𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Wednesday, February 09, 2022
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Generated Thu 10 Feb 02:41:12 GMT 2022
Created by Dr. Roy Schestowitz (𝚛𝚘𝚢 (at) 𝚜𝚌𝚑𝚎𝚜𝚝𝚘𝚠𝚒𝚝𝚣 (dot) 𝚌𝚘𝚖)
Full hyperlinks for navigation omitted but are fully available in the originals
The corresponding HTML versions are at 𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈
Latest in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕 and older bulletins can be found at 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕-𝒂𝒓𝒄𝒉𝒊𝒗𝒆𝒔
Full IPFS index in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔 and as plain text in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔/𝒕𝒙𝒕
Gemini index for the day: gemini://gemini.techrights.org/2022/02/09/
╒═══════════════════ 𝐑𝐄𝐂𝐄𝐍𝐓 𝐁𝐔𝐋𝐋𝐄𝐓𝐈𝐍𝐒 ════════════════════════════════════╕
Previous bulletins in IPFS (past 21 days, in chronological order):
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╒═══════════════════ 𝐈𝐍𝐃𝐄𝐗 ═══════════════════════════════════════════════════╕
⦿ [Meme] Team UPC and Team Battistelli Above the Law, Ignore the Law, Break the Law | Techrights
⦿ The EPO’s Overseer/Overseen Collusion — Part XXXXVI: An Erosion of Fundamental Rights Protection? | Techrights
⦿ Response to Gemini Misconceptions and Mythology (It’s Not Ugly or Just for Geeks) | Techrights
⦿ Despite Occasional Shutdowns, Geminispace Has a Net Gain of About 100 Working Capsules Per Month (It Has Accelerated Further in 2022) | Techrights
⦿ Staff Holding Management at the EPO Accountable | Techrights
⦿ [Meme] Drunk Driving, Like Son of António Campinos | Techrights
⦿ IRC Proceedings: Tuesday, February 08, 2022 | Techrights
䷼ Bulletin articles (as HTML) to comment on (requires login):
http://techrights.org/2022/02/09/breaking-the-law-in-nl/#comments
http://techrights.org/2022/02/09/fundamental-rights-epo/#comments
http://techrights.org/2022/02/09/gemini-not-ugly/#comments
http://techrights.org/2022/02/09/geminispace-1705-working-capsules/#comments
http://techrights.org/2022/02/09/holding-management-accountable/#comments
http://techrights.org/2022/02/09/iloat-ruling-no-4430-and-iloat-ruling-no-4482/#comments
http://techrights.org/2022/02/09/irc-log-080222/#comments
䷞ Followed by Daily Links (assorted news picks curated and categorised):
http://techrights.org/2022/02/09/epic-wants-rootkits-in-linux/#comments
http://techrights.org/2022/02/09/gulag-stadia-failing/#comments
䷩ 𝚕𝚒𝚗𝚎 66
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(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/02/09/breaking-the-law-in-nl/#comments
Gemini version at gemini://gemini.techrights.org/2022/02/09/breaking-the-law-in-nl/
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Gemini_version_available_♊︎
✐ [Meme]_Team_UPC_and_Team_Battistelli_Above_the_Law,_Ignore_the_Law,_Break_the
Law⠀✐
Posted in Europe, Patents at 8:52 am by Dr. Roy Schestowitz
Much can be said about how Team UPC too flagrantly breaks_the_law with the
EPO's_complicity
🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Law? Sorry, not applicable to us.⦈
Summary: In the_Netherlands, EPO management is effectively above the law, so
Benoît_Battistelli and António_Campinos can ignore court rulings, gaslight an
International_Criminal_Court_(ICC)_judge_looking_to_rectify_things_at_the_EPO,
and bribe_Dutch_media to defame actual judges with integrity
🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇António Campinos fronting for Team UPC⦈
Tony fronting for ‘Team UPC’ only 3 days after he became EPO President.
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⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡆⠀⠀⠀⠀⢡⣴⣿⣼⣿⣿⠏⠀⠀⣸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠉⠩⢹⣿⡍⠈⡿⢿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠸⣿⣿⣿⠇⢀⡀⠀⢰⣾⣿⠉⠉⠉⠁⠀⠀⣰⣿⣿⣿⣿⣠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣏⠀⠐⢪⣆⠷⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣷⣾⣟⣿⣿⣿⣿⣾⣿⣿⣿⠏⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣷⣿⣿⣷⣾⣿⣿⣦⣤⣤⣴⣶⣤⣿⣿⡏⣿⣿⣿⣿⣿
⠀⠀⡀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣷⣶⣾⣿⣿⣿⡿⠋⠛⠉⠈⠛⠿⡇⠀⠈⢿⡉⣭⣝⣿⡿⣿⣿⠟⠁⠀⠀⠀⠀⠀⢰⣿⣯⣿⡿⠁⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠙⢿⣿⣿⣿
⠀⢈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣬⣿⣿⡏⣉⣹⣿⣟⣿⣟⠛⠃⠀⠀⠀⣀⣤⣴⣶⣄⠀⠈⠑⠿⠿⠿⣶⣿⣷⣦⣀⠀⠀⠀⠀⢠⣿⡿⣿⣿⠇⠀⠀⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣷⣶⣬⣿⣿
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡷⠀⠀⢀⣘⠛⠙⠋⠙⠋⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣄⠀⣰⣿⠟⠹⣿⡯⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⢻⣿⣿⣿⣿⡟⠀⠀⠉⠉⠁⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣛⣷⣶⣶⣷⣤⣦⣤⣶⣦⣶⡄⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠘⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣧⣰⣶⡖⠉⠛⠛⠛⠉⠙⢿⣿⣿⣿⠟⠈⢿⣿⣿⣿⣿⣿⡿⠀⠙⠟⠻⢿⣿⡧⠄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⢿⣷⡀⠀⠀⠀⠀⠀⠀⠉⠟⠋⠀⠀⠸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣄⣄⣀⣀⣀⣀⣼⠉⠀⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢸⣿⣷⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠋⠛⠋⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⣿⣿⠛⣿⡿⠟⠃⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀
⣿⠿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⣸⣿⣿⣇⠀⠀⠀⠀⢿⣶⡤⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡏⢠⡆⠁⠀⠀⠀⠀⢠⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢸⣻⠁⠀
[16A⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣀⡀⠀⠀⠐
⠀⠀⠉⠉⠉⠉⢉⣭⣭⣭⣭⣿⣿⣿⣿⠋⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣤⣤⣄⣼⣿⣿⣿⣿⣿⣾⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠀⢀⣠⣴⣶⣶
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣷⣴⣦⣄⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⠿⠿⠿⠻⣿⣿⣿⣿⠇⠀⠀⢰⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡃⠀⠾⠀⠰⠆⢀⠙⣿⣿⣿⠀⠀⢠⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣶⡁⠀⠀⠀⢠⣴⣿⣴⣿⣿⠟⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⡿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠇⠀⠀⠀⢾⣿⠋⠉⠉⠉⠀⠀⠀⠈⢿⣿⣿⣠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣇⠀⠐⠪⣏⠳⠀⠈⢻⣿⣿⣿⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⢀⣤⢸⣿⣿⣿⠀⠀⠀⠀⢸⣿⣦⣄⣄⣠⣀⣀⠀⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡿⣿⣷⣶⣾⣟⣶⣶⣶⣿⣿⣿⡏⢀⡴⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣿⣿⠟⠁⠀⠀⠀⠀⠀⢠⣿⣿⣼⣿⣿⠿⣀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠙⢿⣿⣿⣟
⠀⢈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣿⣿⡏⣉⣹⣿⢏⣿⣿⣿⣷⡏⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⣼⣿⠿⣿⣿⣿⠀⡃⠀⢀⣾⣿⣿⣿⣿⣿⣿⢿⠉⠛⢿⣿⣦⣄⡈⢿⣿
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢻⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⣠⣾⣿⠟⢻⣿⣿⠃⠀⠃⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣤⠈⠛⠛⢿⡿⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⢺⣿⡟⠀⠀⠀⠈⠛⣽⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣧⡀⠀⠘⠚⠁⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⠇⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⡇⠀⠘⠛⠛⠻⣿⠷⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣰⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⠿⠋⠘⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⢠⣾⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀
⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠹⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⠰⠚⠫⠁⠀⠀⠀⠀⠀⢀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸⣻⠁⠀
[16A⠐⠒⠒⣲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣆⣰⣶⣶⠶⠶⠒
⠀⠀⠀⢀⡴⠉⣉⣭⣭⣿⣽⣿⣿⣿⣿⠏⠉⢉⣉⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⠉⠁⠙⢛⣻⣵⣶⣶
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣄⡀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⢰⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠛⣟⠋⢉⠋⠹⣿⣿⣿⣿⠀⠀⢠⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠙⠀⡜⢃⣼⣈⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⡿⠿⣿⣿⣿⣿⡇⣠⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡇⠀⠀⣷⣿⣿⡿⣿⡿⠃⠀⠀⠈⢿⣿⣿⣨⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⠀⠘⢸⣆⠓⠀⠀⣿⣿⣿⣿⡿⢁⣸⣿⣿⣿⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣟⣿⠧⣠⣾⣿⣿⡃⠀⠀⠈⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠀⢀⣀⡀⠀⢀⣀⣸⣿⣿⣿⣿⣿⣿⠿⣿⣿⣾⣿⣯⣿⣶⣿⣿⣿⣿⣿⣿⡿⢓⣀⣬⣽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢰⣾⠂⠉⠻⣿⣷⣴⣿⣿⣿⣿⣿⣶⣶⣤⣶⣤⡀⠀⠀⠙⢿⣿⣿⣿
⠀⢀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⡉⣁⣹⣿⢉⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⣾⣿⠁⠀⠀⠙⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠈⢿⣿
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⣿⣿⠀⠀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠛⣿⣿⣦⡀⠀⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠘⠋⠀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠉⠙⢿⣷⡄⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢿⡿⢿⣿⣧⠀⢀⣾⣿⣿⣿⣿⣿⣿⠀⢻⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣫⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠙⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿⠿⠿⠛⠛⠛⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀
⣿⠿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠟⠛⠀⠀⠀⠀⠀⠀⢀⣤⣶⡇⠀⠀⠀⠀⠀⠀⠀⢸⣻⠁⠀
[16A⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠶
⠀⠀⠀⠙⣫⣿⣭⣭⣭⣿⣿⣿⣿⣿⣿⡏⢉⣩⣭⣍⡉⠉⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣶⣶⣶⣆⣀⣈⠉⠉⠉⠉⠀⢀⣠⣴⣶⣶
⠀⠀⠀⠾⠟⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢰⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠁⠀⢠⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡼⢿⣿⣿⡿⣫⡾⠏⠁⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⣀⠀⠀⠀⠀⠀⢹⣿⣿⠟⣿⣯⠁⢹⡄⠈⠿⣿⣿⣿⡄⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⢿⣿⡿⠿⠿⣿⣿⣿⡿⠁⠈⢿⣿⣾⠋⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣿⣦⣤⡏⠀⠀⣋⣡⣾⣆⣿⣿⣿⣷⠀⠈⢿⣿⣷⣨⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⡀⠈⢉⣇⠉⠀⢀⣼⣿⣿⣿⢀⣴⠟⠉⡵⢒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠸⣿⣿⣿⣄⠀⣸⣿⣿⣿⣿⣿⣿⣷⠀⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⢋⢡⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⣤⢄⡀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠙⢿⣿⣿⣿
⠀⢘⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣭⣥⣼⣿⣿⣿⣿⣿⣿⢇⣿⣿⣿⣿⣿⣿⣷⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢰⣿⣯⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠈⢿⣿
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡁⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠹⢿⣿⣦⡀⠀⠀⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⡿⠛⠁⡽⢿⣿⣿⡿⣿⣿⣿⣿⠀⠒⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠈⠉⠻⣷⣤⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⢿⣷⣦⣤⣤⣿⠁⠀⠀⠻⢿⠿⠿⠛⠋⠀⠙⠛⠛⢿⣿⣆⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠟⠀⠀⠀⠀⠀⠘⡂⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⣿⡿⠿⠟⠋⠛⠛⠿⠋⠀⠀⢀⣼⠇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀
⣿⠿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀
[16A⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠖
⠀⠀⢀⣭⡿⠉⣉⣭⣭⣭⣽⣿⣿⣿⣿⣏⡉⢉⣉⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⢀⣶⣦⡀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣯⣤⣬⣉⠉⠉⠉⠁⢀⣠⣴⣶⣶
⠀⠀⠈⠉⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢰⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠙⡟⠿⠏⢹⣿⠀⢰⡆⠀⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⢶⣾⣄⣘⣧⣶⣿⣿⣿⣿⠟⠁⠀⠈⢿⣿⣷⣠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣏⠁⠈⠋⢛⠛⠋⠉⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣿⣿⣿⣿⣿⣿⣿⣭⡉⠉⠀⠀⡼⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⠏⢹⣦⣤⣤⣿⣦⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⠀⠀⠀⠙⢿⣿⣿⣟
⠀⢐⣒⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡿⣿⡿⣿⣿⣋⡙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢰⣿⣯⣈⣻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣷⣄⠀⠀⠀⠈⢿⣿
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣷⣄⣸⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠸⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣟⠷⠀⠀⠈⠉⢿⣿⣧⡀⠀⠀⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠛⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠈⠛⣿⣦⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠹⣿⣿⣿⠟⠀⠉⠛⠛⢿⠿⡦⠀⠀⠀⠐⢿⣿⣿⠟⠙⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⡿⠟⠉⠈⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢘⡿⠸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⣿⣿⣿⣿⢿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⠉⠉⠘⠛⠻⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢉⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀
⣿⠿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⠃⠀⠀⠀⠀⠀⠀⢸⣻⠁⠀
[16A⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣆⠰⠶⠶
⠀⠀⠀⡹⠟⠍⢉⣭⣭⣭⣽⣿⣿⣿⣿⠏⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⠉⠉⠉⢉⣠⣴⣶⣶
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣶⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢰⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⣿⡅⠙⣿⣿⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢯⣭⣀⣿⣷⡞⢇⣶⡏⣿⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⣿⣿⣿⣿⣏⣿⣀⣁⣼⣿⣆⣀⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⣿⠇⠀⠀⠈⢿⣿⣿⣨⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⠿⢿⡀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⡧⢶⣤⣤⣄⠀⠀⠙⣿⣿⣿⣿
⠀⢠⣤⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣶⣼⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⢁⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡿⠛⠉⠉⠀⠀⣰⣾⣸⠁⠉⢿⣿⣷⡄⠀⠀⠘⢿⣿
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢄⣤⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢸⣿⠝⣿⣿⠏⠀⠀⠀⢀⣀⣼⣿⢃⢛⠆⠀⠀⠹⣿⣿⣆⠀⠀⠀⠸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢁⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠘⠃⠀⠀⡝⠀⠀⠀⠀⠘⢿⣿⠇⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⡄⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⡇⠀⢩⣿⣿⣿⣿⣿⣿⡟⠛⢿⣿⣿⣿⣷⡄⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠈⠙⢫⠉⠀⠀⢸⣿⣿⣿⣿⣿⠛⠃⠀⢸⣿⣿⣿⣿⣿⣷⣤⡀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣴⣀⣀⣾⣿⠿⠿⠻⠉⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⣤⣶⣮⣷⣦⣄⣤⣶⣭⣿⢟⠹⢻⡗⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀
⣿⠿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⠃⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠋⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⢸⣻⠁⠀
[16A⠖⠒⠒⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠀⢀⡶⠖
⠀⠀⠀⠉⠉⠉⢉⣭⡭⣿⣿⣿⣿⣿⣿⣿⣿⠉⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣀⣀⣡⣿⣿⣿⣿⣿⣶⣾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⢋⣠⣾⣶⣶
⠀⠀⠘⠀⠀⢀⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢰⣿⣿⣿⣿⣿
⠀⠀⠁⠀⢠⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠟⣿⡟⠻⢿⣿⣿⣿⣿⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿
⠀⠀⢀⡴⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣴⡟⠀⠘⡊⢠⣿⣧⣿⣿⡿⠁⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠞⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣿⣿⣿⣿⡿⠛⢻⣿⣟⡛⠛⡿⢿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⢿⣿⣇⠀⠀⣭⣽⡟⠻⠛⠿⠃⠀⠀⠈⢿⣿⣿⣩⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣷⣤⣼⣿⣿⣧⣶⣷⣾⣿⣿⣿⡏⠀⠀⠀⠀⠀⣀⣤⣴⣿⣿⣿⣶⡆⠀⠀⣽⣿⠁⣀⠀⠈⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⠀⠀⢹⣿⣿⣿⡇⠀⠀⠈⠿⣿⡟⠻⣿⡿⠿⠿⣿⣿⠛⠙⣿⠏⠁⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣁⣀⠀⠀⠠⠟⢀⣿⣟⣿⣷⣶⣦⡄⠀⠙⣿⣿⣿⣿
⠀⢀⣀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⡿⣿⣿⣿⠀⠀⢀⣠⣴⣾⣷⣦⠹⡷⣄⡤⣽⢇⣠⣴⣤⣄⡀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⡿⣸⡇⠈⢹⣿⣿⣆⠀⠀⠘⢿⣿
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠈⢀⣼⣿⣿⣿⣿⣿⣿⣄⠈⠀⠀⠀⣸⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢿⠁⠀⠀⠀⣿⣿⣇⠀⠀⢸⡘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠸⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠃⣿⠀⠀⠀⠀⠀⠹⢻⣿⡀⠀⠀⢠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢵⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⡿⠿⠇⠘⠋⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⢻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⣿⣿⣿⣿⣿⣿⡟⠉⢿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢸⣿⣿⣿⣿⡟⠀⠀⠀⠀⠈⠀⣲⣶⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠺⠿⠿⠿⠛⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀
⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⢿⣿⠇⠋⢻⣿⣿⡿⠛⠛⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⠁⠀
[16A⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠐⣶⣶⣶⠆
⠀⠀⠀⡍⠉⠉⣽⣯⣭⣽⣿⣿⣿⣿⣿⠏⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⣨⣶⣶⣤⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣸⣿⣿⣷
⠀⠀⢠⠁⢀⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⣿⣿⣿⣿⣿
⠀⠀⡌⣠⡾⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠻⢻⠟⠻⠿⠟⡿⠿⣿⣿⣿⡿⠟⢫⣿⣿⣿⣿⣿⣿
⠀⠀⠙⠟⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⢻⣏⡿⠀⠀⠀⠐⠀⢰⣷⣠⣿⣿⡟⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⣹⣿⡇⠀⠀⠀⠀⣭⣾⡟⠛⠛⠿⠁⠀⠀⠈⢿⣿⣷⣠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⠀⢃⣿⣿⠀⢈⣟⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⢀⣠⣸⣿⣛⡄⠀⠀⠀⣿⣿⠁⡀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⠃⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡇⠀⠀⠀⠠⠟⠀⣿⡟⡿⣷⣶⣤⡀⠀⠙⣿⣿⣿⣿
⠀⢀⣀⠀⠀⠀⢀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿⣿⣿⠋⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣽⣿⣇⢀⣀⣹⡏⣨⣿⠟⠉⠀⠀⠀⠀⠀⢠⣿⣇⣻⣿⣿⣿⣿⣷⣄⡀⣠⣴⣾⣿⣷⣿⣙⢻⣿⣿⣆⠀⠀⠘⢿⣿
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠨⣿⡿⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⠉⣾⣿⣿⣷⣦⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠸⠃⣿⣿⡀⠀⠀⠀⠸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢰⣿⣾⠀⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣾⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠐⢻⣿⡇⠀⠀⢠⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣸⣿⡏⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠈⠻⢿⣿⣿⠿⣿⣿⡿⠛⠿⢿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠹⡇⠀⠀⠈⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢸⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠁⠇⠀⠀⠨⣿⣿⣿⣿⡿⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠻⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⣤⣤⣤⣾⣾⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀
⣿⠿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣿⣿⣿⣏⣀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⠁⠀
[16A⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠒
⠀⠀⠀⡍⠉⣽⢫⣭⣭⣿⣿⣿⣿⣿⣭⣭⣈⠁⣠⣼⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠁⠀⣀⣀⣀⣀⣠⣶⣶⣦⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⠉⠉⠀⢀⣠⣴⣶⣶
⠀⠀⢴⣠⡾⠃⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⣾⣿⣿⣿⣿
⠀⠀⠀⠙⠃⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⣿⣿⠀⠀⢠⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⢹⣿⣿⣿⣿⠟⢠⣄⢈⣿⣿⡿⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⠿⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⠿⠛⠁⠀⠢⣻⣿⡾⣿⣿⠇⠀⠀⠈⢿⣿⣷⣠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣭⣾⣿⣁⣀⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣠⣄⣀⡟⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⠛⠁⠀⠀⠀⠀⢀⣴⠦⣿⣿⣷⡀⠀⠀⠀⢻⣿⣀⣶⣶⣤⣤⣀⡀⠀⠀⠙⢿⣿⣿⣟
⠀⢀⣀⣀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣖⢶⣾⣿⣴⣿⣋⡀⠀⠀⠀⠀⠀⠀⣼⣿⣤⠙⣿⣿⡇⠀⠀⠀⠀⣸⣿⣿⣿⣿⡿⢿⣿⣦⠀⠀⠀⠈⢿⣿
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠉⠻⣿⣿⣿⠉⠉⠉⠀⢠⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⣿⡟⠛⠏⣿⣟⣿⣷⣤⣤⣴⣿⣿⣿⣿⠿⠀⠟⣿⣿⣧⠀⠀⠀⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⢀⣼⣿⣿⣿⣷⡀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠻⠃⠀⠀⡿⢻⢿⣿⣿⣿⣿⣿⣿⡿⠹⠀⠀⠀⠈⣿⣿⣦⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⡇⢸⠀⣿⣿⣿⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠻⣿⣦⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠣⠘⠀⣼⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠉⢿⣿⣿⣷⠤⠀⠀⠈⠹⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠋⠀⠘⠻⠇⠀⠀⠀⠀⠀⠀⢈⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢿⣿⣿⣿⣿⡿⢿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀
⣿⠿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠙⣿⡟⠛⠀⠀⠀⢠⡿⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣹⠁⠀
[16A⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠖
⠀⠀⠀⡍⢉⣽⢋⣭⣭⣿⣿⣿⣿⣿⣭⣍⣈⡁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣧⣤⣌⡉⠉⠉⠉⠀⢁⣠⣴⣶⣶
⠀⠀⢺⣿⡿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢰⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣤⣾⣿⣿⣿⣿⣉⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢹⣿⣆⣼⠋⠉⢻⣉⣿⣿⣿⣿⣿⡏⠀⠀⠈⢿⣿⣷⣨⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⠀⠀⠙⠉⠙⠛⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣧⠀⠀⢸⣿⣿⣿⣿⠿⡟⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣦⣤⣾⣷⣦⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⣿⣿⣿⣿⣿⣿⠟⠛⠉⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⡇⠀⣾⣿⣿⣿⣿⣶⡇⠀⠀⠀⠀⠀⠙⢿⣿⣿⣟
⠀⣀⣀⣀⣠⣤⣤⣶⣿⣿⣿⣿⣿⣿⣾⣿⠛⠛⢿⣿⡿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢻⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⣸⣿⠿⣿⣿⣿⣿⣧⠀⠈⠛⠿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠈⢿⣿
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⣿⡗⠀⠘⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⠋⠉⣿⣿⣿⡄⠀⠀⠀⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣺⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢻⠏⠀⢰⣿⣿⣿⣿⣿⣶⣴⣶⣤⣿⠟⠀⠀⠀⠻⣿⣿⣄⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠉⢿⣿⣦⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⠄⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠟⠀⠙⠉⠙⢿⡂⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡍⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠘⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⢿⡿⠿⠷⠒⠀⠀⠀⠶⣴⣠⣤⣾⣷⣶⣾⣿⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀
⣿⠿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢸⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⠁⠀
[16A⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣄⣤⣴⣶
⠀⠀⠀⠉⡉⠉⢉⣭⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠍⠉⠁⠈⢻⣿⣿⣿⣿
⠀⠀⠀⡀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢰⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣴⠋⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢠⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢻⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⠀⠀⠀⠀⠀⠈⣿⣿⣿⢿⢹⡿⣻⣻⣾⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠈⠻⣿⣿⣿⣀⣀⣹⣿⣉⠉⣹⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠈⢿⡀⣾⣾⣷⣿⣶⣿⣿⣿⣿⣿⡟⠀⠀⠈⢿⣿⣷⣠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠘⠃⠉⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⡿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡏⢹⣧⡀⠀⢀⣀⠀⠀⠀⢹⣿⣿⣿⣇⣠⣶⣶⣶⣿⣶⠹⢿⣿⣿⣿⣿⣵⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡆⢻⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⡟⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿
⠀⢀⣀⠀⠀⣀⣀⣤⣾⣿⣿⣿⣿⣿⣦⣼⣿⣿⣿⣿⣿⣷⣦⡴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢸⣿⡿⠁⢸⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⡀⠘⣿⣶⣄⠀⠀⠀⠘⢿⣿
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣍⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⢿⣿⠇⢠⣾⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣇⡀⢸⢿⣿⣆⠀⠀⠀⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣐⡛⠊⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡵⠆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠸⠏⢸⣿⣿⣿⠛⠛⠿⣿⣿⣿⣿⢣⢿⣿⠇⠀⠸⢿⣿⣇⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⣿⠿⠟⠀⠈⢿⠿⢿⣿⡁⠀⠀⠀⢸⣿⣿⡏⠀⠀⠀⠈⣿⡿⢋⡟⠀⠉⠀⠀⠀⠈⠹⣿⣷⡄⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⢹⠟⠀⠀⠀⠀⠀⢙⠙⠀⣿⣄⡀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢀⣴⣶⣿⣿⣿⣿⣿⣴⣆⠀⠀⠀⠀⠀⠀⢀⡐⣶⡿⠿⡿⠝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠽⢿⣿⣿⣿⣿⣿⡿⠟⠁⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠓⠀⠀⠀⠀⠀⠀⠾⠀⡉⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀
⣿⠿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠂⠀⠈⠀⠀⠻⠿⠿⠋⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⠁⠀
[16A⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣆⠀⠀⠀⠀⢰⣶⣶⡶⠶⠖
⠀⠀⠈⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢛⣻⣷⣶⣶
⠀⠀⠀⠀⠀⠁⠀⣨⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣠⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢰⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢿⣻⡿⢙⠉⠙⣿⣿⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡿⠿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠸⣿⠛⣛⢳⡟⢀⡸⢂⣤⣽⣿⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⣧⣹⣧⣀⣠⣿⣧⣀⣨⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⣹⣭⣽⣿⣿⣿⣷⣿⣿⣿⣿⠀⠉⢀⡀⠈⢿⣿⣷⣨⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠈⠉⠀⠘⢿⣿⣿⣿⣿⣿⣿⡿⡿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡄⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡏⠙⠻⣿⣍⡉⠛⠛⠻⠿⠿⠿⢿⣿⣿⣿⣠⣴⣶⣶⣶⡄⠹⣿⣿⣿⢿⢿⣷⣶⣤⣄⠀⠀⠀⠀⠀⠀⢠⣾⡿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠙⣿⣿⣿⣿
⠀⢀⣀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣁⣀⣀⣿⣿⣧⣀⣀⣠⡄⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⢀⣰⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣼⣿⡷⠀⢸⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠘⢿⣿
⣴⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⡗⢀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⣿⣿⠃⠀⠀⡿⠋⠁⠳⣦⣀⡀⠹⣿⣿⣿⣿⣿⢿⣿⣷⡀⠀⠀⠀⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⢷⠄⢄⢀⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⡿⠋⠀⠀⠀⠇⠀⠀⠀⠹⣿⣿⡶⣾⣿⣿⠟⠁⠈⢻⣿⣷⡄⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣀⣼⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠉⠉⠛⠛⠛⠻⢿⣿⣿⡿⠋⠻⠿⢿⣿⣧⡄⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⢸⡿⢡⡿⠛⠁⠀⠀⠀⠀⠘⢿⣿⡆⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠀⠀⠀⠀⢿⡿⠛⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠊⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣿⣿⣿⣿⠿⠏⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⣀⣀⣸⣷⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠳⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⢿⠿⠛⡿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀
⣿⠿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⣻⠁⠀
[16A⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡀⠀⠀⢲⣶⣤⡶⠖
⠀⠀⠀⠉⠉⠉⢉⣭⣭⣿⣿⣿⣿⣿⣿⠏⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣴⣶⣄⣿⣿⣷⣶
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠈⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣰⣶⣶⣾⣿⣿⣿⣿⣿⣿⣦⣀⡀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠿⢫⡟⠉⢩⠠⢀⣰⣾⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣦⡞⠉⢠⠈⠀⣿⡄⣼⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠟⠋⢉⣿⡉⠉⢹⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢩⢭⡍⠐⠀⠀⢐⠀⣿⠿⠻⠿⠃⠀⠀⠈⢿⣿⣷⣨⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⢿⣿⡿⠿⣷⣿⣷⣶⣾⣿⣿⣿⣿⠿⠛⠃⠀⠀⠀⠀⠀⠀⢀⡀⢼⣗⠂⠈⠁⠀⠀⠀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠿⣿⣿⡉⠛⠛⠻⠿⠿⠿⠿⣿⣿⣿⠁⠀⠀⣈⣀⡀⠈⠘⢛⣿⡉⠉⢩⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠻⡦⠀⠀⠀⠀⢘⣿⣇⣿⣷⣶⣶⣤⣄⡀⠀⠙⢿⣿⣿⣟
⠀⢀⣀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⠀⠀⠈⣿⣿⣄⠀⢀⣠⠀⠀⠀⣼⣿⣯⣴⣾⣿⣿⣿⣿⣷⡀⠈⠛⠻⠋⢋⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⣾⣿⡂⠀⢨⡏⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡟⣟⣿⣷⡄⠀⠀⠘⢿⣿
⣴⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣝⠿⠂⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣆⠀⠀⢀⣿⡿⠀⠀⢸⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⡾⢻⣿⣿⡄⠀⠀⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡃⠀⠀⢠⣾⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢸⡿⠃⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡟⠉⠀⠈⢻⢿⣷⡄⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣅⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⣿⣿⣿⣿⣿⡿⠛⢿⣿⣿⣿⣷⡄⠀⠀⠀⢀⣾⣶⣿⣿⡿⠿⠟⣻⣿⣿⠟⠀⠀⠀⠀⠈⠘⣿⣿⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿⣿⣿⡟⠀⠀⠀⣿⣿⣿⣿⠟⠀⠀⠀⠉⠀⠻⣿⣿⣀⡀⠀⠘⠟⠛⠋⢹⣀⣀⣠⣿⡿⠿⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢿⣿⣿⣿⢿⠟⠋⠀⠈⠉⠉⠀⠀⠀⠀⠹⠧⠀⠀⣰⣿⣿⡟⠁⠀⠀⠀⢀⣹⢿⣿⣿⣿⣿⣗⠀⠀⠀⢀⣀⣾⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠘⠛⠉⠉⡀⠀⠀⠀⠀⠚⠛⠋⠁⠉⠙⠛⠃⣠⣶⣶⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀
⣿⠿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣍⠉⠁⠉⠀⢉⣻⠛⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⠀⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⠁⠀
[16A⠀⠀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡖⠐⠶⣦⡄⠒
⣤⣾⣿⡟⠉⠉⢉⣭⣭⣿⣿⣿⣿⣿⣿⠏⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣠⣤⣤⣤⣶⣿⣿⣷⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⣉⠄⠀⢀⣠⣼⣷⣶
⢿⡿⠛⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣶⣶⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⣿⢟⡛⠋⣛⠛⠻⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣼⣯⣵⠏⠈⠁⢀⠐⢀⣤⠀⣽⣿⡟⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⣾⣿⣿⣿⣿⠟⢻⣿⡿⡿⠿⣿⢿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⡄⠀⠀⠀⠔⢘⣿⢾⠻⡿⠃⠀⠀⠈⢿⣿⣷⣠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣷⣄⣤⣿⣿⣅⣤⣧⣼⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢠⣾⣿⣧⣾⠀⠀⠀⢽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠟⣷⡄⠀⠀⠉⠉⠀⠀⠀⣿⣿⣿⠃⠀⠀⠀⠘⠻⠿⠏⠛⢿⣿⠿⠿⣿⣿⠿⠙⠟⠁⠀⠀⠀⠀⠀⠀⢠⣾⡟⢿⣿⣯⣏⡀⠀⠀⢻⣿⠇⢶⣦⣤⣀⣀⠀⠀⠀⠙⢿⣿⣿⣿
⠀⢀⣀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣀⣸⣿⣶⣶⢾⢷⣦⣤⠀⠛⠿⢿⠀⠀⠀⣠⣤⣶⣶⣶⡄⠘⣷⡠⣤⢼⢇⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⣼⣿⣧⣼⣿⣿⣿⣷⣶⣦⣬⣅⣤⣿⣿⣿⣿⡿⣿⣦⠀⠀⠀⠈⢿⣿
⣴⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⢹⣷⣶⣶⣤⡀⠀⣠⣿⣿⣿⣿⣿⣿⣷⡀⠀⠢⠔⠀⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢹⣿⣿⣧⠀⠀⠀⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡁⠐⠀⢸⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⢯⡟⠁⠊⢸⢿⣿⣆⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠉⠁⠀⠀⠀⠀⣰⣿⡟⠁⠀⠀⠀⠚⢿⣿⣧⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠿⠿⠿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⡟⠁⠈⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢸⡄⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠀⠈⠛⣿⡇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣽⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⡿⣟⠀⠀⠀⣿⣿⣿⠿⠋⠀⠀⠛⠛⠉⠙⢿⣿⣿⡿⠃⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⠛⡛⣭⣤⠠⠶⠀⠀⠀⠀⠀⠄⠀⠀⠈⠙⠀⠀⠀⠭⠝⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀
⣿⠿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠸⠇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⠁⠀
[16A⠀⠀⠲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⡶⠶⠖
⠀⠀⠀⠈⠉⠉⠉⣩⣭⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣍⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣨⣶⣾⣿⣶⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣬⡉⠉⠉⠁⠀⢀⣠⣴⣶⣶
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢰⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⠀⠀⢠⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡿⠉⢺⠄⡈⠛⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢿⣿⣿⣿⠿⠛⢿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠈⠛⠁⣿⠏⠀⠘⣀⢰⣿⣤⣿⣿⠏⠀⠀⠈⢿⣿⣷⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠛⠛⠛⠿⠟⠛⠛⠛⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⢿⣿⣿⣄⣠⣼⣿⣌⣀⣽⣭⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠰⣿⣷⣾⡏⠀⠀⠈⣽⣼⡟⠙⠀⠉⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣆⣀⣀⣸⣄⣀⣀⣸⡿⠿⠿⣿⠀⠀⠀⠀⠀⠀⠀⠙⠋⢹⣿⣿⣿⣿⣿⣿⡿⢹⣿⣿⣿⠟⠀⠀⠀⠀⠀⣠⡄⠘⢿⣿⣿⠀⠀⠀⣼⣿⡇⣀⡀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿
⠀⢀⣀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣥⣿⣿⢿⠿⠿⣿⣷⣤⣤⣀⡀⠀⠀⠀⠀⣀⣤⣴⣶⣶⡜⠷⠲⣷⣾⡿⠋⣀⣈⣛⠉⠁⠀⠀⠀⠀⠀⠀⢿⠿⢧⡬⣿⣣⠄⠀⠀⢸⡿⢃⣿⣿⣿⣶⣶⣤⡀⠀⠀⠀⠈⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢤⣦⣜⢿⣿⣿⣿⣿⣿⣦⡀⣠⣾⣿⣿⣿⣿⣿⣧⡀⠀⠉⠉⣠⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⣽⣅⣀⣹⣿⣿⡮⣦⣀⡈⣿⣿⣿⣿⣿⡏⣿⣿⣷⡄⠀⠀⠀⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣈⣘⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣴⣿⣿⡿⠛⣿⣿⣿⣿⣷⣄⣀⣄⣴⣿⣿⣿⣿⣿⣿⠁⠀⠻⠻⢿⣿⣿⢻⠟⠀⠀⢿⣿⣿⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⡻⡄⠸⣿⣿⣿⣍⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⢿⣿⠋⠀⠀⠀⠀⠙⢿⣿⣄⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠙⠿⣿⣿⣿⣿⡇⠀⠀⠀⠉⠿⣿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠋⠀⠀⠀⠀⠀⠈⠫⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠙⠿⠿⠃⠀⠀⣴⣤⣤⡃⠀⠀⠀⠉⠛⠋⠉⠻⠿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⢀⡀⠀⠈⠀⠁⠀⠀⠀⠈⠓⠁⠀⠀⠈⠛⠛⠫⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀
⣿⠿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀
[16A⠶⢶⣶⣶⠖⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⡶⠶⠖
⠀⠀⠀⠁⠀⠈⢩⣭⣽⣿⣿⣿⣿⣿⣿⣯⣭⣿⣭⣭⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⣤⣤⣴⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⣿⣿⣿⣶⣤⣀⣈⠉⠉⠉⠉⠀⢀⣠⣴⣶⣶
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢰⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢠⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡟⣿⠍⢹⡄⠈⠻⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢿⣿⣿⡿⡟⠉⠹⣿⣿⡻⢿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡁⠀⠐⢊⠀⣿⣆⣿⣿⡟⠀⠀⠈⢿⣿⣿⣨⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣏⠉⠉⠛⠛⠛⠉⠉⢙⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠻⣿⢿⣿⣶⣶⣿⣿⣦⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣄⠻⣿⣿⡇⠀⠀⢩⣴⣿⠛⠋⠛⠁⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣆⣀⣤⣾⣦⣤⣤⡼⠟⠛⠛⠷⠀⠀⠀⠀⠀⠀⠀⢉⢨⣷⣦⠉⣿⣿⣿⡿⢻⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⢀⡀⣿⣿⣻⡿⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿
⣂⣤⣴⣶⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣶⣿⡿⠶⠞⢿⣿⣷⣦⣤⣄⡀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣾⣿⠻⣷⣾⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⣿⠇⠈⢻⣿⣷⡀⠀⠀⠸⣿⡿⢸⣿⣶⣤⣤⣄⡀⠀⠀⠀⠈⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣧⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢠⣷⠀⢀⣾⣿⣿⣿⣶⣿⣿⣿⣴⣿⣿⡟⡟⢻⣿⣷⡄⠀⠀⠀⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠋⠀⠀⢹⣿⣿⣷⣿⣿⣿⣿⣿⣿⡟⡗⠁⠉⢻⣿⣿⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠟⢻⣿⣿⣿⣿⣿⣤⠊⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠸⣿⣿⡿⠛⠉⢿⣿⣿⣿⠃⠀⠀⠀⠀⠛⢿⣿⣦⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠉⠀⠀⠀⠙⢛⠿⣿⣿⡏⠀⠀⠀⣿⣿⣿⣿⣿⠃⠀⠘⠛⠛⣿⣿⡤⠀⠀⠀⠀⠈⢻⡏⢄⡀⠀⠀⠻⡟⠁⠀⠀⠀⠀⠀⠀⠈⠙⢿⡷⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⣴⣶⠶⠾⠀⠀⠐⠲⠯⡄⠀⠀⢼⣿⣿⢿⢯⠃⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⢼⢭⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡧⠀⣽⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀
⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠉⠉⢩⣍⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡯⠁⠍⠙⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⠁⠀
[16A⠆⠰⣶⣶⠖⠂⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣄⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⣿⣭⣭⣿⣿⣿⣿⣿⣏⣩⣭⣭⣭⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣶⣶⣬⣍⠉⠉⠁⠸⢟⣧⣾⣶⣶
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢰⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡿⠿⠿⠏⠻⣿⣿⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣟⠀⠽⠄⡨⠇⢠⡙⢻⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢻⣿⣿⣿⣯⣿⠉⠉⣹⣿⠃⠉⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⢀⣴⣾⣯⣹⠀⠀⠀⢡⠄⣿⣧⣿⣿⡏⠀⠀⠈⢿⣿⣿⣨⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠻⠿⠿⠿⠿⢿⣿⣿⣿⠀⠀⠀⠀⠻⣿⣿⣿⡟⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠘⣿⣟⠣⡛⠀⠀⠀⢰⣷⣿⣿⣿⣿⡇⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠋⣿⣄⡀⣀⣠⣆⠀⠀⠀⠹⠿⡇⠀⠀⠀⢀⣴⣿⣿⣿⠃⠸⣿⣿⣿⡿⢻⣾⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⣻⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠙⢿⣿⣿⣟
⠀⢀⣀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⠀⠀⠈⠉⠉⣹⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⡿⠇⢸⣿⣿⣾⣤⠀⠀⠸⠋⢹⣿⣿⣿⣿⣿⣶⣆⠀⠀⠀⠘⢿⣿
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠇⢀⣤⠄⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡷⠀⣾⣿⣿⣿⡟⠧⣴⡇⠀⢸⣿⣿⣿⣿⣻⣿⣿⣷⡀⠀⠀⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡏⠀⢸⣡⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠈⢿⣿⣿⣿⣧⣶⣿⣷⠀⠀⣿⣿⣿⡿⠀⠀⢿⣿⣷⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣠⣶⣿⡇⠀⢸⣿⣿⣿⣿⣿⡟⠙⠿⠿⣿⣿⣤⡀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⡧⣠⣾⣿⡿⠏⠀⠀⠀⠈⠙⢿⣿⣆⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⡀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣸⣿⣿⣿⣿⡟⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢸⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠙⠛⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀
⣿⠿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡟⢃⡸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣹⠁⠀
[16A⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣆⠀⠀⠰⠦⣴⣶⣶⣶⣶⣶⠖
⠀⠘⠀⠀⠉⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠙⠻⢿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣤⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢰⣾⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⡀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡟⢭⠉⢉⡇⠀⢿⣿⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠁⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⠀⠀⠈⠁⡄⠉⣰⡄⢸⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣏⣿⠁⠁⣸⣿⡀⠀⣹⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⣶⣿⣗⢶⠁⠀⠀⠀⠐⣂⣽⡿⠿⢿⣿⣶⣆⠈⢿⣿⣷⣠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠙⠟⠃⠻⢿⣿⣿⣿⣿⣿⡿⡿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣌⡋⠀⠀⠀⠀⠀⣿⣿⠀⠀⢰⣿⣿⣿⣀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⡟⠿⣿⣿⣏⡛⠛⠛⠿⠿⠿⠿⢿⣿⡗⠀⣀⣤⣴⣶⣦⠈⠻⣿⣿⣿⣿⢿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⢶⣮⣿⣧⡀⠀⠀⠀⠐⣿⣿⢰⣶⣾⣿⣿⣿⣿⣧⠙⣿⣿⣿⣟
⠀⢀⣀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣧⣴⣿⣿⣿⣷⣄⠀⣀⣄⠀⠀⣸⣿⣴⣾⣿⣿⣿⣿⣿⣧⡀⠀⠉⠉⣱⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⣎⢸⣿⣿⣿⣿⣦⡀⠀⠀⢉⣠⣼⣿⣿⣿⣿⣿⣿⣿⣧⠀⠘⢿⣿
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠁⣿⣿⣿⣿⡏⡇⠈⢷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡷⠄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠐⣿⣿⣿⣿⡇⢿⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠸⣿⣿⣿⣿⣿⠁⠈⠛⠻⣿⣿⣦⣀⠀⠀⡺⡿⡟⢘⡃⢸⣆⠐⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠿⠿⢿⣿⣿⣿⣿⣿⡿⠉⠙⠻⠿⠿⠏⠀⢸⣿⣿⣿⣿⠁⠀⠀⠀⠀⠙⢿⣿⠛⠀⠀⠠⠀⠀⠀⠀⠈⣿⠂⠀⠀⠉⠙⠛⠻⠿⠟⠉⠈⠉⠀⠉⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⢴⣶⣶⣶⣶⣶⣶⣶⣾⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢳⠚⠛⠛⠉⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀
⣿⠿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣤⣤⣤⣤⣤⣦⣤⣦⣽⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⠁⠀
[16A⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⣶⣶⣦⣤⣤⣤⡒
⠀⠀⠀⠉⠉⠉⢉⣭⣭⣿⣿⣿⣿⣿⣿⠏⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⠉⠉⠈⠹⢿⣿⣿⣿⣿⣷
⠀⠀⢀⣤⣤⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣶⡆⠀⠀⢰⣿⣿⣿⣿⣿
⢠⣾⣿⣿⣿⡆⣽⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣀⣀⣴⣶⣷⣶⣶⣄⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⠛⢭⡉⠉⠄⠀⠻⣿⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠓⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠨⣽⣿⡉⠁⠀⠈⠁⠄⠉⢰⡦⣸⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿
⣿⡿⠛⠁⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⢙⣿⡟⠋⢹⣏⢹⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢠⣶⣷⣬⡇⠀⠀⠀⠀⢐⣆⣾⠿⠿⠿⠃⠀⠀⠈⢿⣿⣷⣠⣿⣿
⠁⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⠟⠳⣶⣿⣿⣿⣿⣿⢿⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣏⣨⡁⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⣶⣶⡄⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⣀⣀⡀⢹⡿⣿⣿⣿⡟⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡀⡀⠀⠀⠀⠈⢿⡷⢸⣶⡆⠘⢻⣿⣦⣀⣙⣿⣿⣿⣟
⠀⢀⣀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⠉⠉⠙⢻⣭⣭⣍⡉⠉⠉⠛⠋⠉⢻⣋⣤⣶⣿⣿⣿⣿⡄⠈⠛⠛⠉⣸⣿⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣿⣄⠀⠀⠀⢀⣤⣾⣿⡅⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿
⣴⣿⣿⣿⣿⣿⣿⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣼⡆⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⣿⣿⣿⣿⡯⡇⠀⢲⣦⣼⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣳⡝⠛⠀⣠⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠐⢿⣿⣿⢹⡇⢱⠀⠈⢻⣿⣿⣭⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣉⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⡟⠙⠿⣿⣿⣿⣇⡀⠀⠀⠙⣿⡏⢸⡇⠸⡆⠀⠀⠙⠛⢿⠇⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⠃⠀⢸⣿⣿⣿⣿⠟⠀⠀⠀⠀⠈⠛⢿⠿⠀⠀⠀⠛⠀⢸⠃⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⡿⠿⢿⣿⠟⠁⠀⠀⠀⠉⢁⣀⠀⡸⠿⡿⠻⠋⠀⠀⠀⠀⠀⠀⠀⢨⣾⣶⣀⠀⠀⠀⠈⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠿⠟⠋⢛⠛⠉⠉
⣿⠿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠐⠐⠂⠀⠀⣄⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⢸⣹⠁⠀
[16A⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠶⠖
⠀⠀⠀⠉⠉⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⣉⣠⣾⣿⣿⣿⣿⣿⣯⣤⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠉⠉⠉⠈⢙⣦⣶⣶⣶
⠀⠀⠀⠀⠄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣤⣤⣴⣿⣿⣿⣿⣿
⠀⠀⠀⣼⣦⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣠⣴⣿⣿⣿⣿⣿⣿⣦⣤⣀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠿⠛⠟⠋⠙⣿⣿⣿⣿⠘⠿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⡰⠿⠿⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣤⣤⣾⣹⠿⠋⠀⠹⠆⠈⠇⢠⡈⢹⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠿⠏⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⡟⠛⢻⣿⠛⡛⢻⡿⢿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⢡⡄⣾⣧⣾⣿⠏⠀⠀⠈⢿⣿⣷⣠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠘⢿⣿⣧⣤⣼⣿⣦⣴⣾⣧⣶⢻⣿⣿⡿⠟⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠐⣷⡿⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠙⠃⠸⡿⠻⣿⣿⣿⠋⠋⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣗⡦⠀⠀⠀⠀⢰⣿⣇⢠⣄⡀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣟
⠀⢀⣀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠉⣉⣹⣿⣿⣤⡀⠀⢀⣄⠀⠀⠻⠇⠀⢀⣀⣤⣴⣶⡄⠀⢸⡿⠟⠉⢠⣴⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣧⢀⠀⠀⠀⠙⠁⣸⣿⣿⢿⣿⣶⣄⠀⠀⠀⠈⢿⣿
⣴⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⣠⣀⠀⠀⣴⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡝⡇⠐⣄⡀⣼⣿⣿⣿⣶⠦⠘⠿⣷⣶⠀⠀⠀⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡈⠉⠠⠀⢀⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⢿⣿⣿⣿⡇⣷⠀⠻⣿⣿⣿⣧⢂⣯⣶⣶⡶⣾⣿⣇⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠴⠆⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣆⠀⠀⠀⠘⣿⠇⢸⡇⢹⡀⠀⠙⠿⣿⢿⣿⡿⠋⠁⠀⠘⠻⣿⣷⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡧⠀⠀⢿⣿⣿⣿⣿⣿⠃⠀⠈⠻⠟⢿⣿⣷⡄⠀⠀⢹⠀⢸⡇⠸⣧⠀⠀⠀⠋⠀⠈⠁⠀⠀⠀⠀⠀⠙⢿⣿⡄⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠁⠈⠉⠉⠻⠃⠀⠀⢼⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⣠⣾⣿⣷⡄⠀⠃⠀⠸⠃⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠈⠉⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠋⠛⢿⣶⡦⠀⠀⠀⠀⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀
⡿⢿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⣹⠁⠀
[16A⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠖
⣿⣿⡟⠉⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⢠⣼⣿⣿⣿⣷⣬⣁⡀⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⣶⣶⣿⣷⣦⣤⣤⠀⠉⠉⠉⠉⠉⠈⢁⣠⣴⣶⣶
⠉⠉⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢰⣾⣿⣿⣿⣿
⠀⠀⠀⢀⠃⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠂⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡛⢋⡏⠈⢿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠸⣿⣿⣿⣿⡿⠿⢿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⢶⣶⣤⣿⡋⠛⠀⠈⠁⠆⠉⣰⡆⣽⣿⣿⠃⠀⠈⢿⣿⣷⣠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠋⠛⠿⠻⠛⠟⠛⠻⣿⣿⣿⣿⠀⠀⠀⠹⢿⣿⣿⣧⣀⣸⣿⣯⣀⣼⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⡇⠀⠀⠀⠀⢘⣇⣿⠿⠛⠛⠃⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⠻⣧⣀⣀⣤⣴⣄⣀⣰⣿⣿⣿⡟⠀⠀⠀⠀⠈⠻⠏⠻⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣀⠀⠀⠀⠀⢈⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣟
⠀⢀⣀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣏⣁⠉⠉⠉⠀⠀⠀⢀⣀⣤⣤⡄⠹⠿⣿⡿⠿⠋⣠⣼⣟⡉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣾⣦⠀⠀⠀⠸⣿⠿⣹⣷⣶⣤⣤⣀⠀⠀⠀⠀⠈⢿⣿
⣴⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣶⣄⠀⣰⣾⣿⣿⣿⣿⣧⠀⠀⠁⠀⢀⣾⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡷⣄⠀⠐⣦⣴⣿⣿⣏⣿⣿⣿⣷⡄⠀⠀⠀⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠸⣿⣿⣿⡏⣷⠊⣿⣾⣿⣿⣏⣿⣿⡟⣿⢹⣿⣿⣄⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣥⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⢹⡇⣿⠇⢯⠀⠘⢿⣿⣿⣿⡏⠀⠻⠿⠏⠻⢿⣿⣧⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⠟⠉⠻⣿⣿⣿⣧⡀⠀⠀⠀⠸⠀⣼⠁⢸⡀⠀⠈⠉⠙⠛⠁⣶⠟⠀⠀⠀⠀⠙⢻⣿⡆⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⠛⠿⠟⠋⠀⠀⠀⠈⠉⠛⢿⠁⠀⠀⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠈⠙⢿⢿⠂⠀⠀⠀⠀⢿⠀⢸⡇⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣿⣿⠏⠁⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⢂⠀⠘⠀⠀⡿⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀
⣿⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠄⠀⠀⠀⠀⠉⠛⠛⠛⢿⣧⣀⡀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⠁⠀
[16A⣲⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⡶⠶⣶
⠿⢿⣿⣿⠇⠀⠈⠉⠛⢿⣿⣿⣿⣿⣿⣯⣉⣉⣉⣩⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣀⣀⣽⣿⣿⣿⣿⣿⣆⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣶⣤⣤⣄⠈⠉⠉⠉⠁⠀⢀⣠⣴⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣛⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢰⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⠀⢠⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⣿⣿⠟⢹⡏⠉⢥⠀⠘⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⠟⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⡛⠻⣿⡟⠛⢿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣫⣡⠀⠀⠀⠰⠁⢠⣆⢸⣿⣿⠃⠀⠈⢿⣿⣷⣠⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡀⠀⢀⣄⡀⠈⠁⣤⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣤⣿⣧⣤⣼⣿⣧⣤⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠘⢛⣽⣏⠀⠀⠀⠀⠀⣯⣼⠟⠛⠛⠃⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⣿⣿⡏⠀⠀⠀⠀⠙⠿⠿⠀⠛⠹⣿⣿⣿⣿⣿⠿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠀⠀⠀⠀⢀⣿⡏⢀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣟
⠀⢀⣀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣯⣭⣽⣿⣿⢣⣤⣤⣀⣀⠀⠀⠀⠀⢀⣀⣤⣴⣤⣄⠀⠈⠛⠛⠛⠉⢰⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡀⠀⠀⠀⠈⠻⠿⢸⣿⡶⣦⣤⣄⡀⠀⠀⠀⠈⢿⣿
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠛⠋⣡⣾⣿⣿⣿⣿⣿⣦⣀⣴⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡇⠄⠀⠀⢀⣴⣾⣟⡇⠙⠻⣿⣿⣄⠀⠀⠀⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠇⠀⢳⣶⣿⣿⢏⣿⠁⢀⣠⣴⣿⣿⣇⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡵⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠈⠻⣿⡷⠘⠿⠿⠿⣿⣿⢻⣿⣿⣿⣿⡆⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⡿⠛⠛⠛⢿⣿⣿⣿⡇⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠛⠻⠃⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⣭⢉⣥⣨⣍⣭⣭⣡⣤⡀⣠⣤⣀⣤⡄⣤⣄⣠⣤⣠⣤⡄⢠⣄⣬⣠⣬⣠⣤⡍⢡⣭⢡⣤⣠⣤⣄⣤⢠⣄⣤⣄⣠⣄⣠⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣠⣤⡀⠀⠀
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠈⠁⠀⣿⢸⣿⣿⣿⣿⣿⢽⣼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣼⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀
⣿⠿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⠀⠀⠀⠉⠉⠉⠉⠉⠈⠉⠉⡁⡀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀
[16A⠂⠀⢀⡀⠀⠀⠀⠲⡶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣆⣰⣶⡔⠀⠲⢶⣶⣶⣶⣶
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣏⣭⣭⣁⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣄⠀⠀⠀⢀⣠⣴⣶⣶
⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣤⣄⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢰⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠿⠛⠛⠛⠁⠈⢿⣿⣿⣿⠀⢠⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⠶⠦⣘⠁⠀⠙⠀⡐⠂⣀⠈⣿⣿⡿⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠿⠉⢹⣿⠁⠉⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠿⣷⠂⠸⠀⠀⠀⠀⢠⢄⣿⣼⣿⡿⠁⠀⠈⢿⣿⣷⣠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡀⠀⣨⣄⠈⠁⢀⣈⣿⣿⣿⣿⠇⠀⠀⢻⣿⣿⣿⡿⣿⣽⣿⣷⣶⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⠇⠀⠀⠀⠀⢸⡾⠃⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠈⠙⠛⠀⠈⠁⠹⣿⣿⣋⠉⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣺⣿⠀⠀⠀⠀⠀⢿⣧⢰⣦⣴⣷⣶⣤⣄⠀⠙⣿⣿⣿⣟
⠀⢀⣀⠀⠀⠀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣯⣭⣉⣿⣿⣏⣠⣀⣈⣙⠁⠀⠀⠀⣠⣶⣾⣿⣿⣶⡀⠀⠈⠙⠋⠀⢨⣿⣷⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇⡀⠀⠀⠀⠀⣠⣼⠿⣿⣿⣿⣿⣿⣷⣆⡀⠘⢿⣿
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣼⣿⣿⣿⣿⣿⣦⣠⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠨⢿⣟⢃⢡⠀⢢⣀⣼⡿⠁⠀⢻⣿⣿⣿⣿⣿⣿⣶⣶⡄⠸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠨⡏⠈⢐⠀⠈⢿⣿⡃⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡟⠐
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠚⠃⢸⠟⠙⠛⠻⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠁⠀⢸⠀⠀⠀⠿⣷⡆⠀⢀⣦⠉⢿⣿⣿⣿⣿⣿⣷⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠙⠛⠛⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠐⣿⢃⠀⣀⣿⡇⠀⠹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣤⢀⣤⣠⣄⣤⣤⣨⣭⡙⣩⣭⣉⣭⡍⣭⣍⣡⣤⣠⣤⡄⢠⣄⣤⣠⣤⣠⣤⡄⢠⣤⢠⣤⣠⣤⣄⣤⢠⣄⣤⣄⣠⣄⣠⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣨⣭⡙⣿⡿
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⢸⣿⣿⣿⣿⣿⢽⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣼⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠈⠀
⡿⠿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⠀⠀⠀⠉⠉⠉⠉⣉⣈⣉⣉⣡⣦⣌⣋⣉⣛⣁⣉⣉⡉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⢀⠉⠁⠙⢋⠀⠙⠋⠈⢻⣹⠁⠀
[16A⠶⠶⣶⣶⣶⣶⡶⠒⠒⠲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣆⣀⡀⣀⣠⣶⣶⣶⣶⣶
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿⣏⣉⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠟⠿⠟⠻⠻⠿⡿⠿⢛⣫⣵⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⢿⡟⠛⠀⣠⠀⢀⡀⠀⠰⣿⣿⣿⠀⢠⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢰⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⠿⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡐⠓⠦⣼⠀⠀⠀⠀⠈⠀⣴⢀⣾⣿⡟⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣾⣿⣿⣿⣿⡿⣿⡁⣁⣼⣿⣄⣀⣼⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⠒⠸⠀⠀⠀⠀⢨⣥⡿⠛⠿⠏⠀⠀⣸⣿⣿⣷⣠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⠟⠿⢿⣿⡿⣿⣿⣿⣿⡟⠀⠙⣿⣿⣿⡟⢿⢿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠛⣿⠃⠀⠀⠀⠀⢸⡏⢀⡀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠏⣿⣧⣄⠀⢀⣀⠀⠀⠀⣿⣿⣿⠁⠀⠀⠀⣈⣭⣄⡀⠀⢻⣿⣧⡄⣨⣿⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣸⠇⢘⣿⣿⠀⠀⠀⠀⠀⠘⠋⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⠀⢀⣀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣤⣼⣿⣿⣿⣿⣿⣷⣄⢰⣿⣿⡟⠀⢠⣶⣿⣿⣿⣿⣿⣄⠀⠈⠉⠗⢓⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⡟⠀⢸⣿⡿⠃⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡉⠉⠉⣰⣿⣿⣿⣇⣠⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠃⠀⢘⣿⡏⠀⠀⠀⠘⣧⣿⣿⣿⣿⣿⣿⠀⠀⠈⠙⢿⡿⠿⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⢒⣿⠇⠀⢸⠀⠀⠙⢿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠈⢻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠟⠋⠉⠻⡿⢿⣿⣧⣄⠀⠀⠀⠀⠈⠀⠀⠐⡆⠀⠀⠀⠻⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⠁⠠⣤⣾⣷⣷⠀⠀⠀⠀⠀⠙⠻⡿⠃⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣭⢉⣭⣩⣍⣭⣭⣩⣭⡙⣩⣭⣉⣥⡅⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣠⣤⣠⣤⡄⢠⣤⢠⣤⣠⣤⣀⣤⢠⣄⣤⣄⣠⣄⣠⣤⣠⡄⣠⣤⢩⣭⣭⣡⣍⠉⣤⣤⣠⣤⡀⠀⠀
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠙⠋⠀⣿⢸⣿⣿⣿⣿⣿⢽⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣼⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀
⣿⢿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⠀⠀⠀⠉⠉⠉⠉⠉⠈⠉⠉⠁⢀⣈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⢀⣉⡁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀
[16A⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠒⠲⠶⠶⣶⣶⣤
⠀⠀⠀⠉⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⡄⠀⢀⣠⣼⣿⣿⣿
⠀⠀⠀⣠⣴⣿⠟⠛⠁⣿⣿⣿⣿⣿⣿⠀⠀⢀⣀⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⡿⠿⢿⠗⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠸⠿⠋⠀⡀⢀⣸⣿⣿⣿⣿⣿⣿⣤⣶⣾⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣱⡟⠀⠀⣀⠀⢀⡀⠀⠘⠛⠛⠉⠉⢙⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⣿⣿⣿⣿⣿⠿⢿⣿⣿⠟⠛⣿⢿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠘⡛⠿⠄⠀⠀⠀⠀⠀⠀⣴⠀⣀⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣻⣀⣀⣽⣿⣅⣀⣦⡄⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣝⡂⠄⠀⠀⠀⠀⢨⣠⡿⠊⠛⠃⠀⠀⠈⣿⣿⣷⣠⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠈⠻⢿⡏⠋⢿⣿⣿⣿⣿⣿⡟⠃⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣦⣀⠀⠀⠀⠀⠀⢰⡏⢀⡀⠀⢀⣤⣤⣴⣻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡟⣿⣿⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣠⣤⣶⣄⠘⠻⢾⡿⣿⡿⣡⣴⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⡼⠀⢠⣼⡟⠀⠀⠀⠀⠀⠈⠋⢸⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⠀⢀⣀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠁⣀⣿⣿⣷⣄⠀⠀⠉⠉⠉⠀⢹⡟⢁⣴⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⡇⠀⢸⣿⠧⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣴⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⣠⡦⠀⢀⡸⢁⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠐⠃⠀⠰⣿⠀⠀⢀⠀⠈⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⠈⠛⠉⠉⠉⠀⣰⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⢦⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠠⣿⠀⠃⢸⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢡
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢿⣿⣿⣿⣿⡟⠀⠈⠛⠋⢻⣿⣷⡄⠀⠀⠀⠐⠀⠀⠈⡆⠀⠀⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⠟⠛⠉⠉⠙⠟⠋⠋⠻⠿⢿⡇⠀⠀⠹⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠈⠻⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⡘⠻⣿⣿⣿⡿⠟⠋⠀⠀⠀⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣭⢉⣭⣩⣍⣭⣭⢠⣤⡀⣠⣤⣀⣤⡀⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣠⣤⣠⣤⡄⢠⣤⢠⣤⣠⣤⣀⣤⢠⣄⣤⣄⣠⣄⣠⣤⣠⡄⣠⣤⢠⣤⣤⣠⣌⠁⣤⣤⣠⣤⡀⠀⠀
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿⠟⠀⣿⢸⣿⡿⣿⣿⣿⢽⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣼⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀
⡿⢿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⠀⢁⣀⣉⣉⡉⠉⠉⠈⠉⠉⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀
[16A⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠖
⠀⠀⠀⠉⠉⠉⠉⣭⣿⣿⣿⣿⣿⣿⣿⠏⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠉⠁⠈⢿⣷⣴⣶⣶
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠛⠛⢿⣿⣿⣿⣿⠀⠀⢰⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⣠⣴⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠿⣿⡿⠛⠉⠙⠀⠀⠈⣿⣿⣿⣷⣴⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⢿⣿⣿⣿⡿⠿⠿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⠃⠀⠃⠀⠐⠀⢀⠈⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠈⢻⣿⣿⣇⣀⣸⣿⣦⣃⣸⡏⡙⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⡏⠀⠀⠀⠀⢠⢰⣿⡼⠿⠏⠀⠀⠈⢿⣿⣶⣠⣼⣿
⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠛⠟⠸⣿⣿⣿⣿⣿⣿⠻⠇⢸⣿⢿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢺⡞⠁⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢀⣠⣤⣄⠻⠷⣶⣾⣿⠏⠀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡤⡄⠀⠀⠀⠀⠀⢸⡷⢰⣦⣤⣀⣀⠀⠀⠀⠘⢿⣿⣿⣟
⠀⢀⣀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠟⠿⠿⢿⡿⠋⠉⠉⠛⠛⢿⣿⣿⠋⠀⣠⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⣚⠀⢠⣶⣿⣿⣿⣴⣄⠀⣀⣠⣼⣿⣿⣿⡿⣿⣦⠀⠀⠀⠈⢿⣿
⣴⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣶⣾⣿⠿⣧⣤⠀⠀⠀⣴⡀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⣴⣿⣾⣿⣿⣿⣿⣿⠿⣿⣷⣾⣿⣿⣿⣿⣿⠀⡿⣿⣧⠀⠀⠀⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⠈⠀⠀⠀⠀⠀⢀⣿⣆⣰⣿⣿⣿⣿⣿⣿⣿⣿⡏⣤⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⢿⡻⡿⠿⢶⣜⢿⣿⣿⣿⣿⣿⡏⡜⢀⣿⣿⣆⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠀⣿⣿⣿⣿⣿⡿⠉⠙⠿⠿⠻⠟⠋⠛⠋⠁⠀⠀⠁⣄⣾⣿⣟⠛⠿⢿⣿⣿⣿⡟⠀⠙⣿⣿⣿⡄⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣤⣤⣼⣿⣿⣿⠿⠿⣿⡿⠋⠙⠿⠻⠿⠃⠀⠀⢺⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⠃⠀⠀⠈⢹⣿⠟⠁⠀⠄⠀⠘⢿⡇⠀⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣭⢉⣥⣠⣄⣭⣥⢠⣤⡉⣠⣤⣀⣤⡀⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣠⣤⣠⣤⡄⢠⣤⢠⣤⣠⣤⣀⣤⢠⣄⣥⣍⣠⣄⣠⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣠⣤⡀⠀⢹
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⡿⣿⣿⣿⢽⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣸⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀
⡿⢿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣶⣷⣀⣉⣉⣉⡉⠉⠈⠉⠉⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⠉⠉⡉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀
[16A⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠶⠖
⠀⠀⠀⠉⠉⠉⢉⣹⣿⣿⣿⣿⣿⣿⣿⠏⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠁⠈⢉⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣦⣤⣤⠀⠈⠉⠉⠉⠉⠈⢀⣠⣴⣶⣶
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⣶⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢰⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⣿⣿⣿⡿⡏⠀⢮⣿⣧⠉⢹⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢸⣿⣿⣿⣿⠏⢠⡆⢸⣿⣿⠃⠀⠈⢿⣿⣷⣠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠸⣿⣿⢧⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠘⠿⠟⠋⠁⠓⣼⠿⠛⠛⠃⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠿⠿⠛⠛⠻⣿⣿⡄⠀⠀⠀⠀⠀⠈⠁⠈⠙⣿⡏⠉⠙⣿⡟⠁⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣷⣤⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣟
⠀⢀⣀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣄⣀⠀⠀⠀⢀⣄⠀⠀⠀⠉⠀⠀⠀⠀⣀⣤⣴⣶⣶⡀⠈⠓⠉⠈⠛⢠⣴⣿⣦⣤⡀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠈⠉⠙⠀⠀⠀⠀⣾⠟⣸⣿⣶⣤⣤⣀⠀⠀⠀⠀⠈⢿⣿
⣴⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠖⠴⠀⠀⣠⣶⣤⡀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠃⠀⠀⠀⢠⣤⠀⠀⡀⠀⢠⣶⣿⣿⣿⡿⢻⣿⣧⠀⠀⠀⠀⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⢀⣾⣿⣿⣿⣦⢠⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⡀⠀⠀⡾⠸⡇⡆⠀⢻⣶⣿⣿⣿⣿⣿⠇⠈⢹⣿⣧⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢶⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠅⢠⠇⣇⠀⠀⠻⣿⣿⣿⣿⣿⠀⠀⠈⠿⣿⣦⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⢻⣿⣿⠄⠀⠀⣿⣿⣿⣿⠟⠋⠛⠛⠛⠛⠉⠉⠀⣸⣿⣷⡄⠀⢸⠀⢸⡄⠀⠀⠙⢿⣿⣿⡟⠀⠀⠀⠀⠘⣿⣷⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣭⢉⣤⣠⣌⣭⣭⣠⣤⡉⣡⣤⣀⣤⡄⣤⣄⢠⣤⣠⣤⡄⢠⣄⣤⣠⣤⣠⣤⡄⢠⣤⢠⣤⣠⣤⡀⣤⢩⣍⣤⣄⣠⣄⣠⣤⣠⡄⣠⣤⢨⣤⣤⣠⣄⠀⣤⣤⣠⣭⡀⠀⠀
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⣿⣿⣿⣿⢽⢼⠇⣙⣿⣽⣿⡇⣿⣿⢻⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣼⡿⢻⡿⠏⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀
⡿⢿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣷⣀⣉⣉⣉⠉⠉⠈⠉⠉⠀⠀⠈⠋⠉⠛⠁⠉⠉⠈⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠀⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀
[16A⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠖
⠀⠀⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⡏⠉⣉⡉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠁⣠⣿⣿⣿⣿⣿⣿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣼⣧⣄⣀⠀⠈⠉⠉⠉⠁⠀⢀⣠⣴⣶⣶
⣶⣾⣿⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⡄⠀⠀⢰⣾⣿⣿⣿⣿
⠀⠈⢿⠿⠋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⢠⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⠿⣿⡿⠛⠿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡍⠉⢹⣿⣿⣿⡏⢁⣄⢹⣿⣿⠇⠀⠈⢿⣿⣷⣠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠟⠉⠛⠛⠛⠛⠟⠛⠛⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣼⣿⣿⣿⣏⢹⣧⣈⣠⣿⣷⣀⣠⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢠⣿⠉⠀⠸⠿⠛⠛⠶⣸⡿⠞⠻⠋⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣄⢀⣀⣤⣦⣀⣀⣸⣾⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠘⢿⣿⡿⠹⡇⣿⣿⣿⠿⠿⣿⡿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠸⢯⡀⠀⠀⠀⠀⠀⠀⢿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣟
⠀⢀⣀⠀⠀⠀⠀⠀⣸⣿⣿⣶⣿⣿⠿⢿⣿⣿⣿⢋⣉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣁⡀⠀⠈⢿⣇⣰⣀⡼⢀⣻⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡄⠀⠀⠀⠀⠀⣸⡿⢸⣿⣶⣤⣤⣀⠀⠀⠀⠀⠈⢿⣿
⣴⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣴⣶⣶⣿⠟⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⣠⣶⣿⣿⣿⣿⣇⠀⠀⠈⠀⠀⢡⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣶⣶⣦⣤⡀⣤⣴⣾⣿⣿⣿⠟⣿⣷⡀⠀⠀⠀⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠻⢿⣾⣿⣿⣿⣿⣿⣿⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⣴⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠈⠉⣿⣷⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣁⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣠⠊⠉⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠻⢿⣿⣆⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⠿⠿⠿⢻⣿⣿⣿⣿⡇⠉⠀⣼⣿⣿⣿⣿⣿⡟⠿⣿⣟⠛⠡⣤⠄⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠻⣿⡇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣭⢉⣭⣩⣍⣭⣭⣡⣤⡀⣩⣤⣀⣤⡄⣤⣄⢠⣤⣠⣤⡄⢠⣄⣤⣠⣬⣩⣭⡍⢠⣬⢩⣥⣠⣤⣄⣤⢠⣄⣤⣄⣠⣄⣠⣤⣨⡅⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣠⣤⡀⠀⠀
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⣿⣿⣿⣿⢽⢼⠇⣙⣿⣽⣿⡇⣿⣿⣾⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣼⡿⢻⡿⢟⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀
⣿⢿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣄⠉⠉⠉⠉⠉⠈⠉⠉⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀
[16A⠀⠀⣲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⡶⠂⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣩⣭⣅⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣤⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣾⣶⣦⣬⣍⡉⠉⠁⠀⢀⣠⣴⣶⣶
⠉⠉⠙⠛⠛⠉⠉⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢰⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⡟⣿⣿⣿⣿⠉⢿⣿⣿⣿⣿⠀⢠⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⢀⢸⡿⠇⠀⠈⢿⣿⡿⠀⠀⠻⣿⣿⡿⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⢿⣿⡿⠿⢿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣾⠂⠀⠨⠀⠀⠀⠈⣁⢠⣿⣰⣿⡿⠃⠀⠈⢿⣿⣷⣠⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⠀⠀⠀⡀⠀⠈⠉⣉⣹⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⢸⣿⣿⣿⡟⢹⣇⠈⣸⣿⣇⠀⠀⢹⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⠀⠀⢨⣼⠏⠁⠈⠁⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣶⣾⣿⣶⣦⣶⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠸⣿⣿⣿⠻⠂⢻⣿⣿⣯⠿⣿⡟⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠦⣼⠃⠀⠀⠀⠀⠀⠘⣿⢠⣤⣀⡀⠀⠀⠀⠀⠘⢿⣿⣿⣟
⠀⢀⣀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⢉⣻⣿⣿⣿⠇⢀⣭⣉⣁⣀⣠⣤⣤⣤⠀⠀⠀⢈⣙⣏⣀⠀⠈⠻⡁⠤⠄⡺⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡿⠀⠀⠀⠀⠀⠀⠐⢋⣸⣿⢹⠹⢿⣿⣦⡀⠀⠀⠘⢿⣿
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣤⣾⣿⣿⣿⣿⣿⣿⣿⡟⣀⣴⣾⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⣠⢽⣷⠄⠀⠀⠀⢄⣀⣠⣿⣿⣏⡾⠀⠀⠘⢹⣿⡄⠀⠀⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠐⠾⠼⡇⠀⠀⠆⠀⠈⢿⣿⣿⣟⡅⠀⠀⠀⠀⠈⣿⣿⣦⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡀⠀⢴⣿⣿⣿⡿⠛⠋⠉⢻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣿⣶⡶⠀⡠⠄⠀⠙⢿⣿⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠛⠿⣿⣿⡿⠛⠉⠉⠙⠙⢻⢿⣿⡇⠁⠀⢸⣿⣿⣿⠁⣠⣀⣴⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⢏⡀⢼⠦⠀⠀⠀⠀⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣭⢉⣥⣠⣄⣤⣤⢠⣤⡀⣠⣤⣀⣤⡄⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣠⣤⣠⣬⡝⢩⣤⢩⣭⣩⣭⣉⣤⢠⣄⣤⣄⣠⣄⣠⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣠⣤⡀⠀⠀
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⣿⣿⣿⣿⢽⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣼⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀
⠿⠿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⠛⠁⠀⠉⠉⠉⠉⠉⠈⠉⠈⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀
[16A⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡀⠀⣀⣲⣶⠀
⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣏⣉⣉⣁⢉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣾⣿⣿⣿⣶⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠁⠐⣿⣭⣿⣷⣶
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠀⠀⢰⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⡟⠟⠛⠛⠿⠛⠀⠙⣿⣿⣿⣿⠀⢠⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣴⣟⢢⣨⠀⠈⠀⢀⠀⠀⣤⢈⣿⣿⡟⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢿⣿⣿⣿⡿⠿⢿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⠂⠀⠀⠀⠀⠤⢸⡿⡾⢿⠟⠀⠀⠈⢿⣿⣷⣠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠁⠉⠛⠛⠿⠿⠻⠿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⡁⣀⣀⣿⣧⣀⣠⣧⣤⢻⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣌⣿⡿⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣤⣠⣤⣤⣀⠀⠀⢠⣿⣿⣿⡿⠁⠀⠀⠀⣰⣿⣿⡿⠀⢽⣿⣿⣿⣿⣿⡏⠃⠘⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠈⠿⢸⣶⢶⢤⣤⢄⡀⠀⠙⣿⣿⣿⣟
⠀⢀⣀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⡿⠀⢛⣛⠛⠿⠇⠀⣰⣶⣾⣿⣿⣶⣷⣦⠈⠛⠉⠉⠛⠛⣠⣴⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⢤⠀⠀⠀⠀⠀⠀⣴⣾⡿⣸⣮⣞⣾⣿⣦⣀⡀⠘⢿⣿
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣴⣿⣿⣿⣿⣶⣄⣼⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠈⣿⣿⣿⠁⠀⠀⠀⠱⣤⡴⠟⠛⠁⢻⣿⠿⣿⣿⣿⣿⣿⣄⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠈⡻⣽⡏⠀⠀⠀⠀⠀⠙⠇⠀⠀⠀⠀⡋⣠⣿⣿⣿⣿⣿⣿⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⡆⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠟⠋⠉⠉⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⠃⠀⠉⠋⠛⠿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⡏⠀⠻⠿⠿⢿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣭⢛⣭⣩⣍⣭⣭⣠⣤⡀⣠⣤⣀⣤⡄⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣠⣤⣨⣤⡍⢡⣤⢠⣤⣠⣤⣄⣤⢠⣄⣤⣄⣠⣄⣠⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣠⣤⡀⠀⠀
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⣿⣿⣿⣿⢽⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣼⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀
⡿⠿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣮⣉⡉⠉⠉⠉⠈⠉⠉⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀
[16A⠶⠖⠀⣠⣶⣶⣶⣶⣶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⣰⡶⠶⠒⣶⡶⠖⠀⠀
⠀⣠⣴⣿⣿⣿⡿⠛⠁⠀⣸⣿⣿⣿⣿⠏⠉⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⠀⠀⠀⢀⣠⣴⣶⣶
⠀⠿⠛⠛⠉⠁⠀⠀⣠⣾⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⡷⠀⠀⢰⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡿⠋⢉⠈⢻⣟⠀⠘⣿⣿⣿⡧⠀⢀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠻⠏⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⣠⡶⢬⠉⠀⠀⠀⠈⠁⢠⡆⢰⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠹⣿⣿⣿⠉⠙⢻⡟⠛⠟⢻⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⣯⡍⠀⠉⠀⠀⠀⠀⠀⣸⠟⠋⠛⠃⠀⠀⠈⢿⣿⣷⣠⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠈⠻⠏⠤⣴⣿⣿⣶⣶⣾⢠⡏⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣘⢛⣦⠀⠀⠀⠀⠀⠸⣏⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡏⢻⣏⠙⠛⠻⠿⣿⣿⡿⠿⣿⣿⣿⠃⠀⠀⠀⢀⣀⢀⣟⢉⣛⣿⣿⡿⠈⢀⣀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠟⢀⣿⣱⣶⣶⣶⣦⡀⠙⣿⣿⣿⣟
⠀⢀⣀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣀⣸⣿⣧⡀⠀⠀⡀⠀⠀⠀⣿⣿⡏⠀⣠⣴⣾⣿⣿⣿⠀⠀⠼⠙⠉⢠⣶⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⡿⣿⢠⠀⠀⠀⠀⠀⠀⣴⠋⠁⠉⢻⣿⣿⣿⡿⢀⡈⠙⢿⣿
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣷⣴⣿⣦⣤⣤⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠐⢊⣿⠈⠀⠀⠀⠰⣤⡾⠃⠀⠀⠀⠀⠙⢿⣿⣦⣿⣟⠀⠀⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠑⠟⠀⠀⠀⠀⠀⠙⠳⠈⠀⠀⠀⠀⠀⠈⣿⣿⠿⣿⡇⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⠛⢸⣿⣿⣿⣿⣿⣿⠛⠻⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⣿⣿⡟⠀⠀⢸⣿⣿⣿⣿⣿⡟⠀⠀⠈⠉⠉⠻⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣭⢋⣭⣩⣍⣤⣤⢠⣭⡙⣩⣭⣉⣤⡄⣤⣄⣠⣤⣠⣤⡄⢠⣄⣬⣡⣤⣠⣤⡄⢠⣤⢠⣤⣠⣤⣀⣤⢠⣄⣤⣄⣠⣄⣠⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣠⣤⡀⠀⠀
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⣿⣿⣿⣿⢹⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣼⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀
⡿⠿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣀⠉⣉⣉⣉⣉⠈⠉⠉⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀
[16A⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⠠⢀⢠⣤⡶⠖
⠀⠀⠀⠉⠉⠉⢩⣭⣭⣿⣿⣿⣿⣿⣿⠏⠉⠉⠁⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⢿⣿⣿⣷⣶
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠻⣿⠛⢱⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣠⣤⣶⣶⣶⣶⣄⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣻⠟⠛⢿⣿⣿⣿⠿⣿⣿⣧⠀⠀⢠⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⡏⠀⠁⢸⣿⣿⣿⡄⢸⣿⡿⠁⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠘⢿⣿⣟⠋⠀⠈⣿⣏⠋⠉⡻⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠠⠏⠀⠀⠀⠸⠟⠋⣿⠟⠋⠛⠁⠀⠀⠈⢿⣿⣶⣠⣼⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⠛⠋⠆⣾⣿⣟⣿⣿⣿⡿⠻⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠄⠀⠀⠀⠀⣼⣏⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⢀⣀⡀⠿⠿⠿⡿⣿⠿⠀⣠⣄⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⡄⠀⠀⠀⠀⠀⠀⠿⠀⣷⡆⣦⣤⣀⠀⠀⠘⣿⣿⣿⣟
⠀⢀⣀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠋⠛⠻⢿⡿⠛⠻⠿⣿⣿⣿⣿⡿⢿⣟⣡⣴⣿⣿⣿⣿⡀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡋⠙⠹⣿⣦⣴⣶⡘⢿⣿
⣤⣿⣿⣿⣿⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⢽⡔⡀⠀⠀⠀⠀⠀⠀⢠⣽⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⢣⡀⣴⣿⣿⣿⣿⠁⠀⠀⠸⣿⣿⣿⠇⠀⠸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⠀⠀⠀⠀⠈⠂⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢸⠀⠂⠀⠀⠀⢳⠉⢿⣿⣿⣽⠀⠀⠀⠀⠸⡿⠁⢀⣤⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⢸⣿⣿⣿⣿⣿⣿⠛⠻⣿⣿⣿⣿⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⡿⠃⣸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠹⠻⣿⡟⠟⠀⠀⢸⣿⣿⣿⣿⣿⠇⠀⠀⠈⠉⠉⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣭⢉⣭⣩⣍⣭⣭⢩⣬⡉⣡⣤⣀⣤⡄⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣠⣤⣠⣤⡄⢠⣤⢠⣤⣠⣤⣀⣤⢠⣄⣤⣄⣠⣄⣠⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣠⣤⡈⠙⠟
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⡿⣿⣿⣿⢹⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣸⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀
⠿⢿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⠀⠉⠉⠉⠉⠉⠈⠉⠉⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀
[16A⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠶⠖
⠀⠀⠀⠉⠉⠉⢩⣽⣭⣿⣿⣿⣿⣿⣿⠏⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⠉⠉⠁⠀⢀⣠⣴⣶⣶
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣰⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⣴⣾⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣷⣷⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠝⠋⢹⣿⣿⣿⡛⢻⠏⠙⢻⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⠫⠉⣿⣏⠉⢹⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠉⢣⠈⣿⣤⠾⠿⠁⠀⠀⠈⢿⣿⣷⣠⣼⣿
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⡿⠛⣶⠘⣿⣷⣶⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠉⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠀⠘⢿⣟⠋⠈⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣳⡆⠀⠀⠀⠀⠀⠹⣧⠀⣄⡀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣟
⠀⢀⣀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⠛⠛⠛⠻⠿⠿⠻⢿⡇⠀⢀⣤⣶⣿⣿⣶⠀⠀⠀⠈⠁⠂⢸⣿⣿⣶⣶⣄⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠋⣠⣿⣷⢿⣶⣤⣀⠀⠀⠀⠘⢿⣿
⣤⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣶⣶⣶⠎⠑⡄⡀⠀⠀⠂⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⡀⠀⢠⣿⣿⣿⣿⡄⣟⣿⣿⡄⠀⠀⠀⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⣸⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢸⡇⠀⠀⡄⠀⢳⡐⠯⣿⣿⣿⡿⠁⠈⠁⣿⣧⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⠛⢸⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⣿⣷⠀⠀⠀⠀⢸⠁⠀⠀⠁⠀⠀⠷⠀⠹⣿⡟⠁⠀⠀⠀⠀⣿⣧⠀⢀⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣴⣿⣿⣿⡿⠿⠟⠋⠙⠙⠻⢿⣿⠟⠂⠀⠸⣿⣿⣿⣿⣿⠏⠀⠀⠙⠛⠛⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⠿⣶⣶⡆⠀⣤⢾⣿⣯⣷⣟⠉⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣭⢉⣥⣠⣄⣬⣭⢠⣤⡉⣠⣤⣀⣤⡀⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣠⣤⣠⣤⡄⢠⣤⢠⣤⣠⣤⣀⣄⢠⣄⣤⣄⣠⣄⣠⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠈⣤⣤⣠⣤⡈⠀⠀
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⡿⣿⣿⣿⢹⢼⠇⣙⢿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣸⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀
⠿⢿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣄⣉⣉⣉⣉⠉⠈⠉⠉⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⣉⣁⣈⣁⠈⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⢉⣉⣀⣉⣁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀
[16A⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠶⠖
⠀⠀⠀⠉⠉⠉⣩⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⣀⣬⣥⣠⣽⣿⣿⣿⣿⣿⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣄⣀⡀⠈⠉⠉⠉⠉⠈⢀⣠⣴⣶⣶
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢰⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠂⢀⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣾⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠸⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢿⡟⠛⢻⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠈⢿⣿⣷⣠⣾⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢰⣿⣿⣿⣿⣿⣿⡛⢻⣿⣄⣀⣼⣿⣴⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠟⠉⠙⠁⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⠂⠀⠀⠹⣿⣿⣿⠏⠙⢿⠘⠿⣿⣿⡿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⠂⠀⠙⠛⠉⠹⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣟
⠀⢀⣀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣷⠶⣶⡾⠓⠶⠄⠀⠉⠛⠛⠀⠀⠀⠀⠀⣈⣭⣀⠀⠀⠀⠀⠉⠻⠴⠤⢸⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⠈⠻⡿⡇⠀⠀⠀⠀⠈⢻⣿⢠⣷⣦⣤⣀⠀⠀⠀⠀⠻⠿⢿⣿
⣴⣿⣿⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⢠⣾⣷⣦⣄⠀⠀⢀⣴⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⣠⣾⣿⣿⢻⣿⣿⠀⠀⠀⠀⠀⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⢰⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⢠⣷⡆⠄⢀⠀⢸⣶⣤⣾⣿⣿⣿⣿⠀⣿⣿⣴⡀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⣿⡿⠀⠘⢸⡀⠀⢿⡟⢿⣿⣿⢿⡇⠀⠉⣼⡟⠃⠀⢀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠉⠉⠹⠿⢿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⠋⠙⣿⣿⣿⣿⣦⣾⡁⣻⠁⠀⣺⡟⢿⡿⣿⡿⣿⢿⣿⣿⠇⠀⠀⠉⠀⠀⠀⠈⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣭⢉⣭⣩⣍⣭⣭⢡⣤⡉⣠⣤⣀⣤⡄⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣠⣤⣩⣥⡄⢠⣤⢠⣭⣩⣭⣄⣤⢠⣄⣤⣄⣩⣍⣠⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣠⣤⡀⠀⠀
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⡿⣿⣿⣿⢽⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣼⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀
⠿⢿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣄⣉⣉⣉⡉⠉⠈⠉⠉⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⣉⣉⣉⣉⣉⣄⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀
[16A⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠖
⠀⠀⠀⠉⢉⣽⢏⣭⣯⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⢀⣨⣴⣤⣤⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⣿⣿⣷⣤⣄⠉⠉⠉⠉⠁⠈⢀⣠⣴⣶⣶
⠀⠀⠀⢴⣿⣿⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢰⣾⣿⣿⣿⣿
⠀⠀⠀⡼⠁⠈⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣶⣦⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⢾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠿⠿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⡿⠿⢿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⣿⣿⣿⣿⣿⡇⢹⠉⠀⠀⠀⣿⣿⣿⣷⣠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⢀⡀⠀⠉⢡⣤⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⢿⣿⠉⢀⣼⣷⣀⣠⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⢿⡟⡇⠀⠀⢹⣿⣿⣧⣿⠛⠁⠀⠀⠀⠀⢸⡏⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣶⣶⣿⣿⣷⣶⣾⣿⣿⢿⣿⣿⠃⠀⠀⠀⠀⠸⣿⣿⣿⣿⢿⠆⠻⣿⣿⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠑⣽⠁⠀⠀⠀⠉⢿⣿⡏⠀⠀⠀⠀⠀⠀⠀⡇⠙⢿⣿⣿⣟
⠀⢀⣀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣏⣉⣉⣹⣿⣿⡃⣠⣀⣀⣁⠀⠀⠀⠀⠀⠀⠈⢻⣿⡏⠀⠀⠀⠘⠿⠵⠶⠒⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡄⠀⢀⠀⠀⠀⠘⣿⣿⢦⣿⣦⣤⣀⠀⠀⠀⠀⠀⠈⢿⣿
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⣼⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣾⣿⣿⣿⣷⡄⠀⠀⠀⠀⠁⢰⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⣰⣿⣿⣿⣾⣿⠀⡀⠀⠀⠋⣡⣾⣿⣿⠻⣿⡗⠀⠀⣠⠀⠀⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⣿⣿⣿⣿⣿⡏⠈⢹⡲⣴⣾⣿⣿⣿⣿⠇⣿⠇⠀⠀⠻⡆⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣠⡟⣿⣿⣿⡿⢱⠀⠀⡇⠈⢿⣿⣿⠋⡇⠀⠉⡀⠀⠀⠀⠃⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⡿⠛⠉⠀⠀⠙⠛⢿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⠟⠻⣿⣿⣿⣿⣿⡟⠻⣿⣿⣵⠃⠀⡀⠀⢿⡀⠈⠻⣿⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣭⢉⣤⣩⣍⣭⣭⣡⣤⡀⣠⣤⣀⣤⡄⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣠⣬⣩⣭⡍⢠⣤⢠⣬⣩⣭⡍⣭⢩⣍⣥⣄⣠⣄⣠⣤⣨⡄⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣠⣤⡀⠀⠀
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⣿⣿⣿⣿⢽⣼⠇⣙⣿⣽⣿⡇⣿⣿⢾⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣼⡿⢻⡿⠏⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀
⣿⢿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣌⡉⠉⠉⠉⠉⠈⠉⠉⣠⣤⡈⠋⠉⠛⠁⠉⠉⠈⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⡈⠁⠀⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀
[16A⠶⠶⣶⣶⣶⣶⣖⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⣶⣶⣶⠶⠶⠶⠖
⠀⠀⠀⠛⣿⣯⠹⣿⣽⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣷⣶⠦⣴⠀⠀⡅⠀⢀⣠⣴⣶⣶
⠀⠀⠀⡰⣿⠿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣾⡿⢿⣿⣯⣴⣾⣿⣿⣿⣿
⠀⠀⠈⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡟⠛⠛⠉⠁⠀⠀⠉⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠏⠀⠀⠅⢠⡀⠀⠀⠀⠀⣀⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠟⠛⠻⡿⠿⢿⣿⡿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠰⣿⣿⣿⣿⡟⠛⢻⣿⣟⡛⠻⡿⠿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⢀⣴⡓⣎⡇⠀⠀⢀⣸⠀⠀⣾⣆⣼⣿⡟⠀⠀⠘⢿⣿⣷⣠⣾⣿
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡀⢱⣀⣦⡀⠈⠁⢰⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⢿⣿⣿⣿⢧⣤⣴⣿⣷⣤⣴⣷⡆⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⢸⣯⡟⠠⡇⠀⠀⣼⣿⡇⣴⡟⠀⠀⠉⠁⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠻⠿⠏⠀⢿⣿⣿⣿⣿⣿⠛⠁⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣿⡆⠀⠀⢰⣿⣿⡿⣿⣧⢠⣄⡀⠀⠀⠀⠀⠀⣙⢿⣿⣿⣟
⠀⢀⣀⣀⣀⣀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣤⣄⣀⣿⣇⠀⠀⠀⠀⠀⣠⣤⣶⣷⣄⠀⠉⠀⠟⠛⠃⣠⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⣰⣿⡿⡀⠀⠀⣼⣿⣿⠇⠟⠛⣸⣿⣿⢿⣶⡆⠀⠀⢿⡄⠈⢿⣿
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣴⣿⣿⣿⣿⣿⣷⣄⡀⣠⣾⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⢀⣿⣿⣇⢀⠂⠀⠿⠛⣿⠀⢠⣾⣿⣿⣿⡀⠟⡇⠀⠀⠀⠃⠀⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣠⣼⣿⣿⣷⢸⠀⠀⠀⠀⡿⠰⣿⣿⣿⡟⡿⠁⠘⠁⡀⠀⢰⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⠉⢉⣛⣛⣛⣛⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⠿⠄⠘⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠈⠀⢀⣠⡾⠃⠀⢻⣿⣿⠿⠃⠀⠀⠘⡅⠀⠘⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⠁⠀⠀⠀⠀⠀⠛⠛⢻⡄⠀⠀⣿⣿⡍⡁⠀⠀⠀⠉⠛⣻⣿⣿⣿⣿⣿⣿⡄⠀⠀⣿⣿⠀⠐⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣭⢉⣭⣩⣍⣭⣭⢩⣭⡁⣠⣤⣀⣤⡄⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣠⣤⣠⣤⡄⢠⣤⢠⣤⣨⣭⣍⣭⢩⣍⣤⣄⣠⣄⣠⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣠⣤⡙⡆⠀
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⠀⣿⢸⣿⣿⣿⣿⣿⢽⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣼⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠁⠀
⡿⢿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⠀⠀⠀⠉⠉⠉⠉⠉⠈⠉⠉⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⢉⣉⣋⣀⣉⣄⣉⣉⣉⣁⣈⣁⣌⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀
[16A⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠖⠒⢲⣶⣶⠶⠶⠶⠖
⠀⠀⠀⠈⣿⡍⢻⣯⣭⣽⣿⣿⣿⣿⣿⣏⣭⣭⣅⣈⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠳⣠⣤⣀⣀⠀⢀⣠⣴⣶⣶
⠀⠀⠀⣼⣿⣿⣎⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⠿⠟⠉⠉⠙⠋⠈⠉⠹⢿⣿⣾⣿⣿⣿⣿⣿
⠀⠀⠈⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠉⠁⠀⠀⢀⣰⡁⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢻⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠈⡿⣿⠁⠀⠀⠁⢸⣿⣿⣿⡄⢸⣿⡿⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⢿⣿⣇⣀⣸⣿⡉⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⢀⣴⡲⡌⡄⠀⠀⢀⣿⣯⣭⣿⠷⠿⠿⠃⠀⠀⠈⢿⣿⣷⣠⣼⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠸⣿⡙⠠⠃⠀⠀⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣀⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣟⠛⠁⠀⠀⠀⠀⠀⠀⢀⣿⣿⣧⣤⣶⣾⠁⣿⣿⣿⡧⢰⣶⣤⣄⣀⠀⠀⠀⢹⣿⣿⣿⣟
⠀⢀⣤⣄⣀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣾⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣇⠀⠙⢿⣇⣠⣾⣿⣿⠙⡿⣿⠃⠀⠘⢿⡈⢿⣿
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠧⣴⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡏⢿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢿⣿⣿⣿⣿⡀⢡⡇⠀⠀⠀⠀⠁⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⡉⠁⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠉⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢣⠀⠀⣾⣿⣿⣿⣿⠁⠀⢀⠀⠀⢠⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⣇⡜⠁⠀⠈⠙⢿⡿⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠈⣿⣿⣿⢟⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⠠⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⣤⢀⣤⣠⣍⣥⣤⢠⣬⡉⣩⣭⣉⣭⡍⣭⣅⣠⣤⣠⣤⡄⢠⣄⣤⣠⣤⣠⣤⡄⢠⣬⢩⣭⣩⣭⣉⣄⢠⣄⣤⣄⣠⡄⣠⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣠⣤⡙⡆⠀
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡁⠀⣿⢸⣿⡿⣿⣿⣿⢽⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣸⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠁⠀
⡿⠿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⠛⠧⠀⠉⠉⠉⠉⠉⠈⠉⠉⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀
[16A⠶⠶⢂⣴⢲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣲⠶⠶⠶⠒
⠀⣷⣿⣿⣧⣿⠉⣭⣭⣿⣿⣿⣿⣿⣿⠏⠉⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⠁⠀⠀⢀⣠⣴⣶⣶
⠀⠈⢿⣿⣿⣏⣠⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⣶⣶⣄⣀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⣀⣀⣰⣾⣿⣿⣿⣿
⠀⠀⠈⠹⠛⠁⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⠿⠻⠟⠋⠉⠛⢟⡛⢟⡶⠿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⡟⠈⠀⠀⠀⣠⣤⣶⣾⣿⣿⣿⣿⠏⠀⢹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣀⣠⣿⣇⣉⣉⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣶⣾⠁⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠈⢿⣿⢶⣠⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠸⡿⣿⣿⣿⣿⠏⢿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⡀⢞⣯⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⣀⣠⣄⡀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⣀⣤⣤⡀⢀⢈⠛⠟⠋⠀⠀⣉⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⢂⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣢⣤⣀⡀⠀⠀⠙⣿⣿⣿⣟
⣿⣿⣿⣿⣶⣄⡀⢠⣿⣿⣿⣿⣿⠿⠋⠉⠉⠁⠀⠀⠉⠉⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠙⡟⣿⣆⠀⠀⠀⠈⢿⣿
⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡇⡿⠀⢰⠋⣿⠄⠀⢰⡄⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⠀⠀⠘⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣿⣿⣿⣿⠿⡿⢿⠋⠹⣿⣿⣿⣽⡷⠀⠀⠰⠉⠀⠀⢸⡇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢌⠉⠛⠻⠿⠿⠿⠿⣿⣿⣧⠀⠀⣿⣿⣿⣿⣿⣿⠋⠀⠈⠛⠁⠀⠀⠀⠀⠈⠉⠋⠀⠀⠀⡇⠈⠀⡄⠉⠻⢿⡟⠇⠀⠀⡀⠀⠀⠀⠈⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⠁⠀⠀⠸⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣷⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⣭⢉⣤⣡⣄⣤⣤⢠⣤⡀⣠⣤⣀⣤⡀⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣠⣤⣠⣤⡄⢠⣤⢠⣤⣠⣤⣀⣄⢠⣄⣬⣄⣠⣄⣠⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣠⣭⡀⠀⠀
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣿⢸⣿⡿⣿⣿⣿⢹⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣸⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀
⠿⠿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣄⣉⠉⠉⠉⠉⠈⠉⠈⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠁⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣩⠁⠀
[16A⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠖
⠀⠀⠀⠉⠉⠉⣉⣭⣭⣿⣿⣿⣿⣿⣿⠏⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⠉⠉⠉⠁⠀⢀⣠⣴⣶⣶
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⠟⡋⠙⣿⣿⣿⣿⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⢸⣿⣿⣿⣿⠿⢿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⡈⠃⢀⢈⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠹⣿⡿⣠⣀⣠⣿⣿⣁⣀⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠙⠃⠀⣾⣿⣿⣿⣿⡆⡀⠀⢘⣿⣿⣷⣠⣼⣿
⣴⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡟⠁⠀⠀⣸⣿⣿⣿⣿⣿⣿⣷⣴⡏⠈⣿⣿⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢀⣀⣀⣀⠈⠋⣍⡿⠿⠋⠀⣠⣹⣏⠁⠀⠀⠀⠀⠀⠀⠀⢸⣶⣦⠀⠙⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣟
⠀⢀⣀⡀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⢹⣿⣿⣾⣿⣿⣿⣿⡀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠸⠿⠿⠆⠀⠀⠀⠀⠀⠘⣻⣿⣿⣿⣿⣿⣿⣿⠄⠀⠈⠙⠻⢿⣿
⣴⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣤⡄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠐⠂⢀⠀⠁⠀⡀⠀⠄⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢉⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣼⡇⠀⠀⢃⠘⡆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢸⣿⣿⣿⣿⣿⡟⠉⠉⠻⠛⠻⣿⣆⠀⠀⠿⠃⠀⠀⢸⡀⢹⠀⠘⣿⣿⣿⣿⣿⠋⢺⣿⣿⡆⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠉⠁⠀⠈⠉⠀⠹⢿⣿⠟⠀⠀⢸⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣇⠀⠃⢸⣿⣿⣿⡿⠀⠀⠈⣽⠿⠁⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣭⢉⣭⣩⣍⣤⣤⢠⣤⡀⣠⣤⣀⣤⡀⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣠⣤⣠⣤⡄⢠⣤⢠⣤⣠⣤⣀⣄⢠⣄⣤⣄⣠⣄⣠⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠉⣤⣤⣠⣤⡀⠀⠀
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣿⢸⣿⡿⣿⣿⣿⢽⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣸⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀
⠿⢿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣛⢣⠀⠉⠉⠉⠉⠉⠈⠉⠈⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀
[16A⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠖
⠀⠀⠀⠉⠉⠉⢉⣭⣭⣿⣿⣿⣿⣿⣿⠏⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢉⣴⣾⣿⣾⣿⣿⣿⣿⣿⣿⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣶⣦⣤⣄⣀⠈⠉⠉⠉⠁⠀⢀⣠⣴⣶⣶
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣠⣤⣤⣾⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠈⠿⣿⣿⣿⡅⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡏⠏⣸⣿⡁⠈⠙⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⡿⠿⠛⠏⠁⣠⡀⣸⣿⡿⠀⠀⠀⠈⢿⣿⣦⣠⣼⣿
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣦⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⢦⣿⠓⠉⠉⠁⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠈⠁⠀⠈⠈⠙⣿⡿⠅⠹⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣇⠀⠀⠀⠀⢾⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣟
⠀⢀⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠁⠉⣙⣻⣿⣃⠀⠀⠉⠛⠿⠋⠉⢿⠋⢀⣠⣤⣶⣶⣶⠀⠀⠀⠀⠀⠀⣰⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠨⡆⠀⠀⠘⠀⠀⠀⠀⠘⠟⢸⣿⣷⣦⣤⡀⠀⠀⠀⠀⠀⠈⢿⣿
