𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Monday, January 02, 2023

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Generated Tue 3 Jan 02:43:47 GMT 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/2023/01/02/

╒═══════════════════ 𝐑𝐄𝐂𝐄𝐍𝐓 𝐁𝐔𝐋𝐋𝐄𝐓𝐈𝐍𝐒 ════════════════════════════════════╕

Previous bulletins in IPFS (past 21 days, in chronological order):

QmdRJwsbsXgydBbvrvinQ8ybSqJWBJpS39D3VBcY5DSd3G

Qmb4EjHKEYahRXurhmzoyhxRGEPvXqTA7AcQPuzLrKfJGh

QmeFrf4tqX8a5FgfN4cMTHFas3gdjg8g34A9iryCnBvtMG

QmVK3bkZbD5g3xuJVLcQEb4nbz82bgKPeuhqrZfSGDbnWj

QmcMmjkkKEkp8tPhvcRuQqQEthfDb2Nksw3RYrGfjUfw3Q

QmfQQhspUHkt3SuJBA5fzqjRPqzZGW5MrbYgrDoP7udz1f

QmVUTRpCU7PcTDC7kj2yHWWkV5Mhg6XD2yLq9ekqQv4xj5

QmVwJZvv6r7xzdhVLH4kTyoCkuFgsArexoVuFbayx9A5N5

QmNhjQG4XJrooeuqLbPUPR9RtcgJkwZXoswD1oPWfgY7kD

QmX23uBSayrQrZ3iRx2A9hTusXL5Qh1iQYgKiEFEXVheje

QmcYNvBka24tu2hBsNQvBVNcTjpuUCQEfzcyW15SJLsr1Y

QmYTdvgUUtSuvEKMNdZJRgJFYocLqB3fhxmt8qv13qfA9k

QmcJ2fTtAvxD5pUALCXvrhAptqfYZYBPhYtyH3LP59jAmm

QmaHh3rcF6g1UkYaeQMy8YKRuBj1LWfFt5DuaV6zofEsKC

QmbuG1onEhQaW6rPEagzCe7S1rrm3GzuhFgsmM6jL2TBZS

QmY4eU9zG8ckdDYJVc11Fmqezkxur7EKvrCfBGK5RtRH44

QmfTYjmBes8TFM2EptMBYjdyJNQoTQsLBJovB5pnSaqAWd

QmUNj8KTWXETvfoRAoK5wetjRTk1KM6eF8ihQQsZ1gAX33

QmNt5eextzQVZUBr2ZtPeFpGEySDSJ3d1mRBqP4t126YvE

QmdcR8a3vTfpFjhLVTL5gCq8WQ4ahnKhbZnPhvZVnGhcHs

QmSqRoGuWGzGPiMq2GgcCee22CrF6E8w7JYJncWSZqw4yj

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

⦿ Analytics India Mag (AIM) is a Microsoft-Funded Propaganda Site (For Years Already) That Attacks Linux With Stigma and Lies | Techrights

⦿ CEO of Sirius ’UK’ Uses Accountants as the Address of His Personal Business Too (Not Just Sirius Open Source/Corporation After 3 Address Rotations in Just 5 Weeks!) | Techrights

⦿ IRC Proceedings: Sunday, January 01, 2023 | Techrights

⦿ Sirius ‘Open Source’ Misleading the International Organization for Standardization (ISO) on Security | Techrights

⦿ Sirius ‘Open Source’ Has Turned Workers Into Serfs/Slaves and Technical Work Into ’Bullshit Jobs’ | Techrights

⦿ Sirius Open Source Inc. - A New Shell Created When Bill Gates Paid the CEO; Then the Company Immediately Turned Ugly and Hostile Towards Its Own Workers | Techrights

⦿ [Meme] Sirius Management Meeting | Techrights

⦿ How Sirius Open Source Presents Itself in Microsoft’s LinkedIn | Techrights

⦿ When Talking About Wrongdoing is Considered Impressible | Techrights

⦿ [Meme] Managers Who Attack Their Own Company, Treating Staff Like Enemies | Techrights

䷼ Bulletin articles (as HTML) to comment on (requires login):

	http://techrights.org/2023/01/02/analytics-india-magazine-is-fud/#comments

	http://techrights.org/2023/01/02/bogus-addresses/#comments

	http://techrights.org/2023/01/02/irc-log-010123/#comments

	http://techrights.org/2023/01/02/retaliation-for-speaking-of-security-failings/#comments

	http://techrights.org/2023/01/02/sirius-divide-and-rule/#comments

	http://techrights.org/2023/01/02/sirius-open-source-inc/#comments

	http://techrights.org/2023/01/02/sirius-open-source-meeting/#comments

	http://techrights.org/2023/01/02/sirius-open-source-microsoft-linkedin/#comments

	http://techrights.org/2023/01/02/talking-about-wrongdoing/#comments

	http://techrights.org/2023/01/02/treating-staff-like-enemies/#comments

䷞ Followed by Daily Links (assorted news picks curated and categorised):

	http://techrights.org/2023/01/02/gnu-chinese-translators-team/#comments

	http://techrights.org/2023/01/02/ultramarine-linux-37-released/#comments

                ䷩ 𝚕𝚒𝚗𝚎 75

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/01/02/analytics-india-magazine-is-fud/#comments

Gemini version at gemini://gemini.techrights.org/2023/01/02/analytics-india-magazine-is-fud/

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Gemini_version_available_♊︎

✐ Analytics_India_Mag_(AIM)is_a_Microsoft-Funded_Propaganda_Site(For_Years

Already)_That_Attacks_Linux_With_Stigma_and_Lies⠀✐

Posted in Deception, FUD, GNU/Linux, Microsoft at 8:35 am by Dr. Roy

Schestowitz

It looks like another_Softpedia:

🄸🄼🄰🄶🄴🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽⦇branded-aim⦈_

🄸🄼🄰🄶🄴🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽⦇aim-microsoft⦈_

Article full of lies and deliberate distortion of history (like the lies

Microsoft paid writers to spread about MINIX and Linux):

🄸🄼🄰🄶🄴🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽⦇Anti-Linux⦈_

Purely provocation (or, as some would say, “trolling” by the same person):

🄸🄼🄰🄶🄴🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽⦇Same_author,less_than_two_days_apart⦈

Summary: For a number of years already we’ve noticed that Analytics India Mag

was behaving like a Microsoft mouthpiece and thus we’ve mostly ignored it; it

now openly admits working with Microsoft and the first two days of 2023 were

spent viciously attacking GNU/Linux with low-grade propaganda, so watch out; it

tries to discourage people in India, where GNU/Linux gained a lot lately (about

10%_on_desktops/laptops), from bringing us the next billion users along with

millions of skilled programmers

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

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⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢿⡿⠉⣿⢩⣭⣽⠉⣭⡍⢻⠉⣿⡏⡍⢿⣿⣿⣿⡏⣭⣭⣏⢹⣿⢉⡏⢩⣭⣽⠉⢻⡏⢹⣭⠉⣭⡟⢩⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡌⢡⡇⣿⠰⠶⢾⠀⠿⠏⣸⠀⡿⢀⣃⠘⡿⢿⣿⡇⠶⠾⣿⡄⠇⣼⡇⠰⠶⢿⢸⣦⡁⢸⣿⠀⣿⡟⠲⠦⢹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⡠⢀⢀⣀⢀⣀⣀⠀⢀⢀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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⣿⣿⣿⣿⣿⣿⣀⣉⣶⣆⣀⣀⣇⣸⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⢿⣿⣿⢛⡻⣿⢛⢻⢟⢿⢛⡻⣛⢛⡟⣿⢻⣛⣻⣛⢿⢛⣻⣟⡛⣻⢛⢻⢻⡟⡟⣛⣟⢛⣻⣿⣿⡿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣛⣼⣛⣻⣸⣔⣿⣸⣞⣬⣜⣸⣔⣿⣸⣇⣮⣸⣒⣺⣾⣺⣒⣸⣿⣇⣿⣸⣸⣘⣣⣗⣊⣿⣸⣿⣟⣛⣿⣒⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⢹⡏⡟⡟⣟⣿⣯⣮⡟⡿⡟⣻⢺⢻⢻⢻⢻⡻⣿⡟⣵⣽⠻⢻⡻⣿⢛⣿⡟⡟⡏⣾⣿⣿⡗⡟⡟⡟⡟⣿⢟⣟⣿⣿⡏⣯⣟⢿⣿⣳⣟⡿⡟⣿⡏⣛⡟⣟⡟⣿⣟⣟⠟⡟⡟⡟⡟⡟⡟⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣾⣷⣷⣷⣾⣿⣷⣶⣿⣶⣷⣿⣾⣷⣾⣶⣾⣶⣿⣿⣶⣾⣶⣾⣶⣿⣶⣿⣿⣶⣷⣿⣿⣶⣷⣷⣷⣷⣶⣷⣷⣷⣿⣿⣷⣿⣷⣾⣿⣿⣷⣾⣷⣿⣷⣶⣿⣾⣷⣾⣿⣿⣼⣷⣶⣷⣷⣷⣶⣷⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡻⡿⡿⡟⣻⣿⠹⣿⢿⣿⣿⡻⡿⡻⡿⡋⡿⡿⣿⡏⡏⡿⣻⡿⡻⡟⣿⣿⢽⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣵⣷⣥⣷⣽⣿⣾⣾⣮⣽⣿⣵⣷⣵⣷⣥⣿⣼⣿⣷⣵⣿⣵⣷⣽⣯⣼⣿⣼⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣉⣉⣋⣩⣉⣹⣉⡽⠋⠉⠉⠉⠉⠏⠏⠉⠉⠹⠉⣏⣩⣉⣉⣩⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠅⠀⣀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⡟⣛⢛⠿⠿⠿⡏⡿⠿⣟⣿⢻⣿⡻⠿⡿⡿⡿⠿⣿⢛⡛⡿⠿⠛⠋⢉⠤⠴⢶⢾⠿⠿⡟⡟⢿⢿⢿⣿⠛⡿⠿⡟⢿⠿⣿⡿⠻⡿⢿⣿⠻⡏⠿⡿⢿⣿⠛⢻⠿⡿⢿⠛⠿⢿⠿⠿⠻⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣼⣬⣬⣤⣧⣧⣥⣿⣿⣬⣽⣤⣧⣧⣥⡧⠬⠛⢈⣡⣤⣤⣼⣼⣼⣼⣼⣼⣬⣤⣷⣧⣧⣽⢀⣾⣧⣦⣥⣥⣧⣽⣤⣿⣧⣦⣧⣤⣿⣬⣧⣧⣦⣴⣿⣴⣶⣤⣦⣿⣼⣤⣼⣬⣼⣬⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⣉⠁⢠⠖⢿⠟⢿⠟⠏⡏⡿⠻⡿⠻⠟⢿⡏⠹⠻⡿⢻⡏⠻⢹⠟⠿⡿⢿⣿⢹⢹⠟⡿⠻⡿⢿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⣉⣤⣴⣶⣿⣿⣴⣼⣤⣼⣨⣼⣤⣦⣧⣧⣤⣧⣧⣧⣿⣧⣧⣥⣧⣿⣧⣧⣼⣤⣶⣴⣼⣿⣬⣼⣤⣦⣤⣧⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⠛⠿⠿⡿⠿⢿⠿⢿⠟⠻⠿⠿⠿⢿⠿⠿⡟⠿⠿⡟⠿⠿⠿⢿⡿⢿⠿⡿⠿⠿⠿⠿⠿⠟⡿⠿⠟⠟⠻⢿⠿⠿⠿⠿⠿⡿⠿⠟⠿⠿⠻⡟⠿⡟⠻⢿⠻⠿⠿⡿⠿⠿⠿⠿⠿⠻⢿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣾⣶⣶⣷⣷⣶⣶⣿⡶⠳⠶⠶⠶⠾⠶⡶⠷⠷⢶⠳⠶⠾⠷⠾⠶⠷⠶⠷⠾⠖⢿⠷⠾⡞⠷⠶⠶⢶⡖⠾⠶⡶⠷⣶⠷⠷⢶⠶⠶⠶⠲⠷⢲⠷⡶⠾⢶⠲⣷⣷⣶⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿

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

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠨⠝⠉⠁⠉⠈⠽⠉⠻⠿⢿⣿⣿⣿⣿⡟⠻⠛⠿⡟⠛⠛⢟⢟⡿⠛⠟⡟⡻⠛⠟⠛⢛⡟⠛⠛⢻⠻⠻⠟⢻⣿

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

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⣿⣿⣿⢿⠿⣿⡿⢿⡿⡿⠛⠻⠛⠻⠛⠛⡛⠻⠛⡛⠻⠻⠛⠻⡻⡿⡛⠛⠻⠛⠛⠛⠻⢻⢻⠟⢻⢟⢛⢟⢟⢟⢟⢟⢟⢟⢟⢟⢿⢿⢿⢿⣟⣿⢟⢟⣟⢿⣿⣿

⣿⣿⣿⣿⡏⠉⡉⠉⠉⠉⡉⠉⠉⣿⢟⡿⣿⣿⣿⣿⣤⣶⣤⣿⣾⣿⣿⣿⣈⣺⣈⢈⣈⡂⡈⡢⡪⡪⡊⡨⡪⠪⡪⡪⡢⡢⡠⡀⠀⡀⠘⢎⡈⣁⣑⣵⣕⢕⢕⢕⢵⢵⣵⣵⣵⢵⣝⣿⣿⣿⣿⣟⣗⣿⣕⣵⣿⣿

⣿⣿⣿⣿⣇⣀⣁⡆⡀⡀⡃⡀⣀⣿⣯⣾⣿⣿⣿⡯⣮⣿⣿⣿⣿⣿⣿⣿⢻⠿⢿⢤⡄⢀⡄⠦⣧⠮⢚⢨⠪⠈⣢⢦⡀⡞⡷⠈⣼⢛⠚⠘⠛⣤⣼⣝⢕⢵⣵⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣷⣽⣿⣟⣿⣿⣿

⣿⣿⣿⣿⣯⣯⡿⣿⣿⡯⡪⡪⣿⣿⣿⣿⡿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣚⢰⢘⢘⣒⡈⣇⠀⢉⢁⠀⢉⣜⢀⠁⣉⣁⣓⣃⡂⢉⣾⢨⣖⣰⠊⣹⣿⣷⣵⣿⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣷⣿⣿

⣿⣿⣿⣿⣿⣺⡻⡺⡪⡺⣮⣾⣿⣿⡿⡿⣿⣿⣺⣻⣿⣿⣿⣿⣿⣿⣿⣿⠝⢔⢕⠄⠀⠁⠁⠀⠔⠄⢔⢓⠕⢐⢕⢅⢔⣇⣤⠁⠘⠸⠠⠠⠀⠠⢸⡻⡺⣻⣿⡻⣿⣻⣼⡿⡻⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣾⡿⡯⡪⣪⡪⡻⡪⣮⣿⣯⡯⡮⡫⣿⣻⣿⣿⣿⣿⣷⢿⢽⢟⢝⢔⢕⢕⠀⠀⢐⣔⢕⠀⢄⠁⢀⢔⠄⢑⢕⢕⠍⢕⠄⠀⠀⠈⠠⡂⠀⡨⡮⡪⡪⡮⡮⣪⡫⡫⡪⡪⡪⡪⣿⣿⡿⣾⡯⣿⣿⣿⡿⣿⣿

⣿⣿⣿⣻⡮⣪⡮⣺⣿⡪⡿⣿⣻⡿⡮⡫⡪⣺⡪⣻⣿⣿⣿⣗⢕⢕⢕⢕⢔⢜⢜⠅⠀⠀⠀⠕⢅⢔⢕⢕⢕⢕⢕⢕⢕⢝⠝⠁⠀⠀⠺⠠⠨⠣⡨⡪⡪⡪⡪⡪⣺⡺⣻⡺⡪⡫⡺⡪⡪⡫⡫⣻⡫⣺⣫⡯⣿⣿

⣿⣿⣿⣿⡮⡪⣪⣯⣯⣿⡻⡪⣺⡪⡪⣾⣿⣻⣾⣿⣯⢿⣿⣕⣕⣕⢕⢵⠑⢑⢕⠀⠐⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠑⠑⠁⠀⠀⢠⠤⢪⠢⠂⠈⡨⡪⡪⡪⡪⡪⡪⡪⡪⡪⡪⡻⡯⣫⡪⡪⡪⣪⣻⣾⣾⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣺⡮⣪⣫⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣗⢽⢝⢗⢀⢁⠸⠅⢀⠅⠔⠄⠀⠀⠀⠀⠀⠀⠀⢀⠄⢴⠜⠂⠠⢨⠨⡠⠨⡪⡪⡪⡪⡪⡪⡪⡪⡪⡪⣪⡫⡪⡫⡮⣻⡾⡾⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣟⣕⢗⣶⣿⢳⡐⠐⠐⠁⡑⡄⠀⠀⠀⠀⠀⠀⠀⢰⢕⠕⣤⠚⢐⠺⠈⠢⡆⠪⡪⡪⡪⡪⡪⡪⡪⡪⡪⡪⡪⡪⡪⡪⡮⡮⣯⡺⣿⣿⣿⣿⣿

⣿⣿⣿⣟⣽⣟⢗⣷⣿⣧⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢿⢸⢹⢈⣉⣸⡇⡅⡅⠀⢰⡄⠀⠀⠀⠀⠈⣍⡷⡦⠾⠈⣸⠦⠀⡠⠪⡪⡪⡪⡫⡮⡪⡪⡪⡪⡪⡪⡪⡪⡪⡪⣿⣾⣺⣿⣿⡿⣿⣿

⣿⣿⣿⢿⢗⢵⣵⣽⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⢸⠠⠸⠛⠃⠀⡆⠂⠀⠀⠀⠀⢀⣀⠀⠀⠠⣷⢛⣴⠐⣸⢰⠚⢃⣨⡺⡮⡪⡪⡪⡪⣮⣮⣾⡮⣫⣫⣪⣪⡪⡿⣾⣿⣾⣿⣿⣿⣿

                ䷩ 𝚕𝚒𝚗𝚎 216

(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/01/02/bogus-addresses/#comments

Gemini version at gemini://gemini.techrights.org/2023/01/02/bogus-addresses/

Gemini_version_available_♊︎

✐ CEO_of_Sirius_‘UK’_Uses_Accountants_as_the_Address_of_His_Personal_Business

Too_(Not_Just_Sirius_Open_Source/Corporation_After_3_Address_Rotations_in_Just

5_Weeks!)⠀✐

Posted in Deception, Finance at 2:53 am by Dr. Roy Schestowitz

The CEO’s one-man business (and formerly a wife):

🄸🄼🄰🄶🄴🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽⦇Tax_link_as_company_address:_Latest_change_on_record;

Accountants'address⦈

🄸🄼🄰🄶🄴🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽⦇Tax_link⦈_

Summary: The company we left a month ago (second of December) operates in a

dodgy way; maybe it should not be so shocking given who’s calling the shots

⣿⣿⡿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⡇⡏⠀⠀⠁⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠸⣿⡇⢀⣀⠈⢿⠁⣀⠙⡟⠋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⡇⣷⠤⣀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠘⠀⢹⡇⢸⣿⠀⢸⠀⣿⠀⣷⣾⠀⣿⢻⠿⠏⠙⣿⣿⣿⣿

⣿⣿⡇⣇⠖⡀⠉⡌⠈⠌⠁⢡⠁⠁⠁⢹⢨⣍⠌⠸⠁⠉⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣼⣿⣷⣤⣧⣤⣤⣴⣿⣦⣤⣴⣿⣿⣤⣿⣰⣤⣦⣃⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢻⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⣩⠉⠉⠉⠉⠉⡏⢍⢸⢀⠈⢉⠍⠈⠉⠉⠉⡉⠉⢸⡁⢨⡄⠈⠉⢙⡇⡘⠁⠉⠈⠉⠉⡉⢹⣿⣿⣿⢸⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣒⣛⣛⣛⣛⣛⣛⣛⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣸⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠏⠉⠩⠏⠙⡉⠅⣽⡏⣭⢨⢹⢉⢹⣭⠋⡍⡏⣉⣿⢩⠝⢩⣹⣿⣩⢉⡙⢭⢫⡝⢩⡍⡅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⡿⠿⠿⠿⠿⠿⠿⢿⠿⠿⠿⡿⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣷⣾⣾⣾⣶⣾⣿⣦⣠⣷⣶⣿⣷⣾⣾⣿⣿⣿⣶⣾⣶⣷⣾⣾⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⡧⢥⣤⣤⣴⣤⣧⣾⠤⣤⣾⢦⣽⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿

⣿⣿⣧⣤⣤⣤⣠⣤⣆⣼⣤⣤⣶⣤⣤⣤⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠛⢹⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠃⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿

⣿⣿⣇⣈⣉⣉⣉⣉⣉⣯⣈⣹⣀⣈⡉⢹⣉⣇⣀⣉⣁⣉⣉⣉⣹⣠⣉⣍⣉⣁⣏⣩⣩⣈⣉⣩⣀⣁⣈⣀⣀⣨⣈⣸⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣼⣿⣿⣿

⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠒⠒⠒⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡉⡝⠛⠛⣿⠋⠟⠉⠋⡛⡛⠛⠛⣿⢩⠙⠛⠙⢛⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⣿⣿⡟⠿⠛⢻⠟⠛⠛⡛⠛⢿⣿⣿⣿⣿⣿⢉⠋⠉⡏⠟⠛⠛⠋⡏⠟⠙⠙⠋⠋⢻⠙⠉⠹⠛⠛⢹⠛⠙⠋⠋⠋⠋⠋⠋⢻⠉⠋⠛⠙⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣷⣿⣿⣿⣶⣷⣶⣷⣶⣿⣿⣿⣿⣿⣿⠚⢱⠀⠁⠲⠆⠁⠒⠑⠈⣾⣶⣷⣷⣾⣾⣶⣾⣶⣾⣾⣾⣶⣷⣶⣷⣷⣷⣶⣾⣾⣶⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠉⠙⠉⠋⠉⠛⣿⣿⣿⣿⣧⡀⠀⠀⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠹⠏⠋⠉⠝⣿⣿⣿⣿⣿⣆⠀⢀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠋⢉⠋⡏⠉⠉⠉⣹⣿⣿⣿⣿⣿⣷⣿⣿⣶⣄⡀⠀⠉⠛⠿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⡟⣿⡟⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⣹⣿⣿⣿⣁⡸⠰⡇⢾⠰⢸⠸⢸⣴⢰⢾⠀⡇⡆⡇⠦⠐⣾⡟⠄⡇⠆⡗⠆⣧⡆⠤⡧⠠⠄⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣇⣌⣉⣉⣹⣈⣉⣈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣷⣮⣉⣏⣈⣉⡉⣉⣏⣹⣀⣉⣇⣈⡉⣈⣈⣩⣉⣨⣆⣆⣈⣉⣇⣉⣉⣏⣉⣹⣈⣈⣩⣉⣀⣉⣙⣏⣉⣁⣇⣈⣹⣀⣉⢁⣁⣉⣩⣏⣉⣹⣍⠉⣈⣈⣉⣉⣇⣈⣈⣇⣉⣭⣙⣇⣉⣹⣨⣸⣿⣿⣿⣿⣿⣿

⣿⣿⣏⣈⢉⣙⣏⣉⢁⣉⣁⣉⢉⣍⣅⣈⣇⣉⣹⣈⣉⣹⣈⣉⣋⣹⣁⣉⣉⢉⣹⣁⣆⣈⡉⣉⣉⣉⣉⣸⣂⣀⣈⣉⣇⣹⣉⣉⣉⣈⣉⣉⣻⣙⢉⣉⣉⣉⣹⣉⣉⣹⣭⣁⣈⣈⣹⣉⣩⣉⣝⣉⣉⣿⣿⣿⣿⣿

⣿⣿⣏⣈⣉⣉⣉⣉⣙⣁⣈⣉⣏⣍⣇⣈⣹⣉⣉⣉⣉⣉⣹⣉⣸⣈⣉⣉⣩⣁⣩⣉⣗⣌⣉⣉⣉⣉⣩⣸⣐⣀⣈⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢻⠛⠋⢘⠛⠛⣛⠋⠏⡋⠋⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⡿⠻⠿⠻⠿⠿⠿⠿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣶⣷⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⣿⣿⣷⣆⣉⣹⣆⣀⣀⣯⣅⣩⣅⣁⣀⣨⣄⣈⣁⣇⣨⣇⣀⣩⣉⣰⣀⣩⣷⣀⣀⣭⣅⣈⣐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⡏⠍⠛⠛⠙⠛⡏⠙⠛⠛⠛⠛⠛⡏⡙⠛⠛⠛⡟⠛⠋⠛⠛⠙⠛⠹⡏⠟⠛⠛⠙⠛⠛⢻⠟⠋⠛⠛⠋⠋⠛⠛⠛⢿⠛⠋⠛⠙⠛⠛⠛⠋⢛⢻⠉⠛⠛⢛⡛⠛⡏⠙⠛⠛⡛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⡏⠙⠛⠛⡛⠛⡫⠋⠛⠛⠛⠛⠺⡫⠙⠛⡛⠛⡏⠝⠛⠛⠛⠛⠋⠓⢻⠉⠚⠛⢙⠛⢛⠚⠛⢹⠙⠝⠛⠛⠛⠻⡏⠌⠩⡏⠋⠛⠛⠛⠛⢻⠍⠛⠙⠋⠋⡏⡝⠓⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣾⣶⣶⡆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⢀⡆⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣧⠀⠀⢰⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠃⠛⠘⠓⠲⠚⠒⠚⠓⠀⠀⠀⠟⠀⠀⠀⠀⠀⡠⣐⣿⣿⣿⣿⣿⣿⣲⠚⠶⠆⠀⠀⠀⠀⠠⢤⠀⣾⣾⣿⣿⣇⢻⡇⠂⠒⠀⠄⠀⠠⠤⡠⢤⠤⠀⠀⠀⣿⣿⠀⡄⢸⣶⣶⣶⣇⡀⠀⠀⠀⠀⠀⢀⠄⡀

⠀⠀⠀⠃⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⣽⣇⣿⣿⣿⣿⣿⣿⣿⣧⣶⣤⠀⠀⠀⠀⠀⠋⢸⣿⣭⣹⣿⣝⠛⢻⣹⣿⣿⣿⣿⣓⣶⣶⣶⡿⠿⠀⠀⣿⣿⣿⣧⣼⣿⣿⣿⣿⣇⣔⣶⠲⡶⣶⣶⣶⢷

⠀⠀⠀⢰⣾⠂⠂⠄⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡄⢸⣿⣿⣿⣿⣿⣄⡼⢿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣾⣶⠶⣿⣗⣴⡈⡏⢹⡝⠛⠻⣏⣽⣿⣿⣿⡟⢻⠛⣿

⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⠀⠀⠀⠀⠀⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣹⠿⢹⣿⣿⣿⡇⠀⣺⣿⣿⣿⣷⣬⣿⣿⣿⣿⣿⣿⣛

⠀⠀⠀⠪⠅⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣧⠠⠼⣿⣿⣿⣧⠀⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣏

⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣻⣿⣿⣿⣿⠿⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣻⣿⣿⣟⣿⣿⣿⣦⣤⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣾⡿⢿⣾⣯⣽⡻⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⡀⢀⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣿⣿⡟⠛⣿⣿⣿⣿⣧⣿⣿⣟⠟⡿⠿⠇⠙⢉⣉⣿⣀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⣁⣐⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣏⣿⣿⣟⢻⣿⠷⠷⣿⣿⣿⣙⠉⠁⣿⣿⣿⡿⠃⠉⠋⠉⠀⠀⠀⠀⠀⠀⠈⠁⠳⠀

⠀⠀⠷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣲⠏⣋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠁⣤⣼⣿⣿⣻⣟⡖⢳⢶⠿⠙⠚⠛⠿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠙⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣽⣿⣯⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣀⠀⢀⣄⡀⠀⠀⠠⡉⠀⠀

⠀⠀⠠⢠⡀⣀⡀⠀⣥⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠟⠻⡀⠀⠀⠀⠀⠌⠀

⠀⠀⠀⠹⠯⡹⣛⣛⣤⣦⠂⠀⠀⠀⠀⠀⠀⠀⠀⠒⢩⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⢿⡿⣿⣿⣿⣿⣿⣿⠛⢻⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⣿⣿⣿⡏⢸⣿⣄⠙⢿⣶⣿⠀⢸⢟⣵⣿⣯⠏⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢐⠠⡀⣻⢟⣳⣴⣜⡠⣀⠀⠀⠀⠀⠀⠠⡈⠂⠐⠛⠟⣿⣿⣿⣿⣿⣷⣿⡆⢸⣿⣿⣿⡄⢻⣿⣿⣧⡈⢻⣿⡟⣵⣶⣶⠏⣿⣿⣿⣿⠀⣿⣿⣿⡇⢸⣿⣿⣧⡈⢻⣿⡄⢠⡈⠻⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢠⡄⠀⠈⢉⣫⣷⣿⣷⡇⠀⠑⡴⣶⠏⠿⢁⠂⡄⠚⠀⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡿⣽⣷⡀⢻⣿⢿⣷⡄⠹⣿⣮⣭⣵⣾⣿⣿⣿⣿⣀⣿⣛⣽⣇⣸⣿⣽⣿⣿⣾⣿⣤⣼⣿⣤⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠘⢁⢤⣮⣽⣓⢾⡿⠯⠝⣡⠂⠉⠉⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀

⠰⠀⢠⣻⢿⣿⠿⢿⠏⠓⠐⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠖⠀⠀⠀⠀⠀⠀

⠀⢐⡿⢟⣴⡾⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⡀⠀⠀⠀⠀

⠀⢘⣶⣿⣿⣇⠀⠀⠀⠀⠐⠀⠀⠀⠠⠦⢀⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣻⡿⡿⣿⢿⣿⣟⣿⣿⡿⣛⣭⣿⣿⣿⣿⡇⠀⠀⠀⠆

⠀⢋⣿⣿⣿⣧⡤⠀⠀⠀⠐⠀⠀⠀⢠⠄⠀⢀⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⡿⣿⣿⣽⣿⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠉⠁⠀⠀⠀⠀

⡁⠀⢻⣿⣿⣟⠀⠀⠀⠀⢀⡄⠔⠷⢠⣤⠀⠈⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠟⠛⠛⠛⠛⠛⠋⠁⠄⠙⠓⠤⢀⠀⠀⠀⠀

⠐⠀⠀⠉⠉⢁⣼⡧⠀⠀⠀⢀⠀⠂⠀⠁⠁⠀⠀⠀⠀⠀⡠⢿⡿⠿⡿⠿⢿⠿⠟⢻⢿⣻⢛⡻⠟⡛⠋⢉⢹⡍⠋⠙⠉⣁⠀⠊⠁⠀⠀⠀⠀⠀⠀⠤⢔⡄⠀⠀⠀⠀⠀⢠⡤⢤⠠⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀

⣄⠀⠀⠀⠀⠙⠛⠘⠴⠤⠂⠀⠈⣀⠀⠀⠀⠀⠀⠀⢀⣄⠀⣈⠓⠀⠘⠁⠂⠀⠀⠹⠂⠈⢀⠀⠄⠂⠈⠀⠀⠀⠀⠀⢈⡙⠁⠀⢧⣤⠀⠀⠀⠀⠁⠂⠸⠃⣸⠀⠐⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀

⣿⡏⣗⣿⣷⣴⣠⣠⢀⡀⠀⠀⠈⠋⠁⠀⢴⡤⠀⠰⠉⠀⠀⠀⠀⠀⠀⠠⠀⢁⠀⠄⠂⠈⠀⠀⠀⠀⠀⠀⠤⠀⠀⠙⠋⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠂⠀⣿⡏⠈⠀⠀⠀⠀⠠⠵⠖⠆⠀⠠⠀⢀⣀⣤⣶⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣾⣿⣤⣦⣅⣀⣠⣀⡀⠀⠾⠁⠀⠀⠀⠀⠀⠀⠀⠄⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀⠈⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣤⣨⣧⣶⣶⣶⢾⠿⢶⣖⣲⣖⣶⣶⣶⣿⣿⣿⣿⣿⣿

⣿⣿⣍⣿⣿⣿⣿⣿⣯⢹⡏⣛⠋⣿⣿⣿⣷⢰⣶⢀⡀⠄⢐⡈⢀⡀⣀⣤⣤⣤⣤⣤⣀⣀⠀⢀⣀⣀⣀⣀⣠⣬⣯⣧⣶⡶⣶⠞⠛⠾⠿⠿⠛⠛⠛⠟⠉⠋⠉⢉⣀⣼⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣾⣿⣿⠻⠻⣽⣤⣝⣆⡕⢽⣿⡛⠯⢾⣘⣳⣟⢓⠠⡇⢠⡀⠙⣶⡛⢛⡿⡿⣿⠿⠿⠟⠛⠛⠙⠙⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⡿⢿⢿⣿⣶⣧⣾⣿⣽⣽⠿⣽⡛⠧⣤⣄⣁⠈⠉⠓⣞⠿⢿⣇⡘⠛⠁⢸⣷⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠠⠀⠀⠂⠀⠀⠈⠁⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉

⣿⣾⡏⣿⣿⣿⢾⣿⣿⣿⠉⣟⣛⢻⣟⣳⣺⡌⣉⠛⠶⣦⣿⢊⣀⣼⡉⠉⠑⠺⣿⣯⣇⣀⣀⠤⠤⠤⠀⣶⠀⠀⠀⠁⠀⠀⡆⠀⠀⢀⣀⠀⠀⠀⠀⠀⠒⠒⠈⠉⠉⠙⢻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣤⣹⣍⣽⡆⢯⣜⣚⣮⢿⡟⣷⠿⢿⠉⠃⠀⠈⢹⠛⠿⠅⢡⡘⢷⠀⠉⠐⠀⢤⣾⣿⣿⠀⢀⣀⣠⣤⠤⠿⠴⠶⠒⡖⠒⠉⠉⠁⠀⣀⡀⠀⢀⠀⠸⠂⠀⠤⠒⠒⠂⠈⠉⠉⠀⠸⠀⠉⠉⠛⠛⠛⠟⠿⠿⠿⠿⠿

⡿⢿⢻⣿⣷⣶⣤⣤⡙⠛⠷⢆⠀⡴⢷⠀⠀⠀⠘⠲⣄⣤⡾⢸⢿⡗⣤⠤⢰⣔⣴⢭⣿⠋⠛⢻⡇⠀⡀⢀⣠⠤⠴⠧⠀⠒⠒⠂⠈⠁⠀⠀⠀⠀⠀⢀⣀⡀⠤⠤⠀⠀⠲⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⢿⣿⣫⣦⣾⣿⡟⢻⠟⠀⠼⣤⣁⠸⠀⠀⠀⠀⠀⣻⣇⠻⠻⢿⡻⡿⣦⣤⠀⢹⣿⣿⠛⠉⠉⠉⠀⠀⣿⣀⣀⢠⡀⠠⠤⠥⠀⠂⢠⡎⠉⠁⠈⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢷

⠀⠰⠆⠀⠀⠀⠀⠀⠀⢰⠤⣄⣇⡁⢦⣐⠀⠀⢂⣁⡆⠀⡄⢸⣿⣿⣿⣿⣿⣿⣿⢼⣿⠀⣀⣄⣠⣠⣇⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣤⣤⣦⣤⣤⣴⣶⣴⣴⣶⣾⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣶⣷⣾

⡀⠀⢀⣀⡀⣀⠀⡀⠀⠨⣭⣻⢂⠅⠀⡄⠀⢀⠀⡄⡄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣻⣿⠤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡿⠴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣸⣼⣯⣿⣻⣿⡖⡷⢴⣇⣲⢀⣁⡠⠈⣇⣰⣸⣀⡻⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣾⣿⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿

⡇⣿⣿⢿⣿⣷⡤⣧⢸⣷⢎⢲⣿⣽⠀⣧⢸⣼⡀⠸⢃⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⢿⣿⠚⠛⢻⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠼⠿⠿⠿⠿⠿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢐⣿⡏⣿⣝⣟⠃⣯⠉⣉⢰⣯⡐⢻⠆⢟⠛⡻⠧⠈⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣤⣸⣴⣾⣷⡆⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⢠⣶⣶⣦⣶⣶⣶⣧⣤⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠈⣿⡟⠺⠷⠢⠗⢿⡦⠟⠂⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣾⣿⣿⣾⣻⣿⠉⡉⢹⣹⣿⣿⡗⢻⣿⣿⣿⣿⣛⣿⣻⣟⣿⡯⣿⡿⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿

⣤⣿⣿⣴⣷⣾⢶⢶⡶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡇⣘⣻⣿⣯⣭⣭⣭⣿⣷⣶⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷

⣻⣎⣷⣮⣿⣼⣯⣵⣥⣮⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣛⣛⣿⣿⣿⣿⣭⣽⣭⣽⣿⣿⣾⣶⣶⣾⣿⠿⠿⠿⠿⣿⣿⣿⣿⡏⣿⢧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣽⣝⣟⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⣢⣍⣀⡂⠀⠃⠀⠈⡀⢘⣯⡻⣿⣿⣿⣟⠋⠉⠀⠀⠀⠀⠀⠀⢀⣩⠿⢿⣷⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿

⠛⠛⠛⠛⠈⠉⠉⠉⠁⠀⠀⠀⣀⣤⣤⣶⣶⣟⡅⠉⠀⠀⠈⠉⠀⠒⠆⠀⠀⠘⠰⠾⠷⠎⣎⢻⣿⣿⣿⣦⣄⠀⠀⢠⣤⣤⣤⣾⣿⡿⠷⠏⣻⣿⣿⢷⣶⣦⣶⣶⣦⣭⣭⣉⣉⣼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣄⣀⣠⣿⣿⣿⣿⣿⣿⣦⣄⡈⣑⣒⣢⣤⣴⣶⣾⣛⠩⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠅⡉⠉⠛⠛⠻⠿⢿⣭⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠀⠂⠉⠁⠀⠀⣠⣿⣯⣥⢭⣽⣿⡿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⢧⡀⠀⠀⠀⠉⠁⠀⠒⠂⠀⠅⠭⠉⣛⣛⠿⠿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣽⣿⡏⠀⢀⡀⠀⠀⠀⣀⠤⠚⠁⠙⠩⠸⣻⠷⣿⣿⣯⣿⣿⣿⣿⣿⣟⣲⣾⣾⣿⣯⣥⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠈⠀⠀⠀⠈⠛⢿⡟⠛⠉⢹⢿⣷⣶⣶⣾⠿⠷⠚⠉⠁⠀⠀⠀⠀⠐⠀⠀⠀⢉⠊⠠⠋⠹⡫⢿⠿⠿⣿⣿⣿⣿⣿⣿⡏

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

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⠭⡉⢉⠛⠛⠛⠿⠿⠿⠟⠛⠉⣠⡠⠢⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢉⡀⠁⠀⠀⣧⢄⡡⣐⣅⡀⠀⠀⢁⡀⢠⣴⡶⠐⡷⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⠟⠛⠋⠉⠉⠿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡡⣘⣇⠲⠋⠡⢿⣿⣿⣾⢿⡻⠲⢏⣛⣭⣥⣶⣿⠀⠙⠝⠆⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⡇⠀⠀⠀⠀⠀⠀⠈⠀⠁⠉⠛⢉⡻⢶⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⢋⠉⡀⢚⣿⢟⣭⣿⣯⠿⠶⠒⡉⠍⠀⠠⢐⣿⣿⡊⠹⣭⣿⠀⠀⢀⠀⠀⢌⠻⣿⣿⣿⣿⣿⣿⣿

⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠝⠘⣇⡘⠀⢻⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣯⣟⣿⣿⣿⣿⠿⠛⠉⠀⢰⣛⣡⣤⠠⢷⣛⠋⢩⣴⣶⡼⡇⣡⣤⣶⣾⣿⣿⣩⠹⠃⡠⠠⣙⠄⠀⠢⠀⠀⠀⠀⣈⢿⣿⣿⣿⣿⣿

⢋⡟⠦⠄⠀⠀⠰⢁⠤⠤⢀⣚⠀⠀⠄⠀⢀⠀⠠⠿⠿⠟⣿⣿⣿⣵⣿⣿⣿⢻⣿⡿⠟⠉⠀⠀⠀⠀⠀⢨⣭⣳⣾⣋⢭⣥⣶⡮⣹⣿⢿⠇⣿⣿⣿⣿⣿⡿⠄⠈⠥⠩⡒⣏⠆⠀⠀⠀⢀⠀⠀⡈⠷⣝⢿⣿⣿⣿

⡀⠀⠠⠀⠀⠀⡸⠥⢤⠋⠀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠤⠄⠹⠛⠎⠹⣿⠟⠛⠋⠁⠀⠀⠀⡀⠀⠀⠀⠀⢸⣷⣾⣿⣿⣿⣿⣿⣇⡻⡯⣯⠂⣯⣿⣿⣾⣿⣿⡄⣰⡶⣇⣴⢔⡀⠀⠀⠃⠚⠀⠀⠀⣱⣜⢿⣿⣿⣿

⠙⠡⠐⠘⠋⠙⠀⠠⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⡀⠅⢰⣿⠔⠀⢸⡯⣿⢹⡯⣿⣶⣿⣧⠤⣶⠴⡦⣿⣿⣿⣿⣿⡯⢇⠬⡛⣿⣿⡫⠃⠀⠀⢀⡄⠀⠀⠸⢸⣿⣟⣿⡿⠛

⠀⠀⠀⠀⠀⣀⠀⠀⠁⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠈⠀⡋⠀⠀⢰⣇⠀⠀⢸⣛⣧⣿⡗⠻⠿⠿⢥⣿⣿⠼⠦⣭⣉⣀⣀⣤⣤⣌⣡⣿⡶⠦⠬⠿⠄⢀⡈⠁⠀⠈⣺⣈⣿⡿⣿⣿⣦

⠐⠂⠀⠀⠉⠀⠠⢤⠠⠀⡠⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠷⠀⠀⠘⠋⠀⠀⣸⣽⣥⣭⠤⠷⠷⠶⠶⠛⠛⢛⠛⠋⢉⠉⠉⢉⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠤⢀⡡⢿⣷⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⣂⡠⠔⠋⠐⠀⢰⠴⠄⡥⡀⠁⠁⠁⠀⠀⠉⢡⡞⠤⠄⠀⣀⢠⡀⠀⠀⠀⠀⠀⠀⠀⢉⣺⠂⠀⠀

⠀⠀⠀⢀⠠⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢩⠂⡄⠀⠀⠀⣼⣯⣴⣿⠄⡖⠒⡒⠒⡂⠀⣦⣯⡑⢛⣿⣉⣻⠇⠀⠀⠀⠀⠀⠀⠀⡀⢾⡇⠀⠀

⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⡂⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢓⠐⠇⡇⠒⠒⠒⡿⣳⣬⣭⡇⡇⠒⡗⠒⡗⠒⣇⣲⣖⢺⠷⠐⢺⠄⠀⠀⠀⢸⠀⠀⠀⡇⣺⡇⠀⠀

⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠀⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⡈⠅⡇⢀⠈⠀⢙⢻⡍⢖⡆⡗⠚⠛⠛⠛⠛⢻⠯⡿⢱⠒⣭⠍⠁⠀⠀⠀⢨⠀⠀⠀⣇⢹⡇⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣀⢧⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠸⠈⠉⠱⣛⣝⣉⢆⣷⠐⠒⣷⣓⣚⢲⡐⠂⠀⠛⠡⠐⠂⠀⠀⠀⢸⡇⠀⠀⠛⠈⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⣾⣶⢷⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⣴⣄⠐⠀⠈⠀⠃⠀⠿⣶⣾⣿⣿⠿⠟⠀⠀⠀⣀⠖⠂⠀⠀⠀⠀⡋⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠶⠦⠤⢠⣤⣄⣀⣀⣀⣘⣿⣷⣤⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠈⢑⠶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠽⠛⠛⠉⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠂⠀⡈⠨⠬⠍⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡀⠈⠱⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠑⠀⠀⠐⠒⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠙⢦⡀⠈⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠙⢦⡀⠀⠈⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣟⢰⣺⢯⠱⠹⠿⠯⡏⣍⠁⠁⠉⠛⡞⠧⠋⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣧⡦⠁⠌⠈⠉⠛⠋⠉⠉⠙⠓⡿⢿⠿⣿⠻⣶⣴⢶⣽⣐⡩⡀⢢⣤⢁⠰⠽⣗⣻⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠓⠳⡷⠾⣷⠠⠔⠀⠘⠞⠀⠈⠀⠀⠂⢒⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⢀⠃⠀⠀⠀⠀⢀⢄⠀⠀⠘⢻⠶⠀⠈⣋⡹⢷⠄⡫⠀⠈⡿⡿⣷⡶⣾⡿⢿⡟⣿⣿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠈⠁⠲⠖⠿⠖⣻⣘⡷⢆⣄⡀⢀⠀⠀⠁⢋⢾⢦⣴⣾⣿⣿⣟⣿⡿⠇⠀⡀⠔⠋⠒⠀⠈⠀⢀⣦⣠⣮⡆⣀⣵⣿⣙⣧⣴⣀⣌⢀⣴⣴⣇⢿⠛⠁⡀⣉⣤⣻⣧⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠄⠀⠀⠀⠀⠀⠀⠀⡯⠷⠽⠛⠉⡟⢳⣀⣄⣤⣆⣸⣿⣿⣿⣿⢿⡻⠉⠁⢎⠀⠀⠀⠀⠀⠀⠁⠚⣭⣫⣻⣿⣿⢆⢃⠘⠉⠋⠛⠟⢿⢿⡟⠉⡊⣐⣆⢼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿

⣦⡀⢤⡦⠀⠀⠀⠀⡀⠀⠛⡆⠀⠐⠋⠁⣯⡘⣿⡿⢟⣿⡿⢿⢦⣔⡆⡈⠠⠀⠀⠀⠀⠀⠀⠀⠘⠙⠇⠘⠅⠏⠦⢀⠂⠀⠀⣀⡄⣾⣿⢿⣷⣄⢙⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣽⣛⡿⠽⠃⠉

⠙⢰⢸⣹⡦⡄⠀⠀⠁⠀⠈⠀⠀⠀⣹⠂⠙⣿⣿⣿⡁⢐⡀⠰⣆⣪⡋⠂⢀⡀⠀⢄⣦⠄⢀⠀⠀⠰⢶⠀⠀⠀⠀⠀⠰⣻⢻⢽⢾⣛⣿⣾⡎⣿⣬⣻⣯⣿⡷⣿⢿⣿⣿⠻⢿⣿⠻⢿⣋⣽⣿⣿⡿⢗⣀⠀⠀⠀

⠀⠨⠿⠷⠌⠀⠠⠀⠀⠀⠀⠀⠀⠀⣸⠀⢨⡇⢑⢸⠘⠋⠑⠃⠈⠉⣱⣴⣮⣡⠭⠤⣯⢯⣬⣤⣤⣤⡀⠈⠀⠁⠐⠅⠡⠻⠖⠊⡉⠻⡿⣿⣿⣿⣿⣮⣿⣥⣀⠒⠂⠉⣉⣧⣔⣿⣿⣶⣶⣭⣿⣷⣿⣻⣿⡦⡤⢄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⢲⢸⠄⠀⠀⣷⣾⢷⡿⡟⡛⠃⠠⠚⠉⠻⣿⣯⣙⡻⠻⣿⢿⣿⣿⣿⣿⡇⢀⣀⠳⠠⠀⢿⣿⣿⣿⣿⣷⣬⣧⣕⢀⣤⣿⣾⣻⣿⣏⣿⢻⡿⣻⣶⡮⢉⣑⠛⣬⡄

⣟⣓⣆⠃⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠈⠉⠉⢫⠂⢀⠀⠍⢹⠛⠀⠀⠛⠀⠀⠀⠠⣼⣯⠑⣿⢻⣯⡟⠈⢘⢫⣿⣿⣇⣌⣈⠅⠨⡀⣼⣿⡿⢿⣿⣿⣿⣿⣷⣼⡿⣻⣿⡽⣞⣿⣷⢯⣮⣌⡀⠀⠁⠌⠜⠸⢟

⣿⡯⢾⠛⠿⢤⠬⢀⡠⠄⠀⠀⠀⠀⡆⠠⢀⡀⢀⣀⢰⣿⣿⠄⠀⠀⠀⢀⠀⠀⠠⠄⡄⠃⠉⠀⠴⠨⣿⠕⠛⠞⣹⣿⣯⣾⡿⢿⣿⣶⣤⣿⡋⢲⣤⡛⣿⣿⣿⣿⣾⣿⣯⢷⣶⣓⣧⡕⣋⠝⡓⢀⢀⠀⢘⠒⠒⠀

⡀⠀⠀⠀⠐⡀⠁⣠⣤⠭⠩⢤⣥⠀⡁⠈⢸⢛⠛⢳⠀⠉⠩⣧⣹⣰⠀⢰⣲⡀⠀⡘⣁⠂⠀⠀⠀⠲⡶⠁⠻⣶⠁⣆⢁⣿⣴⣾⣻⡛⣿⣿⣿⣿⣿⣦⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣵⣾⣦⣾⣖⣶⣤⣤⣤⣄

⢅⠀⢀⡂⡂⠀⡘⣾⣿⣿⣿⣿⣿⠀⡇⠀⢸⢼⡄⢼⠀⠀⢸⣟⣿⢺⠀⢸⣿⠃⡃⠈⠄⠀⠃⠀⡀⢨⡍⠀⢴⣿⢽⣿⣽⣷⣹⢟⡿⠗⡛⣟⡿⣿⣧⣿⣿⣿⣿⣻⣿⣿⠟⡿⠟⢻⠿⡺⢿⣿⣿⣍⣙⣋⣙⠀⠐⠀

⠓⢁⢸⠉⡷⠀⠀⣿⣿⣿⠶⣿⡟⠈⠆⠀⣼⣹⣁⣇⠀⠀⢸⣿⣿⣿⠀⢸⣿⣯⣇⠐⠑⢘⡩⡧⠀⣿⣿⡆⡄⠙⣿⣿⣿⣿⣿⣽⣵⣶⣷⣴⣼⣾⣶⣿⣿⣿⣾⣾⣄⠁⠀⠀⠀⠀⠄⠀⣈⢰⣯⣿⣿⢛⣋⣻⣕⣶

⠀⠀⢾⢛⠻⠟⢛⠟⠛⠛⠻⠛⡗⠒⠒⠒⠗⠒⠒⢖⡖⠒⠒⠒⠒⠒⠒⠒⠒⠒⣦⠀⠀⠠⠘⠘⠀⡟⢠⣿⠵⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠀⠘⠀⠙⠠⠱⠀⠀⠀⠀⠀⠀⠀⠐⠈⣿⢟⠻⣿⣿⣿⣿⢯

⠀⢀⢸⡑⠁⠀⣈⣐⣂⣀⣈⣀⣃⣠⣤⣴⣶⣶⣷⣶⣶⣶⣶⣶⣶⣾⡶⢴⠄⠀⣿⠀⠀⠈⢲⣶⡆⠁⠐⠒⠲⢶⣾⣿⣿⣿⡟⠀⠀⠍⠿⢿⣿⣿⣿⣆⣀⣠⣄⣤⣧⣤⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣧⣤⣤⣴⣶⣬

⣀⣀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣐⠀⠀⠀⣿⠀⠀⠀⠀⠻⠇⠀⠈⠢⠀⡈⣭⣉⣛⢛⠃⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⢛⡛⣹⣇⢀⣀⣀⣿⡄⢄⣠⣤⣀⠀⢀⡶⡀⠀⠧⠿⢿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢂⢤⢺⣛⣛⣛⣟⡿⣭⡍⡭⠽⣛⣳⣞⣌⡭⢹⣽⡷⣒⡶⣿⣋⠉⢙⣿⡿⠛⠻⣿⠃⠀⠁⠁⠀⣁⣀⣀⣠⠠⠦⠋⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⡿⠿⠻⠟⠟⡛⠛⣻⣿⣛⣻⣟⣿⣿⣿⣿⣿⣿⣿⢻⣻⢿⣽⣴⣤⣤⣤⡤⣭⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                ䷩ 𝚕𝚒𝚗𝚎 390

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✐ IRC_Proceedings:_Sunday,_January_01,_2023⠀✐

Posted in IRC_Logs at 2:59 am by Needs Sunlight

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                                     #techrights_log_as_HTML5                                                                                  #boycottnovell_log_as_HTML5

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                                #boycottnovell-social_log_as_HTML5                                                                               #techbytes_log_as_HTML5

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(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/01/02/retaliation-for-speaking-of-security-failings/#comments

Gemini version at gemini://gemini.techrights.org/2023/01/02/retaliation-for-speaking-of-security-failings/

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✐ Sirius_‘Open_Source’_Misleading_the_International_Organization_for

Standardization_(ISO)_on_Security⠀✐

Posted in Deception, Free/Libre_Software, Security at 9:36 pm by Dr. Roy

Schestowitz

What if ISO knew the truth?

🄸🄼🄰🄶🄴🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽⦇International_Organization_for_Standardization_(ISO)brag⦈

Summary: There are no proper and truly compliance-driven procedures that are

being followed, actively used, or even vaguely specified by poor leadership at

Sirius_‘Open_Source’; it’s all improvised, hugely deficient, not even remotely

compliant, and changes are sometimes made retroactively due to lapses and

mistakes (compliance or merely appearance thereof, albeit only “after the

act”); eventually there are attempts to shoot the messengers — those who have

actually cautioned about those concerning things for several years already

THE “Conclusion” part of the report (a document we’ll publish tomorrow as PDF)

is included at the bottom of this post. Worry not, it’s not the end of the

series, only the end of this report; we have plenty left to show and to explain

after that. We’re eager to show to the world what Sirius_‘Open_Source’_Inc./

Limited/Corporation truly is.

“We’re eager to show to the world what Sirius ‘Open Source’ Inc./Limited/

Corporation truly is.”As a teaser of sorts, consider how poorly the company was

handling data and information. It was getting worse over time because skilled

people were leaving the company, making way for the “Google is your friend”

mantra. This aforementioned mantra was something along the lines of, “trust big

companies”, you can give them any data we have. Trust them, they’re big! Sure,

they_also_spy_for_a_government.

Data of high-profile clients, both past and present, was naturally left

scattered all over the place, sometimes even outside the country. And to give

just one example (there are so many; some will be covered later this month and

next month), colleagues have cognition reports and incremental/full load

reports on local — as in personal and offsite — machines (this is indirectly

related to patients’ data) with no protocol or guidelines for removing these.

There’s potentially sensitive data on people’s machines at home and we’ve

already witnessed mistakes made by the clients themselves (like patients’ names

or similar data showing up by mistake/accident).

THIS SHOULD NEVER HAPPEN!

“There are serious ramifications for data protection and adherence to law…”In a

saner world, everything would be uploaded to a firewalled file server located

on the client’s own network, accessible in some secure fashion, without the

data ever leaving the network, not even metadata. But when a company like

Sirius handles its E-mail via AWS and AWS is also the host of OTRS (ticketing),

one is expected to just upload files to AWS and transmit the stuff over E-mail

(i.e. open relays). No encryption. I was repeatedly told off for using PGP in

my E-mails.

There are serious ramifications for data protection and adherence to law, as

there are unpatched old machines and perhaps backups that contain such files —

a ticking time bomb. And even way after they’re no longer a client (years

later), the example above serves to show that the problem does not go away. Not

even when the contract ends (or gets terminated).

“Clients simply come to assume the reputation earned in past decades persists

to date.”The sad reality is that the company, Sirius (so-called ‘open source’),

is terrified about clients finding out how reckless and incompetent the company

gradually became. Clients simply come to assume the reputation earned in past

decades persists to date. They’re trusting a company run by a person divorced

twice, whose kids refuse to even speak to him. How can deep trust be

established with people who (if they get caught) simply pretend nothing bad

happened and instead of apologising would rather get aggressive, even

combative, to cover up the abuse?

The text below mentions ISO, security incidents, and then the company’s

attempts to shoot the messenger (who cautioned about those issues along with

many other issues). The in-depth analysis of the witch-hunt will follow after

this report is published in full (some time tomorrow).

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

⚓ Conclusion⠀⇛

To summarise, Sirius should simply admit out in the open: “we’ve deviated away

from our mission,” and moreover Sirius ignores warnings about security (ISO

deserves to know about phonies and posers at security).

Roy internally cautioned about this several times over the years. Later, when

some providers suffers security breaches (as Roy predicted) Sirius neither

reset the passwords nor left the compromised providers.

To reiterate what was stated at the start, what’s alleged here is factually

correct and evidence-backed. No URLs are provided, but URLs can be provided

shall they be requested. Brevity still matters and much remains to be told.

In regards to the weak accusations leveraged to avoid paying compensation to

Roy and Rianne, here again is the gist of the underlying issue/s:

no due process

no evidence presented (or claims merely alluded to without context/link)

gross accusation inflation

guilt by association (identical letter, too)

the company has a history doing this to couples, e.g. one blind colleague

based in Germany; it was very serious and it went to court (cost the company or

its Directors — the founder and his wife — a lot of money, went on for a long

time, settled at the end)

The document is far from complete. Roy and Rianne have documents, have

screenshots, links to official documents from Companies House etc. █

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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                ䷩ 𝚕𝚒𝚗𝚎 710

(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/01/02/sirius-divide-and-rule/#comments

Gemini version at gemini://gemini.techrights.org/2023/01/02/sirius-divide-and-rule/

Gemini_version_available_♊︎

✐ Sirius_‘Open_Source’_Has_Turned_Workers_Into_Serfs/Slaves_and_Technical_Work

Into_‘Bullshit_Jobs’⠀✐

Posted in Deception, Free/Libre_Software, Law at 12:09 am by Dr. Roy

Schestowitz

 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Don't_mind_vicious_boss;_I_will_always_remember⦈_

Summary: Staff of Sirius_‘Open_Source’ still remembers how badly managers have

treated workers in the past 4 years while keeping them isolated, sometimes even

gagged

IN yesterday’s video ("Sirius_Open_Source_Uses_'Privacy'_as_a_Weapon_Against

Truth-tellers_(Can't_Speak_Outside_Work)") we sought to highlight endless

hypocrisy and disproportionate powers managers gave themselves. It was not

about leadership but about control. Those aren’t the same thing. Leaders

motivate people, but the managers Sirius attracted in recent years are power-

hungry and don’t know how to manage power; they get drunk on power. Some lack

actual experience in management; no, babysitting toddlers or being an assistant

of an assistant doesn’t substitute training and experience at leadership.

Companies would struggle to compel adults to be managed by babysitters.

Programmers and sysadmins are grownups, not toddlers.

