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):

QmPrM5Hu5PNR7zjUmtsvqm8xkZsrE96qx4CaEuQrKFfjFd

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡎⢳⢸⠉⡆⡮⠷⢸⠙⡆⠯⡁⡎⢱⢸⠀⡇⡎⢱⠋⠃⡯⠷⠀⢰⠙⢰⠋⡆⡎⢱⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣄

⠙⠉⠸⠉⠁⠙⠁⠈⠀⠁⠙⠁⠙⠋⠈⠙⠁⠁⠀⠙⠁⠙⠁⠈⠈⠚⠈⠓⠁⠃⠘⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢤⣥

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢦⣶⢲⠀⣂⣆⣶⣴⠀⠀⠀⠀⣶⣶⣴⢔⣴⡄⢦⣖⣶⣴⠀⠀⠀⠀⠀⢰⡤⡢⣶⢶⡆⡠⣢⣴⣔⢴⡆⠀⠀⠀⠰⢰⣴⣦⡂⠐⢀⡤⢴⢲⣠⠂⣤⣴⠠⣲⣲⡆⢔⣴⣶⡆⡆⡖⣦⡂⢴⣶⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠖⣀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣡⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⢉⠏⢹⢛⢻⢻⢻⢻⡿⢛⢹⢟⡻⡛⡟⡿⡛⠏⠹⢛⢿⢛⡻⡟⡛⠟⢿⢛⢻⠛⠋⡀⣺⢛⣻⣿⣛⢻⠉⣻⡟⣭⡙⡟⣛⢿⢛⢻⢛⡻⡟⣛⡟⡛⡟⣿⢻⢛⡻⣛⡿⡛⢿⡿⡛⡿⡛⢿⢛⢛⢻⣿⣿

⣿⣿⣿⣿⣿⣼⣦⣴⣤⣼⣦⣧⣾⣷⣬⣼⣦⣤⣧⣴⣧⣤⣧⣴⣬⣼⢨⣥⣧⣧⣿⡼⠄⣠⣴⣧⣧⣽⣥⣼⣯⣤⣼⣤⣽⣷⣭⣴⡇⣭⣼⣤⣼⣼⣧⣧⣤⣦⣥⣦⣭⣼⣼⣧⣭⣧⣤⣮⣧⣭⣧⣥⣾⣼⣼⣼⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢋⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⡏⡿⠻⣿⣟⡻⣟⣿⣻⠛⡟⣿⢻⡟⡿⢻⣿⡟⣿⡟⠻⠟⣡⠒⣟⣟⣻⡿⠿⣿⣿⡟⠻⣟⣟⡿⣻⣟⣻⣻⣿⡻⣟⡿⢻⣛⡟⢻⢹⢹⡟⣿⢻⣛⣿⢻⡟⠿⠻⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣷⣷⣷⣿⣷⣾⣶⣿⣿⣶⣷⣿⣶⣷⣷⣾⣾⣼⠟⢃⣴⣾⣿⣶⣿⣷⣾⣷⣶⣷⣿⣾⣿⣶⣿⣿⣾⣷⣾⣿⣿⣶⣷⣾⣾⣿⣷⣾⣾⣾⣷⣿⣾⣦⣿⣾⣿⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣡⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣼⣽⣿⣾⣿⣿⣿⣿⣿⣿⣿⠏⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⡿⣯⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿

⣿⣿⣿⣿⣿⣿⣿⣷⣾⣾⣽⣿⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣯⣿⣿⣿⣿⣶⣼⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿

