⠰⢾⠙⡆⠀⣾⠀⣽⠀⠘⠀⠀⡇⠰⢾⣿
⠸⡇⠸⠀⢸⠀⠶⡇⢰⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⢹⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡇⢸⠀⢰⡇⠀⠇⢸⠀⢰⠀⣷⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⡀⡇⠀⣿⠀⢻⠀⡄⠀⠀⡇⠰⢾⡿
⠀⠛⠲⢷⠚⠶⠖⢳⡾⣶⠗⠚⠒⠓⠒⢷⡾⣶⣾⡒⠋⠓⠚⠲⣷⣶⣶⠖⠚⢲⣶⣶⠖⠛⠓⠒⠁⠈⠒⠊⠉⠒⠒⠛⠒⠚⠒⠁⠑⠒⠁⠑⠒⠓⠚⠒⢺⠒⠓⠒⠒⠓⠒⠚⠀⠑⠒⠉⠒⣾⣶⣷⣷⣶⣷⣶⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠦⢄⠀⢹⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠈⢻⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢰⣾⣿⣿⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠀⡆⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠈⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠀⠀⠀⠀⣶⣾⣿⣿⣷⡄⠀⠀⢸⣿⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⣿⣿⣿⡟⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀
⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡑⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣦⡀⣼⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⣿⣿⣿⠇⠀⠀⠀⠀⣠⣿⡿⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀
⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⣿⣿⠟⠀⠀⠀⠀⣰⣿⣿⡧⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀
⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠂⠀⠀⠀⠀⢸⣿⣿⣿⡇⠙⢿⣿⣿⣿⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣶⣿⣿⠿⠋⠀⠀⢸⣿⣿⣶⣶⣶⠀⠀⢹⣿⣿⠇⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀
⠀⣻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⠀⠀⠀⠀⣸⣿⣿⣿⠇⠀⠈⠻⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠇⠀⠀⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣆⠀⠀⠀
⠀⠈⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣄⡀⠀
⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⡇⠈⠉⢹⣿⣿⣿⣿⣯⣽⣿⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠈⠛⣿⣿⡿⠟⠛⢻⣿⣿⡏⠀⢸⣿⣿⣏⣙⣻⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⠗⠀⠀⠀⠀⠀⢈⣠⣢⣷⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣷⠂⠀⠀⠀⠀⠀⠀⠀⡏⡅⢀⠄⠀⠀⠀⣘⣿⣿⣷⣶⣾⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⡿⣿⣿⡛⠸⣿⣿⣯⣿⣯⡅⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣠⣀⣤⣾⣿⣿⣿⣧⣄⣀⡀⠀⠀⠠⢤⠇⠁⢈⣡⣽⣷⣼⣿⣿⣿⣿⣿⣿⠛⢻⣿⣿⣿⡄⠀⣿⣿⣽⣿⣿⠃⢸⣿⡿⢛⣛⣃⠠⣼⣯⣭⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀⠀⢀⣤⣄⣀⠘⣿⣿⣿⣿⣿⣿⣿⠁⣩⣥⢤⣿⣿⣾⣿⣷⡀⣿⣿⢈⣻⣿⣧⣼⣿⠿⠿⠿⠿⠶⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣥⣾⣿
⣿⣿⣿⣿⡟⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣿⠿⠟⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣶⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⡿⠿⠻⣿⣟⣻⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷⣾
⣿⡿⠿⠿⣧⠶⠶⡴⠶⣤⠶⢶⠶⣶⠶⡶⢶⠶⢦⡘⢻⡶⠾⠿⡿⠿⠿⡿⠿⢦⡤⠶⠶⣶⠶⡴⢦⣠⠴⠶⢤⠴⠶⣤⠶⠶⢤⡀⡤⠶⠦⡤⠶⠶⢤⠶⢤⠶⢦⠴⠦⡴⠶⢤⣨⠿⠿⢿⠿⢿⠿⢿⠿⠿⡿⠿⢿⣿
⣿⡇⢸⠤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⡽⠀⠶⡇⢠⠘⡇⠀⡆⢸⡄⠃⣼⢹⠀⠰⡆⠀⡆⢸⠀⠐⢀⡇⡇⠀⠆⡀⠀⠆⣸⠀⢸⠀⠘⠀⠀⡇⠰⢾⠙⡆⠀⣾⠀⣿⠀⠘⠀⠀⡇⠰⢾⣿
⠸⡇⠸⠀⢸⠀⠶⡇⢰⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⢹⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡇⢸⠀⢰⡇⠀⠇⢸⠀⢰⠀⣇⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⡀⡇⠀⣿⠀⢿⠀⡄⠀⠀⡇⠰⢾⣷
⠀⠙⠲⢷⠚⠶⠖⠳⡾⣶⠗⠚⠒⠓⠒⢳⣾⣶⣾⡖⠋⠓⠚⠲⣷⣶⣶⠖⠚⢲⣶⠖⠶⡟⠓⠒⠁⠈⠒⠊⠉⠒⠒⠛⠒⠚⠒⠁⠑⠒⠁⠑⠒⠓⡞⠒⠚⠒⠓⠒⠒⠓⠒⠚⠀⠑⠒⠙⢲⣾⣶⣷⣷⣶⡷⣶⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠥⠶⠦⢄⠉⢹⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⣿⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠀⡆⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⢻⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⣶⣾⣿⣿⣷⡀⠀⠀⢸⣿⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣾⣿⠃⠀⠀⢿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣦⡀⣼⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⣿⣿⣿⠇⠀⠀⠀⠀⠀⣼⣿⡏⠀⠀⠀⠘⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡄⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⣿⣿⠏⠀⠀⠀⠀⠀⣸⣿⣿⡧⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀
⠀⠀⡀⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⢸⣿⣿⣿⡇⠙⢿⣿⣿⣿⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣶⣿⣿⠿⠋⠀⠀⢸⣿⣿⣶⣶⣆⠀⠀⠐⣿⣿⡿⠁⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀
⠀⠈⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⡆⠀⠀⠀⢸⣿⣿⣿⡇⠀⠈⠻⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠆⠀⠀⠹⣿⠇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀
⠀⠀⠉⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡯⠀⠀⠀⠀⣾⣿⣿⣿⣅⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣧⣀⡀⢀
⠀⠀⠀⢼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⡇⠉⠉⢹⣿⣿⣿⣿⣯⣽⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⡸⣿⣿⣿⣿⣿⣿⣿⣿⣾
⠀⠀⠀⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⡧⠀⠀⠀⠈⠛⣿⣿⡿⠟⠛⢻⣿⣿⡏⠁⢸⣿⣿⣏⣛⣻⣿⣿⣿⣧⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⣷⣲⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣽⢙⠀⠄⢀⠀⠀⣀⣿⣿⣷⣶⣾⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⡿⣿⣿⡋⠸⣿⣿⣭⣿⣯⡁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣄⣀⣀⣼⣿⣿⣿⣿⣷⣄⣀⠀⠀⠀⢠⠇⠂⢀⣁⣾⣶⣾⣿⣿⣿⣿⣿⣿⡛⢻⣿⣿⣿⡀⠈⣿⣿⣽⣿⣿⠃⢹⣿⡿⢟⣛⣃⢠⣼⣯⣭⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣬⣤⣀⠘⣸⣿⣿⣿⣿⣿⣿⠁⢩⣭⣤⣾⣿⣾⣿⣷⡀⣿⣿⠉⣿⣿⣧⣼⣿⣿⣿⣿⣿⣶⣿⣿⡿⠿⠿⠿⠷⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣴⣿⣿
⣿⣿⣿⣿⣿⠟⠛⠛⠋⠉⠉⠁⠀⠀⠀⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⡾⠿⠟⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣷⣾⣿⣿
⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣿⠿⠟⢿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣾⣿
⣿⡿⠿⠿⣧⠶⠶⡴⠶⣤⠶⢤⠶⣶⠶⡶⢶⠶⢦⡀⢻⡶⠶⠿⡿⠿⠿⡿⠶⢤⡤⠶⠶⣶⠦⡤⢦⣠⠴⠶⢤⠴⠶⣤⠴⠶⢤⡀⡤⠶⠦⡤⠶⠦⢤⠴⢤⠶⢦⠴⠦⡤⠶⢾⣿⠿⠿⢿⠿⢿⠿⢿⠿⠿⡿⠿⢿⣿
⣿⡇⢸⠤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⡵⠀⠶⡇⢠⠘⡇⠀⡆⢸⡄⠃⣼⢹⠀⠰⡆⠀⡆⢸⠀⠐⢀⡇⡇⠀⠂⡀⠀⠆⣸⠀⢸⠀⠸⠀⠀⡇⠰⢾⠙⡆⠀⣾⠀⣾⠀⠸⠀⠀⡇⠰⢾⣿
⠸⡇⠸⠀⢸⠀⠶⡇⢰⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⢹⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡇⢸⠀⢰⡇⠀⠇⢸⠀⢰⠀⣗⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⠀⡇⠀⣿⠀⢸⠀⡄⠀⠀⡇⠰⢾⣆
⠀⠙⠲⢷⠚⠶⠖⠳⡾⢶⠗⠚⠒⠓⠒⢳⣾⣶⣾⡖⠋⠓⠚⠲⣷⣶⣶⠖⠚⢲⠖⠲⠖⠋⠓⠒⠁⠈⠒⠊⠉⠒⠒⠛⠒⠚⠒⠁⠑⠒⠁⠑⠒⠗⠚⠒⠚⠒⠓⠒⠒⠓⠒⠚⠀⠑⠒⠛⣶⣾⣶⣷⣷⣶⣷⣶⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠬⠶⠦⢄⠁⢹⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⣿⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠀⡆⢸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣿⣷⡀⠀⠀⢸⣿⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⠈⢿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣦⡀⣸⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣶⠀⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⣠⣿⣿⠁⠀⠀⠸⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⣿⣿⠏⠀⠀⠀⠀⠀⢰⣿⣿⣿⠂⠀⠀⠀⢻⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀
⠀⠀⣀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⢸⣿⣿⣿⡇⠙⢿⣿⣿⣿⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣶⣿⣿⠿⠋⠀⠀⢸⣿⣷⣶⣶⣆⠀⠀⠀⣼⣿⣿⠋⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⠀⠀⠀⢸⣿⣿⣿⡇⠀⠈⠻⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠆⠀⠀⠸⣿⠏⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀
⠀⠀⠈⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⣼⣿⣿⣿⣇⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣷⣤⡀⠀⠀
⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⡇⠉⠉⢻⣿⣿⣿⣿⣿⣭⣿⣶⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⢀⣨⣿⣿⣿⣿⣿⣿⣷⣤⣶
⠀⠀⠀⠀⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠛⣿⣿⣿⠿⠛⢻⣿⣿⡏⠉⢸⣿⣿⣏⣛⣿⣿⣿⣿⣧⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⢠⣶⣮⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢹⣿⣿⣯⡄⠀⠀⠀⠀⠀⠀⢸⢹⠀⠀⠠⠀⠀⣀⣿⣿⣷⣶⣶⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⡿⢿⣿⡃⠸⣿⣿⣭⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⠀⢠⣿⣿⣿⣿⣶⣦⡀⠀⠀⠀⢤⡞⠈⠀⡡⣴⣦⣾⣿⣿⣿⣿⣿⣿⡛⢛⣿⣿⣿⡈⠀⣿⣿⣭⣿⣿⠃⣿⣿⡿⢛⣛⣃⢠⣼⣯⣭⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣬⣥⣀⠀⣩⣿⣿⣿⣷⣿⣿⠁⢩⣭⣤⣾⣿⣾⣿⣷⡀⣿⣿⠉⣿⣿⣧⣻⣿⣿⣿⣿⣿⣶⣿⣿⣿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣥⣾⣿⣿
⣿⣿⣿⣿⣿⠟⠛⠛⠛⠉⠉⠁⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⡶⠿⠛⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣶⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⣿⠿⠿⣟⣟⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣾⣿
⣿⡿⠿⠿⣿⠶⠶⡤⠶⣤⠶⢤⠶⣶⠶⡶⢶⠴⢦⡀⢻⡶⠶⠿⡿⠿⠿⡿⠶⢤⡴⠶⠶⣤⠦⡤⢤⣠⠴⠶⢤⠴⠶⣤⠴⠶⢤⡀⡤⠶⠦⡴⠶⠦⢤⠴⢤⠶⢦⠴⠦⡤⠾⢿⣿⠿⠿⢿⠿⢿⠿⢿⠿⠿⡿⠿⢿⣿
⣿⡇⢸⠤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⣿⠀⠶⡇⢠⠈⡇⠀⡆⢸⡄⠃⣼⢹⠀⠰⡆⠀⡆⢸⠀⠐⢀⡇⡇⠀⠆⡀⠀⠆⣸⠀⢸⠀⠘⠀⠀⡇⠰⢾⠙⡆⠀⣾⠀⢺⠀⠘⠀⠀⡇⠰⢾⣿
⠸⡇⠸⠀⢸⠀⠶⡇⢰⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⣟⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡇⢸⠀⢰⡇⠀⠇⢸⠀⢰⠀⣷⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⠀⡇⠀⣿⠀⢻⠀⡄⠀⠀⡇⠰⢾⣎
⠀⠛⠲⢷⠚⠶⠖⠳⣾⢶⠗⠚⠒⠓⠒⢳⣾⣶⣾⡖⠋⠓⠚⠲⣷⣶⣶⠖⠚⢲⠒⠶⠖⠋⠑⠒⠁⠈⠒⠊⠉⠒⠒⠛⠒⠚⠒⠁⠑⠒⠁⠑⡖⠓⠚⠒⠚⠒⠓⠒⠒⠓⠒⠚⠀⠑⠒⠻⣶⣾⣶⣷⣷⣶⣷⣶⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠬⠶⠦⢄⠈⢹⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣾⣿⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠀⠆⢸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣿⣷⡀⠀⠀⢸⣿⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠻⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣦⠀⢸⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣰⣿⣿⡃⠀⢻⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠃⠀⠘⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⢰⣿⣿⣿⡇⠙⢿⣿⣿⣿⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣶⣿⣿⠿⠋⠀⠀⢸⣿⣷⣶⣶⡆⠀⠀⠀⠀⣾⣿⣿⠃⠀⠀⠀⢹⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀
⠀⠀⢘⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠳⠆⠀⠀⢸⣿⣿⣿⡇⠀⠈⠻⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⠆⠀⠀⠈⣿⣿⠏⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀
⠀⠀⠀⠉⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣇⣠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣧⣄⠀⢀⢀
⠀⠀⠀⠀⣸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠉⠉⣿⣿⣿⣿⣿⣿⣭⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⡀⣄⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿
⠀⠀⠀⠀⠸⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠈⠛⣿⣿⣿⠿⠿⢿⣿⣿⡏⠉⢸⣿⣿⡏⣛⣿⣿⣿⣿⣧⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⠂⠀⠀⠀⠀⠀⠀⢰⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣹⣿⣿⣧⠀⠀⠀⠀⠀⠀⢸⢋⠂⠀⠀⡀⠀⠀⣿⣿⣿⣶⣶⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⡟⣿⣿⡿⢿⣿⡇⢸⣿⣿⣭⣿⣭⡀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣠⣠⣄⣠⣾⣿⣿⣿⣿⣷⣤⣤⠀⠀⠄⡼⠘⠀⣠⣿⣶⣷⣿⣿⣿⣿⣿⣿⡛⢛⣿⣿⣿⡉⠈⣿⣿⣭⣿⡿⠃⣿⣿⡿⢟⣛⡃⢠⣽⣯⣭⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢠⣥⣀⠀⢻⣿⣿⣿⣿⣿⣿⠁⢩⣭⣄⣾⣿⣾⣿⣷⡀⣿⣿⠉⢿⣿⣦⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⢀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣴⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛⠉⠉⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⡿⠿⠟⠛⠛⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⢿⠿⠿⢿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣾⣿⣿
⣿⡿⠿⠿⣿⠶⠦⡤⠶⣤⠶⢤⠶⣶⠶⡶⢶⠶⢦⡀⢸⡶⠶⠿⡿⠿⠿⡤⠴⢤⡴⠶⠦⣤⠤⡤⢤⣠⠴⠶⢤⠶⠶⣤⠴⠶⢤⡀⡤⠶⠦⡤⠶⠦⢤⠴⢤⠶⢦⠤⠤⡼⠿⢿⣿⠿⠿⢿⠿⢿⠿⢿⠿⠿⡿⠿⢿⣿
⣿⡇⢸⠤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⡿⠀⠶⡇⢠⠈⡇⠀⡆⢸⡄⠃⣼⢹⠀⠰⡆⠀⡆⢸⠀⠐⢀⡇⡇⠀⠆⡀⠀⠆⣸⠀⢸⠀⠘⠀⠀⡇⠰⢾⠿⡆⠀⣾⠀⣾⠀⠘⠀⠀⡇⠰⢾⣿
⠸⡇⠸⠀⢸⠀⠶⡇⢸⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⣗⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡇⢸⠀⢰⡇⠀⠇⢸⠀⢰⠀⣗⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⠀⡇⠀⣿⠀⢹⠀⡄⠀⠀⡇⠰⢾⣽
⠀⠛⠲⢷⠚⠲⠖⠳⢾⢶⡗⠚⠒⠓⠒⠳⣾⣶⣺⡖⠋⠓⠚⠒⣷⣶⣶⠖⠚⠒⠲⠶⠒⠋⠑⠒⠁⠈⠒⠊⠙⠒⠒⠛⠒⠚⠒⠁⠑⠒⡇⠑⠒⠓⠚⠒⠚⠒⠓⠒⠒⠓⠒⠚⠀⠑⠒⠻⣶⣾⣶⣷⣷⣶⣷⣶⣾⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠾⠯⢄⠁⢹⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣾⣿⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠀⠆⢸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢰⣶⣾⣿⣷⡀⠀⠀⢸⣿⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣦⠀⢸⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠛⢻⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡆⠀⠀⠀⠀⣿⣿⣿⡇⠙⣿⣿⣿⣿⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣶⣿⣿⠿⠋⠀⠀⢸⣿⣷⣶⣶⡄⠀⠀⠀⠀⢰⣿⣿⡿⠁⠀⠀⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣽⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠒⠀⠀⢸⣿⣿⣿⡇⠀⠈⢻⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⠄⠀⠀⠀⢻⣿⣿⠁⠀⠀⠀⢘⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢹⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⢸⣿⣿⣿⣇⣀⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣷⣄⣄⠤⢄⡤
⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠉⠉⣿⣿⣿⣿⣿⣯⣽⣿⣶⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⣤⢀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢻⣿⣿⣦⠀⠀⠀⠀⠀⠀⢸⣿⣿⢄⠀⠀⠀⠛⢿⣿⣿⠿⠿⢿⣿⣿⡏⠉⢹⣿⣿⡏⢛⣿⣿⣿⣿⣧⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⠂⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢨⣿⣿⣿⣦⠀⠀⠀⠀⠀⠈⡏⡇⠀⠀⡀⠄⠀⣿⣿⣿⣦⣶⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⡟⣿⣿⡿⢿⣿⠃⢸⣿⣯⣽⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣠⣄⣦⣿⣿⣿⣿⣿⣿⣼⣦⣄⠀⠠⣼⠃⠀⢠⣵⣿⣷⣿⣿⣿⣿⣿⣿⡟⢛⣿⣿⣿⡉⠉⣿⣿⣭⣿⡿⠃⣿⣿⡿⢟⣛⡂⢤⣽⣯⣭⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⢠⣭⣀⠀⢘⣿⣿⣿⣿⣿⣿⠉⢉⣭⣅⣾⣿⣿⣿⣷⡀⣿⣿⠙⢿⣿⣆⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣤⣾⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠿⠛⠛⠛⠋⠉⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠿⠟⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢿⠿⠿⠿⣿⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷⣿⣿⣿
⣿⡿⠿⠿⣿⠷⠶⡴⠶⣤⠶⢤⠶⣶⠶⡴⢶⠶⢦⡀⢸⡶⠶⠿⡿⠿⠷⡤⠴⢶⡴⠶⠦⣤⠦⡤⢤⣠⠴⠶⢤⠴⠶⣤⠴⠶⢤⡀⡤⠶⠦⡤⠶⠦⢤⠴⢤⠴⢤⠴⠦⡼⠿⢿⣿⠿⠿⢿⠿⢿⠿⢿⠿⠿⡿⠿⢿⣿
⣿⡇⢸⠤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⡽⠀⠶⡇⢠⠈⡇⠀⡆⢸⡄⠃⣼⢹⠀⠰⡆⠀⡆⢸⠀⠐⢀⡗⡇⠀⠆⡀⠀⠆⣸⠀⢸⠀⠘⠀⠀⡇⠰⢾⡿⡆⠀⣾⠀⢸⠀⠘⠀⠀⡇⠰⢾⣿
⠸⡇⠸⠀⢸⠀⠶⡇⢸⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⢹⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡇⢸⠀⢰⡇⠀⠇⢸⠀⠰⠀⣷⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⠰⡇⠀⣿⠀⢸⠀⡄⠀⠀⡇⠰⢾⣿
⠀⠛⠲⢷⠚⠲⠖⠳⢾⠶⡗⠚⠒⠓⠒⠳⣾⣶⣚⡖⠋⠓⠚⠒⣷⣶⣶⠖⠚⠲⠶⠒⠒⠋⠑⠒⠁⠈⠒⠊⠉⠒⠒⠛⠒⠚⠒⠁⠓⠖⠁⠓⠒⠓⠚⠒⠚⠒⠓⠒⠒⠓⠒⠚⠀⠑⠒⢿⣶⣾⣶⣷⣷⣶⣷⣶⠞⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠦⢄⠀⢹⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣾⣿⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠀⡆⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡕⠀⠀⠀⠀⢠⣶⣶⣿⣧⡀⠀⠀⢸⣿⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠆⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣦⠀⢸⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣤⣔⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⣿⣿⣿⡇⠙⣿⣿⣿⣿⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣶⣿⣿⠿⠋⠀⠀⢸⣿⣷⣶⣶⡀⠀⠀⠀⠀⠀⣼⣿⣿⡟⠀⢹⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠃⠀⢰⣿⣿⣿⡇⠀⠈⢻⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣟⠷⠀⠀⠀⠀⠐⣿⣿⡿⠁⠀⠈⢻⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣇⣀⣀⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠹⣿⠇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⡄⢀⠠⢤⣰
⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⣿⠃⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠉⠉⣿⣿⣿⣿⣿⣯⣭⣿⡆⠀⠀⠀⠀⠀⠀⠀⠘⡄⢀⣀⣄⣬⣿⣿⣿⣿⣿⣿⣿⣾⣶⣯⣶
⠀⠀⠀⠀⠀⠀⢿⣿⣷⣦⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠈⠻⢿⣿⣿⠿⠿⢿⣿⣿⡏⠉⢹⣿⣿⡟⢻⣿⣿⣿⣿⣧⣤⣶⣿⣿⣿⣿⣿⣿⣿⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣥⠀⠀⠀⠀⠈⡏⡿⠀⠀⢀⠀⢠⢿⣿⣿⣤⣶⣾⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⠿⣿⠃⢿⣿⣯⣽⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣤⣤⣤⣺⣾⣿⣿⣿⣿⣿⣶⣦⠀⠠⢠⠇⠇⢀⣤⣮⣧⣿⣿⣿⣿⣿⣿⡟⢛⣿⣿⣿⡉⠉⣿⣿⣭⣿⡿⠁⣿⣿⠿⠿⣛⡀⣤⣿⣭⣽⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⣬⣄⠀⠘⣿⣿⣿⣿⣿⣿⠋⢉⣍⡁⣾⣿⣽⣿⣷⡀⣿⣿⠙⢿⣿⣆⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⠿⠿⠿⠄⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣝⣧⣴⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠛⠉⠁⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣽⣿⣿⡿⠿⠿⠟⠛⠛⠛⠛⠋⠋⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢿⡿⠿⠿⠿⣿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣾⣿⣿⣿
⣿⡿⠿⠿⣿⠿⠶⡤⠶⡤⠶⢤⠶⣶⠶⡴⢶⠶⢤⡀⢰⡶⠶⠾⡿⠷⠦⡤⠶⢶⡴⠶⠦⣤⠤⡤⢦⣠⠶⠶⢤⠴⠶⣤⠴⠶⢤⡀⡤⠶⠦⡤⠶⠦⢤⠴⢤⠤⢤⠴⠦⡴⠿⢿⣿⠿⠿⢿⠿⢿⠿⢿⠿⠿⡿⠿⢿⣿
⣿⡇⢸⠤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⣷⠀⠶⡇⢠⠘⡇⠀⡆⢸⡄⠃⣼⢹⠀⠰⡆⠀⡆⢸⠀⠐⢀⣿⡇⠀⠆⡀⠀⠆⣸⠀⢸⠀⠘⠀⠀⡇⠰⢾⡿⡆⠀⣾⠀⢾⠀⠘⠀⠀⡇⠰⢾⣿
⠹⡇⠸⠀⢸⠀⠶⡇⢰⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⣿⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡇⢸⠀⢰⡇⠀⠇⢸⠀⢰⠀⣿⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⠶⡇⠀⣿⠀⢸⠀⡄⠀⠀⡇⠰⢾⣿
⠀⠛⠲⢷⠚⠲⠖⠳⠾⡶⡷⠚⠒⠓⠒⠳⣾⢶⣚⡒⠋⠓⠚⠒⣷⣶⣶⠖⠚⠶⠒⠒⠒⠋⠑⠒⠁⠈⠒⠊⠉⠒⠒⠛⠒⠚⠒⠋⠓⠒⠃⠑⠒⠓⠚⠒⠚⠒⠓⠒⠒⠓⠒⠚⠀⠑⠒⢿⣶⣾⣶⣷⣷⣶⣷⡶⠚⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣇⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣦⣠⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠦⢄⠀⢹⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣿⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠀⠆⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣿⣧⡀⠀⠀⢸⣿⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣆⠀⢸⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣤⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⢀⡀⠀⣿⣿⣿⡏⠙⣿⣿⣿⣿⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣶⣿⣿⠿⠋⠀⠀⢸⣿⣷⣶⣶⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠛⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠈⠀⢀⣿⣿⣿⡇⠀⠈⢻⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠷⠀⠀⠀⠀⠀⢸⣿⣿⠏⠀⠸⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⢸⣿⣿⣿⣇⣀⣀⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠘⢿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣄⠀⠀⢀⡀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠉⠉⣿⣿⣿⣿⣿⣯⣭⣷⡆⠀⠀⠀⠀⠀⠀⠀⠈⢻⣤⣤⡀⣽⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿
⠀⠀⠀⠀⠀⠀⠨⣿⣿⣷⡄⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠈⠻⢿⣿⣿⡿⠿⢿⣿⣿⡏⠉⢹⣿⣿⡟⠻⣿⣿⣿⣿⣧⣤⣴⣿⣿⣿⣿⣿⣿⣿⡿⠷⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⠀⠀⠀⠀⠀⣹⠙⠀⠀⠀⠄⠐⢿⣿⣿⣤⣴⣾⣿⣿⣵⣶⣾⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⠿⣿⠃⣿⣿⣭⣽⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣤⣤⣤⣶⣵⣾⣿⣿⣿⣿⣿⣶⡆⠀⢄⡏⠀⢀⣰⣴⣧⣿⣿⣿⣿⣿⣿⡟⠛⣿⣿⣿⡉⠙⣿⣿⣭⣿⡿⠁⣿⣿⠿⠿⣛⡀⣬⣿⣍⣽⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⣬⣅⡀⠘⣿⣿⣿⣿⣿⣿⠏⢉⣉⡁⣼⣿⣽⣿⣷⡀⣿⣿⠙⣿⣿⣄⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣯⣻⣤⣾⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠁⠀⠀⠉⠛⠻⠿⣾⣿⣿⣿⣿⣿⣷⣾⣿⣽⣿⣿⡿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣿⡿⠿⠿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿
⣿⡿⠿⠿⣿⠿⠶⡤⠶⣤⠶⢤⠴⣶⠶⡴⢶⠶⢤⡀⢠⡶⠶⠾⡿⠶⠤⡤⠶⢶⡴⠶⠦⣤⠤⡤⢦⣠⠴⠶⢤⠴⠶⣤⠴⠶⢤⡀⡴⠶⠦⡤⠶⠦⢤⠤⢤⠴⢦⠴⠦⡴⠿⢿⣿⠿⠿⢿⠿⢿⠿⢿⠿⠿⡿⠿⢿⣿
⣿⡇⢸⠤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⣿⠀⠶⡇⢠⠘⡇⠀⡆⢸⡄⠃⣼⢹⠀⠰⡆⠀⡆⢸⠀⠐⢀⡷⡇⠀⠂⡀⠀⠆⣸⠀⢸⠀⠘⠀⠀⡇⠰⢾⡿⡆⠀⣾⠀⢺⠀⠘⠀⠀⡇⠰⢾⣿
⠹⡇⠸⠀⢸⠀⠶⡇⢰⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⡷⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡇⢸⠀⢰⡇⠀⠇⢸⠀⢰⠀⣷⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⠲⡇⠀⣿⠀⢹⠀⡄⠀⠀⡇⠰⢾⣿
⠀⠛⠲⢷⠚⠒⠖⠳⠾⡶⣷⠚⠒⠓⠒⠳⣾⣶⣚⣒⠋⠓⠚⠒⣷⣶⣶⠖⠺⠖⠒⠒⠒⠋⠑⠒⠁⠈⠒⠊⠉⠒⠒⠛⠒⠚⠒⠁⠳⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠒⠒⠓⠒⠚⠀⠑⠲⣿⣶⣾⣶⣷⣷⣶⣷⡖⢺⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⡀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⣤⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠦⢌⠀⢹⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣿⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠀⡆⢸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠀⠀⠀⠀⢠⣴⣶⣿⣦⡀⠀⠀⢸⣿⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣆⠀⢸⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⣀⠀⣿⣿⣿⡟⠙⣿⣿⣿⣿⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣶⣿⣿⠿⠋⠀⠀⢸⣿⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⣿⣿⣿⡇⠀⠈⢻⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⡻⠧⠀⠀⠀⠀⠀⠀⣿⣿⣿⠋⢿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⢰⣿⣿⣿⡇⣀⣀⣠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠈⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠀⢸⣿⣿⣿⣿⣿⣧⣀⠀⠀⣀⡀⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠉⠉⣿⣿⣿⣿⣿⣯⣭⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⢹⡗⣂⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⢘⣿⣿⣷⡄⠀⠀⠀⢸⣿⣿⡇⠀⠀⠈⠻⢿⣿⣿⡿⠿⢿⣿⣿⡟⠉⢹⣿⣿⡟⠻⣿⣿⣿⣿⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣇⠀⠀⠀⠀⢹⢹⠁⠀⠀⣤⠰⢾⣿⣿⣤⣴⣾⣿⣿⣥⣶⣾⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⠿⢿⠉⣿⣿⣭⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣄⣤⣤⣤⣼⣯⣿⣿⣿⣿⣿⣿⣷⠐⡤⡼⠸⠠⣤⣴⣷⣾⣿⣿⣿⣿⣿⡟⠛⣿⣿⣿⡉⠙⣿⣿⣭⣿⡿⠀⣿⣿⠿⠿⢟⠀⣬⣽⣉⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣠⣅⡀⠀⢻⣿⣿⣿⣿⣿⡏⠉⣋⡁⣼⣿⣽⣿⣷⡀⣿⣿⠙⣿⣿⣄⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⡿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣟⣧⣴⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠋⠀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠾⣿⣿⠿⠿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿
⣿⡿⠿⠿⣿⠿⠷⡴⠶⣤⠶⢤⠴⣶⠶⡶⢶⠶⢤⡀⢀⡷⠶⠾⡿⠶⠤⡴⠶⢦⡤⠶⠤⣤⠤⡴⢦⣠⠴⠶⢤⠴⠶⣤⠴⠶⢤⡀⡤⠶⠦⡤⠶⠦⢤⠤⢤⠶⢦⠴⠦⡴⠾⢿⣿⠿⠿⢿⠿⢿⠿⢿⠿⠿⡿⠿⢿⣿
⣿⡇⢸⠤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⣷⠀⠶⡇⢠⠘⡇⠀⡆⢸⡄⠃⣼⢹⠀⠰⡆⠀⡆⢸⠀⠐⢀⣿⡇⠀⠆⡀⠀⠆⣸⠀⢸⠀⠘⠀⠀⡇⠰⢾⠿⡆⠀⣾⠀⣻⠀⠘⠀⠀⡇⠰⢾⣿
⠹⡇⠸⠀⢸⠀⠶⡇⢰⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⣿⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡇⢸⠀⢰⡇⠀⠇⢸⠀⢰⠀⣿⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⠐⡇⠀⣿⠀⢻⠀⡄⠀⠀⡇⠰⢾⣿
⠀⠛⠲⢷⠚⠲⠖⠳⠾⡶⢷⠚⠒⠓⠒⠓⣾⣶⣚⣒⠋⠓⠚⠒⣷⣶⣶⠒⠾⠒⠒⠒⠒⠋⠑⠒⠁⠈⠒⠊⠉⠒⠒⠛⠒⠚⠒⠋⠓⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠒⠒⠓⠒⠚⠀⠑⠲⣿⣶⣾⣶⣷⣷⣶⡷⠒⢾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣧⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣇⠀⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠦⢄⠀⢹⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣿⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠀⡆⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣾⣦⡀⠀⠀⢸⣿⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣆⠀⢸⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣽⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣶⣶⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⣿⣿⡿⠙⣿⣿⣿⣿⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣶⣿⣿⠿⠋⠀⠀⢸⣿⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠛⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣿⣿⣿⡇⠀⠈⢻⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⡻⠦⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣗⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⢠⣿⣿⣿⡇⢀⣀⣠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠀⢹⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡄⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠉⠉⣿⣿⣿⣛⣿⣯⣭⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣆⠀⠀⠀⠨⣿⣿⡇⠀⠀⠈⠻⢿⣿⣿⣿⠿⢿⣿⣿⡟⠉⢹⣿⣿⡟⠻⣿⣿⣿⣿⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠀⠀⠀⠀⢹⠛⠁⠀⠀⡤⢰⢾⣿⣿⣤⣤⣾⣿⣿⣥⣴⣾⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⠿⠿⠉⣿⣿⣭⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣤⣤⣤⣤⣲⣶⣿⣿⣿⣿⣿⣿⣷⠅⠤⣸⠸⠠⣦⣤⣶⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⡉⠙⣿⣿⣭⣿⡿⠀⣿⣿⠿⠿⢟⠀⣬⣿⣛⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⢠⣅⡀⠀⢻⣿⣿⣿⣿⣿⡏⠉⣋⡁⣼⣿⣿⣿⣷⠀⣿⣿⠙⣿⣿⣄⣿⣿⣿⣿⣿⣧⣽⣿⣿⣿⡿⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣟⣆⣼⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠋⠀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⣿⣯⣿⣿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠾⣿⣿⠿⠿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠿⣿⠿⠷⡤⠶⣤⠶⢤⠴⣶⠶⡶⢶⠶⢦⡀⢀⡶⠶⠾⡷⠴⠤⡴⠶⢦⡤⠶⠦⣤⠦⡴⢦⣠⠴⠶⢤⠴⠶⣤⠴⠶⢤⡀⡤⠶⠦⡤⠶⠤⢤⠴⢤⠶⢦⠴⠶⡴⠾⢿⣿⠿⠿⢿⠿⢿⠿⢿⠿⠿⡿⠿⢿⣿
⣿⡇⢸⠤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⣷⠀⠶⡇⢠⠘⡇⠀⡆⢸⡄⠃⣼⢹⠀⠰⡆⠀⡆⢸⠀⠐⢀⡷⡇⠀⠆⡀⠀⠆⣸⠀⢸⠀⠘⠀⠀⡇⠰⢾⠿⡆⠀⣾⠀⢼⠀⠘⠀⠀⡇⠰⢾⣿
⠹⡇⠸⠀⢸⠀⠶⡇⢰⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⣿⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡇⢸⠀⢰⡇⠀⠇⢸⠀⢰⠀⣷⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⠐⡇⠀⣿⠀⢹⠀⡄⠀⠀⡇⠰⢾⣿
⠀⠛⠲⢷⠚⠲⠖⠳⠺⢶⢷⠚⠒⠓⠒⠓⣾⣶⣞⣒⠋⠓⠚⠒⣷⣶⡶⠲⠞⠒⠒⠒⠒⠋⠑⠒⠁⠈⠒⠊⠉⠒⠒⠛⠒⠚⠒⠃⠓⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠒⠒⠓⠒⠚⠀⠑⠲⣿⣶⣾⣶⣷⣷⣶⡗⠒⢾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⠀⠀⠀⠀⠀⢠⣾⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⡀⠀⢀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠦⢄⠀⢹⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣧⣄⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣾⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠀⡆⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⢠⣤⣶⣾⣦⡀⠀⠀⢸⣿⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣄⠀⢸⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⣶⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠄⣿⣿⣿⣿⠙⣿⣿⣿⣿⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣶⣿⣿⠿⠋⠀⠀⢸⣿⣦⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣀⡈⠻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⣿⣿⣿⡟⠀⠈⢿⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⡻⠦⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠋⠙⠄⠀⢼⣿⣿⡆⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⣿⣿⣿⡇⠀⣀⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⢀⠀⣀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠄⠀⠀⠀⠀⣾⣿⣿⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠹⣿⣿⣿⣛⣿⣿⣭⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣷⡀⠀⠀⠠⣿⣿⣿⡀⠀⠈⠻⢿⣿⣿⣿⠿⢿⣿⣿⡟⠉⢹⣿⣿⡟⠿⣿⣿⣿⣿⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣠⣰⣿⣿⣿⣧⠀⠀⠀⢘⡟⠧⠀⠀⠀⢢⢼⣿⣿⣥⣤⣾⣿⣿⣥⣤⣾⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⡿⠿⠉⣿⣿⣭⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣦⣤⣴⣤⣴⣿⣾⣿⣿⣿⣿⣿⣿⠯⢶⣸⠁⠸⣤⣶⣿⣾⣿⣿⣿⣿⣿⡿⠟⣿⣿⣿⡉⠙⣿⣿⣭⣿⡿⠀⣿⣿⠿⠿⠟⢀⣭⣿⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢠⣥⡀⠀⠻⣿⣿⣿⣿⣿⡏⠉⣛⡁⣴⣿⣿⣿⣷⠀⣿⣿⠙⣿⣷⣄⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⡿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣳⣠⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠛⠁⠀⠈⠙⠛⠿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⣿⣯⣽⣿⣿⡿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠾⢿⣿⡿⠿⠿⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠿⣿⠿⠿⡴⠶⡤⠶⢤⠴⣶⠶⡴⢶⠶⢦⡀⢀⡶⠶⠾⡦⠴⠤⡴⠶⢦⡤⠶⠤⣤⠶⡴⢦⣠⠴⠶⢤⠴⠶⣤⠴⠶⢤⡀⡴⠶⠦⡤⠶⠤⢤⠶⢤⠶⢦⠴⠶⡴⠶⢿⣿⠿⠿⢿⠿⢿⠿⢿⠿⠿⡿⠿⢿⣿
⣿⡇⢸⠤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⡷⠀⠶⡇⢠⠘⡇⠀⡆⢸⡄⠃⣼⢹⠀⠰⡆⠀⡆⢸⠀⠐⢀⡇⡇⠀⠆⡀⠀⠆⣸⠀⢸⠀⠘⠀⠀⡇⠰⢾⠿⡆⠀⣾⠀⢸⠀⠘⠀⠀⡇⠰⢾⣿
⠻⡇⠸⠀⢸⠀⠶⡇⢰⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⣿⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡇⢸⠀⢰⡇⠀⠇⢸⠀⢰⠀⣷⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⠐⡇⠀⣿⠀⢻⠀⡄⠀⠀⡇⠰⢾⣿
⠀⠛⠲⢷⠚⠲⠖⠳⠺⢶⢷⠞⠒⠓⠒⠓⣾⣶⣞⣒⠋⠓⠚⠒⣷⣶⡖⠶⠚⠒⠒⠒⠒⠋⠑⠒⠁⠈⠒⠊⠉⠒⠒⠛⠒⠲⠒⠁⠓⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠒⠒⠓⠒⠚⠀⠓⠲⣿⣶⣾⣶⣷⣷⡶⠓⠒⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⣴⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣧⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣆⠀⠀⠀⣠⣿⡏⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠦⢄⠀⢹⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡄⠀⣰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠀⠆⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣦⡀⠀⠀⢸⣿⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣄⠀⢸⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢨⣿⡇⠀⠀⠀⣿⣿⣿⣿⠹⣿⣿⣿⣿⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣶⣿⣿⠿⠋⠀⠀⢸⣿⣦⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⣠⣤⣤⠙⠻⣿⣿⡄⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⣿⣿⣿⣿⠀⠈⢿⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⣿⣟⠿⠆⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠈⠛⠛⠀⠀⣿⣿⣿⡄⠀⠀⠀⠀⢠⣿⣿⠆⠀⠀⠀⣿⣿⣿⡇⠀⣀⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣧⡀⠀⠀⠀⣼⣿⣿⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⢹⣿⣿⣿⣟⣿⣿⣭⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⡀⠀⠀⣾⣿⣿⠀⠀⠈⠻⢿⣿⣿⣿⡿⢿⣿⣿⡟⠋⢹⣿⣿⡟⠿⣿⣿⣿⣿⣠⣤⣼⣿⣿⣿⣿⣿⣿⣿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣗⣀⡀⠈⡟⡟⠀⠀⠀⡐⣿⣿⣿⣥⣤⣴⣿⣿⣥⣤⣼⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⠿⠩⣿⣿⣽⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣦⣤⣼⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⢿⣆⡇⠏⢶⣶⣶⣷⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⡉⠹⣿⣿⣻⣿⡿⠈⣿⣿⠿⠿⠇⢀⣭⣿⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢀⣨⣀⠀⠸⣿⣿⣿⣿⣿⡟⠉⣛⡁⣴⣿⣿⣿⣷⠀⣿⣟⠹⣿⣷⣜⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣻⣏⣁⣼⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠃⠀⠈⠙⠛⠿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣷⣿⣯⣽⣿⣿⣿⣿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡿⣯⣽⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠾⢿⣿⡿⠿⠿⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠿⣿⠿⠿⡶⠶⡤⠶⢤⠴⣴⠶⡴⢶⠶⢦⡀⢀⡴⠶⠾⡤⠴⠶⡶⠶⢦⡤⠶⠦⣤⠦⡤⢤⣠⠴⠶⢤⠴⠶⣤⠶⠶⢤⡀⡤⠶⠦⡤⠶⠶⢦⠴⢤⠶⢦⠴⠶⡴⠶⢿⣿⠿⠿⢿⠿⢿⠿⢿⠿⠿⡿⠿⢿⣿
⣿⡇⢸⠤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⡿⠀⠶⡇⢠⠘⡇⠀⡆⢸⡄⠃⣼⢹⠀⠰⡆⠀⡆⢸⠀⠐⢀⡷⡇⠀⠆⡀⠀⠆⣸⠀⢸⠀⠘⠀⠀⡇⠰⢾⠿⡆⠀⣾⠀⢻⠀⠘⠀⠀⡇⠰⢾⣿
⠻⡇⠸⠀⢸⠀⠶⡇⢸⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⣿⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡇⢸⠀⢰⡇⠀⠇⢸⠀⢰⠀⣷⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⡀⡇⠀⣿⠀⢽⠀⡄⠀⠀⡇⠰⢾⣿
⠀⠛⠲⢷⠚⠲⠖⠳⠺⢶⢷⡞⠒⠓⠒⠓⢾⣶⣞⣒⠋⠓⠚⠒⣿⣶⠲⠶⠚⠒⠒⠒⠒⠋⠑⠒⠁⠈⠒⠊⠉⠒⠒⠛⠒⠒⠒⠁⠓⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠒⠒⠓⠒⠚⠀⠓⠶⣿⣶⣾⣶⣷⣷⠒⠓⠒⢺⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡄⠀⠀⠀⠀⠀⢀⣾⡿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⡀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠦⢄⠀⢹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⠀⠀⠀⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣶⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠀⡆⢸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⣀⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⢀⣤⣴⣶⣦⡀⠀⠀⢸⣿⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⢮⡇⠀⠀⠀⢸⣿⣿⣿⣿⣷⣄⠀⢸⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠗⠀⠀⠀⠀⠀⢸⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⢸⣿⣿⣿⠹⣿⣿⣿⣿⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣶⣿⣿⠿⠋⠀⠀⢸⣯⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢰⣦⣤⣤⡄⠉⢻⣿⣿⡀⠀⠀⠀⠀⠀⢸⣿⡗⠀⠀⠀⣿⣿⣿⣿⠀⠈⢿⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⣿⣟⢷⡄⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠙⠛⠻⠏⠀⢸⣿⣿⣷⠀⠀⠀⠀⢀⣾⣿⡇⠀⠀⠀⣿⣿⣿⡿⠀⢀⣀⣹⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⣠⢄⣀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣆⠀⠀⠀⣤⣿⣿⠇⠀⢠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠉⠛⢹⣿⣿⣿⣿⣻⣿⣯⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⠀⠈⣿⣿⣿⠁⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢹⣿⣿⡟⠿⣿⣿⣿⣿⣠⣤⣼⣿⣿⣿⣿⣿⣿⣿⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣧⣄⡈⡿⢛⠀⠀⠀⠰⣾⣿⣿⣥⣤⣴⣿⣿⣧⣤⣼⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠿⢹⣿⣿⣿⣿⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣷⣷⣦⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢇⡇⠿⢶⣿⣿⣷⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⡉⠹⣿⣿⣻⣿⡿⢸⣿⣿⠾⠿⠇⢠⣭⣟⣛⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣈⣀⠀⠸⣿⣿⣿⣿⣿⡟⠉⣛⣃⣰⣿⣿⣿⣧⠀⣿⡟⠻⣿⣷⣸⣿⣿⣾⣿⣿⣬⣽⣿⣿⣿⣿⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣟⣻⣉⣠⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠛⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣽⣿⣿⣿⣿⠿⠿⠿⠿⠟⠛⠛⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⢿⣽⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠲⢿⣿⣿⡿⠿⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠿⣿⠿⠿⡷⠶⣤⠶⢤⠴⣴⠶⡴⢶⠶⢦⡀⢀⡴⠶⠦⡤⠴⠶⡶⠶⢤⡤⠶⠦⣤⠦⡤⢤⣠⠴⠶⢤⠴⠶⣤⠴⠶⢤⡀⡤⠶⠤⡤⠶⠶⢦⠴⢤⠶⢦⠴⠶⡴⠶⢼⣿⠿⠿⢿⠿⢿⠿⢿⠿⠿⡿⠿⢿⣿
⣿⡇⢸⠤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⣿⠀⠶⡇⢠⠘⡇⠀⡆⢸⡄⠃⣼⢹⠀⠰⡆⠀⡆⢸⠀⠐⢀⡇⡇⠀⠆⡀⠀⠆⣸⠀⢸⠀⠘⠀⠀⡇⠰⢾⠿⡆⠀⣾⠀⣹⠀⠘⠀⠀⡇⠰⢾⣿
⠻⡇⠸⠀⢸⠀⠶⡇⢰⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⣿⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡇⢸⠀⢰⡇⠀⠇⢸⠀⢰⠀⣷⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⡀⡇⠀⣿⠀⢻⠀⡄⠀⠀⡇⠰⢾⣿
⠀⠙⠲⢷⠚⠲⠖⠳⠺⠶⡗⡞⠒⠓⠒⠓⢾⣶⣞⣒⠋⠓⠚⠒⣷⡖⢶⠖⠚⠒⠒⠒⠒⠋⠑⠒⠁⠈⠒⠊⠉⠒⠒⠛⠒⠒⠒⠁⠓⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠒⠒⠓⠒⠚⠀⠓⠶⣿⣶⣾⣶⣷⡗⠒⠓⠒⢺⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣆⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠦⢄⠀⢹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡄⠀⠀⠀⣠⣿⣿⡃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⣶⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠀⡆⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡀⠀⣰⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢰⣍⠀⠀⠀⠀⣠⣴⣶⣦⡀⠀⠀⢸⣿⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣾⣿⣿⣿⣿⠻⠿⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⢨⣳⠀⠀⠀⢸⣿⣿⣿⣿⣷⣄⠀⢸⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀
⣀⠀⠀⠀⠀⠀⠀⣤⣀⠀⡒⠀⠀⠀⠀⠀⠀⠀⣾⡧⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⣸⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠃⠀⠀⠀⠀⠀⣿⣿⣷⣾⡄⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⢸⣿⣿⣿⠹⣿⣿⣿⣿⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣶⣿⣿⠿⠋⠀⠀⢸⣯⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠾⣶⣷⣶⠈⠉⣿⣿⣿⡀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⣼⣿⣿⣿⠀⠈⢿⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⣿⡿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠋⠙⠛⠃⠀⣿⣿⣿⣇⠀⠀⠀⠀⣼⣿⣟⠀⠀⠀⣿⣿⣿⣿⠀⠀⣀⣹⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣖⣂⣀⣤⣤⣀⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣆⠀⠀⣰⣿⣿⣇⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠉⠛⢻⣿⣿⣿⣿⣻⣿⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣧⠀⣿⣿⣿⡇⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢻⣿⣿⡿⠿⣿⣿⣿⣿⣀⣤⣼⣿⣿⣿⣿⣿⣿⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⣀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣷⡌⢻⢻⠀⠀⡀⢐⣷⣿⣿⣇⣠⣴⣿⣿⣧⣤⣼⣿⣿⣷⣿⣿⣿⢿⣿⣿⣿⣿⠏⢹⣿⣿⣿⣿⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⣇⣼⠸⢮⣿⣾⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⠉⠹⣿⣿⣻⣿⡿⢸⣿⣿⠾⠿⠇⢈⣽⣟⣛⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⣘⣁⡀⠀⢿⣿⣿⣿⣿⡿⠋⢛⡋⣰⣿⣯⣿⣧⢀⣿⡟⠻⣿⣷⣸⣿⣿⣾⣿⣿⣬⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⢯⣉⣽⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣯⣿⣿⣭⣿⣿⣿⣿⡿⠿⠿⠿⠿⠟⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢿⣿⣿⡿⠿⠛⠛⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣾⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠿⣿⠿⠿⡿⠶⣤⠶⢤⠴⡴⠶⡴⢶⠶⢦⡀⢀⡴⠶⠦⡤⠴⠶⡴⠶⢤⡤⠶⠦⣤⠦⡤⢤⣠⠴⠶⢤⠴⠶⣤⠴⠶⢤⡀⡤⠶⠤⡴⠶⠶⢦⠴⢤⠶⢦⠴⠶⡴⠶⢬⣿⠿⠿⢿⠿⢿⠿⢿⠿⠿⡿⠿⢿⣿
⣿⡇⢸⠤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⣿⠀⠶⡇⢠⠘⡇⠀⡆⢸⡄⠃⣼⢹⠀⠰⡆⠀⡆⢸⠀⠐⢀⡗⡇⠀⠆⡀⠀⠆⣸⠀⢸⠀⠘⠀⠀⡇⠰⢾⠿⡆⠀⣾⠀⢺⠀⠘⠀⠀⡇⠰⢾⣿
⠿⡇⠸⠀⢸⠀⠶⡇⢰⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⣿⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡇⢸⠀⢰⡇⠀⠇⢸⠀⢰⠀⣷⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⡀⡇⠀⣿⠀⢿⠀⡄⠀⠀⡇⠰⢾⣿
⠀⠙⠲⢷⠚⠒⠖⠳⠺⠶⡗⡾⠒⠓⠒⠓⢾⣶⣞⣒⠋⠓⠚⠒⢷⠲⡶⠒⠚⠒⠒⠒⠒⠋⠑⠒⠁⠈⠒⠊⠙⠒⠒⠛⠒⠒⠒⠁⠓⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠒⠒⠓⠒⠚⠀⠓⠶⣿⣶⣾⣶⡷⠓⠒⠓⠖⠚⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠦⢄⠀⢹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣧⠀⠀⠀⠀⢀⣾⣿⣏⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⣣⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠀⡆⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣆⠀⠀⢀⣾⣿⣿⣿⣶⣄⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠠⣶⠀⠀⠀⠀⣠⣤⣶⣦⡀⠀⠀⢸⣿⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡄⢀⣾⣿⣿⡿⠉⠉⠋⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⢸⣯⠀⠀⠀⢠⣿⣿⣿⣿⣷⣄⠀⢸⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀
⣤⡀⠀⠀⠀⠀⠀⢠⣤⣄⠀⡧⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⣸⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠏⠀⠀⠀⠀⠀⢸⣿⣿⣶⣆⡀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⣿⣿⠹⣿⣿⣿⣿⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣶⣿⣿⠿⠋⠀⠀⢸⣿⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠘⠞⣷⣾⡆⠀⢹⣿⣿⣷⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⢸⣿⣿⣿⠀⠈⢿⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⣿⡻⣦⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⠋⠑⠀⢸⣿⣿⣿⣇⠀⠀⠀⣾⣿⣿⠀⠀⠀⣾⣿⣿⣿⠀⠀⢀⣹⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣆⡀⡤⢄⡀⣄⣰⣤⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠹⣿⣿⣿⣧⢀⢴⣿⣿⣿⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠛⢻⣿⣿⣿⣿⣛⣿⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⣿⣿⡗⣻⣿⣿⡟⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢻⣿⣿⡿⠿⣿⣿⣿⣿⣀⣠⣼⣿⣿⣿⣿⣿⣿⣿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⡷⡀⠀⠀⠀⠀⢀⣀⣄⣶⣿⣿⣿⣿⣿⣾⢻⢻⡃⠀⠀⣀⣲⣿⣿⣏⣀⣴⣿⣿⣧⣤⣼⣿⣿⣷⣾⣿⣿⢿⣿⣿⣿⣿⠏⢹⣿⣟⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣸⠸⢿⣽⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⠙⠹⣿⣟⣻⣿⡿⢸⣿⣷⠾⠿⠇⣈⣽⣟⣻⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢀⣃⡀⠀⢿⣿⣿⣿⣿⣿⠋⢛⡋⣠⣿⣯⣿⣧⢀⣿⡟⠻⣿⣧⣸⣿⣷⣾⣿⣷⣬⣿⣿⣿⣿⣷⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⣏⣩⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣯⣿⣿⣭⣿⣿⣿⣿⣷⠾⠿⠿⠿⠟⠛⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠿⣿⣿⡿⠿⠟⠛⠛⠛⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣾⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠿⣿⠿⠿⡿⠶⣤⠶⢤⠴⣤⠶⡴⢶⠶⢦⡀⢀⡴⠶⠦⡤⠴⠶⡤⠶⢤⡤⠶⠦⣤⠦⡤⢦⣠⠴⠶⢤⠴⠶⣤⠶⠶⢤⡀⡤⠶⠶⡶⠶⠶⢤⠴⢤⠶⢦⠴⠶⡴⠶⢤⣿⠿⠿⢿⠿⢿⠿⢿⠿⠿⡿⠿⢿⣿
⣿⡇⢸⠤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⣿⠀⠶⡇⢠⠘⡇⠀⡆⢸⡄⠃⣼⢹⠀⠰⡆⠀⡆⢸⠀⠐⢀⡷⡇⠀⠆⡀⠀⠆⣸⠀⢸⠀⠘⠀⠀⡇⠰⢾⠿⡆⠀⣾⠀⣿⠀⠘⠀⠀⡇⠰⢾⣿
⠿⡇⠸⠀⢸⠀⠶⡇⢸⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⣿⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡇⢸⠀⢰⡇⠀⠇⢸⠀⢰⠀⣷⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⡀⡇⠀⣿⠀⢽⠀⡄⠀⠀⡇⠰⢾⣿
⠀⠙⠲⢷⠚⠒⠖⠳⠺⠶⠷⣾⠒⠓⠒⠓⢾⣶⣞⣒⠋⠓⠚⠒⢷⠲⠶⠒⠚⠒⠒⠒⠒⠋⠑⠒⠁⠈⠒⠚⠙⠒⠖⠛⠒⠒⠒⠁⠓⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠒⠒⠓⠒⠚⠀⠓⠶⣿⣶⣾⣶⠓⠓⠒⠳⡶⠚⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠷⠧⢄⠈⢹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣆⠀⠀⠀⠀⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠀⡆⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡄⠀⠀⠀⣼⣿⣿⣿⣿⣷⣤⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡿⠂⠀⠀⠀⣀⣤⣴⣦⡀⠀⠀⢸⣿⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⠀⠀⣼⣿⣿⣿⠟⠛⠹⠛⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⢀⣿⣿⣿⣿⣷⣄⠀⢸⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣾⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀
⣶⣄⠀⠀⠀⠀⠀⠠⣦⣄⠀⢨⡄⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣦⣸⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀
⡿⡿⠁⢀⢀⠀⣀⠐⣿⣿⣧⣼⣅⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⢸⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣶⣿⣿⠿⠋⠀⠀⢸⣧⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠛⢿⣿⣿⣿⡀⢸⣿⣿⣿⡄⠀⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⣿⣿⠀⠈⢿⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⣿⡻⣦⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠛⠛⠃⢸⣿⣿⣿⣿⡀⠀⠀⢾⣿⣿⠀⠀⠀⣾⣿⣿⣿⠀⠀⠀⣻⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣷⣄⣀⣢⣤⣤⣀⣤⣶⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢿⣿⣿⣷⣴⣬⣿⣿⣿⠁⠀⣤⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠛⢻⣿⣿⣿⣿⣟⣻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣾⣿⣿⣿⠂⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢻⣿⣿⡿⢿⣿⣿⣿⣿⣀⣠⣼⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⡄⡀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⣿⢻⠟⣿⡀⣀⣠⣶⣿⣿⣏⣀⣤⣿⣿⣧⣤⣼⣿⣿⣷⣾⣿⣿⢿⣿⣿⣿⣿⠏⢹⣿⣟⣻⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⠙⢻⣿⣟⣻⣿⡿⢸⣿⣷⡾⠿⠇⣈⣿⣛⣻⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢀⣃⡀⠀⢿⣿⣿⣿⣿⣿⠛⢛⡛⣠⣿⣿⣿⣧⢠⣿⡟⠻⣿⣧⣸⣿⣷⣾⣿⣧⣬⣿⣿⣿⣿⣷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⢿⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⠃⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⣿⣶⣿⣯⣿⣿⣭⣿⣿⣿⣿⣷⠾⠿⠿⠿⠟⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢾⣿⣿⡿⠿⠿⠛⠛⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣾⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠿⣿⠿⠿⡿⠶⣤⠶⢤⠶⣤⠶⡶⢶⠶⢦⡀⢀⡴⠶⠦⡤⠶⠶⡤⠶⢤⡤⠶⠦⣤⠦⡤⢦⣠⠴⠶⢤⠴⠶⣤⠴⠶⢤⡀⡤⠶⠶⡶⠶⠷⢤⠴⢤⠶⢦⠴⠶⡴⠶⢤⣽⠿⠿⢿⠿⢿⠿⢿⠿⠿⡿⠿⢿⣿
⣿⡇⢸⠤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⡿⠀⠶⡇⢠⠘⡇⠀⡆⢸⡄⠃⣼⢹⠀⠰⡆⠀⡆⢸⠀⠐⢀⡗⡇⠀⠆⡀⠀⠆⣸⠀⢸⠀⠘⠀⠀⡇⠰⢾⠿⡆⠀⣾⠀⢾⠀⠘⠀⠀⡇⠰⢾⣿
⡿⡇⠸⠀⢸⠀⠶⡇⢰⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⣿⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡇⢸⠀⢰⡇⠀⠇⢸⠀⢰⠀⣿⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⡀⡇⠀⣿⠀⢾⠀⡄⠀⠀⡇⠰⢾⣿
⠀⠙⠲⢷⠚⠲⠖⠳⠺⠖⠷⣺⠒⠓⠒⠓⢾⣶⣞⣒⡋⠓⠚⠒⠗⢶⠖⠒⠚⠒⠒⠒⠒⠋⠑⠒⠁⠈⠒⠊⠙⠲⠒⠛⠒⠒⠒⠁⠓⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠒⠒⠓⠒⠚⠀⠓⠶⣿⣶⣾⣶⠓⠓⠒⢳⡶⠚⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠯⢅⠀⢹⣷⡀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣰⣿⣿⣇⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⣇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠀⡆⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⠀⠀⠀⠀⣰⣿⣿⣿⠿⠿⣿⣶⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⢯⡂⠀⠀⠀⣀⣤⣤⣤⡀⠀⠀⢸⣿⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡆⠀⠀⢠⣿⣿⣿⠏⠀⠀⠉⠉⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⣿⣿⣿⣿⣷⣄⠀⢸⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣄⣠⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀
⣿⣦⡀⠀⠀⠀⠀⠀⢶⣶⣄⠀⢸⡀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣦⣸⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠿⠃⠀⣀⣀⣀⣀⠻⠿⣿⣦⣌⣇⠀⠀⠀⠀⣸⣿⠀⠀⠀⢸⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣶⣿⣿⠿⠋⠀⠀⢸⣧⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠿⣿⣿⣿⣇⠀⣿⣿⣿⣿⡆⠀⠀⠀⣿⣿⡀⠀⠀⢸⣿⣿⣿⠀⠘⢿⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⣿⢿⣦⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠈⠉⠙⠛⠀⣿⡿⣿⣿⣷⡄⠀⣺⣿⣿⡃⠀⠀⢸⣿⣿⣿⠀⠀⠀⣻⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣷⣤⣄⣶⣦⣟⣠⣼⣾⣷
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢹⣿⣿⣿⣾⣿⣿⣿⠁⠀⣠⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⠛⣿⣿⣿⡿⣿⣟⣻⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣲⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠂⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢻⣿⣿⠿⢿⣿⣿⣿⣷⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣵⣣⣀⠀⠀⠀⢀⣤⣤⣤⣾⣿⣿⣿⣿⣿⡿⡟⣿⣲⣤⣄⣶⣿⣿⣏⣀⣤⣿⣿⣃⣤⣼⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⠏⣹⣿⣟⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⠛⢹⣿⣟⣻⣿⡿⢸⣿⣷⣶⠿⠀⣈⣿⣛⣻⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢀⣛⡀⠀⠹⣿⣿⣿⣿⣿⠛⢛⠛⢠⣿⣿⣿⣧⢀⣿⡟⠻⣿⣦⢸⣿⣷⣾⣿⣧⣭⣿⣿⣿⣿⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢯⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠃⠀⠈⠙⠿⢿⣿⣿⣿⣿⣿⣿⣶⣿⣯⣿⣿⣿⣿⣿⣿⣿⣷⡶⠿⠿⠿⠟⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢾⣿⣿⡿⠿⠿⠟⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠿⣿⠿⠿⡿⠷⣤⠶⢤⠴⡤⠶⡶⢶⠶⢦⡀⢠⡴⠶⠦⡤⠶⠶⡤⠶⢤⡤⠶⠦⣤⠦⡤⢤⣠⠴⠶⢤⠴⠶⣤⠶⠶⢤⡀⡤⠶⠶⡶⠾⠷⢤⠴⢤⠶⢦⠴⠶⡴⠶⢤⣽⠿⠿⢿⠿⢿⠿⢿⠿⠿⡿⠿⢿⣿
⣿⡇⢸⠤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⣿⠀⠶⡇⢠⠘⡇⠀⡆⢸⡄⠃⣼⢹⠀⠰⡆⠀⡆⢸⠀⠐⢀⡟⡇⠀⠆⡀⠀⠆⣸⠀⢸⠀⠘⠀⠀⡇⠰⢾⠿⡆⠀⣾⠀⣻⠀⠘⠀⠀⡇⠰⢾⣿
⣿⡇⠸⠀⢸⠀⠶⡇⢰⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⣿⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡇⢸⠀⢰⡇⠀⠇⢸⠀⢰⠀⣷⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⠀⡇⠀⣿⠀⢻⠀⡄⠀⠀⡇⠰⢾⣿
⠀⠙⠲⢷⠚⠲⠖⠳⠺⠖⢷⢺⠒⠓⠒⠓⢺⣶⣾⣒⡋⠓⠚⠒⠓⢶⠖⠒⠚⠒⠒⠒⠒⠋⠑⠒⠁⠈⠒⠊⠙⠖⠒⠛⠒⠒⠒⠁⠑⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠒⠒⠓⠒⠚⠀⠓⢶⣿⣶⣾⠒⠓⠓⠒⢷⣶⠚⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠷⠦⢄⠁⢸⣦⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡤⣤⣀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠀⡆⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡆⠀⠀⠀⠀⢀⣾⣿⣿⠟⠃⠙⢿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⣵⡇⠀⠀⠀⣀⣠⣤⣤⠀⠀⠀⢸⣿⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⠀⠀⠀⢀⣾⣿⣿⠋⠀⠀⠀⠈⠁⠀
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⣿⣿⣿⣿⣷⣄⠀⢸⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣇⠀⠀⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀
⣿⣷⣤⠀⠀⠀⠀⠀⢸⣷⣦⡀⠀⢸⡇⠀⠀⠀⢰⣿⡇⠀⠀⢀⣿⣿⣿⣿⣿⣿⣦⣸⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣦⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠻⠟⠋⠀⣤⣤⣤⣤⣼⠿⢿⣷⣤⠸⣦⠀⠀⠀⢸⣿⠇⠀⠀⢸⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣾⣿⣿⠿⠋⠀⠀⢸⣧⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠙⢻⣿⣿⣿⡄⢸⣿⣿⣿⣿⡇⠀⢀⣿⣿⡇⠀⠀⢸⣿⣿⣿⠀⠘⢿⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⣿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠐⠐⠀⠀⠙⠛⠁⢺⣿⡝⢹⣿⣿⡀⣸⣿⣿⡇⠀⠀⢸⣿⣿⣿⠀⠀⠀⢻⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣷⣤⣤⣴⣰⡞⣀⣰⣳⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠺⣿⣿⣿⣿⣿⣿⡇⠀⣀⣼⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⠛⣿⣿⣿⡿⣿⣟⣛⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣷⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⡏⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢻⣿⣿⠿⢿⣷⣿⣿⣇⣀⣀⣽⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣆⣀⢀⢤⣀⣤⣴⣤⣿⣿⣿⣿⣿⣿⡿⡟⣿⣵⣴⣤⣤⣿⣿⣏⣁⣠⣿⣿⣃⣠⣼⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⠏⣿⣿⣛⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⠛⢻⣿⣟⣻⣿⡟⢸⣿⣷⣶⠿⠀⣉⣿⣛⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠐⣘⡀⠀⠸⣿⣿⣿⣿⣿⠛⠛⠛⢠⣿⣟⣿⣧⢀⣿⡟⢻⣿⣦⢸⣿⣷⣶⣿⣧⣽⣿⣿⣿⣿⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠋⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠃⠀⠈⠙⠿⢿⣿⣿⣿⣿⣿⣿⣤⣾⣟⣿⣿⣿⣿⣿⣿⣿⣷⣶⠿⠿⠿⠿⠟⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠾⣿⣿⣿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠿⣿⠿⠿⡿⠷⣤⠶⢤⠶⡤⠶⡶⢶⠶⢦⡀⢀⡴⠾⠦⡤⠶⠶⡤⠶⢤⡤⠶⠦⣤⠦⡤⢦⣠⠴⠶⢤⠴⠶⣤⠴⠦⢤⡀⡴⠾⠷⡾⠿⠷⢤⠴⢤⠶⢦⠴⠶⡶⠶⢦⣸⠿⠿⢿⠿⢿⠿⢿⠿⠿⡿⠿⢿⣿
⣿⡇⢸⠤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⣿⠀⠶⡇⢠⠘⡇⠀⡆⢸⡄⠃⣼⢹⠀⠰⡆⠀⡆⢸⠀⠐⢀⡷⡇⠀⠆⡀⠀⠆⣸⠀⢸⠀⠘⠀⠀⡇⠰⢾⠿⡆⠀⣾⠀⣿⠀⠘⠀⠀⡇⠰⢾⣿
⣿⡇⠸⠀⢸⠀⠶⡇⢸⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⣿⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡇⢸⠀⢰⡇⠀⠇⢸⠀⢰⠀⣷⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⡀⡇⠀⣿⠀⢿⠀⡄⠀⠀⡇⠰⢾⣿
⠁⠛⠲⢷⠚⠒⠖⠳⠺⠖⢷⢺⡖⠓⠒⠓⠺⣶⣾⣒⡋⠓⠚⠒⠛⡶⠒⠒⠚⠒⠒⠒⠒⠋⠑⠒⠁⠈⠒⠊⠙⠒⠒⠛⠒⠚⠒⠁⠓⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠒⠒⠓⠒⠚⠁⠳⣶⣿⣶⡞⠒⠓⠓⠒⣷⣶⠚⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠷⠦⢌⠀⢸⣦⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠄⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠰⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠀⡆⢸⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⠀⠀⠊⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠀⠀⠀⠀⢻⠏⠀⠀⠀⣀⣠⣤⣤⠀⠀⠀⢸⣿⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇⠀⠀⠀⠀⣼⣿⣿⡃⠀⠀⠀⠀⠀⠀
⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⣿⣿⣿⣷⣄⠀⢸⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡄⠀⠀⣸⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣷⠄⠀⠀⠀⠀⠀⣿⣷⣆⠀⠀⠘⡄⠀⠀⠀⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣦⣸⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⣄⣼⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠻⠛⠀⣠⣤⣤⣤⣤⡛⠻⣿⣷⠀⠀⣄⠀⠀⢸⣿⡇⠀⠀⢰⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣶⣿⣿⠿⠋⠀⠀⢸⣧⣠⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⢹⡿⣿⣿⣦⠀⣿⠏⠂⢀⣿⣄⠀⣼⣿⡇⠀⠀⢸⣿⣿⣿⠀⠘⢿⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⡿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠴⠑⠀⠈⠋⠉⠰⣿⡀⠀⢈⣿⣿⣿⣿⣿⣇⠀⠀⢸⣿⣿⣿⠀⠀⠀⢻⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣶⣦⣴⣶⣤⣧⣤⡶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⢰⣿⣿⣿⣿⣿⡯⠀⣀⣼⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⠛⣿⣿⣿⡿⣿⣿⣛⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣽⣷⣦⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡷⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢻⣿⣿⠿⣿⣷⣿⣿⣇⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣑⣠⣀⣀⣠⣤⣴⣶⣷⣿⣿⣿⣿⣿⣿⣿⢿⣿⣶⣴⣴⣿⣿⣏⣁⣠⣿⣿⣇⣠⣼⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⠏⣿⣿⣛⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⠛⢻⣿⣟⣻⣿⡗⢸⣿⣿⣶⡾⠀⣙⣿⠛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣘⡁⠀⠸⣿⣿⣿⣿⣿⠟⠻⠛⢠⣿⣟⣿⣧⢸⣿⡟⢿⣿⣆⢸⣿⣷⣶⣿⣧⣽⣿⣿⣿⣿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠀⠀⠛⠿⢿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣾⣿⣿⣿⣿⣿⣿⣷⣶⠿⠿⠿⠿⠟⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶⣿⣿⣿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠿⣿⠿⠿⡿⠿⣤⠶⢤⠶⣤⠶⡴⢶⠶⢦⡀⢀⡴⠾⠧⡤⠶⠦⡤⠶⢦⡤⠶⠦⣤⠦⡤⢦⣠⠴⠶⢤⠴⠶⣤⠴⠦⢤⡀⡵⠶⠶⡶⠷⠶⢤⠴⢤⠶⢦⠴⠶⡴⠶⢤⣸⠿⠿⢿⠿⢿⠿⢿⠿⠿⡿⠿⢿⣿
⣿⡇⢸⠤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⣿⠀⠶⡇⢠⠘⡇⠀⡆⢸⡄⠃⣼⢹⠀⠰⡆⠀⡆⢸⠀⠐⢀⡇⡇⠀⠆⡀⠀⠆⣸⠀⢸⠀⠘⠀⠀⡇⠰⢾⠿⡆⠀⣾⠀⣿⠀⠘⠀⠀⡇⠰⢾⣿
⣿⡇⠸⠀⢸⠀⠶⡇⢰⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⣿⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡇⢸⠀⢰⡇⠀⠇⢸⠀⢰⠀⣷⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⡀⡇⠀⣿⠀⢿⠀⡄⠀⠀⡇⠰⢾⣿
⠁⠙⠲⢷⠚⠲⠖⠳⠺⠖⠗⣚⡖⠓⠒⠓⠺⣶⣾⣒⡋⠓⠚⠒⠺⠖⠒⠒⠚⠒⠒⠒⠒⠋⠑⠒⠁⠈⠒⠚⠉⠒⠒⠛⠒⠒⠒⠁⠓⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠒⠒⠓⠒⠚⠀⢳⣶⣿⣶⠚⠒⠓⠓⢲⣷⣶⠚⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡏⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠾⠧⢅⠀⢰⣄⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠇⠀⠀⠒⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠀⡆⢸⣿⡆⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⣼⣿⣿⠏⠀⠀⠈⠰⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⣿⣿⠀⠀⠀⢀⣀⣤⣤⠀⠀⠀⢸⣿⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡄⠀⠀⠀⠀⣼⣿⣿⠟⠀⠀⠀⠀⠁⠈
⣷⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢹⡀⠀⠀⣿⣟⠀⠀⠀⣿⣿⣿⣿⣷⣄⠀⢸⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⠀⠀⠀⣼⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡆⠀⠀⠀⠀⠀⣸⣿⣷⡀⠀⠀⢰⣣⠀⢠⣿⡟⠀⠀⠀⣿⣿⣿⣿⣿⣿⣦⣸⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣇⠀⣴⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠛⠁⠰⣶⣶⣶⣶⣟⠛⣿⣿⡆⠀⠀⣷⡀⢸⣿⣷⠀⠀⢠⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣶⣿⣿⠿⠋⠀⠀⢸⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣤⣟⣿⣿⣿⣿⡆⢿⣿⠓⠀⠰⣿⣷⣾⣿⣿⠀⠀⢸⣿⣿⣿⠁⠘⢿⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⡿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⢀⡠
⠀⡀⠀⠈⢿⡿⠟⠈⠛⠛⣳⣿⣿⠀⠀⢐⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⠀⠀⠀⢻⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣾⣶⣦⣿⣿
⠀⠂⡀⡀⠀⠈⠁⠀⠀⠀⠀⠉⠁⠀⠀⣰⣿⣿⣿⣿⣿⠁⣀⣸⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⣿⣿⣿⡿⣿⣿⣛⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢲⣿⣿⣷⠄⠀⢀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⡄⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢻⣿⣿⠿⣿⣷⣿⣿⣇⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣧⣀⣀⣄⣸⣾⣿⣾⣿⣿⣿⣿⣿⣿⢿⢻⣿⣿⣷⣶⣿⣿⣟⣉⣠⣿⣿⣏⣀⣼⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣻⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⠛⢻⣿⣟⣻⣿⡇⢸⣿⣿⣷⡶⠀⣙⣟⠛⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⣙⣃⠀⠸⣿⣿⣿⣿⣿⠟⠻⠟⢠⣿⣟⣿⣧⢸⣿⡟⢿⣿⣆⢸⣿⣷⣶⣿⣆⣽⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣾⣿⣿⣿⣿⣿⣿⣷⣶⠿⠿⠿⠿⠿⠟⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠿⣿⠿⠿⡿⠿⣦⠶⢤⠶⣤⠶⡶⢶⠶⢦⠀⢀⡴⠶⠯⣤⠶⠦⡤⠶⢦⡤⠶⠦⣤⠦⡤⢦⣠⠴⠶⢤⠴⠶⣤⠴⠶⢤⡀⡴⠶⠶⡶⠿⠦⢤⠴⢤⠶⢦⠴⠶⡶⠶⢤⣨⠿⠿⢿⠿⢿⠿⢿⠿⠿⡿⠿⢿⣿
⣿⡇⢸⠤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⣿⠀⠶⡇⢠⠘⡇⠀⡆⢸⡀⠃⣼⢹⠀⠰⡆⠀⡆⢸⠀⠐⢀⡷⡇⠀⠆⡀⠀⠆⣸⠀⢸⠀⠘⠀⠀⡇⠰⢾⠿⡆⠀⣾⠀⢻⠀⠘⠀⠀⡇⠰⢾⣿
⣿⡇⠸⠀⢸⠀⠶⡇⢰⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⡟⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡇⢸⠀⢰⡇⠀⠇⢸⠀⢰⠀⣿⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⣠⡇⠀⣿⠀⢼⠀⡄⠀⠀⡇⠰⢾⣿
⠉⠛⠲⢷⠚⠲⠖⠳⠺⠖⠗⡞⡖⠓⠒⠓⠺⣶⣾⣒⡋⠓⠚⠒⢻⠖⠒⠒⠚⠒⠒⠒⠒⠋⠑⠒⠁⠈⠒⠞⠙⠒⠒⠛⠒⠚⠒⠁⠓⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠒⠒⠓⠒⠚⠘⣷⣶⣿⡖⠚⠒⠓⠓⢶⣷⣶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠥⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠯⢄⠀⢰⣄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⠀⠀⠐⣒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠀⡆⢸⣿⡄⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣸⣿⣿⡋⠀⠀⠀⠀⠁
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠀⣼⣿⠀⠀⠀⢀⣀⣠⣤⠀⠀⠀⢸⣿⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣧⠀⠀⠀⠀⠀⣼⣿⣿⠏⠀⠀⠀⠀⠀⠀
⣿⣦⣀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠰⡇⠀⣿⣿⠀⠀⠀⣿⣿⣿⣿⣷⡄⠀⢸⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡆⠀⠀⠀⣼⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⠀⠀⠀⠀⠀⢀⣿⣿⣆⠀⠀⠀⠀⣿⢰⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣦⢸⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣷⡀⠀⣴⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠛⠃⠰⣿⣿⣾⣾⣾⡉⢹⣿⣷⠀⠀⠘⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣶⣿⣿⠿⠋⠀⠀⢸⣅⣀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣾⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣷⢸⣿⡟⠀⠀⢰⣿⣿⣿⣿⡄⠀⢠⣿⣿⣿⡇⠘⢿⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⡿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⡀⢀⠀⠀⣀⢠
⠀⡀⡠⢴⣿⡿⡿⠃⠛⠋⠟⢾⣿⠆⠀⠀⣸⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⠀⠀⠈⠻⣿⣿⣿⣿⣦⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠊⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⣿⣶⣷⣿⣿
⠂⢺⣍⣼⣿⠉⠐⠁⢃⠀⠈⠈⠁⠀⠀⢀⣾⣿⣿⣿⣿⠅⢀⣸⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⣿⣿⣿⣿⣿⣿⣟⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⣼⣿⣿⣏⠀⢀⠀⠀⠀⠀⢀⣠⣤⣤⣾⣿⣿⣿⣿⣿⡅⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢻⣿⣿⠿⣿⣿⣿⣿⡇⣀⣀⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣦⣠⣌⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣶⣿⣿⣟⣉⣡⣿⣿⣏⣀⣸⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠛⢻⣿⣿⣻⣿⡇⢹⣿⣿⣿⡶⢀⣛⣿⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢂⣃⠀⠀⢿⣿⣿⣿⣿⠟⠻⠟⢀⣾⣟⣿⣧⢸⣿⡟⢿⣿⣆⢸⣿⣷⣶⣾⣌⣿⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠂⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣦⣾⣿⣾⣿⣿⣿⣿⣿⣿⣷⣶⡿⠿⠿⠿⠿⠿⠻⠛⠛⠙⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠿⣿⠿⠿⡿⠿⣧⠶⢤⠶⣤⠴⡴⢶⠶⢦⡀⢀⡴⠶⠯⣤⠴⠦⡤⠶⢦⡴⠶⠦⣤⠦⡤⢦⣠⠴⠶⢤⠴⠶⣤⠴⠶⢧⡀⡾⠾⠿⡿⠷⠦⢤⠴⢤⠶⢦⠴⠶⡶⠶⢤⣸⠿⠿⢿⠿⢿⠿⢿⠿⠿⡿⠿⢿⣿
⣿⡇⢸⣤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⣿⠀⠶⡇⢠⠘⡇⠀⡆⢸⡄⠃⣼⢹⠀⠰⡆⠀⡆⢸⠀⠐⢀⡧⡇⠀⠆⡀⠀⠆⣸⠀⢸⠀⠸⠀⠀⡇⠰⢾⢿⡆⠀⣾⠀⣿⠀⠸⠀⠀⡇⠰⢾⣿
⣿⡇⠸⠀⢸⠀⠶⡇⢰⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⡿⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡇⢸⠀⢰⡇⠀⠇⢸⠀⢰⠀⣿⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⣼⡇⠀⣿⠀⢿⠀⡄⠀⠀⡇⠰⢾⣿
⠋⠛⠲⢷⠚⠲⠖⠳⠺⠖⠗⡚⡶⠓⠒⠓⠺⣶⣾⣖⡋⠓⠚⠒⠷⠒⠒⠒⠚⠒⠒⠒⠒⠋⠑⠒⠁⠈⢲⠊⠙⠒⠒⠛⠒⠚⠒⠁⠓⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠒⠒⠓⠒⠚⢻⣷⣶⣿⠒⠚⠒⠓⠓⣶⣷⣶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡏⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠾⠧⢄⠀⢰⡄⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠀⡆⢸⣿⡄⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⠀⠀⠀⠀⠀
⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⣿⣿⠀⠀⠀⢀⣀⣠⣤⠀⠀⠀⢸⣿⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣼⣿⣿⠏⠀⠀⠀⠀⠀⠀
⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⣵⡀⣿⣿⠀⠀⠀⣿⣿⣿⣿⣷⡄⠀⢸⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡄⠀⠀⠀⣴⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣧⡀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣦⢸⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣷⡀⠀⣴⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠛⠋⠀⣿⣿⣿⣿⣿⡏⢩⣿⣿⡀⠀⠀⢸⣿⣿⣿⠀⠀⠀⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣶⣿⣿⠿⠋⠀⠀⢸⣁⣀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣼⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⣮⣿⣿⣿⣿⣿⠌⣿⡟⠃⠀⠀⣸⣿⣿⣿⡆⠀⢀⣿⣿⣿⡇⠘⢿⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣀⡀⡀⠀⣀⡀
⡀⠀⠀⠠⣼⣿⣿⡯⠼⡏⢾⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⠇⠀⢸⣿⣿⣿⠁⠀⠈⠻⣿⣿⣿⣿⣦⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠈⠁⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠛⢘⣶⣤⣯⡷⢢⡷⢲⡑⠩⠙⠈⠀⠀⠀⢰⣿⣿⣿⣿⡆⢀⣸⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠟⣿⣿⣿⣿⣿⣿⣟⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣌⣽⣿⣿⣿⡉⠁⠄⠀⣀⢄⣀⣀⣤⣴⣲⣿⣿⣿⣿⣿⡇⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢻⣿⣿⠿⣿⣿⣿⣿⡇⣀⣀⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣦⣤⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⣿⣿⣿⣉⣉⣿⣿⣏⣀⣸⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠛⢻⣿⡿⣻⣿⡇⢹⣿⣿⣿⡶⢀⣛⡿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢀⣃⠀⠀⢿⣿⣿⣿⣿⠟⠻⠟⢀⣾⣟⣿⣧⢸⣿⡟⢿⣿⣆⢻⣿⣷⣶⣾⣌⣿⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡟⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠃⠀⠘⠻⠿⣿⣿⣿⣿⣿⣿⣦⣾⣿⣾⣿⣿⣿⣿⣾⣿⣷⣶⡿⠿⠿⠿⠿⠿⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠾⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠿⣿⠿⠿⡿⠿⣷⠶⢤⠶⣤⠶⡶⢶⠶⢦⠀⢀⡴⠶⠯⣤⠴⠦⡤⠶⢦⡴⠶⠦⣤⠦⡴⢦⣠⠴⠶⢤⠴⠶⣤⠶⠶⢧⡁⡷⠾⠿⡿⠷⠦⢤⠴⢤⠶⢦⠴⠶⡴⠶⢤⣼⠿⠿⢿⠿⢿⠿⢿⠿⠿⡿⠿⢿⣿
⣿⡇⢸⣤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⣿⠀⠶⡇⢠⠘⡇⠀⡆⢸⡄⠃⣼⢹⠀⠰⡆⠀⡆⢸⠀⠐⢀⡧⡇⠀⠆⡀⠀⠆⣸⠀⢸⠀⠸⠀⠀⡇⠰⢾⢿⡆⠀⣾⠀⣿⠀⠸⠀⠀⡇⠰⢾⣿
⣿⡇⠸⠀⢸⠀⠶⡇⢸⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⡿⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡇⢸⠀⢰⡇⠀⠇⢸⠀⢰⠀⣿⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⣾⡇⠀⣿⠀⢿⠀⡄⠀⠀⡇⠰⢾⣿
⠋⠙⠲⢷⠚⠲⠖⠳⠺⠖⠗⡚⣶⠓⠒⠓⠚⣶⣾⣖⡋⠓⠚⠒⡿⠒⠒⠒⠚⠒⠒⠒⠒⠋⠑⠒⠁⠈⠒⠊⠙⠒⠒⠛⠒⠚⠒⠁⠓⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠒⠒⠓⠒⠚⣿⣷⣶⡿⠒⠚⠒⠓⠓⣶⣷⣶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠦⢄⠀⢠⡀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠀⡆⢸⣿⡀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⠀⠀⠀⠀⠀
⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⡀⠀⠀⠀⣀⣀⣄⠀⠀⠀⢸⣿⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⣿⡇⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⣼⣿⣿⠇⠀⠀⠀⠀⠀⠀
⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⢤⣤⡀⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣷⡄⠀⢸⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣧⠀⠀⠀⠀⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡇⢀⣀⣀⠀⠀⣼⣿⣿⣄⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣦⢸⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡆⠀⠀⣰⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠙⠋⠀⢻⣿⣿⣿⣿⣧⠀⣿⣿⡇⠀⠀⠀⣿⣿⣿⡄⠀⠀⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣶⣿⣿⠿⠋⠀⠀⢸⣁⡀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣶⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣇⣿⣿⠁⠀⠀⠀⣿⣿⣿⡷⠀⠀⣿⣿⣿⡇⠘⢿⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣀⢀⠀⡠⣄⣀⣀⡴⣀
⠀⠀⠀⠠⣼⣿⠿⠳⠄⡛⡩⣿⣿⠟⠀⠀⠀⢀⣿⣿⣿⡯⠀⢸⣿⣿⣿⠇⠀⠈⠻⣿⣿⣿⣿⣦⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠉⠁⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣄⣦⣤⡄⠀⠰⠈⠐⠈⠈⠀⠀⠀⠀⣀⣾⣿⣿⣿⡏⢀⣸⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠠⢺⣿⣿⣿⠁⠀⣠⠀⡀⠀⣀⣠⣶⣴⣴⣿⣿⣿⣿⣿⣏⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⢿⣿⣿⣿⣿⡇⢀⣀⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣶⣮⣤⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣉⣉⣿⣿⣏⣀⣸⣿⣿⣴⣶⣿⣿⣿⣿⣿⣿⣿⢛⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠛⢻⣿⡿⣿⣿⡇⣿⣿⣿⣿⡶⢈⣛⡿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢀⣋⠀⠀⢿⣿⣿⣿⣿⡟⠻⠟⢀⣾⣟⣿⣧⢸⣿⡟⢿⣿⣄⢿⣿⣷⣶⣶⣈⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠃⠀⠘⠻⠿⣿⣿⣿⣿⣿⣿⣦⣼⣿⣼⣿⣻⣿⣿⣾⣿⣷⣶⡿⡿⠿⠿⠿⠿⠟⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠿⣿⠿⠿⡿⠿⣷⠶⢤⠶⡤⠶⡶⢶⠶⢦⡀⢀⡴⠶⠯⣤⠴⠦⡤⠶⢦⡤⠶⠦⣤⠦⡤⢦⣠⠴⠶⢤⠴⠶⣤⠶⠾⢯⡉⡷⠿⠾⡿⠷⠦⢤⠴⢤⠶⢦⠴⠶⡴⠶⢤⣿⠿⠿⢿⠿⢿⠿⢿⠿⠿⡿⠿⢿⣿
⣿⡇⢸⡤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⣿⠀⠶⡇⢠⠘⡇⠀⡆⢸⡄⠃⣼⢹⠀⠰⡇⠀⡆⢸⠀⠐⢀⡧⡇⠀⠆⡀⠀⠆⣸⠀⢸⠀⠘⠀⠀⡇⠰⢾⣿⡆⠀⣾⠀⣿⠀⠸⠀⠀⡇⠰⢾⣿
⣿⡇⠸⠀⢸⠀⠶⡇⢸⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⣿⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡇⢸⠀⢰⡇⠀⠇⢸⠀⢰⠀⣿⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⣿⡇⠀⣿⠀⢿⠀⡄⠀⠀⡇⠰⢾⣿
⠛⠙⠲⢷⠚⠲⠖⠳⠺⠖⠗⢚⣶⠓⠒⠓⠚⣶⣾⣖⡋⠓⠚⠒⡟⠒⠒⠒⠚⠒⠒⠒⠒⠋⠑⠒⠁⠘⠒⠚⠙⠒⠒⠛⠒⠚⠒⠁⠓⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠒⠒⠓⠒⠺⣿⣷⣶⡟⠒⠚⠒⠓⢳⣶⣷⣶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠦⢄⠀⢠⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠀⡆⢸⣷⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟⠀⠀⠀⠀⠀⠀
⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⣄⣀⣀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⣿⡆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀
⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⢰⣶⣄⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⣾⣿⣿⣿⣷⡀⠀⢸⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⣿⠁⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡆⠀⠀⠀⠀⣼⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀
⠿⢿⣿⣿⡟⠀⣀⣀⣀⣀⠸⣿⣿⣧⡀⠀⠀⠀⠀⣿⣿⡆⠀⠀⣿⣿⣿⣿⣿⣿⣆⢸⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡀⠀⠀⣾⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠉⠁⠸⢿⣿⣿⣿⣿⡄⢼⣿⣿⠀⠀⠀⠀⣿⣿⡇⠀⠀⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣾⣿⣿⠿⠋⠀⠀⢸⣀⡀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣧⣆⣼⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢤⣌⣻⡿⢿⣿⣇⣸⣿⠁⠀⠀⠀⢸⣿⣿⣧⠂⠀⣿⣿⣿⡇⠘⢿⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣂⠀⢀⣀⣀⣀⣀⡐⣒
⠀⠀⠀⠈⠰⠾⠟⠃⠀⠘⠍⢹⡿⠿⠀⠀⠀⠀⣾⣿⣿⣿⡀⢠⣿⣿⣿⡇⠀⠈⢻⣿⣿⣿⣿⣦⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠖⠉⠁⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿
⠀⠉⣈⢠⣤⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⢀⣸⣿⣿⣿⣧⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⠐⣾⣿⣿⡇⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⢿⣿⣿⣿⣿⡇⢀⣀⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣶⣤⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡋⣉⣿⣿⣟⣀⣸⣿⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⢛⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢻⣿⡿⣿⣿⡇⣿⣿⣽⣿⡧⠈⣛⡿⢿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢈⣋⠀⠀⢿⣿⣿⣿⣿⡟⠻⠿⢀⣾⣟⣿⣧⢸⣿⡟⢿⣿⣄⣿⣿⣶⣶⣶⣈⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠇⠀⠘⢻⠿⣿⣿⣿⣿⣿⣿⣦⣼⣿⣼⣿⣻⣿⣿⣾⣿⣷⣾⡿⡿⠿⠿⠿⠿⠟⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠿⣿⠿⠿⡿⠿⣿⠶⢦⠶⣤⠦⡶⢶⠶⢦⡀⢀⡴⠶⠯⣥⠴⠦⡤⠶⢤⡤⠶⠦⣤⠦⡤⢦⣠⠴⠶⢤⠴⠶⣤⠶⠾⢯⡁⡷⠷⠿⡾⠷⠦⢤⠴⢦⠶⢦⠴⠶⡴⠶⢦⣷⠿⠿⢿⠿⢿⠿⢿⠿⠿⡿⠿⢿⣿
⣿⡇⢸⢤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⡷⠀⠶⡇⢠⠘⡇⠀⡆⢸⡄⠃⣼⢹⠀⠰⡇⠀⡆⢸⠀⠐⢀⡏⡇⠀⠆⡀⠀⠆⣸⠀⢸⠀⠸⠀⠀⡇⠰⢾⣿⡆⠀⣾⠀⣿⠀⠸⠀⠀⡇⠰⢾⣿
⣿⡇⠸⠀⢸⠀⠶⡇⢸⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⣿⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡇⢸⠀⢰⡇⠀⠇⢸⠀⢰⠀⣷⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⣷⡇⠀⣿⠀⢿⠀⡄⠀⠀⡇⠰⢾⣿
⠟⠛⠲⢷⠚⠲⠖⠳⠺⠖⠗⢺⢲⠓⠒⠓⠚⣶⣾⣖⣋⠓⠚⢲⠖⠒⠒⠒⠚⠒⠒⠒⠒⠋⠑⠒⠁⠘⠒⠚⠉⠒⠒⠛⠒⠚⠒⠁⠓⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠒⠒⠓⠒⢺⣿⣷⣶⠛⠒⠚⠒⠓⢷⣶⣷⣶⠚⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡏⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠦⢄⠀⢠⡀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠈⡆⢸⣷⠀⠀⠀⠀⠀⠘⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠇⠀⠀⠀⠀⠀⠀
⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠘⣀⣀⣀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⣿⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢠⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠐⣷⣦⡀⠀⠀⠀⠀⠀⢸⣿⣏⠀⠀⣼⣿⣿⣿⣷⡀⠀⢸⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡀⠀⠀⠀⢀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀
⠿⣿⣿⣿⣿⠁⣀⣀⣀⣀⣰⡿⢿⣷⣄⠀⠀⠀⠀⣸⣿⣯⠀⠀⣿⣿⣿⣿⣿⣿⣆⢸⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣧⠀⠀⠀⣼⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠑⠈⣿⣿⣿⣿⣿⣆⢸⣿⣿⠀⠀⠀⠀⣽⣿⣿⣄⠀⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣾⣿⣿⠿⠋⠀⠀⢘⣀⡀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣦⣀⣾⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣼⣿⡇⠀⠀⠀⢠⣿⣿⣿⣿⠀⣿⣿⣿⡇⠘⢿⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⣧⣄⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣷⣁⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠠⠐⠾⣿⠛⣟⣏⠮⠭⣽⡟⡿⠇⠀⠀⠀⣽⣿⣿⣿⣿⠀⣿⣿⣿⡇⠀⠈⢻⣿⣿⣿⣿⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠉⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠘⠁⢵⣸⣶⡆⣺⠖⣍⠟⡒⠺⡄⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣸⣿⣿⣿⣧⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⢿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢆⣰⣾⣿⣿⣷⠀⢐⢀⠀⣶⣀⣖⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⢿⣿⣿⣿⣿⡇⠀⣀⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣮⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⠋⣉⣿⣿⣟⣀⣸⣿⣿⣤⣼⣿⣿⣿⣿⣿⣿⣿⢛⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢻⣿⡿⢿⣿⡇⣿⣿⣭⣿⡇⠈⣻⡿⢿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣯⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢈⣛⡀⠀⢿⣿⣿⣿⣿⡿⠻⠿⢀⣾⣟⣿⣧⢸⣿⡟⢿⣿⡄⣿⣿⣶⣶⣶⣘⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠀⠘⠻⠿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣼⣿⣛⣿⣿⣾⣿⣷⣾⣿⡿⠿⠿⠿⠿⠟⠟⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⢶⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣽⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠿⣿⠿⠿⡿⠿⣿⠶⢤⠶⣤⠦⡴⢶⠶⢦⡀⢀⡴⠶⠯⣥⠶⠦⡤⠶⢤⡤⠶⠦⣤⠦⡤⢦⣠⠴⠶⢤⠶⠶⣶⠶⠿⢯⡉⡷⠶⠿⡿⠷⠦⢤⠴⢦⠶⢦⠴⠶⡶⠶⢾⣦⠿⠿⢿⠿⢿⠿⢿⠿⠿⡿⠿⢿⣿
⣿⡇⢸⣤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⣿⠀⠶⡇⢠⠘⡇⠀⡆⢸⡄⠃⣼⢹⠀⠰⡆⠀⡆⢸⠀⠐⢀⡏⡇⠀⠂⡀⠀⠆⣸⠀⢸⠀⠸⠀⠀⡇⠰⢾⣿⡆⠀⣾⠀⣿⠀⠸⠀⠀⡇⠰⢾⣿
⣿⡇⠸⠀⢸⠀⠶⡇⢸⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⣿⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡇⣾⠀⢰⡇⠀⠇⢸⠀⢰⠀⣿⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⣷⡇⠀⣿⠀⣿⠀⡄⠀⠀⡇⠰⢾⣿
⠟⠛⠲⢷⠚⠲⠖⠳⠺⠖⠗⢚⢲⠓⠒⠓⠚⢶⣾⣖⣋⠓⠚⢲⠛⠒⠒⠒⠚⠒⠒⠒⠒⠋⠑⠒⠁⠈⠒⠊⠙⠒⠒⠛⠒⠚⠒⠁⠓⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠒⠒⠓⠒⣾⣿⣷⡖⠛⠒⠚⠒⠓⣷⣶⣷⣶⠚⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠦⢄⠀⢀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠈⡆⢸⣧⠀⠀⠀⠀⠀⢻⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀
⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⠀⢐⡀⣀⣀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⣿⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⣰⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⣿⣶⣄⠀⠀⠀⠀⠀⢸⣿⣿⡧⠀⢸⣿⣿⣿⣷⡀⠀⢸⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⣿⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣧⠀⠀⠀⠀⢰⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀
⢿⠿⠿⣿⣿⡇⣤⣤⣤⣠⣤⡿⠿⣿⣦⡄⠀⠀⠀⢸⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣆⢸⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⡏⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡆⠀⠀⢀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠐⠀⠿⣿⣿⣿⣿⣷⡀⣿⣿⠇⠀⠀⠀⣸⣿⣿⣿⡀⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣾⣿⣿⠿⠋⠀⠀⢘⣀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⢀⣾⣿⣿⡟⠀⠀⠀⠀⢀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⣠⣿⣿⣿⢿⣿⣿⣷⣿⣧⠀⠀⠀⢠⣿⣿⣿⣿⡇⣿⣿⣿⡇⠙⢿⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⣧⡀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⢿⣿⣿⣿⣿⣯⣄⣀⣦⣦⣰⣪⣴⣦⣴
⠀⢀⠠⣰⣵⣿⡿⠟⢯⠺⢯⡻⣟⢿⠋⠀⠀⠠⣶⣿⣿⣿⣿⡇⣿⣿⣿⡇⠀⠈⢻⣿⣿⣿⣿⣦⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠊⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠒⣢⣴⣿⣼⢧⣌⢸⡖⣁⠁⠈⢀⠀⠀⠠⣺⣿⣿⣿⣿⣿⣷⣿⣿⣿⣧⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⢿⣿⣿⣿⣿⣿⠿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣵⣆⣿⣿⣿⣷⣹⠧⠅⢼⣻⣶⣶⣷⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢘⣿⣿⣷⣿⣿⣿⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠋⢉⣽⣿⣟⣀⣸⣿⣿⣤⣼⣿⣿⣿⣿⣿⣿⣿⢻⣿⡿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢻⣿⡿⢿⣿⡇⣿⣿⣭⣿⡇⠘⣻⡿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣎⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠈⣘⡀⠀⠹⣿⣿⣿⣿⡿⠻⠿⢀⣾⣟⣿⣧⢸⣿⡟⢿⣿⡄⣿⣿⣵⣶⣶⣘⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠀⠘⠻⠿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣼⣿⣛⣿⣿⣾⣿⣷⣾⣿⣿⠿⡿⠿⠿⠿⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⣆⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢼⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠿⣿⠿⠿⡿⠿⣿⠶⢦⠶⣤⠦⡴⢶⠶⢦⡀⢀⡴⠶⠿⣥⠶⠦⡤⠶⢤⡤⠶⠦⣤⠦⡤⢦⣠⠴⠶⢤⠶⠶⣶⠶⠶⢯⡉⡷⠶⠶⡶⠷⠦⢤⠴⢦⠶⢤⠴⠶⡶⠶⢿⣼⠿⠿⢿⠿⣿⠿⢿⠿⠿⡿⠿⢿⣿
⣿⡇⢸⡤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⣿⠀⠶⡇⢠⠘⡇⠀⡆⢸⡄⠃⣼⢹⠀⠰⡆⠀⡆⢸⠀⠐⢀⡟⡇⠀⠆⡀⠀⠆⣸⠀⢸⠀⠘⠀⠀⡇⠰⢾⢿⡆⠀⣾⠀⣿⠀⠸⠀⠀⡇⠰⢾⣿
⣿⡇⠸⠀⢸⠀⠶⡇⢸⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⣿⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡏⢸⠀⢰⡇⠀⠇⢸⠀⢰⠀⣿⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⣶⡇⠀⣿⠀⣿⠀⡄⠀⠀⡇⠰⢾⣿
⠟⠛⠲⢷⠚⠲⠖⠳⠺⠖⠗⢚⢲⠓⠒⠓⠚⢶⣾⣖⣋⠓⠚⢶⠛⠒⠒⠒⠚⠒⠒⠒⠒⠋⠑⠒⠁⠈⠒⠊⠉⠒⠒⠛⠒⠚⠒⠁⠓⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠒⠒⠓⠲⣾⣿⣷⠖⠛⠒⠚⠒⠓⣷⣶⣷⣶⠚⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠦⢄⠀⢀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁⠀⠀⠀⠀⠀⠀
⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⣄⠀⡆⢸⣧⠀⠀⠀⠀⠈⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⠄⣀⣀⠀⠀⠀⢰⣿⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⠀⠀⠀⠀⠀⢀⣼⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⢸⣿⣦⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢸⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⣿⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡇⠀⠀⠀⠀⣸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀
⢛⢻⠿⣿⣿⣧⣤⣴⣤⣤⣤⡿⠿⣿⣷⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢸⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡀⠀⠀⢰⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠉⠀⣻⣿⣿⣿⣿⣿⡄⣿⣿⠇⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣶⣿⣿⠿⠋⠀⠀⢘⡀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣧⡀⢴⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠄⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡇⠙⢿⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⣦⡀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⠿⣿⣿⣿⣿⣃⡀⢀⣀⣀⣀⣀⣠⣴⣶
⠀⠀⠀⠀⣴⣾⠟⡿⠋⢪⠋⡍⡻⠿⠟⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⢻⣿⣿⣿⣿⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠊⠉⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠡⢀⠀⣮⣿⣿⡟⢾⣊⣲⠺⢛⠩⡀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⢿⣿⣿⣿⣿⣿⡿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣖⣿⣿⣿⣯⡏⣪⣛⡿⢰⣬⣷⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣷⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣷⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠋⢉⣽⣿⣟⣀⣸⣿⣿⣤⣬⣿⣿⣿⣿⣿⣿⣿⢻⣿⡿⢿⣿⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢻⣿⡿⢿⣿⡇⣿⣿⣭⣿⡇⠘⣻⠿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣄⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣘⡁⠀⠹⣿⣿⣿⣿⡿⠿⠿⢂⣼⣟⣿⣧⢸⣿⡿⣿⣿⡄⣿⣿⣵⣶⣶⣘⣿⣿⣿⣿⣵⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠀⠀⠛⠿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣾⣿⣛⣿⣿⣾⣿⣷⣾⣿⡿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡱⡆⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠿⣿⠿⠿⡿⠿⣿⠷⢦⠶⣤⠦⡴⢶⠶⢦⡀⢀⡴⠶⠾⣥⠶⠦⡤⠿⢭⡥⠶⠦⣤⠦⡤⢤⣠⠴⠶⢶⠶⠶⣶⠾⠾⢯⡉⡷⠶⠿⡿⠶⠦⢤⠴⢦⠶⢦⠴⠶⡶⠶⢷⣼⠿⠿⢿⠿⣿⠿⢿⠿⠿⡿⠿⢿⣿
⣿⡇⢸⣤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⣿⠀⠶⡇⢠⠘⡇⠀⡆⢸⡄⠃⣼⢹⠀⠰⡆⠀⡆⢸⠀⠐⢀⡟⡇⠀⠆⡀⠀⠆⣸⠀⢸⠀⠸⠀⠀⡇⠰⢾⢿⡆⠀⣾⠀⣿⠀⠸⠀⠀⡇⠰⢾⣿
⣿⡇⠸⠀⢸⠀⠶⡇⢸⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⣿⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡏⢸⠀⢰⡇⠀⠇⢸⠀⢰⠀⣿⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⣶⡇⠀⣿⠀⣿⠀⡄⠀⠀⡇⠰⢾⣿
⠿⠛⠲⢷⠚⠲⠖⠳⠺⠖⠗⢚⢲⡗⠒⠓⠚⢶⣾⣖⣋⠓⠚⠶⠛⠒⠒⠒⠚⠒⠒⠒⠒⠋⠑⠒⠁⠈⠒⠊⠙⠒⠒⠛⠒⠚⠒⠁⠓⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠚⠒⠓⢲⣾⣿⣷⠒⠛⠒⠚⠒⠳⣷⣶⣷⣶⠚⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠦⢄⠀⢀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠀⠀⠀⠀⠀⠀⠀
⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⣄⠀⡆⢸⣆⠀⠀⠀⠀⠘⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣻⣿⣿⡀⢀⣀⠀⠀⠀⢰⣿⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⣿⠀⠀⠀⠀⠀⢻⣿⣿⣿⣇⠀⠀⠀⠀⠀⢀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⢸⣿⣶⠀⠀⠀⠀⠀⢸⣿⣿⣼⣿⣿⣿⣿⣿⣷⡀⠀⢸⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⣿⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡄⠀⠀⠀⠀⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀
⠻⠿⠿⢿⣿⣷⣤⣤⣤⣤⣤⣾⠟⢿⣿⣆⠀⠀⠀⢸⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣄⢸⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⠀⠀⠀⣸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠛⠁⢙⣿⣿⣿⣿⣿⣄⢸⣿⡟⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣾⣿⣿⠿⠋⠀⠀⢘⡀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣆⠀⣰⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠙⢿⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⣤⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠻⣿⣿⣿⣿⣥⠀⢀⣀⣀⣀⣀⣀⣤⣤
⠀⠀⠀⠀⣰⡷⠟⡿⣛⡿⡮⡯⠿⠟⠏⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⢻⣿⣿⣿⣿⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠊⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⠂⣰⣾⣷⣷⢚⣫⠵⢐⣠⠁⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⠿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡄⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣛⣠⣲⣿⣿⣿⣷⣐⡤⡍⢄⣴⣷⣶⣶⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠅⠀⢸⣿⣿⣷⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣷⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠋⢉⣽⣿⣟⣀⣸⣿⣿⣤⣭⣿⣿⣿⣿⣿⣿⣿⢻⣿⡿⣿⣿⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢻⣿⡿⢿⣿⡇⣿⣿⣭⣿⡇⠘⣻⠿⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣘⡁⠀⠹⣿⣿⣿⣿⡿⠻⠿⢂⣼⣟⣿⣧⢸⣿⡿⣿⣿⡄⣿⣿⣵⣶⣶⣙⣿⣿⣿⣿⣵⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠀⠀⠛⠿⣷⣿⣿⣿⣿⣿⣧⣴⣿⣾⣿⣛⣿⣿⣾⣿⣷⣾⣿⣿⣿⠿⠿⠿⠿⠟⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⡄⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠁⠀⠀⠀⠀⠠⠄⠀⠀⢀⡀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠿⣿⠿⠿⡿⠿⣿⠷⢦⠶⣤⠦⡴⢶⠶⢦⡀⢀⡴⠶⠾⣵⠶⠦⡬⠿⢭⡭⠿⠯⣤⠦⡤⢤⣠⠴⠶⢶⠶⠶⣷⠶⠿⢯⡉⡷⠾⠿⡿⠶⠦⢤⠴⢤⠶⢤⠴⠶⡴⠾⢧⣾⠾⠿⢿⠿⢿⠿⢿⠿⠿⡿⠿⢿⣿
⣿⡇⢸⣤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⣿⠀⠶⡇⢠⠘⡇⠀⡆⢸⡄⠃⣼⢹⠀⠰⡆⠀⡆⢸⠀⠐⢀⡟⡇⠀⠆⡀⠀⠆⣸⠀⢸⠀⠸⠀⠀⡇⠰⢾⣿⡆⠀⣾⠀⣿⠀⠸⠀⠀⡇⠰⢾⣿
⣿⡇⠸⠀⢸⠀⠶⡇⢸⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⣿⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡇⢸⠀⢰⡇⠀⠇⢸⠀⢰⠀⣿⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⣦⡇⠀⣿⠀⣿⠀⡄⠀⠀⡇⠰⢾⣿
⡿⠛⠲⢷⠚⠲⠖⠳⠺⠖⠗⠚⢲⡗⠒⠓⠚⢶⣾⣖⣋⠓⠚⠶⠛⠒⠒⠒⠚⠒⠒⠒⠒⠋⠑⠒⠃⠈⠒⠊⠙⠒⠒⠛⠒⠚⠒⠁⠓⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠒⠒⠓⢶⣾⣿⣷⠒⠛⠒⠚⠒⠳⣷⣶⣷⣶⠚⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡟⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠦⢄⠀⢀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀
⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣠⠖⣫⣶⣿⣿⣿⣦⡄⠀⡆⢸⣆⠀⠀⠀⠀⢸⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣾⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣿⡇⢀⣀⠀⠀⠀⢰⣿⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣼⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⢸⣿⡏⠀⠈⣿⣿⣿⣿⣷⡀⠀⢸⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⣿⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⡀⠀⠀⠀⢸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠙⠿⠿⣿⡇⣠⣾⣶⣤⣶⣾⠟⢻⣿⣶⠀⠀⠀⢸⣿⡏⠀⢀⣿⣿⣿⣿⣿⣿⣄⢸⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⠇⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣇⠀⠀⢀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠂⠘⣿⣿⣿⣿⣿⣧⢸⣿⡟⠀⠀⠀⣼⣿⣗⢄⣺⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣶⣿⣿⠿⠋⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡄⢠⣾⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⠿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠙⢿⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⣄⡀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠉⠻⣿⣿⣿⣿⣦⣄⣤⣄⣀⣦⣴⣶⣴⣵
⠀⠀⠀⠄⣠⣻⠛⠛⠙⢃⠀⠀⠘⠛⠛⠁⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⢻⣿⣿⣿⣿⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠉⠉⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣾⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⠿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣀⣤⣾⣿⣿⡗⠀⠀⢀⠀⣰⣠⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣷⣾⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣧⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢉⣽⣿⡟⢀⣸⣿⣿⣤⣭⣿⣿⣿⣿⣿⣿⡿⢻⣿⡿⢿⣿⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢻⣿⡿⢿⣿⡏⣿⣿⣭⣿⡇⠘⢿⠿⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⢀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣙⡃⠀⠸⣿⣿⣿⣿⡿⠿⠿⢂⣼⣟⣿⣧⢸⣿⡿⣿⣿⡀⣿⣿⣭⣶⣶⣙⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠿⠟⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠀⠀⠛⡿⣷⣾⣿⣿⣿⣿⣧⣴⣷⣾⣿⣛⣿⣿⣾⣿⣧⣾⣿⣿⠿⠿⠿⠿⠟⠟⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣷⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡌⡯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠿⣿⠿⠿⡿⠿⣿⠷⢦⠶⣤⠦⡴⢶⠶⢦⡀⢀⡴⠶⠾⣵⠶⠶⡬⠿⢭⡭⠿⠯⣭⠧⡴⢦⣠⠶⠶⢶⠶⠶⣶⠶⠿⢯⡁⡶⠶⠾⡷⠶⠦⢤⠴⢦⠶⢦⠴⠶⡴⠾⢧⣿⠾⠿⢿⠿⢿⠿⢿⠿⠿⡿⠿⢿⣿
⣿⡇⢸⣤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⣿⠀⠶⡇⢠⠘⡇⠀⡆⢸⡄⠃⣼⢹⠀⠰⡇⠀⡆⢸⠀⠐⢀⡟⡇⠀⠆⡀⠀⠆⣸⠀⢸⠀⠸⠀⠀⡇⠰⢾⣿⡆⠀⣾⠀⣽⠀⠸⠀⠀⡇⠰⢾⣿