“Companies would struggle to compel adults to be managed by babysitters.

Programmers and sysadmins are grownups, not toddlers.”The managers at Sirius

gradually become insecure, knowing they’re not just unqualified for the job but

are in fact failing at their job. Then they try to stop staff from talking

about the issues (failures that repeat themselves, e.g. pension contributions

not being paid). Then start bullying, intimidation etc. It begets spying and

dirt-digging, even habitual insults (like aimlessly accusing staff of “cooking”

without any evidence whatsoever; as noted in the last part’s meme, based on a

real quote). If managers start falsely accusing staff, then the principal

objective is humiliation, hoping to cause guilt and render people more

submissive. That never works!

Then come impediments against dialogue. Staff is divided so as to make people

feel isolated. Let’s use an example. In a grievance letter posted (reproduced)

here last month, a colleague explained that people who work overnight are

already isolated and feeling alone. Why add insult to injury?

“Staff is divided so as to make people feel isolated.”Then comes suppression of

speech in general, like claiming the clients and colleagues deserve total

privacy (in practice, it is about censorship), even outside work where they’re

mentioned not by name, yet the same people who claim this are engaging in overt

acts of surveillance against staff, even outside work.

This_hypocritical_behaviour is also used by the EPO to basically say that staff

cannot speak to one another because of “privacy”, even if the conversations are

about managers’ corruption. They misuse “privacy” for cover-up. Privacy is no

excuse for those who are committing crimes or engaging in all sorts of

wrongdoing.

The icing on the cake is, such rogue management engages in chronic lying while

bullying staff and innocent people are warned not to speak to colleagues

(“divide and rule”) while managers are spying on everybody. This is all about

double-standards. To put it in simple terms, a boss may allege that staff is

violating privacy of people and the boss builds this allegation by violating

the privacy of the accused.

“Privacy is no excuse for those who are committing crimes or engaging in all

sorts of wrongdoing.”Sirius has quite a tradition like this. It effectively

banned staff conversations in Freenode (outside work), way back in its glory

days, not_in_2022. It’s as if colleagues cannot have a personal life and cannot

socialise outside the workplace.

As a reminder, a decade ago the company resorted to shutting_down_the_company's

own_Jabber_server, very likely to prevent workers’ solidarity/empathy towards a

colleague… or even the ability to find out what had happened.

Sirius created a self-defeating culture wherein people are talking to one

another inside the train to avoid detection for fear of committing the “crime”

of speaking to co-workers about facts (like bosses doing unethical things,

including lying, cheating, engaging in extreme nepotism… like bringing 3 sexual

partners to the company in spite of a lack of relevant qualifications).

“It’s as if colleagues cannot have a personal life and cannot socialise outside

the workplace.”Sirius is no longer unique in the sense that after COVID-19

lock-downs many people still don’t commute to work and still don’t meet

colleagues in person (or seldom do). Generally speaking, when people work from

home, and they’re each based in a distant town, they can’t easily meet “down

the pub” and have in-person chat, so if conversations outside the spying

network of the company are frowned upon, and if spyware becomes the norm, how

is staff supposed to be properly informed? Trusting liars? How can a union ever

be formed? As we shall show later, the company pretends to be open to the

concept of a staff union, but that’s just a convenient lie.

The company goes out of its way to prevent and impede communication between

workers, usually by means of blackmail/threats. How unhealthy a work

atmosphere! For instance, staff is not permitted to know if someone is

investigated or disciplined and similarly staff being bullies is explicitly

forbidden from talking about this to anybody. This poses a threat to people’s

health and safety. The company knows that, but it does not care. People are

isolated and asked not to cooperate with their colleagues. It’s not limited to

“bollocking” inside the company as the same goes for salaries, work status etc.

Sirius is just a very secretive company that misuses the name “Open Source” and

conceals the operational aspects. It’s proprietary, intransparent, and truly

dishonest. It lies about its very own people when it suits the managers. As a

result, colleagues are just vanishing without anyone bothering to explain why

(skeletons in the closet), we have had colleagues that say they’re under de

facto gag order and cannot talk about what they know, and it starts to resemble

Life_Is_Beautiful where nobody can speak about the gas in the showers. People

just vanish, no more questions…

“This poses a threat to people’s health and safety.”The workplace inevitably

becomes very mentally unhealthy; as we’ll show later this month, it becomes

physically unhealthy too (some colleagues got diarrhoea from the stress). These

tactics of isolation are being resisted, as colleagues occasionally reach out

to one another, even people who are working from home. Their safety net does

not come from “leaders” but from peers. The leaders are correctly perceived as

dictators, who aren’t to be trusted with anything. There’s no comforting

shoulder. This should not be considered standard business practice, but this is

where Sirius was heading just to ensure workers were always disadvantaged,

underpaid, mistreated, falsely accused. They cannot unite, they can barely even

form a coalition through which to negotiate with management. Things were so out

of hand in Sirius that even to have a colleague as a witness would require

prior permission from management so that the management can ‘tamper’ with the

person a priori (like issuing warnings or curtail freedom of expression).

The tactics employed in 2022 began to resemble authoritarian regimes and

aggressive cops, more so towards the end of the year; relatives were being kept

as pawns and false accusations thrown while distorting facts. Managers very

well understand that scaring workers won’t make them productive; au contraire —

it leads to misery.

We’ve seen these things before. At the EPO, for instance, the union (SUEPO)

explained how a spouse needed to come to the Office to pick up her husband

after he had suffered a mental breakdown (due to ruthless ‘investigation’).

We’ll soon show that Sirius too employed a kind of Reid_method/technique, which

is controversial and likely illegal. This was done to Aaron_Swartz.

“The tactics employed in 2022 began to resemble authoritarian regimes and

aggressive cops, more so towards the end of the year…”One colleague used to

joke that the company’s slogan, “stress-free technology”, took no account of

how workers felt. Workers had no real voice in the company. They were barely

consulted about important things.

Unfortunately, SUEPO uses the same Microsoft spyware that EPO management uses,

probably because of the “installed based” (number of workers who already have

that set up). But since Microsoft_colludes_with_the_EPO they can undermine

communications, spy, and worse. We’ve repeatedly said that a union using the

“bossware” of the boss, controlled by a truly hostile corporation, isn’t a good

idea.

The reason we are writing these detailed reports is clear to those who have had

similar experiences in their career. It’s important because workers would be

empowered if they could identify emergent patterns of technological oppression

and then respond them them, equipped with knowledge of the law in their

country. Don’t let people be subjected to that; don’t be subjected to that

yourself. Workers aren’t supposed to be pointed at for doing perfectly lawful

things, even if their bosses aren’t happy about those things. That can lead to

conflicts in one’s mind, with questions arising like, “are they telling the

truth? Am I overrating or overthinking?”

Remember that sociopaths and pathological liars do this as a matter of routine;

they’ve mastered all these tricks and they keep using them again and again.

“Workers aren’t supposed to be pointed at for doing perfectly lawful things,

even if their bosses aren’t happy about those things.”The staff, they hope, may

remains defenseless after all the gaslighting; when you stop receiving actual

information and get fed disinformation from management, repeatedly even (and

you might even start to believe it!) you may eventually lose a sense of

reality.

In my personal case, working backwards to figure out where and why it started,

it seems like management truly hated how I scrutinised a contract they had

wanted us to sign without any legal advice, challenging the legality of it and

even considering a lawyers’ consultation (advice can take weeks unless it is

treated urgently).

One can assume that managers were maybe worried other people (like colleagues)

would realise what’s going on and follow suit.

“Remember that sociopaths and pathological liars do this as a matter of

routine; they’ve mastered all these tricks and they keep using them again and

again.”That’s when one manager was starting a malicious, vicious, baseless

witch-hunt that backfired so badly. We’ll give more details about this later.

The portion of the report below talks about the awful, centralised, outsourced

telephony system, the “timetracker” which everyone hated (except bosses who

exempted themselves), and the aftermath of these misguided moves, which not

only harmed the company but lowered morale. The timetracker was so

counterproductive that it was quietly dropped, for the second time, a few years

ago. It was more about surveillance than productivity or timekeeping.

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

The company ought to remove the term “Open Source” from its name; the company

has presence only in proprietary platforms but none in “Open Source” ones,

except maybe “legacy” systems from the “old” Sirius era. Over time it’s

gravitating towards 100% proprietary, but people who run the company cannot

even distinguish, so explaining the issue can be an exercise in futility. To

give just recent examples, Sirius moved to a system of telephony that did not

work and did so even faster as a result of it not working (example of extreme

incompetence), resulting in poor service to clients that could previously make

contact effortlessly. This document won’t name the systems, but it’s clear that

improving the ability to answer calls or communicate was not a priority.

‘Freebies’ from Google aren’t free; they’re only temporarily available ‘free

samples’.

To cite an older example, all the staff hated the timetracker and hilariously

enough those who imposed it on staff refused to do the timetracker routines

themselves. When challenged on this (highly hypocritical behaviour that harms

morale), one of them sobbed and went away, unable to actually justify this

arrogant ego trip (imposing unwanted things on people vastly more qualified).

The person who sobbed later messed up the salaries (many times), then did not

respond for months when question on the matter. This resulted in financial

harm. The person responsible for this error was never reprimanded or punished,

neither for these mistakes nor for failing to respond, which is very typical in

today’s Sirius management, even the CEO lying about not receiving E-mails.

No wonder lots of workers left. Those who did not leave constantly face abuse

and are being silenced. Dissent in Sirius isn’t being dealt with by grown-ups.

No wonder associates were openly mocking the CEO for being non-technical and

for writing face-saving cruft to clients. In fact, it seems like a lot of

people either left or became cynical about the company. Those who stayed (and

remains cynical) are now being maliciously targeted and it is truly sad to say

that the company became a bit of a hoax, as it is neither about Open Source nor

caring about the devoted staff that made many personal compromises, only

pretending to care in very shallow ways like annual vouchers (worth less than

one shift). █

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⠀⠀⠀⠈⠛⠛⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀

                ䷩ 𝚕𝚒𝚗𝚎 1013

(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/01/02/sirius-open-source-inc/#comments

Gemini version at gemini://gemini.techrights.org/2023/01/02/sirius-open-source-inc/

Gemini_version_available_♊︎

✐ Sirius_Open_Source_Inc._—_A_New_Shell_Created_When_Bill_Gates_Paid_the_CEO;

Then_the_Company_Immediately_Turned_Ugly_and_Hostile_Towards_Its_Own_Workers⠀✐

Posted in Bill_Gates, Deception, Free/Libre_Software, Microsoft at 4:29 am by

Dr. Roy Schestowitz

One might joke that it looks like Sirius Open Source LTD was ‘sold’ to Bill

Gates; less than 2 months later bullying by the ‘boss’ started (against both

myself and my wife)

🄸🄼🄰🄶🄴🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽⦇microsoft-inc-siriuus⦈_

Who or where is Sirius Open Source Inc. anyway?

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

Summary: The company Sirius_Open_Source_LTD (UK) now presents itself as “Sirius

Open Source Inc.” and says in Microsoft’s LinkedIn that it is "a_company_based

in_Washington." It was founded by totally unknown people around the time all

staff was required (under implicit threats; we’ll show evidence later this

month) to sign a new and mysterious contract; a month later the company above

was incorporated (not by the CEO; he’s not even named!) and months later we

were all told that Bill Gates had passed money to the CEO under NDA (when the

Gates/Epstein_MIT_scandals surfaced in the mainstream media and in_Techrights);

the CEO very clearly said Gates_Foundation had become the first US client and

it now says “Sirius Open Source is a company based in Washington, USA” (close

to Gates); it was incorporated by a person whose name was mentioned in chat/

phone only once; the shell game goes a lot further than it seems on the surface

and it will be discussed in weeks to come; it’s worth adding that Microsoft had

already attacked my job and my livelihood by phoning_the_CEO_in_the_past,

asking for him to take action (he politely declined).

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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣼⣼⣤⣿⣤⣧⣭⣼⣭⣤⣿⣧⣭⣥⣿⢨⣥⣧⣭⣽⣼⣧⣿⣯⣭⣴⣦⣥⣾⣬⣥⣧⣼⣧⣭⣧⣬⣽⣿⣥⣽⣼⣧⣧⣬⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⢫⠉⡍⢋⡉⡍⢫⣋⣉⣉⢉⠋⡝⢉⠉⣍⢋⡋⢹⣿⣿⣿⣿⣿⣿⡏⡄⠠⠤⠤⢤⠤⠤⡤⡤⠤⠠⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠉⠉⠉⢹

⣿⣷⣦⣴⣷⣶⣷⣶⣶⣶⣾⣴⣷⣶⣾⣶⣴⣆⣦⣼⣿⣿⣿⣿⣿⣿⣧⢭⣭⣭⣭⣬⣭⢭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣾

⣿⣶⣤⣤⣤⣤⣤⣤⣤⣼⣤⣦⣤⣤⣤⣤⣤⣼⣤⣤⣼⣿⣿⣿⣿⣿⣿⣾⣶⣶⣶⣶⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣥⣤⣤⣧⣼

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

⣿⠉⣭⠉⡏⢹⠭⢹⣯⡝⢉⣍⠍⠋⡏⠙⣭⡋⣯⠉⡯⡭⠉⣿⢩⡙⠉⡍⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸

⣿⣶⣶⣾⣶⣷⣾⣾⣷⣾⣾⣶⣶⣷⣷⣾⣶⣷⣾⣾⣶⣾⣶⣼⣶⣾⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸

⣿⣿⣿⣿⣿⣿⣧⣤⣥⣥⣥⣬⣤⣭⣿⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸

⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⣧⢤⣤⣿⢤⢤⣼⠿⠿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸

⣿⣿⣿⣿⣿⣿⣶⡶⠶⠶⠶⠶⠶⠶⣿⠶⡶⠼⠶⠶⠶⠶⠶⠷⠶⠾⠦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸

⣿⣿⣿⣿⣿⣿⣿⣷⣶⠶⠶⠶⠶⠶⣿⠶⠶⠶⠶⢾⠶⢶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸

⣿⣿⣿⣿⣿⡟⠿⠿⠿⠶⡖⠶⠲⠶⣿⠒⠒⠒⡶⢒⡲⢺⠛⠛⠻⠟⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸

⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣉⣋⣋⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣉⣉⣍⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠤⠽⠿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠿⠟⠻⠿⣿⠒⠲⠒⠷⠶⠒⠒⠛⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸

⣿⣿⣿⣿⣿⣿⣿⡿⠟⠓⠛⠛⠛⠛⣿⠛⠛⠛⠛⠛⠛⠟⠛⡟⠛⡟⠛⡟⠛⠛⠛⠻⡛⠻⠛⠛⠻⠛⠛⠿⠛⡛⠛⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣍⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸

⣿⣿⣿⣿⣿⣿⣀⣉⣉⣉⣉⣀⣈⣉⣿⡀⣀⣁⡀⢀⠀⠀⢈⣯⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠤⠤⠤⠤⠤⠤⠤⠤⠧⡶⠶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠛⠟⠛⢻⠛⠻⣿⠒⠶⠲⠲⠶⠶⠶⠲⠶⠗⠒⠾⠻⠛⠿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⠉⠉⠉⠉⠉⠉⠹⠈⠍⠉⠉⠉⠏⠩⠉⠉⠉⠉⠉⠉⠋⠉⠙⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⠛⠟⠛⠛⢻⣿⠛⠛⠟⠻⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣹⣉⣉⣉⣹⣿⣉⣉⣋⣙⣉⣉⣉⣙⣉⣉⣉⣉⣙⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⢤⠥⠤⠤⢼⣿⠤⠤⡥⢬⠤⠤⠤⢼⠿⠿⠿⠿⢿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⡏⢸⣒⡒⡒⣺⣿⠒⠒⠒⠲⠀⠐⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣹⣍⣉⣉⣹⣿⣈⣙⣉⣙⣈⣑⣉⣉⣉⣙⣈⣉⣈⡙⣉⣁⣉⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⠘⠦⠦⠤⢼⣿⠀⣀⠁⠌⠠⠄⠠⠨⠀⠠⠀⠄⡈⠀⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⣿⣀⣲⣀⣱⣀⣈⣐⣙⣂⣀⣶⣶⣷⣶⣾⣷⣶⣾⣾⣶⣷⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⡩⠛⠛⠛⢛⠟⠛⢛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⠛⠛⠟⠛⠟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣀⡀⠰⢰⡢⡄⠀⣀⣌⣉⣉⣉⣉⣋⣉⣋⣉⣉⣍⣙⣉⣉⣙⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣶⣶⣧⣼⣾⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                ䷩ 𝚕𝚒𝚗𝚎 1131

(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/01/02/sirius-open-source-meeting/#comments

Gemini version at gemini://gemini.techrights.org/2023/01/02/sirius-open-source-meeting/

Gemini_version_available_♊︎

✐ [Meme]_Sirius_Management_Meeting⠀✐

Posted in Free/Libre_Software, Humour, Law at 12:13 am by Dr. Roy Schestowitz

🄸🄼🄰🄶🄴🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽⦇Punching_wheel:_The_Sirius_staff_must_never_talk_to_other

                                staff⦈_

Summary: A merciless Sirius_‘Open_Source’ does_not_tolerate_colleagues_talking

to_one_another or staff asking_people_to_raise_money_for_a_koala_charity (while

many koalas were burning to death and needed urgent help); a heartless company

such as this deserves nobody’s sympathy when it files_for_bankruptcy

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠟⠛⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣠⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣦⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣄⣤⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣴⣿⡇⢹⣿⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡀⠈⠛⢿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢠⣿⣿⣯⣿⣿⣇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⡄⠀⠀⢻⣿⣿⣿⡿⠧⠀⠀⠀⠀⠀⠀⠠⣤⡀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢸⣿⣿⣁⠘⣿⣿⡆⠀⢀⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠻⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣤⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⡉⢹⣿

⠀⠀⠀⠀⠀⠀⠀⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡁⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠳⣾⣿

⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⢻⠟⠛⠛⠛⠿⠿⠿⠿⠟⠛⠋⠉⠀⠈⠉⠁⠀⠀⠀⠀⠀⠹⣿

⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣾⣿⣿⣿⣿

⠀⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⡿⠋⠉⠉⠉⠉⠛⠻

⠿⣿⡇⠀⠀⠸⣿⣿⣿⣿⣿⡿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⠀⠀⠠⠂⠀⠀⠀

⠀⠀⠈⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠿⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠈⠙⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⢿⣷⡆⣾⣿⣿⣿⣿⠀⣿⣿⣿⡇⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣌⡛⠃⠀⢸⣿⣿⠀⢀⣿⡿⣿⣷⠀⣿⣿⣇⡀⢸⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣛⢿⣿⣆⠀⢸⣿⣿⠀⢸⣿⣇⣿⣿⠀⣿⣿⡟⠃⢸⣿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠿⠷⢶⣶⣷⣾⣿⣿⣆⡀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣨⣿⡿⠀⢸⣿⣿⠀⣼⣿⡟⢿⣿⡇⣿⣿⡇⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠁⠀⠈⠉⠉⠀⠉⠉⠁⠈⠉⠁⠉⠉⠁⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠆⠲⣶⠀⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[29A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣠⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠈⠠⣤⡄⠀⠀⠀⠙⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⠀⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣯⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣰⣿⡇⢹⣿⡀⠀⠀⠀⢸⣿⣿⣿⣿⣷⡀⠉⠻⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢠⣿⣿⣯⣿⣿⣇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⡀⠀⠈⢻⣿⣿⡿⠿⠁⠀⠀⠀⠀⠐⣦⣄⡀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢸⣿⣿⣁⠘⣿⣿⡆⠀⠀⣾⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣄⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣦⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⡉⢹⣿

⠀⠀⠀⠀⠀⠀⠀⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠻⠟⠛⠛⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠉⠉⠛⠛⠟⠛⠛⠿

⣿⣷⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀

⠿⣿⡄⠀⠀⠸⣿⣿⣿⣿⣿⡿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠟⠃⠀⠀⠀⠠⠐⠒⠒⠒

⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠈⠙⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠿⠟⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⢿⣷⡆⣾⣿⣿⣿⣿⠀⣾⣿⣿⡇⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣌⡛⠃⠀⢸⣿⣿⠀⢀⣿⡟⣿⣷⠀⣿⣿⣇⡀⢸⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣛⢿⣿⣆⠀⢸⣿⣿⠀⢸⣿⣇⣿⣿⠀⣿⣿⡟⠃⢸⣿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠿⠷⠶⣶⣶⣾⣿⣷⣆⡀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣠⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠈⠀⣤⡄⠀⠀⠀⠙⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⠀⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣯⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣰⣿⡇⢹⣿⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡀⠉⠻⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢠⣿⣿⣯⣿⣿⣇⠀⠀⠀⢨⣿⣿⣿⣿⣿⣷⡀⠀⠈⢻⣿⣿⡿⠿⠁⠀⠀⠀⠀⠐⢦⣄⡀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠉⠉⠙⠻⠛⠛⠛⠿

⣾⣷⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠈⠙⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠿⠟⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣌⡛⠃⠀⢸⣿⣿⠀⢀⣿⡟⣿⣷⠀⣿⣿⣇⡀⢸⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣛⢿⣿⣆⠀⢸⣿⣿⠀⢸⣿⣇⣿⣿⠀⣿⣿⡟⠃⢸⣿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠿⠶⠶⣶⣷⣾⣿⣷⣆⡀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣨⣿⡿⠀⢸⣿⣿⠀⣼⣿⡟⢿⣿⡇⣿⣿⡇⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣠⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠘⢠⣴⡆⠀⠀⠀⠹⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣮⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣰⣿⡏⢹⣿⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡈⠙⠻⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢠⣿⣿⣯⣿⣿⣇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⡀⠀⠈⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⢤⣄⡀⠀⠀⠀⠙⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢸⣿⣿⣁⠸⣿⣿⣆⠀⢀⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣶⣄⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣶⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⢹⣿

⠀⠀⠀⠀⠀⠀⠀⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠏⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⠿⠿⠋⠉⠁⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣾⣿

⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿

⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿

⠀⣀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠿⣿⡆⠀⠀⢸⣿⣿⣿⣿⣿⡿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒

⠀⠀⠉⠀⠀⠀⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠈⠙⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠚⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣌⡛⠃⠀⢸⣿⣿⠀⢀⣿⡿⣿⣷⠀⣿⣿⣇⡀⢸⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣛⢿⣿⣆⠀⢸⣿⣿⠀⢸⣿⣇⣿⣿⡀⣿⣿⡟⠃⢸⣿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠿⠷⢶⣶⣷⣾⣿⣿⣆⡀⠀⠀

[29A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢠⡐⠆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠘⢢⣴⣦⠀⠀⠈⢻⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⢀⣼⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⣿⣿⣿⣦⡀⠿⠟⠋⠁⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣰⣿⡏⢹⣿⡀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡈⠙⠻⠿⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣧⠀⠀⠀⣸⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢸⣿⣿⣁⠸⣿⣿⣦⠀⣠⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣉⢹⣿

⠀⠀⠀⠀⠀⠀⢀⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢯⣿⣿

⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠻⠛⠛⠛⠿⠟⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⢻⣿

⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿

⣀⣄⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠿⣿⣇⠀⠀⢸⣿⣿⣿⣿⣿⡿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠖⠲⢒⠒

⠀⠀⠉⠀⠀⠸⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣾⡷

⠀⠀⠀⠀⠀⠀⠈⠙⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣜⡛⠃⠀⢸⣿⣿⠀⢠⣿⡿⣿⣷⠀⣿⣿⣇⡀⢸⣿⣇⣀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣛⢿⣿⣦⠀⢸⣿⣿⠀⢸⣿⣇⣿⣿⡀⣿⣿⡟⠃⢸⣿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠙⠛⠛⠛⠻⠿⠷⢶⣾⣿⣿⣿⣿⣦⡀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣸⣿⡿⠀⢸⣿⣿⠀⣼⣿⡟⢿⣿⡇⣿⣿⡇⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠁⠀⠈⠉⠉⠀⠉⠉⠁⠈⠉⠁⠉⠉⠁⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠲⣶⠊⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[29A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣠⣄⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠙⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣠⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⠰⣾⣿⣿⣿⣿⣿⢿⡿⠟⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣷⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣰⣿⡏⢹⣿⡀⠀⠀⠀⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣇⠀⠀⠀⣸⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢸⣿⣿⣁⠸⣿⣿⣦⠀⢀⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣉⢹⣿

⠀⠀⠀⠀⠀⠀⠀⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣼⣿

⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠻⠟⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠋⠉⠁⠈⢿⣿

⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿

⢀⣀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⡿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠔⠒⠂⠀

⠀⠀⠉⠀⠀⠈⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣯⣥⣤⣆⠄

⠀⠀⠀⠀⠀⠀⠈⠙⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣌⡛⠃⠀⢸⣿⣿⠀⢠⣿⡿⣿⣷⠀⣿⣿⣇⡀⢸⣿⣇⣀⠀⠀⠀⠀⠀⠀⠠⣦⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣛⢿⣿⣆⠀⢸⣿⣿⠀⢸⣿⣇⣿⣿⡀⣿⣿⡟⠃⢸⣿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠛⠛⠛⠲⢶⣶⣷⣾⣿⣿⣆⡀⠀⠀

⠀⠖⠲⣶⠀⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[29A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⣶⣤⣶⣾⣿⣿⣦⣄⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⣤⣠⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠛⠛⠛⠋⠉⠉⠁⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⣸⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣴⡦⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠶⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣰⣿⣏⣹⣿⡀⠀⠀⠀⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣧⠀⠀⠀⣸⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢸⣿⣿⣅⢸⣿⣿⣧⠀⣠⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⢽⣿

⠀⠀⠀⠀⠀⠀⢀⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⢹⣿

⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠟⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⠇⠘⣿⣿

⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⣿⣿⠿⣿⣿⡶⠶⠶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠹⣿

⣠⣤⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⣿⣿⡄⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢿⣿⣧⡀⠀⢿⣿⣿⣿⣿⣿⡿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤

⠀⠀⠉⠀⠀⢸⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣾⣿⣿⡿

⠀⠀⠀⠀⠀⠀⠈⠛⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⢿⣷⡆⣾⣿⣿⣿⣿⠀⣿⣿⣿⡇⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣜⡛⠃⠀⢸⣿⣿⠀⢠⣿⡿⣿⣷⠀⣿⣿⣇⡀⢸⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣛⢿⣿⣦⠀⢸⣿⣿⠀⢸⣿⣇⣿⣿⡀⣿⣿⡟⠃⢸⣿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠐⠶⢶⣶⣾⣿⣿⣅⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣸⣿⡿⠀⢸⣿⣿⠀⣼⣿⡟⢿⣿⡇⣿⣿⡇⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀

⠀⠖⠲⣶⠎⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[29A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢠⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⣿⣷⣤⣤⣴⣶⣾⣿⣦⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠉⠼⠿⠁⠀⠀⠾⠋⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⣙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⡀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⣼⣿⣿⡀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣻⣿⣿⣿⣇⠀⠀⠀⠀⠘⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⣀⣤⠀⠀⠀⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⠀⠀⠀⢶⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣰⣿⣿⣹⣿⡀⠀⠀⠀⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣷⠀⠀⠀⣼⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢸⣿⣿⣇⣸⣿⣿⣦⢀⣴⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⢿⣿

⠀⠀⠀⠀⠀⠀⢀⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠟⢿⣿

⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⡇⠂⣾⣿

⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⡶⠶⠒⠀⠀⠹⣿

⣤⣤⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠛⠛⠛⠿⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠉

⣿⣿⡇⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢿⣿⣷⡄⠀⢿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠉⠀⠀⢸⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿

⠀⠀⠀⠀⠀⠀⠈⠙⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⠿⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⢿⣷⡆⣾⣿⣿⣿⣿⠀⣿⣿⣿⡇⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣛⢿⣿⣦⠀⢸⣿⣿⠀⢸⣿⣇⣿⣿⡀⣿⣿⡟⠃⢸⣿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣴⣿⣿⣇⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣸⣿⡿⠀⢸⣿⣿⠀⣼⣿⡟⢿⣿⡇⣿⣿⡇⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀

⠀⠖⠶⣶⠎⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[29A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣦⡄⠀⠀⠀⣀⣰⣦⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣠⣠⣤⣤⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⠛⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡟⠁⠺⣿⣄⠀⠰⠟⠋⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠘⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣶⣦⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⣸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⢿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠶⠇⠀⠀⠀⠀⠀⠀⠀⠘⣿⡗⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢹⣶⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⠀⠀⠀⢶⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣼⣿⣿⣸⣿⡄⠀⠀⠀⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠀⠀⠀⣾⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢸⣿⣿⣇⣸⣿⣿⣧⢀⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿

⠀⠀⠀⠀⠀⠀⣀⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡟⣿⣿

⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⡯⠶⣾⣿

⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⠖⠹⣿

⣠⣤⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⡀⠈⠁⠀⠀⠈⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠁⠀⠀⠙

⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢿⣿⣿⡄⠀⢿⣿⣿⣿⣿⣿⡿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠉⠁⠀⢸⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿

⠀⠀⠀⠀⠀⠀⠉⠛⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠿⠟⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣜⡛⠋⠀⢸⣿⣿⠀⢠⣿⡿⣿⣷⠀⣿⣿⣇⡀⢸⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣛⢿⣿⣦⠀⢸⣿⣿⠀⢸⣿⣇⣿⣿⡀⣿⣿⡟⠃⢸⣿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣾⣿⣇⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣸⣿⣿⠀⢸⣿⣿⠀⣾⣿⡟⢿⣿⡇⣿⣿⡇⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠁⠀⠈⠙⠋⠀⠙⠉⠁⠘⠋⠃⠙⠋⠁⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[29A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣠⣤⣤⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠀⠀⠀⠀⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⢀⣀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠋⠁⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⠀⠀⠀⠶⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣼⣿⣏⣽⣿⡀⠀⠀⠀⢿⣿⣿⣿⣿⣇⠀⠀⠉⠻⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⠀⠀⠀⣼⣿⣿⣿⣿⣿⣦⠀⠀⠀⠈⢿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢸⣿⣿⣁⢸⣿⣿⣦⢀⣤⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣌⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣉⢹⣿

⠀⠀⠀⠀⠀⠀⣀⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠰⣶⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠸⣿

⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠇⢀⠀⠀⠀⠉⠙⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣯⠤⠐⣿

⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣿

⣠⣀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠈

⣿⣿⡆⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⢦⡄⠐⠦⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠛⠙⠭⠛⠁⠀⠀⠀⠀

⠿⣿⣇⠀⠀⢺⣿⣿⣿⣿⣿⡿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠰⢗⣏⣻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤

⠀⠀⠉⠀⠀⢸⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠇⠀⠀⢨⢹⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠈⠛⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣼⣽⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⢿⣷⡆⣾⣿⣿⣿⣿⠀⣿⣿⣿⡇⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⠀⠀⠙⠻⣯⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣜⡛⠃⠀⢸⣿⣿⠀⢠⣿⡿⣿⣷⠀⣿⣿⣇⡀⢸⣿⣇⣀⠀⠀⠀⠀⠀⠙⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣛⢿⣿⣦⠀⢸⣿⣿⠀⢸⣿⣇⣿⣿⡀⣿⣿⡟⠃⢸⣿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣁⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣸⣿⡿⠀⢸⣿⣿⠀⣼⣿⡟⢿⣿⡇⣿⣿⡇⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀

⠀⠖⠶⣶⠊⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[29A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⣤⣤⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣷⣦⣄⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠀⠀⠀⠰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣼⣿⡇⣽⣿⡀⠀⠀⠀⢿⣿⣿⣿⣿⣇⠉⠉⠛⠿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠟⠀⠀⠀⠘⠇⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣸⣿⣿⣷⣿⣿⣇⠀⠀⠀⣼⣿⣿⣿⣿⣿⣆⠀⠀⠀⠙⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢻⣿⣿⣀⢸⣿⣿⣆⠀⣀⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣹⣿

⠀⠀⠀⠀⠀⠀⢀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠰⣶⣿⡿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣶⡌⢹⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿

⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠉⠉⠛⠻⢿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡟⠉⠀⣿

⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣿

⣀⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠈

⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀

⠿⣿⡄⠀⠀⢹⣿⣿⣿⣿⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠉⠀⠀⠸⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶

⠀⠀⠀⠀⠀⠀⠈⠛⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⢿⣷⡆⣾⣿⣿⣿⣿⠀⣿⣿⣿⡇⢀⣿⣿⣿⣿⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡿⣿⣿⣇⡿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣷⣿⣿⡟⠃⣿⣿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣼⣿⣿⢿⣿⡟⣿⣿⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢻⣿⠇⣿⣿⠙⣿⣿⣽⣿⡟⠸⣿⣧⣽⣿⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠲⣶⠊⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠉⠀⠉⠉⠀⠈⠉⠉⠉⠀⠀⠈⠉⠉⠁⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[29A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢄⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣠⣤⣤⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠀⠀⠀⠲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢠⡤⠄⠀⠀⠀⠀⢠⣤⣤⣤⣀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⣾⣿⡇⣿⣯⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⠉⠉⠙⠻⢿⣿⡟⠗⠀⢸⣿⣗⡄⠀⠀⢀⣸⣿⣿⣿⣿⣷⣄⢿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣯⠈⠻⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠀⠀⢿⣿⠗⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢿⣿⣿⣀⢸⣿⣿⣄⠀⣠⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠁⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣇⡀⣹⣿⣿⣿⣿⣿⣿⣿⣯⣉⣹⣿

⠀⠀⠀⠀⠀⠀⣈⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠰⣶⣿⣿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢹⣿

⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠻⠿⠿⠿⠿⠿⣿⣿⣿⣧⣄⣀⣿

⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿

⣠⣀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿

⣿⣿⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿

⠿⣿⣇⠀⠀⢹⣿⣿⣿⣿⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿

⠀⠀⠉⠀⠀⠸⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣿⣿

⠀⠀⠀⠀⠀⠀⠈⠛⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢠⣿⣿⣿⢸⣿⣿⢸⣿⣿⢰⣿⡿⢿⣿⡄⠿⣿⣿⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣾⣿⣿⣿⢸⣿⣿⢸⣿⣿⠸⣿⣷⣬⡉⠁⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢻⣿⡏⣿⣿⢸⣿⣿⢸⣿⣿⢀⣈⡛⢿⣿⡆⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⠇⣿⣿⠘⣿⣿⣼⣿⡟⠸⣿⣧⣼⣿⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣴⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠠⡠⣀⠀⠀⠀⢀⣤⣤⣀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⣾⣿⡁⣿⣧⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠿⠿⠿⠿⢿⣿⣿⡿⠗⠀⠀⠸⣿⣷⡇⠀⠀⠸⣿⣿⣿⣿⣷⣄⢹⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⣦⡀⠀⠀⣿⣿⣷⠀⣠⣶⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢿⣿⣯⣀⢸⣿⣿⡄⠀⣠⣿⣿⣿⣿⣿⣿⡿⠁⠈⠙⠻⠿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠈⢻⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡁⠈⣿⣿⣿⣿⣿⣿⣿⣯⣉⣹⣿

⠀⠀⠀⠀⠀⠀⣈⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠰⢶⣿⣿⡿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⠋⢹⣿

⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠁⠀⠹⠿⠿⠿⢿⢿⣿⣿⣿⣇⠀⠀⢻

⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠴⠶⠶⣶⣶⡶⠶⠶⠶⠶⠾⣿⣿⣿⣶⣶⣾

⣀⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿

⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿

⠿⣿⣇⠀⠀⢹⣿⣿⣿⣿⣿⡟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠛

⠀⠀⠉⠀⠀⠸⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠈⠙⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢀⣿⣿⣿⢸⣿⣿⢸⣿⣿⢰⣿⡿⢿⣿⡄⠿⣿⣿⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣾⣿⣿⣿⢸⣿⣿⢸⣿⣿⠸⣿⣷⣬⡉⠁⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢻⣿⡇⣿⣿⢸⣿⣿⢸⣿⣿⢀⣈⡛⢿⣿⡆⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠲⣶⠂⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠉⠀⠉⠉⠀⠈⠉⠉⠉⠀⠀⠈⠉⠉⠁⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[29A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣴⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣤⣄⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠁⠀⠀⢰⣤⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣰⣿⣿⢸⣿⣅⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠀⠀⠀⠀⠉⠁⠀⠀⢈⣿⣿⣿⣿⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡍⠛⠿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠘⣿⣿⣏⡀⣿⣿⣷⡄⠀⣰⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⣸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣆⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣉⣹⣿

⠀⠀⠀⠀⠀⠀⣈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠠⣶⣾⡿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⢹⣿

⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠉⠙⠛⠻⢷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⡇⠀⢈⣿

⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣶⣿⣿

⣀⣀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿

⣿⣿⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿

⠿⣿⣆⡀⠀⢻⣿⣿⣿⣿⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠛

⠀⠀⠉⠀⠀⠸⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠈⠙⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢠⣿⣿⣿⢸⣿⣿⢸⣿⣿⢰⣿⡿⢿⣿⡄⠿⣿⣿⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣾⣿⣿⣿⢸⣿⣿⢸⣿⣿⠸⣿⣷⣬⡉⠁⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣦⣄⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢻⣿⡏⣿⣿⢸⣿⣿⢸⣿⣿⢀⣈⡛⢿⣿⡆⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀

[29A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⢄⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣶⣤⣴⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⢸⣿⣿⣿⣈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢠⣿⣿⡈⣿⣇⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣆⠙⠻⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣿⣿⣏⣀⢸⣿⣷⡄⠀⢀⣼⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣉⣹⣿

⠀⠀⠀⠀⠀⢈⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣀⣠⡾⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠹⣿

⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠉⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⡅⠀⣤⣿

⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⣶⣶⣶⣶⣤⣼⣿

⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿

⣷⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠛

⠿⢧⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⠿⠿⠿⠋⠀

⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠙⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢀⣿⣿⣿⢸⣿⣿⢸⣿⣿⢰⣿⡿⢿⣿⡄⠿⣿⣿⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣾⣿⣿⣿⢸⣿⣿⢸⣿⣿⠸⣿⣷⣬⡉⠁⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣦⣀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢻⣿⡇⣿⣿⢸⣿⣿⢸⣿⣿⢀⣈⡛⢿⣿⡆⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀

⠀⠖⠲⣶⠀⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠉⠀⠉⠉⠀⠀⠉⠉⠉⠀⠀⠈⠉⠉⠁⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⣶⣶⣾⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⠛⠉⠉⠉⠉⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣶⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⣠⣤⣤⡀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢠⣿⣿⡇⣽⣇⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣿⣿⣿⡯⠿⣿⣄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⠻⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢻⣿⣿⣄⡀⢿⣿⣦⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠹⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣦⣴⣾⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡉⢹⣿

⠀⠀⠀⠀⢀⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠸⣿

⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣴⣶⣾⣿

⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠛⠛⠿⠿

⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠟⠁⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀

⠀⠀⠀⠀⠀⠀⠀⠙⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⡾⠟⠉⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣾⣿⣿⣿⢸⣿⣿⢸⣿⣿⠸⣿⣷⣬⡉⠁⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⣄⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢻⣿⡇⣿⣿⢸⣿⣿⢸⣿⣿⢀⣈⡙⢿⣿⡆⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⠇⣿⣿⠘⣿⣿⣼⣿⡏⠸⣿⣧⣼⣿⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠆⠲⣶⠀⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠉⠀⠉⠉⠀⠀⠉⠉⠉⠀⠀⠈⠉⠉⠁⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⣴⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⠉⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⢸⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣾⣿⣿⡈⣿⡁⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡥⠿⣧⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣀⡀⢻⣿⡄⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⠟⠻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠈⠻⣿⣿⣿⣿⣿⣿⡀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡉⢹⣿

⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠸⣿

⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⡿⠀⠀⣾⡿

⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⡶⣶⣿⣿⣿⣿⣿⣿⡶⠶⠀⠀⠀⠈⠉⠀⠀⠀⠙⠁

⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠉⠛⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣾⣿⣿⣿⢸⣿⣿⢸⣿⣿⠸⣿⣷⣬⡉⠁⠀⣿⣿⡇⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣦⣄⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢻⣿⡇⣿⣿⢸⣿⣿⢸⣿⣿⢀⣈⡙⢿⣿⡆⠀⣿⣿⡇⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀

[29A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣄⣀⣴⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⣿⠿⠛⠛⠛⠋⠠⣤⣤⣈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠸⣿⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠿⣿⢿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣶⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣷⣤⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡉⢹⣿

⠿⠟⠁⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠸⣿

⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⡿⠀⠀⣠⣿

⠀⠀⠀⠀⢀⡀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠀⠀⠘⠏

⠀⠀⣴⣶⣿⣿⣄⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⠿⠿⠿⠿⠿⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀

⠀⠀⣿⣿⣿⣿⣿⣷⣤⣾⣿⣿⡿⠿⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠈⠻⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠉⠛⠿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣾⣿⣿⣿⢸⣿⣿⢸⣿⣿⠸⣿⣷⣬⡉⠁⠀⣿⣿⡇⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⣀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢻⣿⡇⣿⣿⢸⣿⣿⢸⣿⣿⢀⣈⡙⢿⣿⡆⠀⣿⣿⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀

[29A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⣀⣀⣀⣀⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣦⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠁⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣟⠛⠛⣿⣿⣿⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠛⠛⠃⠀⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦

⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⠀⠀⠀⠀⠸⣿⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⠟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣉⢹⣿

⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⢸⣿

⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⡇⠀⢀⣿

⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠀⠘⠻

⠀⣤⣴⣷⣄⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⣿⡿⢿⣿⣿⣿⡿⠿⠿⠋⠁⠀⠀⠀⠀

⠘⣿⣿⣿⣿⣷⣦⣄⣰⣿⡿⠿⠻⠛⠻⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠈⠙⠿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠈⠙⠻⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣾⣿⣿⣿⢸⣿⣿⢸⣿⣿⠸⣿⣷⣬⡉⠁⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢻⣿⡏⣿⣿⢸⣿⣿⢸⣿⣿⢀⣈⡛⢿⣿⡆⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣦⣄⣀⣀⣤⣄⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠁⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡛⠛⢻⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠙⠛⠿⠀⣸⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀

⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦

⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣧⡀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣹⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠆⠀⠀⠀⠀⣤⠀⠀⠀⠀⠸⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⣹⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⣿⡟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣉⣻⣿

⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢹⣿

⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⡇⠀⢈⣻

⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠈⠻

⢀⣤⣤⡀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⣤⠀⠈⠁⠀⠀⠀⠈⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀

⢾⣿⣿⣿⣷⣤⣀⣀⣾⣿⠟⠛⠛⠛⠛⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀

⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠐⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠉⠛⢿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠈⠙⠻⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣿⡏⣿⣿⢸⣿⣿⢸⣿⣿⢀⣈⡛⢿⣿⡆⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀

⠀⠖⠲⣶⠎⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠉⠀⠉⠉⠀⠈⠉⠉⠉⠀⠀⠈⠉⠉⠁⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠁⠀⠀

⠀⠀⠀⠀⠀⣠⣄⣠⣤⣴⣶⣶⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀

⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣽⣿⣿⣋⠉⠙⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶

⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣷⠀⠀⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣿⣿⣷⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⠂⠀⠈⣿⡇⠀⠀⠀⡀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⠍⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠘⠁⠀⠀⠀⠋⠀⠀⠀⠀⢸⣿⣿⣿⡋⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣸⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣴⣿⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⢿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢈⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣉⢹⣿

⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⢸⣿

⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⢿⠄⠀⠀⣻

⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠖⠻

⠀⣀⠀⠀⠀⠀⠻⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀

⣿⣿⣷⣦⣀⠀⠀⠈⡈⠈⠁⠉⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀

⢻⣿⣿⣿⣿⣿⣿⣿⣿⣾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠉⠻⢿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠈⠙⠻⢿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⣤⣤⠀⣤⣤⣤⡄⣤⣤⡀⣤⣤⡄⣤⣤⣤⡄⢠⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣈⣿⣿⣿⣆⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⢿⣿⠇⣿⣿⠿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⡿⠸⣿⣿⡿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[29A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣴⣶⣶⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠁⠀⠀

⠀⠀⠀⠀⣀⣠⣴⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀

⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀

⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶

⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠰⣿⣿⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢠⣾⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⣠⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⡏⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⢿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣶⣶⣦⡀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠻⣿⣆⠀⢉⠀⠀⠈⠉⠙⠻⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⠟⠁⠀⠀⠀⣤⣄⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⢘⣿⣷⣤⡄⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣀⣼⡛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠰⠾⣿⣟⡛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠷⠶⠶⠶⠿⠿⠿⠿⠿⠿⠻⢿

⠀⠀⠀⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⢿

⠀⠀⠀⠹⠂⠻⠿⢿⢿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀

⣦⣄⡀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀

⣿⣿⣿⣷⣷⣶⣴⣤⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠙⠻⠿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠉⠛⠿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⣤⣤⠀⣤⣤⣤⡄⣤⣤⠀⣤⣤⡄⣤⣤⣤⡄⢠⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⣿⣿⠀⣿⣿⠉⠁⣿⣿⡇⣿⣿⠇⣿⣿⠉⠁⢸⣿⡏⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⣿⣿⣿⡇⢸⣿⡇⣿⣿⠀⣿⣿⣿⡇⢸⣿⡿⢿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢻⣿⣿⠀⣿⣿⣀⡀⠘⣿⣿⣿⡟⠀⣿⣿⣀⣀⢸⣿⡇⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠈⠿⠿⠀⠿⠿⠿⠇⠀⠿⠿⠿⠇⠀⠿⠿⠿⠿⠸⠿⢿⣾⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠆⠲⣶⠀⢶⠄⠰⠴⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣴⣶⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠀⠀

⠀⠀⢀⣀⣤⣴⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀

⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶

⣿⣿⡟⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠟⠁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢀⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣠⣿⣿⣿⣿⣿⣦⣼⣿⣿⣿⡝⣿⣿⡛⠋⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠻⣷⣄⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠻⠿⠛⠛⠛⠛⠛⠿⣿⣿⡿⠁⠀⠀⢠⣤⣴⡄⠀⠀⠀⢤⣤⣤⣄⠀⠹⣿⣿⣿⣿⣿⣽⣿⣿

⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢸⣿⣷⡀⢸⣿⣿⠉⠉⢿⣿⡟⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⢀⣻⣿⣿⣿⣷⣄⢸⣿⣿⣿⣿⣿⣿⣿

⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣔⠛⠻⠋⠀⢸⡿⠃⠀⠀⠀⠈⠁⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠀⣴⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠉⠻⢿⣿⣿⣿⣿⣿⣿⣯⡉⠹⣿

⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠐⠾⣿⣟⡛⠛⠻⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⠀⠀⢨⣿⣿⣿⣿⣿⣿⡏⠀⠈⣿

⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⡄⠼⠿⠿⠿⠿⣿⣿⣄⣀⠀⢹

⠀⠀⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠒⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿

⠀⠀⠀⠘⠿⡿⠭⢽⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿

⣀⡀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿

⣿⣿⣷⣶⣴⣤⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉

⠛⠿⢿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠉⠛⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠋⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢻⣿⣿⠀⣿⣿⣀⡀⠘⣿⣿⣿⡿⠀⣿⣿⣀⣀⢸⣿⡇⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠈⠿⠿⠀⠿⠿⠿⠇⠀⠿⠿⠿⠇⠀⠿⠿⠿⠿⠸⠿⠇⠸⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠆⠲⣶⠀⠶⠄⠰⠴⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[29A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀

⠀⣀⣠⣴⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣶

⡿⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣼⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣷⣤⣽⣿⣿⡇⠙⢿⣿⡟⠛⠋⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠻⣷⣄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢿⣿⠿⠿⠿⣿⣿⣿⣿⠏⠀⠀⠀⠘⣿⣾⡧⠀⠀⢀⣾⣿⣿⣿⣦⡀⠹⣿⣿⣿⣿⣿⣸⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣸⣿⣷⠀⠀⠸⣿⡿⠉⠋⢿⣿⣯⢻⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⢿⣿⡇⠀⢀⣾⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⣀⣜⣛⠛⠋⠀⠀⠀⣿⠃⠀⠀⠀⠈⠁⠈⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣇⠀⠈⣿⣿⣿⣿⣿⣿⣿⣏⡉⠸⣿

⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣿⣟⡛⠿⠟⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣤⡄⣿⣿⣿⣿⣿⣿⣿⠏⠀⠈⣿

⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⢙

⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿

⠀⠀⠈⠻⡿⠏⠛⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⣿⣿⣿

⡀⠀⠀⠀⠀⠀⠀⠈⠙⢿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿

⣿⣷⣶⣦⣤⣤⣠⣤⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿

⠛⠿⢿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛

⠀⠀⠀⠈⠙⠻⢿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⣤⣤⠀⣤⣤⣤⡄⣤⣤⠀⣤⣤⡄⣤⣤⣤⡄⢠⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠆⠲⣶⠀⠶⠄⠰⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣠⣄⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀

⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶

⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡿⠿⢿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣶⣄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣧⣤⣿⣿⣿⠄⠈⢿⣿⡿⠿⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠹⣿⣿⣿⣿⣿⡇⠀⠀⠀⣀⡀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠙⣿⣤⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⠀⠛⠛⠻⠿⠟⠀⠀⠀⠀⠙⠛⠃⠀⠀⢰⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿

⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢨⣿⣿⠀⠀⠀⢸⣿⡟⠙⠛⢿⣿⠉⢿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣧⠀⢀⣠⣞⣉⣹⠋⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣄⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡉⢹⣿

⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⣿⣿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠘⣿

⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⠀⠀⠀⣹

⠀⠀⢿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣚⣿

⠀⠀⠸⢿⡇⠈⢻⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠛⠙⠛⠛⠛⠻⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠈⠛⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿

⣿⣶⣦⣤⣤⣤⣤⣴⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿

⠻⠿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋

⠀⠀⠀⠈⠙⠻⢿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⣿⣿⣿⡇⢸⣿⡇⣿⣿⠀⣿⣿⣿⡇⢸⣿⡿⢿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡤⢀⠀⠀⠀

⠀⠆⠲⣶⠀⠲⠄⠰⠴⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣠⣠⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠁⠀⠀

⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠉⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣄⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⠿⢿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣷⣄⣽⣿⣿⠁⠀⠻⣿⣿⡿⠿⠿⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⣿⣿⣿⣏⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠘⢿⣧⣄⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⢸⡿⠀⠈⠙⠁⠀⠹⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⡀⠀⣠⣴⣭⣽⡏⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡉⢹⣿

⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠘⣿

⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⠀⠀⢠⣿

⠀⠨⢻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⠿⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣶⣶⣶⣾⣿

⠀⠀⢻⣧⡀⠙⢿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿

⠈⠂⠀⡀⠀⠀⠀⠉⢻⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿

⣷⣶⣶⣤⣤⣤⣤⣶⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠿⠿

⠻⠿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠉⠙⠻⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⣿⣿⣿⡇⢸⣿⣇⣿⣿⠀⣿⣿⣿⡇⢸⣿⡿⢿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢦⢴⢶⣶⣶⣄⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢻⣿⣿⠀⣿⣿⣀⡀⠘⣿⣿⣿⡿⠀⣿⣿⣀⣀⢸⣿⡇⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀

⠀⠀⠀⠀⢀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀

⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠿⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦

⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⡿⠿⢿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣶⣮⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣡⣤⣐⣿⣿⡁⠀⠈⢻⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿

⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⢻⠿⠿⠿⠿⠛⢿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣪⣿⣿

⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢨⣿⣿⠀⠀⠀⢘⡀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⠛⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣄⠀⢀⣤⣄⣩⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠆⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⡉⢹⣿

⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⢘⣿

⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠟⠿⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⠛⠀⠀⢿⠟

⠀⠀⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣾⣿

⠀⠀⢻⡄⠀⠙⢿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠈⠻⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡏

⣶⣦⣤⣤⣤⣤⣤⣶⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠻⠛⠉⠀

⠀⠀⠀⠉⠙⠻⢿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⣿⣿⠀⣿⣿⠉⠁⣿⣿⡇⣿⣿⠇⣿⣿⠉⠁⢸⣿⡏⢹⣿⡇⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⣿⣿⣿⡇⢸⣿⡇⣿⣿⠀⣿⣿⣿⡇⢸⣿⡿⢿⣿⡁⠀⠀⠀⠀⠀⠀⠈⠈⠈⠀⠀⠀⠀⠀⠲⠶⠶⣶⣶⣶⣶⣶⣄⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢻⣿⣿⠀⣿⣿⣀⡀⠘⣿⣿⣿⡟⠀⣿⣿⣀⣀⢸⣿⡇⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀

⠀⠆⠲⣶⠀⠲⠄⠰⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢀⣤⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀

⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⡀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣷⣦

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣋⣙⣥⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣤⡹⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠘⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡿⠋⠉⠩⣽⣿⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿

⣷⣿⣿⣿⣿⣿⠀⠀⠀⠀⠻⣿⣇⠀⠀⠈⠿⠿⠿⠿⠿⠿⢿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣿⣿

⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⠀⢚⣻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣷⣦⣴⣿⣽⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠉⢸⣿

⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⣠⣿

⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠟⠛⠉⠀⠘⢻⣯

⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⢀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡤⣄⣀⣀⣀⣀⣠⣴⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⣿⣿⠀⣿⣿⠉⠁⣿⣿⡇⣿⣿⠇⣿⣿⠉⠁⢸⣿⡏⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⣿⣿⣿⠇⢸⣿⡇⣿⣿⠀⣿⣿⣿⡇⢸⣿⡿⢿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠚⠛⠛⠲⠶⠶⣶⣶⣴⣶⣶⣄⠀⠀⠀

⠀⠆⠲⣶⠀⠶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⣀⣤⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣷⣦

⣛⣙⣥⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣴⣤⡹⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⠟⠿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡿⠋⠉⠩⣼⣿⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿

⣷⣿⣿⣿⣿⣿⠀⠀⠀⠀⠻⣿⣇⠀⠀⠈⠿⠿⠿⠿⠿⠿⢿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣿⣿

⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⣿⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⠀⠚⣻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⣠⣿

⠀⠛⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⠛⠛⠛⠻⠛⠛⠉⠀⠈⠿⣯

⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚

⠀⠀⢄⠀⠀⠙⢿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡤⣄⣀⣀⣀⣀⣠⣴⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⣿⣿⠀⣿⣿⠉⠁⣿⣿⡇⣿⣿⠇⣿⣿⠉⠁⢸⣿⡏⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⣿⣿⣿⠇⢸⣿⡇⣿⣿⠀⣿⣿⣿⡇⢸⣿⡿⢿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠛⠛⠛⠲⠶⠶⣶⣶⣶⣶⣶⣄⠀⠀⠀

⠀⠀⠀⠀⢀⣠⣤⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀

⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⡀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣷⣦

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⣇⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠿⣿⣿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣋⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣀⣤⣴⣶⣶⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⡿⠿⠛⠛⣻⠃⠀⠙⢿⣿⣿⡿⠿⠿⠿⣿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣯⡉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿

⣿⣠⣶⣶⣾⣿⡄⠀⠀⠈⠻⣿⣿⡀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣿⣿

⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠘⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⢼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣷⣄⣀⣴⡆⣶⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⡉⠸⣿

⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⢀⣿

⠀⠚⣿⣿⣿⣿⣿⡛⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡿⠿⠀⠀⢿⣿

⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠉⠙⠛⠿⢿⣿⣿⣿⣿⣷⣶⡶⠶⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣀⡀⠀⠀⠀⠀⢀⣀⡄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠻⠿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠈⠙⠻⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⣿⣿⠀⣿⣿⠉⠁⣿⣿⡇⣿⣿⠇⣿⣿⠉⠁⢾⣿⡏⢹⣿⡇⠀⠀⠀⠀⢄⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⣿⣿⣿⠇⢸⣿⡇⣿⣿⠀⣿⣿⣿⡇⢸⣿⡿⢿⣿⡁⠀⠀⠆⠀⠀⠁⠁⠈⠀⠈⠁⠈⠀⠐⠒⠲⠶⣶⣶⣶⣶⣶⣄⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢻⣿⣿⠀⣿⣿⣀⡀⠘⣿⣿⣿⡟⠀⣿⣿⣀⣰⣸⣿⡇⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠈⠿⠿⠀⠿⠿⠿⠇⠀⠿⠿⠿⠇⠀⠿⠿⠿⢿⡿⠿⠇⠸⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠆⠲⣶⠀⠲⠄⠰⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[29A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀

⠀⠀⠀⠀⠀⣠⣤⣤⣄⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣷⣦⣶⣶⣦⣄⣠⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀

⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣇⠀⣸⡿⠿⠂⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⡄⠻⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⢻⣿⣿⣿⣥⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠉⣉⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⠿⢿⣿⣿⠀⠈⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣯⣴⣶⣾⣿⣧⠀⠀⠀⠹⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠈⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣼⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣦⣀⣠⣶⣷⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡉⢹⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠘⣿

⠈⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠿⠟⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⡿⠀⠀⢿⣿

⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠉⠀⠀⠀⠀⠀⠙⠛⠛⠿⣿⣿⣿⣿⣶⣶⣶⣶⣶⠶⠶⠖⠀⠀⠀⠀⠀⠈⢻

⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠁⠀⠀⠈⠛⢿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣀⣀⠀⠀⠀⠀⣀⣀⡄⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠛⠿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠉⠛⠿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⡄⢠⣤⣤⣄⠀⢠⣤⡄⠀⢠⣤⡄⢠⣤⡄⠀⢠⣤⣤⣤⣤⡄⢀⣴⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⠉⠁⣿⣿⣿⣿⠀⢸⣿⡇⠀⢸⣿⣇⣿⣿⠁⠀⠈⠉⣿⣿⡏⠁⣿⣿⡇⣿⣿⠀⢰⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢀⣿⣿⢹⣿⡄⢸⣿⡇⠀⢸⣿⣿⣿⣇⠀⠀⠀⠀⣿⣿⡇⠀⣿⣿⡇⣿⣿⠀⠀⠉⠉⠉⠉⠉⠉⠁⠈⠐⠒⠶⠶⢶⣶⣶⣶⣄⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⣾⣿⡇⢸⣿⣇⣀⢸⣿⡏⣿⣿⡀⠀⠀⠀⣿⣿⡇⠀⣿⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠀⠸⠿⠇⠸⠿⠷⠸⠿⠿⠿⠸⠿⠇⠸⠿⠧⠀⠀⠀⠿⠿⠃⠀⠘⠻⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[29A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣦⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀

⠀⠀⠀⣀⣀⣠⣤⣴⣶⣦⣦⣤⣤⣤⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠁⠀⠀

⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⢿⣿⣏⠀⠈⢶⣿⣿⣿⡿⠛⠉⠉⠉⠉⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢻⣿⣦⠸⢿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⡀⠀⠀⠀⠀⠀⠀⠉⠉⡀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠆⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠂⠀⠀⠀⠀⣻⣿⣿⣿⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠉⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣤⣶⣿⣿⣿⣿⣿⣿⡇⠀⠙⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣭⣯⣿⣿⣿⡇⠀⠀⠘⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣠⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣠⣶⣾⣷⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠉⠁⠀⠀⠈⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣹⣿

⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢹⣿

⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠙⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡯⠀⢺⣿

⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠸⣶⠄⠀⠈⠁⠀⠀⠀⠀⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣶⡶⠖⠀⠀⠀⠑