⣟⡛⠿⢿⠿⢿⠿⠿⠿⣿⡻⢿⠿⠿⡿⠿⠿⠿⡿⠿⠿⢿⢿⠿⡟⠿⠿⠿⡿⣿⠿⠿⢿⠿⢿⢿⠻⡿⡿⡿⠿⠿⡿⢿⠿⠿⡿⢻⢿⠿⠻⠿⠟⢿⣟⡿⣿⠿⢿⠿⣿⢻⡿⡿⠿⠿⡿⡿⡿⠿⡿⡿⣿⢿⠿⡻⣿⣿

⣿⣷⣷⣿⣾⣾⣶⣾⣶⣷⣾⣾⢶⣶⣶⢶⣷⣶⣶⣶⣶⣾⠷⣶⣷⣶⣷⣾⣷⣷⣴⣶⣾⣷⣶⣾⣶⣼⣶⣷⣶⣷⣿⣿⣶⡶⣷⣾⣾⣷⣶⣽⣿⣾⣿⣶⣷⠶⣾⣷⣾⣾⣾⣿⣾⣶⣷⣶⣶⣴⣷⣷⣿⣷⣶⣷⣿⣿

⣷⣮⣯⣧⣿⣮⣷⣼⣼⣿⣽⣥⣼⣿⣧⣬⣽⣤⣽⣯⣿⣼⣭⣮⣤⣦⣥⣬⣿⣵⣼⣵⣤⣤⣯⣤⣿⣼⣧⣼⣿⣯⣯⣿⣽⣾⣽⣥⣴⣾⣿⣧⣤⣼⣼⣧⣷⣤⣽⣴⣼⣷⣮⣷⣤⣯⣧⣤⣴⣧⣽⣿⣿⣿⣿⣿⣿⣿

⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣙⣯⣯⣉⣯⣝⣉⣫⣝⢈⣏⣽⣹⣍⣫⣿⣉⣍⣏⣯⣫⣽⣏⡯⣫⣯⡩⣯⣯⣯⣙⣙⣍⣛⣹⣍⣋⣽⣯⣉⠍⣏⣯⣋⢫⣭⣏⣉⣯⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⡆⠀⡆⠂⡦⠆⡄⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢀⠀⣁⠀⠀⠀⡀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠁⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⣿⣿⣿⣿⣿⣿⣿⠿⣿⢿⣿⣿⣿⠀⠀⠀⢠⡍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⡟⢻⡟⣿⢻⡟⢻⠀⣿⢸⣿⠋⠿⠀⠀⠀⠈⠱⠍⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⡇⢸⡇⣿⢸⡇⢸⡀⣿⢸⣿⣦⡄⠀⠀⠀⠀⣄⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣤⣇⣸⡇⣿⢸⡟⢻⠿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡟⢻⡇⣿⢸⣇⣸⣤⣷⣾⣿⣿⡇⠀⠀⠀⠘⠛⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⡇⢸⡇⣿⢹⡏⢹⠉⣿⢹⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⣇⣸⣇⣿⣸⣇⣸⠀⡏⢸⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⡤⡿⢿⣿⣿⣿⡿⢿⢤⣧⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⠀⡇⢸⡏⣿⢹⡇⢸⠀⡟⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⣷⣾⡇⣿⢸⣷⣾⠀⡇⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⡏⢹⡇⣿⢸⡏⢹⠀⡇⢸⣿⣿⡇⠀⠀⠀⠀⢬⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⣇⣸⣇⣿⣨⣇⣸⠀⡇⢸⣿⣿⡇⠀⠀⠀⠀⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣤⣿⣿⣿⣿⣿⣿⣿⣤⣧⣼⣿⡏⠁⠀⠀⠀⠀⢂⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⣿⣿⣿⣿⣿⣿⣿⠀⡇⢸⣿⣇⠀⠀⠀⠀⠀⢲⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⣿⣿⣿⣿⣿⣿⣿⠀⡇⢸⣿⣿⠀⠀⠀⠀⠀⠬⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⣿⣿⣿⣿⣿⣿⣿⠀⡇⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⡟⢻⠛⣿⢛⡟⢻⠀⠇⠸⠿⠿⠇⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣀⣇⣸⠀⢋⣀⣄⣴⣠⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⡿⢁⣴⣿⣿⣿⣿⠀⣿⢸⣿⣿⡇⠀⠀⠀⠀⢸⠀⣲⢠⣍⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⠁⢸⡇⣿⢸⡇⢸⠀⣿⢸⣿⡟⠀⠀⠀⠀⠀⣈⠀⢸⡇⣿⣿⣶⣌⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⡆⢸⣷⣿⣾⡄⡌⠀⢛⢸⠛⠶⠆⠀⠀⠀⠀⠀⠀⠸⠃⢿⣿⣿⣿⣷⣄⠙⢿⡿⢿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠙⠋⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠛⠙⠟⠛⠋⠀⠻⣿⣿⡿⠛⠞⠶⠾⢤⣄⠀⠀⠀⠀⠀⠈⠀⠈⠓⠘⠿⠿⢿⣿⣿⣷⡀⠀⠀⠀⠀⠉⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣤⣤⣄⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⢠⣤⣡⣐⡐⢠⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠛⠋⠉⠉⣋⣉⣭⡟⠛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠀⡄⠀⣤⢄⠀⠀⠀⠀⠁⠀⠀⠁⢉⠹⠎⢛⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠈⠙⠻⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢘⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                ䷩ 𝚕𝚒𝚗𝚎 5962

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/09/06/microsoft-freefall/#comments

Gemini version at gemini://gemini.techrights.org/2023/09/06/microsoft-freefall/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.06.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧

Gemini_version_available_♊︎

✐ Microsoft_and_Its_Proxies_Are_in_a_Freefall⠀✐

Posted in Google, Microsoft, Search at 2:25 pm by Dr. Roy Schestowitz

Summary: Microsoft is a shrinking company; on the client side and the server

side younger companies such as Google are replacing it

MICROSOFT-FUNDED media pretends_that_Microsoft_is_a_valuable_company_that

continues_to_grow, but the exact opposite is true.

“Microsoft is a shrinking company…”Take search for example. Microsoft increased

Bing usage fees, so about 5 months ago Brave dumped that completely and

DuckDuckGo, which is basically a Microsoft proxy, has had a tough couple of

years:

            🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇DDG_market_share_2021-2023⦈_

DuckDuckGo market share as a function of time (data_as_OpenDocument_Format)

Despite all the advertising, people eventually find out that DuckDuckGo is just

a Microsoft ‘skin’ and abandon the false promise of “privacy” (DuckDuckGo is

Microsoft surveillance and by extension NSA surveillance).

