𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Wednesday, September 06, 2023
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Generated Thu 7 Sep 02:52:03 BST 2023
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/2023/09/06/
╒═══════════════════ 𝐑𝐄𝐂𝐄𝐍𝐓 𝐁𝐔𝐋𝐋𝐄𝐓𝐈𝐍𝐒 ════════════════════════════════════╕
Previous bulletins in IPFS (past 21 days, in chronological order):
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QmfR8XxBEMVs1Mue6wS1NKXYG8optDVxN7EFcGCzvD1Q9z
QmbqCQ6R4NusTRm9E3YjVzj9c1FxCfEvrfqShjAZLaCyQS
QmeZFBVX9fk1V5VBuSsZpDpx2dnJBatXxASzUtAm4wrZ26
QmR8687kGyLT5rdVV9a5wwcd599wytXYh8CbSBUtHMqNx6
QmVL6ny5v6haHeg8eGHJrcSY343AUa4deXjfvCw1ZDmDz6
QmWKPms4oLgJhFJZPgySVW8kBSCBHkHuEbpSJ9Hu8w899a
QmYRNEXfEKgCkNrxSJTkmHBQSawGzsT7jTG9zeGBgLZpYW
QmXuNJQvwQEw7vxCEMaH6S2XP6CJWxyQPwQ5XwEnWrbwNY
QmU8r9irxybJVwzTWsCaejmJ4dDWJ8vAHAHHAKEkyeufpQ
QmeryNavwPZxt2XqRC8WzQsxzm8Q2aJpPrHDJjt4MVx7j9
QmV1aDkYP6Y7Yv8Eg5mojpfKfRqGkjzLoJiut9uECHzXbF
QmNRJcNP3MBmn7dGr91i3qjc8AouAjwSZWUmroRDLJDj2W
QmR3skFpi5NU2DwodXGtVWF1yWK1pJNg7U4BHJZ26DXmJr
QmNyZCmQoHYnCZYzsD7hZtwEa43PmCo6mPJQSvxSE2bjMR
QmbHjgPAAcGNUG9Sej4vSKhK8DfUYokfFkXLdKwr1JtGJG
QmdLsuRLzrwb58dZaSmJah6oCmNNZ6cW4ick4chqJmHjmY
QmTNR3uqcbMYjPAbbHjBqyNJb3ib8kytQvdFnATzkBFVvo
QmfCHrqMLfMsHXYnQeAvVuNYt91Zw2AmMJ5mx4RqsrWy3b
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QmWE6ucdKk9Q1pi6ce3ko9xPWd9Y4BjpLij3W7tJ5TMjG3
╒═══════════════════ 𝐈𝐍𝐃𝐄𝐗 ═══════════════════════════════════════════════════╕
⦿ [Meme] Axe-Wielding Microsoft Trolls Impersonating Free Software People Across IRC Networks | Techrights
⦿ IRC Proceedings: Tuesday, September 05, 2023 | Techrights
⦿ Leftover Links 06/09/2023: University of Michigan Admits It Got Cracked (Microsoft TCO) | Techrights
⦿ [Meme] 3 Months | Techrights
⦿ Microsoft and Its Proxies Are in a Freefall | Techrights
⦿ Principal Threat to Security is Microsoft Windows and Proprietary Software | Techrights
⦿ A Blueprint for Digital, Online Oppression (and Threat to Software Freedom Everywhere) | Techrights
⦿ Red Hat Under IBM is Lying to Us, It’s Not Trustworthy Anymore | Techrights
䷼ Bulletin articles (as HTML) to comment on (requires login):
http://techrights.org/2023/09/06/illegal-smear-campaigns/#comments
http://techrights.org/2023/09/06/irc-log-050923/#comments
http://techrights.org/2023/09/06/leftover-links-06092023-university-of-michigan-admits-it-got-cracked-microsoft-tco/#comments
http://techrights.org/2023/09/06/meme-3-months/#comments
http://techrights.org/2023/09/06/microsoft-freefall/#comments
http://techrights.org/2023/09/06/threat-to-security/#comments
http://techrights.org/2023/09/06/threat-to-software-freedom-everywhere/#comments
http://techrights.org/2023/09/06/untrustworthy-ibm/#comments
䷞ Followed by Daily Links (assorted news picks curated and categorised):
http://techrights.org/2023/09/06/arti-1-1-8/#comments
http://techrights.org/2023/09/06/changes-in-zenwalk/#comments
http://techrights.org/2023/09/06/iterating-on-fractals/#comments
http://techrights.org/2023/09/06/recommendation-algorithms/#comments
http://techrights.org/2023/09/06/vanity-onion-address/#comments
䷩ 𝚕𝚒𝚗𝚎 72
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(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/09/06/illegal-smear-campaigns/#comments
Gemini version at gemini://gemini.techrights.org/2023/09/06/illegal-smear-campaigns/
⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.06.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧
Gemini_version_available_♊︎
✐ [Meme]_Axe-Wielding_Microsoft_Trolls_Impersonating_Free_Software_People
Across_IRC_Networks⠀✐
Posted in Deception, Free/Libre_Software, Microsoft at 8:49 pm by Dr. Roy
Schestowitz
🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Winter_is_coming⦈_
Summary: The Free_software-hostile_militants (connected_to_Microsoft) are
impersonating me in IRC networks this week, trying to link me to terrorism;
we’re still planning to write about these vicious and sometimes illegal smear
campaigns until next year because other projects, communities and people are
targeted by the very same Microsoft flock (we have proof, too)
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣈⡺⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠀⢠⣤⣀⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣘⢙⡻⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⡛⣻⣿⡿⠀⠀⠀⠀⠀⠀⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣖⣆⣀⣉⣵⣾⡏⠴
⣿⣿⣿⣿⣿⣿⣿⣿⡏⠆⡃⠀⠛⣂⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣍⢉⠉⢛⣙⡇⣾
⣿⣿⣿⣿⣿⣿⣿⣿⠁⢷⡆⢠⠀⢨⠓⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⢼⣿⢇⣾
⣿⣿⣿⣿⣿⣿⣿⣿⠀⣼⣉⢈⣀⠄⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿
⣿⣿⣿⣿⣿⣿⣿⠇⠀⠈⠙⢿⣿⣡⣽⡟⠛⢿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣷⡄⠀⠅⠀⠀⠉⣽⣿⠀⠀⢸⣿⣿⣿⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣄⠁⣤⠄⠀⣀⡍⠁⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣴⡟⠁⢠⣿⡿⠿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⣠⣿⣿⣷⠀⠉⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⡿⠋⢢⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠘⠿⠋⢿⣤⡀⠘⣿⣿⣿⣿⣿⣿⣿⠏⠻⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡇⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣦⣽⠟⠋⠁⣼⠟⠁⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠀⠁⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⣷⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠁⠈⠻⢿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢹⣿⣿⣶⣤⣜⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠂⠀⠀⠀⠀⠈⠋⠋⠉⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⡀⠀⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣶⣶⣦⣤⣄⣀⣀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⣿⣿⣿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⣁⣛⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠉⠉⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣽⣿⡿⠋⠩⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣰⡟⠁⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣟⣠⣰⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⣄⣤⣴⣤⣼⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⡿⠉⠣⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⣴⣦⠈⠉⠉⠻⣿⣷⣌⠉⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠇⠀⠛⣿⠟⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⡝⢳⣄⠀⠀⠘⠋⠙⣦⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠚⠁⢛⠛⡿⠰⠐⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠆⠀⣰⣶⣾⣿⣦⣄⡀⠀⠀⠉⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢡⣤⣄⢡⣤⣤⠀⣤⣤⡄⣤⣤⠀⣤⣤⠀⣤⣤⢠⣤⣤⣤⣤⣤⣤⣤⣤⡄⢠⣤⣤⣤⣄⠉⢷⣿⣿⣿⣿⡜⢿⣿⣿⣷⣦⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⢸⣿⣿⡆⣿⣿⠀⣿⣿⠀⣿⣿⡇⣿⣿⠈⢹⣿⣿⠉⢹⣿⣿⠉⠁⢸⣿⡏⣿⣿⡆⢰⣬⣽⣿⣿⡅⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣼⣿⣿⣷⣿⣿⠀⣿⣿⠀⣿⣿⣿⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⣶⡆⢸⣿⡷⣿⣟⠀⢿⣿⣿⣿⣿⣷⡄⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⡏⢿⣿⣿⡏⠀⣿⣿⠀⣿⣿⢻⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⠀⠀⢸⣿⡇⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣷⣆⡄⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠸⠿⠿⠇⠸⠿⠿⠇⠰⠿⠿⠀⠿⠿⠘⠿⠿⠀⠸⠿⠿⠀⠸⠿⠿⠿⠇⠸⠿⠇⠿⠿⠇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠙⠻⡟⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠿⠿⠛⠛⠳⢶⣶⣶⠀⠀⠀⠀⠀⠀⠰⠒⠀⠀⠀⠴⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠿⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣶⣿⢿⣿⣆⢹⡏⢠⣾⡿⢿⣷⡄⢠⣾⣿⢿⣷⡄⢸⣿⣿⡇⣼⣿⣿⡇⣿⣿⡇⢸⣿⣇⢸⣿⡇⣰⣾⡿⣿⣶⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣿⣿⣬⡉⠋⢸⡇⢸⣿⡇⢸⣿⡇⢸⣿⡇⢸⣿⡇⢸⣿⣿⣧⣿⣿⣿⡇⣿⣿⡇⢸⣿⣿⣼⣿⡇⣿⣿⡇⠿⠿⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣽⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣈⣛⢿⣿⣦⠈⠀⢸⣿⡇⢠⣤⡄⢸⣿⡇⢸⣿⡇⢸⣿⡿⣿⣿⢹⣿⡇⣿⣿⡇⢸⣿⢿⣿⣿⡇⣿⣿⡟⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣄⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣿⣿⣠⣿⣿⠀⡄⢸⣿⣧⣸⣿⡇⠸⣿⣧⣼⣿⡇⢸⣿⡇⣿⣿⢸⣿⡇⣿⣿⡇⢸⣿⠘⣿⣿⡇⢻⣿⣇⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣛⣛⣠⣌⣙⣛⣋⣡⣾⣷⣄⡉⠛⠛⠉⠀⢠⣉⡛⠛⣉⡀⠘⠛⠃⠙⠃⠘⠛⠁⠙⠛⠃⠘⠛⠀⠙⠛⠁⣀⡙⠛⠉⠛⢁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠚⣿⣿
⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⡀⢀⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢰⣶⣿⣿
⣇⣆⡲⣶⢀⣶⢌⣡⣰⣶⣆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⢸⣿⣿⣿
[69A⠀⠀⠙⢿⠛⣟⣛⣥⣾⣿⡴⠀⠀⠀⠀⣝⡊⠘⢹⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⢲⢿⠆⢋⡼⢽⢷⢰⡸⡋⣊⢟⠉⠷⡿⠎⣿⡟⠑⠇⡐⢹⣫⣵⣽⠰⢠⠚
⠀⠀⠀⣿⡹⣿⣟⣿⣿⣿⣿⠣⣦⠐⠀⣿⣷⣦⣿⣿⣏⠀⠀⠀⣶⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣌⠀⣸⣿⣷⣾⣿⠥⣯⡜⠄⠀⠀⠁⠀⠉⠀⡀⡸⢹⣿⡝⢏⡿⠏⠊⡄
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣇⠋⠀⢳⣿⠸⢹⣿⣿⣿⠀⠀⠀⢺⣷⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠏⢱⣾⣽⣿⢼⡬⠋⠁⠀⠀⠄⠀⢆⣀⣄⣥⣷⡾⠤⠈⠈⡋⣤⡐
⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠇⣤⣼⣿⣿⣿⣿⣿⣯⠀⣰⢈⠃⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠉⠉⠉⠉⠉⠛⠿⣿⣿⣿⣧⣎⠹⢧⣿⡞⠫⡅⠀⠀⠀⢠⣄⢑⡘⢷⣻⠭⡃⠀⡈⠐⠪⢋⢤
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡴⣿⠿⢿⣿⣿⣿⣿⣃⡀⠿⠋⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣗⣿⠛⣹⠂⠀⠀⠄⢀⠊⠴⣟⡃⠈⠀⠀⠀⢀⣿⣎⢷⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣼⣿⣿⣿⣿⣿⠟⠂⠀⠈⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡿⠇⠿⠦⣀⡴⡀⠠⠁⠊⠄⣴⠄⠀⠀⠀⠘⠛⠛⠃⡻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⡀⣴⣄⣀⡀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣧⠀⠀⢀⠀⠀⠀⠀⡀⠤⢿⡏⠁⠈⠀⠀⢐⢾⠷⢿⢐⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠘⡀⠀⠀⠐⠀⠀⣽⠇⣀⠐⠃⠀⠀⠏⠀⠈⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠃⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣧⡀⣤⠃⠀⠀⠀⠘⢹⢟⢁⣁⢤⠀⠀⠫⣄⣠⡄⠀⠐
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠛⠀⠀⠀⠀⣤⡈⡟⠀⣁⠈⠀⠐⠛⢛⣩⣿⣦⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣄⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣧⠀⠀⠀⢀⣿⣟⠀⠄⠰⠀⠈⣴⣷⣿⣿⣿⣟⡩
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣧⡐⠂⠉⠀⠛⠀⡐⠆⠁⠀⠉⠁⠀⢴⣿⣿⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⠐⣿⣯⣌⣳
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠽⠯⢇
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡟⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⢀⡀⡔⠂⠈⠘⠉
⠈⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢄⠀⠀⠀⢸⣿⡿⠉⠈⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡦⠠⠀⢀⣒⠲⣈⡀⠀⠀⠀⠀
⠀⠀⣀⡈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⣀⣴⣿⠇⠀⠀⠸⡿⠁⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⢘⣵⣸⠻⠁⠀⠀⡀⠀
⠀⢠⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡾⠁⠀⣀⣀⠤
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠁⠀⢀⡀⠈⢁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣇⠘⢓⣯⣧⣄⡄⡘⠃
⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠃⠒⠊⢁⡂⠀⠂⠠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣏⡠⡄⠀⠚⣛⣽⡇⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⠰⠀⢮⡁⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⠛⠛⠛⠿⠻⡇⣰
⣿⣿⣿⣿⣿⣿⣿⣿⠯⠡⡂⠀⠀⠲⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⠀⣰⣿⡇⣽
⣿⣿⣿⣿⣿⣿⣿⣿⡀⢹⡷⠰⠄⠐⠁⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⢸⣯
⣿⣿⣿⣿⣿⣿⣿⣿⠃⠘⠷⣤⣶⠅⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡏
⣿⣿⣿⣿⣿⣿⣿⡉⠀⠠⠀⠙⠿⢶⣦⠃⠀⢨⣿⣿⣿⠏⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣇⠀⠈⠀⠀⠀⠘⢻⠄⠀⢸⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠤⠋⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⢰⡟⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠸⣿⣟⠉⠹⠿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡟⠛⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⢓⠁⠁⠀⠀⠙⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠈⢻⡀⠀⠀⠈⠁⢀⣼⣿⣿⣿⣿⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡟⠁⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠻⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⠙⠿⡿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣮⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢨⣿⣿⣦⣄⡀⠀⣼⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠃⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠋⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣦⣀⣀⣠⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⣶⣶⣾⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠖⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣦⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣶⣶⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣄⣀⣀⣀⣀⢉⢉⣙⣛⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠒⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠏⠁⢹⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣦⡶⠲⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡬⠟⠋⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣱⣾⣿⠏⢀⣈⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠃⠀⢀⡀⠈⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⠛⠿⠿⣿⣿⣧⡹⠿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⣹⣿⣿⣿⠟⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⢾⠿⣆⡀⠀⠀⠹⣿⢿⡄⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⠉⠠⠤⠾⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣶⣬⣳⡄⠀⢀⣀⡀⢻⣄⠀⠀⠀⠀⠸⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢡⣤⣄⢡⣤⣤⠀⣤⣤⡄⣤⣤⠀⣤⣤⠀⣤⣤⢠⣤⣤⣤⣤⣤⣤⣤⣤⡄⢠⣤⣤⣤⣄⠘⣥⣀⣼⣿⣟⠚⣿⣷⣦⣄⡀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⢸⣿⣿⡆⣿⣿⠀⣿⣿⠀⣿⣿⡇⣿⣿⠈⢹⣿⣿⠉⢹⣿⣿⠉⠁⢸⣿⡏⣿⣿⡆⢈⠻⢿⣿⣿⡄⠉⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣼⣿⣿⣷⣿⣿⠀⣿⣿⠀⣿⣿⣿⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⣶⡆⢸⣿⡷⣿⣟⠀⣿⣷⣾⣿⣿⣄⠀⠀⠙⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⡏⢿⣿⣿⡏⠀⣿⣿⠀⣿⣿⢻⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⠀⠀⢸⣿⡇⣿⣿⡇⢸⣿⣿⣿⣿⣿⣦⣀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠸⠿⠿⠇⠸⠿⠿⠇⠰⠿⠿⠀⠿⠿⠘⠿⠿⠀⠸⠿⠿⠀⠸⠿⠿⠿⠇⠸⠿⠇⠿⠿⠇⢸⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⠹⣿⣿⣿⡟⠿⢯⣟⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠿⠿⠛⠛⠒⢶⣶⣶⠆⠀⠀⠀⠀⠀⠰⠒⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠿⠛⠛⠛⠻⢿⣿⣿⣿⣿⣮⣤⣬⢿⣿⣧⠀⠀⠈⠉⠘⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣶⣿⢿⣿⣆⠹⡏⢠⣾⡿⢿⣷⡄⢠⣾⣿⢿⣷⡄⢸⣿⣿⡇⣼⣿⣿⡇⣿⣿⡇⢸⣿⣇⢸⣿⡇⣰⣾⡿⣿⣶⡀⢻⣿⣿⣿⣿⣷⣿⣿⣿⣿⡆⠀⠀⠀⠀⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣿⣿⣬⡉⠋⣰⡇⢸⣿⡇⢸⣿⡇⢸⣿⡇⢸⣿⡇⢸⣿⣿⣧⣿⣿⣿⡇⣿⣿⡇⢸⣿⣿⣼⣿⡇⣿⣿⡇⠻⠿⠇⢸⣿⣿⣿⣿⣿⣿⣿⣻⣿⣧⠀⠀⠀⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣈⣛⢿⣿⣦⠘⠃⢸⣿⡇⢠⣤⡄⢸⣿⡇⢸⣿⡇⢸⣿⡿⣿⣿⢹⣿⡇⣿⣿⡇⢸⣿⢿⣿⣿⡇⣿⣿⡟⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣿⣿⣠⣿⣿⠀⠀⢸⣿⣧⣸⣿⡇⠸⣿⣧⣼⣿⡇⢸⣿⡇⣿⣿⢸⣿⡇⣿⣿⡇⢸⣿⠘⣿⣿⡇⢻⣿⣇⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢠⡀⢻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣛⣛⣠⣌⣙⣛⣋⣡⣴⣷⣄⠉⠛⠛⠉⠀⠀⠉⠛⠛⠉⠀⠘⠛⠁⠙⠃⠘⠛⠁⠙⠛⠃⠘⠛⠀⠙⠛⠁⣀⠙⠛⠉⠛⢁⣸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⣿⣾
⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⡆⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣻⢸⣿⣿⣿⣿⡏⠀⠀⠀⢹⣿
⣇⣆⡲⣶⢀⢶⢌⣡⣰⣶⣆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣆⢰⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣷⣧⣿⣿⣿⣿⡿⠀⠀⠀⣴⣿⣿
[69A⠀⠈⢻⣿⣿⣿⣿⠿⣫⣥⡄⠁⠀⠄⠀⢳⡸⢸⢿⣧⣄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣵⢠⣿⠀⠟⣱⢻⣍⣠⣲⠘⠔⡿⠿⣯⣧⡟⣿⡿⠫⠄⠬⣢⣛⡇⣺⡠⢀⠠
⠀⠀⠀⢹⢤⣷⣶⣿⣷⣿⣿⣆⣄⠀⠀⣶⣦⡀⣼⣿⡿⠀⠛⠛⣛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣉⠸⠀⢸⣶⣯⣤⣿⢫⣗⡴⠀⠀⠠⠂⠂⠻⠂⠐⢔⢿⣿⠿⢫⢧⡦⠹⠀
⠀⠀⠀⣿⣾⣽⣿⣿⣿⣿⣿⡏⢿⠂⢠⣿⣻⣿⣿⣿⣷⠀⠀⠀⠺⣯⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣠⡾⢏⣻⣻⣿⣠⡝⠇⠂⠀⠀⠀⠀⠀⠀⣠⣡⣏⣿⠠⠸⠑⢂⣀⠠
⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⢈⣿⣤⣼⣿⣿⣿⠀⠀⠠⠌⠹⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠻⠿⠿⠿⣿⣿⣿⣄⡜⢻⡏⣿⡹⠗⡂⠀⠀⠀⢀⠀⠾⠁⡮⢟⣻⠛⠁⠀⠈⢬⠗⣰
⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣾⣿⣿⣿⣿⣿⣿⡟⠀⣾⡼⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⡴⣾⠿⣷⠄⠁⠀⠀⠀⠜⣨⣿⠄⠐⠉⠈⠀⢀⣷⡰⣦⣾⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣙⣍⣙⣿⣿⣿⣿⣾⣶⡍⠀⠐⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣯⡆⣯⡀⠀⣠⠁⢀⡂⠄⠉⣡⡀⠀⠀⠀⠸⠿⠷⠝⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⢙⡁⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠁⠁⠁⠀⠀⣀⣾⡟⠀⠀⠀⠀⠠⣴⡶⣦⠤⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⢠⣿⣿⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⡰⠀⠀⠀⠠⠁⠀⣺⡇⡀⡰⠂⠀⠈⢎⠀⠈⠈⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⣀⠃⠀⠀⠀⠶⢶⡿⠂⠋⣀⠀⠰⢂⡀⢀⡀⠀⠩
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣔⠿⠀⠀⠀⠈⣀⠙⡶⠈⠃⠈⠀⠠⠾⠿⢻⣷⣄⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣄⠀⠀⠀⠀⣿⡷⠑⠆⢩⠀⠀⣠⣦⣿⣿⣿⡿⣛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣾⣿⣿⣿⣿⣿⣄⠠⠄⠛⠉⠟⠀⠰⡔⠂⠀⠛⠉⠉⣡⣿⣿⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣮⣟⡙⠷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⣠⣈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠁⢐⠀⠀⠄⠀⠀⠐⠋⣿⡟⠏
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠊⠰⠓
⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡀⠀⠀⠀⢰⣿⣿⠛⠙⠫⠉⠁⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣄⠠⠀⠠⠰⠨⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣀⣀⣠⣿⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⢼⣫⣸⠿⠂⠀⠀⠀⠀
⠀⠀⣾⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣶⠆⠀⠀⣁⡀
⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⡛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠉⢙⠀
⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠰⢺⣖⣅⣁⠀⠱⠇
⣃⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⢿⣿⣿⣿⣿⣿⣿⣿⠓⠠⠉⠉⠀⠉⠁⢈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠠⠀⠈⢀⡀⠀⠀⠀⠀⠀⠀⠀⣊⣽⣿⣿⣿⣿⣿⣿⡟⣀⡀⠀⠸⢟⣻⡆⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢈⠉⣙⠋⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠂⠀⠙⠚⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠲⠶⠾⡿⢿⡇⣩
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠈⠀⠈⢑⡐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠴⣾⡇⣹
⣿⣿⣿⣿⣿⣿⣿⣿⡅⠐⣦⢠⡄⠀⡏⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⢱⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⣧⣀⣠⡄⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡟
⣿⣿⣿⣿⣿⣿⣿⠟⠀⢀⠀⠻⠛⠁⠐⠏⠉⢛⣿⣿⣿⡿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⣿⣿⣿⣿⣿⣿⣿⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣄⣄⠀⠢⠄⠝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀⠀⠈⠻⠛⠛⠛⠉⠁⢀⣾⣿⣿⣿⣿⣿⣿⡿⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⠮⠋⠀⠀⠈⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⠻⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⠈⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠏⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠐⣶⣶⣦⡀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣷⠆⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣄⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣤⡆⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⠀⠀⠈⠉⠛⠿⢿⣿⣿⣿⣿⣆⠨⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣹⣶⣦⣤⣀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣤⣾⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠭⣵⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⠛⢹⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣤⣌⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠉⠁⢀⣿⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣼⣿⡿⠃⠐⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡯⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣵⣤⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⢾⣷⣶⣿⣯⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢿⣿⣿⣿⣿⠁⠁⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⣷⣆⠀⠀⠈⠙⣿⢷⡄⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠗⠂⠘⣹⠟⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠅⠉⢧⡀⠀⠀⠉⠀⢹⡄⠀⠀⠀⠀⠹⣿⡿⣟⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢡⣤⣄⢡⣤⣤⠀⣤⣤⡄⣤⣤⠀⣤⣤⠀⣤⣤⢠⣤⣤⣤⣤⣤⣤⣤⣤⡄⢠⣤⣤⣤⣄⠈⠛⠀⢀⣶⡖⠈⢿⣆⠤⡀⠀⠀⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⢸⣿⣿⡆⣿⣿⠀⣿⣿⠀⣿⣿⡇⣿⣿⠈⢹⣿⣿⠉⢹⣿⣿⠉⠁⢸⣿⡏⣿⣿⡆⠸⠿⣿⣿⣷⡀⠘⢿⣿⣾⣕⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣼⣿⣿⣷⣿⣿⠀⣿⣿⠀⣿⣿⣿⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⣶⡆⢸⣿⡷⣿⣟⠀⣾⣦⣤⣿⣿⣄⠀⠈⠹⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⡏⢿⣿⣿⡏⠀⣿⣿⠀⣿⣿⢻⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⠀⠀⢸⣿⡇⣿⣿⡇⢸⣿⣿⣿⣿⣿⣦⡀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⠿⠿⠇⠸⠿⠿⠇⠰⠿⠿⠀⠿⠿⠘⠿⠿⠀⠸⠿⠿⠀⠸⠿⠿⠿⠇⠸⠿⠇⠿⠿⠇⢸⣿⣿⣿⣿⣿⣿⣷⣠⠀⠀⠙⣿⣿⣿⣿⣿⣟⡿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠿⠿⠛⠛⠂⢠⣴⣴⡖⠀⠀⠀⠀⠲⠶⠖⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠞⠛⠛⠛⠻⢿⣿⣿⣿⣿⣈⣀⠈⢿⣿⣷⠀⠉⠙⠢⠙⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣶⣿⢿⣿⣆⢹⡏⢠⣾⡿⢿⣷⡄⢠⣾⣿⢿⣷⡄⢸⣿⣿⡇⣼⣿⣿⡇⣿⣿⡇⢸⣿⣇⢸⣿⡇⣰⣾⡿⣿⣶⡀⢻⣿⣿⣿⣷⣢⣥⡸⣿⣿⡇⠀⠀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣿⣿⣬⡉⠋⣸⡇⢸⣿⡇⢸⣿⡇⢸⣿⡇⢸⣿⡇⢸⣿⣿⣧⣿⣿⣿⡇⣿⣿⡇⢸⣿⣿⣼⣿⡇⣿⣿⡇⠻⠿⠇⢸⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣈⣛⢿⣿⣦⠘⡇⢸⣿⡇⢠⣤⡄⢸⣿⡇⢸⣿⡇⢸⣿⡿⣿⣿⢹⣿⡇⣿⣿⡇⢸⣿⢿⣿⣿⡇⣿⣿⡟⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣿⣿⣠⣿⣿⠀⠀⢸⣿⣧⣸⣿⡇⠸⣿⣧⣼⣿⡇⢸⣿⡇⣿⣿⢸⣿⡇⣿⣿⡇⢸⣿⠘⣿⣿⡇⢻⣿⣇⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣛⣛⣠⣌⣙⣛⣋⣡⣴⣶⣄⡉⠛⠛⠉⠀⠀⠉⠛⠛⠉⠀⠘⠉⠁⠙⠃⠈⠉⠁⠉⠉⠃⠈⠉⠀⠙⠙⠁⢀⠙⠛⠉⠙⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⣌
⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠀⠀⠀⠀⠀⣦⣶⣾⣿⡀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣟⣿⣿⠿⣿⣟⣿⣿⣿⣿⠁⠀⠀⠸⣿
⣇⣆⡲⣶⢀⣶⢌⣡⣰⣶⣆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⡀⢀⢰⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣗⣯⣦⣽⣿⣿⣿⣿⡇⠀⠀⠀⣤⣿
[69A⠿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⡏⠛⣁⠀⠀⢈⠉⠋⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⡉⠁⠈⠀⣋⢤⣟⡍⡒⠅⣭⢻⣋⣿⣿⢻⣮⣯⡿⡿⢖⡡⢒⡓⠈⡃⠀⠀⠀
⠀⠈⠻⣿⣿⣿⣿⣿⡿⢟⠃⠀⠀⠀⠁⢰⣰⠼⣶⣷⣀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠷⣼⡧⠸⢉⢎⣷⡅⣮⡗⠃⠻⠛⠻⡾⠾⢻⡿⠋⠒⢐⣪⣯⣽⣸⠱⣠⠆⠀
⠀⠀⠀⠙⣏⢩⣽⣙⣶⣽⣷⣆⠀⠀⠀⢴⣭⠀⣀⣿⣿⠀⠻⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣁⡂⠀⣿⣿⣶⣾⡏⢾⣷⠃⠀⠀⠊⠈⠈⠃⠂⢑⢝⣿⡏⢏⣿⠾⡂⡅⠀
⠀⠀⠀⢰⣇⣿⣿⣿⣿⣿⣿⣏⢺⡆⢁⣸⡿⣿⣿⣿⣿⠀⠀⠀⠩⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡻⠛⣮⣏⣿⡧⣇⡝⠈⠀⠀⠠⠀⠰⣀⣠⣧⣾⡾⠧⠂⠂⡉⢴⡂⠙
⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠈⣿⣇⣡⣿⣿⣿⠀⠀⢠⢘⠻⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠙⠛⠛⠿⠿⢷⣤⢉⠿⣼⣷⠟⢭⡀⠀⠀⠀⣄⡘⣂⠹⣊⡭⣏⠀⢀⠐⡚⢚⢤⣷
⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⢸⣿⣿⣿⣿⣿⣿⡿⠀⣴⣷⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢺⡟⢋⡿⠀⠀⠠⠀⠜⠠⢼⡟⠂⠁⠀⠀⠀⣼⣷⡹⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⡉⠉⣿⣿⣿⣿⣴⣦⡍⠀⠀⠂⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡙⠷⢤⡠⢖⠀⠔⠈⢉⣰⡖⠀⠀⠀⠀⠉⣉⢙⠌⢻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⡋⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⡀⠀⠀⠀⠀⠠⢨⣿⠁⠑⢀⠀⠀⢝⠟⠛⡇⡅⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡤⢰⣼⣿⣶⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠀⠀⠀⠀⣀⣸⣿⢡⠏⠊⠀⢀⡘⠀⠀⠠⠀⠠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠀⠀⠀⠀⠉⢿⡍⣠⠄⡆⠀⠈⣲⣤⣶⡀⠀⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣮⠉⠀⠀⠀⢠⣦⣘⠋⠄⠄⢐⡀⠉⢉⣥⣾⣿⣶⠮
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣆⠀⠀⢀⡬⠿⡇⠐⡁⢒⠀⢰⣿⠿⠿⢛⣿⣵⠲
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣾⣿⣿⣿⣦⡈⠀⠀⠈⠁⠀⠉⠁⠀⠀⠀⠐⡐⢿⡿⢿⣛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠄⣀⠀⠀⡀⠀⠀⢪⠿⣷⡷⡍
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣦⣽⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠁⠐⠀⠀⠀⠀⠀⠀⡀⠹⡩⠅
⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣟⡿⣿⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⢀⢀⢰⠔⠁⠀⠀⠁⠀
⡇⢸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⢰⡄⠀⠀⢰⣿⡿⠁⠀⠀⠀⠀⠈⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣇⠈⠀⣸⠖⣨⣐⠄⠀⠀⠀⠀
⡇⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⡿⠃⠀⠀⠨⡟⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣵⣯⣛⣩⠄⠀⠀⠂⠀
⡇⠀⢰⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⠰⡖⡁
⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣀⣤⠄⠂⠀⢶⡀
⣧⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣿⣿⣿⣿⣿⣿⣶⣄⣐⡿⠟⠒⠑⡆⠐
⣏⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣲⡦⢤⡄⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣽⣿⣿⣿⣿⣧⡪⣧⣤⣤⣶⣿⡇⢒
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡀⡄⠠⣍⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣷⡄⠠⠄⢉⣬⡇⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠅⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣺⣿⢇⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣙⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⣿⣿⣿⣿⡟⠀⠻⢆⠀⠀⠀⠀⠠⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⣿⠟⠁⠀⠘⢿⣿⣟⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠛⠉⠉⠁⣴⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⢿⣿⣿⡿⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠂⠀⠀⠀⠀⣠⠿⣿⣿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡆⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡄⠀⠀⠀⠀⣵⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⣀⠉⠛⠿⣿⣿⣿⣿⡗⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣿⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠑⣂⡀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠛⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠑⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠛⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣾⠒⠺⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠋⠁⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢉⣵⣿⣿⠁⢀⣌⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⢀⡀⠈⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣷⣿⣿⠻⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠉⠛⠻⠿⣿⣧⡘⠻⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⢿⣿⣿⣿⠇⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⣆⠀⠀⠀⠸⡿⠛⡄⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢡⣤⣄⢡⣤⣤⠀⣤⣤⡄⣤⣤⠀⣤⣤⠀⣤⣤⢠⣤⣤⣤⣤⣤⣤⣤⣤⡄⢠⣤⣤⣤⣄⠈⢳⡀⠀⢀⠀⠀⠹⣄⠀⠀⠀⠀⠸⠿⢻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⢸⣿⣿⡆⣿⣿⠀⣿⣿⠀⣿⣿⡇⣿⣿⠈⢹⣿⣿⠉⢹⣿⣿⠉⠁⢸⣿⡏⣿⣿⡆⢰⣅⡀⢸⣟⠀⠈⢻⣯⣆⠄⡀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣼⣿⣿⣷⣿⣿⠀⣿⣿⠀⣿⣿⣿⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⣶⡆⢸⣿⡷⣿⣟⠀⣤⡉⠙⠻⣿⠦⠀⠈⢻⣿⣷⣮⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⡏⢿⣿⣿⡏⠀⣿⣿⠀⣿⣿⢻⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⠀⠀⢸⣿⡇⣿⣿⡇⢸⣿⣶⣦⣭⣤⡀⠀⠀⠙⠻⣿⣿⣿⣿⣿⡷⣟⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠸⠿⠿⠇⠸⠿⠿⠇⠰⠿⠿⠀⠿⠿⠘⠿⠿⠀⠸⠿⠿⠀⠸⠿⠿⠿⠇⠸⠿⠇⠿⠿⠇⢸⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠿⠟⠛⠛⠃⠂⠀⢠⠖⠀⠀⠀⠂⠴⡶⠆⠀⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠙⠛⢿⣿⣿⣤⣀⠀⠀⠈⠻⣿⣿⡟⠻⢯⡙⠿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣶⣿⢿⣿⣆⢰⡆⢠⣾⡿⢿⣷⡄⢠⣾⣿⢿⣷⡄⢸⣿⣿⡇⣼⣿⣿⡇⣿⣿⡇⢸⣿⣇⢸⣿⡇⣰⣾⡿⣿⣶⡀⢻⣿⣿⡯⡀⠀⠀⠀⢹⣿⣧⠀⠀⠈⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣿⣿⣬⡉⠋⣼⡇⢸⣿⡇⢸⣿⡇⢸⣿⡇⢸⣿⡇⢸⣿⣿⣧⣿⣿⣿⡇⣿⣿⡇⢸⣿⣿⣼⣿⡇⣿⣿⡇⠿⠿⠇⢸⣿⣿⣿⡶⠂⡀⠀⠀⢿⣿⡇⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣈⣛⢿⣿⣦⠘⡇⢸⣿⡇⢠⣤⡄⢸⣿⡇⢸⣿⡇⢸⣿⡿⣿⣿⢸⣿⡇⣿⣿⡇⢸⣿⢿⣿⣿⡇⣿⣿⡟⣿⣿⡇⢸⣿⣿⣿⣿⣶⣾⣠⡀⡘⣿⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣿⣿⣠⣿⣿⠀⡇⢸⣿⣧⣸⣿⡇⠸⣿⣧⣼⣿⡇⢸⣿⡇⣿⣿⢸⣿⡇⣿⣿⡇⢸⣿⠘⣿⣿⡇⢻⣿⣇⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣛⣛⣠⣌⣙⣛⣋⣡⣴⣇⣀⣉⠛⠛⠉⠀⠀⠉⠛⠛⠉⠀⠘⠙⠁⠙⠃⠘⠉⠁⠉⠉⠁⠈⠉⠀⠉⠙⠁⠀⠙⠛⠉⠛⢁⣼⣿⣿⣿⣿⣿⣫⠭⢺⣿⣿⣿⡇⠀⠀⠀
⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣦⣀⠙⣻⡉⠻⣿⣿⠗⠂⢤⣿⣿⣿⡇⠀⠀⢀
⣇⣆⡲⣶⢀⣶⢌⣡⣰⣶⣆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡔⠀⠀⠀⠀⢰⣶⣶⣿⣷⡀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣴⣯⠂⠚⠊⠋⠀⠀⣾⣿⣿⣿⠁⠀⠀⠀
[69A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡢⣂⣻⡿⠿⠀⡁⢠⠟⢸⢿⣄⠽⠁⡺⠧⢿⣿⣿⣟⡿⣶⣿⣯⠝⠘⠴⠀⠢⠀⠀⠀⠀
⠻⣿⣿⣿⣿⣿⣿⣿⣿⣹⢿⣿⠏⠉⡠⠀⠀⣠⠀⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣓⡄⣗⡀⡵⢪⢿⣟⢀⢸⣾⡡⣿⢿⣯⣧⡿⣿⡿⢫⡉⠬⣄⡳⡂⣞⡄⣀⠀⠀
⠀⠈⠻⣿⣿⣿⣿⣿⡿⣛⡁⠐⠀⠀⠀⠹⡰⠸⢿⣧⣄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠙⠙⠅⢰⣯⣵⣹⣼⠎⣦⡶⠀⠀⠉⠛⠆⠻⢂⠠⢴⢯⣿⢿⢫⣷⡦⢁⠀⠀
⠀⠀⠀⠈⣯⣙⣯⣵⣿⣿⣿⣧⢀⠀⡀⣲⣯⣀⣬⣿⣿⠀⠛⠙⣛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡴⢟⣻⣟⣿⢫⢹⠧⠁⠐⠀⡀⠀⡀⠀⣨⣣⣯⣿⡠⠹⡱⣂⡬⠐⠖
⠀⠀⠀⢠⡿⣜⣿⣿⣿⣿⣿⣧⠹⠇⢠⣼⡟⡿⣿⣿⣿⠀⠀⠀⢰⣯⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢘⢻⣎⣿⣼⢟⠃⠀⠀⠀⢀⡠⠾⠹⣮⢿⣻⠓⠁⠀⠬⠮⢯⣰⡤
⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢶⢀⣀⣿⣧⣵⣿⣿⣿⠀⠀⢰⠨⠙⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠁⠀⠀⠀⠉⠛⠛⠳⢾⡿⢷⠖⠉⠀⠀⠄⠜⣩⣿⠇⠜⠉⠈⠁⢀⣷⡜⣶⣿⣯⣧
⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣺⣿⣿⣿⣿⣿⣿⠟⠀⣾⠿⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⢀⢄⢀⠆⠐⠏⣠⠄⠀⠀⠀⠘⠛⠛⠎⡻⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣄⣀⣿⣿⣿⣿⣾⡷⠆⠀⠀⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡉⠀⠁⠀⠀⡈⣲⡟⠃⠞⠄⠀⢐⡾⢗⢿⢐⡀⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⢈⣅⣀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⡿⣰⠢⠃⠀⠀⠿⠀⠀⡀⣒⡠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⢸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢛⣿⡃⣘⠢⡄⠀⠩⣄⣠⣄⠀⠐⠂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⢻⠊⢉⡀⠄⠀⠚⢛⣩⣿⣷⣤⡺
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣺⣿⡃⠝⣨⠆⠈⢰⣷⢿⡿⢿⣿⡥⢶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣠⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⣀⠒⠈⠁⠘⠁⠨⠓⠉⠀⠈⠀⠀⢐⣿⣿⣿⡖
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢹⢿⣶⣬⠧
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢘⡟⣸⡀
⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢰⠰⠃⠁⠀⠉⠀
⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢠⠀⠀⠀⣰⣿⡏⠁⠡⠉⠿⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⠂⠂⠀⣸⡭⣨⣠⠀⠀⠀⠀⠀
⣿⠈⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣾⠇⠀⢰⣿⡏⠁⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣇⢀⣵⡇⣿⣉⠁⠂⠠⠀⠀
⣿⠀⠀⣀⡈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠸⠿⠃⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠓⠀⠀⠤⡖⠀
⣇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢁⢤⡠⠢⠂⠀⣶⠐
⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣢⡀⠹⠶⠖⠢⠴⠌⠠
⣿⠄⠈⠁⠀⠹⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⡯⠀⠈⠐⢠⣤⣬⡀⠀
⠁⠀⠀⠀⠀⠀⠹⢿⣿⠿⠛⠋⠁⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣇⢖⣂⣠⣨⣷⣾⡇⢖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠛⠟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣦⠨⠉⠉⢉⣸⡇⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣪⣿⢇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⡿⠟⠋⢿⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⡟⠁⠀⠀⠀⠀⠐⠛⠟⠿⠿⠿⠛⠋⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⣿⠇⠤⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣾⣿⣦⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠉⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠈⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠈⢿⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⠀⠀⠀⠀⠙⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠻⣿⣿⣶⡀⠀⠀⠀⠀⢲⣿⣿⣿⣧⡀⠀⠀⠀⠀⠈⠻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠘⢿⣿⣷⣀⠀⠀⢀⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣻⢇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠭⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⡻⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣤⢬⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠹⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣼⣿⡿⠁⠐⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣾⢿⣿⣥⣬⣿⡧⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣶⣼⣧⠈⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠿⣿⣿⣿⣿⠀⠁⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⠀⠀⠀⠙⣿⠳⣄⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⣤⣄⢡⣤⣤⠈⣤⣤⡄⣤⣤⠀⣤⣤⠀⣤⣤⢠⣤⣤⣤⣤⣤⣤⣤⣤⡄⢠⣤⣤⣤⣄⠈⢳⡄⠀⠀⠈⠀⠘⣆⠀⠀⠀⠀⠈⣿⣿⢿⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⢸⣿⣿⡆⣿⣿⠀⣿⣿⠀⣿⣿⡇⣿⣿⠈⢹⣿⣿⠉⢹⣿⣿⠉⠁⢸⣿⡏⣿⣿⡆⢠⡙⠀⠀⣶⠂⠀⠙⣦⡠⢀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣼⣿⣿⣷⣿⣿⠀⣿⣿⠀⣿⣿⣿⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⣶⡆⢸⣿⡷⣿⣟⠀⣈⠙⠷⢶⣿⣷⡄⠀⠿⣿⣷⣍⣢⣄⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⡏⢿⣿⣿⡏⠀⣿⣿⠀⣿⣿⢻⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⠀⠀⢸⣿⡇⣿⣿⡇⢸⣿⣦⣀⡸⠏⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣽⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠸⠿⠿⠇⠸⠿⠿⠇⠰⠿⠿⠀⠿⠿⠘⠿⠿⠀⠸⠿⠿⠀⠸⠿⠿⠿⠇⠸⠿⠇⠿⠿⠇⠸⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠙⢿⣿⣿⣿⣿⣯⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠿⠿⠛⠛⠓⠶⣤⠀⠰⠒⠐⠒⠒⠰⡶⠖⠀⠀⠰⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠙⠛⢿⣿⣿⣁⠀⠀⠀⠈⠻⣿⣿⣿⢿⣿⡻⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣶⣿⢿⣿⣆⠀⡀⢠⣾⡿⢿⣷⡆⢠⣾⣿⢿⣷⡄⢸⣿⣿⡇⣼⣿⣿⡇⣿⣿⡇⢸⣿⣇⢸⣿⡇⣰⣾⡿⣿⣶⡀⢻⣿⣿⣷⣀⡀⠀⠀⠙⣿⣿⡀⠈⠙⠂⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣿⣿⣬⡉⠋⣼⡇⢸⣿⡇⢸⣿⡇⢸⣿⡇⢸⣿⡇⢸⣿⣿⣧⣿⣿⣿⡇⣿⣿⡇⢸⣿⣿⣼⣿⡇⣿⣿⡇⠿⠿⠇⢸⣿⣿⣿⡷⡄⢀⠀⠀⠸⣿⣷⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣈⣛⢿⣿⣦⠘⡇⢸⣿⡇⢠⣤⡄⢸⣿⡇⢸⣿⡇⢸⣿⡿⣿⣿⢹⣿⡇⣿⣿⡇⢸⣿⢿⣿⣿⡇⣿⣿⡟⣿⣿⡇⠈⣿⣿⣿⣿⣷⣖⣥⠀⠀⢻⣿⡆⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣿⣿⣠⣿⣿⠀⡇⢸⣿⣧⣸⣿⡇⠸⣿⣧⣼⣿⡇⢸⣿⡇⣿⣿⢸⣿⡇⣿⣿⡇⢸⣿⠘⣿⣿⡇⢻⣿⣇⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣛⣛⣠⣌⣙⣛⣋⣡⣾⣿⡄⡉⠛⠛⠉⠀⠀⠉⠛⠛⠉⠀⠘⠛⠃⠙⠃⠘⠛⠁⠙⠛⠃⠘⠛⠀⠙⠛⠁⠀⠙⠛⠉⠛⢃⣸⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⡆⠀⠀
⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣶⣄⠉⠻⣿⡿⠿⣿⣿⣿⣳⢾⣿⣿⣿⣿⡇⠀⠀
⣇⣆⡲⣶⣀⣶⢌⣡⣰⣶⣆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⣀⣀⣠⣴⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣶⣾⡷⠀⣿⣿⡿⠊⢹⣿⣿⣿⣿⠀⠀⠀
[69A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣴⢅⣚⣿⡿⠷⢈⠁⢰⠃⣸⣇⣨⠟⢑⡿⡿⣻⣿⣟⣯⢿⣾⣿⡧⢟⠀⠴⠈⡦⠠⠀⢀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡟⠟⡀⠀⠉⠉⠛⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣣⢸⣦⠀⡳⢫⢿⡃⢈⣷⢘⣵⡿⢿⣻⣷⢿⣿⡿⣭⠉⠽⣘⣲⢠⣇⡀⡀⠐⠀
⠀⠙⢿⣿⣿⣿⣿⣿⣿⠿⠉⠍⠀⠀⠃⢆⢠⢻⣴⣆⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⠘⠹⠀⣰⣭⣞⣡⣿⢫⡶⢦⠂⠈⠹⠋⠘⠟⢀⠁⡼⣧⡿⡿⣿⣵⠎⢇⠀⠀
⠀⠀⠀⠛⡟⢻⣿⢻⣵⣻⡧⡆⠀⠁⠐⣬⣎⠈⣸⣿⣿⠈⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡷⠠⡾⢟⣻⣿⣿⣬⡿⠮⠀⠀⢀⠀⠀⠀⢀⣱⣱⣿⣏⡨⣏⠶⣊⣌⠲⠀
⠀⠀⠀⢀⣏⣾⣿⣿⣿⣿⣿⡟⢶⡄⠂⢻⢿⣷⣿⣿⣧⠀⠀⠈⢿⡎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⡜⢳⡏⣿⣻⣗⡀⠀⠐⠀⢀⠤⠎⠑⡼⢟⣻⠊⠠⠒⠬⠼⣂⣶⡄
⠀⠀⠀⢸⣯⣿⣿⣿⣿⣿⣿⣿⣌⠀⠈⣿⣋⣉⣿⣿⣿⠀⢀⠀⡉⠿⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠉⠛⠟⢿⣿⣿⣷⠆⠁⠀⠀⠀⢞⣩⣿⠢⠙⠉⠨⠀⢨⣷⡱⣶⣷⣽⡽
⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⣼⣿⣿⣿⣿⣿⣿⡿⠀⣼⡰⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⡀⣢⡁⣘⠆⠒⠉⣤⠄⠀⠐⠀⠘⠛⠻⢘⢿⣿⣿
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣙⠍⠙⣿⣿⣿⣿⣶⣦⡉⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⢀⣿⡟⠐⡃⠀⠀⣰⢿⡟⡷⢲⠀⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⢛⡃⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⣿⠏⣔⠒⠃⠀⠢⠣⠀⠀⠈⣒⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡤⢠⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣟⠑⣕⢤⠀⠘⢡⣄⣤⡄⠀⠐⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡿⢪⣃⢨⠄⠀⠛⣛⣽⣿⣦⣴⡱
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠋⠗⡰⠂⠉⢾⡾⣿⠿⣿⣯⡔⢶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠀⠛⠀⠸⠑⠁⠀⠉⠀⠀⣸⣿⡿⣷⡣
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣻⢿⣦⣬⠅
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣷⡀⠀⠀⠐⠈⠁⠀⠈⠀⠀⠀⢁⢘⢟⠰⠀
⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣈⣉⣁⡀⢻⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⡀⢤⠚⠉⠀⠈⠉⠀
⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣴⣾⠻⠟⢛⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣔⠂⠂⠀⣡⠅⣥⣄⠀⠀⠀⠀⠀
⣿⠘⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄⣠⣾⡄⠀⢠⣾⡟⠀⠐⠀⠀⠀⢪⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⢨⣷⣗⣟⣡⠂⠀⠠⠄⠀
⣿⠀⠀⠈⠉⠀⠀⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠸⡟⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠴⡒⠐
⠉⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣍⣡⣀⣙⣿⣿⣿⣿⣿⣿⣿⠉⣀⢄⡠⠢⠂⠣⣶⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠠⠄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠣⡚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⡑⠹⠾⠖⠢⠤⠌⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⣤⣤⣤⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⡁⣿⣿⣿⣿⣿⣿⣿⡇⢖⣀⣠⣨⣶⣾⡆⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠨⣿⣿⣿⣿⣿⣿⣿⣆⠨⠡⠉⢉⣼⡇⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣞⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣐⣸⣿⢡⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢿⣿⣿⠿⠿⠟⠛⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠉⠀⣀⡀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠀⠀⠀⠀⠀⣀⣴⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣿⣿⠁⠀⠀⠐⠓⠂⠒⢻⣿⣿⣿⣿⣦⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⢂⠉⡛⠂⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠐⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣤⣄⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢸⣿⣯⣴⣿⣄⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠛⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⢿⣿⣿⣿⣶⣶⣦⡀⠈⠁⣦⠀⠀⠀⠀⠀⠀⠀⢦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⠟⠐⠸⠟⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠘⣿⣏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣶⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠙⣷⣤⡀⠀⠀⠀⠀⠠⣾⣿⣧⠀⠀⠀⠀⠀⠈⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡈⠻⣷⡀⠀⠀⠀⣺⣿⣿⣿⣧⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⣿⣶⣶⣾⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠮⡾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠻⠇⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣍⢀⣈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣩⣿⡿⠃⠀⠵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣿⣇⣄⣾⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⣦⣼⣧⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣶⣿⣿⣿⠇⠙⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣄⠀⠀⠀⠉⢿⠷⣄⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⣤⣄⢡⣤⣤⠉⣤⣤⡄⣤⣤⠀⣤⣤⠀⣤⣤⢠⣤⣤⣤⣤⣤⣤⣤⣤⡄⢠⣤⣤⣤⣄⠈⢳⡀⠀⠀⠈⠀⠘⣆⠀⠀⠀⠀⠈⣿⣿⢿⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⢸⣿⣿⡆⣿⣿⠀⣿⣿⠀⣿⣿⡇⣿⣿⠈⢹⣿⣿⠉⢹⣿⣿⠉⠁⢸⣿⡏⣿⣿⡆⢠⡙⠀⠀⢐⡀⠀⠸⣦⡠⢀⠀⠀⠈⢰⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣼⣿⣿⣷⣿⣿⠀⣿⣿⠀⣿⣿⣿⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⣶⡆⢸⣿⡷⣿⣟⠀⢈⠙⠲⠤⣵⣧⣄⠀⠻⣿⣷⣅⣢⣄⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⡏⢿⣿⣿⡏⠀⣿⣿⠀⣿⣿⢻⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⠀⠀⢸⣿⡇⣿⣿⡇⢸⣷⣄⣀⡀⠫⠄⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣽⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠸⠿⠿⠇⠸⠿⠿⠇⠰⠿⠿⠀⠿⠿⠘⠿⠿⠀⠸⠿⠿⠀⠸⠿⠿⠿⠇⠸⠿⠇⠿⠿⠇⠘⣿⣿⣿⣷⣦⣦⣄⠀⠀⠀⠙⢿⣿⣿⣿⣿⣯⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠿⠿⠛⠛⠳⠶⣦⠀⠒⠖⠒⠒⠒⠲⠶⠖⠀⠀⠐⠶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠙⠛⢿⣿⣿⣇⡀⠀⠀⠈⠹⣿⣿⣿⢿⣿⡻⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣶⣿⢿⣿⣆⠈⠁⢠⣾⡿⢿⣷⡆⢠⣾⣿⢿⣷⡄⢸⣿⣿⡇⣼⣿⣿⡇⣿⣿⡇⢸⣿⣇⢸⣿⡇⣰⣾⡿⣿⣶⡀⢹⣿⣿⣿⡂⠀⠀⠀⠹⣿⣿⡆⠉⠙⠢⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣿⣿⣬⡉⠋⣴⡇⢸⣿⡇⢸⣿⡇⢸⣿⡇⢸⣿⡇⢸⣿⣿⣧⣿⣿⣿⡇⣿⣿⡇⢸⣿⣿⣼⣿⡇⣿⣿⡇⠿⠿⠇⢸⣿⣿⣿⣿⣇⠁⠀⠀⠘⣿⣷⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣈⣛⢿⣿⣦⠸⡇⢸⣿⡇⢠⣤⡄⢸⣿⡇⢸⣿⡇⢸⣿⡿⣿⣿⢹⣿⡇⣿⣿⡇⢸⣿⢿⣿⣿⡇⣿⣿⡟⣿⣿⡇⠘⣿⣿⣿⣿⣿⣴⣷⣀⣰⠿⣿⡇⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣿⣿⣠⣿⣿⢀⡇⢸⣿⣧⣸⣿⡇⠸⣿⣧⣼⣿⡇⢸⣿⡇⣿⣿⢸⣿⡇⣿⣿⡇⢸⣿⠘⣿⣿⡇⢻⣿⣇⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣛⣛⣠⣌⣙⣛⣋⣡⣾⣿⣄⠉⠛⠛⠉⠀⠀⠉⠛⠛⠉⠀⠘⠛⠃⠙⠃⠘⠛⠁⠙⠛⠃⠘⠛⠀⠙⠛⠁⠀⠙⠛⠉⠛⢃⣰⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⡇⠀⠀
⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣦⡀⠈⠛⣿⡿⠻⣿⣿⣿⣷⣿⣿⣿⣿⣿⡇⠀⠀
⣇⣆⡲⣶⣀⣶⢌⣡⣰⣶⣆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⢀⡀⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣶⣄⣍⣿⢀⢻⣿⡿⠁⢝⣿⣿⣿⣿⠁⠀⠀
[69A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣛⣬⣽⣿⠛⡆⠄⢀⢏⣰⣿⡢⣽⠃⣺⢿⢻⣿⡿⢿⣿⣿⣿⣿⠜⡡⠰⠆⢺⠀⠄⠀⡄⠀
⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠿⠃⠈⠉⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣍⡆⣶⡆⠸⢛⡟⣭⢁⣜⡆⠱⡿⠿⣯⣯⡟⣿⡿⠫⡄⠨⢲⢛⡇⣾⠥⣠⠠⠁⠀
⠙⢿⣿⣿⣿⣿⣿⣿⣷⡟⠛⠃⠀⠘⢠⠀⡜⣧⣤⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⡎⡉⠇⠠⣷⣾⣭⣼⡟⣿⡲⠆⠀⠀⠓⠀⠹⠁⢄⢴⢷⣾⡻⣻⡧⡏⠘⡀⠀⠀
⠀⠀⠙⢿⠿⡿⠟⣫⣴⣶⣤⠀⠐⠀⢀⣣⠁⠉⣿⣿⡆⢻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡇⢸⠻⣽⢟⣿⣷⣼⠓⠂⠀⠀⠄⠀⠀⠀⣁⣧⣯⣿⣠⠸⢝⣊⡤⡕⠓⠁
⠀⠀⠀⣼⢲⣿⣿⣿⣿⣿⣿⢧⣆⠀⢸⡿⣿⢾⣿⣿⡀⠀⠀⠺⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⢠⣙⣿⣹⣯⠿⣀⠀⠀⠁⠀⡤⢺⠩⢫⠻⠾⡇⠁⢈⠀⠲⢚⣴⡭⠀
⠀⠀⠐⣿⣿⣾⣿⣿⣿⣿⣿⣆⡁⠀⢹⣟⢛⣿⣿⣿⡇⠀⢀⢘⠻⣯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠳⣾⣿⣟⣛⠈⠀⢀⠀⡰⢍⣺⣷⠌⠉⠁⠁⠀⣶⣮⢿⣿⣷⣯⣫
⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⢡⣶⣿⣿⣿⣿⣿⣿⠇⢠⣧⡌⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠁⠀⠀⠀⠀⠉⠙⠻⠶⣄⣄⠂⡭⠐⠂⢠⡦⠀⠀⠃⠀⠋⣛⠃⠝⢿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣞⠋⠙⢻⣿⣿⣿⣧⣦⣝⠉⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⠬⣿⠉⠙⢀⠀⠀⠽⢟⢻⡟⡌⡈⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢛⠁⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⣸⣿⢁⡀⠋⠀⢐⠚⠂⠀⠠⣘⠤⠄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⣴⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⣽⡏⢲⡕⡆⠀⠉⣒⣤⣦⡀⠀⠁⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣹⢇⠅⠀⠐⠀⢉⢉⣥⣿⣿⣶⠮⢣
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠐⣃⢛⠁⢱⣿⠿⠿⢛⣿⣷⠒⢷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠍⠊⠀⠀⠀⠀⠀⣾⡿⠿⣛⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⢪⡿⣿⡷⡖⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆⠀⠀⠀⠂⠐⠁⠀⠀⠀⠀⠀⡀⠻⣁⡅⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣶⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⢀⡀⡦⠋⠀⢀⠀⠀⠀
⠸⣿⣿⣿⡿⠿⠛⠉⠀⠈⢿⣿⣿⣿⣿⣿⠋⠉⠉⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣖⣶⣶⣦⣤⣹⣿⣿⣿⣿⣿⣿⣧⣓⠀⠀⢈⣶⢪⣶⡄⠀⠀⠀⠠⠀
⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣀⣠⣦⠀⠀⢀⣾⡿⠃⠉⠃⣻⠭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣰⣿⣸⣫⠄⠈⠀⠂⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠋⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⢀⣿⡟⠁⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⣀⠲⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⢿⣟⠿⢿⣿⣿⣿⣿⣿⣿⣏⠀⣄⣤⡼⠒⠀⢲⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⣁⣆⣺⣿⣿⣿⣿⣿⣿⣷⣦⣂⣻⠷⠓⠠⡒⠁⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠀⠉⣙⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠗⡿⣾⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⢂⣶⠤⣤⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢺⣿⣿⣿⣿⣿⣿⣿⣰⢷⣄⣤⣴⣾⣿⠘⣎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠈⠐⠄⠀⠀⠀⠀⠀⠀⠀⢸⣼⣿⣿⣿⣿⣿⣿⣷⡀⠀⠤⠈⣥⣿⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣶⣤⣐⣾⡿⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⢷⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢀⡻⠋⠀⢀⠀⠀⠀⣠⣴⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡕
⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣷⣿⠀⠀⠀⠙⠓⠾⠟⣿⣿⣿⣿⣿⡀⠀⢀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏
⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⡿⣾⠟⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠑⢶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠔⠛⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⣬⣟⣁⡀⢺⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢸⣿⣟⣭⣿⣀⣻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⣿⣿⣿⣿⠟⢹⠃⠀⢰⣤⣄⡀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⢹⣿⣿⣷⣤⣤⣄⠀⠘⢻⣿⠃⠀⠀⠀⠀⠈⢻⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢻⣿⣿⣿⣿⣿⡧⠰⢸⠏⠀⠀⠀⠀⠀⠀⠘⠻⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠻⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣇⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣤⣀⢢⣀⠀⠀⠀⠀⠀⢠⣶⡀⠀⠀⠀⠀⠈⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣶⣿⣧⠀⠀⠀⠀⠀⠈⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣶⣶⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠣⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣰⣣⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣲⣿⠀⠀⠘⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠘⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣉⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣿⣇⣄⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⣤⣬⣧⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣶⣿⣿⣿⠏⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⠀⠀⠀⠙⢿⠳⣄⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⣤⣄⢡⣤⣤⠉⣤⣤⡄⣤⣤⠀⣤⣤⠀⣤⣤⢠⣤⣤⣤⣤⣤⣤⣤⣤⡄⢠⣤⣤⣤⣄⠈⢳⡀⠀⠀⠈⠀⠘⣆⠀⠀⠀⠀⠈⣿⣿⢿⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⢸⣿⣿⡆⣿⣿⠀⣿⣿⠀⣿⣿⡇⣿⣿⠈⢹⣿⣿⠉⢹⣿⣿⠉⠁⢸⣿⡏⣿⣿⡆⢠⡙⠀⠀⠐⡀⠀⠸⣦⡠⢀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣼⣿⣿⣷⣿⣿⠀⣿⣿⠀⣿⣿⣿⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⣶⡆⢸⣿⡷⣿⣟⠀⢀⠙⠲⠤⣼⣧⣀⠘⢻⣿⣷⣅⣢⣄⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⡏⢿⣿⣿⡏⠀⣿⣿⠀⣿⣿⢻⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⠀⠀⢸⣿⡇⣿⣿⡇⢸⣿⣤⣀⡉⠭⠁⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣽⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠸⠿⠿⠇⠸⠿⠿⠇⠰⠿⠿⠀⠿⠿⠘⠿⠿⠀⠸⠿⠿⠀⠸⠿⠿⠿⠇⠸⠿⠇⠿⠿⠇⠘⣿⣿⣿⣿⣶⣦⣆⠀⠀⠀⠙⢿⣿⣿⣿⣿⣯⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠻⠿⠿⠛⠛⠳⠶⢖⡀⠐⠖⠒⠒⠲⠲⠶⠖⠂⠀⠐⠶⠖⠂⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠙⠛⢿⣿⣿⣇⡀⠀⠀⠈⠻⣿⣿⣿⢿⣯⡛⢿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣶⣿⢿⣿⣆⠈⠃⢠⣾⡿⢿⣷⡆⢠⣾⣿⢿⣷⡄⢸⣿⣿⡇⣼⣿⣿⡇⣿⣿⡇⢸⣿⣇⢸⣿⡇⣰⣾⡿⣿⣶⡀⢹⣿⣿⣷⡂⠀⡀⠀⠹⣿⣿⡆⠈⠉⠃⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣿⣿⣬⡙⠋⣴⡆⢸⣿⡇⢸⣿⡇⢸⣿⡇⢸⣿⡇⢸⣿⣿⣧⣿⣿⣿⡇⣿⣿⡇⢸⣿⣿⣼⣿⡇⣿⣿⡇⠿⠿⠇⢸⣿⣿⣿⣿⣿⠈⡄⠀⠸⣿⣿⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣈⣛⢿⣿⣦⠸⡇⢸⣿⡇⢠⣤⡄⢸⣿⡇⢸⣿⡇⢸⣿⡿⣿⣿⢹⣿⡇⣿⣿⡇⢸⣿⢿⣿⣿⡇⣿⣿⡟⣿⣿⡇⠈⣿⣿⣿⣿⣿⣧⣾⣀⣼⢿⣿⣇⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣿⣿⣨⣿⣿⢀⡇⢸⣿⣧⣸⣿⡇⠸⣿⣧⣼⣿⡇⢸⣿⡇⣿⣿⢸⣿⡇⣿⣿⡇⢸⣿⠘⣿⣿⡇⢻⣿⣇⣿⣿⡇⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣛⣛⣠⣌⣙⣛⣋⣡⣾⣿⣤⡉⠛⠛⠉⠀⠀⠉⠛⠛⠉⠀⠘⠛⠃⠙⠃⠘⠛⠁⠙⠛⠃⠘⠛⠀⠙⠛⠁⠀⠙⠛⠉⠛⢃⣰⣿⣿⣿⣿⣿⣿⠿⠿⣹⣿⣿⣿⡇⠀⠀
⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣶⡆⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣶⠀⠈⠛⢿⣿⠻⣿⣿⣷⡶⢲⣾⣿⣿⣿⡇⠀⠀
⣇⣆⣲⣶⣀⣶⢌⣡⣰⣶⣆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⢀⣠⣤⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣦⢠⣿⠀⠉⡿⢟⠀⢸⣿⣿⣿⣿⠀⠀⠀
[69A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣏⣪⣼⣿⡛⢃⠐⢀⠞⣁⣿⡷⢔⡃⣪⢿⣪⣿⡿⢿⣵⣿⣿⣿⡞⡃⢱⠇⠨⠂⠀⠀⡄⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠗⠀⠉⠙⠛⠻⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣫⣴⣸⣧⠰⢋⣞⢿⡅⣔⡷⠧⢾⠟⢯⣼⡿⢻⣿⠋⢧⠨⢲⢎⣣⣺⠥⢠⠤⠀⠀⠀
⢿⣿⣿⣿⣿⣿⣿⣷⡯⠛⡋⠀⠘⠡⡄⡐⣧⣴⡀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡆⢁⡁⡀⣿⣶⣧⣷⣟⣸⣚⢃⠀⠀⠐⠐⠈⠇⠄⢲⣳⣾⡟⣟⣾⡝⠞⡀⠀⠀⠀
⠀⠘⢿⡿⡿⠿⣛⣵⣶⣤⡀⠀⠂⢀⣹⠅⠈⢻⣿⡇⠹⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇⠴⠛⣭⡿⣿⣏⣎⣟⠂⠀⠁⠠⠄⠠⣀⢀⣮⣾⣽⣇⠞⠇⡛⣦⠄⠛⠀⠉
⠀⠀⢸⡗⣿⣿⣿⣿⣿⣿⠣⣷⠀⠀⣿⣷⣿⣿⣿⡇⠀⠀⠐⣳⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⢀⣉⠿⣽⣷⡟⢍⡀⠀⠀⡀⣡⠒⡇⠫⡝⡿⠏⠁⢀⠁⠒⠚⢴⣿⠀⢀
⠀⠀⣿⣿⣾⣿⣿⣿⣿⣿⣧⡉⠀⢹⣿⠺⣹⣿⣿⡇⠀⠀⣀⠚⡟⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⢞⣿⣟⣟⠃⠀⠀⠀⠐⠨⣳⣿⡀⠉⠀⠀⠀⣼⣷⡹⣿⣷⣿⣋⣄
⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠋⣶⣾⣿⣿⣿⣿⣿⡗⢀⣼⡥⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠉⠀⠀⠈⠙⠛⢷⣦⣕⡀⠬⠑⡓⢠⣔⠀⡐⠀⠀⠋⣙⢛⠜⢻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⡻⠙⢻⣿⣿⣿⣿⣤⣌⠋⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢈⠀⠨⣿⡏⠙⢑⠀⠀⠽⠿⠝⠇⠧⠈⠉⢻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⠋⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣈⣿⠣⡌⠉⠀⢀⡚⠃⠀⠠⢈⠡⠂⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢀⣾⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⡏⢐⡮⣲⠀⠈⣒⣤⣶⣄⠀⠉⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡁⠤⠰⢀⢈⢉⣭⣾⣿⣷⠮⢸⢲
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠨⢋⠘⡋⠀⣻⠟⠿⢛⣿⣷⡎⠿⠒
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠁⠀⠈⠀⢀⣼⣿⠿⢿⡁⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢀⡀⠀⢀⠀⠐⠒⡿⢿⣷⡶⠂⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠀⠂⠀⠀⠀⠀⢀⢀⠨⢋⡕⠀⠀
⣿⣿⣿⣿⣿⣿⠿⠛⠉⠉⢻⣿⣿⣿⣿⣿⣿⠟⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣅⠀⠀⠀⠀⠀⠀⡀⣶⠉⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣉⣁⡀⢸⣿⣿⣿⣿⣿⣷⣜⠀⠁⠀⡷⡂⣦⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⢀⣤⠀⠀⠀⣴⣾⠿⠛⠿⣯⡿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣄⢰⣾⣯⣧⡤⠁⠀⠐⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⣾⣿⠇⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⡒⠉⠘⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠰⡿⠁⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡤⣒⡬⠓⠀⠐⣷⠈⣩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢛⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠻⠇⠈⣿⣿⣿⣿⣿⣿⣿⣴⡐⣚⠻⢛⠛⢒⠂⠐⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀⣨⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⢳⣶⣾⣾⣿⣻⣿⣿⣿⣿⡗⠀⠀⠀⣲⠶⢦⠄⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣗⠯⣤⣤⣴⣿⢿⡇⢹⣐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠙⠛⠿⠿⠿⠿⠿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠛⠓⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣆⠀⠠⠄⢡⣼⡇⣻⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢿⠁⠀⠀⠀⠀⠀⠀⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣴⣿⢸⣿⢏
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⡿⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡟⠘
⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⡏⠘⠋⠀⢠⣄⣄⣤⣤⣶⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠂
⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣭⣶⣶⡆⠀⠀⠀⠉⠉⠉⠻⢿⣿⣿⣿⣷⠀⢀⣠⣴⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡠
⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⡈⠿⣿⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠉⠑⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠃⠀⢀⠸⢿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⡀⠀⠀⠀⠀⢀⣰⡞⠠⠐⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣧⠀⠀⠀⠀⠈⣿⣿⣿⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢿⣿⣟⣻⡏⠀⣷⣦⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠸⣿⣿⣿⣿⠟⠿⠀⠈⢳⣦⡄⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢻⣿⣿⣧⣀⣄⡀⠀⠛⢿⡿⠀⠀⠀⠀⠀⠛⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⢿⣿⣿⣿⣿⣿⡄⡄⣼⠇⠀⠀⠀⠀⠀⠀⡿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠈⢿⣿⣿⡏⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠈⢻⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⣼⡄⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣤⣴⣄⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠘⢿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣼⣷⠀⠀⠀⠀⠀⠈⢿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣴⣿⣿⣧⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠵⣵⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣝⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠹⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠇⠀⠀⠀⠹⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣇⣀⣰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢦⣤⣼⣧⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⠀⠀⠈⠙⣿⠳⣄⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⣤⣄⢡⣤⣤⠉⣤⣤⡄⣤⣤⠀⣤⣤⠀⣤⣤⢠⣤⣤⣤⣤⣤⣤⣤⣤⡄⢠⣤⣤⣤⣄⠈⢳⡀⠀⠀⠈⠀⠘⡆⠀⠀⠀⠀⠘⣿⠿⣯⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⢸⣿⣿⡆⣿⣿⠀⣿⣿⠀⣿⣿⡇⣿⣿⠈⢹⣿⣿⠉⢹⣿⣿⠉⠁⢸⣿⡏⣿⣿⡆⢠⡙⠀⠀⢔⠀⠀⠻⣶⡠⢀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣼⣿⣿⣷⣿⣿⠀⣿⣿⠀⣿⣿⣿⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⣶⡆⢸⣿⡷⣿⣟⠁⢈⠙⠳⠤⣷⣧⡀⠀⠿⣿⣶⣬⣲⣴⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⡏⢿⣿⣿⡏⠀⣿⣿⠀⣿⣿⢻⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⠀⠀⢸⣿⡇⣿⣿⡇⢸⣿⣄⣀⡉⠏⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠸⠿⠿⠇⠸⠿⠿⠇⠸⠿⠿⠀⠿⠿⠘⠿⠿⠀⠸⠿⠿⠀⠸⠿⠿⠿⠇⠸⠿⠇⠿⠿⠇⠘⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠙⢿⣿⣿⣿⣿⣾⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠻⠿⠟⠛⠛⠳⢶⣶⠀⠤⠖⠒⠒⠢⠶⡶⠖⠂⠀⠐⠶⠖⠂⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠙⠛⢿⣿⣶⣆⣀⠀⠀⠈⡻⣿⣿⣿⢿⣯⡙⠿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣶⣿⢿⣿⣆⠈⠃⢠⣾⡿⢿⣷⡆⢠⣾⣿⢿⣷⡄⢸⣿⣿⡇⣼⣿⣿⡇⣿⣿⡇⢸⣿⣇⢸⣿⡇⣰⣾⡿⣿⣶⡀⢹⣿⣿⣿⣃⠀⡀⠀⠙⣿⣿⡀⠀⠈⠁⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣿⣿⣬⡉⠋⣤⡆⢸⣿⡇⢸⣿⡇⢸⣿⡇⢸⣿⡇⢸⣿⣿⣧⣿⣿⣿⡇⣿⣿⡇⢸⣿⣿⣼⣿⡇⣿⣿⡇⠿⠿⠇⢸⣿⣿⣿⣿⡧⠀⡀⠀⢹⣿⣷⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣈⣛⢿⣿⣦⠸⡇⢸⣿⡇⢠⣤⡄⢸⣿⡇⢸⣿⡇⢸⣿⡿⣿⣿⢹⣿⡇⣿⣿⡇⢸⣿⢿⣿⣿⡇⣿⣿⡟⣿⣿⡇⠈⣿⣿⣿⣿⣿⣤⣟⣠⣏⣿⣿⡆⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣿⣿⣨⣿⣿⢀⣇⢸⣿⣧⣸⣿⡇⠸⣿⣧⣼⣿⡇⢸⣿⡇⣿⣿⢸⣿⡇⣿⣿⡇⢸⣿⠘⣿⣿⡇⢻⣿⣇⣿⣿⡇⢀⣼⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣛⣛⣠⣌⣙⣛⣋⣡⣾⣿⣤⡉⠛⠛⠉⠀⠀⠉⠛⠛⠉⠀⠘⠛⠃⠙⠃⠘⠛⠁⠙⠛⠃⠘⠛⠀⠙⠛⠁⠀⠙⠛⠉⠛⢃⣰⣿⣿⣿⣿⣿⣟⡟⠻⣿⣿⣿⣿⡂⠀⠀
⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣦⠀⠀⠀⠀⠋⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣶⣀⡈⠙⢿⡏⠙⣿⣿⣿⠧⢶⣿⣿⣿⣿⠀⠀⠀
⣇⣆⣲⣶⢀⣶⢌⣡⣰⣶⣆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⢦⣼⡧⡀⢁⡍⡋⠀⢠⣿⣿⣿⡟⠀⠀⠀
[69A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣦⣼⣿⡝⠃⠀⢀⣋⣠⣟⡴⢔⠃⣽⢻⣫⣿⡿⢽⣛⣿⣿⣿⡜⡡⠠⠆⠠⠀⠄⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⠙⠛⠿⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣣⡦⣼⣧⠸⢋⣞⣿⢁⣜⡧⠷⠾⠛⣯⣮⡟⣿⡿⠫⡄⠨⢲⢛⡇⣺⠤⣠⠠⠀⠀⠀⠄
⣿⣿⣿⣿⣿⣿⣶⡝⠟⠛⠀⠰⢠⡄⡰⣆⣤⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡂⣁⡀⠀⣷⣾⣦⣿⡏⣺⣚⠊⠀⠀⠃⠀⠈⠅⠄⢴⢳⣾⡿⣻⣧⡆⠘⡀⠀⠀⢀⠀
⠹⣿⣿⣿⡿⣟⣭⢦⣠⠀⠐⠀⠀⠳⡁⠙⢻⣿⡆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡇⠱⠛⣬⡿⣿⡧⣖⣟⠂⠀⠀⠄⠀⠀⠀⢂⣎⣮⣿⣃⠘⠕⡊⣤⡕⠓⠑⢥⡴
⠀⣼⣤⣿⣶⣿⣿⣿⣿⢆⣆⠀⠈⣿⣷⣾⣿⣿⡏⠀⠀⠰⣾⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢠⣉⠿⣼⣧⠟⢍⡀⠀⠀⠀⡥⠘⠣⢫⠟⡺⡇⠀⢀⠠⠲⢛⣴⡭⠀⡀⠿
⠐⣿⣳⣽⣿⣿⣿⣿⣿⣆⠉⠀⢲⣿⠾⢻⣿⣿⡇⠀⠀⡀⠾⣗⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡞⡟⠛⣗⠁⠀⢀⠀⡐⢁⣳⣷⠌⠋⠁⠁⠀⣾⣮⢻⣿⣶⣮⣣⣨⣭
⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⣶⣾⣿⣷⣿⣿⣿⡧⠀⣰⣥⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠒⠶⢶⣤⣀⣴⠀⡬⠑⡒⢠⡖⠀⠀⠃⠀⠛⡛⠃⠝⢿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣖⠿⡛⢻⣿⣿⣿⣿⣡⣘⠛⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⢀⣀⠀⠨⣿⡉⠙⢐⠀⠀⠽⠿⠹⡛⡎⡈⠙⠻⡱
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⡿⢿⠟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⣸⣿⢦⡍⠋⠀⢀⡚⠂⠀⠡⣘⠤⠄⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⢀⣴⣷⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡏⢐⡭⡲⠀⠈⣒⣤⣦⡀⠀⠁⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠀⠦⠰⠀⠉⢉⣥⣿⣿⣶⠮⢣⢶⠤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢋⢘⡅⠀⣿⠟⠿⢛⣿⣶⠺⠷⡗⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⢀⣾⡿⠿⣭⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⢀⠀⠐⠊⡿⣿⡷⡦⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⠀⠀⢀⢀⠩⢡⡁⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣅⠀⠀⠀⠀⠀⠀⡀⡇⠋⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠋⠉⠉⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡀⠀⣠⣿⣿⣿⣿⣷⣜⠀⠁⢀⡷⣢⣦⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡤⣴⣶⣦⣄⢻⣿⣿⣿⣿⣿⣿⣿⣄⢰⣿⣯⣧⠄⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠉⠉⠀⠀⠀⢀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣴⡇⠀⠀⣠⣾⡿⠹⠋⠗⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⡲⠁⠐⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⠀⢰⣿⠏⠀⠀⠀⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣄⣐⡬⠚⠀⠒⣷⢀⡡⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⢸⠛⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣴⡐⣚⠻⢓⠚⣒⠀⠂⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠭⠝⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡌⠛⠀⣈⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣲⠶⢦⠄⠄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠛⢢⣸⣿⣿⣷⣿⣿⣿⣿⣗⠯⣤⣤⣴⡿⣿⡇⣙⣞⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣿⡟⠻⠿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠠⠀⢠⣾⡿⣻⣍⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠁⠀⠀⠀⠀⠀⠀⠀⢿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠁⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣼⣿⢸⣿⢏⠅