⠀⠀⠀⢀⡀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢹⣮⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠙⠛⠛⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠘⠇⠀⠀⠈⠻⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠻⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⣀⢀⣀⣀⣤⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⡞⢾⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠛⠛⠿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠈⠙⠻⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⡄⣠⣤⣤⣄⠀⢠⣤⡄⠀⢠⣤⡄⢠⣤⡄⠀⢠⣤⣤⣤⣤⡄⢠⣴⣶⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⠉⠁⣿⣿⣿⣿⠀⢸⣿⡇⠀⢸⣿⣇⣿⣿⠁⠀⠈⠉⣿⣿⡏⠁⣿⣿⡇⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢀⣿⣿⢻⣿⡄⢸⣿⡇⠀⢸⣿⣿⣿⣇⠀⠀⠀⠀⣿⣿⡇⠀⣿⣿⡇⣿⣿⡃⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣄⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⣾⣿⡇⢸⣿⣇⣀⢸⣿⡏⣿⣿⡀⠀⠀⠀⣿⣿⡇⠀⣿⣿⡇⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠀⠺⠿⠇⠸⠿⠿⠸⠿⠿⠿⠸⠿⠇⠹⠿⠧⠀⠀⠀⠿⠿⠇⠀⠘⠻⠿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[29A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣦⣤⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀

⠀⠀⠀⣀⣀⣀⣠⣴⣶⣦⣦⣤⣤⣤⣤⣤⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠁⠀⠀

⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⢿⣿⣏⠀⠈⢶⣿⣿⣿⡿⠛⠉⠉⠉⠉⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⡀⠀⠀⠀⠀⠀⠀⠉⠉⡀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷

⠉⠉⣙⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣭⣽⣿⣿⣿⡇⠀⠀⠘⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣠⣶⣿⣷⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠉⠁⠀⠀⠈⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣹⣿

⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢹⣿

⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠙⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡧⠀⢺⣿

⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣶⠄⠀⠈⠁⠀⠀⠀⠀⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡶⠖⠂⠀⠀⠙

⠀⠀⠀⢀⡈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢩⣎⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠙⠛⠻⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀

⠀⠀⡀⠘⠇⠀⠀⠈⠻⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠻⣿⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⡀⠀⠀⣀⣀⣀⣀⣤⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡶⢾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠛⠛⠿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠾⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⡄⣠⣤⣤⣄⠀⢠⣤⡄⠀⢠⣤⡄⢠⣤⡄⠀⢠⣤⣤⣤⣤⡄⢀⣴⣶⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢀⣿⣿⢹⣿⡆⢸⣿⡇⠀⢸⣿⣿⣿⣇⠀⠀⠀⠀⣿⣿⡇⠀⣿⣿⡇⣿⣿⠇⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⣿⣷⣄⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⣾⣿⡇⢸⣿⣇⣀⢸⣿⡏⣿⣿⡀⠀⠀⠀⣿⣿⡇⠀⣿⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠀⠸⠿⠇⠸⠿⠿⠸⠿⠿⠿⠸⠿⠇⠹⠿⠧⠀⠀⠀⠿⠿⠇⠀⠘⠻⠿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠶⣶⠎⢶⠆⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[29A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀

⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣴⣶⣦⣤⣤⣶⣶⣶⣶⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠁⠀⠀

⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣅⠀⠀⠀⠉⠋⠁⠀⠀⠀⠀⠀⢠⣤⣀⡀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀⠀⠹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⢻⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠉⠉⠉⠉⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⣀⣠⣾⣿⣿⣿⣿⣿⣿⠉⠙⢿⣿⣿⠉⠉⠉⠿⠟⠋⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣷⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⠀⠀⠈⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠿⠿⢿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠈⢿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣠⢤⣮⣽⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡈⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣹⣿

⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡟⠀⠀⠀⠹⠏⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⢹⣿

⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠧⠤⠄⣿

⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣾⣷⣶⣾⣶⣶⣶⠂⠙

⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⡤⠀⡠⣤⡀⠈⠓⠀⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀

⠀⠀⠀⠀⠓⠀⠀⠀⠹⢿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠃⠀⠀⠀⢀⢤⢹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⢀⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠛⠻⢶⣶⣶⣾⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣐⣾⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠉⠛⠿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⡄⣠⣤⣤⣄⠀⢠⣤⡄⠀⢠⣤⡄⢠⣤⡄⠀⢠⣤⣤⣤⣤⡄⢀⣴⣶⣾⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⠉⠁⣿⣿⣿⣿⠀⢸⣿⡇⠀⢸⣿⣇⣿⣿⠁⠀⠈⠉⣿⣿⡏⠁⣿⣿⡇⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢀⣿⣿⢹⣿⡆⢸⣿⡇⠀⢸⣿⣿⣿⣇⠀⠀⠀⠀⣿⣿⡇⠀⣿⣿⡇⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⣾⣿⡇⢸⣿⣇⣀⢸⣿⡏⣿⣿⡀⠀⢀⣆⣿⣿⡇⠀⣿⣿⡇⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠀⠸⠿⠇⠸⠿⠿⠸⠿⠿⠿⠸⠿⠇⠹⠿⠧⠀⣸⠿⠿⠿⠃⠀⠘⠻⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠲⣶⠊⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣀⣤⣀⣠⣤⣶⣶⣶⣶⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠀⠀⠀

⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀

⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀

⣤⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⢀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠿⠿⠛⠋⠉⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣦⣄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣈⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣀⣴⣾⡿⠿⠟⢛⣻⡟⠈⠙⣿⣿⡟⠉⠹⠿⠯⠿⠿⠿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⡇⠀⠀⠸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣄⠀⢀⡀⢀⣉⣿⡏⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡍⢹⣿

⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⠁⠀⠀⠀⠀⠀⠐⠿⣿⣟⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠸⣿

⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠙⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠤⠤⠀⣿

⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣷⣾⣶⣶⣶⣶⣶⣶⠖⠙

⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣜⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠘⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⢲⣄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠿⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠐⠲⣶⣤⣴⣶⣶⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⠏⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠈⠙⠻⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡄⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⡄⣠⣤⣤⣄⠀⢠⣤⡄⠀⢠⣤⡄⢠⣤⡄⠀⣾⣿⣿⣦⣤⡄⢀⣴⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⠉⠁⣿⣿⣿⣿⠀⢸⣿⡇⠀⢸⣿⣇⣿⣿⠁⠀⢹⣿⣿⣿⡏⠁⣿⣿⡇⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢀⣿⣿⢹⣿⡄⢸⣿⡇⠀⢸⣿⣿⣿⣇⠀⠀⣼⣿⣿⣿⡇⠀⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⣾⣿⡇⢸⣿⣇⣀⢸⣿⡏⣿⣿⡀⢸⣿⣿⣿⣿⡇⠀⣿⣿⡇⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠀⠸⠿⠇⠸⠿⠷⠸⠿⠿⠿⠸⠿⠇⠸⠿⠧⠸⢿⣿⣿⠿⠃⠀⠘⠻⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠲⣶⠂⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀

⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⠀⠀

⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶

⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠻⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣠⣤⣾⣿⣭⣭⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⣠⣴⣾⡿⢛⣉⣉⣥⣾⠀⠈⢻⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢰⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⠀⠀⠈⢿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢿⡿⠿⠛⠋⠉⠉⠙⠛⠻⢿⡿⠁⠀⠀⠀⣄⣰⡄⠀⠀⠀⣠⣤⣤⣤⣄⠘⢿⣿⣿⣿⣿⣿⣿

⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢻⣷⣿⣿⣿⠟⠹⢿⣿⡿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡋⠀⠀⣰⣿⣿⣿⣿⣿⣷⡈⣿⣿⣿⣿⣿⣿

⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⠀⠀⠉⠁⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠁⢠⣀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⡀⢀⣀⣹⡟⠁⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⡿⠋⠻⣿⣿⣿⣿⣿⣥⡁⢹⣿

⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠁⠀⠀⠀⠀⠰⠾⣿⣟⡛⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣇⠀⠀⢹⣿⣿⣿⣿⡏⠀⠘⣿

⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⡿⠿⠿⠿⠿⠿⠄⠀⠀⢻

⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣶⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠐⢶⣶⣶⣶⣶⠾

⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠛

⠀⠲⣤⣤⣤⣤⣤⣤⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣄⠀⠀

⠀⠀⠀⠙⠛⠿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⡄

⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⡄⢠⣤⣤⣄⠀⢠⣤⡄⠀⢠⣤⡄⢠⣤⡄⠀⢠⣤⣤⣤⣤⡄⢀⣤⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⠉⠁⣿⣿⣿⣿⠀⢸⣿⡇⠀⢸⣿⣇⣿⣿⠁⠀⠈⠉⣿⣿⡏⠁⣿⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢀⣿⡿⢹⣿⡄⢸⣿⡇⠀⢸⣿⣿⣿⣇⠀⠀⠀⠀⣿⣿⡇⠀⣿⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⣾⣿⡇⢸⣿⣇⣀⢸⣿⡏⣿⣿⡀⠀⠀⠀⣿⣿⡇⠀⣿⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀

⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀

⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶

⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠈⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣭⣭⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⣀⣤⣾⡿⢛⣉⣉⣥⣾⠀⠈⢻⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢰⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⠀⠀⠈⢿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢿⡿⠿⠛⠋⠉⠉⠙⠛⠻⢿⡿⠁⠀⠀⠀⣄⡰⣄⠀⠀⠀⣤⣤⣦⣤⣄⠈⢿⣿⣿⣿⣿⣿⣿

⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢻⣷⣿⣿⣿⠟⠻⢿⣿⡿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡃⠀⠀⣰⣿⣿⣿⣿⣿⣧⡈⣿⣿⣿⣿⣿⣿

⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⠀⠀⠉⠁⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠁⢀⣀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⡀⢀⣀⣹⡿⠁⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⡟⠋⠻⣿⣿⣿⣿⣿⣭⡉⢹⣿

⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠁⠀⠀⠀⠀⠰⠾⣿⣟⡛⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣇⠀⠀⢹⣿⣿⣿⣿⠏⠀⠘⣿

⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⡿⠿⠿⠿⠿⠿⠄⠀⠀⢻

⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣶⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⢶⣶⣶⣶⣶⠾

⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⣄

⠀⠀⠀⠙⠛⢿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢀⣿⡿⢹⣿⡄⢸⣿⡇⠀⢸⣿⣿⣿⣇⠀⠀⠀⠀⣿⣿⡇⠀⣿⣿⡇⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣄⣀⣀⠀⢀⣠⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀

⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀

⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶

⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠈⠙⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⠿⢥⡄⢸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣷⣦⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⣠⣴⣿⣿⣿⣩⣶⣤⣶⣿⡇⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⢹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠻⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠉⠉⠙⠛⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠹⣿⣿⣿⠉⠉⠻⢿⠝⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢀⣿⣿⡟⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣤⣠⣤⣼⠋⠁⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⡉⢹⣿

⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠰⣶⣿⡿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠸⣿

⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢶⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣄⠀⠀⣿

⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠂⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⢀⣀⡀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢤⣤⣤⣤⣤⣤⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠿⠿⠿

⠀⠀⠀⠉⠛⠿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣟⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⣿⣷⣶⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⡄⢠⣤⣤⣄⠀⢠⣤⡄⠀⢠⣤⡄⢠⣤⡄⠀⢠⣤⣤⣤⣤⡄⢀⣤⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢀⣿⡿⢹⣿⡄⢸⣿⡇⠀⢸⣿⣿⣿⣇⠀⠀⠀⠀⣿⣿⡇⠀⣿⣿⡇⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣄⣀⡀⠀⣠⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀

⠀⠀⠀⠀⢤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀

⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦

⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣤⣈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠈⠉⠉⠛⣻⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠿⠿⠓⣦⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠘⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⣤⣾⣿⣿⣿⣧⣶⣷⣾⣿⣿⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⢿⣿⣿⠿⠿⣿⡿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢻⣿⡆⠀⠀⠀⠈⢻⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢀⣼⣿⡿⠀⠀⠀⠀⠀⢿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣴⣄⣦⣴⠋⠀⠀⠀⠀⠀⢀⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⡉⢹⣿

⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢤⣴⡿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿

⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠉⠉⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⠀⠀⠠⣿

⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠆⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠛⠛⢛⣿⣍⣉⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠿⠿⠿⠿

⠀⠀⠠⣤⣤⣤⣤⣤⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀

⠀⠀⠀⠈⠛⠻⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢿⣷⣶⣤⣀

⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡿⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⡄⢠⣤⣤⣄⠀⢠⣤⡄⠀⢠⣤⡄⢠⣤⡄⠀⢠⣤⣤⣤⣤⡄⢀⣤⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢀⣿⡿⢹⣿⡄⢸⣿⡇⠀⢸⣿⣿⣿⣇⠀⠀⠀⠀⣿⣿⡇⠀⣿⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⡀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⣾⣿⡇⢸⣿⣇⣀⢸⣿⡏⣿⣿⡀⠀⠀⠀⣿⣿⡇⠀⣿⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀

[29A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣄⡀⠀⠀⣠⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠀⠀⠀

⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠉⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀

⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦

⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠈⠉⠉⣻⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⣠⣶⣿⡿⠿⠿⣟⣳⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣷⣿⣿⡇⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢿⣿⡿⠿⠿⠿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⢹⣿⣄⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠼⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⣧⣦⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⡉⢹⣿

⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⣸⣿

⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⣿⣿⣿⠿⠿⠿⠿⠿⣿⣿⡿⠿⠿⠋⠀⠘⣿⡟

⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠿⠟⠻⠟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⣤⣄⣀⣤⣤⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤

⠀⠀⠀⠈⠙⠻⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⡿⠛

⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠟⠋⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⡄⢠⣤⣤⣄⠀⢠⣤⡄⠀⢠⣤⡄⢠⣤⡄⠀⢠⣤⣤⣤⣤⡄⢀⣴⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢀⣿⣿⢹⣿⡄⢸⣿⡇⠀⢸⣿⣿⣿⣇⠀⠀⠀⠀⣿⣿⡇⠀⣿⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠶⣶⣶⣶⣶⣀⠀⠀⠀

[29A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⣠⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀

⠀⠀⠀⠀⠀⢰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠉⠙⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀

⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦

⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠈⠉⢛⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠿⠻⠟⢓⠄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢠⣶⣿⣿⣿⣿⣷⣿⣷⣾⣿⡇⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢻⣿⡿⠿⠟⠿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿

⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢹⣷⣄⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣧⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠨⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣧⣤⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⡉⢹⣿

⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣸⣿

⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⣿⣿⣿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠟⠋⠀⠘⡿⠟

⠀⠀⠀⠀⠀⠀⠀⠘⠹⢿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠟⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⣤⣄⣀⣠⣤⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤

⠀⠀⠀⠈⠙⠻⢿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⡿⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣤⠀⣤⣤⣤⣤⣤⢠⣤⡄⢠⣤⡄⢠⣤⣤⣤⠀⣤⣤⣤⣤⡀⠀⠀⢀⣤⣶⣶⣤⠀⣤⣤⣤⣤⡤⢀⣤⣤⣤⠀⢠⣤⣤⣤⡄⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⢹⣿⡇⠉⢹⣿⡏⠉⢸⣿⡇⢸⣿⡇⢸⣿⡏⠉⠀⣿⣿⠉⣿⣿⠀⠀⢸⣿⣇⠹⠿⠇⠉⣿⣿⡏⠁⢸⣿⣿⣿⡇⢸⣿⣿⠉⠁⣿⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⡇⠀⢸⣿⡇⠀⢸⣿⣿⣿⣿⡇⢸⣿⣿⣿⠀⣿⣿⢿⣿⣅⠀⠀⠈⠻⢿⣿⣦⡀⠀⣿⣿⡇⠀⣸⣿⠏⣿⣧⢸⣿⣿⣿⠇⣿⣿⣿⡗⠒⠒⠶⣶⣶⣶⣶⣀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⡇⠀⢸⣿⡇⠀⢸⣿⡇⢸⣿⡇⢸⣿⣇⣀⠀⣿⣿⠀⣿⣿⠀⠀⢰⣶⡆⢹⣿⡇⠀⣿⣿⡇⠀⣿⣿⣷⣿⣿⢸⣿⣿⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠟⠁⠀⠸⠿⠇⠀⠸⠿⠇⠸⠿⠇⠸⠿⠿⠿⠃⠿⠿⠀⠿⠿⠀⠀⠈⠻⠿⠿⠟⠁⠀⠻⠿⠇⠀⠿⠿⠀⠿⠿⠾⠿⠿⠀⠀⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⣾⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀

⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣷⣦

⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣭⣟⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣿⣿⣿⡿⠿⢿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣯⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣀⣤⣴⣿⣿⠿⠟⠛⠛⡄⠐⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡇⠀⢹⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⣿⣿⣿⣧⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿

⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⢸⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿

⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠼⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣧⣤⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠉⢹⣿

⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣸⣿

⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣟⡛⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⠛⠻⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠁⠀⠸⠿⠋

⠀⠀⠀⠀⠀⠀⠘⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁⠉⠙⠻⠿⠿⠿⠿⠿⠿⠷⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄

⠀⠀⠀⠀⠀⠀⠀⠿⠀⠸⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢠⣄⣀⣀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠉⠛⠻⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣤⡀⣤⣤⣤⣤⣤⢠⣤⡄⢠⣤⡄⢠⣤⣤⣤⠀⣤⣤⣤⣤⡀⠀⠀⢀⣤⣶⣦⣤⠀⣤⣤⣤⣼⣧⠀⣤⣤⣤⠀⢠⣤⣤⣤⡄⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⢹⣿⡇⠉⢹⣿⡏⠉⢸⣿⡇⢸⣿⡇⢸⣿⡏⠉⠀⣿⣿⠉⣿⣿⠀⠀⢸⣿⣇⠹⠿⠇⠉⣿⣿⡿⣿⢸⣿⣿⣿⡇⢸⣿⣿⠉⠁⣿⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⡇⠀⢸⣿⡇⠀⢸⣿⣿⣿⣿⡇⢸⣿⣿⣿⠀⣿⣿⢿⣿⡅⠀⠀⠈⠻⢿⣿⣦⡀⠀⣿⣿⡇⡿⣸⣿⠏⣿⣧⢸⣿⣿⣿⠇⣿⣿⣿⡗⠶⠶⢶⣤⣶⣶⣶⣀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⡇⠀⢸⣿⡇⠀⢸⣿⡇⢸⣿⡇⢸⣿⣇⣀⠀⣿⣿⠀⣿⣿⠀⠀⢰⣶⡆⢹⣿⡇⠀⣿⣿⡇⠁⣿⣿⣶⣿⣿⢸⣿⣿⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠟⠁⠀⠸⠿⠇⠀⠸⠿⠇⠸⠿⠇⠸⠿⠿⠿⠃⠿⠿⠀⠿⠿⠀⠀⠈⠛⠿⠿⠟⠁⠀⠻⠿⠇⠀⠿⠿⠀⠿⠿⠞⠿⠿⠀⠀⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[29A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣶⣤⣀⣀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⣤⣤⣤⠤⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀

⠀⠀⠀⠀⠀⢰⣶⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⢻⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣤⣾⣿⡟⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⣿⣿⣿⠿⢿⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⣠⣾⣧⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⣿⣿⣶⣦⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀

⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣠⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦

⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠰⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠁⣀⣽⣿⣿⣿⣿⠿⢿⣿⣿⣷⠀⠀⠀⠈⠙⠻⠿⣿⣿⣇⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⢸⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣠⣶⣶⣿⣿⣿⣟⣛⠛⣛⡃⢰⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿

⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠤⠾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣦⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⡉⢹⣿

⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣸⣿

⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠈⠛⠻⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠃⠀⠘⠿⠋

⠀⠀⠀⠀⠀⠀⢻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠿⢿⡷⠶⠖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆

⠀⠀⠀⠀⠀⠀⠘⣿⠀⢸⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢻⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠠⣷⣦⣤⣀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠉⠙⠻⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣤⡀⣤⣤⣤⣤⣤⢠⣤⡄⢠⣤⡄⢠⣤⣤⣤⠀⣤⣤⣤⣤⡀⠀⠀⢀⣤⣶⣶⣤⡀⣤⣤⣤⣼⣧⢀⣤⣤⣤⠀⢠⣤⣤⣤⡄⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⢹⣿⡇⠉⢹⣿⡏⠉⢸⣿⡇⢸⣿⡇⢸⣿⡏⠉⠀⣿⣿⠉⣿⣿⠀⠀⢸⣿⣇⠹⠿⠇⠉⣿⣿⣿⣯⢸⣿⣿⣿⡇⢸⣿⣿⠉⠁⣿⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⡇⠀⢸⣿⡇⠀⢸⣿⣿⣿⣿⡇⢸⣿⣿⣿⠀⣿⣿⢿⣿⣅⠀⠀⠈⠻⢿⣿⣦⡀⠀⣿⣿⡏⠃⣼⣿⠏⣿⣧⢸⣿⣿⣿⠇⣿⣿⣿⡷⠶⠶⢶⣶⣶⣶⣶⣄⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⡇⠀⢸⣿⡇⠀⢸⣿⡇⣸⣿⡇⢸⣿⣇⣀⠀⣿⣿⠀⣿⣿⠀⠀⢰⣶⡆⢹⣿⡇⠀⣿⣿⡇⠀⣿⣿⣷⣿⣿⢸⣿⣿⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠟⠁⠀⠸⠿⠇⠀⠸⠿⠇⠹⠿⠇⠸⠿⠿⠿⠃⠿⠿⠀⠿⠿⠀⠀⠈⠻⠿⠿⠟⠁⠀⠿⠿⠇⡄⠿⠿⠀⠿⠿⠾⠿⠿⠀⠀⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠆⠲⣶⠀⢶⠄⠰⠴⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[29A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⣶⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⢠⣿⡇⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠀⠀⠀

⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣞⠛⠛⠻⣿⣿⣤⣿⣿⠃⠀⠀⠻⠿⠛⠛⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢀⣴⣿⣿⣿⡄⠀⠀⠹⣿⣿⣭⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣶⣦⣜⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀

⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠙⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶

⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠘⠿⠿⢿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣠⣤⣤⣾⣿⣿⣿⣿⣿⣿⡛⢻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⠄⠀⠀⠀⢘⣿⣿⣿⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⣒⣬⡇⢺⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠙⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⣈⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⣠⡚⠛⢻⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠿⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⡉⢹⣿

⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⢸⣿

⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⡏⠀⠀⢿⠟

⠀⠀⠀⠀⠀⠀⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣷⠶⠶⠶⠂⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠹⣿⠀⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣨⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠈⠙⠻⢿⣷⣶⣴⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠈⠙⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣤⡀⣤⣤⣤⣤⣤⢠⣤⡄⢠⣤⡄⢠⣤⣤⣤⠀⣤⣤⣤⣤⡀⠀⠀⢀⣤⣶⣶⣤⡀⣤⣤⣤⣤⣿⣿⣤⣤⣤⠀⢠⣤⣤⣤⡄⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠘⠃⠂⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⢹⣿⡇⠉⢹⣿⡏⠉⢸⣿⡇⢸⣿⡇⢸⣿⡏⠉⠀⣿⣿⠉⣿⣿⠀⠀⢸⣿⣇⠹⠿⠇⠉⣿⣿⡏⣿⢹⣿⣿⣿⡇⢸⣿⣿⠉⠁⣿⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⡇⠀⢸⣿⡇⠀⢸⣿⣿⣿⣿⡇⢸⣿⣿⣿⠀⣿⣿⢿⣿⣍⠀⠀⠈⠻⢿⣿⣦⡀⠀⣿⣿⣷⣿⣾⣿⠏⣿⣧⢸⣿⣿⣿⠇⣿⣿⣿⡇⠀⠀⠀⠀⢴⣾⣶⣄⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⡇⠀⢸⣿⡇⠀⢸⣿⡇⣽⣿⡇⢸⣿⣇⣀⠀⣿⣿⠀⣿⣿⠀⠀⢰⣶⡆⢹⣿⡇⠀⣿⣿⣿⣏⣿⣿⣷⣿⣿⢸⣿⣿⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠟⠁⠀⠸⠿⠇⠀⠸⠿⠇⠸⠿⠇⠸⠿⠿⠿⠃⠿⠿⠀⠿⠿⠀⠀⠈⠻⠿⠿⠟⠁⠀⠿⠿⠇⠀⢿⠿⠀⠿⠿⠾⠿⠿⠀⠀⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠆⠲⣶⠀⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[29A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⣶⣿⠟⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⢠⣿⡇⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠀⠀⠀

⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣞⠛⠛⠻⣿⣿⣤⣿⣿⠃⠀⠀⠻⠿⠛⠛⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣶⣦⣜⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀

⠀⠀⠀⠀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⡛⢻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⠄⠀⠀⠀⢘⣿⣿⣿⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣯⣧⣒⣼⡇⢺⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠙⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣠⡚⠛⢻⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠿⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⡉⢹⣿

⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⡏⠀⠀⢿⠟

⠀⠀⠀⠀⠀⠈⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣷⠶⠶⠶⠂⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣤⡀⣤⣤⣤⣤⣤⢠⣤⡄⢠⣤⡄⢠⣤⣤⣤⠀⣤⣤⣤⣤⡀⠀⠀⢀⣤⣶⣶⣤⡀⣤⣤⣤⣤⣿⣿⣤⣤⣤⠀⢠⣤⣤⣤⡄⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠘⠃⠒⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⡇⠀⢸⣿⡇⠀⢸⣿⣿⣿⣿⡇⢸⣿⣿⣿⠀⣿⣿⢿⣿⣍⠀⠀⠈⠻⢿⣿⣦⡀⠀⣿⣿⣷⣿⣾⣿⠏⣿⣧⢸⣿⣿⣿⠇⣿⣿⣿⡇⠀⠀⠐⠀⢴⣾⣶⣀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠟⠁⠀⠸⠿⠇⠀⠸⠿⠇⠹⠿⠇⠸⠿⠿⠿⠃⠿⠿⠀⠿⠿⠀⠀⠈⠻⠿⠿⠟⠁⠀⠿⠿⠇⠀⢿⠿⠀⠿⠿⠾⠿⠿⠀⠀⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[29A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀

⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠠⣶⣶⣶⣶⣶⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠀⠀⠀

⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⡀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⢿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀

⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶

⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢀⣴⣷⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣧⣒⣭⣿⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠄⠀⠀⠀⠀⠐⡶⠀⠀⠀⠀⢸⣿⣿⣿⡙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠹⠿⠿⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⣸⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⡿⠿⢿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣰⡛⠛⢻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⢀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠀⠀⠀⠀⠀⠘⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⡉⢹⣿

⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠁⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⢸⣿

⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣷⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠯⠀⠀⢼⡟

⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠂⠀⠈⠁

⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠏⠀⠀⠀⠀⠀⠳⠄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀

⡀⠀⠀⠀⠀⠀⠙⠋⠹⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣦⡀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠉⠛⠿⣶⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣤⡀⣤⣤⣤⣤⣤⢠⣤⡄⢠⣤⡄⢠⣤⣤⣤⠀⣤⣤⣤⣤⡀⠀⠀⢀⣤⣿⣶⣤⡀⣤⣤⣤⣤⣤⢀⣿⣷⣤⡀⢠⣤⣤⣤⡄⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠘⠀⠐⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⢹⣿⡇⠉⢹⣿⡏⠉⢸⣿⡇⢸⣿⡇⢸⣿⡏⠉⠀⣿⣿⠉⣿⣿⠀⠀⢸⣿⣏⠻⠿⠇⠉⣿⣿⡏⠉⢸⣿⣿⣿⡇⢸⣿⣿⠉⠁⣿⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⡇⠀⢸⣿⡇⠀⢸⣿⣿⣿⣿⡇⢸⣿⣿⣿⠀⣿⣿⢿⣿⣍⠀⠀⠈⠻⢿⣿⣦⡀⠀⣿⣿⡇⠀⣸⣿⡟⣿⣧⢸⣿⣿⣿⠇⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⡇⠀⢸⣿⡇⠀⢸⣿⡇⣸⣿⡇⢸⣿⣇⣀⠀⣿⣿⠀⣿⣿⠀⠀⢰⣶⡇⢹⣿⡇⠀⣿⣿⡇⠀⣿⣿⣷⣿⣿⢸⣿⣿⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠟⠁⠀⠸⠿⠇⠀⠸⠿⠇⠹⠿⠇⠸⠿⠿⠿⠃⠿⠿⠀⠿⠿⠀⠀⠈⠻⠿⠿⠟⠁⠀⠿⠿⠇⠀⠿⠿⠀⠿⠿⠾⠿⠿⠀⠀⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠆⠲⣶⠂⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[29A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣶⣶⣶⣶⣶⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀

⠀⠀⠀⠀⣶⣿⣿⣿⣷⣶⣶⣤⡀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⡀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠿⠟⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀

⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⠃⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶

⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣄⣀⡀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡩⣭⣽⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⠸⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢘⣿⣄⠀⠀⠀⠀⠀⠀⠀⠹⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣠⡞⠛⢿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⡉⢹⣿

⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠿⢿⣟⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠸⣿

⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⣶⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠯⠀⠀⢰⡿

⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣶⠶⠂⠈⠁

⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⢀⡀⠀⠀⠂⠀⠀⠀⠙⠛⠛⠿⠿⠿⢿⡿⠿⠟⠛⠉⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠈⠛⠋⢿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⠁⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣷⣄⠀⠀⠀⠀⠀⠀⠈⢿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣶⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠛⠿⣷⣤⣄⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄⠈⠹⣿⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠜⣿⣿⣷⡄⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣤⡀⣤⣤⣤⣤⣤⢠⣤⡄⢠⣤⡄⢠⣤⣤⣤⠀⣤⣤⣤⣤⡀⠀⣿⣀⣿⣿⣿⣿⠀⣤⣤⣤⣤⣤⢀⣤⣦⣦⡀⢠⣤⣤⣤⡄⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠿⠏⠑⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⢹⣿⡇⠉⢹⣿⡏⠉⢸⣿⡇⢸⣿⡇⢸⣿⡏⠉⠀⣿⣿⠉⣿⣿⢀⣿⣿⣿⣿⣿⡿⠇⠉⣿⣿⡏⠉⢸⣿⣿⣿⡇⢸⣿⣿⠉⠁⣿⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⡇⠀⢸⣿⡇⠀⢸⣿⣿⣿⣿⡇⢸⣿⣿⣿⠀⣿⣿⢿⣿⣅⠀⣿⣿⣿⣿⣿⣧⡀⠀⣿⣿⡇⠀⣼⣿⡟⣿⣧⢸⣿⣿⣿⠇⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⡇⠀⢸⣿⡇⠀⢸⣿⡇⣸⣿⡇⢸⣿⣇⣀⠀⣿⣿⠀⣿⣿⠀⢻⣿⣿⣿⣿⣿⡇⠀⣿⣿⡇⠀⣿⣿⣿⣿⣿⢸⣿⣿⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠟⠁⠀⠸⠿⠇⠀⠸⠿⠇⠸⠿⠇⠸⠿⠿⠿⠃⠿⠿⠀⠿⠿⠀⠀⠹⠿⠿⠿⠟⠁⠀⠿⠿⠇⠀⠿⠿⠀⠿⠿⠾⠿⠿⠀⠀⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠆⠲⣶⠀⢶⠄⠰⠴⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[29A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀

⠀⠀⠠⣶⣶⣶⣶⣶⣦⣤⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀

⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣦

⠀⠀⠘⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⣿⣿⣿⣿⣿⣿⣯⣍⠭⣩⡧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢿⣿⠄⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡿⠿⣿⣿

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢿⣧⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣴⣶⣄⠀⠀⢠⣶⣶⣤⣤⡀⠙⢿⣿⣿⣿⣿⣠⣿⣿

⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⣹⣷⡀⢸⣿⣿⠿⢿⣿⣿⣿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠛⠋⠉⠉⠁⠉⠉⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣦⠸⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⣰⠚⠛⢿⡿⢸⣿⠇⠀⠀⠈⠛⠛⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⢡⣤⣼⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⠋⠻⣿⣿⣿⣿⣿⣿⣀⠀⠘⣿

⠀⠀⢸⣿⣿⣿⣿⣿⣿⠉⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⢿⣟⡛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣤⣠⣿⣿⣿⣿⣿⣿⠃⠀⠈⣿

⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡙⠻⣿⠿⠿⠿⠿⠿⠿⠅⠀⠀⠀⣻

⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣶⣿⣿⣶⣶⣶⣶⣶⣶⣶⠶⠀⠛

⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠿⠛⠛⠉⠀⠀⢀⣤

⠀⠀⠀⠀⠀⠀⠉⠈⢿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⣦⡀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢿⣿⣷⣶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠙⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣤⠀⣤⣤⣤⣤⣤⢠⣤⡄⢠⣤⡄⢠⣤⣤⣤⠀⣤⣤⣤⣤⡀⠀⠀⢀⣤⣶⣦⣤⠀⣤⣤⣤⣤⡄⠀⣤⣤⣤⠀⢠⣤⣤⣤⡄⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⡇⠀⢸⣿⡇⠀⢸⣿⣿⣿⣿⡇⢸⣿⣿⣿⠀⣿⣿⢿⣿⡅⠀⠀⠈⠻⢿⣿⣦⡀⠀⣿⣿⡇⠀⣸⣿⠏⣿⣧⢸⣿⣿⣿⠇⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⡇⠀⢸⣿⡇⠀⢸⣿⡇⢸⣿⡇⢸⣿⣇⣀⠀⣿⣿⠀⣿⣿⠀⠀⢰⣶⡆⢹⣿⡇⠀⣿⣿⡇⠀⣿⣿⣷⣿⣿⣸⣿⣿⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠟⠁⠀⠸⠿⠇⠀⠸⠿⠇⠸⠿⠇⠸⠿⠿⠿⠃⠿⠿⠀⠿⠿⠀⠀⠈⠛⠿⠿⠟⠁⠀⠻⠿⠇⠀⠿⠿⠀⠿⠿⠟⠿⠿⠀⠀⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠂⠲⣶⠀⠰⠄⠠⠰⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀

⠀⠀⠀⣶⣶⣶⣶⣶⣦⣤⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀

⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣷⣦

⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⣿⣿⣿⣿⣿⣿⣯⣍⠍⣩⡧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢿⣧⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣴⣶⣄⠀⠀⢠⣴⣶⣤⣤⡀⠙⢿⣿⣿⣿⣿⣤⣿⣿

⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⣹⣷⡀⢸⣿⣿⠿⠿⣿⣿⣿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠛⠋⠉⠉⠁⠉⠉⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣦⢸⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⣰⠚⠛⢿⡷⢸⣿⠇⠀⠀⠈⠛⠛⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢡⣦⣾⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⠋⠻⣿⣿⣿⣿⣿⣿⣁⠀⠘⣿

⠀⠀⢸⣿⣿⣿⣿⣿⣿⠉⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⢿⣟⡛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣤⣠⣿⣿⣿⣿⣿⣿⠃⠀⠀⣿

⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⠻⣿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⣻

⠀⠀⠀⠀⠀⠀⠉⠉⢿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⢿⣿⣷⣶⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⡇⠀⢸⣿⡇⠀⢸⣿⡇⢸⣿⡇⢸⣿⣇⣀⠀⣿⣿⠀⣿⣿⠀⠀⢰⣶⡆⢹⣿⡇⠀⣿⣿⡇⠀⣿⣿⣷⣿⣿⢸⣿⣿⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀

⠀⢸⣿⣿⣿⣶⣶⣶⣦⣀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀

⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀⠀⠀

⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣷⣦

⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠈⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢿⣿⣿⣿⣿⣿⣷⣆⢢⣼⣷⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⡀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡞⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠤⠀⠀⠀⠀⢠⣶⣶⣾⣿⣿⣿⣦⣘⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⡄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠈⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⢲⣦⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣿⣿

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⢀⣨⣿⣦⠀⠀⣿⣿⣿⣿⣿⣿⣟⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠈⠉⠙⠛⠁⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢰⣾⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣋⠉⢹⠿⠀⠀⣿⣿⠛⠛⠻⠛⠃⠀⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⠁⢸⣿

⠀⠘⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣾⣿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠘⣿

⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠳⢶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡇⠀⠀⢀⣿

⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣼⠟

⠀⠀⠀⠀⠈⠻⢿⢿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⣿⣿⠿⣿⠿⠿⠟⠛⠋⠉⠀⠀⢈⣥⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿

⣦⣀⣀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠈⠉⠛⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣤⡀⣤⣤⣤⣤⣤⢠⣤⡄⢠⣤⡄⢠⣤⣤⣤⠀⣤⣤⣤⣤⡀⠀⠀⢀⣤⣶⣦⣤⠀⣤⣤⣤⣤⡄⠀⣤⣤⣤⠀⢠⣤⣤⣤⡄⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⡇⠀⢸⣿⡇⠀⢸⣿⣿⣿⣿⡇⢸⣿⣿⣿⠀⣿⣿⢿⣿⡅⠀⠀⠈⠻⢿⣿⣦⡀⠀⣿⣿⡇⠀⣸⣿⠏⣿⣇⢸⣿⣿⣿⠇⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠟⠁⠀⠸⠿⠇⠀⠸⠿⠇⠸⠿⠇⠸⠿⠿⠿⠃⠿⠿⠀⠿⠿⠀⠀⠈⠛⠿⠿⠟⠁⠀⠻⠿⠇⠀⠿⠿⠀⠿⠿⠾⠿⠿⠀⠀⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                ䷩ 𝚕𝚒𝚗𝚎 2611

(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/01/02/sirius-open-source-microsoft-linkedin/#comments

Gemini version at gemini://gemini.techrights.org/2023/01/02/sirius-open-source-microsoft-linkedin/

Gemini_version_available_♊︎

✐ How_Sirius_Open_Source_Presents_Itself_in_Microsoft’s_LinkedIn⠀✐

Posted in Deception, Free/Libre_Software, Microsoft at 3:39 am by Dr. Roy

Schestowitz

🄸🄼🄰🄶🄴🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽⦇Totally_false;_Liability_dodge;_only_1_person_lives_there;

The_company_rewrites_its_history_too_(e.g._founder);_So_it_pretends_to_do

things_that_it_does_not;it's_a_middleman⦈

Summary: Sirius_‘Open_Source’ paints a misleading picture in Microsoft’s

LinkedIn; for instance, it says that “Sirius Open Source is a company based in

Washington, USA” (insiders know that only one or two people are based there;

maybe one, at most, is an American)

⣿⡟⠉⠉⠉⠉⠉⣿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⡇⢠⡄⡄⢤⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⡇⠘⠃⠃⠘⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢙

⣿⣿⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾

⣿⣿⠉⠉⠈⠉⠉⣿⣿⡇⠀⠋⡅⠹⠉⢹⡏⠤⡏⢙⠉⡏⢹⡇⠘⠉⠋⠏⢩⠩⡏⢹⡆⢏⢹⠩⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣷⣷⣷⣶⣾⣿⣶⣧⣾⣷⣷⣿⣷⣾⣶⣷⣶⣾⣷⣷⣾⣷⣿⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣏⡁⠩⠉⡍⢹⠉⣿⣿⣿⣿⣿⣿⣿⡟⣀⠇⢙⠩⡏⠏⠨⣿⣿⣿⣿⣿⣿⣿⡇⣠⠩⡉⢉⠌⢹⣿⣿⣿⣿⣿⣿⣿⢸⠩⡁⠍⠉⣿⣿⣿⣿⣿⣿⣿⡇⣠⠉⡉⢍⠩⡁⡉⢹⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠉⠉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉

⠀⠀⣿⣿⣿⡟⡻⢿⠛⢿⡿⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣿⣿⣿⣧⣥⣴⣤⣦⣧⣦⣤⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣿⣿⣿⡇⡆⣾⠔⡋⡋⡝⣹⠩⠉⠉⡟⠉⢩⡫⢸⠶⢰⣏⠶⠩⣯⠉⠉⢿⠈⢽⡍⠫⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣿⣿⣿⡿⠿⠿⡿⠿⡿⢿⢿⠿⢿⢿⠿⠻⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣏⠙⡻⢛⠛⠙⡻⢻⢋⠛⢹⢻⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣿⠁⣤⣤⣤⣤⣤⣤⣄⣤⣤⣤⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡌⣿⣿⢿⣿⠿⠟⠋⣉⣤⣴⣾⣿⣿⣶⣶⣶⣶⣶⣧⣿⣾⣶⣾⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣿⠀⣿⡏⢽⢹⢿⢝⡉⢫⢻⠛⢛⠛⢛⠋⢛⠻⡛⠛⢻⢻⣿⣿⡇⠟⠁⠀⢠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣿⡀⠛⠓⠚⠚⠓⠒⠒⠒⠛⠒⠚⠒⠐⠒⠒⠁⠓⠒⠚⠚⠛⠛⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣿⣿⣿⡏⢹⡏⠋⡝⡏⠏⣯⠃⠙⢙⠉⠭⣉⣿⡇⠀⢹⣿⡿⠟⠛⠉⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⢟⢻⠿⠻⡿⡟⣻⣿⢿⠿⠿⠟⢿⡟⠿⣿⠿⠿⡿⢿⠿⡿⠿⠿⢿⠿⡿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣷⣶⣤⣀⣰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣬⣽⣧⣜⣰⣧⣼⣧⣦⣮⣤⣧⣼⣧⣼⣿⣬⣧⣤⣼⣬⣬⣤⣿⣼⣥⣤⣧⣿⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⣿⣿⠛⠃⠁⠉⠉⠉⠁⠉⠋⠙⠉⠉⠈⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣿⣿⢸⡿⢿⢿⡿⡿⠿⢿⢿⡿⣿⣿⢿⠿⡿⠟⢿⡿⢿⠿⠿⠿⠿⣿⣿⡇⣿⠿⠛⠋⠉⠿⠿⠿⣿⠹⠉⠋⠉⠉⢉⢻⠋⠫⠋⠉⠙⠩⡟⢙⣽⡙⣿⢹⡯⠋⠋⠋⠋⢩⣿⢋⠛⠙⢹⠉⣽⠙⠙⢹⣿⣿⣿⣿

⠀⠀⣿⣿⢸⣧⣬⣥⣤⣧⣤⣼⣧⣤⣻⣧⣦⣧⣤⣤⣧⣧⣤⣁⣬⣤⣼⣼⣿⡇⣿⣶⣦⣄⣀⣶⣶⣶⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣾⣷⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣿⣿⣈⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣿⣿⣿⡏⠹⡛⠻⡟⠻⡋⠛⠛⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣿⣿⣿⣷⣿⣶⣶⣷⣾⣶⠷⠗⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣿⣿⣿⣷⣸⣀⣀⣃⣸⣤⣄⣀⣤⣤⣤⣤⣤⣤⣿⣿⣿⣷⣰⣎⣸⣗⣑⣵⣀⢀⣁⣷⠌⣿⣆⣈⣠⣄⣘⣈⣸⣀⣂⣿⣎⣁⣐⣊⡤⣹⣘⣪⣊⡇⣀⡃⢘⣷⣔⣝⣀⣀⣨⣨⣖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣿⣿⣿⡟⢻⠿⠟⠿⠟⠿⡿⢻⠿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣿⣿⣿⣧⣴⣤⣦⣦⣤⣤⣿⣼⣦⣤⣼⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣿⣿⣿⡏⠮⡯⠉⠙⡍⡯⠚⠍⠹⠉⡍⠈⠹⡏⠬⡻⠉⠍⠍⢹⠏⢩⠩⠈⣝⠍⢿⡇⠃⠋⢏⡹⠙⠉⡏⠋⢹⡇⠉⢹⣍⠃⠫⡋⡋⠹⡟⢹⡍⠫⣿⠁⡙⡉⡭⠉⣯⢩⣿⠈⣽⠝⢙⠍⢩⠉⡭⠈⢽⠉⣿⣿

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

⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠛⢻⡉⡟⠛⡛⢋⡛⠛⠛⢻⢻⡟⠛⡟⢻⠛⡏⢙⠋⠛⠛⠛⣟⠉⠻⢛⢻⠉⡟⢻⠛⠛⠛⡟⣻⠛⠙⣿⡛⡙⣿⠛⣟⢛⣿⠋⠋⠙⠛⣛⠛⢻⣻⣿⣿⣿

⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

                ䷩ 𝚕𝚒𝚗𝚎 2681

(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/01/02/talking-about-wrongdoing/#comments

Gemini version at gemini://gemini.techrights.org/2023/01/02/talking-about-wrongdoing/

Gemini_version_available_♊︎

✐ When_Talking_About_Wrongdoing_is_Considered_Impressible⠀✐

Posted in Deception, Finance, Free/Libre_Software at 2:15 am by Dr. Roy

Schestowitz

Video_download_link | md5sum 84f018c1290b8f233c66af03884b4fbc

Worker Isolation Tactics

Creative Commons Attribution-No Derivative Works 4.0

http://techrights.org/videos/gagging-of-workers-sirius.webm

Summary: Companies rarely/barely tolerate people who speak about wrongdoing,

whether it is done internally (to management or among colleagues) or externally

without naming anyone; at Sirius there has been a culture of gagging and

isolation, hoping to prevent clients and the wider public finding out what’s

truly going on, but it is time to break the silence

THE latest (and one before last) part of our report is just about the

thirtieth, focusing on how management at Sirius_‘Open_Source’ was trying to

prevent staff talking to one another. This strategy isn’t entirely unique and

there are several names for it.

“This strategy isn’t entirely unique and there are several names for it.”The

video above discusses what went on and why a witch-hunt began. Sirius ‘Open

Source’ is not Open Source and it has been doing unethical as well as illegal

things. It’s trying to prevent staff knowing about it and being able to discuss

such matters. But at the end there’s a bit of a Streisand_effect.

The saddest thing is, the company’s management also lies about itself. For

instance, one new boss was introduced as a person who had created a successful

company, however the public record indicates that this is either a dissolved

two-person company (failed and forcibly de-registered) or a one-man ‘company’

with barely any activity in it. Extravagant claims to impress the easily-

impressionable? If a one-person company is “successful” according to that one

person, does that even mean anything? Look what he has done to Sirius. The

company is shrinking into nothing (more ‘managers’ than technical people).

Big egos turns big companies into tiny boutiques with big debt. █

                ䷩ 𝚕𝚒𝚗𝚎 2743

(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/01/02/treating-staff-like-enemies/#comments

Gemini version at gemini://gemini.techrights.org/2023/01/02/treating-staff-like-enemies/

Gemini_version_available_♊︎

✐ [Meme]_Managers_Who_Attack_Their_Own_Company,_Treating_Staff_Like_Enemies⠀✐

Posted in Free/Libre_Software at 9:42 pm by Dr. Roy Schestowitz

Staff can be an asset, not a “resource”

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

Summary: With hardly_any_staff_left at Sirius_‘Open_Source’ (mostly absent

management and external contractors) it’s not even clear if such a company even

exists (there’s no office and it’s registered at the accountants’ address)

because most of the technical people left and that's_hardly_an_accomplishment

Of note: Twitter now suspends/bans Twitter accounts of former security staff,

preventing them from talking about Twitter. There are serious security

incidents.

⢰⣶⣶⣶⣶⡒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⡶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣶⣶⣶⣶⣶⣶⢴⣶⣶⣶⣶⣶⣶⣶⠆⠀⠀⠀⠀⠀⢲⣶⡆⠀⢲⣶⡆

⢸⣿⣦⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⣿⣟⢀⣤⣤⣴⣤⣶⠀⠀⠀⠀⣿⣿⣿⡿⠟⠛⠿⣿⣿⡿⠏⠀⢰⣿⣿⣿⡿⣿⣿⣿⣆⠋⠀⠀⠀⠀⠘⣿⡇⠀⢸⣿⡇

⢸⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⡿⠿⠁⠀⠀⠀⢻⣿⡄⠀⠀⣿⣿⡿⣿⣿⣩⣽⣿⣯⣀⡀⠀⠀⠀⢠⣾⣷⠀⢸⣿⡇

⢈⣩⣭⣿⣿⣿⣿⠀⣀⡀⢀⣾⠇⠀⠀⠀⢠⣶⡀⠀⠀⠀⣠⡿⠟⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠛⠉⠉⢻⣿⣿⡆⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⣿⣄⠀⠀⣿⣿⡇⣾⣿⣧⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⠉⠀⢸⣿⡇

⢨⣩⣭⣿⣿⣿⣿⣤⣿⣿⡆⢭⣿⣿⡁⠀⠀⢿⣇⠀⢀⠈⠁⠀⠀⠐⣯⠀⠀⢿⣿⣿⣿⣿⠃⠰⠂⠀⠀⠛⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠻⠟⠀⣇⣿⣿⡼⣿⣿⡿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇

⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣇⠀⠀⠸⣿⣦⡸⠀⠀⠀⠀⠀⢹⡄⠀⢸⣿⣿⣿⡿⣷⣶⣆⣆⣀⣸⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣆⠀⠙⠼⣿⣷⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡟⠉⠀⠀⠀⠀⣠⣤⡄⠰⠀⠀⠀⢘⠧⠘⢹⣟⣫⣀⣴⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣿⣿⠯⢀⣤⣂⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇

⠀⠈⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠄⠀⣀⣸⣿⣿⣷⣄⡀⠀⠀⣺⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠄⠀⠀⠀⠀⣠⣿⣿⣿⣿⡁⣾⣿⣿⣶⣶⠟⠀⠀⠀⢀⡀⢀⠀⢀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡯⣿⠀⠀⠀⢀⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣧⠀⠀⠀⢠⣾⣇⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⡦⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⡄⣿⠀⣀⣠⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⣬⣿⣓⣾⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⣰⣗⠞⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣯⣖⣶⣶⣧⡄⠀⠀⠀

⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣇⣊⣁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠙⠛⠛⠛⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀

⢰⣶⣦⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣿⣿⣿⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠛⢿⣿⣿⣿⣿⣿⠟⠋⠛⠛⠋⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠊⠀⠂⠀

⢸⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠉⣿⠙⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠿⢉⣿⣿⣿⣿⣿⣿⣽⡏⠀⠀⢠⡆

⢸⡿⠃⠀⢻⣿⣿⣿⣧⣿⠿⣿⣿⣿⡧⠀⢙⠀⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠏⠀⠀⠀⠀⢀⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⣟⣿⣻⢸⣿⡇⣠⣿⣿⣿⡟⠉⠩⠉⠁⠀⠀⢀⣿⡇

⢘⠁⡀⠀⢸⣿⣿⣿⡟⠛⠉⠀⠀⠉⠀⠀⠘⠤⢿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠹⠛⠀⠀⢀⣷⣾⣿⣿⣿⣿⣿⣿⣷⠀⢀⡀⠀⠀⢰⣿⣿⣧⣴⣷⣿⡟⣸⢻⣿⣿⣿⠿⠛⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇

⢸⣿⣿⡆⢸⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⣰⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⢠⣼⡿⣿⡇

⢸⣿⣿⠇⠘⣿⣿⣿⠛⠀⠀⠀⢀⢶⣦⠀⠀⠀⠀⣸⣿⠿⠛⠋⠈⠉⠙⠙⢻⣿⣿⣿⣿⣿⣿⣀⣄⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⢳⣽⡇

⢸⣿⣿⣀⡀⣿⣿⣿⣀⠀⠀⠀⠘⠸⢻⡅⠀⠐⢱⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠻⠿⣿⣿⣿⡟⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢀⡻⢟⡟⣟⣿⡇

⢸⣿⣿⠏⠁⢿⠿⢿⣿⡇⡄⠀⠀⠀⢸⣇⣤⣾⣿⡅⢀⣀⠀⠀⠀⠀⠀⠀⠀⣏⠃⠀⠀⢺⣿⡿⠁⠀⠀⠀⣿⣿⣿⣟⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢠⡟⢡⣷⣶⣷⣿⡇

⠸⠿⠶⣶⠿⢿⠿⠶⠾⠾⠷⠀⠡⠴⠿⠿⠿⠿⠿⠷⠼⠿⠿⠿⠀⠀⠀⠀⠀⠿⠄⠀⠀⠹⠟⠃⠀⠀⠀⠀⠈⠛⠟⠿⠿⠿⠿⠿⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠿⠃⠾⠿⠿⠻⠿⠇

[21A⢰⣶⡶⢶⣖⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣴⣶⣶⣶⣶⡶⠴⣶⣶⣴⣖⣶⢶⣶⡆⠀⠀⠀⢀⣶⠄⠀⠀⠀⠀⠀⠀

⢸⣿⣦⣼⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣴⣥⠚⢀⣤⣤⣤⣦⣶⠀⠀⠀⠀⢸⣾⣿⣿⠟⠛⠻⣿⣿⡏⠿⠁⢀⣿⣿⣏⣿⣿⣷⣿⣧⠃⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⣿⣿⣿⣿⣿⣟⢾⣿⣿⣿⣿⣿⡀⠀⠀⠀⢸⣿⣿⢧⣤⡀⠀⢹⣿⠅⠀⠀⢺⣿⣿⢻⣿⡈⢁⢿⣿⡀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀

⢨⣭⣭⣿⣿⣿⣿⠀⣀⣀⠀⣸⡇⠀⠀⠀⢠⣶⡀⠀⠀⠀⣠⣼⠿⠀⠀⠀⠀⢹⣿⣿⣿⢯⠧⠜⠉⠉⠹⣿⣿⡇⠀⠀⢀⣼⣿⣿⣿⡿⠷⢿⢾⣿⡅⠀⠀⣿⣟⠇⣼⣿⡇⠀⣻⣿⣇⠀⠀⠀⠀⢰⣿⣿⡧⠀⣾⡆

⢨⣭⣭⣿⣿⣿⣿⠠⣾⣿⡆⠈⣿⣿⠀⠀⠀⢿⣧⠀⠀⡀⠁⠀⠀⠀⢫⠀⠀⢸⣿⣿⡟⠠⣤⣴⣴⣶⣾⣿⣷⣦⣄⣠⡾⠟⠁⠈⠉⠀⠀⠀⠀⠈⠀⠀⠀⢻⣿⡔⢩⣿⣿⢴⣿⣿⠏⠀⡀⠀⠀⠟⠋⠁⠙⣿⠈⠀

⠘⢿⣿⣿⣿⣿⣿⣧⣿⣿⣇⢰⣿⣿⣇⠀⠀⠸⢿⣧⡠⠁⠀⠀⠀⠀⢸⡆⠀⢸⣿⣿⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣿⠛⢻⠜⠉⠁⠀⠄⠀⠀⣴⣶⣄⣀⣤⣿⡆⠀

⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡟⠁⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠐⡳⠄⢺⣿⠉⠀⢸⣿⣿⣿⣿⣿⣿⡿⢫⠇⠀⠀⢠⣄⣀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠁⠀⢸⡆⣠⠀⢀⠰⠀⢺⣿⣿⣿⣿⣿⣿⣷⡇

⠀⠀⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢠⣿⣿⣿⣦⣀⠀⠀⣸⣿⣶⣶⣿⠀⠀⢈⣿⣿⣿⣿⣿⣿⣻⣾⣿⠀⣰⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠘⡄⠀⢸⣷⣿⣠⣰⡀⠀⢘⣿⣿⠉⠁⣈⣀⡈⠃

⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡏⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣾⠇⢸⣿⣿⣿⣿⠟⢿⡿⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣰⣶⣿⣧⣿⣷⣾⠀⠀⠘⣿⡇⣠⣿⣿⣿⣿⠁

⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣿⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⣿⣿⠁⢲⡦⠄⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⡴⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⢴⣦⠤⣟⣿⣿⣿⠏⠉⠋⠀

⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⡎⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠁⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠃⠀⠀⠸⠟⠁⠀⠀⠀⠀

⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠸⣧⠀⠀⣿⣿⡿⠟⠛⠉⠉⠀⠈⠹⣟⣿⣿⣿⣿⣿⣻⣭⣶⣶⣤⣤⠄⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢀⣠⣾⣾⣦⠀⠀⠀⠀

⢰⣶⣶⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣽⣴⡴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡟⠶⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⠿⠉⠉⡀⠀⠀⠀

⢸⣿⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠙⠉⠁⠀⣠⣤⣤⣀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢀⣶⠈⡀

⢸⡿⠀⠀⢸⣿⣿⣿⠟⠸⠿⣿⣹⣿⡷⠀⠀⠀⢀⣀⣿⣿⣿⡿⢀⠀⠀⠀⠨⢉⣿⣿⣿⣿⣇⣀⡀⠀⠀⠀⠀⢀⣾⡇⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢠⡾⢁⣼⡇

⢈⢁⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣏⣋⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⣾⣿⡃⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⡟⢀⣿⣿⡇

⢸⣿⣿⡄⠈⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠀⠀⠀⠀⠀⣾⣿⢿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢹⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⡾⢱⣾⣿⣿⡇

⢸⣿⣿⠇⠀⣇⣠⣀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⢀⣸⣿⣿⠟⠿⠂⠀⠀⠀⢠⡇⠀⠈⣿⡟⠀⠀⣀⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣡⣿⣿⣿⣿⡇

⢸⣿⣿⣀⡀⣿⡿⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⣶⣿⣿⣿⡇⠀⡀⠀⠀⠀⠀⣼⠿⡄⠀⠘⢿⣦⣺⡻⣿⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠟⣿⣿⣿⣿⢡⣿⣿⣿⣿⣿⡇

⢸⣿⠿⠏⠁⢿⠿⢦⣶⠄⠀⠀⠀⣾⣆⣤⣴⣿⣿⣿⣿⣿⣆⡇⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠙⣿⡉⠩⡆⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡙⣿⣿⣿⣿⢿⡿⠉⠉⠀⠀⠙⢿⣿⣧⣾⣿⣿⣿⣿⣿⡇

⠸⠷⠶⣶⠏⢷⠷⠶⠶⠶⠆⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠛⠿⠇⠀⠆⠀⠾⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠁⠀⠀⠀⠿⠿⠿⠿⠃⠿⠿⠿⠿⠿⠿⠿⠿⠻⠇⠈⠋⠙⠃⠀⠲⠐⠀⠀⠀⠀⠸⠿⠿⠿⠿⣿⡿⠿⠿⠇

[21A⢰⣶⡶⠶⢖⡒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⡶⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣴⣶⣶⣶⣶⣶⣴⣶⣶⡠⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⢰⡶⠆⠀⠀⠀⠀

⢸⣾⣦⣼⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣧⣤⡀⠀⣠⣤⣤⣦⣴⡆⠀⠀⠀⢸⣿⣿⣿⡿⠛⠛⠋⠋⠁⠁⠀⠈⠛⠛⠃⢿⢿⣷⣿⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⢸⣿⣿⣟⡛⢷⢺⣿⣿⣿⣿⣿⡇⠀⠀⠀⠘⣿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢡⣿⣿⡄⠄⠀⠀⠀⠀⠆⠀⢀⣤⡄⠀

⢨⣭⣭⣿⣿⣿⣿⠀⣀⣀⠀⢸⡇⠀⠀⠀⢠⣴⡄⠀⠀⠀⢠⣼⠿⠀⠀⠀⠀⢸⣿⣿⣿⢖⠾⠜⠉⠉⠙⣿⣿⡷⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆

⢈⣩⣭⣿⣿⣿⣿⡀⣾⣿⣆⠠⣽⣿⡇⠀⠀⢻⣷⠀⠀⡀⠀⠀⠀⠀⢺⠄⠀⢸⣿⣿⣿⠀⠱⣴⣶⣶⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⢰⣾⣿⣿⣿⣷⣶⣦⠀⠀⠀⠀⠀⠀⠀⣿⣿⠏⠁⠀⠀⠀⠀⠀⠘⠋⠁⠐⠃