“Despite all the advertising, people eventually find out that DuckDuckGo is

just a Microsoft ‘skin’ and abandon the false promise of “privacy” (DuckDuckGo

is Microsoft surveillance and by extension NSA surveillance).”As we noted here

some days ago, Bing_as_per_this_year has had loads_of_layoffs (the media barely

reported on it) and so far this month Microsoft has_fallen_even_further_in_the

global_search_market and Indian_market. Now it’s just 0.9%! Pathetic. It is the

same_in_Russia. Microsoft at 0.9%. At one point are the financial

sustainability and viability aspects going to force Microsoft to exit the

market and shut down Bing? Google_is_turning_25 and despite starting as a

search company it is now slaughtering Microsoft’s monopoly on operating

systems. Android is a lot bigger than Windows now, so the_whole_'ecosystem'_of

broken_Windows_is_collapsing. █

⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⡿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⡇⢸⣿⠀⣿⠀⣿⡏⢹⣿⣿⣿⣿⣿⠀⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⠀⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⣿⣿⣿⠛⣿⠀⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣽⣿⠀⣿⠀⣿⡿⢿⣿⣿⣿⠿⣿⠛⣿⡟⢻⡇⢸⡏⠉⣿⠛⣿⠀⣻⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⠀⢸⡇⢸⡇⢸⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⠀⣿⠀⣿⡇⢸⡏⢹⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⠀⢸⡇⢸⡇⢸⣿⠀⣿⠉⣿⡏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⠀⢸⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⣿⣿⣿⠉⣿⠉⣿⣿⣿⣿⣿⡇⠀⣿⠉⣿⠉⣿

⣿⣟⣿⣻⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⠀⢸⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡏⢹⡏⢹⡇⠀⣿⠀⣿⠀⣿

⣿⣿⣿⣿⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⠀⢸⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿

⣿⣿⣿⣿⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⠀⢸⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿

⣿⣷⣿⣼⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⠀⢸⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿

⣿⣿⣿⣿⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⠀⢸⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿

⣿⣿⣿⣿⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⠀⢸⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿

⣿⣿⣿⣾⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⠀⢸⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿

⣿⣿⣿⣿⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⢿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡿⠀⣿⠀⣿⠀⢸⡇⢸⡇⠸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿

⣿⡿⣿⢿⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⠁⠀⡠⠀⡤⠀⣀⠀⡀⠀⡀⢀⠀⡀⠀⠀⠀⠀⡀⡀⠀⠀⠀⢀⢀⠀⠀⢀⠀⠀⠀⢸⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿

⣿⣿⣿⣿⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣤⠀⣤⠀⢠⡄⢠⡄⢠⣤⠀⣤⠀⣤⡄⢠⡄⢠⡄⠀⣤⠀⣤⠀⢠⡄⢠⡄⠀⣤⠀⣼⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿

⣿⣿⣿⣿⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⠀⢸⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿

⣿⣿⣿⣿⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⢿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⠀⢸⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⠇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿

⣿⣿⣿⣿⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⠀⢸⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿

⣿⣿⣿⣿⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⠀⢸⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢸⡇⢸⡇⠀⣿⠀⣿⠀⣿

⣿⣿⣟⢻⣿⣀⣿⣀⣿⣇⣸⣇⣸⣿⣀⣿⣀⣿⣇⣸⣇⣸⣇⣀⣿⣀⣿⣀⣿⣇⣸⣇⣸⣿⣀⣿⣀⣿⣇⣸⣇⣸⣿⣀⣿⣀⣿⣀⣸⣇⣸⣇⣸⣿⣀⣿⣀⣿⣇⣸⣇⣸⣿⣀⣿⣀⣿⣇⣸⣇⣸⣇⣀⣿⣀⣿⣀⣿

⣿⣿⣿⣿⢿⣻⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⢿⡿⣿⣿⡿⣻⣿⣿⡿⣿⣿⡿⣿⣿⣿⣿⢿⣿⣿⣿⣟⣿⣿⣿⡿⣻⢿⣿⣿⢛⡿⣛⣿⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⢛⡿⣿⣿⡿⣿⢿⣿⣿⣿⣿

⣿⣿⡿⢟⡟⣽⡿⣫⣿⢿⣿⢟⣽⡿⣿⡿⣓⣽⠿⣻⢟⣪⡿⢟⡿⣽⡿⣫⣿⢫⣿⢟⣽⡿⣷⡿⣫⣿⢿⣾⢟⣻⡿⢗⡿⣛⣿⠿⣺⢯⣿⢟⣽⡟⣽⡿⣫⣿⢿⣮⢟⣻⡿⣷⡽⣛⣿⠿⣻⢟⣻⡿⢟⡿⣽⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                ䷩ 𝚕𝚒𝚗𝚎 6046

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/09/06/threat-to-security/#comments

Gemini version at gemini://gemini.techrights.org/2023/09/06/threat-to-security/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.06.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧

Gemini_version_available_♊︎

✐ Principal_Threat_to_Security_is_Microsoft_Windows_and_Proprietary_Software⠀✐

Posted in Microsoft, Security at 12:38 am by Dr. Roy Schestowitz

Video_download_link

http://techrights.org/wp-content/uploads/2023/09/spyware-threats.webm

Summary: Richard Stallman gave this talk some years ago; meanwhile, a leading

technical university got_cracked due to Microsoft* and it won’t dare mention

the culprit

🄸🄼🄰🄶🄴🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽⦇Windows_TCO:_Yes,_it's_true,we_got_cracked⦈


dovetailed with MIT’s Kerberos and would have avoided “AD”, to paraphrase an

associate. Kerberos_was_sabotaged_by_Microsoft and gag_clauses_have_been_in_use

since_the_early_stages_of_“AD”.

So Microsoft has dragged this university’s computing environment down from

world class to that of a year 2021 “Hillsdale College”. To be sure, Oracle and

Cisco also have their fingers in that pie and a role in the demise of the

institution’s role as one of the world leaders in computing. See “Our

Attorney’s_Response_To_Microsoft” (posted by Roblimo) and this_last_article

which brings up a very important point — that Microsoft regards its contracts

as trade secrets so even someone resourceful and tenacious would be unlikely to

succeed in a FOIA request regarding the publicly-funded university’s support

contracts. Microsoft_tried_to_censor_information while crushing_standards.

Those institutions late in weaning themselves from Microsoft Windows can look

at Samba_4_as_an_alternative.

⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⣿⣿⣿⣿⣿⢿⣿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⡇⣭⢹⠩⢝⣿⢸⣿⠈⣭⢹⢩⠻⡙⠭⠋⣭⡩⢽⢩⢨⡹⢏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡇⠀⠀⢿⣿⣿⣆⠀⢀⣼⣿⣿⠇⠀⠀⣿⠿⠼⠧⠿⠼⠮⣵⣿⠮⠥⠧⠿⠼⠼⢦⣷⣭⠶⠿⠮⠵⣼⣬⣓⣾⡿⠿⠿⠿⢿⣿⡿⠿⠿⠿⠿⠿⣿⣿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿

⣿⣿⣿⡇⠀⠀⢸⣿⡟⢿⣷⣿⠟⣿⣿⠀⠀⠀⣿⣷⠀⠀⣶⣦⡀⠈⣿⣶⠀⢰⣶⣶⡄⢸⠟⠁⢠⣴⣶⣦⡀⠀⡟⠁⢀⣴⣶⣦⡀⠈⢷⡆⠀⣶⣦⡀⠈⢻⣷⠀⠀⣶⣶⣦⣄⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾

⣿⣿⣿⡇⠀⠀⣼⣿⣧⡄⠹⠃⣤⣿⣿⡄⠀⠀⣿⣿⠀⠀⠿⠿⠁⢀⣿⣿⠀⠸⠿⠏⢹⡟⠀⠀⣿⣿⣿⣿⣿⣴⠀⠀⣾⣿⣿⣿⣧⠀⠈⡇⠀⠿⠿⠃⢀⣼⣿⡇⠀⣿⣿⣿⣿⡆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡇⠀⠀⠛⠛⠛⠃⠀⠀⠛⠛⠛⠃⠀⠀⣿⣿⠀⠀⣦⡀⠀⢿⣿⣿⠀⢰⣶⣆⣸⣇⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⢿⣿⣿⣿⡟⠀⠀⡇⠀⣶⡀⠀⢻⣿⣿⡇⠀⣿⣿⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢿⣷⡀⠈⢿⡿⠀⠘⠿⠿⠟⠁⣆⠀⠈⠻⠿⠿⠋⣨⣧⡀⠈⠻⠿⠟⠁⢀⣼⠇⠀⢿⣷⡀⠀⢻⣿⠀⠀⠿⠿⠟⠋⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣿⠶⢶⣶⣶⢿⡿⡶⡤⡴⡶⡶⣶⡶⢶⢶⡿⡿⣶⠤⢤⢶⣾⡿⣿⠿⡶⢦⡤⡴⡶⣿⣷⣶⣶⣶⣿⣿⣶⣦⣼⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛

⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣴⣤⣤⣤⣤⣧⣬⣶⣧⣤⣬⣬⣦⣄⣮⣧⣤⣤⣤⣿⣤⣤⣤⣧⣧⣤⣤⣦⣦⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⢻⠛⡟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⣟⠛⣻⡏⠋⣹⣿⡋⣿⣿