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡄⠀⠀⠈⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⢠⢠⣮⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡟⠚⠀
⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⣿⡿⠛⠀⠀⠀⠀⠀⠀⣨⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠁
⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⣴⡟⠀⠀⠺⠾⠶⣶⣾⣿⣿⣿⣿⣿⠀⠀⢀⣠⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⢽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡰⠀
⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢠⣿⣯⣿⡿⠋⠀⠀⠀⠀⠀⠀⠙⠹⣿⣿⣿⣿⣦⣾⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⢺⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⡈⢫⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣤⠄⠁⣨⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣧⠀⠀⠀⠀⠘⣿⣶⣤⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣿⣿⠿⡿⠂⣴⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢸⣷⣾⣿⣶⢾⡟⠁⢳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢿⣿⣿⠀⠘⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀⠀⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠘⣿⣿⣿⣿⣷⣄⢀⢈⣿⠈⠀⠀⠀⠀⠀⢰⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠘⣿⣿⣿⠛⠋⠈⠘⠋⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣠⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠘⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣆⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡄⠒⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣆⠀⠀⠀⠀⢘⣿⡄⠀⠀⠀⠀⠀⢻⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣀⣀⣼⣿⣷⠀⠀⠀⠀⠀⠈⢿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⠀⠉⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⡟⠀⠀⠘⠿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣀⠀⠀⠀⠀⠹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⠠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢴⣤⣤⣷⡌⠿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⡀⠀⠀⠉⠻⡟⢦⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⣤⣄⢡⣤⣤⠉⣤⣤⡄⣤⣤⠀⣤⣤⠀⣤⣤⢠⣤⣤⣤⣤⣤⣤⣤⣤⡄⢠⣤⣤⣤⣄⠁⢄⠀⠀⠀⠁⠀⢷⠀⠀⠀⠀⠀⢿⠿⣻⣽⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⢸⣿⣿⡆⣿⣿⠀⣿⣿⠀⣿⣿⡇⣿⣿⠈⢹⣿⣿⠉⢹⣿⣿⠉⠁⢸⣿⡏⣿⣿⡆⢈⠃⠀⢀⠂⡢⠸⢷⣖⡄⡀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣼⣿⣿⣷⣿⣿⠀⣿⣿⠀⣿⣿⣿⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⣶⡆⢸⣿⡷⣿⣟⠁⠈⠛⠶⣾⣷⣄⠀⡺⣿⣿⣦⣕⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⡏⢿⣿⣿⡏⠀⣿⣿⠀⣿⣿⢻⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⠀⠀⢸⣿⡇⣿⣿⡇⢸⣷⣄⣈⠻⠂⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠸⠿⠿⠇⠸⠿⠿⠇⠰⠿⠿⠀⠿⠿⠘⠿⠿⠀⠸⠿⠿⠀⠸⠿⠿⠿⠇⠸⠿⠇⠿⠿⠇⢸⣿⣿⣿⣿⣷⣶⡀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠿⠟⠛⠛⠳⢶⣶⠐⡓⠶⠒⠒⠓⠶⡶⠶⠒⠒⠢⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠛⠛⢿⣿⣴⣄⡀⠀⠀⠘⣿⣿⣿⠟⠿⣏⡛⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣶⣿⢿⣿⣆⠀⠆⢠⣾⡿⢿⣷⡆⢠⣾⣿⢿⣷⡄⢸⣿⣿⡇⣼⣿⣿⡇⣿⣿⡇⢸⣿⣇⢸⣿⡇⣰⣾⡿⣿⣶⡀⢻⣿⣿⣷⢀⢢⡀⠈⢿⣿⣷⠀⠀⠉⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣿⣿⣬⡙⠋⣀⡀⢸⣿⡇⢸⣿⡇⢸⣿⡇⢸⣿⡇⢸⣿⣿⣧⣿⣿⣿⡇⣿⣿⡇⢸⣿⣿⣼⣿⡇⣿⣿⡇⠿⠿⠇⢸⣿⣿⣿⣿⡟⢃⡀⠈⣿⣿⡆⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣈⣛⢿⣿⣦⠸⡇⢸⣿⡇⢠⣤⡄⢸⣿⡇⢸⣿⡇⢸⣿⡿⣿⣿⢹⣿⡇⣿⣿⡇⢸⣿⢿⣿⣿⡇⣿⣿⡟⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣷⣿⣻⣿⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣿⣿⣨⣿⣿⢀⣇⢸⣿⣧⣸⣿⡇⠸⣿⣧⣼⣿⡇⢸⣿⡇⣿⣿⢸⣿⡇⣿⣿⡇⢸⣿⠘⣿⣿⡇⢻⣿⣇⣿⣿⡇⢠⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡇⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣛⣛⣠⣌⣙⣛⣋⣡⣾⣿⣦⣉⠛⠛⠉⡀⠀⠉⠛⠛⢉⠀⠘⠛⠃⠙⠃⠘⠛⠁⠙⠛⠃⠘⠛⠀⠙⠛⠁⠀⠙⠛⠉⠛⠃⣸⣿⣿⣿⣿⣿⣿⢟⢻⣿⣿⣿⡇⠀⠀⠀
⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣧⡄⠀⠀⠀⠁⠖⠀⠀⠀⠈⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣶⡀⠈⠹⢿⡏⢿⣿⣿⡿⢯⣺⣿⣿⣿⡇⠀⠀⣲
⣇⣆⣲⣶⢁⣶⢌⣡⣰⣶⣆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡧⣼⠇⠈⣸⠻⠃⢲⣿⣿⣿⣿⠇⠀⠀⠈
[69A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣦⣼⣿⡝⠃⠀⢀⣏⣀⠿⡴⣔⠃⣺⢿⢟⣿⣿⢛⡽⣷⣿⣯⠼⠀⢠⠀⣢⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⠈⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣣⡦⣼⣦⠸⢋⣞⣯⣃⣔⡆⠳⢾⠿⣯⣭⡾⣿⣿⢯⡍⠠⢄⠷⡦⣴⡀⢀⡈⠀⠠⢀⠀⠀
⣿⣿⣿⣿⣿⣯⣿⠿⠿⠈⠠⠂⡀⠀⣄⣀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡆⢁⡀⠀⣷⣾⣦⣼⡟⣿⣲⠆⠀⠈⠇⠃⠙⡃⡈⢤⢮⣾⢾⢷⣇⣦⠡⠀⠀⠀⠀⡀⠀
⣿⣿⣿⣿⡿⣫⣥⡄⠁⠀⠄⠀⢳⠻⠸⢿⣷⣦⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠇⠱⠛⣭⡿⣿⣇⣎⠟⠂⠀⠀⠄⠀⠀⠀⢈⣎⣞⣻⢁⢹⡹⢕⣸⠺⠆⠐⢲⡦⢄
⣼⡝⣻⣧⣽⣿⣾⣻⣆⣠⠀⠀⣷⣧⣆⣾⣿⡟⠀⠉⠉⣽⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢠⣉⠿⣼⣧⡟⢙⡀⠀⠀⠀⡀⠰⠃⢛⠿⣚⡇⠁⠔⠪⠤⢗⣰⣆⠀⠸⣧⣃
⣿⢧⣻⣿⣽⣿⣿⣿⣇⠙⠀⠠⣿⣽⡿⣿⣿⣿⠀⠀⠀⢜⣯⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡞⡿⠟⣗⠁⠀⠀⠀⠰⢅⣽⡿⠈⠊⠁⠇⠀⣼⣜⢶⣶⣼⣷⢢⢹⣈⣑
⣿⣿⣿⣿⣿⣿⣿⣿⡟⠗⣤⣼⣿⣧⣶⣿⣿⣿⠀⢠⢐⠒⠘⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡦⠖⣣⡀⠀⡠⡐⡨⠐⡺⢡⡤⠀⠀⠃⠀⠛⠛⠏⡻⣿⣿⣿⣿⣿⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣷⡤⢿⠻⢿⣿⣿⣿⣿⠋⠀⡿⠋⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠓⠈⠙⠳⢶⣦⣌⠀⠀⠀⠨⢿⠉⠙⠀⠀⢀⡾⣟⢺⠰⡈⠙⠛⡿⢱⠦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣴⣿⣿⣿⣿⣿⣿⠂⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦⡀⢸⣿⢇⡒⠋⠀⠐⠾⠂⠀⠀⢑⣠⡄⠁⠂⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⢁⢠⣧⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣟⢠⡤⠦⠀⠈⣧⣄⣤⠀⠀⠂⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⢈⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠗⠈⣁⠠⠀⠘⢉⣡⣿⣷⣤⡆⠦⣤⡀⠠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⡰⠂⠁⣾⡿⠿⢟⣿⣷⢲⣶⠇⠂⠸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠁⠀⠀⠀⠀⣿⡿⢿⣓⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣿⣷⡵⡆⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠻⣃⡅⠀⠀⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡆⠋⠀⠀⠀⠀⠀⠀⠠⠥
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣷⣐⠂⠀⢀⡷⢢⣥⡄⠀⠀⠀⠠⠀⠀⠀⠀
⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠋⠉⠉⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⣾⣿⣿⣿⣿⣿⣿⡀⢨⣿⣿⣧⠄⠈⠀⠂⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠸⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⠀⢤⣤⣶⠿⣶⢦⣹⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠟⠃⡀⣀⡲⠀⠀⠐⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⢀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⡇⠀⠀⣠⣼⡋⠚⠋⠚⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣴⡨⠒⠀⠲⡇⠉⡥⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⢠⣿⠏⠀⠀⠀⠐⠂⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡐⣘⠿⠖⠪⢒⠀⠈⠂⠷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⢼⠃⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡋⠙⢿⣿⣿⣿⣿⣿⡿⠀⠁⢀⣠⣤⣤⠀⠄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠊⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠿⠈⠓⠀⠈⠻⣿⣿⣿⣿⣇⠾⣦⣠⣴⡷⣿⡏⣍⣸⢴⡀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⣴⣶⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⠃⠀⠠⣼⣿⣵⣹⣿⣿⣷⡄⠀⠠⠌⢡⣽⠻⣿⣍⠄⠁
⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠉⠩⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣦⣦⣤⣾⣿⢸⣿⢏⠤⠀
⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠛⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡏⠎⠀⠀
⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⠇⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠋⠀⠀⠀⠁⠀⠀⠀⠀⢠⢀⢅⢞⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠁⡁⠀
⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠟⠁⣀⣄⣀⣀⣠⣤⣶⣿⣿⣦⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠿⠯⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡠⠀⠀
⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣿⣿⠀⠀⠈⠙⠛⠿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣶
⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠿⠻⠻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠠⡛⢻⠃⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣶⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽
⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢀⣐⢙⣿⠓⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠘⣿⣿⢋⢀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣥⣴⣤⣨⣿⠟⢳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢸⣿⠟⠁⠏⠀⠀⣿⣿⣷⣤⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⣿⣷⣴⣶⣄⠀⠉⢻⡟⠫⠄⠀⠀⠀⠀⠸⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠸⣿⣿⣿⠿⠆⠆⠿⠃⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡀⠀⣀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣧⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣾⣿⣦⣄⠀⠀⠀⠀⠀⢶⣷⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢀⣿⣿⣧⠀⠀⠀⠀⠀⠸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⣵⣿⠏⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠏⠀⡀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠋⢀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣠⣤⣤⣸⣆⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠈⠹⣿⢳⡀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⣤⣄⢡⣤⣤⠉⣤⣤⡄⣤⣤⠀⣤⣤⠀⣤⣤⢠⣤⣤⣤⣤⣤⣤⣤⣤⡄⢠⣤⣤⣤⣄⠀⡀⠀⠀⠈⠀⠸⡆⠀⠀⠀⠀⠸⡿⢟⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⢸⣿⣿⡆⣿⣿⠀⣿⣿⠀⣿⣿⡇⣿⣿⠈⢹⣿⣿⠉⢹⣿⣿⠉⠁⢸⣿⡏⣿⣿⡆⠘⠀⠀⠐⡀⠀⠹⣶⡠⢀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣼⣿⣿⣷⣿⣿⠀⣿⣿⠀⣿⣿⣿⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⣶⡆⢸⣿⡷⣿⣟⠁⠐⠶⠤⣿⣧⠀⠘⢿⣿⣷⣌⣢⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⡏⢿⣿⣿⡏⢀⣿⣿⠀⣿⣿⢻⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⠀⠀⢸⣿⡇⣿⣿⡇⢰⣦⣀⠙⠇⠅⠀⠀⠙⠿⣿⣿⣿⣿⣿⡷⣟⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠸⠿⠿⠇⠸⠿⠿⠇⠸⠿⠿⠀⠿⠿⠘⠿⠿⠀⠸⠿⠿⠀⠸⠿⠿⠿⠇⠸⠿⠇⠿⠿⠇⢸⣿⣿⣿⣿⣷⣆⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠻⠿⠿⠛⠛⠳⢶⣶⠶⠦⠖⠒⠀⠳⢶⡴⠖⠒⠒⠓⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⢿⣷⣧⣄⠀⠀⠀⢿⣿⣿⣟⠿⢯⣝⠻⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣶⣿⢿⣿⣆⠉⠀⢠⣾⡿⢿⣷⡆⢠⣾⣿⢿⣷⡄⢸⣿⣿⡇⣼⣿⣿⡇⣿⣿⡇⢸⣿⣇⢸⣿⡇⣰⣾⡿⣿⣶⡀⢹⣿⣿⣇⣀⣄⠒⢻⣿⣿⡄⠀⠀⠀⠀⢻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣿⣿⣬⡉⠋⠠⠀⢸⣿⡇⢸⣿⡇⢸⣿⡇⢸⣿⡇⢸⣿⣿⣧⣿⣿⣿⡇⣿⣿⡇⢸⣿⣿⣼⣿⡇⣿⣿⡇⠿⠿⠇⢸⣿⣿⣿⣷⠋⡂⢀⣹⣿⣿⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣈⣛⢿⣿⣦⠘⡇⢸⣿⡇⢠⣤⡄⢸⣿⡇⢸⣿⡇⢸⣿⡿⣿⣿⢹⣿⡇⣿⣿⡇⢸⣿⢿⣿⣿⡇⣿⣿⡟⣿⣿⡇⢸⣿⣿⣿⣿⣾⣿⣿⣎⣻⣿⡆⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣿⣿⣨⣿⣿⢀⣇⢸⣿⣧⣸⣿⡇⠸⣿⣧⣼⣿⡇⢸⣿⡇⣿⣿⢸⣿⡇⣿⣿⡇⢸⣿⠘⣿⣿⡇⢻⣿⣇⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣛⣛⣠⣌⣙⣛⣋⣡⣾⣿⣦⣉⠛⠛⠉⠀⠀⠉⠛⠛⢉⠀⠘⠛⠁⠙⠃⠘⠛⠁⠙⠛⠃⠘⠛⠀⠙⠛⠁⠀⠙⠛⠉⠛⢃⣼⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⠀⠀⠀⠀
⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠐⠃⠀⠀⠛⡧⠏⠀⠀⠘⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⣦⡄⠙⢿⣿⡟⣿⣿⣿⡿⣿⣿⣿⣿⣿⠀⠀⢠⣦
⣇⣆⣲⣶⣁⣶⢌⣡⣰⣶⣆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣮⣽⠇⣐⣿⠻⠅⣿⣿⣿⣿⡏⠀⠀⠀⢹
[69A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣦⣢⣤⣿⡛⢒⠠⠀⡺⣁⣿⢇⣈⠎⢘⠿⠽⣿⣿⣿⣻⡷⣿⣿⣹⠏⠁⡁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢫⣵⢸⣧⠠⠛⣿⢯⡁⣀⣷⣏⢴⡿⣿⣻⣼⣻⣿⡟⡛⠂⣀⣪⡄⣨⠄⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣟⣿⣿⣿⠟⠋⡀⠀⠀⣈⠉⠋⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡱⢈⡨⠀⢼⣶⣯⣧⣟⢡⡖⠆⠂⠈⠩⠩⠘⡏⠐⣁⢔⣸⣴⣦⡞⣍⢚⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡿⣟⠀⠀⠀⡀⠀⢾⡰⠹⣶⣧⣄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣘⠷⠀⡟⢫⡿⣻⢿⣬⡟⢌⠀⠀⠀⡀⠀⠀⡁⡲⢼⢻⡎⠺⠿⡣⢀⢤⡄⠄⢤⣆⡠⠀
⡟⢻⣛⣹⣾⣿⣷⣇⢀⠀⠀⢤⣵⣀⣤⣿⣿⠇⠙⠛⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⡈⣹⣕⣿⡹⠇⡀⠀⠀⠀⢀⢠⡆⡺⣻⠼⡻⠖⠨⢁⣢⣯⢣⢄⠀⠸⢏⠎⢠
⣏⡿⣿⣿⣿⣿⣿⣏⠺⠂⠀⣰⣟⣿⣿⣿⣿⠀⠀⠀⠹⣿⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣦⣾⠿⢳⠆⠁⠀⠀⠀⠙⢢⣶⠈⠗⠋⠃⠀⣰⣔⣶⣬⣝⣯⢆⢲⠛⠻⣸
⣿⣿⣿⣿⣿⣿⣿⣿⢦⢀⣠⣿⣏⣡⣿⣿⣿⡀⠀⡀⢄⠙⠯⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⡄⣿⡀⠀⢀⠃⢔⠂⠭⢉⡀⠀⠀⠀⠀⠿⠿⡎⢻⣿⣿⣾⣾⣿⡿⡽
⣿⣿⣿⣿⣿⣿⣿⣿⣀⣼⡿⣿⣿⣿⣿⣿⡿⠃⢰⡇⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠃⠉⠁⠀⠀⢑⣾⠟⠲⠢⠀⠀⣤⣶⣶⢥⠝⠹⠿⣿⢫⣅⠡
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣅⣀⣿⣿⣿⣿⣵⣶⣬⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠒⠒⠲⣤⣀⡀⠀⠀⠐⣿⠏⡲⠖⠀⠀⠴⠅⠀⠃⠱⣀⠀⠁⠎⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⠛⣻⡀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠷⠜⢿⡿⠀⣑⢤⠀⠐⡤⡠⣄⠀⠈⠍⠁⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠄⣦⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⣷⠀⢉⢠⠀⠐⠛⣛⣽⣧⣄⣄⢄⣤⠀⢀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠱⠄⠀⣶⡾⣿⡟⣿⣭⠤⣦⡮⠀⠰⠮
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠃⠀⠙⠀⠀⣼⣿⣿⡒⠀⠀⠀⠀⣪
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣿⣿⣦⣟⠀⠀⠀⠀⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠈⠀⠀⠀⠉⢙⢋⠇⠀⠀⠀⠀⠐
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡶⠚⠀⠀⠈⠁⠀⠀⠐⠏⢴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠆⠂⠀⣠⠆⣥⡌⠀⠀⠀⠀⠀⠀⠠⠀⣉
⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣶⡆⠀⣷⣗⣇⡥⠋⠀⠀⠀⠀⠀⠀⠀⣝
⡇⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⡿⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠄⢀⣾⣿⣿⣿⣿⣿⣿⣮⣿⣿⡿⠃⠀⠈⢤⠂⠀⠀⠈⡃⢻
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣔⠒⣶⣦⣻⣿⣿⣿⣿⣿⣿⣿⡏⣁⢄⣐⡲⠀⠳⣦⠠⠋⢠⠀⡆
⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⡇⠀⠀⠀⣠⡌⠅⠀⠬⣿⢦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠹⠿⠖⠠⠄⠉⠀⠁⠾⠇⠛
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⣼⡿⠁⠀⠀⠀⠊⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⠀⢨⣤⣌⡀⡁⠀⠀⠀⠀
⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⢸⠿⠀⠀⠀⠀⠀⠀⢸⣷⠿⣿⠫⠿⡿⣿⣿⣿⣿⡿⡶⣆⣀⣠⣶⣾⡇⠲⡼⢠⡄⠀
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⢭⣛⠻⢿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡙⠷⠀⠈⢻⣿⣿⣿⣿⡄⠠⠨⠀⢉⣽⡧⢿⣟⠂⠀⢐
⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢼⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⢰⣶⣏⢻⣿⣿⣿⣴⣤⣌⣺⣿⢳⣿⡟⡂⠀⠀
⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣽⣽⢩⣿⣿⣿⣿⣿⣿⣿⣿⣾⡟⠸⠀⠐⠀
⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠲⢖⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠂⠡⠁⠀
⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⠄⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠙⠊⠄⠀⠀⠀⠀⠀⠤⣤⢬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⠀⠀⠈
⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⠏⠁⣀⣀⡀⢀⣀⣠⣼⣷⣦⣴⣶⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⣱⣥⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣴⣤
⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠉⣿⣿⡏⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡸⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢼⣯⠀⠀⣿⡟⠁⠀⠀⠀⠀⠀⠨⠿⣿⣿⣿⣿⣟⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢴⣦⠄⢠⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣔⣐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢠⣾⠃⠀⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢘⣅⠁⢾⣿⡿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠈⣿⠟⢻⠏⠀⢙⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢧⣀⣈⡀⠀⠸⠿⣿⢿⣗⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠸⣿⣿⣿⣦⢠⢠⣿⠀⠉⠁⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⢻⣿⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡄⢀⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣤⣄⠀⠀⠀⠀⠀⠀⢀⣼⣿⡀⠀⠀⠀⠀⠸⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣧⡀⠀⠀⠀⢰⣿⣿⣧⠀⠀⠀⠀⠀⢻⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣦⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⣠⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡓⡋⣻⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡇⠀⠐⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠚⠀⠀⢠⣀⣀⣯⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣾⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠉⠻⣿⡷⡄⠉⠁⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢡⣤⣌⢡⣤⣤⠉⣤⣤⡄⣤⣤⠀⣤⣤⠀⣤⣤⢠⣤⣤⣤⣤⣤⣤⣤⣤⡄⢠⣤⣤⣤⣄⠀⠀⠀⠈⠃⠈⣆⠀⠀⠀⠀⠈⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⢸⣿⣿⡆⣿⣿⠀⣿⣿⠀⣿⣿⡇⣿⣿⠈⢹⣿⣿⠉⢹⣿⣿⠉⠁⢸⣿⡏⣿⣿⡆⠀⠀⠀⠀⣀⠸⣦⡠⣀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣼⣿⣿⣷⣿⣿⠀⣿⣿⠀⣿⣿⣿⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⣶⡆⢸⣿⡷⣿⣟⠁⠠⣄⣸⣶⡁⠀⢸⣿⣷⣅⣢⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⡏⢿⣿⣿⡏⠀⣿⣿⠀⣿⣿⢻⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⠀⠀⢸⣿⡇⣿⣿⡇⢀⡈⠘⠿⢃⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠸⠿⠿⠇⠸⠿⠿⠇⠰⠿⠿⠀⠿⠿⠘⠿⠿⠀⠸⠿⠿⠀⠸⠿⠿⠿⠇⠸⠿⠇⠿⠿⠇⣸⣿⣿⣶⣤⣦⡀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠻⠿⠿⠛⠛⠳⢶⣶⣤⠲⠆⠐⠊⠒⠆⡠⠖⠒⠒⠒⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⠛⠛⠛⢿⣝⣀⠀⠀⠀⠻⣿⣿⣿⠻⣯⡙⠻⣻⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣶⣿⢿⣿⣆⠈⠉⢠⣾⡿⢿⣷⡆⢠⣾⣿⢿⣷⡄⢸⣿⣿⡇⣼⣿⣿⡇⣿⣿⡇⢸⣿⣇⢸⣿⡇⣰⣾⡿⣿⣶⡀⢻⣿⡆⢀⢀⠀⠻⢿⣿⡆⠀⠈⠁⠀⢻⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣿⣿⣬⡉⠋⠀⠀⢸⣿⡇⢸⣿⡇⢸⣿⡇⢸⣿⡇⢸⣿⣿⣧⣿⣿⣿⡇⣿⣿⡇⢸⣿⣿⣼⣿⡇⣿⣿⡇⠿⠿⠇⢸⣿⣿⣿⡉⣇⠀⠸⣿⣿⡀⠀⠀⠀⠀⢧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣈⣛⢿⣿⣦⠀⡄⢸⣿⡇⢠⣤⡄⢸⣿⡇⢸⣿⡇⢸⣿⡿⣿⣿⢹⣿⡇⣿⣿⡇⢸⣿⢿⣿⣿⡇⣿⣿⡟⣿⣿⡇⢸⣿⣿⣿⣷⣿⣧⣰⢻⣿⣇⠀⠀⠀⠀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣿⣿⣨⣿⣿⢀⣇⢸⣿⣧⣸⣿⡇⠸⣿⣧⣼⣿⡇⢸⣿⡇⣿⣿⢸⣿⡇⣿⣿⡇⢸⣿⠘⣿⣿⡇⢻⣿⣇⣿⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣣
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣛⣛⣠⣌⣙⣛⣋⣡⣾⣿⣦⡉⠛⠛⠉⠀⠀⠉⠛⠛⢉⠀⠘⠛⠃⠙⠃⠘⠛⠁⠙⠛⠃⠘⠛⠀⠙⠛⠁⠀⠙⠛⠉⠛⢃⣼⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡇⠀⠀⠀⠹
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠠⠀⠀⠠⠿⡟⠟⠀⠀⠷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣤⡈⠙⢻⣿⣟⢻⣿⣿⣿⣳⣜⣿⣿⣿⠇⠀⠀⣦⣀
⣇⣆⣲⣶⢀⣶⢌⣡⣰⣶⣆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣶⡆⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣶⡦⢸⢯⠀⣩⠿⠗⢺⣿⣿⣿⣿⠀⠀⠀⠘⣿
[69A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣕⣤⣽⣿⠛⠆⠀⠀⠟⢰⣿⢅⡹⠋⢽⣟⢿⣿⣿⡿⣿⣴⣿⡇⡿⠛⠛⢨⠈⠀⠀⠐⠈⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣍⡆⣲⡄⠘⢾⢿⣕⠀⢱⡔⢣⣶⣾⠿⣭⡿⣿⣾⠿⠯⠁⠰⣊⠀⣂⠀⠀⠄⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠿⣿⣿⣿⠿⠟⠀⠉⠉⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣭⡎⡉⠅⢀⣮⣵⣛⣼⠟⣥⢥⠉⠀⠛⡛⡉⣿⡋⠌⢠⠍⣞⣽⣨⢓⠠⠒⠀⠀⠀⠂⠀⠀⠀
⣿⣿⣿⣿⣷⡯⠛⡋⠀⠐⠁⡆⢀⢳⣤⡄⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣄⢿⠆⢴⠿⣛⣿⣿⢧⢻⠧⠄⠀⠀⠀⠀⠈⠀⢈⢇⡿⡯⠩⣿⡞⡀⢅⣄⢀⣀⡠⠀⠀⢀
⠿⡿⠟⣫⣴⡶⣤⡀⠀⠀⠁⣙⡜⠈⣹⣿⣷⠘⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣕⠀⢠⠛⣞⢱⡟⣻⠀⠀⠀⠀⠀⠀⣠⠨⡺⣂⣷⡃⠀⡒⢈⣰⡃⣉⠠⠃⣿⢹⠀⣺
⢢⣿⣿⣿⣿⣿⣿⡧⡤⠀⠄⣽⢿⡷⣿⣿⣇⠀⠀⠀⢶⡯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡟⣺⣼⣿⠿⣄⠘⠀⠀⠀⠀⠧⡨⡌⢻⠴⠺⠀⢀⣄⢭⣍⣓⣿⣀⠠⡟⠿⣡⢿
⣽⣾⣿⣿⣿⣿⣿⣧⡀⠀⢠⣿⡟⠛⣿⣿⣿⠀⠀⢀⠠⢿⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣧⢴⠍⠀⠀⡐⢀⠤⠑⡛⠑⡀⠀⠠⠀⠸⢿⣮⠻⣿⣿⣷⣧⣷⣷⣼⣫
⣿⣿⣿⣿⣿⣿⣿⡇⠁⣿⣿⣿⣷⣾⣿⣿⣿⠀⣠⣮⠈⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⠈⠀⠁⠑⠚⠒⠀⢀⠀⢠⣿⠢⡔⡀⠀⢀⣴⢨⣔⣜⠿⣿⣿⡿⣇⢐⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣯⣙⠀⢉⣿⣿⣿⣿⣠⣄⡋⠁⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⡠⠄⠀⠀⠄⠀⢽⣷⠠⢄⠆⠀⢨⡍⠃⠡⠐⡄⠀⠘⢁⠋⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠉⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠐⠒⠲⣶⣄⡀⠂⠶⣾⠇⢌⢄⡀⠀⢖⡄⣀⠁⠐⢚⠓⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣈⠠⣰⣿⣦⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠈⠱⠆⠘⠁⡁⠀⠼⠿⣺⣷⡀⣀⢀⢀⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⠌⣧⠀⢠⣦⣾⣿⢿⣟⡡⣵⣘⡃⠀⣞⠐
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠐⠀⠘⠉⠀⢐⣿⣿⡧⠍⠁⠀⠀⠀⣘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣅⣫⠉⠀⠀⠀⢜⠄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⡶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⠹⡿⢰⠀⠀⠀⠀⠀⠬
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠒⠀⠀⠈⠀⠀⠀⣒⣀⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⢀⡤⢘⣁⠂⠀⠀⠀⡀⠀⠀⠀⢘⣋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣮⣴⠀⢨⣾⣻⣩⡀⠂⠀⠀⠀⠀⠀⠀⢘⣯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣦⣻⣿⣿⠿⠀⠀⠠⡄⠀⠀⠄⠛⠹⠿
⣿⣿⠀⠈⠉⠉⠙⠛⠛⠛⠛⠉⠉⠁⠀⠀⢹⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠦⠀⣾⣿⣿⣿⣿⣿⣿⣟⠉⢁⡤⠢⠌⠡⣔⠀⢒⠀⡂⠠⠍
⣄⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⠀⣀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⣷⣦⣽⣿⣿⣿⣿⣿⣿⣿⡈⠅⢫⣧⠨⡠⠈⠁⠊⢠⡅⠾⠗
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠿⠟⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⡂⠂⠀⠀⢠⣩⡵⡽⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠁⠀⣀⣐⡁⢀⠀⠀⠀⠀⠀
⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⢠⡟⠃⠀⠀⠀⠈⢤⡾⣻⣿⢿⣿⣿⣿⣿⣿⣿⠧⣠⣀⢈⣩⣽⣷⢐⡂⣂⣀⠀⠀
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⢚⠀⠀⠀⠀⠀⠀⠀⡉⡙⣨⠍⠝⢿⣿⣿⣿⣿⡅⠈⠉⣉⠙⣉⣿⣾⣿⠢⠙⠐⠞
⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣛⡿⢿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡶⠉⠡⠀⠈⢹⣿⣿⣿⣿⣧⣤⣀⣁⣽⡇⣾⣿⢣⡀⠀⠁
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠈⣽⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠂⠀⠀⠠⣶⣬⢹⣿⣿⣿⣿⣿⣿⣿⣧⣿⢣⠏⠀⠀⠀
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⣿⣿⣪⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠐⠀⠀⢄
⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠙
⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⠀⠀⠀⠈⠁⠀⠀⠀⣀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡀⣰⣦⣾
⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⡿⠋⢀⣀⣀⠀⣀⣀⣠⣿⣿⣿⣿⡇⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡒⠐⢖⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣯
⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣀⠀⢸⣿⣿⡏⠁⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢸⠁⢀⣾⣿⡟⢣⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠘⠠⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢰⡶⣿⠛⠙⢷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠈⣿⣿⣧⡀⢀⢸⡿⠙⠒⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢹⡿⠛⠃⠉⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣶⡄⠀⠀⠀⠀⠹⣿⣿⣿⡄⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣷⣄⡀⠀⠀⠀⠀⣙⣿⣿⣇⠀⠀⠀⠀⠀⢿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⣠⣿⣿⣿⣿⡄⠀⠀⠀⠀⠘⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡧⢍⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣎⣾⡇⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠨⠉⠁⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠎⠀⠀⢀⠀⢹⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⢀⢶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢷⣿⣌⠉⠋⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢡⣤⣌⢡⣤⣤⠈⣤⣤⡄⣤⣤⠀⣤⣤⠀⣤⣤⢠⣤⣤⣤⣤⣤⣤⣤⣤⡄⢠⣤⣤⣤⣄⠀⠀⠀⠹⠈⢳⡀⠀⠀⠀⠈⢻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⢸⣿⣿⡆⣿⣿⠀⣿⣿⠀⣿⣿⡇⣿⣿⠈⢹⣿⣿⠉⢹⣿⣿⠉⠁⢸⣿⡏⣿⣿⡆⠀⠀⠀⡀⠀⣳⡀⡀⠀⠀⠈⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣼⣿⣿⣷⣿⣿⠀⣿⣿⠀⣿⣿⣿⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⣶⡆⢸⣿⡷⣿⣟⠁⢀⡀⣤⣈⠁⠁⣿⣶⣕⡢⢄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⡏⢿⣿⣿⡏⢀⣿⣿⠀⣿⣿⢻⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⠀⠀⢸⣿⡇⣿⣿⡇⠈⠉⠿⣿⠂⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠸⠿⠿⠇⠸⠿⠿⠇⠸⠿⠿⠀⠿⠿⠘⠿⠿⠀⠸⠿⠿⠀⠸⠿⠿⠿⠇⠸⠿⠇⠿⠿⠇⣸⣶⣶⣬⣰⡄⠀⠀⠈⠻⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠻⠿⠿⠛⠛⠳⢶⣶⣀⡶⠖⠀⠒⠒⠀⠰⠒⠒⠒⠀⠀⠐⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠛⠛⠛⠛⠛⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣝⠿⣟⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣶⣿⢿⣿⣆⠉⠃⢠⣾⡿⢿⣷⡆⢠⣾⣿⢿⣷⡄⢸⣿⣿⡇⣼⣿⣿⡇⣿⣿⡇⢸⣿⣇⢸⣿⡇⣰⣾⡿⣿⣶⡀⢱⣷⡂⠠⠀⠈⢻⣿⣇⠀⠈⠁⠀⠙⡟⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣿⣿⣬⡙⠋⢀⠀⢸⣿⡇⢸⣿⡇⢸⣿⡇⢸⣿⡇⢸⣿⣿⣧⣿⣿⣿⡇⣿⣿⡇⢸⣿⣿⣼⣿⡇⣿⣿⡇⠿⠿⠇⢸⣿⣶⣺⠑⠀⠀⢿⣿⡆⠀⠀⠀⠀⠰⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣈⣛⢿⣿⣦⠀⡀⢸⣿⡇⢠⣤⡄⢸⣿⡇⢸⣿⡇⢸⣿⡿⣿⣿⢹⣿⡇⣿⣿⡇⢸⣿⢿⣿⣿⡇⣿⣿⡟⣿⣿⡇⢸⣿⣿⣿⣾⣗⡀⡜⢿⣷⠀⠀⠀⠀⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣿⣿⣨⣿⣿⢀⣇⢸⣿⣧⣸⣿⡇⠸⣿⣧⣼⣿⡇⢸⣿⡇⣿⣿⢸⣿⡇⣿⣿⡇⢸⣿⠘⣿⣿⡇⢻⣿⣇⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣛⣛⣠⣌⣙⣛⣋⣡⣾⣿⣆⡉⠛⠛⠉⢀⠀⠉⠛⠛⣉⠀⠘⠛⠃⠙⠃⠘⠛⠁⠙⠛⠃⠘⠛⠀⠙⠛⠁⠀⠙⠛⠉⠛⢃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠐⣿
⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⢰⣿⢿⡿⠀⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣄⡈⠙⠿⣿⣿⣿⣿⣿⣿⣿⠾⣿⣿⣿⡿⠀⠀⣠⡀⣿
⣇⣆⣲⣶⢁⣶⢌⣡⣰⣶⣆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠉⠀⠀⠈⠸⠊⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣦⣤⢈⢿⡗⢹⣿⣿⠻⣿⣿⣿⣿⡇⠀⠀⠈⢿⡿
[69A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣖⣠⣈⣿⡿⠧⠈⠀⢠⠏⣸⠏⠉⡓⢟⣾⢷⣿⣿⣿⣿⢟⣴⣿⣟⣷⣿⡟⠮⠀⠄⠀⡄⠄⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣁⢀⣄⠀⠶⢒⣯⠭⠙⣄⠰⣩⣭⣾⡿⣻⣽⣯⣿⣿⡚⡡⠠⠄⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠘⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢘⢫⠘⢛⠀⢠⣽⣞⠇⣾⢟⣐⡉⡋⠹⠾⠾⢺⡿⠛⠆⢈⢲⢛⡃⡺⠄⣀⡈⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣝⡿⠿⠟⠉⠠⠀⠀⢠⡄⢀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠠⣷⠀⣼⠟⢿⢿⣿⣘⣷⣉⠀⠀⠈⠠⠈⠋⠀⢲⢱⣾⡻⡻⣷⡦⢀⠀⠀⠀⡀⡀⡀⠀⠀
⣿⣿⣿⠟⣻⣅⢈⠀⠠⠀⠘⡆⠆⠻⣿⣦⡄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣔⠄⠁⠸⢿⡟⣿⠷⡇⠀⠀⠀⠀⠀⠀⠀⣢⣯⢻⣼⣀⠈⠕⠊⡬⠙⠃⠰⢰⡄⡆⢠⣇
⣛⣯⣥⣽⣿⣿⣛⡄⡄⠀⠐⣾⣦⣶⣾⣿⡇⠈⠉⢙⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣰⢇⣎⣽⣟⣟⡁⠂⠀⠀⠀⢰⣐⣃⠪⢜⡯⠆⠀⢊⠐⠒⢛⢬⡅⠀⡨⢶⣅⣼⡡
⣜⣿⣯⣿⣿⣿⣿⡌⠁⠀⢠⣯⣿⢿⣿⣿⡇⠀⠀⠀⣹⣅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⢼⣈⣘⠂⠀⠀⠄⢀⡂⠼⠗⠐⠁⠀⡀⠀⣾⣧⠻⣿⣾⣭⣡⣩⣥⡇⡷⡂
⣿⣿⣿⣿⣿⣿⣿⠃⢀⣶⣾⣿⣍⣼⣿⣿⡇⠀⢠⠂⠄⠙⢦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⠁⠐⠁⠤⠴⠄⠀⠀⠈⣡⡦⢀⠄⠀⠀⢈⡍⣃⠝⠿⣿⣿⣿⣿⠛⠹⠊
⣿⣿⣿⣿⣿⣿⣿⣶⡔⢟⠛⢻⣿⣿⣿⣿⠃⠠⠿⠈⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⣀⠀⠀⠀⠀⢀⣿⡇⣀⢨⠀⠀⣛⠳⠙⠸⠄⠈⠉⠏⠸⠂⠁⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣾⣿⣿⡿⣷⣿⡷⠄⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢈⠀⠀⠀⠀⢠⢤⣿⢁⠂⠀⠀⢨⢉⠀⠐⠀⠬⠤⠀⠈⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠉⣩⣄⣀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠒⠼⣥⣄⡀⠀⠂⠘⣥⠀⠗⠙⠀⢀⣽⡮⣶⡀⠈⠁⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠈⠙⠻⠿⣾⣦⡜⢀⠲⠈⠀⣠⣠⣾⣿⣿⠎⣑⡍⠟⠀⢠⢊⠰
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢀⠡⠈⠅⠀⠛⠋⠉⣵⣾⣿⣘⠋⠁⠀⠈⠁⠄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠰⣯⣟⢍⡒⠂⠀⠀⢨⢎⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣆⣀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠟⢿⣟⠍⠀⠀⠀⠈⢀⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠄⠈⠐⠃⠀⠀⠠⠄⣠⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠟⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⣫⡾⡏⡡⠀⠀⠀⠀⠀⠀⠀⠐⢟⣃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣦⡰⣿⣿⣿⡇⠀⠐⣂⠀⠀⠀⠲⠼⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⠛⠛⢁⡠⣠⠒⣪⡄⠤⠄⡠⢀⣑⠀
⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⢰⣿⣿⣿⣿⣿⣿⣿⡆⢐⠙⣺⡁⢂⠈⠃⠠⣃⣺⠸⡶⠄
⣷⡀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣀⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣶⣦⣿⣿⣿⣿⣿⣿⣿⣟⠒⠒⠈⠑⠈⠉⠀⠀⠀⠉⠀⠀⠀
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣉⣿⣿⣿⣿⣿⣿⣿⣿⡠⠄⠀⢚⣛⣿⠄⡅⠠⢀⠀⠀⠀
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠄⢉⣟⣿⣿⣿⣿⣿⣿⣗⠈⠙⠛⠙⠛⣻⢧⣿⠮⠙⠀⠠⠂
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠹⣿⣿⣿⣿⣿⣶⣀⣀⠐⢚⣿⢠⣿⠗⠀⠀⠂⠀
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⡾⡹⠈⠀⠀⠀
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢤⣄⢀⠛⠻⠿⠉⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠄⠀⢀⠀
⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢘⢻
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣿⣿⣿⣿⣿⣿⣿⣿⣧⡆⠀⣤⣠⡞
⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢰⡁⠀⢀⣤⣶⣶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⡇
⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⢀⣠⠿⠂⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠇⢠⣤⣤⣄⣤⣤⣴⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠀⠊⠀⠀⠀⠀⠀⠈⢠⠛⠿⠿⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢀⣸⣿⠿⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠈⠃⠀⠀⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢠⣤⣤⡀⠀⠛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠘⣿⣿⠿⠠⠆⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣠⠀⠀⠀⠀⠀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣶⡄⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⡇⠀⠀⠀⠀⠸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⢂⠀⠀⠀⢀⣿⣿⣿⣷⠀⠀⠀⠀⠀⢻⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠈⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢻⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⠀⠀⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⢀⠀⠀⠀⠀⠘⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⠃⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⣦⣿⣄⠛⠿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢡⣤⣄⢡⣤⣤⠀⣤⣤⡄⣤⣤⠀⣤⣤⠀⣤⣤⢠⣤⣤⣤⣤⣤⣤⣤⣤⡄⢠⣤⣤⣤⣄⠀⠀⠹⡏⠣⡀⠀⠀⠀⠙⢻⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⢸⣿⣿⡆⣿⣿⠀⣿⣿⠀⣿⣿⡇⣿⣿⠈⢹⣿⣿⠉⢹⣿⣿⠉⠁⢸⣿⡏⣿⣿⡆⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠛⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣼⣿⣿⣷⣿⣿⠀⣿⣿⠀⣿⣿⣿⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⣶⡆⢸⣿⡷⣿⣟⠀⠀⠀⣀⠀⠈⢻⣥⡂⠄⡀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⡏⢿⣿⣿⡏⠀⣿⣿⠀⣿⣿⢻⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⠀⠀⢸⣿⡇⣿⣿⡇⠰⢲⡿⠆⠀⠘⢻⣿⣶⣾⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠸⠿⠿⠇⠸⠿⠿⠇⠰⠿⠿⠀⠿⠿⠘⠿⠿⠀⠸⠿⠿⠀⠸⠿⠿⠿⠇⠸⠿⠇⠿⠿⠇⣠⣄⣈⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣯⣳⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠻⠿⠿⠛⠛⠳⢶⡶⢲⡶⠂⠀⠐⠀⠀⠴⠒⠂⠀⠒⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠟⠛⠛⠉⠓⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡻⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣶⣿⢿⣿⣆⠀⠎⢠⣾⡿⢿⣷⡄⢠⣾⣿⢿⣷⡄⢸⣿⣿⡇⣼⣿⣿⡇⣿⣿⡇⢸⣿⣇⢸⣿⡇⣰⣾⡿⣿⣶⡀⢠⡀⠀⠀⠈⢻⣿⣯⠉⠙⠂⠈⠛⣿⠿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣿⣿⣬⡉⠋⠀⠀⢸⣿⡇⢸⣿⡇⢸⣿⡇⢸⣿⡇⢸⣿⣿⣧⣿⣿⣿⡇⣿⣿⡇⢸⣿⣿⣼⣿⡇⣿⣿⡇⠿⠿⠇⢸⣧⠠⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⠠⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣈⣛⢿⣿⣦⠀⠀⢸⣿⡇⢠⣤⡄⢸⣿⡇⢸⣿⡇⢸⣿⡿⣿⣿⢹⣿⡇⣿⣿⡇⢸⣿⢿⣿⣿⡇⣿⣿⡟⣿⣿⡇⢸⣿⣿⣄⡐⠀⠈⢿⣿⠀⠀⠀⠀⠀⠱⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣿⣿⣨⣿⣿⢀⡇⢸⣿⣧⣸⣿⡇⠸⣿⣧⣼⣿⡇⢸⣿⡇⣿⣿⢸⣿⡇⣿⣿⡇⢸⣿⠘⣿⣿⡇⢻⣿⣇⣿⣿⡇⠘⣿⣿⣿⣿⣦⣤⣼⣿⡇⠀⠀⠀⠀⢐⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣛⣛⣠⣌⣙⠛⣋⣡⣾⣿⣆⠉⠛⠛⠉⠀⠀⠉⠛⠛⠉⣀⡘⠛⠃⠙⠃⠘⠛⠁⠙⠛⠃⠘⠛⠀⠙⠛⠁⢀⠙⠛⠉⠛⠃⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢪⡅
⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠁⠀⢰⣿⣿⡏⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠉⠻⢿⣿⣿⣿⣿⣿⣿⠋⠀⠀⣿⣿⣿⠀⠀⠀⠀⠠⡇
⣇⣆⣲⣶⣀⣶⢌⣡⣰⣶⣆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠂⠀⠀⠚⣣⠛⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣷⣦⠀⠙⠻⡇⠙⢿⣿⡆⠀⠠⣿⣿⡿⠀⠀⠀⢣⠄⡀
[69A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣖⡠⣈⣿⡿⠧⠈⠀⢠⠏⢸⠟⠁⣳⠟⣼⣷⣿⣿⣿⣿⢟⣭⣿⣿⣿⣷⡞⠌⠀⠄⠀⡀⡄⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠟⣣⢀⣄⠀⢶⢒⡿⠝⠙⣅⠰⢉⢏⣿⡷⢻⣝⣟⣿⣻⡜⡡⠠⠄⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢘⢫⠘⢛⠁⢡⣘⣞⠇⣴⣟⣐⡹⡋⢹⡾⠾⢺⡿⠏⠅⠨⢒⠳⡂⣶⡂⠀⡘⠀⠀⢀⠀⠀⠀⠀
⣿⣿⣿⣿⡻⣿⣿⡿⠛⢁⠀⠀⢈⡉⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⠠⣶⢀⣸⡟⢿⢿⣿⢘⣿⣪⠀⠀⠈⠁⠘⠇⠀⢤⣳⣾⠿⢯⢇⡦⠁⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⠿⡋⠁⠀⢀⠀⠰⡅⠌⢷⣾⣄⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣔⠄⠁⠸⢿⡟⣽⠾⡇⠁⠀⠀⠀⠀⠠⠀⢂⣎⢾⣹⡁⠘⡙⠖⣨⠚⠀⢰⢣⡤⡆⢀⣇
⡛⣟⣋⣷⣿⣿⢶⡀⡀⠀⠠⣼⣄⣤⣽⣿⡧⠈⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣰⠧⣎⣵⣿⣞⠁⠆⠀⠈⠀⢠⡐⠇⢡⠝⡲⠇⠀⠀⠬⠟⢗⡶⡅⠁⢨⣤⡅⣾⣡
⡱⣿⣿⣿⣿⣿⣿⡑⠃⠀⢀⣾⣻⣿⣿⣿⡇⠀⠀⠈⢻⡮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⢼⢉⣼⠁⠀⠀⠄⢈⢈⠴⡵⡀⠋⠀⡁⠀⣾⣎⢿⣶⣿⣌⣢⢩⣜⡁⣷⡂
⣿⣿⣿⣿⣿⣿⣿⠇⠄⣤⣾⣿⡛⣹⣿⣿⡇⠀⢀⠄⢘⢻⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠈⠃⠑⠂⡀⠴⡀⠁⠀⠉⢠⡦⣀⠀⠁⠀⢉⡙⠣⠙⣿⣿⣿⣿⣿⠻⠳⠂
⣿⣿⣿⣿⣿⣿⣿⣦⡨⡟⠿⢿⣿⣿⣿⣿⠟⢀⣾⠐⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⡀⠀⠀⢀⠀⢐⣿⡅⣈⢈⠀⠀⣙⢳⠙⠘⡌⠙⠟⡟⠼⠄⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⣼⣿⣿⣿⣯⣶⣦⡀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢈⠀⠀⠀⠀⢠⢤⣿⢁⢎⠡⠀⢈⠋⠀⠐⠀⡰⠤⠀⠈⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⠛⢛⡃⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠼⡇⠀⠀⠀⠂⠹⣭⠀⡷⠑⠀⢐⣷⡦⣦⡀⠈⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡠⢰⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠋⠉⠉⠛⠳⢶⣤⡀⢺⣧⡟⠀⢵⠐⡀⣀⣠⣾⣿⣿⠖⠊⡕⡖⠀⢠⢰⡂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢻⠁⠣⠀⡁⠀⠟⠋⠛⢹⣿⣟⣙⠿⠋⠀⠊⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢐⣿⡟⠛⡄⠀⠀⠀⢸⣌⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢄⠀⠀⠀⠀⠕⠿⣿⣟⡃⠀⠀⠀⠘⠀⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀⡤⠀⠈⠤⠁⠀⠀⠠⠄⢠⣭
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡀⠗⠄⠀⠀⠀⠀⠀⠀⠀⠨⠟⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣫⡾⡟⡡⠀⠀⠀⠀⠀⠀⠀⠸⣿⡂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣄⢸⣿⣿⣿⡅⠀⠀⢀⠀⡀⠀⡢⠼⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣷⠿⠛⢁⣠⣀⠒⣀⡄⠠⠤⠠⢀⡛⠉
⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡄⢒⠹⣒⠑⠀⠙⠇⠩⢂⣳⢸⣦⠀
⣦⣹⠟⠻⠿⣿⣿⣿⣿⣿⣯⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣒⠸⣿⣿⣿⣿⣿⣿⣿⣑⠂⠎⠉⠡⠉⠎⠀⠁⠈⠉⠀⠀⠀
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⠿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⢷⣿⣿⣿⣿⣿⣿⣿⣯⣀⡀⠀⠚⣛⣷⠨⠀⠠⠄⠀⠀⠀
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠠⡀⠿⣿⣿⣿⣿⣿⣿⡗⠉⠛⠚⠻⠯⢿⢨⣯⣏⠙⠀⢤⠂
⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⢀⡊⠀⠀⠀⠀⠀⠀⠐⠐⠊⠹⣿⣿⣿⣿⣿⣿⣦⠀⡈⠀⣸⣿⢨⣿⣇⠀⠀⠃⠀
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⠘⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣸⡟⡘⠈⠀⠀⠈
⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠻⠿⣿⠛⠛⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⠡⠀⠀⠀⠀
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠸⠯⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠸⢷
⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣣⠂⢀⣄⣴⡎
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⣤⣤⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⠃
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠥⠰⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀
⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣾⣿⠟⠃⠀⠀⠀⠀⠀⢙⣻⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣦
⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡏⠠⣴⣶⣶⣴⣶⣶⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠉⢿⠿⠃⠀⠀⠙⠛⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢸⣿⡿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠐⠘⠏⠀⠈⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢀⣠⣀⠀⠀⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⢸⣿⣿⣷⢀⡄⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠈⣿⠏⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠈⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡄⠀⠀⠀⠀⢻⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠈⢷⡀⠀⠀⠀⢰⣾⣿⣿⡇⠀⠀⠀⠀⠘⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⢷⣶⣴⣶⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⢹⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢀⢸⠛⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣸⠀⠘⠿⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣔⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠻⠀⠈⠀⠀⠀⢻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠰⣤⣀⣧⡈⠿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢡⣤⣄⢡⣤⣤⠈⣤⣤⡄⣤⣤⠀⣤⣤⠀⣤⣤⢠⣤⣤⣤⣤⣤⣤⣤⣤⡄⢠⣤⣤⣤⣄⠀⠉⢿⡓⢄⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⢸⣿⣿⡆⣿⣿⠀⣿⣿⠀⣿⣿⡇⣿⣿⠈⢹⣿⣿⠉⢹⣿⣿⠉⠁⢸⣿⡏⣿⣿⡆⠀⠀⠁⠈⢆⠀⠀⠀⠀⠸⠟⢻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣼⣿⣿⣷⣿⣿⠀⣿⣿⠀⣿⣿⣿⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⣶⡆⢸⣿⡷⣿⣟⠀⠀⠀⢀⠀⠘⣧⣂⠄⡀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⡏⢿⣿⣿⡏⠀⣿⣿⠀⣿⣿⢻⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⠀⠀⢸⣿⡇⣿⣿⡇⠠⢼⣓⡄⠀⠛⣿⣷⣌⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠸⠿⠿⠇⠸⠿⠿⠇⠰⠿⠿⠀⠿⠿⠘⠿⠿⠀⠸⠿⠿⠀⠸⠿⠿⠿⠇⠸⠿⠇⠿⠿⠇⢀⠀⠉⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣟⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠻⠿⠿⠛⠛⠳⢶⣶⢶⡶⠀⠀⠀⠀⠐⠴⠖⠂⠀⠐⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠟⠛⠂⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣶⣿⢿⣿⣆⢀⠎⢠⣾⡿⢿⣷⡄⢠⣾⣿⢿⣷⡄⢸⣿⣿⡇⣼⣿⣿⡇⣿⣿⡇⢸⣿⣇⢸⣿⡇⣰⣾⡿⣿⣶⡀⠀⠀⠀⠀⠙⣿⣿⡈⠙⠒⠌⠑⢿⡿⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣿⣿⣬⡙⠋⠀⠀⢸⣿⡇⢸⣿⡇⢸⣿⡇⢸⣿⡇⢸⣿⣿⣧⣿⣿⣿⡇⣿⣿⡇⢸⣿⣿⣼⣿⡇⣿⣿⡇⠿⠿⠇⠀⠀⠀⠀⠀⠈⢿⣷⠀⠀⠀⠀⠀⠁⠈⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣈⣛⢿⣿⣦⠀⠀⢸⣿⡇⢠⣤⡄⢸⣿⡇⢸⣿⡇⢸⣿⡿⣿⣿⢹⣿⡇⣿⣿⡇⢸⣿⢿⣿⣿⡇⣿⣿⡟⣿⣿⡇⠈⠧⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠈⢤⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣿⣿⣨⣿⣿⠀⡇⢸⣿⣧⣸⣿⡇⠸⣿⣧⣼⣿⡇⢸⣿⡇⣿⣿⢸⣿⡇⣿⣿⡇⢸⣿⠘⣿⣿⡇⢻⣿⣇⣿⣿⡇⠘⢿⢶⠦⠄⠀⠀⢸⣿⠀⠀⠀⠀⠀⠰⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣛⣛⣠⣌⣙⢛⣋⣡⣾⣿⡄⠉⠛⠛⠉⠀⠀⠉⠛⠛⠉⣠⣘⠛⠃⠙⠃⠘⠛⠁⠙⠛⠃⠘⠛⠀⠙⠛⢁⣀⠙⠛⠉⠛⠃⢀⣰⣗⠛⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⢀⠀
⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠏⠀⠀⠀⠀⣼⣿⣿⠏⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢶⣴⣿⣯⢿⣿⣏⠀⠀⠀⠀⢼⣿⡇⠀⠀⠀⠀⢸⠀
⣇⣆⣲⣶⣀⣶⢌⣡⣰⣶⣆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠠⠀⠀⠀⠿⡏⠟⠀⠀⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡴⣆⡀⠀⠛⢧⠈⠙⠻⠄⠀⠀⠀⣿⣽⠇⠀⠀⠀⠀⠈⠀
[69A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣦⣑⣁⣽⡿⠦⠀⠁⢠⠟⢰⡿⡃⢋⠞⣺⡷⣿⣿⣿⣿⢿⣥⣿⡟⣿⡿⡖⠮⠐⠠⠘⡀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣉⡄⣔⡀⠰⢎⣾⡹⠈⢋⢰⢌⣯⣾⣿⡏⣽⣻⣿⣿⡮⢃⠠⠆⠑⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢘⡙⡘⠉⠅⢁⣮⣔⢣⣰⡼⣑⣊⠋⠙⡶⠾⠳⡿⠟⠧⠀⢑⡚⢆⢴⣂⢀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡿⢿⣿⣿⠟⠛⡀⠀⠉⢉⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠀⣷⠄⢨⢟⡻⡿⢿⢆⢿⡎⠀⠀⠈⠀⠌⠋⠀⠐⡸⣴⡿⡼⣽⡤⠸⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡿⠗⠉⠅⠀⡀⡀⡇⢠⢸⣤⣆⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⠀⠁⠠⠻⡜⢿⠺⡞⡀⠀⠀⠈⠀⠀⠀⢀⣙⣼⣽⡇⢌⡏⠔⣠⡑⠃⠠⢪⣡⠄⠀⣄
⣟⣟⣛⣽⣞⣛⣷⠄⢀⠁⠀⣌⣎⡀⣼⣿⣿⠀⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡠⡿⣆⣽⣿⣿⢈⠀⠀⠀⠀⢠⢐⡍⠌⡝⡗⠔⠀⠀⠠⠅⢗⡰⢥⠀⡘⣥⣥⣸⣏
⣇⣾⣿⣿⣿⣿⣾⡟⠀⠀⠂⢼⣻⣿⣿⣿⣷⠀⠀⠀⠻⣮⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢿⢜⢉⢨⠃⠀⠀⠀⢈⣋⠴⣽⠂⠉⠁⢈⠀⣴⣷⡻⣷⣮⣧⣣⣩⣼⡙⢺⠗
⣼⣷⣿⣿⣿⣿⣿⡟⠐⣠⣴⣿⡟⢃⣿⣿⣿⠀⠀⣠⠐⢻⢈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⠈⠘⠒⠀⠰⠢⠁⠂⠀⣁⣦⢀⡀⠈⠀⢉⡙⠓⠝⢿⣿⣿⣿⣿⡟⡗⠗
⣿⣿⣿⣿⣿⣿⣿⣧⡠⢽⠿⢿⣿⣿⣿⣿⠿⠀⣴⡗⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⡀⠀⠀⠀⠀⡁⣾⣇⢈⣊⠀⠀⢹⠛⠞⡉⢂⠘⠟⣿⠱⠄⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣰⣿⣿⣿⣿⣴⣦⣅⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢈⠰⠀⠀⠠⢠⢤⣿⡅⢎⠠⠀⢀⠛⠂⠀⠡⡘⠦⠄⠀⠑⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡞⠛⣋⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠸⠍⠀⠀⠀⠂⠡⢭⢀⠷⠛⠀⢀⣷⣤⢶⡀⠀⠁⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠐⣼⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠓⠓⢦⣤⣀⠀⢺⣷⡘⠀⢤⠈⣀⣀⣠⣶⣿⣿⡶⠂⡃⡶⠀⢀⡴⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⠟⣫⠁⢚⠄⡁⠀⠿⠋⠛⢡⣿⣿⣙⠻⠋⠁⠘⠃⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠈⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠠⣿⣿⡛⣂⠀⠀⠀⢀⣍⠅
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡠⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢄⠀⠀⠀⠀⠁⠿⣿⣟⡗⠀⠀⠀⠈⠁⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣀⡠⠄⠈⠰⢅⠀⠀⠠⠄⢠⣭
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠗⠀⠀⠀⠠⠀⠀⠀⠀⠨⠿⠻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣫⡧⡟⡣⠤⠀⠀⠀⠀⠀⠈⠈⣿⡃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣅⠰⣿⣿⣿⡯⠀⠠⠀⠐⠀⢀⢠⠴⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣷⠿⠛⠉⣀⣀⠐⣈⡄⠀⡤⠠⢀⡺⠉
⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡆⠒⠩⣖⠓⢄⠉⠇⢨⢆⣲⢨⣦⠄
⣦⣼⣿⡿⢿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠠⣿⣿⣿⣿⣿⣿⣿⣑⠂⠊⠉⠩⠈⠚⠀⠁⠀⠋⠀⠀⠀
⣿⣿⣿⠀⠀⠀⠉⠉⠉⠋⠙⠛⠛⠉⠉⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣀⣠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⢶⣼⣿⣿⣿⣿⣿⣿⣿⢀⡀⠀⠚⣓⣷⡤⠂⠠⢄⠀⠀⠀
⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⣿⣿⣿⣿⣿⠏⠁⠀⠈⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⣿⣿⣿⣿⣿⣿⡏⠉⠛⠚⠻⠯⢿⢫⣯⣏⠙⠀⢤⠂
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠇⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠊⣿⣿⣿⣿⣿⣿⣦⢀⡈⠡⣸⣿⢨⣽⡧⠀⠀⠂⠀
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣸⡿⡸⠈⠀⠀⠀
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⢺⣿⣿⡿⠿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁⠀⠀⢀⠀
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢀⡄⠀⠀⠉⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠸⢷
⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠂⠀⣄⣰⡎
⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⠇
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢴⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⡿⠄⠀⠀⠈⠁⠘⢿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣦
⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠏⠀⣀⣀⣀⣀⣀⣠⣴⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠉⢹⣿⠿⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣿⣿⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠟⠁⠈⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢀⣁⠀⠀⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢸⣿⣷⡄⡄⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠈⡏⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⣤⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣧⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⡄⠘⠄⠀⠀⠀⠀⣾⣿⣿⣿⡀⠀⠀⠀⠀⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⢶⣴⣤⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡛⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠘⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣔⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⠀⠈⠀⠀⠀⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢤⣤⣈⣧⠘⠿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢡⣤⣄⢡⣤⣤⠀⣤⣤⡄⣤⣤⠀⣤⣤⠀⣤⣤⢠⣤⣤⣤⣤⣤⣤⣤⣤⡄⢠⣤⣤⣤⣄⠀⠙⣿⠓⣄⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⢸⣿⣿⡆⣿⣿⠀⣿⣿⠀⣿⣿⡇⣿⣿⠈⢹⣿⣿⠉⢹⣿⣿⠉⠁⢸⣿⡏⣿⣿⡆⠀⠈⠀⠈⠆⠀⠀⠀⠀⠸⠟⣹⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣼⣿⣿⣷⣿⣿⠀⣿⣿⠀⣿⣿⣿⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⣶⡆⢸⣿⡷⣿⣟⠀⠀⠀⢀⠀⠘⣦⣂⠄⡀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⡏⢿⣿⣿⡏⠀⣿⣿⠀⣿⣿⢻⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⠀⠀⢸⣿⡇⣿⣿⡇⠠⣼⣳⠄⠀⠿⣿⣦⣬⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠸⠿⠿⠇⠸⠿⠿⠇⠰⠿⠿⠀⠿⠿⠘⠿⠿⠀⠸⠿⠿⠀⠸⠿⠿⠿⠇⠸⠿⠇⠿⠿⠇⠀⠀⠃⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣛⣼⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠻⠿⠿⠛⠛⠓⢶⣶⢶⡶⠀⠀⠀⠀⠐⠤⠖⠂⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠟⠛⠁⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡿⢽⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣶⣿⢿⣿⣆⠀⠚⢠⣾⡿⢿⣷⡆⢠⣾⣿⢿⣷⡄⢸⣿⣿⡇⣼⣿⣿⡇⣿⣿⡇⢸⣿⣇⢸⣿⡇⣰⣾⡿⣿⣶⡀⠀⠀⠀⠀⠹⣿⣯⡈⠙⠢⠉⠚⢿⡿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣿⣿⣬⡉⠋⠀⠀⢸⣿⡇⢸⣿⡇⢸⣿⡇⢸⣿⡇⢸⣿⣿⣧⣿⣿⣿⡇⣿⣿⡇⢸⣿⣿⣼⣿⡇⣿⣿⡇⠿⠿⠇⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠈⡀⠈⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣈⣛⢿⣿⣦⠀⠀⢸⣿⡇⢠⣤⡄⢸⣿⡇⢸⣿⡇⢸⣿⡿⣿⣿⢹⣿⡇⣿⣿⡇⢸⣿⢿⣿⣿⡇⣿⣿⡟⣿⣿⡇⠀⡀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠐⢄⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣿⣿⣨⣿⣿⢀⡇⢸⣿⣧⣸⣿⡇⠸⣿⣧⣼⣿⡇⢸⣿⡇⣿⣿⢸⣿⡇⣿⣿⡇⢸⣿⠘⣿⣿⡇⢻⣿⣇⣿⣿⡇⠀⢿⠶⢀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠨⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣛⣛⣠⣌⡙⢛⣋⣡⣾⣿⣆⠉⠛⠛⠉⠀⠀⠉⠛⠛⠉⣠⡘⠛⠃⠙⠃⠘⠛⠁⠙⠛⠃⠘⠛⠀⠙⠛⢁⣀⠙⠛⠉⠛⠁⢠⣤⡠⠁⠀⠀⠀⢼⣿⡀⠀⠀⠀⠀⢘⠀
⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⣴⣿⣿⠏⠙⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢶⣴⣶⡗⣼⣿⣇⠀⠀⠀⢰⣾⣿⡇⠀⠀⠀⠀⡄⠀
⣇⣆⣲⣶⣀⣶⢌⣡⣰⣶⣆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠠⠄⠀⠀⠟⡏⠟⠀⠀⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡒⣄⡀⠀⠉⠏⠈⠙⠟⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠃⠀
[69A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣴⣿⡝⠁⠀⢀⠞⣁⣿⡫⣈⠎⠩⣿⡻⢿⣿⣿⠿⣷⣾⣿⢹⢿⠿⢍⠂⠁⠂⠀⠀⠂⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠞⣣⡴⣴⣦⠠⠋⡞⢧⠃⠠⣄⠗⣼⣞⡿⠯⣰⢯⣿⣿⠟⢈⠔⡒⠀⠑⠀⠀⢀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣅⡂⢁⠀⠀⣯⣶⣅⣦⡿⢣⠄⡌⠀⠹⠛⠋⣻⡙⠙⠂⡀⢭⡙⣕⡯⠆⡄⠄⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡻⢿⣿⡟⠉⠡⠀⠀⠀⡀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠺⠇⠀⠟⢭⡿⣛⡟⡜⡿⠀⠀⠀⡀⠐⠈⠀⠀⡱⢻⣿⠳⢑⡯⠂⢂⢀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡿⣛⣁⠐⠀⢀⠠⠰⡄⡄⠇⣾⣤⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⢀⠈⢳⣙⣏⠻⡠⠀⠀⠀⠀⠀⢀⠀⣤⣷⠱⠿⠔⠜⢐⢡⡶⠉⠀⡈⣻⢖⠀⢰
⣿⠽⣽⣑⣺⣯⡿⣶⡀⡀⠀⠠⣴⡄⢠⣿⣿⠇⠘⠛⢛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣛⣻⡴⣿⡿⡇⠊⠀⠀⠀⣀⡀⢵⡐⢰⣹⠑⡁⠀⢀⢒⣘⠥⣓⢆⢀⡱⣖⡦⣿
⣿⡸⢿⣟⣿⣿⣿⣿⠑⠀⠈⢐⣏⣿⣿⣿⣿⡆⠀⠀⠈⢻⡊⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⠗⡅⡄⡏⠀⠀⠐⢀⠮⠐⢳⠯⠀⠀⠀⡄⢰⣿⣯⠻⣿⣾⣮⣦⣴⣦⣅⣝
⣷⣿⣿⣿⣿⣿⣿⣿⠂⢰⣶⣿⣿⡉⣸⣿⣿⡇⠀⠀⠤⠉⠏⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠉⠁⠀⠋⠂⠈⢀⠠⣼⠆⡤⡀⠀⢀⣠⡉⣑⡙⠿⣿⣿⣿⠿⠹⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣤⠺⠝⠛⢿⣿⣿⣿⡿⠃⢰⠶⠂⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⡠⠀⠀⠀⠀⠠⢸⣿⠄⡤⠄⠀⢀⣏⠉⠡⠈⡄⠉⠙⢇⠻⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣾⣿⣿⣿⣧⣶⣦⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣄⠀⠀⠀⠂⢖⢾⡷⢘⢄⡂⠀⠬⠉⠀⠀⠢⢙⠒⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⣹⡁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢀⠳⠀⠀⠀⠈⣀⢻⡆⠼⠋⡁⠀⠼⠷⢞⣦⡀⠀⢀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠄⢠⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠚⢷⣤⣤⣀⢈⣿⣧⠀⡐⢆⠈⢤⣤⣾⣿⢿⣿⢋⣪⣸⣃⠀⡤⠩
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠉⠙⠛⠫⡇⠈⠄⠠⠀⠘⠏⠈⢉⣾⣿⡧⡍⠉⠀⠀⢉⠰
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡀⠀⠀⠀⠀⢀⢼⣽⡫⣩⠄⠀⠀⠀⡰⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡄⠀⠀⠀⠀⠸⠻⡿⠹⠁⠀⠀⠀⠀⣐
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠄⠀⠁⠓⠄⠀⠀⠴⢀⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢘⠐⠂⠀⠀⠂⠀⠀⠀⠀⠚⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣶⣻⣩⠄⠂⠀⠀⠀⠀⠀⠀⠺⣛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⢿⣿⣿⡷⠀⠀⢒⠁⠁⠀⠐⠦⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⡟⠛⠉⣠⠄⠜⢂⣵⠠⡴⢀⠄⣈⡃
⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣷⠐⡚⢳⣇⠓⠀⠛⠀⢜⣼⡇⢷⠆
⣷⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣏⡓⠐⠂⢉⠂⠨⠁⠀⠀⠈⠁⠀⠀
⣿⣿⣿⣿⠏⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⢦⣽⣿⣿⣿⣿⣿⣿⣅⠄⠀⠐⣛⣿⡇⢅⠀⠤⡀⠀⠀
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⠟⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣟⠊⠙⠛⠋⠛⢻⡇⣽⠷⠍⠃⠠⠄
⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠻⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣷⣂⣀⠀⠒⣿⢇⣼⡷⡂⠀⠘⠀
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⢀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢳⠃⠀⠀⠀
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⣿⣿⣿⠿⢿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡀⠄⠀⠀⠀
⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠁⠀⢰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠐⢿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣏⡆⠀⣤⣠⣶
⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⡇
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢰⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣷
⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⣈⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏⠉⣿⠿⣿⡆⠀⢾⣿⣶⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣼⠿⣷⠀⠀⢠⠞⠁⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢸⠃⠀⢹⣷⣦⡀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⢠⡄⠀⠘⠿⣿⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢸⣿⡇⢠⢰⡿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡄⠀⠀⠀⠀⢸⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢠⡀⠀⢀⠀⠀⠀⠀⠀⠰⣾⣿⣿⣧⠀⠀⠀⠀⠘⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⢢⠀⠀⠀⠀⣺⣿⣿⣿⣿⡄⠀⠀⠀⠀⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⢳⣶⣶⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠻⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⠻⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠃⠀⠀⠀⠀⠸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠿⢿⣿⣿⠃⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣄⣷⡀⠛⠿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢡⣤⣄⢡⣤⣤⠀⣤⣤⡄⣤⣤⠀⣤⣤⠀⣤⣤⢠⣤⣤⣤⣤⣤⣤⣤⣤⡄⢠⣤⣤⣤⣄⠀⠈⠻⡝⢦⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⢸⣿⣿⡆⣿⣿⠀⣿⣿⠀⣿⣿⡇⣿⣿⠈⢹⣿⣿⠉⢹⣿⣿⠉⠁⢸⣿⡏⣿⣿⡆⠀⠀⠀⠀⢣⠀⠀⠀⠀⠘⠛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣼⣿⣿⣷⣿⣿⠀⣿⣿⠀⣿⣿⣿⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⣶⡆⢸⣿⡷⣿⣟⠀⠀⠀⡀⠀⠈⣷⣄⠠⢀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⡏⢿⣿⣿⡏⠀⣿⣿⠀⣿⣿⢻⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⠀⠀⢸⣿⡇⣿⣿⡇⠐⢸⡧⠀⠀⠙⢿⣷⡤⣙⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠸⠿⠿⠇⠸⠿⠿⠇⠰⠿⠿⠀⠿⠿⠘⠿⠿⠀⠸⠿⠿⠀⠸⠿⠿⠿⠇⠸⠿⠇⠿⠿⠇⣀⣀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣝⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠿⠿⠛⠛⠳⢶⣶⠒⡶⠒⠀⠐⠀⠀⠰⠒⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠛⠛⠋⠀⠀⠀⠀⠀⠀⠻⣿⣿⡿⢿⣟⠿⣿⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣶⣿⢿⣿⣆⠈⠆⢠⣾⡿⢿⣷⡆⢠⣾⣿⢿⣷⡄⢸⣿⣿⡇⣼⣿⣿⡇⣿⣿⡇⢸⣿⣇⢸⣿⡇⣰⣾⡿⣿⣶⡀⠀⠀⠀⠀⠘⢿⣯⠀⠉⠑⠀⠘⢻⠛⢻⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣿⣿⣬⡉⠋⠀⠀⢸⣿⡇⢸⣿⡇⢸⣿⡇⢸⣿⡇⢸⣿⣿⣧⣿⣿⣿⡇⣿⣿⡇⢸⣿⣿⣼⣿⡇⣿⣿⡇⠿⠿⠇⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⡄⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣈⣛⢿⣿⣦⠀⠀⢸⣿⡇⢠⣤⡄⢸⣿⡇⢸⣿⡇⢸⣿⡿⣿⣿⢸⣿⡇⣿⣿⡇⢸⣿⢿⣿⣿⡇⣿⣿⡟⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠈⢤⢄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣿⣿⣠⣿⣿⢀⡆⢸⣿⣧⣸⣿⡇⠸⣿⣧⣼⣿⡇⢸⣿⡇⣿⣿⢸⣿⡇⣿⣿⡇⢸⣿⠘⣿⣿⡇⢻⣿⣇⣿⣿⡇⠀⠲⠀⢀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠈⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣛⣛⣠⣌⡙⠛⣋⣡⣾⣿⣆⡉⠛⠛⠉⠀⠀⠉⠛⠛⠉⣀⠘⠛⠃⠙⠃⠘⠛⠁⠙⠛⠃⠘⠛⠀⠙⠛⠁⢀⠙⠛⠉⠛⠁⢀⣶⡀⠁⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⢐⠀
⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⢰⣿⣿⡇⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠲⠴⣾⣀⠨⣾⢀⠀⠀⠀⠀⢽⣿⠃⠀⠀⠀⠀⠀⠀
⣇⣆⣲⣶⣀⣶⢌⣡⣰⣶⣆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠀⠀⠈⠱⠈⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠃⠄⠀⠀⢁⠀⠈⠁⠀⠀⠀⠀⣮⠏⠀⠀⠀⠀⠀⠀⠀
[69A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⡿⢇⠀⡀⠀⣌⡤⣾⡣⠢⠜⢀⠘⡷⣻⣿⡿⢿⣷⣿⡿⣃⠟⠍⡓⠠⠁⠈⠀⢀⠈⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠨⠞⢰⠟⠀⢈⠼⡱⠎⣠⣲⠘⠢⡿⢟⣫⣲⣻⣾⣿⣛⠁⣄⣩⡅⣀⡅⠀⠀⡀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠟⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡔⠜⢠⣌⠀⢸⣿⣷⣴⣿⢙⣗⠶⠀⠈⠋⠉⠨⡧⠁⠉⢀⣐⣴⢱⣽⣘⠰⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣯⣻⠿⠿⠀⠀⠀⡈⠀⢄⠀⡀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠋⠀⠋⢱⣞⣹⣿⣴⡟⠂⠀⠀⠠⠀⠀⠀⠀⢠⢪⢿⡏⠃⠝⣋⠍⢤⡄⠀⡀⡀⢀⠀
⣿⣿⣿⣿⡿⣫⣥⡀⠁⠀⠄⠔⢣⠠⠸⢹⣷⣆⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢀⠄⡼⢧⣿⣜⠇⡂⠀⠀⠀⢀⢀⠄⠐⢼⣟⣚⠓⠐⠁⢄⣞⢃⠄⠈⠨⠟⠅⢠
⣿⡍⣿⣥⣽⣿⣿⣻⣆⠠⠀⠈⢦⣧⣀⣾⣿⡟⠀⠉⠉⣛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢱⣷⣻⠳⢳⡊⠀⠀⠀⠠⡸⢒⣷⠉⠧⠏⠁⠀⣀⡌⣤⣕⣪⡍⡄⠦⠫⢿⣺
⣿⢧⣻⣿⣽⣿⣿⣿⡅⠁⠀⢡⣿⣽⡿⣿⣿⣿⠀⠀⠀⠉⣍⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡟⠹⡖⢖⠀⠀⢀⠁⠔⠒⠩⠋⡂⠀⠀⠀⠀⠻⢿⣌⢿⣿⣿⣾⣾⣿⣶⣼
⣿⣾⣿⣿⣿⣿⣿⣿⡏⠀⣶⣿⣿⣇⣠⣿⣿⣿⠀⠀⠰⠪⠙⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠂⠉⠂⠀⠀⢀⣶⠟⠰⡡⠀⠀⢤⣆⢠⢥⡙⢻⣿⣿⢟⡃⠂
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣔⠺⠉⢻⣿⣿⣿⣿⠋⠀⠿⠊⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠠⠂⠀⠀⠀⠀⠀⣿⠇⠲⠔⠀⠀⣼⡀⠀⢆⢢⡀⠀⠛⡜⠃⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣾⣿⣿⡿⣿⣾⣷⠆⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠠⣔⡄⠀⠀⠀⠘⢽⡿⠀⣑⢬⠀⢐⣄⠀⡈⠀⠚⡍⠀⠠⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠋⢩⣥⣀⡀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⡍⠃⠀⠀⠀⣠⡌⡿⠐⢋⢈⠀⠐⠛⢃⣽⣦⣀⡀⣄⣀⠀⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡔⢈⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠓⠶⢶⣤⣀⣾⡿⠆⡢⢙⠄⠀⣴⡾⣿⡛⣿⣋⢬⣦⡯⠄⣰⡂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠙⠙⠀⠰⠀⠂⠀⠉⠀⠠⣾⣿⣿⡺⠀⠀⠀⢀⢄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢐⣿⣯⣢⣕⠄⠀⠀⢰⠣
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⢀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠋⢻⠁⠃⠀⠀⠀⠈⠠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠒⠂⠀⠉⠁⠀⠀⠐⡃⢴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢀⣁⠀⠀⠀⠀⠀⠀⠀⠀⢈⣋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣾⣼⣣⠜⠀⠀⠀⠀⠀⠀⠀⢘⣯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⢸⣿⣿⡿⠆⠀⠈⠅⠀⠀⠀⠑⠘⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⠉⠉⡠⢴⠄⠹⣔⡄⣒⠀⡖⠠⠭
⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠄⠃⢹⣯⡉⡀⢈⠃⠠⢱⣽⠸⠗
⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸⣿⣿⣿⣿⣿⣿⣍⠁⠋⠀⣂⢀⡃⢀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣀⣀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣿⣿⣿⣿⣿⣿⡧⣤⡀⢈⣩⣭⢷⢐⣄⡖⣄⠀⠀
⣿⣿⣿⣿⣿⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⢨⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡁⠈⠉⣉⠙⢋⣿⣴⣿⠦⠉⠐⠾
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣆⣄⣀⠠⣿⡇⣶⣿⠣⠀⠀⠁
⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠁⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣾⣿⣿⣿⣧⣿⢧⠎⠀⠀⠀
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠸⣿⣿⡿⠿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⠐⠀⠀⠀⡄
⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠈⠀⠀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⠃⠈⠀⠀⡛
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠐⠬⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣨⠀⣠⣤⣶
⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠠⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡿⣿⠟⠀⠀⠀⠀⠀⠀⠉⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠈⠺⠟⢿⣿⡞⠀⢠⣶⣶⣶⣶⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠰⢻⣅⠀⠠⣾⡿⠇⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄⣹⣇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢠⡀⠀⠛⣿⡿⣏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢸⠿⠠⠆⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣤⣴⣆⠀⠀⠀⠀⠸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣶⡀⠀⠀⠀⠀⠀⠀⠐⣾⣿⣿⣿⣿⡀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣹⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠙⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠙⠋⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠈⣟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⠇⠠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⢶⣼⣆⡙⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢡⣤⣌⢡⣤⣤⠈⣤⣤⡄⣤⣤⠀⣤⣤⠀⣤⣤⢠⣤⣤⣤⣤⣤⣤⣤⣤⡄⢠⣤⣤⣤⣄⠀⠀⠙⠇⠳⡀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⢸⣿⣿⡆⣿⣿⠀⣿⣿⠀⣿⣿⡇⣿⣿⠈⢹⣿⣿⠉⢹⣿⣿⠉⠁⢸⣿⡏⣿⣿⡆⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣼⣿⣿⣷⣿⣿⠀⣿⣿⠀⣿⣿⣿⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⣶⡆⢸⣿⡷⣿⣟⠀⠀⠀⣀⠀⠀⣿⣦⡔⠠⣀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⡏⢿⣿⣿⡏⠀⣿⣿⠀⣿⣿⢻⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⠀⠀⢸⣿⡇⣿⣿⡇⠘⠘⠾⠂⠀⠈⠻⣿⣖⣾⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠸⠿⠿⠇⠸⠿⠿⠇⠰⠿⠿⠀⠿⠿⠘⠿⠿⠀⠸⠿⠿⠀⠸⠿⠿⠿⠇⠸⠿⠇⠿⠿⠇⢰⣤⣀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠿⠿⠛⠛⠳⢶⣶⡂⠰⠆⠀⠒⠒⠀⠀⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠛⠛⠉⠀⠀⠀⠀⠀⠙⢿⣿⡟⠻⣯⡙⠿⡿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣶⣿⢿⣿⣆⠉⠉⢠⣾⡿⢿⣷⡄⢠⣾⣿⢿⣷⡄⢸⣿⣿⡇⣼⣿⣿⡇⣿⣿⡇⢸⣿⣇⢸⣿⡇⣰⣾⡿⣿⣶⡀⠀⠀⠀⠀⠈⠻⣿⡅⠀⠈⠀⠈⠙⠛⠻⢻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣿⣿⣬⡉⠋⠀⠀⢸⣿⡇⢸⣿⡇⢸⣿⡇⢸⣿⡇⢸⣿⣿⣧⣿⣿⣿⡇⣿⣿⡇⢸⣿⣿⣼⣿⡇⣿⣿⡇⠿⠿⠇⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⠀⠀⠀⢀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣈⣛⢿⣿⣦⠀⡀⢸⣿⡇⢠⣤⡄⢸⣿⡇⢸⣿⡇⢸⣿⡿⣿⣿⢹⣿⡇⣿⣿⡇⢸⣿⢿⣿⣿⡇⣿⣿⡟⣿⣿⡇⠀⢀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⢐⠶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣿⣿⣠⣿⣿⢀⡇⢸⣿⣧⣸⣿⡇⠸⣿⣧⣼⣿⡇⢸⣿⡇⣿⣿⢸⣿⡇⣿⣿⡇⢸⣿⠘⣿⣿⡇⢻⣿⣇⣿⣿⡇⠀⠁⠃⢀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣛⣛⣠⣌⣙⠛⣋⣡⣾⣿⣆⡉⠛⠛⠉⠀⠀⠉⠛⠛⢉⠀⠘⠛⠃⠙⠃⠘⠛⠁⠙⠛⠃⠘⠛⠀⠙⠛⠁⠀⠙⠛⠉⠛⠁⢠⡴⠀⠀⠀⠀⠀⠀⣝⡇⠀⠀⠀⠀⢈⠀
⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⢀⠀⠀⢠⢿⠻⠏⠀⠐⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⠈⠛⠫⣷⠘⠻⠖⠀⠀⠀⠀⠆⢽⠇⠀⠀⠀⠀⠈⠀
⣇⣆⡲⣶⣀⢶⢌⣡⣰⣶⣆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠍⠀⠀⠀⠀⠀⠀⠀
[69A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢉⡄⣴⡄⠘⠏⠽⣓⠃⢁⡀⣖⢸⣶⡿⢟⣹⣞⣯⣽⡽⡚⠀⡠⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⣩⡆⠉⠄⠀⣮⣵⣈⣰⡗⣇⡠⡜⠉⢳⡟⠟⢺⡿⠳⠂⠀⢲⢛⡃⣺⠄⢀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡿⢿⣿⣿⡿⠿⠂⠈⠉⠙⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⠀⢾⠄⢠⠿⣛⡿⣿⡇⣚⢾⠀⠀⠀⠀⠀⠈⠃⠄⢰⢳⣾⠿⢻⣇⡦⠠⠀⠀⠀⠂⡀⠀
⣿⣿⣿⣿⣿⣿⣶⠝⠛⠁⠀⠀⣰⠀⠘⡧⣤⡀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠁⠀⠀⠋⣶⢳⡞⢷⢀⠀⠀⠀⠁⠀⠀⠀⣄⣧⢪⣿⡀⠨⠑⠂⡬⠙⠂⠠⢲⡦⡆
⢹⣿⠿⠿⢟⣥⠶⢦⣄⠀⠀⠈⢈⢢⢀⢁⣿⣿⡆⢻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⡮⣠⣩⣿⣳⡊⠔⠀⠀⠀⠀⡄⣊⢠⢩⠛⠲⠃⠀⠂⠨⠚⢚⠴⡁⠀⠨⡦⣑
⣽⣷⣩⣿⣿⣿⣿⣯⡷⠄⠀⠠⢨⡿⣷⢾⣿⣿⡀⠀⠀⠰⣯⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣻⡧⣃⡡⡏⠀⠀⠠⠀⣙⠡⢮⣧⠈⠉⠀⡁⠀⣾⣎⢿⣶⣾⣌⣢⢩⣼⡀
⣿⣏⣮⣽⣷⣿⣿⣿⣿⢀⢀⣠⣾⣿⠿⢻⣿⣿⡇⠀⠀⠀⠽⡞⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠙⠈⠒⢀⠀⢆⠈⠐⠀⢀⣰⡄⣀⠀⠁⠀⢁⠛⠣⠛⣿⣿⣿⣿⣿⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣺⢿⣿⣿⣶⣿⣿⣿⡇⢀⡄⠍⠀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢀⠀⠀⠀⠀⠀⢰⣿⡀⣁⡁⠀⠈⠿⢳⢿⢘⡈⠙⠻⡟⢹⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⡀⠀⣿⣿⣿⣿⢇⣄⡘⠁⠀⠀⢄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠪⠀⠀⠀⠀⣤⣭⡯⠨⠁⠁⠀⢘⠛⠀⠀⣀⢲⣄⠀⠐⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⠿⠿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠱⣞⠀⠀⠀⠀⠈⢿⡅⢰⠌⠆⠀⢰⣦⣤⣄⠀⠐⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠃⢀⣾⣦⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⠀⠀⠀⠀⢐⣯⣌⠇⠀⡀⠀⠀⡀⣨⣾⣿⡶⡴⠐⠲⡖⠀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠁⠀⠈⠉⠻⠶⣴⣻⡋⠰⡉⠒⠁⢹⠿⠛⢛⣸⣿⡆⢾⠾⠂⠀⠼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠁⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⠁⠈⠀⠀⠀⠀⣴⣿⠿⠫⠁⠀⠀⠀⢰
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠐⢽⣿⣷⢞⠁⠀⠀⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣠⡤⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠈⠋⡝⠀⠀⠀⢀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⢉⠀⠀⠀⡀⠁⠀⠀⠁⣰
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡂⣶⠄⡀⠀⠀⠀⠀⠀⠀⠀⣰
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣷⡞⠁⠀⣀⠄⠀⠀⢀⡂⣬
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⣿⣿⠿⠋⠀⢀⡐⠀⠀⢀⠀⠉⢹
⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⡇⢀⢤⣚⡓⡀⠰⣿⠈⢡⢰⡅⣖
⠀⣀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡗⣔⢀⡹⠧⠠⠠⠌⠀⠑⠷⠇⠛
⢸⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠺⣿⣿⣿⣿⣿⣷⠄⠀⠐⣨⣄⣬⠀⠄⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⣿⣿⣿⣿⣿⣿⠢⣦⣄⢤⣶⣾⡇⠵⡼⢽⡄⡀
⢽⣿⣿⣿⣿⣿⡟⠙⠛⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣷⡀⠀⠠⠄⢩⣽⠷⢿⣿⠂⠀⢙
⣸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⡶⣤⣄⣺⣿⢸⣿⠏⡂⠀⠀
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠉⠙⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⣿⣿⣿⣿⣿⣿⣿⣾⡟⠞⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠀⠀⠿⣿⣿⠛⠻⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢽⣿⣿⣿⣿⣿⣿⣿⣇⠁⡀⠀⢰
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⢿⣿⣿⣿⣿⣿⡏⡀⠀⠀⠨
⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢸⣿⣿⣿⣿⣿⣧⡆⢠⣶⣾
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣒⣿⡷⠀⠀⠀⠀⠀⠀⠈⠛⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠙⣿⣿⣿⡇⠀⢀⡂⣀⣤⣴⣾⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢰⣤⠀⢚⣿⣿⣿⠇⠀⠀⠈⠙⠛⠿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢨⣿⣷⣦⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣢⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠉⣿⠙⠄⠈⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠘⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣤⣶⣿⣿⡇⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣦⠀⠀⠀⠀⠀⠀⣘⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢀⣀⣠⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣹⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠤⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣟⢽⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⣀⣀⣹⡍⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣿⢿⣯⣤⣼⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠉⢀⡀⠀⠈⠙⢻⣿⢤⠈⠁⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢡⣤⣄⢠⣤⣤⠀⣤⣤⠄⣤⣤⠀⣤⣤⠀⣤⣤⢠⣤⣤⣤⣤⡄⣤⣤⣤⡄⢠⣤⣤⣤⣄⠀⠀⠀⠁⠀⢣⠀⠀⠀⠀⠈⣿⡿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⣿⣿⢸⣿⣿⡆⣿⣿⠀⣿⣿⠀⣿⣿⡇⣿⣿⠈⢹⣿⣿⠉⠁⣿⣿⠉⠁⢸⣿⡏⣿⣿⡆⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣼⣿⣿⣷⣿⣿⠀⣿⣿⠀⣿⣿⣿⣿⣿⠀⢸⣿⣿⠀⠀⣿⣿⣶⡆⢸⣿⡷⣿⣟⠀⢠⡄⢴⣄⠀⠘⣿⣶⣌⣒⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢿⣿⣿⡇⢿⣿⣿⡇⠀⣿⣿⠀⣿⣿⢻⣿⣿⠀⢸⣿⣿⠀⠀⣿⣿⠀⠀⢸⣿⡇⣿⣿⡇⢀⠀⠙⠛⠀⠀⠈⠿⣿⣿⣿⣿⣿⡷⢏⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠸⠿⠿⠇⠸⠿⠿⠇⠠⠿⠿⠀⠿⠿⠘⠿⠿⠀⠸⠿⠿⠀⠠⠿⠿⠿⠇⠸⠿⠇⠿⠿⠇⢸⣿⣶⣴⣆⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⠿⠿⠛⠛⠳⢶⣶⡶⡄⠒⠀⠂⠂⢦⡤⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠙⠙⠛⢠⡄⠀⠀⠀⠹⣿⣿⡟⠻⠦⢉⠫⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣶⣿⢿⣿⡆⠙⠁⢠⣾⡿⢿⣷⡄⢠⣾⡿⢿⣷⡄⢸⣿⣿⡇⣸⣿⣿⡇⢽⣿⡇⢸⣿⡇⢸⣿⡇⣰⣾⡿⣿⣶⡀⢹⡇⠀⠀⠀⠈⣿⣿⡀⠀⠀⠀⠈⡟⠉⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣿⣿⣌⡉⠉⣠⠀⢸⣿⡇⢸⣿⡇⢸⣿⡇⢸⣿⡇⢸⣿⣿⣧⣿⣿⣿⡇⢾⣿⡇⢸⣿⣿⣼⣿⡇⣿⣿⡇⠻⠻⠇⢸⣯⡄⠀⠀⠀⠸⣿⣷⠀⠀⠀⠀⠸⣄⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣈⣛⢿⣿⣦⠘⡆⢸⣿⡇⢠⣤⡄⢸⣿⡇⢸⣿⡇⢸⣿⡿⣿⣿⢸⣿⡇⣾⣿⡇⢸⣿⢿⣿⣿⡇⣿⣿⡇⣿⣿⡇⠘⣿⣿⣷⣤⣄⢀⣿⣿⡄⠀⠀⠀⢠⣼⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣿⣿⣠⣿⣿⢀⡇⢸⣿⣧⣸⣿⡇⠸⣿⣧⣸⣿⡇⢸⣿⡇⣿⣿⢸⣿⡇⣼⣿⡇⢸⣿⠈⣿⣿⡇⢻⣿⣇⣿⣿⡇⠀⣿⣿⣿⡿⢻⣿⣿⣿⣇⠀⠀⠀⢸⣿⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣉⣉⣠⣌⣙⣛⣋⣡⣾⣿⣦⣉⠛⠛⠉⠀⠀⠉⠛⠛⢉⠀⠈⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠈⠉⠀⠉⠉⠁⠀⠙⠛⠉⠉⠁⣸⣿⣿⡿⡉⢜⢿⣿⣿⣿⠀⠀⠀⢘⣿⠁
⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠉⠱⠉⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣴⣄⣙⢻⡏⢙⣿⡿⣬⢦⣿⣿⣿⡇⠀⠀⢰⣼⣿⠀
⣇⣀⣰⣶⢀⣰⢌⣡⣠⣖⣆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣦⢆⠀⠑⠉⠁⠈⣿⣿⣿⠁⠀⠀⠀⣿⡿⠀
[69A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠋⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡟⠋⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣶⣾⣉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣸⠹⠿⢿⣿⠟⠿⠍⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠠⡿⢁⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⡇⠀⠀⢙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣿⠇⠀⠀⠀⣀⣼⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣀⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢳⠇⠀⣴⣿⡿⣿⣿⣿⣽⣿⣿⣿⣦⠀⠈⠛⢻⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣾⡆⢰⣿⣿⠇⠃⣿⣿⢿⣿⣿⣿⣿⣷⡀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠈⢉⣿⠇⣾⠁⢸⣿⣿⠀⠸⣿⣿⣦⠘⡿⢿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠉⠀⠉⠀⢸⣿⣿⠀⡄⠻⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣀⣸⣿⡇⢰⡆⠀⠈⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢿⣿⡟⠀⣀⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠈⢿⡇⢠⣿⡿⣷⣶⣾⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠀⠀⠀⠀⠘⠁⣼⡟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣿⣿⡏⢹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣀⣐⣄⡰⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢀⣾⣿⣿⣿⣷⣄⠈⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⡿⣿⣿⣿⣿⣿⣿⣧⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⣀⠻⢟⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⠿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣦⠁⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢤⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠁⠀⠀⠀⢿⣿⣿⣿⣿⣿⠏⠉⠉⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠐⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠁⠀⠀⠀⠀⠀⠈⠿⣿⣿⠉⠛⠀⠀⠀⠀⠀⠰⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⣿⡇⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠺⠿⠉⠉⣿⣿⣿⣿⣿⡄⢰⣿⡇⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠿⠛⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⠙⠻⠆⣘⣿⣿⣦⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣀⣬
⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠟⠁⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠁⢿⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡅⢠⣤⣄⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠃⠈⠉⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡄⠀⠀⠀⠀⠀⠀⠀⠐⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⢐⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣿⡁⠀⠀⢀⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠹⢾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣧⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠼⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣶⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣤⣀⣀⣿⣿⣦⣄⡘⢿⣿⣿⣿⣆⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠛⣿⣿⣿⣿⣿⣿⣦⣹⣿⣿⣿⣇⣀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣸⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡄⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⡀⣀⡀⢀⣾⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠐⣻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠈⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠁⠀⠀⠀⢰⣶⣾⣿⣿⣿⣿⡟⢃⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢠⣿⣿⣿⣿⣀⠀⠀⡀⣾⣿⢿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⠿⠿⣿⠿⠿⠿⠿⠿⢿⠿⠿⡿⠿⠿⠿⠿⠿⠿⠶⠿⠿⠿⠿⠿⠿⠿⠷⠶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠠⣤⡄⠀⣤⣤⠀⣠⣤⠀⣤⣤⠀⣤⣤⠀⣤⣤⢠⣤⣤⣤⣤⠀⣤⣤⣤⡄⢠⣤⣤⣤⣄⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣇⢸⣿⣿⠀⣿⣿⠀⣿⣿⠀⣿⣿⡄⣿⣿⠈⠉⣿⣿⠉⠀⣿⣿⠉⠁⢸⣿⡏⢹⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣿⣿⢸⡿⣿⡆⣿⡏⠀⣿⣿⠀⣿⣿⣷⣿⣿⠀⠀⣿⣿⠀⠀⣿⣿⣶⡆⢸⣿⡷⣿⣋⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢹⣿⣾⡇⢹⣷⣿⡇⠀⣿⣿⠀⣿⡇⢹⣿⣿⠀⠀⣿⣿⠀⠀⣿⣿⠀⠀⢸⣿⡇⢸⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠸⠿⠿⠃⠸⠿⠿⠇⠀⠿⠿⠀⠿⠇⠈⠿⠿⠀⠀⠿⠿⠀⠀⠿⠿⠿⠇⠸⠿⠇⠸⠿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠛⠋⠙⠒⠢⣶⣶⠶⠀⠀⠀⠒⠢⠴⠒⠀⠀⠒⠦⠒⠒⠒⠀⠐⠒⠒⠂⠀⠀⠐⠂⠀⠒⠂⠐⠒⠟⠛⠉⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⠀⣴⣿⠿⣷⡄⠈⠏⢀⣶⡿⢿⣶⡄⢀⣶⡿⢿⣶⡀⢸⣿⣿⡆⢸⣿⣿⠀⢸⣿⡇⢸⣿⡆⢸⣿⠀⢠⣾⡿⣿⣦⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⠀⢿⣿⣄⠉⠁⢠⠀⢸⣿⡇⠸⠿⠇⢸⣿⡇⢸⣿⡇⢸⣿⣿⡇⣾⢻⣿⠀⢸⣿⡇⢸⣿⣷⣸⣿⠀⢸⣿⡇⠛⠛⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⠀⠀⠙⠻⣿⣆⠀⠀⢸⣿⡇⢀⣀⡀⢸⣿⡇⢸⣿⡇⢸⣿⡏⣿⣿⢸⣿⠀⢸⣿⡇⢸⣿⢻⣿⣿⠀⢸⣿⡇⢻⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⠀⢿⣿⣀⣿⡿⠀⡀⠘⣿⣇⣸⣿⠇⠸⣿⣇⣸⣿⠇⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⡇⢸⣿⠈⣿⣿⠀⢸⣿⣇⣼⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠉⠉⢀⡀⠉⠉⠉⣀⣴⣷⣄⡈⠉⠉⠁⣠⣄⡈⠉⠉⢁⣀⠈⠉⠁⠈⠁⠈⠉⠀⠈⠉⠁⠈⠉⠀⠈⠉⢀⣀⠉⠉⠁⠉⢁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
[69A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡆⠻⡿⡟⠰⡖⣯⣻⡄⠿⠃⠀⠀⠀⠀⠀⠀⡇⠀⠀⠃⠯⣽⠜⣻⣼⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⢀⡀⠉⠓⠀⠈⠃⠀⠦⣷⠃⠀⠉⠻⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠥⠀⡾⣭⢛⢉⣭⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠈⠩⠄⢀⣙⠀⠀⢐⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⣄⠀⠀⠁⠀⠀⠉⠞⣶⡀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠁⡀⠀⠀⠀⢰⣤⣿⠃⠐⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠐⢭⣄⣠⡄⢰⣷⣽⡄⣐⣷⡦⢀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠉⢩⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠢⠈⠉⠉⠓⠀⢻⣏⠁⠊⢈⣡⡀⠀⠀⢀⡟⠘⠀⠀⠀⠀⠐⠂⠀⠀⠀⠠⠁⢀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠈⠀⢂⣴⣿⡿⠠⣦⠀⠐⢤⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠾⡀⠀⣤⠆⠀⣸⣿⠟⢹⣿⠏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠧⣄⣄⣀⣺⣿⣿⡸⡏⡀⠀⣐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡶⢾⣿⣾⣾⣿⠋⣠⣾⡟⢰
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣷⣦⣶⣽⣿⣿⣿⣿⣿⢻⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⡏⢁⣾⣿⣿⣃⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⠙⠿⣿⣿⣿⣿⣿⣿⣾⡄⠀⠀⠀⠀⣷⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢸⣷⠞⢻⣿⡟⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡇⠀⠙⣿⣿⣿⣿⣿⣯⡇⠀⠀⠀⢰⣿⢠⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢞⣓⣠⣼⣿⢹⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡂⠘⣿⣿⣿⣿⣿⢠⡄⠀⡀⢠⡇⠀⢸⣂⠀⠀⠀⠀⠀⠀⠀⠈⠉⣩⣽⡿⠟⠁⣠⣴⠆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠙⣿⣿⣿⡏⠾⡁⢠⣾⣿⠇⠃⣆⡿⠧⠀⠀⠀⠀⠀⠀⠀⣸⣯⣿⣷⣤⣴⣿⣿⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢼⣿⣿⣿⠇⣞⠂⢸⣿⣿⠀⠰⣿⣧⡀⠀⠀⠀⠀⠀⢀⣬⣿⣿⣿⣿⣿⣿⣿⢧⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡤⣾⣿⣿⠟⠈⡛⣀⣼⣿⡟⠀⠀⢿⣿⣅⣀⣤⣄⣀⣠⢏⣗⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠙⠀⠀⢀⣍⣿⣿⠇⢰⡆⠀⠙⢻⣷⣿⣿⣿⣿⣻⣿⣿⣿⢿⣿⣯⡿⠛⢩⣽
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢸⣿⣿⣿⠀⣆⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⠟⠁⠼⠿⣿⡿⣳⣏⣉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⣿⣿⣿⡇⢰⣿⡷⣠⠀⢸⣿⣿⣿⣿⣿⠛⠋⣁⣉⣾⠇⢟⣴⢋⣏⡛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣔⠀⣿⣿⠿⠁⣾⡿⣷⣿⣀⣿⣿⣿⣿⢻⣃⡡⣀⠔⢫⠉⢈⠈⠉⠻⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⠀⣼⣿⣼⣿⣿⣿⣿⣿⣿⡄⠉⣿⣷⣶⡏⢃⠀⣻⣤⢴⢿⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠙⠙⢿⣿⣿⣿⣿⣿⡿⠇⠢⠋⠛⠿⣶⡄⡆⠨⣽⢇⣺⣿⡷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠄⣤⡄⣇⢙⣿⢳⡆⢀⣼⣿⣯⠀⠃⡰⣳⣿⣿⣿⣯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠅⠄⢶⣔⣦⣿⣿⣷⢾⣿⣿⡇⠀⠀⠀⠻⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⢿⣿⣿⣿⣿⡿⠙⢮⣿⣿⡇⠀⠀⠀⢨⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⣬⣿⣿⢇⣀⠀⠀⠙⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠰⢀⣤⣿⢏⣾⠃⠀⠀⠐⠿⠿⠋⠻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠈⠉⠋⢾⠏⠔⠀⠀⠀⠀⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠂⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⡀⠀⠠⣴⡄⢀⣆⠀⠀⠀⠀⢰⣿⣷⠀
⣿⣿⣿⣿⡿⠀⠙⢿⣿⡯⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡀⠈⠀⠀⠛⠁⡾⠟⠀⠀⠀⠀⣠⣅⡄⠀
⣿⣿⣿⡟⠀⠀⠀⠈⣙⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⠀⠈⠀⠀⠠⣤⣿⣿⠇⠀⠀⠀⠀⠈⠛⠤⢀
⣿⣿⣿⠃⠀⠀⠀⡨⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⠀⠀⠘⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢹⣿⡿⠁⠀⠀⠤⣶⡆⠀⠀⠀
⠏⠁⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠙⣿⣿⣿⣷⠀⠀⠀⢀⡀⠋⡏⠁⠀⠀⠰⢢⡼⡟⠃⡂⠀
⠀⠀⠀⣠⣴⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⣿⣿⣿⣿⡆⠐⠀⠼⣿⡾⠁⠀⠀⠀⢀⠈⠁⠁⠀⠀⠀
⣀⣤⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣄⠘⢿⣿⣿⣷⣤⠀⠀⠉⠈⠀⠀⠀⠀⠀⠛⠒⠀⠀⠀⢀
⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠈⢿⣿⣿⣷⣄⠀⠀⠀⣀⠀⠀⠀⢈⣥⣤⣤⢀⠀
⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠹⣿⣿⣿⣇⠀⠀⠈⠀⠀⠀⢻⠘⠿⣿⣶⣀
⣿⣿⠋⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⠁⠀⠀⠀⠀⢠⠐⣤⡀⠰⡠⣌
⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⠛⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠚⣿⣿⣿⣷⠂⢻
⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣇⣴⣿⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣸⡷⠀⠉⢿⣿⣿⠏⠀⠘
⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠀⣤⡀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⠉⡁⢩⣙⢛⡒⠀⠀
⣿⡆⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢘⢷⣬⣿⣧⠁⠀⠠
⣿⣷⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠒⠀⢐⣶⠃⢀⠀⣄
⢻⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠐⠄⠀⠐⠉⠈⢒
⠀⠈⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⡀⠀⠀⠀⠠
⣀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠿⠀⠀⠀⠀
⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣤⣿⣿⡀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢠⡀⠀⠀⠀
⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠁⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣾⣷⠀⠐
⣿⣿⣿⣷⣤⣀⣀⣀⣠⡄⠀⠀⠀⠀⠉⠙⠛⢉⣿⣿⠿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠓
⠀⠉⠛⠿⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣀⡼⠇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢨⣍⡉⠉⢿⣀⡀⠟⠋⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠸⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣦⡄⠀⠀⠀⣠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⢰⣿⣿⣿⣇⣀⣀⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣥⣤⠀⠀⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⣀⡰⣶⢀⣰⢌⣡⣠⣖⣆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
[69A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⠸⣿⠿⡇⣘⡇⡸⢟⢸⣿⠀⠀⠀⠀⠀⢀⠠⠀⠀⠐⢛⣛⣛⡛⣿⣱⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠐⠲⠄⠀⠹⠛⠀⡘⣨⠅⠴⢰⡷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠀⠐⡀⢈⡟⠲⠿⠛⣛⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠘⠀⠀⠀⠄⠀⠀⢠⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⣻⡏⠈⠈⢹⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠄⠀⠈⠁⠨⠃⠀⠐⢪⣥⡄⠀⠀⠁⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⣠⣶⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠒⠀⠀⠀⠀⠀⣀⣸⣹⠀⢠⡄⠐⠂⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣄⢃⠀⣀⠀⢹⣭⣾⠀⣰⢄⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠛⢻⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠠⡈⠛⠿⠿⡄⠸⣷⠛⠈⠛⠻⡁⠓⢀⠀⢰⡇⠄⠀⠀⠀⠀⡠⠀⠀⠀⠀⣘⠀⢠⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠂⠠⢀⢴⣾⡆⠠⡉⠈⣅⡀⠀⠀⢈⠁⠀⠀⠀⠀⠀⢀⣦⠐⠄⣀⠀⠀⣼⣿⡿⢻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡀⠀⢰⢀⢀⠀⠋⣻⣿⡆⣾⠏⠀⠀⠵⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣉⣤⣼⣿⣶⣴⣿⠃⢀⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣷⣂⣤⣈⣿⣿⣶⣿⣿⡿⡞⠘⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠉⢹⣿⠟⢃⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡙⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣧⣇⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣿⣦⡾⣿⣿⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣷⠀⠘⢻⣿⣿⣿⣿⣿⣻⠀⠀⠀⠀⣼⡇⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢀⠿⠅⣀⣼⡿⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⢠⠈⢿⣿⣿⣿⣿⡏⣀⠀⠀⡀⣹⠁⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠃⠒⣛⣿⣿⠟⠃⣁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠙⢻⣿⣿⣿⢣⡟⠀⣨⣾⡿⠰⢸⣹⣧⡀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣄⣀⣴⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢰⣾⣿⣿⡟⢰⡾⠀⣿⣿⡇⠀⣼⡿⡀⠀⠀⠀⠀⠀⠀⣀⣺⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⣿⣿⣿⡃⡻⢧⣠⣿⣿⠃⠀⢹⣿⣇⠀⢀⣀⠀⠀⣰⠻⢭⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠟⠻⠃⠀⠉⢘⢿⣿⡿⠀⡄⠀⠙⠿⣿⣽⣿⣿⣿⡷⣽⣿⣿⣿⣿⣿⣻⡿⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣿⣿⣿⡇⢠⠃⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⣽⣿⣿⡤⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣆⠀⠀⠀⣶⣿⣿⣿⠀⣴⣧⡀⠀⠀⣿⣿⣿⣿⣿⡿⢿⠓⠐⢦⡴⢸⢏⡼⢛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣷⣄⠀⣿⣿⣿⡏⢸⣿⣟⣾⡃⣰⣿⣿⣿⠿⡟⠑⠀⡈⠽⡛⠃⠀⠛⠳⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⣾⣿⡏⢠⣿⢫⣾⣿⣿⣿⣿⣿⡋⠐⢯⣷⣬⣥⠲⠀⢐⡃⢀⣴⣎
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣯⠀⠺⠿⢿⣿⣿⣿⣿⣿⣿⣏⢠⡺⠻⢿⣯⡠⠱⠁⢛⣷⡡⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⣄⠀⠘⣙⣉⡋⣭⠙⢷⢶⣄⠀⢠⣶⣿⠋⠨⠠⡼⣷⣾⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣦⡀⠂⢈⢡⣈⢥⡻⣿⣿⣴⣷⣾⡷⠁⠀⠈⠺⡯⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣄⣾⣶⣿⣿⣿⣿⠻⣮⣿⣿⣇⠀⠀⠀⠐⣲⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣄⣿⣿⡏⢀⠐⠈⠘⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡄⣈⣿⡿⣱⠯⠀⠀⠀⢼⣿⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠘⠛⠿⢱⡿⠀⠀⠀⠀⠈⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⠀⢤⠀⠀⠺⠃⠀⠀⠀⠀⠀⠁⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⣠⡄⠀⠀⠀⠀⡀⠀⠀⣤⣶
⣿⣿⣿⣿⣿⣿⠏⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠙⠀⠀⣽⡇⢰⣯⠴⠀⠀⠀⢐⡙⠙
⣿⣿⣿⣿⣿⠇⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠑⠀⠀⠀⣀⣶⣶⡖⠀⠀⠀⠀⠸⢿⢇
⠛⣻⣿⣿⡿⠀⠀⠀⠀⢀⣹⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣦⡀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢹⣿⣿⠂⠀⠀⣀⣄⡄⠀⢈
⠰⠿⠁⠀⠀⠀⢀⣤⣤⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣦⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠼⣛⠋⠀⠀⢀⣀⣹⣿⡦⠀
⠀⠀⠀⠀⢠⣤⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡆⠠⠀⢰⣷⣒⠋⠀⠀⠀⠀⠘⠏⠇⠀⠀
⠀⢠⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⢠⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠙⠋⠆⠀⠀⠀⠈⠤⠄⠀⠂⠀
⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⠛⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀
⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠈⢹⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠒⠀⠀⠀⣴⠙⣶⣯⣉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⡀⠴⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠹⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⣈⡰⣀⠈⠙⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢀⡄⠘⢃⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣐⣤⣾⣥⣬⡊
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢸⣧⣤⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠁⢰⣄⠀⡒⠻⣿⣿⡿⠀
⠻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⠶⠻⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣚⣚⡂⠥⠽⠿⢿⣄⡀
⠀⠙⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠉⠛⠛⠓⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣶⠠⣢⠘⣿⡔⠦⠀
⠀⠀⠈⠻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣁⠙⠚⣟⡛⠀⠀
⣄⠀⠀⠀⠙⢿⣿⣿⡆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣤⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⢦⣄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢀⠀⠌⢠⠴⠂
⣿⣷⣄⠀⠀⠀⠙⢿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣇⣀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠣⠀⠀⠀⠀⠘⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣄⠀⠀⠀⠁⠀⠀⠀⠀⠸⣿⣿⣿⢿⣿⣿⣿⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⣢⠈⠀⠀
⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣿⣿⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠈⠁⡀⠀
⠻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⢿⣷⡄⠀⡅⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣀⣄⠀
⣄⠈⢿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⢸⣿⠿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢻⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠀
⣿⣆⠀⠈⠻⢿⣿⣿⣿⣿⣶⣶⣤⡶⠀⠀⠀⠀⠀⠈⠃⠀⠾⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⣿⣿⣷⡀⠀⠀⠈⠉⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡸⠛⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⣀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⢠⣿⡿⠿⠿⠿⣿⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⢿⠿⠿⠿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣴⣶⣶⣶⡌⢁⣴⣶⣷⣶⡄⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣶⣶⣶⠀⠀⠀⣶⣶⣶⣶⣶⢰⣶⣶⣶⣦⡀⢠⣶⣾⣶⣦⡀⣶⣶⡆⠀⢰⣶⡆⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⠸⠿⠷⢸⣿⣿⢸⣿⡇⠀⢸⣿⡏⠀⡀⢸⣿⡏⠀⣸⣿⣿⣿⡇⠀⠀⠀⢸⣿⡏⠀⢸⣿⣿⣸⣿⡇⣾⣿⡇⣿⣿⡇⣿⣿⡇⠀⢸⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⢶⣶⣶⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⢸⡇⢸⣿⡇⠀⣿⣿⢸⣿⣇⠀⠀⠀⢸⣿⡇⠀⢸⣿⣿⢿⣯⡅⣿⣿⡇⣿⣿⡇⣿⣿⡇⠀⢸⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣸⣿⣿⢸⣿⣿⣸⣿⡇⠀⢸⣿⡇⢸⡇⢸⣿⡇⢀⣿⣿⠿⣿⣿⠀⣿⡆⢸⣿⡇⠀⢸⣿⣿⢸⣿⡇⢻⣿⣇⣿⣿⡇⣿⣿⣇⣀⢸⣿⣇⣈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡙⠻⠛⠛⠛⣀⡙⠻⠟⠛⣡⣆⠘⠛⠃⣸⣧⡘⠛⠃⠘⠛⠛⠀⠛⠛⢀⣿⣇⡘⠛⠓⣀⡘⠛⠛⠘⠛⠃⣈⠛⠻⠟⢋⣀⠛⠛⠛⠛⠘⠛⠛⠛⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣛⣋⣙⣉⡛⣛⣉⣉⣛⠻⢛⣉⣉⡙⠻⢛⣛⡛⢛⣛⡛⢛⣉⣉⣛⡛⠿⢛⣛⡛⠿⢛⣉⣉⡛⠛⢋⣉⣙⢋⣉⡙⣋⣉⣛⣛⣛⠛⢛⣉⣙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⠿⣿⣿⠿⠇⣿⣿⡿⠯⢰⣿⡿⢻⣿⡆⢸⣿⣇⢸⣿⡇⢸⣿⣿⢿⣿⡆⢸⣿⡇⢰⣿⡿⢻⣿⡆⢸⣿⣿⢸⣿⡇⠿⢿⣿⡿⠿⣸⣿⡟⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⠀⠀⣿⣿⣧⡄⢸⣿⡇⠸⠿⠿⢸⣿⣿⣾⣿⡇⢸⣿⣿⣼⣿⠇⢸⣿⡇⢸⣿⡇⣘⣛⡃⢸⣿⣿⣾⣿⡇⠀⢸⣿⡇⠀⠹⣿⣷⣭⡉⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⠀⣿⣿⡟⠃⢸⣿⡇⢠⣤⣤⢸⣿⣿⢹⣿⡇⢸⣿⣿⢹⣿⡆⢸⣿⡇⢸⣿⡇⢻⣿⡇⢸⣿⣿⢹⣿⡇⠀⢸⣿⡇⠈⢠⣬⡝⣿⣿⡄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⠀⣿⣿⣷⣶⠸⣿⣷⣼⣿⠇⢸⣿⡇⢸⣿⡇⢸⣿⣿⢸⣿⡇⢸⣿⡇⠸⣿⣷⣼⣿⡇⢸⣿⣿⢸⣿⡇⠀⢸⣿⣇⠀⠸⣿⣧⣿⣿⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣍⣭⣴⣦⣭⣭⣭⣭⣤⣬⣉⣉⣥⣴⣬⣭⣥⣬⣭⣥⣬⣭⣭⣬⣭⣥⣬⣭⣥⣶⣬⣍⣥⣭⣥⣬⣉⣭⣬⣭⣥⣶⣬⣭⣥⣾⣷⣬⣭⣩⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⣆⡲⣶⢏⣶⢌⣡⣰⣶⣆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
[69A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡆⠻⡟⡻⠠⠽⣤⢻⡅⠿⠇⠀⠀⠀⠀⠀⠄⠂⠀⠀⠉⠩⣭⠍⢹⣧⣾⣿⣏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⡀⠉⠓⠀⠀⠃⠁⢠⣡⠆⠐⠃⠿⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠡⠀⢴⣉⡙⡋⡩⣽⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠁⣀⠀⡐⠀⠀⠀⣶⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣿⠀⠀⠀⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠉⠶⣶⡀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠁⠀⠀⠀⠀⢠⣤⡧⡃⠀⠖⠀⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠰⣬⣄⣠⡄⠠⣶⣼⡇⡠⣗⣤⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⠉⣿⣽⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠢⠈⠙⠛⠳⠀⢻⡏⠁⢈⠉⣣⠈⠀⠄⠀⡿⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠠⠅⠀⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠈⠀⠂⣰⣿⡿⠀⣢⡀⠰⢄⠀⠀⠈⡄⠀⠀⠀⠀⠀⢀⢼⡄⠑⣠⡄⠀⢠⣿⠿⠋⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠇⣀⣄⡈⢩⣿⣿⡸⡟⡀⡀⣐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⢶⣿⣿⣷⣿⠏⣀⣼⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⣿⣿⣷⣠⣤⣽⣿⣿⣿⣿⣿⢻⠁⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢻⡟⠉⣼⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣻⣿⣿⠘⠻⣝⣿⣿⣿⣿⣿⣾⡀⠀⠀⠀⠀⣷⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢰⣷⠾⠻⣿⡿⣹
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡇⠀⠁⣿⣿⣿⣿⣿⣯⡇⠀⠀⠀⢰⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠜⣓⣠⣰⣿⢧⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡆⠙⣿⣿⣿⣿⣿⢀⡄⠀⠀⣨⡏⠀⢸⣄⠀⠀⠀⠀⠀⠀⠀⠘⠈⣉⣹⡽⠟⠉⢠⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠙⣿⣿⣿⡏⠔⡃⢠⣶⣿⡇⠃⣎⡿⢴⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣷⣤⣴⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣾⣿⣿⣿⠁⣾⠃⢰⣿⣿⠀⠰⣿⣣⠀⠀⠀⠀⠀⠀⢀⣨⣻⣿⣿⣿⣿⣿⣿⣏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⣼⡿⣿⠟⠨⡛⣄⣼⣿⡏⠀⠀⢿⡿⣆⣀⢤⣄⡀⡠⣋⣷⣾⣿⣿⣿⣿⣿⣿⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠋⠀⠀⢀⣝⣿⣿⠇⢰⡄⠀⠙⢻⣿⣿⣿⣿⣿⣳⣟⣿⣿⣿⣿⣏⡿⠛⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣼⣿⣿⣿⠀⡎⠀⠀⠀⢚⣿⣿⣿⣿⣿⣿⣿⠟⠁⠠⠿⣻⡷⢖⡝
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⢐⣿⣿⣿⡇⢰⣿⣥⣀⠀⢸⣿⣿⣿⣿⣿⠟⠍⣃⣐⣶⠆⠟⣡⠞⣁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⣿⣿⡿⢁⣿⡿⣵⣿⡀⣾⣿⣿⡿⠛⢇⠁⣀⠐⠋⠉⠈⠈⠉⢱⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣽⣿⠀⣼⣟⣽⣿⣿⣿⣿⣿⣿⡀⠉⣺⣷⣶⡆⠁⠀⡺⣀⣤⢶⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠛⠛⢿⣿⣿⣿⣿⣿⡿⠄⠆⠋⠻⢿⣦⡀⣂⢈⢽⠏⠾⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠨⠭⣽⡀⣆⢙⣧⢶⡆⢀⣼⣿⢟⠁⠃⣰⡻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣦⣰⣮⣻⣿⣧⣿⣿⣿⠇⠀⠀⠁⠛⣺⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡟⠹⢜⣿⣿⡄⠀⠀⠀⢉⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠃⠠⣼⣿⣿⢁⡀⠀⠀⠰⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢠⣀⣰⣿⢏⡾⠇⠀⠀⠐⣿⠿⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠈⠙⠋⣾⠗⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠐⠄⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠏⠁⡀⠀⢠⡄⠀⠀⡀⠀⠀⠀⠀⢠⣾⣇
⣿⣿⣿⣿⣿⠿⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠁⠀⠰⠿⠀⣾⠆⠂⠀⠀⠀⢠⣃⠉
⣿⣿⣿⣿⡏⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣿⣿⡗⠀⠁⠀⠀⢀⣴⣶⡷⠂⠀⠀⠀⠀⠛⠟⡀
⢙⣿⣿⠿⠁⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠈⢿⣿⡗⠀⠀⠀⢀⣤⡀⠀⠀
⠟⠋⠀⠀⠀⠀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⠠⢪⡉⠁⠀⠀⠠⢄⣿⠷⠄⠀
⠀⠀⠀⠀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠢⠀⣿⣧⡌⠁⠀⠀⠀⠀⠙⠐⠀⠀⠀
⠀⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡤⠀⠈⠉⠐⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀
⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣦⡀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⠀
⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣶⣆⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠁⠀⠀⠠⠏⠹⣾⢧⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣧⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠄⠤⠡⣄⠀⠉⢉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⡀⠀⠈⣿⠇⠀⠀⠀⠀⠀⠀⢀⣴⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣷⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠴⣾⣷⣶⡮⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢐⠏⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⡿⡄⢸⢑⣿⣿⡷⡃⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢰⣾⣿⣿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⠬⠐⠒⣛⠛⠷⠤⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠘⠋⠉⠛⠻⣷⢄⡀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠒⡦⢹⡷⡜⠂⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⡀⠀⠀⠀⢡⣿⡟⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡡⠄⠈⠱⣅⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⠀⠀⠚⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠄⠀⠁⠔⠋⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠡⠌⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠉⠻⣿⣿⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠰⣔⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠉⠓⠈⣿⡇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣤⣴⡄⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⢟⣻⣿⣆⡠⠤⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⡖⠦⠤⢀⠈⣦⣀⠀⠀⠀⠀⠈⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠁⠀⠀⠀⠀⠻⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠰⢸⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⡿⠿⠿⠷⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⡿⠿⠿⠿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣴⣶⣶⣶⡌⢁⣴⣶⣷⣶⡄⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣶⣶⣶⠀⠀⠀⣶⣶⣶⣶⣶⢰⣶⣶⣶⣦⡀⢠⣶⣶⣶⣦⡀⣶⣶⡆⠀⢰⣶⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⠸⠿⠷⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⠀⡀⢸⣿⡏⠀⣸⣿⣿⣿⡆⠀⠀⠀⢸⣿⡏⠀⢸⣿⣿⣸⣿⡇⣾⣿⡇⣿⣿⡇⣿⣿⡇⠀⢸⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⢶⣶⣶⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⢸⡇⢸⣿⡇⠀⣿⣿⢸⣿⣇⠀⠀⠀⢸⣿⡇⠀⢸⣿⣿⢿⣯⡄⣽⣿⡇⣿⣿⡇⣿⣿⡇⠀⢸⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣸⣿⣿⢸⣿⣿⣸⣿⡇⠀⢸⣿⡇⢸⡇⢸⣿⡇⢀⣿⣿⠿⣿⣿⠀⣿⡆⢸⣿⡇⠀⢸⣿⣿⢸⣿⡇⢻⣿⣇⣿⣿⡇⣿⣿⣇⣀⢸⣿⣇⣈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡙⠻⠛⠛⠛⣀⡙⠻⠟⠛⣡⣆⠘⠛⠃⣸⣧⡘⠛⠃⠘⠛⠛⠀⠛⠛⢀⣿⣇⠘⠛⠃⣀⠘⠛⠛⠘⠛⠃⣈⠛⠻⠟⢋⣀⠛⠛⠛⠛⠘⠛⠛⠛⣠⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣛⣉⣉⣉⡛⣛⣉⣉⣛⠛⢛⣉⣉⡙⠻⢛⣛⣛⢛⣛⡛⢛⣉⣉⣛⡛⠿⢛⣛⡛⠿⢛⣉⣉⡙⠛⢛⣉⣙⢋⣉⡉⣋⣉⣛⣛⣛⠛⢛⣉⣙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⠿⣿⣿⠿⠇⣿⣿⡿⠇⢰⣿⡿⢻⣿⡆⢸⣿⣿⢸⣿⡇⢸⣿⣿⢿⣿⡆⢸⣿⡇⢰⣿⡿⢻⣿⡆⢸⣿⣿⢸⣿⡇⠿⢿⣿⡿⠿⣸⣿⡟⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⠀⠀⣿⣿⣥⡄⢸⣿⡇⠸⠿⠿⢸⣿⣿⣾⣿⡇⢸⣿⣿⣼⣿⠇⢸⣿⡇⢸⣿⡇⣘⣛⡃⢸⣿⣿⣾⣿⡇⠀⢸⣿⡇⠀⠹⣿⣷⣭⡉⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⠀⠀⣿⣿⡟⠃⢸⣿⡇⢠⣤⣤⢸⣿⣿⢹⣿⡇⢸⣿⣿⢹⣿⡆⢸⣿⡇⢸⣿⡇⢻⣿⡇⢸⣿⣿⢹⣿⡇⠀⢸⣿⡇⠈⢠⣬⡝⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⠀⠀⣿⣿⣷⣶⠸⣿⣷⣼⣿⠇⢸⣿⣿⢸⣿⡇⢸⣿⣿⢸⣿⡇⢸⣿⡇⠸⣿⣷⣼⣿⡇⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⠀⠸⣿⣧⣿⣿⠇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣍⣩⣴⣦⣭⣍⣩⣭⣤⣬⣉⣉⣡⣴⣬⣭⣥⣬⣭⣥⣬⣭⣭⣬⣩⣥⣬⣉⣥⣶⣬⣍⣡⣭⣥⣌⣉⣩⣬⣭⣥⣶⣬⣭⣥⣾⣷⣬⣍⣩⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⣆⡲⣶⢄⣶⢌⣡⣰⣶⣆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
[69A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⡈⠉⠑⠂⠀⠙⠈⡰⣨⡴⠀⠊⠹⠗⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠁⠃⠁⢠⣗⡚⠛⢉⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠁⣀⠀⠐⠄⠀⠀⢦⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⡇⠁⠁⢸⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠚⠀⠀⠈⠣⢦⣀⠀⠀⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠁⠀⣤⣾⣿⣿⣿⣿⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⠋⠀⠀⠀⠀⠀⣄⣰⠹⠀⠤⠀⠐⠃⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡟⢠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢌⣂⡀⣀⠀⣹⣌⣺⠀⠴⢤⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠋⢻⢿⣿⣿⣿⠃⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠠⠀⠙⠻⠻⠆⠸⣿⢛⠈⠉⠛⡁⠑⢀⠀⢰⡇⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⡘⠀⢰⣿⣿⣿⣿⡟⢰⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠠⠀⠀⠂⠠⢀⢰⣾⡖⠠⡈⠈⣉⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⣧⠐⠄⣀⠀⠀⣾⣿⠿⢿⣿⢃⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⡀⠀⢰⣀⢀⠀⠉⣻⣿⣷⢸⠏⠀⠀⠭⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣁⣤⣴⣿⣴⣴⣿⠃⢀⣿⠏⣸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣷⠀⠀⣈⣻⣿⣶⣿⣿⣿⣶⠀⠀⠐⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠈⠙⣿⠟⢃⣾⣿⣿⢠⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡙⣿⣿⡇⠀⢿⢻⣿⣿⣿⣿⣿⡅⠃⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⣾⣿⣿⡟⣾⣿⠟⢻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣷⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢠⣯⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡼⠍⣀⣸⣿⣸⣿⡟⡀⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⡀⢻⣿⣿⣿⣿⣿⠁⠀⠀⢀⢘⡇⠈⢰⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⢒⣛⣻⡿⠃⣉⣩⠁⠈⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠈⠻⣿⣿⣿⡟⡨⠁⢀⣬⣽⡇⠆⣏⣶⡄⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣄⡀⣰⣿⡟⣀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢤⣿⣿⣿⠇⣓⠆⢘⣿⣿⠀⢠⣿⢏⠈⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⢗⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣻⣿⣿⡿⠰⢿⡀⢸⣿⣿⠀⠈⣿⣿⡄⠀⣀⡀⠀⠀⡖⣭⣽⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⠇⠟⠀⠀⠁⠺⣿⣿⡇⢀⡄⠈⠳⢷⣛⣾⣷⣶⣮⢯⡷⣿⣿⣿⣿⡟⣿⠿⠛⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢰⣿⣾⣿⠁⡘⠃⠀⠀⠴⣿⣿⣿⣷⣿⣾⣿⡿⠋⢙⣿⣿⣧⣄⠲⠻⡿⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⣾⣿⣿⡟⢀⣷⣆⠀⠀⢸⣿⣿⣿⣿⣿⡿⡿⠆⠠⣤⡄⡿⣡⠞⠱⠶⠲⠞
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⣿⣿⣿⡇⢸⣿⣟⣾⠃⣼⣿⣿⣿⠿⡟⠀⠀⠊⠟⠛⠀⠐⠛⣾⣷⣶⡏⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣛⣿⠍⢠⣿⢯⣾⣿⣷⣿⣿⡿⠋⠐⢦⣦⣄⡤⠂⠀⢰⠀⣀⣬⣵⣿⣗⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢾⠿⣿⣿⣿⣿⣿⣿⣿⡇⣀⠟⢿⣿⣅⡀⠐⠑⣻⡾⣼⣿⣏⠁⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣦⡀⠀⠘⡛⣻⡏⡍⠻⣯⢤⡈⠀⢀⣾⡿⠃⠏⢨⢞⣶⣶⣾⣟⠀⣐
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⡅⠘⢡⡙⣌⢾⣾⣧⣸⣯⢻⡏⠀⠀⠈⢷⢽⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣼⣭⣿⣿⣿⣿⠿⣟⣿⡿⡇⠀⠀⠀⠐⣼⣿⣿⣿⣻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⡿⡟⠀⠐⢿⣿⡇⠀⠀⠁⠈⣿⣿⣿⣹⣋⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⣽⣿⠏⢹⠋⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠛⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⠉⠀⠀⠀
⣿⣿⠇⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⢃⠀⢀⣀
⣿⠃⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⠀⠀⠀⢄⣭
⠟⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡸⣿⠦⠀⠀⢺⣿
⠀⠀⢀⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡐⠀⠀⠀⠀⠘⠋⠀⠀⠈⠀⠈⠀
⠀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠑⠀⠀⠀⠀⠡⠤⠀⠂⠀⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⣦⣤⣀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡀⠀⡀⠀⠁⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠂⠀⠀⢰⡏⢷⣿⣤⠀⠈⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣀⡤⡀⠈⠉⡉⢹⣆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⢿⣿⣿⣿⡿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠠⢷⣶⣿⣶⠯⠈⢏⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢋⡀⠀⢈⣿⣿⣥⣦⠜⢻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠁⡷⡄⢊⢨⣿⣿⡞⠁⠀⠓⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣼⣿⣿⣿⣿⡿⠋⠁⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣉⡀⠐⠂⣛⠛⠧⠤⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠘⡆⢹⡷⠙⠂⠀⢀⡀
⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣤⡀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡡⠄⠈⠹⡭⠀⠀⢀⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⡿⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠈⠀⠈⠉⠐⣉⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠉⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠇⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⠀⠄⠀⠀⠈⠆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣣⣄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠐⠥⠀⠀⠀⠈⢷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠐⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣠⡽⣏⠄⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢿⠛⠿⠟⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣴⣶⡆⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠧⢾⣷⣷⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⢳
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣵⣄⣸⡿⠟⢧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣾⠿⣛⣿⣧⣀⠴⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢸⣦⠠⠤⠀⠀⢱⣄⡀⠋⠀⢀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠄⠀⠀⠸⠯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⣤⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣤⣸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⠿⠿⠿⠿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠺⠿⡿⠿⠿⠿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣴⣶⣶⣶⡌⢁⣴⣶⣷⣶⡄⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣶⣶⣶⠀⠀⠀⣶⣶⣶⣶⣶⢰⣶⣶⣶⣦⡀⢠⣶⣾⣶⣦⡀⣶⣶⡆⠁⢰⣶⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⠸⠿⠷⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⢀⡀⢸⣿⡏⠀⣸⣿⣿⣿⡇⠀⠀⠀⢸⣿⡏⠀⢸⣿⣿⣸⣿⡇⢾⣿⡇⣿⣿⡇⣿⣿⡇⠀⢸⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⢶⣶⣶⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⢸⡇⢸⣿⡇⠀⣿⣿⢸⣿⣇⢀⣤⡀⢸⣿⡇⠀⢸⣿⣿⢿⣯⡄⣿⣿⡇⣿⣿⡇⣿⣿⡇⠀⢸⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣸⣿⣿⢸⣿⣿⣸⣿⡇⠀⢸⣿⡇⢸⡇⢸⣿⡇⢀⣿⣿⠿⣿⣿⠀⣿⡇⢸⣿⡇⠀⢸⣿⡏⢸⣿⡇⢻⣿⣇⣿⣿⡇⣿⣿⣇⣀⢸⣿⣇⣈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡙⠻⠛⠛⠛⣀⡙⠻⠟⠛⣡⣆⠘⠛⢃⣸⣧⡘⠛⠃⠘⠛⠛⠀⠛⠛⣀⣿⣧⡘⠛⠃⣀⠘⠛⠓⠘⠛⠃⣈⠛⠻⠟⢋⣀⠛⠛⠛⠛⠘⠛⠛⠛⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣋⣉⣉⣉⡛⣋⣉⣉⣛⠛⢋⣉⣉⡛⠻⢛⣋⣛⢛⣉⡛⢛⣉⣉⣛⡛⠿⢛⣛⡛⠟⢛⣉⣉⡙⠻⢛⣉⣙⢋⣉⡙⣛⣛⣋⣛⣛⠛⢛⣉⣙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⠿⣿⣿⠿⠇⣿⣿⡿⠧⢰⣿⡿⢻⣿⡆⢸⣿⣿⢸⣿⡇⢸⣿⣿⢿⣿⡆⢸⣿⡇⢰⣿⡿⢻⣿⡆⢸⣿⣿⢸⣿⡇⠿⢿⣿⡿⠿⣸⣿⡟⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⠀⠀⣿⣿⣧⡄⢸⣿⡇⠸⠿⠿⢸⣿⣿⣾⣿⡇⢸⣿⣿⣼⣿⠇⢸⣿⡇⢸⣿⡇⣘⣛⡃⢸⣿⣿⣾⣿⡇⠀⢸⣿⡇⠀⠹⣿⣷⣭⡉⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣿⣿⠀⠀⣿⣿⡟⠃⢸⣿⡇⢠⣤⣤⢸⣿⣿⢹⣿⡇⢸⣿⣿⢹⣿⡆⢸⣿⡇⢸⣿⡇⢻⣿⡇⢸⣿⣿⢹⣿⡇⠀⢸⣿⡇⠈⢠⣬⡝⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⠀⠀⣿⣿⣷⣶⠸⣿⣷⣼⣿⠇⢸⣿⣿⢸⣿⡇⢸⣿⣿⢸⣿⡇⢸⣿⡇⠸⣿⣷⣼⣿⡇⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⠀⠸⣿⣧⣿⣿⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣍⣩⣴⣦⣭⣉⣉⣭⣤⣬⣉⣉⣡⣴⣬⣭⣥⣬⣭⣥⣬⣭⣭⣬⣭⣥⣬⣭⣥⣶⣬⣉⣡⣍⣡⣌⣉⣩⣬⣭⣥⣶⣬⣭⣥⣾⣦⣌⣉⣩⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⣆⡲⣶⢀⣶⢌⣡⣰⣶⣆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
[69A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⢤⡄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠿⠇⠀⠀⣹⣿⣿⣿⣿⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠈⠒⠀⠀⠀⠀⠀⢀⠘⡹⡀⠀⡀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⣟⠫⡁⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⡈⠸⢷⣶⣧⠀⢻⣵⠿⠀⠷⣿⠀⠄⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⢠⣯⣿⣿⣿⢁⣿⣿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠈⠀⠀⠀⡀⠁⢈⣷⢐⠀⠀⠐⠢⠀⠐⠀⠸⠇⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠂⠀⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡄⠀⠀⢀⠀⠀⠀⠰⢾⣿⣌⣀⣵⠀⠉⠲⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠛⠀⢁⣶⢀⢀⣿⡟⠉⣿⡏⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢿⣿⣿⣿⡄⠀⠈⠰⣴⣤⣌⣽⣿⣿⣇⡋⠀⠀⣬⡅⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⡿⠿⠿⣿⣿⡟⢀⣴⡿⢠⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⠛⢿⣿⣿⡄⠀⠰⣾⣿⣿⣿⣿⣿⣟⡇⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡏⢀⣿⣿⣿⣸⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠘
⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣿⣿⣷⠀⠈⠢⢹⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠨⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠛⢻⣿⣏⣿⣿⠁⢻⣾⣿⣿⣿⣿⣿⣿⣿⣏⣁⠁⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠸⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢸⣿⢠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣁⣴⣼⣿⠻⠿⠟⠠⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠙⣿⣿⣿⣿⣿⢀⣄⠀⠀⢤⣧⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣶⠛⠁⢠⣶⡆⠀⠈⣉⢻⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠘⢿⣿⣿⣿⠠⠃⠀⣴⣿⣟⠀⢸⣼⠧⠄⠀⠀⠀⠀⠀⠀⣸⣿⣿⣷⣤⣿⣿⣡⣤⣄⠉⠄⠉⠁⠀⢪⣶⠀⠀⠀⠀⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠄⠐⣯⣿⣾⣿⠨⡽⠀⢸⣿⡗⠀⢾⣿⣄⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⡿⣜⣿⣿⡆⠠⢤⡅⣴⣾⡏⠀⠀⠀⠀⠸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢀⣿⠛⢿⠏⠘⠏⢄⣸⣿⡟⠀⠘⢿⣿⣄⣠⣤⣀⣀⡜⢜⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⠀⡾⣶⣿⡿⠁⠀⠀⠀⠀⠀⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡿⠀⠀⠀⠈⠀⣙⢿⣿⡇⢀⡆⠀⠙⢻⣿⣿⣿⣿⣟⣻⣿⣿⡿⣿⣧⣟⠉⣀⡿⣿⣿⡖⠀⠸⠟⠁⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣿⣿⣿⡇⢨⠁⠀⠀⠘⣿⣿⣿⣿⣿⣿⡷⠃⠤⠚⢻⡿⢫⡎⣀⣋⣹⢿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢰⣽⣿⣿⠁⣴⣯⡄⡀⠀⣿⣿⣿⣿⣿⠟⠉⡡⣬⣿⠈⢣⣎⣤⣍⣴⠶⢘⡁⠁⠀⣀⠀⠀⠀⠀⠀⠀⢰
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠘⣿⠿⣿⠀⣿⡿⣽⣯⢀⣿⣿⣿⡟⢙⢀⠀⠀⠁⠀⢀⠀⠀⣛⣻⣿⡀⠎⠁⢀⣺⣿⣷⠀⠚⢻⡆⠐⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣻⣥⠀⢸⣿⣱⣿⣿⣿⣿⣿⣯⡈⠑⣿⣶⡿⠀⠀⠔⣤⣺⢷⣿⢟⠀⠀⠀⠖⠘⠉⠁⣶⣶⣾⡏⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠻⠻⢿⣿⣿⣿⣿⣿⠿⠂⠂⠈⢛⣿⣶⢨⠀⢸⣫⣽⣿⡗⠀⠀⣼⣿⣿⡇⢠⣿⣿⣿⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠈⠍⢽⡄⣆⢙⣿⢷⡇⢀⡼⣽⡣⠈⠀⢫⣿⣿⣿⣿⣾⣿⣾⣝⠿⠅⠀⠈⢻⣿⠀⠀⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⢀⣰⣄⣦⣿⣿⣿⣾⣿⣾⡇⠀⠀⠀⣗⣿⣿⣿⠿⣿⣿⣿⡜⠟⡀⠀⠀⣯⠀⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡹⣷⣿⣿⣿⣿⡏⠓⣽⣯⣧⠀⠀⠀⢸⣿⣿⣟⣿⠋⠹⣿⣷⣾⣿⣿⠦⠏⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠰⣼⣿⡗⣤⠀⠀⠈⣻⣿⠛⡿⠁⠂⠹⢿⣿⠿⠿⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠰⢤⣼⣿⢻⡏⠀⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠉⠁⣻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⡀⠀⠰⡄⠀⣀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠲⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣷⡿⠆⠀⠀⠀⠀⠈⠛⢋⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢉⡁⠀⠀⠄⠀⠀⢀⣤⣶⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡀⠀⢠⢼⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠉⠀⠀⠈⠀⠙⢿⣿
⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⣿⣿⣿⠿⠋⣉⢿⣿⣿⣿⢿⠿⣿⡿⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠁⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⣿⣿⠛⠛⣀⠀⠀⣨⣿⣿⡾⠿⠁⠈⠟⠻⠛⠒⠀⠈⠀⠚⠛⢻⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣀⣰⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣶⣤⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⡻⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠏⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄⣀⠀⠀⠀⠀⠀⢀⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡄⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣤⡀⠘⢀⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡜⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⣼⣿⡇⣠⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣏⠁⢛⣿⢀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣎⣩⣿⣴⡦⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠥⡁⠋⣿⣿⠿⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⣿⣏⣿⣿⠶⣿⣇⢀⠰⠆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⣿⣿⣿⣿⣿⡟⠻⣿⠛⠁⠚⠉⠉⠡⣀⣀⠈⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠟⡣⠀
⣿⣿⣿⣿⣿⣷⢀⣽⣧⠘⠉⠀⠀⠀⠯⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡀⠀⠀⠀⠀⢀⣴⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣦⡀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠸⠿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠟⠀⠸⠿⠿⣿⣿⠿⠿⠿⢿⣿⡿⠿⢿⣿⡿⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣴⣶⣶⣶⡄⢁⣴⣶⣶⣶⡄⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣶⣶⣶⠀⠀⠀⣶⣶⣶⣶⣶⢰⣶⣶⣶⣦⡀⢠⣶⣾⣶⣦⡀⣶⣶⡆⠁⢰⣶⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⠸⠿⠷⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⠀⠀⢸⣿⡏⠀⣸⣿⣿⣿⡆⢰⣤⡀⢸⣿⡏⠀⢸⣿⣿⣸⣿⡇⣾⣿⡇⣿⣿⡇⣿⣿⡇⠀⢸⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⢶⣶⣶⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⠀⡄⢸⣿⡇⠀⣿⣿⢸⣿⣇⢸⣿⡇⢸⣿⡇⠀⢸⣿⣿⢿⣯⡄⣿⣿⡇⣿⣿⡇⣿⣿⡇⠀⢸⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣸⣿⣿⢸⣿⣿⣸⣿⡇⠀⢸⣿⡇⠀⡇⢸⣿⡇⢀⣿⣿⠿⣿⣿⠀⣿⡇⢸⣿⡇⠀⢸⣿⣿⢸⣿⡇⢻⣿⣇⣿⣿⡇⣿⣿⣇⣀⢸⣿⣇⣈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠙⠻⠛⠛⠛⣀⠙⠻⠟⠛⣡⣆⡘⠛⠃⣸⣇⠘⠛⠃⠘⠛⠛⠀⠛⠛⢀⣿⣇⠘⠛⠃⣠⡘⠛⠛⠘⠛⢃⣈⡛⠻⠟⢋⣀⡛⠛⠛⠛⠘⠛⠛⠛⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣛⣉⣉⣉⡛⣉⣉⣉⣙⠛⢛⣉⣉⡙⠛⢛⣉⣙⢛⣉⡛⢛⣋⣉⣉⡛⠛⢋⣉⡙⠛⢛⣉⣉⡛⠿⢛⣛⣛⢛⣛⡛⣛⣛⣛⣛⣛⠛⢋⣉⣉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠸⠿⣿⣿⠿⠇⣿⣿⠿⠇⢰⣿⡿⢻⣿⡆⢸⣿⣿⢸⣿⡇⢸⣿⣿⢿⣿⡆⢸⣿⡇⢰⣿⡿⢻⣿⡆⢸⣿⣿⢸⣿⡇⠿⢿⣿⡿⠿⣸⣿⡟⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⠀⠀⣿⣿⣥⡄⢸⣿⡇⠸⠿⠿⢸⣿⣿⣾⣿⡇⢸⣿⣿⣼⣿⠇⢸⣿⡇⢸⣿⡇⣘⣛⡃⢸⣿⣿⣾⣿⡇⠀⢸⣿⡇⠀⠹⣿⣷⣭⡉⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⠀⣿⣿⡟⠃⢸⣿⡇⢠⣤⣤⢸⣿⣿⢹⣿⡇⢸⣿⣿⢹⣿⡆⢸⣿⡇⢸⣿⡇⢻⣿⡇⢸⣿⣿⢹⣿⡇⠀⢸⣿⡇⠀⢠⣬⡝⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⠀⣿⣿⣶⣶⠸⣿⣷⣼⣿⠇⢸⣿⣿⢸⣿⡇⢸⣿⣿⢸⣿⡇⢸⣿⡇⠸⣿⣷⣼⣿⡇⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⠀⠸⣿⣧⣿⣿⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣭⣭⣴⣦⣍⣉⣉⣩⣤⣬⣉⣉⣥⣴⣬⣭⣥⣬⣉⣥⣬⣉⣭⣬⣩⣥⣬⣭⣥⣤⣌⣉⣁⣉⣡⣌⣉⣉⣈⣉⣥⣶⣬⣭⣥⣾⣦⣬⣉⣉⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⣆⡲⣶⢀⢶⢌⣡⣰⣶⣆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
[69A⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⡍⠄⢿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣶⣶⠾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠀⠀⢹⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠶⢾⣻
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢤⣈⣭⡀⠀⠀⠀⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣼⣿⡷⠂⢸⣿
⠀⠀⠀⠀⠀⢀⣀⠀⢀⠀⠈⣿⡅⠤⠀⣠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣠⣤⡈
⡄⠀⠀⠀⠀⠀⠙⠻⠾⠷⡄⠈⣿⠟⠃⠐⠻⠯⠀⠤⠀⡀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⢈⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⡖⠀⠉⠉⣠
⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣷⣧⠀⠀⠐⠓⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠠⡄⢀⠀⠐⠀⠈⣿⣿⣿⣿⣾⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⣿⣿⣿⡟⠀⠀⢠⣿
⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠒⠿⣿⣧⣄⢰⡆⠈⠙⢓⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⢠⣶⣀⢰⣿⠟⢹⣿⢻⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⠁⠀⢀⣀⡀
⣿⣿⣿⣿⣦⠀⠀⠀⠀⢾⣶⣤⣽⣿⣿⣿⣦⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠿⠛⠿⢿⣿⡿⢠⣼⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣼⣿⣿⣿⠇⣀⡀⠈⢿⣿
⠉⠻⣿⣿⣿⣷⠀⠀⠐⠚⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⣿⣿⣿⣼⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣿⣿⣿⡿⠀⠉⠁⠀⠀⣺
⣷⣤⡾⢿⣿⣿⣷⡀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣦⣤⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠉⢻⣿⣽⣿⡇⢘⣿⣿⣿⣿⣿⣿⣿⣧⣤⠀⠠⢿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣸⣿⣿⡍⠀⠀⠀⠀⠀⠀⢻
⣿⣿⣿⣾⣿⣿⣿⣷⡄⠀⠀⠀⢻⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⢿⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠥⢾⣿⡿⠙⠛⠁⠛⢿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⢿⠀⢠⣿⣿⣿⣿⡀⠀⠀⠀⠀⣰⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠉⣿⣿⣿⣿⣿⡀⢤⠀⠀⠠⣼⡄⠀⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣏⠀⢠⣿⡇⠀⠠⠄⠿⠿⠟⡻⣛⡷⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⣴⢠⣿⣿⣿⣿⣿⣷⠀⢀⣤⢰⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠄⠀⠈⠛⣿⣿⣿⡀⠽⢁⠀⢾⣿⣇⠀⢹⣿⡓⠂⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⡗⣿⣿⣆⠁⢐⠄⣄⣿⡇⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣧⣽⣿⣿⣿⣿⣿⣿⡿⠁⣈⣉⣾⣿⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢪⣼⣿⣿⡇⢐⣖⠀⢸⣿⣿⠀⠸⣿⣷⡄⠀⠀⠀⠀⠀⢼⣻⣿⣿⣿⣿⣿⣿⣾⣿⣿⠀⢹⣧⣽⣿⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠀⠀⠈⢩⣍⠹⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⣯⠏⠻⠃⠈⡛⢰⣤⣿⣿⡆⠀⠙⢿⣷⣤⢴⣷⣦⣤⣴⣾⣿⣿⣿⣿⣻⠿⠛⣻⣿⣷⡌⠈⣿⠏⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢀⣀⠛⢛⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡿⠀⠀⠀⠀⠀⢈⣟⣿⣿⡇⢸⡆⠀⠉⢹⣿⣿⣿⣿⣷⣿⣿⠟⠉⣿⢿⣶⢾⠋⠻⢻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⠀⠺⡿⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇⢸⣂⡀⠀⠀⢻⣿⣿⣿⣿⣿⢟⠄⠀⣴⠸⢇⡟⣘⣋⣭⡭⠏⡀⠀⢀⠀⠀⠀⡀⠀⢸⡿⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣙⣭
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⣿⣿⣿⣇⠰⣿⣶⣤⡄⢘⣿⣿⣿⣿⡇⠀⠈⠙⠋⠀⠈⠉⠻⣿⣧⡈⠝⠀⢘⣿⣷⡄⠛⣛⡂⠛⠒⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣀⣀⣻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠸⣯⡻⠟⢸⣿⣟⣿⣷⣼⣿⣿⡟⠀⠳⣶⣭⡖⠂⠀⢇⣴⢿⣿⡿⡃⠀⠀⣒⣉⡁⢸⣿⣿⡇⠀⢀⣤⡀⢀⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣌⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⢀⣽⣷⠀⢸⣿⣼⣿⣿⣿⣿⣿⣿⡇⠀⠛⣿⣷⣤⢐⡀⢿⣋⣿⣿⡆⢀⢼⣿⣿⡇⠸⢿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⢀⣀⣭⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣽⡋⠀⠈⠋⠙⠿⠿⡟⡛⠿⣭⣴⣦⠀⣰⣿⣏⠀⠂⢿⣿⣿⣿⣷⣿⣿⣾⣟⣣⡀⠀⠻⣿⠀⢿⣿⣿⣿⣿⣿⣿⣏⣀⣴⣾⣿⣿⣿⣯⣉⠃⠘⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠰⢓⡹⣆⢲⣾⣿⣧⣿⣷⣿⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡬⣵⣤⡄⡿⠀⠘⣏⠀⠘⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠘⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⣲⣻⣿⣿⣿⣿⡟⠯⣻⣿⣦⠀⠀⠀⢻⣿⣿⣿⣯⢙⢻⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣘⣻⣿⣿⣿⣿⡇⠀⣽⣿⣿⢠⡆⠀⠈⣿⣿⠙⠟⠈⠀⠙⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡏⠉⠀⠀⠀⠠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢠⣠⣿⡿⣿⡁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⠉⠃⣻⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⡿⠋⠀⠀⠀⠀⠛⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠐⠂⠀⡈⠀⠀⠀⡀⠀⣸⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⣸⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣺
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⠟⠀⡀⠀⢶⡆⢰⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀⣿⣿⣿⣏⠀⠀⠀⢀⠀⣰⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⡿⠀⠀⠀⠀⠈⢡⣬⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⣤⣼⣿⣿⣿⣿⣦⡀⠀⠀⠀⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠻⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⢿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⠀⠠⣤⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣊⠁⠀⠀⠀⠀⠀⠀⠲⠆⠀⠀⠀⠀⠀⠉⠛⢻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠛⢻⣿⠀⡠⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣜⠠⠄⡊⠈⠀⠀⢹⡆⠀⠀⠠⣶⣷⡀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣃⣐⠀⢤⡀⠀⠈⠻⠖⡧⢠⣈⣿⣿⡄⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠈⠁⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⣴⣦⠀⡱⣤⣤⣽⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠘⢻⣿
⠟⢉⣽⢿⣿⣿⣿⣿⣍⠉⠙⠚⠛⠛⠙⢿⣿⡿⣿⣿⠿⠿⠿⢿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⢀⣿⣿⣦⡀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⣿
⣿⡏⠀⠉⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠘
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠑⠈⠉⠉⠁⠀⠉⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣟⠻⢿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⣼⣿⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣦⢈⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠉⠙⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠛⠁⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠃⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠐⠃⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠃⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣃⡀⠀⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣤⣀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣧⠄⠙⠻⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⡿⠿⠿⢿⣿⠿⠿⢿⣿⡿⠿⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀
⣿⡟⠉⠉⣩⡀⢠⣶⡄⠀⠀⠀⢀⣴⣶⣶⣶⡄⢀⣴⣶⣶⣶⡄⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣶⣶⣶⠀⢻⠀⣶⣶⣶⣶⣶⢰⣶⣶⣶⣦⡈⢡⣶⣾⣶⣦⡀⣶⣶⡆⠉⢰⣶⡆⢹⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀
⣿⣷⣤⠖⠀⠁⠸⠋⡀⠀⠀⠀⢸⣿⣿⠸⠿⠷⢸⣿⣿⢸⣿⡇⠀⢸⣿⡏⠀⠀⢸⣿⡏⠀⣸⣿⣿⣿⡇⢸⣦⡀⢸⣿⡏⠀⢸⣿⣿⣸⣿⡇⣾⣿⡇⣿⣿⡇⣿⣿⡇⠀⢸⣿⡇⢸⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀
⠋⠁⠈⠙⣶⣶⠀⠀⠀⠀⠀⠀⢸⣿⣿⢶⣶⣶⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⠀⠀⢸⣿⡇⠀⣿⣿⢸⣿⣇⠸⣿⡇⢸⣿⡇⠀⢸⣿⣿⢿⣯⡄⣿⣿⡇⣿⣿⡇⣿⣿⡇⠀⢸⣿⡇⢸⣿⣿⣿⣿⣿⣿⣦⣄⣤⣤⡀⠀
⠂⠀⠀⠀⠛⠋⠀⢀⣤⡄⠀⠀⢸⣿⣿⣸⣿⣿⢸⣿⣿⣸⣿⡇⠀⢸⣿⡇⠀⠀⢸⣿⡇⢀⣿⣿⠿⣿⣿⠀⣿⡇⢸⣿⡇⠀⢸⣿⣿⢸⣿⡇⢻⣿⣇⣿⣿⡇⣿⣿⣇⣀⢸⣿⣇⣈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣄⣀⠀⠙⠻⠛⠛⠛⠀⠙⠻⠟⠛⠁⠀⠘⠛⠃⢀⣀⠘⠛⠃⠘⠛⠛⠀⠛⠛⢀⣿⣇⠘⠛⢓⣠⡘⠛⠛⠘⠛⢃⣈⡛⠻⠟⢋⣀⠛⠛⠛⠛⠘⠛⠛⠛⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣤⡄⠀⠀⠀⣸⣿⣿⣿⣿⡟⢀⣀⣀⣀⣀⡀⣀⣀⣀⡀⠀⢀⣀⣀⡀⠚⢋⣉⣙⢋⣉⡛⢛⣉⣉⣉⡛⠻⢛⣛⡛⠿⢛⣉⣉⡛⠿⢛⣛⣛⢛⣛⡛⣛⣙⣙⣉⣛⠛⢋⣉⣙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⣇⠸⠿⣿⣿⠿⠇⣿⣿⠿⠏⢰⣿⡿⢻⣿⡆⢸⣿⡇⢸⣿⡇⢸⣿⣿⢿⣿⡆⢸⣿⡇⢰⣿⡿⢻⣿⡆⢸⣿⣿⢸⣿⡇⠿⢿⣿⡿⠿⣸⣿⡟⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⠀⠀⣿⣿⣥⡄⢸⣿⡇⠸⠿⠿⢸⣿⣿⣾⣿⡇⢸⣿⣿⣼⣿⠇⢸⣿⡇⢸⣿⡇⣘⣛⡃⢸⣿⣿⣾⣿⡇⠀⢸⣿⡇⠀⠹⣿⣷⣭⡉⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⠀⣿⣿⡟⠃⢸⣿⡇⢠⣤⣤⢸⣿⡿⢹⣿⡇⢸⣿⣿⢹⣿⡆⢸⣿⡇⢸⣿⡇⢻⣿⡇⢸⣿⣿⢹⣿⡇⠀⢸⣿⡇⠀⢠⣬⡝⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⠀⣿⣿⣶⣶⠸⣿⣷⣼⣿⠇⢸⣿⡇⢸⣿⡇⢸⣿⣿⢸⣿⡇⢸⣿⡇⠸⣿⣷⣼⣿⡇⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⠀⠸⣿⣧⣿⣿⠇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣍⣩⣴⣦⣭⣍⣉⣭⣴⣬⣍⣉⣥⣶⣬⣭⣥⣬⣉⣥⣬⣭⣭⣬⣉⣥⣌⣉⣥⣤⣬⣉⣁⣉⣡⣬⣉⣭⣬⣭⣥⣶⣬⣉⣥⣾⣦⣌⣉⣉⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⣆⣲⣶⣀⣶⢌⣡⣰⣶⣆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
[69A⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢭⣴⣦⡀⠀⣾⣷⠀⢸⣿⣻⡛⠃⠀⣿⣿⣿⣿⣧⠄⠀⢸⣏⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣿⣔⣿⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠒⠖⢉⣴⣿⣿⣿⣿⣿⣿⣿⣇⢿⣿⣿⣷⣶⣿⣿⣀⣘⣿⣭⣄⡁⠀⣿⣿⣿⣟⡋⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣼⣯⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠺⣭⣉⡩⠉⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣤⣤⣀⡀⠘⢻⡿⠇⣈⣥⣿⣿⣿⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⡟⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣧⠀⠀⢹⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⣛⣿⢿⣿⡿⠿⠀⢹⣿⣿⣿⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡛⢫⣽⣿⣿⠄⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⡿⠃⠈⠻⢿⣿⡀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⣿⣿⣿⣿⣿⣿
⠐⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡀⠀⣻⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣥⠀⠿⠟⢠⣽⡁⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠋⠉⠀⠠⠴⣿⣿⣿⣿⣿⣿
⠀⠛⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠃⠀⢹⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⡂⠀⢰⣿⣿⠃⢀⢀⣴⣾⣿⣿⣿⣟⣿⣟⡁⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⢰⣆⣀⢸⣿⡟⠙⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣟⠀⠀⠈⠉⠛⠋⣹⣿⣿⣿⣿⣿⣏⠉⢛⣿⠃⠀⠀⠀⣼⣿⣿⡟⢿⣿⣿
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⠿⠛⠻⠿⣿⣿⠁⣴⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣿⣿⣿⣿⣀⣚⠻⣿⣿⣿⣿⣿⣿⣿⣿⠛⢻⣶⣿⡿⠀⠀⠀⣸⡏⢀⡿⠀⠘⣿⣿
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣈⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠃⣹⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⣿⣿⣿⠏⠉⠀⠀⠈⣽⣿⣿⡿⣿⣿⣿⣄⣀⣼⡧⣶⣶⠀⠀⠉⠀⠈⠀⠀⠀⣻⡟
⠄⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⣋⠉⣿⣿⣿⣿⡇⢩⣿⣿⣿⣿⣿⣿⣿⣷⡶⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⠅⠀⣿⣿⣧⡀⠈⠁⠀⠀⣹⣿⣿⣷⣿⣿⡿⣿⣿⣿⣿⡿⠛⠃⠀⠀⠀⢠⣤⡄⢸⣿⠃
⠉⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⢾⣿⣿⠏⠉⣁⠈⠛⠿⢿⣿⣿⣿⣿⣿⠁⠀⠀⢠⣿⣿⣿⣿⣿⣿⡟⡂⢸⣿⣿⣿⣷⡀⠀⠀⢠⣿⣿⠟⢻⣿⣿⣿⣯⣤⢾⡏⠀⠀⠀⠀⣀⣤⣿⣿⣷⣿⣿⣶
⣄⠀⠀⠤⣴⣄⠀⠰⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⣅⣀⣸⣿⣄⣀⡀⠀⠛⠋⠉⠺⣿⠁⠀⠀⠈⣿⣿⣿⣿⣿⣿⡇⢷⣿⣿⣿⣿⣿⣷⠀⠛⣸⣿⠋⣠⡄⠙⠛⠿⢻⡇⠈⠁⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠖⠀⠀⢸⣿⣿⡄⠀⢿⣷⣓⠂⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⡟⢽⣿⣧⠀⣬⡅⢾⣿⡇⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣟⡉⠀⠘⢛⠻⡇⣻⡷⠂⠀⠘⣻⣿⣤⣾⣿⣿⡿⠛⠛⠋⢹⣿⣿⣿⣿⣿