⣿⡇⠸⠀⢸⠀⠶⡇⢸⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⣿⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡇⢸⠀⢰⡇⠀⠇⢸⠀⢰⠀⣿⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⣬⡇⠀⣿⠀⢿⠀⡄⠀⠀⡇⠰⢾⣿
⡿⠟⠲⢷⠚⠶⠖⠳⠺⠖⠗⠚⣶⡗⠒⠓⠚⢶⣾⣖⣋⠓⠚⠖⠛⠒⠒⠒⠚⠒⠒⠒⠒⠋⠑⠒⠃⠈⠒⠊⠙⠒⠒⠛⠒⠚⠒⠁⠓⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠒⠒⠓⣶⣾⣿⡗⠒⠛⠒⠚⠒⢳⣷⣶⣷⣶⠚⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⣿⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠦⢄⠀⢀⠀⠀⠀⠀⠸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⢹⣿⣿⠄⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠀⡆⢸⡆⠀⠀⠀⠀⢿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⣿⢁⣀⠀⠀⠀⢰⣿⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⣿⠀⠀⠀⠀⠘⣿⣿⣿⣷⡀⠀⠀⠀⠀⢀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⢀⣿⣿⣆⠀⠀⠀⠀⢀⣿⡇⠀⠀⣿⣿⣿⣿⣷⡀⠀⢸⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⡿⠀⠀⠀⠀⠀⢻⣿⣿⣿⣧⠀⠀⠀⠀⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠻⠻⢿⡿⣤⣶⣶⣶⣶⣾⡟⢻⣿⣷⡀⠀⠀⢸⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣄⢸⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⠇⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡄⠀⠀⢠⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣷⠸⣿⡿⠀⠀⠀⢸⣿⣷⠀⢠⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣶⣿⣿⠿⠋⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⡀⣠⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠠⣾⣿⣿⡿⠟⣿⣻⣾⣿⡇⠀⠀⠀⣿⣿⣷⠀⢸⣿⣿⣿⡇⠙⢿⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⣄⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠈⠻⣿⣿⣿⣇⡀⢄⣄⣔⣤⣔⣤⣦⣤⣵
⠀⠀⠀⠀⠐⢸⠛⠙⠙⠉⠀⠀⠀⠈⠛⠁⠀⠀⣰⣿⣿⣷⣧⣼⣿⣿⣿⡇⠀⠈⢻⣿⣿⣿⣿⣄⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠍⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣦⣾⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⡗⣿⣿⣿⣿⣧⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⠿⢇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣀⣀⣺⣿⣿⣏⠀⠀⠀⠀⠀⢤⣤⣴⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣽⣿⣿⠀⠀⢸⣿⣿⣷⣾⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣆⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣾⣧⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠛⢉⣹⣿⡟⢀⣸⣿⣿⣤⣭⣿⣿⣿⣿⣿⣿⡟⢻⣿⡿⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣟⠺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡿⢿⣿⡏⣿⣿⣭⣽⡇⠘⢿⠿⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣙⡃⠀⠸⣿⣿⣿⣿⡿⠿⠿⠆⣼⣿⣿⣇⢸⣿⡿⣿⣿⡀⣿⣿⣭⣶⣶⣙⣿⣷⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⠿⠗⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠀⠀⠛⠿⣷⣾⣿⣿⣿⣿⣧⣴⣷⣺⣿⣛⣿⣿⣾⣿⣧⣾⣿⣿⠿⠿⠿⠿⠟⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣦⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠋⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⢸⡯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠿⣿⠿⠿⡿⠿⣿⠷⢦⠶⣤⠦⡴⢶⠶⢦⡀⢀⡴⠶⠾⣷⠶⠶⡭⠿⢯⡭⠿⠯⣭⠧⡴⢦⣠⠶⠶⢶⠶⠶⣶⠶⠶⢦⣀⡶⠶⠶⡶⠶⠦⢤⠴⢦⠶⢤⠴⠦⡴⠾⢶⣷⠾⠿⢿⠿⢿⠿⢿⠿⠿⡿⠿⢿⣿
⣿⡇⢸⡤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⣿⠀⠶⡇⢠⠘⡇⠀⡆⢸⡀⠃⣼⢹⠀⠰⡇⠀⡆⢸⠀⠐⢀⡟⡇⠀⠆⡀⠀⠆⣸⠀⢸⠀⠘⠀⠀⡇⠰⢾⣿⡆⠀⣾⠀⣹⠀⠸⠀⠀⡇⠰⢾⣿
⣿⡇⠸⠀⢸⠀⠶⡇⢸⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⣿⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡇⢸⠀⢰⡇⠀⠇⢸⠀⢰⠀⣿⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⣬⡇⠀⣿⠀⢿⠀⡄⠀⠀⡇⠰⢾⣿
⡿⠟⠲⢷⠚⠲⠖⠳⠺⠖⠗⠚⣖⡗⠒⠓⠚⢶⣾⣖⣋⠓⠚⠖⠛⠒⠒⠒⠚⠒⠒⠒⠒⠋⠑⠒⠁⠘⠒⠊⠙⠒⠒⠛⠒⠚⠒⠁⠓⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠒⠒⠓⣶⣾⣿⠓⠒⠛⠒⠚⠒⢷⣷⣶⣷⣶⠚⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠦⢄⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⢸⣿⡀⣦⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠀⡆⢸⡆⠀⠀⠀⠘⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣿⡷⠀⠀⣿⣿⣿⣀⠀⠀⠀⢰⣿⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠟⠛⠶⠀⢸⣷⠀⠀⠀⠀⢹⣿⣿⣿⣧⠀⠀⠀⠀⠀⣸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⢠⣿⣷⠀⠀⢹⣿⣿⣿⣧⡀⠀⢸⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⡿⠀⠀⠀⠀⠈⢿⣿⣿⣿⡆⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠉⠛⠛⢿⣿⣦⣿⣿⣶⣾⣾⡟⠻⣿⣿⡄⠀⠀⢸⣿⡏⠀⠀⣼⣿⣿⣿⣿⣿⣄⢸⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⠇⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⠀⠀⠀⣼⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢉⣟⣿⣿⣿⣷⡄⣿⡿⠃⠀⠀⣸⣿⣷⠀⠀⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣶⣿⣿⠿⠋⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⣀⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀
⠀⠀⠀⠀⠀⢠⣸⣿⣿⣿⠛⠿⣿⣽⣿⡷⠀⠀⠀⣿⣿⣿⠂⠐⣿⣿⣿⡇⠙⢿⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⣄⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⠈⠻⣿⣿⣿⣄⢠⣤⣤⣴⣶⣾⣶⣶⣿⣿
⠀⠀⠀⠐⠬⠑⠛⠋⠉⠁⠂⠄⠉⠉⠉⠁⠀⠀⣺⣿⣿⣿⣆⢰⣿⣿⣿⡇⠀⠈⢻⣿⣿⣿⣿⣀⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠍⠁⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣼⣥⣆⠀⠀⠀⠀⠁⠀⠀⠀⠀⣀⣰⣿⣿⣿⣿⣟⣼⣿⣿⣿⣧⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⡿⢇⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣆⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣀⣸⣿⣿⣿⢀⠐⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣽⣿⣿⠀⠀⢸⣿⣿⣷⣾⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⡆⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣷⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠛⢉⣿⣿⡟⢀⣸⣿⣿⣤⣭⣿⣿⣿⣿⣿⣿⡟⢻⣿⡿⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣏⠲⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡿⢿⣿⡏⣿⣿⣭⣽⡅⠘⢿⠿⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡇⠀⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣙⡃⠀⠸⣿⣿⣿⣿⡿⠿⠿⠆⣼⡟⣿⣇⢸⣿⡿⣿⣿⡀⣿⣿⣭⣶⣦⣙⣿⣷⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠿⠓⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠀⠀⠛⠿⢷⣾⣿⣿⣿⣿⣧⣴⣷⣺⣿⣛⣻⣿⣾⣿⣧⣾⣿⣿⡿⠿⠿⠿⠿⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⣆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢸⡧⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠿⣿⠿⠿⡿⠿⣿⠷⢦⠶⣤⠦⡴⢶⠶⢦⡀⢀⡴⠶⠾⣿⠶⠶⡼⠿⢯⡽⠿⠯⣭⠧⡴⢦⣠⠶⠶⢶⠶⠶⣶⠶⠶⢮⣁⡶⠶⠾⡶⠶⠦⢤⠴⢦⠶⢦⠴⠶⡶⠿⢾⣧⠾⠿⢿⠿⢿⠿⢿⠿⠿⡿⠿⢿⣿
⣿⡇⢸⣤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⣿⠀⠶⡇⢠⠘⡇⠀⡆⢸⡄⠃⣼⢹⠀⠰⡇⠀⡆⢸⠀⠐⢀⡟⡇⠀⠆⡀⠀⠆⣸⠀⢸⠀⠸⠀⠀⡇⠰⢾⣿⡆⠀⣾⠀⣿⠀⠸⠀⠀⡇⠰⢾⣿
⣿⡇⠸⠀⢸⠀⠶⡇⢸⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⣿⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡇⢸⠀⢰⡇⠀⠇⢸⠀⢰⠀⣿⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⣭⡇⠀⣿⠀⢿⠀⡄⠀⠀⡇⠰⢾⣿
⣿⠟⠲⢷⠚⠶⠖⠳⠺⠖⠗⠚⡖⡗⠒⠓⠚⢲⣾⣖⣋⠓⠚⠖⠛⠒⠒⠒⠚⠒⠒⠒⠒⠋⠑⠒⠁⠘⠒⠊⠙⠒⠒⠛⠒⠚⠒⠁⠓⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠚⠒⢳⣶⣾⣿⠑⠒⠛⠒⠚⠒⢷⣷⣶⣷⣶⠚⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠦⢄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠀⡆⢸⡄⠀⠀⠀⠸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢿⡄⢠⣀⠀⠀⠀⢰⣿⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠟⠛⠲⠀⢸⣧⠀⠀⠀⠀⣿⣿⣿⣿⡆⠀⠀⠀⠀⢀⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣷⠆⠀⠀⠀⠀⠀⣿⣿⣧⡀⠀⠀⠀⢀⣿⡧⠀⠀⢹⣿⣿⣿⣧⡀⠀⢸⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⡟⠀⠀⠀⠀⠘⣿⣿⣿⣿⡀⠀⠀⠀⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠉⠙⠛⢿⣿⠢⣾⣷⣶⣶⣿⡏⠉⣿⣿⡆⠀⠀⢸⣿⡗⠀⠀⣼⣿⣿⣿⣿⣿⣄⢸⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⠇⠀⠀⠀⠀⠀⠘⣿⣿⣿⣇⠀⠀⣰⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢉⡻⣿⣿⣿⣿⡆⣿⣿⠃⠀⠀⢸⣿⣇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣶⣿⣿⠿⠋⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠧⣠⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠟⠻⠿⣿⣿⣿⠀⠀⠀⣿⣿⣿⠀⠀⣿⣿⣿⡇⠙⣿⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⣄⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⠈⠻⣿⣿⣧⡀⣤⣤⣆⣐⣦⣕⣶⣦⣬⣶
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠈⠉⠋⠁⠀⠀⢰⣿⣿⣿⠂⠀⣿⣿⣿⡇⠀⠈⢻⣿⣿⣿⣿⣀⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠍⠃⠀⠀⠀⠀⠀⢹⣿⣿⣇⠀⠀⠈⢿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣸⣤⣄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣾⣿⣿⣿⠖⢈⣿⣿⣿⣧⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣠⣺⣿⣿⣿⡂⠀⠀⠀⣀⣴⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣽⣿⣿⠀⠀⢸⣿⣿⣷⣾⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠛⢉⣻⣿⡟⢀⣸⣿⣿⣤⣭⣿⣿⣿⣿⣿⣿⡟⢻⣿⠿⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣍⠰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡿⢿⣿⡏⣿⣿⣭⣿⡅⠘⢿⠿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⡛⡃⠀⠸⣿⣿⣿⣿⡿⠿⠿⠆⣼⡿⣿⣇⢸⣿⡿⣿⣿⡀⣿⣿⣭⣶⣆⣙⣿⣷⣿⣯⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠀⠀⠛⡿⣷⣾⣿⣿⣿⣿⣧⣴⣷⣾⣿⣛⣻⣿⣾⣿⣧⣾⣿⣿⡿⠿⠿⠿⠿⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⡆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⢹⠤⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠿⣿⠿⠿⡿⠿⣿⠷⢤⠶⣤⠦⡴⢶⠶⢦⡀⢀⡴⠶⠾⣿⠶⠶⡽⠿⢯⡽⠿⠿⣽⠷⡴⢶⣠⠶⠶⢶⠶⠶⣶⠶⠾⢦⣉⡶⠶⠾⡶⠶⠦⢤⠴⢦⠶⢦⠴⠶⡶⠿⢾⣧⠼⠿⢿⠿⢿⠿⢿⠿⠿⡿⠿⢿⣿
⣿⡇⢸⣤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⣿⠀⠶⡇⢠⠘⡇⠀⡆⢸⡀⠃⣼⢹⠀⠰⡇⠀⡆⢸⠀⠐⢀⡿⡇⠀⠂⡀⠀⠆⣸⠀⢸⠀⠘⠀⠀⡇⠰⢾⣿⡆⠀⣾⠀⣿⠀⠘⠀⠀⡇⠰⢾⣿
⣿⡇⠸⠀⢸⠀⠶⡇⢸⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⣿⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡇⢸⠀⢰⡇⠀⠇⢸⠀⢰⠀⣿⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⣭⡇⠀⣿⠀⢿⠀⡄⠀⠀⡇⠰⢾⣿
⣿⠟⠲⢷⠚⠲⠖⠳⠺⠖⠗⠚⡖⡗⠒⠓⠚⢲⣾⣖⣋⠓⠚⠖⠛⠒⠒⠒⠚⠒⠒⠒⠒⠋⠑⠒⠁⠘⠒⠊⠙⠒⠒⠛⠒⠚⠒⠁⠓⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠒⠒⢳⣶⣾⣿⠑⠒⠛⠒⠚⠒⣷⣷⣶⣷⣶⠚⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠦⢄⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠀⡆⢸⡄⠀⠀⠀⢹⣿⣿⣿⣇⠀⠀⠀⠀⠀⢀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⡄⠀⣀⠀⠀⠀⢰⣿⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⡇⠀⠀⠀⠈⣿⣿⣿⣿⡄⠀⠀⠀⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⣸⣿⣷⡀⠀⠀⠀⢠⣿⡏⠀⠀⢸⣿⣿⣿⣧⡀⠀⢸⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⡏⠀⠀⠀⠀⠸⣿⣿⣿⣧⠀⠀⠀⢰⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠉⠙⠛⢿⣿⡿⣿⣿⣶⣶⣾⣏⠉⣿⣿⡧⠀⠀⢸⣿⡟⠀⠀⢸⣿⣿⣿⣿⣿⣄⢸⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⠇⠀⠀⠀⠀⠀⠹⣿⣿⣿⡆⠀⠀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠉⣹⣿⣿⣿⣿⣿⣦⣹⣿⠁⠀⠀⣸⣿⣷⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣶⣿⣿⠿⠋⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡟⠢⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣬⣿⣿⣿⡿⢿⣿⣿⣿⣿⠀⠀⠀⣾⣿⣿⠀⠀⣿⣿⣿⡇⠙⣿⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⣀⠀⠀⠀⠀⠀⠘⣿⣿⣧⠀⠈⠻⣿⣿⡀⠄⡀⠀⣄⡤⢀⣀⣤⣶⣼⣽
⠂⢀⠀⠐⠔⣤⣿⣟⡛⢹⠻⡠⠻⣛⠛⠉⠀⠀⢰⣿⣿⣿⡀⠀⣿⣿⣿⡇⠀⠈⢻⣿⣿⣿⣿⣀⣠⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠍⠃⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠄⠀⢀⣮⣾⣭⣀⢞⡂⢌⡯⣣⡘⢀⢀⠀⣸⣿⣿⣿⣿⣇⣸⣿⣿⣿⣧⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣰⣤⣺⣿⣿⣿⡧⡷⣧⣴⡶⣴⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣽⣿⣿⠀⠀⢸⣿⣿⣿⣾⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣷⡀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⠛⠋⣿⣿⡟⠀⣸⣿⣿⣤⣭⣿⣿⣿⣿⣿⣿⡟⢿⣿⠿⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡅⠰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡿⢿⣿⡏⣿⣿⣭⣽⡅⠙⢿⠿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣯⠀⠀⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠙⡋⠀⠸⣿⣿⣿⣿⡿⠿⠿⠆⣼⡿⣿⣇⢸⣿⡿⣿⣿⡀⣿⣿⣭⣷⣆⣛⣿⣶⣿⣯⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠿⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠂⠀⠛⠿⣷⣾⣿⣿⣿⣿⣧⣴⣶⣺⣿⣟⣻⣿⣾⣿⣧⣼⣿⣷⡿⠿⠿⠿⠿⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡅⢿⠤⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠿⣿⠿⠿⡿⠿⣿⠷⢤⠶⡤⠦⡴⢶⠶⢦⡀⢀⡴⠶⠾⣿⠶⠶⡾⠿⢿⡿⠿⠿⣽⠷⡶⢶⣠⠶⠶⢶⠶⠶⣶⠶⠶⢧⣠⡶⠶⠶⡶⠶⠦⢤⠴⢦⠶⢦⠴⠶⡶⠷⢾⣤⠾⠿⢿⠿⢿⠿⢿⠿⠿⡿⠿⢿⣿
⣿⡇⢸⣤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⣿⠀⠶⡇⢠⠘⡇⠀⡆⢸⡀⠃⣼⢹⠀⠰⡇⠀⡆⢸⠀⠐⢀⡿⡇⠀⠆⡀⠀⠆⣸⠀⢸⠀⠘⠀⠀⡇⠰⢾⣿⡆⠀⣾⠀⣿⠀⠘⠀⠀⡇⠰⢾⣿
⣿⡇⠸⠀⢸⠀⠶⡇⢸⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⣿⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡇⢸⠀⢰⡇⠀⠇⢸⠀⢰⠀⣷⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⡍⡇⠀⣿⠀⢿⠀⡄⠀⠀⡇⠰⢾⣿
⣿⠟⠲⢷⠚⠲⠖⠳⠺⠖⠗⠚⡖⡗⠒⠓⠚⢲⣾⣖⣋⠓⠚⠒⠛⠒⠒⠒⠚⠒⠒⠒⠒⠋⠑⠒⠁⠈⠒⠊⠙⠒⠒⠛⠒⠚⠒⠁⠓⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠒⠒⢳⣶⣾⡇⠑⠒⠛⠒⠚⠒⣷⣷⣶⣷⣶⠚⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠦⢄⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⠀⠸⣇⠀⠀⠀⠠⠀⠀⠀⠀⠀⣀⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠀⡆⢸⡄⠀⠀⠀⢻⣿⣿⣿⡆⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣀⡀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢻⡀⠀⣀⠐⠀⠀⢰⣿⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⡇⠀⠀⠀⠘⣿⣿⣿⣿⡀⠀⠀⠀⢀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣸⣿⣿⣄⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⣿⣿⣧⡀⠀⢸⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⡇⠀⠀⠀⠀⠹⣿⣿⣿⣇⠀⠀⠀⣸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠉⠉⠙⠻⣿⡟⣾⣿⣷⣿⣾⣟⠋⢿⣿⣧⠀⠀⢈⣿⡇⠀⠀⣸⣿⣿⣿⣿⣿⣄⢸⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⠃⠀⠀⠀⠀⠀⢹⣿⣿⣿⡄⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⡙⢿⣿⣿⣿⡦⢸⣿⠁⠀⠀⣸⣿⣯⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣶⣿⣿⠿⠋⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡛⠀⣼⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⢛⣿⣻⣿⣿⣿⠀⠀⠀⣾⣿⣿⠀⠀⣿⣿⣿⡇⠙⣿⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⣀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠈⠻⢿⣷⣀⡀⡠⣀⡀⡀⣀⣤⣼⣤⣦⣶
⠀⠀⠀⠀⡀⣈⢚⠊⠙⠁⠀⠟⠟⠉⠉⠁⠀⠀⢰⣿⣿⣿⡁⠀⣿⣿⣿⡇⠀⠈⢿⣿⣿⣿⣿⣀⣠⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠍⠁⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⠀⠈⢻⣶⣷⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣰⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣇⣰⣿⣿⣿⣧⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣄⣸⣿⣿⡿⠁⡀⠀⠀⠀⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣽⣿⣿⠀⠀⢸⣿⣿⣿⣶⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⡀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣾⣷⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⠛⠋⣻⣿⡟⠀⣸⣿⣿⣤⣭⣿⣿⣿⣿⣿⣿⡟⢿⣿⠿⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡿⢿⣿⡏⣿⣿⣯⣭⡅⠛⢿⠿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣇⠀⠀⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠛⡋⠀⠸⣿⣿⣿⣿⡿⠿⠿⠆⣼⡿⣿⣇⢸⣿⡿⣿⣿⡀⣿⣿⣭⣵⣆⣻⣿⣶⣿⣯⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠿⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠂⠀⠛⠿⢷⣶⣿⣿⣿⣿⣧⣴⣶⣾⣿⣟⣻⣿⣾⣿⣧⣼⣿⣷⣿⠿⠿⠿⠟⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣸⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡅⢿⠠⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠿⣿⠿⠿⡿⠿⣿⠿⢦⠶⣤⠦⡴⢶⠶⢦⡀⢀⡴⠶⠾⣿⠶⠶⡾⠿⢿⡿⠿⠿⣽⠷⡶⢶⣠⠶⠶⢶⠶⠶⣶⠶⠾⢯⣠⡶⠶⠶⡶⠶⠦⢤⠴⢦⠶⢤⠴⠶⡴⠷⢾⣤⠾⠿⢿⠿⢿⠿⢿⠿⠿⡿⠿⢿⣿
⣿⡇⢸⡤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⡿⠀⠶⡇⢠⠘⡇⠀⡆⢸⡄⠃⣼⢹⠀⠰⡇⠀⡆⢸⠀⠐⢀⡿⡇⠀⠂⡀⠀⠆⣸⠀⢸⠀⠘⠀⠀⡇⠰⢾⣿⡆⠀⣾⠀⣿⠀⠘⠀⠀⡇⠰⢾⣿
⣿⡇⠸⠀⢸⠀⠶⡇⢸⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⣿⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡇⢸⠀⢰⡇⠀⠇⢸⠀⢰⠀⣷⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⡍⡇⠀⣿⠀⢿⠀⡄⠀⠀⡇⠰⢾⣿
⣿⠟⠲⢷⠚⠲⠖⠳⠺⠖⠗⠚⡖⡗⠒⠓⠚⢲⣾⣖⣋⠓⠚⠒⠛⠒⠒⠒⠚⠒⠒⠒⠒⠋⠑⠒⠁⠈⠒⠊⠙⠒⠒⠛⠒⠚⠒⠁⠓⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠒⠒⢳⣶⣾⡇⠑⠒⠛⠒⠚⠒⣷⣷⣶⣷⣶⠚⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠦⢄⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⠀⠘⣇⠀⠀⠀⠀⠠⠀⠀⠀⠀⣀⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠀⡆⢸⡄⠀⠀⠀⣿⣿⣿⣿⡀⠀⠀⠀⠀⢀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⣿⣏⠀⠀⢿⡀⠀⢀⠀⣿⢶⢰⣾⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⡇⠀⠀⠀⢸⣿⣿⣿⣷⠀⠀⠀⠀⣸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡖⠀⠀⠀⠀⠀⢸⣿⣿⣄⠀⠀⠀⠀⣿⡏⠀⠀⢸⣿⣿⣿⣧⡀⠀⢸⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⡇⠀⠀⠀⠀⢻⣿⣿⣿⡇⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠉⠙⠻⣿⠯⢾⣿⣷⣿⣿⣿⠉⢹⣿⣷⠀⠀⠀⣿⡇⠀⠀⢸⣿⣿⣿⣿⣷⣄⢸⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⠃⠀⠀⠀⠀⠀⢻⣿⣿⣿⡀⠀⣼⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⢉⢛⣿⣿⣿⣦⢸⣿⠃⠀⠀⢰⣿⣗⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣶⣿⣿⠿⠋⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠃⠰⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡴⣿⣿⡿⣫⢿⣿⣿⣿⣿⠇⠀⠀⣼⣿⣿⠀⠀⣿⣿⣿⡇⠙⣿⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⣀⠀⠀⠀⠀⠀⢹⣿⣿⡆⠀⠈⠻⢿⡄⣀⠀⢀⣠⣤⣀⣤⣶⣖⣧⣦⣾
⠀⠀⠀⠀⠀⣀⠸⠋⠉⠊⠘⠧⠇⠈⠋⠁⠀⠀⢠⣿⣿⣿⠄⠀⣿⣿⣿⡇⠀⠈⢿⣿⣿⣿⣿⣀⣠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠍⠁⠀⠀⠀⠀⢸⣿⣿⣷⡀⠀⠀⠈⢻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢨⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣧⢐⣿⣿⣿⣧⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣧⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣄⣰⣿⣿⣿⡠⡀⠀⠀⠀⢠⣦⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣽⣿⣿⠀⠀⢸⣿⣿⣿⣷⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⡀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣷⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⠛⠋⣻⣿⡟⠀⣸⣿⣿⣤⣭⣿⣿⣿⣿⣿⣿⡟⢿⣿⡿⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⡀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡿⢿⣿⡏⣿⣿⣯⣭⡅⠻⢿⠿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡇⠀⠀⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠋⡋⠀⠸⣿⣿⣿⣿⡿⠿⠿⠆⣼⡿⣿⣇⢸⣿⡿⣿⣯⡀⣿⣿⣭⣵⣆⣻⣿⣶⣿⣯⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠿⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠇⠀⠛⠿⣷⣶⣿⣿⣿⣿⣧⣴⣶⣺⣿⣟⣻⣿⣾⣿⣧⣼⣿⣷⣿⠿⠿⠿⠿⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣹⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡛⠛⠉⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡅⣿⠠⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠿⣿⠿⠿⡿⠿⣿⠿⢦⠶⣤⠦⡴⢶⠶⢦⡀⢀⡴⠶⠾⣿⠶⠾⡿⠿⢿⡿⠿⠿⣿⠷⡶⢶⣠⠶⠶⢶⠶⠶⣶⠶⠶⢧⣠⡶⠶⠶⡶⠶⠦⢤⠴⢦⠶⢤⠴⠶⡶⠷⢿⣤⠾⠿⢿⠿⢿⠿⢿⠿⠿⡿⠿⢿⣿
⣿⡇⢸⡤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⣿⠀⠶⡇⢠⠘⡇⠀⡆⢸⡄⠃⣼⢹⠀⠰⡇⠀⡆⢸⠀⠐⢀⡿⡇⠀⠆⡀⠀⠆⣸⠀⢸⠀⠘⠀⠀⡇⠰⢾⣿⡆⠀⣾⠀⣿⠀⠸⠀⠀⡇⠰⢾⣿
⣿⡇⠸⠀⢸⠀⠶⡇⢸⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⣿⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡇⢸⠀⢰⡇⠀⠇⢸⠀⢰⠀⣷⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⡅⡇⠀⣿⠀⢿⠀⡄⠀⠀⡇⠰⢾⣿
⣿⠟⠲⢷⠚⠲⠖⠳⠺⠖⠗⠚⡖⡗⠒⠓⠚⢲⣾⣖⣋⠓⠚⠒⠛⠒⠒⠒⠚⠒⠒⠒⠒⠋⠑⠒⠁⠈⠒⠊⠙⠒⠒⠛⠒⠚⠒⠁⠓⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠒⠒⢳⣶⣾⡇⠑⠒⠛⠒⠚⠒⣷⣷⣶⣷⣶⠚⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠦⢄⠀⠀⠀⠀⠀⢿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠘⣗⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠀⡆⢸⡄⠀⠀⠘⣿⣿⣿⣷⠀⠀⠀⠀⠀⣸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⣼⣿⠀⠀⢻⡀⠀⢀⠀⣰⣿⢷⣾⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⡇⠀⠀⠀⢻⣿⣿⣿⣇⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⣿⣿⣿⣿⣿⡖⠀⠀⠀⠀⠀⢸⣿⣿⣄⠀⠀⠀⠀⣿⡏⠀⠀⢸⣿⣿⣿⣧⡈⠈⢸⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⡇⠀⠀⠀⠀⢻⣿⣿⣿⡀⠀⠀⣼⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠉⠙⠻⣿⡏⣿⣿⣷⣾⣿⣿⠉⢹⣿⣷⠀⠀⠀⣿⣷⠀⠀⢸⣿⣿⣿⣿⣿⣄⢸⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⠃⠀⠀⠀⠀⠈⣿⣿⣿⣧⠀⢠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠉⠉⡙⢻⣿⣿⣿⣷⢸⣿⡇⠀⠀⢰⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣶⣿⣿⠿⠋⠀⠀⠈⠀⠀⠀⠀⠀⠀⠸⣿⣿⣯⠁⠺⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣽⣿⣿⣿⣿⣿⡇⠀⠀⢼⣿⣿⠀⠀⣿⣿⣿⡇⠙⣿⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⣀⠀⠀⠀⠀⠀⢿⣿⣿⡀⠀⠈⠛⢇⠀⠀⢄⢠⣄⣀⢢⣀⣠⣤⣶⣦⣿
⠀⠀⠀⠀⠆⠐⢺⠛⠛⠉⠐⠧⠪⠈⠙⠁⠀⠀⢰⣿⣿⣿⡆⠀⣿⣿⣿⡇⠀⠈⢿⣿⣿⣿⣿⣀⣠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠝⠃⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠈⢻⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣠⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣿⣿⣿⣿⡇⢀⣿⣿⣿⣧⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣧⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣠⣤⣐⣿⣿⣿⣧⠀⠀⠠⡀⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣽⣿⣿⠀⠀⢸⣿⣿⣿⣷⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣧⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠛⠋⣻⣿⡟⠀⣸⣿⣿⣤⣭⣿⣿⣿⣿⣿⣿⡟⢿⣿⡿⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣧⡀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡿⢿⣿⡏⣿⣿⣯⣭⡅⠻⢿⠿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡅⠀⠀⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠉⡋⠀⠸⣿⣿⣿⣿⡿⠿⠿⠆⣼⡿⣿⣇⢸⣿⡿⣿⣯⡀⣿⣿⣭⣵⣆⣻⣿⣶⣿⣯⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠟⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠇⠀⠛⠿⢷⣶⣿⣿⣿⣿⣧⣴⣶⣾⣿⣟⣻⣿⣾⣿⣧⣼⣿⣷⣿⠿⠿⠿⠿⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣹⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠉⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⣿⠠⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠿⣿⠿⠿⡿⠿⣿⠿⢦⠶⣤⠦⡴⢶⠶⢦⡀⢀⡴⠶⠾⣿⠶⠾⡿⠿⢿⡿⠿⠿⣿⠷⡶⢶⣠⠶⠶⢶⠶⠶⣶⠶⠾⢧⣀⡶⠶⠾⡶⠶⠦⢤⠴⢦⠶⢤⠴⠦⡶⠷⢿⣤⠾⠿⢿⠿⢿⠿⢿⠿⠿⡿⠿⢿⣿
⣿⡇⢸⡤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⣿⠀⠶⡇⢠⠘⡇⠀⡆⢸⡄⠃⣼⢹⠀⠰⡇⠀⡆⢸⠀⠐⢀⡿⡇⠀⠆⡀⠀⠆⣸⠀⢸⠀⠘⠀⠀⡇⠰⢾⣿⡆⠀⣾⠀⣿⠀⠘⠀⠀⡇⠰⢾⣿
⣿⡇⠸⠀⢸⠀⠶⡇⢸⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⣿⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡇⢸⠀⢰⡇⠀⠇⢸⠀⢰⠀⣷⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⡅⡇⠀⣿⠀⢿⠀⡄⠀⠀⡇⠰⢾⣿
⣿⠟⠲⢷⠚⠶⠖⠳⠺⠖⠗⠚⡖⡗⠒⠓⠚⢲⣾⣖⣋⠓⠚⠒⠛⠒⠒⠒⠚⠒⠒⠒⠒⠋⠑⠒⠁⠈⠒⠊⠙⠒⠒⠛⠒⠚⠒⠁⠓⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠒⠒⣷⣶⣾⡇⠑⠒⠛⠒⠚⠒⣷⣷⣶⣷⣶⠚⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠦⢄⠀⠀⠀⠀⠈⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠘⣧⠀⠀⠀⠀⠀⢀⡆⠀⠀⣀⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠀⡆⢰⡄⠀⠀⢸⣿⣿⣿⣧⠀⠀⠀⠀⢰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⣽⣿⠀⠀⠘⡄⠀⢀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⡇⠀⠀⠀⢿⣿⣿⣿⡄⠀⠀⠀⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⢰⣿⣿⣆⠀⠀⠀⠀⣿⡗⠀⠀⢰⣿⣿⣿⣧⡀⠉⢸⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⡇⠀⠀⠀⠈⢿⣿⣿⣿⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠉⠙⠻⣿⡟⢽⣿⣿⣷⣾⣿⠉⢹⣿⣿⠀⠀⠀⣿⣷⠀⠀⢸⣿⣿⣿⣿⣿⣄⢸⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⠃⠀⠀⠀⠀⠘⣿⣿⣿⣧⠀⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠉⢀⢉⢻⣿⣿⣿⣷⢸⣿⡇⠀⠀⢸⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣶⣿⣿⠿⠋⠀⠀⢈⠀⠀⠀⠀⠀⠀⠹⣿⣿⣇⠉⠻⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⠯⣝⣛⣿⣿⣿⡇⠀⠀⣸⣿⣿⠀⠀⣿⣿⣿⡇⠙⣿⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠈⠙⢆⢀⠀⠠⠠⠀⣀⣀⣠⣤⣠⣤⣴⣿
⠀⠀⠀⠀⠀⡐⠜⡎⠙⠉⠉⠷⠇⠀⠋⠉⠀⠀⢠⣿⣿⣿⠅⠀⣿⣿⣿⡇⠀⠈⢿⣿⣿⣿⣿⣀⣠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠙⠃⠀⠀⠀⠀⢻⣿⣿⣧⠀⠀⠀⠈⢲⣶⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢠⣶⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣿⣿⣿⣿⣇⢀⣿⣿⣿⣧⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣠⣀⣐⣻⣿⣿⣧⣀⠀⢀⡄⢤⣴⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣽⣿⣿⠀⠀⢸⣿⣿⣿⣷⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣆⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠛⠋⣻⣿⡿⠀⣸⣿⣿⣤⣭⣿⣿⣿⣾⣿⣿⡟⢿⣿⡿⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡿⢿⣿⡏⣿⣿⣿⣭⡅⠻⢿⠿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡄⠀⠀⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠉⡋⠀⠉⣿⣿⣿⣿⡿⠿⠿⠆⣼⡿⣿⣇⢸⣿⡿⣿⣯⡀⣿⣿⣭⣵⣆⣻⣿⣶⣿⣯⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⠏⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠇⠀⠛⠿⢷⣶⣿⣿⣿⣿⣧⣴⣶⣾⣿⣟⣻⣿⣾⣿⣧⣼⣿⣷⣿⠿⠿⠿⠿⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣵⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⡿⠠⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠿⣿⠿⠿⡿⠿⡿⠿⢦⠶⣤⠦⡴⢶⠶⢦⡀⢀⡴⠶⠾⣿⠾⠶⡿⠿⢿⡿⠿⠿⣿⠷⡶⢶⣰⠶⠶⢶⠶⠶⣶⠶⠶⢧⣠⡶⠶⠶⡶⠶⠦⢤⠴⢤⠶⢦⠴⠶⡾⠷⢿⣤⠾⠿⢿⠿⢿⠿⢿⠿⠿⡿⠿⢿⣿
⣿⡇⢸⡤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⣿⠀⠶⡇⢠⠘⡇⠀⡆⢸⡄⠃⣼⢹⠀⠰⡇⠀⡆⢸⠀⠐⢀⡿⡇⠀⠆⡀⠀⠆⣸⠀⢸⠀⠘⠀⠀⡇⠰⢾⣿⡆⠀⣾⠀⣿⠀⠘⠀⠀⡇⠰⢾⣿
⣿⡇⠸⠀⢸⠀⠶⡇⢸⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⣿⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡇⢸⠀⢰⡇⠀⠇⢸⠀⢰⠀⣷⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⡅⡇⠀⣿⠀⢿⠀⡄⠀⠀⡇⠰⢾⣿
⣿⠟⠲⢷⠚⠲⠖⠳⠺⠖⠗⠚⡖⡗⠒⠓⠚⢲⣾⣖⣋⠓⠚⠒⠛⠒⠒⠒⠚⠒⠒⠒⠒⠋⠑⠒⠁⠈⠒⠊⠉⠒⠒⠛⠒⠚⠒⠁⠓⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠒⠒⣷⣶⣾⡇⠑⠒⠛⠒⠚⠒⣷⣷⣶⣷⣶⠚⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠐⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢀⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠦⢄⠀⠀⠀⠀⠸⣿⣿⣿⣧⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠐⠀⠀⠀⠀⠀⠀⣤⡀⠀⣀⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠀⡆⢰⡄⠀⠀⢿⣿⣿⣿⡆⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⢠⣤⣀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠈⡆⠀⢀⠀⠀⢰⣿⣿⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⡇⠀⠀⠘⣿⣿⣿⣿⡀⠀⠀⢸⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⢠⣿⣿⣆⡀⠀⠀⠀⣿⣿⠀⠀⢰⣿⣿⣿⣧⡀⠈⢹⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⡇⠀⠀⠀⠘⣿⣿⣿⣧⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠉⠙⠛⣿⣿⢻⣿⣷⣶⣿⣿⡉⢹⣿⣿⠀⠀⠀⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣄⢸⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⠃⠀⠀⠀⠀⠸⣿⣿⣿⡆⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢈⢉⣻⣿⣿⣿⣷⣸⣿⡇⠀⠀⢨⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣶⣿⣿⠿⠋⠀⠀⠈⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠘⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⣽⣿⣿⣯⣏⣻⣿⣿⣿⡇⠀⠀⣼⣿⣿⠀⠀⣿⣿⣿⡇⠙⣿⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠈⣿⣿⣷⠀⠀⠈⠑⠀⠀⠀⢠⠠⠀⢀⣀⣂⣤⣤⣶⣤⣿
⠀⠀⠀⠀⠀⡀⢲⠛⠙⠙⠉⠛⡎⠁⠉⠉⠀⠀⢰⣿⣿⣿⡃⠀⣿⣿⣿⡇⠀⠈⢿⣿⣿⣿⣿⣀⣀⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠙⠃⠀⠀⠀⠀⣿⣿⣿⣇⠀⠀⠀⠀⢢⣴⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣶⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⠀⣿⣿⣿⣧⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣠⣠⣿⣿⣿⣖⣄⡀⢀⠠⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣽⣿⣿⠀⠀⢸⣿⣿⣿⣷⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡆⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠛⠋⣻⣿⡿⠀⢸⣿⣿⣤⣭⣿⣿⣿⣾⣿⣿⡿⢿⣿⡿⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣦⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡿⢿⣿⡏⣿⣿⣿⣽⡅⠻⢿⠿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠉⡋⠀⠉⣿⣿⣿⣿⡿⠿⠿⠄⣼⡿⣿⣇⢸⣿⡿⣿⣯⡀⣿⣿⣭⣽⣆⣻⣿⣶⣿⣯⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⠇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠇⠀⠚⠿⣿⣶⣿⣿⣿⣿⣧⣤⣶⣺⣿⣟⣻⣿⣾⣿⣧⣼⣿⣷⡿⠿⠿⠿⠿⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣷⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡌⡷⠠⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠿⣿⠿⠿⡿⠿⣿⠿⢦⠶⣤⠦⡴⢶⠶⢦⡀⢀⡴⠶⠾⣿⠶⠶⡾⠿⢿⡿⠿⠿⣿⠷⡶⢶⣰⠶⠶⢶⠶⠶⣶⠶⠶⢧⣀⡶⠶⠶⡶⠶⠦⢤⠶⢤⠶⢤⠴⠶⡾⠷⢿⣤⠾⠿⢿⠿⢿⠿⢿⠿⠿⡿⠿⢿⣿
⣿⡇⢸⣤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⣿⠀⠶⡇⢠⠘⡇⠀⡆⢸⡀⠃⣼⢹⠀⠰⡇⠀⡆⢸⠀⠐⢀⡿⡇⠀⠆⡀⠀⠆⣸⠀⢸⠀⠘⠀⠀⡇⠰⢾⣿⡆⠀⣾⠀⣿⠀⠘⠀⠀⡇⠰⢾⣿
⣿⡇⠸⠀⢸⠀⠶⡇⢸⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⣟⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡇⢸⠀⢰⡇⠀⠇⢸⠀⢰⠀⣷⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⡅⡇⠀⣿⠀⣿⠀⡄⠀⠀⡇⠰⢾⣿
⣿⠟⠲⢷⠚⠲⠖⠳⠺⠖⠗⠚⡖⡗⠒⠓⠚⢲⣾⣖⣋⠓⠚⠒⠛⠒⠒⠒⠚⠒⠒⠒⠒⠋⠑⠒⠁⠈⠒⠊⠙⠒⠒⠛⠒⠚⠒⠁⠓⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠒⠒⣷⣶⣾⡇⠑⠒⠛⠒⠚⠲⣷⣷⣶⣷⣶⠚⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⡇⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠦⢄⠀⠀⠀⠀⢹⣿⣿⣿⣇⠀⠀⠀⠀⢐⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⡃⠀⠀⠀⠀⠀⢀⡄⠀⣀⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠀⡆⢰⡀⠀⠈⣿⣿⣿⣿⡄⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⢶⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⡇⠀⠀⠘⣿⣿⣿⣷⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⣿⣿⣿⣿⣿⣷⢀⠀⠀⠀⠀⢀⣿⣿⣧⡀⠀⠀⠀⣿⣿⠀⠀⢰⣾⣿⣿⣧⡀⠀⢹⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⡇⠀⠀⠀⠘⣿⣿⣿⣧⠀⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠀⠉⠉⠛⣿⣿⣯⣿⣿⣿⣿⣿⡋⠙⣿⣿⠄⠀⢀⣿⣿⠀⠀⢸⣿⣿⣿⣿⣷⣄⢸⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⠃⠀⠀⠀⠀⢹⣿⣿⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⣹⡻⣿⣿⣿⣷⣴⣿⡏⠀⠀⢸⣿⣿⠀⠀⣸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣶⣿⣿⠿⠋⠀⠀⠈⠀⠀⠀⠀⠀⠀⢿⣿⣿⡂⠙⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠒⣿⣿⣿⣿⣹⣿⣻⣿⣿⡇⠀⠀⣾⣿⣿⠀⠀⣿⣿⣿⡇⠙⣿⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠠⢤⡤⡀⠂⣦⢲⣸⣴⣦⣶⣾
⠀⠀⠀⠐⠀⡀⠈⠛⠉⠁⠈⠉⠐⠛⠈⠈⠀⠀⢰⣿⣿⣿⡇⠀⣿⣿⣿⡇⠀⠈⢿⣿⣿⣿⣿⣀⣀⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠙⠃⠀⠀⠀⠈⣿⣿⣿⡄⠀⠀⠀⠀⢸⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣴⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣇⠀⣿⣿⣿⣧⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣠⣠⣤⣾⣿⣿⡇⠀⠠⠀⠀⠀⡀⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣽⣿⣿⠀⠀⢸⣿⣿⣿⣷⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡿⠄⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣾⣷⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠟⠛⣻⣿⡿⠀⣸⣿⣿⣬⣭⣿⣿⣿⣾⣿⣿⡿⢿⣿⡿⣿⣯⠉⠁⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣦⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡿⢿⣿⡍⣿⣿⣿⣭⡅⠻⢿⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠉⠛⠈⠉⣿⣿⣿⣿⣿⠿⠿⠇⣼⡿⣿⣇⢸⣿⡿⣿⣯⡀⣿⣿⣭⣵⣆⣻⣿⣶⣿⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠆⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠇⠀⠚⠿⣿⣶⣿⣿⣿⣿⣧⣤⣶⣾⣿⣟⣿⣿⣾⣿⣧⣼⣿⣷⡿⠿⠿⠿⠟⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣧⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡌⡇⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠿⣿⠿⠿⡿⠿⡿⠿⢦⠶⣤⠦⡴⢶⠶⢦⡀⢀⡴⠶⠶⣿⠷⠾⡿⠿⢿⡿⠿⠿⣿⠷⡶⢶⣰⠶⠶⢶⠶⠶⣶⠶⠶⢦⣠⡶⠶⠶⡶⠶⠦⢤⠴⢦⠶⢤⠴⠶⡾⠷⢿⣠⠶⠿⢿⠿⢿⠿⢿⠿⠿⡿⠿⢿⣿
⣿⡇⢸⣤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⣯⠀⠶⡇⢠⠘⡇⠀⡆⢸⡄⠃⣼⢹⠀⠰⡇⠀⡆⢸⠀⠐⢀⡿⡇⠀⠂⡀⠀⠆⣸⠀⢸⠀⠘⠀⠀⡇⠰⢾⣿⡆⠀⣾⠀⣿⠀⠸⠀⠀⡇⠰⢾⣿
⣿⡇⠸⠀⢸⠀⠶⡇⢸⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⣿⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡇⢸⠀⢰⡇⠀⠇⢸⠀⢰⠀⣷⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⡅⡇⠀⣿⠀⣿⠀⡄⠀⠀⡇⠰⢾⣿
⣿⠿⠲⢷⠚⠲⠖⠳⠺⠖⠗⠚⡒⡗⠒⠓⠚⢲⣾⣶⣋⠓⠚⠒⠛⠒⠒⠒⠚⠒⠒⠒⠒⠋⠑⠒⠁⠈⠒⠊⠙⠒⠒⠛⠒⠚⠒⠁⠓⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠒⠒⣷⣶⣾⡇⠑⠒⠛⠒⠚⠲⣷⣷⣶⣷⣶⠚⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⡻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡇⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣧⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠦⢄⠀⠀⠀⠀⢹⣿⣿⣿⡆⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⢀⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠀⡆⢰⡀⠀⠈⣿⣿⣿⣿⡄⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⢘⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⡇⠀⠀⠘⣿⣿⣿⣷⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⢀⣿⣿⣧⡀⠀⠀⠀⣾⣿⠀⠀⢰⣾⣿⣿⣧⡀⠀⢸⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⡇⠀⠀⠀⠸⣿⣿⣿⣧⠀⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠈⠉⠉⠻⢟⣿⡰⣿⣿⣿⣿⣿⡏⠙⣿⣿⠄⠀⢠⣿⣿⠀⠀⢸⣿⣿⣿⣿⣷⣄⢸⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⠃⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠀⠀⠀⠀⠀⠀⠀⣈⡛⣿⣿⣿⣿⣤⣿⡏⠀⠀⢸⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣶⣿⣿⠿⠋⠀⠀⠈⠀⠀⠀⠀⠀⠀⢿⣿⣿⡀⠙⠿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⣿⣿⣿⡇⠀⠀⣼⣿⣿⠀⠀⣿⣿⣿⡇⠙⣿⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⡀⡀⠀⢄⣀⣤⠤⢴⣼⣷⣶⣾
⠀⠀⠀⠀⠀⠀⠀⠛⠋⠁⠈⠉⠲⠊⠉⠁⠀⠀⢸⣿⣿⣿⡅⠀⣿⣿⣿⡇⠀⠈⢿⣿⣿⣿⣿⣀⣀⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠙⠃⠀⠀⠀⠈⣿⣿⣿⡆⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢠⣦⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣏⠀⣿⣿⣿⣧⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣠⣠⣤⣺⣿⣿⣆⠀⠀⠀⠀⢀⢀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣽⣿⣿⠀⠀⢸⣿⣿⣿⣷⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠄⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣾⣷⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠟⠛⣻⣿⡿⠀⣸⣿⣿⣬⣭⣿⣿⣿⣾⣿⣿⡿⢿⣿⡿⣿⣯⠉⠁⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣆⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡿⢿⣿⡍⣿⣿⣯⣭⡅⠻⠿⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠉⠛⠈⠉⣿⣿⣿⣿⣿⠿⡿⠇⣸⡿⣿⣇⢸⣿⡿⣿⣯⡀⣿⣿⣭⣵⣆⣻⣿⣶⣿⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠇⠀⠚⠿⣿⣶⣿⣿⣿⣿⣧⣤⣶⣾⣿⣟⣿⣿⣾⣿⣧⣼⣿⣷⣿⠿⠿⠿⠟⠛⠟⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣧⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡌⡇⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠿⣿⠿⠿⡿⠿⡿⠿⢦⠶⣤⠦⡴⢶⠶⢦⡀⢀⡴⠶⠾⣿⠶⠶⡿⠿⢿⡿⠿⠿⣿⠷⡶⢶⣰⠶⠶⢶⠶⠶⣶⠶⠶⢦⣰⡶⠶⠶⡶⠶⠦⢤⠴⢦⠶⢦⠴⠶⡾⠷⢷⣠⠶⠿⢿⠿⢿⠿⢿⠿⠿⡿⠿⢿⣿
⣿⡇⢸⣤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⣯⠀⠶⡇⢠⠈⡇⠀⡆⢸⡄⠃⣼⢹⠀⠰⡇⠀⡆⢸⠀⠐⢀⡿⡇⠀⠂⡀⠀⠆⣸⠀⢸⠀⠘⠀⠀⡇⠰⢾⣿⡆⠀⣾⠀⣿⠀⠸⠀⠀⡇⠰⢾⣿
⣿⡇⠸⠀⢸⠀⠶⡇⢸⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⣿⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡇⢸⠀⢰⡇⠀⠇⢸⠀⢰⠀⣿⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⡅⡇⠀⣿⠀⢿⠀⡄⠀⠀⡇⠰⢾⣿
⣿⠿⠲⢷⠚⠲⠖⠳⠺⠖⠗⠚⡒⡗⠒⠓⠚⢲⣾⣶⣋⠓⠚⠒⠛⠒⠒⠒⠚⠒⠒⠒⠒⠋⠑⠒⠁⠈⠒⠊⠙⠒⠒⠛⠒⠚⠒⠁⠓⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠒⠒⣷⣶⣾⡇⠑⠒⠛⠒⠚⠲⣷⣷⣶⣷⣶⠚⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⡟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣇⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠦⢄⠀⠀⠀⠀⢿⣿⣿⣿⡄⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠀⡆⢰⡀⠀⠸⣿⣿⣿⣷⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⡇⠀⠀⠹⣿⣿⣿⣆⠀⢰⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣧⡀⠀⠀⠀⣾⣿⠀⠀⢰⣾⣿⣿⣧⡀⠀⢸⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⡇⠀⠀⠀⢹⣿⣿⣿⣦⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠉⠉⠙⣿⣿⣶⣿⣿⣿⣿⣿⡏⠉⣿⣿⡄⠀⠀⣿⡿⠀⠀⢸⣿⣿⣿⣿⣷⣄⢸⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⠃⠀⠀⠀⠀⢿⣿⣿⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠉⢀⣙⣿⣿⣿⣿⣷⣤⣿⣿⠀⠀⢰⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣶⣿⣿⠿⠋⠀⠀⠈⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠙⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡯⠽⣻⣻⣿⣿⡟⠀⠀⣼⣿⣿⠀⠀⣿⣿⣿⡇⠙⣿⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⠀⢹⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⣔⣤⣴⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠁⠋⠐⠀⠉⠉⠀⠀⢰⣿⣿⣿⡅⠀⣿⣿⣿⡇⠀⠈⢿⣿⣿⣿⣿⣀⣀⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠙⠃⠀⠀⠀⢸⣿⣿⣿⡄⠀⠀⠀⠀⢲⣶⣯⣼⣿⣾⣿⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡏⠀⣿⣿⣿⣧⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⡀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣠⣤⣤⣼⣿⣿⣿⣔⡅⢥⣄⣤⣢⣤⣼⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣽⣿⣿⠀⠀⢸⣿⣿⣿⣷⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡷⠄⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠟⠛⣻⣿⡿⠀⢸⣿⣿⣬⣽⣿⣿⣿⣶⣿⣿⡿⢿⣿⣿⣿⣯⠉⠁⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡆⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢺⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡿⢿⣿⡍⣿⣿⣿⣭⡅⠻⠿⠿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠉⠋⠈⠉⢿⣿⣿⣿⡿⠿⠿⠇⣸⡿⣿⣇⢸⣿⡿⣿⣯⡀⣿⣿⣭⣷⣆⣻⣿⣶⣿⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⡿⠆⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠇⠀⠘⠿⣿⣶⣿⣿⣿⣿⣧⣤⣶⣾⣿⣟⣿⣿⣾⣿⣧⣼⣿⣷⡿⠿⠿⠿⠟⠛⠻⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣦⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡌⡇⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠿⣿⠿⠿⡿⠿⣿⠿⢦⠶⣤⠦⡴⢶⠶⢦⡀⢀⡴⠶⠶⣿⠷⠾⡿⠿⢿⡿⠿⠿⣿⠷⡶⢶⣰⠶⠶⢶⠶⠶⣶⠶⠶⢦⣠⡶⠶⠶⡶⠶⠦⢤⠴⢤⠶⢤⠴⠶⡾⠷⢷⣠⠶⠿⢿⠿⣿⠿⢿⠿⠿⡿⠿⢿⣿
⣿⡇⢸⣤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⣿⠀⠶⡇⢠⠘⡇⠀⡆⢸⡄⠃⣼⢹⠀⠰⡇⠀⡆⢸⠀⠐⢀⡿⡇⠀⠆⡀⠀⠆⣸⠀⢸⠀⠘⠀⠀⡇⠰⢾⣿⡆⠀⣾⠀⣿⠀⠘⠀⠀⡇⠰⢾⣿
⣿⡇⠸⠀⢸⠀⠶⡇⢸⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⣯⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡇⢸⠀⢰⡇⠀⠇⢸⠀⢰⠀⣷⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⡅⡇⠀⣿⠀⣿⠀⡄⠀⠀⡇⠰⢾⣿
⣿⠿⠲⢷⠚⠲⠖⠳⠺⠖⠗⠚⡒⡗⠒⠓⠚⢲⣾⣶⣋⠓⠺⠒⠛⠒⠒⠒⠚⠒⠒⠒⠒⠋⠑⠒⠁⠈⠒⠊⠙⠒⠒⠛⠒⠚⠒⠁⠓⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠒⠒⣷⣶⣾⡇⠑⠒⠛⠒⠚⠲⣷⣷⣶⣷⣶⠚⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣇⠀⠀⠀⠀⠀⣸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡄⠀⠀⠀⠀⣬⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠦⢄⠀⠀⠀⠘⣿⣿⣿⣿⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⢀⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠀⡆⢰⡀⠀⢹⣿⣿⣿⣧⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⣀⠀⠀⠀⢾⣿⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⡇⠀⠀⢻⣿⣿⣿⣆⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⣿⣿⣧⡀⠀⠀⠀⣿⣿⠀⠀⢰⣶⣿⣿⣧⡀⠀⢸⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⡇⠀⠀⠀⢻⣿⣿⣿⣶⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣄⠈⠉⠉⠛⢿⣿⠴⣿⣿⣿⣿⣿⡏⠉⣿⣿⡆⠀⠀⣿⣿⠀⠀⢸⣿⣿⣿⣿⣷⣄⢸⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⠃⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣿⣿⣿⣿⣦⣿⣟⠀⠀⢰⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣶⣿⣿⠿⠋⠀⠀⠈⠀⠀⠀⠀⠀⠘⣿⣿⣷⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣯⢏⣿⢻⣿⣿⡿⠀⠀⣼⣿⣿⠀⠀⣾⣿⣿⡇⠙⣿⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⠀⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠠⠀⡤⠄⡀⣤⣐⣾⣖⣶⣿⣶
⠀⠀⠀⠀⠀⡀⡀⠛⠉⠁⠀⠉⠛⠋⠋⠉⠁⠀⢸⣿⣿⣿⡆⠀⣿⣿⣿⡇⠀⠈⢿⣿⣿⣿⣿⣀⣀⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠙⠃⠀⠀⠀⢸⣿⣿⣿⡀⠀⠀⠀⠀⢲⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣤⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡇⠀⣿⣿⣿⣧⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣠⣤⣤⣸⣿⣿⣇⢀⠀⣀⠀⠄⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣽⣿⣿⠀⠀⢸⣿⣿⣿⣷⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡷⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠟⠛⣻⣿⡿⠀⢸⣿⣿⣬⣭⣿⣿⣿⣶⣿⣿⡿⢿⣿⡿⣿⣯⠉⠁⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡆⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡿⢿⣿⡍⣿⣿⣿⣭⡅⠻⢿⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠉⠛⠈⠉⣿⣿⣿⣿⣿⠿⡿⠇⣼⡿⣿⣇⢸⣿⡿⣿⣯⡀⣿⣿⣭⣵⣆⣻⣿⣶⣿⣯⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡿⠄⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠘⠿⣿⣶⣿⣿⣿⣿⣧⣤⣶⣾⣿⣟⣿⣿⣾⣿⣧⣼⣿⣷⣿⠿⠿⠿⠟⠛⠟⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣧⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⡈⡇⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠿⣿⠿⠿⡿⠿⡿⠿⢦⠶⣤⠦⡴⢶⠶⢦⡀⢀⡴⠶⠶⣿⠷⠶⡿⠿⢿⡿⠿⠿⣿⠷⡶⢶⣰⠶⠶⢶⠶⠶⣶⠶⠶⢧⣠⡶⠶⠶⡶⠶⠦⢤⠶⢤⠶⢤⠴⠶⡾⠷⢷⣠⠶⠿⢿⠿⢿⠿⢿⠿⠿⡿⠿⢿⣿
⣿⡇⢸⡤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⣿⠀⠶⡇⢠⠘⡇⠀⡆⢸⡀⠃⣼⢹⠀⠰⡇⠀⡆⢸⠀⠐⢀⡿⡇⠀⠆⡀⠀⠆⣸⠀⢸⠀⠸⠀⠀⡇⠰⢾⣿⡆⠀⣾⠀⣿⠀⠸⠀⠀⡇⠰⢾⣿
⣿⡇⠸⠀⢸⠀⠶⡇⢸⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⣿⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡇⢸⠀⢰⣇⠀⠇⢸⠀⢰⠀⣷⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⡅⡇⠀⣿⠀⣿⠀⡄⠀⠀⡇⠰⢾⣿