⣿⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣷⣿⣿

⣿⣿⡇⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⣿⣿⣿

⣿⣿⡇⠀⢸⠉⣿⢹⣿⡏⢹⠏⢹⣿⠛⡿⡛⡿⠛⢻⢻⠛⡇⡟⢻⢸⠛⢻⠟⡛⣿⡟⠟⢿⢟⢻⠟⠻⡟⡻⡛⡟⡟⡿⡛⠟⠛⠟⠃⣿⡟⢛⠟⠻⠟⠻⡿⡛⡏⣻⣟⢐⠟⠻⡟⢻⣿⢟⢻⣿⢸⣿⣿⡇⠀⣿⣿⣿

⣿⣿⡇⠀⢸⡄⠿⣸⣤⡇⡆⣸⢸⣿⢸⡇⠄⣇⠿⢸⠸⠀⡇⡇⣿⢸⢸⢸⠂⠥⢿⡇⠸⢸⠡⠸⡂⠌⡓⠌⡇⢠⢁⡇⠗⡀⢸⡘⠇⣿⡇⣿⡠⢀⡒⠌⡇⠄⡇⢿⣿⢸⡘⢇⡇⣿⣿⠡⠸⣿⢸⣿⣿⡇⠀⣿⣿⣿

⣿⣿⡇⠀⢸⠿⣿⢿⠿⣿⠿⡿⣿⠿⠿⡿⣿⡿⣿⣼⢻⢿⣿⣿⣿⣿⣿⣿⣮⣥⢺⣧⠾⢿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿

⣿⣿⡇⠀⢸⠀⣿⢸⢠⠙⡄⡇⡇⣾⡧⡇⣛⡃⣿⡇⣿⢸⣿⠁⣊⡇⠇⡎⣂⣹⠘⠛⣿⢸⣷⢹⣿⢔⢸⢡⣬⢡⣎⡇⡆⡇⣿⢸⢰⠈⡄⣇⠢⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿

⣿⣿⡇⠀⠸⠧⠭⠾⠼⠤⠧⠧⠷⠬⠵⠧⠿⠧⠿⠧⠹⠬⠭⠦⠥⠿⠴⠷⠭⠾⠼⠿⠭⠬⠏⠾⠷⠬⠬⠮⠴⠦⠵⠧⠥⠷⠤⠼⠼⠤⠧⠧⠥⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⣿⣿⣿

⣿⣿⣷⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣿⣿⣿

⣿⣿⣿⣿⣿⠛⠿⡟⡻⠿⠿⠿⡟⠻⠟⢿⣿⣿⣯⢫⠻⢻⠿⣿⣿⢺⣿⣟⢿⣿⣽⢻⢻⣿⠻⢻⣿⡿⠛⢻⠻⣻⣟⡟⢟⡟⢹⣿⢻⡟⣿⠟⡟⣿⠘⡟⠟⣟⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣶⡧⣷⣶⣶⣷⣶⣷⣷⣶⣾⡿⡿⢿⣾⢶⣾⣷⢵⣿⣾⣾⢷⣾⣿⢾⣾⣶⣾⣾⣮⣾⣷⣷⣾⣾⣿⣗⣣⣷⣶⣾⣿⣾⣷⣷⣷⣷⣿⣾⣶⣶⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣤⣤⣤⣶⣦⣦⣦⣤⣾⣤⣤⣤⣿⣷⣴⣤⣤⣤⣴⣔⣎⣧⣮⣦⣮⣤⣤⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣶⣆⣤⣼⣴⣿⣷⣤⣥⣄⣤⣤⣧⣭⣬⣽⣜⣯⣦⣥⣤⣬⣤⣬⣤⣽⣤⣥⣷⣵⣭⣴⣕⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⡭⠙⢛⡯⠝⠋⡛⢛⠛⠙⡛⡟⠋⡏⠋⠟⠋⠋⠛⠿⣻⠙⠛⢻⠛⠛⠛⠋⠟⠛⡻⡟⠙⠟⢻⠛⠛⠛⣛⡛⠛⠋⢻⠙⠛⣻⠋⢹⠹⡍⠋⠙⠭⠉⡟⡭⠟⡻⠛⢹⡿⣽⠛⢛⠟⠛⠛⠻⢻⠙⢻⣿⣿

⣿⣿⣿⣿⣿⠿⡿⢿⠿⠿⡿⢿⢿⡿⢿⠾⡿⡟⣿⡿⠿⢿⡿⣶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣶⣶⣾⣾⣶⣿⣶⣾⣶⣶⣷⣿⣿⣿⣶⣴⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                ䷩ 𝚕𝚒𝚗𝚎 6134

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/09/06/threat-to-software-freedom-everywhere/#comments

Gemini version at gemini://gemini.techrights.org/2023/09/06/threat-to-software-freedom-everywhere/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.06.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧

Gemini_version_available_♊︎

✐ A_Blueprint_for_Digital,Online_Oppression(and_Threat_to_Software_Freedom

Everywhere)⠀✐

Posted in Free/Libre_Software at 2:45 am by Dr. Roy Schestowitz

Video_download_link | md5sum a8a1c95c5af46e06e17653bcf5b2c204

Not About Protecting Kids

Creative Commons Attribution-No Derivative Works 4.0

http://techrights.org/videos/legislating-for-state-power.webm

Summary: The potent and immediate threat to people’s lives has grown greater

with the advance of the latest awful British legislation, which may in turn

jeopardise Free software because it’s harder to mandate/impose back doors on

Free software users

THE latest_episode of The_Cyber|Show was published earlier this month. It

covered what mobile (cellular) phones actually are, what social control

networks do to people, and it debated back doors.