⠘⠿⣿⣿⣿⣿⣿⣥⣿⣿⣟⠀⣿⣿⣇⠀⠀⠘⠿⣧⡀⠇⠀⠀⠀⠀⠀⡇⠀⢘⣿⣿⣿⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠉⡀⠀⠄⠀⠀⠀⠀⢀⣾⣷⣠⣤⡄

⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⡿⠋⠀⠀⠀⠀⢀⣠⣤⠀⠀⠀⠀⠀⡻⠄⠊⣿⡉⠀⠀⠘⣿⣿⡿⢿⣿⡿⠋⠋⠛⠇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⠀⠀⠀⠀⣠⠀⢀⠰⠂⠁⠈⠈⢹⣿⣿⣿⣿⡇

⠀⠀⠉⠙⣿⣿⣿⣿⣿⣿⣿⣷⣿⠃⠀⠀⠀⠀⢀⣿⣯⣿⣦⣀⠀⠀⢐⣿⣶⣦⣿⡀⠀⠀⢀⣿⣿⣿⣿⣿⣷⣿⣿⣿⠀⢸⡇⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠀⠀⠀⣴⣿⣿⣿⣶⡆⠁⠀⠐⠊⣿⠋⠁⣀⡀

⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡟⢹⡅⠀⠀⠀⠀⠘⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣷⣀⣄⣼⡇⣿⣿⣿⠛⠋⠉⠛⣿⠷⢼⣷⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢁⣠⣴⣾⣿⣿⣿⣿⣿⣇⠈⠀⠀⠈⠁⠀⣼⣿⡇

⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣼⡇⠀⠀⠀⠀⢨⡿⠋⠁⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⢿⣿⠃⠈⠿⡟⠀⠰⠲⠀⠀⠀⠀⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠈⠉⠀⠈⠛⠟⠁

⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⡄⠀⠀⢀⠀⢀⣀⣀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣯⠻⣷⣀⡀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢹⣿⣿⣿⡿⠿⠿⠿⣿⣧⠘⣷⢀⠀⣺⣶⣿⣿⣿⣧⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣉⠰⢾⣷⡶⣶⣖⣠⣼⣿⠋⠘⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⢀⣠⣤⣄⠀

⢰⣶⣶⣦⢸⣿⡿⠛⠀⠀⠀⠀⠀⠨⣄⣸⢥⡂⢿⣿⣿⣿⣿⢔⡲⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⠠⣀⠩⠛⠻⠿⠿⠛⠉⠀⠀⣀⣀⣠⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣯⣽⣿⡇

⢸⣿⡿⠁⢾⣿⡇⠀⠀⠀⠀⠀⠀⠀⡏⠀⢉⠁⢠⣿⢿⣿⣿⡇⠁⠂⠀⠀⠈⢹⣿⣿⣿⣿⣿⣟⠀⠀⠒⡂⠀⠀⠀⢀⣤⠀⢀⡋⣹⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣼⠃

⢸⠟⠀⠀⢸⣿⣧⣀⠀⠀⠀⠀⠀⠀⣷⠀⠈⠀⢸⣽⣾⣿⣿⣿⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣶⣶⠀⠀⠀⢀⣾⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡰⣁⡆

⢀⠀⣀⠀⠘⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⡟⠁⠙⠁⠀⠀⣶⣿⣿⣿⣿⣿⣿⣻⣿⡿⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣰⣿⡇

⢸⣿⣿⡄⠀⣿⣿⣿⠴⡶⠀⠀⠀⢰⡄⠀⣶⣿⣿⣿⣿⣿⢀⡆⠀⠀⣀⣸⣿⣿⡏⠉⠉⣷⣿⠛⠀⠀⠀⠀⠀⢿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣽⣿⣿⡇

⢸⣿⣿⠇⠀⣿⣿⣿⣿⠀⠀⠀⠀⠸⣷⣾⣿⣿⣿⣿⣿⣿⢸⢧⣿⣿⣿⣿⣿⣿⣿⣄⡀⠉⣟⣀⠤⣶⡆⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣟⣾⣿⣿⣿⡇

⢸⣿⣯⣀⣀⢹⣿⣿⣿⠀⠀⠀⣆⡀⣿⡿⠻⣿⡿⠋⠙⡁⢼⢸⣿⣿⣿⣿⣿⣿⣯⠀⠁⠀⠙⢿⡵⠉⢿⡀⠀⠀⠀⢻⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⠙⠿⠿⣿⠋⠉⠁⠀⠀⣿⡟⣾⣿⣿⣿⣿⡇

⠀⠹⠿⠟⠉⢸⣿⣿⣿⣧⣤⣠⣿⣿⣇⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⡝⣿⣿⣿⣿⣿⣦⣄⡀⠀⠈⠹⡂⠠⡇⠀⠀⠀⢈⠉⠛⠛⢿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⡇

⠀⠆⠶⣶⠍⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠦⠀⠴⠶⠆⠀⠧⠙⠈⠿⠧⠿⠿⠿⠿⠿⠿⠿⠗⠀⠀⠀⠀⠠⠇⠀⠀⠀⠿⠇⠀⠀⠀⠀⠀⠀⠀⠿⡿⣿⠿⠿⠿⠿⠧⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠽⠿⠿⣿⣿⠿⠿⠇

[21A⢰⣶⡶⠶⠖⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⡦⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⠀⠀⣶⡆

⢸⣾⣦⣤⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⣀⠀⠃⣠⣤⣤⣶⣴⣆⠀⠀⠀⠀⣷⣿⣿⠟⠛⠛⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡄⠀⠟⠁

⢸⣿⣿⣿⣿⣿⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⢸⣿⣿⣿⡇⠂⢰⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⠿⠋⠀⠀⠀⠀⣿⠇⣴⣶⣶⣶⣶⣄⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⡇⢰⠀⠀

⢨⣭⣭⣽⣿⣿⣿⡀⢀⣀⠀⢰⡏⠀⠀⠀⢀⣴⡆⠀⠀⠀⢀⣠⠿⠃⠀⠀⠀⠘⣿⣿⣿⠈⠀⠌⠋⠉⠉⢿⣿⣿⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣹⣜⣿⣿⣿⣯⣤⣴⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⡀

⢈⣩⣥⣽⣿⣿⣗⠀⢰⣿⣷⠀⢹⣿⠀⠀⠀⢻⣿⡀⠀⢀⠈⠀⠀⠀⠐⠀⠀⠀⣿⣿⣿⠀⠀⠀⢰⢶⣶⣶⣿⣿⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣯⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇

⠘⠻⣿⣿⣿⣿⡏⡑⣸⣿⣿⡀⢾⣿⣇⠀⠀⠸⢿⣧⣐⠁⠀⠀⠒⠀⠀⡆⠀⠀⣿⣿⣿⠴⠲⠲⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢨⡁

⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⡿⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⣿⠉⠀⠀⠀⠁⠘⣿⣿⣿⣿⣿⡿⠋⠿⢿⡇⠀⠀⠀⣀⣾⣿⣿⣿⣿⣛⣉⠉⠛⠿⣿⡿⡿⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢠⣿⡇

⠀⠀⠈⠉⣿⣿⣿⣿⡿⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣀⠀⠀⠀⠀⢀⣷⣶⣿⡅⠀⠀⠀⠀⢀⣿⣿⣤⣔⣿⣤⣴⣶⡄⠀⣠⠀⣰⣿⣿⣿⡃⢸⡇⣈⣠⡀⠀⢾⠋⠀⢀⣀⣀⣀⣠⣿⣿⣿⣷⡒⠀⠀⢸⣿⠇

⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⠀⠀⠀⠀⢸⣿⣿⣿⣷⣄⣀⠠⣠⣿⠀⣿⣿⡿⠿⠛⠻⣿⡷⠀⠃⠘⡻⣿⣿⣿⠃⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠈⡇⠀

⠀⠀⠀⠀⣹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⣿⣿⣿⡀⠙⠓⠀⠀⢸⣿⣿⣿⡿⣿⡅⠀⣿⡟⠀⠹⣿⠃⠈⣁⣀⠈⠁⠀⢃⣀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢣⡄

⠀⠀⠀⠀⢸⣿⣿⣿⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣇⠀⠀⠀⠀⠈⢹⣿⣿⣧⣿⣧⠀⠙⣷⡄⠀⠈⠀⠛⠛⠃⠀⠀⢀⣠⣿⣿⣶⣶⣦⣄⡄⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠘⡇

⠀⠀⠀⠀⢸⣿⣿⣏⢻⠃⠀⠀⠀⠀⠀⢰⣤⡀⢸⣿⣿⣿⣿⡇⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣆⣤⠐⣦⣬⣤⣄⣀⡀⡀⠀⢀⣼⠿⣻⣿⣿⠏⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠁

⢰⣶⣶⣦⢸⣿⣿⣧⣏⠀⠰⠆⠀⠀⠀⢸⣿⣿⣾⣿⣿⠀⠘⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠁⠈⠻⠛⠫⣽⣿⣶⣿⡿⠃⠀⠉⢉⣉⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀

⢸⣿⡿⠁⢸⣿⡧⣾⣇⣿⣇⠀⠀⠀⣤⣾⣿⣿⡟⣿⣿⢀⠀⢀⡀⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠘⠆⠀⠉⠉⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⡇

⠀⠈⠀⠀⠈⣿⣿⡿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣟⣻⣼⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠁⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁

⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠟⠉⢀⣾⣿⣿⣿⠟⠻⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡷⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⡄

⠀⠀⠀⣠⣤⣿⣿⣿⣿⣿⣿⣯⠀⠀⠊⠉⢻⣿⠇⠀⠀⡄⢸⣿⣿⢻⣿⣿⣿⣿⣿⡿⠟⠛⣋⣸⣿⣿⠋⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡟⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣼⡇

⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⠀⠀⠀⠁⣀⠀⠀⢃⢸⣿⣿⣾⠛⢿⣿⣿⣿⣧⡀⠀⠹⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠻⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣟⣿⣿⣿⣿⣿⢿⣿⡇

⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣴⣿⣿⣿⣆⠈⡀⣿⣿⣿⠆⢰⣿⣿⣿⠟⠛⠦⠀⠨⣄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⠟⠀⠀⢠⠉⠉⢹⣿⡿⣿⣿⣿⡇

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢡⢻⣿⣿⣾⣿⣿⣿⣿⣧⠀⠀⠀⠀⠘⠢⡀⠀⠀⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣾⠂⠀⠙⠏⢠⣿⣿⣿⡇

⠸⠿⠿⣿⠿⢿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⡿⢿⠷⠄⠨⠸⠿⠿⠇⠬⠥⠽⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣿⣿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠺⠯⠼⢿⣿⠿⠇

[21A⢰⣶⡶⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴⣶⣶⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⡀⠀⣶⡆

⢰⣶⣦⣤⣦⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⢠⣤⣤⣴⣴⣶⠀⠀⠀⠀⢻⣿⣿⡟⠛⠛⠻⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡅⠀⣿⡇

⢸⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⢺⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⠟⠛⠀⠀⠀⠀⢻⣿⠤⢀⣾⣿⣷⡷⠦⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣲⡇⢀⡿⠃

⢈⣩⣩⣽⣿⣿⠈⠀⢀⣀⡀⠀⡿⠀⠀⠀⢀⣴⣆⢀⠀⠠⠤⠶⡿⠃⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠋⠉⠉⠻⣿⣿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⣿⡀⣸⣿⣿⣿⣶⣶⣾⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀

⢈⣁⣤⣬⣿⣿⡆⠀⢰⣿⣷⣀⣸⣿⠀⠀⠀⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⢀⢶⣲⣾⣿⣿⣷⣶⣦⣀⠀⠀⠀⠀⠀⠀⠈⠻⠇⢸⣿⣿⣿⣧⢠⣻⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠘⠛⠛⢿⣿⣿⡷⢠⣼⣿⠛⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠴⠒⠓⠒⢺⣷⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣠⣰⡄⣾⣿⣿⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⢰⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⡄⠀⠀⠀⠀⠀⠠⠀⠂⣿⡏⠀⠀⠀⠀⠀⠀⣿⣿⡿⠿⢿⡿⠋⠛⢿⡇⠀⠀⠀⢴⣿⡿⠛⠀⢹⡏⠠⠤⠀⠈⡙⢿⠿⠿⠃⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡇

⠀⠀⠈⠉⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⡗⠀⢀⠀⠀⠀⠀⣲⣶⣶⣾⡇⠀⠀⠀⠀⠀⢀⡿⣿⣄⣀⣸⣅⣠⣤⡄⠀⣤⣤⡾⣿⣿⡇⠀⡄⠻⢀⣤⣴⣄⣀⣰⣀⣀⣀⣤⣤⣤⣴⣿⣿⣿⣦⠀⠀⢠⡇

⠀⠀⠀⠀⢸⣿⣿⣿⣿⡢⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⠀⠙⠁⠀⠀⢿⣿⣿⣿⣿⣿⣄⡀⠠⠀⣠⣾⠀⣽⣿⡿⠟⠛⠛⣿⡇⠀⠒⢛⠲⠽⡿⠃⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⡇

⠀⠀⠀⠀⢸⣿⣿⣿⡿⠗⠂⠀⠀⠀⠀⠀⠀⠀⢿⡿⣻⡖⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⡟⠀⠸⣿⠇⠀⣉⠀⠀⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠸⡇

⠀⠀⠀⠀⢸⣿⣿⣿⣾⣿⡀⠀⠆⠀⠀⠀⢰⣦⣸⣿⠿⡯⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣼⣷⠀⠀⠙⢷⡄⠀⠈⠀⠘⠛⠃⠀⠀⠀⢠⣿⣷⣶⣶⣦⣤⡀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠐⠃

⠀⠀⠀⠀⢸⣿⣿⣟⣯⢽⣿⡆⠀⠀⢀⣀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣇⢠⣄⠰⣢⣬⣤⣄⣀⠀⠀⠀⢀⣴⠟⢻⣿⣟⠉⠉⣉⣭⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀

⠀⠀⠀⠀⠘⣿⣏⡉⡘⣾⣿⣧⣤⣤⣿⣿⣿⠻⣿⡇⠀⠀⣠⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⡿⢿⣏⠉⠂⣛⠿⠛⠩⣽⣯⣶⣶⡟⠁⠀⠈⣩⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⠀⠀⠀⢠⣾⣿⣿⣶⣻⣿⣿⣿⣿⣿⣿⣗⣛⣾⣈⡟⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡇⠀⠀⠀⠲⠀⠈⠈⠉⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀

⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣿⣿⣿⠛⠙⠿⠻⢀⣿⣷⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀

⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠘⠛⢿⠿⠂⠀⠀⠆⠸⣿⣿⢈⣿⠗⣿⣿⣿⣿⣿⣻⣿⡿⡿⢿⣿⣦⣶⠆⠀⠀⠀⠀⣀⣿⡀⣼⣿⣿⠟⠉⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆

⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣿⣿⣿⣇⠀⢸⣿⣿⣿⣯⠈⠋⠀⠀⢰⣿⣿⠋⠀⠀⠀⠀⠀⠈⣿⡇⠙⢯⣃⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣄⣀⣠⣤⣰⣤⡀⠀⠂⢻⣿⣿⡇⠄⣿⠟⠛⠛⠇⠀⠀⠀⢺⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠈⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⡀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⢌⡿⠟⠁⢀⣤⣤⠀⠀⠀⠀⠆⣄⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢳⣿⡿⠗⠹⣷⠆

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣽⣿⢢⣶⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱⢀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢿⣿⠀⠀⠐⣿⡆

⠸⠿⠿⣿⠿⢿⠿⠿⠿⠿⠿⠋⠿⢿⣿⡿⠿⠿⠿⠧⠠⠿⠿⠃⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⣿⣿⣿⣿⠿⣿⣿⢿⠿⠿⠿⠿⠇⠰⠿⠟⠁⠀⠸⠿⠇

[21A⢰⣶⡶⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴⣶⣶⢰⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄⠀⣶⡆

⢰⣶⣦⣤⣄⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⠀⣠⣤⣤⣴⣴⣶⠀⠀⠀⠀⢻⣿⣿⡟⠛⠛⠻⣿⣿⠸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡁⠀⢿⡇

⢸⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠐⣾⣿⣿⡟⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⠿⠛⠀⠀⠀⠀⢹⣿⠀⠐⠂⣠⣿⣶⣶⠶⠄⢄⡀⠀⠀⠀⠀⠀⠀⠀⢶⡇⠀⢸⡇

⢈⣩⣭⣭⣿⣿⠀⠀⢀⣀⡀⠀⡟⠀⠀⠀⢀⣴⣦⠴⠒⠒⠦⢶⡿⠃⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠋⠉⠈⠻⣿⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⣯⣿⣿⣷⡶⣶⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀

⢈⣁⣤⣼⣿⣿⡄⠀⢰⣿⣷⣀⣨⣿⠀⠀⡼⠛⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⣐⠒⣾⣿⣿⣿⣿⣷⣢⣀⠀⠀⠀⠀⠀⠈⠻⠇⠀⣯⣿⣹⣿⣇⡐⢀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠘⠛⠛⠻⣿⣿⡷⢀⣼⣿⠟⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠴⠒⠒⠂⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣀⡀⠀⠀⢹⣿⣿⡟⢻⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠰⣼⣿⣿⣷⣶⡍⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣴⠄⠀⠀⠀⠀⠀⠠⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⢸⣿⡿⠿⠿⣿⠏⠉⠙⢿⠀⠀⠀⣰⣿⡻⠃⠀⠀⢸⡟⢁⣤⠀⠉⢻⣿⣿⢿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠉⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣿⠉⣹⠁⠀⡀⠀⠀⠀⠀⣰⣶⣶⣼⡇⠀⠀⠀⠀⠀⠀⣼⢿⣇⣀⣠⣿⣄⣄⣠⠀⠠⣤⠿⣿⣿⡇⠀⡄⠀⠀⢇⣠⣤⣀⣀⣈⣁⣀⣁⣀⣀⣄⣠⣿⣿⣶⣦⡀⠀⡄

⠀⠀⠀⠀⠀⠙⣿⣿⣟⣸⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠆⠈⠋⠀⠀⠚⢻⣿⣿⣿⣿⣿⣄⡀⡀⠀⠀⣾⡏⠸⣿⣿⠟⠛⠉⠛⢿⠇⠀⠻⠛⢟⣿⠇⠀⠀⠀⠀⠘⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⡇

⠀⠀⠀⠀⠀⢠⣿⣿⡟⠋⠁⠀⠀⠀⠀⠀⢀⠸⣿⠓⣒⡀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⠃⠀⠻⡿⠀⢩⣥⠀⠀⠀⠀⢁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⡇

⠀⠀⠀⠀⠀⠸⠻⣿⣿⣷⡀⠘⠃⠀⠀⠀⣤⣤⣿⠿⠯⠁⠀⠀⣠⣼⣿⣿⣿⣿⣿⣯⣼⣷⠀⠀⠀⠙⠷⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⣼⣿⣷⣾⣶⣶⣤⡀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠐⠀

⠀⠀⠀⠀⢀⣀⣷⣯⡺⢻⣿⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣇⢠⣤⡆⠉⣤⣶⣶⣤⣀⣀⠀⠀⣠⠾⢋⣽⣿⠏⠉⠉⠩⣉⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀

⠀⠀⠀⣴⣿⣿⣿⣿⣞⣻⣿⣇⢀⣀⣶⣿⠘⢿⡆⣀⠀⢀⣄⣀⣴⣼⣿⣿⣿⣿⣿⣿⣿⡿⢿⣯⣄⠈⢙⡟⢋⡁⢬⣵⣶⣶⠿⠁⠀⠈⢉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀

⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣙⣓⣤⣹⣘⡇⢸⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⣾⣿⣿⠀⠀⠀⠲⠂⠀⡤⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆

⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⣵⣿⣿⣛⠉⠘⠟⠁⢸⡇⣿⣿⣾⠽⣿⣿⣿⣿⣿⡷⣾⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠛⠻⠯⠟⠀⠀⢰⠀⢸⣿⣇⢀⣻⠀⣿⣿⣿⣿⣿⡇⣿⡿⠛⠻⢿⣧⣾⠇⠀⠀⠀⠀⣀⣾⠀⠀⣿⣿⣿⠛⠉⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢸⣿⣿⣿⡇⠀⣸⣿⣿⣿⣿⠄⠉⠀⠀⢀⣿⡟⠁⠀⠀⠀⠀⠀⠙⣿⠀⠀⠻⢿⣁⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣦⣀⣀⣀⣀⣀⠀⠘⣷⢸⣿⣿⣿⠁⣐⠟⠋⠉⠙⠛⠀⠀⠀⠸⣿⠏⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠉⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠙⢸⣏⣿⡛⠀⣠⣶⠆⠀⠀⠀⠀⠐⢠⡀⠐⣆⠀⠀⠀⠀⠀⠀⠀⠰⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣼⣿⠟⢿⡆

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⣿⡿⠅⠟⠛⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⠀⠀⣠⠀⠀⠀⠀⠿⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢘⣻⠁⠀⠸⠃

⠸⠿⠿⣿⠿⢿⠿⠿⠿⠿⠿⠋⠻⠿⠿⠿⠿⠿⠿⠀⠛⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⡿⠿⢿⣿⣿⣿⣿⡿⢿⡿⠿⠿⠿⠿⠀⠚⠛⠁⠀⠄⠄

[21A⢰⣶⡶⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴⣶⣶⢰⣶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡄⠀⣶⡆

⢠⣶⣦⣤⣬⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⣠⣤⣤⣴⣴⣶⠀⠀⠀⠀⢻⣿⣿⡟⠛⠛⠻⣿⣿⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡁⠀⢿⡇

⢸⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠐⣾⣿⣿⡏⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⠿⠛⠀⠀⠀⠀⢻⣿⠀⠀⠐⢀⣾⣷⣶⡺⠴⠀⣀⠀⠀⠀⠀⠀⠀⠀⢶⡇⠀⢸⡇

⢈⣩⣭⣽⣿⣿⡀⠀⢀⣀⡀⠀⡟⠀⠀⠀⢀⣴⣦⠴⠂⠒⠦⣶⡿⠃⠀⠀⠀⢸⣿⣿⡯⠀⠀⠀⠋⠉⠈⠻⣿⣿⠄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⣸⣿⣿⣿⣶⣶⣾⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠀

⢈⣁⣤⣼⣿⣿⡇⠀⢰⣿⣷⣀⣸⣿⠀⠀⡼⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⢠⡋⢽⣿⣿⣿⣿⣿⢲⣄⡀⠀⠀⠀⠀⠈⠻⠇⠀⡄⣿⣏⣿⣿⡀⢂⣹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠘⠛⠛⠻⣿⣿⡗⠀⣼⡿⠛⠓⠂⠁⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠔⠒⠒⠂⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⡀⡀⠀⠀⠁⣿⣿⣿⠛⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢐⣼⣿⣿⣷⣶⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⠄⠀⠀⠀⠀⠀⠠⠀⠀⢿⡏⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠿⣿⠟⠁⠉⠻⠇⠀⢀⣰⣟⣻⠃⠀⠀⠀⢿⠋⣠⡤⠀⠙⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠈⠉⠀⠉⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠙⣿⠁⠀⠀⠀⠀⠀⠀⣴⣶⣶⣼⡇⠀⠀⠀⠀⠀⠀⣰⠟⣷⣀⣀⣾⣤⣠⣤⡄⠀⣴⡟⣿⣿⡇⠀⠄⠀⠀⠘⣀⣤⣀⣀⣀⣉⣀⣉⣀⣀⣠⣀⣼⣿⣷⣶⡄⠀⠀

⠀⠀⠀⠀⠀⠉⣿⣟⡃⡇⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠀⠘⠉⠀⠀⠛⢻⣿⣿⣿⣿⣿⣄⡀⡠⠀⠀⣴⣏⠀⣿⣿⠟⠛⠋⠙⠻⠇⠀⠛⠍⠿⡛⠇⠀⠀⠀⠀⠀⢻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡇

⠀⠀⠀⠀⠀⢠⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⡀⢹⣿⠿⠶⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⠃⠀⠙⢿⠀⠨⠥⠄⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠃

⠀⠀⠀⠀⠀⠸⢻⣿⡷⣦⠀⠒⠀⠀⠀⠀⣤⣠⣿⣾⠿⠁⠀⠀⢀⣰⣿⣿⣿⣿⣿⣯⣼⣷⠀⠀⠀⠉⠿⠀⢀⠀⠀⠁⠀⠀⠀⠀⠀⣰⣿⣷⣶⣶⣶⣦⣀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⠀

⠀⠀⠀⠀⣀⣀⣷⣭⠯⢿⣧⠀⠀⠀⠀⢀⣿⡿⠁⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢠⣤⡄⠈⢥⣶⣶⣤⣄⣀⡀⠀⢀⡾⠛⣹⣿⠟⠉⠈⢉⣉⣱⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀

⠀⠀⢀⣴⣿⣿⣿⣿⣶⣺⣿⡀⠀⢀⣤⣿⢹⣿⡄⢰⠀⠀⡀⠀⣠⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣁⠈⠛⡛⢻⡍⢠⣵⣶⣶⡾⠋⠀⠈⠉⣁⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄

⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠟⢒⣀⣣⢹⡄⢨⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣼⣿⣿⠃⠀⠀⠰⠇⠀⢤⡀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣹⣿⣿⠟⠉⠻⡟⠃⢸⡏⣿⣿⣽⢹⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠁⠀⠀⡄⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠠⠟⢿⣿⡧⠀⠀⠀⠀⢸⣧⡏⠛⣿⠀⣿⣿⣿⣿⣿⡏⢹⣿⠟⠛⢿⣧⣶⠆⠀⠀⠀⠀⢀⣾⡇⠀⢸⣿⡿⠟⠋⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠈⠀⠀⠀⣶⠀⢸⣿⣷⣼⡏⠀⢹⣿⣿⣿⣿⡃⠘⠁⠀⠀⣾⡿⠋⠀⠀⠀⠀⠀⠘⣿⡃⠀⠸⢿⣃⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⡄⠀⠀⠀⠀⠀⠀⢹⣇⢸⣿⣿⣿⠃⢀⡾⠛⠛⠻⣿⠀⠀⠀⠀⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢷⢺⣛⣿⢷⠈⢉⣤⠀⠀⠀⠐⠀⠀⢀⡀⠀⢦⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢓⣽⣿⡿⢿⡆

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣠⣾⡿⠉⠶⢾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⠀⢠⠀⠀⠀⠀⠿⠁⠀⠀⠀⠀⠀⠀⠀⠄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢈⣻⡋⠀⡜⠃

⠸⠿⠿⣿⠿⢿⠿⠿⠿⠿⠿⠏⠻⠿⠿⠿⠿⠿⠿⠀⠿⠃⠡⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠿⠿⣿⣿⣿⣿⡿⡿⢿⠿⠿⠿⠿⠀⠘⠿⠋⠀⠐⠄

[21A⢰⣶⣶⡶⠖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣦⢰⣶⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⣶⡆

⢨⣽⣦⣀⣠⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⢀⣀⣠⣤⣤⡄⠀⠀⠀⠀⣷⣿⣿⡿⠛⠻⢿⣿⣿⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢿⡇

⢸⣿⣿⣿⣿⣯⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠰⣾⣿⣿⡏⠀⠀⠀⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢻⡿⠟⠁⠀⠀⠀⢻⣿⠀⠀⢠⡆⢀⣶⣶⣶⣶⣤⢠⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇

⢈⣉⣉⣻⣿⣿⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⢀⣠⣄⣀⣀⣤⣄⣤⣿⠇⠀⠀⠀⢹⣿⣿⣧⠀⠀⠀⠛⠋⠉⢿⣿⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⣯⠀⠀⠀⠀⣞⣿⣿⣯⣥⣤⣤⣷⡀⠀⠀⠀⠀⠀⠀⠁⢀⠌⠀

⢈⣉⣉⣹⣿⣿⡂⠀⢨⣿⣷⠀⢹⣞⠀⠀⡹⢟⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⡞⢛⣿⣿⣿⣿⣿⡞⣄⡀⠀⠀⠀⠀⠈⢻⠁⠀⡀⢿⣿⢛⣿⣿⠹⠉⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠘⠻⠿⠿⣿⣿⣷⢀⣸⣿⠿⠭⠉⠛⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠴⠶⠶⠤⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣀⠠⠀⠀⠁⢸⣿⣿⣿⢿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠠⣼⣿⣿⣧⣼⠋⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢀⠀⠀⣿⣏⠁⠀⠀⠀⠀⠀⠀⣿⣿⠿⠿⣿⡿⠋⠈⠻⡇⠀⠀⣴⣾⡿⠗⠀⠀⠀⢸⡿⢋⣀⡈⠉⢿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠰⠖⠚⠋⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⣿⠏⠁⠀⠀⠀⠀⠀⣷⣶⣤⣼⡇⠀⠀⠀⠀⠀⠀⢠⡟⣿⣦⣀⣼⣥⣀⣠⡤⠀⣤⠟⣿⣿⠁⠀⡄⠀⠀⠀⠇⣠⣤⣠⣤⣈⣟⣟⣛⣁⣀⣀⣀⣶⣶⣦⣄⠀⠀

⠀⠀⠀⠀⠙⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢸⣷⣤⣿⡀⠠⣴⠀⠀⠶⢾⣿⣿⣿⣿⣷⣄⡀⡀⠀⠀⣠⣿⠀⢿⣿⠟⠛⠋⠙⠻⡷⠀⠘⠻⢿⡿⠆⠀⠀⠀⠀⠀⠘⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⡇

⠀⠀⠀⠀⠀⣾⣿⣿⣴⡦⠀⠀⠀⠀⠀⠀⠈⣿⣿⣟⣁⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣿⡋⠀⠘⢿⠀⠀⠏⠄⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠄

⠀⠀⠀⠀⠠⣿⣿⣿⣯⡀⠠⠆⠀⠀⠀⠀⣀⢨⣿⣶⡶⠂⠀⠀⠀⢨⣿⣿⣿⣿⣿⣟⣹⣷⠀⠀⠀⠈⠽⢇⣀⡀⠀⠁⠀⠀⠀⠀⠀⢀⣿⣷⣶⣶⣶⣦⣄⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⠀

⠀⠀⠀⠀⠀⢿⣻⣿⡿⢷⣄⠀⠀⠀⠀⢐⣿⣿⠉⠉⠁⠀⠀⠀⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣤⣶⠈⠡⣴⣶⣦⣄⣀⡀⠀⠀⣰⠟⣡⣿⡿⠉⠉⠉⣉⢉⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀

⠀⠀⠀⣤⣾⣿⣿⣟⠟⣸⣿⠀⠀⠀⣀⣾⢻⣵⠐⢠⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣢⡀⠲⡟⢿⣟⠠⣿⣤⣼⣶⠟⠁⠀⠋⠉⢁⣠⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⢀⣾⣿⣿⣿⣿⣿⣷⣿⣿⣷⣶⣾⡿⣿⣘⡟⠇⢺⡀⠀⣶⣴⣿⢿⣿⣿⣿⣿⣿⣿⣿⠄⣼⣿⣿⠇⠀⠀⠰⠎⠠⢤⣬⡁⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣧⣶⣶⠶⢾⣾⡇⠀⢹⠺⣿⣻⢻⣿⣾⣿⣿⣿⣿⢸⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠙⠃⠀⡠⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣾⣿⣿⣅⠀⠀⢃⠀⠀⣿⡄⠻⢻⠆⢿⣿⣿⣿⣿⣿⢸⣿⠟⠛⠿⣧⣴⡦⠀⠀⠀⠀⢀⣸⡇⠀⢘⣿⣿⣿⡿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠈⠉⠻⠋⠄⠀⣾⠀⠀⡟⣧⣠⡾⠀⢸⣿⣿⣿⣿⡇⠸⠁⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠘⣿⡇⠀⠘⠿⣇⣀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠄⠀⢻⣦⠀⣁⣿⣿⡷⠀⢸⣿⣿⣿⣿⠇⠀⠀⠀⢾⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠁⠈⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡇

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣤⡀⠈⣿⢀⣷⣿⣿⢡⡤⠞⠁⠈⠙⢻⠀⠀⢀⣀⠀⠱⡄⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣼⣿⢿⡇

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⠸⣿⣿⣿⡿⢁⣴⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⢠⡄⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣹⣏⡼⠃

⠸⠿⠿⣿⠿⢿⠿⠿⠿⠿⠿⠯⠿⢿⢿⡿⠿⠿⠿⠀⠠⠿⠿⠝⠟⠻⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠿⡿⢿⣿⣿⣿⣿⣿⡿⢿⣿⠿⠿⠿⠀⠘⠿⠋⠰⠄

[21A⢰⣶⣶⢲⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣀⠀⠀⠀⠀⠀⣴⣶⣶⣶⡶⠶⠶⠶⠒⠂⠀⠀⠐⠶⠶⢶⣦⠀⠀⠀⠀⢀⡀⢀⣀⣀⣤⡄

⢸⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣠⡞⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠙⢶⣿⣿⣿⣿⣾⣿⣿⣿⡇

⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡿⠋⠉⠀

⢸⣿⣿⣿⣿⡀⢠⣶⣦⠀⢼⣿⡇⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⡅⢸⣿⣿⣆⠈⣿⣿⣿⣿⣿⡇⠀⠀⠘⣿⣿⣿⣇⠀⠀⠀⠀⠀⣇⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠈⠻⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣷⣠⣿⣿⡏⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠈⣿⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⢠⠤⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣇⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⡄⠀⠀⠀⣷⣄⣀⠀⠀⣠⠴⠿⠟⠻⣿⣿⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⠀⠀⠀⠀⢹⣿⣿⣿⠿⠣⠀⠀⢠⣿⣿⣿⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⣿⣿⣿⣿⣥⡀⠀⠀⠀⠘⠛⠋⠀⠀⠀⠀⠀⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠄⠀⠀⡸⣠⣄⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⢀⣐⡲⢀⣀⣀⣀⡀⠀⣐⣿⣿⣿⣿⣿⣟⣻⠿⢿⣲⣿⣿⠓⠁⠀⠀⠀⠀⠀⠀⡄

⢸⣿⣿⣿⣿⣿⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣇⣠⣾⡄⠀⠀⠀⠀⠀⠀⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⣿⡏⢹⣿⠆⢸⣿⣿⣼⣿⣿⢻⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⢰⡇

⢸⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⠟⠉⠀⠀⠀⠀⠀⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠘⢿⣿⣧⠻⣿⣶⣄⠀⢸⣿⣿⢻⣿⣿⣿⣛⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣷⡗⠀⠀⠀⠀⠀⠃

⢸⣿⣿⣿⣿⡏⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠏⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠘⠉⠀⣤⣌⣽⣿⡇⢸⣿⣿⢸⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⢽⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀

⠈⠉⠉⠙⢿⡇⠀⠀⠘⣿⣿⣿⡟⢸⣿⣿⣿⣿⡏⣀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⠇⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣻⢿⣾⣿⣷⢺⣿⣿⣸⡿⣿⢿⢿⢿⢿⣿⣿⣿⣿⣿⣿⣿⠏⠻⠿⣾⠿⠃⡀⠀⠀⠀⠀⠀⠀⠇

⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⣿⣿⣆⣿⣿⣿⣿⣿⣯⣿⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣤⣶⣿⣿⣿⣄⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣚⣒⣢⣠⠄⠀⠀⠀⠀⠀⠀⢠⡆

⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⡀⣀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠀⣶⣶⡎⣿⣿⣿⣿⣿⣿⣶⣶⣻⣶⣶⣿⣱⣾⣶⣟⣿⣿⣿⡿⣿⣿⣿⣿⣷⣶⡆⢰⣶⡶⣶⣦⠀⢸⡇

⠀⠀⠀⠀⣸⡇⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⢿⣿⢿⣿⣿⢸⣿⣿⣿⣿⣿⣄⡀⢸⣿⣇⣸⣿⠀⢸⡇

⠀⠀⠀⣴⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⡌⣿⣿⠰⣿⣿⣼⣿⣿⢛⠃⢸⣿⡟⢻⣶⣀⣿⡇

⠀⠀⠀⢿⣿⣿⣶⣤⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡿⣿⣿⡟⢿⣿⣜⣿⣿⣿⣿⣿⣾⣾⣿⣿⡇⢸⣿⣿⣿⠀

⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⠟⠛⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣷⣿⣯⣭⣿⣿⣽⣿⣿⣿⣿⣿⣷⣾⣿⣽⣧⡀

⠀⠖⠲⣿⠿⢿⠿⠿⠿⠿⠧⠀⠹⠿⠿⠄⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠯⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⢿⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇

[21A⢰⣶⣖⠒⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣦⣀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⠶⠶⠖⠒⠂⠀⠐⠲⠶⠶⣶⣄⠀⠀⠀⠀⢀⡀⢀⣀⣀⣤⡄

⢸⣿⣿⡿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡐⠉⠉⢴⢤⠔⠒⠒⢀⣀⡀⠀⠀⠀⠀⠀⠀⠉⠳⢶⣿⣿⣿⣿⣾⣿⣿⣿⡇

⢸⣿⣷⣿⣿⠀⠀⠀⠀⠀⢀⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡿⠋⠉⠀

⢸⣿⣿⣿⣿⠀⢠⣶⣦⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡯⠈⠀⠀⠀⠀

⢸⣿⣿⣿⣿⡀⢸⣿⣿⡦⠀⣽⣿⣿⣿⣿⡿⠀⠀⠘⣿⣿⣿⣇⠀⠀⠀⠀⠀⣃⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⡇⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣧⣠⣿⣿⡏⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⢹⣿⣿⣿⣦⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣤⣤⣴⣄⠀⠘⣿⣆⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣷⣿⣿⣷⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⡄⠀⠀⠀⣦⣀⣀⠀⠀⢠⡴⠿⠛⠻⣿⣿⢿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠹⠟⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⠇⠀⠀⠀⢸⣿⣿⡿⠟⢃⠀⠀⢀⣿⣿⣿⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣿⣿⣿⣿⡁⠀⠀⠀⠀⠛⠋⠉⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⣻⣿⣿⣟⣋⡁⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢐⠅⡤⠄⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⢀⣀⡀⢀⣀⣀⣀⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣿⣿⣟⣛⣛⢏⠀⠀⠀⠀⠀⠀⠀⡄

⢸⣿⣿⣿⣿⣿⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣴⣦⠀⠀⠀⠀⠀⠀⠀⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢠⣿⡏⢹⣿⠆⢼⣿⣗⢸⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢰⡇

⢸⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣽⣿⡟⠋⠁⠀⠀⠀⠀⠀⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⢻⣿⣧⠻⣿⣶⣄⠀⢸⣿⣿⢾⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠃⠀⠀⠀⠀⠀⠃

⢸⣿⣿⣿⣿⡏⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠁⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠘⠛⠁⣤⡌⣽⣿⡇⢸⣿⣿⢸⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠍⣭⣭⢽⣿⣯⠋⠀⠀⠀⠀⠀⠀⠀

⠘⠛⠛⠛⢿⡇⠀⠀⠸⣿⣿⣿⡟⢘⣿⣿⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠇⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢻⢿⣾⠿⢣⣼⣿⣿⣸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⠻⠿⡾⠿⣣⡄⠀⠀⠀⠀⠀⠀⠇

⠀⠀⠀⠀⢸⡇⠀⠀⠀⢹⣿⣿⣄⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣦⣿⣿⣿⣿⣧⣴⣾⣿⣿⡄⠀⠀⠀⠀⠀⢻⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⢠⡇

⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣀⣀⢀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⠀⣶⣶⡎⣿⣿⣿⣿⣿⣿⣿⣿⣻⣶⣶⣿⣹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⡆⢰⣶⡶⣶⣦⠀⢸⡇

⠀⠀⠀⠀⣸⡇⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡇⣟⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⢿⣿⢿⣿⣿⢹⣿⣿⣿⣿⣿⣆⡀⢸⣿⣇⣸⣿⠀⢸⠃

⠀⠀⠀⣰⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⡇⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣸⣿⣬⣿⣿⠰⣿⣿⣼⣿⣿⢛⠃⢸⣿⡟⢻⣶⣀⣾⡇

⠀⠀⠀⢻⣿⣿⣦⣄⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡟⢿⣿⣔⣿⣿⣿⣿⣿⣾⣼⣿⣿⡇⢸⣿⣿⣿⠁

⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣬⣯⣽⣇⡀

⠀⠖⠲⣿⠿⢿⠿⠿⠿⠿⠧⠈⠻⠿⠇⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇

[21A⢰⣶⣒⠲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⣀⣤⡄

⢸⣿⣟⠏⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣠⣀⣀⣤⣴⣶⣾⠆⠀⠚⠛⠓⠂⣤⡀⠀⠀⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⡇

⢸⣿⣷⣿⣶⠀⠀⠀⠀⠀⢀⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣷⡖⣿⣿⠿⠟⠿⠿⠿⠿⠆⠀⠀⠀⠀⠀⠈⠉⢷⣆⣻⣿⣿⣿⣿⣿⣿⡿⠋⠉⠀

⢸⣿⣿⣿⣿⠀⢰⣶⣆⠀⢼⣿⡃⠀⠀⠀⠀⠀⠀⢀⣠⣤⣦⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⡟⠈⠀⠀⠀⠀

⢸⣿⣿⣿⣿⡀⢸⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⠆⠀⠀⢻⣿⣿⣇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⡇⢸⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠘⣿⣿⣿⣆⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠘⣿⣿⡄⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣸⣿⣿⣷⠠⣿⣿⣿⣿⣿⣿⠀⠀⠀⢠⣿⣿⣿⣿⡄⠀⠀⠀⣀⡀⡀⠀⠀⢀⣴⠿⠟⠛⣿⡿⠿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣷⡄⠀⠀⠻⣿⠇⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⠟⠀⠀⣼⣿⣿⠟⠻⠿⠇⠀⠀⠀⣼⣿⣿⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣿⣿⣿⡿⣇⠀⠀⠀⢉⠁⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠘⠁⠦⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⢀⣀⡀⢸⣿⣿⣿⡿⠿⣛⣤⢠⣋⣻⣿⣏⣛⢲⢾⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⡄

⢸⣿⣿⣿⣿⣟⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣾⣦⣀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⣿⡏⢹⣿⣆⢸⣿⡇⢸⣿⣿⣿⣿⣤⣿⣿⣼⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡇

⢸⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠂⠀⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡻⣿⣾⣄⢸⢸⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⡔⠇⠀⠀⠀⠀⠀⠃

⢸⣿⣿⣿⣿⡏⠀⠘⢿⣿⣿⣿⣿⡿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⢠⡀⠀⢀⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠈⠚⠁⣤⡄⣹⣿⡿⣿⣿⣧⣸⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀

⠘⠋⠛⠛⢿⡇⠀⠀⠘⣿⣿⣿⡿⢀⣿⣿⣿⣧⡆⠀⠀⠀⠀⠀⠈⢩⡀⣼⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣾⠿⠃⠸⢿⣿⣻⣿⣿⣿⣿⣿⡿⠿⠉⠙⠿⢷⠿⢿⣿⣿⣿⣿⡿⢃⠀⠀⠀⠀⠀⠀⠀⠆

⠀⠀⠀⠀⢸⡇⠀⠀⠀⢹⣿⣿⡇⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣥⣴⣾⣿⣷⡄⠀⠀⠀⠀⠀⢻⣿⣿⡇⢠⣶⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⠀⠐⠀⠀⠀⠈⢿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⢠⡆

⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⣿⣿⣷⣿⣿⣿⣿⣿⡇⣠⣠⣤⣠⣠⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⠀⣶⣶⡎⣿⣿⣿⣾⣿⣿⣶⣶⣻⣾⣿⣿⣿⣶⣶⡆⣶⣦⣶⡿⣶⣶⣾⣿⣶⣶⡆⢰⣶⡶⣶⣦⠀⢸⡇

⠀⠀⠀⠀⢸⡇⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⡇⣟⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣿⣆⡀⢸⣿⣇⣸⣿⠀⢸⡃

⠀⠀⠀⣠⣾⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⡟⢸⣿⣽⣿⣿⢹⣿⣿⣸⣿⣿⢛⠃⢸⣿⡟⢻⣶⣀⡼⠄

⠀⠀⠀⢺⣿⣿⣶⣤⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡟⣻⣿⡗⢿⣿⣜⣿⣿⣿⣿⣿⣿⣤⣾⣿⡇⢸⣿⣿⣿⠁

⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢿⣿⣿⣿⣿⣿⣯⣯⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣥⣷⣯⣯⣿⣽⣿⣽⣿⣿⣯⣿⣿⣥⣬⣭⣽⣇⡀

⠀⠶⠲⣿⠿⢿⠿⠿⠿⠿⠿⠋⠹⠀⠼⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠿⡿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇

[21A⢰⣶⣒⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣀⣤⡄

⢸⣿⣟⡭⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢀⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡇

⢸⣿⣯⣿⣧⠀⠀⠀⠀⠀⢀⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⣷⣶⠀⣀⣀⣀⣠⣾⣿⣿⡿⠀⠒⠛⠛⠙⠶⣦⣄⠀⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠀

⢸⣿⣿⣿⣿⠀⢰⣶⣄⠀⢸⣿⡃⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠺⣿⣿⣿⣿⠿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠈⠙⢷⣿⣿⣿⣿⣿⡏⠉⠀⠀⠀⠀

⢸⣿⣿⣿⣿⠀⢸⣿⣿⡆⠈⣿⣿⣿⣿⣿⣿⡆⠀⠀⠻⣿⣿⣇⠀⠀⠀⠀⠀⣅⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠨⠭⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⠇⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣇⢸⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⡆⠀⠀⠀⠀⢿⠋⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡄⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣺⣿⣿⣧⠀⣿⣿⣿⣿⣿⣿⡇⠀⣀⣄⣿⣿⣿⣿⡀⠀⠀⠀⢨⣀⡀⠀⠀⢀⣴⡿⠿⠻⠿⣿⣿⣿⣿⣿⣿⠟⠘⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⣀⣀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡿⢷⣿⡿⠟⠙⠻⢿⣿⠇⠀⠀⠀⣽⣿⣿⠆⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⣿⣿⣿⣿⠇⠀⠈⣇⠀⠀⠀⠀⠀⠉⠀⠀⠀⣸⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠛⠛⠂⠀⠀⠀⠀⢖⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⢀⣀⡀⢀⣸⣿⣿⡿⣿⣛⣻⢻⣻⣿⣿⣿⣿⠿⢿⣻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⡄

⢸⣿⣿⣿⣿⣯⠀⢹⣿⣿⣿⣿⣿⣿⣿⣷⣠⣿⣶⣤⠀⠀⠀⠀⠀⠈⡀⠀⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⣿⡏⢹⣿⡆⢸⣿⡇⢸⣿⣿⣻⣿⠹⣿⣿⢤⣿⣿⣿⣿⣿⠀⣿⣿⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⡇

⢸⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠸⠿⠆⠀⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⢸⣿⣧⡻⣿⣾⣅⠀⢸⣿⡇⢸⣿⣿⣿⣿⣴⣿⣿⣶⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⡀⠰⠖⠀⠀⠀⠀⠀⠁

⢸⣿⣿⣿⣿⡟⠀⠘⣿⣿⣿⣿⣿⡿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣧⠀⠀⢀⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠋⠋⣤⡄⣹⣿⡇⣼⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀

⠈⠋⠛⠛⢿⡇⠀⠀⠸⣿⣿⣿⣿⠁⣸⣿⣿⡗⠀⠀⠀⠀⠀⠈⣿⣇⡀⣼⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⣾⡿⠃⢸⣿⣧⣸⣿⣿⣿⣿⣿⣿⣿⢽⠛⠿⣿⡿⢟⣿⣿⣿⣿⣿⣣⣄⠀⠀⠀⠀⠀⠀⠆

⠀⠀⠀⠀⠈⡇⠀⠀⠀⢹⣿⣿⣇⣸⣿⣿⣿⡆⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣟⣤⣴⣾⣿⣷⡄⠀⠀⠀⠀⠀⢿⣿⣿⡇⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠀⠘⠉⠉⠻⢿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⢠⡆

⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣇⣠⣴⣦⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⠀⣶⣶⡎⣿⣿⣿⣶⣦⣶⣾⣷⣻⣾⣿⣿⣿⣷⣶⡆⢀⣠⣶⡿⣶⣦⠀⣿⣿⣷⡆⢰⣶⡶⣶⣦⠀⢸⡇

⠀⠀⠀⠀⢰⡇⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣿⣿⡇⣟⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⢴⣿⣿⢸⣿⣿⣻⣿⣿⣆⡀⢸⣿⣇⣸⣿⠀⢸⠃

⠀⠀⠀⣠⣾⡇⠀⠀⠀⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⡟⢸⣿⣾⣿⣿⣶⣿⣿⣿⣿⣿⢛⡃⢸⣿⡟⢻⣶⡀⡌⠄

⠀⠀⠀⢸⣿⣿⣶⣤⣀⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣼⣿⡟⢻⣿⡟⢿⣿⣟⣿⣿⣹⣿⣿⣾⣤⣼⣿⡇⢸⣿⣿⣿⠁

⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⡟⣿⣿⣿⣿⣿⣯⣯⣭⣤⣭⣥⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣮⣭⣉⣃⣉⣯⣭⣭⣽⣿⣿⣿⣯⣿⣿⣥⣬⣭⣽⣏⠀

⠀⠖⠶⣿⠿⢿⠿⠿⠿⠿⠿⠉⠀⠈⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠰⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇

[21A⢰⣶⣒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡄

⢸⣿⡿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢠⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡇

⢸⣿⣯⣷⣶⠀⠀⠀⠀⠀⠀⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣷⣶⠀⠀⣀⣀⣀⣼⣶⣶⣾⠟⠀⠾⠛⠛⠷⣦⣄⡈⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠀

⢸⣿⣿⣿⣿⠀⢠⣶⣄⠀⢸⣿⡃⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢾⣿⣿⣿⣿⣿⣿⣯⡄⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⣿⣿⣿⡇⠉⠀⠀⠀⠀

⢸⣿⣿⣿⣟⠀⢸⣿⣿⡆⠈⣿⣿⣿⣿⣿⣿⣷⠀⠀⠛⢿⣿⣇⠀⠀⠀⠀⠀⣅⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠭⠥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠇⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⡇⢘⣿⣿⡟⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⢻⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣺⣿⣿⣧⢀⣿⣿⣿⣿⣿⣿⣧⢀⣀⣀⣸⣿⣿⣿⡀⠀⠀⠀⢰⣀⠀⠀⠀⢀⣴⡿⠿⠻⢿⣿⣿⠿⢿⣿⣿⠟⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢻⡧⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠛⠻⣿⣿⡇⠀⠀⠀⣼⣿⣿⠇⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣿⣿⣿⣿⠋⠁⢩⡁⠀⠀⠀⠀⠘⢛⠓⠀⠀⣰⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠜⠋⠐⠀⠀⠀⠀⢨⣻⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⢀⣀⡀⢀⣀⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⡄

⢸⣿⣿⣿⣿⣏⠀⢻⣿⣿⣿⣿⣿⣿⣿⣆⣴⣷⣦⠄⠀⠀⠀⠀⠀⢉⠀⠀⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⢠⣿⡏⢹⣿⠆⢸⣿⡇⢸⣿⣿⣻⣿⢹⣿⣿⣠⣿⣿⣿⣿⣿⠀⣿⣿⢽⣿⡇⠀⠀⠀⠀⠀⠀⠀⡇

⢸⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢀⡿⠿⠅⠀⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⢘⣿⣧⡻⣿⣾⣄⠀⢸⣿⡇⢸⣿⣿⣿⣟⣤⣿⣿⣿⣿⣿⣿⣿⣿⣴⣻⣿⣿⣿⡇⠀⠴⠀⠀⠀⠀⠀⠁

⢸⣿⣿⣿⣿⡟⠀⠘⢿⣿⣿⣿⣿⡿⣿⣿⣿⠁⠀⠀⠀⠀⠀⣿⣷⠀⠀⢀⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠈⠿⠋⣤⡄⣹⣿⡇⢸⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀

⠈⠉⠛⠻⢿⡇⠀⠀⠸⣿⣿⣿⣿⠃⢸⣿⣿⠂⠀⠀⠀⠀⠀⢘⣿⣂⠀⣸⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣾⠿⠃⠸⣿⣧⠸⢿⣿⣿⣿⣿⣿⣿⢻⠟⠿⣿⣿⠿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠇

⠀⠀⠀⠀⠀⡇⠀⠀⠀⢹⣿⣿⡯⣰⣿⣿⣿⠀⠀⠀⠀⠀⠀⢷⣿⣿⣷⣿⣿⣿⡟⣠⣤⣶⣿⣷⡄⠀⠀⠀⠀⠀⢿⣿⣿⡆⠀⠀⠙⢹⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠘⠋⠉⠻⢿⣿⣿⣿⡿⠉⠁⠀⠀⠀⠀⢀⡆

⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣀⣠⣤⣦⣴⣤⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⠀⣶⣶⡎⣿⣿⣿⣶⣦⣤⣶⣿⣻⣾⣿⣿⣿⣿⣶⡆⠀⣠⣶⡿⣶⣦⠀⣿⣿⣿⡆⢰⣶⡶⣶⣦⠀⢸⡇

⠀⠀⠀⠀⢀⡇⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡇⣟⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⢤⣿⣿⢰⣿⣿⣶⣿⣿⣈⡀⢸⣿⣇⣸⣿⠀⠸⠁

⠀⠀⠀⢀⣾⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⡟⢸⣿⣼⣿⣿⣰⣿⣿⣾⣿⣿⢛⠃⢸⣿⡟⢻⣶⡀⣊⠇

⠀⠀⠀⢸⣿⣿⣶⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣇⢿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⡟⢻⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣼⣬⣾⣿⡇⢸⣿⣿⣿⠁

⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⡟⣿⣿⣿⣿⣿⣿⣧⣭⣤⣭⣧⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣮⣭⣉⡓⠩⣫⣯⣭⣼⣽⣿⣿⣿⣿⣿⣥⣬⣭⣽⡏⠀

⠀⠖⠶⣾⠿⢿⠿⠿⠿⠿⠿⠁⠀⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠡⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇

[21A⢰⣶⣒⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣀⣤⡄

⢸⣿⣿⣭⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡀⠀⠀⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡇

⢸⣿⣿⣿⡧⠀⠀⠀⠀⠀⢀⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣶⡆⠀⠀⢀⣀⣀⣿⣶⣶⣾⣿⠋⠙⠞⠛⠉⠳⢶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀

⢸⣿⣿⣿⣷⠀⢰⣶⣄⠀⢾⣿⠃⠀⠀⠀⠀⠀⠀⢀⣠⣤⣦⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢾⣿⣿⣿⣶⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⡇⠉⠀⠀⠀⠀

⢸⣿⣿⣿⣿⠀⢸⣿⣿⡆⠈⣿⣿⣿⣿⣿⣿⣷⠀⠀⠛⢿⣿⣇⠀⠀⠀⠀⠀⣋⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠤⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⠇⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⡇⢸⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠸⣿⣿⣆⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣷⣿⣿⣿⣧⠀⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢠⣿⣿⣿⡄⠀⠀⠀⣸⣄⣀⠀⠀⢀⣼⠿⠿⠿⣿⣿⣿⠿⣿⣿⣿⣿⡟⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢂⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠻⢿⣿⣿⡂⠀⠀⠀⣾⣿⣿⠇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⠄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠈⠃⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⡟⠉⢙⣁⠀⠀⠀⠀⠀⠉⣉⡁⠀⠀⣼⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠘⠟⠳⠀⠀⠀⠀⠀⣿⣿⡄⠜⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⢀⣀⡀⢀⣀⣀⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡀

⢸⣿⣿⣿⣿⣇⠀⢿⣿⣿⣿⣿⣿⣿⣆⣰⣷⣤⡄⠀⠀⠀⠀⠀⡉⢑⠰⠀⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⢠⣿⡏⢹⣿⠆⢸⣿⡇⢸⣿⣿⣻⣿⣹⣿⣿⢤⣿⣿⣿⣿⣿⠀⣿⣿⢽⣿⣿⡇⠀⠀⠀⠀⠀⠀⡇

⢸⣿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⡿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⣿⣿⠿⠆⠀⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⢿⣿⣧⡻⣿⣾⣄⠀⢸⣿⡇⢸⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣴⣻⣿⣷⣿⣿⡇⠀⡀⠀⠀⠀⠀⠁

⢸⣿⣿⣿⣿⡟⠁⠸⣿⣿⣿⣿⠁⠨⢿⣿⡃⠀⠀⠀⠀⠀⢰⣿⣿⡀⠀⢠⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠸⠿⠃⣤⡌⣹⣿⡇⢸⣿⣧⢸⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀

⠈⠉⠛⠛⠿⠇⠀⠀⠹⣿⣿⣿⣶⠀⢸⣿⠂⠀⠀⠀⠀⠀⠘⡏⠈⠀⠀⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣾⠿⠃⠸⠿⣿⣾⢿⣿⣿⣿⣿⣿⣿⢿⡝⠿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠁⠀⠀⠀⢿⣿⣿⣿⣠⣾⣿⠀⠀⠀⠀⠀⠀⣾⣿⣿⣶⣴⣿⣿⣿⢇⣠⣤⣶⣿⣷⡀⠐⠂⠀⠀⠀⣿⣿⣿⡀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠛⠉⠛⠿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⢀⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⣀⣠⣤⣤⣴⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⠀⣶⣶⡎⣿⣿⣷⣶⣦⣤⣶⣶⣻⣾⣿⣿⣿⣿⣷⡆⠀⣠⣶⣿⣶⣦⠀⣾⣿⣿⡏⢰⣶⡶⣶⣦⠀⢸⡇

⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣿⣿⡇⣟⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⢸⣿⣿⣲⣿⣿⣿⡃⢸⣿⣇⣸⣿⠀⠘⡁

⠀⠀⠀⢀⣼⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⡇⣿⣇⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⡇⣿⡟⢸⣿⣼⣿⣿⣴⣿⣿⣾⣿⣿⠛⠃⢸⣿⡟⢻⣶⡀⣊⡆

⠀⠀⠀⠘⣿⣷⣦⣼⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡏⢿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⡟⢿⣿⣿⣿⣿⢻⣿⣿⣾⣯⣾⣿⡇⢸⣿⣿⣿⠀

⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣯⣯⣭⣤⣽⣧⣼⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣮⣭⣁⣀⣉⢋⣭⣭⣼⣭⣿⣿⣿⣿⣿⣥⣬⣭⣽⡏⠀

⠀⠖⠶⣾⠿⢿⠿⠿⠿⠿⠿⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠹⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇

[21A⢰⣶⣶⣶⡖⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⣀⣤⡄

⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⣶⣶⣾⣶⣿⣿⣿⣿⣿⣿⣿⡇

⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣷⡖⠀⠀⢀⣀⣀⣿⣶⣶⣾⣿⠟⠹⠟⠛⠙⠷⢶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠀

⢸⣿⣿⣿⣿⠁⢰⣶⣄⠀⣾⣿⡃⠀⠀⠀⠀⠀⠀⢀⣤⣬⣶⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠉⠿⣿⣿⣿⣿⡯⠉⠀⠀⠀⠀