⣿⠿⠲⢷⠚⠲⠖⠳⠺⠖⠗⠚⡒⡗⠒⠓⠚⢲⣾⣶⣋⠓⠺⠒⠛⠒⠒⠒⠚⠒⠒⠒⠒⠋⠑⠒⠁⠈⠒⠊⠙⠒⠒⠛⠒⠚⠒⠁⠓⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠒⠒⣷⣶⣾⡅⠑⠒⠛⠒⠚⠲⣷⣷⣶⣷⣶⠚⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡆⠀⠀⠀⠀⢨⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠀⠀⠀⠀⢰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠦⢄⠀⠀⠀⠸⣿⣿⣿⣧⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⢀⡈⣀⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠈⡆⢰⡀⠀⢹⣿⣿⣿⣆⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⢠⠀⠀⠀⢾⣿⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⡇⠀⠀⢻⣿⣿⣿⣆⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣿⣿⣧⣀⠀⠀⠀⣿⡿⠀⠀⢰⣶⣿⣿⣧⡀⠀⢸⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⡇⠀⠀⠀⢿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠉⠉⠛⣿⣿⢶⣿⣿⣷⣿⣿⡏⠉⣿⣿⡆⠀⠀⣿⣿⠀⠀⢸⣿⣿⣿⣿⣷⣄⢸⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⠃⠀⠀⠀⠈⣿⣿⣿⡿⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣛⣹⣿⣿⣿⣿⣤⣿⣟⠀⠀⢠⣿⣷⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣶⣿⣿⠿⠋⠀⠀⠈⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⢽⢿⣿⣿⣿⡿⠀⠀⣾⣿⣿⠀⠀⣿⣿⣿⡇⠙⣿⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⠀⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠄⡤⢀⣄⣖⣶⣮⣴
⠀⠀⠀⠀⠀⠀⠀⠛⠙⠉⠀⠈⢘⠉⠋⠉⠀⠀⢴⣿⣿⣿⡄⠀⣿⣿⣿⡇⠀⠈⢿⣿⣿⣿⣿⣀⣀⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠙⠃⠀⠀⠀⢻⣿⣿⣷⡀⠀⠀⠀⠀⢰⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⣿⣿⣿⣧⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⢙⣿⣿⣧⡀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⣀⣤⣤⣸⣿⣿⣿⣠⢀⠄⠀⢀⣄⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣽⣿⣿⠀⠀⢸⣿⣿⣿⣷⣿⣿⣇⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡷⠄⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠟⠛⣻⣿⡿⠀⢸⣿⣿⣬⣭⣿⣿⣿⣶⣿⣿⡿⢿⣿⡿⣿⣯⠉⠁⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡄⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡿⢿⣿⡍⣿⣿⣿⣭⡅⠻⠿⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⡋⠀⠉⢿⣿⣿⣿⣿⠿⠿⠇⣼⡿⣿⣆⢸⣿⡿⣿⣯⡀⣿⣿⣭⣵⣆⣻⣿⣶⣿⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⡿⠆⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠇⠀⠘⠿⣿⣶⣿⣿⣿⣿⣧⣤⣶⣾⣿⣟⣿⣿⣾⣿⣧⣼⣿⣷⡿⠿⠿⠿⠟⠛⠻⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣦⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⡈⡇⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠿⣿⠿⠿⡿⠿⡿⠿⢦⠶⣤⠦⡴⢶⠶⢦⡀⢠⡴⠶⠾⣿⠶⠶⡿⠿⢿⡿⠿⠿⣿⠷⡶⢶⣰⠶⠶⢶⠶⠶⣶⠶⠶⢦⣠⡶⠶⠶⡶⠶⠦⢤⠴⢦⠶⢤⠴⠶⡾⠷⢧⣠⠶⠿⢿⠿⢿⠿⢿⠿⠿⡿⠿⢿⣿
⣿⡇⢸⣤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⣿⠀⠶⡇⢠⠘⡇⠀⡆⢸⡄⠃⣼⢹⠀⠰⡇⠀⡆⢸⠀⠐⢀⡿⡇⠀⠂⡀⠀⠆⣸⠀⢸⠀⠸⠀⠀⡇⠰⢾⣿⡆⠀⣾⠀⣿⠀⠸⠀⠀⡇⠰⢾⣿
⣿⡇⠸⠀⢸⠀⠶⡇⢸⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⣿⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡇⢸⠀⢰⡇⠀⠇⢸⠀⢰⠀⣷⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⡅⡇⠀⣿⠀⣿⠀⡄⠀⠀⡇⠰⢾⣿
⣿⠿⠲⢷⠚⠲⠖⠳⠺⠖⠗⠚⡒⡗⠒⠓⠚⢲⣾⣶⣋⠓⠺⠒⠛⠒⠒⠒⠚⠒⠒⠒⠒⠋⠑⠒⠁⠈⠒⠊⠙⠒⠒⠛⠒⠚⠒⠁⠓⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠒⠒⣷⣶⣾⠁⠑⠒⠛⠒⠚⠲⣷⣷⣶⣷⣶⠚⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠅⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣧⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠦⢄⠀⠀⠀⢻⣿⣿⣿⣇⠀⠀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠮⣀⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠀⡆⢰⡀⠀⢿⣿⣿⣿⣆⢀⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⢀⠄⠀⠀⢺⣿⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⡇⠀⠈⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⢿⣿⣿⣿⣿⣿⡆⡀⠀⠀⠀⠀⣿⣿⣷⣀⠀⠀⠀⣿⣿⠀⠀⢰⣶⣿⣿⣧⡀⠀⢸⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⡇⠀⠀⠈⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠉⠉⠛⢻⣿⢵⣿⣿⣿⣿⣿⣏⠉⣿⣿⡇⠀⠀⣿⣿⠀⠀⢸⣿⣿⣿⣿⣷⣄⢸⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⠃⠀⠀⠀⠘⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣘⣽⣿⣿⣿⣿⣦⣿⣿⠀⠀⢠⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣶⣿⣿⠿⠋⠀⠀⠈⠀⠀⠀⠀⠀⢹⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⣟⡿⣿⣿⣿⡿⠀⠀⣾⣿⣿⠀⠀⣿⣿⣿⡇⠙⣿⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⠈⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣠⣶⣼⣷⣶⣿⣷
⠀⠀⠀⠐⠀⠀⡈⠛⠋⠁⠈⠉⠪⠛⠋⠉⠀⠀⢸⣿⣿⣿⡅⠀⣿⣿⣿⡇⠀⠈⢿⣿⣿⣿⣿⣀⣀⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠙⠃⠀⠀⠀⢿⣿⣿⣷⠀⠀⠀⠀⠀⢠⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡗⠀⣿⣿⣿⣇⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⢙⣿⣿⣧⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣀⣠⣄⣸⣿⣿⡷⣄⠀⠄⠀⣠⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣽⣿⣿⠀⠀⢸⣿⣿⣿⣷⣿⣿⣇⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡷⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠟⠛⣻⣿⡿⠀⢸⣿⣿⣬⣽⣿⣿⣿⣶⣿⣿⡿⢿⣿⣿⣿⣯⠉⠁⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡄⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡿⢿⣿⡍⣿⣿⣿⣭⡁⠻⠿⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠛⠈⠉⢿⣿⣿⣿⣿⠿⠿⠇⣼⡿⣿⣆⢸⣿⡿⣿⣯⡀⣿⣿⣭⣵⣆⣻⣿⣶⣿⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡿⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠘⠿⣿⣶⣿⣿⣿⣿⣧⣤⣶⣾⣿⣿⣿⣿⣾⣿⣧⣼⣿⣷⣿⠿⠿⠿⠟⠛⠟⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣦⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⡘⡇⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠿⣿⠿⠿⡿⠿⣿⠿⢦⠶⣤⠦⡴⢶⠶⢦⡀⢀⡴⠶⠾⣿⠿⠿⡿⠿⢿⡿⠿⠿⣿⠷⡶⢶⣴⠶⠶⢶⠶⠶⣶⠶⠶⢧⣰⡶⠶⠶⡶⠶⠦⢤⠴⢤⠶⢦⠴⠶⡾⠶⢧⣠⠶⠿⢿⠿⢿⠿⢿⠿⠿⡿⠿⢿⣿
⣿⡇⢸⣤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⣿⠀⠶⡇⢠⠘⡇⠀⡆⢸⡀⠃⣼⢹⠀⠰⡇⠀⡆⢸⠀⠐⢀⡿⡇⠀⠆⡀⠀⠆⣸⠀⢸⠀⠸⠀⠀⡇⠰⢾⣿⡆⠀⣾⠀⣿⠀⠘⠀⠀⡇⠰⢾⣿
⣿⡇⠸⠀⢸⠀⠶⡇⢸⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⣿⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡇⢸⠀⢰⡇⠀⠇⢸⠀⢰⠀⣷⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⡅⡇⠀⣿⠀⣿⠀⡄⠀⠀⡇⠰⢾⣿
⣿⠿⠲⢷⠚⠲⠖⠳⠺⠖⠗⠚⡒⡷⠒⠓⠚⢲⣾⣶⣋⠓⠺⠒⠛⠒⠒⠒⠚⠒⠒⠒⠒⠋⠑⠒⠁⠈⠒⠊⠙⠒⠒⠛⠒⠚⠒⠁⠓⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠒⠒⣷⣶⣾⠁⠑⠒⠛⠒⠚⠲⣷⣷⣶⣷⣶⠚⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡄⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣧⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠦⢄⠀⠀⠀⢻⣿⣿⣿⣆⠀⢨⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⡆⣀⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠀⡆⢰⡀⠀⢿⣿⣿⣿⣦⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⣤⣄⡀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⢸⠀⠀⢾⣿⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⡇⠀⠈⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⢿⣿⣿⣿⣿⣿⠆⢀⠀⠀⠀⠀⣾⣿⣷⣀⠀⠀⠀⣿⣿⠀⠀⢰⣶⣿⣿⣧⡀⠀⢸⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⡇⠀⠀⠘⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠈⠉⠛⢻⣿⡶⣿⣿⣿⣿⣿⣟⠉⣿⣿⡇⠀⠀⣿⣿⠀⠀⢸⣿⣿⣿⣿⣷⣄⢸⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⠃⠀⠀⠀⠸⣿⣿⣿⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠁⣘⣽⣿⣿⣿⣿⣆⣿⣿⠀⠀⢰⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣶⣿⣿⠿⠋⠀⠀⠈⠀⠀⠀⠀⠀⢹⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⢿⢿⣿⣿⣿⡿⠀⠀⣾⣿⣿⡀⠀⣾⣿⣿⡇⠙⣿⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⠘⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣴⣴⣴⣦⣷⣷⣿
⠀⠀⠀⠀⠀⢄⢌⠋⠉⠁⠈⠉⠫⠚⠛⠉⠀⠀⢠⣿⣿⣿⡧⠀⣿⣿⣿⡇⠀⠈⢿⣿⣿⣿⣿⣀⣀⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠙⠃⠀⠀⠐⢿⣿⣿⣧⠀⠀⠀⠀⠀⢰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⡿⠀⣿⣿⣿⣇⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⢹⣿⣿⣧⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣀⣠⣤⣘⣿⣿⣯⡀⠀⠀⠀⣀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣽⣿⣿⠀⠀⢸⣿⣿⣿⣷⣿⣿⣇⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡃⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠟⠛⣻⣿⡿⠀⢸⣿⣿⣬⣭⣿⣿⣿⣶⣿⣿⡿⢿⣿⣿⣿⣯⠉⠁⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡿⢿⣿⡍⣿⣿⣿⣭⡁⠻⠿⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠋⠈⠉⣿⣿⣿⣿⣿⠿⠿⠇⣼⡿⣿⣇⢸⣿⡿⣿⣯⡀⣿⣿⣭⣵⣆⣻⣿⣶⣿⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡿⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠘⠿⣿⣶⣿⣿⣿⣿⣧⣤⣶⣾⣿⣿⣻⣿⣾⣿⣧⣼⣿⣷⡿⠿⠿⠿⠟⠛⠟⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣧⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⢸⡇⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠿⣿⠿⠿⡿⠿⡿⠿⢦⠶⡤⠦⡴⢶⠶⢦⡀⢀⡴⠶⠶⣿⠶⠾⡿⠿⢿⡿⠿⠿⣿⠷⡶⢶⣴⠶⠶⢶⠶⠶⣶⠶⠶⢮⣠⡶⠶⠶⡶⠶⠦⢤⠶⢤⠶⢦⠴⠶⡾⠶⢧⣠⠾⠿⢿⠿⢿⠿⢿⠿⠿⡿⠿⢿⣿
⣿⡇⢸⣤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⣿⠀⠶⡇⢠⠘⡇⠀⡆⢸⡀⠃⣼⢹⠀⠰⡇⠀⡆⢸⠀⠐⢀⡿⡇⠀⠂⡀⠀⠆⣸⠀⢸⠀⠸⠀⠀⡇⠰⢾⣿⡆⠀⣾⠀⣿⠀⠸⠀⠀⡇⠰⢾⣿
⣿⡇⠸⠀⢸⠀⠶⡇⢸⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⣿⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡇⢸⠀⢰⣇⠀⠇⢸⠀⢰⠀⣷⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⡅⡇⠀⣿⠀⣿⠀⡄⠀⠀⡇⠰⢾⣿
⣿⠿⠲⢷⠚⠲⠖⠳⠺⠖⠗⠚⡒⡷⠒⠓⠚⢲⣾⣶⣋⠓⠚⠒⠛⠒⠒⠒⠚⠒⠒⠒⠒⠋⠑⠒⠁⠈⠒⠊⠙⠒⠒⠛⠒⠚⠒⠁⠓⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠒⠒⣷⣶⣾⠁⠑⠒⠛⠒⠚⢲⣷⣷⣶⣷⣶⠚⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣇⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠦⢄⠀⠀⠀⢿⣿⣿⣿⣆⠀⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⢀⡏⣀⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠀⡆⢰⡀⠘⣿⣿⣿⣿⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⣤⣄⡀⠀⠀⠀⠀⣻⣿⠀⠀⠀⠀⠀⠀⢘⣦⠀⢸⣿⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⡇⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⢿⣿⣿⣿⣿⣿⡆⠀⡀⠀⠀⠀⣾⣿⣷⣀⠀⠀⠀⣿⣿⠀⠀⢰⣶⣿⣿⣧⡈⠀⢸⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⡇⠀⠀⠘⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠤⡀⠉⠉⠛⠻⣿⠃⣿⣿⣿⣿⣿⣏⠉⣿⣿⡇⠀⠀⣿⣿⠀⠀⢸⣿⣿⣿⣿⣷⣄⢸⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⠃⠀⠀⠀⠸⣿⣿⣿⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣈⡛⢿⣿⣿⣿⡆⣿⣿⠀⠀⢠⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣶⣿⣿⠿⠋⠀⠀⠈⠀⠀⠀⠀⠀⢻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣺⣿⣿⡿⢿⣿⣟⣿⣿⣿⠀⢀⣿⣿⣿⡀⠀⣾⣿⣿⡇⠙⣿⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⢘⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⡀⠤⣐⢀⣠⣴⣤⣽⣯⣿⣿⣾
⠀⠀⠀⠀⠐⠴⢔⠛⠁⠀⠀⠀⠥⠼⠝⠉⠁⠀⢰⣿⣿⣿⣧⠀⣿⣿⣿⡇⠀⠈⢿⣿⣿⣿⣿⣀⣀⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡮⠙⠂⠀⠀⠐⢿⣿⣿⣧⠀⠀⠀⠀⠀⢲⣾⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣦⣼⣠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣟⠀⣿⣿⣿⣇⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⢹⣿⣿⣧⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⣀⣀⣤⣺⣿⣿⣷⠄⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣽⣿⣿⠀⠀⢸⣿⣿⣿⣷⣾⣿⣇⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡣⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠟⠋⣻⣿⡿⠀⢸⣿⣿⣬⣽⣿⣿⣿⣶⣿⣿⡿⢿⣿⣿⣿⣯⠉⠁⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⡄⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡿⢿⣿⡍⣿⣿⣿⣭⡅⠻⠿⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣦⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⡋⠈⠉⣿⣿⣿⣿⣿⠿⡿⠇⣸⡿⣿⣆⢸⣿⡿⣿⣯⡀⣿⣿⣭⣵⣆⣻⣿⣶⣿⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠘⠿⣿⣶⣿⣿⣿⣿⣧⣤⣶⣾⣿⣿⣿⣿⣾⣿⣧⣼⣿⣷⣿⠿⠿⠿⠟⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣦⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⢸⡇⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠿⣿⠿⠿⡿⠿⣿⠿⢦⠶⡤⠦⡴⢶⠶⢦⡀⢠⡴⠶⠾⣿⠷⠾⡿⠿⢿⡿⠿⠿⣿⠷⡶⢶⣰⠶⠶⢶⠶⠶⣶⠶⠶⢦⣠⡶⠶⠶⡶⠶⠦⢤⠴⢤⠶⢤⠴⠶⡾⠶⢧⣠⠾⠿⢿⠿⢿⠿⢿⠿⠿⡿⠿⢿⣿
⣿⡇⢸⣤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⣿⠀⠶⡇⢠⠘⡇⠀⡆⢸⡀⠃⣼⢹⠀⠰⡇⠀⡆⢸⠀⠐⢀⡿⡇⠀⠆⡀⠀⠆⣸⠀⢸⠀⠸⠀⠀⡇⠰⢾⣿⡆⠀⣾⠀⣿⠀⠸⠀⠀⡇⠰⢾⣿
⣿⡇⠸⠀⢸⠀⠶⡇⢸⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⣿⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡇⢸⠀⢰⣇⠀⠇⢸⠀⢰⠀⣷⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⡁⡇⠀⣿⠀⣿⠀⡄⠀⠀⡇⠰⢾⣿
⣿⠿⠲⢷⠚⠲⠖⠳⠺⠖⠗⠚⡒⡷⠒⠓⠚⢲⣾⣶⣋⠓⠺⠒⠛⠒⠒⠒⠚⠒⠒⠒⠒⠋⠑⠒⠁⠈⠒⠊⠙⠒⠒⠛⠒⠚⠒⠁⠓⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠒⠒⣷⣶⣾⠁⠑⠒⠛⠒⠚⢲⣷⣷⣶⣷⣶⠚⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡪⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣧⠀⠀⢀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡆⠀⢀⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠶⢄⠀⠀⠀⢿⣿⣿⣿⣦⣼⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡆⣀⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠀⡆⢰⡀⠘⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⣤⣄⡀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⢸⣗⣾⣿⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⡇⠀⠸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣼⣿⣷⣀⠀⠀⠀⣿⣿⠀⠀⢰⣶⣿⣿⣧⡈⠙⢼⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⡇⠀⠀⠹⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⡀⠀⠈⠛⠻⣿⠇⢿⣿⣾⣿⣿⣏⠉⣿⣿⡇⠀⠀⣿⣿⠀⠀⢸⣿⣿⣿⣿⣷⣄⢸⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⠃⠀⠀⠀⠹⣿⣿⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣈⣹⣿⣿⣿⣿⣆⣿⣿⠁⠀⣨⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣶⣿⣿⠿⠋⠀⠀⠈⠀⠀⠀⠀⠀⢻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡟⠿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⡀⠀⣼⣿⣿⡇⠙⣿⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⢸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⡠⣄⡀⣆⣄⣤⣴⣽⣷⣶⣾
⠀⠀⠀⠀⠀⠠⢎⠙⠉⠀⠀⠀⠃⠟⠙⠉⠀⠀⢠⣿⣿⣿⣧⠀⣿⣿⣿⡇⠀⠈⢿⣿⣿⣿⣿⣀⣀⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡮⠙⠂⠀⠀⠀⢿⣿⣿⣧⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣴⣶⡔⢉⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣏⠀⣿⣿⣿⣇⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢹⣿⣿⣧⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⣀⣀⣰⣼⣿⣿⣷⣂⠀⠀⠀⢀⡀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣽⣿⣿⠀⠀⢸⣿⣿⣿⣷⣾⣿⣇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡃⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠟⠛⣻⣿⡿⠀⢸⣿⣿⣬⣽⣿⣿⣿⣶⣿⣿⡿⢿⣿⣿⣿⣯⠉⠁⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⡄⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡿⢿⣿⡍⣿⣿⣿⣭⡁⠻⠿⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣧⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠋⠈⠉⣿⣿⣿⣿⣿⠿⡿⠏⣼⡿⣿⣆⢸⣿⡿⣿⣯⡀⣿⣿⣭⣵⣆⣻⣿⣶⣿⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠘⠿⣿⣶⣿⣿⣿⣿⣧⣤⣶⣾⣿⣟⣻⣿⣾⣿⣧⣼⣿⣷⡿⠿⠿⠿⠟⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣧⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⢸⡇⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠿⣿⠿⠿⡿⠿⡿⠿⢦⠶⣤⠦⡴⢶⠶⢦⡀⢠⡴⠶⠾⣿⠷⠶⡿⠿⢿⡿⠿⠿⣿⠷⡶⢶⣠⠶⠶⢶⠶⠶⣶⠶⠶⢦⣠⡶⠶⠶⡶⠶⠦⢤⠴⢤⠶⢤⠴⠶⡾⠶⢧⣤⠶⠿⢿⠿⢿⠿⢿⠿⠿⡿⠿⢿⣿
⣿⡇⢸⣤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⣿⠀⠶⡇⢠⠘⡇⠀⡆⢸⡀⠃⣼⢹⠀⠰⡇⠀⡆⢸⠀⠐⢀⡿⡇⠀⠆⡀⠀⠆⣸⠀⢸⠀⠘⠀⠀⡇⠰⢾⣿⡆⠀⣾⠀⣿⠀⠘⠀⠀⡇⠰⢾⣿
⣿⡇⠸⠀⢸⠀⠶⡇⢸⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⣿⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡇⢸⠀⢰⣇⠀⠇⢸⠀⢰⠀⣷⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⡁⡇⠀⣿⠀⣿⠀⡄⠀⠀⡇⠰⢾⣿
⣿⠿⠲⢷⠚⠲⠖⠳⠺⠖⠗⠚⡒⡷⠒⠓⠚⢲⣾⣶⣋⠓⠺⠒⠛⠒⠒⠒⠚⠒⠒⠒⠒⠋⠑⠒⠁⠈⠒⠊⠉⠒⠒⠛⠒⠚⠒⠁⠓⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠒⠒⣷⣶⣾⠁⠑⠒⠛⠒⠚⠲⣷⣷⣶⣷⣶⠚⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣆⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠶⢄⠀⠀⠈⣿⣿⣿⣿⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣵⣀⣸⡇⣀⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠀⡆⢰⡀⠘⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣦⣀⡀⠀⠀⠀⠀⠀⠀⣤⣄⡀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⡇⠀⠹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣼⣿⣷⣄⠀⠀⠀⣾⣿⠀⠀⢠⣶⣿⣿⣧⡀⠙⢿⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⡇⠀⠀⠹⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠤⡀⠈⠉⠛⢿⣿⣓⢻⣿⣿⣿⣿⣟⠉⣿⣿⡇⠀⠀⣿⣿⠀⠀⢸⣿⣿⣿⣿⣷⣄⢸⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⠃⠀⠀⠀⢻⣿⣿⣟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⣉⡝⣻⣿⣿⣿⣦⣿⣿⠁⠀⣰⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣶⣿⣿⠿⠋⠀⠀⠈⠀⠀⠀⠀⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠻⣟⣿⣿⣿⣿⠀⠀⣾⣿⣿⡀⠀⣽⣿⣿⡇⠙⣿⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣢⢄⣀⣰⣥⣿⣷⣶⣿
⠀⠀⠀⠀⠀⢠⣔⣉⠉⠀⠀⠀⠉⠷⠍⠉⠀⠀⢸⣿⣿⣿⣧⠀⣿⣿⣿⡇⠀⠈⢿⣿⣿⣿⣿⣀⣀⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡮⠙⠂⠀⠀⠘⣿⣿⣿⣧⠀⠀⠀⠀⠀⢰⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣴⣷⣤⠅⠀⡀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣟⠀⣿⣿⣿⣇⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣹⣿⣿⣦⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣠⣀⣤⣼⣿⣿⣿⣆⠀⠀⠀⡀⣄⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣽⣿⣿⠀⠀⢸⣿⣿⣿⣷⣾⣿⣇⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡃⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠟⠛⣻⣿⡿⠀⢸⣿⣿⣬⣽⣿⣿⣿⣶⣿⣿⡿⢿⣿⣿⣿⣯⠉⠁⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡿⢿⣿⡍⣿⣿⣿⣭⡅⠻⠿⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣦⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠛⠈⠉⢿⣿⣿⣿⣿⠿⡿⠇⣼⡿⣿⣆⢸⣿⡿⣿⣯⡀⣿⣿⣭⣵⣆⣻⣿⣶⣿⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠘⠿⣿⣶⣿⣿⣿⣿⣧⣤⣶⣾⣿⣟⣻⣿⣾⣿⣧⣼⣿⣷⡿⠿⠿⠿⠟⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣦⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⢸⡇⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠿⣿⠿⠿⡿⠿⣿⠿⢦⠶⡤⠦⡴⢶⠶⢦⡀⢠⡴⠶⠶⣿⠷⠾⡿⠿⢿⡿⠿⠿⣿⠷⡶⢶⣰⠶⠶⢶⠶⠶⣶⠶⠶⢦⣠⡶⠶⠶⡶⠶⠦⢤⠴⢤⠶⢤⠴⠶⡾⠶⢧⣠⠶⠿⢿⠿⢿⠿⢿⠿⠿⡿⠿⢿⣿
⣿⡇⢸⣤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⣿⠀⠶⡇⢠⠘⡇⠀⡆⢸⡀⠃⣼⢻⠀⠰⡇⠀⡆⢸⠀⠐⢀⡿⡇⠀⠆⡀⠀⠆⣸⠀⢸⠀⠘⠀⠀⡇⠰⢾⣿⡆⠀⣾⠀⣿⠀⠘⠀⠀⡇⠰⢾⣿
⣿⡇⠸⠀⢸⠀⠶⡇⢸⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⣿⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡇⢸⠀⢰⣇⠀⠇⢸⠀⢰⠀⣷⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⡅⡇⠀⣿⠀⣿⠀⡄⠀⠀⡇⠰⢾⣿
⣿⠿⠲⢷⠚⠲⠖⠳⠺⠖⠗⠚⡒⡷⠒⠓⠚⢲⣾⣶⣋⠓⠺⠒⠛⠒⠒⠒⠚⠒⠒⠒⠒⠋⠑⠒⠁⠈⠒⠊⠙⠒⠒⠛⠒⠚⠒⠁⠓⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠒⠒⣷⣶⣾⠁⠑⠒⠛⠒⠚⢲⣷⣷⣶⣷⣶⠚⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣷⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠦⢄⠀⠀⠘⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⡇⢀⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠀⡆⢰⡀⢹⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣧⣀⡀⠀⠀⠀⠀⠀⠀⢤⣄⡀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⡇⠀⠹⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣸⣿⣷⣄⠀⠀⠀⣿⣿⠀⠀⢠⣶⣿⣿⣧⡀⠈⢾⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⡇⠀⠀⢹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠉⠉⠛⠻⣿⣗⢻⣿⣿⣿⣿⣏⠉⣻⣿⡇⠀⠀⣿⣿⠀⠀⢸⣿⣿⣿⣿⣷⣄⢸⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⠃⠀⠀⠀⢻⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣙⡝⣻⣿⣿⣿⣦⣿⣿⠃⠀⢠⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣶⣿⣿⠿⠋⠀⠀⠈⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡝⢿⣿⣿⣿⣿⡿⠀⠀⣼⣿⣿⠀⠀⣾⣿⣿⡇⠙⣿⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⢹⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⢄⣤⣤⣼⣮⣦⣾
⠀⠀⠀⠀⠀⠀⠀⢘⠉⠀⠀⠀⠸⠩⠛⠉⠀⠀⢠⣿⣿⣿⣆⠀⣿⣿⣿⡇⠀⠈⢿⣿⣿⣿⣿⣀⣀⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠙⠂⠀⠀⠸⣿⣿⣿⣆⠀⠀⠀⠀⠀⢠⣴⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣠⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣗⠀⣿⣿⣿⣇⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣻⣿⣿⣆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⢀⣀⣠⣠⣿⣿⣿⡦⠀⠀⠀⢀⡀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣽⣿⣿⠀⠀⢸⣿⣿⣿⣷⣿⣿⣇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡃⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠟⠛⣻⣿⡿⠀⢸⣿⣿⣬⣽⣿⣿⣿⣶⣿⣿⡿⢿⣿⣿⣿⣯⠉⠁⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡿⢿⣿⡍⣿⣿⣿⣭⡁⠻⠿⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡆⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠛⠈⠉⣿⣿⣿⣿⣿⠿⡿⠇⣸⡿⣿⣆⢸⣿⡿⣿⣯⡀⣿⣿⣭⣵⣆⣻⣿⣶⣿⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⡿⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠘⠿⣿⣶⣿⣿⣿⣿⣧⣤⣶⣶⣿⣟⣻⣿⣾⣿⣧⣼⣿⣷⣿⠿⠿⠿⠟⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣦⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⢸⡇⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠿⣿⠿⠿⡿⠿⣿⠿⢦⠶⣤⠦⡴⢶⠶⢦⡀⢠⡴⠶⠶⣿⠷⠶⡿⠿⢿⡿⠿⠿⣿⠷⡶⢶⣤⠶⠶⢶⠶⠶⣶⠶⠾⢦⣠⡶⠶⠶⡶⠶⠦⢤⠴⢤⠶⢤⠴⠶⡾⠶⢧⣠⠶⠿⢿⠿⢿⠿⢿⠿⠿⡿⠿⢿⣿
⣿⡇⢸⢤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⣿⠀⠶⡇⢠⠘⡇⠀⡆⢸⡀⠃⣼⢻⠀⠰⡇⠀⡆⢸⠀⠐⢀⡿⡇⠀⠆⡀⠀⠆⣸⠀⢸⠀⠘⠀⠀⡇⠰⢾⣿⡆⠀⣾⠀⣿⠀⠸⠀⠀⡇⠰⢾⣿
⣿⡇⠸⠀⢸⠀⠶⡇⢸⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⣟⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡇⢸⠀⢰⣇⠀⠇⢸⠀⢰⠀⣷⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⡁⡇⠀⣿⠀⣿⠀⡄⠀⠀⡇⠰⢾⣿
⣿⠿⠲⢷⠚⠲⠖⠳⠺⠖⠗⠚⡒⡷⠒⠓⠚⢲⣾⣶⣋⠓⠚⠒⠛⠒⠒⠒⠚⠒⠒⠒⠒⠋⠑⠒⠁⠈⠒⠊⠙⠒⠒⠛⠒⠚⠒⠁⠓⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠒⠒⣷⣶⣾⠁⠑⠒⠛⠒⠚⢲⣷⣷⣶⣷⣶⠚⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣇⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣷⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣴⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠦⢄⠀⠀⠸⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⣀⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠀⡆⢰⡀⢹⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⢤⣄⡀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠟⠛⠲⠀⢸⡇⠀⢹⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣸⣿⣷⣄⠀⠀⠀⣾⣿⠀⠀⢰⣶⣿⣿⣧⡀⠀⢼⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⡇⠀⠀⢻⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠉⠙⠻⠿⡗⢻⣿⣷⣿⣿⣟⠉⣿⣿⣇⠀⠀⣿⣿⠀⠀⢸⣿⣿⣿⣿⣷⣄⢸⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⠃⠀⠀⠈⢿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠂⠀⠀⠀⠀⠀⠈⣹⣟⣿⣿⣿⣿⣦⣾⣿⠃⠀⢠⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣶⣿⣿⠿⠋⠀⠀⠈⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢀⣀
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠠⣿⣿⣿⠀⠀⣾⣿⣿⡇⠙⣿⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⢻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢬⣖⣴⣸⣻⣿⣵⣶
⠀⠀⠀⠀⠀⢀⢦⠟⠋⠁⠁⠀⠸⠛⠛⠉⠉⠀⢸⣿⣿⣿⣗⠀⣿⣿⣿⡇⠀⠈⢿⣿⣿⣿⣿⣀⣀⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠙⠂⠀⠀⠹⣿⣿⣿⣇⠀⠀⠀⠀⠀⢲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣰⣾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣾⣿⣿⣿⣿⠀⣿⣿⣿⣇⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠈⣿⣿⣿⣦⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⢀⣀⣤⣴⣿⣿⣿⣆⠀⠀⠀⣠⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣽⣿⣿⠀⠀⢸⣿⣿⣿⣷⣾⣿⣇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠂⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠟⠛⣻⣿⡿⠀⢸⣿⣿⣬⣽⣿⣿⣿⣶⣿⣿⡿⢿⣿⣿⣿⣯⠉⠁⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡿⢿⣿⡍⣿⣿⣿⣭⠁⠻⠿⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡦⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠋⠈⠉⣿⣿⣿⣿⣿⠿⡿⠏⣸⡿⣿⣇⢸⣿⡿⣿⣯⡀⣿⣿⣭⣵⣆⣻⣿⣶⣿⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠘⠿⣿⣶⣿⣿⣿⣿⣧⣤⣶⣶⣿⣿⣻⣿⣾⣿⣧⣼⣿⣷⡿⠿⠿⠿⠟⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣦⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⢸⡇⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠿⣿⠿⠿⡿⠿⣿⠿⢦⠶⡤⠦⡴⢶⠶⢦⡀⢠⡴⠶⠾⣿⠿⠷⡿⠿⢿⡿⠿⠿⣿⠷⡶⢶⣴⠶⠶⢶⠶⠶⣶⠶⠶⢦⣠⡶⠶⠶⡶⠶⠦⢤⠶⢤⠶⢤⠴⠶⡾⠶⢧⣤⠾⠿⢿⠿⢿⠿⢿⠿⠿⡿⠿⢿⣿
⣿⡇⢸⣤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⣿⠀⠶⡇⢠⠘⡇⠀⡆⢸⡀⠃⣼⢻⠀⠰⡇⠀⡆⢸⠀⠐⢀⡿⡇⠀⠆⡀⠀⠆⣸⠀⢸⠀⠸⠀⠀⡇⠰⢾⣿⡆⠀⣾⠀⣿⠀⠸⠀⠀⡇⠰⢾⣿
⣿⡇⠸⠀⢸⠀⠶⡇⢸⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⣿⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡇⢸⠀⢰⣇⠀⠇⢸⠀⢰⠀⣿⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⡁⡇⠀⣿⠀⣿⠀⡄⠀⠀⡇⠰⢾⣿
⣿⠿⠲⢷⠚⠲⠖⠳⠺⠖⠗⠚⡒⡷⠒⠓⠚⢲⣾⣶⣋⠓⠺⠒⠛⠒⠒⠒⠚⠒⠒⠒⠒⠋⠑⠒⠁⠈⠒⠊⠙⠒⠒⠛⠒⠚⠒⠁⠓⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠒⠒⣷⣶⣾⠁⠑⠒⠛⠒⠚⢲⣷⣷⣶⣷⣶⠚⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣧⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠦⢄⠀⠀⠻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡧⢀⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠈⡆⢰⡀⢻⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⡇⠀⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣸⣿⣷⣄⠀⠀⠀⣾⣿⠀⠀⢠⣶⣿⣿⣧⡀⠀⢼⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⡇⠀⠈⢿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠄⠉⠉⠙⢻⣿⡃⣻⣿⣿⣿⣿⣟⠉⣻⣿⡇⠀⠀⣿⣿⠀⠀⢸⣿⣿⣿⣿⣷⣄⢸⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⠃⠀⠀⠈⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣽⣟⣿⣿⣿⣿⣦⣼⣿⠁⠀⢰⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣾⣿⣿⠿⠋⠀⠀⠈⠀⠀⠀⠀⠘⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⡟⠟⢿⡛⣿⣿⣿⠂⠀⣽⣿⣿⠀⠀⣼⣿⣿⡇⠙⣿⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⢻⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣠⣦⣥⣶⣷⣬
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠓⠁⠉⠁⠀⢰⣿⣿⣿⣆⠀⣿⣿⣿⡇⠀⠈⢿⣿⣿⣿⣿⣀⣀⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡮⠙⠂⠀⠀⠸⣿⣿⣿⣆⠀⠀⠀⠀⠀⢢⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⣿⣿⣿⣇⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠈⣿⣿⣿⣦⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣐⢢⣄⣠⣴⣿⣿⣿⡆⠄⠀⡀⠀⣀⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣽⣿⣿⠀⠀⢸⣿⣿⣿⣷⣾⣿⣇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠂⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠟⠋⣻⣿⡿⠀⢸⣿⣿⣨⣽⣿⣿⣿⣶⣿⣿⡿⢿⣿⣿⣿⣯⠉⠁⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡿⢿⣿⡍⣿⣿⣿⣭⠁⠻⠿⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡦⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⢋⠈⠉⢿⣿⣿⣿⣿⠿⡿⠇⣸⡿⣿⣇⢸⣿⡿⣿⣯⡀⣿⣿⣭⣽⣆⣻⣿⣶⣿⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠘⠿⣿⣶⣿⣿⣿⣿⣧⣤⣶⣶⣿⣟⣻⣿⣾⣿⣧⣼⣿⣷⡿⠿⠿⠿⠟⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣦⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⢸⡇⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠿⣿⠿⠿⡿⠿⡿⠿⢦⠶⣤⠦⡴⢶⠶⢦⡀⢠⡴⠶⠶⣿⠿⠶⡿⠿⢿⡿⠿⠿⣿⠷⡶⢶⣴⠶⠶⢶⠶⠶⣶⠶⠶⢦⣰⡶⠶⠶⡶⠶⠦⢤⠴⢦⠶⢤⠴⠶⡾⠶⢧⣠⠶⠿⢿⠿⢿⠿⢿⠿⠿⡿⠿⢿⣿
⣿⡇⢸⡤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⣿⠀⠶⡇⢠⠘⡇⠀⡆⢸⡄⠃⣼⢻⠀⠰⡇⠀⡆⢸⠀⠐⢀⡿⡇⠀⠆⡀⠀⠆⣸⠀⢸⠀⠸⠀⠀⡇⠰⢾⣿⡆⠀⣾⠀⣿⠀⠸⠀⠀⡇⠰⢾⣿
⣿⡇⠸⠀⢸⠀⠶⡇⢸⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⣿⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡇⢸⠀⢰⡇⠀⠇⢸⠀⢰⠀⣷⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⡁⡇⠀⣿⠀⣿⠀⡄⠀⠀⡇⠰⢾⣿
⣿⠿⠲⢷⠚⠲⠖⠳⠺⠖⠗⠚⡒⡗⠒⠓⠚⢲⣾⣶⣋⠓⠺⠒⠛⠒⠒⠒⠚⠒⠒⠒⠒⠋⠑⠒⠁⠈⠒⠊⠙⠒⠒⠛⠒⠚⠒⠁⠓⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠒⠒⣷⣶⣾⠁⠑⠒⠛⠒⠚⢲⣷⣷⣶⣷⣶⠚⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣧⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠦⢄⠀⠀⢻⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣀⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠈⡆⢰⡀⢿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⡇⠀⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢸⣿⣿⣄⠀⠀⠀⣿⣿⠀⠀⢠⣶⣿⣿⣧⡀⠀⢼⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⡇⠀⠈⢿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠉⠙⠻⣿⣟⣻⣿⣶⣿⣿⣿⠉⣻⣿⣷⠀⠀⣿⣿⠀⠀⢸⣿⣿⣿⣿⣷⣄⢸⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⠃⠀⠀⠈⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣻⣟⣿⣿⣿⣿⣶⣿⣿⠃⠀⢠⣿⣯⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣾⣿⣿⠿⠋⠀⠀⠈⠀⠀⠀⠀⠘⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀
⠀⠀⠀⠀⠀⠀⡀⢾⣿⣿⣿⠿⣿⣿⣿⣿⣿⠀⠀⣾⣿⣿⠀⠀⣼⣿⣿⡇⠙⣿⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢂⣠⣴⣤⣴⣮⣶⣾
⠀⠀⠀⠀⠀⠠⠘⠉⠉⠉⠁⠀⠨⠛⠘⠉⠁⠀⢴⣿⣿⣿⣆⠀⣿⣿⣿⡇⠀⠈⢿⣿⣿⣿⣿⣀⣀⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠙⠂⠀⠀⠹⣿⣿⣿⣄⠀⠀⠀⠀⠀⢰⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣤⣴⣄⠀⠀⠀⡀⠀⠀⠀⠀⢀⢀⣾⣿⣿⣿⡿⠀⣿⣿⣿⣇⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠈⣿⣿⣿⣦⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣰⣂⣤⣤⣵⣿⣿⣿⣦⠄⢐⢄⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣽⣿⣿⠀⠀⢸⣿⣿⣿⣷⣾⣿⣇⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠂⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠟⠋⣻⣿⡿⠀⢸⣿⣿⣨⣽⣿⣿⣿⣶⣿⣿⡿⢿⣿⣿⣿⣯⠉⠁⠀⠀⠀⠀⠀⠀⠺⣿⣿⣷⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡿⢿⣿⡍⣿⣿⣿⣭⠁⠻⠿⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣆⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⢛⠈⠉⢿⣿⣿⣿⣿⠿⡿⠇⣸⡿⣿⣆⢸⣿⡿⣿⣯⡀⣿⣯⣭⣽⣆⣻⣿⣶⣿⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠘⠿⣿⣶⣿⣿⣿⣿⣧⣤⣶⣶⣿⣟⣿⣿⣾⣿⣧⣼⣿⣷⡿⠿⠿⠿⠟⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣦⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⠛⠁⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⢸⡇⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠿⣿⠿⠿⡿⠿⣿⠿⢦⠶⣤⠦⡴⢶⠶⢦⡀⢠⡴⠶⠶⣿⠷⠶⡾⠿⢿⡿⠿⠿⣿⠷⡶⢶⣴⠶⠶⢶⠶⠶⣶⠶⠶⢮⣰⡶⠶⠶⡶⠶⠦⢤⠴⢦⠶⢤⠴⠶⡾⠶⢧⣠⠾⠿⢿⠿⣿⠿⢿⠿⠿⡿⠿⢿⣿
⣿⡇⢸⡤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⣿⠀⠶⡇⢠⠘⡇⠀⡆⢸⡀⠃⣼⢻⠀⠰⡇⠀⡆⢸⠀⠐⢀⡿⡇⠀⠆⡀⠀⠆⣸⠀⢸⠀⠸⠀⠀⡇⠰⢾⣿⡆⠀⣾⠀⣿⠀⠸⠀⠀⡇⠰⢾⣿
⣿⡇⠸⠀⢸⠀⠶⡇⢸⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⣷⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡇⢸⠀⢰⡇⠀⠇⢸⠀⢰⠀⣷⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⡁⡇⠀⣿⠀⣿⠀⡄⠀⠀⡇⠰⢾⣿
⣿⠿⠲⢷⠚⠲⠖⠳⠺⠖⠗⠚⡒⣷⠒⠓⠚⢲⣾⣶⣋⠓⠺⠒⠛⠒⠒⠒⠚⠒⠒⠒⠒⠋⠑⠒⠁⠈⠒⠊⠙⠒⠒⠛⠒⠚⠒⠁⠓⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠒⠒⣷⣶⣾⠁⠑⠒⠛⠒⠚⢲⣷⣷⣶⣷⣶⠚⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣽⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠦⢄⠀⠀⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣇⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠈⡆⢰⡈⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⣺⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⡇⠈⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⢿⣿⣿⣿⣿⣿⡖⠀⠀⠀⠀⠀⢸⣿⣿⣄⠀⠀⠀⣻⣿⠀⠀⢰⣶⣿⣿⣧⡀⠀⢿⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⡇⠀⠈⢿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠉⠙⠿⣿⡟⣿⣿⣿⣷⣿⣿⠉⢹⣿⣷⠀⠀⣿⣿⠀⠀⢸⣿⣿⣿⣿⣷⣄⢸⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⠃⠀⠀⠘⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠀⠀⠀⠀⠀⠀⣑⣟⣻⣿⣿⣿⣦⣸⣿⠁⠀⢰⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣶⣿⣿⠿⠋⠀⠀⠈⠀⠀⠀⠀⠹⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⣿⣿⣻⣿⣿⣿⡆⠀⣾⣿⣿⠀⠀⣾⣿⣿⡇⠙⣿⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣀⣀⣤⣄⣶⣤⣤
⠀⠀⠀⠀⠁⠀⠀⠒⠋⡋⠁⠀⠛⡿⠋⠋⠈⠀⢰⣿⣿⣿⣧⠀⣿⣿⣿⡇⠀⠈⢿⣿⣿⣿⣿⣀⣀⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠙⠂⠀⠀⠺⣿⣿⣿⡆⠀⠀⠀⠀⠀⢲⣾⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣼⣷⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡧⠀⣿⣿⣿⣇⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠈⣿⣿⣿⣆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⣀⣠⣈⣿⣿⣿⡇⠀⠀⢀⣄⣔⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣷⣿⣿⣇⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠃⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣽⣿⣿⣿⣿⣿⣿⣷⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠟⠛⣻⣿⡿⠀⢸⣿⣿⣨⣽⣿⣿⣿⣶⣿⣿⡿⢿⣿⣿⣿⣯⠉⠁⠀⠀⠀⠀⠀⠀⠺⣿⣿⣷⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡿⢿⣿⡍⣿⣿⣿⣭⡁⠻⠿⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡆⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⢏⠈⠉⢿⣿⣿⣿⣿⠿⡿⠇⣸⡿⣿⣆⢸⣿⡿⣿⣯⡀⣿⣯⣭⣽⣆⣻⣿⣶⣿⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠘⠿⣿⣶⣿⣿⣿⣿⣧⣤⣶⣶⣿⣟⣿⣿⣾⣿⣧⣼⣿⣷⡿⠿⠿⠿⠟⠻⠟⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣦⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⢸⡇⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠿⣿⠿⠿⡿⠿⣿⠿⢦⠶⡤⠦⡴⢶⠶⢦⡀⢠⡴⠶⠶⣿⠷⠶⡿⠿⢿⡿⠿⠿⣿⠷⡶⢶⣴⠶⠶⢶⠶⠶⣶⠶⠶⢦⣰⡶⠶⠶⡶⠶⠦⢤⠴⢤⠶⢤⠴⠶⡾⠶⢧⣠⠶⠿⢿⠿⢿⠿⢿⠿⠿⡿⠿⢿⣿
⣿⡇⢸⡤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⣿⠀⠶⡇⢠⠘⡇⠀⡆⢸⡀⠃⣼⢻⠀⠰⡇⠀⡆⢸⠀⠐⢀⡿⡇⠀⠆⡀⠀⠆⣸⠀⢸⠀⠸⠀⠀⡇⠰⢾⣿⡆⠀⣾⠀⣿⠀⠸⠀⠀⡇⠰⢾⣿
⣿⡇⠸⠀⢸⠀⠶⡇⢸⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⣿⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡇⢸⠀⢰⡇⠀⠇⢸⠀⢰⠀⣿⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⡁⡇⠀⣿⠀⣿⠀⡄⠀⠀⡇⠰⢾⣿
⣿⡿⠲⢷⠚⠲⠖⠳⠺⠖⠗⠚⡲⡷⠒⠓⠚⢲⣾⣶⣋⠓⠺⠒⠛⠒⠒⠒⠚⠒⠒⠒⠒⠋⠑⠒⠁⠈⠒⠊⠙⠒⠒⠛⠒⠚⠒⠁⠓⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠒⠒⣷⣶⣾⠁⠑⠒⠛⠒⠚⢲⣷⣷⣶⣷⣶⠚⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡪⡻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠅⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠦⢄⠀⠈⢿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣆⠀⣀⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠈⡆⢰⡈⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⣺⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⡇⠈⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⢿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢸⣿⣿⣄⠀⠀⠀⣾⡿⠀⠀⢰⣶⣿⣿⣧⡀⠀⢽⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⡇⠀⠈⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠴⠀⠈⠉⠙⠿⣿⣷⣿⣿⣿⣿⣿⣿⠉⢹⣿⡷⠀⠀⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣄⢸⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⠃⠀⠀⠘⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠁⢙⣿⣿⣿⣿⣿⣧⣼⣿⠃⠀⢰⣿⣷⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣶⣿⣿⠿⠋⠀⠀⠈⠀⠀⠀⠀⠹⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⡿⣻⣿⣿⣿⣿⠆⠀⣼⣿⣿⠀⠀⣼⣿⣿⡇⠙⣿⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⣢⡔⣀⢴⡄⣼⣶⣶
⠀⠀⠀⠀⠀⠀⠐⠘⠫⠙⠁⠈⠙⠟⡛⠉⠂⠀⢰⣿⣿⣿⣇⠀⣿⣿⣿⡇⠀⠈⢿⣿⣿⣿⣿⣀⣀⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠙⠂⠀⠀⠻⣿⣿⣿⡄⠀⠀⠀⠀⠀⢰⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣤⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⡏⠀⣿⣿⣿⣇⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠈⣿⣿⣿⣆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣄⣂⣀⣤⣎⣿⣿⣿⣷⡤⠀⠠⣄⣄⣽⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣷⣾⣿⣇⠀⠀⠀⠀⠀⠀⠹⣿⣿⣟⠃⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠟⠛⣻⣿⡿⠀⢸⣿⣿⣬⣽⣿⣿⣿⣶⣿⣿⡿⢿⣿⣿⣿⣯⠉⠁⠀⠀⠀⠀⠀⠀⠺⣿⣿⣷⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡿⢿⣿⡍⣿⣿⣿⣭⡁⠻⠿⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡆⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⢏⠈⠉⢿⣿⣿⣿⣿⠿⡿⠇⣸⡿⣿⣆⢸⣿⡿⣿⣯⡀⣿⣿⣭⣽⣆⣻⣿⣶⣿⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⡿⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠘⠿⣿⣶⣿⣿⣿⣿⣧⣤⣶⣶⣿⣟⣿⣿⣾⣿⣧⣼⣿⣷⡿⠿⠿⠿⠟⠻⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣦⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⢸⡇⠠⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠿⣿⠿⠿⡿⠿⣿⠿⢦⠶⣤⠦⡴⢶⠶⢦⡀⢠⡴⠶⠾⣿⠷⠶⡿⠿⢿⡿⠿⠿⣿⠷⡶⢶⣴⠶⠶⢶⠶⠶⣶⠶⠶⢦⣰⡶⠶⠶⡶⠶⠦⢤⠴⢤⠶⢤⠴⠶⡾⠶⢧⣠⠶⠿⢿⠿⢿⠿⢿⠿⠿⡿⠿⢿⣿
⣿⡇⢸⣤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⣷⠀⠶⡇⢠⠘⡇⠀⡆⢸⡀⠃⣼⢻⠀⠰⡇⠀⡆⢸⠀⠐⢀⡿⡇⠀⠆⡀⠀⠆⣸⠀⢸⠀⠸⠀⠀⡇⠰⢾⣿⡆⠀⣾⠀⣿⠀⠸⠀⠀⡇⠰⢾⣿
⣿⡇⠸⠀⢸⠀⠶⡇⢸⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⣿⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡇⢸⠀⢰⡇⠀⠇⢸⠀⢰⠀⣷⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⡁⡇⠀⣿⠀⣿⠀⡄⠀⠀⡇⠰⢾⣿
⣿⠿⠲⢷⠚⠲⠖⠳⠺⠖⠗⠚⡒⣷⠒⠓⠚⢲⣾⣶⣋⠓⠺⠒⠛⠒⠒⠒⠚⠒⠒⠒⠒⠋⠑⠒⠁⠈⠒⠊⠙⠒⠒⠛⠒⠚⠒⠁⠓⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠚⠒⣷⣶⣾⠁⠑⠒⠛⠒⠚⢲⣷⣷⣶⣷⣶⠚⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠶⢄⠀⠈⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⢀⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠈⡆⢰⡘⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⡇⠘⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢸⣿⣿⣄⠀⠀⠀⣾⣇⠀⠀⢰⣶⣿⣿⣧⡀⠀⢿⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⡇⠀⠘⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠈⠙⠿⡿⢗⣺⣿⣾⣶⣿⣯⠉⢹⣿⣷⠀⠀⣿⡿⠀⠀⢸⣿⣿⣿⣿⣷⣄⢸⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⠁⠀⠀⠸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢑⣙⣻⣿⣿⣿⣦⢸⣿⠀⠀⢀⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣶⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠯⣿⣿⣿⣿⡿⠆⠀⣼⣿⣿⠀⠀⣼⣿⣿⡇⠙⣿⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣀⣰⣤⣠
⠀⠀⠀⠀⠀⠀⠀⠐⠉⠉⠀⠀⠛⠾⠊⠈⠀⠀⢠⣿⣿⣿⣦⠀⣿⣿⣿⡇⠀⠈⢿⣿⣿⣿⣿⣀⣀⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡮⠙⠂⠀⠀⠻⣿⣿⣿⡄⠀⠀⠀⠀⠀⢰⣲⣶⣶⣦⣿⣾⣾⣶⣷⣿⣿⣿
⠀⠀⠀⠀⠀⣰⣶⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡧⠀⣿⣿⣿⣇⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠈⣿⣿⣿⣄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿
⠀⠀⣀⣀⣂⣿⣿⣿⡧⠀⢀⠤⣀⣤⣲⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣽⣿⣿⠀⠀⢸⣿⣿⣿⣷⣾⣿⣇⠀⠀⠀⠀⠀⠀⠹⣿⣿⣟⠂⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣴⣾⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠟⠋⣻⣿⡿⠀⢸⣿⣿⣬⣽⣿⣿⣿⣶⣿⣿⡿⢿⣿⣿⣿⣯⠉⠁⠀⠀⠀⠀⠀⠀⠺⣿⣿⣷⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡿⢿⣿⡍⣿⣿⣿⣭⠁⠻⠿⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡆⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⢏⠀⠉⢿⣿⣿⣿⣿⠿⡿⠇⣸⡿⣿⣆⢸⣿⡿⣿⣯⡀⣿⣿⣭⣽⣆⣻⣿⣶⣿⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⡿⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠘⠿⣿⣶⣿⣿⣿⣿⣧⣠⣶⣶⣿⣟⣿⣿⣾⣿⣧⣼⣿⣷⡿⠿⠿⠿⠟⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣦⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⢸⡇⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠿⣿⠿⠿⡿⠿⡿⠿⢦⠶⣤⠦⡴⢶⠶⢦⡀⢠⡴⠶⠾⣿⠷⠶⡾⠿⢿⡿⠿⠿⣿⠷⡶⢶⣰⠶⠶⢶⠶⠶⣶⠶⠶⢦⣠⡶⠶⠶⡶⠶⠦⢤⠴⢤⠶⢤⠴⠶⡾⠶⢧⣠⠶⠿⢿⠿⢿⠿⢿⠿⠿⡿⠿⢿⣿
⣿⡇⢸⢤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⡿⠀⠶⡇⢠⠘⡇⠀⡆⢸⡄⠃⣼⢻⠀⠰⡆⠀⡆⢸⠀⠐⢀⡿⡇⠀⠆⡀⠀⠆⣸⠀⢸⠀⠘⠀⠀⡇⠰⢾⣿⡆⠀⣾⠀⢸⠀⠘⠀⠀⡇⠰⢾⣿
⣿⡇⠸⠀⢸⠀⠶⡇⢸⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⡿⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡇⢸⠀⢰⡇⠀⠇⢸⠀⢰⠀⣷⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⡀⡇⠀⣿⠀⢸⠀⡄⠀⠀⡇⠰⢾⣿
⣿⠿⠲⢷⠚⠲⠖⠳⠺⠖⠗⠚⡒⡷⠒⠓⠚⢲⣾⣶⣋⠓⠺⠒⠛⠒⠒⠒⠚⠒⠒⠒⠒⠋⠑⠒⠁⠈⠒⠊⠙⠒⠒⠛⠒⠚⠒⠁⠓⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠒⠒⣷⣶⣾⠁⠑⠒⠛⠒⠚⢲⣷⣷⣶⣷⣶⠚⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠶⢄⠀⠘⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠈⡆⢰⡘⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⡇⠘⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠻⢿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⢰⣿⣿⣄⠀⠀⠀⢾⣧⠀⠀⢰⣶⣿⣿⣧⡀⠈⢽⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⡇⠀⠘⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠉⠙⠿⡿⡿⢼⣿⣾⣷⣶⣮⠉⢹⣿⣷⠀⠀⣿⣿⠀⠀⢸⣿⣿⣿⣿⣷⣄⢸⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⠁⠀⠀⠸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠐⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣧⢸⣿⡁⠀⢰⣿⣏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣶⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢐⣾⣿⣿⢻⣿⣿⣿⣿⣿⡃⠀⣼⣿⣿⠀⠀⣼⣿⣿⡇⠙⣿⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡠⣀⣆⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠘⠍⠉⠉⠑⠛⠓⠁⠉⠀⠀⢠⣿⣿⣿⣤⠀⣿⣿⣿⡇⠀⠈⢿⣿⣿⣿⣿⣀⣀⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠙⠂⠀⠀⠻⣿⣿⣿⡄⠀⠀⠀⠀⠀⢰⣰⢦⣦⣶⣾⣿⣾⣶⣿⢿⣿⣟
⠀⠀⠀⠀⠀⣴⣧⣔⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠦⠀⣿⣿⣿⣇⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠨⣿⣿⣿⣄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⠀⣀⣄⣮⣿⣿⣿⡷⠀⡠⢀⢤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣽⣿⣿⠀⠀⢸⣿⣿⣿⣷⣾⣿⣇⠀⠀⠀⠀⠀⠀⠹⣿⣿⣟⠂⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣾⣿⣿⣿⣿⣿⣿⣷⣶⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠟⠋⣻⣿⡿⠀⢸⣿⣿⣨⣽⣿⣿⣿⣶⣿⣿⡿⢿⣿⣿⣿⣯⠉⠁⠀⠀⠀⠀⠀⠀⠺⣿⣿⣷⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡿⢿⣿⡍⣿⣿⣿⣭⠁⠻⠿⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡆⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠏⠈⠉⢿⣿⣿⣿⣿⠿⡿⠇⣸⡿⣿⣆⢸⣿⡿⣿⣯⡀⣿⣯⣭⣵⣆⣻⣿⣶⣿⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⡿⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠘⠿⣿⣶⣿⣿⣿⣿⣧⣠⣶⣶⣿⣟⣿⣿⣾⣿⣧⣼⣿⣷⡿⠿⠿⠿⠟⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣦⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⢸⠇⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠿⣿⠿⠿⡿⠿⣿⠿⢦⠶⣤⠦⡴⢶⠶⢦⡀⢠⡴⠶⠶⣿⠷⠶⡾⠿⢿⡿⠿⠿⣿⠷⡶⢶⣠⠶⠶⢶⠶⠶⣶⠶⠶⢦⣠⡶⠶⠶⡶⠶⠦⢤⠴⢤⠶⢤⠴⠶⡾⠶⢧⣠⠶⠿⢿⠿⣿⠿⢿⠿⠿⡿⠿⢿⣿
⣿⡇⢸⠤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⣿⠀⠶⡇⢠⠘⡇⠀⡆⢸⡄⠃⣼⢻⠀⠰⡆⠀⡆⢸⠀⠐⢀⡿⡇⠀⠆⡀⠀⠆⣸⠀⢸⠀⠘⠀⠀⡇⠰⢾⣿⡆⠀⣾⠀⣿⠀⠘⠀⠀⡇⠰⢾⣿