“Andy’s articles have done a spectacular job explaining the issues.”When we

started mentioning_the_show it was because of one of the hosts (Andy), who

contributed some articles to Techrights while he still worked at a university.

Now he spends his time writing and talking about important issues, including

Software Freedom.

“Thanks so much to you and your team for the enthusiastic support,” Andy told

me this week. Andy’s articles have done a spectacular job explaining the

issues.

The video above contains some personal thoughts on the episode contained below.

Your browser does not support the audio element.

                ䷩ 𝚕𝚒𝚗𝚎 6194

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/09/06/untrustworthy-ibm/#comments

Gemini version at gemini://gemini.techrights.org/2023/09/06/untrustworthy-ibm/

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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 ═════════════════════════════════════════════╕

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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

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Gemini_version_available_♊︎

✐ Gemini_Links_06/09/2023:_Reddit’s_New_Tracking_URLs_and_Iterating_On

Fractals⠀✐

Posted in News_Roundup at 12:05 am by Dr. Roy Schestowitz

🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈

§ Contents⠀➾

* Gemini*_and_Gopher

      o Personal/Opinions

      o Science

      o Technology_and_Free_Software

            # Internet/Gemini

            # Programming

* § Gemini* and Gopher⠀➾

      o § Personal/Opinions⠀➾

            # ⚓ Show_notes_23-35⠀⇛

                   This week i have been preparing to move back to

                   university, and have been streamlining my workflow

                   for learning chinese. Recently i have been

                   neglecting certain aspects, and in general doing

                   far too many flash cards.

                   I know that a lot of people swear by anki, but i am

                   less convinced. Often the cards used are low

                   quality, so the information recall can be hardly

                   that helpful either. Instead, i have been

                   increasing the amount of reading i do, which should

                   have the same general effect as word flashcards,

                   but with added context of sentences and plot.

      o § Science⠀➾

            # ⚓ Astronomy_Season_Begins_(publ._2023-09-05)⠀⇛

                   For me here in Fairbanks, Alaska, astronomy season

                   doesn’t start until September, since there isn’t

                   enough darkness before that for practical

                   stargazing. I’m on an early-morning life schedule,

                   so it doesn’t work for me to stay up until midnight

                   to see the stars. But now there is enough darkness

                   for me to be able to do early morning sessions

                   (around 4am) before work.

                   Most nights these last few weeks have been overcast

                   skies, but there was a forecast of partly cloudy

                   early this morning, so I decided to head out early

                   to the boatlaunch, away from the light pollution,

                   and give it a try. Indeed, it was partly cloudy

                   this morning, but I was thwarted by a thick, low-

                   lying fog, which blocked out all the stars and

                   obscured the third-quarter moon.

      o § Technology and Free Software⠀➾

            # ⚓ let’s_talk_about_AI_art_i_guess⠀⇛

                   unavoidable subject i suppose. as i mentioned in my

                   microlog, i don’t know why everyone’s talking about

                   their hatred for AI art these days; it’s not

                   exactly the same as when dall-e 2 was unveiled and

                   half of art twitter was running to the hills,

                   panicking about their jobs [1]. it’s less fear and

                   more… contempt? disgust? just sheer *hatred*?

                   now, i don’t wanna come across as a techbro or

                   something. i get rather defensive when i hear

                   people talking shit about AI art; only natural

                   given that’s my research and how a lot of my work

                   has involved GAN generated images for the past year

                   and a half (since october 2020 to be exact) [2].

                   but don’t think this a blind defense of the

                   corporations and exploitative systems behind

                   current state of art AI image generation. i would

                   like to talk about the medium or the technology

                   itself (not that it can be understood in a vacuum,

                   but let’s cross that bridge when we get to it).

            # ⚓ Gemini_PDA_vs_Emacs_Native_Android⠀⇛

                   However, there were deal breaking issues. The

                   android sandbox the app lives in is the main one. I

                   was unable to get files I wanted to edit into emacs

                   to edit them. I could make a new file and save it

                   to /storage/emulated/0/Downloads, for example, but

                   if I created the file in another app, like vim in

                   termux, it would not open it. Access denied. This

                   device is rooted, so I even created a new directory

                   – /tmp – and chown’d to u0_a96 (the android system

                   generated user for my particular emacs

                   installation), chmod’ing /tmp/ 0777. No dice.

            # ⚓ Re:_FLOSS_Equivalent_of_Wordpad⠀⇛

                   Ted is a very old program. It looks dated as all

                   hell because it uses xlib instead of a “modern”

                   toolkit like Gtk4 or QT6. I do not consider this a

                   bad thing. It’s very small, very light, and has

                   very few dependencies. It hasn’t really changed in

                   years. It’s software that has achived that

                   remarkable (for today) state of being “finished”.

                   What Ted actually does give you is a pretty good

                   word processor using the Rich Text Format (.rtf)

                   that is the native Wordpad format. No more than

                   that, and no less. It does that job and that job

                   alone.