⣤⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢟⠸⡇⠀⠀⠛⠀⢀⡀⠈⣴⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠘⢣⠄⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⢋⡟⢿⣧⠀⠀⠀⠀⠀⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⢀⡌⠀⢰⠀⡄⠀⢰⣾⣿⣿⡏⠋⢀⣤⣎⣿⣇⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣷⣀⠀⠀⢸⠃⠀⠀⡇⠸⡄⠀⢹⣿⣿⠀⢀⣾⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠿⡿⠛⠋⠀⠉⠉⠛⠻⣿⣿⣝⡀⠀⠀⣿⣿⣿⣿⣿⡏⠀⠀⠙⠋⠙⠛⠿⠀⠀⠘⠀⠀⠀⢹⠀⠳⠀⢀⣿⡿⠀⠲⠿⠏⠸⣿⠁⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣭⢉⣭⣠⣄⣤⣭⢡⣤⡀⣠⣤⣀⣤⡀⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣡⣤⣡⣤⡄⢠⣤⢠⣤⣠⣤⣀⣤⢠⣄⣤⣄⣠⣌⣠⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠁⣤⣤⣠⣤⡀⠀⠀
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⡿⣿⣿⣿⢽⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣸⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀
⠿⠿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣄⡉⣉⡉⠉⠉⠈⠉⠈⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⢉⣉⣉⣉⣉⣀⣉⣁⣙⣋⣀⡙⢋⡈⢻⣹⠁⠀
[16A⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⡶⠶⠖
⠀⠀⠀⠉⠉⠉⣩⣽⣭⣿⣿⣿⣿⣿⣿⠏⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⢀⣈⡁⢀⣭⣿⣿⣿⣦⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣥⣀⣀⠀⠀⠉⠉⠉⠉⠁⠀⢀⣠⣴⣶⣶
⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣴⣶⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡀⠀⠀⠀⣰⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢠⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠟⠻⠉⠉⠁⠀⢹⣿⣿⣿⡏⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⣿⠋⠙⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠈⠁⠀⠚⢀⡈⢹⣿⣿⠇⠀⠀⠈⢿⣿⣷⣠⣼⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠻⠿⠿⢿⠿⠿⣿⣿⣿⡿⠀⢸⣿⣿⣿⣿⣯⡙⣿⣧⣤⣴⣿⣷⣼⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣤⣎⢃⡏⠀⠀⠀⠀⣦⣼⣧⠾⠿⠛⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡏⢹⣦⡀⠀⠀⣀⡀⠀⠀⣸⣿⣿⡇⠀⠘⣿⣿⣿⡏⠙⠯⢹⣿⣿⣿⡟⢻⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣦⡀⠇⠀⠀⠀⠀⢽⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣟
⠀⢀⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣀⣨⣿⣿⣿⣿⠋⠋⣤⠀⠉⠛⠻⠃⠀⠀⠈⢉⣛⣁⡀⠀⠀⠈⠛⠛⠉⠉⣁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡟⠀⠀⠀⠀⠀⢸⡷⢸⣿⢶⣤⣄⣀⠀⠀⠀⠀⠀⡎⢿⣿
⣴⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠟⠫⠉⣼⣿⣷⣦⡀⢀⣴⣾⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⣠⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠆⠀⢼⣿⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⠹⣿⣿⣧⡀⠀⠀⠘⢧⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠐⣿⡇⠀⠀⠐⡰⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡟⡅⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⣀⣿⠃⠀⠰⠀⠱⠀⠈⢿⣿⣿⣿⣿⠘⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠃⠀⠀⠀⠉⠻⠿⣿⣿⠇⠀⠀⢸⣿⣿⣿⣿⣿⠋⠙⢿⣿⣿⣏⣿⣾⣿⡏⠀⠀⠀⡆⠀⠀⠀⠈⢿⣿⣿⣿⣦⠁⠿⠙⠁⠀⠀⢀⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣭⢉⣭⣩⣍⣭⣭⢡⣤⡀⣠⣤⣀⣤⡄⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣠⣭⣩⣥⡄⢠⣤⢩⣭⣩⣭⣅⣭⢡⣄⣤⣄⣠⣄⣠⣤⣠⡄⣠⣬⢩⣭⣭⣠⣄⠀⣤⣤⣠⣤⡁⠀⠀
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⡿⣿⣿⣿⢹⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣼⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀
⠿⠿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣀⠉⠉⠉⠉⠉⠈⠉⠉⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀
[16A⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣶⣶⣶⣶⣶⠶⠖⠒⠒
⠀⠀⠀⠉⠉⠉⣩⣭⣭⣿⣿⣿⣿⣿⣿⣿⣯⣭⣅⣉⣉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⣴⣾⣾⣷⣦⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⣶⣶⣄⠀⠉⠛⠛⠋⠈⢉⣠⣴⣶⣶
⣿⣿⡆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⢰⣿⣿⣿⣿⣿
⣿⠟⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠿⠿⠿⠿⠿⢻⣿⣿⣿⡿⠀⢀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣛⡿⣇⠉⠀⠴⠄⠀⠀⠀⢸⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡿⠻⢿⣿⡿⢿⢿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢟⠋⠻⣿⠉⠙⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣶⢯⣑⡆⠀⠀⠀⠀⢐⡀⣰⣾⣿⣿⡿⠀⠀⠈⢿⣿⣷⣠⣾⣿
⠀⠀⢀⣀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣇⠀⠀⢡⡀⠈⠀⢀⣹⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣯⡘⣿⣦⣤⣾⠿⣦⣴⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡈⠃⠀⠀⠀⠀⠀⣿⣿⣾⣿⣟⠁⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠀⢠⣿⣿⣷⣤⣄⢠⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣶⣾⣿⢿⣿⣿⠁⠀⠀⠀⢿⣿⣿⡿⠙⠇⠸⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡗⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣻⡆⠀⠀⠀⠀⠙⣿⣿⣿⣟
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⢁⣄⣀⣄⣉⠀⠀⠀⠀⠀⣉⣿⣇⣀⠀⠀⠈⠛⠛⠉⠹⣡⣤⣀⡀⠀⠀⠀⠀⠀⠀⡄⣼⣿⡿⠀⠀⠀⠀⠀⠀⡈⠹⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⢠⠉⢿⣿
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠉⣠⣾⣿⣿⣿⣿⣷⣄⣠⣶⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⢠⣾⣿⡇⠀⠀⠀⠀⢀⣀⡇⠀⠈⣿⣿⡏⠀⠻⣿⣷⡄⠀⠈⠀⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⣼⣿⣿⡇⠀⠀⠀⣷⣿⣿⠇⠀⠀⠈⠁⠀⠀⠀⢻⣿⣿⡄⠀⢰⣧⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⢿⣿⣿⣿⣿⣿⡅⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡤⢟⠟⠛⠁⢀⣾⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡇⠀⠈⣿⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⡇⠀⠀⢸⡟⠛⠛⠻⠿⠿⠛⢻⠟⢛⣿⣧⠀⠀⠀⢠⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣤⢀⣤⣨⣍⣭⣭⣡⣤⡀⣠⣤⣀⣤⡄⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣠⣤⣠⣤⡄⢠⣤⢠⣤⣠⣤⣀⣤⢠⣄⣤⣍⣩⣍⣡⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣠⣤⡀⠀⠻
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡆⠀⣿⢸⣿⡿⣿⣿⣿⢽⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣼⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀
⡿⢿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣧⣀⠉⠉⠉⠉⠉⠈⢉⣉⣀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⣙⡉⢉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀
[16A⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⡐⢶⡶⠖⠒⡆⠀⢶⠶⠖⠒
⠀⠹⣿⣿⣿⢋⣭⣭⣭⣿⣿⣿⣿⣿⣿⣏⣭⣍⣁⣉⣉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⣤⣶⣿⣿⣿⣿⣿⣿⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⠀⠀⠀⢀⣠⣴⣶⣶
⠀⠀⠀⠠⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⢀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢰⣾⣿⣿⣿⣿
⡄⠀⠀⠁⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⡏⠿⠟⠁⡀⠈⠉⠻⠯⣿⣿⣿⣿⣿⢣⣿⣿⣿⣿⣿⣿
⠃⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⡐⢯⡑⠀⠀⠀⠉⠀⠀⠀⠀⢹⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⠿⡿⠛⠟⣿⣿⠉⠙⡟⢿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⣿⣏⠂⡇⠀⠀⠀⠀⠀⢠⣤⣾⣿⣿⡿⠟⠁⠈⢿⣿⣷⣠⣼⣿
⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣦⠃⣤⣴⣿⣿⣦⣴⣷⣿⡿⠿⠟⠀⠀⠀⠀⠀⠀⠀⣼⣿⡧⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠛⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⣀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠈⠙⠻⠋⠈⠀⠙⡿⠓⠛⢻⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⠀⠀⠀⣰⣿⣿⠟⠁⠀⡤⣤⣀⠀⠀⠙⣿⣿⣿⣟
⠙⢙⣛⡛⢀⣈⠛⣇⣸⣿⣿⣾⣦⣄⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢀⣤⣴⣶⣿⣶⡄⠀⠀⠈⠁⠘⢵⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠃⣻⣿⡏⠀⠀⠀⠀⠀⣴⣿⣿⣧⡄⠀⠀⠀⠻⣿⣷⡄⠀⠀⠈⣿⣿
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣤⣔⣶⣾⣿⣿⣿⣿⣿⣿⣶⣄⣴⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⢸⣿⣿⡇⠀⠀⠀⢀⣼⣿⡿⢻⣿⠃⠀⠀⠀⠀⠸⢿⣿⣆⠀⠀⢻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠠⢼⣿⡟⠃⠀⠀⠀⠸⢿⠉⠁⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠻⠇⠀⠀⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠉⠙⠛⠛⠻⣿⣿⡍⠉⠉⠉⠉⠉⠙⢿⣿⣿⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣷⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡒⠒⠒⣤⡀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠉⠉⠉⠙⠛⣻⣿⡿⠀⠀⠘⠉⠈⠻⠿⠇⠀⠀⠀⠀⠀⠔⠖⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣭⢉⣥⣨⣍⣤⣤⢠⣤⡀⣠⣤⣀⣤⡄⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣠⣤⣠⣤⡄⢠⣤⢠⣤⣠⣤⣄⣤⢠⣄⣤⣄⣠⣄⣠⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣠⣤⡀⠀⠀
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⣿⣿⣿⣿⢽⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣼⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀
⡿⠿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣄⡉⠉⠉⢉⣉⠈⠉⠉⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀
[16A⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣀⣰⣦⡀⠀⠒⠲⠶⠲⣶⡀⠰⠶⠶⠒
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣉⣩⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⢀⣤⣴⣶⣶
⡔⠿⠛⠛⠻⠛⣻⣿⢿⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠽⠟⠋⡉⠙⠛⠿⠿⠿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⡠⢭⣓⠀⠀⠀⠉⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠉⢿⣿⣿⠟⠙⠻⣿⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢸⣿⠣⢸⠀⠀⠀⠀⠀⢠⣄⣿⣴⣾⣿⣿⣿⣿⣿⣿⣷⣠⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡄⠀⠀⢠⠀⠈⢛⠋⠀⢻⣿⣿⠀⠀⠀⠀⠀⠙⠛⠀⣤⣼⣿⣤⣤⣼⡧⡦⠘⢿⡿⠿⠟⠀⠀⠀⠀⠀⠀⢨⣿⣧⠈⠀⠀⠀⠀⠀⢸⡟⢻⣿⣿⣿⣿⠟⠁⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠙⢿⡀⠀⢸⠀⢠⠃⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⢀⣀⡀⠘⠛⠛⠿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⢸⣿⡟⠀⠀⠀⠀⠀⠀⠈⣸⣿⣿⣿⣿⣿⣤⡀⠀⠙⣿⣿⣿⣟
⠀⢀⣀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣦⣤⣷⣤⣿⣄⡞⠀⠀⢀⡈⠙⠃⠀⠀⣠⣶⣿⣿⣿⣿⡀⠀⠉⠉⠛⢁⣶⣿⣿⣿⣷⣦⣀⠀⠀⠀⢀⣿⠇⣼⣿⠁⠀⠀⠀⠀⠀⢀⣶⣿⠏⣿⡃⠀⠛⢿⣷⣄⠀⠀⠈⣿⣿
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣼⣿⣿⣷⣄⣀⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠸⠛⣾⣿⣿⠀⠀⠀⠀⡀⢰⣿⡿⢃⣼⡏⠀⠀⠀⠙⠿⣿⣦⠀⠀⢿⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠙⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⣿⣿⡇⠀⠀⠀⠀⠙⠾⡍⠀⣺⠏⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⠸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠙⠿⣿⣿⠛⠛⠛⠛⠛⠻⣿⣿⣿⡿⠛⠻⠏⠉⠀⣿⣿⣿⣿⣿⣿⠟⠙⢿⣿⡿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠶⣶⣄⠀⠉⠈⠀⠀⠀⠀⠀⠘⢿⡿⠛⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠈⠻⠛⠁⠀⠀⠀⠀⠠⠚⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣭⢉⣥⣨⣍⣭⣤⣠⣤⡀⣠⣤⣀⣤⡄⣤⣄⣠⣤⣠⣤⡄⢠⣄⣬⣩⣭⣡⣤⡄⢠⣤⢠⣤⣠⣤⣀⣤⢠⣄⣤⣄⣠⣄⣠⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣠⣤⡀⠀⠀
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⣿⣿⣿⣿⢽⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣼⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀
⣿⠿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣮⣉⡉⠉⣉⡉⠈⠉⠉⠁⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⢉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀
[16A⠖⢀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠆⠒⠲⣶⣶⣄⡀⠀⠀⠰⠶⠶⠖
⠀⠸⠟⠋⠉⠈⠈⣩⣭⣿⣿⣿⡿⠉⠙⠻⣿⣿⣯⣉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠉⠻⠇⠀⢀⣠⣴⣶⣶
⠀⠀⠀⢰⣶⠀⢲⣿⣿⣿⣿⠟⠁⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⢰⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠟⠀⠀⠻⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢸⣿⢏⣿⠿⠛⠛⠻⠿⠟⢻⣿⣿⣿⣿⠀⢠⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣶⣦⡀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⣯⣸⠋⠀⠐⠃⠀⠀⠀⢸⣿⣿⣿⣏⣠⣼⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠙⠿⠋⠛⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠆⠀⠀⠀⠀⠀⠀⠹⠟⠀⠀⠀⠀⠀⣀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣠⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⣀⢸⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⣤⣿⣆⣀⣈⣿⠛⠻⢿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⣾⠞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠇⢹⣿⡇⠀⠀⡉⠀⢻⡿⠋⠉⢻⠇⠀⠀⠀⠀⢀⣀⡀⠙⠐⠻⣿⣿⡿⠀⠀⠈⠛⠛⠛⠁⠀⠀⠀⠀⢀⡆⠀⠙⣷⡄⠀⠀⠀⠀⠀⠌⠀⠘⣿⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣟
⠀⢀⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣤⣤⣿⣷⣀⣶⢧⣤⠄⠀⠀⠀⢾⠀⠀⣠⣴⣿⣿⣿⣧⠀⠀⠈⠉⠉⢀⣶⣾⣿⣿⣷⣦⣀⠀⠀⠀⠀⣾⠇⠀⢀⣻⠃⠀⠀⠀⠀⠀⡀⠀⠀⠀⣼⣿⣿⣿⣿⡓⠀⢠⠛⢿⣿
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠙⠀⢀⣤⣄⡀⠀⣼⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⢀⡟⠀⠀⠈⠆⠀⠀⠠⡀⢀⣴⠃⠀⠀⣼⣿⡿⠻⣿⣿⡇⠀⠸⠀⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⡿⣯⣴⣾⣿⡟⠁⠀⠘⣿⣷⠀⠀⣴⡄⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⠻⢿⡟⠀⠘⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⠈⠉⢸⣿⣿⣿⣿⣿⣿⠟⠉⠻⣿⡿⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠻⠋⠀⠀⠀⠀⠀⠿⠀⠀⢻⣷⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⠀⠀⠳⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⡟⠀⠀⠀⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣭⢀⣤⣠⣄⣤⣤⢠⣤⡀⣠⣤⣀⣤⡄⣤⣄⣠⣤⣠⣤⡄⢠⣄⣬⣩⣤⣠⣤⡄⢠⣤⢠⣤⣠⣤⣀⣤⢠⣄⣤⣄⣠⣄⣠⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣠⣤⡀⠸⡇
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⡿⣿⣿⣿⢽⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣼⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠁
⡿⠿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣆⣉⣉⠉⠉⠉⠈⠉⠉⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀
[16A⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⡆⣲⣶⢲⠶⠶⠶⠖
⠀⠀⠀⠉⠉⠉⣩⣭⣭⣿⣿⣿⣿⣿⣿⠏⢉⣩⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⣿⣿⣿⣿⣶⣦⣩⣿⣿⣷⣧⡀⣀⣤⣴⣶⣶
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣄⡀⠀⠀⢨⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⠟⠛⠻⣿⣿⠉⠀⠀⠀⠘⢿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠈⠻⣿⣿⠟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⣴⡀⣼⣿⡟⠀⠀⠈⢿⣿⣲⣠⣼⣿
⠀⢠⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠁⢀⣀⣼⣯⣀⣉⡛⠿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⡿⠋⠁⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠀⠘⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⠿⠭⠿⣿⡿⠅⠀⠻⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⣿⡄⣄⣀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣟
⠀⢀⣀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠙⣿⣿⣿⡟⠛⣿⣿⠟⠁⣠⣴⣶⣿⣷⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⢠⡌⢿⣿
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⢸⣿⣿⠀⢠⣿⡏⣠⣾⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⣦⡀⠀⢀⣺⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⠹⣿⣿⡇⠀⠀⠸⣿⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠸⣿⣿⣶⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠈⢒⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⢰⠿⣿⣷⠀⠀⠀⠙⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠼⠸⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⢻⣿⣿⣷⠀⠀⣻⣿⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣄⠀⣀⣤⣿⣿⣿⣿⣿⠟⠋⠉⠉⠉⠈⠉⠛⣯⣿⠀⠀⠀⢿⣿⣿⣿⣿⡿⠀⠀⠈⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⣿⡟⠁⠀⠀⠘⠃⠀⠀⢀⡄⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣭⢉⣤⣠⣄⣤⣬⢠⣤⡁⣠⣤⣀⣤⡀⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣠⣤⣨⣤⡄⢠⣤⢠⣤⣠⣤⣀⣄⢠⣄⣤⣄⣠⣄⣠⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣠⣤⡁⠀⠀
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⢸⣿⡿⣿⣿⣿⢹⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣸⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀
⠿⠿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣀⠉⠉⠉⠉⠉⠈⠉⠈⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀
[16A⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠖
⠀⠀⠀⠉⠉⠉⢛⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠈⠉⠀⠉⠁⠈⠉⠁⢈⣩⣬⣭⣥⣽⣿⣯⣿⡅⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣀⣀⡀⠈⠉⠉⠉⠉⠉⠉⢁⣠⣴⣶⣶
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣆⠀⠀⠀⢰⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣤⣤⣤⣴⣿⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢠⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣦⣤⣼⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡿⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⠉⠈⢀⣿⣿⣿⣿⣿⣦⠈⣿⣿⣿⣿⣿⣿⣿⣿⣷⣠⣼⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠘⣿⣿⣿⣏⡉⢻⣏⣁⣠⣿⣄⡀⣸⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠶⠛⠛⠀⠹⣿⣿⡿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠿⠿⣿⠟⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠈⠋⠁⠈⠏⠰⢿⣿⣿⠟⠻⠋⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠠⣀⡀⠀⠘⠿⠛⠡⣿⠃⠀⠀⠀⠀⠀⠈⠉⠁⠙⢿⣿⣿⣟
⠀⢀⣀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⠀⠘⣿⣿⡄⠀⠀⢈⠿⠋⠉⠙⣿⡏⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠙⠁⠀⠀⢀⣈⠉⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣿⡇⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠈⢿⣿
⣴⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣾⣿⡟⣿⣷⠀⠄⠘⠀⠀⠀⣼⡿⠀⢀⣤⣶⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣦⣄⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣴⣿⣿⣿⢿⣿⣦⠀⠀⠀⠀⠀⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠈⠩⠀⠀⠀⠀⢠⣾⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠰⡆⠀⠀⠀⣤⣿⣿⣿⣿⣿⢸⣿⣿⣧⠀⠀⠀⠠⣤⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⢀⣾⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣟⣁⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠁⠀⠀⠀⠀⠀⡇⠀⢀⠔⣿⣿⣿⣿⣿⡇⠘⠙⣿⣿⡆⠀⠀⠈⠿⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣶⣴⣿⠟⠿⠿⠟⠁⠀⠀⠀⠙⠛⠿⠿⢿⠋⠈⠀⢸⣿⣿⣿⣿⣿⠏⠉⠻⣿⣿⢿⣏⠀⠀⠀⠀⠀⠀⢹⡀⠀⠑⢸⣿⣿⣿⣿⡇⠀⠀⠻⣿⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣭⢉⣤⣠⣌⣭⣭⢡⣤⡀⣠⣤⣀⣤⡄⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣠⣬⣩⣭⡄⢠⣤⢠⣤⣠⣤⣀⣤⢠⣄⣤⣄⣠⣄⣠⣤⣠⡄⣠⣤⢩⣥⣤⣠⣄⠀⣤⣤⣠⣤⡀⠀⠀
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣿⢸⣿⡿⣿⣿⣿⢹⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣸⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀
⡿⠿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣶⣧⡀⠉⠉⠉⠉⠉⠈⠉⠈⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀
[16A⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠒
⠀⠀⠀⠉⠉⠉⣉⣯⣽⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠈⠁⠀⠉⠀⠈⠉⠀⣈⣁⣈⠉⣁⣭⣭⣬⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣧⣤⣀⡀⠉⠉⠉⠉⠉⠈⢀⣠⣴⣶⣶
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⣶⣾⣷⣶⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⢰⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⠀⠀⢀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢿⡿⢿⡿⣿⣿⡿⢯⡀⠈⠿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⣿⠛⠻⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⡼⠀⢹⣿⠛⠀⢀⣦⠀⣿⣿⡟⠀⠀⠈⢿⣿⣲⣠⣼⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⡛⢻⣿⣧⣀⣠⡿⣦⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠃⠀⠘⡏⠀⠐⣼⡿⠚⠛⠛⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⢻⣷⣄⠀⠀⢀⡀⠀⠀⠈⣿⣿⡿⠀⠀⠸⣿⣿⣿⡿⠛⠻⠀⠻⣿⣿⣿⡿⢟⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠃⠀⠠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣟
⠀⢀⣀⡀⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣀⣹⣿⣿⣿⡿⠗⠂⠀⠘⠿⢿⠇⠀⠀⠀⠈⠙⣻⡁⠀⠀⠀⠀⠉⠻⠛⠛⠉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢈⣴⣶⠘⠀⠀⠀⠀⠀⣿⠷⣼⣷⣦⣤⣀⡀⠀⠀⠀⠀⢸⣿⣿
⣴⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⠻⠿⠏⠘⠄⠚⣰⣿⣶⣤⡀⠀⢀⣤⣶⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣶⣤⡀⠀⠀⠀⣰⣿⣿⣿⣿⣦⣴⡄⠀⠀⠀⢀⣴⣿⡯⣏⢻⣿⣿⣆⠀⠀⠀⠘⢿⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣶⣴⣾⣿⣿⣿⣿⣿⣿⡿⠁⠠⠀⣴⣿⣿⣿⣻⡿⠀⣿⣿⣿⣆⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠿⣿⣿⣿⣿⣿⣿⠇⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⢸⣿⣿⣿⠟⠀⠀⠁⠻⣿⣿⠀⠀⠆⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⠿⠛⠁⠀⠀⠀⠙⠛⠿⠿⣿⡿⠀⠀⠀⣿⣿⣿⣿⣿⠏⠉⠛⠿⣿⣿⣿⡿⠟⠉⠁⠀⠀⢸⡀⠀⠀⠀⠹⣿⣿⠁⠀⠀⠀⠈⠻⣿⠀⠀⢀⡆⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣭⢉⣥⣠⣍⣭⣭⢠⣤⡀⣠⣤⣀⣤⡄⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣠⣬⣩⣭⡄⢠⣤⢠⣤⣨⣭⣁⣄⢠⣄⣤⣄⣠⣄⣠⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣠⣤⡈⢿⠀
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⡿⣿⣿⣿⢹⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣸⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠘⠀
⡿⠿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣧⣀⠉⠉⠉⠉⠉⠈⠉⠉⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⣁⣈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀
[16A⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣴⣤⣴⠲⠖⠀⠀
⠀⠀⠀⠉⠉⠉⣩⣭⣽⣿⣿⣿⣿⣿⣿⣯⣭⣭⣉⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣤⣤⣵⣾⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣶⣶⣍⠉⠉⠙⢿⠍⢃⣠⣴⣶⣶
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⡆⠀⠀⠀⢰⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⠻⠛⠃⠀⠀⢻⣿⣿⣿⣧⠀⠀⢀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠁⠨⠆⠀⠀⠀⠀⠉⣿⣿⡿⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⣿⡁⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠳⢣⠀⠀⠀⠀⢀⣸⣶⣾⣿⣿⠃⠀⠀⠈⢿⣿⣷⣠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠁⢨⠙⠃⠉⠙⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⡙⣿⣿⣤⣶⣟⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣕⣤⣤⣴⣶⣀⣴⣿⣿⣿⠃⠉⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⢿⣷⣶⣶⡿⢷⣤⢀⣼⣿⣿⣿⠁⠀⠀⠻⣿⣿⣿⡟⠙⠿⠙⣿⣿⣿⣿⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣟
⠀⢀⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣯⣻⣿⠃⣈⣉⠛⠓⠀⠀⠀⠀⠈⣩⣿⣅⣀⠀⠀⠀⠉⠛⠛⠋⢡⣶⣶⣤⣀⠀⠀⠀⠀⠀⢰⣆⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⣿⣷⣄⠀⠀⠀⢸⢿⣿
⣴⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣟⠛⠿⠿⠛⠃⣴⣿⣿⣿⣦⣄⠀⣠⣾⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⡀⠀⠀⠈⠀⠈⠉⠛⠙⠛⠛⢛⣿⣿⣧⣿⠄⢹⣿⣿⣧⠀⠀⠸⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⣠⡄⣀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠁⠀⠀⠈⣿⣿⣧⠀⠀⣴⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠛⠻⢿⣿⣿⣿⣿⣿⠣⠀⠘⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⡿⢠⣿⣿⡟⠀⠀⠀⢀⠀⠀⠀⠻⣿⡟⠁⠀⠀⠀⠀⠘⢻⣿⠀⠀⢻⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠋⠛⠁⠀⠀⠀⠀⠉⠿⠟⠿⣿⢿⠀⠀⠀⣿⣿⣿⣿⣿⠃⠀⣈⣿⠃⠀⣠⣿⣿⡿⠇⠀⠀⠀⡎⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠘⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣭⢀⣤⣠⣍⣥⣤⢠⣤⡀⣠⣤⣀⣤⡄⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣠⣤⣨⣥⡄⢨⣭⢩⣤⣠⣤⣌⣭⢠⣄⣤⣄⣠⣄⣠⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣠⣤⡀⠀⢻
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⢸⣿⡿⣿⣿⣿⢽⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣼⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀
⡿⠿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⡟⢿⡀⠉⠉⠉⠉⠉⠈⠉⠉⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⢉⣡⡈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀
[16A⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⠀⠀⠀⠀⢀⢶⠶⠖⠒
⡿⠋⠀⠉⠉⠉⣩⣭⣭⣿⣿⣿⣿⣿⣿⠋⢉⣉⣉⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠈⠉⠀⠀⠀⠀⢛⣠⣴⣶⣶
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⡿⠙⠿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠉⠁⠀⢀⠀⢸⣿⣿⣿⣗⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⢛⡛⠣⣰⣶⡄⠉⠁⣿⣿⣿⣿⣷⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⣿⣿⣿⣿⣿⣿⡟⠻⠉⣿⣇⠀⢈⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠦⣹⣿⣿⣿⡇⠀⠀⠙⣿⣿⣿⣿⣿⣆⠀⠈⢿⣿⣶⣠⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣄⠀⠈⠀⡉⠛⠉⠉⢻⣿⣿⡿⠀⠀⣿⣿⣿⣿⣷⡌⢿⣶⣾⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠙⠻⣿⣿⣿⠁⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠻⢿⣷⣶⣞⣿⣦⡄⢀⣾⣿⣿⠇⠀⠀⠙⠿⣿⡟⠀⠁⠈⢿⣿⡋⣉⣹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡷⠀⠠⠀⠀⠀⠀⠀⠘⠿⣦⡄⠀⠙⣿⣿⣿⣟
⠀⢀⣀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣤⣾⣿⣏⣙⠉⣿⡏⢉⣉⠛⠛⠀⠀⠀⠀⣀⣤⣾⣦⣤⠀⠀⠈⠉⠀⠀⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⡿⠁⠀⠀⢀⣤⣄⠀⡀⠀⠀⣿⣿⣦⠀⠀⠿⢿⣿
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⣿⣛⡛⠍⣠⣿⣿⣿⣦⣄⢀⣴⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⣹⣿⣿⣿⣿⣿⡟⠀⠀⠀⣤⣼⣿⠟⣴⠁⠀⠀⠉⣿⣿⣄⠀⠀⣤⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠉⠋⡾⠃⠀⠀⠀⠀⠐⠿⣿⠀⠀⢻⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠋⠉⠉⠙⠻⣿⣿⣿⣿⣿⣿⠓⠀⠘⠁⠙⢿⣿⣿⣿⡛⠛⠻⠛⠉⠸⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⢿⡿⢛⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣦⣄⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡟⠉⣭⢁⣤⣠⣄⣤⣤⢠⣤⡀⣠⣤⣀⣤⡄⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣠⣤⣠⣤⡌⢩⣭⢩⣥⣠⣤⣀⣄⢠⣄⣤⣄⣠⣄⣠⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣠⣤⡀⠀⠀
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡀⠀⠀⣿⢸⣿⡿⣿⣿⣿⢽⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣼⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀
⡿⢿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣷⡀⠉⠉⠉⠉⠉⠈⠉⠈⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀
[16A⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣦⣤⡄⠐⠀⠀⢠⣴⠶⠶⠖⠒
⠀⠋⠀⠉⠉⠉⣩⣭⣭⣿⣿⣿⣿⣿⣿⣏⣉⣭⣉⣉⣉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⡆⠀⠘⢃⣠⣴⣶⣶
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣦⡁⠀⢰⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⢰⣿⣿⣿⣹⠋⠉⡀⠉⠹⡿⣿⣿⡟⠋⢿⣿⡿⠁⢀⣿⣿⣿⣿⣿⣿
⣇⣀⡀⠀⠀⡀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠸⠿⣿⣷⡟⠀⠀⠀⠁⠀⢾⡹⠿⠏⢀⢎⡟⠁⠀⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣆⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠈⢿⣿⣿⡿⠉⠀⢹⣿⡙⠀⢹⡉⠙⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠈⢼⠁⠀⠀⠀⠀⠀⣸⡁⠀⠀⠈⠟⠀⠀⠀⠈⢿⣿⣶⣠⣼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡉⠛⠛⠻⢿⣿⠿⢿⣿⣿⣿⠇⠀⠘⢿⣿⠟⢱⣶⣿⣿⣿⣶⣿⢻⠁⠿⠛⣿⠁⠀⠀⠀⠀⠀⠀⠸⢛⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⢀⡀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⣧⣀⡀⢠⡄⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢻⣉⣉⣙⣿⣟⢀⣀⣀⣠⣿⣿⡀⠀⠀⠀⠀⠀⠀⠺⢆⠀⠀⠀⠀⠀⠀⠈⠋⠀⣸⡇⢀⠈⠳⢳⣦⡀⠙⣿⣿⣿⣟
⣿⣿⣿⣿⣿⠿⠻⣽⣿⣿⣿⣿⣿⣿⣷⣦⡾⣿⣿⢿⠿⠛⠂⠀⢸⠿⣿⠀⠀⢀⣠⣴⣾⣿⣦⠀⠈⠋⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⡄⡈⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠍⡼⠀⠀⣿⢿⣷⠀⠀⣿⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠙⠁⠤⠀⠀⠀⣼⣿⣷⣄⠀⣴⣿⣿⣿⣿⣿⣿⣇⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠜⠙⢧⣴⠃⠀⠀⠀⠸⣿⡀⠀⠀⣀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠋⢳⣆⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠛⢧⠀⠀⢻⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠠⠟⠙⠓⠠⣶⡀⠉⠙⠛⠻⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠩⠟⢻⠀⠀⠀⠀⠀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠖⠀⣤⢀⣤⣠⣄⣤⣤⢠⣤⡀⣠⣤⣀⣤⡄⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣠⣤⣠⣤⡄⢠⣤⢠⣤⣠⣤⣀⣄⢠⣄⣤⣄⣠⣄⣠⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣠⣤⡀⠀⠀
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⡇⠀⣿⢸⣿⡿⣿⣿⣿⢽⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣸⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀
⡿⠿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣄⠉⠉⠉⠉⠉⠈⠉⠈⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀
[16A⠶⣶⣶⣐⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⡠⣶⣶⡆⠀⠀⠀⠀⢰⠶⠶⠒
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠈⠁⠀⠉⠀⠈⣭⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣶⣆⠀⠐⠻⠿⠿⣧⠀⠀⢰⣿⣦⣴⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⣤⣴⣿⣶⣶⣶⣶⣤⣄⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢠⣤⣶⣾⣤⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣿⣿⡟⠹⣿⡿⠿⢿⣿⣿⠛⢿⡿⠆⠀⣸⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿
⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⠉⠉⢹⣟⠹⠟⢿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠉⠙⠀⢀⠇⠀⠀⠀⠁⢹⡆⠀⠀⠀⢠⣿⣿⡟⠈⠘⢿⣿⢲⣠⣼⣿
⠀⠘⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠙⠏⢰⣶⣿⣿⣶⣶⡿⣪⠙⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⡤⡼⠀⠀⠀⠀⢠⣾⣧⠀⠀⠀⠀⢿⠏⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠛⠻⢿⣿⣿⡿⣿⣿⣿⡿⠁⠀⠀⠀⠐⣿⢸⣿⣿⣿⠁⠈⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠉⠻⠗⠀⠇⠀⠃⠀⠀⣲⣄⠀⠙⣿⣿⣿⣟
⣾⣿⣿⡿⠿⠛⠁⠀⠀⠉⢹⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠈⣿⡿⠀⣀⣤⣶⣶⣆⠀⠉⣿⣿⠏⠀⣤⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⠂⡀⠀⠀⣿⣿⡇⠀⠀⠘⢿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠘⠂⠀⠀⣸⣏⣤⣾⣿⣿⣿⣿⣿⡀⠀⢠⣿⡀⣸⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⠃⣰⠃⠀⠀⠋⢻⣧⠀⠀⢀⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠽⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄⠘⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠏⣰⣇⠀⠀⠀⠀⢩⣿⠀⠀⠸⢀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠓⠗⠀⣹⣿⣿⣿⣿⠿⠛⢿⣿⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⢿⡿⠁⠀⠀⠀⠀⠀⡄⠀⠀⢸⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠈⠉⠛⠛⠿⠯⠅⠀⠀⠘⠀⣿⣿⣿⣿⠟⠀⠀⠀⠉⠀⠈⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣤⢀⣤⣠⣄⣤⣤⢠⣤⡀⣠⣤⣀⣤⡀⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣠⣤⣠⣤⡄⢠⣤⢠⣤⣠⣤⣀⣄⢠⣄⣤⣄⣠⣄⣠⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣠⣤⡀⠀⠀
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⡿⣿⣿⣿⢹⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣸⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀
⠿⠿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣄⣉⡉⠉⠉⠉⠈⠉⠈⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣩⠁⠀
[16A⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠲⣶⣶⣶⡆⠀⠰⠶⠶⠒
⠀⠀⠀⠉⠉⠉⣭⣭⣭⣿⣿⣿⣿⣿⣿⠋⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⣠⣬⣷⣾⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣶⣄⠀⠀⠀⠀⠀⠈⠹⣿⣿⣟⠁⢀⣠⣴⣶⣶
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⣰⣦⣍⣿⡿⣰⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣤⣤⣤⣤⣶⣶⣶⣶⣤⣄⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⢻⣿⣿⡀⠀⠀⠀⠁⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡏⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠋⣟⣿⣟⠛⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⠏⠐⢶⡀⠛⠛⠁⠀⠀⠀⠀⠀⠈⢿⣿⣶⣠⣼⣿
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣜⢷⣤⣴⣿⣿⣤⣤⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⣺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠃⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠁⠘⡿⠻⠛⠻⣿⡟⢻⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⠀⠐⣿⣿⣄⠀⣄⠀⣀⡞⠀⠀⠀⠀⠘⢿⣿⣿⣟
⣴⢆⣀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⡀⣾⣿⣾⣦⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣧⣤⣄⠀⠀⠂⠀⠀⠃⢀⣤⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠠⢄⡤⠀⠀⠀⠀⠀⠀⠙⠁⢠⣣⣾⠏⠻⡿⣿⣦⡀⠀⠀⠈⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡀⠀⠀⡀⠀⠀⠈⣽⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠙⠓⠄⠀⠀⠀⠀⠀⠀⣰⣿⠟⠁⠀⠀⠈⠉⢹⣷⡄⠀⠀⠀⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠈⠁⢀⣰⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣧⣤⡄⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢡⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡟⠿⡟⣥⣄⣀⠀⠋⡿⠋⠉⠈⠉⠉⠿⠿⣿⠿⠇⠀⠀⢸⣻⣿⣿⣿⣿⣿⣡⠀⠻⠿⠟⠋⠃⠀⠀⠈⠿⠀⠀⠀⣠⣿⣿⡿⠟⠻⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣭⢉⣬⣡⣄⣭⣤⢠⣤⡀⣠⣤⣀⣤⡀⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣠⣤⣡⣤⡝⢩⣤⢠⣤⣠⣤⣀⣄⢠⣄⣤⣄⣠⣄⣠⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣠⣤⡀⠀⠘
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡿⠀⣿⢸⣿⡿⣿⣿⣿⢹⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣸⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀
⠿⠿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⠚⢷⠀⠉⠉⠉⠉⠉⠈⠉⠈⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣩⠁⠀
[16A⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠖
⠀⠀⠀⠉⠉⠉⣩⣭⣽⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣀⣅⣠⣈⣠⣶⣿⣦⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⡀⠀⠀⠀⠀⠉⠉⠉⠁⠀⢀⣠⣴⣶⣶
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢠⣤⣶⣶⣶⣾⣿⣿⣷⣦⣄⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡇⣈⠛⠛⢿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠛⠻⣿⠛⠛⣿⣿⣿⣿⠁⠀⠀⢠⣾⣤⣿⣿⣿⣿⣿⡏⠁⠘⠀⣤⠀⢿⣿⡇⠀⠀⠀⠀⠈⢿⣿⣷⣠⣼⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠹⣿⣎⣀⣴⢿⣤⣤⣿⣿⣿⣿⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⡇⠀⠈⠙⣻⣟⣹⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠙⠇⠙⠿⢿⠿⠟⠻⠿⣿⣿⡿⠁⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢰⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣟
⠀⢀⣀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢻⣿⣿⣿⠀⠀⠀⠈⠉⠙⢿⡟⠁⠀⣀⣀⠀⠀⠀⠀⠀⠦⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠙⠿⠃⣸⣿⢘⠳⣶⣶⣄⠀⠀⠀⠈⢿⣿
⣤⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⠿⠋⠒⠀⠐⠂⠀⠀⠀⣠⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣦⣀⠀⠀⠀⠘⠿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⢨⠀⠀⠸⢿⣷⣄⠀⠀⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠈⠀⠀⠀⠀⣀⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⢛⣠⣶⣴⠯⡿⢧⡇⠀⠀⠀⠸⢿⣿⡆⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⢸⡄⣮⣯⣽⠉⠉⠉⠀⢰⡇⢼⠇⠀⠀⠀⠀⠀⠻⠧⠀⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡶⠿⣿⡿⠏⠉⠉⠉⢻⣿⠿⡿⠟⠃⠉⠀⢸⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⣹⠃⠿⠿⠃⠀⠀⠀⠀⠀⠇⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣭⢉⣥⣠⣄⣤⣭⢠⣤⡀⣠⣤⣀⣤⡄⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣠⣤⣠⣤⡄⢨⣭⢩⣭⣩⣥⣀⣤⢠⣄⣤⣄⣠⣄⣠⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣠⣤⡀⠀⠀
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⢸⣿⡿⣿⣿⣿⢹⢼⠇⣙⢿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣸⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀
⠿⠿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣷⣀⣉⣉⣉⡉⠉⠈⠉⠈⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⢁⣌⣉⣉⣉⡙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀
[16A⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢐⠒⠶⢦⣤⠐⠒
⠀⠀⠈⠉⠉⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠀⠁⠀⠈⠁⠀⠉⠀⠈⢉⣀⣈⣁⣨⣽⣷⣿⣭⣨⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⡄⠀⠉⠉⠉⠁⣧⣀⣀⣨⣿⣶⣶
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣶⣶⣶⣶⣶⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⠟⠛⢿⣿⣿⣿⣷⡆⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠁⠀⢤⠈⠉⢻⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⠛⠛⣿⣿⣿⡏⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⣶⣶⢸⣿⣿⠇⠀⠀⠀⠈⢿⣿⣦⣠⣼⣿
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡿⣿⣟⠛⠻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⣿⣍⢁⣸⣿⣤⣠⣿⣿⡟⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣹⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⠃⢸⣿⣇⡀⠀⠀⠀⠈⠁⠈⢿⣿⣿⠛⠛⣿⣿⡏⠙⠇⠀⠿⢿⡿⢿⠟⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡿⢠⣾⣿⣿⣧⠀⢀⣀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣟
⠀⢀⣀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣀⣀⣈⣿⣿⣿⡛⠓⠀⠀⢀⣾⣿⠇⠀⠀⠀⢉⣁⡀⠀⠀⠀⠀⠒⠀⠀⣆⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣷⣿⣿⣿⣿⠟⠁⣿⡇⠈⠛⠿⣷⣦⡀⠀⠀⠈⢿⣿
⣴⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡯⠘⠈⠀⠀⠀⠀⣠⣼⣿⡛⠀⢀⣴⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⣾⣿⡇⡇⠀⠀⠿⢻⣷⣄⠀⠀⠀⣸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⢀⣴⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡵⠁⠀⠀⠀⠘⢻⣿⣦⠀⠀⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⢸⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⠙⢑⠼⠁⠀⠀⠀⠀⠀⠀⠈⠻⡇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⢿⣿⠟⠉⠀⠀⠈⢻⣿⣿⢿⡿⠅⠁⠀⣽⡿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⠿⢿⠿⠿⡟⠙⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣭⢉⣭⣠⣌⣭⣭⢡⣤⡀⣠⣤⣀⣤⡀⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣠⣤⣠⣤⡍⢩⣭⢩⣭⣩⣭⣉⣄⢠⣄⣤⣄⣠⣄⣠⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣠⣤⡀⠀⠀
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⡿⣿⣿⣿⢹⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣸⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀
⠿⠿⣿⣿⣿⣿⣿⣿⡿⢾⣿⣿⣾⣷⣀⡉⠉⡉⠉⠉⠈⠉⠈⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣩⠁⠀
[16A⠒⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣄⡀⢠⣠⠒⠀
⠀⠀⠀⠀⠀⠉⣩⣽⣿⣿⣿⣿⣿⣿⣿⣷⣮⣥⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣶⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣾⣿⣿⡉⠉⠉⠹⠛⢡⣤⣽⣷⣶
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢰⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⠃⠈⢻⣿⣿⣿⣿⠀⠀⢀⣿⣿⣿⣿⣿⣿
⣿⣶⣦⣄⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡇⠈⠀⠀⠉⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿
⣛⣿⣿⣿⣿⣦⡘⢿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⡿⠿⣿⣿⣿⡛⠻⡏⠹⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣄⢰⣿⣤⣿⣿⠏⠀⠀⠈⢿⣿⣶⣠⣾⣿
⣿⣿⣿⡿⠿⠛⠁⣾⣿⣿⣿⣿⣿⣿⡇⠀⠈⢁⠉⠙⠋⠉⠻⣿⣿⣿⣿⠀⠀⢾⣿⣿⣿⣏⠀⣀⣠⣿⣧⣤⣴⣷⠰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠈⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠛⠉⠀⠂⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⠿⣷⣶⣿⣷⣤⣄⣴⣾⣿⣿⣿⡏⠀⠀⠈⠻⠿⣿⠁⠀⠘⠿⢭⣟⢿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢠⣤⢠⣀⣀⣀⠀⠀⠘⣿⣿⣿⣟
⠀⢀⣀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣤⣿⠉⢉⠉⠻⠏⠉⣉⣉⡛⠛⠀⠀⠀⠀⢀⣠⣴⣦⡄⠀⠀⠈⠉⠙⠋⣴⣶⣶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠛⢿⣿⣿⣿⣿⣿⣥⣾⡟⣮⠈⠛⣿⣷⣄⠀⠀⠘⢿⣿
⣴⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⣿⣿⡂⠌⠀⠀⠀⣼⣿⣿⣿⣷⣄⡀⣠⣾⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⢿⠛⠀⠀⠀⠽⠿⣿⣿⣿⣿⢧⠇⠀⠀⠙⢿⣿⣧⡀⠀⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢹⠀⢀⡷⠀⠀⠀⠘⢿⠟⣡⠞⠀⠀⠀⠀⠈⠹⢿⣷⣄⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⢿⣿⣿⣿⣿⣿⡏⠆⠀⠙⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢸⡀⢸⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠉⠀⠀⠀⠀⠘⠟⠛⠿⠿⡇⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠿⣿⣿⣿⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣭⢁⣤⣠⣌⣭⣤⢡⣤⡀⣠⣤⣀⣤⡄⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣠⣤⣠⣤⡄⢨⣭⢩⣥⣠⣤⣀⣤⢠⣄⣤⣄⣠⣄⣠⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣠⣤⡀⠀⠀
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⢸⣿⡿⣿⣿⣿⢽⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣸⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀
⡿⠿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⢿⣷⡀⠉⠉⠉⠉⠉⠈⠉⠈⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀
[16A⠶⢶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣀⣀⠀⠀⠀⠀⠀
⠀⢠⠀⠀⠉⠉⣭⣭⣽⣿⣿⣿⣿⣿⣿⣏⣈⣁⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠸⢗⣶⣶⣶⣶
⠀⣿⣷⣄⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣭⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⣿⣿⣿⣷⠀⢰⣾⣿⣿⣿⣿
⠀⢻⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢻⣿⣿⣿⡟⢀⣿⣿⣿⣿⣿⣿
⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠛⠿⠛⠋⠁⣾⣿⣿⣿⣿⣿⡇⠀⠈⢻⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠸⣿⣿⣿⡟⠛⠻⣿⠟⠻⠿⣿⠿⢿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡏⢰⣿⣠⣾⣿⠟⠀⠈⢿⣿⣷⣠⣼⣿
⠀⠀⠀⠀⠘⣿⠟⠋⠹⣿⣿⣿⣿⣿⠀⠀⢈⣀⠀⠛⠈⠉⢻⣿⣿⣿⡿⠀⠀⠀⠈⢻⣿⣧⣀⣴⣿⣦⣀⣴⣿⣰⠂⠹⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣶⠟⠁⠀⠉⠁⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⢿⣷⣟⣛⣶⣤⣤⣶⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⠏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠸⠀⣰⡆⠠⣤⣄⣀⠀⠀⠘⢿⣿⣿⣟
⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣾⠏⢉⡉⠈⠛⠉⢈⣉⣉⣛⠃⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢀⣶⣿⣿⣿⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡜⠀⠀⢀⣴⣿⡇⡯⠈⠉⣿⣷⣄⠀⠀⠘⢿⣿
⣴⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣟⠒⠂⠀⠀⣠⣾⣿⣿⣿⣷⣦⡀⣠⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⢀⣼⣿⠟⣴⠋⠀⠀⠋⣿⣿⣧⠀⠀⠀⠸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢾⣿⠧⠒⠀⠀⠀⠈⢿⣿⣷⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠉⠁⠤⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⠟⠉⠻⣿⠟⠻⢟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢚⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣬⢉⣤⣠⣄⣤⣤⢠⣤⡀⣠⣤⣀⣤⡄⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣠⣤⣠⣤⡄⢠⣤⢠⣤⣠⣤⣀⣄⢠⣄⣤⣄⣠⣄⣠⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣠⣤⡀⠀⠀
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⠋⠀⣿⢸⣿⡿⣿⣿⣿⢹⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣸⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀
⠿⢿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣾⣄⡀⠉⠉⠉⠉⠉⠈⠉⠈⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀
[16A⠶⣶⣦⣶⣶⢲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡖⣶⣶⣶⣶⣶⠂⠀⠀⠀⠀⠀⠀⠒
⠀⠀⢸⣿⣿⠝⣛⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣉⣉⠉⠉⠈⠀⠀⠈⠁⠀⠉⠀⢈⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣦⣄⠀⢀⣠⣴⣶⣶
⠄⠀⢸⣿⡿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢰⣿⣿⣿⣿⣿
⠀⠀⠈⠙⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣻⣄⢻⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿
⠀⡴⣆⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣄⠈⠛⢿⠟⠛⢻⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣿⡁⢨⣿⣿⠏⠈⢿⣿⣢⣠⣼⣿
⣶⣿⣿⣷⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⠀⠀⠙⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⢰⢠⣼⣿⣄⣀⣽⡝⠻⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⢡⠟⠓⠿⠟⠋⠀⠀⠈⣿⣿⣿⣿⣿
⣽⣿⣿⣿⣿⣿⠟⠁⡲⢻⣿⣿⣿⣿⠿⣧⣤⣤⣶⣀⠀⠀⠀⣸⣿⣿⡿⠻⣿⣧⠀⠀⠀⠀⠹⠋⠿⢿⣿⡿⠃⠃⠈⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡘⠀⠸⠀⣤⡀⣀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣟
⣿⣿⣿⡟⠋⠁⠀⠠⣶⣾⣿⣿⣿⣿⣤⣿⠛⠷⠷⠉⠛⠀⠘⢻⣿⣿⠁⠀⠹⣿⠆⠀⣶⣶⡀⠀⠉⠙⠏⠁⢀⣴⣿⣿⣿⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠃⠀⢀⣠⣿⡇⡏⠿⣿⣶⡀⠀⠀⠀⠈⢿⣿
⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣇⠀⠒⠀⠀⠀⢀⣾⣿⣿⣶⣄⠀⣠⡿⠇⠀⣿⣿⣷⡀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢀⠀⠰⠀⠀⢀⣾⣿⡿⣸⠇⠀⣸⣿⣿⣄⠀⠀⠀⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⢈⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢀⣾⣿⣿⣿⡆⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣸⣿⣿⣿⡏⡀⠀⠈⢹⣿⣿⡄⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠛⠛⠿⠿⠿⠿⠿⠿⠛⠋⠉⠉⠂⠺⣿⣿⣿⣿⠐⠛⠘⣿⣿⣿⣿⣿⣿⠏⠉⠻⠿⠛⠛⠊⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠿⠃⠀⠀⠈⣿⣿⣿⡆⠀⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⠋⠙⠿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠻⠿⠂⠀⠘⣿⣿⣏⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠇⠀⠀⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣤⢀⣤⣠⣄⣤⣤⢠⣤⡀⣠⣤⣀⣤⡀⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣡⣬⣠⣤⡄⢠⣤⢠⣤⣠⣤⣀⣄⢠⣄⣤⣄⣠⡄⣠⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣠⣤⡀⠀⠸
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⣿⢸⣿⡿⣿⣿⣿⢹⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣺⣿⣸⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀
⠿⢿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⡀⠀⠀⠉⠉⠉⠉⠉⠈⠉⠈⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣩⠁⠀
[16A⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠖⠒
⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⠏⠈⣡⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣍⡉⠉⠁⠀⢀⣠⣴⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣷⣶⣦⣄⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣰⣾⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠉⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠉⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠙⣿⣿⠟⠛⢻⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢿⣿⣷⣠⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠁⠀⣤⣼⣿⣦⣤⣼⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⠟⡋⣹⣿⣿⣿⣿⣿⡿⠃⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢿⣯⣿⣿⣿⡟⠙⠉⠿⢿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⢸⠃⢠⠀⢺⠋⣀⠀⠀⠁⠀⠀⠀⠀⠘⢿⣿⣿⣟
⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⣼⣿⡟⠀⠀⣠⣴⣾⣿⣦⠀⢻⣿⣿⣿⣀⣴⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠔⣂⠀⠀⠀⠀⠀⡘⠀⡆⠀⠈⢀⣿⣿⣶⣦⣤⡀⠀⠀⠀⠀⠈⢿⣿
⣴⣿⣿⣿⣿⣿⣿⣶⣶⣿⣆⡀⣳⣸⣿⣿⣿⣿⣿⣿⣿⠁⠀⢀⣴⣿⣿⡀⣠⣾⣿⣿⣿⣿⣿⡄⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠙⠀⠀⠀⢠⠀⡧⣰⠀⠀⣾⣿⣿⣿⣟⢿⣿⣿⡄⠀⠀⠀⠀⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠈⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠨⡄⠀⠟⢸⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⡀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠈⠛⢿⠟⠛⠛⠻⢿⣿⣿⣿⣿⣿⠁⠙⠀⠀⠀⠀⠈⠙⢿⠋⠉⠻⣿⠿⠿⢿⡆⠀⠀⠀⠀⠀⠛⠀⠀⠀⠙⢻⣿⣿⣿⣿⠎⠉⣿⣿⣧⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⠇⠀⠀⠀⢀⣀⡀⣠⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠟⠁⠀⠈⣿⣿⣿⡆⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣤⢀⣤⣠⣄⣤⣤⢠⣤⡀⣠⣤⣀⣤⡄⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣠⣤⣠⣤⡄⢠⣤⢠⣤⣠⣤⣀⣄⢠⣄⣤⣄⣠⣄⣠⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠈⣭⣭⣡⣤⡀⠀⠀
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⢸⣿⡿⣿⣿⣿⢹⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣸⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀
⠿⠿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣷⣄⡉⠉⠉⠉⠉⠈⠉⠉⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀
[16A⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠒
⠀⠀⠀⠉⠉⢉⣭⣭⣿⣿⣿⣿⣿⣿⣿⠏⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣠⣤⣵⣶⣿⣿⣿⣿⣷⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣶⣶⣦⣈⠉⠉⠉⠁⠈⢀⣠⣴⣶⣶
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡀⠀⢰⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣤⣶⣿⣿⣿⣿⣿⣷⣶⣶⣄⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣟⠁⣾⣽⣿⡿⠛⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣾⣿⣿⣿⡏⠀⠀⢹⣿⣿⡿⠉⢿⣿⣶⣠⣾⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⡿⠀⢁⣸⣿⣀⣀⡽⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏⢹⣿⣿⣿⣷⣿⣆⣼⣿⡿⠃⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡏⠛⠿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠀⠹⠈⢿⣿⡿⠿⣿⣿⠇⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⣠⣤⣤⠠⢾⡟⠀⢸⣿⣿⣿⣿⣿⡏⠛⠁⠀⠀⠀⠀⠘⢿⣿⣿⣟
⠀⢀⣀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠁⠀⣀⣾⣿⡆⠉⠛⠻⠿⢿⠿⠛⢻⣿⡟⠉⢀⣠⣤⣀⠀⠀⠱⠀⠀⠐⢃⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⣶⢃⠈⣽⣷⡎⠀⢀⣿⣿⣿⣿⣿⣿⣷⣦⡀⠁⠀⠀⠀⠀⠀⠈⢿⣿
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⡀⠀⠀⠀⠀⠀⠀⣸⠛⣠⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠟⠷⠀⠀⠁⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠙⠁⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⣰⣿⣿⠿⠟⠛⠻⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⢸⣈⠿⣿⠟⢻⣿⣿⣿⣿⡆⢿⣿⣿⡀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⢠⣼⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡟⣥⠀⠰⠟⠉⠀⠀⠀⠀⠀⣹⣿⣿⣿⣷⠀⠀⠀⠀⠀⠘⡄⠀⢸⣦⠸⣿⣿⣿⣿⡇⢹⣿⣿⣇⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢛⡃⣀⣀⣀⠈⠉⠉⠀⠀⠀⠀⠉⠉⡿⠿⠿⠿⠇⠀⠀⠀⠀⠀⢀⣀⡠⠀⠀⠙⠿⠿⠛⠯⠀⠀⠀⠀⠀⠀⣧⠀⠀⠁⠄⢿⣿⣿⣿⠇⠈⣾⣿⣿⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⣤⢁⣤⣠⣄⣤⣤⢠⣤⡀⣠⣤⣀⣤⡄⣤⣄⢠⣤⣠⣤⡄⢠⣄⣤⣠⣤⣠⣤⡄⢠⣤⢠⣤⣠⣤⣀⣄⢠⣄⣤⣄⣠⣄⣠⣤⣠⡄⣠⣤⢩⣤⣤⣠⣌⠉⣭⣤⣠⣤⡀⠀⠀
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡹⣿⡇⠀⣿⢸⣿⡿⣿⣿⣿⢹⢼⠇⣙⣿⣽⣿⡇⣿⣿⣹⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣸⡿⢻⡿⢯⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀
⡿⢿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⠚⠃⠀⠉⠉⠉⠉⠉⠈⠉⠈⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀
[16A⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠒
⠀⠀⠀⠉⠉⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠁⠀⠈⠁⠈⠉⠀⠈⠉⠀⢉⣵⣯⣭⣈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣶⣦⣄⠀⠉⠉⠉⠉⠁⠉⢁⣠⣴⣶⣶
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⢰⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣤⣶⣦⣤⣶⣾⣿⣷⣶⣤⣀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⠋⠁⠘⣿⣿⣿⣿⡏⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⡻⡿⠉⠀⠐⠀⠀⠘⣿⣿⣿⠀⠈⢿⣿⣷⣠⣼⣿
⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⡟⠑⠀⣹⣧⠀⠀⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠞⠀⠀⠀⠀⡄⢸⣇⣸⣿⡿⠃⠀⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠏⠛⠿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢶⡈⠻⣶⣾⣯⣻⣿⡿⡿⠛⠛⠁⠀⠀⠀⠀⠀⢀⣠⣄⠀⢝⢿⠀⠀⠀⠀⢰⡄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣟
⠀⢀⣀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣾⣿⣇⠀⠀⠀⠉⢻⡿⠿⢿⡿⠋⠉⠻⠿⠀⠀⠁⠀⠈⠛⠉⠁⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⠿⠿⠆⠀⠀⠆⠀⠀⣠⡟⠀⢀⣠⣴⣿⣶⣤⡀⠀⠀⠀⠀⠀⢠⣾⣿⣶⣶⣄⠀⠀⠀⠀⢸⡇⠀⠀⢲⡆⠀⢀⠀⣀⣴⣿⣤⣼⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⢀⣶⣿⣧⣴⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣦⡀⠀⠸⠁⠀⠀⡄⠁⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢀⠰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⡟⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠓⢹⣿⣿⡄⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣾⣿⣿⣿⠿⠛⠉⠙⠻⠿⣿⣿⣿⡟⠇⠃⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⡇⠀⠘⣿⣿⣿⣿⡇⠻⣿⣿⣿⡇⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣭⢉⣭⣠⣄⣤⣥⢠⣤⡀⣠⣤⣀⣤⡄⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣠⣤⣨⣭⡝⢩⣤⢨⣭⣡⣤⣀⣤⢠⣄⣤⣄⣠⣌⣠⣤⣠⡄⣠⣤⢡⣤⣤⣠⣌⠙⣥⣤⣠⣤⡀⠀⠀
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⡿⣿⣿⣿⢹⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣼⣿⣼⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀
⡿⠿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣄⠉⠉⠉⠉⠉⠈⠉⠈⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀
[16A⠲⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠖⠒
⠀⠀⠀⠀⠈⢉⣭⣽⣿⣿⣿⣿⣿⣿⣿⠏⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⣤⣄⣀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣿⣾⣿⣿⣿⣿⣆⡀⠉⠉⠉⠀⠀⢀⣠⣴⣶⣶
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⣶⣶⣶⣾⣿⣶⣶⣦⡀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢰⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠟⠻⣿⣿⣿⣿⣿⠇⠀⢀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢋⡿⢋⣉⠁⠀⠀⠘⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⠁⠀⠀⠀⠀⢠⡄⢈⣿⣿⡟⠀⠀⠈⢿⣿⣦⣠⣼⣿
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⢻⡋⠂⢀⣿⣆⠀⢘⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡈⠀⠀⠀⠀⠂⣸⠟⠊⠋⠉⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡄⠀⠀⠀⠀⠈⠉⠙⣿⣿⣿⠋⢹⣿⣿⣿⠟⢦⠈⢳⣶⣾⣍⣿⣿⡿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠈⠀⠀⠀⠀⢻⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣟
⢀⣴⣶⣄⡀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣁⣠⣽⣿⣿⡖⠛⠂⠀⠀⢰⣿⣿⠃⠀⠀⠙⠿⢿⠀⠀⠀⠀⠙⠇⠠⠥⠸⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢀⣽⡇⠀⠀⠀⠀⠀⠀⠛⢸⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠈⢿⣿
⣼⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⠀⠀⠀⠀⠀⣠⣶⣿⣝⠀⠀⣠⣴⣶⣿⣷⣦⡀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣶⣦⣀⠀⠀⠀⢸⠇⠀⢸⣿⠀⡀⢀⢀⠀⠀⢠⣴⣿⣿⣿⠙⣿⣿⣆⠀⠀⠀⠀⠀⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⣴⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣷⣄⠀⠈⠀⠀⢸⡏⠀⢡⠈⠘⠀⣾⣿⣿⣿⣿⣿⠀⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⢐⡇⠀⢘⣄⣀⣀⡘⣿⣿⣿⣟⢁⠠⢾⣿⣿⣿⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡿⠟⠉⠉⠙⠻⠿⣿⣿⡿⡇⠙⠀⢸⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣆⠀⢠⣷⣶⣿⣿⣿⣿⠇⠉⢻⣿⣿⣾⠀⠢⠛⣿⣿⡆⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣭⢉⣭⣩⣍⣭⣥⢠⣤⡀⣠⣤⣀⣤⡀⣤⣄⣡⣤⣠⣤⡄⢠⣄⣤⣠⣤⣩⣭⡍⢠⣤⢨⣭⣩⣤⣀⣤⢠⣌⣭⣍⣩⣍⣩⣤⣠⡄⣠⣤⢩⣭⣤⣠⣄⠀⣤⣭⣠⣤⡀⠀⠀
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⡿⣿⣿⣿⢽⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣸⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀
⠿⠿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣀⣉⣉⡉⠉⠉⠈⠉⠈⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⢉⡉⣉⡉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀
[16A⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣄⣰⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠖⠒
⠀⠀⠀⠈⠉⠉⣭⣭⣭⣿⣿⣿⣿⣿⣿⣯⣭⣭⣀⣉⣁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣾⣿⣿⣿⣿⣧⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⣿⣿⣿⡿⠙⢻⡄⠀⠉⠉⠉⠀⠀⢀⣠⣴⣶⣶
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⡀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿
⠀⠀⣠⣦⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠿⠋⠙⣿⣿⣿⣿⡇⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿
⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠙⠿⣟⣯⡏⠤⠀⠀⠀⠀⠙⢿⣿⣿⡗⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠠⠙⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢠⡉⠂⠀⠀⠀⠀⣰⣆⠸⠿⠿⠋⠀⠀⠀⠈⢿⣿⢶⣠⣼⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣯⠀⠉⠙⠛⠛⠛⠛⠿⣿⣿⣿⣿⠃⠀⠸⣿⣿⣿⡟⠛⠉⠉⢹⣿⡙⠀⢸⡅⣹⣿⣿⡿⠀⠀⠀⠀⠀⠀⠈⣒⠠⠈⠇⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠙⣦⣤⣤⣦⣀⠀⠀⢠⣿⣿⣿⡿⠀⠀⠀⠹⣿⣿⡏⠀⠀⢶⡾⠿⢻⣶⡿⠁⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠀⠘⢿⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣟
⠀⢀⣀⠀⠀⠀⠀⠀⠈⠉⢿⣿⣿⣿⣤⣼⡟⠷⠆⠁⠰⠀⠈⠙⠛⠻⠁⠀⠀⠀⠀⢀⣨⣄⡀⠀⠀⠁⠤⠍⠙⢃⣤⣄⣀⡀⠀⠀⠀⠀⠀⢀⠆⠀⣤⣿⠁⠀⠀⠀⠀⠀⠈⠁⣼⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠈⢿⣿
⣤⣿⣿⣿⣿⣿⣷⣦⣴⣾⣿⣿⣿⣿⣿⣿⣻⢛⣃⡠⠀⢀⣾⣿⣿⣶⣄⠀⢀⣴⣾⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⣤⡀⠀⠀⠸⠀⠀⢹⡇⠀⡄⠀⣤⠀⢀⣰⣿⣿⣿⢙⣋⣿⣿⣷⡀⠀⠀⠀⠀⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⣁⣀⣴⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢼⡇⠀⢃⠀⠘⠀⢾⣿⣿⣿⡏⢿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⡀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⢸⠀⠀⠘⡀⠀⠀⠈⠻⣿⣿⣿⣯⡗⠙⠻⣿⣿⣇⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⡿⠿⡿⠛⠉⠀⠀⠀⢹⣿⣿⣿⡻⠃⠈⠀⣸⣿⣿⣿⣿⣿⡿⠛⢻⣿⣿⣿⣿⣷⣀⡈⠀⠀⠀⠰⠀⠀⠀⠀⠈⣿⣿⣿⣇⠀⠙⢻⣿⣿⡆⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣭⢁⣤⣠⣌⣭⣭⢡⣤⡀⣠⣤⣀⣤⡄⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣠⣬⣩⣭⡍⢡⣤⢠⣤⣠⣤⣀⣭⢠⣄⣤⣄⣠⣄⣠⣤⣠⡄⣠⣭⢩⣭⣭⣠⣄⠀⣤⣭⣡⣤⡀⠀⠀
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⡿⣿⣿⣿⢽⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣸⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀
⠿⠿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣀⣉⡉⠉⠉⠉⠈⠉⠈⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⢁⣈⣉⣉⣉⣙⣉⣉⣉⠉⠉⠉⠉⠉⠉⠀⠉⢁⣙⣋⣄⠙⠋⠈⢻⣹⠁⠀
[16A⠶⠒⠀⠀⠀⣰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣴⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠖⠒
⠀⣀⣀⠀⣴⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣏⣩⣭⣤⣍⣁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣷⣿⣿⣿⣿⣿⣿⣿⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⠙⣿⣆⠀⠀⠉⠉⠉⠁⠀⢀⣠⣴⣶⣶
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣏⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿
⠉⠸⠟⠛⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠻⣿⣿⣿⡽⡁⠀⠨⠭⠀⡀⢹⣿⣿⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠈⢿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣈⣙⠃⠀⠀⠀⠀⢾⡷⠜⠛⠓⠀⠀⠀⠀⠀⠈⢿⣿⣷⣠⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢮⣿⣿⣿⡇⠀⠉⠙⠛⠛⠛⠛⠿⣿⣿⣿⣿⠀⠀⠀⠀⠹⢿⡿⠀⠀⣸⣯⠀⠁⢹⡟⠛⢿⣿⣿⣿⡟⠀⠀⠀⠀⠀⡼⠒⠌⢲⠀⠀⠀⢠⣿⡇⢸⣦⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣹⣿⠳⣤⣤⣴⣧⣀⠀⠀⢰⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠹⠛⢛⣿⣿⣿⠇⠃⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠐⢿⣦⠀⠀⠀⠀⠈⢻⣷⣾⣿⣧⣤⣶⡀⠀⠀⠀⠀⠘⢿⣿⣿⣟
⠀⢀⣀⡀⢀⡀⣰⣶⣼⣿⣿⣿⣿⣿⣤⣾⣛⣲⠂⠉⠂⠀⢉⣙⡛⠻⠀⠀⠀⠀⣀⣤⣶⣶⣆⠀⠀⠤⣬⣯⢁⣤⣶⣶⣶⣦⣄⠀⠀⠀⠀⢰⠀⢠⣼⡿⠀⠀⢀⣤⡄⠀⠀⠸⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠈⢿⣿
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣽⣧⠔⠀⣰⣿⣿⣿⣷⣄⠀⣠⣾⣿⣿⣿⣿⣿⣆⠀⣤⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠸⠀⠐⣿⡇⢀⣾⣿⣿⣇⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠘⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⢹⣷⣾⣿⣿⣿⣿⡀⠀⠀⠸⣿⣿⣿⣟⢿⣿⣿⡆⠀⠀⠀⠀⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⡿⠿⡿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣷⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠹⣿⣿⣿⡄⠙⣿⣿⡄⠀⠀⢀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⠋⠙⠛⠁⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠹⢻⣿⣿⠃⠀⠘⠻⠟⠛⠁⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠘⢿⣿⠃⠀⠹⢿⡇⠀⠀⢀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣭⢀⣤⣠⣍⣭⣭⢡⣤⡀⣠⣤⣀⣤⡄⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣠⣤⣨⣤⡄⢠⣤⢠⣤⣠⣤⣀⣤⢨⣍⣭⣍⣩⣍⣩⣭⣩⡄⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣡⣤⡀⢸⡆
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⡿⣿⣿⣿⢽⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣼⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠈⠀
⠿⢿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⠟⠛⠀⠉⠉⠉⠉⠉⠈⠉⠈⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⣉⣙⣉⣉⣉⣉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀
[16A⠠⠦⢤⠆⠀⢠⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⠶⠶⠖⠒
⣶⣶⣶⣶⣶⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣯⣭⣭⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠉⠉⠈⠀⠀⢀⣠⣴⣶⣶
⠿⠿⠿⢿⣿⣻⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿
⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢀⣤⣦⣤⣤⣿⣿⣿⣿⣿⣿
⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣾⣿⣿⡿⢛⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿
⠀⠀⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠙⠿⡿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠈⠙⠻⢋⡸⠁⢠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠈⢿⣿⢢⣠⣼⣿
⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡏⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠁⠀⣠⣿⣄⠈⢉⡟⠻⠿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⢙⡇⣠⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⠏⠀⠀⠈⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠇⠀⠀⢀⡄⠀⠀⠀⢈⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠁⠙⠿⣿⣿⠟⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠻⢿⣃⡀⠀⠀⠀⠙⢿⣿⣿⣟
⣿⣿⣿⣿⣿⣿⣿⠟⠁⠙⢿⣿⣿⣿⣤⡄⠀⠈⠉⠉⠒⠀⢐⣻⣿⣿⣿⣦⣴⣶⣴⣶⣿⣿⡆⠀⠀⠂⠙⠃⠀⣴⣾⣿⣿⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠘⢿⣿⣆⠀⠀⠀⠀⢘⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⢨⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠟⠛⠛⢿⣿⣿⡀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠨⠛⠟⣿⣿⣿⣶⣶⢰⠀⢾⡟⣿⣧⠀⠀⠀⢸⣷⡘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠈⠱⠀⢡⣤⡀⣀⣀⣀⣀⣴⣾⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⢸⣿⣿⣿⡶⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⡀⠀⠀⠀⢹⢏⣿⣿⣿⣼⠀⠈⠀⣿⣿⡇⠀⠀⠀⠙⠇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠐⢦⣶⣿⣦⣴⣿⣟⣻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠻⣿⣿⣿⠇⠘⠸⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⢰⠀⠀⠀⡘⠀⢹⣿⣱⡇⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠟⠉⠈⠁⠀⠀⠀⠀⠀⠀⠉⠙⠿⣿⠆⠀⠀⣿⣿⣿⣿⣿⡿⠃⠀⠈⠛⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⢿⡿⠃⠀⠀⠀⠀⠙⣿⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠛⠉⣭⢉⣤⣠⣄⣤⣤⢠⣤⡀⣠⣤⣀⣤⡀⣤⣄⣠⣤⣠⣤⡄⢠⣄⣬⣡⣤⣠⣤⡄⢠⣤⢠⣤⣠⣤⣀⣄⢠⣄⣤⣄⣠⣄⣠⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣠⣤⡀⢲⠀
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣾⡇⠀⣿⢸⣿⡿⣿⣿⣿⢽⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣸⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣼⣿⣽⡇⣹⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠈⠀
⠿⠿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣄⠉⠉⠉⠉⠉⠈⠉⠈⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣩⠁⠀
[16A⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠖⠒
⠀⠀⠀⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⢀⣠⣴⣶⣶
⠀⠀⢀⣀⣀⠀⡰⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⣿⣿⣷⣶⣷⣶⣶⣦⡀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿
⠀⣰⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢠⣆⠀⢀⣿⣿⣿⣿⣿⣿
⠀⢈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣴⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿
⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠈⠹⣿⣿⠟⠛⢿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠘⢿⣿⠏⠉⠉⢻⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⢹⡿⠀⠀⠘⣿⣿⢢⣠⣼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠉⠀⢀⣰⣿⣄⣀⣸⡟⠻⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⣦⣶⣿⠇⠀⠀⠀⠈⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⠛⠿⠿⠿⠿⢿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠘⠋⠹⠿⣿⡟⠁⠀⠛⠻⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢹⣿⣿⣿⣿⣤⠈⠉⠹⠏⡀⠀⠀⠀⠀⠘⢿⣿⣿⣟
⣿⣿⣿⡿⣿⠿⠿⠿⢿⣿⠏⠉⠉⠁⢻⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⣠⣤⣾⣿⣦⠀⠀⠐⠂⠊⠀⣰⣾⣿⣶⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡟⠀⠀⠀⢸⢿⣷⡄⠀⠀⠀⠀⠈⢿⣿
⣴⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⣠⣾⣿⡀⣠⣾⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⡅⡀⠠⠀⠀⢻⠟⣿⣆⠀⠀⠀⠀⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⢆⠀⡏⢹⡇⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠉⠛⢻⡟⡇⡇⠀⡆⠀⠈⠀⣿⣿⣆⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢨⣦⣷⣾⣆⠀⠀⠀⠀⣴⣿⣿⣿⣿⡿⠿⠿⠛⠛⠿⠿⣿⣿⣷⣴⣶⣿⣿⣿⣿⣿⣿⡿⠛⢿⣿⣿⣿⠟⠀⠀⠀⠀⠀⢢⠀⠀⡂⡜⠀⠃⣷⡀⡃⠀⠀⠀⠸⢿⣿⠀⠀⢀⣧⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⣿⣿⣿⣿⣿⡆⠀⠀⠘⠏⠙⠛⠛⠁⠀⠀⠀⠀⠀⠂⠀⠀⠈⠉⠛⠛⠿⣿⣿⣿⣿⣿⠇⠀⠀⠛⠉⠀⠉⠀⠀⠀⠂⠀⠀⠀⠐⡐⠀⠀⠀⢹⠟⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣭⢉⣥⣠⣄⣤⣤⢠⣤⡀⣠⣤⣀⣤⡄⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣠⣤⣨⣥⡄⢠⣤⢠⣤⣠⣤⣀⣄⢠⣄⣤⣄⣠⣄⣠⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣠⣤⡀⢀⠀
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⡿⣿⣿⣿⢹⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣸⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣽⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠈⠁
⠿⠿⣿⣿⣿⣿⣿⣿⡿⢾⣿⣿⣿⣿⣄⡉⠉⠉⠉⠉⠈⠉⠈⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣩⠁⠀
[16A⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠒
⠀⠀⠀⠉⠉⠉⣭⣭⣭⣿⣿⣿⣿⣿⣿⠏⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⣴⣶⣶⣿⣿⣿⣿⣿⣿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⢀⣠⣴⣶⣶
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣤⣾⣷⣶⣿⣿⣿⣿⣶⡄⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⢿⣿⡟⠻⣿⣿⣿⣿⣿⣶⡄⠀⠸⢿⣿⡿⠛⠋⠉⠉⢻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⢿⣿⣢⣠⣼⣿
⠀⠀⠀⠀⠀⠰⢚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣁⠿⣀⣀⣼⣿⣧⣤⡜⣿⣿⣿⣿⠟⠀⠀⠀⠀⠉⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⡏⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠀⠘⠀⠻⢿⠟⠻⢿⣿⠇⠛⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣣⢀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣟
⠀⢀⣀⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢀⣀⣀⣿⣿⡋⠙⠿⣿⣿⣿⣿⠿⢿⣿⠟⠋⢀⣠⣤⣤⠀⠀⠙⠀⠀⠐⢃⣴⣦⣤⣤⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠐⣿⣿⣿⣿⡟⠃⠍⠀⠀⠀⢶⣤⡀⠀⠀⠀⠀⠈⠙⢿⣿
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣿⠥⠀⠀⠀⠀⠀⠀⠀⠘⠁⣠⣾⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⣤⡀⠀⠰⠎⠙⢻⣶⣞⣿⣿⣿⣿⣷⣾⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⠀⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⣰⣷⣾⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⣿⡏⠀⡀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢀⣨⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣴⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣾⣿⣿⣿⣿⣿⣿⠃⠋⠀⠀⢧⠀⠀⠀⠀⠀⠀⠻⣿⣧⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⣤⣀⣤⠊⠙⠛⠁⠀⠀⠀⠀⠙⠿⢿⡿⠿⠇⠀⠀⢸⣿⣿⣿⣿⣿⠟⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠘⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⣬⢉⣥⣠⣄⣤⣤⢠⣤⡀⣠⣤⣀⣤⡀⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣠⣤⣨⣥⡄⢠⣤⢠⣤⣠⣤⣀⣤⢨⣍⣭⣍⣡⣄⣠⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣠⣤⡀⠀⢀
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⢸⣿⡿⣿⣿⣿⢹⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣸⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠸
⠿⠿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⢀⠉⠉⠉⠉⠉⠈⠉⠈⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀
[16A⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠒
⠀⠀⠀⠉⠉⢉⣭⣭⣭⣿⣿⣿⣿⣿⣿⠏⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣶⣦⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⢀⣠⣴⣶⣶
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣤⣤⣤⣤⣶⣶⣤⣄⡀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⣿⡛⠛⢻⣿⣿⡟⠁⠀⠀⠀⠻⣿⡿⠁⠀⢰⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠐⠀⠈⢿⣿⣷⣠⣼⣿
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠙⣿⣿⣄⣤⣿⣷⣴⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⡇⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⢷⠘⢿⣿⡿⠿⠟⠻⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢼⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣟
⠀⢀⣀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣸⣿⣿⡟⠋⠉⠛⢿⣿⣿⣿⣿⠟⠛⠛⢛⡁⠀⠀⠀⠀⠈⠑⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢸⣿⣿⣿⣿⣿⢿⣿⣿⠀⠙⢷⣶⣦⡀⠀⠀⠀⠀⠈⢿⣿
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⠿⠇⠀⠀⢀⠀⠙⠋⠉⠁⢀⣴⣶⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠄⠀⠀⠸⣿⣿⣿⠋⠀⣸⣿⣻⠀⠀⠀⠛⠻⣿⣦⠀⠀⠀⠀⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣠⣶⣧⣴⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣂⢺⡭⡇⡇⠀⠀⠀⠀⠀⠿⣿⡇⠀⠀⢂⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⣠⣾⣿⡿⠋⠀⠈⠉⠀⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣤⣤⣴⡘⠛⢻⠟⠁⠀⠉⠉⠛⣿⣿⣿⣿⣿⠈⠀⠀⣿⣿⣿⣿⣿⡿⠛⢿⣿⣿⣿⣯⣤⣴⣾⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣭⢉⣥⣠⣄⣭⣤⢠⣤⡀⣠⣤⣀⣤⡄⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣠⣬⣩⣭⡍⢠⣤⢠⣬⣩⣭⣉⣭⢩⣍⣭⣍⣩⣅⣠⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣠⣤⡀⠀⣿
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⢸⣿⡿⣿⣿⣿⢹⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣸⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠈
⠿⠿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⡀⣉⣉⡉⠉⠉⠈⠉⠈⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⣤⣉⣉⠉⠁⢈⣁⣈⣉⣉⣉⡙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀
[16A⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠒
⠀⠀⠀⠉⠉⢉⣭⣭⣭⣿⣿⣿⣿⣿⣿⠏⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⣴⣶⣾⣶⣤⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣷⣦⣴⣶⣄⠀⠀⠀⠀⠉⣩⣿⣯⡉⢀⣠⣴⣶⣶
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣤⣤⣤⣴⣶⣶⣶⣶⣦⣄⡀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⣿⣿⣿⣷⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣆⠀⠀⠈⠛⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⣿⣿⠛⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⢹⣿⠁⢉⣿⣿⠋⠀⠀⠀⠀⠀⠀⠉⠉⡝⣿⣿⣿⣿⠏⠉⣤⡀⠸⠿⠆⠀⠀⠀⠀⠀⠈⢿⣿⣶⣠⣼⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⠿⣿⡟⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡙⣿⣷⣴⣾⣿⣷⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣼⣿⠉⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⡇⠀⢿⣿⡂⠀⠀⠀⠉⠙⠛⢻⣿⣿⡿⠻⣿⣿⣿⡉⠙⠇⠙⢿⣿⡟⠛⠉⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠙⡏⠀⠀⠀⠀⢿⣆⢀⣄⠀⣀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣟
⠀⢀⣀⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣀⣠⣤⣿⣿⡦⠀⠰⠂⠀⠀⣸⣿⡏⠀⠀⠀⠙⣻⣀⡀⠀⠀⠀⠉⠙⠙⠒⣥⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⠀⠀⠀⠀⠀⠈⠉⣾⣿⠃⠈⠻⢿⣷⣄⠀⠀⠀⠀⠈⢿⣿
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣇⠀⠀⠀⠀⠀⣴⣿⣿⠀⠀⣠⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⣽⠇⠀⠀⠀⠀⠀⣠⣿⡿⠸⠀⠀⠀⠈⠉⣿⠀⠀⠀⠀⠀⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⠀⠀⠀⢀⣾⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⣴⣿⣧⣶⠀⠀⠀⢘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⣤⣀⣸⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣷⣾⣿⣿⡿⠿⣿⠟⠋⠀⠀⠀⠙⣿⠿⠿⣿⣿⠈⠀⠀⣿⣿⣿⣿⣿⡟⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣭⢉⣭⣩⣍⣭⣥⢠⣤⡀⣠⣤⣀⣤⡀⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣨⣬⣠⣥⡍⢠⣤⢠⣭⣩⣭⣉⣭⢩⣍⣭⣌⣨⣍⣩⣭⣠⡄⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣠⣤⡀⠀⠉
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⡿⣿⣿⣿⢹⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣸⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀
⠿⠿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣀⣉⣉⡉⠉⠉⠈⠉⠈⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⢀⣉⣉⣉⣁⣌⣁⣌⣉⣉⣉⣙⡉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀
[16A⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡖⣦⠄⠰⣶⣶⣶⣶⣴⣶⣶⣶⠶⠶⠶⠒
⠀⠀⠀⠈⠉⢉⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣯⠄⠐⠛⠻⢿⣿⣿⡍⠀⠀⢀⣠⣴⣶⣶
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠈⠉⠀⠀⢰⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠉⠛⢿⠟⢿⣿⣿⣿⣿⣿⣿⢶⣶⣤⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢺⣿⣿⣿⣿⠛⣇⠈⣺⣿⣇⣀⣨⡉⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⣴⣿⣿⣿⣿⣿⣿⣸⣿⠏⠁⠀⠀⠀⠘⢿⣿⣷⣠⣼⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⣿⡀⠀⠀⣄⠈⠃⠀⠙⣿⣿⣿⡏⠀⠀⣿⣿⣿⡿⠇⢻⣿⣿⣿⣿⣿⡿⠳⠿⠋⠁⠀⠀⠀⠀⠀⠀⢰⣿⣼⣙⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⠇⠙⣿⣿⣿⡛⢷⣦⣀⣾⣿⣿⡿⠁⠀⠀⠈⠻⠿⠃⠀⠀⠻⣿⡿⣿⣿⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣤⡄⣀⣀⣀⠀⠀⠀⠀⠙⣿⣿⣿⣟
⠀⢀⣀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣧⣽⡁⢰⡟⢀⣀⣉⠙⠃⠀⠀⢀⣠⣴⣾⣷⣶⡄⠀⠈⠀⠀⢀⣿⣿⣿⣿⣶⣦⣀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⣿⠀⣿⡇⠀⠙⢻⣿⣦⠀⠀⠀⠀⠈⢿⣿
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠀⠀⢀⣾⣿⣿⣿⣦⡀⣠⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⢸⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⢱⠡⠹⠀⠀⠀⠀⠀⣿⣧⠀⠀⢸⠀⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣼⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠁⠀⠈⠁⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⢿⠿⢯⣿⣤⣿⣿⣿⣿⣿⣿⡿⠛⠿⠿⠟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠯⠿⢿⣿⣿⣿⠿⠿⠟⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣭⢉⣤⣠⣌⣥⣬⢡⣤⡀⣠⣤⣀⣤⡄⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣠⣭⣠⣤⡄⢠⣤⢠⣤⣠⣤⣈⣭⢩⣍⣭⣍⣩⣍⣩⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣠⣤⡀⠀⠈
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⡿⣿⣿⣿⢽⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣸⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀
⡿⠿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣄⡉⠉⠉⠉⠉⠈⠉⠈⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⣉⡙⣉⡉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣄⣀⡀⢀⠀
⠀⢸⣷⣦⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢰⣶⣶⣶⣾⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⢸⡇
⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⢰⣿⣿⣿⣿⣿⣿⢸⣧
⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⢸⣿⣿⣿⣿⣿⣼⣿
⠀⢸⣿⣿⣿⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣿⣿⡏⠛⠭⠿⠿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⣿⣿⣿⣿⢸⡿
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✐ The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXXXVI:_An_Erosion_of
Fundamental_Rights_Protection?⠀✐
Posted in Courtroom, Europe, Law, Patents at 8:40 am by Dr. Roy Schestowitz
Series parts:
Endorsement?
Courage
Pusillanimous_Hibernia
Cheese
Controversial_Christian_Bock
Battistelli’s_Swiss_Apprentice?
Facilitators_–_Spain
Facilitators_–_Portugal
Austrian_Double-Dipper
Nordic_Bloc
Doyen_and_His_“Protégée”
North_Macedonia_and_Albania
Bulgaria
Romania
Fresh_Blood_or_Same_Old,_Same_Old?
Budget_and_Finance_Committee
Loyal_“Habibi”
States_–_Monaco_and_Malta
Perfidious_Betrayal_of_Liberty
Belgium”?
Dubious”_Proposal
Independent_Slovenia
Tentacles_of_the_SAZAS_Octopus
to_Capture
Italians
Self-Service?
Land
“Waite_and_Kennedy”
🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Kicking_Fundamental_Rights⦈_
Recent judgments of the European Court of Human Rights appear to have eroded
the obligation of ECHR states to protect fundamental rights in cases where the
alleged violations involve an international organisation.
Summary: What the European Court of Human Rights means to EPO workers in light
of more recent developments, especially 5 years ago (Supreme Court of the
Netherlands)
In the last part we saw how the European Court of Human Rights (ECtHR) has
ruled that states which are signatories of the European Convention on Human
Rights (ECHR) have a responsibility to ensure that their membership of
international organisations does not lead to a breach of their ECHR
obligations.
“…it has become evident that the overriding priority of the Court is to protect
the autonomy of international organisations at the expense of the fundamental
rights of their staff (and other individuals adversely affected by the acts of
such organisations).”In other words, ECHR signatory states must ensure that
adequate provision is made for an “equivalent protection” of fundamental rights
inside any international organisation which they join.
This has implications for the internal justice systems of international
organisations on which staff are obliged to rely for legal redress, because of
their lack of access to national courts.
According to the “Waite_and_Kennedy_v._Germany” judgment, such internal justice
systems must provide staff of an international organisation with “reasonable
alternative means to protect effectively their rights under the [European]
Convention [on Human Rights]“.
However, following the delivery of ECtHR judgments in the cases of Klausecker
v. Germany (application_no._415/07) and Perez_v._Germany [PDF] (no._15521/08)
in January 2015, it has become evident that the overriding priority of the
Court is to protect the autonomy of international organisations at the expense
of the fundamental rights of their staff (and other individuals adversely
affected by the acts of such organisations).
“There was now a distinct possibility that international organisations and
their member states could get away with applying a different and less rigorous
standard of human rights protection to the acts and omissions of an
international organisation.”The Klausecker and Perez judgments prompted the
legal scholar Anne-Marie Thévenot-Werner to express concern about an_erosion_of
the_obligation_of_states_to_protect_the_fundamental_rights_enshrined_in_the
ECHR.
In an article published in the legal journal Revue de droit allemande in 2015
Thévenot-Werner acknowledged that the ECtHR had formally reaffirmed its case
law requiring the provision of “reasonable alternative means” for the
protection of fundamental rights inside international organisations.
However, at the same time the Court signalled that it would not hold a state to
account for a breach of the ECHR involving an international organisation unless
the protection available via the organisation’s internal justice system was
shown to be “manifestly deficient”.
Thévenot-Werner warned that the approach taken by the Court in these cases
risked creating a loophole with respect to the protection of fundamental rights
enshrined in the ECHR.
“It deserves to be emphasised at this point that these are matters which are
not merely of academic and theoretical interest.”There was now a distinct
possibility that international organisations and their member states could get
away with applying a different and less rigorous standard of human rights
protection to the acts and omissions of an international organisation. In such
situations, states would only be called to account if it could be established
to the satisfaction of the Court that the level of protection available was
“manifestly deficient”.
The risk of such an erosion of legal protection exists even in the case of
organisations where all participating states are signatories to the ECHR (which
is the case for the EPO).
It deserves to be emphasised at this point that these are matters which are not
merely of academic and theoretical interest.
The saga of Benoît_Battistelli‘s “Strike Regulations” at the EPO provides a
striking illustration of their practical significance for the staff of
international organisations.
“The Gerechtshof judgment showed that at least some judges in the Netherlands
were serious about setting limits to the “immunity” enjoyed by an international
organisation in order to prevent abuses involving clear-cut violations of
fundamental rights.”As noted in an_earlier_part_of_this_series, Battistelli’s
controversial “Strike Regulations” were one of a long litany of grievances
which the EPO staff union SUEPO attempted to litigate before the national
justice system in the Netherlands.
During the litigation procedure, the Gerechtshof den Haag (Appeal Court of The
Hague) decided that breaches of fundamental rights by EPO management were so
severe that they justified lifting the organisation’s immunity from
jurisdiction.
This lead to a judgment, delivered on 17_February_2015, in which the
Gerechtshof ordered_the_EPO [PDF] to rescind several amendments to the
organisation’s staff regulations, including the undue restrictions on
industrial actions imposed by the impugned “Strike Regulations”.
In addition to this, the EPO was ordered by the court to uphold the rule-of-law
and social dialogue standards in_line_with_the_European_Convention_on_Human
Rights_and_ILO_Conventions_No._87,_on_the_right_to_organise_in_trade_unions,
and_No._98_on_the_right_to_collective_bargaining. [PDF]
The Gerechtshof judgment showed that at least some judges in the Netherlands
were serious about setting limits to the “immunity” enjoyed by an international
organisation in order to prevent abuses involving clear-cut violations of
fundamental rights.
The European Public Service Union (EPSU) reported on the judgment under the
headline “European_Patent_Office_does_not_live_in_a_Dutch_no_man’s_land”.
“The problem with the Gerechtshof judgment was that it set a worrying precedent
which had political ramifications going far beyond the EPO.”Unfortunately, both
SUEPO’s legal victory and EPSU’s optimism turned out to be short-lived.
Less than two years later, the Gerechtshof judgment was set aside, thereby
confirming what many had long suspected: the European Patent Office does indeed
live in a Dutch no man’s land!
🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Gerechtshof_den_Haag⦈_
An independent judicial review of violations of fundamental rights by the EPO
carried out by the Gerechtshof den Haag led to a short-lived lifting of the
organisation’s immunity in February 2015. This was overruled in January 2017
when the Supreme Court proclaimed that Dutch courts had “no jurisdiction in the
EPO dispute”.
The problem with the Gerechtshof judgment was that it set a worrying precedent
which had political ramifications going far beyond the EPO.
“The Hoge Raad attempted to justify its findings on the basis that the
fundamental rights of EPO staff “were sufficiently protected by the internal
dispute settlement procedure provided for by EPOrg”.”It was a veritable thorn
in the flesh not only for Battistelli and his clique at the EPO, but also for
the Dutch government which reaps significant economic benefits from the
country’s status as a host to a large number of international organisations.
This led to the Dutch government joining forces with Team Battistelli in
support of an application for “cassation” of the judgment.
Finally, on January 2017, the Hoge Raad (Supreme Court of the Netherlands)
issued a ruling to the effect that Dutch courts had no_jurisdiction_in_the_EPO
dispute:
“According to the European Court of Human Rights (ECtHR), granting
jurisdictional immunity to an international organisation constitutes
a limitation of the right of access to a court as referred to in
article 6 of the Convention for the Protection of Human Rights and
Fundamental Freedom Rights (ECHR). This limitation is acceptable
provided that litigants have a reasonable alternative means of
protecting their rights effectively.
The Supreme Court found that such alternative means exist. The rights
of VEOB [the Netherlands branch of SUEPO] and SUEPO are sufficiently
protected by the internal dispute settlement procedure provided for
by EPOrg, under which individual employees and staff representatives
can ultimately take their complaint to the Administrative Tribunal of
the International Labour Organization in Geneva. According to the
Supreme Court, this means that the essence of their right of access
to a court has not been impaired.”
The Hoge Raad attempted to justify its findings on the basis that the
fundamental rights of EPO staff “were sufficiently protected by the internal
dispute settlement procedure provided for by EPOrg”.
But is this really the case?
“In the upcoming parts, we will take a closer look at the EPO’s internal
justice system and the role which it played in “Strike Regulations” affair.”Not
everybody would agree. Indeed, many would argue that the facts tell a very
different story and that the judgment delivered by the Hoge Raad in January
2017 was driven by political expediency and a misplaced desire to tell the
Dutch government and the EPO what they wanted to hear rather than what they
needed to hear.
In the upcoming parts, we will take a closer look at the EPO’s internal justice
system and the role which it played in “Strike Regulations” affair.
In particular, we will see how a former judge of the European Court of Human
Rights played a bizarre and incongruous role in prolonging the suppression of
the fundamental right to “freedom of association” at the EPO. █
⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⢀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣀⡀⠀⠀
⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣍⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡻⣿⠛⡍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀
⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣍⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡾⣶⠈⡄⣧⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠀⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣝⡻⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⢳⢷⡇⠀⠃⢸⣿⣿⣿⣿⣿⣿⠊⢾⡿⣿⣿⠿⢿⣿⣿⣿⡿⣿⣿⣧⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⢀⣿⣗⠍⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⣪⣝⡻⣿⣿⡇⡿⣿⣿⡿⡣⢟⣮⡟⠰⠰⣾⣿⣿⣿⣿⣿⡿⣬⢻⣾⣯⣿⣿⣷⣶⣶⣿⣭⣳⣝⢻⣖⠽⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠸⣿⣿⣿⣾⣮⡛⢿⣿⣿⣿⣿⣿⡿⠋⣩⣿⣎⣿⣿⣿⣿⣿⣮⢙⢿⣴⢸⡟⣕⡯⡈⢏⢋⠂⢦⣿⣿⣿⣿⣿⣿⢧⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣽⣗⣯⣽⣭⣟⡮⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠀⣿⣿⣿⣿⣿⣿⣦⡙⢿⣿⣿⢿⣷⣿⣿⣿⣿⣿⣿⣿⣎⣿⣿⡟⣁⡮⡒⡎⣪⠃⠀⢨⣉⡘⣾⣿⣿⣿⣿⣿⡟⣾⣿⡖⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣆⣾⣿⣿⣿⣿⣿⣮⣷⡝⡿⢟⡻⢻⣿⣿⣿⣿⣿⡇⠀
⠀⢰⣿⣿⣿⣿⣿⣿⡿⣇⢳⣝⡻⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⢁⣀⣸⡟⣿⢂⣤⣬⣍⢱⣿⣿⣿⣿⣿⣿⢡⣿⣿⣷⡞⣿⣿⣿⣿⣿⣿⣿⣿⡿⢶⢸⣿⣿⣿⣿⣿⣿⣿⡿⣿⣾⣖⢴⣿⣿⣿⣿⣿⣿⡃⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⡽⣦⣹⣿⢳⢑⡻⢿⣿⣿⣿⣿⣿⡿⢁⢦⣿⣟⢛⡻⢁⣴⣿⡟⢦⢄⣟⣛⣛⣛⣛⣛⡿⣞⣛⣛⣻⣰⢻⣛⣛⣛⣛⣛⣛⣻⠓⡆⣟⣛⣛⣛⣛⣛⡽⣽⣛⢿⣟⣿⣓⣛⣛⣛⣛⣛⣛⡃⠀
⠀⠈⠻⣿⣿⣿⣿⣿⣿⣽⣿⣽⢿⣳⡌⣿⣿⣿⣿⣻⢿⡟⣰⣼⠟⠋⠀⢩⣶⣿⣿⢋⣮⢅⣾⣿⣿⣿⣿⣿⣿⢱⣿⣿⣿⣿⡟⡟⣿⣿⣿⣿⣿⣿⡏⢹⢸⣿⣿⣿⣿⣿⣿⣿⣟⣏⣻⢿⡿⢿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠀⠬⡪⣻⢿⣿⣿⣿⣿⣿⣿⣯⣿⣇⣙⣿⣿⣿⣿⡿⣼⣿⡿⠀⠀⣰⣿⣿⡿⡡⡣⣢⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣧⣷⢻⣿⣿⣿⣿⡿⣀⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⢷⣿⣿⣿⣷⠝⠻⣿⣿⡇⠀
⠀⠀⠀⠈⠳⢕⢝⢿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⡿⡁⢾⡟⠃⠀⢰⣿⣿⠏⢜⢄⣾⣿⣿⣿⣿⣿⣿⣿⡿⠼⠻⡻⣿⣿⣿⣟⠎⠈⠙⡛⠏⢹⢣⣹⣏⠿⠿⠿⠿⠿⠿⠿⣿⠟⣿⢀⣼⣻⡹⢇⣢⣴⣞⣿⣿⠃⠀
⠀⠀⠀⠀⠀⠀⠳⣕⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢡⡳⣿⣿⡇⠀⣸⣿⡏⢌⢪⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡲⣶⣶⣶⣶⣶⣶⣶⡿⣕⣽⡆⣏⢾⡟⢹⣿⣿⣿⣿⣷⣶⡆⠀⢀⢫⣉⣟⣻⣷⡿⣟⠿⣿⣿⠿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣝⢿⣿⣿⣿⣿⣿⣿⠟⡈⣹⣽⣿⣿⠇⢠⣿⡟⢬⠊⠊⡝⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣾⣿⣭⣿⡿⢒⣽⣿⣿⣷⢸⣿⣷⣾⣿⣿⣿⣿⠿⠋⢀⣴⣿⣷⣿⣿⡟⠗⢋⠭⠤⢀⣀⣰⡆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢵⡹⣻⢿⢟⢡⣟⣵⡾⢻⣿⣿⢀⣾⡿⣌⠆⠀⡼⣹⢿⣿⣿⣿⠿⠋⠀⠀⠀⠀⣠⣿⣿⡿⢋⣴⡿⢿⢟⠛⡥⣘⣿⢐⣿⣿⣿⠟⠁⢀⣴⣿⣿⣿⣿⣿⣿⣿⣗⢱⣤⣭⠩⠽⠶⠅⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠗⠋⣆⢤⢹⠻⢿⡿⣣⣾⡿⣙⢎⠢⣹⢳⠇⠘⠛⠉⠀⠀⠀⠀⠀⣠⣾⣿⣿⣷⣤⣀⣗⢌⡈⡶⡝⣲⡯⢥⣄⠤⠫⡀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣇⣈⣀⣀⣀⣀⣤⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢝⡕⡦⣼⣻⣿⣁⡞⠢⢱⢧⠏⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⡿⠉⠑⠯⢕⣲⠾⢟⣻⣯⣙⢥⣉⡎⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀
⠀⠀⢳⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠥⢭⠱⢟⣀⣀⢏⠎⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⡀⠀⠀⠉⠉⠐⠒⠒⠒⣾⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠀⣾⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠯⠬⠎⠀⠀⠐⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣴⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣀⣀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠉⠋⠛⠍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠛⠚⠓⠛⠛⢿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⣠⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠎⠀⠀⠀⠘⠙⠿⡤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠀⠀⠀⠀⠐⠤⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣽⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠈⠛⠛⢹⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢤⡂⠸⠦⣠⣄⣈⣿⣿⣿⣿⣿⣿⣿⣿⣯⠆⠀⠀⠀⠀⠀⠀⣨⣧⣶⣿⣿⣿⣿⣵⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⣿⣿⣿⣿⣿⣿⡛⠈⠀⠀⠀⠀⠀⠀⠀⠐⠹⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⠃⠀⢰⡀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢹⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠊⣠⣿⣿⣿⣿⣿⣿⣿⣟⠿⠃⠈⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡟⢀⡇⢸⣽⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣽⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⡼⡏⠽⠟⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⡀⠸⣿⣿⣿⣿⣿⣿⣿⠁⣔⠀⣼⣿⣧⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣴⡠⠀⠀⠀⠃⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣔⣶⣟⡀⢛⣿⣿⣿⣿⣿⡅⣰⣿⠀⣿⣿⣿⣤⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢱⣿⣿⣿⡿⡿⠿⠟⠛⠁⠀⣀⣀⣤⣶⣯⠄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠂⠁⠈⠉⠉⠙⠃⠈⢿⣿⣿⡟⠛⠀⠙⠉⠈⠉⠉⠉⠙⠂⠙⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣯⡉⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⢴⣾⠗⣀⣀⠀⠀⠀⠀⠀⠀⣠⣤⣿⣿⣿⣿⣤⡄⡀⠀⠀⠀⠀⠀⣀⢠⢼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡚⠐⠳⠧⠀⠀⠙⠁⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡣⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣀⣀⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣷⣶⣿⣿⣿⣿⣿⣿⠿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣴⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠝⠛⠛⠀⠸⡿⠛⠙⠻⣿⣿⣿⡇⠀⢄⠀⢀⠽⠋⠛⠟⡻⡻⠛⠛⢟⠀⠘⠙⢯⠟⠉⠙⢿⠏⠙⠫⢿⠛⠛⠛⠻⢯⠙⠙⠙⡟⠛⠛⠏⡽⠉⠉⠻⢏⡇⢘⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢐⡠⠀⠰⠀⠀⠁⠀⣿⣿⣿⡇⠀⡀⠀⣼⠀⠀⠀⠀⠂⠀⠤⡄⣞⠀⢠⡂⢨⣠⠀⠰⣾⡀⠈⠐⢾⠀⠠⡤⠀⢹⠀⢰⣤⠆⠈⠀⠀⡵⠀⠈⠀⢸⡇⠀⠀⢼⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⣠⣼⣧⣄⣀⣴⣿⣿⣿⣇⣤⣷⣄⣸⣦⣄⣀⣤⣴⣦⣀⣠⣴⣤⣜⣇⣸⣿⣄⣀⣼⣄⣀⣤⡼⠀⢠⣀⣠⣝⣤⣜⣧⣤⣀⣀⣤⣧⣄⣀⣤⣼⣇⣸⣤⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠻⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⡟⢛⣿⣿⢿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣟⡎⢛⣻⣿⠛⠛⠟⢿⢿⣿⣿⣿⣿⣿⣿⣟⡟⢻⣿⠻⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠠⣟⠓⠺⠍⠉⠉⠍⢉⠍⠩⠉⠟⢉⣉⠁⢈⡉⣫⠀⡍⠉⠁⠇⢈⠉⡋⠉⠍⠹⠄⢨⣽⣷⠀⣿⡄⢨⠋⠍⠉⠍⢡⠙⣿⣿⡇⢘⡛⢸⡍⠩⠙⠏⠩⠉⡟⢩⡍⢹⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣄⣉⣁⣸⡂⢀⢠⣇⣨⣤⣀⣀⡃⡈⡉⣁⣸⣂⣙⣀⡡⣀⣀⣁⣨⣀⡧⣀⠁⢸⣂⣾⣿⣿⣀⣉⣠⢾⣀⣀⣴⣂⣊⣀⣿⣿⣃⣸⣟⢈⢁⣀⣀⣇⣈⣀⡆⢈⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣰⣽⣿⣿⣿⣿⣿⣿⣿⣿
䷩ 𝚕𝚒𝚗𝚎 1632
╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕
(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/02/09/gemini-not-ugly/#comments
Gemini version at gemini://gemini.techrights.org/2022/02/09/gemini-not-ugly/
⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.09.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧
Gemini_version_available_♊︎
✐ Response_to_Gemini_Misconceptions_and_Mythology_(It’s_Not_Ugly_or_Just_for
Geeks)⠀✐
Posted in Deception, Free/Libre_Software, FUD, Protocol, Standard at 7:54 am by
Dr. Roy Schestowitz
Video_download_link | md5sum 420621d8ea77533494fdde5e187ca23a
Gemini Misconceptions
Creative Commons Attribution-No Derivative Works 4.0
http://techrights.org/videos/gemini-myths.webm
Summary: Another gemini:// FUD response; this time we deal with this_new
article, a polite article, which nevertheless makes Gemini as a whole seem
crude and ugly; in reality, depending how it’s presented, Gemini can be
beautiful, expressive, and feature-rich (depending on the creativity of
pertinent capsules)
THE RISE of Gemini isn’t a subjective thing. It is measurable. It’s objective.
🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇1700 Gemini capsules approached⦈ As shown in the image to
the right, Gemini is growing fast. On January 16th we_wrote_about_1,600_active
capsule and now we’re flirting with 1,700. Almost 100 active capsules in net
gain in 3.5 weeks is nothing to sneeze at (not the same as 100 new capsules as
it’s possible that 10 of the existing ones shut down while 110 new ones
emerged).
“Almost 100 active capsules in net gain in 3.5 weeks is nothing to sneeze at
(not the same as 100 new capsules as it’s possible that 10 of the existing ones
shut down while 110 new ones emerged).”Over the past few months I’ve seen a
number of Gemini-bashing posts that were mostly based on misunderstandings.
Sometimes there’s almost outdated information or misinformation. “I had a
discussion with someone about Gemini,” one person told me this morning, “a
couple of years ago.” That’s like the time Gemini was only months old. A lot
has changed since then. The number of capsules grew from a couple hundred to
over 2,000, with probably around a million pages in them (Lupa alone has
retrieved and analysed almost half a million pages).
That same person then asked me and another Gemini proponent: “What are the
advantages you two see in Gemini?”
“The number of capsules grew from a couple hundred to over 2,000, with probably
around a million pages in them (Lupa alone has retrieved and analysed almost
half a million pages).”“Speaking for myself,” I replied, “self-hosting is one.
The Web became far too bloated, so it’s difficult to host from one’s
residential perimeter, hence people move to centralised platforms and
datacentres.”
“But people’s connections have gotten faster, it’s just the Web that changed.
Why can’t people take back control of the Internet? In his talks about
Freedombox, Eben Moglen raised this point.”
The person then asked: “Does Gemini use HTML? Could we post the same pages HTML
pages we have now on a gemini server, or would they need to be modified and
adapted?”
Some people wrongly believe that Gemini Protocol is only for transmission or
only for ‘markup’. It’s actually both. HTML is very complicated for a lot of
people. Setting up a Web server is also hard compared to Gemini. So lesser
technical people cannot easily participate, unless they create some accounts in
Blogspot (Gulag) or Facebook…
“There are already dozens of Gemini clients (like Web browsers) and over a
dozen Gemini server implementations.”Gemini uses GemText, which is simple
enough to teach to 6 year olds. It’s also a lot simpler to program with, owing
to this simplicity.
There are many good HTML→GemText (and vice verse) converters. Anyone with basic
coding skills can write one in a few hours, as many people have. “XSLT might
also be an option for HTML→GemText,” an associate of ours notes.
There are already dozens_of_Gemini_clients_(like_Web_browsers)_and_over_a_dozen
Gemini_server_implementations.
Our hope is that better understanding of Gemini, owing to media coverage (the
mainstream media is paid to push ads and lies, so it won’t help Gemini grow),
can help without it resembling “advocacy”/”evangelism” (religious term) or
“marketing”. As it turns out, some mainstream media already_embraces_Gemini and
it has become big enough for Microsoft_to_attempt_to_hijack/undermine_it. █
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣇⢿⣿⡟⡇⡇⡷⣹⡜⡇⢿⢸⢸⡱⣼⢬⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣾⣀⣇⣾⣈⣿⣟⣼⣷⣇⣸⣿⣏⣾⣃⣿⣸⣽⣿⣯⣺⣢⣗⣺⣐⣟⣸⣻⣧⣽⣼⣟⣿⣿⣉⣇⣸⣿⣧⣻⣇⣵⣯⣾⣠⣗⣺⣐⣇⣿⣃⣇⣿⣸⣞⣿⣿⣒⣗⣺⣇⣿⣸⣬⣵⣷⣺⣡⣗⣿⣿
⣿⣿⣿⣿⣿⢿⡿⣿⡿⣿⢿⡿⡿⣿⢻⢿⣿⣿⣿⣿⢿⣿⣟⣿⢻⢿⣿⢿⣿⡿⣿⢿⣿⣿⢻⣿⠿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣾⣷⣿⣿⣯⣿⣷⣷⣿⣼⣧⣿⣿⣯⣿⣿⣿⣿⣿⣵⣿⣿⣾⣿⣿⣿⣿⣿⣿⣾⣿⣶⣽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
䷩ 𝚕𝚒𝚗𝚎 1753
╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕
(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/02/09/geminispace-1705-working-capsules/#comments
Gemini version at gemini://gemini.techrights.org/2022/02/09/geminispace-1705-working-capsules/
⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.09.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧
Gemini_version_available_♊︎
✐ Despite_Occasional_Shutdowns,_Geminispace_Has_a_Net_Gain_of_About_100_Working
Capsules_Per_Month_(It_Has_Accelerated_Further_in_2022)⠀✐
Posted in Site_News at 9:37 am by Dr. Roy Schestowitz
🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇January 2021: ~400; June 2021: 1000; December 2021: 1500;
January 2022: 1600; Today (Feb. 9th): Over 1700⦈
🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇1705_capsules⦈_
Summary: With almost 2,100 known Gemini capsules, about 82% of which are online
and accessible, the_growth_continues_unabated (net gain of about 100 in just 3
weeks or roughly 5 per day, on average)
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⢰⣶⡆⢰⣶⣶⡏⠉⣷⣦⢰⣶⡆⣶⣶⢱⣶⡏⢹⣶⣶⡏⢻⣶⣶⣶⣬⢱⣶⡄⣶⡾⢻⡟⣵⣶⣶⣍⢋⣵⣶⣶⣍⢫⣴⣶⣦⡙⣛⣩⣾⢹⣿⣿⣿⣿⣿⣿⣿⣿⡟⣵⣶⣶⠈⣽⣶⣶⣭⠛⣽⣶⣶⣌⠻⣿
⠿⡇⢸⣿⡇⢸⣿⣿⣿⠀⣿⣿⣾⣿⡇⣿⣿⢸⣿⡇⣼⣿⣿⣷⢸⣿⣿⣽⣿⠀⣿⣷⣿⢇⣿⣾⠿⢇⣿⣿⢸⣿⡇⣿⣿⠸⠿⢠⣿⡇⠛⣿⣿⢈⣿⣿⣿⢟⣛⡛⠛⡛⢱⡿⣿⣿⢸⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠉
⠀⠀⢸⣿⡇⣿⣿⣸⣿⡄⣿⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣹⣿⢸⣿⣿⢿⣷⠀⢸⣿⡟⣸⣿⣿⢃⣾⡿⠃⢸⣿⡇⣿⣿⠀⣠⣿⡟⢰⡇⣿⣿⠘⣛⣿⣷⣟⣉⡛⢛⠃⣿⣇⣿⣿⣸⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠀
⠀⢠⣼⣿⡇⣿⣿⢻⣿⡇⣿⡇⢿⣿⡇⢿⣿⣼⣿⢧⣿⡿⢻⣿⣿⣿⣿⢸⣿⠀⢸⣿⡇⠹⡿⢡⣿⣿⣥⣤⠸⣿⣧⣿⡟⢰⣿⣯⣤⡄⠁⣿⣿⢰⣶⡏⢿⣿⣿⠿⠟⠘⠛⠛⣿⣿⠋⢿⣧⣿⡿⠘⣿⣧⣿⡿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣤⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠉⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⠿⣿⣆⠀⠀⠀⢀⣰⣾⣿⣿⣿⡆⠀⠀⠀⠀⢰⣟⣷⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⣠⣶⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀
⠀⠠⠠⠤⡤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣧⣄⣀⣀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠠⠄⠀
⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⠤⠤⠤⠶⠶⠶⠒⣲⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⠍⠀⠀⠀⠈⠉⠉⠐⠶⢦⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠛⠙⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠿⠋⠙⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣷⣶⣶⡒⠲⠤⠤⠤⠤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣴⣿⠷⢿⣿⣿⣿⣿⣿⡿⠟⠉⠉⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣷⣶⣶⣦⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀
⠄⠠⠒⠒⠚⠛⡛⠋⢹⣟⠁⠀⣻⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣀⣠⣿⣿⣿⣿⣿⣴⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⢀⠠⠤⣶⣾⣿⣿⣿⣿⣿⡿⠋⡌⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀
⠀⠖⠶⣶⠏⢶⠄⠱⠶⠶⣆⡹⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡿⠉⠀⠀
[22A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⢰⣶⡆⢰⣶⣶⡏⠉⣷⣦⢰⣶⡆⣶⣶⢱⣶⡏⢹⣶⣶⡏⢻⣶⣶⣶⣬⢱⣶⡄⣶⡾⢻⡟⣵⣶⣶⣍⢋⣵⣶⣶⣍⢫⣴⣶⣦⡙⣛⣩⣾⢹⣿⣿⣿⣿⣿⣿⣿⣿⡟⣵⣶⣶⠈⣽⣶⣶⣭⠛⣽⣶⣶⣌⠻⣿
⠻⡇⢸⣿⡇⢸⣿⣿⣿⠀⣿⣿⣾⣿⡇⣿⣿⢸⣿⡇⣼⣿⣿⣷⢸⣿⣿⣹⣿⠀⣿⣷⣿⢇⣿⣾⠿⢇⣿⣿⢸⣿⡇⣿⣿⠸⠿⢠⣿⡇⠛⣿⣿⢈⣿⣿⣿⢟⣛⡛⠛⡛⢰⡿⣿⣿⢰⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠉
⠀⠀⢸⣿⡇⣿⣿⣸⣿⡄⣿⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣹⣿⢸⣿⣿⢿⣷⠀⢸⣿⡟⣸⣿⣿⢃⣾⡿⠃⢸⣿⡇⣿⣿⠀⣠⣿⡟⢰⡇⣿⣿⠘⣛⣿⣷⣟⣉⡛⠛⠃⣿⣇⣿⣿⣸⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠀
⠀⢠⣼⣿⡇⣿⣿⢻⣿⡇⣿⡇⢿⣿⡇⢿⣿⣼⣿⢧⣿⡿⢻⣿⣿⣿⣿⢸⣿⠀⢸⣿⡇⠹⡿⢡⣿⣿⣥⣤⠸⣿⣧⣿⡟⢰⣿⣯⣤⡌⠁⣿⣿⢰⣶⡏⢿⣿⣿⠿⠟⠘⠛⠛⣿⣿⠋⢿⣧⣿⡿⠘⣿⣧⣿⡿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣤⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠉⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⠿⣿⣆⠀⠀⠀⢀⣰⣾⣿⣿⣿⡄⠀⠀⠀⠀⢰⣞⣷⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⣠⣶⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀
⠀⠄⠠⠤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣧⣀⣀⣀⠀⠀⠀⠠⠤⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⡤⠤⠤⠴⠶⠶⠖⣲⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠉⠀⠀⠀⠈⠉⠉⠒⠶⢦⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠂⠉⠉⠉⠋⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⠿⠋⠉⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣷⣶⣶⡒⠦⠤⠤⠤⢤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣴⣿⡷⢶⣿⣿⣿⣿⣿⡿⠟⠉⠉⠛⠋⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣶⣶⣶⣤⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀
⠄⠠⠒⠒⠚⠛⠛⠋⢽⡿⠁⠁⣿⣶⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣀⣠⣿⣿⣿⡿⣋⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⢀⠠⠤⣶⣾⣿⣿⣿⣿⣿⡿⠋⡀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀
⠀⠖⠲⣶⠏⢶⠄⠱⠶⢶⣆⡹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡿⠿⠛⠀⠀
[22A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⢰⣶⡆⢰⣶⣶⡏⠉⣷⣦⢰⣶⡆⣶⣶⢱⣶⡏⢹⣶⣶⡏⢻⣶⣶⣶⣬⢱⣶⡄⣶⡾⢻⡟⣵⣶⣶⣍⢋⣵⣶⣶⣝⢫⣴⣶⣦⡙⣛⣩⣾⢹⣿⣿⣿⣿⣿⣿⣿⣿⡟⣵⣶⣶⠈⣽⣶⣶⣭⠛⣽⣶⣶⣌⠻⣿
⠿⡇⢸⣿⡇⢸⣿⣿⣿⠀⣿⣿⣾⣿⡇⣿⣿⢸⣿⡇⣼⣿⣿⣷⢸⣿⣿⣽⣿⠀⣿⣷⣿⢇⣿⣾⠿⢇⣿⣿⢸⣿⡇⣿⣿⠸⠿⢠⣿⡇⠛⣿⣿⢈⣿⣿⣿⢟⣛⡛⠟⡛⢱⡿⣿⣿⢸⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠁
⠀⠀⢸⣿⡇⣿⣿⣸⣿⡄⣿⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣹⣿⢸⣿⣿⢿⣷⠀⢸⣿⡟⣸⣿⣿⢃⣾⡿⠃⢸⣿⡇⣿⣿⠀⣠⣿⡟⢰⡇⣿⣿⠘⣛⣿⣷⣟⣉⡛⠛⠃⣿⣇⣿⣿⣸⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠀
⠀⢠⣼⣿⣇⣿⣿⢻⣿⡇⣿⡇⢿⣿⡇⢿⣿⣼⣿⢧⣿⡿⢻⣿⣿⣿⣿⢸⣿⠀⢸⣿⡇⠹⡿⢡⣿⣿⣥⣤⠸⣿⣧⣿⡟⢰⣿⣯⣤⡄⠁⣿⣿⢰⣶⡏⢿⣿⣿⠿⠟⠘⠛⠛⣿⣿⠋⢿⣧⣿⡿⠘⣿⣧⣿⡿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⡄⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠉⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⠀⠀⠀⠀⠀⠠⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⢿⣿⣄⠀⠀⠀⢀⣲⣿⣿⣿⣿⡄⠀⠀⠀⠀⢰⣾⣧⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⣠⣾⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣯⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣁⣀⣀⣀⠀⠀⠠⠤⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⡤⠤⠤⠴⠶⠶⠖⣲⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠉⠀⠀⠀⠈⠉⠉⠒⠶⢤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠉⠉⠋⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠿⠋⠉⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣷⣶⣶⡒⠦⠤⠤⠤⢤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣴⣾⡶⢾⣿⣿⣿⣿⣿⡿⠏⠉⠈⠛⠛⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣷⣶⣶⣤⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀
⠤⠠⠔⠒⠚⠛⠛⠋⢹⡏⠁⠁⣲⣶⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣿⣿⣿⡿⣋⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⢀⠠⠤⣶⣶⣿⣿⣿⣿⣿⡿⠋⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀
⠀⠖⠶⣶⠏⢶⠄⠱⠶⢶⣆⡹⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡿⠁⠀⠀
[22A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⢰⣶⡆⢰⣶⣶⡏⠉⣷⣦⢰⣶⡆⣶⣶⢱⣶⡏⢹⣶⣶⡏⢻⣶⣶⣶⣭⢱⣶⡄⣶⡾⢻⡟⣵⣶⣶⣍⢋⣵⣶⣶⣝⢫⣴⣶⣦⡙⢛⣩⣾⢹⣿⣿⣿⣿⣿⣿⣿⣿⡟⣵⣶⣶⠈⣽⣶⣶⣭⠛⣽⣶⣶⣬⠻⣿
⠻⡇⢸⣿⡇⢸⣿⣿⣿⠀⣿⣿⣾⣿⡇⣿⣿⢸⣿⡇⣼⣿⣿⣷⢸⣿⣿⣽⣿⠀⣿⣷⣿⢇⣿⣾⠿⢇⣿⣿⢸⣿⡇⣿⣿⠸⠿⢠⣿⡇⠛⣿⣿⢈⣿⣿⣿⢟⣛⡛⠛⡛⢰⡿⣿⣿⢰⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠉
⠀⠀⢸⣿⡇⣿⣿⣸⣿⡄⣿⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣹⣿⢸⣿⣿⢿⣷⠀⢸⣿⡟⣸⣿⣿⢃⣾⡿⠃⢸⣿⡇⣿⣿⠀⣠⣿⡟⢰⡇⣿⣿⠘⣛⣿⣷⣟⣉⡛⠛⠃⣿⣇⣿⣿⣸⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠀
⠀⢠⣼⣿⣇⣿⣿⢻⣿⡇⣿⡇⢿⣿⡇⢿⣿⣼⣿⢧⣿⡿⢻⣿⣿⣿⣿⢸⣿⠀⢸⣿⡇⠹⡿⢡⣿⣿⣥⣤⠸⣿⣧⣿⡟⢰⣿⣯⣤⡄⠁⣿⣿⢰⣶⡏⢿⣿⡿⠿⠟⠘⠛⠛⣿⣿⠋⢿⣧⣿⡿⠘⣿⣧⣿⡿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡄⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠉⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣛⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡄⠀⠀⠀⠀⠀⢠⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣷⡄⠀⠀⠀⢐⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⣲⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣦⣴⣾⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⣠⣾⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀
⠀⠀⠀⢄⣤⣤⣤⣤⣤⣤⣤⣤⣠⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡿⣀⣀⣀⣀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⡤⠤⠤⠤⠶⠶⠖⣲⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡝⠉⠀⠀⠀⠈⠉⠉⠒⠶⢤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠂⠘⠛⠋⠙⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠋⠙⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣷⣶⣶⡒⠦⠤⠤⢤⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣦⣶⡶⢶⣿⣿⣿⣿⣿⡿⠟⠉⠙⠛⠛⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣷⣶⣶⣤⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀
⠀⠠⠰⠒⠚⠛⠛⠋⠻⠏⠉⠀⣩⣶⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⣠⣿⣿⣿⣿⣏⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃
⠀⠀⠀⠀⠀⠤⣶⣶⣿⣿⣿⣿⣿⡿⠋⠈⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀
⠀⠖⠶⣶⠏⢶⠄⠱⠶⢶⣆⠹⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠿⠉⠀⠀
[22A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⢰⣶⡆⢰⣶⣶⡏⠉⣷⣦⢰⣶⡆⣶⣶⢱⣶⡏⢹⣶⣶⡏⢻⣶⣶⣶⣬⢱⣶⡄⣶⡾⢻⡟⣵⣶⣶⣍⢋⣵⣶⣶⣝⢫⣴⣶⣦⡙⣛⣩⣾⢹⣿⣿⣿⣿⣿⣿⣿⣿⡟⣵⣶⣶⠈⣽⣶⣶⣭⠛⣽⣶⣶⣬⠻⣿
⠿⡇⢸⣿⡇⢸⣿⣿⣿⠀⣿⣿⣾⣿⡇⣿⣿⢸⣿⡇⣼⣿⣿⣷⢸⣿⣿⣽⣿⠀⣿⣷⣿⢇⣿⣾⠿⢇⣿⣿⢸⣿⡇⣿⣿⠸⠿⢠⣿⡇⠛⣿⣿⢈⣿⣿⣿⢟⣛⡛⠛⡛⢱⡿⣿⣿⢸⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠉
⠀⠀⢸⣿⡇⣿⣿⣸⣿⡄⣿⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣹⣿⢸⣿⣿⢿⣷⠀⢸⣿⡟⣸⣿⣿⢃⣾⡿⠃⢸⣿⡇⣿⣿⠀⣠⣿⡟⢰⡇⣿⣿⠘⣛⣿⣷⣟⣉⡛⠛⢃⣿⣇⣿⣿⣸⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠀
⠀⢠⣼⣿⣇⣿⣿⢻⣿⡇⣿⡇⢿⣿⡇⢿⣿⣼⣿⢧⣿⡿⢻⣿⣿⣿⣿⢸⣿⠀⢸⣿⡇⠹⡿⢡⣿⣿⣥⣤⠸⣿⣧⣿⡟⢰⣿⣯⣤⡄⠁⣿⣿⢰⣶⡏⢿⣿⡿⠿⠟⠘⠛⠛⣿⣿⠋⢿⣧⣿⡿⠘⣿⣧⣿⡿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠉⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⢀⣼⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣿⣿⣧⡀⠀⠀⠀⢐⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣰⣲⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢻⣿⣷⣤⣴⣾⣿⣿⣿⣿⣿⣿⣷⣤⣀⣀⣤⣿⠏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀
⠀⠀⠠⢤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠂⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣀⣀⣀⣀⠀⠄⠀⠄⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⠤⠤⠤⠶⠶⠖⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡙⠋⠀⠀⠀⠈⠉⠉⠒⠶⣤⣄⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠐⠚⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠙⠛⠋⠋⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣷⣶⣶⡒⠤⠤⠤⠤⣤⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣴⣷⡾⢿⣿⣿⣿⣿⣿⡿⠟⠉⠛⠛⠛⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣷⣶⣦⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀
⠀⠤⠔⠒⠒⠛⠟⠛⢻⡛⠉⠁⣵⣶⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣀⣠⣿⣿⣿⣿⣏⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢀⠠⠤⣶⣶⣿⣿⣿⣿⣿⡿⠋⠈⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀
⠀⠖⠲⣶⠏⢶⠄⠱⠶⢶⣖⡙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠟⠋⠁⠀
[22A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⢰⣶⡆⢰⣶⣶⡏⠉⣷⣦⢰⣶⡆⣶⣶⢱⣶⡏⢹⣶⣶⡏⢻⣶⣶⣶⣬⢱⣶⡄⣶⡾⢻⡟⣵⣶⣶⣍⢋⣵⣶⣶⣝⢫⣴⣶⣦⡙⢛⣩⣾⢹⣿⣿⣿⣿⣿⣿⣿⣿⡟⣵⣶⣶⠈⣵⣶⣶⣭⠛⣽⣶⣶⣌⠻⣿
⠻⡇⢸⣿⡇⢸⣿⣿⣿⠀⣿⣿⣾⣿⡇⣿⣿⢸⣿⡇⣼⣿⣿⣷⢸⣿⣿⣽⣿⠀⣿⣷⣿⢇⣿⣾⠿⢇⣿⣿⢸⣿⡇⣿⣿⠸⠿⢠⣿⡇⠛⣿⣿⢈⣿⣿⣿⢟⣛⡛⠛⡛⢱⡿⣿⣿⢰⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠉
⠀⠀⢸⣿⡇⣿⣿⣸⣿⡄⣿⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣹⣿⢸⣿⣿⢿⣷⠀⢸⣿⡟⣸⣿⣿⢃⣾⡿⠃⢸⣿⡇⣿⣿⠀⣠⣿⡟⢰⡇⣿⣿⠘⣛⣿⣷⣟⣉⡛⠛⠃⣿⣇⣿⣿⣸⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠀
⠀⢠⣼⣿⣇⣿⣿⢻⣿⡇⣿⡇⢿⣿⡇⢿⣿⣼⣿⢧⣿⡿⢻⣿⣿⣿⣿⢸⣿⠀⢸⣿⡇⠹⡿⢡⣿⣿⣥⣤⠸⣿⣧⣿⡟⢰⣿⣯⣤⡄⠁⣿⣿⢰⣶⡏⢿⣿⡿⠿⠟⠘⠛⠛⣿⣿⠋⢿⣧⣿⡿⠘⣿⣧⣿⡿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠉⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣾⣄⠀⠀⠀⠀⢺⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣔⣲⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⣿⣿⣦⣠⣴⣾⣿⣿⣿⣿⣿⣿⣶⣤⣀⢀⣠⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀
⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣄⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠐⠒⠒⠂⠂⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣀⣀⣀⣀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠄⠀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⡤⠤⠤⠶⠶⠶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡙⠃⠀⠀⠀⠉⠉⠉⠒⠶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠒⠘⠋⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠋⠙⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣶⣶⡤⠤⠤⠤⢤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣴⣶⡶⢶⣾⣿⣿⣿⣿⡿⠛⠉⠉⠛⠛⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀
⠠⠤⠔⠒⠚⠛⠛⠛⢻⡋⠉⠉⣬⣶⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⣀⣠⣿⣿⣿⡿⣋⣤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠤⣴⣶⣿⣿⣿⣿⣿⡿⠋⠩⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀
⠀⠖⠲⣶⠏⢶⠄⠱⠶⢶⣆⡙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠿⠓⠀⠀
[22A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⢱⣶⡆⢰⣶⣶⡏⠉⣷⣦⢰⣶⡆⣶⣶⢱⣶⡏⢹⣶⣶⡏⢻⣶⣶⣶⣬⢱⣶⡄⣶⡾⢻⡟⣵⣶⣶⣍⢋⣵⣶⣶⣝⢫⣴⣶⣦⡙⣛⣩⣾⢹⣿⣿⣿⣿⣿⣿⣿⣿⡟⣵⣶⣶⠈⣵⣶⣶⣭⠛⣽⣶⣶⣬⠻⣿
⠿⡇⢸⣿⡇⢸⣿⣿⣿⠀⣿⣿⣾⣿⡇⣿⣿⢸⣿⡇⣼⣿⣿⣷⢸⣿⣿⣹⣿⠀⣿⣷⣿⢇⣿⣾⠿⢇⣿⣿⢸⣿⡇⣿⣿⠸⠿⢠⣿⡇⠛⣿⣿⢈⣿⣿⣿⢟⣛⡛⠛⡛⢱⡿⣿⣿⢰⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠉
⠀⠀⢸⣿⡇⣿⣿⣸⣿⡄⣿⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣹⣿⢸⣿⣿⢿⣷⠀⢸⣿⡟⣸⣿⣿⢃⣾⡿⠃⢸⣿⡇⣿⣿⠀⣠⣿⡟⢰⡇⣿⣿⠘⣛⣿⣷⣟⣉⡛⠛⠃⣿⣇⣿⣿⣸⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠀
⠀⢠⣼⣿⣇⣿⣿⢻⣿⡇⣿⡇⢿⣿⡇⢿⣿⣼⣿⢧⣿⡿⢻⣿⣿⣿⣿⢸⣿⠀⢸⣿⡇⠹⡿⢡⣿⣿⣥⣤⠸⣿⣧⣿⡟⢰⣿⣯⣤⡄⠁⣿⣿⢰⣶⡎⢿⣿⡿⠿⠟⠘⠛⠛⣿⣿⠋⢿⣧⣿⡿⠘⣿⣧⣿⡿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣦⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠉⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣯⣿⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣔⢶⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠹⣿⣿⣄⣀⣤⣶⣿⣿⣿⣿⣿⣿⣶⣄⡀⢀⣤⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀
⠀⠀⠀⣀⣀⣀⣠⣤⣄⣄⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠒⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣄⣀⣀⣀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⡤⠤⠤⠤⠶⠶⣲⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡙⠋⠀⠀⠀⠉⠉⠉⠒⠶⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠂⠚⠛⠛⠛⠙⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠋⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣶⣶⣖⡠⠤⠤⠤⢤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣴⣶⡶⣶⣶⣿⣿⣿⣿⡿⠟⠉⠙⠛⠛⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣷⣶⣤⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀
⠀⠤⠤⠖⠒⠛⠛⠛⢛⡉⠉⠠⣤⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣀⣰⣿⣿⣿⣿⣏⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁
⠀⠀⠀⠀⠀⠤⣴⣶⣾⣿⣿⣿⣿⡿⠋⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀
⠀⠖⠶⣶⠏⢶⠄⠱⠶⢶⣖⡹⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡿⠟⠁⠀⠀
[22A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⢱⣶⡆⢱⣶⣶⡏⠉⣷⣦⢰⣶⡆⣶⣶⢱⣶⡏⢹⣶⣶⡏⢻⣶⣶⣶⣬⢱⣶⡄⣶⡾⢻⡟⣵⣶⣶⣍⢋⣵⣶⣶⣝⢫⣴⣶⣦⡙⣛⣩⣾⢹⣿⣿⣿⣿⣿⣿⣿⣿⡟⣵⣶⣶⠈⣵⣶⣶⣭⠛⣽⣶⣶⣬⠻⣿
⠿⡇⢸⣿⡇⢸⣿⣿⣿⠀⣿⣿⣾⣿⡇⣿⣿⢸⣿⡇⣼⣿⣿⣷⢸⣿⣿⣹⣿⠀⣿⣷⣿⢇⣿⣾⠿⢇⣿⣿⢸⣿⡇⣿⣿⠸⠿⢠⣿⡇⠛⣿⣿⢈⣿⣿⣿⢟⣛⡛⠛⡛⢱⡿⣿⣿⢸⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠉
⠀⠀⢸⣿⡇⣿⣿⣸⣿⡄⣿⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣹⣿⢸⣿⣿⢿⣷⠀⢸⣿⡟⣸⣿⣿⢃⣾⡿⠃⢸⣿⡇⣿⣿⠀⣠⣿⡟⢰⡇⣿⣿⠘⣛⣿⣷⣟⣉⡛⠛⠃⣿⣇⣿⣿⣸⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠀
⠀⢠⣼⣿⣇⣿⣿⢻⣿⡇⣿⡇⢿⣿⡇⢿⣿⣼⣿⢧⣿⡿⢻⣿⣿⣿⣿⢸⣿⠀⢸⣿⡇⠹⡿⢡⣿⣿⣥⣤⠸⣿⣧⣿⡟⢰⣿⣯⣤⡄⠁⣿⣿⢰⣶⡏⢿⣿⡿⠿⠟⠘⠛⠛⣿⣿⠋⢿⣧⣿⡿⠘⣿⣧⣿⡿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡆⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠉⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⡤⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⢻⣿⣦⣄⣀⣠⣴⣿⣿⣿⣿⣿⣿⣦⣄⠀⢀⣠⣿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀
⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠒⠒⠒⠂⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠠⠄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⡤⠤⠤⠴⠶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠛⠋⠀⠀⠀⠉⠉⠉⠒⠶⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠒⠒⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠻⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣦⣤⡤⠤⠤⢤⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣷⣦⡀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣴⣶⡶⢶⣶⣿⣿⣿⣿⣿⠟⠉⠙⠛⠛⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣷⣶⣦⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀
⠀⠤⠤⠖⠲⠛⠛⠛⣿⠋⠉⠡⣦⣶⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢀⣰⣿⣿⣿⣿⣋⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠤⣤⣶⣾⣿⣿⣿⣿⡿⠋⡈⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠖⠶⣶⠏⢶⠄⠱⠶⢶⣖⡙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⠿⠇⠀⠀
[22A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⢱⣶⡆⢰⣶⣶⡎⠉⣷⣦⢰⣶⡎⣷⣾⢱⣶⡏⢹⣶⣶⡏⢻⣶⣶⣶⣭⢱⣶⡄⣶⡾⢻⡟⣵⣶⣶⣍⢋⣵⣶⣶⣝⢫⣴⣶⣦⡙⣛⣩⣾⢹⣿⣿⣿⣿⣿⣿⣿⣿⡟⣵⣶⣶⠈⣵⣶⣶⣭⠛⣽⣶⣶⣌⠻⣿
⠿⡇⢸⣿⡇⢸⣿⣿⣿⠀⣿⣿⣾⣿⡇⣿⣿⢸⣿⡇⣼⣿⣿⣷⢸⣿⣿⣽⣿⠀⣿⣷⣿⢇⣿⣾⠿⢇⣿⣿⢸⣿⡇⣿⣿⠸⠿⢠⣿⡇⠛⣿⣿⢈⣿⣿⣿⢟⣛⡛⠛⡛⢱⡿⣿⣿⢸⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠉
⠀⠀⢸⣿⡇⣿⣿⣸⣿⡄⣿⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣹⣿⢸⣿⣿⢿⣷⠀⢸⣿⡟⣸⣿⣿⢃⣾⡿⠃⢸⣿⡇⣿⣿⠀⣠⣿⡟⢰⡆⣿⣿⠘⣛⣿⣷⣟⣉⡛⠛⢃⣿⣇⣿⣿⣸⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠀
⠀⢠⣼⣿⣇⣿⣿⢻⣿⡇⣿⡇⢿⣿⡇⢿⣿⣼⣿⢧⣿⡿⢻⣿⣿⣿⣿⢸⣿⠀⢸⣿⡇⠹⡟⢡⣿⣿⣥⣤⠸⣿⣧⣿⡟⢰⣿⣯⣤⡄⠀⣿⣿⢰⣶⡎⢿⣿⡿⠿⠟⠘⠛⠛⣿⣿⠋⢿⣧⣿⡿⠘⣿⣧⣿⡿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡆⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠉⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⢾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣲⡄⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣤⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠿⢿⣿⣤⡀⠀⣀⣤⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⣠⣿⠿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀
⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢀⣀⡀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠐⠒⠒⠒⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠠⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⠤⠤⠤⠤⠶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡻⠏⠀⠀⠀⠉⠉⠙⠒⠶⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠒⠚⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠻⠟⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣷⣤⣴⡤⠤⠤⢤⣤⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣷⣤⡀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣴⣦⣶⢶⣶⣿⣿⣿⣿⡿⠟⠉⠹⠟⠛⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣶⣦⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀
⠀⠤⠤⠶⠞⠟⠛⠛⢿⠍⠉⢻⣧⣶⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣸⣿⣿⣿⡿⠋⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅
⠀⠀⠀⠀⠀⠤⣴⣶⣾⣿⣿⣿⣿⡿⠋⠈⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀
⠀⠖⠶⣶⠏⢶⠄⠱⠶⢶⣖⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⢿⡅⠀⠀
[22A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⢱⣶⡆⢱⣶⣶⡎⠋⣷⣦⢰⣶⡎⣷⣾⢱⣶⡏⢹⣶⣶⡏⢻⣶⣶⣶⣭⢱⣶⡄⣶⡾⢻⡟⣵⣶⣶⣍⢋⣵⣶⣶⣝⢫⣴⣶⣦⡙⣛⣩⣾⢹⣿⣿⣿⣿⣿⣿⣿⣿⡟⣵⣶⣶⠈⣴⣶⣶⣬⠛⣵⣶⣶⣌⠻⣿
⠿⡇⢸⣿⡇⢸⣿⣿⣿⠀⣿⣿⣾⣿⡇⣿⣿⢸⣿⡇⣼⣿⣿⣷⢸⣿⣿⣽⣿⠀⣿⣷⣿⢇⣿⣾⠿⢇⣿⣿⢸⣿⡇⣿⣿⠸⠿⢠⣿⡇⠛⣿⣿⢈⣿⣿⣿⢟⣛⡛⠛⡛⢱⡿⣿⣿⢰⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠉
⠀⠀⢸⣿⡇⣿⣿⣸⣿⡄⣿⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣹⣿⢸⣿⣿⢿⣷⠀⢸⣿⡟⣸⣿⣿⢃⣾⡿⠃⢸⣿⡇⣿⣿⠀⣠⣿⡟⢠⡆⣿⣿⠘⣛⣿⣷⣟⣉⡛⠛⢃⣿⣇⣿⣿⣸⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠀
⠀⢠⣼⣿⣇⣿⣿⢻⣿⡇⣿⡇⢿⣿⡇⢿⣿⣼⣿⢧⣿⡿⢻⣿⣿⣿⣿⢸⣿⠀⢸⣿⡇⠙⠿⢡⣿⣿⣥⣤⠸⣿⣧⣿⡟⢰⣿⣯⣤⡄⠀⣿⣿⢰⣶⡎⢿⣿⡿⠿⠛⠘⠛⠛⣿⣿⠋⢿⣧⣿⡿⠘⣿⣧⣿⡿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡄⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠉⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣯⢽⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣼⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢤⡄⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣠⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣬⣷⣶⣷⡀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣷⣤⡀⠀⠀⣠⣿⣶⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢹⣿⣿⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀
⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⣀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠄⠀⠀⠀⠀⠒⠒⠒⠂⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠤⠤⠤⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠠⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⡤⠤⠤⠤⠴⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠟⠃⠀⠀⠉⠉⠙⠒⠶⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠒⠒⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠛⠿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣶⣤⣤⡤⠤⠤⢤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣷⣦⡀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⣦⣴⣶⣶⣾⣿⣿⣿⡿⠟⠉⠙⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣷⣶⣦⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀
⠀⠠⠤⠴⠶⠟⠛⠛⣻⠉⠉⢉⣥⣶⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⣸⣿⣿⣿⡿⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠠⣤⣴⣶⣿⣿⣿⣿⡿⠉⠑⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀
⠀⠖⠲⣶⠏⢶⠄⠱⠶⢶⣆⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠟⠋⠀⠀
[22A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⢱⣶⡎⢰⣶⣶⡎⠉⣷⣦⢰⣶⡎⣷⣾⢱⣶⡏⢹⣶⣶⡏⢻⣶⣶⣶⣭⢱⣶⡄⣶⡾⢻⡟⣵⣶⣶⣍⢋⣵⣶⣶⣝⢫⣴⣶⣦⡙⣛⣩⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⡟⣵⣶⣶⠈⣴⣶⣶⣭⠛⣵⣶⣶⣌⠻⣿
⠿⡇⢸⣿⡇⣸⣿⣿⣿⠀⣿⣿⣾⣿⡇⣿⣿⢸⣿⡇⣼⣿⣿⣷⢸⣿⣿⣽⣿⠀⣿⣷⣿⢇⣿⣾⠿⢇⣿⣿⢸⣿⡇⣿⣿⠸⠿⢠⣿⡇⠛⣿⣿⢈⣿⣿⣿⢟⣛⡛⠛⡛⢱⡿⣿⣿⢰⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠉
⠀⠀⢸⣿⡇⣿⣿⣸⣿⡄⣿⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣹⣿⢸⣿⣿⢿⣷⠀⢸⣿⡟⣸⣿⣿⢃⣾⡿⠃⢸⣿⡇⣿⣿⠀⣠⣿⡟⢠⡆⣿⣿⠘⢛⣿⣷⣟⣉⡛⠛⠃⣿⣇⣿⣿⣸⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠀
⠀⢠⣼⣿⣇⣿⣿⢻⣿⡇⣿⡇⢿⣿⡇⢿⣿⣼⣿⢧⣿⡿⢻⣿⣿⣿⣿⢸⣿⠀⢸⣿⡇⠙⠟⢡⣿⣿⣥⣤⠸⣿⣧⣿⡟⢰⣿⣯⣤⡄⠀⣿⣿⢰⣶⡊⢿⣿⠿⠿⠟⠘⠛⠛⣿⣿⠋⢿⣧⣿⡿⠘⣿⣧⣿⡿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡆⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠉⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢷⢼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⡄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣤⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⠛⢿⣿⣦⡀⠀⣀⣤⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⣠⣿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀
⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠐⠒⠒⠒⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⣤⠤⠤⠤⠤⠤⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⠤⠤⠤⠤⣴⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡙⠋⠁⠀⠀⠉⠉⠓⠒⢦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠒⠒⠒⠚⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣶⣤⣤⡤⠤⠤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣤⡀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⠟⠋⠙⠛⠻⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣶⣶⣤⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀
⡀⠠⠤⠴⠖⠿⠛⠛⡛⠉⠉⢉⣥⣶⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠅
⠀⠀⠀⠀⠀⢠⣤⣴⣶⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠖⠲⣶⠏⢶⠄⠱⠶⢶⡆⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⠿⠁⠀⠀
[22A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⢱⣶⡆⢱⣶⣶⡎⠋⣷⣦⢰⣶⡎⣷⣾⢱⣶⡏⢹⣶⣶⡏⢻⣶⣶⣶⣭⢱⣶⡌⣶⡾⢻⡟⣵⣶⣶⣍⢋⣵⣶⣶⣝⢫⣴⣶⣦⡙⣛⣩⣾⢹⣿⣿⣿⣿⣿⣿⣿⣿⡟⣵⣶⣶⠈⣴⣶⣶⣬⠛⣵⣶⣶⣌⠻⣿
⠿⡇⢸⣿⡇⢸⣿⣿⣿⠀⣿⣿⣾⣿⡇⣿⣿⢸⣿⡇⣼⣿⣿⣷⢸⣿⣿⣽⣿⠀⣿⣷⣿⢇⣿⣾⠿⢇⣿⣿⢸⣿⡇⣿⣿⠸⠿⢠⣿⡇⠛⣿⣿⢈⣿⣿⣿⢟⣛⡛⠛⡛⢱⡿⣿⣿⢸⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠉
⠀⠀⢸⣿⡇⣿⣿⣸⣿⡄⣿⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣹⣿⢸⣿⣿⢿⣷⠀⢸⣿⡟⣸⣿⣿⢃⣾⡿⠃⢸⣿⡇⣿⣿⠀⣠⣿⡟⢠⡆⣿⣿⠘⢛⣿⣷⣟⣉⣛⠛⢃⣿⣇⣿⣿⣸⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠀
⠀⢠⣼⣿⣇⣿⣿⢻⣿⡇⣿⡇⢿⣿⡇⢿⣿⣼⣿⢧⣿⡿⢻⣿⣿⣿⣿⢸⣿⠀⢸⣿⡇⠹⠟⢡⣿⣿⣥⣤⠸⣿⣧⣿⡟⢰⣿⣯⣤⡄⠀⣿⣿⢰⣶⡎⢿⣿⠿⠿⠟⠘⠛⠛⣿⣿⠋⢿⣧⣿⡿⠘⣿⣧⣿⡿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡆⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠉⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠻⢼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⡆⠀⠀⠀⠀⠀⢰⣶⣶⣿⣿⣇⠀⠀⠀⠀⠀⣤⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢻⣿⣦⡀⠀⣀⣤⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⣠⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐⠒⠒⠒⠂⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣥⣾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⣀⣀⣀⣀⣤⣠⣄⣀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⡤⠤⠤⠤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣯⡛⠋⠀⠀⠈⠉⠉⠓⠲⢦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠒⠒⠒⠚⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠟⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣶⣤⣤⡤⠤⢤⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣷⣤⡀⠀⠀⠀⠉⠉⠉⠉⠉⠑⠐⠂⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣴⣤⣤⣶⣶⣿⣿⣿⣿⣿⠟⠻⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣶⣶⣤⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀
⠀⡀⠤⠴⠶⠿⠛⢻⠛⠋⠉⢹⣥⣶⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⣼⣿⣿⣿⡿⢋⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢠⣤⣴⣶⣾⣿⣿⣿⡿⠋⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀
⠀⠖⠲⣶⠏⢶⠄⠱⠶⢶⡆⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⠟⠁⠀
[22A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛
⠀⠈⠁⠈⠉⠛⠛⠛⠿⠿⠟⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠈⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠋⠉⠉⠈⠉⠛⠛⠿⠿⢿⢿⣿⠿⠿⠿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠯⠧⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢷⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣖⣻⡀⠀⠀⠀⠀⢀⣴⣤⣿⣿⣷⠀⠀⠀⠀⠀⢠⠴⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⣿⣷⣤⣀⣤⣴⣾⣿⣿⣿⣿⣿⣷⣤⣀⣀⣤⣾⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠒⠂⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⣩⣥⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⣀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⡤⠤⠤⠤⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠁⠀⠀⠉⠉⠓⠒⢦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠒⠒⠒⠚⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠉⠉⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣶⣤⣤⡤⠤⢄⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣤⡀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣶⣾⣿⣿⣿⡿⠛⠋⠛⠟⠻⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣷⣶⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠠⠤⠶⠾⠟⠛⠛⠉⠉⠉⣁⣶⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⣠⣤⣶⣾⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀
⠀⠖⠲⣶⠏⢶⠄⠱⠶⢶⠖⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⡿⠃⠄⠀⠀
[22A⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠻⠟⠛⠻⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⢿⣿⣿⡿⠛⡛⠻⢿⣿⠿⢿⡿⢿⣿⡿⠿⣻⠿⢿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⡿⠿⢿⡿⠿⣛⠿⢿⣿⡿⠛⡛⠛⢿⣿⠿⢿⡻⠿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⡈⣿⣿⢸⣿⣿⣿⣏⣿⡏⣾⣿⢻⣿⣆⢰⣿⡿⢿⣷⡌⣴⣿⠿⣿⣧⣩⣴⣾⣿⠸⣿⣿⣿⢯⣥⣾⣿⠁⣾⣿⠿⣿⣦⠉⣾⣿⢻⣿⣆⢠⣾⣿⢻⣿⡎⣿⣿⣿⣿⣿
⠿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⣧⣿⣿⢸⣿⣿⣠⣿⣿⣾⣛⠛⣼⣿⡏⢸⣿⡇⢸⣿⡇⣛⡛⣰⣿⡿⣉⢹⣿⣿⢠⣬⡝⣿⣮⡉⣿⣿⠀⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡗⠹⣿⠿⠿⠋
⠀⠈⠁⠉⠁⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡿⣿⣿⣿⢸⣿⣿⠛⣳⣿⣿⢏⣼⣿⠟⠀⢸⣿⡇⢸⣿⡇⠛⣴⣿⡿⣱⣿⢸⣿⣿⠘⠛⢣⣿⣿⡇⣿⣿⠀⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣼⣿⣿⠘⣿⣿⣼⣿⡿⢸⣿⡇⢻⣿⣿⢸⣿⣿⣤⡌⠻⢁⣾⣿⣯⣤⡄⢸⣿⣇⣼⣿⠇⣼⣿⣯⣤⣭⠉⢸⣿⣿⢠⣤⡄⠙⠛⠀⣿⣿⠀⢿⣿⣤⣿⡿⠈⣿⣿⣸⣿⡿⠸⣿⣿⣸⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠉⠁⠀⠈⠙⠛⠉⠀⠈⠉⠁⠈⠉⠉⠈⠉⠉⠉⠁⠀⠈⠉⠉⠉⠉⠁⠀⠉⠛⠛⠁⠀⣉⣉⣉⠉⠉⠀⠈⠉⠉⠈⠉⠁⠀⠀⠀⠉⠉⠁⠈⠙⠛⠋⠁⠀⠈⠙⠛⠉⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⠷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢷⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣖⣻⠀⠀⠀⠀⠀⢀⣴⣤⣿⣿⣷⠀⠀⠀⠀⠀⣠⠴⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⣿⣷⣤⣀⣤⣶⣾⣿⣿⣿⣿⣿⣶⣤⣀⣀⣤⣾⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠐⠒⠒⠒⠂⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠁⠀⠀⠉⠁⠈⠉⠉⠉⠀⠀⠉⠉⠉⠉⠉⠁⠈⠀⠀⣩⣥⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⠤⠤⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠁⠀⠈⠉⠉⠓⠒⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠒⠒⠒⠒⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠉⠉⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢻⣶⣤⣤⡤⠤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣤⡀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠐⠂⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣤⣤⣤⣶⣾⣿⣿⣿⣿⠟⠛⠛⠿⠻⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣶⣦⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀
⡀⠠⠤⠤⠶⠿⠟⠛⠛⠛⠉⢩⣥⣶⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠃
⠀⠀⠀⠀⠀⠀⣤⣤⣶⣶⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡯⡋⠀
⠀⠖⠶⣶⠏⢶⠄⠱⠶⣶⡖⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⡿⠛⠀⠀
[22A⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠛⠟⠛⠻⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⢿⣿⣿⡿⠛⡛⠻⢿⣿⠿⢿⡿⠿⣿⡿⠿⣻⠿⢿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⡿⠿⢿⡿⠿⣛⠿⢿⣿⡿⠟⡛⠛⢿⣿⠿⢿⡻⠿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⡈⣿⣿⢸⣿⣿⣿⣏⣿⠏⣾⣿⢻⣿⣆⢰⣿⡿⢿⣷⡌⣼⣿⠿⣿⣧⣩⣴⣿⣿⠸⣿⣿⣿⢯⣥⣾⣿⠁⣾⣿⠿⣿⣦⠉⣾⣿⢻⣿⣦⢠⣾⣿⢻⣿⡎⣿⣿⣿⣿⣿
⠿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⣧⣿⣿⢸⣿⣿⣠⣿⣿⣾⣛⠛⣼⣿⡏⢸⣿⡇⢸⣿⡇⢛⠛⣰⣿⡿⣉⢹⣿⣿⢠⣬⡝⣿⣮⡉⣿⣿⠀⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡇⠹⣿⠿⠟⠋
⠀⠈⠁⠉⠁⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡿⣿⣿⣿⢸⣿⣿⠛⣳⣿⣿⢏⣼⣿⠟⠀⢸⣿⡇⢸⣿⡇⠛⣴⣿⡿⣡⣿⢸⣿⣿⠈⠛⢣⣿⣿⡇⣿⣿⠀⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣼⣿⣿⠘⣿⣿⣼⣿⡿⢸⣿⡇⢻⣿⣿⢸⣿⣿⣤⡌⠛⢁⣾⣿⣯⣤⡄⢸⣿⣇⣾⣿⠇⣼⣿⣯⣤⣭⠉⢸⣿⣿⢠⣤⡆⠙⠛⠀⣿⣿⠀⢿⣿⣤⣿⡿⠈⣿⣿⣸⣿⡿⠸⣿⣿⣸⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠉⠁⠀⠈⠙⠛⠉⠀⠈⠉⠁⠈⠉⠉⠈⠉⠉⠉⠁⠀⠈⠉⠉⠉⠉⠁⠀⠉⠛⠛⠉⠀⢉⣉⣉⠉⠉⠀⠈⠉⠉⠈⠉⠁⠀⠀⠀⠉⠉⠁⠈⠙⠛⠋⠁⠀⠈⠙⠛⠉⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡁⠀⠀⠀⠀⠀⠸⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣿⣿⣇⠀⠀⠀⠀⢀⣤⣤⣿⣿⣿⡀⠀⠀⠀⠀⢠⣚⣦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⣤⣴⣾⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⣴⣾⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⠀⠀⠀⠐⠒⠒⠒⠒⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠈⠈⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⣩⣭⣿⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⠀⢀⡀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⠤⠤⣤⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡻⠛⠁⠀⠈⠉⠙⠓⠂⢤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠒⠒⠒⠶⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠟⠉⠉⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣶⣤⣤⡤⢄⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣷⣤⡀⠀⠈⠉⠉⠉⠉⠉⠛⠐⠒⠂⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣴⣾⣿⣿⣿⡿⠟⠛⠻⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣶⣦⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀
⢀⣀⣤⡤⠶⠶⠾⠟⠛⠛⠋⢉⣍⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣾⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⢀⣤⣤⣶⣶⣿⣿⣿⡟⠋⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁
⠀⠖⠲⣶⠏⢶⠄⠱⠶⣶⡖⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⡿⡿⠍⠀⠀
[22A⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠛⠟⠛⠻⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⢿⣿⣿⡿⠛⡛⠻⢿⣿⠿⢿⡿⠿⣿⡿⠿⣻⠿⢿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⡿⠿⣿⡿⠟⣛⠿⢿⣿⡿⠟⡛⠛⢿⣿⠿⢿⡻⠿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⡈⣿⣿⢸⣿⣿⣿⣏⣿⠏⣾⣿⢻⣿⣆⢱⣿⡿⣿⣷⡌⣼⣿⠿⣿⣧⣩⣴⣿⣿⠸⣿⣿⣿⢯⣥⣾⣿⠁⣾⣿⠿⣿⣦⠉⣾⣿⢻⣿⣦⢠⣾⣿⢻⣿⡎⣿⣿⣿⣿⣿
⠿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⣧⣿⣿⢸⣿⣿⣠⣿⣿⣾⣛⠛⣼⣿⡏⢸⣿⡇⢸⣿⡇⢛⡛⣰⣿⡿⣉⢹⣿⣿⢠⣤⡝⣿⣮⡉⣿⣿⠀⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡗⠹⣿⠿⠟⠋
⠀⠈⠁⠈⠁⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡿⣿⣿⣿⢸⣿⣿⠛⣳⣿⣿⢏⣼⣿⠟⠀⢸⣿⡇⢸⣿⡇⠛⣴⣿⡿⣱⣿⢸⣿⣿⠈⠛⢣⣿⣿⠇⣿⣿⠀⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣼⣿⣿⠘⣿⣿⣼⣿⡿⢸⣿⡇⢻⣿⣿⢸⣿⣿⣤⡌⠛⢁⣾⣿⣯⣤⡄⢸⣿⣇⣼⣿⠇⣼⣿⣯⣤⣭⠉⢸⣿⣿⢠⣤⡆⠙⠛⠀⣿⣿⠀⢿⣿⣤⣿⡿⠈⣿⣿⣸⣿⡿⠸⣿⣿⣸⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠉⠁⠀⠈⠙⠛⠉⠀⠈⠉⠁⠈⠉⠉⠈⠉⠉⠉⠁⠀⠈⠉⠉⠉⠉⠁⠀⠉⠛⠛⠁⠀⠉⣉⣉⡉⠉⠀⠈⠉⠉⠈⠉⠁⠀⠀⠀⠉⠉⠁⠈⠙⠛⠋⠁⠀⠈⠙⠛⠉⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠹⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⡿⣧⠀⠀⠀⠀⠀⠀⠿⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⠿⢿⣷⡀⠀⠀⠀⢀⣀⣀⣿⣿⣿⡀⠀⠀⠀⠀⣴⣌⣧⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣤⣴⣾⣿⣿⣿⣿⣿⣿⣷⣶⣶⣄⣤⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠒⠒⠒⠒⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣁⣬⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⠤⠤⣤⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠁⠀⠈⠉⠙⠒⠢⢤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠲⠲⠶⠒⠒⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠁⠀⠀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⠟⠿⠟⠛⠉⠉⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣶⣤⣤⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣶⣤⡀⠀⠈⠉⠉⠉⠉⠉⠒⠒⠂⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣴⣿⣿⣿⣿⡿⠟⠛⠿⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣶⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⢀⣤⡤⢶⠶⠾⠿⠛⠛⠛⢩⣭⣷⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⢀⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠅
⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⠟⠋⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣯⠏⠀
⠀⠖⠶⣶⠏⢶⠄⠱⠶⣶⡖⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⡿⠿⠋⠁⠀
[22A⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠛⠛⠛⠻⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⢿⣿⣿⡿⠛⡛⠻⢿⣿⠿⢿⡿⠿⣿⡿⠿⣻⠿⢿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⡿⠿⢿⡿⠿⣛⠿⢿⣿⡿⠟⡛⠛⢿⣿⠿⢿⡻⠿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⡈⣿⣿⢸⣿⣿⣿⣏⣿⠏⣾⣿⢻⣿⣆⢱⣿⡿⣿⣷⡌⣼⣿⠿⣿⣧⣩⣴⣿⣿⠸⣿⣿⣿⢯⣥⣾⣿⠁⣾⣿⠿⣿⣦⠉⣾⣿⢻⣿⣦⢠⣾⣿⢻⣿⡎⣿⣿⣿⣿⣿
⠿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⣧⣿⣿⢸⣿⣿⣠⣿⣿⣾⣛⠛⣼⣿⡏⢸⣿⡇⢸⣿⡇⢛⠛⣰⣿⡿⣉⢹⣿⣿⢠⣤⡝⣿⣯⡉⣿⣿⠀⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡗⠹⣿⡿⠟⠋
⠀⠈⠁⠉⠁⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡿⣿⣿⣿⢸⣿⣿⠛⣷⣿⣿⢏⣼⣿⠟⠀⢸⣿⡇⢸⣿⡇⠛⣴⣿⡿⣡⣿⢸⣿⣿⠈⠛⢣⣿⣿⠇⣿⣿⠀⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣼⣿⣿⠘⣿⣿⣼⣿⡿⢸⣿⡇⢻⣿⣿⢸⣿⣿⣤⡌⠛⢁⣾⣿⣯⣤⡄⢸⣿⣇⣼⣿⠇⣼⣿⣯⣤⣭⠉⢸⣿⣿⢠⣤⡄⠙⠛⠀⣿⣿⠀⢿⣿⣤⣿⡿⠈⣿⣿⣸⣿⡿⠸⣿⣿⣸⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠉⠁⠀⠈⠙⠛⠉⠀⠈⠉⠁⠈⠉⠉⠈⠉⠉⠉⠁⠀⠈⠉⠉⠉⠉⠁⠀⠉⠛⠛⠉⠀⠉⣉⣉⣉⠉⠀⠈⠉⠉⠈⠉⠁⠀⠀⠀⠉⠉⠁⠈⠙⠛⠋⠁⠀⠈⠙⠛⠉⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡻⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠛⢿⣿⡄⠀⠀⠀⢀⣀⡀⣼⣿⣿⡄⠀⠀⠀⠀⢴⣭⣧⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣾⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠒⠒⠒⠂⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⣩⣬⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⠤⠤⣤⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠁⠀⠈⠉⠙⠒⠢⢤⣄⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠒⠖⠖⠒⠒⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⠛⠿⠻⠟⠉⠙⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣶⣤⣤⣄⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣶⣄⡀⠀⠉⠉⠉⠉⠉⠉⠐⠒⠂⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣠⣤⣤⣴⣾⣿⣿⣿⡿⠟⠛⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣶⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⠠⠤⠶⠶⠾⠿⠛⠛⠛⣯⣅⣾⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⠟⠋⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀
⠀⠖⠶⣶⠏⢶⠄⠱⠶⣶⡖⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⡿⠟⠀⠀
[22A⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠛⠛⠛⠻⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⢿⣿⣿⡿⠛⡛⠻⢿⣿⠿⢿⡿⠿⣿⡿⠿⣻⠿⢿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⡿⠿⣿⡿⠿⣛⠿⢿⣿⡿⠟⡛⠛⠿⣿⠿⢿⡻⠿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⡈⣿⣿⢸⣿⣿⣿⣏⣿⡏⣾⣿⢻⣿⣆⢱⣿⡿⣿⣷⡌⣼⣿⠿⣿⣧⣩⣴⣿⣿⠸⣿⣿⣿⢯⣥⣾⣿⠁⣾⣿⠿⣿⣦⠉⣾⣿⢻⣿⣆⢠⣾⣿⢻⣿⡎⣿⣿⣿⣿⣿
⠿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⣧⣿⣿⢸⣿⣿⣠⣿⣿⣾⣛⠛⣼⣿⡏⢸⣿⡇⢸⣿⡇⢛⠛⣰⣿⡿⣉⢹⣿⣿⢠⣬⡝⣿⣯⠉⣿⣿⠀⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡗⠸⣿⠿⠟⠋
⠀⠈⠁⠉⠁⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡿⣿⣿⣿⢸⣿⣿⠛⣷⣿⣿⢏⣼⣿⠟⠀⢸⣿⡇⢸⣿⡇⠛⣴⣿⡿⣱⣿⢸⣿⣿⠈⠛⠃⣿⣿⠇⣿⣿⠀⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣼⣿⣿⠘⣿⣿⣼⣿⡿⢸⣿⡇⢻⣿⣿⢸⣿⣿⣤⡌⠛⢁⣾⣿⣯⣤⡄⢸⣿⣇⣾⣿⠇⣼⣿⣯⣤⣬⠉⢸⣿⣿⢠⣤⡄⠉⠋⠀⣿⣿⠀⢿⣿⣤⣿⡿⠈⣿⣿⣸⣿⡿⠸⣿⣿⣸⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠉⠁⠀⠈⠙⠛⠉⠀⠈⠉⠁⠈⠉⠉⠈⠉⠉⠉⠁⠀⠈⠉⠉⠉⠉⠁⠀⠉⠛⠛⠁⠀⠉⢉⣉⣉⡉⠀⠈⠉⠉⠈⠉⠁⠀⠀⠀⠉⠉⠁⠈⠙⠛⠋⠁⠀⠈⠙⠛⠉⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣔⣄⠀⠀⠀⠀⠀⠀⢰⣟⡻⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣿⣿⣽⡄⠀⠀⠀⠀⠀⠚⠻⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠟⠛⣿⣷⡀⠀⠀⢀⡀⠀⠀⣿⣿⡇⢀⠀⠀⠀⣴⣛⣿⣴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣦⣤⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠤⠄⠀⠐⠒⠒⠒⠒⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⢀⣠⢾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⡤⠤⣤⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⠁⠀⠈⠉⠙⠒⠢⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠴⠶⠶⠶⠶⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠁⠀⠀⢀⣀⣴⣾⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠏⠉⠛⠛⠿⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⣦⣤⣤⢤⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣶⣤⡀⠀⠈⠉⠉⠉⠙⠓⠒⠒⠒⠂⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣾⣿⣿⣿⡿⠟⠛⠻⠟⠻⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣶⣤⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣠⣤⣴⠶⠶⠿⠟⠛⠋⢋⣉⣽⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢐⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁
⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣿⣿⣿⠟⠉⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠖⠶⣶⠏⢶⠄⠱⠶⣶⡖⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⠿⡉⠀⠀
[22A⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠛⠛⠛⠻⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⢿⣿⣿⡿⠛⡛⠻⢿⣿⠿⢟⡿⠿⣿⡿⠿⣛⠿⢿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⡿⠿⣿⡿⠿⣛⠿⢿⣿⡿⠟⡛⠛⠿⣿⠿⢿⡻⠿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⡈⣿⣿⢸⣿⣿⣿⣏⣿⠏⣾⣿⢻⣿⣆⢱⣿⡿⢿⣷⡌⣴⣿⠿⣿⣧⣩⣴⣾⣿⠸⣿⣿⣿⢯⣥⣾⣿⠃⣾⣿⠿⣿⣦⠉⣾⣿⢻⣿⣦⢠⣾⣿⢻⣿⡎⣿⣿⣿⣿⣿
⠿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⣧⣿⣿⢸⣿⣿⣠⣿⣿⣾⣛⠛⣼⣿⡏⢸⣿⡇⢸⣿⡇⢛⠛⣰⣿⡿⣉⢹⣿⣿⢠⣤⡝⣿⣯⠉⣿⣿⠀⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡗⠸⣿⠿⠟⠋
⠀⠈⠁⠈⠁⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡿⣿⣿⣿⢸⣿⣿⠛⣷⣿⣿⢏⣼⣿⠟⠀⢸⣿⡇⢸⣿⡇⠛⣴⣿⡿⣱⣿⢸⣿⣿⠘⠛⠃⣿⣿⠇⣿⣿⠀⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣼⣿⣿⠘⣿⣿⣼⣿⡿⢸⣿⡇⢻⣿⣿⢸⣿⣿⣤⡌⠙⢁⣾⣿⣯⣤⡄⢸⣿⣇⣾⣿⠇⣼⣿⣯⣤⣬⠁⢸⣿⣿⢠⣤⡄⠉⠋⠀⣿⣿⠀⢿⣿⣤⣿⡿⠈⣿⣿⣸⣿⡿⠸⣿⣿⣸⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠉⠁⠀⠈⠙⠛⠉⠀⠈⠉⠁⠈⠉⠉⠈⠉⠉⠉⠁⠀⠈⠉⠉⠉⠉⠁⠀⠉⠛⠛⠁⠀⠉⢉⣉⣉⡉⠀⠈⠉⠉⠈⠉⠁⠀⠀⠀⠉⠉⠁⠈⠙⠛⠋⠁⠀⠈⠙⠛⠉⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⡤⠀⠀⠀⠀⠀⠀⣰⣟⠒⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠚⢿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠟⠻⣿⣦⡀⠀⠀⣀⣀⣂⣸⣿⣿⡇⣀⡄⠀⠀⢰⣎⣿⣶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣶⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠤⠀⠀⠀⠒⠒⠒⠒⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⢀⣤⣿⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡤⠤⣤⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠁⠀⠈⠉⠙⠒⠢⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠴⠶⠶⠶⠶⠾⠟⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠁⠀⠀⢀⣀⣴⣾⣿⣿⣿⣿⣿⣿⡿⠛⠻⠛⠋⠈⠙⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣦⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⡿⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣶⣤⡀⠀⠉⠉⠉⠉⠙⠓⠒⠒⠒⠂⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣴⣾⣿⣿⣿⡿⠟⠛⠻⠟⠻⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣦⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣀⣀⣤⣴⠶⠶⠿⠟⠛⠋⠋⢉⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⣾⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉
⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣾⣿⣿⠟⠋⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀
⠀⠖⠶⣶⠏⢶⠄⠱⠶⢶⠆⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⡿⠇⠀⠀
[22A⣿⣿⣿⣿⣿⡿⠿⠿⠿⠟⠛⠛⠛⠻⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⢿⣿⣿⡿⠛⡛⠻⢿⣿⠿⢟⡛⠿⣿⡿⠿⣛⠿⢿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⡿⠿⢿⡿⠟⣛⠿⢿⣿⡿⠟⡛⠛⠻⡿⠿⢿⡻⠿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⡈⣿⣿⢸⣿⣿⣿⣏⣿⠏⣾⣿⢻⣿⣆⢱⣿⡿⣿⣷⡌⣼⣿⠿⣿⣧⣩⣴⣾⣿⠘⣿⣿⣿⢯⣥⣾⣿⠃⣾⣿⠿⣿⣦⠉⣾⣿⢻⣿⣆⢠⣾⣿⢻⣿⡎⢿⣿⣿⣿⣿
⠻⣿⣿⣿⣷⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⣧⣿⣿⢸⣿⣿⣠⣿⣿⣾⣛⠛⣼⣿⡏⢸⣿⡇⢸⣿⡇⢛⠛⣰⣿⡿⢉⢹⣿⣿⢠⣤⡝⣿⣯⠉⣿⣿⠀⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣷⠸⠿⠟⠛⠉
⠀⠈⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡿⣿⣿⣿⢸⣿⣿⠛⣷⣿⣿⢇⣼⣿⠟⠀⢸⣿⡇⢸⣿⡇⠛⣴⣿⡿⣡⣿⢸⣿⣿⠈⠛⠃⣿⣿⠆⣿⣿⠀⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡷⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣼⣿⣿⠘⣿⣿⣼⣿⡿⢸⣿⡇⢻⣿⣿⢸⣿⣿⣤⡌⠙⢁⣾⣿⣯⣤⡄⢸⣿⣧⣾⣿⠇⣼⣿⣿⣤⣬⠁⢸⣿⣿⢠⣤⡄⠈⠉⠀⣿⣿⠀⢿⣿⣤⣿⡿⠘⣿⣿⣸⣿⡿⠸⣿⣿⣸⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠉⠁⠀⠈⠙⠛⠉⠀⠈⠉⠁⠈⠉⠉⠈⠉⠉⠉⠁⠀⠈⠉⠉⠉⠉⠁⣀⠉⠛⠛⠉⠀⠉⣉⣉⣉⠉⠀⠈⠉⠉⠈⠉⠁⠀⠀⠀⠉⠉⠁⠈⠙⠛⠋⠁⠀⠈⠙⠛⠉⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠁⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⣰⣛⣳⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡿⣿⣿⡇⠀⠀⠀⣽⣾⣿⣿⠀⢠⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣷⡾⢛⠀⠀⠀⣤⣾⣿⣿⣿⣷⣾⣿⣄⡀⢠⣶⣻⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⠁⠘⣿⣿⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⣀⣀⣀⡀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣠⣾⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠄⣀⣠⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠋⠁⠈⠉⠛⠒⠠⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠠⠀⠒⠒⠒⠒⠒⠛⠛⠛⠛⠉⠉⠉⠉⠉⠁⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⡿⠛⠛⠟⠋⠈⠙⠛⠿⠿⠿⠿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⣦⣀⣀⡀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣶⣄⡀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣾⣿⣿⣿⡿⠟⠿⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠠⠴⠖⠒⠛⠋⠉⢉⣴⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣄⣀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀
⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⢶⣶⠖⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⡿⡿⠿⠁⠀⠀⠀
[22A⣿⣿⣿⣿⣿⡿⠿⠿⠿⠟⠛⠛⠛⠻⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⢿⣿⣿⡿⠛⡛⠻⢿⣿⠿⢟⡛⠿⣿⡿⠟⣛⠿⢿⣿⣿⠿⠟⢿⣿⣿⣿⣿⣿⡿⠿⣿⡿⠟⣛⠿⢿⣿⡿⠟⡛⠛⠻⠿⠿⢿⡛⠿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⡈⣿⣿⢸⣿⣿⣿⣏⣿⠏⣾⣿⢻⣿⣆⢱⣿⡿⣿⣷⡌⣴⣿⠿⣿⣧⣩⣴⣿⣿⠈⣿⣿⣿⢯⣥⣾⣿⠃⣾⣿⠿⣿⣦⠉⣾⣿⢻⣿⣦⢠⣾⣿⢻⣿⡎⢿⣿⣿⣿⣿
⠛⣿⡿⣿⡷⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⣧⣿⣿⢸⣿⣿⣠⣿⣿⣾⣛⠛⣼⣿⡏⢸⣿⡇⢸⣿⡇⢛⠛⣰⣿⡿⢉⢹⣿⣿⢠⣤⡝⣿⣮⠉⣿⣿⠀⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣷⠘⠟⠛⠋⠁
⠀⠈⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡿⣿⣿⣿⢸⣿⣿⠛⣷⣿⣿⢇⣼⣿⠟⠀⢸⣿⡇⢸⣿⡇⠊⣴⣿⡿⣡⣿⢸⣿⣿⠈⠛⠃⣿⣿⠆⣿⣿⠀⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣼⣿⣿⠘⣿⣿⣼⣿⡿⢸⣿⡇⢻⣿⣿⢸⣿⣿⣤⡌⠙⢁⣾⣿⣯⣤⡄⢸⣿⣧⣾⣿⠇⣼⣿⣿⣤⣬⠁⢸⣿⣿⢠⣤⡄⠈⠁⠀⣿⣿⠀⣿⣿⣤⣿⡿⠈⣿⣿⣸⣿⡿⠸⣿⣿⣸⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠉⠉⠁⠀⠈⠙⠛⠉⠀⠈⠉⢁⡈⠉⡉⠈⠉⠉⠉⠁⠀⠈⠉⠉⠉⠉⠁⣀⠉⠛⠛⠉⠀⠉⣉⣉⣉⠉⠀⠈⠉⠉⠈⠉⠁⠀⠀⠀⠉⠉⠁⠈⠙⠛⠋⠁⠀⠈⠙⠛⠉⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢟⠻⣿⡟⡯⠈⠁⠀⣒⣾⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣰⣛⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡐⠠⠀⠀⠀⢺⣿⣿⣿⣿⣿⡿⣿⣿⡧⠀⠀⠀⣽⣾⣿⣿⢠⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢸⣿⣿⣿⣿⣿⣷⡿⣿⢡⡀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣷⣄⢠⣶⣻⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⠻⠝⠚⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⢀⣀⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠏⠁⠈⠉⠓⠒⠠⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠒⠒⠒⠒⠒⠒⠚⠛⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⡿⠛⠿⠿⠋⠉⠙⠛⠿⠿⠿⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⣦⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⠿⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣾⣿⣿⣿⣿⠿⠻⠿⠟⠻⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣦⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠠⠀⠒⠒⠚⠉⠉⢁⣴⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣾⣿⣿⠟⠋⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡛⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⢶⣶⡖⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⡿⠿⠀⠀⠀⠀⠀
[22A⣿⣿⣿⣿⣿⡿⠿⠿⠿⠟⠛⠛⠛⠻⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⢿⣿⣿⡿⠛⡛⠻⢿⣿⠿⢛⡛⠿⣿⡿⠟⣛⠿⢿⣿⣿⠿⠛⢿⣿⣿⣿⣿⣿⠿⠿⢿⡿⠟⣛⠻⢿⣿⡿⠟⡛⠉⠀⠿⠻⢿⡛⠿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⡈⣿⣿⢸⣿⣿⣿⣏⣿⠏⣾⣿⢻⣿⣆⢱⣿⡿⣿⣷⡌⣼⣿⠿⣿⣧⣩⣴⣿⣿⠀⣿⣿⣿⢫⣥⣾⣿⠃⣾⣿⠿⣿⣦⠉⣾⣿⢻⣿⣦⢠⣾⣿⢻⣿⡎⢻⣿⣿⣿⣿
⠛⣿⡿⣿⡷⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⣧⣿⣿⢸⣿⣿⣠⣿⣿⣾⣛⠛⣼⣿⡏⢸⣿⡇⢸⣿⡇⢛⠛⣰⣿⡿⢉⢹⣿⣿⢠⣤⡌⣿⣮⠉⣿⣿⠀⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣷⠘⠛⠋⠉⠀
⠀⠈⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡿⣿⣿⣿⢸⣿⣿⠛⣷⣿⣿⢇⣼⣿⠟⠀⢸⣿⡇⢸⣿⡇⠊⣴⣿⡿⣡⣿⢸⣿⣿⠘⠛⠃⣾⣿⠀⣿⣿⠀⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣼⣿⣿⠘⣿⣿⣼⣿⡿⢸⣿⡇⢻⣿⣿⢸⣿⣿⣤⡌⠙⢁⣾⣿⣯⣤⡄⢸⣿⣧⣾⣿⠇⣼⣿⣿⣤⣤⠀⢸⣿⣿⢠⣤⡆⠀⠀⠀⣿⣿⠀⣿⣿⣤⣿⡿⠘⣿⣿⣸⣿⡿⠸⣿⣿⣸⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠉⠉⠁⠀⠈⠙⠛⠋⣀⣈⠉⣁⣈⣉⣉⣈⣉⠉⠉⢁⣤⣈⣉⣉⣉⣉⣁⣀⡉⠛⠛⠉⢀⣩⣉⣉⣉⠉⠀⠈⠉⠉⠈⠉⠁⠀⠀⠀⠉⠉⠁⠈⠙⠛⠋⠁⠀⠈⠙⠛⠉⠀⠀⠈⠛⠛⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠝⠊⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⣾⢻⡻⣿⣿⠄⣶⡤⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⠿⠿⣟⢿⡽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⣀⣽⣿⣿⣿⣿⣾⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠙⠋⡈⠫⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣴⢖⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠓⠝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠉⠙⠓⠒⠠⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠐⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠋⠉⠛⠿⠿⠿⠿⠿⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⢿⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⣿⣿⠿⠿⠿⠟⢿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⠿⠋⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⢶⣶⡖⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⡇⠁⠀⠀⠀⠀⠀
[22A⣿⣿⣿⣿⣿⡿⠿⠿⠿⠟⠛⠛⠛⠻⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⢿⣿⣿⡿⠛⡛⠻⢿⣿⠿⢛⡛⠿⣿⡿⠟⣛⠿⢿⣿⣿⠿⠛⢿⣿⣿⣿⣿⣿⠿⠿⢿⡿⠟⣛⠻⢿⣿⡿⠟⡋⠁⠀⠘⠛⢿⡛⠿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⡈⣿⣿⢸⣿⣿⣿⣏⣿⠏⣾⣿⢻⣿⣆⢱⣿⡿⣿⣷⡌⣼⣿⠿⣿⣧⣩⣴⣿⣿⠀⣿⣿⣿⢫⣥⣾⣿⠃⣾⣿⠿⣿⣦⠉⣾⣿⢻⣿⣦⢠⣾⣿⢻⣿⡎⢻⣿⣿⣿⡿
⠛⣿⡿⣿⡧⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⣧⣿⣿⢸⣿⣿⣠⣿⣿⣾⡛⠛⣼⣿⡏⢸⣿⡇⣾⣿⡇⢛⠛⣰⣿⡿⢉⢹⣿⣿⢠⣤⡌⢿⣮⠉⣿⣿⠀⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣷⠘⠛⠉⠁⠀
⠀⠈⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡿⣿⣿⣿⢸⣿⣿⠛⣷⣿⣿⢇⣼⣿⠟⠀⢸⣿⡇⣿⣿⡇⠈⣴⣿⡿⣡⣿⢸⣿⣿⠘⠛⠃⢾⣿⠀⣿⣿⠀⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠠⣼⣿⣿⠘⣿⣿⣼⣿⡿⢸⣿⡇⢻⣿⣿⢸⣿⣿⣤⡌⠹⢁⣾⣿⣯⣤⡄⢸⣿⣧⣿⣿⠇⣼⣿⣿⣤⣤⠀⢸⣿⣿⢠⣤⡆⠀⠀⠀⣿⣿⡀⣿⣿⣤⣿⡿⠘⣿⣿⣸⣿⡿⠸⣿⣿⣸⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠉⠉⠁⢀⠈⠙⠛⠋⣀⣈⣉⣁⣈⣉⣉⣈⣉⡉⣉⣁⣴⣈⣉⣉⣉⣉⣁⣄⣉⠛⠛⢉⣀⣍⣉⣉⢉⠉⢠⠈⠉⠉⠈⠉⠁⠀⠀⠀⠉⠉⠁⠈⠙⠛⠋⠁⠀⠈⠙⠛⠉⠀⠀⠈⠛⠛⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠙⠻⠻⠻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠎⣿⢿⣿⣿⣿⣷⣿⣿⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠣⣠⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢘⢏⣟⡛⡻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⡍⠈⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠻⠿⢿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠙⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣀⣠⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠋⠀⠉⠙⠓⠒⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠋⠙⠻⠿⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⢿⣿⣿⡿⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⡿⠿⡿⠿⢿⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣿⣿⣿⣿⣿⣿⠓⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⠿⢋⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⠽⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⢶⣶⡖⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⡇⠀⠀⠀⠀⠀⠀
[22A⣿⣿⣿⣿⣿⠿⠿⠿⠿⠟⠛⠛⠛⠻⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⢿⣿⣿⡿⠛⡛⠻⢿⣿⠟⢛⡛⠿⣿⡿⠟⣛⠻⢿⣿⡿⠿⠛⠳⣤⣼⣿⣿⣿⠿⠿⢿⡿⠟⣛⠻⢿⣿⡿⠟⡁⠀⠀⠀⠘⢛⡛⠿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⡈⣿⣿⢸⣿⣿⣿⣏⣿⠏⣾⣿⢻⣿⣆⢱⣿⡿⣿⣷⡌⣼⣿⠿⣿⣧⣩⣴⣿⣿⠀⢿⣿⣿⢫⣥⣾⣿⠇⣾⣿⠿⣿⣧⠉⣾⣿⢿⣿⣦⢠⣾⣿⢻⣿⡎⢻⣿⣿⣿⠿
⠙⣿⡿⣿⡧⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⣧⣿⣿⢸⣿⣿⣠⡿⣿⣾⡛⠛⣼⣿⡏⢸⣿⡇⣿⣿⡇⢛⠛⣰⣿⡿⢉⢹⣿⣿⢠⣤⡌⢿⣮⠉⣿⣿⠀⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣷⠘⠛⠉⠀⠀
⠀⠈⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡿⣿⣿⣿⢸⣿⣿⠛⣳⣿⣿⢇⣼⣿⠟⠀⢸⣿⡇⣿⣿⡇⠈⣴⣿⡿⢡⣾⢸⣿⣿⠘⠛⠃⢸⣿⠀⣿⣿⠀⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⣼⣿⣿⠘⣿⣿⣼⣿⡿⢸⣿⡇⢻⣿⣿⢸⣿⣿⣤⡌⠹⢁⣾⣿⣯⣤⡄⢸⣿⣧⣿⣿⠇⣼⣿⣿⣤⣤⠀⢸⣿⣿⢠⣶⡆⠀⠀⠀⣿⣿⡀⣿⣿⣤⣿⡿⠘⣿⣿⣸⣿⡿⠸⣿⣿⣸⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠉⠉⠁⣀⣈⠙⠛⢋⣠⣌⣉⣁⣈⣉⣉⣈⣉⣉⣉⣁⣴⣌⣉⣉⣉⣉⣁⣤⣉⠛⠛⢉⣠⣍⣉⣉⣉⠉⣠⡈⠉⠉⠈⠉⠁⠀⠀⠀⠉⠉⠁⠈⠙⠛⠋⠁⠀⠈⠙⠛⠉⠀⠀⠈⠛⠛⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⣿⣿⣿⣿⣿⣿⣿⣗⠄⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢫⢛⠻⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠋⢉⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡻⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠈⠩⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠙⠹⠛⠿⢻⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣮⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠈⠉⠚⠒⠲⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠋⠛⠿⢿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⡿⢿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⠟⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣷⣶⣶⣦⣤⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⢛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⠿⡛⠴⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⣶⣶⣖⠹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⡄⠀⠀⠀⠀⠀⠀
[22A⣿⣿⣿⣿⣿⠿⠿⠿⠿⠛⠛⠟⠛⠻⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⢿⣿⣿⡿⠛⡛⠻⢿⣿⠟⢛⡛⠿⣿⡿⠟⣛⠻⢿⣿⡿⠟⠃⠀⢀⣠⣾⣿⣿⠿⠻⢿⡿⠟⣛⠻⢿⣿⡿⠟⡀⠀⠀⠀⠀⢛⡛⠻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⡘⣿⣿⢸⣿⣿⣿⣏⣿⠏⣾⣿⢻⣿⣆⢰⣿⡿⣿⣷⡄⣼⣿⠿⣿⣧⣩⣴⣿⣿⠀⠻⣿⣿⢫⣥⣾⣿⡇⣾⣿⢿⣿⣧⠉⣾⣿⢿⣿⣦⢠⣾⣿⢿⣿⡎⢹⣿⣿⣿⠟
⠙⣿⡿⣿⡧⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⣧⣿⣿⢸⣿⣿⣠⡿⣿⣾⡛⠛⣼⣿⡏⢸⣿⡇⣾⣿⡇⢛⠛⣰⣿⡿⠉⢹⣿⣿⢠⣤⡌⢿⣮⠉⣿⣿⠁⣿⣿⢰⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣷⠈⠋⠁⠀⠀
⠀⠈⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡿⣿⣿⣿⢸⣿⣿⠛⣷⣿⣿⢇⣼⣿⠟⠀⢸⣿⡇⣿⣿⡇⠀⣴⣿⡿⢡⣾⢸⣿⣿⠘⠛⠃⢸⣿⠀⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⣼⣿⣿⠘⣿⣿⣼⣿⡿⢸⣿⡇⢻⣿⣿⢸⣿⣿⣤⡌⢻⢁⣾⣿⣯⣤⡄⢸⣿⣧⣿⣿⠇⣼⣿⣿⣤⣤⠀⢸⣿⣿⢠⣶⡆⠀⠀⠀⣿⣿⡆⣿⣿⣼⣿⣿⠘⣿⣿⣸⣿⡿⠸⣿⣿⣸⣿⡏⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠉⠉⢁⣤⣈⡙⠛⣋⣠⣌⣉⣁⣌⣉⣉⣈⣉⣉⣉⣡⣾⣌⣉⣉⣉⣉⣁⣤⣉⠛⠛⢉⣤⣍⣉⣉⣉⢉⣠⠌⠉⠉⠈⠉⠁⠀⠀⠀⠉⠉⠁⠈⠙⠛⠋⠁⠀⠈⠙⠛⠋⠀⠀⠈⠛⠛⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⠿⡛⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠚⠘⠉⠟⢯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠣⠒⡊⡟⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠁⢁⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠈⠉⠛⠒⠶⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠋⠻⠿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⠟⠋⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣟⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⡍⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⡿⣿⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⣶⣶⡖⠹⠁⠈⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⡄⠀⠀⠀⠀⠀⠀
[22A⣿⣿⣿⣿⣿⠿⠿⠿⠿⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⡿⠛⡛⠻⢿⣿⠟⢛⡛⠿⣿⡿⠟⣛⠛⢿⣿⡿⠟⠃⠀⠀⢠⣼⣿⣿⠿⠻⢿⡿⠟⣛⠻⢿⣿⡿⠛⡀⠀⠀⠀⠀⢛⡛⠻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⡸⣿⣿⢸⣿⣿⣿⣏⣿⠏⣾⣿⢻⣿⣆⢰⣿⡿⣿⣷⡄⣼⣿⠿⣿⣧⣩⣴⣿⣿⠀⠀⣿⣿⢫⣥⣾⣿⡇⣾⣿⢿⣿⣦⢉⣾⣿⢿⣿⣦⢠⣾⣿⢿⣿⡎⢹⣿⣿⣿⠟
⠉⣿⡟⣿⠧⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⣧⣿⣿⢸⣿⣿⣤⡿⣿⣾⡛⠛⣼⣿⡏⢸⣿⡇⣿⣿⡇⠛⠛⣰⣿⡿⠉⢹⣿⣿⢠⣤⡌⢿⣮⠉⣿⣿⠀⣿⣿⢰⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⠈⠋⠁⠀⠀
⠀⠈⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡿⣿⣿⣿⢸⣿⣿⠛⣳⣿⣿⢇⣼⣿⠟⠀⢸⣿⡇⣿⣿⡇⠀⣴⣿⡿⢡⣾⢸⣿⣿⠘⠛⠃⠸⣿⠀⣿⣿⠆⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⣼⣿⣿⠘⣿⣿⣼⣿⡿⢸⣿⡇⢻⣿⣿⢸⣿⣿⣤⡌⢻⢁⣾⣿⣯⣤⡄⢸⣿⣧⣿⣿⠇⣼⣿⣿⣤⣤⠀⢸⣿⣿⢠⣶⡆⠀⠀⠀⣿⣿⡆⣿⣿⣼⣿⣿⠘⣿⣿⣸⣿⡿⠸⣿⣿⣸⣿⡏⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠉⠉⢁⣤⣈⡙⠛⣋⣠⣌⣉⣁⣌⣉⣉⣈⣉⣉⣉⣡⣾⣌⣉⣉⣉⣉⣡⣤⣉⠛⠛⣉⣤⣍⣉⣉⣉⢉⣠⠈⠉⠉⠈⠉⠁⠀⠀⠀⠉⠉⠁⠈⠙⠛⠋⠁⠀⠈⠙⠛⠉⠀⠀⠈⠛⠛⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠨⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠟⠻⢺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠿⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠙⢙⠿⠻⠿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠈⠙⠛⠒⠶⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠋⠻⠿⣿⣿⣿⣿⡿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⡿⢿⣿⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⠛⠋⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣷⣶⣖⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣟⣩⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⠏⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⣶⣶⡖⠙⠋⠀⠃⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⡆⠀⠀⠀⠀⠀⠀
[22A⣿⣿⣿⣿⣿⠿⠿⠿⠿⠛⠛⠿⠛⠿⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⢿⣿⣿⡿⢛⡛⠻⢿⣿⠟⢛⡛⠿⣿⡿⠛⣛⠛⢿⣿⡿⠟⠃⠀⠀⠀⣤⣿⣿⠿⠛⢿⠿⠛⣛⠻⢿⣿⡿⠛⡀⠀⠀⠀⠀⢘⡛⠛⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⡘⣿⣿⢸⣿⣿⣿⣇⣿⠏⣾⣿⢻⣿⣆⢰⣿⡿⣿⣷⡄⣼⣿⠿⣿⣧⣩⣴⣿⣿⠀⠀⠐⣿⢫⣤⣾⣿⡇⣾⣿⢿⣿⣧⢁⣾⣿⢿⣿⣦⢠⣾⣿⢿⣿⡎⢹⣿⣿⣿⠟
⠙⣿⡿⠿⡧⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⣧⣿⣿⢸⣿⣿⣠⡿⣿⣾⡛⠛⣼⣿⡏⢸⣿⡇⣿⣿⡇⠛⠛⣰⣿⡿⠉⢹⣿⣿⢠⣤⡄⢻⣎⠉⣿⣿⡇⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣷⠈⠉⠁⠀⠀
⠀⠈⠁⠀⠁⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡿⣿⣿⣿⢸⣿⣿⠛⣳⣿⣿⢃⣼⣿⠟⠀⢸⣿⡇⣿⣿⡇⠀⣴⣿⡿⢡⠶⢸⣿⣿⠘⠛⠃⠸⡿⠀⣿⣿⡁⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⣼⣿⣿⠘⣿⣿⣼⣿⡿⢸⣿⡇⢻⣿⣿⢸⣿⣿⣤⡌⢿⢁⣾⣿⣯⣤⡄⢸⣿⣧⣿⣿⠇⣼⣿⣿⣤⣤⠀⢸⣿⣿⢠⣶⡆⠀⠀⠀⣿⣿⡇⣿⣿⣼⣿⣿⠘⣿⣿⣸⣿⡿⠸⣿⣿⣸⣿⡏⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠉⢉⣁⣤⣌⣙⢛⣋⣤⣬⣉⣡⣌⣉⣉⣈⣉⣉⣉⣡⣾⣮⣉⣉⣉⣉⣡⣤⣉⡛⠛⣉⣴⣍⣉⣉⣉⢉⣤⡈⠉⠉⠈⠉⠁⠀⠀⠀⠉⠉⠁⠈⠙⠛⠋⠁⠀⠈⠙⠛⠋⠀⠀⠈⠛⠛⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠨⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠩⠂⠓⠐⠋⠊⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠙⠛⣻⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠽⢧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠐⠒⠲⠦⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠻⢿⣿⣿⣿⣿⡿⠟⠟⠁⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⠟⠛⠟⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⣶⣶⣖⠙⠃⠘⠉⠃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⡆⠀⠀⠀⠀⠀⠀
[22A⣿⣿⣿⣿⣿⠿⠟⠿⠿⠛⠛⠿⠛⠿⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⢿⣿⣿⡿⠛⡛⠻⢿⣿⠟⢛⡛⠻⣿⡿⠛⣛⠛⢿⣿⡿⠛⠁⠀⠀⠀⣠⣿⣿⠟⠛⢿⠿⠛⣛⠻⢿⣿⠟⠛⡀⠀⠀⠀⠀⢘⡛⠛⢿⣿⣿⣿⣿⣿
⣿⡿⢿⣿⣷⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⡘⣿⣿⢸⣿⣿⣿⣇⣿⠏⣾⣿⢻⣿⣆⢰⣿⡿⣿⣷⡄⣼⣿⠿⣿⣧⣩⣴⣿⣿⠀⠀⠀⡛⢫⣤⣾⣿⡇⣾⣿⢿⣿⣧⢀⣾⣿⢿⣿⣦⢠⣾⣿⢿⣿⡎⢉⣿⣿⡿⠟
⠉⣿⡿⠿⡦⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⣧⣿⣿⢸⣿⣿⣤⡿⣿⣾⡛⠛⣼⣿⡏⢸⣿⡇⣿⣿⡇⠛⠛⣰⣿⡿⠉⢹⣿⣿⢠⣤⡄⠻⣎⠉⣿⣿⡇⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⠀⠉⠀⠀⠀
⠀⠈⠁⢐⠇⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡿⣿⣿⣿⢸⣿⣿⠛⣳⣿⣿⢃⣼⣿⠟⠀⢸⣿⡇⣿⣿⡇⠀⣴⣿⡿⠡⠶⢸⣿⣿⠘⠛⠃⠸⠿⠀⣿⣿⡁⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⣼⣿⣿⠘⣿⣿⣼⣿⡿⢸⣿⡇⢻⣿⣿⢸⣿⣿⣤⡌⢻⢁⣾⣿⣯⣤⡄⢸⣿⣧⣿⣿⠇⣼⣿⣿⣤⣤⠀⢸⣿⣿⢠⣶⡆⠀⠀⠀⣿⣿⡇⣿⣿⣼⣿⣿⠘⣿⣿⣸⣿⡿⠸⣿⣿⣸⣿⡏⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠉⠉⣁⣤⣌⣙⢛⣋⣤⣬⣉⣡⣌⣉⣉⣌⣉⣉⣉⣡⣿⣮⣉⣉⣉⣉⣡⣤⣉⡛⢛⣉⣤⣍⣉⣉⣉⢉⣤⡈⠉⠉⠈⠉⠁⠀⠀⠀⠉⠉⠁⠈⠙⠛⠋⠁⠀⠈⠙⠛⠋⠀⠀⠈⠛⠛⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣾⣿⣿⣿⣿⣷⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠍⠛⠉⠫⠿⡺⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠣⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠌⠿⢷⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣀⣬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠑⠐⠒⠲⠦⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠿⠿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⠟⠛⠛⠋⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣯⡅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⣶⣶⣖⠹⠋⠈⠛⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣆⠀⠀⠀⠀⠀⠀
[22A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣦⠀⠀⠀⠀⢸⣿⢿⣿⣿⣿⣿⣿⣿
⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⢰⣿⠾⢿⣋⣿⡿⠿⠟
⠙⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡀⠀⠀⠀⠈⣷⡶⠿⠋⠉⠁⠀⠀
⠀⠈⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣤⠀⠀⠀⠰⠿⠿⠿⠿⠿⠿⠿⠿⠻⠟⠛⠟⠛⠛⠃⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡝⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢚⡿⠿⠿⡻⡟⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠠⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⣛⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⠓⠲⠶⠦⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠿⢿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠬⠛⣛⠿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⠿⡿⠟⠛⠋⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣧⡤⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠶⠶⣶⠿⢷⠖⢰⣶⣶⣶⠹⢿⣿⡿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣆⠀⠀⠀⠀⠀⠀
[22A⣿⣿⡿⠛⠻⠿⠿⡿⠿⠿⠿⡿⠿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⠟⠛⠻⣿⠛⠛⠁⠀⠀⠀⠀⠸⢿⡿⠛⢿⣿⣿⣿⣿⠎⠷⠆⠰⠄⠀⠀⠀⠀⠰⠿⠟⠛⠉⠻⣿⣿⣿
⣽⡿⠂⣿⣿⣿⣷⢸⣿⡿⠇⣴⣿⢻⣷⡀⣿⡿⠿⣿⣿⣷⣸⣿⣿⢸⣿⣿⣷⡄⣿⣿⠿⢸⣿⡿⣿⡎⠛⢰⣿⢿⣷⡄⣾⡟⣿⣦⢰⣿⢻⣷⣤⣴⣿⡇⠿⢿⢩⣴⣾⡇⣿⣿⠿⠿⢠⣾⡟⣿⣆⣰⣿⢻⣷⡀⠿⠟
⠙⣥⠀⣿⣿⣿⣿⢸⣿⣷⡆⣿⣿⠘⠛⠃⣿⣷⣶⣹⣿⣿⣿⣿⣿⢸⣿⣿⣿⡃⣿⣿⣶⢸⣿⣷⣿⡃⢾⡎⢉⣼⡿⢻⣿⡇⣿⣿⠈⢉⣾⡿⠀⢸⣿⣷⣶⠀⡷⠈⣿⡇⠿⠿⢻⣿⣼⣿⡇⣿⣿⣿⣿⢸⣿⡇⠀⠀
⠀⠈⠀⣿⣿⣿⣿⢸⣿⣇⣀⣿⣿⣸⣿⠇⣿⣯⣀⢻⣿⢿⣿⣿⣿⢸⣿⣿⣿⡇⣿⣿⣀⢸⣿⡏⣿⡇⠘⢁⣾⣿⣁⡸⣿⡇⣿⣿⢠⣿⣟⣀⠀⢸⣿⣇⣀⠸⠟⠀⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⡿⢿⣿⢸⣿⠇⠀⠀
⠀⠀⠀⠛⠛⠛⢋⣘⣛⣛⣛⣈⣛⣛⣋⣄⣛⣛⣛⣙⣛⣘⣋⣛⣛⣘⣛⣛⣛⣁⣛⣛⣛⣘⣛⣋⡛⣃⣤⣜⡛⠛⠛⢃⠙⠛⠛⠁⠙⠛⠛⠛⠀⠘⠛⠛⠛⠀⠀⠀⠛⠃⠈⠛⠛⠋⠀⠙⠛⠛⠁⠈⠛⠛⠋⠀⠀⠀
⠀⠀⠐⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡐⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠓⢛⢟⣛⠿⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠈⠈⠈⠘⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⣋⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⠓⠲⠶⠦⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠬⠛⠛⠶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⠿⡿⡟⠋⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠶⠶⣶⠟⢷⠖⢰⣶⣶⣶⠹⢟⣿⡿⠟⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣆⠀⠀⠀⠀⠀⠀
[22A⣿⣿⡿⠛⠻⠿⠿⠿⠿⠿⠿⡿⠿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡿⠟⠛⠛⠟⠙⠛⠀⠀⠀⠀⠀⠘⢻⡭⠙⢥⣭⣵⣬⣤⠄⠰⠄⠀⠀⠀⠀⠀⠀⠀⠿⠛⠛⠁⠰⢿⠟⠛
⣽⡷⠂⣿⣿⣿⣷⢸⣿⡿⠇⣴⣿⢻⣷⡀⣿⡿⠿⢻⣿⣷⣸⣿⣿⢸⣿⣿⣷⡄⣿⣿⠿⢸⣿⡿⣿⡆⠛⢰⣿⢻⣷⡄⣾⡟⣿⣦⢰⣿⢻⣷⣤⣴⣿⡇⠻⠟⢡⣴⣾⡇⣿⣿⠿⠿⢠⣾⡟⣿⣆⣰⣿⢻⣷⡀⠸⠏
⠉⣥⠀⣿⣿⣿⣿⢸⣿⣷⡆⣿⣿⠘⠛⠃⣿⣷⣶⢸⣿⣿⣿⣿⣿⢸⣿⣿⣿⡃⣿⣿⣶⢸⣿⣷⣿⡃⢺⡌⢉⣼⡿⢳⣿⡇⣿⣿⠈⢉⣾⡿⠀⢸⣿⣷⣶⠀⡀⠈⣿⡇⠿⠿⢻⣿⣼⣿⡇⣿⣿⣿⣿⢸⣿⡇⠀⠀
⠀⠈⠀⣿⣿⣿⣿⢸⣿⣇⣀⣿⣿⣸⣿⠇⣿⣯⣀⢺⣿⣿⣿⣿⣿⢸⣿⣿⣿⡇⣿⣿⣀⢸⣿⡇⣿⡇⠘⢁⣾⣿⣁⡘⣿⡇⣿⣿⢠⣿⣟⣀⠀⢸⣿⣇⣀⠘⠟⠀⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⡿⢿⣿⢸⣿⠇⠀⠀
⠀⠀⠀⠛⠛⠛⣋⣘⣛⣛⣛⣈⣛⣛⣋⣄⣛⣛⣛⣙⣛⣘⣋⣛⣛⣘⣛⣛⣛⣁⣛⣛⣛⣘⣛⣋⡛⢃⣤⣘⣛⠛⠛⣃⠙⠛⠛⠁⠘⠛⠛⠛⠀⠘⠛⠛⠛⠀⠀⠀⠛⠃⠈⠛⠛⠋⠀⠙⠛⠛⠁⠈⠛⠛⠋⠀⠀⠀
⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠨⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠈⠀⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠻⠛⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⠒⠲⠶⠦⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠿⢿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠘⠛⣻⣷⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⡿⠟⠙⠛⠋⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣯⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢶⠄⢰⣶⣶⣶⠹⢛⠛⠻⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣆⠀⠀⠀⠀⠀⠀
[22A⣿⣿⡿⠛⠛⠿⠿⠿⠿⠿⠿⡿⠿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡿⠟⠛⠛⠟⠙⠛⠀⠀⠀⠀⠀⠈⠙⠭⠉⢠⣬⣤⣤⡤⠄⠠⠄⠀⠀⠀⠀⠀⠀⠀⠿⠋⠉⠁⠐⠿⠂⠋
⣥⡷⠂⣿⣿⣿⣷⢸⣿⡿⠇⣴⣿⢻⣷⡀⣿⡿⠿⢹⣿⣷⣸⣿⣿⢸⣿⣿⣷⡄⣿⣿⠿⢸⣿⡿⣿⡆⠛⢰⣿⢻⣷⡄⣾⡟⣿⣦⢰⣿⢻⣷⣤⣴⣿⡇⠙⠟⢡⣴⣾⡇⣿⣿⠿⠿⢠⣾⡟⣿⣆⣰⣿⢻⣷⡀⠰⠋
⠉⣥⠀⣿⣿⣿⣿⢸⣿⣷⡆⣿⣿⠘⠛⠃⣿⣷⣶⢸⣿⣿⣿⣿⣿⢸⣿⣿⣿⡃⣿⣿⣶⢸⣿⣷⣿⡃⢸⡌⢉⣼⡿⢳⣿⡇⣿⣿⠈⢉⣾⡿⠀⢸⣿⣷⣶⠀⠀⠈⣿⡇⠿⠿⢻⣿⣼⣿⡇⣿⣿⣿⣿⢸⣿⡇⠀⠀
⠀⠈⠀⣿⣿⣿⣿⢸⣿⣇⣀⣿⣿⣸⣿⠇⣿⣧⣀⢸⣿⢿⣿⣿⣿⢸⣿⣿⣿⡇⣿⣿⣀⢸⣿⡏⣿⡇⠸⢁⣾⣿⣁⡘⣿⡇⣿⣿⢠⣿⣟⣀⠀⢸⣿⣇⣀⠘⠟⠀⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⡿⢿⣿⢸⣿⠇⠀⠀
⠀⠀⠀⠛⠛⠛⢋⣘⣛⣛⣛⣈⣛⣛⣋⣄⣛⣛⣛⣘⣛⣘⣋⣛⣛⣘⣛⣛⣛⣁⣛⣛⣛⣘⡛⣃⢛⣃⣤⣘⣛⡛⠛⣃⠙⠛⠛⠁⠘⠛⠛⠛⠀⠘⠛⠛⠛⠀⠀⠀⠛⠃⠈⠛⠛⠋⠀⠙⠛⠛⠁⠈⠛⠛⠋⠀⠀⠀
⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⢹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⢹⢿⠿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠈⠀⠁⠀⠘⠙⢻⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣄⣤⣂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠟⠻⢛⣛⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠑⠒⠲⠶⠤⣄⣀⣿⣿⣿⣯⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠛⠿⢿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⡿⠯⠛⠛⠉⠋⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⡿⠕⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠟⢶⠄⢰⣶⣶⣶⠹⢋⠛⠟⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣆⠀⠀⠀⠀⠀⠀
[22A⣿⣿⡿⠛⠛⠿⠿⠿⠿⠿⠿⡿⠿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡿⠟⠛⠛⠏⠈⠉⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⣀⣠⣄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠉⠀⠀⠶⠀⠈
⣴⡷⠀⣿⣿⣿⣷⢸⣿⡿⠇⣴⣿⢻⣷⡀⣿⡿⠿⢸⣿⣷⣸⣿⣿⢸⣿⣿⣷⡄⣿⣿⠿⢸⣿⡿⣿⡆⠛⢰⣿⢻⣷⡄⣾⡟⣿⣆⢰⣿⢻⣷⣤⣴⣿⡇⠈⠉⢡⣴⣾⡇⣿⣿⠿⠿⢠⣾⡟⣿⣆⣰⣿⢻⣷⡀⠀⠀
⠉⣤⠀⣿⣿⣿⣿⢸⣿⣷⡆⣿⣿⠘⠛⠃⣿⣷⣶⢸⣿⣿⣿⣿⣿⢸⣿⣿⣿⡃⣿⣿⣶⢸⣿⣷⣿⡃⢰⡌⢉⣼⡿⢣⣿⡇⣿⣿⠈⢉⣾⡿⠀⢸⣿⣷⣶⠀⠀⠈⣿⡇⠿⠿⢻⣿⣼⣿⡇⣿⣿⣿⣿⢸⣿⡇⠀⠀
⠀⠈⠀⣿⣿⣿⣿⢸⣿⣇⣀⣿⣿⣸⣿⠇⣿⣧⣀⢸⣿⢿⣿⣿⣿⢸⣿⣿⣿⡇⣿⣿⣀⢸⣿⡏⣿⡇⠘⢁⣾⣿⣁⡘⣿⡇⣿⣿⢠⣿⣟⣀⠀⢸⣿⣇⣀⠐⠛⠀⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⡿⢿⣿⢸⣿⠇⠀⠀
⠀⠀⠀⠛⠛⠛⣋⣘⣛⣛⣛⣈⣛⣛⣋⣄⣛⣛⣛⣘⣛⣘⣋⣛⣛⣘⣛⣛⣛⣁⣛⣛⣛⣘⣛⣃⡛⣃⣤⣘⣛⣛⠛⣃⠙⠛⠛⠁⠘⠛⠛⠛⠀⠘⠛⠛⠛⠀⠀⠀⠛⠃⠈⠛⠛⠋⠀⠙⠛⠛⠁⠈⠛⠛⠋⠀⠀⠀
⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⠚⠛⠉⠩⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣠⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⢛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠑⠒⠶⠶⠤⣄⣀⣿⢿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⡿⠿⠛⠛⠉⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⡟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠟⢶⠄⢰⣶⣶⣖⠙⠃⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣆⠀⠀⠀⠀⠀⠀
[22A⡿⣿⡿⠛⠛⠿⠿⠿⠿⠿⠿⡿⠿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠟⠿⠿⢿⣿⡿⠟⠋⠉⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀
⣤⡷⠀⣿⣿⣿⣷⢸⣿⡿⠇⣴⣿⢻⣷⡀⣿⡿⠿⢸⣿⣷⣸⣿⣿⢸⣿⣿⣷⡄⣿⣿⠿⢸⣿⡿⣿⡆⠋⢰⣿⢻⣷⡄⣾⡟⣿⣦⢰⣿⢻⣷⣤⣴⣿⡇⠀⠀⢠⣴⣾⡇⣿⣿⠿⠿⢠⣾⡟⣿⣆⣰⣿⢻⣷⡀⠀⠀
⠉⣤⠀⣿⣿⣿⣿⢸⣿⣷⡆⣿⣿⠘⠛⠃⣿⣷⣶⢸⣿⣿⣿⣿⣿⢸⣿⣿⣿⡃⣿⣿⣶⢸⣿⣷⣿⡃⢰⡌⢉⣼⡿⢳⣿⡇⣿⣿⠈⢉⣾⡿⠀⢸⣿⣷⣶⠀⠀⠈⣿⡇⠿⠿⢻⣿⣼⣿⡇⣿⣿⣿⣿⢸⣿⡇⠀⠀
⠀⠋⠀⣿⣿⣿⣿⢸⣿⣇⣀⣿⣿⣸⣿⠇⣿⣧⣀⢸⣿⢿⣿⣿⣿⢸⣿⣿⣿⡇⣿⣿⣀⢸⣿⡏⣿⡇⠘⢁⣾⣿⣁⡘⣿⡇⣿⣿⢠⣿⣟⣀⠀⢸⣿⣇⣀⠀⠃⠀⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⡿⢿⣿⢸⣿⠇⠀⠀
⠀⠀⠀⠛⠛⠛⣋⣘⣛⣛⣛⣌⣛⣛⣋⣄⣛⣛⣛⣘⣛⣘⣋⣛⣛⣘⣛⣛⣛⣁⣛⣛⣛⣘⣛⣃⣛⣃⣤⣘⣛⣛⡛⣃⠙⠛⠛⠁⠘⠛⠛⠛⠀⠘⠛⠛⠛⠀⠀⠀⠛⠃⠈⠛⠛⠋⠀⠙⠛⠛⠁⠈⠛⠛⠋⠀⠀⠀
⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠟⠿⠿⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢻⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠑⠶⠶⠶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠻⢿⣿⣿⣿⣿⣿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠘⠟⠳⢶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⡿⠟⠛⠛⠋⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⡟⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡅⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢶⠄⢰⣶⣶⡶⠙⠙⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣆⠀⠀⠀⠀⠀⠀
[22A⣼⣿⡿⠛⠛⠿⠿⡿⠿⠿⠿⡿⠿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡿⠟⠛⠉⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀
⣤⡷⠂⣿⣿⣿⣷⢸⣿⡿⠇⣴⣿⢻⣷⡀⣿⡿⠿⢸⣿⣷⣸⣿⣿⢸⣿⣿⣷⡄⣿⣿⠿⢸⣿⡿⣿⡆⠋⢰⣿⢻⣷⡄⣾⡟⣿⣦⢰⣿⢻⣷⣤⣴⣿⡇⠀⠀⢠⣴⣾⡇⣿⣿⠿⠿⢠⣾⡟⣿⣆⣰⣿⢻⣷⡀⠀⠀
⠉⣤⠀⣿⣿⣿⣿⢸⣿⣷⡆⣿⣿⠘⠛⠃⣿⣷⣶⢸⣿⣿⣿⣿⣿⢸⣿⣿⣿⡃⣿⣿⣶⢸⣿⣷⣿⡃⢴⡌⢉⣼⡿⢻⣿⡇⣿⣿⠈⢉⣾⡿⠀⢸⣿⣷⣶⠀⠀⠈⣿⡇⠿⠿⢻⣿⣼⣿⡇⣿⣿⣿⣿⢸⣿⡇⠀⠀
⠀⠉⠀⣿⣿⣿⣿⢸⣿⣇⣀⣿⣿⣸⣿⠇⣿⣯⣀⢸⣿⣿⣿⣿⣿⢸⣿⣿⣿⡇⣿⣿⣀⢸⣿⡏⣿⡇⠸⢁⣾⣿⣁⡘⣿⡇⣿⣿⢠⣿⣟⣀⠀⢸⣿⣇⣀⠀⠀⠀⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⡿⢿⣿⢸⣿⠇⠀⠀
⠀⢠⡀⠛⠛⢛⣋⣘⣛⣛⣛⣌⣛⣛⣋⣤⣛⣛⣛⣘⣛⣘⣋⣛⣛⣘⣛⣛⣛⣁⣛⣛⣛⣘⣛⣃⣛⣃⣤⣘⣛⣛⣛⡃⠙⠛⠛⠁⠘⠛⠛⠛⠀⠘⠛⠛⠛⠀⠀⠀⠛⠃⠈⠛⠛⠋⠀⠙⠛⠛⠁⠈⠛⠛⠋⠀⠀⠀
⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠂⠉⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⢿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠑⠶⠶⠶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠩⠟⠳⢶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⠟⠛⠋⠛⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⠣⠗⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠶⠶⣶⠿⢷⠔⢰⣶⣶⣶⠹⠋⠛⠟⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⠀⠀⠀⠀⠀⠀
[22A⢽⣿⡿⠛⠛⠿⠿⡿⠿⠿⢿⡿⠿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⡿⠀⣿⣿⣿⣷⢸⣿⡿⠇⣴⣿⢻⣷⡀⣿⡿⠿⢸⣿⣷⣸⣿⣿⢸⣿⣿⣷⡄⣿⣿⠿⢸⣿⡿⣿⡆⠛⢰⣿⢻⣷⡄⣾⡟⣿⣦⢰⣿⢻⣷⣤⣴⣿⡇⠀⠀⢠⣴⣾⡇⣿⣿⠿⠿⢠⣾⡟⣿⣆⢰⣿⢻⣷⡀⠀⠀
⠉⣤⠀⣿⣿⣿⣿⢸⣿⣷⡆⣿⣿⠘⠛⠃⣿⣷⣶⢸⣿⣿⣿⣿⣿⢸⣿⣿⣿⡃⣿⣿⣶⢸⣿⣷⣿⡃⢴⡌⢉⣼⡿⢻⣿⡇⣿⣿⠈⢉⣾⡿⠀⢸⣿⣷⣶⠀⠀⠈⣿⡇⠿⠿⢻⣿⣼⣿⡇⣿⣿⢸⣿⢸⣿⡇⠀⠀
⢈⡯⠀⣿⣿⣿⣿⢸⣿⣇⣀⣿⣿⣸⣿⠇⣿⣯⣀⢸⣿⣿⣿⣿⣿⢸⣿⣿⣿⡇⣿⣿⣀⢸⣿⡏⣿⡇⠸⢁⣾⣿⣁⡘⣿⡇⣿⣿⢠⣿⣟⣀⠀⢸⣿⣇⣀⠀⠀⠀⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⡿⢸⣿⢸⣿⠇⠀⠀
⠀⣿⣀⠛⠛⢛⣋⣘⣛⣛⣛⣌⣛⣛⣋⣤⣛⣛⣛⣘⣛⣘⣋⣛⣛⣘⣛⣛⣛⣁⣛⣛⣛⣘⣛⣛⣛⣃⣴⣘⣛⣛⡛⣃⠙⠛⠛⠁⠘⠛⠛⠛⠀⠘⠛⠛⠛⠀⠀⠀⠛⠃⠈⠛⠛⠋⠀⠙⠛⠛⠁⠈⠛⠛⠋⠀⠀⠀
⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠹⠉⠉⠉⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣀⣀⣠⡶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⢿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠳⠶⠶⢦⣤⣄⣀⣿⡾⣿⣿⣽⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠉⢿⣿⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠁⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠛⠻⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡟⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡿⠓⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢶⠆⢰⣶⣶⣶⠹⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣦⠀⠀⠀⠀⠀⠀
[22A⣿⣿⡿⠛⠛⠿⠿⡿⠿⠿⢿⡿⠿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣵⡷⠂⣿⣿⣿⣷⢸⣿⡿⠇⣴⣿⢻⣷⡀⣿⡿⠿⢸⣿⣷⣸⣿⣿⢸⣿⣿⣷⡄⣿⣿⠿⢸⣿⡿⣿⡆⠛⢰⣿⢻⣷⡄⣾⡟⣿⣦⢰⣿⢻⣷⣤⣴⣿⡇⠀⠀⢠⣴⣾⡇⣿⣿⠿⠿⢠⣾⡟⣿⣆⢰⣿⢻⣷⡀⠀⠀
⠉⣤⠀⣿⣿⣿⣿⢸⣿⣷⡆⣿⣿⠘⠛⠃⣿⣷⣶⢸⣿⣿⣿⣿⣿⢸⣿⣿⣿⡃⣿⣿⣶⢸⣿⣷⣿⡃⢴⡌⢉⣼⡿⢳⣿⡇⣿⣿⠈⢉⣾⡿⠀⢸⣿⣷⣶⠀⠀⠈⣿⡇⠿⠿⢻⣿⣼⣿⡇⣿⣿⣿⣿⢸⣿⡇⠀⠀
⠈⡟⠀⣿⣿⣿⣿⢸⣿⣇⣀⣿⣿⣸⣿⠇⣿⣷⣀⢸⣿⢿⣿⣿⣿⢸⣿⣿⣿⡇⣿⣿⣀⢸⣿⡏⣿⡇⠸⢁⣾⣿⣁⡘⣿⡇⣿⣿⢠⣿⣟⣀⠀⢸⣿⣇⣀⠀⠀⠀⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⡿⢻⣿⢸⣿⠇⠀⠀
⠀⣳⣀⠛⠛⢛⣋⣘⣛⣛⣛⣌⣛⣛⣋⣤⣛⣛⣛⣘⣛⣘⣋⣛⣛⣘⣛⣛⣛⣁⣛⣛⣛⣘⣛⣓⣛⣃⣶⣘⣛⣛⢛⠃⠙⠛⠛⠁⠘⠛⠛⠛⠀⠘⠛⠛⠛⠀⠀⠀⠛⠃⠈⠛⠛⠋⠀⠙⠛⠛⠁⠈⠛⠛⠋⠀⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠐⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠙⠉⠉⠋⠉⠉⠯⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠳⠶⠶⢦⣤⣄⣰⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢈⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠁⠉⠁⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⠿⠛⠍⠉⠉⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⢿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠛⣛⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢶⠆⢰⣶⣶⣶⠹⠋⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⠀⠀⠀⠀⠀⠀
[22A⣿⣿⠿⠛⠻⠿⠿⡿⠿⠿⢿⡿⠿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡿⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣴⡷⠂⣿⣿⣿⣷⢸⣿⡿⠇⣴⣿⢻⣷⡀⣿⡿⠿⢸⣿⣷⣸⣿⣿⢸⣿⣿⣷⡄⣿⣿⠿⢸⣿⡿⣿⡆⠛⢰⣿⢻⣷⡄⣾⡟⣿⣦⢰⣿⢻⣷⣤⣴⣿⡇⠀⠀⢠⣴⣾⡇⣿⣿⠿⠿⢠⣾⡟⣿⣆⢰⣿⢻⣷⡀⠀⠀
⢙⣤⠀⣿⣿⣿⣿⢸⣿⣷⡆⣿⣿⠘⠛⠃⣿⣷⣶⢸⣿⣿⣿⣿⣿⢸⣿⣿⣿⡃⣿⣿⣶⢸⣿⣷⣿⡃⢴⡌⢉⣼⡿⢳⣿⡇⣿⣿⠈⢉⣾⡿⠀⢸⣿⣷⣶⠀⠀⠈⣿⡇⠿⠿⢻⣿⣼⣿⡇⣿⣿⣿⣿⢸⣿⡇⠀⠀
⠘⣏⠀⣿⣿⣿⣿⢸⣿⣇⣀⣿⣿⣸⣿⠇⣿⣧⣀⢸⣿⢿⣿⣿⣿⢸⣿⣿⣿⡇⣿⣿⣀⢸⣿⡏⣿⡇⠸⢁⣾⣿⣁⡘⣿⡇⣿⣿⢠⣿⣟⣀⠀⢸⣿⣇⣀⠀⠀⠀⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⡿⢻⣿⢸⣿⠇⠀⠀
⠀⣷⣀⠛⠛⢛⣋⣘⣛⣛⣛⣌⣛⣛⣋⣤⣛⣛⣛⣘⣛⣘⣋⣛⣛⣘⣛⣛⣛⣁⣛⣛⣛⣘⣛⣃⣛⣃⣶⣘⣛⣛⠛⢃⠙⠛⠛⠁⠘⠛⠛⠛⠀⠘⠛⠛⠛⠀⠀⠀⠛⠃⠈⠛⠛⠋⠀⠙⠛⠛⠁⠈⠛⠛⠋⠀⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠨⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠙⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠈⠚⠛⠛⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠶⠦⢤⣤⣀⣰⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣬⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⢉⢿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠉⠉⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠻⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⠿⠋⠉⠛⠉⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠟⣝⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠟⢶⠄⢰⣶⣶⣶⠙⠋⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣦⠀⠀⠀⠀⠀⠀
[22A⣼⣿⡿⠛⠛⠿⠿⠿⠿⠿⢿⡿⠿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢔⡿⠂⣿⣿⣿⣷⢸⣿⡿⠇⣴⣿⢻⣷⡀⣿⡿⠿⢹⣿⣷⣸⣿⣿⢸⣿⣿⣷⡄⣿⣿⠿⢸⣿⡿⣿⡆⠙⢰⣿⢻⣷⡄⣾⡟⣿⣦⢰⣿⢻⣷⣤⣴⣿⡇⠀⠀⢠⣴⣾⡇⣿⣿⠿⠿⢠⣾⡟⣿⣆⢰⣿⢻⣷⡀⠀⠀
⢘⣤⠀⣿⣿⣿⣿⢸⣿⣷⡆⣿⣿⠘⠛⠃⣿⣷⣶⢸⣿⣿⣿⣿⣿⢸⣿⣿⣿⡃⣿⣿⣶⢸⣿⣷⣿⡃⢴⡌⢉⣼⡿⢻⣿⡇⣿⣿⠈⢉⣾⡿⠀⢸⣿⣷⣶⠀⠀⠈⣿⡇⠿⠿⢻⣿⣼⣿⡇⣿⣿⣿⣿⢸⣿⡇⠀⠀
⠈⣟⠀⣿⣿⣿⣿⢸⣿⣇⣀⣿⣿⣸⣿⠇⣿⣿⣀⢸⣿⢿⣿⣿⣿⢸⣿⣿⣿⡇⣿⣿⣀⢸⣿⡏⣿⡇⠸⢁⣾⣿⣁⡸⣿⡇⣿⣿⢠⣿⣟⣀⠀⢸⣿⣇⣀⠀⠀⠀⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⡿⢿⣿⢸⣿⠇⠀⠀
⠀⢻⡀⠛⠛⢛⣋⣘⣛⣛⣛⣈⣛⣛⣋⣄⣛⣛⣛⣘⣛⣘⣋⣛⣛⣘⣛⣛⣛⣁⣛⣛⣛⣘⣛⣋⣛⣃⣶⣘⣛⡛⠛⢃⠙⠛⠛⠁⠘⠛⠛⠛⠀⠘⠛⠛⠛⠀⠀⠀⠛⠃⠈⠛⠛⠋⠀⠙⠛⠛⠁⠈⠛⠛⠋⠀⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠆⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠊⠙⠿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠶⠦⢤⣤⣀⣀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠹⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⡿⠫⠉⠙⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⠛⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⢻⣿⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠟⢷⠖⣰⣶⣶⣶⠙⠋⠻⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣧⠀⠀⠀⠀⠀⠀
[22A⣻⣿⠿⠛⠻⠿⠿⠿⠿⠿⢿⡿⠿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢹⡿⠆⣿⣿⣿⣷⢸⣿⡿⠇⣴⣿⢻⣷⡀⣿⣿⠿⢹⣿⣷⣼⣿⣿⢸⣿⣿⣷⡄⣿⣿⠿⢸⣿⡿⣿⡆⠙⢰⣿⢿⣷⡄⣾⡟⣿⣦⢰⣿⢻⣷⣤⣴⣿⡇⠀⠀⢠⣴⣾⡇⣿⣿⠿⠿⢠⣾⡟⣿⣆⢰⣿⢻⣷⡀⠀⠀
⢈⣷⠀⣿⣿⣿⣿⢸⣿⣷⡆⣿⣿⠘⠛⠃⣿⣿⣶⢸⣿⣿⣿⣿⣿⢸⣿⣿⣿⡃⣿⣿⣶⢸⣿⣿⣿⡃⢰⡌⢉⣼⡿⢻⣿⡇⣿⣿⠈⢉⣾⡿⠀⢸⣿⣷⣶⠀⠀⠈⣿⡇⠿⠿⢻⣿⣼⣿⡇⣿⣿⣿⣿⢸⣿⡇⠀⠀
⠀⣟⠀⣿⣿⣿⣿⢸⣿⣇⣀⣿⣿⣸⣿⠇⣿⣿⣀⢸⣿⣿⣿⣿⣿⢸⣿⣿⣿⡇⣿⣿⣀⢸⣿⣏⣿⡇⠸⢁⣾⣿⣁⡸⣿⡇⣿⣿⢠⣿⣟⣀⠀⢸⣿⣇⣀⠀⠀⠀⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⡿⢻⣿⢸⣿⠇⠀⠀
⠀⢻⣀⠛⠛⠛⣋⣘⣛⣛⣛⣈⣛⣛⣋⣄⣛⣛⣛⣘⣛⣘⣋⣛⣛⣘⣛⣛⣛⣁⣛⣛⣛⣘⣛⣛⣛⣃⣴⣼⣛⡛⡛⢃⠙⠛⠛⠁⠘⠛⠛⠛⠀⠘⠛⠛⠛⠀⠀⠀⠛⠃⠈⠛⠛⠋⠀⠙⠛⠛⠁⠈⠛⠛⠋⠀⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣅⣄⣐⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⡉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠻⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⢘⢽⡻⠑⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⢶⣾⣧⣼⣧⣢⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣽⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠹⠿⣿⠿⣿⣿⠷⢦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⠋⠉⠉⠁⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣷⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⠻⠛⠿⠻⠻⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡝⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠶⠶⣶⠿⢷⠶⣰⣶⣾⣶⠹⡻⣿⢿⠿⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣧⡀⠀⠀⠀⠀⠀
[22A⠸⣿⠿⠛⠛⠿⠿⠿⠿⠿⢿⡿⠿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⡿⠂⣿⣿⣿⣷⢸⣿⡿⠇⣴⣿⢻⣷⡀⣿⣿⠿⢸⣿⣷⣸⣿⣿⢸⣿⣿⣷⡄⣿⣿⠿⢸⣿⣿⣿⡆⠉⢰⣿⢿⣷⡄⣾⡟⣿⣦⢰⣿⢻⣷⣤⣴⣿⡇⠀⠀⢠⣴⣾⡇⣿⣿⠿⠿⢠⣾⡟⣿⣆⢰⣿⢻⣷⡀⠀⠀
⠀⣤⠀⣿⣿⣿⣿⢸⣿⣷⡆⣿⣿⠘⠛⠃⣿⣿⣶⢸⣿⣿⣿⣿⣿⢸⣿⣿⣿⡃⣿⣿⣶⢸⣿⣿⣿⡃⢰⡌⢉⣼⣿⢻⣿⡇⣿⣿⠈⢉⣾⡿⠀⢸⣿⣷⣶⠀⠀⠈⣿⡇⠿⠿⢻⣿⣼⣿⡇⣿⣿⣿⣿⢸⣿⡇⠀⠀
⠀⠟⠀⣿⣿⣿⣿⢸⣿⣇⣀⣿⣿⣸⣿⠇⣿⣿⣀⢸⣿⣿⣿⣿⣿⢸⣿⣿⣿⡇⣿⣿⣀⢸⣿⣿⣿⡇⠸⢁⣾⣿⣁⡸⣿⡇⣿⣿⢠⣿⣟⣀⠀⢸⣿⣇⣀⠀⠀⠀⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⡿⢻⣿⢸⣿⠇⠀⠀
⠀⢠⣀⠛⠛⢛⣋⣘⣛⣛⣛⣈⣛⣛⣋⣄⣛⣛⣛⣘⣛⣘⣋⣛⣛⣘⣛⣛⣛⣁⣛⣛⣛⣘⣛⣛⣛⣃⣶⣜⡛⡛⠛⣃⠙⠛⠛⠁⠘⠛⠛⠛⠀⠘⠛⠛⠛⠀⠀⠀⠛⠃⠈⠛⠛⠋⠀⠙⠛⠛⠁⠈⠛⠛⠋⠀⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣐⣤⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠐⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠁⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⠛⡛⡿⠻⠿⠿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣽⠝⣍⢆⡄⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⣶⣾⣷⣿⣿⣁⣿⠇⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠹⠿⠿⠻⡟⠿⠷⣦⣤⣤⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠉⠉⠠⠁⠐⠉⠉⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⡟⠿⠛⠿⠟⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠶⠶⣶⠿⢷⠶⣰⣶⣾⣶⠹⢿⣿⡿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⡀⠀⠀⠀⠀⠀
[22A⠼⣿⡿⠛⠛⠿⠿⡿⠿⠿⢿⡿⠿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢴⡿⠆⣿⣿⣿⣷⢸⣿⡿⠇⣴⣿⢻⣷⡈⣿⣿⠿⣿⣿⣷⣼⣿⣿⢸⣿⣿⣷⡄⣿⣿⠿⢸⣿⣿⣿⡆⠉⢰⣿⢿⣿⣄⣾⡟⣿⣦⣰⣿⢻⣷⣤⣶⣿⡇⠀⠀⢠⣴⣾⡇⣿⣿⠿⠿⢠⣾⡟⣿⣆⣰⣿⢻⣷⡀⠀⠀
⠚⣶⠀⣿⣿⣿⣿⢸⣿⣷⡆⣿⣿⠘⠛⠃⣿⣿⣶⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡃⣿⣿⣶⢸⣿⣿⣿⡃⣴⡌⢉⣼⣿⢻⣿⡇⣿⣿⠈⢉⣾⡿⠀⢸⣿⣷⣶⠀⠀⠈⣿⡇⠿⠿⢻⣿⣼⣿⡇⣿⣿⣿⣿⢸⣿⡇⠀⠀
⠘⣛⠀⣿⣿⣿⣿⢸⣿⣇⣀⣿⣿⣸⣿⠇⣿⣿⣀⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡇⣿⣿⣀⢸⣿⣿⣿⡇⠸⢁⣾⣿⣁⡸⣿⣇⣿⣿⢠⣿⣟⣁⠀⢸⣿⣇⣀⠀⠀⠀⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⡿⢿⣿⢸⣿⠇⠀⠀
⠀⣶⡀⠛⠛⢛⣋⣘⣛⣛⣛⣈⣛⣛⣋⣄⣛⣛⣛⣙⣛⣘⣛⣛⣛⣘⣛⣛⣛⣁⣛⣛⣛⣘⣛⣛⣛⣃⣾⣞⣛⣛⡛⣃⡙⠛⠛⣁⠙⠛⠛⠛⠀⠘⠛⠛⠛⠀⠀⠀⠛⠃⠈⠛⠛⠋⠀⠙⠛⠛⠁⠈⠛⠛⠋⠀⠀⠀
⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠛⢛⡻⣻⡻⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⠁⠀⠀⠀⠀⣀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠄⠀⠉⠺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⡛⠭⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠙⣿⣿⣿⣿⣿⡿⢿⣿⠿⣿⣿⣿⡿⣿⠟⣻⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠶⠶⣶⠿⢷⠶⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⢭⠛⠛⠛⠻⠿⠿⠿⠿⠿⡿⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠟⠛⠿⢿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⡷⠆⣿⣿⣿⣷⢸⣿⡿⠇⣴⣿⢿⣷⡀⣿⣿⠿⣿⣿⣷⣼⣿⣿⢸⣿⣿⣿⡄⣿⣿⠿⢸⣿⣿⣿⡆⠈⢰⣿⢿⣿⣄⣾⡟⣿⣦⣰⣿⢻⣷⣤⣶⣿⡇⠀⠀⢠⣴⣾⡇⣿⣿⠿⠿⢠⣾⡟⣿⣆⣰⣿⢻⣷⡀⠀⠀
⠀⣶⠀⣿⣿⣿⣿⢸⣿⣷⡆⣿⣿⠘⠛⠃⣿⣿⣶⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡃⣿⣿⣶⢸⣿⣿⣿⡃⢰⡌⢉⣼⣿⢻⣿⡇⣿⣿⠈⢉⣾⡿⠀⢸⣿⣷⣶⠀⠀⠈⣿⡇⠿⠿⢻⣿⣼⣿⡇⣿⣿⣿⣿⢸⣿⡇⠀⠀
⠀⠛⠀⣿⣿⣿⣿⢸⣿⣇⣀⣿⣿⣸⣿⠇⣿⣿⣀⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡇⣿⣿⣀⢸⣿⣿⣿⡇⠸⢁⣾⣿⣁⡸⣿⣇⣿⣿⢠⣿⣟⣁⠀⢸⣿⣇⣀⠀⠀⠀⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⡿⢿⣿⢸⣿⡇⠀⠀
⠀⢠⣀⠛⠛⣛⣋⣘⣛⣛⣛⣈⣛⣛⣋⣄⣛⣛⣛⣛⣛⣘⣛⣛⣛⣘⣛⣛⣛⣁⣛⣛⣛⣘⣛⣛⣛⣣⣶⣜⣛⣛⢛⣃⠙⠛⠛⢁⠙⠛⠛⠛⠀⠘⠛⠛⠛⠀⠀⠀⠛⠃⠈⠛⠛⠋⠀⠙⠛⠛⠁⠈⠛⠛⠋⠀⠀⠀
⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠳⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠰⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠁⠒⠹⠚⡫⠈⠉⠟⢹⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠭⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠆⠀⠀⣾⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⠂⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠐⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠁⠀⠀⠀⠉⠀⠛⠛⠙⠛⢋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠶⠶⣶⠿⢷⠶⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⢀⠙⠛⠛⠻⠿⠿⠿⠿⠿⡿⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠛⠿⠿⠟⠛⠻⠿⣯⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡷⠆⣿⣿⣿⣷⢸⣿⡿⠇⣴⣿⢿⣷⡈⣿⣿⠿⣿⣿⣷⣼⣿⣿⢸⣿⣿⣿⡄⣿⣿⠿⢸⣿⣿⣿⡆⠁⢰⣿⢿⣿⣄⣾⡟⣿⣦⣰⣿⢻⣷⣤⣶⣿⡇⠀⠀⢠⣴⣾⡇⣿⣿⠿⠿⢠⣾⡟⣿⣆⣰⣿⢻⣷⡄⠀⠀
⠀⣤⠀⣿⣿⣿⣿⢸⣿⣷⡆⣿⣿⠘⠛⠃⣿⣿⣶⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡃⣿⣿⣶⢸⣿⣿⣿⡃⢠⡈⢉⣼⣿⢻⣿⡇⣿⣿⠉⢉⣾⡿⠀⢸⣿⣷⣶⠀⠀⠈⣿⡇⠿⠿⢻⣿⣼⣿⡇⣿⣿⣿⣿⢸⣿⡇⠀⠀
⠀⠋⠀⣿⣿⣿⣿⢸⣿⣇⣀⣿⣿⣸⣿⠇⣿⣿⣀⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡇⣿⣿⣀⢸⣿⣿⣿⡇⠸⢁⣾⣿⣁⡸⣿⣇⣿⣿⢠⣿⣟⣁⠀⢸⣿⣇⣀⠀⠀⠀⣿⡇⣿⣿⣸⣿⣿⣿⡇⣿⡿⢿⣿⢸⣿⡇⠀⠀
⠀⢰⣀⠛⠛⣛⣋⣘⣛⣛⣛⣈⣛⢛⣋⣔⣛⣛⣛⣛⣛⣘⣛⣛⣛⣘⣛⣛⣛⣁⣛⣛⣛⣘⣛⣛⣛⣣⣾⣾⣛⣛⠛⣃⡙⠛⠛⠁⠙⠛⠛⠛⠀⠘⠛⠛⠛⠀⠀⠀⠛⠃⠈⠛⠛⠋⠀⠙⠛⠛⠁⠈⠛⠛⠋⠀⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⢿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠫⠅⠐⠊⠛⠻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡀⡀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡒⣾⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠰⠒⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣻⠶⠺⠳⠄⠀⠈⠻⠿⣿⡿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⣿⣾⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠿⠟⠛⠋⠉⠉⠉⠉⠉⠛⠻⠿⣿⠛⠉⠁⠚⠈⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠑⠚⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠶⠶⣶⠿⢷⠶⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠙⠛⠛⠿⠿⠿⠿⠿⠿⠿⠻⠿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡿⠿⠛⠻⠿⠛⠛⠛⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠷⠆⣿⣿⣿⣷⢸⣿⡿⠇⣼⣿⢿⣷⡈⣿⣿⠿⣿⣿⣷⣼⣿⣿⢸⣿⣿⣿⡄⣿⣿⠿⢸⣿⣿⣿⡆⠀⢰⣿⢿⣿⣄⣾⡿⣿⣦⣰⣿⢻⣷⣤⣶⣿⡇⠀⠀⢠⣴⣾⡇⣿⣿⠿⠿⢠⣾⡟⣿⣆⣰⣿⢻⣷⡄⠀⠀
⠀⣤⠀⣿⣿⣿⣿⢸⣿⣷⡆⣿⣿⠘⠛⠃⣿⣿⣶⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡃⣿⣿⣶⢸⣿⣿⣿⡃⢠⠈⢉⣼⣿⢻⣿⡇⣿⣿⠉⢉⣾⡿⠀⢸⣿⣷⣶⠂⠀⠈⣿⡇⠿⠿⢻⣿⣼⣿⡇⣿⣿⣿⣿⢸⣿⡇⠀⠀
⠀⠋⠀⣿⣿⣿⣿⢸⣿⣇⣀⣿⣿⣸⣿⠇⣿⣿⣀⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡇⣿⣿⣀⢸⣿⣿⣿⡇⠈⢀⣾⣿⣁⡸⣿⣇⣿⣿⢠⣿⣟⣁⠀⢸⣿⣇⣀⠀⠀⠀⣿⡇⣿⣿⣸⣿⣿⣿⣇⣿⡿⢿⣿⢸⣿⡇⠀⠀
⠀⢳⣀⠛⠛⣛⣋⣜⣛⣛⣛⣈⡛⠛⣋⣀⣛⣛⣛⣛⣛⣘⣛⣛⣛⣘⣛⣛⣛⣁⣛⣛⣛⣘⣛⣛⣛⣣⣶⣾⣛⡛⠛⣃⡙⠛⠛⠁⠙⠛⠛⠛⠀⠘⠛⠛⠛⠀⠀⠀⠛⠃⠈⠛⠛⠋⠀⠙⠛⠛⠁⠈⠛⠛⠋⠀⠀⠀
⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣼⣧⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢩⣝⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⡻⡿⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢀⣄⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⡭⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⠿⠿⠿⠿⠋⠁⠀⠀⠀⠸⢿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣍⣾⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⢝⡿⡿⡻⠛⠀⠝⠻⠻⣿⣿⣿⠿⠿⢛⠉⠈⠀⠘⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠈⢰⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢄⠰⠙⠩⣿⣷⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢰⢉⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠅⠙⠉⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠶⠶⣶⠿⢷⠶⠴⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣼⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣦⣴⣦⢉⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡲⢾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡂⠙⡩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠀⠀⠄⠹⠝⠟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⢪⣜⡯⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠍⡋⠇⠪⡥⣿⠿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢊⣊⡥⠫⠯⠁⣩⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡟⡿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢑⡝⢯⣿⢣⣽⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣽⣹⣿⢿⣫⣻⡉⣛⢷⣶⡿⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣻⡶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣻⡻⠀⠼⣿⢡⡰⣩⠿⠙⢫⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠰⠿⠷⣶⠿⢿⠶⡾⠾⠿⡿⠚⠻⠿⠿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠄⠳⢃⣘⠗⠑⠭⠂⠈⠰⠝⠽⣯⣿⠿⠿⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⢷⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠷⢶⢠⣤⡄⢠⣤⣤⡌⢩⣤⡍⣭⣭⢩⣥⡌⣭⣬⠉⣥⣤⣤⠉⣥⣤⣤⣭⡡⣤⡄⣡⣤⠄⠀⣠⣤⣤⣄⠀⣠⣤⣤⡀⢀⣤⣤⣤⡀⣠⣤⣤⣄⠀⠀⠀⠀⠀⣠⣤⢀⣠⣤⣤⡀⢀⣤⣤⣤⡀⢀⣤⣤⣤⡀⠀⠀
⠀⣤⡄⢸⣿⡇⣼⣿⣿⣧⢸⣿⣿⣼⣿⢸⣿⡇⣿⣿⢀⣿⣿⣿⡆⣿⣿⣿⣿⡇⢻⣿⣿⡟⠀⠀⠿⠏⣽⣿⢸⣿⡏⣿⣿⠸⠿⢹⣿⡇⠿⠏⣿⣿⢀⣀⠀⠘⠻⣿⣿⢸⣿⣏⣛⡛⢸⣿⡏⣿⣷⣾⣿⣿⣿⡇⠀⠀
⠀⠈⠁⢸⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⣿⢸⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⣿⣿⣿⡅⠘⣿⣿⠁⣼⡦⢀⣼⣿⠏⢸⣿⡇⣿⣿⠀⣠⣿⡿⠁⠀⣼⣿⠏⠘⠿⠀⠀⠀⣿⣿⢸⣿⡟⣿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⢠⣼⣿⣧⣿⣿⢻⣿⣾⣿⡟⣿⣿⠸⣿⣧⣿⣿⣸⣿⡟⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⠀⣿⠁⣾⣿⣧⣤⠸⣿⣧⣿⡿⢰⣿⣿⣤⡄⣾⣿⣧⣤⢠⣤⠀⠀⠀⣿⣿⢸⣿⣧⣿⡿⢸⣿⣧⣿⡟⢻⣿⣿⣿⡇⠀⠀
⠀⠀⠀⣉⣉⣬⣭⣭⣬⣭⣍⣉⣡⣉⣉⣤⣈⣉⣉⣁⣉⣉⣥⣭⣭⣭⣭⣭⣭⣥⣶⣭⣭⣾⣿⣮⣭⣭⣭⣽⣶⣬⣉⣉⣤⣈⢉⣉⣉⡁⠉⠉⠉⠉⠈⠉⠀⠀⠀⠉⠉⠀⠈⠉⠉⠀⠀⠉⠉⠉⠀⠀⠉⠉⠉⠀⠀⠀
⠀⠀⡱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣵⣿⣗⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠉⢯⡿⢿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠩⣿⣿⣿⣿⣿⡯⠓⠶⡳⢭⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⠹⠉⡉⠛⢙⠁⠉⠀⠬⠒⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⢀⣴⣶⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡂⠀⠀⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡇⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠠⠀⠀⠀⠈⠙⠿⠿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢐⠷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣯⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠙⠹⣿⡟⢻⠉⠋⠛⠛⠻⣿⠿⠿⢟⠟⠋⠉⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡮⣶⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡴⠃⠻⢇⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠶⠶⣶⠿⢷⠶⠴⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠽⢟⢻⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠶⢶⢠⣤⡄⢠⣤⣤⡄⢠⣤⡄⣤⣤⢠⣤⡄⣤⣤⠈⣤⣤⣤⠉⣤⣤⣤⣤⡠⣤⡄⣠⣤⠄⠀⣠⣤⣤⣄⠀⣠⣤⣤⡀⢀⣤⣤⣤⡀⣠⣤⣤⣄⠀⠀⠀⠀⠀⣠⣤⢀⣠⣤⣤⡀⢀⣤⣤⣤⡀⢀⣤⣤⣤⡀⠀⠀
⠀⣤⡄⢸⣿⡇⣼⣿⣿⣧⢸⣿⣿⣼⣿⢸⣿⡇⣿⣿⢀⣿⣿⣿⡆⣿⣿⣿⣿⡇⢻⣿⣿⡟⠀⠀⠿⠏⣽⣿⢸⣿⡏⣿⣿⠸⠿⢹⣿⡇⠿⠏⣿⣿⢀⣀⠀⠘⠻⣿⣿⢸⣿⣏⣛⡛⢸⣿⡏⣿⣷⣾⣿⣿⣿⡇⠀⠀
⠀⠈⠁⢸⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⣿⢸⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⣿⣿⣿⡅⠘⣿⣿⠁⣀⠂⢀⣼⣿⠏⢸⣿⡇⣿⣿⠀⣠⣿⡿⠁⠀⣼⣿⠏⠘⠻⠀⠀⠀⣿⣿⢸⣿⡟⣿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⢀⣼⣿⣧⣿⣿⢻⣿⣾⣿⡟⣿⣿⠸⣿⣧⣿⣿⣸⣿⡟⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⠀⣿⠀⣾⣿⣧⣤⠸⣿⣧⣿⡿⢰⣿⣿⣤⡄⣾⣿⣧⣤⢠⣤⠀⠀⠀⣿⣿⢸⣿⣧⣿⡿⢸⣿⣧⣿⡟⢻⣿⣿⣿⡇⠀⠀
⠀⠀⠈⣉⣉⣬⣭⣭⣬⣍⣉⣉⠁⠉⠉⠀⡈⠉⠉⢁⣉⣉⣁⣉⣉⣍⣭⣭⣭⣥⣦⣭⣭⣴⣿⣮⣭⣭⣭⣽⣶⣬⣉⣩⣤⣉⢉⢉⣉⡁⠉⠉⠉⠉⠈⠉⠀⠀⠀⠉⠉⠀⠈⠉⠉⠀⠀⠉⠉⠉⠀⠀⠉⠉⠉⠀⠀⠀
⠀⠀⢹⣿⢿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠐⣂⠀⣢⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣼⣿⣷⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠿⠯⠽⠻⣻⣿⣿⠩⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠂⠀⠊⠩⠋⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠍⠀⢠⣴⣾⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠍⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡇⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⢿⠎⠀⠀⠀⠀⠈⠙⠿⠿⠿⠛⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣟⠵⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠿⠿⠿⠿⠛⠟⠻⣿⡿⠟⠻⠟⠏⠋⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠗⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⠁⢋⢳⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠘⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠂⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠶⠶⣶⠿⢷⠶⠴⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠶⢶⢠⣤⡄⢠⣤⣤⡄⢠⣤⡄⣤⣤⢠⣤⡄⣤⣤⠀⣤⣤⣤⠀⣤⣤⣤⣤⡠⣤⡄⣠⣤⠄⠀⣠⣤⣤⣄⠀⣠⣤⣤⡀⢀⣤⣤⣤⡀⣠⣤⣤⣄⠀⠀⠀⠀⠀⣠⣤⢀⣠⣤⣤⡀⢀⣤⣤⣤⡀⢀⣤⣤⣤⡀⠀⠀
⠀⣤⡄⢸⣿⡇⣼⣿⣿⣧⢸⣿⣿⣼⣿⢸⣿⡇⣿⣿⠀⣿⣿⣿⡆⣿⣿⣿⣿⡇⢻⣿⣿⡟⠀⠀⠿⠏⣽⣿⢸⣿⡏⣿⣿⠸⠿⢹⣿⡇⠿⠏⣿⣿⢀⣀⠀⠘⠻⣿⣿⢸⣿⣏⣛⡛⢸⣿⡏⣿⣷⣾⣿⣿⣿⡇⠀⠀
⠀⠈⠁⢸⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⣿⢸⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⣿⣿⣿⡅⠘⣿⣿⠁⠀⠀⢀⣼⣿⠏⢸⣿⡇⣿⣿⠀⣠⣿⡿⠁⠀⣼⣿⠏⠘⠿⠀⠀⠀⣿⣿⢸⣿⡟⣿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⠀⣼⣿⣧⣿⣿⢻⣿⣾⣿⡟⣿⣿⠸⣿⣧⣿⣿⣸⣿⡟⣿⣷⣿⣿⣿⣿⡇⠀⣿⣿⠀⠀⠀⣾⣿⣧⣤⠸⣿⣧⣿⡿⢰⣿⣿⣤⡄⣾⣿⣧⣤⢠⣤⠀⠀⠀⣿⣿⢸⣿⣧⣿⡿⢸⣿⣧⣿⡟⢻⣿⣿⣿⡇⠀⠀
⠀⠀⠈⣉⢉⣨⣍⣩⣌⣉⡉⠉⠁⠉⠉⠀⠈⠉⠉⠁⠉⣉⣁⣉⣉⣉⣩⣭⣉⣡⣤⣍⣉⣴⣿⣮⣭⣉⣭⣽⣶⣮⣉⣩⣄⠈⡉⢉⡉⠁⠉⠉⠉⠉⠈⠉⠀⠀⠀⠉⠉⠀⠈⠉⠉⠀⠀⠉⠉⠉⠀⠀⠉⠉⠉⠀⠀⠀
⠀⠀⠀⠉⠿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠛⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢆⣤⣶⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⡺⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⢻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠙⠍⠁⠀⠈⠙⠛⠛⠛⠋⠛⠍⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠽⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠽⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢛⠿⠛⠛⠙⠛⠛⠟⣿⡿⡿⠿⡛⠟⠛⠉⠉⠉⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢩⣗⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⢼⢙⡷⣧⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢆⢒⠌⠉⠉⠋⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠶⠶⣶⠿⢷⠶⠴⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠲⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠲⢦⢠⣤⡄⢠⣤⣤⡄⢠⣤⡄⣤⣤⢠⣤⡄⣤⣤⠀⣤⣤⣤⠀⣤⣤⣤⣤⡠⣤⡄⣠⣤⠄⠀⣠⣤⣤⣄⠀⣠⣤⣤⡀⢀⣤⣤⣤⡀⣠⣤⣤⣄⠀⠀⠀⠀⠀⣠⣤⢀⣠⣤⣤⡀⢀⣤⣤⣤⡀⢀⣤⣤⣤⡀⠀⠀
⠀⣤⡄⢸⣿⡇⣼⣿⣿⣧⢸⣿⣿⣼⣿⢸⣿⡇⣿⣿⢀⣿⣿⣿⡆⣿⣿⣿⣿⡇⢻⣿⣿⡟⠀⠀⠿⠏⣽⣿⢸⣿⡏⣿⣿⠸⠿⢹⣿⡇⠿⠏⣿⣿⢀⣀⠀⠘⠻⣿⣿⢸⣿⣏⣛⡛⢸⣿⡏⣿⣷⣾⣿⣿⣿⡇⠀⠀
⠀⠈⠁⢸⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⣿⢸⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⣿⣿⣿⡅⠘⣿⣿⠁⠀⠀⢀⣼⣿⠏⢸⣿⡇⣿⣿⠀⣠⣿⡿⠁⠀⣼⣿⠏⠘⠿⠀⠀⠀⣿⣿⢸⣿⡟⣿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⢀⣼⣿⣧⣿⣿⢻⣿⣾⣿⡟⣿⣿⠸⣿⣧⣿⣿⣸⣿⡟⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⠀⣄⠀⣾⣿⣧⣤⠸⣿⣧⣿⡿⢰⣿⣿⣤⡄⣾⣿⣧⣤⢠⣤⠀⠀⠀⣿⣿⢸⣿⣧⣿⡿⢸⣿⣧⣿⡟⢻⣿⣿⣿⡇⠀⠀
⠀⠀⠀⢉⣉⣨⣉⣩⣈⠉⠉⠉⠁⠉⠉⠀⠈⠉⠉⠁⠉⠉⣁⣉⣉⣉⣉⣉⣉⣁⢀⣍⣩⣼⣿⣾⣭⣉⣭⣽⣶⣮⣉⣩⣄⣈⠉⠉⠉⠁⠉⠉⠉⠉⠈⠉⠀⠀⠀⠉⠉⠀⠈⠉⠉⠀⠀⠉⠉⠉⠀⠀⠉⠉⠉⠀⠀⠀
⠀⠀⠀⠘⢟⠛⡿⣿⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣀⣠⡤⡂⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⠘⢉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠛⠛⠋⠉⠀⠁⠈⠙⠛⠛⠿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⢀⢈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠿⠿⠿⠛⠛⠛⠿⢿⣿⣿⣿⠿⠿⠿⠛⠛⠋⠋⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢠⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⢥⠻⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣡⠄⡁⠆⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⠌⢉⡻⣄⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠣⠂⠀⠋⠀⠀⠀⠀⠀⠀⣰⣶⣾⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⢁⠂⠈⠈⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠶⠶⣶⠿⢷⠶⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠲⢦⢠⣤⡄⢠⣤⣤⡄⢠⣤⡄⣤⣤⢠⣤⡄⣤⣤⠀⣤⣤⣤⠀⣤⣤⣤⣤⡠⣤⡄⣠⣤⠄⠀⣠⣤⣤⣄⠀⣠⣤⣤⡀⢀⣤⣤⣤⡀⣠⣤⣤⣄⠀⠀⠀⠀⠀⣠⣤⢀⣠⣤⣤⡀⢀⣤⣤⣤⡀⢀⣤⣤⣤⡀⠀⠀
⠀⣤⡄⢸⣿⡇⣼⣿⣿⣧⢸⣿⣿⣸⣿⢸⣿⡇⣿⣿⠀⣿⣿⣿⡆⣿⣿⣿⣿⡇⢻⣿⣿⡟⠀⠀⠿⠏⣽⣿⢸⣿⡏⣿⣿⠸⠿⢹⣿⡇⠿⠏⣿⣿⢀⣀⠀⠘⠻⣿⣿⢸⣿⣏⣛⡛⢸⣿⡏⣿⣷⣾⣿⣿⣿⡇⠀⠀
⠀⠈⠀⢸⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⣿⢸⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⣿⣿⣿⡅⠘⣿⣿⠁⠀⠀⠀⣼⣿⠏⢸⣿⡇⣿⣿⠀⣠⣿⡿⠁⠀⣼⣿⠏⠘⠿⠀⠀⠀⣿⣿⢸⣿⡟⣿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⢀⣼⣿⣧⣿⣿⢻⣿⣾⣿⡟⣿⣿⠸⣿⣧⣿⣿⣸⣿⡟⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⠀⣄⠀⣾⣿⣧⣤⠸⣿⣧⣿⡿⢰⣿⣿⣤⡄⣾⣿⣧⣤⢠⣤⠀⠀⠀⣿⣿⢸⣿⣧⣿⡿⢸⣿⣧⣿⡟⢻⣿⣿⣿⡇⠀⠀
⠀⠀⠈⠉⠉⣌⡉⠉⠈⠉⠉⠉⠁⠉⠉⠀⠈⠉⠉⠁⠉⠉⠁⠉⣉⣉⣉⢉⢉⢁⣤⣭⣭⣾⣿⣯⣍⣉⣭⣽⣶⣮⣍⣉⣀⡈⠉⠉⠉⠁⠉⠉⠉⠉⠈⠉⠀⠀⠀⠉⠉⠀⠈⠉⠉⠀⠀⠉⠉⠉⠀⠀⠉⠉⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣿⣷⣿⣿⣿⣬⣢⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣶⢒⣤⣄⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠈⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⠛⠉⠀⠀⠀⠉⠉⠛⠻⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡛⢛⠛⠋⠻⠿⠿⢿⣿⡿⡿⠟⠿⠟⠛⠛⠙⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠛⠿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠔⡠⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡠⠀⠀⠙⢞⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⠈⠊⠈⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠶⠶⣶⠿⢷⠶⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠲⠆⢠⣤⡄⢠⣤⣤⡄⢠⣤⡄⣤⣤⢠⣤⡄⣤⣤⠀⣤⣤⣤⠀⣤⣤⣤⣤⡠⣤⡄⣠⣤⠄⠀⣠⣤⣤⣄⠀⣠⣤⣤⡀⢀⣤⣤⣤⡀⣠⣤⣤⣄⠀⠀⠀⠀⠀⣠⣤⢀⣠⣤⣤⡀⢀⣤⣤⣤⡀⢀⣤⣤⣤⡀⠀⠀
⠀⣠⡄⢸⣿⡇⣼⣿⣿⣧⢸⣿⣿⣼⣿⢸⣿⡇⣿⣿⠀⣿⣿⣿⡆⣿⣿⣿⣿⡇⢻⣿⣿⡟⠀⠀⠿⠏⣽⣿⢸⣿⡏⣿⣿⠸⠿⢹⣿⡇⠿⠏⣿⣿⢀⣀⠀⠘⠻⣿⣿⢸⣿⣏⣛⡛⢸⣿⡏⣿⣧⣼⣿⣿⣿⡇⠀⠀
⠀⠈⠀⢸⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⣿⢸⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⣿⣿⣿⡅⠘⣿⣿⠁⠀⠀⠀⣼⣿⠏⢸⣿⡇⣿⣿⠀⣠⣿⡿⠁⠀⣼⣿⠏⠘⠻⠀⠀⠀⣿⣿⢸⣿⡟⣿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⠀⣼⣿⣇⣿⣿⢻⣿⣾⣿⡟⣿⣿⠸⣿⣧⣿⣿⣸⣿⡟⣿⣷⣿⣿⣿⣿⡇⠀⣿⣿⠀⠀⠀⣾⣿⣧⣤⠸⣿⣧⣿⡿⢰⣿⣿⣤⡄⣾⣿⣧⣤⢠⣤⠀⠀⠀⣿⣿⢸⣿⣧⣿⡿⢸⣿⣧⣿⡟⢻⣿⣿⣿⡇⠀⠀
⠀⠀⠀⠉⢉⠈⠉⠉⠈⠉⠉⠉⠁⠉⠉⠀⠈⠉⠉⠁⠉⠉⠁⠉⢉⣉⣉⣉⣉⣁⣄⠉⠉⢀⣴⣆⣉⣭⣭⣽⣶⣮⣍⣉⣀⠈⠉⠉⠉⠁⠉⠉⠉⠉⠈⠉⠀⠀⠀⠉⠉⠀⠈⠉⠉⠀⠀⠉⠉⠉⠀⠀⠉⠉⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣄⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣾⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢹⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠹⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠍⠀⠀⠀⠈⠙⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢾⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠈⠟⠍⠙⠻⠿⠛⠛⠛⠛⠋⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠶⠶⣶⠿⢷⠶⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠒⠆⢠⣤⡄⢠⣤⣤⡄⢠⣤⡄⢠⣤⢠⣤⡄⣤⣤⠀⣤⣤⣤⠀⣤⣤⣤⣤⡠⣤⡄⣠⣤⠄⠀⣠⣤⣤⣄⠀⣠⣤⣤⡀⢀⣤⣤⣤⡀⣠⣤⣤⣄⠀⠀⠀⠀⠀⣠⣤⢀⣠⣤⣤⡀⢀⣤⣤⣤⡀⢀⣤⣤⣤⡀⠀⠀
⠀⣤⡀⢸⣿⡇⣼⣿⣿⣧⢸⣿⣿⣸⣿⢸⣿⡇⣿⣿⠀⣿⣿⣿⡆⣿⣿⣿⣿⡇⢻⣿⣿⡟⠀⠀⠿⠏⣽⣿⢸⣿⡏⣿⣿⠸⠿⢹⣿⡇⠿⠏⣽⣿⢀⣀⠀⠘⠻⣿⣿⢸⣿⣏⣛⡛⢸⣿⡏⣿⣧⣼⣿⣿⣿⡇⠀⠀
⠀⠈⠀⢸⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⣿⢸⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⣿⣿⣿⡅⠘⣿⣿⠁⠀⠀⠀⣼⣿⠋⢸⣿⡇⣿⣿⠀⣠⣿⡿⠁⠀⣼⣿⠏⠘⠻⠀⠀⠀⣿⣿⢸⣿⡟⣿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⠀⣼⣿⣇⣿⣿⢻⣿⣼⣿⡟⣿⣿⠸⣿⣧⣿⡿⣸⣿⡟⣿⣷⣿⣿⣿⣿⡇⠀⣿⣿⠀⠀⠀⣾⣿⣧⣤⠸⣿⣧⣿⡿⢰⣿⣯⣤⡄⣾⣿⣧⣤⢠⣤⠀⠀⠀⣿⣿⠸⣿⣧⣿⡿⢸⣿⣧⣿⡟⢹⣿⣿⣿⡇⠀⠀
⠀⠀⠀⠉⡉⠈⠉⠉⠈⠉⠉⠉⠁⠉⠉⠀⠈⠉⠉⠁⠉⠉⠁⠉⢉⣉⣉⣉⣉⣁⡀⠉⠉⢀⣼⣄⣉⣩⣭⣽⣶⣮⣉⣉⣀⠉⠉⠉⠉⢁⠉⠉⠉⠉⠈⠉⠀⠀⠀⠉⠉⠀⠈⠉⠉⠀⠀⠉⠉⠉⠀⠀⠉⠉⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⣿⣿⣿⡿⠃⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣆⣀⣿⣧⣶⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠇⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠠⡨⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⢸⡚⢀⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣂⡀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⡾⢹⡑⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠻⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡧⠀⠀⠀⠀⠈⠙⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢉⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠋⠛⠛⠛⠛⠛⠋⠙⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠶⠶⣶⠿⢷⠶⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠒⠆⢠⣤⡄⢠⣤⣤⡄⢠⣤⡄⢠⣤⢠⣤⡄⣤⣤⠀⣤⣤⣤⠀⣤⣤⣤⣄⡠⣤⡄⣠⣤⠀⠀⣠⣤⣤⣄⠀⣠⣤⣤⡀⢀⣤⣤⣤⡀⣠⣤⣤⣄⠀⠀⠀⠀⠀⣠⣤⠀⣠⣤⣤⡀⢀⣤⣤⣤⡀⢀⣤⣤⣤⡀⠀⠀
⠀⣠⡀⢸⣿⡇⣸⣿⣿⣧⢸⣿⣿⣸⣿⢸⣿⡇⣿⣿⠀⣿⣿⣿⡆⣿⣿⣿⣿⡇⢻⣷⣿⡟⠀⠀⠿⠏⣽⣿⢸⣿⡏⣿⣿⠸⠿⢹⣿⡇⠿⠏⣽⣿⢀⣀⠀⠐⠻⣿⣿⢸⣿⣏⣛⡛⢸⣿⡏⣿⣧⢸⣿⢹⣿⡇⠀⠀
⠀⠈⠀⢸⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⣿⢸⣿⡇⣿⣿⢸⣿⣟⣿⡇⣿⣿⣿⣿⡅⠘⣿⣿⠁⠀⠀⠀⣼⣿⠋⢸⣿⡇⣿⣿⠀⣠⣿⡟⠁⠀⣼⣿⠏⠘⠛⠀⠀⠀⣿⣿⢸⣿⡏⣿⣿⢸⣿⡇⣿⣿⢽⣿⢸⣿⡇⠀⠀
⠀⠀⠀⣼⣿⣇⣿⣿⢻⣿⣼⣿⡏⣿⣿⠸⣿⣧⣿⡿⢸⣿⡟⣿⣷⣿⣿⣿⣿⡇⠀⣿⣿⠀⠀⠀⣾⣿⣧⣤⠸⣿⣧⣿⡿⢰⣿⣯⣤⡄⣾⣿⣧⣤⢠⣤⠀⠀⠀⣿⣿⠸⣿⣧⣿⡿⢸⣿⣧⣿⡏⢸⣿⣼⣿⡇⠀⠀
⠀⠀⠀⠉⠉⠈⠉⠉⠈⠉⠉⠉⠁⠉⠉⠀⠈⠉⠉⠀⠉⠉⠁⠉⠉⠉⠉⠉⠉⠁⠀⠉⠉⢀⣄⢀⣉⣉⣩⣽⣶⣮⣉⣉⣠⣌⣉⣉⣉⣡⣍⣉⠉⠉⠈⠉⠀⠀⠀⠉⠉⠀⠈⠉⠉⠀⠀⠉⠉⠉⠀⠀⠉⠉⠉⠠⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠐⣠⡄⠀⡀⠀⢠⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡆⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡇⠀⠁⠠⠅⠘⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣟⠀⠀⠀⠀⠈⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⣤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠈⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⠯⠀⠀⠨⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣧⡦⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠫⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⠉⠿⣿⣿⣿⣿⣿⣿⣔⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠈⠉⠉⠉⠁⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠈⠀⠀⠀⠀⠀⠀⠋⠂⠉⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣷⣦⠀⠀⠀⠀⠀⡀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢶⠆⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠒⠄⢠⣤⡄⢠⣤⣤⡄⢠⣤⡄⢠⣤⢠⣤⡄⣤⣤⠀⣤⣤⣤⠀⣤⣤⣤⣄⡠⣤⡄⣠⣤⠀⠀⣠⣤⣤⣀⠀⣠⣤⣤⡀⢀⣤⣤⣄⡀⣠⣤⣤⣄⠀⠀⠀⠀⠀⣠⣤⠀⣠⣤⣤⡀⢀⣤⣤⣤⡀⢀⣤⣤⣄⡀⠀⠀
⠀⠠⠀⢸⣿⡇⣸⣿⣿⣧⢸⣿⣿⣸⣿⢸⣿⡇⣿⣿⠀⣿⣿⣿⡆⣿⣿⣹⣿⡇⢻⣷⣿⡟⠀⠀⠿⠏⣽⣿⢸⣿⡇⣿⣿⠸⠿⢹⣿⡇⠿⠏⣽⣿⢀⣀⠀⠐⠻⣿⣿⢸⣿⣇⣛⡛⢸⣿⡏⣿⣧⢸⣿⢹⣿⡇⠀⠀
⠀⠀⠀⢸⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⣿⢸⣿⡇⣿⣿⢰⣿⣟⣿⡇⣿⣿⣿⣿⡅⠘⣿⣿⠁⠀⠀⠀⣼⣿⠋⢸⣿⡇⣿⣿⠀⢠⣿⡟⠁⠀⣼⣿⠏⠘⠛⠀⠀⠀⣿⣿⢸⣿⡏⣿⣷⢸⣿⡇⣿⣿⢸⣿⢸⣿⡇⠀⠀
⠀⠀⠀⣼⣿⣇⣿⣿⢻⣿⣼⣿⡏⣿⣿⠸⣿⣧⣿⡿⢸⣿⡟⣿⣷⣿⣿⣿⣿⡇⠀⣿⣿⠀⠀⠀⣾⣿⣧⣤⠸⣿⣇⣿⡿⢰⣿⣯⣤⡄⣾⣿⣧⣤⢠⣤⠀⠀⠀⣿⣿⠸⣿⣧⣿⡿⢸⣿⣧⣿⡏⢸⣿⣼⣿⡇⠀⠀
⠀⠀⠀⠉⠉⠈⠉⠉⠈⠉⠉⠉⠁⠉⠉⠀⠈⠉⠉⠀⠉⠉⠁⠉⠉⠉⠉⠉⢉⡁⡀⠉⣉⣠⣦⠀⣉⣉⣭⣭⣶⣌⣉⣉⣠⣌⣉⣉⣉⣥⣍⣉⣉⡉⠈⠉⠐⠂⠀⠉⠉⠀⠈⠉⠉⠀⠀⠉⠉⠉⠀⠀⠉⠉⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢵⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣸⣹⣄⢀⠀⢄⡖⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣼⣿⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⡿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠉⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣤⡔⠚⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢉⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠩⠨⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣦⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠅⢹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠏⠉⠀⠀⠀⠀⠀⠈⠫⠙⡿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢛⠿⣿⣿⣿⣿⣿⡿⣿⢿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣷⣄⠀⠀⠀⠀⣄⡀⢴⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠐⠁⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠒⠄⢠⣤⡄⢠⣤⣤⡄⢠⣤⡄⢠⣤⢠⣤⡄⣤⣤⠀⣤⣤⣤⠀⣤⣤⣤⣄⡠⣤⡄⣠⣤⠀⠀⣠⣤⣤⣀⠀⣠⣤⣤⡀⢀⣤⣤⣄⠀⣠⣤⣤⣄⠀⠀⠀⠀⠀⣠⣤⠀⣠⣤⣤⡀⢀⣤⣤⣤⡀⢀⣤⣤⣄⡀⠀⠀
⠀⢠⠀⢸⣿⡇⣸⣿⣿⣧⢸⣿⣿⣸⣿⢸⣿⡇⣿⣿⠀⣿⣿⣿⡆⣿⣿⣹⣿⡇⢻⣷⣿⡟⠀⠀⠿⠏⣽⣿⢸⣿⡇⣿⣿⠸⠿⢹⣿⡇⠿⠏⣽⣿⢀⣀⠀⠐⠻⣿⣿⢸⣿⣇⣛⡛⢸⣿⡏⣿⣧⢸⣿⢹⣿⡇⠀⠀
⠀⠀⠀⢸⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⣿⢸⣿⡇⣿⣿⢰⣿⣟⣿⡇⣿⣿⣿⣿⡅⠘⣿⣿⠁⠀⠀⠀⣼⣿⠋⢸⣿⡇⣿⣿⠀⢠⣿⡟⠁⠀⣼⣿⠏⠘⠛⠀⠀⠀⣿⣿⢸⣿⡏⣿⣷⢸⣿⡇⣿⣿⢸⣿⢸⣿⡇⠀⠀
⠀⠀⠀⣼⣿⣇⣿⣿⢻⣿⣼⣿⡏⣿⣿⠸⣿⣧⣿⡿⢸⣿⡟⣿⣷⣿⣿⣿⣿⡇⠀⣿⣿⠀⠀⠀⣾⣿⣧⣤⠸⣿⣇⣿⡿⢰⣿⣯⣤⡄⣾⣿⣧⣤⢠⣤⠀⠀⠀⣿⣿⠸⣿⣇⣿⡿⢸⣿⣧⣿⡏⢸⣿⣼⣿⡇⠀⠀
⠀⠀⠀⠉⠉⠈⠉⠁⠈⠉⠉⠉⠁⠉⠉⠀⠈⠉⠉⠀⠉⠉⠁⠉⠉⠉⠉⠉⠉⢁⢀⣉⣉⣤⡄⢀⣉⣭⣭⣭⣦⣌⣉⣉⣠⣌⣉⣉⣉⣥⣍⣉⣉⠉⠈⢉⠐⠂⠀⠉⠉⠀⠈⠉⠉⠀⠀⠉⠉⠉⠀⠀⠉⠉⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣸⣻⣆⠀⠀⣠⡆⠀⠀⠄⠀⠀⡀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣽⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣦⣽⣿⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⡿⠿⢿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣷⣦⣄⠚⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⢈⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⢉⠤⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠅⢹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠍⠉⠀⠀⠀⠀⠀⠉⠉⠉⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⢿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣦⡀⠀⠀⠀⠀⡀⠀⣄⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠊⠁⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠒⠄⢠⣤⡄⢠⣤⣤⡄⢠⣤⡄⢠⣤⢠⣤⡄⣤⣤⠀⣤⣤⣤⠀⣤⣤⣤⣄⡠⣤⡄⣠⣤⠀⠀⣠⣤⣤⣀⠀⣠⣤⣤⡀⢀⣤⣤⣄⡀⣠⣤⣤⣄⠀⠀⠀⠀⠀⣠⣤⠀⣠⣤⣤⡀⢀⣤⣤⣤⡀⢀⣤⣤⣄⡀⠀⠀
⠀⠠⠀⢸⣿⡇⣸⣿⣿⣧⢸⣿⣿⣸⣿⢸⣿⡇⣿⣿⠀⣿⣿⣿⡆⣿⣿⣹⣿⡇⢻⣷⣿⡟⠀⠀⠿⠏⣽⣿⢸⣿⡇⣿⣿⠸⠿⢹⣿⡇⠿⠏⣽⣿⢀⣀⠀⠐⠻⣿⣿⢸⣿⣇⣛⡛⢸⣿⡏⣿⣧⢸⣿⢹⣿⡇⠀⠀
⠀⠀⠀⢸⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⣿⢸⣿⡇⣿⣿⢰⣿⣟⣿⡇⣿⣿⢿⣿⡅⠘⣿⣿⠁⠀⠀⠀⣼⣿⠋⢸⣿⡇⣿⣿⠀⢠⣿⡟⠁⠀⣼⣿⠏⠘⠛⠀⠀⠀⣿⣿⢸⣿⡏⣿⣷⢸⣿⡇⣿⣿⢸⣿⢸⣿⡇⠀⠀
⠀⠀⠀⣼⣿⣇⣿⣿⢻⣿⣼⣿⡏⣿⣿⠸⣿⣧⣿⡿⢸⣿⡟⣿⣷⣿⣿⣿⣿⡇⠀⣿⣿⠀⠀⠀⣾⣿⣧⣤⠸⣿⣇⣿⡿⢰⣿⣯⣤⡄⣾⣿⣧⣤⢠⣤⠀⠀⠀⣿⣿⠸⣿⣇⣿⡿⢸⣿⣧⣿⡏⢸⣿⣼⣿⡇⠀⠀
⠀⠀⠀⠉⠉⠈⠉⠉⠈⠉⠉⠉⠁⠉⠉⠀⠈⠉⠉⠀⠉⠉⠁⠉⠉⠉⠉⠉⠉⠁⠀⠉⠉⢀⣠⣀⣉⣭⣭⣭⣦⣌⣉⣉⣠⣌⣉⣉⣉⣥⣍⣉⣉⠉⠈⢉⠐⠀⠀⠉⠉⠀⠈⠉⠉⠀⠀⠉⠉⠉⠀⠀⠉⠉⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣜⣹⣆⠀⠀⣤⡆⠀⠀⠄⠀⠀⡀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠴⣲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣦⣾⣿⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⡿⠟⠛⢿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣷⣤⣄⠘⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢈⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢉⠀⠄⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢿⣿⣿⣿⣿⣿⣯⢿⣿⣻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠍⠀⠀⠀⠈⠉⠉⠉⠉⠉⠽⠟⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⢝⡿⢿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠋⠉⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠂⠀⢠⣤⡄⢠⣤⣤⡄⢠⣤⡄⢠⣤⢠⣤⡄⣤⣤⠀⣤⣤⣤⠀⣤⣤⣤⣄⡠⣤⡄⣠⣤⠀⠀⣠⣤⣤⣀⠀⣠⣤⣤⡀⢀⣤⣤⣄⠀⣠⣤⣤⣄⠀⠀⠀⠀⠀⣠⣤⠀⣠⣤⣤⡀⢀⣤⣤⣤⡀⢀⣤⣤⣄⡀⠀⠀
⠀⠀⠀⢸⣿⡇⣸⣿⣿⣧⢸⣿⣿⣸⣿⢸⣿⡇⣿⣿⠀⣿⣿⣿⡆⣿⣿⣹⣿⡇⢻⣷⣿⡟⠀⠀⠿⠏⣽⣿⢸⣿⡇⣿⣿⠸⠿⢹⣿⡇⠿⠏⣽⣿⢀⣀⠀⠐⠻⣿⣿⢸⣿⣇⣛⡛⢸⣿⡏⣿⣧⢸⣿⢹⣿⡇⠀⠀
⠀⠀⠀⢸⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⣿⢸⣿⡇⣿⣿⢰⣿⣟⣿⡇⣿⣿⢿⣿⡅⠘⣿⣿⠁⠀⠀⠀⣼⣿⠋⢸⣿⡇⣿⣿⠀⢠⣿⡟⠁⠀⣼⣿⠏⠘⠛⠀⠀⠀⣿⣿⢸⣿⡏⣿⣷⢸⣿⡇⣿⣿⢸⣿⢸⣿⡇⠀⠀
⠀⠀⠀⣼⣿⣇⣿⣿⢻⣿⣼⣿⡏⣿⣿⠸⣿⣧⣿⡿⢸⣿⡟⣿⣷⣿⣿⣾⣿⡇⠀⣿⣿⠀⠀⠀⣾⣿⣧⣤⠸⣿⣇⣿⡿⢰⣿⣯⣤⡄⣾⣿⣧⣤⢠⣤⠀⠀⠀⣿⣿⠸⣿⣇⣿⡿⢸⣿⣧⣿⡏⢸⣿⣼⣿⡇⠀⠀
⠀⠀⠀⠉⠉⠈⠉⠁⠈⠉⠉⠉⠁⠉⠉⠀⠈⠉⠉⠀⠉⠉⠁⠉⠉⠉⠉⠉⠉⠁⠀⠉⠉⠀⣸⣤⣩⣭⣭⣭⣦⣌⣉⣉⣠⣌⣉⣉⣉⣥⣍⣉⣉⠉⠈⢉⠀⠀⠀⠉⠉⠀⠈⠉⠉⠀⠀⠉⠉⠉⠀⠀⠉⠉⠉⢀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⢀⣰⣀⠀⠀⢠⡄⠀⠀⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣧⡤⣠⢤⣿⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⢷⡞⠯⠘⠿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣶⣤⡄⠘⠀⢀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠆⢈⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠕⢁⠄⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣓⣾⣿⣿⣦⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠿⠟⠩⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠟⠻⢿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠯⠄⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⢿⠿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠍⠃⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣤⡄⢠⣤⣤⡄⢠⣤⡄⢠⣤⢠⣤⡄⣤⣤⠀⣤⣤⣤⠀⣤⣤⣤⣄⡠⣤⡄⣠⣤⠀⠀⣠⣤⣤⣀⠀⣠⣤⣤⡀⢀⣤⣤⣄⠀⣠⣤⣤⣄⠀⠀⠀⠀⠀⣠⣤⠀⣠⣤⣤⡀⢀⣤⣤⣤⡀⢀⣤⣤⣄⡀⠀⠀
⠀⠀⠀⢸⣿⡇⣸⣿⣿⣧⢸⣿⣿⣸⣿⢸⣿⡇⣿⣿⠀⣿⣿⣿⡆⣿⣿⣹⣿⡇⢻⣷⣿⡟⠀⠀⠿⠏⣽⣿⢸⣿⡇⣿⣿⠸⠿⢹⣿⡇⠿⠏⣽⣿⢀⣀⠀⠐⠻⣿⣿⢸⣿⣇⣛⡛⢸⣿⡏⣿⣧⢸⣿⢹⣿⡇⠀⠀
⠀⠀⠀⢸⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⣿⢸⣿⡇⣿⣿⢰⣿⣟⣿⡇⣿⣿⢿⣿⡅⠘⣿⣿⠁⠀⠀⠀⣼⣿⠋⢸⣿⡇⣿⣿⠀⢠⣿⡟⠁⠀⣼⣿⠏⠘⠛⠀⠀⠀⣿⣿⢸⣿⡏⣿⣷⢸⣿⡇⣿⣿⢸⣿⢸⣿⡇⠀⠀
⠀⠀⠀⣼⣿⣇⣿⣿⢻⣿⣼⣿⡏⣿⣿⠸⣿⣧⣿⡿⢸⣿⡟⣿⣷⣿⣿⣿⣿⡇⠀⣿⣿⠀⠀⠀⣾⣿⣧⣤⠸⣿⣇⣿⡿⢰⣿⣯⣤⡄⣾⣿⣧⣤⢠⣤⠀⠀⠀⣿⣿⠸⣿⣇⣿⡿⢸⣿⣧⣿⡏⢸⣿⣼⣿⡇⠀⠀
⠀⠀⠀⠉⠉⠈⠉⠁⠈⠉⠉⠉⠁⠉⠉⠀⠈⠉⠉⠀⠉⠉⠁⠉⠉⠉⠉⠉⠉⠁⠀⠉⠉⠀⣾⣦⣩⣭⣭⣭⣦⣌⣉⣉⣠⣬⣉⣉⣉⣥⣍⣉⣉⠉⠈⢉⠀⠀⠀⠉⠉⠀⠈⠉⠉⠀⠀⠉⠉⠉⠀⠀⢉⠉⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⢀⣱⣀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣿⣿⠤⣠⢀⣽⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣦⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⢷⡿⠟⠛⠟⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣦⣤⣄⠈⠀⢀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠆⢌⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠕⢀⠄⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣾⣿⣿⣦⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡾⠿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠟⠻⢿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠄⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠲⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠒⠉⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠒⠄⢠⣤⡄⢠⣤⣤⡄⢠⣤⡄⢠⣤⢠⣤⡄⣤⣤⠀⣤⣤⣤⠀⣤⣤⣤⣄⡠⣤⡄⣠⣤⠀⠀⣠⣤⣤⣀⠀⣠⣤⣤⡀⢀⣤⣤⣄⠀⣠⣤⣤⣄⠀⠀⠀⠀⠀⣠⣤⠀⣠⣤⣤⡀⢀⣤⣤⣤⡀⢀⣤⣤⣄⡀⠀⠀
⠀⠀⠀⢸⣿⡇⣸⣿⣿⣧⢸⣿⣿⣸⣿⢸⣿⡇⣿⣿⠀⣿⣿⣿⡆⣿⣿⣹⣿⡇⢻⣷⣿⡟⠀⠀⠿⠏⣽⣿⢸⣿⡇⣿⣿⠸⠿⢹⣿⡇⠿⠏⣽⣿⢀⣀⠀⠐⠻⣿⣿⢸⣿⣇⣛⡛⢸⣿⡏⣿⣧⢸⣿⢹⣿⡇⠀⠀
⠀⠀⠀⢸⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⣿⢸⣿⡇⣿⣿⢰⣿⣟⣿⡇⣿⣿⢿⣿⡅⠘⣿⣿⠁⠀⠀⠀⣼⣿⠋⢸⣿⡇⣿⣿⠀⢠⣿⡟⠁⠀⣼⣿⠏⠘⠛⠀⠀⠀⣿⣿⢸⣿⡏⣿⣷⢸⣿⡇⣿⣿⢸⣿⢸⣿⡇⠀⠀
⠀⠀⠀⣼⣿⣇⣿⣿⢻⣿⣼⣿⡏⣿⣿⠸⣿⣧⣿⡿⢸⣿⡟⣿⣷⣿⣿⣾⣿⡇⠀⣿⣿⠀⠀⠀⣾⣿⣧⣤⠸⣿⣇⣿⡿⢰⣿⣯⣤⡄⣾⣿⣧⣤⢠⣤⠀⠀⠀⣿⣿⠸⣿⣇⣿⡿⢸⣿⣧⣿⡏⢸⣿⣼⣿⡇⠀⠀
⠀⠀⠀⠉⠉⠈⠉⠁⠈⠉⠉⠉⠁⠉⠉⠀⠈⠉⠉⠀⠉⠉⠁⠉⠉⠉⠉⠉⢉⡁⣀⣉⣉⣤⢰⣄⣭⣭⣭⣭⣦⣌⣉⣉⣠⣌⣉⣉⣉⣥⣍⣉⣉⠉⠈⢉⠀⠀⠀⠉⠉⠀⠈⠉⠉⠀⠀⠉⠉⠉⠀⠀⢉⠉⠉⠀⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⣀⣰⣀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣽⣿⡤⣠⣄⣷⣶⣰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣦⣔⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠓⡟⠿⠙⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣶⣤⡤⠘⠁⢠⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠇⠄⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠕⢀⠀⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠋⠩⢻⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡆⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠿⠿⠿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠲⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⠆⠖⠙⠿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠂⠄⢠⣤⡄⢠⣤⣤⡄⢠⣤⡄⢠⣤⢠⣤⡄⣤⣤⠀⣤⣤⣤⠀⣤⣤⣤⣄⡠⣤⡄⣠⣤⠀⠀⣠⣤⣤⣀⠀⣠⣤⣤⡀⢀⣤⣤⣄⠀⣠⣤⣤⣄⠀⠀⠀⠀⠀⣠⣤⠀⣠⣤⣤⡀⢀⣤⣤⣤⡀⢀⣤⣤⣄⡀⠀⠀
⠀⠀⠀⢸⣿⡇⣸⣿⣿⣧⢸⣿⣿⣸⣿⢸⣿⡇⣿⣿⠀⣿⣿⣿⡆⣿⣿⣹⣿⡇⢻⣷⣿⡟⠀⠀⠿⠏⣽⣿⢸⣿⡇⣿⣿⠸⠿⢹⣿⡇⠿⠏⣽⣿⢀⣀⠀⠐⠻⣿⣿⢸⣿⣇⣛⡛⢸⣿⡏⣿⣧⢸⣿⢹⣿⡇⠀⠀
⠀⠀⠀⢸⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⣿⢸⣿⡇⣿⣿⢰⣿⣟⣿⡇⣿⣿⣿⣿⡅⠘⣿⣿⠁⠀⠀⠀⣼⣿⠋⢸⣿⡇⣿⣿⠀⢠⣿⡟⠁⠀⣼⣿⠏⠘⠛⠀⠀⠀⣿⣿⢸⣿⡏⣿⣷⢸⣿⡇⣿⣿⢸⣿⢸⣿⡇⠀⠀
⠀⠀⠀⣼⣿⣇⣿⣿⢻⣿⣼⣿⡏⣿⣿⠸⣿⣧⣿⡿⢸⣿⡟⣿⣷⣿⣿⣿⣿⡇⠀⣿⣿⠀⠀⠀⣾⣿⣧⣤⠸⣿⣇⣿⡿⢰⣿⣯⣤⡄⣾⣿⣧⣤⢠⣤⠀⠀⠀⣿⣿⠸⣿⣇⣿⡿⢸⣿⣧⣿⡏⢸⣿⣼⣿⡇⠀⠀
⠀⠀⠀⠉⠉⠈⠉⠁⠈⠉⠉⠉⠁⠉⠉⠀⠈⠉⠉⠀⠉⠉⠁⠉⠉⠉⠉⢉⣉⣁⣄⣉⣉⣤⢶⣄⣩⣭⣭⣭⣦⣌⣉⣉⣤⣌⣉⣉⣉⣥⣉⣉⣉⠉⠈⢉⡀⠀⠀⠉⠉⠀⠈⠉⠉⠀⠀⠉⠉⠉⠀⠀⠉⠉⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⣺⣂⠀⠀⢰⡏⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢙⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣿⠴⣦⣤⣿⣷⣲⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣷⡾⠿⠛⢛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣦⡦⠘⠁⠠⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗⠄⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⡐⠥⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠩⢹⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣄⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⠿⠿⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠲⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⡒⠤⠻⡿⠂⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⡀⣹⣧⣌⣵⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠲⣾⣷⣶⠶⢄⣰⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⣀⣀⣠⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣤⡄⠠⠀⠀⢐⠻⠟⠿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣧⣀⡀⠀⠀⠀⡄⢤⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢿⡿⠋⠋⠁⢀⣤⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⣐⣹⣿⣿⣷⣶⣤⣤⣤⣦⣦⣀⠀⡀⣬⣢⣿⢰⠇⠋⡝⠈⠀⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣢⣬⡿⠃⠄⠀⠀⠀⣸⡿⠋⠀⠀⣴⣮⠇⠃⢐⣦⣤⣴⣶⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡺⣿⣽⣿⣗⡋⠴⢀⠀⡀⠀⣀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⢽⡿⡋⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣿⣿⠌⠁⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣜⣿⣯⢝⣿⣾⡄⠁⠀⠅⠀
⠀⠀⠀⠀⠀⠀⠠⡈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⢿⠋⡀⠀⠓⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢯⢧⠀⣠⠀⢠⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣯⠙⠂⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⢀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⡗⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠉⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⢃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡆⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣄⣦⣥⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣵⡿⣷⣘⣾⠆⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣏⣿⣿⣿⣿⣿⡿⠃⠀⡁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⠿⣟⣟⣿⣟⠛⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠙⠫⣟⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠪⢙⠃⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣠⣲⣶⣖⣆⣴⣶⣂⣾⣞⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠶⠶⣶⠿⢷⠶⠴⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠾⢭⢶⣿⣿⣿⣿⣿⣿⣿⡿⢙⠂⡙⠛⢫⣿⣿⣿⣟⡟⠝⣙⣛⢿⢿⣿⣿⣿⣿⠿⠿⠿⡿⣿⣿⣶⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠲⢾⣶⣶⠾⠄⠠⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠷⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣤⡄⠠⠀⠄⠀⠻⠻⢿⣿⢿⣿⣿⣿⣿⡻⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⡄⠤⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀
⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⢿⣿⣿⠿⠟⠋⠀⠀⣠⡤⠀⠀⠀⣠⣤⣤⣤⡀⠀⠀⠀⠀⠀⢀⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⣹⢿⣿⣷⣤⣤⣦⣠⣤⣠⣤⡀⣐⣨⣕⣿⠰⠗⢊⡍⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⡷⠃⠔⠂⠀⠀⢾⠟⠁⠀⢀⣾⣿⣿⣿⣿⣿⡆⠀⠀⠀⣰⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡺⣿⣺⣾⣗⣹⠐⠂⠀⠀⠀⣀⠀
⠀⠀⠀⠀⠀⠀⠀⣰⡿⡛⠋⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠙⣺⣷⣻⢺⢶⡄⡀⠀⠄⠀
⠀⠀⠀⠀⠀⠀⠀⡾⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠟⠋⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠻⣏⠉⡄⠀⠛⠀⠀⠀
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⠦⠀⣀⠀⠠⠄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢿⠙⠁⠀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠂⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠯⠩⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢚⣍⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡮⢥⢀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣿⣿⣿⣲⣿⢔⡀⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢻⣿⣿⣿⣿⡿⠎⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣷⣤⣫⡻⠙⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⠈⠸⠻⠟⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡊⣙⠇⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣶⣼⣛⣦⣄⣬⣹⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⡔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⡟⢹⣿⣯⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠶⠶⣶⠿⢷⠶⠴⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣟⠏⠍⠁⠈⠘⠭⡇⠋⣛⣿⣿⣿⣿⣿⣿⣿⡿⠫⠃⠑⣋⣻⣿⣿⣿⣿⣿⢿⠹⠛⢻⢿⣿⣿⣿⣿⣿⣿⠿⣿⣿⡿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⡀⠀⠀⠀⣐⣿⣅⣩⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠲⢾⣶⣶⡾⢄⣨⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣤⡄⠠⠀⠄⠔⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⣿⣿⣿⣦⣅⠀⠀⠀⢠⣄⡤⠄⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⢠⡀⠀⠀⣀⠀⢀⡀⠀⠀⠀⠀
⠀⠈⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⣿⠏⠁⠀⢀⣦⣴⠀⠀⠀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⠈⣀⣿⣿⣿⣷⣶⣴⣦⣴⣦⣤⢤⣀⣐⣬⣓⣿⢰⡇⣃⡌⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣈⣎⣿⡟⠂⠄⠀⠀⢸⣿⠟⠀⠀⢠⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⢿⣼⡿⣓⣻⡘⢂⠀⡀⠀⣀⠀
⠀⠀⠀⠀⠀⠀⠀⣔⣿⠟⠁⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⡲⣿⠞⡿⢷⡄⠀⠀⠆⠀
⠀⠀⠀⠀⠀⠀⠀⣥⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠟⠋⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⡂⠀⠛⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡅⠀⣠⠀⠠⠄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⢝⠙⠡⠀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⢷⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⠛⠔⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡴⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⠦⠈⠊⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣾⣷⣽⣷⣶⡁⠀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣿⣿⣿⣿⣿⣿⠟⠌⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣝⣻⣿⠟⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠛⢿⠯⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠗⢛⠏⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣷⣿⣤⣡⣲⣗⣧⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠄⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠶⠶⣶⠿⢷⠶⠴⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⠯⡿⢿⣿⡿⠏⡻⡿⣟⣿⣿⣿⣿⣿⣿⣿⡯⠓⠑⠐⠚⡿⣿⣿⣿⣿⣿⡿⠷⠿⠿⢿⣿⢿⣿⣿⣿⣿⣿⡿⣿⣿⣗⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠒⠆⠀⠠⠲⠄⠀⠀⠀⠀⠘⠛⠛⠛⠛⠓⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠿⣿⡿⢷⣿⢻⣦⣿⡟⣿⡆⣿⣿⡟⣿⣼⡟⠀⣼⡟⢸⣿⠿⣿⡿⠇⣿⣿⣷⠀⠀⠀⣾⣿⣷⡼⣿⡿⢿⣿⢸⣿⠻⣿⠀⠀⠀⣾⡟⣿⣼⣿⢸⣿⢸⣿⠗⣿⡿⣷⡀⢠⣶⣿⠛⢻⣿⣾⡟⣷⣰⣿⢻⣧⠀⠀
⠀⠀⠀⣿⡇⢸⣿⢸⣿⣿⡇⣿⡇⣿⣿⣷⢹⣿⠃⠀⣿⡇⢸⣿⠗⣿⡿⠇⣿⣿⣿⠀⠀⠀⢿⣿⣿⡇⣿⡇⢸⣿⢿⣿⠀⣿⠘⠃⠀⣿⡇⣿⡏⣿⣿⡿⢸⣿⠇⣿⡿⣿⡀⠀⢸⣿⠀⣿⡇⣿⡇⣿⣿⣿⢸⣿⠀⠀
⠀⠀⠀⠿⠇⠘⠿⠾⠏⠿⠷⠿⠻⠿⠹⠿⠸⠿⠀⠀⠻⠷⠸⠿⠀⠿⠷⠆⠿⠿⠿⠰⠆⠀⠻⠿⠿⠁⠿⢇⡸⠿⠼⠿⠴⠿⠰⠆⣀⠻⢷⠿⠃⠿⠿⠇⠸⠿⠶⠿⠇⠿⠇⡀⠸⠿⠸⠿⠁⠻⠷⠿⠙⠿⠾⠟⠠⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣿⣿⣷⣶⣶⣾⣶⣶⣶⣶⡖⠀⠀⠀⣄⠀⠈⠀⠀⠄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡶⢿⣿⣉⣖⢘⣀⡀⠰⠂⠀⠀⠀⠀⠀⠈⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣻⣿⠟⡏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠊⠇⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢴⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠉⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣒⠛⠀⠸⣿⣿⣿⣿⣿⡟⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡠⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠍⠀⠀⠀⠀⠉⠩⠋⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠙⠛⠿⠿⠿⠿⠿⢿⢿⣿⣿⣿⣿⣿⡿⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠖⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣡⣠⣶⣿⣾⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠒⠆⠀⠠⠲⠄⠀⠀⠀⠀⠛⠛⠛⠛⠛⠊⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠿⣿⡿⢷⣿⢻⣦⣿⡟⣿⡆⣿⣿⡏⣿⣼⡟⠀⣼⡟⢸⣿⠟⣿⡿⠇⣿⣿⣷⠀⠀⠀⣾⣿⣷⡼⣿⡿⢿⣿⢸⣿⠻⣿⠀⠀⠀⣾⡟⣿⣼⣿⢸⣿⢸⣿⠗⣿⡿⣷⡀⢠⣶⣿⠛⢻⣿⣾⡟⣷⣠⣿⢻⣧⠀⠀
⠀⠀⠀⣿⡇⢸⣿⢸⣿⣿⡇⣿⡇⣿⣿⣷⢹⣿⠃⠀⣿⡇⢸⣿⠗⣿⡿⠇⣿⣿⣿⠀⠀⠀⢿⣿⣿⡇⣿⡇⢸⣿⢿⣿⠀⣿⠘⠃⠀⣿⡇⣿⡏⣿⣿⡿⢸⣿⠇⣿⡿⣿⡀⠀⢸⣿⠀⣿⡇⣿⡇⣿⣿⣿⢸⣿⠀⠀
⠀⠀⠀⠿⠇⠘⠿⠾⠏⠿⠷⠿⠻⠿⠹⠿⠸⠿⠀⠀⠻⠷⠸⠿⠀⠿⠷⠆⠿⠿⠿⠰⠆⠀⠿⠿⠿⠁⠿⢇⡸⠿⠼⠿⠴⠿⠰⠆⣀⠻⢷⠿⠃⠿⠿⠇⠸⠿⠶⠿⠇⠿⠇⡀⠸⠿⠸⠿⠁⠻⠷⠿⠙⠿⠾⠟⠠⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣷⣶⣶⣶⣾⣶⣿⣿⣷⣶⣶⣾⣶⣴⣦⣴⣖⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣖⢿⣿⣌⣒⣘⣀⠂⠰⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡁⠒⠀⠀⠀⠀⠠⠀⠀⠂⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣻⣿⢿⠧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣏⠂⠇⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⠼⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣕⠻⠴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠉⢋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠼⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⢛⣿⣿⣿⣿⣿⣿⣿⣋⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢄⠑⠂⠀⢨⣿⣿⣿⣿⣿⣿⠝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠋⠉⠝⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠡⠙⠛⣿⣟⠟⠿⡿⢿⣿⣿⣿⣿⣿⡿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⡦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢶⠆⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣁⣠⣶⣿⣾⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⡿⢿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠒⠆⠀⠠⠲⠄⠀⠀⠀⠀⠉⠛⠛⠛⠃⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠿⣿⡿⢷⣿⢻⣦⣿⡟⣿⡆⣿⣿⡏⣿⣼⡟⠀⣼⡟⢸⣿⠟⣿⡿⠇⣿⣿⣷⠀⠀⠀⣾⣿⣷⡼⣿⡿⢿⣿⢸⣿⠛⣿⠀⠀⠀⣾⡟⣿⣼⣿⢸⣿⢸⣿⠇⣿⡿⣷⠀⢠⣶⣿⠛⢻⡿⣾⡟⣷⣠⣿⢻⣧⠀⠀
⠀⠀⠀⣿⡇⢸⣿⢸⣿⣿⡇⣿⡇⣿⣿⣷⢹⣿⠃⠀⣿⡇⢸⣿⠗⣿⡿⠇⣿⣿⣿⠀⠀⠀⢿⣿⣿⡇⣿⡇⢸⣿⢿⣿⠀⣿⠘⠃⠀⣿⡇⣿⡏⣿⣿⡟⢸⣿⠇⣿⡿⣿⠀⠀⢸⣿⠀⣿⡇⣿⡇⣿⣿⣿⢸⣿⠀⠀
⠀⠀⠀⠿⠇⠘⠿⠾⠏⠿⠷⠿⠻⠿⠹⠿⠸⠿⠀⠀⠻⠷⠸⠿⠀⠿⠷⠆⠿⠿⠿⠰⠆⠀⠻⠿⠿⠁⠿⢇⡸⠿⠸⠿⠴⠿⠰⠆⣀⠻⠷⠿⠃⠿⠿⠇⠸⠿⠶⠿⠇⠿⠀⡀⠸⠿⠸⠿⠁⠻⠷⠿⠙⠿⠾⠟⠠⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠄⠀⢤⣶⣶⣶⣶⣶⣶⣿⣾⣿⣿⣿⣶⣶⣶⣶⣷⣿⣿⣿⣶⣶⣶⣶⡐⣦⣦⣖⠀⠀⢀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣤⠆⣺⣿⣌⣒⡈⡀⠀⠰⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠒⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢻⣿⠋⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣉⠀⠆⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⠴⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣽⠺⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠉⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠉⠁⠈⣹⣿⣻⣋⣛⣾⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠟⠂⠀⠀⠀⠀⠀⠉⠉⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠈⠛⠿⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⡿⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢂⠀⣤⣶⡔⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠒⠆⠀⠀⠲⠀⠀⠀⠀⠀⠚⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠿⣿⡿⢳⣿⢻⣦⣿⡟⣿⡆⣿⣿⡏⣿⣼⡟⠀⣼⡟⢸⣿⠟⣿⡿⠇⣿⣿⣷⠀⠀⠀⣾⣿⣷⡼⣿⡿⢿⣿⢸⣿⠛⣿⠀⠀⠀⣾⡟⣿⣼⣿⢸⣿⢸⣿⠇⣿⡟⣷⠀⠠⣶⣿⠛⢻⡿⣾⡟⣷⣠⣿⢻⣧⠀⠀
⠀⠀⠀⣿⡇⢸⣿⢸⣿⣿⡇⣿⡇⣿⣿⣷⢹⣿⠁⠀⣿⡇⢸⣿⠇⣿⡿⠇⣿⣿⣿⠀⠀⠀⢿⣿⣿⡇⣿⡇⢸⣿⢿⣿⠀⣿⠘⠃⠀⣿⡇⣿⡏⣿⣿⡟⢸⣿⠇⣿⡿⣿⠀⠀⢸⣿⠀⣿⡇⣿⡇⣿⣿⣿⢸⣿⠀⠀
⠀⠀⠀⠿⠇⠘⠿⠾⠏⠿⠷⠿⠻⠿⠹⠿⠸⠿⠀⠀⠹⠷⠸⠿⠀⠿⠷⠆⠿⠿⠿⠰⠆⠀⠻⠿⠿⠁⠿⠇⡸⠿⠸⠿⠴⠿⠰⠆⠀⠻⠷⠿⠃⠿⠿⠇⠸⠿⠶⠿⠇⠿⠀⡀⠸⠿⠸⠿⠁⠻⠷⠿⠙⠿⠾⠟⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠢⠰⠔⠀⠀⠀⠀⠀⢀⣼⣷⣶⣾⣿⣷⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣷⣶⣶⣶⡶⠀⢴⣤⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣥⣅⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⢹⣿⣈⡐⣈⣀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠙⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡷⣍⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⠤⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣙⠪⠄⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠉⠓⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡍⠀⠀⠀⠀⠀⠙⠟⢛⠁⣀⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⠋⠃⠀⠀⠀⠀⠀⠀⠈⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⡷⠿⠿⠿⠿⠿⠿⠿⠃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣯⠻⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠒⠂⠀⠠⠲⠀⠀⠀⠀⠀⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠿⣿⡿⢳⣿⢻⣦⣿⡟⣿⡆⣿⣿⡏⣿⣼⡟⠀⣼⡟⢸⣿⠟⣿⡿⠇⣿⣿⣷⠀⠀⠀⣾⣿⣷⡼⣿⡿⢿⣿⢸⣿⠛⣿⠀⠀⠀⣾⡟⣿⣼⣿⢸⣿⢸⣿⠇⣿⡟⣷⠀⢠⣶⣿⠛⢻⡿⣾⡟⣷⣠⣿⢻⣧⠀⠀
⠀⠀⠀⣿⡇⢸⣿⢸⣿⣿⡇⣿⡇⣿⣿⣷⢹⣿⠃⠀⣿⡇⢸⣿⠇⣿⡿⠇⣿⣿⣿⠀⠀⠀⢿⣿⣿⡇⣿⡇⢸⣿⢿⣿⠀⣿⠘⠃⠀⣿⡇⣿⡏⣿⣿⡟⢸⣿⠇⣿⡿⣿⠀⠀⢸⣿⠀⣿⡇⣿⡇⣿⣿⣿⢸⣿⠀⠀
⠀⠀⠀⠿⠇⠘⠿⠾⠏⠿⠷⠿⠻⠿⠹⠿⠸⠿⠀⠀⠹⠷⠸⠿⠀⠿⠷⠆⠿⠿⠿⠰⠆⠀⠻⠿⠿⠁⠿⠇⡸⠿⠸⠿⠴⠿⠰⠆⠀⠻⠷⠿⠃⠿⠿⠇⠸⠿⠶⠿⠇⠿⠀⠀⠸⠿⠸⠿⠁⠻⠷⠿⠙⠿⠾⠟⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣶⣾⣿⣷⣿⣿⣿⣿⣶⣶⣶⣾⣾⣿⣷⣶⣶⣶⣦⠀⢶⣦⡀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣥⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣷⣤⣂⢸⣿⣄⣀⣈⣀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢙⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣯⣅⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⠠⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣙⠪⠆⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢿⠋⠛⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠀⠀⠀⠀⠀⠹⠛⠛⠁⣀⠰⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠝⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠐⠟⡿⡿⠿⠿⠿⠿⢿⠿⡳⢟⠯⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢦⡶⣦⣤⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠹⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠒⠆⠀⠠⠲⠀⠀⠀⠀⠚⠛⠛⠛⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠿⣿⡿⢷⣿⢻⣦⣿⡟⣿⡆⣿⣿⡏⣿⣼⡟⠀⣼⡟⢸⣿⠿⣿⡿⠇⣿⣿⣷⠀⠀⠀⣾⣿⣷⡼⣿⡿⢿⣿⢸⣿⠛⣿⠀⠀⠀⣾⡟⣿⣼⣿⢸⣿⢸⣿⠗⣿⡟⣷⠀⢠⣶⣿⠛⢻⡿⣾⡟⣷⣠⣿⢻⣧⠀⠀
⠀⠀⠀⣿⡇⢸⣿⢸⣿⣿⡇⣿⡇⣿⣿⣷⢹⣿⠃⠀⣿⡇⢸⣿⠗⣿⡿⠇⣿⣿⣿⠀⠀⠀⢿⣿⣿⡇⣿⡇⢸⣿⢿⣿⠀⣿⠘⠃⠀⣿⡇⣿⡏⣿⣿⡿⢸⣿⠇⣿⡿⣿⠀⠀⢸⣿⠀⣿⡇⣿⡇⣿⣿⣿⢸⣿⠀⠀
⠀⠀⠀⠿⠇⠘⠿⠾⠏⠿⠷⠿⠻⠿⠹⠿⠸⠿⠀⠀⠻⠷⠸⠿⠀⠿⠷⠆⠿⠿⠿⠰⠆⠀⠿⠿⠿⠁⠿⢇⡸⠿⠼⠿⠴⠿⠰⠆⡀⠻⠷⠿⠃⠿⠿⠇⠸⠿⠶⠿⠇⠿⠄⠀⠸⠿⠸⠿⠁⠻⠷⠿⠙⠿⠾⠟⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣾⣶⣶⣶⣿⣶⣿⣿⣿⣷⣶⣶⣶⣾⣿⣿⣿⣶⣶⣶⣶⠴⣦⣦⡄⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⠑⢂⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣶⣦⣺⣿⣤⣜⣈⣀⣀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⣹⣿⠟⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠲⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠢⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣙⡒⠷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠉⠛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⡟⢛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠁⠸⢿⠿⡓⣊⣱⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠃⠀⠀⠀⠀⠀⠈⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⠹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠹⢿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣰⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠛⣻⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠟⢷⠔⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⡷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠒⠆⠀⠠⠲⠄⠀⠀⠀⠈⠛⠛⠛⠃⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠿⣿⡿⢷⣿⢻⣦⣿⡟⣿⡆⣿⣿⡏⣿⣼⡟⠀⣼⡟⢸⣿⠟⣿⡿⠇⣿⣿⣷⠀⠀⠀⣾⣿⣷⡼⣿⡿⢿⣿⢸⣿⠛⣿⠀⠀⠀⣾⡟⣿⣼⣿⢸⣿⢸⣿⠗⣿⡟⣷⠀⢠⣶⣿⠛⢻⡿⣾⡟⣷⣠⣿⢻⣧⠀⠀
⠀⠀⠀⣿⡇⢸⣿⢸⣿⣿⡇⣿⡇⣿⣿⣷⢹⣿⠃⠀⣿⡇⢸⣿⠗⣿⡿⠇⣿⣿⣿⠀⠀⠀⢿⣿⣿⡇⣿⡇⢸⣿⢿⣿⠀⣿⠘⠃⠀⣿⡇⣿⡏⣿⣿⡟⢸⣿⠇⣿⡿⣿⠀⠀⢸⣿⠀⣿⡇⣿⡇⣿⣿⣿⢸⣿⠀⠀
⠀⠀⠀⠿⠇⠘⠿⠾⠏⠿⠷⠿⠻⠿⠹⠿⠸⠿⠀⠀⠻⠷⠸⠿⠀⠿⠷⠆⠿⠿⠿⠰⠆⠀⠻⠿⠿⠁⠿⢇⡸⠿⠸⠿⠴⠿⠰⠆⡀⠻⠷⠿⠃⠿⠿⠇⠸⠿⠶⠿⠇⠿⠄⠀⠸⠿⠸⠿⠁⠻⠷⠿⠙⠿⠾⠟⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⣠⣶⣶⣶⣶⣿⣶⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣷⣶⣶⣶⣦⠤⣶⣦⡄⠀⠀⢀⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⠙⢪⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⣽⣿⣤⣌⣌⡄⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡇⠉⡀⠀⠀⠀⠀⠂⠀⠈⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡋⣹⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⠀⠒⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⡲⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣙⠓⠷⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠙⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⡿⣿⣿⣿⣿⣿⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⠁⠀⠀⠀⠁⢸⢿⣿⠿⠊⣰⠢⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠈⠀⠉⠈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⢀⣰⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠟⢷⠄⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠁⢿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⠝⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠒⠂⠀⠀⠲⠀⠀⠀⠀⠀⠛⠛⠛⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠿⣿⡿⢳⣿⢻⣦⣿⡟⣿⡆⣿⣿⡏⣿⣼⡟⠀⣼⡟⢸⣿⠟⣿⡿⠇⣿⣿⣷⠀⠀⠀⣾⣿⣷⡼⣿⡿⢿⣿⢸⣿⠛⣿⠀⠀⠀⣾⡟⣿⣼⣿⢸⣿⢸⣿⠇⣿⡟⣷⠀⢠⣶⣿⠛⢻⡿⣾⡟⣷⣠⣿⢻⣧⠀⠀
⠀⠀⠀⣿⡇⢸⣿⢸⣿⣿⡇⣿⡇⣿⣿⣷⢹⣿⠁⠀⣿⡇⢸⣿⠇⣿⡿⠇⣿⣿⣿⠀⠀⠀⢿⣿⣿⡇⣿⡇⢸⣿⢿⣿⠀⣿⠘⠃⠀⣿⡇⣿⡏⣿⣿⡟⢸⣿⠇⣿⡿⣿⠀⠀⢸⣿⠀⣿⡇⣿⡇⣿⣿⣿⢸⣿⠀⠀
⠀⠀⠀⠿⠇⠘⠿⠾⠏⠿⠷⠿⠻⠿⠹⠿⠸⠿⠀⠀⠹⠷⠸⠿⠀⠿⠷⠆⠿⠿⠿⠰⠆⠀⠻⠿⠿⠁⠿⢇⡸⠿⠸⠿⠴⠿⠰⠆⠀⠻⠷⠿⠃⠿⠿⠇⠸⠿⠶⠿⠇⠿⠀⠀⠸⠿⠸⠿⠁⠻⠷⠿⠙⠿⠾⠟⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣲⣆⣰⣾⣶⣶⣶⣿⣿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⣷⣶⣶⣶⣦⠀⣶⣦⠀⠀⠀⢀⣢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⠛⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡔⣂⣸⣿⣦⣌⣄⣤⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣟⣋⢉⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡿⠡⠀⠐⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⡢⠾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣉⡒⠷⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⡛⢿⣿⣿⠿⠿⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠀⠀⠀⠀⠁⠘⠿⠷⠂⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠁⠊⠉⠉⠀⠀⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣰⣾⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⡗⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠙⠻⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⢷⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠒⠆⠀⠠⠲⠀⠀⠀⠀⠘⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠿⣿⡿⢳⣿⢻⣦⣿⡟⣿⡆⣿⣿⡏⣿⣸⡟⠀⣼⡟⢸⣿⠟⣿⡿⠇⣿⣿⣷⠀⠀⠀⣾⣿⣷⡼⣿⡿⢿⣿⢸⣿⠛⣿⠀⠀⠀⣾⡟⣿⣼⣿⢸⣿⢸⣿⠇⣿⡟⣷⠀⠠⣶⣿⠛⢻⡿⣾⡟⣷⣠⣿⢻⣧⠀⠀
⠀⠀⠀⣿⡇⢸⣿⢸⣿⣿⡇⣿⡇⣿⣻⣷⢹⣿⠁⠀⣿⡇⢸⣿⠇⣿⡿⠇⣿⣿⣿⠀⠀⠀⢿⣿⣿⡇⣿⡇⢸⣿⢿⣿⠀⣿⠘⠃⠀⣿⡇⣿⡏⣿⣿⡟⢸⣿⠇⣿⡟⣿⠀⠀⢸⣿⠀⣿⡇⣿⡇⣿⣿⣿⢸⣿⠀⠀
⠀⠀⠀⠿⠇⠘⠿⠾⠏⠿⠷⠿⠻⠿⠹⠿⠸⠿⠀⠀⠹⠷⠸⠿⠀⠿⠷⠆⠿⠿⠿⠰⠆⠀⠻⠿⠿⠁⠿⠇⡸⠿⠸⠿⠴⠿⠰⠆⠀⠻⠷⠿⠁⠿⠿⠇⠸⠿⠶⠿⠇⠿⠀⠀⠸⠿⠸⠿⠁⠻⠷⠿⠙⠿⠾⠟⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣶⣾⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣿⣿⣷⣶⣶⣶⣆⠀⣴⣦⡀⠀⠀⠀⣠⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⡄⡀⣸⣿⣦⣬⣄⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣟⡋⡈⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠩⠀⠐⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⡆⠾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣉⡒⠖⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⢿⣿⣿⠟⠛⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠙⠁⠀⠀⠀⠁⠘⠿⠗⠂⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣴⣟⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠒⠂⠀⠠⠲⠀⠀⠀⠀⠘⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠿⣿⡿⢳⣿⢻⣦⣿⡟⣿⡆⣿⣿⡏⣿⣸⡟⠀⣼⡟⢸⣿⠟⣿⡿⠇⣿⣿⣷⠀⠀⠀⣾⣿⣷⡼⣿⡿⢿⣿⢸⣿⠛⣿⠀⠀⠀⣾⡟⣷⣼⣿⢸⣿⢸⣿⠇⣿⡟⣷⠀⠠⣶⣿⠛⢻⡿⣾⡟⣷⣠⣿⢻⣧⠀⠀
⠀⠀⠀⣿⡇⢸⣿⢸⣿⣿⡇⣿⡇⣿⣻⣷⢹⣿⠁⠀⣿⡇⢸⣿⠇⣿⡿⠇⣿⣿⣿⠀⠀⠀⢿⣿⣿⡇⣿⡇⢸⣿⢿⣿⠀⣿⠘⠃⠀⣿⡇⣿⡏⣿⣿⡟⢸⣿⠇⣿⡟⣿⠀⠀⢸⣿⠀⣿⡇⣿⡇⣿⣿⣿⢸⣿⠀⠀
⠀⠀⠀⠿⠇⠘⠿⠾⠏⠿⠷⠿⠻⠿⠹⠿⠸⠿⠀⠀⠹⠷⠸⠿⠀⠿⠷⠆⠿⠿⠿⠰⠆⠀⠻⠿⠿⢁⠿⠇⡸⠿⠸⠿⠴⠿⠰⠆⠀⠻⠷⠿⠁⠿⠿⠇⠸⠿⠶⠿⠇⠿⠀⠀⠸⠿⠰⠿⠁⠻⠷⠿⠙⠿⠾⠟⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣶⣾⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣶⢂⠀⣶⣤⡀⠀⠀⢀⣤⢀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣷⡆⣀⣸⣿⣤⣬⣄⡄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠿⢿⣟⠃⠈⢽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡷⠠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⡂⠾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣀⡚⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣗⣿⣿⣿⣿⠄⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣿⣿⠿⣏⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⢻⡿⣿⠍⠁⠘⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠀⠀⠀⠀⠁⠘⠻⠒⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠙⠙⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣳⡟⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠒⠂⠀⠀⠲⠀⠀⠀⠀⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠿⣿⡿⢳⣿⢻⣦⣿⡟⣿⡆⣿⣿⡏⣿⣸⡟⠀⣼⡟⢸⣿⠟⣿⡿⠇⣿⣿⣷⠀⠀⠀⣾⣿⣷⡼⣿⡿⢿⣿⢸⣿⠛⣿⠀⠀⠀⣾⡟⣷⣼⣿⢸⣿⢸⣿⠇⣿⡟⣷⠀⠠⣶⣿⠛⢻⡿⣾⡟⣷⣠⣿⢻⣧⠀⠀
⠀⠀⠀⣿⡇⢸⣿⢸⣿⣿⡇⣿⡇⣿⣻⣷⢹⣿⠁⠀⣿⡇⢸⣿⠇⣿⡿⠇⣿⣿⣿⠀⠀⠀⢿⣿⣿⡇⣿⡇⢸⣿⢿⣿⠀⣿⠘⠃⠀⣿⡇⣿⡏⣿⣿⡟⢸⣿⠇⣿⡟⣿⠀⠀⢸⣿⠀⣿⡇⣿⡇⣿⣿⣿⢸⣿⠀⠀
⠀⠀⠀⠿⠇⠘⠿⠾⠏⠿⠷⠿⠻⠿⠹⠿⠸⠿⠀⠀⠹⠷⠸⠿⠀⠿⠷⠆⠿⠿⠿⠰⠆⠀⠻⠿⠿⣁⠿⠇⠸⠿⠸⠿⠴⠿⠰⠆⠀⠻⠷⠿⠁⠿⠿⠇⠸⠿⠶⠿⠇⠿⠀⠀⠸⠿⠰⠿⠁⠻⠷⠿⠙⠿⠾⠟⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣶⣶⣾⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣿⣿⣷⣶⣶⣶⡀⠀⣴⣤⡀⠀⠀⢀⣤⠄⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⡆⣀⡸⣿⣦⣬⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠿⢿⣟⠋⠀⢽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠠⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⡂⠾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⣃⡚⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠄⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⢻⣿⣿⠟⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠙⠉⠀⠀⠀⠁⠈⠻⠲⠒⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀⠀⠀⠉⠙⠛⠋⠛⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢲⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⣾⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠒⠆⠀⠀⠲⠀⠀⠀⠀⠙⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠿⣿⡿⢳⣿⢻⣦⣿⡟⣿⡆⣿⣿⡏⣿⣸⡟⠀⣼⡟⢸⣿⠟⣿⡿⠇⣿⣿⣷⠀⠀⠀⣾⣿⣷⡼⣿⡿⢿⣿⢸⣿⠛⣿⠀⠀⠀⣾⡟⣷⣼⣿⢸⣿⢸⣿⠇⣿⡟⣷⠀⠠⣶⣿⠛⢻⡿⣾⡟⣷⣠⣿⢻⣧⠀⠀
⠀⠀⠀⣿⡇⢸⣿⢸⣿⣿⡇⣿⡇⣿⣻⣷⢹⣿⠁⠀⣿⡇⢸⣿⠇⣿⡿⠇⣿⣿⣿⠀⠀⠀⢿⣿⣿⡇⣿⡇⢸⣿⢿⣿⠀⣿⠘⠃⠀⣿⡇⣿⡏⣿⣾⡟⢸⣿⠇⣿⡟⣿⠀⠀⢸⣿⠀⣿⡇⣿⡇⣿⣿⣿⢸⣿⠀⢀
⠀⠀⠀⠿⠇⠘⠿⠾⠏⠿⠷⠿⠻⠿⠹⠿⠸⠿⠀⠀⠹⠷⠸⠿⠀⠿⠷⠆⠿⠿⠿⠰⠆⠀⠻⠿⠿⣁⠿⠇⠸⠿⠸⠿⠴⠿⠰⠆⠀⠻⠷⠿⠁⠿⠿⠇⠸⠿⠶⠿⠇⠿⠀⠀⠸⠿⠰⠿⠁⠻⠷⠿⠙⠿⠾⠟⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣶⣶⣾⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣷⣶⣶⣶⣂⠀⠴⣦⡀⠀⠀⢀⣤⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⡆⣠⣘⣿⣦⣤⣀⡀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡞⢿⣟⣋⡀⢽⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠡⠄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⡆⠞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠞⣃⡚⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⢿⣿⣿⡟⠉⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠋⠀⠀⠀⠁⠈⠻⠗⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣦⣄⠀⠉⠙⠛⠻⢿⠿⠟⠻⠿⠟⠟⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠒⠆⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠿⣿⡿⢳⣿⢻⣦⣿⡟⣿⡆⣿⣿⡏⣿⣼⡟⠀⣼⡟⢸⣿⠟⣿⡿⠇⣿⣿⣷⠀⠀⠀⣾⣿⣷⡼⣿⡿⢿⣿⢸⣿⠻⣿⠀⠀⠀⣾⡟⣿⣼⣿⢸⣿⢸⣿⠇⣿⡟⣷⠀⢠⣶⣿⠛⢻⡿⣾⡟⣷⣠⣿⢻⣧⠀⠀
⠀⠀⠀⣿⡇⢸⣿⢸⣿⣿⡇⣿⡇⣿⣿⣷⢹⣿⠁⠀⣿⡇⢸⣿⠇⣿⡿⠇⣿⣿⣿⠀⠀⠀⢿⣿⣿⡇⣿⡇⢸⣿⢿⣿⠀⣿⠘⠃⠀⣿⡇⣿⡏⣿⣿⡟⢸⣿⠇⣿⡿⣿⠀⠀⢸⣿⠀⣿⡇⣿⡇⣿⣿⣿⢸⣿⠀⢠
⠀⠀⠀⠿⠇⠘⠿⠾⠏⠿⠷⠿⠻⠿⠹⠿⠸⠿⠀⠀⠻⠷⠸⠿⠀⠿⠷⠆⠿⠿⠿⠰⠆⠀⠻⠿⠿⣁⡿⢇⠸⠿⠸⠿⠴⠿⠰⠆⠀⠻⠷⠿⠁⠿⠿⠇⠸⠿⠶⠿⠇⠿⠀⠀⠸⠿⠸⠿⠁⠻⠷⠿⠙⠿⠾⠟⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣶⣶⣾⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣷⣶⣶⣶⡂⠀⢶⣤⡀⠀⠀⢀⣠⠄⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⡄⣀⠐⣿⣦⣤⣀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⢿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⢿⣛⣇⡀⢹⠗⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠣⠄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣒⠚⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣂⡘⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⡿⠋⠉⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠈⠿⠷⠖⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡁⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠻⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⠁⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣤⡀⠙⠟⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠻⠿⠅⠀⠀⠀⠀⠀⠀⠸⠽⢟⢻⣿⣴⣦⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡀⠀⠀⠁⠩⠋⠉⠀⠈⠉⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠈⠠⢷⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠁⠁⠉⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣶⣄⠀⠀⠀⠀⠀⠀⠠⠉⠘⢻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⠷⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠒⠆⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠿⣿⡿⢳⣿⢻⣦⣿⡟⣿⡆⣿⣿⡏⣿⣼⡟⠀⣼⡟⢸⣿⠟⣿⡿⠇⣿⣿⣷⠀⠀⠀⣾⣿⣷⡼⣿⡿⢿⣿⢸⣿⠻⣿⠀⠀⠀⣾⡟⣿⣼⣿⢸⣿⢸⣿⠇⣿⡟⣷⠀⢠⣶⣿⠛⢻⡿⣾⡟⣷⣠⣿⢻⣧⠀⠀
⠀⠀⠀⣿⡇⢸⣿⢸⣿⣿⡇⣿⡇⣿⣿⣷⢹⣿⠁⠀⣿⡇⢸⣿⠇⣿⡿⠇⣿⣿⣿⠀⠀⠀⢿⣿⣿⡇⣿⡇⢸⣿⢿⣿⠀⣿⠘⠃⠀⣿⡇⣿⡏⣿⣿⡟⢸⣿⠇⣿⡿⣿⠀⠀⢸⣿⠀⣿⡇⣿⡇⣿⣿⣿⢸⣿⠀⠠
⠀⠀⠀⠿⠇⠘⠿⠾⠏⠿⠷⠿⠻⠿⠹⠿⠸⠿⠀⠀⠻⠷⠸⠿⠀⠿⠷⠆⠿⠿⠿⠰⠆⠀⠻⠿⠿⣁⡿⢇⠸⠿⠼⠿⠴⠿⠰⠆⠀⠻⠷⠿⠁⠿⠿⠇⠸⠿⠶⠿⠇⠿⠀⠀⠸⠿⠸⠿⠁⠻⠷⠿⠙⠿⠾⠟⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣶⣾⣿⣿⣿⣿⣶⣶⣶⣶⣾⣿⣾⣿⣷⣶⣶⣶⣀⠀⢶⣦⡀⠀⠀⠀⣴⠂⢀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⡆⣀⣐⣿⣶⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⢿⣿⡷⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣏⣅⡀⢹⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢐⠚⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣂⡘⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⠟⠉⠉⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠈⠻⠷⠆⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠃⠸⠀⢀⠁⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⢿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⠿⠿⠿⠁⠀⠀⠀⠀⠀⠈⢼⠺⢛⠿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⡄⣠⡀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠶⠙⠏⠻⡅⠉⠁⠊⠠⢠⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠝⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⠛⠙⠓⠟⠚⠔⡺⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠠⠀⠀⠀⠀⠀⠀⠀⠐⠂⠊⣻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠛⠻⠿⠿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠒⠆⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠿⣿⡿⢷⣿⢻⣦⣿⡟⣿⡆⣿⣿⡏⣿⣼⡟⠀⣼⡟⢸⣿⠟⣿⡿⠇⣿⣿⣷⠀⠀⠀⣾⣿⣷⡼⣿⡿⢿⣿⢸⣿⠻⣿⠀⠀⠀⣾⡟⣿⣼⣿⢸⣿⢸⣿⠇⣿⡟⣷⠀⢠⣶⣿⠛⢻⡿⣾⡟⣷⣠⣿⢻⣧⠀⠀
⠀⠀⠀⣿⡇⢸⣿⢸⣿⣿⡇⣿⡇⣿⣿⣷⢹⣿⠁⠀⣿⡇⢸⣿⠇⣿⡿⠇⣿⣿⣿⠀⠀⠀⢿⣿⣿⡇⣿⡇⢸⣿⢿⣿⠀⣿⠘⠃⠀⣿⡇⣿⡏⣿⣿⡟⢸⣿⠇⣿⡿⣿⠀⠀⢸⣿⠀⣿⡇⣿⡇⣿⣿⣿⢸⣿⠀⠠
⠀⠀⠀⠿⠇⠘⠿⠾⠏⠿⠷⠿⠻⠿⠹⠿⠸⠿⠀⠀⠻⠷⠸⠿⠀⠿⠷⠆⠿⠿⠿⠰⠆⠀⠿⠿⠿⢁⡿⢇⡸⠿⠼⠿⠴⠿⠰⠆⡀⠻⠷⠿⠁⠿⠿⠇⠸⠿⠶⠿⠇⠿⠀⠀⠸⠿⠸⠿⠁⠻⠷⠿⠙⠿⠾⠟⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣶⣶⣾⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⡀⠀⣶⣦⠀⠀⠀⠀⣰⠢⢀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠈⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⣀⣿⣷⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⡯⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣏⣍⣀⢸⠏⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠆⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⠚⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢂⣐⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⡟⠋⠛⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠈⠻⡧⠤⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠫⢀⠀⠁⠒⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣶⣔⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠏⠁⠀⠀⠀⠀⠀⠀⢼⢽⣿⣷⣾⣶⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢡⣾⣿⣿⣷⣦⣾⣿⣿⣿⣿⣿⣿⡄⠈⠐⠺⢿⢛⣿⢟⣟⠙⠯⠯⢴⣆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠸⠯⠛⠛⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠈⠍⢻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠟⢶⠆⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠙⠛⠋⠛⠟⠉⠙⠛⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠡⠊⠉⠉⠛⠛⠿⠿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠒⠆⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠿⣿⡿⢷⣿⢻⣦⣿⡟⣿⡆⣿⣿⡏⣿⣼⡟⠀⣼⡟⢸⣿⠟⣿⡿⠇⣿⣿⣷⠀⠀⠀⣾⣿⣷⡼⣿⡿⢿⣿⢸⣿⠛⣿⠀⠀⠀⣾⡟⣿⣼⣿⢸⣿⢸⣿⠇⣿⡟⣷⠀⠠⣶⣿⠛⢻⡿⣾⡟⣷⣠⣿⢻⣧⠀⠀
⠀⠀⠀⣿⡇⢸⣿⢸⣿⣿⡇⣿⡇⣿⣿⣷⢹⣿⠁⠀⣿⡇⢸⣿⠇⣿⡿⠇⣿⣿⣿⠀⠀⠀⢿⣿⣿⡇⣿⡇⢸⣿⢿⣿⠀⣿⠘⠃⠀⣿⡇⣿⡏⣿⣿⡟⢸⣿⠇⣿⡿⣿⠀⠀⢸⣿⠀⣿⡇⣿⡇⣿⣿⣿⢸⣿⠀⠠
⠀⠀⠀⠿⠇⠘⠿⠾⠏⠿⠷⠿⠻⠿⠹⠿⠸⠿⠀⠀⠹⠷⠸⠿⠀⠿⠷⠆⠿⠿⠿⠰⠆⠀⠻⠿⠿⢁⡿⢇⡸⠿⠼⠿⠴⠿⠰⠆⠀⠻⠷⠿⠁⠿⠿⠇⠸⠿⠶⠿⠇⠿⠀⠀⠸⠿⠸⠿⠁⠻⠷⠿⠙⠿⠾⠟⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⡀⠀⢶⣦⠀⠀⠀⠀⣰⠂⢄⠀⠄⠀⠀⡤⠀⠀⠀⠀⠀⠀⠈⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡄⣀⣀⣿⣷⣴⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⡯⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢻⣏⡅⡀⢸⠏⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠆⡀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⠒⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⣊⣐⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡽⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⡿⠋⠃⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠈⠻⡧⠤⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⠣⣀⠀⠈⠢⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣶⣼⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⢿⠿⠁⠀⠀⠀⠀⠀⠀⠯⢻⣿⣷⣶⣶⣤⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣶⣤⣾⣿⣿⣿⣿⣿⣿⠀⠈⠐⠿⠿⡿⡟⠻⡟⢻⢛⡜⣛⡥⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠙⠽⢟⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠹⠞⠛⠙⠉⠀⠀⠀⠀⠀⢡⣶⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠠⠐⠛⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠑⠛⢿⠿⣽⠟⠃⠉⠛⠻⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠔⠀⠀⠉⠛⠛⠿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⡖⠀⠂⠀⢀⢀⡀⣀⢀⢀⢀⠀⡀⣿⢀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠧⠀⠄⠶⠸⢸⡇⠟⠈⠳⠸⠠⠇⠿⠸⠌⠨⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢹⢰⢠⠀⠄⡄⢠⠠⠀⠀⠀⢠⠀⡄⠄⠀⢈⠅⡮⣆⢕⠨⠅⠀⢠⠠⠀⡄⠀⠠⠀⡄⡄⠁⢠⠀⠄⡀⠀⠀⠀⡤⢣⠠⠀⠀⠄⢠⢠⠀⠄⠀⢠⠀⠄⡀⢀⠀⠁⡄⡄⡇⠈⠀⢄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠁⠀⠁⠀⠀⠁⠀⠀⠈⠀⠀⠈⠁⠈⠀⠁⠈⠁⠀⠀⠁⠈⠀⠈⠀⠁⠈⠁⠉⠀⠁⠈⠀⠁⠀⠀⠀⠀⠁⠀⠀⠉⠀⠁⠈⠀⠉⠀⠁⠈⠀⠉⠀⠀⠈⠀⠉⠈⠁⠈⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡔⢠⢢⠐⠂⠐⢠⠢⠔⡀⡗⢰⠂⡔⡇⠀⢰⠂⡔⢤⢂⠐⠂⡖⠐⣂⠈⠀⢤⠀⠀⢺⠀⠒⠀⠀⢸⠀⡙⠨⠁⡏⠀⠀⠐⠂⠚⠀⠀⢸⠂⠒⢠⠢⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⢃⠠⡇⡄⠄⣄⢠⠀⢀⠄⢠⠠⢠⢠⢠⢠⢠⠠⢀⠠⣠⠠⠀⢀⠀⠠⡀⠄⢄⣄⢠⠀⠀⢀⣠⢠⠀⠀⡇⠄⠄⡀⠀⡄⡄⡄⡄⡄⡄⠄⡇⠄⣄⡄⡤⠀⡀⢄⠨⠁⢠⢠⠠⠠⢠⠠⠌⡠⠀⠀⠠⠀⠠⠀⠀
⠀⠀⠐⠊⠁⠃⠑⠂⠒⠉⠂⠈⠒⠈⠒⠘⠘⠘⠘⠘⠐⠊⠒⠘⠐⠀⠈⠒⠐⠐⠐⠊⠒⠉⠂⠐⠊⠒⠐⠂⠀⠑⠂⠸⠀⠀⠃⠃⠑⠃⠃⠃⠂⠓⠂⠑⠂⠃⠀⠑⠂⠐⠀⠀⠃⠃⠐⠊⠐⠐⠘⠒⠒⠂⠢⠒⠆⠀
⠀⠀⠀⠀⢀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⡸⢸⠒⡁⢀⢀⢘⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡴⢡⢦⠀⠀⠒⢐⢦⢂⠆⠶⠀⠀⡰⡄⠀⠀⠀⢺⢰⣶⠐⠀⠒⡀⠀⠐⡂⠒⠀⠀⠈⠀⢝⢨⠀⡇⡇⢼⠀⠀⡇⢸⢜⠀⠀⠖⠀⠀⠐⡆⠶⢰⠂⠀⠀⢒⢐⠆⡖⡄⢖⠀⡀⢸⢠⢦⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⢀⡀⢀⠀⡀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢎⠲⠿⠈⠀⠎⠀⡇⠀⠀⢉⠰⡑⢎⠄⠀⠰⠀⢸⠀⣱⠀⠁⠉⠄⡡⠀⠀⠈⠀⠀⢈⡆⠀⠀⠀⠀⠀⠂⠐⠀⢗⠟⡺⠀⠀⢇⠸⠊⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
䷩ 𝚕𝚒𝚗𝚎 3574
╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕
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Gemini version at gemini://gemini.techrights.org/2022/02/09/holding-management-accountable/
⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.09.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧
Gemini_version_available_♊︎
✐ Staff_Holding_Management_at_the_EPO_Accountable⠀✐
Posted in Europe, Patents at 2:37 pm by Dr. Roy Schestowitz
Video_download_link | md5sum 3e57c063cb4318309a3e810ef7b45ce7
Consequences for Rogues at the EPO
Creative Commons Attribution-No Derivative Works 4.0
http://techrights.org/videos/epo-action-and-impunity.webm
Summary: It seems possible that in months to come the administrative body of
the EPO will finally acknowledge that “breaking point” has been reached and
it’s time to reboot the Office
THE immunity and impunity of EPO management has been a theme of recent coverage
here. We last wrote about it earlier_today, focusing on what Benoît_Battistelli
had done in the Netherlands. After 3 years at the Office António_Campinos is
starting to see it all crumbling or falling down, starting with last summer’s
ILOAT ruling no. 4430 and then ILOAT ruling no. 4482, which is still very
fresh. But why did it take so long? As noted in the video above, many of the
people wronged are already dead, unable to claim_or_collect_compensation_from
the_Office.
