𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Monday, February 07, 2022

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Generated Tue 8 Feb 02:41:16 GMT 2022

Created by Dr. Roy Schestowitz (𝚛𝚘𝚢 (at) 𝚜𝚌𝚑𝚎𝚜𝚝𝚘𝚠𝚒𝚝𝚣 (dot) 𝚌𝚘𝚖)

Full hyperlinks for navigation omitted but are fully available in the originals

The corresponding HTML versions are at 𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈

Latest in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕 and older bulletins can be found at 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕-𝒂𝒓𝒄𝒉𝒊𝒗𝒆𝒔

Full IPFS index in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔 and as plain text in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔/𝒕𝒙𝒕

Gemini index for the day: gemini://gemini.techrights.org/2022/02/07/

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

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

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QmWMn5rx4mwf86jmAsH6KUasKtr2WVybRVa9b2sJECtwpz

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

⦿ [Meme] Drunk on Power and Diplomatic Immunity | Techrights

⦿ EPO Pays Out Millions of Euros in Compensation - to Thousands of Workers Who Deserve a Lot More for Moral Damage - for Battistelli’s Illegal Acts (But Battistelli Himself Has Not Been Punished at All, Nor Have His Enablers) | Techrights

⦿ Self-Hosted Gemini Proxy (HTTP and HTTPS) | Techrights

⦿ The EPO’s Overseer/Overseen Collusion — Part XXXXIV: Immunity = Impunity? | Techrights

⦿ IRC Proceedings: Sunday, February 06, 2022 | Techrights

⦿ Microsoft GitHub Exposé — Part XVII — Backsliding Into 1990s-Style Digital Slavery by Microsoft | Techrights

⦿ Nobody Should be Above the Law | Techrights

⦿ The EPO is Bleeding in Courts | Techrights

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

	http://techrights.org/2022/02/07/epo-diplomatic-immunity-meme/#comments

	http://techrights.org/2022/02/07/epo-moral-damage/#comments

	http://techrights.org/2022/02/07/http-and-https-gemini-proxy/#comments

	http://techrights.org/2022/02/07/immunity-and-impunity/#comments

	http://techrights.org/2022/02/07/irc-log-060222/#comments

	http://techrights.org/2022/02/07/monday-github-outline/#comments

	http://techrights.org/2022/02/07/the-above-the-law-complex/#comments

	http://techrights.org/2022/02/07/the-epo-is-bleeding-in-courts/#comments

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

	http://techrights.org/2022/02/07/fragments-2-0/#comments

	http://techrights.org/2022/02/07/openmandriva-lx-4-3/#comments

                ䷩ 𝚕𝚒𝚗𝚎 69

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/02/07/epo-diplomatic-immunity-meme/#comments

Gemini version at gemini://gemini.techrights.org/2022/02/07/epo-diplomatic-immunity-meme/

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Gemini_version_available_♊︎

✐ [Meme]_Drunk_on_Power_and_Diplomatic_Immunity⠀✐

Posted in Europe, Humour, Patents at 9:08 am by Dr. Roy Schestowitz

🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Slippy guy: Internal appeals, ILOAT, Dutch Supreme Court⦈

Summary: When you let unqualified (in the area of patents) psychopaths run the

EPO you can expect the worst; Benoît_Battistelli and António_Campinos have

repeatedly misused diplomatic immunity to avoid investigation and possible

prosecution

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠿⡛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠁⠈⠀⠈⠙⠋⠉⠛⠻⠿⠋⠀⠙⠉⠙⠉⠉⠁

⠋⠛⢶⢀⡀⠀⠂⣀⡀⡀⠀⠀⠚⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣦⣤⣄⣨⣿⣧⣼⣿⣿⣯⣿⡬⣿⣿⡶⠂⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣶⣶⡶⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[32A⣤⣤⣤⣤⣤⣴⣤⣤⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣙⠛⠛⣛⣛⠛⣛⡛⢛⣛⣛⡛⠛⣛⣛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣷⣸⣿⡿⠿⣿⡿⠿⣿⣿⠿⠇⣿⣿⢻⣿⡆⣿⣿⡄⣿⡇⢸⣿⣿⣷⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⣿⣿⡇⢸⣿⡇⠀⣿⣿⣶⡆⣿⣿⢾⣟⡃⣿⣿⣷⣿⡇⣿⣿⢸⣿⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡇⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⡏⣿⣿⡇⢸⣿⡇⠀⣿⣿⣀⡀⣿⣿⢸⣿⡇⣿⡏⣿⣿⡇⣿⣿⣾⣿⡄⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡇⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠛⠃⠙⠛⠃⠘⠛⠃⠀⠛⠛⠛⠃⠛⠛⠘⠛⠃⠛⠛⠘⠛⠛⠛⠛⠘⠛⢓⡛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣇⣀⣀⣀⣀⣀⣀⣀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢸⣿⡿⣿⡆⣿⣿⣿⣿⡆⣿⣿⠿⠀⣿⣿⣿⡆⢸⣿⡇⢀⣾⡿⣿⣷⠈⠛⠛⠛⠛⡛⢛⠛⣛⠛⠛⠛⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⣿⣇⢸⣿⣧⣿⡇⣿⣿⣿⣿⡇⣿⣿⣤⢠⣿⡟⣿⡇⢸⣿⡇⠈⢿⣿⣯⡍⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣷⣶⣶⣦⣤⣶⣶⣤⣶⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣶⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡛⠛⣛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣀⣀⠀⠀⠘⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣠⣄⠀⠀⠀⠸⢿⡧⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⡀⠀⠈⣁⠀⠀⠀⠀⠀⠀⣀⣸⣛⣻⣿⡇

⣿⣿⣿⣿⡿⣿⣿⣿⡟⠋⠙⠛⠛⠿⠿⠿⣿⢿⣿⠿⠉⠁⠀⠀⠀⢠⣦⡀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣀⣹⣿⣿⣿⣿⣿⡇

⠿⠛⠛⣿⠿⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸⣿⣷⡀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠭⠉⠉⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠁⠀⠈⠛⠛⠛⠟⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠿⡍⠛⠻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠁⠙⠋⠙⠋⠙⠛⠻⠿⠿⠋⠁⠙⠉⠉⠉⠉⠁

⠉⠓⣦⣀⡀⠀⠂⣀⢀⣀⢀⠀⠶⢦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣤⣤⣄⣸⣿⣤⣽⣿⣿⣿⣥⣼⣿⡷⡔⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣿⣯⠀⠀⠐⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣷⣶⣶⣶⠎⠂⠀⠠⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[32A⣤⣤⣤⣤⣤⣴⣤⣤⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣙⠛⠛⣛⡛⠛⣛⡛⢛⣛⣛⡛⠛⣛⣛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣷⣸⣿⡿⠿⣿⡿⠿⣿⣿⠿⠇⣿⣿⢻⣿⡆⣿⣿⡄⣿⡇⢸⣿⣿⣷⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⡏⣿⣿⡇⢸⣿⡇⠀⣿⣿⣀⡀⣿⣿⢸⣿⡇⣿⡏⣿⣿⡇⣿⣿⣾⣿⡄⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡇⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠛⠃⠙⠛⠃⠘⠛⠃⠀⠛⠛⠛⠃⠛⠛⠘⠛⠃⠛⠛⠘⠛⠛⠛⠛⠘⠛⢓⡛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡇⣀⣈⣀⣀⣀⣀⣀⣨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢸⣿⡿⣿⡆⣿⣿⣿⣿⡆⣿⣿⠿⠀⣿⣿⣿⡆⢸⣿⡇⢠⣾⡿⣿⣷⠀⠻⡟⣟⣛⣟⣛⡛⣛⣛⣛⡛⢛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⣇⢸⣿⣧⣿⡇⣿⣿⣿⣿⡇⣿⣿⣤⢠⣿⡟⣿⡇⢸⣿⡇⠈⢿⣿⣯⡍⠀⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣷⣦⣶⣦⣤⣶⣶⣤⣶⣦⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡛⠛⣛⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣄⣀⣀⠀⠀⠘⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣠⣄⠀⠀⠀⠼⢿⡧⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⡀⠀⠘⣁⠀⠀⠀⠀⠀⢀⣀⣘⣛⣻⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠙⠛⠛⠿⠿⢿⣿⢿⣿⣿⣿⠏⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣀⣹⣿⣿⣿⣿⣿⡇

⠿⠟⠟⢿⡽⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠠⠼⠊⠉⠉⠁⠀⠀⠀⠀⠀⢠⣿⣦⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠍⠁⠁⠀⠀⠀⠀⠀⠀⠘⠿⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠈⠛⠛⠛⠟⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢥⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣷⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠟⢟⠛⣻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠁⠉⠉⠉⠋⠙⠋⠻⠿⠿⠋⠀⠙⠉⠉⠉⠉⠁

⠉⠳⣤⣀⡀⠐⠒⡀⢀⣀⢀⠀⠶⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣤⣤⣀⣸⣿⣧⣼⣿⣿⣿⣥⣼⣿⣷⡔⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣿⡏⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣷⣶⣶⡶⠄⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[32A⣤⣦⣤⣤⣤⣴⣤⣤⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣙⠛⠛⣛⡛⠛⣛⡛⢛⣛⣛⡛⠛⣛⣛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣷⣸⣿⡿⠿⣿⡿⠿⣿⣿⠿⠇⣿⣿⢻⣿⡆⣿⣿⡄⣿⡇⢸⣿⣿⣷⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡇⠀⢀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠛⠃⠙⠛⠃⠘⠛⠃⠀⠛⠛⠛⠃⠛⠛⠘⠛⠃⠛⠛⠘⠛⠛⠛⠛⠘⠛⢓⡛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡇⣀⣀⣀⣀⣀⣀⣀⣨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢸⣿⡿⣿⡆⣿⣿⣿⣿⡆⣿⣿⠿⠀⣿⣿⣿⡆⢸⣿⡇⢀⣾⡿⣿⣷⠀⠛⢛⢻⣟⣛⣛⣛⣛⣛⢛⠛⣛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⣇⢸⣿⣧⣿⡇⣿⣿⣿⣿⡇⣿⣿⣤⢠⣿⡟⣿⡇⢸⣿⡇⠈⢿⣿⣯⡍⠀⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣷⣦⣶⣦⣤⣶⣶⣤⣶⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡛⠛⣛⣻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣄⣀⣀⠀⠀⠘⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣠⣄⠀⠀⠀⠸⢿⡧⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⡀⠀⠘⣁⠀⠀⠀⠀⠀⠀⣀⣘⣛⣻⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠙⠛⠛⠿⢿⠿⣿⢿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣀⣹⣿⣿⣿⣿⣿⡇

⠻⠛⠛⡿⠷⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢠⠔⣞⠟⢻⡿⠛⠋⠉⠀⠀⠀⠀⠀⢰⣶⡄⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡄⠈⠛⠛⠛⠿⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡶⢠⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠏⠛⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠁⠘⠉⠙⠋⠛⠛⠛⠿⠿⠋⠀⠙⠉⠉⠉⠉⠃

⠉⠳⣤⣀⠀⠐⠒⡂⠀⠀⢀⠀⣶⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣤⣤⣄⣸⣿⣤⣸⣿⣿⣿⣥⣼⣿⡷⠦⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣿⡏⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣷⣶⣶⠶⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[32A⣤⣤⣤⣤⣤⣼⣤⣤⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣙⠛⠛⣛⣛⠛⣛⡛⢛⣛⣛⡛⠛⣛⣛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡏⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣷⣸⣿⡿⠿⣿⡿⠿⣿⣿⠿⠇⣿⣿⢻⣿⡆⣿⣿⡄⣿⡇⢸⣿⣿⣷⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⡏⣿⣿⡇⢸⣿⡇⠀⣿⣿⣀⡀⣿⣿⢸⣿⡇⣿⡏⣿⣿⡇⣿⣿⣾⣿⡆⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡇⣀⣈⣀⣀⣀⣀⣀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢸⣿⡿⣿⡆⣿⣿⣿⣿⡆⣿⣿⠿⠀⣿⣿⣿⡆⢸⣿⡇⢀⣾⡿⣿⣷⠀⠳⠒⠖⢒⣒⣒⡒⡒⢒⡖⣗⢛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⣿⣇⢸⣿⣧⣿⡇⣿⣿⣿⣿⡇⣿⣿⣤⢠⣿⡟⣿⡇⢸⣿⡇⠈⢿⣿⣯⡍⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇⠿⠿⠸⠿⠇⠀⠀⠿⠿⠇⠀⠀⠿⠿⠿⠿⠿⠇⠿⠿⠸⠿⠿⠇⠻⢿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣷⣦⣴⣤⣤⣶⣶⣤⣶⣦⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡛⠛⣛⣻⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣶⣶⣶⣤⣤⣤⣤⣤⣤⣄⣀⣀⡀⠀⠀⠚⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣃⣄⠀⠀⠀⡠⢿⡇⠀⠀⠀⠀⠄⠀⠀⢿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⡀⠀⠘⠁⠀⠀⠀⠀⠀⢀⣀⣘⣛⡻⣿⡇

⣿⣿⣻⣿⣿⣿⣿⣿⠿⠋⠛⠛⠛⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣷⣶⣶⣶⣀⣹⣿⣿⣿⣿⣿⡇

⠿⠟⠛⠫⠿⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⢠⡔⣺⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠙⠛⠛⠛⠿⠛⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠏⠙⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠉⠉⠋⠉⠋⠙⠛⠛⠿⠿⠋⠀⠛⠉⠙⠉⠉⠃

⠉⠳⡤⣀⠀⠐⠂⣒⡂⠀⢀⡀⡴⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣤⣤⣄⣸⣿⣤⣺⣿⣿⣿⣥⣽⣿⣶⡤⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣷⣶⣶⡶⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[32A⣤⣤⣤⣤⣤⣼⣤⣤⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣙⠛⠛⣛⡛⠛⣛⡛⢛⣛⣛⡛⠛⣛⣛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡅⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣷⣸⣿⡿⠿⣿⡿⠿⣿⣿⠿⠇⣿⣿⢻⣿⡆⣿⣿⡄⣿⡇⢸⣿⣿⣷⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡇⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⡏⣿⣿⡇⢸⣿⡇⠀⣿⣿⣀⡀⣿⣿⢸⣿⡇⣿⡏⢿⣿⡇⣿⣿⣾⣿⡄⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠛⠃⠙⠛⠃⠘⠛⠃⠀⠛⠛⠛⠃⠛⠛⠘⠛⠃⠛⠛⠘⠛⠛⠛⠛⠘⠛⢓⡛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡇⣀⣈⣈⣀⣀⣀⣀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠿⠿⠿⠿⠿⠿⠿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢸⣿⡿⣿⡆⣿⣿⣿⣿⡆⣿⣿⠿⠀⣿⣿⣿⡆⢸⣿⡇⢀⣾⡿⣿⣷⠀⠳⠒⠖⠒⠲⣒⡒⣒⡒⡒⡗⢟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⣇⢸⣿⣧⣿⡇⣿⣿⣿⣿⡇⣿⣿⣤⢠⣿⡟⣿⡇⢸⣿⡇⠈⢿⣿⣯⡍⠀⠀⠀⠀⠁⠉⠉⠉⠉⠈⠉⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿⢸⣿⡏⠉⠀⣿⣿⡏⠉⠀⣿⣿⠉⢸⣿⣷⣿⣿⢸⣿⡇⠀⣶⣮⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡛⠛⣛⣻⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣶⣶⣶⣤⣤⣤⣤⣤⣤⣄⣀⣀⡀⠀⠀⠚⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣃⣀⠀⠀⠀⡠⢿⡇⠀⠀⠀⠀⠄⠀⠀⢿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⡀⠀⠘⠁⠀⠀⠀⠀⠀⢀⣀⣘⣛⡻⣿⡇

⣿⣿⣿⢿⡿⣿⣿⣿⠟⠋⠛⠛⠛⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣷⣶⣶⣶⣀⣹⣿⣿⣿⣿⣿⡇

⠟⠟⠛⢻⡯⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⢠⡕⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⢀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠟⠁⠀⠀⠀⠀⠉⠿⠏⠉⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉⠉⠋⠉⠋⠙⠛⠻⠿⠿⠏⠀⠛⠉⠙⠉⠉⠃

⠋⠳⣤⣀⠀⠐⠂⠒⠀⠀⢀⠀⠴⢤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣤⣤⣄⣸⣿⣥⣼⣿⣿⣿⣤⣿⣿⡧⡤⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣿⡇⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣷⣶⣶⡶⠮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[32A⣶⣶⡷⠶⠶⠷⠾⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣛⠛⠛⣛⣛⠛⣛⡛⢛⣉⣉⡉⠙⣛⣛⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢈⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣷⣸⣿⡿⠿⣿⡿⠿⣿⣿⠿⠇⣿⣿⢻⣿⡆⣿⣿⡄⣿⡇⢸⣿⣿⣷⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⣿⣿⡇⢸⣿⡇⠀⣿⣿⣶⡆⣿⣿⢾⣟⡃⣿⣿⣷⣿⡇⣿⣿⢸⣿⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⡏⣿⣿⡇⢸⣿⡇⠀⣿⣿⣀⡀⣿⣿⢸⣿⡇⣿⡏⢿⣿⡇⣿⣿⣾⣿⡆⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠛⠃⠙⠛⠃⠘⠛⠃⠀⠛⠛⠛⠃⠛⠛⣘⡛⠃⠛⠛⠘⠛⠛⠛⠛⠘⠛⢓⡛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣤⣤⣤⣤⣤⣤⣤⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠿⠿⠿⠶⠾⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢸⣿⡿⣿⡆⣿⣿⣿⣿⡆⣿⣿⠿⠀⣿⣿⣿⡆⢸⣿⡇⢀⣾⡿⣿⣷⠈⡛⠛⠛⠻⡿⣛⣛⡛⣛⣛⠛⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⣿⣇⢸⣿⣧⣿⡇⣿⣿⣿⣿⡇⣿⣿⣤⢠⣿⡟⣿⡇⢸⣿⡇⠈⢿⣿⣯⡍⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣶⣴⣦⣤⣴⣶⣤⣴⣶⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⡇⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⠛⠛⣛⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⣀⣀⣤⣤⣤⣄⣘⣁⡀⠀⠀⠚⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣶⣄⠀⠀⠈⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣋⣃⣄⡀⠀⠀⡠⢿⡷⠀⠀⠀⠀⠄⠀⠀⢿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⡀⠀⠘⠁⠀⠀⠀⠀⠀⠀⣀⣘⣛⠻⣿⡇

⣿⡿⣿⣿⣿⣿⣿⣿⠻⠛⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣷⣶⣶⣶⣀⣹⣿⣿⣿⣿⣿⡇

⠿⠟⢛⣿⡟⠉⠉⠁⠀⠀⠀⠀⠀⠈⠁⠸⢓⣿⣿⣿⣿⡟⢿⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠤⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠎⠹⠫⠁⠥⠂⠀⠨⢿⣦⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠛⠛⠻⢿⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠲⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠏⠙⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠃⠀⠂⠈⠙⠛⠛⠛⠻⡿⡿⠟⠉⠙⠛⠛⠛⠛⠃

⠳⣄⡀⠀⠠⠤⠔⠒⡒⠀⠀⠰⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣤⣀⣘⣷⣞⣷⣿⣿⣿⣯⣛⣾⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣷⣶⣶⠦⠴⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[32A⣶⣶⡷⠶⠶⠷⠾⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣛⠛⠛⣛⣛⠛⣛⡛⢛⣉⣉⡉⠙⣛⣛⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠛⠃⠙⠛⠃⠘⠛⠃⠀⠛⠛⠛⠃⠛⠛⣘⡛⠃⠛⠛⠘⠛⠛⠛⠛⠘⠛⢓⣛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠾⠿⠿⠷⠾⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢸⣿⡿⣿⡆⣿⣿⣿⣿⡆⣿⣿⠿⠀⣿⣿⣿⡆⢸⣿⡇⢀⣾⡿⣿⣷⠈⠛⠛⠛⠿⠛⣛⢛⡛⣛⣛⠛⢛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⣿⣇⢸⣿⣧⣿⡇⣿⣿⣿⣿⡇⣿⣿⣤⢠⣿⡟⣿⡇⢸⣿⡇⠈⢿⣿⣯⡍⠀⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⠛⢛⣛⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⢀⣀⣀⣤⣄⣤⣄⣘⣁⡀⠀⠀⠚⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⡀⠀⠘⠃⠀⠀⠀⠀⠀⠀⣀⣘⣛⠻⣿⡇

⣿⣿⢿⣿⣿⣿⣿⣿⠻⠛⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣷⣶⣶⣶⣀⣹⣿⣿⣿⣿⣿⡇

⠿⠿⠻⣿⡟⠉⠉⠁⠀⠀⠀⠀⠀⠈⠁⢸⢻⣿⣿⣿⣿⡿⢿⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠤⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠎⠹⠋⠣⠬⠀⠀⠘⢿⣦⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⢿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠙⠛⠻⢿⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠲⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠏⠛⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠊⠀⠒⠉⠙⠛⠛⠛⠻⢿⡿⠟⠉⠙⠛⠛⠛⠛⠃

⠳⡄⡀⠀⠠⡤⠖⠒⡒⠀⠀⠰⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣤⣀⣘⣷⣝⣟⣿⣿⣿⣯⣛⣷⣶⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⡯⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣷⣶⣶⡦⠴⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[32A⠿⠿⠿⠿⠿⠿⠿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣈⣛⠛⠛⣉⣉⠉⣉⡉⢉⣉⣉⡉⠙⣛⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣷⣸⣿⡿⠿⣿⡿⠿⣿⣿⠿⠇⣿⣿⢻⣿⡆⣿⣿⡄⣿⡇⢸⣿⣿⣷⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⣿⣿⡇⢸⣿⡇⠀⣿⣿⣶⡆⣿⣿⢾⣟⡃⣿⣿⣷⣿⡇⣿⣿⢸⣿⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⡏⣿⣿⡇⢸⣿⡇⠀⣿⣿⣀⡀⣿⣿⢸⣿⡇⣿⡏⣿⣿⡇⣿⣿⣾⣿⡄⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠛⠃⠙⠛⠃⠘⠛⠃⠀⠛⠛⠛⠃⠛⠛⣘⠛⠃⠛⠛⠘⠛⠛⠛⠛⠘⠛⢓⣛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣤⣤⣤⣤⣤⣤⣤⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠛⠛⠛⠗⠲⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢸⣿⡿⣿⡆⣿⣿⣿⣿⡆⣿⣿⠿⠀⣿⣿⣿⡆⢸⣿⡇⢠⣾⡿⣿⣷⠈⡙⠛⠛⠿⢿⣛⣛⢛⢛⣛⡛⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢠⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣷⣦⣶⣤⣤⣶⣶⣤⣶⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣀⡀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡛⠛⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠚⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣆⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⢰⣷⣾⣿⣿⣿⣧⡀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣃⡀⠀⠀⠀⡠⢿⡷⠀⠀⠀⠀⠄⠀⠀⢿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⡀⠀⠘⠃⠀⠀⠀⠀⠀⠀⣀⣘⡛⠻⣿⡇

⣿⣿⢿⣿⣿⣿⣿⡿⠿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠁⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣷⣶⣶⣶⣀⣸⣿⣿⣿⣿⣿⡇

⡿⠿⣿⣿⠟⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⡹⣻⣿⣿⣿⣿⡟⠛⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠽⠛⠃⠍⠀⠀⠺⢷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⢿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠙⠛⠛⠛⢿⠟⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠲⠶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⠙⠛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠃⠀⠑⠛⠻⠟⠛⠻⠿⢿⣿⠟⠉⠙⠛⠛⠛⠛⠃

⣦⣀⠀⠀⣠⣤⡤⠀⠂⠒⠂⢶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣀⣈⣻⣤⣒⣷⣿⣿⣿⣚⣢⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣤⣤⣤⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⢿⣿⣿⣿⣿⣷⣶⠦⠤⠦⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[32A⠿⠿⠿⠿⠿⠿⠿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣈⣛⠛⠛⣋⣉⠉⣉⡉⢉⣉⣉⡉⠛⣛⣋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣷⣸⣿⡿⠿⣿⡿⠿⣿⣿⡿⠇⣿⣿⢻⣿⡆⣿⣿⡆⣿⡇⢸⣿⣿⣷⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⣿⣿⡇⢸⣿⡇⠀⣿⣿⣶⡆⣿⣿⢾⣟⡃⣿⣿⣷⣿⡇⣿⣿⢸⣿⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⡏⣿⣿⡇⢸⣿⡇⠀⣿⣿⣆⡀⣿⣿⢸⣿⡇⣿⡏⣿⣿⡇⣿⣿⣾⣿⡆⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠛⠃⠙⠛⠃⠘⠛⠃⠀⠛⠛⠛⠃⠛⠛⣘⠛⠃⠛⠛⠘⠛⠛⠛⠛⠘⠛⣓⡛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣤⣤⣤⣤⣤⣤⣤⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠛⠛⠛⠟⠺⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢸⣿⡿⣿⡆⣿⣿⣿⣿⡆⣿⣿⠿⠀⣿⣿⣿⡆⢸⣿⡇⢠⣾⡿⣿⣷⠈⢙⡛⠛⢿⣛⣛⣛⣛⣛⣛⡛⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⣿⣇⢸⣿⣧⣿⡇⣿⣿⣿⣿⡇⣿⣿⣤⢠⣿⡟⣿⡇⢸⣿⡇⠈⢿⣿⣯⡍⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣷⣶⣶⣦⣤⣶⣦⣤⣶⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢠⣿⡄⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡇⢀⣀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡛⠛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣄⣀⣀⡀⠀⠀⠋⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⢀⣄⡀⣸⣿⣿⣧⡀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣋⣠⡀⠀⠀⠀⡼⣿⡇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⡀⠀⠘⡁⠀⠀⠀⠀⠀⢀⣀⣘⣛⡿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⠿⠛⠻⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠿⠟⠉⠁⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⠀⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣶⣶⣶⣀⣹⣿⣿⣿⣿⣿⡇

⠿⢻⣿⣿⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢈⣽⣿⣿⣿⣿⣿⡏⠛⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠾⠻⠯⠁⠬⠉⠀⠾⢿⡇⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⢿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠛⠛⠻⢿⠟⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠒⠲⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠫⠙⠋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠁⠘⠓⠛⠛⠛⠛⠛⠿⣿⠿⠋⠈⠙⠛⠛⠛⠛⠃

⢧⣄⠀⠀⣰⣤⠦⢒⠐⠒⠀⢶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣄⣈⣻⣶⣛⣿⣿⣿⣿⣝⣷⣾⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣷⣶⠦⠤⠦⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[32A⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣘⣛⠛⠛⣛⣛⠛⣛⡛⢛⣛⣛⡛⠟⣛⣛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣷⣸⣿⡿⢿⣿⡿⠿⣿⣿⡿⠇⣿⣿⢻⣿⡆⣿⣿⡆⣿⡇⢸⣿⣿⣷⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⣿⣿⡇⢸⣿⡇⠀⣿⣿⣷⡆⣿⣿⢾⣟⡃⣿⣿⣷⣿⡇⣿⣿⢸⣿⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⡏⣿⣿⡇⢸⣿⡇⠀⣿⣿⣇⡀⣿⣿⢸⣿⡇⣿⣏⣿⣿⡇⣿⣿⣾⣿⡆⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠛⠃⠛⠛⠃⠘⠛⠃⠀⠛⠛⠛⠃⠛⢛⡘⠛⠃⠛⠛⠘⠛⠛⠛⠛⠘⠛⣓⡛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣤⣤⣤⣤⣤⣤⣤⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢸⣿⡿⣿⡆⣿⣿⣿⣿⡎⣿⣿⠿⠀⣿⣿⣿⡆⢸⣿⡇⢠⣾⡿⣿⣷⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⣿⣇⢸⣿⣧⣿⡇⣿⣿⣿⣿⡇⣿⣿⣤⢠⣿⡟⣿⡇⢸⣿⡇⠈⢿⣿⣯⡍⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿⢸⣿⡏⠉⠀⣿⣿⡏⠉⠀⣿⣿⠉⢸⣿⣷⣿⣿⢸⣿⡇⠰⣶⣮⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇⠿⠿⠸⠿⠇⠀⠀⠿⠿⠇⠀⠠⠿⠿⠿⠿⠿⠇⠿⠿⠸⠿⠿⠇⠻⢿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣷⣶⣶⣦⣤⣶⣶⣤⣾⣷⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⣶⣶⣦⣤⣤⣤⣤⣀⣀⡀⠀⠘⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⡀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣿⣿⣁⣡⣤⠀⠀⠀⢼⣿⡿⠀⠀⠀⠀⠇⠀⠀⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣠⣤⣤⣾⣿⣿⣿⣿⣄⠀⠀⠀⢤⣤⣄⡀⠀⢸⣿⣿⣿⣿⣿⣶⣤⣀⡀⣈⣁⠀⠀⠀⠀⠀⢠⣀⣽⣛⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⠟⠋⠙⠛⠛⠿⠿⢿⡿⢿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⠿⠟⠉⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢸⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣠⣿⣿⣿⣿⣿⣿⣿⡇

⡿⣿⣿⡿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣯⠛⠂⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠾⠿⠿⠿⠿⠿⠏⠑⠿⢿⣿⠀⠈⠁⠑⠀⠀⠀⠀⠀⠀⠰⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣂⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠙⠛⠛⠛⠛⠻⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⡀⡀⠒⣙⣿⢷⠦⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⡄⠀⠴⠂⢤⡕⡁⠀⠀⢀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⠙⠉⠙⠛⠛⠛⢿⣿⠿⠏⠀⠙⠉⠉⠙⠋⠹⠇

⢳⣦⣄⣔⣺⣺⣿⣿⣇⣭⣸⣿⣿⠖⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⢄⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠆⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⡟⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⢿⣿⣿⣿⣿⣷⣶⣶⣷⡿⠆⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀

[32A⣶⣾⣶⠶⠶⠶⠶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣙⣛⠛⠛⣛⣛⠛⣛⡛⢛⣛⣛⡛⠟⣛⣛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣷⣸⣿⡿⢿⣿⡿⠿⣿⣿⡿⠇⣿⣿⢻⣿⡆⣿⣿⡆⣿⡇⢸⣿⣿⣷⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⣿⣿⡇⢸⣿⡇⠀⣿⣿⣶⡆⣿⣿⢾⣟⡃⣿⣿⣷⣿⡇⣿⣿⢸⣿⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⡏⣿⣿⡇⢸⣿⡇⠀⣿⣿⣇⡀⣿⣿⢸⣿⡇⣿⣏⣿⣿⡇⣿⣿⣾⣿⡆⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠛⠃⠙⠛⠃⠘⠛⠃⠀⠛⠛⠛⠃⠛⢛⡘⠛⠃⠛⠛⠘⠛⠛⠛⠛⠘⢛⣓⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠻⠟⠻⠷⠿⠿⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢸⣿⡿⣿⡆⣿⣿⣿⣿⡆⣿⣿⠿⠀⣾⣿⣿⡆⢸⣿⡇⢠⣾⡿⣿⣷⠈⢻⡿⠿⢿⣿⣿⣿⢿⡿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⣿⣇⢸⣿⣧⣿⡇⣿⣿⣿⣿⡇⣿⣿⣤⢠⣿⡟⣿⡇⢸⣿⡇⠈⢿⣿⣯⡍⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣷⣶⣶⣦⣴⣶⣶⣴⣾⣶⣤⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣤⣤⣤⣤⣄⣀⣀⡀⠀⠙⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣀⣥⣄⠀⠀⠀⡼⢿⡧⠀⠀⠀⠐⠀⠀⠘⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣷⣦⣤⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⡀⠀⣈⣀⠀⠀⠀⠀⠀⣠⣀⣽⣛⣻⣿⣿⡇

⣽⣿⣿⣿⣿⣿⡿⠟⠉⠙⠋⠛⠿⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⡿⠿⠏⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣠⣿⣿⣿⣿⣿⣿⣿⡇

⠛⢻⣿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⣿⣟⠛⠂⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠮⠿⠻⠿⠟⠟⠃⠀⠘⢻⣿⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠘⠋⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⣀⠚⠙⠻⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠻⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⡀⠀⠤⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠙⠋⠀⠁⠀⠈⠋⠙⠙⠛⠿⠟⠁⠀⠉⠉⠉⠉⠉⠹⠇

⢳⣄⣀⠀⡒⢒⣛⣫⣀⣀⡐⣿⡵⠂⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣤⣤⣿⣿⣭⣿⣿⣿⣿⣽⣿⣿⣿⣶⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⡇⠀⠀⠀⠂⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠿⣿⣿⣿⣿⣿⣿⣶⣶⣶⡶⠫⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀

[32A⠿⠿⠿⠿⠛⠛⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣘⣛⣉⠉⠛⣉⣉⠉⣉⡉⢉⣉⣉⡛⠟⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣷⣸⣿⡿⢿⣿⡿⠿⣿⣿⡿⠇⣿⣿⢻⣿⡆⣿⣿⡆⣿⡇⢸⣿⣿⣷⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⣿⣿⡇⢸⣿⡇⠀⣿⣿⣷⡆⣿⣿⢾⣟⡃⣿⣿⣷⣿⡇⣿⣿⢸⣿⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⡏⣿⣿⡇⢸⣿⡇⠀⣿⣿⣇⡀⣿⣿⢸⣿⡇⣿⣏⣿⣿⡇⣿⣿⣾⣿⡆⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠛⠃⠙⠛⠃⠘⠛⠃⠀⠛⠛⠛⠃⠛⢛⠘⠛⠃⠛⠛⠘⠛⠛⠛⠛⢘⣛⡓⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣶⣶⣶⣶⣶⣶⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠛⠃⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢸⣿⡿⣿⡆⣿⣿⣿⣿⡎⣿⣿⠿⠀⣿⣿⣿⡆⢸⣿⡇⢠⣾⡿⣿⣷⠈⢉⣉⣋⣽⣟⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⣿⣇⢸⣿⣧⣿⡇⣿⣿⣿⣿⡇⣿⣿⣤⢠⣿⡟⣿⡇⢸⣿⡇⠈⢿⣿⣯⡍⠀⠀⠀⠀⠈⠉⠉⠁⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣷⣶⣿⣿⣶⣿⣿⣷⣾⣶⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⣀⡀⠀⠀⠀⠀⠀⠀⣶⣶⣤⣤⣤⣤⡀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣀⠀⠀⠸⢿⡿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣶⣤⣀⣤⣤⣄⡀⠀⠀⠀⣠⣤⣤⣭⣽⣿⣿⣿⡇

⣿⣿⣿⣿⣿⡿⠋⠉⠉⠉⠉⠙⠻⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⡇

⣻⣿⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⣿⣿⣿⡯⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣿⠃⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠙⠛⠉⠉⢱⣤⡀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠛⠿⠛⠛⠿⠿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⣀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⡠⠄⠉⠻⠿⠿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⣿⣿⣿⣿⠿⢿⣿⢿⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⡇

⠐⠈⡐⠐⠀⠀⠀⠀⣀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⡅⠀⠈⠀⠀⠀⠀⠈⠁⠁

⢲⣖⡊⣛⣯⣭⣽⣦⣭⣝⣻⣗⠃⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣥⣼⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡛⡃⢀⣠⣤⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢍⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⠶⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[32A⠛⠛⠛⠛⠛⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣙⣛⣉⠉⠉⣉⣉⠉⣉⡉⢉⣉⣀⡛⠟⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣷⣸⣿⡿⢿⣿⡿⠿⣿⣿⡿⠇⣿⣿⢻⣿⡆⣿⣿⡆⣿⡇⢸⣿⣿⣷⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⣿⣿⡇⢸⣿⡇⠀⣿⣿⣷⡆⣿⣿⢾⣟⡃⣿⣿⣷⣿⡇⣿⣿⢸⣿⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⡏⣿⣿⡇⢸⣿⡇⠀⣿⣿⣇⡀⣿⣿⢸⣿⡇⣿⣏⣿⣿⡇⣿⣿⣾⣿⡆⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠛⠃⠛⠛⠃⠘⠛⠃⠀⠛⠛⠛⠃⠛⡛⠘⠛⠃⠛⠛⠘⠛⠛⠛⠛⢘⣛⠓⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣶⣶⣶⣶⣶⣶⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠛⠃⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢸⣿⡿⣿⡆⣿⣿⣿⣿⡎⣿⣿⠿⠀⣿⣿⣿⡆⢸⣿⡇⢠⣾⡿⣿⣷⠈⠉⢹⣭⣿⣏⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⣿⣇⢸⣿⣧⣿⡇⣿⣿⣿⣿⡇⣿⣿⣤⢠⣿⡟⣿⡇⢸⣿⡇⠈⢿⣿⣯⡍⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣾⣿⣻⣶⣿⣿⣷⣿⣷⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⠆⠀⠀⠀⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣀⣀⢀⠀⠀⠀⠀⠀⢠⣶⣶⣤⣤⣤⣤⡀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⣤⣀⣤⣤⣄⡀⠀⠀⠀⣤⣤⣦⣭⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⠿⠉⠉⠉⠉⠉⠙⠛⠛⢟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⡇

⣿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⣿⣿⣿⣿⡏⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣿⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠉⠙⠛⠋⠂⠸⣇⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠟⠛⠿⠿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⢀⣀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⢀⠤⢀⢍⠿⠿⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⡇

⠘⠛⣒⣲⣀⣀⣀⣀⣀⣀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢺⣎⣚⣹⣿⣿⣿⣾⣿⣿⣿⣟⣃⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣥⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣀⣠⣄⠀⠐⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⣍⡤⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⠿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⡶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[32A⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣘⡛⣀⣀⣀⠀⠀⣀⣀⠀⣀⡀⢀⣛⣛⡀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣷⣸⣿⡿⢿⣿⡿⠿⣿⣿⡿⠇⣿⣿⢻⣿⡆⣿⣿⡆⣿⡇⢸⣿⣿⣷⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⣿⣿⡇⢸⣿⡇⠀⣿⣿⣶⡆⣿⣿⢾⣟⡃⣿⣿⣷⣿⡇⣿⣿⢸⣿⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⡏⣿⣿⡇⢸⣿⡇⠀⣿⣿⣄⡀⣿⣿⢸⣿⡇⣿⣏⣿⣿⡇⣿⣿⣾⣿⡆⣿⣿⣀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣤⣤⣤⣤⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠛⠃⠙⠛⠃⠘⠛⠃⠀⠛⠛⠛⠃⠛⠛⠘⠛⠃⠛⠛⠘⠛⠛⠛⠛⠘⠛⠓⠛⠛⠛⠠⣤⣤⣤⣤⣤⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠒⠒⠒⠒⠒⠚⠓⠒⠀⠀⠀⠐⠂⠀⠐⠒⠒⠚⠚⠛⠛⠛⠛⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢸⣿⡿⣿⡆⣿⣿⣿⣿⡆⣿⣿⠿⠀⣿⣿⣿⡆⢸⣿⡇⢀⣾⡿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⣿⣇⢸⣿⣧⣿⡇⣿⣿⣿⣿⡇⣿⣿⣤⢠⣿⡟⣿⡇⢸⣿⡇⠈⢿⣿⣯⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣤⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⡖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣉⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⡀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢼⣿⠉⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠈⠉⠀⠀⠀⠀⠀⢀⣀⣍⠉⣻⣿⣿⣿⣭⣽⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣤⣦⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⠟⠛⠉⠉⠉⠉⠛⠛⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣼⣿⣿⣿⣿⣤⣀⠀⠀⠀⣾⣷⡄⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⢻⣻⡿⣿⣿⣿⣿⣿⣿⢿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢰⣿⣿⣿⣿⣿⣿⡿⠀⠀⣰⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠈⠁⠀⠁⠉⠉⠉⠉⠀⠈⠉⠘⠉⠉⠈⠈⠉⠉⠉⠁⠀⠀⠈⠛⠉⠉⠛⠛⠛⠁⠀⣰⣿⣯⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⢠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣀⣀⡶⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠃

⣿⠛⠋⣀⣀⣠⣤⣤⠦⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀

⢹⣻⣿⣴⣾⣿⣿⣿⣿⣿⣿⣷⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢳⣄⣀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣦⣤⣶⣾⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠿⠛⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣠⣼⣿⣅⣧⣤⠴⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣥⣤⣄⡀⠀⠀⠀⠀⢀⣤⡠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[32A⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣘⡛⣀⣀⣀⠀⠀⣀⡀⠀⣀⡀⢀⣛⣋⡀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣷⣸⣿⡿⠿⣿⡿⠿⣿⣿⠿⠇⣿⣿⢻⣿⡆⣿⣿⡄⣿⡇⢸⣿⣿⣷⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⡏⣿⣿⡇⢸⣿⡇⠀⣿⣿⣀⡀⣿⣿⢸⣿⡇⣿⡏⣿⣿⡇⣿⣿⣾⣿⡄⣿⣿⣀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣤⣤⣤⣤⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠛⠃⠙⠛⠃⠘⠛⠃⠀⠛⠛⠛⠃⠛⠛⠘⠛⠃⠛⠛⠘⠛⠛⠛⠛⠘⠛⠓⠛⠛⠛⠠⡤⣤⢤⣤⣤⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠓⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀⠐⠂⠀⠀⠒⠒⠚⠒⠚⠉⠛⠃⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⣇⢸⣿⣧⣿⡇⣿⣿⣿⣿⡇⣿⣿⣤⢠⣿⡟⣿⡇⢸⣿⡇⠈⢿⣿⣯⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣤⣀⣀⣀⣀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⡖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠈⠉⠀⠀⠀⠀⠀⢀⣀⣍⠉⣻⣿⣿⣿⣭⣽⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣤⣦⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⠟⠛⠉⠉⠉⠉⠙⠛⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣼⣿⣿⣿⣿⣤⣀⠀⠀⠀⣾⣷⡄⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠽⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⡿⢛⣻⡿⣿⣿⣿⣿⣿⡿⢿⣿⣟⣟⣻⣿⣿⣿⣿⣿⣿⠃⠀⢰⣿⣿⣿⣿⣿⣿⡿⠀⠀⣰⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠁⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠉⠁⠀⠈⠉⠉⠉⠁⠀⠀⠈⠉⠉⠉⠛⠛⠛⠁⠀⢰⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣀⣀⠴⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠁

⣗⠁⠈⢀⣀⣤⡤⣤⠄⣀⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀

⢙⣛⣷⣠⣶⣿⣿⣿⣿⣷⣿⣷⣤⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⢳⣄⣀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣤⣤⣰⣾⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠿⠛⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣠⣤⣏⣠⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⢀⣤⡠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠯⠿⠾⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⡏⣿⣿⡇⢸⣿⡇⠀⣿⣿⣀⡀⣿⣿⢸⣿⡇⣿⡏⣿⣿⡇⣿⣿⣾⣿⡄⣿⣿⣀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣤⣤⣤⣤⣼⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠛⠃⠙⠛⠃⠘⠛⠃⠀⠛⠛⠛⠃⠛⠛⠘⠛⠃⠛⠛⠘⠛⠛⠛⠛⠘⠛⠓⠛⠛⠛⠠⡤⣤⢤⣤⣤⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀⠐⠂⠀⠀⠒⠒⠚⠒⠛⠉⠛⠃⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢸⣿⡿⣿⡆⣿⣿⣿⣿⡆⣿⣿⠿⠀⣿⣿⣿⡆⢸⣿⡇⢠⣾⡿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣤⣀⣀⣀⣀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣉⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⡀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⢼⣿⠉⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠀⠀⠀⠀⠀⢀⣀⣍⠉⣻⣿⣿⣿⣭⣽⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⣿⣿⣦⣄⠀⠀⠀⢰⣿⣇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣤⣦⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⠟⠛⠉⠉⠉⠉⠛⠛⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣿⣿⣿⡟⠀⠀⣴⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⡹⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣿⣿⣻⣿⣛⢻⡿⣿⣿⣿⣿⣿⡿⠿⢿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⠿⠀⠀⣶⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠁⠀⠀⠈⠉⠉⠁⠀⠀⠀⠈⠉⠁⠁⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠈⠁⠀⠀⠾⣿⣿⣿⣯⣽⣿⣿⣧⠀⠀⠠⣤⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⢀⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⠄⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⡇

⣀⣠⣤⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠃

⣟⠋⠁⢀⣀⣤⡤⣤⠄⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⠀⠀⠀⠀

⢙⣻⣷⣴⣶⣿⣿⣿⣿⣿⣿⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣤⣤⣴⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣬⣏⣀⣀⡀⠀⠀⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣄⣄⠀⠀⠀⠀⠀⢀⣀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠯⠿⠿⠿⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[32A⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣘⡛⣀⣀⣀⠀⠀⣀⡀⠀⣀⡀⢀⣛⣛⡀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣷⣸⣿⡿⠿⣿⡿⠿⣿⣿⠿⠇⣿⣿⢻⣿⡆⣿⣿⡄⣿⡇⢸⣿⣿⣷⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⣿⣿⡇⢸⣿⡇⠀⣿⣿⣶⡆⣿⣿⢾⣟⡃⣿⣿⣷⣿⡇⣿⣿⢸⣿⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⡏⣿⣿⡇⢸⣿⡇⠀⣿⣿⣀⡀⣿⣿⢸⣿⡇⣿⡏⣿⣿⡇⣿⣿⣾⣿⡄⣿⣿⣀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣤⡤⣤⣤⣤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠛⠃⠙⠛⠃⠘⠛⠃⠀⠛⠛⠛⠃⠛⠛⠘⠛⠃⠛⠛⠘⠛⠛⠛⠛⠘⠛⠓⠛⠛⠛⠠⠤⣤⣴⣶⡶⢾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠛⠙⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠓⠒⠒⠒⠒⠓⠚⠒⠒⠀⠀⠀⠐⠂⠀⠐⠒⠒⠒⠚⠒⠒⠚⠓⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⣿⣇⢸⣿⣧⣿⡇⣿⣿⣿⣿⡇⣿⣿⣤⢠⣿⡟⣿⡇⢸⣿⡇⠈⢿⣿⣯⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣶⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣶⣶⣶⣦⣤⣄⣀⣀⣀⣄⣀⣀⣀⣀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⣉⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠼⣿⠀⠁⠀⠀⠂⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠉⡀⠀⠀⠀⠀⢠⣄⣌⣉⣹⣿⣿⣿⣯⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣧⣷⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⡿⠛⠋⠀⠀⠀⠉⠉⠛⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣼⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠶⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣏⣋⠉⡙⠿⠿⢿⡿⣿⣿⠿⠿⢟⣿⣿⡟⠿⠿⣿⣿⣿⡿⠿⢿⣿⣿⣿⠆⠀⠀⠸⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠉⠁⠀⠀⠀⠀⠈⢿⣿⣿⢯⣽⣿⣶⣶⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠠⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⡄⣼⡿⠿⠿⠿⢿⣿⣿⣿⡇

⣠⣤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠈⠀⠀⠀⠁

⣥⡁⣀⣀⡤⠤⠤⢴⣄⣠⣄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡤⢟⣷⣦⣾⣿⡿⣿⣿⣿⣿⣿⠤⠄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣤⣤⣬⣍⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣨⣏⣀⡀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⢠⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠽⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[32A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣙⡛⣀⣀⣀⠀⠀⣀⡀⠀⣀⡀⢀⣛⣋⡀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣷⣸⣿⡿⠿⣿⡿⠿⣿⣿⡿⠇⣿⣿⢻⣿⡆⣿⣿⡆⣿⡇⢸⣿⣿⣷⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⡏⣿⣿⡇⢸⣿⡇⠀⣿⣿⣆⡀⣿⣿⢸⣿⡇⣿⡏⣿⣿⡇⣿⣿⣾⣿⡄⣿⣿⣀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣶⣶⣶⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠛⠃⠙⠛⠃⠘⠛⠃⠀⠛⠛⠛⠃⠛⠛⠘⠛⠃⠛⠛⠘⠛⠛⠛⠛⠘⠛⠓⠛⠛⠛⠰⣾⡿⠶⣶⢶⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠓⠒⠛⠛⠛⠓⠚⠛⠂⠀⠀⠀⠐⠂⠀⠀⠐⠒⠒⠒⠒⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣷⣿⣿⣽⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣦⣤⣤⣤⣦⣄⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠀⠀⠀⠀⠂⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⣶⣶⣶⠀⠀⠀⠀⠀⢀⣷⣦⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣠⣤⣯⣩⣽⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠸⢿⣿⠀⠀⠀⠀⠐⠻⢿⣿⣿⣇⠀⠀⠀⠀⠘⠻⣾⣧⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⠟⠛⠉⠀⠀⠀⠀⠉⠉⠉⣹⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠙⠛⠻⣿⣄⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠎⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⠋⠽⠿⠿⠿⢿⠿⢿⡿⠿⠻⠛⣻⣿⡿⠿⠿⠿⡿⣿⠿⠿⢿⣿⣿⠇⠀⢸⣦⠀⠀⠈⢿⣷⣶⣆⡀⠀⠀⠀⠀⠀⠈⠉⠁⠶⠆⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠊⠉⠀⠀⠀⠈⠉⠹⠿⣿⣶⣶⣶⣶⣶⣶⣄⠀⠀⢀⣶⣄⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠴⢴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠟⠃⠉⠀⠀⠀⠀⠿⠿⠿⠿⠿⡿⢿⡇

⣤⣾⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣍⡀⠀⠤⠤⠤⠤⣤⣠⣴⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠦⣯⣿⣶⣿⣿⡿⣿⣿⣿⣿⣿⠦⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣷⣶⣶⣿⣯⣄⣠⣤⡄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣇⣠⠤⣄⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣦⣶⣤⣤⣄⣀⣀⣄⡀⣠⣤⣤⣤⣄⣀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[32A⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣛⡃⣀⣀⣀⠀⠀⣀⣀⠀⣀⡀⢈⣛⣁⡀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣷⣸⣿⡿⠿⣿⡿⠿⣿⣿⡿⠇⣿⣿⢻⣿⡆⣿⣿⡆⣿⡇⢸⣿⣿⣷⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⣿⣿⡇⢸⣿⡇⠀⣿⣿⣶⡆⣿⣿⢾⣟⡃⣿⣿⣷⣿⡇⣿⣿⢸⣿⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⡏⣿⣿⡇⢸⣿⡇⠀⣿⣿⣆⡀⣿⣿⢸⣿⡇⣿⡏⣿⣿⡇⣿⣿⣾⣿⡄⣿⣿⣀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣤⣤⣤⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠛⠃⠙⠛⠃⠘⠛⠃⠀⠛⠛⠛⠃⠛⠛⠘⠛⠃⠛⠛⠘⠛⠛⠛⠛⠘⠛⠓⠛⠛⠛⠠⣤⣤⣤⡤⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠋⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠚⠛⠒⠒⠒⠛⠒⠒⠒⠂⠀⠀⠀⠒⠂⠀⠒⠒⠒⠒⠒⠒⠚⠃⠛⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣶⣶⣶⣾⣏⣶⣾⣿⣶⣶⣶⣶⣶⣦⣤⣤⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣉⣉⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣀⣀⠀⠀⠀⠀⢀⣴⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠻⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣦⣤⣿⣿⣣⣿⣿⣿⡇⣈⣿⣿⡇

⣿⣿⣿⠟⠛⠁⠀⠉⠉⠉⠛⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡇

⠏⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣻⣛⡻⣿⡽⠿⢿⣿⢿⣿⡿⠿⣿⣟⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢰⣶⡀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠈⠉⠉⠀⠀⠀⠈⠈⠈⠀⠀⠉⠙⠀⠀⠛⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⠿⠿⠿⠻⠿⢿⠿⠿⠿⠿⠿⠿⠿⢿⣿⠿⣿⣿⡇

⣠⣤⡃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃

⡋⠁⣀⣠⣤⠤⠤⣦⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⠄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣧⣴⣦⣻⣃⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣽⣏⣠⣄⣤⣀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣧⣄⣀⠀⠀⠀⠠⢠⣤⣤⣄⣀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[32A⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣶⣶⣶⣤⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⡤⠤⠼⠿⣧⡤⣤⢤⣤⣤⣤⣤⣤⣤⣤⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠀⠀⠀⠒⠒⠒⠒⠚⠓⠓⠓⠚⠚⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⠀⣤⣤⣤⡄⠀⠀⢀⣤⣤⣶⣤⣄⡀⠀⠀⣤⣤⣤⣤⡄⠀⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⣿⣿⣿⡇⠀⢀⣿⣿⣿⠛⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⠀⠻⠿⣿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⣿⣿⣿⠀⢸⣿⣿⢻⣿⣿⡀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⣿⣿⣿⠀⣾⣿⣿⢸⣿⣿⡇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣤⠀⠀

⣶⣿⣶⣾⣿⣶⣾⣿⣷⣾⣷⣶⣶⣶⣤⣤⣄⣀⣀⣀⠀⣿⣿⣿⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⣿⣿⣿⢀⣿⣿⣿⣾⣿⣿⣇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⠀⣿⣿⣿⣷⣶⡎⣿⣿⣿⣤⣿⣿⡿⢸⣿⣿⣿⠛⣿⣿⣿⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣩⣿⣿⣿⣿⣿⣿⣖⣛⣛⣛⣀⣛⣛⣛⣛⣛⣳⠌⠙⠿⠿⠟⠋⠀⠘⠛⠛⠛⠀⠛⠛⠛⠃⠀⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣶⣄⠀⠀⠈⠁⠀⠀⠀⠀⠀⣄⣀⣉⣉⣻⣿⣿⣿⣭⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⢿⣿⡇⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⠟⠛⠉⠀⠉⠉⠉⠛⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠘⣿⡇⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠏⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⡿⣻⡿⠿⢿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣟⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠈⠀⠀⠀⠀⠀⠉⠁⠀⠈⠉⠉⠉⠉⠁⠀⠁⠉⠉⠀⠀⠉⠉⠉⠀⠀⠀⠀⠈⠻⠄⠀⢠⣤⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠠⣦⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠉⠻⠿⠿⠿⠿⢿⠿⠿⢿⠿⠿⡿⠿⠿⠿⢿⣿⣿⣿⣿⡇

⣤⣼⣷⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃

⡟⢁⣤⣤⣤⠤⠴⣶⣠⣶⣶⣄⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢽⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⠆⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣯⣶⣶⣿⣏⠁⣠⣠⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣽⣷⣬⣤⣄⢠⠶⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣯⣤⣤⡀⠀⢀⢀⣀⣤⣤⣤⣤⣀⣀⡀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀

[32A⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

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

⣶⣶⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⠤⠤⠼⠿⣧⣤⣤⣥⣤⣤⣼⣷⣦⣤⣶⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠒⠀⠀⠀⠒⠒⠒⠒⠚⠚⠒⠓⠚⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⣿⣿⣿⡇⠀⢀⣿⣿⣿⠛⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⠀⠻⠿⣿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⣿⣿⣿⠀⢸⣿⣿⢻⣿⣿⡀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣦⣄⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⣿⣿⣿⠀⣾⣿⣿⢸⣿⣿⡇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠀⠀

⣿⣿⣶⣿⣿⣷⣾⣿⣿⣿⣿⣶⣶⣶⣶⣦⣤⣄⣀⣠⠀⣿⣿⣿⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⣿⣿⣿⢀⣿⣿⣿⣾⣿⣿⣇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⠀⣿⣿⣿⣷⣶⡆⣿⣿⣿⣤⣿⣿⡿⢸⣿⣿⣿⠛⣿⣿⣿⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣿⣿⣿⣿⣿⣿⣖⣛⣛⣛⣀⣛⣛⣛⣛⣛⣳⡎⠙⠿⠿⠟⠋⠀⠘⠛⠛⠛⠀⠛⠛⠛⠃⠀⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣶⣄⡀⠀⠈⢁⠀⠀⠀⠀⠀⣤⣀⣉⣉⣻⣿⣿⣿⣭⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⢤⣿⣿⠃⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⠟⠛⠉⠀⠈⠁⠉⠛⠛⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⡿⢽⡿⠿⢿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⠀⠀⠀⠀⣻⣿⣶⡆⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠉⠉⠉⠉⠉⠈⠁⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠉⠀⠀⠉⠉⠉⠀⠀⠀⠀⠘⠻⣿⣷⣶⢤⡄⠀⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⢠⣦⣤⣄⣀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠀⠀⠻⠻⠿⠿⠿⢿⠿⣿⢿⠿⠿⣿⠿⠿⡿⢿⣿⣿⣿⣿⡇

⣤⣾⣷⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃

⣯⢀⣤⣤⣤⠤⠶⣦⣴⣶⣶⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢼⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⠆⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣯⣶⣾⣿⣯⡁⣠⣄⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣽⣷⣬⣤⣄⢔⢞⠂⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣯⣤⣤⡀⠀⢠⣀⣀⣤⣤⣤⣤⣤⡀⣀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[32A⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

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

⣶⣶⣾⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⠤⠤⠼⠿⣧⣤⣤⣿⣬⣦⣾⣷⣾⣿⣶⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠀⠀⠀⠒⠒⠒⠒⠛⠛⠒⠓⠚⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣤⠀⣤⣤⣤⡄⠀⠀⢀⣤⣤⣶⣤⣄⡀⠀⠀⣤⣤⣤⣤⡄⠀⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⣿⣿⣿⡇⠀⢀⣿⣿⣿⠛⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⠀⠿⠿⣿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⣿⣿⣿⠀⢸⣿⣿⢻⣿⣿⡀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀

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

⣿⣿⣶⣿⣿⣵⣾⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣄⣀⣠⠀⣿⣿⣿⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⣿⣿⣿⢀⣿⣿⣿⣾⣿⣿⣇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣿⣿⣿⣿⣿⣿⣖⣛⣛⣛⣀⣛⣛⣛⣛⣛⣣⣎⠙⠿⠿⠟⠋⠀⠘⠛⠛⠛⠀⠛⠛⠛⠃⠀⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⢠⡤⠈⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⢀⣾⣿⣿⣶⣄⡀⠀⠈⢁⠀⠀⠀⠀⠀⣤⣀⣉⣉⣻⣿⣿⣿⣭⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⢴⣿⣿⣿⣿⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⠟⠛⠉⠀⠈⠉⠉⠙⠛⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠘⣿⣿⣿⣿⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠀⠀⠀⠀⣻⣿⣿⣿⣷⣄⡀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⢀⠀⠤⠈⠉⠉⠉⠉⠈⠉⠁⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠉⠉⠉⠉⠀⠀⠀⠈⠉⠀⠀⠉⠉⠉⠀⠀⠀⠀⠻⠿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠠⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⠆⠠⠼⠿⠿⠿⢿⣿⣿⠿⠿⠿⣿⠿⠿⡿⢿⣿⣿⣿⣿⡇

⣤⣾⣿⢶⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃

⣟⢁⣥⣤⡴⣶⣶⣶⣴⣶⣶⡆⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠦⠀⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣧⣶⣾⣿⣟⣁⣠⣄⣀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣴⣦⣴⣔⣿⠂⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣾⣿⣤⣤⡄⠐⣤⣤⣤⣦⣶⣤⣤⣤⣀⡀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠎⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀

[32A⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

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

⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣤⣤⣤⣤⣬⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣤⣤⣤⢤⡤⣤⣤⣤⢤⡤⣼⣿⣧⣤⡤⣤⣤⣤⢤⢤⣤⣤⣤⣤⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠀⠀⠀⠘⠒⠒⠓⠚⠛⠛⠛⠒⠚⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⣿⣿⣿⡇⠀⢀⣿⣿⣿⠛⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⠀⠿⠿⣿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⣿⣿⣿⠀⢸⣿⣿⢻⣿⣿⡀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣶⣶⣶⣶⣿⣳⣶⣿⣷⣶⣶⣶⣶⣦⣤⣤⣀⣀⣀⣀⠀⣿⣿⣿⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⣿⣿⣿⢀⣿⣿⣿⣾⣿⣿⣇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⠀⣿⣿⣿⣷⣶⡆⣿⣿⣿⣤⣿⣿⡿⢸⣿⣿⣿⠛⣿⣿⣿⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣍⣉⣩⣽⣿⣿⣿⣿⣖⣛⣛⣛⣀⣛⣛⣛⣛⣛⣳⡎⠙⠿⠿⠟⠋⠀⠘⠛⠛⠛⠀⠛⠛⠛⠃⠀⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⡀⣀⢀⣀⡀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⢀⡀⠀⠀⠀⠀⠴⣾⠑⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣶⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⣀⣍⠋⣻⣿⣿⣿⣭⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠸⣷⣤⣄⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⡿⠟⠛⠁⠉⠉⠉⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⢀⡀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠎⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠈⠉⠉⠈⠉⠁⠀⠈⠁⠉⠁⠀⠈⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠙⠙⠃⠀⠀⠀⠀⠹⠿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⣠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠹⠛⠛⠛⠛⠋⠉⠛⠻⢿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣤⣤⡷⠰⢤⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁⠈⠃

⣟⡋⣀⣀⣤⣤⠴⢶⣦⣴⣦⣄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢜⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⡦⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣤⣶⣾⣟⡇⢀⣄⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣾⣿⣀⣤⣄⡰⢠⡄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣬⣤⣇⣀⠀⠀⠀⠀⠀⣠⣄⣤⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀

[32A⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣤⣤⣤⣤⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣤⣤⢤⡤⢤⣤⡤⠤⣤⢤⡿⢧⣤⡤⣤⣤⣤⣤⣤⡤⣤⣤⣤⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠚⠛⠛⠒⠛⠂⠀⠀⠘⠓⠂⠁⠐⠛⠛⠛⠛⠒⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣶⣶⣶⣶⣶⣷⣶⣾⣷⣶⣶⣶⣶⣤⣄⣀⣀⣀⣀⣀⠀⣿⣿⣿⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⣿⣿⣿⢀⣿⣿⣿⣾⣿⣿⣇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⠀⣿⣿⣿⣷⣶⡆⣿⣿⣿⣤⣿⣿⡿⢸⣿⣿⣿⠛⣿⣿⣿⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣉⣉⣉⣹⣿⣿⣿⣿⣖⣛⣛⣛⣀⣛⣛⣛⣛⣛⣣⠌⡙⠿⠿⠟⠋⠀⠘⠛⠛⠛⠀⠛⠛⠛⠃⠀⠛⠛⠛⠀⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⡀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡄⠀⠀⠀⠀⠀⢠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠘⠉⢻⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣄⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣾⣿⣿⣷⣶⣶⣯⣄⡀⠈⠈⠉⠀⠀⠀⠀⠀⢀⠀⠀⠀⣼⣿⣿⣿⣏⣹⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⡆⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣀⣨⣿⣶⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⠿⠛⠋⠉⠉⠉⠙⠛⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⡾⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⣰⣶⣾⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⡿⣿⣻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⠉⠉⠉⠀⠈⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠍⠉⠛⠻⠿⠿⠿⠿⠿⢿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣤⣤⣦⣥⠀⠄⣄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠈⠃

⣿⢏⢁⣀⣠⣤⡴⢶⣆⣴⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣯⣬⣿⣿⣿⣿⣧⣴⣶⣿⠒⠀⡀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣂⣼⣟⣀⣤⡀⠀⠀⠄⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⣤⣤⣠⡀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀

[32A⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

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

⣤⣤⣤⣤⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣤⣤⢤⣤⣤⣤⣤⢤⣤⣤⣿⣿⣤⣤⣤⣤⣤⠤⡤⣤⣤⣤⣤⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠓⠒⠛⠛⠓⠛⠂⠀⠀⠘⠚⠂⠃⠐⠛⠛⠛⠓⠚⠛⠛⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⣿⣿⣿⠀⢸⣿⣿⢻⣿⣿⡀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀

⣶⣶⣶⣶⣶⣷⣶⣾⣿⣶⣶⣶⣶⣦⣤⣤⣀⣀⣀⣀⠀⣿⣿⣿⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⣿⣿⣿⢀⣿⣿⣿⣾⣿⣿⣇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⠀⣿⣿⣿⣷⣶⡆⣿⣿⣿⣤⣿⣿⡿⢸⣿⣿⣿⠛⣿⣿⣿⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣉⣉⣉⣹⣿⣿⣿⣿⣖⣛⣛⣛⣀⣛⣛⣛⣛⣛⣣⣌⠙⠿⠿⠟⠋⠀⠘⠛⠛⠛⠀⠛⠛⠛⠃⠀⠛⠛⠛⠀⢸⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⣀⡀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⡟⢓⣠⡀⠀⠀⢠⣼⣶⡆⠂⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣷⣾⣿⣯⣅⡀⠈⠀⠉⠁⠀⠀⠀⠀⢀⡀⢈⡙⢻⣿⣿⣿⣿⣹⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⢀⠀⠀⠀⠀⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣄⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⠿⠛⠋⠉⠉⠉⠙⠛⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣿⣄⠀⠀⠀⢻⣷⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⡾⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣿⣿⠀⠀⠀⠸⣿⣦⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠈⠉⠉⠁⠉⠉⠉⠉⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠈⠉⠉⠀⠀⠀⠀⠏⠉⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⢀⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠻⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣤⣤⣾⠤⠄⠄⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠈⠃

⣿⡏⢁⣀⣠⣤⡴⢶⣆⣴⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣧⣴⣾⣿⡓⠀⣠⣄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⣀⣠⣄⢀⠀⠤⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣤⣤⣤⣤⡀⠀⠀⠀⠀⠠⢤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠈⠁⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀

[32A⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣤⣤⣤⣤⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣤⣤⠤⢤⣤⣤⣤⣤⣤⣤⣿⣿⣤⡤⠤⢤⡤⣤⠤⢤⣤⣤⣤⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠓⠒⠛⠛⠓⠚⠂⠀⠀⠐⠒⠀⠀⠀⠒⠒⠒⠒⠀⠐⠒⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⣿⣿⣿⠀⢸⣿⣿⢻⣿⣿⡀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠿⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⣿⣿⣿⠀⣾⣿⣿⢸⣿⣿⡇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢤⣶⡄⠀⠀⠀⠀⠀⠀

⣶⣶⣶⣶⣾⣷⣶⣾⣿⣶⣶⣶⣶⣦⣤⣤⣄⣀⣀⣀⠀⣿⣿⣿⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⣿⣿⣿⢀⣿⣿⣿⣾⣿⣿⣇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣍⣉⣉⣹⣿⣿⣿⣿⣖⣛⣛⣛⣀⣛⣛⣛⣛⣛⣣⣌⠙⠿⠿⠟⠋⠀⠘⠛⠛⠛⠀⠛⠛⠛⠃⠀⠛⠛⠛⠀⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⣀⡀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⢓⣠⡀⠀⠀⢠⣤⣶⡆⠂⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣶⣷⣾⣿⣿⣄⡀⠈⠀⠉⠁⠀⠀⠀⠀⢀⡀⢈⡙⢻⣿⣿⣿⣯⣹⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣤⣄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⠿⠛⠋⠈⠉⠉⠙⠛⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣿⣿⣄⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⡾⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣫⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠉⠉⠁⠉⠉⠉⠈⠉⠉⠀⠉⠉⠉⠉⠀⠈⠉⠉⠉⠉⠈⠈⠉⠉⠉⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⢠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠝⠫⠿⠻⠿⠿⠿⢿⡿⢿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣠⣤⣴⠱⠀⠤⠤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠈⠃

⣿⠟⢁⣀⣠⣤⠴⢶⣆⣰⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣼⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣴⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⣿⣿⣴⣾⡿⡓⠀⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣜⣟⣂⣠⡀⠀⠠⠤⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣤⣴⣤⡀⠀⠀⠀⠀⠀⣠⣤⣀⣀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⠈⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀

[32A⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣤⣤⣤⣤⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣤⣤⡤⠤⣤⡤⠤⠤⡤⠤⠿⠿⠤⠤⠤⠤⣤⠤⠤⠤⢤⠤⢤⢼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠓⠒⠛⠛⠛⠒⠂⠀⠀⠐⠒⠀⠀⠀⠚⠒⠒⠒⠒⠐⠒⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣷⣶⣶⣶⣾⣟⣶⣾⣿⣶⣶⣶⣶⣶⣤⣤⣄⣀⣀⣀⠀⣿⣿⣿⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⣿⣿⣿⢀⣿⣿⣿⣾⣿⣿⣇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⠀⣿⣿⣿⣷⣶⡆⣿⣿⣿⣤⣿⣿⡿⢸⣿⣿⣿⠛⣿⣿⣿⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣍⣉⣉⣭⣿⣿⣿⣿⣖⣛⣛⣛⣀⣛⣛⣛⣛⣛⣣⡈⠙⠿⠿⠟⠋⠀⠘⠛⠛⠛⠀⠛⠛⠛⠃⠀⠛⠛⠛⣰⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⢀⡀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣽⣿⡿⢃⣠⠀⠀⠀⢀⡤⣤⡄⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢰⣆⡀⠀⠀⠀⠀⠀⢠⣶⣶⣾⣿⣿⣿⣿⣿⣾⣿⣿⣦⡀⠈⠀⠉⠁⠀⠀⠀⠀⢀⡀⢈⡙⠹⣿⣿⣿⣯⣽⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⠿⠛⠁⠀⠉⠉⠙⠛⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠜⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⢛⣋⣙⠿⢿⣿⣿⣿⠿⠿⣛⣋⣻⣿⣿⢿⣿⡷⠀⠀⣼⣿⣿⣿⣿⡆⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠈⠀⠀⠀⠁⠉⠁⠀⠀⠉⠀⠉⠁⠀⠀⠁⠁⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⢠⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠛⠿⠻⠿⠿⠿⠿⢿⢿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣀⣤⡴⢀⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠈⠃

⣟⠏⢀⣀⣤⡤⠤⠤⣄⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠤⣅⣾⣶⣶⣾⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⣿⣥⣴⣶⡟⠃⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣬⣛⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣬⣅⡀⠀⠀⠀⠀⠀⢀⣤⣠⡀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀

[32A⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣤⣤⣤⣤⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⣤⣤⡤⡤⣤⣤⣤⣤⣤⢤⡿⣿⡤⠤⠤⢤⣤⠤⣤⣤⣤⣤⣤⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠓⠚⠛⠛⠓⠛⠂⠀⠀⠐⠚⠒⠓⠚⠚⠓⠓⠛⠚⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⠀⣿⣿⣿⣷⣶⡆⣿⣿⣿⣤⣿⣿⡿⢸⣿⣿⣿⠛⣿⣿⣿⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠲⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⣉⣉⣩⣿⣿⣿⣿⣖⣛⣛⣛⣀⣛⣛⣛⣛⣛⣣⣌⡙⠿⠿⠟⠋⠀⠘⠛⠛⠛⠀⠛⠛⠛⠃⢀⠛⠛⠛⠀⠀⠈⠑⠀⠀⠀⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⢀⡀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣷⣤⣤⣤⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢀⡽⣶⡇⠀⠀⠀⠠⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢠⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠈⠀⠉⠁⠀⠀⠀⠀⠀⡀⢀⡛⠹⣿⣿⣿⣿⣹⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⣿⣿⣿⣿⣿⣿⣦⣤⣄⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⠿⠛⠉⠈⠉⠉⠙⠛⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⡾⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⣰⣶⣾⣿⣿⣿⣿⣟⣿⠿⣿⣿⣿⣿⠿⢿⣿⣋⣿⣿⣿⣿⡇⠀⠉⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠉⠁⠀⠈⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠈⠉⠉⠉⠉⠉⠙⠁⠀⠀⠀⠿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⢠⣄⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠈⠻⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣄⣤⣦⠥⢤⠤⢤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠙⡁⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠘⠃

⣟⣏⣀⣀⣤⣤⣶⢶⣆⣴⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢮⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣯⣴⣿⣿⣿⣿⣵⣴⣶⡿⠓⠀⣀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⣟⣃⣀⡀⠀⠠⡀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣬⣄⡀⠀⠀⠀⠀⠀⣤⣤⣀⡄⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⠈⠁⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀

⣤⣤⣤⣤⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⣤⣤⣤⡤⣤⣤⢤⣤⡤⢤⡿⣿⡤⠤⡤⢤⡤⡤⡤⣤⣤⣤⣤⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠓⠒⠛⠛⠛⠓⠂⠀⠀⠐⠛⠒⠓⠒⠛⠓⠒⠒⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⣉⣉⣭⣿⣿⣿⣿⣖⣛⣛⣛⣀⣛⣛⣛⣛⣛⣣⣌⠙⠿⠿⠟⣋⡀⠘⠛⠛⠛⠀⠛⠛⠛⠃⣄⡛⠛⠛⠀⠻⣿⣷⠆⠀⠀⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⢀⡀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠿⠛⣀⡀⠀⠀⢀⡽⣶⡇⠀⠀⠀⠠⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢹⣿⣿⣦⠀⠀⠀⣾⣿⣿⣅⡀⠈⠀⠉⠁⠀⠀⠀⠀⠀⡀⢈⡙⠹⣿⣿⣿⣿⣹⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⠿⠛⠋⠉⠉⠉⠙⠛⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⡾⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⣰⣶⣾⣿⣿⣿⣿⣿⣽⠿⣿⣿⣿⣿⠿⢿⣿⣋⣿⣿⡿⠇⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠉⠁⠀⠈⠉⠉⠉⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⣽⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⢠⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠿⠿⠿⢿⣿⢿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣤⣤⣖⠠⢤⡀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠙⠋⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠈⠃

⣿⣯⣀⣀⣠⣤⠴⢶⣆⣰⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣯⣴⣿⣿⣿⣿⣧⣴⣶⣿⠗⠀⡀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣸⣟⣀⣀⡠⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣬⣅⡀⠀⠀⠀⠀⠀⢠⣤⣠⣄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⠿⠿⠿⠿⠿⠿⠿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠌⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀

[32A⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣤⣤⣤⣤⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⣤⣤⡤⠤⣤⡤⠤⠤⠤⠤⠿⠿⠤⠤⠤⠤⡤⠤⠤⢤⡤⣤⣤⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠛⠋⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠓⠒⠛⠛⠛⠓⠂⠀⠀⠐⠒⠂⠀⠐⠓⠒⠒⠒⠚⠚⠚⠓⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣷⣶⣶⣶⣾⣏⣶⣾⣿⣶⣶⣶⣶⣶⣤⣤⣤⣀⣀⣀⠀⣿⣿⣿⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⣿⣿⣿⢀⣿⣿⣿⣾⣿⣿⣇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⠀⣿⣿⣿⣷⣶⡆⣿⣿⣿⣤⣿⣿⡿⢸⣿⣿⣿⠛⣿⣿⣿⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠺⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⣉⣉⣭⣿⣿⣿⣿⣖⣛⣛⣛⣀⣛⣛⣛⣛⣛⣣⡌⠙⠿⠿⠟⣋⣀⣘⣛⠛⠛⠀⠛⠛⠛⠃⠀⠛⠛⠛⣰⣿⣿⣷⠆⠀⠀⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠛⣀⣄⠀⠀⢠⡽⣶⡇⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣾⣿⣿⣅⣀⠈⠀⠉⠁⠀⠀⠀⠀⠀⡀⢀⡙⠹⣿⣿⣿⣿⣩⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⠟⠛⠃⠀⠉⠉⠙⠛⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣏⣫⣻⣏⣹⠿⢿⣿⣿⣿⠿⠿⢛⠋⣿⡛⠋⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠉⠉⠉⠀⠀⠁⠀⠀⠁⠉⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠈⠁⠀⠀⠀⠀⢹⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⢠⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢝⡛⣿⠿⠟⠿⡿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣀⣤⡦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠉⠈⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠃

⣿⡇⢀⣀⣤⠤⠤⠤⣆⣰⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢤⣿⣶⣶⣶⣾⣿⡿⣿⣿⣿⣿⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣶⣤⣿⣿⣿⣿⣥⣴⣶⡾⠓⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣷⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣽⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣅⣀⠀⠀⠀⠀⠀⠀⣤⣠⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⡿⠿⠿⠿⠿⠶⠿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣤⣤⣤⣤⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⣤⣤⠤⠤⣤⡤⠤⠤⠤⢤⠿⠿⠤⠤⠤⠤⡤⢤⠤⢤⣤⡤⢤⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠛⠋⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠒⠒⠛⠛⠚⠒⠂⠀⠀⠐⠒⠂⠀⠀⠒⠒⠒⠒⠀⠐⠐⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⠀⣿⣿⣿⣷⣶⡆⣿⣿⣿⣤⣿⣿⡿⢸⣿⣿⣿⠛⣿⣿⣿⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣍⣉⣉⣩⣿⣿⣿⣿⣖⣛⣛⣛⣀⣛⣛⣛⣛⡛⠃⠈⠙⠿⠿⠟⣋⣀⡘⠛⠛⠛⠀⠛⠛⠛⣣⣀⠛⠛⠛⠀⠸⣿⣿⠆⠀⠀⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⡀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣸⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⣸⣿⣿⣿⣷⣤⡀⠀⠘⠛⣠⣄⠀⠀⢀⡽⣶⡇⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⠆⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣷⣆⠀⠈⢻⣿⣥⡀⠈⠀⠉⠁⠀⠀⠀⠀⠀⡀⢀⡙⠹⣿⣿⣿⣿⣩⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢰⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⠟⠛⠉⠈⠉⠉⠉⠛⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠈⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠾⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣏⠉⣛⣋⣹⠿⢿⣿⣿⣿⠿⠟⢙⠉⠀⠀⠀⣌⣿⣿⣿⣿⡿⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠉⠉⠉⠀⠈⠀⠀⠀⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠉⠋⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⢿⣿⡿⠿⠿⠿⣿⠿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣀⣤⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠙⠈⠋⠛⠛⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠃

⣿⡇⢀⣀⣤⡤⠤⠤⣄⣰⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢤⣭⣶⣶⣶⣿⣿⠿⣿⣿⣿⣧⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣾⣤⣿⣿⣿⣿⣥⣤⣦⡎⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⡿⠿⠿⠿⠷⠶⠿⠷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣤⣤⣤⣤⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⣤⣤⢤⠤⣤⣤⠤⠤⠤⠤⠿⠿⢤⠤⠤⢤⡤⠤⠤⠤⣤⠤⢤⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠒⠒⠛⠛⠛⠒⠂⠀⠀⠐⠒⠀⠀⠀⠒⠒⠒⠒⠒⠀⠐⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣷⣶⣶⣶⣶⣗⣶⣾⣿⣶⣶⣶⣶⣦⣤⣄⣀⣀⣀⣀⠀⣿⣿⣿⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⣿⣿⣿⢀⣿⣿⣿⣾⣿⣿⣇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣍⣉⣉⣩⣿⣿⣿⣿⣖⣛⣛⣛⣀⣛⣛⡛⠛⠛⠃⣈⣙⠿⠿⠟⠋⠀⠘⠛⠛⠛⠀⠛⠛⢛⣣⣀⡛⠛⠛⠀⠀⠙⠿⠆⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⢀⠀⠀⢀⡀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣠⣿⣿⣿⣿⠀⠀⢀⡄⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⢠⡽⣶⡇⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣶⣶⡾⠁⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡀⠀⠀⢡⣀⠈⠀⠉⠁⠀⠀⠀⠀⠀⡀⢈⡙⠹⣿⣿⣿⣯⣩⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⠓⠂⠀⣸⣿⣦⣤⣄⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⠟⠛⠋⠀⠉⠉⠉⠛⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⢻⣿⣿⣿⣿⣿⡿⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠾⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣍⡉⣿⣋⣙⠿⢿⣿⣿⣿⠁⠀⠀⠀⠌⢟⠿⣿⣿⠏⠁⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠀⠉⠉⠁⠀⠀⠀⠀⠀⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠰⣾⣿⣿⠿⠿⠿⣿⢿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣀⣤⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⠈⠉⠋⠛⣛⠀⠀⠀⠀⠀⠀⠀⠘⠛⠂⠈⠁

⣯⠏⢀⣀⣠⡤⠤⠤⢄⣰⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢤⣭⣶⣶⣶⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣥⣤⣠⡏⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣐⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣤⣤⣅⡀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣾⡿⠿⠿⠿⠷⠿⠿⠷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀

[32A⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⣤⣤⣤⣤⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⣤⣤⣤⡤⣤⣤⣤⢤⠤⢤⠿⢿⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⣤⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠓⠛⠛⠛⠓⠂⠀⠀⠐⠚⠂⠀⠐⠚⠛⠒⠚⠛⠛⠚⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣷⣶⣶⣶⣾⣏⣶⣾⣿⣶⣶⣶⣶⣶⣤⣤⣄⣀⣀⣀⠀⣿⣿⣿⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⣿⣿⣿⢀⣿⣿⣿⣾⣿⣿⣇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⣉⣉⣭⣿⣿⣿⣿⣖⣛⣛⢛⡀⠛⠛⠛⠛⣛⣣⠈⠙⠿⠿⠟⠋⠀⠘⠛⠛⠛⠀⠛⠛⠛⠃⠀⠛⠛⠛⢰⣿⣿⣿⠆⠀⠀⠉⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⣿⣿⠀⠀⠀⢀⣀⣤⠔⠀⠀⠀⠀⠀⢀⣼⣿⣿⣦⣤⡀⠀⠈⢻⡿⢛⣠⣄⠀⠀⢠⡽⣶⡇⠂⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⠋⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣷⣄⠀⠀⠹⣾⣿⣿⣧⣀⠈⠀⠉⠁⠀⠀⠀⠀⢀⣀⢨⡙⢹⣿⣿⣿⣯⣭⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣄⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⠿⠛⠋⠈⠉⠉⠉⠛⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⣰⣶⣾⣿⣿⣟⣿⣏⣿⢿⣿⣿⣿⣿⠿⠿⣿⠻⠛⠉⠉⠁⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠈⠁⠀⠈⠉⠉⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠉⠛⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⢠⣄⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠴⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣀⣤⣴⣶⣴⠤⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠐⠉⠋⠘⠛⠋⠛⢛⣿⡇⠀⠀⠀⠀⠀⠀⠘⠛⠁⠈⠃

⣿⡏⢁⣥⣤⣤⡶⠶⣆⣴⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠘⠉⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣤⣿⣶⣶⣾⣿⣿⡿⣻⣿⣿⣿⣤⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣾⣶⣿⣿⣿⣿⣥⣤⣤⣿⠃⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣨⣽⣄⣀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣬⣥⣄⠀⠀⠀⠀⠀⢀⣤⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⡿⠿⠿⠿⠿⠿⠿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀

[32A⠀⠀⠀⠀⠀⣄⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣿⠬⠭⡖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣿⠀⠠⢁⡀⠀⡀⣄⠀⠀⠀⠀⠠⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣿⠀⠂⠐⠀⠀⠫⠑⣀⣀⣀⣀⣀⡐⡀⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣶⣤⣷⣦⣤⡿⠀⠉⠐⣨⣹⣀⠀⡇⠀⠀⠀⠀⡇⠀⢛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⣤⣤⣤⣤⣥⣬⣭⣭⣬⣤⣿⢿⣤⣬⣭⣿⣾⣿⣯⣭⣿⣿⣿⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣷⣶⣾⣶⣶⣿⣷⡆⠅⠀⠀⠀⠀⡅⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⡄⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠀⠀⠐⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡷⣈⠀⢀⡀⠔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣦⡂⢐⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢉⣙⣿⣿⡟⣿⣿⣦⠘⢿⣿⣿⡿⠉⣿⡍⠉⢉⡛⠛⣿⡍⢩⣿⡟⢿⣿⡏⠁⡿⢃⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣾⣿⢁⠸⣿⣿⣇⠈⢿⡿⠁⠀⢿⡇⠀⢸⡇⠀⣿⡇⢸⣿⡇⢀⠻⡇⠀⠇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⢿⡇⣘⡀⢹⣿⢹⣧⠈⠃⡄⠀⠸⡇⠀⢰⣴⣾⢣⣤⣤⣤⠀⣤⣤⣤⡄⠇⠘⢁⣤⣴⣶⣤⣄⡀⠀⠀⣤⣤⣤⣤⣄⠀⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣦⣭⣾⣥⣿⣷⣤⣿⣼⣿⣦⣾⣿⠀⠀⠃⢀⣘⣿⣿⠈⣿⣿⣿⠀⣿⣿⣿⡇⠘⢀⣿⣿⣿⠛⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⠀⠿⠿⣿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⠐⣿⣿⣿⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⣿⣿⣿⠀⢸⣿⣿⢿⣿⣿⡀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢘⣿⣿⣿⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⣿⣿⣿⢀⣿⣿⣿⣾⣿⣿⣇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠨⣿⣿⣿⠀⣿⣿⣿⣷⣶⡎⣿⣿⣿⣤⣿⣿⡿⢸⣿⣿⣿⠛⣿⣿⣿⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠛⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢜⣛⠛⢛⣀⣛⣛⠛⠛⠛⠃⠈⠙⠿⠿⠟⠋⠁⠘⠛⠛⠛⠀⠛⠛⠛⠃⠀⠛⠛⢛⣲⣿⣿⣿⠆⠀⠀⠉⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⢿⣿⣦⣀⣀⣀⣀⣀⣠⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⣤⠀⠀⠀⠛⣿⣿⣿⢛⣢⣄⡀⠀⢠⡼⣿⡏⠁⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣽⢧⡿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⠿⠉⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣷⣦⡀⠀⢸⣿⣿⣿⣿⣿⣷⣄⠈⠁⠉⠁⠀⠀⠀⠀⠀⣄⣨⣉⢙⣿⣿⣿⣿⣭⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣆⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣇⡿⣾⣹⣹⢫⣧⣷⣵⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠉⠉⠉⠈⠙⠛⠛⠛⠻⣿⡿⠿⠿⣿⣿⣿⣿⣿⡇⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇

⠀⠀⠀⠈⠉⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⠛⠃⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠛⠛⠛⠛⣻⣿⣿⣿⣿⠀⠀⠀⠀⢀⠁⠘⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠙⠝⠻⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⢾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠰⣟⡟⠂⠁⠀⠀⠀⠀⢀⡀⣀⣀⠀⠀⠀

⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣧⣤⣴⣶⣾⣄⣀⣀⡀⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣗⣷⢦⡇⠀⠀⣠⣄⣅⣀⠀⠀⠀⠀⠀

⠀⠸⠿⠻⢻⡿⠿⠿⡿⠣⠺⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠼⠝⠿⠿⠇⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀

[32A⠀⠀⠀⠀⠀⣄⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣿⠼⠯⣷⠗⠀⠁⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢿⣼⣯⣭⡧⣠⡀⣔⠌⠀⠀⠀⠠⠜⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢺⠞⣾⡶⠗⡡⠯⠑⣀⣀⣀⣀⣀⡀⡀⢖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣦⣤⣿⣶⣥⣾⠯⡿⢝⣭⣻⣅⠀⡇⠀⠀⠀⠀⡇⠁⢛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⣤⣤⣥⣬⣭⣭⣭⣭⣥⣥⣿⣿⣧⣭⣯⣯⣿⣿⣿⣽⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣶⣿⣶⣶⣿⣷⡆⠇⠀⠀⠀⠀⡅⣷⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠐⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣈⠀⢀⡀⠔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡆⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢋⣝⣿⣿⡟⣿⣿⣦⠙⢿⣿⣿⡿⠉⣿⡍⠉⢙⡛⠛⣿⡍⢩⣿⡟⢿⣿⡯⠉⡿⢃⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⣿⢁⠸⣿⣿⣇⠈⢿⡿⠁⠀⢿⡇⠀⢸⡇⠀⣿⡇⢸⣿⡇⢀⠻⡇⠀⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⡇⣘⡀⢹⣿⢹⣧⠈⠃⡄⠀⢸⡇⠀⢰⣶⣾⢣⣤⣤⣤⠀⣤⣤⣤⡄⠇⠘⢁⣤⣴⣶⣤⣄⡀⠀⢀⣤⣤⣤⣤⣄⠀⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣦⣭⣾⣥⣿⣷⣤⣿⣼⣿⣧⣾⣿⡀⠀⢃⣀⣘⣿⣿⢸⣿⣿⣿⠀⣿⣿⣿⡇⡿⢠⣿⣿⣿⠛⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⠀⠿⠿⣿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⢨⣿⣿⣿⠀⣿⣿⣿⡇⡇⢸⣿⣿⣿⠀⣿⣿⣿⠀⢸⣿⣿⢿⣿⣿⡀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣿⠀⣿⣿⣿⡇⠃⢸⣿⣿⣿⠀⣿⣿⣿⢀⣿⣿⣿⣾⣿⣿⣇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣿⣷⣶⡎⣿⣿⣿⣤⣿⣿⡿⢸⣿⣿⣿⠛⣿⣿⣿⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠚⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣛⡛⢛⣀⣛⣛⡛⠛⠛⠃⠈⠛⠿⠿⠟⠋⠁⠘⠛⠛⠛⠀⠛⠛⠛⠃⢆⣛⣛⣛⣺⣿⣿⣿⠇⠀⠀⠉⠉⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣛⣣⣄⡀⠀⠀⡼⣿⡏⠁⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠁⠉⠁⠀⠀⠀⠀⠀⣀⣀⣙⢙⣿⣿⣿⣿⣭⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣴⣿⣿⣿⣿⣿⡀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣦⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠇⢀⣤⣤⣤⣤⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇

⢿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣇⡿⣾⣹⣹⢫⣧⣷⣱⣿⣿⣿⣿⣿⢿⣷⣿⣿⣿⣿⡟⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⢠⠈⠛⠛⠻⠛⢿⣿⣿⣿⣿⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇

⠀⠀⠀⠈⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠉⠀⠀⠀⠀⠠⠾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣛⠋⠛⠛⠛⠛⠻⣿⣿⣿⣿⣿⡁⠙⠁⠃⢠⡁⠘⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠴⢦⣟⡿⠻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡩⡐⠛⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⠻⠋⢱⣿⣿⣿⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠗⠾⠗⠆⢿⣿⣿⣿⠗⠅⠀⠀⠀⢀⣠⣀⣀⣀⠀⠀⠀

⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣬⣿⣶⣿⣧⣤⣤⣄⣠⡀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣷⣾⣀⢤⣤⣤⣭⣄⠀⠁⠀⠀⠀

⠀⠾⠿⠿⢻⡿⠿⠿⡿⠣⠻⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⡿⠿⠿⣿⡿⠿⠿⠿⠷⠶⠶⠦⠦⠤⠴⠶⠅⠴⠴⠤⠦⠴⠦⠿⠿⠿⠿⠿⠷⠇⠈⠈⠋⠉⠉⠉⠀⠄⠀⠀⠀

[32A⠀⠀⠀⠀⠀⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣿⠭⡿⣳⡆⠈⡁⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢿⣽⣯⢉⣥⢼⣈⣕⢌⠀⠀⠀⠠⡜⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢸⠿⡾⠶⢏⡡⠯⠑⣀⣀⣀⣀⣀⡒⡒⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣷⣵⣿⣷⣷⣿⠾⠿⢕⣭⣻⣁⠀⡇⠀⠀⠀⠀⡇⠁⢛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣤⣤⣤⣥⣤⣤⣥⣭⣬⣧⣿⣿⣧⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣽⣿⣿⣿⣿⣶⣿⣾⣶⣿⣷⡆⡇⠀⠀⠀⠀⡅⣷⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠐⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣷⣈⠀⢀⡀⠔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢉⣝⣿⣿⡟⣿⣿⣦⠙⢿⣿⣿⡿⠉⣿⡍⠉⢩⡛⠛⣿⡍⢩⣿⡟⢿⣿⡏⠉⡿⢃⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⡇⣘⡀⢹⣿⢻⣧⠈⠃⡄⠀⢸⡇⠀⢰⣶⣾⢫⣤⣤⣤⠀⣤⣤⣤⡄⡇⠘⢁⣤⣴⣶⣤⣄⡀⠀⠀⣤⣤⣤⣤⣄⠀⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣦⣭⣾⣥⣿⣷⣤⣿⣼⣿⣦⣾⣿⡀⠀⠃⢀⣘⣿⣿⢸⣿⣿⣿⠀⣿⣿⣿⡇⡟⢠⣿⣿⣿⠛⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⠀⠿⠿⣿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣿⡇⠃⢸⣿⣿⣿⠀⣿⣿⣿⠀⢸⣿⣿⢿⣿⣿⡀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⣿⣿⣿⢀⣿⣿⣿⣾⣿⣿⣇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣿⣷⣶⡎⣿⣿⣿⣤⣿⣿⡿⢸⣿⣿⣿⠛⣿⣿⣿⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠚⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣛⡛⢛⣀⣛⣛⡛⠛⠛⠃⠈⠙⠿⠿⠟⠋⠁⠘⠛⠛⠛⠀⠛⠛⠛⠃⠀⢛⣛⣛⣺⣿⣿⣿⡇⠀⠀⠈⠉⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡛⠻⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣟⣣⣤⡀⠀⠀⡼⣿⡏⠁⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠁⣰⡄⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠁⠉⠁⠀⠀⠀⠀⠀⣀⣀⣉⢙⣿⣿⣿⣿⣭⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡯⢜⣤⣣⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡇⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣦⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⢿⣿⣿⣿⣷⣿⣷⣶⣶⣶⣾⣿⣿⣿⣿⣧⣄⠀⠀⣤⣦⣤⣤⣤⣤⣤⣤⣴⣿⣿⣿⣷⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧

⢿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣇⡿⣾⣹⣹⢫⣧⣷⣽⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠈⠉⠉⠉⠉⠛⠛⠻⠿⢻⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧

⠀⠀⠀⠈⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣛⢝⡻⠻⠛⠟⠛⢻⣿⣿⣿⣿⠃⠙⠫⠛⢩⠁⠘⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠾⢿⠿⠿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠈⣀⠙⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡐⡑⠋⢲⣾⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠀⠀⠀⣀⡀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⠲⠻⠠⣳⣿⣿⣿⡟⠅⠀⠀⠀⢀⣀⡄⣠⡀⠀⠀⠀

⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣶⣾⣷⣶⣿⣥⣤⣤⣤⣤⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡭⣿⣿⣿⣷⣾⡀⣠⣤⣤⣬⣄⠀⠁⠀⠀⠀

⠀⠾⠿⠿⢻⡿⠿⠿⡿⠣⠻⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⡿⠿⠿⠿⢿⠿⠿⠿⠷⠶⠶⠦⠶⠤⠴⠾⠤⠁⠤⠤⠦⠤⠶⠼⠿⠿⠿⠿⠿⠏⠀⠈⠹⠋⠋⠉⠀⠄⠀⠀⠀

[32A⠀⠀⠀⠀⠀⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣿⠭⠝⣳⠆⠀⡀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢽⣽⣯⢉⣡⣮⣈⣔⠌⠀⠀⠀⠀⠜⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢸⡿⡾⠶⢏⡹⠯⠑⣀⣀⣀⣀⣀⡐⡂⢖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣷⣷⣾⠯⡿⢝⣭⣻⣉⠀⡇⠀⠀⠀⠀⡇⠁⢛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣤⣤⣤⣬⣥⣥⣭⣬⣿⣧⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣽⣿⣿⣿⣿⣶⣿⣾⣶⣿⣷⡆⡇⠀⠀⠀⠀⡇⣷⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠁⠀⠐⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢋⣝⣿⣿⡟⣿⣿⣦⠙⢿⣿⣿⡿⠉⣿⡍⠉⢩⡛⠛⣿⡍⢩⣿⡟⢿⣿⡯⠉⡿⢃⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⡇⣘⡀⢹⣿⢻⣧⠈⠃⡄⠀⢸⡇⠀⢰⣶⣾⢫⣤⣤⣤⠀⣤⣤⣤⡄⡇⠘⢁⣤⣴⣶⣤⣄⡀⠀⢀⣤⣤⣤⣤⣄⠀⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣦⣭⣾⣥⣿⣷⣤⣿⣼⣿⣦⣾⣿⠀⠀⢃⣀⣘⣿⣿⢘⣿⣿⣿⠀⣿⣿⣿⡇⡿⢠⣿⣿⣿⠛⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⠀⠿⠿⣿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣿⡇⠇⢸⣿⣿⣿⠀⣿⣿⣿⠀⢸⣿⣿⢿⣿⣿⡀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣿⡇⠇⢸⣿⣿⣿⠀⣿⣿⣿⢀⣿⣿⣿⣾⣿⣿⣇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⣿⠀⣿⣿⣿⣷⣶⡎⣿⣿⣿⣤⣿⣿⡿⢸⣿⣿⣿⠛⣿⣿⣿⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠚⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣛⡛⢛⣀⣛⣛⠛⠛⠛⠣⣌⠛⠿⠿⠟⠋⠁⠘⠛⠛⠛⠀⠛⠛⠛⠃⠀⢛⣛⣛⣺⣿⣿⣿⡧⠀⠀⠈⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡛⢹⠋⠀⠝⠛⠃⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣟⣣⣤⡀⠀⠀⡼⣿⡏⠁⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣱⢇⡿⣿⣿⣿⣿⣿⣿⣿⣹⣁⠁⣠⣬⡶⠆⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠁⠉⠁⠀⠀⠀⠀⠀⣀⣀⣉⢙⣿⣿⣿⣿⣭⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡯⣜⣤⡿⠋⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣧⣠⣽⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⢿⣿⣿⣿⣿⣿⣷⣶⣿⣷⣾⣿⣿⣿⣿⡄⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣧⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇

⢿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣇⡿⣾⣹⣹⢫⣷⣷⣽⣿⣿⣿⣿⣿⣿⣇⣀⠀⠙⣿⣿⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠇⠛⠉⠉⠉⠋⠉⠉⠙⠛⠻⠟⢿⣿⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇

⠀⠀⠀⠈⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣛⡋⣿⠛⢟⠟⠛⣻⣿⣿⣿⣿⠁⠙⠫⠛⢩⠁⠘⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⢾⣿⢿⢿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⣠⠹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡐⠓⠓⣺⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⠀⣀⡀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠶⠿⠠⢾⣿⣿⣿⡟⠅⠀⠀⡀⠀⣀⡀⣠⡀⠀⠀⠀

⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣷⣶⣿⣥⣤⣤⣤⣤⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣗⣾⠠⢤⣤⣤⣭⣄⠀⠀⠀⠀⠀

⠀⠾⠿⠿⢻⡿⠿⠿⡿⠣⠻⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⠿⣿⠿⢿⢿⠿⠿⠷⠶⠶⠦⠶⠴⠶⠾⠥⠽⠤⠤⠦⠴⠶⠾⠿⠿⠿⠿⠿⠏⠉⠉⠹⠩⠋⠉⠀⠄⠀⠀⠀

[32A⠀⠀⠀⠀⠀⣤⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢿⠽⡏⢳⠆⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢼⣿⣿⣋⣡⣴⣂⣄⢈⠀⠀⠀⠠⡜⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢸⡿⡾⠷⢏⡡⠯⠑⣀⣀⣀⣀⣐⡒⡂⢖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣷⣾⠯⣿⢽⣩⣻⣁⠀⡇⠀⠀⠀⠀⡇⡂⢛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣤⣤⣬⣭⣤⣦⣭⣭⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣭⣭⣿⣿⣿⣿⣶⣿⣾⣶⣿⣷⡆⠇⠀⠀⠀⠀⡇⣷⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⡄⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠃⠀⠐⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡷⣈⠀⢀⡀⢔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢉⣝⣿⣿⡟⣿⣿⣦⠙⢿⣿⣿⡿⠉⣿⡍⠉⢉⡛⠛⣿⡍⢩⣿⡟⢿⣿⡏⠉⡿⢃⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⡇⣘⡀⢹⣿⢻⣧⠈⠃⡄⠀⢸⡇⠀⢰⣶⣾⢣⣤⣤⣤⠀⣤⣤⣤⡄⡇⠘⢁⣤⣴⣶⣤⣄⡀⠀⢀⣤⣤⣤⣤⣄⠀⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣦⣭⣾⣥⣿⣷⣤⣿⣼⣿⣧⣾⣿⠀⠀⠃⣀⣘⣿⣿⢸⣿⣿⣿⠀⣿⣿⣿⡇⡿⢠⣿⣿⣿⠛⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⠀⠿⠿⣿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⢨⣿⣿⣿⠀⣿⣿⣿⡇⠇⢸⣿⣿⣿⠀⣿⣿⣿⠀⢸⣿⣿⢿⣿⣿⡀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢨⣿⣿⣿⠀⣿⣿⣿⡇⠁⢸⣿⣿⣿⠀⣿⣿⣿⠀⣾⣿⣿⢸⣿⣿⡇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⣿⣿⣿⢀⣿⣿⣿⣾⣿⣿⣇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠰⣿⣿⣿⠀⣿⣿⣿⣷⣶⡎⣿⣿⣿⣤⣿⣿⡿⢸⣿⣿⣿⠛⣿⣿⣿⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⠀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣛⡛⢛⣀⣛⠛⠛⠛⠛⠣⡌⠙⠿⠿⠟⠋⠁⠘⠛⠛⠛⠀⠛⠛⠛⠃⠀⠛⠛⣛⣺⣿⣿⣿⡷⠀⠀⠈⠉⢀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⡛⢹⠃⠀⠀⣤⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣟⣳⣤⡀⠀⠀⡤⢿⡏⠘⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⡷⣱⢇⡾⣼⢳⠿⣹⠹⡏⢟⢱⣁⠁⣀⡀⠀⠀⠉⠉⠁⠀⠠⠖⠂⠉⠀⠀⢦⣤⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠁⠈⠁⠀⠀⠀⠀⠀⣀⣀⣍⣛⣿⣿⣿⣿⣭⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡫⣜⢤⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣧⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⡆⠠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣷⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣇⡿⣾⣹⣹⢫⣧⣷⣽⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⣰⣶⣿⣿⣿⣿⣷⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⠟⠛⠉⠀⠀⠀⠀⠈⠉⠛⠻⠿⢿⣿⡟⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇

⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣛⡩⣿⠿⠿⠛⠛⣿⣿⣿⣿⣿⡇⠈⠒⠛⢣⡍⠈⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⢾⢿⠿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡊⡀⠘⣿⣿⣿⣿⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⠛⠋⢱⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢄⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⠠⠿⠎⠳⣿⣿⣯⡟⠃⠀⠀⠀⠀⣠⣄⣀⣀⠀⠀⠀

⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣦⣼⣷⣶⣾⣥⣤⣤⣤⣤⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣾⣿⣿⣷⣶⠀⢠⣤⣤⣬⣥⠀⠀⠀⠀⠀

⠀⠾⠿⠿⢻⡿⠿⠿⡿⠣⠻⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⠿⠿⠷⠶⠴⠤⠶⠤⠶⠾⠤⠁⠤⠤⠴⠤⠶⠾⠿⠿⠿⠿⠷⠍⠉⠉⠹⠉⠉⠉⠁⠀⠀⠀⠀

[32A⠀⠀⠀⠀⠀⣤⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢼⡭⠯⢗⠆⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢸⣿⣯⣛⣅⣼⣂⣄⢈⠀⠀⠀⠠⣜⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠁⠀⢸⡿⠾⠶⢏⠠⠯⠑⣀⣀⣀⣀⣀⡒⡂⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣾⠿⣽⢝⣩⣻⣉⠀⡇⠀⠀⠀⠀⡇⡆⢛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣤⣤⣬⣥⣥⣤⣬⣽⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣭⣭⣿⣿⣿⣿⣶⣿⣾⣾⣿⣷⡆⡇⠀⠀⠀⠀⡇⣷⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠃⠀⠐⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣈⠀⢀⡀⠔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢉⣝⣿⣿⡟⣿⣿⣦⠙⢿⣿⣿⡿⠉⣿⡍⠉⢉⡛⠛⣿⡍⢩⣿⡟⢿⣿⡯⠉⡿⢃⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⡇⣘⡀⢹⣿⢻⣧⠈⠃⡄⠀⢸⡇⠀⢰⣶⣾⢣⣤⣤⣤⠀⣤⣤⣤⡄⡇⠘⢁⣤⣴⣶⣤⣄⡀⠀⠀⣤⣤⣤⣤⣄⠀⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣦⣭⣾⣥⣿⣷⣤⣿⣼⣿⣦⣾⣿⠀⠀⠃⣀⣘⣿⣿⢸⣿⣿⣿⠀⣿⣿⣿⡇⡻⢠⣿⣿⣿⠛⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⠀⠿⠿⣿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⢨⣿⣿⣿⠀⣿⣿⣿⡇⠂⢸⣿⣿⣿⠀⣿⣿⣿⠀⢸⣿⣿⢿⣿⣿⡀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢈⣿⣿⣿⠀⣿⣿⣿⡇⡁⢸⣿⣿⣿⠀⣿⣿⣿⠀⣾⣿⣿⢸⣿⣿⡇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⣿⠀⣿⣿⣿⣷⣶⡎⣿⣿⣿⣤⣿⣿⡿⢸⣿⣿⣿⠛⣿⣿⣿⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⠀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣛⡛⢛⣀⣛⣛⡛⡛⢛⣣⣌⡙⠿⠿⠟⠋⠁⠘⠛⠛⠛⠀⠛⠛⠛⠃⠀⠛⠛⢛⣺⣿⣿⣿⡷⠀⠀⠈⠉⢀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠟⠛⠃⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣟⣳⣤⡀⠀⠀⡤⢿⡯⠘⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣹⢇⡿⣾⣿⡿⣹⢻⣟⣿⣻⣛⠿⣸⣉⠀⠀⣀⣆⠤⠀⠀⠀⣀⡴⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣷⣤⠀⠁⠈⠁⠀⠀⠀⠀⠀⣀⣀⣉⣛⣿⣿⣿⣿⣭⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣹⡯⣞⣤⡓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣿⣿⡿⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣧⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⢿⣿⣿⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⣟⣯⡀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⡉⢉⡀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣇⡿⣾⣹⣹⢫⣧⣧⢱⣿⣿⣿⣿⣿⣿⣷⣶⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣾⣿⠀⠉⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠓⠀⠀⠀⠀⠀⠀⠒⠒⠲⠾⠿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣛⣋⣟⠛⠛⠿⠛⣿⣿⣿⣿⣿⡇⠀⠋⠛⢫⡌⠀⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⢾⣿⠿⠿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⣀⠙⣿⣿⣿⡟⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⢛⠋⢰⣾⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠰⠻⠂⢫⢿⣿⣯⡟⠁⠀⠀⠠⠀⣠⡄⣀⣀⠀⠀⠀

⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⣼⣶⣶⣾⣥⣄⣤⣤⣄⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣻⣿⣿⣿⣶⢀⢠⣤⣤⣬⣤⠀⠀⠀⠀⠀

⠀⠾⠿⠿⢻⡿⠿⠿⡿⠣⠻⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠧⠤⠤⠖⠦⠤⠔⠾⠤⠁⠤⠤⠶⠤⠶⠼⠿⠿⠿⠿⠷⠍⠉⠉⠹⠯⠉⠉⠁⠀⠀⠀⠀

[32A⠀⠀⠀⠀⠀⣠⣤⣄⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢸⡿⢟⣗⠆⠀⡀⢔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢸⣟⣫⣋⣣⣮⣂⣄⠀⠀⠀⠀⠀⠜⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠁⠀⢸⣿⣾⢷⢇⣡⠫⠁⣀⣀⣀⣀⣀⡀⡒⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⡿⠿⠑⣩⣻⣁⠀⡇⠀⠀⠀⠀⡇⡂⢛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣭⣭⣯⣿⣿⣿⣶⣾⣶⣶⣿⣷⡆⡇⠀⠀⠀⠀⡇⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠃⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢋⣝⣿⣿⡟⣿⣿⣦⠙⢿⣿⣿⡿⠉⣿⡍⠉⢩⡛⠛⣿⡍⢩⣿⡟⢿⣿⣏⠉⡿⢃⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⣿⢁⠸⣿⣿⣇⠈⢿⡿⠁⠀⣿⡇⠀⢸⡇⠀⣿⡇⢸⣿⡇⢀⠻⡇⠀⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⡇⣘⡀⢹⣿⢹⣧⠈⠃⡄⠀⢸⡇⠀⢰⣶⣾⢫⣤⣤⣤⠀⣤⣤⣤⡄⡇⠘⢁⣤⣴⣶⣤⣄⡀⠀⢀⣤⣤⣤⣤⣄⠀⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣦⣭⣾⣥⣿⣷⣤⣿⣼⣿⣧⣾⣿⠀⠀⢃⣀⣘⣿⣿⢸⣿⣿⣿⠀⣿⣿⣿⡇⣿⢠⣿⣿⣿⠛⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⠀⠿⠿⣿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣿⡇⡏⢸⣿⣿⣿⠀⣿⣿⣿⠀⢸⣿⣿⢿⣿⣿⡀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢰⣿⣿⣿⠀⣿⣿⣿⡇⠁⢸⣿⣿⣿⠀⣿⣿⣿⢀⣿⣿⣿⣾⣿⣿⣇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢨⣿⣿⣿⠀⣿⣿⣿⣷⣶⡎⣿⣿⣿⣤⣿⣿⡿⢸⣿⣿⣿⠛⣿⣿⣿⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⠁⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣛⡛⢛⣀⣛⣛⣛⡛⣛⣣⡈⠛⠿⠿⠟⠋⠁⠘⠛⠛⠛⠀⠛⠛⠛⠃⠀⠛⠛⠛⢺⣿⣿⣿⡷⠀⠀⠈⠉⢁⡀⢀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠿⠛⠋⠁⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣬⠄⠀⠀⠀⠀⠀⠈⣿⣿⣟⣻⣤⡀⠀⠀⡴⢿⡯⠘⠀⠀⠐⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣽⢧⡿⣿⣿⣿⣿⢿⣿⣿⣹⣁⠁⡠⡠⠀⣠⣿⡇⠀⠀⠀⠐⠀⠀⣠⠔⠂⠂⠀⠉⠀⠀⠀⠀⣤⠀⢰⣿⣿⣿⣿⣿⣷⣶⡀⠁⠈⣁⠀⠀⠀⠀⠀⣠⣀⣭⣉⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣹⡫⢞⣤⡋⠂⠈⠛⠛⠋⠀⠀⠀⠐⠚⠁⠀⠀⠀⠀⣀⡀⢰⣿⠿⠟⠃⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⢿⣿⣿⣿⣷⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣭⣭⠈⠁⣄⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣇⡿⣾⡹⣹⢫⣧⣧⢠⣾⣿⣿⣿⣿⣿⣽⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡇⠀⠈⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣶⣶⡶⠒⠀⠀⠀⠀⠐⠀⠀⠐⠒⠻⠻⣿⣿⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣯⣻⠿⢿⢿⣿⣿⣿⣿⣿⣿⡇⠘⠉⠛⠉⡄⠀⠛⠉⠛⠃

⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠾⢿⡿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠸⣋⣅⡘⣿⣿⣿⣿⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢤⣦⡻⢁⣽⣿⣿⣿⡟⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠛⠯⣿⣽⣿⣿⡟⠂⠀⠀⠤⠀⣤⡄⡀⣀⡀⠀⠀

⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣴⣾⣷⣷⣮⣥⣤⣤⣤⣤⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢉⣻⣿⣿⣿⣶⢀⣠⣤⣴⣽⣤⠀⠀⠀⠀⠀

⠀⠿⠿⠿⢻⡿⠿⠿⡿⠣⠻⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⠿⠿⠧⠤⠤⠶⠶⠦⠶⠶⠠⠅⠰⠴⠦⠤⠶⠶⠿⠿⠿⠿⠗⠏⠁⠈⠹⠭⠉⠉⠁⠀⠀⠀⠀

[32A⠀⠀⠀⠀⠀⣤⣠⣄⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢿⠿⢟⢷⢖⠂⡀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢸⣟⣫⣉⡣⢼⣈⣔⠈⠀⠀⠀⠀⠔⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢀⠀⠁⢀⢸⣿⣿⣷⠇⣡⠯⠁⣀⣀⣀⣀⣀⡐⡐⢖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⠯⠟⢐⢨⣻⣊⠀⡇⠀⠀⠀⠀⡇⡀⢛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣭⣭⣽⣿⣿⣿⣶⣾⣶⣶⣿⣷⡆⡇⠀⠀⠀⠀⡇⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠀⠉⠉⠉⠛⠛⠛⠛⠉⠛⠛⠋⠀⠀⠀⠉⠋⠛⠉⠛⠛⠛⠛⠛⠉⠛⠋⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣈⠂⢀⡀⠔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢋⣝⣿⣿⡟⣿⣿⣦⠙⢿⣿⣿⡿⠉⣿⡍⠉⢩⡛⠛⣿⡍⢩⣿⡟⢿⣿⡏⠉⡿⢃⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⡇⣘⡀⢹⣿⢹⣧⠈⠃⡄⠀⠸⡇⠀⢰⣶⣾⢣⣤⣤⣤⠀⣤⣤⣤⡄⡇⠘⢁⣤⣴⣶⣤⣄⡀⠀⢀⣤⣤⣤⣤⣄⠀⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣦⣭⣾⣥⣿⣷⣤⣿⣼⣿⣧⣾⣿⠀⠀⢃⢀⣘⣿⣿⢸⣿⣿⣿⠀⣿⣿⣿⡇⡿⢠⣿⣿⣿⠛⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⠀⠿⠿⣿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⠀⣿⣿⣿⡇⠧⢸⣿⣿⣿⠀⣿⣿⣿⢀⣿⣿⣿⣾⣿⣿⣇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠨⣿⣿⣿⠀⣿⣿⣿⣷⣶⡎⣿⣿⣿⣤⣿⣿⡿⢸⣿⣿⣿⠛⣿⣿⣿⠀⠀⣿⣿⣿⠀⣀⠀⠀⠀⠀⠀⠀⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣛⡛⢛⣀⣛⣛⡛⠛⠛⠃⡈⠛⠿⠿⠟⠋⠁⠘⠛⠛⠛⠀⠛⠛⠛⠃⠀⠛⠛⠛⢺⣿⣿⣿⡟⠀⠀⠈⠉⠁⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡛⡿⡛⠹⢋⢰⡿⠰⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠲⠆⠀⠀⠀⠀⠀⢹⣿⣿⣏⣧⣤⡀⠀⠀⡴⢿⡇⠈⠀⠀⠐⠂⠀⠈⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣽⢷⡿⣿⣿⡿⣻⠻⡏⢾⢱⡁⠁⢠⣬⣾⣿⡨⠇⠀⠀⠀⠀⠀⠀⠐⢁⠀⠀⠀⠚⠅⠀⠀⢠⣶⠀⢸⣿⣿⣿⣿⣿⣷⣶⡀⠁⠈⣁⠀⠀⠀⠀⠀⣠⣤⣭⣭⣻⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠿⣹⣫⣞⣤⣿⣿⣿⣿⢯⠄⠀⠀⠀⢀⠀⠔⠃⠀⠀⠀⠀⠀⠠⣴⣿⡿⠃⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣛⢿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡿⠊⠀⠀⠀⠐⠒⠉⠀⠀⠀⠀⠀⢠⣤⣤⠀⠉⠋⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇

⢿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣇⡿⡼⠱⢱⢂⣧⣷⣵⣿⣿⣿⣿⣿⣿⣝⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣾⣷⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠠⣤⠀⠀⠀⠚⠛⠛⠻⢿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⢽⢟⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠀⠉⠃⡄⠀⠛⠉⠙⠃

⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⢿⣿⢿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⣕⣌⢈⣿⣿⣿⣿⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣴⠻⢁⣵⣿⣿⣿⡟⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠟⠁⢷⣿⣿⣿⡿⠅⠀⠠⡤⠄⣤⡄⡠⣀⠀⠀⠀

⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣶⣮⣷⣶⣤⣥⣤⣤⣤⣤⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣧⣾⣠⣠⣤⣶⣼⣤⠀⠀⠀⠀⠀

⠄⠿⠿⠿⢻⡿⠿⠿⡿⠣⠻⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⠿⡿⣿⡿⠿⠧⠤⠤⠶⠶⠦⠤⠴⠆⠫⠰⠶⠶⠴⠶⠶⠷⠿⠿⠿⠗⠏⠈⠈⠹⠭⠉⠉⠀⠀⠀⠀⠀

[32A⠀⠀⠀⠀⠀⣤⣠⣄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢽⠴⣇⢲⢆⠂⡀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢸⣟⣫⣙⡉⣮⣊⣔⠈⠀⠀⠀⠀⠌⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢸⣿⣿⢷⢟⡡⠿⠁⣀⣀⣀⣀⣀⡐⡀⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⠿⡟⢘⠨⣻⣋⠀⡇⠀⠀⠀⠀⡇⠂⢛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣭⣭⣽⣿⣿⣿⣶⣷⣶⣶⣿⣷⡆⡇⠀⠀⠀⠀⡇⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠀⠉⠛⠛⠛⠛⠛⠛⠋⠛⠛⠛⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⡏⣘⡀⢹⣿⢹⣧⠈⠃⣄⠀⢸⡇⠀⢰⣶⣾⢫⣤⣤⣤⠀⣤⣤⣤⡄⡇⠘⢁⣤⣴⣶⣤⣄⡀⠀⢀⣤⣤⣤⣤⣄⠀⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣦⣭⣾⣥⣿⣷⣤⣿⣼⣿⣧⣾⣿⠀⠀⢃⢀⣘⣿⣿⢸⣿⣿⣿⠀⣿⣿⣿⡇⣿⢠⣿⣿⣿⠛⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⠀⠿⠿⣿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣿⡇⡇⢸⣿⣿⣿⠀⣿⣿⣿⠀⢸⣿⣿⢿⣿⣿⡀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⠀⣿⣿⣿⡇⠃⢸⣿⣿⣿⠀⣿⣿⣿⢀⣿⣿⣿⣾⣿⣿⣇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣿⣷⣶⡎⣿⣿⣿⣤⣿⣿⡿⢸⣿⣿⣿⠛⣿⣿⣿⠀⠀⣿⣿⣿⠀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣛⡛⢛⣀⣛⡛⠛⠛⠛⠃⠈⠛⠿⠿⠟⠋⠁⠘⠛⠛⠛⠀⠛⠛⠛⠃⠀⠛⠛⢛⣺⣿⣿⣿⡟⠀⠀⠈⠉⢀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡿⣻⢿⢋⢔⡇⠀⠅⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢠⣽⠁⠀⠀⠀⠀⢻⣿⣿⣿⣟⣧⣤⡀⠀⠀⡴⢿⡇⠈⠀⠀⠐⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡏⢾⣱⣁⠁⣸⣬⡾⠁⠀⡇⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⢿⡆⠀⠀⣠⠀⢸⣿⣿⣿⣿⣿⣿⣷⣶⡀⠁⠈⣁⠀⠀⠀⠀⠀⣠⣀⣭⣉⣻⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⠿⣻⣯⣞⣴⣿⣿⣷⣶⠤⡁⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⢠⣤⣿⡏⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣛⢿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠠⠀⠊⠁⠀⠀⠀⠀⠀⣀⣀⠈⠛⠋⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣇⡿⡾⡱⢱⢀⣧⣷⣵⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣰⣶⣿⣿⣇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⠁⠀⠀⠀⠀⠈⠁⡠⠀⠀⠚⠛⠻⢻⣿⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧

⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⠻⣟⣿⣿⣿⣿⣿⣿⣿⣿⡅⠈⠈⠋⠉⡄⠀⠛⠉⠙⠃

⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣾⢏⣷⡍⣿⣿⣿⣟⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣵⡛⣃⣹⣿⣿⣿⡏⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠟⠓⣿⣿⣿⣿⡾⠆⠀⠀⠤⠠⢤⡄⢠⣀⠀⠀⠀

⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣴⣤⣶⣷⣬⣥⣤⣤⣤⣤⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢱⣿⣿⣿⣗⣾⢠⣠⣴⣶⣼⣤⠀⠀⠀⠀⠀

⠄⠾⠿⠿⢻⡿⠿⠿⡿⠣⠻⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⢿⡿⡿⠿⠿⠧⠤⠤⠤⠴⠦⠤⠄⠤⠡⠴⠶⠦⠶⠶⠶⠿⠿⠿⠿⠶⠏⠉⠈⠩⠭⠉⠉⠁⠀⠀⠀⠀

[32A⠀⠀⠀⠀⠀⣤⣠⣤⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢿⠿⢿⢿⠆⠀⡀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢼⣝⣿⣉⡣⣪⣈⣄⢀⠀⠀⠀⠀⡜⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢸⡿⣾⣷⢏⡠⠯⠑⣀⣀⣀⣀⣐⡒⡂⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⠿⠿⠑⣨⣻⣉⠀⡇⠀⠀⠀⠀⡇⡂⢛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣭⣭⣭⣿⣿⣿⣶⣷⣶⣶⣿⣷⡆⡇⠀⠀⠀⠀⡇⣷⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠂⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣈⠂⢀⡀⠔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢋⣝⣿⣿⡟⣿⣿⣦⠙⢿⣿⣿⡿⠉⣿⡍⠉⢹⡛⠛⣿⡍⢩⣿⡟⢿⣿⡯⠉⡿⢃⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⡇⣘⡀⢹⣿⢹⣧⠈⠃⡄⠀⠸⡇⠀⢰⣶⣾⢫⣤⣤⣤⠀⣤⣤⣤⡄⡇⠘⢁⣤⣴⣶⣤⣄⡀⠀⢀⣤⣤⣤⣤⣄⠀⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣦⣭⣾⣥⣿⣷⣤⣿⣼⣿⣦⣾⣿⠀⠀⢃⣀⣘⣿⣿⠨⣿⣿⣿⠀⣿⣿⣿⡇⡽⢠⣿⣿⣿⠛⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⠀⠿⠿⣿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⢰⣿⣿⣿⠀⣿⣿⣿⡇⡇⢸⣿⣿⣿⠀⣿⣿⣿⠀⢸⣿⣿⢿⣿⣿⡀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⠀⣿⣿⣿⡇⠂⢸⣿⣿⣿⠀⣿⣿⣿⢀⣿⣿⣿⣾⣿⣿⣇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣿⣷⣶⡎⣿⣿⣿⣤⣿⣿⡿⢸⣿⣿⣿⠛⣿⣿⣿⠀⡄⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣛⡛⢛⣀⣛⡛⠛⠛⠛⠃⡈⠛⠿⠿⠟⠋⠁⠘⠛⠛⠛⠀⠛⠛⠛⣣⣇⣛⣛⣛⣺⣿⣿⣿⡷⠀⠀⠈⠉⢁⠀⢀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢹⠃⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⣤⡴⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣟⣣⣤⡀⠀⠀⡤⢿⡏⠘⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⢷⡿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠁⣠⠀⠀⠀⣶⡃⠀⠀⠀⠀⠀⠀⠀⠀⠏⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠁⠈⢁⠀⠀⠀⠀⠀⣠⣀⣍⣙⣿⣿⣿⣿⣭⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣴⢟⣸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣧⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠡⢹⣿⣿⠃⠀⢀⣴⣶⣤⣀⡀⠀⠀⠀⣀⡀⢀⡀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷

⢿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣇⡿⣾⣹⣹⢫⣧⣷⣵⣿⣿⣿⣿⣗⠑⣀⣾⡿⠊⠀⣰⣿⣿⣿⣿⣿⣿⣶⣀⣀⣠⡆⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⡏⠆⠐⠉⠉⠉⠉⠉⠙⠛⠛⠿⠿⠿⣷⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣯⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠛⠋⠋⡅⠈⠛⠉⠛⠃

⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠳⠿⠿⣿⠿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣰⠩⣂⠉⣿⣿⣿⣿⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣾⠚⠓⢫⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠒⠛⠛⣯⣿⣿⣿⡿⠆⠀⠀⠤⠀⢠⣤⣠⣀⡀⠀⠀

⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣠⣤⣤⣄⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⣿⣿⣗⣾⢠⣄⣤⣤⣶⣧⠀⠁⠀⠀⠀

⠄⠾⠿⠿⢻⡿⠿⠿⡿⠣⠻⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⠿⠿⠆⠀⠤⠠⠤⠤⠰⠤⠀⠀⠰⠤⠶⠴⠶⠶⠿⠿⠿⠿⠷⠍⠀⠈⠹⠯⠏⠉⠀⠀⠀⠀⠀

[32A⠀⠀⠀⠀⠀⣤⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣿⠴⢭⠓⠂⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢽⣿⢻⣋⡣⣠⣀⣄⠀⠀⠀⠀⠀⠔⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢸⡟⡚⡷⠏⡡⠯⠑⣀⣀⣀⣀⣐⡒⡂⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣾⠯⠿⢒⣨⣻⣈⠀⡇⠀⠀⠀⠀⡇⡂⢛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣭⣭⣽⣿⣿⣿⣶⣾⣶⣶⣿⣷⡆⡇⠀⠀⠀⠀⡇⣷⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠂⠀⠐⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡷⣈⠂⢀⡀⠔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢋⣝⣿⣿⡟⣿⣿⣦⠘⢿⣿⣿⡿⠉⣿⡍⠉⢩⡛⠛⣿⡍⢩⣿⡟⢿⣿⡏⠉⡿⢃⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⡏⣘⡀⢹⣿⢹⣧⠈⠃⡄⠀⠸⡇⠀⢰⣶⣾⢣⣤⣤⣤⠀⣤⣤⣤⡄⡇⠘⢁⣤⣴⣶⣤⣄⡀⠀⠀⣤⣤⣤⣤⣄⠀⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣦⣭⣾⣥⣿⣷⣤⣿⣼⣿⣦⣾⣿⠀⠀⠃⢀⣘⣿⣿⢘⣿⣿⣿⠀⣿⣿⣿⡇⡻⢠⣿⣿⣿⠛⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⠀⠿⠿⣿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⠸⣿⣿⣿⠀⣿⣿⣿⡇⠃⢸⣿⣿⣿⠀⣿⣿⣿⠀⢸⣿⣿⢿⣿⣿⡀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢘⣿⣿⣿⠀⣿⣿⣿⡇⠰⢸⣿⣿⣿⠀⣿⣿⣿⢀⣿⣿⣿⣾⣿⣿⣇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⣿⠀⣿⣿⣿⣷⣶⡎⣿⣿⣿⣤⣿⣿⡿⢸⣿⣿⣿⠛⣿⣿⣿⠀⡀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣛⡛⢛⣀⣛⠛⠛⠛⠛⠃⡈⠙⠿⠿⠟⠋⠁⠘⠛⠛⠛⢀⣛⣛⣛⣳⣇⣛⣛⣛⣺⣿⣿⣿⡷⠀⠀⠈⠉⢀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢻⠃⠀⠘⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣣⣤⡀⠀⠐⡼⣿⡏⠈⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣻⣷⡿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡗⣠⡄⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⣰⣶⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠁⠈⠁⠀⠀⠀⠀⠀⣄⣀⣉⣙⣿⣿⣿⣿⣭⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⡗⠀⢰⠟⠀⠀⠀⠀⠀⠀⠐⡟⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣦⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠂⠀⣯⠃⠀⠀⢀⣀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧

⢿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣇⡿⣾⣹⣹⢫⣧⣷⣽⣿⣿⣿⣿⣟⣿⡷⠀⠐⣊⠀⠀⠀⣿⣿⣿⣿⣶⣶⣤⣶⡀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏⠑⠀⢈⠁⠀⠀⠀⠉⠉⠉⠙⠛⠛⠿⠻⡇⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⠿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣻⣯⢻⡿⠿⣿⣿⣿⣿⣿⣿⣿⡄⠙⠛⠛⢫⡁⠈⠛⠋⠛⠃

⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠷⠿⡿⣿⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣶⠉⣀⠉⢿⣿⣿⡿⠀⠀⠀⠉⠀⢀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠬⡏⡻⠃⣡⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠒⠛⠒⡾⣿⢿⣿⡟⢄⠀⠀⠤⠀⣤⣤⣤⣀⡀⠀⠀

⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣀⣄⣀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣽⣾⣿⣗⣾⢠⣤⣤⣴⣾⣷⠀⠀⠀⠀⠀

⠄⠾⠿⠿⢻⡿⠿⠿⡿⠣⠻⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠆⠀⠀⠠⠤⠤⠠⠄⠀⠀⠤⠤⠶⠤⠴⠶⠷⠿⠿⠿⠶⠏⠁⠈⠻⠹⠏⠉⠀⠀⠀⠀⠀

[32A⠀⠀⠀⠀⢠⣄⣠⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢸⡯⢿⣟⣶⡆⠂⡀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣿⣙⣫⣹⡧⣮⡀⣄⢈⠀⠀⠀⠀⡜⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢀⠀⠀⠀⠀⣿⢿⣿⣷⠟⡢⠫⠙⣀⣀⣀⣀⣀⡒⡒⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⣿⣿⠀⡀⣀⣀⣀⣀⣀⡀⠀⠀⣀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⡟⠾⡟⢕⠠⣻⡓⠀⡇⠀⠀⠀⠀⡇⠃⢛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣭⣭⣽⣿⣿⣿⣶⣾⣶⣶⣿⣷⡆⡇⠀⠀⠀⠀⡇⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⣿⢁⠸⣿⣿⡇⠈⢿⡿⠁⠀⢿⡇⠀⢸⡇⠀⣿⡇⢸⣿⡇⢀⠻⡇⠀⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⡇⣘⡀⢹⣿⢹⣧⠈⠃⡄⠀⢸⡇⠀⢰⣶⣾⢫⣤⣤⣤⠀⣤⣤⣤⡄⡇⠘⢁⣤⣴⣶⣤⣄⡀⠀⠀⣤⣤⣤⣤⣄⠀⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣦⣭⣼⣥⣿⣷⣤⣿⣼⣿⣧⣾⣿⡀⠀⠃⢀⣘⣿⣿⠸⣿⣿⣿⠀⣿⣿⣿⡇⣾⢠⣿⣿⣿⠛⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⠀⠿⠿⣿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⠰⣿⣿⣿⠀⣿⣿⣿⡇⣿⢸⣿⣿⣿⠀⣿⣿⣿⠀⢸⣿⣿⢿⣿⣿⡀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⠀⣿⣿⣿⡇⠇⢸⣿⣿⣿⠀⣿⣿⣿⢀⣿⣿⣿⣾⣿⣿⣇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⣰⣶⠀⠀⠀⠀⠰⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣿⣷⣶⡎⣿⣿⣿⣤⣿⣿⡿⢸⣿⣿⣿⠛⣿⣿⣿⠐⡀⣿⣿⣿⢀⣄⣀⣀⠀⠀⠁⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣛⠛⠛⣀⠛⠛⠛⠛⠛⢃⣈⠙⠿⠿⠟⠋⠁⠘⠛⠛⠛⠀⠛⠛⢛⣳⣇⣛⣛⣛⣺⣿⣿⣿⠁⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣶⣦⣄⣀⣀⣀⣀⣀⡀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠿⡛⡿⡛⢹⣿⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣤⠄⠀⠰⠛⣿⠇⠀⠀⠀⠘⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢾⣱⣁⢱⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣀⣀⣈⣄⠀⠀⠀⠀⢠⣶⣶⣿⣽⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡯⣞⣽⣿⣿⣿⣿⡇⠀⢀⣿⣷⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣼⣿⡟⠀⠀⠀⢠⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗

⢻⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣇⡿⣾⣹⣹⢫⣧⣧⠡⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢿⠿⠁⠀⠀⠀⠸⣇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠈⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠤⠘⠽⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢿⣿⡿⢿⠿⢿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⢮⣽⣾⣛⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⠟⣿⣿⣿⣿⣿⡇⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢤⢤⠠⢶⣡⣤⢘⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣰⣶⢾⡯⡉⣼⣿⣿⣿⡇⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠉⠀⠿⣽⣿⣿⣖⡇⠀⠐⠒⠖⢾⠧⠴⠄⠀⠀⠀

⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣶⣦⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣿⣿⣿⣿⡇⠲⢲⣶⣾⣦⣤⠀⠀⠀⠀⠀

⠄⠾⠿⠿⢻⡿⠿⠿⡿⠣⠻⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠿⠦⠤⠤⠴⠶⠤⠶⠆⠀⠠⠶⠶⠶⠾⠶⠾⠷⠿⠿⠿⠿⠀⠀⠀⠈⠈⠀⠈⠀⠀⠀⠀⠀

[32A⠀⠀⠀⠀⢠⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢸⡧⠶⢖⡖⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣿⣈⣩⣃⡡⢀⡀⣄⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢀⢀⠀⠀⢀⣿⠟⣺⣶⢄⠀⠫⠑⣀⣀⣀⣀⣀⡀⡐⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⣿⣿⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⣀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⡟⠮⠛⠑⠨⣻⡊⠀⡇⠀⠀⠀⠀⡇⠀⢚⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣭⣭⣽⣿⣿⣷⣾⣾⣷⣶⣿⣷⡆⡇⠀⠀⠀⠀⡇⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢋⣙⣿⣿⡟⣿⣿⣦⠙⢿⣿⣿⡿⠉⣿⡍⠉⢩⡛⠛⣿⡍⢩⣿⡟⢿⣿⡏⠉⡿⢃⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⡇⣘⡀⢹⣿⢹⣧⠈⠃⡄⠀⢸⡇⠀⢰⣶⣾⢣⣤⣤⣤⠀⣤⣤⣤⡄⡇⠘⢁⣤⣴⣶⣤⣄⡀⠀⠀⣤⣤⣤⣤⣄⠀⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣦⣭⣾⣥⣿⣷⣤⣿⣼⣿⣧⣾⣿⠀⠀⠃⣀⣘⣿⣿⢸⣿⣿⣿⠀⣿⣿⣿⡇⣿⢠⣿⣿⣿⠛⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⠀⠿⠿⣿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⠸⣿⣿⣿⠀⣿⣿⣿⡇⡟⢸⣿⣿⣿⠀⣿⣿⣿⠀⢸⣿⣿⢿⣿⣿⡀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⠀⣿⣿⣿⡇⠃⢸⣿⣿⣿⠀⣿⣿⣿⢀⣿⣿⣿⣾⣿⣿⣇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⣰⣶⠀⠀⠀⠀⠰⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣿⣷⣶⡎⣿⣿⣿⣤⣿⣿⡿⢸⣿⣿⣿⠛⣿⣿⣿⠐⡀⣿⣿⣿⢀⣄⣀⣀⠀⠀⠉⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣛⠛⠛⠀⠛⠛⠛⠛⠛⢃⡈⠙⠿⠿⠟⠋⠁⠘⠛⠛⠛⠀⠛⠛⢛⣳⣇⣛⣛⣛⣺⣿⣿⣿⠁⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣶⣶⣄⣀⣀⣀⣀⣀⡀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣟⠿⡛⡿⡛⢸⣿⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣴⣤⠄⠀⠰⠛⣿⠇⠀⠀⠀⠘⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⢧⡿⣾⣿⣿⣿⢿⣏⢞⣱⣁⢱⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣀⣀⣈⣄⠀⠀⠀⠀⢠⣶⣶⣿⣽⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⣼⣿⡟⠀⠀⠀⢠⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢻⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⢇⡿⣾⡹⣹⢫⣧⣧⠡⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢿⠿⠁⠀⠀⠀⠸⣇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣾⣷⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⠙⠝⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠿⣿⠿⠿⡿⢿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣬⣯⣾⣻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠿⠿⣿⣿⣿⣿⣿⡇⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⢤⣠⢤⣧⣁⣤⢘⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⢶⡾⣏⠩⣼⣿⣿⣿⡇⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⡿⣾⣿⣿⣂⡇⠀⠐⠂⠐⠿⠦⠰⠄⠀⠀⠀

⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣶⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣝⣿⣿⣿⣿⡇⠰⢦⣶⣶⣤⣤⠀⠀⠀⠀⠀

⠄⠾⠿⠿⢻⡿⠿⠿⡿⠣⠻⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠿⠦⠄⠤⠴⠴⠤⠴⠶⠠⠠⠶⠶⠶⠾⠶⠾⠷⠿⠿⠿⠿⠄⠀⠀⠀⠈⠀⠈⠀⠄⠀⠀⠀

[32A⠀⠀⠀⠀⢠⣄⣤⣤⣤⣴⣦⣶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣛⣿⢗⡁⠄⡰⠤⠀⠀⠂⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣝⡚⠅⠀⠀⠩⣟⠀⡁⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢿⠙⣂⣀⣀⣀⣒⡒⣲⢖⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣟⠀⡇⠀⠀⠀⠀⡇⡃⢛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣭⣭⣿⣿⣿⣿⣾⣿⣿⣾⣿⣿⡆⡇⠀⠀⠀⠀⡇⣷⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢋⣝⣿⣿⡟⣿⣿⣦⠙⢿⣿⣿⡿⠉⣿⡍⠉⢹⡛⠛⣿⡍⢩⣿⡟⢿⣿⣏⠉⡿⢃⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⡇⣘⡀⢹⣿⢹⣧⠈⠃⣄⠀⢸⡇⠀⢰⣶⣾⣿⡇⢸⣿⡇⢸⣷⡄⠀⣇⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣦⣭⣾⣥⣿⣷⣤⣿⣼⣿⣧⣾⣿⡀⠀⠃⣀⣘⣿⣿⣿⣧⣼⣿⣥⣼⣿⣿⣾⣿⣶⣴⣾⡦⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⢰⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⣤⣶⣀⣀⣤⣄⠀⠀⠀⠀⠀⠙⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣯⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠉⠁⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢘⠿⡛⡿⡛⢽⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣫⣤⣤⠄⠀⢠⠾⣿⡇⠀⠀⠀⠒⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱⡏⢞⣱⣁⣿⣾⣿⣿⣿⡿⢡⣶⣄⠀⠀⠀⠀⠈⣷⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⠀⣉⡀⠀⠀⠀⠀⢀⣦⣼⣭⣹⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣯⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣧⠀⠀⠀⠀⢸⡇⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⢿⣿⣿⣿⣿⣿⣿⣶⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⣿⣿⣿⡇⠀⠀⠀⠈⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣇⡿⣾⣹⣹⢋⢧⣧⠡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠉⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏

⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠚⠉⠉⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷

⠀⠀⠀⠈⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠿⠿⠿⠿⠿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏

⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣽⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠉⠋⠁⠀⠈⠉⠉⠉⠀

⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⢤⡤⣴⢦⣉⣷⣻⣿⣿⣿⡇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⣿⣛⣍⢽⣿⣿⣿⡇⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠛⠛⠙⣿⣿⣿⣿⣽⡇⠀⠀⠤⠤⢶⠤⠤⠀⠀⠀⠀

⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣶⣤⣤⣤⣤⣤⣤⣤⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣧⣿⣿⣿⣿⡇⣤⣠⣤⣦⣽⣷⡄⡀⠀⠀⠀

⠄⠾⠿⠿⢻⡿⠿⠿⡿⠣⠻⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⡿⢿⣿⠿⠿⠿⠦⠤⠤⠤⠤⠤⠴⠤⠴⠴⠶⠶⠶⠶⠾⠿⠿⠿⠿⠿⠿⠇⠀⠈⠿⠟⠉⠉⠀⠀⠀⠀⠀

[32A⠀⠀⠀⠀⢠⣤⣤⣤⢤⣤⣶⢶⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢀⢸⣿⣿⣿⣿⢷⣯⣻⠖⡁⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢠⠀⠠⣿⣿⣿⣿⣿⣿⣺⣕⣏⠁⠀⠀⠲⣗⠤⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠈⠀⠠⣿⣿⣿⣿⣿⣿⡿⠙⣂⣀⣀⣀⣒⡒⡖⢖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣻⠀⡇⠀⠀⠀⠀⡇⡇⢛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣧⣤⣯⣭⣭⣵⣿⣿⣽⡽⠧⣿⣿⣦⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⡆⡇⠀⠀⠀⠀⡇⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣌⠂⢀⡀⢔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢋⣝⣿⣿⡟⣿⣿⣦⠙⢿⣿⣿⡿⠉⣿⡍⠉⢹⡛⠛⣿⡍⢩⣿⡟⣿⣿⡯⠉⡿⢃⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⡇⣘⡀⢹⣿⢻⣧⠈⠃⣄⠀⢸⡇⠀⢰⣶⣾⣿⡇⢸⣿⡇⢸⣷⡄⠀⣇⠸⠿⠀⣀⡀⠀⠀⠀⠀⠠⠜⠂⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣦⣭⣾⣥⣿⣷⣬⣿⣼⣿⣧⣾⣿⡀⠀⠃⣀⣘⣿⣿⣿⣧⣼⣿⣥⣼⣿⣿⣶⣿⣶⣴⣾⠛⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⢠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣤⣤⣤⣀⡀⣀⡀⠀⠀⠀⠀⠀⠛⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢀⣀⠁⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠉⠁⣀⠀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠿⡛⡿⡛⢿⢋⢾⣿⡏⠀⠀⠀⠀⠀⠀⠳⣾⣿⣿⣧⡀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣛⣤⣄⡀⠀⢠⠾⣿⡇⠁⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡏⢞⣱⣁⠁⣸⣬⣾⣿⣷⣆⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⠈⠀⠉⠁⠀⠀⠀⠀⢀⣄⣸⣍⣹⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣯⣞⣴⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣦⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣇⡿⣾⣹⣹⢫⣧⣧⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡛⠿⡿⠁⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟

⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠿⠚⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷

⠀⠀⠀⠈⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟

⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⠛⠛⢣⠀⠙⠛⠋⠋⠃

⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢉⡿⠿⢿⣿⢿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⢀⣤⣀⣤⣿⣸⣿⣻⣿⣿⣿⡇⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠫⣿⣿⡿⠟⢻⣿⣿⣿⡇⠀⠀⠀⠀⠶⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠾⠻⠟⢿⣿⣿⣿⣿⡇⠀⠠⢄⣄⣤⡄⣠⣀⠀⠀⠀

⠀⠤⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣠⣤⣤⣤⣤⣤⣠⣀⣄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣳⣿⣿⣿⣿⡇⣀⢤⣤⣷⣭⣥⡀⠀⠀⠀⠀

⠀⠾⠿⠿⢻⡿⠿⠿⡿⠣⠻⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⡿⠿⠿⣿⢿⠿⠿⠿⠆⠀⠀⠀⠄⠀⠀⠄⠀⠀⠴⠤⠶⠶⠶⠾⠿⠿⠿⠿⠿⠇⠁⠈⠹⠿⠉⠙⠀⠄⠀⠀⠀

[32A⠀⠀⠀⠀⢠⡀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢘⡧⠽⢕⡒⠖⠀⡢⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣿⣹⡪⣇⡡⣢⡀⣄⠀⠀⠀⠀⠠⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣧⢟⣾⡶⣟⠱⠫⠑⣀⣀⣀⣀⣀⡀⠀⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣤⣤⣶⣦⣴⡿⢺⠿⢟⣪⣻⡂⠀⡇⠀⠀⠀⠀⡇⠀⢛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣧⣤⣤⣤⣤⣤⣴⣦⣦⣦⣤⣿⣿⣤⣤⣤⣤⣤⣤⣤⣥⣤⣤⣤⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣷⣾⣿⣶⣾⣿⣷⡆⠇⠀⠀⠀⠀⡅⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⡄⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡆⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡀⠀⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢉⣝⣿⣿⡟⣿⣿⣦⠘⢿⣿⣿⡿⠉⣿⡍⠉⢹⡛⠛⣿⡍⢩⣿⡝⢿⣿⡯⠉⡿⢃⣤⠀⠀⠀⠀⠀⠂⠀⠀⠘⠁⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⣿⢁⠸⣿⣿⣇⠈⢿⡿⠁⠀⢿⡇⠀⢸⡇⠀⣿⡇⢸⣿⡇⢀⠻⡇⠀⡇⢸⣿⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⡇⣘⡀⢹⣿⢹⣧⠈⠃⡄⠀⢸⡇⠀⢰⣶⣾⣿⡇⢸⣿⡇⢸⣷⣄⠀⣇⠸⠿⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣦⣭⣾⣥⣿⣷⣤⣿⣼⣿⣦⣾⣿⠀⠀⠃⢀⣘⣿⣿⣿⣧⣼⣿⣥⣼⣿⣿⣾⣿⣦⣴⡆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠌⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⠉⠉⠁⠨⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⣀⣹⡷⠀⠀⠀⠛⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⢀⣀⣀⡀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡛⡿⡋⢹⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢓⣠⣀⡀⠀⢠⣽⣶⡇⠂⠀⠀⠠⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⣿⣿⣿⣿⣿⣏⢞⣱⣁⠁⣠⠀⣶⡀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣧⣀⠈⠀⠉⠁⠀⠀⠀⠀⢀⣀⢨⡛⢻⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡯⣞⣤⣏⣼⠿⠿⠿⠄⠀⠀⠀⠀⠀⠀⠘⢿⡿⠿⠿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣡⡍⣶⣶⣶⣦⢰⣶⣶⣶⠶⣶⡶⠆⣶⡖⣶⡄⣶⡆⣶⡎⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧

⢿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣇⡿⣾⣹⣹⢫⣧⣷⣵⣿⣿⣿⣿⣿⢂⣽⡇⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⡇⠛⠃⣿⣷⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠁⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⣇⣿⡇⣿⡇⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇

⠀⠀⠀⠈⠉⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠋⠀⠉⠉⠉⠁⠀⠉⠉⠁⠀⠉⠁⠀⠈⠉⠉⠀⠉⠁⠉⠁⠼⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏

⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠉⠉⢉⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⢠⣤⣤⣤⢠⣤⣤⣤⣤⣤⢠⣤⡄⣤⣤⣤⠀⠀⣤⣤⣤⠀⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⣠⣤⣤⣤⡌⣻⣿⡿⠀⠛⠓⠘⢂⠁⠙⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣙⢹⣿⣿⣿⡇⣿⣇⣿⢿⣿⣿⡿⢸⣿⣇⣸⣿⣿⣼⣿⡇⣿⣿⣀⠀⢸⣿⡸⠿⢾⣿⣿⣿⣿⣿⣿⣿⡇⣿⣇⣿⠇⢸⣿⡇⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡝⣿⣿⣿⣿⣿⡇⣿⡏⠉⢸⣿⣿⣿⢸⣿⣏⣹⣿⢸⣿⣿⡇⣿⣿⣉⠀⢸⣿⣱⣶⢺⣿⣿⣿⡿⣿⣿⣿⡇⣿⡇⣿⡇⢸⣿⡇⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠙⠛⠋⠁⠛⠃⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠘⠋⠛⠓⠛⠛⠛⠀⠈⠛⠛⠋⠈⠙⠛⠛⠀⠙⠛⠛⠁⠛⠃⠛⠃⠘⠛⠃⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⢼⣯⡟⠂⡅⠀⠀⠀⣀⣠⣀⣀⣀⠀⠀⠀

⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⣷⣶⡇⠀⢀⣀⣄⣉⢁⠈⠈⠀⠀⠀

⠀⠸⠿⠻⢻⡿⠿⠿⡷⠣⠺⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠄⠀⠀⠾⠿⠿⠟⠿⠃⠀⠈⠉⠫⠉⠙⠀⠀⠀⠀⠀

[32A⠀⠀⠀⠀⢠⣀⡀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢀⢸⡯⠽⢏⡲⠖⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣿⣸⣤⣃⡡⢄⣀⣄⢀⠀⠀⠀⠠⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣧⢞⣒⠶⠏⠠⠫⠑⣀⣀⣀⣀⣀⡒⠀⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣤⣤⣶⣦⣤⡿⢪⠟⠟⣸⣻⣈⠀⡇⠀⠀⠀⠀⡇⠂⢛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣧⣤⣦⣤⣴⣦⣶⣦⣶⣦⣧⣿⣿⣤⣤⣤⣥⣤⣥⣭⣭⣤⣤⣤⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣷⣾⣾⣾⣶⣿⣷⡆⡇⠀⠀⠀⠀⡅⣴⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⡄⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣷⣈⠂⢀⡀⠔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢉⣝⣿⣿⡟⣿⣿⣦⠙⢿⣿⣿⡿⠉⣿⡍⠉⢙⡛⠛⣿⡍⢩⣿⡟⢿⣿⡯⠉⡿⢃⣤⠀⠀⠀⠀⠀⠒⠀⠀⠘⠁⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⣿⢁⠸⣿⣿⣇⠈⢿⡿⠁⠀⢿⡇⠀⢸⡇⠀⣿⡇⢸⣿⡇⢀⠻⡇⠀⡇⢸⣿⠀⠀⠀⠁⠀⡀⠀⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⡏⣘⡀⢹⣿⢹⣧⠈⠃⡄⠀⠸⡇⠀⢰⣶⣾⣿⡇⢸⣿⡇⢸⣷⣄⠀⣇⠸⠿⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣦⣭⣾⣥⣿⣷⣤⣿⣼⣿⣧⣾⣿⠀⠀⠃⢀⣘⣿⣿⣿⣧⣼⣿⣥⣼⣿⣿⣶⣿⣦⣤⡆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠖⠋⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡻⢻⣿⢿⡿⠇⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢔⠇⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡷⠋⠉⠀⠁⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⣙⡷⠀⠀⠀⠛⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡛⡿⡋⠉⠂⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢓⣠⣀⠀⠀⢠⣽⣶⡇⠂⠀⠀⠠⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣽⢷⡿⣾⣿⣿⣿⣿⡏⢾⣱⣁⠁⡀⠀⣴⡀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣧⣄⠈⠀⠉⠁⠀⠀⠀⠀⢀⣀⢨⡛⢻⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣹⡯⣞⣠⣇⣼⠿⠿⠿⠄⠀⠀⠀⠀⠀⠀⠘⢿⣿⠿⠿⣿⡿⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡏⣶⣶⣶⣦⢰⣶⣶⣶⠶⣶⡶⠆⣶⡖⣶⡄⣶⡆⣶⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧

⢿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣇⡿⣾⣹⣹⢫⣧⣷⣽⣿⣿⣿⣿⣿⣟⣽⡇⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⡇⠛⠃⣿⣷⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⣇⣿⡇⣿⡇⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧

⠀⠀⠀⠈⠉⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠿⠿⠋⠀⠉⠉⠉⠁⠀⠉⠉⠁⠀⠉⠁⠀⠈⠉⠉⠀⠉⠁⠉⠁⠼⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏

⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠉⠉⢉⣤⣤⣤⢡⣤⣤⣤⡄⣤⣤⣤⢠⣤⣤⣤⢠⣤⣤⣤⣤⣤⢠⣤⡄⣤⣤⣤⠀⠀⣤⣤⣤⢀⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⣠⣤⣤⣤⡌⣻⣿⣿⠀⠙⠓⠘⢂⠁⠛⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣙⢹⣿⣿⣿⡇⣿⣇⣿⢿⣿⣿⡿⢸⣿⣇⣸⣿⣿⣼⣿⡇⣿⣿⣀⠀⢸⣿⡸⠿⢾⣿⣿⣿⣿⣿⣿⣿⡇⣿⣇⣿⠇⢸⣿⡇⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡝⣿⣿⣿⣿⣿⡇⣿⡏⠉⢸⣿⣿⣿⣸⣿⣏⣹⣿⢸⣿⣿⡇⣿⣿⣉⠀⢸⣿⣱⣶⢺⣿⣿⣿⡿⣿⣿⣿⡇⣿⡇⣿⡇⢸⣿⡇⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠠⠒⣿⣿⡿⠃⡅⠀⠀⠀⠀⣠⡀⣀⣀⠀⠀⠀

⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣠⡀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⡇⠀⠀⣀⣀⣍⣠⠀⠀⠀⠀⠀

⠀⠼⠿⠻⢻⡿⠿⠿⡷⠣⠺⠟⠿⠻⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠠⠰⠷⠽⠿⠿⠿⠃⠀⠈⠉⠛⠉⠙⠀⠀⠀⠀⠀

[32A⠀⠀⠀⠀⢀⣄⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢀⢘⡧⠽⢌⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣿⠀⠠⠁⡁⠀⡀⣄⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣧⠀⠂⠐⠀⠠⠫⠁⣀⣀⣀⣀⣀⡀⠀⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢤⣤⣶⣤⣤⡟⠠⠛⠐⣨⣻⡁⠀⡆⠀⠀⠀⠀⡇⠀⢛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣧⣤⣤⣤⣴⣤⣴⣦⣶⣦⣤⣿⣿⣤⣤⣤⣤⣮⣥⣬⣥⣤⣤⣤⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣷⣶⣾⣾⣶⣿⣷⡆⠇⠀⠀⠀⠀⡅⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⡄⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡆⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⠀⣤⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠡⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢉⣙⣿⣿⡟⣿⣿⣦⠙⢿⣿⣿⡿⠉⣿⡍⠉⢉⡛⠛⣿⡍⢩⣿⡟⢿⣿⡯⠉⡿⢃⣤⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⣿⢁⠸⣿⣿⣇⠈⢿⡿⠁⠀⢿⡇⠀⢸⡇⠀⣿⡇⢸⣿⡇⢀⠻⡇⠀⡇⢸⣿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⡇⣘⡀⢹⣿⢹⣧⠈⠃⡄⠀⠸⡇⠀⢰⣶⣾⣿⡇⢸⣿⡇⢸⣷⡄⠀⡇⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣦⣭⣾⣥⣿⣧⣤⣿⣼⣿⣧⣾⣿⠀⠀⠃⢀⣘⣿⣿⣿⣧⣼⣿⣥⣼⣿⣿⣦⣿⣦⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣧⠉⠀⠀⠀⠀⢠⡏⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠄⠀⠀⠀⠄⠈⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⣦⣤⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠳⠙⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠿⠿⠏⠄⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠀⠀⠛⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⢀⣀⣀⡀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡛⡿⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣠⡀⠀⠀⢠⣽⣶⡇⠂⠀⠀⠠⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣽⢧⡿⣾⣿⣿⣿⢿⣿⣞⣑⣁⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣥⣀⠈⠁⠉⠁⠀⠀⠀⠀⢀⡀⢨⡛⢻⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣖⣤⡛⠀⠠⠷⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⡿⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡓⠀⣶⣶⣶⣦⢰⣶⣶⣶⠶⣶⡶⠆⣶⡖⣶⡄⣶⡆⣶⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣇⡿⣾⡹⣹⢫⣧⣷⣵⣿⣿⣿⣿⣿⣗⣷⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⡇⠛⠃⣿⣷⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠇⣾⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⣇⣿⡇⣿⡇⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠽⠋⠀⠉⠉⠉⠁⠀⠉⠉⠁⠀⠉⠁⠀⠈⠉⠉⠀⠉⠁⠉⠁⠰⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠉⠉⢉⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⢠⣤⣤⣤⢠⣤⣤⣤⣤⣤⢠⣤⡄⣤⣤⣤⠀⠀⣤⣤⣤⠀⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⣠⣤⣤⣤⡌⣿⣿⣿⠀⠙⡋⠚⢂⠃⠙⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠙⠛⠋⠁⠛⠃⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠘⠋⠛⠃⠛⠛⠛⠀⠈⠛⠛⠋⠈⠙⠛⠛⠀⠙⠛⠛⠁⠛⠃⠛⠃⠘⠛⠃⣼⣿⣿⡇⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠄⠠⢾⣿⣿⠋⡅⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀

⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣶⡇⠀⠀⣀⣄⣌⣁⠀⠉⠀⠀⠀

⠀⠼⠿⠿⢻⡿⠿⠿⡷⠣⠺⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠼⠿⠿⠿⠃⠀⠈⠋⠉⠉⠉⠀⠀⠀⠀⠀

[32A⠀⠀⠀⠀⢀⣄⡀⢀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢀⢈⡯⢴⡟⢒⠖⠀⡠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣿⣼⡤⣏⡱⢀⣀⣄⢀⠀⠀⠀⠠⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣷⢺⣺⡷⢟⠱⢯⠑⣀⣀⣀⣀⣀⡒⠀⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣤⣤⣶⣦⣤⡿⡻⠟⢟⣪⣻⣃⠀⡇⠀⠀⠀⠀⡇⠇⢛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣧⣤⣤⣤⣤⣤⣤⣦⣦⣦⣤⣿⣿⣤⣤⣤⣤⣭⣤⣤⣤⣤⣤⣤⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣷⣾⣾⣿⣶⣿⣷⡆⡇⠀⠀⠀⠀⡇⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣷⣌⠂⢀⡀⠔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡆⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⡄⠀⢲⡖⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠘⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢉⣝⣿⣿⡟⣿⣿⣦⠙⢿⣿⣿⡿⠉⣿⡍⠉⣹⡛⠛⣿⡍⢩⣿⡝⢿⣿⡯⠉⡿⢃⣤⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⣿⢁⠸⣿⣿⣇⠈⢿⡿⠁⠀⢿⡇⠀⢸⡇⠀⣿⡇⢸⣿⡇⢀⠻⡇⠀⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⡏⣘⡀⢹⣿⢻⣧⠈⠃⡄⠀⢸⡇⠀⢰⣶⣾⣿⡇⢸⣿⡇⢸⣷⣄⠀⡇⠸⠟⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣦⣭⣾⣥⣿⣷⣬⣿⣼⣿⣧⣾⣿⡀⠀⠃⣀⣘⣿⣿⣿⣧⣼⣿⣥⣼⣿⣿⣦⣿⣦⣠⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡁⠀⠀⠀⠀⢠⡏⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠈⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡒⠀⠀⠀⡆⠀⠀⠀⢰⣾⣶⣤⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠙⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠯⡦⠀⠀⠀⠁⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠀⠀⠛⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⣀⡀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡿⡛⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣠⡀⠀⠀⢠⣽⣶⡇⠂⠀⠀⠠⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣷⡿⣿⣿⣿⣿⣿⣿⣿⣹⣁⠁⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣥⣀⠈⠁⠉⠁⠀⠀⠀⠀⢀⡀⢨⡛⢻⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣞⣤⣏⠏⠀⠀⠾⢷⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠥⠀⣶⣶⣶⣦⢰⣶⣶⣶⠶⣶⡶⠆⣶⡖⣶⡄⣶⡆⣶⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣇⡿⣾⣹⣹⢫⣧⣷⣽⣿⣿⣿⣿⣿⣿⣔⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⡇⠛⠃⣿⣷⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⣇⣿⡇⣿⡇⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠈⠉⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠋⠁⠉⠉⠉⠁⠀⠉⠉⠁⠀⠉⠁⠀⠈⠉⠉⠀⠉⠁⠉⠁⠀⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠉⠉⢉⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⢠⣤⣤⣤⢠⣤⣤⣤⣤⣤⢠⣤⡄⣤⣤⣤⠀⠀⣤⣤⣤⠀⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⣠⣤⣤⣤⡌⣿⣿⣿⠀⠛⡻⠟⣇⠃⠹⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣙⢹⣿⣿⣿⡇⣿⣇⣿⢿⣿⣿⡿⢸⣿⣇⣸⣿⣿⣼⣿⡇⣿⣿⣀⠀⢸⣿⡸⠿⢾⣿⣿⣿⣿⣿⣿⣿⡇⣿⣇⣿⠇⢸⣿⡇⢰⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠙⠛⠋⠁⠛⠃⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠘⠋⠛⠓⠛⠛⠛⠀⠈⠛⠛⠋⠈⠙⠛⠛⠀⠙⠛⠛⠁⠛⠃⠛⠃⠘⠛⠃⣼⣿⣿⡇⠈⠒⠀⠀⡤⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠰⠅⠡⣾⣿⡿⠋⡇⠀⠀⢀⣀⣀⣀⣂⣀⠀⠀⠀

⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣠⡀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⡇⠀⢤⣠⣦⣝⣥⠉⠉⠁⠀⠀

⠀⠼⠿⠿⢻⡿⠿⠿⡷⠣⠺⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠤⠄⠀⠶⠾⠿⠿⠿⠇⠀⠈⠋⠿⠉⠙⠁⠄⠀⠀⠀