            # § Internet/Gemini⠀➾

                  # ⚓ Beware_Reddit’s_New_Tracking_URLs⠀⇛

                         Reddit recently implemented a new feature for

                         tracking the activity of it’s users and site

                         visitors, even if not logged in. This is a

                         privacy concern for everyone, even if you’ve

                         never used Reddit.

                         If a user using the official app shares a

                         link, they will be given a special tracking

                         URL that links their account to the post

                         being shared. These tracking links look like

                         this: https://reddit.com/r/subredditname/s/

                         tracking_token where the tracking_token is a

                         bunch of gibberish.

                         Opening this link resolved to a normal Reddit

                         URL with tracking parameters: https://

                         www.reddit.com/r/subredditname/comments/

                         post_id/post_title/?share_id=more_gibberish

                         Take note of the share_id parameter. This is

                         a unique identifier that reports to Reddit

                         who shared the link that is being opened.

                  # ⚓ RE:_Why_would_students_use_gemini?⠀⇛

                         This is an update to my original post asking

                         for help in a course I’m teaching on web

                         technologies, collaboration and the internet

                         to undergrad Computer Science students.

                  # ⚓ RE:_Accross_the_Spiderverse⠀⇛

                         Circadian makes a number of great

                         observations. I actually loved “Across the

                         Spiderverse” myself, but would likely point

                         out some of the same flaws if pressed. That

                         said, I’ve felt for a long time that there is

                         something wrong with our attention span in

                         modern times, and it overflows into our

                         expectations for entertainment. Thinking on

                         this, and on one of his biggest complaints,

                         got me thinking about pacing, and how

                         different it used to be.

            # § Programming⠀➾

                  # ⚓ Re:_Fast_Thoughts_on_a_Fast_Language⠀⇛

                         slondr has written up four thoughts on the

                         Ada programming language. As the maintainer

                         of one of the world’s most widely used Ada

                         programs, I couldn’t resist weighing in.

                         Sadly this program is used for cheating on

                         Latin translation homework, rather than Ada’s

                         more glamorous niches of aerospace or

                         security kernels.

                  # ⚓ Iterating_On_Fractals⠀⇛

                         In my recent post about print nozzle sizes I

                         showed a print of a super-fine fractal

                         pyramid.

=> =============================================================================

World Wide Web but a lot lighter.

                ䷩ 𝚕𝚒𝚗𝚎 8898

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Gemini_version_available_♊︎

✐ Gemini_Links_06/09/2023:_Recommendation_Algorithms,_IPv6_Adoption⠀✐

Posted in News_Roundup at 8:23 pm by Dr. Roy Schestowitz

🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈

§ Contents⠀➾

* Gemini*_and_Gopher

      o Personal/Opinions

      o Technology_and_Free_Software

            # Internet/Gemini

* § Gemini* and Gopher⠀➾

      o § Personal/Opinions⠀➾

            # ⚓ review:_the_genesis_of_misery_by_neon_yang⠀⇛

                   “the genesis of misery” is a sci-fi / fantasy mech

                   novel from the author of the “tensorate” series of

                   novellas. **this review is quite spoiler heavy**

                   but i’ll preface by saying i really disliked the

                   book and do not recommend it, so i think you won’t

                   be losing anything. it did get a fair amount of

                   praise? but i felt very similar to “the house of

                   hunger” (bad).

            # ⚓ Rescuing_(or_Replacing?)_the_Big_Bang_(publ._2023-09-06)⠀⇛

                   Short version: An astrophysicist from Canada

                   recognizes the glaring contradictions between what

                   we are seeing with JWST, and the standard model.

                   JWST is believed to give us a window into the far

                   distant past. But what we are finding is “mature”

                   galaxies popping up in places where the universe is

                   supposed to be in its infancy, according to the

                   supposed 13.8 billion year age of the universe. And

                   this astrophysicist is trying to put together a new

                   model, which allows for these ancient galaxies,

                   without hopefully adding too much time to the age

                   estimate. What will the new age turn out to be?

                   Nineteen billion? Twenty-nine billion?

            # ⚓ Shallow_Year,_or_failing_at_Depth_Year_(2023)⠀⇛

                   An online friend of mine did a Depth Year in 2022.

                   He documented both his successes and failures each

                   month, and ultimately felt rewarded but exhausted

                   after his pursuits. I thought that fulfillment and

                   exhaustion that comes with a year-long project was

                   something that I desperately needed, and so I

                   embarked upon my Depth Year on January 2023, with

                   the intention of deepening my understanding of

                   habit and my relationship with my hobbies and

                   studies.

      o § Technology and Free Software⠀➾

            # ⚓ Recommendation_algorithms:_all_fail⠀⇛

                   Is there a best practice of automated

                   recommendation systems? Clearly there are lots of

                   bad recommendation algorithms out there. Either

                   they don’t work as intended, or they do but have

                   undesirable side effects. I’ve touched on music

                   recommendation in a previous post (rewilding

                   music), here I will focus on video.