⢸⣿⣿⣿⣿⡇⢼⣿⣿⡏⢹⣿⣿⣿⣿⣿⣿⣿⠂⠈⠛⢿⣿⣇⠀⠀⠀⠀⢠⣿⣇⣀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠼⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⠇⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣷⣾⣿⣿⡟⢰⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠸⣿⣿⣆⠀⠀⠀⠸⣿⣿⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⣸⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⢰⣿⣿⣿⡄⠀⠀⠀⣿⣧⣀⡀⠀⣠⣼⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⠀⠀⠀⠀⠈⠀⢠⡆⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣗⠀⠀⠀⣿⣿⣿⠇⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⡤⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠸⠃⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢹⣁⡀⠀⠀⠀⠀⠙⣿⣿⡄⠀⣼⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣼⠿⠷⠦⠀⠀⠀⠀⣿⣿⣷⡾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢰⡄

⢸⣿⣿⣿⣿⣏⠈⣿⣿⣿⣿⣿⣿⣿⣆⣼⣿⣶⣤⠀⠀⠀⠀⢀⣿⣿⣿⡇⣿⣷⣀⠈⠀⠀⠀⠀⠀⠀⢠⣤⣄⣀⣀⣠⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⣭⣭⣿⣿⣿⣿⣯⠩⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⡇

⢸⣿⣿⣿⣿⣿⡇⣻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⣿⣿⣿⠿⠁⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⠿⣿⠀⠀⢸⢀⡀⠀⢸⣿⣿⣿⣿⣦⣴⣿⣷⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⡇⠠⣶⠀⠀⠀⠀⠁

⢸⣿⣿⣿⣿⡿⠁⠿⣿⣿⣿⣿⠁⣸⣿⣿⡇⠀⠀⠀⠀⠀⢰⣿⣿⣧⠀⢰⣿⣿⣿⡿⠇⠀⠀⠀⠀⠂⢿⣿⣿⡟⠁⠀⣼⠀⠀⠈⢸⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠉⠀⠀⠀⠀⠀

⠘⠛⠛⠿⢿⡇⠀⠀⠹⣿⣿⣿⣶⠉⢸⣿⠇⠀⠀⠀⠀⠀⢹⡏⢹⡿⣭⣿⣿⣿⣿⠇⠀⠀⠀⠀⢸⣷⡆⠈⠉⠀⣀⣾⣿⠀⠀⠀⠸⣿⣷⣸⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠇

⠀⠀⠀⠀⠀⡇⠀⠀⠀⢿⣿⣿⣿⣠⣾⣿⠀⠀⠀⠀⠀⠐⣿⣿⣿⣷⣿⣿⣿⣿⢿⣦⣤⣾⣿⣷⡄⢿⣷⠂⠀⠀⣿⣿⣿⡂⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠈⠛⠉⠛⢿⣿⣿⣿⣿⡟⠻⠷⠆⠀⠀⢠⡇

⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣀⣤⣤⣶⣴⣾⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣃⡀⠀⣿⣿⣿⣿⣶⣤⣴⣠⣾⣿⣿⣿⣿⣿⣿⡏⠀⠀⣀⣘⣛⣛⡀⠀⠈⣿⣿⣿⠃⠀⠀⠀⠀⠀⣼⡇

⠀⠀⠀⠀⢠⡇⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣶⣶⣿⣿⠏⠀⠀⠀⠀⠀⠀⢹⡇

⠀⠀⠀⢀⣾⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⣠⣿⡇

⠀⠀⠀⢸⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⣿⣿⠇

⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣭⣛⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⡀

⠠⠶⠶⣿⣿⢿⠿⠿⠿⠿⠿⠀⠹⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠹⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⡿⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⡿⠿⠿⠿⠿⠿⠇

[21A⢰⣶⣶⣶⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⣠⣤⡄

⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣰⣶⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⡇

⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⣰⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣶⡇⠀⠀⠀⣠⣴⣿⣦⣶⣾⣿⡿⠛⠟⠛⠋⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀

⢸⣿⣿⣿⣯⠀⣴⣦⡄⢠⣿⣿⠁⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⠀⠀⠀⠀⠀⢸⣧⢀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⠿⠿⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡏⠉⠀⠀⠀⠀

⢸⣿⣿⣿⣿⡀⣿⣿⣿⡖⢻⣿⣿⣿⣿⣿⣿⣿⡆⠘⠛⢿⣿⣇⠀⠀⠀⠀⢸⣿⣈⣀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠨⠿⠖⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠃⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣷⣿⣿⣿⡗⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠘⣿⣿⡆⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢀⣿⣿⣿⡀⠀⠀⠸⣿⣿⣤⠀⠀⣠⣾⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢰⡆⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡶⣿⣿⣿⣿⣇⠀⠀⢀⣿⣿⣿⠂⠊⠁⠀⠀⠀⠀⠀⠀⠉⠙⠿⣿⣿⣿⡿⠄⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢸⠇⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢻⣇⡀⠀⠀⠀⠈⠀⠉⣿⣧⠀⢀⣾⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣼⡿⣿⠦⠀⠀⠀⠀⠀⣻⣿⣷⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢠⡄

⢸⣿⣿⣿⣿⣏⠸⣿⣿⣿⣿⣿⣿⣇⣰⣿⣦⣤⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⡀⠁⠀⠀⠀⠀⠀⢠⣀⢀⠀⢀⠀⣰⣿⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠿⠯⣭⣽⣿⣿⣿⣿⠅⠶⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⡇

⢸⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⠿⣿⣿⡿⠉⠁⠀⠀⠀⠀⢴⣶⣿⣿⣿⢸⣿⣿⣿⣤⠀⠀⠀⠀⠀⣻⣿⣿⣾⣿⡿⣿⣿⠀⠀⠈⡇⣤⡀⠀⣿⣿⣿⣿⣷⣶⣾⣿⣾⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⠀⢰⠀⠀⠀⠀⠁

⢸⣿⣿⣿⣿⡿⠃⢿⣿⣿⣟⠁⠀⣼⣿⡇⠀⠀⠀⠀⠀⣰⣾⣿⣿⣯⢀⣸⣿⣿⣿⣿⠁⠀⠀⠀⢨⣿⣿⣿⡿⠉⠀⣸⣿⠀⠀⠀⠁⣿⣇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀

⠘⠻⠿⠿⢿⡇⠀⠀⢿⣿⣿⣦⡄⠋⣿⡇⠀⠀⠀⠀⠀⠙⣏⠈⠙⡗⢨⣿⣿⣿⡟⠁⠀⠀⠀⠀⣵⠁⠈⠉⠁⢀⣤⣿⣿⠀⠀⠀⠀⢹⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿⡿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣧⣴⣿⡄⠀⠀⠀⠀⠀⣾⣿⣷⣶⣽⣿⣿⣿⣿⢯⣤⣴⣾⣿⣦⠘⣿⣶⠄⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠙⠋⠉⠻⢿⣿⣿⣿⣿⠛⠛⠀⠀⠀⢀⡄

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣶⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣄⠀⢰⣿⣿⣿⣷⣦⣤⣀⠄⣴⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣐⣛⣛⡓⠀⠀⢹⣿⣿⡟⠀⠀⠀⠀⠀⣾⡇

⠀⠀⠀⠀⢠⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⢹⡇

⠀⠀⠀⢠⣾⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡀⠀⠀⠀⠀⢀⣿⡇

⠀⠀⠀⢸⣿⣷⣾⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⣿⣿⡇

⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⡌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣙⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⡄

⠠⠶⠶⣾⣿⢿⠿⠿⠿⡿⠿⠈⠹⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⡿⠿⠿⠿⠿⠇

[21A⢰⣶⣶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⢰⡖⠀⠐⣶⠆⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⡀⢀⣀⣠⣤⡄

⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢀⣴⣦⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣠⣀⠀⠀⣀⣺⣿⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⣿⣿⣿⡧⠀⠀⠀⠀⠀⣸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⣿⣿⣿⣿⠀⠀⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⣾⣦⣆⠀⠈⠛⠛⠷⠚⠋⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀

⢸⣿⣿⣿⣟⠀⣶⣦⡀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⣤⣆⠀⠀⠀⠒⠈⠀⢠⣧⣸⠀⠀⠀⠀⠇⠀⢸⣿⣿⣿⣿⠀⠀⣿⣿⡏⠀⠀⠀⠀⠈⠀⠀⡿⠿⠾⢷⣤⣤⡀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡏⠉⠀⠀⠀⠀

⢸⣿⣿⣿⣿⠀⣿⣿⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⠇⠘⠛⢿⣿⣆⠀⠀⠐⠀⣿⣿⣉⣄⡀⠀⠀⢢⣤⣾⣿⣿⣿⣿⣀⣠⣿⣿⣷⣀⠀⠀⠀⠠⠀⠀⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠃⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣧⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠘⣿⣿⡄⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢠⣿⣿⣷⡀⠀⠀⢸⣿⣿⣍⠀⠀⣠⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣰⣾⡇⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⣷⣶⣿⣿⣿⣿⡆⠀⠀⢠⣿⣿⣿⠂⠚⠁⠀⠀⠀⠈⠁⠀⠉⠻⢿⣿⣿⣿⣿⠤⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢿⡇⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⢿⣁⠀⠀⠀⠀⠉⠀⠉⣿⣇⡀⢀⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣿⡿⣷⠄⠀⠀⠀⠀⠀⣿⣿⣷⣽⣿⡏⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢠⡄

⢸⣿⣿⣿⣿⣏⢹⣿⣿⣿⣿⣿⣿⡄⣾⣿⣤⣼⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⡀⠉⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣼⡧⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⠯⣭⣭⣿⣿⣿⣿⠅⠼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⡇

⢸⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠠⣶⣾⣿⣿⡿⢹⣿⣿⣧⣤⠀⠀⠀⠀⣨⣿⣿⣶⣾⣿⣼⣿⣯⠀⠀⢀⡏⢠⡀⠀⢸⣿⣿⣿⣷⣦⣾⣿⣾⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⡇⢰⠄⠀⠀⠀⠁

⢸⣿⣿⣿⣿⣿⠃⣿⣿⣿⡟⠀⠀⣼⣿⠇⠀⠀⠀⠀⢀⣶⣿⣿⣿⣷⢃⣾⣿⣿⣿⡿⠀⠀⠀⠀⣽⣿⣿⣿⠟⠀⢀⣿⣧⠀⠀⠈⠁⣿⣇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⠀⠀⠀⠀⠀

⠸⠿⠿⠿⢿⠁⠀⠈⣿⣿⣷⣄⡀⢋⣿⠃⠀⠀⠀⠀⠀⢻⡇⠉⠙⡯⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣿⣏⠙⠋⠆⢀⣾⣿⣿⠀⠀⠀⠀⢸⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⡿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣧⣾⣿⠀⠀⠀⠀⠀⠰⣿⣿⣶⣤⣿⣿⣿⣿⣿⢿⣀⣤⣾⣿⣆⠙⣿⣧⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠙⠋⠉⠻⢿⣿⣿⣿⣿⠟⠛⠆⠀⠀⢀⡆

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣀⣠⣤⣤⣤⣶⣿⣿⣿⣿⡿⢿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣶⣿⣿⣆⠀⢸⣿⣿⣿⣷⣦⣤⣀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⣐⣛⣛⣓⠂⠀⠹⣿⣿⡿⠀⠀⠀⠀⠀⣾⡇

⠀⠀⠀⠀⢀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢹⡇

⠀⠀⠀⢠⣿⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⢀⣿⡇

⠀⠀⠀⢸⣿⣷⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠠⣿⣿⡇

⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⡄

⠠⠶⠶⣾⣿⢿⢿⠿⠿⡿⠿⠉⠹⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠼⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⡿⠿⠿⠿⠿⠇

[21A⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠂⢀⣤⣤⣄⠀⢲⣶⣶⡆⠀⣲⣶⣶⠀⢰⡖⠂⠲⣶⡖⠒⣶⣶⣶⠒⢶⣶⣶⣶⡶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆

⢸⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠈⠛⠛⠿⢿⣿⣿⣿⠁⠀⣿⣿⡟⠀⢀⣴⣶⣾⣿⠃⠀⣿⣿⡏⠀⢸⣿⣿⣿⠃⠀⣿⣿⡟⠁⢠⣤⣤⡀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⠿⣷⣶⣤⣄⠀⠙⣿⣿⠀⠀⣿⣿⡇⠀⢸⣿⣿⣿⣿⠀⠀⣿⣿⡇⠀⢸⣿⣿⣿⠀⠀⣿⣿⣇⠀⠘⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣿⣧⡀⠉⠛⠛⠋⠀⣠⣿⣿⠀⠀⣿⣿⡇⠀⢸⣿⣿⣿⣿⠀⢀⣿⣿⡇⠀⢸⣿⣿⡿⠀⠀⣿⣿⡿⢿⣶⣦⣤⡀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⣶⣶⣶⣿⣿⣿⣿⣦⣶⣿⣿⣧⣤⣾⣿⣿⣿⣿⣀⣸⣿⣿⣷⣀⡀⠉⣉⣤⠀⢀⣿⣿⣄⠀⠙⠛⠛⠃⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡇

⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠏⠁⠀⠀⠸⣿⡿⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢻⣿⢻⣻⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⢿⣯⣯⢻⣏⣏⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣿⣳⣳⣿⣿⣾⣾⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⠟⡛⠙⠉⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡯⡟⠟⠉⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣧⡆⠀⢀⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠾⡋⣀⣀⣶⠺⠏⠀⠁⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⠰⠁⢨⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣦⠠⠴⠾⣿⡆

⢠⣄⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣠⠀⢠⡆

⢸⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣴⣿⣄⡤⠈⠠⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣿⣿⣷⣶⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠳⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠟⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⢀⣴⣶⣶⣶⣶⢾⣿⣆⠀⠀⠰⠊⣐⣿⣿⣿⢷⢄⠀⠓⠀⠀⢀⣴⣶⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡄⠀⠀⠀⠐⣇⡀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⢻⣿⣿⣿⣿⣭⡟⢿⣁⡀⠀⠀⠉⠉⠉⠈⠀⠀⠙⠀⠀⠀⠘⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⣿⣿⡆

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠘⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⣿⣿⣿⣿⣧⣿⡟⣿⡯⠀⠠⣄⡀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠘⢿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠿⣿⡇

⠸⠿⠿⣿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠷⠦⠀⠀⠘⢿⣿⠷⠸⠀⠀⠀⠙⠿⠿⠿⠿⠿⠸⠿⠿⠿⠏⠉⠁⠋⠁⠀⠀⠘⠿⠦⠀⠀⠀⠀⠀⠳⠀⠀⠀⠸⠿⠿⠿⠏⠿⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡿⡇

[21A⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠂⢀⣤⣤⣄⠀⢲⣶⣶⡆⠀⢲⣶⣶⠀⢰⡖⠂⢲⣶⡖⠒⣶⣶⣶⠖⢶⣶⣶⣶⡶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆

⢸⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠈⠛⠛⠿⢿⣿⣿⣿⠁⠀⣿⣿⡿⠀⢀⣴⣶⣾⣿⠃⠀⣿⣿⡟⠀⢸⣿⣿⣿⠃⠀⣿⣿⡟⠁⢠⣤⣤⡀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣿⣿⣿⣿⣿⠿⣷⣶⣤⣄⠀⠙⣿⣿⠀⠀⣿⣿⡇⠀⢸⣿⣿⣿⣿⠀⠀⣿⣿⡇⠀⢸⣿⣿⣿⠀⠀⣿⣿⣇⠀⠘⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣧⡀⠈⠛⠛⠋⠀⣠⣿⣿⠀⠀⣿⣿⡇⠀⢸⣿⣿⣿⣿⠀⠀⣿⣿⡇⠀⢸⣿⣿⡿⠀⠀⣿⣿⡿⢿⣶⣦⣤⡀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣷⣶⣶⣶⣿⣿⣿⣿⣦⣴⣿⣿⣧⣤⣾⣿⣿⣿⣿⣀⣸⣿⣿⣷⣀⠀⠉⣉⣤⠀⢀⣿⣿⣄⠀⠙⠛⠛⠃⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡇

⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡟⠁⠀⠀⠸⣿⡟⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢻⣿⢻⢻⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⢿⣯⣯⢻⣯⣏⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢛⣻⣳⣳⣿⣿⣾⣾⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⣿⣿⣿⡿⠛⠛⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠟⠟⠋⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠉⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣯⡤⠠⢠⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡫⠾⠏⢍⣄⣴⠚⠛⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⠰⠀⢈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⡄⠴⠶⣿⡷⠀

⢠⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣷⢀⡄⢀⣴⡆

⢸⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣴⣾⣄⡤⡉⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⣿⣿⣿⣿⣿⣿⣇⠁⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣿⣿⣷⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠑⠄⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠉⡀⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⣴⣶⣶⣶⣶⡾⣿⣆⠀⠀⠠⡎⠁⣾⣿⣿⣿⣦⡀⠘⠀⠀⢀⣤⣶⣾⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⢺⣤⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠻⣿⣿⣿⣿⣥⣝⢿⣅⣄⠀⠀⠀⠉⠀⠀⠈⠀⠘⠂⠀⠀⠸⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⢸⣿⣿⡇

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠘⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢿⣿⣿⣿⣧⡽⡟⢿⡿⠁⠀⣤⡀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠘⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠸⠿⣿⡇

⠸⠿⠿⣿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠷⠦⠀⠀⠘⢿⢿⡿⠸⠍⠀⠉⠙⠿⠿⠿⠿⠿⠜⠿⠿⠟⠿⠅⠁⠨⠁⠄⠀⠈⠿⠷⠤⠀⠀⠀⠀⠘⠆⠀⠀⠸⠿⠿⠿⠟⠻⠇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠆

[21A⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠂⢀⣤⣤⣄⠀⢲⣶⣶⡆⠀⣶⣶⣶⠀⢰⡖⠂⢲⣶⡖⠒⣶⣶⣶⠒⢶⣶⣶⣶⡶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆

⢸⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠈⠛⠛⠿⢿⣿⣿⣿⠁⠀⣿⣿⡟⠀⢀⣴⣶⣾⣿⠃⠀⣿⣿⡇⠀⢸⣿⣿⣿⠃⠀⣿⣿⡟⠁⢠⣤⣤⡀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⣿⣿⣿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣿⣿⣿⣿⣿⠿⣷⣶⣤⣄⠀⠙⣿⣿⠀⠀⣿⣿⡇⠀⢸⣿⣿⣿⣿⠀⠀⣿⣿⡇⠀⢸⣿⣿⣿⠀⠀⣿⣿⣇⠀⠘⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢻⣿⣧⡀⠈⠛⠛⠋⠀⣠⣿⣿⠀⠀⣿⣿⡇⠀⢸⣿⣿⣿⣿⠀⠀⣿⣿⡇⠀⢸⣿⣿⡿⠀⠀⣿⣿⡿⢿⣶⣦⣤⡀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣦⣶⣿⣿⣧⣤⣾⣿⣿⣿⣿⣀⣸⣿⣿⣷⣀⡀⠉⣉⣤⠀⢀⣿⣿⣄⠀⠙⠛⠛⠃⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡇

⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠉⠀⠀⠸⣿⡿⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢻⣿⢻⢻⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢛⣻⣳⣳⣻⣿⣾⣾⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣻⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⣿⣿⣿⡿⠛⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠿⠗⠋⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠉⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣯⡦⠠⢠⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡫⠾⠟⢌⣄⣴⠖⠚⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⠰⠀⢈⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⡀⠴⢶⣿⠧⠀

⢠⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣇⢠⡀⢠⣴⠂

⢸⣿⣿⣿⣷⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⣴⣾⣤⣤⡈⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⣿⣿⣿⣿⣿⣿⡈⠁⠀⠈⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣿⣿⣿⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡘⠆⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠋⠀⡀⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⣴⣶⣶⣶⣶⡾⣿⣆⠀⠀⠠⣞⠁⣺⣿⣿⣿⡦⡀⠐⠂⠀⢀⣤⣶⣾⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⣷⣀⢀⡀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠻⣿⣿⣿⣿⣧⣝⢻⣅⣄⠀⠉⠀⠉⠈⠀⠉⠀⠈⠃⠀⠀⠸⣿⣿⣿⣿⣿⣧⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⢸⣿⣾⡇

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣧⡄⢿⣿⣿⣿⣷⣽⡟⢿⡻⠁⠀⣤⣀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠘⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠸⠿⣿⡇

⠸⠿⠿⣿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠷⠦⠀⠀⠘⢿⡿⡷⠘⠀⠀⠀⠙⠿⠿⠿⠿⠿⠌⠿⠿⠛⠏⠁⠁⠠⠁⠄⠀⠈⠿⠿⠦⠀⠀⠀⠀⠈⠇⠀⠀⠸⠿⠿⠿⠏⠻⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡿⠷⠆

[21A⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠂⢀⣤⣤⣄⠀⢲⣶⣶⡆⠀⢲⣶⣶⠀⢰⡖⠂⢲⣶⡖⠒⣶⣶⣶⠒⢶⣶⣶⣶⡶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆

⢸⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠈⠛⠛⠿⢿⣿⣿⣿⠁⠀⣿⣿⡟⠀⢀⣴⣶⣾⣿⠃⠀⣿⣿⡏⠀⢸⣿⣿⣿⠃⠀⣿⣿⡟⠁⢠⣤⣤⡀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⣿⣿⣿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣿⣿⣿⠿⣷⣶⣤⣄⠀⠙⣿⣿⠀⠀⣿⣿⡇⠀⢸⣿⣿⣿⣿⠀⠀⣿⣿⡇⠀⢸⣿⣿⣿⠀⠀⣿⣿⣇⠀⠘⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢻⣿⣧⡀⠈⠛⠛⠛⠀⣠⣿⣿⠀⠀⣿⣿⡇⠀⢸⣿⣿⣿⣿⠀⢀⣿⣿⡇⠀⢸⣿⣿⡿⠀⠀⣿⣿⡿⢿⣶⣦⣤⡀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣦⣶⣿⣿⣧⣤⣾⣿⣿⣿⣿⣀⣸⣿⣿⣷⣀⡀⠉⣉⣤⠀⢀⣿⣿⣄⠀⠙⠛⠛⠃⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠋⠀⠁⠸⣿⡟⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢻⣿⢻⢻⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⢿⣯⣯⢻⣯⣏⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢛⣻⣳⣻⣻⣿⣾⣾⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣻⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⡿⡟⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⠟⠟⠋⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠉⠉⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣯⣧⠠⠠⢰⣿⣧⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡩⠾⠟⢍⣤⣴⠗⠛⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠼⠈⢈⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⡄⠤⢶⣾⠿⠄⠀

⢠⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⡄⠀⣠⣧⠀

⢸⣿⣿⣿⣷⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⣠⡀⠀⢴⣾⣴⣤⠍⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠄⢸⣿⣿⣿⣿⣿⠆⠉⠁⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣿⣿⣿⣶⣿⣿⣿⣿⣷⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⠂⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠛⢯⠉⠁⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⣠⣶⣶⣶⣶⡾⣿⣇⡀⠀⠠⢾⠁⢸⣿⣿⣿⣶⣄⠀⠃⠀⢀⣤⣶⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⢰⣄⠀⢠⡄

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠙⣿⣿⣿⣿⣧⢍⢻⣇⣄⠀⠘⠀⠉⠉⠁⠈⠀⠈⠃⠀⠀⠸⣿⣿⣿⣿⣿⣿⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣷⣿⡇

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠘⣿⣿⣿⡿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣄⢺⣿⣿⣿⣷⣼⡿⢻⡿⠁⠀⢠⣄⠀⠀⠀⠀⠀⠀⢡⠀⠀⠘⢿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢿⣿⡇

⠸⠿⢿⣿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠦⠀⠀⠘⢿⣿⡷⠈⠀⠈⠀⠉⠻⠿⠿⠿⠿⠇⠻⠿⠛⠿⠃⠁⠸⠁⠄⠀⠀⠻⠿⠦⠀⠀⠀⠀⠀⠣⠀⠀⠸⠿⠿⠿⠟⠻⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠮⠁

[21A⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠂⢀⣤⣤⣄⠀⢲⣶⣶⡆⠀⣲⣶⣶⠀⢰⡖⠂⢲⣶⡖⠒⣶⣶⣶⠒⢶⣶⣶⣶⡶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆

⢸⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠈⠛⠛⠿⢿⣿⣿⣿⠁⠀⣿⣿⡟⠀⢀⣴⣶⣾⣿⠃⠀⣿⣿⡟⠀⢸⣿⣿⣿⠃⠀⣿⣿⡟⠁⢠⣤⣤⡀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢿⣿⣧⡀⠈⠛⠛⠛⠀⣠⣿⣿⠀⠀⣿⣿⡇⠀⢸⣿⣿⣿⣿⠀⢀⣿⣿⡇⠀⢸⣿⣿⡿⠀⠀⣿⣿⡿⢿⣶⣦⣤⡀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣦⣶⣿⣿⣧⣤⣾⣿⣿⣿⣿⣀⣸⣿⣿⣷⣀⡀⠉⣉⣤⠀⢀⣿⣿⣄⠀⠙⠛⠛⠃⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠛⠀⠁⠸⣿⡟⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢻⣿⢻⢻⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣯⣯⢿⣯⣏⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢛⣻⣳⣳⣻⣿⣾⣾⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⡿⡟⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠟⠟⠋⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣯⡧⠠⢠⢰⣿⣧⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡩⠾⠟⢭⣄⣴⠒⠚⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡼⠈⢈⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⠠⠶⠾⠿⠷⠀⠀

⢠⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡆⣰⡀⢀⠴⠄⠀

⢸⣿⣿⣿⣷⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⣾⣧⣤⢌⠑⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⠛⠋⠁⠈⠁⠈⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣿⣿⣿⣶⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠂⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢮⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⣠⣶⣦⣴⣶⡶⣿⣆⡀⠀⠠⢾⠁⢸⣿⣿⣿⣦⣄⠀⠃⠀⢀⣤⣶⣾⣿⣶⡄⠘⣿⡇⠀⠀⠀⠀⠀⠈⠘⠀⠀⠀⠀⣆⠀⠀⢠⡄

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠸⣿⣿⣿⣿⣇⣝⢻⣇⣄⠀⠘⠀⠉⠙⠋⠈⠀⠈⠃⠀⠀⠘⣿⣿⣿⣿⣿⣷⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⣿⡇

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠘⣿⣿⣿⡿⢿⣿⠟⡿⣿⣿⣿⣿⣷⡄⢻⣿⣿⣿⣷⣽⡿⢿⡿⠁⠀⢠⣀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠈⢿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⡇

⠸⠿⠿⣿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠦⠀⠀⠘⢿⣿⣷⠈⠈⠂⠁⠈⠻⠿⠿⠿⠿⠎⠻⠿⠟⠿⠃⠁⠸⠁⠄⠀⠀⠿⠿⠦⠀⠀⠀⠀⠀⠣⠀⠀⠘⠿⠿⠿⠟⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠾⠝⠃

⢸⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠈⠛⠛⠿⢿⣿⣿⣿⠁⠀⣿⣿⡟⠀⢀⣴⣶⣾⣿⠃⠀⣿⣿⡏⠀⢸⣿⣿⣿⠃⠀⣿⣿⡟⠁⢠⣤⣤⡀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⢻⣿⣧⡀⠈⠛⠛⠛⠀⣠⣿⣿⠀⠀⣿⣿⡇⠀⢸⣿⣿⣿⣿⠀⠀⣿⣿⡇⠀⢸⣿⣿⡿⠀⠀⣿⣿⡿⢿⣶⣦⣤⡀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣦⣶⣿⣿⣧⣤⣾⣿⣿⣿⣿⣀⣸⣿⣿⣷⣀⡀⠉⣉⣤⠀⢀⣿⣿⣄⠀⠙⠛⠛⠃⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡇

⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠛⠁⠀⠸⣿⡿⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣿⣻⣻⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠛⢻⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣯⢯⢻⣧⣯⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣻⣳⣳⢻⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⡿⡟⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠟⠋⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣧⠠⠠⢰⣿⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠾⠟⢩⣄⣴⠖⠚⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡼⠈⢈⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⠀⠒⠾⠿⠷⠄⠀

⢠⣀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠆⣴⣀⠠⠴⠅⠀

⢸⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⣾⣧⣤⣍⠑⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠿⣿⠋⠉⠀⠀⠈⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⢀⣿⣿⣷⣴⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠂⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠈⠀⠀⠀⡎⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⣠⣶⣦⣤⣶⡶⣿⣗⡀⠀⠀⢶⠁⢸⣿⣿⣿⣦⣄⠀⠃⠀⠀⣤⣶⣾⣿⣶⡄⠛⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⢀⡄

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠘⣿⣿⣿⣿⣇⢝⢻⣇⣄⠀⠈⠀⠉⠙⠋⠉⠀⠈⠃⠀⠀⠘⣿⣿⣿⣿⣿⣧⠀⠀⠑⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣴⣿⡇

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠘⣿⣿⣿⡿⣿⣿⠿⣿⣿⣿⣿⣿⣷⡄⢺⣿⣿⣿⣷⣽⣿⢿⣿⠁⠀⢠⣀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠈⢿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⣿⣿⡇

⠸⠿⠿⣿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠦⠀⠀⠘⢿⣿⣿⠈⠓⠊⠂⠙⠿⠿⠿⠿⠿⠎⠻⠿⠟⠿⠃⠁⠸⠁⠀⠀⠀⠻⠷⠦⠀⠀⠀⠀⠀⠣⠀⠀⠘⠿⠿⠿⠟⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠾⠝⠃

⢸⣿⣿⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⠿⣷⣶⣤⣄⠀⠙⣿⣿⠀⠀⣿⣿⡇⠀⢸⣿⣿⣿⣿⠀⠀⣿⣿⡇⠀⢸⣿⣿⣿⠀⠀⣿⣿⣇⠀⠘⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠹⣿⣧⡀⠈⠛⠛⠋⠀⣠⣿⣿⠀⠀⣿⣿⡇⠀⢸⣿⣿⣿⣿⠀⠀⣿⣿⡇⠀⢸⣿⣿⡿⠀⠀⣿⣿⡿⢿⣶⣦⣤⡀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣷⣶⣶⣶⣿⣿⣿⣿⣶⣶⣿⣿⣧⣤⣾⣿⣿⣿⣿⣀⣸⣿⣿⣷⣀⡀⠉⣉⣤⠀⢀⣿⣿⣄⠀⠙⠛⠛⠃⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡇

⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠏⠁⠀⠸⣿⡿⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⣿⡽⣾⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠛⢻⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣷⢣⣻⣷⣷⡃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣻⣻⣽⣽⣻⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⡋⠉⠉⠉⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠛⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⠽⠻⠊⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣽⠡⠠⣰⣿⣿⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢵⢟⢩⣤⣴⠖⠚⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⢀⣀⣀⣄⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡾⠀⠀⡕⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⠙⠛⠋⡀⠀

⢠⣄⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⠿⠋⠀⢾⠤⠰⠚⠃⠀

⢸⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⣠⠀⠀⢠⣶⣧⣤⣍⠙⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⣻⣿⣷⣦⣾⣿⣿⣿⣷⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠙⠈⡇⠀⠀⠀⣄⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢀⣴⣶⣴⣶⡶⢾⣗⡀⠀⠀⢴⠁⢸⣿⣿⣿⣶⣄⠀⠃⠀⠀⣤⣶⣾⣿⣦⠀⣻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣆⡀⠀⣠⡄

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠈⢿⣿⣿⣯⣏⣹⡻⣯⣠⡀⠀⠀⠈⠉⠉⠀⠀⠈⠓⠀⠀⠘⢿⣿⣿⣿⣿⡄⠀⢀⣿⣶⣶⣢⢀⡀⠀⠀⠀⠀⠀⠸⣿⣿⣾⣿⡇

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠈⢿⣿⣿⡟⣿⣿⢿⠿⣿⣿⣿⣿⣷⣄⠰⣿⣿⣿⣿⣼⣿⢻⣿⠍⠀⠀⣀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠈⢻⣿⣿⣿⣷⣤⣾⣿⣿⣿⡿⠻⠀⠀⠀⠀⠀⠀⣄⣛⠛⢿⣿⡇

⠸⠿⠿⣿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠄⠀⠈⠿⣿⣿⠄⠘⠉⠀⠀⠻⠿⠿⠿⠿⠧⠻⠿⠟⠻⠉⠉⠀⠌⠀⠀⠀⠹⠿⠦⠀⠀⠀⠀⠀⠣⠀⠀⠀⠿⠿⠿⠹⠿⠿⠿⠿⠿⠃⠀⠀⠂⠀⠀⠀⠀⠹⠿⠿⠿⠍⠁

⢸⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠛⠛⠿⢿⣿⣿⣿⠁⠀⣿⣿⡟⠀⢀⣴⣶⣾⣿⠃⠀⣿⣿⡏⠀⢸⣿⣿⣿⠃⠀⣿⣿⡟⠁⢠⣤⣤⡀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⠿⣷⣶⣤⣄⠀⠙⣿⣿⠀⠀⣿⣿⡇⠀⢸⣿⣿⣿⣿⠀⠀⣿⣿⡇⠀⢸⣿⣿⣿⠀⠀⣿⣿⣇⠀⠘⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⣿⣧⡀⠈⠛⠛⠛⠀⣠⣿⣿⠀⠀⣿⣿⡇⠀⢸⣿⣿⣿⣿⠀⠀⣿⣿⡇⠀⢸⣿⣿⡿⠀⠀⣿⣿⡿⢿⣶⣦⣤⡀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣷⣶⣶⣶⣿⣿⣿⣿⣦⣶⣿⣿⣧⣤⣾⣿⣿⣿⣿⣀⣸⣿⣿⣷⣀⡀⠉⣉⣤⠀⢀⣿⣿⣄⠀⠙⠛⠛⠃⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣽⡇

⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠟⠁⠀⠸⣿⡿⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡻⣿⡟⡟⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡾⠛⢻⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡻⣿⣷⣻⣿⣷⣳⡃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣻⣟⣜⣾⣿⣷⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣯⡥⡀⠈⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠿⠻⠚⠁⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣽⠅⠄⡄⣾⣿⡆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠵⠿⢫⣡⣤⡖⠒⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢀⣠⣠⣤⣄⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡦⠆⠀⡡⠉⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣉⠉⠉⠁⠀⠀

⢠⣤⣀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⣛⠻⠿⢿⣿⣿⡿⠛⠉⠀⠀⠿⠄⠐⠉⠁⠀

⢸⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⣀⠀⡀⠀⣴⣯⣤⣌⠉⠻⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠌⠓⠀⡀⠠⣤⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⢀⣹⣿⣷⣤⣶⣿⣿⣿⣿⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃⠀⠀⠀⣆⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⢀⣴⣶⣤⣶⣶⢾⣷⣂⠀⠀⠰⡏⢀⣿⣿⣿⡶⣄⠀⠃⠀⠀⣠⣴⣶⡤⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⡀⠀⣰⡆

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⢿⣿⣿⣯⣯⣨⡛⣿⣀⡄⠀⠀⠈⠁⠀⠀⠀⠈⠓⠀⠀⠀⢿⣿⣿⣷⣠⠀⢀⣸⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿⡇

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠈⢿⣿⣿⣟⢿⣿⣿⡿⣿⣿⣿⣿⣷⣆⠀⣿⣿⣿⣿⣬⣿⠟⣿⠯⠀⠀⣀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠹⣿⣿⣿⣧⣸⡿⠿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⣤⣙⡙⠿⣿⡇

⠸⠿⠿⣿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠦⠀⠀⠻⣿⣿⠄⠙⠐⠀⠁⠿⠿⠿⠿⠿⠧⠘⠿⠿⠻⠟⠉⠀⠏⠀⠀⠀⠘⠿⠦⠀⠀⠀⠀⠀⠱⠀⠀⠀⠋⠿⠿⠿⠿⠇⠀⠀⠀⠉⠉⠛⠉⠛⠃⠀⠀⠿⠿⠿⠷⠙⠁

⢸⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠛⠛⠿⣿⣿⣿⣿⠁⠀⣿⣿⡟⠀⢀⣴⣶⣾⣿⠃⠀⣿⣿⡏⠀⢸⣿⣿⣿⠃⠀⣿⣿⡟⠁⢠⣤⣤⡀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⠿⣷⣶⣤⣄⠀⠙⣿⣿⠀⠀⣿⣿⡇⠀⢸⣿⣿⣿⣿⠀⠀⣿⣿⡇⠀⢸⣿⣿⣿⠀⠀⣿⣿⣇⠀⠘⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣧⡀⠈⠛⠛⠋⠀⣠⣿⣿⠀⠀⣿⣿⡇⠀⢸⣿⣿⣿⣿⠀⠀⣿⣿⡇⠀⢸⣿⣿⡿⠀⠀⣿⣿⡿⢿⣶⣦⣤⡀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣦⣶⣿⣿⣧⣤⣾⣿⣿⣿⣿⣀⣰⣿⣿⣷⣀⡀⠉⣉⣤⠀⢀⣿⣿⣄⠀⠙⠛⠛⠃⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣽⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡟⠁⠀⠸⣿⡿⠀⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⣿⡟⡟⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠛⠻⢛⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡻⣿⣷⣻⣿⣷⣹⡃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣻⣟⣜⡞⣿⣷⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣿⣿⣿⣿⠿⢿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣭⣭⡭⡉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠿⠒⠁⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣭⠌⠄⡀⣾⣿⡆⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠾⠫⣡⣤⡶⠒⠃⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢠⣤⣤⣴⣆⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡦⠆⠀⡡⠉⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⣀⠉⠉⠀⠀⠀

⢠⣤⣀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠿⡣⣉⠛⠹⠿⠛⠿⣏⠀⠀⠀⠀⠗⠂⠘⠉⠀⠀

⢸⣿⣿⣿⣿⣿⣶⣶⣄⡀⠀⠀⠀⠀⢀⣠⠀⡀⠀⣴⣯⣤⣤⡉⠳⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠄⠀⠹⠿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢀⣻⣿⣷⣤⣴⣿⣿⣿⣿⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⣴⣶⣦⣴⣶⢾⣿⣂⠀⠀⠠⠏⠀⣿⣿⣿⡷⢄⠀⠒⠀⠀⢠⣤⠦⠠⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⡀⢀⣴⡇

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⢄⠀⢻⣿⣿⣯⣿⣩⡛⢿⣅⣄⠀⠀⠈⠉⠁⠀⠀⠀⠳⠀⠀⠀⠻⣿⣷⣷⣷⡀⢢⡌⠒⠻⢿⣿⣷⡄⠀⠀⠀⠀⠀⢿⣿⣷⣿⣿⡇

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠈⢻⣿⣿⣟⢿⣿⣿⣿⢿⣿⣿⣿⣷⣦⠀⢿⣿⣿⣿⣤⣿⡟⣿⡯⠁⠀⢀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠹⣿⣿⣿⣇⣼⡆⠀⠀⠈⠉⠙⠛⠀⠀⠀⠀⢰⣤⣍⠘⢿⣿⡇

⠸⠿⠿⣿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠦⠀⠀⠻⣿⣿⠌⠃⠁⠀⠈⠻⠿⠿⠿⠿⠷⠘⠿⠿⠻⠟⠉⠀⠃⠁⠀⠀⠈⠿⠦⠀⠀⠀⠀⠀⠑⠀⠀⠀⠹⠿⠿⠿⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠧⠉⠁

[21A⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠂⢀⣤⣤⣄⠀⢲⣶⣶⡆⠀⣲⣶⣶⠀⢰⡖⠂⢲⣶⡖⠒⣶⣶⣶⠖⢶⣶⣶⣶⡶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆

⢸⣿⣿⣿⣿⡿⠿⠟⠙⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠛⠛⠿⢿⣿⣿⣿⠁⠀⣿⣿⡟⠀⢀⣴⣶⣾⣿⠃⠀⣿⣿⡟⠀⢸⣿⣿⣿⠃⠀⣿⣿⡟⠁⢠⣤⣤⡀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⣿⣿⣿⣿⠿⣷⣶⣤⣄⠀⠙⣿⣿⠀⠀⣿⣿⡇⠀⢸⣿⣿⣿⣿⠀⠀⣿⣿⡇⠀⢸⣿⣿⣿⠀⠀⣿⣿⣇⠀⠘⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⣧⡀⠈⠛⠛⠛⠀⣠⣿⣿⠀⠀⣿⣿⡇⠀⢸⣿⣿⣿⣿⠀⠀⣿⣿⡇⠀⢸⣿⣿⡿⠀⠀⣿⣿⡿⢿⣶⣦⣤⡀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣶⣶⣿⣿⣧⣤⣾⣿⣿⣿⣿⣀⣰⣿⣿⣷⣀⡀⠉⣉⣤⠀⢀⣿⣿⣄⠀⠙⠛⠛⠃⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠸⣿⡿⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣿⣏⣯⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠛⠻⢛⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣿⣿⡽⣽⣿⣼⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠂⠀⢽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣛⣟⣾⣞⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣿⣿⠿⠛⠋⠉⠙⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣭⣽⡻⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠽⠻⠚⠁⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠄⠄⡀⣿⣿⡧⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠿⠩⣥⣤⡶⠋⠁⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠒⠶⠶⠿⠣⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠃⠀⡐⠁⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⢰⠀⠀⡀⠀⠀⠀

⢠⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠛⠉⢠⣾⡿⡄⠀⠀⠀⠈⠉⠀⠁⠀⠀⠀

⢸⣿⣿⣿⣿⣷⣶⣦⣄⡀⠀⠀⠀⠀⣠⣤⡀⠃⠀⢰⣾⣴⣦⢈⠑⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣻⣿⣿⣦⣴⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠐⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⣠⣶⣶⣴⣶⡶⣿⣗⡀⠀⠀⠎⠀⣿⣿⣿⡷⣄⠀⠒⠀⠀⢀⣔⣒⣶⣿⣿⣷⣤⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣿⣷⣄⠀⣠⣾⡇

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⡀⠘⣿⣿⣿⣽⣁⣝⢻⣇⣠⠀⠀⠀⠉⠀⠀⠀⠀⠳⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠘⠃⠀⠀⠀⠀⠀⠹⣿⣿⣾⣿⣿⡇

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⢻⣿⣿⣿⠿⣿⣿⡿⢿⣿⣿⣿⣿⣦⡀⢺⣿⣻⣿⣧⣽⡿⢻⣿⠍⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⣶⣮⣅⣙⢿⣿⡇

⠸⠿⠿⣿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠦⠄⠀⠹⣿⣿⠆⠉⠃⠑⠈⠛⠿⠿⠿⠿⠿⠄⠻⠿⠟⠿⠋⠁⠸⠁⠀⠀⠀⠸⠦⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠿⠿⠿⠿⠿⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠮⠙⠃

⢸⣿⣿⣿⣿⠿⠟⠋⠉⠉⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠛⠛⠿⢿⣿⣿⣿⠁⠀⣿⣿⡟⠀⢀⣴⣶⣾⣿⠃⠀⣿⣿⡏⠀⢸⣿⣿⣿⠇⠀⣿⣿⡟⠁⢠⣤⣤⡀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⣿⣿⣿⣿⠿⣷⣶⣤⣄⠀⠙⣿⣿⠀⠀⣿⣿⡇⠀⢸⣿⣿⣿⣿⠀⠀⣿⣿⡇⠀⢸⣿⣿⣿⠀⠀⣿⣿⣇⠀⠘⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣿⣧⡀⠈⠛⠛⠋⠀⣠⣿⣿⠀⠀⣿⣿⡇⠀⢸⣿⣿⣿⣿⠀⠀⣿⣿⡇⠀⢸⣿⣿⡿⠀⠀⣿⣿⡿⢿⣶⣦⣤⡀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣶⡶⠿⢿⣧⣤⣾⣿⣿⣿⣿⣀⣸⣿⣿⣷⣀⡀⠉⣉⣤⠀⢀⣿⣿⣄⠀⠙⠛⠛⠃⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠸⣿⡟⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣯⢿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⠟⢛⢻⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⣞⣟⣿⣞⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⢼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢻⣿⣫⣯⠾⠿⠿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠟⠁⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⣉⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠈⠈⠛⠛⠿⠃⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⠄⠀⠀⠎⠉⠻⣿⣿⢿⣟⠋⠉⠀⠀⠀⣴⡀⢀⡀⠀⠀⠀⠀

⢠⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣇⠘⢿⡮⢧⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣷⣶⣦⣄⡀⠀⠀⠀⠀⣠⣴⡄⠉⠀⢰⣶⣷⣶⣤⠉⠳⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣼⣿⣿⣦⣴⣾⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠈⠃⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⠀⠀⠀⠀⣰⡄

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⢀⣴⣶⣶⣶⡶⢾⣿⣂⠀⠀⠀⠸⣿⣿⣦⣄⠀⠐⠀⠀⠀⢀⣴⣾⣿⣿⣷⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄⢀⣴⣾⣿⡇

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣀⠀⢻⣿⣿⣯⣏⣩⡛⣿⣠⡄⠀⠀⠉⠉⠀⠀⠳⡀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠁⠀⠀⠀⠀⠺⣿⢻⣿⣿⣿⣿⡇

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠹⣿⣿⣿⠻⣿⣻⣿⠿⣿⣿⣿⣿⣷⣆⠰⣿⣿⣿⣿⣸⣿⠻⣿⠏⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠸⣷⣦⣄⡙⣿⣿⣿⠃

⠸⠿⠿⣿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠄⠀⠹⢿⣿⡧⠈⠀⠀⠀⠈⠻⠿⠿⠿⠿⠷⠹⠿⠟⠿⠋⠉⠀⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠹⠿⠿⠿⠿⠿⠿⠿⠿⠄⠀⠀⠀⠀⠻⠿⠿⠿⠌⠛⠿⠃

⢸⣿⣿⣿⣿⠿⠟⠋⠉⠋⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠈⠛⠛⠿⣿⣿⣿⣿⠁⠀⣿⣿⡿⠀⢀⣴⣶⣾⣿⠇⠀⣿⣿⡏⠀⢸⣿⣿⣿⠃⠀⣿⣿⡟⠁⢠⣤⣤⡀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠛⣿⣿⣿⣿⠿⣷⣶⣤⣄⠀⠙⣿⣿⠀⠀⣿⣿⡇⠀⢸⣿⣿⣿⣿⠀⠀⣿⣿⡇⠀⢸⣿⣿⣿⠀⠀⣿⣿⣇⠀⠘⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣧⡀⠈⠛⠛⠋⠀⣠⣿⣿⠀⠀⣿⣿⡇⠀⢸⣿⣿⣿⣿⠀⠀⣿⣿⡇⠀⢸⣿⣿⡿⠀⠀⣿⣿⡿⢿⣶⣦⣤⡀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣶⡶⠿⠿⣧⣤⣾⣿⣿⣿⣿⣀⣸⣿⣿⣷⣀⡀⠉⣉⣤⠀⢀⣿⣿⣄⠀⠙⠛⠛⠃⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠸⣿⡟⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⢻⡃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠟⠛⢻⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣮⣿⣿⣏⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠀⠼⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢛⡿⠳⠃⠛⠛⠛⠿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠟⠋⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢀⣀⠀⡀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⢿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣀⡀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠈⠉⠛⠛⠋⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠙⠂⠀⠀⣘⣿⣿⠿⣟⣻⣯⡀⠀⠀⠀⢸⣅⡀⢤⠀⠀⠀⠀⠀

⢠⣤⣀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡙⠛⠻⡆⠙⠻⠏⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣶⣶⣤⣀⠀⠀⠀⠀⢠⣤⣄⢉⠀⢠⣶⣿⣶⣤⡌⠙⠶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡄

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢬⣿⣿⣦⣤⣾⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⠀⠀⠀⣠⣿⡆

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⣰⣶⣦⣶⣶⢶⣿⣂⠀⠀⠀⠐⣿⣆⡀⠀⠂⠀⠀⠀⠀⠀⢹⣿⣿⣿⣷⣿⣿⣷⣶⣄⠤⠀⠀⠀⠀⢸⣿⣷⣄⣴⣿⣿⣿⡇

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠙⣿⣿⣯⣏⣨⡛⣿⣅⣄⠀⠀⠈⠉⠙⢦⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⡈⠿⡟⣿⣿⣿⣿⣿⡇

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠘⣿⣿⣿⡟⢿⣿⡿⣿⣿⣿⣿⣿⣿⣦⠀⢿⣿⣿⣿⣜⣿⠿⣿⡯⠁⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⢿⣷⣤⣈⢻⣿⣿⣿⠃

⠸⡿⠿⣿⠿⢿⠿⠿⠿⠿⡿⠿⠿⠿⠿⠷⠤⠀⠘⢿⣿⡷⠈⠙⠂⠀⠀⠹⠿⠿⠿⠿⠿⠘⠿⠿⠻⠟⠉⠀⠏⠁⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠿⠿⠿⠿⠿⠿⠄⠀⠀⠘⠻⠿⠿⠦⠙⠻⠿⠃

⢸⣿⣿⣿⣿⡿⠿⠛⠉⠉⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⡀⠈⠛⠛⠿⣿⣿⣿⣿⠁⠀⣿⣿⡿⠀⢀⣴⣶⣾⣿⠃⠀⣿⣿⡟⠀⢸⣿⣿⣿⠃⠀⣿⣿⡟⠁⢠⣤⣤⡀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢻⣿⣿⣿⠿⣷⣶⣤⣄⠀⠙⣿⣿⠀⠀⣿⣿⡇⠀⢸⣿⣿⣿⣿⠀⠀⣿⣿⡇⠀⢸⣿⣿⣿⠀⠀⣿⣿⣇⠀⠘⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣹⣧⡀⠈⠛⠛⠋⠀⣠⣿⣿⠀⠀⣿⣿⡇⠀⢸⣿⣿⣿⣿⠀⠀⣿⣿⡇⠀⢸⣿⣿⡿⠀⠀⣿⣿⡿⢿⣶⣦⣤⡀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣦⡶⠿⠿⠧⣤⣾⣿⣿⣿⣿⣀⣰⣿⣿⣷⣀⡀⠉⣉⣤⠀⢀⣿⣿⣄⠀⠙⠛⠛⠃⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠹⣿⡿⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣻⣿⣿⣽⡅

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠏⠉⢻⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠫⠳⠻⠷⠿⢿⣷⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠻⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⠷⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⠁⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠙⠚⠻⠶⠶⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠿⣿⡋⠉⠀⠀⠄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⠿⣿⢿⣿⡟⠁⠛⢿⣿⠻⡄⠀⠀⠀⠋⠒⠈⠁⠀⠀⠀⠀⠀⠀

⢰⣤⣤⣀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⠓⠀⠀⠛⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⡄

⢸⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⣤⣼⡈⠁⢠⣤⣾⣿⣶⣦⢌⠙⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡇

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣷⣆⣴⣿⣿⣿⣿⣿⣶⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣶⣶⣤⣴⣤⣀⠀⠀⠀⠀⠀⠀⠀⣿⣆⠀⠀⠀⣠⣼⣿⣿⡇

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⣴⣶⣦⣤⢤⣶⣓⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⣻⣿⣷⣠⣾⣿⣿⣿⣿⡇

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠸⣿⣯⣟⣩⡛⢿⣏⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣧⠀⢠⣈⠛⠛⣿⣿⣿⣿⣿⣿⠇

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⢻⣿⣿⣯⠻⣿⠟⠛⠛⢻⣿⣿⣿⣿⣦⡀⢟⣿⣿⣜⣿⡟⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣦⣬⠛⣿⣿⣿⣿⠀

⠸⠿⠿⣿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠄⠀⠹⣿⣿⠆⠀⠀⠀⠀⠀⠹⠿⠿⠿⠿⠷⠸⠟⠳⠛⠉⠀⠏⠁⠄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠿⠿⠧⠉⠻⠿⠿⠧⠌⠛⠛⠛⠁

[21A⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠂⢀⣤⣤⣄⠀⢲⣶⣶⡆⠀⣲⣶⣶⠀⢰⡖⠒⢲⣶⡖⠒⣶⣶⣶⠖⢶⣶⣶⣶⡶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆

⢸⣿⣿⣿⣿⣿⠿⠟⠋⠉⠉⠉⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⡀⠈⠛⠛⠿⣿⣿⣿⣿⠃⠀⣿⣿⡿⠀⢀⣴⣶⣾⣿⠃⠀⣿⣿⡏⠀⢸⣿⣿⣿⠃⠀⣿⣿⡟⠁⢠⣤⣤⡀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⢿⣿⣿⠿⣷⣶⣤⣄⠀⠙⣿⣿⠀⠀⣿⣿⡇⠀⢸⣿⣿⣿⣿⠀⠀⣿⣿⡇⠀⢸⣿⣿⣿⠀⠀⣿⣿⣇⠀⠘⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣧⡀⠈⠛⠛⠛⠀⣠⣿⣿⠀⠀⣿⣿⡇⠀⢸⣿⣿⣿⣿⠀⢀⣿⣿⡇⠀⢸⣿⣿⡿⠀⠀⣿⣿⡿⣿⣶⣦⣤⡀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣦⣶⠿⠿⠧⠤⢾⣿⣿⣿⣿⣀⣸⣿⣿⣷⣀⡀⠉⣉⣤⠀⢀⣿⣿⣄⠀⠙⠛⠛⠃⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡟⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⡟⣟⣿⣟⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⠉⢛⣿⢿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠁⠀⠀⠀⠀⠀⠀⠈⠹⣿⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣍⣙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡦⠙⣿⣿⣿⣿⣿⣿⣿⡿⠠⢤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠀⠀⠀⢸⣿⣿⣿⡿⠟⠋⠀⡀⢀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣻⣧⡄⠀⠀⠀⠀⣿⢄⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣾⣿⡿⠛⠈⠙⠻⠿⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣼⡇

⢰⣶⣶⣤⣄⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣸⣿⡇

⢸⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡀⠀⠀⠀⢀⣦⣿⠀⠀⣤⠀⣾⣿⣷⣷⡆⠙⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⡇

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠸⣿⣿⣷⣄⣼⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢶⣄⣀⣀⣀⡀⠀⠀⠀⠀⢸⣷⣀⠀⠀⣠⣶⣿⣿⣿⣿⡇

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⢠⣶⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠰⣴⣶⣄⡄⠀⠀⠀⡀⠀⠈⠻⢿⣿⣿⣿⣿⣷⣦⠀⢸⣿⣿⣴⣾⣿⣿⣿⣿⣿⣿⠇

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠈⣿⡥⣬⣙⣿⣤⣦⡀⠀⠀⠀⠀⣿⣿⣿⣧⣤⣾⣿⠃⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷⣦⣉⠁⠹⣿⣿⣿⣿⣿⣿⣿⠁

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠘⢿⣿⣿⡟⢿⣽⡛⠻⠛⠿⣿⣿⣿⣿⣷⡀⠸⣧⣿⣿⠻⣿⠇⠁⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⢀⠊⠙⣿⣿⣿⣿⣿⣿⣶⣎⠻⣿⣿⣿⣿⣿⠀

⠸⠿⠿⣿⠿⢿⠿⠿⠿⠿⠿⠿⢿⠿⠿⠿⠿⠦⠀⠈⠿⣿⣿⠌⠿⠀⠀⠀⠈⠙⠿⠿⠿⠿⠿⠆⠉⠁⠁⠘⠏⠀⠄⠀⠀⠀⠀⠀⠛⠿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠏⠹⠿⠿⠿⠦⠌⠉⠉⠉⠉⠀

[21A⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠂⢀⣤⣤⣄⠀⢲⣶⣶⡆⠀⣲⣶⣶⠀⢰⡖⠒⢲⣶⡖⠒⣶⣶⣶⠒⢶⣶⣶⣶⡶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆

⢸⣿⣿⣿⣿⣿⠿⠛⠛⠉⠉⠉⠉⠉⠙⠻⣿⣿⣿⣿⣿⣿⡀⠈⠛⠛⠿⣿⣿⣿⣿⠃⠀⣿⣿⡿⠀⢀⣴⣶⣾⣿⠇⠀⣿⣿⡟⠀⢸⣿⣿⣿⠇⠀⣿⣿⡿⠁⢠⣤⣤⡀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⣿⣿⠿⣷⣶⣤⣄⠀⠙⣿⣿⠀⠀⣿⣿⡇⠀⢸⣿⣿⣿⣿⠀⠀⣿⣿⡇⠀⢸⣿⣿⣿⠀⠀⣿⣿⣇⠀⠘⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠈⠛⠛⠛⠀⣠⣿⣿⠀⠀⣿⣿⡇⠀⢸⣿⣿⣿⣿⠀⢀⣿⣿⡇⠀⢸⣿⣿⡿⠀⠀⣿⣿⡿⢿⣶⣦⣤⡀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣦⡶⠿⠿⠇⠀⠺⢿⣿⣿⣿⣄⣸⣿⣿⣷⣄⡀⠉⣉⣤⠀⢀⣿⣿⣄⠀⠙⠛⠛⠃⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⡿⠟⠛⠉⠉⠛⠛⠛⠟⣿⣿⣷⡃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠉⠙⣿⣿⡿⠻⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠙⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣭⣍⡙⠻⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣶⣬⣻⣿⣿⣿⣿⣿⠟⠒⠖⠶⠶⢤⠀⠀⠀⠀⠀⠀⠀⠀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢈⣿⠿⣿⣿⠏⠉⢉⣿⣿⠟⠋⠁⠀⠄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⣿⠇⠀⠀⠀⣐⣠⣮⣟⣷⡄⠀⠀⠀⠀⠿⠦⠀⠒⠀⠀⠀⠀⠀⠀⠀⣤⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⡿⠋⠉⠉⠻⠿⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⣼⣿⡇

⢸⣷⣶⣦⣤⣄⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣠⠀⠠⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣼⣿⣿⡇

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⣸⣽⡇⠀⢴⡄⣠⣿⣿⣿⣷⡂⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣠⣾⣾⣿⣿⡇

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣆⣰⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⢸⣿⣄⠀⢀⣤⣾⣿⣿⣿⣿⣿⡇

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⢠⣶⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣠⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣷⡆⠘⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡂

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⣦⣽⣿⣷⣷⣄⠀⠀⠀⠀⠀⠀⠸⣿⣿⣶⣾⡿⠋⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣶⣌⡁⠘⢿⣿⣿⣿⣿⣿⣿⡿⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⢻⣿⣿⣯⢻⣿⡟⠛⢟⣿⠻⣿⣿⣿⣿⣿⠀⠻⠟⢹⣿⡓⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⢀⠏⠈⢻⣿⣿⣿⣿⣶⣦⠹⣿⣿⣿⣿⣿⣷⠀

⠸⠿⠿⣿⠿⢿⠿⠿⠿⠿⠿⠿⢿⢿⠿⠿⠿⠦⠀⠀⠻⣿⣿⡆⠙⠋⠅⠀⠀⠀⠹⠿⠿⠿⠿⠷⠆⠀⠸⠃⠀⠢⠀⠀⠀⠀⠄⠄⠀⠸⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠿⠿⠹⠿⠿⠿⠷⠤⠉⠉⠉⠉⠉⠀