⠠⣭⡇⠀⢹⣿⣿⡀⠘⣿⣿⣦⡄⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣐⠗⢿⣿⠁⠀⠀⠀⠀⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣐⡿⢿⣿⣿⢃⣤⠄⠀⠻⠿⡾⠛⣿⣿⣆⣀⣠⣴⣾⣿⣿⣿⣿⣿
⠀⠿⠇⣤⣄⣿⣿⣧⠀⠈⠻⠿⣷⣤⣶⣿⣶⣶⣤⣶⣿⣿⣿⣿⣯⣟⠋⣙⣿⣿⣿⡀⠈⠛⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡄⠘⣿⢛⡿⠃⢰⣾⣷⣶⣷⠖⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠿⣿⣿⣿⡆⢰⡄⠀⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠿⢻⡟⢻⣄⣧⠼⠿⡷⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠨⢵⣷⣤⣾⣯⣿⣿⡟⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣷⠸⡇⣀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠏⠀⣀⣸⡎⠃⠿⢴⣦⣿⠁⢽⠇⠀⣴⣦⡀⠖⠷⡄⠻⠉⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡴⣶⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⣿⣿⣿⣿⡀⢽⣷⣶⣤⡄⠘⣿⣿⣿⡿⠿⠀⠀⠀⠁⠀⢀⠀⢠⣭⣿⣷⠀⠀⢠⠽⠛⠁⣶⣾⣿⠀⠀⣴⣄⢀⣿⣿⣿⣿⣿⠛⠋⠙⠿⣿⣷⣿⣿⣿⣿⣻⣿⣿⡇⠀⠀⠈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠙⡿⠻⢿⡇⢸⣿⡿⣿⣿⣦⣿⣿⣿⣏⠀⠹⣷⣶⡇⠀⠀⠰⢿⡽⢿⣿⡅⠀⢰⣿⣾⡦⠾⣿⣿⡄⠀⣼⣿⣿⣿⣿⣿⣿⠁⢀⠀⠀⠀⠉⠙⠛⢺⣿⣿⣿⣿⣿⠇⠀⠀⠐⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣦⠀⠀⠀⠀⠀⠑⣂⣄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠉⢻⣿⣿⠖⠂⢹⣷⣿⣿⣿⣴⣶⣿⣿⢃⣀⠈⠛⣷⠀⢻⡿⠻⢿⣿⣿⣿⣶⡆⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡄⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣤⡀⠀⠀⠙⢿⡿⠀⠈⠛⠛⠻⣿⡿⣟⠫⢏⡰⣶⣦⣄⢠⣿⣻⡆⠀⠈⠛⠛⣿⣿⣿⣿⣿⣿⣯⢏⣤⣤⣹⠃⠈⠣⢤⠜⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠼⣿⣿⣿⡏⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣾⣦⡚⢷⣤⣀⠀⠀⠀⠀⠲⢜⠳⣖⡶⣮⣿⣿⣿⣿⣿⣿⡄⠀⠀⠉⢿⣿⣿⣿⣋⡙⢿⣿⣿⣿⡯⠀⠀⠀⡀⠀⣿⣿⣿⡟⠀⠀⠀⠀⢀⡄⠀⠀⠠⢾⣿⠉⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣯⡁⠀⠀⠀⠀⠀⣨⣻⣿⣿⣿⣿⣿⡏⠙⢻⣿⣿⡆⠀⠀⠈⢻⣿⡟⠿⠙⠀⠉⠛⠉⠁⠀⠀⠀⡇⠀⠛⠿⠟⠀⠀⠀⠀⠀⠉⠙⠀⠀⠀⠚⠿⠦⣤⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⡈⢛⣿⣿⣿⣿⣿⣿⠀⠐⢛⣿⣷⣿⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣍⣸⣿⣿⣿⣿⣿⣿⡇⠐⠾⠿⠇⣿⠂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⣀⠀⠘⠁⠀⠀⠀⠀⠰⣿⠦⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⡆⠀⠀⠀⣴⠀⢨⡀⠀⠀⠀⢰⣶⠀⠰⣾⣿⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠃⠀⠀⠀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠻⡟⠁⠐⠄⠀⠻⢇⣘⣣⠀⠀⠀⠈⡉⠉⠈⢲⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣠⣾⣿⣿⣿⣿⣿⣶⣤⣀⣀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⢠⣟⣀⠀⠀⠀⠀⢴⣿⣿⡄⠀⠐⠚⢿⣶⠄⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣼⣿⣿⡆⠀⠀⠀⠀⠙⡿⠇⠀⠀⠉⠿⠇⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢤⣥⠇⠀⠀⠀⠂⠤⠮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠋⠀⠀⠀⠀⠤⠄⣨⡟⠳⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣂⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡞⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠈⠁⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣠⣜⡇⠀⠍⠙⠂⠀⠄⣀⣀⣹⣿⣿⣧⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⣼⣿⣿⣧⡀⠂⠈⣿⣷⣐⠚⢿⣿⣿⣿⣿⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣷⣔⡄⢹⣿⣿⣧⣿⣿⣿⣿⡟⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⠀⠉⠛⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⡿⠋⠉⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⠉⠻⣿⣿⣿⣿⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠈⠋⢸⣿⣿⠯⠹⠛⣿⠿⠛⠛⠿⠿⠏⠁⠙⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠛⠋⠉⠁⠁⠀⠀⠀⠀⠀⠀⠸⠿⠋⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⢿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⡿⠿⠿⢿⣿⡿⠿⢿⣿⡿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⡄⢀⣴⣶⣶⣶⡄⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣶⣶⣶⠈⣿⡃⣶⣶⣶⣶⣶⢰⣶⣶⣶⣦⡈⢡⣶⣾⣶⣦⡀⣶⣶⡆⠉⢰⣶⡆⢀⣴⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠸⠿⠷⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⠀⠀⢸⣿⡏⠀⣸⣿⣿⣿⡇⢹⣷⡄⢸⣿⡏⠀⢸⣿⣿⣸⣿⡇⣾⣿⡇⣿⣿⡇⣿⣿⡇⠀⢸⣿⡇⢸⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢶⣶⣶⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⠀⠀⢸⣿⡇⠀⣿⣿⢸⣿⣇⢸⣿⡇⢸⣿⡇⠀⢸⣿⣿⢿⣯⡄⣿⣿⡇⣿⣿⡇⣿⣿⡇⠀⢸⣿⡇⢸⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣸⣿⣿⢸⣿⣿⣸⣿⡇⠀⢸⣿⡇⠀⠀⢸⣿⡇⢀⣿⣿⠿⣿⣿⠀⣿⡇⢸⣿⡇⠀⢸⣿⣿⢸⣿⡇⢻⣿⣇⣿⣿⡇⣿⣿⣇⣀⢸⣿⣇⣈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠛⠛⠛⠀⠙⠻⠟⠛⠁⠀⠘⠛⠃⠀⠀⠘⠛⠃⠘⠛⠛⠀⠛⠛⢀⣿⣧⡘⠛⢓⣠⡘⠛⠛⠘⠛⢃⣈⡛⠻⠟⢋⣀⠛⠛⠛⠛⠘⠛⠛⠛⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⣀⣀⣀⡀⠀⢀⣀⣀⡀⠀⢀⣀⣀⢈⣉⡛⢛⣉⣉⣙⡛⠿⢛⣛⡛⠿⢛⣉⣉⡛⠿⢛⣛⣛⢛⣛⡛⣛⣉⣛⣉⣙⠛⢋⣉⣙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⠿⠇⣿⣿⠿⠇⢰⣿⡿⢻⣿⡆⢸⣿⣿⢸⣿⡇⢸⣿⣿⢿⣿⡆⢸⣿⡇⢰⣿⡿⢻⣿⡆⢸⣿⣿⢸⣿⡇⠿⢿⣿⡿⠿⢸⣿⡟⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⣥⡄⢸⣿⡇⠸⠿⠿⢸⣿⣿⣾⣿⡇⢸⣿⣿⣼⣿⠇⢸⣿⡇⢸⣿⡇⣘⣛⡃⢸⣿⣿⣾⣿⡇⠀⢸⣿⡇⠀⠹⣿⣷⣭⡉⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⡟⠃⢸⣿⡇⢠⣤⣤⢸⣿⣿⢹⣿⡇⢸⣿⣿⢹⣿⡆⢸⣿⡇⢸⣿⡇⢻⣿⡇⢸⣿⣿⢹⣿⡇⠀⢸⣿⡇⠀⢠⣬⡝⣿⣿⡆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⣶⣶⠸⣿⣷⣼⣿⠇⢸⣿⣿⢸⣿⡇⢸⣿⣿⢸⣿⡇⢸⣿⡇⠸⣿⣷⣼⣿⡇⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⠀⠸⣿⣧⣿⣿⠇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠉⠉⠉⣉⣤⣬⣉⣉⣥⣴⣬⣭⣥⣬⣩⣥⣬⣭⣭⣬⣭⣥⣬⣭⣥⣶⣬⣉⣡⣭⣥⣬⣭⣭⣬⣭⣥⣶⣬⣉⣥⣴⣦⣌⣉⣉⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠆⠲⣶⠀⢶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
[69A⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠇⠀⢿⣙⣿⣿⣧⣾⣿⡄⣴⡄⠀⠀⠀⠠⡐⠐⠿⣿⡀⠀⠤⣽⣿⣿⣶⣦⣤⣤⣦⣀⣴⣾⣷⣦⣼⣇⣀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠐⠒⣒⠛⢿⣿⣿⡿⢾
⠀⠰⣾⣇⠀⠈⣿⣛⣛⠛⠀⠸⣿⣿⣿⣿⣟⡀⠀⠈⡇⢿⣿⣏⠀⠀⠀⠁⠇⠀⠀⠀⠀⠃⠀⡬⢀⣀⠀⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⣛⣻⣿⣶⣄⠀⠀⠀⢀⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⣨⡿⠓⡛⣯⣿
⣷⣾⣿⣿⣄⣀⣸⣭⣭⣉⡁⠀⣿⣿⣿⡿⠟⠀⠀⠀⠧⠈⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⣾⣿⣤⣿⣿⣿⣿⣿⣯⣿⣿⣿⣋⣿⣿⡿⣾⣿⣿⣿⣿⣿⣿⣷⣤⣼⡇⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣤⠘⠛⠋⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣶⣶⣦⣄⣀⣀⣀⡀⠀⠀⠀⢠⣤⣤⡄⠸⢾⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⡭⣤⣾⣿⣿⣿⣿⡯⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠿⠋⢿⣛⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⣠⡤⢁⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣭⠶⣿⣾⣿⠛⠋⠀⣽⣿⣿⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣦⡄⠈⠀⠀⠀⠒⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣰⣿⣷⠂⠻⣿⣿⡁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⡿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⠀⣶⡍⢛⡷⠀⠀⠀⠉⣽⣿⣿⣿⣿⣿⠿⠟⠃⢀⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⡟⠀⠀⠰⠀⠀⠀⠀⠀⠀
⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡄⠀⠀⣾⣿⠆⠀⢀⣤⣿⣿⣿⣿⢿⣿⠀⠀⠈⠄⢿⣿⣿⣿⣿⣿⣿⣿⡟⣿⠿⠀⠉⢻⣿⣟⢀⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀
⣧⢿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⡇⡀⠈⠛⠻⠖⢺⣿⣿⣿⣿⣿⡛⠺⢻⡇⠀⠀⠀⣾⣿⣿⢿⣿⣿⣿⣿⢇⣄⡴⢀⣴⣿⣿⣿⣿⣿⣿⠱⠤⠀⠀⠀⠀⠀⠀
⣿⠘⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⡇⢠⠘⢻⣷⣶⣿⣿⣿⣿⣿⠟⢿⣴⣿⣧⠀⠀⢰⡟⢙⡏⠀⣿⣿⣿⣿⣿⡻⢠⣾⣿⣿⣿⣿⣿⠿⠿⠀⢀⣀⣶⣄⠀⠀⠀
⣿⣷⣸⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢹⣿⣿⡿⠋⠡⠀⠐⣽⣿⣿⡿⣿⣿⣇⣀⣹⣷⣶⣦⠀⠈⠁⠈⠁⠀⢸⣿⠑⡿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠈⠀⠾⣟⣿⣿⣿⠀⠀⠀
⣿⣿⡟⣿⣿⡄⠙⣾⣿⣿⣿⣿⣿⣿⣿⣤⣄⠀⠸⠿⣿⣿⣿⣿⣿⣿⣿⣏⠀⢸⣿⣿⣄⠀⠀⠀⠀⢹⣿⣿⣶⣿⣿⡿⣿⣿⣿⣿⠛⡃⠀⠀⠀⣶⣶⣾⣿⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡋⠁⠀⠀⠀⢤⢾⣿⣷⣄⠀
⣾⣿⣿⠝⠛⠓⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠗⡀⢼⣿⣿⣿⣦⡀⠀⡀⣼⣿⣿⠻⣿⣿⣿⣯⡾⢿⡇⠀⣀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢼⠀⠉⣹⣿⣿
⣿⣿⠋⠀⠀⣾⣦⠀⠀⠀⠈⠻⠿⢛⠻⣻⡗⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡆⢧⣾⣿⣿⣿⣿⣷⠀⠛⣼⣿⡁⣴⡀⠉⠛⣻⣧⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣅⣀⡀⠀⠀⠀⠀⠀⣹⣴⣿⣿⣿
⣿⣿⣿⣶⣶⣿⣿⡷⢿⣶⣤⡀⠀⣀⡠⡼⣿⡀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣉⠀⠉⢻⣝⣗⣻⡟⠀⠀⢉⣿⡷⣿⣿⣿⡏⠉⠋⢘⣿⣿⣿⣿⣿⣯⣷⣿⣿⣿⣿⣿⡯⠁⠀⠀⠀⠀⣐⡋⠉⢉⠿⠀
⣿⣿⣿⣿⣿⣿⣿⣯⣌⣿⣿⣧⠀⠩⡧⣽⣿⡇⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣰⠿⠛⢻⣿⣧⣶⠆⣈⣝⣻⣏⣹⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠧⠀⠀⣠⠀⠠⣿⣿⣗⣒⣻⠀⠀
⢚⣻⣿⣿⣿⣿⣿⡿⡿⠟⢻⣿⣿⣦⠄⠉⠿⠃⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡄⠉⢯⣿⡇⢀⣿⣿⣿⣿⢥⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠒⠂⡄⠀⠹⠃⠀⣿⣿⣿⣿⣿⠁⠀
⣗⣻⣿⣿⡿⠛⢻⣿⣧⣤⣖⠋⠻⠻⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠘⠛⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠇⠀⠀⠀⠀⢿⣿⣿⣿⣿⠴⣿
⣿⣿⣿⣿⡇⠀⠀⣉⡸⢿⢸⡋⣛⣩⡭⢈⣣⡄⠀⣠⣤⡀⠤⢶⠤⠰⠯⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⠟⠁⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠇⠀⠀⠀⢸⣿⡿⢿⣿⣷⡀⢿
⣿⣿⣿⡟⠁⠀⠐⠶⠇⠀⠈⠉⠻⠿⣷⣤⠀⠁⠀⣘⡿⠟⠠⣴⣿⡇⠀⠠⣴⣄⣠⣿⣿⣿⣿⠟⠉⠀⢈⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⣌⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣠⣾⡿⢋⣾⣿⠿⢿⡗
⣿⣿⡟⠓⣀⣀⠀⠀⠀⠀⠐⢀⣸⠿⣿⣿⡇⠀⠀⢥⣶⣶⣄⢿⣿⣿⡄⠀⢹⣿⣿⣿⣿⣿⣿⠆⣠⣾⣿⣿⣯⣍⡀⣹⣿⡇⠀⠀⠀⠀⠂⠸⠟⠛⠋⠛⠛⠉⠉⠉⠉⠉⠉⠛⢻⣤⣄⡀⠺⣿⣿⣧⣴⣿⠏⡀⠈⠙
⣿⣿⣇⡈⠉⢻⣿⣿⣆⣀⠀⠉⠹⣟⣩⣿⣿⣧⣠⣽⣛⣿⡧⣀⠈⠙⠿⣤⠘⣿⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣾⣿⣿⣿⣿⣿⣇⠸⠀⠀
⣿⣿⣿⣿⠀⠀⠘⠻⣿⣿⡗⠈⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣣⣤⣄⣻⠀⠈⠃⢶⠘⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠙⠿⣿⣿⣿⠋⠋⠀⠀⠀⠀
⣛⠋⢙⣷⣬⣷⣆⢠⣿⣭⣿⣆⠀⠀⠀⠠⢽⣿⣿⣿⡿⠟⠻⣿⣿⣿⣿⡧⠀⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣷⣤⣀⡀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀
⣌⣭⣤⣝⣻⣿⣿⣷⣿⢿⣿⣿⣦⡀⠀⠀⠘⢿⣿⣿⡿⣿⠓⠈⠙⠛⠋⠀⠀⠁⠀⠘⠀⢈⣹⣿⣟⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠦⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀
⣤⣿⣶⣿⣿⣿⣿⣿⡬⠉⠺⢿⣿⣷⢠⣄⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣧⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠿⢿⣿⣿⣿⣍⣉⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣷⡀⠉⠛⣿⣿⡾⣯⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀
⣤⢈⣿⣿⣿⣿⣿⣿⣿⣷⠙⠚⠿⠻⠇⢻⡇⠀⠀⠀⠀⠀⢠⣿⣤⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠉⠛⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣤⣤
⠒⠘⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣠⡀⠀⣲⣿⣷⣿⣿⣆⡀⠀⢀⣤⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣄⠀⠻⠿⣿⣿⣿⣿⡟⣿⣿⡄⠀⠀⠀⢰⣦⡄⢰⡖⠀⠀⠀⠀⠋⠋⠀⠀⢼⣿⣿⣿⣿⠁⠀⠀⠉⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣆⠀⠹⣿⣿⣿⡟⠻⣿⠃⠀⠢⠄⠀⠛⠋⣤⣶⡆⠀⠀⢀⣴⣷⣤⠤⠈⠛⠉⠩⠅⠀⠀⠀⠀⠤⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠿
⣿⣿⣿⡆⠀⢻⣿⣿⠇⠀⣸⡆⠀⠠⠀⠀⠀⠐⠿⣿⣿⠄⠀⠀⠤⣿⣟⠀⠀⠐⠀⠀⠗⠀⠀⠀⠀⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⣀⣀⣀
⣿⣿⣿⣿⣆⢸⣿⢃⠀⠀⣿⣿⣿⡄⠀⠀⠀⠀⠀⠨⡏⣄⠀⠀⠀⠠⢁⡤⠆⠀⠉⢅⡀⠀⠀⠀⠀⢌⣄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣞⣡⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢰⣶⡭⠀⠀⠀⠀⠀⠀⢱⣶⣯⣄⣤⣄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡶⠃⠁⠀⠀⠀⠀⠤⠀⠀⠛⠁⠓⠀⠀⠀⠀⠀⠨⠙⠫⠉⠶⠿⠃⠀⠤⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⣶⣶⣾⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠁⠄⠀⠛⣿⣿⣿⡍⠙⠀⢀⣴⣾⡇⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡿⣿⣿⣷⡤⠀⠊⠉⠻⠃⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢑⡸⢛⣭⠶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⣀⣀⣄⣀⢀⠄⣋⣄⡰⣬⣿⣿⡅⢰⠂⠀⠄⠀⠀⠀⠀⢰⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣛⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣟⢿⡿⢈⠈⠽⠓⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢀⣵⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡠⠀⠈⠀⣀⠀⠶⠀⠀⠀⠀⠀⣀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⡀⠈⠀⠀⠀⠀⠀⡤⠌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢀⣽⣾⣬⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠛⣿⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣼⣦⣐⡆⢀⣼⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿
⡇⢹⣿⣿⠿⠛⣿⠿⠛⠟⠉⠁⠀⠀⠁⠀⠀⠀⠀⠀⠈⠤⠤⠽⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢿⣿
⠃⢸⣿⣿⠏⢁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰
⠀⢸⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⡿⠿⠿⢿⣿⡤⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⡄⢀⣴⣶⣶⣶⡄⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣶⣶⣶⠈⣿⡃⣶⣶⣶⣶⣶⢰⣶⣶⣶⣦⡈⢡⣶⣾⣶⣦⡀⣶⣶⡆⠉⢰⣶⡆⢀⢀⣀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠸⠿⠷⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⠀⡀⢸⣿⡏⠀⣸⣿⣿⣿⡇⢻⣷⡄⢸⣿⡏⠀⢸⣿⡇⣸⣿⡇⢾⣿⡇⣿⣿⡇⣿⣿⡇⠀⢸⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢶⣶⣶⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⠀⠁⢸⣿⡇⠀⣿⣿⢸⣿⣇⢸⣿⡇⢸⣿⡇⠀⢸⣿⡿⢿⣯⡄⢿⣿⡇⣿⣿⡇⣿⣿⡇⠀⢸⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣸⣿⣿⢸⣿⣿⣸⣿⡇⠀⢸⣿⡇⠀⠀⢸⣿⡇⢀⣿⣿⠿⣿⣿⠈⣿⡇⢸⣿⡇⠀⢸⣿⣷⢸⣿⡇⢻⣿⣇⣿⣿⡇⣿⣿⣇⣀⢸⣿⣇⣈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠛⠛⠛⠀⠙⠻⠟⠛⠁⠀⠘⠛⠃⢠⣆⠘⠛⠃⠘⠛⠛⣀⠛⠛⣠⣿⣧⡘⠛⢃⣠⡘⠛⠛⠘⠛⠃⣈⠛⠻⠟⢋⣀⡛⠛⠛⠛⠘⠛⠛⠛⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⣀⣀⣀⡀⠀⢀⣀⣀⡀⠒⢋⣉⣛⢋⣉⡛⢛⣛⣛⣛⡛⠿⢛⣛⡛⠿⢛⣉⣉⡛⠿⢛⣛⣛⢛⣙⡛⣛⣙⣛⣛⣛⠛⢋⣉⣉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⠿⠇⣿⣿⠿⠇⢰⣿⡿⢻⣿⡆⢸⣿⣿⢸⣿⡇⢸⣿⣿⢿⣿⡆⢸⣿⡇⢰⣿⡿⢻⣿⡆⢸⣿⣿⢸⣿⡇⠿⢿⣿⡿⠿⣸⣿⡟⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⣥⡄⢸⣿⡇⠸⠿⠿⢸⣿⣿⣾⣿⡇⢸⣿⣿⣼⣿⠇⢸⣿⡇⢸⣿⡇⣘⣛⡃⢸⣿⣿⣾⣿⡇⠀⢸⣿⡇⠀⠹⣿⣷⣭⡉⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⡟⠃⢸⣿⡇⢠⣤⣤⢸⣿⣿⢹⣿⡇⢸⣿⣿⢹⣿⡆⢸⣿⡇⢸⣿⡇⢻⣿⡇⢸⣿⣿⢹⣿⡇⠀⢸⣿⡇⠀⢠⣬⡝⣿⣿⡆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⣶⣶⠸⣿⣷⣼⣿⠇⢸⣿⣿⢸⣿⡇⢸⣿⣿⢸⣿⡇⢸⣿⡇⠸⣿⣷⣼⣿⡇⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⠀⠸⣿⣧⣿⣿⠇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠉⠉⠉⠉⠀⠈⣉⣉⣥⣤⣬⣉⣥⣬⣭⣥⣬⣭⣭⣬⣭⣥⣬⣭⣥⣶⣬⣍⣥⣭⣥⣬⣍⣭⣬⣉⣥⣤⣌⣉⣡⣴⣦⣌⣉⣉⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠆⠲⣶⠀⢶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
[69A⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⠀⠐⢿⣹⣿⣿⣷⣿⣿⡆⣼⡄⠀⠀⠀⠀⡐⠒⠿⣿⡃⠀⠬⠽⣿⣿⣷⣤⣤⣤⣄⣀⣩⣴⣾⣤⣼⣇⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠤⠤⣼⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿
⢹⣿⣭⣟⡃⠀⢻⣿⣿⣿⣿⣛⡀⠀⠘⡆⢿⣿⣟⠀⠀⠀⠈⠆⠀⠀⠀⠀⠋⠀⣨⠍⣀⡀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⣝⣻⣿⣦⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠁⣶⡿⠽⣟⣻⣿⣿⣿⣿⣿⣿
⣤⣿⣿⣤⣀⠀⠰⣿⣿⣿⡿⠟⠀⠀⠀⠧⠉⠉⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡶⣶⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣟⢻⣿⣿⣷⣿⣿⣿⣿⣿⣷⣦⣀⣸⡇⠈⠒⠀⠀⠀⠀⠀⠒⠈⢉⡁⠶⠿⣿⣿⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣀⣀⣀⡀⠀⠀⠀⠠⣤⣤⡤⠸⠷⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠁⠸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⣾⣯⢥⣴⣶⣿⣿⣿⣿⡅⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⠟⣻⠟⣿⣿⣿⣿⣿⣿⣿⣶⣄⣀⠀⠀⠀⣀⡔⢀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣯⡵⢿⣿⣿⡟⠛⠁⢹⣿⣿⣷⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣥⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣦⡀⠉⠁⠀⠀⠤⠀⠀⠀⠀⠉⢛⡟⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣾⣿⡶⠸⣿⣿⣏⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣯⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡁⢰⣦⣛⣻⡆⠀⠀⠈⠉⣿⣿⣿⣿⣿⣿⠿⠛⠉⣹⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣷⣧⡄⠀⢠⣿⣷⠀⠀⢀⣴⣿⡿⣿⡿⣿⡧⠀⠀⠈⠠⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠇⠈⠹⣿⣿⠉⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢿⣿⣿⣿⠇⡀⠘⠛⠿⠖⢺⣿⣿⣿⣿⣿⠟⣿⣿⡆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⢀⣀⠆⢠⣾⣿⣿⣿⣿⣿⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⣿⡇⠤⠞⣿⣶⣶⣿⣿⣿⣿⣿⠿⢷⣴⣿⡇⠀⠀⢸⡏⢹⡇⠸⣿⣿⣿⣿⣟⡧⣰⣿⣿⣿⣿⣿⡿⠿⠅⠀⢀⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⡿⠛⠩⠀⠐⣿⣿⣿⣿⣿⣿⣇⣈⣹⣧⣶⣤⠀⠙⠁⠈⠀⠀⣿⣿⢸⠿⣿⣿⣿⣿⣿⣿⣿⡿⠒⠀⠴⡟⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀
⡌⠑⢾⣿⣿⣿⣿⣿⣿⣿⣯⣤⡄⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⡅⠀⠀⠀⠀⢹⣿⣿⣶⣿⣿⡿⣿⣿⣿⣿⠛⡃⠀⠀⠀⣴⣿⣿⣟⠉⣠⣿⣿⣿⣿⣿⣿⣿⣟⠋⠀⠀⠀⢠⡼⣿⣷⣆⠀⠀⠀⠀⠀⠀
⠷⠐⠻⣿⣿⣿⣿⣿⣿⣿⣿⣟⠃⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠧⠀⣸⣿⣿⣿⣦⡀⠀⠀⢸⣿⣿⠻⣿⣿⣿⣯⣼⢿⡇⠀⢀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠠⡇⠈⢹⣿⣿⣦⡀⠀⠀⠀
⣶⣦⠀⠀⠀⠉⠹⢿⠿⢛⣛⣻⠆⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡆⢧⣿⣿⣿⣿⣿⣷⠀⠻⢸⣿⡋⣤⡄⠉⠛⢛⣿⡈⠁⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⣠⡀⠀⠀⠀⠀⢘⣧⣿⣿⣿⢟⡇⠀⠀⠀
⣿⣿⣷⣶⣶⣦⡀⠀⠀⠅⢀⣿⣧⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣋⠀⠉⢛⣛⣷⣹⣿⠀⠀⠉⣿⣷⢿⣿⣿⡏⠉⠋⢀⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⠯⠀⠀⠀⠀⢐⣚⠉⢋⡿⠃⠀⠀⠀⠀⠀
⣿⣿⣿⣀⣿⣿⣿⡄⠈⢻⣈⣿⣿⡄⠀⠀⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⢀⣿⢛⣻⣿⣿⣶⡖⢀⣭⣻⣟⣹⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⣠⠀⠰⣿⣿⣀⣹⡅⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠿⣿⣿⣷⣼⠀⠛⣿⠅⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⠈⢿⣿⣟⠀⣿⣿⣿⣿⡯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡒⢂⡄⠀⠛⠀⢰⣿⣿⣿⣿⣇⠀⣠⣴⠀⠀⠀
⣿⢿⣷⣾⣄⣠⡽⠿⡿⢿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠛⢿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⢈⣿⣿⣿⣿⡯⢺⣿⣿⣇⠀⠀
⠅⠀⠛⠋⢿⡏⣿⠖⠷⢚⣛⠙⢇⡤⠀⢠⣀⠀⣀⣦⣄⠸⣿⡓⠀⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣻⣿⣿⣿⣿⣿⣿⣏⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⠧⠀⠀⠀⢺⣿⡟⢻⣿⣇⠘⠿⢿⣿⢀⠀
⠀⠀⣨⣽⡆⠁⠛⠒⢿⣿⣧⣀⠍⠃⠀⠨⢿⡿⠂⣤⣾⣶⠀⠀⣤⣄⣀⣿⣿⣿⣿⣿⠋⠉⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣴⣿⡟⠩⣿⡿⠻⢿⡇⣸⣿⣯⠤
⠀⠀⡀⠁⠀⠀⠠⠀⢰⣶⣿⣿⣇⠀⠀⢘⣥⣤⣄⢹⣿⣿⣆⠀⢹⣿⣿⣿⣿⣿⣿⣧⠀⣤⣿⣿⣿⣯⣉⢈⣿⣿⣿⣿⠇⠀⠀⠀⠀⠈⣿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠿⠧⣤⣄⢹⣿⣿⣧⣾⣿⠁⣄⠀⠈⢡⣿⣿⡆
⠲⣶⣶⣶⡀⠀⠀⠙⢳⡶⢻⣿⣳⣦⣀⣘⠿⢿⣿⡄⠈⠙⠿⣦⠀⢿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠁⠘⣻⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡇⠛⠀⠀⠛⠿⠿⠃
⠀⠛⠻⢿⣿⣿⣦⠒⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⡷⣀⣠⡹⡇⠈⠙⠠⣦⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠈⠝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠈⠙⢿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠰
⢤⣤⠀⢈⣿⡿⣷⡄⠀⠀⠉⢉⣹⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡅⢀⠀⠀⡄⠈⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣾⣿⣿⣿⣧⣄⠀⠀⠀⠀⠋⠀⢠⠂⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣷⣴⣿⣿⣿⣿⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⡶⠌⠛⠿⠿⠋⠁⠘⠀⠀⢣⠀⠈⢻⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣾⣿⡿⠓⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣿⣿
⣾⣿⣿⣿⠳⠽⢻⣿⣿⣷⡀⡀⠀⠀⠙⣿⡿⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣄⣴⣿⣿⣧⡄⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⡿⢿⣿
⣿⣿⣿⣿⣏⠀⠬⢭⣿⣿⣇⣿⡆⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠻⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠙⠻⢿⣿⣿⣿⣿⣿⣿⣧⣤⣤⡀⠀⠀⠈⠉⠉⠉⠉⠉⣠⣾⣿
⣿⣿⣿⣿⣿⣧⠠⣠⣼⣿⣿⢸⣿⠀⠀⠀⠀⠀⠀⢠⣦⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠋⠿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣴⣶⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡧⠀⠈⠀⠀⠀⠛⠂⠀⠀⠀⣀⠀⠘⠿⢉⠀⠀⢴⣶⣦⣿⣿⣤⠀⠀⢀⣈⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠋⠀⣠⡄⠀⣥⡀⠀⠀⠀⠘⡿⠷⠄⠋⢽⣿⣿⣿⣿⠇⠀⡈⠉⠍⣸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢻⣿⣿⣿⣿⣹⣿⣿⠀⢀⡀⠀⠙⣿⠇⢘⣣⡀⠀⠀⢀⣠⣦⣀⣀⠈⠿⠟⠛⡋⠀⠀⠀⠀⠀⣾⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠉⠉⣹⣿⣿
⠈⢻⣿⣿⣿⠈⠹⣏⠀⠀⠈⠀⠀⠀⣨⣿⣿⣧⠀⠀⠉⣉⣿⡿⠁⠀⠠⠀⠀⡲⠀⠀⠀⠀⠰⠛⠋⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣾⣿⣿⣿
⠀⠈⣿⣿⡟⠀⠠⣿⣤⣤⠀⠁⠀⠀⠀⠉⠻⡿⠃⠀⠀⠀⠉⠛⣀⡀⠀⠐⢒⠅⡀⠀⠀⠀⠀⢄⡴⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣦⢀⣿⣿⢃⣀⣠⣿⣿⣿⣆⠀⠀⠀⠀⠀⢀⣁⠽⠀⠀⠀⠈⠈⠉⠷⣤⣔⣂⣉⣀⠈⠀⠀⠀⠍⠁⣽⣿⣧⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⣶⣶⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣽⣿⣿⣿⣛⣻⣻⠛⠀⠀⠀⠀⠀⠈⢿⠟⠖⠀⠀⠀⠀⠀⠘⠛⢿⠛⢩⣿⡟⠀⠠⡆⠀⢰⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⡀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⢿⠉⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠠⣴⣶⣶⣖⠐⠆⠀⢠⣴⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣷⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⣿⣿⣿⣆⣀⠠⠛⠛⠿⠿⡿⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠐⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣴⣆⣀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⡙⠍⠿⢟⣫⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣙⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠈⠀⡠⢑⠈⢀⣻⣿⣾⡀⡰⠓⠠⡀⠀⠠⠾⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣶⣈⡾⣿⣿⡎⠋⠙⣿⠇⠁⣀⡀⠙⠷⠂⠄⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠉⣀⠁⠒⠂⠀⠠⣤⣄⡀⠀⢀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⡀⠀⠈⠹⠀⠒⠂⢄⣦⡄⠈⠂⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠈⢿⣿⣿⡄⠀⠻⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢸⣿⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡒⠾⢿⠉⠉⠀⠠⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡄⠶⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⠀⠀⠀⣹⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⣸⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠘⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿
⣿⣿⣿⣿⣿⡿⣿⠟⠛⠋⠉⠙⠉⠀⠀⠀⠀⠀⠙⢷⠦⠝⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙
⣿⣯⠤⠊⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⡿⠿⠿⢷⣾⡶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀
⣿⡃⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⡄⢀⣴⣶⣶⣶⡄⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣶⣶⣶⠈⣿⠃⣶⣶⣶⣶⣶⢰⣶⣶⣶⣦⡈⢡⣶⣾⣶⣦⡀⣶⣶⡆⠀⢰⣶⡆⢰⣶⣶⣶⣶⣾⣿⣿⣷⣀⡀⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠸⠿⠷⢸⣿⣿⢸⣿⡇⠀⢸⣿⡏⢀⡀⢸⣿⡏⠀⣸⣿⣿⣿⡇⢻⣶⡄⢸⣿⡏⠀⢸⣿⣿⣸⣿⡇⣾⣿⡇⣿⣿⡇⣿⣿⡇⠀⢸⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢶⣶⣶⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⢸⡇⢸⣿⡇⠀⣿⣿⢸⣿⣇⢸⣿⡇⢸⣿⡇⠀⢸⣿⣿⢿⣯⡄⣿⣿⡇⣿⣿⡇⣿⣿⡇⠀⢸⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣸⣿⣿⢸⣿⣿⣸⣿⡇⠀⢸⣿⡇⢸⡇⢸⣿⡇⢀⣿⣿⠿⣿⣿⠈⣿⡇⢸⣿⡇⠀⢸⣿⣿⢸⣿⡇⢻⣿⣇⣿⣿⡇⣿⣿⣇⣀⢸⣿⣇⣈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠛⠛⠛⠀⠙⠻⠟⠛⣁⠀⠘⠛⠃⣸⣇⡘⠛⠃⡘⠛⠛⣀⠛⠛⣠⣿⣧⡘⠛⢓⣠⡘⠛⠛⠘⠛⢃⣈⠛⠻⠟⢋⣀⠛⠛⠛⠛⠘⠛⠛⠛⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⣀⣀⣀⡀⠀⢉⣁⣀⡀⠘⢛⣉⣛⢛⣛⡛⢛⣛⣛⣛⡛⠿⢛⣛⡛⠿⢛⣉⣙⡛⠿⢛⣛⣛⢛⣛⡛⣛⣛⣛⣛⣛⠛⢋⣉⣙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⠿⠇⣿⣿⠿⠇⢰⣿⡿⢻⣿⣆⢸⣿⣏⢸⣿⡇⢸⣿⣿⢿⣿⡆⢸⣿⡇⢰⣿⡿⢻⣿⡆⢸⣿⣿⢸⣿⡇⠿⢿⣿⡿⠿⣸⣿⡟⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⣥⡄⢸⣿⡇⠸⠿⠿⢸⣿⣿⣾⣿⡇⢸⣿⣿⣼⣿⠇⢸⣿⡇⢸⣿⡇⣘⣛⡃⢸⣿⣿⣾⣿⡇⠀⢸⣿⡇⠀⠹⣿⣷⣭⡉⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⡟⠃⢸⣿⡇⢠⣤⣤⢸⣿⣿⢹⣿⡇⢸⣿⣿⢹⣿⡆⢸⣿⡇⢸⣿⡇⢻⣿⡇⢸⣿⣿⢹⣿⡇⠀⢸⣿⡇⠀⢠⣬⡝⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⣶⣶⠸⣿⣷⣼⣿⠇⢸⣿⡇⢸⣿⡇⢸⣿⣿⢸⣿⡇⢸⣿⡇⠸⣿⣷⣼⣿⡇⢸⣿⣿⢸⣿⡇⠀⢸⣿⣇⠀⠸⣿⣧⣿⣿⠇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠉⠉⠉⠉⠀⢈⣉⣉⣥⣴⣬⣭⣥⣬⣭⣥⣬⣭⣭⣬⣭⣥⣬⣭⣥⣶⣬⣭⣥⣭⣥⣬⣍⣩⣌⣉⣡⣤⣌⣉⣡⣴⣦⣌⣉⣉⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠆⠲⣶⠀⢶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
[69A⡆⠿⢿⣿⣿⣿⣿⣿⣃⡀⢻⣭⣿⣿⣿⡿⠿⣷⢸⣷⠀⠀⠀⠀⢤⡃⠸⢿⣿⠀⠠⣬⣿⣿⣿⣷⣦⣥⣤⣄⣀⣽⣾⣧⣴⣿⣄⡇⡅⠀⠀⠀⠀⢠⡇⠀⠤⠀⠅⠀⠠⢀⣤⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣉⡀⠸⣿⣿⣿⣿⣯⡥⠀⠀⢗⢻⣿⣿⡀⠀⠀⠀⠨⠁⠀⠀⠀⠘⡁⢀⡭⢀⣀⠀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠉⣛⣿⣷⣤⡀⠀⡀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠛⣰⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣄⡀⣿⣿⣿⣿⣛⠁⠀⠀⠾⠀⠉⠽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⣾⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣶⣿⣿⣿⣿⣿⣾⣆⣀⣿⢀⠙⠃⠀⠀⠀⠀⠐⠒⠛⡋⢰⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣶⣄⣠⣅⣀⡀⠀⠀⢤⣶⣶⡆⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠀⠀⠀⠀⠀⠄⠀⠀⢀⠉⠀⠀⠈⠉⠁⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣭⣤⣾⣿⣿⣿⣿⣿⠍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⢟⣿⠟⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⣀⠂⡀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣭⠴⣿⣿⣿⡟⠛⠀⢹⣿⣿⣷⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣥⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⣄⠈⠉⠀⠁⠠⠄⠀⠀⠀⠈⠙⣿⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣱⣿⣿⡆⠘⣿⣿⣏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠸⠛⠿⠁⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡀⢰⣮⠙⣻⠆⢀⠀⠈⠉⣿⣿⣿⣿⣿⡿⠿⠛⠉⣹⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡟⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣧⠀⠀⢰⣿⣿⠀⢀⢀⣼⣿⡿⣿⡿⣿⡷⠀⠀⠩⠠⣿⣿⣿⣿⣿⣿⣿⣿⢻⡿⡇⠈⢻⣿⣿⠈⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⠇⡀⠈⠛⠿⠖⢺⣿⣿⣿⣿⣿⠛⢿⢿⡆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⢀⣠⠆⣠⣿⣿⣿⣿⣿⣿⢱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⣿⡇⡤⠾⣿⣶⣶⣿⣿⣿⣿⣿⡿⢷⣼⣿⣧⠀⠀⢸⡏⢙⡇⠘⣿⣿⣿⣿⣟⡧⣰⣿⣿⣿⣿⣿⠿⠿⠄⢀⣀⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣿⣿⣿⡿⠛⢩⠉⠐⣿⣿⣿⣿⣿⣿⣧⣈⣹⣿⣶⣦⡀⠸⠁⠈⠁⠀⣿⣿⣸⡿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠾⡟⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣧⣤⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢸⣿⣿⣅⠀⠀⠀⠀⢙⣿⣿⣷⣿⣿⡿⣿⣿⣿⣿⠟⡃⠀⢀⠀⣴⣿⣿⣿⠈⢠⣿⣿⣿⣿⣿⣿⣿⣟⠉⠀⠀⠀⢠⢾⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠧⠄⢸⣿⣿⣿⣦⡄⠀⠀⢸⣿⣿⠟⣿⣿⣿⣿⣵⢿⣿⠀⢀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠰⡇⠉⣹⣿⣿⣤⠀⠀⢀⠀⠀⠀⠀
⠀⠉⡉⠿⣿⠿⢛⣛⣿⠦⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡆⢧⣾⣿⣿⣿⣿⣿⡆⠻⢺⣿⡏⣠⣄⠉⠛⢟⣿⡄⠁⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⡀⠀⠀⠀⠀⢸⣷⣿⣿⣿⢻⡂⠀⠀⠀⠀⠀⠀
⣶⣶⣌⠁⠀⠠⠅⣈⣿⣆⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣟⡁⠉⢛⣿⣻⣞⣿⡃⠀⠈⢹⣿⡾⣿⣿⣿⠉⠘⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⠀⠀⠀⠀⣀⣿⠉⢋⡛⠃⠀⠁⠀⠀⠀⠀⠀⠀
⣘⣿⣿⣧⠀⠙⣻⣈⣿⣿⡄⠀⠀⠀⠈⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢀⣿⡟⣛⣿⣿⣵⣶⢂⣹⣟⣿⣋⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⣠⡀⠰⣿⣿⣭⣭⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣷⣦⣼⠈⠻⣿⡃⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡈⠹⣿⣿⠃⢸⣿⣿⣿⣿⢭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⠀⡖⠀⠙⠃⢠⣿⣿⣿⣿⣧⣀⣴⣶⠀⠀⠀⠀⠀⠀
⣯⣁⣠⡿⠿⡿⢿⣦⣤⡈⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠘⠿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣿⣿⣿⣿⡿⢻⣿⣿⣶⡀⠀⠀⠀⠀
⠛⣿⡏⣷⠶⠥⢞⣛⠻⣟⣃⠀⠀⣀⠀⢀⣠⣄⡀⣿⣿⠐⠴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⣿⣿⣿⣿⣿⣿⣿⡁⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠻⠀⠀⠀⢸⣿⣟⢻⣿⣧⣈⡿⢿⣿⣠⠀⠢⡄⠀
⣳⡌⠃⠿⠶⣶⣾⣯⡀⢛⠓⠀⠈⣿⣿⠆⣀⣽⣶⠀⠀⣠⣤⣀⢹⣿⣿⣿⣿⡿⠉⠉⢹⣟⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠈⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⢈⣶⣿⣿⠑⣿⣿⠙⢻⣇⡼⣿⣷⠆⠀⠀⠀
⠉⠀⠀⢀⠀⢠⣽⣿⣿⣧⠀⠀⠐⣊⣥⣄⠘⣿⣿⣧⡀⠈⣿⣿⣿⣿⣿⣿⣿⡆⢠⣼⣿⣿⣿⣍⣁⢹⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢸⣿⣿⠿⠿⣿⣿⣿⣿⣿⣇⣠⣠⠈⣿⣿⣿⣾⣿⡇⢢⠀⠀⣠⣿⣿⡄⠀⠀⠀
⣦⠀⠀⠀⠗⠾⣧⠿⢿⣿⣦⡀⠨⢿⣿⣿⣏⠉⠛⠻⣷⣄⠸⣿⡿⡿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⠏⠀⢙⣿⣿⣿⡿⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⠿⠈⠀⠀⠉⠛⠛⢀⡄⠀⠀
⣿⣷⣶⣤⠠⠌⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣭⢿⣆⣀⣨⢿⠄⠙⠧⣤⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⢉⣿⡟⠃⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⡇⠀⠀⠀⠀⠠⠀⠀⠀⠘⢩⣈⣿
⠘⣿⣿⣿⡄⠀⠈⠙⠛⠻⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣯⡀⠀⠀⢠⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣿⣧⡀⠀⠀⠀⠈⠀⢠⣾⣀⠀⠀⠀⠀⢀⣠⣼⣭⣿
⡸⣿⣷⣿⣿⣄⠀⠀⠀⠉⢻⣿⣿⣿⣿⣧⡭⠙⠿⠿⠿⠛⠀⠛⠀⠀⠇⠀⠉⢿⣿⣻⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡿⢿⣿⣿⠛⠀⠀⠀⠀⠀⠀⢻⠾⠛⠻⣿⣿⣿⣿⣿⣿⣿
⣿⢯⣛⡿⣿⣿⣷⡄⠀⠀⠈⠙⢻⣿⣯⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷⣤⣾⣿⣿⠒⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣿⣿⣿⣿⣿⣿⣿
⣿⣖⠂⢈⣛⣻⣿⣷⢸⣧⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠛⣻⢿⣿⣿⣿⣿⣿⡇⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡿⠿⣿⣿⣿⣿⣿⣿⣶⣶⣄⡀⠀⠀⠉⠛⠛⠛⠛⣋⣿⣿⣿⣿⣿⣿
⣿⣿⣦⠀⡈⢙⣿⣿⡟⣿⡆⠂⠀⠀⠀⠈⠀⢠⣄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠋⢿⣿⣿⣿⣿⣿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⣿⣿⣿⣧⠉⠙⠋⠙⠃⠹⠷⠀⠀⠀⠀⠀⠀⠹⡟⠃⠀⢐⢤⣶⣤⣿⣿⡄⠀⠀⢀⢈⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣄⠀⠀⠴⠆⠀⡀⠀⢐⣀⠀⠉⠀⠀⠱⣿⠤⠄⢝⣹⣿⣿⣿⣿⠇⠀⠈⠉⠉⣹⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⣿⣿⣆⠀⠀⠀⠈⢿⣷⡀⠻⢃⠀⠀⠀⠀⣠⣄⣀⠀⠘⣿⠟⠛⡋⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⠀⠀⢀⣠⣾⣿⣿⣿⣿
⣿⣿⡛⠻⣿⠃⠀⠑⠂⠀⠈⠁⢲⣾⣿⣄⠀⠀⠚⠛⣿⣿⠋⠀⢀⠀⠀⣰⠄⠀⠀⠀⠠⠟⠋⢸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠇⠀⢸⣇⠀⠀⠂⠀⠀⠀⠙⠻⢿⣿⠆⠀⠀⠉⠛⠟⠁⡠⠀⠀⠂⠅⠀⠀⠈⠀⠀⢁⡤⢿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⣀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡆⠀⢸⣿⣿⣷⠈⠀⠀⠀⠀⠀⠐⠇⢶⡀⠀⠀⠐⠐⠋⠿⣄⡤⢌⢉⣁⡈⠀⠀⠀⠉⠉⢼⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣟⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠸⣿⡖⠤⠀⠀⠀⠀⠀⠀⠿⠿⠿⢋⣽⡿⠆⠀⣄⠀⠐⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⠞⠁⠁⠀⠀⠀⠶⠄⠀⠙⠀⠀⠀⠀⠀⠄⠀⠀⠡⣬⣴⣶⣶⠛⠆⠀⢀⣤⣾⣿⣿⣿⡿⠈⡁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠈⣙⠛⠻⣿⣿
⣿⣿⣿⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⣬⣿⣿⣿⣇⢀⠀⠞⠻⢿⠿⣿⠇⠀⠀⢘⠶⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡄⠀⠻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠹
⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠰⣍⢛⡿⢟⣭⠄⠀⠀⠀⠀⠀⠀⠀⣀⣌⣻⡆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⣀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠐⠂⢀⡽⠖⠈⢲⣿⣿⣇⢀⡌⠀⢄⠀⠀⢴⣿⣿⣿⣷⡀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⣶⣬⡖⢩⣶⣷⣮⠛⠛⣟⣿⠘⠀⠀⠘⠻⠖⠠⠄⣿⣿⣿⣷⡀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡙⢋⠐⠠⠤⠀⠀⢤⣤⣀⠀⠀⣀⠀⣈⣻⣿⣿⣇⠀⠀⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡞⠄⠀⠠⠒⠃⠀⠐⠠⣴⣦⡀⠙⢿⣿⣿⣿⣿⠀⣴⣿⣿⡿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⠀⠀⠀⡄⠹⣿⣿⣷⣽⣿⣿⣿⣿⡄⠿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠄⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠈⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⠶⠿⣯⠉⠙⢿⣿⣿⣿⣿⣿⣦⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣰⡆⠀⣼⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣋⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠉⠉⢩⣍⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠽
⣿⣿⣿⡿⣿⡟⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠙⠛⠋⠉⠉⠙⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⡿⠿⠿⢿⣿⡦⠄⠀⠀⠀⠀⢀⣀⣀⣀⣀⣴⣶⣶⡄⠀⠀⠀⠀⠀
⠥⠚⠋⠀⠊⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⡄⢀⣴⣶⣷⣶⡄⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣶⣶⣶⠈⣿⡇⣶⣶⣶⣶⣶⢰⣶⣶⣶⣦⡉⢡⣶⣾⣶⣦⡀⣶⣶⡆⠁⢰⣶⡆⢹⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣀
⡄⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠸⠿⠷⢸⣿⣿⢸⣿⡇⠀⢸⣿⡏⢀⡀⢸⣿⡏⠀⣸⣿⣿⣿⡇⢸⣷⡄⢸⣿⡏⠀⢸⣿⣿⣸⣿⡇⣼⣿⡇⣿⣿⡇⣿⣿⡇⠀⢸⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢶⣶⣶⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⢸⡇⢸⣿⡇⠀⣿⣿⢸⣿⣇⢸⣿⡇⢸⣿⡇⠀⢸⣿⣿⢿⣯⡅⣿⣿⡇⣿⣿⡇⣿⣿⡇⠀⢸⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣸⣿⣿⢸⣿⣿⣸⣿⡇⠀⢸⣿⡇⢸⡇⢸⣿⡇⢀⣿⣿⠿⣿⣿⠈⣿⡇⢸⣿⡇⠀⢸⣿⣿⢸⣿⡇⢻⣿⣇⣿⣿⡇⣿⣿⣇⣀⢸⣿⣇⣈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠛⠛⠛⠀⠙⠻⠟⠛⠁⠀⠘⠛⠃⣸⣧⡘⠛⢃⡘⠛⠛⣀⠛⠛⣠⣿⣧⡘⠛⢓⣠⡘⠛⠛⠘⠛⢃⣈⡛⠻⠟⢋⣀⡛⠛⠛⠛⠘⠛⠛⠛⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⣀⣀⣀⣀⠂⢀⣀⣀⡀⠛⢛⣛⣛⢛⣛⡛⢛⣛⣛⣛⡛⠿⢛⣛⡛⠿⢛⣋⣙⡛⠿⢛⣛⣛⢛⣛⡛⣛⣛⣛⣛⣛⠛⢛⣉⣙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⠿⠇⣿⣿⡿⠏⢰⣿⡿⢻⣿⣆⢸⣿⣿⢸⣿⡇⢸⣿⣿⢿⣿⡆⢸⣿⡇⢰⣿⡿⢻⣿⡆⢸⣿⣿⢸⣿⡇⠿⢿⣿⡿⠿⣸⣿⡟⣿⣿⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⣧⡄⢸⣿⡇⠸⠿⠿⢸⣿⣿⣾⣿⡇⢸⣿⣿⣼⣿⠇⢸⣿⡇⢸⣿⡇⣘⣛⡃⢸⣿⣿⣾⣿⡇⠀⢸⣿⡇⠀⠹⣿⣷⣭⡉⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⡟⠃⢸⣿⡇⢠⣤⣤⢸⣿⣿⢹⣿⡇⢸⣿⣿⢹⣿⡆⢸⣿⡇⢸⣿⡇⢻⣿⡇⢸⣿⣿⢹⣿⡇⠀⢸⣿⡇⠀⢠⣬⡝⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⣷⣶⠸⣿⣷⣼⣿⠇⢸⣿⣿⢸⣿⡇⢸⣿⣿⢸⣿⡇⢸⣿⡇⠸⣿⣷⣼⣿⡇⢸⣿⣿⢸⣿⡇⠀⢸⣿⣇⠀⠸⣿⣧⣿⣿⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠉⠉⠉⠉⣤⣌⣉⣉⣥⣴⣬⣭⣥⣬⣭⣥⣬⣭⣭⣬⣭⣥⣬⣭⣥⣶⣬⣍⣥⣭⣥⣬⣍⣭⣌⣉⣥⣤⣌⣉⣡⣴⣦⣬⣉⣉⣥⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠆⠲⣶⠈⢶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
[69A⣿⣿⣿⢗⠀⠈⢟⣻⣿⣿⣿⠛⠛⠃⠻⣇⠀⠀⠁⠀⢻⠄⢙⡿⠯⠀⠐⠶⣿⣿⣿⣿⣷⣶⣶⣦⣤⣾⣿⣷⣶⣿⣀⡇⡄⠀⠀⠀⠀⣸⡇⡀⣿⢨⠃⠀⠠⠤⡴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡖⠀⠀⢸⡌⢿⡿⡗⠀⠀⠀⠀⠋⠀⠀⠀⠀⠈⠀⣲⣖⣨⣤⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢀⣿⣿⣷⣧⣀⣐⡔⠀⣤⣀⣄⣣⠀⠀⠀⠀⢘⣯⣶⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣯⣥⣀⣀⠊⢣⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣿⢫⠹⠃⠀⠀⠀⠀⠘⠋⣋⣃⠾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣾⣷⣦⣶⣦⣤⣄⣀⠀⡛⣿⣿⠄⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡈⠀⠀⠀⠀⠄⠀⠀⣀⠉⠀⠀⠈⠉⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠿⣿⣿⣿⣿⣿⡞⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣺⡿⠟⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⣀⣤⢂⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣶⠛⢿⣿⣿⣏⡉⠀⠸⢿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⣤⡈⠉⠀⠀⠰⠄⠀⠀⠀⠈⠙⡟⣿⣿⣿⣿⣿⡿⣿⡿⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠇⠈⠿⣿⣯⡀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠁⠸⠙⠛⠀⠋⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣄⠸⠷⠽⢬⣇⢀⠀⠀⠁⣿⣿⣿⣿⣿⣿⠻⠿⠁⣠⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣟⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠻⣿⣿⣿⣿⡆⠀⢐⣿⣿⠃⢀⣀⣶⣿⣿⣻⣿⢿⣿⡂⠀⠈⠀⢻⣿⣿⣿⣿⣿⣿⣿⡏⡿⢳⠈⠙⣿⣿⣂⣽⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢹⣿⣿⣿⡃⠄⠀⠩⠙⠛⢉⣿⣿⣿⣿⣿⣟⠻⣿⣷⠀⠀⠀⢸⣿⣿⠿⣿⣿⣿⣿⣃⣄⠜⢀⣾⣿⣿⣿⣿⣿⡱⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⣿⣿⣿⣧⢱⣚⡻⣿⣿⣿⣿⣿⣿⣿⣿⠛⣷⣿⣿⠄⠀⠀⣿⠁⣿⠀⢻⣿⣿⣿⣿⣽⣠⣿⣿⣿⣿⣿⡿⠿⠇⣀⣠⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣷⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢹⣿⣿⣿⠘⠉⠆⠀⢫⣿⣿⣿⢿⣿⣿⣄⣠⣿⣶⣶⣦⠀⠏⠀⠁⠀⣸⣿⣧⣿⢿⣿⣿⣿⣿⣿⣿⣿⣋⡁⠘⢿⠻⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣤⣤⠀⠘⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠨⣿⣿⣿⡄⠉⠁⠀⠀⣿⣿⣿⣾⣿⣿⣻⣿⢿⣿⡿⠹⡁⠀⠀⢀⣾⣿⣿⣿⣁⣼⣿⣿⣿⣿⣿⣿⣿⠍⠁⠀⠀⠰⣞⢿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡛⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⢂⠰⣿⣿⣿⣿⣶⡀⠀⡀⣿⣿⡿⠹⣿⣿⣿⣷⣿⢿⡇⠀⣠⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠃⠀⠀⠀⠀⠀⢿⣀⢨⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠟⢛⣛⣿⠦⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣷⠘⣴⣿⣿⣿⣿⣿⣷⠈⣛⣼⣿⣉⣴⣄⠉⠙⣛⣿⡄⢀⣦⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣷⣶⣤⣦⠀⠀⠀⠀⢀⣿⣿⣿⣿⠋⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤
⠀⠸⠁⢈⣿⣦⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣉⡀⠉⣻⣿⣿⣽⣿⡁⠀⠀⣿⣿⣿⣿⣿⣏⠀⠈⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⢠⣭⣇⣈⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠔⡫
⠀⠛⣻⣈⣾⣿⡄⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣰⣿⠟⠻⣿⣿⣾⣞⢂⣿⣽⣿⣭⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⢠⣦⠀⢻⣿⣿⣤⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣦⣼⡈⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠈⠹⣽⣿⡀⣸⣿⣿⣿⣿⠶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣡⡇⠀⠉⠀⢸⣿⣿⣿⣿⣇⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀⣀⠒
⢿⣿⢿⣦⣤⡈⢀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠙⢻⣿⣿⣿⣿⣿⣟⡂⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣨⣿⣿⣿⣿⡋⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣲⣶
⡦⣥⠾⢿⠟⢿⣚⣀⠀⣀⡀⠀⢀⣦⣄⣸⣿⣟⠓⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠙⠀⣀⠀⣽⣿⢯⣿⣿⣷⣬⠛⣿⣇⠆⠈⠒⠀⠀⢀⣻⣿
⡤⣶⣾⣿⡁⢒⡛⠢⠀⢻⣿⡷⠌⣈⣽⣶⠀⠉⣠⣅⢈⢹⣿⣿⣿⣿⣿⠉⠁⢩⣟⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠘⠿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⡀⢽⣿⣿⣏⣸⣿⡏⠉⠿⠶⢿⣿⡏⠀⠀⠀⠀⢸⣿⣿
⠀⠀⣭⣿⣿⣿⡀⠀⠀⢒⣉⣠⡀⢹⣿⣿⣦⡀⠈⣿⣿⣿⣿⣿⣿⣿⡆⢠⣼⣿⣿⣿⣭⣅⢹⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡇⣶⣴⡈⣿⣿⣿⣿⣿⡄⣧⠀⢀⣾⣿⣿⠀⠀⠀⣀⣬⣿⣿
⡖⢾⣯⣻⣿⣿⠧⡄⠐⠽⣿⣿⣿⣍⠉⠛⢿⣧⡀⠻⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢈⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠈⠉⠉⠉⠑⠛⠿⠇⣿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠉⠁⣴⡄⢀⣹⣿⣿⣿
⡠⡄⢻⣷⣾⣿⣿⣿⣼⣿⣷⣾⣿⣩⣷⣄⢀⣸⣿⠀⠙⠳⣤⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⢿⣿⠉⢀⠀⢐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠇⠀⣀⠀⠀⠂⠁⠀⠀⠠⠷⣾⣿⣿⣿⣿
⣇⠈⠈⠛⠿⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠈⠁⠘⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⣈⣿⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠸⢿⣤⣀⣀⣠⣤⣴⣾⣿⣿⣶⣿⣿⣭
⣿⣆⠀⠀⠀⠐⠒⣿⣿⣿⣿⣿⣯⣍⠻⢿⣿⡿⠛⠀⠻⠀⠀⢇⠀⠉⢻⣿⡿⣿⣿⣿⣿⣿⠀⠀⠈⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠿⢻⣿⣿⡉⠀⠀⠀⠀⠀⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣷⣄⠀⠀⠀⠘⠻⢿⣿⣟⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢘⣿⣿⣿⣯⣿⣿⣿⣧⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣾⡿⠿⠿⠆⠀⠀⠐⠚⠛⠛⠛⠉⠉⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛
⠾⠿⣿⣿⡆⣶⣀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠆⢹⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣷⣶⣤⣀⣀⣀⣀⣐⣒⣒⣒⣻⣽⣿⣿⣿⣿⣿⣿⣿⣆⠀⣠
⠙⠛⢻⣿⣿⢹⣯⡄⠄⠀⠀⠀⠘⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠹⣿⣿⣿⣿⣿⣷⣦⣄⣄⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣴⣿
⡙⠖⠿⠿⠿⠆⢻⣧⠀⠀⠀⠀⠀⠀⠹⣿⠷⠀⠀⣆⣤⣤⣼⣿⣧⠀⠀⠀⢀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⠀⠀⢀⣠⡀⠀⠈⠀⠠⠀⠀⠒⠀⠀⠹⣾⣦⡀⠚⢛⣿⣿⣿⣿⡗⠀⠀⠙⠛⢉⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿
⣿⣷⡐⠤⠀⠀⠰⣿⣧⠈⢿⡇⠀⠀⠀⠀⠁⣀⠀⠀⠈⢿⡿⠿⠿⠃⠀⠈⠁⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡇⠀⠦⡄⠀⠘⠛⠡⣤⣾⣇⠀⠀⠠⠼⢿⣿⡷⠡⠀⣀⠀⠈⣤⠀⠀⠀⠀⠼⠟⠃⣼⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⢻⡄⠀⠀⣀⠀⠀⠀⠐⠿⣿⣿⡆⠀⠀⠐⠺⠿⠟⠀⡀⠁⠤⠔⠀⠀⠀⠁⠀⠐⣀⠴⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢺⣿⣦⣦⠀⠀⠀⠀⠀⠀⠀⠿⢡⡀⠀⠀⠀⠆⠴⠚⣇⣀⣀⠙⠊⠀⠐⠀⠀⠀⠉⠁⣼⣿⣿⣿⣿⣿⣿⡟⠂⠀⠀⠀⠀⠀⣼⣿⣿⣿⣦⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣼⣿⣿⣿⣧⠀⠀⠀⠀⠀⠠⣶⣦⠍⡀⠀⠀⠀⠀⠀⠸⣿⣷⡷⣛⣿⡶⠀⢀⣄⠀⠰⣿⣿⣿⣿⣿⠏⠀⢀⣲⡄⠀⠀⠀⠀⢿⣿⣿⣿⣿⣧⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⣿⣿⣿⣿⣿⣿⣿
⣟⣿⣿⣿⡿⠛⠀⠀⠀⣀⡀⠀⢘⠏⡐⠒⠀⠀⠀⡀⠀⠀⣀⣠⣥⣬⣽⠳⡄⠀⢀⣤⣾⣿⣿⣿⡟⠈⡁⠈⣹⣿⣿⣄⠀⠀⠀⢸⣿⣿⣿⣿⣿⡆⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠘⠀⠀⠙⢻⣿⣿⣿
⣿⣿⣿⡯⡀⠀⠀⠀⠀⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⢊⣹⣿⣿⣿⡤⠀⠀⠾⠻⣿⠿⣿⠇⠀⠀⢙⠳⣿⣿⣿⣿⣶⣄⠀⠀⠉⢻⣿⣿⣿⣿⡀⣈⣭⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠹⣿⣿
⣿⣿⣿⣷⣤⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⢻⣛⢿⣿⢟⣫⠄⠀⠀⠀⠀⠀⠀⠀⣀⣌⣹⣿⣿⣿⣿⣿⣿⣷⣦⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢹⣿
⣿⣿⣿⣿⣿⣧⣤⣤⣴⣿⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢄⣲⠭⠊⢱⣿⣭⣇⢀⡤⠀⢄⡀⠀⠴⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣇⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⣸⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⢀⠀⣀⣀⣀⣄⣒⠢⢊⣵⣦⣔⠾⠻⢿⣿⠘⠁⠀⠀⠛⠶⠠⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣝⢻⠛⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠻⠟⠀⠀⠉⠅⠀⢺⣥⣄⡀⠀⣀⣀⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡾⡖⠀⠀⠒⢲⠀⠍⠀⣤⣦⡄⠌⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣄⠀⠀⠀⡅⠘⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠠⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣔⡲⠾⢿⡏⠉⠙⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⣶⡀⢠⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣻⣟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠹⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣭⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡄⠀⠀⠀⠀⠀⠉⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠐⠀⠉⢙⣿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⡿⠿⠿⢿⣶⡤⠄⣤⣶⡾⠿⢿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣀⠀⠀
⣿⣿⣿⡿⠟⠛⠛⠉⠉⠀⠀⠀⢀⣴⣶⣷⣶⡄⢀⣴⣶⣷⣶⡄⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣶⣶⣶⠈⣿⡇⣶⣶⣶⣶⣶⢰⣶⣶⣶⣦⡉⢡⣶⣾⣶⣦⡀⣶⣶⡆⠉⢰⣶⡆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠟⠡⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠸⠿⠷⢸⣿⣿⢸⣿⡇⠀⢸⣿⡏⢀⡀⢸⣿⡏⠀⣸⣿⣿⣿⡇⢻⣷⡄⢸⣿⡏⠀⢸⣿⣿⣸⣿⡇⣾⣿⡇⣿⣿⡇⣿⣿⡇⠀⢸⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢶⣶⣶⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⢸⡇⢸⣿⡇⠀⣿⣿⢸⣿⣇⢸⣿⡇⢸⣿⡇⠀⢸⣿⣿⢿⣯⡅⣿⣿⡇⣿⣿⡇⣿⣿⡇⠀⢸⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣸⣿⣿⢸⣿⣿⣸⣿⡇⠀⢸⣿⡇⢸⡇⢸⣿⡇⢀⣿⣿⠿⣿⣿⠘⣿⡇⢸⣿⡇⠀⢸⣿⣿⢸⣿⡇⢻⣿⣇⣿⣿⡇⣿⣿⣇⣀⢸⣿⣇⣈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠛⠛⠛⠀⠙⠻⠟⠛⠁⠀⠘⠛⠃⣸⣧⡘⠛⢃⡘⠛⠛⣀⠛⠛⣀⣿⣧⡘⠛⢓⣠⡘⠛⠛⠘⠛⢃⣈⡛⠻⠟⢋⣀⡛⠛⠛⠛⠘⠛⠛⠛⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⣀⣀⣀⡀⠀⢀⣀⣀⡙⠻⢛⣛⣛⢛⣛⡛⢛⣛⣛⣛⡛⠿⢛⣛⡛⠿⢛⣋⣉⡛⠿⢛⣛⣛⢛⣛⡛⣛⣛⣛⣛⣛⠛⢛⣉⣙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⠿⠇⣿⣿⡿⠯⢰⣿⡿⢻⣿⣆⢸⣿⣿⢸⣿⡇⢸⣿⣿⢿⣿⡆⢸⣿⡇⢰⣿⡿⢻⣿⡆⢸⣿⣿⢸⣿⡇⠿⢿⣿⡿⠿⣸⣿⡟⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⣧⡄⢸⣿⡇⠸⠿⠿⢸⣿⣿⣾⣿⡇⢸⣿⣿⣼⣿⠇⢸⣿⡇⢸⣿⡇⣘⣛⡃⢸⣿⣿⣾⣿⡇⠀⢸⣿⡇⠀⠹⣿⣷⣭⡉⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⡟⠃⢸⣿⡇⢠⣤⣤⢸⣿⣿⢹⣿⡇⢸⣿⣿⢹⣿⡆⢸⣿⡇⢸⣿⡇⢻⣿⡇⢸⣿⣿⢹⣿⡇⠀⢸⣿⡇⠀⢠⣬⡝⣿⣿⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⣷⣶⠸⣿⣷⣼⣿⠇⢸⣿⣿⢸⣿⡇⢸⣿⣿⢸⣿⡇⢸⣿⡇⠸⣿⣷⣼⣿⡇⢸⣿⣿⢸⣿⡇⠀⢸⣿⣇⠀⠸⣿⣧⣿⣿⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠉⠉⣉⣩⣤⣌⣉⣩⣥⣴⣬⣭⣥⣬⣭⣥⣬⣭⣭⣬⣭⣥⣬⣭⣥⣶⣬⣍⣥⣭⣥⣬⣉⣭⣌⣉⣥⣤⣌⣉⣡⣼⣦⣌⣉⣉⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠆⠲⣶⠏⢶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
[69A⠀⠈⡖⠿⣿⣿⡏⠀⠀⠀⢩⠧⠀⠀⠀⠀⠺⠁⢀⣛⠋⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡿⠛⣿⣿⣺⣀⠀⠀⣀⡀⠘⡟⠀⢸⡁⠇⠀⠐⢒⣶⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⠿⠈⠙⢹⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⣿⣵⣾⣿⣄⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢿⣿⣿⣆⣷⣾⣿⣿⣦⣰⣿⣃⢰⡆⡦⣾⠇⠀⠀⠀⠀⣿⣿⣿⠿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣦⣤⣶⣀⠀⣰⠀⠀⠀⠀⠀⣠⣄⣠⠀⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣾⣾⡇⡇⠏⠀⠀⠀⠀⠈⠉⠬⣥⠘⠻⢻⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣄⣥⣿⣟⡂⣤⣼⣷⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠑⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣷⣟⣻⣿⣟⣿⣿⣿⠟⠸⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢸⠿⢼⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠠⣴⡏⠤⠀⠀⠀⠀⠀⢹⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣍⢙⣿⣿⣯⡖⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣾⣿⣿⣿⣿⣿⡿⣿⣿⣿⣙⣿⣦⠀⠀⠀⠀⠓⠀⠀⠀⠀⠉⢿⢹⣿⣿⡿⣿⠟⢿⠟⠋⠉⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣘⠿⡻⣦⠀⠀⠀⠻⢻⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁⠋⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣶⠈⠛⠃⢰⣾⣄⠂⠀⠀⢸⣿⣿⣿⣿⣿⡏⠙⠂⡠⠞⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢿⣿⣿⣿⢿⣇⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⢿⣿⣿⣿⣯⠀⠀⢽⣿⣏⣀⣤⣾⣿⣿⣯⣿⣿⣿⣯⡀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠹⠟⠃⠀⣸⣿⣿⣤⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣾⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣯⢐⠀⣀⣆⣉⣁⣼⣿⣿⣿⣿⣿⣏⠙⣽⡇⠀⠀⠀⣿⢿⣿⠻⣿⣿⣿⣿⣴⣴⠃⣴⣿⣿⣿⣿⣿⣿⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠷⢀
⡏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢹⣿⣿⣿⡆⣭⡭⠻⢿⣿⣿⣿⣿⣿⣿⣏⠉⠿⣿⠿⠀⠀⢰⡿⠀⡿⠀⢻⣿⣿⣿⣿⣾⣼⣿⣿⣿⣿⣿⣛⠛⢀⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾
⠟⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⡇⢁⣘⠁⠀⢾⣿⣿⡟⣻⣿⣿⣦⣶⣿⣿⣿⣧⠀⠀⠐⠀⢠⣼⣿⣷⣿⢻⣿⣿⣿⣿⣿⣿⣿⣤⠄⠙⠃⠛⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⣾⠀⠘⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢹⣿⣿⣷⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣹⡿⣿⣿⡟⠙⠄⠀⠂⢸⣿⣿⣿⣧⣤⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠘⡟⠿⢿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋
⣍⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠋⡆⢸⣿⣿⣿⣿⣷⡀⢀⡀⣿⣿⡏⠹⠿⣿⣿⣿⡟⠻⠇⠀⣴⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠁⠀⠀⠀⠀⠈⠣⡴⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀
⣿⠗⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣇⢱⣾⣿⣿⣿⣿⣿⣯⢨⣯⣿⣿⡴⣾⣄⠀⠈⢭⣿⣆⣠⣶⣿⣿⠿⢿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡷⠀⠀⠀⠀⣰⡿⣿⣿⡟⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⠂⠀⠀
⢿⣷⡀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⢈⣿⣿⣿⣿⣿⢀⠀⠀⣿⣿⣿⣿⣿⣿⡀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⣰⣾⡦⠴⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠊⠀⠀⠀
⣽⣿⣇⠀⠀⠀⠀⠀⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡬⠿⠋⢽⣿⣿⣿⡿⢡⣿⣿⣿⣴⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⡁⡀⠰⣿⠀⢸⣿⣿⣾⣿⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀
⠙⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠙⢿⣿⣄⣸⣿⣿⣿⣿⠓⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡇⠀⠀⠀⠸⣿⣿⣿⣿⣷⣾⣿⣇⡀⠀⠀⠀⠀⠀⠨⠍⣁⢈⣠⡄
⣤⣀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣈⣛⣿⣿⣿⣿⣿⣿⡥⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣧⠀⠀⠀⢰⣿⣿⣿⣿⡅⠿⣿⣿⠃⠀⢀⡀⠀⠀⣈⣿⣿⣿⣿⡆
⠿⢻⣟⣣⠀⢀⣀⠀⠀⣰⣤⣄⢹⣿⣿⠓⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠁⢤⣀⣼⣿⢓⣿⣿⣿⣶⠀⣿⣾⣃⠈⠉⠀⠀⢨⣿⣿⣿⣿⣿
⣍⠐⣚⠓⠀⠘⣿⣿⡦⢀⣨⣷⣶⠀⠀⣠⣥⣀⣸⣿⣿⣿⣿⡿⠁⠀⢨⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠆⠀⠈⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⢀⡲⣿⣿⣿⣰⣿⡏⡀⠉⠛⢹⣿⣆⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿
⣿⣿⣇⠂⡀⠀⢖⣉⣠⡀⢻⣿⣿⣦⡀⠉⣿⣿⣿⣿⣿⣿⣿⡗⢒⣾⣿⣿⣿⣧⣥⡀⢿⣿⣿⣿⣿⡦⠀⠀⡿⠋⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⢸⣾⡆⣾⣿⣿⣿⣿⣧⡸⠀⠐⠿⡿⡯⢀⠀⠐⢴⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⠀⠀⢽⣿⣿⣿⣍⠉⠛⢿⣷⣄⠹⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡂⠀⢽⣿⣿⣿⡇⠀⢀⡇⠀⠀⠀⠀⠹⠟⠛⠛⠛⠻⠿⠷⢾⣿⣷⣿⣿⣿⡟⠋⠁⠀⠀⢀⠀⠀⠀⠾⣆⢲⣾⣿⣿⣿⣿⣿⣿
⣴⣿⣿⣿⣿⣾⣿⣶⣿⣿⣩⣷⣄⣀⣈⢻⡆⠈⠻⢤⣶⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠼⣿⣏⠀⢀⣦⡁⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠃⠀⣤⠀⠀⠁⠀⠀⠀⣠⣿⣻⣿⡿⣿⢿⣿⣿⣿
⠻⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡃⠀⠀⠀⡌⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⣠⣼⣿⣶⣾⡿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣯⣽
⠀⠀⠐⠿⣿⣿⣿⣿⣿⣯⣉⠻⢿⣿⣿⠟⠃⠸⠇⠀⠸⡀⠈⠙⣿⣿⣻⣿⣿⣿⣿⡇⠀⠀⢀⠁⣾⣿⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠋⣿⣿⣧⡀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠀⠀⠛⠿⣿⣿⣟⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⣻⣿⣿⣿⣾⣿⣿⣿⡆⠀⠀⠀⢀⣾⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠿⠿⠿⠟⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠉⠀⣹⣿⣿
⣿⡄⣦⡄⠀⠀⠺⠿⠛⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠛⣿⢿⣿⣿⣿⣿⣿⣇⠀⠀⠸⠇⢿⣿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣶⣤⣄⣀⣀⣀⣀⣀⣤⣤⣀⣤⣼⣿⣿⣿⣿⣿⣿⡟⠛⠀⣴⣿⣟⠛
⣿⣷⢻⣯⡀⡀⠀⠀⠀⠐⠂⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣾⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣿⣿⣿⠭⠟
⣿⣿⡎⢿⣇⠀⠀⠀⠀⠀⠀⠘⣿⡷⡄⠀⠠⣀⣤⣤⣿⣿⡄⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠈
⠀⢀⠀⠈⠉⠆⢀⡀⠄⠂⠀⠀⠈⣵⣶⣀⢐⡻⢻⣿⣿⣿⣿⡆⠀⠈⠙⠋⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣗⣀⣠
⡈⠙⠁⠀⣴⣵⡀⢶⣶⠀⢀⠀⠀⠌⢉⡀⠀⠀⠹⣿⡿⠿⠟⠁⠀⠙⢀⠄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣀⡀⠀⠹⠿⢗⣀⣥⣦⠀⠀⠀⠲⠿⣿⣷⠆⠀⠉⢀⠀⠨⡄⠀⠀⠀⠀⠾⠛⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⣦⣤⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠉⠀⠀⠀⠀⣿⣿⣿⣧⠀⠀⠀⠔⢿⣿⠓⠀⠀⠁⠤⢜⠀⠀⠀⠀⠀⠐⣀⡴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⣼⣿⣿⣦⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⠉⡁⠀⠀⠀⠀⠉⢹⡟⣀⠀⠀⠀⠀⠄⡤⢾⣆⣀⣀⠑⠂⠀⠀⠀⠀⠀⠉⠁⣽⣿⣿⣿⣿⣿⡿⠟⠻⣿⣿⣦⡀⠀⠀⠀⠸⡿⢿⣿⣷⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⠀⠀⠀⠀⠀⠀⢠⣥⣙⡃⠀⠀⠀⠀⠀⠈⢹⣿⣶⡧⢛⣿⡶⠀⢀⣄⠀⠰⣿⣿⣿⣿⣿⡏⠀⢀⣼⣿⣿⣿⣿⣦⣀⣀⠀⠀⠀⣿⣿⣷⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣭⠙⠻⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠁⠀⠀⠀⢀⠈⣿⠏⠪⠅⠀⠀⠀⠀⠀⠀⠀⣀⣠⣬⣭⠧⡄⠀⢀⣤⣾⣿⣿⣿⠟⠈⡁⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠙⠿⠻⠇⠀⢛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿
⣿⡏⠁⠀⠀⠀⠰⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢉⣹⣿⣿⣿⡦⠀⠀⠾⠿⣿⣿⣿⠇⠀⠀⢈⣓⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⡀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠸⣿⣿⣿⣿
⣿⣔⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⢫⠿⢿⣿⡿⣋⠅⠀⠀⠁⠀⠀⠀⠀⣀⣮⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣧⡀⠀⠁⣠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠦⡋⠜⢥⣾⣯⣷⠀⡤⠀⠀⡀⠀⠔⡿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣾⣧⣿⣿⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⡀⠤⣄⠔⣩⣦⣌⢶⠿⣿⣿⡄⢃⠀⠀⠛⠷⠂⠄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠈⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣦⣼⣛⡿⠿⠢⠄⣈⠉⠀⠸⣧⣄⣀⠀⢀⣀⣠⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣡⡖⣀⠀⡠⠒⡀⠨⠁⢤⣴⣤⡒⠙⣻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⡀⠀⠀⢨⠀⠹⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡄⠀⠀⠤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡒⠶⠟⢿⡉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡤⠔⣿⠀⣾⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠈⠉⠛⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣤⣀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣶⣿⣿⣿⣶⣤⣤⣄⣀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠷⠾⠿⠿⠿⠿⠿⣿⣿⡿⠿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⡿⠿⠿⠿⠿⡿⠿⠿⠿⣿⣿⣿⡿⠿⠿⣿⣶⡾⠿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀
⣿⣿⣿⣿⣿⣿⣿⡯⠄⠀⠀⠀⢀⣴⣶⣷⣶⡄⢁⣴⣾⣷⣶⡄⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣶⣶⣶⠈⣿⡇⣶⣶⣶⣶⣶⢰⣶⣶⣶⣦⡉⢡⣶⣾⣷⣦⡀⣶⣶⡆⠉⢰⣶⡆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⣿⡿⠟⠛⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⣿⠸⠿⠷⢸⣿⣿⢸⣿⡇⠀⢸⣿⡏⢀⡀⢸⣿⡏⠀⣸⣿⣿⣿⡇⢻⣷⡄⢸⣿⡏⠀⢸⣿⣿⣸⣿⡇⣾⣿⡇⣿⣿⡇⣿⣿⡇⠀⢸⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢶⣶⣶⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⢸⡇⢸⣿⡇⠀⣿⣿⢸⣿⣇⢸⣿⡇⢸⣿⡇⠀⢸⣿⣿⢿⣯⡅⣿⣿⡇⣿⣿⡇⣿⣿⡇⠀⢸⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣸⣿⣿⢸⣿⣿⣸⣿⡇⠀⢸⣿⡇⢸⡇⢸⣿⡇⢀⣿⣿⠿⣿⣿⠈⣿⡇⢸⣿⡇⠀⢸⣿⣿⢸⣿⡇⢻⣿⣇⣿⣿⡇⣿⣿⣇⣀⢸⣿⣇⣈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠛⠛⠛⠀⠙⠻⠟⠛⢁⣄⠘⠛⢃⣼⣧⡘⠛⠃⡘⠛⠛⣀⠛⠛⣠⣿⣧⡘⠛⢓⣠⡘⠛⠛⠘⠛⢃⣈⡛⠻⠟⢋⣀⡛⠛⠛⠛⠘⠛⠛⠛⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⣀⣀⣀⣀⠀⢈⣉⣉⡙⠻⢛⣛⣛⢛⣛⡛⢛⣛⣛⣛⡛⠿⢛⣛⡛⠿⢛⣋⣉⡛⠿⢛⣛⣛⢛⣛⡛⣛⣛⣛⣛⣛⠛⢛⣉⣙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⠿⠇⣿⣿⡿⠯⢰⣿⡿⢻⣿⣆⢸⣿⣿⢸⣿⡇⢸⣿⣿⢿⣿⡆⢸⣿⡇⢰⣿⡿⢻⣿⡆⢸⣿⣿⢸⣿⡇⠿⢿⣿⡿⠿⣸⣿⡟⣿⣿⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⣧⡄⢸⣿⡇⠸⠿⠿⢸⣿⣿⣾⣿⡇⢸⣿⣿⣼⣿⠇⢸⣿⡇⢸⣿⡇⣘⣛⡃⢸⣿⣿⣾⣿⡇⠀⢸⣿⡇⠀⠹⣿⣷⣭⡉⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⡟⠃⢸⣿⡇⢠⣤⣤⢸⣿⣿⢹⣿⡇⢸⣿⣿⢹⣿⡆⢸⣿⡇⢸⣿⡇⢻⣿⡇⢸⣿⣿⢹⣿⡇⠀⢸⣿⡇⠀⢠⣬⡝⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⣷⣶⠸⣿⣷⣼⣿⠇⢸⣿⣿⢸⣿⡇⢸⣿⣿⢸⣿⡇⢸⣿⡇⠸⣿⣷⣼⣿⡇⢸⣿⣿⢸⣿⡇⠀⢸⣿⣇⠀⠸⣿⣧⣿⣿⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⣉⣉⣉⣩⣤⣌⣉⣉⣥⣶⣬⣭⣭⣬⣭⣥⣬⣭⣭⣬⣭⣥⣬⣭⣥⣶⣬⣭⣥⣭⣥⣬⣉⣭⣬⣉⣥⣤⣌⣉⣡⣾⣦⣬⣉⣉⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠆⠲⣶⠏⢶⠄⠠⠲⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
[69A⠿⢿⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠘⢄⣰⣶⣠⣵⡆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⣛⣳⣷⣧⡀⡠⡤⡇⣹⠃⣁⣷⠈⠀⠀⠀⠹⣯⣽⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣷⣖⣿⡇⣿⠿⠀⠀⠀⠀⣸⠿⠿⡟⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣶⣤⣤⣄⣀⠀⣖⢿⣿⡇⢙⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣾⣿⣿⣿⣿⣿⣿⣇⡟⠀⠀⠀⠀⡀⠀⠀⠛⠷⠈⠉⠹⠟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣲⣾⣿⣿⣿⣿⣿⣿⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣻⡿⢿⣿⣿⣿⣿⣿⣷⣾⣤⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠁⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢿⣿⡶⠿⣿⣾⣿⠛⡋⠀⢹⣿⣿⣷⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣻⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠐⠿⠃⠃⠀⡀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠂⠺⣿⣿⣟⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣾⣿⣧⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠇⢻⢿⡿⢻⡟⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀⢰⣮⢹⣙⡧⢀⠀⠀⠋⢹⣿⣿⣿⣿⣿⣿⣿⡏⠉⣻⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡏⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡻⢿⣿⣿⣾⣧⠀⠀⠠⣾⣿⡆⠁⠀⢠⣽⣿⣿⣿⣿⣿⡧⠀⠀⢒⠫⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡇⠛⢿⣿⣿⠙⣧⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣶⣰
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⣿⡧⠀⡐⠻⣿⠦⠶⣻⣿⣿⣿⣿⣿⠷⣿⣷⡆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢈⠃⡥⢀⣶⣿⣿⣾⣿⣿⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠿⠃⠉⢈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠸⣿⣿⣿⣇⢓⡰⠶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣷⣨⣾⣧⠀⠀⠀⣿⠙⣿⠉⣿⣿⣿⣿⣾⢿⢁⣾⣿⣿⣿⣿⣿⣿⡈⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⡦⠀⠀⡘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢻⣿⣿⣿⡞⡟⣓⠻⢹⢻⣿⣿⣿⣿⣿⣧⠀⢛⣿⣭⣄⡀⠘⡟⢀⠛⠀⢹⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⠧⠊⢰⡾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⣀⣴⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⣿⣿⣿⡃⠠⠬⠀⠀⠛⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⢿⠄⠀⠀⠀⣤⣾⣿⣿⠿⣨⣿⣿⣿⣿⣿⣿⣿⠶⠃⠀⠉⢉⣹⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣷⡋⠃⠀
⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⣿⣿⣿⣿⣄⣀⠀⠀⠀⣿⣿⣿⢿⣿⣿⣾⣟⣭⣿⡏⠈⠁⠀⢈⣰⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⣇⠙⢻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠟⠀⠀⠀⠐
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠈⡄⣿⣿⣿⣿⣿⣿⣀⢰⣄⣿⣿⠇⢈⠛⠿⠿⣿⣿⠙⠛⡀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣁⣦⠀⠀⠀⠀⠙⣿⣽⣿⣿⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡎⠀⠀⠀⠀⠀
⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣇⣹⣿⣿⣿⣿⣿⣿⠷⠀⠦⣿⣿⣾⢿⣷⠤⠀⠓⢿⣷⣤⣿⣿⣿⠟⠻⠋⢻⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣟⠁⠀⠀⠀⣐⡟⠹⢻⠟⠈⠃⠀⠀⠀⠀⠀⠀⠀⣀⠹⡿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡤⣐⣺⣿⣿⣷⣿⣆⣀⡄⣸⣿⣿⡿⣿⣿⣦⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⣠⠀⢴⣿⣿⣒⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣟⣋⡲⢿⡿⣿⡟⢃⣾⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠄⢠⠀⠻⠇⢐⣿⣿⣿⣿⣇⣠⣴⡆⠀⠀⠀⠀⠀⠀⢀⡀⠄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⢓⣿⣧⣤⣿⣿⣿⣿⣏⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠀⠀⠀⠈⣻⣿⣿⣿⡿⢻⣿⣿⣤⠀⠀⠀⠀⠀⠀⣡⣤⣤⣼⡂⠀⠀⢀
⠆⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠛⢿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣆⣤⣬⣿⣿⣿⣿⣿⣿⣷⠂⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣆⠀⠀⠘⣿⣿⢻⣿⣧⣙⡿⣿⡏⣄⠐⣤⠀⠀⠨⣿⣿⣿⣿⣧⣄⣀⣠
⡄⠀⢤⣄⡀⢀⣼⣶⣤⠿⢿⣿⠛⡿⢿⢿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢐⢳⣾⣿⠏⢿⣿⡛⢻⣇⣾⣿⡗⠂⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟
⠃⠄⠈⢿⣿⡷⢀⣤⣿⣷⠀⠀⣴⣶⣤⣨⣿⣿⣿⣿⣿⠇⠀⣠⣾⣿⣿⢿⡿⣿⣿⣿⣿⣿⡟⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣆⠦⢻⣿⣿⣷⣿⣏⢰⡀⠐⣰⣿⣿⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠂⠀⠀⣊⣁⣤⡀⢹⣿⣿⣧⡀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣈⣷⣿⣿⣿⣿⣶⣦⠹⢿⣿⣿⣿⣿⠂⠀⢸⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡼⣿⣿⣿⣿⣿⠮⠁⠀⠉⠛⠛⢁⡄⡀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣛
⣤⠀⠂⢽⣿⣿⣿⣍⠉⠛⠻⣿⣤⡘⢿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⡀⠀⠿⣿⣿⡿⠀⠀⢸⣿⡇⠀⠀⠀⠛⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢀⠔⠀⠀⢉⣸⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣾⣿⣶⣿⣿⣩⢿⡆⣀⣀⡻⡇⠀⠙⠶⢶⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠛⣿⣆⠀⣠⣧⣿⡃⢀⡀⠀⠀⠀⠀⠀⠲⠀⠈⠉⠉⠛⠿⣿⡿⠉⠀⣰⣇⣀⠀⠀⣀⣀⣤⣷⣾⣿⣯⣽⣿⣛⣿⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⡀⠀⢸⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢤⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣯⣑⡛⠿⣿⣿⡟⠓⠀⠿⠀⠀⢇⠀⢉⢹⣿⣟⣿⣿⣿⣿⣿⠀⠀⠀⠀⠠⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⣠⣶⣶⣶⡄⠀⠀⢠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠍⠿⣿⣿⣿⣿⣿
⠀⠹⢿⣿⣿⣿⠻⠏⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠃⢈⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢀⣬⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⣿⣿⣿⠇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⢀⣼⣿⣿⠿⠛⣿
⡀⠀⠀⠚⠿⠏⠂⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠘⢻⠿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠘⠁⠿⣿⣿⣷⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣀⣀⣀⠀⠈⠉⠙⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣀⣠⣾⣿⣿⣦⣤⠴⠟
⣿⡀⡀⠀⠀⠀⠀⠂⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠹⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⢀
⢿⣷⠐⠀⠀⠀⠀⠈⠀⢾⣿⠦⠀⠀⢤⣠⣤⣸⣿⣧⡄⠀⠀⠀⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢘
⠀⠛⢇⠀⣀⠀⠠⠤⠀⠀⢩⣴⣆⣀⢔⠻⣿⣿⣿⣿⣷⠀⠀⠈⠉⠏⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣏⣀⣀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⡟
⠀⣠⣔⡄⢱⣦⡄⠀⠀⠀⠠⠙⢉⠉⠀⠈⢿⣿⡿⠿⠟⠀⠀⠉⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠙⣿⡿⠆⣙⣵⡄⠀⠀⣀⣠⣿⣷⣶⢖⠀⠉⠀⠀⢡⡄⠀⠀⠀⠀⠾⠛⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⢸⣿⣧⡀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠂⠀⠀⠀⣩⣿⣿⣷⣆⠀⠀⠀⠼⣿⣯⠒⢀⠈⠁⡤⢈⠀⠀⠀⠀⠀⠀⢄⡴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠈⠿⢿⣷⣄⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠒⠀⠀⠀⠈⠉⠛⢿⡿⡀⠀⠀⠀⠠⠄⣤⢾⡄⢀⣀⠓⠂⠀⠀⠀⠀⠀⠉⢀⣽⣿⣿⣿⣿⣿⡿⠏⢉⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠙⣿⣆⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⡟⣩⣿
⡀⠀⠀⠀⠀⠀⠀⣙⡁⢗⠀⠀⠀⠀⠀⠀⠈⢹⣷⣴⣦⢟⣿⣶⠀⢀⣀⠀⠀⣿⣿⣿⣿⣿⡇⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡉⠋⠀⠘⠿⡿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠃⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⠿
⣷⠀⠄⠁⠀⠀⢀⠙⣿⠏⠓⠂⠀⠀⠄⠀⠀⠀⠉⢛⣠⣬⣭⠷⢤⠀⢀⣠⣾⣿⣿⣿⠿⠀⢄⠠⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠃⣠
⠈⠀⠀⢀⠴⠦⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠠⠀⠍⢹⣿⣿⣿⡧⠀⠀⡼⠿⢿⡿⣿⠟⠀⠀⠀⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢠⡀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠫⡿⢿⣿⣿⢟⡅⠀⠀⠁⠀⠀⠀⠀⢀⣰⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⣴⣛⣿⣿⡟⢘⣿
⣖⠀⠒⠀⢀⡁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⢀⠤⣝⠉⠫⣶⣿⣷⡀⢠⠄⠠⢀⠀⠀⠻⢿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿
⣿⣶⣤⣶⣿⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠀⠠⢛⣥⣀⢦⡿⢿⣿⣧⠙⠀⠀⠈⠻⠆⠐⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣴⣶⣶⣿⣶⣮⣴⣻⠿⣿⠃⠄⢒⣋⠉⠀⢯⣤⣄⡀⠀⠄⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣀⣶⠤⡀⢀⠔⢂⠀⠕⠀⢦⣶⣄⣊⢹⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣄⡌⠁⠀⠀⠡⠈⢻⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⠀⠀⠳⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡚⠛⠛⢿⡀⠈⢻⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡴⠼⠇⣰⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠛⠻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣴⣿⣿⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⢏⣩⣿⣿⠿⠿⠿⠿⣿⣿⡿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⡿⠿⠿⣿⣿⡿⠿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀
⣿⣿⣿⣿⣿⣿⠟⠁⠘⠛⠛⡋⢁⣴⣶⣷⣶⡌⢁⣴⣾⣷⣶⡄⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣶⣶⣶⠘⣿⡇⣶⣶⣶⣶⣶⢰⣶⣶⣶⣦⡉⢡⣶⣾⣷⣦⡀⣶⣶⡆⠉⢰⣶⡆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⣿⣿⣿⣿⣿⠿⠂⠀⠀⠀⠀⠀⢸⣿⣿⠸⠿⠷⢸⣿⣿⢸⣿⡇⠀⢸⣿⡏⢀⡄⢸⣿⡏⠀⣼⣿⣿⣿⡇⢿⣷⡄⢸⣿⡏⠀⢸⣿⣿⣸⣿⡇⣾⣿⡇⣿⣿⡇⣿⣿⡇⠀⢸⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢶⣶⣶⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⢸⡇⢸⣿⡇⠀⣿⣿⢸⣿⣇⢸⣿⡇⢸⣿⡇⠀⢸⣿⣿⢿⣯⡅⣿⣿⡇⣿⣿⡇⣿⣿⡇⠀⢸⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣸⣿⣿⢸⣿⣿⣸⣿⡇⠀⢸⣿⡇⢸⡇⢸⣿⡇⢀⣿⣿⠿⣿⣿⠘⣿⡇⢸⣿⡇⠀⢸⣿⣿⢸⣿⡇⢻⣿⣇⣿⣿⡇⣿⣿⣇⣀⢸⣿⣇⣈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠛⠛⠛⠀⠙⠻⠟⠛⣡⣆⠘⠛⢃⣼⣧⡘⠛⠃⡘⠛⠛⣀⠛⠛⣠⣿⣧⡘⠛⢓⣀⡘⠛⠛⠘⠛⢃⣌⡛⠻⠟⢋⣀⡛⠛⠛⠛⠘⠛⠛⠛⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⣀⣀⣀⣀⠙⢋⣉⣉⡛⠿⢛⣛⣛⢛⣛⡛⢛⣛⣛⣛⡛⠿⢛⣛⡛⠿⢛⣋⣉⡛⠿⢛⣛⣛⢛⣛⡛⣛⣛⣛⣛⣛⠛⢛⣋⣙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⠿⠇⣿⣿⡿⠏⢰⣿⡿⢻⣿⡆⢸⣿⣿⢸⣿⡇⢸⣿⣿⢿⣿⡆⢸⣿⡇⢰⣿⡿⢻⣿⡆⢸⣿⣿⢸⣿⡇⠿⢿⣿⡿⠿⣸⣿⡟⣿⣿⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⣧⡄⢸⣿⡇⠸⠿⠿⢸⣿⣿⣾⣿⡇⢸⣿⣿⣼⣿⠇⢸⣿⡇⢸⣿⡇⣘⣛⡃⢸⣿⣿⣾⣿⡇⠀⢸⣿⡇⠀⠹⣿⣷⣭⡉⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⡟⠃⢸⣿⡇⢠⣤⣤⢸⣿⣿⢹⣿⡇⢸⣿⣿⢹⣿⡆⢸⣿⡇⢸⣿⡇⢻⣿⡇⢸⣿⣿⢹⣿⡇⠀⢸⣿⡇⠀⢠⣬⡝⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⣷⣶⠸⣿⣷⣼⣿⠇⢸⣿⣿⢸⣿⡇⢸⣿⣿⢸⣿⡇⢸⣿⡇⠸⣿⣷⣼⣿⡇⢸⣿⣿⢸⣿⡇⠀⢸⣿⣇⠀⠸⣿⣧⣿⣿⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⣉⣉⣉⣉⣤⣬⣉⣉⣥⣶⣬⣭⣥⣬⣭⣥⣬⣭⣭⣬⣭⣥⣬⣭⣥⣶⣬⣭⣥⣭⣥⣬⣉⣭⣬⣉⣡⣤⣌⣉⣡⣼⣦⣬⣉⣩⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠆⠲⣶⠏⢶⠄⠠⠲⠶⠆⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
[69A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣭⣷⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣷⣶⣶⣿⣿⣿⣦⣺⡏⡇⣾⡆⡇⣿⠀⠀⠀⠀⢨⣿⣿⣿⠽⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⠀⠀⠀⣤⢲⣴⣆⠸⠷⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⡏⠀⠀⠀⠀⠘⠉⢽⣧⠸⠿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣦⣼⣼⣿⣍⣀⣶⣾⣿⣿⣿⣿⣏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⣀⡄⠀⠀⠘⠀⠰⣵⡍⠀⠀⠘⠥⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟
⣿⣿⣿⣿⣿⣻⣿⣿⣛⣭⣿⣿⣿⣿⣿⡟⠒⢿⣿⣿⣏⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢾⠿⢼⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⢀⣰⡟⣡⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠋⠀⠀⠀
⣿⣿⣿⣿⣿⣟⢩⣿⣿⣄⢘⣿⣿⣿⡖⠂⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣾⣾⣾⣿⣿⣿⣿⣿⡿⣿⣿⣿⢛⣷⣆⠈⠀⠀⠀⠂⠀⠀⠀⠈⠙⣿⢻⣿⣿⣿⣿⡿⣿⡿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣈⡹⣿⣯⡀⠀⠀⠘⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠚⠋⠟⠈⠏⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⠄⠛⠓⢐⣶⣧⠰⠀⠀⠀⢾⣿⣿⣿⣿⡿⡏⠛⠃⣀⡾⣧⣻⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣟⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣷⡍⢿⣿⣿⣿⣿⠄⠀⢈⣿⣿⡃⣀⣤⣾⣿⣿⣿⣿⣟⢿⣿⡀⠀⠀⠂⢻⣿⣿⣿⣿⣿⣿⣿⡇⡿⢻⠀⢙⣿⣿⣀⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⡿⡿⠶⠀⠀⠚
⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⡅⡤⢀⣨⣛⡙⣉⣿⣿⣿⣿⣿⣿⣍⠻⣹⡗⠀⠀⠀⢸⣿⣿⡿⣿⣿⣿⣿⣃⣆⡼⢀⣾⣿⣿⣿⣿⣿⡵⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⡈⠀⠀⢰⡃⠀⠀
⣿⣿⣿⣿⣿⣿⠀⠸⣿⣿⣿⣷⢰⣚⡉⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⣾⣿⡿⡄⠀⠀⣿⡇⣹⡇⢹⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⡿⠿⠇⢀⣠⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⢀⡞⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡆⠀⢻⣿⣿⣿⡎⠋⠷⠀⠘⣽⣿⣿⡿⢿⣿⣿⣄⣠⣿⣶⣷⣦⡀⠋⠀⠍⠀⣀⣿⣿⣽⡿⣿⣿⣿⣿⣿⣿⣿⣟⣉⠐⠿⠹⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⣰⡿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣏⠀⠈⣿⣿⣿⣅⠉⠉⠀⠀⠁⣿⣿⣿⣾⣿⣿⡿⣿⡿⣿⣿⠟⣇⠀⠠⠀⣰⣿⣿⣿⣍⣡⣿⣿⣿⣿⣿⣿⣿⡯⠉⠀⠀⠀⢶⢻⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠻⠃⠀⢀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡿⢢⠀⣿⣿⣿⣿⣷⣤⠈⠀⠀⣿⣿⣿⢻⣿⣿⣿⣿⣼⡿⣿⠀⢀⣀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⠃⠀⠀⠀⠀⠸⣆⣬⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣷⠘⣆⣿⣿⣿⣿⣿⣿⣧⠐⠷⣸⣿⡏⣤⣌⠉⠛⢿⣻⣇⠁⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣷⣦⣼⣦⠀⠀⠀⠀⢸⣿⣿⣿⠟⢽⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⡌⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⠛⠈⠓⠻⣟⣿⣞⣿⡗⠀⠈⠩⣿⣷⢿⣿⣿⣏⠁⠃⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⣨⣽⣁⣡⡟⠁⠀⠄⠀⠀⠀⠀⠀⠀⠰⠊⠭⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠓⢿⣿⠿⣿⣿⣇⣶⣶⢘⣿⣻⣽⣹⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠂⠀⢠⣦⠀⢻⣿⣷⣴⣯⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣽⣥⡄⠚⢿⣻⣿⠁⢸⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣁⡆⠀⠉⠀⢸⣿⣿⣿⣿⣦⣿⣿⡠⠀⠀⠀⠀⠀⠀⣒⠒⠀⢀⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⠻⣿⣶⣾⣿⣿⣿⣿⠄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢠⣿⣿⣿⣿⡋⣿⣿⣿⠇⠀⠀⠀⠀⠀⢲⣿⣿⣿⣧⠀⠀⠀⠂⠀⠀
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣏⣻⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣤⣶⣶⣿⣿⣿⣿⣿⣿⣟⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠙⠂⢀⡀⣸⣿⡯⣽⣿⣷⣬⠉⣿⣼⠆⠙⠂⠀⠈⣻⣿⣿⣿⣿⣶⣦⣶⠁⠀⠀
⣤⣀⠀⠼⢷⡦⡘⠿⢿⠈⠻⠹⠟⣿⣿⣿⣿⣿⣿⠿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠨⣿⣿⣿⢈⣿⡟⠉⠛⠲⢻⣿⣏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⠀
⢿⣿⠗⠠⣴⣿⣿⡀⠀⠰⣾⣦⣤⣿⣿⣿⣿⣿⡟⡀⢠⣼⣿⣿⡟⠿⠙⣿⣿⣿⣿⣿⣇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣦⣖⢹⣿⣿⣿⣿⣷⢹⠀⠠⣾⣿⣿⠀⠀⠠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀
⣋⣤⣤⣄⣘⣿⣿⣷⣤⠀⠸⣿⣿⣿⣿⣿⣿⣿⣧⣨⣿⣿⣿⣿⣿⣿⣗⠛⠿⣿⣿⣿⣿⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣸⣿⣿⣿⠟⠋⠁⠀⠀⠀⠁⠈⣼⡆⢤⣾⣿⣿⣿⣿⣿⣿⣿⣶⣿⣆⣴
⠽⣿⣿⣿⣧⡀⠈⠙⠿⣷⣄⠹⣿⡟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠘⠛⣿⣿⠟⠀⢀⡻⣿⣿⡟⠉⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⡀⠀⠘⠁⠀⠀⠀⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣿⣭⡿⣷⢄⣤⣾⢿⠀⠈⠛⠺⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⠀⠀⠀⠙⣿⣦⣀⣼⣷⣿⣿⡇⠀⠀⠀⠀⠉⠉⠉⢽⡟⠛⠿⢿⣿⡟⠋⠀⠀⠺⣗⣦⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣶⣛⣯⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⡁⢀⠀⠀⢂⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠐⠶⠿⣿⣿⣿⣿⣿⣿⣧⠐⠛⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠓⢤⡀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣭⣈⠻⠿⣿⡿⠛⠁⠘⠇⠀⠈⢆⠀⢀⣹⣿⣯⡿⣿⣿⣿⡿⠀⠀⠀⠂⢐⣿⣿⣿⣿⣿⣟⠋⠀⠀⠀⠀⠀⠀⠀⣴⣶⣦⣤⣤⣀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠈⣹⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡻⠿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢨⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢠⠰⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠩⠻⣿⣿⣿⡏⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⣴⣿⣟⠛⠁⣸⡿⣿⣿
⠐⠿⠟⠃⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠘⡹⢿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠈⠀⣛⣿⣿⣿⣿⣦⢒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⣿⠟⠛⠋⠉⢁⣿⣿
⠀⠀⠀⠀⠐⠄⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠛⠸⢻⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣷⣿
⠠⠀⠀⠀⠀⠁⠐⣿⡷⠆⠀⠠⢄⣰⣤⣼⣿⣧⡄⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⢡⣿⣿⣿⣿⣿⣿⣿⣿⣀⣤⣤⣠⣾⣿⣿
⡀⠀⠀⠀⠤⠄⠀⠀⢧⣶⣄⣀⢐⠟⣿⣿⣿⣿⣿⠀⠀⠈⠉⠅⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣹⣿
⣦⠈⣤⣴⠀⠀⠀⠀⠀⠋⢉⠁⠀⠉⢿⣿⡿⠿⠟⠁⠀⠁⠀⠀⢰⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠉
⣿⣷⡈⢛⣤⠀⠁⠀⢠⣴⣿⣷⣶⢖⠀⠉⠀⠀⠩⡄⠀⠀⠀⠀⠘⠋⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠘⣿⣿⣄⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶
⠉⠀⣻⣿⣿⣷⡀⠀⠀⠀⠼⣿⣯⠒⠀⡈⠁⠤⢜⠀⠀⠀⠁⠀⠈⢠⣸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠙⠿⠿⣷⡄⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡁
⠀⠈⠙⠛⠻⣿⠿⠀⠀⠀⠀⢠⡕⣤⢼⡄⢀⣀⡑⠂⠀⠐⠀⠀⠀⠠⠀⣐⣿⣿⣿⣿⣿⡿⠛⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⡀⢹⣿⡄⠈⢿⣿⣿⣿⣿⣿⣿⡟⠀⡭⠙⠻⢿⣿⣿⣿⣿⣿⣥⣾⣿⣿⣾
⠀⠀⠀⠀⠀⢙⣈⠷⠄⠀⠀⠀⠀⠀⠈⢹⣿⣤⣾⠞⣻⣷⠆⠀⣠⡀⠀⣿⣿⣿⣿⡿⣿⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠁⠀⢠⣤⣼⣿⣿⣿⣿⣿⡶⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⠋⢩⣿⣿
⠀⠀⠀⠀⠈⠛⣿⡯⢵⡂⠀⠀⠄⠀⠀⡀⠉⢉⣂⣬⣭⠽⢦⠀⠀⣠⣴⣿⣿⣿⡿⠃⠠⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣶⣿⣿⣿
⠀⠀⣠⠤⠈⠊⠛⠀⡀⠀⠀⠀⠐⠀⠠⢄⠈⠛⣿⣿⣿⣷⠄⠀⠰⠟⠿⡿⠿⡟⠁⠀⠀⢨⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢀⡿⣿⣿⡿⠹⣿⣿⣿
⠀⠀⠠⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⠿⣿⣿⢟⣫⠀⠀⠈⠀⠀⠀⠀⠀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣷⣿⣿⣥⣼⣿⣿⣿
⠆⠀⠐⠓⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⢽⡋⠙⢵⣿⣯⣆⠀⡄⠀⠠⣀⠀⠚⠿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠉⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣠⣾⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⡔⣪⣄⡱⣼⠿⣿⣿⡄⠣⢀⡀⠉⠛⠀⠌⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣦⣀⣀⣀⣠⣤⣤⣴⣶⣮⣁⣺⠟⣿⡿⠀⠐⣚⡉⠁⠀⣴⣦⣄⠄⠠⠤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⣠⠤⣀⠀⠠⠒⡆⠐⠒⠴⣼⣷⣎⣄⠹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣤⣠⡀⠀⠀⠁⠇⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠓⣺⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠙⠛⠙⢳⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⣻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡒⠚⠣⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠹⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠟⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣶⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡿⠿⠿⢿⣿⣿⡿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡿⠿⠿⢿⣿⣿⣿⡿⠿⠿⠿⠿⡿⠿⠿⠿⣿⣿⣿⡿⠿⠿⣿⣿⡿⠿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀
⣿⣿⣿⣿⣿⣿⠿⣭⣴⣿⡿⠿⢁⣴⣾⣷⣶⡌⢁⣴⣾⣷⣶⡄⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣶⣶⣶⠘⣿⡇⣶⣶⣶⣶⣶⢰⣶⣶⣶⣦⡉⢡⣶⣾⣶⣦⡀⣶⣶⡆⠉⢰⣶⡆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⣁⠀⠉⠀⠐⢶⡆⢸⣿⣿⠸⠿⠷⢸⣿⣿⢸⣿⡇⠀⢸⣿⡏⢠⡄⢸⣿⡏⠀⣸⣿⣿⣿⡇⢿⣷⡄⢸⣿⡏⠀⢸⣿⣿⣸⣿⡇⣾⣿⡇⣿⣿⡇⣿⣿⡇⠀⢸⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠈⠁⢸⣿⣿⢶⣶⣶⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⢸⡇⢸⣿⡇⠀⣿⣿⢸⣿⣇⢸⣿⡇⢸⣿⡇⠀⢸⣿⣿⢿⣯⡅⣿⣿⡇⣿⣿⡇⣿⣿⡇⠀⢸⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣸⣿⣿⢸⣿⣿⣸⣿⡇⠀⢸⣿⡇⢸⡇⢸⣿⡇⢀⣿⣿⠿⣿⣿⠘⣿⡇⢸⣿⡇⠀⢸⣿⣿⢸⣿⡇⢻⣿⣇⣿⣿⡇⣿⣿⣇⣀⢸⣿⣇⣈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠙⠻⠛⠛⠛⠀⠙⠻⠟⠛⣡⣆⡘⠛⢃⣼⣧⡘⠛⠃⡘⠛⠛⡀⠛⠛⣠⣿⣧⡘⠛⢓⣠⡘⠛⠛⠘⠛⢃⣈⡛⠻⠟⢋⣀⡛⠛⠛⠛⠘⠛⠛⠛⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⣀⣈⣉⣙⠛⢛⣉⣉⡛⠿⢛⣛⣛⢛⣛⡛⢛⣛⣛⣛⡛⠿⢛⣛⡛⠿⢛⣋⣉⡛⠿⢛⣛⣛⢛⣛⡛⣛⣛⣛⣛⣛⠛⢛⣉⣙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⠿⠇⣿⣿⡿⠯⢰⣿⡿⢻⣿⣆⢸⣿⣿⢸⣿⡇⢸⣿⣿⢿⣿⡆⢸⣿⡇⢰⣿⡿⢻⣿⡆⢸⣿⣿⢸⣿⡇⠿⢿⣿⡿⠿⣸⣿⡟⣿⣿⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⣧⡄⢸⣿⡇⠸⠿⠿⢸⣿⣿⣾⣿⡇⢸⣿⣿⣼⣿⠇⢸⣿⡇⢸⣿⡇⣘⣛⡃⢸⣿⣿⣾⣿⡇⠀⢸⣿⡇⠀⠹⣿⣷⣭⡉⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⡟⠃⢸⣿⡇⢠⣤⣤⢸⣿⣿⢹⣿⡇⢸⣿⣿⢹⣿⡆⢸⣿⡇⢸⣿⡇⢻⣿⡇⢸⣿⣿⢹⣿⡇⠀⢸⣿⡇⠀⢠⣬⡝⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⣷⣶⠸⣿⣷⣼⣿⠇⢸⣿⣿⢸⣿⡇⢸⣿⣿⢸⣿⡇⢸⣿⡇⠸⣿⣷⣼⣿⡇⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⠀⠸⣿⣧⣿⣿⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⢀⣉⡉⣉⡉⣠⣬⣉⣉⣥⣶⣬⣭⣥⣬⣭⣥⣬⣭⣭⣬⣭⣥⣬⣭⣥⣶⣬⣍⣥⣭⣥⣬⣉⣭⣌⣉⣥⣤⣌⣉⣡⣾⣦⣬⣉⣩⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠆⠲⣶⠏⢶⠄⠠⠲⠶⠆⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
[69A⠀⢀⢀⣀⣀⢠⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣙⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣧⣧⣿⡇⣿⠿⠀⠀⠀⠀⣸⠿⣿⡟⢭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣄⣸⣸⣿⠿⠄⣩⣍⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡏⢣⠀⠀⠀⢠⠁⢠⣟⡿⠈⠙⢹⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⢿⣿⣯⣷⡿⣿⣿⣿⣿⣿⣿⣞⢻⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⡟⣻⣿⢿⣿⣿⣿⣿⣿⣷⣦⣧⡄⠀⠀⠀⠈⣿⠇⠀⠀⠀⠈⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠟⠉⠛⠁
⣿⣿⣷⡿⢿⣾⡞⠛⣿⣿⣿⣟⢛⠀⠨⣿⢿⣿⣷⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣻⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠐⠾⠏⠲⠀⡀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠉⠁⠀⠀⠀⠠⢴
⣿⣿⣿⣮⣾⣿⣿⠂⢘⢿⣿⣿⡄⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠉⢀⠀⠀⠀⠀⠻⢸⣿⣿⠿⣿⠟⠿⠋⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡏⡀⢰⣦⡋⣋⣳⡄⠀⠀⠘⠋⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⢻⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡻⣿⣿⣿⣿⣯⡄⠀⠀⢦⣿⣷⡈⠀⠀⣤⣿⣿⣿⣿⣿⣿⣇⠀⠀⠖⠋⣿⣾⣿⣿⣿⣿⣿⣿⡟⣿⣯⠘⠿⣿⣿⡟⢿⣄⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⢠⠀⠀⣀⠀⠀
⣿⣿⣷⠈⣿⣿⣿⣿⣯⠀⠀⠚⠿⢿⣴⠼⣿⣿⣿⣿⣷⣿⡧⣿⣷⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠛⢉⡄⢠⣿⣿⣷⣾⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⠟⠟⠙⡀⠀⠈⠀⠀
⣿⣿⣿⡇⠘⣿⣿⣿⣿⡌⡄⣤⣾⣤⣤⣤⣿⣿⣿⣿⣿⣿⣦⢈⣾⣯⠀⠀⠀⢸⡟⢿⡏⢿⣿⣿⣿⣧⣷⡎⢠⣿⣿⣿⣿⣿⣿⡧⠋⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠛⣔⠀⠀⠸⠇⠀⠀⠀⠀
⣿⣿⣿⣧⠀⠹⣿⣿⣿⣧⢳⠶⡎⢛⢻⢿⣿⣿⣿⣿⣿⣧⠈⠻⢿⣟⣃⡀⠀⢿⠇⠸⠃⠈⣿⣿⢿⣿⣷⣧⣿⣿⣿⣿⣿⣿⡽⠉⣡⣶⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⣠⠇⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡆⠀⢻⣿⣿⣿⠂⣀⣋⠀⠨⠾⣿⣿⣟⣻⣿⣿⣷⣾⣿⣿⣿⣿⣆⠈⠀⠁⢀⣠⣿⣿⡾⡏⣻⣿⣿⣿⣿⣿⣿⣯⣤⠂⠉⠋⠛⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⡼⠟⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣇⠀⢸⣿⣿⣿⣦⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣏⣿⢟⣻⣿⠃⠓⠀⠀⠂⣸⣿⣿⣿⣧⣴⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢙⡟⠿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣿⠋⠁⠀⠠⠂⠀⠀⠀⠈
⣿⣿⣿⣿⡇⢂⠈⣿⣿⣿⣿⣿⣷⡀⢀⡀⢿⣿⣿⠙⠿⣿⣿⣿⣿⡟⠿⠆⠀⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠁⡀⠀⠀⠀⠈⠳⣖⣾⣿⣿⣷⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢨⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣷⠘⣦⣿⣿⣿⣿⣿⣿⣷⠈⡟⣾⣿⣧⣶⣷⡀⠀⠙⣽⣷⣄⣸⣶⣿⣿⡿⢿⠿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣶⡿⠂⠀⠀⠀⢰⡿⣿⢿⡟⠘⠆⠀⠀⠀⠀⠀⠀⠀⠘⣿⡏⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀
⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣩⡄⡈⣝⣿⣝⣯⣽⣯⠀⠀⠀⣿⣿⣿⣿⣿⣿⡀⢈⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⢠⣾⣧⠴⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀
⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠉⣺⡿⠻⢿⣿⣯⣾⡿⢂⣽⣍⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣉⢀⠀⢿⡆⠨⣿⣿⣿⣿⡇⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣶⠉⠹⣭⣿⡁⢘⣿⣿⣿⣿⡷⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣾⠀⠀⠀⠐⣿⣿⣿⣿⣿⣾⣿⣗⡀⠀⠀⠀⠀⠀⠸⣃⣀⣠⣴⠀⠀⠀⠀⠄⠀⠀⠊
⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣧⠀⠘⠻⣿⣿⣿⣿⣿⣿⣗⡀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡄⠀⠀⠀⣾⣿⣿⣿⣏⠸⣿⣿⡗⡂⢀⣀⠀⠀⢰⣿⣿⣿⣿⣆⠀⢀⣁⠀⠀⠀⠠
⠀⣀⡀⠀⢻⣿⣿⣣⣙⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠉⠄⣤⢠⣿⡟⣺⣿⡿⢿⡇⣸⣷⣯⡄⠉⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀
⡀⠾⠻⣖⣊⠛⠟⠆⢸⠈⠛⢻⣿⣿⣿⣿⣿⠟⠋⠙⣻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⣀⢺⣿⣿⣇⣾⣿⢁⡈⠉⢍⣿⣿⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⣴⠆⠀⠀
⠋⠰⣾⣿⣿⡄⠀⠘⢿⣷⣶⣾⣿⣿⣿⣿⣯⠠⣀⣶⣿⣿⣿⣛⣋⢻⣿⣿⣿⣿⣿⡄⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣾⡄⣿⣿⣿⣿⣿⣇⠃⠀⠚⢿⠿⠃⡀⠀⠲⣿⣿⣿⣿⣿⣿⣿⡿⢿⡃⠀⠀⢄
⣶⣤⣈⣿⣿⣿⣧⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣿⣿⣿⣿⡿⠌⠙⣻⣿⣿⣿⡇⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣿⣿⣿⡟⠉⠀⠀⠀⡠⠀⠀⠙⢻⣐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿
⣿⣿⣶⣄⠈⠉⠻⢿⣦⠈⢻⣿⠛⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡖⠀⠉⢹⣿⡟⠁⠀⣜⢻⣿⣿⣿⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⣤⠀⠀⠀⠀⠀⣀⣭⣿⣿⣿⣛⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⡿⣿⢠⣠⣼⡿⡇⠀⠈⠛⠻⠎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⢹⣿⣤⣰⣿⣿⣿⣿⣿⠀⠀⠀⠈⠛⠛⢿⣿⣿⣿⣿⣿⠿⠈⠀⠀⠈⢹⣽⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⢿⣯⣿⣿⣿⣿⡤⠀⡄⠀⠸⡀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠐⠛⢻⣿⣿⣿⣿⣿⣿⣿⣠⠔⠂⠀⠀⠀⠀⣸⣿⠀⠀⠉⠲⣄⡀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣯⣭⣬⡛⠿⣿⡿⠏⠁⠀⠛⠀⠀⠱⡀⠀⣌⣿⣿⣽⣿⣿⣿⣿⡃⠀⠀⠈⠀⢭⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠴⣿⣿⣤⣀⡀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⣰⣿⣿⡿⠿⣿⣿⣿⣿⣿
⣿⡟⠻⡆⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣤⢻⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⣿⣿⠇⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢉⣸⣿⡿⠤⣀⡴⡿⢿⣿⣿⣿
⠿⠁⠂⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠉⠟⣻⣿⣿⣿⣿⣿⣿⣦⣀⠀⠁⢈⣽⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠁⠀⢀⣾⣿⣿⣿
⠀⠀⠀⠆⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠁⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢘⣿⣿⣿⣿
⠀⠀⠀⠈⠀⢺⣿⢶⠀⠀⠤⣤⣶⣤⣿⣿⣤⠀⠀⠀⣠⣼⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡋⠀⢀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣷⡿⠿⢿⣿⣿
⠀⠀⠠⠤⠀⠀⠩⢴⣦⣀⡐⡻⢻⣿⣿⣿⣿⡧⠀⢀⡈⠉⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡴⠿⠿⢿
⢡⣤⡄⠀⠀⠀⠠⠙⠉⡁⠀⠀⠹⢿⣿⠟⠟⠃⠀⠀⠁⠐⠀⢾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⢰⣶⣆⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⣠⣄
⡄⠛⣣⡄⠈⠀⠀⢤⣾⣿⣶⡷⡂⠈⠁⠀⠀⢡⠄⠀⠀⠀⠀⠛⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢀⠀⠀⠀⠘⣿⣿⣷⣄⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢿
⢚⣿⣿⣿⣄⠀⠀⠀⢠⢽⣿⣕⠂⢀⠈⠠⠤⠃⠀⠀⠀⠀⠀⠈⣠⠞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠈⠻⠿⣿⣷⡀⠹⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣿⣿⣗⣴⣿
⠉⠛⠻⢿⡿⠇⠀⠀⠀⠀⢌⢠⡤⢿⡀⢀⣀⠓⠋⠀⠁⢀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⠟⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠈⣿⣷⣌⣉⠉⢹⣿⣿⣿⣇⡐⠃⠀⠉⠻⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿
⠀⠀⠀⠘⢓⣹⠦⠀⠀⠀⠀⠀⠀⠈⢻⣷⣤⡦⢟⣿⣶⠄⠀⢤⠀⠀⣿⣿⣿⣿⡿⠇⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⠁⠙⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠘⣿⣿⣿⣿⣗⢠⣼⣿⣿⣿
⠀⠀⠀⠘⢿⣶⠯⠴⡀⠀⠀⠀⠀⢀⠀⠉⢙⣠⣬⣭⠟⢦⠀⠀⣤⣾⣿⣿⣿⠟⠁⠰⣄⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣀⡀⠂⠘⠃⠀⠀⠀⠀⠄⠐⠀⠠⢀⠘⢙⣿⣿⣿⣷⠄⠀⠸⠛⠿⡿⠿⠟⠀⠀⠀⠼⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⣼⣹⣿⣿⠃⢽⣿⣿⣿⣿
⠈⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⡿⠿⣿⣿⢟⡩⠀⠀⠀⠀⠀⠀⠀⢀⣼⣶⣾⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠹⠆⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠠⢝⡃⠉⢵⣿⣿⣇⢀⡄⠀⠀⣄⡀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢠⣖⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣈⣁⢈⠔⣪⣄⡡⣼⠿⣿⣻⡄⢡⣀⠀⠉⠙⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣦⣀⠀⢀⣀⣀⣠⣤⣴⣮⣼⣁⣾⣿⣿⡿⠀⠐⣊⠉⠀⠈⢿⣶⠤⡀⠀⠒⡶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⢠⠤⠀⠀⠀⠊⡇⠀⠂⡐⢸⣿⣦⣤⡘⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣀⣤⣠⣄⠀⠀⠀⠆⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠐⣐⣿⣿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⠩⠉⠉⢛⣆⠀⣸⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣝⠂⢑⣰⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣈⣻⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠉⠉⠹⠟⠿⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣾⣿⣿⣶⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠘⠹
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⡿⠿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⢿⣿⣿⣿⡿⠿⠿⠿⠿⡿⠿⠿⠿⣿⣿⣿⡿⠿⠿⣿⣿⡿⠿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤
⣿⣿⣿⣿⣿⣿⠿⣩⣼⣿⣿⡿⢁⣴⣾⣷⣶⡌⢁⣴⣾⣷⣶⡄⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣶⣶⣶⠘⣿⡇⣶⣶⣶⣶⣶⢰⣶⣶⣶⣦⡉⢡⣶⣾⣷⣦⡁⣶⣶⡆⠉⢰⣶⡆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠋⠈⠛⠛⢛⣍⣉⠁⢸⣿⣿⠸⠿⠷⢸⣿⣿⢸⣿⡇⠀⢸⣿⡏⢀⡄⢸⣿⡏⠀⣸⣿⣿⣿⡇⢿⣷⡄⢸⣿⡏⠀⢸⣿⣿⣸⣿⡇⣾⣿⡇⣿⣿⡇⣿⣿⡇⠀⢸⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠧⠒⠀⠀⠀⠀⠙⠻⠂⢸⣿⣿⢶⣶⣶⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⢸⡇⢸⣿⡇⠀⣿⣿⢸⣿⣇⢸⣿⡇⢸⣿⡇⠀⢸⣿⣿⢿⣯⡅⣿⣿⡇⣿⣿⡇⣿⣿⡇⠀⢸⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣸⣿⣿⢸⣿⣿⣸⣿⡇⠀⢸⣿⡇⢸⡇⢸⣿⡇⢀⣿⣿⠿⣿⣿⠈⣿⡇⢸⣿⡇⠀⢸⣿⣿⢸⣿⡇⢻⣿⣇⣿⣿⡇⣿⣿⣇⣀⢸⣿⣇⣈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠛⠛⠛⠀⠙⠻⠟⠛⣡⣆⡘⠛⢃⣼⣧⡘⠛⠃⡘⠛⠛⡀⠛⠛⣠⣿⣧⡘⠛⠓⣠⡘⠛⠛⠘⠛⢃⣈⡛⠻⠟⢋⣀⡛⠛⠛⠛⠘⠛⠛⠛⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⣀⣉⣉⣙⠛⢛⣉⣙⡛⠿⢛⣛⣛⢛⣛⡛⢛⣛⣛⣛⡛⠿⢛⣛⡛⠿⢛⣉⣙⡛⠿⢛⣛⣛⢛⣛⡛⣛⣛⣛⣛⣛⠛⢛⣋⣛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⠿⠇⣿⣿⡿⠯⢰⣿⡿⢻⣿⣆⢸⣿⣿⢸⣿⡇⢸⣿⣿⢿⣿⡆⢸⣿⡇⢰⣿⡿⢻⣿⡆⢸⣿⣿⢸⣿⡇⠿⢿⣿⡿⠿⣸⣿⡟⣿⣿⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⣧⡄⢸⣿⡇⠸⠿⠿⢸⣿⣿⣾⣿⡇⢸⣿⣿⣼⣿⠇⢸⣿⡇⢸⣿⡇⣘⣛⡃⢸⣿⣿⣾⣿⡇⠀⢸⣿⡇⠀⠹⣿⣷⣭⡉⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⡟⠃⢸⣿⡇⢠⣤⣤⢸⣿⣿⢹⣿⡇⢸⣿⣿⢹⣿⡆⢸⣿⡇⢸⣿⡇⢻⣿⡇⢸⣿⣿⢹⣿⡇⠀⢸⣿⡇⠀⢠⣬⡝⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⣷⣶⠸⣿⣷⣼⣿⠇⢸⣿⣿⢸⣿⡇⢸⣿⣿⢸⣿⡇⢸⣿⡇⠸⣿⣷⣼⣿⡇⢸⣿⣿⢸⣿⡇⠀⢸⣿⣇⠀⠸⣿⣧⣿⣿⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⡀⠉⠉⠉⢉⣤⣌⣉⣩⣥⣶⣬⣭⣥⣬⣭⣥⣬⣭⣭⣬⣭⣥⣬⣭⣥⣶⣬⣍⣥⣭⣥⣬⣉⣩⣬⣉⣥⣤⣌⣉⣡⣾⣦⣬⣉⣩⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠆⠲⣶⠏⢶⠄⠠⠰⠶⠆⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
[69A⣿⣧⠈⣋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠧⡀⠀⠀⠀⡀⢉⠹⢿⡎⠛⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣶⣼⣿⣿⣿⣿⣿⣿⣯⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣳⣀⠀⠀⠁⠀⠿⣷⠁⠀⠐⠙⠆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠻⢿⣟
⣻⣿⣯⡴⢿⣷⣿⣿⡿⠿⠉⠙⣿⣿⣿⣧⣙⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡉⢸⡟⢪⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⣄⣶⡏⡄⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠉⠀⠀⠀⠁⡀⠀⠃
⣢⣿⣿⣶⠀⠿⣿⣿⣷⠉⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣻⣷⡄⠉⠀⠀⠐⠆⠀⠀⠀⠉⢻⡟⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠁⠀⠀⠄⠀⠀⠀⠀⠀⠙⠃⠀⠀
⣿⣿⣿⠟⠀⢠⣍⡿⡻⣦⠀⠀⠀⠘⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠁⠼⠻⠟⠹⠋⠈⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀
⣿⣿⣿⣽⣦⠘⠋⠁⣩⣿⣧⠐⠀⠀⢀⢻⣿⣿⣿⣿⣿⣟⠙⠊⢀⢰⢿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⡇⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢻⣿⢿⣿⣿⡧⠀⠀⢹⣿⣿⡁⣀⣤⣾⣿⣿⣯⣿⣿⢻⣿⡄⠀⠀⠐⠸⣿⣿⣿⣿⣿⣿⣿⣿⠹⡿⢧⠈⢙⣿⣿⣈⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣶⢶⣿⡧⡇⠀⠐⠆⠀⠀⠀⠀
⠄⢻⣿⣿⣿⣿⠡⡤⢀⣙⡙⡙⡋⣽⣿⣿⣿⣿⣿⣏⠙⢟⣿⠀⠀⠀⠀⣿⣿⣿⢿⣿⣿⣿⣿⣀⣄⡞⢠⣾⣿⣿⣿⣿⣿⣱⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣏⡛⠀⠉⣶⠀⠀⠀⠀⠀⠀⠀
⡆⠈⢿⣿⣿⣿⣇⢳⣛⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⢳⣿⣿⢧⠀⠀⢠⣿⠈⣿⠀⢿⣿⣿⣿⣿⣿⢆⣿⣿⣿⣿⣿⣿⡿⡧⠀⣀⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⣡⡗⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀
⣷⠀⠘⣿⣿⣿⣿⡜⠏⢧⠘⠘⣭⣿⣿⣿⣿⣿⣿⣧⣀⣭⣿⣶⣶⣄⠈⠏⠀⠉⠀⢸⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡟⢋⠠⢿⢻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡇⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡇⠀⢸⣿⣿⣿⣅⠒⠒⠂⠀⠉⢻⣿⣿⣶⣿⣿⣿⢿⣿⣿⣿⣿⠻⡇⠀⢠⠀⣦⣿⣿⣿⡙⢡⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠁⢤⢿⣿⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⢿⠋⠀⢀⠀⠀⠀⠀⠄⠀⠀
⣿⡇⡀⢸⣿⣿⣿⣿⣦⣄⠀⠂⠀⢸⣿⣿⡟⣿⣿⣿⣿⣏⣶⣿⣧⠀⢈⣀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢸⣇⡉⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⡶
⣿⣇⠰⡀⣿⣿⣿⣿⣿⣿⣧⡀⢶⡌⣿⣿⠃⣩⡙⠛⠿⡿⢿⡈⠉⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣬⣐⣄⠀⠀⠀⠀⢘⣧⣿⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀
⣿⣿⣄⣹⣿⣿⣿⣿⣿⣿⡿⠆⠰⠼⣿⡿⣯⡻⣷⡤⠀⠙⢻⣿⣤⣾⣿⣿⡿⠛⠟⠉⣿⣿⣿⣿⣿⣯⣷⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⣺⡏⠛⡿⠃⠈⠁⠀⠀⠀⠀⠀⠀⠰⠴⣛⠃⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⢐⢔⣾⣿⣾⣷⣿⡇⣄⣄⣸⣿⢿⣾⠿⣿⣿⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠀⠀⣠⠀⠸⣿⣿⣉⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣰⣟⡃⡒⢿⣿⣿⣿⠛⣰⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠒⢠⠀⠹⠇⢈⣿⣿⣿⣿⣇⣰⣿⣆⠀⠀⠀⠀⠀⠀⢬⠽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⡀
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠑⣺⣿⣄⣼⣿⣿⣿⣿⣝⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣻⣿⣿⣿⡿⢻⣿⣷⡆⠀⠀⠀⠀⠀⢩⣶⣶⣾⣿⠀⠀⠠⠄⠀⠀⠀⠀⠐⠀
⠈⣿⣿⣿⣟⢿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣧⡀⣌⣙⣿⣿⣿⣿⣿⣿⣧⠄⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢦⡀⠀⠀⣿⣿⣛⣿⣷⣍⡟⢿⣇⣆⠐⠦⠀⠀⢺⣿⣿⣿⣿⣶⣤⣴⠂⠀⠀⠀⠀⠀⠀
⡀⠘⣿⣿⡏⠶⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠑⣻⣴⣿⡏⢻⣿⠟⠻⣧⡼⣿⣷⠂⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠁⢀⠀⠀⠀⠉⠀
⣻⣧⡌⠙⠛⣀⣇⠈⠉⣿⣿⣿⣿⣿⣿⠉⠀⠈⣿⣹⣿⣿⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡰⠜⣿⣿⣿⣿⣿⡔⣆⠀⣡⣿⣿⡆⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢀⢀⠀
⣿⣿⣷⡀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⡷⠒⣤⣿⣿⣿⣷⣬⣤⢺⣿⣿⣿⣿⣿⡦⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣧⢿⣿⣿⣿⣿⠗⠋⠀⠈⠙⠋⢃⣦⢀⣨⣿⣿⣿⣿⣿⣿⣿⣯⣽⣄⣠⣮⣴⣿⣶
⠽⠿⣿⣿⣦⡀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠂⠈⢽⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠂⢀⠔⠁⠀⠈⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⣄⠀⠈⠛⢿⣦⡈⠻⣯⣈⣜⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠸⢿⣿⠀⠀⣰⣍⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠁⠀⣿⣦⣄⣀⣀⣤⣴⣾⣿⣷⣾⣿⣿⣽⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣮⣻⣇⣦⣶⣾⡻⡅⠀⠀⠉⠻⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⣨⣿⣷⣾⣿⣿⣿⣿⣿⣿⠃⠀⠀⠙⠿⢿⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⣿⣾⣿⣿⣿⣿⡦⢰⡄⠀⠸⡄⠀⠿⢿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠈⡉⢹⣿⣿⣿⣿⣿⣿⣿⣿⡆⢀⣤⠀⠀⠀⠀⢹⣿⠏⠒⠦⣤⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣭⣍⠙⠿⠿⠿⠊⠀⠀⠁⠀⠀⠑⡄⠀⣤⣿⣿⣾⣿⣿⣿⣿⣧⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁⠀⠀⠰⣿⣿⣿⡀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠧⢀⣼⣿⠛⠋⠉⣿⣿⣿⣿⣿⣿⣿
⠻⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⢰⠙⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠈⠙⠿⠻⠿⡖⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣾⣿⣯⠭⠖⠋⠋⣹⣿⣿⣿⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠛⣽⣿⣿⣿⣿⣿⣿⣷⣦⣄⣠⣀⣼⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿
⠐⠂⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠀⠀⠈⠁⠊⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣾⣿⠿⠋⠉⢉⣿⣿⣿⣿⣿⣿⣿⣇⣀⣤⣄⣴⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢿⣿⢷⠀⠀⢖⣤⣶⣦⣿⣿⣶⡀⠀⠀⢴⣾⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣽⣿⣿⣿⣿
⠠⠤⠀⠀⠩⢼⣶⣀⠐⠟⣻⣿⣿⣿⣿⣿⠀⠀⡀⠀⠂⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠘⣿⣿
⠀⠀⠀⠀⠠⠙⠋⣃⠀⠀⠈⢿⣿⠟⠛⠃⠀⠀⠀⠀⠐⢺⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⣼⣿⣧⣀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣿⣿
⣩⡀⠉⠀⠀⢤⣾⣿⣷⡶⠈⠂⠀⡀⠀⢐⡄⠀⠀⡀⠀⠈⠉⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣤⣄⠀⠀⠈⢿⣿⣿⣷⣄⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣏⢀⣽⣿⣿
⣿⣯⡄⠀⠀⠀⢠⢽⣿⣝⠂⢀⠀⠁⠤⠈⠀⠀⠀⠀⠀⠀⠰⠴⠛⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠙⠿⢿⣿⣧⡐⠛⠛⠻⣿⣿⠉⣹⠛⠻⢿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿
⠻⢿⡿⠇⠀⠀⠀⠀⢠⢀⣤⢾⣆⣀⣀⡉⢊⣀⡈⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡟⠉⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠻⣿⣿⣿⣶⣾⣿⣿⣶⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⠋⢹⣿⣿⣿⣿⣿
⠀⠘⠗⣙⠦⠀⠀⠀⠀⠀⠀⠈⢹⣿⣶⣾⢞⣻⣿⠇⠀⠤⠄⠀⣸⣿⣿⣿⣿⠻⠄⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠈⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠸⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿
⠀⠸⢿⣷⠞⠤⡄⠀⠀⠀⠀⠀⡀⠉⠑⣠⣥⣭⣕⠒⠆⠀⢠⣶⣿⣿⣿⡿⠋⠀⠲⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⢀⡿⣿⣿⡿⣹⣿⣿⣿⣿⣿⣿
⡀⠂⠚⠛⠠⠤⠀⠀⠠⠀⠀⠀⠄⡨⠋⣻⣿⣿⣿⣦⢀⡀⠟⠛⡿⠛⠻⠁⠀⠀⢀⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠿⠿⣿⡿⣫⠄⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢤⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠬⣟⠈⠡⣾⣯⣿⣆⢰⡂⠀⠂⣄⡀⠘⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⣈⣀⡡⢒⣥⣈⠦⡿⢿⣟⣿⡈⠀⠤⠀⠀⠉⠀⠀⠈⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣤⡀⠀⠀⣀⣀⣀⣠⣴⣦⣥⣖⣰⣿⣿⣿⡗⠀⢀⡉⠥⠀⠘⠶⠷⠖⢄⡀⢓⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⣠⠤⠀⠀⠐⠙⠄⠈⡁⡘⢾⣿⣷⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣀⣤⣠⣦⣀⡀⠈⠇⠄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⣈⣬⣿⣿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣼⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣘⠉⠈⢩⣆⠀⣼⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⣉⣩⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣽⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⣿⡿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣾⣷⣄⣀⣀⣀⡀⠀⠀⠀⠀⠈⠀⢛⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠙⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠐⠼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣽
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⡿⠿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⠿⠿⢿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⡿⠿⠿⣿⣿⣿⠿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠿⣻⣿⣿⣿⡿⢋⣴⣾⣷⣶⡌⢁⣴⣾⣷⣶⡄⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣶⣶⣶⠘⣿⡇⣶⣶⣶⣶⣶⢰⣶⣶⣶⣦⡉⢡⣶⣾⣷⣦⡀⣶⣶⡆⠉⢰⣶⡆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⢿⣵⡾⠿⠿⠿⠿⡇⢸⣿⣿⠸⠿⠷⢸⣿⣿⢸⣿⡇⠀⢸⣿⡏⢀⡄⢸⣿⡏⠀⣸⣿⣿⣿⡇⢿⣷⡄⢸⣿⡏⠀⢸⣿⣿⣸⣿⡇⣾⣿⡇⣿⣿⡇⣿⣿⡇⠀⢸⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠋⡀⠀⠀⠀⠘⢿⣿⣶⠆⢸⣿⣿⢶⣶⣶⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⢸⡇⢸⣿⡇⠀⣿⣿⢸⣿⣇⢸⣿⡇⢸⣿⡇⠀⢸⣿⣿⢿⣯⡅⣿⣿⡇⣿⣿⡇⣿⣿⡇⠀⢸⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣸⣿⣿⢸⣿⣿⣸⣿⡇⠀⢸⣿⡇⢸⡇⢸⣿⡇⢀⣿⣿⠿⣿⣿⠈⣿⡇⢸⣿⡇⠀⢸⣿⣿⢸⣿⡇⢻⣿⣇⣿⣿⡇⣿⣿⣇⣀⢸⣿⣇⣈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠛⠛⠋⢀⡙⠻⠟⠛⣡⣦⡘⠛⢃⣼⣧⡘⠛⠃⡘⠛⠛⣀⠛⠛⣠⣿⣧⡘⠛⢓⣠⡘⠛⠛⠘⠛⢃⣈⡛⠻⠟⢋⣀⡛⠛⠛⠛⠘⠛⠛⠛⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⣉⣉⣉⣛⠛⢛⣉⣙⡛⠿⢛⣛⣛⢛⣛⡛⢛⣛⣛⣛⡛⠿⢛⣛⡛⠿⢛⣋⣉⡛⠿⢛⣛⣛⢛⣛⡛⣛⣛⣛⣛⣛⠛⢛⣉⣙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⠿⠇⣿⣿⡿⠿⢰⣿⡿⢻⣿⡆⢸⣿⣿⢸⣿⡇⢸⣿⣿⢿⣿⡆⢸⣿⡇⢰⣿⡿⢻⣿⡆⢸⣿⣿⢸⣿⡇⠿⢿⣿⡿⠿⣸⣿⡟⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⣧⡄⢸⣿⡇⠸⠿⠿⢸⣿⣿⣾⣿⡇⢸⣿⣿⣼⣿⠇⢸⣿⡇⢸⣿⡇⣘⣛⡃⢸⣿⣿⣾⣿⡇⠀⢸⣿⡇⠀⠹⣿⣷⣭⡉⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⡟⠃⢸⣿⡇⢠⣤⣤⢸⣿⣿⢹⣿⡇⢸⣿⣿⢹⣿⡆⢸⣿⡇⢸⣿⡇⢻⣿⡇⢸⣿⣿⢹⣿⡇⠀⢸⣿⡇⠀⢠⣬⡝⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⣷⣶⠸⣿⣷⣼⣿⠇⢸⣿⣿⢸⣿⡇⢸⣿⣿⢸⣿⡇⢸⣿⡇⠸⣿⣷⣼⣿⡇⢸⣿⣿⢸⣿⡇⠀⢸⣿⣇⠀⠸⣿⣧⣿⣿⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠉⠉⣉⣩⣴⣬⣍⣩⣥⣶⣬⣭⣭⣬⣭⣥⣬⣭⣭⣬⣭⣥⣬⣭⣥⣶⣬⣉⣥⣭⣥⣬⣉⣭⣬⣉⣥⣴⣬⣉⣥⣾⣶⣬⣉⣩⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣦⣤⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠆⠲⣶⠏⢶⠄⠠⠰⠶⠆⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
[69A⣿⣿⣿⣿⣿⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣇⣙⣅⠀⠀⠰⠀⠸⣿⣿⠃⠀⠼⢿⡃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛
⣽⣿⣯⣿⣿⣿⣿⠓⠹⣿⣿⣿⣟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡟⠛⣾⡯⣹⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⢀⣸⠏⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠛⡃⠉⡹⠀⠀⠀
⣤⠈⣿⣿⣿⣷⠒⠀⠀⠛⢻⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢦⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⣄⠙⠛⠈⠁⢠⡀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠉⠀⠀⠀⠀⠀⣤⠆⠃⠀⠀⠀
⡟⠀⢊⠛⣿⢿⣅⠀⠀⠀⠘⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠘⠧⣿⢻⡿⢿⡟⠹⠟⠁⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣲⣄⠸⠿⠇⠓⣾⣇⠠⡄⠀⠁⢸⣿⣿⣿⣿⣿⣿⡿⠿⠃⠀⣽⣏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⣿⣿⡇⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀
⣿⣿⣆⠀⠀⢺⣿⣿⠆⠀⣀⣰⣾⣿⣿⢿⣿⡿⣾⡇⠀⠀⠋⠁⢿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⡄⠛⢿⣿⣿⠙⣧⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣀⡄⠀⣀⡄⠀⠀⠀⠀⠀⠀
⣿⣿⣷⢀⠀⠉⠻⡻⠷⠗⢻⣿⣿⣿⣿⣿⣿⠷⢿⢿⣆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⢈⠃⡥⠀⣾⣿⣿⣶⣿⣿⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⡿⠹⠫⣃⠀⠁⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡆⢂⣴⠶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣷⣠⣶⣷⡀⠀⠀⢸⡿⠻⡏⠹⣿⣿⣿⣿⣾⢿⡁⣼⣿⣿⣿⣿⣿⣿⡞⠉⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⢗⣆⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠁⠀
⣿⣿⣿⣿⡸⡟⢗⡘⠏⡟⣿⣿⣿⣿⣿⣿⣧⠀⠛⣻⣏⣇⣀⠀⢸⠗⢰⠟⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠭⢁⣴⢶⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣇⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢻⣿⣿⣟⡇⢠⢼⠅⠀⠸⢻⣿⣿⣏⣹⣿⣿⣷⣾⣿⣿⣿⣿⣷⡀⠁⠈⠀⣀⣾⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣷⡴⠀⠙⠞⠛⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣥⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⣿⣿⣿⣿⣄⠀⠀⢀⠀⠀⣿⣿⣿⣿⣿⣿⣯⣿⡿⣻⣿⡟⠘⠂⠀⠐⢀⣿⣿⣿⣿⣦⣵⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢛⡝⠿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡿⠙⠀⠀⠠⠀⠀⠀⠀⠁⠀⣀⠀⠀
⡀⣿⣿⣿⣿⣿⣿⣦⠀⢀⡀⢿⣿⣿⠙⠿⣿⣿⣿⣾⣿⢻⡷⠀⢰⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⢁⡀⠀⠀⠀⠘⠳⣆⣿⣿⣿⣷⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠊⠁⠀
⢣⣿⣿⣿⣿⣿⣿⣿⣗⠈⣛⣼⣿⣯⣤⣷⣄⠈⢙⣋⣿⣥⠀⣴⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣶⡿⠀⠀⠀⠀⣰⡿⢿⢿⡟⠸⡄⠀⠀⠀⠀⠀⠀⠀⠚⣶⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣿⣿⣍⡀⠉⣙⣿⣿⣷⣛⣿⡋⠀⠀⢸⣿⣿⣿⣿⣿⣏⠀⠁⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⢠⣶⣧⠠⣾⠁⠀⠂⠀⠀⠀⠀⠀⠀⠈⠋⠚⠂⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠙⣺⣿⡿⣿⣿⣿⣳⣶⢖⢘⣿⣻⣿⣹⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣋⠀⠀⢾⡆⠈⣿⣿⣶⣿⡆⢀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⢀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣯⣤⡔⠛⣟⣻⣟⠀⢾⣿⣿⣿⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣸⠀⠈⠁⠀⢿⣿⣿⣿⣷⣶⣿⣷⣀⠀⠀⠀⠀⠀⠬⢋⣀⣁⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠈⠿⣿⣶⣾⣿⣿⣿⣿⡧⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⣼⣿⣿⣿⣯⠸⣿⣿⡟⠀⢀⡀⠀⠀⣨⣿⣿⣿⣿⡄⠀⠈⡁⠀⠀⠀⠀⠀⠀⠘⠀
⣿⣿⣝⠿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⠃⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠙⢆⣤⡀⣿⣿⢧⣿⣿⣷⣎⢹⣷⣗⡀⠉⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠠⠀⠀⠀
⣿⣿⡟⢻⡟⡿⢿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⠪⣿⣿⣿⢨⣿⡗⡀⠛⡛⣹⣿⡇⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣦⣤⠆⠀⠀⠀⠀⠀⢐
⠀⠈⢱⣴⣧⣁⣸⣿⣿⣿⣿⣿⣿⡀⠀⣤⣷⣾⣿⠿⠟⢿⣿⣿⣿⣿⣿⡁⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣮⣇⢹⣿⣿⣿⣿⣧⠹⠀⠰⠿⣿⡧⢂⠀⢲⣾⣿⣿⣿⣿⣿⣿⡿⢿⠋⠀⡀⢔⣴⣀⣰⣿
⣧⣀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣏⢉⣾⣿⣿⣿⣿⣷⣶⠘⠻⣿⣿⣿⣿⡟⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣿⣿⣼⣿⣿⣿⠛⠋⠁⠀⢀⡈⠀⠐⠟⣖⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿
⠿⣿⣦⣀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣁⠀⠺⠻⣿⣿⠇⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢠⡄⠀⠊⠀⠀⠀⣰⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠈⠉⢿⣷⡈⠻⢧⣤⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠐⠻⣿⣄⠀⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠚⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣶⣿⣧⡽⠀⢀⠀⠀⢙⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠙⠻⣿⣿⠿⣿⣿⣏⠁⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢆⢺⡆⠀⠘⡆⠀⠙⠻⣿⣿⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠠⢿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⢀⡀⠈⠉⠙⣿⣿⡟⠿⣾⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣾⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⠛⠟⠛⠀⠀⠀⠁⠀⠀⠈⢆⠀⢶⣿⣿⣿⣯⣿⣿⣿⣷⡄⠀⠁⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠏⠉⠀⠀⢾⣿⣿⡇⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⢁⣾⣿⠭⣁⣠⢿⢻⣿⣿⣿⣟⣿⣿⣾
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠐⠃⠹⢿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠙⠿⠿⠶⠆⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠍⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⡽⢻⣿⣿⣿⣿⣿⣿⣿⣶⣤⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⠀⠀⠀⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣶⣶⣷⣾⠻⢿⣿⣿⣿⣿⣿⣿
⠈⢿⣿⠗⠀⠀⢘⢶⣾⣶⣾⣿⣷⣆⠀⠀⢰⠿⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠿⠿⠻⣿⣿⣿⣿
⠀⠀⠙⣼⣷⣄⡐⠽⣋⣿⣿⣿⣿⣿⠀⠀⢤⠀⠈⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣠⣄⣽⣿⣿⣿
⠀⠀⠠⠜⠂⣅⠀⠀⠀⠻⣿⠟⠙⢋⠀⠀⠀⠀⠂⠀⣿⡿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⣿⣿⣿⣦⣀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢻⣿⣿⣿⣿
⠈⠀⠀⢤⣼⣿⣿⡿⠎⠄⠀⣀⠀⢀⡶⠀⠀⠀⠀⠈⠁⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣼⣶⣄⠀⠀⠈⢿⣿⣿⣿⣷⣄⠹⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣹⣿⣿⣣⣿⣿⣿⣿⣿
⣤⠀⠀⠀⣠⠼⣿⣯⡚⠀⡀⠀⠡⢂⠅⠀⠀⠀⠀⠀⠂⠴⠋⢽⣿⣿⣿⣿⣿⣿⣟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠙⢿⣿⣿⣿⣷⣤⣄⣀⣁⠐⠃⠀⠉⠻⣿⣿⣿⣿⣿⡿⠟⣿⣿⣿⣿⣿⣿⣿
⣿⠇⠀⠀⠀⠀⠀⡄⣤⠼⣷⣀⣀⡌⡉⣁⣀⠀⠠⠀⠀⠄⠀⣺⣿⣿⣿⣿⣿⠋⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠘⣿⣿⣿⣿⣁⣴⣿⣿⣿⣿⣿⣿⣿
⠻⢘⡷⠄⠀⠀⠀⠀⠀⠀⠉⣿⣿⣾⡷⣋⣿⣿⠂⠀⠲⠄⢀⣼⣿⣿⣿⡏⠛⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢈⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⣷⡞⠢⢤⠀⠀⠀⠀⠀⢠⠀⠀⢂⣥⣴⣶⡚⠳⠀⠈⣶⣾⣿⣿⣿⡟⠀⠀⢳⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣠⣾⣽⣿⣟⠑⣿⣿⣿⣿⣿⣿⣿⣿
⢸⠿⠀⠬⠅⠀⠀⠄⠀⠀⠠⢀⠉⢙⣿⣿⣿⣿⣂⣀⠰⠋⠛⠿⠛⠛⠁⠀⠀⡔⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡿⢿⢿⣿⢟⣵⡂⠀⠀⠄⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⢀⢬⡉⠈⢡⣿⣭⣿⡄⢴⠀⠀⠰⢤⣄⠈⡍⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣉⡈⡰⣊⣤⣌⣼⠿⠿⣿⣷⡈⣦⡄⠀⠀⠈⠈⠀⢀⣬⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⡀⠀⠀⠀⠀⢀⣀⣀⣐⣬⣽⣊⣾⣿⣿⣿⠂⠄⠈⠭⠄⢀⠸⠻⡛⠚⢠⣈⠭⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠠⣄⠤⠀⠀⠒⠈⠆⠈⡐⡈⠻⣿⣿⣷⣮⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣀⣠⣤⣶⣦⣀⡀⠀⠣⣄⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣿⣿⣿⣟⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⢬⣾⣿⣿⡉⠉⢻⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⡀⣀⣸⣿⢀⣾⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⣿⣿⣿⣿⣿⣿⣷⣶⣦⣄⠀⠀⠀⠀⠉⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⢼⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣼⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⡿⠿⠿⢿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⢿⣿⣿⣿⡿⠿⠿⠿⢿⡿⠿⠿⠿⣿⣿⣿⡿⠿⠿⣿⣿⡿⠿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣴⣾⣷⣶⡌⢁⣴⣾⣷⣶⡄⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣶⣶⣶⠘⣿⡇⣶⣶⣶⣶⣶⢰⣶⣶⣶⣦⡉⢡⣶⣾⣷⣦⡁⣶⣶⡆⠉⢰⣶⡆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⢋⣵⣿⣿⣿⣿⣿⡇⢸⣿⣿⠸⠿⠷⢸⣿⣿⢸⣿⡇⠀⢸⣿⡏⢀⡄⢸⣿⡏⠀⣸⣿⣿⣿⡇⢿⣷⡄⢸⣿⡏⠀⢸⣿⣿⣸⣿⡇⣾⣿⡇⣿⣿⡇⣿⣿⡇⠀⢸⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡟⠉⠙⠛⠋⣹⣤⣬⣭⣽⠇⢸⣿⣿⢶⣶⣶⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⢸⡇⢸⣿⡇⠀⣿⣿⢸⣿⣇⢸⣿⡇⢸⣿⡇⠀⢸⣿⣿⢿⣯⡅⣿⣿⡇⣿⣿⡇⣿⣿⡇⠀⢸⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠴⠂⠀⠀⠀⠀⠘⠛⠋⠀⠀⢸⣿⣿⣸⣿⣿⢸⣿⣿⣸⣿⡇⠀⢸⣿⡇⢸⡇⢸⣿⡇⢀⣿⣿⠿⣿⣿⠈⣿⡇⢸⣿⡇⠀⢸⣿⣿⢸⣿⡇⢻⣿⣇⣿⣿⡇⣿⣿⣇⣀⢸⣿⣇⣈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠛⠛⠛⣀⡙⠻⠟⠛⣡⣦⡘⠛⢃⣼⣧⡘⠛⠃⡘⠛⠛⣀⠛⠛⣠⣿⣧⡘⠛⢓⣠⡘⠛⠛⠘⠛⢃⣈⡛⠻⠟⢋⣀⡛⠛⠛⠛⠘⠛⠛⠛⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡘⣋⣉⣉⣛⠻⢛⣋⣙⡛⠿⢛⣛⣛⢛⣛⡛⢛⣛⣛⣛⡛⠿⢛⣛⡛⠿⢛⣋⣙⡛⠿⢛⣛⣛⢛⣛⡛⣛⣛⣛⣛⣛⠛⢛⣉⣙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⠿⠇⣿⣿⡿⠿⢰⣿⡿⢻⣿⣆⢸⣿⣿⢸⣿⡇⢸⣿⣿⢿⣿⡆⢸⣿⡇⢰⣿⡿⢻⣿⡆⢸⣿⣿⢸⣿⡇⠿⢿⣿⡿⠿⣸⣿⡟⣿⣿⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⣧⡄⢸⣿⡇⠸⠿⠿⢸⣿⣿⣾⣿⡇⢸⣿⣿⣼⣿⠇⢸⣿⡇⢸⣿⡇⣘⣛⡃⢸⣿⣿⣾⣿⡇⠀⢸⣿⡇⠀⠹⣿⣷⣭⡉⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⡟⠃⢸⣿⡇⢠⣤⣤⢸⣿⣿⢹⣿⡇⢸⣿⣿⢹⣿⡆⢸⣿⡇⢸⣿⡇⢻⣿⡇⢸⣿⣿⢹⣿⡇⠀⢸⣿⡇⠀⢠⣬⡝⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⣷⣶⠸⣿⣷⣼⣿⠇⢸⣿⣿⢸⣿⡇⢸⣿⣿⢸⣿⡇⢸⣿⡇⠸⣿⣷⣼⣿⡇⢸⣿⣿⢸⣿⡇⠀⢸⣿⣇⠀⠸⣿⣧⣿⣿⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢉⣉⣉⣭⣴⣬⣍⣭⣥⣶⣬⣭⣭⣬⣭⣥⣬⣭⣭⣬⣭⣥⣬⣭⣥⣶⣬⣉⣡⣭⣥⣬⣭⣭⣬⣉⣥⣶⣬⣉⣥⣾⣶⣬⣭⣭⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⣀⣠⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠆⠲⣶⠏⢶⠄⠰⠲⠶⠆⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
[69A⣿⣿⣿⣿⠿⠸⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⠿⢫⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠈⠀⠀⢻⡏⠀⠀⠀⠘⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠟⠿⢿⡁⠀⠀⠇⠀
⣿⣿⣧⠵⠀⠁⠿⢿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣘⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡐⠺⣿⠰⠆⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⠀⠀⠀⠈⣀⡀⠎⠀⠀⠀⠀⠀
⠿⣿⣿⣇⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣹⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣯⣿⣿⡄⠀⠀⠀⠈⠀⠀⠀⠀⠈⠹⡯⣿⣿⣿⣿⣿⢿⣿⠟⠛⠉⠀⠀⠐⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀
⣶⣏⢣⣝⣆⠀⡀⠀⠘⠉⣿⣿⣿⣿⣿⣿⣿⣿⡿⡉⠉⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠚⠹⠋⠸⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⣾⣿⣆⠁⠀⠀⣤⣿⣿⣿⣿⣿⣯⣿⡀⠀⠠⠊⢛⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⢿⣿⣷⣿⢿⣇⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⢀⠀⠐⢿⣿⣧⣠⡼⣷⣿⣿⣿⣷⣾⣿⣼⣿⣧⠀⠀⠈⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠸⠛⣃⠀⣹⣿⣿⣀⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣿⡷⡇⠀⠖⠃⠀⠀⠀⠀⠀⠀⠀⠸
⡆⢷⢂⣤⣭⣡⣨⣠⣿⣿⣿⣿⣿⣿⣷⡄⢳⣽⡇⠀⠀⠀⢸⡿⣿⡟⢿⣿⣿⣿⣿⣰⣴⠏⣰⣿⣿⣿⣿⣿⣿⡽⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣏⡏⠀⠋⣶⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀
⣿⡤⣯⣭⠜⡿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠻⣾⣿⡿⠆⠀⠀⣼⡇⢨⣧⠈⣿⣿⣿⣿⣿⣽⣢⣿⣿⣿⣿⣿⡿⠿⠇⢀⣀⣾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢡⡗⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣷⠙⠐⡖⠈⠘⣼⣿⣿⣿⠿⣿⣿⣷⣄⣴⣿⣷⣿⣶⣄⠘⠅⠸⠁⠀⣸⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣟⢉⡀⠿⡿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡯⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣯⡄⠋⠉⠀⠀⠁⢹⣿⣿⣷⣿⣿⣿⡿⣿⣿⣿⣿⡿⢻⡀⠀⢀⠀⣶⣿⣿⣿⡙⢥⣿⣿⣿⣿⣿⣿⣿⣿⡙⠀⠀⠀⢤⡿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⢿⠏⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣦⣤⠈⠀⠀⢸⣿⣿⣿⢻⣿⣿⣿⣿⣽⣾⣿⣇⠀⢀⣀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⣧⢈⣻⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⡔⠄⠀⠀⠀
⣿⣿⣿⣿⣿⣧⡀⢶⡌⣿⣿⡷⣘⣘⠛⠻⢿⡿⣷⠘⠉⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣬⣁⣦⡀⠀⠀⠀⠈⣿⣿⣿⣿⢿⡆⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡗⠐⢾⣿⣿⣿⣟⣿⣦⠤⠘⠓⢻⣷⣤⣿⣿⣿⡿⠛⠿⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⣐⣟⠝⢻⠿⠈⢁⠀⠀⠀⠀⠀⠀⠀⡌⢞⠇⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣶⡄⣄⣮⣿⣾⣿⣾⣿⣦⣀⡀⢸⣿⣿⣽⢿⣿⣿⣄⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⡀⠠⣿⣿⣆⣻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⣡⣽⠿⠋⢛⣿⣿⣾⣿⠛⢰⣿⣾⣿⣶⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠤⠀⡄⠘⠿⠀⣿⣿⣿⣿⣿⣀⣦⣦⠀⠀⠀⠀⠀⠀⠀⠭⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⠯⢞⣿⣀⣹⣿⣿⣿⣿⡿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇⠀⠀⠀⠙⣿⣿⣿⣿⡟⣿⣿⣷⠄⠀⠀⠀⠀⠈⢥⣶⣶⣿⡂⠀⠀⠤⠃⠀⠀⡠⠀⠀⢠⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⡙⠻⣿⣿⣿⣿⣿⣿⣯⡄⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣄⠀⠀⢸⣿⡿⢿⣿⣆⣻⠿⣿⢩⡀⢦⡄⠀⠐⢿⣿⣿⣿⣧⣤⣠⡔⠀⠀⠀⠂⠀⠀⠈⠀⠀⠀
⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣟⣿⣿⣿⣿⣿⣿⣿⣆⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠘⢔⢦⣾⣿⡫⣿⣿⡛⢿⣤⡿⣿⡶⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠀⠀⢀⣀⣤
⠉⢻⠹⠛⢿⣿⣿⣿⣿⣿⣿⠛⠋⠛⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡆⣌⠻⣿⣿⣧⣿⣏⢠⡀⠘⣸⣿⣿⠀⠀⢀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⡀⡀⠀⣰⣿⣿
⠿⣿⣷⣴⣼⣿⣿⣿⣿⣿⣭⣆⣀⣶⣿⣿⣿⣛⣋⠹⣿⣿⣿⣿⣿⣦⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢻⣿⡆⣿⣿⣿⣿⣿⠮⠃⠀⠉⠛⠻⣠⣄⡀⣻⣿⣿⣿⣿⣿⣿⣯⣽⣧⣄⣴⣤⣾⣶⣾⣿⣿⣿
⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⠎⠉⢿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⣿⣿⣿⡏⠁⠀⠀⢀⠔⠀⠀⠉⣽⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣤⡙⢻⣿⡿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠈⠉⣿⣿⡟⠀⠀⣼⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⣶⣀⠀⠀⢀⣀⣤⣿⣾⣿⣿⣿⣭⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣈⣿⣷⠄⠙⠻⡶⣿⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠀⠀⠀⠉⢻⣷⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⢹⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣟⠀⢀⠀⠀⢨⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠚⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⡛⢹⣿⣿⣤⣀⣀⣀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⠿⣍⠹⡗⠀⠀⢧⠀⠈⠙⢿⣿⣝⣿⣿⣿⣿⣿⠇⠀⢀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠈⠙⠟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣾⡿⠿⠋⢹⣿⣿⣿⣿⣿⣿⣿⣟⣭⠂
⠛⠏⠀⠀⠀⠀⠀⠀⠀⠱⠀⢹⣿⣿⣿⣿⣾⣿⣿⣿⣷⠀⠀⠀⢠⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣠⠤⠆⠀⢀⣾⣿⣧⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣠⣾⣿⣿⡶⠖⠛⠋⣿⣿⣿⣿⣾⣿⣿⣏⠁
⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠉⠀⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠙⠻⢿⠶⠆⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠈⠀⠀⢸⣯⣿⣿⣿⣿⣿⣿⣿⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡰⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⣭⣽⣿⣿⠟⠛⠛⣿⣿⣿⣿⣿⣿⣿⡇⣀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⡀⠀⠀⠀⠀⢀⠀⢰⣤⡄⠀⠀⠀⠀⠐⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣏⣀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣩⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡛⠂⠀⠘⢵⣾⣿⣿⣿⣿⣧⡄⠀⠀⠾⠿⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠻⣿⣿⣿⣿⣿
⠘⢺⣿⣦⡄⠙⠉⣿⣿⣿⣿⣿⡧⠀⠀⠂⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⣁⠀⠀⠀⠀⠀⠀⣤⣀⣀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣾⣿⣿⣿⣿⣿
⠀⠬⠃⣠⣄⠀⠀⠘⠿⡟⠋⠉⠀⠀⠀⠀⠈⠀⣨⡿⠟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⠀⠀⠀⠀⢴⣿⣿⣿⣷⣄⡀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣏⢠⣿⣿⣿⣿⣿⣿
⠀⣐⣾⣿⣿⣿⡷⢁⠀⢄⡄⠀⢸⠂⠀⠀⠄⠀⠀⠄⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣦⣄⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠻⡿⠏⠛⠛⠿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡴⢻⣿⡯⠃⢠⡀⠀⠒⣠⢀⡀⢀⠀⠀⠈⠘⠛⠒⣻⣿⣿⣿⣿⣿⡿⠟⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⡈⠻⣿⣿⣿⣿⣿⣷⣶⣦⠄⠀⠀⠀⠙⣿⣿⣿⣿⡿⠋⣹⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⢠⡶⢻⣇⣠⠤⢌⢉⣀⣄⡀⠀⠀⠀⠁⠀⣿⣿⣿⣿⣿⡏⠁⠀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠉⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠘⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣳⠆⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⡿⠞⣽⣿⡟⠀⠐⠓⠀⣠⣿⣿⣿⣿⠏⢁⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⡿⣿⣿⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⡓⠤⡄⠀⠀⠄⠀⠀⠄⠀⢀⣭⣴⣶⣾⡉⠛⠀⢀⣾⣿⣿⣿⣿⠋⠀⠈⢙⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠇⠀⠭⠀⠀⠠⠀⠀⠀⠤⠨⣉⣹⣿⣿⣿⣷⣂⡀⠜⠉⠝⠋⠉⠃⠀⠀⠀⣌⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠫⡿⣿⣿⡿⣫⣖⡂⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠐⠒⠄⠀⠀⠀⠀⠀⢈⠁⠊⢺⣿⣿⣿⡄⢼⠀⠀⠰⠦⡄⢀⠌⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣁⢀⠜⣩⣦⡔⠾⠛⠿⣿⡷⠀⡁⣆⡀⢀⠀⢀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣀⣀⣦⣭⣾⣡⣾⢟⣿⣿⠂⠄⠩⠵⠀⢠⠘⢛⠋⢉⣴⣤⡐⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣠⡴⠠⠀⠀⡊⠈⠂⠀⠔⡄⠹⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣀⣤⣦⣮⣷⣤⡄⠀⠑⢦⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠶⠶⠿⢿⠄⠀⢹⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣌⣄⠥⠼⠿⢤⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⢙⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣽⢿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣿⣷⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣽⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣀⣽⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⡿⠿⠿⢿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⠿⠿⢿⣿⣿⣿⡿⠿⠿⠿⠿⡿⠿⠿⠿⣿⣿⣿⡿⠿⠿⣿⣿⣿⠿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣴⣾⣷⣶⡌⢁⣴⣾⣷⣶⡄⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣶⣶⣶⠘⣿⡇⣶⣶⣶⣶⣶⢰⣶⣶⣶⣦⡉⢡⣶⣾⣷⣦⡁⣶⣶⡆⠉⢰⣶⡆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⣋⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⠸⠿⠷⢸⣿⣿⢸⣿⡇⠀⢸⣿⡏⢠⡄⢸⣿⡏⠀⣸⣿⣿⣿⡇⢿⣷⡄⢸⣿⡏⠀⢸⣿⣿⣸⣿⡇⣾⣿⡇⣿⣿⡇⣿⣿⡇⠀⢸⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠟⢳⡾⠿⢿⣋⣛⠛⡻⣿⠇⢸⣿⣿⢶⣶⣶⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⢸⡇⢸⣿⡇⠀⣿⣿⢸⣿⣇⢸⣿⡇⢸⣿⡇⠀⢸⣿⣿⢿⣯⡅⣿⣿⡇⣿⣿⡇⣿⣿⡇⠀⢸⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣁⡀⠀⠀⠀⠙⠻⠿⠿⠋⠁⠀⢸⣿⣿⣸⣿⣿⢸⣿⣿⣸⣿⡇⠀⢸⣿⡇⢸⡇⢸⣿⡇⢀⣿⣿⠿⣿⣿⠘⣿⡇⢸⣿⡇⠀⢸⣿⣿⢸⣿⡇⢻⣿⣇⣿⣿⡇⣿⣿⣇⣀⢸⣿⣇⣈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠛⠛⢛⣀⡙⠻⠟⠛⣡⣦⡘⠛⢃⣼⣧⡘⠛⢃⡘⠛⠛⣀⠛⠛⣠⣿⣧⡘⠛⢓⣤⡘⠛⠛⠘⠛⢃⣈⡛⠻⠟⢋⣀⡛⠛⠛⠛⠘⠛⠛⠛⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣈⡛⣛⣉⣙⣛⠻⢛⣋⣙⡛⠿⢛⣛⣛⢛⣛⡛⢛⣛⣛⣛⡛⠿⢛⣛⡛⠿⢛⣋⣙⡛⠿⢛⣛⣛⢛⣛⡛⣛⣛⣛⣛⣛⠛⢛⣛⣛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡞⡿⡆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⠿⠇⣿⣿⡿⠿⢰⣿⡿⢻⣿⣆⢸⣿⣿⢸⣿⡇⢸⣿⣿⢿⣿⡆⢸⣿⡇⢰⣿⡿⢻⣿⡆⢸⣿⣿⢸⣿⡇⠿⢿⣿⡿⠿⣸⣿⡟⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⣧⡄⢸⣿⡇⠸⠿⠿⢸⣿⣿⣾⣿⡇⢸⣿⣿⣼⣿⠇⢸⣿⡇⢸⣿⡇⣘⣛⡃⢸⣿⣿⣾⣿⡇⠀⢸⣿⡇⠀⠹⣿⣷⣭⡉⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⡟⠃⢸⣿⡇⢠⣤⣤⢸⣿⣿⢹⣿⡇⢸⣿⣿⢹⣿⡆⢸⣿⡇⢸⣿⡇⢻⣿⡇⢸⣿⣿⢹⣿⡇⠀⢸⣿⡇⠈⢠⣬⡝⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⣷⣶⠸⣿⣷⣼⣿⠇⢸⣿⣿⢸⣿⡇⢸⣿⣿⢸⣿⡇⢸⣿⡇⠸⣿⣷⣼⣿⡇⢸⣿⣿⢸⣿⡇⠀⢸⣿⣇⠀⠸⣿⣧⣿⣿⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠤⣉⣉⣩⣭⣴⣬⣭⣭⣥⣶⣮⣭⣭⣬⣭⣥⣬⣭⣭⣬⣭⣥⣬⣭⣥⣶⣬⣍⣥⣭⣥⣬⣭⣭⣬⣉⣥⣴⣬⣉⣥⣾⣶⣬⣭⣩⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⣉⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠆⠲⣶⠏⢶⠄⠠⠰⠶⠆⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
[69A⣹⠅⠀⠸⣿⣿⣿⣷⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⢹⣟⡓⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⣤⣾⢩⡄⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠙⠁⠉⠇⠈⡌⠇⠀⠀⠁⠀⠈⠀
⡧⠀⠀⠃⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣟⣻⣷⡌⠉⠀⠀⠐⠄⠀⠀⠀⠙⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⣀⡀⠀⠀⠀⠀⠀⠶⠇⠁⠀⠀⠀⠀⠀⠀⠀
⣻⣦⠀⡀⠀⠘⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠿⣿⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠃⢽⠿⡿⢻⡟⠉⡛⠁⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣽⣿⣦⠘⠀⠀⢀⡸⣿⣿⣿⣿⣿⡿⣏⠙⠒⢀⣴⢿⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⡇⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⡀⠚⠀
⣿⣿⣿⡁⣀⣴⣼⣿⣿⣿⣽⣿⣟⢻⡿⡀⠀⠀⠐⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡿⠆⠉⠻⣿⣿⠈⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣆⣄⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀
⠀⢽⠙⠛⠋⢹⣿⣿⣿⣿⣿⣿⣟⠻⡟⣿⡄⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⢠⡁⡾⢀⣾⣿⣿⣿⣿⣿⡧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⠏⠏⢟⡀⠈⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀
⣟⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢧⣾⣿⣧⡀⠀⠀⣿⡏⠹⣇⠘⣿⣿⣿⣿⣿⣿⡅⣾⣿⣿⣿⣿⣿⣿⣷⡉⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠛⣶⠀⠁⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡟⣯⠈⠅⢞⣿⣿⣿⣿⣿⣿⣿⣎⠈⢋⣿⣭⣥⣄⠀⢻⠇⢸⠋⠀⢹⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⠬⠉⣴⡶⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠼⠀⠀⠸⠻⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠈⠀⣄⣾⣿⣿⣿⡏⣽⣿⣿⣿⣿⣿⣿⣿⢶⠆⠈⠓⠛⢻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⣽⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣆⠀⠀⠠⠀⠀⢿⣿⣿⣿⣿⣿⣿⣯⣿⢿⣿⣿⡏⠘⠂⠀⠘⢀⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠈⣫⠻⢿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠏⠃⠀⠠⠄⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣷⡀⠀⣄⢸⣿⣿⣏⢻⢻⣿⣿⣿⣿⣟⠻⠷⠀⢰⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠯⣀⠀⠀⠀⠀⠛⢶⣶⣿⣿⣿⡆⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⡀⣛⣣⣿⣿⣅⣾⣦⡀⠉⢹⣋⣿⣥⠀⣰⣾⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣷⣾⣧⠀⠀⠀⠀⣸⡿⣿⣿⡏⠷⠀⠀⠀⠀⠀⠀⠀⠐⢶⣶⠃⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⡟⣇⢈⢛⠻⣟⣻⣮⣻⣿⠁⠀⠈⢸⣿⣿⢿⣿⣿⣿⡀⠈⢀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠊⠀⠀⠀⢰⣾⣄⣠⡏⠁⠀⠂⠀⠀⠀⠀⠀⠀⠘⠨⡏⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥
⣿⣿⣿⣿⣿⡜⠗⣽⣿⠿⢿⣿⣿⣫⣶⣦⢘⣽⡻⣿⣛⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⣶⡀⢹⣿⣿⣶⣿⡆⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣠⠀⠁⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣷⣼⣿⣭⣨⠉⠿⡿⢿⡿⠉⢼⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣁⣾⠀⠈⠁⠸⣿⣿⣿⣿⣷⣾⣿⣧⡀⠀⠀⠀⠀⠀⠼⢉⡀⣠⣄⠀⠀⠀⢀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠙⣿⣿⣦⣴⣿⣿⣿⣿⣧⡁⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣼⣿⣿⣿⣟⢹⣿⣿⡿⠄⢀⠀⠀⠀⢸⣿⣿⣿⣷⠀⠀⠘⡀⠀⠀⢐⠀⠀⠀⠇⠀⠀⠀⠀
⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣷⣀⣤⣭⣿⣿⣿⣿⣿⣿⣿⡖⠀⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠳⡀⣀⠀⣿⣿⢭⣿⣿⣶⡏⢹⣧⣷⡈⠛⠀⠀⣨⣿⣿⣿⣿⣿⣶⣿⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢰
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⢭⣾⣿⣿⣹⣿⡇⠉⠟⠾⣻⣿⡅⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣤⣤⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿
⡘⠉⢻⣿⣿⣿⣿⣿⣿⠉⠀⠈⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣜⣆⢹⣿⣿⣾⣿⣦⢷⠀⠡⣿⣿⡇⠄⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⡀⢄⣄⣈⣼⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⠿⣤⣿⣿⣿⣿⣦⣭⡄⣿⣿⣿⣿⣿⣿⡦⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣸⣿⣿⣿⠿⠟⠁⠀⠀⢀⠁⠁⡿⡔⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⡗⠀⠈⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⡈⠀⠜⠁⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣀⠹⣿⣝⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⣸⢿⣿⠀⠀⣰⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠸⣿⣶⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣶⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⠆⠈⠙⠛⢿⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⣈⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⢀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋
⣯⣃⢠⡄⠀⠸⡄⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠙⠩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣼⣿⣿⣶⣴⣦⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠈⣽⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀
⡿⠇⠌⢿⠀⠀⠹⣄⠀⢀⣹⣿⣷⣿⢿⣿⣿⣿⣟⠀⠀⠄⠈⠈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠂⣾⣿⣏⡉⣀⣿⢿⣿⣿⣿⡿⣿⣯⣾⠇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠂⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⡎⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢀⣨⣿⣿⠀⠉⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⠒⢞⠁⠀⣼⢿⣿⣿⣿⣿⣿⣿⣄⠠⠀
⠀⠦⡀⠀⠀⠀⠀⠀⠀⠀⠛⣿⢿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⢨⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠙⠿⣿⣿⠇⢠⠾⠟⢛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⠆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠟⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⡿⠟⠉⠈⣩⣿⣿⣿⣿⣿⣿⣿⣤⣶⣶⣶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅
⠀⠀⠀⡀⠀⣀⠐⣶⣶⣀⠀⠀⠀⠀⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡾⠿⢿⣿⣿⣿⣿⣿⣿⣿
⣃⠀⠈⢽⣿⣿⣿⣿⣿⣿⣦⠀⠀⠘⠛⢛⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢸⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣄⣽⣿⣿⣿⣿⣿⣿
⣿⣷⠤⠉⠊⢼⣿⣿⣿⣿⣿⠀⠀⠲⠀⠀⠈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠈⠙⢁⡀⠀⠀⠀⠀⠀⣤⣀⣀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⣿⣿⣿⣿⣿⣿⣿
⠉⣠⣤⡀⡀⢀⠙⠿⠋⠉⠠⠀⠀⠀⠀⠀⠀⡾⠟⠃⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣼⣧⡀⠀⠀⠀⣼⣿⣿⣿⣷⣦⣀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢩⣿⣿⣢⣾⣿⣿⣿⣿⣿⣿⣿
⢲⣿⣿⣿⣿⢃⠊⠀⠤⡀⠁⡟⠀⠀⠀⠀⠀⠀⣀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣼⣿⣿⣷⣄⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣶⣌⠲⠾⠍⠙⠻⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠠⠾⣿⣷⠍⢀⣄⠀⠀⠃⣆⡀⠀⢀⠀⠀⠈⠐⠋⠠⣿⣿⣿⣿⣿⣿⠿⠏⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠈⢿⣿⣿⣿⣇⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠄⢴⠞⣿⣤⣤⠤⡀⣠⣤⣄⡀⠂⠀⠐⠀⠨⣿⣿⣿⣿⣿⡇⠀⣀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠙⠻⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠈⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠄⠀⠀⠀⠀⠀⠐⠀⢹⣿⣿⠿⠫⡼⢿⣍⠀⠈⡃⢀⣴⣿⣿⣿⣿⠀⢁⡠⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢰⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣴⣏⣿⣿⡃⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡢⢤⠀⠀⠠⠄⠀⠠⠄⠀⣡⣵⣶⣿⣯⡉⠃⠀⢸⣿⣿⣿⣿⣿⠁⠀⠀⢹⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠨⠅⠀⠀⠄⠐⠀⠠⠄⠍⣉⣽⣿⣿⣿⣷⣦⡤⠋⠉⠙⠋⠉⠁⠀⠀⢀⣮⣽⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⡛⣛⣻⠟⣡⣾⡄⠀⢐⠂⠀⠀⠀⠀⣺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠐⠢⠀⠀⠀⠀⠀⠐⣉⠔⡁⣺⣿⣾⣿⡆⠾⠀⠀⠘⠲⠆⠀⠂⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣁⣬⡡⢠⢟⣱⣥⣔⠾⠛⢿⣿⠿⠄⢶⣊⣀⣀⠀⠠⠤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣠⣐⣮⣭⣟⣱⣿⠟⣿⣟⢀⠀⠡⠔⠂⢠⡘⠩⠭⢡⣵⣶⣌⣁⠹⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡠⠶⠀⠀⠀⠈⠐⠃⠀⠃⣆⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣽⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣴⣶⣶⣿⣴⡆⠀⠉⠹⠨⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⢀⢒⡻⡛⠻⣢⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣧⣦⣐⠒⠛⣲⣾⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⢈⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠛⢿⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⡀⢀⣽⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡙⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⡿⠿⠿⢿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⠿⠿⢿⣿⣿⣿⡿⠿⠿⠿⠿⡿⠿⠿⠿⣿⣿⣿⡿⠿⠿⣿⣿⣿⠿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣴⣾⣷⣶⡌⢉⣴⣾⣷⣶⡄⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣶⣶⣶⠘⣿⡇⣶⣶⣶⣶⣶⢰⣶⣶⣶⣦⡉⢡⣶⣾⣷⣦⡉⣶⣶⡆⠉⢰⣶⡆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠿⣻⣿⣿⣿⣿⣿⣿⡏⢸⣿⣿⠸⠿⠷⢸⣿⣿⢸⣿⡇⠀⢸⣿⡏⢠⡄⢸⣿⡏⠀⣼⣿⣿⣿⡇⢿⣷⡄⢸⣿⡏⠀⢸⣿⣿⣸⣿⡇⣾⣿⡇⣿⣿⡇⣿⣿⡇⠀⢸⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣥⣾⣿⠿⠿⠿⢿⣿⣿⡇⢸⣿⣿⢶⣶⣦⢸⣿⣿⢸⣿⡏⠀⢸⣿⡇⢸⡇⢸⣿⡇⠀⣿⣿⢸⣿⣇⢸⣿⡇⢸⣿⡇⠀⢸⣿⣿⢿⣯⡅⣿⣿⡇⣿⣿⡇⣿⣿⡇⠀⢸⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⠉⠀⠸⢿⣿⣶⠖⠋⠀⠀⢸⣿⣿⣸⣿⣿⢸⣿⣿⣸⣿⡇⠀⢸⣿⡇⢸⡇⢸⣿⡇⢀⣿⣿⠿⣿⣿⠘⣿⡇⢸⣿⡇⠀⢸⣿⣿⢸⣿⡇⢻⣿⣇⣿⣿⡇⣿⣿⣇⣀⢸⣿⣇⣈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⠻⠛⠛⢛⣀⡙⠻⠟⢛⣡⣦⡘⠛⢃⣼⣧⡘⠛⠃⡘⠛⠛⣀⠛⠛⣠⣿⣧⡘⠛⢓⣠⡘⠛⠛⠘⠛⢃⣈⡛⠻⠟⢋⣄⡛⠛⠛⠛⠘⠛⠛⠛⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣈⣙⡛⣛⣉⣙⣛⠿⢛⣋⣙⡛⠿⢛⣛⣛⢛⣛⡛⢛⣛⣛⣛⡛⠿⢛⣛⡛⠿⢛⣋⣙⡛⠿⢛⣛⣛⢛⣛⡛⣛⣛⣛⣛⣛⠛⢛⣉⣛⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣤⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⠿⠇⣿⣿⡿⠿⢰⣿⡿⢻⣿⡆⢸⣿⣿⢸⣿⡇⢸⣿⣿⢿⣿⡆⢸⣿⡇⢰⣿⡿⢻⣿⡆⢸⣿⣿⢸⣿⡇⠿⢿⣿⡿⠿⣸⣿⡟⣿⣿⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⣧⡄⢸⣿⡇⠸⠿⠿⢸⣿⣿⣾⣿⡇⢸⣿⣿⣼⣿⠇⢸⣿⡇⢸⣿⡇⣘⣛⡃⢸⣿⣿⣾⣿⡇⠀⢸⣿⡇⠀⠹⣿⣷⣭⡉⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⡟⠃⢸⣿⡇⢠⣤⣤⢸⣿⣿⢹⣿⡇⢸⣿⣿⢹⣿⡆⢸⣿⡇⢸⣿⡇⢻⣿⡇⢸⣿⣿⢹⣿⡇⠀⢸⣿⡇⠈⢠⣬⡝⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⣷⣶⠸⣿⣷⣼⣿⠇⢸⣿⣿⢸⣿⡇⢸⣿⣿⢸⣿⡇⢸⣿⡇⠸⣿⣷⣼⣿⡇⢸⣿⣿⢸⣿⡇⠀⢸⣿⣇⠀⠸⣿⣧⣿⣿⠇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢀⣤⣍⣉⣭⣭⣴⣬⣭⣭⣥⣶⣮⣭⣭⣬⣭⣥⣬⣭⣭⣬⣭⣥⣬⣭⣥⣶⣬⣍⣥⣭⣥⣬⣭⣭⣬⣉⣡⣶⣬⣉⣥⣾⣷⣬⣭⣩⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠆⠲⣶⠏⢶⠄⠠⠲⠶⠆⠀⠀⠀⢸⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