[32A⠀⠀⠀⠀⢀⡄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢀⢘⡧⠵⢍⡒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣿⠀⠨⢁⠁⠀⡀⣄⢀⠀⠀⠀⠀⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣧⠀⠂⠐⠀⠠⠫⠑⣂⣀⣀⣀⣀⡒⠀⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢤⣤⣶⣤⣤⡟⠀⠉⢐⡩⢻⡁⠀⡅⠀⠀⠀⠀⡇⠂⢛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣥⣤⣿⣿⣤⣤⣬⣥⣬⣤⣤⣤⣤⣤⣤⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣿⣷⡆⠇⠀⠀⠀⠀⡅⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠛⠛⠛⠻⠛⠛⠛⠛⠛⠛⠛⠛⠀⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣷⣈⠀⢀⡀⠔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡆⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢉⣉⣿⣿⡟⣿⣿⣦⠙⢿⣿⣿⡿⠉⣿⡍⠉⢙⡛⠛⣿⡍⢩⣿⡟⢿⣿⡏⠉⡿⢁⡤⠀⠀⠀⠀⠿⠏⡄⡆⠄⠀⡜⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⣿⢁⠸⣿⣿⣇⠈⢿⡿⠁⠀⢿⡇⠀⢸⡇⠀⣿⡇⢸⣿⡇⢀⠻⡇⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠒⠀⠁⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⡇⣘⡀⢹⣿⢹⣧⠈⠃⡄⠀⢸⡇⠀⢰⣶⣾⣿⡇⢸⣿⡇⢸⣷⡄⠀⡇⠸⠷⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣦⣭⣾⣥⣿⣷⣬⣿⣼⣿⣧⣾⣿⠀⠀⠃⢀⣘⣿⣿⣿⣧⣼⣿⣥⣼⣿⣿⣦⣿⣦⣤⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠃⠀⠀⠀⢧⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠏⠄⠀⠀⠀⠀⠀⠰⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠉⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣠⣄⡀⠀⢠⡽⣿⡇⠁⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣽⣧⡿⣿⣿⣿⣻⢿⣿⣿⣿⣿⡿⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠈⠀⠉⠁⠀⠀⠀⠀⢀⣀⣨⣙⢻⣿⣿⣿⣿⣽⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠇⠃⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣆⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠁⠀⣶⣶⣶⣦⢰⣶⣶⣶⠶⣶⡶⠆⣶⡖⣶⡄⣶⡆⣶⡆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣇⡿⣾⣹⣹⢫⣧⣷⣵⣿⣿⣿⣿⣿⢸⠀⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⡇⠛⠃⣿⣷⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⣇⣿⡇⣿⡇⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠈⠉⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠗⠇⠀⠀⠀⠉⠉⠉⠁⠀⠉⠉⠁⠀⠉⠁⠀⠈⠉⠉⠀⠉⠁⠉⠁⠸⢿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠉⠉⢉⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⢠⣤⣤⣤⢠⣤⣤⣤⣤⣤⢠⣤⡄⣤⣤⣤⠀⠀⣤⣤⣤⠀⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⣠⣤⣤⣤⡌⣿⣿⣿⠀⠈⠑⠈⢁⠁⠘⠛⠙⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡝⣿⣿⣿⣿⣿⡇⣿⡏⠉⢸⣿⣿⣿⢸⣿⣏⣹⣿⢸⣿⣿⡇⣿⣿⣉⠀⢸⣿⣱⣶⢺⣿⣿⣿⡟⣿⣿⣿⡇⣿⡇⣿⡇⢸⣿⡇⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠙⠛⠋⠁⠛⠃⠀⠘⠛⠛⠛⠚⠛⠛⠛⠛⠘⠋⠛⠃⠛⠛⠛⠀⠈⠛⠛⠋⠈⠙⠛⠛⠀⠙⠛⠛⠁⠛⠃⠛⠃⠘⠛⠃⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠠⠶⠄⠠⣾⣟⣟⠃⡄⠀⠀⠀⠀⣠⡀⣀⣀⠀⠀⠀

⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣀⡀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣹⣿⣿⣶⡇⠀⢀⣠⣤⣭⣀⠀⠉⠀⠀⠀

⠀⠼⠿⠹⢻⡿⠿⠿⡷⠣⠺⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠤⠴⠠⠀⠖⠽⠿⠿⠾⠇⠁⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀

[32A⠀⠀⠀⠀⢀⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢘⡇⠵⢥⡖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣿⠀⠨⠁⠀⠀⡀⣄⠀⠀⠀⠀⠀⠔⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣷⠀⠀⠐⠀⠠⠫⠁⣀⣀⣀⣀⣀⡀⠂⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢤⣤⣶⣤⣤⡿⠀⠉⠀⣨⣻⡁⠀⡅⠀⠀⠀⠀⡇⠁⢛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣧⣤⣤⣤⣤⣤⣤⣬⣬⣥⣤⣿⣿⣤⣤⣭⣭⣯⣥⣴⣭⣭⣬⣥⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣷⣶⣾⣶⣶⣿⣿⡆⠇⠀⠀⠀⠀⡅⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠛⠛⠛⠻⠛⠛⠛⠛⠛⠛⠛⠛⠀⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣷⣈⠀⢀⡀⠔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢋⣝⣿⣿⡟⣿⣿⣦⠙⢿⣿⣿⡿⠉⣿⡍⠉⢙⡛⠛⣿⡍⢩⣿⡟⢿⣿⡏⠉⡿⢁⣤⠀⠀⠀⠀⠿⠇⡄⡆⠄⠀⡜⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⣿⢁⠸⣿⣿⣇⠈⢿⡿⠁⠀⢿⡇⠀⢸⡇⠀⣿⡇⢸⣿⡇⢀⠻⡇⠀⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠒⠀⠁⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⡇⣘⡀⢹⣿⢹⣧⠈⠃⡄⠀⢸⡇⠀⢰⣶⣾⣿⡇⢸⣿⡇⢸⣷⡄⠀⡇⠸⠿⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣦⣭⣾⣥⣿⣷⣤⣿⣼⣿⣧⣾⣿⠀⠀⠃⢀⣘⣿⣿⣿⣧⣼⣿⣥⣼⣿⣿⣦⣿⣦⣤⠄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⢠⡇⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡄⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠇⠀⠀⠀⢧⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⢿⠿⠅⠀⠀⠀⠀⠸⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠉⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣠⣄⡀⠀⢠⡽⣿⡇⠃⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣽⣧⡿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⡠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠈⠀⠉⠁⠀⠀⠀⠀⢀⣀⣨⣙⢻⣿⣿⣿⣿⣽⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣿⠛⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣆⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⣶⣶⣶⣦⢰⣶⣶⣶⠶⣶⡶⠆⣶⡖⣶⡄⣶⡆⣶⡆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣇⡿⣾⣹⣹⢫⣧⣷⣽⣿⣿⣿⣿⣿⣿⣄⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⡇⠛⠃⣿⣷⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣿⣿⡃⠃⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⣇⣿⡇⣿⡇⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠃⠀⠀⠉⠉⠉⠁⠀⠉⠉⠁⠀⠉⠁⠀⠈⠉⠉⠀⠉⠁⠉⠁⠸⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠉⠉⢉⣤⣤⣤⢡⣤⣤⣤⡄⣤⣤⣤⢠⣤⣤⣤⢠⣤⣤⣤⣤⣤⢠⣤⡄⣤⣤⣤⠀⠀⣤⣤⣤⠀⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⣠⣤⣤⣤⡌⣿⣿⣿⠀⠈⠋⠀⢂⠁⠘⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣙⢹⣿⣿⣿⡇⣿⣇⣿⢿⣿⣿⡿⢸⣿⣇⣸⣿⣿⣼⣿⡇⣿⣿⣀⠀⢸⣿⡸⠿⢾⣿⣿⣿⣿⣿⣿⣿⡇⣿⣇⣿⠇⢸⣿⡇⢰⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡝⣿⣿⣿⣿⣿⡇⣿⡏⠉⢸⣿⣿⣿⣸⣿⣏⣹⣿⢹⣿⣿⡇⣿⣿⣉⠀⢸⣿⣳⣶⢺⣿⣿⣿⡿⣿⣿⣿⡇⣿⡇⣿⡇⢸⣿⡇⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠙⠛⠛⠁⠛⠃⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠘⠋⠛⠃⠛⠛⠛⠀⠈⠛⠛⠋⠈⠙⠛⠛⠀⠙⠛⠛⠁⠛⠃⠛⠃⠘⠛⠃⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠠⠖⠄⠰⣿⣿⣿⠇⡅⠀⠀⠀⠀⣠⡀⣀⣀⠀⠀⠀

⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣀⣀⣀⢀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣶⡇⠀⠠⣠⣄⣍⣁⠀⠉⠀⠀⠀

⠀⠼⠿⠿⢻⡿⠿⠿⡷⠣⠺⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠤⠴⠴⠤⠰⠾⠿⠿⠿⠿⠇⠀⠈⠉⠙⠉⠉⠁⠀⠀⠀⠀

[32A⠀⠀⠀⠀⢠⡀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢸⡧⠵⢭⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⡯⠐⠨⠁⠁⠀⡀⣄⠀⠀⠀⠀⠠⠔⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣧⠄⠒⠰⠀⠠⠫⠑⣀⣀⣀⣀⣀⡀⡀⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣶⣤⣷⣶⣴⡟⠀⠉⠀⣨⣻⣀⠀⡇⠀⠀⠀⠀⡇⠁⢛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣧⣤⣥⣤⣤⣤⣬⣭⣭⣿⢥⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣯⣽⣿⣿⣿⣷⣶⣶⣶⣶⣿⣷⡆⠇⠀⠀⠀⠀⡅⣵⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⡦⠂⠋⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠂⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡷⣈⠀⢀⡀⠔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠺⠺⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡆⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢀⡆⠄⡄⠀⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢋⣝⣿⣿⡟⣿⣿⣦⠘⢿⣿⣿⡿⠉⣿⡍⠉⢙⡛⠛⣿⡍⢩⣿⡟⢿⣿⡏⠉⡿⢃⣤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠣⠞⠀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⣿⢁⠸⣿⣿⣇⠈⢿⡿⠁⠀⢿⡇⠀⢸⡇⠀⣿⡇⢸⣿⡇⢀⠻⡇⠀⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⡏⣘⡀⢹⣿⢹⣧⠈⠃⡄⠀⢸⡇⠀⢰⣶⣾⣿⡇⢸⣿⡇⢸⣷⣄⠀⡇⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣦⣭⣾⣥⣿⣷⣤⣿⣼⣿⣧⣾⣿⠀⠀⠃⢀⣘⣿⣿⣿⣧⣼⣿⣥⣼⣿⣿⣶⣿⣦⣤⡆⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⠾⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣻⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠟⠂⠀⠀⠀⠀⠀⢠⡇⠀⠀⠸⢳⣶⣤⣤⣤⣀⡀⡀⠀⠀⠀⠀⠀⠀⠛⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠉⠁⣀⠀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⣿⣿⣿⣿⣿⣟⣛⣤⣄⡀⠀⢠⠼⣿⡇⠁⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣽⢧⡿⣾⣿⣿⣻⢿⣿⣿⣿⣿⠋⡠⡌⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠈⠀⠉⠁⠀⠀⠀⠀⢠⣄⣸⣉⣹⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣤⡗⠃⠀⠀⠀⢤⡿⠿⡿⠿⠿⠿⠦⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠥⠀⣶⣶⣶⣦⢰⣶⣶⣶⠶⣶⡶⠆⣶⡖⣶⡄⣶⡆⣶⡆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣇⡿⣾⣹⣹⢫⣧⣷⣽⣿⣿⣿⣿⣿⢿⣽⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⡇⠛⠃⣿⣷⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⣇⣿⡇⣿⡇⣿⡇⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧

⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⢿⡿⠿⠿⠋⠀⠉⠉⠉⠁⠀⠉⠉⠁⠀⠉⠁⠀⠈⠉⠉⠀⠉⠁⠉⠁⠀⠠⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠉⠉⢉⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⢠⣤⣤⣤⢠⣤⣤⣤⣤⣤⢠⣤⡄⣤⣤⣤⠀⠀⣤⣤⣤⠀⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⣠⣤⣤⣤⡌⣿⣿⣿⠀⠈⠁⠀⢂⠀⠙⠛⠉⠙⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠒⠀⠨⣿⣿⡏⠋⡇⠀⠀⠀⠀⢠⡄⡀⣀⠀⠀⠀

⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣤⣤⣤⣤⣤⣄⣤⣄⣀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⢶⡇⠀⠠⣠⣤⣥⣀⠀⠀⠀⠀⠀

⠀⠾⠿⠽⢻⡿⠿⠿⡷⠣⠺⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠷⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠠⠤⠰⠦⠤⠠⠿⠿⠿⠿⠿⠇⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀

[32A⠀⠀⠀⠀⢠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢸⠤⠿⢇⣓⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢸⣿⣙⣻⣅⡅⣆⣀⣄⢀⠀⠀⠀⠠⡔⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠸⣧⠿⡚⠶⠇⡂⠯⠑⣀⣀⣀⣀⣀⡒⡐⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⡟⠾⠛⢒⣨⣻⣊⠀⡇⠀⠀⠀⠀⡇⠃⢛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⠟⠃⠉⠁⠉⠉⠀⠘⠛⠿⠿⠿⠿⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣭⣭⣿⣿⣿⣷⣾⣾⣿⣶⣿⣿⡆⡇⠀⠀⠀⠀⡅⣷⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣴⠶⠆⠀⠀⠘⠛⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡷⣈⠀⢀⡀⠔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡆⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠀⠘⠆⢀⣀⠀⠀⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠴⠁⠰⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢋⣝⣿⣿⡟⣿⣿⣦⠙⢿⣿⣿⡿⠉⣿⡍⠉⢩⡛⠛⣿⡍⢩⣿⡟⢿⣿⡏⠉⡿⢃⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⣿⢁⠸⣿⣿⣇⠈⢿⡿⠁⠀⢿⡇⠀⢸⡇⠀⣿⡇⢸⣿⡇⢀⠻⡇⠀⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⡏⣘⡀⢹⣿⢻⣧⠈⠃⣄⠀⢸⡇⠀⢰⣶⣾⣿⡇⢸⣿⡇⢸⣷⡄⠀⡇⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣦⣭⣾⣥⣿⣷⣤⣿⣼⣿⣧⣾⣿⠀⠀⢃⣀⣘⣿⣿⣿⣧⣼⣿⣥⣼⣿⣿⣦⣿⣦⣤⡆⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣻⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⡌⠁⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⢠⠤⠼⠀⠀⠀⠀⣠⣤⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠁⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠉⢁⣀⠀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢻⠋⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣟⣫⣤⣄⠀⠀⢤⠾⣿⠇⠁⠀⠀⠂⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⣿⣿⣿⣿⣿⣿⣿⣿⣁⠁⣠⡈⠄⠀⠀⠀⢀⣰⣶⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠈⠀⠉⡀⠀⠀⠀⠀⢠⣄⣸⣍⣹⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣞⣤⣷⣋⠀⠤⠼⢿⡿⠿⡿⠿⠿⠿⠿⣧⡄⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣶⣶⣶⣦⢰⣶⣶⣶⠶⣶⡶⠆⣶⡖⣶⡄⣶⡆⣶⡆⠀⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣇⣿⣾⣹⣹⢫⣷⣷⣽⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⡇⠛⠃⣿⣷⣿⡇⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⣇⣿⡇⣿⡇⣿⡇⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇

⠀⠀⠀⠈⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠁⠉⠉⠉⠁⠀⠉⠉⠁⠀⠉⠁⠀⠈⠉⠉⠀⠉⠁⠉⠁⠤⠀⠀⠀⠀⣠⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠉⠉⢉⣤⣤⣤⢡⣤⣤⣤⡄⣤⣤⣤⢠⣤⣤⣤⢠⣤⣤⣤⣤⣤⢠⣤⡄⣤⣤⣤⠀⠀⣤⣤⣤⠀⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⣠⣤⣤⣤⡌⣿⣿⡇⠀⠉⠃⠈⠀⠀⠛⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣙⢹⣿⣿⣿⡇⣿⣇⣿⢿⣿⣿⡿⢸⣿⣇⣸⣿⣿⣼⣿⡇⣿⣿⣀⠀⢸⣿⡸⠿⢞⣿⣿⣿⣿⣿⣿⣿⡇⣿⣇⣿⠇⢸⣿⡇⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡝⣿⣿⣿⣿⣿⡇⣿⡏⠉⢸⣿⣾⣿⣼⣿⣏⣹⣿⢹⣿⣿⡇⣿⣿⣉⠀⢸⣿⣳⣶⢺⣿⢿⣿⡿⣿⣿⣿⡇⣿⡇⣿⡇⢸⣿⡇⢸⣿⣿⡇⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠙⠛⠛⠁⠛⠃⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠘⠋⠛⠓⠛⠛⠛⠀⠈⠛⠛⠋⠈⠙⠛⠛⠀⠙⠛⠛⠁⠛⠃⠛⠃⠘⠛⠃⢼⣿⣿⡇⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣨⢸⠇⠀⠀⠀⠠⢤⡄⡀⠀⠀⠀⠀

⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣴⣶⣤⣤⣤⣤⣤⣄⣀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣿⣿⢺⡇⢀⢤⣥⣆⣯⣠⠀⠀⠀⠀⠀

⠀⠾⠿⠿⢻⡿⠿⠿⡿⠣⠻⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⡿⠿⠿⡿⠿⠿⠿⠷⠀⠀⠀⠠⠄⠄⠠⠀⠀⠠⠠⠤⠴⠶⠴⠴⠿⠿⠿⠿⠼⠀⠀⠈⠉⠉⠉⠉⠀⠆⠀⠀⠀

[32A⠀⠀⠀⠀⢠⢀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢸⠀⠿⢟⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢸⠭⣙⣻⣃⡅⢠⡀⣄⠀⠀⠀⠀⠠⠔⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢸⡧⠿⠺⡷⠟⡀⠯⠑⣀⣀⣀⣀⣀⡀⡐⢖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠒⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⠇⠎⠝⢔⣨⣻⣈⠀⡇⠀⠀⠀⠀⡇⡂⢛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠀⠀⠂⠀⠀⠀⠀⣀⠸⠿⠿⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣭⣭⣽⣿⣿⣶⣾⣾⣾⣶⣿⣷⡆⠇⠀⠀⠀⠀⡇⣷⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠐⠚⠋⠀⠘⠓⠟⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠛⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡷⣈⠀⢀⡀⠔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡆⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠢⠐⠀⠾⠧⠀⢺⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠋⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢋⣝⣿⣿⡟⣿⣿⣦⠘⢿⣿⣿⡿⠉⣿⡍⠉⢩⡛⠛⣿⡍⢩⣿⡟⢿⣿⡏⠉⡿⢃⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⢀⠤⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⣿⢁⠸⣿⣿⣇⠈⢿⡿⠁⠀⢿⡇⠀⢸⡇⠀⣿⡇⢸⣿⡇⢀⠻⡇⠀⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠇⠀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⡇⣘⡀⢹⣿⢻⣧⠈⠃⡄⠀⢸⡇⠀⢰⣶⣾⣿⡇⢸⣿⡇⢸⣷⡄⠀⡇⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣦⣭⣾⣥⣿⣷⣤⣿⣼⣿⣦⣾⣿⠀⠀⠃⣀⣘⣿⣿⣿⣧⣼⣿⣥⣼⣿⣿⣦⣿⣦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡘⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠟⠇⠀⠀⠀⠀⠀⠄⠁⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠰⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠒⠀⠼⠴⠂⠀⡄⢠⣤⣶⣀⣀⣄⣀⠀⠀⠀⠀⠀⠁⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠉⢀⢀⣀⡀⠀⠀⠀⠀⠀⠀⣤⣀⣀⣀⣀⣀⣀⣀⡀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣟⣫⣤⡤⠀⠀⢴⠾⣿⠇⠁⠀⠀⠃⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡌⠂⠀⠀⠀⠀⠀⣀⣴⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⣉⡀⠀⠀⠀⠀⣰⣤⣼⣍⣽⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣗⠇⠀⠀⠀⢤⡾⠿⡿⠿⠿⠿⠿⣿⡷⠄⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠀⣶⣶⣶⡦⢰⣶⣶⣶⠶⣶⡶⠆⣶⡖⣶⡄⣶⡆⣶⡆⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣇⡿⣾⣹⣹⢫⣷⣷⣵⣿⣿⣿⣿⣿⣝⣗⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⡇⠛⠃⣿⣷⣿⡇⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⣇⣿⡇⣿⡇⣿⡇⠀⠀⠀⠀⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠈⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠀⠉⠉⠉⠁⠀⠉⠉⠁⠀⠉⠁⠀⠈⠉⠉⠀⠉⠁⠉⠡⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡿⢿⡿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠉⠉⢉⣤⣤⣤⢡⣤⣤⣤⡄⣤⣤⣤⢠⣤⣤⣤⢠⣤⣤⣤⣤⣤⢠⣤⡄⣤⣤⣤⠀⢀⣤⣤⣤⠀⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⣠⣤⣤⣤⡄⣿⣿⡇⠀⠀⠈⠀⠀⠀⠉⠀⠀⠈⠀

⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣙⢹⣿⣿⣿⡇⣿⣇⣿⢿⣿⣿⡿⢸⣿⣇⣸⣿⣿⣼⣿⡇⣿⣿⣀⠀⢸⣿⡸⠿⢞⣿⣿⣿⣿⣿⣿⣿⡇⣿⣇⣿⠇⢸⣿⡇⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡝⣿⣿⣿⣿⣿⡇⣿⡏⠉⢸⣿⣾⣿⣸⣿⣏⣹⣿⢹⣿⣿⡇⣿⣿⣉⠀⢸⣿⣳⣶⢪⣿⢿⣿⡿⣿⣿⣿⡇⣿⡇⣿⡇⢸⣿⡇⢹⣿⣿⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠙⠛⠛⠁⠛⠃⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠘⠋⠛⠓⠛⠛⠛⠀⠈⠛⠛⠋⠈⠙⠛⠛⠀⠙⠛⠛⠁⠛⠃⠛⠃⣘⠛⠃⢸⣿⣿⡇⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠁⠀⠐⡀⢹⡆⠀⠀⠠⢤⠤⠄⠠⠀⠀⠀⠀

⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣶⣷⣶⣤⣤⣤⣤⣤⣄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣶⣿⢾⡇⣠⣤⣤⣴⣶⣤⠀⠀⠀⠀⡀

⠀⠾⠿⠿⢻⡿⠿⠿⡿⠣⠻⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⡿⢿⠿⡿⠿⠿⠀⠠⠤⠠⠄⠠⠤⠀⠀⠀⠴⠦⠦⠦⠰⠴⠿⠿⠿⠿⠠⠀⠀⠈⠅⠉⠉⠉⠀⠂⠀⠀⠀

[32A⠀⠀⠀⠀⢠⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢸⠈⠾⢟⡗⠇⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢸⠭⢙⢻⣋⡁⢀⡀⣄⠀⠀⠀⠀⠠⠔⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢸⡧⠿⠚⠶⢿⠁⠫⠑⣀⣀⣀⣀⣀⡀⠐⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠒⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣷⣿⠇⠮⠙⢔⢨⣻⣀⠀⡇⠀⠀⠀⠀⡇⡂⢛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠀⠀⠂⠀⠀⠀⠀⣀⠸⠿⠿⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣭⣭⣽⣿⣿⣶⣾⣾⣾⣶⣿⣷⡆⡇⠀⠀⠀⠀⡇⣷⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠐⠚⠋⠀⠘⠓⠟⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡷⣈⠀⢀⡀⠔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡆⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠢⠐⠀⠾⢦⠀⢺⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⡇⣘⡀⢹⣿⢹⣧⠈⠃⡄⠀⢸⡇⠀⢰⣶⣾⣿⡇⢸⣿⡇⢸⣷⡄⠀⡇⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣦⣭⣾⣥⣿⣷⣤⣿⣼⣿⣧⣾⣿⠀⠀⠃⣀⣘⣿⣿⣿⣧⣼⣿⣥⣼⣿⣿⣦⣿⣦⣤⠄⠀⠀⠀⠀⠀⠀⠀⢘⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡘⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠁⠀⠀⠀⠀⠀⠄⠁⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠰⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠒⠤⠸⠴⠆⠀⡄⢠⣤⣶⣀⣀⣄⣀⠀⠀⠀⠀⠀⠁⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠟⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣟⣫⣤⡤⠀⠀⢴⠾⣿⠇⠁⠀⠀⠃⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡌⠂⠀⠀⠀⠀⠀⣀⣴⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⣉⡀⠀⠀⠀⠀⣰⣤⣼⣭⣽⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⡗⠗⠁⠀⠀⢤⡾⠿⡿⠿⠿⠿⠿⣿⡷⠄⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⣶⣶⣶⣦⢰⣶⣶⣶⠶⣶⡶⠆⣶⡖⣶⡄⣶⡆⣶⡆⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣇⡿⣾⣹⣹⢫⣧⣷⣽⣿⣿⣿⣿⣿⣯⢋⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⡇⠛⠃⣿⣷⣿⡇⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⣇⣿⡇⣿⡇⣿⡇⠀⠀⠀⠀⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠈⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠀⠉⠉⠉⠁⠀⠉⠉⠁⠀⠉⠁⠀⠈⠉⠉⠀⠉⠁⠉⠡⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⢿⡿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠉⠉⢉⣤⣤⣤⢡⣤⣤⣤⡄⣤⣤⣤⢠⣤⣤⣤⢠⣤⣤⣤⣤⣤⢠⣤⡄⣤⣤⣤⠀⠀⣤⣤⣤⠀⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⣠⣤⣤⣤⡄⣿⣿⡇⠀⠀⠈⠀⠀⠀⠉⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠙⠛⠛⠁⠛⠃⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠘⠋⠛⠓⠛⠛⠛⠀⠈⠛⠛⠋⠈⠙⠛⠛⠀⠙⠛⠛⠁⠛⠃⠛⠃⣘⠛⠃⢸⣿⣿⡇⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠁⠀⠐⡂⢸⡇⠀⠀⠀⢤⠤⠄⠠⠀⠀⠀⠀

⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣶⣷⣦⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⣾⢾⡇⡤⣤⣤⣤⣶⣤⠀⠀⠀⠀⡀

⠀⠾⠿⠿⢻⡿⠿⠿⡿⠣⠻⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⡿⠿⠿⡿⠿⠿⠀⠀⠤⠠⠄⠀⠤⠀⠀⠀⠴⠦⠦⠦⠤⠤⠾⠿⠿⠿⠤⠀⠀⠈⠃⠉⠉⠉⠀⠀⠀⠀⠀

[32A⠀⠀⠀⠀⢀⡀⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢸⠠⠶⠏⡖⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢸⠼⣛⣻⣃⡥⢠⣀⣄⢀⠀⠀⠀⠠⡔⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢸⠢⠟⠾⡷⠗⠠⠫⠑⣀⣀⣀⣀⣀⡒⡀⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⡂⠎⠹⢄⢠⣻⣈⠀⡇⠀⠀⠀⠀⡇⡂⢛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠿⠓⠒⣶⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣭⣭⣭⣿⣿⣶⣾⣾⣾⣶⣿⣷⡆⡇⠀⠀⠀⠀⡇⣷⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠉⠉⠁⠀⠀⠘⠛⠛⠛⣻⣯⣤⣤⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣷⣈⠀⢀⡀⠔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡆⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⠀⣠⡤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⣞⡿⣏⠉⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢋⣝⣿⣿⡟⣿⣿⣦⠙⢿⣿⣿⡿⠉⣿⡍⠉⢹⡛⠛⣿⡍⢩⣿⡟⢿⣿⡏⠉⡿⢃⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣮⡿⠔⠃⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⣿⢁⠸⣿⣿⣇⠈⢿⡿⠁⠀⢿⡇⠀⢸⡇⠀⣿⡇⢸⣿⡇⢀⠻⡇⠀⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠴⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⡏⣘⡀⢹⣿⢻⣧⠈⠃⡄⠀⢸⡇⠀⢰⣶⣾⣿⡇⢸⣿⡇⢸⣷⡄⠀⡇⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡟⠀⢀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣦⣭⣾⣥⣿⣷⣤⣿⣼⣿⣧⣾⣿⠀⠀⢃⣀⣘⣿⣿⣿⣧⣼⣿⣥⣼⣿⣿⣮⣿⣦⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣦⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠁⠀⣼⠀⠀⠀⠀⡀⣀⣤⣄⡀⣀⢀⠀⠀⠁⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠂⠀⠀⠘⠿⠿⠟⠀⠀⠀⠀⡇⢿⣿⣿⣿⣿⡏⠀⠀⠈⠁⢀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣶⣄⣀⣀⣀⣀⣀⣀⡀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣟⣡⣤⡤⠀⠀⠴⠿⣿⠀⠀⠀⠐⠃⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣷⣶⣤⡀⢀⣉⡀⠀⠀⠀⠀⣰⣦⣾⣭⣽⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⡼⠿⢷⣤⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣶⣶⣶⣦⢰⣶⣶⣶⠶⣶⡶⠆⣶⡖⣶⡄⣶⡆⣶⡆⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣇⡿⣾⣹⣹⢫⣷⣷⣽⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⡇⠛⠃⣿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⣇⣿⡇⣿⡇⣿⡇⢰⡄⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠁⠉⠉⠉⠁⠀⠉⠉⠁⠀⠉⠁⠀⠈⠉⠉⠀⠉⠁⠉⠁⠼⠿⠦⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⠿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠉⠉⢉⣤⣤⣤⢡⣤⣤⣤⡄⣤⣤⣤⢠⣤⣤⣤⢠⣤⣤⣤⣤⣤⢠⣤⡄⣤⣤⣤⠀⠀⣤⣤⣤⠀⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⣠⣤⣤⣤⡌⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣙⢹⣿⣿⣿⡇⣿⣇⣿⢿⣿⣿⡿⢸⣿⣇⣸⣿⣿⣼⣿⡇⣿⣿⣀⠀⢸⣿⡸⠿⢞⣿⣿⣿⣿⣿⣿⣿⡇⣿⣇⣿⠇⢸⣿⡇⢰⣿⣿⡇⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡝⣿⣿⣿⣿⣿⡇⣿⡏⠉⢸⣿⣾⣿⣼⣿⣏⣹⣿⢹⣿⣿⡇⣿⣿⣉⠀⢸⣿⣳⣶⢪⣿⢿⣿⡿⣿⣿⣿⡇⣿⡇⣿⡇⢸⣿⡇⠸⣿⣿⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠙⠛⠛⠁⠛⠃⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠘⠋⠛⠓⠛⠛⠛⠀⠈⠛⠛⠋⠈⠙⠛⠛⠀⠙⠛⠛⠁⠛⠃⠛⠃⠘⠛⢃⣾⣿⢿⡇⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢄⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢯⡭⠆⢸⡇⠀⠀⠀⠴⠷⠀⠀⠀⠀⠀⠀

⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣽⣿⣿⣾⣦⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠸⢇⡤⣤⣦⣴⣶⡖⠀⠀⠀⠀⡄

⠀⠼⠿⠿⢻⡿⠿⠿⡿⠣⠻⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠦⠴⠦⠶⠶⠤⠄⠀⠤⠤⠴⠶⠶⠶⠶⠴⠶⠾⠿⠿⠆⠀⠀⠀⠃⠈⠀⠁⠠⠂⠀⠀⠁

[32A⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢸⠀⠤⢉⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢸⠼⠀⠊⢁⡀⠀⡀⣄⠀⠀⠀⠀⠀⠔⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢸⠀⠈⠂⠐⠀⠠⠫⠑⣀⣀⣀⣀⣀⡀⠐⢖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣷⣿⠀⠀⠉⠐⣠⣹⣀⠀⡇⠀⠀⠀⠀⡇⠀⢛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣭⣭⣯⣿⣿⣶⣶⣶⣶⣶⣿⣷⡆⠇⠀⠀⠀⠀⡇⣷⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⢛⣀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡷⣈⠀⢀⡀⢔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠹⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡆⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⢧⣿⣿⡟⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢉⣝⣿⣿⡟⣿⣿⣦⠙⢿⣿⣿⡿⠉⣿⡍⠉⢩⡛⠛⣿⡍⢩⣿⡟⢿⣿⣏⠉⡟⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣩⡇⣶⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⣿⢁⠸⣿⣿⣇⠈⢿⣿⠁⠀⢿⡇⠀⢸⡇⠀⣿⡇⢸⣿⡇⢀⠻⡇⠀⡇⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢘⡷⠋⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⡏⣘⡀⢹⣿⢹⣧⠈⠃⡄⠀⢸⡇⠀⢰⣶⣾⣿⡇⢸⣿⡇⢸⣷⡄⠀⡇⠸⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣦⣭⣾⣥⣿⣷⣤⣿⣼⣿⣧⣾⣿⠀⠀⠃⢀⣘⣿⣿⣿⣧⣼⣿⣥⣼⣿⣿⣦⣿⣦⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣤⠁⢰⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⡿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣦⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⣀⡀⠀⠀⠀⠀⠁⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠐⣶⣶⣾⠄⠀⠀⢰⠀⠀⢸⣿⣿⣿⡏⠀⠀⠈⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣶⣄⣀⣀⣀⣀⣀⣀⡀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠸⣿⣿⣟⣡⣤⡄⠀⠀⠴⠻⣿⠀⠀⠀⠘⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣽⢧⡿⣾⣿⣿⣿⢿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣷⣶⣤⠀⢀⣉⡀⠀⠀⠀⠀⣰⣦⣾⣭⣽⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⣄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣶⣶⣶⣦⢰⣶⣶⣶⠶⣶⡶⠆⣶⡖⣶⡄⣶⡆⣶⡆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣇⡿⣾⣹⣹⢫⣧⣷⣽⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⡇⠛⠃⣿⣷⣿⡇⠀⠀⠀⠀⠀⠈⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⣇⣿⡇⣿⡇⣿⡇⢰⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠀⠉⠉⠉⠁⠀⠉⠉⠁⠀⠉⠁⠀⠈⠉⠉⠀⠉⠁⠉⠁⠸⠿⠦⠤⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⡿⠙⣿⣿⣿⣿⠿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣙⢹⣿⣿⣿⡇⣿⣇⣿⢿⣿⣿⡿⢸⣿⣇⣸⣿⣿⣼⣿⡇⣿⣿⣀⠀⢸⣿⡸⠿⢾⣿⣿⣿⣿⣿⣿⣿⡇⣿⣇⣿⠇⢸⣿⡇⢰⣿⣿⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡝⣿⣿⣿⣿⣿⡇⣿⡏⠉⢸⣿⣿⣿⣼⣿⣏⣹⣿⢹⣿⣿⡇⣿⣿⣉⠀⢸⣿⣳⣶⢾⣿⣿⣿⡿⣿⣿⣿⡇⣿⡇⣿⡇⢸⣿⡇⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠙⠛⠛⠁⠛⠃⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠘⠋⠛⠓⠛⠛⠛⠀⠈⠛⠛⠋⠈⠙⠛⠛⠀⠙⠛⠛⠁⠛⠃⠛⠃⠘⠛⠃⣼⣿⣿⠆⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⠂⢸⠂⠀⠀⠀⠰⠷⠀⠀⠀⠀⠀⠀

⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣿⣿⣶⣦⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣾⡿⠸⠀⢤⣠⣦⣴⣦⡖⠀⠀⠀⠀⡄

⠀⠼⠿⠽⢻⡿⠿⠿⡿⠣⠺⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠦⠤⠦⠶⠴⠤⠀⠠⠠⠠⠴⠶⠶⠶⠦⠶⠿⠿⠿⠿⠆⠀⠀⠀⠂⠈⠀⠁⠠⠀⠀⠀⠁

[32A⠀⠀⠀⠀⢀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢸⠠⠬⠍⡒⠆⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢸⠼⣙⢫⣃⡁⣀⣀⣄⢀⠀⠀⠀⠠⠔⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢸⠂⠟⠚⠶⠟⠠⠫⠑⣀⣀⣀⣀⣀⡒⡀⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⠀⠊⠹⠖⣨⣻⣈⠀⡇⠀⠀⠀⠀⡇⡀⢛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣭⣭⣭⣿⣿⣶⣶⣾⣶⣶⣿⣷⡆⡇⠀⠀⠀⠀⡇⣷⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣷⣈⠀⢀⡀⠔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣦⡆⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣤⣴⣾⣷⣶⡢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢋⣝⣿⣿⡟⣿⣿⣦⠙⢿⣿⣿⡿⠉⣿⡍⠉⢩⡛⠛⣿⡍⢩⣿⡟⢿⣿⡏⠉⡿⢃⣤⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠛⠛⣥⡱⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⣿⢁⠸⣿⣿⣇⠈⢿⡿⠁⠀⢿⡇⠀⢸⡇⠀⣿⡇⢸⣿⡇⢀⠻⡇⠀⠇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢹⠷⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⡏⣘⡀⢹⣿⢹⣇⠈⠃⣄⠀⢸⡇⠀⢰⣶⣾⣿⡇⢸⣿⡇⢸⣷⡄⠀⡇⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⡟⠀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣦⣭⣾⣥⣿⣷⣤⣿⣼⣿⣧⣾⣿⠀⠀⠃⢀⣘⣿⣿⣿⣧⣼⣿⣥⣼⣿⣿⣦⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣦⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣀⣠⣾⣄⠀⠀⠀⠀⠀⠀⠀⢹⣿⡏⠀⠀⠈⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣶⣄⣀⣀⣀⣀⣀⣀⡀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠃⠀⠀⠉⠙⠛⠛⠀⠀⠀⠀⠀⠠⡀⠘⣏⣡⣤⡄⠀⠀⠴⠻⣿⠀⠀⠀⠘⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣽⢷⡿⣾⣿⣿⣿⢿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀⢸⣿⣿⣷⣶⣤⠀⢀⣉⡀⠀⠀⠀⠀⣰⣦⣾⣭⣽⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠘⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣶⣶⣶⣦⢰⣶⣶⣶⠶⣶⡶⠆⣶⡖⣶⡄⣶⡆⣶⡆⠀⠀⠀⠀⠛⣷⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣇⡿⣾⣹⣹⢫⣧⣷⣽⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⡇⠛⠃⣿⣷⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⣇⣿⡇⣿⡇⣿⡇⢠⠀⠀⠀⠀⠀⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠀⠉⠉⠉⠁⠀⠉⠉⠁⠀⠉⠁⠀⠈⠉⠉⠀⠉⠁⠉⠁⠸⠄⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⡿⠙⣿⣿⡿⣿⠿⣿⣿⡿⣿⡇

⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣙⢹⣿⣿⣿⡇⣿⣇⣿⢿⣿⣿⡿⢸⣿⣇⣸⣿⣿⣼⣿⡇⣿⣿⣀⠀⢸⣿⡸⠿⢾⣿⣿⣿⣿⣿⣿⣿⡇⣿⣇⣿⠇⢸⣿⡇⢰⣿⣿⡇⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡝⣿⣿⣿⣿⣿⡇⣿⡏⠉⢸⣿⣿⣿⣼⣿⣏⣹⣿⢹⣿⣿⡇⣿⣿⣉⠀⢸⣿⣳⣶⢺⣿⣿⣿⡿⣿⣿⣿⡇⣿⡇⣿⡇⢸⣿⡇⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠙⠛⠛⠁⠛⠃⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠘⠋⠛⠓⠛⠛⠛⠀⠈⠛⠛⠋⠈⠙⠛⠛⠀⠙⠛⠛⠁⠛⠃⠛⠃⠘⠛⢃⣬⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡐⢸⠂⠀⠀⠀⠐⠳⠀⠀⠀⠀⠀⠀

⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣴⣿⣿⣶⣦⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣾⣿⠼⠀⠀⢠⣤⣤⣤⡆⠀⠀⠀⠀⡀

⠀⠼⠿⠿⢻⡿⠿⠿⡿⠣⠺⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠖⠶⠦⠶⠶⠦⠤⠠⠄⠠⠦⠶⠶⠶⠶⠼⠷⠿⠿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀

[32A⠀⠀⠀⠀⠀⠀⠀⢠⠄⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢸⠠⠥⢌⡓⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢸⠜⠀⠊⢁⡁⠀⡀⣄⠀⠀⠀⠀⠠⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢸⠀⠌⠒⠐⠀⠠⠫⠑⣀⣀⣀⣀⣀⡀⠀⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣷⣿⠀⠀⠉⠐⣈⣻⡀⠀⡇⠀⠀⠀⠀⡇⠀⢚⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣭⣭⣯⣿⣿⣶⣶⣾⣶⣶⣾⣷⡆⠇⠀⠀⠀⠀⡇⣷⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣷⣈⠀⢀⡀⠔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡆⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⠻⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢋⣝⣿⣿⡟⣿⣿⣦⠘⢿⣿⣿⡿⠉⣿⡍⠉⢩⡛⠛⣿⡍⢩⣿⡟⢿⣿⡯⠉⡿⢃⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⣿⢁⠸⣿⣿⣇⠈⢿⡿⠁⠀⢿⡇⠀⢸⡇⠀⣿⡇⢸⣿⡇⢀⠻⡇⠀⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣰⠾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⡇⣘⡀⢹⣿⢹⣧⠈⠃⡄⠀⢸⡇⠀⢰⣶⣾⣿⡇⢸⣿⡇⢸⣷⡄⠀⡇⠸⠿⠀⠀⠀⠀⠀⠀⢠⠇⠈⠀⠆⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣦⣭⣾⣥⣿⣷⣤⣿⣼⣿⣦⣾⣿⠀⠀⠃⢀⣘⣿⣿⣿⣧⣼⣿⣥⣼⣿⣿⣮⣿⣦⣤⠆⠀⠀⠀⠀⠀⡆⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡇⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣿⣿⣿⣿⣻⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠃⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⣦⠀⠀⠀⠀⡄⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠀⠀⠀⠀⠁⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⣶⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡏⠀⠀⠈⠁⢀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣶⣄⣀⣀⣀⣀⣀⣀⡀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⡟⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣟⣡⣤⡄⠀⠀⠴⠻⣿⠀⠀⠀⠘⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣽⣧⡿⣾⣿⣿⣿⢿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣷⣶⣤⠀⢈⣁⡀⠀⠀⠀⠀⣰⣦⣾⣭⣽⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⡿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣶⣶⣶⣦⢰⣶⣶⣶⠶⣶⡶⠆⣶⡖⣶⡄⣶⡆⣶⡆⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣇⡿⣾⣹⣹⢫⣧⣷⣽⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⡇⠛⠃⣿⣷⣿⡇⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⣇⣿⡇⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠀⠉⠉⠉⠁⠀⠉⠉⠁⠀⠉⠁⠀⠈⠉⠉⠀⠉⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠿⢿⣿⣿⣿⡿⠙⣿⣿⡿⡿⠿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠉⠉⢉⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⢠⣤⣤⣤⢠⣤⣤⣤⣤⣤⢠⣤⡄⣤⣤⣤⠀⠀⣤⣤⣤⠀⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⣠⣤⣤⣤⡌⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣙⢹⣿⣿⣿⡇⣿⣇⣿⢿⣿⣿⡿⢸⣿⣇⣸⣿⣿⣼⣿⡇⣿⣿⣀⠀⢸⣿⡸⠿⢾⣿⣿⣿⣿⣿⣿⣿⡇⣿⣇⣿⠇⢸⣿⡇⠀⠀⠀⠉⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡝⣿⣿⣿⣿⣿⡇⣿⡏⠉⢸⣿⣿⣿⣼⣿⣏⣹⣿⢹⣿⣿⡇⣿⣿⣉⠀⢸⣿⣳⣶⢾⣿⣿⣿⡿⣿⣿⣿⡇⣿⡇⣿⡇⢸⣿⡇⠀⠀⠀⠀⠐⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠙⠛⠛⠁⠛⠃⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠘⠋⠛⠓⠛⠛⠛⠀⣈⡛⠛⢋⣬⡙⠛⠛⠀⠙⠛⠛⠁⠛⠃⠛⠃⠘⠛⠃⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠄⠀⠀⢀⣀⠀⠀⠀⠸⢿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢠⠀⠈⠛⠛⠻⠧⠀⠀⠀⠀⠀⠀

⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣮⣿⣿⣶⣦⣤⣤⣤⣤⣤⣍⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣾⣾⣿⠼⠀⡤⣠⣤⣤⣴⡖⠀⠀⠀⠀⡀

⠀⠼⠿⠿⢻⡿⠿⠿⡿⠣⠺⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠤⠾⠦⠶⠶⠦⠦⠤⠀⠀⠴⠶⠶⠶⠶⠾⠿⠿⠿⠿⠆⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠁

[32A⠀⠀⠀⠀⡄⠀⠀⢀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢡⠀⠤⠉⡖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢸⠸⠈⠉⢁⡁⠀⡀⣄⢀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢸⠂⠀⠂⠐⠀⠀⠫⠑⣀⣀⣀⣀⣀⡀⠀⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣷⣿⠀⠂⠉⠐⣠⣹⣈⠀⡇⠀⠀⠀⠀⡇⡀⢚⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣭⣭⣭⣿⣿⣶⣶⣶⣶⣶⣿⣷⡆⡇⠀⠀⠀⠀⡇⣷⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠈⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠉⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢋⣝⣿⣿⡟⣿⣿⣦⠘⢿⣿⣿⡿⠉⣿⡍⠉⢩⡛⠛⣿⡍⢩⣿⡟⢿⣿⣏⠉⡿⢃⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⡇⣘⡀⢹⣿⢹⣧⠈⠃⡄⠀⢸⡇⠀⢰⣶⣾⣿⡇⢸⣿⡇⢸⣷⡄⠀⡇⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣦⣭⣾⣥⣿⣷⣤⣿⣼⣿⣦⣾⣿⠀⠀⠃⢀⣘⣿⣿⣿⣧⣼⣿⣥⣼⣿⣿⣾⣿⣦⣤⡆⠀⠀⠀⠀⢀⣶⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠐⠏⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⡇⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠿⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣦⠀⠀⠀⠀⡆⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⣀⣀⠀⠀⠈⠃⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡇⠀⠀⠈⠀⢀⣀⣀⢀⠀⠀⠀⠀⠀⢀⣶⣄⣀⣀⣀⣀⣀⣀⡀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠙⢿⣿⣏⣡⣤⡄⠀⠀⠼⢻⡿⠀⠀⠀⠘⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣿⣧⡿⣾⣿⣿⣿⢿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣷⣶⣤⠀⣈⣡⡀⠀⠀⠀⠀⣲⣦⣾⣭⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⡿⠿⡿⠿⠿⠇⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣶⣶⣶⣦⢰⣶⣶⣶⠶⣶⡶⠆⣶⡖⣶⡄⣶⡆⣶⡆⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣇⡿⣾⣹⣹⢫⣧⣷⣽⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⡇⠛⠃⣿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⣇⣿⡇⣿⡇⣿⡇⢠⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠀⠉⠉⠉⠁⠀⠉⠉⠁⠀⠉⠁⠀⠈⠉⠉⠀⠉⠁⠉⠁⠰⠿⠿⠟⠦⡀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⡿⠹⣿⣿⡿⡿⠿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠉⠉⢉⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⢠⣤⣤⣤⢠⣤⣤⣤⣤⣤⢠⣤⡄⣤⣤⣤⠀⠀⣤⣤⣤⠀⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⣠⣤⣤⣤⡄⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣙⢹⣿⣿⣿⡇⣿⣇⣿⢿⣿⣿⡿⢸⣿⣇⣸⣿⣿⣼⣿⡇⣿⣿⣀⠀⢸⣿⡸⠿⢾⣿⣿⣿⣿⣿⣿⣿⡇⣿⣇⣿⠇⢸⣿⡇⠀⠀⠈⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡝⣿⣿⣿⣿⣿⡇⣿⡏⠉⢸⣿⣿⣿⣼⣿⣏⣹⣿⢹⣿⣿⡇⣿⣿⣉⠀⢸⣿⣳⣶⢺⣿⣿⣿⡿⣿⣿⣿⡇⣿⡇⣿⡇⢸⣿⡇⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠙⠛⠛⠁⠛⠃⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠘⠋⠛⠓⠛⠛⠛⠀⠈⠛⠛⠋⠈⠙⠛⠛⣠⣙⠛⠛⠁⠛⠃⠛⠃⠘⠛⠃⠀⠀⠀⠀⠀⠀⢿⣾⣧⡀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠦⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣤⠀⠀⠀⠀

⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣶⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠈⠛⣿⣿⠀⠀⠠⡄

⠀⠼⠿⠿⢻⡿⠿⠿⡿⠣⠺⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠷⠶⠼⠴⠳⠶⠾⠶⠝⠤⠤⠶⠶⠶⠶⠶⠴⠿⠾⠿⠿⠇⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠁

[32A⠀⠀⠀⠀⡄⠀⠀⢄⡠⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⣗⠀⠶⠍⡒⠆⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢸⢽⠑⢫⣁⡥⠠⡀⣄⢀⠀⠀⠀⠀⠔⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢸⠢⠞⠚⠷⠏⠀⠫⠑⣀⣀⣀⣀⣀⡀⡐⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣷⣿⠀⠊⠙⠐⣨⣹⣀⠀⡇⠀⠀⠀⠀⡇⠀⢛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣭⣭⣽⣿⣿⣶⣶⣶⣶⣾⣿⣷⡆⠇⠀⠀⠀⠀⡇⣷⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠈⠉⠉⠉⠉⠉⠉⠉⠉⠛⠙⠉⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⡇⣘⡀⢹⣿⢹⣧⠈⠃⡄⠀⠸⡇⠀⢰⣶⣾⣿⡇⢸⣿⡇⢸⣷⡄⠀⡇⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣦⣭⣾⣥⣿⣷⣤⣿⣼⣿⣧⣾⣿⠀⠀⠃⣀⣘⣿⣿⣿⣧⣼⣿⣥⣼⣿⣿⣮⣿⣦⣤⡂⠀⠀⠀⣰⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠿⠃⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣦⠀⠀⠀⠀⡆⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣄⣀⣀⠀⠀⠈⠃⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢠⣶⣤⣀⣀⣀⣀⣀⣀⡀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠐⡄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠛⢿⣿⣏⣥⣤⡄⠀⠀⠝⢻⡿⠀⠀⠀⠘⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣽⣧⡿⣾⣿⡿⣿⢿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢱⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠹⣿⣿⣿⣶⣶⣄⠀⣈⣠⡀⠀⠀⠀⠀⣶⣶⣾⣭⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⡿⠿⡿⠿⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣶⣶⣶⣦⢰⣶⣶⣶⠶⣶⡶⠆⣶⡖⣶⡄⣶⡆⣶⡆⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣇⡿⣾⣹⣹⢫⣧⣷⣽⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⡇⠛⠃⣿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⣇⣿⡇⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠀⠉⠉⠉⠁⠀⠉⠉⠁⠀⠉⠁⠀⠈⠉⠉⠀⠉⠁⠉⠁⠀⠀⠐⠶⠤⣄⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡿⢹⣿⣿⢿⡿⠿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠉⠉⢉⣤⣤⣤⢡⣤⣤⣤⡄⣤⣤⣤⢠⣤⣤⣤⢠⣤⣤⣤⣤⣤⢠⣤⡄⣤⣤⣤⠀⠀⣤⣤⣤⠀⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⣠⣤⣤⣤⡄⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣙⢹⣿⣿⣿⡇⣿⣇⣿⢿⣿⣿⡿⢸⣿⣇⣸⣿⣿⣼⣿⡇⣿⣿⣀⠀⢸⣿⡸⠿⢾⣿⣿⣿⣿⣿⣿⣿⡇⣿⣇⣿⠇⢸⣿⡇⠀⠀⠉⠇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡝⣿⣿⣿⣿⣿⡇⣿⡏⠉⢸⣿⣿⣿⣸⣿⣏⣹⣿⢹⣿⣿⡇⣿⣿⣉⠀⢸⣿⣳⣶⢺⣿⣿⣿⡿⣿⣿⣿⡇⣿⡇⣿⡇⢸⣿⡇⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠙⠛⠛⠁⠛⠃⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠘⠋⠛⠓⠛⠛⠛⠀⠈⠛⠛⠋⠈⠙⠛⠛⠀⠙⠛⠛⠁⠛⠃⠛⠃⠘⠛⠃⢀⣶⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⢷⣀⣓⡒⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀

⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⣿⣿⣿⣿⣤⠀⠀⠀⢀⡄

⠀⠾⠿⠿⢻⡿⠿⠿⡿⠣⠺⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⡿⢿⠿⠿⠿⠿⠶⠬⠤⠷⠶⠦⠆⠦⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀

[32A⠀⠀⠀⠀⡄⠀⡀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⣇⠀⠽⠈⡗⠖⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢳⠝⠉⣺⣁⡅⠀⡀⣔⠀⠀⠀⠀⠀⠔⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢸⠢⠞⠺⡷⢏⠀⠫⠁⣀⣀⣀⣀⣀⡀⠀⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⠀⠎⠙⠔⣨⢹⣀⠀⡇⠀⠀⠀⠀⡇⠀⢚⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣭⣭⣭⣿⣿⣶⣶⣾⣶⣶⣿⣷⡆⠆⠀⠀⠀⠀⡇⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢉⣙⣿⣿⡟⣿⣿⣦⠙⢿⣿⣿⡿⠉⣿⡍⠉⢩⡛⠛⣿⡍⢩⣿⡟⢿⣿⡏⠉⡿⢃⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⡇⣘⡀⢹⣿⢻⣧⠈⠃⡄⠀⠸⡇⠀⢰⣶⣾⣿⡇⢸⣿⡅⢸⣷⣄⠀⡇⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣦⣭⣾⣥⣿⣷⣤⣿⣼⣿⣦⣾⣿⠀⠀⠃⢀⣘⣿⣿⣿⣧⣼⣿⣥⣼⣿⣿⣶⣿⣦⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣿⣿⣿⣿⣻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠫⠅⠀⠀⠇⢀⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣦⠀⠀⠀⠀⡶⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣸⣿⠃⠀⠀⠀⠀⠀⠀⠰⣶⣶⣤⣤⣤⣄⣀⣀⡀⠀⠉⢃⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠇⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢠⣶⣤⣀⣀⣀⣀⣀⣀⡀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣏⣥⣤⡄⠀⠀⠛⢻⡿⠀⠀⠀⠘⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⣧⡿⣾⣿⣿⣽⢿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣶⣶⣄⢀⣈⣠⡀⠀⠀⠀⠀⣶⣶⣾⣽⣿⣿⣿⣿⣿⣿⡆

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⡿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣶⣶⣶⣦⢰⣶⣶⣶⠶⣶⡶⠆⣶⡖⣶⡄⣶⡆⣶⡆⠀⠀⢀⣀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢻⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⢇⡿⣾⣹⣹⢫⣧⣷⣽⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⡇⠛⠃⣿⣷⣿⡇⠀⠀⣿⣿⣿⣦⣉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⣇⣿⡇⣿⡇⣿⡇⠀⠀⠘⣿⣿⣿⣿⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠀⠉⠉⠉⠁⠀⠉⠉⠁⠀⠉⠁⠀⠈⠉⠉⠀⠉⠁⠉⠁⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠹⡿⣿⠿⠿⠿⣿⣿⡿⠿⡇

⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠉⠉⢉⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⢠⣤⣤⣤⢠⣤⣤⣤⣤⣤⢠⣤⡄⣤⣤⣤⠀⠀⣤⣤⣤⠀⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⣡⣤⣤⣤⡄⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣙⢹⣿⣿⣿⡇⣿⣇⣿⢿⣿⣿⡿⢸⣿⣇⣸⣿⣿⣼⣿⡇⣿⣿⣀⠀⢸⣿⡸⠿⢾⣿⣿⣿⣿⣿⣿⣿⡇⣿⣇⣿⠇⢸⣿⡇⢰⣿⣿⡇⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡝⣿⣿⣿⣿⣿⡇⣿⡏⠉⢸⣿⣿⣿⢸⣿⣏⣹⣿⢸⣿⣿⡇⣿⣿⣉⠀⢸⣿⣱⣶⢺⣿⣿⣿⡟⣿⣿⣿⡇⣿⡇⣿⡇⢸⣿⡇⣾⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠙⠛⠋⠁⠛⠃⠀⠘⠛⠛⠛⠚⠛⠛⠛⠛⠘⠋⠛⠓⠛⠛⠛⠀⠈⠛⠛⠋⠈⠙⠛⠛⠀⠙⠛⠛⠁⠛⠃⠛⠃⠘⠛⠃⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠶⣢⡛⣢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠀⠀⠀⠒⠦⠀⠀⠀⠀⠀⠀

⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⣿⣿⣧⣴⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⢠⢠⡄⣠⡄⠀⠀⠀⠀⡄

⠀⠾⠿⠻⢻⡿⠿⠿⡿⠣⠺⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠠⠤⠥⠟⠟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[32A⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⡇⠀⠠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣄⢀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢰⠀⠀⠀⠐⠀⠀⠋⠁⣀⣀⣀⣀⣀⡀⠀⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢀⣀⡀⣀⣀⣀⣀⡀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣲⣖⣻⣶⡟⠀⠀⠀⠀⠀⢹⡀⠀⡃⠀⠀⠀⠀⠇⠀⢚⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣥⣭⣭⣿⣿⣶⣶⣶⣶⣶⣾⣷⡆⠆⠀⠀⠀⠀⡇⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡂⠐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢉⣉⣿⣿⡟⣿⣿⣦⠘⢿⣿⣿⡿⠉⣿⡍⠉⢉⡙⠛⣿⡍⢩⣿⡟⢿⣿⡏⠉⡿⢁⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣾⣿⢁⠘⣿⣿⡇⠈⢿⡿⠁⠀⢿⡇⠀⢸⡇⠀⣿⡇⢸⣿⡇⢀⠻⡇⠀⠇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣟⡇⣘⡀⢹⣿⢹⣇⠀⠃⡄⠀⠸⡇⠀⢰⣶⣾⣿⡇⢸⣿⠄⢸⣧⡄⠀⡇⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣦⣭⣼⣥⣿⣧⣤⣿⣼⣿⣦⣾⣿⠀⠀⠃⢀⣘⣿⣿⣿⣧⣼⣿⣤⣼⣿⣿⣦⣿⣦⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣿⣿⣿⣻⣹⢿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡛⠙⠀⠀⠀⠀⠀⢰⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⡦⠀⠀⠀⠀⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢻⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣄⣀⣀⡀⠀⠈⢁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⣷⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢰⣶⣦⣄⣀⣀⣀⣀⣀⡀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢠⠁⠀⠈⠛⢿⣿⠁⠙⠛⣿⣿⣿⣿⣿⣿⣏⣤⣦⠄⠀⠀⠛⢻⠿⠀⠀⠀⠈⠃⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣽⣧⡿⣾⣿⣿⣿⢿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣀⣀⣤⡀⠀⠀⠀⠀⣶⣶⣾⣿⣿⣿⣿⣿⣶⣿⡆

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⡿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣶⣶⣶⣦⢰⣶⣶⣶⠶⣶⡶⠆⣶⡖⣶⡄⣶⡆⣶⡆⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢹⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⢇⡿⣾⡹⣹⢫⣧⣷⣽⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⡇⠛⠃⣿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⣇⣿⡇⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠀⠉⠉⠉⠁⠀⠉⠉⠁⠀⠉⠁⠀⠈⠉⠉⠀⠉⠁⠉⠁⠀⠀⠀⠀⠀⠀⠠⠿⠿⣿⣿⠿⠿⣿⣿⣿⣿⡟⠹⠿⠿⠿⠿⠿⣿⠿⠿⠿⡇

⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠉⠉⢉⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⢠⣤⣤⣤⢠⣤⣤⣤⣤⣤⢠⣤⡄⣤⣤⣤⠀⠀⣤⣤⣤⠀⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⣠⣤⣤⣤⡄⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣙⢹⣿⣿⣿⡇⣿⣇⣿⢿⣿⣿⡿⢸⣿⣇⣸⣿⣿⣼⣿⡇⣿⣿⣀⠀⢸⣿⡸⠿⢾⣿⣿⣿⣿⣿⣿⣿⡇⣿⣇⣿⠇⢸⣿⡇⢠⣾⣿⡇⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡝⣿⣿⣿⣿⣿⡇⣿⡏⠉⢸⣿⣿⣿⢸⣿⣏⣹⣿⢸⣿⣿⡇⣿⣿⣉⠀⢸⣿⣰⣶⢺⣿⣿⣿⡟⣿⣿⣿⡇⣿⡇⣿⡇⢸⣿⡇⠘⠿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠙⠛⠋⠁⠛⠃⠀⠘⠛⠛⠛⠚⠛⠛⠛⠛⠘⠋⠛⠓⠛⠛⠛⠀⠈⠛⠛⠋⠈⠙⠛⠛⠀⠙⠛⠛⠁⠛⠃⠛⠃⠘⠛⠃⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠶⣀⡚⢒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣀⣸⣧⠀⠠⠀⠀⠀⠀

⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⡄

⠀⠸⠿⠻⢺⡿⠿⠿⡿⠣⠺⠟⠿⠻⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠄⠀⠀⠠⠶⠆⠀⠀⠀⠤⠶⠶⠴⠴⠦⠂⠀⠠⠄⠀⠀⠀⢽⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀

[32A⠀⠀⠀⠀⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⣇⠀⠕⢄⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠄⠀⠀⠀⠁⠀⠀⣄⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢸⠀⠈⠂⠐⠀⠀⠋⠁⣀⣀⣀⣀⣀⡀⠀⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⡀⠀⣀⣀⣀⡀⢸⣿⡇⢀⢀⡀⣀⣀⣀⣀⠀⠀⡀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣻⣿⣿⣿⣿⠀⠀⠈⠀⠀⢻⠈⠀⡇⠀⠀⠀⠀⡇⠀⢚⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣭⣭⣭⣿⣿⣶⣶⣶⣶⣶⣾⣷⡆⠇⠀⠀⠀⠀⡇⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⡄⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡷⣈⠀⢀⡀⠔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡂⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢉⣙⣿⣿⡟⣿⣿⣦⠘⢿⣿⣿⡿⠉⣿⡍⠉⢉⡙⠛⣿⡍⢩⣿⡟⢿⣿⡯⠉⡿⢃⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⡇⣘⡀⢹⣿⢻⣧⠈⠃⡄⠀⢸⡇⠀⢰⣶⣾⣿⡇⢸⣿⡇⢸⣷⡄⠀⡇⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣦⣭⣼⣥⣿⣷⣤⣿⣼⣿⣦⣾⣿⠀⠀⠃⢀⣘⣿⣿⣿⣧⣼⣿⣥⣼⣿⣿⣶⣿⣦⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣿⣻⣿⣻⣻⢿⣿⣿⡟⠀⠀⣼⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⠋⠀⠀⣿⣿⣿⣿⣶⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡦⠀⠀⠀⠀⠖⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣷⣶⣶⣶⣤⣤⣤⣤⣤⣄⡀⠀⠈⢁⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠈⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣄⣀⣀⣤⣠⣤⡄

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣧⣤⣶⠄⠀⠀⠛⠻⠿⠀⠀⠀⠈⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⢧⡿⣾⣿⣿⣿⢿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⡀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢿⣿⣿⣿⣷⣶⣦⣀⣠⣴⣀⡀⠀⠀⠀⣶⣶⣶⣿⣿⣿⣿⣿⣶⣿⡆

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣶⣶⣶⣦⢰⣶⣶⣶⠶⣶⡶⠆⣶⡖⣶⡄⣶⡆⣶⡆⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢹⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⢇⡿⡾⣹⣹⢫⣧⣷⣱⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⡇⠛⠃⣿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⣇⣿⡇⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠀⠉⠉⠉⠁⠀⠉⠉⠁⠀⠉⠁⠀⠈⠉⠉⠀⠉⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣿⠿⠿⢿⣿⣿⣿⡟⠙⠿⠿⠿⠿⠿⡿⠿⠿⠿⡇

⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠉⠉⢉⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⢠⣤⣤⣤⢠⣤⣤⣤⣤⣤⢠⣤⡄⣤⣤⣤⠀⠀⣤⣤⣤⠀⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⣠⣤⣤⣤⡄⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣙⢹⣿⣿⣿⡇⣿⣇⣿⢿⣿⣿⡿⢸⣿⣇⣸⣿⣿⣼⣿⡇⣿⣿⣀⠀⢸⣿⠸⠿⢾⣿⣿⣿⣿⣿⣿⣿⡇⣿⣇⣿⠇⢸⣿⡇⢠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡝⣿⣿⣿⣿⣿⡇⣿⡏⠉⢸⣿⣿⣿⢸⣿⣏⣹⣿⢸⣿⣿⡇⣿⣿⣉⠀⢸⣿⣰⣶⢺⣿⣿⣿⡟⣿⣿⣿⡇⣿⡇⣿⡇⢸⣿⡇⠘⣿⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠗⣀⡐⣢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠸⡓⠀⠀⠀⠀⠀⠀

⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⣼⣿⣿⣷⣦⣤⡀⢠⡆⠀⠀⠀⠀⡄

⠀⠾⠿⠿⢻⡿⠿⠿⡿⠣⠺⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠿⠿⠤⠤⠄⠤⠶⠆⠤⠄⠠⠰⠶⠶⠦⠦⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⠷⠀⠀⠀⠀⠀⠀⠀

[32A⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠔⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢰⠀⠀⠀⠐⠀⠀⠋⠑⣀⣀⣀⣀⣀⡀⠀⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣀⣀⡀⣀⣀⣀⣀⢸⣿⡇⢀⢀⡀⣀⣀⣀⣀⡀⢀⡀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣛⣟⣿⣿⡟⠀⠀⠀⠀⠀⢻⠈⠀⠇⠀⠀⠀⠀⡇⠀⢚⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣭⣭⣽⣿⣿⣶⣶⣶⣶⣶⣾⣷⡆⠆⠀⠀⠀⠀⡇⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⡄⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡆⠐⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢉⣙⣿⣿⡟⣿⣿⣦⠘⢿⣿⣿⡿⠉⣿⡍⠉⢉⡙⠛⣿⡍⢩⣿⡝⢿⣿⡏⠁⡿⠁⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣾⣿⢁⠸⣿⣿⡇⠈⢿⡿⠁⠀⢿⡇⠀⢸⡇⠀⣿⡇⢸⣿⡇⢀⠻⡇⠀⠃⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣟⡇⣘⡀⢹⣿⢹⣇⠀⠃⡄⠀⠸⡇⠀⢰⣶⣾⣿⡇⢸⣿⡄⢸⣷⡄⠀⡅⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣿⣻⡿⣛⣹⢿⣿⣿⣟⣡⣴⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣻⣛⡋⢸⣿⣿⣿⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡦⠀⠀⠀⠀⠖⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣤⣤⣤⣄⡀⠀⠈⢁⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣆⠀⠀⠀⠙⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣄⣀⣠⣤⣠⣤⡄

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣧⣤⣶⠄⠀⠀⠛⠻⠿⠀⠀⠀⠈⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣽⢧⡿⣾⣿⣿⣿⢿⣿⣿⣿⣷⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⠁⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠻⣿⣿⣿⣿⣷⣶⣦⣀⣠⣴⣀⡀⠀⠀⠀⣶⣶⣶⣿⣿⣿⣿⣿⣶⣿⡆

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⡿⠿⠿⠷⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣶⣶⣶⣦⢰⣶⣶⣶⠶⣶⡶⠆⣶⡖⣶⡄⣶⡆⣶⡆⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢹⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⢇⡿⡾⡹⣹⢫⣧⣷⣱⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⡇⠛⠃⣿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⣇⣿⡇⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣙⢹⣿⣿⣿⡇⣿⣇⣿⢿⣿⣿⡿⢸⣿⣇⣸⣿⣿⣼⣿⡇⣿⣿⣀⠀⢸⣿⠸⠿⢾⣿⣿⣿⣿⣿⣿⣿⡇⣿⣇⣿⠇⢸⣿⡇⢠⣿⣿⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡝⣿⣿⣿⣿⣿⡇⣿⡏⠉⢸⣿⣿⣿⢸⣿⣏⣹⣿⢸⣿⣿⡇⣿⣿⣉⠀⢸⣿⣰⣶⢺⣿⣿⣿⡟⣿⣿⣿⡇⣿⡇⣿⡇⢸⣿⡇⠸⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢷⣀⡐⣒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠘⠓⠀⠀⠀⠀⠀⠀

⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣷⡆⠠⡄⠀⠀⠀⠀⡄

⠀⠼⠿⠽⢻⡿⠿⠿⡿⠣⠺⠟⠿⠻⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠤⠄⠄⠶⠶⠆⠤⠦⠀⠴⠶⠶⠶⠖⠀⠀⣶⣶⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀

[32A⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢀⠀⠤⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢸⠀⠀⠂⠐⠀⠀⠋⠁⣀⣀⣀⣀⣀⡀⠀⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣀⣀⢀⡀⠀⣀⣀⢸⣿⡇⠀⠀⡀⢀⢀⣀⡀⣀⣀⡀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣛⣿⣿⣿⡿⠀⠀⠀⠀⠀⢹⠀⠀⡇⠀⠀⠀⠀⠇⠀⢚⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠿⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣤⣤⣭⣿⣿⣶⣶⣶⣶⣶⣾⣷⡆⠄⠀⠀⠀⠀⡇⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡂⠐⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢋⣉⣿⣿⡟⣿⣿⣦⠘⢿⣿⣿⡿⠉⣿⡍⠉⢉⡙⠛⣿⡍⢩⣿⡟⢿⣿⡏⠁⡿⠁⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⣿⢁⠘⣿⣿⡇⠈⢿⡿⠁⠀⢿⡇⠀⢸⡇⠀⣿⡇⢸⣿⡇⢀⠻⡇⠀⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣟⡇⣘⡀⢹⣿⢹⣇⠀⠃⡄⠀⠸⡇⠀⢰⣶⣾⣿⡇⢸⣿⡅⢸⣷⡄⠀⡆⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⢻⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣛⠀⠀⣀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠀⠀⠀⠀⠆⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣷⣿⣧⣴⣶⣶⣤⣤⣤⡄⠀⠀⢡⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢠⣀⣀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣦⣤⣤⣦⣤⣶⡆

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡄⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⣿⣿⣿⣧⣴⣶⡄⠀⠀⠛⠻⠟⠀⠀⠀⠈⠁⠀⠀⠿⣿⣿⣿⣿⣿⡿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⢷⡿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⢿⣿⣿⣿⣿⣷⣶⣠⣤⣶⣄⡀⠀⠀⠀⣶⣶⣷⣾⣿⣿⣿⣿⣶⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⡿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣛⢿⣿⣿⣿⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏⣶⣶⣶⣦⢰⣶⣶⣶⠶⣶⡶⠆⣶⡖⣶⡄⣶⡆⣶⡆⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢹⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣇⡿⡾⡹⣹⢫⣧⣷⣱⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⡇⠛⠃⣿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⣇⣿⡇⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠀⠉⠉⠉⠁⠀⠉⠉⠁⠀⠉⠁⠀⠈⠉⠉⠀⠉⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⣿⠿⠿⢿⣿⣿⣿⡟⠙⠿⠿⠿⠿⠿⠿⠿⠟⠿⡇

⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠉⠉⢉⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⢠⣤⣤⣤⢠⣤⣤⣤⣤⣤⢠⣤⡄⣤⣤⣤⠀⠀⣤⣤⣤⠀⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⣠⣤⣤⣤⡄⢻⣿⡇⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣙⢹⣿⣿⣿⡇⣿⣇⣿⢿⣿⣿⡿⢸⣿⣇⣸⣿⣿⣼⣿⡇⣿⣿⣀⠀⢸⣿⠸⠿⢾⣿⣿⣿⣿⣿⣿⣿⡇⣿⣇⣿⠇⢸⣿⡇⢠⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡝⣿⣿⣿⣿⣿⡇⣿⡏⠉⢸⣿⣿⣿⢸⣿⣏⣹⣿⢸⣿⣿⡇⣿⣿⣉⠀⢸⣿⣰⣶⢺⣿⣿⣿⡟⣿⣿⣿⡇⣿⡇⣿⡇⢸⣿⡇⢘⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢗⣀⣄⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⢿⣤⣤⣤⣤⡙⠓⠀⠀⠀⠀⠀⠀

⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣦⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⢸⣿⣿⣿⣿⣷⠄⡄⠀⠀⠀⠀⠄

⠀⠾⠿⠿⢻⡿⠿⠿⡿⠣⠺⠟⠿⠻⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠤⠠⠄⠴⠶⠆⠴⠠⠤⠶⠶⠶⠾⠶⠦⠲⠴⠦⠀⠀⢾⣿⣿⡿⠿⠁⠀⠀⠀⠀⠀⠀⠀

[32A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢀⠀⠤⠀⠒⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢸⠄⠀⠠⠀⠀⠀⡀⣄⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢸⠂⠘⠐⠒⠀⠀⠋⠁⣀⣀⣀⣀⣀⡀⠀⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢀⠀⡀⠀⠀⢀⣀⢸⣿⡇⠀⠀⠀⢀⣀⡀⠀⣀⠀⡀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⠀⠀⠈⠀⠀⢹⡀⠀⡅⠀⠀⠀⠀⠇⠀⢚⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠛⠛⠛⣻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣤⣤⣽⣶⣷⣶⣶⣶⣶⣶⣾⣷⡆⠇⠀⠀⠀⠀⡇⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⡄⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣤⡆⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢉⣙⣿⣿⡟⣿⣿⣦⠘⢿⣿⣿⡿⠉⣿⡍⠉⢉⡙⠛⣿⡍⢩⣿⡟⢿⣿⡏⠁⡿⠃⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣾⣿⢁⠘⣿⣿⣇⠈⢿⡿⠁⠀⢿⡇⠀⢸⡇⠀⣿⡇⢸⣿⡇⢀⠻⡇⠀⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⡟⡇⣘⡀⢹⣿⢹⣇⠀⠃⡄⠀⠸⡇⠀⢰⣶⣾⣿⡇⢸⣿⡅⢸⣷⡄⠀⡆⠸⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣦⣭⣾⣥⣿⣧⣤⣿⣼⣿⣦⣾⣿⠀⠀⠃⢀⣘⣿⣿⣿⣧⣼⣿⣥⣼⣿⣿⣦⣿⣦⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣫⢿⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣛⣿⣋⠀⠀⣀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠶⠀⠀⠀⠀⠂⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣶⣶⣦⣤⣤⡄⠀⠀⠠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣀⠀⠀⠉⠉⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢰⣄⣀⠀⠀⠀⠀⡀⠀⢰⣶⣶⣶⣤⣶⣶⣴⣶⡆

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠛⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⢿⣿⣿⣧⣴⣶⣄⠀⠀⠛⠻⠿⠀⠀⠀⠀⠁⠀⠀⠿⣿⣿⣿⣿⣿⡿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣿⢧⡿⣾⣷⣿⣿⢿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣿⣿⣿⣷⣶⣤⣤⣶⣆⣀⠀⠀⠀⣶⣶⣷⣶⣾⣿⣿⣿⣷⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⡿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣛⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣶⣶⣶⣦⢰⣶⣶⣶⠶⣶⡶⠆⣶⡖⣶⡄⣶⡆⣶⡆⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢹⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣇⡿⡾⣹⢹⢫⣧⣧⣱⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⡇⠛⠃⣿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠀⠉⠉⠉⠁⠀⠉⠉⠁⠀⠉⠡⣶⣬⣉⣉⠀⠉⠁⠉⠁⠀⠀⠀⠀⠀⠀⠠⠽⠿⠿⠿⠿⠿⢿⣿⣿⣿⡏⠘⠿⠟⠛⠿⠻⠿⠿⠿⠿⡇

⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠉⠉⢉⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⢠⣤⣤⣤⢠⣤⣤⣤⣤⣤⢠⣤⡄⣤⣤⣤⠙⠋⣤⣤⣤⠀⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⣠⣤⣤⣤⡄⢻⣿⡇⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣙⢹⣿⣿⣿⡇⣿⣇⣿⢿⣿⣿⡿⢸⣿⣇⣸⣿⣿⣼⣿⡇⣿⣿⣀⠀⢸⣿⡸⠿⢾⣿⣿⣿⣿⣿⣿⣿⡇⣿⣇⣿⠇⢸⣿⡇⢠⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡝⣿⣿⣿⣿⣿⡇⣿⡏⠉⢸⣿⣿⣿⢸⣿⣏⣹⣿⢸⣿⣿⡇⣿⣿⣉⠀⢸⣿⣱⣶⢺⣿⣿⣿⡟⣿⣿⣿⡇⣿⡇⣿⡇⢸⣿⡇⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠙⠛⠋⠁⠛⠃⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠘⠋⠛⠃⠛⠛⠛⠀⠈⠛⠛⠋⠈⠙⠛⠛⠀⠙⠛⠛⠁⠛⠃⠛⠃⠘⠛⣣⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢛⣤⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡟⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀

⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠛⢿⠓⠀⠀⠐⠘⠀⠀⠄⠀⠀⠀⠀⠀

⠀⠾⠿⠻⢻⡿⠿⠿⡿⠣⠺⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠦⠀⠄⠴⠶⠦⠷⠤⠴⠶⠶⠶⠶⠶⠷⠶⠿⠷⠶⠾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢰⠠⠤⠄⡒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢸⢈⠀⠠⠁⡀⠀⡀⣄⢀⠀⠀⠀⠀⠔⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣀⢀⠀⠀⣸⠠⠜⠒⠔⠀⠀⠋⠁⣀⣀⣀⣀⣀⡀⠀⢖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⢸⣿⡇⠀⠀⠀⣀⣀⣀⠀⢀⣀⣀⣀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⠀⠀⠉⠀⣠⣻⡁⠀⠅⠀⠀⠀⠀⠇⠀⢛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠛⠛⠛⣻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣾⣷⡆⠄⠀⠀⠀⠀⡇⣴⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡂⢐⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢉⣙⣿⣿⡟⣿⣿⣦⠘⢿⣿⣿⡿⠉⣿⡍⠉⢉⡛⠛⣿⡍⢩⣿⡟⢿⣿⡏⠁⡿⢁⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣾⣿⢁⠘⣿⣿⡇⠈⢿⡿⠁⠀⢿⡇⠀⢸⡇⠀⣿⡇⢸⣿⡇⢀⠻⡇⠀⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣟⡇⣘⡀⢹⣿⢹⣧⠀⠃⡄⠀⠸⡇⠀⢰⣶⣾⣿⡇⢸⣿⡇⢸⣷⡄⠀⡆⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣦⣭⣼⣥⣿⣷⣤⣿⣼⣿⣦⣾⣿⠀⠀⠃⢀⣘⣿⣿⣿⣧⣼⣿⣤⣼⣿⣿⣦⣿⣦⣄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⢿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣯⣉⡀⠀⣀⣀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠶⠀⠀⠀⠀⠂⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡟⠋⠉⠙⣿⡿⠿⠿⣿⣧⣴⣶⣶⣦⣤⣤⡄⠀⠀⠠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡶⡶⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢰⣄⣀⠀⠀⠀⠀⡀⠀⢰⣶⣶⣶⣦⣶⣶⣴⣶⡆

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢧⣴⣶⣄⠀⠀⠛⠻⠿⠀⠀⠀⠀⠁⠀⠀⠿⣿⣿⣿⣿⣿⡿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣿⣧⡿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣷⣶⣤⣤⣶⣆⣀⠀⠀⠀⣶⣶⣷⣶⣾⣿⣿⣿⣷⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⡿⠿⠿⠿⠿⠿⠿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣛⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣶⣶⣶⣦⢰⣶⣶⣶⠶⣶⡶⠆⣶⡖⣶⡄⣶⡆⣶⡆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢹⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⢇⡿⡾⡹⣹⢫⣧⣷⣱⣿⣿⣿⣿⣿⣿⣿⠄⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⡇⠛⠃⣿⣷⣿⡇⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⣇⣿⡇⣿⡇⣿⡇⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠀⠉⠉⠉⠁⠀⠉⠉⠁⠀⠉⠁⠀⠈⠉⠉⠀⠉⠁⠉⠁⠀⠀⠀⠀⠀⠤⢾⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⡏⠸⠿⠿⢻⠿⠻⠿⠿⠿⠿⡇

⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠉⠉⢉⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⢠⣤⣤⣤⢠⣤⣤⣤⣤⣤⢠⣤⡄⣤⣤⣤⠀⠀⣤⣤⣤⠀⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⣠⣤⣤⣤⡄⢻⣿⡇⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡝⣿⣿⣿⣿⣿⡇⣿⡏⠉⢸⣿⣿⣿⢸⣿⣏⣹⣿⢸⣿⣿⡇⣿⣿⣉⠀⢸⣿⣱⣶⢺⣿⣿⣿⡟⣿⣿⣿⡇⣿⡇⣿⡇⢸⣿⡇⢘⢿⣏⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠙⠛⠋⠁⠛⠃⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠘⠋⠛⠓⠛⠛⠛⠀⠈⠛⠛⠋⠈⠙⠛⠛⠀⠙⠛⠛⠁⠛⠃⠛⠃⠘⠛⠃⠀⠈⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⣨⣔⣕⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠘⠛⠀⠐⠀⠀⠀⠀

⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠃⠀⠀⠲⠘⠄⠠⠄⠀⠀⠀⠠⠀

⠀⠾⠿⠽⢻⡿⠿⠿⡿⠣⠻⠟⠿⠻⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠄⠀⠠⠤⠤⠦⠤⠀⠀⠠⠶⠶⠶⠶⠶⠶⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀

[32A⠀⠀⠀⠀⢀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢰⠠⢼⣬⡖⠖⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢸⢌⣈⣨⣧⡡⠠⡀⣔⠀⠀⠀⠀⠀⠔⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣀⢀⠀⢀⣸⠠⠝⠚⡶⠔⠠⠋⠁⣀⣀⣀⣀⣀⡀⠀⠒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⡀⡀⠀⡀⣀⠀⠀⢀⢸⣿⣇⣀⣀⣀⣀⣀⣠⣀⣀⣄⣀⣀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡿⠿⠿⠿⢿⠀⠈⠉⠕⣨⣻⢀⠀⡇⠀⠀⠀⠀⠇⠀⢘⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣤⣤⣶⣶⣶⣶⣶⣾⣷⣶⣿⣷⡆⠇⠀⠀⠀⠀⡅⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢉⣙⣿⣿⡟⣿⣿⣦⠘⢿⣿⣿⡿⠉⣿⡍⠉⢉⡙⠛⣿⡍⢩⣿⡟⢿⣿⡏⠁⡿⠁⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣾⣿⢁⠘⣿⣿⣇⠈⢿⡿⠁⠀⢿⡇⠀⢸⡇⠀⣿⡇⢸⣿⠇⢀⠻⡇⠀⡃⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⡿⡇⣘⡀⢹⣿⢹⣇⠀⠃⡄⠀⠸⡇⠀⢰⣶⣾⣿⡇⢸⣿⡇⢸⣷⡄⠀⡆⠸⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣦⣭⣼⣥⣿⣧⣤⣿⣼⣿⣦⣾⣿⠀⠀⠃⢀⣘⣿⣿⣿⣧⣼⣿⣥⣼⣿⣿⣦⣿⣦⣄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⢿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣍⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡖⡶⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡥⢤⡄⠀⠀⠀⠀⠀⠀⠘⠉⠲⠶⣶⣶⣦⣤⡄⠀⠀⢠⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠇⠀⠀⠀⠀⢰⣆⣠⠀⠀⠀⢀⡀⠀⠰⣿⣿⣶⣶⣶⣶⣶⣶⡆

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣴⣿⣄⡀⠀⠛⠻⠟⠀⠀⠀⠀⠀⠀⠀⡸⠿⢿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣻⢷⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣶⣦⣶⣶⣦⣄⡀⡀⠀⢶⣶⣷⣶⣾⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⡿⠿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣛⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣶⣶⣶⣦⢰⣶⣶⣶⠶⣶⡶⠆⣶⡖⣶⡄⣶⡆⣶⡆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢹⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣇⡿⡾⡹⢹⢫⣧⣧⣱⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⡇⠛⠃⣿⣷⣿⡇⠀⠀⠀⠀⠀⠸⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⣇⣿⡇⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠀⠉⠉⠉⠁⠀⠉⠉⠁⠀⠉⠁⠀⠈⠉⠉⠀⠉⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠿⠛⠛⠛⠙⠿⠿⠿⠿⠇

⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠉⠉⢉⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⢠⣤⣤⣤⢠⣤⣤⣤⣤⣤⢠⣤⡄⣤⣤⣤⠀⠀⣤⣤⣤⠀⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⣠⣤⣤⣤⡄⠀⠘⣿⣿⡄⠀⠀⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣙⢹⣿⣿⣿⡇⣿⣇⣿⢿⣿⣿⡿⢸⣿⣇⣸⣿⣿⣼⣿⡇⣿⣿⣀⠀⢸⣿⠸⠿⢾⣿⣿⣿⣿⣿⣿⣿⡇⣿⣇⣿⠇⢸⣿⡇⠀⠀⢀⣘⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡝⣿⣿⣿⣿⣿⡇⣿⡏⠉⢸⣿⣿⣿⢸⣿⣏⣹⣿⢸⣿⣿⡇⣿⣿⣉⠀⢸⣿⣰⣶⢺⣿⣿⣿⡟⣿⣿⣿⡇⣿⡇⣿⡇⢸⣿⡇⠀⠀⠈⠻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣛⣴⣽⣛⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠊⠀⠀⠀⠀

⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣤⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠐⢘⠂⠐⠄⠀⠀⠀⠀⠀

⠀⠾⠿⠻⢻⡿⠿⠿⡿⠣⠺⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠕⠄⠢⠶⠶⠶⠦⠤⠠⠾⠿⠿⠶⠿⠿⠿⠶⠿⠿⠿⠇⠀⠀⠀⠁⠀⠀⠀⠀⠰⠀⠀⠀

⠀⠀⠀⠀⢰⠠⠼⣬⡖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢸⠈⠀⢨⢁⡁⠀⡀⣄⠀⠀⠀⠀⠀⠔⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢀⠀⠀⠀⢸⠀⠈⠂⠐⠀⠀⠋⠁⣀⣀⣀⣀⣀⡀⠀⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⡀⠀⠀⡀⡀⡀⠀⢀⢸⣿⣇⣀⣀⣀⣀⣀⣠⣄⣀⣀⣀⣀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠿⠿⠿⠿⠿⠀⠀⠉⠐⣠⢹⣈⠀⡇⠀⠀⠀⠀⠇⠀⢘⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⡆⠇⠀⠀⠀⠀⡇⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡷⣈⠀⢀⡀⢔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢉⣙⣿⣿⡟⣿⣿⣦⠘⢿⣿⣿⡿⠉⣿⡍⠉⢉⡛⠛⣿⡍⢩⣿⡟⢿⣿⡏⠁⡿⠃⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣾⣿⢁⠘⣿⣿⣇⠈⢿⡿⠁⠀⢿⡇⠀⢸⡇⠀⣿⡇⢸⣿⠇⢀⠻⡇⠀⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⡇⣘⡀⢹⣿⢹⣇⠀⠃⡄⠀⠸⡇⠀⢰⣶⣾⣿⡇⢸⣿⡇⢸⣷⡄⠀⡇⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣦⣭⣾⣥⣿⣧⣤⣿⣼⣿⣦⣾⣿⠀⠀⠃⢀⣘⣿⣿⣿⣧⣼⣿⣥⣼⣿⣿⣦⣷⣦⣄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⢿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣅⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡖⡶⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡥⢡⡄⠀⠀⠀⠀⠀⠀⠘⠉⠲⠶⣶⣶⣦⣤⡄⠀⠀⢠⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠇⠀⠀⠀⠀⢰⣆⣠⠀⠀⠀⠀⡀⠀⠰⣿⣿⣶⣶⣶⣶⣶⣶⡆

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣻⢧⡿⣾⣿⣿⣿⢿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣶⣦⣶⣶⣦⣄⡀⡀⠀⢶⣶⣷⣶⣾⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣛⢿⣿⣿⣿⣷⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡏⣶⣶⣶⣦⢰⣶⣶⣶⠶⣶⡶⠆⣶⡖⣶⡄⣶⡆⣶⡆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢹⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣇⡿⡾⡹⣹⢫⣧⣧⣱⣿⣿⣿⣿⣿⣿⣿⠄⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⡇⠛⠃⣿⣷⣿⡇⠀⠀⠀⠀⠀⠸⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠀⠉⠉⠉⠁⠀⠉⠉⠁⠀⠉⠁⠀⠈⠉⠉⠀⠉⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠻⠛⠛⠛⠙⠿⠿⠿⠿⠇

⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠉⠉⢉⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⢠⣤⣤⣤⢠⣤⣤⣤⣤⣤⢠⣤⡄⣤⣤⣤⠀⠀⣤⣤⣤⠀⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⣠⣤⣤⣤⡄⠀⠘⢿⣿⡄⠀⠀⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣙⢹⣿⣿⣿⡇⣿⣇⣿⢿⣿⣿⡿⢸⣿⣇⣸⣿⣿⣼⣿⡇⣿⣿⣀⠀⢸⣿⠸⠿⢾⣿⣿⣿⣿⣿⣿⣿⡇⣿⣇⣿⠇⢸⣿⡇⠀⠀⠀⣘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡝⣿⣿⣿⣿⣿⡇⣿⡏⠉⢸⣿⣿⣿⢸⣿⣏⣹⣿⢸⣿⣿⡇⣿⣿⣉⠀⢸⣿⣰⣶⢺⣿⣿⣿⡟⣿⣿⣿⡇⣿⡇⣿⡇⢸⣿⡇⠀⠀⠈⠛⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⣴⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠂⠀⠀⠀⠀

⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⠐⠀⠀⠀⠸⠂⠀⠂⠀⠀⠀⠀⠀

⠀⠾⠿⠽⢻⡿⠿⠿⡿⠣⠺⠟⠿⠻⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠧⠄⠠⠷⠶⠶⠦⠤⠴⠶⠿⠾⠶⠿⠾⠷⠷⠿⠿⠧⠇⠀⠀⠀⠁⠀⠀⠀⠀⠴⠖⠀⠀

[32A⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢸⠠⢶⠴⠖⢖⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢸⢌⣈⢨⣃⡥⠀⡀⣔⠀⠀⠀⠀⠠⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣀⣠⣀⣀⣸⠢⠟⠚⠷⠗⠠⢋⠁⣀⣀⣀⣀⣀⡀⠀⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣇⣀⣄⣤⣠⣤⣤⣤⣤⣤⣤⣀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠿⠯⠿⠿⠿⠀⠈⠉⢄⣨⣻⣁⠀⡇⠀⠀⠀⠀⡇⠀⢘⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⢿⡿⡿⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣤⣤⣶⣶⣶⣶⣶⣾⣶⣶⣿⣷⡆⡇⠀⠀⠀⠀⡇⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡷⣈⠀⢀⡀⠔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢉⣙⣿⣿⡟⣿⣿⣦⠙⢿⣿⣿⡿⠉⣿⡍⠉⢩⡛⠛⣿⡍⢩⣿⡟⢿⣿⣯⠉⡿⢃⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⣿⢁⠘⣿⣿⣇⠈⢿⡿⠁⠀⢿⡇⠀⢸⡇⠀⣿⡇⢸⣿⡇⢀⠻⡇⠀⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⡏⣘⡀⢹⣿⢻⣧⠈⠃⡄⠀⠸⡇⠀⢰⣶⣾⣿⡇⢸⣿⡇⢸⣷⡄⠀⡇⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣻⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣭⣁⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡖⣶⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⣶⣶⣶⡆⠀⠀⢠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⠇⠀⠀⠀⠀⢲⣦⣠⠄⠀⠀⢀⡀⠀⠸⣿⣿⣷⣶⣶⣶⣶⣶⡆

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⡀⠀⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⡺⠿⢿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣽⢷⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⣶⣶⣶⣶⣦⣤⡀⡀⠀⢾⣶⣷⣶⣾⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⡿⠿⠿⠿⠿⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣛⢿⣿⣿⣿⣷⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡏⣶⣶⣶⣦⢰⣶⣶⣶⠶⣶⡶⠆⣶⡖⣶⡄⣶⡆⣶⡆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢹⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⢇⡿⡾⡹⢹⢫⣧⣧⣱⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⡇⠛⠃⣿⣷⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⣇⣿⡇⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠀⠉⠉⠉⠁⠀⠉⠉⠁⠀⠉⠁⠀⠈⠉⠉⠀⠉⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠿⣿⡾⠟⠛⠿⠛⠙⠿⠿⠿⠿⠇

⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠉⠉⢉⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⢠⣤⣤⣤⢠⣤⣤⣤⣤⣤⢠⣤⡄⣤⣤⣤⠀⠀⣤⣤⣤⠀⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⣠⣤⣤⣤⡄⠀⣤⣯⣯⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣙⢹⣿⣿⣿⡇⣿⣇⣿⢿⣿⣿⡿⢸⣿⣇⣸⣿⣿⣼⣿⡇⣿⣿⣀⠀⢸⣿⡸⠿⢾⣿⣿⣿⣿⣿⣿⣿⡇⣿⣇⣿⠇⢸⣿⡇⠰⠛⠉⠙⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡝⣿⣿⣿⣿⣿⡇⣿⡏⠉⢸⣿⣿⣿⢸⣿⣏⣹⣿⢸⣿⣿⡇⣿⣿⣉⠀⢸⣿⣱⣶⢺⣿⣿⣿⡟⣿⣿⣿⡇⣿⡇⣿⡇⢸⣿⡇⠀⠀⠀⠰⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣳⣿⣿⣧⣀⢱⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⠀⠀⠀⢀⠈⠁⠀⠊⠀⠀⠀⠀

⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⠀⠀⠀⢀⠀⡀⠀⠀⠀⢀⠀⡀⠀⠀⣀⣌⣷⣿⣦⡋⠀⠀⠀⢘⠀⠐⠇⠀⠀⠀⠀⠀

⠄⠾⠿⠹⢻⡿⠿⠿⡿⠣⠻⠟⠿⠻⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠷⠮⠶⠾⠿⠾⠿⠿⠿⠷⠿⠿⠿⠿⠇⠀⠀⠀⠁⠀⠀⠀⠠⠰⠴⠀⠀

[32A⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢹⠠⠴⢜⡖⠇⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢸⢌⣈⣨⣏⡧⠀⡀⣔⢀⠀⠀⠀⠠⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣀⣠⣀⣠⣼⠢⠟⠚⠷⠄⠠⠋⠁⣀⣀⣀⣀⣀⡀⠀⠒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣀⣀⣀⣀⣀⣄⣀⣄⣤⣄⣸⣿⣇⣠⣦⣤⣤⣤⣴⣦⣤⣤⣤⣤⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠿⠿⠿⠿⠿⠀⠀⠈⢄⣨⣻⡊⠀⡃⠀⠀⠀⠀⡇⠀⢘⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣦⡂⠐⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢉⣉⣿⣿⡟⣿⣿⣦⠘⢿⣿⣿⡿⠉⣿⡍⠉⢉⡙⠛⣿⡍⢩⣿⡟⢿⣿⡏⠁⡿⠁⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣾⣿⢁⠘⣿⣿⣇⠈⢿⡿⠁⠀⢿⡇⠀⢸⡇⠀⣿⡇⢸⣿⠇⢀⠻⡇⠀⠇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⡇⣘⡀⢹⣿⢹⣇⠀⠃⡄⠀⠸⡇⠀⢰⣶⣾⣿⡇⢸⣿⡇⢸⣷⡄⠀⡆⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣦⣭⣾⣥⣿⣷⣤⣿⣼⣿⣦⣾⣿⠀⠀⠃⢀⣘⣿⣿⣿⣧⣼⣿⣥⣼⣿⣿⣦⣿⣦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣻⣩⢿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣭⣀⣀⣤⣤⡀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡖⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢲⣶⣶⡆⠀⠀⠠⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇⡀⠀⠀⠀⣲⣦⣤⠦⠀⠀⢀⡀⠀⠸⣿⣿⣷⣶⣶⣶⣶⣶⡆

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⡀⠀⠛⠙⠛⠀⠀⠀⠀⠀⠀⠀⡻⠿⢿⣿⣿⣿⣟⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣽⢧⡿⣾⣿⣿⣻⢿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣶⣶⣶⣶⣦⣤⣀⡀⠀⢾⣶⣷⣶⣾⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⡿⠿⠿⠿⠿⠇⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣛⢿⣿⣿⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⠏⣶⣶⣶⣦⢰⣶⣶⣶⠶⣶⡶⠆⣶⡖⣶⡄⣶⡆⣶⡆⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢹⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣇⡿⡾⡹⢹⢫⣧⣷⣱⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⡇⠛⠃⣿⣷⣿⡇⢀⠀⠀⠀⠀⠄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⣇⣿⡇⣿⡇⣿⡇⠈⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠀⠉⠉⠉⠁⠀⠉⠉⠁⠀⠉⠁⠀⠈⠉⠉⠀⠉⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠿⠷⠿⠿⠿⠿⠿⠿⠿⠿⡏⠀⠛⠻⠯⠛⠉⠿⠿⠿⠿⠇

⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠉⠉⢉⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⢠⣤⣤⣤⢠⣤⣤⣤⣤⣤⢠⣤⡄⣤⣤⣤⠀⠀⣤⣤⣤⠀⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⣠⣤⣤⣤⡄⠀⠈⢣⣄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣙⢹⣿⣿⣿⡇⣿⣇⣿⢿⣿⣿⡿⢸⣿⣇⣸⣿⣿⣼⣿⡇⣿⣿⣀⠀⢸⣿⡸⠿⢾⣿⣿⣿⣿⣿⣿⣿⡇⣿⣇⣿⠇⢸⣿⡇⠀⠀⠀⠈⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡝⣿⣿⣿⣿⣿⡇⣿⡏⠉⢸⣿⣿⣿⢸⣿⣏⣹⣿⢸⣿⣿⡇⣿⣿⣉⠀⢸⣿⣱⣶⢺⣿⣿⣿⡿⣿⣿⣿⡇⣿⡇⣿⡇⢸⣿⡇⠀⠀⠀⠘⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣧⣼⣭⣷⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢸⡷⡄⣀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀

⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣀⣶⣾⣷⣯⡛⠀⠀⠉⠛⠒⠒⠃⠀⠀⠀⠀⠀

⠀⠿⠿⠿⢻⡿⠿⠿⡿⠣⠻⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠧⠇⠷⠾⠷⠶⠦⠦⠤⠶⠿⠿⠷⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠁⠀⠀⠀⠀⠶⠰⠀⠀

⠀⠀⠀⠀⢱⠠⠴⢌⡖⠖⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢸⢌⣨⣨⣃⡡⠀⡀⣔⢀⠀⠀⠀⠠⠔⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣀⣤⣀⣀⣼⠢⠟⠚⠷⠞⠠⠋⠁⣀⣀⣀⣀⣀⡀⠀⠒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣀⣀⣀⣄⣤⣤⣤⣤⣤⣤⣸⣿⣇⣠⣴⣦⣶⣶⣶⣦⣤⣤⣤⣤⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠿⠽⠿⠿⠿⠀⠂⠉⠐⣨⢻⡁⠀⡇⠀⠀⠀⠀⡇⠀⢐⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣦⣤⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⡆⠇⠀⠀⠀⠀⡇⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣤⡂⠐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢉⡙⣿⣿⡟⣿⣿⣦⠘⢿⣿⣿⡿⠉⣿⡍⠉⢉⡙⠛⣿⡍⢩⣿⡟⢿⣿⡏⠁⡿⠁⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣦⣭⣾⣥⣿⣷⣤⣿⣼⣿⣦⣾⣿⠀⠀⠃⣀⣘⣿⣿⣿⣧⣼⣿⣥⣼⣿⣿⣦⣿⣦⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣫⣿⣿⣿⡟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⣤⣄⣠⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡎⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢲⣶⣶⡆⠀⠀⠠⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠇⣀⠀⠀⠀⣸⣦⣴⠦⠀⠀⠀⡀⠀⠸⣿⣿⣿⣶⣶⣶⣶⣿⡆

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣆⡀⠀⠛⠙⠛⠀⠀⠀⠀⠀⠀⠀⡟⠿⢿⣿⣿⣿⣟⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣽⢷⡿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⣶⣶⣶⣶⣦⣀⣀⠀⢺⣷⣿⣶⣾⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⡿⠿⠿⠿⠿⠀⠀⠘⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣛⢿⣿⣿⣿⣷⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠏⣶⣶⣶⣦⢰⣶⣶⣶⠶⣶⡶⠆⣶⡖⣶⡄⣶⡆⣶⡆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢹⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⢇⡿⡾⡹⢹⢫⣧⣧⣱⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⡇⠛⠃⣿⣷⣿⡇⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⣇⣿⡇⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠁⠉⠉⠉⠁⠀⠉⠉⠁⠀⠉⠁⠀⠈⠉⠉⠀⠉⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠩⠶⠿⠿⠿⠿⠿⠿⠿⠿⢯⣀⠻⠿⠏⠛⠉⠿⠿⠿⠿⠇

⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠉⠉⢉⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⢠⣤⣤⣤⢠⣤⣤⣤⣤⣤⢠⣤⡄⣤⣤⣤⠀⠀⣤⣤⣤⠀⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⣠⣤⣤⣤⡄⠀⠀⠈⢻⣥⠀⠀⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣙⢹⣿⣿⣿⡇⣿⣇⣿⢿⣿⣿⡿⢸⣿⣇⣸⣿⣿⣼⣿⡇⣿⣿⣀⠀⢸⣿⡸⠿⢾⣿⣿⣿⣿⣿⣿⣿⡇⣿⣇⣿⠇⢸⣿⡇⠀⠀⠀⠀⠈⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡝⣿⣿⣿⣿⣿⡇⣿⡏⠉⢸⣿⣿⣿⢸⣿⣏⣹⣿⢸⣿⣿⡇⣿⣿⣉⠀⢸⣿⣱⣶⢺⣿⣿⣿⡿⣿⣿⣿⡇⣿⡇⣿⡇⢸⣿⡇⠀⠀⠀⠀⠘⢳⣾⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣯⣭⣾⣿⣧⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣩⡧⡄⣀⠀⠀⠀⠀⠀⠃⡀⠀⠀⠀⠀⠀

⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⢠⡀⣖⣿⣿⣾⡛⠀⠀⠘⠒⠂⠐⠃⠀⠀⠀⠀⠀

⠀⠾⠿⠽⢻⡿⠿⠿⡿⠣⠻⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠶⠎⠷⠾⠿⠶⠧⠤⠠⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠁⠀⠀⠀⠀⠶⠴⠀⠀

[32A⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢡⠠⠤⢠⡔⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢸⢄⠀⠀⢁⡁⠀⡀⣄⢀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣀⣤⣠⣠⣾⠀⠘⠚⠐⠀⠠⠫⠁⣀⣀⣀⣀⣀⡀⠀⠒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣀⣠⣀⣤⣤⣦⣤⣤⣤⣴⣸⣿⣧⣠⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠿⠯⠿⠿⠿⠀⠀⠀⠀⣀⢻⡀⠀⡇⠀⠀⠀⠀⡇⠀⢘⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠍⠉⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣤⣤⣶⣶⣶⣶⣶⣾⣶⣶⣿⣷⡆⠇⠀⠀⠀⠀⡇⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡷⣈⠂⢀⡀⠔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣤⡂⢐⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢉⣉⣿⣿⡟⣿⣿⣦⠙⢿⣿⣿⡿⠉⣿⡍⠉⢩⡙⠛⣿⡍⢩⣿⡟⢿⣿⣯⠉⡿⢃⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣟⡇⣘⡀⢹⣿⢻⣧⠈⠃⡄⠀⠸⡇⠀⢰⣶⣾⣿⡇⢸⣿⡇⢸⣷⡄⠀⡇⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣦⣭⣾⣥⣿⣷⣤⣿⣼⣿⣧⣾⣿⠀⠀⠃⣀⣘⣿⣿⣿⣧⣼⣿⣥⣼⣿⣿⣶⣿⣦⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣫⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡎⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⡆⠀⠀⠠⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⠇⣀⠀⠀⠀⣸⣦⣴⠶⠀⠀⠀⡀⠀⠸⣿⣿⣿⣶⣶⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣆⡀⠀⠛⠙⠛⠀⠀⠀⠀⠀⢀⠀⡛⠿⢿⣿⣿⣿⣟⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣽⢧⡿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠈⠉⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⣶⣶⣶⣶⣦⣀⣀⠀⣺⣿⣿⣶⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⡿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣛⢿⣿⣿⣿⣷⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡏⣶⣶⣶⣦⢰⣶⣶⣶⠶⣶⡶⠆⣶⡖⣶⡄⣶⡆⣶⡆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢹⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⢇⡿⡾⡹⢹⢫⣧⣷⣱⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⡇⠛⠃⣿⣷⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⣇⣿⡇⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠈⠉⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠁⠉⠉⠉⠁⠀⠉⠉⠁⠀⠉⠁⠀⠈⠉⠉⠀⠉⠁⠉⠁⠀⠀⠀⠀⠀⠀⠘⠿⠿⠟⠛⠿⠻⠿⠟⠛⠉⠉⣿⣿⣿⠯⠉⠉⠿⠿⠿⠿⠇

⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠉⠉⢉⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⢠⣤⣤⣤⢠⣤⣤⣤⣤⣤⢠⣤⡄⣤⣤⣤⠀⠀⣤⣤⣤⠀⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⣠⣤⣤⣤⡄⠀⠀⢠⡿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣙⢹⣿⣿⣿⡇⣿⣇⣿⢿⣿⣿⡿⢸⣿⣇⣸⣿⣿⣼⣿⡇⣿⣿⣀⠀⢸⣿⠸⠿⢾⣿⣿⣿⣿⣿⣿⣿⡇⣿⣇⣿⠇⢸⣿⡇⠀⠘⠛⠋⠀⠸⢿⠆⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡝⣿⣿⣿⣿⣿⡇⣿⡏⠉⢸⣿⣿⣿⢸⣿⣏⣹⣿⢸⣿⣿⡇⣿⣿⣉⠀⢸⣿⣰⣶⢺⣿⣿⣿⡟⣿⣿⣿⡇⣿⡇⣿⡇⢸⣿⡇⠀⠀⠀⠀⠀⠀⣷⠆⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠙⠛⠋⠁⠛⠃⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠘⠋⠛⠓⠛⠛⠛⠀⠈⠛⠛⠋⠈⠙⠛⠛⠀⠙⠛⠛⠁⠛⠃⠛⠃⠘⠛⠃⠠⠠⠠⠀⠀⠉⠁⠀⡀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣯⣴⣯⣽⣧⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣼⣾⡤⣀⠀⠀⠀⠀⠈⠉⡀⠁⠀⠀⠀⠀

⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⡂⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀⠀⢀⣐⣲⣿⣷⣧⡛⠀⠀⠙⠐⠛⠐⠃⠀⠀⠀⠀⠀

⠀⠾⠿⠿⢻⡿⠿⠿⡿⠣⠺⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠮⠽⠾⠷⠾⠶⠮⠴⠽⠿⠿⠶⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠁⠀⠀⠀⠠⠴⠶⠄⠀

[32A⠀⠀⠀⠀⢀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢸⠠⠼⢤⠖⠖⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢸⢬⣈⣬⣃⡥⠂⡀⣄⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣤⣤⣤⣶⣾⠢⠟⠚⠳⠗⠀⠮⠑⣀⣀⣀⣀⣀⡐⠀⠒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣤⣦⣴⣶⣶⣶⣶⣦⣶⣦⣼⣿⣧⣠⣶⣶⣦⣶⣶⣤⣤⣤⣤⣤⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠿⠿⠿⠿⠿⠀⠂⠉⠀⣨⣻⣂⠀⡃⠀⠀⠀⠀⡇⠀⢚⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠭⠍⠈⠉⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣤⣤⣶⣶⣶⣶⣶⣾⣶⣶⣾⣷⡆⠆⠀⠀⠀⠀⡇⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⠷⣈⠀⢀⡀⠔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢉⡉⢿⣿⡟⣿⣿⣦⠘⢿⣿⣿⡿⠉⣿⡍⠉⢉⡙⠛⣿⡍⢩⣿⡟⢿⣿⡯⠉⡿⢃⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⣿⢁⠘⣿⣿⡇⠈⢿⡿⠁⠀⢿⡇⠀⢸⡇⠀⣿⡇⢸⣿⠇⢀⠻⡇⠀⠇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⡇⣘⡀⢹⣿⢹⣧⠀⠃⡄⠀⠸⡇⠀⢰⣶⣾⣿⡇⢸⣿⡇⢸⣷⡄⠀⡇⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣦⣭⣼⣥⣿⣧⣤⣿⣼⣿⣦⣾⣿⠀⠀⠃⢀⣘⣿⣿⣿⣧⣼⣿⣥⣼⣿⣿⣶⣿⣦⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣟⡿⣿⣿⣿⣿⣩⣿⣿⣿⡷⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡎⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣦⠀⠀⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠇⣀⠀⠀⠀⣘⣶⣶⠖⠂⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣄⠀⠋⠉⠛⠀⠀⠀⠀⠀⢀⡀⣚⠻⣿⣿⣿⣿⣟⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣽⢷⡿⣾⣿⣿⣹⢿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣶⣶⣶⣶⣶⣀⣄⠀⣺⣿⣿⣷⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⡿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣛⢿⣿⣿⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⡏⣶⣶⣶⣦⢰⣶⣶⣶⠶⣶⡶⠆⣶⡖⣶⡄⣶⡆⣶⡆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢹⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⢇⡿⡾⡹⢹⢫⣧⣧⣱⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⡇⠛⠃⣿⣷⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⣇⣿⡇⣿⡇⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠀⠉⠉⠉⠁⢤⣉⣉⣥⣦⠉⠁⠀⠈⠉⠉⠀⠉⠁⠉⠁⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠉⠉⠉⠉⠉⠀⠹⣿⣾⡟⠉⠉⠉⠈⠿⠿⠿⠟⠇

⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠉⠉⢉⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⢠⣤⣤⣤⢠⣤⣤⣤⣤⣤⢠⣤⡄⣤⣤⣤⠀⠀⣤⣤⣤⠀⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⣠⣤⣤⣤⡄⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣙⢹⣿⣿⣿⡇⣿⣇⣿⢿⣿⣿⡿⢸⣿⣇⣸⣿⣿⣼⣿⡇⣿⣿⣀⠀⢸⣿⠸⠿⢾⣿⣿⣿⣿⣿⣿⣿⡇⣿⣇⣿⠇⢸⣿⡇⠀⠀⠀⠈⠛⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡝⣿⣿⣿⣿⣿⡇⣿⡏⠉⢸⣿⣿⣿⢸⣿⣏⣹⣿⢸⣿⣿⡇⣿⣿⣉⠀⢸⣿⣰⣶⢺⣿⣿⣿⡟⣿⣿⣿⡇⣿⡇⣿⡇⢸⣿⡇⠀⠀⠀⠀⢺⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠙⠛⠋⠁⠛⠃⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠘⠋⠛⠓⠛⠛⠛⠀⠈⠛⠛⠋⠈⠙⠛⠛⠀⠙⠛⠛⠁⠛⠃⠛⠃⠘⠛⠃⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣽⣦⣾⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣸⣧⡤⣀⠀⠀⢀⡄⠀⢉⠀⠀⠀⠀⠀⠀

⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡀⠀⠀⣀⡀⠀⠀⠀⠀⢀⣄⣀⡄⠀⢠⣤⣟⣿⣷⣶⡛⠀⠀⠙⠛⡃⠐⠃⠀⠀⠀⠀⠀

⠀⠿⠿⠿⢻⡿⠿⠿⡿⠣⠻⠟⠿⠻⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠷⠿⠿⠶⠧⠶⠴⠾⠿⠿⠿⠿⠿⠿⠿⠿⠷⠿⠇⠀⠀⠀⠁⠀⠀⠀⠰⠤⠴⠆⠀

[32A⠀⠀⠀⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢸⠠⠴⠧⡒⠖⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢸⢬⣀⣠⣃⡥⠀⡀⣄⠀⠀⠀⠀⠠⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣤⣤⣤⣶⣾⠢⠟⡚⠷⠖⠀⠮⠑⣀⣀⣀⣀⣀⡀⠂⠒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⣶⣶⣶⣶⣶⣶⣶⣶⣴⣼⣿⣧⣠⣶⣴⣶⣶⣶⣦⣤⣤⣤⣤⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠿⠿⠿⠿⠿⠀⠈⠉⠐⣸⣻⡂⠀⡃⠀⠀⠀⠀⡇⠀⢚⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠯⠍⠉⠉⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣦⣤⣶⣶⣶⣶⣶⣾⣶⣶⣿⣷⡆⡇⠀⠀⠀⠀⡇⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢉⣉⣿⣿⡟⣿⣿⣦⠙⢿⣿⣿⡿⠉⣿⡍⠉⢩⡛⠛⣿⡍⢩⣿⡟⢿⣿⡯⠉⡿⢃⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⣿⢁⠘⣿⣿⡇⠈⢿⡿⠁⠀⣿⡇⠀⢸⡇⠀⣿⡇⢸⣿⡇⢀⠻⡇⠀⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣦⣭⣼⣥⣿⣧⣤⣿⣼⣿⣧⣾⣿⠀⠀⠃⢀⣘⣿⣿⣿⣧⣼⣿⣥⣼⣿⣿⣶⣿⣦⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣥⣤⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡞⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣶⣦⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠇⣀⠀⠀⠀⣘⣰⣶⡖⠆⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣄⠀⠙⠉⠛⠁⠀⠀⠀⠀⢀⡀⣚⠻⣿⣿⣿⣿⣟⣻⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣽⣷⡿⣾⣿⣿⣽⢿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣶⣶⣶⣶⣶⣄⣄⠀⣺⣿⣿⣷⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⡿⠏⠀⠀⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣛⢿⣿⣿⣿⣷⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡏⣶⣶⣶⣦⢰⣶⣶⣶⠶⣶⡶⠆⣶⡖⣶⡄⣶⡆⣶⡆⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⢹⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⢇⡿⡾⡹⣹⢫⣧⣧⣱⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⡇⠛⠃⣿⣷⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⣇⣿⡇⣿⡇⣿⡇⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠈⠉⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠀⠉⠉⠉⠁⠀⠉⠉⠁⠀⠉⠁⠀⠈⢉⣉⡀⠉⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⠿⢿⣿⣿⡏⠀⠋⠛⠉⠉⠉⠿⠿⠿⠟⠇

⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠉⠉⢉⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⢠⣤⣤⣤⢠⣤⣤⣤⣤⣤⢠⣤⡄⣤⣤⣤⠘⠋⣤⣤⣤⠀⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⣠⣤⣤⣤⡄⢙⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣙⢹⣿⣿⣿⡇⣿⣇⣿⢿⣿⣿⡿⢸⣿⣇⣸⣿⣿⣼⣿⡇⣿⣿⣀⠀⢸⣿⡸⠿⢾⣿⣿⣿⣿⣿⣿⣿⡇⣿⣇⣿⠇⢸⣿⡇⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡝⣿⣿⣿⣿⣿⡇⣿⡏⠉⢸⣿⣿⣿⢸⣿⣏⣹⣿⢸⣿⣿⡇⣿⣿⣉⠀⢸⣿⣱⣶⢺⣿⣿⣿⡟⣿⣿⣿⡇⣿⡇⣿⡇⢸⣿⡇⠀⠀⢻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠙⠛⠋⠁⠛⠃⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠘⠋⠛⠓⠛⠛⠛⠀⠈⠛⠛⠋⠈⠙⠛⠛⠀⠙⠛⠛⠁⠛⠃⠛⠃⠘⠛⠃⢀⠀⠈⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣝⣿⣧⣾⣿⣷⣄⣀⣀⣂⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢰⣄⣯⣿⣤⣸⡀⠀⢀⣄⠀⠉⠓⠁⠂⠀⠀⠀

⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⠠⡁⣤⣈⠂⣤⢀⠁⢤⣤⣠⣤⣤⣤⣴⣾⣿⣿⣿⡙⠀⠀⠘⠛⡓⠘⠒⠀⠀⠀⠀⠀

⠀⠿⠿⠿⢻⡿⠿⠿⡿⠣⠻⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠯⠿⠿⠿⠿⠾⠦⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠁⠀⠀⠀⠰⠤⠴⠆⠀

                ䷩ 𝚕𝚒𝚗𝚎 2658

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/02/07/epo-moral-damage/#comments

Gemini version at gemini://gemini.techrights.org/2022/02/07/epo-moral-damage/

Gemini_version_available_♊︎

✐ EPO_Pays_Out_Millions_of_Euros_in_Compensation_—_to_Thousands_of_Workers_Who

Deserve_a_Lot_More_for_Moral_Damage_—for_Battistelli’s_Illegal_Acts(But

Battistelli_Himself_Has_Not_Been_Punished_at_All,_Nor_Have_His_Enablers)⠀✐

Posted in Courtroom, Europe, Law, Patents at 11:36 am by Dr. Roy Schestowitz

🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇The people who committed these crimes Are still in power!⦈

Summary: The staff union of the EPO (SUEPO) is pushing ahead for justice after

more than a decade of chronic, ongoing, systematic injustice, which saw the

rule of law abolished, patent quality as “collateral damage”, and Europe’s

reputation/leadership in tatters

SUEPO Central is circulating_this_letter_today [PDF]. Of course we’ve managed

to get a copy (the EPO is getting more leaky as corruption grows there and

people feel desperate to speak out). “SUEPO expresses again its solidarity to

all staff in the HR Department,” it says, “who strived to conclude all payments

by the end of the year 2021 to repair the damages caused by their upper

management.”

“Over the years we heard from aggrieved and unhappy workers from the HR

Department.”The short story is, payments were made to 4,523 workers, in effect

undoing penalties but not paying anything in compensation for moral harm,

amongst other aspects. How many more industrial actions would have been

possible if it weren’t for the illegal “strike regulations” persisting

illegally for 8 years?

Over the years we heard from aggrieved and unhappy workers from the HR

Department. Some left, some stayed while hating the grossly under-qualified

boss, and we still have some stories we can share one day. People hate her guts

more than she can possibly imagine, but in order to pay the mortgage people

need to maintain a shallow, superficial, appearance of an amicable

relationship.

“Some of the people responsible are still clinging onto top positions at the

Office!”Of importance and of note in this case: nobody was punished for these

illegal acts! Not the people who voted for something illegal. Not the

management that proposed these illegal regulations. Some of the people

responsible are still clinging onto top positions at the Office!

Welcome to the EPO, where immunity means that crimes pay off and doing illegal

things is the “smart” thing to do. Like trying to kick off the UPC, even though

it is patently and manifestly illegal, as_per_the_simple_treaties. This will be

a permanent injury not just to the image of the EPO but also the EU’s (UPC is

an EU system). What have we sunken to and how can these crises be rectified?

Just like cops who never pay for their crimes (the police departments pay

compensation to victims — however rarely — at taxpayers’ expense), Battistelli

paid nothing and instead got rewarded with huge compensations upon his

departure in 2018. To make matters worse, he also wasted an unbelievable sum of

money trying to “get even” (ego-tripping) with judges by illegally sending them

to Haar. Those spendings did not come out of his own pocket. █

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣵⣾⣿⣿⡏⠁⠹⠁⡇⢿⣿⢹⠃⣷⡟⢿⣿⣿⡿⠃⠤⡄⠙⠠⢼⡿⠿⠿⠀⡀⢀⣤⣷⣽⣿⣿⣿⣿⣿⣿⣿⡇⠚⠛⠒⠓⠓⠛⠘⠚⠒⠚⠒⠚⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠝⠃⠀⠀⠀⠀⠀⠉⠈⠙⠘⢈⡏⠁⠉⠀⠋⠀⠀⠈⠀⢀⠀⡀⠈⠂⡀⣠⣷⣾⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣽⣿⣿⣿⠗⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢿⣿⣿⣿⣿⣿⣿⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣚⣽⣿⣯⠉⠀⠀⠀⢀⣀⣤⣤⣶⣶⣶⣶⣶⣦⣤⣴⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠒⢒⠂⠺⣿⣿⣿⡏⢻⠿⢷⢲⠇⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⡿⡻⠄⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⡟⠙⠛⠃⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣯⣵⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣠⠌⡄⠀⣐⢐⣒⣶⢙⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⣟⠛⠛⠋⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢀⣠⣘⡃⢄⣶⢿⣿⣿⣿⣟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⠄⠀⠀⠉⠹⣿⣿⣿⣿⠟⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣽⣟⣿⡆⠾⡭⠕⠋⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣴⣶⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠋⠀⠈⠀⠀⣸⣿⣿⣿⣟⣀⠀⠀⠀⠀⠈⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠻⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠹⠿⠿⡿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠘⡷⠀⠀⠀⢀⣼⣷⣿⣯⠼⢉⣠⠤⣄⠀⠀⠀⠀⣰⣿⣿⣿⣿⠘⠿⠿⠇⠰⠤⣈⣽⣿⣿⣿⣷⣾⣿⢰⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⡴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⣾⣿⣿⣿⣷⣧⣗⠂⠀⢈⣧⣴⣶⣄⣿⣿⣿⣿⣿⡄⣠⡀⣄⡤⠤⢌⡉⢻⣿⣿⣿⠆⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⣠⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣇⣈⢀⣿⣤⠻⣿⣿⡀⠘⣇⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⡯⠇⠃⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢅⣀⡨⣿⣿⠉⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡤⠆⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢣⡇⣇⢸⣿⣿⣿⣿⣿⣿⡿⣹⣿⣿⣷⣾⣿⣷⣘⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣂⢀⡀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣞⡇⢿⣿⣿⣿⣿⣿⣿⣿⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⢿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣻⣿⣿⣿⣿⣿⣿⡿⡄⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⢗⢡⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠁⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠉⠉⠉⠉⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⢁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠠⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠘⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⠛⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⢆⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⡀⠀⠀⠀⠀⠀⠈⠉⠛⠋⣀⡀⠀⠀⢋⢻⣿⣿⣿⣿⣾⣷⡝⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠆⠈⢾⣿⣿⣿⣿⣿⣿⣿⣿⣉⣭⣍⣟⣉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠈⢺⣿⣿⣿⣿⣿⣿⣿⣧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢻⣿⣷⡄⠀⠀⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣾⣿⣿⣿⣆⠀⠀⠀⠀⠉⠋⠹⣟⡛⢿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⣠⣶⣶⣶⣿⡏⠀⠀⠀⠀⠀⠹⠿⠿⠿⠿⠿⠿⠿⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⡀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠀⠀⣀⡠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣹⣿⡉⣽⣿⣩⣠⣤⣶⣶⣦⡀⣴⣶⣷⣶⡰⣶⣶⢾⣷⡾⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣇⢻⣿⣿⣿⣟⣿⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣟⣩⣭⣯⢹⣿⡧⠠⢿⣾⣿⣿⣾⢿⣿⡿⣯⣅⣿⣿⡘⠛⠻⣿⣿⢸⣿⡇⣿⣿⢸⣿⡇⣿

⡀⠀⠀⡀⢠⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢿⣿⣽⣿⣟⠃⢳⣦⣠⣤⣤⢤⠀⠀⢀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣶⣶⣿⣖⢸⣿⣿⣟⣿⢙⢿⣼⣇⣻⣋⣿⣿⣷⣿⡇⣿⣿⣼⣿⡇⣿⣿⢸⣿⡇⢿

⣔⣶⣴⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠙⠿⣿⣽⡊⡈⡿⣿⣿⢟⡟⠜⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⠛⠛⠛⠁⠀⢻⢏⢻⣯⡼⠾⠻⠛⠟⠋⠈⠙⠋⠉⠀⠀⠉⠉⠉⠀⠉⠉⠀⠉⠁⠀

⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠰⢞⠯⢹⠇⠐⣀⠚⠏⠀⠀⠈⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡄⠀⠀⠀⠠⠚⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣻⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠇⠀⠀⠛⠣⠃⠁⠈⠑⠀⠀⠀⠀⠀⠉⠿⠿⠿⠿⠿⠿⢿⠇⠿⠿⣿⡿⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⠾⣟⣟⣟⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⠛⣿⣿⣿⡇⣿⡟⠃⡀⣿⡟⣿⣾⣿⡟⢳⣿⢻⣷⢸⣿⢻⡇⣿⡇⢸⣿⠛⣼⢸⣿⣼⣿⢸⣿⣿⣿⣿⡇⣾⡟⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀

⣿⡾⣿⣿⣿⡏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⡇⣿⡿⠇⠀⣿⣿⠿⢻⣿⡿⢸⣿⢸⣿⢸⣿⠿⠃⣿⡇⢸⣿⠿⣽⡼⣿⣿⣿⣿⡟⣿⣿⣿⡇⣿⡇⣿⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⣤⡶⠘⣷⡄⠀⠀⠀

⣈⢯⡿⣿⣿⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠴⡿⠿⠿⢇⡿⠷⠆⠀⠿⠿⣸⡸⠿⠷⠞⠿⠾⠟⠸⠿⢸⠂⠿⠷⠾⠿⠶⣹⣇⠿⢿⡸⠿⢇⠿⠿⠿⢇⣻⠷⠿⠃⣀⣀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣧⠀⣿⣿⡄⠀⠀

⠂⢘⣉⣁⠋⢼⣛⣻⠿⣛⣻⢟⣛⡿⣛⣋⢀⣀⡙⣛⣟⣛⣛⣛⣂⣀⣙⣛⣛⡛⣂⣀⣀⠐⠐⣛⣛⣛⢋⣀⣀⡻⣛⣛⡻⢟⣛⣻⢿⣛⣛⢻⣿⢛⣛⡻⢟⣛⣓⡦⣘⣻⢀⣀⡻⣛⣛⢛⣉⣁⢀⣀⣀⢿⣿⣿⡄⠀

⡇⣼⣿⣿⡇⣿⡏⣿⡇⣿⣿⣼⣿⡇⣿⣿⣾⣿⡇⣿⡏⢹⣿⢩⣹⣿⠋⣿⣿⡁⣿⡏⣿⡇⣠⢹⣿⡏⢸⣿⣿⡇⣿⣟⡁⣿⣏⡿⢸⣿⣋⢼⢰⣿⣿⣿⢸⣿⣹⣿⢹⣿⢸⣿⣷⣿⣿⢸⣿⡉⣿⣏⡿⢺⣿⣿⣿⣦

⣧⢿⣿⣤⡄⣿⡇⣿⡇⣿⢻⡿⣿⡇⣿⢻⡿⣿⡇⣿⡇⢸⣿⢸⣾⣿⠀⣿⣿⠃⣿⡇⣿⡇⣿⢸⣿⡇⢸⣿⣿⡇⣿⡟⠃⣬⡟⣿⣼⣿⠛⢼⣾⣿⣧⣤⢸⣿⢹⣷⢸⣿⢸⡟⣿⢿⣿⢸⣿⠛⣬⡟⣿⡞⣿⣿⣿⣿

⣿⣜⣻⣿⣷⣽⠿⢻⣡⣟⣚⣃⡛⠃⡛⢘⣃⣛⣃⡛⣳⣜⣛⣾⣟⣛⣶⣛⣛⣛⣛⣛⣛⣳⣿⣞⣛⣃⡘⣛⣛⣃⣛⣛⣛⣝⣻⣛⣝⣛⣛⣿⣧⣛⣿⣛⣜⣛⣘⣛⣚⣛⣘⣃⣛⣘⣛⣘⣛⣛⣙⡛⠛⢱⣿⣿⣿⣿

[39A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣵⣾⣿⣿⡏⠁⠙⠀⡆⢻⣿⢹⠃⢷⡛⢿⣿⣿⡿⢃⠤⠄⠙⠀⢴⣤⣤⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⠛⠒⠓⠓⠛⠘⠚⠒⠒⠒⠚⠂

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡴⠁⢳⡁⠆⣴⣾⣿⣿⠝⠃⠀⠀⠀⠀⠀⠈⠀⠙⠈⠀⡎⠁⠈⠀⠋⠀⠀⠈⠀⠀⠀⡀⠈⠻⡇⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⢠⣐⡀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⡜⠑⣈⣽⣿⣿⣿⠗⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡘⣿⠺⠄⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣚⣽⣿⣯⠁⠀⠀⠀⢀⣀⣤⣤⣶⣶⣶⣶⣶⣦⣤⣴⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠂⠸⣿⣿⣿⣧⣾⣿⣶⣿⣶⣲⡶⠀⠀⠁⠓⣿⣾⣿⣿⣿⣁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⡿⡻⠄⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣕⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣵⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢠⠘⢿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⡀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⣟⠛⠛⠋⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢀⣠⣌⣂⢌⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢿⣿⡇⠀⠀⠀⠀

⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⠀⠀⠀⠈⠘⣿⣿⣿⣿⠛⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣭⣟⣻⡆⠺⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀

⣴⣶⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠋⠀⠀⠀⠀⡰⣿⣿⣿⣟⣀⠀⠀⠀⠀⠉⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠻⡷⠐⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠘⠻⠟⠿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠘⡷⠀⠀⠀⢀⣼⣿⣿⣯⠼⢉⡠⠤⣀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠘⠿⠻⠃⠰⠤⣈⣽⣿⣿⣿⣷⣼⣿⢰⠈⠀⠈⠉⠉⢤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⡴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⣾⣿⣿⣿⣶⣦⣗⠂⠀⢈⣷⣤⣶⣄⣿⣿⣿⣿⣿⡄⣠⡀⣄⡤⠤⢄⡉⢻⣿⣿⣿⡆⣿⠂⠀⠀⠀⠀⠀⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⣠⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣇⣈⢀⣿⣤⠻⣿⣿⠀⠘⣇⠀⢄⠀⠀⠀⢸⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠛⠸⣞⠀⠀⠀⠀⠀⠹⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⡀⡝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢰⣟⣀⣀⠀⠀⠀⠀⡀⣠⣦⣤⣦⣄⠀⢀⠀⢠⣠⡀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⡯⠇⠃⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠃⣀⠠⣿⣿⠉⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣂⡀⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣶⣄⡀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢣⡇⣇⢸⣿⣿⣿⣿⣿⣿⡿⣱⣿⣿⣷⣾⣿⣶⣘⣿⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡊⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⣿⣞⡇⢿⣾⣿⣿⣿⣿⣿⡿⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⢿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠗⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠂⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⣛⣁⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠉⠉⠉⠉⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣈⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣾⣿⣿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠿⣻⡿⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⠈⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣛⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡄⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡬⠆⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣷⠆⠈⢻⣿⣿⣿⣿⣿⣿⣿⣟⣉⣍⣍⣟⣉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠈⠹⠃⠀⠀⠀⠉⠁⠀⠈⠉⠉⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣶⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢹⣿⣷⡀⠀⠀⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣾⣿⣿⣿⣆⠀⠀⠀⠀⠉⠋⠹⣍⡛⢿⣿⣷⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣀⠀⢀⣴⣶⣶⣾⣏⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⡀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⣀⡠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⣶⣆⢠⣿⡄⢸⣿⢋⣁⣤⣴⣶⣦⡀⣴⣿⣿⣶⡄⣿⣶⢶⣷⡶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣇⢻⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣟⣛⣯⣿⠻⣿⣯⠀⢿⣿⣿⣿⣯⣿⣿⣿⣿⣍⣾⣿⡟⠛⠓⣿⣿⣸⣿⣇⣿⣿⢸⣿⡇⢻

⡀⠀⠀⡀⢠⣄⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢿⣿⣽⣿⣿⠃⢳⣤⣤⣤⣤⢀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣶⣷⣿⣦⠰⣿⣻⣿⣹⠋⢿⣽⡇⣻⣟⣿⣿⣇⣿⡷⢿⣿⣿⣿⡿⣿⣿⡟⣿⣿⢸

⣄⣶⣴⣶⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠙⢿⣿⣽⡈⠈⡿⣿⣿⠟⡗⠄⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⠛⠛⠛⠋⠀⢻⣏⠹⣿⣤⠶⠿⠛⠿⠛⠁⠙⠛⠋⠁⠀⠉⠉⠉⠀⠈⠉⠁⠁⠁⠀

⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠠⠞⠿⢹⡇⠐⣀⠚⠏⠀⠀⠈⠚⢻⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡄⠀⠀⠀⠀⠜⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣻⣻⣿⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠇⠀⠀⠛⠂⠁⠀⠈⠐⠀⠀⠀⠀⠀⠉⠿⠿⠿⠿⠿⠿⢿⠇⠺⠿⣿⡿⢿⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡿⠾⣋⣟⣝⣻⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⠛⣿⣿⣿⡇⣿⡟⠃⡀⣿⣿⣿⣾⣿⡟⢳⣿⢻⣷⢸⣿⢻⡇⣿⡇⢸⣿⠛⣼⢸⣿⣼⣿⢸⣿⢹⣿⣿⡇⣾⡟⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢿⡾⢿⣿⣿⡏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⡇⣿⡿⠇⠀⣿⣿⠟⢻⣿⡿⢸⣿⢸⣿⢸⣿⠿⠃⣿⡇⢸⣿⠿⣽⡾⣿⣿⣿⣿⡟⣾⣿⣿⡇⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠊⠓⢀⣠⡴⠀⢰⣿⡆⠀⠀

⢀⢾⡾⣿⣿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠤⡿⠿⠿⢇⡿⠷⠆⠀⠿⠿⣸⡸⠿⠷⠞⠿⠾⠟⠸⠿⢸⠂⠿⠷⠾⠿⠶⣹⣇⠿⢿⡸⠿⢇⠿⠿⠿⢇⣻⠷⠿⠃⢰⣢⠀⠀⢀⣼⣷⣿⣿⣿⣿⣧⠞⢻⣿⠁⠀⠀

⠂⢘⣉⣁⠋⢼⣛⣻⠿⣛⣻⢟⣛⡿⣛⣋⢀⣀⡙⣛⣛⣛⣛⣛⣂⣀⣘⣛⣛⡛⣀⣀⣀⠀⠐⣛⣛⣛⢋⣀⣀⡻⣛⣛⡻⢟⣛⣻⢿⣛⣛⠿⣿⢛⣛⡛⢟⣛⣓⡦⣈⣻⢀⣀⡘⣛⣻⢛⣛⣉⢀⣀⣀⢸⣿⣧⠀⠀

⡇⣼⣿⣿⡇⣿⡏⣿⡇⣿⣿⣾⣿⡇⣿⣿⣾⣿⡇⣿⡏⢹⣿⢩⢹⣿⠋⣿⣿⡁⣿⡏⣿⡇⣠⢹⣿⡏⢸⣿⣿⡇⣿⣟⡁⣿⣏⡿⢸⣿⣋⢴⢰⣿⣿⣿⢸⣿⣹⣿⢸⣿⢸⣿⣷⣿⣿⢸⣿⡉⣿⣏⡿⢂⣿⣿⣷⣤

⣧⢿⣿⣤⡄⣿⡇⣿⡇⣿⢻⡿⣿⡇⣿⢻⡿⣿⡇⣿⡇⢸⣿⢸⢾⣿⠀⣿⣿⠃⣿⡇⣿⡇⣿⢸⣿⡇⢸⣿⣿⡇⣿⡟⠃⣬⡟⣿⣼⣿⠛⢼⣼⣿⣧⣤⢸⣿⢹⣷⢸⣿⢸⡟⣿⢿⣿⢸⣿⠋⣬⡝⣿⡆⣿⣿⣿⣿

⣿⣜⡻⣿⣷⣽⠿⢻⣁⣛⣚⣃⠛⠃⡛⢘⣃⣛⣃⡛⣳⣜⣛⣾⣟⣛⣴⣛⣛⣛⣛⣛⣛⣣⣿⣞⣛⣃⠘⣛⣛⣃⣛⣛⣛⣝⣻⣛⣝⣛⣛⣿⣧⣛⣿⣛⣘⣛⣘⣛⣚⣛⣘⣃⣛⣘⣛⣘⣛⣛⣝⡛⠛⠁⣿⣿⣿⣿

[39A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣵⣾⣿⣿⡎⠁⠙⠂⡆⢻⣿⢹⠋⢿⡿⢿⣿⣿⡿⢃⠄⠄⠙⠄⢴⣤⣴⡄⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡘⠛⠒⠓⠓⠓⠘⠚⠚⠚⠒⠚⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⣴⣾⣿⣿⠝⠋⠀⠀⠀⠀⠀⠈⠀⠉⠈⠄⡞⠁⠘⠀⠋⠀⠀⠈⠁⢠⠀⠀⠀⠀⠁⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣽⣿⣿⣿⡗⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢦⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣚⣽⣿⣯⠁⠀⠀⠀⢀⣀⣤⣤⣶⣶⣶⣶⣶⣦⣤⣴⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠸⣿⣿⣿⡟⢿⠿⠿⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⡿⡻⠄⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣿⣿⣿⣿⣿⣵⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠁⠀⢠⠜⢹⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣼⡅⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⣟⠛⠛⠋⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⢀⣠⣌⣃⢌⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘⠏⠀⠀⠀⠀⠀

⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⠐⠉⠑⣿⣿⣿⣿⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣟⣻⣦⠹⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠄⠀⠀⠀⠀

⣴⣶⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠋⠀⠀⠀⠀⡰⣿⣿⣿⣟⣠⠀⠀⠀⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣷⠀⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠹⠻⠿⡿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠘⡷⠀⠈⠀⢀⣼⣿⣿⣯⠼⢉⡠⠤⣄⡀⠀⠀⠀⣴⣿⣿⣿⣿⠘⠿⠿⠗⠴⠦⢈⣽⣿⣿⣿⣿⣮⣿⠳⡁⠀⠈⠻⠿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⡴⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⣾⣿⣿⣿⣷⣦⣛⠂⠀⢈⣿⣤⣶⣄⣿⣿⣿⣿⣿⡄⢀⣤⣤⣤⠤⢤⡉⠻⣿⣿⣿⡇⢻⠃⠀⠀⠀⠀⠈⣿⣿⣷⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⣠⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⢈⣹⣦⡹⣿⣿⡆⠘⣶⠀⢀⠀⠀⠀⢻⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠘⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠙⠘⡎⠀⠀⠀⠈⠋⢿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⡁⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⡀⢰⡗⣀⢀⠀⠀⠀⠀⣿⣿⣧⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⡯⡇⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠃⣀⡠⣿⣿⠉⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢀⡀⣼⣿⣷⣶⣦⣠⣤⣾⣿⣿⣿⣿⣿⣶⣦⣤⣀⣠⣠⣀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣣⡇⣗⢸⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⣷⣾⣿⣷⣘⣿⣾⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣷⣴⣢⣆⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣟⡇⣿⣿⣿⣿⣿⣿⣿⣿⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡪

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢛⣁⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠉⠉⠉⠉⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣽⡙⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡧⣯⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡄⣿⡄⢈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣽⡕⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣷⠎⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣭⣭⣟⣉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠟⣿⡏⠙⠛⠛⠛⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡎⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢫⣿⣷⣄⠀⠉⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣦⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣾⣿⣿⣿⣆⠀⠀⠀⠀⠙⠋⢿⣿⡻⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢀⠀⠀⣴⣦⣶⣾⣿⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⡀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠉⠀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢳⣶⣦⢀⣿⣇⢨⣿⡟⣉⣠⣤⣤⣤⡄⣠⣿⣿⣶⡄⣷⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣇⢿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣿⠛⣿⣿⠀⢸⣿⣿⣿⣯⡿⣿⣿⢿⣏⣹⣿⡇⠛⠛⣿⣿⡏⣿⣿⢹⣿⡇⣿⣿⢸

⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⠀⠀⢠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣾⣷⣷⣾⣦⠀⣷⡻⣿⣻⡏⢻⣯⡿⢙⣿⣻⣿⣧⣾⣿⢸⣿⣧⣿⣿⢸⣿⡇⣿⣿⢸

⢀⣲⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠻⢿⣿⣿⡿⡞⣿⣿⣿⣿⣿⡾⢷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠁⢻⣿⠙⣿⣥⡶⠿⠟⠻⠟⠁⠙⠛⠛⠁⠀⠉⠉⠉⠁⠈⠉⠁⠉⠉⠀

⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠠⡟⡿⣿⣷⠘⣁⠟⠏⠉⠈⠘⠻⠻⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⡄⠀⠀⠀⠀⠼⠋⠃⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⢿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠇⠀⠈⠓⠢⡧⠂⠈⠛⠀⠀⠀⠀⠀⠉⠿⠿⠿⠿⠿⠿⢿⠏⠸⠿⣿⡿⢿⡤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢿⠾⢏⣿⣝⣻⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⠛⣿⣿⣿⡇⣿⡟⠃⡀⣿⣟⣿⣾⣿⡟⢳⣿⢻⣷⢸⣿⢻⡇⣿⡇⢸⣿⠛⣼⢸⣿⣼⣿⢸⣿⣿⣿⣿⡇⣾⡟⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀

⢓⡾⣿⣿⣿⡏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⡇⣿⡿⠇⠅⣿⣿⠿⢻⣿⡿⢸⣿⢸⣿⢸⣿⠿⠃⣿⡇⢸⣿⠿⣽⡼⣿⣿⣿⣿⡟⣿⣿⣿⡇⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠜⠻⠋⡈⠉⠀⢠⣾⣧⠀⠀

⡊⢾⣼⣿⣟⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢦⡿⠿⠿⢇⡿⠷⠆⠀⠿⠧⣸⡸⠿⠷⠞⠿⠾⠟⠸⠿⣸⠆⠿⠷⠾⠿⠶⣹⣇⠿⢿⡸⠿⣇⠿⠿⠿⢇⣻⠷⠿⠃⢠⣚⡄⠀⠀⣰⣷⣶⣶⣼⣿⣷⠞⠋⠉⠁⠀⠀

⡄⢚⣁⣃⠋⢸⣛⣻⠿⣛⣻⢟⣛⡿⣛⣋⢀⣀⡹⣛⣟⣛⣛⣛⣂⣀⣙⣛⣛⡛⣂⣀⣀⠀⠀⣛⣛⣛⢋⣀⣀⡺⣛⣛⡻⢟⣛⣻⢿⣛⣛⠿⣿⣛⣛⡻⢟⣛⣓⡦⣈⣻⢇⣀⡘⣛⣻⢟⣛⣋⢁⣀⣀⠀⠀⠀⠀⠀

⡆⣼⣿⣿⡇⣿⡏⣿⡇⣿⣿⣾⣿⡇⣿⣿⣾⣿⡇⣿⡏⢹⣿⢩⢹⣿⠋⣿⣿⡁⣿⡏⣿⡇⣠⢹⣿⡏⢸⣿⣿⡇⣿⣟⡁⣿⣏⡿⢸⣿⣋⢴⢰⣿⣿⣿⢸⣿⣹⣿⢹⣿⢸⣿⣷⣿⣿⢸⣿⡉⣿⣏⡿⠂⠀⠀⠀⠀

⣧⢿⣿⣤⡄⣿⡇⣿⡇⣿⢻⣿⣿⡇⣿⢻⡿⣿⡇⣿⡇⢸⣿⢸⣸⣿⠀⣿⣿⠃⣿⡇⣿⡇⣿⢸⣿⡇⢸⣿⣿⡇⣿⡟⠃⣬⡟⣿⣼⣿⠛⢼⣿⣿⣧⣤⢸⣿⢹⣷⢸⣿⢸⡟⣿⢿⣿⢸⣿⠋⣬⡟⣿⡆⠀⠀⠀⠀

⣿⣞⡻⣿⣷⣿⠿⢻⢁⣛⣚⣃⠛⣃⡛⢘⣃⣛⣃⡛⣳⣜⣛⣾⣟⣛⣶⣛⣛⣛⣛⣛⣛⣳⣿⣞⣛⣃⡘⢛⣛⣃⣛⣛⣛⣝⣻⣛⣝⣛⣛⣿⣧⣛⣿⣛⣜⣛⣘⣛⣚⣛⣘⣃⣛⣘⣛⣘⣛⣛⣝⡛⠛⠁⠀⠀⠀⠀

[39A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣵⣾⣿⣿⡎⠁⠙⠂⡆⢻⣿⢹⠋⢿⡿⢿⣿⣿⡿⢃⠤⠄⠙⠄⢴⣤⣴⡄⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡘⠛⠒⠓⠓⠛⠘⠚⠚⠚⠒⠚⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣴⣾⣿⣿⠝⠋⠀⠀⠀⠀⠀⠈⠀⠉⠈⠄⡞⠁⠘⠀⠋⠀⠀⠈⠁⢠⠀⠀⠀⠀⠁⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣽⣿⣿⣿⡟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣚⣽⣿⣯⠁⠀⠀⠀⢀⣀⣤⣤⣶⣶⣶⣶⣶⣦⣤⣴⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠸⣿⣿⣿⡟⢿⠿⠻⠟⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⡿⡻⠄⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣿⣿⣿⣿⣿⣵⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠁⠀⢠⠜⢹⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡄⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⣟⠛⠛⠋⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⢀⣰⣄⣃⢌⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠺⠏⠀⠀⠀⠀⠀

⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⠉⠙⣿⣿⣿⣿⠻⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⣟⣻⣦⠹⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀

⣴⣶⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠋⠀⠈⠀⠀⣰⣿⣿⣿⣟⣂⠀⠀⠀⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣷⠀⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠹⠻⠿⡿⣯⣄⠀⠀⠀⠀⠀⠀⠀⠘⡷⠀⠈⠀⢀⣼⣿⣿⣯⠼⢉⡠⠤⣄⡀⠀⠀⠀⣰⣿⣿⣿⣿⠘⠿⠿⠓⠴⠦⣈⣽⣿⣿⣿⣷⣮⣿⠳⡁⠀⠈⠻⠿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⡴⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⣾⣿⣿⣿⣷⣦⣛⠂⠀⢈⣿⣤⣶⣄⣿⣿⣿⣿⣿⡄⢀⣤⣤⣤⠤⢤⡉⠻⣿⣿⣿⡇⢻⠃⠀⠀⠀⠀⠀⣿⣿⣷⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⣠⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⢈⣹⣦⡹⣿⣿⡆⠘⣶⠀⢀⠀⠀⠀⢻⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠘⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠙⠘⡏⠀⠀⠀⠈⠉⢻⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⡁⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⡀⢰⡗⣀⢀⠀⠀⠀⠀⣿⣿⣏⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⡯⡇⡇⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠃⣀⡠⣿⣿⠉⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢀⡀⣼⣿⣷⣾⣧⣤⣤⣾⣿⣿⣿⣿⣿⣶⣦⣤⣀⣠⣤⡀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣣⡇⣗⢸⣿⣿⣿⣿⣿⣿⡿⣳⣿⣿⣷⣾⣿⣷⣘⣿⣾⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣿⣗⣂⡠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣟⡇⢿⣿⣿⣿⣿⣿⣿⣿⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡥

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢟⢛⡁⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠉⠉⠉⠉⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣽⡹⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣣⣯⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡁⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡆⣿⡆⢈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣽⡅⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣷⠆⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣍⣭⣟⣉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠟⣿⡏⠉⠛⠛⠛⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡎⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢫⣿⣷⣄⠀⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣦⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣾⣿⣿⣿⣆⠀⠀⠀⠀⠙⠟⢿⣟⡻⢿⣿⣷⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢀⠀⠀⣴⣦⣶⣾⣿⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠁⠀⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢳⣶⣦⢀⣿⣇⢨⣿⡟⣉⣠⣤⣤⣤⡄⣡⣿⣿⣶⡄⣿⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣇⢻⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣿⠛⣿⣿⠀⢸⣿⣿⣿⣯⡿⣿⣿⢿⣏⣹⣿⡇⠛⠛⣿⣿⡏⣿⣿⢹⣿⡇⣿⣿⢸

⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⢿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⠀⠀⢠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣾⣷⣷⣾⣦⠀⣷⡻⣿⣻⡏⢻⣯⡿⢙⣿⣻⣿⣧⣾⣿⢸⣿⣧⣿⣿⢸⣿⡇⣿⣿⢸

⢀⣲⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠻⢿⣿⣿⡿⡞⣿⣿⣿⣿⡿⡜⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠁⢻⣿⠙⣿⣥⡶⠿⠟⠻⠟⠁⠙⠛⠛⠁⠀⠉⠉⠉⠁⠈⠉⠁⠉⠉⠀

⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠠⡛⡿⣿⣇⠘⣉⠿⠟⠉⠈⠈⠻⠻⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⡄⠀⠀⠀⠀⠼⠋⠃⠉⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠇⠀⠈⠓⠢⡆⠀⠈⠻⠀⠀⠀⠀⠀⠉⠿⠿⠿⠿⠿⠿⢿⠏⠸⠿⣿⡿⢿⡤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢿⠾⢏⣿⣝⣻⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⠛⣿⣿⣿⡇⣿⡟⠃⡀⣿⡟⣿⣾⣿⡟⢳⣿⢻⣷⢸⣿⢻⡇⣿⡇⢸⣿⠛⣼⢸⣿⣼⣿⢸⣿⣿⣿⣿⡇⣾⡟⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀

⢳⡾⣿⣿⣿⡏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⡇⣿⡿⠇⠅⣿⡿⠿⢻⣿⡿⢸⣿⢸⣿⢸⣿⠿⠃⣿⡇⢸⣿⠿⣽⡼⣿⣿⣿⣿⡟⣿⣿⣿⡇⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠜⠻⠃⡈⠉⠀⢠⣿⣦⠀⠀

⡊⢾⣼⣿⣟⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢴⡿⠿⠿⢇⡿⠷⠆⠀⠿⠧⣸⡸⠿⠷⠞⠿⠾⠟⠸⠿⣸⠀⠿⠷⠾⠿⠶⣹⣇⠿⢿⡸⠿⣇⠿⠿⠿⢇⣻⠷⠿⠃⢠⣚⡄⠀⠀⣰⣷⣶⣶⣼⣿⣷⠖⠋⠉⠁⠀⠀

⡄⢘⣁⣋⠋⢸⣛⣻⠿⣛⣻⢟⣛⡿⣛⣋⢀⣀⡹⣛⣟⣛⣛⣛⣂⣀⣙⣛⣛⡛⣂⣀⣀⠀⠀⣛⣛⣛⢋⣀⣀⡺⣛⣛⡻⢟⣛⣻⢿⣛⣛⠿⣿⢛⣛⡻⢟⣛⣓⡦⣈⣻⢇⣀⡘⣛⣻⢟⣛⣋⢁⣀⣀⠀⠀⠀⠀⠀

⡆⣼⣿⣿⡇⣿⡏⣿⡇⣿⣿⣼⣿⡇⣿⣿⣾⣿⡇⣿⡏⢹⣿⢩⣹⣿⠋⣿⣿⡁⣿⡏⣿⡇⣠⢹⣿⡏⢸⣿⣿⡇⣿⣟⡁⣿⣏⡿⢸⣿⣋⢴⢰⣿⣿⣿⢸⣿⣹⣿⢸⣿⢸⣿⣷⣿⣿⢸⣿⡉⣿⣏⡿⠂⠀⠀⠀⠀

⣧⢿⣿⣤⡄⣿⡇⣿⡇⣿⢻⣿⣿⡇⣿⢻⡿⣿⡇⣿⡇⢸⣿⢸⣻⣿⠀⣿⣿⠃⣿⡇⣿⡇⣿⢸⣿⡇⢸⣿⣿⡇⣿⡟⠃⣬⡟⣿⣼⣿⠛⢼⣿⣿⣧⣤⢸⣿⢹⣷⢸⣿⢸⡟⣿⢿⣿⢸⣿⠋⣬⡟⣿⡆⠀⠀⠀⠀

⣿⣞⡻⣿⣷⣽⠿⢻⢁⣛⣚⣃⠛⠃⡛⢘⣃⣛⣃⡛⣳⣜⣛⣾⣟⣛⣶⣛⣛⣛⣛⣛⣛⣳⣿⣞⣛⣃⡘⢛⣛⣃⣛⣛⣛⣝⣻⣛⣝⣛⣛⣿⣧⣛⣿⣛⣜⣛⣘⣛⣚⣛⣘⣃⣛⣘⣛⣘⣛⣛⣝⡛⠛⠁⠀⠀⠀⠀

[39A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⣿⡾⠁⠈⡃⢾⠙⣿⢾⠋⠸⡿⢻⣿⣿⡿⢇⡠⡤⠈⠃⠤⣤⣄⣀⣀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣧⡘⠛⠒⠒⠒⠑⠘⠚⠒⠒⠒⠚⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣰⣾⣿⣿⡿⠙⠀⠀⠀⠀⠀⠈⠀⠇⠉⠀⡼⠁⠀⠉⠘⠁⡀⠀⠁⠀⡀⠀⠀⠀⠈⠉⠛⠂⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠂⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⣿⡿⢿⠿⠓⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⢤⣀⣄⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣞⣿⣿⣿⠁⠀⠀⠀⢀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣾⣶⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠀⢾⣝⣷⣶⠗⠿⠿⣿⣿⠿⠿⠿⠿⠿⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣛⡦⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⢼⣾⣿⣿⣷⣿⣼⣬⣠⣄⣀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⢿⣿⣿⣿⢽⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢀⡌⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⣿⣛⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢀⣀⣅⣑⠠⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⡦⢀⡘⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣿⣻⣧⠸⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣴⣶⣿⣷⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠋⠁⠨⠁⢰⣿⣿⣿⣿⣿⣿⣿⣷⣿⣙⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠟⣿⠂⢼⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠈⠙⠟⠿⣥⣄⠀⠀⠀⠀⠀⠀⠀⠐⠻⠀⠘⠀⢠⣿⣿⣿⣿⣿⣿⡿⠶⢤⣬⣿⠿⠀⢠⣿⣿⣿⣿⠈⠿⠿⠟⠳⠶⢀⣼⣿⣿⣿⣿⣦⣿⡗⠀⠀⣼⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⡴⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣃⡈⢀⣿⡿⣴⣆⣼⣿⣿⣿⣿⣆⢀⣄⢀⣤⠤⠄⣉⠛⣿⣿⣿⡇⢸⡗⠀⠀⠛⠋⠉⠉⠑⠀⣤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⣠⣿⡿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣀⡈⣸⣧⡘⣿⣿⡇⠘⢷⠀⠀⠀⠀⠀⠀⢀⡴⣻⣷⣿⡅⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠘⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⠇⢷⠀⠀⠀⠀⠈⠒⣼⡿⠻⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢸⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢀⡜⢀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠃⣀⡀⣿⣿⠏⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢐⡀⢸⣃⣮⡀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣣⣿⣿⣷⣾⣿⣿⣍⣿⣾⣶⣬⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⢹⣿⣿⣿⣿⣷⣦⣤⣤⣤⣶⣶⣿⣿⣿⣷⣶⣶⣶⣤⣠⣄⣤⡄⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣇⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉⠉⠉⠉⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡠⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠈⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣉⣉⣟⣋⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣆⡀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠈⠙⢻⣿⣿⠋⠉⠻⠟⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣴⣴⣶⣾⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⡛⣋⣏⣩⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⡷⠘⣶⣶⡄⢰⣿⡀⣽⣿⢋⣉⣠⣤⣤⣭⠉⣽⣿⣿⣦⢹⣷⣶⣶⣶⣴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢻⠿⣿⢸⣿⡿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣻⡟⢻⣿⡇⠀⢿⣿⣿⣿⣽⢿⣿⡿⣿⣉⣿⣿⠹⠿⢻⣿⣿⢹⣿⡏⣿⣿⢸⣿⡇

⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣸⣿⣿⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣿⣾⣾⣿⡄⢰⣌⢿⣟⣿⠙⣯⣽⠏⠿⢟⣿⣿⣱⣶⡦⣿⣿⣼⣿⡇⣿⣿⢸⣿⡇

⠀⣀⣦⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡹⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡟⠛⠛⠛⠛⠋⠘⣿⡎⢻⣏⣤⡼⠿⠛⡿⠋⠉⠛⠛⠋⠁⠈⠛⠛⠉⠀⠉⠉⠈⠉⠁

⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣿⣿⣿⣄⠀⠀⠀⠀⢀⠟⠛⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠇⠻⠿⠿⠿⣿⠿⠿⠿⠟⠀⠙⠻⠟⠛⠿⠿⠟⠿⠿⠿⢿⡿⠸⠿⣿⡿⠿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⠛⣿⣿⣿⡇⣿⡟⠃⡇⣿⡟⣿⣾⣿⡟⢳⣿⢻⣷⢸⣿⢻⡇⣿⡇⢸⣿⠛⣼⢸⣿⣼⣿⢸⣿⢸⣿⣿⡇⣾⡟⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⡇⣿⡿⠇⡇⣿⣿⢟⢻⣿⡿⢸⣿⢸⣿⢸⣿⠿⠃⣿⡇⢸⣿⠻⣽⡼⣿⣿⣿⣿⡟⢸⣿⣿⡇⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣤⡿⠿⠿⢇⡿⠷⠆⣁⠿⠿⣼⡼⠿⠷⠞⠿⠾⠟⠸⠿⣸⡆⠿⠷⠾⠿⠶⣹⣇⠿⢿⡸⠿⢇⠿⠿⠿⢇⡻⠷⠿⠃⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⢟⣛⣛⠛⢹⣛⣻⠿⣛⣻⢟⣛⡿⣛⣛⢁⣀⡻⣛⣛⣛⣛⣛⣂⣙⣛⣛⣛⡛⣛⣛⣛⢿⡟⣛⣛⣛⢛⣁⣈⡸⣛⣛⡻⢟⣛⣻⢿⣛⣛⢿⣿⢛⣛⡻⢟⣛⣓⡦⣀⣘⢟⣀⡀⣚⣛⢋⣁⣀⢀⣀⣀⠀⠀⠀⠀⠀

⣇⣼⣿⣿⡇⣿⡏⣿⡇⣿⣿⣾⣿⡇⣿⣿⣾⣿⡇⣿⡏⢹⣿⢩⢹⣿⠋⣿⣿⡁⣿⡏⣿⡇⣧⢹⣿⡏⢸⣿⣿⡇⣿⣟⡁⣿⣏⡿⢸⣿⣋⢴⢰⣿⣿⣿⢸⣿⣹⣿⢸⣿⢸⣿⣷⣿⣿⢸⣿⡉⣿⣏⡿⠂⠀⠀⠀⠀

⣧⢿⣿⣤⡄⣿⡇⣿⡇⣿⢻⡿⣿⡇⣿⢻⡿⣿⡇⣿⡇⢸⣿⢸⢸⣿⠀⣿⣿⠃⣿⡇⣿⡇⣿⢸⣿⡇⢸⣿⣿⡇⣿⡟⠃⣬⡟⣿⣼⣿⠛⢼⣿⣿⣧⣤⢸⣿⢹⣷⢸⣿⢸⡟⣿⢿⣿⢸⣿⠋⣬⡝⣿⡆⠀⠀⠀⢀

⣿⣞⡻⢿⣷⣽⣿⢻⠅⣛⣚⣃⣛⣃⡛⢘⣃⣛⣃⣛⣳⣜⣛⣾⣞⣛⣴⣛⣛⣛⣛⣛⣛⣡⣿⣜⣛⣃⣘⢛⣛⣃⣛⣛⣛⣙⣻⣛⣝⣛⣛⣿⣧⣛⣿⣛⣘⣛⣘⣛⣘⣛⣘⣃⣛⣘⣛⣘⣛⣛⣝⣛⠛⠁⠀⠀⠀⢼

[39A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⣿⣿⣿⠁⠈⠁⢺⠃⣿⡏⡋⡸⣿⢻⣿⣿⡿⢟⡠⢤⢈⠣⠲⣾⣿⠿⣥⣤⣤⣼⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣞⡛⠒⠓⢓⠓⠚⠚⠚⠚⠒⠚⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣰⣾⣿⣿⡿⠙⠀⠀⠀⠀⠀⠈⠀⠁⠁⠁⣹⠁⠀⠁⠘⠁⠀⠀⠁⠠⡀⢠⠀⠀⠀⠀⠈⠉⠉⠋⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⣈⣽⣿⣿⡿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠰⣿⣿⣶⣶⡄⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠇⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⠉⠀⠀⠀⢀⣠⣤⣴⣶⣿⣿⣶⣶⣶⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠐⠒⡒⠀⢶⣼⣻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⡻⠋⠛⠍⠒⢐⡑⡀⡀⢀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣛⡧⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⢉⠘⣿⣿⡆⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣿⣿⣿⢵⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠀⢀⡤⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⣿⣛⠛⢋⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢀⣀⣧⣙⡠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿

⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⠦⠀⠀⠀⠉⣿⣿⣿⣿⠟⠻⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋

⣴⣶⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠋⠀⠈⠀⠀⣰⣿⣿⡿⣿⡀⠀⠀⠀⠀⠀⠛⠛⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡟⢿⠆⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠙⠻⠿⠿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠘⢻⠄⠈⠀⠀⣼⣿⣿⠯⠜⢁⡠⠤⢤⡀⠀⠀⠀⢠⣾⣿⣿⣿⡀⠻⠿⠟⠓⠶⠀⣼⣿⣿⣿⣿⣧⣿⡗⠂⠀⣼⣿⣿⣿⣿⣿⣿⣿⡿⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⡴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠠⠐⠂⠀⠀⣸⣿⣿⣿⣧⣿⣼⡃⠈⠀⣿⡤⣴⣦⣼⣿⣿⣿⣿⣇⢀⣤⠄⣤⠤⠀⣈⠙⣿⣿⣿⣷⢸⡟⠀⠀⡿⡟⠋⠉⠀⠐⠀⠄⠾⣿⣷⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⣠⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠂⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣀⡁⣸⣷⡌⣿⣿⣧⠐⢳⡀⠀⡄⠀⠀⠀⠀⠀⠀⠐⢹⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡦⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⠃⢷⠇⠀⠀⠀⠀⠀⠀⠀⢘⢟⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢸⡇⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⡼⢀⣄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡯⢇⠙⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠋⣀⡀⣽⣿⠏⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠑⡀⢰⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⢀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⡿⣶⣸⣿⣿⣿⣿⣿⣿⣿⢣⣿⣿⣷⣶⣿⣿⣍⣿⣾⣷⣬⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣿⣽⣇⣿⣿⣿⣿⣿⣿⣿⣿⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠃⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠉⠉⠉⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡾⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢂⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣉⣉⣿⣛⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣆⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣄⠀⠈⠙⠿⣿⡿⠃⠉⠛⠋⠙⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢯⣿⣷⣀⠀⠀⠉⠻⢿⣽⣿⣿⣿⣿⣿⣿⣧⡈⣿⣿⣿⣿⣿⣿⣿⣿⣫⣾⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠸⠿⠻⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣭⣴⣾⣿⣿⢹⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⢀⠀⠀⣴⣤⣶⣶⣟⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠁⠀⢀⢰⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⢠⣿⡄⢸⣿⢟⣉⣁⣤⣤⣤⡀⣩⣿⣿⣯⡍⣿⣿⣿⣷⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣇⢻⣿⣿⣿⡿⡿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣿⠛⣿⣿⡉⣻⣿⣿⣾⣯⣿⣿⣿⢿⣋⣽⣿⡟⠿⠗⣿⣿⣼⣿⣷⣿⣿⡼⣿⣧

⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⢿⣿⣿⣧⣎⣏⣿⣦⣀⣀⣀⣄⠀⠀⠀⣠⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣧⣦⣿⣦⠀⣶⢿⣿⣻⠟⢷⣽⡏⠻⠿⣻⣿⣇⣶⣶⢿⣿⣯⣿⣿⢹⣿⡇⣿⣿

⠀⣀⣦⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠹⣿⣿⣽⡏⠅⢻⣿⣟⢿⢷⣤⢢⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠟⠛⠛⠛⠁⢛⣏⠻⣿⣠⣤⠿⠟⢻⠟⠉⠛⠛⠛⠁⠈⠙⠛⠋⠁⠈⠉⠁⠉⠉

⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⡹⢿⣻⡧⠐⣉⡽⠿⡀⠙⠙⠩⠿⢿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣆⠀⠀⠀⠀⠀⡼⠛⠃⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣳⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠇⠀⠈⠺⠐⠁⠈⠈⠳⠂⠀⠀⠀⠀⠀⠼⠿⠟⠿⠿⠿⢿⡿⠸⠿⣿⡿⢿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠗⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢿⣽⡟⣿⣻⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⠛⣿⣿⣿⡇⣿⡟⠃⠀⣿⡟⣿⣾⣿⡟⢳⣿⢻⣷⢸⣿⢻⡇⣿⡇⢸⣿⠛⣼⢸⣿⣼⣿⢸⣿⣿⣿⣿⡇⣾⡟⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣶⣼⣿⣿⣿⡿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⡇⣿⡿⠇⠀⣿⡿⠿⢻⣿⡿⢸⣿⢸⣿⢸⣿⠿⠃⣿⡇⢸⣿⠿⣽⡼⣿⣿⣿⣿⡟⣿⣿⣿⡇⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⠀⠀⠀⠀

⢌⡷⣺⣿⡟⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣤⡿⠿⠿⢇⡿⠷⠆⠀⠿⠿⣸⡸⠿⠷⠞⠿⠾⠟⠸⠿⢸⡄⠿⠷⠾⠿⠶⣹⣇⠿⢿⡸⠿⢇⡿⠿⠿⢇⡻⠷⠿⠃⠀⠀⢀⠀⠀⠀⣰⣷⣶⣶⣿⣿⣇⡀⠀⠀⠀⠀

⠌⢘⣁⣉⠛⢸⣛⣻⠿⣛⣻⢟⣛⡿⣛⣛⢁⣀⡻⣛⣟⣛⣛⣛⣂⣀⣘⣛⣛⡛⣃⣀⣀⠐⠀⣘⣛⣛⢛⣁⣀⡸⣛⣛⡻⢟⣛⣻⢿⣛⣛⢿⣿⣛⣛⡻⢟⣛⣛⡦⣀⣘⢟⣂⡀⣘⣻⣟⣛⣛⢉⣁⣀⠀⠀⠀⠀⠀

⡅⣼⣿⣿⡇⣿⡏⣿⡇⣿⣿⣼⣿⡇⣿⣿⣾⣿⡇⣿⡏⢹⣿⢩⣹⣿⠋⣿⣿⡁⣿⡏⣿⡇⢀⢹⣿⡏⢸⣿⣿⡇⣿⣟⡁⣿⣏⡿⢸⣿⣋⢰⢰⣿⣿⣿⢸⣿⣹⣿⢸⣿⢸⣿⣷⣿⣿⢸⣿⣉⣿⣏⡿⠀⠀⠀⠀⠀

⣧⢿⣿⣤⡄⣿⡇⣿⡇⣿⢻⡿⣿⡇⣿⢻⡿⣿⡇⣿⡇⢸⣿⢸⣺⣿⠀⣿⣿⠃⣿⡇⣿⡇⣾⢸⣿⡇⢸⣿⣿⡇⣿⡟⠃⣬⡟⣿⣼⣿⠛⣾⣿⣿⣧⣤⢸⣿⢹⣷⢸⣿⢸⡿⣿⢿⣿⢸⣿⠋⣬⡟⣿⡆⡆⠀⠀⠀

⣿⣞⣻⢿⣷⣽⣿⠿⠵⢛⣚⣃⡛⠃⡛⢘⣃⣛⣃⣛⣳⣜⣛⣾⣟⣛⣶⣛⣛⣛⣛⣛⣛⣣⣿⣞⣛⣃⡘⢛⣛⣃⣛⣛⣛⣙⣻⣛⣝⣛⣛⣿⣧⣛⣿⣛⣜⣛⣘⣛⣚⣛⣘⣃⣛⣘⣛⣚⣛⣛⣝⣻⠛⣱⣷⠀⠀⠠

[39A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⣿⣿⣿⠁⠈⠁⢺⠋⣿⡏⡋⡸⣿⢻⣿⣿⡿⢟⡠⢤⢈⠳⠲⣿⣿⡿⣧⣤⣤⣼⣷⣽⢿⣿⣿⣿⣿⣿⣿⣿⣞⠛⠒⠓⢓⠓⠘⠚⠚⠚⠒⠚⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣰⣾⣿⣿⡿⠑⠀⠀⠀⠀⠀⠈⠀⠁⠁⠁⣹⠁⠀⠁⠘⠁⠀⠀⠁⠠⡀⢠⠀⠀⠀⠀⠈⠉⠉⠋⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⣈⣽⣿⣿⡿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠰⣿⣿⣶⣶⡄⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⠉⠀⠀⠀⢀⣠⣤⣴⣶⣾⣿⣶⣶⣶⣴⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠐⠒⡒⠀⢲⣼⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⠿⠏⠻⠍⠐⢀⠂⡂⡀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣻⡧⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⢙⠐⣿⡿⣦⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣿⣿⣿⢿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠀⢀⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⢨⣷⣷⣲

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⣿⣛⠛⢋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢀⣀⣧⣙⡠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿

⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⠦⠀⠀⠀⠉⣿⣿⣿⣿⠟⠻⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋

⣴⣶⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⠈⠀⠀⣰⣿⣿⡿⣿⡀⠄⠀⠀⠀⠀⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡟⢿⠆⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠹⠻⠿⡿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠘⢻⠄⠘⠀⠀⣼⣿⣿⠯⠜⢁⡠⠤⢤⡀⠀⠀⠀⢠⣾⣿⣿⣿⡀⠻⠿⠟⠓⠶⢀⣼⣿⣿⣿⣿⣷⣿⡗⠂⠀⣼⣿⣿⣿⣿⣿⣿⣿⡿⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⡴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠠⠐⠂⠀⠀⣸⣿⣿⣿⣧⣿⣼⡃⠈⠀⣿⡤⣴⣦⣼⣿⣿⣿⣿⣇⢀⣤⢄⣤⠤⠀⣈⠙⣿⣿⣿⣧⢸⡟⠀⠀⡿⡟⠋⠉⠀⠀⠀⡠⡿⣿⣿⣶⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⣠⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠂⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣀⡁⣸⣷⡌⣿⣿⣇⠰⢻⡀⠀⡄⠀⠀⠀⠀⠀⠀⠐⢾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡦⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠃⢷⡃⠀⠀⠀⠀⠀⠀⠀⠘⠛⢻⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢸⡇⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⡼⢀⣄⡆⠀⠀⠀⠀⠀⠀⠈⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡯⢇⠘⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠋⣀⡀⣽⣿⠏⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠑⣀⢰⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⡀⣠⣀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⡿⣶⣸⣿⣿⣿⣿⣿⣿⣿⢣⣿⣿⣷⣶⣿⣿⣍⣿⣾⣷⣬⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣠⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠉⠉⠉⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣮⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⢘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠂⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣉⣉⣿⣛⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣆⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣄⠀⠈⠙⠿⢿⡿⠃⠉⠛⠏⠙⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢯⣿⣷⣄⠀⠀⠉⠻⢿⣽⣿⣿⣿⣿⣿⣿⣧⡘⣿⣿⣿⣿⣿⣿⣿⣿⣻⣾⣿⣿⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠸⠿⠻⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣽⣴⣾⣿⣿⢹⣿⣿⣿⣿⣿⣿⣶⣦⠀⠀⠀⢀⠀⠀⣴⣤⣶⣶⣟⠁⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⢀⣺⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⢠⣿⡄⢸⣿⢟⣉⣁⣤⣤⣤⡀⣩⣿⣿⣯⡍⣿⣿⣿⣷⣤

⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⢿⣿⣿⣧⣎⣟⣿⣦⣀⣀⣀⣄⠀⠀⠀⣠⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣷⣦⣿⣦⠀⣶⢿⣿⣻⠟⢷⣽⡏⠻⠿⣻⣿⣇⣶⣶⢿⣿⣯⣿⣿⢹⣿⡇⣿⣿

⠀⣀⣦⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠹⣿⣿⣽⡏⠅⣻⣿⣟⢿⡷⣤⢢⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠟⠛⠛⠛⠁⢻⣏⠻⣿⣠⣤⠿⠟⢻⠟⠉⠛⠛⠛⠁⠈⠙⠛⠋⠁⠈⠉⠁⠉⠉

⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠹⢿⣿⡧⠐⣉⡻⠿⢀⠉⠉⠩⠿⢿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣆⠀⠀⠀⠀⠀⡼⠛⠃⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣣⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠇⠀⠈⠛⠃⠁⠈⠈⠳⠂⠀⠀⠀⠀⠀⠼⠿⠟⠿⠿⠿⢿⠿⠸⠿⣿⡿⢿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠗⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣽⡟⣿⣻⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⠛⣿⣿⣿⡇⣿⡟⠃⠀⣿⡟⣿⣾⣿⡟⢳⣿⢻⣷⢸⣿⢻⡇⣿⡇⢸⣿⠛⣼⢸⣿⣼⣿⢸⣿⣿⣿⣿⡇⣾⡟⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣶⣽⣿⣿⣿⡿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⡇⣿⡿⠇⠀⣿⡿⠿⢻⣿⡿⢸⣿⢸⣿⢸⣿⠿⠃⣿⡇⢸⣿⠿⣽⡼⣿⣿⣿⣿⡟⣿⣿⣿⡇⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⠀⠀⠀⠀

⢌⡷⣺⣿⡟⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣤⡿⠿⠿⢇⡿⠷⠆⠀⠿⠷⣸⡸⠿⠷⠞⠿⠾⠟⠸⠿⣸⡄⠿⠷⠾⠿⠶⣹⣇⠿⢿⡸⠿⢇⡿⠿⠿⢇⡻⠷⠿⠃⠀⠀⢀⠀⠀⠀⣰⣷⣶⣶⣿⣿⣇⡀⠀⠀⠀⠀

⡌⢘⣁⣉⠛⢸⣛⣻⠿⣛⣻⢟⣛⡿⣛⣛⢁⣀⡻⣛⣛⣛⣛⣛⣂⣀⣘⣛⣛⡛⣃⣀⣀⠐⠀⣘⣛⣛⢛⣁⣀⡸⣛⣛⡻⢟⣛⣻⢿⣛⣛⢿⣿⣛⣛⡻⢟⣛⣛⡦⣀⣘⢟⣂⡀⣘⣻⣟⣛⣛⢉⣁⣀⠀⠀⠀⠀⠀

⡇⣼⣿⣿⡇⣿⡏⣿⡇⣿⣿⣼⣿⡇⣿⣿⣾⣿⡇⣿⡏⢹⣿⢩⣹⣿⠋⣿⣿⡁⣿⡏⣿⡇⢀⢹⣿⡏⢸⣿⣿⡇⣿⣟⡁⣿⣏⡿⢸⣿⣋⢰⢰⣿⣿⣿⢸⣿⣹⣿⢸⣿⢸⣿⣷⣿⣿⢸⣿⡉⣿⣏⡿⠀⠀⠀⠀⠀

⣧⢿⣿⣤⡄⣿⡇⣿⡇⣿⢻⡿⣿⡇⣿⢻⡿⣿⡇⣿⡇⢸⣿⢸⢸⣿⠀⣿⣿⠃⣿⡇⣿⡇⣾⢸⣿⡇⢸⣿⣿⡇⣿⡟⠃⣬⡟⣿⣼⣿⠛⣾⣿⣿⣧⣤⢸⣿⢹⣷⢸⣿⢸⡿⣿⢿⣿⢸⣿⠋⣬⡝⣿⡆⡆⠀⠀⠀

⣿⣞⣻⢿⣷⣽⣿⠿⠵⢛⣚⣃⡛⠃⡛⢘⣃⣛⣃⣛⣳⣜⣛⣾⣟⣛⣶⣛⣛⣛⣛⣛⣛⣣⣿⣞⣛⣃⡘⢛⣛⣃⣛⣛⣛⣙⣻⣛⣝⣛⣛⣿⣧⣛⣿⣛⣜⣛⣘⣛⣘⣛⣘⣃⣛⣘⣛⣘⣛⣛⣝⣻⠛⣱⣷⠀⠀⠠

[39A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⢿⢿⠉⠈⠋⢻⠇⣿⡯⡏⡙⣿⢻⣿⣿⣿⢟⡠⢠⢈⠻⠲⣷⠁⠀⠀⠀⠀⠀⠀⠙⠛⠟⠀⠀⢸⣿⣿⣧⠚⠛⠒⠛⠓⡓⠚⠛⠚⠚⠒⠚⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣾⣿⣿⣿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⣳⠁⠈⠁⠈⠁⠀⠀⠁⠤⣄⢀⠀⠀⠀⠀⠀⠀⣷⣤⣠⡀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⡒⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠰⣶⣶⣤⡄⠀⠙⠁⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠁⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣾⣿⣿⣿⠏⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⣷⣶⣶⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠐⠒⣒⠀⢳⣶⣽⢿⣖⣲⣶⣶⣿⣦⣿⣟⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣻⣧⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣿⣿⣿⣿⢿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠈⠀⠀⣤⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣛⠛⢋⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣀⣾⣙⡤⢹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡖⠀⠀⠉⠛⣿⣿⣿⣿⡿⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣷⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠐⠨⠀⠀⣴⣿⣿⣿⣿⡷⠄⠀⠀⠀⠈⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡟⢿⡗⢸⣹⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⠄⠈⠀⢀⣼⣿⣿⡿⠽⢋⡠⠤⢤⣀⠀⠀⠀⢠⣾⣿⣿⣿⡇⠻⠿⠿⠿⠶⢤⣽⣿⣿⣿⣿⣷⣿⡟⡆⠁⣸⣿⣿⣿⣿⣿⡿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠃⠀⠀⣸⣿⣿⣿⣿⣿⣾⡃⠈⠀⣿⡤⣶⣦⣼⣿⣿⣿⣿⣧⢀⣤⠄⣤⡤⠄⣈⠙⣿⣿⣿⣿⠸⣟⠂⠀⡾⢿⠿⠏⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣁⣩⣷⣌⢿⣿⣷⠀⢻⡆⠀⣦⣞⠀⠀⠀⠀⠀⠀⠀⠀⢠⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⠈⠳⢻⣿⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢸⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢀⠀⣾⣿⣿⣧⣄⣄⢠⣭⠈⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡮⢗⠻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠫⣀⡀⣽⣿⡏⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣀⢠⣿⣿⣿⣿⣿⣿⣾⣾⣿⣄⣤⣦⣷⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⡿⣾⣸⣿⣿⣿⣿⣿⣿⣿⢯⣿⣿⣿⣾⣿⣿⣍⣿⣿⣷⣦⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⢧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⣿⣿⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉⠉⠉⠉⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣉⣉⣿⣛⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠙⠻⠿⠛⠛⠛⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡏⣿⣿⣄⠀⠉⠉⠻⢿⣽⣿⣿⣿⣿⣿⣿⣧⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣄⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢻⣿⠿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⡀⠄⣠⣦⣴⣶⣾⡋⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠙⠉⠋⠉⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣾⣇⢀⣿⡟⣋⣉⣠⣤⣤⣄⢀⣴⣿⣯⣍⢹⣿⣿⣿⣦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣧⢻⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣻⡛⣿⣿⡍⣹⣿⣿⣿⣿⣻⣿⣿⣿⣛⣻⣿⣿⠿⠿⢸⣿⡇⣿⣿⣸⣿⣇⣿⣿

⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⢻⣿⣿⣿⣿⣿⣿⣶⣄⣤⣤⣤⣀⠀⠀⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣿⣵⣼⣧⡄⣷⡿⣿⣿⡿⢻⣯⣿⠹⠿⢻⣿⣿⣰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⣀⣰⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠻⣿⣿⣿⡟⣯⣿⣿⣿⣿⣿⣷⢷⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠿⠛⠛⠛⠁⢘⣿⡙⣿⣇⣧⡽⡿⢻⡿⠋⠙⠛⠛⠋⠀⠙⠛⠛⠋⠈⠛⠋⠈⠉

⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⠨⡽⣿⣿⣿⡵⣉⣿⠿⢏⡛⢻⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣦⠀⠀⠀⠀⠀⣠⠟⠓⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠧⠀⠘⠻⠟⡻⠘⠈⠳⠆⠈⠀⠀⠀⠀⠽⠿⠟⠿⠿⠿⢿⡿⠁⠿⣿⡿⢿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⡿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⠛⣿⣿⣿⡇⣿⡟⠃⡀⣿⣿⣿⣾⣿⡟⢳⣿⢻⣷⢸⣿⢻⡇⣿⡇⢸⣿⠛⣼⢸⣿⣼⣿⢸⣿⣿⣿⣿⡇⣾⡟⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣽⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⡇⣿⡿⠇⠀⣿⣿⠿⢻⣿⡿⢸⣿⢸⣿⢸⣿⠿⠃⣿⡇⢸⣿⢿⣽⡾⣿⣿⣿⣿⡟⣿⣿⣿⡇⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠀⠀⠀⠀

⣽⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣶⡿⠿⠿⢇⡿⠷⠆⠀⠿⠿⣼⡸⠿⠷⠞⠿⠾⠟⠸⠿⣸⡇⠿⠷⠾⠿⠶⣹⣇⠿⢿⡸⠿⣇⡿⠿⠿⢇⡻⠷⠿⠃⠀⠀⠀⡀⠀⠀⢠⣿⣶⣶⣾⣿⣿⡀⠀⠀⠀⠀

⡜⢘⣋⣛⠛⢹⣛⣻⠿⣛⣻⢟⣛⡿⣛⣛⢉⣀⡻⣛⣿⣛⣛⣛⣂⣀⣘⣛⣛⡛⣃⣁⣈⠐⠀⣘⣛⣛⢛⣁⣀⣰⣛⣛⡻⢟⣛⣻⢿⣛⣛⢿⣿⣟⣛⡻⢟⣛⣛⡶⣄⣈⢛⣃⡀⣀⣻⣟⣛⣛⢋⣉⣁⠀⠀⠀⠀⠀

⡇⣼⣿⣿⣇⣿⡏⣿⡇⣿⣿⣾⣿⡇⣿⣿⣿⣿⡇⣿⡏⢹⣿⢩⣹⣿⠋⣿⣿⡁⣿⡏⣿⡇⢀⢹⣿⡏⢸⣿⣿⡇⣿⣟⡃⣿⣏⡿⢸⣿⣋⢼⣲⣿⣿⣿⢸⣿⣹⣿⢹⣿⢸⣿⣷⣿⣿⢸⣿⣉⣿⣏⡿⢂⠀⠀⠀⠀

⣯⢿⣿⣤⡄⣿⡇⣿⡇⣿⢻⣿⣿⡇⣿⢻⣿⣿⡇⣿⡇⢸⣿⢸⣿⣿⠀⣿⣿⠃⣿⡇⣿⡇⣾⢸⣿⡇⢸⣿⣿⡇⣿⡟⠃⣬⡟⣿⣼⣿⠛⣾⣿⣿⣧⣤⢸⣿⢹⣷⢹⣿⢸⡿⣿⢿⣿⢸⣿⠛⣬⡟⣿⡎⣧⠀⠀⠀

⣿⣞⣻⢿⣷⣿⣿⡿⠵⢛⣚⣃⣛⣃⡛⢘⣃⣛⣃⣛⣻⣜⣛⣾⣟⣛⣶⣛⣛⣛⣛⣛⣛⣣⣿⣞⣛⣣⣘⢛⣛⣓⣛⣛⣛⣙⣿⣛⣝⣛⣛⣿⣧⣟⣿⣛⣜⣛⣘⣛⣛⣛⣘⣃⣛⣘⣛⣚⣛⣛⣝⣻⡛⢡⣿⠄⠀⠀

[39A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣾⣿⠿⠿⠁⠀⠁⠰⡋⢻⡇⡏⠘⣻⠉⢿⣿⣿⠛⠠⢀⠂⡉⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠘⠛⠒⠒⠓⠓⠐⠒⠒⠘⠒⠚⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣾⣿⣾⠷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠁⠀⠀⠀⠁⠀⠀⠀⠄⠀⠀⠄⠀⠀⠀⠒⠒⠲⠶⠶⣦⣴⠀⠀⠁⠀⠀⠀⠀⠀⠐⠛⠿⠿⠖⠒⠂⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣶⣄⣀⠀⠀⠀⠀⠀⢀⣀⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣺⣷⣿⣿⠇⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠂⠙⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣧⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣛⣂⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⢀⠀⠀⠲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⢾⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣤⠈⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⡋⠉⠉⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀⣼⣌⡄⢌⠀⠈⠀⠉⠙⠛⠻⠿⠋⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠆⠀⠀⠈⠉⢿⣿⣿⣿⠯⠻⠟⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣭⣿⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠈⠀⠀⠀⠀⣠⣿⣿⣿⢟⡂⠀⠀⠀⠀⠀⠉⠙⠻⣿⣿⣿⡿⣿⣿⣿⣿⠿⠻⡿⣿⣿⣿⣿⡿⣿⣟⠻⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⣴⣿⣿⠧⠔⠃⡠⠄⠤⣄⢀⠀⠀⢀⣾⣿⣿⣿⡇⠙⠛⠛⠛⠒⠀⣴⣿⣿⣿⣿⣷⢼⣟⠂⠀⢠⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠃⠀⠀⣸⣿⣿⣿⣯⣿⣾⣋⠀⢀⣸⡥⣶⣧⣼⣿⣿⣿⣿⣷⠀⣠⠄⣠⠶⠂⢀⡈⢻⣿⣿⣿⠀⣿⠂⠀⢸⣇⠀⠘⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣄⣀⣠⣿⣦⢻⣿⣿⠀⠟⡇⠀⣼⡼⠆⠒⣿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠑⠸⣿⣿⣶⣶⣽⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⢸⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣮⢇⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠛⣀⣀⢼⣿⡏⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣖⣤⣤⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⣾⢰⡘⣿⣿⣿⣿⣿⣿⣿⢋⣾⣿⣿⣶⣿⣿⣌⣻⣿⣷⣦⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⠄⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⣵⡿⣸⣾⣿⣿⣿⡿⣿⣿⢇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣧⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣧⢸⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠀⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠉⠉⠉⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⡿⠟⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⠄⠀⢀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢻⣧⣿⣻⣿⣿⣿⣿⣿⣿⣝⡻⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢁⢋⡅⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠈⢱⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿⠿⠟⠛⠿⠿⠿⣿⣿⣿⢟⠐⠚⠃⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⠆⠀⢻⣻⣿⣿⣿⣿⣿⣿⣟⣋⣉⣉⣛⣛⣉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡖⣽⣿⣄⠀⠀⠉⠛⢿⣽⣿⣿⣿⣿⣿⣿⣷⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣷⣿⣿⣿⣧⡀⠀⠀⠀⠈⠿⠛⡿⠿⠿⠿⣿⣿⣿⣿⣿⢿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁⠀⠀⡀⣾⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⢿⣿⡟⣛⣋⣡⣤⣤⡀⢀⣤⣤⣤⡄⣤⣤⣤⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣧⢻⣿⣿⣿⡟⣿⡣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⠿⢟⣛⣛⣛⠛⣛⣻⡉⣻⣿⣿⣾⣯⣿⣾⣿⢿⣛⢹⣿⡏⠿⠿⣿⣿⡏⣿⣿⢹⣿⡇⣿

⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠻⣿⣟⣿⣯⣛⣸⣢⣄⣀⣀⡀⠀⠀⠀⢠⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣤⣽⣯⠀⣶⣿⣿⢻⡟⣷⣿⣿⣾⡿⢻⣿⣇⣶⣶⢻⣿⣇⣿⣿⢸⣿⡇⣿

⠀⠀⣀⣤⣴⣶⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠙⢿⣷⣵⠇⢁⢹⢿⣟⠿⢷⢧⠲⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠿⠿⠿⠟⠁⢻⢟⠻⣿⣙⣯⡿⡿⢿⠿⠋⠛⠿⠛⠋⠀⠙⠛⠛⠉⠘⠛⠃⠙

⣾⣿⣿⣿⣿⣿⡏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⡙⠿⡻⠶⠀⠈⠙⠏⠈⠈⠈⠱⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣸⣿⣿⣷⡀⠀⠀⠀⠀⠀⡨⠖⠂⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠷⠀⠀⠀⠀⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠨⠿⠟⠻⠿⠿⠿⠿⠃⠿⣿⡿⢿⡷⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣠⣷⣾⣤⣤⣤⣤⣤⣤⣤⡀⠀

⣿⣿⡗⢫⣻⢿⣇⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⠛⣿⣿⣿⡇⣿⡟⠃⠀⣿⡟⣿⣾⣿⡟⢳⣿⢻⣷⢸⣿⢻⡇⣿⡇⢸⣿⠛⣼⢸⣿⣼⣿⢸⣿⢹⣿⣿⡇⣾⡟⣿⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤

⡾⣭⣿⣷⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⡇⣿⡿⠇⠀⣿⡿⠟⢻⣿⡟⢸⣿⢸⣿⢸⣿⠿⠃⣿⡇⢸⣿⠻⣽⡼⣿⣿⣿⣿⡟⣾⣿⣿⡇⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠍⣳⣻⣿⣿⡏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⠿⣤⡿⠿⠿⢇⡿⠷⠆⠀⠿⠿⣸⡸⠿⠷⠞⠿⠾⠟⠸⠿⢸⡀⠿⠷⠾⠿⠶⣸⣇⠿⢿⡸⠿⢇⡿⠿⠿⢇⡻⠷⠿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿

⡄⢀⣉⣙⠛⢐⣛⣻⠿⣛⣻⢟⣛⡿⣛⣛⢋⣀⡙⣛⣛⣛⣛⣛⣂⣀⣈⣛⣛⡛⣀⣀⣈⠀⠀⣈⣓⣛⢛⣃⣀⡀⣛⣛⡻⢟⣛⣻⢿⣛⣛⠻⡿⢟⣛⡛⢟⣛⣛⡿⣟⣻⢟⣛⡿⣛⣻⢟⣛⣻⢟⣛⣻⢿⣿⣿⠏⠁

⡅⣼⣿⣿⡇⣿⡏⣿⡇⣿⣿⣾⣿⡇⣿⣿⣾⣿⡇⣿⡏⢹⣿⢩⢹⣿⠋⣿⣿⡁⣿⡏⣿⡇⢀⢹⣿⡏⢸⣿⣿⡇⣿⣟⡁⣿⣏⡿⢸⣿⣋⢰⢰⣿⣿⣿⢸⣿⣹⣿⢸⣿⢸⣿⣷⣿⣿⢸⣿⡉⣿⣏⡿⣿⣿⡏⠀⠀

⣇⢿⣿⣤⡄⣿⡇⣿⡇⣿⢻⡿⣿⡇⣿⢻⡿⣿⡇⣿⡇⢸⣿⢸⢸⣿⠀⣿⣿⠃⣿⡇⣿⡇⣼⢸⣿⡇⢸⣿⣿⡇⣿⡟⠃⣬⡟⣿⣼⣿⠛⢼⣿⣿⣧⣤⢸⣿⢹⣷⢸⣿⢸⡟⣿⢿⣿⢸⣿⠋⣬⡝⣿⡞⣿⡇⠀⠀

⣿⣞⣻⢿⣷⣽⣿⣻⠥⠛⡚⣃⣛⠃⠛⠘⣃⣛⣃⣛⣳⣜⣛⣼⣞⣛⣴⣛⣛⣛⣛⣛⣛⣣⣿⣜⣛⣣⠘⠛⣛⣃⣛⣛⣛⣙⣻⣛⣝⣛⣛⣻⣧⣛⣟⣛⣘⣛⣘⣛⣚⣛⣘⣃⣛⣘⣛⣘⣛⣛⣙⣛⣛⣽⣿⡇⠀⠀

[39A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣾⣿⠿⠿⠁⠀⠁⠰⡋⢻⡇⡏⠘⣻⠉⢿⣿⡿⠛⠠⢐⠂⡉⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠘⠛⠒⠒⠓⠓⠐⠒⠒⠘⠒⠚⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣾⣿⣿⠷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠲⠶⠶⢦⣶⠀⠀⠁⠀⠀⠀⠀⠀⠐⠛⠿⠿⠞⠒⠂⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣷⣦⣄⠀⡀⠀⠀⠀⠀⢀⣀⣰⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣺⣷⣿⣿⠇⠀⠀⠀⢀⣠⣤⣴⣾⣿⣿⣿⣷⣶⣶⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠂⠙⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣛⣒⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⢾⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣤⠈⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⡋⠉⠉⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀⣴⣌⣄⢌⠀⠈⠀⠉⠙⠛⠛⠻⠛⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠆⠀⠀⠀⠉⣿⣿⣿⣿⠯⠻⠟⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣭⣿⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠈⠀⠀⠀⠀⣠⣿⣿⣿⣟⡃⠠⠀⠀⠀⠀⠉⠙⠻⣿⣿⣿⡿⣿⣿⣿⣿⠿⠻⡿⣿⣿⣿⣿⡿⣿⡟⠻⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⣴⣿⣿⠧⠔⠃⡠⠄⠠⣄⢀⠀⠀⠀⣾⣿⣿⣿⡇⠙⠛⠛⠛⠒⠀⣤⣿⣿⣿⣿⣷⢼⣟⠀⠀⢠⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠃⠀⠀⣸⣿⣿⣿⣯⣿⣾⣉⠀⢀⣸⡥⣶⣧⣼⣿⣿⣿⣿⣷⠀⣠⠄⣠⠶⠂⢀⡈⢻⣿⣿⣿⠀⣿⠂⠀⢸⣧⠀⠘⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣾⣄⣀⣠⣿⣦⢻⣿⣿⠀⠛⡇⠀⣼⠾⠂⠒⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠑⠸⣿⣿⣷⣶⣾⣿⣿⣿⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⡇⣸⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣬⢇⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠛⣀⣀⢼⣿⡏⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⣾⢰⡘⣿⣿⣿⣿⣿⣿⣿⢋⣼⣿⣿⣶⣿⣿⣌⣻⣿⣷⣦⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⠭⠄⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⣵⡿⣸⣼⣿⣿⣿⡿⣿⣿⢇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣇⢀⡂⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣧⠸⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠀⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉⠉⠉⠉⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⢄⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢻⣧⣿⣿⣿⣿⣿⣿⣿⣿⣝⡿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢾⠃⠞⠂⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠈⢱⣿⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⡿⠿⠟⠛⠻⠿⠿⢿⣿⣿⢿⠐⠻⠼⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⠆⠀⢻⣻⣿⣿⣿⣿⣿⣿⣟⣋⣉⣉⣛⣛⣉⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠟⠀⠀⠀⠀⠈⠀⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡆⣿⣿⣄⠀⠀⠉⠛⢿⣽⣿⣿⣿⣿⣿⣿⣧⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣧⣿⣿⣿⣧⠀⠀⠀⠀⠘⠿⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⢿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁⠀⠀⡀⣾⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⡿⢿⣿⡟⣛⣋⣡⣤⣤⡀⢀⣤⣤⣤⡄⣤⣤⣤⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣧⢹⣿⣿⣿⣿⣟⡧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠿⢟⣛⣛⣛⠛⣛⣻⡉⣻⣿⣿⣾⣯⣿⣾⣿⢿⣛⢹⣿⡏⠿⠿⣿⣿⡏⣿⣿⢸⣿⡇⣿

⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠻⣿⣏⣿⣯⢟⡸⣦⣄⣀⣀⡀⡀⠀⠀⢠⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣤⣽⣯⠀⣶⣿⣿⢻⡟⣷⣿⣿⣾⡿⢻⣿⣇⣶⣶⢻⣿⣇⣿⣿⢸⣿⡇⣿

⠀⠀⣀⣤⣴⣶⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠙⢿⣷⣥⡆⢁⢹⢿⣟⢿⢷⢧⠢⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠿⠿⠿⠛⠁⢻⢿⠻⣿⣘⣯⡿⡿⢿⠿⠋⠛⠿⠛⠋⠀⠛⠛⠛⠉⠘⠛⠃⠙

⣾⣿⣿⣿⣿⣿⡏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⡙⠿⡿⠖⠀⠈⠘⠛⠈⠁⠈⠹⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣸⣿⣿⣷⡀⠀⠀⠀⠀⠀⡸⠒⠂⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠨⠿⠿⠻⠿⠿⢿⠿⠃⠿⣿⡿⠿⡷⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣠⣷⣾⣤⣤⣤⣤⣤⣤⣤⡀⠀

⣿⣿⡷⢻⣿⢷⣧⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⠛⣿⣿⣿⡇⣿⡟⠃⠀⣿⡟⣿⣾⣿⡟⢳⣿⢻⣷⢸⣿⢻⡇⣿⡇⢸⣿⠛⣼⢸⣿⣼⣿⢸⣿⢹⣿⣿⡇⣾⡟⣿⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤

⠾⣭⣿⣧⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⠀⣿⣿⣿⡇⣿⡿⠇⠀⣿⡿⠟⢻⣿⡟⢸⣿⢸⣿⢸⣿⠿⠃⣿⡇⢸⣿⠻⣽⡼⣿⣿⣿⣿⡟⣾⣿⣿⡇⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠍⣱⣻⣿⣿⡏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣤⡿⠿⠿⢇⡿⠷⠆⠀⠿⠯⣸⡸⠿⠷⠞⠿⠾⠟⠸⠿⢸⡀⠿⠷⠾⠿⠶⣸⣇⠿⢿⡸⠿⢇⡿⠿⠿⢇⡻⠷⠿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿

⡔⢁⣉⣉⠛⢑⣛⣻⠿⣛⣻⢟⣛⡿⣛⣛⢋⣀⡙⣛⣛⣛⣛⣛⣂⣀⣈⣛⣛⡛⣀⣀⣈⠀⠀⣈⣓⣛⢛⣃⣀⡀⣛⣛⡻⢟⣛⣻⢿⣛⣛⠻⡿⢟⣛⡛⢟⣛⣛⡿⣟⣻⢟⣛⡿⣛⣻⣟⣛⣻⢟⣛⣻⢿⣿⣿⠏⠁

⣇⢿⣿⣤⡄⣿⡇⣿⡇⣿⢻⡿⣿⡇⣿⢻⡿⣿⡇⣿⡇⢸⣿⢸⢸⣿⠀⣿⣿⠃⣿⡇⣿⡇⣼⢸⣿⡇⢸⣿⣿⡇⣿⡟⠃⣬⡟⣿⣼⣿⠛⢼⣿⣿⣧⣤⢸⣿⢹⣷⢸⣿⢸⡟⣿⢿⣿⢸⣿⠛⣬⡝⣿⡞⣿⡇⠀⠀

[39A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⡾⣿⠻⠟⠁⠀⠁⠐⡁⢻⠇⡇⠀⣱⠉⠿⠟⡿⠋⠀⠠⠀⠀⠀⠲⢌⣤⣀⣀⣀⠀⠘⠃⠛⠻⠿⠿⣿⣷⡄⠀⠐⠂⢒⠒⠒⠐⠀⠒⠒⠐⠒⠚⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣄⣀⣀⠀⠀⠀⠀⠀⣀⣤⣦⣭⡤⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⠟⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣫⣵⣿⡿⠃⠀⠀⠀⢀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣶⣶⣷⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣋⣂⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣻⣿⣿⠺⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⢠⠈⠎⠉⠙⠙⠛⠋⠛⠿⢿⠿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⠿⠍⠉⠁⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⢀⣤⣤⡄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⣿⢿⠃⠀⠀⠀⠀⣿⣿⣿⣿⡏⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡸⣮⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠈⠀⠀⠀⠀⣰⣿⣿⡿⣿⡉⠒⠀⠀⠀⠀⠘⠛⢻⣿⣿⣿⡿⣿⣿⣿⡿⠿⠛⠛⣿⣿⣿⣿⡿⢿⣏⠛⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⣼⣿⣿⢿⡛⢃⡤⠖⠢⣄⠀⠀⠀⢠⣿⣿⣿⣿⡇⠙⠛⠋⠉⠐⠀⢤⣾⣿⣿⣿⣟⠼⣿⠀⠀⢀⣸⣤⣦⣀⣸⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠃⠀⠀⣸⣿⣿⣿⣿⣿⣾⣍⣀⣀⣸⡔⣾⣷⣼⣿⣿⣿⣿⣷⣀⣤⠀⣠⠖⠂⠀⡈⠹⣿⣿⣿⠀⢿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣾⣤⣀⣠⣿⣦⣹⣿⣿⠀⠈⡇⠀⢸⣿⣿⢿⡿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⢀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠉⠘⣿⣿⣿⡰⠄⢿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⣀⢀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣧⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠓⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢰⣿⣿⣅⡄⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠠⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣬⢿⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⢠⣤⢼⣿⡏⠀⠀⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⠀⣿⣿⣿⣿⣷⣄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡟⡃⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⣼⢸⡜⣿⣿⣿⣿⣿⣿⣿⢃⣾⣿⣿⣿⣿⣿⣇⣻⣿⣿⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠇⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⢠⠐⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣯⣤⣿⢸⣿⣿⣿⣿⣿⣿⣿⢇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⢿⡆⡿⠉⢉⣤⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠙⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⠸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣾⣿⣧⣤⡈⠋⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠈⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠛⠉⠁⠀⠀⠉⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢉⣻⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣵⡌⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠈⠛⠿⣿⣿⡝⠛⠛⠟⠛⠙⠛⠛⠿⣿⣿⣿⣿⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠈⢹⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠿⣷

⠀⠀⣰⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣅⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣉⣡⣄⣉⣉⣉⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠺⠿⡿⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⡃⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡖⣽⣿⣆⡀⢥⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣷⡄⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⡟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣇⣿⣿⣿⣷⡀⠀⠀⠀⠘⣭⡍⣿⠿⠿⠿⣿⣿⣿⣿⠿⠿⣛⢿⣦⣶⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣋⣯⣿⣄⠀⣠⣤⣤⣄⢠⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣷⠹⣿⣿⣿⣿⣿⡗⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣻⣿⣿⣿⣿⣿⠾⠟⣛⣛⣛⡛⢛⣛⣋⢙⣿⣿⣷⣿⣹⣷⣿⡿⣟⡋⣿⣿⠹⠿⢾⣿⣿⢹⣿⡇⣿⣿⢸

⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠹⣿⣿⣿⣿⡿⣿⣷⣤⣤⣤⣄⠀⠀⠀⠀⢠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣥⣬⣯⡅⢰⣿⣿⣟⣿⢻⣾⣿⣷⣿⢟⣿⣿⣰⣶⡾⣿⣿⣸⣿⡇⣿⣿⢸

⠀⠀⣀⣤⣴⣶⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠙⢿⣿⣾⡇⢡⣿⣿⣿⣻⣿⢷⠦⠄⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠿⠿⠟⠛⠃⠘⠿⠛⢿⣇⣻⡽⠿⠿⡿⠛⠙⠻⠟⠛⠁⠙⠛⠛⠋⠁⠛⠛⠈

⣶⣿⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠙⣿⡽⡶⠈⢉⣼⠿⢚⠊⠀⠠⠎⠻⢿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⢀⠔⠒⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⡿⣿⢿⡇⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠷⠀⠀⠁⠀⠁⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠽⠛⠻⠿⠿⠿⠿⠃⠸⣿⡿⠿⠿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢸⣸⣇⣀⣀⣠⣄⣀⠀⠀⠀

⣿⡻⠃⢀⠉⠎⣇⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⠛⣻⣿⣿⡇⣿⡟⠃⠀⣿⡟⣿⣾⣿⠛⢳⣿⢻⣷⢸⣿⢻⡆⣿⡇⢸⣿⠛⣼⢸⣿⣸⣿⢸⣿⢸⣿⣿⡇⣾⡟⣿⡎⣿⣿⣿⣿⣷⣶⣦⣾⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀

⠆⣤⣒⣀⣙⣾⢸⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⠀⣿⣿⣿⡇⣿⡿⠃⠀⣿⡿⠟⢻⣿⡟⢸⣿⢸⣿⢸⣿⠿⠃⣿⡇⢸⣿⠻⣼⡼⣿⣿⣿⣿⡟⢸⣿⣿⡇⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾

⠀⣠⠘⡭⣟⡏⣾⣿⣿⣿⣿⣿⣿⣿⣿⡾⠿⣤⡿⠿⠿⢇⠿⠷⠆⠀⠿⠧⣸⡸⠿⠷⠞⠿⠾⠟⠸⠿⢸⡀⠿⠷⠾⠿⠶⣸⣇⠿⠿⡸⠿⢇⡼⠿⠿⠇⡹⠷⠿⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿

⠀⠀⣁⣉⠉⢀⣛⣛⠿⣛⣛⢟⣛⡻⣛⣛⢋⣀⡙⣛⣛⣛⣛⣛⣃⣀⣀⣛⣛⡋⣁⣀⣀⠀⠀⣈⣀⣘⢋⣃⣀⡀⣛⣛⡻⢟⣛⣻⢿⣛⣛⠻⠿⢟⣛⡛⢟⣛⣛⡻⣟⣛⢟⣛⡻⣛⣻⢟⣛⣻⢟⣛⣛⢿⣿⡏⠀⠀

⡄⣸⣿⣿⡇⣿⡏⣿⡇⣿⣿⣼⣿⡇⣿⣿⣾⣿⡇⣿⡏⢹⣿⢩⢹⣿⠋⣿⣟⡁⣿⡏⣿⡇⠀⢙⣿⡋⢸⣿⣿⡇⣿⣟⡁⣿⣏⠿⢸⣿⣋⢰⢰⣿⢻⣿⢸⣿⣹⣷⢸⣿⢸⣿⣷⣿⣿⢸⣿⡉⣿⣏⡿⣺⣿⠀⠀⠀

⡇⢻⣿⣤⡄⣿⡇⣿⡇⣿⢻⡿⣿⡇⣿⢻⡿⣿⡇⣿⡇⢸⣿⢸⢸⣿⠀⣿⣟⠃⣿⡇⣿⡇⣰⢸⣿⡇⢸⣿⣿⡇⣿⡟⠃⣬⡟⣿⣼⣿⠛⢼⣽⣿⢡⣤⢸⣿⢹⣷⢸⣿⢸⡟⣿⢿⣿⢸⣿⠋⣬⡝⣿⡞⣿⣇⠀⠀

⣿⣜⣻⢟⣧⣽⣿⣻⠥⠛⡚⣃⡛⠃⠛⠘⣃⣛⣃⣛⣳⣜⣛⣼⣞⣛⣴⣛⣛⣛⣛⣛⣛⣡⣿⣜⣛⣣⠘⠛⣛⣃⣛⣛⣓⣙⣻⣛⣝⣛⣛⣻⣧⣛⢛⣛⣘⣛⣘⣛⣘⣛⣘⣃⣛⣘⣛⣘⣛⣛⣙⣛⣛⣽⣿⣿⣷⡄

[39A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⡿⣯⠛⠋⠀⠀⠀⠘⠀⠸⠇⡇⠀⣸⠀⠻⠟⡿⢉⠀⠨⠁⠀⠈⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠄⠀⠀⠐⠀⠒⠒⠒⠐⠀⠒⠒⠀⠒⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠶⠂⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⠻⠛⠁⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⡀⠀⠀⠐⠳⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣫⣵⣿⡿⠃⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠁⠁⠘⡷⣦⠀⠀⠀⠀⠀⠀⠀⢤⣼⣷⣶⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣫⣁⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⡀⠀⠁⢋⠙⠀⠀⠀⠀⠀⠀⠀⠈⠫⢿⢿⣿⣓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣛⣻⣿⡿⢚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⢀⢰⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⠿⠍⠈⠁⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣿⣧⣅⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢿⢿⠂⠀⠀⠀⠀⢻⣿⣿⣿⣿⡛⡟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠈⠀⠀⠀⠀⣠⢾⣿⣿⣿⣿⠿⠶⢷⣄⡙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠹⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠂⠀⠀⠀⣴⢫⣿⣿⣟⣿⡷⠛⠳⣾⣿⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⢿⣿⣿⣿⣿⣿⠿⣿⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⢰⢿⣿⣿⣿⣿⣿⣯⣀⣡⣾⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢛⠳⣌⢻⣿⣿⣿⠇⣿⡅⠀⠀⠀⣤⢠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠼⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣬⣤⣿⣿⣿⣿⣿⡆⠾⣧⢀⢠⣼⡇⣼⠃⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡆⠙⠘⣿⣿⣿⡟⠀⠀⠀⠀⠀⠠⣿⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢘⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⠟⠃⢿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠁⠀⢰⣿⡿⣿⠇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣬⢁⠀⠀⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣈⠛⣦⣤⣾⣿⣿⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣧⣀⣾⣿⣿⣿⠀⠀⠀⢀⣄⣴⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⣼⢀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⢻⡿⠻⠟⢠⠀⠀⠐⠛⢻⣻⣿⣿⣿⣿⣿⣿⡿⠆⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣧⣀⡻⠘⢠⣼⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡿⠀⠀⠀⠀⣤⠀⠀⠀⠀⢰⣾⠞⣿⣿⣿⣿⣿⣿⣼⡭⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣿⣧⠀⢤⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣀⠀⠈⢀⣴⣿⣷⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠃⠀⠘⠡⢻⣿⣷⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠉⠉⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⡇⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡏⣿⣿⣿⣿⣿⣦⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠉⢁⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠁⠉⠉⠃⠉⠉⠈⠈⠁⠉⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠈⣺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡇⠀⠀⠰⢼⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡖⣹⣿⣄⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⡇⣿⣿⣿⣷⣆⠀⠓⣤⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷⣄⠹⡧⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⡿⢿⣿⣿⣿⣋⣩⣭⣯⡁⢠⣤⣤⣤⡀⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣿⣿⣿⣿⣿⣄⣄⡀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⢛⣛⣛⠛⣛⣋⠉⣻⣿⣿⣾⣏⢿⣾⣿⢿⣛⣻⣿⡏⠿⠷⣿⣿⣿⣿⣷⢻⣿⡇

⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣭⣭⣭⣥⣤⣽⣅⠀⣮⢿⣿⣻⡟⣷⣿⣿⣿⡿⣻⣿⣇⣶⣶⢿⣿⣇⣿⣿⢸⣿⡇

⠀⠀⣀⣠⣴⣶⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠻⠻⠿⠿⠛⠋⠀⠛⠟⠻⣿⣘⣭⠿⠿⣿⠟⠋⠛⠿⠛⠋⠈⠛⠛⠛⠁⠘⠛⠃

⣶⣿⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠠⠐⠂⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠿⣿⠿⠿⠿⠿⠿⠟⠿⠟⠻⠿⠿⠿⠿⠿⠿⢿⡿⠟⠸⣿⡿⠿⠿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⠅⣿⣿⣿⣿⣿⣿⣿⣇⢻⣿⠛⣹⣏⣿⡇⣿⡟⠃⡇⣿⡟⣿⡞⣿⠛⢳⣿⢻⣷⢸⣿⢻⡆⣿⡇⢸⣿⠛⣼⢸⣿⣸⣿⢸⣿⢸⣿⣿⡇⣾⡟⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣹⡿⣿⡇⣿⡿⠃⡇⣿⡿⢟⢣⣿⠟⢸⣿⢸⣿⢸⣿⠿⠃⣿⡇⢸⣿⠻⣼⡼⣿⣿⢿⣾⡏⢸⣿⣿⡇⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⡼⠿⣠⡾⠧⠿⠇⠿⠷⠆⡀⠿⠇⣼⡸⠿⠷⠎⠿⠾⠟⠸⠿⣸⡇⠿⠷⠸⠿⠶⣸⣇⠿⠿⡸⠿⢇⡼⠿⠿⠇⡹⠷⠿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⠟⣛⣛⠻⢃⣛⣛⠿⣛⣛⢟⣛⡻⣛⣛⢋⣁⡙⣛⣛⣛⣛⣛⣓⣙⣛⣛⣛⡛⣛⣛⣛⢿⡟⣛⣛⣛⢛⣛⣚⡀⣚⣛⡻⢟⣛⣻⢿⣛⣛⢻⡿⢟⣛⡛⢟⣛⣛⡻⢗⣂⢀⣀⡀⣀⣀⢀⣀⣀⢀⣀⣀⠀⠀⠀⠀⠀

⡇⢸⡟⣿⡇⣿⡏⣿⡇⣿⣿⣼⣿⡇⣿⣿⣼⣿⡇⣿⡏⢹⣿⢩⢹⣿⠉⣿⣟⡁⣿⡏⣿⡇⣤⠙⣿⠋⢸⣿⣿⡇⣿⣟⡁⣿⣏⠿⢸⣿⣋⢼⣧⣿⢹⣿⢸⣿⣹⣷⢸⣿⢸⣿⣧⣿⣿⢸⣿⡉⣿⣏⡿⠀⠀⠀⠀⠀

⣇⢸⡏⣤⡄⣿⡇⣿⡇⣿⢻⡿⣿⡇⣿⢻⡿⣿⡇⣿⡇⢸⣿⢸⢸⣿⠀⣿⡟⠃⣿⡇⣿⡇⣿⠈⣿⠀⢸⣿⣿⡇⣿⡟⠃⣬⡟⣿⣼⣿⠛⢼⡿⣿⢠⣤⢸⣿⢹⣷⢸⣿⢸⡟⣿⢻⣿⢸⣿⠃⣬⡝⣿⡄⠀⠀⠀⠀

⣿⣜⣻⢛⣧⣝⣛⣛⡥⠛⣚⣃⣛⣃⣛⠘⣃⣛⣃⣛⣣⣜⣛⣼⣞⣛⣤⣛⣛⣛⣛⣛⣛⣡⣿⣞⣛⣢⣘⠛⢛⣃⣛⣛⣃⣙⣛⣛⣝⣛⣛⣻⣧⣛⣛⣋⣜⣛⣘⣛⣘⣛⣘⣃⣛⣘⣛⣘⣛⣛⣙⡛⣛⣥⣶⡀⠀⠀

[39A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⢿⣏⠛⠋⠀⠀⠀⠸⠀⠟⠇⠇⠄⡿⠀⠻⠋⠟⠱⠀⠘⠀⠀⠈⠱⠃⣺⣿⣶⣶⣦⣤⣤⣄⡀⠀⠉⠉⠋⠉⠋⠐⠂⠒⠒⠒⠐⠈⠒⠒⠐⠒⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⢀⣠⣴⣵⣿⣿⠇⢐⠁⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⡿⠟⠛⠁⠀⠀⠀⠀⢀⣀⣀⣀⡀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠈⠡⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣯⣷⣿⡿⠃⠀⠀⠀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠄⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⣿⣿⣿⣫⣇⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠑⢫⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠊⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣛⣻⣿⣿⢺⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⢲⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠻⠿⢛⠆⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⠿⠍⠉⠁⠈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠠⢴⣦⣆⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⠂⠀⠀⠀⠀⣹⣿⣿⣿⠋⠙⠉⠙⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣴⣻⣿⠿⡻⠅⠀⠀⠀⠀⠀⠀⠀⢩⣿⣿⣿⡟⣿⣿⣿⣟⣛⠉⠉⣿⣿⣿⣿⣟⢻⡟⠙⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠂⠀⠀⠀⣼⣿⠟⢓⠊⢀⣔⠂⠐⣤⠀⢀⡀⠀⣿⣿⣿⣿⡇⠈⠉⠉⠁⠉⠑⠾⢿⣿⣿⣿⣿⠻⣿⠐⠀⢠⣀⣤⣤⣴⣾⡇⠀⠀⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠀⣸⣷⣿⣿⣿⣾⣮⣅⣀⣠⣾⣞⣾⣷⣾⣿⣿⣿⣿⣿⣀⣴⣂⢴⠛⠁⠀⣄⠹⣿⣿⣿⠀⢿⡀⠀⠘⣲⣿⣿⣿⣿⢿⠀⠠⠦⢠⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣿⣷⣼⣿⣿⠀⠀⣧⢀⣰⣿⣿⣿⣿⡏⠘⠀⠀⠀⠰⣿⣿⣿⣿⣦⣤⡀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠀⢠⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⠈⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣷⣶⣆⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⠛⠑⢿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢰⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⣮⢃⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣈⠁⣠⣤⡸⣿⣇⣀⠀⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣤⣀⣾⣿⣿⣿⣿⠟⣿⣿⣅⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⣾⢸⠀⣿⣿⣿⣿⣿⣿⣿⢡⣿⣿⣿⣿⣷⣿⣦⣭⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⠿⢿⣿⡿⡟⠐⠛⣿⣿⡷⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⣴⡿⠸⣴⣿⣿⣿⣿⣿⣿⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣇⡾⠔⠀⠀⠀⠀⣶⠀⢸⣯⣶⣶⣶⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣷⠀⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⣶⣶⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠁⠀⠩⡻⢻⣿⣿⣿⣿⣿⣿⡿⠙⠙⠁⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡇⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⣟⣿⣿⣿⣿⣿⣷⣄⣀⣀⣀⣀⣀⣀⢀⠀⠀⠀⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠙⠟⣽⣿⣿⣿⣿⣿⣮⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠈⢛⡻⣿⡏⠉⠉⠉⠉⠉⠀⠈⠙⠋⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡁⠀⠀⡓⡸⢿⣿⣿⣿⣿⣿⣥⣤⣤⣤⣀⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠠⣧⣇⠀⠀⠐⠼⢯⣿⠿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡖⣹⣿⣆⠀⠀⠀⠈⠳⠈⣾⣽⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣧⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠿⡿⠿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢿⣿⡿⣿⣟⣋⣿⣿⣿⢿⣤⣤⣤⣄⢠⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⡌⢱⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢛⣛⣻⡛⣛⣛⡉⢹⣿⣿⣷⣯⣻⣾⣿⣿⣟⣻⣿⣿⠿⠿⢾⣿⣏⣿⣿⣸⣿⣇

⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠹⢿⣍⡁⡄⡐⢀⠳⣄⣀⣀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⠉⣩⣭⣭⣥⣽⣯⡄⢰⣿⣿⣟⡿⢻⣿⣿⣿⣿⢿⣿⣿⢰⣶⣾⣿⣿⣿⣿⡏⣿⣿

⠀⠀⣀⣠⣴⣶⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠘⠿⣷⣦⡇⠀⠈⠛⢯⠙⠂⠀⠀⠄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣆⠈⠙⠿⠿⠟⠛⠃⠘⠿⠛⣿⣇⣯⡽⡿⢿⡿⠋⠙⠻⠟⠛⠀⠙⠛⠛⠋⠀⠛⠛

⣶⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢉⠷⡍⠒⠄⠀⠀⠁⠀⠀⠀⠀⠘⢻⢿⣿⣿⣿⣿⣿⣿⣿⢱⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⢀⠔⠒⠘⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⡿⡯⢿⢻⡇⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠷⠀⠀⠁⠀⠘⠀⠀⠁⠀⠀⠀⠀⠀⠀⠨⠴⠛⠻⠿⠟⠿⠿⠏⠸⣿⡿⠿⠿⠷⠄⠀⠀⠂⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠾⠾⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣫⡇⢂⠏⠞⣄⣿⣿⣿⣿⣿⣿⣿⣏⢻⣿⠛⣿⣿⣿⡇⣿⡟⠃⠀⣿⡟⣿⣾⣿⠛⢳⣿⢻⣷⢸⣿⢻⡆⣿⡇⢸⣿⠛⣼⢸⣿⣸⣿⢸⣿⢸⣿⣿⡇⣾⡟⣿⡞⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠷⣤⣖⣥⣛⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⡇⣿⡿⠃⠀⣿⡿⠟⢻⣿⠟⢸⣿⢸⣿⢸⣿⠿⠃⣿⡇⢸⣿⠻⣼⡸⣿⣿⣿⣿⡟⢸⣿⣿⡇⣿⡇⣿⡇⣸⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠈⢱⣐⣻⣿⡏⣼⣿⣿⣿⣿⣿⣿⣿⣿⡼⠿⣤⡿⠿⠿⢇⠿⠷⠆⠀⠿⠧⣸⡸⠿⠷⠞⠿⠾⠟⠸⠿⢸⡀⠿⠷⠸⠿⠶⣸⣇⠿⠿⡸⠿⢇⡼⠿⠿⠇⡹⠷⠿⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀

⡄⠀⣁⣉⠙⢀⣛⣛⠿⣛⣛⢟⣛⡻⣛⣛⢉⣀⡙⣛⣛⣛⣛⣛⣓⣀⣀⣛⣛⡋⣁⣈⣀⠀⠀⣀⣐⣚⢛⣁⣀⡀⣚⣛⡻⢟⣛⣻⢿⣛⣛⠙⡿⢟⣛⡛⢟⣛⣛⡻⣟⣛⢟⣛⡿⣛⣻⢟⣛⣛⢛⣉⣀⠀⠀⠀⠀⠀

⡄⣸⣿⣿⡇⣿⡏⣿⡇⣿⣿⣼⣿⡇⣿⣿⣼⣿⡇⣿⡏⢹⣿⢩⢹⣿⠉⣿⣟⡁⣿⡏⣿⡇⠀⠹⣿⡋⢸⣿⣿⡇⣿⣟⡁⣿⣏⠿⢸⣿⣋⢤⢰⣿⢻⣿⢸⣿⣹⣷⢸⣿⢸⣿⣷⣿⣿⢸⣿⡉⣿⣏⡿⠂⠀⠀⠀⠀

⡇⢺⣿⣤⡄⣿⡇⣿⡇⣿⢻⡿⣿⡇⣿⢻⡿⣿⡇⣿⡇⢸⣿⢸⢸⣿⠀⣿⡟⠃⣿⡇⣿⡇⣴⠐⣿⡇⢸⣿⣿⡇⣿⡟⠃⣬⡟⣿⣼⣿⠛⢼⡾⣿⢣⣤⢸⣿⢹⣷⢸⣿⢸⡟⣿⢿⣿⢸⣿⠃⣬⡝⣿⡆⡄⠀⠀⠀

⣿⣜⡻⢟⣧⣽⣿⣻⠥⠛⡚⣃⣛⠃⠛⠘⣃⣛⣃⡛⣣⣜⣛⣼⣞⣛⣴⣛⣛⣛⣛⣛⣛⣡⣿⣜⣛⣣⡘⠛⢛⣃⣛⣛⣓⣝⣛⣛⣝⣛⣛⣿⣧⣛⡛⣛⣘⣛⣘⣛⣘⣛⣘⣃⣛⣘⣛⣘⣛⣛⣙⣛⣛⣥⡋⠀⠀⠀

[39A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⢿⣯⠟⠛⠀⠀⠁⠸⠀⡟⡏⠁⢌⠿⠘⠟⢛⠟⠑⠈⠞⠀⠈⠈⠓⠀⠀⠀⠀⣀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠐⠂⠒⠒⠓⠓⠈⠒⠒⠀⠒⠚⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣼⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣦⣄⡿⠒⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⡟⠛⠁⠀⠀⠀⠀⣀⣀⣀⣀⣀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣴⣶⣶⣶⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣭⣿⣿⡿⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣰⣿⣿⣿⣿⡇⠂⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠑⢫⠛⠋⠉⠁⠈⠈⠀⠈⠁⠉⠛⠛⠻⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣛⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢀⢲⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠿⠅⠍⠀⣨⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⢴⣶⣶⣦⠂⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⣿⣿⠀⠀⠀⠀⠁⣻⣿⣿⣿⡋⠙⠉⠙⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠁⢀⠀⠀⠀⣼⣿⣿⢿⡿⠗⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⡟⣿⣿⣿⣿⣛⠉⢉⣿⣿⣿⣿⣟⢿⣯⠉⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠂⠈⠀⢀⣾⣿⢟⡓⠊⢀⡒⢃⠐⣦⠠⢀⡀⢰⣿⣿⣿⣿⡇⠈⠉⠁⠀⠈⠑⠿⢿⣿⣿⣿⣿⠻⣿⠐⠀⢀⡀⠀⠀⢰⣴⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠘⠁⠀⠀⣼⣿⣿⣿⣷⣿⣿⣄⣠⣤⣿⣟⣾⣷⣾⣿⣿⣿⣿⣿⣤⣶⣠⣶⠋⠁⠄⣄⠹⣿⣿⣿⠀⢿⡀⠀⠘⠀⢠⣔⣿⣿⡿⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢠⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣴⣿⣷⣼⣿⣿⠀⠀⣇⢀⣰⢷⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢸⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⡀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⠈⣿⣾⣿⣿⣿⣿⠡⠀⠀⠀⠀⠀⣹⣿⣿⣿⣷⣄⢀⡀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⡇⢠⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠘⢿⣿⡿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣮⢃⠀⢠⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣀⣁⣴⣄⠺⣿⣇⣀⠀⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣤⣀⣿⣿⣿⣿⣿⣿⠛⣿⣦⡄⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⢻⡄⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⣿⢸⡄⣿⣿⣿⣿⣿⣿⡿⣱⣿⣿⣿⣿⣿⣿⣦⣽⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠛⠛⠻⠿⠿⠋⠀⠹⣿⣗⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣻⣷⠄⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣿⣴⡟⢾⣶⣿⣿⣿⣿⣿⣿⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣇⣿⠄⠀⠀⠀⠀⠀⠀⠀⠸⣯⣤⣀⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣧⠈⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⣠⣾⣦⡀⠀⠀⠀⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠁⠀⢻⣿⢻⣿⣿⣿⣿⣿⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡉⣿⣿⣿⣿⣿⣿⣷⣄⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣦⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠋⠁⢿⢿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠙⠹⡇⠉⠉⠁⠈⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⣫⣻⢻⣿⣿⣿⣿⣿⣿⣟⣿⡿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡁⠀⠹⣟⣿⣿⣿⣿⣿⣿⣿⣥⣤⣤⣤⣀⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣷⣇⠀⠀⠽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡖⣽⣿⣦⠀⠀⠀⠈⠻⢾⣿⣿⣿⣿⣿⣿⣿⡆⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣧⣿⣿⣿⣧⡀⠀⠀⠀⠘⠙⠛⠿⠿⢿⠿⢿⡿⠿⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⡿⣿⣿⢿⣿⣋⣿⣿⣿⡛⣿⣤⣤⣤⡀⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠘⣿⡿⣿⣟⣿⡗⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡟⠿⠿⠿⢛⣛⡟⢛⣛⣋⢉⣿⣽⣿⣿⣽⣷⣿⣿⣾⣛⣿⣿⡿⠿⠷⣿⣿⣹⣿⣇⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠹⣿⣯⡽⣾⡝⢻⢳⣤⣤⣤⡄⢠⠀⠀⢠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠉⢉⣩⣽⣥⣬⣿⡅⢰⣼⣿⣿⣿⠻⣿⣿⣿⣿⡿⣿⣿⡇⣶⣶⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣀⣠⣴⣶⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠘⠿⣿⣮⡇⠀⣼⡟⣿⡛⢟⣏⡴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣦⠀⠙⠙⠿⠿⠿⠋⠈⠻⠟⢻⣟⣸⣭⢿⠿⣿⠟⠉⠛⠿⠛⠃⠈⠛⠛⠛⠁⠘⠛

⣶⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢙⢿⡭⠲⠆⠀⡀⠻⠯⠁⠀⠽⠟⢿⢿⣿⣿⣿⣿⣿⣿⣿⢳⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⡤⠚⠊⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⡿⣿⣿⢿⡇⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠀⠀⠁⠂⡨⠀⠀⠁⠀⠀⠀⠀⠀⠀⠨⠵⠻⠻⠿⠿⠿⠿⠟⠸⣿⡿⠿⠿⠷⠤⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠰⠲⠃⠀⠀⠀⠀⣀⣤⡤

⣿⣯⣇⣮⣏⠞⣇⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⠛⣿⣿⣿⡇⣿⡟⠃⠀⣿⡟⣿⣾⣿⠟⢳⣿⢻⣷⢸⣿⢻⡇⣿⡇⢸⣿⠛⣼⢸⣿⣼⣿⢸⣿⢸⣿⣿⡇⣾⡟⣿⡞⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠺⠛⠁⠀

⣿⣮⣿⣷⣟⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⢺⣿⠀⣿⣿⣿⡇⣿⡿⠃⠀⣿⡿⠟⢻⣿⡟⢸⣿⢸⣿⢸⣿⠿⠃⣿⡇⢸⣿⠻⣼⡼⣿⣿⣿⣿⡟⢸⣿⣿⡇⣿⡇⣿⡇⣿⣿⣿⣟⣷⣾⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢈⣱⣹⣿⣿⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣾⠿⣤⡿⠿⠿⢇⠿⠷⠆⠀⠿⠯⣸⡸⠿⠷⠞⠿⠾⠟⠸⠿⢸⡀⠿⠷⠾⠿⠶⣸⣇⠿⠿⡸⠿⢇⡿⠿⠿⠇⡹⠷⠿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀

⡕⠁⣁⣙⠙⢀⣛⣛⠿⣛⣻⢟⣛⡻⣛⣛⢋⣀⡙⣛⣛⣛⣛⣛⣓⣀⣀⣛⣛⡛⣋⣀⣀⠀⠂⣀⣒⣚⢛⣃⣀⡀⣚⣛⡻⢟⣛⣻⢿⣛⣛⠙⡟⢛⣛⡛⢟⣛⣛⡻⣟⣛⢟⣛⡿⣛⣻⢛⣛⣛⢛⣀⣀⠀⠀⠀⠀⠀

⡄⣸⣿⣿⡇⣿⡏⣿⡇⣿⣿⣼⣿⡇⣿⣿⣾⣿⡇⣿⡏⢹⣿⢩⢹⣿⠋⣿⣿⡁⣿⡏⣿⡇⠀⢹⣿⡏⢸⣿⣿⡇⣿⣟⡁⣿⣏⠿⢸⣿⣋⢤⣰⣿⣻⣿⢸⣿⣹⣿⢸⣿⢸⣿⣷⣿⣿⢸⣿⡉⣿⣏⡿⠂⠀⠀⠀⠀

⡇⢻⣿⣤⡄⣿⡇⣿⡇⣿⢻⡿⣿⡇⣿⢻⡿⣿⡇⣿⡇⢸⣿⢸⢸⣿⠀⣿⣿⠃⣿⡇⣿⡇⣴⢸⣿⡇⢸⣿⣿⡇⣿⡟⠃⣬⡟⣿⣼⣿⠛⢼⣿⣿⣧⣤⢸⣿⢹⣷⢸⣿⢸⡟⣿⢿⣿⢸⣿⠋⣬⡝⣿⡆⠀⠀⠀⠀

⣿⣜⣻⢿⣧⣽⣿⣻⠥⠛⡚⣃⣛⡃⠛⠘⣃⣛⣃⡛⣳⣜⣛⣼⣞⣛⣴⣛⣛⣛⣛⣛⣛⣡⣿⣜⣛⣣⡘⠛⢛⣃⣛⣛⣓⣝⣻⣛⣝⣛⣛⣿⣧⣛⣟⣛⣘⣛⣘⣛⣘⣛⣘⣃⣛⣘⣛⣘⣛⣛⣝⣛⣛⣥⣄⠀⠀⠀

[39A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⢿⣿⠛⠋⠀⠀⠀⠙⠀⠛⠈⠀⢠⠃⠈⠛⠹⠋⠀⠀⠂⠀⠀⠈⠓⠀⠰⢿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠐⠀⠒⠒⠒⠐⠈⠒⠒⠀⠒⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄⣾⣿⣿⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣷⣷⣆⣤⣄⣢⣤⣐⣷⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠿⠛⠋⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣭⣿⣿⠿⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⢿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣰⣿⣿⣿⣭⡄⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠘⠱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣛⣿⣿⡟⢒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠲⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡟⠏⠁⠉⠀⠈⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⢴⢶⣆⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⡿⡿⠀⠀⠀⠀⠀⣿⣿⣿⡿⠀⠉⠉⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡇⠁⠀⠀⠀⢀⣾⣿⡿⢋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠋⣿⣿⣿⠋⡉⠉⠉⣿⣿⣿⣿⡟⢻⡇⠉⠃⠀⠀⠀⠀⠀⣠⣠⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠀⠀⠀⢠⣾⡻⢛⡐⠈⣀⡒⢁⠐⣄⠀⢀⠀⢰⣿⣿⣿⣿⡄⠈⠀⠀⠀⠀⠁⠛⢿⣿⣿⣿⣍⠚⣧⠀⠀⠠⠀⡄⣀⢴⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠘⠀⠀⠀⣼⣼⣿⣿⣷⣿⣷⣄⣠⣤⣧⣊⣪⣷⡞⣿⣿⣿⣿⣷⣤⣶⣠⣾⠋⠀⠤⣄⠹⣿⣿⣿⠀⠿⡀⠀⠘⠀⣠⡟⣿⣿⣿⠁⠀⠀⠀⠀⠀⢀⣖⣆⡀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣴⣿⣷⣼⣿⣿⠀⠀⡇⢀⣸⣻⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣀⣀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⡆⠎⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⠋⠘⢿⣿⡿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⢻⣿⣸⡆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡎⢁⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣀⣀⣤⢄⠸⣿⣁⣀⠀⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣠⣀⣿⣿⣿⣿⣿⣿⡏⠈⢹⣿⣷⡄⠀⠸⣿⣿⣿⣿⣿⣿⣿⢿⣿⣧⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠃⡏⡀⢸⣿⣿⣿⣿⣿⣿⡏⣰⣿⣿⣿⣿⣷⣿⣦⣽⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢹⠀⠀⠀⠉⠉⠉⢀⡄⠀⣿⡿⠇⠀⠀⢻⣿⣿⣿⣿⣿⡶⣼⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣧⣴⡇⠻⣼⣿⣿⣿⣿⣿⣿⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣇⣾⣼⡀⠀⢠⣄⡀⠈⠁⠀⢸⣷⣶⣷⡄⠈⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⡇⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡥⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣸⣿⣿⠀⠀⠀⠘⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠙⠛⣿⣿⣿⣿⣿⣿⣿⡿⠈⠉⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⣿⣿⣿⣿⣿⣷⣄⣀⣀⣀⣀⣀⣀⣀⡀⡀⢀⣠⣽⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠈⢿⠿⠟⠻⠿⠟⠻⠿⠻⠻⠿⢿⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠙⢿⣿⣿⣿⣿⣿⣿⣌⡹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣡⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⡟⢿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⡀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣯⣠⣤⣤⣀⣀⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣇⠀⠀⠀⠹⣿⡿⠿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡖⣹⣿⣆⠀⠀⠀⠈⠀⠐⢻⣿⣟⢋⣿⣿⣷⠄⢸⣿⣿⣿⣿⢿⠻⠟⠏⣵⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣇⣿⡿⣿⣧⠀⠀⠀⠀⠀⠀⠉⠛⠘⠿⠿⠿⠿⠿⠟⠛⠛⣋⣠⣦⣾⣾⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⣿⣿⡏⠉⡈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣯⢸⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣙⣿⣿⣿⢿⣿⣷⣤⣀⢠⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣷⠸⣯⠇⡼⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣋⣿⣿⣿⣿⣿⣇⠀⠈⠻⠿⠟⣛⠛⣟⣛⡉⣹⣯⣿⣾⣏⣿⣾⣿⣷⣟⢻⣿⣏⠿⠿⢼⣿⡏⣿⣿⢸⣿

⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠹⢿⣄⠀⠄⠀⢀⠑⡄⣤⡄⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠈⠙⠩⣤⣽⣭⠀⣦⣿⣿⢻⡟⣷⣿⣿⣾⣿⢿⣿⣿⢰⣶⣾⣿⣿⣿⣿⣿⣿

⠀⠀⢀⣠⣤⣶⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⠊⠓⢄⠃⠀⠀⠙⢮⠙⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣦⠀⠀⠀⠀⠉⠛⠟⠀⠙⠟⠻⣿⣙⣯⣿⡿⢿⠿⠋⠙⠿⠟⠋⠀⠙⠛⠛⠋⠀⠛

⣶⣿⣿⣿⣿⣿⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠃⠉⠒⠀⠀⠀⠁⠀⠀⠀⠀⠈⠻⢻⣿⣿⣿⣿⣿⣿⣿⢡⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⡿⡏⢟⢫⡇⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠷⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠻⠿⠟⠿⠿⠟⠸⣿⡿⠿⠿⠷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣀⣀⣀⢀⣶⣾⣀⣤⣀⣠⣤⣤⣤

⣿⣋⠇⠀⠏⠖⣄⣿⣿⣿⣿⣿⣿⣿⣇⢻⣿⠛⢹⣏⣿⡇⣿⡟⠃⠀⣿⡟⣿⣾⣿⠛⢳⣿⢻⣷⢸⣿⢻⡆⣿⡇⢸⣿⠛⣼⢸⣿⣸⣿⢸⣿⢸⣿⣿⡇⣾⡟⣿⡎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛

⠡⣤⣒⣅⢙⣾⢸⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⡿⣿⡇⣿⡿⠃⠀⣿⡿⠟⢻⣿⠟⢸⣿⢸⣿⢸⣿⠿⠃⣿⡇⢸⣿⠛⣼⡸⣿⣿⢿⣿⡏⢸⣿⣿⡇⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣽⣿

⠀⢱⠱⡋⣟⠏⣼⣿⣿⣿⣿⣿⣿⣿⣿⡼⠿⣠⡿⠧⠿⢇⠿⠷⠆⠀⠿⠇⣸⡸⠿⠷⠎⠿⠾⠟⠸⠿⢈⡀⠿⠷⠾⠿⠶⣸⣇⠿⠿⡸⠿⢇⡼⠿⠿⠇⡹⠷⠿⣣⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡄⠀⣁⣈⠉⢀⣛⣛⠿⣛⣛⢟⣛⡻⣛⣛⢉⣀⡙⣛⣛⣛⣛⣛⣓⣀⣀⣙⣛⡋⣀⣀⣀⠀⠀⣀⣐⣐⢋⣁⣀⡀⣘⣛⡻⢟⣛⣻⢿⣛⣛⠉⠛⢛⣛⡛⢟⣛⣛⡻⢛⣛⢛⣛⡛⣛⣛⢟⣛⣻⢟⣛⣻⢿⣿⣿⣿⣿