⣿⡇⠸⠀⢸⠀⠶⡇⢸⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⣿⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡇⢸⠀⢰⡇⠀⠇⢸⠀⢰⠀⣷⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⡀⡇⠀⣿⠀⣿⠀⡄⠀⠀⡇⠰⢾⣿
⣿⠿⠲⢷⠚⠲⠖⠳⠺⠖⠗⠚⡒⡷⠒⠓⠚⢲⣾⣶⣋⠓⠺⠒⠛⠒⠒⠒⠚⠒⠒⠒⠒⠋⠑⠒⠁⠈⠒⠊⠙⠒⠒⠛⠒⠚⠒⠁⠓⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠒⠒⣷⣶⣾⠀⠑⠒⠛⠒⠚⢲⣷⣷⣶⣷⣶⠚⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠶⢄⠀⠘⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣻⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠈⡆⢰⡙⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⡇⠘⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⢿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⢰⣿⣿⣆⠀⠀⠀⣾⡷⠀⠀⢰⣶⣿⣿⣧⡀⠙⢽⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⡇⠀⠸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⠀⠉⠙⠛⢿⡗⢸⣿⣿⣿⣿⣿⠉⢹⣿⣷⠀⠀⣿⣟⠀⠀⢸⣿⣿⣿⣿⣷⣄⢸⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⠃⠀⠀⠹⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⣿⣿⣿⣿⣷⢼⣿⡃⠀⢀⣿⣯⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣶⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡻⣟⣛⣿⣿⣿⡇⠀⣸⣿⣿⠀⠀⣾⣿⣿⡇⠙⣿⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠈⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡄⣠⣔⡂⣴⣴⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠓⠉⠋⠀⠁⠀⢨⣿⣿⣿⣦⠀⣿⣿⣿⡇⠀⠈⢿⣿⣿⣿⣿⣀⣀⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠙⠂⠀⠀⠻⣿⣿⣿⡄⠀⠀⠀⠀⠀⢰⣖⣴⣶⣦⣿⣿⣷⣿⣿⣿⣿⣯
⠀⠀⠀⠀⢀⢠⣤⣆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡏⠀⣿⣿⣿⣇⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠨⣿⣿⣿⣄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣰⠀⣂⣠⣖⣿⣿⣿⣯⠀⣤⣠⣠⣅⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣽⣿⣿⠀⠀⢸⣿⣿⣿⣷⣾⣿⣇⠀⠀⠀⠀⠀⠀⠹⣿⣿⣟⠂⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠟⠋⣻⣿⡿⠀⢸⣿⣿⣨⣽⣿⣿⣿⣶⣿⣿⡿⢿⣿⣿⣿⣯⠉⠁⠀⠀⠀⠀⠀⠀⠺⣿⣿⣷⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡿⢿⣿⡍⣿⣿⣿⣭⠁⠻⠿⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡆⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠏⠀⠉⢿⣿⣿⣿⣿⠿⠿⠇⣸⡿⣿⣆⢸⣿⡿⣿⣯⡀⣿⣯⣭⣵⣆⣻⣿⣶⣿⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⡿⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠘⠿⢿⣶⣿⣿⣿⣿⣧⣤⣶⣶⣿⣟⣿⣿⣾⣿⣧⣼⣿⣷⡿⠿⠿⠿⠟⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣦⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⢸⠇⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠿⣿⠿⠿⡿⠿⡿⠿⢦⠶⣤⠦⡴⢶⠶⢦⡀⢠⡴⠶⠶⣿⠷⠶⡿⠿⢿⡿⠿⠿⣿⠷⡶⢶⣰⠶⠶⢶⠶⠶⣶⠶⠶⢦⣠⡶⠶⠶⡶⠶⠦⢤⠴⢤⠶⢤⠴⠶⡾⠶⢧⣤⠶⠿⢿⠿⢿⠿⢿⠿⠿⡿⠿⢿⣿
⣿⡇⢸⡤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⣿⠀⠶⡇⢠⠘⡇⠀⡆⢸⡄⠃⣼⢻⠀⠰⡆⠀⡆⢸⠀⠐⢀⡿⡇⠀⠆⡀⠀⠆⣸⠀⢸⠀⠘⠀⠀⡇⠰⢾⣿⡆⠀⣾⠀⢸⠀⠘⠀⠀⡇⠰⢾⣿
⣿⡇⠸⠀⢸⠀⠶⡇⢸⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⣿⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡇⢸⠀⢰⡇⠀⠇⢸⠀⢰⠀⣷⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⡀⡇⠀⣿⠀⢸⠀⡄⠀⠀⡇⠰⢾⣿
⣿⠿⠲⢷⠚⠲⠖⠳⠺⠖⠗⠚⡒⡷⠒⠓⠚⢲⣾⣶⣋⠓⠺⠒⠛⠒⠒⠒⠚⠒⠒⠒⠒⠋⠑⠒⠁⠈⠒⠊⠙⠒⠒⠛⠒⠚⠒⠁⠓⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠒⠒⣷⣶⣾⠁⠑⠒⠛⠒⠚⢲⣷⣷⣶⣷⣶⠚⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠶⢄⠀⠸⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣻⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠈⡆⢰⡙⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⢼⣿⠀⠀⠀⠀⠀⠀⠀⢠⣿⢻⣿⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⡇⠘⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⢿⣿⣿⣿⣿⣿⡷⡀⠀⠀⠀⠀⢸⣿⣿⣆⠀⠀⠀⣿⣿⠀⠀⢠⣶⣿⣿⣧⡀⠙⢸⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⡇⠀⠹⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⠀⠉⠙⠿⢿⡿⣼⣿⣿⣿⣿⣿⠉⢹⣿⣿⠀⢀⣿⣿⠀⠀⢸⣿⣿⣿⣿⣷⣄⢸⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⠃⠀⠀⠹⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣍⣿⣿⣿⣿⣷⣸⣿⡃⠀⢰⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣶⣿⣿⠿⠋⠀⠀⠈⠀⠀⠀⠀⢻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⢿⣿⣿⣿⣿⣿⡇⠀⣼⣿⣿⠀⠀⣼⣿⣿⡇⠙⣿⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠘⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣠⣔⣂⡶⣔⣷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠙⠃⠠⡶⠙⠋⠉⠁⠀⢰⣿⣿⣿⣦⠀⣿⣿⣿⡇⠀⠈⢿⣿⣿⣿⣿⣀⣀⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠙⠂⠀⠈⠻⣿⣿⣿⡄⠀⠀⠀⠀⠀⢲⣴⣷⣶⣶⣿⣷⣷⣿⣿⣿⣿⣿
⢀⠀⠀⠀⢀⢠⣤⣆⣐⠀⠀⠀⠁⠀⠀⠀⠀⢀⣽⣿⣿⣿⡯⠀⣿⣿⣿⣇⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠨⣿⣿⣿⣄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣰⢢⣀⣠⣼⣿⣿⣿⣿⣀⣀⣈⠔⣥⣾⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣽⣿⣿⠀⠀⢸⣿⣿⣿⣷⣾⣿⣇⠀⠀⠀⠀⠀⠀⠹⣿⣿⣟⠂⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣷⣾⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠟⠋⣻⣿⡿⠀⢸⣿⣿⣨⣽⣿⣿⣿⣶⣿⣿⡿⢿⣿⣿⣿⣯⠉⠁⠀⠀⠀⠀⠀⠀⠺⣿⣿⣷⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡿⢿⣿⡍⣿⣿⣿⣭⠁⠻⠿⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡆⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠟⠈⠉⢿⣿⣿⣿⣿⠿⡿⠇⣸⡿⣿⣆⢸⣿⡿⣿⣯⡀⣿⣿⣭⣽⣆⣻⣿⣶⣿⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⡿⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠘⠿⢿⣶⣿⣿⣿⣿⣧⣠⣶⣶⣿⣟⣿⣿⣾⣿⣧⣼⣿⣷⡿⠿⠿⠿⠟⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣦⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⢸⡇⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠿⣿⠿⠿⡿⠿⡿⠿⢦⠶⣤⠦⡴⢶⠶⢦⠀⢠⡴⠶⠶⣿⠷⠶⡾⠿⢿⡿⠿⠿⣿⠷⡶⢶⣰⠶⠶⢶⠶⠶⣶⠶⠶⢦⣠⡶⠶⠶⡶⠶⠦⢤⠴⢤⠶⢤⠴⠶⡾⠶⢧⣠⠶⠿⢿⠿⢿⠿⢿⠿⠿⡿⠿⢿⣿
⣿⡇⢸⣤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⡿⠀⠶⡇⢠⠘⡇⠀⡆⢸⡄⠃⣼⢻⠀⠰⡆⠀⡆⢸⠀⠐⢀⡿⡇⠀⠆⡀⠀⠆⣸⠀⢸⠀⠘⠀⠀⡇⠰⢾⣿⡆⠀⣾⠀⢸⠀⠘⠀⠀⡇⠰⢾⣿
⣿⡇⠸⠀⢸⠀⠶⡇⢸⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⣿⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡇⢸⠀⢰⡇⠀⠇⢸⠀⢰⠀⣷⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⡀⡇⠀⣿⠀⢸⠀⡄⠀⠀⡇⠰⢾⣿
⣿⠿⠲⢷⠚⠲⠖⠳⠺⠖⠗⠚⡒⣷⠒⠓⠚⢲⣾⣶⣋⠓⠺⠒⠛⠒⠒⠒⠚⠒⠒⠒⠒⠋⠑⠒⠁⠈⠒⠊⠙⠒⠒⠛⠒⠚⠒⠁⠓⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠒⠒⣷⣶⣾⠁⠑⠒⠛⠒⠚⢲⣷⣷⣶⣷⣶⠚⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠦⢄⠀⠸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣻⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠀⡆⢸⡹⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢠⡇⢰⣾⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⡇⠸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠻⢿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⢠⣿⣿⣄⠀⠀⠀⣼⡏⠀⠀⢠⣶⣿⣿⣧⡈⠁⢸⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⡇⠀⠹⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠙⠟⠿⠣⠤⣿⣶⣶⣶⣦⠉⢙⣿⣷⠀⠀⣿⣯⠀⠀⢸⣿⣿⣿⣿⣷⣄⢸⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⠁⠀⠀⢹⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⢻⣿⣿⣿⣷⢸⣿⠃⠀⢰⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣶⣿⣿⠿⠋⠀⠀⠈⠀⠀⠀⠀⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⡿⣗⠻⠹⢻⣾⣿⡆⠀⣺⣿⣿⠀⠀⣼⣿⣿⡇⠙⣿⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠛⠀⠁⠀⠀⠀⢠⣿⣿⣿⣆⠀⣿⣿⣿⡇⠀⠈⢿⣿⣿⣿⣿⣀⣀⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠙⠂⠀⠀⠻⣿⣿⣷⡄⠀⠀⠀⠀⠀⢰⣄⣠⡴⣤⣇⣶⣶⣶⣰⣾⣖⡤
⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣸⣿⣿⣿⡆⠀⣿⣿⣿⣇⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢨⣿⣿⣷⣄⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⡀⣀⣠⣄⣾⣿⢿⣧⡄⡀⠀⣀⢀⣄⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣷⣾⣿⣇⠀⠀⠀⠀⠀⠀⠻⣿⣿⣟⠂⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣬⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠟⠛⣻⣿⡿⠀⢸⣿⣿⣨⣽⣿⣿⣿⣶⣿⣿⡿⢿⣿⣿⣿⣏⠉⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣇⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡿⢿⣿⡍⣿⣿⣿⣭⠁⠻⠿⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡄⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠏⠈⠉⢿⣿⣿⣿⣿⠿⡿⠇⣸⡿⣿⣆⢸⣿⡿⣿⣯⡀⣿⣿⣭⣽⣆⣻⣿⣶⣿⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⡷⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠘⠿⢿⣶⣿⣿⣿⣿⣧⣠⣶⣶⣿⣟⣻⣿⣾⣿⣧⣼⣿⣷⡿⠿⠿⠿⠟⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣦⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⢸⠇⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠿⣿⠿⠿⡿⠿⣿⠿⢦⠶⡤⠤⡴⢶⠶⢦⠀⢠⡴⠶⠶⣿⠷⠶⡾⠿⢿⡿⠿⠿⣿⠷⡶⢶⣠⠶⠶⢶⠶⠶⣶⠶⠶⢦⣀⡶⠶⠶⡶⠶⠦⢤⠴⢤⠴⢤⠴⠶⡾⠶⢧⣠⠶⠿⢿⠿⢿⠿⢿⠿⠿⡿⠿⢿⣿
⣿⡇⢸⠤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⣿⠀⠶⡇⢠⠘⡇⠀⡆⢸⡄⠃⣼⢻⠀⠰⡇⠀⡆⢸⠀⠐⢀⡿⡇⠀⠂⡀⠀⠆⣸⠀⢸⠀⠘⠀⠀⡇⠰⢾⣿⡆⠀⣾⠀⢸⠀⠘⠀⠀⡇⠰⢾⣿
⣿⡇⠸⠀⢸⠀⠶⡇⢸⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⣟⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡇⢸⠀⢰⡇⠀⠇⢸⠀⢰⠀⣷⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⡀⡇⠀⣿⠀⢸⠀⡄⠀⠀⡇⠰⢾⣿
⣿⠿⠲⢷⠚⠲⠖⠳⠺⠖⠗⠚⠒⡷⠒⠓⠚⢲⣾⣶⣋⠓⠺⠒⠛⠒⠒⠒⠚⠒⠒⠒⠒⠋⠑⠒⠁⠈⠒⠊⠙⠒⠒⠛⠒⠚⠒⠁⠓⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠒⠒⣷⣶⣾⠁⠑⠒⠛⠒⠚⢲⣷⣷⣶⣷⣶⠚⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠦⢄⠀⢸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣺⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠀⡆⢰⡹⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣽⠀⢰⣾⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠻⠟⠶⠀⢸⡇⠹⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠻⢿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠠⣿⣿⣆⠀⠀⠀⣼⣿⠀⠀⢠⣶⣿⣿⣧⡈⠁⢸⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⡇⠀⠹⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠉⠙⠻⢻⣧⠰⣿⣶⣶⣿⣧⠉⢹⣿⣿⠀⠀⣿⣿⠀⠀⢸⣿⣿⣿⣿⣷⣄⢸⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⠁⠀⠀⢹⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣉⣻⣿⣿⣿⣷⢸⣿⠃⠀⢰⣿⣇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣾⣿⣿⠿⠋⠀⠀⠈⠀⠀⠀⠀⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⡽⣿⢿⣿⣿⡆⠀⣼⣿⣿⠀⠀⣼⣿⣿⡇⠙⣿⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⠀⡀⣠⣔⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠁⠉⠏⠈⠁⠈⠀⢠⣿⣿⣿⣆⠀⣿⣿⣿⡇⠀⠈⢿⣿⣿⣿⣿⣀⣀⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠙⠂⠀⠀⠻⣿⣿⣿⡀⠀⠀⠀⠀⠀⢰⣤⣴⣶⣴⣿⣷⣿⣷⣿⣾⣯⣽
⠀⠀⠀⠀⠁⢠⣶⣄⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⣽⣿⣿⣿⡯⠀⣿⣿⣿⣇⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢨⣿⣿⣿⣄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿
⣀⢀⣀⣀⣄⣿⣿⣿⡇⠀⣀⠀⠀⣠⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣷⣾⣿⣇⠀⠀⠀⠀⠀⠀⠻⣿⣿⣟⠂⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣦⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠟⠛⣻⣿⡿⠀⢸⣿⣿⣨⣽⣿⣿⣿⣶⣿⣿⡿⢿⣿⣿⣿⣯⠉⠁⠀⠀⠀⠀⠀⠀⠻⣿⣿⣧⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡿⢿⣿⡍⣿⣿⣿⣭⠁⠻⠿⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡆⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠏⠈⠉⢿⣿⣿⣿⣿⠿⠿⠇⣸⡿⣿⣆⢸⣿⡿⣿⣯⡀⣿⣿⣭⣽⣆⣻⣿⣶⣿⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⡷⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠘⠿⢿⣶⣿⣿⣿⣿⣧⣠⣶⣶⣿⣟⣿⣿⣾⣿⣧⣼⣿⣷⡿⠿⠿⠿⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣦⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⢸⡇⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠿⣿⠿⠿⡿⠿⣿⠿⢦⠶⣤⠤⡴⢶⠶⢦⠀⢠⡴⠶⠾⣿⠷⠶⡿⠿⢿⡿⠿⠿⣿⠷⡶⢶⣰⠶⠶⢶⠶⠶⣶⠶⠶⢦⣠⡶⠶⠶⡶⠶⠦⢤⠴⢤⠶⢤⠴⠶⡾⠶⢧⣤⠶⠿⢿⠿⢿⠿⢿⠿⠿⡿⠿⢿⣿
⣿⡇⢸⡤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⣿⠀⠶⡇⢠⠘⡇⠀⡆⢸⡄⠃⣼⢻⠀⠰⡇⠀⡆⢸⠀⠐⢀⡿⡇⠀⠂⡀⠀⠆⣸⠀⢸⠀⠘⠀⠀⡇⠰⢾⣿⡆⠀⣾⠀⢹⠀⠘⠀⠀⡇⠰⢾⣿
⣿⡇⠸⠀⢸⠀⠶⡇⢸⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⣗⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡇⢸⠀⢰⡇⠀⠇⢸⠀⢰⠀⣷⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⡀⡇⠀⣿⠀⢸⠀⡄⠀⠀⡇⠰⢾⣿
⣿⠿⠲⢷⠚⠲⠖⠳⠺⠖⠗⠚⡒⡷⠒⠓⠚⢲⣾⣶⣋⠓⠚⠒⠛⠒⠒⠒⠚⠒⠒⠒⠒⠋⠑⠒⠁⠈⠒⠊⠙⠒⠒⠛⠒⠚⠒⠁⠓⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠒⠒⣷⣶⣾⠁⠑⠒⠛⠒⠚⢲⣷⣷⣶⣷⣶⠚⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡩⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠦⢄⠀⢸⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠈⡆⢸⡹⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣷⠀⢰⣾⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⡇⠹⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠻⢿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⣿⣿⣆⠀⠀⠀⣽⣿⠀⠀⢠⣶⣿⣿⣧⡉⠀⢸⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⡇⠀⢹⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠉⠙⠻⢿⢿⣴⣿⣶⣶⣿⣯⠉⢹⣿⣿⠀⠀⣿⣟⠀⠀⢸⣿⣿⣿⣿⣷⣄⢸⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⠃⠀⠀⢻⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⣻⣿⣿⣿⣷⢸⣿⡏⠀⢰⣿⣇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣶⣿⣿⠿⠋⠀⠀⠈⠀⠀⠀⠈⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⢿⣿⣿⣿⣿⡇⠀⣾⣿⣿⠀⠀⣼⣿⣿⡇⠙⣿⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⠀⣀⣄⣤⣤
⠀⠀⠀⠀⠀⡀⡀⠀⠈⠘⠁⠋⣘⢚⣇⠉⠉⠀⢠⣿⣿⣿⣔⠀⣿⣿⣿⡇⠀⠈⢿⣿⣿⣿⣿⣀⣀⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠙⠂⠀⠈⠻⣿⣿⣷⡀⠀⠀⠀⠀⠀⢲⣤⣴⣶⣾⣿⣿⣿⣾⣿⣿⣶⣿
⠀⠀⠀⠈⠀⢠⣶⣆⡀⠀⡀⠈⠁⠘⠀⠀⠀⢀⣸⣿⣿⣿⡟⠀⣿⣿⣿⣇⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢨⣿⣿⣿⣄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣠⣀⣄⣠⣄⣿⣿⣿⣯⣤⢅⡀⣤⣰⣾⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣷⣿⣿⣇⠀⠀⠀⠀⠀⠀⠻⣿⣿⣟⠂⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠟⠛⣻⣿⡿⠀⢸⣿⣿⣬⣽⣿⣿⣿⣶⣿⣿⡿⣿⣿⣿⣿⣯⠉⠁⠀⠀⠀⠀⠀⠀⠻⣿⣿⣧⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡿⢿⣿⡍⣿⣿⣿⣭⠁⠻⠿⢿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡄⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠏⠈⠉⢿⣿⣿⣿⣿⠿⡿⠇⣸⡿⣿⣆⢸⣿⡿⣿⣯⡀⣿⣿⣭⣽⣆⣻⣿⣶⣿⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⡷⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠘⠿⢿⣶⣿⣿⣿⣿⣧⣠⣶⣶⣿⣿⣿⣿⣾⣿⣧⣼⣿⣷⡿⠿⠿⠿⠟⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣦⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⢸⡇⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠿⣿⠿⠿⡿⠿⣿⠿⢦⠶⣤⠦⡴⢶⠶⢦⡀⢠⡴⠶⠾⣿⠷⠶⡾⠿⢿⡿⠿⠿⣿⠷⡶⢶⣴⠶⠶⢶⠶⠶⣶⠶⠶⢦⣠⡶⠶⠶⡶⠶⠦⢤⠴⢤⠶⢤⠴⠶⡾⠶⢧⣠⠶⠿⢿⠿⢿⠿⢿⠿⠿⡿⠿⢿⣿
⣿⡇⢸⢤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⣿⠀⠶⡇⢠⠘⡇⠀⡆⢸⡄⠃⣼⢻⠀⠰⡇⠀⡆⢸⠀⠐⢀⡿⡇⠀⠆⡀⠀⠆⣸⠀⢸⠀⠸⠀⠀⡇⠰⢾⣿⡆⠀⣾⠀⣿⠀⠸⠀⠀⡇⠰⢾⣿
⣿⡇⠸⠀⢸⠀⠶⡇⢸⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⣿⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡇⢸⠀⢰⡇⠀⠇⢸⠀⢰⠀⣷⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⡀⡇⠀⣿⠀⣿⠀⡄⠀⠀⡇⠰⢾⣿
⣿⠿⠲⢷⠚⠲⠖⠳⠺⠖⠗⠚⡒⣷⠒⠓⠚⢲⣾⣶⣋⠓⠺⠒⠛⠒⠒⠒⠚⠒⠒⠒⠒⠋⠑⠒⠁⠈⠒⠊⠙⠒⠒⠛⠒⠚⠒⠁⠓⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠒⠒⣷⣶⣾⠁⠑⠒⠛⠒⠚⢲⣷⣷⣶⣷⣶⠚⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠦⢄⠀⢸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣻⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠀⠆⢸⡻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⡄⠀⢰⣾⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⡇⠹⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⢿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⣿⣿⣆⡀⠀⠀⣼⣿⠀⠀⢠⣶⣿⣿⣧⡁⠀⢸⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⡇⠀⢻⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠉⠉⢟⢻⣿⡶⣾⣶⣶⣷⣿⠉⢙⣿⣿⡀⠀⣿⣿⠀⠀⢸⣿⣿⣿⣿⣷⣄⢸⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⠁⠀⠀⢻⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣍⣻⣿⣿⣿⣷⢨⣿⡋⠀⢰⣿⣷⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣾⣿⣿⠿⠋⠀⠀⠈⠀⠀⠀⠈⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣯⠯⣿⢿⣿⣿⡇⠀⣼⣿⣿⠀⠀⣼⣿⣿⡇⠙⣿⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⢸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⣀⣄⡠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠀⠊⠛⠝⠉⠁⠁⢰⣿⣿⣿⣆⠀⣿⣿⣿⡇⠀⠈⢿⣿⣿⣿⣿⣀⣀⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡮⠙⠂⠀⠈⠻⣿⣿⣷⡀⠀⠀⠀⠀⠀⢰⣶⣤⣶⣶⣿⣿⣿⣶⣿⣿⣦⣿
⠀⠀⠀⠀⠀⢀⣴⣦⢄⠁⠀⠀⠀⠈⠀⠀⠀⠀⣼⣿⣿⣿⠞⠀⣿⣿⣿⣇⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢨⣿⣿⣷⣄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣄⣠⣤⣠⣄⣿⣿⣿⡯⡤⡆⠀⡠⣠⣴⣶⣶⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣷⣾⣿⣇⠀⠀⠀⠀⠀⠀⠻⣿⣿⣟⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠟⠛⣻⣿⡿⠀⢸⣿⣿⣨⣽⣿⣿⣿⣶⣿⣿⡿⢿⣿⣿⣿⣯⠉⠁⠀⠀⠀⠀⠀⠀⠻⣿⣿⣧⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡿⢿⣿⡍⣿⣿⣿⣭⠁⠻⠿⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡆⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠋⠈⠉⢿⣿⣿⣿⣿⠿⠿⠆⣸⡿⣿⣆⢸⣿⡿⣿⣯⡀⣿⣿⣭⣵⣆⣻⣿⣶⣿⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⡷⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠘⠿⢿⣶⣿⣿⣿⣿⣧⣠⣶⣶⣿⣟⣻⣿⣾⣿⣧⣼⣿⣷⡿⠿⠿⠿⠟⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣦⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⢸⡇⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠿⣿⠿⠿⡿⠿⣿⠿⢦⠶⣤⠦⡴⢶⠶⢦⠀⢠⡴⠶⠶⣿⠷⠶⡾⠿⢿⡿⠿⠿⣿⠷⡶⢶⣴⠶⠶⢶⠶⠶⣶⠶⠶⢦⣠⡶⠶⠶⡶⠶⠦⢤⠴⢤⠶⢤⠴⠶⡾⠶⢧⣠⠶⠿⢿⠿⢿⠿⢿⠿⠿⡿⠿⢿⣿
⣿⡇⢸⡤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⣿⠀⠶⡇⢠⠘⡇⠀⡆⢸⡄⠃⣼⢻⠀⠰⡆⠀⡆⢸⠀⠐⢀⡿⡇⠀⠆⡀⠀⠆⣸⠀⢸⠀⠘⠀⠀⡇⠰⢾⣿⡆⠀⣾⠀⣿⠀⠘⠀⠀⡇⠰⢾⣿
⣿⡇⠸⠀⢸⠀⠶⡇⢸⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⣿⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡇⢸⠀⢰⡇⠀⠇⢸⠀⢰⠀⣷⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⡁⡇⠀⣿⠀⣿⠀⡄⠀⠀⡇⠰⢾⣿
⣿⠿⠲⢷⠚⠲⠖⠳⠺⠖⠗⠚⡒⡷⠒⠓⠚⢲⣾⣶⣋⠓⠺⠒⠛⠒⠒⠒⠚⠒⠒⠒⠒⠋⠑⠒⠁⠈⠒⠊⠙⠒⠒⠛⠒⠚⠒⠁⠓⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠒⠒⣷⣶⣾⠁⠑⠒⠛⠒⠚⢲⣷⣷⣶⣷⣶⠚⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠦⢄⠀⢸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠀⡆⢸⡿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠠⣤⣀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠔⠀⠀⢰⣾⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠻⠟⠶⠀⢸⡇⢻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⢿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣿⣿⣆⠀⠀⠀⣼⡿⠀⠀⢠⣶⣿⣿⣧⡀⠀⢸⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⡇⠀⢻⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠉⠙⠛⠻⢿⠒⣶⣶⣶⣾⣿⠉⠙⣿⣿⠀⠀⣿⣟⠀⠀⢸⣿⣿⣿⣿⣷⣄⢸⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⠁⠀⠀⢻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣻⣿⣿⣿⣷⣠⣿⡏⠀⢰⣿⣯⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣾⣿⣿⠿⠋⠀⠀⠈⠀⠀⠀⠈⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠛⢛⢽⣿⣿⡇⠀⣸⣿⣿⠀⠀⣸⣿⣿⡇⠙⣿⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠸⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⡀⣀⡤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⠀⠙⠁⠁⠀⠀⢰⣿⣿⣿⡄⠀⣿⣿⣿⡇⠀⠈⢿⣿⣿⣿⣿⣀⣀⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡮⠙⠂⠀⠈⠻⣿⣿⣷⡀⠀⠀⠀⠀⠀⢰⣤⣤⣴⣢⡲⣾⣯⣾⣶⣯⣿⣿
⠀⠀⠀⠀⠀⢀⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡏⠀⣿⣿⣿⣇⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢨⣿⣿⣷⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣀⣀⣀⣻⣿⣿⡇⡄⡀⠀⠠⠠⣰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣷⣾⣿⣇⠀⠀⠀⠀⠀⠀⠻⣿⣿⣟⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣼⣿⣿⣿⣿⣿⣿⣿⣾⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠟⠛⣻⣿⡿⠀⢸⣿⣿⣨⣽⣿⣿⣿⣶⣿⣿⡿⢿⣿⡿⣿⣯⠉⠁⠀⠀⠀⠀⠀⠀⠻⣿⣿⣇⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡿⢿⣿⡍⣿⣿⣿⣭⠁⠻⠿⢿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡄⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠏⠈⠉⢿⣿⣿⣿⣿⠿⡿⠆⣸⡿⣿⣇⢸⣿⡿⣿⣯⡀⣿⣯⣭⣽⣆⣻⣿⣶⣿⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⡷⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠘⠿⢿⣶⣿⣿⣿⣿⣧⣠⣶⣶⣿⣟⣿⣿⣾⣿⣧⣼⣿⣷⡿⠿⠿⠿⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣦⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⢸⡇⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠿⣿⠿⠿⡿⠿⡿⠿⢦⠶⣤⠦⡴⢶⠶⢦⡀⢠⡴⠶⠶⣿⠷⠶⡿⠿⢿⡿⠿⠿⣿⠷⡶⢶⣰⠶⠶⢶⠶⠶⣶⠶⠶⢦⣠⡶⠶⠶⡶⠶⠦⢤⠴⢤⠶⢤⠴⠶⡾⠶⢧⣠⠶⠿⢿⠿⢿⠿⢿⠿⠿⡿⠿⢿⣿
⣿⡇⢸⠤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⣿⠀⠶⡇⢠⠘⡇⠀⡆⢸⡄⠃⣼⢻⠀⠰⡇⠀⡆⢸⠀⠐⢀⡿⡇⠀⠂⡀⠀⠆⣸⠀⢸⠀⠘⠀⠀⡇⠰⢾⣿⡆⠀⣾⠀⢸⠀⠘⠀⠀⡇⠰⢾⣿
⣿⡇⠸⠀⢸⠀⠶⡇⢸⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⣿⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡇⢸⠀⢰⡇⠀⠇⢸⠀⢰⠀⣷⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⡀⡇⠀⣿⠀⢸⠀⡄⠀⠀⡇⠰⢾⣿
⣿⠿⠲⢷⠚⠲⠖⠳⠺⠖⠗⠚⡒⣷⠒⠓⠚⢲⣾⣶⣋⠓⠺⠒⠛⠒⠒⠒⠚⠒⠒⠒⠒⠋⠑⠒⠁⠈⠒⠊⠙⠒⠒⠛⠒⠚⠒⠁⠓⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠒⠒⣷⣶⣾⠀⠑⠒⠛⠒⠚⢲⣷⣷⣶⣷⣶⠚⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠦⢄⠀⢸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣸⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠀⡆⢸⡿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠠⣤⣀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠨⠅⠀⠀⢰⣾⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠻⠻⠲⠀⢸⡇⢻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⢿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣿⣿⣆⡀⠀⠀⣼⡷⠀⠀⢠⣶⣿⣿⣧⡀⠀⢸⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⡇⠀⢻⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠉⠙⠻⡿⠿⢶⣾⣶⣶⣾⣿⡉⠙⣿⣿⠀⠀⣿⣟⠀⠀⢸⣿⣿⣿⣿⣷⣄⢸⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⠁⠀⠀⢻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⢻⣿⣿⣿⣷⢠⣿⡃⠀⢰⣿⣏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣶⣿⣿⠿⠋⠀⠀⠈⠀⠀⠀⠈⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠟⣻⢿⣿⣿⡇⠀⣼⣿⣿⠀⠀⣾⣿⣿⡇⠙⣿⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⢸⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠐⠑⠈⠉⠁⠀⢰⣿⣿⣿⣄⠀⣿⣿⣿⡇⠀⠈⢿⣿⣿⣿⣿⣀⣀⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠙⠂⠀⠈⠻⣿⣿⣷⡀⠀⠀⠀⠀⠀⠠⣢⣤⣶⣶⣖⣿⣿⣶⣾⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣾⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡅⠀⣿⣿⣿⣇⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢸⣿⣿⣷⡄⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣀⣀⣀⣻⣿⣿⡷⡀⠀⢀⣠⡄⣠⣖⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣽⣿⣿⠀⠀⢸⣿⣿⣿⣷⣾⣿⣇⠀⠀⠀⠀⠀⠀⠻⣿⣿⣏⠂⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣶⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠟⠋⣻⣿⡿⠀⢸⣿⣿⣨⣽⣿⣿⣿⣶⣿⣿⡿⢿⣿⣿⣿⣯⠉⠁⠀⠀⠀⠀⠀⠀⢻⣿⣿⣇⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡿⢿⣿⡍⣿⣿⣿⣭⠁⠻⠿⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡄⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠏⠈⠉⢿⣿⣿⣿⣿⠿⡿⠆⣸⡿⣿⣆⢸⣿⡿⣿⣯⡀⣿⣿⣭⣽⣆⣻⣿⣶⣿⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⡷⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠘⠿⢿⣶⣿⣿⣿⣿⣧⣠⣶⣶⣿⣿⣿⣿⣾⣿⣧⣼⣿⣷⡿⠿⠿⠿⠟⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣦⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⢸⡇⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠿⣿⠿⠿⡿⠿⡿⠿⢦⠶⣤⠤⡴⢶⠶⢦⡀⢠⡴⠶⠾⣿⠷⠾⡿⠿⢿⡿⠿⠿⣿⠷⡶⢶⣠⠶⠶⢶⠶⠶⣶⠶⠶⢦⣠⡶⠶⠶⡶⠶⠦⢤⠴⢤⠶⢤⠴⠶⡾⠶⢧⣠⠶⠿⢿⠿⢿⠿⢿⠿⠿⡿⠿⢿⣿
⣿⡇⢸⠤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⣿⠀⠶⡇⢠⠘⡇⠀⡆⢸⡄⠃⣼⢻⠀⠰⡇⠀⡆⢸⠀⠐⢀⡿⡇⠀⠂⡀⠀⠆⣸⠀⢸⠀⠘⠀⠀⡇⠰⢾⣿⡆⠀⣾⠀⢸⠀⠘⠀⠀⡇⠰⢾⣿
⣿⡇⠸⠀⢸⠀⠶⡇⢸⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⣿⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡇⢸⠀⢰⡇⠀⠇⢸⠀⢰⠀⣷⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⡀⡇⠀⣿⠀⢸⠀⡄⠀⠀⡇⠰⢾⣿
⣿⠿⠲⢷⠚⠲⠖⠳⠺⠖⠗⠚⡒⣷⠒⠓⠚⢲⣾⣶⣋⠓⠺⠒⠛⠒⠒⠒⠚⠒⠒⠒⠒⠋⠑⠒⠁⠈⠒⠊⠙⠒⠒⠛⠒⠚⠒⠁⠓⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠒⠒⣷⣶⣾⠁⠑⠒⠛⠒⠚⢲⣷⣷⣶⣷⣶⠚⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠦⢄⠀⢸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣸⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠀⡆⢸⡿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢩⠀⠀⠀⢰⣾⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⡇⢻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠻⢿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣿⣿⣦⡀⠀⠀⣿⣿⠀⠀⢠⣶⣿⣿⣧⡀⠀⢸⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⡇⠀⢻⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠉⠙⢿⠿⠿⠦⣾⣶⣶⣾⣿⡉⠙⣿⣿⠄⠀⣿⣿⠀⠀⢸⣿⣿⣿⣿⣷⣄⢸⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⠁⠀⠈⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣻⣿⣿⣿⣷⣄⣿⡇⠀⢰⣿⣏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣶⣿⣿⠿⠋⠀⠀⠈⠀⠀⠀⠘⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⡿⢛⢛⣿⣿⣿⡷⠀⣾⣿⣿⠀⠀⣾⣿⣿⡇⠙⣿⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⢹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⢁⠐⠀⠽⠋⠈⠁⠁⢰⣿⣿⣿⣄⠀⣿⣿⣿⡇⠀⠈⢿⣿⣿⣿⣿⣀⣀⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠙⠂⠀⠈⠻⣿⣿⣷⡀⠀⠀⠀⠀⠀⢠⣤⣴⣶⣶⣶⣷⣿⣾⣵⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣶⣦⡀⠀⠈⠀⠀⠁⠀⠀⠀⢀⣼⣿⣿⣿⡧⠀⣿⣿⣿⣇⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢸⣿⣿⣷⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⠁⣀⣀⣄⣻⣿⣿⣿⠄⠄⠀⢀⣀⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣷⣿⣿⣇⠀⠀⠀⠀⠀⠈⠻⣿⣿⣏⠂⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣴⣿⣿⣿⣿⣿⣿⣿⣾⣷⣧⣾⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠟⠛⣻⣿⡿⠀⢸⣿⣿⣬⣽⣿⣿⣿⣶⣿⣿⡿⢿⣿⣿⣿⣯⠉⠁⠀⠀⠀⠀⠀⠀⠻⣿⣿⣧⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡿⢿⣿⡍⣿⣿⣿⣭⠁⠻⠿⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡄⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⢏⠈⠉⢿⣿⣿⣿⣿⠿⡿⠆⣸⡿⣿⣆⢸⣿⡿⣿⣯⡀⣿⣿⣭⣽⣆⣻⣿⣶⣿⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⡿⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠘⠿⣿⣶⣿⣿⣿⣿⣧⣤⣶⣶⣿⣟⣿⣿⣾⣿⣧⣼⣿⣷⡿⠿⠿⠿⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣦⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⢸⡇⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠿⣿⠿⠿⡿⠿⣿⠿⢦⠶⣤⠦⡴⢶⠶⢦⠀⢠⡴⠶⠾⣿⠷⠶⡿⠿⢿⡿⠿⠿⣿⠷⡶⢶⣴⠶⠶⢶⠶⠶⣶⠶⠶⢦⣰⡶⠶⠶⡶⠶⠦⢤⠶⢤⠶⢤⠴⠶⡾⠶⢧⣠⠶⠿⢿⠿⢿⠿⢿⠿⠿⡿⠿⢿⣿
⣿⡇⢸⣤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⣯⠀⠶⡇⢠⠘⡇⠀⡆⢸⡀⠃⣼⢻⠀⠰⡇⠀⡆⢸⠀⠐⢀⡿⡇⠀⠆⡀⠀⠆⣸⠀⢸⠀⠸⠀⠀⡇⠰⢾⣿⡆⠀⣾⠀⣿⠀⠸⠀⠀⡇⠰⢾⣿
⣿⡇⠸⠀⢸⠀⠶⡇⢸⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⣏⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡏⢸⠀⢰⡇⠀⠇⢸⠀⢰⠀⣿⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⡁⡇⠀⣿⠀⣿⠀⡄⠀⠀⡇⠰⢾⣿
⣿⠿⠲⢷⠚⠲⠖⠳⠺⠖⠗⠚⡒⣷⠒⠓⠚⢲⣾⣶⣋⠓⠺⠒⠛⠒⠒⠒⠚⠒⠒⠒⠒⠋⠑⠒⠁⠈⠒⠊⠙⠒⠒⠛⠒⠚⠒⠁⠓⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠒⠒⣷⣶⣾⠁⠑⠒⠛⠒⠚⢲⣷⣷⣶⣷⣶⠚⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠦⢄⠀⢸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠈⡆⢸⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣄⣀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⢺⣿⠀⠀⠀⠀⠀⢄⠀⠀⠀⢰⣾⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⡇⢻⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠻⢿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢀⣿⣿⣧⡀⠀⠀⣾⡿⠀⠀⢠⣶⣿⣿⣧⡀⠀⢸⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⡇⠀⢻⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠉⠛⣿⢿⠴⣾⣿⣾⣿⣿⡉⠙⣿⣿⡆⢀⣿⣿⠀⠀⢸⣿⣿⣿⣿⣷⣄⢸⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⠃⠀⠀⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠀⠀⠀⠀⠀⠀⠀⣝⣻⣿⣿⣿⣷⣤⣿⡟⠀⢴⣿⣯⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣶⣿⣿⠿⠋⠀⠀⠈⠀⠀⠀⠘⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⠛⢿⣿⣿⣿⡯⠀⣿⣿⣿⠀⠀⣼⣿⣿⡇⠙⣿⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⢻⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⢀⣠⡠⣠⣤
⠀⠀⠀⠀⣀⠀⢀⠐⠋⠙⠃⠀⠀⡐⠚⠉⠉⠁⢰⣿⣿⣿⣄⠀⣿⣿⣿⡇⠀⠈⢿⣿⣿⣿⣿⣀⣀⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡮⠙⠂⠀⠈⠻⣿⣿⣷⡀⠀⠀⠀⠀⠀⢲⣶⣴⣶⣾⣷⣿⣿⣿⣿⣿⣿⣾
⠀⠀⠀⠈⠈⢁⣾⣶⣀⠀⡀⠀⠀⠉⠁⠀⠀⢀⣾⣿⣿⣿⡷⠁⣿⣿⣿⣇⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢸⣿⣿⣷⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣠⢂⣀⣠⣄⣺⣿⣿⣷⡖⡤⢀⣀⡠⣲⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣷⣾⣿⣇⠀⠀⠀⠀⠀⠀⠻⣿⣿⣏⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠟⠛⣻⣿⡿⠀⢸⣿⣿⣬⣽⣿⣿⣿⣶⣿⣿⡿⢿⣿⣿⣿⣯⠉⠁⠀⠀⠀⠀⠀⠀⢻⣿⣿⣇⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡿⢿⣿⡍⣿⣿⣿⣭⠁⠻⠿⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡄⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⢏⠈⠉⢿⣿⣿⣿⣿⠿⡿⠇⣸⡿⣿⣆⢸⣿⡿⣿⣯⡀⣿⣿⣭⣽⣆⣻⣿⣶⣿⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⡷⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠘⠿⢿⣶⣿⣿⣿⣿⣧⣠⣶⣶⣿⣟⣿⣿⣾⣿⣧⣼⣿⣷⡿⠿⠿⠿⠟⠛⠟⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣦⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⢸⡇⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠿⣿⠿⠿⡿⠿⣿⠿⢦⠶⣤⠦⡴⢶⠶⢦⡀⢠⡴⠶⠶⣿⠷⠶⡿⠿⢿⡿⠿⠿⣿⠷⡶⢶⣰⠶⠶⢶⠶⠶⣶⠶⠶⢦⣠⡶⠶⠶⡶⠶⠦⢤⠴⢤⠴⢤⠴⠶⡾⠶⢧⣤⠶⠿⢿⠿⢿⠿⢿⠿⠿⡿⠿⢿⣿
⣿⡇⢸⡤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⣿⠀⠶⡇⢠⠘⡇⠀⡆⢸⡄⠃⣼⢻⠀⠰⡇⠀⡆⢸⠀⠐⢀⡿⡇⠀⠆⡀⠀⠆⣸⠀⢸⠀⠸⠀⠀⡇⠰⢾⣿⡆⠀⣾⠀⣿⠀⠸⠀⠀⡇⠰⢾⣿
⣿⡇⠸⠀⢸⠀⠶⡇⢸⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⣿⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡇⢸⠀⢰⡇⠀⠇⢸⠀⢰⠀⣷⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⡁⡇⠀⣿⠀⣿⠀⡄⠀⠀⡇⠰⢾⣿
⣿⠿⠲⢷⠚⠲⠖⠳⠺⠖⠗⠚⡒⣷⠒⠓⠚⢲⣾⣶⣋⠓⠺⠒⠛⠒⠒⠒⠚⠒⠒⠒⠒⠋⠑⠒⠁⠈⠒⠊⠙⠒⠒⠛⠒⠚⠒⠁⠓⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠒⠒⣷⣶⣾⠁⠑⠒⠛⠒⠚⢲⣷⣷⣶⣷⣶⠚⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠦⢄⠀⢸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠈⡆⢸⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣄⣀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⡇⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠻⢿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣿⣿⣧⡀⠀⠀⣿⣟⠀⠀⢰⣶⣿⣿⣧⡀⠀⢸⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⡇⠀⢿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠉⠛⣻⣿⠰⣿⣿⣾⣿⣿⡉⠉⣿⣿⡆⠀⣿⣿⠀⠀⢸⣿⣿⣿⣿⣷⣄⢸⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⠃⠀⠈⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠀⠀⠀⠀⠀⠀⠀⣙⣛⣿⣿⣿⣷⡄⣿⡿⠀⣸⣿⣟⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣶⣿⣿⠿⠋⠀⠀⠈⠀⠀⠀⠘⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠿⠿⣿⣿⣿⣿⡯⠠⣾⣿⣿⠀⠀⣼⣿⣿⡇⠙⣿⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⢻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣴⡤⣀
⠀⠀⠀⠀⠀⠀⠀⡐⠑⠈⠁⠀⠀⠘⠛⠉⠁⠀⢠⣿⣿⣿⣄⠀⣿⣿⣿⡇⠀⠈⢿⣿⣿⣿⣿⣀⣀⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡮⠙⠂⠀⠈⠻⣿⣿⣧⡀⠀⠀⠀⠀⠀⢢⣤⣤⣶⣴⣾⣾⣿⣷⣾⣿⣿⣿
⠀⠀⠀⠀⠀⢈⣤⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡯⠀⣿⣿⣿⣇⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢸⣿⣿⣷⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣄⣀⣀⣠⣄⣼⣿⣿⣷⣠⡄⢀⣄⣀⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣷⣿⣿⣇⠀⠀⠀⠀⠀⠀⠻⣿⣿⣏⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠟⠋⣻⣿⡿⠀⢸⣿⣿⣬⣽⣿⣿⣿⣶⣿⣿⡿⢿⣿⣿⣿⣯⠉⠁⠀⠀⠀⠀⠀⠀⠻⣿⣿⣧⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡿⢿⣿⡍⣿⣿⣿⣭⠁⠻⠿⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡄⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠏⠈⠉⢿⣿⣿⣿⣿⠿⡿⠇⣸⡿⣿⣆⢸⣿⡿⣿⣯⡀⣿⣿⣭⣽⣆⣻⣿⣶⣿⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⡷⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠘⠿⢿⣶⣿⣿⣿⣿⣧⣠⣶⣶⣿⣟⣿⣿⣾⣿⣧⣼⣿⣷⡿⠿⠿⠿⠟⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣦⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⢸⡇⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠿⣿⠿⠿⡿⠿⣿⠿⢦⠶⣤⠦⡴⢶⠶⢦⡀⢠⡴⠶⠾⣿⠷⠶⡾⠿⢿⡿⠿⠿⣿⠷⡶⢶⣰⠶⠶⢶⠶⠶⣶⠶⠶⢦⣠⡶⠶⠶⡶⠶⠦⢤⠴⢦⠶⢤⠴⠶⡾⠶⢧⣤⠶⠿⢿⠿⢿⠿⢿⠿⠿⡿⠿⢿⣿
⣿⡇⢸⡤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⣿⠀⠶⡇⢠⠘⡇⠀⡆⢸⡀⠃⣼⢻⠀⠰⡇⠀⡆⢸⠀⠐⢀⡿⡇⠀⠆⡀⠀⠆⣸⠀⢸⠀⠸⠀⠀⡇⠰⢾⣿⡆⠀⣾⠀⣿⠀⠸⠀⠀⡇⠰⢾⣿
⣿⡇⠸⠀⢸⠀⠶⡇⢸⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⣿⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡇⢸⠀⢰⡇⠀⠇⢸⠀⢰⠀⣷⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⡁⡇⠀⣿⠀⣿⠀⡄⠀⠀⡇⠰⢾⣿
⣿⠿⠲⢷⠚⠲⠖⠳⠺⠖⠗⠚⡒⣷⠒⠓⠚⢲⣾⣶⣋⠓⠺⠒⠛⠒⠒⠒⠚⠒⠒⠒⠒⠋⠑⠒⠁⠈⠒⠊⠙⠒⠒⠛⠒⠚⠒⠁⠓⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠒⠒⣷⣶⣾⠁⠑⠒⠛⠒⠚⢲⣷⣷⣶⣷⣶⠚⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠦⢄⠀⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣨⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠈⡆⢸⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣄⣀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⢼⣿⠀⠀⠀⠈⠁⠀⠀⠀⠀⢰⣾⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⡇⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⢿⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⣿⣿⣧⡀⠀⠀⣾⣿⠀⠀⢰⣶⣿⣿⣧⡀⠀⢸⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⡇⠈⢿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠉⠛⢿⣿⡵⣾⣾⣶⣿⣷⡉⠉⣿⣿⠆⠀⣿⡿⠀⠀⢸⣿⣿⣿⣿⣷⣄⢸⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⠃⠀⠈⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠁⠀⠀⠀⠀⠀⠀⣹⣻⣿⣿⣿⣷⡄⣿⣿⠀⢸⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣶⣿⣿⠿⠋⠀⠀⠈⠀⠀⠀⠘⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢜⣿⣿⣯⠛⢿⣿⣿⣿⡿⠀⣾⣿⣿⠀⠀⣾⣿⣿⡇⠙⣿⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⢿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠍⠅⠁⠈⡰⠒⠁⠉⠁⢸⣿⣿⣿⣴⡀⣿⣿⣿⡇⠀⠈⢿⣿⣿⣿⣿⣀⣀⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠙⠂⠀⠈⠻⣿⣿⣧⡀⠀⠀⠀⠀⠀⢲⣤⣠⣤⣶⣶⣾⣿⣾⣿⣾⣿⣿
⠀⠀⠀⠈⠀⠈⣴⣦⡄⠄⡈⠀⠀⠘⠀⠀⠀⢀⣼⣿⣿⣿⡇⠀⣿⣿⣿⣇⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢼⣿⣿⣷⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣠⣠⣀⣀⣄⣽⣿⣿⣿⡌⢀⡀⣀⣄⣔⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣷⣿⣿⣇⠀⠀⠀⠀⠀⠀⢻⣿⣿⣏⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠟⠋⣻⣿⡿⠀⢸⣿⣿⣬⣽⣿⣿⣿⣶⣿⣿⡿⢿⣿⣿⣿⣯⠉⠁⠀⠀⠀⠀⠀⠀⢻⣿⣿⣇⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡿⢿⣿⡍⣿⣿⣿⣭⠁⠻⠿⠿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡄⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⢏⠈⠉⢿⣿⣿⣿⣿⠿⡿⠇⣸⡿⣿⣆⢸⣿⡿⣿⣯⡀⣿⣿⣭⣽⣆⣻⣿⣶⣿⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⡷⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠘⠿⢿⣶⣿⣿⣿⣿⣧⣠⣶⣶⣿⣟⣿⣿⣾⣿⣧⣼⣿⣷⡿⠿⠿⠿⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣦⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⢸⡇⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠿⣿⠿⠿⡿⠿⣿⠿⢦⠶⣤⠦⡴⢶⠶⢦⡀⢠⡴⠶⠶⣿⠷⠶⡾⠿⢿⡿⠿⠿⣿⠷⡶⢶⣴⠶⠶⢶⠶⠶⣶⠶⠶⢦⣠⡶⠶⠶⡶⠶⠦⢤⠴⢦⠶⢤⠴⠶⡾⠶⢧⣤⠾⠿⢿⠿⢿⠿⢿⠿⠿⡿⠿⢿⣿
⣿⡇⢸⢤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⣿⠀⠶⡇⢠⠘⡇⠀⡆⢸⡀⠃⣼⢻⠀⠰⡇⠀⡆⢸⠀⠐⢀⡿⡇⠀⠆⡀⠀⠆⣸⠀⢸⠀⠸⠀⠀⡇⠰⢾⣿⡆⠀⣾⠀⣿⠀⠸⠀⠀⡇⠰⢾⣿
⣿⡇⠸⠀⢸⠀⠶⡇⢸⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⣿⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡇⢸⠀⢰⡇⠀⠇⢸⠀⢰⠀⣿⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⡀⡇⠀⣿⠀⣿⠀⡄⠀⠀⡇⠰⢾⣿
⣿⠿⠲⢷⠚⠲⠖⠳⠺⠖⠗⠚⡒⣷⠒⠓⠚⢲⣾⣶⣋⠓⠺⠒⠛⠒⠒⠒⠚⠒⠒⠒⠒⠋⠑⠒⠁⠈⠒⠊⠙⠒⠒⠛⠒⠚⠒⠁⠓⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠒⠒⣷⣶⣾⠁⠑⠒⠛⠒⠚⢲⣷⣷⣶⣷⣶⠚⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠦⢄⠀⢸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣜⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠈⡆⢸⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⡇⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠿⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⣿⣿⣧⡀⠀⠀⣿⣿⠀⠀⢰⣶⣿⣿⣧⡀⠀⢸⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⡇⠈⢿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠉⠛⠿⢿⠶⣾⣿⣾⣿⣿⡌⠉⣿⣿⡆⢀⣿⣿⠀⠀⢸⣿⣿⣿⣿⣷⣄⢸⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⠃⠀⠈⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠁⠀⠀⠀⠀⠀⠀⢈⣙⣿⣿⣿⣷⡄⣿⣏⠀⢸⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣶⣿⣿⠿⠋⠀⠀⠈⠀⠀⠀⠸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⢤⣿⣿⡯⠟⣯⣿⣿⣿⣿⠀⣿⣿⣿⠀⠀⣿⣿⣿⡇⠙⣿⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠒⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠁⠀⠀⠐⡚⠁⠁⠁⢰⣿⣿⣿⣦⣄⣿⣿⣿⡇⠀⠈⢿⣿⣿⣿⣿⣀⣀⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠙⠂⠀⠈⠻⣿⣿⣧⡀⠀⠀⠀⠀⠀⢢⣤⣤⣶⣦⣦⣶⣶⣶⣿⣿⣷⣾
⠀⠀⠀⠀⠀⢀⣴⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⡯⣿⣿⣿⣇⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢸⣿⣿⣷⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣄⣀⣀⣀⣽⣿⣿⣿⣆⡀⠀⡀⣀⣢⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣷⣿⣿⣇⠀⠀⠀⠀⠀⠀⢻⣿⣿⣏⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠟⠛⣻⣿⡿⠀⢸⣿⣿⣬⣽⣿⣿⣿⣶⣿⣿⡿⢿⣿⣿⣿⣯⠉⠁⠀⠀⠀⠀⠀⠀⢻⣿⣿⣇⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡿⢿⣿⡍⣿⣿⣿⣭⠁⠻⠿⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡄⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣽⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⢏⠈⠉⢿⣿⣿⣿⣿⠿⡿⠇⣸⡿⣿⣆⢸⣿⡿⣿⣯⡀⣿⣿⣭⣽⣆⣻⣿⣶⣿⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⡷⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠘⠿⣿⣶⣿⣿⣿⣿⣧⣠⣶⣶⣿⣟⣿⣿⣾⣿⣧⣼⣿⣷⡿⠿⠿⠿⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣦⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⢸⠇⠠⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠿⣿⠿⠿⡿⠿⣿⠿⢦⠶⣤⠦⡴⢶⠶⢦⡀⢠⡴⠶⠶⣿⠿⠶⡿⠿⢿⡿⠿⠿⣿⠷⡶⢶⣴⠶⠶⢶⠶⠶⣶⠶⠶⢶⣠⡶⠶⠶⡶⠶⠦⢤⠴⢤⠶⢤⠴⠶⡾⠶⢧⣤⠶⠿⢿⠿⢿⠿⢿⠿⠿⡿⠿⢿⣿
⣿⡇⢸⢤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⣿⠀⠶⡇⢠⠘⡇⠀⡆⢸⡀⠃⣼⢻⠀⠰⡇⠀⡆⢸⠀⠐⢀⡿⡇⠀⠆⡀⠀⠆⣸⠀⢸⠀⠘⠀⠀⡇⠰⢾⣿⡆⠀⣾⠀⣿⠀⠘⠀⠀⡇⠰⢾⣿
⣿⡇⠸⠀⢸⠀⠶⡇⢸⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⣿⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡇⢸⠀⢰⡇⠀⠇⢸⠀⢰⠀⣷⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⡁⡇⠀⣿⠀⣿⠀⡄⠀⠀⡇⠰⢾⣿
⣿⠿⠲⢷⠚⠲⠖⠳⠺⠖⠗⠚⠒⣷⠒⠓⠚⢲⣾⣶⣋⠓⠺⠒⠛⠒⠒⠒⠚⠒⠒⠒⠒⠋⠑⠒⠁⠈⠒⠊⠙⠒⠒⠛⠒⠚⠒⠁⠓⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠒⠒⣷⣶⣾⠁⠑⠒⠛⠒⠚⢲⣷⣷⣶⣷⣶⠚⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣝⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠦⢄⠀⢸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣌⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⠖⣫⣶⣿⣿⣷⣦⡄⠈⡆⢸⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⠀⠀⠞⣡⣾⡟⠀⠀⠈⠛⠛⠛⠲⠀⢸⡇⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⢿⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⣿⣿⣧⡀⠀⠀⣾⣿⠀⠀⢰⣶⣿⣿⣧⡀⠀⢸⣿⣿⣿⠀⠀⣼⣿⣿⠀⠀⢰⣶⣶⣶⣶⣷⠀⢸⡇⠈⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠉⠉⠻⣿⣿⣶⣿⣷⣾⣿⣷⡍⠉⣿⣿⡆⢀⣿⣟⠀⠀⢸⣿⣿⣿⣿⣷⣄⢸⣿⣿⣿⠀⣼⢿⣿⣿⣇⠀⠈⢉⣿⣿⣿⠏⠀⢸⠃⠀⠈⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣛⣿⣿⣿⣷⡄⣿⣟⠀⣾⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠀⣿⡌⠛⢿⣿⣿⣶⣿⣿⠿⠋⠀⠀⠈⠀⠀⠀⠘⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠋⠿⣿⣿⣿⣷⠀⣿⣿⣿⠀⠀⣿⣿⣿⡇⠙⣿⣿⣿⣿⣿⣿⠀⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⢿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⠀⢠⣤⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢈⠁⡀⠀⢙⠋⠃⠈⠀⢰⣿⣿⣿⣶⡠⣿⣿⣿⡇⠀⠈⢿⣿⣿⣿⣿⣀⣀⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠙⠂⠀⠈⠻⣿⣿⣧⡀⠀⠀⠀⠀⠀⢲⣤⣦⣶⣶⣷⣾⣿⣴⣷⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣤⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡷⠯⣿⣿⣿⣇⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢼⣿⣿⣷⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣄⡄⣀⣀⣤⣹⣿⣿⣿⡤⢀⢠⣄⣠⣾⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣷⣾⣿⣇⠀⠀⠀⠀⠀⠀⠻⣿⣿⣏⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣽⣿⣿⣿⣿⣿⣿⣿⣷⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠟⠋⣻⣿⡿⠀⢸⣿⣿⣨⣽⣿⣿⣿⣶⣿⣿⡿⢿⣿⣿⣿⣯⠉⠁⠀⠀⠀⠀⠀⠀⢻⣿⣿⣇⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡿⢿⣿⡍⣿⣿⣿⣭⠁⠻⠿⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡄⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⢏⠈⠉⢿⣿⣿⣿⣿⠿⡿⠇⣸⡿⣿⣆⢸⣿⡿⣿⣯⡀⣿⣿⣭⣵⣆⣻⣿⣶⣿⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⡷⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠘⠿⢿⣶⣿⣿⣿⣿⣧⣠⣶⣶⣿⣿⣿⣿⣾⣿⣧⣼⣿⣷⡿⠿⠿⠿⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣦⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⢸⠇⠠⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠿⣿⠿⠿⡿⠿⣿⠿⢦⠶⣤⠦⡴⢶⠶⢦⠀⢠⡴⠶⠶⣿⠿⠶⡿⠿⢿⡿⠿⠿⣿⠷⡶⢶⣴⠶⠶⢶⠶⠶⣶⠶⠶⢦⣠⡶⠶⠶⡶⠶⠦⢤⠶⢦⠶⢤⠴⠶⡾⠶⢧⣠⠾⠿⢿⠿⢿⠿⢿⠿⠿⡿⠿⢿⣿
⣿⡇⢸⡤⣼⠀⠶⡇⠀⠁⠀⢸⠀⣿⠀⠃⢸⠀⢸⠓⣾⡇⠰⠀⣿⠀⠶⡇⢠⠘⡇⠀⡆⢸⡄⠃⣼⢻⠀⠰⡇⠀⡆⢸⠀⠐⢀⡿⡇⠀⠆⡀⠀⠆⣸⠀⢸⠀⠘⠀⠀⡇⠰⢾⣿⡆⠀⣾⠀⣿⠀⠘⠀⠀⡇⠰⢾⣿
⣿⡇⠸⠀⢸⠀⠶⡇⢸⠀⡇⢸⠀⣿⠀⡀⢸⠀⢸⠿⣿⡇⢸⠀⣿⠀⠾⠃⢈⠀⡇⠀⠇⢸⡇⠀⡇⢸⠀⢰⣇⠀⠇⢸⠀⢰⠀⣷⡇⠀⡖⡇⠀⡇⢸⠀⢸⠀⡆⢸⠀⡇⠰⢾⡀⡇⠀⣿⠀⣿⠀⡄⠀⠀⡇⠰⢾⣿
⣿⠿⠲⢷⠚⠲⠖⠳⠺⠖⠗⠚⡒⣷⠒⠓⠚⢲⣾⣶⣋⠓⠺⠒⠛⠒⠒⠒⠚⠒⠒⠒⠒⠋⠑⠒⠁⠈⠒⠊⠙⠒⠒⠛⠒⠚⠒⠁⠓⠒⠁⠑⠒⠓⠚⠒⠚⠒⠓⠒⠒⣷⣶⣾⠁⠑⠒⠛⠒⠚⢲⣷⣷⣶⣷⣶⠚⠀