[69A⠰⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⣤⡉⠛⠃⠃⠀⡀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠙⠛⠀⠀⠀⠀⢉⣤⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢻⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢻⠸⣿⣿⣿⣿⠟⢿⠟⠙⠁⠀⠀⠐⠲⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠐⠄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡟⠿⠿⠀⢨⣿⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠛⠀⠋⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠄⠊⠀
⡷⠀⢀⣀⣾⣾⣿⣿⢿⣿⡿⣿⣷⠀⠀⠙⢉⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣇⠻⢿⣿⣿⡟⢿⣄⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠠⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⢁⡀⠀⠀
⠿⢾⠟⣻⣿⣿⣿⣿⣿⣿⠷⢿⣿⣷⡀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠘⠏⢹⠀⢠⣿⣿⣷⣼⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣿⢿⢾⠄⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀
⣶⣦⣶⣿⣿⣿⣿⣿⣿⣿⣷⡄⣱⣿⣇⠀⠀⠀⢸⣿⢿⡟⢻⣿⣿⣿⣿⣤⣷⡟⢠⣿⣿⣿⣿⣿⣿⣧⠻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣍⡁⠸⠈⡞⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠂⠀⠀
⢿⢻⣿⣿⣿⣿⣿⣿⣿⣯⡨⠹⠿⣿⠿⡆⠀⠀⢼⡧⠀⡿⠀⢻⣿⣿⣿⣿⣷⣗⣾⣿⣿⣿⣿⣿⡟⡿⠒⣠⣤⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⣸⡇⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣷⣿⣿⣿⣿⢻⣿⣿⣷⣤⣶⣿⣿⣿⣿⣤⠘⠀⠘⠀⠀⣨⣿⣿⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣋⣡⠸⢿⣹⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠁⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀
⡀⠀⠈⠈⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⡿⢹⡃⠀⢸⠀⢱⣿⣿⣿⣏⢻⣼⣿⣿⣿⣿⣿⣿⣿⣏⠉⠀⠀⠀⣴⢿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢾⠛⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡄⠁⠀⠀⣻⣿⣿⡟⣿⣿⣿⣿⣿⣽⣿⣿⣇⠀⢀⣀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠄⠀⠀⢰⣇⣉⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠉⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀
⣿⣄⠠⣶⣸⣿⣿⠗⢸⡙⠛⠿⢿⡿⣿⡌⠋⢠⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣑⣦⠀⠀⠀⠀⠘⣿⣿⣿⣿⢿⡀⠀⠁⠀⠀⠀⠀⠀⣀⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠠⡤
⣿⣿⠄⠶⣿⣿⣿⣿⡻⣿⣦⡤⠘⠲⢿⣿⣤⣾⣿⣿⣿⠟⠻⠟⢹⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣟⠇⠀⠀⠀⢐⣟⠹⢻⠿⠈⢃⠀⠀⠀⠀⠀⠀⠀⡌⢿⢗⠀⠀⠀⠀⠀⠀⢐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀
⣿⣷⣦⢠⣰⣽⣷⣯⣿⣾⣿⡦⡀⡀⠸⣿⣿⣯⣿⣿⣿⣦⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢀⡀⠠⣿⣿⣖⣻⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠀⠀⠀⠀⠀⠉⠀
⣿⣿⣿⣏⢨⣿⡿⠽⠽⣿⣿⣿⣿⡿⢩⣽⣮⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠥⠄⡀⠸⣷⠀⢾⣿⣿⣿⣿⠀⣴⣦⠀⠀⠀⠀⠀⠀⢀⣲⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠠⠀⠀⠀⠀⠈⠀
⣿⣿⣿⣿⣿⣾⣶⣶⣌⠉⢯⣹⣿⡁⢙⣿⣿⣿⣿⣿⠿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡇⠀⠀⠀⠙⣿⣿⣿⣿⡿⣿⣿⣯⡄⠀⠀⠀⠀⠐⣫⣦⣤⣾⡆⠀⠀⣠⠂⠀⠀⠀⠠⠁⢠⠀⠀⠁⠀⠀⠀
⣿⣿⡿⣿⣿⣿⣿⣿⣿⣄⠀⠚⠿⣿⣿⣿⣿⣿⣿⣿⣒⡀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⡀⠀⠀⢸⣿⣿⢿⣿⣆⠻⣿⣿⢡⡀⢤⡀⠀⠠⣿⣿⣿⣿⣧⣄⣀⡤⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣶⣾⣿⣿⣿⣿⣿⣿⣯⡀⠀⠘⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠙⠴⣦⣸⣿⡟⣾⣿⠿⢿⣇⣿⣿⣥⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠐⠀⠀⠀⢀⣀⣤⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⠐⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣌⢾⣿⣿⣇⣾⣿⢡⡈⠩⢁⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣾⠇⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿
⣸⣿⣿⣿⣿⣿⡿⡄⠀⣠⣿⣷⣿⡿⢿⠻⢿⣿⣿⣿⣿⣿⣁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣾⡅⣿⣿⣿⣿⣿⣇⣗⠀⠚⢻⠿⠊⡄⠈⢻⣿⣿⣿⣿⣿⣿⣿⣛⣯⠀⣤⣢⣷⣵⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡛⣳⣾⣿⣿⣿⣿⣶⣶⠘⠿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣽⣿⣿⣿⠉⠁⡀⠀⣠⠄⠀⠘⢻⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣁⠀⠸⠿⣿⣿⡿⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⣠⡄⡐⠁⠀⠀⣀⣽⣯⣿⣿⣿⣟⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡴
⢿⣧⡀⣬⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠛⣿⣧⠀⢠⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠀⠀⠛⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠈⠙⠻⠟⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣏⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⠀⠀
⠴⣦⠀⠈⢣⠀⠘⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠠⡈⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣰⣿⣿⠟⢛⣿⣿⣿⣿⣿⣿⣿⢿⣋⠐⠀⠀⠀
⠂⠹⠇⠀⠈⠣⡀⠀⣤⣿⣿⣾⣟⣿⣿⣿⣿⣅⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡈⣩⣿⣿⣶⣤⠞⠟⣿⣿⣿⣿⣽⣿⣿⠏⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠙⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠸⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠙⠛⠛⣻⣿⠉⠉⠉⢹⡿⠟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠐⠁⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣂⠀⠀⠀
⠄⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⣄⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡤⠈⠀⠀⠘⠻⣿⣿⠃⢀⣭⣶⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠀⢀⡀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⡤⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠹⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⢿⣿⣿⠟⠁⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠄
⠀⢀⡀⢠⣀⣸⣾⣇⡀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿
⠀⡉⣻⣿⣿⣿⣿⣿⣷⡆⠀⠀⠉⠙⠅⡨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢰⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿
⡶⠦⠐⠡⢿⣿⣿⣿⣿⡗⠀⠀⠉⠀⡄⠠⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠸⣼⣿⣿⡀⠀⠀⠀⠀⢠⣄⣀⡀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡁⣽⣿⣿⣿⣿⣿⣿⣿⣿
⣴⣄⣀⡄⡨⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠰⠟⠋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢄⣿⣿⣿⣧⠀⠀⠀⠀⣼⣿⣿⣿⣿⣦⣀⠀⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣇⣼⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣟⡀⠂⠢⠆⠀⢰⠋⢀⠀⠐⠀⠀⡘⢀⣬⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣷⡀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠈⠰⠤⠜⢿⣿⣿⣿⣿⡟⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠶⠻⢿⠾⠁⢀⡆⠠⠈⢡⣆⢄⠀⠄⠀⠀⠀⠉⠁⢑⣿⣿⣿⣿⣿⣿⠛⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢻⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠲⠬⠶⠛⣷⣤⣶⢖⡄⣤⣤⣤⡀⠀⠀⡀⠀⠸⣿⣿⣿⣿⢿⡇⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠙⢿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⢀⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢿⣿⠿⠟⠡⠿⣿⣅⡀⠉⠁⢀⣾⣿⣿⣿⡿⠀⠠⣐⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⢠⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣶⣿⣿⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠄⠀⠀⠠⠀⠀⠠⠀⠀⣡⣶⣾⣿⣯⡀⠃⠀⣸⣿⣿⣿⣿⡿⠀⠀⠀⢨⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⡀⠀⠄⠀⠀⠠⠄⠌⣁⣿⣿⣿⣿⣿⣥⠄⠋⠀⠋⠁⠈⠁⠀⠀⣀⣦⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⠉⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢙⣛⣛⣿⢟⣵⣯⣄⠀⢀⠀⠀⠀⠀⠠⠽⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠒⠢⠀⠀⠀⠀⠀⠒⣫⠔⣑⣺⣿⣾⣿⣆⠺⡀⠀⠈⠑⡂⠀⠁⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣡⣥⡤⣠⢚⣵⣧⣴⠺⠛⢛⡿⠿⠄⢀⣧⣤⣀⠄⠠⠖⡶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣀⣐⣭⣭⣟⣱⣿⠿⡿⣿⠄⠀⠠⠒⢂⢰⡄⠩⡗⠲⢼⣷⣮⣥⣜⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣟⣻⣿⣿⣿⣿⣿
⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡠⠶⠂⠀⠀⢌⡀⠁⠀⠀⣥⣈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣯⣽⣻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣼⣶⣷⣿⣶⡖⠀⠀⠙⢖⣻⣿⡿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⡹⠿⠏⠙⣻⡆⢠⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣦⣋⢉⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣾⣿⡿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣶⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣉⠻⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣅⣈⣽
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⡿⠿⠿⢿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⠿⠿⢿⣿⣿⣿⡿⠿⠿⠿⠿⣿⠿⠿⢿⣿⣿⣿⡿⠿⠿⣿⣿⣿⠿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⠹⠟⠋⢹⣦⣦⣤⣬⠿⠋⠉⠁⢸⣿⣿⣸⣿⣿⢸⣿⣿⣸⣿⡇⠀⢸⣿⡇⢸⡇⢸⣿⡇⢀⣿⣿⠿⣿⣿⠘⣿⡇⢸⣿⡇⠀⢸⣿⣿⢸⣿⡇⢻⣿⣇⣿⣿⡇⣿⣿⣇⣀⢸⣿⣇⣈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⣀⣀⠀⠁⠀⠀⠄⠀⠀⠀⠀⠀⠸⠿⣿⣿⠿⠇⣿⣿⡿⠿⢰⣿⡿⢻⣿⡆⢸⣿⣿⢸⣿⡇⢸⣿⣿⢿⣿⡆⢸⣿⡇⢰⣿⡿⢻⣿⡆⢸⣿⣿⢸⣿⡇⠿⢿⣿⡿⠿⣸⣿⡟⣿⣿⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⣧⡄⢸⣿⡇⠸⠿⠿⢸⣿⣿⣾⣿⡇⢸⣿⣿⣼⣿⠇⢸⣿⡇⢸⣿⡇⣘⣛⡃⢸⣿⣿⣾⣿⡇⠀⢸⣿⡇⠀⠹⣿⣷⣭⡉⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⡟⠃⢸⣿⡇⢠⣤⣤⢸⣿⣿⢹⣿⡇⢸⣿⣿⢹⣿⡆⢸⣿⡇⢸⣿⡇⢻⣿⡇⢸⣿⣿⢹⣿⡇⠀⢸⣿⡇⠈⢠⣬⡝⣿⣿⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⣷⣶⠸⣿⣷⣼⣿⠇⢸⣿⣿⢸⣿⡇⢸⣿⣿⢸⣿⡇⢸⣿⡇⠸⣿⣷⣼⣿⡇⢸⣿⣿⢸⣿⡇⠀⢸⣿⣇⠀⠸⣿⣧⣿⣿⠇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠄⠉⠉⣀⣤⣭⣩⣭⣭⣴⣬⣭⣭⣥⣶⣮⣭⣭⣬⣭⣥⣬⣭⣭⣬⣭⣥⣬⣭⣥⣶⣬⣍⣥⣭⣥⣬⣭⣭⣬⣉⣥⣴⣬⣉⣥⣾⣷⣬⣍⣭⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠆⠲⣶⠏⢶⠄⠠⠲⠶⠆⠀⠀⠀⣷⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
䷩ 𝚕𝚒𝚗𝚎 2795
╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕
(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/09/06/irc-log-050923/#comments
Gemini version at gemini://gemini.techrights.org/2023/09/06/irc-log-050923/
⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.06.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧
Gemini_version_available_♊︎
✐ IRC_Proceedings:_Tuesday,_September_05,_2023⠀✐
Posted in IRC_Logs at 5:05 am by Needs Sunlight
Also available via the Gemini protocol at:
* gemini://gemini.techrights.org/irc-gmi/irc-log-techrights-050923.gmi
* gemini://gemini.techrights.org/irc-gmi/irc-log-050923.gmi
* gemini://gemini.techrights.org/irc-gmi/irc-log-social-050923.gmi
* gemini://gemini.techrights.org/irc-gmi/irc-log-techbytes-050923.gmi
Over HTTP:
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#techrights_log_as_HTML5 #boycottnovell_log_as_HTML5
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#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
QmSFK9NEvNoyG6iZaAKCLTzcUifDCCii76UnQFQBpYA88q #boycottnovell 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
(full IRC log
as HTML)
IRC log for
#boycottnovell
QmWjCbaTQN6n7MU35YEztMVc65JJ1PQAhqEAjo2coWMaBa (full IRC log 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
as plain/ASCII
text)
IRC log for
#boycottnovell-
QmWuouZf8jesTnaRY8D3ymHKdoDb9VHKRk3a286xPeNpZ3 social 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
(full IRC log
as HTML)
IRC log for
#boycottnovell-
QmSzhJSzWYySg8YurZmDgNgbenRYhScNJByWFAdKEg3von social 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
(full IRC log
as plain/ASCII
text)
IRC log for
QmfF7yFQKUqCDNw99HycSsXcNqkPvXyA1XRagG5AnoYv8g #techbytes 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
(full IRC log
as HTML)
IRC log for
#techbytes
Qme8FN51n6g6AzStu1BJha1tJY48m4pGRw2zkdjj6dikKg (full IRC log 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
as plain/ASCII
text)
IRC log for
QmdjXXZSdRkRKaKJ3gqk5qRtsHSyKkdPcRxxFLE9cSS8sQ #techrights 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
(full IRC log
as HTML)
IRC log for
#techrights
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as plain/ASCII
text)
🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇IPFS logo⦈
§ Bulletin for Yesterday⠀➾
Local_copy | CID (IPFS): QmWE6ucdKk9Q1pi6ce3ko9xPWd9Y4BjpLij3W7tJ5TMjG3
䷩ 𝚕𝚒𝚗𝚎 2922
╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕
(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/09/06/leftover-links-06092023-university-of-michigan-admits-it-got-cracked-microsoft-tco/#comments
Gemini version at gemini://gemini.techrights.org/2023/09/06/leftover-links-06092023-university-of-michigan-admits-it-got-cracked-microsoft-tco/
⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.06.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧
Gemini_version_available_♊︎
✐ Leftover_Links_06/09/2023:University_of_Michigan_Admits_It_Got_Cracked
(Microsoft_TCO)⠀✐
Posted in Site_News at 1:01 pm by Dr. Roy Schestowitz
🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈
§ Contents⠀➾
* Leftovers
o Science
o Education
o Hardware
o Health/Nutrition/Agriculture
o Proprietary/Artificial_Intelligence_(AI)
o Security
# Integrity/Availability/Authenticity
# Privacy/Surveillance
o Defence/Aggression
o Environment
# Energy/Transportation
# Overpopulation
o Finance
o AstroTurf/Lobbying/Politics
o Censorship/Free_Speech
o Freedom_of_Information_/_Freedom_of_the_Press
o Civil_Rights/Policing
o Internet_Policy/Net_Neutrality
o Monopolies
# Patents
# Trademarks
# Copyrights
* § Leftovers⠀➾
o ⚓ Chris Coyier ☛ $38,000⠀⇛
That’s what WordPress.com is asking for web hosting,
domain ownership, and support for a hundred years. They
are essentially saying they’ll be helping your anointed
heir with the /wp-admin/ password after you die.
o ⚓ CoryDoctorow ☛ Pluralistic:_Naomi_Klein’s_“Doppelganger”_(05
September_2023)⠀⇛
Wolf’s politics were always more Sheryl Sandberg than
bell hooks (or Emma Goldman). While Klein talked about
capitalism and class and solidarity, Wolf wanted to
“empower” individual women to thrive in a market system
that would always produce millions of losers for every
winner. Fundamentally: Klein is a leftist, Wolf was a
liberal.
o § Science⠀➾
# ⚓ Hackaday ☛ Electro-Optical_Control_Of_Lasers_With_A
Licorice_Twist⠀⇛
You’ve got to hand it to [Les Wright]; he really
knows how to dig into optical arcana and present
topics in an interesting way. Case in point: an
electro-optical control cell that’s powered by
ouzo.
o § Education⠀➾
# ⚓ Futurism ☛ Professor_Caught_Using_ChatGPT_When_Scientific
Paper_Was_Full_of_Errors⠀⇛
As Retraction Watch reports, Natural History Museum
of Denmark myriapodologist Henrik Enghoff suspected
the authors of the paper from China and Africa used
OpenAI’s ChatGPT to dig up academic references —
and as it turns out, his hunch was right.
The offending paper was initially taken down by
Preprints.org, a preprint archive run by the
academic publisher MDPI, in June after Enghoff’s
colleague, the University of Copenhagen’s David
Richard Nash, notified editors of the errors.
Now, the paper has seemingly resurfaced online,
hallucinated references and all, on a different
preprint platform called Research Square.
# ⚓ Rlang ☛ Spatial_Data_Science_Using_R_in_Berlin,_Germany⠀⇛
The Berlin R User Group fosters a diverse and
vibrant R community in Berlin. Rafael Camargo
shared some insights from his experience regarding
the potential of R and some anecdotes for
organizers of RUGs. The Berlin RUG is currently
looking for sponsors to host their physical events,
and companies interested in hosting the group can
contact Rafael.
# ⚓ APNIC ☛ Event_Wrap:_National_Conference_on_Information
Technology⠀⇛
The event welcomed 200 participants to discuss the
theme: Enhancing National and Regional Economies
through Sustainable and Equitable Technology. View
the agenda for more information on the topics
discussed.
# ⚓ New York Times ☛ Americans_Are_Losing_Faith_in_the_Value_of
College._Whose_Fault_Is_That?⠀⇛
A decade later, Americans’ feelings about higher
education have turned sharply negative. The
percentage of young adults who said that a college
degree is very important fell to 41 percent from 74
percent. Only about a third of Americans now say
they have a lot of confidence in higher education.
Among young Americans in Generation Z, 45 percent
say that a high school diploma is all you need
today to “ensure financial security.” And in
contrast to the college-focused parents of a decade
ago, now almost half of American parents say they’d
prefer that their children not enroll in a four-
year college.
# ⚓ Pro Publica ☛ Idaho_Created_a_$25M_Fund_to_Fix_Schools._Why
Is_Nobody_Using_It?⠀⇛
As a member of the school board in the remote
Central Idaho town of Salmon, Josh Tolman worried
that an earthquake would turn the elementary and
middle schools to rubble. The foundations of the
schools were crumbling. The floors buckled. The
district canceled school whenever a few inches of
snow fell for fear the roofs would cave in.
But Tolman and the school district were in a bind:
They couldn’t convince enough voters to support a
tax increase that would allow the district to build
a new facility. The school board ran six bond
elections in seven years. But even though 53% of
the community supported the bond in one of their
first attempts in 2006, it wasn’t enough. Idaho is
one of two states that require two-thirds of voters
to support a bond for it to pass.
o § Hardware⠀➾
# ⚓ Silicon Angle ☛ Huawei’s_latest_smartphone_showcases
China’s_chip_manufacturing_breakthrough⠀⇛
Huawei Technologies Co. Ltd. has teamed up with
China’s leading chipmaking firm, Semiconductor
Manufacturing International Corp., to build an
advanced, seven-nanometer processor that sits at
the heart of its latest flagship smartphone.
# ⚓ Tom’s Hardware ☛ U.S._Aims_to_‘Choke’_China’s_Military
Advances_with_Chip_Sanctions⠀⇛
U.S. denies China advanced supercomputer chip
exports amid military concerns.
# ⚓ Techdirt ☛ Foxconn’s_Shriveled_Wisconsin_Subsidy_Scam
Stumbles_Forth_With_Sale_Of_Two_Key_Buildings⠀⇛
In 2017 the Wisconsin GOP, with Donald Trump and
Paul Ryan at the head of the parade, struck what
they claimed was an incredible deal with Foxconn to
bring thousands of high paying jobs to the state.
The project, which Trump dubbed the “the eighth
wonder of the world,” provided the former president
with several years’ worth of endless free marketing
for his “job creation” skills.
# ⚓ Hackaday ☛ Clean_Up_Your_Resin-Printing_Rinse_With
Dialysis⠀⇛
There’s a lot to like about resin 3D printing. The
detail, the smooth surface finish, the mechanical
simplicity of the printer itself compared to an FDM
printer. But there are downsides, too, not least of
which is the toxic waste that resin printing
generates. What’s one to do with all that resin-
tainted alcohol left over from curing prints?
# ⚓ Hackaday ☛ Finally,_A_Machine_To_Organize_Resistors!⠀⇛
Perhaps it’s a side-effect of getting older, but it
seems like reading the color bands on blue metal-
film resistors is harder than it was on the old
brown carbon ones. So often the multimeter has to
come out to check, but it’s annoying. Thus we
rather like [Mike]’s Resistorganizer, which
automates the process of keeping track of the
components.
# ⚓ Hackaday ☛ Spooky_Noise_Box_Has_Post-Halloween_Potential⠀⇛
There’s more than one way to scare people on
Halloween. Sure, there’s always the low-brow jump
scare, but that will generally just annoy the
person and possibly cause a heart attack. No, what
you need is a sustained soundscape of hellish
audio. And where does one find hellish audio? Well,
you make your own with a spooky-sounds noise box.
# ⚓ CNX Software ☛ Using_SenseCAP_T1000_LoRaWAN_GPS_Tracker_for
cattle_tracking⠀⇛
SenseCAP T1000 is a credit-size GPS tracker using
LoRaWAN low-power long-range connectivity. Smart
Agriculture is one specific application that can
leverage IoT and LoRaWAN to analyze and manage
soil, crops, and water, but also to track the
location of livestock. This is an important aspect
of farming, and we’ll use the SenseCAP T1000
LoRaWAN GPS tracker to track cattle in this
article/review. SenseCAP T1000 unboxing The package
contains the SenseCAP T1000 GPS Tracker device,
which is about the size of a credit card, and a
charging cable.
# ⚓ Ruben Schade ☛ Another_Am386_30-pin_SIMM_replacement⠀⇛
I’ve been messing with some shadow memory settings
on my working Am386 machine again, but in the
process it exposed another memory issue. I think.
Get it, because it’s about memory, and I’m feigning
memory loss about a… shaddup.
View_all_posts_about_my_Am386_machine
Uncovering another flaky SIMM was a relief in a
way, because it exposed some instability and errant
behavior I’d been experiencing of late. Drivers and
TSRs would fail to load for no reason, and Windows
3.1 bluescreened with even more regularity than I
remembered.
I used MemTest86 to track down the failed module,
and tried my best to save it with more isopropyl
alcohol and contact cleaner, but I think it was a
gone. I’ve put it in my small drawer of dubious
computer parts for a future time when I might have
more skills to fix things. It joins the other
module I removed in July:
# ⚓ Alan Pope ☛ Alan_Pope:_Every_cellphone_I_have_owned⠀⇛
Time for a listicle!
# ⚓ Tom’s Hardware ☛ TSMC’s_Troubled_Arizona_Fab_Gets_Vote_of
Confidence_From_AMD⠀⇛
AMD set to use TSMC’s Arizona fab despite delays as
it needs geographic diversity.
# ⚓ Jeff Geerling ☛ Testing_10_GbE_throughput_on_Windows_–
iperf3_is_outdated [Ed: Microsoft is technically behind]⠀⇛
Recently I upgraded_my_AMD-based_PC on a
livestream, and I installed an Innodisk_EGPL-T101
10_Gbps_M.2_NIC (link_to_Innodisk_product_page).
Under Linux, I could get through 9.4 Gbps using
iperf3 between the PC and my Mac Studio. But under
Windows, I could only get up to about 4.5 Gbps
(tested around 1h_27m_into_the_stream)!
# ⚓ Intel_Foundry_Services_and_Tower_Semiconductor_Announce_New
US_Foundry_Agreement⠀⇛
Intel Foundry Services (IFS) and Tower
Semiconductor (Nasdaq: TSEM), a leading foundry for
analog semiconductor solutions, today announced an
agreement where Intel will provide foundry services
and 300mm manufacturing capacity to help Tower
serve its customers globally. Under the agreement,
Tower will utilize Intel’s advanced manufacturing
facility in New Mexico. Tower will invest up to
$300 million to acquire and own equipment and other
fixed assets to be installed in the New Mexico
facility, providing a new capacity corridor of over
600,000 photo layers per month for Tower’s future
growth, enabling capacity to support forecasted
customer demand for 300mm advanced analog
processing.
o § Health/Nutrition/Agriculture⠀➾
# ⚓ The Straits Times ☛ Japan_to_WTO:_China’s_Fukushima-related
seafood_ban_‘totally_unacceptable’⠀⇛
Tokyo also urged Beijing to immediately repeal the
action.
# ⚓ University of Michigan ☛ You’re_probably_eating_enough
protein⠀⇛
This past July, the term “cottage cheese” reached a
19-year high in Google search interest. While some
people simply spread it on bread, others throw it
into a blender with fruit and honey and call it ice
cream. The versatility of cottage cheese was
highlighted by TikTok’s recent obsession with this
supermarket staple.
# ⚓ Reason ☛ The_University_of_Michigan_Will_Force_Students
With_COVID_To_Leave_Campus⠀⇛
A likely consequence: Sick students will avoid
going to the university hospital.
# ⚓ University of Michigan ☛ Study_shows_forced_sexual
intercourse_rates_rose_during_pandemic⠀⇛
The rate of forced intercourse in early adulthood
rose during the COVID-19 pandemic, leading to a
potential increase in unintended pregnancies and
other sexual, reproductive and mental health
problems.
# ⚓ Off Guardian ☛ Fauci_just_admitted_masks_don’t_work…but
why?⠀⇛
A few days ago former White House chief medical
adviser Dr Anthony Fauci admitted the evidence
supporting mask mandates was weak. Why would he do
this as they appear to be gearing up Pandemic 2.0?
Is it a sign Fauci is going to be made a scapegoat?
Or is something else going on?
# ⚓ Gregory Hammond ☛ My_realistic,_not_training_guide_to
walking_5_km⠀⇛
Running is not just about training, or following
the advice of those who have done long races, or
not run at all. You can’t do a long distance
without working your way up to it. You need to be
comfortable and safe, and have the time to get out.
It’s ok to somewhat plan your route and not go the
entire distance. You may need to remember things to
bring and have a backup plan. Know why you are
doing this, and when you should see a licensed
expert.
# ⚓ Mexico News Daily ☛ Voces_de_Guiraa’:_Giving_disabled
children_a_voice⠀⇛
Viridiana Pacheco, a young, speech therapist set up
the foundation Voces de Guiraa’ with the support of
two expats back in 2017 in Oaxaca.
# ⚓ Techdirt ☛ Yet_Another_Study_Shows_No_Link_At_All_Between
Social_Media_And_Teen_Anxiety_And_Depression⠀⇛
I know that we’ve already pointed to a whole bunch
of studies, using a variety of different methods
that all show no evidence of any link at all
between social media and teen depression, but it’s
time to highlight another one.
# ⚓ Reason ☛ Rescheduling_Marijuana_Would_Leave_Federal
Prohibition_Essentially_Untouched⠀⇛
Although the HHS-recommended change would benefit
researchers and the cannabis industry, it would not
resolve the conflict between state and federal
marijuana laws.
o § Proprietary/Artificial Intelligence (AI)⠀➾
# ⚓ WinBuzzer ☛ Gizmodo_Replaces_Spanish_Staff_with_AI
Translation [Ed: Machine translations are decades old; now
they just add buzzwords to cause a panic.]⠀⇛
# ⚓ Futurism ☛ Gannett_Sports_Writer_on_Botched_AI-Generated
Sports_Articles:_“Embarrassing”⠀⇛
For young athletes, there are few moments as
exciting as when they first see their name in the
newspaper — preferably for a goal scored, or a save
made, and extra points if a local reporter asks for
a quote.
That dynamic is now on the line at Gannett, the
publisher of USA Today and many other regional
newspapers, where it was forced to pause the
publication of abysmally low quality AI-generated
articles about high school sports.
We were curious: how would a sports writer at a
Gannett publication feel about the AI articles? So
we asked one, though we’re keeping them anonymous
and not sharing which newsroom they work at to
protect their job.
# ⚓ Digital Music News ☛ Queen’s_Brian_May_Goes_Full_Dystopian
on_AI⠀⇛
Queen’s Brian May becomes the latest musician to
voice concerns over generative AI and the future of
the music industry: “We might look back on 2023 as
the last year when humans really dominated the
music scene.”
In a recent interview with Guitar Player, Queen’s
Brian May admitted his apprehension about potential
authorship issues as society strides forth into the
era of generative AI. The seasoned musician is also
a scientist with a Ph.D. in astrophysics from
Imperial College London — so he acknowledges that
AI will bring great benefit, especially its
capacity for problem-solving. But May believes we
will soon see more implications generative AI
creates for the music industry.
# ⚓ The Register UK ☛ You_patched_yet?_Years-old_Microsoft
security_holes_still_hot_targets_for_cyber-crooks⠀⇛
It’s generally accepted that security flaws in
Microsoft’s products are a top magnet for crooks
and fraudsters: its sprawling empire of hardware
and software is a target-rich ecosystem in that
there is a wide range of bugs to exploit, and a
huge number of vulnerable organizations and users.
And so we can believe it when Qualys yesterday said
15 of the 20 most-exploited software
vulnerabilities it has observed are in Microsoft’s
code.
# ⚓ Krebs On Security ☛ Experts_Fear_Crooks_are_Cracking_Keys
Stolen_in_LastPass_Breach⠀⇛
In November 2022, the password manager service
LastPass disclosed a breach in which hackers stole
password vaults containing both encrypted and
plaintext data for more than 25 million users.
Since then, a steady trickle of six-figure
cryptocurrency heists targeting security-conscious
people throughout the tech industry has led some
security experts to conclude that crooks likely
have succeeded at cracking open some of the stolen
LastPass vaults.
# ⚓ Wladimir Palant ☛ A_year_after_the_disastrous_breach,
LastPass_has_not_improved⠀⇛
In September last year, a breach at LastPass’
parent company GoTo (formerly LogMeIn) culminated
in attackers siphoning out all data from their
servers. The criticism from the security community
has been massive. This was not so much because of
the breach itself, such things happen, but because
of the many obvious ways in which LastPass made
matters worse: taking months to notify users,
failing to provide useful mitigation instructions,
downplaying the severity of the attack, ignoring
technical issues which have been publicized years
ago and made the attackers’ job much easier. The
list goes on.
Now this has been almost a year ago. LastPass
promised to improve, both as far as their
communication goes and on the technical side of
things. So let’s take a look at whether they
managed to deliver.
TL;DR: They didn’t. So far I failed to find
evidence of any improvements whatsoever.
# ⚓ Security Week ☛ Norfolk_Southern_Says_a_Software_Defect_—
Not_a_Hacker_—_Forced_It_to_Park_Its_Trains_This_Week⠀⇛
Norfolk Southern believes a software defect — not a
hacker — was the cause of the widespread computer
outage that forced the railroad to park all of its
trains for most of a day earlier this week.
# ⚓ Tedium ☛ Art_Fights_Back⠀⇛
A comic artist took a journalistic dive into the
knotty debates around generative AI—and found
artists worried about the people even more than the
tech.
# ⚓ The Register UK ☛ The_Anti_Defamation_League_is_Musk’s
latest_excuse_for_Twitter’s_tanking_ad_revenue⠀⇛
In December, the ADL said it noticed an increase in
antisemitic content on the social network, as well
as the “return of extremists of all kinds to the
platform [that] has the potential to supercharge
the spread of extremist content.” The ADL further
noted the return of what it said were “extremists
and conspiracy theorists” emboldened by Twitter’s
content amnesty policies, and further alleged that
X wasn’t enforcing its own rules against
antisemetic content.
# ⚓ Reason ☛ ‘Free_Speech_Absolutist’_Elon_Musk_Threatens_Anti-
Defamation_League_With_Defamation_Lawsuit⠀⇛
Plus: The doubling of the deficit, young Americans
souring on college, and more…
# ⚓ Techdirt ☛ Hey_Elon:_The_ADL_Convincing_Advertisers_To_Run
Away_From_Your_Site_Is_Part_Of_The_Free_Speech_You_Pretend_To
Support⠀⇛
Not this shit again.
# ⚓ Vice Media Group ☛ Twitter_Users_Are_Warning_Each_Other
About_Its_Junk_Ads_With_Community_Notes⠀⇛
Users are warning each other about misleading ads
on Twitter as Musk lashes out over declining
revenue.
# ⚓ Vice Media Group ☛ Musk_Melts_Down_Over_Ad_Revenue,
Amplifies_Conspiracies,_Threatens_Lawsuit_In_Typical
Weekend⠀⇛
A weekend meltdown full of conspiracies and threats
is now a routine occurrence for the billionaire
Twitter owner.
# ⚓ CCIA ☛ New_Research:_Hate_Speech_Hurts_Social_Media_Sites,
Brands,_and_the_Digital_Economy⠀⇛
U.S. policymakers are increasingly considering
“must-carry” laws for the internet, which would
require digital intermediaries…
# ⚓ Neowin ☛ Zoom’s_CEO_thinks_the_US_government_should_look
into_Microsoft’s_bundling_of_Teams⠀⇛
Last week, Microsoft announced it would offer its
Teams online conferencing and collaboration service
as a stand-alone product in much of Europe starting
on October 1. This was in response to the European
Commission’s announcement that it was launching an
investigation into whether or not Microsoft’s
bundling of Teams with Microsoft 365 was an anti-
competitive move.
Now, the head of the company that offers a
competing product to Teams believes that a similar
investigation should happen in the US as well.
Bloomberg reports that Zoom CEO Eric Yuan, during a
presentation at the Goldman Sachs Communacopia +
Technology Conference, was asked about Microsoft
breaking off Teams from Microsoft 365 in Europe.
Yuan stated, “You should ask this question to the
FTC as well”.
# § Windows TCO⠀➾
# ⚓ University of Michigan ☛ U-M_requiring_password_reset
for_all_UMICH_(Level-1)_accounts⠀⇛
The University of Michigan has mandated that
passwords for all UMICH (Level-1) accounts be
rest by the end of Sept. 12.
o § Security⠀➾
# ⚓ OSTechNix ☛ How_To_Prevent_SSH_Brute_Force_Attacks_Using
Fail2ban_In_Linux⠀⇛
Linux is a popular operating system for servers and
other devices. It is known for its stability,
security, and flexibility. However, no operating
system is immune to attack. One of the most common
types of attacks against Linux servers is a brute-
force attack. In this step-by-step guide, we’ll
show you how to install and configure fail2ban on a
Linux system and how to prevent SSH brute force
attacks with Fail2ban.
# ⚓ Bruce Schneier ☛ Inconsistencies_in_the_Common
Vulnerability_Scoring_System_(CVSS)⠀⇛
Interesting research:
Shedding Light on CVSS Scoring
Inconsistencies: A User-Centric Study on
Evaluating Widespread Security
Vulnerabilities
Abstract: The Common Vulnerability
Scoring System (CVSS) is a popular method
for evaluating the severity of
vulnerabilities in vulnerability
management. In the evaluation process, a
numeric score between 0 and 10 is
calculated, 10 being the most severe
(critical) value. The goal of CVSS is to
provide comparable scores across
different evaluators. However, previous
works indicate that CVSS might not reach
this goal: If a vulnerability is
evaluated by several analysts, their
scores often differ. [...]
# ⚓ Security Week ☛ Developers_Warned_of_Malicious_PyPI,_NPM,
Ruby_Packages_Targeting_Macs⠀⇛
Malicious packages uploaded to PyPI, NPM, and Ruby
repositories are targeting macOS users with
information stealing malware.
# ⚓ Security Week ☛ United_Airlines_Says_the_Outage_That_Held
Up_Departing_Flights_Was_Not_a_Cybersecurity_Issue⠀⇛
United Airlines flights were halted nationwide on
Sept. 5, because of an “equipment outage,”
according to the FAA.
# ⚓ IT Wire ☛ Three_Australian_firms_latest_to_be_hit_by_Alphv
ransomware_gang⠀⇛
While Core_Desktop has not yet made any public
statement about the attacks, the ABC claimed to
have seen a letter sent by the company to its
clients saying it had become of the intrusion on 22
August.
The three companies that were attacked are
pathology services provider TissuPath, real estate
agent Barry Plant and strata management firm Strata
Plan.
# ⚓ Security Week ☛ 7_Million_Users_Possibly_Impacted_by
Freecycle_Data_Breach⠀⇛
Freecycle.org is prompting millions of users to
reset their passwords after their credentials were
compromised in a data breach.
# ⚓ Security Week ☛ 9_Vulnerabilities_Patched_in_SEL_Power
System_Management_Products⠀⇛
Nine vulnerabilities patched in SEL electric power
management products, adding to the 19 other flaws
fixed earlier this year.
# § Integrity/Availability/Authenticity⠀➾
# ⚓ Cendyne Naga ☛ Breaking_Into_Secure_Facilities_With
OSDP⠀⇛
Facilities like hospitals, banks, data
centers, airports, power and natural gas
plants, and government institutions secure
their properties with authorization hardware
built to use the Open Supervised Device
Protocol (OSDP). Unfortunately, there are
both design weaknesses and poor practices
which can be realistically exploited in the
real world. OSDP advertises itself as an
encrypted protocol, yet many installations
use unencrypted modes. While it has defenses
against trivial replay attacks, it has such a
small counter inside that with enough samples
one could replay communications on the wire.
It also uses a truncated Message
Authentication Code (MAC), which exposes OSDP
systems to brute-force attacks. And lastly,
OSDP is by design easy to misuse: installers
can leave the controller perpetually in
“install” mode which allows any device to ask
for secret credentials for another device
without any encryption on a shared
communication line.
# ⚓ David Rosenthal ☛ Microsoft_Keys⠀⇛
Below the fold I update this sorry state of
affairs, which I first started cataloging a
decade ago.
The technology used to secure Internet
communication, for example via TLS, the basis
for the HTTPS protocol, and for protecting
the software supply chain, is based on public
key encryption. For example, to start an
HTTPS connection between Alice and Bob using
Diffie-Hellman-Merkle key exchange, they each
use their private key and the other’s public
key to compute aa shared secret key used to
encrypt the communication.
# § Privacy/Surveillance⠀➾
# ⚓ The Register UK ☛ Mozilla_calls_cars_from_25
automakers_‘data_privacy_nightmares_on_wheels’⠀⇛
The foundation, the Firefox browser maker’s
netizen-rights org, assessed the privacy
policies and practices of 25 automakers and
found all failed its consumer privacy tests
and thereby earned its Privacy Not Included
(PNI) warning label.
In research published Tuesday, the org warned
that car manufacturers may collect and
commercially exploit much more than location
history, driving habits, in-car browser
histories, and music preferences. Instead,
some makers may handle deeply personal data,
such as – depending on the privacy policy –
sexual activity, immigration status, race,
facial expressions, weight, health, and even
genetic information, the Mozilla team found.
# ⚓ [Repeat] OpenRightsGroup ☛ Online_Safety_Bill:_US_and
UK_campaigners_warn_of_dangers_of_age_verification⠀⇛
“The Online Safety Bill could present
websites like Wikipedia, Tik Tok and Twitter
with the choice of blocking content to ensure
their platforms are suitable for children or
forcing users to verify their age. The first
would lead to a huge restriction in the
content we can all see, create and share. The
second would pose a threat to our privacy and
security.
“Keeping children safe online is a worthy
goal but we need to ensure that we do not
restrict children’s right to information by
banning them from large swathes of the
[Internet], or expose them to intrusive age
assurance.
# ⚓ Sedishj Authority for Privacy Protection ☛
Administrative_fine_of_SEK_35_million_against_Trygg-
Hansa⠀⇛
Trygg-Hansa’s security flaws have meant that
information about 650,000 customers has been
accessible to unauthorized persons via the
internet. The Swedish Authority for Privacy
Protection (IMY) is now issuing an
administrative fine of SEK 35 million against
the company.
# ⚓ EFF ☛ Montana’s_New_Genetic_Privacy_Law_Caps_Off_Ten
Years_of_Innovative_State_Privacy_Protections⠀⇛
2013 is a good starting point for this story.
That year, Montana passed a law requiring
police to get a warrant before they could
obtain location information generated by
electronic devices. At the time, there were
no state or federal laws that explicitly
protected this data. And the police were
already getting and using location data in
thousands of criminal cases across the
country every year.
Montana’s straightforward law went into
effect two and a half years before
California’s landmark privacy law, CalECPA,
codified similar protections for location
data—and five years before the Supreme Court,
in Carpenter v. United States, explicitly
recognized the Fourth Amendment requires a
warrant for access to cell site location
information.
Montana may have only a little more than a
million residents, but since 2013, it has
passed a significant number of other
important privacy laws. These run the gamut
from prohibiting government face surveillance
and limiting face recognition, to providing
Montana consumers with explicit privacy
rights in their online data and preventing
energy utilities from selling or sharing
individual advanced meter energy data without
consumer consent. In 2021, Montana expressly
restricted familial searches of government-
maintained DNA databases and became one of
only two states to require a warrant to
search consumer DNA databases like genetic
genealogy sites. Also in 2021, Montana
residents overwhelmingly supported (by 80%) a
constitutional amendment that added
electronic data and communications to the
state constitution’s search and seizure
protections.
# ⚓ EFF ☛ Digital_Rights_Updates_with_EFFector_35.11⠀⇛
Learn more about all of the latest news by
reading the full newsletter here, or you can
listen to the audio version below!
# ⚓ Techdirt ☛ Techdirt_Podcast_Episode_364:_Thinking
About_Decentralization⠀⇛
We’ve got a another cross-post episode for
you this week, on a subject near and dear to
our hearts: protocols over platforms, and
restoring decentralization online. Mike
recently joined Danny O’Brien on the DWeb
Decoded podcast to talk all about these
topics, as well as tell a little story about
Danny’s role in the founding of Techdirt, and
you can listen to the whole conversation here
on this week’s episode.
# ⚓ Techdirt ☛ Apple_Irritates_Interest_Groups,_Law
Enforcement_With_Its_(Reasonable)_Refusal_To_Restart
Its_Client-Side_Scanning_Program⠀⇛
After years of irritating the DOJ with its
refusal to compromise encryption, Apple
suddenly went the other way after receiving
criticism over its perceived inability to
stop the distribution of CSAM (child sexual
abuse material) via its devices and services.
# ⚓ Techdirt ☛ NYPD’s_New_Labor_Day_Tradition_Involves
Drone_Surveillance_Of_People’s_Private_Parties_And
Property⠀⇛
Never let it be said the NYPD doesn’t know
how to have a good time. The question remains
as to whether it’s possible for the NYPD to
allow others to have a good time.
o § Defence/Aggression⠀➾
# ⚓ Federal News Network ☛ Vice_President_Harris_will_face
doubts_and_dysfunction_at_the_Southeast_Asian_nations
summit⠀⇛
Vice President Kamala Harris has left Washington
for Indonesia, where she’ll attend the Association
of Southeast Asian Nations summit. President Joe
Biden decided to skip the event. The White House
says Harris will demonstrate American commitment to
Southeast Asia on her fourth trip to Asia since
taking office. Harris’ plane left Washington on
Monday morning. Southeast Asia has been a focal
point of competition between the United States and
China. The summit is not expected to resolve
longstanding issues such as the military coup in
Myanmar or territorial disputes in the South China
Sea.
# ⚓ France24 ☛ Myanmar_crisis,_South_China_Sea_headline_ASEAN
summit_in_Indonesia⠀⇛
Southeast Asian leaders met in Indonesia on Tuesday
to seek a united voice on the years-long Myanmar
crisis and tackle rifts over China’s growing
assertiveness in the South China Sea.
# ⚓ India Times ☛ TikTok’s_Irish_data_centre_up_and_running_as
European_privacy_project_gets_under_way⠀⇛
TikTok has been under scrutiny by European and
American regulators over concerns that sensitive
user data may end up in China. TikTok is owned by
ByteDance, a Chinese company that moved its
headquarters to Singapore in 2020.
# ⚓ The Atlantic ☛ How_American_Democracy_Fell_So_Far_Behind⠀⇛
Despite its flaws, the U.S. Constitution was a
pioneering document. America became the first large
nation to rule itself without a monarchy and
instead fill its most important political offices
via regular elections. Over the next century, the
American Constitution served as a model for
republican and democratic-minded reformers across
the world.
The United States no longer seems like a good model
today. Since 2016, America has experienced what
political scientists call “democratic backsliding.”
The country has seen a surge in political violence;
threats against election workers; efforts to make
voting harder; and a campaign by the then-president
to overturn the results of an election—hallmarks of
a democracy in distress. Organizations that track
the health of democracies around the world have
captured this problem in numerical terms. Freedom
House’s Global Freedom Index gives countries a
score from 0 to 100 each year; 100 indicates the
most democratic. In 2015, the United States
received a score of 90, roughly in line with
countries such as Canada, France, Germany, and
Japan. But since then, America’s score has declined
steadily, reaching 83 in 2021. Not only was that
score lower than every established democracy in
Western Europe; it was lower than new or
historically troubled democracies such as
Argentina, the Czech Republic, Lithuania, and
Taiwan.
# ⚓ JURIST ☛ Sweden_oil_executives_face_landmark_trial_over
alleged_Sudan_war_crimes⠀⇛
Schneiter and Lundin are charged with “complicity
in grave war crimes.” In November 2021, Swedish
prosecutors indicted Lundin and Schneiter for
Lundin Oil’s operations in Sudan from 1999 to 2003.
Lundin Energy calls the charges “impossible and
grossly inaccurate.” The defendants also vehemently
deny any wrongdoing. Prosecutors allege that Lundin
Oil was complicit in war crimes committed by the
government of Sudan while the company operated oil
fields in Sudan.
# ⚓ EDRI ☛ Digital_Sovereignty_Conference⠀⇛
Join Disco Slovenia for an electrifying event that
brings together passionate activists, legal experts
and engineers who understand the significance of
owning the means of digital production. Only
through empowered control and ownership over
technology, data, and infrastructure can we truly
attain independence and wield influence over the
course of our digital future!
# ⚓ France24 ☛ Dozens_of_schoolgirls_sent_home_for_flouting
France’s_new_ban_on_Muslim_abayas⠀⇛
Attal said the girls refused entry were given a
letter addressed to their families saying that
“secularism is not a constraint, it is a liberty”.
If they showed up at school again wearing the dress
there would be a “new dialogue”, the minister said.
# ⚓ Democracy Now ☛ Racist_Shootings_“Don’t_Happen_in_a
Vacuum”:_Bishop_Barber_on_DeSantis,_Trump_&_Those_Who_Spread
Hate⠀⇛
As federal law enforcement opens an investigation
into the Jacksonville, Florida, shooting where a
white gunman killed three Black people at a Dollar
General as a possible hate crime and act of
domestic violent extremism, we speak with civil
rights leader Bishop William Barber about the
increasing number of racist attacks in America
fueled by racism. “There is this history of not
just who kills, but what kills and what creates the
atmosphere,” says Barber, who calls for a political
movement of love to force out hateful politicians.
Barber specifically condemns the Republican Party
and Florida Governor Ron DeSantis for attacking
cultural issues as a distraction for policy
failures. “The racist rhetoric and the culture wars
and the hatred toward women, the hatred toward
immigrants, the hatred toward the trans community
is a form of deflection,” says Barber. “He’s
decided that this is his way to office:
distraction, division, deflection, focusing on
culture wars so that he cannot be labeled as a
failed governor.”
# ⚓ Democracy Now ☛ “Doing_Harm”:_Roy_Eidelson_on_the_American
Psychological_Association’s_Embrace_of_U.S._Torture_Program⠀⇛
A military judge at Guantánamo has thrown out the
confessions of Saudi man Abd al-Rahim al-Nashiri
because he had been tortured and waterboarded at
secret CIA black sites in Afghanistan, Thailand,
Poland, Romania and Morocco before being sent to
Guantánamo. Psychologists James Mitchell and John
Bruce Jessen, who were paid at least $81 million by
the CIA to develop and then implement the CIA’s
post-9/11 torture program, had waterboarded al-
Nashiri at a CIA black site. We get response from
Roy Eidelson and discuss his new book, Doing Harm,
which investigates the American Psychological
Association’s complicity in post-9/11 torture
programs and the struggle to reform the psychology
field. “We felt there was a lot at stake,” says
Eidelson. “It took over a decade for us to bring
change in terms of APA’s policy toward
interrogation and detention operations.” As the
U.N. calls for al-Nashiri’s release, Eidelson warns
that APA leadership and military personnel are once
again pushing guidelines that expand psychologists’
role in torture. “They want to expand the
opportunities that are available for psychologists
to work in this arena where ‘do no harm’ is, at
best, secondary, and sometimes off the table
entirely,” says Eidelson. “It feels as though APA
is slipping — slipping back into positions that led
to awful things.”
# ⚓ JURIST ☛ Sweden_oil_executives_face_landmark_trial_over
alleged_Sudan_war_crimes⠀⇛
Executives of Lundin Oil (now Orrön Energy) Ian
Lundin and Alex Schneiter’s criminal trial for
alleged war crimes in Sudan began on Tuesday.
Schneiter and Lundin are charged with “complicity
in grave war crimes.” In November 2021, Swedish
prosecutors indicted Lundin and Schneiter for
Lundin Oil’s operations in Sudan from 1999 to 2003.
# ⚓ Hong Kong Free Press ☛ Taiwan_president_heads_to_last
African_ally_Eswatini⠀⇛
President Tsai Ing-wen headed to Eswatini on
Tuesday to cement ties with Taiwan’s only
diplomatic ally in Africa, as China intensifies
political pressure on the island. In a pre-
departure speech, Tsai acknowledged support from
Eswatini in the face of “many international
challenges such as the expansion of
authoritarianism” in recent years.
# ⚓ RFERL ☛ Kyrgyz_Border-Deal_Detainees_Say_Cell_Transfers
Amount_To_Torture⠀⇛
Opposition politicians who are among dozens of
members of the Kempir-Abad Defense Committee placed
in pretrial detention last year following protests
against Kyrgyzstan’s decision to cede water
supplies to Uzbekistan have said they are facing
pressure in custody that amounts to torture.
# ⚓ RFERL ☛ War_Crimes_Trial_Opens_For_Bosnian_Serbs_Accused_Of
Rapes,_Torture_At_Prison_Camps_During_1992-95_War⠀⇛
The war crimes trial of three men accused of
abusing non-Serb citizens in prison camps during
the Bosnian War opened on September 5 in Bosnia-
Herzegovina.
# ⚓ RFA ☛ Junta_troops_detain_more_than_70_civilians_in
Myanmar’s_Mandalay_region⠀⇛
Soldiers tortured them and used them as human
shields.
# ⚓ ADF ☛ In_Eritrea,_China_and_Russia_Seek_Red_Sea_Dominance⠀⇛
Sometimes called a hermit state, Eritrea is one of
the most diplomatically isolated countries in the
world. A history of repression, human rights abuses
and conflict with neighboring countries has left it
with few allies on the world stage.
# ⚓ New York Times ☛ This_is_how_military_service_is_sold_on
Russian_TV.⠀⇛
# ⚓ Mint Press News ☛ When_the_Torturer_is_the_Savior:_Can
BRICS_Help_Us_Escape_the_West’s_Hegemony_and
Contradictions?⠀⇛
At the zenith of the mass protests in Egypt on
January 25, 2011, Twitter, Facebook and other
Western-based social media platforms appeared to be
the most essential tools for the Egyptian
Revolution.
# ⚓ New York Times ☛ Earthquake_sensors_are_helping_document
Russian_bombings_in_new_detail.⠀⇛
# ⚓ RFERL ☛ Russian_Mathematician_Held_In_Custody_On_New
Charges_Of_Justifying_Terrorism⠀⇛
A Russian Court decided to detain mathematician
Azat Miftakhov until November 3 on new charges of
justifying terrorism
# ⚓ RFERL ☛ Saudi_Arabia,_Russia_Extend_Oil_Cuts_Through
December⠀⇛
Saudi Arabia and Russia on September 5 said they
would extend voluntary oil cuts until the end of
the year, continuing their campaign to bolster
prices.