⡀⢸⣿⣿⡇⣿⡏⣿⡇⣿⣿⣼⣿⡇⣿⣿⣾⣿⡇⣿⡏⢹⣿⢩⢹⣿⠉⣿⣟⡁⣿⡏⣿⡇⠀⢹⣿⠋⢸⣿⣿⡇⣿⣟⡁⣿⣏⠿⢸⣿⣋⢤⢠⣿⢹⣿⢸⣿⣹⣷⢸⣿⢸⣿⣧⣿⣿⢸⣿⡉⣿⣏⡿⣸⣿⣿⣿⣿

⡇⢸⣿⣤⡄⣿⡇⣿⡇⣿⢻⡿⣿⡇⣿⢻⡿⣿⡇⣿⡇⢸⣿⢸⢸⣿⠀⣿⡟⠃⣿⡇⣿⡇⢴⢸⣿⠀⢸⣿⣿⡇⣿⡟⠃⣬⡟⣿⣼⣿⠛⢼⡼⣿⢠⣤⢸⣿⢹⣷⢸⣿⢸⡟⣿⢿⣿⢸⣿⠃⣬⡝⣿⡞⣿⣿⣿⣿

⣿⣜⡻⢟⣧⣝⣟⣛⠥⠛⠚⢃⣛⠃⠛⠘⣃⣛⣃⡛⣣⣜⣛⣼⣞⣛⣤⣛⢛⣛⣛⣛⣛⣡⣿⣜⣛⣢⡘⠛⢛⣃⣛⣛⣃⣙⣛⣛⣝⣛⣛⣻⣧⣛⡛⣋⣘⣛⣘⣛⣘⣛⣘⣃⣛⣘⣛⣘⣛⣛⣙⣛⣛⣽⣿⣿⣿⣿

[39A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⢿⣿⠛⠋⠀⠀⠀⠙⠀⠛⠈⠀⢠⠃⠈⠛⠹⠋⠀⠀⠂⠀⠀⠈⠓⠀⠠⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠐⠀⠒⠒⠒⠐⠈⠒⠒⠀⠒⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄⣾⣿⣿⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣦⣦⣤⣒⣷⣾⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣭⣾⣿⠿⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣸⣿⣿⣿⣭⡄⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠘⠱⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠛⠻⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⣛⣿⣿⡟⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠲⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡟⠏⠁⠉⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⣴⢶⣆⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⡿⡿⠀⠀⠀⠀⠀⣿⣿⣿⣷⠈⠈⠉⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡇⠁⠀⠀⠀⢀⣾⣿⡿⢋⠡⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠋⣿⣿⣿⠋⡉⠉⠉⣿⣿⣿⣿⡟⢻⡇⠉⠃⠀⠀⠀⠀⠀⣠⣠⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠀⠀⠀⢠⣾⡿⢋⡐⠈⣀⡒⢁⠐⣄⠀⢀⠀⢸⣿⣿⣿⣿⡄⠈⠀⠀⠀⠀⠁⠛⢿⣿⣿⣿⣍⠚⣧⠀⠀⠠⠀⡀⠀⣤⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠘⠀⠀⠀⣼⣼⣿⣿⣷⣿⣷⣄⣠⣤⣧⣊⣪⣷⡞⣿⣿⣿⣿⣷⣤⣶⣠⣾⠋⠀⠤⣄⠙⣿⣿⣿⠀⠿⡀⠀⠈⠐⣤⣟⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣖⣄⡀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣴⣿⣷⣼⣿⣿⠀⠀⡇⢀⣸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣄⣀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⡆⠎⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⠋⠘⢿⣿⡿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⢹⣿⣸⡆⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡌⢁⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣀⣀⣤⢆⠸⣿⣁⣀⠀⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣠⣀⣿⣿⣿⣿⣿⣿⡏⠀⢹⣿⣷⡄⠀⠸⣿⣿⣿⣿⣿⣿⣿⢿⣿⣧⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠃⡏⡀⢸⣿⣾⣿⣿⣿⣿⡟⣰⣿⣿⣿⣿⣿⣿⣦⣽⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢹⠀⠀⠀⠉⠉⠉⢀⡄⠀⣿⡿⠇⠀⠀⢻⣿⣿⣿⣿⣿⡶⢺⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣧⣴⡇⠻⣼⣿⣿⣿⣿⣿⡿⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣇⣾⣼⡀⠀⢠⣄⡀⠈⠁⠀⢸⣷⣶⣷⡄⠈⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⡇⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣭⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣸⣿⣿⠀⠀⠀⠘⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠙⠁⠀⠛⠿⣿⣿⣿⣿⣿⣿⣿⠿⠈⠉⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⣄⣀⣀⣀⣀⣀⣀⣀⡀⡀⢀⣠⣽⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠘⢿⠿⠟⠻⠿⠟⠿⠿⠿⠻⠿⣿⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣿⣿⣿⣿⣿⣿⣌⡽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣡⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠈⢶⡀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⡟⢿⡿⠿⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⡀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣯⣠⣤⣤⣀⣀⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠹⣿⡿⠿⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢡⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡖⣹⣿⣄⠀⠀⠀⠈⠀⠀⢻⣽⣟⢙⣿⣿⣷⠄⢹⣿⣿⣿⣿⢿⠻⠟⠍⣴⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣇⣿⡿⣿⣧⠀⠀⠀⠀⠀⠀⠉⠋⠨⠿⠿⠿⠿⠿⠟⠛⠛⣃⣴⣦⣾⣾⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⣿⣿⡟⠙⡈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣯⢹⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣙⣿⣿⣿⢿⣿⣷⣤⡀⢠⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣷⠸⣯⡅⡼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣋⣿⣿⣿⣿⣿⣇⠀⠈⠻⠿⠟⣛⠛⣟⣛⡉⣹⣯⣿⣾⣏⣿⣾⣿⣷⣟⢻⣿⣏⠿⠿⢼⣿⡏⣿⣿⢸⣿

⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠹⣷⣄⡀⠄⠀⢀⠑⡄⣤⣄⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠈⠙⢩⣤⣽⣭⠀⣦⣿⣿⢻⡟⢷⣿⣿⣾⣿⢿⣿⣿⢰⣶⣾⣿⣿⣿⣿⣿⣿

⠀⠀⢀⣠⣤⣶⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⠘⠓⢄⠃⠀⠀⠉⢮⠙⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣦⠀⠀⠀⠀⠉⠛⠟⠀⠙⠟⠻⣿⣙⣯⣽⡿⢿⠿⠋⠙⠿⠟⠋⠈⠙⠛⠛⠋⠀⠛

⣶⣿⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠈⠂⠉⠒⠀⠀⠀⠁⠀⠀⠀⠀⠈⠫⢻⣿⣿⣿⣿⣿⣿⣿⢡⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⡿⡏⢟⢫⡇⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠷⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠻⠿⠟⠿⠿⠟⠸⣿⡿⠿⠿⠷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣀⣀⣀⢀⣶⣾⣀⣤⣀⣠⣤⣤⣤

⣿⣋⡇⠀⠎⠆⣄⣿⣿⣿⣿⣿⣿⣿⣇⢻⣿⠛⣻⣏⣿⡇⣿⡟⠃⠀⣿⡟⣿⣾⣿⠛⢳⣿⢻⣷⢸⣿⢻⡆⣿⡇⢸⣿⠛⣼⢸⣿⣸⣿⢸⣿⢸⣿⣿⡇⣾⡟⣿⡎⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛

⠡⣤⣒⣥⠙⣾⢸⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⡿⣿⡇⣿⡿⠃⠀⣿⡿⠟⢻⣿⠟⢸⣿⢸⣿⢸⣿⠿⠃⣿⡇⢸⣿⠛⣼⡸⣿⣿⢿⣿⡏⢸⣿⣿⡇⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣽⣿

⠀⢱⠰⡋⣟⠏⣼⣿⣿⣿⣿⣿⣿⣿⣿⡼⠿⣠⡿⠧⠿⢇⠿⠷⠆⠀⠿⠇⣸⠸⠿⠷⠎⠿⠾⠟⠸⠿⢈⡀⠿⠷⠾⠿⠶⣸⣇⠿⠿⡸⠿⢇⡼⠿⠿⠇⡹⠷⠿⣣⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡄⠀⣁⣈⠉⢀⣛⣛⠿⣛⣛⢟⣛⡻⣛⣛⢉⣀⡙⣛⣛⣛⣛⣛⣃⣀⣀⣙⣛⡋⣁⣀⣀⠀⠀⣀⣐⣐⢋⣁⣀⡀⣘⣛⡻⢟⣛⣻⢿⣛⣛⠉⠛⢛⣛⡛⢟⣛⣛⡻⢛⣛⢛⣛⡛⣛⣛⢟⣛⣻⢟⣛⣻⢿⣿⣿⣿⣿

⡇⢸⣿⣤⡄⣿⡇⣿⡇⣿⢻⡿⣿⡇⣿⢻⡿⣿⡇⣿⡇⢸⣿⢸⢸⣿⠀⣿⡟⠃⣿⡇⣿⡇⣤⢸⣿⠀⢸⣿⣿⡇⣿⡟⠃⣬⡟⣿⣼⣿⠛⢼⡼⣿⢠⣤⢸⣿⢹⣷⢸⣿⢸⡟⣿⢿⣿⢸⣿⠃⣬⡝⣿⡞⣿⣿⣿⣿

⣿⣜⡻⢟⣧⣝⣟⣛⠥⠛⠚⢃⣛⠃⠛⠘⣃⣛⣃⡛⣣⣜⣛⣼⣞⣛⣤⣛⢛⣛⣛⣛⣛⣡⣿⣜⣛⣢⡘⠛⢛⣃⣛⣛⣃⣝⣛⣛⣝⣛⣛⣻⣧⣛⡛⣋⣘⣛⣘⣛⣘⣛⣘⣃⣛⣘⣛⣘⣛⣛⣙⣛⣛⣵⣿⣿⣿⣿

[39A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣿⣿⠛⠋⠀⠈⠀⠧⢸⠻⠹⢰⡽⠃⠻⠛⡿⠃⢋⠑⠋⢙⠁⠈⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠒⠒⠓⠑⠀⠚⠒⠒⠒⠚⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⠛⠛⠀⠀⠀⠀⢀⣤⣤⣤⣤⣄⣤⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣹⣽⣿⣿⠿⠈⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠒⢰⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡗⡀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠠⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⣔⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠯⠩⢉⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣾⣯⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⠊⣠⠬⠚⢻⣿⣿⣿⣿⣿⠛⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠁⣉⠂⠀⢠⣿⣿⡿⣿⠿⠛⠓⠀⠀⠀⠀⠉⢙⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣟⣿⣧⡙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠟⠀⢐⠀⣰⣿⣿⣿⣟⡉⣴⡛⠉⠳⣄⠀⣀⠀⣾⣿⣿⣿⣿⡄⠉⠁⠀⡀⣈⠙⠻⢿⣿⣿⣿⣿⠻⣿⡁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠚⠀⠀⢀⣿⣿⣿⣿⣿⣿⣷⣤⣤⣼⣷⣿⣿⣷⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⠉⠌⢳⣄⠻⣿⣿⣿⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⢀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣷⣽⣿⣿⠀⠙⣧⢤⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠈⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠈⠘⡇⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠙⣿⣿⡟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠘⠀⠀⠀⠀⣴⡿⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⡿⣣⡧⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣀⣠⣶⣎⢿⣿⣤⣄⡸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣥⣄⠁⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⡟⣿⣽⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣾⡧⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣧⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠠⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣮⣦⡀⢀⣯⣶⠀⠀⠀⠀⠀⢂⣤⠀⠀⢀⣥⣀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠀⠀⠀⠀⠀⠈⠁⠀⠰⠿⣿⣿⣷⣄⡀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣀⣠⣤⣤⣄⣀⣀⣀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠉⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡧⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣶⣾⣥⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠂⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡞⣿⣿⣦⡀⢝⠋⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣧⣿⣿⣿⣿⡌⢠⠀⠠⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡘⠀⠀⢹⠋⠀⠀⠁⠀⢠⡄⣴⣬⣼⣿⣿⣿⣿⣿⣿⣿⣿⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⠿⣿⣿⣿⣿⣋⣯⣿⣟⠛⣿⣧⣤⣤⣠⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⢀⠀⢀⢠⠂⠑⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠈⠙⠿⠟⢟⡿⢿⣿⡇⢘⣿⣿⣷⣿⣹⣷⣿⣿⣿⡛⣿⣿⠹⠿⢷⣿⣿⢹⣿⡇⣿

⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣶⣤⣴⣶⣶⡀⢞⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⢈⠟⣥⣼⣯⡁⢸⡽⣿⡿⣿⠻⣾⣿⡷⣿⡿⣿⣿⣧⣶⣾⣿⣿⣾⣿⣿⣿

⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠻⣿⣿⣿⣿⢿⣿⣿⣿⣻⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠐⠁⠀⠈⠙⠻⠃⠘⣿⡛⢿⣏⣲⣽⣿⠿⣿⠟⠙⠻⠿⠟⠁⠉⠛⠛⠛⠁⠙

⣶⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢀⡿⠓⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠷⠀⠈⠛⠿⡿⠌⠂⠹⠶⠉⠁⠀⠀⠈⠹⠿⠿⠿⠿⠿⢿⡿⠟⠸⣿⡿⢿⡿⠿⡶⠄⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠁⠀⣀⣰⣶⣆⣀⣄⣀⣤⣤⣤

⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⠛⣿⣿⣿⡇⣿⡟⠃⡄⣿⣿⣿⣾⣿⡟⢳⣿⢻⣷⢸⣿⢻⡇⣿⡇⢸⣿⠛⣼⢸⣿⣼⣿⢸⣿⣿⣿⣿⡇⣾⡟⣿⡆⢿⣿⣿⣿⡇⠀⣀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿

⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⣿⣿⣿⡇⣿⡿⠇⠄⣿⣿⠿⢻⣿⡿⢸⣿⢸⣿⢸⣿⠿⠃⣿⡇⢸⣿⠿⣽⡾⣿⣿⣿⣿⡟⣿⣿⣿⡇⣿⡇⣿⡇⠈⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣽⣿⣿⣿⣿⡏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣤⡿⠿⠿⢇⡿⠷⠆⠀⠿⠿⣼⡸⠿⠷⠞⠿⠾⠟⠸⠿⣸⡅⠿⠷⠾⠿⠶⣹⣇⠿⢿⡸⠿⣇⡿⠿⠿⢇⡻⠷⠿⣣⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡿⢋⣋⣙⠛⢓⣛⣻⠿⣛⣻⢟⣛⡿⣛⣛⢋⣁⡻⣛⣟⣛⣛⣛⣓⣀⣀⣛⣛⡛⣛⣘⣓⠃⠒⣀⣛⣛⢛⣛⣀⡀⣘⣛⡻⢟⣛⣻⢿⣛⣛⠍⡿⢛⣛⡻⢟⣛⣛⡻⣟⣻⢟⣛⡿⣛⣻⣟⣛⣻⢿⣛⣻⢿⣿⣿⣿⣿

⡇⣼⣿⣿⡇⣿⡏⣿⡇⣿⣿⣾⣿⡇⣿⣿⣾⣿⡇⣿⡏⢹⣿⢩⣹⣿⠋⣿⣿⡁⣿⡏⣿⡇⢀⢹⣿⡏⢸⣿⣿⡇⣿⣟⡁⣿⣏⡿⢸⣿⣛⣶⣵⣿⣿⣿⢸⣿⣹⣿⢹⣿⢸⣿⣷⣿⣿⢸⣿⡉⣿⣏⡿⣿⣿⣿⣿⣿

⣇⢿⣿⣤⡄⣿⡇⣿⡇⣿⢻⣿⣿⡇⣿⢻⣿⣿⡇⣿⡇⢸⣿⢸⣿⣿⠀⣿⣿⠃⣿⡇⣿⡇⣿⢸⣿⡇⢸⣿⣿⡇⣿⡟⠃⣬⡟⣿⣼⣿⠛⣾⣿⣿⣧⣤⢸⣿⢹⣷⢸⣿⢸⡿⣿⢿⣿⢸⣿⠛⣬⡟⣿⣾⣿⣿⣿⣿

⣿⣞⣻⣿⣷⣿⣿⣿⡵⠛⡚⣃⣛⣃⣛⠘⣃⣛⣃⣛⣳⣜⣛⣾⣟⣛⣶⣟⣛⣛⣛⣛⣛⣷⣿⣞⣛⣣⡘⣛⢛⣃⣛⣛⣻⣝⣻⣛⣝⣛⣛⣿⣧⣛⣿⣛⣜⣛⣘⣛⣚⣛⣘⣃⣛⣘⣛⣚⣛⣛⣝⣻⣛⣽⣿⣿⣿⣿

[39A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣿⣿⠛⠋⠀⠈⠀⠇⠸⠻⠱⢰⡽⠇⠻⠛⡿⠃⢋⠑⠋⠙⠀⠈⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠒⠒⠓⠑⠀⠚⠒⠒⠒⠚⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⠛⠋⠀⠀⠀⠀⢀⣤⣤⣤⣤⣄⣤⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡗⡀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠠⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⣄⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠯⠡⢉⢄⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣾⣏⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⠂⢠⠤⠚⢻⣿⣿⣿⣿⣿⠛⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠁⡉⠂⠀⢠⣿⣿⡿⣿⠿⠛⠓⠀⠀⠀⠀⠉⢙⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣟⣿⣧⡙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠟⠀⢀⠀⣰⣿⣿⣿⡟⡉⣴⡚⠉⠲⣄⠀⣀⠀⣾⣿⣿⣿⣿⡄⠉⠉⠀⡀⣈⠙⠻⢿⣿⣿⣿⣿⠻⣷⡁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠘⠀⠀⢀⣿⣿⣿⣿⣿⣿⣷⣤⣤⣴⣷⣿⣿⣷⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⠉⠌⢳⣄⠻⣿⣿⣿⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⢀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣷⣽⣿⣿⠀⠘⣧⢠⡀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠈⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠈⠘⡇⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠙⣿⣿⡟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠈⢀⠀⠀⠀⣠⡿⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⡿⣣⡇⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣀⣠⣶⣆⢿⣿⣤⣄⡸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡥⣄⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢧⡟⣿⣹⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣾⡇⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣧⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠠⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣎⣦⡀⢀⣮⣶⠀⠀⠀⠀⠀⢐⡀⠀⠀⣀⣁⣀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠁⠀⠐⠿⣿⣿⣷⣄⡀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣀⣠⣤⣤⣀⣀⣀⣀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⢈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣶⣾⣥⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡞⣿⣿⣦⡀⠙⠛⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣧⣿⣿⣿⣿⡄⢠⠀⠠⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡘⠀⠀⢹⠙⠀⠀⠀⠀⢠⣄⣴⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⠿⣿⣿⣿⣿⣋⣯⣿⣟⠛⣿⣧⣤⣤⣠⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⢀⢡⠄⠑⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠈⠙⠿⠟⢟⡟⢿⣿⡇⢈⣿⣿⣷⣿⣹⣷⣿⣿⣿⡛⣿⣿⠹⠿⢷⣿⣿⢹⣿⡇⣿

⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣴⣤⣴⣶⣶⡀⢾⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⢈⠟⣥⣼⣯⡁⢸⡽⣿⡿⣿⠻⣾⣿⡷⣿⡿⣿⣿⣧⣶⣾⣿⣿⣾⣿⣿⣿

⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠻⣿⣿⣿⣿⢿⣿⣿⣿⣻⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠁⠀⠈⠙⠻⠃⠈⣿⡛⢿⣏⣲⣽⣿⠿⣿⠟⠙⠻⠿⠟⠁⠉⠛⠛⠛⠁⠙

⣶⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⠂⣿⣿⣿⣿⣿⣿⣹⢿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢀⡿⠓⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠈⠛⣾⣿⣾⡂⢽⣶⣭⠀⠀⠀⠈⣽⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⣿⣶⣄⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠁⠀⣀⣰⣶⣆⣀⣄⣀⣤⣤⣤

⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣾⣿⣿⣦⣨⢻⢧⡀⠀⠀⠀⣼⢿⣿⣿⣿⣿⣿⡿⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇⠀⣀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿

⣿⣽⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠙⣿⣿⣿⣧⣿⣷⣶⠶⠖⠒⢿⣿⣿⣿⣿⣿⡟⠁⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠈⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣽⣿⣿⣿⣿⡏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⠟⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡿⣯⣿⣿⣿⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⢻⣿⣿⣿⣿⣿⣷⡀⠈⣿⣿⣿⣿⣽⡻⡇⠻⢸⣿⣿⣿⡟⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣟⣿⣿⣿⡟⣾⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⣀⣠⠈⣿⣿⣿⣿⣿⣿⣷⣸⣿⣿⣿⣿⣿⣿⣗⣸⣿⣿⣿⣿⠀⠰⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⡿⠋⣠⡀⢸⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣷⣿⣿⣿⣿⡿⠟⣋⣤⣴⣿⣷⠞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

[39A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⡿⠛⠏⠈⠘⠘⠇⢹⠻⡿⢸⡿⠃⠿⠟⡟⠙⡫⠺⡏⣻⠃⠘⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠒⠛⠓⠓⠘⠛⠚⠚⠒⠚⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣿⣿⣿⣿⡟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠈⠀⠐⠉⠈⢲⡃⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⢻⠋⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣄⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠭⢥⣄⢢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣹⣿⣿⣿⠿⠌⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⢻⢻⣲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣓⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠢⠁⠈⢙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⣾⢿⡕⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠯⠯⣩⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣯⠙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢿⣿⣿⠋⣤⡽⠛⣿⣿⣿⣿⣿⣿⠛⠉⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠉⡉⠂⠀⣸⣿⣿⣿⣿⠿⠛⠓⠂⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠟⠀⣑⠀⣰⣿⣿⣿⣟⡅⣔⠋⡙⢳⣤⡤⣀⠀⣿⣿⣿⣿⣿⡎⠉⠉⢁⣀⣉⡙⠻⢿⣿⣿⣿⣿⣿⣷⡕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠚⠀⠂⣠⣿⣿⣿⣿⣿⣿⣷⣤⣤⣼⣷⣿⣿⣷⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⠉⠼⢳⣄⣻⣿⣿⣿⠘⣿⡐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠈⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣷⣿⣿⣿⠀⠹⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠀⠈⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠛⣿⣿⠟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠠⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⡿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣱⣶⣾⣿⣿⣤⣄⡸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣧⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠃⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣀⣠⣤⣤⣄⣀⣀⣀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣥⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⢣⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡞⣿⣿⣦⡙⢽⣛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣷⣿⣿⣿⣿⡝⢳⣆⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡛⠻⠿⢿⡿⣿⣽⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣤⣄⢀⣾⡆⢸⣿⡟⠛⣉⣉⣤⣀⡀⢀⣤⣤⣤⣄⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣆⡀⢀⠀⢠⠁⣈⢉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⣀⢀⠤⠤⠀⢺⣿⣿⣾⣟⣿⣾⣿⣿⣟⢻⣿⣿⡿⠿⣿⣿⣏⣿⣿⣼

⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⡠⠋⠀⠓⠄⠀⣮⢿⣿⢿⡟⢿⣟⣿⢻⣿⢿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿

⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠊⠀⠀⠀⠀⠀⠀⢹⣯⠻⣿⣃⣮⣿⡷⢿⡿⠛⠛⠿⠿⠛⠈⠛⠛⠛⠋⠘

⣴⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣸⠿⠇⠛⠋⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣉⠀⠋⣹⣽⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⡀⠀⢀⡈⣀⣀⣀⣶⣶⣀⣀⣀⣀⣀⣀

⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⢤⢤⢤⣿⣿⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠃⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠻⣿⣿⣿⣿⣿⣿⣿⣷⡿⡶⣿⣿⣿⣿⣿⣿⡟⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⢻⣿⣿⣿⣿⣰⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⡟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠐⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠂⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣯⣿⣿⣿⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⢻⣿⣿⣿⣿⣿⣷⡀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣀⣠⠈⣿⣿⣿⣿⣿⣿⣷⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⣴⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⠟⣡⣰⢸⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣷⣿⣿⣿⣿⣿⠿⣏⣥⣶⣿⣷⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

[39A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⡟⠛⠃⠀⠈⠘⠇⠹⠏⡏⢻⡿⢁⠟⠟⠟⠙⡩⠺⡑⣩⠃⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠒⠚⠓⠓⠐⠛⠚⠚⠒⠚⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣴⣿⣿⣿⣿⠽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⠀⠂⠁⠀⠖⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⢻⠋⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣄⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠠⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣹⣽⣿⣿⠿⡌⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠓⢠⣲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣓⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠢⠁⢀⡙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⣮⢿⡁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠯⠯⣩⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⠿⣏⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢿⣿⣿⠃⣤⡝⠛⣿⣿⣿⣿⣿⡿⠋⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⡉⠂⠀⣸⣿⣿⡿⣿⠟⠛⠓⠂⠀⠀⠀⠉⢻⣿⣿⣿⣿⢿⣿⣿⣿⣿⣽⣟⣿⣿⣿⣿⣿⣯⣿⡷⡝⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡟⠀⡁⠀⣰⣿⣿⣿⣟⠅⣔⠋⡙⢳⡤⡄⣀⠀⣿⣿⣿⣿⣿⡀⠀⠀⢀⣀⣈⡙⠻⢿⣿⣿⣿⣿⢿⣷⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠚⠀⠂⣠⣿⣿⣿⣿⣿⣿⣷⣤⣤⣼⣷⣿⣿⣷⣿⣿⣿⣿⣿⣷⣾⣿⣿⡿⠁⠼⢳⣄⡻⣿⣿⣿⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠈⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣷⣿⣿⣿⠀⠹⣧⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⠀⠈⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠻⣿⣿⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⡿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣱⣶⣾⣿⣿⣤⣄⡸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡥⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣧⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡪

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠃⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣠⣤⣠⣤⣤⣄⣀⣀⣀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣸⠎⢐⢶⣀⣰⣯⡷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⢀⣀⣀⠄⣉⠳⣿⣦⣧⣯⡺⣝⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣧⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣒⠻⣛⢿⠋⠓⠓⠼⣷⣌⠛⠩⠍⠚⠑⢕

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⢃⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠽⢯⡻⣿⣷⠁⡤⠈⣉⣾⣝⢳⠔⡙⠒⠋⣐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣿⣿⣦⣉⢿⠋⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣻⠑⡛⠍⡠⡬⣥⡤⠼⠨⠟⢒⣮⣽⣧⣎⠁⠀⠀⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣷⣿⣿⣿⣿⡌⢲⣄⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠔⠊⠋⡁⠊⢀⣤⣤⣤⣶⡖⠊⠛⠑⠁⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⠐⠈⢿⠻⠏⠙⠫⠅⣿⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣤⡀⢰⣿⠀⣺⣿⠟⠋⣉⣉⣄⣀⠀⣠⣤⣤⣤⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⢀⡚⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⡀⣠⠤⠄⠀⣿⣿⣷⣿⣻⣷⣿⣿⣾⡛⣿⣿⣻⣿⢷⣿⣿⢹⣿⣧

⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣶⣴⣶⣶⣦⡤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⢀⠜⠡⠘⢢⡀⢰⡽⣿⡿⣿⠻⣿⣻⡟⣿⡿⣿⣿⡧⣶⣶⣿⣿⣿⣿⣿

⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠔⠁⠀⠀⠀⠀⠀⠘⣿⡝⢿⡟⣀⣹⣿⠶⣾⠿⠛⠿⠿⠿⠃⠙⠻⠿⠛⠋

⣥⣶⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⡿⠿⠜⠟⠉⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠛⣿⣿⣿⣿⣿⣿⣿⡿⣁⠀⠈⢉⣭⣿⣿⣿⣿⣿⣿⣿⣿⢁⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⢁⣀⣀⣰⣦⣆⣀⣀⣀⣤⣤

⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢸⣿⣿⣿⣯⣭⣿⣿⣎⢀⠀⣁⣸⢿⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣯

⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠻⣿⣿⣿⣿⣿⣿⣷⡶⠖⢒⢾⣿⣿⣿⣿⣿⡿⠃⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠈⠻⣿⣿⣿⣿⣿⡏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⢿⣿⣿⣿⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⡈⢿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⡿⢁⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠹⣿⣿⣿⣿⣷⣦⣻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣯⣿⣿⣿⢧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⢻⣿⣿⣿⣿⣿⣷⡄⠊⣿⣿⣿⣿⣿⣿⣯⣽⣾⣿⣿⣿⡿⠁⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⢀⣠⠈⣿⣿⣿⣿⣿⣿⣿⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⢱⣿⣿⣿⣿⣿⣿⣿⠟⢡⠰⢰⣿⣿⣷⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡜⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢟⣡⣰⣾⣷⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

[39A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⡟⠛⠃⠀⠈⠘⠇⠹⠿⡏⢻⡿⢣⠟⠟⠟⠹⡩⠺⡁⣩⠃⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠒⠛⠓⠓⠚⠛⠚⠛⠒⠚⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣴⣿⣿⣿⣿⠿⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⠀⠂⠉⠀⠿⡁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⢻⠋⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⠤⢢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣹⣽⣿⣿⠿⡜⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠳⢠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⣾⢿⡁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⢯⠯⣫⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡿⣏⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢿⣿⣿⠃⣦⡽⠛⣿⣿⣿⣿⣿⡿⠟⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⡉⠂⠈⣸⣿⣿⣿⣿⠿⠛⠓⠂⠀⠀⠀⠙⣻⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣷⡝⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡟⠀⡁⠀⣰⣿⣿⣿⣟⡅⣔⠋⡙⢳⡤⡆⣀⠀⣿⣿⣿⣿⣿⡀⠀⠀⢀⣀⣈⡙⠻⢿⣿⣿⣿⣿⢿⣷⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠚⢀⠂⣠⣿⣿⣿⣿⣿⣿⣷⣤⣤⣼⣷⣿⣿⣷⣿⣿⣿⣿⣿⣷⣾⣿⣿⡿⠁⠼⢷⣄⡻⣿⣿⣿⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠈⢔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣷⣿⣿⣿⠀⠹⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⠀⠈⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠻⣿⣿⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⡁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣱⣶⣾⣿⣿⣤⣄⡸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣺

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣷⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠠⠠⠀⠀⣾⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣠⣤⣤⣤⣤⣄⣀⣀⣀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣴⣾⢶⠀⠐⣜⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣧⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣴⣷⣿⠿⡿⠿⠿⠿⠿⠿⠿⠿⠟⣛⣛⠻⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣿⣿⣮⣿⣿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⣿⡿⢿⡿⠿⢿⣿⠿⠟⠀⠀⠀⠀⣀⣤⣀⠠⣤⡄⢠⣤⡄⣴⣶⢰⣶⡶⠆⢻⣿⠿⣿⡄⢿⣿⠀⣿⣿⡿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⡷⠿⠿⡿⠿⠈⢓⣀⢀⣛⠛⣉⣉⠛⢩⣭⡝⣿⡟⢱⣶⡆⣶⣦⠸⣿⡆⣿⢸⣿⡟⣿⡇⢼⣿⢹⣿⡇⣿⣧⢸⣿⣇⣿⣿⢸⣿⣧⣄⢸⣿⣶⣿⡃⢸⣿⠀⠉⠉⠀⠀

⠀⠀⣀⣀⣀⠀⣤⣤⣤⣤⠀⣤⣶⣿⣻⣿⢳⣾⠿⣷⡆⠿⣿⣿⠛⢸⣿⡄⣿⣿⠀⢸⣿⡇⢿⣧⢸⣿⡇⢹⣿⣧⣿⡇⣿⡀⣿⣧⣿⡟⢸⣿⠈⣿⡇⢸⣿⣾⡟⣿⣿⣿⠀⣿⡏⠽⢸⣿⡇⣿⣷⢘⣛⣀⣤⣤⣤⡀

⠀⠀⣿⣿⣿⡀⢸⣿⢉⣿⡇⢻⣿⣐⣻⣿⡼⣿⣶⣍⡐⡇⣿⣿⠀⢸⣿⡇⢿⣿⠀⢸⣿⡇⢨⣷⠘⣿⡇⢸⣿⢻⣿⡇⢿⡇⣿⣿⠀⠀⠸⣿⣇⣿⡇⠈⣿⣿⡇⢻⣿⣿⡀⠿⠿⠿⠌⠿⣇⣛⠛⣬⢟⣿⣿⢹⣿⣧

⠀⠀⣿⡇⣿⣇⢸⣿⡟⣿⡆⢸⣿⡟⣿⣿⡯⣤⡍⣿⣷⠀⢸⣿⠀⠘⣿⡇⢸⣿⣤⡄⣿⣷⣶⢸⡄⣿⠧⠸⠿⢈⠿⢧⣼⣧⣛⡛⠀⠀⠀⢉⠍⠉⠐⢢⡀⢠⡼⣷⡿⣿⠻⣾⣻⡗⣿⡿⣿⣿⡧⣶⣶⣿⣿⣿⣿⣿

⠀⠀⣿⡿⢿⣿⠸⣿⡇⣿⣿⢸⣿⣷⣾⣿⣧⣻⠷⠿⠋⣴⣘⣛⣃⣄⣛⣡⣬⣩⣭⣥⣥⣤⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⢿⣿⣿⡄⠀⠔⠁⠀⠀⠀⠈⠀⠘⣿⡝⣿⣟⣀⣹⣿⠶⣾⠿⠛⠿⠿⠿⠋⠙⠻⠿⠛⠋

⣥⣦⣿⣧⣮⣭⣥⣹⣷⣶⣶⣿⣶⣾⣿⣿⣿⣿⣿⣿⡜⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⡿⠿⠞⠟⠋⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣍⠀⠈⢉⣭⣿⣿⣿⣿⣿⣿⣿⣿⢁⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⢁⣀⣀⣰⣶⣆⣀⣀⣀⣤⣤

⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣹⣿⣿⣿⣿⣿⣿⣿⣾⣤⡀⣉⣽⢿⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯

⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⠶⢲⣿⣿⣿⣿⣿⣿⣿⠃⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠈⠻⣿⣿⣿⣿⣿⡏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢁⠄⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠹⣿⣿⣿⣿⣿⣮⣻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣯⣿⣿⣿⢧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⢻⣿⣿⣿⣿⣿⣷⡄⠋⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⡿⠁⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⢀⣠⠈⣿⣿⣿⣿⣿⣿⣿⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⢳⣿⣿⣿⣿⣿⣿⣿⠟⢡⣰⢰⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣡⣶⣾⣷⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

[39A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⡟⠛⠃⠀⠈⠘⠇⠻⠯⡇⢺⠟⢡⠟⠏⠟⠙⠉⠺⡁⣉⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠒⠚⠓⠓⠚⠛⠚⠛⠒⠚⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣰⣿⣿⣿⣿⢽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⠀⠂⠁⠀⠟⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⢻⠋⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣄⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠠⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢹⣽⣿⣿⠷⡘⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⢰⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣓⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠠⠀⢀⡈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⣦⢿⡅⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⢯⠯⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡿⣿⡑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⢿⣿⣿⠃⣤⡽⠻⣿⣿⣿⣿⣿⣿⠋⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⡩⠂⠁⣸⣿⣿⣿⣿⠿⠛⠓⠂⠀⠀⠀⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣯⣿⡷⡝⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡟⠀⣑⠀⣰⣿⣿⣿⣟⠇⣔⠋⡙⢳⡴⡤⣀⠀⣿⣿⣿⣿⣿⡀⠀⠀⢀⣀⣈⣙⠛⢿⣿⣿⣿⣿⠿⣷⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠚⠀⠂⣠⣿⣿⣿⣿⣿⣿⣷⣤⣤⣼⣷⣿⣿⣷⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⠁⠴⢳⣆⡻⣿⣿⣿⠈⣿⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠘⢔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣷⣿⣿⣿⠀⠙⣷⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠈⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠻⣿⣿⠟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣵⣶⣾⣿⣿⣤⣄⡸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣷⣿⣿⡿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⡿⠟⢀⡀⠀⠀⣀⣤⣀⠠⣤⡄⢠⣤⡄⣴⣶⢰⣶⡶⠇⢻⣿⠿⣿⡄⢿⣿⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡿⠿⠿⡿⠿⠋⢓⣁⢚⣙⠛⣋⣙⠛⢩⣭⡝⣿⡿⢱⣶⡆⣶⣶⠸⣿⡏⣿⢸⣿⡟⣿⡇⢼⣿⢹⣿⡇⣿⣧⢸⣿⣇⣿⣿⢸⣿⣧⣄⢸⣿⣶⣿⡃⢸⣿⠀⠀⠀⠀⠀

⠀⠀⣀⣀⣀⠀⣠⣤⣤⣤⠀⣤⣶⣾⣻⣿⢳⣾⠿⣷⡄⠿⣿⣿⠛⢸⣿⡄⣿⣿⠀⢸⣿⡇⢿⣧⢸⣿⡇⢹⣿⣧⣿⡇⣿⡀⣿⣧⣿⡟⢸⣿⠈⣿⡇⢸⣿⣾⡟⣿⣿⣿⠀⣿⡏⠽⢸⣿⡇⣿⣷⢘⣛⡀⣠⣤⣤⣄

⠀⠀⣿⣿⣿⡀⢸⣿⢙⣿⡇⢻⣿⣐⣻⣿⡼⣿⣶⣭⡱⡇⣿⣿⠐⢸⣿⡇⣿⣿⠀⢸⣿⡇⢸⡗⠘⣿⡇⢸⣿⢻⣿⡇⣿⡇⣿⣿⠀⠀⠸⣿⣇⣿⡗⠈⣿⣿⡇⢻⣿⣿⣄⠿⠿⠿⣌⠿⢇⣛⣛⢸⣿⣷⣿⣿⣿⣿

⠀⠀⣿⡇⣿⣇⢸⣿⡟⣿⡆⢸⣿⡟⣿⣿⣯⣤⡍⣿⣷⠀⢸⣿⠀⠘⣿⡇⢸⣿⣤⡄⣿⣷⣶⢸⡄⣿⡧⠸⠿⢈⠿⢧⣼⣧⣛⣛⠀⠀⠀⠉⣉⠉⠄⠳⢄⠀⢢⢿⣾⣿⣿⢷⣟⣿⠿⣿⣿⣿⣿⢰⣶⣾⣿⣿⣿⣿

⠀⠀⣿⡿⢿⣿⢸⣿⡇⣿⣿⢸⣿⣷⣾⣿⣧⣻⠿⠿⠋⣴⣘⣛⣣⣆⣛⣡⣬⣩⣭⣥⣥⣤⣶⣾⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠞⠁⠀⠀⠀⠀⠀⢹⣷⠻⣿⡇⣊⣿⣿⢶⣶⠟⠻⠿⠿⠟⠉⠛⠿⠿⠟

⣠⣤⣿⣷⣮⣭⣥⢭⣷⣶⣶⣿⣶⣿⣿⣿⣿⣿⣿⣿⡌⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠷⠻⠛⠉⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣍⡁⠈⣋⣯⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣴⣴⣆⣀⣀⣠⣤

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢠⣸⣿⣿⣿⣿⣿⣿⣿⣿⣤⡦⣉⣽⣿⣿⣿⣿⣿⣿⣿⠏⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡁⠀⠀⠐⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡁⢹⣿⣿⣿⣿⣽⣿⣿⣿⠷⢾⣿⣿⣿⣿⣿⣿⣿⠋⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛

⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⡄⢿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣿⣿⣿⣿⠃⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⢻⣿⣿⣿⣿⣿⣿⡄⠉⣿⣿⣿⣿⣿⣿⢯⣿⣾⣿⣿⣿⣿⠇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣿⣿⣿⣿⣿⣿⣀⣀

⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⣀⠌⣿⣿⣿⣿⣿⣿⣿⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⢧⣿⣿⣿⣿⣿⣿⣿⡿⢃⡤⡔⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣾⣿⣿⣿⣿⡿⠟⢩⣴⣼⣿⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

[39A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⡟⠛⠃⠀⠈⠘⠇⠻⠿⡇⢺⠟⢣⠟⠏⠟⠙⠉⠺⡁⣉⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠒⠚⠓⠓⠚⠛⠚⠚⠒⠚⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣰⣿⣿⣿⣿⢵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⠀⠂⠁⠀⠝⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⢻⠃⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣄⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠠⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢹⣽⣿⣿⠷⡘⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⢰⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣓⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠠⠀⢀⡈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⣦⢿⡁⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⢯⠯⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡿⣿⡑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢿⣿⣿⠃⣤⡽⠛⣿⣿⣿⣿⣿⡿⠋⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⡉⠂⠁⣸⣿⣿⣿⣿⠿⠛⠓⠂⠀⠀⠀⠉⣻⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣯⣿⡷⡝⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠻⣿⣿⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣵⣶⣾⣿⣿⣤⣄⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠋⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣠⣤⣤⣤⣤⣄⣀⣀⣀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣯⣿⣿⡿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⠿⠟⢀⡀⠀⠀⣀⣤⣀⠠⣤⡄⢠⣤⡄⣴⣶⢰⣶⡶⠇⢻⣿⠿⣿⡆⢿⣿⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡿⠿⠿⡿⠿⠛⢓⣀⢊⣙⠛⣋⣙⠛⢩⣭⡝⣿⡿⢱⣶⡆⣶⣶⠸⣿⡇⣿⢸⣿⡟⣿⡇⢼⣿⢹⣿⡇⣿⣧⢸⣿⣇⣿⣿⢸⣿⣧⣄⢸⣿⣶⣿⡃⢸⣿⠀⠀⠀⠀⠀

⠀⠀⣀⣀⣀⠀⣠⣤⣤⣤⠀⣤⣶⣾⣻⣿⢳⣾⠿⣷⡆⠿⣿⣿⠛⢸⣿⡄⣿⣿⠀⢸⣿⡇⢿⣧⢸⣿⡇⢹⣿⣧⣿⡇⣿⡀⣿⣧⣿⡟⢸⣿⠈⣿⡇⢸⣿⣾⡟⣿⣿⣿⠀⣿⡏⠽⢸⣿⡇⣿⣷⢘⣛⡀⣠⣤⣤⣄

⠀⠀⣿⣿⣿⡀⢸⣿⢙⣿⡇⢻⣿⣐⣻⣿⡼⣿⣶⣭⡱⡇⣿⣿⠐⢸⣿⡇⣿⣿⠀⢸⣿⡇⠸⣗⠘⣿⡇⢸⣿⢻⣿⡇⣿⡇⣿⣿⠀⠀⠸⣿⣇⣿⡗⠈⣿⣿⡇⢻⣿⣿⣄⠿⠿⠿⣌⠿⢇⣛⣛⢸⣿⣷⣿⣿⣿⣿

⠀⠀⣿⡇⣿⣇⢸⣿⡟⣿⡆⢸⣿⡟⣿⣿⣯⣤⡍⣿⣷⠀⢸⣿⠀⠘⣿⡇⢸⣿⣤⡄⣿⣷⣶⢸⡄⣿⡧⠸⠿⢈⠿⢧⣼⣧⣛⣛⠀⠀⠀⠉⣉⠉⠄⠳⢄⠀⢦⢿⣾⣿⣿⢷⣟⣿⠿⣿⣿⣿⣿⢴⣶⣾⣿⣿⣿⣿

⠀⠀⣿⡿⢿⣿⠸⣿⡇⣿⣿⢸⣿⣷⣾⣿⣧⣻⠿⠿⠋⣼⣘⣛⣣⣄⣛⣡⣬⣩⣭⣥⣥⣤⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠞⠁⠀⠀⠀⠀⠀⢻⣷⠻⣿⡇⣊⣿⣿⢶⣷⠟⠻⠿⠿⠟⠉⠛⠿⠿⠟

⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⠸⣿⣿⣿⣿⣿⣿⣿⣿⣍⡁⠈⣋⣫⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣴⣴⣆⣀⣀⣠⣤

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠠⣸⣿⣿⣿⣿⣿⣿⣿⣿⣤⡦⢍⣽⣿⣿⣿⣿⣿⣿⣿⠏⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡁⠀⠀⠐⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡁⢹⣿⣿⣿⣿⣽⣿⣿⣿⠶⢾⣿⣿⣿⣿⣿⣿⣿⠏⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛

⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⡌⢿⣿⣿⣿⣿⣿⣷⣾⣿⣾⣿⣿⣿⣿⣿⠃⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⢻⣿⣿⣿⣿⣿⣿⡄⠉⣿⣿⣿⣿⣿⣿⢯⣿⣾⣿⣿⣿⣿⠃⠄⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⣿⣀⣀

⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⣀⡈⣿⣿⣿⣿⣿⣿⣿⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⠎⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⢧⣿⣿⣿⣿⣿⣿⣿⡿⢃⡤⡴⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

[39A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⠿⣿⡟⠛⠀⠀⠀⠈⠀⠘⠃⠇⢠⠞⠁⠋⠋⠟⠀⠁⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣸⡄⠀⠐⠀⠒⠒⠒⠐⠀⠒⠒⠀⠒⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⢟⠛⠃⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣧⣤⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣾⣿⠿⠈⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢐⣾⣶⣤⣶⣴⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣟⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠈⠹⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣗⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⢀⠻⠌⠙⣿⣿⣿⣿⣿⡈⣁⠀⠀⣀⣠⣿⣿⣿⣦⣌⠻⣿⣿⣿⢿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣾⡿⠏⠉⠉⠀⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⣺⡛⣷⡉⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣷⣴⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣇⠀⠀⠀⠀⠘⣿⣿⣿⣟⠈⠋⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⠀⠀⢀⣾⣿⡿⢛⠍⠁⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠹⣿⣿⠿⠿⠥⠈⣹⣿⣿⣿⣿⣏⢹⣇⠈⠓⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢷⠀⠀⠀⢠⣾⣿⣛⡂⠁⣄⠂⠈⢲⣄⠀⢀⠀⢸⣿⣿⣿⣿⡀⠀⠀⠀⠀⣀⡈⠛⠿⣿⣿⣿⣯⠘⣿⠄⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠰⠀⠀⠀⣾⣿⣿⣿⣿⣷⣧⣤⣤⣼⣇⣹⣾⣷⣿⣿⣿⣿⣿⣷⣴⣻⡴⣿⠁⠀⠒⣆⡘⣿⣿⣿⠀⠻⡄⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣷⣾⣿⣿⡄⠀⠷⠠⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⢸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠉⠁⠀⠀⠀⠀⢠⣴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⠠⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⠉⠙⣿⣿⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠂⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣘⠃⠀⢨⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣀⣀⣶⣆⠹⣿⣤⣄⡀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⢤⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⣼⢠⠸⣿⣿⣿⣿⣿⣿⡏⣴⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⡇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡆⡀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⡿⢸⣼⣿⣿⣿⣿⣿⣿⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣤⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣿⣧⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠤⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠏⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⣀⣀⣄⣄⣀⣀⣀⣀⣀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢻⣽⣿⢿⣿⣿⣿⣿⣿⣿⣮⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿⠟⢃⠈⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣗⠀⠉⢽⣿⣿⣿⣿⣿⣿⣿⣥⣤⣤⣤⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠤⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⡿⣟⣛⢿⣿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢹⣿⣧⡀⠀⠈⠉⠻⣿⣿⡿⣿⣿⣿⣿⣿⣆⣸⣿⣿⣿⠿⠿⠿⠿⢿⣿⠟⠛⠋⠁⠀⠀⣀⣤⣀⠠⣤⡝⢩⣭⡍⣵⣶⢰⣶⡶⠆⢹⣿⠿⣿⡄⢻⣿⠀⠁⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠔⣨⣴⣾⡿⠘⠿⠿⠓⠀⠀⣀⢀⣈⠉⣁⣉⠉⢩⣭⡙⠿⠟⢰⣶⡆⣶⣦⠘⣿⡄⣿⠸⣿⡟⣿⡇⢸⣿⢹⣿⡇⣿⣇⢸⣿⡇⣿⣿⢸⣿⣧⡄⢸⣿⣴⣿⡃⢸⣿⠀⠀⠀⠀⠀

⠀⠀⣀⣀⣀⠀⢠⣤⣤⣄⠀⣤⣴⣶⢹⣿⢱⣾⠿⣷⡄⠿⣿⣿⠛⢸⣿⡀⣿⣿⠀⢸⣿⡇⠀⠀⢸⣿⡇⢸⣿⣧⣿⡇⣿⠀⣿⣧⣾⠇⢸⣿⠀⣿⡇⢸⣿⣾⡟⣿⣿⣿⠀⣿⡏⠉⢸⣿⡇⣿⣇⢈⣛⡀⠀⢀⣠⣤

⠀⠀⣿⣿⣿⡀⢸⣿⢉⣿⡇⢹⣿⣀⡺⣿⡸⣿⣶⣅⡀⠀⣿⣿⠀⢸⣿⡇⢻⣿⠀⠸⣿⡇⠀⠀⠈⣿⡇⢸⣿⢻⣿⡇⢹⡄⣿⣷⠀⠀⠸⣿⣇⣿⡇⠈⣿⣿⡇⢻⣿⡿⣀⠿⠿⠿⣀⣿⠃⠛⣛⣤⢛⣷⣦⣿⣿⣻

⠀⠀⣿⡇⣿⣇⢸⣿⡟⣿⡆⢸⣿⡛⣷⣿⡏⣤⡍⢿⣷⠀⢸⣿⠀⠈⣿⡇⢸⣿⣤⡄⣿⣷⣶⠠⠀⡿⠧⠸⠿⠀⠿⠇⣸⣇⣛⣛⠀⠀⠀⠉⠉⠉⠐⠃⠀⢤⠀⠀⡰⣾⡿⣿⢷⣝⢻⡏⣿⣷⣿⣿⡇⣤⣤⣿⣿⣿

⠀⠀⣿⡿⢿⣿⠸⣿⡇⣿⣷⢸⣿⣷⡦⣻⣧⡻⠷⠿⠋⢠⠘⠛⠂⠀⠛⠁⢌⡉⠉⡅⠁⢀⣤⣾⣷⣶⣶⣿⣶⣿⣿⣿⣿⡿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠹⣷⡟⢀⣹⣿⣵⣶⡶⠛⠿⣷⡿⠋⠙⠿⠿

⠀⣀⣻⣥⣮⣭⣥⡍⣵⣶⣶⣷⣶⣶⣿⣿⣿⣿⣿⣿⣆⠀⠈⢻⣝⡳⡄⠀⠀⠙⠲⠁⠀⠈⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠼⠟⠛⠉⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⢿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠈⠒⠁⠀⠈⠂⠀⠀⠀⠀⠀⠀⣩⣵⣿⣿⣿⣿⣿⣿⡟⢰⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣦⠀⣀⣀

⣿⣿⠿⠋⢻⢟⣾⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣸⢓⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠎⣽⣿⣿⣿⣿⡿⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⢰⣶⣤⣶⣶⣆⡀⠀⣾⢿⣿⣷⣌⣿⣿⣿⣿⣿

⣿⡋⠚⣢⠀⢠⡼⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⣿⣶⣆⣀⣐⡤⠄⠀⠀⠀⠶⢿⣿⣿⣿⣿⠟⠁⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡘⣿⣿⣿⣿⣿⣷⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠋⠩⢛⢳⡿⠶⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⢿⣿⣿⣿⡿⣷⡄⠂⠀⠈⣾⣿⣿⣿⡟⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠁⠋⠆⠏⠓⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠹⣿⣿⣿⣿⣿⣿⣆⠀⠸⣿⣿⣿⣧⣡⡠⠁⠀⠀⣿⣿⣿⡟⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣏⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿

⡙⠀⢋⠈⡄⢃⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⡀⢻⣿⣿⣿⣿⣿⣿⣆⢠⣿⣿⣿⣿⣾⣶⠀⠀⢀⣿⣿⣿⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣷⣿⣾⡆⣸⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢰⣿⣷⠈⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣷⣷⣿⣿⣿⣿⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⢧⣿⣿⣿⣿⣿⡿⠋⠁⣀⣲⡤⢸⣿⣿⣷⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣗⠀⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

[39A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡾⣿⣿⠛⠋⠀⠈⠀⠃⠸⠻⠙⢰⡞⠃⠛⠋⠝⠁⠉⠐⠁⠈⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠘⠁⠒⠒⠒⠐⠀⠒⠒⠐⠒⠚⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣾⣿⣿⣿⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠛⠟⠀⠀⠀⠀⢀⣀⣤⣤⣤⣀⣄⣀⣠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣿⣿⠄⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣷⢀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡷⣀⣀⠀⠀⠀⠀⠀⠀⢀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣟⡆⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢀⠹⢻⣷⣿⣦⣶⣶⣴⣿⠿⣿⠟⢿⣿⣿⣿⠌⠽⢞⣧⡀⣀⣰⣮⣉⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⡘⠄⢙⣿⣿⣿⣾⣿⣿⣿⠃⡿⣄⣀⠿⣿⣿⣷⣼⠄⠻⢿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⡿⠿⠉⠉⢁⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣿⣟⢻⣌⢫⣿⣿⣿⣿⣿⣿⣀⠷⠋⠁⠄⡀⣹⣿⣟⣧⡀⠐⠉⠏⠁⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣟⠀⠀⠈⠀⠘⣿⣿⣿⣿⡉⠛⠉⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢿⣿⠀⣙⠛⢩⣿⣿⣿⣷⣶⣧⣾⣿⣾⣿⣿⣿⣿⣷⣶⣾⣤⣀⣰⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣾⣿⣿⢟⡿⠛⠀⠀⠀⠀⠀⠀⢈⣽⣿⣿⣿⡏⣿⣿⣿⠿⢧⣌⣹⣿⣿⣿⣿⣷⣙⣿⠄⠉⠀⣸⣷⣿⣿⣿⣿⣟⣫⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⠆⠀⠀⢀⣾⣿⣟⡓⡉⣠⡒⢁⠳⣦⢀⢀⡀⢸⣿⣿⣿⣿⣇⠀⠀⠀⠀⣀⡀⠙⠻⢿⣿⣿⣿⡌⢻⠢⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⠂⠀⠀⣸⣿⣿⣿⣷⣿⣿⣤⣤⣤⣷⣹⣷⣿⣾⣿⣿⣿⣿⣿⣶⣿⣴⣻⠁⠀⠀⣧⣘⢿⣿⣿⡇⠸⣧⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣶⣿⣿⡇⠀⠸⠆⢦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⡄⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⢰⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠋⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⣿⢸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⢿⣿⡟⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠐⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠉⠀⠀⠀⠀⠀⠀⣠⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⡻⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣶⣦⠸⣿⣧⣤⣀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⡴⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣴⢷⡌⣿⣿⣿⣿⣿⣿⡿⣱⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡄⣤⠀⠀⡂⠀⠀⢠⣤⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣼⢸⣿⣿⣿⣿⣿⣿⣿⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡏⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡄⣠⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠯⠽⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⠿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣀⣀⣤⣤⣠⣀⣀⣀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠛⠟⠋⢀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡌⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣴⣶⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡔⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⡿⣟⣛⢿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⣿⣷⣀⠀⠈⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣷⣸⣿⣿⣿⠿⢿⡿⠿⢿⣿⠟⠛⠛⠀⠀⠀⣀⣤⣀⠠⣤⡄⢡⣬⡍⣰⣶⢰⣶⡶⠇⢹⣿⠿⣿⡄⢻⣿⢸⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠇⠿⠿⠛⠂⠀⣀⢀⣈⠉⣉⣉⠉⢩⣭⡙⠿⠟⢰⣶⡆⣶⣦⠘⣿⡄⣿⠸⣿⡟⣿⡇⢸⣿⢹⣿⡇⣿⣧⢸⣿⡇⣿⣿⠸⣿⣧⡄⢸⣿⣴⣿⡃⢸⣿⠈⠟⠋⠉⠀

⠀⠀⣀⣀⣀⠀⣠⣤⣤⣄⠀⣤⣶⣶⢸⣿⢱⣾⠿⣷⡄⠿⣿⣿⠛⢸⣿⡀⣿⣿⠀⢸⣿⡇⠀⠀⢸⣿⡇⢸⣿⣧⣿⡇⣿⠀⣿⣧⣿⠗⢸⣿⠀⣿⡇⢸⣿⣾⡟⣿⣿⣿⠀⣿⡏⠉⢸⣿⡇⣿⣧⢈⣛⡀⡀⠀⢀⣠

⠀⠀⣿⣿⣿⡀⢸⣿⢉⣿⡇⢻⣿⣀⡺⣿⡸⣿⣶⣅⡐⠆⣿⣿⠀⢸⣿⡇⢻⣿⠀⠸⣿⡇⠀⠀⠈⣿⡇⢸⣿⢻⣿⡇⢻⡆⣿⣷⠀⠀⠸⣿⣇⣿⡇⠈⣿⣿⡇⢻⣿⡿⢀⠿⠿⠿⣀⣿⣃⠛⠛⣤⣛⢳⣿⣦⣿⣿

⠀⠀⣿⡇⣿⣇⢸⣿⡟⣿⡆⢸⣿⡛⣷⣿⡯⣤⡍⣿⣷⠀⢸⣿⠀⠘⣿⡇⢸⣿⣤⡄⣿⣷⣶⠠⡀⣿⠧⠸⠿⠈⠿⠇⣸⣧⣛⣛⣄⠀⠀⠉⠉⠉⢀⠔⡀⠠⣄⠀⢀⢻⣿⡿⣿⢿⣝⣿⠿⣿⡷⣿⣿⣠⣤⣼⣿⣿

⡀⠀⣿⡿⢿⣿⠸⣿⡇⣿⣷⢸⣿⣷⡦⣿⣧⡻⠷⠿⠋⠠⡘⠛⣃⠄⠛⢁⣌⣉⠉⣡⢡⣤⣤⣾⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣆⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠸⣧⠻⣷⡏⢈⣻⣿⣴⣾⡶⠻⢿⣿⡿⠃⠙⠿

⠀⢀⣛⣥⣬⣭⣥⣭⢱⣶⣶⣷⣶⣶⣿⣿⣿⣿⣿⣿⣷⡀⠌⢻⣿⣻⣦⠈⡍⢹⢷⣟⠿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡟⣼⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣪⠦⠹⠟⠋⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠉⠯⣟⣻⣴⡌⣳⣄⠄⠁⠀⠀⢀⣉⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀

⣿⣿⡿⣿⣿⡿⣿⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢨⣿⣿⣥⠈⠣⡆⠀⠀⠀⠀⢸⠿⣿⣿⣿⣿⣿⣿⠃⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣘⠀⠀⣠⣴⣶⣶⡶⣶⣶⣶⣶⣿⣺⣶⣶⣭⣿⣷⣿⣿

⣿⣿⡟⣿⣿⣵⣭⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠙⣿⣿⣿⣄⣐⣶⣤⡤⠤⠀⢶⣿⣿⣿⣿⣿⡿⠋⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿

⣿⡯⣿⣿⣿⣿⡿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠈⢻⣿⣿⣿⣿⣿⣧⠒⠀⠈⣾⣿⣿⣿⡿⠃⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣝⡿⣿⣿⣿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠙⣿⣿⣿⣿⣿⣿⣷⡀⠈⣿⣿⣿⣿⣯⣭⢍⠑⠀⣿⣿⣿⣿⠃⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⢿⣿⣯⣿⡟⣸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢀⠘⣿⣿⣿⣿⣿⣿⣷⡀⣿⣿⣿⣿⣿⣿⣧⠤⢀⣿⣿⣿⡇⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣾⣿⣿⢱⣿⣿⣿⣿⣿⣿⣿⠟⢁⠀⢰⣿⣿⡄⢻⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣇⡀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⡏⣾⣿⣿⣿⣿⡿⠟⢁⣀⣼⣦⠌⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

[39A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡾⣿⣿⠛⠋⠀⠀⠀⠃⠸⠳⠙⢰⡞⠃⠛⠉⠝⠁⠉⠐⠁⠈⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠘⠀⠒⠒⠒⠐⠀⠒⠒⠒⠒⠚⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣾⣿⣿⣿⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠛⠛⠀⠀⠀⠀⢀⣀⣤⣤⣄⣀⣄⣀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣾⣿⣿⡀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣷⢁⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡷⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣟⡆⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢀⠹⢻⣷⣿⣦⣶⣶⣴⣿⢿⣿⠟⢻⣿⣿⣿⠍⠽⢮⣧⠀⣀⣰⣦⣈⣲

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⡘⠄⢙⣿⣿⣿⣿⣿⣿⣿⠃⡟⢄⢀⠿⣿⣿⣶⣬⠄⠻⢿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⡿⠿⠉⠉⠁⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣿⣟⢿⣈⢫⣿⣿⣿⣿⣿⣿⠀⠷⠋⠃⠀⡀⣽⣿⣟⢤⡀⠐⠡⠎⠁⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣟⠐⠀⠈⠀⠘⣿⣿⣿⣿⡈⠛⠉⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢿⣿⠀⡙⠛⢩⣿⣿⣿⣷⣦⣶⣿⣿⣼⣿⣿⣿⣷⣷⣾⣾⣤⣀⢸⡤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣾⣿⣿⢟⡽⠙⠀⠀⠀⠀⠀⠀⢈⣽⣿⣿⣿⡏⣿⣿⣿⠿⢯⣌⣹⣿⣿⣿⣿⣿⣙⣿⠄⠉⠀⣸⣿⣿⣿⣿⣿⣯⣏⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⠆⠀⠀⢀⣾⣿⣟⡓⡉⣠⡒⢁⠲⣦⠀⢀⡀⢸⣿⣿⣿⣿⣇⠀⠀⠀⠀⣀⡀⠙⠻⢿⣿⣿⣿⡍⢻⠢⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⠂⠀⠀⣸⣿⣿⣿⣷⣿⣿⣤⣤⣤⣷⣹⣷⣿⣿⣿⣿⣿⣿⣿⣶⣿⣵⣻⠁⠀⠀⣧⣘⢻⣿⣿⡇⠹⣧⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣿⡇⠀⠸⠆⢦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⡆⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⢰⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⣿⢸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⢿⣿⡟⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠐⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠉⠀⠀⠀⠁⠀⢀⣠⣴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⡻⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣶⣦⠸⣿⣧⣤⣀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⡴⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠙⠃⢀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣴⢷⡜⣿⣿⣿⣿⣿⣿⡿⣱⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡆⡤⠀⠂⡀⠀⢀⢀⣤⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣼⢸⣿⣿⣿⣿⣿⣿⣿⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡏⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡄⣠⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠯⠽⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⣀⣤⣤⣠⣀⣀⣀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠛⠟⠋⣐⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣴⣴⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡖⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡿⣿⡿⠿⠿⠿⡿⣛⣛⢿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠇⠿⠿⠛⠂⠀⣀⢀⣈⠉⣉⣉⠉⢩⣭⡝⠿⠟⢰⣶⡆⣶⣦⠘⣿⡄⣿⠸⣿⡟⣿⡇⢸⣿⢹⣿⡇⣿⣇⢸⣿⡇⣿⣿⢸⣿⣧⡄⢸⣿⣴⣿⡃⢸⣿⠈⠟⠋⠉⠀

⠀⠀⣀⣀⣀⠀⣠⣤⣤⣄⠀⣤⣶⣶⢸⣿⢱⣾⠿⣷⡄⠿⣿⣿⠛⢸⣿⡀⣿⣿⠀⢸⣿⡇⠀⠀⢸⣿⡇⢸⣿⣧⣿⡇⣿⠀⣿⣧⣿⠗⢸⣿⠀⣿⡇⢸⣿⣾⡟⣿⣿⣿⠀⣿⡏⠉⢸⣿⡇⣿⣧⢈⣛⡀⡀⠀⢀⣀

⠀⠀⣿⣿⣿⡀⢸⣿⢉⣿⡇⢻⣿⣀⡺⣿⡸⣿⣶⣅⡀⠆⣿⣿⠀⢸⣿⡇⢻⣿⠀⠸⣿⡇⠀⠀⠘⣿⡇⢸⣿⢻⣿⡇⢹⡆⣿⣷⠀⠀⠸⣿⣇⣿⡇⠈⣿⣿⡇⢻⣿⡿⢀⠿⠿⠿⣀⣿⣃⠛⠛⣤⣛⢳⣿⣶⣿⣿

⠀⠀⣿⡇⣿⣇⢸⣿⡟⣿⡆⢸⣿⡛⣷⣿⡯⣤⡍⣿⣷⠀⢸⣿⠀⠘⣿⡇⢸⣿⣤⡄⣿⣷⣶⠀⡀⣿⠧⠸⠿⠈⠿⠇⣸⣇⣛⣛⡄⠀⠀⠉⠉⠉⢀⠔⡀⠠⣄⠀⢀⢻⣿⡿⣿⢿⣝⣿⠿⣿⡷⣿⣿⣠⣤⣼⣿⣿

⠀⢀⣛⣥⣬⣭⣥⣭⢱⣶⣶⣷⣶⣶⣿⣿⣿⣿⣿⣿⣷⡐⠌⣻⣿⣻⣦⠌⡌⠹⢷⣟⠿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡟⣼⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠦⠹⠟⠋⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠈⠯⣟⣻⣴⡈⡳⣄⠄⠀⠀⠀⢀⣉⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀

⣿⣿⡿⣿⣿⡿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⣨⣿⣿⣥⠈⠧⠆⠀⠀⠀⠀⢸⠿⣻⣿⣿⣿⣿⣿⠃⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣘⠀⠀⣠⣴⣶⣶⡶⣶⣶⣶⣶⣿⣺⣶⣶⣯⣿⣷⣿⣿

⣿⣿⡟⣿⣿⣷⣭⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠙⣿⣿⣿⣄⣰⣶⣤⡤⠤⠀⢾⣿⣿⣿⣿⣿⡿⠋⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿

⣿⡯⣿⣿⣿⣿⡿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠈⢻⣿⣿⣿⣿⣿⣧⠐⠀⠈⣾⣿⣿⣿⡿⠃⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣟⣟⣿⣿⣿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠙⣿⣿⣿⣿⣿⣿⣷⡀⠈⣿⣿⣿⣿⣿⣭⢍⠑⠀⣽⣿⣿⣿⠃⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⢿⣿⣯⣿⡟⣸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢀⠘⣿⣿⣿⣿⣿⣿⣷⡀⣿⣿⣿⣿⣿⣿⣷⠄⢀⣿⣿⣿⡇⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

[39A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⢾⢿⣿⠛⠉⠀⠀⠀⠘⠀⠻⠘⠀⡸⠃⠘⠙⠙⠁⠈⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⡿⠿⠿⣯⡚⠛⠒⠚⠓⠒⠘⠒⠒⠘⠒⠒⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣿⣿⡏⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣋⡁⠀⠀⠀⠀⠀⠀⢈⠻⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡟⠛⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣀⣠⣠⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣽⣾⡯⠇⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⣢⢼⣶⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⡇⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⡁⠛⣿⣷⣶⣤⣤⣀⣠⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⣠⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⢀⠳⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⠿⠉⠉⠁⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣽⣿⣻⣇⠙⣿⣿⣿⣿⣿⣿⣿⡟⠛⡿⠿⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣿⣿⡐⠀⠀⠀⠀⢻⣿⣿⣿⡃⠙⠉⠙⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⡿⣿⠆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠃⠀⠀⠀⠀⣠⣿⣿⢟⡿⠇⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⣿⡏⢿⣿⡿⠿⠿⢬⣙⣿⣿⣿⣿⣿⣎⣿⡆⠈⠁⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⣴⣿⣟⣓⠋⢠⣖⠉⠙⢦⡀⢀⡀⠀⣿⣿⣿⣿⣧⠀⠀⢀⠀⣀⡀⠈⠙⢿⣿⣿⣿⣇⢹⡇⠀⠀⢸⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣉⣻⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠇⠀⠀⢠⣿⣿⣿⣿⣿⣿⣦⣤⣤⣾⣮⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣧⣺⡇⠐⠐⣲⣄⠹⣿⣿⣇⠈⢳⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠀⠈⠃⠰⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⡀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠉⠉⢹⣿⡿⠋⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡜⠇⠀⣼⣿⣿⣿⣿⣿⣿⣿⢻⣿⣧⣀⣴⣶⠀⢿⣧⣤⣄⡸⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡴⢆⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠋⠉⠁⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢧⡇⡀⣿⣿⣿⣿⣿⣿⣿⢣⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⢀⣀⣀⣰⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣟⣸⡇⢿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣼⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣀⢀⣤⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣧⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠯⠤⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠟⠃⠨⣿⡿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⡿⣿⣿⣿⣿⣿⣦⣄⣤⣄⣤⣤⣤⣄⣀⣀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⣻⡃⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⠛⠛⠀⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡀⠀⠀⠀⣶⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠠⣷⣿⣿⣿⣿⣿⣿⣿⣦⣶⣶⣧⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠀⠀⠀⡻⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⡇⠀⠀⠈⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⠿⡿⣟⣛⢿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢹⣿⣄⠀⠐⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⠿⠿⠿⠟⢻⣿⠟⠛⠛⠛⠸⠃⣀⣤⣀⠠⣤⡄⢠⣤⡍⣰⣶⢰⣶⡶⠆⢸⣿⠻⣿⡄⢻⣿⢸⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣀⠀⠀⣠⣴⡿⠟⠸⠿⠛⠃⠀⣀⢀⣀⠈⣉⣉⠉⢩⣭⡉⠿⠟⢰⣶⡆⣶⣦⠘⣿⡀⣿⠸⣿⡟⣿⡇⢸⣿⢹⣿⡇⣿⣇⢸⣿⡇⣿⣿⢸⣿⣧⡄⢸⣿⣴⣿⡃⢸⣿⢸⣿⣿⣿⣿

⠀⠀⣀⣀⣀⠀⢠⣤⣤⣄⠀⣤⣴⣶⢸⣿⢱⣾⠿⣷⡄⠿⣿⣿⠛⢸⣿⡀⣿⣿⠀⢸⣿⡇⠀⡄⢸⣿⡇⢸⣿⣧⣿⡇⣿⠀⣿⣧⣾⠇⢸⣿⠀⣿⡇⢸⣿⣾⡟⣿⣿⣿⠀⣿⡏⠩⢸⣿⡇⣿⣧⢈⣛⡘⣿⡛⠛⣉

⠀⠀⣿⣿⣿⡀⢸⣿⢉⣿⡇⢹⣿⣀⡺⣿⡸⣿⣦⣅⡀⠀⣿⣿⠀⢸⣿⡇⢻⣿⠀⠸⣿⡇⠀⠀⠈⣿⡇⢸⣿⢻⣿⡇⢹⡆⣿⣷⠀⠀⠸⣿⣇⣿⡇⠀⣿⣿⡇⢻⣿⡿⡀⠿⠿⠿⢀⣿⣃⣛⠛⢀⣛⣧⢿⣿⣼⣿

⠀⠀⣿⡇⣿⣇⢸⣿⡟⣿⡆⢸⣿⡛⣷⣿⡏⣤⡍⢿⣷⠀⢸⣿⠀⠈⣿⡇⢸⣿⣤⡄⣿⣷⣶⠀⠀⡿⠧⠸⠿⠀⠿⠇⣸⣇⣛⣛⣤⡀⠀⠉⠉⠉⠀⢀⠀⠀⠠⡀⠀⢈⢿⣿⢿⣿⢯⡛⣿⢹⣿⣾⣿⣿⢠⣤⣼⣿

⣀⠀⣿⡿⢿⣿⠸⣿⡇⣿⣷⢸⣿⣷⡦⣻⣧⡻⠷⠿⡋⠀⠘⠛⣂⣀⠋⣁⣈⣉⣉⣥⣥⡤⣤⣾⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣷⡀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠸⡎⢻⣾⡇⢈⣻⣿⣴⣾⠾⠻⢿⣾⠿⠃⠛

⠥⠄⣛⣥⣬⣭⣥⣭⢅⣶⣶⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⡆⠀⢹⣿⣿⣷⣿⣿⣯⣿⢾⣱⠻⠿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠤⠿⠟⠋⠉⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀

⣾⣿⣿⣿⣿⢿⣿⢿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⠻⣿⣿⣯⣉⣽⣷⢶⣍⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀

⣿⣿⣿⢿⣩⣽⣿⡿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢼⣿⣿⣿⡉⡹⢿⡦⢠⠀⠀⡀⣿⣿⣿⣿⣿⣿⣿⡟⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠠⡀⢠⣤⣴⣦⡆⣰⣤⡶⢉⣾⣶⣿

⣿⣿⣻⢻⣿⣿⣯⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠙⢻⣿⣿⣷⣥⣶⣮⣧⠷⠆⠰⣿⣿⣿⣿⣿⣿⠟⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣠⣼⣶⣦⣷⣌⢻⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿

⣿⡿⢽⣿⣿⣷⣾⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣧⠙⢿⣿⣿⣿⣿⠏⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡜⠒⡳⢿⣿⣿⠟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⢻⣿⣿⣿⣿⣿⣿⣄⠀⢹⣿⣿⣿⣿⣿⡯⡭⡆⣹⣿⣿⣿⠇⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣯⣻⣶⣿⢿⣷⢠⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢀⠀⢿⣿⣿⣿⣿⣿⣿⣆⢸⣿⣿⣿⣿⣿⣷⡧⠽⣻⣿⣿⣿⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿

⣿⣿⣶⣿⣿⡏⣾⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⣾⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣂⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⠿⠋⣀⣠⣶⠄⢿⣿⣿⣦⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢡⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

[39A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⣿⡿⠛⠁⠀⠀⠈⠇⠘⠃⠇⢘⠏⠁⠉⠋⠋⢈⠀⠈⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠿⠞⠛⠒⠛⠓⠛⠚⠛⠚⠛⠒⠚⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⣿⣿⣿⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣯⡤⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡋⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡛⠟⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠠⠄⠀⠀⠀⠀⣰⡿⠋⠁⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣇⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣿⣿⣿⣽⡀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠂⡇⠀⠀⠀⢠⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣦⡀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣟⡆⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢀⠐⢀⠀⠀⣾⣿⣿⣿⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⢰⡈⣓⢀⡀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⡿⠿⠉⠍⢉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣼⣿⣻⣦⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⣻⣿⠏⠉⠉⣛⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣟⠆⠀⠈⠀⠘⣿⣿⣿⣿⡈⠋⠁⠉⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⠂⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠀⠀⠀⠀⣼⣿⣿⢻⠟⠊⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠃⠿⠿⠿⠟⠳⢧⣽⣿⣿⣿⣿⣿⣌⣿⠠⠈⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⠆⠀⠀⠀⣾⣿⣿⣟⡁⣴⡎⠉⠙⡦⣀⣠⡀⢸⣿⣿⣿⣿⣇⠀⣀⡀⣀⡤⠄⢉⠙⢿⣿⣿⣿⡆⢹⡅⠀⠀⣿⣿⣿⣿⣿⣿⣿⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣉⣉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡠⠆⠀⠀⣸⣿⣿⣿⣷⣿⣿⣤⣤⣴⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⡀⠀⢉⣷⣤⢻⣿⣿⡇⠘⢷⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⠂⢲⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢀⠃⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⢸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡏⠁⠈⣿⣿⡏⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠈⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⡿⡈⠰⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣦⣤⣿⣧⡘⢿⣶⣦⣄⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡖⣆⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⡿⣄⣿⣿⣿⣿⣿⣿⡟⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⢹⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⡙⠛⠁⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣽⠷⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣽⣷⡾⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠣⡈⠀⠀⢐⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠗⠚⠟⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣔⣼⣿⣿⣿⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠛⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠋⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⡀⣄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠘⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗⠀⠀⡀⠿⠂⠐⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠁⠀⠀⠀⠒⠀⠀⠀⢻⣿⣿⣿⣿⠿⠿⠿⠿⡿⣟⣛⢿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢻⣿⣄⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⠿⠿⠿⠿⢿⣿⠿⠛⠛⠛⠿⠟⣁⣤⣀⠠⣤⡄⢠⣤⡄⣰⣶⢰⣶⡶⠆⢹⣿⠿⣿⡄⢻⣿⢸⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣠⡶⠿⠇⠿⠛⠛⠓⣀⢀⣀⠀⣉⣉⠉⢩⣭⡉⠛⠛⢰⣶⡆⣶⣦⠘⣿⡄⣿⠸⣿⡟⣿⡇⢸⣿⢹⣿⡇⣿⣇⢸⣿⡇⣿⣿⢸⣿⣧⡄⢸⣿⣴⣿⡃⢸⣿⢸⣿⣿⣿⣿

⠀⠀⣀⣀⣀⠀⢠⣤⣤⣄⠀⣤⣴⣶⢠⣾⢱⣾⠿⣷⡄⠿⣿⣿⠛⢸⣿⡀⣿⣿⠀⢸⣿⡇⠀⠀⢸⣿⡇⢸⣿⣧⣿⡇⣿⠀⣿⣧⣾⠗⢸⣿⠀⣿⡇⢸⣿⣾⡟⣿⣿⣿⠀⣿⡏⠩⢸⣿⡇⣿⣧⢈⣛⡘⠻⣿⣿⡿

⠀⠀⣿⣿⣿⡀⢸⣿⢉⣿⡇⢹⣿⣀⣺⣿⡸⣿⣶⣅⡐⡆⣿⣿⠀⢸⣿⡇⢻⣿⠀⠸⣿⡇⠀⠀⠈⣿⡇⢸⣿⢻⣿⡇⢹⡆⣿⣷⢠⡀⠸⣿⣇⣿⡇⠈⣿⣿⡇⢻⣿⡿⠀⠿⠿⠿⣀⡿⣃⣛⣛⣤⠛⢳⣿⡟⣿⣿

⠀⠀⣿⡇⣿⣇⢸⣿⡟⣿⡆⢸⣿⡛⣷⣿⡯⣤⡍⢿⣷⠀⢸⣿⠀⠘⣿⡇⢸⣿⣤⡄⣿⣷⣶⠀⠀⡿⠧⠸⠿⠀⠿⠇⣸⣇⣛⣛⣼⣷⡀⠉⠉⠉⠀⠀⠀⡠⠂⠐⢤⠀⠀⡘⣿⣿⢿⡿⣯⡿⣿⢽⣿⣾⣿⣿⢠⣤

⠀⠀⣿⡿⢿⣿⠸⣿⡇⣿⣷⢸⣿⣷⡦⣿⣧⡻⠷⠿⣋⡄⠘⠛⢂⣄⣛⢁⣈⣉⣭⣡⢥⣤⣤⣶⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣷⣄⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⢿⡜⢿⣾⠃⢙⣿⣧⣶⣿⠞⠿⣿⣾⠿

⣷⡀⠛⣁⣬⣭⣵⣿⣷⣦⣶⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢻⣿⣿⣿⡿⠏⣹⡿⠿⠉⠋⠁⠚⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡱⡌⠿⠞⠋⠉⠁⠈⠁⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠙⣿⣿⣧⡆⠈⠦⠆⠀⠀⠀⠀⠨⣽⣿⣿⣿⣿⣿⣿⣿⠏⢸⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤

⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢸⣿⣿⡆⡀⡈⠀⠀⠀⠀⠀⠀⡸⢿⣿⣿⣿⣿⣿⡟⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀

⣿⣿⣿⣿⢻⣳⣿⣯⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢹⣿⣷⣦⣤⣶⣦⣖⠲⠒⠰⡿⣿⣿⣿⣿⣿⠏⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⢀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣠⣤

⣿⣿⠿⢽⣿⣿⣿⣿⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠙⣿⣿⣿⣿⣿⣿⠖⣲⠀⠴⣿⣿⣿⣿⠋⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⣼⣦⡀⠀⢸⣿⣶⣄⢀⣾⣿⣿

⢻⠸⠀⠱⢻⣿⣿⡏⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⢻⣿⣿⣿⣿⣿⣿⣄⠀⢹⣿⣿⣿⣿⣽⡧⡅⠂⢰⣿⣿⣿⠇⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡗⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣈⣿⣿⣿⣿⣿⣿⣿

⣾⣇⣿⣲⣾⢽⣽⢡⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⠈⣿⣿⣿⣿⣿⣿⣿⣆⢸⣿⣿⣿⣿⣿⣿⣾⠍⣺⣿⣿⡿⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣶⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡿⢃⠀⠀⣾⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣌⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⠟⢋⣀⣠⣷⠄⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣿⢡⣿⣿⣿⣿⣿⣿⣿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

[39A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⣿⡿⠛⠁⠀⠈⠈⠇⠘⠃⠇⢘⠏⠁⠉⠋⠋⢈⠀⠈⡀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠿⠟⠛⠓⠛⠛⠛⠚⠛⠚⠛⠒⠚⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⣿⣿⣿⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣯⡄⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡻⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡛⠟⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣄⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⠄⠀⠀⠀⠀⣀⡿⠋⠁⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣇⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣿⣿⣿⣿⡄⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⢢⡧⠀⠀⠀⢠⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣦⡀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣟⡆⡀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢀⠐⢀⠀⠀⣾⣿⣿⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⢰⡘⣓⢀⡀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⡿⠿⠉⠍⢉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣼⣟⣻⣧⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢛⣻⡿⠏⠉⢉⣛⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣟⠒⠀⠈⠀⠘⣿⣿⣿⣿⡉⠋⠉⠉⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⠂⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠀⠀⠀⠀⣾⣿⣿⢻⠿⠋⠁⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠃⠿⠿⠿⠟⠷⢧⣽⣿⣿⣿⣿⣿⣬⣿⠠⠈⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⠆⠀⠀⠀⣾⣿⣿⣟⡁⣴⡎⠉⠙⡦⣀⣠⡀⢸⣿⣿⣿⣿⣇⠀⣀⡀⣀⡤⠤⢉⠙⢿⣿⣿⣿⡆⢹⡅⠀⠀⣿⣿⣿⣿⣿⣿⣿⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⣙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⠆⠀⠀⣸⣿⣿⣿⣿⣿⣿⣤⣤⣴⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⡀⠀⢉⣷⣤⢻⣿⣿⡇⠘⣷⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⠃⢲⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⢸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡏⠁⠈⣿⣿⡏⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠈⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⣿⠈⠰⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣦⣤⣿⣷⡘⢿⣶⣦⣄⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡖⣦⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⡿⣄⣿⣿⣿⣿⣿⣿⡟⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⢹⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡩⡋⠃⠀⠐⠂⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠷⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣽⣷⡾⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠡⣀⠀⠀⡔⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠗⠚⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣼⣿⣿⣷⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠟⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠋⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠠⣄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠸⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗⠀⠀⠀⢿⠇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠒⠉⠀⠀⠀⠲⠀⠀⠀⢻⣿⣿⣿⣿⠿⠿⠿⠿⡿⣟⣛⢿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢻⣿⣤⠀⠈⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⠿⠿⡿⠿⢿⣿⠿⠛⠛⠛⠿⠛⣁⣤⣀⠠⣤⡄⢠⣤⡄⣴⣶⢰⣶⡶⠆⢹⣿⠿⣿⡄⢻⣿⢸⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣠⡶⠿⠇⠿⠛⠛⢓⣀⢀⣀⠀⣉⣉⠋⢩⣭⡉⠻⠛⢰⣶⡆⣶⣦⠘⣿⡄⣿⠸⣿⡟⣿⡇⢸⣿⢹⣿⡇⣿⣇⢸⣿⡇⣿⣿⢸⣿⣧⡄⢸⣿⣴⣿⡃⢸⣿⢸⣿⣿⣿⣿