                    ䷩ 𝚕𝚒𝚗𝚎 2442

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

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⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 11.26.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ IRC_Proceedings:_Wednesday,_November_24,_2021⠀✐


Posted in IRC_Logs at 2:39 am by Needs Sunlight


Also available via the Gemini protocol at:


    * gemini://gemini.techrights.org/tr_text_version/irc-log-techrights-
      241121.txt
    * gemini://gemini.techrights.org/tr_text_version/irc-log-241121.txt
    * gemini://gemini.techrights.org/tr_text_version/irc-log-social-241121.txt
    * gemini://gemini.techrights.org/tr_text_version/irc-log-techbytes-
      241121.txt
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                                      🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇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
 QmX63zsjBPaBN3jJW6yYERciSfwTDW8VLKL9TD2WqrVeTK #boycottnovell  🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell
 QmQxFF2XaYCsK43N67mt14oCTVE4rVQegmLcPiYmxxPZWe (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
                                                 #boycottnovell-
 QmR8pUMdKNnfUB18vrb2P3bMKVnsDCCC87fjfNxipfbvUb social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell-
 Qmdfchdv9o2WtNEeLMwg5bqWpgw8nSTsT6peAesq4ZJ92B social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 (full IRC log
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
 QmRB8w1EbTSWeZYe18r2HFbV6wiS1A3YSxeBUjGjrkVcRg #techbytes      🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #techbytes
 QmeSs9D4s7EYCXr13eYaKKu9g175uzVU9Q1opcAeya8bLK (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
 QmWfPoJ4ymwgSzdzW55cFzzQ58zM29vn7A5o4kE6w5SCSF #techrights     🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #techrights
 QmfLv1QstKik7aqLGDQG7Rm4EPaVrmy9tZvoBQhLF3ggRC (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇IPFS logo⦈


§ Bulletin for Yesterday⠀➾


Local_copy | CID (IPFS): QmWM7VYrVdqPgZh8JgwKyiXxRcVGNjoM8cBVEUyQXKcR5T



                    ䷩ 𝚕𝚒𝚗𝚎 2571

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/11/26/irc-log-251121/#comments
    Gemini version at gemini://gemini.techrights.org/2021/11/26/irc-log-251121/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 11.26.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ IRC_Proceedings:_Thursday,_November_25,_2021⠀✐


Posted in IRC_Logs at 2:56 am by Needs Sunlight


Also available via the Gemini protocol at:


    * gemini://gemini.techrights.org/tr_text_version/irc-log-techrights-
      251121.txt
    * gemini://gemini.techrights.org/tr_text_version/irc-log-251121.txt
    * gemini://gemini.techrights.org/tr_text_version/irc-log-social-251121.txt
    * gemini://gemini.techrights.org/tr_text_version/irc-log-techbytes-
      251121.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
 QmaxBR1oY5qrYHqQ4fZ2fYRVSKCfcT7nEwYEsNj1u1sH8B #boycottnovell  🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell
 QmVzG7m7gS3L5YT26iD96TCHiEEH6bwm56iZzuegC27C9y (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
                                                 #boycottnovell-
 QmZpGqE43WQv5TYp1zUZFgLFwXQdFcbi3QkLQ9TMgjYv3d social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell-
 QmZpTf7DjmCvMKNYTz9owwFEbRBsUPYvpELJsVBN9Bdrcp social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 (full IRC log
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
 QmQG4S9rSU66VXjzoSxXK44sbqGhHBGzEzK4TRSigc4cjQ #techbytes      🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #techbytes
 QmR4zB6ugZ3UDEoFAMHHN6hauHFUi8q8PPWXasvcYvkkob (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
 QmUtgGpQP1TRuetLoaf51v17XwfLwbsFiGV6wmGMdpVzDe #techrights     🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #techrights
 QmUk2jw4pufeu8CtL7yLqe7yS8dzSeqfAsv3ffMAeJ6FAD (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇IPFS logo⦈


§ Bulletin for Yesterday⠀➾


Local_copy | CID (IPFS): QmWSgWCNaXdj4bqpVXJtFwGUpuJtUjJhMJNpvzpyfvb343



                    ䷩ 𝚕𝚒𝚗𝚎 2700

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 11.26.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_26/11/2021:_New_Complaint_About_Microsoft_Competition_Crimes_in_Europe,
EuroLinux_8.5,_GhostBSD_21.11.24,_and_Kiwi_TCMS_10.5_Released⠀✐


Posted in News_Roundup at 5:21 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⠀➾


                # ⚓ Tuxedo_releases_the_Tiger_Lake-H-powered_InfinityBook_S17_–
                  Gen6,_its_smallest_17-inch_Linux_laptop_yet_–
                  NotebookCheck.net_News⠀⇛


                       Tuxedo is launching the InfinityBook S17 – Gen6
                       thin and light Linux laptops with Intel Tiger Lake-
                       H processors. Even though these new models are
                       touted as desktop replacement devices, they do not
                       feature a discrete GPU. Nevertheless, users can
                       benefit from the included Thunderbolt 4 connector
                       that enables the use of external GPUs.


                       The InfinityBook S17 – Gen6 features a 17.3-inch
                       Full-HD IPS display with thin screen bezels all
                       around, so the screen-to-body factor almost matches
                       that of a 15.6-inch model. Thus, its dimensions are
                       quite compact at 395 x 250.7 x 19.8 mm, making it
                       the smallest 17-incher in the Tuxedo portfolio, and
                       it only weighs 2.25 kg (4.96 lbs).


                       Despite its lightness, the InfinityBook S17 – Gen6
                       still packs enough power to match your average
                       desktop. Processor options include the Intel Core
                       i5-11300H with Iris Xe G7 80 EUs iGPU and the Core
                       i7-11370H with Iris Xe G7 96 EUs iGPU, which can be
                       coupled with up to 64 GB of DDR4-3200 RAM and up to
                       4 TB of NVMe SSD storage through a PCIe 4.0 x4 +
                       PCIe 3.0 x4 M.2 2280 slot combo. Port selection
                       comes with a Thunderbolt 4 connector with DP and
                       power delivery capabilities, USB-C 3.2 Gen2x2, USB-
                       A 3.2 Gen2, USB 2.0, HDMI 1.4b video output, 2-in-
                       1 audio and GbE jacks, plus a handy microSD card
                       reader.


                       Other notable features include an ergonomic and
                       cooling-optimized Lift-Up hinge, a large 73 Wh
                       battery that can last up to 6-7 hours in practical
                       office workloads, a FlexiCharger BIOS option that
                       can limit the battery charging to increase
                       lifespan, Wi-Fi 6 + Bluetooth 5.2 + GbE NIC, HD
                       webcam with Windows Hello support, and TPM 2.0
                       security.


          o § Audiocasts/Shows⠀➾


                # ⚓ Distro_Rating_Wallpapers_=_Distro_Review_|_Sudo_25k_Special
                  –_Invidious⠀⇛


                       I recently heard about Ubuntu Unity and I was
                       curious how usable Unity 7 would be like in 2021,
                       if it’s exciting I might make a followup video
                       about my thoughts.


                # ⚓ Linux_overview_|_deepin_20.3_–_Invidious⠀⇛


                       In this video, I am going to show an overview of
                       deepin 20.3 and some of the applications pre-
                       installed.


          o § Kernel Space⠀➾


                # ⚓ Linux_5.10.82⠀⇛


                # ⚓ Linux_5.4.162⠀⇛


                # ⚓ Linux_4.19.218⠀⇛


                # ⚓ Linux_4.14.256⠀⇛


                # ⚓ Linux_4.9.291⠀⇛


                # ⚓ Linux_4.4.293⠀⇛


                # ⚓ Intel_Compute-Runtime_Updated_With_DG2/Alchemist_Support_–
                  Phoronix⠀⇛


                       Intel’s open-source engineers today released the
                       Compute-Runtime 21.47.21710 as their latest update
                       to this open-source compute stack for Linux systems
                       enabling their graphics processors to enjoy
                       performant OpenCL and oneAPI Level Zero support.


                       Notable with today’s Compute Runtime update is that
                       v21.47.21710 is the first having DG2 “Alchemist”
                       graphics card support in place. This goes along
                       with other DG2/Alchemist enablement going on in the
                       Linux kernel and Mesa, etc. When pairing the latest
                       kernel now with Intel Compute-Runtime should yield
                       preliminary support for OpenCL and oneAPI L0 on
                       Alchemist but expect more refinements and
                       optimizations to come over the months ahead.


