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
QmR2rr1yXDANjQBEz2oGtd2UMgy9U37FHdjpUhPfAk7h5z
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

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

(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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⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢰⡀⠀⠀⢠⣿⡟⠏⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢠⡭⢉⣤⡀⠀⠀⠀⠀
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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:


                                      🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇H                                     🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇HTML5_logs⦈_


                                         #techrights_log_as_HTML5                                                                                  #boycottnovell_log_as_HTML5


                                      🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇H                                     🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇HTML5_logs⦈_


                                    #boycottnovell-social_log_as_HTML5                                                                               #techbytes_log_as_HTML5


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


                                          #techrights_log_as_text                                                                                   #boycottnovell_log_as_text


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


                                     #boycottnovell-social_log_as_text                                                                                #techbytes_log_as_text


                          Enter_the_IRC_channels_now


===============================================================================
§ IPFS Mirrors⠀➾


CID                                              Description     Object type


                                                 IRC log for
 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
 QmRfPhvwdvzyQ7gzwWUHadm4FsJc8JnH3p2UrTRyMqzfrw (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 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


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡎⢳⢸⠉⡆⡮⠷⢸⠙⡆⠯⡁⡎⢱⢸⠀⡇⡎⢱⠋⠃⡯⠷⠀⢰⠙⢰⠋⡆⡎⢱⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣄
⠙⠉⠸⠉⠁⠙⠁⠈⠀⠁⠙⠁⠙⠋⠈⠙⠁⠁⠀⠙⠁⠙⠁⠈⠈⠚⠈⠓⠁⠃⠘⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢤⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢦⣶⢲⠀⣂⣆⣶⣴⠀⠀⠀⠀⣶⣶⣴⢔⣴⡄⢦⣖⣶⣴⠀⠀⠀⠀⠀⢰⡤⡢⣶⢶⡆⡠⣢⣴⣔⢴⡆⠀⠀⠀⠰⢰⣴⣦⡂⠐⢀⡤⢴⢲⣠⠂⣤⣴⠠⣲⣲⡆⢔⣴⣶⡆⡆⡖⣦⡂⢴⣶⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠖⣀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣡⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢉⠏⢹⢛⢻⢻⢻⢻⡿⢛⢹⢟⡻⡛⡟⡿⡛⠏⠹⢛⢿⢛⡻⡟⡛⠟⢿⢛⢻⠛⠋⡀⣺⢛⣻⣿⣛⢻⠉⣻⡟⣭⡙⡟⣛⢿⢛⢻⢛⡻⡟⣛⡟⡛⡟⣿⢻⢛⡻⣛⡿⡛⢿⡿⡛⡿⡛⢿⢛⢛⢻⣿⣿
⣿⣿⣿⣿⣿⣼⣦⣴⣤⣼⣦⣧⣾⣷⣬⣼⣦⣤⣧⣴⣧⣤⣧⣴⣬⣼⢨⣥⣧⣧⣿⡼⠄⣠⣴⣧⣧⣽⣥⣼⣯⣤⣼⣤⣽⣷⣭⣴⡇⣭⣼⣤⣼⣼⣧⣧⣤⣦⣥⣦⣭⣼⣼⣧⣭⣧⣤⣮⣧⣭⣧⣥⣾⣼⣼⣼⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢋⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡏⡿⠻⣿⣟⡻⣟⣿⣻⠛⡟⣿⢻⡟⡿⢻⣿⡟⣿⡟⠻⠟⣡⠒⣟⣟⣻⡿⠿⣿⣿⡟⠻⣟⣟⡿⣻⣟⣻⣻⣿⡻⣟⡿⢻⣛⡟⢻⢹⢹⡟⣿⢻⣛⣿⢻⡟⠿⠻⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣷⣷⣿⣷⣾⣶⣿⣿⣶⣷⣿⣶⣷⣷⣾⣾⣼⠟⢃⣴⣾⣿⣶⣿⣷⣾⣷⣶⣷⣿⣾⣿⣶⣿⣿⣾⣷⣾⣿⣿⣶⣷⣾⣾⣿⣷⣾⣾⣾⣷⣿⣾⣦⣿⣾⣿⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣡⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣼⣽⣿⣾⣿⣿⣿⣿⣿⣿⣿⠏⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⡿⣯⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣾⣾⣽⣿⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣯⣿⣿⣿⣿⣶⣼⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿
⣟⡛⠿⢿⠿⢿⠿⠿⠿⣿⡻⢿⠿⠿⡿⠿⠿⠿⡿⠿⠿⢿⢿⠿⡟⠿⠿⠿⡿⣿⠿⠿⢿⠿⢿⢿⠻⡿⡿⡿⠿⠿⡿⢿⠿⠿⡿⢻⢿⠿⠻⠿⠟⢿⣟⡿⣿⠿⢿⠿⣿⢻⡿⡿⠿⠿⡿⡿⡿⠿⡿⡿⣿⢿⠿⡻⣿⣿
⣿⣷⣷⣿⣾⣾⣶⣾⣶⣷⣾⣾⢶⣶⣶⢶⣷⣶⣶⣶⣶⣾⠷⣶⣷⣶⣷⣾⣷⣷⣴⣶⣾⣷⣶⣾⣶⣼⣶⣷⣶⣷⣿⣿⣶⡶⣷⣾⣾⣷⣶⣽⣿⣾⣿⣶⣷⠶⣾⣷⣾⣾⣾⣿⣾⣶⣷⣶⣶⣴⣷⣷⣿⣷⣶⣷⣿⣿
⣷⣮⣯⣧⣿⣮⣷⣼⣼⣿⣽⣥⣼⣿⣧⣬⣽⣤⣽⣯⣿⣼⣭⣮⣤⣦⣥⣬⣿⣵⣼⣵⣤⣤⣯⣤⣿⣼⣧⣼⣿⣯⣯⣿⣽⣾⣽⣥⣴⣾⣿⣧⣤⣼⣼⣧⣷⣤⣽⣴⣼⣷⣮⣷⣤⣯⣧⣤⣴⣧⣽⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣙⣯⣯⣉⣯⣝⣉⣫⣝⢈⣏⣽⣹⣍⣫⣿⣉⣍⣏⣯⣫⣽⣏⡯⣫⣯⡩⣯⣯⣯⣙⣙⣍⣛⣹⣍⣋⣽⣯⣉⠍⣏⣯⣋⢫⣭⣏⣉⣯⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡆⠀⡆⠂⡦⠆⡄⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⠀⣁⠀⠀⠀⡀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⣿⣿⣿⣿⣿⣿⣿⠿⣿⢿⣿⣿⣿⠀⠀⠀⢠⡍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⡟⢻⡟⣿⢻⡟⢻⠀⣿⢸⣿⠋⠿⠀⠀⠀⠈⠱⠍⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⡇⢸⡇⣿⢸⡇⢸⡀⣿⢸⣿⣦⡄⠀⠀⠀⠀⣄⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣤⣇⣸⡇⣿⢸⡟⢻⠿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡟⢻⡇⣿⢸⣇⣸⣤⣷⣾⣿⣿⡇⠀⠀⠀⠘⠛⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⡇⢸⡇⣿⢹⡏⢹⠉⣿⢹⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⣇⣸⣇⣿⣸⣇⣸⠀⡏⢸⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⡤⡿⢿⣿⣿⣿⡿⢿⢤⣧⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⠀⡇⢸⡏⣿⢹⡇⢸⠀⡟⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⠛⠋⠉⠉⣋⣉⣭⡟⠛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠀⡄⠀⣤⢄⠀⠀⠀⠀⠁⠀⠀⠁⢉⠹⠎⢛⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠈⠙⠻⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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(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/