The EPO got infiltrated by white-collar criminals, who in effect fronted for
international (non-European) or multinational corporations with their patent
litigation staff (in-house) and/or outside law firms. The solution to such a
dire crisis must come from the outside, but the_EU_too_is_infiltrated. The EPO
conflict has exposed a rotting unregulated system, which extends_to_EUIPO and
even some courts. It won’t be pretty, but “ordinary” EPO staff (such as patent
examiners) are on the right side of history. █
䷩ 𝚕𝚒𝚗𝚎 3626
╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕
(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/02/09/iloat-ruling-no-4430-and-iloat-ruling-no-4482/#comments
Gemini version at gemini://gemini.techrights.org/2022/02/09/iloat-ruling-no-4430-and-iloat-ruling-no-4482/
⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.09.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧
Gemini_version_available_♊︎
✐ [Meme]_Drunk_Driving,_Like_Son_of_António_Campinos⠀✐
Posted in Europe, Patents at 2:47 pm by Dr. Roy Schestowitz
Benoît_Battistelli is notorious for misusing EPO funds to build himself a_pub;
António_Campinos received a lot of negative press after his son had_gotten
drunk,_crashed_the_car,_and_wanted_to_borrow_dad's_diplomatic_immunity (his
grandpa Jorge did not live long enough to see such a disgrace; he died_in_a_car
accident_in_1993)
🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇ILOAT ruling no. 4430 and ILOAT ruling no. 4482⦈
Summary: In the Netherlands, the drunk-on-power EPO may have gotten its way (an
above-the-law status), but ILOAT keeps delivering much-belated rulings (4430,
4482, maybe more to come) which curtail the illegal actions of the EPO albeit
without any consequences for the perpetrators
⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠨⣲⣍⡩⣿⡯⠻⠿⠿⠿⠿⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣀⠠⡀⠉⠃⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠐⠏⠁⠛⠋⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢠⡀⠄⣤⣆⡰⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⠭⡝⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣜⣍⢿⢿⣿⣷⠿⢻⣤⡄⠀⣸⣿⣷⣭⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣓⣻⢾⣿⣿⡿⠀⣿⣿⠀⣨⣿⣹⣿⣿⣿⣿⡗⠾⣭⣟⡛⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣧⣬⠝⠃⠀⢻⣟⣿⣶⣯⣽⣿⡷⢧⣿⣾⠃⣠⣿⣾⠙⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠋⣽⠷⠫⠠⢼⢿⡿⣬⣿⣿⣿⣿⣿⣿⣿⢀⣼⣿⡏⢴⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⣼⣿⣼⣶⣶⣤⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⣿⣿⡟⠐⣿⡿⠬⣿⣿⣮⣆⣿⣿⣿⣿⣿⣿⣿⣯⢀⢹⣿⠗⢺⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡿⣿⢸⣿⠻⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠇⣼⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡏⢹⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠉⢋⣛⢹⡿⣸⣿⣾⣧⡟⢟⣻⣿⡟⣿⣿⠛⣿⣿⣟⣿⣿⡟⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⢿⠟⣷⣆⣀⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡝⠈⠅⢈⣋⣛⢹⣠⡌⣿⣿⠀⣿⣿⠃⣿⣿⢸⣿⣿⡇⣿⣾⣿⣿⣿⣿⠆⢿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣸⢿⣶⢈⣈⣷⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣰⠀⡏⠀⠗⠀⣢⠉⠘⠁⠗⠛⡿⠀⣿⣿⠀⢿⡟⠀⣿⣿⡇⢻⣽⣿⣿⣿⠃⠀⠀⠙⠿⣿⠀⢻⣿⣿⣿⣿⣿⣟⡷⢾⡟⠓⣿⣿⣿⣿⣿⣿⣸⠽⠻⠻⠍⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⡟⠀⠀⠀⠀⢰⡦⣤⣷⡇⠀⠀⠛⠀⢸⣇⠀⠸⢷⣷⣾⣿⡇⢸⣽⣿⣹⠃⠐⠛⠀⠀⠀⠉⠀⠸⣿⠿⡿⠿⠦⢴⣇⣸⢻⠄⣿⣼⣿⣿⣧⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠓⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⡇⠀⠀⠀⠀⢸⣿⢳⣿⠁⠀⠀⠀⠀⠈⣿⠀⢸⠈⠛⣿⢿⡇⢸⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠯⠿⠀⠀⠀⠀⠀⠀⠀⠉⠉⢩⡙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠒⠀⠀⠀⠀⠀⢸⣇⣿⠏⠀⠀⠀⠀⠀⠀⠏⠀⢐⢀⡀⠙⢼⠃⠛⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣦⣀⠀⠀⠀⠘⠛⠛⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣯⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⢠⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢺⣈⣃⠈⠀⠀⠀⠠⢠⠦⠤⠀⠒⢸⢩⠧⠀⠀⠀⠀⡀⠉⠛⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡄⠀⠀⠀⠀⠀⠁⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠀⠈⠀⠉⠀⠀⠈⠑⠂⠀⠀⠀⠀⠀
⢀⠄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⢴⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠀⠀⠐⠀⠂
⠂⠄⠰⢠⠀⠀⠀⡠⠠⠄⠂⠀⠀⠀⠀⠀⠀⠒⠙⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[20A⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣈⢉⣓⣍⡹⣿⡮⠟⠿⠿⠿⠿⡿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠃⠃⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠐⠏⠁⠙⠋⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢄⢰⣄⡤⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⠭⡍⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣿⣿⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣘⣍⢿⢷⣿⣷⠿⢻⣤⡄⠀⣸⣿⣷⣭⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣓⡻⢾⣿⣿⣿⠀⣿⣿⠀⣨⣿⣹⣿⣿⣿⣿⡗⠾⣭⣟⡋⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣧⣬⠛⠃⠀⢻⣟⣿⣶⣯⣽⣻⡷⢧⣿⣾⠃⣠⣿⣾⠩⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠋⣽⠷⠫⠠⢼⢿⡿⣬⣿⣿⣿⣿⣿⣿⣿⢀⣼⣿⡏⢴⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⣼⡿⣼⣶⣶⣤⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⣿⣿⡟⠐⣿⡿⠬⣿⣿⣮⣆⣿⣿⣿⣿⣿⣷⣿⣯⢀⢹⣿⠗⢺⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡿⣿⢸⣿⠻⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠆⣼⣿⣽⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡏⡏⢹⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠈⢉⣛⢹⡿⣸⣿⣾⣧⡟⢟⢻⣿⡟⣿⣿⠛⣿⣿⣟⣿⣿⡟⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⢿⠟⣷⣆⣀⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠓⠈⡁⢈⣋⣛⢹⣠⡌⣿⣿⠀⣿⣿⠂⣿⣿⢸⣿⣿⡇⣿⣾⣿⣿⣿⣿⠆⢿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⢸⢿⣶⢈⣈⣷⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢠⠀⡋⠀⠗⠀⣂⠉⠘⠁⠗⠛⣿⠀⣻⣿⠀⢿⡟⠑⣿⣿⡇⢻⣽⣿⣿⣿⠃⠀⢀⠙⠿⣿⠀⢻⣿⣿⣿⣿⣿⣟⡷⢾⡟⠓⣿⣾⣿⣿⣿⣿⣸⠽⠻⠻⠍⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⡟⠀⠀⠀⠀⢰⡦⣠⣷⡇⠀⠀⠛⠀⢸⣇⠀⠸⢷⣷⣾⣿⡇⢨⣯⣿⣹⠃⠐⠛⠀⠀⠀⠁⠀⠸⣿⣿⡿⠿⠦⠴⣧⣼⢻⠄⣿⣼⣿⣿⣧⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠻⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⡇⠀⠀⠀⠀⢸⡿⢰⣿⠁⠀⠀⠀⠀⠈⣿⠀⢸⠈⠛⣿⢿⡇⢸⣿⡟⠁⠀⠀⠐⠀⠀⠀⠀⠀⠂⣿⡿⠻⠃⠀⠀⠀⠀⠀⠉⡍⠉⠉⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠁⠀⠀⠀⠀⢸⣇⣿⠇⠀⠀⠀⠀⠀⠀⠏⠀⢐⢀⡀⠙⢼⠃⠛⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣦⣀⠀⠀⠀⠘⠛⠛⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠚⠓⢠⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣄⡀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢀⣈⣃⠈⠀⠀⠀⠠⢠⠦⠤⠀⠒⢸⢩⠧⠀⠀⠀⠀⡀⠉⠛⠉⠉⠉⠉
⠀⠀⠀⡀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⠆⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠤⠄⠈⠀⠉⠀⠀⠈⠑⠂⠂⠀⠀⠀⠀
⢀⠄⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⢴⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠀⠀⠀⠀⠂
⠃⠄⠰⢠⠀⠀⠀⡠⠠⠄⠂⠀⠀⠀⠀⠀⠀⠒⠙⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[20A⠀⠀⠀⠀⠀⠀⠀⠀⠀⣊⣈⢉⣡⣍⡹⣿⡿⠛⠿⠿⠿⠿⡿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠃⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠰⠏⠁⠙⠋⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠠⡀⡄⣔⣄⡤⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⠭⡍⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣿⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣘⣍⢿⢷⣿⣷⠿⢻⣤⡄⠀⣸⣿⣷⣭⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣛⡻⢾⣿⣿⣿⠀⣿⣿⠀⣨⣿⣹⣿⣿⣿⣿⡗⠾⣭⣟⡛⡽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣧⣬⠛⠃⠀⢻⣟⣿⣶⣯⣽⣻⡷⢧⣿⣾⠃⣠⣿⣾⠩⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠋⣽⠷⠫⠠⢼⢿⡿⣬⣿⣿⣿⣿⣿⣿⣿⢀⣼⣿⡏⢴⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⣼⣿⣼⣶⣶⣤⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⣿⣿⡟⠐⣿⡿⠬⣿⣿⣮⣆⣿⣿⣿⣿⣿⣿⣿⣯⢀⢹⣿⠗⢺⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡿⣿⢸⣿⠻⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠃⣸⣿⣽⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡏⢹⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠋⠁⢉⣛⢹⡿⣸⣿⣾⣧⡟⢟⣻⣿⡟⣿⣿⠛⣿⣿⣟⣿⣿⡟⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⢿⠟⣷⣆⣀⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠝⠀⡅⢈⣋⣛⢹⣠⡌⣿⣿⠀⣿⣿⠃⣿⣿⢘⣿⣿⡇⣿⣾⣿⣿⣿⣿⠆⢿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⢸⢿⣶⢈⣈⣷⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢠⠀⡋⠀⠓⠀⣢⠉⠘⠁⠗⠛⡿⠀⣿⣿⠀⢿⡟⠐⣿⣿⡇⢻⣽⣿⣿⣿⠃⠀⢀⠙⠿⣿⠀⢻⣿⣿⣿⣿⣿⣟⡷⢾⣟⠓⣿⣾⣿⣿⣿⣿⣘⠹⠻⠻⠍⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⡟⠀⠀⠀⠀⢰⡦⣤⣷⡇⠀⠀⠛⠀⢸⣇⠀⠸⢷⣷⣾⣿⡇⢸⣯⣿⣹⠃⠐⠛⠀⠀⠀⠉⠀⠸⣿⣿⣿⡽⠧⠴⣧⣼⢻⠄⣿⣼⣿⣿⣧⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠻⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⡇⠀⠀⠀⠀⢸⡿⢰⣿⠁⠀⠀⠀⠀⠈⣿⠀⢸⠈⠻⣿⢿⡇⢸⣿⡏⠁⠀⠀⠐⠀⠀⠀⠀⠀⠂⣿⣿⡿⠀⠖⠀⠀⠀⠀⠀⠉⠉⠉⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣇⣿⠇⠀⠀⠀⠀⠀⠀⠏⠀⢐⢀⡀⠙⢾⠃⠛⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠒⣦⣀⠀⠀⠀⠘⠛⠛⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣯⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⢠⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣭⡅⠂⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣀⠈⠀⠀⠀⠠⢠⠦⠤⠀⠒⢸⢩⠧⠀⠀⠀⠀⡀⠉⠛⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⡀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠀⠈⠀⠉⠀⠀⠈⠑⠂⠂⠀⠀⠀⠀
⢀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⢴⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠀⠀⠀⠀⠂
⠀⠄⠰⢠⠀⠀⠀⠠⠠⠄⠂⠀⠀⠀⠀⠀⠀⠒⠙⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[20A⠀⠀⠀⠀⠀⠀⠀⠀⠉⣪⣭⣉⣓⣭⡻⣿⡿⠻⠿⠿⠿⠿⡿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡝⠋⠃⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠐⠏⠁⠙⠋⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠠⡄⣤⣴⣄⡶⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⠬⡍⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣐⣍⢿⢷⣿⣷⠿⢻⣤⡄⠀⣸⣿⣷⣭⣝⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣓⡻⢾⣿⣿⣿⠀⣿⣿⠀⣨⣿⣹⣿⣿⣿⣿⡗⠾⣭⣟⡋⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣧⣬⠛⠃⠀⢻⣟⣿⣶⣯⣽⣻⡷⢦⣿⣾⠃⣠⣿⣾⠫⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠋⣽⠷⠫⠠⢼⢿⡿⣬⣿⣿⣿⣿⣿⣿⣿⢀⣼⣿⡏⢴⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⣼⣿⣼⣶⣶⣤⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⣿⣿⡟⠐⣿⡿⠬⣿⣿⣾⣆⣿⣿⣿⣿⣿⣿⣿⣯⢀⢹⣿⠗⢺⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡿⣿⢸⣿⠻⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠃⣼⣿⣼⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡏⢹⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠁⠛⣛⢹⡿⣸⣿⣾⣧⡟⢟⣻⣿⡟⣿⣿⠛⣿⣿⣟⣿⣿⡟⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⢿⠟⣷⣆⣀⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠝⠈⠅⢈⣋⣻⢹⣠⡌⣽⣿⠀⣿⣿⠃⣿⣿⢸⣿⣿⡇⣿⣾⣿⣿⣿⣿⠆⢿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣸⢿⣶⢈⣈⣷⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣠⠀⡇⠀⠗⠀⣢⠉⠘⠁⡗⠛⣿⠀⣻⣿⠀⢿⡟⠀⣿⣿⡇⢻⣽⣿⣿⣿⠃⠀⠀⠙⠿⣿⠀⢻⣿⣿⣿⣿⣿⣟⡷⢾⡟⠓⣿⣾⣿⣿⣿⣿⣸⠹⠻⠻⠍⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⡟⠀⠀⠀⠀⢰⡦⢠⣷⡇⠀⠀⠛⠀⢸⣇⠀⠸⢷⣷⣾⣿⡇⢨⣭⣿⣹⠃⠐⠋⠀⠀⠀⠉⠀⠸⣿⣿⣿⣽⣧⡴⠧⣼⢻⠄⣿⣼⣿⣿⣧⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠻⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⡇⠀⠀⠀⠀⢸⡿⢰⣿⠁⠀⠀⠀⠀⠈⣿⠀⢸⠈⠻⣿⣿⡇⠸⣿⡟⠁⠀⠀⠄⠀⠀⠀⠀⠀⠂⣿⣿⣿⣼⠃⠰⠀⠀⠀⠀⠉⠉⠉⠘⠒⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣗⣿⠇⠀⠀⠀⠀⠀⠀⠏⠀⢐⢀⡀⠙⢿⠃⠃⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡯⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣦⣀⠀⠀⠀⠘⠛⠛⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠚⠓⢠⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣭⡱⠢⠄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⠦⠤⠀⠒⢸⢩⠧⠀⠀⠀⠀⡀⠉⠛⠉⠉⠉⠉
⠀⠀⠀⡀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⡄⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠀⠈⠀⠁⠀⠀⠈⠑⠂⠀⠀⠀⠀⠀
⢀⠄⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⢴⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠀⠀⠂
⠃⠄⠰⢠⠀⠀⠀⠠⠠⠄⠂⠀⠀⠀⠀⠀⠀⠒⠙⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[20A⠀⠀⠀⠀⠀⠀⠀⠀⠈⡪⣨⢉⣓⣭⡫⣿⡿⠿⠿⠿⠿⠿⡿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡐⡙⠏⠃⠛⠉⠉⠀⠀⠈⠀⠀⠀⠰⠐⠏⠁⠙⠋⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⡀⠤⢄⣄⡤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⠭⡍⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣐⣍⢿⢷⣿⣷⠿⢻⣤⡄⠀⣸⣿⣷⣭⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣓⡻⢾⣿⣿⣿⠀⣿⣿⠀⣨⣿⣹⣿⣿⣿⣿⡗⠾⣭⣟⡛⡽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣧⣬⠛⠃⠀⢻⣟⣿⣶⣯⣽⣻⡷⢤⣿⣾⠃⣠⣿⣾⠩⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠋⣽⠷⠫⠠⢼⢿⡿⣬⣿⣿⣿⣿⣿⣿⣿⢀⣼⣿⡏⢴⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⣼⡿⣼⣶⣶⣤⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⣿⣿⡟⠐⣿⡿⠬⣿⣿⣮⣆⣿⣿⣿⣿⣿⣿⣿⣯⢀⢹⣿⠗⢺⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡿⣯⢸⣿⠻⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠃⣸⣿⣼⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡏⢹⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠈⠛⣛⢹⡿⣸⣿⣾⣧⡟⢟⢻⣿⡟⣿⣿⠛⣿⣿⣟⣿⣿⡟⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⢿⠟⣷⣆⣀⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠝⠈⠅⢈⣋⣛⢹⣠⡌⣿⣿⠀⣿⣿⠂⣿⣿⢸⣿⣿⡇⣿⣾⣿⣿⣿⣿⠆⢿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣸⢿⣶⢈⣈⣷⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢠⠀⡋⠀⠓⠀⣂⠈⠘⠁⠗⠛⣿⠀⣻⣿⠀⢿⡟⠐⣿⣿⡇⢻⣽⣿⣿⣿⠃⠀⠀⠙⠿⣿⠀⢻⣿⣿⣿⣿⣿⣟⡷⢾⣟⠓⣿⣾⣿⣿⣿⣿⣸⠹⠻⠻⠍⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⡟⠀⠀⠀⠀⢰⡦⣤⣷⡇⠀⠀⠛⠀⢸⣇⠀⠸⢷⣷⣾⣿⡇⢨⣭⣽⣹⠃⠐⠛⠀⠀⠀⠉⠀⠸⣿⣿⣿⣽⣧⣴⣧⡼⢻⠄⣿⣼⣿⣿⣧⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠻⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⡇⠀⠀⠀⠀⢸⣿⣰⣿⠁⠀⠀⠀⠀⠈⣿⠀⢸⠈⠻⣿⣿⡇⠸⣿⡟⠁⠀⠂⠄⠀⠀⠀⠀⠀⠂⣿⣿⣿⣼⣿⠏⠆⠀⠀⠀⠈⠉⠉⠘⠒⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣗⣿⠇⠀⠀⠀⠀⠀⠀⠯⠀⢐⢀⡀⠙⢿⠃⠃⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡾⣿⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠒⣦⣀⠀⠀⠀⠘⠛⠛⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣯⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⢠⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣝⡧⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⠦⠤⠀⠒⢸⢩⠧⠀⠀⠀⠀⡀⠉⠛⠉⠉⠉⠉
⠀⠀⠀⡀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⠄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠄⠈⠀⠁⠐⠀⠈⠑⠂⠀⠀⠀⠀⠀
⢀⠄⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⢴⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠀⠀⠀⠀⠂
⠁⠄⠰⢠⠀⠀⠀⠠⠠⠄⠂⠀⠀⠀⠀⠀⠀⠒⠙⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[20A⠀⠀⠀⠀⠀⠀⠀⠀⠉⢤⣊⣉⣑⣍⡩⢿⡻⠛⠟⠿⠿⠿⡿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⠏⠋⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠰⠏⠁⠙⠋⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠤⣄⣀⡠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⠭⡍⠛⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣗⣿⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣐⣍⢿⢷⣿⣷⠿⢻⣤⡄⠀⣸⣿⣷⣭⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣯⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣓⡻⢾⣿⣿⣿⠀⣿⣿⠀⣨⣿⣸⣿⣿⣿⣿⡗⠾⣭⣟⡛⡽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣧⣬⠛⠃⠀⢻⣟⣿⣶⣯⣽⣻⡷⢦⣿⣾⠃⢠⣿⣾⠉⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠋⣽⠷⠫⠠⢼⢿⡾⣬⣿⣿⣿⣿⣿⣿⣿⢀⣼⣿⡏⢴⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⣼⡿⣼⣶⣶⣤⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⣿⣿⡟⠐⣿⡿⠬⣿⣿⣮⣆⣿⣿⣿⣿⣿⣿⣿⣯⢀⢹⣿⠗⢺⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡿⣿⢸⣿⠻⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠂⣼⣿⣼⣿⡿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡏⢹⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠀⠛⣛⢹⡿⣸⣿⣶⣧⡟⢟⢻⣿⡟⣿⣿⠛⣿⣿⣟⣿⣿⡟⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⢿⠟⣷⣆⣀⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠐⠀⠁⢈⣋⣛⢹⢠⡌⣿⣿⠀⣿⣿⠃⣿⣿⢸⣿⣿⡇⣿⣾⣿⣿⣿⣿⠆⢿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⢸⢿⣶⢈⣀⣷⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢠⠀⡇⠀⠓⠀⣂⠈⠘⠁⠗⠛⣿⠀⣻⣿⠀⢿⡟⡑⣿⣿⡇⢻⣽⣿⣿⣿⠃⠀⠀⠙⠿⣿⠀⢻⣿⣿⣿⣿⣿⣟⡷⢾⡟⠓⣿⣾⣿⣿⣿⣿⣜⠹⠻⠻⠍⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⡟⠀⠀⠀⠀⢰⡦⣠⣷⡇⠀⠀⠛⠀⢸⣇⠀⠸⢷⣷⣾⣿⡇⢨⣯⣽⣹⠃⠐⠋⠀⠀⠀⠉⠀⠸⣿⣿⣿⣽⣧⣴⣇⡸⢻⠄⣿⣼⣿⣿⣧⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠻⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⡇⠀⠀⠀⠀⢸⣿⣰⣿⠁⠀⠀⠀⠀⠈⣿⠀⢸⠈⠻⣿⢿⡇⠸⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⣿⣿⣿⣼⣿⡿⠭⠖⠀⠀⠀⠉⠉⠘⠒⠀⠠⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣷⣿⠇⠀⠀⠀⠀⠀⠀⠛⠀⠼⢀⡀⠙⢿⠃⠁⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⢾⡏⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⠁⢀⠀⠀⠀⠀⠀⠒⣦⣀⠀⠀⠀⠘⠛⠛⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣧⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⢠⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡧⠤⠤⠤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⠦⠤⠀⠒⢸⢩⠧⠀⠀⠀⠀⡀⠉⠛⠉⠉⠉⠉
⠀⠀⠀⡀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠤⠤⠤⠀⠈⠀⠁⠐⠀⠈⠑⠂⠀⠀⠀⠀⠀
⢀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⢴⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠂
⠂⠄⠰⢠⠀⠀⠀⠠⠠⠄⠂⠀⠀⠀⠀⠀⠀⠚⠙⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[20A⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣊⣉⣑⣩⡹⣿⡯⠿⠿⠿⠿⠿⡿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡡⡱⠟⠃⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠐⠏⠁⠛⠏⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠄⣄⣐⠤⠕⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⠭⡍⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣟⣾⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣐⣍⢿⢷⣿⣷⠿⢻⣤⡄⠀⣸⣿⣷⣯⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣓⡻⢾⣿⣿⣿⠀⣿⣿⠀⣨⣿⣹⣿⣿⣿⣿⡗⠾⣭⣟⡋⡽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣧⣬⠛⠃⠀⢻⣟⣿⣶⣯⣽⣻⡷⢦⣿⣾⠃⣠⣿⣾⠉⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠋⣽⠷⠫⠠⢼⢿⡾⣬⣿⣿⣿⣿⣿⣿⣿⢀⣼⣿⡏⢴⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⣼⡿⣼⣶⣶⣤⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⣿⣿⡟⠐⣿⡿⠬⣿⣿⣮⣆⣿⣿⣿⣿⣿⣿⣿⣯⢀⢹⣿⠗⢺⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡿⣿⢸⣿⠻⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠃⣼⣿⣽⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡏⢹⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠈⢛⣛⢹⡿⣸⣿⣾⣧⡟⢟⣻⣿⡟⣿⣿⠛⣿⣿⣟⣿⣿⡟⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⢿⠟⣷⣆⣀⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠟⠈⠅⢈⣋⣛⢹⣠⡌⣿⣿⠀⣿⣿⠃⣿⣿⢸⣿⣿⡇⣿⣾⣿⣿⣿⣿⠆⢿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⢸⢿⣶⢈⣈⣷⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣠⠀⡏⠀⠷⠀⣂⠈⠘⠁⠗⠋⣿⠀⣿⣿⠀⢿⡟⠑⣿⣿⡇⢻⣽⣿⣿⣿⠃⠀⠀⠙⠿⣿⠀⢻⣿⣿⣿⣿⣿⣟⡷⢾⡟⠓⣿⣾⣿⣿⣿⣿⣼⠹⠻⠻⠍⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⡟⠀⠀⠀⠀⢰⡦⣠⣷⡇⠀⠀⠛⠀⢸⣇⠀⠸⢷⣷⣾⣿⡇⢨⣯⣿⣹⠃⠐⠙⠀⠀⠀⠉⠀⠸⣿⣿⣿⣽⣧⣴⣧⡼⢻⠄⣿⣼⣿⣿⣧⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⡇⠀⠀⠀⠀⢸⡿⣳⣿⠁⠀⠀⠀⠀⠀⣿⠀⢸⠈⠻⣿⢿⡇⠸⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⣿⣿⣿⣼⣿⡿⠯⠭⠠⠀⠀⠈⠉⠈⠒⠂⠠⠤⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣇⣿⠇⠀⠀⠀⠀⠀⠀⠋⠀⠸⢢⡀⠙⢿⠃⠈⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⡍⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⠀⡀⠀⠀⠀⠀⠒⣦⣀⠀⠀⠀⠘⠛⠛⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣟⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⢠⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⡧⠤⠤⠤⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⠦⠤⠀⠒⢸⢩⠧⠀⠀⠀⠀⡀⠉⠛⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠤⠤⠤⠀⠈⠀⠁⠐⠀⠈⠑⠂⠀⠀⠀⠀⠀
⢀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⢴⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠀⠀⠀⠀⠂
⠀⠄⠰⢠⠀⠀⠀⠠⠠⠄⠂⠀⠀⠀⠀⠀⠀⠰⠙⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[20A⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣌⣉⣁⣍⡹⣿⡯⠟⠟⠿⠿⠿⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⠈⡙⠋⠛⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠰⠏⠁⠛⠋⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠤⢄⣀⡱⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⠭⡍⠛⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣐⣍⢿⢷⣿⣷⠿⢻⣤⡄⠀⣸⣿⣷⣭⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣓⡻⢾⣿⣿⣿⠀⣿⣿⠀⣨⣿⣹⣿⣿⣿⣿⡗⠾⣭⣟⡋⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣧⣬⠛⠃⠀⢻⣟⣿⣶⣯⣽⣻⡷⢦⣿⣾⠃⣠⣿⣾⠉⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠋⣽⠷⠫⠠⢼⢿⡾⣬⣿⣿⣿⣿⣿⣿⣿⢀⣼⣿⡏⢴⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⣼⡿⣼⣶⣶⣤⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⣿⣿⡟⠐⣿⡿⠬⣿⣿⣮⣆⣿⣿⣿⣿⣿⣿⣿⣯⢀⢹⣿⠗⢺⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡿⣟⢸⣿⠻⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠂⣼⣟⣼⣿⡿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡏⡏⢹⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠚⠈⠋⢛⢹⡿⣸⣿⣾⣧⡟⢟⢻⣿⡟⣿⣿⠛⣿⣿⣟⣿⣿⡟⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⢿⠟⣷⣆⣀⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠙⠈⡁⢈⣋⣻⢹⢠⡌⣿⣿⠀⣿⣿⠃⣿⣿⢹⣿⣿⡇⣿⣾⣿⣿⣿⣿⠆⢿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⢸⢿⣶⢈⣀⣷⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢠⠀⡇⠀⠗⠀⣂⠈⠘⠁⠗⠉⣿⠀⣿⣿⠀⢿⡟⠀⣿⣿⡇⢻⣽⣿⣿⣿⠃⠀⢀⠙⠿⣿⠀⢻⣿⣿⣿⣿⣿⣟⡷⢾⣟⠃⣿⣾⣿⣿⣿⣿⣸⠹⠻⠻⠍⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⡟⠀⠀⠀⠀⢰⡦⢠⣷⡇⠀⠀⠛⠀⢸⣇⠀⠸⢷⣷⣾⣿⡇⢨⣯⣽⣹⠃⠐⠉⠀⠀⠀⠉⠀⠸⣿⣿⣿⣽⣧⣴⣧⡸⢻⠄⣿⣼⣿⣿⣧⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠻⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⡇⠀⠀⠀⠀⢸⡿⢰⣿⠁⠀⠀⠀⠀⠀⣿⠀⢸⡈⠻⣿⢿⡇⠸⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⣿⣿⣿⣼⣿⡿⠯⠭⣀⢠⠁⠈⠉⠉⠒⠂⠀⠤⠤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣇⣿⠇⠀⠀⠀⠀⠀⠀⠏⠀⠘⢂⡀⠘⢿⠃⠘⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠍⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘⢁⡀⠀⠀⠀⠒⣦⣀⠀⠀⠀⠘⠛⠛⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣧⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⢠⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣶⡧⠤⠤⠄⠀⣈⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠦⠤⠀⠒⢸⢩⠧⠀⠀⠀⠀⡀⠉⠛⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⠄⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠤⠤⠤⠀⠈⠀⠀⠐⠀⠈⠑⠂⠀⠀⠀⠀⠀
⢀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⢴⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠀⠀⠀⠀⠒
⠁⠄⠰⢠⠀⠀⠀⠠⠠⠄⠂⠀⠀⠀⠀⠀⠀⠒⠙⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[20A⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⡪⢉⣑⣉⡹⣿⡻⠻⠟⠿⠿⠿⡿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡠⡙⠊⠃⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠐⠏⠁⠛⠋⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠠⣄⡂⠨⠕⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⠭⡍⠛⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣟⣾⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣐⣍⢿⢷⣿⣷⠿⢻⣤⡄⠀⣸⣿⣷⣯⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣓⡻⢾⣿⣿⣿⠀⣿⣿⠀⣨⣿⣹⣿⣿⣿⣿⡗⠾⣭⣟⡋⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣧⣬⠙⠃⠀⢻⣟⣿⣶⣯⣽⣻⡷⢦⣿⣾⠃⣠⣿⣾⠋⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠋⣽⠷⠫⠠⢼⢿⡿⣬⣿⣿⣿⣿⣿⣿⣿⢀⣼⣿⡏⢴⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⣼⡿⣼⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⣿⣿⡟⠐⣿⡿⠬⣿⣿⣮⣆⣿⣿⣿⣿⣿⣿⣿⣯⢀⢹⣿⠗⢺⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡿⣟⢸⣿⠻⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠂⣼⣷⣸⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡏⡏⢹⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠋⠀⢋⣙⢹⡿⣸⣿⣾⣧⡏⢟⣻⣿⡟⣿⣿⠛⣿⣿⣟⣿⣿⡟⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⢿⠟⣷⣆⣀⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠚⠀⡁⢈⣋⣛⢸⣠⡌⣽⣿⠀⣿⣿⠃⣿⣿⢸⣿⣿⡇⣿⣾⣿⣿⣿⣿⠆⢿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⢸⢿⣶⢈⣀⣷⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢠⠀⡏⠀⠧⠀⣢⠀⠘⠁⠗⠛⣿⠀⣻⣿⠀⢿⡟⠀⣿⣿⡇⢻⣽⣿⣿⣿⠃⠀⠀⠙⠿⣿⠀⢻⣿⣿⣿⣿⣿⣟⡷⢾⣟⠃⣿⣿⣿⣿⣿⣿⣸⠹⠻⠻⠍⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⡟⠀⠀⠀⠀⢰⡦⢠⣷⡇⠀⠀⠛⠀⢸⠇⠀⠸⢷⣷⣾⣿⡇⢨⣯⣽⣹⠃⠐⠉⠀⠀⠀⠉⠀⠸⣿⣿⣿⣽⣧⣴⣧⡸⢻⠄⣿⣼⣿⣿⣧⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠻⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⡇⠀⠀⠀⠀⢸⡿⢰⣿⠁⠀⠀⠀⠀⠀⣿⠀⢸⠈⠻⣿⣻⡇⢸⣿⡟⠁⠀⠀⠐⠀⠀⠀⠀⠀⠂⣿⣿⣿⣼⣿⡿⠯⠭⣀⣀⢫⠍⠉⠉⠒⠂⠀⠤⠤⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣇⣿⠇⠀⠀⠀⠀⠀⠀⠏⠀⠀⢀⡀⠘⢿⠇⠘⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡏⠍⠙⠋⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠸⢂⡀⠀⠀⠒⣦⣀⠀⠀⠀⠘⠛⠛⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣗⡟⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠚⠓⢠⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣾⡧⠤⠤⠄⠀⣈⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠦⠤⠀⠒⢸⢩⠧⠀⠀⠀⠀⡀⠉⠛⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡄⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠤⠤⠤⠀⠉⠀⠀⠀⠀⠈⠑⠂⠀⠀⠀⠀⠀
⢀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⢴⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠂
⠁⠄⠰⢠⠀⠀⠀⡠⠠⠄⠂⠀⠀⠀⠀⠀⠀⠒⠙⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[20A⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣎⢉⣡⣉⡹⣿⡫⠛⠿⠿⠿⠿⡿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⡀⡝⠏⠃⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠰⠏⠁⠛⠏⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣄⣂⠄⠝⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⠭⡍⠛⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣮⣶⣶⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣐⣍⢿⢷⣿⣷⠿⢻⣤⡄⠀⣸⣿⣷⣭⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣓⡻⢾⣿⣿⣿⠀⣿⣿⠀⣨⣿⣹⣿⣿⣿⣿⡗⠾⣭⣟⡋⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣧⣬⠛⠃⠀⢻⣟⣿⣶⣯⣽⣻⡷⢦⣿⣾⠃⣠⣿⣾⠉⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠋⣽⠷⠫⠠⢼⢿⡯⣬⣿⣿⣿⣿⣿⣿⣿⢀⣼⣿⡏⢴⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⣼⡿⣼⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⣿⣿⡟⠐⣿⡿⠬⣿⣿⣮⣆⣿⣿⣿⣿⣿⣿⣿⣯⢀⢹⣿⠗⢺⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡿⣿⢸⣿⠻⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⣸⣿⣼⡿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡏⡏⢹⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠀⢋⡋⢹⡿⣸⣿⣾⣧⡟⢟⢻⣿⡟⣿⣿⠛⣿⣿⣟⣿⣿⡟⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⢿⠟⣷⣆⣀⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠙⠈⠁⢈⣋⣛⢸⢠⡌⣽⣿⠀⣿⣿⠃⣿⣿⢸⣿⣿⡇⣿⣾⣿⣿⣿⣿⠆⢿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⢸⢿⣶⢈⣀⣷⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢠⠀⡇⠀⠷⠀⣢⠀⠘⠁⠗⠛⣿⠀⣿⣿⠀⢿⡏⠐⣿⣿⡇⢻⣽⣿⣿⣿⠃⠀⢀⠙⠿⣿⠀⢻⣿⣿⣿⣿⣿⣟⡷⢾⡟⠃⣿⣿⣿⣿⣿⣿⣸⠹⠻⠻⠍⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⡟⠀⠀⠀⠀⢰⡦⢠⣷⡇⠀⠀⠛⠀⢸⠇⠀⠸⢷⣷⣾⣿⡇⢨⣯⣽⣹⠃⠐⠉⠀⠀⠀⠉⠀⠸⣿⣿⣿⣽⣧⣴⣧⡸⢻⠄⣿⣼⣿⣿⣧⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠻⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⡇⠀⠀⠀⠀⢸⡿⢰⣿⠁⠀⠀⠀⠀⠀⣾⠀⢰⠈⠛⣿⣿⡇⢸⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⣿⣿⣿⣼⣿⡿⠯⠭⣀⣀⣿⡋⠉⠉⠀⠂⠀⠤⠤⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣇⣿⠇⠀⠀⠀⠀⠀⠀⠏⠀⠼⢡⡀⠈⢿⠁⠈⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡏⠍⠙⠋⠀⠀⠀⠀⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠚⠸⡰⣃⠀⠀⠒⣦⣀⠀⠀⠀⠘⠛⠛⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣯⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⠗⠠⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⡧⠤⠤⠀⠀⢈⣀⣀⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠒⢸⢩⠧⠀⠀⠀⠀⡀⠉⠛⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡄⠀⠀⠀⠀⠀⠈⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⠤⠤⠀⠉⠀⠁⠐⠀⠈⠑⠂⠀⠀⠀⠀⠀
⢀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⢴⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠀⠀⠀⠀⠂
⠀⠄⠰⢠⠀⠀⠀⠠⠠⠄⠂⠀⠀⠀⠀⠀⠀⠒⠙⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣂⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[20A⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢈⢉⣑⣍⡩⣿⡿⠟⠿⠿⠿⠿⡿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡂⡑⠓⠃⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠐⠏⠁⠛⠋⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠠⣀⣀⠠⠕⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⠬⡍⠛⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣾⣶⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣐⣍⢟⢷⣿⣷⠿⢻⣤⡄⠀⣸⣿⣷⣭⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣓⡻⢾⣿⣿⣿⠀⣿⣿⠀⣨⣿⣹⣿⣿⣿⣿⡗⠾⣭⣟⡋⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣧⣬⠛⠃⠀⢻⣟⣿⣶⣯⣽⣻⡷⢦⣿⣾⠃⣠⣿⣾⠉⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠋⣽⠷⠫⠠⢼⢿⡿⣬⣿⣿⣿⣿⣿⣿⣿⢀⣼⣿⡏⢴⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⣼⡿⣼⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⣿⣿⡟⠐⣿⡿⠬⣿⣿⣮⣆⣿⣿⣿⣿⣿⣿⣿⣯⢀⢹⣿⠗⢺⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡿⣟⢸⣿⠻⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠂⣼⣿⣼⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡏⡏⢹⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠚⠀⠋⣛⢹⡿⣸⣿⣾⣧⡟⢟⢻⣿⡟⣿⣿⠛⣿⣿⣟⣿⣿⡟⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⢿⠟⣷⣆⣀⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠚⠈⠁⢈⣋⣛⢸⢠⡌⣿⣿⠀⣿⣿⠃⣿⣿⢘⣿⣿⡇⣿⣾⣿⣿⣿⣿⠆⢿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⢸⢿⣶⢈⣀⣷⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢠⠀⡃⠀⠇⠀⣂⠀⠘⠁⠗⠛⣿⠀⣻⣿⠀⢿⡟⡁⣿⣿⡇⢻⣽⣿⣿⣿⠃⠀⠀⠙⠿⣿⠀⢻⣿⣿⣿⣿⣿⣟⡷⢾⡟⠃⣿⣿⣿⣿⣿⣿⣼⠹⠻⠻⠍⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⡟⠀⠀⠀⠀⢰⡦⢠⣷⡇⠀⠀⠛⠀⢸⠇⠀⠸⢷⣷⣾⣿⡇⢨⣯⣽⣹⠃⠐⠛⠀⠀⠀⠉⠀⠸⣿⣿⣿⣽⣧⣴⣧⡸⢻⠄⣿⣼⣿⣿⣧⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠻⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⡇⠀⠀⠀⠀⢸⡿⢰⣿⠁⠀⠀⠀⠀⠀⣿⠀⢰⠈⠛⠿⢿⡇⠸⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⣿⣿⣿⣼⣿⡿⠭⠭⣀⣀⣿⣛⡛⠈⠀⠀⠀⠤⠤⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣇⣿⠇⠀⠀⠀⠀⠀⠀⠋⠀⢬⢅⡀⠙⢿⠁⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡏⠉⠙⠋⠀⠀⠀⠀⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠰⡹⣁⠀⠒⣦⣀⠀⠀⠀⠘⠛⠛⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⡟⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⠠⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣾⡧⠤⠤⣀⠀⢈⣀⣈⠹⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠒⢸⢩⠧⠀⠀⠀⠀⡀⠉⠛⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠄⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠤⠤⠤⠀⠉⠀⠁⠐⠀⠈⠑⠂⠀⠀⠀⠀⠀
⢀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⢴⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠀⠀⠀⠀⠂
⠀⠄⠰⢠⠀⠀⠀⠠⠠⠄⠂⠀⠀⠀⠀⠀⠀⠒⠙⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[20A⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣈⣈⢄⣍⡩⢿⡮⠻⠿⠿⠿⠿⡿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡅⠎⠋⠛⠉⠁⠀⠀⠈⠀⠀⠀⠸⠰⠏⠁⠛⠋⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣐⠴⠊⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⠭⡍⠛⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣔⣾⣶⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣐⣍⢿⢷⣿⣷⠿⢻⣤⡄⠀⣸⣿⣷⣭⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣓⡻⢾⣿⣿⡿⠀⣿⣿⢀⣨⣿⣸⣿⣿⣿⣿⡗⠾⣭⣟⡛⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⣿⣿⣿⣿⣿⣧⣬⠙⠃⠀⢻⣟⣿⣶⣯⣽⣻⡷⢶⣿⣾⠃⢠⣿⣾⠉⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠉⣿⠷⠋⢠⣼⢿⡮⣬⣽⣿⣿⣿⣿⣿⣿⢀⣼⣿⡏⢴⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⣼⡿⣼⣶⣶⣤⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⣿⣿⡟⠐⣿⡿⠬⣾⣿⣔⣇⣿⣿⣿⣿⣿⣿⣿⣯⢠⢹⣿⠗⢺⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⡿⣿⢸⣿⠻⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠃⣼⣟⣼⡿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡏⢽⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠓⠀⠉⣛⢹⡿⣸⣿⣾⣧⡏⢟⢻⣿⡟⣿⣿⠛⣿⣿⣟⣿⣿⡟⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⢿⠟⣿⣆⣀⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠝⠀⠁⢈⣋⣛⢹⢠⡌⣿⣿⠀⣿⣿⠃⣿⣿⢘⣿⣿⡇⣿⣾⣿⣿⣿⣿⠆⢿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣸⢿⣶⢈⣀⣷⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢠⠀⡇⠀⠗⠀⣂⠀⠘⠁⠗⠋⣿⠀⣻⣿⠀⢿⡟⠀⣿⣿⡇⢻⣽⣿⣿⣿⠃⠀⠀⠙⠿⣿⠀⢻⣿⣿⣿⣿⣿⣟⡷⢾⡟⠃⣿⣾⣿⣿⣿⣿⣸⠹⠻⠻⠅⠙⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⡟⠀⠀⠀⠀⢰⡦⣠⣷⡇⠀⠀⠛⠀⢘⠃⠀⠸⢷⣷⣾⣿⡇⢨⣯⣽⣹⠃⠐⠉⠀⠀⠀⠉⠀⠸⣿⣿⣿⣽⣧⣴⣧⡸⠻⠄⣿⣼⣿⣿⣧⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠻⠃⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⡇⠀⠀⠀⠀⢸⣿⣷⣿⠁⠀⠀⠀⠀⠀⣾⠀⢰⠈⠛⡆⣻⡇⠐⡿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⣿⣿⣿⣼⣿⡿⠭⠭⣀⢀⣿⣛⡛⠉⠀⠀⠀⠀⠠⠄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣷⣿⠇⠀⠀⠀⠀⠀⠀⠋⠀⠀⢀⡀⠀⠹⠁⡀⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡏⠍⠙⠋⠀⠀⠀⠀⠻⠿⡿⣷⣦⠀⠀⠀⠀⠀⠂⠑⡠⠟⣽⡙⠐⣦⣀⠀⠀⠀⠘⠛⠛⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⠠⠀⠀⠀⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⡧⠤⠀⢀⠀⠀⣀⡸⢿⡿⣇⣛⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠒⢸⢩⠧⠀⠀⠀⠀⡀⠉⠛⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠄⠤⠤⠀⠉⠀⠁⠀⠀⠈⠁⠂⠀⠀⠀⠀⠀
⢀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⢴⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠄⠰⢠⠀⠀⠀⠠⠠⠄⠂⠀⠀⠀⠀⠀⠀⠐⠙⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[20A⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⢈⡈⣉⡩⢿⡾⠛⠿⠿⠿⠿⡿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡥⠌⠋⠛⠉⠁⠀⠀⠈⠀⠀⠀⠸⠰⠏⠁⠛⠋⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⠀⡄⣀⠴⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⠭⡍⠛⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣆⣾⣶⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣐⣍⢿⢷⣿⣷⠿⢻⣤⡄⠀⣸⣿⣷⣯⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣓⡻⢾⣾⣿⣿⠀⣿⣿⢀⣨⣿⣸⣿⣿⣿⣿⡗⠾⣭⣟⡛⡽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⣿⣿⣿⣿⣿⣧⣬⠙⠃⠀⢻⣟⣿⣶⣯⣽⣻⡷⢶⣿⣾⠃⢠⣿⣾⠉⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠋⣽⠷⠋⢠⣼⢿⡮⣬⣽⣿⣿⣿⣿⣿⣿⢀⣼⣿⡏⢴⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⣼⣿⣼⣶⣶⣤⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⣿⣿⡟⠐⣿⡿⠤⣼⣿⣴⢆⣿⣿⣿⣿⣿⣿⣿⣯⢀⢹⣿⠗⢺⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⡿⣯⢸⣿⠻⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⡼⣟⣸⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡟⡏⢹⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠃⠈⠉⢙⢹⡿⣨⣿⣶⣧⡏⢟⢻⣿⡟⣿⣿⠛⣿⣿⣟⣿⣿⡟⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⢿⠟⣿⣆⣀⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠑⠀⠁⢈⣋⣛⢹⢠⡌⣿⣿⠀⣿⣿⠃⣿⣿⢸⣿⣿⡇⣿⣾⣿⣿⣿⣿⠆⢿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣸⢿⣶⢈⣈⣷⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢠⠀⡏⠀⠗⠀⣂⠀⠘⠁⠗⠛⣿⠀⢿⣿⠀⢿⡏⠀⣿⣿⡇⢻⣽⣿⣿⣿⠃⠀⠀⠙⠿⣿⠀⢻⣿⣿⣿⣿⣿⣟⡷⢾⡟⠃⣿⣾⣿⣿⣿⣿⣼⠹⠻⠻⠅⠙⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⡟⠀⠀⠀⠀⢰⡦⣠⣷⡇⠀⠀⠛⠀⢘⠃⠀⠸⢲⣷⠾⢾⡇⠸⣯⣽⣹⠃⠐⠉⠀⠀⠀⠉⠀⠸⣿⣿⣿⣽⣧⣴⣧⡸⢻⠄⣿⣼⣿⣿⣧⡏⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠻⠃⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⡇⠀⠀⠀⠀⢸⣿⣷⣿⠁⠀⠀⠀⠀⠀⣾⠀⢰⠈⠙⡀⠘⡇⠀⡿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⣿⣿⣿⣼⣿⡿⠭⠭⣀⣀⣿⣛⡛⠉⠀⠀⠀⠀⠀⠀⣄⣀⣀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣧⣿⡏⠀⠀⠀⠀⠀⠀⠋⠀⠀⢀⡀⠀⠰⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡏⠍⠙⠋⠀⠀⠀⠀⠻⠿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠴⢑⣠⣏⣽⡳⢦⣀⠀⠀⠀⠘⠛⠛⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣾⡧⠄⠀⣀⠀⢀⣀⡹⢿⡿⣇⣛⣃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⢸⢩⠧⠀⠀⠀⠀⡀⠉⠛⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢯⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⠀⠠⠤⠀⠉⠀⠁⠀⠀⠈⠁⠂⠀⠀⠀⠀⠀
⢀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⠴⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠂
⠁⠄⠰⢠⠀⠀⠀⠠⠠⠄⠂⠀⠀⠀⠀⠀⠀⠐⠙⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[20A⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣈⣙⣂⣍⣋⢽⡿⠿⠿⠿⠿⠿⡿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⠀⠀⢀⠤⠈⠃⠛⠉⠉⠀⠀⠈⠀⠀⠀⠰⠰⠏⠁⠛⠋⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣀⣀⠴⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⠭⡍⠛⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣗⣾⣷⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣐⣍⢿⢷⣿⣷⠿⢻⣤⡄⠀⣸⣿⣷⣭⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣓⡻⢾⣿⣿⣿⠀⣿⣿⠀⣨⣿⣹⣿⣿⣿⣿⡗⠾⣭⣟⡛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⣿⣿⣿⣿⣿⣧⣬⠛⠃⠀⢻⣟⣿⣶⣯⣽⣻⡷⢦⣿⣾⠃⢠⣿⣾⠉⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣻⣿⡆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠋⣽⡷⠋⢠⣼⢿⡮⣬⣽⣿⣿⣿⣿⣿⣿⢀⣼⣿⡏⢴⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⣼⡿⣼⣶⣶⣤⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⣿⣿⡟⠐⣿⡿⠬⣾⡿⣴⣆⣿⣿⣿⣿⣿⣿⣿⣯⢀⢹⣿⠗⢺⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⡿⣿⢸⣿⠻⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠂⣼⣿⣼⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡟⡏⢹⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠂⠀⠉⡛⢹⡿⣸⣿⣾⣧⡟⢟⢻⣿⡟⣿⣿⠛⣿⣿⣟⣿⣿⡟⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⢿⠟⣿⣆⣀⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠑⠀⠁⢈⣋⣛⢹⢠⡌⣿⣿⠀⣿⣿⠃⣿⣿⢸⣿⣿⡇⣿⣾⣿⣿⣿⣿⠆⢿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣸⢿⣶⢈⣀⣷⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣠⠀⡏⠀⠣⠀⣂⠈⠘⠁⠗⠋⣿⠀⢻⣿⠀⢿⡟⠀⣿⣿⡇⢻⣽⣿⣿⣿⠃⠀⢀⠙⠿⣿⠀⢻⣿⣿⣿⣿⣿⣟⡷⢾⡟⠃⣿⣾⣿⣿⣿⣿⣜⠹⠻⠻⠅⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⡟⠀⠀⠀⠀⢰⡦⣠⣷⡇⠀⠀⠛⠀⢸⡇⠀⠸⢳⣷⠚⠛⡇⠈⠭⠽⢹⠃⠐⠉⠀⠀⠀⠁⠀⠸⣿⣿⣿⣽⣧⣴⣧⡸⢻⠄⣿⣼⣿⣿⣧⡏⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠻⠃⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⡇⠀⠀⠀⠀⢸⣿⣳⣿⠁⠀⠀⠀⠀⠀⣾⠀⢠⠈⠙⡀⠀⡇⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣿⣿⣿⣼⣿⡿⠭⠭⣀⢀⣿⣛⡛⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣧⣿⡏⠀⠀⠀⠀⠀⠀⠋⠀⠀⢀⡀⠀⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡏⠉⠙⠋⠀⠀⠀⠀⠻⣿⢿⣷⣦⣄⢀⠀⠀⠀⠀⠀⢰⣛⣛⣛⣟⡆⣀⠀⠀⠀⠘⠛⠛⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⡧⠄⠀⣀⠀⣀⣀⠿⣿⢿⣃⣛⣃⣈⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢸⢩⠧⠀⠀⠀⠀⡀⠉⠛⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣿⠁⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠂⠀⠀⠄⠠⠠⠄⠉⠀⠁⠀⠀⠈⠁⠂⠀⠀⠀⠀⠀
⢀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⢴⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠂
⠁⠄⠰⢠⠀⠀⠀⠠⠠⠄⠂⠀⠀⠀⠀⠀⠀⠐⠙⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[20A⠀⠀⠀⠀⠀⠀⠀⠁⠉⢀⢈⣈⣀⣥⡿⣿⣿⠿⠿⠿⠿⠿⡿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⢀⡵⠅⠃⠋⠉⠉⠀⠀⠈⠀⠀⠀⠸⠰⠏⠁⠛⠋⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢄⡡⡼⠎⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⠭⡍⠛⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡶⣼⣺⣿⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣐⣍⢿⢷⣿⣷⠿⢻⣤⡄⠀⣸⣿⣷⣭⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣓⣻⢾⣿⣿⣿⠀⣿⣿⠀⣨⣿⣹⣿⣿⣿⣿⡗⠾⣭⣟⡛⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣌⢿⣿⡇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣧⣬⠛⠃⠀⢻⣟⣿⣶⣯⣽⣻⡷⢦⣿⣾⠃⢠⣿⣾⠉⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣯⢻⡆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠉⣽⢷⠋⢠⣼⢿⡿⣬⣿⣿⣿⣿⣿⣿⣿⢀⣼⣿⡏⢴⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⣼⡿⣼⣶⣶⣤⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⣿⣿⡟⠐⣿⡿⠬⣾⣿⣴⣆⣿⣿⣿⣿⣿⣿⣿⣯⢀⢹⣿⠗⢺⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡿⣿⢸⣿⠻⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠂⣼⣿⣼⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡏⡏⢹⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠈⢛⣛⢹⡿⣨⣿⣾⣧⡟⢟⢻⣿⡟⣿⣿⠛⣿⣿⣟⣿⣿⡟⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⢿⠟⣿⣆⣀⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠙⠀⡁⢈⣋⣛⢹⣠⡌⣿⣿⠀⣿⣿⠃⣿⣿⢸⣿⣿⡇⣿⣾⣿⣿⣿⣿⠆⢿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣸⢿⣶⢈⣈⣷⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣠⠀⡋⠀⠗⠀⣂⠈⠘⠁⠗⠛⣿⠀⣻⣿⠀⢿⡟⠀⣿⣿⡇⢻⣽⣿⣿⣿⠃⠀⠀⠙⠿⣿⠀⢻⣿⣿⣿⣿⣿⣟⡷⢾⡟⠃⣿⣿⣿⣿⣿⣿⣘⠹⠻⠻⠅⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⡟⠀⠀⠀⠀⢰⡦⣠⣷⡇⠀⠀⠛⠀⢸⣇⠀⢸⢶⣷⠞⠛⡇⠈⠛⠛⢹⠃⠈⠋⠀⠀⠀⠉⠀⠸⣿⣿⣿⣽⣧⣴⣧⡸⢻⠄⣿⣼⣿⣿⣧⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠻⠃⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⡇⠀⠀⠀⠀⢸⣿⣷⣿⠁⠀⠀⠀⠀⠈⣿⠀⢰⠈⠙⡀⠀⡇⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣿⣿⣿⣼⣿⡿⠭⠭⣀⣀⣿⣛⡛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣧⣿⡏⠀⠀⠀⠀⠀⠀⠏⠀⠀⢀⡀⠀⠲⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠯⡉⠙⠋⠀⠀⠀⠀⠻⠿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⣛⣋⣛⣛⣖⡂⠀⠀⠀⠘⠛⠛⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⣉⡁⢀⣀⠀⣀⣘⣿⡿⣿⣃⣛⣃⣈⣃⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⢩⠧⠀⠀⠀⠀⡀⠉⠛⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⠍⠅⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠂⠀⠠⠄⠠⠄⠉⠀⠁⠀⠀⠈⠁⠂⠀⠀⠀⠀⠀
⢀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⢴⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠂
⠂⠄⠰⢠⠀⠀⠀⠠⠠⠄⠂⠀⠀⠀⠀⠀⠀⠒⠙⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[20A⠀⠀⠀⠀⠀⠈⢀⠩⡉⣻⣻⣿⣿⣿⡿⣿⡿⠿⡿⠿⠿⠿⡿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠀⠀⠀⣤⣭⣶⣿⡿⠟⠛⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠸⠏⠡⠛⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡔⣧⣾⣞⣿⡽⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⡭⡍⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣐⣍⢿⢷⣿⣷⠿⢻⣤⡆⠀⣸⣿⣷⣯⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣛⣻⢾⣿⣿⣿⠀⣿⣿⢀⣨⣿⣹⣿⣿⣿⣿⡗⠾⣭⣟⡛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣧⣬⠛⠃⠀⢻⣟⣿⣶⣯⣽⣿⡷⢶⣿⣾⠃⣴⣿⣾⠹⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡋⣿⣷⠋⢠⣼⢿⡿⣭⣿⣿⣿⣿⣿⣿⣿⢀⣼⣿⡏⢵⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⣼⣿⣼⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⣿⣿⡟⠐⣿⡿⠬⣿⣿⣶⣆⣿⣿⣿⣿⣿⣿⣿⣯⢠⢹⣿⡗⢺⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣿⣗⣿⣿⡿⣿⢷⢸⣿⣿⣶⣦⣤⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⠁⢸⣿⠆⣀⣺⣇⣿⢸⣿⢹⣿⣿⣿⣿⣿⡿⣿⢸⣿⠻⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠿⠸⠿⢿⣿⣿⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣻⣤⣾⣿⠉⢹⣿⢓⡏⣿⡇⣾⣿⣿⣿⣿⣿⡏⡏⢹⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠉⠉⠛⠻⠿⠃⠀⠀⠀⢤⣟⣻⣿⣿⣿⣏⣀⠿⠟⠉⠼⣿⢸⢳⣿⢱⣿⣿⣽⣿⣿⣿⣿⠟⣿⣆⣀⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⢻⣿⡗⠀⣀⡿⣿⢘⡽⣼⣿⣻⣿⣿⣿⣿⣸⢿⣶⢈⣈⣷⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡟⠛⢫⣽⣷⣆⣒⣔⣀⣹⣧⡏⣿⡇⣿⡿⣿⣿⣿⣿⣟⡷⢾⣟⠓⣿⣿⣿⣿⣿⣿⣽⠻⠻⠻⠅⠛⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⢀⣀⣀⠀⡀⠀⠀⠀⠀⠀⠀⢠⣬⣭⡭⠿⠟⠛⠛⠛⠛⠣⠭⠼⠙⣿⣿⣿⣽⣧⣴⣧⡸⢻⠄⣿⣼⣿⣿⣧⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠉⠉⠉⠉⠛⠋⠁⠀⠘⣴⠀⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣵⣿⣼⣿⡿⠯⠭⣄⣐⣿⣛⡛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠲⠤⠤⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢘⣻⣍⣷⠒⡂⠀⠀⠘⠛⠛⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠓⠢⡈⢛⣃⣛⣃⣈⣃⠂⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠂⠧⠀⠀⠀⠀⡀⠉⠛⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠤⠄⠠⠀⠀⠁⠐⠀⠈⠑⠂⠂⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠉⠀⠀⠈⠈⠀⠂⠂⠒
⠀⠀⠲⢶⠀⠰⠄⠠⠰⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[20A⠀⠀⠀⠀⠀⠈⠁⠁⠉⠈⣸⣝⣫⢝⣯⣿⣿⠿⡿⠿⠿⠿⡿⡿⠿⠯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣄⠢⡯⠖⠛⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠰⠏⠡⠛⠋⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠠⢄⢄⣶⠼⠞⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⠭⡍⠛⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣐⣍⢿⢷⣿⣷⠿⢻⣤⡄⠀⣸⣿⣷⣯⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣓⣻⢾⣿⣿⣿⠀⣿⣿⠀⣨⣿⣹⣿⣿⣿⣿⡗⠾⣭⣟⡛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣧⣬⠛⠃⠀⢛⣟⣿⣶⣯⣽⣿⡷⢶⣿⣾⠃⣠⣿⣾⠙⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠋⣽⣷⠋⢠⣼⢿⡿⣬⣿⣿⣿⣿⣿⣿⣿⢀⣼⣿⡏⢵⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⣼⣿⣼⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⣿⣿⡟⠐⣿⡿⠬⣾⣿⣶⣆⣿⣿⣿⣿⣿⣿⣿⣯⢀⢹⣿⠗⢺⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣿⣗⣿⣿⡿⣿⢧⢸⣿⣿⣶⣦⣤⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⠁⢸⣿⠆⣀⣺⣇⣿⢸⣿⢹⣿⣿⣿⣿⣿⡿⣿⢸⣿⠻⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠿⠸⠿⢿⣷⣿⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣻⣤⣾⣿⠉⠹⣿⢳⡏⣿⡇⣾⣿⣿⣿⢿⣿⡏⡏⢹⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠉⠉⠛⠛⠿⠃⠀⠀⠀⢠⣟⣻⣿⣿⣿⣏⡀⠿⠟⠉⠼⣿⢸⢡⣿⢱⣿⣿⣽⣿⣿⣿⢻⠟⣿⣆⣀⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠿⢻⣿⡗⠀⣀⡿⣿⢘⡽⣼⣿⣻⣿⣿⣿⣿⣸⢿⣶⢈⣈⣷⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡟⠛⢫⣽⣷⣆⣒⣅⣀⣹⣧⡏⣿⡇⣿⡿⣿⣿⣿⣿⣟⡷⢾⡟⠓⣾⣿⣿⣿⣿⣿⣼⠻⠻⠻⠍⠙⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⢀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⣬⣭⣭⣿⣿⣛⡛⠿⠿⠣⠍⠼⠽⠿⠯⠿⣽⣧⣴⣧⡸⢳⠄⣿⣼⣿⣿⣧⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠉⠉⠉⠉⠛⠋⠁⠀⠘⠔⠐⠚⢛⠛⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⢼⣿⣭⣭⣀⣐⣿⣛⡛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠹⠿⠿⠷⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠋⢑⡒⡒⠀⠀⠘⠛⠛⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠠⣶⡆⣶⣶⠀⢠⣶⢶⣤⠀⢰⣶⣶⢰⣶⣶⣶⠀⠀⣶⣶⣶⣄⢰⣶⡆⣶⡆⢰⣶⠀⢰⣶⠀⣶⡆⢰⡆⢀⣴⢶⣦⡀⠀⢰⣶⡀⣶⡆⢨⣷⢶⣤⠀⠀⠀⠀⢀⣶⣶⠀⠀⣶⣶⡆⢠⣶⢶⣄⠈⣽⡶⣦⡌⠉
⠀⠀⠀⣿⡇⣿⣿⠀⣿⣿⢸⣿⠀⣿⡟⣿⡀⢸⣿⠀⠀⠀⣿⣧⣼⡿⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⣷⣼⡇⢸⣿⠀⠛⡃⠀⢸⣿⣧⣿⡇⣿⣿⢸⣿⠀⠀⠀⠀⣼⢻⣿⠀⣸⡟⣿⡇⠉⢉⣼⡟⠀⣿⡇⣿⡇⠀
⠀⠀⠀⣿⡇⣿⣿⠀⢿⣿⢸⣿⢀⣿⣧⣿⡇⢸⣿⠀⠀⠀⣿⡏⢹⣷⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⡻⣿⡇⢸⣿⠈⣿⡇⠀⢸⣿⢻⣿⡇⣿⣿⢸⣿⠀⠀⠀⢰⣿⣼⣿⣤⣿⣤⣿⣧⢴⣦⢹⣿⠀⣿⡇⣿⡇⠀
⠀⠀⠰⢿⠇⠿⠟⠻⠸⠿⠾⠋⠘⠛⠁⠛⠃⠘⠛⠀⠀⠀⠛⠃⠘⠛⠈⠛⠷⠟⠁⠘⠛⠛⠘⠛⠀⠛⠃⠛⠃⠈⠻⠟⠛⠃⠀⠘⠛⠈⠛⠃⠘⠻⠾⠋⠘⠛⠀⠀⠀⠘⠛⠀⠀⠘⠛⠃⠘⠻⠾⠋⠀⠛⠷⠟⠁⠀
[20A⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⣻⣻⣯⣿⣿⣿⣿⠿⡿⠿⠿⠿⡿⡿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠀⠀⠀⠀⠀⢤⢸⡽⠝⠛⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠰⠏⠡⠛⠋⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠠⣤⣤⣿⠼⠞⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⠭⡍⠛⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣐⣍⢿⢷⣿⣷⠿⢻⣤⡄⠀⣸⣿⣷⣯⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣛⣻⣾⣿⣿⣿⠀⣿⣿⠠⣨⣿⣹⣿⣿⣿⣿⡗⠾⣭⣟⡛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣧⣬⠛⠃⠀⢛⣟⣿⣶⣯⣽⣻⡷⢶⣿⣾⠃⣠⣿⣾⠙⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣿⣿⣿⣿⠋⣿⣷⠋⢠⣼⢿⡿⣬⣿⣿⣿⣿⣿⣿⣿⢀⣼⣿⡏⢴⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⣼⣿⣼⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⣿⣿⡟⠐⣿⡿⠬⣿⣿⣶⣇⣿⣿⣿⣿⣿⣿⣿⣯⢠⢹⣿⡗⢺⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣿⣗⣿⣿⡿⣿⢧⢸⣿⣿⣶⣦⣤⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⠁⢸⣿⠆⣀⣺⣇⣿⢸⣿⢹⣿⣿⣿⣿⣿⡿⣿⢸⣿⠻⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠿⠸⠿⢿⣷⣿⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣻⣤⣾⣿⠉⢹⣿⢳⡏⣿⡇⣾⣿⣿⣿⣿⣿⡏⡏⢹⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠉⠉⠛⠛⠿⠃⠀⠀⠀⢦⣟⣻⣿⣿⣿⣏⣀⠿⠟⠉⠸⣿⠸⢣⣿⢱⣿⣿⣽⣿⣿⣿⣿⠟⣿⣆⣀⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⢻⣿⡗⠀⣀⡿⣿⢘⡽⣼⣿⣻⣿⣿⣿⣿⣸⢿⣶⢈⣈⣷⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡟⠛⢫⣽⣷⣆⣐⣅⣀⣹⣧⡏⣿⡇⣿⡿⣿⣿⣿⣿⣟⡷⢾⣟⠓⣿⣿⣿⣿⣿⣿⣼⠹⠻⠻⠍⠛⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⢀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⣬⣭⣭⣿⣿⣟⣛⣻⠟⠃⠉⠸⠽⠿⠯⠿⠽⠧⢴⣧⡸⢻⠄⣿⣼⣿⣿⣧⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠉⠉⠉⠉⠙⠋⠁⠀⠘⠒⠚⠚⠛⢿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢑⢢⢿⣛⡛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠒⠢⠤⠤⡀⠀⠀⠀⠀⠀⠀⢘⠓⢒⢒⠄⠀⠘⠛⠛⢿⣿⣿⣿⣿⣿⣿
⠀⠀⢠⣶⡆⣶⣶⠀⢠⣶⢶⣤⠀⢰⣶⣶⢰⣶⣶⣶⠀⠀⣶⣶⣶⣄⢰⣶⡆⣶⡆⢰⣶⠀⢰⣶⠀⣶⡆⢰⡆⢀⣴⢶⣦⡀⠀⢰⣶⡀⣶⡆⢩⣶⢶⣤⠀⠀⠀⠀⢀⣶⣶⠀⠁⣶⣶⡆⢠⣶⢶⣄⠈⣽⡶⣦⡌⠉
⠀⠀⢸⣿⡇⣿⣿⠀⣿⣿⢸⣿⠀⣿⡟⣿⡀⢸⣿⠀⠀⠀⣿⣧⣼⡿⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⣷⣼⡇⢸⣿⢀⢛⡃⠀⢸⣿⣧⣿⡇⣿⣿⢸⣿⠀⠐⠂⠀⣼⢻⣿⠀⣸⡟⣿⡇⠉⢉⣼⡟⠀⣿⡇⣿⡇⠀
⠀⠀⢸⣿⡇⣿⣿⠀⣿⣿⢸⣿⢀⣿⣧⣿⡇⢸⣿⠀⠀⠀⣿⡏⢹⣷⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⡻⣿⡇⢸⣿⠈⣿⡇⠀⢸⣿⢻⣿⡇⣿⣿⢸⣿⠀⠀⠀⢰⣿⣼⣿⣤⣿⣤⣿⣧⢴⣦⢹⣿⠀⣿⡇⣿⡇⠀
⠀⠀⠸⢿⠇⠿⠟⠻⠸⠿⠾⠋⠘⠛⠁⠛⠃⠘⠛⠀⠀⠀⠛⠃⠘⠛⠈⠛⠷⠟⠁⠘⠛⠛⠘⠛⠀⠛⠃⠛⠃⠈⠻⠟⠛⠃⠀⠘⠛⠈⠛⠃⠘⠻⠾⠋⠘⠛⠀⠀⠀⠘⠛⠀⠀⠘⠛⠃⠘⠻⠾⠛⠀⠛⠷⠟⠁⠀
[20A⠀⠀⠀⠀⠀⠈⠀⠉⠉⠙⢻⣟⣯⣿⣿⣿⣿⠿⡿⠿⠿⠿⡿⡿⠿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⠀⢀⢸⡽⠝⠻⠋⠉⠉⠀⠀⠈⠀⠀⠀⠸⠸⠋⠡⠛⠋⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⢤⣤⣄⣶⠼⠞⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⠭⡍⠛⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣾⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣐⣍⢿⢷⣿⣷⠿⢻⣤⡄⠀⣸⣿⣷⣯⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣛⣻⢾⣿⣿⣿⠀⣿⣿⠀⣨⣿⣹⣿⣿⣿⣿⡗⠾⣭⣟⡋⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣧⣬⠛⠃⠀⢻⣟⣿⣶⣯⣽⣻⡷⢶⣿⣾⠃⣰⣿⣾⠩⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠋⣿⣷⠋⢠⣼⢿⡯⣬⣿⣿⣿⣿⣿⣿⣿⢀⣼⣿⡏⢴⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⣼⣿⣼⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⣿⣿⡟⠐⣿⡿⠬⣿⣿⣶⣆⣿⣿⣿⣿⣿⣿⣿⣯⢠⢹⣿⠗⢺⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣿⣗⣿⣿⡿⣿⢧⢸⣿⣿⣶⣦⣤⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⠁⢸⣿⠆⣀⣺⣇⣿⢸⣿⢹⣿⣿⣿⣿⣿⡿⣿⢸⣿⠻⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠿⠸⠿⢿⣷⣿⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣻⣤⣾⣿⠉⢹⣿⢳⡏⣿⡇⣾⣿⣿⣿⣿⣿⡏⡏⢹⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠉⠉⠛⠛⠿⠃⠀⠀⠀⢦⣟⣻⣿⣿⣿⣏⣀⠿⠟⠉⠼⣿⢸⢣⣿⢱⣿⣿⣽⣿⣿⣿⢿⠟⣿⣆⣀⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⡿⢻⣿⡟⠀⣀⡿⡻⠘⡿⣼⣿⣻⣿⣿⣿⣿⢸⢿⣶⢈⣈⣷⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡟⠛⢫⣽⣷⣆⣒⣅⣀⣹⣧⡏⣾⡇⣿⡿⣿⣿⣿⣿⣟⡷⢾⣟⠓⣿⣿⣿⣿⣿⣿⣼⠹⠿⠿⠅⠛⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⢀⣀⠀⡀⡀⠀⠀⠀⠀⠀⠀⢠⣬⣭⣭⣿⣿⣟⣛⣻⠟⢃⠉⠸⡙⣿⣏⣿⣽⡧⠴⠧⠼⠿⠄⠿⠼⠿⣿⣧⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠉⠉⠉⠉⠘⠉⠁⠀⠘⠒⠚⣿⢻⡟⣿⣿⣿⣿⣿⣿⠆⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠉⠈⠓⠶⠤⠀⠀⢀⣄⣀⣀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⠗⠿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠴⠬⢥⠀⠲⠒⠢⠤⠘⠛⠛⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠠⣶⡆⣶⣶⠀⢠⣶⢶⣤⠀⢰⣶⣶⢰⣶⣶⣶⠀⠀⣶⣶⣶⣄⢰⣶⡆⣶⡆⢰⣶⠀⢰⣶⠀⣶⡆⢰⡆⢀⣴⢶⣦⡀⠀⢰⣶⡀⣶⡆⢠⣶⢶⣤⠀⠀⠀⠀⢀⣶⣶⠀⠁⣶⣶⡆⢠⣶⢶⣄⠈⣽⡶⣦⡌⠉
⠀⠀⠀⣿⡇⣿⣿⠀⣿⣿⢸⣿⠀⣿⡟⣿⡀⢸⣿⠀⠀⠀⣿⣧⣼⡿⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⣷⣼⡇⢸⣿⢀⢛⡃⠀⢸⣿⣧⣿⡇⣿⣿⢸⣿⠀⠀⠀⠀⣼⢻⣿⠀⣸⡟⣿⡇⠉⢉⣼⡟⠀⣿⡇⣿⡇⠀
⠀⠀⠀⣿⡇⣿⣿⠀⢿⣿⢸⣿⢀⣿⣧⣿⡇⢸⣿⠀⠀⠀⣿⡏⢹⣷⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⡻⣿⡇⢸⣿⠈⣿⡇⠀⢸⣿⢻⣿⡇⣿⣿⢸⣿⠀⠀⠀⢰⣿⣼⣿⣤⣿⣤⣿⣧⢴⣦⢹⣿⠀⣿⡇⣿⡇⠀
⠀⠀⠰⢿⠇⠿⠟⠻⠸⠿⠾⠋⠘⠛⠁⠛⠃⠘⠛⠀⠀⠀⠛⠃⠘⠛⠈⠛⠷⠟⠁⠘⠛⠛⠘⠛⠀⠛⠃⠛⠃⠈⠻⠟⠛⠃⠀⠘⠛⠈⠛⠃⠘⠻⠾⠋⠘⠛⠀⠀⠀⠘⠛⠀⠀⠀⠛⠃⠘⠻⠾⠋⠀⠛⠷⠟⠁⠀
[20A⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣻⣿⣯⣽⣿⣿⣿⠿⡿⠿⠿⠿⡿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⠀⢀⢰⡍⠝⠛⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠸⠏⠡⠛⠋⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠠⣤⣠⣶⡽⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⠭⡍⠛⡋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣐⣏⢿⢿⣿⣷⠿⢻⣤⡄⠀⣸⣿⣷⣯⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣛⣻⣾⣿⣿⣿⠀⣿⣿⢠⣨⣿⣹⣿⣿⣿⣿⡗⠾⣭⣟⡋⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡏⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣧⣬⠛⠃⠀⢻⣟⣿⣶⣯⣽⣿⡷⢦⣿⣾⠃⣠⣿⣾⠩⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠋⣿⣷⠋⢠⣼⢿⡿⣬⣿⣿⣿⣿⣿⣿⣿⢀⣼⣿⡏⢴⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⣼⣿⣼⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⣿⣿⡟⠐⣿⡿⠬⣿⣿⣶⣆⣿⣿⣿⣿⣿⣿⣿⣯⢠⢹⣿⡗⢺⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣿⣗⣿⣿⡿⣿⢧⢸⣿⣿⣶⣦⣤⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⠁⢸⣿⠆⣀⣞⣇⣿⢸⣿⢹⣿⣿⣿⣿⣿⡿⣿⢸⣿⠻⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠿⠸⠿⢿⣷⣿⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣻⣤⣾⣿⠉⢹⣿⢳⡏⣿⡇⣾⣿⣿⣿⣿⣿⡏⡏⢹⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠉⠉⠛⠻⠿⠃⠀⠀⠀⢦⣏⣻⣿⣿⣿⣏⣀⠿⠿⠩⠸⣿⢸⢧⣿⢱⣿⣿⣽⣿⣿⣿⢿⠟⣷⣆⣀⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⢻⣿⡟⠀⣀⡿⣻⢘⡹⣼⣿⣻⣿⣿⣿⣿⢸⢿⣶⠈⣈⡷⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡟⠛⢫⣽⣷⣆⣓⣅⣀⣹⣧⡏⣿⡇⣿⡿⣿⣿⣿⣿⣟⡷⢾⡟⠓⣿⣿⣿⣿⣿⣿⣼⠻⠿⠿⠅⠙⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⢀⠀⢀⣀⡀⡀⡀⠀⠀⠀⠀⠀⠀⢠⣬⣭⣭⣿⣿⣟⣛⣻⠟⢃⠉⠸⡙⣿⣏⣿⣽⣧⣴⠧⠼⠛⠐⠛⢚⠛⠛⠃⠯⢄⣀⡀⠀⠀⠀⠀⠀⠉⠉⠿⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠉⠉⠉⠙⠛⠉⠁⠀⠘⠒⡚⣿⢻⡿⣿⣿⣿⣿⣿⣿⣖⠸⠀⠀⠁⠉⠁⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⢀⣒⣀⢤⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠸⠼⠿⠿⠿⠿⠛⢛⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⠑⠢⠤⠜⠛⠛⢿⣿⣿⣿⣿⣿⣿
⠀⠀⢠⣶⡆⣶⣶⠀⢠⣶⢶⣤⠀⢰⣶⣶⢰⣶⣶⣶⠀⠀⣶⣶⣶⣄⢰⣶⡆⣶⡆⢰⣶⠀⢰⣶⠀⣶⡆⢰⡆⢀⣴⢶⣦⡀⠀⢰⣶⡀⣶⡆⢠⣶⢶⣤⠀⠀⠀⠀⢀⣶⣶⠀⠈⣶⣶⡆⢠⣶⢶⣤⠈⣽⡶⣦⡌⠉
⠀⠀⢠⣿⡇⣿⣿⠀⣿⣿⢸⣿⠀⣿⡟⣿⡀⢸⣿⠀⠀⠀⣿⣧⣼⡿⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⣷⣼⡇⢸⣿⠀⡛⡃⠀⢸⣿⣧⣿⡇⣿⣿⢸⣿⠀⠀⠀⠀⣼⢻⣿⠀⣸⡟⣿⡇⠉⢉⣼⡟⠀⣿⡇⣿⡇⠀
⠀⠀⢈⣿⡇⣿⣿⠀⣿⣿⢸⣿⢀⣿⣧⣿⡇⢸⣿⠀⠀⠀⣿⡏⢹⣷⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⡿⣿⡇⢸⣿⠈⣿⡇⠀⢸⣿⢻⣿⡇⣿⣿⢸⣿⠀⠀⠀⢰⣿⣼⣿⣤⣿⣤⣿⣧⢴⣦⢹⣿⠀⣿⡇⣿⡇⠀
⠀⠀⠸⢿⠇⠿⠟⠻⠸⠿⠾⠋⠘⠛⠁⠛⠃⠘⠛⠀⠀⠀⠛⠓⠘⠛⠈⠛⠷⠟⠁⠘⠛⠛⠘⠛⠀⠛⠃⠛⠃⠈⠻⠟⠛⠃⠀⠘⠛⠈⠛⠃⠘⠻⠾⠋⠘⠛⠀⠀⠀⠘⠛⠀⠀⠈⠛⠃⠘⠻⠾⠋⠀⠛⠷⠟⠁⠀
[20A⠀⠀⠠⠀⠀⠉⠉⣉⣉⣿⣻⣿⣯⣿⣿⣿⣿⠿⠿⠿⠿⠿⡿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⠀⢤⢤⣶⣺⡿⠟⠛⠋⠉⠉⠀⠀⠈⠀⠀⠀⠸⠸⠏⠡⠛⠋⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣳⣶⣾⣾⣿⣿⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⠭⡍⠛⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣔⣍⢿⢿⣿⣷⠿⢻⣤⡄⠀⣸⣿⣷⣯⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣛⣻⣾⣿⣿⣿⠀⣿⣿⢠⣨⣿⣹⣿⣿⣿⣿⡗⠾⣭⣟⡛⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣧⣬⠛⠃⠀⢻⣟⣿⣶⣯⣽⣿⡷⢦⣿⣾⠃⣠⣿⣾⠹⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠋⣿⣷⠋⢤⣼⢿⡿⣭⣿⣿⣿⣿⣿⣿⣿⢀⣼⣿⡏⢴⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⣼⣿⣼⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⣿⣿⡟⢐⣿⡿⠬⣿⣿⣶⣆⣿⣿⣿⣿⣿⣿⣿⣯⢨⢹⣿⠗⢺⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣿⣷⣿⣿⡿⣿⢧⢸⣿⣿⣶⣦⣤⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⠁⢸⣿⠆⣀⣾⣇⣿⢸⣿⢹⣿⣿⣿⣿⣿⡿⣿⢸⣿⠿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠿⠸⠿⢿⣷⣿⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣻⣿⣻⣤⣾⣿⠈⢹⣿⢳⡏⣿⡇⣿⣿⣿⣿⣿⣿⡏⡏⢹⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠉⠙⠛⠻⠿⠃⠀⠀⠀⢤⣏⣿⣿⣿⣿⣏⡀⠿⠿⠉⠸⣛⢸⢣⢿⢱⣿⣿⣽⣿⣿⣿⢿⠟⣿⣆⣀⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⡿⢻⣿⡟⠀⣀⡿⣿⢘⡿⣼⣿⣻⣿⣿⣿⣿⣸⢿⣶⠈⣈⡷⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡟⠛⢫⣽⣷⣆⣛⣗⣀⣹⣧⡏⣿⡇⣿⡿⣿⣿⣿⣿⣟⡷⢾⣟⠓⣿⣿⣿⣿⣿⣿⣼⠽⠿⠿⠅⠛⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⢀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣬⣭⣭⣿⣿⣟⣛⣻⠟⢃⠉⠸⡙⣿⣏⣿⣽⣧⣴⣧⠼⠟⠐⠋⠈⠉⠭⣥⠍⠉⠒⠒⠂⠠⠄⠠⠤⠉⠙⣛⣓⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠉⠉⠉⠙⠉⠉⠁⠀⠘⣴⠚⣿⢻⢿⣿⣿⣿⣿⣿⣿⣖⢸⠐⣆⠁⠋⠁⠉⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⡬⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠃⠸⠸⠿⠿⠿⠿⠛⢛⠿⠸⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠜⠛⠛⢿⣿⣿⣿⣿⣿⣿
⠀⠀⢠⣶⡆⣶⣶⠀⢠⣶⢶⣤⠀⢰⣶⣶⢰⣶⣶⣶⠀⠀⣶⣶⣶⣄⢰⣶⡆⣶⡆⢰⣶⠀⢰⣶⠀⣶⡆⢰⡆⢀⣴⢶⣦⡀⠀⢰⣶⡀⣶⡆⢠⣶⢶⣤⠀⠀⠀⠀⢀⣶⣶⠀⠀⣶⣶⡆⢠⣶⢶⣤⠈⣽⡶⣦⡌⠉
⠀⠀⠀⣿⡇⣿⣿⠀⣿⣿⢸⣿⠀⣿⡟⣿⡀⢸⣿⠀⠀⠀⣿⣧⣼⡿⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⣷⣼⡇⢸⣿⢀⢛⡃⠀⢸⣿⣧⣿⡇⣿⣿⢸⣿⠀⠀⠂⠀⣼⢻⣿⠀⣸⡟⣿⡇⠉⢉⣼⡟⠀⣿⡇⣿⡇⠀
⠀⠀⠀⣿⡇⣿⣿⠀⣿⣿⢸⣿⢀⣿⣧⣿⡇⢸⣿⠀⠀⠀⣿⡏⢹⣷⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⡿⣿⡇⢸⣿⠈⣿⡇⠀⢸⣿⢻⣿⡇⣿⣿⢸⣿⠀⠀⠀⢰⣿⣼⣿⣤⣿⣤⣿⣧⢴⣦⢹⣿⠀⣿⡇⣿⡇⠀
⠀⠀⠰⢿⠇⠿⠟⠻⠸⠿⠾⠋⠘⠛⠁⠛⠓⠘⠛⠀⠀⠀⠛⠓⠘⠛⠈⠛⠷⠟⠁⠘⠛⠛⠘⠛⠀⠛⠃⠛⠃⠈⠻⠟⠛⠃⠀⠘⠛⠈⠛⠃⠘⠻⠾⠋⠘⠛⠀⠀⠀⠘⠛⠀⠀⠘⠛⠃⠘⠻⠾⠛⠀⠛⠷⠟⠁⠀
[20A⠀⠀⠀⠀⠈⠈⢈⣩⣝⢿⣛⣻⣯⣿⣿⣿⣿⠿⡿⠿⠿⠿⡿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢄⠀⣠⣤⣿⣾⡿⠟⠛⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠸⠏⠡⠛⠋⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⢿⣶⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⠭⡍⠛⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣔⣏⢿⢿⣿⣷⠿⢻⣤⡄⠀⣸⣿⣷⣯⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣛⣻⣾⣿⣿⣿⠀⣿⣿⢠⣸⣿⣹⣿⣿⣿⣿⡷⠾⣭⣟⡛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣧⣬⠛⠃⠀⢻⣟⣿⣶⣯⣽⣻⡷⢦⣿⣾⠃⣰⣿⣾⠻⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣿⣿⣿⣿⣿⣿⡉⣿⣷⠋⢤⣼⢿⡿⣮⣿⣿⣿⣿⣿⣿⣿⢀⣼⣿⡏⢴⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⣼⡿⣼⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⣿⣿⡟⠐⣿⡿⠬⣿⣿⣶⣇⣿⣿⣿⣿⣿⣿⣿⣯⢨⢹⣿⡗⢺⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣿⣷⣿⣿⣿⣿⢧⢸⣿⣿⣶⣦⣤⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⠁⢸⣿⡆⣀⣿⣇⣿⢸⣿⢹⣿⣿⣿⣯⣿⡿⣿⢸⣿⠿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠿⠸⠿⢿⣷⣿⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣻⣤⣾⣿⠉⢙⣿⢳⡏⣿⡇⣿⣿⣿⣿⣿⣿⡟⡟⢹⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠙⠛⠛⠿⠃⠀⠀⠀⢠⣿⣿⣿⣿⣿⣏⣁⠿⠿⠡⠼⣿⢸⢳⣶⢳⣿⣿⣽⣿⣿⣿⢿⠟⣿⣆⣀⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⡿⢻⣿⡿⠀⣀⡿⣿⢘⡿⣼⣿⣻⣿⣿⣷⣿⣸⢿⣶⢈⣈⣷⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡟⠛⢫⣽⣷⣆⣛⣗⣀⣹⣧⡏⣾⡇⣿⡿⣿⣿⣿⣿⣟⡷⢾⣟⠓⣿⣿⣿⡿⠿⠿⠼⠿⢿⣿⣁⣛⠟⣿⠿⠿⠿⢛⣛⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⢀⠀⢀⣀⣀⠀⡀⠀⠀⠀⠀⠀⠀⣠⣬⣭⣭⣿⣿⣟⣛⣻⠟⢃⠉⠸⡙⣿⣏⣿⣿⣧⣴⣧⡸⠿⠀⠉⠀⠀⠰⣦⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠉⠉⠉⠉⠉⠉⠁⢠⠘⣴⠚⣿⢻⢻⣿⣿⣿⣿⣿⣿⣆⢸⠐⣆⣅⣿⠷⠋⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠘⠋⠸⠺⠿⠿⠿⠿⠛⢛⠿⠸⡀⢹⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠤⠼⠛⠛⢿⣿⣿⣿⣿⣿⣿
⠀⠀⢰⣶⡆⣶⣶⠀⢠⣶⢶⣤⠀⢰⣶⣶⢰⣶⣶⣶⠀⠀⣶⣶⣶⣄⢰⣶⡆⣶⡆⢰⣶⠀⢰⣶⠀⣶⡆⢰⡆⢀⣴⢶⣦⡀⠀⢰⣶⡀⣶⡆⢠⣶⢶⣤⠀⠀⠀⠀⢀⣶⣶⠀⠀⣶⣶⡆⢠⣶⢶⣤⠈⣽⡶⣦⡌⠉
⠀⠀⢸⣿⡇⣿⣿⠀⣿⣿⢸⣿⠀⣿⡟⣿⡀⢸⣿⠀⠀⠀⣿⣧⣼⡿⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⣷⣼⡇⢸⣿⢀⣛⡃⠀⢸⣿⣧⣿⡇⣿⣿⢸⣿⠀⠀⠐⠀⣼⢻⣿⠀⣸⡟⣿⡇⠉⢉⣼⡟⠀⣿⡇⣿⡇⠀
⠀⠀⢸⣿⡇⣿⣿⠀⣿⣿⢸⣿⢀⣿⣧⣿⡇⢸⣿⠀⠀⠀⣿⡏⢹⣷⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⡿⣿⡇⢸⣿⠈⣿⡇⠀⢸⣿⢻⣿⡇⣿⣿⢸⣿⠀⠀⠀⢰⣿⣼⣿⣤⣿⣤⣿⣧⢴⣦⢹⣿⠀⣿⡇⣿⡇⠀
⠀⠀⠸⢿⠇⠿⠟⠻⠸⠿⠾⠋⠘⠛⠁⠛⠃⠘⠛⠀⠀⠀⠛⠓⠘⠛⠈⠛⠷⠟⠁⠘⠛⠛⠘⠛⠀⠛⠃⠛⠃⠈⠻⠟⠛⠃⠀⠘⠛⠈⠛⠃⠘⠻⠾⠋⠘⠛⠀⠀⠀⠘⠛⠀⠀⠘⠛⠃⠘⠻⠾⠛⠀⠛⠷⠟⠁⠀
[20A⠀⠀⠀⠢⠉⢉⢫⣭⣝⣿⣿⣿⣯⣿⣿⣿⣿⠿⡿⠿⠿⠿⡿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⡀⠔⣴⣖⣥⣦⣿⣿⡿⠟⠻⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠸⠏⠡⠛⠋⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢿⣷⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⡭⡝⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣔⣏⢿⢿⣿⣷⠿⢻⣥⡄⠀⣸⣿⣷⣯⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣛⣻⣾⣿⣿⣿⠀⣿⣿⢠⣸⣿⣹⣿⣿⣿⣿⡷⠾⣭⣟⡛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣧⣬⠟⠃⠀⢻⣟⣿⣶⣯⣽⣿⡷⢷⣿⣾⠃⣰⣿⣾⠻⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⣿⣿⣿⣿⣿⣿⡋⣿⣷⠫⢤⣼⢿⡿⣮⣿⣿⣿⣿⣿⣿⣿⢄⣼⣿⡏⢴⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⣼⡿⣾⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⣿⣿⡟⠐⣿⡿⠬⣿⣿⣶⣇⣿⣿⣿⣿⣿⣿⣿⣯⢨⢹⣿⡗⢺⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣿⣷⣿⣿⣿⣿⢧⢸⣿⣿⣶⣦⣤⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⠁⢸⣿⠆⠀⢾⣇⣿⢸⣿⢹⣿⣿⣿⣿⣿⡿⣿⢸⣿⠿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠿⠸⠿⢿⣿⣿⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣤⣾⣿⠉⢸⣿⢳⡇⣶⡆⣿⣿⣿⣿⣿⣿⡟⡏⢹⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠙⠛⠛⠿⠃⠀⠀⠀⢤⣿⣿⣿⣿⣿⣏⣁⠿⠿⠩⠼⣿⢸⢣⣿⢱⣿⣿⣽⣿⣿⣿⣿⠟⣿⣆⣀⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢛⣛⣯⠭⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⢻⣿⡿⠀⣀⣿⣿⢘⡿⣼⣿⣻⣿⣿⣷⣿⣸⢿⣶⠈⣈⣷⣿⣿⠿⠿⠛⠛⠛⠉⠙⠛⠉⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡟⠛⢫⣽⣷⣆⣛⣗⣀⣹⣧⡏⣿⡇⣿⡿⣿⣿⣿⣿⣟⡷⢾⣟⠓⠿⠋⠁⢠⣶⠞⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⢀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣠⣬⣭⣭⣿⣿⣟⣛⣻⠟⢃⠉⠸⡙⣿⣟⣿⣿⣯⣴⣧⡼⠋⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠉⠉⠉⠉⠙⠏⠁⠀⠘⣜⠚⣿⢻⢻⣿⣿⣿⣿⣿⣿⣶⢸⡐⣆⣅⣿⣷⣿⣼⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⠘⠛⠸⠺⠿⠿⠿⠿⠛⢛⠿⢸⡃⢹⢟⢹⠏⠉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠒⠆⠀⠀⠐⠤⠼⠛⠛⢿⣿⣿⣿⣿⣿⣿
⠀⠀⢰⣶⡆⣶⣶⠀⢠⣶⢶⣤⠀⢰⣶⣶⢰⣶⣶⣶⠀⠀⣶⣶⣶⣄⢰⣶⡆⣶⡆⢰⣶⠀⢰⣶⠀⣶⡆⢰⡇⢀⣴⢶⣦⡀⠀⢰⣶⡀⣶⡆⢠⣶⢶⣤⠀⢻⣪⠀⢢⣶⣶⠀⠀⣶⣶⡆⢠⣶⢶⣤⠈⣽⡶⣦⡌⠉
⠀⠀⢸⣿⡇⣿⣿⠀⣿⣿⢸⣿⠀⣿⡟⣿⡀⢸⣿⠀⠀⠀⣿⣧⣼⡿⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⣿⣼⡇⢸⣿⢀⣛⡃⠀⢸⣿⣧⣿⡇⣿⣿⢸⣿⠀⠀⠀⠀⣼⢻⣿⠀⣸⡟⣿⡇⠉⢉⣼⡟⠀⣿⡇⣿⡇⠀
⠀⠀⢸⣿⡇⣿⣿⠀⣿⣿⢸⣿⢀⣿⣧⣿⡇⢸⣿⠀⠀⠀⣿⣏⢹⣷⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⡿⣿⡇⢸⣿⠈⣿⡇⠀⢸⣿⢻⣿⡇⣿⣿⢸⣿⠀⠀⠀⢰⣿⣼⣿⣤⣿⣤⣿⣧⢴⣦⢹⣿⠀⣿⡇⣿⡇⠀
⠀⠀⠸⢿⠇⠿⠟⠻⠸⠿⠾⠋⠘⠛⠁⠛⠃⠘⠛⠀⠀⠀⠛⠛⠘⠛⠈⠛⠷⠟⠁⠘⠛⠛⠘⠛⠀⠛⠃⠛⠃⠈⠻⠟⠛⠃⠀⠘⠛⠈⠛⠃⠘⠻⠾⠋⠘⠛⠀⠀⠀⠘⠛⠀⠀⠘⠛⠃⠘⠻⠾⠛⠀⠛⠷⠟⠁⠀
[20A⠀⠀⠠⠒⢛⢉⢩⣿⣟⣿⣿⣿⣯⣿⣿⣿⣿⢿⣿⠿⠿⠿⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⡀⡑⣶⣏⣌⣢⣿⣿⡿⠟⠿⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠸⠏⠡⠛⠏⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⡭⡍⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣔⣏⢿⢿⣿⣷⠿⢻⣥⡆⠀⣸⣿⣷⣯⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣛⣻⣾⣿⣿⣿⠀⣿⣿⢠⣸⣿⣽⣿⣿⣿⣿⡷⠾⣭⣟⡛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣧⣬⠟⠃⠀⢻⣟⣿⣶⣯⣽⣿⡷⢷⣿⣾⠃⣰⣿⣾⠻⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⣿⣿⣿⣿⣿⣿⡋⣿⣷⠫⢤⣼⢿⡿⣬⣿⣿⣿⣿⣿⣿⣿⢄⣼⣿⡟⢴⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⣼⡿⣾⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⣿⣿⡟⢐⣿⡿⠬⣿⣿⣶⣇⣿⣿⣿⣿⣿⣿⣿⣯⢨⢹⣿⡗⢺⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣿⣷⣿⣿⣿⣿⢷⢸⣿⣿⣶⣦⣤⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⠃⢸⣿⡆⢀⣛⣇⣿⢸⣿⢹⣿⣿⣿⣿⣿⡿⣿⢸⣿⠿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠿⠸⠿⢿⣿⣿⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣤⣾⣿⠉⢹⣿⢳⡏⣿⡇⣿⣿⣿⣿⣿⣿⡟⡟⢹⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠭⠟⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠙⠛⠛⠿⠃⠀⠀⠀⢤⣿⣿⣿⣿⣿⣏⣁⠿⠿⠩⠼⣿⢸⢣⣿⢱⣿⣿⣽⣿⣿⣿⢿⠟⣿⣆⣀⣿⣽⣿⣿⣿⣿⠿⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⢻⣿⡿⠀⣀⣿⣿⢘⡿⣼⣿⣻⣿⣿⣿⣿⣸⢿⣶⢈⣈⡷⠟⠋⣉⣤⠤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡟⠛⢫⣽⣷⣆⣛⣗⣀⣹⣧⡏⣿⣇⣿⡿⣿⣿⣿⣿⣟⡷⢾⡟⠃⠉⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⢀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢠⣬⣭⣭⣿⣿⣟⣛⣻⠟⢃⠉⠸⡙⣿⣟⣿⣽⣯⣴⣧⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠉⠉⠉⠉⠟⠋⠁⠀⠘⠾⠚⣿⠻⣿⣿⣿⣿⣿⣿⣿⣾⢸⡐⣆⣅⣿⣷⣿⣼⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⠘⠛⠰⠻⠿⠿⠿⠿⠛⢛⠿⢸⠇⢹⠏⠻⠏⢉⣉⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⡀⠀⠀⠀⠂⡦⠀⠀⠀⠠⠼⠛⠛⢿⣿⣿⣿⣿⣿⣿
⠀⠀⢰⣶⡆⣶⣶⠀⢠⣶⢶⣤⠀⢰⣶⣶⢰⣶⣶⣶⠀⠀⣶⣶⣶⣄⢰⣶⡆⣶⡆⢰⣶⠀⢰⣶⠀⣶⡆⢸⡎⢀⣴⢶⣦⡀⠀⢰⣶⡀⣶⡆⢠⣶⢶⣤⠀⠀⠈⠻⢠⣶⣶⠀⠀⣶⣶⡆⢠⣶⢶⣤⠈⣽⡶⣦⡌⠉
⠀⠀⢸⣿⡇⣿⣿⠀⣿⣿⢸⣿⠀⣿⡟⣿⡀⢸⣿⠀⠀⠀⣿⣧⣼⡿⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⣿⣼⡇⢸⣿⢀⣛⡃⠀⢸⣿⣧⣿⡇⣿⣿⢸⣿⠀⠀⠀⠀⣼⢻⣿⠀⣸⡟⣿⡇⠉⢉⣼⡟⠠⣿⡇⣿⡇⠀
⠀⠀⢸⣿⡇⣿⣿⠀⣿⣿⢸⣿⢀⣿⣧⣿⡇⢸⣿⠀⠀⠀⣿⣏⢹⣷⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⡿⣿⡇⢸⣿⠘⣿⡇⠀⢸⣿⢻⣿⡇⣿⣿⢸⣿⠀⠀⠀⢰⣿⣼⣿⣤⣿⣤⣿⣧⢴⣦⢹⣿⠀⣿⡇⣿⡇⠀
⠀⠀⠸⢿⠇⠿⠟⠻⠸⠿⠾⠋⠘⠛⠁⠛⠓⠘⠛⠀⠀⠀⠛⠓⠘⠛⠈⠛⠷⠟⠁⠘⠛⠛⠘⠛⠀⠛⠃⠛⠃⠈⠻⠟⠛⠃⠀⠘⠛⠈⠛⠃⠘⠻⠾⠋⠘⠛⠀⠀⠀⠘⠛⠀⠀⠘⠛⠃⠘⠻⠾⠛⠀⠛⠷⠟⠃⠀