[21A⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆

⢸⣿⣿⣿⣿⣿⠿⠛⠛⠉⠉⠉⠉⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠛⠛⠛⠟⣿⢿⣷⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠉⠙⣿⣿⠿⠻⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠙⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣭⣍⡙⠻⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣌⡻⣿⣿⣿⣿⣿⠟⠒⠂⠶⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢈⣻⠿⣿⣿⠏⠉⢉⣿⣿⠟⠋⠁⠀⠄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⣿⠃⠀⠀⠀⠀⣠⣮⣝⣷⡄⠀⠀⠀⠀⠿⠢⠀⠒⠀⠀⠀⠀⠀⠀⠀⣠⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⡿⠋⠈⠉⠻⠏⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡇

⢸⣷⣶⣦⣤⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣴⣿⣿⡇

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⣨⣽⡄⠀⢴⡄⣠⣿⣿⣿⣷⡀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⡇

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣆⣰⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⢸⣷⣄⠀⢀⣤⣾⣿⣿⣿⣿⣿⡇

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢠⣶⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣠⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣷⡆⠈⢿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿⢿⢿⣿⣿⣿⣿⣿⣦⡀⠀⣦⣼⣿⣷⣷⣄⠀⠀⠀⠀⠀⠀⠘⣿⣿⣤⣾⡿⠃⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣶⣄⡁⠘⢿⣿⣿⣿⣿⣿⣿⠟⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⢻⣿⣿⣧⠘⣇⠀⠈⠉⠙⠛⣿⣿⣿⣿⣧⠀⠹⠏⢙⣿⡓⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⢀⠏⠈⢻⣿⣿⣿⣿⣶⣦⠹⢿⣿⣿⣿⣯⣷⠀

⠸⠿⠿⣿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠦⠀⠀⠻⢿⣿⠆⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠷⠄⠀⠸⠃⠀⠢⠀⠀⠀⠀⠄⠀⠀⠘⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠹⠿⠿⠿⠷⠤⠈⠉⠉⠉⠀⠀

⢸⣿⣿⣿⣿⣿⠿⠛⠋⠁⠀⠀⠀⠀⠉⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠋⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠋⠉⠉⠛⠛⠻⢿⣿⣿⣿⣿⡇

⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⣿⡇

⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠏⠉⢿⣿⡿⠻⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇

⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣉⣛⢿⣿⣿⣿⣿⡧⢄⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣿⠿⠿⠋⠁⠀⠀⠈⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠘⠿⢿⣿⡿⠿⣅⡀⠀⠀⠀⠁⣾⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣿⡿⠗⠾⠟⠻⢿⣷⡟⢳⡀⠀⠀⠀⠉⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠦⣽⣿⠇⠂⠀⠀⠀⠈⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣰⣿⣿⣿⡇

⢸⣿⣷⣶⣦⣤⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣀⣄⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡇

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⢠⣯⣿⠀⢰⡆⠀⣠⣴⣿⣿⣿⣧⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡇

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣷⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣄⠀⣿⣷⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣀⠻⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠘⣿⣿⣿⣿⣿⠿⠯⠙⠛⠿⣿⣿⣿⣿⣿⣷⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠻⢿⣿⣶⣤⡀⠻⣿⣿⣿⣿⣿⣿⠛⠋⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠘⣿⣿⣿⡌⢿⣄⠀⠀⠀⠀⠘⢻⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣴⡘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠻⣿⣿⣿⣷⡈⢿⣿⣿⣿⣯⣿⠷⠄⠀

⠸⠿⠿⣿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠄⠀⠘⠿⣿⡷⠀⠐⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠿⠦⠀⠀⠀⠀⠀⠀⠿⠿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠘⠿⠿⢿⠿⠦⠀⠀⠉⠉⠁⠀⠀⠀

⢸⣿⣿⣿⣿⣿⡿⠛⠋⠉⠀⠀⠀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⡇

⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇

⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠏⠉⢻⣿⡿⠛⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇

⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇

⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠿⣿⣿⣿⠏⠒⠴⢶⣤⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠷⠈⠋⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣰⣿⣫⣟⣷⡄⠀⠀⠀⠀⣿⣤⠀⢤⠄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣶⣿⡟⠋⠉⠙⠿⡿⠏⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⣠⣿⣿⣿⣿⡇

⢸⣿⣿⣶⣶⣤⣴⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⡇

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⣼⣿⡀⠠⣦⠀⢀⣴⣾⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⡇

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠰⣿⣿⣿⣄⣸⣶⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⣿⣷⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⠙⠿⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠈⢿⣿⣿⣿⠿⣿⡋⠈⠍⠻⠿⡿⣿⣿⣿⣿⣕⠀⠀⠀⣴⣿⡿⠁⠀⠀⣀⠀⢠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣤⣀⡙⠿⣿⣿⣿⣿⣿⣟⠉⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠈⢿⣿⣿⡆⢻⠌⢈⠀⠀⠀⠀⠛⣿⣿⣿⣿⣧⡀⠀⢿⣿⣿⣄⠀⣼⣿⣿⢾⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠘⢿⣿⣿⣿⡄⠹⢿⣿⣿⣿⣯⣿⠶⠄⠀

⠸⠿⠿⣿⠿⢿⠿⠿⠿⠿⠿⠿⢿⣿⣿⡿⠿⠿⠦⠀⠈⠿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠿⠿⠿⠄⠀⠿⠿⠷⠄⠈⠋⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠿⠿⠿⠿⠶⠤⠀⠀⠉⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣿⠟⠛⠉⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⡇

⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡇

⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇

⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠋⠉⣻⣿⡿⠻⢿⣿⣿⣿⣦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇

⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠸⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇

⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢿⣿⣿⣿⣿⣿⠧⢤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇

⠘⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠋⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠘⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣩⣻⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⣄⠀⠀⠀⠀⠈⠛⠛⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⠿⠿⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣼⣿⣿⣿⣿⡇

⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠹⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⣾⣿⣿⣿⣿⣿⡇

⢸⣿⣿⣿⣷⣶⣦⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣠⣤⣖⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⡇

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⢠⣵⣯⡀⢰⡆⢀⣤⣾⣿⣿⣿⣎⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢸⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⠇

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠘⣿⣿⣿⡟⠻⡋⠉⠙⠿⢿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⣶⠶⢠⣤⣠⣤⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢼⣿⣦⣄⣈⠛⢿⣿⣿⣿⣿⣿⣏⠉⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠙⣿⣿⣿⡀⢛⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠛⢻⣿⣿⣿⣯⡅⠀⠀⠀⠀⠀⠀⠀⠒⠖⠋⠉⠙⢿⣿⣿⣿⣧⠘⢿⣿⣿⣿⣯⣿⣷⣶⡀⠀⠀

⠸⠿⠿⣿⠿⢿⠿⠿⠿⠿⠿⠿⢿⢿⡿⡿⠿⠿⠷⠄⠀⠘⢿⣿⡷⠘⠁⠑⠀⠀⠀⠀⠉⠙⠿⠿⠿⠧⠀⠀⠀⠀⠹⠾⠿⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⢿⠿⠷⠄⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣿⡿⠛⠋⠉⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⡇

⢸⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⡇

⢸⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠟⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇

⢸⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡇

⢸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠃⠈⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡇

⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇

⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠟⠟⠛⢻⣿⡇⠈⠀⠑⠶⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇

⠈⠘⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣤⣴⣿⣟⡁⠀⠀⠀⠀⢸⣧⣀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣷⣯⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠗⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⠟⠙⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⣴⣿⣿⣿⣿⣿⣿⡇

⢠⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⡇

⠀⣿⣿⣿⣿⣿⣷⣶⣷⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⡇

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⢀⣥⣿⡀⢰⣦⣤⣾⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠸⣿⣿⣿⣾⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⣤⡴⠀⢸⣿⡇⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⣿⣧⡀⠀⠀⠀⠀⠀⠈⠻⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠿⣿⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣟⢙⣿⣿⣿⣆⠀⠀⠀⠀⣿⣤⡄⠈⠛⢿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠈⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠘⣿⣿⣿⡽⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⠿⠿⢤⣤⡤⠖⠻⣿⣿⣿⣿⠀⢽⣿⣿⣿⣯⣽⡻⣶⣤⡀⠀⠀⠀

⠸⠿⠿⣿⠿⢿⠿⠿⠿⠿⠿⠿⠿⢿⡿⢿⡿⡿⠿⠷⠄⠀⠘⠿⣿⣿⠘⠻⠿⠟⠿⠿⠿⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠷⠌⠙⠛⠛⠛⠛⠛⠃⠈⠁⠀⠀⠀

[21A⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠒⠀⠀⠀⠀⠐⠒⠲⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆

⢸⣿⣿⣿⣿⣿⣿⡿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡇

⢸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇

⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡇

⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇

⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣿⣿⣿⣾⠛⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡇

⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⠿⣿⣿⣿⣿⠟⠈⠛⠾⢷⣶⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡇

⢸⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠘⠛⠛⠁⠀⣄⠀⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡇

⠘⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣷⣦⡀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⣶⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣤⡀⠀⠀⠀⠀⣠⣴⣶⣶⣾⣶⣶⣿⣿⣿⣿⣿⣿⡟⢷⡀⠀⠀⠈⠛⠙⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣶⣤⣤⣶⣿⣿⣿⣿⡿⠟⠂⠀⠀⠈⠉⠛⠟⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣺⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⡿⠟⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⣷⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢠⣤⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣼⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣻⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠈⠉⣿⣿⣿⣿⣿⣶⣾⣦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⣠⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣶⣾⣿⣶⣤⣄⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⣿⣦⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢺⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣀⠀⠀⠀⠀⠀⣽⣿⡇⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢻⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠟⢿⣿⣿⣦⠀⠀⠀⡈⠿⠗⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⢻⣿⣿⣷⣠⣤⣄⣀⣠⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠉⠛⠛⠃⠀⠀⣿⣦⣄⣀⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠁⠀⠀⠙⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⣿⣿⣿⣿⣆⠹⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⠀⠀⠀⠀

⢸⣿⢿⣿⠿⢿⣿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⡿⠷⠄⠀⠈⠻⣿⣿⠿⠿⠿⠿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠄⠿⠿⠿⢿⠿⠦⠙⠛⠿⠿⠿⠿⠿⠟⠛⠛⠃⠀⠀⠀

[21A⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆

⢸⣿⣿⣿⣿⠿⠟⠋⠉⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇

⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡇

⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡇

⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⢿⡿⡟⠻⣿⣿⣿⣿⣷⡝⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠋⠀⠀⠙⠛⠾⣤⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣀⠄⠀⠀⠀⠔⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀⠀⠀⠀⠀⠠⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣻⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣶⣿⡿⣦⠀⠀⠀⠀⣾⣅⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣶⣤⡀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⠗⠺⠛⠿⣿⣿⣿⡿⠘⢧⠀⠀⠀⠉⠈⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣪⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣷⣄⡀⠀⣾⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠉⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣴⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⣻⣿⣿⡿⠇⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡆⠉⠀⢠⡶⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠈⠉⣾⣿⣷⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣶⣾⣿⣿⣶⣶⣶⣤⣀⢰⣆⠀⠀⠀⠀⠀⠈⣿⣄⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃

⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢾⣿⣿⣧⠀⠀⠀⠀⡀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⢿⣿⣆⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠈⢿⣿⣿⣇⠀⠀⡀⠀⠀⠀⢜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠈⠙⠿⣿⣷⡄⢠⡄⠻⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠈⣿⣿⣿⣶⣾⣭⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠁⠐⣿⣶⣄⣀⣙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠉⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣧⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀

⢸⣿⢿⣿⠿⢿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⡿⠿⠿⠦⠄⠀⠀⠹⢿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠄⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠿⠿⠿⠿⠿⠧⠌⠛⠿⠿⠿⠿⠿⠿⠟⠛⠛⠀⠀⠀⠀

[21A⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠒⠂⠀⠀⠀⠀⠐⠲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠘⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠁⠀⠀⠸⠿⠟⠉⠙⣿⡿⠟⠛⣿⣿⣿⣿⣷⡜⠻⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠒⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣝⣿⣿⣯⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡿⠟⠛⠉⠙⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣾⣟⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⠟⠛⠻⠿⡿⠏⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣆⣀⡀⠆⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣼⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠀⣋⣿⣿⣿⣿⣿⣿⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣿⣿⣿⣿⡏⠉⠀⠀⠹⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠇

⢸⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣦⣤⣠⣿⣿⡿⠟⠋⠀⠀⠀⠀⠘⠀⠀⠀⣠⣦⣄⣤⣤⣤⣤⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠀

⢸⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠄⠀⠀⣴⣆⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠿⠛⠛⠻⠀

⢸⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣉⣩⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⠉⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠳⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡏⡁⠁⠀⠀⡀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢸⣿⣿⣿⣿⣷⣦⠀⠀⢀⣉⣛⣋⠁⠈⠀⠀⠀⠀⣯⡄⠀⠀⠀

⠸⠿⠿⣿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠶⠤⠤⠤⠼⠿⢿⠿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠹⠿⠿⠿⠿⠿⠿⠿⠿⠿⠏⠁⠻⠿⠿⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠷⠤⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀

[21A⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

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

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⡿⠿⠉⠙⣿⣿⠿⠛⢿⣿⣿⣿⣧⡼⠻⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣷⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡇

⠰⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠉⠻⠿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣝⡻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣧⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⠀⠀⠀⢠⣶⣤⣄⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⣄⢀⣼⣿⣿⣿⣿⡟⠉⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣷⡀⠀⢺⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⢛⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢿⣿⡿⠟⠁⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⣿⣶⣿⣿⣿⣿⣿⣿⣷⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠛⠉⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⣙⣿⣿⣯⣿⣿⣿⡭⠉⠉⠛⠛⠻⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⠀⠀⠀⠀

⠀⠀⠄⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⣀⣉⡹⡏⣹⣿⣿⣿⣿⣾⠆⠀⠀⠀⠀⠠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀

⢰⣒⠒⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣿⣿⣇⡀⠉⠙⠿⣿⣦⠀⠀⠀⠀⠀⠀⠀⣑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣾⣿⣿⣿⠧⠀⠀⠀⠀⠀⠀

⢸⣿⣷⣤⡀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣰⡄⠀⠀

⢸⣿⣿⣿⣿⣶⣤⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣿⣶⣶⣶⣶⣶⣦⣀⠀⠀⠈⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢸⡏⠀⠀

⠸⠿⠿⣿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠦⠄⠀⠉⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀

[21A⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆

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

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

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠈⠉⠉⠉⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣽⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠀⠀⠈⣿⠿⠉⠙⣿⣿⡿⠻⢿⣿⣿⣿⣧⡝⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡇

⠐⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣷⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠻⢿⣿⡂⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠛⠏⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⠿⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣟⣷⡶⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣷⣽⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡿⠛⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⣀⠀⣾⣿⣿⣿⣿⣿⣿⠿⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⢹⣿⠁⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣦⡄⠀⢸⣿⣵⣤⣬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠒⢻⣿⣿⣿⣿⣿⣷⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠿⣿⣧⣾⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄⣿⣿⣿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⣾⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⠓⠰⣏⡿⠿⠿⠿⠿⠿⠏⠄⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀

⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠘⡿⠙⣿⢹⣟⡟⠉⠀⠀⠀⠀⢈⢻⣩⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀

⢸⣿⡔⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣶⣾⣿⣿⣀⠀⠉⠪⠉⠒⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⣦⡀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣶⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⣶⣶⣤⣄⡈⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀

⠸⠿⠿⣿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠶⠶⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆

[21A⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⣿⣿⣿⣿⣿⠿⠛⠙⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣧⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡖⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠙⠛⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⣽⣿⣿⣿⣿⣿⣿⣿⡇

⢸⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⡿⠟⠉⠉⠙⣿⣿⠛⠻⣿⣿⣿⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡷⠖⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠉⠀⠀⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡿⠟⠛⠁

⠘⠛⠁⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀

⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣄⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣦⠀⡀⠀⠀⠀⠀⠀⠀

⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⠼⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣶⣤⣴⣤⣤⠀⣠⣤⣴⣾⣿⣿⡿⣿⣿⣿⣿⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀

⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⣰⣿⣿⣿⣿⣯⣿⣿⣝⢐⢍⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣶⣦⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣦⡀⠀⠀⠀⣶⣅⠄⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⣿⣿⣿⣿⣿⠿⠛⠋⠙⠋⠘⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣷⣶⣦⣄⡀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠋⠉⠹⢻⣿⣿⣿⡿⠿⠛⠛⠛⠋⠋⠁⠀⠀⠻⣿⣿⣿⡛⠀⠀⠀⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣠⣴⣶⣾⣧⡀⠀⠀⠀⠀⠁⠀⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣾⣿⣿⣿⣿⣿⡆

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⡶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆

⠸⠿⠿⣿⠿⢿⠿⠿⠿⠿⠿⠯⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠯⠸⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⡿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠹⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀

[21A⢰⣶⣶⣶⣶⣒⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠂⠀⠀⠀⠀⠀⢲⣶⡆⠀⢶⣶⡆

⢸⣿⣴⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢀⣤⣠⣤⣤⣦⠀⠀⠀⠀⢻⣿⣿⡿⠿⠛⢿⣿⣿⠿⠟⠀⢰⣿⣿⣿⣿⣿⣿⣿⣦⠈⠀⠀⠀⠀⠘⣿⡇⠀⢹⣿⡇

⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⢻⡿⠟⠀⠀⠀⠀⢻⣿⠀⠀⠀⢿⣿⣿⣿⣿⣭⣿⢿⣧⣀⡄⠀⠀⠀⠠⣯⣧⠀⢸⣿⡇

⢨⣭⣭⣿⣿⣿⣿⡀⣀⡀⢀⣿⠃⠀⡀⠀⢠⣶⡀⠀⠀⢀⣤⡾⠏⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠛⠉⠉⢻⣿⣿⡆⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⣿⣿⣷⣽⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠈⠉⠀⢸⣿⡇

⢨⣭⣭⣿⣿⣿⣿⣦⣾⣿⡆⢸⣿⣿⡇⠀⠀⢻⣧⠀⢀⠈⠀⠀⠀⠐⢇⠀⠀⢿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠻⠇⠀⣆⣿⣿⡄⣽⣿⡇⢽⣿⡿⠿⠀⠀⠀⠀⠀⠀⡀⠀⠈⣿⡇

⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢠⣿⣿⣇⠀⠀⠸⢿⣦⠜⠀⠀⠀⠀⠀⣼⡆⠀⢸⣿⣿⣿⣛⠲⠴⠄⠀⠀⠸⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⠘⠸⣿⣿⡿⠛⣷⠞⢡⡅⠠⠄⠀⠀⠀⠤⠀⠀⠀⠀⣿⡇

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡟⠉⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⢘⠿⠘⢹⣟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡿⠇⠀⠀⠀⠈⣿⠀⠀⣿⡦⣤⢁⠀⠗⠚⠃⠉⠈⣁⢀⠀⠀⣿⡇

⠀⠀⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⣸⣿⣿⣷⣄⡀⡀⢀⣿⣿⣶⣼⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠀⡼⠇⠀⠀⠀⠙⠀⠀⣿⣷⣿⣾⠄⠀⠀⠇⠀⡙⡇⠀⠀⠀⣿⡇

⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⣀⡀⠀⢠⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠂⠃⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡷⢀⡀⠀⠀⠀⡍⣃⠀⠀⠀⢻⡇

⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⣿⡄⠀⠦⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠀⠀⠀⢼⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⣿⣿⠿⠀⠐⠀⠀⠀⠀⢠⣼⣿⣿⡟⠛⠓⠀⠀⠂⠀⠀⣉⠁⣀⡀⠂⢘⡇

⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⡌⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⡆⠀⠀⠀⢨⣿⣿⡀⠀⠀⠀⢀⢰⡆⠀⠰⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠨⡏⢹⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⡆

⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⡗⢠⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣄⣤⣶⣞⣿⣿⣿⣶⣤⣤⣿⣿⣿⠀⠀⢀⣀⣴⣿⣯⣄⠀⠀⠀⠀⠀⣦⡾⣼⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇

⢰⣷⣶⡤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣧⣜⢿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠟⠀⠀⣾⣿⣿⣿⣿⣿⣆⣀⣼⢃⣠⣟⡟⣿⢯⡉⠉⠋⠀⠀⠈⠀⠈⠀⠀⠀⠀⢸⡇

⢸⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⢾⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠽⢹⣿⠀⢽⣿⠁⠀⢰⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⢿⣿⣷⣯⡜⣷⣶⢀⠀⠀⠀⠭⠌⡔⠀⠀⠀⠀⡇

⢸⡿⠁⠀⢻⣿⣿⣿⣧⡿⠿⣿⣿⣿⡇⠀⠘⣺⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢼⣿⠀⠉⠋⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⢿⢸⡿⠃⣹⣿⡄⠀⠀⠉⠍⠁⠅⠀⠀⠀⠀⡇

⢸⡁⠀⠀⢸⣿⣿⣿⣿⠙⠉⠁⠀⠀⠀⠀⠰⠼⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⠀⠀⠀⠀⠀⣿⣿⣿⢇⣿⣿⣿⣿⣿⣿⣿⣷⣿⣙⣹⠁⣿⠿⣟⢀⡀⠀⠆⠈⠋⠃⠀⠀⠀⠀⡇

⢸⣿⣿⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠆⠀⠀⠀⠀⠈⠉⢻⡏⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⡿⠀⢸⣾⣻⣿⣿⣷⣦⣤⣭⣥⣤⣤⣶⣶⡇

⢸⣿⣿⠀⠈⣿⣿⣿⠋⠀⠀⠀⢠⢶⣖⠀⠀⠀⢀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣷⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⣾⠥⣰⢁⡄⠀⠉⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⣿⣿⣀⡀⣿⣿⣿⣀⠀⠀⠀⠙⠘⢻⡅⠀⠀⢝⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠈⣽⣿⣿⣿⣿⣿⡇⠷⠠⢻⣦⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⣿⣿⠿⠁⢿⠿⣿⣿⣀⡐⠀⠀⠀⢸⢗⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣶⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠸⠷⠶⣷⠿⢿⠿⠶⠾⠾⠧⠀⠀⠴⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠯⠻⠿⠿⠁⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇

[21A⢰⣶⣶⣶⣶⣒⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣆⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⣶⠂⠀⠀⠀⠀⠀⢲⣶⡆⠀⢶⣶⡆

⢸⣿⣤⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣻⣟⢀⣤⣠⣤⣤⣦⠀⠀⠀⠀⢻⣿⣿⡿⠟⠛⢿⣿⣿⠿⠏⠀⢰⣿⣿⣿⣟⣿⣿⣿⣦⠀⠀⠀⠀⠀⠈⣿⡇⠀⢹⣿⡇

⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⢺⡿⠟⠀⠀⠀⠀⢻⣿⠀⠀⠀⢿⣿⣿⢿⣿⣭⣿⢿⣧⣀⠀⠀⠀⠀⠠⣯⣧⠀⢸⣿⡇

⢨⣭⣭⣿⣿⣿⣷⠀⣀⡀⢀⣿⠃⠀⡀⠀⢠⣶⡀⠀⠀⠀⣤⡾⠏⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠛⠉⠉⠻⣿⣿⠆⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⣿⣿⢧⣼⣿⣿⣿⣻⣿⣇⠀⠀⠀⠀⠀⠀⠉⠀⢸⣿⡇

⢨⣭⣭⣿⣿⣿⣿⣦⣾⣿⡄⢸⣿⣿⡇⠀⠀⢻⣧⠀⢀⠈⠀⠀⠀⠐⢅⠀⠀⢻⣿⣿⣿⡻⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⠇⠀⣄⣿⣿⡄⣼⣿⡇⢙⣿⠿⠟⠁⠀⠀⠀⠀⠀⡀⠀⠀⣿⡇

⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢠⣿⣿⡇⠀⠀⠸⢿⣦⠘⠀⠀⠀⠀⠀⢸⡄⠀⢸⣿⣿⣽⡛⠒⠴⠄⠀⠀⠸⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⠘⠸⢿⣿⡿⠛⣷⠞⢁⠄⠠⠄⠀⠀⠀⠄⠀⠀⠀⠀⣿⡇

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡟⠉⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⢘⠯⠘⢹⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡿⠇⠀⠀⠀⠈⣿⠀⠀⣿⡦⣤⢀⠀⠗⠊⠁⠉⠀⣀⢀⠀⠀⣿⡇

⠀⠀⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣰⣿⣿⣷⣄⡀⠀⢀⣿⣿⣶⣼⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠠⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠀⡴⠇⠀⠀⠀⠙⠀⠀⣿⣧⣿⣾⠄⠀⠀⠄⠀⡙⡃⠀⠀⠀⣿⡇

⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⡀⠀⠀⠀⢀⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠃⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡗⢀⡀⠀⠀⠀⡍⠃⠀⠀⠀⢻⡇

⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⣿⡄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⢤⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⡿⠿⠀⠐⠀⠀⠀⠀⢠⣼⣿⡿⡟⠛⠃⠀⠀⠀⠀⠀⣉⠁⣀⡠⠀⢘⡇

⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⠄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⡄⠀⠀⠀⢨⣯⣿⡀⠀⠀⠀⢀⠀⠆⠀⠰⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠨⡏⢹⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡆

⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⡇⢀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣷⣿⣿⣄⣤⣦⣚⣿⣿⣿⣶⣀⡀⣾⣯⣲⠀⠀⢀⣀⣴⣾⣟⣀⠀⠀⠀⠀⠀⣄⡾⣼⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇

⢰⣶⣶⡤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣇⢘⠿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠓⠀⠀⣼⣿⣿⣿⣿⣿⣆⣀⣴⢃⢠⣟⡛⡿⢏⡉⠁⠋⠀⠀⠈⠀⠈⠀⠀⠀⠀⢸⡇

⢸⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⢩⠸⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠩⢉⣿⠀⢸⡇⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡟⣿⣾⢾⣿⣷⣯⡜⣷⣆⠀⠀⠀⠀⠁⠈⠐⠀⠀⠀⠀⡇

⢸⡟⠁⠀⢻⣿⣿⣿⣧⣾⣿⣿⣿⣿⡇⠀⠘⠸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠼⡿⠀⠀⠋⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⢿⢸⡟⠃⣹⣽⡀⠀⠀⠀⠋⠁⠁⠀⠀⠀⠀⡇

⢸⡁⠀⠀⢸⣿⣿⣿⣿⠓⠈⠉⠉⠁⠀⠀⠀⢌⢿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣾⣿⣿⠉⣿⣿⣿⣿⣿⣿⣷⣧⣿⣙⣸⠁⣟⠿⡏⢁⡀⠀⠂⠀⠂⠃⠀⠀⠀⠀⡇

⢸⣿⣿⠀⢸⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡿⠆⠀⠀⠀⠀⠀⠛⢻⡏⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⡿⠀⢸⣾⣻⣿⣿⣷⣦⣤⣤⣥⣤⣠⣤⣶⡇

⢸⣿⣿⠀⠈⣿⣿⣿⠋⠀⠀⠀⠠⢴⡆⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣷⠀⠀⠀⠀⠀⠀⢸⡿⣿⢻⣿⡟⣿⡿⣿⢥⣰⠁⡄⠀⠋⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⣿⣿⣀⡀⣿⣿⣿⣀⠀⠀⠀⠘⠘⢻⠀⠀⠀⢙⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠈⣹⣿⣿⣿⣿⣿⡇⠷⠠⢻⣤⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢸⣿⣿⠿⠁⢿⠿⢿⣧⢀⡐⠀⠀⠀⢸⡆⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣷⣿⣯⣷⣿⣿⣿⣶⣦⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠸⠷⠶⣶⠿⢿⠿⠶⠾⠾⠧⠀⠀⠴⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⢿⡿⢿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⡿⢿⠿⠿⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇

[21A⢰⣶⣶⣶⣶⣒⣒⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠆⠀⠀⠀⠀⠀⢲⣶⡆⠀⣶⣶⡆

⢸⣿⣴⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣀⣤⣠⣤⣤⣦⠀⠀⠀⠀⢻⣿⣿⡿⠿⠻⢿⣿⣿⡿⠟⠁⢸⣿⣿⣿⣿⣿⣿⣿⣶⠛⠀⠀⠀⠀⠘⣿⣇⠀⢹⣿⡇

⢸⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⣿⡿⠿⠁⠀⠀⠀⢻⣿⠇⠀⠀⣿⣿⣿⣿⣿⣭⣿⣿⣯⣀⡄⠀⠀⠀⠠⣿⣧⠀⢸⣿⡇

⢨⣭⣭⣿⣿⣿⣿⡆⣀⡀⢀⣿⠃⠀⠀⠀⢠⣤⡀⠀⠀⢀⣤⡾⢏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠟⠋⠉⢻⣿⣿⡆⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠠⣿⣿⣷⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠈⠉⠀⢸⣿⡇

⢨⣭⣭⣿⣿⣿⣿⣦⣿⣿⡤⢹⣿⣿⡅⠀⠀⢿⣧⠀⢀⠈⠀⠁⠀⠐⣇⠀⠀⢿⣿⣿⣿⣿⠇⠠⠀⠀⠀⠋⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠻⠯⠀⣄⣿⣿⡌⣻⣿⣇⢿⣿⡿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇

⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⡇⠀⠀⠸⣿⣦⡼⠀⠀⠀⠀⠀⣽⣆⠀⢸⣿⣿⣿⣿⠶⠴⠤⠀⠀⠸⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡄⠀⠙⠸⣿⣿⣿⠛⣷⡾⢹⡇⠢⡄⠀⠀⠀⡀⠀⢀⠀⠀⣿⡇

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡿⠁⠀⠀⠀⠀⣀⣠⡀⠀⠀⠀⠀⢸⣿⠻⢹⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⡿⠇⠀⠀⠀⠈⣿⠀⠀⣿⣧⣼⣁⡀⠷⠚⠆⠹⠀⠀⢀⠀⠀⣿⡇

⠀⠈⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⢄⡀⠀⣼⣿⣿⣧⣄⠀⠀⠀⣾⣿⣶⣼⣟⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠀⣼⠧⠀⠀⠀⢹⠀⠀⣿⣷⣿⣶⠦⠀⠈⡇⠈⠺⡏⡈⠀⠀⣿⡇

⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢱⣇⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠂⠓⠁⠀⠀⠀⠀⢷⣶⣿⣿⣿⡷⢖⡀⠀⠀⠀⡏⠇⠀⠀⠀⢻⡇

⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⣿⡀⠀⣿⣷⠓⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠸⠩⣿⣿⠿⠚⢠⣴⣶⢆⠀⢠⣼⡿⠟⠛⠿⠗⠈⠁⠆⠄⣈⣙⡋⣀⣠⠤⢘⡇

⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣰⡟⠓⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢀⣀⣴⣶⣦⣶⣶⣀⠀⠀⣠⢾⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠲⠨⡇

⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⡷⣧⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇

⢰⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣟⣾⣿⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⢀⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇

⢸⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⣿⣿⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇

⢸⡿⠁⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠹⣾⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣱⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇

⢸⡃⠀⠀⢸⣿⣿⣿⣿⠛⠊⠉⠉⠉⠁⠀⠰⠿⠿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢠⣖⣄⣤⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇

⢸⣿⣿⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡟⣂⣾⣶⣿⣯⠀⠀⠀⠀⢀⣠⣤⣤⡇

⢸⣿⣿⡀⠘⣿⣿⣿⠋⠀⠀⠀⣰⢶⣶⡀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠟⠋⠀⠈⠉⠙⠛⠻⣿⣿⣿⣿⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇

⢸⣿⣿⣁⡀⣿⣿⣿⣄⠀⠀⠈⢙⠘⢿⡇⠀⠀⢛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠃⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⢰⣿⣿⣿⣿⡇

⢸⣿⣿⠿⠁⢿⠿⣿⣿⣀⡞⠀⠀⠀⢸⣗⣦⣶⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⣿⣦⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠟⠙⠋⠀⠀⠀⣼⣿⣿⣿⣿⡇

⠸⠷⠶⣷⠿⢿⠿⠷⠾⠿⠷⠀⠀⠴⠾⠿⠿⠿⠿⠿⠿⠟⠁⠀⠀⠀⠀⠉⠙⠿⠿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠇

                ䷩ 𝚕𝚒𝚗𝚎 3746

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

Gemini_version_available_♊︎

✐ Links_02/01/2023:_GNU_Chinese_Translators_Team_Reports_Progress⠀✐

Posted in News_Roundup at 7:53 am by Dr. Roy Schestowitz

🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈

§ Contents⠀➾

* GNU/Linux

      o Linux_Magazine

      o Applications

      o Instructionals/Technical

      o Games

      o Desktop_Environments/WMs

            # K_Desktop_Environment/KDE_SC/Qt

            # GNOME_Desktop/GTK

* Distributions_and_Operating_Systems

      o BSD

      o Fedora_Family_/_IBM

      o Canonical/Ubuntu_Family

      o Devices/Embedded

      o Open_Hardware/Modding

      o Mobile_Systems/Mobile_Applications

* Free,_Libre,_and_Open_Source_Software

      o SaaS/Back_End/Databases

      o GNU_Projects

      o Programming/Development

            # Rust

      o Standards/Consortia

* Leftovers

      o Hardware

      o Health/Nutrition/Agriculture

      o Proprietary

      o Security

            # Privacy/Surveillance

      o Defence/Aggression

      o Environment

            # Energy/Transportation

            # Wildlife/Nature

      o Finance

      o AstroTurf/Lobbying/Politics

      o Censorship/Free_Speech

      o Civil_Rights/Policing

      o Digital_Restrictions_(DRM)

      o Monopolies

            # Patents

            # Copyrights

* Gemini*_and_Gopher

      o Personal

      o Technical

            # Programming

* § GNU/Linux⠀➾

      o § Linux Magazine⠀➾

            # ⚓ Linux Magazine ☛ Synchronize_your_data_across_multiple

              devices_with_Syncthing⠀⇛

            # ⚓ Linux Magazine ☛ Zack’s_Kernel_News⠀⇛

            # ⚓ Linux Magazine ☛ Programming_Snapshot_–_Go_Password

              Manager⠀⇛

            # ⚓ Linux Magazine ☛ This_month_in_Linux_Voice.⠀⇛

            # ⚓ Linux Magazine ☛ Choosing_a_graphical_backup_tool⠀⇛

            # ⚓ Linux Magazine ☛ Shell_Programming_in_Python⠀⇛

            # ⚓ Linux Magazine ☛ Code_Care⠀⇛

            # ⚓ Linux Magazine ☛ Quick_Service⠀⇛

            # ⚓ Linux Magazine ☛ System_Under_Control⠀⇛

            # ⚓ Linux Magazine ☛ Fast_and_easy_backups_with_Restic_and

              Jarg⠀⇛

            # ⚓ Linux Magazine ☛ On_the_DVD:_Linux_Mint_21_Cinnamon_and

              Kali_Linux_2022.4⠀⇛

            # ⚓ Linux Magazine ☛ Initial_Support_for_Rust_in_the_Linux

              Kernel_is_Finally_Released⠀⇛

            # ⚓ Linux Magazine ☛ Whatever_happened_to_Mandrake?⠀⇛

            # ⚓ Linux Magazine ☛ FOSSPicks⠀⇛

            # ⚓ Linux Magazine ☛ Natural_language_processing_with_neural

              networks⠀⇛

            # ⚓ Linux Magazine ☛ Tutorial_–_Skrooge⠀⇛

            # ⚓ Linux Magazine ☛ Doghouse_–_Starting_Out⠀⇛

            # ⚓ Linux Magazine ☛ Back_up_your_data_with_BorgBackup_and

              Vorta⠀⇛

            # ⚓ Linux Magazine ☛ An_improved_front_end_for_Apt⠀⇛

            # ⚓ Linux Magazine ☛ Watering_Pi⠀⇛

            # ⚓ Linux Magazine ☛ A_desktop_command-line_widget⠀⇛

      o § Applications⠀➾

            # ⚓ It’s FOSS ☛ 10_Awesome_Open_Source_Tools_I’d_Recommend_You

              to_Use_in_2023⠀⇛

                   In 2022, we noticed a lot of users preferring to

                   use open-source tools for the sake of transparency.

                   Whether you are a Linux user or not, there are a

                   lot of open-source solutions.

                   Open-source options have several benefits. So, if

                   you are wondering the same, let me tell you about

                   some of the most useful open-source tools I’ve

                   encountered that you should use in 2023.

                   The tools should help improve your online privacy,

                   security, and work productivity and provide you

                   with a better online/computing experience overall.

      o § Instructionals/Technical⠀➾

            # ⚓ Learn Ubuntu ☛ How_to_Get_User_ID_(UID)_in_Ubuntu_Command

              Line⠀⇛

                   User ID (UID), is nothing but a numeric value

                   defined by your system to identify the users.

                   And if your system is running with multiple users,

                   UID can be handy when you want to manage them.

            # ⚓ Check_If_You_Are_Using_SystemD_or_Not_in_Linux⠀⇛

                   This article will show you three methods for

                   determining whether your Linux system is using

                   systemd or another init system.

                   If you are unfamiliar with this term, check the

                   following section; otherwise, skip to the next

                   section.

            # ⚓ Controversy_of_‘init’_and_‘systemd’_in_Linux⠀⇛

                   The init (short for “initialization”) is the first

                   (or parent) process loaded by your kernel that

                   swamps other (child) processes to make your system

                   work in a systematic manner, and it is assigned

                   with “PID=1” (process identifiers are assigned in

                   sequential order).

                   As this is the parent of all processes, it has the

                   responsibility to keep running until the user sends

                   a halt signal; otherwise, you might experience the

                   stage called “Kernel Panic”.

                   When you hear the term “init” in conjunction with

                   it, you will also hear the term “System V init”,

                   which is essentially the first commercial system

                   designed based on init, which many future Linux

                   distributions adopted (until systemd came).

                   The init is respected for many things, but for now

                   I’ll focus on one major one: “Do one thing and do

                   it well”. This referred to the init behavior of

                   starting one process after the previous one had

                   completed in serial.

            # ⚓ Preetam Jinka ☛ HTTP_request_case_sensitivity⠀⇛

                   I only recently learned that HTTP methods are case-

                   sensitive. In order to save myself from future

                   debugging headaches, I decided to do a quick search

                   to see what else is case-sensitive.

                   This is what the RFC says. Real applications may

                   treat things differently!

            # ⚓ IT Tavern ☛ Visual_guide_to_SSH_tunneling_and_port

              forwarding⠀⇛

                   SSH tunneling and port forwarding can be used to

                   forward TCP traffic over a secure SSH connection

                   from the SSH client to the SSH server, or vice

                   versa. TCP ports or UNIX sockets can be used, but

                   in this post I’ll focus on TCP ports only.

                   I won’t go into details, but the following post

                   should show enough examples and options to find use

                   in your day-to-day work.

            # ⚓ Make Use Of ☛ How_to_List_Current_Logged-In_Users_on

              Linux⠀⇛

                   Linux being a multi-user system allows multiple

                   users to log in and run various programs at the

                   same time. As a normal Linux user or system admin,

                   you may sometimes need to check which users are

                   currently logged into your system.

                   This information can be useful for various reasons

                   such as for troubleshooting performance issues,

                   monitoring user activity, or for simply checking

                   who else is using the system.

            # ⚓ It’s Ubuntu ☛ Make_Ubuntu_Terminal_Look_Like_Kali_Linux_

              [2023]_|_Itsubuntu.com⠀⇛

                   In this Ubuntu Tutorial Post, we will help you to

                   make your Ubuntu terminal look like Kali Linux.

                   Ubuntu is a popular Linux-based operating system

                   and is most preferred by beginners while Kali Linux

                   is popular for security purposes.

            # ⚓ DebugPoint ☛ How_to_Force_Auto_Dark_Mode_in_Chrome_and

              Chromium⠀⇛

                   Dark mode in websites is an option which the

                   website itself should provide. Most of the time,

                   it’s handled by the website’s CSS and usually comes

                   with a toggle button. However, at debugpoint – we

                   do have a dark mode toggle switch.

                   But most of the websites don’t have dark mode

                   enabled. Google Chrome and all Chromium-based web

                   browser feature a flag where you can force dark

                   mode for all websites, all the time.

                   Here’s how to enable it.

            # ⚓ Trend Oceans ☛ Display_Memory_Information_Using_Ramfetch_in

              Linux⠀⇛

                   Neofetch, Screenfetch, etc., which display your

                   system information like the Linux OS version,

                   hostname, processor, kernel, memory, desktop

                   environment, resolution, CPU, GPU, and many more.

                   Despite the fact that this information can be read

                   from a file present in the root directory, you can

                   still use this tool to get clean output.

            # ⚓ Pi My Life Up ☛ How_to_use_the_date_Command_–_Pi_My_Life

              Up⠀⇛

                   You can use the date command to view the current

                   date and time on your Linux system. The command

                   allows you to format the output, view the last

                   modified date on files, set the date and time, and

                   more. It is an incredibly useful command which I

                   highly recommend taking the time to learn.

                   There are many ways you can utilize this command,

                   but you will likely need it when creating bash

                   scripts that require the current date and time. You

                   can also set the time using the command, but it is

                   unlikely you will ever need to use this

                   functionality.

                   This tutorial will take you through the syntax,

                   options, and several examples of how you can use

                   the date command.

            # ⚓ UNIX Cop ☛ How_to_fix_“Briefly_unavailable_for_scheduled

              maintenance”_error_on_WordPress?⠀⇛

                   If you have a WordPress site, you will know that

                   sometimes some unwanted errors occur that can give

                   us a headache. So, the error in question is

                   “Briefly unavailable for scheduled maintenance” on

                   WordPress. Let’s take a look at it.

            # ⚓ Linux Capable ☛ How_to_Install_PowerShell_on_Ubuntu_22.04_|

              20.04 [Ed: Microsoft traps like these should be replaced by

              Bash or similar]⠀⇛

                   Utilizing PowerShell, developers and IT

                   professionals can unlock the power of automation.

                   An open-source CLI tool with code lets users

                   streamline their tasks and quickly configure

                   settings. The following tutorial will teach you how

                   to install PowerShell on Ubuntu 22.04 LTS Jammy

                   Jellyfish or Ubuntu 20.04 Focal Fossa LTS. The

                   tutorial will use the command line terminal with

                   complete steps to install the official repository

                   and tips on updating and removing the software

                   securely and adequately.

            # ⚓ Pi My Life Up ☛ How_to_Find_your_Mac_Address_on_Ubuntu_–_Pi

              My_Life_Up⠀⇛

                   A mac address is a unique identifier used by your

                   Ubuntu systems network interfaces to identify

                   itself on your network.

                   For example, if you have a Wi-Fi network controller

                   and an ethernet one, they will have different mac

                   addresses.

                   Network routers often use a mac address to identify

                   your device within the network. It allows the

                   router, for example, to assign your Ubuntu device a

                   static IP address.

                   Please note that you can spoof a mac address, so it

                   isn’t a flawless way of tracking or identifying a

                   device within a network. For example, iPhones by

                   default will fake a mac address for different Wi-Fi

                   networks to improve privacy.

                   Over the following sections we will show you how to

                   find the mac address on Ubuntu using either the

                   terminal or desktop interface. Both methods are

                   very straightforward to use even if you aren’t the

                   most confident with Ubuntu.

            # ⚓ Pi My Life Up ☛ How_to_Check_Disk_Space_on_Ubuntu_–_Pi_My

              Life_Up⠀⇛

                   There are a couple of ways that you can check the

                   disk space on the Ubuntu operating system that we

                   will be exploring.

                   If you are running a version of Ubuntu that has a

                   graphical interface, this process is made very

                   simple by two inbuilt applications. These

                   applications allow you to get the free disk space

                   of every filesystem in just a few clicks.

                   There is even a built-in tool to quickly see what

                   files are consuming the disk space on your Ubuntu

                   system.

                   Regarding the terminal side of things, we can

                   utilize a handy built-in tool that goes by the name

                   “df“. While not as versatile as the desktop tools,

                   it allows you to quickly get the disk space usage

                   of your filesystems.

                   Hopefully, by the end of the following two

                   sections, you will be able to check the disk space

                   usage of your Ubuntu filesystems quickly.

            # ⚓ Pi My Life Up ☛ How_to_Add_a_Repository_on_Ubuntu_–_Pi_My

              Life_Up⠀⇛

                   A repository is where your Ubuntu system will

                   download and install packages from whenever you use

                   the apt package manager.

                   While Ubuntu provides numerous packages through its

                   official repositories, it may not include all the

                   packages you need. There is also a chance the

                   packages included are older than what that software

                   is releasing itself.

                   Luckily the apt package manager that Ubuntu relies

                   on allows you to add your repositories to download

                   packages from.

                   In the following sections, we will show how you can

                   manually add a package repository to your Ubuntu

                   system and add a PPA repository.

      o § Games⠀➾

            # ⚓ Engadget ☛ 2022_was_an_incredible_year_for_handheld_gaming

              |_Engadget⠀⇛

                   Valve started rolling out the Steam Deck in

                   February, and by October it had shipped more than 1

                   million of these beasts across the western world,

                   with plans to expand into additional regions.

      o § Desktop Environments/WMs⠀➾

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

                  # ⚓ Kraft_on_Windows [Ed: Wasting time on company and

                    platform intolerant of software freedom]⠀⇛

                         Kraft, which was released as version 1.0

                         after long time of active development, is

                         targetted to the Linux desktop. My firm

                         conviction is that the Linux desktop is very

                         suitable for the target group of Kraft: In

                         the small office of craftsmen for example, a

                         Linux desktop is a great work horse which is

                         stable, very well adoptable and has a great

                         amount of applications that are stable and

                         maintained.

            # § GNOME Desktop/GTK⠀➾

                  # ⚓ DebugPoint ☛ Colorblind_Filters:_GNOME_Extension_to

                    help_Color-blind_Users⠀⇛

                         Accessibility is a critical aspect of

                         computing and operating systems. It includes

                         well-managed settings for vision impairment,

                         color blind and many other health symptoms.

                         Popular Linux desktop environments such as

                         GNOME and KDE Plasma feature accessibility

                         settings to help all those scenarios.

                         Thanks to the GNOME Extensions ecosystem, a

                         huge number of specialised extensions are

                         available to aid those users. One of the

                         extensions I came across is “Colorblind

                         Filters”.

                         Here’s how to install and use it.

* § Distributions and Operating Systems⠀➾

      o ⚓ [Old] Birdhouse Arts Collective ☛ He_Who_Controls_the

        Bootloader⠀⇛

             There is no technical reason why CompUSA customers

             shouldn’t be able to walk out of the shop with a machine

             that asks “Which OS do you want to use today?” upon boot.

             And yet, even today, after several years of relentless

             news about how Linux is ready for the general desktop and

             business customer, one does not find dual-boot Win/Linux

             machines from large commercial OEMs at any consumer

             outlet or web shop I know of. Yes, you can get dual-boot

             machines at some of the smaller shops, but these are the

             ones that slip under Microsoft’s radar, and there’s no

             guarantee that Microsoft won’t decide to take action

             against these vendors at some point. And yes, you can buy

             Linux-only machines from vendors such as IBM. But think

             about it: Why would IBM sell Windows machines and Linux

             machines, but no dual-boot Win/Linux machines? The

             absence is conspicuous.

             A few years ago, Be’s CEO Jean-Louis Gassée used the

             phrase “peaceful co-existence with Windows” to describe

             his company’s intended relationship with Microsoft on the

             consumer’s hard drive. Later, when it became clear that

             Microsoft had no intention of co-existing with a rival OS

             vendor peacefully, Gassée recanted, saying, “I once

             preached peaceful coexistence with Windows. You may laugh

             at my expense — I deserve it.”

      o § BSD⠀➾

            # ⚓ [Semibug]_Crazy_unix_shell_prompts⠀⇛

                   I tripped across an idea recently which I'm not

                   sure if

                   it is brilliant or evil.  But I kinda like it.

                   Standard unix shell prompt is a $ or # (or a number

of

                   other things, if you like unusual shells).  Every

                   operating

                   system I've used in the last 40 years has some kind

of

                   prompt...but that's not exactly a requirement.  And

                   most of

                   us start cramming other info into the prompt, for

                   example,

                   my standard prompt has grown to three lines -- a

                   blank line,

                   username at hostname, then the full path and the $

                   or #.

            # ⚓ [bsdcan-announce]_BSDCan_2023_call_for_papers⠀⇛

                   BSDCan 2023 will be held May 19-20 (Fri-Sat) May

                   2023 in Ottawa,

                   at the University of Ottawa. It will be preceded by

two

                   days of tutorials on 17-18 May (Wed-Thu).

                   Also: do not miss out on the Goat BOF on Tuesday 16

                   May (more

                   details to follow later).

                   We are now accepting proposals for talks.

                   The talks should be designed with a very strong

                   technical content bias.

                   Proposals of a business development or marketing

                   nature are not

                   appropriate.

            # ⚓ FreeBSD ☛ 2022_in_Review:_Continuous_Integration_and

              Quality_Assurance_Update_|_FreeBSD_Foundation⠀⇛

                   The year 2022 was a busy and productive one for the

                   FreeBSD Foundation. Continuous Integration (CI) and

                   Quality Assurance (QA) is but one of many

                   successful efforts the Foundation continues to

                   support as a dedicated resource. We spoke with Li-

                   Wen Hsu, one of the Foundation’s Software

                   Engineers, to discuss his work on this project over

                   the past year, and the plans he has for it this

                   coming year.

            # ⚓ FreeBSD ☛ Conference_Report:_Rocky_Mountain_Celebration_of

              Women_in_Computing_|_FreeBSD_Foundation⠀⇛

                   We were thrilled to be part of the Rocky Mountain

                   Celebration of Women in Computing Conference

                   September 29-30, 2022 here in Boulder, Colorado!

                   Just a few years ago, we were gaining momentum on

                   showcasing FreeBSD at women in computing

                   conferences and university groups. But, that came

                   to a standstill when Covid hit. We are now

                   kickstarting that effort to attend more of these

                   types of events, from meetups to celebration of

                   women in computer conferences. So, I was thrilled

                   when I saw the local Rocky Mountain Celebration of

                   Women in Computing was taking place here in Boulder

                   Colorado in September!

            # ⚓ pkgsrc-2022Q4_branch_released⠀⇛

                   The pkgsrc developers are proud to announce the

                   77th quarterly release

                   of pkgsrc, the cross-platform packaging system.

                   pkgsrc is available

                   with more than 27,000 packages, and supports 23

                   platforms, of which 10

                   are currently known to be working.  More

                   information on pkgsrc itself

                   is available at https://www.pkgsrc.org/

                   In total, 215 packages were added, 63 packages were

                   removed, and 2326

                   package updates (to 1687 unique packages) were

                   processed since the

                   pkgsrc-2022Q3 release.  Updates include 56 perl5

                   packages, 570 Python

                   packages, 184 Ruby packages, and 39 TeX packages.

                   This announcement takes a high-level view, grouping

                   related packages

                   under a single name, and treating multiple versions

                   of an upstream

                   package as a logical unit.  Thus, 'gcc 12', while a

                   new entry

                   'lang/gcc12', is an update to 'lang/gcc*'.

      o § Fedora Family / IBM⠀➾

            # ⚓ Fedora Magazine ☛ Docker_and_Fedora_37:_Migrating_to_Podman

              –_Fedora_Magazine⠀⇛

                   In previous installments (Fedora 32, Fedora 35),

                   there was a strong focus on making things work with

                   Docker on Fedora Linux. This article will focus on

                   the final stage of this long journey. It will focus

                   on migrating a cross-platform production set-up

                   from Docker to Podman.

            # ⚓ Red Hat ☛ C#_11:_pattern_matching_and_static_abstract

              interfaces [Ed: Tom Deseyn still works for Microsoft while

              taking the salary from IBM]⠀⇛

            # ⚓ Data Swamp ☛ Export_Flatpak_programs_from_a_computer_to

              another⠀⇛

                   As a flatpak user, but also someone with a slow

                   [Internet] connection, I was looking for a way to

                   export a flatpak program to install it on another

                   computer. It turns out flatpak supports this, but

                   it’s called “create-usb” for some reasons.

                   So today, I’ll show how to export a flatpak program

                   from a computer to another.

      o § Canonical/Ubuntu Family⠀➾

            # ⚓ [Older] Linuxiac ☛ Canonical_Considering_IPO_in_2023:_What

              It_Means_for_Ubuntu_Users⠀⇛

                   Specifically, once a company goes public, the focus

                   shifts to ensuring the financial well-being of the

                   shareholders rather than satisfying expectations

                   and listening to the voice of users who are simply

                   consuming the final product offered to them for

                   free – in this case, Ubuntu.

            # ⚓ [Older] TechCrunch ☛ Canonical_now_hopes_to_IPO_in_2023⠀⇛

                   He stressed that Canonical is not in a situation

                   where it has to raise outside money and that going

                   public for him is not about fundraising. He noted

                   that Canonical’s revenue last year was $175 million

                   and that the company’s biggest challenge right now

                   is that demand is bigger that the company’s ability

                   to service it, in large part because there isn’t

                   enough talent on the market for the company to

                   hire.

            # ⚓ Ubuntu ☛ Hybrid_cloud_infrastructure_modernisation⠀⇛

                   Public clouds enabled digital transformation at

                   unprecedented speed. But their operational costs

                   over time can be exacting as compute needs

                   increase. Hybrid clouds emerged as an alternative

                   to gain the benefits of both worlds: private

                   infrastructure that allows for lower operational

                   expenditures and tighter control, and public clouds

                   that can scale with ease.

                   Organisations looking to adopt a hybrid cloud

                   architecture should carefully consider their

                   options for private cloud vendors, as well as their

                   implications for application design and

                   development, workload orchestration and long-term

                   maintenance.

      o § Devices/Embedded⠀➾

            # ⚓ Russell Graves ☛ Battle_of_the_Boards_2023:_Rock5B_and

              Kernel_Builds⠀⇛

                   It’s another year, and for me, that means it’s a

                   good time to start with another Battle of the

                   Boards – this time, with the Rock5 included! I’m

                   going to be talking more about these boards in the

                   coming weeks and flushing out some old posts on

                   some older SBCs that I still use on a daily basis.

                   But one could comfortably call this post, “The

                   Rock5B Crushes All Others.”

            # ⚓ Linux Gizmos ☛ Open_source_ESP32_module_supports_5G_and_GPS

              connectivity⠀⇛

                   The Walter is an upcoming embedded device equipped

                   with the ESP32-S3 microcontroller along with a

                   GM02SP module for NB-IoT, LTE-M and GPS protocols.

                   The board will also be CE and FCC certified to

                   accelerate customers’ product development.

            # ⚓ Hackaday ☛ LEDCard:_The_Pocketable_Ring_Light⠀⇛

                   How many times have you found yourself fumbling

                   about with lighting while trying to get a clear up-

                   close shot of an object? Although smartphones come

                   with pretty nice cameras these days, properly

                   lighting an object and taking impressive macro

                   shots isn’t exactly their strong suit. This is

                   where [MisterHW]’s LEDCard is a very welcome

                   companion. Not only does it provide a credit card

                   sized ring light, it also allows for a molded

                   acrylic lens to be inserted for high-quality macro

                   shots.

      o § Open Hardware/Modding⠀➾

            # ⚓ [Old] History Computer ☛ Everything⠀⇛

                   The Apollo Guidance Computer was the first computer

                   ever built whose operation was based entirely on

                   silicon integrated circuits.

                   The drive to create the Apollo Guidance Computer’s

                   software essentially established software

                   engineering as an autonomous field. In fact,

                   Margaret Hamilton, one of the principal software

                   engineers who worked on the project, is credited

                   with coining the term “software engineering.”

            # ⚓ CNX Software ☛ Walter_ESP32-S3_board_supports_NB-IoT,_LTE-

              M,_and_GPS_–_CNX_Software⠀⇛

                   QuickSpot Walter is an ESP32-S3 development board

                   with built-in WiFi 4 and Bluetooth LE/Mesh

                   connectivity, as well as NB-IoT, LTE-M, and GNSS

                   support through a Sequans GM02SP 5G IoT modem that

                   appears to be a variant of the Sequans Monarch 2

                   GM02S with GNSS support.

      o § Mobile Systems/Mobile Applications⠀➾

            # ⚓ SlashGear ☛ How_To_Extend_Your_Android_Phone’s_Ring_Time⠀⇛

            # ⚓ SlashGear ☛ How_To_Make_Custom_App_Icons_On_Android

              Phones⠀⇛

            # ⚓ Notebook Check ☛ Redmi_12C:_An_intriguing_look_for_fairly

              ordinary_Android_smartphone_specs_at_a_reasonable_price_–

              NotebookCheck.net_News⠀⇛

            # ⚓ Phone Arena ☛ Google_testing_new_look_for_Android_YouTube

              app_–_PhoneArena⠀⇛

            # ⚓ Here_Are_Some_Android_Features_You_Should_Immediately

              Disable_for_Better_Performance_/_Digital_Information_World⠀⇛

            # ⚓ Android’s_Weight_Loss_Apps_Help_Monitor_Progress_But

              Interfere_With_Digital_Privacy_As_Per_New_Study_/_Digital

              Information_World⠀⇛

            # ⚓ Hectic Geek ☛ Best_10_Tech_News_Top_Apps_for_Android_in

              2023⠀⇛

                   Time changes and technology is evolving swiftly

                   with every passing day. If you are in the tech

                   industry, you must stay in touch with all these

                   rapid changes and the coming trends to stay up to

                   date.

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

      o § SaaS/Back End/Databases⠀➾

            # ⚓ Preetam Jinka ☛ SQLite’s_automatic_indexes⠀⇛

                   Why is it that SQLite automatically creates an

                   index for this join and PostgreSQL doesn’t?

      o § GNU Projects⠀➾

            # ⚓ GNU ☛ GNU_Chinese_Translators_Team_–_News:_Summary_of

              2022⠀⇛

                   Dear CTT team:

                   Thank you very much for you contribution in 2022.

                   There have been a few new comers joining our team,

                   like Wind. Their work is appreciated.

                   The whole team have been doing a good job in 2022.

                   Here is official letter from GNU.

                   Dear GNU translators!

                   This year was relatively quiet; the total number of

                   new translations

                   was considerably lower than in 2021, especially in

                   terms of size.

                   Almost two of every three translations were made in

                   the "Simplified"

                   Chinese team; the Albanian and Turkish teams

                   significantly reduced

                   the percentage of their outdated translations.

                         General Statistics

                   In November, we reached new maximum values of

                   translations per file

                   in important directories, 9.44 translations per

                   file (0.12 more

                   than in 2021) and 8.85 translations weighted with

                   size of articles

                   (0.46 more than in 2021), 50 Mi in 3300 files

                   total.

                   Meanwhile, the percent of outdated translations was

                   as high

                   as at the end of 2021 (about twice as high as the

                   historical

                   minimum in 2014-2015).

                   The table below shows the number and size of newly

                   translated

                   articles in important directories and typical

                   number of outdated

                   GNUNified translations throughout the year.

      o § Programming/Development⠀➾

            # ⚓ Rlang ☛ Using_Emacs_for_R⠀⇛

                   To start using R, or almost anything else in Emacs

                   you basically need to know 3 things: 1) How to move

                   in Emacs, meaning understanding what is what and

                   learning a few key commands; 2) What is the

                   configuration file and how to use it and 3) How to

                   use packages to extend Emacs. In the first half of

                   this post I will try to show how easy it is to

                   cover these 3 points even for people who are

                   inexperienced in programming. If you don’t believe

                   me I invite you to read just the first paragraph of

                   the next section to give you an idea of how easy it

                   really is. During the second half I will show how

                   I’m using R in Emacs to give you a starting point

                   of a fully functional environment for R, and will

                   conclude with some topics that can be further

                   explored.