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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. █


⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⣿⣿⣿⣿⣿⠀⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⣿⣿⣿⠛⣿⠀⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣽⣿⠀⣿⠀⣿⡿⢿⣿⣿⣿⠿⣿⠛⣿⡟⢻⡇⢸⡏⠉⣿⠛⣿⠀⣻⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⠀⢸⡇⢸⡇⢸⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⣿⠀⣿⡇⢸⡏⢹⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⠀⢸⡇⢸⡇⢸⣿⠀⣿⠉⣿⡏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⠀⢸⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⣿⣿⣿⠉⣿⠉⣿⣿⣿⣿⣿⡇⠀⣿⠉⣿⠉⣿
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⣿⣿⣿⣿⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⠀⢸⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿
⣿⣷⣿⣼⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⠀⢸⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿
⣿⣿⣿⣿⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⠀⢸⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿
⣿⣿⣿⣿⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⠀⢸⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿
⣿⣿⣿⣾⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⠀⢸⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿
⣿⣿⣿⣿⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⢿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡿⠀⣿⠀⣿⠀⢸⡇⢸⡇⠸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿
⣿⡿⣿⢿⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⠁⠀⡠⠀⡤⠀⣀⠀⡀⠀⡀⢀⠀⡀⠀⠀⠀⠀⡀⡀⠀⠀⠀⢀⢀⠀⠀⢀⠀⠀⠀⢸⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿
⣿⣿⣿⣿⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣤⠀⣤⠀⢠⡄⢠⡄⢠⣤⠀⣤⠀⣤⡄⢠⡄⢠⡄⠀⣤⠀⣤⠀⢠⡄⢠⡄⠀⣤⠀⣼⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿
⣿⣿⣿⣿⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⠀⢸⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿
⣿⣿⣿⣿⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⢿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⠀⢸⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⠇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿
⣿⣿⣿⣿⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⠀⢸⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿
⣿⣿⣿⣿⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⠀⢸⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 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⦈_