                # ⚓ Several_Older_NVIDIA_Tegra_Powered_Tablets_To_Be_Supported
                  By_Linux_5.17_–_Phoronix⠀⇛


                       For those that happen to have older ASUS
                       Transformer tablets powered by a NVIDIA Tegra SoC,
                       the Linux 5.17 kernel cycle early next year is
                       enabling a number of them to work off the mainline
                       kernel.


                       A batch of patches were sent out this week intended
                       for the Linux 5.17 cycle for improving the older
                       NVIDIA Tegra support with the mainline kernel.


                # § Graphics Stack⠀➾


                      # ⚓ Venus_on_QEMU:_Enabling_the_new_virtual_Vulkan
                        driver⠀⇛


                             With virtualization we can create multiple
                             virtual machines over a single physical
                             computer. The benefits of virtualization are
                             countless, from being able to create virtual
                             representation of different machines, to
                             efficiently use the currently available
                             hardware. Clearly a virtual machine, like any
                             real computer, needs an operating system
                             (OS). In this context it is called a Guest
                             OS, as opposed to the one running on real
                             hardware, called Host OS.


                             Running graphics applications in a Guest OS
                             can be annoying as they are generally greedy
                             of computing resources, and that can slow you
                             down or give you a bad experience in terms of
                             graphics performance. Being able to
                             accelerate all this by offloading the
                             workload to the hardware can be a great deal.
                             The VirtIO-GPU virtual GPU device comes into
                             play here, allowing a Guest OS to send
                             graphics commands to it through OpenGL or
                             Vulkan. While we are already there with
                             OpenGL, we can not say the same for Vulkan.
                             Well, until now.


                      # ⚓ Getting_Experimental_Vulkan_Within_QEMU_VMs_Using
                        Linux_5.16+_Paired_With_Mesa’s_Venus_–_Phoronix⠀⇛


                             When running on the very latest Linux 5.16
                             Git kernel paired with recent Mesa and
                             various experimental components to the
                             virtualization stack, it is possible getting
                             at least basic Vulkan acceleration working
                             within QEMU guest virtual machines that in
                             turn is accelerated by the host.


                             Getting experimental Vulkan API support
                             working within guest virtual machines on QEMU
                             currently requires a number of steps,
                             including the use of yet-to-be-upstreamed
                             code in some areas.


          o § Applications⠀➾


                # ⚓ The_rocky_road_to_better_Linux_software_installation_•_The
                  Register⠀⇛


                       Linux cross-platform packaging format Flatpak has
                       come under the spotlight this week, with the
                       “fundamental problems inherent in [its] design”
                       criticised in a withering post by Canadian software
                       dev Nicholas Fraser.


                       Fraser wrote in a blog published on 23 November
                       that “these are not the future of desktop Linux
                       apps,” citing a litany of technical, security and
                       usability problems. His assertions about disk usage
                       and sharing of runtimes between apps were hotly
                       disputed by Will Thompson, director of OS at
                       Endless OS Foundation a day later in a post titled:
                       “On Flatpak disk usage and deduplication,” but
                       there is no denying it is horribly inefficient.


                       Most people don’t care about that any more, one
                       could argue. But they should.


                       The Linux world has been trying to invent a cross-
                       platform packaging format for years, but leading
                       contenders – the older, vendor-neutral older,
                       AppImage format as well as Ubuntu’s Snap and
                       Fedora’s Flatpak – all have serious issues.


          o § Instructionals/Technical⠀➾


                # ⚓ How_to_install_Hugin_panoramic_image_editor_on_Linux⠀⇛


                       Hugin is an open-source image editing tool for
                       Linux, Mac OS, Windows, and BSD. It allows users to
                       stitch photographs together and create panoramas
                       digitally. In this guide, we’ll show you how to
                       install Hugin on Linux.


                # ⚓ How_to_play_Total_War:_WARHAMMER_II_on_Linux⠀⇛


                       Total War: WARHAMMER II is the sequel to Total War:
                       WARHAMMER. It is a turn-based real-time tactics
                       video game developed by Creative Assembly and
                       published by Sega. Here’s how you can play the game
                       on your Linux system.


                # ⚓ How_to_Use_the_Linux_Screen_Command⠀⇛


                       In Linux, you often need to run lengthy processes
                       to execute in the background and independently
                       (such as ping commands to a server for an extended
                       period of time) .


                # ⚓ How_to_install_VRoid_Studio_1.0_on_a_Chromebook⠀⇛


                       Today we are looking at how to install VRoid Studio
                       1.0 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_Run_Multiple_Commands_in_Linux_at_Once⠀⇛


                       The Linux terminal is a powerful tool that allows
                       you to perform a wide range of operations using
                       commands. These commands enable you to accomplish a
                       variety of computing tasks, including file
                       manipulation, program management, and service
                       automation.


                       Ideally, when you need to run a bunch of terminal
                       commands, you do it one-by-one. However, it turns
                       out that there’s a better way to do this, and it
                       involves running multiple commands at once.


                       Follow along as we demonstrate the different ways
                       to run multiple terminal commands in Linux.


                # ⚓ Easily_Install_and_Setup_PowerDNS_on_Debian_11/Debian_10_–
                  kifarunix.com⠀⇛


                       This tutorial is about how to easily install and
                       setup PowerDNS on Debian 11/Debian 10. PowerDNS “is
                       a premier supplier of open source DNS software,
                       services and support“. It provides both the
                       Authoritative Server and the Recursor DNS products.


                # ⚓ How_to_Set_the_Date_and_Time_on_Linux⠀⇛


                       Keeping software on your device up to date is an
                       important part of having a robust and secure
                       system, but even more important is having an up-to-
                       date time and date.


                       Accurate time and date on a system not only tells
                       you the correct time but also allows you to execute
                       automated tasks as expected and connect to services
                       over the internet seamlessly.


                       This guide will show you how to review, adjust, and
                       configure the time and date on Linux from the
                       command line using the timedatectl command.


                # ⚓ How_to_install_MediaWiki_on_CentOS_8_–_Unixcop_the_Unix_/
                  Linux_the_admins_deams⠀⇛


                       MediaWiki is a collaboration and documentation
                       platform brought to you by a vibrant community.


                       It helps you collect and organize knowledge and
                       make it available to people.


                       MediaWiki is a free and open source software that
                       helps users collect and organize information. It is
                       a centralized place where users collaborate and
                       share knowledge. Wikipedia is an example of
                       MediaWiki’s software use case, as it was initially
                       developed for creating Wikipedia.


                       In this tutorial, We will show you how to install
                       Mediawiki in your CentOS 8 system.


                # ⚓ How_To_Tune_UP_Ngnix_For_the_Upcoming_2022_h⠀⇛


                       Nginx is a free open source high performing and
                       lightweight web server that is used as the load
                       balancer, reverse proxy, HTTP cache, and mail
                       proxy. Although Nginx is quite new as compared to
                       other web servers, its popularity is rising due to
                       its high performance. With your default Nginx
                       configuration, you might get fast performance but
                       we can boost the Nginx performance at its best by
                       changing some configurations.


                       In this article, you will get to know 8 different
                       best ways to boost Nginx for better performance. To
                       demonstrate the example in this article I have
                       installed Nginx on the Ubuntu 20.04 LTS system.


                # ⚓ How_To_Install_Parabola_GNOME_on_a_Virtual_Machine⠀⇛


                       This tutorial will explain step by step to install
                       Parabola computer operating system with GNOME
                       Desktop to a virtual machine. Let’s practice!


                # ⚓ How_to_Set_up_Pritunl_VPN_Server_on_Rocky_Linux_8⠀⇛


                       Pritunl is an open-source VPN and IPsec server with
                       user management and horizontal scaling for small
                       and large organizations. It gives the user a choice
                       to use OpenVPN and Wireguard protocols. It comes
                       with an easy to use GUI interface and supports
                       clients on most devices and platforms. All the
                       traffic between clients and the server is
                       encrypted. Pritunl is built on MongoDB, a reliable
                       and scalable database that can be quickly deployed
                       and with built-in support for replication, making
                       deploying the Pritunl cluster easy.


                       This tutorial will teach you about how to install
                       the Pritunl VPN server on Rocky Linux 8. We will
                       also explore how to connect to the VPN using a
                       Linux Client.


                # ⚓ How_to_Install_TeamSpeak_Server_on_Ubuntu_20.04_–_VITUX⠀⇛


                       Teamspeak is a free voice chat software that can be
                       used by teams, groups, and communities. It’s
                       popular among gamers because it allows them to
                       communicate complex strategies in real-time while
                       playing their favorite game. Teamspeak has many
                       other uses besides gaming though. It can also be
                       used for running online conferences or meetings,
                       distance learning courses, language lessons, and
                       much more.


                # ⚓ How_To_Install_Zabbix_on_Debian_11_–_idroot⠀⇛


                       In this tutorial, we will show you how to install
                       Zabbix on Debian 11. For those of you who didn’t
                       know, Zabbix is an open-source monitoring tool for
                       servers, applications, and network devices. It is
                       used to monitor networks, servers, applications,
                       services as well as cloud resources. It also
                       supports the monitoring of storage devices,
                       databases, virtual machines, telephony, IT security
                       resources, and much more.


                       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 Zabbix open-source
                       monitoring tool on a Debian 11 (Bullseye).


                # ⚓ How_to_install_MySQL_8.0_Server_on_Debian_11_Bullseye_–
                  Linux_Shout⠀⇛


                       MySQL doesn’t need any introduction, it has been
                       around for years and widely used open source
                       Database management system. Here we learn how to
                       install MySQL server and client on Debian 11
                       Bullseye.


                       Well, just like Debian 10 Buster, the 11 Bullseye
                       also got the MariaDB as the default MySQL variant
                       to install. Yes, you won’t be able to install the
                       Oracle MySQL using the default repository of Debain
                       11. Well, being a fork of MySQL, MariaDB will work
                       similar and also stable. And compatible with all
                       application that required the MYSQL.


                       Nevertheles, still those who want Oracle’s MySQL
                       and only its features they can add its repository
                       manually using this tutorial to get it.


                # ⚓ The_APT_package_manager_has_been_patched_to_prevent_the
                  uninstallation_of_essential_components_–_LinuxStoney⠀⇛


                       Last week was a bitter for bit System76 . Aside
                       from its conflict with GNOME , the company had to
                       see its operating system, Pop! _OS , being exposed
                       on the YouTube channel Linus Tech Tips after an
                       attempt to install Steam took away the desktop
                       environment.


                       Linus Sebastian, the protagonist of the Linus Tech
                       Tips channel, tried to use or test Linux as a
                       desktop operating system. To do this, he first
                       opted for Pop! _OS, one of NVIDIA’s most user-
                       friendly and graphics-friendly distributions.
                       Everything seemed to be going apparently fine until
                       he started installing Steam . He first tried the
                       store, but after failing, he tried through APT.
                       Despite the warning that jumped him, Linus decided
                       to go ahead with the installation of the
                       application, which resulted in the uninstallation
                       of the desktop environment . After rebooting,
                       obviously, there was no graphical interface.


                # ⚓ How_To_Make_Plasma_Panel_Fit_Content_(Like_A_Dock)!_–
                  Kockatoo_Tube⠀⇛


                # ⚓ Full_Circle_Magazine_#175⠀⇛


                # ⚓ How_To_Install_phpIPAM_on_Ubuntu_20.04_LTS_–_idroot⠀⇛


                       In this tutorial, we will show you how to install
                       phpIPAM on Ubuntu 20.04 LTS. For those of you who
                       didn’t know, phpIPAM is a free PHP-based web IP
                       Address management tool whose goal is to provide
                       modern, lightweight, and useful IP address
                       management and administration. It is a PHP-based
                       application with MySQL database backend, using
                       jQuery libraries, ajax, and some HTML5/CSS3
                       features.


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


                # ⚓ Create_an_S3_Bucket_on_AWS_using_Terraform⠀⇛


                       In this article, I will show you how to use
                       Terraform to create an S3 bucket on AWS. Before
                       proceeding, I assume that you are familiar with S3
                       bucket if not then you can click here to see the
                       steps to create an S3 bucket from the AWS console.


                # ⚓ How_To_Change_File_Attributes_in_Linux_With_Chattr
                  Command⠀⇛


                       File attributes are certain properties that are
                       associated with the file. The attributes allow a
                       file to have some characteristics that are valid
                       for all users.


                       You may be familiar with the file permissions on
                       Linux. As Linux is a multi-user operating system,
                       it is possible to assign different file or folder
                       permissions for different users.


                       File attributes are quite similar to permissions on
                       Linux. However, while basic permissions are only
                       limited to read, write, and execute, the attribute
                       allows the files or folders to have some extended
                       sets of rules that apply on them.


                       We can change or modify file/folder permissions
                       with the chmod command. If you are not familiar
                       with the Linux permissions, we recommend you to
                       take a look at our comprehensive guide on the
                       matter. Knowledge of file or folder permissions are
                       not required to follow this tutorial.
                       An important thing to remember about the attributes
                       is that the attributes generally apply to all the
                       users in the system (even root).


                       For example, if a file were to be assigned the
                       read-only attribute, that file would not allow any
                       user (including root) to modify it. Obviously, the
                       root user could modify the file, but only after
                       removing the read-only attribute.


                # ⚓ Apt_vs_Apt-get_Commands_Explained:_Which_One_To_Use?⠀⇛


                       As a regular Ubuntu or Debian Linux user, you might
                       have noticed that some package installer, removal,
                       or updating commands use the apt command instead of
                       the apt-get command. Now, as a day-to-day Linux
                       user, you would not get to know what they are and
                       which command is used for what! But as a power
                       Linux/Ubuntu user, you definitely must know the
                       difference between apt vs apt-get commands.


                       In the default command lists of Ubuntu, the apt-get
                       command has been widely used for a long while. The
                       new apt command was introduced a few years ago to
                       increase the work efficiency and make the commands
                       process simpler. Though there are some packages
                       that only work with apt-get, hence most cache
                       loading and cache removing or updating functions
                       are nowadays done by the apt command.


                # ⚓ How_to_install_Ajenti_2_Control_Panel_on_Debian_11⠀⇛


                       Ajenti 2 is an open-source, web-based control panel
                       that can be used for a large variety of server
                       management tasks. It can install packages and run
                       commands, and you can view basic server information
                       such as RAM in use, free disk space, etc. All this
                       can be accessed from a web browser. Optionally, an
                       add-on package called Ajenti V allows you to manage
                       multiple websites from the same control panel.


                       In this tutorial, we are going to install Ajenti 2
                       on our Debian 11 server.


                # ⚓ Josef_Strzibny:_Summer_and_winter_time_changes_with
                  DateTime⠀⇛


                       Developers usually think of timezones, but European
                       summertime changes can be easily overlooked. I have
                       to admit I overlooked them when parsing dates with
                       DateTime.from_naive!/2.


                       What’s the issue, you ask?


          o § Games⠀➾


                # ⚓ Scientific_evolution_sim_Thrive_is_now_available_on_itch.io
                  and_Steam_|_GamingOnLinux⠀⇛


                       Thrive is a free and open source evolution sim,
                       that is now available from the itch.io and Steam
                       stores where you can pay to support the
                       development. It’s in Early Access and they have a
                       very long road ahead until it’s complete, and
                       they’re estimating multiple years to go yet until
                       it’s finished.


                       “In Thrive, you take control of an organism on an
                       alien planet, beginning with the Last Universal
                       Common Ancestor (LUCA). Your goal is to survive in
                       the environment, adapt your species by adding
                       mutations, and thrive. Other species will emerge to
                       compete with yours. They will evolve via a
                       population dynamics driven simulation with random
                       mutations – you must improve and spread your
                       species to surpass them. The success of your
                       species depends both on your skill in surviving as
                       an individual cell and the changes you make in the
                       editor.”


                # ⚓ Linux_gaming_takes_a_big_step_forward_with_full_Nvidia_DLSS
                  support_in_Proton_|_TechRadar⠀⇛


                       The latest version of Proton comes with full
                       support for Nvidia DLSS, among other benefits such
                       as better compatibility with anti-cheat software.


                       For the uninitiated, Proton is the compatibility
                       layer which allows Windows games to be played under
                       Valve’s SteamOS operating system, and version 6.3-
                       8 delivers official support for DLSS in DX11 and
                       DX12 games. This follows Nvidia making its frame
                       rate boosting tech available for Vulkan titles
                       earlier in the year (meaning the likes of Doom
                       Eternal got the benefit of DLSS).


                # ⚓ Linux_Release_Roundup_#21.48:_Pinta_1.7.1,_Proton_6.3-8,
                  Deepin_20.3,_and_More_Releases_–_It’s_FOSS_News⠀⇛


                       In the Linux Release Roundup series, we summarize
                       the new distribution and application version
                       releases in the past week. This keeps you informed
                       of the latest developments in the Linux world.


                       [...]


                       Proton compatibility layer 6.3-8 release introduces
                       support for a bunch of new games that include Age
                       of Empires 4, Assassin’s Creed, COD: Black Ops II,
                       and many more.


                # ⚓ Godot_Engine_–_Release_candidate:_Godot_3.4.1_RC_1⠀⇛


                       Godot 3.4 was released earlier this month, and it
                       went fairly smoothly! Many thanks to all the
                       contributors who worked on it, including all
                       testers who tried beta and RC releases to ensure
                       that the 3.4-stable branch would be an easy and
                       worthwhile upgrade path for all users.


                       No software release is perfect though, so there
                       will always be some things to iron out, which is
                       why we usually provide maintenance releases for
                       stable branches, focusing on bugfixing and
                       preserving compatibility (see our release policy).
                       A number of fixes have been queued already in the
                       3.4 branch for Godot 3.4.1, so here’s a first
                       release candidate to validate them.


                # ⚓ X4:_Tides_of_Avarice_expansion_coming_early_2022,_plus_AMD
                  FSR⠀⇛


                       “Encountering and interacting with previously
                       unknown, lawless pirate and scavenger factions,
                       will challenge your perception of social order and
                       justice in the X universe. In new sectors and
                       dangerous regions, you will not only discover new
                       ships and stations, but also encounter stellar
                       phenomena that will significantly influence your
                       plans and actions. What is it all about, and who
                       are the mysterious manipulators that have learned
                       to master a rare and vital resource? Your journey
                       will lead you towards the answers. Set out and
                       discover a new chapter of X4: Foundations.”


                       Expect to see the likes of a “terrifying pirate
                       battleship with an experimental and unusual energy
                       source” and the complete opposite with an
                       “incredibly lavish and luxurious yacht”. Plus you
                       will also get the ability to salvage shipwrecks to
                       recycle resources.


                # ⚓ Canonical_want_your_feedback_on_Ubuntu_Gaming⠀⇛


                       Looks like Canonical, the creator of Ubuntu, want
                       to get in on more Linux Gaming with their Desktop
                       Product Manager starting a new series of blog posts
                       and your feedback is needed.


                       The first blog post goes over using Steam and
                       Proton, which won’t be news to any of our readers,
                       especially with our full guide existing for some
                       time now. What’s interesting though, that I had no
                       idea, is that their Desktop Product Manager is
                       Oliver Smith, who previously worked for Creative
                       Assembly as a Producer on the likes of Alien
                       Isolation – which got ported natively to Linux by
                       Feral Interactive.


                       As for the actual guide, it’s a pretty good intro
                       for those who need to point newer users to get
                       setup ready with Steam and try out Proton.


                # ⚓ Creator_Day_is_live_on_itch.io_giving_100%_to_developers⠀⇛


                       The anti-Black Friday event is live once again on
                       the itch.io store, where developers get 100% of
                       purchases as itch forgoes its cut for a day.


                       Continuing to buck the trend here, itch always does
                       things a bit differently. They have an open revenue
                       sharing model, where by default itch only takes a
                       10% cut but developers can set it to whatever they
                       want — even zero.


                # ⚓ Capcom_shows_off_official_video_of_Devil_May_Cry_5_on_the
                  Steam_Deck_|_GamingOnLinux⠀⇛


                       As more developers get their hands on a Steam Deck
                       devkit, we’re seeing plenty more show their games
                       and now Capcom has taken a turn with Devil May Cry
                       5.


                       Unlike a lot of what we’ve seen previously via
                       small clips or plain pictures on Twitter, Capcom
                       went a tiny step further by making a video on their
                       official Capcom USA YouTube Channel – that’s quite
                       a bit of extra advertisement power there for the
                       Steam Deck.


                # ⚓ Open_source_re-implementation_of_Caesar_III,_Augustus_v3.1
                  is_out_|_GamingOnLinux⠀⇛


                       Augustus is an open source game engine re-
                       implementation for Caesar III, forked from another
                       called Julius that aims to add in new features.


                       Version 3.1 is out now adding in plenty of new
                       goodies like: a volume slider, a Hippodrome betting
                       system, roofed garden walls, palisades for cheaper
                       walls, a new difficulty option to adjust the max
                       number of allowed grand temples per city, new
                       hotkeys, resource stockpiling is now an option to
                       production buildings and warehouses, an option to
                       have number separators for larger numbers and many
                       more improvements and bug fixes. It’s making it
                       easily one of the best ways to play the classic
                       city-builder.


          o § Desktop Environments/WMs⠀➾


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


                      # ⚓ New_Icons,_Iconoclast_Pipeline_›_Ken_Vermette⠀⇛


                             As was the method for Blue Ocean on the
                             desktop widgets and design, the icons will be
                             a gradual rollout over a few releases. We do
                             have a strategy in place to ensure that this
                             won’t be too jarring or inconsistent during
                             the transition. The current plan is to update
                             both all mimetypes and all places in time for
                             the 5.24 release.


                             Like our current icons the new icons have
                             adaptive capabilities. Beyond that some
                             additional select icons such as the new
                             desktop icon are also adaptive, and there are
                             plans for other icons to also take advantage
                             of this feature where it would not be
                             obnoxious. Compared to existing icons the
                             refreshed content will be softer, more
                             detailed, and less flat. These icons are also
                             prepared with future capabilities in mind,
                             and as enhancements are made to KDE
                             Frameworks these icons may expose new and
                             interesting features.


                             Finally, we’re expanding the number of sizes
                             the icons come in, so they look ideal at more
                             zoom levels in your file browser. Currently
                             colour places icons are offered in 32, 48,
                             64, and 96 pixel sizes, and mimetypes are
                             offered in 32 and 64 pixel sizes. Refreshed
                             icons in both places and mimetypes will be
                             offered in 32, 48, 64, 96, 128, and 256 pixel
                             sizes with no missing graphics. We already
                             have all folders in all of the above sizes,
                             and in under a month while also writing our
                             software we have over doubled the number of
                             folder icons in Breeze. We’re estimating we
                             will more than triple in the number of
                             mimetype icons.


                             To get this work done we’ve built new tools
                             for the express purpose of making mass
                             iconography far easier for even individual
                             artists, so I’m very pleased to state that a
                             new icon and SVG pipeline is underway and
                             despite being unfinished is producing
                             results. This Python-written pipeline is
                             capable of adding guides, rulers, and setting
                             up grids for existing icons, standardizing
                             existing icon colours, assembling entirely
                             new icons from templates and components, and
                             aggressively optimizing icons. With this
                             authors will be able to have a “golden copy”
                             of their icon sets where they can focus
                             purely on design, letting the software take
                             care of cleaning up the documents and
                             assembling the individual pieces. The folders
                             in the above image were assembled by the
                             pipeline, with no hand-tuning.


                # § GNOME Desktop/GTK⠀➾


                      # ⚓ 13_Best_Dark_GTK_Themes_for_Your_Linux_Desktop_–_It’s
                        FOSS⠀⇛


                             With the near infinite customization options
                             you have on any given Linux distribution, the
                             most visually noticeable difference is
                             customizing the theme. Let’s take a look at
                             some of the GTK themes with dark mode.


                             Yeah, we have covered the best Linux themes
                             in the past but this one is specifically
                             dedicated to the dark themes. There was a
                             time when only programmers and sysadmins
                             preferred dark mode but that’s not the case
                             anymore. Dark mode is loved by normal people
                             as well and hence I compiled this list of
                             dark themes for desktop Linux users like you.


                             [...]


                             McMojave is a GTK theme which takes
                             inspiration from the macOS style user
                             interface. This theme is offered in dark
                             mode, obviously, but also in light mode, for…
                             umm… whoever may want it.


                             The McMojave GTK theme obviously supports GTK
                             based Desktop Environments like Pantheon,
                             Gnome, XFCE, Mate etc; but, this theme is
                             also available for KDE users.


                      # ⚓ #20_Colorful_Characters_·_This_Week_in_GNOME⠀⇛


                             Update on what happened across the GNOME
                             project in the week from November 19 to
                             November 26.


          o § Distributions⠀➾


                # § Reviews⠀➾


                      # ⚓ Cutefish_OS_Review_–_Impressive_Linux_Distribution_in
                        the_Making⠀⇛


                             We review the Debian/Ubuntu based Cutefish OS
                             Linux Distribution that features the stunning
                             Cutefish Desktop.


                # § New Releases⠀➾


                      # ⚓ blog.ipfire.org_–_IPFire_2.27_–_Core_Update_161
                        released⠀⇛


                             Today, we are releasing a brand new version
                             of IPFire: 2.27 – Core Update 161. Amongst a
                             huge performance improvement for the
                             Intrusion Prevention System, it comes with a
                             brand new kernel and various security and bug
                             fixes.


                             Before we talk about what is new, I would
                             like to ask you for your support. IPFire is a
                             small team of people and like many of our
                             open source friends, we’ve taken a hit this
                             year and would like to ask you to help us
                             out. Please follow the link below where your
                             donation can help fund our continued
                             development: https://www.ipfire.org/donate.


                             Please note, that this update will reconnect
                             any PPP connections and we recommend
                             performing a reboot after the update has been
                             installed.


                # § BSD⠀➾


                      # ⚓ GhostBSD_21.11.24_ISO_is_now_available⠀⇛


                             This new ISO contains kernel, OS, and
                             software updates. In addition, I added a new
                             command-line software called ghostbsd-version
                             that gives you the GhostBSD version, FreeBSD
                             version, kernel version, and OS version. At
                             the date of this release, if you run
                             ghostbsd-version or ghostbsd-version -v, it
                             should output 21.11.24. This version number
                             will be increment by the date of new packages
                             built on packages every update performed. The
                             ISO version is now following the last
                             package’s build version instead of an ISO’s
                             build date in the hope of removing confusion
                             about the ISO version.


                # § SUSE/OpenSUSE⠀➾


                      # ⚓ Git,_curl,_systemd_Roll_with_Tumbleweed⠀⇛


                             openSUSE Tumbleweed gave rolling release
                             users a snapshot every day this past week.


                             The latest snapshot to be released was
                             20211124. This snapshot brought systemd
                             249.7, which focused on package tests and
                             updated dependencies for the testsuite. The
                             text editor vim had a minor update to version
                             8.2.3640, but it was filled with many fixes;
                             some of the fixes included taking care of a
                             memory leak, crashes and performance issues
                             related to GTK. The removal of a redundant
                             script header was made in the update of
                             dracut and optimal compression parameters
                             were made for zstd in the Linux-boot process
                             package. Other packages to update in the
                             snapshot were autoyast2 4.4.22, embedded
                             Linux library ell 0.46, GNOME’s document
                             viewer evince 41.3 and gtk-vnc 1.3.0.


                      # ⚓ openSUSE_Tumbleweed_–_Review_of_the_week_2021/47_–
                        Dominique_a.k.a._DimStar_(Dim*)⠀⇛


                             Winter has come – at least that’s what I
                             heard some colleagues talk about these days.
                             Luckily, for me, there is no snow out yet and
                             Tumbleweed has sufficient grip to roll ahead
                             without getting stuck. As such, we have
                             published 7 snapshots this week (1118…1124).


                # § IBM/Red Hat/Fedora⠀➾


                      # ⚓ EuroLinux_8.5_Release_Notes_–_EuroLinux
                        Documentation⠀⇛


                             EuroLinux 8.5 is the first minor release
                             created in a continuous way. It was also the
                             first version when we deployed our engineer
                             to remote sites (in most cases virtual) to
                             provide support for organisations that
                             rebuild RHEL/EuroLinux from sources with Gaia
                             build system. This version code name is
                             Tirana – the capital city of Albania.


                             Below you can find the essential changes in
                             EuroLinux 8.5 release for x86_64
                             architecture. The aarch64 GA release is
                             slightly delayed. Release notes for aarch64
                             will be provided in a separate document.


                      # ⚓ Fedora_Community_Blog:_Friday’s_Fedora_Facts:_2021-
                        47⠀⇛


                             Here’s your weekly Fedora report. Read what
                             happened this week and what’s coming up. Your
                             contributions are welcome (see the end of the
                             post)!


                             Fedora Linux 33 will reach end of life on
                             Tuesday 30 November. The F35 retrospective
                             survey is open through 4 December.


                      # ⚓ 4_unexpected_ways_to_use_Ansible_|_Enable_Sysadmin⠀⇛


                             Ansible is well-known for automating
                             traditional IT tasks, like server
                             administration, networking, application
                             deployments, and more. But Ansible can do a
                             whole lot more. In Jeff Geerling’s
                             AnsibleFest 2021 presentation, Automating the
                             uncommon—Ansible automates everything, he
                             shared some of the creative ways he uses
                             Ansible.


                # § Canonical/Ubuntu Family⠀➾


                      # ⚓ Craft_Parts_–_Reusable_code,_Snapcraft_style_|
                        Ubuntu⠀⇛


                             Throughout the ages, humans have always used
                             simpler tools and materials to create more
                             complex ones. Wood and stone for smelting
                             bronze and iron; iron to create steel; vacuum
                             tubes to create logical gates; logical gates
                             to create advanced arithmetic engines, and so
                             on. Modern software is no different.


                             With Snapcraft in particular, the snap
                             building process comprises a number of steps.
                             Source artifacts are collected, there’s
                             compilation and assembly of binary products,
                             and then, these are packaged into a single
                             final archive. This process is very similar
                             to how various other Canonical solutions
                             work, and applicable to many different use
                             cases outside of the snap world. To that end,
                             the Snapcraft team has created a portable,
                             reusable mechanism called Craft Parts.


          o § Devices/Embedded⠀➾


                # ⚓ Seaberry_Turns_A_Raspberry_Pi_4_Into_A_Linux_Powered_ITX
                  System_–_PC_Perspective⠀⇛


                       Since it’s inception the Raspberry Pi has evolved
                       from it’s start as a nifty sounding hobby board to
                       a rather powerful multi-core small form factor
                       computer which is capable of quite a lot. The
                       enhancement to it’s capabilities has continued to
                       expand at a pace roughly equal to it’s growing
                       popularity, to the point where there is an
                       effective compute module which can be added to the
                       your Pi to give it more versatility.


                       Thanks to the compatibility improvements for that
                       computer module we will see in 5.16 release of the
                       Linux kernel, the Raspberry Pi will be capable of
                       yet another impressive feat with the help of a
                       product from a Canadian company called ALFTEL.
                       Their Seaberry Compute Module 4 carrier board will
                       give your Raspberry Pi 4 PCIe support. Once
                       attached, your Pi will have access to a variety of
                       PCIe interfaces including a 16x slot with a single
                       PCIe lane, four PCIe 1x Mini slots, four M.2 Key E
                       with two lanes each and one single lane PCIe M.2
                       Key M port.


                # § Mobile Systems/Mobile Applications⠀➾


                      # ⚓ Truecaller_users_on_Android_get_video_call_ID,_call
                        recording_features_|_TechRadar⠀⇛


                      # ⚓ Top_5_Google_Maps_Android_tricks_to_make_your_life
                        easier;_check_list_and_how_to_use⠀⇛


                      # ⚓ 60_paid_Android_apps_and_games_that_are_free_on
                        Google_Play_today,_November_17_–_Market_Research
                        Telecast⠀⇛


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


                      # ⚓ Deals:_The_Android_App_Development_Course_–_Geeky
                        Gadgets⠀⇛


                      # ⚓ How_to_record_calls_on_Android_smartphone_using
                        Truecaller⠀⇛


                      # ⚓ Android_Circuit:_Samsung_Galaxy’s_Massive_Upgrade,
                        OnePlus_10_Details,_Pixel_6A_Leaks⠀⇛


                      # ⚓ postmarketOS_revolutionizes_smartphone_hacking⠀⇛


                             I briefly mentioned postmarketOS in my
                             Pinephone review two years ago, but after
                             getting my Dutch SIM card set up in my
                             Pinephone and having another go at using
                             postmarketOS, I reckon they deserve special
                             attention.


                             Let’s first consider the kind of ecosystem
                             into which postmarketOS emerged: smartphone
                             hacking in the XDA Forums era. This era was
                             dominated by amateur hackers working
                             independently for personal prestige, with
                             little to no regard for the values of free
                             software or collaboration. It was common to
                             see hacked-together binary images shipped
                             behind adfly links in XDA forum threads in
                             blatant disregard of the GPL, with pages and
                             pages of users asking redundant questions and
                             receiving poor answers to the endless
                             problems caused by this arrangement.


                             The XDA ecosystem is based on Android, which
                             is a mess in and of itself. It’s an enormous,
                             poorly documented ball of Google code, mixed
                             with vendor drivers and private kernel trees,
                             full of crappy workarounds and locked-down
                             hardware. Most smart phones are essentially
                             badly put-together black boxes and most smart
                             phone hackers are working with their legs cut
                             off. Not to mention that the software
                             ecosystem which runs on the platform is full
                             of scammers and ads and theft of private user
                             information. Android may be Linux in
                             implementation, but it’s about as far from
                             the spirit of free software as you can get.


                             postmarketOS, on the other hand, is based on
                             Alpine Linux, which happens to be my favorite
                             Linux distribution. Instead of haphazard
                             forum threads collecting inscrutable ports
                             for dozens of devices, they have a single git
                             repository where all of their ports are
                             maintained under version control, complete
                             with issue trackers and merge requests, plus
                             a detailed centralized wiki providing a
                             wealth of open technical info on their
                             supported platforms. And, by virtue of being
                             a proper Linux distribution, they essentially
                             opt-out of the mess of predatory mobile apps
                             and instead promote a culture of trusted
                             applications which respect the user and are
                             built by and for the community instead of by
                             and for a corporation.


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


                # § Web Browsers⠀➾


                      # § Mozilla⠀➾


                            # ⚓ Thunderbird_&_no_email_associated_to_perform
                              action_error⠀⇛


                                   A new weird little problem has landed
                                   into my lap. On one of me Windows
                                   boxes, I upgraded Thunderbird, the mail
                                   client program, to the new release. I
                                   went from 78.x to 91.x, and in the
                                   process, I also received a gratis error
                                   message.


                                   It would pop up on every program
                                   startup, and it reads: There is no
                                   email program associated to perform the
                                   requested action. Please install an
                                   email program or, if one is already
                                   installed, create an association in the
                                   Default Programs control panel. Clunky
                                   language aside, Control Panel is sadly
                                   no longer the goto place for default
                                   apps in Windows 10/11. Plus, the error
                                   shows up during Thunderbird startup.
                                   Every time. Let’s fix this.


                            # ⚓ Mozilla_Performance_Blog:_Performance_Sheriff
                              Newsletter_(October_2021)⠀⇛


                                   In October there were 303 alerts
                                   generated, resulting in 45 regression
                                   bugs being filed on average 5.2 days
                                   after the regressing change landed.


                                   Welcome to the October 2021 edition of
                                   the performance sheriffing newsletter.
                                   Here you’ll find the usual summary of
                                   our sheriffing efficiency metrics. If
                                   you’re interested (and if you have
                                   access) you can view the full
                                   dashboard.


                # § Content Management Systems (CMS)⠀➾


                      # ⚓ Kiwi_TCMS_10.5⠀⇛


                             We’re happy to announce Kiwi TCMS version
                             10.5 which celebrates the very positive
                             reception we had at WebSummit 2021!


                # § Programming/Development⠀➾


                      # ⚓ PHP_8.1_is_Here_Studded_with_Highly_Requested
                        Features⠀⇛


                             PHP 8.1 has been officially released and
                             brings numerous innovations, such as
                             enumerations, fibers and performance
                             improvements.


                             PHP is a server side scripting language that
                             is used to develop web applications.
                             According to W3Techs’ data, PHP is used by
                             78.2% of all websites with a known server-
                             side programming language. In other words,
                             almost 8 out of every 10 websites that you
                             visit on the Internet are using PHP in some
                             way.


                             The language continues to evolve, by
                             releasing their newest PHP 8.1 update, just a
                             couple of days after the formation of a PHP
                             Foundation was announced. This new version,
                             released November 25, 2021, contains many new
                             features, including enums, readonly
                             properties, first-class callable syntax,
                             fibers, intersection types, performance
                             improvements and more.


                             Let’s take a quick look at some of the new
                             features, performance tweaks and other
                             reasons why you should migrate to PHP 8.1.


                      # ⚓ LLVM_Prepares_New_ThreadSanitizer_Runtime_That_Is
                        Faster,_Lower_Memory_Use_–_Phoronix⠀⇛


                             LLVM developers have been working recently to
                             land their new ThreadSanitizer run-time. The
                             TSan as a reminder is the compiler
                             instrumentation with associated run-time
                             library for being able to detect data races.


                             ThreadSanitizer is successful at detecting
                             data race conditions even within large and
                             complex code-bases. But unfortunately it’s
                             quite burdensome to enable with performance
                             slowing down in the range of 5~15x while the
                             run-time memory overhead can be in the range
                             of 5~10x.


                      # ⚓ xcrun:_error:_invalid_active_developer_path_–
                        buildVirtual⠀⇛


                      # ⚓ Why_PHP_Is_Getting_a_Foundation_and_Why_That_Matters
                        –_FOSS_Force⠀⇛


                             The PHP Foundation is an effort by 10 key PHP
                             vendors to assure adequate funding to keep
                             the popular scripting language viable.


                      # ⚓ Qt_5.12.12_Released⠀⇛


                             We have released Qt 5.12.12 today. This is
                             the last release from Qt 5.12 LTS series and
                             the standard support of Qt 5.12 LTS ends in
                             December 2021.


                             Qt 5.12.12 contains ~ 30 bug fixes compared
                             to the Qt 5.12.11. Please check details about
                             the release from Qt 5.12.12 Release Note.


                             Note that Qt 5.12 LTS standard support ends
                             in December 2021. It has been quite a long
                             journey with it; big thanks to everyone
                             involved!


                      # § Perl/Raku⠀➾


                            # ⚓ Perl_Weekly_Challenge_140:_Add_Binary⠀⇛


                            # ⚓ My_Favorite_Warnings:_experimental_|_Tom_Wyant_
                              [blogs.perl.org]⠀⇛


                                   Perl has had experimental features ever
                                   since I started using it at about
                                   version 5.6. These were things that
                                   were considered useful, but about which
                                   there was doubt — about their final
                                   form, whether a satisfactory
                                   implementation existed, or whatever.


                                   Until Perl 5.18, experimental features
                                   were simply documented as experimental.
                                   At that point, an experimental warning
                                   category was added, with sub-categories
                                   experimental::lexical_subs,
                                   experimental::lexical_topic,
                                   experimental::regex_sets, and
                                   experimental::smartmatch.


                                   Most of the features covered by the
                                   original Perl 5.18 warning categories
                                   were actually introduced in Perl 5.10
                                   as back-ports from Raku (or Perl 6, as
                                   it was then called), and not documented
                                   as experimental. My impression was that
                                   the relevant experimental:: warnings
                                   were introduced becaue the
                                   corresponding features were recognized
                                   as being more experimental than
                                   originally believed. Programmers
                                   already familiar with a feature might
                                   not notice an extra sentence in the
                                   documentation, but they will surely
                                   notice if their code starts spitting
                                   out experimental warnings.


                      # § Python⠀➾


                            # ⚓ OpenFaaS:_How_to_Add_Python_Requirements_and
                              Dependencies_–_Anto_./_Online⠀⇛


                                   This guide will show you how to add
                                   requirements and dependencies for a
                                   Python project using OpenFaaS.


                                   Python dependencies are software
                                   components that your project needs for
                                   it to work. You can manually use PyPI
                                   (the Python Package Index) to provide
                                   packages that you need, but OpenFaaS
                                   can automate this for you.


                      # § Java⠀➾


                            # ⚓ LWJGL_–_The_Lightweight_Java_Game_Library
                              Version_3.3_Released⠀⇛


                                   The part to note in this definition is
                                   that LWJGL provides access to native
                                   APIs through Java. That it is a wrapper
                                   over the APIs doesn’t mean that you
                                   should not be familiar with the
                                   semantics of the underlying API. Hence
                                   to get the most out of LWJGL a good
                                   understanding of the native APIs is
                                   essential too.


                                   At this point it is important to
                                   disambiguate between a library and a
                                   framework. LWJGL is a library and as
                                   such is low level; it is not a gamedev
                                   framework like libgdx (which itself
                                   uses LWJGL under the covers!) or a
                                   gamedev engine like GoDot which provide
                                   higher level of abstractions. For this
                                   reason, it is not recommended for
                                   novice programmers to start out writing
                                   games with it.


                                   And, of course, it is debatable whether
                                   Java is a good language for gamedev
                                   over the classic value of C++. Some
                                   advantages of using Java are its
                                   support of multiple operating systems
                                   and, of course, the easy learning curve
                                   in comparison to C++. Minuses could be
                                   garbage collection, performance and a
                                   smaller dev community. In any case, it
                                   depends on the use case; as they say,
                                   choose the best tool for the job at
                                   hand.


          o § Standards/Consortia⠀➾


                # ⚓ Bitrot_resistance_of_next-generation_image_formats⠀⇛


                       What happens when a single bit gets corrupted in an
                       image file you cherish? The results can range from
                       absolutely nothing to an imperceptible visual
                       change to a complete loss of the image. The hero
                       image below is somewhere in the middle of the
                       scale; where the top half of the image is perfect,
                       and the lower half is reduced to meaningless
                       digital noise.


                       Whether due to mechanical failure or transmission
                       interference like cosmic radiation: bitrot happens.
                       A rotted bit, or flipped bit, is when one bit of
                       RAM or persistent storage unintentionally flips its
                       state between zero and one. You can only do so much
                       to protect your system from random failure.
                       Multiple backups and data verification is the only
                       proven strategy to protect against it.


                       Traditional JPEG images (referred to as JPEG
                       troughing the article as opposed to JXL),
                       especially with progressive encoding, handle bitrot
                       remarkably well. You might see a single pixel shift
                       its color almost imperceptibly, or one of the
                       encoding layers may shift slightly. The effects are
                       so well understood that you can even find free
                       software that can automatically recover corrupted
                       JPEG photos.


                       However, the next-generation image formats pack
                       data much more densely than in the legacy image
                       formats. There’s isn’t just less redundancy, but
                       every single bit means more to the complete image.
                       This means the effects of bitrot produce a much
                       greater loss of visual fidelity and decodes to more
                       abstract results. The newer encoding techniques
                       include predictive models that can get thrown off
                       completely by a single bit out of place. The
                       digital hellfire in the lower half of the above
                       hero image is a perfect example of this.


    * § Leftovers⠀➾


          o § Integrity/Availability⠀➾


                # § Proprietary⠀➾


                      # § Security⠀➾


                            # ⚓ Fake_Windows_Update_Messages_in_Windows_10_Edge
                              Browser_via_Google_Picture_search_(searchterm:
                              Cosmos)⠀⇛


                                   naive users without deeper knowledge of
                                   technology might want to click that
                                   button.


                            # ⚓ Security_updates_for_Friday⠀⇛


                                   Security updates have been issued by
                                   Fedora (freerdp, gnome-boxes, gnome-
                                   connections, gnome-remote-desktop,
                                   guacamole-server, hydra, java-1.8.0-
                                   openjdk-aarch32, medusa, mingw-
                                   gstreamer1, mingw-gstreamer1-plugins-
                                   bad-free, mingw-gstreamer1-plugins-
                                   base, mingw-gstreamer1-plugins-good,
                                   php, pidgin-sipe, remmina, vinagre, and
                                   weston), openSUSE (kernel and netcdf),
                                   and SUSE (kernel and netcdf).


                            # ⚓ Proposed_UK_Law_Bans_Default_Passwords⠀⇛


                                   Following California’s lead, a new UK
                                   law would ban default passwords in IoT
                                   devices.


          o § Finance⠀➾


                # ⚓ Web3:_the_risk_of_naming⠀⇛


                       In the last few weeks, I’ve heard from many –
                       mainly not technical – people the expression
                       “Web3”. In a way, it is excellent that people that
                       are not tech-savvy start to learn about the Web,
                       how it works, and where it might go, since they are
                       using it consciously or not to perform the majority
                       of tasks in their lives. The issue I have with
                       this, though, is that no one of them could explain
                       how it would work or why they are so confident that
                       the future is going in that direction. The only
                       thing they could associate with Web3 was that
                       cryptocurrencies would be the future, and their
                       value would go to the moon.


                       I’m not a pessimist about the future of
                       cryptocurrency and blockchain, but I’m not sure
                       that it will happen either. I’ve been interested in
                       the technology space for the last 20 years, and I
                       have seen many technologies been proposed as the
                       game-changer failing and being completely
                       forgotten. Some were inherently flawed, others were
                       technically sound, but they did not deliver on the
                       promised success. Those 20 years taught me to
                       approach any new technology that promises to change
                       the world with a healthy amount of skepticism, and
                       blockchain and cryptocurrency are no exception.


                # ⚓ The_Tim_Dillon_Show_with_Whitney_Webb⠀⇛


                       Whitney joins Tim Dillon to discuss vaccine
                       mandates, digital ID and the 4th industrial
                       revolution and how their implementation threatens
                       human society and freedom globally.


          o § Monopolies⠀➾


                # ⚓ EU_coalition_urges_EU_to_push_back_against_gate_keeping_by
                  Microsoft,_files_official_complaint⠀⇛


                       A coalition of EU software and cloud businesses
                       joined Nextcloud GmbH in respect of their formal
                       complaint to the European Commission about
                       Microsoft’s anti-competitive behavior in respect of
                       its OneDrive (cloud) offering. In a repeat from
                       earlier monopolistic actions, Microsoft is bundling
                       its OneDrive, Teams and other services with Windows
                       and aggressively pushing consumers to sign up and
                       hand over their data to Microsoft. This limits
                       consumer choice and creates a barrier for other
                       companies offering competing services.


                       Over the last few years have grown their market
                       share to 66% of the EU market, while local
                       providers lost out from 26 to 16%. By heavily
                       favoring their own products and services (so-called
                       “self-preferencing”) or outright blocking other
                       vendors they leverage their position as gate
                       keepers to extend their reach in more and more
                       neighbouring markets and push users deeper into
                       their ecosystems. Local, more specialised vendors
                       are unable to compete “on the merits” as the key to
                       success is not a good product but the ability to
                       distort competition and block market access.


                       “This is quite similar to what Microsoft did when
                       it killed competition in the browser market,
                       stopping nearly all browser innovation for over a
                       decade. Copy an innovators’ product, bundle it with
                       your own dominant product and kill their business,
                       then stop innovating. This kind of behavior is bad
                       for the consumer, for the market and, of course,
                       for local businesses in the EU. Together with the
                       other members of the coalition, we are asking the
                       antitrust authorities in Europe to enforce a level
                       playing field, giving customers a free choice and
                       to give competition a fair chance,” said Frank
                       Karlitschek, CEO and founder of Nextcloud GmbH



                    ䷩ 𝚕𝚒𝚗𝚎 4440

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 11.26.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_26/11/2021:_F35_Elections,_Whonix_16.0.3.7,_OSMC’s_November_Refresh
With_Kodi_19.3⠀✐


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


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


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


          o § Desktop/Laptop⠀➾


                # ⚓ TUXEDO_InfinityBook_S_17_Linux_Laptop_Unveiled_with_11th
                  Gen_Tiger_Lake_CPUs,_Compact_Design⠀⇛


                       Dubbed as the smallest 17-inch business TUXEDO
                       notebook in a 15-inch form factor, the TUXEDO
                       InfinityBook S 17 Gen6 is here with an above-
                       average screen-to-body ratio and a large 17.3-inch
                       Full-HD IPS anti-reflective / non-glare display,
                       partial aluminum chassis (display lid and bottom
                       panel), as well as an ergonomic and cooling-
                       optimized Lift-Up hinge that acts as a stand.


          o § Server⠀➾


                # ⚓ Kubernetes_Blog:_Quality-of-Service_for_Memory_Resources⠀⇛


                       Kubernetes v1.22, released in August 2021,
                       introduced a new alpha feature that improves how
                       Linux nodes implement memory resource requests and
                       limits.


          o § Audiocasts/Shows⠀➾


                # ⚓ mintCast_374.5_–_“Smart”_Phones⠀⇛


                       1:46 Linux Innards
                       42:07 Vibrations from the Ether
                       51:07 Check This Out
                       54:28 Announcements & Outro


          o § Applications⠀➾


                # ⚓ Best_Free_and_Open_Source_Alternatives_to_Apple’s_Products
                  –_LinuxLinks⠀⇛


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


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


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


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


                # ⚓ Best_Free_and_Open_Source_Alternatives_to_Apple_FaceTime_–
                  LinuxLinks⠀⇛


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


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


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


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


          o § Instructionals/Technical⠀➾


                # ⚓ How_to_Install_PostgreSQL_14_in_RHEL_8_Linux⠀⇛


                       PostgreSQL is a well-known object-relational
                       database system. The open-source nature of this
                       relational database management system has kept it
                       under an active development status for over 30
                       years. These development milestones have earned
                       PostgreSQL the attributes of being robust,
                       performant, and reliable.