[20A⠈⢀⠩⢿⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣅⣤⣽⣿⣷⣾⣿⣿⣿⡿⠟⠿⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠸⠏⠡⠛⠏⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⡭⡍⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣔⣏⢿⢿⣿⣷⠿⢻⣥⡆⠀⣸⣿⣷⣯⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣛⣻⣾⣿⣿⣿⠀⣿⣿⢠⣸⣿⣽⣿⣿⣿⣿⡷⠾⣭⣟⡛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣯⣬⠟⠃⠀⢻⣟⣿⣶⣯⣽⣿⡷⢷⣿⣾⠃⣱⣿⣾⠻⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⣿⣿⣿⣿⣿⣿⡋⣿⣷⠫⢤⣼⢿⡿⣯⣿⣿⣿⣿⣿⣿⣿⢄⣼⣿⡏⢴⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⣼⡿⣾⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⣿⣿⡟⢐⣿⡿⠬⣿⣿⣶⣇⣿⣿⣿⣿⣿⣿⣿⣯⣨⣹⣿⡗⢺⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣿⣷⣿⣿⣿⣿⢷⢸⣿⣿⣶⣦⣤⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⠓⢸⣿⡆⣀⣿⣧⣿⢸⣿⢹⣿⣿⣿⣿⣿⡿⣿⣸⣿⠿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠫⠭⠋⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠿⠸⠿⢿⣿⣿⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣤⣾⣿⠉⢹⣿⢻⡏⣿⡇⣿⣿⣿⣿⣿⣿⡟⡟⢹⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠙⠛⠻⠿⠃⠀⠀⠀⢤⣿⣿⣿⣿⣿⣏⣁⠿⠿⠩⠼⣿⢸⢳⣿⢳⣿⣿⣽⣿⣿⣿⣿⠟⣿⣆⣀⣿⣽⠿⠟⢋⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢻⣿⡿⠀⣀⣿⣿⢘⡿⣼⣿⣻⣿⣿⣿⣿⣸⢿⣶⠈⠈⠃⣡⡔⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡟⠛⢫⣽⣷⣆⣛⣗⣀⣹⣧⡏⣿⣇⣿⡿⣿⣿⣿⣿⣟⡷⢺⠟⠁⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⢀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣠⣬⣭⣭⣿⣿⣟⣛⣻⠟⢃⠉⠸⡙⣿⣟⣿⣿⣯⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠈⠉⠉⠉⠉⠍⠛⠋⠁⠀⠸⠿⠺⣿⠟⣿⣿⣿⣿⣿⣿⣿⣾⢸⡐⣆⣇⣿⣷⣿⣼⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡂⠀⠠⠀⠀⠘⠸⠘⠛⠠⠿⠿⠿⠿⠿⠛⢛⠿⢸⡇⢹⡏⠻⢏⣉⣭⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠀⠀⠀⠀⠒⣦⡀⠀⠐⠀⠼⢛⡛⢿⣿⣿⣿⣿⣿⣿
⠀⠀⢰⣶⡆⣶⣶⠀⢠⣶⢶⣤⠀⢰⣶⣶⢰⣶⣶⣶⠀⠀⣶⣶⣶⣄⢰⣶⡆⣶⡆⢰⣶⠀⢰⣶⠀⣶⡎⢱⡏⢁⣴⢶⣦⡀⠀⢰⣶⡀⣶⡆⢠⣶⢶⣤⠀⠀⠀⠀⢀⣷⣶⠂⠀⣶⣶⡆⣠⣶⢶⣤⠈⣽⡶⣦⡌⠉
⠀⠀⢸⣿⡇⣿⣿⠀⣿⣿⢸⣿⠀⣿⡟⣿⡀⢸⣿⠀⠀⠀⣿⣧⣼⡿⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⣿⣼⡇⢸⣿⢀⣛⡃⠀⢸⣿⣧⣿⡇⣿⣿⢸⣿⠀⠀⠀⠀⣼⢻⣿⠀⣸⡟⣿⡇⠉⢉⣼⡟⠠⣿⡇⣿⡇⠀
⠀⠀⢸⣿⡇⣿⣿⠀⣿⣿⢸⣿⢀⣿⣧⣿⡇⢸⣿⠀⠀⠀⣿⣏⢹⣷⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⡿⣿⡇⢸⣿⠘⣿⡇⠀⢸⣿⢻⣿⡇⣿⣿⢸⣿⠀⠀⠀⢰⣿⣼⣿⣤⣿⣤⣿⣧⢴⣦⢹⣿⠀⣿⡇⣿⡇⠀
⠀⠀⠸⢿⠇⠿⠟⠻⠸⠿⠾⠋⠘⠛⠁⠛⠓⠘⠛⠀⠀⠀⠛⠓⠘⠛⠈⠛⠷⠟⠁⠘⠛⠛⠘⠛⠀⠛⠃⠛⠃⠈⠻⠟⠛⠃⠀⠘⠛⠈⠛⠃⠘⠻⠾⠋⠘⠛⠀⠀⠀⠘⠛⠀⠀⠘⠛⠃⠘⠻⠾⠛⠀⠛⠷⠟⠃⠀
[20A⠀⠀⠡⢾⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠿⠿⠿⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣠⣽⣾⣾⣿⣿⣿⣿⡿⠟⠻⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠸⠏⠡⠛⠛⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⡭⡝⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣔⣏⢿⢿⣿⣷⠿⢻⣥⡆⠀⣸⣿⣷⣯⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣛⣻⣿⣿⣿⣿⠀⣿⣿⢠⣸⣿⣹⣿⣿⣿⣿⣷⠾⣭⣟⡛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣯⣬⠟⠃⠀⢻⣟⣿⣶⣯⣽⣿⡷⢷⣿⣾⠇⣰⣿⣾⠻⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⣿⣿⣿⣿⣿⣿⡋⣿⣷⠫⢤⣼⢿⡿⣯⣿⣿⣿⣿⣿⣿⣿⢄⣼⣿⡏⢴⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⣼⡿⣾⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⣿⣿⡟⢐⣿⡿⠬⣿⡿⣶⣇⣿⣿⣿⣿⣿⣿⣿⣯⢨⣹⣿⡗⢺⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⡫⠭⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣿⣷⣿⣿⣿⣿⢷⢸⣿⣿⣶⣦⣤⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⠃⢸⣿⡆⣀⣾⣯⣿⢸⣿⢹⣿⣿⣿⣿⣿⣿⣿⢸⣿⠿⣿⣯⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠿⠸⠿⢿⣿⣿⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣻⣤⣾⣿⠉⢹⣿⢻⡏⣿⡇⣿⣿⣿⣿⣿⣿⡟⡟⢽⡿⣇⣿⣮⣿⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠙⠛⠻⠿⠃⠀⠀⠀⢤⣿⣿⣿⣿⣿⣏⣁⠿⠿⠩⠼⣿⢸⢷⣿⢳⣿⣿⣽⣿⣿⣿⣿⠟⣿⣆⣀⡿⠉⣡⡤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢻⣿⡿⠀⣀⣿⣿⢘⡿⣼⣿⣻⣿⣿⣿⣿⣸⢿⣶⠄⠈⢄⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡟⠛⢫⣽⣷⣖⣛⣗⣀⣹⣧⡏⣿⣇⣿⡿⣿⣿⣿⣿⣟⡷⠺⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⢀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣠⣬⣭⣭⣿⣿⣟⣛⣻⠟⢃⠉⠸⡙⣿⣟⣿⣿⣯⣴⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠉⠉⠩⡍⠉⠛⠋⠁⠀⠘⣾⠻⣿⠟⣿⣿⣿⣿⣿⣿⣿⣾⢸⡐⣆⣇⣿⣷⣿⣼⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠄⠀⠠⠀⠀⠈⠸⠘⠛⠐⠿⠿⠿⠿⠿⠛⢛⠿⢸⡇⢻⠏⠿⣏⣩⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠕⠦⠀⠀⠒⣦⣀⠀⠐⠀⠸⠟⣛⢿⣿⣿⣿⣿⣿⣿
⠀⠀⢰⣶⡆⣶⣶⠀⢠⣶⢶⣤⠀⢰⣶⣶⢰⣶⣶⣶⠀⠀⣶⣶⣶⣄⢰⣶⡆⣶⡆⢰⣶⠀⢰⣶⠀⣶⡇⢹⡟⢁⣴⢶⣦⡀⠀⢰⣶⡀⣶⡆⢠⣶⢶⣤⠀⠀⠀⠀⢀⣶⣾⠐⠂⣶⣶⡆⢠⣶⢶⣤⠈⣽⡶⣦⡌⠉
⠀⠀⢸⣿⡇⣿⣿⠀⣿⣿⢸⣿⠀⣿⡟⣿⡀⢸⣿⠀⠀⠀⣿⣧⣼⡿⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⣿⣼⡇⢸⣿⢀⣛⡃⠀⢸⣿⣧⣿⡇⣿⣿⢸⣿⠀⠀⠀⠀⣼⢻⣿⠀⣸⡟⣿⡇⠉⢉⣼⡟⢰⣿⡇⣿⡇⠀
⠀⠀⢸⣿⡇⣿⣿⠀⣿⣿⢸⣿⢀⣿⣧⣿⡇⢸⣿⠀⠀⠀⣿⣏⢹⣷⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⡿⣿⡇⢸⣿⠘⣿⡇⠀⢸⣿⢻⣿⡇⣿⣿⢸⣿⠀⠀⠀⢰⣿⣼⣿⣤⣿⣤⣿⣧⢶⣦⢹⣿⠈⣿⡇⣿⡇⠀
⠀⠀⠸⢿⠇⠿⠟⠻⠸⠿⠾⠋⠘⠛⠁⠛⠓⠘⠛⠀⠀⠀⠛⠛⠘⠛⠈⠛⠿⠟⠁⠘⠛⠛⠘⠛⠀⠛⠃⠛⠃⠈⠻⠟⠛⠃⠀⠘⠛⠈⠛⠃⠘⠻⠾⠋⠘⠛⠀⠀⠀⠘⠛⠀⠀⠘⠛⠃⠘⠻⠾⠛⠀⠛⠷⠟⠃⠀
[20A⠈⠀⢩⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⠿⠿⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣶⣽⣿⣿⣿⣿⣿⣿⣿⠟⠿⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠸⠏⠡⠛⠟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⣭⡝⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⣜⣏⢿⢿⣿⣷⠿⢻⣵⡆⠀⣸⣿⣷⣯⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣛⣻⣾⣿⣿⣿⠀⣿⣿⢠⣨⣿⣽⣿⣿⣿⣿⡷⠾⣭⣟⡛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣯⣬⠟⠃⠀⢻⣟⣿⣶⣯⣽⣿⡷⢷⣿⣾⠇⣱⣿⣾⠻⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⣿⣿⣿⣿⣿⣿⡋⣿⣿⠋⢠⣼⢿⡿⣯⣿⣿⣿⣿⣿⣿⣿⢄⣼⣿⡏⢴⡿⣿⣿⣿⣿⣿⣿⠟⠋⠐⠖⠀⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⣼⡿⣾⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣽⣿⣿⣿⡟⢐⣿⡿⠬⣿⣿⣶⣇⣿⣿⣿⣿⣿⣿⣿⣯⢨⢹⣿⣗⢺⣿⣽⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣿⣷⣿⣿⣿⣿⢷⢸⣿⣿⣶⣦⣤⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⠃⢸⣿⡆⣀⣾⣧⣿⢸⣿⢹⣿⣿⣿⣿⣿⡿⣿⢸⣿⠿⣿⣯⣿⣿⠯⠑⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠿⠸⠿⢿⣿⣿⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣻⣤⣾⣿⠉⢹⣿⢳⡏⣿⡇⣿⣿⣿⣿⣿⣿⡟⡟⢹⡿⣇⡟⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠙⠛⠻⠿⠃⠀⠀⠀⢦⣿⣿⣿⣿⣿⣏⣁⠿⠿⠩⠼⣿⢸⢳⣿⢳⣿⣿⣽⣿⣿⣿⣿⠟⣿⡆⠈⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣨⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢻⣿⡿⡀⣀⣿⣿⢘⡿⣼⣿⣻⣿⣿⣿⣿⣸⠿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡟⠛⢫⣽⣷⣆⣛⣗⣀⣹⣧⡏⣿⣇⣿⡿⣿⣿⣿⣿⣟⡷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠏⠛⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⢀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣠⣬⣭⣭⣿⣿⣟⣛⣻⠟⢃⠉⠸⡙⣿⣟⣿⣿⣧⣔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⡩⠉⠉⠉⠉⠛⠋⠁⠀⠘⢿⢛⣿⠟⣿⣿⣿⣿⣿⣿⣿⣾⢸⡐⣆⣇⣿⣷⣿⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠄⠀⠀⠀⠈⠸⠘⠛⠸⠿⠿⠿⠿⠿⠛⢛⠿⢸⡇⠻⢯⣛⣉⣽⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢑⢦⣀⠀⠀⠀⠘⠛⣛⢿⣿⣿⣿⣿⣿⣿
⠀⠀⢰⣶⡆⣶⣶⠀⢠⣶⢶⣤⠀⢰⣶⣶⢰⣶⣶⣶⠀⠀⣶⣶⣶⣄⢰⣶⡆⣶⡆⢰⣶⠀⢰⣶⠈⣶⡏⢻⡏⢁⣴⢶⣦⡀⠀⢰⣶⡀⣶⡆⢠⣶⢶⣤⠀⠀⠀⠀⢀⣶⣶⠀⠀⣶⣶⡆⣠⣶⢶⣤⠈⣽⡶⣦⡍⠉
⠀⠀⢸⣿⡇⣿⣿⠀⣿⣿⢸⣿⠀⣿⡟⣿⡀⢸⣿⠀⠀⠀⣿⣿⣼⡿⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⣿⣼⡇⢸⣿⢀⣛⡃⠀⢸⣿⣧⣿⡇⣿⣿⢸⣿⠀⠀⠀⠀⣼⢻⣿⠀⣸⡟⣿⡇⠉⢉⣼⡟⢰⣿⡇⣿⡇⠀
⠀⠀⢸⣿⡇⣿⣿⠀⣿⣿⢸⣿⢀⣿⣧⣿⡇⢸⣿⠀⠀⠀⣿⣿⢹⣷⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⡿⣿⡇⢸⣿⠘⣿⡇⠀⢸⣿⢻⣿⡇⣿⣿⢸⣿⠀⠀⠀⢰⣿⣼⣿⣤⣿⣤⣿⣧⣴⣦⢹⣿⠘⣿⡇⣿⡇⠀
⠀⠀⠸⢿⠇⠿⠟⠻⠸⠿⠾⠋⠘⠛⠁⠛⠓⠘⠛⠀⠀⠀⠛⠛⠘⠛⠈⠛⠿⠟⠁⠘⠛⠛⠘⠛⠀⠛⠃⠛⠃⠈⠻⠟⠛⠃⠀⠘⠛⠈⠛⠃⠘⠻⠾⠋⠘⠛⠀⠀⠀⠘⠛⠀⠀⠘⠛⠃⠘⠻⠾⠛⠀⠛⠷⠟⠃⠀
[20A⠀⢉⠭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⠿⠿⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⣰⣽⣿⣿⣿⣿⣿⣿⡿⠟⠿⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠹⠏⠱⠛⠟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⡭⡟⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣘⣍⢿⢿⣿⣷⠿⢻⣵⡆⠀⣸⣿⣷⣯⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣛⣻⣿⣿⣿⣿⠀⣿⣿⢠⣨⣿⣹⣿⣿⣿⣿⣷⠾⣭⣟⡛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣧⣬⠟⠃⠀⢛⣟⣿⣶⣯⣽⣿⡷⢷⣿⣿⠇⣱⣿⣾⠹⣸⣿⣿⣿⣿⣿⣿⠿⢛⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⣿⣿⣿⣿⣿⣿⡋⣿⣿⠋⢠⣼⢿⡿⣮⣿⣿⣿⣿⣿⣿⣿⢄⣼⣿⡏⢵⡿⣿⣿⣿⣿⠏⠁⠀⠉⠀⠐⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⣼⡿⣾⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣽⣿⣿⣿⡟⢐⣿⡿⠬⣿⣿⣶⣇⣿⣿⣿⣿⣿⣿⣿⣯⢨⢹⣿⡗⢺⣿⣽⣿⠏⠁⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣿⣷⣿⣿⣿⣿⢷⢸⣿⣿⣶⣦⣤⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⠃⢸⣿⡆⣀⣾⣧⣿⢸⣿⢹⣿⣿⣿⣿⣿⡿⣿⢸⣿⠿⣿⢯⠭⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠿⠸⠿⢿⣿⣿⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣻⣤⣾⣿⠉⢹⣿⢳⡏⣿⡇⣿⣿⣿⣿⣿⣿⡟⡟⢹⡿⠃⠛⠁⠀⠀⠂⠀⠀⠀⠀⠠⢀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠙⠛⠻⢿⠇⠀⠀⠀⢦⣿⣿⣿⣿⣿⣏⣁⠿⠿⠩⠼⣿⢸⢳⣿⢳⣿⣿⣽⣿⣿⣿⣿⠟⡏⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢻⣿⡿⡀⣀⣿⣿⢘⡿⣼⣿⣻⣿⣿⣿⣿⣸⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡟⠛⢫⣽⣷⣆⣛⣗⣀⣹⣧⡏⣿⣇⣿⡿⣿⣿⣿⣿⣟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠻⠏⠛⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⢀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣠⣬⣭⣭⣿⣿⣟⣛⣻⠟⢃⠉⠸⡙⣿⣟⣿⣿⣧⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠨⠉⠉⠉⠉⠉⠛⠋⠁⠀⠘⢿⢻⣿⠿⣿⣿⣿⣿⣿⣿⣿⣾⢸⡐⣆⣇⣿⣷⣿⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⣀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠤⠀⠀⠀⠄⠠⠀⠀⠀⠸⠘⠛⠰⠿⠿⠿⠿⠿⠛⢛⠿⠸⠇⢽⣏⣩⣭⣯⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⢒⢄⡀⠀⠘⠛⣛⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢰⣶⡆⣶⣶⠀⢠⣶⢶⣤⠀⢰⣶⣶⢰⣶⣶⣶⠀⠀⣶⣶⣶⣄⢰⣶⡆⣶⡆⢰⣶⠀⢰⣾⠀⣷⡏⢻⡏⢁⣴⢶⣦⡀⠀⢰⣶⡀⣶⡆⢨⣷⢶⣤⠀⠀⠀⠀⢀⣶⣶⠀⠀⣶⣶⡆⢠⣶⢶⣤⠈⣽⡶⣦⡍⠉
⠀⠀⢸⣿⡇⣿⣿⠀⣿⣿⢸⣿⠀⣿⡟⣿⡀⢸⣿⠀⠀⠀⣿⣧⣼⡿⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⣿⣼⡇⢸⣿⢀⣛⡃⠀⢸⣿⣧⣿⡇⣿⣿⢸⣿⠀⠀⠀⠀⣼⢻⣿⠀⣸⡟⣿⡇⠉⢉⣼⡟⢰⣿⡇⣿⡇⠀
⠀⠀⢸⣿⡇⣿⣿⠀⣿⣿⢸⣿⢀⣿⣧⣿⡇⢸⣿⠀⠀⠀⣿⣯⢹⣷⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⡿⣿⡇⢸⣿⠘⣿⡇⠀⢸⣿⢻⣿⡇⣿⣿⢸⣿⠀⠀⠀⢰⣿⣼⣿⣤⣿⣤⣿⣧⣴⣦⢹⣿⠈⣿⡇⣿⡇⠀
⠀⠀⠸⢿⠇⠿⠟⠻⠸⠿⠾⠋⠘⠛⠁⠛⠓⠘⠛⠀⠀⠀⠛⠓⠘⠛⠈⠛⠿⠟⠁⠘⠛⠛⠘⠛⠀⠛⠃⠛⠃⠈⠻⠟⠛⠃⠀⠘⠛⠈⠛⠃⠘⠻⠾⠋⠘⠛⠀⠀⠀⠘⠛⠀⠀⠘⠛⠃⠘⠻⠾⠛⠀⠛⠷⠟⠃⠀
[20A⡈⢉⢡⢿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⠿⠿⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣥⣶⣽⣿⣿⣿⣿⣿⣿⡿⠟⠿⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠹⠏⠱⠛⠟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⡭⡍⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⣘⣏⢿⢿⣿⣷⠿⢻⣵⡆⠀⣸⣿⣷⣯⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣛⣻⣿⣿⣿⣿⠀⣿⣿⠠⣨⣿⣽⣿⣿⣿⣿⣷⠾⣭⣟⡛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡏⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣯⣬⠛⠃⠀⢻⣟⣿⣶⣯⣽⣿⡷⢷⣿⣾⠇⣱⣿⣾⠻⣸⣿⣿⣿⣿⠟⠋⢭⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⣿⣿⣿⣿⣿⣿⡋⣿⣿⠋⢤⣼⢿⡿⣬⣿⣿⣿⣿⣿⣿⣿⢄⣼⣿⡏⢵⡿⣿⣿⠟⠁⠀⠀⠀⠀⠐⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⣼⡿⣾⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣽⣿⣿⣿⡟⢐⣿⡿⠬⣿⣿⣶⣇⣿⣿⣿⣿⣿⣿⣿⣯⢨⢹⣿⣗⢺⣿⡏⠃⠀⠀⠀⠀⠀⠀⠀⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣿⣷⣿⣿⣿⣿⢷⢸⣿⣿⣶⣦⣤⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⠃⢸⣿⡆⣀⣾⣧⣿⢸⣿⢹⣿⣿⣿⣿⣿⡿⣿⢸⣿⠻⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠿⠸⠿⢿⣿⣿⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣻⣤⣾⣿⠉⢹⣿⢳⡏⣿⡇⣿⣿⣿⣿⣿⣿⡟⡟⠹⠫⠊⠀⠀⠀⠁⠀⠀⠀⠀⠀⣢⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠙⠛⠻⢿⠃⠀⠀⠀⢤⣿⣿⣿⣿⣿⣏⣁⠿⠿⠩⠼⣿⢸⢳⣿⢳⣿⣿⣽⣿⣿⣿⣿⠟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢻⣿⡿⡀⣀⣿⣿⢘⡿⣼⣿⣻⣿⣿⣿⣿⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡟⠛⢫⣽⣷⣆⣛⣗⣀⣹⣧⡏⣿⣇⣿⡿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠻⠏⠛⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⢀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣠⣬⣭⣭⣿⣿⣟⣛⣻⠟⢃⠉⠸⡙⣿⣿⣿⣿⡇⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠉⠉⠉⠛⠋⠁⠀⠘⣿⢛⣿⠻⣿⣿⣿⣿⣿⣿⣿⣾⢸⡐⡆⣇⣿⣷⣿⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠤⠤⠀⠀⠀⠄⠠⠀⠀⠀⠹⠘⠛⠰⠿⠿⠿⠿⠿⠛⢛⠿⠸⢇⣗⣯⣯⣯⣽⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⠘⠛⢛⢿⣿⣿⣿⣿⣿⣿
⠀⠀⢰⣶⡆⣶⣶⠀⢠⣶⢶⣤⠀⢰⣶⣶⢰⣶⣶⣶⠀⠀⣶⣶⣶⣄⢰⣶⡆⣶⡆⢰⣶⠀⢰⣶⠈⣶⡏⢳⡎⢀⣴⢶⣦⡀⠀⢰⣶⡀⣶⡆⢨⣷⢶⣤⠀⠀⠀⠀⢀⣶⣶⠀⠀⣶⣶⡆⢡⣶⢶⣤⠈⣽⡶⣦⡍⠉
⠀⠀⢸⣿⡇⣿⣿⠀⣿⣿⢸⣿⠀⣿⡟⣿⡀⢸⣿⠀⠀⠀⣿⣿⣼⡿⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⣿⣼⡇⢸⣿⢀⣛⡃⠀⢸⣿⣧⣿⡇⣿⣿⢸⣿⠀⠀⠀⠀⣼⢻⣿⠀⣸⡟⣿⡇⠉⢉⣼⡟⠀⣿⡇⣿⡇⠀
⠀⠀⢸⣿⡇⣿⣿⠀⣿⣿⢸⣿⢀⣿⣧⣿⡇⢸⣿⠀⠀⠀⣿⣿⢹⣷⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⡿⣿⡇⢸⣿⠘⣿⡇⠀⢸⣿⢻⣿⡇⣿⣿⢸⣿⠀⠀⠀⢰⣿⣼⣿⣤⣿⣤⣿⣧⢴⣦⢹⣿⠈⣿⡇⣿⡇⠀
⠀⠀⠸⢿⠇⠿⠟⠻⠸⠿⠾⠋⠘⠛⠁⠛⠓⠘⠛⠀⠀⠀⠛⠛⠘⠛⠈⠛⠷⠟⠁⠘⠛⠛⠘⠛⠀⠛⠃⠛⠃⠈⠻⠟⠛⠃⠀⠘⠛⠈⠛⠃⠘⠻⠾⠋⠘⠛⠀⠀⠀⠘⠛⠀⠀⠘⠛⠃⠘⠻⠾⠛⠀⠛⠷⠟⠃⠀
[20A⠀⠀⠩⣿⣿⣻⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⢿⣿⠿⠿⠿⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣅⡴⣽⣿⣿⣿⣿⣿⣿⣿⠟⠿⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠹⠏⠱⠛⠟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⡭⡍⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣘⣍⢿⢿⣿⣷⠿⢻⣵⡆⠀⣸⣿⣷⣯⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣛⣻⣿⣿⣿⣿⠀⣿⣿⢠⣸⣿⣽⣿⣿⣿⣿⣷⠾⣭⣟⡛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣧⣬⠟⠃⠀⢳⣟⣶⣶⣮⣽⣿⡷⢷⣿⣾⠇⣱⣿⣾⠹⣸⣿⣿⡿⠋⠩⠏⠙⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⣿⣿⣿⣿⣿⣿⡋⣿⣿⠋⢠⣼⢿⡿⣬⣿⣿⣿⣿⣿⣿⣿⢄⣼⣿⡏⢵⡿⡟⠁⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⣼⡿⣾⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣽⣿⣿⣿⡟⢐⣿⡿⠬⣿⣿⣶⣇⣿⣿⣿⣿⣿⣿⣿⣯⢨⢹⣿⡗⣺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣿⣷⣿⣿⣿⣿⢷⢸⣿⣿⣶⣦⣤⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⠃⢸⣿⠆⣀⣾⣧⣿⢸⣿⢹⣿⣿⣿⣿⣿⡿⣿⢸⡿⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠿⠸⠿⢿⣿⣿⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣻⣤⣾⣿⠉⢹⣿⢳⡏⣿⡇⣿⣿⣿⣿⣿⣿⡿⡟⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠙⠛⠻⢿⠇⠀⠀⠀⢦⣿⣿⣿⣿⣿⣏⣁⠿⠿⠩⠼⣿⢸⢳⣿⢳⣿⣿⣽⣿⣿⣿⡯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢻⣿⡿⡀⣀⣿⣿⢘⡿⣼⣿⣻⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡟⠛⢫⣽⣷⣦⣛⣗⣀⣹⣧⡏⣿⣇⣿⡿⣿⣿⣿⡏⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠻⠿⠻⠏⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⢀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣠⣬⣭⣭⣿⣿⣟⣛⣻⠟⢃⠉⠸⡙⣿⣟⣿⣿⠱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠇⠈⠉⠉⠉⠉⠉⠛⠋⠁⠀⠘⣽⢛⣿⠻⣿⣿⣿⣿⣿⣿⣿⣾⢸⡐⡆⣅⣿⣷⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠂⠀⠀⠀⠀⠀⠀⠀⠐⠠⠄⠄⠄⠀⠀⠀⠄⠠⠀⠀⠀⠹⠘⠛⠰⠿⠿⠿⠿⠿⠛⢛⠿⢘⣃⣧⣮⣽⣭⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠺⢛⠛⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢰⣶⡆⣶⣶⠀⢠⣶⢶⣤⠀⢰⣶⣶⢰⣶⣶⣶⠀⠀⣶⣶⣶⣄⢰⣶⡆⣶⡆⢰⣶⠀⢱⣾⠉⣶⡏⢺⡆⢀⣴⢶⣦⡀⠀⢰⣶⡀⣶⡆⢨⣷⢶⣤⠀⠀⠀⠀⢀⣶⣶⠀⠀⣶⣶⡆⢠⣶⢶⣤⠈⣽⡶⣦⡍⠉
⠀⠀⢸⣿⡇⣿⣿⠀⣿⣿⢸⣿⠀⣿⡟⣿⡀⢸⣿⠀⠀⠀⣿⣿⣼⡿⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⣿⣼⡇⢸⣿⢀⣛⡃⠀⢸⣿⣧⣿⡇⣿⣿⢸⣿⠀⠀⠀⠀⣼⢻⣿⠀⣸⡟⣿⡇⠉⢉⣼⡟⠠⣿⡇⣿⡇⠀
⠀⠀⢸⣿⡇⣿⣿⠀⣿⣿⢸⣿⢀⣿⣧⣿⡇⢸⣿⠀⠀⠀⣿⣿⢹⣷⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⡿⣿⡇⢸⣿⠘⣿⡇⠀⢸⣿⢻⣿⡇⣿⣿⢸⣿⠀⠀⠀⢰⣿⣼⣿⣤⣿⣤⣿⣧⢴⣦⢹⣿⠀⣿⡇⣿⡇⠀
⠀⠀⠸⢿⠇⠿⠟⠻⠸⠿⠾⠋⠘⠛⠁⠛⠓⠘⠛⠀⠀⠀⠛⠛⠘⠛⠈⠛⠷⠟⠁⠘⠛⠛⠘⠛⠀⠛⠃⠛⠃⠈⠻⠟⠛⠃⠀⠘⠛⠈⠛⠃⠘⠻⠾⠋⠘⠛⠀⠀⠀⠘⠛⠀⠀⠘⠛⠃⠘⠻⠾⠛⠀⠛⠷⠟⠃⠀
[20A⠀⠌⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⠿⠿⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣴⣽⣿⣿⣿⣿⣿⣿⡿⠿⠫⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠸⠏⠡⠛⠟⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⡭⡍⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣘⣏⢿⢿⣿⣷⠿⢻⣥⡄⠀⣸⣿⣷⣯⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣛⣿⣾⣿⣿⣿⠀⣿⣿⠠⣨⣿⣽⣿⣿⣿⣿⣷⠾⣭⣟⡛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣧⣬⢟⠃⠀⢺⣟⣿⣶⣮⣽⣿⡷⢷⣿⣾⠇⣠⣿⣾⠙⠜⠋⠀⠒⠂⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⣿⣿⣿⣿⣿⣿⡋⣿⣷⠋⢤⣼⢿⡿⣬⣿⣿⣿⣿⣿⣿⣿⢄⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⣾⣿⣾⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣽⣿⣿⣿⡟⢐⣿⡿⠬⣿⣿⣶⣇⣿⣿⣿⣿⣿⣿⣿⣯⢨⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣿⣷⣿⣿⣿⣿⢷⢸⣿⣿⣶⣦⣤⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⠃⢸⣿⠆⣀⣾⣧⣿⢸⣿⢹⣿⣿⣿⣿⣿⡿⡟⠈⠈⠀⠀⡀⠀⠀⠀⠀⢀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠿⠸⠿⢿⣿⣿⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣻⣤⣾⣿⠉⢹⣿⢳⡏⣿⡏⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠙⠛⠻⠿⠇⠀⠀⠀⢦⣯⣿⣿⣿⣿⣏⣁⠿⠿⠩⠼⣿⢸⢳⣿⢳⣿⣿⣽⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢻⣿⡿⡀⣀⣿⣿⢘⡿⣼⣿⣻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡟⠛⢫⣽⣷⣶⣛⣗⣂⣹⣧⡏⣿⣇⣿⡿⣿⣿⢳⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣽⠻⠿⠿⠍⠛⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⢀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣠⣬⣭⣽⣿⣿⣟⣛⣻⠟⢃⠉⠸⡙⣿⣟⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⠀⠀⠀⡇⠈⠉⠉⠉⠉⠙⠛⠋⠁⠀⠘⣽⢛⣿⠻⣿⣿⣿⣿⣿⣿⣿⣾⢸⡐⣆⣇⣿⣧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠄⠀⠀⠄⠀⠀⠀⠀⠹⠘⠛⠲⠿⠿⠿⠿⠿⠛⠛⣻⣼⣦⣥⣯⣽⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠉⠀⠁⠈⠉⠙⡛⢿⣿⣿⣿⣿⣿
⠀⠀⢰⣶⡆⣶⣶⠀⢠⣶⢶⣤⠀⢰⣶⣶⢰⣶⣶⣶⠀⠀⣶⣶⣶⣄⢰⣶⡆⣶⡆⢰⣶⠀⢹⣶⠉⣶⡎⢰⡆⢀⣴⢶⣦⡀⠀⢰⣶⡀⣶⡆⢨⣷⢶⣤⠀⠀⠠⢀⢢⣶⣶⠀⠀⣶⣶⡆⢠⣶⢶⣤⠀⣼⡶⣦⡌⣉
⠀⠀⢸⣿⡇⣿⣿⠀⣿⣿⢸⣿⠀⣿⡟⣿⡀⢸⣿⠀⠀⠀⣿⣿⣼⡿⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⣿⣼⡇⢸⣿⢀⣛⡃⠀⢸⣿⣧⣿⡇⣿⣿⢸⣿⠀⠀⠀⠀⣼⢻⣿⠀⣸⡟⣿⡇⠉⢉⣼⡟⠀⣿⡇⣿⡇⠀
⠀⠀⢸⣿⡇⣿⣿⠀⣿⣿⢸⣿⢀⣿⣧⣿⡇⢸⣿⠀⠀⠀⣿⣿⢹⣷⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⡿⣿⡇⢸⣿⠘⣿⡇⠀⢸⣿⢻⣿⡇⣿⣿⢸⣿⠀⠀⠀⢰⣿⣼⣿⣤⣿⣤⣿⣧⢴⣦⢹⣿⠀⣿⡇⣿⡇⠀
⠀⠀⠸⢿⠇⠿⠟⠻⠸⠿⠾⠋⠘⠛⠁⠛⠓⠘⠛⠀⠀⠀⠛⠛⠘⠛⠈⠛⠿⠟⠁⠘⠛⠛⠘⠛⠀⠛⠃⠛⠃⠈⠻⠟⠛⠃⠀⠘⠛⠈⠛⠃⠘⠻⠾⠋⠘⠛⠀⠀⠀⠘⠛⠀⠀⠘⠛⠃⠘⠻⠾⠛⠀⠛⠷⠟⠃⠀
[20A⠈⢍⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⠿⠿⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣦⣶⣽⣿⣿⣿⣿⣿⣿⡿⠟⠻⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠹⠏⠡⠛⠟⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠆⠀⣤⡀⠀⣾⣿⡿⠁⣭⡍⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣘⣏⢿⢿⣿⣷⠿⢻⣥⡆⠀⣸⣿⣷⣯⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣛⣿⣾⣿⣿⣿⢀⣿⣿⢠⣨⣿⣽⣿⣿⣿⣿⣷⠾⣭⣟⡛⡿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣧⣼⢟⠃⠀⢛⣟⢿⣦⣯⣽⣿⡿⢷⣿⣾⠇⣡⣿⣾⠉⠁⠀⠉⠂⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⣿⣿⣿⣿⣿⣿⡋⣿⣿⠫⢤⣼⢿⡿⣮⣿⣿⣿⣿⣿⣿⣿⢄⣼⠟⠁⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⣾⣿⣾⣶⣶⣤⡌⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣽⣿⣿⣿⡟⢐⣿⡿⠬⣿⣿⣶⣇⣿⣿⣿⣿⣿⣿⣿⣯⢨⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣿⣷⣿⣿⣿⣿⢷⢸⣿⣿⣶⣦⣤⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⠃⢸⣿⠆⣀⣾⣧⣿⢸⣿⢹⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⢀⠀⠀⠀⠀⠀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠿⠸⠿⢿⣿⣿⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣻⣤⣾⣿⠉⢹⣿⢿⡏⣿⡏⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠙⠛⠻⠿⠇⠀⠀⠀⢦⣯⣿⣿⣿⣿⣏⣁⠿⠿⠩⢼⣿⢸⢳⣿⢳⣿⣿⣽⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢻⣿⡿⡀⣀⣿⣿⢘⡿⣼⣿⣻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡟⠛⢫⣽⣷⣦⣛⣗⣂⣹⣧⡏⣿⣇⣿⡿⣿⡏⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣽⠻⠿⠿⠏⠟⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⢀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣠⣬⣭⣭⣿⣿⣟⣛⣻⠟⢃⠉⠸⡙⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⡀⠀⠀⠀⡇⠈⠉⠉⠉⠉⠙⠛⠋⠁⠀⠘⣷⢛⣿⠻⣿⣿⣿⣿⣿⣿⣿⣾⢸⡐⣆⣇⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠄⠄⠀⠀⠄⠀⠀⠀⠀⠈⠘⠋⠂⠿⠿⠿⠿⠿⠛⢻⢿⣴⣥⣯⣭⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣦⠀⠀⠀⠀⠈⠉⠙⠛⢛⠻⢿⣿⣿⣿
⠀⠀⢰⣶⡆⣶⣶⠀⢠⣶⢶⣤⠀⢰⣶⣶⢰⣶⣶⣶⠀⠀⣶⣶⣶⣄⢰⣶⡆⣶⡆⢰⣶⠉⢹⣾⠁⣾⡇⢰⡆⢀⣴⢶⣦⡀⠀⢰⣶⡀⣶⡆⢨⣷⢶⣤⠀⠀⠨⠀⢢⣶⣶⠀⠀⣶⣶⡆⢠⣶⢶⣤⠀⣵⡶⣦⡍⠉
⠀⠀⢸⣿⡇⣿⣿⠀⣿⣿⢸⣿⠀⣿⡟⣿⡀⢸⣿⠀⠀⠀⣿⣿⣼⡿⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⣿⣼⡇⢸⣿⢀⣛⡃⠀⢸⣿⣧⣿⡇⣿⣿⢸⣿⠀⠀⠀⠀⣼⢻⣿⠀⣸⡟⣿⡇⠉⢉⣼⡟⠀⣿⡇⣿⡇⠀
⠀⠀⢸⣿⡇⣿⣿⠀⣿⣿⢸⣿⢀⣿⣧⣿⡇⢸⣿⠀⠀⠀⣿⣿⢹⣷⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⡿⣿⡇⢸⣿⠘⣿⡇⠀⢸⣿⢻⣿⡇⣿⣿⢸⣿⠀⠀⠀⢰⣿⣼⣿⣤⣿⣤⣿⣧⢴⣦⢹⣿⠀⣿⡇⣿⡇⠀
⠀⠀⠸⢿⠇⠿⠟⠻⠸⠿⠾⠋⠘⠛⠁⠛⠓⠘⠛⠀⠀⠀⠛⠛⠘⠛⠈⠛⠿⠟⠁⠘⠛⠛⠘⠛⠀⠛⠃⠛⠃⠈⠻⠟⠛⠃⠀⠘⠛⠈⠛⠃⠘⠻⠾⠋⠘⠛⠀⠀⠀⠘⠛⠀⠀⠘⠛⠃⠘⠻⠾⠛⠀⠛⠷⠟⠃⠀
[20A⠀⠈⠩⣿⣭⣿⣿⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⠿⠿⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣄⡠⣽⣯⣽⣿⣿⣿⣿⡿⠟⠻⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠹⠏⠡⠛⠏⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⣭⡍⠟⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣘⣏⢿⢿⣿⣷⠿⢻⣥⡄⠀⣸⣿⣷⡯⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣛⣻⣾⣿⣿⣿⠀⣿⣿⢠⣨⣿⣽⣿⣿⣿⣿⣷⠾⣭⣟⡋⡿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡏⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣧⣼⢟⠃⠀⢻⣟⣿⣖⣯⣽⣿⡷⢷⣿⣿⠃⣠⡿⠊⠁⠀⠉⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⣿⣿⣿⣿⣿⣿⡋⣿⣿⠋⢤⣼⢿⡶⣮⣿⣿⣿⣿⣿⣿⣿⢄⠈⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⣾⡿⣾⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣽⣿⣿⣿⡟⢐⣿⡿⠬⣿⣿⣶⣇⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣿⣷⣿⣿⣿⣿⢷⢸⣿⣿⣶⣦⣤⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⠃⢸⣿⢆⣀⣾⣇⣿⢸⣿⢹⣿⣿⣿⣿⣿⡏⠂⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠿⠸⠿⢿⣷⣿⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣻⣤⣾⣿⠉⢹⣿⢷⡏⣿⡇⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠙⠛⠻⠿⠇⠀⠀⠀⢤⣯⣿⣿⣿⣿⣏⣁⠿⠿⠩⠼⣿⢸⢳⣿⢳⣿⣿⣽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢻⣿⡿⡀⣀⣿⣿⢘⡿⣼⣿⣻⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡟⠛⢫⣽⣷⣦⣛⣗⣀⣹⣧⡏⣿⣇⣿⡿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣽⠻⠿⠿⠏⠝⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⢀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣠⣬⣭⣭⣿⣿⣟⣛⣻⠟⢃⠉⠸⡙⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⡀⠀⠀⠀⠀⡇⠈⠉⠉⠉⠉⠙⠛⠋⠁⠀⠘⣿⢛⣿⠻⣿⣿⣿⣿⣿⣿⣿⣾⢸⡐⣆⢇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠤⠁⠀⠀⠈⠀⠀⠀⠀⠀⠤⠄⠄⠀⠀⠀⠄⠀⠀⠀⠀⠈⠘⠋⠂⠿⠿⠿⠿⠛⢻⠿⣧⣤⣼⣭⣾⡟⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣦⣀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠿⣿⣿
⠀⠀⢰⣶⡆⣶⣶⠀⢠⣶⢶⣤⠀⢰⣶⣶⢰⣶⣶⣶⠀⠀⣶⣶⣶⣄⢰⣶⡆⣶⡆⢰⣾⠉⢹⣶⠀⣷⡆⢰⡆⢀⣴⢶⣦⡀⠀⢰⣶⡀⣷⡆⢨⣷⢶⣤⠀⠀⠬⠀⢢⣶⣶⠂⠈⣶⣶⡆⢠⣶⢶⣤⠀⣴⡶⣦⡌⠫
⠀⠀⢸⣿⡇⣿⣿⠀⣿⣿⢸⣿⠀⣿⡟⣿⡀⢸⣿⠀⠀⠀⣿⣧⣼⡿⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⣿⣼⡇⢸⣿⢀⣛⡃⠀⢸⣿⣧⣿⡇⣿⣿⢸⣿⠀⠀⠀⠀⣼⢻⣿⠀⣸⡟⣿⡇⠉⢉⣼⡟⠀⣿⡇⣿⡇⠀
⠀⠀⢠⣿⡇⣿⣿⠀⣿⣿⢸⣿⢀⣿⣧⣿⡇⢸⣿⠀⠀⠀⣿⣏⢹⣷⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⡿⣿⡇⢸⣿⠘⣿⡇⠀⢸⣿⢻⣿⡇⣿⣿⢸⣿⠀⠀⠀⢰⣿⣼⣿⣤⣿⣤⣿⣧⢴⣦⢹⣿⠀⣿⡇⣿⡇⠀
⠀⠀⠸⢿⠇⠿⠟⠻⠸⠿⠾⠋⠘⠛⠁⠛⠓⠘⠛⠀⠀⠀⠛⠛⠘⠛⠈⠛⠷⠟⠁⠘⠛⠛⠘⠛⠀⠛⠃⠛⠃⠈⠻⠟⠛⠃⠀⠘⠛⠈⠛⠃⠘⠻⠾⠋⠘⠛⠀⠀⠀⠘⠛⠀⠀⠘⠛⠃⠘⠻⠾⠛⠀⠛⠷⠟⠃⠀
[20A⠀⠀⠡⡭⢉⠯⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⢿⣿⠿⠿⠿⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣴⣵⣆⣼⣿⣿⣿⣿⡿⠟⡫⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠹⠏⠡⠛⠟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣯⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⣭⡝⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣘⣏⢿⢿⣿⣷⠿⢻⣥⡄⠀⣸⣿⣷⣯⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣛⣻⣾⣿⣿⣿⠀⣿⣿⠠⣸⣿⣽⣿⣿⣿⣿⣗⠾⣭⣟⡛⡽⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡏⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣧⣬⠟⠃⠀⢻⣟⣿⣶⣯⣽⣿⡷⢷⣿⣿⠇⠀⠃⠀⠀⠉⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⣿⣿⣿⣿⣿⣿⠋⣿⣿⠫⢤⣼⢿⡿⣬⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⣾⡿⣼⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣽⣿⣿⣿⡟⢐⣿⡿⠬⣿⣿⣶⣇⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣿⣷⣿⣿⡿⣿⢷⢸⣿⣿⣶⣦⣤⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⠃⢸⣿⡆⣀⣾⣇⣿⢸⣿⢹⣿⣿⣿⣿⡯⠈⠀⠀⠀⠀⠀⠀⠀⢀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠿⠸⠿⢿⣿⣿⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣻⣤⣾⣿⠉⢹⣿⢳⡏⣿⡇⣾⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠙⠛⠻⠿⠇⠀⠀⠀⢤⣿⣿⣿⣿⣿⣏⣁⠿⠿⠩⠸⣿⢸⢳⣿⢳⣿⣿⡝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢻⣿⡿⡀⣀⣿⣿⢘⡿⣼⣿⣻⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡟⠛⢫⣽⣷⣦⣛⣗⣀⣹⣧⡏⣿⣇⣿⡿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣽⠿⠿⠿⠏⠟⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⢀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣠⣬⣭⣭⣿⣿⣟⣛⣻⠟⢃⠉⠸⡙⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡀⠀⠀⠀⠀⠀⡇⠈⠉⠉⠉⠉⠙⠛⠋⠁⠀⠘⣿⢛⣿⠻⣿⣿⣿⣿⣿⣿⣿⣾⢸⡐⣆⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠤⠁⠀⠈⠀⠀⠀⠀⠀⠀⠤⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠈⠘⠃⠇⠿⠿⠿⠛⢛⠿⣯⣥⣼⣬⣽⣼⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣄⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣦⣀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠻⠿⢿
⠀⠀⢰⣶⡆⣶⣶⠀⢠⣶⢶⣤⠀⢰⣶⣶⢰⣶⣶⣶⠀⠀⣶⣶⣶⣄⢰⣶⡆⣶⡆⢰⣾⠉⢱⣶⠉⣶⡆⢰⡆⢀⣴⢶⣦⡀⠀⢰⣶⡈⣶⡆⢨⣷⢶⣤⠀⠀⠬⢀⢢⣶⣶⠂⠈⣶⣶⡆⢠⣶⢶⣄⠀⣴⡶⣦⡄⠀
⠀⠀⢸⣿⡇⣿⣿⠀⣿⣿⢸⣿⠀⣿⡟⣿⡀⢸⣿⠀⠀⠀⣿⣧⣼⡿⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⣿⣼⡇⢸⣿⢀⣛⡃⠀⢸⣿⣧⣿⡇⣿⣿⢸⣿⠀⠀⠀⠀⣼⢻⣿⠀⣸⡟⣿⡇⠉⢉⣼⡟⠀⣿⡇⣿⡇⠀
⠀⠀⢰⣿⡇⣿⣿⠀⣿⣿⢸⣿⢀⣿⣧⣿⡇⢸⣿⠀⠀⠀⣿⣏⢹⣷⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⡿⣿⡇⢸⣿⠘⣿⡇⠀⢸⣿⢻⣿⡇⣿⣿⢸⣿⠀⠀⠀⢰⣿⣼⣿⣤⣿⣤⣿⣧⢴⣦⢹⣿⠀⣿⡇⣿⡇⠀
⠀⠀⠸⢿⠇⠿⠟⠻⠸⠿⠾⠋⠘⠛⠁⠛⠓⠘⠛⠀⠀⠀⠛⠛⠘⠛⠈⠛⠷⠟⠁⠘⠛⠛⠘⠛⠀⠛⠃⠛⠃⠈⠻⠟⠛⠃⠀⠘⠛⠈⠛⠃⠘⠻⠾⠋⠘⠛⠀⠀⠀⠘⠛⠀⠀⠘⠛⠃⠘⠻⠾⠛⠀⠛⠷⠟⠁⠀
[20A⠀⠀⠡⠉⢩⣫⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⢿⡿⠿⠿⠿⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡄⣄⣥⣤⣾⣿⣿⣿⣿⡿⠟⠻⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠱⠏⠡⠛⠟⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣯⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⣭⡝⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣘⣏⢿⢿⣿⣷⠿⢻⣴⡆⠀⣸⣿⣷⣯⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣛⣻⣿⣿⣿⣿⠀⣿⣿⢠⣸⣿⣽⣿⣿⣿⣿⡗⠾⣭⣟⡟⡿⠿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣧⣼⠟⠃⠀⢻⣟⣿⣶⣯⣽⣿⡷⢷⣿⠟⠁⠀⠈⠈⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⣿⣿⣿⣿⣿⣿⡋⣿⣷⠫⢠⣼⢿⡿⣬⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠂⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⣼⡿⣼⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⣿⣿⡟⠐⣿⡿⠤⣾⣿⣶⣆⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣿⣷⣿⣿⣿⣿⢷⢸⣿⣿⣶⣦⣤⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⠁⢸⣿⡆⣀⣾⣇⣿⢸⣿⢹⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢰⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠿⠸⠿⢿⣷⣿⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣤⣾⣿⠉⢹⣿⢳⡏⣿⡇⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠐⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠙⠛⠻⢿⠇⠀⠀⠀⢤⣿⣿⣿⣿⣿⣏⣁⠿⠿⠉⠸⣿⢸⢳⣿⢳⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⢻⣿⡿⡀⣀⣿⣿⢘⡿⣼⣟⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡟⠛⢫⣽⣷⣖⣛⣗⣀⣹⣧⡏⣿⣇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣽⠿⠿⠿⠏⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⢀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣠⣬⣭⣭⣿⣿⣟⣛⣻⠟⢃⠉⠸⡙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠉⠉⠉⠉⠛⠋⠁⠀⠘⢿⢛⡿⠻⣿⣿⣿⣿⣿⣿⣿⣞⢸⡐⣆⡅⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠤⠀⠁⠀⠀⠀⠀⠀⠀⠀⠤⠄⠄⠀⠀⠀⠄⠀⠀⠀⠀⠈⠘⠃⠃⠿⠟⠛⠿⢭⣥⣤⣧⣬⣧⡟⠿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣦⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣦⣀⠀⠀⠀⠘⠛⠻⢿⡿⠿⠿⠿⠿⠿
⠀⠀⢰⣶⡆⣶⣶⠀⢠⣶⢶⣤⠀⢰⣶⣶⢰⣶⣶⣶⠀⠀⣶⣶⣶⣄⢰⣶⡆⣶⡆⢰⣾⠈⢸⣷⠀⣶⡆⢰⡆⢀⣴⢶⣦⡀⠀⢰⣶⡉⣷⡆⢨⣷⢶⣤⠀⠀⠬⢀⢂⣶⣶⠂⠈⣶⣶⡆⢠⣶⢶⣄⠀⣴⡶⣦⡄⠀
⠀⠀⢸⣿⡇⣿⣿⠀⣿⣿⢸⣿⠀⣿⡟⣿⡀⢸⣿⠀⠀⠀⣿⣧⣼⡿⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⣷⣼⡇⢸⣿⢀⣛⡃⠀⢸⣿⣧⣿⡇⣿⣿⢸⣿⠀⠀⠐⠀⣼⢻⣿⠀⣸⡟⣿⡇⠉⢉⣼⡟⠀⣿⡇⣿⡇⠀
⠀⠀⢸⣿⡇⣿⣿⠀⣿⣿⢸⣿⢀⣿⣧⣿⡇⢸⣿⠀⠀⠀⣿⡏⢹⣷⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⡿⣿⡇⢸⣿⠈⣿⡇⠀⢸⣿⢻⣿⡇⣿⣿⢸⣿⠀⠀⠀⢰⣿⣼⣿⣤⣿⣤⣿⣧⢴⣦⢹⣿⠀⣿⡇⣿⡇⠀
⠀⠀⠸⢿⠇⠿⠟⠻⠸⠿⠾⠋⠘⠛⠁⠛⠃⠘⠛⠀⠀⠀⠛⠓⠘⠛⠈⠛⠷⠟⠁⠘⠛⠛⠘⠛⠀⠛⠃⠛⠃⠈⠻⠟⠛⠃⠀⠘⠛⠈⠛⠃⠘⠻⠾⠋⠘⠛⠀⠀⠀⠘⠛⠀⠀⠘⠛⠃⠘⠻⠾⠛⠀⠛⠷⠟⠁⠀
[20A⠀⠀⠡⠉⠉⢫⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⢿⣿⠿⠿⠿⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⣠⣥⣤⣾⣿⣿⣿⣿⡿⠟⠫⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠹⠏⠡⠛⠟⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⣭⡍⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣘⣏⢿⢿⣿⣷⠿⢻⣥⡄⠀⣸⣿⣷⣭⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣛⣻⣿⣿⣿⣿⠀⣿⣿⢠⣸⣿⣽⣿⣿⣿⣿⡗⠾⣭⣟⠛⢻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣧⣼⠟⠃⠀⢻⣟⣿⣶⣯⣽⣿⡷⢷⠟⠀⠀⠈⠈⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⣿⣿⣿⣿⣿⣿⡋⣿⣷⠫⢠⣼⢿⡿⣬⣿⣿⣿⡿⢁⠀⠀⠀⠀⠀⠃⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⣾⡿⣼⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⣿⣿⡟⢐⣿⡿⠮⣿⣿⣶⢆⣿⣿⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣿⣷⣿⣿⣿⣿⢧⢸⣿⣿⣶⣦⣤⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⠃⢸⣿⡆⣀⣾⣇⣿⢸⣿⢹⣿⡟⠀⠀⠀⠀⠀⠄⠀⠀⠀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠿⠸⠿⢿⣷⣿⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣻⣤⣾⣿⠉⢹⣿⢳⡏⣿⡇⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠙⠛⠻⢿⠃⠀⠀⠀⢤⣿⣿⣿⣿⣿⣏⡁⠿⠿⠉⠸⣿⢸⢳⣿⢱⡟⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢻⣿⡿⡀⣀⣿⣿⢘⡽⣼⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡟⠛⢫⣽⣷⣆⣛⣗⣀⣹⣧⡏⣿⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣿⣿⣿⣽⠿⠻⠿⠏⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⢀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣠⣬⣭⣭⣿⣿⣟⣛⣻⠟⢃⠉⠸⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠉⠉⠉⠉⠛⠋⠁⠀⠚⢿⢛⡿⠻⣿⣿⣿⣿⣿⣿⣿⣾⢸⡐⣆⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠤⠉⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠈⠘⠃⠃⠟⠛⠿⢭⢭⣤⣧⣬⣿⡇⡛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⣿⣦⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣦⣀⠀⠀⠀⠘⠛⠛⢿⣿⣿⡿⠿⠿⠿
⠀⠀⠰⣶⡆⣶⣶⠀⢠⣶⢶⣤⠀⢰⣶⣶⢰⣶⣶⣶⠀⠀⣶⣶⣶⣄⢰⣶⡆⣶⡆⢰⣶⠈⢱⣶⠀⣶⡆⢰⡆⢀⣴⢶⣦⡀⠀⢰⣶⡉⣷⡆⢨⣷⢶⣤⠀⠀⠬⢀⢂⣶⣶⠂⠈⣶⣶⡆⢠⣶⢶⣄⠀⣵⡶⣦⡄⠀
⠀⠀⠀⣿⡇⣿⣿⠀⣿⣿⢸⣿⠀⣿⡟⣿⡀⢸⣿⠀⠀⠀⣿⣧⣼⡿⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⣷⣼⡇⢸⣿⠀⣛⡃⠀⢸⣿⣧⣿⡇⣿⣿⢸⣿⠀⠐⠐⠀⣼⢻⣿⠀⣸⡟⣿⡇⠉⢉⣼⡟⠀⣿⡇⣿⡇⠀
⠀⠀⠀⣿⡇⣿⣿⠀⣿⣿⢸⣿⢀⣿⣧⣿⡇⢸⣿⠀⠀⠀⣿⡏⢹⣷⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⡿⣿⡇⢸⣿⠈⣿⡇⠀⢸⣿⢻⣿⡇⣿⣿⢸⣿⠀⠀⠀⢰⣿⣼⣿⣤⣿⣤⣿⣧⢴⣦⢹⣿⠀⣿⡇⣿⡇⠀
⠀⠀⠰⢿⠇⠿⠟⠻⠸⠿⠾⠋⠘⠛⠁⠛⠃⠘⠛⠀⠀⠀⠛⠛⠘⠛⠈⠛⠷⠟⠁⠘⠛⠛⠘⠛⠀⠛⠃⠛⠃⠈⠻⠟⠛⠃⠀⠘⠛⠈⠛⠃⠘⠻⠾⠋⠘⠛⠀⠀⠀⠘⠛⠀⠀⠘⠛⠃⠘⠻⠾⠛⠀⠛⠷⠟⠁⠀
[20A⠀⠀⠡⣉⠩⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⠿⠿⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡄⣠⣥⣦⣼⣿⣿⣿⣿⡿⠟⠫⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠹⠏⠡⠛⠟⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⣭⡝⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣘⣏⢿⢿⣿⣷⠿⢻⣵⡆⠀⣸⣿⣷⣯⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣛⣻⣿⣿⣿⣿⠀⣿⣿⢠⣸⣿⣽⣿⣿⣿⣿⡗⠾⣭⡟⢛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣧⣼⢟⠃⠀⢻⣟⣿⣶⣯⣽⣿⡷⠇⠁⠀⠐⠁⠀⠈⠻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⣿⣿⣿⣿⣿⣿⠋⣿⣷⠫⢠⣼⢿⡿⣮⣿⣿⡿⠁⠀⠀⠀⠀⠀⠁⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⣼⡿⣼⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⣿⣿⡟⢐⣿⡿⠬⢿⣿⣶⣆⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣿⣷⣿⣿⣿⣿⢷⢸⣿⣿⣶⣦⣤⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⠃⢸⣿⡆⣀⣾⣇⣿⢸⣿⢹⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠿⠸⠿⢿⣿⣿⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣤⣾⣿⠉⢹⣿⢳⡏⣿⡇⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠙⠛⠻⢿⠃⠀⠀⠀⢤⣿⣿⣿⣿⣿⣏⡁⠿⠿⠉⠸⣿⢸⢳⣿⢳⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢻⣿⡿⡀⣀⣿⣿⢘⡿⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡟⠛⢫⣽⣷⣖⣛⣗⣀⣹⣧⡏⣿⣇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣽⠿⠿⠿⠏⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⢀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣠⣬⣭⣭⣿⣿⣟⣛⣻⠟⢃⠉⠸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⣿⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠉⠉⠉⠉⠛⠋⠁⠀⠚⢿⢛⡿⠻⣿⣿⣿⣿⣿⣿⣿⣞⢸⡐⣆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠨⠘⠃⠇⠛⠿⠯⠽⠷⠷⢤⢿⣼⡇⡋⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡆⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣦⣀⠀⠀⠀⠘⠛⠛⢿⣿⣿⣿⣿⠿⠿
⠀⠀⠰⣶⡆⣶⣶⠀⢠⣶⢶⣤⠀⢰⣶⣶⢰⣶⣶⣶⠀⠀⣶⣶⣶⣄⢰⣶⡆⣶⡆⢰⣶⠉⢰⣶⠀⣶⡆⢰⡆⢀⣴⢶⣦⡀⠀⢰⣾⡈⣶⡇⢨⣷⢶⣤⠀⠀⠬⢀⢢⣶⣶⠂⠈⣶⣶⡆⢠⣶⢶⣄⠀⣽⡶⣦⡄⠀
⠀⠀⠀⣿⡇⣿⣿⠀⣿⣿⢸⣿⠀⣿⡟⣿⡀⢸⣿⠀⠀⠀⣿⣧⣼⡿⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⣷⣼⡇⢸⣿⢀⣛⡃⠀⢸⣿⣧⣿⡇⣿⣿⢸⣿⠀⠐⠒⠀⣼⢻⣿⠀⣸⡟⣿⡇⠉⢉⣼⡟⠀⣿⡇⣿⡇⠀
⠀⠀⠀⣿⡇⣿⣿⠀⣿⣿⢸⣿⢀⣿⣧⣿⡇⢸⣿⠀⠀⠀⣿⡏⢹⣷⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⡿⣿⡇⢸⣿⠈⣿⡇⠀⢸⣿⢻⣿⡇⣿⣿⢸⣿⠀⠀⠀⢰⣿⣼⣿⣤⣿⣤⣿⣧⢴⣦⢹⣿⠀⣿⡇⣿⡇⠀
⠀⠀⠰⢿⠇⠿⠟⠻⠸⠿⠾⠋⠘⠛⠁⠛⠓⠘⠛⠀⠀⠀⠛⠓⠘⠛⠈⠛⠷⠟⠁⠘⠛⠛⠘⠛⠀⠛⠃⠛⠃⠈⠻⠟⠛⠃⠀⠘⠛⠈⠛⠃⠘⠻⠾⠋⠘⠛⠀⠀⠀⠘⠛⠀⠀⠘⠛⠃⠘⠻⠾⠛⠀⠛⠷⠟⠁⠀
[20A⠀⠀⠀⠉⢩⣫⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⢿⣿⠿⠿⠿⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⢠⣤⣤⣾⣿⣿⣿⣿⡿⠟⠫⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠹⠏⠡⠛⢟⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣯⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⡭⡍⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣘⣏⢿⢿⣿⣷⠿⢻⣵⡆⠀⣸⣿⣷⣯⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣛⣻⣿⣿⣿⣿⠀⣿⣿⢠⣨⣿⣽⣿⣿⣿⣿⡗⢾⡝⢟⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣧⣼⠛⠃⠀⢻⣟⣿⣶⣯⣽⣿⠏⠇⠀⠑⠀⠀⠀⠾⠻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠃⣿⣿⣿⣿⣿⣿⡋⣿⣷⠫⢠⣼⢿⡿⣬⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⣼⡿⣼⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⣿⣿⡟⢑⣿⡿⠬⣿⣿⣶⣇⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣿⣷⣿⣿⣿⣿⢷⢸⣿⣿⣶⣦⣤⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⠁⢸⣿⠆⣀⣾⣇⣿⢸⣿⠹⠀⠀⠀⠀⠀⠐⠀⠀⠀⢰⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠿⠸⠿⢿⣿⣿⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣻⣤⣾⣿⠉⢹⣿⢳⡏⣿⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠙⠛⠻⢿⠃⠀⠀⠀⢤⣿⣿⣿⣿⣿⣏⣁⠿⠿⠉⠸⣿⢸⢳⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢻⣿⡿⡀⣀⣿⣿⢘⡽⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡟⠛⢫⣽⣷⣆⣚⣗⣀⣹⣧⡏⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣽⠿⠿⠿⠏⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⢀⠀⢀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⣠⣬⣭⣭⣿⣿⣟⣛⣻⠟⢃⠉⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠉⠉⠉⠙⠛⠋⠁⠀⠚⢻⠛⡿⠻⢿⣿⣿⢿⣿⣿⣿⣞⢸⠐⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣚⣛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠨⠘⠃⠃⠿⠽⠽⠷⠶⢶⠿⣿⢸⡇⡋⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡅⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣦⣀⠀⠀⠀⠘⠛⠛⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠰⣶⡆⣶⣶⠀⢠⣶⢶⣤⠀⢰⣶⣶⢰⣶⣶⣶⠀⠀⣶⣶⣶⣄⢰⣶⡆⣶⡆⢰⣾⠀⢰⣶⠀⣶⡆⢰⡆⢀⣴⢶⣦⡀⠀⢰⣶⡉⣶⡆⢨⣷⢶⣤⠀⠀⠨⢀⢢⣶⣶⠂⠈⣶⣶⡆⢠⣶⢶⣄⠀⣽⡶⣦⡌⠁
⠀⠀⠀⣿⡇⣿⣿⠀⣿⣿⢸⣿⠀⣿⡟⣿⡀⢸⣿⠀⠀⠀⣿⣧⣼⡿⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⣷⣼⡇⢸⣿⢀⣛⡃⠀⢸⣿⣧⣿⡇⣿⣿⢸⣿⠀⠐⠒⠀⣼⢻⣿⠀⣸⡟⣿⡇⠉⢉⣼⡟⠀⣿⡇⣿⡇⠀
⠀⠀⠀⣿⡇⣿⣿⠀⣿⣿⢸⣿⢀⣿⣧⣿⡇⢸⣿⠀⠀⠀⣿⡏⢹⣷⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⡿⣿⡇⢸⣿⠈⣿⡇⠀⢸⣿⢻⣿⡇⣿⣿⢸⣿⠀⠀⠀⢰⣿⣼⣿⣤⣿⣤⣿⣧⢴⣦⢹⣿⠀⣿⡇⣿⡇⠀
⠀⠀⠰⢿⠇⠿⠟⠻⠸⠿⠾⠋⠘⠛⠁⠛⠃⠘⠛⠀⠀⠀⠛⠓⠘⠛⠈⠛⠷⠟⠁⠘⠛⠛⠘⠛⠀⠛⠃⠛⠃⠈⠻⠟⠛⠃⠀⠘⠛⠈⠛⠃⠘⠻⠾⠋⠘⠛⠀⠀⠀⠘⠛⠀⠀⠈⠛⠃⠘⠻⠾⠋⠀⠛⠷⠟⠁⠀
[20A⠀⠀⠀⠉⢉⣭⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⠿⠿⡿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣠⣤⣤⣾⣿⣿⣿⣿⡿⠟⠫⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠹⠏⠡⠛⢟⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣿⣿⣯⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⡭⡍⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣘⣏⢿⢿⣿⣷⠿⢻⣵⡆⠀⣸⣿⣷⣯⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣛⣻⣾⣿⣿⣿⠀⣿⣿⢠⣸⣿⣹⣿⣿⣿⡿⡷⠾⣭⣟⡛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣧⣬⠛⠃⠀⢻⣟⣿⣶⣯⠝⠁⠈⠃⠀⠀⠁⢴⣿⣾⠻⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠂⣿⣿⣿⣿⣿⣿⡏⣿⣷⠋⢠⣼⢿⡿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⢷⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⣼⡿⣼⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠄⢰⣯⣽⣿⣿⣿⡟⠑⣿⡿⠬⣿⡿⣶⢧⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡗⢺⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣿⣷⣿⣿⣿⣿⢷⢸⣿⣿⣶⣦⣤⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⠃⢸⣿⣆⣀⣿⣇⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠿⠸⠿⢿⣿⣿⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣤⣾⣿⠉⢹⣿⢳⡏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠙⠛⠻⢿⠃⠀⠀⠀⢤⣿⣿⣿⣿⣿⣏⣁⠿⠿⠩⠸⣿⢸⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣀⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢻⣿⡿⠀⣀⣿⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣈⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡟⠛⢫⣽⣷⣖⣚⣗⣀⣹⣧⡏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣽⠿⠿⠿⠏⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⢀⠀⢀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⣠⣬⣭⣭⣿⣿⣟⣛⣻⠟⢃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⣼⣿⣿⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠉⠉⠉⠉⠛⠋⠁⠀⠘⢺⠚⡿⠻⢿⠿⠿⢿⣿⣿⣿⣮⢸⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣾⣝⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠒⠁⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠈⠘⠁⠳⠾⠿⠾⠶⠾⣿⡟⠿⢸⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠟⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣦⣀⠀⠀⠀⠘⠛⠛⢿⣿⣿⣿⣿⣿⣿
⠀⠀⢰⣶⡆⣶⣶⠀⢠⣶⢶⣤⠀⢰⣶⣶⢰⣶⣶⣶⠀⠀⣶⣶⣶⣄⢰⣶⡆⣶⡆⢰⣶⠀⢰⣶⠀⣶⡆⢰⡆⢀⣴⢶⣦⡀⠀⢰⣶⡀⣾⡆⢨⣷⢶⣤⠀⠀⠨⢀⢂⣶⣶⠂⠈⣶⣶⡆⢠⣶⢶⣤⠈⣽⡶⣦⡍⠉
⠀⠀⠸⣿⡇⣿⣿⠀⣿⣿⢸⣿⠀⣿⡟⣿⡀⢸⣿⠀⠀⠀⣿⣧⣼⡿⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⣷⣼⡇⢸⣿⢀⢛⡃⠀⢸⣿⣧⣿⡇⣿⣿⢸⣿⠀⠐⠒⠀⣼⢻⣿⠀⣸⡟⣿⡇⠉⢉⣼⡟⠀⣿⡇⣿⡇⠀
⠀⠀⢠⣿⡇⣿⣿⠀⣿⣿⢸⣿⢀⣿⣧⣿⡇⢸⣿⠀⠀⠀⣿⡏⢹⣷⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⡿⣿⡇⢸⣿⠈⣿⡇⠀⢸⣿⢻⣿⡇⣿⣿⢸⣿⠀⠀⠀⢰⣿⣼⣿⣤⣿⣤⣿⣧⢴⣦⢹⣿⠀⣿⡇⣿⡇⠀
⠀⠀⠸⢿⠇⠿⠟⠻⠸⠿⠾⠋⠘⠛⠁⠛⠃⠘⠛⠀⠀⠀⠛⠓⠘⠛⠈⠛⠷⠟⠁⠘⠛⠛⠘⠛⠀⠛⠃⠛⠃⠈⠻⠟⠛⠃⠀⠘⠛⠈⠛⠃⠘⠻⠾⠋⠘⠛⠀⠀⠀⠘⠛⠀⠀⠘⠛⠃⠘⠻⠾⠛⠀⠛⠷⠟⠁⠀
[20A⠀⠀⠡⣩⣩⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⠿⠿⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⣴⣥⣦⣾⣿⣿⣿⣿⣿⠟⠿⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠹⠏⠡⠛⢟⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⣭⡍⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣜⣏⢿⢿⣿⣷⠿⢻⣵⡆⠀⣸⣿⣷⣯⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣛⣻⣾⣿⣿⣿⠀⣿⣿⢠⣸⣿⣹⣿⣿⣿⣿⡷⠾⣭⣟⡛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣧⣬⠛⠃⠀⢻⣟⣿⡶⠋⠁⠢⠀⠀⠉⢿⠇⣴⣿⣾⠻⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠃⣿⣿⣿⣿⣿⣿⡏⣿⣿⠫⢠⣼⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⢷⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⣼⣿⣼⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣽⣿⣿⣿⡟⠑⣿⡿⠬⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⠗⢺⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣿⣷⣿⣿⣿⣿⢷⢸⣿⣿⣶⣦⣤⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⠃⢸⣿⡇⣀⣾⣇⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣸⣿⠿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠿⠸⠿⢿⣿⣿⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣤⣾⣿⠉⢹⣿⢳⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠙⠛⠻⢿⠇⠀⠀⠀⢤⣿⣿⣿⣿⣿⣏⣅⠿⠿⠩⠸⣿⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⣀⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢻⣿⡟⠀⣀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣈⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡟⠛⢫⣽⣷⣖⣛⣗⣂⣹⣧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⣿⣿⣿⣿⣿⣽⠿⠿⠿⠏⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⢀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣠⣬⣭⣭⣿⣿⣟⣛⣻⠟⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⣻⣼⣿⣿⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠉⠉⠉⠙⠛⠋⠁⠀⠘⢻⢛⡿⠻⠿⠿⠿⣿⣿⣿⣿⣞⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣶⣶⡝⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠒⠁⠀⠀⠀⠀⠄⠀⠀⠠⠤⠀⠀⠀⢀⣀⠄⠠⠀⣀⠀⠈⠈⠓⠶⠾⠾⠶⠾⢿⣟⣛⠿⢸⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣣⣶⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣦⣀⠀⠀⠀⠘⢛⡛⢿⣿⣿⣿⣿⣿⣿
⠀⠀⢠⣤⠀⣤⡄⠀⣠⣤⣤⡀⢠⣤⣤⠠⣤⣤⣤⡄⠀⢠⣤⣤⡀⢠⣤⠀⣬⡌⣤⡤⠀⢠⣤⢠⣤⠀⣤⡄⢀⣤⣤⡀⠀⠀⣤⡄⢩⣥⠛⣡⣬⣅⠈⠀⠀⠀⠀⣤⣤⠀⠀⣢⣬⡍⢃⣤⣤⡄⠀⣠⣬⣍⠉⠉⠉⠉
⠀⠀⢸⣿⠀⣿⡇⠀⣿⡇⣿⡇⢸⣿⣿⡇⠉⣿⡏⠁⠀⢸⣿⣸⡿⢸⣿⠀⣿⡇⣿⡇⠀⢸⣿⢨⣿⣇⣿⡇⣿⡇⠸⠿⠀⠀⣿⣿⣸⣿⢸⣿⠀⣿⡇⠀⠀⠀⢰⢿⣿⠀⢰⡟⣿⡇⠸⣧⣸⡿⠘⠛⢰⣿⠀⠀⠀⠀
⠀⠀⢸⣿⠀⣿⡇⠀⣿⡇⣿⡇⣼⣧⣼⣇⠀⣿⡇⠀⠀⢸⣿⢹⣶⢸⣿⠀⣿⡇⣿⡇⠀⢸⣿⢐⣿⢻⣿⡇⣿⡇⢻⣿⠀⠀⣿⡟⣿⣿⢸⣿⠀⣿⡇⠀⠀⠀⣿⣸⣿⣄⣾⣀⣿⣇⢸⡏⢹⣷⠀⣰⡿⠃⠀⠒⠒⠒
⠀⠀⠸⢿⠀⠿⠷⠦⠻⠷⠿⠃⠿⠏⠹⠿⠀⠿⠇⠀⠀⠸⠿⠸⠿⠈⠻⠶⠟⠁⠿⠿⠶⠸⠿⠰⠿⠈⠿⠇⠙⠷⠞⠿⠀⠀⠿⠇⠹⠿⠈⠻⠶⠟⠁⠿⠀⠀⠉⠹⠿⠁⠉⠉⠿⠇⠘⠷⠾⠟⠰⠿⠷⠶⠀⠀⠀⠀
[20A⠀⠀⠨⠽⢉⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⠿⠿⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣴⣅⣤⣾⣿⣿⣿⣿⣿⠟⠿⠛⠋⠉⠀⠀⠈⠀⠀⠀⠘⠹⠏⠱⠛⣟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠆⠠⣤⡀⠀⣾⣿⡟⢁⣭⡝⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣔⣏⢿⢿⣿⣷⠿⢻⣵⡆⠀⣸⣿⣷⣯⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣛⣿⣾⣿⣿⣿⠀⣿⣿⢠⣨⣿⣹⣿⣿⣿⣿⣷⠾⣭⣟⡛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣧⣬⠟⠃⠀⢻⣟⡿⠂⠙⠆⠀⠀⠰⠿⣾⠇⣴⣿⣾⠻⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⣿⣿⣿⣿⣿⣿⡏⣿⣿⠫⣰⣼⠟⠀⠀⠀⠀⠀⠁⠀⠀⠈⣄⣼⣿⡏⢷⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⣾⡿⣼⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣽⣿⣿⣿⡟⠑⣿⡿⠤⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⢹⣿⣗⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣿⣷⣿⣿⣿⣿⢷⢸⣿⣿⣶⣦⣤⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⠉⢸⣿⣆⣀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⢸⣿⠿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠿⠸⠿⢿⣿⣿⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣤⣾⣿⠉⢹⣿⡃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢏⢹⡟⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠙⠛⠻⢿⠇⠀⠀⠀⢤⣿⣿⣿⣿⣿⣏⣅⠿⠿⠩⢸⣿⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣆⣀⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢻⣿⡗⠀⣀⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠈⣌⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡟⠛⢫⣽⣷⣖⣛⣗⣀⣹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣿⣿⣿⣿⣽⠿⠿⠿⠏⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⢀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣠⣬⣭⣭⣿⣿⣟⣛⣻⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⢼⣿⣿⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠉⠉⠉⠙⠛⠋⠁⠀⠚⢻⢻⡿⠻⠿⠿⢿⣿⣿⣿⣿⣮⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣷⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠒⠁⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⢀⣀⠄⠀⢀⢀⠀⠈⠚⠖⠾⠶⢶⠶⢿⣿⠛⣛⠿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣫⣶⣶⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣦⣀⠀⠀⠀⠘⢛⠛⢿⣿⣿⣿⣿⣿⣿
⠀⠀⢠⣤⠀⣤⡄⠀⣠⣤⣤⡀⢠⣤⣤⠠⣤⣤⣤⡄⠀⢠⣤⣤⡀⢠⣤⠈⣤⡄⣤⡄⠀⢠⣤⢠⣤⠀⣤⡄⢀⣤⣤⡀⠀⠀⣤⡌⢩⣥⠛⣡⣬⣅⠈⠀⠀⠀⠀⣤⣤⠀⠀⣠⣬⡍⢃⣤⣤⡄⠀⣠⣬⣍⠋⠉⠉⠉
⠀⠀⢸⣿⠀⣿⡇⠀⣿⡇⣿⡇⢸⣿⣿⡇⠉⣿⡏⠁⠀⢸⣿⣸⡿⢸⣿⠀⣿⡇⣿⡇⠀⢸⣿⢨⣿⣇⣿⡇⣿⡇⠸⠿⠀⠀⣿⣿⣸⣿⢸⣿⠀⣿⡇⠀⠐⠀⢰⢿⣿⠀⢰⡟⣿⡇⠸⣇⣸⡿⠘⠛⢰⣿⠀⠀⠀⠀
⠀⠀⢸⣿⠀⣿⡇⠀⣿⡇⣿⡇⣸⣧⣼⣇⠀⣿⡇⠀⠀⢸⣿⢹⣶⢸⣿⠀⣿⡇⣿⡇⠀⢸⣿⢐⣿⢻⣿⡇⣿⡇⢻⣿⠀⠀⣿⡟⣿⣿⢸⣿⠀⣿⡇⠀⠀⠀⣿⣸⣿⣄⣾⣀⣿⣇⢸⡏⢹⣷⠀⣰⡿⠃⠀⠒⠒⠒
⠀⠀⠸⢿⠀⠿⠷⠦⠻⠷⠿⠃⠿⠏⠹⠿⠀⠿⠇⠀⠀⠸⠿⠸⠿⠈⠻⠶⠟⠁⠿⠿⠶⠸⠿⠰⠿⠈⠿⠇⠙⠷⠞⠿⠀⠀⠿⠇⠹⠿⠈⠻⠶⠟⠁⠿⠀⠀⠉⠹⠿⠁⠉⠉⠿⠇⠘⠷⠾⠟⠰⠿⠷⠶⠀⠀⠀⠀
[20A⠀⠀⠨⠽⢩⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⠿⠿⡿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣠⣦⣕⣴⣾⣿⣿⣿⣿⣿⠟⠿⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠹⠏⠱⠛⣏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠆⠠⣤⡀⠀⣾⣿⡟⢁⣭⡝⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣐⣏⢿⢿⣿⣷⠿⢻⣴⡆⠀⣸⣿⣷⣯⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣛⣻⣾⣿⣿⣿⠀⣿⣿⢠⣸⣿⣹⣿⣿⣿⣿⣷⠾⣭⣟⡛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣧⣬⠟⠃⠁⠛⢛⡏⠁⠉⢽⣿⡷⢷⣿⣾⠇⣴⣿⣾⠻⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⣿⣿⣿⣿⣿⣿⡏⣿⣿⠋⠀⠀⠀⠀⠀⠂⠀⠀⠈⢿⣿⣿⢄⣼⣿⡏⢵⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⣼⣿⣼⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣽⣿⣿⣿⡟⢑⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣯⢨⢹⣿⣗⢺⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣿⣷⣿⣿⣿⣿⢷⢸⣿⣿⣶⣦⣤⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⠉⢸⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⣿⢸⣿⠿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠿⠸⠿⢿⣿⣿⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣤⣾⣿⠉⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⡏⢹⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠙⠛⠻⢿⠃⠀⠀⠀⢤⣿⣿⣿⣿⣿⣏⣁⠿⠿⠉⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠟⣿⣆⣀⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢻⣿⡿⠀⡘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣶⢈⣈⣷⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡟⠛⢫⣽⣷⣖⣛⣗⣀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠓⣿⣿⣿⣿⣿⣿⣽⠿⠿⠿⠏⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⢀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣠⣬⣭⣭⣿⣿⣟⣛⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣤⣻⣼⣿⣿⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠉⠉⠉⠙⠛⠋⠁⠀⠚⢻⠻⠿⠻⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⡿⣸⡛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠒⠁⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⢀⣀⠄⠀⠀⠀⠐⠒⠒⠒⠳⠶⠿⣿⠿⠿⠛⣛⠿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣷⣶⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣦⣀⠀⠀⠀⠘⠛⠛⢿⣿⣿⣿⣿⣿⣿
⠀⠀⢠⣤⠀⣤⡄⠀⣠⣤⣤⡀⢠⣤⣤⠠⣤⣤⣤⡄⠀⢠⣤⣤⡀⢨⣤⠀⣤⡄⣤⡄⠀⢠⣤⢠⣤⠀⣤⡄⢀⣤⣤⡀⠀⠀⣤⡌⢩⣥⠛⣡⣬⣅⠈⠀⠀⠀⠀⣤⣤⠀⠀⣢⣬⡍⢃⣤⣤⡄⠀⣠⣬⣍⠉⠉⠉⠉
⠀⠀⢸⣿⠀⣿⡇⠀⣿⡇⣿⡇⢸⣿⣿⡇⠉⣿⡏⠁⠀⢸⣿⣸⡿⢸⣿⠀⣿⡇⣿⡇⠀⢸⣿⠘⣿⣇⣿⡇⣿⡇⠸⠿⠀⠀⣿⣿⣸⣿⢸⣿⠀⣿⡇⠀⠐⠀⢰⠿⣿⠀⢠⡟⣿⡇⠸⣧⣸⡿⠘⠛⢰⣿⠀⠀⠀⠀
⠀⠀⢸⣿⠀⣿⡇⠀⣿⡇⣿⡇⣸⣧⣼⣇⠀⣿⡇⠀⠀⢸⣿⢹⣶⢸⣿⠀⣿⡇⣿⡇⠀⢸⣿⠰⣿⢻⣿⡇⣿⡇⢻⣿⠀⠀⣿⡟⣿⣿⢸⣿⠀⣿⡇⠀⠀⠀⣿⣠⣿⣄⣾⣀⣿⣇⢸⡏⢹⣷⠀⣰⡿⠃⠀⠒⠒⠒
⠀⠀⠸⢿⠀⠿⠷⠦⠻⠷⠿⠃⠿⠏⠹⠿⠀⠿⠇⠀⠀⠸⠿⠸⠿⠈⠻⠶⠿⠁⠿⠿⠶⠸⠿⠰⠿⠈⠿⠇⠙⠷⠞⠿⠀⠀⠿⠇⠹⠿⠈⠻⠶⠟⠁⠿⠀⠀⠉⠹⠿⠁⠉⠉⠿⠇⠘⠷⠾⠟⠰⠿⠷⠶⠀⠀⠀⠀
[20A⠀⠀⠨⢽⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⠿⠿⠿⡿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣂⣤⣔⣶⣿⣿⣿⣿⣿⣿⠟⡿⠛⠋⠉⠀⠀⠈⠀⠀⠀⠸⠹⠏⠡⠻⣏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⣭⡝⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣘⣏⢿⢿⣿⣷⢿⢻⣤⡆⠀⣸⣿⣷⣯⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣛⣻⣾⣿⣿⣿⠀⣿⣿⢠⣸⣿⣹⣿⣿⣿⣿⣷⠾⣭⣟⡛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣧⣬⠿⠃⢀⣛⠛⠛⠲⣯⣿⣿⡷⢷⣿⣿⠇⣴⣿⣾⠻⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⣿⣿⣿⣿⣿⣿⡏⣿⣿⠋⠀⠁⠀⠐⠀⠠⠈⠹⣿⣿⣿⣿⢄⣼⣿⡏⢵⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⣼⣿⣼⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣽⣿⣿⣿⡟⢑⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣯⢨⢹⣿⣗⢺⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣿⣷⣿⣿⣿⣿⣷⢸⣿⣿⣶⣦⣤⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⠁⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡿⣿⢸⣿⠿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠿⠸⠿⢿⣿⣿⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣤⣾⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡏⡏⢽⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠙⠛⠻⢿⠃⠀⠀⠀⢦⣿⣿⣿⣿⣿⣏⣅⠿⠿⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠟⣿⣆⣀⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢻⣿⡿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⢿⣶⠈⣈⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡟⠛⢫⣽⣷⣖⣛⣗⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣟⠓⣿⣿⣿⣿⣿⣿⣽⠿⠿⠿⠏⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⢀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣠⣬⣭⣭⣿⣿⣟⣛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⣦⡻⣼⣿⣿⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠉⠉⠉⠙⠛⠋⠁⠀⢚⠻⠛⠿⠻⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣣⣟⡛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⢀⣀⠄⠀⠀⠐⠒⠒⠂⠓⠶⠺⣿⡿⠿⠿⠛⣛⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢿⣿⣷⣶⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣦⣀⠀⠀⠀⠘⠛⠻⢿⣿⣿⣿⣿⣿⣿
⠀⠀⢠⣤⠀⣤⡄⠀⣠⣤⣤⡀⢠⣤⣤⠀⣤⣤⣤⡄⠀⢠⣤⣤⡀⢠⣤⠀⣤⡄⣤⡄⠀⢠⣤⢠⣤⠀⣤⡄⢀⣤⣤⡀⠀⠀⣬⡌⢩⣥⠛⣡⣬⣅⠈⠀⠀⠀⠀⣤⣤⠀⠀⣢⣬⡍⢃⣤⣤⡄⠀⣠⣬⣍⠉⠉⠉⠉
⠀⠀⢸⣿⠀⣿⡇⠀⣿⡇⣿⡇⢸⡿⣿⡇⠉⣿⡏⠁⠀⢸⣿⣸⡿⢸⣿⠀⣿⡇⣿⡇⠀⢸⣿⠐⣿⣇⣿⡇⣿⡇⠸⠿⠀⠀⣿⣿⣸⣿⢸⣿⠀⣿⡇⠀⠐⠀⢰⢿⣿⠀⢠⡟⣿⡇⠸⣇⣸⡿⠘⠛⢰⣿⠀⠀⠀⠀
⠀⠀⢸⣿⠀⣿⡇⠀⣿⡇⣿⡇⣸⣧⣼⣇⠀⣿⡇⠀⠀⢸⣿⢹⣶⢸⣿⠀⣿⡇⣿⡇⠀⢸⣿⠰⣿⢻⣿⡇⣿⡇⢻⣿⠀⠀⣿⡟⣿⣿⢸⣿⠀⣿⡇⠀⠀⠀⣿⣸⣿⣄⣾⣀⣿⣇⢸⡏⢹⣷⠀⣰⡿⠃⠀⠒⠒⠒
⠀⠀⠸⢿⠀⠿⠷⠦⠻⠷⠿⠃⠿⠏⠹⠿⠀⠿⠇⠀⠀⠸⠿⠸⠿⠈⠻⠶⠟⠁⠿⠿⠶⠸⠿⠰⠿⠈⠿⠇⠙⠷⠞⠿⠀⠀⠿⠇⠹⠿⠈⠻⠶⠟⠁⠿⠀⠀⠉⠹⠿⠁⠉⠉⠿⠇⠘⠷⠾⠟⠰⠿⠷⠶⠀⠀⠀⠀
[20A⠀⠀⠀⠀⠉⢩⣽⣽⣿⣿⢿⣿⣿⣿⣿⣿⡿⢿⡿⠿⠿⠿⡿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡦⣠⣄⣤⣼⣾⣿⣿⣿⣿⠟⡯⠛⠋⠉⠀⠀⠈⠀⠀⠀⠸⠹⠏⠡⠛⠏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⠷⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⣭⡝⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣐⣏⢿⢿⣿⣷⠿⢻⣤⡆⠀⣸⣿⣷⣯⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣛⣻⣿⣿⣿⣿⠀⣿⣿⢠⣸⣿⣹⣿⣿⣿⣿⣷⠾⣭⣟⡛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣧⣬⢛⠃⠀⠿⠟⣿⣶⣯⣽⣿⡷⢷⣿⣿⠃⣵⣿⣾⠻⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⣿⣿⣿⣿⣿⣿⡏⣿⠉⠑⠀⠀⠀⠈⠈⠙⣿⣿⣿⣿⣿⣿⢄⣼⣿⡏⢷⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⣾⣿⣼⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⣿⣿⡟⢑⠇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣯⢨⢹⣿⣗⢺⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣿⣷⣿⣿⣿⣿⢷⢸⣿⣿⣶⣦⣤⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣯⣿⡿⣿⢸⣿⠿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠿⠸⠿⢿⣿⣿⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣤⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡏⡏⢽⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠙⠛⠻⢿⠃⠀⠀⠀⢦⣿⣿⣿⣿⣿⣏⣁⠿⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⢿⠟⣿⣆⣀⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣸⢿⣶⢈⣈⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡟⠛⢫⣽⣷⣖⣛⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⡟⠓⣿⣿⣿⣿⣿⣿⣽⠿⠻⠻⠏⠟⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⢀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣠⣬⣭⣭⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣿⣦⢿⣼⣿⣿⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠉⠉⠉⠙⠛⠋⠁⠀⡘⠳⠺⠿⡻⢿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣋⣾⣛⡛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⢀⣀⠄⠀⠐⠂⠒⠂⠒⠒⠺⣿⡿⠿⠿⠿⠛⣛⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⣷⣶⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣦⣀⠀⠀⠀⠘⠛⢛⢿⣿⣿⣿⣿⣿⣿
⠀⠀⢠⣤⠀⣤⡄⠀⣠⣤⣤⡀⢀⣤⣤⠀⣤⣤⣤⡄⠀⢠⣤⣤⡀⢠⣤⠀⣤⡄⣤⡄⠀⢠⣤⢠⣤⠀⣤⡄⢀⣤⣤⡀⠀⠀⣬⡌⢩⣥⠛⣡⣬⣅⠈⠀⠀⠀⠀⣤⣤⠀⠀⣢⣬⡍⢃⣤⣤⡄⠀⣠⣬⣍⠉⠉⠉⠉
⠀⠀⢸⣿⠀⣿⡇⠀⣿⡇⣿⡇⢸⡿⣿⡇⠉⣿⡏⠁⠀⢸⣿⣸⡿⢸⣿⠀⣿⡇⣿⡇⠀⢸⣿⠠⣿⣇⣿⡇⣿⡇⠸⠿⠀⠀⣿⣿⣸⣿⢸⣿⠀⣿⡇⠀⠐⠀⢰⠿⣿⠀⢠⡟⣿⡇⠸⣇⣸⡿⠘⠛⢠⣿⠀⠀⠀⠀
⠀⠀⢸⣿⠀⣿⡇⠀⣿⡇⣿⡇⣸⣧⣼⣇⠀⣿⡇⠀⠀⢸⣿⢹⣶⢸⣿⠀⣿⡇⣿⡇⠀⢸⣿⠀⣿⢻⣿⡇⣿⡇⢻⣿⠀⠀⣿⡟⣿⣿⢸⣿⠀⣿⡇⠀⠀⠀⣿⣠⣿⣄⣾⣀⣿⣇⢸⡏⢹⣷⠀⣰⡿⠃⠀⠒⠒⠒
⠀⠀⠸⢿⠀⠿⠷⠦⠻⠷⠿⠃⠿⠏⠹⠿⠀⠿⠇⠀⠀⠸⠿⠸⠿⠈⠻⠶⠟⠁⠿⠿⠶⠸⠿⠰⠿⠈⠿⠇⠙⠷⠞⠿⠀⠀⠿⠇⠹⠿⠈⠻⠶⠟⠁⠾⠀⠀⠉⠹⠿⠁⠉⠉⠿⠇⠘⠷⠾⠟⠰⠿⠷⠶⠀⠀⠀⠀
[20A⠀⠀⠨⢙⣭⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠿⠿⠿⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣢⣤⣌⣶⣿⣿⣿⣿⣿⣿⠟⡻⠛⠋⠉⠀⠀⠈⠀⠀⠀⠸⠹⠏⠡⠛⢏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⣭⡝⠟⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣘⣏⢿⢿⣿⣷⠿⢻⣤⡆⢀⣸⣿⣷⣯⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣛⣻⣿⣿⣿⣿⠀⣿⣿⢠⣸⣿⣹⣿⣿⣿⣿⣷⠾⣭⣟⡛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣧⣼⢛⠃⠀⢻⡟⠿⣶⣯⣽⣿⡷⢷⣿⣿⠃⣴⣿⣾⠻⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⣿⣿⣿⣿⣿⣿⡋⢟⡋⠁⠀⠘⠛⠻⣬⣿⣿⣿⣿⣿⣿⣿⢄⣼⣿⡯⢷⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⣾⡿⣼⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠄⢰⣯⣽⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣯⢩⣹⣿⣗⢺⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣿⣷⣿⣿⣿⣿⢷⢸⣿⣿⣶⣦⣤⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢹⣿⣿⣿⣯⣿⡿⣿⢸⣿⠿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠿⠸⠿⢿⣿⣿⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡟⡏⢹⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠙⠛⠻⢿⠇⠀⠀⠀⢦⣿⣿⣿⣿⣿⣏⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠟⣿⣆⣀⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣸⢿⣶⢈⣈⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡟⠛⢫⣽⣷⣖⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⡾⠟⠓⣿⣿⣿⣿⣿⣿⣽⠿⠿⠿⠏⠟⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⢀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣠⣬⣭⣭⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⠀⣿⣼⣿⣿⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠉⠉⠉⠙⠛⠋⠁⠀⠘⠳⠺⣿⠻⢿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣈⣿⣛⡛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠄⠀⢀⡀⠀⠀⠂⠂⠂⠒⠒⠘⢿⡿⠿⠿⠿⠿⠛⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡿⢿⣿⣷⣶⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣦⣀⠀⠀⠀⠘⠛⠛⢿⣿⣿⣿⣿⣿⣿
⠀⠀⢠⣤⠀⣤⡄⠀⣠⣤⣤⡀⢠⣤⣤⠠⣤⣤⣤⡄⠀⢠⣤⣤⡀⢠⣤⠀⣤⡄⣤⡄⠀⢠⣤⢠⣤⠀⣤⡄⢀⣤⣤⡀⠀⠀⣤⡌⢩⣥⠛⣡⣬⣅⠈⠀⠀⠀⠀⣤⣤⠀⠀⣢⣬⡍⢃⣤⣤⡄⠀⣠⣬⣍⠉⠉⠉⠉
⠀⠀⢸⣿⠀⣿⡇⠀⣿⡇⣿⡇⢸⣿⣿⡇⠉⣿⡏⠁⠀⢸⣿⣸⡿⢸⣿⠀⣿⡇⣿⡇⠀⢸⣿⠀⣿⣇⣿⡇⣿⡇⠸⠿⠀⠀⣿⣿⣸⣿⢸⣿⠀⣿⡇⠀⠀⠀⢰⢿⣿⠀⢠⡟⣿⡇⠸⣇⣸⡿⠘⠛⢰⣿⠀⠀⠀⠀
⠀⠀⢸⣿⠀⣿⡇⠀⣿⡇⣿⡇⣸⣧⣼⣇⠀⣿⡇⠀⠀⢸⣿⢹⣶⢸⣿⠀⣿⡇⣿⡇⠀⢸⣿⠨⣿⢻⣿⡇⣿⡇⢻⣿⠀⠀⣿⡟⣿⣿⢸⣿⠀⣿⡇⠀⠀⠀⣿⣸⣿⣄⣾⣀⣿⣇⢸⡏⢹⣷⠀⣰⡿⠃⠀⠒⠒⠒
⠀⠀⠸⢿⠀⠿⠷⠦⠻⠷⠿⠃⠿⠏⠹⠿⠀⠿⠇⠀⠀⠸⠿⠸⠿⠈⠻⠶⠟⠁⠿⠿⠶⠸⠿⠰⠿⠈⠿⠇⠙⠷⠞⠿⠀⠀⠿⠇⠹⠿⠈⠻⠶⠟⠁⠾⠀⠀⠉⠹⠿⠁⠉⠉⠿⠇⠘⠷⠾⠟⠰⠿⠷⠶⠀⠀⠀⠀
[20A⠀⠀⠠⢝⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⠿⠿⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣦⣢⣅⣶⣽⣿⣿⣿⣿⣿⠟⡻⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠹⠏⠱⠛⢟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠆⠀⣤⣀⠀⣾⣿⡟⠁⣭⡝⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⣘⣍⢿⢿⣿⣷⢿⢻⣤⡆⠀⣸⣿⣷⣯⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣛⣻⣾⣿⣿⣿⠂⣿⣿⢠⣸⣿⣹⣿⣿⣿⣿⣷⠾⣭⣟⡛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣧⣼⢟⠃⠀⢻⣟⣿⣶⣯⣽⣿⡿⢷⣿⣾⠇⣵⣿⣾⠻⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠃⣿⣿⣿⣿⣿⣿⡋⣿⣿⠋⢠⣼⢿⡶⣮⣿⣿⣿⣿⣿⣿⣿⢄⣼⣿⡯⢷⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⣾⣿⣼⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠄⢰⣿⣽⣿⢿⣟⠉⠀⠉⠉⠈⠻⣿⣶⣧⣿⣿⣿⣿⣿⣿⣿⣯⢩⢻⣿⣗⢾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣿⣷⣿⣿⣿⣿⣷⢸⣿⣿⣶⣦⣤⠁⠀⠀⠀⣸⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢇⣿⢸⣿⢹⣿⣿⣿⣿⣿⡿⣿⢸⣿⠿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠿⠸⠿⢿⣿⣿⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⡇⣿⣿⣿⣿⣿⣿⡟⡟⢹⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠙⠛⠻⢿⠃⠀⠀⠀⢦⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠻⣿⣽⣿⣿⣿⣿⠟⣿⣆⣀⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣸⢿⣶⢌⣈⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡟⠛⢫⣵⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣍⣟⢾⣟⠓⣿⣿⣿⣿⣿⣿⣽⠿⠿⠿⠏⠟⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⢀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢠⣬⣭⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠟⠃⢿⢄⣿⣼⣿⣿⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠉⠉⠉⠙⠛⠋⠁⠀⠘⠿⡚⣿⠻⢿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣆⣈⣿⣛⡛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠄⠀⠀⠀⠀⠀⠀⠈⠀⠘⠻⠿⠾⡸⠿⠿⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠿⢿⣿⣷⣶⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣦⣀⠀⠀⠀⠘⠛⠛⢿⣿⣿⣿⣿⣿⣿
⠀⠀⢠⣤⠀⣤⡄⠀⣠⣤⣤⡀⢠⣤⣤⠠⣤⣤⣤⡄⠀⢠⣤⣤⡀⢠⣤⠀⣤⡄⣤⡄⠀⢠⣤⢠⣤⠀⣤⡄⢀⣤⣤⡀⠀⠀⣤⡌⢩⣥⠛⣡⣬⣅⠈⠀⠀⠀⠀⣤⣤⠀⠀⣢⣬⡍⢃⣤⣤⡄⠀⣠⣬⣍⠉⠉⠉⠉
⠀⠀⢸⣿⠀⣿⡇⠀⣿⡇⣿⡇⢸⣿⣿⡇⠉⣿⡏⠁⠀⢸⣿⣸⡿⢸⣿⠀⣿⡇⣿⡇⠀⢸⣿⠀⣿⣇⣿⡇⣿⡇⠸⠿⠀⠀⣿⣿⣸⣿⢸⣿⠀⣿⡇⠀⠐⠀⢰⠿⣿⠀⢠⡟⣿⡇⠸⣇⣸⡿⠘⠛⢰⣿⠀⠀⠀⠀
⠀⠀⢸⣿⠀⣿⡇⠀⣿⡇⣿⡇⣸⣧⣼⣇⠀⣿⡇⠀⠀⢸⣿⢹⣶⢸⣿⠀⣿⡇⣿⡇⠀⢸⣿⠀⣿⢻⣿⡇⣿⡇⢻⣿⠀⠀⣿⡟⣿⣿⢸⣿⠀⣿⡇⠀⠀⠀⣿⣠⣿⣄⣾⣀⣿⣇⢸⡏⢹⣷⠀⣰⡿⠃⠀⠒⠒⠒
⠀⠀⠸⢿⠀⠿⠷⠦⠻⠷⠿⠃⠿⠏⠹⠿⠀⠿⠇⠀⠀⠸⠿⠸⠿⠈⠻⠶⠟⠁⠿⠿⠶⠸⠿⠰⠿⠈⠿⠇⠙⠷⠞⠿⠀⠀⠿⠇⠹⠿⠈⠻⠶⠟⠁⠾⠀⠀⠉⠹⠿⠁⠉⠉⠿⠇⠘⠷⠾⠟⠰⠿⠷⠶⠀⠀⠀⠀
[20A⠀⠀⠠⠝⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⠿⠿⠿⡿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣦⣶⣅⣶⣿⣿⣿⣿⣿⣿⠟⠻⠛⠋⠉⠀⠀⠈⠀⠀⠀⠸⠹⠏⠱⠛⣏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠆⠠⣤⣀⠀⣾⣿⡟⢁⣭⡝⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⣘⣍⢿⢿⣿⣷⢿⢻⣥⡆⠀⣸⣿⣷⣯⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣛⣻⣾⣿⣿⣿⠀⣿⣿⢠⣸⣿⣹⣿⣿⣿⣿⣷⠾⣭⣟⡛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣧⣼⠟⠃⠀⢻⣟⣿⣶⣯⣽⣿⡿⢷⣿⣾⠇⣵⣿⣾⠻⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠃⣿⣿⣿⣿⣿⣿⡋⣿⣷⠋⢠⣼⢿⡷⣬⣽⣿⣿⣿⣿⣿⣿⢄⣼⣿⡯⢶⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⣾⣿⣼⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⡿⠿⠿⠑⠿⡿⠬⣿⣿⣶⣇⣿⣿⣿⣿⣿⣿⣿⣯⢩⣹⣿⣗⢾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣿⣷⣿⣿⣿⣿⢷⢸⣿⣿⣶⣦⣤⠁⠀⠀⠀⣸⣿⡻⠫⠀⠀⠀⠀⠀⠀⢂⣾⣇⣿⢸⣿⢹⣿⣿⣿⣿⣿⡿⣿⢸⣿⠿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠿⠸⠿⢿⣿⣿⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⡏⣿⡇⣿⣿⣿⣿⣿⣿⣟⡟⢹⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠙⠛⠻⠿⠇⠀⠀⠀⢤⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠻⢳⣿⣿⣽⣿⣿⣿⣿⠟⣿⣆⣀⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣸⢿⣶⢌⣈⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⣯⣍⡳⢾⣟⠓⣿⣿⣿⣿⣿⣿⣽⠿⠿⠿⠏⠟⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⢀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠡⡼⢻⢄⣿⣼⣿⣿⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠉⠉⠉⠙⠛⠋⠁⠀⠺⣿⠛⣿⠻⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣭⣄⣈⣿⣛⡛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠄⠀⠀⠀⠀⠀⠀⠀⠛⠻⠟⠾⡸⠿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠿⢿⣿⣷⣶⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣦⣀⠀⠀⠀⠘⠛⠛⢿⣿⣿⣿⣿⣿⣿
⠀⠀⢠⣤⠀⣤⡄⠀⣠⣤⣤⡀⢠⣤⣤⠠⣤⣤⣤⡄⠀⢠⣤⣤⡀⢠⣤⠀⣤⡄⣤⡄⠀⢠⣤⢠⣤⠀⣤⡄⢀⣤⣤⡀⢈⠀⣤⡌⢩⣥⠛⣡⣬⣅⠈⠀⠀⠀⠀⣤⣤⠀⠀⣢⣬⡍⢃⣤⣤⡄⠀⣠⣬⣍⠉⠉⠉⠉
⠀⠀⢸⣿⠀⣿⡇⠀⣿⡇⣿⡇⢸⣿⣿⡇⠉⣿⡏⠁⠀⢸⣿⣸⡿⢸⣿⠀⣿⡇⣿⡇⠀⢸⣿⠈⣿⣇⣿⡇⣿⡇⠸⠿⠀⠀⣿⣿⣸⣿⢸⣿⠀⣿⡇⠀⠐⠀⢰⢿⣿⠀⢰⡟⣿⡇⠸⣇⣸⡿⠘⠛⢰⣿⠀⠀⠀⠀
⠀⠀⢸⣿⠀⣿⡇⠀⣿⡇⣿⡇⣸⣧⣼⣇⠀⣿⡇⠀⠀⢸⣿⢹⣶⢸⣿⠀⣿⡇⣿⡇⠀⢸⣿⢀⣿⢻⣿⡇⣿⡇⢻⣿⠀⠀⣿⡟⣿⣿⢸⣿⠀⣿⡇⠀⠀⠀⣿⣸⣿⣄⣾⣀⣿⣇⢸⡏⢹⣷⠀⣰⡿⠃⠀⠒⠒⠲
⠀⠀⠺⢿⠀⠿⠷⠦⠻⠷⠿⠃⠿⠏⠹⠿⠀⠿⠇⠀⠀⠸⠿⠸⠿⠈⠻⠶⠿⠁⠿⠿⠶⠸⠿⠰⠿⠈⠿⠇⠙⠷⠞⠿⠀⠀⠿⠇⠹⠿⠈⠻⠶⠟⠁⠿⠀⠀⠉⠹⠿⠁⠉⠉⠿⠇⠘⠷⠾⠟⠰⠿⠷⠶⠀⠀⠀⠀
[20A⠀⠀⠨⠙⢩⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⠿⣿⠿⠿⠿⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣠⣠⣅⣦⣿⣿⣿⣿⣿⣿⠟⡻⠛⠋⠉⠀⠀⠈⠀⠀⠀⠸⠹⠏⠱⠛⢟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠆⠠⣤⡀⠀⣾⣿⡟⢁⣭⡝⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣘⣍⢿⢿⣿⣷⠿⢻⣤⡆⠀⣸⣿⣷⣯⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣛⣻⣾⣿⣿⣿⠀⣿⣿⢠⣸⣿⣹⣿⣿⣿⣿⣷⠾⣭⣟⡛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣧⣼⢟⠃⠀⢻⣟⣿⣶⣯⣽⣿⡿⢷⣿⣾⠇⣵⣿⣾⠻⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠃⣿⣿⣿⣿⣿⣿⡏⣿⣿⠋⢤⣼⢿⡯⣬⣿⣿⣿⣿⣿⣿⣿⢄⣼⣿⡯⢷⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⣾⣿⣼⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⣿⣿⡿⠑⣿⡿⠬⣿⣿⣶⣇⣿⣿⣿⣿⣿⣿⣿⣯⢨⣹⣿⣗⢾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣿⣷⣿⣿⣿⣿⣷⢸⣿⣿⣶⣦⣤⠁⠀⠀⠀⣸⣿⠟⠛⠿⠛⠃⠸⣿⡆⣀⣾⣇⣿⢸⣿⢹⣿⣿⣿⣿⣿⡿⣿⣸⣿⠿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠿⠸⠿⢿⣿⣿⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⡜⠃⠀⠀⠀⠀⠀⠀⠹⠈⢹⣿⢻⡏⣿⡇⣿⣿⣿⣿⣿⣿⡟⡟⢹⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠙⠛⠻⢿⠃⠀⠀⠀⢦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠸⢳⣿⢳⣿⣿⣽⣿⣿⣿⣿⠟⣿⣆⣀⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠺⢿⣻⣿⣿⣿⣿⣸⢿⣶⢌⣈⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠛⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⢮⡯⠙⣿⢾⣟⠓⣿⣿⣿⣿⣿⣿⣽⠿⠿⠿⠏⠟⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⢀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠘⢷⡼⢻⢄⣿⣼⣿⣿⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠉⠉⠉⠙⠛⠋⠁⠀⢼⢻⠛⣧⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⡼⠭⣄⣈⣿⣛⡛⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠘⠟⠏⠛⠾⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠿⢿⣿⣷⣶⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣦⣀⠀⠀⠀⠘⢛⢛⢿⣿⣿⣿⣿⣿⣿
⠀⠀⢠⣤⠀⣤⡄⠀⣠⣤⣤⡀⢠⣤⣤⠀⣤⣤⣤⡄⠀⢠⣤⣤⡀⢠⣤⠀⣤⡄⣤⡄⠀⢠⣤⢠⣤⠀⣤⡄⢀⣤⣤⡀⠈⠀⣤⡌⢩⣥⠛⣡⣬⣅⠈⠀⠀⠀⠀⣤⣤⠀⠀⣢⣬⡍⢃⣤⣤⡄⠀⣠⣬⣍⠉⠉⠉⠉
⠀⠀⢸⣿⠀⣿⡇⠀⣿⡇⣿⡇⢸⡿⣿⡇⠉⣿⡏⠁⠀⢸⣿⣸⡿⢸⣿⠀⣿⡇⣿⡇⠀⢸⣿⠈⣿⣇⣿⡇⣿⡇⠸⠿⠀⠀⣿⣿⣸⣿⢸⣿⠀⣿⡇⠀⠐⠀⢰⢿⣿⠀⢠⡟⣿⡇⠸⣇⣸⡿⠘⠛⢰⣿⠀⠀⠀⠀
⠀⠀⢸⣿⠀⣿⡇⠀⣿⡇⣿⡇⣸⣧⣼⣇⠀⣿⡇⠀⠀⢸⣿⢹⣶⢸⣿⠀⣿⡇⣿⡇⠀⢸⣿⢀⣿⢻⣿⡇⣿⡇⢻⣿⠀⠀⣿⡟⣿⣿⢸⣿⠀⣿⡇⠀⠀⠀⣿⣸⣿⣄⣾⣀⣿⣇⢸⡏⢹⣷⠀⣰⡿⠃⠀⠒⠒⠒
⠀⠀⠸⢿⠀⠿⠷⠦⠻⠷⠿⠃⠿⠏⠹⠿⠀⠿⠇⠀⠀⠸⠿⠸⠿⠈⠻⠶⠟⠁⠿⠿⠶⠸⠿⠰⠿⠈⠿⠇⠙⠷⠞⠿⠀⠀⠿⠇⠹⠿⠈⠻⠶⠟⠁⠾⠀⠀⠉⠹⠿⠁⠉⠉⠿⠇⠘⠷⠾⠟⠰⠿⠷⠶⠀⠀⠀⠀
[20A⠀⠀⠈⠝⣫⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⠿⣿⠿⠿⠿⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣦⣢⣥⣶⣻⣿⣿⣿⣿⣿⠿⡻⠛⠋⠉⠀⠀⠈⠀⠀⠀⠸⠹⠏⠹⠛⢏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠆⠠⣤⡀⠀⣾⣿⡟⢁⣭⡝⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⣜⣏⢿⢿⣿⣷⠿⢻⣥⡆⢀⣸⣿⣷⣯⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣛⣻⣾⣿⣿⣿⠀⣿⣿⢠⣸⣿⣽⣿⣿⣿⣿⣷⠾⣭⣟⡛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣧⣼⢟⠃⠀⢻⣟⣿⣶⣯⣽⣿⡿⢷⣿⣿⠇⣵⣿⣾⠻⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⣿⣿⣿⣿⣿⣿⡏⣿⣿⠋⢠⣼⢿⡟⣭⣿⣿⣿⣿⣿⣿⣿⢄⣼⣿⡯⢷⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⣾⣿⣼⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠄⢰⣯⣽⣿⣿⣿⡿⢑⣿⡿⠬⣿⣿⣶⣧⣿⣿⣿⣿⣿⣿⣿⣯⢨⣻⣿⣗⢾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣿⣷⣿⣿⣿⣿⣷⢸⣿⣿⣶⣦⣤⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⠁⢸⣿⡆⣀⣾⣇⣿⢸⣿⢹⣿⣿⣿⣿⣿⡿⣿⣸⣿⠿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠿⠸⠿⢿⣿⣿⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠟⠛⠛⠋⠉⠛⢦⣾⣿⠉⢸⣿⢷⡏⣿⡇⣿⣿⣿⣿⣿⣿⡟⡟⢹⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠙⠛⠻⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠩⠸⣿⢸⢳⣿⢳⣿⣿⣽⣿⣿⣿⣿⠟⣿⣆⣀⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠘⠿⣼⢿⣻⣿⣿⣿⣿⣸⢿⣶⢌⣈⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠦⡖⡮⢻⣟⡿⢾⣟⠓⣿⣿⣿⣿⣿⣿⣽⠿⠿⠿⠏⠟⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⢀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣲⣷⡼⢻⢄⣿⣼⣿⣿⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠉⠉⠉⠙⠛⠛⠁⠠⣰⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠘⠫⠭⣄⣘⣿⣛⡛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠄⠀⠀⠀⠀⠀⠀⠈⠻⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⠁⠿⢿⣿⣷⣶⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣦⣀⠀⠀⠀⠘⢛⢛⢿⣿⣿⣿⣿⣿⣿
⠀⠀⢠⣤⠀⣤⡄⠀⣠⣤⣤⡀⢠⣤⣤⠠⣤⣤⣤⡄⠀⢠⣤⣤⡀⢠⣤⠀⣤⡄⣤⡄⠀⢠⣤⢠⣤⠀⣤⡄⢀⣬⣤⡀⠈⠀⣤⡌⢩⣥⠛⣡⣬⣅⠈⠀⠀⠀⠀⣤⣤⠀⠀⣢⣬⡍⢃⣤⣤⡄⠀⣠⣬⣝⠉⠉⠉⠉
⠀⠀⢸⣿⠀⣿⡇⠀⣿⡇⣿⡇⢸⡿⣿⡇⠉⣿⡏⠁⠀⢸⣿⣸⡿⢸⣿⠀⣿⡇⣿⡇⠀⢸⣿⠀⣿⣇⣿⡇⣿⡇⠸⠿⠀⠀⣿⣿⣸⣿⢸⣿⠀⣿⡇⠀⠐⠀⢰⠿⣿⠀⢠⡟⣿⡇⠸⣇⣸⡿⠘⠛⢰⣿⠀⠀⠀⠀
⠀⠀⢸⣿⠀⣿⡇⠀⣿⡇⣿⡇⣸⣧⣼⣇⠀⣿⡇⠀⠀⢸⣿⢹⣶⢸⣿⠀⣿⡇⣿⡇⠀⢸⣿⢀⣿⢻⣿⡇⣿⡇⢻⣿⠀⠀⣿⡟⣿⣿⢸⣿⠀⣿⡇⠀⠀⠀⣿⣠⣿⣄⣾⣀⣿⣇⢸⡏⢹⣷⠀⣰⡿⠃⠀⠒⠒⠲
⠀⠀⠺⢿⠀⠿⠷⠦⠻⠷⠿⠃⠿⠏⠹⠿⠀⠿⠇⠀⠀⠸⠿⠸⠿⠈⠻⠶⠟⠁⠿⠿⠶⠸⠿⠰⠿⠈⠿⠇⠙⠷⠞⠿⠀⠀⠿⠇⠹⠿⠈⠻⠶⠟⠁⠾⠀⠀⠉⠹⠿⠁⠉⠉⠿⠇⠘⠷⠾⠟⠰⠿⠷⠶⠀⠀⠀⠀
[20A⠀⠀⠩⠙⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⠿⠿⠿⡿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⣤⣥⣶⢻⣿⣿⣿⣿⡿⠟⠻⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠸⠏⠱⠻⣏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣾⢿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠆⠀⣤⣀⠀⣾⣿⡟⠁⣭⡝⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⣔⣏⢿⢿⣿⣷⠿⢻⣤⡆⠀⣸⣿⣷⣯⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣛⣻⣾⣿⣿⣿⠀⣿⣿⣨⣸⣿⣽⣿⣿⣿⣿⣷⠾⣭⣟⡛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣧⣼⣟⠃⠀⢻⣟⣿⣶⣯⣽⣿⡷⢷⣿⣿⠃⣴⣿⣾⠻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⣿⣿⣿⣿⣿⣿⡏⣿⣷⠋⠤⣼⢿⡿⣯⣿⣿⣿⣿⣿⣿⣿⢄⣼⣿⡯⢵⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⣼⡿⣼⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣽⣿⣿⣿⡿⢑⣿⡿⠬⣿⣿⣾⣆⣿⣿⣿⣿⣿⣿⣿⣯⢨⢻⣿⡗⢾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣿⣷⣿⣿⣿⣿⢷⢸⣿⣿⣶⣦⣤⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⠁⢸⣿⡆⣀⣾⣇⣿⢸⣿⢹⣿⣿⣿⣿⣿⡿⣿⣸⣿⠿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠿⠸⠿⢿⣷⣿⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣤⣾⣿⠉⠹⣿⣳⡏⣿⡇⣾⣿⣿⣿⣿⣿⡟⡟⢽⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠙⠛⠻⠿⠃⠀⠀⠀⢤⣯⣿⣯⣿⣿⣏⣁⠿⠟⠉⠹⣿⢹⢣⣿⢳⣿⣿⣽⣿⣿⣿⣿⠟⣿⣆⣀⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⢿⣿⣿⡿⢻⣿⡗⠀⣀⣿⣿⢘⡽⣼⣿⣻⣿⣿⣿⣿⣸⢿⣶⢈⣈⣷⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠀⠁⠈⠁⠀⠙⠃⠋⠛⠁⠡⠈⠹⣿⣿⣿⣟⡷⢾⣟⠓⣿⣿⣿⣿⣿⣿⣽⠿⠻⠻⠏⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⢀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⣶⣧⡼⢻⢄⣿⣼⣿⣿⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠿⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠉⠉⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⢹⡿⠭⠭⣀⣘⣿⣛⡛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⠀⠀⢠⠀⠿⢿⣿⣷⣶⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣦⣀⠀⠀⠀⠘⢛⠛⢿⣿⣿⣿⣿⣿⣿
⠀⠀⢠⣤⠀⣤⡄⠀⣠⣤⣤⡀⢠⣤⣤⠠⣤⣤⣤⡄⠀⢠⣤⣤⡀⢠⣤⠀⣤⡄⣤⡄⠀⢠⣤⢠⣤⠀⣤⡄⢀⣤⣤⡀⠈⠀⣤⡌⢩⣥⠛⣡⣬⣅⠈⠀⠀⠀⠀⣤⣤⠀⠀⣠⣬⡍⢃⣤⣤⡄⠀⣠⣬⣝⠉⠉⠉⠉
⠀⠀⢸⣿⠀⣿⡇⠀⣿⡇⣿⡇⢸⡿⣿⡇⠉⣿⡏⠁⠀⢸⣿⣸⡿⢸⣿⠀⣿⡇⣿⡇⠀⢸⣿⠀⣿⣇⣿⡇⣿⡇⠸⠿⠀⠀⣿⣿⣸⣿⢸⣿⠀⣿⡇⠀⠐⠀⢰⢿⣿⠀⢠⡟⣿⡇⠸⣧⣸⡿⠘⠛⢰⣿⠀⠀⠀⠀
⠀⠀⢸⣿⠀⣿⡇⠀⣿⡇⣿⡇⣸⣧⣼⣇⠀⣿⡇⠀⠀⢸⣿⢹⣶⢸⣿⠀⣿⡇⣿⡇⠀⢸⣿⢀⣿⢻⣿⡇⣿⡇⢻⣿⠀⠀⣿⡟⣿⣿⢸⣿⠀⣿⡇⠀⠀⠀⣿⣸⣿⣄⣾⣀⣿⣇⢸⡏⢹⣷⠀⣠⡿⠃⠀⠒⠂⠲
⠀⠀⠺⢿⠀⠿⠷⠦⠻⠷⠿⠃⠿⠏⠹⠿⠀⠿⠇⠀⠀⠸⠿⠸⠿⠈⠻⠶⠿⠁⠿⠿⠶⠸⠿⠰⠿⠈⠿⠇⠙⠷⠞⠿⠀⠀⠿⠇⠹⠿⠈⠻⠶⠟⠁⠿⠀⠀⠉⠹⠿⠁⠉⠉⠿⠇⠘⠷⠾⠟⠰⠿⠷⠶⠀⠀⠀⠀
䷩ 𝚕𝚒𝚗𝚎 4662
╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕
(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/02/09/irc-log-080222/#comments
Gemini version at gemini://gemini.techrights.org/2022/02/09/irc-log-080222/
⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.09.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧
Gemini_version_available_♊︎
✐ IRC_Proceedings:_Tuesday,_February_08,_2022⠀✐
Posted in IRC_Logs at 2:05 am by Needs Sunlight
Also available via the Gemini protocol at:
* gemini://gemini.techrights.org/irc-gmi/irc-log-techrights-080222.gmi
* gemini://gemini.techrights.org/irc-gmi/irc-log-080222.gmi
* gemini://gemini.techrights.org/irc-gmi/irc-log-social-080222.gmi
* gemini://gemini.techrights.org/irc-gmi/irc-log-techbytes-080222.gmi
Over HTTP:
🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇H 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇HTML5_logs⦈_
#techrights_log_as_HTML5 #boycottnovell_log_as_HTML5
🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇H 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇HTML5_logs⦈_
#boycottnovell-social_log_as_HTML5 #techbytes_log_as_HTML5
🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇t 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇text_logs⦈_
#techrights_log_as_text #boycottnovell_log_as_text
🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇t 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇text_logs⦈_
#boycottnovell-social_log_as_text #techbytes_log_as_text
Enter_the_IRC_channels_now
=> =============================================================================
§ IPFS Mirrors⠀➾
CID Description Object type
IRC log for
QmSPUPU5ZqHxTQsd3apxwT4G1nMn7JEgsmxe71kfJUA86Q #boycottnovell 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
(full IRC log
as HTML)
IRC log for
#boycottnovell
QmZNvwnCvTaTdc3QWDJPKffdcGDFfuVYe7PBXqoLQS1iHK (full IRC log 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
as plain/ASCII
text)
IRC log for
#boycottnovell-
QmaY3dKt7BTd8tptvq7N6n68PgSFSJhpiWLig31U8MWYcJ social 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
(full IRC log
as HTML)
IRC log for
#boycottnovell-
Qmeo8oAfrK6cb5eJuYgsWEdsPeQR72AUZNht7GsS4Zrb7u social 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
(full IRC log
as plain/ASCII
text)
IRC log for
QmZ1bdTSeqAGWrkhHaAgv4xRVVfsmxscv5gLnSfRfN71gs #techbytes 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
(full IRC log
as HTML)
IRC log for
#techbytes
QmfUrmap41BA4T33JqUekFtEoo9ELRmrFCQrfgsgZ5WmQ9 (full IRC log 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
as plain/ASCII
text)
IRC log for
QmSpmWXjBZoyq7JvUVZzbbF5nUig5NwMPdN7FXiswiNmxQ #techrights 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
(full IRC log
as HTML)
IRC log for
#techrights
QmSBquW9Y8DFmjXvikR4GwDGMzHgCwVJ7hbZ9K7nRC6N2b (full IRC log 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
as plain/ASCII
text)
🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇IPFS logo⦈
§ Bulletin for Yesterday⠀➾
Local_copy | CID (IPFS): QmYBkNNgDtvjiZGy3f7RwY487FEsQEUQkXJN3yYkKnMGUa
䷩ 𝚕𝚒𝚗𝚎 4789
╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕
⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.09.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧
Gemini_version_available_♊︎
✐ Links_10/2/2022:_Epic_Wants_Rootkits_in_Linux_and_Serial_GPL_Violator_VMware
Launches_Vicious_FUD_Attack_on_Linux⠀✐
Posted in News_Roundup at 8:27 pm by Dr. Roy Schestowitz
🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈
§ Contents⠀➾
* GNU/Linux
o Distributions
o Devices/Embedded
* Free_Software/Open_Source
* Leftovers
* § GNU/Linux⠀➾
o ⚓ Chrome_OS_98_Stable_Channel_arrives:_What_you_need_to_know⠀⇛
According to the official Chrome Release blog, the Chrome
OS 98 Stable Channel was released on Monday night. All
supported Chromebooks, Chromeboxes and Chrome OS tablets
should see the update now, or in the coming days.
As of Tuesday morning, the main Google site did not have
any information as to what’s in this update. So here’s a
rundown on the new features and functions found so far in
the Chrome OS 98 Stable Channel. Many are experimental
features.
o § Desktop/Laptop⠀➾
# ⚓ Compulab’s_Fitlet3_mini-PC_offers_Elkhart_Lake_and_triple
M.2⠀⇛
Compulab has launched a highly customizable
“Fitlet3” industrial mini-PC that starts at about
$260 and runs Linux or Windows on Elkhart Lake.
Standard features include 2x GbE, 6x USB, HDMI,
mini-DP, FACET expansion, and M.2 M-, B- and E-key
slots.
Compulab has updated its five-year old, Apollo Lake
based Fitlet2 mini-PC. The Fitlet3 advances to
Intel’s 10nm Elkhart Lake. Aside from the much
faster Atom x6000 processor, the Fitlet3 ships with
up to 32GB, 3200MT/s DDR4. That is is twice the RAM
of the Fitlet2, which is also available as the
Linux Mint optimized MintBox Mini 2.
# ⚓ Fitlet3_is_a_compact,_fanless_Elkhart_Lake_mini_PC_for_IoT
and_industrial_applications⠀⇛
Fitlet3 fanless mini PC based on a choice of three
Atom or Celeron Elkhart Lake processors is an
upgrade to the Compulab Fitlet2 mini PC introduced
in 2017 with Apollo Lake processors.
Designed to be used as a fanless industrial mini PC
or an IoT gateway, Fitlet3 comes with up to 32GB
RAM, supports SATA and NVMe storage, offers two 4K
video outputs, up to four Gigabit Ethernet ports,
optional WiFi 6E, Bluetooth 5.2, and/or 4G/5G
cellular connectivity, as well as a wide range 7V
to 42V power input.
# ⚓ Windows,_macOS,_Chrome_OS,_or_Linux:_Which_Operating_System
Is_Best?⠀⇛
You don’t have a great many choices when it comes
to your computer’s operating system, but the choice
that you make can have wide-ranging consequences.
The five OSes included here are your most viable
options. That’s not a huge number, but these
operating systems differ distinctly in strengths
and weaknesses. Four come from gargantuan
commercial tech giants, while one, the Linux-based
Ubuntu, is a free, open-source option. Windows and
macOS are generally the most powerful in terms of
hardware and software selection as well as
interface conveniences and utilities, while Chrome
OS is more lightweight and runs on inexpensive
hardware.
# ⚓ Best_desktop_Linux_for_pros_2022:_Our_top_5_choices_|
ZDNet⠀⇛
You knew Fedora, Red Hat’s community Linux
distribution, would be first on my list. It’s the
mainstream distro that pushes Linux’s limits. It
comes powered by the newest Linux kernel and with
the latest open-source software.
In particular, Fedora is the Linux of choice for
programmers. No less a figure than Linus Torvalds
uses Fedora for his development work. Need I say
more?
Sometimes, however, when you’re running a leading-
edge distro, you can cut yourself. There’s a reason
why Fedora’s also known as a bleeding-edge Linux.
On the other hand, Fedora is easy to install and
set up. You don’t need to be a Linux expert to get
up and running with it.
For programmers, Fedora also boasts an excellent
Developer Portal. It features dedicated guides on
developing command line, desktop, mobile, and web
apps.
The Fedora Developer Portal also comes with an
excellent guide for developing hardware devices
such as Arduino and Raspberry Pi. Last but not
least, it comes with such development tools as the
top-notch integrated development environment (IDE)
Eclipse for Java, C/C++, and PHP and Vagrant, a
tool for creating reproducible, portable container
or virtual machine (VM)-based development
environments.
Unless you’re working on the Debian/Ubuntu family
programs, Fedora should be your first choice for a
development operating system. For developers in
that group, I recommend the newest version of
Ubuntu.
# ⚓ Best_Linux_distros_for_beginners_in_2022:_You_can_do_this!
|_ZDNet⠀⇛
Some people still insist that using Linux is hard.
Sure, it was difficult — when I started with the
Linux desktop back in the 1990s. But that was a
long time ago. Today, the easiest desktop of all,
Chrome OS, is simply Linux with the Chrome web
browser on top of it. The more full-featured Linux
desktop distributions are as easy to use in 2021 as
Windows or macOS.
Yes, you can get a lot more from Linux if you know
how to do shell programming and the like. But
that’s also true of Windows and PowerShell. With
both operating systems, you don’t need to know the
deep ins and outs of either one to get your work
done.
o § Kernel Space⠀➾
# ⚓ From_Prototype_to_Post_Deployment:_Linux_Decision_Points⠀⇛
There were four options given:
1) Choose roll-your-own based on Yocto Project
Linux, Debian, or something similar: 27 %
2) Choose Linux provided through a semiconductor or
board vendor: 17 %
3) Choose Linux from a commercial open source
provider: 10 %
4) Continue evaluating whether you want to use
Linux: 45 %
It is interesting that the number of respondents
choosing Linux from a commercial OS provider is not
higher than 10%. Additionally, given recent trends
around the migration to Linux for embedded
development, it is surprising that 45% of the
audience was still evaluating whether to use Linux
at all.
# § Graphics Stack⠀➾
# ⚓ AMD_looking_for_more_Linux_help_to_reach_client-
stages_on_the_open-source_platform⠀⇛
# ⚓ Intel’s_Open-Source_Linux_Driver_now_offers_Vulkan
“ANV”_ray-tracing_support⠀⇛
With the impending launch of Intel Arc GPUs
with new ray-tracing technology approaching
soon, the company has introduced further
open-source “ANV” Vulkan support for the
Linux operating system. In the latest driver
update, this new support is filed under
“VK_KHR_ray_query.”
o § Applications⠀➾
# ⚓ DeskCut_Helps_You_to_Create_Linux_Desktop_Shortcuts_with
Ease⠀⇛
This article explains briefly how to create useful
and standard-compliant desktop entries on Linux by
using the DeskCut app.
Have you ever installed a program in Linux from an
outside source and wished that it had a convenient
entry in your desktop environment’s menu? While
most GUI programs automatically create their
desktop shortcut during installation, some
applications may require you to set up associated
shortcuts manually.
And this is where DeskCut comes on the scene. But
before that, let’s explain what Linux shortcuts
actually are.
o § Instructionals/Technical⠀➾
# ⚓ How_To_Install_Plex_Media_Server_on_Fedora_35_–_idroot⠀⇛
In this tutorial, we will show you how to install
Plex Media Server on Fedora 35. For those of you
who didn’t know, Plex Media Server is a self-hosted
media player system for storing your movies, shows,
music, and photos. Over time Plex Media Server has
grown much and now supports many platforms.
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 Plex Media Server on a Fedora
35.
# ⚓ How_to_Install_Nginx_on_WHM/cPanel_With_Engintron_–
RoseHosting⠀⇛
In this tutorial, we are going to explain how to
Install Nginx with Engintron on a server with WHM/
cPanel control panel installed.
Engintron is a free WHM/cPanel plugin that can be
used for installing the Nginx web server as a
reverse proxy of the default Apache webserver. The
reason for using the Nginx as a reverse proxy of
Apache on our WHM/cPanel server is that the Apache
will server the dynamic content such as PHP, Perl
and etc, and the Nginx will be responsible for
serving the static content like CSS, Javascript,
and images.
Installing Nginx with Engintron to your cPanel
server can take a few minutes and is a very easy
process. Let’s get to work!
# ⚓ How_to_install_InfluxDB_2_on_Debian_11_–_NextGenTips⠀⇛
InfluxDB is an open-source time-series database. It
is used for storage and retrieval of time series
data in fields such as operation monitoring,
operations metrics, internet of things sensor data,
and real-time analytics. In this tutorial, we are
going to learn how to install InfluxDB on Debian
11.
By default, InfluxDB uses the following network
ports for communication.
# ⚓ How_to_install_Google_PageSpeed_to_improve_NGINX
performance_–_News_Update⠀⇛
Google PageSpeed is an open-source module, created
by Google, to help make web pages load faster. This
added speed is achieved by rewriting them for
better latency and decreasing bandwidth. Although
PageSpeed has been around for some time, it’s not
often used. However, by adding it to your NGINX or
Apache websites, you’ll find they perform
considerably better.
I’m going to show you how to install both NGINX and
PageSpeed, so your users can enjoy a much-improved
experience with your web pages. We are going to
install everything from scratch, so you’ll want to
do this on a non-production machine first. Once
you’ve mastered this, move it to production and
then migrate your sites to the new web server.
# ⚓ How_to_easily_install_minix_3.3.0⠀⇛
This is an screen by screen guide on how to install
minix 3.3.0.
# ⚓ Install_and_use_WPscan_(WordPress_security_scanner)_in
Linux⠀⇛
WPScan is a free, for non-commercial use, black box
WordPress security scanner written for security
professionals and blog maintainers to test the
security of their sites.
# ⚓ Install_Metasploit_Framework_on_Ubuntu_22.04/Ubuntu_20.04_–
kifarunix.com⠀⇛
In this tutorial, you will learn how to install
Metasploit Framework on Ubuntu 22.04/Ubuntu 20.04
LTS. Metasploit Framework provides a platform and
tools for performing deep system security auditing
as well as penetration testing to unearth, exploit
and validate every other would-be vulnerability.
# ⚓ How_to_install_Peppermint_OS_2022-02-02_–_Invidious⠀⇛
# ⚓ How_to_install_OpenVPN_Client_on_Debian_11_Bullseye_–_Linux
Shout⠀⇛
Learn the steps to install OpenVPN client on Debian
11 Bullseye Linux to connect VPN server for
establishing a secure connection. It was programmed
by James Yonan and was first released in 2001 under
the open-source license.
OpenVPN is a popular open-source software freely
available. It is available in a client-server
architecture and can be installed on computers,
servers, or network devices such as routers and
supports operating systems such as Windows, Linux,
macOS, Solaris, OpenBSD, Android, and many more.
It can be used to implement encrypted private
networks between individual clients or entire
networks. For the connection to be established, the
OpenVPN software must be available and suitably
configured on both sides. The software transmits
the user data via TCP or UDP packets. The VPN
software can also be used across NAT borders (NAT –
Network Address Translation). The data exchanged in
the VPN is via SSL/ TLSencrypted. The OpenSSL
library is used for encryption.
# ⚓ Ubuntu_Linux_PC_Won’t_Boot?_5_Common_Issues_and_Fixes⠀⇛
You’ve switched on your computer, preparing to do
some work, edit a document, mix a composition, or
just play a game… but something goes wrong.
Ubuntu won’t boot.
Sadly, as reliable as Linux is in general, and as
popular as Ubuntu is, sometimes it runs into
problems, just like Windows 10 or macOS. In most
cases, you’ll be able to work around this.
Whether you’re using Ubuntu desktop or Ubuntu
Server, here’s what to do if Ubuntu doesn’t boot.
# ⚓ What_Is_Log4Shell_and_How_to_Protect_Your_Linux_System
Against_It⠀⇛
The Log4Shell (CVE-2021-44228) vulnerability is
described by many cybersecurity researchers and
experts to be the most critical zero-day
vulnerability of all time. It affects a widely-used
Java utility by the name of Log4j, which has been
around since 2001 for logging and communicating
events, such as routine system operations and
software errors. Here we show you how to protect
your Linux system against it.
# ⚓ 100%_easy_Open-source_VPN_and_Proxy_with_podman⠀⇛
OpenConnect VPN is not officially supported by or
associated in any way with Cisco Systems, Juniper
Networks, Pulse Secure, Palo Alto Networks, F5,
Fortinet, or any of the companies whose protocols
we may support in the future. It just happens to
interoperate with their equipment. Trademarks
belong to their owners in a somewhat tautological
and obvious fashion.
An openconnect VPN server (ocserv), which
implements an improved version of the Cisco
AnyConnect protocol, was also written.
OpenConnect VPN server is an SSL VPN server that is
secure, small, fast, and configurable. It
implements the OpenConnect SSL VPN protocol and has
also (currently experimental) compatibility with
clients using the AnyConnect SSL VPN protocol. The
OpenConnect protocol provides a dual TCP/UDP VPN
channel and uses the standard IETF security
protocols to secure it. The OpenConnect client is
multi-platform and available here. Alternatively,
you can try connecting using the official Cisco
AnyConnect client (Confirmed working on Android).
For the HAproxy tutorial, you can try the link.
# ⚓ Failed_to_download_metadata_for_repo⠀⇛
# ⚓ Bash_Scripting:_Check_if_file_exists⠀⇛
# ⚓ Bash_Scripting:_Check_if_directory_exists⠀⇛
When writing a Bash script, it is common that
you’ll run into the need to check for the existence
of a directory. Based on the result, your Bash
script can proceed with the appropriate action.
This functionality can be written into a Bash
script or used directly from the command line,
without writing a script for it. In this tutorial,
you will see how to check if a directory exists in
Bash on Linux systems.
# ⚓ MySQL:_Allow_user_access_to_database⠀⇛
After installing MySQL on your Linux system and
creating a new database, you will need to setup a
new user to access that database, granting it
permissions to read and/or write data to it.
It is not recommended to use the root account, but
rather create a new account and grant privileges as
needed. In this tutorial, you will see how to allow
a user to access a MySQL database on Linux.
# ⚓ MySQL:_Allow_access_from_specific_IP_address⠀⇛
If you need to allow remote access to your MySQL
server, a good security practice is to only allow
access from one or more specific IP addresses. This
way, you are not needlessly exposing an attack
vector to the entire internet.
In this tutorial, we will take you through the step
by step instructions to allow remote connections to
a MySQL server from a specific IP address on a
Linux system. These instructions should work
independently of whichever Linux distro you are
using.
# ⚓ MySQL:_Allow_remote_connections⠀⇛
After installing a MySQL server on a Linux system,
by default it will only accept incoming connections
from itself (i.e. the loopback address 127.0.0.1).
This default configuration works perfectly fine if
you are only trying to read or write information
from the database on the same server. So users that
host their website and MySQL server on the same box
won’t need to do any extra configuration to allow
remote connections.
If you want to allow remote connections to your
MySQL server, because you have other computers and/
or users that need to access that data, you will
need to bind the MySQL service to a public IP
address on your server, and perhaps allow incoming
MySQL connections through your system firewall.
In this tutorial, we will take you through the step
by step instructions to allow remote connections to
a MySQL server on a Linux system. These
instructions should work independently of whichever
Linux distro you are using.
# ⚓ Building_a_Docker_image_in_Jenkinsfile_and_publishing_to
ECR_–_Octopus_Deploy⠀⇛
In this post, you learn how to build and push the
Octopus Deploy underwater app to Amazon Elastic
Container Registry (ECR) using Jenkins.
o § Games⠀➾
# ⚓ Lilbits:_Fortnite_for_Linux_isn’t_happening,_Vivo_NEX_5
specs_leaked,_MAME_turns_25_–_Liliputing⠀⇛
While Valve’s game client has been able to run on
Linux for years, as of last month just over 1% of
Steam users were running Linux (and fewer than 3%
were using macOS, with Windows holding a 96%
share). It’ll be interesting to see if that starts
to change once the Steam Deck hits the streets. And
if it does, maybe we’ll see more game makers add
support for Linux… but one of the most popular
games around isn’t going to add Linux support
anytime soon: Epic CEO Tim Sweeney says the company
has no plans to port Fortnite to Linux.
He says it’s because Epic doesn’t “have confidence
that we’d be able to combat cheating at scale under
a wide array of kernel configurations including
custom ones,” but it’s an interesting take since
Epic has already ported its anti-cheat software to
support Mac and Linux devices including the Steam
Deck.
That means third-party games that use Epic’s Easy
Anti-Cheat software should be compatible with the
Steam Deck. But Epic’s own Fortnite won’t be one of
those games.
Then again, Fortnite also isn’t available in the
Steam Store, so it’s not like it’s a huge surprise
that the company doesn’t want to make it too easy
for you to play its massively popular game on a
device that may lock you into a rival’s ecosystem.
But the Steam Deck is basically a PC, and while it
will ship with Steam OS, it’s also capable of
running Windows. And that could provide folks
willing to install an alternate operating system a
way to play Fortnite or any other games that may
not be available or play well under Linux.
# ⚓ Fortnite_Is_Never_Coming_To_The_Steam_Deck_–_Invidious⠀⇛
With EAC and Battleye now being supported on Linux
and by extension the Steam Deck someone asked Tim
Sweeney if Fortnite is coming to the Steam Deck and
he had a simple answer no, but his reasoning is
interesting
# ⚓ Epic_Is_Worried_About_Fortnite_Cheaters_on_Linux [Ed:
Worried about the freedom of the platform, Epic wants to put
rootkits in Linux]⠀⇛
Epic Games makes Fortnite, which is one of the
biggest video game phenomenons in recent history.
Because the game is so popular, fans wondered
whether it would make its way to Valve’s Steam
Deck, but it appears Epic is too worried about
cheaters on Linux to make it happen.
# ⚓ Tim_Sweeney_has_a_point_about_Fortnite_EAC_support_|
GamingOnLinux⠀⇛
One of the big topics of discourse in the Linux
gaming sphere recently has been Tim Sweeney’s
statement on porting Fortnite to the Steam Deck,
where Sweeney argues that Linux would be too
difficult of a target and the market not big enough
to warrant the amount of resources it would take to
bring all of Fortnite on the platform.
The central crux of the issue, from Sweeney’s point
of view, is that making Easy Anti-Cheat, with all
of its capabilities, run on Steam Deck (and thus on
Linux) would be extremely difficult. He argues,
that for a game of Fortnite’s size this would open
the flood-gates to significant influx of cheaters.
There have been some responses to this from the
Linux side, with some accusing Sweeney of
exaggerating the difficulty of such a port or that
his statements are conflicting, because he
simultaneously believes the Linux market is too
small to be worthwhile but also would provide a way
for too many cheaters. I will address some of these
aspects a bit later, but for now let’s focus on the
main technical blocker, which is Easy Anti-Cheat.
# ⚓ Proton_vs_Native:_Is_There_Really_A_Difference?_–_Boiling
Steam⠀⇛
The debate over emulation or translation and native
games is at least as old as projects like Wine for
Linux, and more generally as old as gaming
platforms. More recently Proton and DXVK are the
stars, but there have been other tools in the past,
like VOGL (to translate DirectX 9 to OpenGL, used
in CS:Go, for example). Rather than rehash the same
debate here, what I would like to do is explore and
pose some questions. Not questions like which is
“better” (for whatever your definition of
“better”), but to think a bit more deeply about
another aspect of this debate. To me, much of the
endless back and forth comes down to this: is there
really a difference between native and tools like
Proton?
Hold your flames and passioned arguments please!
I’m not here to make the case for one side or the
other or throw my hands up to say “it doesn’t
matter,” but to attempt to go beyond our surface
arguments and see where that may lead us.
# ⚓ Valheim_developers_have_another_fireside_chat_filled_with
teasers_|_GamingOnLinux⠀⇛
Ready for even more content to come to Valheim?
Well, there’s still a bit of a wait and the
developers teased biome updates previously but
there’s more to see – and hear.
In a fresh fireside chat, with a much upgraded
seating area that’s no longer just a fire in a
forest, three members of Iron Gate had a talk about
the game now it’s one year on from the Early Access
release. The fun thing is that this is clearly an
unreleased build, as there’s multiple sneaky new
things surrounding them. Their official Twitter
account even teased “How many sneak peeks can you
spot?”.
# ⚓ Godot_Engine_–_Dev_snapshot:_Godot_4.0_alpha_2⠀⇛
Two weeks ago we finally released Godot 4.0 alpha 1
― the first official alpha build of our upcoming
major milestone, enabling all interested users to
try it out and report bugs, as well as provide
feedback on the new features.
We got lots of bug reports and many have been fixed
already in these two weeks! To keep iterating on
stabilizing the 4.0 branch, we’re going to release
new alpha builds every other week, so that testers
can always have a recent version to test the latest
changes.
So here’s Godot 4.0 alpha 2 with a great deal of
fixes and new features!
Be aware that during the alpha stage the engine is
still not feature-complete or stable. There will
likely be breaking changes between this release and
the first beta release. Only the beta will mark the
so-called “feature freeze”.
As such, we do not recommend porting existing
projects to this and other upcoming alpha releases
unless you are prepared to do it again to fix
future incompatibilities. However, if you can port
some existing projects and demos to the new
version, that may provide a lot of useful
information about critical issues still left to
fix.
Most importantly: Make backups before opening any
existing project in Godot 4.0 alpha builds. There
is no easy way back once a project has been
(partially) converted.
# ⚓ Wordle_Reverse-Engineering_And_Automated_Solving_|
Hackaday⠀⇛
We don’t know about you, but we have mixed feelings
about online puzzle fads. On one hand, they are
great tool to help keep one sharp, but they’re just
everywhere. The latest social-media driven fad,
Wordle, may be a little bit too prevalent for our
liking, with social media timelines stuffed with
updates about the thing. [Ed Locard] was getting a
bit miffed with friends’ constant posts about
‘Today’s Wordle’, and was hoping they’d get back to
posting pictures of their dogs instead, so did what
any self-respecting hacker would do, and wrote a
python script to automate solving Wordle puzzles,
in a likely futile attempt to get them to stop
posting.
o § Desktop Environments/WMs⠀➾
# ⚓ Give_Your_Linux_Mint_and_Xubuntu_a_Visual_Uplift_Using
Twister_UI⠀⇛
Twister UI is the easiest way to give your Linxu
Mint and XUbuntu a visual uplift using pre-loaded
themes. Here’s how.
# § K Desktop Environment/KDE SC/Qt⠀➾
# ⚓ KDE_Community_releases_Plasma_5.24:_It’s_eccentric,
just_like_many_old-timers⠀⇛
The new release of KDE’s Plasma desktop
brings a GNOME Shell-like instant overview
and other improvements.
KDE is fairly mature now. The FOSS community
was founded in 1996, allowing it to call last
year’s Plasma release, 5.23, the 25th
Anniversary Edition. KDE 1.0 came out in
1998, making it the first FOSS desktop for
Linux. It does also support FreeBSD, although
not always the latest version.
# ⚓ Plasma_Mobile_Gear_22.02_is_Out⠀⇛
The Plasma Mobile team is happy to announce
the Plasma Mobile updates for January to
February 2022.
Plasma 5.24 was released on February 8th,
with many changes to the Plasma Mobile shell.
The primary shell repository (and
corresponding package name for distributions)
has been renamed from plasma-phone-components
to plasma-mobile. Devin Lin did a lot of work
on the shell for this release.
# ⚓ KDE_Neon_vs_Kubuntu_vs_KDE_Plasma⠀⇛
One of the best aspects of using a Linux
system is that there are many popular desktop
environments to choose from. If you do not
like the style or behavior of yours, it is
simple enough to install a different one.
When it comes to the KDE Plasma desktop
environment, there are a few different ways
to experience it. KDE Plasma comes not only
as a graphical user interface, but also
includes a slew of applications (over 200;
some installed by default and some not) that
integrate into the desktop environment and
give the user a more unified experience that
flows together.
If you are ready to try out KDE Plasma, you
have a few choices. First of all, you can
install it the same way you would any other
desktop environment – right from your
system’s package manager. But you can also
choose from the KDE Neon and Kubuntu Linux
distributions.
So, which one should you choose? We will go
over all the details in this article and help
you make an informed decision.
# ⚓ More_wlroots_with_KWinFT_5.24_–_subdiff.org⠀⇛
In the last year our development focus for
KWinFT was on the integration with the
wlroots library. In a single sentence our
goal with this is to share underlying
architecture, patterns and ideas across the
Wayland ecosystem, instead of reimplementing
things again and again for each and every big
project while leaving smaller ones behind.
Only a few months ago in October a first
iteration of this integration was released
with KWinFT 5.23. I talked about it here on
this blog and at X.Org Developer Conference
(XDC) 2021 in a talk including a primer on
wlroots itself.
If you’re interested in that first part of
integration specifically or a wlroots primer
in general check out my talk on YouTube.
# § GNOME Desktop/GTK⠀➾
# ⚓ GNOME_42_Adds_’Dark_Wallpaper’_Support⠀⇛
Simply put: when the new standardised dark
mode setting is enabled in GNOME 42 a ‘dark’
version of the default wallpaper is applied.
When light mode is enabled, a ‘light’ version
of the wallpaper is applied. If this all
sounds a bit familiar it’s probably because I
mentioned this was on the way last month when
I wrote about the streamlining of wallpaper
options in GNOME 42.
Naturally, you are free to override this
behaviour and set any image you like as the
desktop background, regardless of whatever
dark mode preference is active.
# ⚓ Turbocharging_GNOME_Nightly_and_GNOME_OS
infrastructure⠀⇛
Mistakes were made¹, and after recent
maintenance, Jordan asked Infrastructure Team
if there is a chance GNOME Nightly (and its
younger sibling GNOME OS) could be moved
somewhere with faster network and more
storage. After short discussion, we decided
to move it to AWS (thanks to promotional
credits for open source projects). The new
server has three times more space, uses SSD
instead of HDD, and should offer up to 10
Gbps of network bandwidth.
It quickly became apparent we underestimated
GNOME Nightly popularity by a large margin.
On the second day, the new server transmitted
almost 500 GB of data. As we wanted to limit
potential egress costs, we reached out to
CDN77, and they quickly agreed to help us.
CDN77 team aren’t stranger to the open source
world, helping other projects like KDE,
Gentoo and Manjaro.
# ⚓ 7_New_Features_That_Make_GNOME_42_an_Awesome_Release
–_It’s_FOSS_News⠀⇛
GNOME 42 will be an interesting release.
It includes noticeable visual changes and
improvements to the desktop experience. Of
course, the changes in GNOME 41 compliments
the new release as well.
GNOME 42 is due on March 23, 2022, but it has
almost reached beta (scheduled for February
12, 2022).
o § Distributions⠀➾
# ⚓ Theme_in_EasyOS_3.3⠀⇛
The snapshot was taken on a 1024×768 monitor, which
is the smallest resolution that is practical to use
with EasyOS. You can see the icons along the top,
anything less than 1024 pixels, say 800 pixels, is
going to be a problem.
In a running Easy, you will see there is a file /
root/.packages/default-theme. This is used in woofQ
to set the theme, and is included in the release
build so that users can see the choices made. Here
is the file for Easy 3.3…
# ⚓ Icon-free_desktop_peach_theme⠀⇛
By using the ‘xdotool’ utility, the “Drives” menu
will now automatically popup whenever a drive is
plugged in.
On a screen that is smaller than 1920 pixels wide,
the app labels automatically do not display. Here
is a snapshot on a 1024×768 screen…
# ⚓ Experimental_icon-free_desktop⠀⇛
I have wanted to try this for a long time, a
desktop completely free of icons. You could then
have, say, a beautiful nature scene filling almost
the entire screen, unmarred by icons. Also, you
will no longer have to shove windows aside to get
at underlying icons.
ROX-Filer is not just a file manager, it also
manages the desktop icons and wallpaper. However,
it is possible for JWM window manager to display
all of the icons, in one or more trays, and also be
responsible for the wallpaper.
One big problem is the drive partition icons, that
will dynamically change as partitions are mounted
and unmounted, and drives plugged in and removed.
Implementing dynamic drive icons in a JWM tray is
not feasible; however, it can be done as a menu.
# § BSD⠀➾
# ⚓ Why_you_should_read_Section_8_of_the_Unix_User’s
Manual_•_The_Register⠀⇛
If, like me, you were a computer-science
graduate student who cut your teeth on
Berkeley Unix – complete with the first open-
source implementation of TCP/IP – you know
Section 8 as the cryptic System Maintenance
Commands section of the Unix User’s Manual.
It was obvious, to me, that this concluding
section warranted a closer look because the
introduction warned: “Information in this
section is not of great interest to most
users.” Judging by my taste in research
problems over the years, reading Section 8
turned out to be a pretty good investment.
But before getting to Section 8, you first
learned about the rest of Unix, where you
discovered how empowering it is to be able to
build new internet applications. Anyone
interested in how targeted investments in
open-source software, coupled with affordable
hardware, can spur innovation should study
the role of the Berkeley Software
Distribution (BSD) in the success of the
internet.
# § PCLinuxOS/Mageia/Mandriva/OpenMandriva Family⠀➾
# ⚓ Mozilla_Thunderbird_update_»_PCLinuxOS⠀⇛
Thunderbird, the email client from Mozilla
has been updated to 91.6.0 and shipped to the
PCLinuxOS Software Repository.
# ⚓ Firefox_browser_update_»_PCLinuxOS⠀⇛
Firefox, the web browser from Mozilla has
been updated to 97.0 and sent to the software
repository.
# ⚓ Kernel_updates_available_»_PCLinuxOS⠀⇛
Current kernels:
kernel-5.4.178-pclos1-1-1pclos2022.x86_64.rpm
kernel-5.10.99-pclos1-1-1pclos2022.x86_64.rpm
kernel-5.15.22-pclos1-1-1pclos2022.x86_64.rpm
kernel-5.16.8-pclos1-1-1pclos2022.x86_64.rpm
# § IBM/Red Hat/Fedora⠀➾
# ⚓ 3_ideas_for_bringing_innersource_to_your_company_|
Opensource.com⠀⇛
As workforces become more distributed and new
tools and processes enable more effective
asynchronous communication, innersource is
very likely to keep changing the work culture
as we know it.
# ⚓ Comparison_of_Fedora_Flatpaks_and_Flathub_remotes_–
Fedora_Magazine⠀⇛
In the previous article in this series, we
looked at how to get started with Fedora
Flatpaks and how to use it. This article
compares and contrasts between the Fedora
Flatpaks remote and the Flathub remote.
Flathub is the de-facto standard Flatpak
remote, whereas Fedora Flatpaks is the Fedora
Project’s Flatpak remote. The things that
differ between the remotes include but are
not limited to their policies, their ways of
distribution, and their implementation.
# ⚓ GitOps_using_Red_Hat_OpenShift_console_4.9_and_4.10_|
Red_Hat_Developer⠀⇛
This article introduces new Red Hat OpenShift
developer console features supporting GitOps
processes for applications running in the
cloud. Learn about improvements and updates
to the OpenShift GitOps Operator, then watch
a video showing how to manage cluster
configurations and deliver cloud-native
applications using Red Hat OpenShift GitOps
in the developer console.
[...]
OpenShift GitOps supports GitOps processes
for cloud-native applications. It is built on
top of Argo CD, a declarative GitOps
continuous delivery tool for Kubernetes, and
includes OpenShift’s GitOps Operator and
Pipelines Operator, both available from the
OpenShift OperatorHub. Figure 1 shows the
development flow and tools OpenShift GitOps
provides.
# ⚓ The_State_of_Customer_Experience_at_Red_Hat:_Where
we’ve_been_and_where_we_are_going⠀⇛
In the final part of our three-part blog
series on the state of customer experience at
Red Hat, we will cover enhancements that our
marketing teams made in 2021 based on
customer feedback. In addition, we will recap
where we have been and will look ahead at the
plans we have as an organization in 2022 to
continue to advance and improve the customer
experience.
# ⚓ Automating_Content_Management_in_Satellite_6.9_with
Ansible_Automation_Platform:_Part_2⠀⇛
If you recall from part one of the Automating
Content Management series, we are working to
minimize the management effort of maintaining
the Red Hat Satellite managed content for a
large fleet of servers. We developed a simple
plan that aligns with the guide to Building a
Red Hat Enterprise Linux Standard Operating
Environment (SOE) and allows us to automate
our process.
The simple model is: update the content,
publish the content, validate the content,
promote the content to the next life cycle
environment, rinse and repeat.
# ⚓ Agile_adoption:_6_strategic_steps_for_IT_leaders_|
The_Enterprisers_Project⠀⇛
At Thales Group, our IT organization has been
working on a transformation known as NextGen
IT for a couple years. One of the key
elements is to change from a waterfall
delivery model to an agile one.
As part of this enterprise initiative, my
North America leadership team and I took on
the challenge of reworking our entire
operation to adopt agile principles for both
product and service delivery. We knew what we
wanted to achieve: squads, operating using
agile methods, driven by user stories, and
ultimately delivering incremental value.
As we embarked on this journey, something
dawned on us early on: The only way we could
truly be effective in leading the
organization through an agile transformation
is if we transformed our leadership team
first.
We did this by adopting agile principles and
adapting the agile process to our leadership
team. Here’s what we learned.
# § Debian Family⠀➾
# ⚓ Writing_Debian_New_Contributor_Guide_–_ひとりしずかに。⠀⇛
Recently, I’ve wrote Debian New Cotributor
Guide in Japanese.
Here is the photo of on-demand printed
version.
This book (JIS-B5 128p) was published for
online event – Techbookfest 12th. It covers
how to package a new software in Debian.
# § Canonical/Ubuntu Family⠀➾
# ⚓ Ubuntu_Blog:_Canonical_and_CoreSpace_Announce
Partnership_To_Offer_Organizations_‘One-Stop_Shopping’
for_Private_Clouds⠀⇛
Canonical, the publisher of Ubuntu, and
CoreSpace, a leading Infrastructure-as-a-
Service provider, announced a partnership
today that makes it easier and more
economical for organizations to set up,
customize, and manage private clouds.
Hybrid or multi-cloud environments that allow
organizations to run workloads where it makes
the most sense have become common in the
modern enterprise. Because private workloads
remain essential for most companies, high-
performing private clouds are playing a
critical role in their containerisation,
cloud, and digital transformation strategies.
The Canonical-CoreSpace alliance enables
organizations to adopt and get the most out
of private clouds. It does this through an
end-to-end solution that combines Canonical’s
leadership in designing, building, operating,
and supporting private clouds with
CoreSpace’s infrastructure technology and
expertise. With the announcement, CoreSpace
becomes Canonical’s first cloud delivery
partner in the United States.
o § Devices/Embedded⠀➾
# ⚓ Vestel_puts_TikTok_on_Linux-based_TVs_|_Light_Reading⠀⇛
Vestel, the largest TV manufacturer in Europe, is
today announcing the arrival of TikTok on its vast
range of Smart TVs. The app collaboration will see
Vestel now bring the video sharing phenomenon to
more than twenty high-profile and premium TV
brands, including its own portfolio of brand
licences.
Especially designed for TV, the TikTok app is
already available on all Vestel-designed Android
Smart TV ranges for brands in the UK, Germany and
France. The roll out of TikTok for Vestel Linux-
based Smart TVs started on the 20th, January, with
the app set to launch on Vestel 2021 UHD TV ranges
in early February, and on Vestel 2020 UHD TVs by
the end of March.
Supporting the display of high definition TikTok
content, the Vestel-manufactured Smart TVs bring
more detail, vibrancy, and colour to the screen for
a larger-than-life home viewing experience.
# § Open Hardware/Modding⠀➾
# ⚓ Intel_Makes_Massive_Investment_in_RISC-V⠀⇛
Intel has joined RISC-V International, the
global open hardware standards organization,
and has announced creation of a billion-
dollar fund that aims to speed innovation and
development of RISC-V.
Intel’s Nios® V processors are already based
on RISC-V, but according to the announcement,
the company’s investment “will strengthen the
overall ecosystem and drive commercialization
of RISC-V.”
# § Mobile Systems/Mobile Applications⠀➾
# ⚓ 6_secret_settings_for_better_browsing_in_Chrome_on
Android_|_Computerworld⠀⇛
# ⚓ OnePlus_&_Oppo_tipped_to_merge_designs_in_Android_13
–_9to5Google⠀⇛
# ⚓ Google_patched_a_critical_Android_12_security_flaw
today_–_PhoneArena⠀⇛
# ⚓ Android_12L_is_coming_to_Samsung_tablets_–
9to5Google⠀⇛
# ⚓ OnePlus’s_first_tablet_may_come_with_Android_12L_OS_–
PhoneArena⠀⇛
# ⚓ Android_12L_Beta_3_rolling_out,_including_for_Pixel_6
and_6_Pro_–_9to5Google⠀⇛
# ⚓ Android_12L_Beta_3_now_available,_adds_support_for
Pixel_6_series⠀⇛
# ⚓ Google_releases_Android_12L_Beta_3_with_support_for
the_Pixel_6_series_|_Android_Central⠀⇛
# ⚓ Galaxy_S22_gets_Android_12′s_Material_You_design,_so
you_can_change_all_the_colors_–_CNET⠀⇛
# ⚓ How_to_install_Android_12L_Beta_on_Google_Pixel_–
9to5Google⠀⇛
# ⚓ Android_12L_beta_3_now_available_on_Pixel_phones_—
here’s_how_to_get_it⠀⇛
# ⚓ Here’s_everything_new_in_Android_12L_Beta_3_[Gallery]
–_9to5Google⠀⇛
# ⚓ Wallpaper_Wednesday:_Android_wallpapers_2022-02-09_–
Android_Authority⠀⇛
# ⚓ Google_just_added_the_Pixel_6_and_Pixel_6_Pro_to_its
Android_beta_program⠀⇛
# ⚓ Samsung_phones_will_get_an_extra_year_of_Android
updates_versus_Google’s_Pixel_–_The_Verge⠀⇛
# ⚓ Samsung_Galaxy_S22_Ultra:_stylus-equipped_Android
superphone_launched_|_Samsung_|_The_Guardian⠀⇛
# ⚓ Samsung_promises_“up_to”_four_major_Android_updates
for_some_devices_(and_five_years_of_security_updates)_–
Liliputing⠀⇛
# ⚓ The_best_mobile_video_editing_app_is_coming_to
Android,_with_a_little_help_from_Samsung⠀⇛
# ⚓ Samsung_leapfrogs_Google_by_announcing_4-year_Android
OS_upgrade_commitment⠀⇛
o § Free, Libre, and Open Source Software⠀➾
# ⚓ syslog-ng-future.blog?_Is_this_a_fork_or_what?_–_syslog-ng-
future.blog⠀⇛
I mentioned in the previous post that I would like
to focus on syslog-ng and put it more into the
spotlight. I also mentioned that Balabit, the
company I was a founder of and the commercial
sponsor behind syslog-ng, was acquired by One
Identity ~4 years ago. How does this add up? Who
owns the Intellectual Property (IP) for syslog-ng?
Who am I or this blog affiliated with?
I felt this post was important to set things
straight and make it easier to understand my
motivation. If you are not much into Free Software
and Open Source licenses or not interested too much
in administrative nuisances of FLOSS projects, feel
free to skip this post.
# § Web Browsers⠀➾
# § Mozilla⠀➾
# ⚓ Firefox_97.0_Released!_Support_New_Overlay
Scrollbars_in_Windows_11⠀⇛
Mozilla Firefox web browser 97.0 was
released a day ago with few new
features and various bug-fixes.
The release does not include any
exciting new features for Linux, but
only adds new minimal overlay scrollbar
support for Windows 11. As well, system
font loading on macOS has been improved
to make opening and switching to new
tabs faster in certain situations.
# ⚓ This_Week_in_Glean:_Migrating_Legacy_Telemetry
Collections_to_Glean⠀⇛
One of the things I’ve spent a fair
amount of time helping with on the
Glean Team are the migrations from
legacy telemetry to Glean being
performed by different Mozilla
products. This includes everything from
internal tools and libraries to the
mobile browsers and even desktop
Firefox. As it turns out, there were
quite a few projects and products that
needed to be migrated. While we have
started migrating all of our active
products, each of them are at different
stages and have different timelines for
completion. I thought it might be
helpful to take a little narrative look
through what the migration process
looks like, and so here we go!
# § FSF⠀➾
# § GNU Projects⠀➾
# ⚓ GNU_Binutils_2.38_released⠀⇛
Version 2.38 of the GNU Binutils tool
set has been released. Changes include
new hardware support (including for the
LoongArch architecture), various
Unicode-handling improvements, a new
–thin option to ar for the creation of
thin archives, and more.
# § Programming/Development⠀➾
# ⚓ QtQuick3D_Realtime_Reflections⠀⇛
Reflections enhance the realism of a rendered
3D scene and without it we can not have
objects like mirrors or puddles of water that
reflect the surrounding environment. Raster
rendering pipelines like QtQuick3D can
approximately calculate reflections using
different methods to get good results, as
opposed to Ray Tracing where reflections can
be calculated accurately by following the
light rays and checking where they bounce
from. In this blog post, we are going to
discuss two different techniques to do
reflections in QtQuick3D.
# ⚓ Qt_for_MCUs_2.0.1_Released⠀⇛
Qt for MCUs 2.0.1 has been released and is
available for download. This is the first
patch release made on top of the new Qt for
MCUs 2.0 series. As a patch release, Qt for
MCUs 2.0.1 provides bug fixes and other
improvements, and maintains source
compatibility with Qt for MCUs 2.0.0. It does
not add any new functionality.
# ⚓ Qt_for_Android_Automotive_6.2.3_released⠀⇛
We are happy to announce the release of Qt
for Android Automotive 6.2.3!
This release comes with several fixes that
improve the stability and developer
experience of QAA. Big thanks to our
technology preview users for reporting the
issues!
# ⚓ Raspberry_Pi:_This_new_feature_could_help_you_get
started_more_easily⠀⇛
The makers of Raspberry Pi computers have
released a new boot loader that lets users
install an operating system like the official
OS directly on the compute board rather than
via a separate computer.
Until now, Raspberry Pi owners needed the
imager on a macOS, Windows or Ubuntu desktop
to install the OS on a Pi device. It could
also be done via another Pi device by
connecting SD card readers on each of them.
The new Raspberry Pi bootloader delivers
network installation, cutting out the need
for a second computer to install the OS.
# ⚓ Getting_Started_with_C++_and_InfluxDB [Ed:
"InfluxData sponsored this post." The so-called 'media'
or so-called 'news' sites on the Web have become
nothing short of webspam]⠀⇛
# § Perl/Raku⠀➾
# ⚓ gfldex:_Fuzzy_commands⠀⇛
Reading can make one learned. Today I
had a peak into lizmat´s new module
shorten-sub-commands and learned about
Parameter.constraint_list. We need this
method to introspect a routines literal
parameters.
# § Shell/Bash/Zsh/Ksh⠀➾
# ⚓ how_to_use_vim’s_build_in_history_(re_run_re
play_commands)_by_line_number
⠀⇛
# ⚓ Using_the_Linux_fold_command_to_make_text_more
readable_|_Network_World⠀⇛
The Linux fold takes lines of text and
breaks them into chunks based on the
arguments that you provide. With no
arguments, fold will break lines at 80
characters.
The first example below uses a single-
line text file that includes
indications of character positions.
First, we count the number of
characters and lines in the file using
the wc -l and wc -l command…
# § Rust⠀➾
# ⚓ Dare_to_ask_for_more_#rust2024⠀⇛
Last year, we shipped Rust 2021 and I
have found the changes to be a real
improvement in usability. Even though
the actual changes themselves were
quite modest, the combination of
precise capture closure and simpler
formatting strings (println!(“{x:?}”)
instead of println!(“{:?}”, x)) is
making a real difference in my “day to
day” life.1 Just like NLL and the new
module system from Rust 2018, I’ve
quickly adapted to these new
conventions. When I go back to older
code, with its clunky borrow checker
workarounds and format strings, I die a
little inside.2
As we enter 2022, I am finding my
thoughts turning more and more to the
next Rust edition. What do I want from
Rust, and the Rust community, over the
next few years? To me, the theme that
keeps coming to mind is dare to ask for
more. Rust has gotten quite a bit nicer
to use over the last few years, but I
am not satisfied. I believe that there
is room for Rust to be 22x more
productive3 and easy to use than it is
today, and I think we can do it without
meaningfully sacrificing reliability,
performance, or versatility.
# § Java⠀➾
# ⚓ Java_break_and_continue_Statements⠀⇛
The continue statement is used in the
body of a while, do and for loop. The
break statement is used in these loops,
as well as in the switch statement.
Iteration can be considered the
execution of a loop’s body, over and
over. The break statement stops the
iteration. The continue statement skips
one execution (rest of the statements
below) of the body. This article
explains the employment of the continue
and break statements in Java. The
while-loop compound statement will be
used. For the break statement, the
switch compound statement will also be
used.
o § Standards/Consortia⠀➾
# ⚓ MIPI_CSI-2_v4.0_adds_features_for_always-on,_low_power
machine_vision_applications_–_CNX_Software⠀⇛
While MIPI CSI-2 standard was first introduced in
2005 as a high-speed protocol for the transmission
of still and video images from image sensors to
application processors, the standard has evolved
over the years, and the latest MIPI CSI-2 v4.0
introduces features to better support always-on,
low power machine vision applications, high-
resolution sensors, and high-dynamic-range
automotive image sensors.
The main changes for v4.0 include support for a
two-wire interface (MIPI I3C) to lower cost and
complexity, multi-pixel compression for the latest
generation of advanced image sensors, and RAW28
color depth for better image quality and an
improved signal-to-noise (SNR) ratio.
* § Leftovers⠀➾
o ⚓ Heart-Shaped_Pizza_History:_Less_Pizza_for_the_Same_Price⠀⇛
It doesn’t matter that the heart symbol doesn’t look like
an actual human heart, and never has. It nonetheless has
become our general symbol for what we think of as love.
The symbol is everywhere—on greeting cards, in emoji. But
there’s one particular heart-shaped thing that I can’t
stop thinking about right now: The heart-shaped pizza. It
seems like the most crass of romantic gestures, to put
tomato sauce and cheese on bread, but in a way, it’s
genius. And seemingly every major chain that’s not
Domino’s is offering a heart-shaped pizza. (Hey, if two
people are sharing, it makes splitting it kind of easy, I
guess.) I can’t stop thinking about the fact that lots of
people are expected to buy cheap, rubbery Papa John’s
pizza as a way to show off their love. (Papa John’s
doesn’t even use heart-shaped pepperonis!) Today’s
Tedium, in our first Valentine’s-themed post in our
seven-year history, talks about our cultural tendency to
make heart-shaped food. Especially pizza.
o § Hardware⠀➾
# ⚓ China_Loves_Battery_Swapping_EVs,_But_Will_They_Ever_Make
It_Here?_|_Hackaday⠀⇛
Electric vehicles promise efficiency gains over
their gas-fuelled predecessors, but the issue of
recharging remains a hurdle for many eager to jump
on board with the technology. The problem is only
magnified for those that regularly street park
their vehicles or live in apartments, without
provision to charge a vehicle overnight at home.
Battery swapping promises to solve that issue,
letting drivers of EVs change out their empty
battery for a freshly charged one in a matter of
minutes. The technology has been widely panned and
failed to gain traction in the US.
However, as it turns out, battery swapping for EVs
is actually thing in China, and it’s catching on at
a rapid rate.
# ⚓ Build_Your_Own_CRT_TV_|_Hackaday⠀⇛
There was a time following the Second World War
when TV sets for the nascent broadcast medium were
still very expensive, but there was an ample supply
of war-surplus electronic parts including ex-radar
CRTs. Thus it wasn’t uncommon at all for
electronics enthusiasts of the day to build their
own TV set, and magazines would publish designs to
enable them. With a burgeoning consumer electronics
industry the price of a new TV quickly dropped to
the point of affordability so nobody would consider
building one themselves today. Perhaps that should
be amended to almost nobody, because [Retro Tech or
Die] has assembled a small black-and-white CRT TV
from a kit he found on AliExpress.
# ⚓ That_Clock_On_The_Wall_Is_Actually_A_Network_Ping_Display_|
Hackaday⠀⇛
We’ve all been online from home a bit more than
usual lately, in ways that often stretch the limits
of what our ISP can muster. You know the signs —
audio that drops out, video sessions that make you
look like [Max Headroom], and during the off-hours,
getting owned in CS:GO by pretty much everyone. All
the bandwidth in the world won’t make up for high
latency, and knowing where you stand on that score
is the point of this ping-tracking clock.
# ⚓ It’s_Always_Floppy_Time!_|_Hackaday⠀⇛
On [Jan Derogee]’s desk is something that wouldn’t
look out of place for many of us, a pile of
computer magazines with a case of 3.5″ floppy disks
on top of it. The causal observer would see nothing
more than the detritus of a retrocomputer
enthusiast’s existence, but stick around. In fact
it’s a clock, and one of the most unusual ones
we’ve seen in a long time.
# ⚓ A_Guide_To_Milling_PCBs_At_Home_|_Hackaday⠀⇛
If you keep up with various retro vacuum tube
projects, you probably have run across
[UsagiElectric] aka [David]’s various PCBs that he
makes on his own Bridgeport EZ-Track 3-axis milling
machine — massively oversized for the job, as he
puts it. In a recent video, [David] walks us
through the steps of making a sample PCB,
introducing the various tools and procedures of his
workflow. He points out that these are the tools he
uses, but the overall process should be similar no
matter what tools you use.
# ⚓ Mystery_Effect_Causing_LEDs_To_Glow_During_Reflow_|
Hackaday⠀⇛
Sometimes you notice something small that
nevertheless you can’t explain. [Greg Davill] found
himself in just such a situation this week when he
noticed some green LEDs glowing dimly when
reflowing some boards. Naturally, [Greg] set out to
investigate.
The green LEDs were wired up as power indicators,
and [Greg] suspected that the polymer caps on the
board might be generating a small current somehow
that was causing the LEDs to light up ever so
slightly. A simple test hooked a polymer cap
directly up to a multimeter. When warmed with a
heat gun, the meter showed a small current “in the
5-10 uA range.”
[...]
It’s a curious case, and has many speculating as to
the causative mechanism on Twitter. Explanations
from thermoelectric effects to chemical reactions
inside the capacitor. If you’ve got the inside
scoop on what’s going on here, don’t hesitate to
let us know in the comments. Meanwhile, check out
some of [Greg]’s best work – a glowing D20 dice
featuring a whopping 2400 LEDs.
# ⚓ Working_Model_Reveals_Amazing_Engineering_Of_Webb’s_Mirror
Actuators_|_Hackaday⠀⇛
We end up covering a lot of space topics here on
Hackaday, not because we’re huge space nerds —
spoiler alert: we are — but because when you’ve got
an effectively unlimited budget and a remit to make
something that cannot fail, awe-inspiring
engineering is often the result. The mirror
actuators on the James Webb Space Telescope are a
perfect example of this extreme engineering, and to
understand how they work a little better, [Zachary
Tong] built a working model of these amazing
machines.
The main mirror of the JWST is made of 18 separate
hexagonal sections, the position of each which must
be finely tuned to make a perfect reflector. Each
mirror has seven actuators that move it through
seven degrees of freedom — the usual six that a
Stewart platform mechanism provides, plus the
ability to deform the mirror’s curvature slightly.
[Zach]’s model actuator is reverse-engineered from
public information (PDF) made available by the
mirror contractor, Ball Aerospace. While the OEM
part is made from the usual space-rated alloys and
materials, the model is 3D printed and powered by a
cheap stepper motor.