                   Youtube’s algorithms have been criticised for

                   promoting inaccurate information, serving scary

                   content to toddlers, and much more. Since the

                   algorithms are tightly kept secrets the criticism

                   must be based on their observable effects, which

                   partly depend on the interaction with millions or

                   billions of users. And with individual

                   customisation, each viewer will see different

                   recommendations.

                   The panic about misinformation has hit hard on

                   those who are critical of the current order of

                   things, regardless of whether they present accurate

                   information or deranged misconceptions. Project Owl

                   in 2017 had the ostensible goal of diminishing the

                   spread of false information, and if it succeeded at

                   that it also had a deleterious effect on

                   independent news sites of high quality, who may

                   have presented opinion pieces that were not well

                   aligned with establishment views.

            # ⚓ From_Terminal_to_terminal⠀⇛

                   Yes, that’s all…Ok, maybe a terminal ? It’s also

                   very usefull.

                   No problem for a PC under GNU/Linux of course but

                   for the other computer that (almost) everyone has,

                   the smartphone, it’s not so easy.

            # § Internet/Gemini⠀➾

                  # ⚓ Finally_reachable_over_IPv6⠀⇛

                         Up until now, this site has been hosted on

                         sourcehut pages. It was quite easy to get

                         started since it integrates very well into

                         the sourcehut ecosystem: the build gets

                         triggered automatically on git push and it

                         automatically gets the permission to publish

                         the page.

                  # ⚓ Trying_Gemini_(again)⠀⇛

                         I’ve been feeling increasingly disillusioned

                         with the bloat and maintenance of my website,

                         and the constant need to move social networks

                         as each hub collapses.

=> =============================================================================

World Wide Web but a lot lighter.

                ䷩ 𝚕𝚒𝚗𝚎 9054

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⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.06.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧

Gemini_version_available_♊︎

✐ Gemini_Links_06/09/2023:Vanity.onion_Address_and_Trying_Gemini⠀✐

Posted in News_Roundup at 12:27 pm by Dr. Roy Schestowitz

🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈

§ Contents⠀➾

* Gemini*_and_Gopher

      o Personal/Opinions

      o Technology_and_Free_Software

            # Internet/Gemini

* § Gemini* and Gopher⠀➾

      o § Personal/Opinions⠀➾

            # ⚓ 🔤SpellBinding:_DGYOTUH_Wordo:_RIFTS⠀⇛

      o § Technology and Free Software⠀➾

            # ⚓ Re:_FLOSS_Equivalent_of_Wordpad?⠀⇛

                   I use AbiWord on machines like my OpenPandora. It’s

                   lightweight and does even more than Wordpad did.

                   Sadly the GTK3 (or higher) versions are much slower

                   than the old GTK2 versions i prefer :/

            # § Internet/Gemini⠀➾

                  # ⚓ Taking_Accountability_for_My_Vanity_.onion_Address⠀⇛

                         Some folks probably already know that my

                         website, gopherhole, gemini capsule, and

                         finger server can be accessed over the tor

                         network at the .onion address

                         vigreyd6wrsvudjto7ccmt45avabdstveitqej2f4or75sjxkrijv3qd.onion.

                         Heck, if you are reading this blog post using

                         the Tor Browser, you likely would have been

                         redirected to that .onion address. The first

                         6 characters are “vigrey”, just like the

                         first 10 characters of the DuckDuckGo .onion

                         address are “duckduckgo” and the first 8

                         characters of the Facebook .onion address are

                         “facebook”. I am currently of the opinion

                         that making a vanity .onion address was a

                         morally wrong choice for me to make, even if

                         it was a mindless choice at the time.

                         Generating a vanity .onion address is

                         essentially the same process as Proof-of-Work

                         systems like Bitcoin use or trying to crack a

                         hashed and salted password. In all of those

                         cases, you make a random guess, see that your

                         guess was likely horribly wrong, throw that

                         guess away, and guess again. Do that over and

                         over again until luck is on your side. All

                         you had to do was waste a bunch of

                         electricity on the way. In the case of my

                         vanity .onion address, I statistically would

                         have generated about 32^6 (1073741824) .onion

                         addresses, likely throwing away over 1

                         billion addresses that didn’t start with

                         “vigrey”. I did that once before and lost

                         that .onion address’s private key, so I did

                         this twice in total… I also did this when

                         .onion addresses were only 16 characters in

                         length, so I likely threw away at least 3

                         billion .onion addresses needlessly.

                  # ⚓ Trying_Gemini_(again)⠀⇛

                         I want to give Gemini and its community

                         another try. Earlier this year I visited the

                         geminispace in a curious but fleeting manner,

                         and had a lot of fun in it, but it was more

                         of a chance encounter than a move.

                         I’ve been feeling increasingly disillusioned

                         with the bloat and maintenance of my website,

                         and the constant need to move social networks

                         as each hub collapses. I am hoping that this

                         will be a more sustainable way to document my

                         thoughts and socialise in a way that is

                         fulfilling but not so reliant on specific

                         services.

=> =============================================================================

World Wide Web but a lot lighter.

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