____
* The University of Michigan developed LDAP (which_became_OpenLDAP) which
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.


⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⣿⣿⣿⣿⣿⢿⣿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⡇⣭⢹⠩⢝⣿⢸⣿⠈⣭⢹⢩⠻⡙⠭⠋⣭⡩⢽⢩⢨⡹⢏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⢿⣿⣿⣆⠀⢀⣼⣿⣿⠇⠀⠀⣿⠿⠼⠧⠿⠼⠮⣵⣿⠮⠥⠧⠿⠼⠼⢦⣷⣭⠶⠿⠮⠵⣼⣬⣓⣾⡿⠿⠿⠿⢿⣿⡿⠿⠿⠿⠿⠿⣿⣿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿
⣿⣿⣿⡇⠀⠀⢸⣿⡟⢿⣷⣿⠟⣿⣿⠀⠀⠀⣿⣷⠀⠀⣶⣦⡀⠈⣿⣶⠀⢰⣶⣶⡄⢸⠟⠁⢠⣴⣶⣦⡀⠀⡟⠁⢀⣴⣶⣦⡀⠈⢷⡆⠀⣶⣦⡀⠈⢻⣷⠀⠀⣶⣶⣦⣄⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾
⣿⣿⣿⡇⠀⠀⣼⣿⣧⡄⠹⠃⣤⣿⣿⡄⠀⠀⣿⣿⠀⠀⠿⠿⠁⢀⣿⣿⠀⠸⠿⠏⢹⡟⠀⠀⣿⣿⣿⣿⣿⣴⠀⠀⣾⣿⣿⣿⣧⠀⠈⡇⠀⠿⠿⠃⢀⣼⣿⡇⠀⣿⣿⣿⣿⡆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠛⠛⠛⠃⠀⠀⠛⠛⠛⠃⠀⠀⣿⣿⠀⠀⣦⡀⠀⢿⣿⣿⠀⢰⣶⣆⣸⣇⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⢿⣿⣿⣿⡟⠀⠀⡇⠀⣶⡀⠀⢻⣿⣿⡇⠀⣿⣿⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢿⣷⡀⠈⢿⡿⠀⠘⠿⠿⠟⠁⣆⠀⠈⠻⠿⠿⠋⣨⣧⡀⠈⠻⠿⠟⠁⢀⣼⠇⠀⢿⣷⡀⠀⢻⣿⠀⠀⠿⠿⠟⠋⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣿⠶⢶⣶⣶⢿⡿⡶⡤⡴⡶⡶⣶⡶⢶⢶⡿⡿⣶⠤⢤⢶⣾⡿⣿⠿⡶⢦⡤⡴⡶⣿⣷⣶⣶⣶⣿⣿⣶⣦⣼⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛
⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣴⣤⣤⣤⣤⣧⣬⣶⣧⣤⣬⣬⣦⣄⣮⣧⣤⣤⣤⣿⣤⣤⣤⣧⣧⣤⣤⣦⣦⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⢻⠛⡟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⣟⠛⣻⡏⠋⣹⣿⡋⣿⣿
⣿⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣷⣿⣿
⣿⣿⡇⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⣿⣿⣿
⣿⣿⡇⠀⢸⠉⣿⢹⣿⡏⢹⠏⢹⣿⠛⡿⡛⡿⠛⢻⢻⠛⡇⡟⢻⢸⠛⢻⠟⡛⣿⡟⠟⢿⢟⢻⠟⠻⡟⡻⡛⡟⡟⡿⡛⠟⠛⠟⠃⣿⡟⢛⠟⠻⠟⠻⡿⡛⡏⣻⣟⢐⠟⠻⡟⢻⣿⢟⢻⣿⢸⣿⣿⡇⠀⣿⣿⣿
⣿⣿⡇⠀⢸⡄⠿⣸⣤⡇⡆⣸⢸⣿⢸⡇⠄⣇⠿⢸⠸⠀⡇⡇⣿⢸⢸⢸⠂⠥⢿⡇⠸⢸⠡⠸⡂⠌⡓⠌⡇⢠⢁⡇⠗⡀⢸⡘⠇⣿⡇⣿⡠⢀⡒⠌⡇⠄⡇⢿⣿⢸⡘⢇⡇⣿⣿⠡⠸⣿⢸⣿⣿⡇⠀⣿⣿⣿
⣿⣿⡇⠀⢸⠿⣿⢿⠿⣿⠿⡿⣿⠿⠿⡿⣿⡿⣿⣼⢻⢿⣿⣿⣿⣿⣿⣿⣮⣥⢺⣧⠾⢿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿
⣿⣿⡇⠀⢸⠀⣿⢸⢠⠙⡄⡇⡇⣾⡧⡇⣛⡃⣿⡇⣿⢸⣿⠁⣊⡇⠇⡎⣂⣹⠘⠛⣿⢸⣷⢹⣿⢔⢸⢡⣬⢡⣎⡇⡆⡇⣿⢸⢰⠈⡄⣇⠢⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿
⣿⣿⡇⠀⠸⠧⠭⠾⠼⠤⠧⠧⠷⠬⠵⠧⠿⠧⠿⠧⠹⠬⠭⠦⠥⠿⠴⠷⠭⠾⠼⠿⠭⠬⠏⠾⠷⠬⠬⠮⠴⠦⠵⠧⠥⠷⠤⠼⠼⠤⠧⠧⠥⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⣿⣿⣿
⣿⣿⣷⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣿⣿⣿
⣿⣿⣿⣿⣿⠛⠿⡟⡻⠿⠿⠿⡟⠻⠟⢿⣿⣿⣯⢫⠻⢻⠿⣿⣿⢺⣿⣟⢿⣿⣽⢻⢻⣿⠻⢻⣿⡿⠛⢻⠻⣻⣟⡟⢟⡟⢹⣿⢻⡟⣿⠟⡟⣿⠘⡟⠟⣟⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣶⡧⣷⣶⣶⣷⣶⣷⣷⣶⣾⡿⡿⢿⣾⢶⣾⣷⢵⣿⣾⣾⢷⣾⣿⢾⣾⣶⣾⣾⣮⣾⣷⣷⣾⣾⣿⣗⣣⣷⣶⣾⣿⣾⣷⣷⣷⣷⣿⣾⣶⣶⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⣿⣿⣿⣿⣿⣶⣆⣤⣼⣴⣿⣷⣤⣥⣄⣤⣤⣧⣭⣬⣽⣜⣯⣦⣥⣤⣬⣤⣬⣤⣽⣤⣥⣷⣵⣭⣴⣕⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⣿⣿⣿⣿⣿⡭⠙⢛⡯⠝⠋⡛⢛⠛⠙⡛⡟⠋⡏⠋⠟⠋⠋⠛⠿⣻⠙⠛⢻⠛⠛⠛⠋⠟⠛⡻⡟⠙⠟⢻⠛⠛⠛⣛⡛⠛⠋⢻⠙⠛⣻⠋⢹⠹⡍⠋⠙⠭⠉⡟⡭⠟⡻⠛⢹⡿⣽⠛⢛⠟⠛⠛⠻⢻⠙⢻⣿⣿
⣿⣿⣿⣿⣿⠿⡿⢿⠿⠿⡿⢿⢿⡿⢿⠾⡿⡟⣿⡿⠿⢿⡿⣶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣶⣶⣾⣾⣶⣿⣶⣾⣶⣶⣷⣿⣿⣿⣶⣴⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 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 &amp; 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.


===============================================================================
* Gemini_(Primer) links can be opened using Gemini_software. It’s like the
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.


===============================================================================
* Gemini_(Primer) links can be opened using Gemini_software. It’s like the
World Wide Web but a lot lighter.



                    ䷩ 𝚕𝚒𝚗𝚎 9054

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 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.


===============================================================================
* Gemini_(Primer) links can be opened using Gemini_software. It’s like the
World Wide Web but a lot lighter.


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