# ⚓ LRT ☛ Abducted_child_returned_from_Russia_to_Lithuania⠀⇛
A girl abducted and unlawfully taken to Russia’s
Kaliningrad by her father has been returned to
Lithuania, the National Crisis Management Centre
(NKVC) has confirmed.
# ⚓ France24 ☛ Fatal_stabbing_of_Gabonese_student_highlights
‘daily’_racism_faced_by_Africans_in_Russia⠀⇛
François Ndzhelassili, a doctoral student from
Gabon at the Ural Federal University in
Yekaterinburg, Russia, was killed on August 18 by a
group of Russian men after they harassed him and
called him racial slurs. The murder is just the
latest case of discrimination and violence against
Black people living in Russia despite ongoing
initiatives meant to encourage Africans to study in
the country.
# ⚓ Defence Web ☛ Presidency_publishes_Lady_R_report_summary
but_new_questions_arise_over_UAE_involvement⠀⇛
<
The South African Presidency has published the
long-awaited executive summary of the report
looking into the arrival of the Lady R cargo vessel
in Simon’s Town more than nine months ago,
concluding no weapons were loaded for Russia.
However, questions remain over what was delivered
by the Russian vessel, and from which country.
# ⚓ Latvia ☛ State_defense_concept_adopted_in_Latvia⠀⇛
Defense is likely to receive funding equivalent
to 3% of gross domestic product next year, Defense
Minister Ināra Murniece (National Alliance) said in
a press briefing on Tuesday, September 5. It is
also planned to further increase the strength of
the National Armed Forces (NBS) and to expand the
presence of NATO troops in Latvia.
# § Russia, Belarus, and War in Ukraine⠀➾
# ⚓ AntiWar ☛ Is_CIA_Director_Bill_Burns_a_Biden_Yes-Man,
a_Putin_Apologist,_or_a_Peacemaker?⠀⇛
Lost in a chaotic hall of mirrors of its own
creation, the CIA has generally failed in its
one and only legitimate task, to provide U.S.
policymakers with accurate intelligence about
the world beyond the Washington echo-chamber
to inform U.S. decision-making.
# ⚓ Meduza ☛ Putin_says_‘Western_managers_put_an_ethnic
Jew_in_charge_of_Ukraine’_to_mask_its_‘anti-human
nature’_—_Meduza⠀⇛
# ⚓ Atlantic Council ☛ Ukraine’s_long_and_sordid_history
of_treason⠀⇛
# ⚓ Atlantic Council ☛ Removal_of_defense_minister_shows
wartime_Ukraine_is_changing⠀⇛
The removal of Ukrainian Defense Minister
Oleksii Reznikov in early September came
following a series of minor but damaging
corruption scandals and signaled a zero
tolerance approach to graft in wartime
Ukraine, writes Melinda Haring.
# ⚓ Meduza ☛ ‘Even_the_SS_troops_didn’t_consider_it
possible’_Putin_says_‘local_nationalists_and_anti-
Semites’_killed_1.5_million_Jews_in_Ukraine_during_WWII
—_Meduza⠀⇛
# ⚓ Meduza ☛ Russia’s_‘post-imperial_syndrome’_A
scholar’s_essay_on_the_myths_of_Kremlin_propaganda
leads_to_dismissal,_a_smear_campaign_from_critics,_and_
(attempted)_solidarity_from_colleagues_—_Meduza⠀⇛
# ⚓ Meduza ☛ Occupying_authorities_in_Zaporizhzhia_say
Russian_forces_‘tactically’_withdrew_from_village_of
Robotyne_—_Meduza⠀⇛
# ⚓ Meduza ☛ Purported_leaked_mobilization_order_calls
for_200K_new_Russian_conscripts._Government_officials
denounce_it_as_‘fake.’_—_Meduza⠀⇛
# ⚓ Meduza ☛ Erdogan_says_‘no_prospects_for_peace_on_the
horizon’_after_meeting_with_Putin_—_Meduza⠀⇛
# ⚓ Meduza ☛ Belarusian_diplomatic_missions_to_stop
issuing_passports_to_citizens_living_abroad_—_Meduza⠀⇛
# ⚓ Meduza ☛ Ukraine’s_Defense_Intelligence_vows_to_pay
$500K_to_Russian_helicopter_pilot_who_turned_his_Mi-
8_over_to_Ukraine_—_Meduza⠀⇛
# ⚓ Meduza ☛ Russian_mathematician_and_anarchist_Azat
Miftakhov_arrested_on_new_charges_immediately_after
release_from_prison_—_Meduza⠀⇛
# ⚓ Meduza ☛ Cuban_authorities_uncover_human_trafficking
network_recruiting_Cubans_living_in_Russia_to_fight_in
Ukraine_—_Meduza⠀⇛
# ⚓ Meduza ☛ Security_Service_of_Ukraine_indicts_oligarch
investment_banker_Mikhail_Fridman_for_financing
Russia’s_military-industrial_complex_—_Meduza⠀⇛
# ⚓ The Nation ☛ Advocates_for_Negotiations_to_End_the
Ukraine_War_Need_to_Come_Out_of_the_Closet⠀⇛
War is a great destroyer of audacious plans,
with dreams of quick victory often turning
into nightmarish quagmires. Vladimir Putin
learned this harsh lesson soon after
launching his criminal invasion of Ukraine in
February 2022. The Russian autocrat and many
of his political allies expected that the
attack would be a romp. Their underlying
premise was that Ukraine was not a real
nation, just a Western-created house of cards
waiting to be blown over by a strong show of
force by the Russian army.
# ⚓ LRT ☛ Belarus_to_stop_issuing_passports_at_embassies,
a_blow_to_émigré_opposition_–_media⠀⇛
Belarusian diplomatic missions will no longer
issue passports to citizens permanently
residing abroad, the independent online
newspaper Zerkalo has reported, a blow to the
Belarusian émigré communities.
# ⚓ RFERL ☛ Lukashenka_Orders_Belarusian_Embassies_To
Stop_Issuing_Passports⠀⇛
Belarusian authoritarian leader Alyaksandr
Lukashenka has ordered the country’s
embassies to stop issuing passports to
Belarusians living abroad.
# ⚓ Latvia ☛ Proposal_to_give_Russians_more_time_for
exams_advances_in_Saeima⠀⇛
The Saeima Defense, Internal Affairs and
Corruption Prevention Committee has decided
to direct amendments to the Immigration
Law, which will provide for the possibility
for Russian citizens living in Latvia to
apply for a temporary residence permit for a
period of two years during which the official
language exam has to be completed, for
viewing in the parliament, Latvian Radio
reported September 5.
# ⚓ New York Times ☛ Battlefield_Update:_The
entrenchments_Ukraine_is_encountering_are_‘not_as
strong,’_an_army_spokesman_says.⠀⇛
# ⚓ New York Times ☛ Cuba_Uncovers_a_Russian_Human
Trafficking_Ring_For_the_War_in_Ukraine⠀⇛
The Cuban government said it had begun
criminal proceedings against a “trafficking
network” that had been recruiting its
citizens in both Russia and Cuba for Russia’s
armed forces.
# ⚓ New York Times ☛ Graft_in_military_spending_becomes_a
headache_for_Ukraine.⠀⇛
The removal of Ukraine’s defense minister
highlights the enduring challenge of
corruption in Ukraine, which has emerged as a
rare area of criticism of President Volodymyr
Zelensky’s leadership.
# ⚓ New York Times ☛ Slovakia_Election_Could_Shift
Sentiment_in_a_Fierce_Ukraine_Ally⠀⇛
The vote in Slovakia this month will be a
test of European unity on Ukraine, and of
Russia’s efforts to undermine it. The front-
runner wants to halt arms shipments to Kyiv.
# ⚓ New York Times ☛ North_Korea_Finds_New_Leverage_in
the_Ukraine_War⠀⇛
Kim Jong-un is likely to seek missile and
warhead technology in an expected visit to
Russia, and he is already getting a public
embrace he has long sought.
# ⚓ New York Times ☛ Russia-Ukraine_War:_Ukraine_Seeks_to
Punch_2nd_Hole_in_Russian_Lines_in_South⠀⇛
Ukrainian forces have made it past more
Russian entrenchments in their campaign to
reach the Sea of Azov, but minefields and
more enemy troops lie ahead, analysts say.
# ⚓ New York Times ☛ Ukraine_Tries_to_Breach_Russian
Lines_in_Another_Patch_of_Territory⠀⇛
Ukrainian soldiers are trying to build on a
new breach in enemy lines, but the battle
will not be easy, military analysts said.
# ⚓ YLE ☛ Ukraine_accuses_Finnish_drinks_company_Hartwall
of_supporting_Russia’s_war⠀⇛
Ukraine’s anti-corruption agency added the US
multinational drinks company PepsiCo to a
boycott list at the beginning of this month.
Hartwall manufactures PepsiCo products in
Finland.
# ⚓ teleSUR ☛ Russia_Destroys_Drones_in_Kaluga_and_Moscow
Regions⠀⇛
Previously, Russian diplomat Zakharova warned
that Ukraine’s actions will not be left
unpunished.
# ⚓ RFERL ☛ Zelenskiy_Returns_From_Visits_With_Ukrainian
Brigades_Saying_Soldiers’_Requests_Will_Be_Addressed⠀⇛
Ukrainian President Volodymyr Zelenskiy has
returned to Kyiv after two days in eastern
and southern Ukraine for meetings with
commanders and Ukrainian troops to hear their
requests, which he said would be passed on to
top generals and other officials and
addressed.
# ⚓ RFERL ☛ Ukraine_War_Spurs_Jump_In_Use_Of_Cluster
Munitions,_Report_Shows⠀⇛
Attacks using cluster munitions by both
Russia and Ukraine since the start of the
Kremlin’s full-scale invasion last year have
helped lead to a “dramatic” increase in the
use of such weapons, highlighting the need
for more countries to join a global ban.
# ⚓ RFERL ☛ Ukrainian_Lawmakers_Approve_Defense
Minister’s_Resignation⠀⇛
Ukraine’s parliament has approved the
resignation of Defense Minister Oleksiy
Reznikov, paving the way for Rustem Umerov to
take over the post amid Russia’s full-scale
invasion of the country.
# ⚓ RFERL ☛ Uzbek_Payment_Services_Oson,_Pay_Way_Suspend
Transfers_On_Sanctions_Risk⠀⇛
Uzbekistan’s leading payment services Oson
and Pay Way said they have suspended foreign
money transfers as of September 5 amid
warnings from the central bank over avoiding
the violation of Western sanctions imposed
against Russia for its full-scale invasion of
Ukraine.
# ⚓ RFERL ☛ Ukraine_Rejects_Turkish_Call_For_Kyiv_To
Soften_Stance_On_Grain_Deal⠀⇛
A senior Ukrainian official on September 5
rebuffed a suggestion by Turkey that Kyiv
should soften its stance to revive the Black
Sea grain deal, saying Ukraine would not
support sanctions relief for Moscow or a
policy of “appeasement.”
# ⚓ JURIST ☛ Russia_opens_investigation_into_US
journalist_‘discrediting’_its_armed_forces⠀⇛
The SHOT Telegram channel reported on Sunday
that a case was opened on Thursday by the
Russian Investigative Committee into Masha
Gessen, a journalist from New York, who has
been providing insights into the atrocities
taking place during Russia’s war of
aggression in Ukraine.
# ⚓ RFERL ☛ Top_U.S._Diplomat_Set_To_Arrive_In_Kyiv_For
Unannounced_Visit⠀⇛
U.S. Secretary of State Antony Blinken is set
to arrive in the Ukrainian capital for an
unannounced visit.
# ⚓ RFERL ☛ Romanian_President_Says_Russian_Attacks_Have
Come_Close_But_Haven’t_Hit_His_Country⠀⇛
Romanian President Klaus Iohannis on
September 5 said attacks are occurring close
to Romania’s border with Ukraine but no drone
or other device landed in Romania during a
weekend attack by Russian forces on Ukrainian
port infrastructure.
# ⚓ ADF ☛ Despite_Loss_of_Leader,_Wagner_Group_Likely_to
Continue_African_Operations⠀⇛
Nothing could rattle the foundation of
Russia’s mercenary Wagner Group more than the
death of founder Yevgeny Prigozhin. Yet even
that dramatic news is not expected to
significantly impact the group’s operations
in Africa.
# ⚓ Silicon Angle ☛ How_Kremlin-backed_social_media
campaigns_continue_to_spread_disinformation⠀⇛
A new report sponsored by the European
Commission has found that social media has
played a key role in the spread of Russian-
backed disinformation campaigns since their
war with Ukraine began. /blockquote>
# ⚓ RFERL ☛ Germany_Sees_More_Aggressive_Russian
Disinformation_Campaigns_Since_Invasion_Of_Ukraine⠀⇛
Russia has increased its disinformation
campaigns in Germany since its invasion of
Ukraine, the German domestic intelligence
agency said in Berlin on September 5.
# ⚓ France24 ☛ ‘You_will_be_provided_with_everything_you
need’:_How_Ukraine_tries_to_fuel_Russian_defections⠀⇛
A rare video aired on Ukrainian television on
Sunday allegedly showing a Russian pilot who
had defected and encouraging other Russian
soldiers to do the same. His dramatic escape
allegedly took six months to plan, and was
carried out in cooperation with Ukraine’s
intelligence services. Whether the video is
authentic remains unclear, but one thing is
certain: Ukraine is doing everything it can
to fuel Russian defections.
# ⚓ France24 ☛ 🔴_Live:_Deadly_Russian_drone_attacks_hit
port_district_in_Ukraine’s_Odesa_region⠀⇛
Russian drone attacks early on Wednesday
killed one person and damaged agricultural
infrastructure in Izmail, a port district in
the Odesa region, its governor Oleg Kiper
said. Ukrainian air defence systems shot down
Russian missiles that targeted Kyiv in
another early morning attack.
# ⚓ Scoop News Group ☛ Bilyana_Lilly_on_Western
cybersecurity_assistance_to_Ukraine⠀⇛
Western aid to Kyiv has played a key role in
keeping Ukraine’s government up and running
and in the fight against Russian forces.
# ⚓ LRT ☛ Closing_border_with_Belarus_is_no_longer
relevant_–_Lithuanian_president⠀⇛
The issue of completely closing Lithuania’s
border with Belarus is losing relevance as
the Wagner mercenary group is leaving the
neighbouring country, says President Gitanas
Nausėda.
# ⚓ The Straits Times ☛ Xi,_Putin_missing_G-20_summit_not
unusual,_says_India’s_foreign_minister⠀⇛
September 06, 2023 12:50 PM
Their absence has nothing to do with India,
says Mr Subrahmanyam Jaishankar.
# ⚓ RFERL ☛ Russia’s_‘General_Armageddon,’_Not_Seen_Since
Wagner_Mutiny,_Reappears_In_Telegram_Photo⠀⇛
General Sergei Surovikin, who has not been
seen publicly since the June mutiny by Wagner
Group mercenaries, has reappeared in a new
photograph online, adding further mystery to
the fate of the Russian commander.
# ⚓ RFERL ☛ Ukrainian_Foreign_Ministry_Rebukes_Putin_For
Latest_Anti-Semitic_Comments⠀⇛
The Ukrainian Foreign Ministry has said the
latest statements by Russian President
Vladimir Putin about Ukrainian President
Volodymyr Zelenskiy’s Jewish roots are
“another manifestation of deep-rooted anti-
Semitism of the Russian elites.”
# ⚓ France24 ☛ Zelensky_visits_frontline_troops_near
Bakhmut_in_east_Ukraine⠀⇛
President Volodymyr Zelensky visited the war-
battered town of Bakhmut in eastern Ukraine
and spoke to troops leading a
counteroffensive against Russia, Ukraine said
Tuesday. Earlier on Tuesday, the Kremlin
declined to confirm a potential upcoming
summit, which US officials expect to take
place, between President Vladimir Putin and
North Korean leader Kim Jong Un in Russia.
# ⚓ France24 ☛ Russia_extends_the_battlefield_to_its
history_books⠀⇛
As Russian students headed back to school
this year, many were given updated history
textbooks – part of an attempt by Russian
President Vladimir Putin to reaffirm his
chosen narrative of Russia’s place in the
world. The new books include a glorified
account of Russia’s history, derision aimed
at its enemies and justifications for the
invasion of Ukraine.
# ⚓ Defence Web ☛ Russia_in_Africa:_Prigozhin’s_death
exposes_Putin’s_real_motives_on_the_continent⠀⇛
The apparent assassination of Yevgeny
Prigozhin in the crash of his private jet
between Moscow and St. Petersburg represents
an inflection point in Russian-African
relations. Prigozhin, as leader of the
notorious Wagner Group, had been the point
man for Russia in Africa since Wagner first
began operations on the continent in 2017.
o § Environment⠀➾
# ⚓ The Straits Times ☛ Storms_from_Typhoon_Haikui_drench
China’s_Fujian_province⠀⇛
The typhoon lost strength and became a tropical
storm after its landfall around 5am.
# ⚓ Truthdig ☛ Why_the_United_States_Undercounts_Climate-Driven
Deaths⠀⇛
Maricopa County’s enhanced heat surveillance
system, which essentially counts each heat-related
death by hand, is something of a state-level gold
standard. Even so, the system only gives the county
a concrete lower bound. That’s valuable, Parks
said, because the county is able to know at least
how many heat-related deaths occurred in a given
year. But it’s almost guaranteed to be an
underestimate. “The perception that that’s the true
number is really rather pervasive,” he said. “It’s
a very conservative estimate.” That even a rigorous
system like Maricopa County’s cannot provide a full
accounting illuminates the challenges of counting
climate-related deaths nationwide.
# ⚓ US News And World Report ☛ Panama_Canal_Water_Levels_at
Historic_Lows,_Restrictions_to_Remain⠀⇛
Experts have warned about maritime trade
disruptions ahead of what is shaping up to be an
even drier period next year. They argue that a
potential early start to Panama’s dry season and
hotter-than-average temperatures could increase
evaporation and result in near-record low water
levels by April.
# ⚓ Reuters ☛ Focus:_Historic_drought,_hot_seas_slow_Panama
Canal_shipping⠀⇛
More than 14,000 ships crossed the canal in 2022.
Container ships are the most common users of the
Panama Canal and transport more than 40% of
consumer goods traded between Northeast Asia and
the U.S. East Coast.
# ⚓ France24 ☛ Cyclone_kills_at_least_21_in_southern_Brazil,
more_flooding_expected⠀⇛
Torrential rain and winds caused by an
extratropical cyclone have left at least 21 people
dead in southern Brazil, officials said Tuesday,
warning more flooding may be coming.
# ⚓ France24 ☛ At_least_seven_dead_in_flooding_in_Greece,
Turkey,_Bulgaria⠀⇛
Fierce rainstorms battered neighboring Greece,
Turkey and Bulgaria on Tuesday, triggering flooding
that caused at least seven deaths, including two
holidaymakers swept away by a torrent that raged
through a campsite in northwestern Turkey.
# § Energy/Transportation⠀➾
# ⚓ RFA ☛ China’s_average_coal_power_emissions_rise_by_a
third,_report_says⠀⇛
Australia, South Korea and China are top coal
electricity polluters per capita.
# ⚓ New York Times ☛ Chinese_Cars_Star_at_Munich_Auto
Show,_Underscoring_German_Economic_Woes⠀⇛
China, an electric-vehicle juggernaut, will
have at least seven brands on display, while
Germany’s automakers are now a drag on their
home economy.
# ⚓ Ruben Schade ☛ Banning_electric_scooters⠀⇛
Jason from NotJustBikes, and Alan Fisher from
the Armchair Urbanist did a great podcast
episode last March about micro-mobility
devices like e-bikes and scooters.
The_Big_Problem_with_Small_Vechiles
# ⚓ DeSmog ☛ Climate_Science_Denial_Looms_Large_in_GB
News_Linked_‘ARC’_Venture⠀⇛
“The arc of the moral universe is long but it
bends towards justice”. This Martin Luther
King quote was used by Conservative peer
Baroness Stroud to introduce the Alliance for
Responsible Citizenship (ARC), which launched
in March.
Set up by the owners of GB News and involving
“senior leaders from politics, media,
culture, business, and academia”, ARC claims
that it will address the six “fundamental
issues of our time”, including “energy and
resources” and “environmental stewardship”.
# ⚓ DeSmog ☛ Jordan_Peterson_Generates_Millions_of
YouTube_Hits_for_Climate_Crisis_Deniers⠀⇛
Fringe climate crisis deniers who claim that
the earth is “cooling” and greenhouse
emissions are good for “biological
productivity” are getting exposed to millions
more people than they normally would on
YouTube thanks to conservative influencer
Jordan Peterson.
That’s according to viewership data newly
reviewed by DeSmog, which reveals a massive
visibility boost for public figures who’ve
been active in the climate denial movement
for years but whose ideas — such as the claim
that plants are growing much better due to
increased carbon dioxide in the atmosphere —
are now rarely taken seriously by most legacy
media outlets.
# ⚓ The Straits Times ☛ Despite_green_energy_boom,_dash
for_coal_clouds_China’s_climate_goals⠀⇛
China’s energy policies have a huge impact on
the pace of global climate change.
# ⚓ New York Times ☛ A_$700_Million_Bonanza_for_the
Winners_of_[Cryptocurrency]’s_Collapse:_Lawyers⠀⇛
Lawyers, accountants, consultants,
cryptocurrency analysts and other
professionals have racked up more than $700
million in fees since last year from the
bankruptcies of five major [cryptocurrency]
firms, including the digital currency
exchange FTX, according to a New York Times
analysis of court records. That sum is likely
to grow significantly as the cases unfold
over the coming months.
# ⚓ Common Dreams ☛ 500_Groups_Endorse_NYC_March_to_End
Fossil_Fuels⠀⇛
Groups including the NAACP, Sierra Club, and
Sunrise Movement have signed on to support
the march and its demands for Pres. Biden to
take bold action on fossil fuels in the wake
of a deadly, record-breaking summer of
extreme heat and climate disasters. They join
the key groups organizing the march,
including the Center for Biological
Diversity, Center for Popular Democracy,
Climate Organizing Hub, Food & Water Watch,
Fridays For Future USA & NYC, Earthworks,
Greenfaith, Indigenous Environmental Network,
New York Communities for Change, Oil Change
International and Oil & Gas Action Network.
# § Overpopulation⠀➾
# ⚓ US News And World Report ☛ Water_Conservation
Measures_Announced_for_Grand_Canyon_National_Park⠀⇛
Last year, the park implemented similar
conservation measures on the South Rim in
parts of July, August and September until the
water tank levels returned to normal.
# ⚓ Los Angeles Times ☛ Colorado_River_Basin_ranks_among
the_world’s_most_water-stressed_regions,_analysis
finds⠀⇛
The analysis by researchers with the World
Resources Institute found that all seven
states that rely on the Colorado River face
high or extremely high water stress. Arizona
ranked first for the most severe water stress
in the country, followed by New Mexico and
Colorado, while California ranked fifth.
o § Finance⠀➾
# ⚓ The Straits Times ☛ Despite_Rome’s_scepticism,_China_says
Belt_and_Road_cooperation_with_Italy_‘fruitful’⠀⇛
In 2019, Italy became the first major Western
nation to join China’s Belt and Road.
# ⚓ Silicon Angle ☛ GitLab_shares_rise_on_better-than-expected
earnings_and_revenue⠀⇛
As of the end of the quarter, GitLab had 7,815 base
customers, including 810 customers with a turnover
in excess of $100,000, up 37% year-over-year. Total
users of GitLab’s platform passed 30 million users,
with more than 50% of Fortune 100 now GitLab
customers. The company’s revenue run rate sat at
$558 million as of the end of July and its dollar-
based net retention rate was 124%, meaning it’s
getting significantly more business from existing
customers.
# ⚓ Roku_cuts_10%_of_workforce,_slows_down_on_new_hiring⠀⇛
Roku Inc. is cutting 10% of its workforce and
curbing hiring plans in an effort to lower
expenses, the company said Wednesday in a
regulatory filing.
The video streaming company laid out a series of
cost-cutting measures that it says will bring down
its annual headcount expense growth rate.
# ⚓ Forbes ☛ 2023_Layoff_Tracker:_Roku_Slashes_10%_Of
Workforce⠀⇛
Digital media giant Roku is laying off roughly 10%
of its workforce, it announced Wednesday, marking
the latest in a series of large corporate layoffs
over the past year as employers continue to
restructure their workforces amid lingering
recession fears (see Forbes’ layoff tracker from
the first quarter here).
# ⚓ Tech Times ☛ Roku_Slashes_Workforce_by_10%,_Limits_Hiring
Amid_Cost-Cutting_Measures⠀⇛
Roku Inc. plans to reduce its personnel by around
10%, equivalent to 360 workers, as part of a
strategic move to stop a string of quarterly
losses. The prominent streaming platform also
intends to restrict new hires to meet its cost-
cutting goals.
Roku’s workforce reduction was in response to its
updated financial forecast. This move follows
Roku’s altered financial forecast. Roku now expects
third-quarter 2023 sales of $835 million to $875
million, up from a projection of $815 million in
July. Investor confidence boosted Roku’s shares by
8% to $90.48 in early trading.
o § AstroTurf/Lobbying/Politics⠀➾
# ⚓ New York Times ☛ Vanuatu_Prime_Minister_Ousted_Amid
Criticism_of_Being_Pro-West⠀⇛
The prime minister of Vanuatu lost his job after he
was criticized for veering too close to the West.
He accuses his successor of being too cozy with
China.
# ⚓ India Times ☛ Elon_Musk_borrowed_$1_billion_from_SpaceX_in
same_month_of_Twitter_deal:_report⠀⇛
SpaceX approved the $1 billion loan, which was
backed by some of Musk’s SpaceX stock in October
and Musk drew all of it down the same month,
according to the report, citing documents. Musk
took ownership of Twitter in October.
# ⚓ Security Week ☛ CISA_Hires_‘Mudge’_to_Work_on_Security-by-
Design_Principles⠀⇛
The U.S. government’s cybersecurity agency CISA on
Monday confirmed the addition of Peiter ‘Mudge’
Zatko to its roster of prominent voices preaching
the gospel of security-by-design and secure-by-
default development principles.
Zatko, most recently the CISO at Twitter who blew
the whistle on the social media giant’s security
shortcomings, is joining the agency in a part-time
capacity to work on the “security and resilience by
design” pillar of the Biden administration’s
National Cybersecurity Strategy.
# ⚓ Security Week ☛ MITRE_and_CISA_Release_Open_Source_Tool_for
OT_Attack_Emulation⠀⇛
MITRE and CISA introduce Caldera for OT, a new
extension to help security teams emulate attacks
targeting operational technology systems.
# ⚓ It’s_long_past_time_for_Apple_to_stop_advertising_on
Twitter⠀⇛
At this point advertising on Twitter is directly
extending financial support to neo-Nazis. It’s long
past time that companies like Apple,1 which resumed
advertising on the platform in December 2022, just
stopped.
But it won’t, which is finally putting the lie to
the idea that the company’s leadership team care
one iota about about the impact its actions make on
the culture of the country which nurtured it. “You
support rampant anti-semitism on your service? No
problem! Here’s some money. You explicitly allow
transphobic hate speech on the service? That’s fine
with us! Here, have some more money.”
# ⚓ Michael Geist ☛ Why_The_Government’s_Bill_C-18_Draft
Regulations_Do_Little_to_Ensure_More_Spending_on_Journalists
or_News_Content⠀⇛
The government released its draft Bill C-18
regulations on Friday ahead of the Labour Day
weekend, but ironically those regulations do very
little to ensure that new funding will be allocated
toward employing journalists. While the regulations
establish what amounts to a minimum 4% link tax on
Google and Meta if they link to news content, they
set no minimum requirements to spend the resulting
revenues on journalists or news content. In fact,
the government specifically dictates to the CRTC
that the legislative requirement that an
“appropriate portion of the compensation will be
used for the production of local, regional and
national news content” will involve no minimum
amount and the agreements need only reference that
“some” of the compensation will be used for that
purpose. As a result, in the best case scenario for
the government in which the Internet platforms pay
for links by reaching commercial agreements with
news outlets, the big beneficiaries such as Bell,
Rogers, the CBC, and Postmedia would be free to
spend the vast majority of the money generated by
those deals on executive salaries, debt repayment,
or any other purpose.
# ⚓ Gizmodo ☛ Facebook_Is_Killing_the_News_Tab_in_Several
Countries⠀⇛
However, despite Meta’s assurances that news
outlets will still be able to post content for
viewers to see, recent reports have surfaced
revealing Meta has quietly reduced referral traffic
to media outlets, according to a report by the
prominent UK news outlet, Reach PLC. Digital
revenue in the UK dropped by 14.5% in the first
quarter of 2023, and Reach claimed the root cause
stems from “recent changes to the way Facebook
presents news content, causing a reduction in
referred traffic across the sector.”
# ⚓ Press Gazette ☛ Meta_to_wind_down_Facebook_News_tab_and
stop_funding_Community_News_Project⠀⇛
Since the start of 2021, most major UK publishers
have received payments from Facebook to use their
content in its News tab. The tab was previously
curated by a team of around 15 journalists at
Upday, but this contract ended last year as Meta
turned it into a fully automated product.
# ⚓ IT Wire ☛ Facebook_says_it_will_cut_back_on_news_in_Europe
in_December⠀⇛
The announcement comes after Meta blocked_access_to
news_feeds_in_Canada after that country passed a
media law known as the Online News Act earlier this
year.
Meta started blocking Canadian news feeds at the
beginning of August, even though the Canadian law
will take effect only by the end of the year.
/blockquote>
# ⚓ Pro Publica ☛ Texas_AG_Ken_Paxton_Repeatedly_Refuses_to
Represent_State_Agencies,_Documents_Reveal⠀⇛
When Texas Attorney General Ken Paxton held a news
conference in May decrying state lawmakers’
anticipated vote to impeach him, he framed the
decision as not only a threat to his political
career but as one that endangered the slew of
lawsuits he’d filed against the Biden
administration.
Paxton, who has since been suspended from office,
faces an impeachment trial that starts today. He
has long positioned himself as one of the country’s
strongest conservative attorneys general,
relentlessly pursuing nearly 50 lawsuits against
the federal government on issues that include
immigration, health care and the environment. Such
messaging raised Paxton’s national profile,
appealed to his base of conservative supporters and
helped him tamp down political pushback stemming
from allegations of wrongdoing that have dogged his
eight-year tenure.
o § Censorship/Free Speech⠀➾
# ⚓ CPJ ☛ Iran_blocks_Entekhab’s_website_and_social_media_over
report_criticizing_foreign_policy⠀⇛
On Monday, September 4, the Press Supervisory Board
of Iran’s Ministry of Culture and Islamic Guidance
revoked Entekhab’s operating license indefinitely
and blocked the outlet’s website and social media
accounts in the country.
# ⚓ Reason ☛ SCOTUS’_Ruling_in_Gay_Wedding_Website_Case_Was_a
Defeat_for_Compelled_Speech⠀⇛
“The opportunity to think for ourselves and to
express those thoughts freely is among our most
cherished liberties,” Justice Neil Gorsuch wrote in
the majority opinion.
# ⚓ EDRI ☛ The_Future_of_Speech_Online_2023:_Generative_AI⠀⇛
Join the Center for Democracy & Technology (CDT)’s
seventh annual Future of Speech Online event, on
October 4-5, to explore how to build a rights-
respecting future where people benefit from
generative AI.
# ⚓ Reason ☛ Arbitrators,_Like_Judges,_Are_Immune_from_Libel
Lawsuits_Based_on_Their_Opinions⠀⇛
From today’s decision by Judge Jia Cobb in Seltzer
v. Financial Industry Regulatory Authority:
Plaintiff Susan Seltzer participated in an
arbitration proceeding before the Financial
Industry Regulatory Authority (FINRA). The
arbitration concluded with a written award that was
published online.
o § Freedom of Information / Freedom of the Press⠀➾
# ⚓ CPJ ☛ Tunisian_authorities_jail_journalist_Khalifa_Guesmi
over_national_security_charge⠀⇛
Guesmi was initially arrested on March 18, 2022,
and held for a week after authorities alleged that
his reporting about the dismantling of a terrorist
cell illegally disclosed information about
government surveillance. On November 29, a court
sentenced Guesmi to one year in prison. On May 16,
2023, an appeals court increased his sentence to
five years.
# ⚓ Techdirt ☛ First_Lawsuit_Filed_Over_Raid_Of_Small_Town
Kansas_Newspaper⠀⇛
Shocking the conscience. That’s the legal term for
government actions that are so far from acceptable
no one, not even cop-friendly courts, can deem them
acceptable.
# ⚓ Meduza ☛ Kremlin_spokesman_tells_AFP_journalist_not_to_ask
him_about_Russian_General_Sergey_Surovikin_—_Meduza⠀⇛
# ⚓ Meduza ☛ The_New_York_Times’_sources_say_Russian_General
Sergey_Surovikin_released_—_Meduza⠀⇛
# ⚓ The Dissenter ☛ Blinken,_Assange,_And_The_20th_Anniversary
Of_The_Palestine_Hotel_Bombing⠀⇛
# ⚓ IT Wire ☛ Six_Australian_MPs_to_visit_US_and_lobby_for
Assange’s_release⠀⇛
The MPs are former Nationals leader Barnaby Joyce,
Liberal Senator Alex Antic, Labor MP Tony Zappia,
Independent MP Monique Ryan and Greens Senators
David Shoebridge and Peter Whish-Wilson.
The planned visit comes ahead of Prime Minister
Anthony Albanese’s scheduled state visit to the US
in October.
o § Civil Rights/Policing⠀➾
# ⚓ Reason ☛ Police_Tore_Up_His_Protest_Sign._Now_They_Owe_Him
$50,000⠀⇛
Last year, Delaware police prevented 54-year-old
Jonathan Guessford from holding a sign warning
drivers about a speed trap and wrongfully cited him
for “improper hand signal” after he flipped off the
officers who seized and tore up his sign. Police
have now agreed to pay Guessford $50,000 as part of
a settlement reached in a lawsuit alleging that
police violated his civil rights.
# ⚓ BIA Net ☛ Layoffs_in_Amnesty_International_Turkey_branch⠀⇛
Amnesty International’s Turkey branch, which fights
for human rights worldwide and works to end
violations, has laid off one-third of its
employees. In the branch, which has 24
employees,eight people have been let go, two of
them being institution managers. The institution
cited “restructuring” as the reason.
The employees criticized the layoffs, attributing
them to “union-related” reasons, as Amnesty
International had withdrawn from collective
bargaining negotiations with the DİSK Sosyal-İş
Union on June 7.
# ⚓ The Nation ☛ How_Inequality_Was_Redefined_as
“Poverty”—Letting_Capitalism_Off_the_Hook⠀⇛
The discovery of poverty as a national problem in
the late 1950s and early ’60s redefined economic
inequality from a description of relative material
circumstances to a cultural issue deriving from the
inadequacies of individuals or groups. Debate
within and around the John F. Kennedy and Lyndon B.
Johnson administrations on how to understand and
thus respond to “poverty” overlapped with the
debate about structural unemployment. Figures like
Labor Secretary W. Willard Wirtz, labor and civil
rights leaders like Walter Reuther, A. Philip
Randolph, and Bayard Rustin, and labor economists
like Charles Killingsworth continued to argue that
poverty stemmed primarily from the economy’s
inability to generate sufficient gainful
employment. In their view, the most effective anti-
poverty strategy would involve the kind of
substantial federal intervention that would tighten
labor markets—including public investment, serious
job training, and direct job creation.
# ⚓ Pro Publica ☛ Why_the_Destruction_of_Shoe_Lane_Matters_to
Me_—_and_Should_Matter_to_Everyone⠀⇛
As a high school sprinter in Virginia’s Tidewater
region, I often participated in meets at
Christopher Newport University’s Freeman Center,
which had one of the few indoor tracks in the area.
I won 500-meter races against top runners, and my
high school was team champion.
Track and field was a huge part of my identity. I
looked forward to crossing the Monitor-Merrimac
bridge over the James River to Newport News, and I
saw the opportunity to display my skill at
Christopher Newport as a way to impress colleges
and earn an athletic scholarship. It wouldn’t be
until 20 years later that I understood the
underlying irony. The construction of Christopher
Newport, where Black athletes like me competed
alongside our white counterparts, had displaced
Black homeowners whose hopes and aspirations were
dashed by racism.
# ⚓ Pro Publica ☛ How_a_Virginia_College_Expanded_by_Uprooting
a_Black_Neighborhood⠀⇛
Katie Luck was sitting in her yard under a magnolia
tree one afternoon in April when a school bus
passed by. A white elementary school student
shouted at her from a window, “You don’t belong
here.”
The 81-year-old grandmother and retired teacher,
who is Black, was so distressed that she called
James and Barbara Johnson, who live down the road
from her on Shoe Lane in Newport News, Virginia.
The Johnsons, perhaps better than anyone, knew just
how wrong the elementary schooler was. The stacks
of files and photo albums on their dining room
table are a shrine to what the Shoe Lane area used
to be — and what it might have become.
# ⚓ Meduza ☛ Human_rights_lawyer_Tatyana_Solomina_receives
death_threats_from_family_of_Chechen_man_she_assisted_—
Meduza⠀⇛
# ⚓ EFF ☛ UK_Online_Safety_Bill_Will_Mandate_Dangerous_Age
Verification_for_Much_of_the_Web⠀⇛
Under new age verification rules in the UK’s
massive Online Safety Bill, all internet platforms
with UK users will have to stop minors from
accessing ‘harmful’ content, as defined by the UK
Parliament. This will affect adult websites, but
also user-to-user services – basically any site,
platform, or app that allows user-generated content
that could be accessed by young people. To prevent
minors from accessing ‘harmful’ content, sites will
have to verify the age of visitors, either by
asking for government-issued documents or using
biometric data, such as face scans, to estimate
their age.
This will result in an enormous shift in the
availability of information online, and pose a
serious threat to the privacy of UK internet users.
It will make it much more difficult for all users
to access content privately and anonymously, and it
will make many of the most popular websites and
platforms liable if they do not block, or heavily
filter, content for anyone who does not verify
their age. This is in addition to the dangers the
Bill poses to encryption.
# ⚓ New York Times ☛ Leaders_of_Canadian_Trucker_Protest_Go_on
Trial⠀⇛
Two key organizers of the 2022 trucker protest
argued that their efforts were a form of free
speech, as prosecutors asserted that “this case is
not about their political views.”
o § Internet Policy/Net Neutrality⠀➾
# ⚓ APNIC ☛ Understanding_the_Japanese_Internet_with_the
Internet_Yellow_Pages⠀⇛
Moving to Tokyo was a once-in-a-lifetime experience
for me. Discovering another culture brings a lot of
surprises, one of them was the ‘Disaster
Preparedness Tokyo’ book that came with my new
apartment. The level of preparedness for natural
disasters in Japan is way beyond anything I have
seen in other parts of the world. And I believe
this also applies to the Internet in Japan,
something I’d like to convey in this article.
# ⚓ RIPE ☛ The_RIPE_Chair_Team_Reports_–_September_2023⠀⇛
Making RIPE more visible, taking part in industry
events, keeping up with policy discussions, and
preparing for a RIPE Meeting in Rome – as we go
into September, the RIPE Chair Team reports on the
work ahead in the months to come.
# ⚓ Linux Links ☛ Best_Free_and_Public_DNS_Servers⠀⇛
This article focuses on four user-friendly DNS
servers: Gcore Public DNS, OpenDNS, Quad9, and
1.1.1.1 Public DNS.
o § Monopolies⠀➾
# ⚓ Silicon Angle ☛ FTC_antitrust_lawsuit_against_Amazon_will
likely_come_later_this_month_after_talks_break_down⠀⇛
The Federal Trade Commission is reportedly going
ahead with an antitrust lawsuit against Amazon.com
Inc. after the company’s lawyers offered no
concessions in recent talks with the regulator,
according to a report today in the Wall Street
Journal.
# § Patents⠀➾
# ⚓ Unified Patents ☛ The_Public_Has_Spoken:_Stakeholders
Overwhelmingly_Oppose_Proposed_Restrictions_on_Patent
Trial_and_Appeal_Board_Review⠀⇛
Public comments responding to U.S. Patent and
Trademark Office proposals have been posted
onregulations.govon a rolling basis. This
analysis has been updated from the original
version – July 23, 2023 – to reflect comments
posted on regulations.gov as of August 22,
2023.
# ⚓ Dennis Crouch/Patently-O ☛ Mandamus_for_Improper
Venue⠀⇛
The U.S. Court of Appeals for the Federal
Circuit recently declined to issue a writ of
mandamus directing the U.S. District Court
for the Eastern District of Texas (Judge
Gilstrap) to dismiss a patent infringement
lawsuit against Charter Communications based
upon improper venue. In re Charter Commc’ns,
Inc., No. 2023-136 (Fed. Cir. Sept. 5, 2023).
Although non-precedential, the decision
highlights a key difference between motions
to dismiss for improper venue under 28 U.S.C.
§ 1406 and motions to transfer venue for
convenience under 28 U.S.C. § 1404. It also
shows the high bar for obtaining the
“extraordinary remedy” of mandamus relief
from denial of an improper venue motion.
>
# ⚓ Kluwer Patent Blog ☛ Patent_case:_Bot_M8_LLC_v._Sony
Interactive_Entertainment_LLC,_USA⠀⇛
Substantial evidence supported a Patent Trial
and Appeal Board (PTAB) decision finding the
challenged claims were obvious. A PTAB
decision finding that Sony Interactive
Entertainment had shown that a Bot M8’s
patent directed to a video game
authentication system was obvious over prior
art has been affirmed by the U.S. Court of
Appeals…
# ⚓ Unified Patents ☛ Phelan_Group_automotive_patent
challenged⠀⇛
On August 31, 2023, Unified Patents filed an
ex parte reexamination proceeding against
U.S._Patent_10,259,470, owned and asserted by
the Phelan Group, LLC, an NPE. The ’470
patent generally relates to a vehicle control
system for authenticating and monitoring a
driver and their operation of a vehicle to
improve safety.
# ⚓ Unified Patents ☛ Vision_Works_IP_automotive_patent
instituted⠀⇛
On August 25, 2023, less than two months
after Unified filed_an_ex_parte
reexamination, the Central Reexamination Unit
(CRU) granted Unified’s request, finding a
substantial new question of patentability on
the challenged claims of U.S._Patent
8,437,935, owned and asserted by Vision Works
IP Corp., an NPE.
# § Trademarks⠀➾
# ⚓ TTAB Blog ☛ TTABlog_Test:_How_Did_These_Three_Appeals
from_Section_2(d)_Refusals_Turn_Out?⠀⇛
A TTAB judge once told me that one can
predict the outcome of a Section 2(d) case
95% of the time just by looking at the marks
and the goods/services. Here are three recent
appeals from Section 2(d) refusals. How do
you think these came out? Answers will be
found in the first comment. [No hints this
time].
In_re_Puma_SE, Serial No. 90600590 (August
29, 2023) [not precedential] (Opinion by
Judge Christopher C. Larkin). [Section 2(d)
refusal of the mark PWRSHAPE for “Clothing,
namely, pants, skirts” and “Clothing, namely,
pullovers, jackets, shirts, T-shirts,
sweaters, and coats,” in view of the
registered mark POWERSHAPE for “bras.”
# § Copyrights⠀➾
# ⚓ Digital Music News ☛ Miley_Cyrus_‘Bangerz’_Tour
Grossed_$63_Million—But_Cyrus_“Didn’t_See_a_Dime”⠀⇛
Why hasn’t Miley Cyrus gone on tour since her
‘Bangerz’ tour in 2014? The singer bares all
on TikTok, revealing the 70+ date “didn’t
earn her a dime.” Miley Cyrus has posted a
series of videos to TikTok sharing some
inside information about the industry.
# ⚓ Bjoern Brembs ☛ Is_this_Smits’_tripleC_moment?⠀⇛
Jeffrey “predatory journals” Beall famously
catapulted himself out of any serious debate
with an article in the journal TripleC,
entitled “The Open-Access Movement is Not
Really about Open Access“. In it, Beall
claimed that OA proponents don’t care about
access, but that they form an “anti-
corporatist movement that wants to deny the
freedom of the press to companies it
disagrees with”. The article is so replete
with similarly unhinged fairy tales that
Beall quickly lost all standing with the
scholarly community.
# ⚓ Walled Culture ☛ China_fully_embraces_Western
copyright,_and_inevitably_suffers_from_its_ills⠀⇛
The export of the West’s obsession with
enforcing copyright monopolies has brought
with it the inevitable rise of copyright
madness. Here’s a good example of that,
reported on the Sixth Tone site. It involves
a professional Chinese astrophotographer, Dai
Jianfeng, and Visual China Group (VCG),
China’s largest stock photo provider. The
latter demanded that Dai should pay
compensation to VCG for publishing his own
photos: [...]
# ⚓ WBUR Radio ☛ Artist:_Known_—_Illustrator_for_‘A
Wrinkle_in_Time’_gets_long-overdue_credit⠀⇛
The answer isn’t on any page of google, or
any page of the physical book itself — not
the copyright page where the rest of the
credit information is, not the front or back
cover, NOWHERE. Sarah posed the question in
the Unresolved Mysteries subreddit. “This
would be the kind of thing that the folks
over at Endless Thread would have a field day
over,” someone commented.
And, indeed… we did! In this episode, Amory
uncovers the artist behind this iconic
illustration.
# ⚓ Digital Music News ☛ Streaming_Dominates_French_Music
Industry_H1_2023⠀⇛
SNEP also revealed some interesting stats
about the French music industry as a whole.
The 200 most listened-to tracks in paid audio
streaming accounted for 10.5% of the total
number of paid streams. Those top 200 tracks
streamed in H1 2023 accounted for around 3.8
billion streams from paid subscribers. The
entire top ten best-selling artists for H1
2023 in France were all local acts. 17 of the
Top 20 best-selling album sin the country
were also made by local acts, while 75% of
the Top 200 were French productions.
# ⚓ Society for Scholarly Publshing ☛ Appeals_Court_Rules
That_Library_of_Congress_Can_No_Longer_Require_Deposit
of_Published_Works⠀⇛
Title 17, Section 407 of the U.S. Code
requires that the copyright holder in a
printed work or sound recording published in
the United States “deposit, within three
months after the date of such publication,
two complete copies of the best edition… in
the Copyright Office for the use or
disposition of the Library of Congress.”
Failure to do so subjects the copyright
holder to “a fine of not more than $250 for
each work” as well as “the total retail price
of the copies… demanded” and an additional
“fine of $2,500… if such person willfully or
repeatedly fails or refuses to comply” with
the deposit requirement.
A few years ago, a small publisher called
Valancourt Books sued the government,
challenging the constitutionality of this
requirement, and initially lost its suit. But
last week the District of Columbia Court of
Appeals reversed the district court’s
decision.
# ⚓ Torrent Freak ☛ ‘Books3’_Takedown:_Anti-Piracy_Group
Calls_for_More_AI_Training_Transparency⠀⇛
With AI initiatives developing at a rapid
pace, copyright holders are on high alert. Of
particular concern is technology companies
using their content as training data, without
any form of compensation. Last month, Danish
anti-piracy group Rights Alliance was the
first to successfully send a DMCA takedown
notice for the Books3 training dataset, and
is now calling for more transparency.
# ⚓ Creative Commons ☛ CC’s_#BetterSharing_Collection_|
September:_Open_Is_Beautiful⠀⇛
Each month throughout 2023, we will be
spotlighting a different CC-licensed
illustration from the collection on our
social media headers and the CC blog. For
September, we’re excited to showcase “Open Is
Beautiful” by Ukrainian illustrator, Tanya
Korniichuk. The piece, licensed under CC BY-
NC-SA 4.0, was inspired by a quote from
Cecília Oliveira, Executive Director of Fogo
Cruzado:
# ⚓ Creative Commons ☛ Hardiansyah_—_Open_Culture_VOICES,
Season_2_Episode_23⠀⇛
Open Culture VOICES is a series of short
videos that highlight the benefits and
barriers of open culture as well as
inspiration and advice on the subject of
opening up cultural heritage. Hardi is the
Deputy General Secretary for Internal Affairs
and Partnership Manager of Wikimedia
Indonesia and has been working in open
culture since he started with Wikipedia.
# ⚓ Torrent Freak ☛ ACE_Shuts_Down_Three_Piracy_Rings_in
Egyptian_Whack-a-Mole⠀⇛
Anti-piracy coalition ACE reports that
Egyptian law enforcement authorities have
shut down three anti-piracy rings, which
operated sports, TV, and movie piracy sites.
These successes are the result of close
cooperation between rightsholders and the
local authorities. While these successes
should not be understated, most brands live
on, as copycat sites thrive.
# ⚓ Digital Music News ☛ One_Media_iP_Announces_Deal_for
‘Licensor’s_Income_Share’_of_15,000-Track_Catalog_—
Including_Works_Performed_by_Ray_Charles,_Dean_Martin,
and_More⠀⇛
Days after inking an expanded distribution
deal with Sony Music’s The Orchard, One Media
iP has announced the acquisition of the
“licensor’s income share” of an over 15,000-
track catalog. One Media iP reached out to
Digital Music News today with word of the
investment, which was executed specifically
via its “Harmony IP” royalty-advance program.
䷩ 𝚕𝚒𝚗𝚎 5849
╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕
(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/09/06/meme-3-months/#comments
Gemini version at gemini://gemini.techrights.org/2023/09/06/meme-3-months/
⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.06.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧
Gemini_version_available_♊︎
✐ [Meme]_3_Months⠀✐
Posted in Deception, IBM, Red_Hat at 3:00 am by Dr. Roy Schestowitz
🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇June_6,_2023:_New_developments_at_Opensource.com⦈_
🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_website_Opensource.com_has_been_supported_by_a
commercial_entity_for_12_years.But_the_people(that's_you_and_me)_that_make_up
the_Opensource.com_community_aren't_commercial_entities,_we're_people._In_one
month,_Opensource.com_is_going_to_resolve_that_bug._Stay_tuned!⦈_
🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Did_I_tell_you_the_joke_about_opensource.com?⦈_
Summary: The company from North Carolina cannot_be_trusted; its words are as
credible as North Korea’s
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡎⢳⢸⠉⡆⡮⠷⢸⠙⡆⠯⡁⡎⢱⢸⠀⡇⡎⢱⠋⠃⡯⠷⠀⢰⠙⢰⠋⡆⡎⢱⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣄
⠙⠉⠸⠉⠁⠙⠁⠈⠀⠁⠙⠁⠙⠋⠈⠙⠁⠁⠀⠙⠁⠙⠁⠈⠈⠚⠈⠓⠁⠃⠘⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢤⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢦⣶⢲⠀⣂⣆⣶⣴⠀⠀⠀⠀⣶⣶⣴⢔⣴⡄⢦⣖⣶⣴⠀⠀⠀⠀⠀⢰⡤⡢⣶⢶⡆⡠⣢⣴⣔⢴⡆⠀⠀⠀⠰⢰⣴⣦⡂⠐⢀⡤⢴⢲⣠⠂⣤⣴⠠⣲⣲⡆⢔⣴⣶⡆⡆⡖⣦⡂⢴⣶⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠖⣀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣡⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢉⠏⢹⢛⢻⢻⢻⢻⡿⢛⢹⢟⡻⡛⡟⡿⡛⠏⠹⢛⢿⢛⡻⡟⡛⠟⢿⢛⢻⠛⠋⡀⣺⢛⣻⣿⣛⢻⠉⣻⡟⣭⡙⡟⣛⢿⢛⢻⢛⡻⡟⣛⡟⡛⡟⣿⢻⢛⡻⣛⡿⡛⢿⡿⡛⡿⡛⢿⢛⢛⢻⣿⣿
⣿⣿⣿⣿⣿⣼⣦⣴⣤⣼⣦⣧⣾⣷⣬⣼⣦⣤⣧⣴⣧⣤⣧⣴⣬⣼⢨⣥⣧⣧⣿⡼⠄⣠⣴⣧⣧⣽⣥⣼⣯⣤⣼⣤⣽⣷⣭⣴⡇⣭⣼⣤⣼⣼⣧⣧⣤⣦⣥⣦⣭⣼⣼⣧⣭⣧⣤⣮⣧⣭⣧⣥⣾⣼⣼⣼⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢋⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡏⡿⠻⣿⣟⡻⣟⣿⣻⠛⡟⣿⢻⡟⡿⢻⣿⡟⣿⡟⠻⠟⣡⠒⣟⣟⣻⡿⠿⣿⣿⡟⠻⣟⣟⡿⣻⣟⣻⣻⣿⡻⣟⡿⢻⣛⡟⢻⢹⢹⡟⣿⢻⣛⣿⢻⡟⠿⠻⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣷⣷⣿⣷⣾⣶⣿⣿⣶⣷⣿⣶⣷⣷⣾⣾⣼⠟⢃⣴⣾⣿⣶⣿⣷⣾⣷⣶⣷⣿⣾⣿⣶⣿⣿⣾⣷⣾⣿⣿⣶⣷⣾⣾⣿⣷⣾⣾⣾⣷⣿⣾⣦⣿⣾⣿⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣡⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣼⣽⣿⣾⣿⣿⣿⣿⣿⣿⣿⠏⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⡿⣯⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣾⣾⣽⣿⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣯⣿⣿⣿⣿⣶⣼⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿
⣟⡛⠿⢿⠿⢿⠿⠿⠿⣿⡻⢿⠿⠿⡿⠿⠿⠿⡿⠿⠿⢿⢿⠿⡟⠿⠿⠿⡿⣿⠿⠿⢿⠿⢿⢿⠻⡿⡿⡿⠿⠿⡿⢿⠿⠿⡿⢻⢿⠿⠻⠿⠟⢿⣟⡿⣿⠿⢿⠿⣿⢻⡿⡿⠿⠿⡿⡿⡿⠿⡿⡿⣿⢿⠿⡻⣿⣿
⣿⣷⣷⣿⣾⣾⣶⣾⣶⣷⣾⣾⢶⣶⣶⢶⣷⣶⣶⣶⣶⣾⠷⣶⣷⣶⣷⣾⣷⣷⣴⣶⣾⣷⣶⣾⣶⣼⣶⣷⣶⣷⣿⣿⣶⡶⣷⣾⣾⣷⣶⣽⣿⣾⣿⣶⣷⠶⣾⣷⣾⣾⣾⣿⣾⣶⣷⣶⣶⣴⣷⣷⣿⣷⣶⣷⣿⣿
⣷⣮⣯⣧⣿⣮⣷⣼⣼⣿⣽⣥⣼⣿⣧⣬⣽⣤⣽⣯⣿⣼⣭⣮⣤⣦⣥⣬⣿⣵⣼⣵⣤⣤⣯⣤⣿⣼⣧⣼⣿⣯⣯⣿⣽⣾⣽⣥⣴⣾⣿⣧⣤⣼⣼⣧⣷⣤⣽⣴⣼⣷⣮⣷⣤⣯⣧⣤⣴⣧⣽⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣙⣯⣯⣉⣯⣝⣉⣫⣝⢈⣏⣽⣹⣍⣫⣿⣉⣍⣏⣯⣫⣽⣏⡯⣫⣯⡩⣯⣯⣯⣙⣙⣍⣛⣹⣍⣋⣽⣯⣉⠍⣏⣯⣋⢫⣭⣏⣉⣯⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡆⠀⡆⠂⡦⠆⡄⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⠀⣁⠀⠀⠀⡀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⣿⣿⣿⣿⣿⣿⣿⠿⣿⢿⣿⣿⣿⠀⠀⠀⢠⡍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⡟⢻⡟⣿⢻⡟⢻⠀⣿⢸⣿⠋⠿⠀⠀⠀⠈⠱⠍⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⡇⢸⡇⣿⢸⡇⢸⡀⣿⢸⣿⣦⡄⠀⠀⠀⠀⣄⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣤⣇⣸⡇⣿⢸⡟⢻⠿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡟⢻⡇⣿⢸⣇⣸⣤⣷⣾⣿⣿⡇⠀⠀⠀⠘⠛⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⡇⢸⡇⣿⢹⡏⢹⠉⣿⢹⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⣇⣸⣇⣿⣸⣇⣸⠀⡏⢸⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⡤⡿⢿⣿⣿⣿⡿⢿⢤⣧⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⠀⡇⢸⡏⣿⢹⡇⢸⠀⡟⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⣷⣾⡇⣿⢸⣷⣾⠀⡇⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⡏⢹⡇⣿⢸⡏⢹⠀⡇⢸⣿⣿⡇⠀⠀⠀⠀⢬⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⣇⣸⣇⣿⣨⣇⣸⠀⡇⢸⣿⣿⡇⠀⠀⠀⠀⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣤⣿⣿⣿⣿⣿⣿⣿⣤⣧⣼⣿⡏⠁⠀⠀⠀⠀⢂⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⣿⣿⣿⣿⣿⣿⣿⠀⡇⢸⣿⣇⠀⠀⠀⠀⠀⢲⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⣿⣿⣿⣿⣿⣿⣿⠀⡇⢸⣿⣿⠀⠀⠀⠀⠀⠬⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⣿⣿⣿⣿⣿⣿⣿⠀⡇⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⡟⢻⠛⣿⢛⡟⢻⠀⠇⠸⠿⠿⠇⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣀⣇⣸⠀⢋⣀⣄⣴⣠⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⡿⢁⣴⣿⣿⣿⣿⠀⣿⢸⣿⣿⡇⠀⠀⠀⠀⢸⠀⣲⢠⣍⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⠁⢸⡇⣿⢸⡇⢸⠀⣿⢸⣿⡟⠀⠀⠀⠀⠀⣈⠀⢸⡇⣿⣿⣶⣌⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⡆⢸⣷⣿⣾⡄⡌⠀⢛⢸⠛⠶⠆⠀⠀⠀⠀⠀⠀⠸⠃⢿⣿⣿⣿⣷⣄⠙⢿⡿⢿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠙⠋⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠛⠙⠟⠛⠋⠀⠻⣿⣿⡿⠛⠞⠶⠾⢤⣄⠀⠀⠀⠀⠀⠈⠀⠈⠓⠘⠿⠿⢿⣿⣿⣷⡀⠀⠀⠀⠀⠉⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣤⣤⣄⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⢠⣤⣡⣐⡐⢠⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠋⠉⠉⣋⣉⣭⡟⠛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠀⡄⠀⣤⢄⠀⠀⠀⠀⠁⠀⠀⠁⢉⠹⠎⢛⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠈⠙⠻⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢘⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
䷩ 𝚕𝚒𝚗𝚎 5962
╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕
(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/09/06/microsoft-freefall/#comments
Gemini version at gemini://gemini.techrights.org/2023/09/06/microsoft-freefall/
⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.06.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧
Gemini_version_available_♊︎
✐ Microsoft_and_Its_Proxies_Are_in_a_Freefall⠀✐
Posted in Google, Microsoft, Search at 2:25 pm by Dr. Roy Schestowitz
Summary: Microsoft is a shrinking company; on the client side and the server
side younger companies such as Google are replacing it
MICROSOFT-FUNDED media pretends_that_Microsoft_is_a_valuable_company_that
continues_to_grow, but the exact opposite is true.
“Microsoft is a shrinking company…”Take search for example. Microsoft increased
Bing usage fees, so about 5 months ago Brave dumped that completely and
DuckDuckGo, which is basically a Microsoft proxy, has had a tough couple of
years:
🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇DDG_market_share_2021-2023⦈_
DuckDuckGo market share as a function of time (data_as_OpenDocument_Format)
Despite all the advertising, people eventually find out that DuckDuckGo is just
a Microsoft ‘skin’ and abandon the false promise of “privacy” (DuckDuckGo is
Microsoft surveillance and by extension NSA surveillance).
“Despite all the advertising, people eventually find out that DuckDuckGo is
just a Microsoft ‘skin’ and abandon the false promise of “privacy” (DuckDuckGo
is Microsoft surveillance and by extension NSA surveillance).”As we noted here
some days ago, Bing_as_per_this_year has had loads_of_layoffs (the media barely
reported on it) and so far this month Microsoft has_fallen_even_further_in_the
global_search_market and Indian_market. Now it’s just 0.9%! Pathetic. It is the
same_in_Russia. Microsoft at 0.9%. At one point are the financial
sustainability and viability aspects going to force Microsoft to exit the
market and shut down Bing? Google_is_turning_25 and despite starting as a
search company it is now slaughtering Microsoft’s monopoly on operating
systems. Android is a lot bigger than Windows now, so the_whole_'ecosystem'_of
broken_Windows_is_collapsing. █
⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⡇⢸⣿⠀⣿⠀⣿⡏⢹⣿⣿⣿⣿⣿⠀⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⣿⣿⣿⠛⣿⠀⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣽⣿⠀⣿⠀⣿⡿⢿⣿⣿⣿⠿⣿⠛⣿⡟⢻⡇⢸⡏⠉⣿⠛⣿⠀⣻⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⠀⢸⡇⢸⡇⢸⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⣿⠀⣿⡇⢸⡏⢹⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⠀⢸⡇⢸⡇⢸⣿⠀⣿⠉⣿⡏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⠀⢸⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⣿⣿⣿⠉⣿⠉⣿⣿⣿⣿⣿⡇⠀⣿⠉⣿⠉⣿
⣿⣟⣿⣻⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⠀⢸⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡏⢹⡏⢹⡇⠀⣿⠀⣿⠀⣿
⣿⣿⣿⣿⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⠀⢸⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿
⣿⣿⣿⣿⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⠀⢸⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿
⣿⣷⣿⣼⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⠀⢸⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿
⣿⣿⣿⣿⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⠀⢸⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿
⣿⣿⣿⣿⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⠀⢸⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿
⣿⣿⣿⣾⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⠀⢸⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿
⣿⣿⣿⣿⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⢿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡿⠀⣿⠀⣿⠀⢸⡇⢸⡇⠸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿
⣿⡿⣿⢿⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⠁⠀⡠⠀⡤⠀⣀⠀⡀⠀⡀⢀⠀⡀⠀⠀⠀⠀⡀⡀⠀⠀⠀⢀⢀⠀⠀⢀⠀⠀⠀⢸⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿
⣿⣿⣿⣿⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣤⠀⣤⠀⢠⡄⢠⡄⢠⣤⠀⣤⠀⣤⡄⢠⡄⢠⡄⠀⣤⠀⣤⠀⢠⡄⢠⡄⠀⣤⠀⣼⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿
⣿⣿⣿⣿⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⠀⢸⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿
⣿⣿⣿⣿⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⢿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⠀⢸⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⠇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿
⣿⣿⣿⣿⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⠀⢸⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿
⣿⣿⣿⣿⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⠀⢸⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿
⣿⣿⣟⢻⣿⣀⣿⣀⣿⣇⣸⣇⣸⣿⣀⣿⣀⣿⣇⣸⣇⣸⣇⣀⣿⣀⣿⣀⣿⣇⣸⣇⣸⣿⣀⣿⣀⣿⣇⣸⣇⣸⣿⣀⣿⣀⣿⣀⣸⣇⣸⣇⣸⣿⣀⣿⣀⣿⣇⣸⣇⣸⣿⣀⣿⣀⣿⣇⣸⣇⣸⣇⣀⣿⣀⣿⣀⣿
⣿⣿⣿⣿⢿⣻⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⢿⡿⣿⣿⡿⣻⣿⣿⡿⣿⣿⡿⣿⣿⣿⣿⢿⣿⣿⣿⣟⣿⣿⣿⡿⣻⢿⣿⣿⢛⡿⣛⣿⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⢛⡿⣿⣿⡿⣿⢿⣿⣿⣿⣿
⣿⣿⡿⢟⡟⣽⡿⣫⣿⢿⣿⢟⣽⡿⣿⡿⣓⣽⠿⣻⢟⣪⡿⢟⡿⣽⡿⣫⣿⢫⣿⢟⣽⡿⣷⡿⣫⣿⢿⣾⢟⣻⡿⢗⡿⣛⣿⠿⣺⢯⣿⢟⣽⡟⣽⡿⣫⣿⢿⣮⢟⣻⡿⣷⡽⣛⣿⠿⣻⢟⣻⡿⢟⡿⣽⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
䷩ 𝚕𝚒𝚗𝚎 6046
╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕
(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/09/06/threat-to-security/#comments
Gemini version at gemini://gemini.techrights.org/2023/09/06/threat-to-security/
⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.06.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧
Gemini_version_available_♊︎
✐ Principal_Threat_to_Security_is_Microsoft_Windows_and_Proprietary_Software⠀✐
Posted in Microsoft, Security at 12:38 am by Dr. Roy Schestowitz
Video_download_link
http://techrights.org/wp-content/uploads/2023/09/spyware-threats.webm
Summary: Richard Stallman gave this talk some years ago; meanwhile, a leading
technical university got_cracked due to Microsoft* and it won’t dare mention
the culprit
🄸🄼🄰🄶🄴🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽⦇Windows_TCO:_Yes,_it's_true,we_got_cracked⦈
dovetailed with MIT’s Kerberos and would have avoided “AD”, to paraphrase an
associate. Kerberos_was_sabotaged_by_Microsoft and gag_clauses_have_been_in_use
since_the_early_stages_of_“AD”.
So Microsoft has dragged this university’s computing environment down from
world class to that of a year 2021 “Hillsdale College”. To be sure, Oracle and
Cisco also have their fingers in that pie and a role in the demise of the
institution’s role as one of the world leaders in computing. See “Our
Attorney’s_Response_To_Microsoft” (posted by Roblimo) and this_last_article
which brings up a very important point — that Microsoft regards its contracts
as trade secrets so even someone resourceful and tenacious would be unlikely to
succeed in a FOIA request regarding the publicly-funded university’s support
contracts. Microsoft_tried_to_censor_information while crushing_standards.
Those institutions late in weaning themselves from Microsoft Windows can look
at Samba_4_as_an_alternative.
⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⣿⣿⣿⣿⣿⢿⣿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⡇⣭⢹⠩⢝⣿⢸⣿⠈⣭⢹⢩⠻⡙⠭⠋⣭⡩⢽⢩⢨⡹⢏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⢿⣿⣿⣆⠀⢀⣼⣿⣿⠇⠀⠀⣿⠿⠼⠧⠿⠼⠮⣵⣿⠮⠥⠧⠿⠼⠼⢦⣷⣭⠶⠿⠮⠵⣼⣬⣓⣾⡿⠿⠿⠿⢿⣿⡿⠿⠿⠿⠿⠿⣿⣿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿
⣿⣿⣿⡇⠀⠀⢸⣿⡟⢿⣷⣿⠟⣿⣿⠀⠀⠀⣿⣷⠀⠀⣶⣦⡀⠈⣿⣶⠀⢰⣶⣶⡄⢸⠟⠁⢠⣴⣶⣦⡀⠀⡟⠁⢀⣴⣶⣦⡀⠈⢷⡆⠀⣶⣦⡀⠈⢻⣷⠀⠀⣶⣶⣦⣄⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾
⣿⣿⣿⡇⠀⠀⣼⣿⣧⡄⠹⠃⣤⣿⣿⡄⠀⠀⣿⣿⠀⠀⠿⠿⠁⢀⣿⣿⠀⠸⠿⠏⢹⡟⠀⠀⣿⣿⣿⣿⣿⣴⠀⠀⣾⣿⣿⣿⣧⠀⠈⡇⠀⠿⠿⠃⢀⣼⣿⡇⠀⣿⣿⣿⣿⡆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠛⠛⠛⠃⠀⠀⠛⠛⠛⠃⠀⠀⣿⣿⠀⠀⣦⡀⠀⢿⣿⣿⠀⢰⣶⣆⣸⣇⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⢿⣿⣿⣿⡟⠀⠀⡇⠀⣶⡀⠀⢻⣿⣿⡇⠀⣿⣿⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢿⣷⡀⠈⢿⡿⠀⠘⠿⠿⠟⠁⣆⠀⠈⠻⠿⠿⠋⣨⣧⡀⠈⠻⠿⠟⠁⢀⣼⠇⠀⢿⣷⡀⠀⢻⣿⠀⠀⠿⠿⠟⠋⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣿⠶⢶⣶⣶⢿⡿⡶⡤⡴⡶⡶⣶⡶⢶⢶⡿⡿⣶⠤⢤⢶⣾⡿⣿⠿⡶⢦⡤⡴⡶⣿⣷⣶⣶⣶⣿⣿⣶⣦⣼⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛
⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣴⣤⣤⣤⣤⣧⣬⣶⣧⣤⣬⣬⣦⣄⣮⣧⣤⣤⣤⣿⣤⣤⣤⣧⣧⣤⣤⣦⣦⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⢻⠛⡟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⣟⠛⣻⡏⠋⣹⣿⡋⣿⣿
⣿⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣷⣿⣿
⣿⣿⡇⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⣿⣿⣿
⣿⣿⡇⠀⢸⠉⣿⢹⣿⡏⢹⠏⢹⣿⠛⡿⡛⡿⠛⢻⢻⠛⡇⡟⢻⢸⠛⢻⠟⡛⣿⡟⠟⢿⢟⢻⠟⠻⡟⡻⡛⡟⡟⡿⡛⠟⠛⠟⠃⣿⡟⢛⠟⠻⠟⠻⡿⡛⡏⣻⣟⢐⠟⠻⡟⢻⣿⢟⢻⣿⢸⣿⣿⡇⠀⣿⣿⣿
⣿⣿⡇⠀⢸⡄⠿⣸⣤⡇⡆⣸⢸⣿⢸⡇⠄⣇⠿⢸⠸⠀⡇⡇⣿⢸⢸⢸⠂⠥⢿⡇⠸⢸⠡⠸⡂⠌⡓⠌⡇⢠⢁⡇⠗⡀⢸⡘⠇⣿⡇⣿⡠⢀⡒⠌⡇⠄⡇⢿⣿⢸⡘⢇⡇⣿⣿⠡⠸⣿⢸⣿⣿⡇⠀⣿⣿⣿
⣿⣿⡇⠀⢸⠿⣿⢿⠿⣿⠿⡿⣿⠿⠿⡿⣿⡿⣿⣼⢻⢿⣿⣿⣿⣿⣿⣿⣮⣥⢺⣧⠾⢿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿
⣿⣿⡇⠀⢸⠀⣿⢸⢠⠙⡄⡇⡇⣾⡧⡇⣛⡃⣿⡇⣿⢸⣿⠁⣊⡇⠇⡎⣂⣹⠘⠛⣿⢸⣷⢹⣿⢔⢸⢡⣬⢡⣎⡇⡆⡇⣿⢸⢰⠈⡄⣇⠢⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿
⣿⣿⡇⠀⠸⠧⠭⠾⠼⠤⠧⠧⠷⠬⠵⠧⠿⠧⠿⠧⠹⠬⠭⠦⠥⠿⠴⠷⠭⠾⠼⠿⠭⠬⠏⠾⠷⠬⠬⠮⠴⠦⠵⠧⠥⠷⠤⠼⠼⠤⠧⠧⠥⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⣿⣿⣿
⣿⣿⣷⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣿⣿⣿
⣿⣿⣿⣿⣿⠛⠿⡟⡻⠿⠿⠿⡟⠻⠟⢿⣿⣿⣯⢫⠻⢻⠿⣿⣿⢺⣿⣟⢿⣿⣽⢻⢻⣿⠻⢻⣿⡿⠛⢻⠻⣻⣟⡟⢟⡟⢹⣿⢻⡟⣿⠟⡟⣿⠘⡟⠟⣟⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣶⡧⣷⣶⣶⣷⣶⣷⣷⣶⣾⡿⡿⢿⣾⢶⣾⣷⢵⣿⣾⣾⢷⣾⣿⢾⣾⣶⣾⣾⣮⣾⣷⣷⣾⣾⣿⣗⣣⣷⣶⣾⣿⣾⣷⣷⣷⣷⣿⣾⣶⣶⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣤⣤⣤⣶⣦⣦⣦⣤⣾⣤⣤⣤⣿⣷⣴⣤⣤⣤⣴⣔⣎⣧⣮⣦⣮⣤⣤⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣶⣆⣤⣼⣴⣿⣷⣤⣥⣄⣤⣤⣧⣭⣬⣽⣜⣯⣦⣥⣤⣬⣤⣬⣤⣽⣤⣥⣷⣵⣭⣴⣕⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡭⠙⢛⡯⠝⠋⡛⢛⠛⠙⡛⡟⠋⡏⠋⠟⠋⠋⠛⠿⣻⠙⠛⢻⠛⠛⠛⠋⠟⠛⡻⡟⠙⠟⢻⠛⠛⠛⣛⡛⠛⠋⢻⠙⠛⣻⠋⢹⠹⡍⠋⠙⠭⠉⡟⡭⠟⡻⠛⢹⡿⣽⠛⢛⠟⠛⠛⠻⢻⠙⢻⣿⣿
⣿⣿⣿⣿⣿⠿⡿⢿⠿⠿⡿⢿⢿⡿⢿⠾⡿⡟⣿⡿⠿⢿⡿⣶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣶⣶⣾⣾⣶⣿⣶⣾⣶⣶⣷⣿⣿⣿⣶⣴⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
䷩ 𝚕𝚒𝚗𝚎 6134
╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕
(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/09/06/threat-to-software-freedom-everywhere/#comments
Gemini version at gemini://gemini.techrights.org/2023/09/06/threat-to-software-freedom-everywhere/
⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.06.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧
Gemini_version_available_♊︎
✐ A_Blueprint_for_Digital,Online_Oppression(and_Threat_to_Software_Freedom
Everywhere)⠀✐
Posted in Free/Libre_Software at 2:45 am by Dr. Roy Schestowitz
Video_download_link | md5sum a8a1c95c5af46e06e17653bcf5b2c204
Not About Protecting Kids
Creative Commons Attribution-No Derivative Works 4.0
http://techrights.org/videos/legislating-for-state-power.webm
Summary: The potent and immediate threat to people’s lives has grown greater
with the advance of the latest awful British legislation, which may in turn
jeopardise Free software because it’s harder to mandate/impose back doors on
Free software users
THE latest_episode of The_Cyber|Show was published earlier this month. It
covered what mobile (cellular) phones actually are, what social control
networks do to people, and it debated back doors.
“Andy’s articles have done a spectacular job explaining the issues.”When we
started mentioning_the_show it was because of one of the hosts (Andy), who
contributed some articles to Techrights while he still worked at a university.
Now he spends his time writing and talking about important issues, including
Software Freedom.
“Thanks so much to you and your team for the enthusiastic support,” Andy told
me this week. Andy’s articles have done a spectacular job explaining the
issues.
The video above contains some personal thoughts on the episode contained below.
█
Your browser does not support the audio element.
䷩ 𝚕𝚒𝚗𝚎 6194
╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕
(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/09/06/untrustworthy-ibm/#comments
Gemini version at gemini://gemini.techrights.org/2023/09/06/untrustworthy-ibm/
⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.06.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧
Gemini_version_available_♊︎
✐ Red_Hat_Under_IBM_is_Lying_to_Us,_It’s_Not_Trustworthy_Anymore⠀✐
Posted in Deception, GNU/Linux, IBM, Red_Hat at 1:45 am by Dr. Roy Schestowitz
Video_download_link | md5sum 47b8912f2621159a583815c31a06eb86
Three Months of OpenSource.com Silence
Creative Commons Attribution-No Derivative Works 4.0
http://techrights.org/videos/ibm-open-source-neglect.webm
Summary: IBM never had an interest in bringing back OpenSource.com (in any
shape or form); 3 months later we remind people of the empty promises and
hollow gestures
ANOTHER month passes_by without IBM fulfilling its empty promises regarding
OpenSource.com. The site was essentially killed off with the layoffs (this past
spring) and there’s no sign of it coming back. It issued a terse statement in
June a day or so after we had noted the demise of OpenSource.com and it went
sort of ‘viral’.
“Thankfully, in 2023, there are still many alternatives available (but fewer
over time).”The video above discusses what IBM has done to Fedora, RHEL,
CentOS, and even Container_Linux_(CoreOS), which was completely discontinued.
OpenSource.com was not the only Red Hat site that IBM decided to shut down and
it’s not because the Web is declining but because IBM is declining its
obligations to the Free software community. This isn’t going to end to well.
People ought to consider adoption of community-run distros which don’t just
copy everything from Fedora (IBM), i.e. they have a go at taking back control
over the stack. Thankfully, in 2023, there are still many alternatives
available (but fewer over time). █
䷩ 𝚕𝚒𝚗𝚎 6246
╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕
⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.06.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧
Gemini_version_available_♊︎
✐ Links_06/09/2023:_Istio_1.19.0_and_Arti_1.1.8⠀✐
Posted in News_Roundup at 12:48 pm by Dr. Roy Schestowitz
🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈
§ Contents⠀➾
* GNU/Linux
o Server
o Audiocasts/Shows
o Graphics_Stack
o Instructionals/Technical
o WINE_or_Emulation
o Games
o Desktop_Environments/WMs
# K_Desktop_Environment/KDE_SC/Qt
* Distributions_and_Operating_Systems
o New_Releases
o Gentoo_Family
o SUSE/OpenSUSE
o Arch_Family
o Fedora_Family_/_IBM
o Canonical/Ubuntu_Family
o Open_Hardware/Modding
o Mobile_Systems/Mobile_Applications
* Free,_Libre,_and_Open_Source_Software
o Web_Browsers/Web_Servers
# Mozilla_and_Tor
o SaaS/Back_End/Databases
o Content_Management_Systems_(CMS)
o Programming/Development
* § GNU/Linux⠀➾
o § Server⠀➾
# ⚓ Kubecost_Embraces_GCP_to_Control_Kubernetes_Costs⠀⇛
Kubecost made its platform for managing the cost of
Kubernetes clusters available on the Google Cloud
Platform (GCP).
# ⚓ Can_a_Cloud_Center_of_Excellence_Help_You_Become_Cloud
Native?⠀⇛
A cloud center of excellence (CCoE) can be an
extremely valuable asset for an organization
looking to build and migrate cloud-native
applications.
o § Audiocasts/Shows⠀➾
# ⚓ Ubuntu_Podcast_from_the_UK_LoCo:_Using_Two_GPUs_at_Once⠀⇛
Exploring the secrets of the TPM, running Radeon
and NVIDIA GPUs in one PC, and getting ongoing data
from an EV.
# ⚓ Tux Digital ☛ Destination_Linux_338:_Reverse_Psychology
Tech_Support⠀⇛
On this episode of Destination Linux (338), we deep
dive a community feedback that takes us into
encrpytion, learning the cli, and containerization.
Then we’re going to discuss some new AI tricks that
might leave you feeling creeped out. Plus, we have
our tips, tricks and software picks for you.