                       RHEL 8 on the other hand offers its users a quick
                       Cybersecurity response, flexible subscription
                       options, secure design, open APIs, and thorough
                       product testing.


                       Therefore, whether you are working on analytics,
                       geospatial, mobile, or web applications on an RHEL
                       8 environment, PostgreSQL’s flexibility with both
                       structured and unstructured data makes it a
                       reliable data warehouse/store.


                # ⚓ Install_a_full_desktop_on_a_Multipass_VM_for_easier_Linux
                  development_–_TechRepublic⠀⇛


                       Install a full desktop on a Multipass VM for easier
                       Linux development


                # ⚓ Check_External_IP_From_Linux_Command_Line_–_Linux_Nightly⠀⇛


                       There are a few different ways to check a system’s
                       external IP address from the Linux command line.
                       Check out some of the methods below to retrieve
                       your public IP address using Linux commands.


                # ⚓ Install_Fail2ban_on_Debian_11_–_Unixcop_the_Unix_/_Linux
                  the_admins_deams⠀⇛


                       See how to use the dig, curl, and wget Linux
                       commands to view a system’s external/public IP
                       address from command line terminal.


          o § Games⠀➾


                # ⚓ FUTEX2_futex_waitv_Wired_Up_For_Other_Architectures_With
                  Linux_5.16-rc3_–_Phoronix⠀⇛


                       FUTEX2 as in the new futex_waitv system call landed
                       in Linux 5.16 back during the merge window for
                       improving the efficiency of running Windows games
                       on Linux for those that rely on Windows’
                       WaitForMultipleObjects functionality with
                       futex_waitv is now the ability to wait on multiple
                       futexes. That new system call is now supported on
                       more architectures with the next Linux 5.16 release
                       candidate.


                       Back with the original FUTEX2/futex_waitv patches
                       the system call was wired up for x86/x86_64 and
                       Arm. Patches since then enabled the system call for
                       MIPS, s390, parisc,and s390. Landing today was
                       enabling the system call for the rest of the
                       supported CPU architectures by the Linux kernel,
                       not that it’s too important for those archs from
                       the gaming aspect but for other use-cases in
                       wanting to wait on multiple futexes.


                # ⚓ DOSBox_Basics_on_Linux_–_CubicleNate’s_Techpad⠀⇛


                       DOSBox is an excellent DOS environment that you can
                       enjoy on modern Linux systems. I was never really
                       into DOS all that much in my early computer years.
                       I used it but I didn’t really enjoy it. I much
                       preferred Commodore 64 because it was far more
                       colorful, later the Amiga, because it was far
                       better in sound and graphics and I got my first x86
                       based system in the Windows 98 years where I only
                       used DOS to do gaming. That said, I do have many
                       happy memories of playing DOS based games like
                       Space Quest, Police Quest, Simant and many others.
                       Games like Descent and Doom have been ported to
                       Linux so there is no benefit in running the DOS
                       version.


                       I got the “hankering” to play some old DOS games,
                       specifically Oregon Trail and Sim Ant for some
                       unknown reason, perhaps it was head injury induced,
                       I can’t say for sure. As I was playing with DOSBox,
                       I couldn’t help but think how much I was enjoying
                       the experience and started thinking, “Can I easily
                       integrate these games in my openSUSE Tumbleweed,
                       Plasma Desktop experience?”


          o § Desktop Environments/WMs⠀➾


                # § GNOME Desktop/GTK⠀➾


                      # ⚓ 13_Best_Dark_GTK_Themes_for_Your_Linux_Desktop⠀⇛


                             Yeah, we have covered the best Linux themes
                             in the past but this one is specifically
                             dedicated to the dark themes. There was a
                             time when only programmers and sysadmins
                             preferred dark mode but that’s not the case
                             anymore. Dark mode is loved by normal people
                             as well and hence I compiled this list of
                             dark themes for desktop Linux users like you.


                             If you are new to theme-ing your desktop
                             environment, you can take a look at our guide
                             to install themes in GNOME.


          o § Distributions⠀➾


                # ⚓ MX_Linux_21_‘AHS’_Is_Now_Available:_What_Is_AHS?⠀⇛


                       You might’ve heard of MX Linux. It is the most
                       popular Linux distro according to the Distrowatch
                       rankings. Developers of the same recently released
                       MX Linux 21 AHS. So what exactly is AHS? In this
                       article, let’s look at everything that’s new in MX
                       Linux 21 AHS.


                       AHS stands for Advanced Hardware Support, which,
                       according to the MX Linux blog, is a repository
                       that allows users to install new graphics firmware
                       such as mesa packages, Xorg drivers, etc. “The
                       target is those users with things like newer amdgpu
                       hardware, or later intel graphics sets, or those
                       requiring newer mesa packages. The primary focus is
                       the graphics stack,” AHS – MX Linux Blog.


                # § New Releases⠀➾


                      # ⚓ Clonezilla_Live_2.8_Disk_Cloning/Imaging_Tool
                        Released_with_Linux_Kernel_5.14,_More⠀⇛


                             Coming three months after the Clonezilla Live
                             2.7.3 release and more than a year after the
                             Clonezilla Live 2.7 series, Clonezilla Live
                             2.8 is here as a modest update that bumps the
                             kernel from Linux 5.10 LTS to the newer Linux
                             5.14 series, which is no longer supported
                             upstream.


                             Linux kernel 5.14.6 is included in Clonezilla
                             Live 2.8 mainly to provide users with better
                             hardware support, but there won’t be any
                             further updates released to this kernel
                             branch, at least not upstream.


                      # ⚓ Stable_Clonezilla_live_2.8.0-27_Released⠀⇛


                             This release of Clonezilla live (2.8.0-27)
                             includes major enhancements and bug fixes.
                             ENHANCEMENTS and CHANGES from 2.7.3-19


                      # ⚓ Endless_OS_4_makes_the_jump_to_Debian_11,_strengthens
                        Flatpak_and_improves_privacy_–_LinuxStoney⠀⇛


                             Endless OS 4 has been published to continue
                             the mission of the foundation that develops
                             it to reduce the digital divide in the world
                             . This time we find another operating system
                             based on excellent Debian 11 Bullseye , which
                             incorporates more applications in Flatpak
                             format and which maintains the atomic update
                             system OSTree as one of its main pillars.


                             As a derivative of Debian 11 Bullseye that it
                             is, Endless OS 4 inherits many of the
                             characteristics of the operating system on
                             which it is based, but the first novelty
                             highlighted by those responsible for the
                             distribution is the possibility of being able
                             to quickly switch between users without
                             logging out.


                             The second novelty mentioned by the
                             foundation is the printing support without
                             drivers thanks to IPP-over-USB , which treats
                             any device connected by USB (in this case,
                             printers) as if it were working through a
                             network, thus making it dispensable. , at
                             least initially, the use of drivers. Endless
                             warns that updating to version 4 of your
                             system will delete all the printers that the
                             user has configured.


                      # ⚓ Endless_OS_4.0_Biggest_Update_Available_to_Download
                        and_Upgrade_–_itsfoss.net⠀⇛


                             Endless OS 4.0 Biggest Update Available to
                             Download and Upgrade, Endless OS is a Linux-
                             based operating system which provides a
                             simplified and streamlined user experience
                             using a customized desktop environment forked
                             from GNOME Shell.


                             The project’s latest release is Endless OS
                             4.0.0 which introduces long-term support.
                             With Endless OS 4, we are introducing a long-
                             term support version of the OS, which will be
                             supported for a number of years even after
                             Endless OS 5 is released. By default, Endless
                             OS 4 systems will automatically update to
                             Endless OS 5 when it is released, as with all
                             past versions of the OS. However, it is now
                             possible to remain on Endless OS 4 and
                             continue to receive critical bug fixes and
                             security updates even after Endless OS 5 is
                             released, keeping the same OS functionality
                             and appearance for several years. Please see
                             the Long-Term Support documentation for more
                             details, including how to configure a system
                             to use the LTS version of Endless OS. We have
                             updated our low-level software platform, for
                             improved hardware support, performance, and
                             stability Linux kernel 5.11 and updated
                             linux-firmware, bringing support for the
                             latest PC hardware and several fixes to
                             existing drivers and core kernel code.”
                             Additional information is provided in the
                             project’s release announcement.


                      # ⚓ Deepin_20.3_Update_Available_to_Download_–
                        itsfoss.net⠀⇛


                             Deepin 20.3 Update Available to Download,
                             Deepin 20.3 is a Debian-based distribution
                             which features its own, custom desktop
                             environment – the Deepin Desktop Environment
                             (DDE). The project’s latest release is deepin
                             20.3 which includes an updated kernel and
                             better support for NTFS partitions.


                             In deepin 20.3, the Stable kernel is upgraded
                             to version 5.15 with better compatibility,
                             system security vulnerabilities are fixed,
                             some deepin applications come with new
                             features and optimizations to meet the needs
                             under different scenarios, and DDE issues are
                             fixed and optimized to improve the overall
                             user experience. The Stable kernel is
                             upgraded to version 5.15 with better support
                             for Intel 12th Gen processors and NTFS file
                             systems, and better system compatibility.
                             Both LTS and Stable kernels can be installed
                             and manually upgraded in deepin. Album
                             provides a better batch selection of photos
                             and new buttons for quick actions, supports
                             importing, previewing, and searching videos,
                             displays the number of photos and videos
                             separately in the status bar, and improves
                             the interactions of main functions, making
                             photo and video management more convenient.”
                             Additional information can be found in the
                             distribution’s release announcement (Chinese,
                             English).


                      # ⚓ Deepin_20.3_improves_image_management_and_screenshots
                        –_LinuxStoney⠀⇛


                             Deepin 20.3 is the new version of the most
                             popular Chinese distro on the scene and as it
                             has been happening with its latest releases,
                             it is presented as little more than a
                             maintenance update, although there are news.


                             We reviewed the latest movements of Deepin on
                             the occasion of its previous version, and
                             this year the project has assumed several
                             changes in its development and launch
                             calendar, now more together than ever and,
                             therefore, with less news than never.


                             Deepin 20.3 is no exception and like the most
                             recent versions of the distribution, regular
                             updates of the environment and applications
                             account for the bulk of the changes, although
                             it presents a couple of novelties that stand
                             out on their own, in the style of what has
                             already been seen.


                      # ⚓ OSMC’s_November_update_is_here_with_Kodi_19.3⠀⇛


                             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.


                      # ⚓ Whonix_16.0.3.7_–_for_VirtualBox_–_Point_Release!⠀⇛


                # § Slackware Family⠀➾


                      # ⚓ Slackware_15.0_RC2_Available_to_Download⠀⇛


                             Patrick Volkerding has announced that the
                             development branch of Slackware Linux has
                             reached “release candidate 2” status. As a
                             result, the highly anticipated release of
                             version 15.0 of the world’s oldest surviving
                             Linux distribution is just around the corner:
                             “Clearly we’re going to have to trend more
                             carefully for things to settle down, so
                             consider this RC2 and a much harder freeze.


                # § IBM/Red Hat/Fedora⠀➾


                      # ⚓ Fedora_Community_Blog:_F35_Elections_voting_now
                        open!⠀⇛


                             Voting in the Fedora Linux 35 elections is
                             now open. Go to the Elections app to cast
                             your vote. Voting closes at 23:59 UTC on
                             Thursday 9 December. Don’t forget to claim
                             your “I Voted” badge when you cast your
                             ballot. Links to candidate interviews are
                             below.


                      # ⚓ Fedora_Community_Blog:_Mindshare_election:_Interview
                        with_Fernando_Fernández_Mancera_(ffmancera)⠀⇛


                      # ⚓ Fedora_Community_Blog:_Mindshare_election:_Interview
                        with_Till_Maas_(till)⠀⇛


                      # ⚓ Fedora_Community_Blog:_Mindshare_election:_Interview
                        with_Stephen_Snow_(jakfrost)⠀⇛


                      # ⚓ Fedora_Community_Blog:_FESCo_election:_Interview_with
                        Fabio_Valentini_(decathorpe)⠀⇛


                      # ⚓ Fedora_Community_Blog:_FESCo_election:_Interview_with
                        Kevin_Fenzi_(kevin)⠀⇛


                      # ⚓ Fedora_Community_Blog:_FESCo_election:_Interview_with
                        Miro_Hrončok_(churchyard)⠀⇛


                      # ⚓ Fedora_Community_Blog:_FESCo_election:_Interview_with
                        Zbigniew_Jędrzejewski-Szmek_(zbyszek)⠀⇛


                      # ⚓ Fedora_Community_Blog:_FESCo_election:_Interview_with
                        Tom_Stellard_(tstellar)⠀⇛


                      # ⚓ Fedora_Community_Blog:_FESCo_election:_Interview_with
                        David_Cantrell_(dcantrell)⠀⇛


                      # ⚓ Normalize_web_services_with_Camel_K_and_AtlasMap,
                        Part_2_|_Red_Hat_Developer⠀⇛


                             Part 1 of this series introduced a simple
                             approach to normalizing and connecting web
                             services using Camel K, a lightweight cloud-
                             integration platform based on Apache Camel
                             that runs natively on Kubernetes. In this
                             article, we’ll walk through the Camel K
                             implementation step-by-step. We’ll also cover
                             how to simplify data mapping with AtlasMap.


                             Note: Many organizations today face the
                             challenge of using many different services,
                             often as a result of partnerships or
                             acquisitions. These systems are implemented
                             with a range of technologies, each with its
                             own access protocol. The previous article
                             discussed how Apache Camel makes it easy to
                             normalize the APIs in this scenario.


                      # ⚓ Change_management:_How_to_build_resilience_into_your
                        processes⠀⇛


                             IT leaders have experienced and witnessed
                             some incredible flexibility, adaptability,
                             and downright heroism since the beginning of
                             the COVID-19 pandemic – among their team
                             members, across their organizations, within
                             themselves. As the pressure on technology
                             teams has persisted, however, many have
                             turned their attention to identifying and
                             preventing burnout on their teams – learning
                             how to toe the line between building healthy
                             resilience within themselves and their teams
                             and demanding too much change of their
                             organizations.


                             One way to ease the impact of uncertainty and
                             volatility on people is to build more
                             resiliency into processes.


                             “This past eighteen months has shown us how
                             quickly our normal can change, and we’re
                             still dealing with things that will challenge
                             our processes some time into our future
                             including supply chain and labor shortages,”
                             says Janele Lynn, owner of the Lynn
                             Leadership Group, which helps leaders build
                             trusting relationships through emotional
                             intelligence. “We’ll need to focus our
                             attention on not only what matters most to
                             our organizations but also changes that will
                             allow our organizations the most opportunity
                             to flex if needed.”


                             People are only as good (or as flexible or as
                             resilient) as the processes they are a part
                             of, says Noelle Akins, leadership coach and
                             founder of Akins & Associates. “While we
                             build personal and team resilience, let’s
                             also look at how our processes either build
                             or drain resilience,” Akins advises. “As
                             Edward Deming said, ‘A bad system will beat a
                             good performer every time.’ It takes a
                             systemic approach for resilience to be
                             sustainable.”


                      # ⚓ Red_Hat_honors_APAC_partners_for_supporting_customers
                        in_their_digital_transformation_with_open_source
                        innovation [Ed: "Clown" TOP PARTNER… Microsoft]⠀⇛


                             The Red Hat partner ecosystem is an integral
                             part of how Red Hat develops and delivers
                             business and technical value to customers. As
                             key players in digital transformation, Red
                             Hat partners help organizations and
                             businesses navigate the ever changing IT
                             landscape through open source solutions.


                             The Red Hat Asia Pacific Partner Awards 2021
                             recognize commercial and public sector
                             partners for their continued efforts to
                             develop innovative solutions using Red Hat
                             technologies to meet customers needs and
                             improve business outcomes. This year’s
                             partner award winners have not only acted as
                             catalysts for customer success, but have been
                             important multipliers of enterprise open
                             source by adopting Red Hat solutions, from
                             emerging technologies to hybrid cloud
                             infrastructure. In today’s evolving
                             marketplace, it is more important than ever
                             to work openly and collaboratively to
                             generate meaningful results for organizations
                             throughout their cloud journey.


                             Selected based on their commitment to
                             innovation, dedication to driving change with
                             open source, and demonstration of
                             collaborative and transparent working
                             ecosystems, we are pleased to announce this
                             year’s Red Hat Asia Pacific Partner Award
                             winners:


          o § Devices/Embedded⠀➾


                # § Open Hardware/Modding⠀➾


                      # ⚓ Bring_A_Minitel_Terminal_Back_To_Life_WIth_An_ESP32_|
                        Hackaday⠀⇛


                             Most of us who are old enough are likely to
                             have had our first experience of an online
                             service some time in the 1990s, either
                             through the likes of Compuserve or via an
                             ISP. For our French readers the online
                             experience will have come much earlier, as a
                             forward-thinking telecommunications
                             environment led to every household in the
                             country receiving a viewdata terminal. The
                             Minitel system as it was called was a runaway
                             success, and was only finally turned off as
                             late as 2012. Many of the terminals survive
                             to make a great basis for projects, and it’s
                             one of these that [Louis H] has taken and
                             enhanced with an ESP32.


                      # ⚓ Fifty_Shades_Of_Brown:_3D_Printing_With_Sugar_|
                        Hackaday⠀⇛


                             Success was somewhat variable, as the gloopy
                             material is notoriously fickle to work with,
                             but the setup did produce some structures
                             that stayed in one piece, at least for a
                             while. Initially [Norbert] tried it real
                             slow, effectively printing with the liquified
                             sweet stuff, by dragging a molten blob of it
                             around on the end of the extruder nozzle.
                             Whilst this did work, the resulting print
                             resolution did leave something to be desired.
                             The next thing tried was increased print
                             speed. This produced clearer prints, as the
                             sugar did not have time to caramelise, or
                             form a noticeable blob, but as soon as the
                             bed started to cool, it caused it to crack
                             badly.


                      # ⚓ Espressif_introduces_ESP32-S3-BOX_AI_development_kit
                        for_online_and_offline_voice_applications_–_CNX
                        Software⠀⇛


                             Espressif Systems has very recently
                             introduced the ESP32-S3-BOX AI voice devkit
                             designed for the development of applications
                             with offline and online voice assistants, and
                             whose design I find similar to the M5Stack
                             Core2 devkit, but the applications will be
                             different.


                             The ESP32-S3-BOX features the latest ESP32-S3
                             processor with WiFi and BLE connectivity, AI
                             capabilities, as well as a 2.4-inch
                             capacitive touchscreen display, a 2-mic
                             microphone array, a speaker, and I/
                             O connectors with everything housed in a
                             plastic enclosure with a stand.


                      # ⚓ IoThing_Digital_IO_board_handles_up_to_300V_for
                        Arduino,_Raspberry_Pi,_and_various_other_boards_
                        (Crowdfunding)_–_CNX_Software⠀⇛


                             AlterStep’s IoThing Digital is a digital I/
                             O module with two high-power Omron G5Q-14
                             relays and two isolated AC or DC input
                             channels based on Texas Instruments ISO1211
                             that can handle up to 300 V.


                             The board also integrates a DC-DC converter
                             and mikroBUS slot that allows it to be used
                             with compatible MCU boards, and the company
                             also provides adapters for popular form
                             factors such as Arduino, Raspberry Pi,
                             Adafruit Feather, Teensy, and others.


                      # ⚓ Celebrating_the_community:_Cian⠀⇛


                # § Mobile Systems/Mobile Applications⠀➾


                      # ⚓ One_UI_4.0_hands-on:_Android_12_for_Samsung_devices_–
                        9to5Google⠀⇛


                      # ⚓ Glodroid_brings_Android_12_to_the_PinePhone_(sort_of)
                        –_Liliputing⠀⇛


                      # ⚓ Android_11_is_finally_rolling_out_to_the_ASUS_ROG
                        Phone_2_–_TalkAndroid.com⠀⇛


                      # ⚓ Free_instead_of_$2.49:_Edit_photo_metadata_with_this
                        Android_app_|_NextPit⠀⇛


                      # ⚓ 6_useful,_affordable_gifts_for_the_Android_lover_on
                        your_list⠀⇛


                      # ⚓ Best_Android_smartwatch_2021:_Top_picks_for_the
                        holidays_–_9to5Google⠀⇛


                      # ⚓ How_to_record_audio_from_Android_apps⠀⇛


                      # ⚓ How_to_Update_Your_Android_Phone⠀⇛


                      # ⚓ Here’s_how_to_track_your_screen_time_on_Android
                        phones_–_Information_News⠀⇛


                      # ⚓ Truecaller_Version_12_to_add_more_features_for
                        Android_users:_Find_out_what’s_new_on_the_updated_app-
                        Technology_News,_Firstpost⠀⇛


                      # ⚓ Android_Auto_and_Spotify_Car_View_mode_not_working
                        together?_You’re_not_alone_|_T3⠀⇛


                      # ⚓ 190_Android_apps_with_trojan_malware_were_installed
                        9.3_million_times_–_PhoneArena⠀⇛


                      # ⚓ How_to_Auto-delete_Google_Search_History_on_Your
                        Android_Device⠀⇛


                             With the advancement of technology, anyone
                             can gather any knowledge or information from
                             internet searching nowadays. And, to do so,
                             we all prefer the Google search engine
                             because of its ease & user-friendliness. You
                             can search for whatever you want in any
                             search engine if you own an Android device
                             and access the internet from it. Speaking of
                             search engines, you might not be aware that
                             Android keeps your Google search history.
                             Regardless of what you’ve searched for,
                             Android keeps an ongoing record of that
                             search. You may not consider it a major
                             issue, but to some people, it is. Thankfully,
                             there is a simple trick by which you can get
                             rid of this permanently. That’s awesome!
                             Don’t you think? Auto-delete of Google search
                             history on your Android is quite easy and
                             simple to do.


                             And for doing that, you shouldn’t miss a word
                             of the entire post if you are someone who is
                             concerned about keeping their p


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


                # ⚓ 10_holiday_gift_ideas_for_open_source_enthusiasts⠀⇛


                       Are you looking for cool gifts for people on your
                       holiday shopping list or ideas for your own
                       wishlist? If so, consider one of the ten
                       suggestions below. Each of these gift suggestions
                       connects in some way to the open source ethos. From
                       DIY projects to computers to books, this list
                       provides gift suggestions that foster creativity,
                       learning, and exploring.


                       If the person on your shopping list already has
                       everything (or does not want any tangible gifts),
                       consider making a charitable donation to an open
                       source project in their name. Opensource.com’s list
                       of open source organizations has plenty of
                       organizations you can select from. You, the person
                       whose name the donation was made in, and the
                       organization that received your donation can all be
                       content in knowing that your gift has helped make
                       open source better.


    * § Leftovers⠀➾


          o ⚓ Opinion_|_When_a_Community_Is_Smashed⠀⇛


                 The first time it happened was bad enough.


          o ⚓ Living_on_a_Sci-Fi_Planet⠀⇛


                 I know that because I recently reread H.G. Wells’s 1898
                 novel War of the Worlds, while revisiting an early moment
                 in my own life. Admittedly, I wasn’t in London when those
                 Martian machines, hooting away, stalked boldly into that
                 city, hungry in the most literal fashion imaginable for
                 human blood. No surprise there, since that was almost a
                 century and a quarter ago. Still, at 77, thanks to that
                 book, I was at least able to revisit a moment that had
                 been mine long enough ago to seem almost like fiction.


                 Yes, all those years back I had been reading that very
                 same novel for the very first time under the covers by
                 flashlight. I still remember being gripped, thrilled, and
                 scared, at a time when my parents thought I was asleep.
                 And believe me, if you do that at perhaps age 12 or 13,
                 you really do feel as if you’ve been plunged into a
                 futuristic world from hell, ululations and all.


          o ⚓ The_Anti-Pilgrim:_The_Life_and_Times_of_Thomas_Morton⠀⇛


                 As Mount St. Mary’s University Professor of English,
                 William Heath pointed out in a 2007 article for the
                 Journal of American Studies, Morton remains one of the
                 best sources on New England’s indigenous culture and
                 ecology at the time of English settlement. Not
                 surprisingly, some of his observations were off the mark;
                 he concluded, for example, that the Natives were remnants
                 of “the scattered Trojans,” and that they had no religion
                 to speak of, the same mistake made by Columbus on his
                 first day in America. But other observations are quite
                 acute. For example, Morton noted that the Indians set
                 fire to the country periodically, thereby cleaning away
                 underbrush and creating more grasslands for the deer to
                 feed on. He was also quick to praise them when he found
                 their conduct superior to that of the Puritans and
                 Separatists. In New English Canaan he wrote, “I have
                 found the Massachusetts Indians more full of humanity
                 than the Christians, and have had much better quarter
                 with them.”


                 The details of Morton’s early life in England are scanty.
                 Heath speculates that he could have been from the
                 southwestern county of Devon, a region famed for its
                 adherence to old English folk customs, Anglo-Catholic
                 ritual, and “good hospitality,” as well as for its
                 swashbuckling, sea-faring sons, including Sir Francis
                 Drake, Sir Humphrey Gilbert, and Sir Walter Raleigh. The
                 just published, The Trials of Thomas Morton by USC
                 Professor of Humanities, History and Anthropology, Peter
                 C Mancall places Morton’s birth at around 1575 or 76
                 possibly in Somerset, also in the southwest of England.
                 As Heath notes, Morton’s family could afford to send him
                 to the Inns of the Court, England’s peculiar combination
                 of law school and professional association, so it can be
                 presumed that he was an aristocrat of sorts whose
                 education was probably similar, if not superior, to that
                 of Shakespeare.


          o ⚓ Tribe_That_Helped_Pilgrims_Survive_First_Thanksgiving_Regrets_It
            400_Years_Later⠀⇛


          o ⚓ The_First_Thanksgiving_is_a_Key_Chapter_in_America’s_Origin
            Story,_But_What_Happened_in_Virginia_Four_Months_Later_Mattered
            Much_More⠀⇛


                 But what happened four months later, starting in March
                 1622 about 600 miles south of Plymouth, is, I believe,
                 far more reflective of the country’s origins – a story
                 not of peaceful coexistence but of distrust, displacement
                 and repression.


                 As a scholar of colonial New England and Virginia, I have
                 often wondered why Americans tend to pay so much less
                 attention to other English migrants of the same era.


          o ⚓ Opinion_|_On_Thanksgiving’s_400th_Anniversary,_We_Must_Change_the
            Way_We_Celebrate⠀⇛


                 Today, the United States officially marks Thanksgiving.
                 This holiday with vague roots in centuries-old European
                 harvest festivals has had peculiarly American – and
                 highly problematic – iconography and mythology
                 constructed around it since the mid-19th century. In its
                 modern incarnation, Thanksgiving is also inescapably
                 associated with capitalism.


          o ⚓ A_THANKSGIVING_TOAST⠀⇛


                 But I will remind them of this nation’s resilience, and
                 the many ways the future could be bright. And when we
                 raise our glasses for a toast, I will ask that they never
                 give up fighting for a more just society. Happy
                 Thanksgiving, friends.


          o ⚓ Opinion_|_Indigenous_Resistance_Rising_as_Thanksgiving_Turns
            400⠀⇛


                 Wampanoag. Massachusett. Nipmuc. Mohegan. Pequot.
                 Narragansett. Passamaquoddy. Miꞌkmaq. These are just some
                 of the indigenous nations of the land now called New
                 England, the home of that original Thanksgiving dinner
                 that occurred 400 years ago, in the fall of 1621. The
                 myth of that shared meal has evolved over the centuries,
                 depicting friendship and cooperation between the English
                 settlers in Plymouth, Massachusetts and the Wampanoag
                 people who had been there for at least 10,000 years.
                 While that gathering was peaceful, it was at best a token
                 respite from the European settler colonists’ genocide
                 against native peoples that was already well underway.
                 While families gather across the country for this year’s
                 Thanksgiving celebration, frontline indigenous
                 communities that have survived centuries of violence,
                 displacement and systemic racism remain in resistance,
                 defending land, water and their very existence.


          o § Hardware⠀➾


                # ⚓ Ken_Shirriff_Breaks_Open_The_Yamaha_DX7_|_Hackaday⠀⇛


                       For better or worse, this synthesizer was king in
                       the 1980s music scene. Sure, there had been
                       synthesizers before, but none acheived the sudden
                       popularity of Yamaha’s DX7. “Take on Me?” “Highway
                       to the Dangerzone”? That harmonica solo in “What’s
                       Love Got to Do With It?” All DX7. This synth was
                       everywhere in pop music at the time, and now we can
                       all get some insight from taking a look at this de-
                       capped chip from [Ken Shirriff].


                       To be clear, by “look” that’s exactly what we mean
                       in this case, as [Ken] is reverse-engineering the
                       YM21280 — the waveform generator of the DX7 — from
                       photos. He took around 100 photos of the de-capped
                       chip with a microscope, composited them, and then
                       analyzed them painstakingly. The detail in his
                       report is remarkable as he is able to show
                       individual logic gates thanks to his powerful
                       microscope. From there he can show exactly how the
                       chip works down to each individual adder and array
                       of memory.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ Enough_Colonial_Pageantry._Let’s_Rally_Behind_Criminalized
                  Water_Protectors.⠀⇛


                # ⚓ Opinion_|_On_This_Thanksgiving,_Celebrate_AgriCULTURE,_Not
                  AgriBUSINESS⠀⇛


                       In December 1972, I was part of a nationwide
                       campaign that came tantalizingly close to getting
                       the U.S. Senate to reject Earl Butz, Richard
                       Nixon’s choice for secretary of agriculture.


                # ⚓ Covid_Year_2:_About_Suffering_the_Old_Masters_Were_Never
                  Wrong⠀⇛


                       How many deaths can you live with?


                # ⚓ Not_Everyone_Is_Feasting._Food_Insecurity_Is_Much_Higher
                  Than_Before_COVID.⠀⇛


                # ⚓ Schumer_Got_$66K_From_Top_Health_Insurance_Lobbyist_Amid
                  Build_Back_Better_Talks⠀⇛


          o § Integrity/Availability⠀➾


                # § Proprietary⠀➾


                      # § Security⠀➾


                            # § Privacy/Surveillance⠀➾


                                  # ⚓ he_Joint_Parliamentary_Committee_on_the
                                    Personal_Data_Protection_Bill,_2019_has
                                    adopted_its_final_report._What_now?
                                    #SaveOurPrivacy⠀⇛


                                         The Joint Parliamentary Committee
                                         on the Personal Data Protection
                                         Bill, 2019 has adopted the final
                                         version of its report, and is
                                         expected to table it in
                                         Parliament during the upcoming
                                         Winter Session. Here, we look at
                                         the possible ways forward for the
                                         Data Protection Bill and
                                         highlight some of the issues that
                                         may emerge from the final report
                                         of the Committee. We guide you
                                         through the parliamentary
                                         process, next steps and the
                                         fundamental issues at play.


          o § Defence/Aggression⠀➾


                # ⚓ Opinion_|_True_Measures_of_Justice_Goes_Beyond_Verdicts_in
                  the_Rittenhouse_or_Arbery_Trials⠀⇛


                # ⚓ “They_Should_Have_Shot_More_Students:”_From_Kent_State_to
                  Kenosha⠀⇛


                       Joy or glee at the killing and wounding of those
                       who differ with the opinions and actions of some
                       within and outside of the governments and the
                       apparatus of empire of the US goes way back in our
                       history. Readers need only view the horrific
                       photographs of the crowds enjoying the spectacle of
                       lynchings in the US South during the first half of
                       the 20th century and beyond to have that premise
                       validated. Now, with the far right a clear and
                       present danger in the US, both in government and at
                       street level, there is a minority that plans and
                       enjoys murder, to paraphrase the late Israeli
                       scientist Israel Shahak. The minority of those who
                       protest injustices is increasingly in grave danger.
                       Jacob Blake was not the first Black person shot by
                       officials of the government, in his case the
                       police, and he was far from the first person of
                       color in US history whose shooting was cheered by
                       those with hate in their hearts and guns and ropes
                       in their hands.


                       The words self-defense appeared from a relative on
                       my Facebook feed within hours of the verdict
                       freeing Kyle Rittenhouse in Wisconsin. Self-defense
                       is the cause célèbre of police who kill unarmed
                       civilians in many cases with impunity. Self-defense
                       was on the lips of some of those in the Ohio
                       National Guard in 1970, when they killed and
                       wounded students. Self-defense was on the lips of
                       Kyle Rittenhouse.  I know something about the
                       military-style semi-automatic rifle Rittenhouse
                       used to kill two protesters in Wisconsin, who
                       were protesting the shooting of Jacob Blake (New
                       York Times, October 26, 2021). The US government
                       taught me how to become a sharpshooter with this
                       kind of weapon and its lethality is so monstrous
                       that the thought of taking a rifle like this to a
                       demonstration and then claiming self-defense is
                       more than obscene! It was the weapon (semi-
                       automatic military assault rifles) of choice at
                       Sandy Hook Elementary School, Columbine High
                       School, at a concert in Nevada, and in countless
                       other public places. Second Amendment/self-defense:
                       Bullshit! A person with this kind of military-style
                       semi-automatic rifle is pretty much invincible. And
                       as if in some bizarre accident of time and place,
                       the military also taught me how to use the M-
                       ! rifle, the weapon of choice on the battlefields
                       of World War II and the weapon that the Ohio
                       National Guard used against unarmed protesting
                       students at Kent State.


                # ⚓ We’re_Spending_Money_on_War_When_We_Could_Be_Building
                  Roads⠀⇛


                       As a Navy spouse of 10 years and counting, my life
                       offers an up-close view of our country’s priorities
                       when it comes to infrastructure and government
                       spending.


                # ⚓ Did_the_CIA_kill_JFK?_Oliver_Stone_on_his_explosive_new
                  film⠀⇛


                # ⚓ Let’s_Talk_Turkey:_Glen_Ford_Carves_Up_the_American
                  Empire⠀⇛


                       Well, that’s how I read the energy and intention of
                       Ford’s “No More American Thanksgivings,” the
                       opening evisceration of the mightiest, whitiest
                       American holiday of them all. His screed is a
                       triumphant tonic,  a P’au Revere trumpet blast to
                       open  Black Agenda (OR Books, 2021). Ford begins
                       his carve-up of the butterball day traditionally
                       associated with the beginning of the Christmas
                       shopping period (Black Friday), with some
                       nastiness. Smallpox blankets that would make Wuhan
                       blush. Stolen corn from gravesites probably filled
                       with victims of that smallpox, leaving a wide open
                       area, reminiscent, later, of a trailer park swathe.
                       Indian heads on totemic poles. Indians sold into
                       slavery and sent to Caribbean. Ford sums it up with
                       words of Governor John Winthrop, “This day forth
                       shall be a day of celebration and thanksgiving for
                       subduing the Pequots.”


                       In 2003, Ford writes, for The Black Commentator (a
                       forerunner to Black Agenda Report),


                # ⚓ The_Problem_of_Sanctions_Against_North_Korea⠀⇛


                       These sanctions have contributed to isolating North
                       Korea from the rest of the world. The country has
                       not entirely welcomed this isolation. Despite
                       longstanding suspicions of outside influences,
                       Pyongyang has shown considerable interest in
                       engaging with the West and with the global economy
                       more generally. Economic sanctions have severely
                       limited this interaction.


                       There is currently little political support in the
                       United States for lifting sanctions against North
                       Korea. Despite claims to the contrary, the Biden
                       administration has settled into the same de facto
                       policy of “strategic patience” adopted by the Obama
                       administration. The new administration has not even
                       reversed the Trump administration’s re-designation
                       of North Korea as a state sponsor of terrorism.


                # ⚓ Takeover_of_German_manufacturer:_Rheinmetall_re-enters_the
                  drone_business⠀⇛


                       Equipping the German Army’s reconnaissance force
                       with new LUNA drones seems to be secured, so a sale
                       of the insolvent German manufacturer to Israel is
                       off the table. The Bundeswehr has also commissioned
                       a study for kamikaze drones, such a system is also
                       offered by Rheinmetall.


                # ⚓ November_25,_International_Day_for_the_Elimination_of
                  Violence_Against_Women⠀⇛


                # ⚓ ‘No_More_Violence,_No_More_Silence!’:_Women_Worldwide
                  Demand_End_to_Gender-Based_Abuse⠀⇛


                       Leaders at the United Nations and civil society
                       groups marked the International Day for the
                       Elimination of Violence Against Women on Thursday
                       to highlight the global scourge of gender-based
                       violence that has escalated during the last 20
                       months of the Covid-19 pandemic and which only
                       focused and urgent action can help bring to an end.


                       “In all of our own neighborhoods, there are women
                       and girls living in danger.”


                # ⚓ Coalition_Against_Stalkerware_Celebrates_Two_Years_of_Work
                  to_Keep_Technology_Safe_for_All⠀⇛


                       Stalkerware makes it possible to intrude into a
                       person’s private life and is a tool for abuse in
                       cases of domestic violence and stalking. By
                       installing these applications on a person’s device,
                       abusers can get access to someone’s messages,
                       photos, social media, geolocation, audio or camera
                       recordings (in some cases, this can be done in
                       real-time). Such programs run hidden in the
                       background, without a victim’s knowledge or
                       consent.


                       This year, the Coalition welcomed new supporters
                       like INTERPOL and members, among them CyberPeace
                       Institute; Gendarmerie Nationale; the Gradus
                       Project; Kandoo; Luchadoras; the Florida Institute
                       for Cybersecurity Research; National Center for
                       Victims of Crime (US); North Carolina A&T State
                       University’s Center of Excellence for Cybersecurity
                       Research, Education, and Outreach; Refuge UK;
                       Sexual Violence Law Center (US), and The Tor
                       Project. 


                       Fulfilling one of the founding missions, the
                       Coalition’s partners in July launched a new
                       technical training on stalkerware aimed at helping
                       increase capacity-building among nonprofit
                       organizations that work with survivors and victims,
                       as well as law enforcement agencies and other
                       relevant parties. In addition, the Coalition has
                       put together a revised page with advice for
                       survivors who suspect they may have stalkerware on
                       their device.


                # ⚓ Coordination_by_Europol:_Special_Intervention_Units_train
                  with_drone_carrying_explosives_and_robot_dog⠀⇛


                       Since this year, the ATLAS network has had a
                       Support Office at Europol, with which the police
                       agency coordinates cross-border operations of units
                       from Schengen states. Most of the money from the
                       coming budget will again go to police forces from
                       Germany.


          o § Environment⠀➾


                # § Energy⠀➾


                      # ⚓ Electric_Car_Delusions⠀⇛


                             Things, however, had changed. COP26, pressure
                             from other countries, and potential electoral
                             pressure within traditional Coalition seats,
                             had made the prime minister shift his
                             position.  In a joint press release from the
                             Prime Minister and Energy Minister Angus
                             Taylor, the government promised, as part of
                             the Future Fuels Fund investment, $250
                             million on vehicle charging and hydrogen
                             fuelling infrastructure; heavy and long-
                             distance vehicle technologies; commercial
                             fleets and household smart charging.


                             In terms of numbers, 400 businesses, 50,000
                             households will be affected, and 1000 public
                             charging stations created.  With an eye
                             towards private investment, the hope is that
                             there will be over $500 million “of combined
                             private and public co-investment directed
                             into the update of future fuels in Australia
                             and the creation of more than 2,600 new
                             jobs.”


                      # ⚓ Consumers_Getting_Hosed_at_the_Pump_Again⠀⇛


                             Despite the longstanding propaganda about
                             “energy independence,” the simple truth is
                             that we have been betrayed by lawmakers who
                             once again kow-tow to the demands of the oil
                             and gas industry.


                             You’d have to be a certain age to remember
                             the Arab oil embargo of 1973-74 and the
                             scenes of Americans waiting in long lines to
                             get gas before the stations ran out — which
                             many did. The Arab members of the
                             Organization of Petroleum Exporting Countries
                             (OPEC) quadrupled the price of its oil and
                             simply stopped all oil shipments to the
                             United States and other nations that
                             supported and re-supplied Israel during the
                             1973 Yom-Kippur Arab-Israeli War.


                # § Wildlife/Nature⠀➾


                      # ⚓ Killer_Apes_and_Global_Ecocide⠀⇛


                             Crucially, this also means that we are
                             descendants of the chimpanzees and not of the
                             neighbors next door – the bonobos, who were
                             mistakenly also known as pygmy chimpanzees,
                             once. Essentially, our chimpanzee ancestors
                             are very different from the bonobos who have
                             never been just a little version of
                             chimpanzees.


                             Our departure from chimpanzees marks not only
                             the fact that we are part of the Warrior
                             Apes, it also marks us out as being closely
                             linked to the wrong crowd – the chimpanzees,
                             and not the bonobos. While both appear
                             similar in look and size, chimpanzees and
                             bonobos are very different when it comes to
                             the way they live.


          o § Finance⠀➾


                # ⚓ ’Tis_the_Season_for_DeJoy’s_Removal⠀⇛


                       The Thanksgiving holiday weekend opens the most
                       demanding season of the year for America’s postal
                       workers. Last year, according to the United States
                       Postal Service, “13 billion letters, cards, and
                       packages were processed and delivered under some of
                       the most difficult circumstances we’ve faced in the
                       past century.” This year, postal workers will again
                       provide outsize service to this country, while
                       continuing to face unprecedented challenges.


                # ⚓ What_Would_Have_Worked_Better_Than_Building_Back_Anything⠀⇛


                       But the most serious problem is the tendency of
                       those voters who do vote to nonetheless identify
                       themselves with one of the lousy candidates and
                       parties and its statements and actions year-in-and-
                       year-out so that a larger phenomenon than lesser-
                       evil voting is total lesser-evil existing. The
                       extremely rare individual actually votes with his
                       or her nose appropriately pinched, containing the
                       voting to a single moment while rejecting the hype
                       and keeping a free mind every other day.


                       This problem is compounded by, and its prevalence
                       exaggerated by, the tendency of commentators to
                       invent explanations for votes based only on who was
                       voted for and not on who was voted against — and
                       certainly not on what would have been voted for had
                       it been anywhere to be found.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ Opinion_|_Pundits_Want_You_To_Think_Biden’s_Low_Approval
                  Rating_Means_Democrats_Should_Move_Center⠀⇛


                       Recent polls show that President Joe Biden’s
                       approval rating has declined significantly since he
                       took office.


                # ⚓ Dialogue_of_the_Deaf:_Debating_Ted_Koppel_on_Communism⠀⇛


                       By late afternoon in Los Angeles, Tracy called from
                       New York. I’d be on with Angela Davis and Melor
                       Sturua, a Russian columnist for Izvestia on leave
                       at the Carnegie Endowment.


                       I drove east across Los Angeles toward the ABC
                       studio. At the studio they make me up and sit me
                       down. The drill with Koppel is that you look into a
                       camera and listen to your earphone. You can’t see
                       what’s happening on the show. You have to keep
                       looking at the camera because you don’t know when
                       Koppel, the only person who can see all the people
                       on the show, who controls everything, is going to
                       call on you. Swivel your eyes away from the camera
                       and millions will think you’ve got something to
                       hide.


                # ⚓ These_Biden_Nominees_are_Foxes_Guarding_Industry_Henhouse⠀⇛


                       The nomination of Vilsack in 2008 by then-
                       President-elect Obama was lauded by industry
                       players such as the Corn Refiners Association, the
                       National Grain and Feed Association and biotech
                       organizations. In fact, Vilsack, a former governor
                       of Iowa, “was named Governor of the Year by the
                       Biotechnology Industry Organization, an industry
                       lobbying group,” reports Wikipedia.


                       Vilsack did not disappoint.


                # ⚓ The_Chilean_Elections,_50_Years_After_How_to_Read_Donald
                  Duck⠀⇛


                       We never anticipated that our essay would become an
                       international best seller, translated into dozens
                       of languages. It had been born, quite modestly, as
                       a way of participating in the unique Chilean
                       experiment of building socialism, for the first
                       time in history, through electoral and nonviolent
                       methods, without eliminating our adversaries. This
                       meant that the government of Salvador Allende,
                       which had captured the presidency in September
                       1970, would have to win the battle for public
                       opinion in a situation of considerable inequality,
                       since most of the media was in the hands of the
                       enemies of the revolution.


                       In this struggle to define Chile’s identity and
                       leave behind the obstacles and prejudices of the
                       past, the Allende government had acquired an
                       important asset: the most important publishing
                       house in the country. Renamed Quimantú (“sun of
                       knowledge” in Mapuche), it gave our peaceful
                       revolution the means to bring out millions of books
                       at inexpensive prices, as well as an assortment of
                       magazines, including children’s and adult comics
                       that would have to compete for readers in a market
                       saturated with foreign products. If we were to
                       devise progressive alternatives, it was urgent to
                       probe how those imported stories worked, and Armand
                       and I therefore set out to analyze the most popular
                       comics in Chile—and in the world: those generated
                       by the immense corporation founded by Walt Disney.


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


                # ⚓ Democracy_Now!_at_25:_Celebrating_a_Quarter-Century_of
                  Independent_News_on_the_Frontlines⠀⇛


                       Democracy Now! first aired on nine community radio
                       stations on February 19, 1996, on the eve of the
                       New Hampshire presidential primary. In the 25 years
                       since that initial broadcast, the program has
                       greatly expanded, airing today on more than 1,500
                       television and radio stations around the globe and
                       reaching millions of people online. We celebrate 25
                       years of The War and Peace Report with an hour-long
                       retrospective, including highlights from the show’s
                       early years, some of the most controversial
                       interviews, and groundbreaking reports from East
                       Timor, Standing Rock, Western Sahara and more.


          o § Civil Rights/Policing⠀➾


                # ⚓ Humanitarians_Demand_End_of_‘Hostile’_UK_Policies_After_27
                  Migrants_Perish_in_English_Channel⠀⇛


                       Over two dozen migrants—including young
                       children—attempting to cross the English Channel
                       from France perished at sea Wednesday, sparking
                       outpourings of grief and renewed demands that both
                       the U.K. government and leaders across Europe end
                       their woeful immigration policies that force
                       desperate individuals and families to risk ever
                       more dangerous and deadly journeys to attain
                       refuge, asylum, or a better life.


                       “How many more times must we see people lose their
                       life trying to reach safety in the U.K. because of
                       the woeful lack of safe means to do so?”


                # ⚓ How_I_Fight_Racism_in_the_World_and_Within_Me⠀⇛


                       Before the murder of George Floyd, I didn’t focus
                       on racism I had experienced. Floyd was just a
                       normal Black man trying to get through another day,
                       like my father, uncle, or older cousins. It had
                       infuriated me enough to see that I couldn’t ignore
                       any more of the microaggressions I often faced, and
                       I had to take a long look in the mirror. This story
                       was produced for Student Nation, a program of the
                       Nation Fund for Independent Journalism, which is
                       dedicated to highlighting the best of student
                       journalism. For more Student Nation, check out our
                       archive or learn more about the program here.
                       StudentNation is made possible through generous
                       funding from The Puffin Foundation. If you’re a
                       student and you have an article idea, please send
                       pitches and questions to [email protected]


          o § Monopolies⠀➾


                # ⚓ Human_Rights_Defenders_Threaten_Legal_Action_Against
                  Countries_Fueling_Vaccine_Inequality⠀⇛


                       More than a year after South African and Indian
                       officials first proposed waiving intellectual
                       property barriers for Covid-19 treatments and
                       vaccines, human rights lawyers and advocacy groups
                       on Thursday threatened legal action against the
                       governments of several wealthy countries that are
                       opposing the waiver.


                       “The consequences of a failure to adopt the TRIPS
                       waiver could be millions of lives.”


                # § Patents⠀➾


                      # ⚓ 130_Social_Justice_Groups_Are_Calling_on_WTO_to_Adopt
                        Patent_Waiver⠀⇛


                      # ⚓ 130+_Global_Groups_Demand_WTO_Postpone_Meeting_Until
                        Vital_Patent_Waiver_Is_Adopted⠀⇛


                             A group of over 130 national and
                             international civil society organizations is
                             demanding the World Trade Organization
                             postpone its upcoming ministerial meeting
                             unless it first agrees to adopt a patent
                             waiver for Covid-19 vaccines seen by social
                             justice campaigners as crucial to ending
                             “vaccine apartheid.”


                             The groups laid out their demand in an open
                             letter to WTO members just ahead of the in-
                             person 12th ministerial conference set to
                             begin Nov. 30 in Geneva, the latest sign of
                             growing pressure on rich nations—including
                             the U.S.—to move more urgently to end the
                             pandemic.


                # § Copyrights⠀➾


                      # ⚓ Filmmakers_Want_ISP_to_Share_Personal_Info_of
                        Thousands_of_Pirates⠀⇛


                             As part of an ongoing lawsuit, a group of
                             independent movie companies wants Colorado-
                             based Internet provider WOW! to disclose the
                             personal details of thousands of persistent
                             pirates. The filmmakers also request the
                             option to file separate lawsuits against
                             these alleged pirates, but that clearly goes
                             a step too far for the Internet provider.


                      # ⚓ Online_Piracy_Increases_Among_Young_Finns,_But_Legal
                        Consumption_is_Up_Too⠀⇛


                             It is often said that the only workable long-
                             term solution to the piracy problem is making
                             content widely available at a fair price. A
                             new study from Finland finds that an
                             increasing number of people are indeed
                             turning to legitimate options. While overall
                             piracy levels are generally static, tech-
                             savvy young people are again bucking the
                             trend.


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