            # ⚓ Fred Herbert ☛ A_Bridge_Over_a_River_Never_Crossed⠀⇛

                   This was the sort of situation I was finding myself

                   in for the protocol: I wanted to build everything

                   correctly the first time around, but I had no damn

                   idea about how to wire up only one fine half to

                   nothing just to figure out what shape exactly

                   should a whole exchange have. I couldn’t do it

                   right all at once.

            # ⚓ Linux Hint ☛ How_to_Create_an_Array_of_Strings_Using_Malloc

              ()_in_C_Programming⠀⇛

                   C programming language is one of the famous

                   structured languages that includes many basic

                   components, and arrays are one of them. Arrays are

                   referred to as a collection of similar types of

                   items stored in contiguous memory blocks. These are

                   of two types: static array and dynamic array. In

                   the static array, the size of the array is fixed.

                   But in a dynamic array, memory is allocated

                   dynamically.

            # ⚓ Of0x ☛ Spice_up_your_persistence:_loading_PHP_extensions

              from_memory_–_Adepts_of_0xCC⠀⇛

                   Dear Fellowship, today’s homily is about how to

                   improve persistences based on PHP extensions. In

                   this gospel we will explain a way to keep a PHP

                   extension loaded on the server without it being

                   backed up by a file on disk. Please, take a seat

                   and listen the story.

            # ⚓ A_table_of_results_for_frequentist_mixed-effects_models:

              Grouping_variables_and_specifying_random_slopes_|_Pablo

              Bernabeu⠀⇛

                   Here I share the format applied to tables

                   presenting the results of frequentist models in

                   Bernabeu (2022; the table for Bayesian models is

                   covered in this other post). The sample table

                   presents a mixed-effects model that was fitted

                   using the R package lmerTest (Kuznetsova et al.,

                   2022). The mixed effects were driven by the maximal

                   principle (Brauer & Curtin, 2018). The format of

                   the table resembles one of the examples published

                   by the American Psychological Association. However,

                   there are also deviations from those examples. For

                   instance, in the present table, the effects are

                   grouped under informative labels to facilitate the

                   readers’ comprehension, using the kableExtra

                   package (Zhu, 2022). Furthermore, the random slopes

                   are specified using superscript letters and a

                   footnote. The table can be reproduced using the

                   materials at https://osf.io/gt5uf.

            # ⚓ A_table_of_results_for_Bayesian_mixed-effects_models:

              Grouping_variables_and_specifying_random_slopes_|_Pablo

              Bernabeu⠀⇛

                   Here I share the format applied to tables

                   presenting the results of Bayesian models in

                   Bernabeu (2022; the table for frequentist models is

                   covered in this other post). The sample table

                   presents a Bayesian mixed-effects model that was

                   fitted using the R package brms (Bürkner et al.,

                   2022). The mixed effects were driven by the maximal

                   principle (Brauer & Curtin, 2018). The format of

                   the table resembles one of the examples published

                   by the American Psychological Association. However,

                   there are also deviations from those examples. For

                   instance, in the present table, the effects are

                   grouped under informative labels to facilitate the

                   readers’ comprehension, using the kableExtra

                   package (Zhu, 2022). Furthermore, the random slopes

                   are specified using superscript letters and a

                   footnote. The table can be reproduced using the

                   materials at https://osf.io/gt5uf.

            # ⚓ OpenSource.com ☛ 7_Git_articles_every_open_source

              practitioner_should_read⠀⇛

                   Understanding the Git version control system is

                   foundational for many open source practitioners.

                   Whether you are an advanced user or you want 2023

                   be the year to get started, Opensource.com has

                   plenty of resources for you. Here are a few recent

                   Git articles that I recommend:

                   The first in a series by Dwayne McDaniels, Git

                   concepts in less than 10 minutes, assures us that,

                   yes, Git can seem intimidating, but knowing and

                   understanding the basic building blocks can break

                   down the barriers. Six basic commands and concepts

                   are explained so you can move on to more advanced

                   Git tools and commands.

                   5 Git configurations I make on Linux by Alan Formy-

                   Duval is a straightforward guide to getting started

                   working with Git on Linux. There are so many

                   configuration options, and Alan suggests starting

                   with global configuration to help make set up

                   easier every time.

                   How to rename a branch, delete a branch, and find

                   the author of a branch in Git is a straightforward

                   article about the most common commands around Git

                   branching.

            # § Rust⠀➾

                  # ⚓ OpenSource.com ☛ How_to_read_and_write_files_in

                    Rust⠀⇛

                         Knowing how to read and write files can be

                         useful for various purposes. In Rust, this

                         task is done using the file system module

                         (std::fs) in the standard library. In this

                         article, I’ll give you an overview on how to

                         use this module.

      o § Standards/Consortia⠀➾

            # ⚓ Cloudflare ☛ The_state_of_HTTP_in_2022⠀⇛

                   So what happened at all of those working group

                   meetings, specification documents, and side events

                   in 2022? What are implementers and deployers of the

                   web’s protocol doing? And what’s coming next?

            # ⚓ Hackaday ☛ Use_USB-C_Chargers_To_Top_Up_Li-Ion_Packs_With

              This_Hack⠀⇛

                   In USB-C Power Delivery (PD) standard, the PPS

                   (Programmable Power Supply) mode is an optional

                   mode that lets you request a non-standard voltage

                   from a charger, with the ability to set a current

                   limit of your choice, too. Having learned this,

                   [Jason] from [Rip It Apart] decided to investigate

                   — could this feature be used for charging Li-Ion

                   battery packs, which need the voltage and current

                   to vary in a specific way throughout the charging

                   process? Turns out, the answer is a resounding

                   “yes”, and thanks to a USB-C tester that’s

                   programmable using Lua scripts, [Jason] shows us

                   how we can use a PPS-capable USB-C charger for

                   topping up our Li-Ion battery packs, in a project

                   named DingoCharge.

* § Leftovers⠀➾

      o ⚓ Counter Punch ☛ Letter_from_London:_Exile_on_Main_Street⠀⇛

             The traffic. I couldn’t hear it. Where the hell was it?

             The cars? The buses? The hundreds of lorries (trucks)?

             The white vans? Fast ones weaving in and out? Slow ones

             not giving a damn? Where was that ever-constant urban din

             of four-stroke combustion cycles, intaking, compressing,

             combusting, exhausting? This was like our London of old,

             at the height of the pandemic. Silent. Void. Weirdly

             placated. (A time I enjoyed.) What has happened to our

             noisy, clattery, impulsive capital? Oh. Wait a minute.

             This was not the capital. This was not us by our hectic

             busy road. This was me rubbing my eyes in relative

             countryside, barely awake after my first proper night’s

             sleep in ages. I had entirely forgotten. We four members

             of the immediate family had decamped together the day

             before on a long green train from London to celebrate

             Christmas with the artist’s family. In short, I was

             waking up in exile.

      o ⚓ Counter Punch ☛ Ten_People_Who_Actually_Didn’t_Suck_in_2022⠀⇛

             2022 sucked. That’s how I usually introduce this annual

             list of people who miraculously didn’t, and I wouldn’t be

             totally off base to do so again. 2022 was a year as chock

             full of horrors as any other year you might expect to

             survive during this dark age of Cthulhu. After all, this

             year was decimated on every conceivable front by a

             grotesque imperial proxy war in Ukraine that seems

             frighteningly likely to end in a thermonuclear third-

             world war. On a far more intimate front, gender outlaws

             like myself have never faced such well-publicized

             vitriol, with the partisan industrial complex using us as

             their go-to props for their latest midterm election

             circus.

             I get called groomer six times a day with mushroom clouds

             blooming on the horizon. For all intents and purposes, it

             really is the end of the world as I know it. So, why then

             do I feel strangely fine? Could it be the estrogen

             finally coursing through my veins after 34 years of

             testosterone poisoning? Or maybe something that my

             therapist suggested about rewiring my grim brain in the

             positive finally clicked. I don’t know. But for whatever

             reason, 2022 was a heinously apocalyptic year that didn’t

             quite suck and here are at least ten reasons why.

      o ⚓ Salon ☛ TikTok’s_use_of_music_poses_a_threat_to_artis⠀⇛

             Radio has been haunted repeatedly by enquiries about

             “payola” (potentially illegal payments for radio play)

             and the power of the major music companies to control the

             market. Similar questions are being asked of TikTok.

      o ⚓ Hackaday ☛ A_DIY_Pulse_Tube_Cryocooler_In_The_Quest_For_Home-Made

        Liquid_Nitrogen⠀⇛

             What if you have a need for liquid nitrogen, but you do

             not wish to simply order it from a local supplier? In

             that case you can build your very own pulse tube

             cryocooler, as [Hyperspace Pirate] is in the process of

             doing over at YouTube. You can catch part 1 using a

             linear motor and part 2 using a reciprocating piston-

             based version also after the break. Although still very

             much a work-in-progress, the second version of the

             cryocooler managed to reduce the temperature to a chilly

             -75°C.

      o ⚓ TruthOut ☛ I’m_Immunocompromised._Here’s_How_I_Feel_About_Masking

        in_2023.⠀⇛

      o § Hardware⠀➾

            # ⚓ Ruben Schade ☛ Rubenerd:_Fascinating_new_pencil_soldering

              irons⠀⇛

                   There seem to be a few major benefits. They’re much

                   smaller, which lets you be more nimble around tiny

                   ICs and other components. Yet advances in

                   technology mean they heat up just as fast, or even

                   faster, than traditional soldering irons and

                   stations. Again, for someone with almost no free

                   space, this seems really compelling.

            # ⚓ Hackaday ☛ AIOC:_The_Ham_Radio_All-In-One_Cable_For_Audio

              And_APRS⠀⇛

                   The Ham Radio All-in-one cable (AIOC) is a small

                   PCB attachment for a popular series of radio

                   transceivers which adds a USB-attached audio

                   interface and virtual TTY port for programming and

                   the push-to-talk function. The STM32F373

                   microcontroller (which, sadly is still hard to find

                   in the usual channels) is a perfect fit for this

                   application, with all the needed hardware

                   resources.

            # ⚓ Hackaday ☛ Snow_Plowing_By_Bicycle⠀⇛

                   There are few challenges more difficult or

                   dangerous than trying to get around the majority of

                   North American cities by bicycle. Not only is the

                   bicycle infrastructure woefully inadequate for safe

                   travel (if it exists at all), but it’s often not

                   maintained to any reasonable standard, either. This

                   goes double in colder areas, where bike paths can

                   essentially become abandoned in the winter after a

                   snowfall. [Phil] found himself in this situation

                   recently after a snowfall in western Canada and

                   decided to DIY his own bike-powered snowplow to

                   help keep his bike paths cleared.

            # ⚓ Hackaday ☛ Electronics_Explained_With_Mechanical_Devices⠀⇛

                   It can be surprisingly hard to find decent

                   analogies when you’re teaching electronics basics.

                   The water flow analogy, for instance, is decent for

                   explaining Ohm’s law, but it breaks down pretty

                   soon thereafter.

            # ⚓ Hackaday ☛ DIYson_Lamp_Hides_Cables_Between_The_Seams⠀⇛

                   [Steven Bennett] is so fond of Dyson’s new

                   Lightcycle lamp that he’s decided to clone his own

                   version in the spirit of the original. Dyson,

                   however, knows what makes their lamp so special —

                   so much that they patented their technique for

                   tucking away the power wiring. Undaunted,

                   [Steven]’s latest challenge has been to create a

                   cable management solution that captures the

                   elegance of the original without making a flat-out

                   duplicate.

      o § Health/Nutrition/Agriculture⠀➾

            # ⚓ Reason ☛ Top_10_Attacks_on_Free-Range_Parenting_in_2022⠀⇛

                   It was another tough year for many parents who

                   sincerely thought they were doing their best—until

                   the busybodies said otherwise. Here are the 10

                   worst free-range kids moments of 2022 (and one

                   encouraging counterexample).

            # ⚓ CNN ☛ TikTok_is_‘digital_fentanyl,’_incoming_GOP_China

              committee_chair_says⠀⇛

                   Gallagher also called for “reciprocity,” noting

                   that Chinese officials are allowed on apps like

                   Twitter but Chinese citizens are not allowed access

                   to those same apps. He said he would like to see an

                   arrangement under which “if your government doesn’t

                   allow your citizens access to the platform, we’re

                   going to deny your government officials access to

                   that same platform.”

            # ⚓ Gannett ☛ Ancient_farming_practice_makes_a_comeback_as

              climate_change_puts_pressure_on_crops⠀⇛

                   Each is part of a small but growing movement to

                   bring back an ancient agricultural practice called

                   cover cropping that was once used to rejuvenate

                   soil but now also likely comes with the added

                   benefits of mitigating climate change and

                   protecting against its ravages.

                   It’s increasingly getting a push from Department of

                   Agriculture programs and even companies that buy

                   commodities. But mostly, farmers say it saves them

                   money and protects their land.

      o § Proprietary⠀➾

            # ⚓ [Old] Wired ☛ DVD-Cracking_Teen_Acquitted⠀⇛

                   Jon Lech Johansen was 15 when he developed and

                   posted his program, called DeCSS, on the Internet

                   in late 1999, enraging the film industry because it

                   feared the software would allow illegal copying of

                   its films.

                   The three-member Oslo City Court found Johansen,

                   now 19 and a household name as DVD-Jon in Norway,

                   innocent on all counts in a unanimous 25-page

                   ruling in the latest setback for the film

                   industry’s drive to prevent film copying.

            # ⚓ New York Times ☛ The_Shameful_Open_Secret_Behind

              Southwest’s_Failure⠀⇛

                   Well, if you are a corporate executive whose

                   compensation is tied to stock prices and earnings

                   statements released every three months, there are

                   strong incentives to address any immediate problem

                   by essentially adding a bit of duct tape and wire

                   to what you already have, rather than spending a

                   large amount of money — updating software is costly

                   and difficult — to address the root problem. Then

                   you can cross your fingers and hope that whatever

                   catastrophe may be in the making, it erupts under

                   someone else’s future tenure. Such bets often pay

                   off since, increasingly, the plight of a company’s

                   customers and employees is divorced from the

                   immediate fortunes of its current top executives.

            # ⚓ NBC ☛ Wickr_Me,_Amazon’s_encrypted_chat_app,_stops

              accepting_new_users⠀⇛

                   The decision, first announced in November, follows

                   several controversies surrounding the ultra-secure

                   chat app, which allowed users to sign up without a

                   phone number or other potentially identifying

                   information, making it a favorite for security-

                   minded groups including hackers, drug dealers and

                   journalists.

      o § Security⠀➾

            # ⚓ SANS ☛ InfoSec_Handlers_Diary_Blog_–_SANS_Internet_Storm

              Center⠀⇛

                   There are a variety of services listening for

                   connections on DShield honeypots [1]. Different

                   systems scanning the internet can connect to these

                   listening services due to exceptions in the

                   firewall. Any attempted connections blocked by the

                   firewall are logged and can be analyzed later. This

                   can be useful to see TCP port connection attempts,

                   but it’s usefulness is limited. Without the ability

                   to complete the SYN, SYN-ACK, ACK handshake process

                   other protocol data may not be sent.

            # § Privacy/Surveillance⠀➾

                  # ⚓ Counter Punch ☛ New_Year’s_Resolution:_Protect_Your

                    Own_Privacy⠀⇛

                         “Here’s some free advice for 2023,”  Erin

                         Keller writes at the New York Post: “Delete

                         all your personal information — and sexual

                         content — from your electronic devices before

                         donating them to Goodwill.”

                         The advice may be free, but it’s worth far

                         more than we’re paying for it.

                  # ⚓ JURIST ☛ Google_to_pay_Indiana_$20M_to_settle

                    location_tracking_suit⠀⇛

                         The agreement orders Google to pay Indiana $2

                         million within 60 days, and the proceeds may

                         be used for any purpose allowable under

                         Indiana law. Additionally, the agreement

                         mandates that Google have “pop-up”

                         notifications to inform users if their

                         location history is enabled. The agreement

                         also orders Google to maintain a webpage

                         disclosing its practices and policies

                         concerning customer location information.

                         Lastly, Google must provide instructions to

                         users about location-related settings and has

                         to report its compliance with the agreement.

                  # ⚓ OpenRightsGroup ☛ Response_To_Call_For_Information:

                    Unauthorised_Access_To_Online_Accounts_And_Personal

                    Data⠀⇛

                         1. We welcome the opportunity to respond to

                         the Home Office consultation on “Unauthorised

                         access to online accounts and personal data”.

                         Having contributed to the previous call for

                         information regarding the Computer Misuse Act

                         1990 (CMA),1 we wish to reiterate some of the

                         issues raised in that regard in light of the

                         plans to introduce a Cyber Security Duty to

                         Protect.

                  # ⚓ Futurism ☛ Fiends_Allegedly_Swatted_Victims,_Use

                    Hacked_Ring_Cameras_To_Livestream_It⠀⇛

                         According to a press release by the US

                         Department of Justice, two young men

                         allegedly accessed a dozen Ring cameras

                         through currently-unknown methods and carry

                         out a weeklong spree of next-level attacks.

                         During the alleged incidents, the schemers

                         were said to have swatted their victims and

                         using the hacked doorbell cameras to

                         livestream the attacks and sometimes issue

                         verbal threats to the responding officers,

                         too. The charges are grisly, but also once

                         again underline the grim privacy implications

                         of allowing connected cameras and microphones

                         into our homes — not to mention underlining

                         the irony that a device designed to be easily

                         be accessed by police is instead being

                         leveraged by criminals to weaponize cops

                         against their victims.

      o § Defence/Aggression⠀➾

            # ⚓ Quartz ☛ The_new_US_defense_bill_includes_a_budget_for

              music_diplomacy⠀⇛

                   Administered by the Bureau of Educational and

                   Cultural Affairs, the program will fund musical

                   curricula focused on conflict resolution and

                   foreign exchange programs for young musicians

                   across the globe. Harvey Mason Jr., a well-known

                   R&B producer who has worked with stars such as

                   Michael Jackson and Beyonce, will assist with the

                   rollout.

                   The bill was sponsored by House member Michael

                   McCaul, a Texas Republican, and had bipartisan

                   support.

            # ⚓ Common Dreams ☛ Negotiate_Now!_A_Call_for_Diplomacy_in

              Ukraine⠀⇛

                   The Russo-Ukrainian War drags on like a bad dream.

                   Admittedly, there are slight glimmers of hope:

                   Russian President Vladimir Putin stated his

                   readiness to participate in an international peace

                   conference; but Ukraine must firstrecognize Russian

                   annexations, especially Crimea and territories

                   around Kherson, demilitarize, and also guarantee

                   Russian security. Meanwhile, Ukrainian President

                   Volodymyr Zelensky has stated that he, too, is

                   willing to negotiate; but Russia must first meet

                   ten conditions including withdrawal from all

                   Ukrainian territories including Crimea. The

                   insincerity on both sides is striking: negotiations

                   are unnecessary when the demands of each have been

                   met in advance.

            # ⚓ Scheerpost ☛ The_Chris_Hedges_Report:_A_New_Book_of_Migrant

              Stories_Exposes_Europe’s_War_on_Refugees⠀⇛

                   In their book, ‘Map of Hope and Sorrow,’ co-authors

                   Helen Benedict and Eyad Awwadawnan trace the

                   stories of five refugees trapped in Greece’s brutal

                   refugee camps.

            # ⚓ Counter Punch ☛ Ukraine_May_Secure_a_Victory_Against_Russia

              in_Name,_But_the_World_won’t_Escape_the_War’s_Aftermath⠀⇛

                   Seldom in European history has an invading power so

                   exaggerated its own strength, and underestimated

                   that of its enemy to the degree that Russia did

                   when it attacked Ukraine on 24 February. Ten months

                   after President Vladimir Putin ordered the Russian

                   army to conquer Ukraine, the tragic absurdity of

                   his giant blunder remains staggering.

                   Russia has never recovered politically or

                   militarily from that initial miscalculation about

                   the likely success of an invasion – and it is

                   difficult to see how it can do so in future.

            # ⚓ Counter Punch ☛ Decry_the_Merchants_of_Death⠀⇛

                   Peace activists take on the Pentagon and its

                   corporate outposts.

                   Days after a U.S. warplane bombed a Doctors Without

                   Borders/Médecins Sans Frontières (MSF) hospital in

                   Kunduz, Afghanistan, killing forty-two people,

                   twenty-four of them patients, the international

                   president of MSF, Dr. Joanne Liu walked through the

                   wreckage and prepared to deliver condolences to

                   family members of those who had been killed. A

                   brief video, taped in October, 2015, captures her

                   nearly unutterable sadness as she speaks about a

                   family who, the day before the bombing, had been

                   prepared to bring their daughter home. Doctors had

                   helped the young girl recover, but because war was

                   raging outside the hospital, administrators

                   recommended that the family come the next day.

                   “She’s safer here,” they said.

            # ⚓ Counter Punch ☛ The_Price_of_Betraying_Palestine:_Moroccans

              Challenge_Normalization_with_Israel⠀⇛

                   Two years ago, Morocco and Israel signed the US-

                   brokered “Joint Declaration”, thus officially

                   recognizing Israel and instating diplomatic ties.

                   Though other Arab countries had already done the

                   same, the Moroccan official recognition of

                   Apartheid Israel was particularly devastating for

                   Palestinians.

                   Years ago, a close Moroccan friend told me that the

                   ‘first time’ he was arrested was during a

                   solidarity protest for Palestine in Rabat which

                   took place many years ago.

            # ⚓ Counter Punch ☛ Why_Do_I_Feel_Like_a_Human_Shield?⠀⇛

                   I am not a total pacifist, but I hate war. Time has

                   shown me that it is always better to talk than to

                   kill. As someone who lives in a nation long

                   considered the greatest purveyor of military

                   violence in the world, I believe one of the most

                   important actions anti-imperialist and anti-

                   militarist people living in the United States can

                   take is to build a movement to challenge and

                   confront the US war machine on the homefront. If

                   this opposition were to happen in a consistent and

                   concerted manner, war would not be Washington’s go-

                   to solution. At this point in time, the possibility

                   of such a movement seems far-fetched and far away.

                   However, one could have said the same thing about

                   the possibility of a movement against the US war on

                   the Vietnamese in 1963.

                   While I understand that there are times when self-

                   defense requires an armed response, the time for

                   that is over in Ukraine. There’s little to nothing

                   to gain by continuing the military conflict. The

                   war itself has clearly become what it always was–a

                   proxy war between Moscow and Washington. The fact

                   of Russia’s invasion and Kyiv’s reaction to it is

                   overshadowed by the greater possibility of a much

                   wider, even nuclear, war. This is true no matter

                   where one stands regarding who holds the greater

                   blame for the situation in Ukraine prior to

                   Russia’s February 2022 invasion. It’s one thing to

                   defend one’s nation from military aggression; it’s

                   quite another thing to forcibly reject calls from

                   governments and people around the world to

                   negotiate a cessation of hostilities. Likewise, it

                   is wrong to reject peace talks while sending (or

                   demanding) billions of dollars worth of arms The

                   ongoing escalation in Ukraine, the growing economic

                   suffering of people around the world and the

                   increasing danger of a wider conflict should be

                   telling those in power that the energy put into

                   warfare must be turned towards negotiating peace.

                   Instead, the powerful in capitals of all nations

                   involved continue their bluster while their

                   sponsors in the war business count their coin.

            # ⚓ Common Dreams ☛ Woe_for_the_Children_Maimed,_Displaced,_and

              Killed_by_the_Merchants_of_War⠀⇛

                   Days after a U.S. warplane bombed a Doctors Without

                   Borders/Médecins Sans Frontières (MSF) hospital in

                   Kunduz, Afghanistan, killing forty-two people,

                   twenty-four of them patients, the international

                   president of MSF, Dr. Joanne Liu walked through the

                   wreckage and prepared to deliver condolences to

                   family members of those who had been killed. A

                   brief video, taped in October, 2015, captures her

                   nearly unutterable sadness as she speaks about a

                   family who, the day before the bombing, had been

                   prepared to bring their daughter home. Doctors had

                   helped the young girl recover, but because war was

                   raging outside the hospital, administrators

                   recommended that the family come the next day.

                   “She’s safer here,” they said.

      o § Environment⠀➾

            # ⚓ Counter Punch ☛ Call_of_the_Sandpiper:_New_Year’s

              Resolutions_in_the_Time_of_Climate_Breakdown⠀⇛

                   Another year over, and the business-as-usual

                   attitudes are breathtaking. As though everything

                   were hunky dory in the Anthropocene. Some people

                   are even pointing at December’s flash freeze to

                   poke fun at climate science. But our industrial-

                   strength impact on the planet is melting ice

                   sheets, researchers at the University of Bristol

                   noted a few years back, weakening the polar

                   gravitational pull. “Wavy” polar vortices are also

                   linked to global heating. Can the cold, chaotic

                   lashings from the poles be kept in check by an

                   increasingly warm and torpid jet stream?

                   The most recent lashing brought a prodigious

                   snowfall and buried holiday drivers. Four people

                   died in a 46-car pileup on the Ohio Turnpike. In

                   Buffalo, a blizzard raged for 37 hours, leaving at

                   least 39 people dead—some stuck in cars or caught

                   in snowbanks.

            # § Energy/Transportation⠀➾

                  # ⚓ Merchants of Doubt ☛ [Cryptocurrency]_investors_lost

                    3.5B_dollars_to_scammers_in_2022_–_Study⠀⇛

                         Regarding 2022, news generated throughout the

                         year showed that from several thousand

                         dollars in cryptocurrencies were scammed from

                         university students, to smaller amounts that

                         victims transferred when scammed by scammers.

                  # ⚓ Positech Games ☛ 2022:_A_year_spent_trying_to_build_a

                    solar_farm⠀⇛

                         Luckily, the price of those panels went up,

                         and I am currently still ahead of the game on

                         this. Assuming they get taken out of storage

                         on schedule (hopefully April), I wont have

                         actually lost out anything except the

                         transport costs for the panels to the site.

                         (Originally that was included, but they

                         needed to be left at a port warehouse

                         instead.

                         So what else happened?

                  # ⚓ TruthOut ☛ Colorado_Law_Could_Force_Boulder_to_Sell

                    Oil_and_Gas_to_a_Private_Company⠀⇛

            # § Wildlife/Nature⠀➾

                  # ⚓ Common Dreams ☛ Seals,_Satellites,_and_Dung_Beetles_—

                    What_Links_Them?⠀⇛

                         Imagine hunting for a fish dinner in the

                         middle of the ocean, in the middle of the

                         night without flashlight, compass, or iPhone

                         . . . and then to find a way back to land.

                         This is what seals must accomplish on a

                         regular basis to survive. These pinnipeds, so

                         often seen posing with a ball balanced

                         perfectly on a whiskered nose or bowing

                         gracefully for a circus display, have skills

                         that cannot be seen on the stage. In fact,

                         they give our close relatives the chimpanzees

                         something to envy.

      o § Finance⠀➾

            # ⚓ TruthOut ☛ Some_of_the_Biggest_Labor_Contracts_Are_Expiring

              in_2023⠀⇛

            # ⚓ TruthOut ☛ When_It_Comes_to_Greed_and_Tax_Dodging,_Sanders

              Points_Out_“Trump_is_Not_Alone”⠀⇛

            # ⚓ Common Dreams ☛ ‘Stand_Up_and_Fight’:_Sanders_Delivers_New

              Year’s_Message_on_2023_Priorities⠀⇛

                   Sen. Bernie Sanders issued a New Year’s Day message

                   on Sunday as he gets ready to take over as chair of

                   the powerful Health, Education, Labor and Pensions

                   Committee in the U.S. Senate when Congress comes

                   back into session later this month.

            # ⚓ Counter Punch ☛ Capitalism’s_Court_Jester:_Slavoj_Žižek⠀⇛

                   One of the most prominent intellectuals in the

                   contemporary world was named to the list of the

                   “Top 100 Global Thinkers” in Foreign Policy

                   magazine in 2012.[1] He shares this distinction

                   with the likes of Dick Cheney, Recep Tayyip

                   Erdoğan, Benjamin Netanyahu, and former Mossad

                   director Meir Dagan. The theorist’s best

                   idea—according to this well-known publication that

                   is a virtual arm of the U.S. State Department—is

                   that “the big revolution the left is waiting for

                   will never come.”[2]

                   Other ideas were surely strong contenders, and we

                   could add to the list more recent positions. To

                   select but a few examples, this top global thinker

                   has described 20th-century communism, and more

                   specifically Stalinism, as “maybe the worst

                   ideological, political, ethical, social (and so on)

                   catastrophe in the history of humanity.”[3] As a

                   matter of fact, he adds for emphasis that “if you

                   measure at some abstract level of suffering,

                   Stalinism was worse than Nazism,” apparently

                   regretting that the Red Army under Stalin defeated

                   the Nazi war machine.[4] The Third Reich was not as

                   “radical” in its violence as communism, he insists,

                   and “the problem with Hitler was that he was not

                   violent enough.”[5] Perhaps he could have taken

                   some tips from Mao Zedong who, according to this

                   theoretical grandee, made a “ruthless decision to

                   starve tens of millions to death.”[6] This

                   undocumented assertion positions its author well to

                   the right of the anti-communist Black Book of

                   Communism, which recognized that Mao did not intend

                   to kill his compatriots.[7] Such information is of

                   no import, however, to this theorist since he

                   operates on the assumption that the worst ‘crime

                   against humanity’ in the modern world was not

                   Nazism or fascism, but rather communism.

      o § AstroTurf/Lobbying/Politics⠀➾

            # ⚓ Thomas Depierre ☛ I_am_not_a_supplier⠀⇛

                   It may feel a bit legalese, and yes, it shouts at

                   you, but I can summarise it pretty easily. If you

                   use this, I owe you nothing. At all. We have no

                   relationship. I put this up online on the condition

                   that if you use it, all the risks are on you.

                   What it means is that there is no supply chain

                   here. Because there is no supplier. I am not

                   providing you something that you bought for me.

                   There is no relationship. I put something online

                   because I wanted to. The fact you made your product

                   depend on it is your responsibility. Not mine. Not

                   the one of the providers. We provide libraries. We

                   do not supply them. You cannot apply rules to me.

                   And quite honestly, I am not going to accept them.

                   I barely have time to spend on doing the work on

                   the FOSS libraries I maintain and doing so

                   regularly burns out the people doing it.

            # ⚓ Michał Woźniak ☛ Why_I_quit_Twitter…_a_decade_ago⠀⇛

                   And so it has come to this. I finally quit Twitter…

                   almost exactly a decade ago.

                   I could spin yarn and claim it was some major feat

                   of clairvoyance, of course. That I foresaw all that

                   happened lately with Twitter and decided to bail

                   early. But it wasn’t that, really. I just felt

                   strongly that centralized services are dangerous

                   and unethical, and I decided to stop using them.

                   Back then, Twitter was the last one on the chopping

                   block for me.

            # ⚓ 4StateNews ☛ ‘Open_source_it’:_Facebook_whistleblower_dares

              Elon_Musk_to_‘publish_the_algorithms’_controlling_Twitter⠀⇛

                   On Sunday’s edition of Meet the Press, former

                   Facebook executive-turned-whistleblower Frances

                   Haugen said that if Twitter owner Elon Musk is

                   truly interested in transparency and championing

                   free speech that he should make public the

                   algorithms that determine what users see on their

                   timelines. Musk pledged to do that earlier this

                   year, and while he has yet to follow through,

                   Haugen believes that it would be a huge step in

                   fostering safer experiences online.

            # ⚓ India Times ☛ Twitter_bans_48,624_accounts_for_policy

              violations_in_India⠀⇛

                   Under the new IT Rules 2021, big digital and social

                   media platforms, with more than 5 million users,

                   have to publish monthly compliance reports.

            # ⚓ Common Dreams ☛ Brazil_Celebrates_Lula’s_Return_as_Right-

              Wing_Reign_of_Bolsonaro_Comes_to_an_End⠀⇛

                   Hundreds of thousands took to the streets across

                   Brazil on Sunday to celebrate the inauguration of

                   leftist President Luiz Inácio Lula da Silva, whose

                   return to the nation’s highest office also marked

                   the exit of far-right Jair Bolsonaro who left his

                   country and arrived in the U.S. state of Florida

                   ahead of the weekend’s transfer of power.

            # ⚓ Scheerpost ☛ Everything_to_Know_About_Lula’s_Inauguration⠀⇛

                   The Workers’ Party leader will begin his third term

                   with an official ceremony, artistic performances

                   and representation of 120 countries.

            # ⚓ Common Dreams ☛ I’m_a_Professional_Comedy_Writer_—_The_GOP

              Has_a_‘Punching_Down’_Problem⠀⇛

                   There’s one rule in comedy so universal that it

                   connects comics of every background, genre, and

                   skill level: never punch down.

            # ⚓ TruthOut ☛ Exposé_Reveals_Lobbyists_Bought_Access_to

              Supreme_Court_Justices_With_Donations⠀⇛

            # ⚓ Counter Punch ☛ NYT:_When_the_Data_Doesn’t_Fit_the

              Narrative,_Ignore_it⠀⇛

                   Can someone buy the NYT Internet access? For some

                   reason the paper insists on ignoring data from the

                   Census Bureau when telling readers about the

                   housing market. Last month it repeatedly told

                   readers that young people, minorities, and lower

                   income households were unable to buy homes when the

                   Census Bureau data showed rapid increases in

                   homeownership for these groups since the start of

                   the pandemic.

                   The paper is doing its misinformation routine again

                   today, telling readers…

            # § Misinformation/Disinformation/Propaganda⠀➾

                  # ⚓ Friends of Earth ☛ Merchants_Of_Poison:_How_Monsanto

                    Sold_the_World_on_a_Toxic_Pesticide⠀⇛

                         Ten years ago, pesticide and processed food

                         companies spent $45 million — roughly $1

                         million a day — to defeat a ballot initiative

                         to label genetically modified foods (GMOs) in

                         California. The anti-transparency campaign

                         led by Monsanto, one of the largest producers

                         of GMOs, blitzed the state with misleading

                         messages amplified by a wide range of

                         seemingly independent third parties: from

                         universities, professors, and scientists to

                         many groups that claimed expertise on matters

                         of food, health, nutrition, and science. But

                         investigations would eventually reveal close

                         ties between these so-called neutral groups

                         and the companies fighting transparency.

      o § Censorship/Free Speech⠀➾

            # ⚓ NCAC ☛ Remembering_Joyce_Meskis:_Free_Speech_Defender⠀⇛

                   From the beginning, Meskis was deeply committed to

                   defending free speech. She would later attribute

                   her interest to a college course that introduced

                   her to Areopagitica, Milton’s classic statement on

                   the danger of censorship.

            # ⚓ Jacobin Magazine ☛ Why_the_Twitter_Files_Are_in_Fact_a_Big

              Deal⠀⇛

                   On the Left, there’s been a temptation to dismiss

                   the revelations about Twitter’s internal censorship

                   system that have emerged from the so-called Twitter

                   Files project. But that would be a mistake: the

                   news is important and the details are alarming.

                   [...]

                   That Berenson espouses nonsense doesn’t make this

                   revelation less disturbing: to accept this

                   precedent is to accept that any future White House

                   can press Twitter or any other social media firm to

                   remove accounts it decides is spreading

                   misinformation.

                   [...]

                   Many have been quick to dismiss or ignore all of

                   this because so many of the illustrative examples

                   disclosed so far have been genuinely repugnant

                   people or politically unsympathetic. But this is a

                   classic mistake.

            # ⚓ Reason ☛ Teacher_Can_Proceed_With_First_Amendment_Lawsuit

              Over_Threatened_Punishment_for_Wearing_MAGA_Hat_to_Training⠀⇛

                   Principal Garrett allegedly threatened Dodge with

                   punishment for wearing the MAGA hat, and Garrett

                   sued.

                   [...]

                   It goes without saying that Dodge disputes this

                   characterization of his political views as

                   evidenced by his testimony explaining why he liked

                   the MAGA message of his hat. Accepting Principal

                   Garrett’s arguments that Dodge’s hat created

                   disruption that warranted restricting his

                   expression would be akin to picking which of their

                   competing political viewpoints is superior.

                   It would be one thing if Principal Garrett was

                   enforcing a generally applicable policy that banned

                   all political expression. A government employer can

                   categorically prohibit political speech as a valid

                   administrative interest such that the prohibition

                   does not favor or disfavor any particular view. But

                   that is not what happened here….

      o § Civil Rights/Policing⠀➾

            # ⚓ Gannett ☛ Protocols_to_stop_mass_school_shootings_are

              spreading._Are_students’_right_being_violated?⠀⇛

                   The processes too often target students already at

                   risk of not succeeding in school, including

                   students with disabilities, who may then be denied

                   an education, advocates say.

            # ⚓ TruthOut ☛ Fighting_to_Close_Prisons_and_Jails⠀⇛

            # ⚓ Common Dreams ☛ A_Celebration_of_Baseball_Rebel_Jim

              Bouton⠀⇛

                   Amidst the current upsurge of social activism among

                   professional athletes, it is worth recalling the

                   enormous contribution of Jim Bouton, one of the

                   most politically outspoken sports figures in

                   American history. Among professional team sports,

                   baseball may be the most conservative and

                   tradition-bound, but throughout its history, rebels

                   and mavericks have emerged to challenge the status

                   quo in baseball and the wider society, none more so

                   than Bouton.

            # ⚓ Counter Punch ☛ Drag_Story_Hour_and_Cultural

              Appropriation⠀⇛

                   Media reports about the debate over Drag Story Hour

                   in the United States typically offer two positions

                   to choose from: A liberal embrace of diversity or a

                   conservative articulation of traditional values.

                   On the left, an endorsement of drag queens reading

                   to children in libraries is presented as

                   celebrating diverse sexualities and challenging the

                   restrictive gender norms of the dominant culture.

                   For many on the right, Drag Story Hour undermines

                   traditional gender norms and validates

                   homosexuality, with the more strident voices

                   suggesting it’s an attempt to recruit children into

                   unhealthy lifestyles. No doubt there are many

                   people who do not have strong feelings either way

                   and find the practice hard to understand, and so

                   stay as far away from the question as possible.

            # ⚓ Counter Punch ☛ Vivienne_Westwood:_Activism_and_the

              Godmother_of_Punk⠀⇛

                   There was the punk scene, Malcolm McLaren, their

                   racy clothes shop at 430 King’s Road that started

                   out as Let it Rock, the creation of a look, and the

                   gathering of the earth rumbling Sex Pistols.  In

                   fact, the late Dame Vivienne Westwood was already a

                   proven stirrer, suggesting that she, not Sex

                   Pistols frontman John Lydon, a.k.a Johnny Rotten,

                   came up with the title for the barnstorming

                   “Anarchy in the UK”.  Boldly, she claimed that

                   prior to McLaren and herself, there was no punk.

                   The Westwood look became ubiquitous with

                   enthusiastic teens of the late 1970s, the use of

                   studs, clothes replete with antisocial indignation,

                   and the jarring, spiky hair to match.  In the

                   opinion of Dame Zandra Rhodes, “We’d had flower

                   power… then suddenly you had this very-hard hitting

                   punk.”

      o § Digital Restrictions (DRM)⠀➾

            # ⚓ EFF ☛ Fighting_for_the_Digital_Future_of_Books:_2022_in

              Review⠀⇛

                   EFF client Internet Archive has created one of

                   those spaces. Through Controlled Digital Lending

                   (“CDL”), the Internet Archive and other nonprofit

                   libraries make and lend digital scans of print

                   books in their collections, at no cost to their

                   patrons.  CDL allows people to check out digital

                   copies of books for two weeks or less, and only

                   permits patrons to check out as many copies as the

                   Archive and its partner libraries physically own.

                   That means that if the Archive and its partner

                   libraries have only one copy of a book, then only

                   one patron can borrow it at a time, just like any

                   other library. Through CDL, the Internet Archive is

                   helping to foster research and learning by helping

                   its patrons access books and by keeping books in

                   circulation when their publishers have lost

                   interest in them.

                   CDL is fundamentally the same as traditional

                   library lending; it’s just another way of getting a

                   book to the one patron who borrowed it.  But four

                   of the biggest publishers in the world want to shut

                   it down. In 2020, they sued the Internet Archive

                   for copyright infringement. In 2022, both sides

                   filed briefs asking the court to decide the

                   question as a matter of law. Supported by authors,

                   libraries, and scholars, the Internet Archive’s

                   briefs explained that CDL is a lawful fair use that

                   serves copyright’s ultimate purpose: enriching our

                   common culture. The publishers, for their part,

                   claim that the Internet Archive’s CDL program harms

                   their ebook licensing market. But their theory has

                   a fundamental flaw: even with unlimited access to

                   years of sales data, they cannot point to a dime

                   they have lost or are likely to lose because of the

                   Internet Archive’s digital lending.

                   The outcome of this case is likely to define the

                   future of books in the U.S. CDL makes it easier for

                   patrons who live far from a brick-and-mortar

                   library, or who have print disabilities, to access

                   books.  But that’s just the beginning. The Internet

                   Archive’s CDL program also helps fight

                   disinformation by facilitating ongoing easy access

                   to authoritative sources for Wikipedia articles.

                   It helps fight censorship by giving librarians a

                   way to curate and share books banned by local

                   school districts.  Like all library lending, it

                   helps the public discover new works that they love

                   enough to purchase their own copies. Digital

                   lending also makes it possible for patrons to

                   access books without having their reading habits

                   tracked by commercial entities, like OverDrive and

                   Amazon, that may not share librarians’ traditional

                   commitment to protecting privacy. Perhaps most

                   importantly, it gives librarians the power to

                   curate their own digital collections, just as they

                   curate their physical collections.

            # ⚓ Ars Technica ☛ New_York_governor_signs_modified_right-to-

              repair_bill_at_the_last_minute_|_Ars_Technica⠀⇛

                   New York state governor Kathy Hochul has signed the

                   Digital Fair Repair Act into law, months after it

                   had passed both chambers of the state’s legislature

                   with overwhelming bipartisan majorities. The bill

                   had originally passed in June, but it was only

                   formally sent to Hochul’s desk earlier this month;

                   the governor had until midnight on December 28th to

                   sign the bill, veto it, or allow it to pass into

                   law without her signature.

                   The Digital Fair Repair Act is the country’s first

                   right-to-repair bill that has passed through a

                   state legislature (as opposed to being implemented

                   via executive order), and has been hailed as

                   “precedent-setting” by right-to-repair advocacy

                   groups like iFixit. The law will require companies

                   to provide the same diagnostic tools, repair

                   manuals, and parts to the public that they provide

                   to their own repair technicians.

      o § Monopolies⠀➾

            # ⚓ NPR ☛ A_bill_to_fight_expensive_prison_phone_call_costs

              heads_to_Biden’s_desk⠀⇛

                   One reason for high rates is that jails and prisons

                   typically develop an exclusive contract with one

                   telecommunications company. That means incarcerated

                   people and their families are stuck with one

                   provider even if the company charges high rates.

                   Another factor is site commissions — that activists

                   call kickbacks — that county sheriffs or state

                   corrections departments receive. Some local

                   officials argue that site commissions are crucial

                   to fund staff who will monitor inmate phone calls

                   for any threats to the community.

            # § Patents⠀➾

                  # ⚓ EFF ☛ Seeing_Patent_Trolls_Clearly:_2022_in_Review⠀⇛

                         Patent trolls are companies that are focused

                         on suing and threatening over patents, not on

                         offering actual goods or services. Very

                         often, they use software patents to sue over

                         basic business processes, like making picture

                         menus or taking event photographs. It’s all

                         too easy to get patents on things like this

                         because the patent system is just a bad fit

                         for software.

                         In the first 3 quarters of 2022, 64% of all

                         patent lawsuits were filed by patent

                         trolls—companies whose primary focus is

                         making money from patents, not providing

                         services or goods. In the high-tech space,

                         patent trolls filed 88% of all lawsuits.

                         Since EFF has started working to improve the

                         patent system, we’ve seen a few big steps

                         forward, like the introduction of inter

                         partes review (IPR), and the 2014 Alice v.

                         CLS Bank Supreme Court ruling.

            # § Copyrights⠀➾

                  # ⚓ Torrent Freak ☛ LaLiga:_Court_Orders_Google_to_Wipe

                    IPTV_Smarters_Pro_From_Play_Store⠀⇛

                         A court in Spain has handed down an order

                         that requires Google to remove popular IPTV

                         app ‘IPTV Smarters Pro’ from the Google Play

                         Store. Filed by top-tier football league

                         LaLiga, the initial complaint received

                         support from UDEV, a police unit tackling

                         specialist and violent crime, including

                         national and international copyright cases.

                  # ⚓ Torrent Freak ☛ Bungie’s_$7.7m_Lawsuit_Against_‘DMCA

                    Fraudster’_Set_For_Jury_Trial…..in_2024⠀⇛

                         Bungie’s $7.7m lawsuit, against a gamer who

                         allegedly sent fraudulent DMCA notices while

                         claiming to represent Bungie, is heading for

                         trial. Bungie alleges that Destiny gamer

                         Nicholas Minor caused substantial damage to

                         its reputation and goodwill. Minor disputes

                         that, and the rest of Bungie’s claims too.

                         The case is now scheduled for a jury

                         trial….in April 2024.

                  # ⚓ Off Guardian ☛ The_Day_the_Music_Died⠀⇛

                         These attempts were so prominent people

                         thought that stealing [sic] intellectual

                         [sic] property [sic] was just the way you got

                         this stuff if you were smart and didn’t want

                         to pay a fortune for it. But before you could

                         do such things, you still had the convenience

                         of owning the material it was embedded in. If

                         you didn’t duplicate it illegally, you could

                         still give away a vinyl record, or a CD

                         (remember them?) or a book.

                         You had the right to keep the material

                         forever, to keep it in an old box, or on a

                         bookshelf, always there and ready to pull

                         down and listen to, read, or fire up on your

                         computer. No one but you controlled what you

                         paid good money for. Not anymore. You never

                         owned the copyright, but now you don’t even

                         own the packaging the software or music, or

                         whatever, comes in.

                  # ⚓ The Economist ☛ A_treasure_trove_of_Hollywood

                    intellectual_[sic]_property_[sic]_is_heading_for_the

                    public_domain⠀⇛

                         For Hollywood executives 95 years may feel

                         all too fleeting, but copyright terms used to

                         be much shorter. The first modern copyright

                         law in the English-speaking world, published

                         in 1710, gave rights-holders in England up to

                         28 years’ ownership of their work. America

                         followed suit with its first federal

                         copyright law in 1790. By 1909 the term was

                         56 years. This held until the 1970s. Then,

                         just as Hollywood’s treasures were about to

                         become public property, Congress stepped in

                         to lengthen the term to 75 years. In 1998, as

                         Domesday approached once more, Congress

                         passed the “Mickey Mouse Protection Act”, as

                         it was mockingly known, extending the

                         copyright term to 95 years.

                         Many expected a further extension. None has

                         materialised. The reason, in a number of

                         ways, is the [Internet]. First, it has turned

                         voters into copyright liberals. In the 1990s

                         the subject of copyright was of interest only

                         to “educators, historians and librarians”,

                         says Mitch Stoltz of the Electronic Frontier

                         Foundation, a free-speech pressure group.

                         With the advent of the internet, people saw

                         how easily information could be copied, and

                         how copyright rules curtailed their ability

                         to share music or images, or to post on

                         social media.

                  # ⚓ New York Times ☛ Mickey’s_Copyright_Adventure:_Early

                    Disney_Creation_Will_Soon_Be_Public_Property⠀⇛

                         This is a company that once forced a Florida

                         day care center to remove an unauthorized

                         Minnie Mouse mural. In 2006, Disney told a

                         stonemason that carving Winnie the Pooh into

                         a child’s gravestone would violate its

                         copyright. The company pushed so hard for an

                         extension of copyright protections in 1998

                         that the result was derisively nicknamed the

                         Mickey Mouse Protection Act.

                         For the first time, however, one of Disney’s

                         marquee characters — Mickey himself — is set

                         to enter the public domain. “Steamboat

                         Willie,” the 1928 short film that introduced

                         Mickey to the world, will lose copyright

                         protection in the United States and a few

                         other countries at the end of next year,

                         prompting fans, copyright experts and

                         potential Mickey grabbers to wonder: How is

                         the notoriously litigious Disney going to

                         respond?

                  # ⚓ Cartooon Brew ☛ What_Happens_When_‘Steamboat_Willie’

                    Hits_The_Public_Domain_In_2024?⠀⇛

                         What does that mean for Mickey and the

                         Steamboat Willie short? After expiration,

                         anyone will be able to screen the original

                         short without permission from Disney. It can

                         also be sold by third parties, although

                         Disney has already made the film free online,

                         so sales will likely be minimal. The film and

                         its characters can also be used by anyone

                         wishing to feature the characters in original

                         stories or artwork.

                  # ⚓ Boston Globe ☛ Mickey’s_copyright_adventure:_Early

                    Disney_creation_will_soon_be_public_property⠀⇛

                         Here is where it gets tricky: Disney also

                         holds trademarks on its characters, including

                         the “Steamboat Willie” version of Mickey

                         Mouse, and trademarks never expire as long as

                         companies keep submitting the proper

                         paperwork. A copyright covers a specific

                         creation (unauthorized copying), but

                         trademarks are designed to protect against

                         consumer confusion — to provide consumers

                         assurance about the source and quality of a

                         creation.

                  # ⚓ Joe Brockmeier ☛ Happy_Public_Domain_Day!_Or_is_it?_:

                    Dissociated_Press⠀⇛

                         Today isn’t just the start of a new year,

                         it’s Public Domain Day in the United States.

                         Works from 1927 enter the public domain

                         today, making them free to copy, share and

                         remix.

                         Some heavy hitters in the mix this year,

                         including Sherlock Holmes, Agatha Christie’s

                         The Big Four, Fritz Lang’s Metropolis, and

                         “Puttin’ on the Ritz” (music and words) by

                         Irving Berlin. (But the iconic number from

                         Young Frankenstein with Gene Wilder and Peter

                         Boyle is still under copyright.)

                         Really, it’s less cause to celebrate and more

                         an occasion to note what’s been stolen from

                         the public. Thanks to Congress extending the

                         already too-generous 75 year copyright term

                         to 95 years, works that should’ve been in the

                         public domain 20 years ago are just now

                         seeing copyright expire. The copyright

                         holders, for the most part, had expired long

                         before the copyright did.

* § Gemini* and Gopher⠀➾

      o § Personal⠀➾

            # ⚓ Looking_Back_on_2022,_and_Forward_to_2023⠀⇛

                   A new year is upon us, and during these days I find

                   myself reflecting on the year that has passed as

                   well as the year to come.

                   I went through a lot of personal growth in 2022.

                   Much of that growth was scary or painful, but it

                   was necessary. I feel like I’m a very different

                   person than I was at the start of last year, and

                   that change has been for the better. My

                   relationships, for all the turbulence they endured,

                   are now stronger than ever–I value the

                   companionship of my wife and the support of my

                   friends in a very different way than I did twelve

                   months ago.

            # ⚓ Review:_The_Black_Company⠀⇛

                   I read Malazan: Book of the Fallen for the first

                   time about 3 years ago and fell in love.

                   The massive scope, the cast, the humour, the

                   action; everything about it was what I wanted in a

                   book, pondourous sections included.

                   I used to have a review for it on this site and

                   can’t for the life of me remember why I removed it.

                   In any case, Malazan has cemented itself as one of

                   my favorite book series of all time, and I’ve

                   reread the whole series once and the first 5 books

                   perhaps a half dozen more times.

            # ⚓ Review:_Legends_and_Lattes⠀⇛

                   *Note: this review is spoiler-free.*

                   The last few books I’ve read have been a bit more

                   serious in tone or ponderous; The Black Company,

                   WWZ, Gormenghast (still working on this one).

                   Minus Discworld, I can’t say I’ve read any

                   lighthearted fantasy books, let alone a slice-of-

                   life one.

                   Legends and Lattes was recommended quite a bit

                   online, so I figured I’d give it a shot.

            # ⚓ 🔤SpellBinding:_AEUKLMI_Wordo:_ALACK⠀⇛

            # ⚓ XR_UK’s_new_line⠀⇛

                   It seems like it’ll be difficult for them to

                   rebrand into a kumbaya hug fest (and they make a

                   good point why such a hug fest is needed: to build

                   solidarity vs the politicians) after all the hate

                   points they’ve racked up. It’d be easier for a new

                   group with a new name to fill that role, while at

                   the same time, I still see some merit in their old

                   role and old tactics.

      o § Technical⠀➾

            # § Programming⠀➾

                  # ⚓ Cross_compiling_HitchHiker_with_Musl⠀⇛

                         My little Linux distro HitchHiker may be

                         getting a pretty dramatic makeover in the

                         form of moving from Glibc to Musl. This is a

                         change that I’ve been considering for a long

                         time and had even done some work towards

                         implementing, but until today had not been

                         able to fully realize compiling the entire

                         base system after swapping out the C library.

                  # ⚓ Crash_Course:_How_to_solve_a_problem_in_J⠀⇛

                         Every year I try to pick up a new programming

                         language to increase the size of my

                         development toolbox. Learning new and

                         different paradigms, trying to pick a

                         language based on the problem. In 20+ years

                         of development I’ve probably got 15 different

                         languages out in production in some shape or

                         form.

                         Last year my interest was peaked when YouTube

                         started suggesting I watch some presentations

                         on APL. This was my first Array programming

                         language, and first language to use a very

                         esoteric glyph syntax. Its interesting to

                         look at, requires a special keyboard setup or

                         a special IDE. To find all prime numbers up

                         to R…

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

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

World Wide Web but a lot lighter.

                ䷩ 𝚕𝚒𝚗𝚎 6319

Gemini_version_available_♊︎

✐ Links_02/01/2023:_Ultramarine_Linux_37_Released,_Nitrux_2.6.0_Released,_and

Archcraft+Arch_Linux_ISOs_for_2023⠀✐

Posted in News_Roundup at 9:03 pm by Dr. Roy Schestowitz

🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈

§ Contents⠀➾

* GNU/Linux

      o Audiocasts/Shows

      o Kernel_Space

      o Applications

      o Instructionals/Technical

      o Desktop_Environments/WMs

            # GNOME_Desktop/GTK

* Distributions_and_Operating_Systems

      o New_Releases

      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 Programming/Development

            # Perl_/_Raku

            # Python

            # Shell/Bash/Zsh/Ksh

      o Standards/Consortia

* Leftovers

      o Science

      o Hardware

      o Health/Nutrition/Agriculture

      o Proprietary

      o Security

      o Environment

      o Finance

      o Internet_Policy/Net_Neutrality

* Gemini*_and_Gopher

      o Personal

      o Technical

            # Internet/Gemini

* § GNU/Linux⠀➾

      o ⚓ AIM ☛ ‘Toxic’_Linux_Community_Acts_As_the_Perfect_Repellent_for

        New_Users [Ed: See the “Note”; seems_like_a_Microsoft_propaganda

        site_and_Microsoft_is,_in_fact,_a_media_partner]⠀⇛

             Although, these bad apples do not make a majority of the

             community surrounding Linux, since many forums are

             actually friendly towards new users, the negative users

             create enough noise in the community to turn newcomers

             away from the platform, thus creating a negative

             perception of the ecosystem.

      o ⚓ LWN ☛ 20_Years_of_DistroWatch_[LWN.net]⠀⇛

             DistroWatch Weekly celebrates its 1000th issue and 20

             years of publication.

      o ⚓ OMG! Linux ☛ Linux_Format_Magazine_Issue_297_is_Now_On_Sale_–

        OMG!_Linux⠀⇛

             A new year, and a brand new issue of the FOSS-focused

             technology magazine Linux Format is available to buy.

             Linux Format 297 includes a comprehensive feature about

             escaping Microsoft Windows. Aimed at first-time Linux

             users, the guide looks at using the user-friendly

             Elementary OS distribution to get started with Linux and

             related software.

             There’s an in-depth guide to open source RAW photography

             that could (no promises) help you create better looking

             snaps, with ample tips, advice, software, and tool

             recommendations provided.

      o § Audiocasts/Shows⠀➾

            # ⚓ Video ☛ Kodachi_Linux:_Is_It_Worth_the_Hype?_–_Invidious⠀⇛

                   Today we look at Kodachi Linux from a standpoint of

                   what it is and how it is created rather than

                   looking at the distro directly. I identify a few

                   major issues with the distro and why other

                   platforms are better for security and privacy

                   models.

            # ⚓ Video ☛ Here’s_something_challenging_for_your_new_year

              resolution_🐧_–_Invidious⠀⇛

                   Comment below which distro you are going to try!

            # ⚓ Video ☛ These_community-made_Steam_Deck_boot_movies_are

              AWFUL._(And_there_are_a_few_good_ones,_too)_–_Invidious⠀⇛

                   What’s going on in the world of Steam Deck

                   customization? Bad boot movies. That’s what. From

                   pre-made motion graphic templates with the Deck

                   logo poorly shoehorned in to “Adult Swim” to the OP

                   re-emergence of “Bonzi Buddy”, there’s something

                   for every (poor) taste on SteamDeckRepo.com!

            # ⚓ Linux_User_Space:_A_Pause_for_Health⠀⇛

                   Hey everyone, and welcome to the Linux User Space!

                   Normally we’d be releasing a new episode today, but

                   we have to pause due to some health issues.

                   We’ll pick back up with episode 14 of season 3

                   featuring Gecko Linux in two weeks. So stay tuned

                   and check out our Youtube and TILVids in the mean

                   time.

            # ⚓ Tux Digital ☛ 306:_2023_Linux_Predictions,_Xfce_4.18,_Steam

              Winter_Sale_–_More!_–_Destination_Linux_–_TuxDigital⠀⇛

                   This week’s episode of Destination Linux, we’re

                   going to discuss our predictions for 2023 as well

                   as our hopes and dreams for this coming year. Then

                   we discuss the latest release of Xfce with Xfce

                   4.18. Plus, we have our tips/tricks and software

                   picks. All this and more coming up right now on

                   Destination Linux to keep those penguins marching!