# ⚓ A_Tuning_Fork_Clock,_With_Discrete_Logic_|_Hackaday⠀⇛
[Willem Koopman aka Secretbatcave] was looking at a
master clock he has in his collection which was
quite a noisy device, but wanted to use the
matching solenoid slave clock mechanism he had to
hand. Willem is a fan of old-school ‘sector’
clocks, so proceeded to build his ideal time piece
— Vibrmatic — exactly the way he wanted. Now, since
most time keeping devices utilise a crystal
oscillator — which is little more than a lump of
vibrating quartz — why not scale it up a bit and
use the same principle, except with a metal tuning
fork? (some profanity, just to warn you!)
o § Integrity/Availability⠀➾
# § Proprietary⠀➾
# ⚓ Microsoft_Teams_will_soon_have_LinkedIn_and_OneDrive
integration [Ed: While Microsoft keeps antitrust
regulators busy with “GAFA” or “Big Tech” [1, 2]]⠀⇛
# ⚓ Microsoft_February_2022_Patch_Tuesday:_48_bugs
squashed,_one_zero-day_resolved [Ed: Charlie Osborne of
Microsoft_ZDNet failing to mention that Microsoft
intentionally_leaves_holes_for_the_NSA]⠀⇛
# ⚓ Microsoft_365_will_tell_your_boss_almost_immediately
if_you_send_an_inappropriate_message_|_TechRadar [Ed:
TechRadar is posting promotional ‘articles’ (ads) that
are painting spyware as “protection”]⠀⇛
Microsoft will soon roll out a new system
that will help businesses identify
inappropriate messages sent by employees over
its productivity and collaboration software.
# § Security⠀➾
# ⚓ Linux_kernel_developer_Alan_Cox_on_Microsoft
security_practices._“I_pointed_out_that_they_ship
an_OpenSSL_from_2017_and_they_won’t_even
respond.”._–_BaronHK’s_Rants⠀⇛
Linux kernel developer Alan Cox on
Microsoft security practices. “I
pointed out that they ship an OpenSSL
from 2017 and they won’t even
respond.”.
OpenSSL is a deeply troubled project
that Big Tech uses extensively. It has
a long history of disastrous security
flaws, thousands, some of which have
THEIR OWN Wikipedia articles, which
routinely compromise the security of
the connection between your computer
and a Web server. So it’s not like
shipping a recent version is important
or anything.
Shipping it in the first place is
stupid when it has a community fork
that removes poorly written and little-
used code and audits and fixes the
rest. But that’s Microsoft/Big Tech/
what most “Linux” distributions have
become under their guiding hand.
# ⚓ Breaking_256-bit_Elliptic_Curve_Encryption_with
a_Quantum_Computer_–_Schneier_on_Security⠀⇛
In other words: no time soon. Not even
remotely soon. IBM’s largest ever
superconducting quantum computer is 127
physical qubits.
# ⚓ The_impact_of_hardware_specifications_on
reaching_quantum_advantage_in_the_fault_tolerant
regime⠀⇛
# ⚓ 2021_Trends_Show_Increased_Globalized_Threat_of
Ransomware [Ed: Could they they type this with a
straight face without_mentioning_Microsoft_or
Windows?]⠀⇛
CISA, the Federal Bureau of
Investigation (FBI), the National
Security Agency (NSA), the Australian
Cyber Security Centre (ACSC), and the
United Kingdom’s National Cyber
Security Centre (NCSC-UK) have released
a joint Cybersecurity Advisory (CSA)
highlighting a global increase in
sophisticated, high-impact, ransomware
incidents against critical
infrastructure organizations in 2021.
This CSA provides observed behaviors
and trends as well as mitigation
recommendations to help network
defenders reduce their risk of
compromise by ransomware.
# § Fear, Uncertainty, Doubt/Fear-mongering/
Dramatisation⠀➾
# ⚓ Deterrence,_diplomacy,_in_hybrid_war._UK
Foreign_Office_hacked._Threats_to_Linux-
based_multi-cloud_environments._Patch
Tuesday. [Ed: They're calling everything
"Linux", even things that have nothing to
do with Linux]⠀⇛
Russia stages more general
purpose forces near Ukraine
(notably moving amphibious
assault ships from the
Mediterranean through the
Dardanelles and toward Ukraine’s
Black Sea coast) while diplomatic
efforts to reduce tension
continue. Belarus continues to
emerge as an important staging
point for Russian conventional
forces. No fresh, large-scale
cyber activity, however, is being
reported. The New York Times
reviews the current state of
multilateral negotiations and
sees, if not stalemate, at least
stasis. Its analysis foresees “a
drawn-out and dangerous
diplomatic slog toward a
difficult settlement.”
# ⚓ Threat_actors_view_Linux_servers_as_their
ticket_to_accessing_multi-cloud
environments [Ed: Only weeks after Dirk
left VMware the company has launched an
anti-Linux FUD campaign in the media, maybe
in order to distract from the back doors in
its own products and blame Linux itself
(while violating GPL, too)]⠀⇛
# ⚓ How_cybercriminals_are_using_malware_to
target_Linux-based_operating_systems [Ed:
Ransomware is a Windows issue (more than
90% of the time, but VMware now pays the
media to shift attention to Linux]⠀⇛
As the most common cloud
operating system, Linux is a core
part of digital infrastructure
and is quickly becoming an
attacker’s ticket into a multi-
cloud environment. Current
malware countermeasures are
mostly focused on addressing
Windows-based threats, leaving
many public and private cloud
deployments vulnerable to attacks
that target Linux-based
workloads, VMware reveals.
# ⚓ Cybercriminals_Are_Using_Malware_To
Target_Linux-Based_Systems [Ed: Microsoft-
connected sites are at it, too]⠀⇛
# ⚓ Cybercriminals_Target_Linux‑based_Systems
with_Ransomware_and_Cryptojacking_Attacks_–
VMware_News⠀⇛
# ⚓ Cybercriminals_Target_Linux-based_Systems
With_Ransomware_and_Cryptojacking_Attacks
[Ed: VMware is attacking Linux again with
FUD as paid press releases, adding to its
GPL_violations etc.]⠀⇛
# ⚓ Linux_Malware_on_the_Rise [Ed: Blindly
repeating the talking points]⠀⇛
o § Environment⠀➾
# § Energy⠀➾
# ⚓ The_Environmental_Costs_of_Cryptocurrency⠀⇛
New Scientist defines Bitcoin as a digital
currency that relies on peer-to-peer software
and cryptography. A public ledger (or
blockchain) records all Bitcoin transactions,
and copies of those transactions are held on
servers (or nodes) around the world.
“Consensus on who owns which coins is reached
cryptographically across these nodes rather
than relying on a central source of trust
like a bank.”
To acquire Bitcoin, you can buy it, you can
sell something and be paid in Bitcoin, or you
can mine it. Each cryptocurrency transaction,
however, involves an immense amount of
processing power, with this article
estimating that each Bitcoin transaction
consumes more than $100 worth of electricity.
o § Internet Policy/Net Neutrality⠀➾
# ⚓ #SocialMediaComplianceWatch:_analysis_of_Social_Media
Compliance_Reports_of_November,_2021⠀⇛
Google (including YouTube), Facebook, Instagram,
ShareChat, Snap, Twitter and WhatsApp released
their reports in compliance with Rule 4(1)(d) of
the IT Rules 2021 for the month of November, 2021.
The reports were made available in January 2022 and
they exhibit similar shortcomings. This outlines
lack of effort on the part of the SSMIs and the
government to further transparency and
accountability in platform governance. The SSMIs
have continued to not report on government
requests, used misleading metrics, and not
disclosed how they use algorithms for proactive
monitoring. You can read our analysis of the
previous reports here.
o § Monopolies⠀➾
# § Copyrights⠀➾
# ⚓ A_Paper_Archaeology:_Piranesi’s_Ruinous_Fantasias_–
The_Public_Domain_Review⠀⇛
From the vast confines of his imaginary
prisons to the billowy scenes that comprise
his grotteschi, the early works of Giovanni
Battista Piranesi wed the exacting details of
first-hand observation with the farthest
reaches of artistic imagination. Susan
Stewart journeys through this 18th-century
engraver-architect’s paper worlds.
䷩ 𝚕𝚒𝚗𝚎 6972
╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕
⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.09.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧
Gemini_version_available_♊︎
✐ Links_9/2/2022:_GNU_Binutils_2.38_and_Google_Stadia_Failing⠀✐
Posted in News_Roundup at 2:01 pm by Dr. Roy Schestowitz
🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈
§ Contents⠀➾
* GNU/Linux
o Distributions
o Devices/Embedded
* Free_Software/Open_Source
* Leftovers
* § GNU/Linux⠀➾
o § Audiocasts/Shows⠀➾
# ⚓ Shockingly_Pragmatic_|_Coder_Radio_452_|_Jupiter
Broadcasting⠀⇛
Mike makes a shocking admission, and Chris wishes
he had a time machine.
o § Applications⠀➾
# ⚓ Best_Free_and_Open_Source_Alternatives_to_Atlassian
Trello⠀⇛
Atlassian Corporation Plc is a software company
founded in 2002 that develops products for software
developers, project managers and other software
development teams. It employs over 7,000 people and
is headquartered in Sydney, Australia.
Atlassian’s range of proprietary software includes
software for collaboration, development, and issue
tracking software for teams. Atlassian dominates
several markets where it still has intense
competition.
o § Instructionals/Technical⠀➾
# ⚓ Checking_out_a_Git_branch_further_back_than_the_head⠀⇛
It’s possible to move a branch (including ‘main’)
back to an older commit while staying on the
branch. This avoids Git complaints about being in a
detached HEAD state and makes ‘git status’ do
useful things like report how many commits you are
behind the upstream tip. As far as I know so far,
the way you do this is: [...]
# ⚓ Ignore_A_Package_From_Being_Upgraded_In_Arch_Linux_–
OSTechNix [Ed: Updated after 5 years]⠀⇛
Sometimes, you may want to ignore a package from
being upgraded in your Arch Linux system. It is
true that the outdated packages might be vulnerable
and not safe to our system. Yes! We need to update
the Arch Linux system regularly to get latest
packages and make our system more secure. However,
we need to hold a package or group of packages from
being upgraded for certain reasons.
# ⚓ How_to_install_WhatsApp_on_Linux⠀⇛
WhatsApp is a telecommunications application to
provide video, chat and voice communication between
computers, tablets, and mobile devices over the
Internet connection. All you need is a phone number
to sign up, and then you can send messages from
your Linux system.
There is no official Linux client for WhatsApp,
unfortunately. The good news is that it is still
possible to download WhatsApp clients made by
users, which will use WhatApp’s web interface to
create a seamless experience. Using this method, we
are able to have WhatsApp on Linux and have it
resemble the same client you would get on a Windows
PC.
# ⚓ How_to_install_PHP_on_Ubuntu_Linux⠀⇛
PHP is one of the most used languages when it comes
to programming dynamic web sites. If you are a web
developer, or just hosting a website that requires
PHP, you will need to install the software on your
server in order for your website to make use of its
PHP code.
PHP is also required by various content management
systems, including the most popular one in the
world, WordPress. In this tutorial, we will take
you through the step by step instructions to
install PHP on Ubuntu Linux.
# ⚓ How_to_install_Grub_Customizer_on_Linux_(all_major
distros)⠀⇛
Grub Customizer is a software package that does
exactly as the name would imply. It allows the user
to customize different aspects of the grub boot
menu – such as the order that entries appear in the
list, how long grub waits before selecting a
default system to boot to, etc.
The good news is that you can use this application
on all major Linux distros. In this tutorial, we
will show you how to install the Grub Customizer
package on all Linux systems.
# ⚓ How_to_fix_Kubernetes_namespaces_stuck_in_the_terminating
state_|_Enable_Sysadmin⠀⇛
A Kubernetes namespace isolates specific system
resources usually visible to all processes. Each
namespace has its own services, pods, and
deployments in the cluster. A namespace in
Kubernetes is essentially the same as a project in
OpenShift.
These days, most products are containerized and can
easily be deployed on Kubernetes or OpenShift. This
requires continuous application deployment and
testing. I recently worked on test automation that
involves the creation of namespaces, resources, and
data in the namespace, followed by running the test
suite, and then removing the data and namespace
once the tests are complete.
While frequently creating and deleting namespaces
in Kubernetes, I stumbled upon an issue where a
namespace got stuck in the Terminating state and
just refused to delete.
I use minikube to run Kubernetes locally, but you
can use the following steps and commands in any
Kubernetes or OpenShift environment.
# ⚓ How_to_Fix_“Unacceptable_TLS_certificate”_Error_in_Linux?⠀⇛
When it comes to SSL/TLS certificates, you may come
across a variety of issues, some related to the
browser or a problem in a website’s back-end.
One such error is “Unacceptable TLS certificate” in
Linux.
Unfortunately, there’s no “one-solves-it-all’
answer to this. However, there are some potential
solutions that you can try, and here, I plan to
highlight those for you.
# ⚓ How_to_Add_Linux_Host_to_Nagios_Ubuntu_Server_–_Part_2⠀⇛
This article assumes that you already have Nagios
installed on your Ubuntu system. If not, follow the
Part 1 tutorial guide article which is succeeded by
this one.
# ⚓ How_To_Install_Podman_on_Linux_Mint_20_–_idroot⠀⇛
In this tutorial, we will show you how to install
Podman on Linux Mint 20. For those of you who
didn’t know, Podman (POD Manager) is a tool for
managing OCI containers and pods. It’s an open-
source project that can be used in most of the
Linux distributions that use Demon-less container
Engines. It exposes the same command-line interface
as Docker but runs containers unprivileged by
default.
This article assumes you have at least basic
knowledge of Linux, know how to use the shell, and
most importantly, you host your site on your own
VPS. The installation is quite simple and assumes
you are running in the root account, if not you may
need to add ‘sudo‘ to the commands to get root
privileges. I will show you the step-by-step
installation of a PHP 8.1 on a Linux Mint 20
(Ulyana).
# ⚓ Create_a_data_stream_with_Amazon_Kinesis_|_Red_Hat
Developer⠀⇛
Streaming data is key to many modern applications.
This tutorial walks you through setting up a data
stream using Amazon Kinesis and Node.js.
# ⚓ Getting_started_with_Arduino⠀⇛
The Arduino is an advanced form of a
microcontroller which is comparatively easier to
work on. Similarly, it is a kind of plug and play
device and is much easier for the beginners to
learn how to make different projects related to
embedded systems. Arduino has different types of
microcontroller boards having different
specifications and the most common Arduino board is
the Arduino Uno board. All the Arduino boards can
be configured using the Arduino IDE software. This
discourse explains how to use the Arduino Uno board
# ⚓ seife’s_assorted_rants:_dracut:_fix_hibernate_after_fresh
install⠀⇛
Just for fun, I finally installed a fresh
Tumbleweed on one of my machines to actually find
out if I’m missing out on new features that are
masked by just always updating the old
installation.
One feature that I had missed was, that hibernation
was no longer working. Or, to be more exact,
hibernation was working, but resume was not.
Investigating the issue, I found that dracut’s
“resume” module was not included in the initramfs,
which in turn lead to initramfs not even trying to
resume.
The dracut mechanism has some logic to actually
find out if suspend and resume is configured, and
when it decides it is not, it will just skip adding
the “useless” resume module.
Unfortunately, the check is faulty IMHO. It checks,
if the resume device is configured in the kernel,
and if it is, it adds the module to dracut. The
problem is, that this kernel config is written by
the resume code in the initrd… so during
installation this is not the case, and as a result
the module is not added to initrd, which leads to
the config not being set on next reboot…
# ⚓ Install/Upgrade_XanMod_Kernel_LTS_on_Rocky_Linux_8_–
LinuxCapable⠀⇛
XanMod is a free, open-source general-purpose Linux
Kernel alternative to the stock kernel that is on
Rocky Linux. It features custom settings and new
features and is built to provide a responsive and
smooth desktop experience, especially for new
hardware.
Installing a third-party kernel may be for you for
users seeking to have their system kernel up to
date and not wanting to install kernels or use the
testing/unstable repositories manually.
Currently, the XanMod LTS kernel is supported and
not the latest bleeding-edge using the rmnscnce/
kernel-xanmod.
# ⚓ Install/Upgrade_MakeMKV_on_Debian_11_Bullseye_–
LinuxCapable⠀⇛
MakeMKV is a free, open-source tool that can
convert video clips from DVDs and Blu-rays, which
are usually encrypted. The output will have most
information preserved but not changed in any way;
it’s perfect for people who want their media
without hassle or headache caused by software
limitations like those found with some other
transcoder apps.
In the following tutorial, you will learn how to
install or upgrade to the latest version of MakeMKV
on Debian 11 Bullseye using a recommended
repository by the MakeMKV team to provide the most
up-to-date version.
# ⚓ Install_Podman_on_Debian_11_–_Unix_/_Linux_the_admins
Tutorials⠀⇛
Podman is an alternative to Docker that is backed
by Red Hat and IBM. The open-source project has a
great ease of use, which is a big draw among
developers.
Well, one of the differences is that it is not
based on daemons (services in the *nix world). One
of the advantages is that Docker has a single
daemon that when it handles many containers grows
and grows, becoming much heavier.
This last point is where Podman wants to be a solid
alternative to Docker and is where Podman bases its
reason.
As you would expect, Podman has great support for
all the Linux distributions out there. This is also
the case for Debian 11 where the installation is
effortless.
# ⚓ Install_Htop_on_Debian_11_Bullseye_–_LinuxCapable⠀⇛
Htop is a free, open-source, cross-platform
interactive process viewer. It is a text-mode
application (for console or X terminals) and
requires ncurses. The terminal UI is a great way to
see what your system looks like inside, both in
terms of processes and other info. It’s also
completely customizable, so you can change colors
or add different widgets for more visual
representation!
In the following tutorial, you will learn how to
install Htop Interactive Process Viewer on Debian
11 Bullseye desktop or server.
# ⚓ 6_Linux_metacharacters_I_love_to_use_on_the_command_line_|
Opensource.com⠀⇛
Early in my Linux journey, I learned how to use the
command line. It’s what sets Linux apart. I could
lose the graphical user interface (GUI), but it was
unnecessary to rebuild the machine completely. Many
Linux computers run headless, and you can
accomplish all the administrative tasks on the
command line. It uses many basic commands that all
are familiar with—like ls, ls-l, ls-l, cd, pwd,
top, and many more.
o § Games⠀➾
# ⚓ Google_Stadia’s_Failure_Is_Almost_Complete⠀⇛
While Google’s Stadia game streaming service
arrived with a lot of promise, it generally landed
with a disappointing thud. A limited catalog,
deployment issues, and a quality that couldn’t
match current gen game consoles meant the service
just never saw the kind of traction Google (or a
lot of other people) originally envisioned. In the
years since, developers have been consistently
abandoning the platform, and Google has
consistently sidelined the service, even shutting
down its own development efforts as a parade of
executives headed for the exists.
# ⚓ How_to_Connect_Xbox_Controller_with_Raspberry_Pi⠀⇛
For those who want to enjoy a better gaming
experience, they certainly need an Xbox controller
in order to play games with great control. Getting
a wireless Xbox controller is a bit expensive so
most people stick with buying an affordable wired
Xbox controller. So, if you are one of those people
who have a wired Xbox USB controller and you want
to play games with it on your Raspberry Pi OS then
you certainly need help in configuring it on the
device.
# ⚓ Wadjet_Eye_Games_brings_Shardlight_over_to_Linux_|
GamingOnLinux⠀⇛
Is there no stopping Wadjet Eye Games? Shardlight,
another quality point and click adventure from 2016
has now been ported over to Linux. This adds to the
list of titles that Wadjet Eye Games has recently
upgraded and ported (or re-ported) to Linux
including Resonance, Technobabylon, Unavowed,
Gemini Rue, The Blackwell Bundle.
# ⚓ ChimeraOS_30_is_out_with_big_OneXPlayer_improvements⠀⇛
ChimeraOS continues to provide a full-screen
console-like Linux experience for those that want
it, and ChimeraOS 30 is now live with some great
upgrades.
First, the usual upgrades to the major parts like
Linux Kernel 5.16.5, Mesa drivers 21.3.5, NVIDIA
drivers 510.47.03 and upgrades to their own special
compositor and Chimera software. Plus, a bump for
RetroArch to version 1.10.0. The bigger changes
come for those who have a OneXPlayer handheld
device as it should work vastly better with
ChimeraOS now thanks to controller detection fixes,
screen orientation fixes, a fix for custom
resolution support and a default resolution set
properly to 1280×800. So out of the box, OneXPlayer
devices should work nicely.
# ⚓ SimAirport_getting_some_great_upgrades_ready_for_the_Steam
Deck_|_GamingOnLinux⠀⇛
A little building and management on the go?
SimAirport from LVGameDev LLC sounds like it might
be a good choice, with the developer highlighting
upcoming changes and improvements for the Steam
Deck and it will help all platforms.
You probably don’t need a big explanation to begin
with on this one, the name SimAirport speaks for
itself really. You construct and manage an Airport
from a single plane to a massive international
terminal filled to the brim with passengers, staff
and it’s your job to keep everything flying
smoothly.
# ⚓ WRAEK_think_they_can_change_PC_gaming_with_the_Tactonic_Pro
|_GamingOnLinux [Ed: Looks to me like paid-for spam; is Liam
Dawe selling itself out like Phoronix?]⠀⇛
What’s really great to see though, is how Linux has
clearly been making more waves – enough for this
hardware vendor to target it too. They said their
software is fully compatible with Linux!
# ⚓ With_You_looks_like_a_sweet_co-op_experience_and_it’s_free
|_GamingOnLinux⠀⇛
Need a new casual co-op game to play with a
partner? With You recently released on Steam and
itch.io and it looks adorable. It’s free to, so
you’ve got nothing to lose but a few moments of
your time, and perhaps a fun memory to gain from
it.
o § Desktop Environments/WMs⠀➾
# § K Desktop Environment/KDE SC/Qt⠀➾
# ⚓ KDE_Plasma_5.24_LTS_Releases_with_Updated_Breeze
Theme_and_New_Overview_Effect⠀⇛
We have been keeping an eye on KDE Plasma
5.24 for a while.
From spotting the GNOME-Style overview effect
to the addition of fingerprint support. If
you have been following our coverages, you
already know about the changes introduced
with KDE Plasma 5.24.
Now that KDE Plasma 5.24 stable release is
finally here, let me highlight the key
additions and improvements below.
[...]
KDE Plasma 5.24 is a long-term support
release that will receive updates until the
final Plasma 5 release (and the transition to
Plasma 6).
With this release, you do not get to see
massive visual changes, but you can find
various functional improvements and subtle
visual refinements.
# ⚓ KDE/Plasma_5.24_for_Debian⠀⇛
Yesterday, KDE released version 5.24 of the
Plasma desktop with the usual long list of
updates and improvements. This release will
be considered a LTS release. And Plasma 5.24
is now available for all Debian releases.
(And don’t forget KDE Gears/Apps 21.12!)
# ⚓ KDE_Plasma_5.24_LTS_desktop_environment_brings
fingerprint_support,_performance_and_user_interface
improvements_and_more⠀⇛
The developers of the open source KDE Plasma
desktop environment for Linux distributions
have released Plasma 5.24, which brings a
number of performance improvements, visual
tweaks, and new features.
It’s also a long term support (LTS) release,
which means it will continue to receive bug
fixes and other updates until the next major
update, which will be Plasma 6.
# ⚓ Plasma_5.24_available_on_Kubuntu_21.10⠀⇛
We are pleased to announce that Plasma 5.24
is now available in our backports PPA for
Kubuntu 21.10 (Impish Indri).
The release announcement detailing the new
features and improvements in Plasma 5.24 can
be found here.
# ⚓ Plasma_Mobile_Gear_22.02_Is_Out_with_Many_Changes_to
the_Plasma_Mobile_Shell_and_Apps⠀⇛

Coming hot on the heels of the KDE Plasma
5.24 desktop environment, which is also
available for mobile devices as Plasma
Mobile, the Plasma Mobile Gear 22.02 software
suite is here to update some of your favorite
mobile apps, as well as the Plasma Mobile
shell.
In fact, Plasma Mobile Gear 22.02 is packed
with great improvements for the Plasma Mobile
shell, including a revamped Quick Settings
panel with support for media and
notifications widgets, as well as a new
landscape format for tablets, a smoother
gesture experience, a revamped task switcher
to use a single row of thumbnails with
gesture support, and a revamped app drawer
open/close gesture.
# § GNOME Desktop/GTK⠀➾
# ⚓ Best_Audio_and_Video_Players_for_Gnome_Desktop⠀⇛
To take a break from our everyday routines,
most unwind by watching movies, TV shows,
listening to music, and indulging in other
forms of entertainment. Aside from that,
videos can be utilized for business
information sharing, product advertisements,
and a variety of other tasks in which digital
media is at the center of business marketing.
There are quite a number of video and audio
players. They provide features like subtitle
synchronization, support for a variety of
video formats, and the ability to play
YouTube videos directly without
advertisements.
o § Distributions⠀➾
# ⚓ VA_Linux⠀⇛
In 1999, one of the hottest IPOs was an open source
company named VA Linux ($LNUX). The stock opened
10x in its first day of trading. The stock was
offered at $30, opened at $300, and was $8.50 a
year later. The company later launched SourceForge.
In 2015, it become a subsidiary of Gamestop.
VA Linux was the largest vendor of pre-installed
Linux computers. Red Hat had just gone public
earlier that year. The company had Intel and
Sequoia as investors in its seed round, and the
founder was classmates at Stanford with Yahoo
founders Jerry Yang and David Filo.
# § IBM/Red Hat/Fedora⠀➾
# ⚓ Comparison_of_Fedora_Flatpaks_and_Flathub_remotes⠀⇛

In the previous article in this series, we
looked at how to get started with Fedora
Flatpaks and how to use it. This article
compares and contrasts between the Fedora
Flatpaks remote and the Flathub remote.
Flathub is the de-facto standard Flatpak
remote, whereas Fedora Flatpaks is the Fedora
Project’s Flatpak remote. The things that
differ between the remotes include but are
not limited to their policies, their ways of
distribution, and their implementatio
# § Debian Family⠀➾
# ⚓ Testing_Slax_11.2_based_on_Debian_Bullseye_–_Slax
Linux⠀⇛
I made my first attempt to build Slax based
on Debian Bullseye (version 11.2). Here is a
work in progress (well, it is mostly finished
I guess so lets call it RC1). Some of the
applications are no longer available, such as
leafpad, wicd, and I replaced pcmanfm with
tuxCommander.
Please feel free to suggest a small simple
GUI app (GTK-based) for network
configuration.
This version does not include chromium
browser due to its size, but if you click the
icon, it will install automatically before
first use.
Debian also no longer supports aufs, so it
has been replaced by overlayfs in Slax. This
is internal change which affects the use of
‘slax activate’ command (it will no longer
work). I am investigating possibilities to
make it work again but as far as I can see,
there is no way to modify the existing
overlay filesystem on the fly as it was
possible with AUFS, this means it is no
longer possible to add new modules on the fly
while running Slax. You can of course still
add modules to your ISO (or USB directory
tree). Suggestions welcome.
o § Devices/Embedded⠀➾
# ⚓ Raspberry_Pi_4_GPIO_Pinout⠀⇛
Raspberry Pi 4 has come up with more advanced
features as compared to the previous model of the
Raspberry Pi. It was launched in June 2019 and has
come up with a much-improved processing speed of
about 90% as compared to previous version due to
the inclusion of 4GB and 8GB RAM memory. Its
General-Purpose Input Output (GPIO) pins have also
maintained the previous standard set by the
Raspberry Pi models, and are now more functional
and performing flawlessly.
The Raspberry Pi 4 has 40 GPIO pins that can be
easily configured to read inputs or write outputs.
If you are unfamiliar with the operation of these
GPIO pins, this article will assist you in
understanding the operation of each pin.
# ⚓ Raspberry_Pi_4_to_support_Network_install_to_a_blank
MicroSD_card⠀⇛
The Raspberry Pi 4 will soon be able to install
Raspberry Pi OS without the need for external
hardware to flash the image. Raspberry Pi Network
install will allow users to install a blank MicroSD
card into their board, which will trigger the
launch of Raspberry Pi Imager on the Raspberry Pi,
and flash the image downloaded from the Raspberry
Pi website.
So far in order to install Raspberry Pi OS, you had
to download Raspberry Pi Imager on a computer or a
working Raspberry Pi, insert the MicroSD card into
the host, and flash the image, before moving the
MicroSD card into the Raspberry Pi board. This
works just fine for most people, but if the
Raspberry Pi is your only computing device, as may
be the case in developing countries, that does not
work. Network Installs may also speed up the
installation process in the classroom where
multiple boards may need to be set up.
# ⚓ How_to_List_Installed_Packages_in_Raspberry_Pi_OS⠀⇛
You already know that your Raspberry Pi OS has so
many different packages installed in it. However,
you don’t know what packages are installed on the
Raspberry Pi OS. Finding those packages used to be
a difficult task as it requires your time in
searching for those packages. As it becomes
necessary for you to look for those packages, there
should be a solution that can help you in finding
those packages on your Raspberry Pi OS. If you are
still searching for the right solution then this
article will provide you with the solution so that
you can easily list the pre-installed packages in
Raspberry Pi OS.
# ⚓ How_to_Mine_Crypto_on_Raspberry_Pi⠀⇛
Nowadays, cryptocurrency is becoming much popular
among the young generation and the reason is it
provides them the opportunity to earn a lot of
money. Cryptocurrency can be obtained by two
methods which are purchasing and mining. The
purchasing method of Cryptocurrency is hard for
most of the people because they don’t have enough
money in their pockets. The second method is a
better one to start with but it requires some
effort and hard work.
Cryptocurrency mining has long affected the passion
of technology addicts, pushing them to design new
algorithms to defend networks, mining pools, and
innovative ways to build mining systems. If you are
among the Raspberry Pi users and you want to start
your Cryptocurrency mining journey, you can do it
on your Raspberry Pi operating system. This
requires your efforts and some time so that you can
begin mining Cryptocurrency on Raspberry Pi.
# § Mobile Systems/Mobile Applications⠀➾
# ⚓ Android_vs._iOS:_Is_iPhone_Better_Than_Android_or
Vice_Versa?⠀⇛
# ⚓ Exclusive:_Material_You-style_theming_will_soon_be
required_for_phones_getting_Android_12⠀⇛
# ⚓ OnePlus_Pad_tablet_tipped_to_ship_with_Android_12L⠀⇛
# ⚓ Google_fixes_“critical”_Android_12_security_flaw_|
TechRadar⠀⇛
# ⚓ Which_phones_and_cars_can_use_Android_digital_car
key?_|_Android_Central⠀⇛
# ⚓ How_to_forward_calls_on_Android_–_Phandroid⠀⇛
# ⚓ Vivaldi_5.1_arrives_for_desktop_and_Android_–_gHacks
Tech_News⠀⇛
# ⚓ Top_10_Android_MMORPGs_of_2022:_RuneScape,_Albion,
Adventure_Quest_3D,_and_More_|_Tech_Times⠀⇛
# ⚓ Top_10_Best_Third-Party_Android_App_Stores_–_2022⠀⇛
# ⚓ OnePlus_Pad_rumored_to_get_Android_12L._Would_you_buy
it?⠀⇛
# ⚓ Motorola’s_first_smartphone_receiving_Android_12
stable_update_was_launched_in_2020_–_GSMArena.com
news⠀⇛
# ⚓ Critical_Android_12_bug_fixed_in_February_security
patches_•_The_Register⠀⇛
# ⚓ OnePlus_Unified_OS_to_Debut_in_Second_Half_of_2022,
OnePlus_Pad_to_Run_Android_12L:_Reports_|_Technology
News⠀⇛
# ⚓ Smartphone_Lifespan:_How_Long_Android_Phones_From
Samsung,_Xiaomi,_Realme_And_Others_Will_Last
‘Officially’⠀⇛
# ⚓ YouTube_Music_For_Android_Gets_A_New_Playback
Shortcut⠀⇛
# ⚓ 6_secret_settings_for_better_browsing_in_Chrome_on
Android_|_Computerworld⠀⇛
o § Free, Libre, and Open Source Software⠀➾
# § FSF⠀➾
# § GNU Projects⠀➾
# ⚓ GNU_Binutils_2.38_has_been_released⠀⇛
Hi Everyone,
We are pleased to announce that version
2.38 of the GNU Binutils project
sources have been released and are now
available for download at:
https://ftp.gnu.org/gnu/binutils
https://sourceware.org/pub/binutils/
releases/
The SHA256 checksums are as follows:
070ec71cf077a6a58e0b959f05a09a35015378c2d8a51e90f3aeabfe30590ef8
binutils-2.38.tar.bz2
6e54170356709d401f1cb781f86bb59656b99b398412047f5c44f0fbc633fa4d
binutils-2.38.tar.bz2.sig
b3f1dc5b17e75328f19bd88250bee2ef9f91fc8cbb7bd48bdb31390338636052
binutils-2.38.tar.gz
864d330b71f2b40120d96e68ebed43a07c5286d9c28f3a3893ae4ae7ec25ede9
binutils-2.38.tar.gz.sig
807ccfa77ccfc3e09b1f760cd73e13839180c6950a37843df1c1e7a58c777dc9
binutils-2.38.tar.lz
49ee3c3b5803dea2acb15a3fa4c8ad0daebf142ba284a8b3d3524a52823a0ceb
binutils-2.38.tar.lz.sig
e316477a914f567eccc34d5d29785b8b0f5a10208d36bbacedcc39048ecfe024
binutils-2.38.tar.xz
41301d67da78df1ad6df04aefe9e7bea8235484b0323cee52caa8f7435385014
binutils-2.38.tar.xz.sig
This release contains numerous bug
fixes and improvements, along with
the following new features:
Assembler:
General:
* Add support for the LoongArch
architecture.
* Add an option to control how
multibyte characters are handled in
the assembler. Using the
option warnings can be generated when
such characters are encountered
in symbol names, or anywhere in
the input source file(s).
AArch64 and ARM:
* Add support for more system
registers.
* Add support for Scalable Matrix
Extension.
* Add support for Cortex-R52+,
Cortex-A510, Cortex-A710,
Cortex-X2, Cortex-A710 cores.
* Add support for 'v8.7-a',
'v8.8-a', 'v9-a', 'v9.1-a',
'armv9.2-a' and 'armv9.3-a'
architecture extensions.
X86:
* Add a command-line option to
encode aligned vector move as
unaligned vector move.
* Add support for Intel
AVX512_FP16 instructions.
* The outputs of .ds.x directive
and .tfloat directive with hex
input have been reduced from 12
bytes to 10 bytes to match the
output of .tfloat directive.
Linker:
* Add support for the LoongArch
architecture.
* Add -z pack-relative-relocs/-z no
pack-relative-relocs to x86 ELF
linker to pack relative
relocations in the DT_RELR section.
* Add -z indirect-extern-access/-
z noindirect-extern-access to x86
ELF linker to control canonical
function pointers and copy
relocation.
Other Binary Tools:
* elfedit: Add --output-abiversion
option to update ABIVERSION.
* Tools which display symbols or
strings (readelf, strings, nm,
objdump) have a new command line
option which controls how unicode
characters are handled. By
default they are treated as normal for
the tool. Using --unicode=locale
will display them according to
the current locale. Using --
unicode=hex will display them as hex
byte values, whilst --
unicode=escape will display them as
escape
sequences. In addition using --
unicode=highlight will display
them as unicode escape sequences
highlighted in red (if supported
by the output device).
* readelf -r dumps RELR relative
relocations now.
* Support for efi-app-aarch64, efi-
rtdrv-aarch64 and
efi-bsdrv-aarch64 has been added
to objcopy in order to enable
UEFI development using binutils.
* ar: Add --thin for creating thin
archives. -T is a deprecated
alias without diagnostics. In
many ar implementations -T has a
different meaning, as specified
by X/Open System Interface.
Our thanks go out to all of the
binutils contributors, past and
present, for helping to make this
release possible.
Cheers
Nick Clifton
GNU Binutils Chief Maintainer
# § Programming/Development⠀➾
# ⚓ Sunsetting_gzip_substitutes_availability⠀⇛
Starting next month (2022/03/01), the build
farm known as ci.guix.gnu.org will no longer
offer gzip-compressed binary substitutes. The
Guix daemon has known to use lzip for
substitutes since 2019; unless you are
running a very outdated daemon, you have no
need to worry about this change.
This idea was first discussed about a year
ago, when it was found that gzip-compressed
substitutes accounted for about only 1% of
the downloaded substitutes. Since then, the
daemon has gained support for zstd on top of
gzip and lzip, and the build farm has happily
generated compressed substitutes for all of
these compression schemes.
# ⚓ I_would_like_a_job_writing_Haskell⠀⇛
Perhaps someone out there wants to take a
chance on a senior programmer with thirty
years of experience who wants to make a move
into Haskell.
# § Java⠀➾
# ⚓ Hashset_vs_Hashmap_in_Java⠀⇛
The Java programming language has two
distinct yet similar types of data
containers, HashMap and HashSet . Both
use a hash table to store data. A table
is a table of values that uses a hash
function to determine where to look and
store data. This allowsquick access to
data because a value does not have to
be searched. Instead, the hash function
can provide the exact location of the
value. Despite so much use of hash
tables, HashMap and HashSet are quite
different from each other.
# ⚓ Java_assert⠀⇛
Assertion in Java is a statement based
on the reserved word, assert, having a
boolean expression and ending with a
semicolon. It happens that certain
conditions in a program may prevent it
from working properly. The assert
statement checks if such conditions
exist in a program. Java assert is
explained in this article.
# ⚓ How_do_You_write_Comparable_in_Java?⠀⇛
Examples of Java lists are; Vector,
Stack, AttributeList, ArrayList, and
LinkedList. The Java Collections class
has overloaded methods to sort a list
of predefined objects. The Java Arrays
class has overloaded methods to sort an
array of predefined objects.
The predefined sort() methods are to
sort predefined objects. What about
user-defined objects? Java has an
interface called Comparable. An
interface is a kind of class whose
methods are declarations without
definitions (bodies). So, a class must
be implemented from an interface for
the methods to be defined (given
bodies). From the implemented class,
objects can be instantiated from a name
given by the programmer.
Java has a predefined Comparable class.
The sort() methods in Collections and
Arrays use the predefined comparable
class to sort predefined objects.
However, in order to sort a list or
array of user-defined objects, the
programmer has to implement (define) a
user Comparable class from the
Comparable interface. This user
implemented (defined) class enables the
sorting of user-defined objects in a
list or array. So, a predefined
Comparable class enables sorting of
predefined objects, while a user-
defined Comparable class enables
sorting of user-defined objects. User-
defined objects are not literals, so a
class of user-defined objects needs its
own user-defined Comparable
implementation.
This article illustrates how to write
Comparable in Java.
# ⚓ Hashtable_in_Java⠀⇛
A hash table is for key/value pairs.
Internally, the values are stored in an
array. Each key is converted into an
index of the array. This conversion is
known as hashing. It is done by a hash
function internally. In other words,
the keys do not have to be stored. All
that is the hash-table, in java and in
other computer languages. This article
explains two constructors of the Java
hastable and its commonly used methods.
# ⚓ How_AJAX_works⠀⇛
AJAX comprises a set of useful web
development techniques utilized to
develop dynamic and speedy web pages.
Behind the scenes, it shares small
chunks of the data, permitting the web
pages to be updated asynchronously.
This states that by using AJAX, HTML
page elements will be updated without
reloading.
This write-up will discuss the
components of AJAX and how AJAX works.
We will talk about the working of AJAX
in some top web-based applications.
Moreover, a comparison between the
conventional and AJAX model will be
provided. So, let’s start!
o § Standards/Consortia⠀➾
# ⚓ Gemini_Isn’t_The_Solution_To_The_Broken_Web⠀⇛
I’m not sure if you heard, but The Web Is F*cked
and techies everywhere are touting the Gemini
protocol as its saviour. I disagree. A lot.
When I wrote The Web Is F*cked, I had a number of
people reach out asking why I didn’t mention
Gemini, as it’s the saviour of the web…apparently.
Well, I didn’t mention Gemini because I think it
actually does more harm than good when it comes to
the web. Let me explain…
* § Leftovers⠀➾
o ⚓ Todd_Gitlin_Told_His_Truth_Everywhere_He_Went⠀⇛
I met Todd Gitlin on October 23, 1987. It was the
beginning of what would become a decades-long “beautiful
friendship.” (We shared a favorite movie in Casablanca.)
I can pin down the date because our meeting took place at
the ridiculous Second Thoughts conference in which
apostate liberals and New Leftists were gathered to
denounce their former selves and embrace the new right.
It took place at the Grand Hyatt hotel in Washington,
D.C., and was organized by left-wing Stalinists turned
right-wing Stalinists David Horowitz and Peter Collier,
with funding from a Christian conservative foundation led
by the son of the far-right Alabama Senator Jeremiah
Denton, together with the Bradley and Olin foundations.
Funnily enough, it took place just days after Ronald
Reagan’s Iran/Contra plot was revealed and the largest
single drop in the stock market since 1929. These week’s
events signaled the long-awaited end to the Reaganite
hegemony these folks had gathered to celebrate.
o ⚓ Everyday_Specters⠀⇛
Last fall, I was in the English countryside on a research
trip and decided to visit Blo’ Norton Hall, the moated,
16th-century manor house in Norfolk where a prince I was
writing about had once lived. It was almost dusk when I
arrived, but there were several people my age walking the
grounds: guests, I assumed, of the bed-and-breakfast to
which the house had been converted after the prince’s
death. I tried to maintain a friendly distance.
As I walked around the house’s rear, the four young men,
holding glasses of beer, strolled directly past me, and I
smiled at them—but none appeared to see me. Moments
later, I realized that this was not, in fact, a bed-and-
breakfast through which I was welcome to perambulate but
a single, large holiday home, and I was trespassing on
some friends’ private vacation. Mortified, I ran back to
my car, reversed for several minutes down the long gravel
driveway, and hightailed it home. It felt like a close
call. The occupants could have interrogated me or even
called the police. But one more chilling possibility also
struck me: Had those men seen me at all? Or had I been
somehow invisible to them—perhaps as an interloper from
another realm, or perceived as the type of grounds staff
some are trained not to see? Was I, in other words, a
sort of ghost passing through their domain?
o ⚓ Anatomy_of_a_Cancellation⠀⇛
Again with no ill will towards anyone in the DSA, I’m
hoping this might be a teachable moment. In order for it
to be one, we need to do some unpacking. There is a
diverse cast of characters involved.
I’ll just assume everyone knows who the Democratic
Socialists of America are. If not, you can look them up
easily enough, but they probably represent the biggest
organized political group to the left of the Democratic
Party today (or on the left of the Democratic Party,
depending). As any sensible democratic socialist
organization would do, they are actively supporting the
Portland city workers in their contract negotiations with
the city, and their plan for an imminent strike.
o ⚓ CNN_Could_Face_a_Reset_Once_Under_Discovery_Control⠀⇛
One prominent Discovery shareholder, John Malone, has
already been vocal. “I would like to see CNN evolve back
to the kind of journalism that it started with, and
actually have journalists, which would be unique and
refreshing,” the entrepreneurial media investor told CNBC
in November. Malone will serve on the Discovery board,
but no longer has a commanding block of super-voting
shares as he once did, leaving Zaslav at the helm.
o ⚓ Joe_Rogan_Calls_Backlash_Over_His_Use_of_N-Word_a_‘Political_Hit
Job’⠀⇛
“That video had always been out there. It’s like, this is
a political hit job,” Rogan said. He continued, “And so
they’re taking all this stuff I’ve ever said that’s wrong
and smushing it all together.”
o ⚓ ViacomCBS_Elevates_Alex_Berkett_to_Chief_Corporate_Development
and_Strategy_Officer_Role⠀⇛
ViacomCBS has promoted veteran dealmaker Alex Berkett to
the role of chief corporate development and strategy
officer.
His previous title was executive vp, corporate
development & strategy. Berkett will continue to report
to ViacomCBS CFO Naveen Chopra and to serve on the
company’s senior leadership team and global inclusion
advisory committee.
o § Education⠀➾
# ⚓ Hunger-Striking_Teachers_Say_School_Closures_Will_Hurt
Black_and_Brown_Kids⠀⇛
o § Hardware⠀➾
# ⚓ CR+LF_has_a_long_history…⠀⇛
There is one exception: carriage return [CR]. The
carriage is released within the 100ms time, but the
carriage is on a spring, and does not get back to
the left within 100ms if it is too far over to the
right. The usual fix is to send another non
printing character, such as a line feed [LF], as
the next character, where CR and LF are used for
each new line. The paper advances whilst the
carriage is returning so giving the carriage a
whole 200ms to complete the return. This allows
enough time to get to the left, but can leave the
carriage still bouncing and mean the first
printable character is not well aligned. The fact
that 200ms is enough is usually fine, unless you
are particularly fussy. The fix to this is to send
another non printing character, such as a NULL,
another CR, or even a rub out [RO]. The standard
HEREIS drum coding even specifies CR, LF and RO at
the start.
# ⚓ Nvidia_Deal_to_Buy_Arm_From_SoftBank_Is_Off_After
Setbacks⠀⇛
Nvidia, a fast-growing company whose chips are best
known for rendering images in video games, in
September 2020 offered cash and stock then valued
at $40 billion for Arm, making it the most
expensive deal ever among chip companies. Nvidia
made the offer to buy Arm from SoftBank, the
Japanese conglomerate that has owned the British
company since 2016. Nvidia’s rising stock price
later sent the transaction’s value much higher,
settling at about $60 billion on Monday.
But the blockbuster deal encountered setbacks that
included a Federal Trade Commission lawsuit in
December to block the acquisition, as well
opposition from regulators in Britain.
Nvidia and SoftBank said early Tuesday they agreed
to terminate the planned deal because of
“significant regulatory challenges.”
# ⚓ SoftBank_dumps_sale_of_Arm_over_regulatory_hurdles,_to_IPO
instead⠀⇛
On a company earnings call on Tuesday, SoftBank CEO
Son, who had said the company initially considered
listing Arm but opted to sell it instead due to the
pandemic, sought to put a positive spin on the
scrapped sale.
o § Health/Nutrition/Agriculture⠀➾
# ⚓ Worse_than_ineffective:_Two_independent_studies_have
confirmed_that_EpiVacCorona_is_a_worthless_vaccine_—_and_it
should_be_taken_off_the_market⠀⇛
Despite a recent report that Russia’s Health
Ministry has stopped placing orders of the
EpiVacCorona vaccine, its manufacturer is
optimistic and claims to expect the next production
order to come in February. Meanwhile, scientists,
as well as journalists at Meduza, have obtained
convincing evidence that EpiVacCorona is
ineffective and gives recipients a completely false
sense of security (unlike Sputnik V, which has been
proven to protect recipients from COVID-19’s most
severe effects). Meduza explains the two studies
that led to that conclusion.
# ⚓ Opinion_|_On_What_Just_Happened_to_Medicare_for_All_in
California—and_the_Organizing_We_Need_to_Win⠀⇛
Why is a healthcare system—Medicare for All—that
costs less described as “too expensive?”
# ⚓ Covid_Survivors_at_Higher_Long-Term_Risk_of_Cardiovascular
Damage:_Study⠀⇛
Covid-19 survivors are at an elevated long-term
risk of developing heart disease, strokes, blood
clots, and other cardiovascular disorders,
according to new peer-reviewed research out Monday.
Published in Nature Medicine, the study finds that
individuals who survive Covid-19 are more likely to
suffer from cardiovascular disease one year later.
That’s true even if they “were not hospitalized
during the acute phase of the infection,” although
disease risks and burdens are higher for patients
who were hospitalized and especially for those who
were admitted to intensive care units (ICUs).
o § Integrity/Availability⠀➾
# § Proprietary⠀➾
# ⚓ Windows_11_–_six_months_later,_still_totally_meh⠀⇛
Early in July 2021, I reviewed the Dev Build
of Windows 11. I was underwhelmed on so many
levels. The new operating system, if it can
be called that, was raw, unfinished, and came
with a slew of bugs and ergonomic annoyances.
But that was then. Since, this thing has been
officially released, and it even received a
handful of big, critical patches, designed to
help resolve some of the early problems.
# ⚓ Vivaldi_5.1_Introduces_Horizontal_Scrollable_Tabs_and
a_New_Reading_List
⠀⇛
Vivaldi is a pretty good option for Linux
users. They focus on Linux as one of the
first-party platforms, which is impressive.
With Vivaldi 5.0 release, it proved to be a
versatile Chromium-based option for many
Linux users. Now, Vivaldi 5.1 is finally
here!
# ⚓ Microsoft_Patch_Tuesday,_February_2022_Edition⠀⇛
# ⚓ How_a_Texas_[crack]_changed_the_ransomware_business
forever [iophk: Windows TCO]⠀⇛
Last year, a security analyst named Dmitry
Smilyanets had a long online chat with
someone who claimed to be a member of REvil’s
management team. He went by the online handle
‘Unknown.’
“Unknown was not a hacker. He was the
operator. He was the manager,” Smilyanets
said. “His job was to control the
infrastructure, make sure it all works. Make
sure that communication lines with victims
were up and that payments go through.”
# ⚓ Protecting_your_business_in_the_age_of_ransomware
[iophk: Windows TCO]⠀⇛
The GDPI survey uncovered that 64% of leaders
are concerned they’ll experience a disruptive
event, such as data loss or downtime, in the
next year. With the frequency of ransomware
attacks on the rise, all businesses should
expect an attack. Whether or not you should
be fearful depends on how prepared you are.
# § Security⠀➾
# ⚓ Security_updates_for_Wednesday_[LWN.net]⠀⇛
Security updates have been issued by
CentOS (aide), Debian (connman), Fedora
(perl-App-cpanminus and rust-
afterburn), Mageia (glibc), Red Hat
(.NET 5.0, .NET 6.0, aide, log4j,
ovirt-engine, and samba), SUSE
(elasticsearch, elasticsearch-kit,
kafka, kafka-kit, logstash, openstack-
monasca-agent, openstack-monasca-log-
metrics, openstack-monasca-log-
persister, openstack-monasca-log-
transformer, openstack-monasca-
persister-java, openstack-monasca-
persister-java-kit, openstack-monasca-
thresh, openstack-monasca-thresh-kit,
spark, spark-kit, venv-openstack-
monasca, zookeeper, zookeeper-kit and
elasticsearch, elasticsearch-kit,
kafka, kafka-kit, logstash, openstack-
monasca-agent, openstack-monasca-
persister-java, openstack-monasca-
persister-java-kit, openstack-monasca-
thresh, openstack-monasca-thresh-kit,
spark, spark-kit, storm, storm-kit,
venv-openstack-monasca, zookeeper,
zookeeper-kit), and Ubuntu (bluez,
linux, linux-aws, linux-aws-5.4, linux-
gcp, linux-gcp-5.4, linux-hwe-5.4,
linux-ibm, linux-kvm, linux-oracle,
linux-oracle-5.4, nvidia-graphics-
drivers-450-server, nvidia-graphics-
drivers-470, nvidia-graphics-drivers-
470-server, nvidia-graphics-drivers-
510, python2.7, and util-linux).
# § Privacy/Surveillance⠀➾
# ⚓ ‘Party_of_Union_Busters’:_McCarthy
Opposes_Congressional_Staff_Union⠀⇛
The sincerity of the GOP’s
attempt to rebrand as a party of
workers was called into further
question Monday when Rep. Kevin
McCarthy—the Republican leader in
the U.S. House—spoke out against
congressional staffers’ nascent
unionization push, which has won
the enthusiastic support of
progressive lawmakers and
Democratic leaders.
“I don’t think it would be
productive for the government,”
McCarthy (R-Calif.), a top ally
of former President Donald Trump,
told Punchbowl News of the
unionization effort by Capitol
Hill aides, many of whom are paid
annual salaries in the low
$20,000 range and struggle to
afford basic necessities in one
of the nation’s most expensive
cities.
# ⚓ Interview_With_Eugene_Shablygin_–
WWPass⠀⇛
Eugene Shablygin: My background
is in fundamental physics, but at
some point, I realized I wasn’t
really a good physicist. In my
opinion, I was not on par with
good physicists like Einstein,
and I didn’t feel the essence of
physics. However, I felt that I
understood how data flows through
different computers.
# ⚓ Faith_Leaders_Denounce_Zuckerberg’s
Instagram-for-Children_Scheme⠀⇛
Saying that “children’s wellbeing
must come first” above profit,
dozens of faith leaders on
Tuesday told Facebook chief Mark
Zuckeberg to permanently end any
plans for a version of the photo-
and video-sharing app Instagram
for kids under 13.
“Childhood should be all
movement, play, messiness, and
wriggle—life-affirming against
the sleek, flat, rapacious world
of screens.”
# ⚓ Private_Internet_Access_Releases_Updated
Transparency_Report_in_Q1_2022⠀⇛
The requests were as follows:
# ⚓ UK_Government_Refreshes_Its_Terrible
‘Online_Safety_Bill,’_Adds_Even_More
Content_For_Platforms_To_Police⠀⇛
The UK’s internet censorship bill
rebranded from “Online Harms” to
“Online Safety” last spring. The
name change did nothing to limit
the breadth of the bill, despite
supposedly shifting the focus
from “harm” to “safety.” Whatever
the name, it’s still being touted
by supporters as a fix for
anything anyone doesn’t like
about the internet.
# ⚓ If_EARN_IT_Passes,_What_Happens_On_Your
iPhone_Won’t_Stay_On_Your_iPhone⠀⇛
Now, Congress wants to force
Apple’s hand—along with
essentially every company that
allows users to store or share
messages or content—and
essentially mandate such
scanning.
While Apple’s plan would have put
the privacy and security of its
users at risk, the EARN IT Act
compromises security and free
speech for everyone. The bill
would create serious legal risk
for business that hosts
content—messages, photos stored
in the cloud, online backups—and,
potentially, even cloud-hosting
sites like those using Amazon Web
Services, unless they use
government-approved scanning
tools.
# ⚓ Ohio:_Don’t_Give_Big_Tech_a_Pass_On
Privacy⠀⇛
The OPPA would enshrine privacy
violating practices from Big Tech
and other companies, and place
the responsibility for managing
privacy entirely on
individuals—without actually
improving protections for the
people of Ohio or offering them a
way to stand up for their own
privacy. If it is not
substantially improved before it
is enacted, it risks locking in
industry-friendly provisions that
would directly benefit tech
giants such as Facebook, Google,
and Amazon. In many ways, passing
this bill would be worse for the
everyday consumer than passing
nothing at all.
# ⚓ Send_Surveillance_Robot_Dogs_to_the
Pound,_Not_the_Border⠀⇛
The dogs are not yet in the
field, but having been pushed
through early stages of testing,
they are undergoing evaluation in
El Paso, Texas. The robot dogs
would eventually be expected to
walk miles through the remote
terrain at the border, all the
while filming and scanning.
People who live along the border
are some of the most heavily
surveilled people in the United
States. A massive amalgamation of
federal, state, and local law
enforcement and national security
agencies are flying drones,
putting up cameras, and just
generally attempting to negate
civil liberties—capturing the
general goings-on of people who
live and work in proximity to the
border. But the civil liberties
of these communities are of no
concern to a government with
nearly limitless resources to
throw at putting entire regions
of the United States under
surveillance.
Even if you live hundreds of
miles from the border, don’t
think these “innovations” can’t
or won’t affect you. As we saw
when Customs and Border
Protection drones flew over a
protest in Minneapolis, the $68
billion border surveillance
industry won’t stop expanding if
there’s money to be made further
inland.
# ⚓ More_Fallout_For_NSO_And_Israel:_Gov’t
Police_Illegally_Deployed_Malware_Against
Person_Involved_In_Netanyahu_Bribery
Trial⠀⇛
More troubling developments for
both NSO Group and the country it
calls home.
# ⚓ Apple_says_a_‘small_portion’_of_iPhones
recorded_interactions_with_Siri_even_if_you
opted_out⠀⇛
Apple’s release of iOS 15.4 beta
2 fixes a bug that may have
recorded interactions with Siri
on some devices, regardless of
whether you opted out, according
to a report from ZDNet. The bug,
which was first introduced in iOS
15, automatically enabled the
Improve Siri & Dictation setting
that gives Apple permission to
record, store, and review your
conversations with Siri.
# ⚓ How_to_delete_your_Instagram_account⠀⇛
If you’ve made the decision to
delete Instagram, whether because
you’ve outgrown the need for a
certain finsta or because its
parent company Meta is courting
controversy again, doing so isn’t
as quick or easy as it should be.
Up until recently, it couldn’t
even be done from within the
Instagram app.
Go ahead and take a moment to
make an obligatory “I’m deleting
Instagram” post if you’d like.
After that, you have two ways you
can go about it.
# ⚓ Companies_Should_Mandate_Two-Factor
Authentication,_Says_Head_of_National
Cybersecurity_Alliance⠀⇛
The interim executive director of
a non-profit that has on its
board members from Lenovo,
Facebook, Microsoft and a number
of other prominent tech firms
said that companies should
mandate two-factor
authentication.
Lisa Plaggemier of the National
Cybersecurity Alliance, which
advocates for cybersecurity
across the country, made the
comment at an event hosted by
Axios Media on Tuesday.
# ⚓ A_safer_Internet_starts_with_more
encryption⠀⇛
The Internet has been vital to
help parents balance work and
parenting through a lingering
pandemic, yet it’s hard to ignore
the societal issues increasingly
amplified online. And with
children increasingly learning
and socializing online, the
reality is we can’t always be
there to hold their hand.
What’s even more frightening is
when government proposals
undermine people’s best efforts
to keep kids safe online by
ignoring a simple truth: security
is crucial to a safer Internet.
It might seem like an obvious
statement, but it’s not.
o § Defence/Aggression⠀➾
# ⚓ Internal_Investigation_Confirms_Border_Patrol_Failures
Leading_Up_to_a_16-Year-Old’s_Death_on_the_Floor_of_His
Cell⠀⇛
A government investigation into the 2019 death of a
Guatemalan teenager in Border Patrol custody has
found serious problems with the agency’s handling
of sick detainees.
The report, obtained by ProPublica through a public
records request, concludes that Border Patrol
agents did not check on 16-year-old Carlos
Hernandez Vasquez, who died of the flu after
writhing on the floor of his cell in Weslaco,
Texas. The report also found that the case
reflected broader problems with care in a detainee
system that at the time was overwhelmed with
migrants, many of whom were ill.
# ⚓ Wave_of_Coups_Disrupts_Africa_as_U.S.-Trained_Soldiers_Play
Key_Role_in_Overthrowing_Governments⠀⇛
The African Union is condemning a wave of coups in
Africa, where military forces have seized power
over the past 18 months in Mali, Chad, Guinea,
Sudan and, most recently, in January, Burkina Faso.
Several were led by U.S.-trained officers as part
of a growing U.S. military presence in the region
under the guise of counterterrorism, which is a new
imperial influence that supplements the history of
French colonialism, says Brittany Meché, assistant
professor at Williams College. Some coups have been
met with celebration in the streets, signaling
armed revolt has become the last resort for people
dissatisfied with unresponsive governments.
“Between the U.S.-led war on terror and the wider
international community’s fixation on ‘security,’
this is a context that centers, if not privileges,
military solutions to political problems,” adds
Samar Al-Bulushi, contributing editor for Africa Is
a Country.
# ⚓ The_Nightmare_Continues⠀⇛
We Own the World
The United States Department State Department
continued in its QAnon-like claim that Russia is
planning to fabricate a mass casualty event as a
pretext to invade Ukraine – an allegation for which
“State” provided no, um, evidence. It was vaguely
reminiscent of the George W. Bush administration’s
unsubstantiated Weapons of Mass Destruction (WMD)
and al-Qaeda alliance claims against Iraq before
the criminal, mass-murderous US petro-imperialist
invasion of that country.
# ⚓ US_Sanctions_Caused_Mass_Civilian_Deaths_in_Iraq._Afghan
Civilians_Are_Up_Next.⠀⇛
# ⚓ Israeli_Policies_Satisfy_the_Definition_of_Apartheid_Under
International_Law⠀⇛
# ⚓ Policing_on_Trial:_Attorney_Ben_Crump_on_Fed_Case_Against
Three_Cops_Involved_in_George_Floyd_Murder⠀⇛
The Minneapolis judge who signed the no-knock
warrant that led to the fatal police shooting of
22-year-old Black man Amir Locke also presided over
the trial of Derek Chauvin, the ex-police officer
convicted for the murder of George Floyd. The trial
of three officers facing lesser charges — Tou Thao,
Thomas Lane and J. Alexander Kueng — is currently
underway after being delayed when one of the
defendants tested positive for COVID. The trial
will show the importance of accountability even
from police who are bystanders to murder, says
Benjamin Crump, part of the legal team for George
Floyd’s family.
# ⚓ Cover-Up_in_Minneapolis?_Police_“Executed”_Amir_Locke_in
“No-Knock”_Raid,_Say_His_Parents,_Activists⠀⇛
Protests are continuing in Minneapolis after police
fatally shot 22-year-old Amir Locke during an
early-morning “no-knock” raid on February 2.
Bodycam video shows that Locke appeared to be
asleep on the couch and wrapped in a blanket when a
SWAT team entered the apartment. Locke held a gun
he was legally licensed to carry, and was not named
in the warrant. Minneapolis interim city Police
Chief Amelia Huffman claimed Locke pointed his
weapon in the direction of the officers, and
suggested he could have been connected to crime,
despite not being a suspect in their investigation.
“It was very jarring for many people in our
community to see Amir painted almost like a
criminal,” says attorney and police accountability
activist Nekima Levy Armstrong. No-knock warrants,
which Mayor Jacob Frey promised to eliminate but
never did, “have deadly consequences for innocent
Black people like Amir Locke and Breonna Taylor and
so many others,” says civil rights attorney
Benjamin Crump, part of the legal team for Amir
Locke’s family. This week the Biden administration
responded to the raid saying it may consider a
federal policy that limits the use of no-knock
warrants.
# ⚓ Mass_Student_Walkouts_Over_Police_Killing_of_Amir_Locke⠀⇛
Demanding accountability from local leaders,
hundreds of high school students in Minneapolis and
St. Paul walked out of their classes on Tuesday at
noon in protest of the fatal police shooting of
Amir Locke during a no-knock raid.
The youth-led group MN Teen Activists organized the
walkout, which included students at St. Paul
Central High School and Capitol Hill Magnet School
in St. Paul and Southwest, Roosevelt, and Washburn
high schools in Minneapolis, as well as other
schools in the surrounding suburbs.
# ⚓ Opinion_|_America’s_Strategic_Blunders_of_the_Past_That
Created_This_Crisis_Over_Ukraine⠀⇛
Understandably enough, commentaries on the crisis
between Russia and the West tend to dwell on
Ukraine. After all, more than 100,000 Russian
soldiers and a fearsome array of weaponry have now
been emplaced around the Ukrainian border. Still,
such a narrow perspective deflects attention from
an American strategic blunder that dates to the
1990s and is still reverberating.
# ⚓ Opinion_|_Memo_to_Congress:_Diplomacy_for_Ukraine_Is
Spelled_M-I-N-S-K⠀⇛
While the Biden administration is sending more
troops and weapons to inflame the Ukraine conflict
and Congress is pouring more fuel on the fire, the
American people are on a totally different track.
# ⚓ ‘Beyond_the_War_Paradigm’:_Report_Offers_Alternative_to_20
Years_of_Post-9/11_Failures⠀⇛
After more than two decades of the widely condemned
“global war on terror” launched by the United
States government in the wake of the 9/11 attacks,
a report released Tuesday offers 10 alternatives to
the nation’s militarized approach to national
security.
“A reevaluation of the U.S. approach to
counterterrorism is a moral and strategic
imperative.”
# ⚓ ‘My_task_is_to_kill_you’_Domestic_violence_victim_who_fled
Dagestan_describes_family_members’_thwarted_attempt_to_kidnap
her_in_Moscow⠀⇛
Aishat Khiramagomedova fled her family home in
Dagestan in October 2021, after reaching out to
Krepost (Fortress), a charity organization that
assists victims of domestic abuse. She made it to
Moscow, where Krepost provided her with shelter and
access to a psychologist. Within a few months she
was starting to find her feet — she had a job and
was looking for an apartment with her boyfriend.
But on February 4, Aishat’s family tried to kidnap
her and bring her back to Dagestan.
# ⚓ Ukraine_and_the_Threat_of_Nuclear_War⠀⇛
As the crisis in Ukraine deepens, it is appropriate
to consider what the actual consequences of war
there might be. An armed conventional conflict in
Ukraine would be a terrible humanitarian disaster.
# ⚓ Behind_the_Olympic_Curtain⠀⇛
# ⚓ China’s_Olympic_Battle_for_Legitimacy:_the_Prehistory_of
the_2022_Beijing_Games⠀⇛
In 1949, the Communist Party of China decisively
prevailed over Chiang Kai-shek’s Kuomintang (KMT)
after 22 years of civil war, forcing the latter to
flee to Taiwan. The founding of the People’s
Republic of China (PRC) brought a definitive end to
a “century of humiliation” inaugurated by the First
Opium War, which had seen colonial powers reduce
China to the “sick man of Asia.” This sickness had
been a byword for the weakness, internal rupture,
and forced narcotic dependency of the Chinese body
politic—transposed inevitably onto the racialized
Chinese body.
Overcoming these scars, in all their physical and
psychological manifestations, was the guiding
principle for sports policy in the PRC. Only
through this lens can we understand why it fought
in such an obstinate, pugnacious, and unabashedly
political way for a place in the Olympic movement
on its own sovereign terms. China turned the
Olympics into a battleground in its contest for
legitimacy with the KMT regime on Taiwan and its
imperialist backers, elevating the dispute to “the
main burden of Olympism,” in the words of Otto
Mayer, chancellor of the International Olympic
Committee (IOC) from 1946 to 1964. And as with the
parallel struggle for recognition by the United
Nations, this one ended after three eventful
decades in unqualified triumph. University of Hong
Kong historian Xu Guoqi relates this fascinating
saga in his 2008 book Olympic Dreams: China and
Sports, 1895-2008.
# ⚓ Helsinki_2.0⠀⇛
You might think that’s an overstatement. NATO is
alive and well. The Organization for Security and
Cooperation (OSCE) in Europe is still functioning
at a high level.
Of course, there’s the possibility of a major war
breaking out between Russia and Ukraine. But would
Russian President Vladimir Putin really take such
an enormous risk? Moreover, periodic conflicts in
that part of the world—in Ukraine since 2014, in
Georgia in 2008, in Transnistria between 1990 and
1992—have not escalated into Europe-wide wars. Even
the horrific bloodletting of Yugoslavia in the
1990s was largely contained within the borders of
that benighted former country, and many of the
Yugoslav successor states have joined both the
European Union and NATO.
# ⚓ Bernie_Sanders_Says_US_War_With_Russia_Over_Ukraine_Must_Be
Avoided_at_All_Costs⠀⇛
Warning of the potentially catastrophic
consequences of what could be the deadliest
European conflict since World War II, U.S. Sen.
Bernie Sanders on Tuesday stressed the imperative
for a diplomatic solution to the Russia-Ukraine
crisis that’s brought the world’s two nuclear
superpowers perilously close to war.
“Wars rarely turn out the way the experts tell us
they will. Just ask the officials who provided rosy
scenarios for the wars in Vietnam, Afghanistan, and
Iraq.”
# ⚓ Aid_Groups_Warn_Biden_Not_to_Revive_Trump’s_Terror
Designation_for_Houthis_in_Yemen⠀⇛
Twenty international aid groups on Tuesday urged
U.S. President Joe Biden to refrain from restoring
the Trump administration’s terrorist designation
for the Houthis—warning that reinstating the label
would have devastating impacts on civilians already
struggling to survive amid a worsening humanitarian
catastrophe in Yemen.
Biden was praised last year by peace and anti-
hunger advocates for rejecting former Secretary of
State Mike Pompeo’s eleventh-hour designation of
Ansar Allah—as the Houthi movement is officially
called—as a “Foreign Terrorist Organization” (FTO)
and a “Specially Designated Global Terrorist”
(SDGT).
# ⚓ Opinion_|_North_Carolina’s_New_Education_Bill_Promotes
Historical_Erasure_and_White_Supremacy⠀⇛
In the state of North Carolina, the legislature saw
fit to pass House Bill 324 in response to the
Critical Race Theory madness set off by a FOX News
interview. The bill outlaws teaching that includes
the following:
# ⚓ Up_to_90_more_new_tanks_for_police_in_Germany⠀⇛
The Federal Police and the riot police of the
federal states are paying € 81 million for armoured
vehicles from Rheinmetall. Some procured them
already for their special forces
# ⚓ Not_another_no-fly_list⠀⇛
In a letter first reported by Reuters and first
published in full by The Points Guy, CEO Edward
Bastian of Delta Air Lines has called on Attorney
General Merrick Garland to “support our efforts
with respect to… putting any person convicted of an
on-board disruption on a national, comprehensive,…
‘no-fly’ list that would bar that person from
traveling on any commercial air carrier.”
The latest letter from Delta steps up a lobbying
campaign the airline began last fall, and which
remains as misguided as ever. The letter highlights
the urgent need for Congress to enact the Freedom
to Travel Act (H.R. 6030) to make clear the rights
of travelers, the duties of airlines and other
common carriers, and the limitations on when, by
what authority, on what grounds, and according to
what procedures the right to travel can be
restricted.
# ⚓ Baloch_insurgency_and_continued_tale_of_apathy_and
violence⠀⇛
The province of Balochistan is once again in the
vortex of turmoil and violence. On February 5,
2022, Pakistani military said it has killed at
least 20 rebels in Balochistan after two army posts
were attacked within hours of each other on
February 2.[1] The attacks targeted paramilitary
post in the town of Panjgur, about 450km (280
miles) south of the provincial capital, Quetta, and
another one in Noshki, about 330km (205 miles)
north of the first attack spot. Following the twin
attacks, in a statement emailed to the media, the
ethnic Baloch separatist group Baloch Liberation
Army (BLA) claimed responsibility for the attacks.
Jeayand Baloch, the BLA’s spokesman, said the raids
were carried out by attackers who were prepared to
“self-sacrifice”.[2]
o § Environment⠀➾
# ⚓ Montana_Plaintiffs_Announce_First_Children’s_Climate_Trial
in_History_of_US⠀⇛
# ⚓ Climate_Expert_Debunks_Big_Oil’s_Lies_About_Carbon_Capture,
Nature-Based_Solutions⠀⇛
A world-renowned climatologist made clear to
Congress on Tuesday that some of fossil fuel
companies’ key proposals to reduce planet-heating
emissions are talking points rather than
“meaningful” solutions to the climate emergency the
industry created.
“The climate crisis… is real and it is here. In
order to confront it, we need real solutions that
are proven to work and to keep our planet safe.”
# ⚓ Climate_Coalition_Calls_on_Biden_to_Cease_All_Gulf_of
Mexico_Drilling_Operations⠀⇛
A new legal petition filed Tuesday calls on the
Biden administration to stop all fossil fuel
exploration and extraction plans throughout the
Gulf of Mexico, saying its ongoing approval of such
activities violate federal requirements to properly
assess climate impacts.
The filing with the Interior Department, signed by
a diverse collection of 310 groups, begins with a
blunt assertion that “fossil fuels are killing us
and killing our planet” and points to a federal
judge’s ruling last month blocking the
administration’s planned oil and gas lease sale of
over 80 million acres in the Gulf of Mexico.
# § Energy⠀➾
# ⚓ Footage_of_Offshore_Oil_Accident_Highlights_Risks_of
Deepwater_Drilling⠀⇛
Video footage obtained by DeSmog shows an
offshore oil drilling incident in which heavy
equipment fell from a drillship onto an oil
and gas wellhead deep below the ocean’s
surface.
The three short clips offer those on land an
unusual window into the world of offshore
drilling accidents. Two experts who reviewed
the footage for DeSmog said that the videos
appear to show a blowout preventer (BOP) — a
kind of heavy oilfield equipment that is used
to control or seal the flow of oil and gas
from wells — falling suddenly during a
relatively routine procedure. An additional
video appears to show the resulting
underwater damage filmed from a remotely
operated vehicle. Text displayed in one clip
reads, in part, “Monitoring BOP Unlatch” and
“Pontus,” and a second video of the incident
bears the date November 20, 2021.
# ⚓ ‘Obscene’:_BP_Profits_Hit_8-Year_High_Amid_Climate
Emergency⠀⇛
Fueled by rising oil and gas prices that have
left millions struggling to afford energy
bills, British fossil fuel giant BP reported
its highest yearly profits in nearly a decade
on Tuesday while rejecting calls for a tax on
its financial windfall.
The company raked in $12.8 billion in profits
in 2021—more than its annual income for the
past eight years. The announcement comes a
week after BP’s rival Shell reported $19.3
billion in profits last year.
# ⚓ PG&E_is_on_the_Loose_Again⠀⇛
What were the terms of probation he had been
asked to oversee? In Judge Alsup’s statement,
“Rehabilitation of a criminal offender
remains the paramount goal of probation.
During these five years of criminal
probation, we have tried hard to rehabilitate
PG&E. As the supervising district judge,
however, I must acknowledge failure.”
An ordinary citizen on probation is
admonished not to break any laws, deal in
guns, drugs, and so on. Probation officers
supervise the probationers with weekly
visits. At the discovery of a single
violation, the probationer is remanded to
prison, with an additional burden of time on
their sentence.
# ⚓ Nornickel’s_Potanin_sees_bright_future_for_NFTs,_not
cryptocurrencies⠀⇛
Risky cryptocurrencies, such as much-hyped
Bitcoin, will give place to asset-backed
digital financial assets like non-fungible
tokens (NFTs) in the long-term due to the
latter’s reliability, Vladimir Potanin, one
of Russia’s richest men with assets in
different industries and countries, including
Finland, told Bloomberg in an interview.
Last week, Atomyze Russia, a fintech startup
backed by Potanin’s conglomerate Interros,
became the first in Russia to obtain the
central bank’s license to issue digital
financial assets.
# ⚓ How_Much_Electricity_Does_Bitcoin_Mining_Use?⠀⇛
Researchers from Cambridge University
estimates that the mining process devours 143
terawatt-hours (TWh) of electricity annually,
which is more than the yearly electricity
consumption of some countries. For instance,
Norway consumes only 124 TWh, and Bangladesh
consumes 71. Also, Bitcoin mining requires
more energy than the largest technology
companies like Google and Facebook.
# ⚓ ‘The_Entire_Cryptocurrency_Market_Is_Basically_a
Ponzi_Scheme’⠀⇛
Janine Jackson interviewed Sohale Mortazavi
about cryptocurrency for the February 4,
2022, episode of CounterSpin. This is a
lightly edited transcript.
# ⚓ Crossing_the_Wires_of_Energy_and_Cryptocurrency
Policy:_U.S._Congress_Investigates_the_Environmental
Impact_of_Crypto_Mining⠀⇛
There are currently two primary ways that
network participants lend their processing
power, which are framing part of the modern
energy policy debates around cryptocurrency.
The first form is “proof of work,” which is
the original method that Bitcoin and Ethereum
1.0 employ. When a group of transactions (a
block) needs to be verified, all of the
“mining” computers race to solve a complex
math puzzle, and whoever wins gets to add the
block to the chain and is rewarded in coins.
The competitive nature of proof of work
consensus systems has led to substantial
increases in computing power provided by
institutional cryptocurrency mining
operations and, with that, higher energy
demands.
# ⚓ 7_countries_where_cryptocurrencies_are_banned⠀⇛
Besides, the report found that the number of
countries subjecting crypto to anti-money
laundering and tax laws has surged 3 times
since 2018. For example, all the members of
the European Union, except Bulgaria, have
currently put these regulations in place.
Here are some countries that decided to say
no to crypto and why.
# ⚓ A_cringe_rapper_slash_Forbes_contributor_allegedly
found_with_billions_in_stolen_Bitcoin⠀⇛
The Department of Justice has finally found
almost all of the billions worth of Bitcoin
stolen during the 2016 hack of cryptocurrency
exchange Bitfinex — in the hands of a
published Forbes and Inc. writer and rapper,
who calls herself the “Crocodile of Wall
Street,” and her startup founder husband.
The DOJ says it seized about $3.6 billion
worth of the cryptocurrency, allegedly held
by Heather Morgan and her husband, Ilya
Lichtenstein. The couple is accused of trying
to cover their tracks by laundering the
stolen funds through “a labyrinth of
cryptocurrency transactions.” It’s the
department’s “largest financial seizure
ever,” according to a Tuesday press release.
o § Finance⠀➾
# ⚓ Amazon_Dodged_$5.2_Billion_in_Taxes_Last_Year,_Report
Finds⠀⇛
# ⚓ ‘Class_Warfare’_in_Action:_Amazon_Dodged_$5.2_Billion_in
Taxes_in_2021⠀⇛
An analysis released Monday shows that Amazon
utilized several perfectly legal mechanisms to
avoid paying $5.2 billion in federal corporate
income taxes in 2021, a year in which the online
retail behemoth saw its profits and sales
skyrocket.
Matthew Gardner, a senior fellow at the Institute
on Taxation and Economic Policy (ITEP), estimated
that given Amazon’s record-breaking $35 billion in
U.S. pretax income for fiscal year 2021, the
Seattle-based corporate giant paid an “effective
federal income tax rate of 6%”—far lower than the
statutory corporate tax rate of 21%.
# ⚓ Opinion_|_Paying_Rate_of_Just_6%,_Amazon_Avoided_More_Than
$5_Billion_in_Taxes_Last_Year⠀⇛
Amazon’s latest annual financial report released
last Friday paints a vivid picture of a company
that is edging toward monopoly status—and doing so
at the expense of U.S. taxpayers.
o § AstroTurf/Lobbying/Politics⠀➾
# ⚓ Opinion_|_Will_US_Turn_Away_From_Fascism_and_Abandon_This
GOP_Death_Cult_Before_It’s_Too_Late?⠀⇛
While Republican successes in blocking legislation,
judges and even presidential nominations may seem
like the Party is on a roll, the reality is that
the GOP is in the midst of an existential crisis as
severe as any party has seen since the Whigs died
out in the early 19th century.
# ⚓ Manchin_Says_He’s_Skeptical_of_Congressional_Workers’_Union
Drive⠀⇛
# ⚓ Palin_Redux⠀⇛
Refusing the vaccine means freedom, she says, And
no one can ever negate hers. The shots would be
o’er her dead body, she says. But what if the
body’s the waiter’s?
# ⚓ ALEC_Is_Driving_Laws_to_Blacklist_Companies_That_Boycott
the_Oil_Industry⠀⇛
# ⚓ Is_Korea_Heading_Toward_a_Political_Crossroads?⠀⇛
The two candidates, who are currently running neck-
and-neck in opinion polls, present a stark
contrast. Lee Jae-myung of the ruling Democratic
Party advocates South Korea taking the lead on
inter-Korean relations, in contrast to President
Moon Jae-in’s unwillingness to adopt any measure
that would elicit Washington’s disapproval. “In
succeeding the Moon Jae-in administration, the Lee
Jae-myung government should act as a more
independent and active mediator and problem
solver,” Lee announced late last year. [1] That
will come as a welcome change in direction if it
comes to fruition.
Lee is also disinclined to accede to U.S. demands
to join the anti-China campaign, questioning why
South Korea should be forced to choose between
China, its leading trading partner, and the U.S.,
with whom it has a military alliance. “I think the
situation is coming where we can make decisions
independently, putting our national interests
first. Any thinking that we have to choose between
the two is a very disgraceful approach,” Lee
argues. [2]
# ⚓ Biden_Claims_Credit_for_ISIS_Leader’s_Death,_But_It_Will_Do
Little_Damage_to_Terror_Group⠀⇛
Islamic State (IS) is much reduced from the all-
conquering force it was for several years after
2014 when it had surprised the world by capturing
the city of Mosul in northern Iraq. It went on to
seize an area the size of Great Britain in western
Iraq and eastern Syria, but lost all this territory
between 2016 and 2019. The fact that al-Qurayshi
was killed so far from previous IS strongholds may
indicate that the movement no longer has any bases
that it considers secure.
But as a guerrilla group that no longer tries to
hold territory, it has recently shown renewed
strength with an attack on a prison in Hasakah, a
Kurdish controlled city in north east Syria. IS
leaders who had escaped the prison were at first
believed by locals in Idlib to be the target of the
US raid.
# ⚓ No_Attack_on_Voting_Rights_Is_Too_Racist_for_This_Supreme
Court⠀⇛
I honestly do not know what kind of attack a state
would have to launch against the voting rights of
its Black citizens to make the current Supreme
Court step in and stop it. I do not know what form
of voter-suppression law, intimidation tactic, or
redistricting map would be so racist that this
court would strike it down. We are back to the Jim
Crow era, not just in terms of the laws that states
are passing against the franchise but also in how
the Supreme Court refuses to enforce the
constitutional amendments prohibiting apartheid. We
have literally been here before, when the Supreme
Court remained inert as the 14th and 15th
Amendments were violated with impunity by any state
with enough aggrieved whites to do so. All that’s
missing is the violent enforcement of these racist
voting rules… but we’ll see what happens when Black
people still try to vote this fall.
# ⚓ What_America’s_Voting_Rights_Activists_Can_Learn_From
Previous_Civil Rights_Movements⠀⇛
Senate Democrats Joe Manchin of West Virginia and
Kyrsten Sinema of Arizona joined Senate Republicans
in blocking both the Freedom to Vote Act and the
John Lewis Voting Rights Advancement Act. These
bills would have combated voter suppression by
creating a national automatic voter registration
system, and they also would have banned partisan
gerrymandering.
In the wake of the vote, President Joe Biden said
he was “profoundly disappointed that the United
States Senate has failed to stand up for
democracy.”
# ⚓ The_Five_(Rosa)_Luxembergs⠀⇛
Today, many know Rosa Luxemburg as Rosa Luxemburg
but when she was born – 5th March 1871 – her real
name was actually Róża Luksemburg. Rosa was also
known as Rozalia Luksenburg. On 13th June, 1919, an
unimaginably large funeral procession walked
through Germany’s capital, Berlin almost five
months after Rosa Luxemburg was murdered. Germany’s
digital library shows thousands and thousands of
workers have lined Berlin’s streets to pay tribute
to Rosa Luxemburg.
Yet, among one of the largest number of people ever
seen at a Berlin rally were also four people with
whom Rosa Luxemburg knew extremely well during the
forty-eight years before her murder by right-wing
death squads known as free corps. During the 1918/
19 revolution, Germany’s majority social-democratic
party, the SPD, had, what Rosa Luxemburg would call
a choice between Socialism or Barbarity. It used
Gustav Noske – known as the bloodhound – and the
free corps to shoot a massive amount of workers
and, thereby ending the revolution.
# ⚓ Peter_Thiel_to_Exit_Meta’s_Board_to_Support_Trump-Aligned
Candidates⠀⇛
Mr. Thiel has been on Meta’s board since 2005, when
Facebook was a tiny start-up and he was one of its
first institutional investors. But scrutiny of Mr.
Thiel’s position on the board has steadily
increased as the company was embroiled in political
controversies, including barring Mr. Trump from the
platform, and as the venture capitalist has become
more politically active.
# ⚓ White_House_science_adviser_Lander_quits_over_bullying
claims⠀⇛
Ms Wallace told Politico that Professor Lander
“retaliated against staff for speaking out and
asking questions by calling them names, disparaging
them, embarrassing them in front of their peers,
laughing at them, shunning them, taking away their
duties, and replacing them or driving them out of
the agency. Numerous women have been left in tears,
traumatised, and feeling vulnerable and isolated.”
o § Misinformation/Disinformation⠀➾
# ⚓ Homeland_Security’s_Attempts_to_“Combat_Misinformation”_Are
Suspect⠀⇛
# ⚓ Neil_Young_urges_Spotify_employees_to_quit⠀⇛
Spotify has also said it will add advisories to any
podcast episodes that discuss Covid-19.
# ⚓ Joe_Rogan_Offered_$100M_to_Quit_Spotify_for_Right-Wing
Platform⠀⇛
The controversial podcaster was offered $100
million on Monday to quit Spotify and join a right-
wing platform.
Chris Pavlovski, the CEO of the Canadian video-
sharing platform Rumble, tried to entice Rogan to
jump ship in a letter posted to the company’s
Twitter account Monday.
o § Censorship/Free Speech⠀➾
# ⚓ Techdirt_Podcast_Episode_310:_A_Global_History_Of_Free
Speech⠀⇛
We talk a lot about free speech in different
countries, and about the history of free speech in
the US — but what about the global history of this
fundamental concept? A new book released today,
Free Speech: A History from Socrates to Social
Media by Jacob Mchangama, tackles exactly this
subject in great and insightful detail. This week,
Jacob joins us on the podcast to discuss the
sweeping story of free speech throughout the ages
and around the world.
# ⚓ Book_Bans_Are_on_the_Rise._But_Librarians_and_Authors_Are
Fighting_Back.⠀⇛
The idea of banning books conjures images of piles
of hardcovers in the street going up in flames. But
over the past few decades in the United States,
book banning has taken on a decidedly more genteel
character. It has taken place in deliberative
school board meetings and in quick after-school
chats between librarians and concerned parents.
# ⚓ Israel_Gets_Georgia_to_Strip_Free_Speech_Rights_(Again)⠀⇛
# ⚓ Opinion_|_Divestment_Is_Wisdom,_Not_Censorship⠀⇛
We live in a time when bribery, in the form of
campaign donations, is construed by our nation’s
Supreme Court as free speech, and divestment of the
kind that helped pressure South Africa to dismantle
its apartheid system is equated in the corporate
media as censorship. These are signs that the
culture in our democracy is unhealthy, diseased.
# ⚓ Platform_vs._Publishers⠀⇛
How do you distinguish between a platform and a
publisher? The debate has been reignited with the
backlash against Joe Rogan’s Spotify podcast. Some
have accused Rogan of spreading misinformation
about COVID on Spotify. Spotify isn’t taking Rogan
down and its important to note that Spotify has a
$100mm+ exclusive deal with Rogan for his content.
Is Spotify a neutral audio platform? Or is Spotify
a publisher?
# ⚓ TikTok_bans_misgendering,_deadnaming_trans_people⠀⇛
In updated community guidelines, the company noted
that it is “adding clarity on the types of hateful
ideologies prohibited on our platform,” stating
that it will ban deadnaming, or using a transgender
person’s pre-transition name, and misgendering,
using incorrect pronouns.
# ⚓ TikTok_is_banning_misgendering,_deadnaming,_and_content
promoting_disordered_eating⠀⇛
The company announced today it would begin removing
videos that promote disordered eating symptoms like
short-term fasting and overexercising. Content
promoting eating disorders is already banned on the
platform, but news reports have repeatedly shown
users are exposed to videos featuring unhealthy
eating habits. During an October congressional
hearing, senators pressed TikTok representatives on
further protecting young users.
# ⚓ [Updated:]_EARN_IT_Act_—_an_attack_on_free_expression_and
privacy_—_is_back⠀⇛
A civil society coalition letter voicing opposition
to the EARN It Act was delivered to the U.S. Senate
Judiciary Committee leadership in advance of the
Committee markup. Access Now is a signatory to the
letter, signed by over 60 organizations and led by
the Center for Democracy and Technology.
o § Freedom of Information/Freedom of the Press⠀➾
# ⚓ BBC_News_Russian:_Nearly_half_of_people_labeled_‘media
foreign_agents’_have_left_or_are_preparing_to_leave_Russia⠀⇛
Russia has designated 75 individuals as “media
foreign agents.” And according to BBC News Russian,
at least 32 of these people have left or are
preparing to leave the country. Another 14
individuals had already left Russia due to pressure
from the authorities before they were added to the
“foreign agent” blacklist.
# ⚓ Journalist_Mary_Heaton_Vorse_Spent_Decades_on_the_Front
Lines_of_Labor⠀⇛
Coverage of labor, unions, and workers’ rights
issues has exploded across a variety of media,
particularly as the Covid-19 pandemic exposes the
plight of vulnerable workers and changes the nature
of work itself. Mainstream publishing behemoths are
now trying to catch up to the left-leaning
publications that have always cared about such
stories. The organizing streaks of media unions
like the Writers Guild of America, East (for which
I’m a council member), and the NewsGuild have
resulted in a generation of labor-savvy media
workers with a fierce commitment to improving their
workplaces. (This is how I unexpectedly morphed
from a heavy metal journalist into a labor
reporter!)
# ⚓ Update_on_Julian_Assange_Case,_Future_of_Gulf_of_Mexico
Drilling,_and_is_Graphika_Really_a_Fake_News_Watchdog?_–_The
Project_Censored_Show⠀⇛
Notes: Kevin Gosztola is the managing editor of
ShadowProof as well as other press-freedom and
whistleblower cases. Jayeesha Dutta is co-founder
of AnotherGulf.com; she also works with the Climate
Justice Alliance. Kevin Gosztola is the managing
editor of ShadowProof. He has covered the Julian
Assange legal proceedings in the UK from the
beginning. Alan MacLeod is a media scholar and a
senior staff writer at Mint Press News.
# ⚓ Didn’t_Those_Now_Enraged_at_Boris_Johnson’s_‘Smears’_of
Keir_Starmer_Defame_Corbyn_at_Every_Turn?⠀⇛
The reason? Last week the British prime minister,
Boris Johnson, blamed Starmer, now the Labour party
leader, for failing to prosecute Jimmy Savile, a TV
presenter and serial child abuser, when his case
came under police review in 2009. Between 2008 and
2013, Starmer was head of the Crown Prosecution
Service (CPS). Savile died in 2011 before he could
face justice.
Johnson accused Starmer, who at the time was
Director of Public Prosecutions, of wasting “his
time prosecuting journalists and failing to
prosecute Jimmy Savile”.
# ⚓ ‘They_were_mostly_shouting_about_Assange!’_Tory_MP_hits
back_at_Boris-Starmer_row⠀⇛
“I’ve also watched the clip in full, it’s about
three minutes long and these people were mostly
talking about Julian Assange for some reason that I
don’t understand.
# ⚓ Keir_Starmer:_No_10_has_no_intention_of_apologising_after
protesters_surround_Labour_leader⠀⇛
“Why did you go after Julian Assange, why did you
go after journalists?” one man shouted.
# ⚓ Police_rescue_Sir_Keir_Starmer_from_mob_who_surround_him
and_accuse_him_of_‘protecting_paedophiles’⠀⇛
o § Civil Rights/Policing⠀➾
# ⚓ Russia’s_Justice_Ministry_seeks_dissolution_of_charitable
foundation_behind_Russian_LGBT_Network⠀⇛
The St. Petersburg branch of the Russian Justice
Ministry has asked the courts to liquidate the
charitable foundation Sfera, the operator of the
Russian LGBT Network.
# ⚓ Sanders_Unveils_Bill_to_Boost_Understaffed_US_Fire
Departments⠀⇛
Citing the “unprecedented challenges” in
“recruiting and retaining” career and volunteer
firefighters across the United States, Sen. Bernie
Sanders on Monday introduced legislation aimed at
tackling the staffing crisis in the essential
profession.
“The difficulty in recruiting and retaining
personnel is an absolute crisis.”
# ⚓ Religious_Support_for_Democratic_World_Federation⠀⇛
But some religious groups and leaders have rejected
the idea that warfare is a necessary part of human
nature and human history.
In order to eliminate the war system and solve
humanity’s many global problems–such as genocide,
terrorism, violations of human rights, and
environmental degradation due to global
warming–they have advocated for the creation of a
democratic world federal government that would
create just world laws and prosecute individuals
who violate them. Violent conflicts would be
settled and global problems would be solved through
a nonviolent democratic process.
# ⚓ The_Black_Migrant_Trail_of_Tragedies⠀⇛
Julliana Essengue arrived in Tapachula, Mexico,
from São Paulo, Brazil, in March 2020. She was
broke but determined to reach the United States.
After nearly two months traversing rain forests,
borders, and rivers by bus, car, boat, and foot,
she needed money. At first, Essengue and her travel
companions squatted. “We slept on the floor for two
weeks in a hallway,” she told me. “There were
Africans, Haitians—everybody was sleeping on the
floor.”1This story was published with the support
of a fellowship from Columbia University’s Ira A.
Lipman Center for Journalism and Civil and Human
Rights.
# ⚓ Ohio_Supreme_Court_Rejects_Republican-Drawn_Congressional
Maps_–_Again⠀⇛
# ⚓ Affirmative_Action_on_the_Block⠀⇛
# ⚓ Connecting_the_Dots_and_Rejecting_the_“Rule_of_Law”
Hypocrisy⠀⇛
Lindiwe Sisulu’s parents, Walter and Albertina
Sisulu, were leading figures with Nelson Mandela in
the African National Congress (ANC) movement that
resisted the racist apartheid regime of South
Africa. Their daughter’s opinion column shows that
she inherited her parents’ zeal for justice.
“Whose law is it anyway” bristles with truth about
economic reparation, a subject that the
beneficiaries of colonization always try to avoid.
Consider the following excerpt:
# ⚓ ‘They_Are_Firing_the_Entire_Committee!’_Memphis_Workers_Say
Starbucks_Targeting_Union_Organizers⠀⇛
Workers at a Memphis Starbucks who were fired
Tuesday after launching a unionization effort vowed
to carry on their fight, with one employee invoking
the legacy of the Rev. Martin Luther King Jr.—who
was assassinated in the Tennessee city while
campaigning for workers’ rights.
“Starbucks has been fighting desperately to silence
us because we did not back down or let them shake
us.”
# ⚓ Hunger-Striking_Teachers_Say_Oakland_Plan_to_Close_Schools
Will_Hurt_Black_&_Brown_Communities⠀⇛
We go to Oakland, where a group of teachers are on
a hunger strike to protest a plan to close and
merge over a dozen schools due to under-enrollment.
This comes ahead of a critical school board vote
Tuesday that will decide whether to proceed with
the plan. Activists argue the move threatens to
divert resources to charter schools and displace
hundreds of Black and Brown children from their
neighborhood schools. The hunger strike across
multiple different schools has empowered many to
speak up against longtime systemic racism, says
Moses Omolade, one of the striking workers and a
community schools manager at Westlake Middle
School. “The school board is attempting to close
predominantly Black and Brown schools without
engaging with us at all.”
# ⚓ How_a_Cooperative_Run_by_the_Formerly_Incarcerated_is
Reshaping_Chicago’s_Food_Industry⠀⇛
These school meals were supplied by
megacorporations like PepsiCo Inc., Tyson Foods
Inc., Pilgrim’s Pride Corporation, Cherry Meat
Packers Inc., Central Valley Meat Co. Inc.,
American Beef Packers Inc. and Jennie-O Turkey
Store LLC. As detailed in a 2020 article by
Jennifer E. Gaddis in the professional journal for
educators Phi Delta Kappan, 95 percent of U.S.
public schools participate in the government-
subsidized National School Lunch Program, and this
program is made up almost entirely of contracts by
giant corporate food brands. Gaddis writes:
It happened again in 2020 when the Trump
administration proposed making the rules more
flexible, Gaddis adds.
# ⚓ The_student_forced_out_after_standing_up_for_women⠀⇛
Yet from the minute it was announced, it became a
target for militant trans activists among the
university students – who objected to Woman’s Place
UK’s stance on gender recognition issues, and
demanded the event be cancelled.
Why? “The issue they had was with the meeting
taking place at all,” Rosario Sanchez replies.
“They didn’t want women to have these
conversations.”
# ⚓ Why_This_Feminist_Is_Taking_the_University_of_Bristol_to
Court⠀⇛
Next week, I am taking my university to court. To
my knowledge, it is the first time an academic
institution has been forced, at trial, to justify
why it prioritises trans rights over women’s
rights. The other party in the case is the
University of Bristol, which one might suppose to
be an unlikely defendant given its distinction as
the first higher-education establishment in England
to have admitted women on an equal basis to men.
Unfortunately, the university has more recently
become known as a hotbed for anti-feminist
militancy.
# ⚓ LABOR_After_Amazon_Tragedy,_Workers_Come_Together_to_Demand
Safe_Working_Conditions⠀⇛
o § Digital Restrictions (DRM)⠀➾
# ⚓ Automakers_Can’t_Give_Up_The_Idea_Of_Turning_Everyday
Features_Into_Subscription_Services_With_Fees⠀⇛
At the same time car companies are fighting the
right to repair movement (and the state and federal
legislation popping up everywhere), they’re
continuing the quest to turn everyday features —
like heated seats — into something users have to
pay a recurring fee for.
# ⚓ What_on_Earth_is_going_on_with_Peloton?⠀⇛
In 2020, Peloton’s supply chain was struggling to
keep up with the unexpected surge in demand created
by people suddenly eager to work out at home.
Facing months-long fulfillment delays, Peloton
decided to heavily invest in building out its
manufacturing capabilities. It dropped millions to
expedite shipping and another $420 million buying
Precor, one of the world’s largest commercial
fitness equipment makers. It spent another $400
million on a factory in Ohio. The company was
positioning itself to rapidly build bikes and
treadmills for a market that couldn’t get enough.
o § Monopolies⠀➾
# § Patents⠀➾
# ⚓ Pfizer_Forecasts_Record-Breaking_2022_Profits_—_as
Billions_Remain_Unprotected⠀⇛
# ⚓ Pfizer_Forecasts_Record_Vaccine_Revenue_for_2022_as
Billions_Remain_Unprotected⠀⇛
Pfizer projected Tuesday that it will
generate a record-shattering $32 billion in
revenue from its publicly funded coronavirus
vaccine in 2022 as the U.S. pharmaceutical
giant refuses to share its technology with
other nations, leaving billions of people
around the world without access to lifesaving
shots as the pandemic continues to rage.
“We’ve let Pfizer withhold this essential
medical innovation from much of the world.”
# § Trademarks⠀➾
# ⚓ Apple_Opposes_Trademark_For_Indie_Film_‘Apple-Man’
Claiming_Potential_Confusion⠀⇛
When it comes to silly trademark disputes,
Apple has come up for discussion many, many
times. The mega-corporation is a jealous
defender of all of its IP, but most of our
stories have focused on its disputes with
companies that created logos that involve any
sort of apple or other fruit. Sometimes it’s
not even companies that Apple is fighting
with, but entire foreign political parties.
The idea here is that when it comes to logos
or trade dress, Apple appears to think that
it owns all the apples.
# § Copyrights⠀➾
# ⚓ Appeals_Court_Can_Rule_That_DMCA’s_Anti-Circumvention
Rules_Are_Unconstitutional⠀⇛
As you hopefully know, there are two main
parts to the DMCA law that was passed in
1998. There’s DMCA 512, which is what you
hear about most of the time. That’s the part
that includes the rules for notice and
takedown regimes for user uploaded content
(among other things). It’s got problems, but
in its current form has also enabled many
important services to exist. The other part,
which is much more problematic, is DMCA 1201,
which is the anti-circumvention rules — or
you could call it the “DRM” part of the law.
This has no redeeming value whatsoever. Under
1201 basically any attempt to circumvent a
“technological” protection measure, can be
deemed infringing even if the underlying
content is never infringed upon. This part of
the law is not only not necessary, but it’s
drafted in a manner that has been regularly
abused — enabling everyone from printer
manufacturers to garage door opener companies
to argue that simple reverse engineering to
create competition is “infringement.”
# ⚓ Do_not_feed_the_trolls⠀⇛
Recently, there has been an increase in
threatened and actual lawsuits involving CC
licensed works, and in some cases, license
enforcement has even become a business model.
We have now learned that even long-time
friend and contributor to Creative Commons,
Cory Doctorow, has been targeted.
Put simply, “license-enforcement-as-business
model” is a perversion of the founding ideals
of Creative Commons. We condemn this
behavior. These aggressive enforcement
actions lessen trust in open licensing, and
they erode the good faith ecosystem that is
the basis of the commons.
# ⚓ MPA_&_ACE_Embed_Staff_at_US_Govt._IPR_Center_To_Fight
Movie_&_TV_Show_Piracy⠀⇛
The Motion Picture Association and anti-
piracy coalition Alliance for Creativity and
Entertainment will embed their own personnel
at the US Government’s National Intellectual
Property Rights Coordination Center. Under
the umbrella of the Department of Homeland
Security and Immigration and Customs
Enforcement, they hope to tackle movie and TV
show piracy more effectively.
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