# ⚓ 338:_Reverse_Psychology_Tech_Support⠀⇛
SHOW NOTES ►► https://tuxdigital.com/podcasts/
destination-linux/dl-338/
# ⚓ mintCast Podcast ☛ mintCast_420_–_“Puff_Puff_Pass”⠀⇛
First up in the news: Mint Monthly News – August,
New Asahi Linux Mac GPU beats Apple, Gnome improves
Epiphany, Budgie 10.8 is out, Bodhi 7.0.0 is
released, QEMU 8.1 released, LibreOffice gets a new
number, Linux Turns 32, Mageia 9 released, Linux
Kernel 6.5 is out, and Firefox loses users
In security and privacy: Nothing. We have nothing.
Then in our Wanderings: Joe and Moss return to the
fold, and welcome Eric Adams to join us
Download
o § Graphics Stack⠀➾
# ⚓ Free Desktop ☛ [ANNOUNCE]_mesa_23.2.0-rc3⠀⇛
Hi list,
After a very long time, here is mesa 23.2.0-rc3.
From my side we've had
some techincal issues plus some personal issues for
me. There's a lot
here, and I'm expecting we may have some
regressions here, so I've added
another rc. I'm hoping to run on a compressed
schedule, and possibly
have another rc by the end of the week.
Dylan
o § Instructionals/Technical⠀➾
# ⚓ It’s FOSS ☛ How_to_Create_Persistent_Live_USB_of_Ubuntu⠀⇛
Enjoy live USB with persistence so that your
changes made in live sessions are saved. Learn to
create a persistent USB in this tutorial.
# ⚓ Ubuntu Handbook ☛ Linux_Kernel_6.5_is_Ready_to_Install_in
Ubuntu_22.04_LTS⠀⇛
Want to install the latest Linux Kernel 6.5? It’s
there in your Ubuntu 22.04 system repository!
# ⚓ Own HowTo ☛ How_to_fix_bash:_reboot:_command_not_found
error_on_Debian_12⠀⇛
reboot is a simple command that is used to reboot
your machine. On Debian 12 this command doesn’t
work when you execute it because reboot is not a
known command to the system.
# ⚓ Ubuntu Handbook ☛ Enable_Mouse_Scroll_Switching_Workspaces
in_Ubuntu_23.10⠀⇛
Ubuntu 23.10 with GNOME 45 has replaced the top-
left ‘Activities’ with a workspace indicator. By
hovering over it, you can use mouse scroll to
switch workspaces. This is done by a simple
extension called “Workspace Scroll”.
# ⚓ LinuxTuto ☛ How_to_Install_NextCloud_on_Debian_12⠀⇛
Nextcloud is a versatile and community-driven
project, making it a popular choice for
individuals, businesses, and organizations looking
for a secure and self-hosted cloud storage…
# ⚓ Log_Analysis_and_Beyond:_Correlating_Data_with_Nagios_Log
Monitoring_Addons⠀⇛
# ⚓ Data_at_a_Glance:_Visualizing_Monitoring_with_Nagios
Graphing_Addons⠀⇛
# ⚓ Unlocking_Monitoring_Potential:_Exploring_Third-Party
Nagios_Addons⠀⇛
# ⚓ Crafting_Custom_Nagios_Plugins:_Building_From_the_Ground
Up⠀⇛
# ⚓ Installing_and_Managing_Nagios_Plugins:_A_Step-by-Step
Guide⠀⇛
# ⚓ Demystifying_Nagios_Plugins:_Unveiling_the_Architecture⠀⇛
# ⚓ Case_Study:_Integrating_Nagios_Alerts_into_DevOps
Workflows⠀⇛
# ⚓ Case_Study:_Scaling_Enterprise_Notifications_for_Complex
Infrastructures⠀⇛
# ⚓ Case_Study:_Small_Business_Alert_Setup_in_Nagios⠀⇛
# ⚓ Refining_Your_Strategy:_Regularly_Reviewing_and_Improving
Notifications⠀⇛
# ⚓ What_is_LEMP_Stack?⠀⇛
In the world of web development, terms like MEAN,
MERN, LEMP, and PERN are frequently encountered.
These terms refer to web stacks, which are bundles
of software, frameworks, and libraries used for
building full-stack web applications. One such
popular web stack is LEMP. In this comprehensive
guide, we will explore what the LEMP stack is, its
components, how it works, and why it is popular in
web development.
# ⚓ Make Tech Easier ☛ Get_Your_Own_Self-hosted_RSS_Reader_With
Tiny_Tiny_RSS⠀⇛
Tiny Tiny RSS is a simple, yet highly flexible web-
based RSS reader that you can install on your own
server. It allows you to create your own personal
library of RSS feeds that can automatically update
and you can read feeds straight from your browser.
This article will show you how you can install Tiny
Tiny RSS in Ubuntu.
# ⚓ sos_report_–_The_Swiss_Army_Knife_of_Diagnostic_Tools⠀⇛
The sosreport command has been around since 2009.
Written in Python the tool is designed to gather
comprehensive diagnostic data from a Linux system.
The tool has been modified and improved by the open
source community over the years and is now run
using the command sos report. sos report does not
make modifications to your system configuration.
# § idroot⠀➾
# ⚓ ID Root ☛ How_To_Install_Bauh_on_Ubuntu_22.04_LTS⠀⇛
In this tutorial, we will show you how to
install Bauh on Ubuntu 22.04 LTS. Bauh is a
versatile application manager for Linux that
bridges the gap between multiple package
managers, making it a powerful and efficient
tool for managing software.
# ⚓ ID Root ☛ How_To_Install_Yarn_on_Debian_12⠀⇛
In this tutorial, we will show you how to
install Yarn on Debian 12. JavaScript has
firmly established itself as a dominant force
in modern web development. With its expansive
ecosystem of libraries and frameworks,
managing JavaScript packages efficiently is
paramount.
# ⚓ ID Root ☛ How_to_Use_Dos2unix_Command_on_Linux⠀⇛
In the ever-evolving landscape of technology,
the need for seamless compatibility across
various platforms remains a constant
challenge. One often-overlooked factor that
can wreak havoc on cross-platform file
sharing is the difference in text file
formats between DOS and Unix systems.
o § WINE or Emulation⠀➾
# ⚓ It’s FOSS ☛ Good_News!_Wii_U_Emulator_Cemu_2.0_Goes_Open
Source_With_Linux_Support⠀⇛
If you have been following us, you might have
noticed some new projects switching to open-source.
One of them is a live debugger tool, Sidekick, and
the other one is a privacy-focused Evernote
alternative…
Now, we have another exciting project to join the
list, i.e., Cemu Wii U emulator.
Wii U was one of the most loved video game consoles
developed by Nintendo in 2012.
Of course, Wii U games were popular back then, and
now that it is no longer available as a new
product, gamers use emulators to enjoy those games.
o § Games⠀➾
# ⚓ Vice Media Group ☛ Video_Game_Workers_Are_Now_Voting
Whether_to_Strike_Over_AI,_Wages⠀⇛
SAG-AFTRA says video game companies have not
addressed adequate on-set protections or proper
regulations on using artificial intelligence.
# ⚓ Torrent Freak ☛ Bungie_&_Teenage_Destiny_2_Cheat_Settle
Differences_With_$500K_Permaban⠀⇛
A teenager who reportedly cheated in Destiny 2,
evaded multiple bans, threatened Bungie employees,
and generally made the developer’s life a
nightmare, has reached a settlement with the gaming
company. In addition to a laundry list of
restrictions moderating his future behavior, the
teenager has accepted Bungie’s $500,000 offer to
put this matter behind them.
# ⚓ GamingOnLinux ☛ STAR_WARS_Jedi:_Survivor_more_playable_on
Steam_Deck_with_Patch_7⠀⇛
STAR WARS Jedi: Survivor just had Patch 7 released,
and Respawn noted it includes some performance
improvements. So what does this mean for the Steam
Deck? Here’s what.
# ⚓ GamingOnLinux ☛ Humble_Choice_has_Tiny_Tina’s_Wonderlands,
Patch_Quest,_Deceive_Inc_+_more⠀⇛
Another pretty great sounding bundle of games, with
the monthly Humble Choice live for September.
Here’s a run over the compatibility for Steam Deck
and desktop Linux.
# ⚓ GamingOnLinux ☛ Broken_Sword_–_Shadow_of_the_Templars
getting_remastered,_plus_a_whole_new_adventure⠀⇛
Revolution Software recently announced two huge
bits of news for adventure game fans! Not only will
there be a whole new game with Broken Sword –
Parzival’s Stone but Broken Sword – Shadow of the
Templars: Reforged is coming too.
# ⚓ GamingOnLinux ☛ Linux_updates_tease_Valve_‘Galileo’_and
‘Sephiroth’_–_Steam_Deck_refresh?_Or_new_VR?⠀⇛
Here’s something that could be exciting but also
could be a whole lot of nothing. So keep
expectations firmly in check, but work submitted
for Linux kernel 6.6 show something interesting
from Valve. Potentially a Steam Deck refresh or
their new VR headset perhaps?
# ⚓ GamingOnLinux ☛ Half-Life_Alyx_NoVR_mod_to_get_a_huge
upgrade_in_October⠀⇛
The work going into the Half-Life Alyx NoVR mod is
quite amazing, and while it was already very
playable the next major update coming in October is
going to really expand it.
# ⚓ GamingOnLinux ☛ Zoom_Platform_adds_Syberia_and_Syberia_II
powered_by_ScummVM⠀⇛
It’s now easier than ever to play the classic
adventures Syberia and Syberia II from Microids, as
the Zoom Platform has added them with cross-
platform support. For those who don’t know, Zoom
Platform is a DRM-free store dedicated to keeping
classics and modern games alive and they support
Linux too.
# ⚓ GamingOnLinux ☛ Game_porter_Ethan_Lee_offers_services_to
maintain_old_games_for_developers⠀⇛
Ethan Lee, otherwise known as flibitijibibo (really
rolls off the tongue huh), who created FNA and has
ported a ton of games to Linux, macOS and more has
announced a new game maintenance service for
developers.
# ⚓ GamingOnLinux ☛ Get_a_bunch_of_live-action_FMV_games_from
Humble_Bundle⠀⇛
Love live-action FMV games? Wales Interactive
teamed up with Humble Bundle to give you a bunch of
them so here’s the compatibility to expect on Steam
Deck and desktop Linux.
# ⚓ GamingOnLinux ☛ Valve_goes_for_the_smurfs_banning_90,000
people_in_Dota_2⠀⇛
After the rather exciting launch of the Summer
Update bringing with it new matchmaking and tools
to get rid of bad experiences, Valve goes for the
smurfs next.
o § Desktop Environments/WMs⠀➾
# § K Desktop Environment/KDE SC/Qt⠀➾
# ⚓ DebugPoint ☛ Join_the_KDE_Plasma_6_Wallpaper_Contest,
Win_a_Framework_Laptop⠀⇛
The countdown to the highly anticipated KDE
Plasma 6 release is officially on, and the
KDE team is reaching out to the creative
minds in the Linux community to help shape
the new desktop environment’s visual
identity.
KDE team have just announced the “KDE Plasma
6 Wallpaper Competition,” inviting artists
and designers to showcase their talents and
compete for a chance to leave an indelible
mark on the upcoming Plasma 6.0 release. The
first release of the 6-series!
* § Distributions and Operating Systems⠀➾
o § New Releases⠀➾
# ⚓ Linux Magazine ☛ Linux_From_Scratch_12.0_is_Now_Available⠀⇛
If you’re looking to roll your own Linux
distribution, the latest version of Linux From
Scratch is now available with plenty of updates.
o § Gentoo Family⠀➾
# ⚓ Gentoo ☛ My_thin_wrapper_for_emerge(1)⠀⇛
I’ve recently written a thin wrapper over emerge
that I use in my development environment. It does
the following: [...]
o § SUSE/OpenSUSE⠀➾
# ⚓ SUSE’s Corporate Blog ☛ Getting_granular_on_GCC_12⠀⇛
Once again, experts from our SUSE toolchain
development team (Jan Hubička, Michael Matz,
Richard Biener) led by Martin Jambor have joined
forces with Brent Hollingsworth from AMD, to
publish a new SUSE Best Practices guide. >
# ⚓ OpenSUSE ☛ Survey_Reveals_Community_Preferences_for
openSUSE’s_Future_Direction⠀⇛
The openSUSE contributor community recently
completed a comprehensive survey last week aimed at
determining the project’s future direction. The
results were obtained from 327 respondents, and it
sheds some light on various aspects of openSUSE’s
development, deployment and upgrade plans.
A pdf of the survey can be found on the openSUSE
Wiki.
[...]
I’d prefer no Leap replacement and just use
Tumbleweed: 15.29%
The results of this comprehensive survey offer a
clear snapshot of the openSUSE community’s
preferences and priorities, which will undoubtedly
influence the project’s future direction.
o § Arch Family⠀➾
# ⚓ DebugPoint ☛ Manjaro_23_“Uranos”_Delivers_Exciting
Updates⠀⇛
Manjaro, the user-friendly Arch-based Linux
distribution, has just released its latest version,
Manjaro 23, codenamed “Uranos”. Since the release
of Talos in April 2023, the Manjaro team has been
diligently working to bring you this exciting
update. In this article, we’ll recap the key
features and improvements you can expect in Manjaro
23 across various desktop environments.
o § Fedora Family / IBM⠀➾
# ⚓ Announcing_Istio_1.19.0⠀⇛
We are pleased to announce the release of Istio
1.19. This is the third Istio release of 2023. We
would like to thank the entire Istio community for
helping get the 1.19.0 release published. We would
like to thank the Release Managers for this
release, Kalya Subramanian from Microsoft, Xiaopeng
Han from DaoCloud, and Aryan Gupta from Google. The
release managers would specially like to thank the
Test & Release WG lead Eric Van Norman (IBM) for
his help and guidance throughout the release cycle.
We would also like to thank the maintainers of the
Istio work groups and the broader Istio community
for helping us throughout the release process with
timely feedback, reviews, community testing and for
all your support to help ensure a timely release.
# ⚓ Istio_1.19.0_Change_Notes⠀⇛
§ Deprecation Notices
These notices describe functionality that will be
removed in a future release according to Istio’s
deprecation_policy. Please consider upgrading your
environment to remove the deprecated functionality.
# ⚓ Istio_1.19_Upgrade_Notes⠀⇛
When you upgrade from Istio 1.18.x to Istio 1.19.x,
you need to consider the changes on this page.
These notes detail the changes which purposefully
break backwards compatibility with Istio 1.18.x.
The notes also mention changes which preserve
backwards compatibility while introducing new
behavior.
Changes are only included if the new behavior would
be unexpected to a user of Istio 1.18.x.
§ Use the canonical filter names for EnvoyFilter
If you are using EnvoyFilter API, please use
canonical filter names. The use of deprecated
filter name is not supported. See the Envoy
documentation for further details.
§ base Helm Chart removals
A number of configurations previously present in
the the base Helm chart were copied to the istiod
chart in a previous releases.
In this release, the duplicated configurations are
fully removed from the base chart.
Below shows a mapping of old configuration to new
configuration: [...]
# ⚓ Packit_Team:_Call_for_volunteers:_help_to_test_us_the
release_syncing_using_staging_instance⠀⇛
In the upcoming months, we plan to migrate our
service to a new cluster. However, this may affect
propose_downstream
and pull_from_upstream jobs due to the new firewall
rules. The problematic aspects could be:
# commands you run in your actions during
syncing the release involving interactions
with external servers
# downloading your sources from various hosting
services (crates.io, npm, gems, etc.)
To smoothen this transition, we kindly encourage
you to enable one of these jobs on our already
migrated staging instance.
This recommendation is particularly important if
you belong to one of the groups affected by the two
previous points.
This proactive step will help us identify and
address any issues promptly.
Both instances can be run at the same time and the
behaviour can be configured via the
packit_instances configuration key, which is by
default set to ["prod"].
# ⚓ CentOS ☛ CentOS_Hyperscale_SIG_Quarterly_Report_for
2023Q2⠀⇛
This report covers work that happened between April
4th 2023 and August 31st 2023. For previous work,
see the 2023Q1 report. Purpose The Hyperscale SIG
focuses on enabling CentOS Stream deployment on
large-scale infrastructures and facilitating
collaboration on packages and tooling. Membership
update Since the last update, the SIG gained four
new members (Raymond Colebaugh, […]
o § Canonical/Ubuntu Family⠀➾
# ⚓ OMG Ubuntu ☛ Ubuntu_23.10_Mascot_Art,_Default_Wallpaper
Revealed⠀⇛
Ubuntu 23.10’s default wallpaper and mascot artwork
draws heavily on the motifs afforded to it by its
mythological moniker – to a greater degree than I
think many of us had expected.
Most Ubuntu mascot artwork has, during the past 5
years or so, been fashioned from geometric shapes,
simplistic lines, or concentric circles. But Mantic
is a far more complex beast. The ‘bull’ head is
present but it is not as linearly distinct as
mascots past.
Instead, Ubuntu’s designers have chosen to
encapsulate the mascot image within a maze1, rather
than a labyrinth like the Minotaur of legend. It’s
still a clever intertwining and creates a
conceptually bold centerpiece for the wallpaper –
ancient and classical yet modern and dynamic…
o § Open Hardware/Modding⠀➾
# ⚓ Hackaday ☛ Raspi-Powered_Typewriter_Is_A_Real_MUSE⠀⇛
Thanks to parenting and life in general, [Brendan]
had fallen out of the habit of writing and wasn’t
happy about it. If you write anything ever, you
already know there are endless distractions when it
comes to doing so on a computer. Sure, there always
typewriters, but it’s difficult to do anything with
the fruits of a typewriter other than scan it in or
make copies, and it’s basically un-editable except
by hand.
# ⚓ Tom’s Hardware ☛ Raspberry_Pi_Projects:_September_2023⠀⇛
These are the best Raspberry Pi projects we’ve had
the honor of covering over the last month for
September 2023.
# ⚓ Hackaday ☛ Jenny’s_Daily_Drivers:_Raspberry_Pi_Desktop⠀⇛
One of the more exciting prospects upon receiving
one of the earliest Raspberry Pi boards back in
2012 was that it was a fully-functional desktop
computer in the palm of your hand. In those far-off
days, the Debian OS distro for the board wasn’t
even yet called Raspbian, but it would run a full-
on desktop on your TV and you could use it after a
fashion to browse the web or do wordprocessing. It
wasn’t in any way fast, but it was usable enough to
be more than a novelty. I’ve said before on these
pages that the Raspberry Pi folks’ key product is
their OS rather than their computers. While they
rarely have the fastest or highest spec hardware,
you can depend on Raspberry Pi OS being updated and
supported through the life of the board unlike many
of their competitors. I can download their latest
OS image and still run it on that 2012 board, which
to me ranks as a very laudable achievement.
# ⚓ Linux Gizmos ☛ Libre_Computer_showcases_low-cost_SBC_with
PoE_support⠀⇛
Yesterday, Libre Computer unveiled a new variant of
the Le Potato Single Board Computer launched a few
years ago. The new Sweet Potato board is also based
on the Amlogic S905X SoC as its predecessor, but
targets commercial and consumer applications
instead.
# ⚓ Arduino ☛ This_gargantuan_3D-printed_robot_hand_is_just_the
beginning⠀⇛
Ivan Miranda has a humble dream: he wants to build
a massive 3D-printed robot that he can ride upon.
In other words, he wants a mech. But that is
obviously a very challenging project that will take
an incredible amount of time and money.
# ⚓ Arduino ☛ Bipedal_robot_walks_with_a_single_motor⠀⇛
A popular goal among roboticists is animal-like
locomotion. Animals move with a fluidity and grace
that is very hard to replicate artificially. That
goal has led to extremely complex robots that
require a multitude of motors and sensors, along
with heavy processing, to walk. But even those
don’t quite match biological movement.
# ⚓ Hackaday ☛ Streaming_Video_From_An_ESP32⠀⇛
The ESP32, while first thought to be little more
than a way of adding wireless capabilities to other
microcontrollers, has quickly replaced many of them
with its ability to be programmed as its own
platform rather than simply an accessory. This also
paved the way for accessories of its own, such as
various sensors and even a camera. This guide goes
over taking the input from the camera and streaming
it out over the network to multiple browsers.
# ⚓ Jeff Geerling ☛ Testing_the_Coral_TPU_Accelerator_(M.2_or
PCIe)_in_Docker⠀⇛
I recently tried setting up an M.2 Coral TPU on a
machine running Debian 12 ‘Bookworm’, which ships
with Python 3.11, making the installation_of_the
pyCoral library very difficult (maybe impossible
for now?).
Some of the devs responded ‘just install an older
Ubuntu or Debian release’ in the GitHub issues, as
that would give me a compatible Python version (3.9
or earlier)… but in this case I didn’t want to do
that.
# ⚓ 10_Free_Online_Gerber_Viewers:_View_Your_PCB_Files_on_the
Go⠀⇛
Gerber files are the standard way to store PCB
design images. Gerber viewers let you see the
content of a Gerber file. These files usually come
in .gbr, .gbx, .top, .bot, etc file extensions. You
can open and check Gerber files from your browser
with online Gerber viewers. No download or
installation is needed.
o § Mobile Systems/Mobile Applications⠀➾
# ⚓ Silicon Angle ☛ Android_is_getting_new_features_to_keep
people_productive_and_connected⠀⇛
The Android team at Google LLC is applying
artificial intelligence to make the operating
system that runs phones and other devices easier
for people to use. Google is putting AI to use with
its Assistant At A Glance widget that can bring
users useful information right on their home
screen.
# ⚓ Android Police ☛ Google_is_killing_the_Play_Movies_&_TV_app
for_Android_TV⠀⇛
# ⚓ The Sun ☛ Millions_of_Android_owners_receive_huge_free_‘AI
assistance’_upgrade_that_instantly_boosts_their_smartphones_|
The_US_Sun⠀⇛
# ⚓ India Today ☛ Android_14_could_be_released_to_everyone_on
October_4_at_Google_Pixel_8_launch_event_–_India_Today⠀⇛
# ⚓ The Register UK ☛ ‘android’_rebranded_as_‘Android’,_in_3D_•
The_Register⠀⇛
# ⚓ SamMobile ☛ Google_has_delayed_the_release_of_stable
Android_14_update_–_SamMobile⠀⇛
# ⚓ Florian Müller ☛ FOSS_Patents:_Three_dozen_U.S._states_are
about_to_settle_Android_app_store_antitrust_case_with_Google,
leaving_Epic_Games_and_Match_Group_as_two_remaining
plaintiffs:_San_Francisco_trial_starts_in_November⠀⇛
# ⚓ Lifewire ☛ What_Does_‘Sent_as_SMS_via_Server’_Mean_on
Android,_and_How_Do_You_Fix_It?⠀⇛
* § Free, Libre, and Open Source Software⠀➾
o ⚓ Terence Eden ☛ Should_the_WordPress_scheduler_use_datetime-
local?⠀⇛
There’s a brilliant post by WordPress about how they’ve
optimised some of the backend code to make it more
efficient. So here’s a suggestion for something else
which can be optimised.
o ⚓ Linux Links ☛ Best_Free_and_Open_Source_Alternatives_to_IBM
Watson⠀⇛
IBM Watson is a data analytics processor that uses
natural language processing, technology that analyzes
human speech for meaning and syntax.
o ⚓ Linux Links ☛ Machine_Learning_in_Linux:_Piper⠀⇛
Piper is billed as a fast, local neural text to speech
system. It’s free and open source software written in C++
and Python.
o ⚓ 80_Essential_Linux_Applications_for_Every_User_in_2023⠀⇛
2022 was an exceptional year for numerous applications,
particularly those that are both free and open source.
o § Web Browsers/Web Servers⠀➾
# § Mozilla and Tor⠀➾
# ⚓ Tor ☛ Arti_1.1.8_is_released:_Onion_service
infrastructure⠀⇛
Arti is our ongoing project to create a next-
generation Tor client in Rust. Now we’re
announcing the latest release, Arti 1.1.8.
This release continues our work on support
for onion services in Arti. It includes
backend support for nearly all of the
functionality needed to launch and publish an
onion service and accept incoming requests
from onion service clients. This
functionality is not yet usable, however: we
still need to connect it all together, test
and debug it, and provide high-level APIs to
allow the user to actually turn it on.
# ⚓ Mozilla ☛ The_Mozilla_Blog:_A_New_York_Times_Magazine
editor_on_her_internet_obsessions⠀⇛
New York Times Magazine editor Iva Dixit
talks about being ratioed on Twitter, an
internet equivalent of a “healing sound bath”
and the pieces she rereads to take a break
from online discourse.
Here at Mozilla, we are the first to admit
the internet isn’t perfect, but we know the
internet is pretty darn magical. The internet
opens up doors and opportunities, allows for
human connection, and lets everyone find
where they belong — their corners of the
internet. We all have an internet story worth
sharing.
# ⚓ Mozilla ☛ Hacks.Mozilla.Org:_Faster_Vue.js_Execution
in_Firefox⠀⇛
Speedometer_3 is a cross-industry effort to
build a modern browser benchmark rooted in
real-world user experiences. Its goal is to
focus browser engineering effort towards
making the Web more smooth for actual users
on actual pages. This is hard to do and most
browser benchmarks don’t do it well, but we
see it as a unique opportunity to improve
responsiveness broadly across the Web.
This requires a deliberate analysis of the
ecosystem — starting with real user
experiences and identifying the essential
technical elements underlying them. We built
several new tests from scratch, and also
updated some existing tests from Speedometer
2 to use more modern versions of widely-used
JavaScript frameworks.
# ⚓ LinuxSecurity ☛ Critical_Memory_Safety_Bug,_Other
Severe_Vulns_Fixed_in_Thunderbird⠀⇛
A critical memory safety bug has been
discovered in Thunderbird 115.0 and
Thunderbird 102.13 ( CVE-2023-4056 ). Due to
the severity of this vulnerability’s threat
to the confidentiality, integrity, and
availability of impacted systems, it has
received a National Vulnerability Database
base score of 9.8 out of 10. Other severe
vulnerabilities have also been found in
Thunderbird, including improper validation of
the Text Direction Override Unicode Character
in filenames ( CVE-2023-3417 ) and copying of
an untrusted input stream to a stack buffer
without checking its size ( CVE-2023-4050 ).
o § SaaS/Back End/Databases⠀➾
# ⚓ Martijn Braam ☛ Squirrel_Strings⠀⇛
The possibility for injection vulnerabilities is
everywhere. Most famously SQL injections where
string templating or concatenation is used to build
SQL commands. It’s still very easy to create one of
these vulnerabilities because the APIs are perfect
for injection.
# ⚓ Peter Eisentraut ☛ PostgreSQL_make_install_times
revisited⠀⇛
We continue our exploration of PostgreSQL build
system performance. A long time ago, I wrote an
article about how to optimize the performance of
make install. This was quite helpful, as it reduced
the time from 10.493 s by default to 1.654 s with
some tweaks (6x faster). Now, with different
hardware, a much newer PostgreSQL, and a new build
system looming, let’s take another look.
# ⚓ TecAdmin ☛ GROUP_BY_Statement_in_MySQL⠀⇛
In the realm of relational databases, data
retrieval and manipulation form the crux of most
operations. MySQL, one of the most popular open-
source relational database management systems,
offers a plethora of SQL statements and clauses to
cater to these needs.
o § Content Management Systems (CMS)⠀➾
# ⚓ Andrea_Corbellini:_My_journey_from_Disqus_to_Remark42⠀⇛
Readers of this blog might have noticed a few
changes recently. For example, I’ve been working on
improving the look of the blog (maybe with
questionable results), as well as improving the
experience on mobile. But one of the biggest
changes that perhaps some have noticed is that all
of the comments on all of my articles have suddenly
disappeared since February 2023. Now, almost 7
months later, all comments have finally been
restored.
o § Programming/Development⠀➾
# ⚓ Chris Coyier ☛ Rewrite_&_Rethink⠀⇛
Baldur wrote up some thoughts about how companies
don’t typically reward refactoring code. There
isn’t a lot of incentive at many companies for slow
work, rewriting old code, refactoring toward better
ideas, paying down technical debt, and that kind of
thing. I get that impression anyway, I don’t have
much first-hand experience as I’ve spent the last
decade at CodePen.
# ⚓ University of Toronto ☛ Having_ClamAV_reject_email_using
the_Malwarepatrol_database_seems_unwise⠀⇛
In practice, ClamAV is both a virus and malware
recognition engine and a collection of malware
signatures. ClamAV only comes with a limited set of
signatures, so supplementing it with additional
third party sources is popular (and perhaps almost
essential). Often people use update tools and
scripts to configure and fetch these additional
signatures, such as Fangfrisch. One of the popular
providers of third party signatures is Malware
Patrol, who have a number of tiers of access,
including a (free) tier for educational
institutions. Since we are an educational
institution, we signed up for this tier and added
it to the configuration of the third party update
script we were using at the time so that it would
be part of our email anti-spam filtering (when we
switched over to ClamAV from our prior solution).
Well, we thought we’d added it; in fact we’d made a
configuration mistake such that we were silently
failing to fetch the Malware Patrol database. We
only noticed and fixed this mistake when we
switched to Fangfrisch for our third party updates.
# ⚓ Dirk Eddelbuettel ☛ Dirk_Eddelbuettel:_RcppInt64_0.0.1_on
CRAN:_New_Package!⠀⇛
Happy to share that a new package RcppInt64 arrived
on CRAN earlier today after a brief one-day
inspection round. RcppInt64 collects some of the
previous conversions between 64-bit integer values
in R and C++, and regroups them in a single
package.
# ⚓ Qt ☛ Qt_Visual_Studio_Tools_3.0_Released [Ed: Qt is
spreading proprietary software and helps Microsoft's too]⠀⇛
We are happy to announce the release of the Qt
Visual Studio Tools version 3.0.1. Installation
packages are now available at the Visual_Studio
Marketplace and download.qt.io.
# ⚓ Russell_John:_Tips_for_Competitive_Programmers⠀⇛
I received the following question on my AMA section
and thought of writing a blog post instead of
answering in a few lines. I like Linux but I do not
enjoy competitive programming (sport programming).
How can I enjoy competitive programming?
# ⚓ Linux Links ☛ 10_Best_Free_and_Open_Source_Web-Based_Git
Clients⠀⇛
Git is an open source distributed version control
system which was originally designed by Linus
Torvalds, the creator of Linux, in 2005 for Linux
kernel development. We explore our recommended web-
based tools.
䷩ 𝚕𝚒𝚗𝚎 7407
╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕
⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.06.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧
Gemini_version_available_♊︎
✐ Links_06/09/2023:_Manjaro_23_Released_and_Changes_in_Zenwalk⠀✐
Posted in News_Roundup at 1:15 am by Dr. Roy Schestowitz
🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈
§ Contents⠀➾
* GNU/Linux
o Audiocasts/Shows
o Applications
o Instructionals/Technical
o Desktop_Environments/WMs
# K_Desktop_Environment/KDE_SC/Qt
# GNOME_Desktop/GTK
* Distributions_and_Operating_Systems
o Reviews
o New_Releases
o BSD
o SUSE/OpenSUSE
o Arch_Family
o Fedora_Family_/_IBM
o Debian_Family
o Canonical/Ubuntu_Family
o Devices/Embedded
o Open_Hardware/Modding
o Mobile_Systems/Mobile_Applications
* Free,_Libre,_and_Open_Source_Software
o GNU_Projects
* Leftovers
o Education
o Proprietary/Artificial_Intelligence_(AI)
o Pseudo-Open_Source
# Openwashing
o Security
# Privacy/Surveillance
o Defence/Aggression
o Environment
# Wildlife/Nature
o Finance
o Censorship/Free_Speech
o Freedom_of_Information_/_Freedom_of_the_Press
o Civil_Rights/Policing
o Internet_Policy/Net_Neutrality
o Monopolies
# Patents
* § GNU/Linux⠀➾
o § Audiocasts/Shows⠀➾
# ⚓ Late_Night_Linux_–_Episode_245⠀⇛
Hacking 2-way radios, upgrading Debian from 10 to
12, sshing into the Ubuntu Server installer, a new
version of a minimal keyboard-focused browser,
establishing the true health of your laptop
battery, playing Wipeout in the browser, RSS
aggregators, and more.
o § Applications⠀➾
# ⚓ ZDNet ☛ This_tool_is_my_new_favorite_way_to_monitor_and
manage_apps_on_the_Linux_desktop⠀⇛
I’ve been using the Linux operating system for a
very long time. I’ve watched so many apps come and
go, all the while making promises to help ease the
confusion of controlling apps and viewing system
resources. Whenever a new app pops up with claims
that it’s all you need for those tasks, I generally
brush it aside.
But every now and then, an app appears and
instantly grabs my attention — and that was the
case with Mission Center. The aim of this app is to
simplify the process of monitoring your CPU,
memory, disk, network, and GPU usage. The app also
gives you the opportunity, via a well-designed GUI,
to view every app and process running on the
system, and even stop any wayward application that
might be causing problems.
# ⚓ 5_Great_Free_Security_Tools_(and_How_to_Use_Them)⠀⇛
If it’s open source, yes, you can. Open source is a
way of developing software that provides
transparency to the end-users. They can obtain the
source code that makes up the application and
review it. They can verify for themselves that it
isn’t doing anything sinister or sneaky with their
data.
As well as reviewing the source code, users can
modify that source code – if they are a programmer
– to fix bugs or to add new features. The changes
are submitted to the maintainers of the product. If
the maintainers like the changes, they will find
their way into the product.
This benefits both the users of the open-source
application – known as the community – and the
developers of the products. The more eyes that
review the code, the better.
# ⚓ PCLOS Official ☛ Filen-desktop_2.0.24⠀⇛
Filen-desktop is an encrypted cloud storage client.
Zero knowledge end-to-end encrypted cloud storage,
similar to Dropbox but better. 10 Gig free storage
limit. Pay for more. Requires sign up at https://
filen.io/ This is the desktop client. Web access is
also available. Protect your privacy with filen-
desktop.
# ⚓ TecMint ☛ 10_Tools_to_Take_or_Capture_Desktop_Screenshots
in_Linux⠀⇛
o § Instructionals/Technical⠀➾
# ⚓ TechRepublic ☛ Securing_Linux_Policy⠀⇛
Linux is a powerful and customizable operating
system that has been the backbone of many
businesses for decades. This policy from
TechRepublic Premium provides guidelines for
securing Linux on company computers and computers
used to conduct company business. It assumes
administrative knowledge of Linux servers and/or
workstation environments.
# ⚓ Linux Hint ☛ How_to_Fix/Resolve_Text_Message_Notifications
Not_Functioning_on_Android⠀⇛
To fix text messages notification not working check
and adjust app notification settings, network
connection, battery optimization settings or
restart phone.
# ⚓ Dive_Tool:_Explore_Docker_Image_Layers_and_Optimize_Size⠀⇛
The Dive tool is only helpful to individuals
looking for a way to identify each layer of a
Docker image. The reason could be reducing the
image size or understanding the function of each
layer.
# ⚓ How_to_Mount_NFS_Drives_in_Linux⠀⇛
Setting up network storage can be a game-changer
for both individual users and organizations,
allowing seamless file sharing and data backups
over a network. One of the most popular methods to
achieve this is through Network File System (NFS),
a protocol that enables users to mount remote
directories on their machine as if they were local.
Every Linux distribution available can mount an NFS
share—as long as the right software is installed.
While NFS might sound daunting for newcomers to
Linux, the process is more straightforward than it
appears.
Keep reading as I demystify the steps involved in
mounting an NFS drive in Linux, offering a
detailed, step-by-step guide to get you up and
running. Whether you’re a system administrator or a
curious tinkerer, learn how to mount NFS drives in
Linux below.
# ⚓ Make Use Of ☛ 5_Ways_to_Fix_the_“E:_Unable_to_Locate
Package”_Error_on_Ubuntu⠀⇛
Ubuntu is a user-friendly Linux distro well-known
for its stability and vast software catalog.
However, even the most seasoned Ubuntu users are
likely to encounter the “E: Unable to locate
package” error. This error message usually appears
when you are trying to install a package via APT.
We’ll show you how you can fix the “E: Unable to
locate package” error message on Ubuntu. Whether
you are a novice or a seasoned admin, knowing how
to overcome this error will greatly enhance your
ability to use Ubuntu.
# ⚓ Linux Journal ☛ How_to_Change_the_Hostname_in_Debian_12
BookWorm⠀⇛
In the vast realm of networked computers, each
device needs a unique identifier—a name that allows
it to be distinguishable from the crowd. This
unique identifier is known as the “hostname.”
Whether you are working in a large corporate
network or simply tinkering with a personal Linux
box, you might find yourself needing to change this
hostname at some point. This comprehensive guide
walks you through the process of changing the
hostname in Debian 12 BookWorm, one of the latest
iterations of the popular Linux distribution
Debian.
# ⚓ How_To_Fix_ifconfig_Not_Found⠀⇛
It’s a versatile command, especially in Linux,
where it can display Wi-Fi and Ethernet IP
addresses. That makes it all the more frustrating
when you get the dreaded “ipconfig Not Found”
error.
# ⚓ Setting_up_cgminer_for_Dogecoin_Mining_on_Linux⠀⇛
Cryptocurrency mining has become increasingly
popular in recent years, especially with the rise
of meme coins like Dogecoin. Dogecoin mining can be
a fun hobby that allows you to earn some extra
digital coins while supporting the Dogecoin
network. However, it does require some technical
know-how, especially when it comes to configuring
the mining software. One of the most popular mining
software programs for Dogecoin on Linux is cgminer.
Setting up cgminer properly is key to getting the
most out of your Dogecoin mining experience.
o § Desktop Environments/WMs⠀➾
# § K Desktop Environment/KDE SC/Qt⠀➾
# ⚓ Unicorn Media ☛ KDE_Gear_23.08_Arrived_With_Plenty_of
Changes:_Here’s_What’s_New⠀⇛
A few weeks ago KDE released KDE Gear 23.08,
which featured numerous changes to key
applications. So many changes, in fact, that
I thought it might be a good idea to go
through them to offer an overview of what’s
changed in this new release.
KDE Gear, for those who don’t know, is a
collection of 100 essential applications that
are maintained and developed by KDE for its
Plasma desktop environment. I say they’re
essential, because they’re generally
necessary components for running a computer,
being things like terminal emulators, file
managers, text editors, and the like. KDE
Gear apps are generally cross-platform, and
will run on both Windows and Linux machines,
but like Plasma (which is also cross-
platform) they are generally used on Linux.
# § GNOME Desktop/GTK⠀➾
# ⚓ Medium ☛ Pratham_Gupta:_GUADEC_2023_in_Riga,_Latvia⠀⇛
§ My experience at
This summer I traveled to Riga to attend my
first international conference, Gnome Users
And Developers European Conference (GUADEC)
2023and true to its promise, the experience
that unfolded was nothing short of amazing.
* § Distributions and Operating Systems⠀➾
o ⚓ 9to5Linux ☛ Manjaro_23_Released_with_Linux_6.5,_KDE_Plasma_5.27
LTS,_GNOME_44.4,_and_Xfce_4.18⠀⇛
Manjaro 23 “Uranos” appears to be one of the first GNU/
Linux distributions that have shipped a stable live/
installation media powered by the recently released Linux
6.5 kernel series. Linux kernel 6.5 introduces new
features like Wi-Fi 7 support, MIDI 2.0 support, improved
support for AMD “Zen” systems, and much more.
For older hardware, this release offers two long-term
supported kernels, namely Linux 6.1 LTS and Linux 5.15
LTS. These kernels are available for installation via the
default package manager of each Manjaro Linux edition.
o ⚓ DebugPoint ☛ CutefishOS_“Reborn”_Arrives_with_Debian_12_and
Ubuntu_22.04⠀⇛
CutefishOS arrives in the news every now and then. Last
year, the project was discontinued, and early this year,
there was news about the name change of the project.
A recent SourceForge repository appeared last week
featuring a new BETA release of CutefishOS featuring a
test build based on Debian 12 “Bookworm” and Ubuntu 22.04
LTS “Jammy Jellyfish”. This project seems to be from an
independent developer with a new name, “CutefishOS
Reborn”.
o ⚓ Linuxiac ☛ What_a_Typical_Linux_Distribution_Looks_Like_in_2023⠀⇛
Linux distributions, often called “distros,” have come a
long way from their humble beginning. In the early 90s,
Linux was primarily the domain of tech enthusiasts and
system administrators.
It has become a user-friendly, versatile, and powerful
platform that appeals to a broad audience, including
developers, gamers, professionals, and everyday computer
users.
At the same time, all of the components that make up a
Linux distribution have also evolved during this
evolution, leaving some in the past replaced by new and
modern solutions.
o ⚓ Syncthing_added_to_Zenwalk_with_custom_tray_icon⠀⇛
Syncthing is a continuous file synchronization program.
It synchronizes files between two or more computers in
real time, safely protected from prying eyes.
o ⚓ New_unified_GTK4/3/2/QT_ready_artwork⠀⇛
I’ve been working on a new Adwaita based theme with
unified look for GTK4, GTK3, GTK2 and QT applications.
o § Reviews⠀➾
# ⚓ DebugPoint ☛ Nitrux_3.0.0_Review:_Is_This_Your_Next_Linux
Daily_Driver?
⠀⇛
It has been almost a year since we reviewed Nitrux
OS. The last review of Nitrux 2.0 was not that
great since I faced a few challenges.
Since then, Nitrux has been steadily gaining
acclaim for its unique features and stunning
aesthetics has just unveiled its major 3.0.0
release. Let’s dive in and explore what’s new and
improved in Nitrux 3.0.0 – codenamed “ut.”
o § New Releases⠀➾
# ⚓ ZDNet ☛ Bodhi_Linux_7.0_is_its_best,_most_user-friendly
release_yet⠀⇛
Bodhi Linux has been a long-time favorite operating
system of mine. This is partially due to it having
a desktop based on Enlightenment, but also because
the development team has always delivered a rock-
solid system that’s as fun as it is easy to use.
And although the changes to 7.0 are sometimes
subtle, they come together to make this the best
release yet.
For those who don’t know, Bodhi Linux is an open-
source operating system that is based on the latest
LTS (Long Term Support) release of Ubuntu Linux,
which in this case means Ubuntu 22.04. Bodhi Linux
has held true to a philosophy of desktop minimalism
combined with high customization. And, once again,
the developers have delivered on that idea — only
this time giving users an even more seamless
experience.
# ⚓ It’s FOSS ☛ Linux_Lite_6.6_Release_Features_an_Updated
Welcome_App_and_Icon_Theme⠀⇛
Linux Lite is one of the best lightweight Linux
distros that offers a Windows-like experience.
We last looked at it earlier this year when Linux
Lite 6.4 added some significant changes. Now, we
have yet another point release that promises a slew
of improvements.
o § BSD⠀➾
# ⚓ Ruben Schade ☛ @Omegatron_on_the_POPCAKE⠀⇛
The_POPCAKE_airport_lounge_pancake_maker
@Omegatron_Via_Twitter
I love these things so much that I looked into
getting one, but it turns out: a) they are rather
expensive machines and b) they use an expensive
premix packet that goes in the top, gets squeezed
out like a tube of toothpaste and only lasts a few
days once it’s opened 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇:(⦈
Darn! I assumed it was a resovoir of sorts, that
anyone could pour batter into. I wonder how
hackable it is? Could I put NetBSD on it, and
attach a funnel?
o § SUSE/OpenSUSE⠀➾
# ⚓ OWASP_ModSecurity_(CRS)_for_everyone_on_openSUSE.⠀⇛
As an active member of the openSUSE Linux developer
community and Chapter Leader for OWASP SP, I am now
responsible for maintaining and updating the
ModSecurity CRS packages on the openSUSE platform,
as well as managing other important packages such
as the official ZAP Core. For more information and
supporting documentation, please refer to the lin:
https://build.opensuse.org/package/view_file/
openSUSE:Factory/owasp-modsecurity-crs/owasp-
modsecurity-crs.spec
o § Arch Family⠀➾
# ⚓ Beta News ☛ Manjaro_Linux_23.0_‘Uranos’_is_here_with_GNOME,
Plasma,_and_XFCE_editions⠀⇛
The developers of Manjaro have delivered version
23.0 of the operating system, and this time, it’s
code-named “Uranos.” Following the lauded release
of Talos in April 2023, the developers at Manjaro
haven’t taken a moment’s rest. Whether you’re in
the GNOME, Plasma, or XFCE camp, there’s a lot to
unwrap, so let’s dive in.
First on our list is the GNOME edition, which has
been tuned to the melodious notes of the GNOME 44
series, a release that originally made its debut
back in March. The point releases from 44.1 to 44.4
have each added their own layer of polish and
precision, and for those interested in the details,
the release notes are your go-to source.
# ⚓ Linuxiac ☛ Manjaro_23_‘Uranos’_Released_with_Updated
Desktop_Sets⠀⇛
Manjaro Linux has gained popularity for its balance
between the cutting-edge nature of Arch Linux and
its user-friendly approach. It caters to beginners
and experienced Linux users, making it an
attractive choice for those looking for a flexible
and up-to-date Linux distribution.
More than four months after the previous 22.1
‘Talos’ release, Manjaro 23, codenamed ‘Uranos,’ is
here, so let’s see what has changed.
o § Fedora Family / IBM⠀➾
# ⚓ The Register UK ☛ Fedora_and_Asahi_Linux_pals_revamp
installation_process⠀⇛
The forthcoming Asahi/Fedora distro for Arm64 Macs
will use the Calamares installer – but the
mainstream Fedora 39 might get a new, simpler
installation program too.
According to a Mastodon post from one of the
project leads, Hector Martin, the Asahi project’s
upcoming Fedora-based release for Apple Silicon
Macs will use the Calamares cross-platform
installer.
Last month, the Asahi project announced it was
switching to Fedora for the first native Arm64
distro for M1 and M2 Mac hardware. The flagship
desktop is going to be KDE Plasma, which is a
departure from Fedora’s default GNOME. Now it looks
like the installer will be different too. Quite a
few distros use Calamares – we have mentioned its
use in the Snap-free Xubuntu, Zinc, OpenMandriva
Rome, and even the officially sanctioned Lubuntu
flavor.
# ⚓ Anaconda_Advanced_Partitioner_(Blivet-GUI)_on_Fedora_39_KDE
Spin_(Nightly_Build_09/04/23)⠀⇛
Just several screenshots during VENV installation
are posted below
# ⚓ Weekly_status_of_Packit_Team:_Week_35_in_Packit⠀⇛
The variables represent paths where the respective
git repositories are cloned (packit-service#2166)
# ⚓ Fedora Project ☛ Fedora_Community_Blog:_Community_Blog
monthly_summary:_August_2023⠀⇛
In August, we published seven posts. The site had
3,172 visits from 2,175 unique viewers. 163 visits
came from search engines, while 4 came from Fedora
Discussion, and 2 came from Reddit.
# ⚓ Red Hat ☛ A_beginner’s_guide_to_Python_containers⠀⇛
Python has emerged as a go-to language for
students, new programmers, and experienced
developers. This general-purpose programming
language is dynamically typed, memory-managed, and
supports multiple programming paradigms. Python is
popular for web development, data_science,
artificial_intelligence_and_machine_learning_(AI/
ML), scripting for Linux, and more.
o § Debian Family⠀➾
# ⚓ 9to5Linux ☛ Tails_5.17_Anonymous_Linux_OS_Renames_Tails
Installer_to_Tails_Cloner⠀⇛
Based on the Debian GNU/Linux 12.1 “Bookworm”
release, Tails 5.17 is here to rename the Tails
Installer to Tails Cloner because Tails Installer
is no longer the preferred way of installing Tails
on a USB flash drive and it can only be used for
cloning a Tails system either for installing or for
upgrading purposes.
For those who also use a printer with their Tails
system, the new release brings more printer drivers
pre-installed by default via the printer-driver-
brlaser package to support Brother printers, and it
also adds the ability to enable all printers
automatically.
o § Canonical/Ubuntu Family⠀➾
# ⚓ Ubuntu ☛ Into_the_Labyrinth:_Revealing_the_Mantic
Minotaur⠀⇛
Few creatures from mythology have captured the
imagination of mankind quite like the legendary
Minotaur. A half-man, half-bull behemoth that is
said to guard the halls of the impenetrable
labyrinth of Crete. The ancient sagas stated that
only the bravest of warriors would be able to match
its incredible strength and escape its mystifying
maze.
Computing, on the other hand, should not feel like
you’re trapped in a maze. In just a few short
weeks, all will be able to experience the freedom
that Ubuntu 23.10 Mantic Minotaur has to offer.
Access the latest and greatest open source software
built on a trusted, secure and stable foundation.
This upcoming release represents another important
step in our quest to craft a desktop experience
that fully embodies our future vision and values.
# ⚓ Ubuntu News ☛ Ubuntu_Weekly_Newsletter_Issue_803⠀⇛
Welcome to the Ubuntu Weekly Newsletter, Issue 803
for the week of August 27 – September 2, 2023. The
full version of this issue is available here.
# ⚓ Ubuntu Fridge ☛ The_Fridge:_Ubuntu_Weekly_Newsletter_Issue
803⠀⇛
o § Devices/Embedded⠀➾
# ⚓ CNX Software ☛ Raspberry_Pi_CM4_compatible_RISC-V_SoM
features_StarFive_JH7110_SoC⠀⇛
We’ve seen many Arm-based system-on-modules
following the Raspberry Pi CM4 form factor, but
we’ve now got a RISC-V one courtesy of the Milk-
V Mars CM CPU module powered by a StarFive JH7110
quad-core RISC-V SoC.
The RISC-V module comes with up to 8GB RAM, a 16MB
SPI flash, an optional eMMC flash, onboard GbE PHY,
and a wireless module with WiFi 5 and Bluetooth 5.2
plus the two 100-pin board-to-board connectors
offering (partial) compatibility with carrier
boards made for the Raspberry Pi Compute Module 4.
o § Open Hardware/Modding⠀➾
# ⚓ Liliputing ☛ Purism’s_Librem_5_Linux_smartphone_now_takes
just_2_weeks_to_ship_(but_costs_$1,299)⠀⇛
The Purism Librem 5 is a smartphone that ships with
PureOS, the same free and open source GNU/Linux
distribution that ships on Purism’s laptop and
desktop computers. The company first began taking
pre-orders for the phone through a crowdfunding
campaign that launched in 2017, began shipping
hardware more than two years later, and then spent
another four years scrambling to try to fulfill
orders… with some customers waiting years for
either a phone or a refund.
Now Purism says it’s finally reached shipping
parity, which means that it’s caught up with its
backlog and now if you place an order for a new
Librem 5 phone, it should ship within two weeks.
But it won’t be cheap.
# ⚓ CNX Software ☛ STARLIGHT_–_A_Raspberry_Pi_RP2040_board_for
rockets⠀⇛
Circuit Wizardry’s STARLIGHT is a rocket control
board based on Raspberry Pi RP2040 microcontroller
and designed for small 75mm model rockets. The
board features rocket control-specific I/Os such as
Igniter and Ejection pins each connected to a
MOSFET, two headers for 5V servos, plus some
sensors and 3.3V or 5V GPIOs for expansion.
STARLIGHT specifications: Microcontroller –
Raspberry Pi RP2040 dual-core Arm Cortex-M0+ MCU @
133 MHz with 264KB SRAM Storage – 16MB flash for
firmware and flight data USB – 1x Micro USB port
for programming Rocket control Igniter via 2-pin
terminal block and AO3400 MOSFET (pulse current up
to 30A) used with ignition systems to automatically
light your engine.
# ⚓ Tom’s Hardware ☛ Milk-V_Reveals_RISC-V_Raspberry_Pi_Compute
Module_4_Compatible_Board⠀⇛
Milk-V has a new Raspberry Pi Compute Module 4
compatible board powered by a RISC-V-based CPU.
o § Mobile Systems/Mobile Applications⠀➾
# ⚓ Android_now_digitises_the_cards_you_hate_to_carry_|_Trusted
Reviews⠀⇛
# ⚓ 9to5Google ☛ Android_Auto_bug_ruins_audio_quality_after
using_Assistant⠀⇛
# ⚓ Sportskeeda ☛ PUBG_Mobile_2.8_update_direct_APK_download
link_for_Android⠀⇛
# ⚓ TechCrunch ☛ Google_is_changing_Android_branding_with_a_3D
logo_|_TechCrunch⠀⇛
# ⚓ The Verge ☛ Google’s_latest_Android_feature_updates_come
with_a_refreshed_logo_–_The_Verge⠀⇛
# ⚓ 9to5Google ☛ Xiaomi_gives_five_years_of_updates_to_latest
Android_phone⠀⇛
# ⚓ 9to5Google ☛ ‘OnePlus_Pad_Go’_could_be_a_more_affordable
Android_tablet⠀⇛
# ⚓ The_Best_Local_Multiplayer_Games_for_Android_–_Droid
Gamers⠀⇛
# ⚓ Tech Advisor ☛ How_To_Share_Your_Location_on_Android_Using
Google_Maps_–_Tech_Advisor⠀⇛
# ⚓ Android Authority ☛ We_asked,_you_told_us:_You_really_miss
small_Android_tablets⠀⇛
# ⚓ Notebook Check ☛ Doogee_unveils_a_new_rugged_phone
alongside_a_trio_of_Android_tablets_–_NotebookCheck.net
News⠀⇛
# ⚓ SlashGear ☛ How_To_Stop_Android_Apps_From_Using_Data_In_The
Background⠀⇛
# ⚓ Neowin ☛ MEmu_Android_Emulator_9.0.5.1_(offline_installer)
–_Neowin⠀⇛
# ⚓ Pocket Lint ☛ Android_is_slowly_taking_over_your_car_and
we’re_only_just_getting_started⠀⇛
# ⚓ Android_14_Delayed_to_October?⠀⇛
# ⚓ Giz China ☛ Android_14_Eligible_Devices:_Checkout_Full_List
–_Gizchina.com⠀⇛
# ⚓ TechCrunch ☛ A_closer_look_at_e/OS:_Murena’s_privacy-first
‘deGoogled’_Android_alternative_|_TechCrunch⠀⇛
# ⚓ TechCrunch ☛ Google’s_quarterly_Android_updates_include
Zoom_and_Webex_support_in_cars_|_TechCrunch⠀⇛
# ⚓ 9to5Google ☛ Xiaomi_gives_five_years_of_updates_to_latest
Android_phone⠀⇛
# ⚓ The Verge ☛ Google’s_latest_Android_feature_updates_come
with_a_refreshed_logo_–_The_Verge⠀⇛
* § Free, Libre, and Open Source Software⠀➾
o § GNU Projects⠀➾
# ⚓ FSF ☛ FSF_Events:_GNU40:_Hacker_meeting_in_Switzerland⠀⇛
The GNU System is turning forty. In honor of this
event, the GNU Project is organizing a hacker
meeting in Switzerland.
* § Leftovers⠀➾
o ⚓ Off Guardian ☛ AUDIO:_Iain_Davis_on_Perspective_with_Jesse
Zurawell_–_Sept_2nd_2023⠀⇛
Iain Davis returns to Perspective to discuss his on-going
series of articles on “Synthetic Hegemonic Currency”
(available on Geopolitics & Empire).
o ⚓ Ruben Schade ☛ The_Pacific_Motorway,_and_building_for_trucks⠀⇛
A few years ago, I was in the car with friends as we
drove from Sydney to Newcastle on the Pacific Motorway.
It’s a long, wide stretch of road that meanders through a
national park, with some jaw dropping scenery. Check out
the Wikipedia article for some photos if you’re
interested.
Wikipedia:_Pacific_Motorway_(Sydney–Newcastle)
It was late in the evening, and my brother-in-law was
increasingly agitated at the number of large trucks
boxing us in on all sides. To make matters worse, it was
clear some of the drivers were exhausted, inattentive, or
bored, based on how they veered in and out of their lanes
like iron serpents. There’s a reason this stretch of road
has so many fatalities and accidents, which are only
exacerbated by the road’s relative remoteness.
Anyway, he slowed the car down, moved to another lane,
and attempted to distance us from the hoard. As we
settled into our new position, someone in the car (I
forget who) shouted “why are these things on the road!?”
We all had a nervous laugh… and I haven’t been able to
get the though out of my head since.
o § Education⠀➾
# ⚓ The Straits Times ☛ South_Korea’s_education_minister
withdraws_discipline_warning_to_teachers_over_strike⠀⇛
Minister vows to communicate weekly with teachers
to resolve school-related issues.
o § Proprietary/Artificial Intelligence (AI)⠀➾
# ⚓ New York Times ☛ Douglas_Lenat,_Who_Tried_to_Make_A.I._More
Human,_Dies_at_72⠀⇛
He spent decades working on artificial
intelligence, striving to create computers that
could replicate common sense.
# ⚓ Silicon Angle ☛ Microsoft_to_discontinue_the_default
WordPad_word_processor_in_Windows⠀⇛
Microsoft Corp. plans to phase out WordPad, the
free word processor that has shipped with Windows
for the past 28 years. The company disclosed the
move in a support note released on Friday. “WordPad
is no longer being updated and will be removed in a
future release of Windows,” Microsoft stated in the
brief announcement.
# ⚓ Tom’s Guide ☛ Microsoft_is_killing_WordPad_in_Windows_11:
What_you_need_to_know⠀⇛
o § Pseudo-Open Source⠀➾
# § Openwashing⠀➾
# ⚓ The Next Platform ☛ HashiCorp_Retools_Licenses_And
Software_To_Grow_Its_Business_–_The_Next_Platform⠀⇛
It is hard to make a living in the open
source software business, although it is
possible, through the contributions of many,
to make great software. In many ways,
HashiCorp is arguably the standard bearer for
the next wave of commercialized open source,
much the way Red Hat was two and a half
decades ago with the second wave the saw the
rise of Linux and the death, pretty much, of
Unix.
The first wave of open source, of course, was
in the academic roots of computing, when
Unix, C, a zillion databases and file systems
and all kinds of stuff for Unix platforms
were created. Once software became
copyrightable in 1974 and once computing
became a big business as Moore’s Law
exponentially scaled down the cost of
hardware and ever-inflating human costs
continually scaled up the cost of software in
the next decade, it was inevitable that
software would start closing up code and
opening up shop.
o § Security⠀➾
# ⚓ SANS ☛ Common_usernames_submitted_to_honeypots,_(Tue,_Sep
5th)⠀⇛
# ⚓ Cybernews ☛ Flaw_in_AtlasVPN_Linux_clients_discovered,
patch_is_on_the_way⠀⇛
A simple code snippet in a webpage could disconnect
instances of AtlasVPN’s Linux Client, exposing a
user’s IP address. The zero-day flaw was discovered
and shared by a user on Reddit and the company is
now working on a fix.
AtlasVPN has a vulnerability in Linux clients that
can be exploited by malicious users to obtain the
user’s real IP address.
# ⚓ LWN ☛ Security_updates_for_Tuesday⠀⇛
Security updates have been issued by Debian (file
and thunderbird), Fedora (exercism, libtommath,
moby-engine, and python-pyramid), Oracle (cups and
kernel), Red Hat (firefox, kernel, kernel-rt,
kpatch-patch, and thunderbird), SUSE (amazon-ecs-
init, buildah, busybox, djvulibre, exempi, firefox,
gsl, keylime, kubernetes1.18, php7, and sccache),
and Ubuntu (docker-registry and linux-azure-5.4).
# § Privacy/Surveillance⠀➾
# ⚓ The Verge ☛ Apple_and_Microsoft_reportedly_want
iMessage_and_Bing_off_the_EU’s_tech_‘gatekeeper’_list⠀⇛
Microsoft and Apple are reportedly pushing to
keep Bing and iMessage, respectively, off a
list of “gatekeepers” subject to new European
regulations.
# ⚓ Digital Music News ☛ Meta_May_Introduce_Paid,_Ad-Free
Subscriptions_to_Europe_in_Response_to_Data_Privacy
Regulations⠀⇛
Meta may introduce paid, ad-free plans for
Facebook and Instagram in response to
European data privacy laws. Here’s the
latest. A new report from The New York Times
suggests Zuckerberg may borrow a page from
Musk’s playbook in asking users to pay a
subscription fee.
o § Defence/Aggression⠀➾
# ⚓ New York Times ☛ He’s_Wanted_in_a_1970_Bombing._The_F.B.I.
Aged_His_Photo_to_Seek_Tips.⠀⇛
The suspect, Leo F. Burt, has evaded capture since
the anti-Vietnam War bombing at the University of
Wisconsin, which was considered the largest act of
domestic terrorism at the time.
# ⚓ RFERL ☛ Pakistani_PM_Claims_Weapons_Left_Behind_In
Afghanistan_Add_To_Security_Threats⠀⇛
Pakistan’s caretaker prime minister says that
weapons and military equipment left behind by U.S.
and other foreign forces in Afghanistan are being
used against Pakistan, worsening the security
situation in the country.
# ⚓ The Straits Times ☛ New_Vanuatu_PM_to_‘revisit’_security
pact_with_Australia:_Report⠀⇛
The pact was a major reason for the ouster of
former leader Ishmael Kalsakau.
# ⚓ New York Times ☛ Can_Kenya_Bring_Order_to_Haiti?⠀⇛
The African country has volunteered to put boots on
the ground in the Caribbean nation by the end of
the year. But the plan is facing pushback even as
Haiti’s security crisis spirals out of control.
o § Environment⠀➾
# ⚓ European Commission ☛ Speech_by_President_von_der_Leyen_at
the_Africa_Climate_Summit⠀⇛
# ⚓ France24 ☛ Several_dead_as_torrential_rains_sweep_drought-
hit_Spain⠀⇛
At least three people died and another three were
missing on Monday after heavy rains lashed drought-
hit Spain, triggering flash floods that closed
Madrid metro lines and high-speed rail links.
# ⚓ New York Times ☛ Burning_Man_Updates:_Attendees_Begin_to
Leave_Festival_Site⠀⇛
After days of torrential rain, an exodus from the
Nevada site began on Monday. The festival’s fiery
climax, postponed twice, finally took place.
# § Wildlife/Nature⠀➾
# ⚓ Federal News Network ☛ Fish_with_a_funny_float_gets_a
CT_scan_at_the_Denver_Zoo⠀⇛
A fancy-looking French angelfish that was
found one day with a funny float has its
buoyancy back after taking some time out of
its tropical trappings to get a CT scan at
the Denver Zoo. A zoo worker recently noticed
the blue and yellow fish was swimming with a
tilt, prompting a visit last week to the
facility’s on-site hospital. The seven-inch
fish was sedated, balanced on a sponge and
had water poured over its gills to keep it
alive as the CT scan took place. The
diagnosis: Inflamed intestines were causing
increased internal gas affecting the fish’s
buoyancy. Zoo spokesperson Jake Kubie said
Monday that the fish was treated with
antibiotics and is again swimming upright.
o § Finance⠀➾
# ⚓ Latvia ☛ Rimi_says_retailers_are_not_to_blame_for_high
prices⠀⇛
The main culprits for food inflation are not
retailers, Valdis Turlais, Chairman of the board of
Rimi Latvia, said in an interview with LETA on
September 5.
# ⚓ Ars Technica ☛ “AI_took_my_job,_literally”—Gizmodo_fires
Spanish_staff_amid_switch_to_AI_translator⠀⇛
Last week, Gizmodo parent company G/O Media fired
the staff of its Spanish-language site Gizmodo en
Español and began to replace their work with AI
translations of English-language articles, reports
The Verge.
Former Gizmodo writer Matías S. Zavia publicly
mentioned the layoffs, which took place via video
call on August 29, in a social media post. On
August 31, Zavia wrote, “Hello friends. On Tuesday
they shut down @GizmodoES to turn it into a
translation self-publisher (an AI took my job,
literally).”
# ⚓ Bennett, Coleman & Company Ltd ☛ Quiet_Cutting_is_the
New_Word!_Here’s_How_Companies_Remove_Positions_Without
Firing_Employees⠀⇛
o § Censorship/Free Speech⠀➾
# ⚓ YLE ☛ One_in_three_hate_speech_suspects_have_party-
political_links,_Yle_investigation_finds⠀⇛
In recent years the highest number of suspects have
been members of either the Finns Party or Finnish
People First.
# ⚓ Silicon Angle ☛ Elon_Musk_says_he_might_sue_the_Anti-
Defamation_League_for_…_defamation⠀⇛
X Corp. boss Elon Musk today partly blamed the
Anti-Defamation League, or ADL, for his company’s
steep decline in advertising revenue since he
became boss of what was then Twitter Inc.
o § Freedom of Information / Freedom of the Press⠀➾
# ⚓ The Straits Times ☛ Australian_lawmakers_to_urge_release_of
Julian_Assange_during_US_visit⠀⇛
They will urge the US to drop attempts to extradite
the WikiLeaks founder from a British prison.
o § Civil Rights/Policing⠀➾
# ⚓ OpenRightsGroup ☛ Online_Safety_Bill:_US_and_UK_campaigners
warn_of_dangers_of_age_verification⠀⇛
Proposals aimed at protecting children could force
tech platforms to choose between freedom of speech
and the right to privacy, a new briefing by digital
rights campaigners, Open Rights Group and EFF has
warned.
o § Internet Policy/Net Neutrality⠀➾
# ⚓ APNIC ☛ Unlocking_the_power_of_Internet_alarms_correlation
and_aggregated_reports⠀⇛
Guest Post: Enhancing network monitoring,
situational awareness, and decision-making in real
time.
o § Monopolies⠀➾
# § Patents⠀➾
# ⚓ EPO_concludes_working_agreement_on_search_co-
operation_with_Slovenian_Intellectual_Property_Office_
(SIPO) [Ed: Slovenian complicity in rigging UPC vote
still noteworthy; they helped ratify something both
illegal and unconstitutional in direct violation of
international conventions]⠀⇛
Agreement to foster collaboration and co-
ordination among the EPO and SIPO in high-
quality search operations.
# ⚓ JUVE ☛ Pinsent_Masons_hires_senior_patent_partner
from_Taylor_Wessing [Ed: JUVE, a propaganda machine of
Team UPC (paid to lie and promote the illegal), has
just published more spam under the guise of
'journalism'; how is the hiring of one low-level person
newsworthy?]⠀⇛
Pinsent Masons has once again bolstered its
ranks in London, this time with the hire of
James Marshall from Taylor Wessing. The
addition of Marshall means the firm’s UK-
based IP partnership is now 13-strong, which
includes both litigators and one patent
attorney in a move towards a mixed-firm
model.
䷩ 𝚕𝚒𝚗𝚎 8666
╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕
⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.06.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧
Gemini_version_available_♊︎
✐ Gemini_Links_06/09/2023:_Reddit’s_New_Tracking_URLs_and_Iterating_On
Fractals⠀✐
Posted in News_Roundup at 12:05 am by Dr. Roy Schestowitz
🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈
§ Contents⠀➾
* Gemini*_and_Gopher
o Personal/Opinions
o Science
o Technology_and_Free_Software
# Internet/Gemini
# Programming
* § Gemini* and Gopher⠀➾
o § Personal/Opinions⠀➾
# ⚓ Show_notes_23-35⠀⇛
This week i have been preparing to move back to
university, and have been streamlining my workflow
for learning chinese. Recently i have been
neglecting certain aspects, and in general doing
far too many flash cards.
I know that a lot of people swear by anki, but i am
less convinced. Often the cards used are low
quality, so the information recall can be hardly
that helpful either. Instead, i have been
increasing the amount of reading i do, which should
have the same general effect as word flashcards,
but with added context of sentences and plot.
o § Science⠀➾
# ⚓ Astronomy_Season_Begins_(publ._2023-09-05)⠀⇛
For me here in Fairbanks, Alaska, astronomy season
doesn’t start until September, since there isn’t
enough darkness before that for practical
stargazing. I’m on an early-morning life schedule,
so it doesn’t work for me to stay up until midnight
to see the stars. But now there is enough darkness
for me to be able to do early morning sessions
(around 4am) before work.
Most nights these last few weeks have been overcast
skies, but there was a forecast of partly cloudy
early this morning, so I decided to head out early
to the boatlaunch, away from the light pollution,
and give it a try. Indeed, it was partly cloudy
this morning, but I was thwarted by a thick, low-
lying fog, which blocked out all the stars and
obscured the third-quarter moon.
o § Technology and Free Software⠀➾
# ⚓ let’s_talk_about_AI_art_i_guess⠀⇛
unavoidable subject i suppose. as i mentioned in my
microlog, i don’t know why everyone’s talking about
their hatred for AI art these days; it’s not
exactly the same as when dall-e 2 was unveiled and
half of art twitter was running to the hills,
panicking about their jobs [1]. it’s less fear and
more… contempt? disgust? just sheer *hatred*?
now, i don’t wanna come across as a techbro or
something. i get rather defensive when i hear
people talking shit about AI art; only natural
given that’s my research and how a lot of my work
has involved GAN generated images for the past year
and a half (since october 2020 to be exact) [2].
but don’t think this a blind defense of the
corporations and exploitative systems behind
current state of art AI image generation. i would
like to talk about the medium or the technology
itself (not that it can be understood in a vacuum,
but let’s cross that bridge when we get to it).
# ⚓ Gemini_PDA_vs_Emacs_Native_Android⠀⇛
However, there were deal breaking issues. The
android sandbox the app lives in is the main one. I
was unable to get files I wanted to edit into emacs
to edit them. I could make a new file and save it
to /storage/emulated/0/Downloads, for example, but
if I created the file in another app, like vim in
termux, it would not open it. Access denied. This
device is rooted, so I even created a new directory
– /tmp – and chown’d to u0_a96 (the android system
generated user for my particular emacs
installation), chmod’ing /tmp/ 0777. No dice.
# ⚓ Re:_FLOSS_Equivalent_of_Wordpad⠀⇛
Ted is a very old program. It looks dated as all
hell because it uses xlib instead of a “modern”
toolkit like Gtk4 or QT6. I do not consider this a
bad thing. It’s very small, very light, and has
very few dependencies. It hasn’t really changed in
years. It’s software that has achived that
remarkable (for today) state of being “finished”.
What Ted actually does give you is a pretty good
word processor using the Rich Text Format (.rtf)
that is the native Wordpad format. No more than
that, and no less. It does that job and that job
alone.
# § Internet/Gemini⠀➾
# ⚓ Beware_Reddit’s_New_Tracking_URLs⠀⇛
Reddit recently implemented a new feature for
tracking the activity of it’s users and site
visitors, even if not logged in. This is a
privacy concern for everyone, even if you’ve
never used Reddit.
If a user using the official app shares a
link, they will be given a special tracking
URL that links their account to the post
being shared. These tracking links look like
this: https://reddit.com/r/subredditname/s/
tracking_token where the tracking_token is a
bunch of gibberish.
Opening this link resolved to a normal Reddit
URL with tracking parameters: https://
www.reddit.com/r/subredditname/comments/
post_id/post_title/?share_id=more_gibberish
Take note of the share_id parameter. This is
a unique identifier that reports to Reddit
who shared the link that is being opened.
# ⚓ RE:_Why_would_students_use_gemini?⠀⇛
This is an update to my original post asking
for help in a course I’m teaching on web
technologies, collaboration and the internet
to undergrad Computer Science students.
# ⚓ RE:_Accross_the_Spiderverse⠀⇛
Circadian makes a number of great
observations. I actually loved “Across the
Spiderverse” myself, but would likely point
out some of the same flaws if pressed. That
said, I’ve felt for a long time that there is
something wrong with our attention span in
modern times, and it overflows into our
expectations for entertainment. Thinking on
this, and on one of his biggest complaints,
got me thinking about pacing, and how
different it used to be.
# § Programming⠀➾
# ⚓ Re:_Fast_Thoughts_on_a_Fast_Language⠀⇛
slondr has written up four thoughts on the
Ada programming language. As the maintainer
of one of the world’s most widely used Ada
programs, I couldn’t resist weighing in.
Sadly this program is used for cheating on
Latin translation homework, rather than Ada’s
more glamorous niches of aerospace or
security kernels.
# ⚓ Iterating_On_Fractals⠀⇛
In my recent post about print nozzle sizes I
showed a print of a super-fine fractal
pyramid.
=> =============================================================================
World Wide Web but a lot lighter.
䷩ 𝚕𝚒𝚗𝚎 8898
╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕
⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.06.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧
Gemini_version_available_♊︎
✐ Gemini_Links_06/09/2023:_Recommendation_Algorithms,_IPv6_Adoption⠀✐
Posted in News_Roundup at 8:23 pm by Dr. Roy Schestowitz
🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈
§ Contents⠀➾
* Gemini*_and_Gopher
o Personal/Opinions
o Technology_and_Free_Software
# Internet/Gemini
* § Gemini* and Gopher⠀➾
o § Personal/Opinions⠀➾
# ⚓ review:_the_genesis_of_misery_by_neon_yang⠀⇛
“the genesis of misery” is a sci-fi / fantasy mech
novel from the author of the “tensorate” series of
novellas. **this review is quite spoiler heavy**
but i’ll preface by saying i really disliked the
book and do not recommend it, so i think you won’t
be losing anything. it did get a fair amount of
praise? but i felt very similar to “the house of
hunger” (bad).
# ⚓ Rescuing_(or_Replacing?)_the_Big_Bang_(publ._2023-09-06)⠀⇛
Short version: An astrophysicist from Canada
recognizes the glaring contradictions between what
we are seeing with JWST, and the standard model.
JWST is believed to give us a window into the far
distant past. But what we are finding is “mature”
galaxies popping up in places where the universe is
supposed to be in its infancy, according to the
supposed 13.8 billion year age of the universe. And
this astrophysicist is trying to put together a new
model, which allows for these ancient galaxies,
without hopefully adding too much time to the age
estimate. What will the new age turn out to be?
Nineteen billion? Twenty-nine billion?
# ⚓ Shallow_Year,_or_failing_at_Depth_Year_(2023)⠀⇛
An online friend of mine did a Depth Year in 2022.
He documented both his successes and failures each
month, and ultimately felt rewarded but exhausted
after his pursuits. I thought that fulfillment and
exhaustion that comes with a year-long project was
something that I desperately needed, and so I
embarked upon my Depth Year on January 2023, with
the intention of deepening my understanding of
habit and my relationship with my hobbies and
studies.
o § Technology and Free Software⠀➾
# ⚓ Recommendation_algorithms:_all_fail⠀⇛
Is there a best practice of automated
recommendation systems? Clearly there are lots of
bad recommendation algorithms out there. Either
they don’t work as intended, or they do but have
undesirable side effects. I’ve touched on music
recommendation in a previous post (rewilding
music), here I will focus on video.
Youtube’s algorithms have been criticised for
promoting inaccurate information, serving scary
content to toddlers, and much more. Since the
algorithms are tightly kept secrets the criticism
must be based on their observable effects, which
partly depend on the interaction with millions or
billions of users. And with individual
customisation, each viewer will see different
recommendations.
The panic about misinformation has hit hard on
those who are critical of the current order of
things, regardless of whether they present accurate
information or deranged misconceptions. Project Owl
in 2017 had the ostensible goal of diminishing the
spread of false information, and if it succeeded at
that it also had a deleterious effect on
independent news sites of high quality, who may
have presented opinion pieces that were not well
aligned with establishment views.
# ⚓ From_Terminal_to_terminal⠀⇛
Yes, that’s all…Ok, maybe a terminal ? It’s also
very usefull.
No problem for a PC under GNU/Linux of course but
for the other computer that (almost) everyone has,
the smartphone, it’s not so easy.
# § Internet/Gemini⠀➾
# ⚓ Finally_reachable_over_IPv6⠀⇛
Up until now, this site has been hosted on
sourcehut pages. It was quite easy to get
started since it integrates very well into
the sourcehut ecosystem: the build gets
triggered automatically on git push and it
automatically gets the permission to publish
the page.
# ⚓ Trying_Gemini_(again)⠀⇛
I’ve been feeling increasingly disillusioned
with the bloat and maintenance of my website,
and the constant need to move social networks
as each hub collapses.
=> =============================================================================
World Wide Web but a lot lighter.
䷩ 𝚕𝚒𝚗𝚎 9054
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⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.06.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧
Gemini_version_available_♊︎
✐ Gemini_Links_06/09/2023:Vanity.onion_Address_and_Trying_Gemini⠀✐
Posted in News_Roundup at 12:27 pm by Dr. Roy Schestowitz
🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈
§ Contents⠀➾
* Gemini*_and_Gopher
o Personal/Opinions
o Technology_and_Free_Software
# Internet/Gemini
* § Gemini* and Gopher⠀➾
o § Personal/Opinions⠀➾
# ⚓ 🔤SpellBinding:_DGYOTUH_Wordo:_RIFTS⠀⇛
o § Technology and Free Software⠀➾
# ⚓ Re:_FLOSS_Equivalent_of_Wordpad?⠀⇛
I use AbiWord on machines like my OpenPandora. It’s
lightweight and does even more than Wordpad did.
Sadly the GTK3 (or higher) versions are much slower
than the old GTK2 versions i prefer :/
# § Internet/Gemini⠀➾
# ⚓ Taking_Accountability_for_My_Vanity_.onion_Address⠀⇛
Some folks probably already know that my
website, gopherhole, gemini capsule, and
finger server can be accessed over the tor
network at the .onion address
vigreyd6wrsvudjto7ccmt45avabdstveitqej2f4or75sjxkrijv3qd.onion.
Heck, if you are reading this blog post using
the Tor Browser, you likely would have been
redirected to that .onion address. The first
6 characters are “vigrey”, just like the
first 10 characters of the DuckDuckGo .onion
address are “duckduckgo” and the first 8
characters of the Facebook .onion address are
“facebook”. I am currently of the opinion
that making a vanity .onion address was a
morally wrong choice for me to make, even if
it was a mindless choice at the time.
Generating a vanity .onion address is
essentially the same process as Proof-of-Work
systems like Bitcoin use or trying to crack a
hashed and salted password. In all of those
cases, you make a random guess, see that your
guess was likely horribly wrong, throw that
guess away, and guess again. Do that over and
over again until luck is on your side. All
you had to do was waste a bunch of
electricity on the way. In the case of my
vanity .onion address, I statistically would
have generated about 32^6 (1073741824) .onion
addresses, likely throwing away over 1
billion addresses that didn’t start with
“vigrey”. I did that once before and lost
that .onion address’s private key, so I did
this twice in total… I also did this when
.onion addresses were only 16 characters in
length, so I likely threw away at least 3
billion .onion addresses needlessly.
# ⚓ Trying_Gemini_(again)⠀⇛
I want to give Gemini and its community
another try. Earlier this year I visited the
geminispace in a curious but fleeting manner,
and had a lot of fun in it, but it was more
of a chance encounter than a move.
I’ve been feeling increasingly disillusioned
with the bloat and maintenance of my website,
and the constant need to move social networks
as each hub collapses. I am hoping that this
will be a more sustainable way to document my
thoughts and socialise in a way that is
fulfilling but not so reliant on specific
services.
=> =============================================================================
World Wide Web but a lot lighter.
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