            # ⚓ Video ☛ Ultramarine_Linux_–_Perfect_Fedora_Spin_|_Now_With

              A_Customized_KDE_Desktop_–_Invidious⠀⇛

                   Ultramarine Linux – Perfect Fedora Spin | Now With

                   A Customized KDE Desktop

                   A video covering the newest release of Ultramarine

                   Linux. The perfect Fedora spin now with the KDE

                   desktop environment. Take a look and let me know

                   what you think in the comments below.

            # ⚓ Linux Made Simple ☛ How_to_install_Rosegarden_on_a

              Chromebook⠀⇛

                   Today we are looking at how to install Rosegarden

                   on a Chromebook.

            # ⚓ Video ☛ Keep_Your_TODO_List_–_Notes_Simple_With_Dooit_–

              Invidious⠀⇛

                   There are many todo list/todo manager applications

                   out there and today we’re looking at one of the

                   simpler ones, this is terminal tui based solution

                   called dooit which while very simple does

                   everything you might need. This video has been

                   sitting in my backlog since September.

            # ⚓ Video ☛ RPCS3_hits_a_new_compatibility_milestone!_–

              Invidious⠀⇛

            # ⚓ Video ☛ How_to_install_Visual_Studio_Code_on_KDE_Neon_–

              Invidious [Ed: Terrible idea as it is proprietary spyware

              controlled by the company attacking GNU/Linux the most; don't

              advise people to install this or help them give Microsoft

              control]⠀⇛

            # ⚓ Video ☛ Ubuntu_22.04_|_Install_–_Setup_a_Minecraft_Server_–

              Invidious [Ed: KeepItTechie helping Microsoft spread

              proprietary software now ]⠀⇛

            # ⚓ Video ☛ deepin_20.8_Quick_overview_–_Invidious⠀⇛

                   A Quick Overview of deepin 20.8

            # ⚓ Video ☛ How_to_install_Manjaro_22.0_Gnome_Edition_–

              Invidious⠀⇛

                   In this video, I am going to show how to install

                   Manjaro 22.0 Gnome Edition.

      o § Kernel Space⠀➾

            # ⚓ OMG! Linux ☛ New_Intel_Xe_Graphics_Driver_for_Linux_in

              Development_–_OMG!_Linux⠀⇛

                   The new Intel Xe kernel graphics driver was

                   announced before Christmas. It will support Intel’s

                   11th gen integrated graphics and newer, as well as

                   discrete Intel Xe graphics cards.

                   Though under active development at present, Intel

                   say the new driver will be production-ready this

                   year.

                   But why build a new Intel graphics driver at all?

                   Isn’t the existing one good enough?

      o § Applications⠀➾

            # ⚓ Linux Links ☛ Best_Free_and_Open_Source_Alternatives_to

              Google_Sheets⠀⇛

                   Google has a firm grip on the desktop. Their

                   products and services are ubiquitous. Don’t get us

                   wrong, we’re long-standing admirers of many of

                   Google’s products and services. They are often high

                   quality, easy to use, and ‘free’, but there can be

                   downsides of over-reliance on a specific company.

                   For example, there are concerns about their privacy

                   policies, business practices, and an almost

                   insatiable desire to control all of our data, all

                   of the time.

                   What if you are looking to move away from Google

                   and embark on a new world of online freedom, where

                   you are not constantly tracked, monetised and

                   attached to Google’s ecosystem.

                   In this series we explore how you can migrate from

                   Google without missing out on anything. We

                   recommend open source solutions.

            # ⚓ Carl Schwan ☛ Tokodon_23.01.0_release⠀⇛

                   Happy new year! To get a good start in this new new

                   year, I’m happy to announce that Tokodon 23.01.0 is

                   out! This is a new major release for Tokodon and

                   while it’s been only 2 weeks since the last major

                   release, this release is packed with new features

                   and improvements.

                   Tokodon is a Mastodon/Pleroma/Nextcloud Social

                   client built with Kirigami that I started back in

                   spring 2021. Tokodon has a great integration with

                   KDE Plasma and Plasma Mobile, but it also work on

                   other desktop environments and even Windows and

                   macOS.

            # ⚓ Make Use Of ☛ The_4_Best_sudo_Alternatives_for_Linux_Worth

              Considering⠀⇛

                   For those who don’t fancy sudo and find it bloated,

                   there are several sudo alternatives you can try

                   instead.

                   sudo is probably one of the most used Linux

                   commands. It allows you to gain administrative or

                   elevated privileges on a Linux machine.

                   You normally need elevated privileges to execute

                   actions such as installing software, managing

                   services, and deleting critical system files. But

                   did you know there are alternatives to the sudo

                   command on Linux?

      o § Instructionals/Technical⠀➾

            # ⚓ UNIX Cop ☛ Using_vnStat_on_Debian_11_to_monitor_the

              network⠀⇛

                   In this post, you will learn how to install and use

                   vnStat on Debian 11 to monitor the network in a

                   quick and easy way without too much complexity.

            # ⚓ ByteXD ☛ How_to_Use_Fasd_in_Linux_for_Quick_Access_to_Files

              &_Directories⠀⇛

                   Linux users often rely on the command line, but

                   tedious and time-consuming tasks can make it

                   frustrating. Navigating and moving between

                   directories using cd and ls commands, plus typing

                   long path files to access, copy or list files, can

                   be annoying for even advanced users.

                   To solve the problem of directory navigation and

                   accessing files from other locations in the system

                   using command lines, the fasd tool has been created

                   exactly for this purpose. fasd is a command line

                   utility written in Shell that serves as an advanced

                   version of the autojump and z command utilities; we

                   can call also: Autojump plus z with support for

                   files.

                   This Linux tool allows the user to quick access a

                   previously visited directories and files from any

                   location in the system.

                   Fasd can be described as a faster solution to

                   navigate and access the user’s frequent and recent

                   directories and files. This helpful utility saves

                   the frequently visited directories and files (i.e.

                   History) from the command line into a database in

                   order to render filesystem navigation possible and

                   quite easy just by typing small patterns.

                   In this article you will learn how to use fasd to

                   easily access files and directories without

                   specifying their full path or executing numerous cd

                   commands.

            # ⚓ TecAdmin ☛ 5_Practical_Examples_to_Check_If_a_Port_is_Open

              –_TecAdmin⠀⇛

                   In Linux, a port is a numbered network connection

                   that allows a device to communicate with other

                   devices over the internet or a local network. It is

                   important to ensure that the desired ports are open

                   and accessible to ensure the smooth functioning of

                   network services. There are various ways to check

                   if a port is open in Linux, and in this article, we

                   will discuss five of them.

            # ⚓ Linux Hint ☛ Sort_Command_in_Linux_with_Examples⠀⇛

                   To organize the data in a precise sequence or sort

                   the file, use the sort command. The file’s data is

                   sorted line by line using the sort command. If a

                   record is in alphabetical order, the file is sorted

                   alphabetically. Otherwise, it is sorted in

                   ascending order if the record contains numeric

                   information. Linux’s sorting feature offers a

                   variety of flags from which we can choose to sort

                   in reverse or by column, etc. We will utilize a few

                   of its flags in this article.

            # ⚓ ID Root ☛ How_To_Install_NoMachine_on_Ubuntu_22.04_LTS_–

              idroot⠀⇛

                   In this tutorial, we will show you how to install

                   NoMachine on Ubuntu 22.04 LTS. For those of you who

                   didn’t know, NoMachine is a comprehensive remote

                   desktop solution that allows users to access and

                   control a remote computer from a local machine.

                   Interestingly, NoMachine supports an unlimited

                   number of remote servers on a single server. Its

                   support for multiple platforms and features such as

                   audio and video streaming make it a popular choice

                   for many users.

                   This article assumes you have at least basic

                   knowledge of Linux, know how to use the shell, and

                   most importantly, you host your site on your own

                   VPS. The installation is quite simple and assumes

                   you are running in the root account, if not you may

                   need to add ‘sudo‘ to the commands to get root

                   privileges. I will show you the step-by-step

                   installation of the NoMachine on Ubuntu 22.04

                   (Jammy Jellyfish). You can follow the same

                   instructions for Ubuntu 22.04 and any other Debian-

                   based distribution like Linux Mint, Elementary OS,

                   Pop!_OS, and more as well.

            # ⚓ Beginners_Guide_for_Wall_Command_in_Linux⠀⇛

                   If you are a sysadmin, then wall command can be

                   your next favorite Linux tool, thinking why? With

                   the help of this tool, you can broadcast messages

                   to all logged-in users on your system, either

                   locally or via SSH.

                   This tool comes in handy, especially when you

                   intend to start maintenance work (or something

                   else) on your server and want to notify other users

                   in advance.

                   Stick with this article until the end to learn more

                   about the wall command and its different options

                   (with practical examples).

            # ⚓ LinuxTuto ☛ How_To_Secure_Apache_with_Let’s_Encrypt_on

              Ubuntu_22.04_–_LinuxTuto⠀⇛

                   Let’s Encrypt is a free, automated, and open

                   certificate authority (CA). Let’s Encrypt offer

                   free 90-day SSL certificates.

                   Let’s Encrypt provide two types of certificates.

                   The standard single-domain SSL and the Wildcard

                   SSL, which covers not only a single domain, but all

                   of its subdomains too.

                   In this tutorial, we will use Certbot a free, open-

                   source software tool for automatically issuing the

                   Let’s Encrypt SSL Certificate and verify that your

                   certificate is set up to renew automatically.

            # ⚓ First_steps_with_Mermaid,_a_diagramming_and_charting_tool⠀⇛

                   Mermaid is a Javascript-based tool that renders

                   Markdown-inspired text definitions to create

                   diagrams. In this tutorial you’ll learn how to

                   start and render your first diagram.

            # ⚓ Make Use Of ☛ Linux_USB_Not_Detected_or_Not_Working?_5

              Common_Issues_and_Fixes⠀⇛

                   USB devices not detected in Linux? Try these

                   troubleshooting tips to get things working again.

                   You’ve hooked up a USB flash drive or a keyboard or

                   mouse to your Linux PC. But nothing is happening.

                   What’s going on? Why is your pen drive not detected

                   in Ubuntu 22.04 LTS or some other distro? Is it a

                   Linux thing, or has your USB device stopped

                   working? Here’s what to do on Linux if your USB

                   drive is not detected or recognized.

            # ⚓ Make Use Of ☛ What_Is_PPA_and_How_Does_It_Install_Software

              on_Ubuntu_Linux?⠀⇛

                   Unlike traditional packages, PPAs aren’t maintained

                   or distributed by Ubuntu or Canonical. So what are

                   they? And should you use them on your PC?

                   PPAs or Personal Package Archives are a type of

                   repository used in Linux systems to store and

                   distribute software packages.

                   Let’s learn what a PPA is, how they differ from

                   standard repositories, how to add and remove PPAs,

                   whether PPAs are safe to use, and finally, the

                   advantages of using PPAs.

            # ⚓ Red Hat Official ☛ 10_top_networking_guides_for_sysadmin

              success_|_Enable_Sysadmin⠀⇛

                   Get plugged into the top 10 networking articles of

                   2022 to learn how to troubleshoot network problems,

                   automate your network, balance traffic, and more.

            # ⚓ TecAdmin ☛ Understanding_the_su_Command_in_Linux_–

              TecAdmin⠀⇛

                   If you’ve ever wanted to run commands as a

                   different user without having to log out and log

                   back in again, then the su command is the perfect

                   tool for you! This command not only allows you to

                   switch users seamlessly but also provides a number

                   of other useful features that can supercharge your

                   Linux experience.

                   In this article, we’ll take a look at some examples

                   of the su command in action, discuss best practices

                   for using it, explore some alternatives, and cover

                   some important security considerations. So let’s

                   get started!

            # ⚓ 5_Easy_Steps_to_Mastering_TCPdump_for_Network

              Troubleshooting_–_buildVirtual⠀⇛

                   TCPdump is a powerful command-line tool for

                   analyzing and debugging network traffic. It allows

                   you to capture and examine packets transmitted over

                   a network, providing valuable insights into network

                   performance and security.

                   If you’re new to TCPdump, don’t worry! In this blog

                   post, we’ll walk you through the basics and provide

                   you with the skills you need to get started.

            # ⚓ It’s FOSS ☛ Getting_Started_With_Manjaro⠀⇛

                   As we mentioned in our Manjaro Linux review, it is

                   Arch Linux for Human Beings.

                   While Arch Linux can be intimidating, Manjaro is

                   much more comforting and easier to use.

                   But that doesn’t mean that there is no learning

                   curve involved.

                   If you are new to Manjaro Linux, these tutorials

                   will help you use Manjaro Linux more smoothly and

                   effectively.

            # ⚓ OSTechNix ☛ Apply_Updates_Automatically_With_dnf-automatic

              –_OSTechNix⠀⇛

                   Applying updates regularly should be the top

                   priority in the day-to-day tasks of a System

                   administrator. Running unpatched systems for a long

                   time is quite risky. There are many ways to patch

                   your Linux systems. Today, we will learn how to

                   apply updates automatically with dnf-automatic in

                   RHEL and its clones like AlmaLinux and Rocky Linux.

            # ⚓ Video ☛ How_To_Save_Your_Desktop_Notifications_–

              Invidious⠀⇛

                   One of the interesting things with Linux desktop

                   notifications is that they are not permanently

                   saved anywhere on your system. Well, with some

                   Google-fu and some minor configuration file edits,

                   we can have our desktop notifications automatically

                   save to a log file that we can read anytime we

                   want.

            # ⚓ Beginners_Guide_for_Pstree_Command_in_Linux⠀⇛

                   The ps and top commands are the most popular and

                   commonly used command-line programs to view the

                   currently running processes on your Linux system.

                   The pstree is also similar to them, except that it

                   outputs the running process in the form of a tree;

                   if no arguments are passed, then it will list the

                   complete process.

                   This way of inspecting the running processes in the

                   form of a hierarchy is more convenient and visually

                   appealing, especially for beginners (even if they

                   don’t understand the output).

                   In this article, you will learn how to use the

                   pstree command and how to use the different

                   available options with it (with practical

                   examples).

            # ⚓ LinuxConfig ☛ How_to_manage_power_profiles_over_D-Bus_with

              power-profiles-daemon_on_Linux⠀⇛

                   Power-profiles-daemons is a free and open source

                   project designed to handle system power profiles

                   over D-Bus. The two major Linux desktop

                   environment, GNOME and KDE Plasma, are nicely

                   integrated with it, allowing the user to easily

                   manage power profiles from their dedicated power

                   manager interfaces, but it is also possible to

                   switch profiles and retrieve information about them

                   from the command line, using a dedicated utility.

                   In this tutorial we learn how to install power-

                   profiles-daemon, and how to use it to manage power

                   profiles on Linux.

      o § Desktop Environments/WMs⠀➾

            # ⚓ 9to5Linux ☛ Xfce’s_Apps_Update_for_December_2022:_New

              Releases_of_Ristretto,_Thunar,_Screenshooter,_and_More_–

              9to5Linux⠀⇛

                   The December and last issue of my exclusive “Xfce’s

                   Apps Update” monthly roundup for 2022 is here with

                   news about the latest releases of your favorite

                   Xfce applications, plugins, tools, and more.

                   As you all know, the biggest news for fans of the

                   Xfce desktop environment in December 2022 was the

                   release of Xfce 4.18, which is already available

                   for installation on some of the most popular GNU/

                   Linux distributions out there, as well as on some

                   less known distros.

                   After the release of Xfce 4.18, the rest of

                   December brought us a new release of the Thunar

                   file manager to version 4.18.1, which fixes several

                   thumbnailing issues, addresses a crash with the

                   location bar, fixes an issue to prevent building on

                   the NixOS distro, no longer resets zoom-level for

                   directory specific settings, fixes the ‘replace’

                   option when copying ‘*.partial~’ files, and

                   preserves the trusted state when copying launchers.

            # § GNOME Desktop/GTK⠀➾

                  # ⚓ OMG Ubuntu ☛ Easily_Monitor_Stock_Prices_with_these

                    GNOME_Extensions_–_OMG!_Ubuntu!⠀⇛

                         Here are two GNOME extensions you can use to

                         keep an eye on stock prices from your Linux

                         desktop without needing to open a web browser

                         or a dedicated app.

                         In a fast-paced world folks want quick and

                         easy access to real-time stock market data.

                         While there are websites that let you view

                         stock prices online, it’s often more

                         convenient to get the information through the

                         OS itself.

                         So the GNOME extensions in this article will

                         satisfy those who spend a lot of time at

                         their computer and want to see the latest

                         stock prices for specific companies/stocks.

                         There’s no need to keep a browser tab open,

                         or fish a smartphone out of your pocket as

                         you can view the latest stock prices hassle-

                         free.

                         Why not invest in one of these time-savers?

* § Distributions and Operating Systems⠀➾

      o ⚓ FOSS Post ☛ Best_Linux_Distribution_of_2022_Goes_to_Pop!_OS

        22.04⠀⇛

             Pop!_OS 22.04 is a fantastic Linux distribution which has

             been heavily modified to provide the best experience for

             power users. It ships with a lot of custom software and

             tweaks, making it one of the best Ubuntu derivatives out

             there.

             Although mainly developed by System76 for their own

             hardware that they sell, it can be used like any other

             normal distribution on any suitable hardware.

             Additionally, many users report that it was able to

             revive their older hardware thanks to the CPU tweaks done

             on it.

             It has a fantastic future as one of the best Linux

             distributions out there for professionals and creators.

      o ⚓ Make Use Of ☛ The_Top_8_Weird_and_Funny_Meme_Linux

        Distributions⠀⇛

             If you’re looking to have a little bit of fun while

             distro-hopping, consider taking these funny, meme Linux

             distros for a spin.

             Linux distributions are the most versatile and valuable

             OSes in the market. Given their customizations and

             flexibility, they inspire developers to create new,

             improved versions of the operating system, usually to

             meet specific goals.

             Even though most Linux OSes are tailor-made to cater to a

             specific purpose, a few are bound to make you laugh or

             wonder about their true meaning.

             If you are a fan of Linux and want to review a few

             unconventional, funny, and weird distros, check out this

             list of meme Linux distributions.

      o § New Releases⠀➾

            # ⚓ January_2023_Release_Available_(Distribution_Release_of

              Archcraft_2023.01.01)⠀⇛

                   You need to re-install Archcraft for this update.

                   After that, you can update to next release with

                   pacman

            # ⚓ Nitrux ☛ Release_Announcement:_Nitrux_2.6.0_“ff”⠀⇛

                   We are pleased to announce the launch of Nitrux

                   2.6.0. This new version combines the latest

                   software updates, bug fixes, performance

                   improvements, and ready-to-use hardware support.

            # ⚓ OS News ☛ Vanilla_OS_22.10_released_–_OSnews⠀⇛

                   Vanilla OS has released its first version. Vanilla

                   OS is an immutable desktop Linux distribution that

                   brings some interesting new technologies to the

                   table, such as the Apx package manager.

      o § Arch Family⠀➾

            # ⚓ 9to5Linux ☛ Arch_Linux’s_First_ISO_Release_in_2023_Is_Out

              and_It’s_Powered_by_Linux_Kernel_6.1_–_9to5Linux⠀⇛

                   Arch Linux is the first GNU/Linux distribution to

                   kick off 2023 with a new ISO release targeting

                   those who want to deploy Arch Linux on new

                   computers, chroot into an existing one to repair

                   it, or just reinstall their systems.

                   Arch Linux 2023.01.01 is not only Arch Linux’s

                   first ISO release in 2023, but it’s also Arch

                   Linux’s first ISO release powered by the latest and

                   greatest Linux 6.1 kernel series. This means that

                   you’re getting better hardware support out of the

                   box when booting the new Arch Linux ISO on some

                   computers.

                   Linux kernel 6.1.1 is being used by default on the

                   new Arch Linux ISO release since the latest Linux

                   6.1.2 kernel release that arrived on New Year’s Eve

                   is still in the Testing repos (you’ll get it as an

                   update after the installation). Linux kernel 6.1

                   arrived in Arch Linux’s repositories on December

                   22nd, 2022, for existing users.

            # ⚓ Linuxiac ☛ The_Numbers_Don’t_Lie:_Arch_Linux_Reigns_Supreme

              on_Reddit⠀⇛

                   As of January 1, 2023, Arch is the most popular

                   Linux distribution based on the number of members

                   in individual Linux communities on Reddit.

                   The popularity of individual Linux distributions

                   has always piqued the interest of the Linux

                   community. Every year, new ones emerge, with some

                   gaining popularity at the expense of others losing

                   it for various reasons. In other words, the

                   popularity of different Linux distributions is

                   dynamic and challenging to track metrics.

                   For many years, Distrowatch has been used as an

                   example in measuring this factor. However, the

                   metric used there, unique page views of a specific

                   Linux distribution, is hard to accept without

                   reservation, even though it provides a good

                   indication of popularity.

      o § Fedora Family / IBM⠀➾

            # ⚓ DebugPoint ☛ Ultramarine_Linux_37_Release_Adds_Pop_OS-Style

              KDE_Plasma,_Drops_Cutefish⠀⇛

                   A new release of Ultramarine Linux is here:

                   Ultramarine Linux 37 with new custom repo, KDE

                   Plasma flavour and goodies.

                   If you are unaware, Ultramarine Linux is a Fedora-

                   based distribution which offers Budgie, Pantheon,

                   GNOME and other desktops. This distro gives you the

                   best Fedora experience with this awesome desktop

                   environment.

                   Recently, this small project is acquired by

                   FyraLabs, the company behind PhotonBrowser and

                   tauOS. And this enables the Ultramarine project

                   with the necessary manpower and funding for

                   infrastructure to continue building the distro.

            # ⚓ Enterprisers Project ☛ Digital_transformation:_4_security

              tips_for_2023_|_The_Enterprisers_Project⠀⇛

                   Digital advances offer countless competitive

                   advantages and can be a great equalizer for those

                   they serve. However, organizations must consider

                   the risks involved when generating a tidal wave of

                   data and connections.

                   As businesses spend millions of dollars on

                   developing strategic, long-term plans to digitize

                   their processes, enhancing IT and cyber risk

                   management functions should be at the forefront. In

                   fact, 14 percent of C-suite executives indicate

                   their organizations have no cyber threat defense

                   plans.

            # ⚓ Enterprisers Project ☛ 10_DevOps_lessons_IT_leaders_learned

              in_2022_|_The_Enterprisers_Project⠀⇛

                   Upskilling, burnout, containers—oh my! These are

                   the topics swirling within the minds of developers

                   and IT professionals. This year, IT leaders shared

                   both their success stories and failures when it

                   comes to DevOps. Although embracing cloud-native

                   technology like Kubernetes is exciting, honing in

                   on the emotional side of DevOps is just as

                   important and even more challenging. As you enter

                   into the new year, read these articles to reflect

                   on how to strengthen your organization’s culture of

                   DevOps.

      o § Debian Family⠀➾

            # ⚓ Gunnar Wolf ☛ Gunnar_Wolf:_Refueling_the_blog⠀⇛

                   So… yes, there is a clear downwards trend towards

                   the last few years. And it does make sense, all in

                   all: Not only have I managed to keep myself busier

                   than before, but… Blogging is a social endeavor.

                   And as people have moved over to the different

                   flavors of social networks, there is somewhat less

                   fueling us to share our thoughts and experiences in

                   this fashion.

                   So this connects me to my first point: Staring at

                   Noodles’ Emptiness, I got to a campaign to Bring

                   Back Blogging. I stand by all of what they suggest:

                   Blogs are a great invention, they allow the sharing

                   of a great insight into a person’s mind, ideas and

                   worldview (and even more so if, like mine, it shows

                   already a window of almost two decades of life!

                   This year my blog will be old enough to vote!),

                   they are completely decentralized, and can be

                   easily grouped according to each readers’

                   preferences via the RSS format.

                   Anyway – I do want to write a post summing up 2022,

                   as well as sharing some hopes and projects I have

                   for 2023. But I don’t want to make it too long to

                   read. So… That shall be the blog post for today!

            # ⚓ Sparky GNU/Linux ☛ Sparky_news_2022/12_–_SparkyLinux⠀⇛

                   The 12th monthly Sparky project and donate report

                   of 2022:

                   – Linux kernel updated up to 6.1.2 & 5.15.86-LTS &

                   4.9.336-LTS49, and the new one 6.2-RC1 as well

                   – Added to repos: Harmonoid

                   – the US1 mirror server is back online

                   – Sparky 2022.12 & 2022.12 Special Editions of the

                   rolling line released

                   Good news!

                   In December, You sent a little more than 100% of

                   donations, it’s something we have not been able to

                   do for the past few years.

                   We also got 100% of the amount for the VPN server

                   for the next year, just a few days before the

                   deadline.

            # ⚓ Ben_Hutchings:_Debian_LTS_work,_December_2022⠀⇛

                   In December I was assigned 15 hours by Freexian’s

                   Debian LTS initiative and carried over 9 hours from

                   November. I worked all of those hours.

                   I merged the latest bullseye point release into the

                   linux-5.10 package, uploaded that, and issued DLA-

                   3244-1.

      o § Canonical/Ubuntu Family⠀➾

            # ⚓ Ubuntu Fridge ☛ The_Fridge:_Ubuntu_Weekly_Newsletter_Issue

              768⠀⇛

            # ⚓ Ubuntu News ☛ Ubuntu_Weekly_Newsletter_Issue_768⠀⇛

                   Welcome to the Ubuntu Weekly Newsletter, Issue 768

                   for the week of December 25 – 31, 2022.

      o § Devices/Embedded⠀➾

            # ⚓ Mighty Gadget ☛ CES_2023:_MediaTek_Genio_700_Chipset_for

              Smart_Home_IoT_Devices_launched⠀⇛

                   The Genio 700 SDK allows designers to customize

                   products using Yocto Linux, Ubuntu, and Android.

                   With this support, customers can easily develop

                   their own products with a minimal amount of effort,

                   regardless of application type.

            # ⚓ MediaTek_Expands_IoT_Platform_with_Genio_700_for_Industrial

              and_Smart_Home_Products⠀⇛

                   The Genio 700 SDK allows designers to customize

                   products using Yocto Linux, Ubuntu, and Android.

                   With this support, customers can easily develop

                   their own products with a minimal amount of effort,

                   regardless of application type.

            # ⚓ MediaTek_Genio_700,_IoT_SoC_for_Industrial_and_Smart_Home

              Products_|_Ubergizmo⠀⇛

                   The Genio 700 SDK will allows developers to create

                   and customize industrial and smart home products

                   running on Yocto Linux, Ubuntu, and Android.

      o § Open Hardware/Modding⠀➾

            # ⚓ TuxPhones ☛ Purism_Librem_5_receives_major_camera_update,

              video_recording_capabilities⠀⇛

                   As we tend to mention often, cameras are one of the

                   areas where Linux phones are often seen as lacking

                   behind their Android alternatives. This is partly

                   due to extreme fragmentation of sensor drivers,

                   with most mainlined devices not having any kind of

                   Linux camera support, and just partly due to the

                   lack of a software infrastructure for acquisition

                   and post-processing.

                   The first camera app for Linux phones was

                   Megapixels, developed by Martijn Braam as a Python

                   GTK3 app for the PinePhone, and now the standard

                   choice for Linux mobiles. Megapixels can be easily

                   extended to new phones with a working kernel camera

                   driver through configuration files, which specify

                   sensor drivers to use, colour processing matrices,

                   how previews are to be displayed, and much more.

            # ⚓ peppe8o ☛ Private_streaming_server_with_Raspberry_Pi_and

              Emby_on_Docker⠀⇛

                   Install and configure your private Streaming Server

                   on Raspberry PI and Emby.

            # ⚓ Hackster ☛ Vlad_Tomoiagă’s_FakePGA_Turns_a_Raspberry_Pi

              Pico_or_Other_RP2040_Board_Into_a_Slow,_Cheap_“FPGA”_–

              Hackster.io⠀⇛

                   Electronics engineering student Vlad Tomoiagă has

                   come up with a neat way to experiment with field-

                   programmable gate array (FPGA) concepts without

                   having to splash out on an actual FPGA — by

                   simulating one on a Raspberry Pi Pico or other

                   RP2040-based microcontroller board.

                   “This project aims to simulate Verilog HDL

                   [Hardware Description Language] designs on a

                   Raspberry Pi Pico (or any other RP2040-based

                   board),” Tomoiagă explains of FakePGA. “It achieves

                   this by using Verilator to compile the RTL

                   [Register Transfer Level code] into a cycle-

                   accurate C++ model of your design which can then be

                   executed on the microcontroller. This allows you to

                   access the signals of the simulated design through

                   the GPIO [General-Purpose Input/Output] pins of the

                   board, which gives a more hands-on experience than

                   simulating on a computer.”

      o § Mobile Systems/Mobile Applications⠀➾

            # ⚓ Support_the_development_of_/e/OS_&_Murena⠀⇛

                   Since 2017, when I announced that I wanted to

                   “Leave Apple & Google”, the /e/OS project has done

                   tremendous progresses: we have succeeded to design

                   and release a modern and realistically usable

                   operating system and cloud services that protect

                   their users from permanent personal data collection

                   and from surveillance capitalism…

                   /e/OS can be installed on more than 250 different

                   smartphones, and we have succeeded to bring it to

                   long awaited devices such as the Fairphone 3 and

                   Fairphone 4, among others.

                   We have introduced unique features, such as the

                   “Advanced Privacy” module, that informs /e/OS’

                   users about trackers and ads triggered by mobile

                   applications and websites, and cut them in real

                   time. Advanced Privacy can even fake one’s

                   geolocation or… IP address, to stay under the

                   radar.

            # ⚓ CNX Software ☛ MECOOL_KM7_Plus_runs_Google_TV_OS_on_Amlogic

              S905Y4_SoC_–_CNX_Software⠀⇛

            # ⚓ Indian Express ☛ How_to_put_a_call_on_hold_on_Android

              devices_|_Technology_News,The_Indian_Express⠀⇛

            # ⚓ 9to5Google ☛ LineageOS_20_based_upon_Android_13_officially

              launches⠀⇛

            # ⚓ SamMobile ☛ Galaxy_A03_bags_Android_13_with_its_latest

              software_update_–_SamMobile_–_SamMobile⠀⇛

            # ⚓ SamMobile ☛ Galaxy_F12_starts_receiving_Android_13_(One_UI

              5.0)_update_in_India_–_SamMobile⠀⇛

            # ⚓ Hindustan Times ☛ Best_Android_App_Development_Companies_in

              India_–_Top_10_List_–_Hindustan_Times⠀⇛

            # ⚓ Sportskeeda ☛ Are_the_rewards_of_rooting_an_Android_phone

              worth_the_risks_in_2023?⠀⇛

            # ⚓ HowTo Geek ☛ LineageOS_20_Brings_Android_13_to_Older

              Phones⠀⇛

            # ⚓ Express ☛ Supercharged_Android_upgrade_is_coming_to

              millions_of_phones_this_year_|_Express.co.uk⠀⇛

            # ⚓ Phone Arena ☛ Can_you_guess_which_Android_phones_were_the

              first_to_be_updated_in_2023?_–_PhoneArena⠀⇛

            # ⚓ Linux On Mobile ☛ LINMOB.net_–_Weekly_GNU-like_Mobile_Linux

              Update_(52/2022):_Year_In_Review_and_other_topics⠀⇛

            # ⚓ Sailfish_Community_News,_29th_December,_Happy_New_Year!_–

              Community_News_–_Sailfish_OS_Forum⠀⇛

                   As we reach the end of 2022 it’s time to take our

                   usual look back at the year, while also glancing

                   forward to what 2023 has to offer. It’s been an

                   unusual year for Sailfish OS, but still with plenty

                   to celebrate. And the newsletter has something to

                   celebrate too, with this being the 50th issue. With

                   all of the crazy non-Sailfish related news that’s

                   been happening around the world this year, we’re

                   pleased that you’re still taking time to read about

                   your favourite mobile operating system in the

                   newsletter as well.

            # ⚓ Make Tech Easier ☛ 10_Wallpaper_Changer_Apps_to_Make_Your

              Android_Phone_Pop⠀⇛

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

      o ⚓ Major Hayden ☛ Second_try_at_self-hosting_Mastodon_–_Major

        Hayden⠀⇛

             Mastodon caught my attention at the end of 2022 in the

             wake of all the Twitter shenanigans. At a high level,

             Mastodon is an implementation of ActivityPub and you can

             use it for “micro-blogging” much like you would use

             Twitter. (This is a really quick, high-level explanation

             and I skipped over plenty of detail.)

             This post covers my journey on Mastodon that led me to

             self-host my own Mastodon instance in a fairly reliable

             way.

      o § Programming/Development⠀➾

            # ⚓ Hubert Figuière ☛ Niepce_December_2022_updates_–_Hubert

              Figuière⠀⇛

                   Here is some udpdate on Niepce work done in

                   December 2022. Mostly changes under the hood, but

                   important ones to move forward with improving the

                   features. The short version: it feels great to

                   remove C++ code.

            # ⚓ Qt ☛ Commercial_LTS_Qt_6.2.7_Released [Ed: conflating non-

              free/proprietary with "commercial"]⠀⇛

                   We have released Qt 6.2.7 LTS for commercial

                   license holders today. As a patch release, Qt 6.2.7

                   does not add any new functionality but provides bug

                   fixes and other improvements.

            # ⚓ Linux Hint ☛ Std_List_C++⠀⇛

                   In C++, std::list is like a container that stores

                   the elements on the non-contagious memory location.

                   The “std::list” is implemented as a doubly linked

                   list. We can insert or remove any element of the

                   list that is stored in any location, which makes

                   the lists bidirectional and sequential.

                   Bidirectional because we can access the list

                   elements from the front and back of the list (from

                   any location). Sequential because we can access the

                   elements anywhere in the sequence. Lists behave as

                   doubly linked lists. Doubly linked lists can store

                   their elements anywhere in the memory and they can

                   be accessed from any location on the runtime. The

                   list belongs to a standard template library like

                   arrays and vectors but lists do not allow a fast

                   access comparable to other data structures. Let’s

                   discuss “std::list” in this article with the

                   practical implementation of lists with different

                   operations.

            # ⚓ Matt Rickard ☛ 2023_Predictions⠀⇛

                   The loss function in optimization is a function

                   that serves as a proxy for the underlying

                   performance measurement. In many cases, it’s one of

                   the most important components of any form of

                   machine learning.

                   It’s also sometimes referred to as the cost

                   function, objective function, error function, or

                   reward function, depending on what you’re doing.

                   Those terms capture the essence of what I’d like to

                   get out of my 2023 predictions – a measured error

                   and a way to derive a path to improvement (i.e., a

                   metaphorical gradient).

            # § Perl / Raku⠀➾

                  # ⚓ Perl ☛ Keeping_Your_Valuables_Under_Lock_and_Key⠀⇛

                  # ⚓ Rakulang ☛ 2023.01_Humming_Away_–_Rakudo_Weekly

                    News⠀⇛

                         Rawley Fowler has created a simple web-

                         framework called Humming-Bird, inspired

                         mainly by Opium, Sinatra and Express. And

                         introduced it in a post on /r/rakulang, with

                         quite a few reactions.

                         [...]

                         Anton Antonov released a new module called

                         DSL::Bulgarian allowing one to specify

                         computational workflows using natural

                         language commands in Bulgarian, and

                         introduced it in a dedicated blog post.

            # § Python⠀➾

                  # ⚓ Adafruit ☛ The_Python_on_Hardware_Newsletter:_Happy

                    New_Year,_please_subscribe_now⠀⇛

                         The Python on Microcontrollers newsletter is

                         the place for the latest news involving

                         Python on hardware (microcontrollers AND

                         single board computers like Raspberry Pi).

                  # ⚓ Adafruit ☛ John_Park’s_CircuitPython_Parsec:_Using

                    Super_Nintendo_Controllers⠀⇛

                         How to use Super Nintendo (SNES) controllers

                         in CircuitPython with the keypad library.

            # § Shell/Bash/Zsh/Ksh⠀➾

                  # ⚓ Linux Hint ☛ How_to_Use_$IFS_in_Bash?⠀⇛

                         The IFS is an abbreviation for Internal Field

                         Separator which is an environment variable in

                         the shell to determine the separator. The

                         $IFS specifies how the words on the command

                         prompt are delimited. By default, field

                         separators (IFS) are the space, tab, and

                         newline but we can alter this in our script

                         to match the requirements. It is mostly used

                         for loops to manipulate the elements in the

                         specified list. We use the $IFS variable in

                         our Bash script to split the string because

                         Bash does not include a built-in mechanism

                         for string splitting.

                  # ⚓ Linux Hint ☛ Delete_a_Folder_in_Bash⠀⇛

                         There are two alternative ways to delete a

                         directory, file, or folder in Bash. We can

                         delete the folders or directories using two

                         different commands. The “rmdir” command is

                         used to delete the empty folders or

                         directories. The “rm” command is used to

                         delete the folders or directories that are

                         not empty. However, we will use the “rm”

                         command to delete the folders in this

                         article. Additionally, we delete some files

                         from the Linux desktop.

                  # ⚓ Linux Hint ☛ What_is_AWK_NF?⠀⇛

                         The “AWK” function is a Linux utility that is

                         used for text analysis that offers strong

                         data control. To use the Linux computer

                         program and “AWK” function, users can

                         evaluate, modify, and generate the prepared

                         results. The “AWK NF” variable is used to

                         show how many files, elements, or other items

                         are contained in a line of any file.

      o § Standards/Consortia⠀➾

            # ⚓ Emmanuel_Kasper:_Ensuring_someone_is_listening_before

              telling_a_joke⠀⇛

* § Leftovers⠀➾

      o ⚓ Amos Wenger ☛ We_need_to_talk_about_Dropout⠀⇛

             Let’s talk about big TV and movie studios. About the life

             and death of CollegeHumor, about what makes Dropout

             interesting, and how their video platform could be

             improved!

      o § Science⠀➾

            # ⚓ Science News ☛ A_new_supercomputer_simulation_animates_the

              evolution_of_the_universe⠀⇛

                   The infant universe transforms from a featureless

                   landscape to an intricate web in a new

                   supercomputer simulation of the cosmos’s formative

                   years.

                   An animation from the simulation shows our universe

                   changing from a smooth, cold gas cloud to the lumpy

                   scattering of galaxies and stars that we see today.

                   It’s the most complete, detailed and accurate

                   reproduction of the universe’s evolution yet

                   produced, researchers report in the November

                   Monthly Notices of the Royal Astronomical Society.

            # ⚓ Medium ☛ DeepMind_–_Google’s_ML-Based_GraphCast_Outperforms

              the_World’s_Best_Medium-Range_Weather_Forecasting_System_|_by

              Synced_|_SyncedReview_|_Dec,_2022_|_Medium⠀⇛

                   Medium-range weather forecasts play a crucial role

                   in agriculture, construction, travel and other

                   industries. They also bring practical value to

                   people’s daily lives, enabling us to plan outings

                   and keeping us safe from extreme weather events.

      o § Hardware⠀➾

            # ⚓ CNX Software ☛ $150_Axelera_M.2_AI_accelerator_module

              claims_to_deliver_up_to_214_TOPS_–_CNX_Software⠀⇛

                   Axelera M.2 AI accelerator module is said to

                   deliver up to 214 TOPS of AI inference and up to

                   3200 FPS with ResNet -50 in a compact M.2 2280 form

                   factor.

                   Few details are available at this time, but the

                   module is based on the company’s Metis AIPU (AI

                   Processing Unit) using in-memory computing based on

                   arrays of SRAM memory devices used to “store a

                   matrix and perform matrix-vector multiplications

                   “in-place” without intermediate movement of data”.

                   This technology is said to “radically” increase the

                   number of operations per computer cycle with

                   without suffering from issues such as noise or

                   lower accuracy.

            # ⚓ Engadget ☛ German_Bionic_debuts_its_lightest_powered

              exosuit_to_date_at_CES_2023

              ⠀⇛

                   German Bionic, the robotic exoskeleton startup

                   behind the Cray X, will be showing off two new

                   posture-protecting products at the Consumer

                   Electronics Show in Las Vegas, Nevada this week.

                   The Apogee is the company’s latest and lightest

                   powered exosuit built for commercial and industrial

                   use while the Smart SafetyVest will “bring

                   ergonomic monitoring and protection to every

                   worker,” per a Monday release.

      o § Health/Nutrition/Agriculture⠀➾

            # ⚓ PC Mag ☛ Cambridge_University_Researchers_Develop_VR_Tool

              for_Cancer_Treatment_|_PCMag⠀⇛

                   Virtual reality software has become an unlikely

                   tool in the fight against cancer.

                   In a bid to help doctors better understand how to

                   treat cancer, video game designers and cancer

                   researchers have teamed up at the University of

                   Cambridge, England, to turn spreadsheet data into

                   highly detailed VR imagery of cancer cells, ITV

                   reports.

                   [...]

                   Speaking to ITV News, Own Harris, IMAXT

                   Laboratory’s lead video game designer said: “It’s

                   so much easier to notice differences, to notice

                   features, to notice peculiarities when you’re

                   actually in a thing than when you’re looking at a

                   spreadsheet or a photograph.

      o § Proprietary⠀➾

            # ⚓ BBC ☛ Guardian_newspaper_hit_by_suspected_ransomware_attack

              –_BBC_News [Ed: Microsoft Windows in action. Both the BBC and

              The Guardian routinely bag bribes from Bill Gates, so they're

              not likely to name the real culprit.]⠀⇛

            # ⚓ OMG! Linux ☛ Microsoft_Teams_Progressive_Web_App_Available

              for_Linux [Ed: Joey Sneddon promoting proprietary Microsoft

              spyware in a site called "Linux".]⠀⇛

            # ⚓ Linux Shell Tips ☛ 7_Best_GitHub_Repositories_for_Linux

              Developers [Ed: No, Ravi Saive, Microsoft proprietary

              software is not for Linux; go back to Microsoft]⠀⇛

      o § Security⠀➾

            # ⚓ Hacker News ☛ WordPress_Security_Alert:_New_Linux_Malware

              Exploiting_Over_Two_Dozen_CMS_Flaws [Ed: This is a WordPress

              plugins issue (not WordPress, not Linux); calling this Linux

              is like calling an Adobe Photoshop bug a "Windows bug";

              WordPress runs not only on Linux]⠀⇛

                   WordPress sites are being targeted by a previously

                   unknown strain of Linux malware that exploits flaws

                   in over two dozen plugins and themes to compromise

                   vulnerable systems.

            # ⚓ NetBSD ☛ Reproducible_Builds_Summit_Venice_2022⠀⇛

                   The sixth Reproducible Builds Summit took place

                   exactly two months ago in Venice, Italy. These

                   three days of workshops were filled with a

                   succession of interactive sessions, where everyone

                   attending had the opportunity to present or learn

                   about anything related to Build Reproducibility.

                   This included the status of specific Open Source

                   projects, techniques to locate, analyse, and

                   understand issues, or also how to explain and

                   communicate better around this topic.

            # ⚓ Can_we_encrypt_data_using_Elliptic_Curves?_–_Andrea

              Corbellini⠀⇛

                   From time to time, I hear people saying that

                   Elliptic Curve Cryptography (ECC) cannot be used to

                   directly encrypt data, and you can only do key

                   agreement and digital signatures with it. This is a

                   common misconception, but it’s not actually true:

                   you can indeed use elliptic curve keys to encrypt

                   arbitrary data. And I’m not talking about hybrid-

                   encryption schemes (like ECIES or HPKE): I’m

                   talking about pure elliptic curve encryption, and

                   I’m going to show an example of it in this article.

                   It’s true however that pure elliptic curve

                   encryption is not widely used or standardized

                   because, as I will explain at the end of the

                   article, key agreement is more convenient for most

                   applications.

                   [...]

                   I wrote an in-depth article about elliptic curve

                   cryptography in the past on this blog, and here is

                   a quick recap: points on an elliptic curve from an

                   interesting algebraic structure: a cyclic group.

                   This group lets us do some algebra with the points

                   of the elliptic curve: if we have two points $A$

                   and $B$, we can add them ($A + B$) or subtract them

                   ($A – B$). We can also multiply a point by an

                   integer, which is the same as doing repeated

                   addition ($n A$ = $A + A + \cdots + A$, $n$ times).

                   We know some efficient algorithms for doing

                   multiplication, but the reverse of multiplication

                   is believed to be a “hard” problem for certain

                   elliptic curves, in the sense that we know

                   efficient methods for computing $B = n A$ given $n$

                   and $A$, but we do not know very efficient methods

                   to figure out $n$ given $A$ and $B$. This problem

                   of reversing a multiplication is known as Elliptic

                   Curve Discrete Logarithm Problem (ECDLP).

            # ⚓ LWN ☛ Security_updates_for_Monday_[LWN.net]⠀⇛

                   Security updates have been issued by Debian (cacti,

                   emacs, exuberant-ctags, libjettison-java, mplayer,

                   node-loader-utils, node-xmldom, openvswitch, ruby-

                   image-processing, webkit2gtk, wpewebkit, and xorg-

                   server), Fedora (OpenImageIO, systemd, w3m, and

                   webkit2gtk3), Mageia (curl, freeradius, libksba,

                   libtar, python-ujson, sogo, thunderbird, and

                   webkit2), Red Hat (bcel), and SUSE (ffmpeg, ffmpeg-

                   4, mbedtls, opera, saphanabootstrap-formula, sbd,

                   vlc, and webkit2gtk3).

            # ⚓ Compromised_PyTorch-nightly_dependency_chain_between

              December_25th_and_December_30th,_2022._|_PyTorch⠀⇛

                   If you installed PyTorch-nightly on Linux via pip

                   between December 25, 2022 and December 30, 2022,

                   please uninstall it and torchtriton immediately,

                   and use the latest nightly binaries (newer than Dec

                   30th 2022).

            # ⚓ Naked Security ☛ PyTorch:_Machine_Learning_toolkit_pwned

              from_Christmas_to_New_Year_–_Naked_Security⠀⇛

                   Unfortunately, the project was compromised by means

                   of a supply-chain attack during the holiday season

                   at the end of 2022, between Christmas Day [2022-12-

                   25] and the day before New Year’s Eve [2022-12-30].

                   The attackers malevolently created a Python package

                   called torchtriton on PyPI, the popular Python

                   Package Index repository.

            # ⚓ LWN ☛ Nightly_PyTorch_builds_compromised_[LWN.net]⠀⇛

                   Anybody who installed a nightly release from the

                   PyTorch machine-learning library between December

                   25 and 30 will want to uninstall it immediately…

      o § Environment⠀➾

            # ⚓ uni Yale ☛ State,_local_governments_increasingly_turn_to

              zoning_reforms_»_Yale_Climate_Connections⠀⇛

                   Transportation is the largest source of greenhouse

                   gases in the United States, and passenger vehicles

                   — the cars most Americans rely on to meet their

                   daily needs — account for more than half of

                   transportation emissions.

                   Conversations about reducing these emissions

                   typically focus on electric vehicles. But

                   increasingly, government officials across the

                   country are aiming not just to get Americans into

                   different kinds of cars, but to radically reduce

                   the need to drive in the first place.

      o § Finance⠀➾

            # ⚓ Ruben Schade ☛ Rejected_cards_and_waking_an_IT_team_up [Ed:

              This never happens when cash is used; there are many other

              advantages associated with cash]⠀⇛

                   One of my payment cards has been flaky the last few

                   days, to the point where multiple cafes and shops

                   have timed out or rejected accepting it. The card

                   has plenty of balance and isn’t physically damaged;

                   I suspect it’s an issue at the payment processor.

                   [...]

                   The cloud isn’t “just someone else’s computer”,

                   just like commercial aviation isn’t just someone

                   else’s Cessna. It’s also someone else’s rosters,

                   architecture, monitoring, maintenance, upgrades,

                   and fixes, often times with significant complexity

                   and (hopefully) redundancy. But despite the best

                   efforts of certain marketing teams claiming

                   otherwise, there’s no magic behind any of it. It’s

                   people all the way down.

      o § Internet Policy/Net Neutrality⠀➾

            # ⚓ Public_search_engines_may_fragment_the_internet_|_Stop_at

              Zona-M⠀⇛

                   There is no question that the current internet is

                   plagued, among other things by surveillance,

                   profiling and polarization at all levels. Two years

                   ago, two UK researchers proposed, as one part of a

                   larger solution, “a public sector challenge to the

                   private interests that have colonised the search

                   functions on which we all depend.”

            # ⚓ as_days_pass_by_–_What_to_do_about hotlinking⠀⇛

                   Hotlinking, in the context I want to discuss here,

                   is the act of using a resource on your website by

                   linking to it on someone else’s website. This might

                   be any resource: a script, an image, anything that

                   is referenced by URL.

                   It’s a bit of an anti-social practice, to be

                   honest. Essentially, you’re offloading the

                   responsibility for the bandwidth of serving that

                   resource to someone else, but it’s your site and

                   your users who get the benefit of that. That’s not

                   all that nice.

                   Now, if the “other person’s website” is a CDN —

                   that is, a site deliberately set up in order to

                   serve resources to someone else — then that’s

                   different. There are many CDNs, and using resources

                   served from them is not a bad thing. That’s not

                   what I’m talking about. But if you’re including

                   something direct from someone else’s not-a-CDN

                   site, then… what, if anything, should the owner of

                   that site do about it?

            # ⚓ Wladimir Palant ☛ South_Korea’s_online_security_dead_end_|

              Almost_Secure⠀⇛

                   Last September I started investigating a South

                   Korean application with unusually high user

                   numbers. It took me a while to even figure out what

                   it really did, there being close to zero

                   documentation. I eventually realized that the

                   application is riddled with security issues and,

                   despite being advertised as a security application,

                   makes the issue it is supposed to address far, far

                   worse.

                   That’s how my journey to the South Korea’s very

                   special security application landscape started.

                   Since then I investigated several other

                   applications and realized that the first one wasn’t

                   an outlier. All of them caused severe security and

                   privacy issues. Yet they were also installed on

                   almost every computer in South Korea, being a

                   prerequisite for using online banking or government

                   websites in the country.

                   [...]

                   Originally, these applications used Microsoft’s

                   proprietary ActiveX technology. This only worked in

                   Internet Explorer and severely hindered adoption of

                   other browsers in South Korea.

            # ⚓ Finding_and_Fixing_DOM-based_XSS_with_Static_Analysis⠀⇛

                   Despite all the efforts of fixing Cross-Site

                   Scripting (XSS) on the web, it continuously ranks

                   as one of the most dangerous security issues in

                   software.

                   In particular, DOM-based XSS is gaining increasing

                   relevance: DOM-based XSS is a form of XSS where the

                   vulnerability resides completely in the client-side

                   code (e.g., in JavaScript). Indeed, more and more

                   web applications implement all of their UI code

                   using frontend web technologies: Single Page

                   Applications (SPAs) are more prone to this

                   vulnerability, mainly because they are more

                   JavaScript-heavy than other web applications. An

                   XSS in Electron applications, however, has the

                   potential to cause even more danger due to the

                   system-level APIs available in the Electron

                   framework (e.g., reading local files and executing

                   programs).

* § Gemini* and Gopher⠀➾

      o § Personal⠀➾

            # ⚓ 2023⠀⇛

                   the new year is a celebration of the recent past

                   and the near future, but i have something a little

                   bit different in mind this year. i am very close to

                   achieving some very big goals – i’m about to become

                   a professional software engineer, i’ll finally be

                   able to move away from my hometown and forget about

                   my less-than-optimal job and i’ll finally have the

                   opportunity to start my life, “for real this time.”

                   this is all on the horizon. after years and years

                   of dreaming of it, i can see it in the distance.

                   i’ve got an article coming soon about this very

                   topic, in fact; i am obsessed with the future and

                   so is the rest of humanity.

            # ⚓ ulises_and_the_NY_walkers⠀⇛

                   when I was 6 years old I met my best friend for a

                   while (at least until 5th grade). I don’t like

                   complaining much but I think I did not socialize

                   much with other kids because of my parents’ rules

                   on going out. ulises lived in front of the

                   elementary school (the second one I attended) and

                   lived with his mother and two younger siblings. his

                   dad was in an unspecified place in america (I don’t

                   know what kind of job he had). this is very common

                   in guanajuato, but of course at the time I had no

                   idea.

            # ⚓ Moving_onward_to_2023⠀⇛

                   As I try to get myself back into something that

                   resembles a routine after the holiday break I

                   started to poke around at some things that have

                   been needing attention. It seems that my microblog

                   to gemini renderer has been broken for about a

                   month. A quick fix and it seems to be functioning

                   but that gave me an excuse to tweak the overall

                   layout. Previously I rendered gemtext headings for

                   the years and the months, leaving the individual

                   entries as just simple paragraphs, however it seems

                   more logical to expose individual entries so you

                   can navigate the in-reply-to chain using your user-

                   agent, assuming it has the ability to navigate

                   headings (Lagrange does).

            # ⚓ Day_002:_The_warning⠀⇛

                   You enter a small room, with four visible doors and

                   an altar.

                   Enshrined in the upper part of the altar, you see a

                   jewelled dagger, the symbol of Abbathor, the dwarf

                   god of greed, pointing to the ceiling. Engraved on

                   the vertical part of the altar, an inscription in

                   Dwarvish: “Abbathor rewards those who know the

                   price of things and never pay more than they can

                   gain. What is the price of blood?”.

            # ⚓ I_used_to_take_photos⠀⇛

                   I looked at some old prints of photos taken on film

                   the other day. I found it a bit overwelming: things

                   that happened so long ago, many of which I could

                   only barely remember.

                   “Did we really go on holiday there?”

                   “I remember that social event, but I have no idea

                   who half the people are.”

                   I had to stop looking. The weight of the past was

                   too much.

      o § Technical⠀➾

            # ⚓ PocketBook_Basic_4_review⠀⇛

                   I read lots of books, so I bought an e-reader for

                   myself, the PocketBook Basic 4, also known as the

                   PocketBook 606 in some regions. It was one of the

                   cheapest options available, while not selling your

                   data to Amazon or Kobo. This is a review after 2

                   months of usage.

                   It has no touch screen, being navigable using a 4-

                   way touch pad. That was one of the selling points

                   for me, as I didn’t want this to be a glorified

                   phone, and besides, less screen wiping. It’s made

                   out of plastic, which makes it really light at

                   around 140g, perfect for carrying around. The e-ink

                   display is HD, perfect for reading any sorts of

                   books. It supports all popular e-book formats and

                   PDFs. Best of all, it runs Linux! More

                   specifically, the kernel version is 3.0, I don’t

                   think the interface is FOSS though. It doesn’t

                   connect to the Internet whatsoever, which is a huge

                   plus for me, it helps you stay disconnected. The

                   battery is rated at around one month, although

                   personally at my reading-rate, I see it lasts

                   around 2 weeks. If you put an SD card in, then plug

                   it into a computer, it’ll act as an SD card reader

                   which is really awesome! For example, on Linux it

                   adds two new devices, the internal memory which is

                   8GB, and the SD card. This way you don’t need a

                   converter in order to load your favorite books.

            # ⚓ Booting_Gentoo_on_a_BTRFS_from_multiple_LUKS_devices⠀⇛

                   This is mostly a reminder for myself. I installed

                   Gentoo on a machine, but I reused the same BTRFS

                   filesystem where NixOS is already installed, the

                   trick is the BTRFS filesystem is composed of two

                   partitions (a bit like raid 0) but they are from

                   two different LUKS partitions.

            # § Internet/Gemini⠀➾

                  # ⚓ internet_nostalgia_–_an_incoherent_rambling_about_how

                    new_internet_culture_sucks⠀⇛

                         ay mates, lelkins here. this might be a

                         pretty short post. i keep remembering memes

                         that used to be the biggest things on the

                         internet. like current ones that just fizzled

                         out fast like ronaldinho soccer 64,

                         megalovania (this one is still kind of

                         popular), so many examples that i can’t put

                         them in (and cause i actually forgot most of

                         them. reason why later). and more common in

                         my head are ones that i used to see as a kid

                         from the era of “fads”, like hotel mario

                         edits where every noun is replaced with a

                         random clip, “the king has a new computer”,

                         one youtube poop where mario and luigi fight

                         eachother in a pokemon battle and mario

                         charges a pinesol bottle and luigi just uses

                         za warudo from jojo. the internet was wild

                         and quality always differed.

                  # ⚓ emerging_from_darkness⠀⇛

                         With the release of version 4 of Mastodon [1]

                         there has been a problem of links to profile

                         pages or conversation threads “going dark”

                         within shell based browsers, such as Lynx

                         [2]. In version 3.x you would get a text

                         rendering of each page, but now you only get

                         a terse *”To use the Mastodon web

                         application, please enable JavaScript”*

                         message.

                         I had been following the philosophy of *”do

                         the minimum thing that works”* with Epicyon

                         [3], but after Mastodon 4, just linking

                         directly to Mastodon web content was no

                         longer sufficient to be universally legible.

                         So I have now replaced those direct links

                         with a *conversation view* and a different

                         way of viewing Mastodon profiles in which the

                         html is all rendered by Epicyon itself. This

                         brings back the otherwise Javascript-shrouded

                         fediverse content, and also has the added

                         advantage that it fully supports *authorized

                         fetch*, which in Mastodon is known as “secure

                         mode”. It also makes the user interface more

                         consistent looking in shell browsers.

                  # ⚓ Gemlog_responses_–_bacardi55′s_concept_without_CGI⠀⇛

                         Gemlog discussions are frequently happening,

                         which is a good sign for an active community.

                         Due to the simplistic nature of the gemini

                         protocol these discussions happen with much

                         less automation and more handwork than in the

                         world wide web. The usual way is to publish a

                         reply with the link to the original gemlog

                         and inform the original author via email

                         about the reply.

                  # ⚓ [Old] re:_“I_kind_of_resent_blogs”_by_adiabatic⠀⇛

                         is it? there isn’t really a built-in

                         mechanism through which you would be made

                         aware whether your work is being noticed or

                         not, and that’s by design. I don’t know how

                         common this is, but I don’t find it to

                         require much effort to keep up with

                         everything that shows up on the main CAPCOM/

                         spacewalk instances so I keep up with it

                         regularly.

                         there wasn’t any contact information anywhere

                         in your gemini capsule, so I can’t reach out

                         and tell you that I’ve responded to your

                         post, so I guess we’ll see if you notice

                         this. this gemlog doesn’t have a feed of any

                         kind, so if you see it, I guess content *can*

                         be noticed without an atom feed.

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

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

World Wide Web but a lot lighter.

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