⠀⠀⣀⣀⣀⠀⢠⣤⣤⣄⠀⣤⣶⣶⢠⣾⢱⣾⠿⣷⡄⠿⣿⣿⠛⢸⣿⡀⣿⣿⠀⢸⣿⡇⠀⠀⢸⣿⡇⢸⣿⣧⣿⡇⣿⠀⣿⣧⣾⠗⢸⣿⠀⣿⡇⢸⣿⣾⡟⣿⣿⣿⠀⣿⡏⠩⢸⣿⡇⣿⣧⢈⣛⡘⠻⣿⣿⡿

⠀⠀⣿⡇⣿⣇⢸⣿⡟⣿⡆⢸⣿⡛⣷⣿⡯⣤⡍⢿⣷⠀⢸⣿⠀⠈⣿⡇⢸⣿⣤⡄⣿⣷⣶⠀⠀⡿⠧⠸⠿⠀⠿⠇⣸⣇⣛⣛⣼⣷⡀⠉⠉⠉⠀⠀⠀⡠⠂⠐⢦⠀⠀⡘⣿⣿⢿⡿⣯⡿⣿⢽⣿⣾⣿⣿⢠⣤

⠀⠀⣿⡿⢿⣿⠸⣿⡇⣿⣷⢸⣿⣷⡦⣿⣧⡻⠷⠿⣋⡄⠘⠛⢂⣄⣛⢁⣈⣉⣭⣡⢥⣤⣤⣶⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣷⡄⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⢿⡜⢿⣾⠃⣙⣿⣧⣶⣿⠞⠿⣿⣾⠿

⣷⡀⠛⣁⣬⣭⣵⣿⣷⣦⣶⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢻⣿⣿⣿⡿⠏⣙⡿⢿⠉⠋⠉⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡱⡌⠿⠞⠋⠉⠁⠈⠁⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠹⢿⣿⣷⡅⠉⠦⠆⠀⠀⠀⠀⠨⣽⣿⣿⣿⣿⣿⣿⣿⠏⢸⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤

⣿⣿⣿⣿⢿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣺⣿⣿⡇⡀⡈⠀⠀⠀⠀⠀⠀⡸⢿⣿⣿⣿⣿⣿⡟⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀

⣿⣿⣿⣿⢿⣻⣿⣯⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠁⢻⣿⣷⣦⣤⣶⣦⣖⠲⠒⠰⡿⣿⣿⣿⣿⣿⠏⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⢀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣠⣤

⣿⣿⡟⢽⣿⣿⣿⣿⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠙⣿⣿⣿⣿⣿⣿⠖⣲⠀⢸⣿⣿⣿⣿⠋⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⣼⣦⡀⠀⢸⣿⣶⣄⢀⣾⣿⣿

⠻⠐⠄⠱⢻⣿⣿⡏⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⢻⣿⣿⣿⣿⣿⣿⣄⠀⢹⣿⣿⣿⣿⣿⡧⡅⠆⢸⣿⣿⣿⠇⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣈⣿⣿⣿⣿⣿⣿⣿

⣾⣎⣿⣶⣿⢽⣽⢡⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⠈⣿⣿⣿⣿⣿⣿⣿⣆⢸⣿⣿⣿⣿⣿⣿⣾⠝⣻⣿⣿⣿⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣾⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡿⢃⠀⠀⣾⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡿⣄⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⠟⢋⣠⣠⣷⠄⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣿⢡⣿⣿⣿⣿⣿⣿⣿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

[39A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⢿⣿⠟⠉⠀⠀⠁⠹⠀⠛⠘⠀⡽⠁⠘⠉⠘⠀⠁⠈⠠⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠏⠚⠛⠓⠛⠓⠛⠘⠛⠚⠛⠒⠚⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⡏⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⠄⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡟⢛⠃⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠐⠤⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡄⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⣽⣿⣯⣇⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣄⠀⠀⠀⠀⠀⠀⠐⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣆⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣷⢂⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⡀⠃⡀⠀⠀⠀⢠⣿⣿⣷⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⣆⣙⡂⣀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⠿⠟⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⠿⠏⠩⢉⡉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣝⣷⡌⠄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣝⣩⣵⡄⠉⠀⠈⣀⣠⣶⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡓⠀⠀⠀⠀⢿⣿⣿⣿⣇⠙⠉⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⡗⠀⡀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⣰⣿⣿⣟⡿⠛⠉⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡏⠻⠿⠿⠿⠻⠶⣼⣿⣿⣿⣿⣿⣷⣽⡇⠄⠁⠀⠄⣾⣿⣿⣿⣿⣿⣿⡿⠟⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡷⠀⠀⠀⣰⣿⣿⣻⢋⢠⣾⠉⠉⢷⢔⣀⣄⢀⣿⣿⣿⣿⣷⡀⢀⣀⢄⣠⠤⠈⡉⠻⣿⣿⣿⣷⠨⣿⠀⠀⢸⣀⣿⣿⣿⣿⣿⣟⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠸⠀⠀⢀⣿⣿⣿⣿⣿⣿⣧⣤⣤⣾⣯⣽⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣿⣇⣐⠈⣹⣦⡝⣿⣿⣿⠀⢻⡆⠀⢈⣿⠍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠳⠘⢶⢻⡗⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⡈⠀⠁⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠉⠀⢹⣿⡟⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠁⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣼⢏⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⣿⣆⢿⣷⣶⣦⣜⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⢲⡄⠀⠀⠀⠀⠀⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠁⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣯⣾⢧⣸⣿⣿⣿⣿⣿⣿⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢘⡇⠀⠀⠀⠀⠀⣿⣹⣿⣿⣿⣿⣿⣿⣿⣾⣯⣿⠐⠢⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠮⢀⡀⠄⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠒⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣄⣔⠁⢄⣴⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠟⠋⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠘⠻⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠐⠃⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡔⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⠿⠿⠿⡿⣛⣛⢿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⣿⣷⡄⠀⠈⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⠿⡿⠿⢿⣿⠟⠛⠛⠛⠿⠛⣉⣤⣀⠠⣤⡄⢠⣤⡄⣰⣶⢰⣶⡶⠆⢹⣿⠿⣿⡄⢻⣿⢸⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡴⠾⢿⠼⠟⠛⢛⣂⢀⣀⠀⣈⣉⠋⢩⣥⡉⠛⠟⢰⣶⡆⣶⣦⠘⣿⡄⣿⠸⣿⡟⣿⡇⢸⣿⢹⣿⡇⣿⣧⢸⣿⡇⣿⣿⢸⣿⣧⡄⢸⣿⣴⣿⡃⢸⣿⢸⣿⣿⣿⣿

⠀⠀⣀⣀⣀⠀⣠⣤⣤⣄⠀⣤⣶⣶⢀⣴⢱⣾⠿⣷⡄⠿⣿⣿⠛⢸⣿⡀⣿⣿⠀⢸⣿⡇⠀⠀⢸⣿⡇⢸⣿⣧⣿⡇⣿⠀⣿⣧⣾⠇⢸⣿⠀⣿⡇⢸⣿⣾⡟⣿⣿⣿⠀⣿⡏⠩⢸⣿⡇⣿⣧⢈⣛⡸⡿⠻⣿⣿

⠀⠀⣿⣿⣿⡀⢸⣿⢉⣿⡇⢻⣿⣀⡺⣿⡸⣿⣶⣍⡀⠇⣿⣿⠀⢸⣿⡇⢻⣿⠀⠸⣿⡇⠀⠀⠘⣿⡇⢸⣿⢻⣿⡇⢹⡆⣿⣷⢰⣆⠸⣿⣇⣿⡇⠈⣿⣿⡇⢻⣿⡿⠀⠿⠿⠿⣀⣿⡃⣛⣛⣤⣛⠷⢿⣿⡿⣿

⠀⠀⣿⡇⣿⣇⢸⣿⡟⣿⡆⢸⣿⡛⣷⣿⡏⣤⡍⢿⣷⠀⢸⣿⠀⠘⣿⡇⢸⣿⣤⡄⣿⣷⣶⠀⠀⣿⠧⠸⠿⠀⠿⠇⣼⣇⣛⣛⣸⣿⣦⠉⠉⠉⠀⠀⠀⠀⡠⠂⠐⢤⠀⠀⡸⣿⣿⢿⡿⣿⢿⣿⣿⣷⣾⣿⣧⣠

⠀⠀⣿⡿⢿⣿⠸⣿⡇⣿⣷⢸⣿⣷⡦⣿⣧⡻⠷⠿⣋⣦⠘⠛⣂⣄⣛⡁⣈⣉⣩⣅⡥⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣧⡀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⢷⡙⣿⣿⠁⣙⣿⣧⣶⣿⠞⠿⣿⣿

⣻⣦⡛⢁⣨⣭⣵⣿⣷⣶⣶⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠙⣿⣿⣿⣿⡛⣹⡿⡿⡋⠛⠙⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡵⡜⠿⠞⠋⠉⠁⠈⠁⠀⠀⠀⠀

⣻⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠉⢻⣿⣿⣾⡨⠱⠶⠀⠀⠀⠀⠠⣽⣿⣿⣿⣿⣿⣿⣿⡿⠁⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤

⣿⣿⣿⣿⡿⣿⣿⣿⣿⢧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⢐⣿⣿⣿⢄⣀⠱⠂⠀⠀⠀⠀⢸⢿⣿⣿⣿⣿⣿⣿⠃⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣘⠂⠀⣀⣠⣄⣀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣿⣿⣿⣿⣿⣻⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠙⢿⣿⣿⣤⣼⣶⣶⠒⠖⠒⢿⢿⣿⣿⣿⣿⡿⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⣀

⣿⣿⣿⡯⣿⣿⣿⣿⡟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠈⢻⣿⣿⣿⣿⣿⣿⣟⣦⠀⣿⣿⣿⣿⡿⠁⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣦⠀⢀⣾⣿

⡟⣧⣷⣘⣟⣿⣿⣿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠙⣿⣿⣿⣿⣿⣿⣷⡀⠈⣿⣿⣿⣿⣿⣿⢠⠰⠀⣿⣿⣿⡿⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿

⣿⣿⣿⠗⣾⣿⣿⡏⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⢀⡀⢹⣿⣿⣿⣿⣿⣿⣷⡀⣿⣿⣿⣿⣿⣿⣿⣗⢩⣿⣿⣿⡇⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⠏⣀⠀⢸⣿⣿⣄⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠻⣿⣿⣿⣿⣿⢧⣿⣿⣿⣿⣿⡿⠋⣁⣤⣾⡧⠸⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣼⣿⣿⣿⣿⣿⣿⣿⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

[39A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⡿⣿⡟⠛⠁⠀⠀⠘⠃⠙⠏⠃⢆⠟⠈⠋⠉⠃⠈⠀⠁⠄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣎⣚⠛⠓⠚⠓⠐⠀⠚⠒⠚⠒⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⢩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡛⠟⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠢⡄⠀⠀⠀⠀⠀⠀⠀⢠⣾⣥⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣿⣿⣿⣽⠨⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠠⡗⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡗⡀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢠⠘⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⣀⣈⣒⢠⡀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣉⣽⣿⠉⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⡿⠿⠉⠍⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⣿⣿⣻⣦⠁⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣟⠂⢀⠈⠀⢸⣿⣿⣿⣿⣜⠋⠉⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠻⣿⠂⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⢀⠀⠀⢀⣾⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠙⠿⠿⠟⠛⠲⢦⣿⣿⣿⣿⣿⣿⣬⣿⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⠆⠈⠀⢀⣾⣿⣿⣟⣅⣤⡏⠉⠹⡦⣂⣠⡀⣿⣿⣿⣿⣿⣆⠀⣀⡠⣀⡤⠄⣉⠙⢿⣿⣿⣿⡆⣿⡆⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠃⠀⠀⣼⣿⣿⣿⣿⣿⣷⣤⣤⣼⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣀⡀⢁⣷⣌⢻⣿⣿⡄⠈⣷⠀⠀⡀⣤⣶⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⠀⠓⠸⠟⠉⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡏⠀⠈⣿⣿⠋⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠈⠀⠈⢀⡇⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⣿⣽⢼⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣤⣴⣿⣷⡹⣿⣶⣶⣤⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢤⡖⣦⠀⠈⠓⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⢿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⢹⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣽⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠓⠚⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠻⠿⠃⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣦⣶⣤⣤⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⢤⠄⣀⣴⢼⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢂⣀⡌⠄⠈⡠⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠡⠀⠆⠀⠀⠀⠁⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠂⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡿⠿⠿⠿⡿⣛⣛⢿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⢻⣿⣯⡨⢍⣙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⠿⠿⠿⢿⣿⠟⠛⠛⠛⠿⠛⣉⣭⣉⠫⣤⡄⢠⣤⡄⣰⣶⢰⣶⡶⠇⢹⣿⠿⣿⡄⢿⣿⢸⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡠⠶⢿⡇⠛⠛⢛⣓⢈⣁⠀⣈⣉⠛⢩⣭⡉⠿⠟⢰⣶⡆⣶⣦⠘⣿⡄⣿⠸⣿⡟⣿⡇⢸⣿⢹⣿⡇⣿⣧⢸⣿⡇⣿⣿⢸⣿⣧⡄⢸⣿⣴⣿⡃⢸⣿⢸⣿⣿⣿⣿

⠀⠀⣀⣀⣀⠀⣠⣤⣤⣄⠀⣤⣴⣶⠀⣠⢰⣾⠿⣷⡄⠿⣿⣿⠛⢸⣿⡀⣿⣿⠀⢸⣿⡇⠀⠀⢸⣿⡇⢸⣿⣧⣿⡇⣿⠀⣿⣧⣾⠇⢸⣿⠀⣿⡇⢸⣿⣾⡟⣿⣿⣿⠀⣿⡏⠩⢸⣿⡇⣿⣧⢈⣛⡸⣿⡿⠿⣿

⠀⠀⣿⣿⣿⡀⢸⣿⢉⣿⡇⢻⣿⣀⣺⣿⡸⣿⣶⣅⡰⠀⢿⣿⠀⢸⣿⡇⢻⣿⠀⠸⣿⡇⠀⠀⠈⣿⡇⢸⣿⢻⣿⡇⢹⡆⣿⣷⢰⣶⠸⣿⣇⣿⡇⠈⣿⣿⡇⢻⣿⡿⠀⠿⠿⠿⢀⣿⣃⠛⣛⣤⣻⣧⡷⣿⣿⣿

⠀⠀⣿⡇⣿⣇⢸⣿⡟⣿⡆⢸⣿⡛⣷⣿⡯⣤⡍⢿⣷⠀⢸⣿⠀⠘⣿⡇⢸⣿⣤⡄⣿⣷⣶⠀⠀⡿⠧⠸⠿⠀⠿⠇⣸⣇⣛⣛⣼⣿⣷⡍⠉⠉⠀⠀⠀⠀⠀⡰⠂⠰⢄⠀⠀⡻⣿⣿⣿⣿⣝⢿⡿⣿⣷⣿⣿⡇

⣀⠀⣿⡿⢿⣿⠸⣿⡇⣿⣷⢸⣿⣷⡦⣿⣧⡻⠷⠿⣋⣾⡘⠛⢂⣄⣛⣁⣈⣉⣭⣥⣥⣤⣤⣾⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣆⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠐⣷⠹⣷⣿⠀⢙⣿⣧⣬⣵⠞⢿⣿

⢛⣢⣟⠁⣈⣩⣥⣿⣷⣶⣶⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣵⡸⡿⠞⠋⠉⠁⠈⠁⠀⠀⠀

⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠈⠛⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠠⠭⣿⣿⣿⣿⣿⣿⣿⣿⠏⢸⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⣻⣿⣿⡿⡭⡟⠯⠄⠀⠀⠀⠀⡻⣿⣿⣿⣿⣿⣿⡟⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣸⠀⠀⣀⣠⣀⣀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣻⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠈⠻⣿⣿⣧⣴⣿⣶⣶⠒⠒⠺⣿⣿⣿⣿⣿⣿⠏⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠙⣿⣿⣿⣿⣿⣿⣾⣱⠄⢘⣿⣿⣿⣿⠇⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⢀⣶

⣿⢻⣽⣦⣷⣻⣿⣿⡟⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⢻⣿⣿⣿⣿⣿⣿⣆⠀⢹⣿⣿⣿⣿⣿⡟⣄⠂⢰⣿⣿⣿⠇⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣿⣿

⣿⣿⣯⣿⢶⣿⣿⣿⢣⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⣀⠈⣿⣿⣿⣿⣿⣿⣿⣆⢸⣿⣿⣿⣿⣿⣿⣷⡊⣽⣿⣿⣿⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡿⠃⡀⠀⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⡄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡾⢿⣿⣿⣿⣿⡿⣼⣿⣿⣿⣿⣿⠟⢉⣰⣴⣷⠄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢡⣿⣿⣿⣿⣿⣿⣿⣏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

[39A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⡿⣿⡿⠛⠁⠀⠀⠘⠃⠙⠏⠃⢆⠟⠈⠋⠉⠃⠈⠀⠁⠄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣎⣚⠛⠓⠚⠓⠐⠀⠚⠚⠚⠒⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⢩⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡻⠟⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠢⡄⠀⠀⠀⠀⠀⠀⠀⢠⣾⣥⡀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣿⣿⣿⣽⠈⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠢⡗⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⣀⣈⣓⢠⡀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣉⣽⣿⠋⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⡿⠿⠉⠍⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣯⣻⣦⠁⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣟⠂⢀⠈⠀⢸⣿⣿⣿⣿⣌⠋⠉⠉⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣾⠻⣿⠂⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⢁⠀⠀⢀⣾⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠘⠿⠿⠟⠛⠲⢦⣿⣿⣿⣿⣿⣿⣬⣿⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣥⣴⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⠆⠈⠀⢀⣾⣿⣿⣟⣁⣤⡏⠉⠹⡦⣂⣠⡀⣿⣿⣿⣿⣿⣆⠀⣀⡠⣀⡤⠄⣉⠙⢿⣿⣿⣿⡆⣿⡆⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠂⠀⠀⣼⣿⣿⣿⣿⣿⣿⣤⣤⣼⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣀⡀⢁⣷⣌⢻⣿⣿⡆⠘⣷⠀⠀⡀⣤⣶⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⠂⠃⠸⠟⠉⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⣿⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡏⠀⠈⣿⣿⠋⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠈⠀⠈⢀⡇⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⣿⡽⢼⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣦⣴⣿⣷⡸⣿⣶⣶⣄⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⡖⣦⠀⠈⠃⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⠀⠀⠀⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡃⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣽⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠓⠚⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠃⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡠⢤⠄⠀⣴⢜⠄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣂⣂⡉⡄⠈⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠡⠈⠆⠀⠀⠀⠩⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠂⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡿⠿⠿⠿⡿⣛⣛⢿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⢻⣿⣯⡀⢉⣙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⢿⡿⠿⢿⣿⠟⠛⠛⠛⠿⠛⣋⣭⣉⠩⣤⡄⢠⣤⡄⣰⣶⢰⣶⡶⠆⢹⣿⠿⣿⡄⢻⣿⢸⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡠⠶⢿⡇⠛⠛⠛⣓⢈⣁⠀⣈⣉⠛⢩⣭⡉⠿⠟⢱⣶⡆⣶⣦⠘⣿⡄⣿⠸⣿⡟⣿⡇⢸⣿⢹⣿⡇⣿⣧⢸⣿⡇⣿⣿⢸⣿⣧⡄⢸⣿⣴⣿⡃⢸⣿⢸⣿⣿⣿⣿

⠀⠀⣿⣿⣿⡀⢸⣿⢉⣿⡇⢻⣿⣀⡺⣿⡸⣿⣶⣅⡰⠀⢿⣿⠀⢸⣿⡇⢻⣿⠀⠸⣿⡇⠀⠀⠈⣿⡇⢸⣿⢻⣿⡇⢹⡆⣿⣷⢰⣶⠸⣿⣇⣿⡇⠈⣿⣿⡇⢻⣿⡿⠀⠿⠿⠿⢀⣿⣃⠛⣛⣤⣻⣧⡷⣿⣿⣿

⠀⠀⣿⡇⣿⣇⢸⣿⡟⣿⡆⢸⣿⡛⣷⣿⡏⣤⡍⢿⣷⠀⢸⣿⠀⠈⣿⡇⢸⣿⣤⡄⣿⣷⣶⠀⠀⡿⠧⠸⠿⠀⠿⠇⣸⣇⣛⣛⣼⣿⣷⡍⠉⠉⠀⠀⠀⠀⠀⡰⠂⠰⢄⠀⠀⡻⣿⣿⣿⣿⣟⢿⡿⣿⣷⣿⣿⣇

⣀⠀⣿⡿⢿⣿⠸⣿⡇⣿⣷⢸⣿⣷⡦⣻⣧⡻⠷⠿⣋⣾⡘⠛⢂⣄⣛⣁⣈⣉⣭⣥⣥⣤⣤⣾⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣆⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠐⣷⠹⣷⣿⠀⢙⣿⣧⣬⣵⠾⢿⣿

⢛⣦⣟⠁⣈⣩⣥⣽⣷⣶⣶⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠊⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡸⡿⠟⠋⠉⠁⠈⠁⠀⠀⠀

⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⠙⣿⣿⣿⣿⣿⣿⠿⢄⠀⠀⠠⢭⣿⣿⣿⣿⣿⣿⣿⣿⠏⢸⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⣺⣿⣿⡿⡽⡟⠻⢎⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⡟⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣸⠀⠀⣀⣠⣀⣀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠁⢻⣿⣿⣷⣴⣿⣷⣶⠖⠒⠺⣿⣿⣿⣿⣿⣿⠏⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠙⣿⣿⣿⣿⣿⣿⣾⣳⠀⠘⣿⣿⣿⣿⠃⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⢀⣶

⣿⣻⣽⣦⣵⣻⣿⣿⡏⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⢻⣿⣿⣿⣿⣿⣿⣆⠀⢹⣿⣿⣿⣿⣿⡟⣄⠆⢸⣿⣿⣿⠇⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣿⣿

⣿⣿⣯⣿⣶⣿⣽⣿⢱⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⣀⡈⣿⣿⣿⣿⣿⣿⣿⣆⢸⣿⣿⣿⣿⣿⣿⣿⠈⣽⣿⣿⣿⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⢿⣿⣿⣿⣿⡿⣼⣿⣿⣿⣿⣿⠟⢉⣰⣴⣷⠄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢁⣿⣿⣿⣿⣿⣿⣿⣏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                ䷩ 𝚕𝚒𝚗𝚎 3981

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/02/07/http-and-https-gemini-proxy/#comments

Gemini version at gemini://gemini.techrights.org/2022/02/07/http-and-https-gemini-proxy/

Gemini_version_available_♊︎

✐ Self-Hosted_Gemini_Proxy_(HTTP_and_HTTPS)⠀✐

Posted in Site_News at 10:12 am by Dr. Roy Schestowitz

Video_download_link | md5sum 86afc898cafbc432ca6331cdfc14f165

A Gemini Proxy Unveiled

Creative Commons Attribution-No Derivative Works 4.0

http://techrights.org/videos/gemini-proxy-site.webm

Summary: Easing people’s transition to Geminispace using a Web proxy is a_long-

term_objective, seeing that some people are intimidated by the idea of using

something other than a Web browser for hypertext (interconnected pages with

textual formatting)

THE Gemini_proxy_of_Techrights has been working for about 2 days, but we needed

to deal with bugs and edge cases, some of which remain. It’s not perfect, but

it mostly works. So the address gemini.techrights.org no longer responds only

to requests over gemini:// protocol (port 1965) but also HTTP/S (ports 80 and

443, which apparently replaces 80 almost_entirely, caveats_notwithstanding).

I’ve decided to do a detailed video about the proxy even though it is still

“work in progress” so to speak. The proxy, which I think is ready for wider use

by now, isn’t meant to actually be used, we just try to lower the entry barrier

for people who haven’t yet installed Gemini_client_software. We’ve already

reviewed many clients and other tools. They’re maturing and they continue to

broaden in reach and usage, which in turn motivates further development and

maturity/stability. In the video above I show 3 graphical Gemini clients:

Kristall, Lagrange, and Moonlander. Here is the_latest_(generated_today_at_1AM)

graph_of_Gemini’s_growth. The orange curve shows the number of active capsules

as a function of time. January was a surge. Lupa, which keeps track of

Geminispace in Stéphane Bortzmeyer’s Gemini server, knows_of_nearly_1,690

working_capsules_right_now. █

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

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

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

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠻⣿⠟⣿⡏⠋⠻⣿⢛⡿⠛⣻⣿⣿⠋⣿⢭⣟⠛⢿⣻⠟⠙⣛⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣓⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢻⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣛⣛⣛⣻⣿⣍⢿⠟⠋⡟⠽⢻⢿⢛⢿⡛⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⢿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣟⢩⣡⣿⡇⣿⣿⣿⣿⣿⣿⠛⠿⠿⡿⣿⡿⠿⡿⣻⠿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠁⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣷⣠⣾⣿⣿⡇⣿⣿⣿⣿⣿⣿⣾⣶⣶⣿⣿⣷⣴⣷⣶⣶⣾⣶⣾⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⢻⠋⠁⠈⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⠛⣿⡃⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⠿⠻⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⡿⢯⣲⣽⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣷⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣶⣾⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⡿⢛⢊⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿

⣿⣿⠿⣿⣯⣕⣼⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣑⣿⣿⣿⣿⠿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⡀⠠⠰⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣵⣿⡿⣟⢌⣴⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿

⣿⣿⠒⣿⣿⣾⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠁⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿

⣿⣿⠀⣿⣿⣿⠿⠝⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⣠⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿

⣿⣿⠙⣻⣟⡓⣸⣾⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⢀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣒⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣟⡹⣡⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⡀⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣾⣿⣿⡇⣿⣿⣿⣿⣿⣿⠿⠛⠁⣠⣾⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⡻⣿⡇⣿⣿⡟⠉⠁⠀⣀⣀⣚⣛⣛⡃⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣏⢰⣴⣿⡇⣿⣿⣧⡄⣾⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⢻⢋⣿⡇⣿⣿⣯⡅⣭⣭⣭⣭⣭⣭⣭⡅⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣽⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⠿⣿⠇⠿⠿⠿⠇⠿⠿⠿⠿⠿⠿⠿⠇⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢸⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡿⡿⣷⣿⣿⣿⣿⣿⡿⡟⣷⣿⣿⣿⣿⣿⡿⠟⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⠿⢻⣾⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠿⡻⡽⣭⣼⣾⣿⣿⢿⣻⡹⣭⣼⣾⣿⣿⠿⡻⡽⣭⣼⣾⣿⣿⡿⡛⡝⣥⣼⣾⣿⣿⡿⣟⣏⢯⣥⣿⣿⣿⡿⢟⢫⢫⣮⣷⣿⣿⣿⢿⢫⢹⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣇⣮⣷⣿⣿⣿⣿⣿⣎⣤⣷⣿⣿⣿⣿⣿⣆⣦⣷⣿⣿⣿⣿⣿⣗⣪⣶⣿⣿⣿⣿⣿⣷⣡⣼⣾⣿⣿⣿⣿⣿⣐⣽⣾⣿⣿⣿⣿⣿⣞⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀

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

                ䷩ 𝚕𝚒𝚗𝚎 4104

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✐ The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXXXIV:Immunity=_Impunity?⠀✐

Posted in Europe, Fraud, Law, Patents at 2:52 pm by Dr. Roy Schestowitz

Series parts:

The_EPO’s_Overseer/Overseen_Collusion_—_Part_I:_Let_the_Sunshine_In!

The_EPO’s_Overseer/Overseen_Collusion_—_Part_II:A“Unanimous”

  Endorsement?

The_EPO’s_Overseer/Overseen_Collusion_—_Part_III:_Three_Missing_Votes

The_EPO’s_Overseer/Overseen_Collusion_—_Part_IV:_The_Founding_States

The_EPO’s_Overseer/Overseen_Collusion_—_Part_V:Germany_Says“Ja”

The_EPO’s_Overseer/Overseen_Collusion_—_Part_VI:_A_Distinct_Lack_of_Dutch

  Courage

The_EPO’s_Overseer/Overseen_Collusion_—_Part_VII:_Luxembourgish_Laxity

The_EPO’s_Overseer/Overseen_Collusion_—_Part_VIII:_Perfidious_Albion_and

  Pusillanimous_Hibernia

The_EPO’s_Overseer/Overseen_Collusion_—_Part_IX:_More_Holes_Than_Swiss

  Cheese

The_EPO’s_Overseer/Overseen_Collusion_—_Part_X:_Introducing_the

  Controversial_Christian_Bock

The_EPO’s_Overseer/Overseen_Collusion_—Part_XI:“General_Bock”_–

  Battistelli’s_Swiss_Apprentice?

The_EPO’s_Overseer/Overseen_Collusion_—_Part_XII:_The_French_Connection

The_EPO’s_Overseer/Overseen_Collusion_—_Part_XIII:_Battistelli’s_Iberian

  Facilitators_–_Spain

The_EPO’s_Overseer/Overseen_Collusion_—_Part_XIV:_Battistelli’s_Iberian

  Facilitators_–_Portugal

The_EPO’s_Overseer/Overseen_Collusion_—_Part_XV:_Et_Tu_Felix_Austria…

The_EPO’s_Overseer/Overseen_Collusion_—_Part_XVI:_The_Demise_of_the

  Austrian_Double-Dipper

The_EPO’s_Overseer/Overseen_Collusion_—_Part_XVII:_The_Non-Monolithic

  Nordic_Bloc

The_EPO’s_Overseer/Overseen_Collusion_—_Part_XVIII:_Helsinki’s_Accord

The_EPO’s_Overseer/Overseen_Collusion_—_Part_IXX:_The_Baltic_States

The_EPO’s_Overseer/Overseen_Collusion_—_Part_XX:_The_Visegrád_Group

The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXI:The_Balkan_League–_The

  Doyen_and_His_“Protégée”

The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXII:The_Balkan_League–

  North_Macedonia_and_Albania

The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXIII:The_Balkan_League–

  Bulgaria

The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXIV:The_Balkan_League–

  Romania

The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXV:The_Balkan_League–

  Fresh_Blood_or_Same_Old,_Same_Old?

The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXVI:_A_Trojan_Horse_on_the

  Budget_and_Finance_Committee

The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXVII:_Cypriot_Complicity

The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXVIII:_Benoît_and_António’s

  Loyal_“Habibi”

The_EPO’s_Overseer/Overseen_Collusion_—_Part_IXXX:_The_EPOnian_Micro-

  States_–_Monaco_and_Malta

The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXX:_San_Marino_and_the

  Perfidious_Betrayal_of_Liberty

The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXXI:_The_Abstentionists

The_EPO’s_Overseer/Overseen_Collusion_—Part_XXXII:“Plucky_Little

  Belgium”?

The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXXIII:_Swedish_Scepticism

The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXXIV:An“Extremely

  Dubious”_Proposal

The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXXV:_Slovakian_Scruples

The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXXVI:_Serbian_Sour_Grapes

The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXXVII:_Stubbornly

  Independent_Slovenia

The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXXVIII:_Ensnared_in_the

  Tentacles_of_the_SAZAS_Octopus

The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXXIX:_On_the_Slippery_Slope

  to_Capture

The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXXX:_The_Idiosyncratic

  Italians

The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXXXI:_Public_Service_or

  Self-Service?

The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXXXII:_A_Parcel_of_Rogues?

The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXXXIII:_A_Legal_No-Man’s

  Land

YOU ARE HERE ☞ Immunity = Impunity?

               🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Diplomatic immunity⦈

According to reputable legal experts, the immunity granted to international

organisations “encourages or at least allows IO managers and executives to

engage in illegal or unlawful practices which would otherwise expose them and

their organizations to civil or criminal liability in national courts there.”

Summary: The EPO‘s administration has come to the point where it shamelessly

and systematically misuses “immunity” to break the law without any consequences

either to ringleaders such as Benoît_Battistelli and António_Campinos or their

facilitators, whom they typically appoint based on loyalty rather than skills;

this erodes confidence in the institutions they run, whose impact can be highly

corrosive or detrimental to their original/stated goals

In the last part we saw how international organisations suffer from a lack of

transparency and accountability and how those who become implicated in serious

maladministration or other wrong-doings seldom – if ever – get called to

account or suffer any prejudice to their “career”.

A key issue here is the bubble of “immunity” in which international

organisations operate and which effectively shields them from any external

oversight or control.

“A key issue here is the bubble of “immunity” in which international

organisations operate and which effectively shields them from any external

oversight or control.”Immunity is granted to these organisations for the

ostensible purpose of ensuring their political and financial independence and,

thus, their impartiality. However, like any other kind of legal privilege, it

is open to abuse.

The immunity accorded to international organisations has long been recognised

as a contentious issue by legal scholars and lawyers who represent the staff of

these organisations in disputes before international tribunals such as the

ILOAT.

In an article published in 2010 under the title “International_Organisation

Reform_or_Impunity?_Immunity_is_the_problem”, legal practitioners Greta Rios

and Ed Flaherty explored the topic in detail.

“The immunity accorded to international organisations has long been recognised

as a contentious issue by legal scholars and lawyers who represent the staff of

these organisations in disputes before international tribunals such as the

ILOAT.”According to the authors, the immunity granted to international

organisations “encourages or at least allows IO managers and executives to

engage in illegal or unlawful practices which would otherwise expose them and

their organizations to civil or criminal liability in national courts there.”

Due to the absence of a threat of criminal sanction or substantial civil

damages awards, “the normal incentive of civil society for managers and

executives to run their organizations lawfully and/or in accord with best

practices is non-existent, encouraging rather than preventing unacceptable

behavior within IOs which clearly also has a negative effect on their

performance and effectiveness.”

“And so the rank-and-file staff of international organisations like the EPO

continue to be exposed to the abuses of managers and senior executives for whom

“immunity” all too often translates into “impunity”.”But despite extensive

academic literature on the subject, there has been little follow-up on a

political level.

It almost seems like those who call the shots in the corridors of power have a

vested interest in the status quo and are not particularly keen about pushing

for the badly-needed reforms of this sector.

Of course there are occasional attempts to pay lip-service to calls for reform

such as the resolution “Accountability_of_international_organisations_for_human

rights_violations” (No. 1979) which was adopted by the Parliamentary Assembly

of the Council of Europe in 2014.

But to date there are no visible signs of concrete political action as a

follow-up to such parliamentary grandstanding.

And so the rank-and-file staff of international organisations like the EPO

continue to be exposed to the abuses of managers and senior executives for whom

“immunity” all too often translates into “impunity”.

              🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Immunity and impunity⦈

For senior executives of international organisation, “immunity” effectively

                      translates into “impunity”.

In the upcoming parts we will take a closer look at the internal justice

systems of international organisations on which staff are obliged to rely in

order to safeguard and assert their rights. And we shall also see how these

systems often turn out to be hopelessly dysfunctional. █

⣿⣿⣿⣿⣿⣿⠋⡴⣨⠡⢿⡿⠿⢿⡿⠿⡿⠿⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣽⣶⣶⣯⣟⢿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⠃⣼⢿⠃⣔⠘⡀⣁⣚⣰⣀⣃⣛⣃⣑⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣷⡟⢛⡏⢹⣶⠀⣿⣿⠀⣿⠀⣾⠙⣛⠿⠿⣟⣫⣽⣿⡏⠡⣼⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣦⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢿⣟⣿⣟⣻⣿⡿⠁⣼⠃⣸⣿⢠⣿⡿⠀⣿⠀⡿⢀⡿⢢⣿⣿⣿⡿⠟⠁⠀⠀⢙⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⠿⠿⠿⠛⠋⣠⡾⠃⣠⡿⢃⣾⡿⣃⣘⣋⡸⠃⠼⠃⠼⣟⣻⣿⣆⠀⠀⢀⣴⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⠁⡄⢸⠀⡇⠰⠈⡇⣿⣿⠀⡆⢸⠀⠘⠀⢸⡇⡀⢻⡄⢠⣿⠀⡏⢠⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠒⠒⠒⠚⠋⣁⣤⠾⢋⣤⣾⡿⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⠀⠇⣸⠀⡇⢰⣿⡁⠛⢻⠀⠃⣼⠀⣦⡇⠸⢀⡄⢸⡇⢸⡟⢸⣇⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣘⡛⠛⠛⠛⣉⣩⣤⣶⣿⠟⠋⣠⣾⠎⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠿⣛

⣿⣿⣿⣿⣿⡷⢾⠿⢿⡿⢿⡟⠿⣿⠿⢿⠿⣿⢿⢿⢿⢿⡿⠿⠿⠿⠟⢻⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣈⣉⡉⠙⠛⠛⠛⠛⠋⣉⣠⣴⡾⠛⢁⣴⠟⠘⣿⣿⣿⣿⣿⢿⣻⣽⣶⡿⠿⣿⣿⡿⣛⣵⣿⣿

⣿⣿⣿⣿⣿⡇⢸⠀⡈⡀⢸⡇⢀⠀⡀⢸⠀⡟⢸⠀⠈⢸⡇⣶⡆⣴⣿⡄⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣬⣍⣉⠙⠳⣦⢀⣟⡿⠛⠛⢋⣡⣴⡾⠟⢁⣴⡿⢹⣿⠀⠀⠻⣿⣷⣶⣿⣿⡿⣛⣽⣾⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣅⣾⣀⣿⣇⣸⣇⣸⣿⣇⣸⣄⣁⣼⣀⣇⣸⣇⣿⣇⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠫⢶⣤⣌⡙⠻⡦⣰⣿⣿⣷⡝⣛⣛⣉⣡⣴⡾⠛⠉⣠⠞⣿⡄⠀⠀⠈⠻⣿⣟⣵⣿⣿⣿⣿⡿⣟⣭⣶

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣭⣿⣾⣿⣷⣦⣌⢙⣻⣴⣾⣿⣿⣿⣿⢇⣉⣉⣉⡌⣡⣤⠶⠛⣁⠄⣿⣿⣖⠀⠀⠀⠀⠀⠈⢿⣿⣿⣛⣻⣭⣿⠷

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣛⣛⡻⠯⣻⡿⣾⣿⣿⣿⣿⣿⣿⡟⣈⣉⣉⣉⡄⣩⣤⡴⠞⢁⡴⢿⣏⣿⢱⡦⠀⠀⠀⠀⠈⢿⠿⣟⣻⣽⣾⣿

⣿⣿⣿⡟⢛⢻⠛⣛⣟⠛⣻⣿⣿⢋⠹⡟⠛⢻⡛⢛⣿⣿⡟⡙⣿⢛⣻⣿⣿⣿⢻⡟⠛⣿⢻⡟⣿⡿⣡⢡⣘⣁⣿⣿⣿⣿⣿⣿⣿⡇⣄⣉⣠⣤⡤⢠⠤⠴⠚⣁⡴⠸⣿⣿⣏⣿⣆⢀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡇⠮⢹⠀⠶⣿⠀⣿⣿⣿⠸⢠⣇⠀⣸⡇⢸⣿⣿⡇⠇⣿⢰⣾⣿⣿⠻⢸⠇⡀⢿⢸⡇⠿⣶⣮⣥⡵⠛⣿⣿⣿⣿⣿⣿⣿⣷⢬⣭⣭⣤⡶⠆⠶⠖⠛⢁⡴⢃⣬⡻⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡩⡢⣡⡭⣻⣿⣿⡉⢲⡌⣿⣎⢉⣡⣤⣴⠞⢃⣐⣚⣉⡴⣿⣿⣷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠩⣽⠉⠙⡏⢭⣽⠉⠭⣿⣿⣿⣿⣿⣿⣿⠇⡔⠐⢩⣿⣿⣿⣷⣬⣉⣴⣿⣿⣿⣥⣴⣶⣿⣿⣷⣭⣠⢤⣶⣿⡟⣿⣿⣿⣞⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣾⠀⠀⡇⠐⢻⡀⠒⣿⣿⣿⣿⣿⣿⣿⣬⣉⣁⣸⣿⣿⣿⣿⣿⣿⠛⠩⣌⠋⢐⠨⠍⣼⣿⣿⣿⣿⣷⣽⣿⣿⢹⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⠷⢞⣃⣐⣚⣰⣿⣿⣿⣿⣿⣿⣷⣻⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠘⣿⠀⡇⢿⠇⠀⢸⠀⠀⢻⢸⠀⣦⡄⣤⣆⠻⢁⣾⣿⣿⠃⢻⠀⢻⢸⢠⡌⣿⣿⡇⡇⠸⡟⢸⠀⡄⠁⢸⢸⠀⢿⢸⢸⣦⠀⣴⣄⠻⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⢀⠃⠀⡇⠘⠀⠀⢸⠀⠀⡄⢸⠀⣿⡇⣿⣿⡆⣿⣿⣿⡟⢘⠘⠀⡌⢸⢸⡇⣿⣿⡇⡇⠀⠃⢸⠀⣴⡇⢸⢸⠀⡈⢸⢸⣿⠀⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣼⣴⣤⣧⣧⣧⣾⣦⣶⣦⣿⣼⣤⣿⣧⣿⣿⣧⣿⣿⣿⣧⣿⣧⣤⣷⣼⣤⣴⣿⣿⣧⣧⣴⣼⣼⣤⣿⣷⣤⣾⣤⣷⣼⣼⣿⣤⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢋⣡⣴⣶⣮⣭⣭⣍⣙⣿⣶⣤⡈⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣈⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⡿⢡⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢸⣿⣿⣿⡿⣭⣽⢩⡝⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠘⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⡇⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣿⣿⡇⣿⣿⢨⡕⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠸⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣾⣼⣧⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡆⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⡿⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣉⣉⣉⣉⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⣭⣯⠹⠏⣽⢩⡙⠉⣿⣿⠏⢻⡏⡏⢻⠉⠉⣭⡏⢩⠙⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣭⣿⠇⠸⣿⢨⣴⠀⣿⡿⠐⠘⡇⡇⡄⠀⠀⣭⡇⢸⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

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

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⢹⣏⣯⢽⣨⣿⢗⢣⢯⣏⢫⣏⡍⡟⣍⣏⡍⣽⡿⣼⢹⣹⡹⣽⣿⣿⢷⢫⣏⡍⡏⣽⠹⣿⢹⢩⣏⢿⢡⡽⢯⣿⢻⡹⣽⡟⣽⢹⣿⡹⡏⡝⣽⢹⣩⢫⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣼⣾⣾⣿⣾⣿⣿⣾⣿⣾⣿⣾⣾⣷⣷⣿⣾⣷⣷⣷⣷⣿⣾⣷⣿⣾⣿⣾⣾⣾⣷⣳⣷⣷⣷⣿⣿⣾⣾⣾⣣⣿⣿⣾⣿⣿⣷⣷⣿⣿⣷⣷⣷⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡻⡟⣻⡿⡽⣛⢟⢻⢛⠻⡻⣿⡿⡿⣛⢿⣝⣛⣿⢻⣟⣱⢟⢟⡻⡟⣛⢟⢿⣿⢛⣻⢿⡟⡿⣛⡿⣟⣻⢿⡻⡿⡻⣛⡿⣛⡟⣛⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⣣⢷⣿⣧⣷⣏⣿⣞⣾⣸⣻⣝⣣⣷⣟⣏⣇⣻⣱⣿⣇⣏⣿⣜⣣⣷⣇⣟⣾⡏⣛⣽⣘⣹⣹⣧⣧⣓⣸⣼⣻⣸⣷⣇⣇⣒⣷⣏⣇⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                ䷩ 𝚕𝚒𝚗𝚎 4349

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/02/07/irc-log-060222/#comments

Gemini version at gemini://gemini.techrights.org/2022/02/07/irc-log-060222/

Gemini_version_available_♊︎

✐ IRC_Proceedings:_Sunday,_February_06,_2022⠀✐

Posted in IRC_Logs at 2:36 am by Needs Sunlight

Also available via the Gemini protocol at:

* gemini://gemini.techrights.org/irc-gmi/irc-log-techrights-060222.gmi

* gemini://gemini.techrights.org/irc-gmi/irc-log-060222.gmi

* gemini://gemini.techrights.org/irc-gmi/irc-log-social-060222.gmi

* gemini://gemini.techrights.org/irc-gmi/irc-log-techbytes-060222.gmi

Over HTTP:

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

                                     #techrights_log_as_HTML5                                                                                  #boycottnovell_log_as_HTML5

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

                                #boycottnovell-social_log_as_HTML5                                                                               #techbytes_log_as_HTML5

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

                                      #techrights_log_as_text                                                                                   #boycottnovell_log_as_text

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

                                 #boycottnovell-social_log_as_text                                                                                #techbytes_log_as_text

                      Enter_the_IRC_channels_now

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

§ IPFS Mirrors⠀➾

CID Description Object type

                                             IRC log for

QmeLVi6dD7nB8edEkgxmQ1sCn5KARFU3ffe2SBU8kkBpKQ #boycottnovell 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈

                                             (full IRC log

                                             as HTML)

                                             IRC log for

                                             #boycottnovell

QmcJcUAm5cqifPhNEsZ8DaVqgKuC4yksh1y5VVrZL14cHj (full IRC log 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈

                                             as plain/ASCII

                                             text)

                                             IRC log for

                                             #boycottnovell-

QmVUu15hBfJYFxX4EZZ6rWNviPtC9MLQnLMRcp3paLbWum social 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈

                                             (full IRC log

                                             as HTML)

                                             IRC log for

                                             #boycottnovell-

QmWedfgviFwwQb7Js8MQVwLDVBUa56W2EmYgxMJa66hRBu social 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈

                                             (full IRC log

                                             as plain/ASCII

                                             text)

                                             IRC log for

QmdSkBiDQY66cYwZtE5xp5Bx6VRkR8Fr4QXgfi7PgoKG6E #techbytes 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈

                                             (full IRC log

                                             as HTML)

                                             IRC log for

                                             #techbytes

Qma3nHQ3L3FWvoSKsBDXLfsjywui19iuYjvjQFvoe1hwbD (full IRC log 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈

                                             as plain/ASCII

                                             text)

                                             IRC log for

QmW99xw5Xgz9tFztLWQ9k3mNgZGyL7kcN2mwwEpePtjvvB #techrights 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈

                                             (full IRC log

                                             as HTML)

                                             IRC log for

                                             #techrights

QmNfkp6hdJP3Bo4wEk82wXxGyeLHb4Jhsh6dZJ9RdwpJYn (full IRC log 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈

                                             as plain/ASCII

                                             text)

🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇IPFS logo⦈

§ Bulletin for Yesterday⠀➾

Local_copy | CID (IPFS): QmQdk83ourWknf8WYXr4Z6LnuaLWYmqhpidR9Crga89wZn

                ䷩ 𝚕𝚒𝚗𝚎 4476

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/02/07/monday-github-outline/#comments

Gemini version at gemini://gemini.techrights.org/2022/02/07/monday-github-outline/

Gemini_version_available_♊︎

✐ Microsoft_GitHub_Exposé_—Part_XVII—_Backsliding_Into_1990s-Style_Digital

Slavery_by_Microsoft⠀✐

Posted in Microsoft at 7:43 pm by Dr. Roy Schestowitz

Series parts:

Microsoft_GitHub_Exposé_—Part_I—_Inside_a_Den_of_Corruption_and

  Misogynists

Microsoft_GitHub_Exposé_—Part_II—_The_Campaign_Against_GPL_Compliance

  and_War_on_Copyleft_Enforcement

Microsoft_GitHub_Exposé_—Part_III—_A_Story_of_Plagiarism_and_Likely

  Securities_Fraud

Microsoft_GitHub_Exposé_—Part_IV—_Mr._MobileCoin:_From_Mono_to

  Plagiarism…_and_to_Unprecedented_GPL_Violations_at_GitHub_(Microsoft)

Microsoft_GitHub_Exposé_—Part_V—_Why_Nat_Friedman_is_Leaving_GitHub

Microsoft_GitHub_Exposé_—Part_VI—_The_Media_Has_Mischaracterised_Nat

  Friedman’s_Departure_(Effective_Now)

Microsoft_GitHub_Exposé_—Part_VII—_Nat_Friedman,_as_GitHub_CEO,_Had_a

  Plan_of_Defrauding_Microsoft_Shareholders

Microsoft_GitHub_Exposé_—Part_VIII—_Mr._Graveley’s_Long_Career_Serving

  Microsoft’s_Agenda_(Before_Hiring_by_Microsoft_to_Work_on_GitHub’s_GPL

  Violations_Machine)

Microsoft_GitHub_Exposé_—Part_IX—_Microsoft’s_Chief_Architect_of_GitHub

  Copilot_Sought_to_be_Arrested_One_Day_After_Techrights_Article_About_Him

Microsoft_GitHub_Exposé_—Part_X—_Connections_to_the_Mass_Surveillance

  Industry_(and_the_Surveillance_State)

Microsoft_GitHub_Exposé_—Part_XI—_Violence_Against_Women

Microsoft_GitHub_Exposé_—Part_XII—_Life_of_Disorderly_Conduct_and_Lust

Microsoft_GitHub_Exposé_—Part_XIII—_Nihilistic_Death_Cults_With

  Substance_Abuse_and_Sick_Kinks

Microsoft_GitHub_Exposé_—Part_XIV—_Gaslighting_Victims_of_Sexual_Abuse

  and_Violence

Microsoft_GitHub_Exposé_—Part_XV—_Cover-Up_and_Defamation

Microsoft_GitHub_Exposé_—Part_XVI—_The_Attack_on_the_Autonomy_of_Free

  Software_Carries_on

YOU ARE HERE ☞ Backsliding Into 1990s-Style Digital Slavery by Microsoft

Video_download_link | md5sum f567010fa87bcd06249a2194c4f4450d

GitHub is a Threat

Creative Commons Attribution-No Derivative Works 4.0

http://techrights.org/videos/microsoft-untrustworthy-for-code.webm

Summary: The fake “social justice” claims or posturing by Microsoft ought to

have been exposed by recent affairs, involving the very CEO or public face of

GitHub, who moreover thinks_rape_jokes_are_appropriate

A few weeks ago we published the arrest_record_of_Balabhadra_(Alex)_Graveley,

but as court days are being scheduled we await the latest developments, which

implicate not only Graveley but also GitHub’s CEO Nat Friedman and his_wife,

whom we’ll pay more attention to later in this series.

Microsoft has a terrible track record with women, and moreover this goes all

the way up to the top (CEO who says things_like_this and co-founder who treats

women like sexual objects while he flies_the_Lolita_Express_with_Jeffrey

Epstein).

🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GitHub: Because you want Microsoft as your boss.⦈ That

Microsoft treated the Graveley situation so poorly is well documented [1, 2].

It would rather protect men who assault women than admit (possibly to the

public) that it was hiring and employing criminals, elevating them to

management positions based on nepotism (GitHub CEO) and in spite of a bad track

record with women.

Microsoft is — as I’ve long put it (for well over a decade for sure) — run by

crooks, criminals, and liars. They’re shamelessly committing the crimes and

then selling us a Microsoft that is “woke” because it changed the default name

of Git branches while keeping the highly controversial (racist) contract with

ICE (because that's_just_what_Microsoft_truly_believes_in as long as the

Pentagon_can_bail_it_out).

The video above discusses the GitHub situation. In relative terms they lose

market share and people should definitely object to Microsoft ‘bossing’ them

(and their projects) through GitHub. Over time more and more realise this, so

we expect that one day GitHub will fold just_like_CodePlex_did. █

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⡖⢀⣶⡄⢶⣴⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠠⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠰⠿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⡀⠀⣀⣀⣤⡀⠀⠀⠀⠀⠀⠉⡂⢀⡀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣅⣀⣼⣿⠿⣧⡄⢠⣼⠀⠀⢸⣷⣿⡇⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⢀⠀⠒⠘⠿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣾⣷⣶⣶⣿⣿⣾⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣶⠀⠀⠀⠀⠀⠀⠈⢩⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠛⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠰⠷⢆⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣿⣿⣿⣿⡟⠀⠀⠀⣰⣿⣿⣿⣇⡀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣼⣿⣿⣿⣿⣿⣿⠇⠀⠀⣰⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡷⠆⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡿⣹⠏⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢀⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢳⡏⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣼⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢯⡿⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢰⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣟⡾⠁⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣄⢀⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣰⣾⠿⣿⣿⣿⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣁⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢰⣿⡟⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⢰⡄⣶⣾⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣸⣽⣿⣿⣿⣶⣆⡀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣤⣼⣿⣷⣦⣶⣶⣶⣶⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠈⠙⢿⣿⡋⠉⢹⣿⡿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠶⠶⣶⠿⢷⠶⠸⠿⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[29A⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠚⢢⣶⣆⢰⣦⣶⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡤⠄⠀

⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⡹⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀

⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⡙⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠿⠂⠀⠀⠀⠀⠤⠤⠄⠀⠀⠤⣶⣿⣿⣿⣷⣾⣾⣿⣿⣿⣿⣶⣶⣴⣰⣴⡄⠀⣴⠿⠿⠿⠿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣨⠷⢭⣽⣦⡙⢿⣿⣿⣿⠟⠛⠛⠋⠀⢠⠷⠀⣤⣀⣴⣿⣿⠧⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠙⠙⢷⡌⢿⣿⣿⣆⠀⠀⠀⠠⡬⢠⣤⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢆⠻⣽⣿⡇⠀⠀⣠⣿⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣜⣿⣿⡆⡼⠛⢋⠉⠙⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡷⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⢁⡈⠅⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⢀⣀⣠⣀⠀⠐⠀⠀⠀⠉⣒⢄⣀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣈⣉⣁⣨⣿⣿⣧⣀⠀⣤⡇⠀⠠⣿⣾⣏⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⣀⠀⠀⠘⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣶⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣷⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢾⣿⣧⣄⠈⠁⠰⠆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠉⠉⠋⠀⠀⠸⢿⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠐⢈⡗⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣴⣶⣾⣿⣿⣿⢸⠇⠀⠀⣠⣿⣆⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣏⣿⠀⠀⢠⣿⣿⣿⡆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢡⠀⠀⠀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⢫⡿⠁⠀⢠⣿⣿⣿⣿⡟⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠋⠛⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡟⣱⠟⠀⠀⣴⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡾⠋⠀⣠⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡾⠁⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣼⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣰⣿⠿⣿⣿⣿⠿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣤⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢰⣿⡟⠀⠀⠀⠀⠀⢿⣿⡆⠀⠀⠀⠀⠀⠀⢰⡄⣶⣼⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠉⠉⠙⢿⣿⡋⠉⢹⣿⡿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

[29A⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠿⣴⣶⡄⣴⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠀⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠

⠀⠸⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣆⡻⡿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠿⠀⠀⠀⠂⠀⠀⠤⠤⠀⠀⠀⠠⠄⠀⠄⠀⠀⠠⣤⣽⣿⣿⣷⣾⣾⣿⣿⣿⣷⣦⣤⣤⣤⡴⠻⠿⠟⡛⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣩⡯⢿⣿⣯⠿⣿⣿⣿⣿⠟⠿⢿⠟⠀⣤⣄⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠉⠁⠀⠈⠻⢛⣷⡹⣿⣿⣿⣇⢰⣎⣠⣶⣿⣿⣿⣿⡿⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠀⢱⣄⢻⣿⣿⣾⣿⣿⣿⣿⡿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⢧⣹⡿⡛⠉⠁⠀⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⢹⡿⠀⠀⠀⠀⠀⠂⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠈⠄⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠙⢂⢄⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠀⠀⠀⠀⠀⠈⠘⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣉⣉⣁⣨⣿⣯⣧⣀⠀⣤⡆⠀⠀⣷⢸⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢠⣶⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣾⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣶⣶⣶⣿⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠈⠿⠿⠿⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⣰⣶⣄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠤⠀⠀⠀⢸⡆⠀⠀⠀⠾⣿⢷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣴⣶⣶⣾⣷⣶⣶⣇⠀⢷⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠒⠀⠀⠀⠀⢐⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⢸⡇⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣤⡿⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⣴⠟⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠟⠁⣠⡾⠃⣰⣾⡆⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣷⣤⡾⠋⣠⣾⣿⣿⣷⣆⠀⠀⠾⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣰⣿⠿⣿⣿⣿⠿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡏⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣤⣴⣦⣾⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢰⣿⡟⠀⠀⠀⠀⠀⢿⣿⡆⠀⠀⠀⠀⠀⠀⢰⡄⣶⡄⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢀⣀⣀⣀⣀⣀⣀⣈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣴⣾⣿⣿⣶⣤⣤⣤⣤⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠉⠉⠹⢿⣿⡏⠉⢹⣿⡿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛

[29A⣀⡀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠄⠀⠀⠘⡶⠶⣿⣦⣤⡄⢴⣶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⡆⠀⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠄⢹⣿⣿⠘⣻⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠙⠻⠇⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣧⡘⢿⣿⣿⣿⣿⡄⠀⠀⠀⣠⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠙⠿⠿⠃⠀⠀⠀⠠⠀⠴⠶⠀⠀⠀⠠⠄⠠⠤⠀⠀⠤⢤⣽⣿⣿⣿⣿⣾⣿⣿⣿⣿⣶⣴⡾⠙⠛⠛⠙⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣉⡻⣿⣿⣿⡻⢿⣿⣿⣿⣿⠛⠁⣶⣦⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠁⠀⠀⠀⠀⠛⣿⣿⣌⢿⣿⣿⣟⣴⣶⣿⣿⣿⣿⡿⠜⠄⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⣿⣦⣽⣿⣿⣿⣿⣿⡟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⢟⠋⠙⠚⠈⢧⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⡼⠀⠀⠀⠀⢠⢻⣟⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠆⠀⠀⠀⠀⡘⢦⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⡇⠀⠀⠀⠀⡀⠀⠃⠘⠆⣷⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠰⡔⡟⣣⡄⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡯⠄⠀⠀⠀⠘⣧⢜⡹⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢇⡄⢀⣀⣀⣀⠀⠀⠀⠀⠀⠉⢓

⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠉⠹⢧⠀⠀⠀⠀⠀⠀⠈⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⣈⣁⣨⣿⣿⣯⣄⡀⣤⡄⠀⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣶⣶⣶⣶⣾⣾⣿⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠐⢿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠸⣆⢀⣴⣶⣤⠀⠤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡴⠀⠀⠀⢻⡄⠀⢻⣀⡽⢿⠿⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣶⣶⣷⣿⣿⣧⠀⠀⠀⢿⡀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠒⠂⠀⠀⠀⣀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⡇⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣠⡿⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣼⠟⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⡾⠋⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣁⡰⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣰⣿⠿⣿⣿⣿⠿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣇⢿⣿⣿⣿⣿⣷⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢰⣿⡟⠀⠀⠀⠀⠀⢿⣿⡆⠀⠀⠀⠀⠀⠀⢰⡄⣶⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣶⣾⣿⣿⣶⣶⣶⣴⣤⣿⣿⣿⣶⣶⣶⣶⣾⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠉⠉⠹⣿⣿⡏⠉⢹⣿⡿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛

⠀⠶⠶⣶⠿⢷⠶⠼⠿⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[29A⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠈⠶⠾⣿⣿⣆⣀⠠⢦⣶⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢿⣿⠇⠀⢼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠁⠀⠀⠁⠀⠙⠋⣼⣿⡟⠿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⣀⣀⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣄⢻⣿⣿⣿⣿⣷⣴⣶⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠻⠿⠃⠀⠻⠿⠇⠀⠀⠠⠄⠀⠰⠶⠄⠀⠀⠀⠤⠤⠤⠤⠄⠠⢤⣼⣿⣿⣿⣷⣿⣿⣿⣿⣟⡙⠛⠋⢉⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣛⠿⣿⣿⣿⣟⣿⠉⠀⣾⣶⣿⣿⣿⢓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠈⢿⣿⣿⣏⣼⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢻⡟⠁⠐⠹⢻⣷⡄⠀⠀⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠁⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣾⠂⠀⢠⠀⠨⣿⣷⡀⠀⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠇⠀⠀⠀⠀⡀⢼⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡤⣠⣤⡄⠀⠀⠀⢹⣿⣆⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠙⠁⣴⣶⠀⡤⠀⠀⠀⠻⣿⣦⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠗⠀⠀⠼⣿⡅⠴⠀⠀⠀⠀⠸⢿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀⠀⣀⣀⣀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⣠⠄⠀⢉⡀⠀⠀⢰⡄⠀⠒⠂⠀⠀⠀⠀⡇⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⣉⣉⣈⣽⣿⣿⣄⡀⢠⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⢰⣶⣾⣆⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣶⣶⣶⣶⣷⣿⣷⣶⣶⣷⣶⣶⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⡿⠸⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠙⣷⠀⠀⣴⣶⣤⠀⣤⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠙⣧⣀⡹⠿⠿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣾⣿⣿⣿⣶⣿⡆⠀⠀⠀⢸⣷⣦⠈⢷⡀⠛⣿⣿⣿⣿⣿⣿⣿⠖⠂⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⢸⣿⠏⠀⣼⠇⢠⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⡟⠀⣸⡟⢀⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⡏⠀⣰⡟⢠⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣤⡍⠀⣰⠟⢠⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢲⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣶⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣰⣿⠿⣿⣿⣿⠿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢰⣿⡟⠀⠀⠀⠀⠀⢿⣿⡆⠀⠀⠀⠀⠀⢀⣰⡄⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣀⣀⣀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣶⣶⣶⣶⣶⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠉⠉⠹⣿⣿⡏⠉⢹⣿⣿⠏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠷⠶⣶⠿⢷⠶⠼⠿⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[29A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠦⠀⡷⢒⣿⣿⣂⣶⣆⣶⣾⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠸⣿⠇⠀⢰⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠁⣾⣿⡗⢿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣤⣿⣿⣿⣿⣷⣷⣶⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠘⠿⠃⠀⠹⠿⠇⠀⠀⠀⠀⠀⠰⠶⠄⠀⠀⠀⠠⠄⠤⠄⠀⠤⢤⣬⣿⣿⣿⣿⣿⣿⣟⡙⠛⠉⢉⣿⣿⣷⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣙⠿⣿⣿⣿⠋⠀⣿⣷⣿⣿⣿⢿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠛⣿⣯⣾⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡟⠁⢐⡄⠻⢿⣿⣿⣷⡄⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⢰⡏⠄⠸⣿⣿⣿⣿⣄⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠈⠘⠀⢀⣿⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⣦⣤⠁⠀⠀⠈⣹⡂⠛⢿⣿⣧⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⣷⣖⡆⠀⠀⠀⠈⠹⠇⠀⠀⠹⣿⣧⡀⠀⢠⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⠶⢼⡅⠀⠀⠂⠀⠈⠁⠀⠀⠀⠈⢿⣿⣀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⣀⣀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠑⠐⠀⡃⠀⠀⢂⠀⠀⠀⠀⢸⡆⠀⠐⠂⠀⠀⠀⠀⡃⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣁⣁⣀⣬⣿⠼⠄⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⣶⣶⣦⠀⠀⢃⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣶⣶⣷⣷⣶⣿⣷⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⡟⠀⠲⣌⠁⠸⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠙⣧⡀⠙⣧⠀⠀⠀⣐⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠈⢳⡄⠈⢷⡀⢀⡨⠿⠿⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢰⣿⣿⣶⠄⢹⡄⠘⣿⣿⣿⣿⣿⡿⠃⠂⠀⠀⢀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⣾⣿⣿⡟⠀⢸⡏⢀⣿⣿⣿⣿⣿⡇⠀⠁⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢰⣿⣿⡿⠀⢠⡿⠁⣾⣿⣿⣿⣿⠏⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣸⣿⣿⠃⠀⣾⠃⣼⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⢸⣿⣿⠃⠀⣼⠃⢰⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢰⣿⣿⣿⣿⣾⣿⣶⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣰⣿⠿⣿⣿⣿⠿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢰⣿⡟⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⠀⢀⢲⣌⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣀⣀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠉⠉⠹⣿⣿⡏⠉⢹⣿⡿⠏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

[29A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠒⠀⠲⡦⣸⠟⣶⣶⣆⣶⣴⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠀⠀⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠅⠀⠀⠁⠀⠀⠀⣾⣿⣿⠫⣿⣿⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⣺⣿⣷⣿⣿⣧⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠻⠟⠀⠀⠐⠲⠆⠰⠶⠦⠀⠀⠀⠠⠤⠤⠤⠄⠤⠤⣭⣿⣿⣿⣿⠋⠛⠋⠉⣹⣿⣿⣶⣦⣤⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣝⣻⡟⠁⢰⣶⣼⣿⣿⣿⠟⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⢸⣿⣶⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠿⠿⣿⣿⣟⣽⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠒⠀⢿⣿⣷⠙⣿⣿⣿⣿⣿⣆⠀⠀⢴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠘⡟⣿⡇⠸⣿⣿⣿⣿⣿⣦⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⠀⠀⠀⠀⠀⠀⣧⢸⣿⠀⠈⠉⠻⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡍⠀⠀⠀⠀⠈⠀⠹⣦⣿⠀⠀⠀⠀⠘⢿⣿⣷⡀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢗⣀⣀⠀⠀⠀⠀⠀⠀⢹⣿⠁⠀⠀⠀⠀⠀⠙⢿⣷⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⢘⢋⡐⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⠀⠀⢀⠀⠀⠿⣿⣇⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠘⡇⠀⠀⠂⠂⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⣀⣀⣠⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣶⡖⠂⠀⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⠀⠀⠀⠀⠈⣷⡀⠀⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠘⣷⡀⠸⣯⠀⠀⠀⠀⠀⠀⠀⢠⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⣿⡀⠒⠂⠀⠀⠀⢀⣀⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠹⣧⣼⣽⣿⣿⣿⣿⣿⣿⣿⡟⠂⠀⠀⠀⢀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⡆⠀⢹⡇⢻⣿⣿⣿⣿⣿⣿⡏⠀⠁⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⢀⣾⠇⠀⣼⡇⢸⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⣴⣿⡿⠀⢰⡿⠀⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⣠⣾⣿⣿⠁⠀⣾⠃⣰⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⣠⣾⣿⣿⣿⣟⠀⣼⣿⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣰⣿⠿⣿⣿⣿⠿⣿⣆⠀⠀⠀⠀⠀⠀⠐⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢰⣿⡿⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⠀⠀⢰⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⢀⠀⢀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣷⣶⣶⣷⣶⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

[29A⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡀⠀⠠⣦⢠⡾⢧⣴⣄⣾⡤⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⢸⣿⣿⡱⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⣻⣿⣿⣿⣿⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠘⠿⠀⠀⠀⠐⠶⠀⠶⠶⠀⠀⠀⠀⠤⠠⠤⠀⠠⠤⣬⣿⣿⣿⠉⠋⠋⢉⣽⣿⣿⣶⣤⣤⣤⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣽⠋⠀⣾⣦⣿⣿⣿⣿⣿⠟⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡿⠛⢿⣿⣿⡟⠯⢿⣻⣯⣽⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠆⢠⡿⣿⣿⡄⠊⠙⢻⣿⣟⣿⣿⣦⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⡇⢿⣿⣿⠂⠀⠸⣿⣿⣿⣿⣿⣧⡀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⣷⠘⣿⣿⠀⠀⠀⠈⠉⠻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠀⠀⠀⠀⠀⠀⢰⣆⠹⣿⡆⠀⠀⠀⠀⠀⠈⠻⣿⣿⡄⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠈⠻⣷⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠀⠀⢰⡄⠀⠀⠀⠀⠻⣷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣄⠀⠀⢸⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⣸⡗⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣇⡀⠈⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢸⣯⠄⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⢠⢷⠀⠀⠀⠄⠀⠀⠀⠘⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠉⠉⠀⠰⠀⠀⠀⠀⠀⣸⣷⣄⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣶⣶⣶⣶⣶⣦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⡇⠀⠀⠀⠀⠀⣿⠀⠀⠰⣾⣿⡿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⠀⠀⠀⠀⠀⠒⠀⢀⠀⠀⠀⢹⡇⠀⠈⠀⠠⠀⡶⠆⠒⠒⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣾⣿⣿⣿⡟⠿⠂⠀⠀⠀⠀⢐⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠘⣧⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⣿⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⢀⡀⠀⢻⡆⢸⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠀⠀⣀⣴⣿⣷⠀⠸⣇⢸⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣷⣾⣿⣿⣿⣿⡆⠀⣿⣾⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣰⣿⠿⣿⣿⣿⠿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣻⣯⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢰⣿⡟⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⠀⠀⢴⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠉⠈⠹⣿⣿⡏⠉⢹⣿⡿⠏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

[29A⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡂⠀⠀⢀⣸⣶⣿⣶⣤⣤⡀⣠⣰⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠷⠀⠀⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⢹⣿⣿⢏⣹⣿⣿⣷⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣾⣿⣯⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠻⠇⠀⠀⠴⠶⠀⠲⣶⠦⠀⠀⠀⠠⠄⢤⣄⣀⡤⣤⡟⠙⠛⠋⢙⣻⣿⣿⣿⣿⣷⣤⣤⣠⣠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡟⠉⢀⣶⣶⣿⣿⣿⣿⢿⣿⣿⣿⠿⠖⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠟⠛⢻⣻⣿⣿⠋⠙⠙⠛⢽⢿⣻⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠘⣗⣿⣿⣦⠀⠀⠀⢠⠀⠙⣽⣿⣿⣿⣿⣄⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⡟⣛⠃⠀⠀⠘⣿⣿⣿⣿⣿⣆⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠻⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡎⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠛⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠙⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡤⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⡀⠀⢀⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠐⢀⠟⠀⠀⠀⠀⠀⠈⠻⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣂⠀⠉⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠈⠁⠙⠛⠃⠀⠀⠀⠀⠀⣴⣿⣿⠧⠀⠀⠀⠀⠀⠀⡀⠘⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠢⠀⠀⠀⠀⠁⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠴⣻⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢘⡻⠿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⠀⠀⠀⢸⡇⠀⠀⠀⢺⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢠⠴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠾⠟⠂⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠘⣷⠠⠆⠀⠀⠄⢠⠖⠐⠒⠃⠀⠀⠀⠀⠀⠠⠶⠶⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠸⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣇⠄⠀⠀⠀⢸⣿⣿⣷⣾⣿⣿⣿⣾⣿⡿⠷⠀⠀⠀⠀⢰⡖⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣧⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⣿⠸⣄⣰⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢨⣿⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣷⣦⣺⣿⢀⣾⣿⣿⣿⣿⣿⣿⣿⢗⠆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣰⣿⠿⣿⣿⣿⠿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢰⣿⡿⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⠀⢀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⢀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣷⣶⣶⣶⣶⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

[29A⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⢸⢲⡿⠶⣤⣄⡀⠠⣠⣲⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠷⠀⠀⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⢹⣿⣿⠍⣹⣿⣿⣷⡵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣶⣿⣯⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠻⠇⠀⠀⠠⠶⠀⠰⡶⠆⠀⠀⠀⠠⠄⢠⣄⠀⠀⣤⡟⠙⠉⠋⢉⣻⣿⣿⣿⣿⣧⣤⣤⣠⣠⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡞⠉⢀⣶⣦⣿⣿⣿⣿⢿⣿⣿⣿⠓⠒⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠟⠛⢻⣻⣿⣿⠋⠙⠙⠛⠭⠉⢹⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠘⣗⣿⣿⣆⠀⠀⠀⢀⠀⠐⢽⣿⣿⣿⣿⡄⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⡟⣒⠁⠀⠀⠘⣿⣿⣿⣿⣿⣆⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠻⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡎⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠛⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠙⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡤⠀⠀⠀⠀⠀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⡀⠀⢀⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠀⢀⠟⠀⠀⠀⠀⠀⠈⠻⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣂⠀⠉⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠙⠃⠀⠀⠀⠀⠀⣴⣿⣿⠆⠀⠀⠀⠀⠀⠀⡀⠘⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠁⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠴⣻⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢘⠻⠿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠟⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠈⣷⠠⠆⠀⠀⠀⢠⠖⠐⠒⠃⠀⠀⠀⠀⠀⠠⠦⠶⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠈⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡇⠀⠀⠀⠀⢸⣿⣿⣷⣾⣿⣿⣿⣶⣾⡿⠗⠀⠀⠀⠀⠰⡖⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣧⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢰⣿⠸⡄⣰⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢨⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣻⣿⣷⣆⢸⡿⠀⣼⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⡻⣻⣿⣿⣼⣇⣠⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡻⣾⣿⠿⢿⡿⢿⣿⣿⣿⣿⣿⣿⠀⡀⠀⠀⠀⠀⢀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣀⣤⣤⣴⣴⣦⣤⣤⣤⣤⣤⣴⣶⣶⣦⣴⣶⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣯⣈⣽⣧⣬⣟⣛⣻⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠁⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

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

[29A⠀⠀⣼⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠲⠤⢿⡄⠀⡀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⣼⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠀⠀⠰⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢾⣿⡌⠛⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠹⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣧⣥⡘⣷⠐⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠘⠛⠀⠀⠀⠠⠄⠀⢶⡶⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠉⠉⠉⣉⣿⣿⣾⣆⣿⣷⣶⡄⣀⠀⢀⢐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠉⠀⣰⣦⣰⣿⣿⡿⠁⠀⠹⣿⣿⣿⠖⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣾⣿⣿⣿⣿⣿⣿⠷⡄⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠿⠛⠻⡝⣿⣿⡟⠋⠉⠛⠃⠀⠁⠀⠰⣄⠹⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠀⠀⠀⠀⠘⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢫⣷⣝⣿⣿⣆⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠉⠿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠓⠂⠘⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣆⠀⠀⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠘⠿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠃⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠈⠻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠈⠻⣷⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠗⡀⠀⠀⠀⠀⢸⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡄⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡆⠀⠀⠀⠀⠉⠛⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣇⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⣇⣦⣬⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⡸⠻⣿⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠠⡻⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠈⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠿⠆⠀⠀⢸⡇⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠰⠀⠀⡴⠂⠐⠀⠀⠀⠀⠀⠀⠠⢾⠿⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⠇⠀⢠⣄⠀⠀⠀⠘⣿⣿⣿⣾⣶⣶⣾⣷⣶⠶⠆⠀⠀⠀⠐⠂⢀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⣀⣀⡀⢀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣼⣀⣠⣿⣃⢀⣀⠀⣀⡿⣿⣿⣿⣟⣿⣿⣿⢟⣀⢀⣀⢠⣶⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⡆⣿⡟⢳⣿⢻⣿⢸⣿⣿⣸⣿⣿⣿⢸⣿⡿⠇⣿⡟⢻⠏⣿⣼⡟⣾⡟⣿⣾⣿⣿⣿⢸⢸⣿⣾⣿⣼⣿⣾⣿⣷⢸⣿⣼⣿⢻⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⡆⣿⡟⢻⣿⢨⣭⣸⣿⣿⡿⣿⣿⣿⢨⣿⣿⡆⣿⡟⠃⠀⢹⣿⠁⣿⡇⣿⡿⣿⣿⣿⠈⠸⣿⣿⣿⣿⡇⣿⣿⣿⣸⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠃⠛⠛⠋⠻⣿⣛⣟⣋⣛⣃⣻⣿⣻⣼⣻⢿⡃⠛⠛⠃⠀⠘⣛⣼⣟⣿⣟⣥⣿⣿⠛⠀⠀⠛⠛⠙⠛⠃⠛⠛⣛⣛⣻⣛⣻⣾⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⢀⣤⣤⣄⣠⣤⣤⡀⣠⣤⣝⢛⣯⣽⡿⣻⣿⣿⢿⣿⣿⣿⣯⣥⡄⠀⣤⣤⡰⣿⣿⣿⢿⣿⣿⣿⡯⣠⣤⣄⢠⣤⢠⣤⣤⣤⣤⣻⡿⣿⣿⣿⡿⣿⣿⣟⢿⣿⣿⡻⣿⣿⣟⣿⣿⣿⣿⣿

⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢸⣿⠹⠿⣿⣿⣿⢷⣿⣿⣿⣼⣿⣿⡃⣿⡏⣿⣿⣿⣯⣍⣿⣏⣁⣰⣿⣿⡇⣿⣿⣛⣾⣟⣿⣿⠃⣿⣿⣿⣾⣿⢸⣿⣿⣿⣿⢯⡇⣿⣯⣿⢻⣿⣿⣿⢻⣿⣟⠛⣿⣿⣛⣿⣿⣿⣿⣿

⠀⠀⠀⢸⣿⢿⣿⣿⣿⣿⢸⣿⣰⣶⣿⣿⣿⡟⣿⣿⣿⢳⣾⣿⡷⣿⣇⣿⢿⣿⣿⡿⣿⡿⠿⢻⣿⣿⣷⣶⣿⣿⣾⣿⢹⣿⠀⣿⣿⣿⢿⣿⣸⣿⣿⣿⣿⡏⡇⣿⣏⣿⡿⣿⣿⣿⢰⣾⣿⡗⣶⣿⣿⣘⣻⣿⣿⣿

⣀⣀⣤⣬⣭⣬⣥⣭⣭⣭⣤⣽⣯⣥⣭⣭⣭⣥⣭⣿⣽⣾⣽⣯⣷⣮⣿⣿⣾⣭⣿⣧⣍⣡⣤⣌⣉⣈⣩⣯⣿⣽⣿⣿⣮⣭⣶⣭⣿⣭⣶⣽⣿⣷⣯⣭⣭⣽⣿⣯⣭⣽⣷⣯⣿⣵⣿⣽⣯⣷⣯⣿⣽⣯⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

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

[29A⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠐⢲⠆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣾⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⣀⣰⣿⡿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣿⣿⡄⠀⠀⠀⠡⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠻⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠘⠃⠀⠀⠠⠤⠀⠠⢤⡆⠀⠀⠀⠀⠀⡰⠛⠙⠛⠋⢛⣿⣿⣷⣶⣶⣾⡀⣻⣶⣦⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢼⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⣤⡀⣴⣿⣿⣯⠁⠈⠃⠀⠀⠻⠿⠿⠖⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣶⣶⣿⣿⣿⣿⣿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠈⣧⣬⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡿⢿⢻⣿⣿⠿⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠈⠙⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠌⠀⢠⠀⢈⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⣿⣷⡀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠙⢿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⣸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣄⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠹⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠢⠀⠀⢀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢤⡀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣧⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⠁⠙⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠃⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠢⠀⠀⠀⠂⠈⠁⠛⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠰⢿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⢹⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠂⠀⠆⠀⠄⠀⢤⠀⢠⠶⠀⠂⠀⠀⠀⠀⠀⣀⠾⡿⠷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⢰⠃⠀⠀⣰⣿⣿⣷⣄⠀⠀⠀⠙⣿⣿⣿⣷⣶⣶⣶⣶⣾⠄⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣶⣶⣶⣶⣶⣶⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⣀⣀⡀⢀⣘⡿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣋⠀⣀⣰⣿⣿⣿⣿⣃⠀⣀⡀⢠⣿⣿⣿⣿⣿⣿⢟⣿⢂⣀⢀⣀⣴⣶⣶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⣿⡆⣿⡟⢳⣿⢻⣿⢸⣿⣿⣸⣿⣿⣿⢸⣿⡿⠇⣿⡟⢿⣏⣿⣼⡟⣾⡟⣿⣾⣿⣿⣿⢸⢸⣿⣾⣿⣼⣿⣾⣿⣷⢸⣿⣼⣿⢻⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⣿⡆⣿⡟⢻⣿⢨⣭⣸⣿⣿⡯⣿⣿⣿⢨⣿⣿⡆⣿⡟⣿⣿⢹⣿⠁⣿⡇⣿⡿⣿⣿⣿⢸⡿⣿⣿⣿⣿⡇⣿⣿⣿⣸⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠃⠛⠛⠋⡻⣿⣛⣛⣋⣛⣃⣻⣿⣛⠘⠻⠟⣣⣛⣛⣿⡿⠘⠛⠀⠙⣿⣟⣥⣿⣿⣻⣿⡇⠛⠛⠙⠛⠃⠛⠛⣛⣛⣻⣛⣻⣾⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⢀⣤⣤⣄⣠⣤⣤⡀⣠⣤⣝⢛⣯⣽⡿⣻⣭⣿⢿⣯⣤⣤⣤⣿⣿⡿⣿⣿⣶⣤⣤⣼⢿⣿⣿⣿⡿⣻⣭⣅⢠⣤⢠⣤⣤⣤⣤⣻⡿⣿⣭⣿⠿⣿⣿⣟⢿⣿⣿⡻⣿⣽⣟⣿⣿⣿⣿⣿

⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢸⣿⠸⠿⣿⣿⣿⢷⣿⣿⣿⣸⣿⣟⡃⣿⡏⣿⣿⣿⣯⣉⣿⡏⣿⢰⣿⣿⡇⣿⣿⣛⣾⣟⣿⣿⠃⣿⣿⣿⣾⣿⢸⣿⣿⣿⣿⢯⡇⣿⣯⣿⢻⣿⣿⣿⢻⣿⣟⠛⣿⣿⣛⣾⣿⣿⣿⣿

⠀⠀⠀⢸⣿⢿⡿⣿⣿⣿⢸⣿⣰⣶⣿⣿⣿⡟⣿⣿⣿⢱⣾⣿⡷⣿⣇⣿⢿⣿⡿⠏⣿⡇⣿⢸⣿⣿⣷⣶⣿⣿⣾⣿⢹⣿⡶⣿⣿⣿⢿⣿⣸⣿⣿⣿⣿⡏⡇⣿⣏⣿⡿⣿⣿⣿⢰⣾⣿⡗⣶⣿⣿⣘⣻⣿⣿⣿

⣤⣤⣤⣬⣭⣬⣥⣭⣭⣭⣤⣽⣯⣥⣭⣭⣭⣥⣭⣿⣽⣾⣽⣯⣷⣮⣿⣽⣬⣭⣥⣤⣍⣉⣉⣭⣽⣮⣭⣍⣿⣽⣿⣿⣮⣽⣿⣯⣿⣭⣶⣭⣿⣥⣭⣭⣭⣿⣿⣭⣭⣭⣶⣯⣿⣵⣾⣽⣯⣷⣯⣿⣽⣯⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

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

[29A⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠐⠀⢠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠄⠀⠀⠀⣀⣀⠀⠀⠀⢽⣿⣧⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠛⠀⠀⠀⠤⠤⠀⠶⣶⠄⠀⠀⣠⠞⠻⠿⠛⠻⣷⣦⣭⣽⣿⣶⣤⣦⡆⢸⣿⣦⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢠⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⣠⡀⣠⣾⣿⣏⣀⣀⡀⠀⠈⠀⠀⠘⠟⠿⠓⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤

⠆⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣎⣤⣤⣿⣿⣿⣿⣿⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠩⣤⡜⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⡿⠟⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠈⠿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠛⠩⠹⠟⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠁⠀⠠⠄⢠⣿⣿⡆⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣦⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠃⠀⠀⠤⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡄⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠀⠀⠉⣼⣿⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣄⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠘⠃⠀⠾⠷⣶⣤⠀⠙⠻⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠐⠚⠛⠂⠘⠛⠀⡠⠀⠀⠀⣠⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠀⠀⠁⠀⠐⠂⠿⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠨⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣢⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠂⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⡱⢿⠿⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾⣿⣿⣿⣿⣿⣿⡟⣾⠀⠀⠀⣼⣿⣿⣿⣷⣤⠀⠀⠀⠙⣿⣿⣿⣿⣷⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⣀⣀⡀⢀⣘⢿⣿⣿⣿⣿⣿⣿⣿⡿⣷⣃⠀⣀⣸⣿⣿⣿⢿⣿⠇⣀⡀⠀⣀⣿⣿⣿⣿⣿⣿⣿⢏⣈⢀⣀⣠⣤⣴⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⣿⡆⣿⡟⢳⣿⢻⣿⢸⣿⣿⣸⣿⣿⣿⢸⣿⡿⠇⣿⡟⢿⣏⣿⣼⡟⣾⡟⣿⣾⣿⣿⣿⢸⢸⣿⣾⣿⣼⣿⣾⣿⣷⢸⣿⣼⣿⢻⣿⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⣿⡆⣿⡟⢻⣿⢨⣭⣸⣿⣿⡿⣿⣿⣿⢨⣿⣿⡆⣿⡟⣿⣿⢹⣿⠁⣿⡇⣿⡿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡇⣿⣿⣿⣸⣿⣿⣿⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠃⠛⠛⠋⡻⣿⣛⣟⣋⣟⣃⣻⣿⡛⠘⠻⢿⣣⣛⣛⣿⣿⣿⡛⠀⠙⠿⢟⣥⣿⣿⣻⣿⣷⡛⠛⠙⠛⠃⠛⠛⢛⣛⣻⣛⣻⣞⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⢀⣤⣤⣄⣠⣤⣤⡀⣠⣬⣝⢛⣯⣽⡿⣻⣯⣿⢻⣥⣤⣤⣽⣿⣿⡿⣿⣿⣿⣷⣤⣄⢀⣾⣿⣿⡿⣻⣿⣟⢣⣤⢠⣤⣤⣤⣤⣸⣿⣿⣿⣿⠟⣻⣿⣟⢿⣿⣿⡻⣿⣿⣟⣿⣿⣿⣿⣿

⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢸⣿⠸⠿⣿⣿⣿⢷⣿⣿⣿⣸⣿⣿⡃⣿⡏⣿⣿⣿⣯⠉⣿⡏⣿⣷⣿⣿⡇⣿⣿⣛⣾⣟⣿⣿⢃⣿⣿⣿⣾⣿⢸⣿⣿⣿⣿⢧⡇⣿⣯⣿⢳⣿⣿⣿⢻⣿⣟⠛⣿⣿⣛⣿⣿⣿⣿⣿

⠀⠀⠀⢸⣿⢿⣿⣿⣿⣿⢸⣿⣰⣶⣿⣿⣿⡟⣿⣿⣿⢱⣾⣿⡷⣿⣇⣿⢿⣿⣿⣇⣿⡇⣿⢹⣿⣿⣷⣶⣿⣿⣾⣿⢹⣿⡶⣿⣿⣿⢿⣿⣸⣿⣿⣿⣿⡇⡇⣿⣏⣿⡿⣿⣿⣿⢰⣾⣿⡇⣶⣿⣿⣘⣻⣿⣿⣿

⣤⣤⣤⣬⣭⣬⣥⣭⣭⣭⣤⣽⣯⣥⣭⣭⣭⣥⣭⣿⣽⣾⣽⣯⣷⣮⣿⣭⣬⣭⣥⣍⣉⣽⣿⣯⣽⣮⣽⣯⣿⣭⣻⣿⣮⣽⣿⣯⣿⣽⣦⣭⣿⣥⣭⣭⣭⣵⣿⣯⣭⣽⣷⣯⣿⣵⣾⣽⣯⣷⣯⣿⣽⣯⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠈⠉⠈⠀⠈⠉⠉⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

[29A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡿⠯⠹⠛⠿⠟⠆⠀⠀⠀⠀⠁⠀⠀⠀⠄⢀⠀⠀⠐⣴⠤⣤⣔⢴⢶⢿⣞⣻⣟⣿⣿⣻⣿⣼⣿⣟⠾⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠿⠋⠂⠀⠀⠀⠀⠀⠘⠂⠠⣴⠵⠀⠀⢻⡿⠗⠈⠀⠀⠀⢈⠋⠀⠀⢸⣷⣭⠏⣩⣽⡿⣿⣯⣿⣿⣿⣿⣿⣽⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢒⡀⢀⠀⠀⠁⠂⠀⢘⢳⢴⣾⣏⣃⡠⣠⠒⠛⠨⣿⣻⣿⣿⣿⢻⣾⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠠⠀⠀⠖⣢⠈⣸⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠙⠛⠁⠀⠻⠿⠋⢰⣶⣶⣿⣶⣾⡿⢻⡟⠿⠿⣿⣿⣤⣴⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⣶⣦⣴⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠨⠠⠠⣧⢠⡄⢸⣿⣷⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠚⠛⠓⠼⣿⠇⢀⣤⣀⣾⣿⣿⠟⣙⣉⣀⣉⣙⣿⡿⢿⣟⣯⡻⣿⣿⣿⡟⠿⠿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠠⣶⡼⢿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣤⣼⣿⣿⣿⣿⣿⡄⠈⠛⠛⠟⠋⠉⠀⠀⠊⢿⣿⡉⢻⢿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀

⠀⠀⠀⠀⠈⠘⢿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢛⣻⣿⢠⡀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⡠⢄⣼⣿⣿⣿⣿⣿⡿⠿⡁⠂⠀⠀⠁⠀⡖⠶⠀⠐⢰⣿⣿⣿⣈⠻⣷⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠘⣭⣏⣬⠏⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣠⣾⣿⡟⠻⣻⣿⣿⡗⣂⠁⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢰⠗⠉⠞⢄⢀⣸⣶⣆⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀

⢐⣠⣤⡄⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠺⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⣽⠂⠙⠇⠀⢿⡏⣿⠿⠿⠿⠿⡯⠄⠿⢿⠿⠿⠿⠟⠛⣺⠀⠀⠀⣽⣿⣿⣿⣿⣦⠀⠘⡿⠀⠀⠀⠀⠀⠀⠀⠀

⠐⠹⣿⣏⡀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣄⠀⠀⠀⠀⠀⠀⢡⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢹⠟⠃⢤⢠⣄⣿⡇⠿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠉⠻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣦⠀⠀⠀⠀⠀⠀⢹⠂⠀⠀⠀⠀⠀⠀⠀⠀⢈⠼⠀⢀⠀⡼⠛⠻⣤⣼⣠⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠶⣦⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡄⠀⠀⠀⢸⡄⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠀⠙⠊⠀⠀⠀⠉⠉⠛⠳⠶⠶⣤⣧⣄⡀⠀⠀⠀⠀⠀⠹⠰⠄⠀⠀⠀⠀⠀⠀⠙⢿⣿⣄⠀⠀⢸⡇⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠈⠈⠡⠁⢀⡦⣤⡀⠀⠀⠻⣿⣿⣿⠿⠂⠀⢀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢻⣿⣇⡀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢿⢿⣿⢃⠀⠀⠀⠎⡅⢠⣈⠙⠋⡁⠀⠀⠀⠤⡏⠁⢀⢤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠐⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠒⢠⣆⠀⠀⠀⡿⣿⡆⢾⣧⠄⠆⢀⣈⡇⠒⠉⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡗⠀⠀⠀⢠⡾⢿⡀⢼⡗⣶⠴⠛⠁⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢁⣼⡇⠀⡀⠀⠍⣿⣿⣿⣿⣟⠟⠀⠂⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣶⠒⣴⡿⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡀⠀⠀⠀⡀⠀⢀⣀⡀⠀⠀⣿⡦⡀⠀⠁⠐⠀⢺⣿⣛⣩⣼⡿⣻⡖⠃⣿⢆⣐⡾⠦⠷⠀⠸⠀⠀⠒⠂⠗⠲⠀⠀⠀⠀⣈⡿⣿⡿⣖⡋⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠑⢢⡄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡗⠀⠖⣔⣶⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠈⠁⠀⠲⠶⠿⠯⣿⠯⣿⣿⣿⡿⠿⣿⡿⡿⣿⡇⢀⡀⣾⢷⢀⠀⠀⡘⣿⣿⢿⣿⢿⣿⣿⠿⣿⣿⡿⠛⢃⠸⢿⡿⠿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠉⠄⠉⠙⢣⣯⠩⢐⢰⣿⣛⣹⣿⣏⣉⣰⣿⠿⠅⠀⠈⣿⣿⡿⡬⡆⣾⡟⠛⡿⣿⡳⠾⢿⢬⡭⠎⠙⠎⢱⠈⢉⣠⢸⣯⢸⡿⣛⣉⣹⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣤⠀⠈⠀⠇⠉⠃⠀⣨⣭⣭⡄⢮⡏⣾⣿⣞⠛⠀⠿⠇⠀⣌⣭⣩⣭⣿⣗⠚⠒⠄⠄⠃⠂⠀⠰⢨⣩⠉⠁⣿⣶⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⣉⣹⣶⣢⣤⣀⣀⣀⡆⣄⡀⠘⠨⣤⣤⣀⣛⣿⣿⣿⠛⠀⠀⠤⣠⣬⣯⡥⣨⣿⣷⣒⠊⠀⠀⠐⠀⠘⢀⣂⣀⣀⣠⣦⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⢀⢠⣤⣄⡀⡨⠝⣍⢙⡯⣽⡻⣿⢯⣛⢫⣠⣠⣾⣟⢿⣿⡿⣿⣟⣿⡤⢤⣠⠀⠿⢟⢿⡿⣻⣭⡿⢿⣠⠀⠀⠄⠤⣤⣸⣿⢿⡹⣛⣿⣯⣽⣟⡿⡏⣍⠻⢟⣹⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠠⠀⡄⠀⠃⠀⠁⠰⠀⠠⠀⢦⢤⡆⠩⠎⠑⢐⡂⠭⡇⠀⢟⣛⣻⠿⠶⠆⣿⣥⣭⣛⣇⡿⠯⠟⣤⣬⣭⣷⢳⠚⠁⠀⠉⠉⡂⠺⠀⠀⢈⠃⠗⣒⣂⣀⢶⣛⠹⣹⢭⣙⡙⣓⡙⠙⣻⣿⣯⣿⣿⣿

⠀⠀⠀⠀⠀⠃⠀⠀⠃⠀⡀⠀⠄⠐⠀⠀⠀⡄⠸⢇⣐⢤⣶⣄⣚⠉⡇⠀⢾⣿⣶⣇⣉⣓⣿⠋⠙⢒⣺⡷⠄⢸⢿⣿⣈⣁⣝⠛⠀⠀⠄⣀⣶⣶⣤⣤⡆⠇⡀⠿⠇⠬⡍⠉⠨⠀⠴⢖⠖⠁⡐⠀⢙⠛⡿⣿⣿⣿

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

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

⠀⠆⠐⠄⠀⢶⠂⠐⠂⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[29A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠟⠛⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠗⠂⣾⣿⣾⣿⣶⣾⣶⣶⣶⣷⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠰⠆⡠⠿⠂⠀⠸⠿⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⣿⠃⠀⠀⠬⠽⢨⠉⣿⣿⣿⢻⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⣀⣺⣏⣀⡠⠈⠀⠀⠀⠀⠀⠀⢮⣿⣿⣿⡜⠵⢿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠘⠛⠃⠠⣶⣶⣾⠟⠿⠛⠛⢿⣿⣶⣤⠤⢤⡤⢤⠤⣶⣿⣿⣿⣿⣾⣾⣿⣿⣿⣷⣶⣶⣴⣦⣤⣧⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢠⣄⠀⣼⣷⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡟⠀⢴⣤⣰⣿⣿⡿⠀⠀⠀⢀⣀⣀⣀⣀⣨⣏⠅⣽⣯⡉⠘⣿⣿⡿⠛⠛⠛⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢤⣶⠿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢲⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣠⣶⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠘⠛⠛⠉⠁⠀⠀⠀⠀⠛⠀⠈⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠀⢶⡀⠿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠐⢭⣭⡤⠟⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠉⠉⠩⣽⡿⠀⠐⣓⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠁⡀⣀⣿⣶⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀

⠀⠀⣠⡀⣠⣤⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣬⠀⠈⠀⠦⠀⣹⢷⠀⠽⠿⠿⠿⠿⠧⠄⠀⠐⠾⠟⠛⠛⢋⣉⡇⠀⠀⢠⣿⣿⣿⣿⣧⡀⠀⢙⠀⠀⠀⠀⠀⠀

⠀⠠⠿⠉⢿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡹⡅⠀⠀⠀⡼⢿⣿⡆⡇⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣧⡀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⣼⠷⠀⢀⠄⢙⠀⠂⠉⠳⣮⡄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⠀⠀⠀⢠⣆⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⢐⠛⠂⡭⠀⢀⠀⠀⠀⠛⠲⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⡀⠀⠸⡿⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠈⠀⠀⠐⠀⠛⠀⠀⠀⢀⠀⠀⠈⣩⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⡿⠟⢃⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⠀⠀⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘⣶⣼⡀⠀⠀⡗⢲⡄⡆⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⣠⣾⣿⣷⣏⣀⣸⣟⡛⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣤⡀⢠⡾⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⣆⠀⠀⠀⢀⠀⠀⠀⠀⠀⠸⡇⠀⢀⣿⣯⢿⣿⣷⣂⡙⣋⣀⡿⠿⡇⣀⣐⡃⠀⠺⠀⠀⠀⠠⠆⠠⣴⠂⠘⠚⠀⠀⠀⠀⢀⡰⠿⠿⢶⡂⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⢾⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣛⣸⢇⣘⢛⣹⣿⣿⣿⣿⣿⣿⠿⣿⣿⡿⣿⣿⣯⣹⢿⣿⣿⡿⢿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠏⠉⠇⠉⡙⢣⣿⠭⢵⢰⣿⣻⣹⣿⣿⣛⣰⣿⠿⠇⠉⡍⠃⠈⣿⡮⡟⣿⡟⠻⡿⣿⣻⣿⣿⣿⣿⣎⣙⠜⢻⠈⢩⡨⢸⣿⢼⣿⣻⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡆⠀⠂⠠⠤⢠⣤⠨⠍⠀⡇⣭⣽⢀⣨⣭⣭⡆⣾⡏⣣⣆⢸⣿⢀⣿⡇⠒⣿⣿⣽⣿⣽⣷⠾⠛⣭⠿⠇⠂⠀⠰⢨⣩⠉⠁⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠚⠒⠂⠀⠈⣉⣻⣶⣲⣥⣔⣀⣠⣆⣅⣜⣼⠩⠥⢂⣓⣛⣿⣿⡜⠛⠘⣯⣿⣿⣿⣯⣵⣪⣿⣿⡛⠋⠈⠉⠐⠀⠈⠀⠂⣘⣒⣶⣵⣒⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⠀⠄⠤⠀⠀⠀⣀⠤⠤⢄⢠⣤⣤⡀⣨⣭⣽⢝⣿⣿⡻⣿⣿⣿⣿⣿⣭⣤⣬⣿⣿⡿⣿⣿⡷⣠⣤⣹⢿⣿⣟⢿⡿⣿⣿⣟⢡⣤⠠⢄⡤⢄⣤⡀⠀⣿⣿⣟⣿⣿⣿⣿⣿⡏⣿⡻⢿⣻⣟⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠌⠢⠀⡄⠀⠀⠀⠀⠰⠀⠘⠄⢦⣶⡎⠩⠎⠑⢹⡓⣿⡇⠈⢿⣿⣻⡟⣶⡆⣼⣷⣿⣛⣇⣿⣯⡿⣾⣯⣭⣷⢳⣿⠁⠀⠈⠉⡀⠺⠀⠀⢀⠇⠀⣛⣋⣀⢾⣿⠿⣹⢻⣿⣝⢓⡻⢝⣻⣿⣿⣿⣿⣿

⠀⠀⠀⢀⠀⠃⠀⠀⠃⠀⡀⠀⠈⠱⠀⠰⠀⠄⠸⢇⣐⢴⣶⣄⣣⢭⡇⠀⢶⣿⣾⣆⣉⣏⣿⠹⠭⢶⣷⡷⡖⠨⢿⣿⢨⣭⣝⠛⠀⠀⠄⣀⣶⣶⣤⣤⡆⠇⡀⣿⣇⣬⣏⣉⡨⠀⢴⣖⠖⠑⡶⢆⢙⠙⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁⠉⠁⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠆⠐⠀⠀⠶⠀⠰⠆⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[29A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠋⠙⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣿⣷⠟⠲⡶⣿⣿⣿⡆⣧⣠⣶⡶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠚⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠅⠀⠀⠈⠙⠟⠉⢹⣿⣿⣾⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⠀⢀⣠⣤⣤⣄⣀⠐⠆⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⡏⠇⠻⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣼⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠛⢳⠋⠉⠉⠉⠛⣻⣷⣦⠀⠠⠤⠤⠤⠤⣤⠤⡤⢴⣾⣿⣿⣿⣶⣷⣿⣿⣿⣿⣶⣦⣤⣤⡤⣼⠄⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣄⣠⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠏⠀⢰⣦⣴⣿⣿⡟⠂⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣈⣀⣼⡥⠹⠿⡉⠈⠻⣿⡿⠛⠛⠛⠃⠉⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠠⣴⡿⢿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢀⡶⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠁⠀⠀⠀⠀⠈⠀⠀⠹⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣻⡇⣀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣮⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⢰⣆⠸⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠂⣭⣡⠼⠁⠀⠀⠀⢀⢿⣿⠒⠉⠁⠸⣿⡆⠀⠀⡆⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠈⡀⠀⣸⣶⡀⠀⠀⠀⡄⠀⠀

⡀⠀⠀⠀⠀⣶⣖⣦⣤⣥⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⣦⡆⠀⠀⢠⡀⠈⣻⣧⡶⣶⡤⠀⠠⠾⠿⠟⠻⠓⠀⠀⠀⠈⠛⠚⠿⠋⡉⣩⠀⠀⠀⣼⣾⣿⣿⣧⡀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣿⢿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠙⠊⠻⣇⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⢃⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⢠⠀⠐⠀⠂⠀⠼⢧⡀⡤⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⣀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠌⠀⠀⠀⠈⠻⣧⣄⠠⣤⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠃⠀⠀⠀⠀⠀⣸⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣧⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡿⠇⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢠⣾⣿⣷⡄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡉⠈⠀⠐⣲⣀⠀⠀⠀⢀⣄⠀⠀⣿⠿⠟⠃⢀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⣰⣿⣿⡷⣀⠀⢸⠗⠀⠀⣾⢐⡣⠄⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⢻⡿⣿⠇⠀⠸⡈⢃⣘⣿⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠾⠷⣖⡒⠀⠀⠀⣀⠀⠀⠀⠘⣷⠀⠈⣿⡮⠼⠿⣿⣿⣆⣈⣋⣁⣙⡛⠓⠀⠀⠀⠀⠀⠀⠀⠖⢠⢶⠤⢠⡖⠀⠓⠃⠀⠀⠀⠀⣀⠾⠿⠷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠈⢷⡰⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣄⠐⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⣀⣀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣃⡀⢀⣀⢸⣇⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣃⢚⣻⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠉⠇⠉⡝⢣⣿⠯⢵⢹⣿⣻⣸⣿⣿⣿⢸⣿⠿⠇⡍⡍⠃⠈⣿⣮⡟⣾⡟⠻⡿⣿⣻⣿⣿⣿⣿⣎⣙⠜⢻⠈⢩⡸⢹⣿⢼⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡆⠀⠊⠣⠤⢠⣥⠸⠏⠀⣇⣭⣼⢭⣨⣭⣭⡆⣾⡏⠃⣴⢻⣿⣰⣿⡇⠒⣿⣿⣽⣿⣿⣷⣾⣛⣯⠿⠇⠂⠀⢰⢸⣻⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠚⠒⠂⠀⠈⣉⣻⣶⣲⣵⣶⣀⣠⣆⣅⣸⣾⣩⣥⡆⠓⢛⡿⠃⢘⣛⣿⣯⣿⣿⣿⣯⣵⣺⣿⣷⠛⠛⠈⠉⠐⠀⠈⠀⢂⣸⣶⣾⣿⣛⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⠄⠄⠤⠠⠀⣤⣀⠤⠤⣄⢠⣤⣤⡀⣨⣭⣟⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣏⣥⣤⡈⣿⣿⣻⣿⣿⣟⢿⡿⣻⣿⣏⢠⣤⢠⣄⡤⢄⣤⡀⠘⣿⣿⣟⣿⣿⣿⣿⣿⣯⣿⡿⢿⣿⣟⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠢⠀⡄⠹⠀⠀⠁⠱⠀⠸⠄⢤⣶⡎⠩⠎⠙⢻⡓⣿⡇⠈⣿⣿⣫⣍⣾⡷⣿⣿⣿⣛⣇⣿⣯⣟⣾⣏⣽⣷⢳⣿⠇⠀⠈⠉⠆⠺⠀⠘⢀⠇⠀⣿⣏⣊⢾⣿⠽⣽⢻⣿⣟⢟⡻⢝⣛⣿⣿⣿⣿⣿

⠀⠀⠀⢀⠀⠃⠐⠀⠃⠀⡀⠀⠈⠱⠀⠸⠀⠄⠸⣇⣘⢵⣶⣄⣳⢭⡇⠀⢾⣿⣿⣗⣿⡇⣿⣻⣿⣶⣷⡷⡖⠨⢿⣿⢩⣭⣝⠛⠀⠀⠄⣀⣷⣾⣤⣤⡆⠇⡀⣿⣇⣭⡏⣉⡨⠀⢴⣖⣖⡑⡶⢖⢛⠙⣿⣿⣿⣿

⣾⣿⣶⣶⣭⣬⣥⣭⣬⣭⣶⣽⣯⣶⣯⣽⣯⣵⣿⣿⣿⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⣭⣯⣭⣭⣭⣭⣯⣭⣿⣿⣿⣿⣿⣿⣽⣿⣶⣷⣭⣷⣯⣭⣥⣴⣷⣯⣭⣽⣷⣾⣯⣷⣾⣾⣿⣷⣿⣿⣷⣷⣾⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠁⠀⠁⠉⠉⠉⠉⠉⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠆⠒⠀⠀⠶⠀⠰⠦⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[29A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠋⠉⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣿⡷⠟⠒⡶⣶⣿⣿⡆⣦⣠⣦⡶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠀⠀⠚⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠍⠀⠀⠀⠭⠟⠉⢽⣿⣿⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⠀⢀⣠⣤⣤⣄⣀⠘⠂⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡏⠇⠻⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣼⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠛⢳⠋⠉⠉⠉⠛⣻⣷⣦⠀⠠⠤⠤⠤⠤⢤⠤⡤⢴⣾⣿⣿⣿⣶⣷⣿⣿⣿⣿⣶⣤⣤⣤⠤⣼⡄⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣀⣠⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠏⠀⢰⣦⣴⣿⣿⡟⠂⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣬⡭⠸⠿⡉⠀⠻⣿⡿⠛⠛⠛⠃⠉⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠠⣴⡶⢿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢀⡶⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠁⠀⠀⠀⠀⠘⠀⠀⠹⣵⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣻⡇⣀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣮⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⢰⡀⠸⠿⡆⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣭⣁⠼⠁⠀⠀⠀⢀⠯⣿⠒⠉⠁⠸⣿⡆⠀⠀⡆⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠈⡀⠀⣸⣶⠀⠀⠀⠀⡄⠀⠀

⠀⠀⠀⠀⠀⣲⣆⣦⣤⣤⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⣦⡆⠀⠀⢠⡀⠈⣻⣧⡶⣦⠤⠀⠠⠾⠿⠝⠻⠓⠀⠀⠀⠈⠛⠚⠿⠋⡈⣨⠀⠀⠀⣼⣷⣿⣿⣧⡀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⡿⠿⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⢙⠈⠻⣇⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⡁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣄⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣿⠁⠀⢠⠀⠐⠀⠂⠀⠼⢧⡀⡤⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⣾⣦⡀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⣀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠻⣧⣄⠠⣤⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠃⠀⠀⠀⠀⠀⣸⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣧⡀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡿⠇⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⣾⣿⣷⡄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡈⠈⠀⠐⣲⣀⠀⠀⠀⢐⣄⠀⠀⣿⠿⠟⠃⢀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⣤⣿⣿⡷⣀⠀⢸⠗⠀⠀⣾⢐⡣⠄⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⢻⡿⣿⠇⠀⠺⡈⢃⣘⣿⡸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠶⠷⣖⡂⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠈⣿⡦⠼⠿⣿⣿⣆⣈⣋⣁⣘⡛⠓⠀⠀⠀⠀⠀⠀⠀⠖⢀⢶⠤⢠⡖⠀⠓⠃⠀⠀⠀⠀⣀⠾⠿⠷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠈⢷⡰⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡀⠐⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⣀⣀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣃⡀⢀⣀⢸⣇⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣃⢊⣻⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠛⠇⠉⡝⢣⣿⠯⢽⢹⣿⣻⣹⣿⣿⣿⢸⣿⠿⠇⡍⡝⠃⠈⣿⣮⡟⣾⡟⠻⡿⣿⣻⣿⣿⣿⣿⣎⣹⠘⢻⠈⢩⡹⢹⣿⣼⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡆⠀⠊⢣⣤⢠⣥⠸⠏⠀⣯⣿⣿⣿⣨⣭⣭⡆⣾⡏⠃⣴⢻⣿⣰⣿⡇⠒⣿⣿⣿⣿⣿⣷⣾⣛⣭⠿⠇⠂⠀⢸⢸⣻⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠚⠒⠂⠀⠈⣉⣻⣾⣻⣵⣦⣀⣠⣆⣅⣹⣾⣩⣥⡆⠛⢛⡿⠃⢘⣛⣿⣯⣿⣿⣿⣯⣵⣺⣿⣿⠛⠛⠈⠉⠐⠀⠈⠀⢊⣹⣶⣾⣿⣛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⠄⠄⠤⠠⠀⣤⣀⠠⠤⣄⢠⣤⣤⡀⣨⣭⣟⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣏⣤⣤⡈⣿⣿⣿⣿⣿⣟⢿⡿⣻⣿⣏⢠⣤⢠⣄⡤⢄⣤⡀⠘⣿⣿⣟⣿⣿⣿⣿⣿⣯⣿⡿⣿⣿⣟⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠢⠀⡀⠹⠀⠀⠁⠱⠀⠸⠄⢧⣶⡎⠩⠎⠙⢻⡓⣿⡇⠛⣿⣿⣫⡉⣾⡿⣿⣿⣿⣻⣇⣿⣯⣟⣿⣯⣽⣷⢳⣿⠇⠀⠈⠉⠆⠺⠀⠘⢀⠇⠀⣿⣏⣊⢾⣿⠽⣽⢻⣿⣟⢟⡻⢝⣛⣿⣿⣿⣿⣿

⠀⠀⠀⢀⠀⠃⠐⠀⠃⠀⡀⠀⠈⠱⠀⠸⠀⠄⠸⣇⣘⢵⣶⣄⣳⢭⣇⣀⢿⣿⣿⣗⣿⡇⣿⣿⣿⣶⣷⡷⡖⠨⢿⣿⢩⣭⣟⣛⣀⡀⠆⣀⣷⣾⣤⣤⡆⠇⡀⣿⣇⣭⡏⣉⡫⠘⢴⣖⣒⡑⡶⢖⢛⠙⣿⣿⣿⣿

⣾⣿⣶⣶⣭⣬⣥⣭⣬⣭⣶⣽⣯⣶⣯⣽⣯⣵⣿⣿⣿⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⣭⣯⣭⣭⣭⣭⣯⣭⣿⣿⣿⣿⣿⣿⣽⣿⣶⣷⣭⣷⣯⣭⣥⣴⣷⣯⣭⣽⣷⣾⣯⣷⣾⣾⣿⣷⣿⣿⣵⣷⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

[29A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠟⠋⠁⠥⠃⠈⠣⠠⣀⢀⠐⣠⣀⡤⡠⡲⠲⠴⡂⠀⠀⠀⠀⠀⢀⣼⣿⡿⣿⣿⣿⣿⣿⣶⣿⣿⣥⣾⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡿⠋⠀⠀⡀⠀⠜⠐⠀⠺⠺⠘⡷⠺⠂⠘⠿⢯⡀⠍⠀⠀⠀⠀⠀⠀⠀⣸⡝⠁⣀⣿⠉⠬⣿⣻⣿⣿⣷⣿⢍⣻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠟⠉⠀⠀⢀⠀⠀⠀⠀⠠⢡⢀⠀⠀⢁⠀⠀⣠⣶⣶⣦⣤⣄⠈⡤⠀⠛⢂⠔⠿⠨⠆⠀⠀⠀⠀⢡⣿⣿⣿⣿⡸⣝⢿⢻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠒⡆⣄⣰⣄⣠⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠛⢁⣿⠋⠈⠉⠉⣋⣽⣿⣿⣶⣶⡆⢠⡤⣄⢤⡤⢠⣦⣤⣶⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣶⣶⣶⣶⣶⡧⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢐⢚⣦⣻⣿⣿⣿⠿⠋⠀⠀⠐⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣻⠁⠀⣾⣷⣾⣿⣿⡟⠀⠐⠖⠂⠀⠘⠓⠀⠀⠀⣀⣀⣀⣀⣉⣨⣿⢷⠿⢧⡁⠹⢿⡿⠟⠛⠛⠛⠛⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣴⣾⢿⣿⣿⣿⢿⣿⣷⡀⠀⠀⠀⢀⣀⠠⣀⠀⡐⢶⣶⡄⠀⠀⠀⠀⠀⢏⣴⡿⣿⣿⣿⣿⣿⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠉⠈⠀⠈⠀⠀⠀⠀⠈⢱⣷⡀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣿⣿⣿⣿⣿⣆⠀⢰⡾⠀⠀⠁⠀⠘⢛⣻⣿⢨⡀⠀⠀⣰⣿⣿⣿⣿⢿⣯⠋⠬⡁⠀⠀⠀⠐⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠒⠀⢠⡼⢿⣿⡄⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣽⣿⣿⣿⣧⡈⠀⠀⠀⠀⠀⠀⠸⣭⣍⡬⠟⠀⢸⣿⣿⠛⣊⠉⣻⣿⢀⣀⣀⣂⣀⣺⠂⠀⢸⠃⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⡂⠀⠚⡻⢇⢘⣿⣆⠀⠀⠀⢠

⢀⣀⣀⡀⠀⠀⠀⣾⣶⢿⣴⣿⡇⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠸⠟⠁⠀⠐⣯⡟⠀⡀⢡⡀⢨⣿⢺⣿⣿⣿⣾⣷⡆⠠⣽⠟⠹⠛⠿⠆⠀⠿⠶⠿⠟⢺⠏⣋⣩⡇⠀⠀⢸⣿⣿⣿⣿⣦⡀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⣿⣿⣻⣿⣿⣇⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠰⡄⠀⢰⠗⠀⠀⠀⠈⢂⠙⢿⡎⠉⠋⠋⠉⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠉⠹⢿⢿⡄⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣧⡀⠀⠀⠀⠀⠀⠙⢧⣿⡇⠐⠹⠄⠀⠀⠂⠐⣿⡀⠀⠀⠀⢤⠀⢀⡄⡀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠲⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣄⡀⠀⠀⠀⠀⡯⠎⠁⠀⠀⠂⠀⠀⠀⠀⠈⣷⣀⠀⠀⣾⣰⠀⣤⡄⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠁⠀⠀⠀⠀⠀⠻⣿⣆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠏⠀⠀⠀⣸⣭⠁⠀⠀⠀⠀⡆⠀⠀⣀⡀⠘⠻⣧⡄⠿⠞⢌⣿⡆⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠯⠂⠠⠀⣀⣌⡄⠠⠀⠘⠿⠿⣦⠀⣘⣻⣯⡀⠀⢩⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⢸⡉⠀⢄⢀⣖⠀⢀⣤⡄⢿⣿⣿⣿⠀⢾⡇⡀⠀⠀⡀⡇⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⢘⢷⣆⠴⣿⣿⣖⡾⣿⣷⠌⢻⡿⠛⠀⢸⡗⣶⠴⠊⠁⠇⠀⠀⠀⠀⠀⠀⠀⢐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣤⡤⠀⠀⢄⠀⠀⠊⢩⢻⣆⠀⢻⣿⣃⣻⣏⡙⡚⣧⣸⡄⣿⣟⡟⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢸⣀⠀⠀⡀⠀⠀⠀⠐⡀⠒⠀⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠀⠀⣀⣠⠾⠿⣾⣶⣂⢀⠀⠀⠀⠨⡀⠹⣧⠈⣹⣷⣯⡯⢿⣿⣿⣷⣀⠙⡋⠘⠋⠁⠀⠀⠀⠈⣀⣿⣂⠿⢂⣴⠧⢄⣶⠆⠒⠚⠀⠀⠀⠀⣀⡼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢸⣿⣷⠘⣷⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠉⡙⠙⠚⠻⠛⣻⢿⣿⡿⣿⣿⣿⣿⡿⡿⡿⣿⣃⣀⠀⠘⣿⢟⡀⡿⠋⣹⡿⣿⣿⡿⣿⣿⣿⢿⡿⠿⣿⢛⣻⣿⡿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠏⠓⡇⢛⡗⢣⣿⠯⢴⠘⠛⢚⣹⣿⣿⣽⠀⠙⠿⠆⡯⠝⠃⡅⣿⡬⡍⡽⡟⠉⡬⣥⠨⣍⢸⡦⠭⣎⣱⠈⠩⠈⢉⣑⢱⣾⣐⣿⡻⠿⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠂⠀⣁⣥⡤⢄⣐⡷⠶⢖⣛⠈⡩⠙⡃⣵⡆⠂⠀⢩⣭⠁⠉⠁⠀⣏⣭⡩⢭⢼⢖⠚⠒⠦⠤⠄⠂⠀⠸⢠⢠⠈⢘⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠾⠓⠂⠀⠈⠀⣠⠼⣛⣐⣢⣄⣠⣀⢌⣍⣌⣩⣤⣤⢭⣽⡃⢠⣜⠛⣸⣟⣷⣲⣰⢢⣄⣠⣾⣧⠭⠍⠀⠀⠁⠀⠘⠀⣈⣩⣤⣴⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿

⠀⠀⠀⠀⠄⠀⠀⠠⠀⠤⣀⠠⠄⢀⢠⣤⣄⡀⡠⣄⡉⠙⢉⣽⡿⣿⡿⣿⢫⣿⢭⢿⣿⢿⣟⣿⣿⣿⣷⣾⣿⣿⣿⣹⡿⢿⡿⣻⠟⢏⠠⢤⠀⢠⠄⢤⣄⠀⠿⣿⣿⢿⣻⣿⣿⣿⣟⣭⣽⡿⠻⢹⡻⣿⣿⣿⣿⣷

⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠃⠰⠀⠸⠀⢢⣤⠂⠉⠌⠙⠒⠂⠭⡗⠛⣶⣶⣻⡿⠿⢯⣿⢇⣉⠿⠇⢾⣯⣲⣼⣏⠿⠭⢣⠿⡁⠀⠄⠀⠍⠉⠀⠘⢈⠃⠀⠤⠄⢀⢬⣭⡯⠭⢀⣙⣛⠓⡙⠑⣺⣾⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠂⠀⠀⠃⠀⠀⠀⠄⠐⠀⠈⠀⡄⠰⣀⣀⢄⣤⠄⢀⠀⠇⠀⠧⠤⣘⠧⣭⠿⣿⣰⣶⣤⡶⠳⠆⠈⣾⣿⢉⡁⢚⣉⣇⣀⠄⣀⢴⣾⠀⠀⡆⠁⡄⣉⡆⠈⡈⡉⠇⠰⢶⣔⣄⡷⣶⣲⣿⢙⣿⣿⢿⣿

⣿⣿⣾⣦⣭⣤⣤⣤⣤⣀⡰⣠⣆⣴⣮⡵⣷⣶⣿⣴⣼⣿⣴⣶⣷⣦⣴⣞⣄⣤⣷⣿⣽⣷⣾⣭⣥⣽⣿⣤⣽⣴⣿⣿⣾⣵⣧⣶⣶⣾⣶⣷⣯⣷⣦⣬⣧⣴⣷⣿⣿⣶⣶⣦⣶⣷⣾⣾⣿⣿⣮⣿⣷⣿⣿⣿⣿⣿

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

⠀⠀⠒⠄⠀⢀⠂⠰⠀⠆⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[29A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡟⡻⠃⠠⡤⢶⠄⠀⠤⡄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⠶⠿⣿⣿⣶⣾⣷⣽⣧⣼⣤⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠿⠋⠀⠀⢀⡀⠆⠀⢑⠁⠆⠳⠓⠆⠏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢸⣏⡽⠀⠠⠟⠹⠿⠋⢿⣿⣿⡹⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣴⣶⣷⣶⣦⣌⠁⠀⠀⠂⠀⠀⠐⠓⠀⠹⠏⠁⠀⠀⠀⠀⠀⠐⣿⣿⣿⣇⠉⠻⣿⣿⣷⡄⠀⠀⠀⠀⠀

⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⣆⣐⣄⣴⠄⣼⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠉⢉⣭⣿⡷⢸⣶⣶⡶⢶⣶⣶⠀⠤⠤⠤⢤⣤⣤⣤⡤⢴⣾⣿⣿⣿⣷⣿⣿⡷⣿⣿⣶⠄⣴⣦⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢘⣾⣽⣏⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⠀⢰⣿⣶⣿⣿⣿⠁⠀⠚⠛⠂⠀⠒⠃⠀⠀⠒⠀⠀⠀⠀⣀⣀⣀⣀⣀⣿⡶⠏⠻⣌⠁⠛⣿⠛⠛⠛⠛⠛

⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣶⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⣀⡀⢀⡄⠀⠒⣶⣦⡀⠘⢡⣼⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠁⠁⠀⠀⠀⠀⠈⠀⠀⠀⠒⣆⡀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣷⡄⠀⢀⡾⠀⠀⠁⠀⠀⢛⣿⢗⣤⣿⣿⣷⢿⣿⣯⠁⠫⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠆⠀⠀⠘⢿⣧⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣄⠁⠀⠀⠀⠀⠀⠀⢯⣭⣿⡿⠿⠃⠉⢙⣿⡏⠀⠀⠀⢀⣀⢀⡀⣀⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠈⠸⣀⣈⣿⣿⣆

⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⣾⣾⣿⣿⣿⡄⠀⠀⠀⠀⠙⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢿⡿⡉⠀⠀⠀⠀⣯⢰⡀⠀⠀⠀⢼⣶⣤⣶⣿⠄⠀⠼⠽⠙⠿⠿⠷⠡⠠⠄⠏⠍⠛⠿⠟⠋⣹⠀⠀⠀⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠐⠀⢠⡍⠐⠰⣿⢴⡆⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠙⠿⣟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣄⠀⠀⠀⠀⣸⡆⠀⢾⠀⠀⣴⣿⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣦⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⡀⣿⠗⠀⠀⠀⠀⢺⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠂⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠃⣾⣿⠆⠀⠀⠀⠀⢈⣿⣅⣀⢀⣀⣀⣀⣀⡀⠀⢠⠇⠁⠀⢈⠀⠀⠀⠀⠠⠇⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⢀⣀⢠⠀⠸⢿⡿⠿⢿⡿⣿⣿⣿⠀⠘⠃⠀⠀⢸⠀⠀⠀⠀⠰⠂⠀⡀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠄⠀⢼⡡⠹⡄⣤⣽⣿⡤⠄⣀⣼⣿⡄⠀⢨⣥⠀⠀⣿⠆⠀⠀⢀⣰⡆⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣿⣄⠀⣿⣿⣿⣿⠈⠛⢿⣿⡅⠀⢸⡿⠀⠀⣾⠖⠦⠔⠊⠙⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⣦⣤⣤⣀⠀⠀⠀⠡⡹⣧⠀⠉⢿⡍⠀⠀⢀⣽⢷⣆⢺⡃⢀⠘⣋⣘⠏⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⢀⠀⢀⣀⣰⠿⠇⠈⠀⠠⢄⡀⢈⠈⢷⡄⢘⣿⣤⣤⡼⠿⢿⣯⠿⠿⠀⠀⠉⠁⠀⠈⠘⣀⡃⡺⢤⣴⣦⠠⠿⢀⣼⠦⢠⡶⠀⠒⠛⠐⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⣺⣿⣿⣿⡆⢻⣞⢻⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣶⣲⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⡀⣀⡒⢛⠿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡿⣟⠃⣀⠀⡀⣿⣿⣿⣿⠃⠸⡿⢘⣿⣿⢿⣿⣿⣿⣿⡿⢿⣿⢿⣛⢿⣯⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠄⣁⡇⠛⡛⠣⠭⠉⢹⠘⠛⠚⢠⣭⡅⢹⣘⣛⠭⠇⡟⡟⢳⣿⣙⠬⠍⣮⡛⠛⠾⠯⢽⣿⢽⣟⡛⡂⢉⠌⠙⠘⠻⠲⢹⣾⣸⣻⢙⣙⣛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠂⠀⠀⢃⣀⡁⢥⠐⢂⣐⣷⣿⡆⠛⠀⣄⠙⠂⣇⡈⣿⣿⣿⣿⠀⣿⡗⠛⣇⣀⣸⣿⣽⣶⢾⣛⡭⣿⡇⠁⠀⢰⢸⣳⠛⢳⣱⣶⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠶⠓⠂⠀⠈⢁⣺⣶⣚⣁⣐⣀⣠⣄⣄⣤⣾⠩⠤⠂⢧⣽⣿⣿⡏⠉⣰⡟⠷⣶⣦⣄⣤⣤⣿⣿⡿⠖⠀⠀⠑⠀⠘⠀⣢⣜⣂⣰⣾⣛⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿

⠀⠀⠀⠀⠀⠄⠤⠀⠀⠀⠀⠀⢠⣄⢀⣀⠀⡀⣠⣬⣿⢿⣯⣽⡻⣿⣿⠛⣷⣿⣯⣤⣤⡬⢾⣿⠻⢿⣿⣿⣯⣤⣽⣿⣿⣿⠿⣣⢽⣿⠡⠠⠠⠄⠠⠤⠠⠀⣿⣿⣿⣍⣿⡿⠿⣿⣟⡫⠿⡿⣻⣿⣿⣿⣿⣿⢿⡿

⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠠⠀⠰⠄⣣⢿⠃⠀⠄⠘⠐⠂⣛⡇⠀⣶⣶⣙⣾⠿⣯⣿⣯⣿⠽⡏⢽⣯⣿⣾⡇⣾⣿⢒⣭⠁⠀⠅⠀⡂⠀⠀⠀⢀⠅⣿⣛⣃⣿⢯⣉⡿⠉⢀⣘⣐⠓⠾⢗⣲⣾⣿⣿⣟⣿

⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠀⠀⠐⠀⠸⠀⡄⠸⣀⣀⠰⣶⠄⠠⢴⣇⣀⢖⣒⡿⠯⣉⡻⣿⡟⠉⢀⡁⠒⠖⠈⢹⣷⢸⣯⢋⠛⢀⣀⠆⣀⠗⠒⠀⠀⡆⠁⣿⣛⣃⣉⡐⠀⠯⢨⢔⣓⣖⡧⣶⣶⣿⢙⣿⣿⣿⣿

⣶⣶⣴⣶⣭⣦⣼⣭⣿⣭⣶⣦⣶⣖⣧⣴⣧⣶⣶⣯⣷⣿⣦⣦⣾⣯⣿⣿⣿⣿⣷⣷⣭⣭⣿⣯⣿⣶⣾⣦⣤⣼⣿⣿⣾⣿⣿⣶⣦⣶⣶⣷⣭⣷⣯⣽⣷⣶⣿⣿⣽⣿⣿⣶⣶⣿⣟⣮⣮⣶⣯⣿⣷⣿⣾⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠉⠉⠉⠁⠈⠉⠈⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠉⠉⠉⠉

⠀⠆⠂⠄⠀⢆⠀⠰⠢⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[29A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠟⠠⠀⠄⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣷⠷⢷⢶⣿⠷⢾⣷⣴⣦⣰⣶⠻⣶⡄⠀⠀⠀⠀⠀

⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠙⠀⠀⠐⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢩⠑⠀⠀⠈⠛⠢⢸⣿⣿⡇⠿⣧⣽⣧⡀⠀⠀⠀⠀

⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠠⣀⣤⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠃⠀⠆⠈⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⠉⠻⡉⢿⣆⠀⠀⠀

⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⢠⡀⢀⢀⣖⢀⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡏⠀⠀⠈⢉⣭⣿⡇⠀⠀⠰⣶⡾⣶⠶⣶⣶⡆⠀⠤⠤⣤⢤⣤⠤⠤⠤⣶⣿⣿⣿⣿⣶⣾⣷⢼⣿⣷⣶⣤

⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⢻⡀⣼⣮⡹⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢸⣿⣶⣿⣿⣿⠁⠀⠀⠀⠚⠛⠋⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⢀⣀⣀⣀⣀⣠⣽⠷⠙⢧⡉⠘⢿⡿⠛⠛

⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣴⣾⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢀⣀⠀⡀⠀⠀⢰⣶⣦⡾⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠂⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣦⠀⠀⡼⠃⠀⠁⠀⠙⠛⣿⡿⠿⢾⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⢀⡀⠰⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣧⡈⠀⠀⠀⠀⠀⠀⠹⠿⢁⠀⠃⠽⣿⡿⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠰⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢁⣀⡉

⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢰⣿⣿⣯⣽⣧⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⢈⡀⠀⠀⠅⠀⢹⣿⠀⠀⠀⠀⠀⠀⢰⣷⣶⣶⠶⡶⠄⠀⠺⠿⠿⠿⠿⠧⠄⠀⠜⠺⠛⠙⠟⠉⠀⡀⠀⠀⠸⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣆⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢘⣿⡄⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡀⠀⢠⣏⠀⠀⠀⢠⡆⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡄⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣠⠏⠀⠀⠀⠂⠙⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢷⠀⢤⡀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⠇⠀⠛⠆⠀⠀⠀⠀⠈⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⢸⠀⠀⢴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠘⠛⡀⠀⠀⠀⠀⠿⠿⡿⣿⣿⣿⣿⣿⡧⠀⠛⢀⠀⠀⡇⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢂⣠⣥⡄⠀⠀⠀⠀⠀⠀⢠⣄⣰⣿⣧⠀⠀⣬⡌⠀⢸⡧⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣘⡂⠀⠀⠀⠀⠀⠙⠿⢿⣿⠆⠀⡿⠃⠀⢸⡗⢲⠤⠂⠀⠧⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠂⠹⣿⡙⢩⡅⠀⠀⠀⠀⠀⠀⠀⢀⣿⡓⡒⠃⠀⡀⢛⣁⠻⠁⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠶⠀⠀⠀⠀⠸⣇⢈⣇⠀⢀⠀⠀⠀⣤⣤⡯⠯⠿⠽⠟⠀⠀⠈⠉⠀⡘⣛⠃⢁⣰⢦⣤⣶⡆⠴⠄⣠⡏⠄⣴⠆⠐⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢁⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢻⣧⢷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⢰⣢⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⡀⣀⡀⢈⡙⡿⣿⣿⡿⣿⣿⣿⣿⣿⡿⣿⠿⣛⣃⡀⢀⣀⢆⣈⠿⡞⣻⣿⣿⣿⣿⣿⣿⣿⣿⡟⢙⣂⢙⣻⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠏⣁⡇⠛⡟⠣⠭⠛⢹⢘⣻⣺⣨⣭⣹⣿⣘⣛⠿⠇⡿⡟⢃⣬⣿⡬⡍⣮⡟⠛⡿⠿⣽⣿⣽⣿⣿⡟⢛⠌⠹⠘⢻⣿⢹⣾⣼⣿⢹⣽⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡆⠀⠚⢃⣀⠡⢥⠸⢗⣐⣿⣿⣿⣿⢤⣾⠿⠆⣇⡘⣿⣿⣿⣿⠀⣿⡇⠛⣟⣛⣻⣿⣿⣾⢾⣛⡯⣿⡇⠀⠀⢰⢸⣻⠛⢳⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠶⠓⠂⠀⠈⠉⠺⣾⣛⣑⣲⣆⣠⣄⣥⡐⠘⠫⠥⣢⣧⣽⣿⣿⣯⠭⢰⡟⠷⣶⣦⣄⣥⣠⣿⣿⡿⠟⠀⠀⠓⠀⠈⢀⣪⣼⣂⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠄⠄⠤⠠⠀⠤⠀⠠⢠⣄⢠⣄⣀⡀⣠⣤⣌⢻⣯⣽⡿⣿⣿⣿⣿⣿⣤⣤⣼⡿⢿⣿⣿⣿⡋⣠⣽⣥⢢⣿⣿⣿⡿⣯⣽⣿⠧⢤⠠⠄⠠⠄⣤⡀⢿⣿⣿⣿⣿⣿⣿⣿⣟⣯⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠌⠢⠀⠀⠀⠀⠀⠁⠸⡇⠸⠄⣣⢿⡇⠈⠔⠙⢛⠃⣛⡇⠀⣾⣿⣽⣾⣿⣿⣿⣯⣿⣿⣇⣿⣯⣟⣼⡏⣿⣿⢓⣿⡇⠈⠷⠿⢊⣉⠀⠀⢀⠇⠀⣿⣯⣿⢯⣉⡿⠉⢂⣘⣒⣗⡾⢗⣺⣿⣿⣿⣟⣿

⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠀⠈⠱⠇⠸⠀⡄⠸⣇⣀⢴⣶⣄⣡⢴⣇⣀⢞⣛⣿⣿⣭⣿⣿⠿⠿⢥⣷⢷⣖⣈⣽⣿⢸⣿⢏⠛⢇⣀⠆⣀⠗⠒⠀⠀⡆⠁⡀⣿⣇⣭⡍⠉⡯⢨⢔⣒⣖⡷⣶⣶⣿⣙⣿⣿⣿⣿

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

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

⠀⠆⠂⠀⠀⢆⠀⠰⠢⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[29A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣃⡠⣶⢶⣲⣦⣾⣿⣿⣿⣿⣿⣿⢏⢐⣊⣔⡼⣦⢴⠂⠀⠀⠀⠄⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⡌⢿⣷⡽⣟⣻⣿⣿⣿⣴⣦⣴⣰⣺⣷⣄⡀

⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣺⣿⣿⣿⣿⣾⣿⣿⣿⣿⡿⠛⡗⠒⠚⢋⢻⠘⠝⠉⠈⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠈⡯⠧⠺⠛⠽⠿⠻⠿⠋⣻⣿⡟⠋⣿⣽⣿⣇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⢿⣿⣿⣿⣾⣿⣿⣿⡿⠋⠁⠀⡀⠀⢠⣠⠶⣿⣶⣿⣦⣤⠀⠀⠐⠀⠂⠀⠰⠀⠀⠑⠀⠀⠛⠀⠀⠇⠐⠀⠀⠀⠀⠀⠁⢀⣿⣿⣿⢜⢩⠹⣿⣿

⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⢠⣀⣀⣡⣦⡤⣐⡰⣼⣿⣿⣿⣴⣿⣿⡿⠋⠐⠀⠁⠀⠀⢁⣧⠯⠀⢀⠧⢉⣿⣿⡇⠀⠀⠂⠶⠀⠰⣾⣶⣶⣶⣶⣶⡆⠠⠤⢤⣤⣤⣤⣤⣤⣴⣶⣿⣿⣿⣿⣽⣷⣿⣋

⠀⠀⠠⣤⡬⢄⡀⠀⠁⠀⠀⠀⢠⠀⠨⠄⢩⠆⣾⡽⢿⣿⣯⣏⣿⣿⣿⣿⡿⠋⠀⠀⠠⠀⠀⠀⠀⢸⠇⣀⣸⣿⣶⣿⣿⣯⠁⠀⠀⠀⠐⠒⠒⠘⠛⠁⠀⠽⠛⠀⠀⠒⠂⠀⠀⠀⣀⣀⣀⣀⣈⣠⣬⠝⣽⠷⡌⠉

⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣅⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠰⡀⣰⣶⣿⣿⣿⣿⣿⣿⣿⣿⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠁⠀⠀⠀⠈⠀⠋⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣖⠀⢨⣿⣿⣿⠟⠻⣿⣿⣿⣯⣿⡋⠍⠄⠀⠀⠀⠐⠈⢄⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠷⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀⡀⠁⠀⢈⢻⣿⣿⣿⣿⣿⣏⠋⢿⠘⢩⡶⠀⢿⠻⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⢀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⣽⣿⣿⣿⣿⣧⠄⢸⡿⡿⠹⢿⣿⣿⣿⣿⣟⣀⠀⠀⠀⠘⠏⠘⣿⣿⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢜⣯⣴⣦⣴⡾⠆⠰⣿⡿⠿⠿⠁⠧⠀⠀⠈⠙⠛⠖⠛⢛⣀⡄⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⣿⣿⣿⣿⠀⠉⠐⠈⠠⢯⠉⢿⣿⣿⢩⣭⡿⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠟⠛⠛⠻⠂⠀⠀⠀⠀⠀⠀⠀⢸⠋⣤⠈⠁⠀⠀⠀⠠⣂⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⡄⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠐⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣲⣄⠀⢿⠀⠀⠀⠀⠀⡀⣀⣀⣀⡀⣀⠀⠀⡟⠀⠀⠀⡄⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢼⡇⠀⠀⠰⣎⣅⣉⣷⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠑⡟⠂⠀⢱⡇⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡄⠀⠀⠀⠀⠀⢠⣶⣶⣦⠀⣯⠃⠐⢴⢶⣿⣽⡉⠀⠀⠈⠀⠀⢻⣶⣴⣭⣿⣞⠀⢰⣭⠆⠀⢾⡧⠀⠀⠁⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣯⡂⣿⠀⠀⠙⡻⠿⡿⠟⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣯⡄⢸⡿⠃⠀⢼⡗⣶⠴⠊⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠉⣿⡠⠀⢀⣿⡟⠇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣟⣗⡛⡃⢰⡀⣻⣕⠟⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣀⣰⣀⣐⢿⡇⢀⡆⢹⣇⣁⣀⢀⠀⢀⣀⡤⠈⢠⣤⣴⠿⡿⠛⠽⠿⠀⠀⠙⣉⢸⣿⣿⣃⣣⣰⠦⣴⣷⡆⢺⠄⣰⡯⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢐⡙⢻⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣾⣧⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⣄⣶⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡉⢂⣁⠙⠛⠛⡿⣿⢿⡿⠿⣿⢿⠿⣿⠿⣿⣿⣏⣿⢄⠀⢀⣿⣿⣿⣿⡿⢿⣿⡿⢿⡿⠛⢙⠋⢘⣿⢿⡿⢿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠌⠅⢀⡝⠣⠿⢠⠝⠸⣿⠿⢌⣓⡈⠉⠾⢷⠿⡇⡶⠏⠋⠈⣽⡬⠍⠈⠉⠓⠮⠿⣟⣒⢹⣾⡷⠚⢓⠊⠹⠌⣩⢵⠠⠭⠄⠑⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡄⠂⠀⠈⠂⠀⠡⢍⠘⠋⠈⣎⣉⣁⣀⢀⣺⠿⡆⣷⡎⠃⠀⢹⣿⠀⣶⡇⠀⣐⣒⣛⣛⣿⠗⠚⠻⠉⠛⠃⠁⠠⠠⠐⢲⠚⢒⢿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠂⠀⠁⠁⠠⠬⠁⠶⣂⣁⣀⣆⣼⣺⣿⣫⣤⣄⠧⠽⠇⣠⢬⣭⢸⣤⣄⣤⣈⣉⣹⣺⣿⠘⠿⠟⠀⠀⠀⠀⠐⢀⣃⣀⣀⣠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⠀⢤⣀⠀⠠⠠⡀⣨⣠⣁⠀⣤⣬⡿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⣆⣼⣿⡸⣻⣬⣿⣿⣟⣿⢿⡻⣻⡡⢤⠠⣄⢀⣀⠀⠠⢤⡸⡿⢿⣿⣻⢿⣿⣽⣿⣿⣿⣽⡿⣻⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢑⠀⢟⠀⠃⠀⠀⠠⠀⠠⠀⡣⢠⡆⠈⢥⣉⣝⠃⠭⡇⠈⣺⣿⣿⡅⠶⢾⣿⣿⣶⠀⢇⢋⣀⣽⣿⡟⣽⣛⠑⣿⡇⠈⠷⠿⢏⣉⠀⠀⠂⠇⠀⣶⣦⣉⠳⠿⠊⠁⢻⠯⣝⢏⠻⢭⠩⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⡀⠀⠂⠀⠀⠀⠀⠂⠰⢇⣈⠑⠶⡄⠀⠀⠇⠀⢾⣿⣷⡶⠒⠆⡿⠳⣶⢶⣦⣷⣶⣘⣼⣶⣹⣿⡆⣉⣃⣀⠆⠀⢶⣶⠀⠀⠁⠃⠀⣒⣂⣹⡗⠀⠀⠀⢔⣀⡄⠟⠦⠋⠹⢙⢿⣿⣿⣿

⣿⣻⣿⣶⣭⣦⣬⣭⣿⣭⣷⣴⣶⣴⣶⣤⣦⣶⣶⣦⣶⣿⣧⣤⣾⣮⣦⣶⣾⣭⣿⣿⣿⣿⣿⣮⣷⣦⣤⣤⣴⣬⣿⣿⣥⣿⣿⣿⣶⣶⣶⣶⣦⣷⣦⣤⣵⣴⣷⣿⣯⣿⣶⣶⣴⣧⣷⣥⣴⣾⣶⣦⣶⣶⣷⣿⣿⣿

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

⠀⠆⠀⠄⠀⢆⠆⠐⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                ䷩ 𝚕𝚒𝚗𝚎 5186

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/02/07/the-above-the-law-complex/#comments

Gemini version at gemini://gemini.techrights.org/2022/02/07/the-above-the-law-complex/

Gemini_version_available_♊︎

✐ Nobody_Should_be_Above_the_Law⠀✐

Posted in Europe, Law, Patents, Site_News at 8:48 am by Dr. Roy Schestowitz

Video_download_link | md5sum 8fac8245e0f6ad5c568ad4b61870d0c8

EPO and Immunity

Creative Commons Attribution-No Derivative Works 4.0

http://techrights.org/videos/epo-immunity-issues.webm

Summary: The EPO regime of Benoît_Battistelli and António_Campinos has

demonstrated that immunity begets impunity, which in turn gives an incentive to

commit crimes, making corruption the “norm”; if European_officials_fail_to

tackle_this_problem, the EU too will be at risk due to legitimacy_problems

THE “immunity complex” (or syndrome, unrelated to immune_complex) in Europe’s

second-largest institution was_covered_here_last_night… with more to come

regarding impunity tonight.

Why is it that some people are effectively above the law? Is it a coincidence

that officials who are above the law are placed there mostly to serve the

financial interests of multinational corporations and oligarchs? What does that

tell us about the state of the law in Europe? Seeing that Team UPC is pushing

and compelling officials to do something illegal, shouldn’t they too be held

accountable for incitement_to_break_the_law?

“Why is it that some people are effectively above the law?”In any event, I’ve

put my thoughts in the video above. Towards the end I show these_3_comments (3

at the time of recording) on a post mentioned_by_SUEPO_last_week, along with

translations (“Translation is available in German, the French translation will

follow soon”). █

                ䷩ 𝚕𝚒𝚗𝚎 5240

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/02/07/the-epo-is-bleeding-in-courts/#comments

Gemini version at gemini://gemini.techrights.org/2022/02/07/the-epo-is-bleeding-in-courts/

Gemini_version_available_♊︎

✐ The_EPO_is_Bleeding_in_Courts⠀✐

Posted in Europe, Patents at 7:59 pm by Dr. Roy Schestowitz

Video_download_link | md5sum 11baf7038f147c5e9f122d2285ad9748

EPO Immunity Backfiring and Media is Silent

Creative Commons Attribution-No Derivative Works 4.0

http://techrights.org/videos/epo-immunity-and-media-deficit.webm

Summary: The abuses of the EPO are causing an embarrassment; media in the

pockets of the EPO’s management isn’t covering that, but sooner or later the

truth will come out regardless

Mondays are typically the time when we cover bigger stories because during the

weekends there’s a sort of ‘backlog’ of developments. So far today we’ve

published quite a lot about EPO President António_Campinos and his appointer,

Benoît_Battistelli, whose legal of crime was covered up and moreover extended

by Campinos.

🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Dr Evil Jesper Kongstad Laughing; Worst-case scenario: I

move to another job⦈ There’s a bit of a positive development; aside from ILOAT

confirming further violations, as we noted here the other day, the Office now

admits culpability by paying over 4,500 EPO workers after wrong punishment,

based upon unlawful regulations which should never have materialised in the

first place. There’s a lot to be learned from all this; even Team UPC should

take a moment to consider or reconsider what it’s trying to do by force-feeding

an unlawful system, bound_to_explode for obvious_reasons. █

⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⢌⠱⡯⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣤⣅⠀⠀⠠⡀⠐⢢⣈⣙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣕⣴⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢷⣿⣯⣭⣿⡅⠀⠞⠲⢕⠁⢀⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⡿⡇⠀⠀⠀⠀⠀⠀

⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣲⣏⣩⣿⠛⡃⣀⣀⣀⣁⠎⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⣾⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣄⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⢿⣿⣿⣿⣞⣘⢧⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣲⡾⠟⠛⣿⣿⣿⢿⣟⣗⣀⣟⣸⢿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢸⣾⣿⣷⣿⡁⠀⠀⣤⣴⡾⠄⠙⣿⣿⣿⠟⢣⣼⣿⣿⣿⣿⣏⣿⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⠀⠀⠀⣸⣿⣿⣿⣟⠙⠁⠀⠀⠈⢩⣿⣿⠿⠛⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠐⣾⣿⣿⣇⣬⡀⠀⠀⠈⠄⠀⠀⠀⠈⢻⣿⡝⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⡿⣿⣿⣶⣷⡄⢀⣿⣿⣷⣿⣟⣫⡞⠀⠀⠀⢠⣯⡉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⢹⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⢿⣿⣿⣿⠋⠈⠿⣿⣿⣿⠇⢾⠁⠀⠀⢀⣮⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠹⣿⠗⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠘⢿⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠋⠸⠻⢥⣴⠤⢢⠀⠈⠋⠀⠈⠀⠀⠀⠌⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢻⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⢾⣷⠙⢸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢧⠌⠀⠐⢷⣘⠅⢻⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣿⠆⢽⣿⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠙⠀⠚⣰⠿⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⢢⣤⡈⣿⣼⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢉⣿⣿⣿⠀⠀⠀⠀⠀⣀⡄⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠛⣌⣿⠛⢸⠋⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠟⠀⠀⠀⠀⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠁⠀⠀⠼⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠔⡶⡅⠀⠀⠀⠃⠀⠀⠀⠤⠴⠄⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⣿⣾⢆⣿⣾⢀⣾⣾⣷⣷⣿⣿⣶⣷⡟⣸⣿⣾⣿⠈⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠲⣶⠎⢶⠄⢴⣿⡿⠿⠃⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⠈⠀⢹⣾⣾⣾⣾⣾⣶⣷⣾⣾⣤⡅⠁⠀⣡⣥⣨⣤⢁⢨⣧⠁⠈⡈⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠌⠡⡯⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣶⣤⣄⠀⢀⢤⣄⠀⣂⣩⡑⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣴⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠻⢿⣿⣯⣭⣿⡌⠐⡘⣹⣷⣏⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⡆⠀⠀⠀⠀⠀⠀

⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣁⣼⣟⠛⣇⣀⣀⣔⢫⡧⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣻⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⢤⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⢻⣿⣿⣿⣮⢪⣧⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣭⢺⡾⠛⠛⣿⣿⣿⠿⡿⣗⣀⣜⠹⢿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢈⣿⣿⣷⣿⡄⠀⢀⣤⣶⣿⠀⠙⣿⣿⡿⡟⠃⣤⣿⣿⣿⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⠀⠀⠀⢸⣿⣿⣿⣟⢉⠁⠀⠁⠀⠁⣿⣯⡿⠛⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣴⡄⠀⠀⠉⠁⠀⠀⠀⠈⢿⣿⡌⠀⢹⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⡄⢀⣿⣿⣿⢻⣟⣫⡞⠀⠀⠀⢠⣯⡟⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡀⢸⣿⣿⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠈⠿⣿⣿⣿⠇⢼⠁⠀⠀⢀⣮⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠹⣿⠟⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠈⢿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠋⠸⠻⣥⣴⢤⢢⠁⠉⠋⠀⠈⠀⠀⠀⡈⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⣼⣷⠙⠜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢧⠄⠀⠐⢷⣘⠁⢻⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣿⠆⢹⣿⣄⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠙⠀⠚⣰⠿⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⢠⣤⡈⣿⣶⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⣀⡄⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠛⣼⡿⠟⢹⣿⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠄⠛⠁⠀⠼⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠴⡶⡅⠀⠀⠀⠃⠀⠀⠀⠤⠴⠄⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⣿⣾⢆⣿⣾⢀⣾⣾⣷⣷⣿⣿⣶⣷⡟⣸⣿⣾⣿⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠲⣶⠎⢶⠄⢴⣾⣿⡿⠃⠀⠈⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⠈⠀⢹⣾⣾⣾⣾⣾⣶⣷⣾⣮⣤⡅⠁⠀⣡⣥⣨⣤⢁⢨⣧⠁⠈⡌⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠌⠰⡯⡛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢏⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣶⣤⣄⠀⠀⡄⠄⠀⢢⢨⠙⠓⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣎⣴⣶⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠻⣿⣿⣥⣭⣶⡀⠀⢠⠨⠠⠨⠅⢢⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡿⡇⠀⠀⠀⠀⠀⠀

⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣮⣠⣿⡟⢻⡇⣀⣀⣠⢫⡄⣳⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠹⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠠⣴⣶⢄⡀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⠃⣿⣿⣿⣯⠻⡵⡑⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣯⣭⢲⡾⠛⠛⣿⣿⢿⠿⡿⡛⣀⡈⢹⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡅⠀⢀⣤⣶⡿⠀⠙⣿⣿⡿⡿⠓⣤⣿⣿⣿⣿⣿⣰⡶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⠀⠀⠀⣸⣿⣿⣿⣟⣙⡍⠀⠀⠈⠉⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢷⣿⣿⣿⣡⡄⠀⠀⠈⠀⠀⠀⠀⠈⢿⣿⡌⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡄⠀⣿⣿⣿⣿⣟⣛⡴⠀⠀⠀⢐⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⢸⣿⣿⡯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠋⠈⠻⠿⣿⢿⡗⢸⠃⠀⠀⠀⣘⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠸⣿⡿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⢻⣿⣇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠟⠁⠊⠸⠻⣥⣶⠤⢢⠁⠀⠘⠀⠈⠀⠀⠀⠀⠁⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠁⢸⣷⠙⠜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣣⠄⠀⠀⢷⣘⠁⢻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣿⠆⠘⣿⣄⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠙⠀⠚⣴⠿⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⡟⢰⣤⡈⣿⣿⣷⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣀⡄⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠛⣌⣿⠿⢹⣿⠇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⡀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠁⠀⠼⣿⡿⣿⣿⣿⠿⣿⣿⡿⠿⠛⠛⠃⠀⠀⠀⠴⡶⡅⠀⠀⠀⠃⠀⠀⠀⠤⠴⠄⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⣿⣾⢆⣿⣾⢀⣾⣾⣷⣷⣿⣿⣶⣷⡟⣸⣿⣾⣿⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠲⣶⠎⢶⠄⢴⣾⣿⡿⠃⠀⠈⠀⠁⠁⠀⠈⠀⠀⠈⠈⠀⢨⠈⠁⠈⠀⠁⠈⠈⠀⢹⣾⣾⣾⣾⣾⣶⣷⣾⣾⣶⡅⠁⠀⣡⣥⣨⡤⢁⢨⣧⠁⠈⠈⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠰⠯⡟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣶⣤⡄⠀⢀⠠⡄⠒⠠⡨⠙⠓⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⣤⣶⣶⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣧⣷⣷⣶⡀⠀⠀⠋⣵⠰⡃⠢⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀

⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣦⣼⣿⠛⢻⢃⣀⣀⣁⢠⣂⣰⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣦⡅⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⢄⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠃⣿⣿⣿⣮⡛⠻⣑⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡭⣶⡟⠛⠛⣿⣿⢿⡿⣿⣛⢂⣬⠙⢿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠈⣷⣿⣿⣾⡄⠀⢀⣤⣶⡿⠀⠙⣿⣿⠿⡟⠑⣤⣿⣿⣿⣿⣿⣾⣴⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⠀⠀⠀⢸⣿⣿⣿⣿⡛⡏⡀⠀⠉⠈⣿⣿⣵⠾⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢺⣷⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡜⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⡄⢠⣿⣿⣿⡿⣿⣛⣵⠀⠀⠀⠀⣿⢿⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡔⢸⣿⣿⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⢿⢿⣿⡿⠃⠈⠟⢿⡿⢿⡟⢸⠇⠀⠀⠀⣜⡅⠐⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠸⣿⡿⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⠀⢻⣿⣇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠉⠸⡻⣤⣶⢄⢆⠁⠀⠘⠀⠈⠀⠀⠀⠀⠁⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠁⢸⣷⠙⠌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡧⠀⠀⠰⢗⣚⠁⢺⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣿⠂⠸⢿⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠃⠀⠃⣴⠟⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⡟⢠⣤⠈⣿⣿⣾⣿⣿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢠⠄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠓⢍⡛⠁⣿⠟⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠐⠉⠀⠀⢸⣿⡿⣿⣿⣿⢿⣿⣿⠛⠛⠋⠃⠀⠀⠀⠠⢴⡶⡄⠀⠀⠐⠀⠀⠀⠀⠤⠴⠄⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⣿⣾⢆⣿⣾⢀⣾⣾⣷⣷⣿⣿⣶⣷⡟⣸⣾⣾⣿⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠲⣶⠎⢶⠄⢴⣾⣿⡿⠃⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠨⠈⠁⠈⠀⠁⠈⠈⠀⢹⣾⣾⣾⣾⣾⣶⣷⣾⣾⣶⣧⠁⠀⣥⣥⣨⡄⢁⢸⡧⠁⢈⠈⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠌⠰⡭⡟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣤⡄⠀⠀⠀⠀⠀⠀⠈⠑⠓⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⣴⣶⣾⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠻⣿⣧⣷⣶⣶⠀⠀⠠⠔⠇⠽⠏⠈⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀

⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣥⣼⣿⠛⣻⢂⣀⣈⣁⠌⢢⢡⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠘⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢤⣴⣶⠤⡀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠁⣿⣿⣷⣷⡕⠱⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡤⣶⠛⠛⠻⣿⣿⣿⡿⢿⢿⣃⡤⠟⢿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣇⠀⢀⣴⣶⡿⠀⠙⣿⣿⠿⡟⠁⣦⣾⣿⣿⣿⣿⣱⣼⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠏⡀⠀⠀⣿⣿⣿⣿⣿⡛⡫⠉⠀⠈⠀⣽⡿⣣⡾⠂⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣤⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡌⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⣶⣧⠀⣠⣿⣿⣿⣯⣿⣟⣥⠃⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄⢸⣿⣿⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣿⣿⣿⡿⣿⢿⣿⡿⠁⠘⠛⣿⣿⡿⡿⢠⡏⠀⠀⠀⣼⣫⠁⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠸⣿⡿⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠀⢻⣿⣏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢀⠁⠘⡯⣴⡶⢔⡄⠀⠘⠁⠁⠀⠀⠀⠀⠀⠉⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠁⢸⣿⠙⠌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡧⠀⠀⠸⠇⡻⠘⢈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠄⠀⠀⠠⣴⣦⣤⣿⠂⠘⢿⣆⣄⢚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠃⠀⠃⡼⠟⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⡟⢠⣤⠘⣿⣿⢿⣿⣿⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⣠⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠰⡀⢠⣿⠟⠁⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠇⠀⠀⠀⠀⡀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣿⣿⣿⣿⣿⣭⠈⠋⠁⠀⠀⠀⠠⢴⡶⡅⠀⠀⠀⠀⠀⠀⡀⠤⠴⠀⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⣿⣾⢆⣿⣾⢀⣾⣾⣷⣷⣿⣿⣶⣷⡗⣸⣿⣾⣿⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠲⣶⠎⢶⠄⢴⣾⣿⠿⠃⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠁⠈⠈⠁⠈⠀⠁⠈⠈⠀⣽⣾⣾⣾⣾⣾⣶⣷⣾⣾⣶⣥⠁⠀⣥⡥⣨⡀⢁⢸⡧⠁⠈⠈⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠌⠰⡭⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣤⡄⠀⠀⠀⡀⠀⠠⡨⠑⠳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣤⣶⣾⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠻⣿⣧⣿⣷⣾⠀⠀⠠⠔⡂⠱⠅⡨⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀

⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣦⣼⣿⠛⣻⢂⣀⣈⣁⡈⢨⢡⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠘⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣄⡀⠀⠀⠀⠀⠀⠠⣼⣿⣿⣿⣿⣿⠁⣿⣿⣷⣷⡜⢵⣗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡴⣶⠛⠛⠻⣿⣿⢿⡿⢿⣿⣣⡤⠛⢿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣾⣇⠀⢀⣴⣶⡿⠀⠙⣿⣿⡿⡟⠑⣤⣿⣿⣿⣿⣿⣿⢹⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠏⡀⠀⠀⣿⣿⣿⣿⣿⡛⡋⠉⠁⠈⠀⣽⡿⣣⡾⠂⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣤⠀⠀⠈⠀⠀⠀⠀⠈⣿⣿⡌⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣧⠀⢠⣿⣿⣿⣯⣿⣟⣥⠃⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄⢸⣿⣿⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡿⣿⢿⣿⡿⠁⠘⠛⣟⣿⣿⡿⢠⡏⠀⠀⠀⣼⣫⠀⠂⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠸⣿⡿⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠀⢻⣿⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢀⠁⠘⡯⣤⡶⢔⡄⠀⠘⠁⠁⠀⠀⠀⠀⠀⠉⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠁⢸⣿⠙⠌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡧⠀⠀⠸⠇⡫⠘⢘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠄⠀⠀⠠⣴⣦⣤⣿⠂⠘⢻⣆⣄⢚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠃⠀⠃⡼⠟⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⡟⢠⣤⠈⣿⣿⢿⣿⣿⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣠⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠰⡀⢠⣿⡟⠃⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠇⠀⠀⠀⠀⡀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣿⣿⣿⣿⣿⣯⠈⠋⠁⠀⠀⠀⠠⢴⡶⡅⠀⠀⠀⠀⠀⠀⡀⠤⠔⠀⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⣿⣾⢆⣿⣾⢀⣾⣾⣷⣷⣿⣿⣶⣷⡗⣸⣾⣾⣿⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠲⣶⠎⢶⠄⢴⣾⣿⡿⠃⠀⠀⠀⠁⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⠈⠀⣿⣾⣾⣾⣾⣾⣶⣷⣾⣾⣶⣥⠁⠀⣥⡥⣨⡄⢁⢸⡧⠁⠈⠈⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⡯⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡅⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣦⡄⠀⠀⠀⢀⠀⠂⡈⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣴⣶⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠻⣿⢗⣷⣶⣾⠀⠀⠀⠐⡃⣀⡐⠏⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀

⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣠⣿⡋⢹⡂⢄⣀⣁⡪⣯⣽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣤⣴⣶⡄⡀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⠁⢹⣿⣿⣶⡜⢫⣦⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡴⡶⠻⠛⠻⣿⣿⣿⣿⣿⠿⣿⣛⣤⣌⣻⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢷⣿⣿⣶⡆⠀⢀⣤⣶⡞⠀⠹⣿⡿⠿⡟⠁⢴⣼⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠁⠀⠀⠀⣾⣿⣿⣿⣿⣿⣟⢛⠉⠁⠀⠈⢿⣿⣟⣰⡶⠂⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠸⣿⣾⣿⣏⡤⠀⠀⠁⠀⠀⠀⠀⠘⣿⣿⡌⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣦⡀⣠⣿⣿⣿⣿⣿⣿⣟⣋⡼⠀⠀⡀⣴⣯⡟⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄⠸⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠟⠁⠘⠿⠿⣿⣿⣿⣿⠇⣼⠁⠀⠸⢡⣋⣭⠄⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠘⣿⡟⢳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡀⢻⣿⣏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠈⠛⠻⠮⠖⣖⠄⠀⠚⠙⠁⠃⠁⠁⠀⠀⠂⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠁⢸⣿⠙⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⠿⠀⠀⠀⣘⡀⠁⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣦⣿⠂⠈⣹⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⠟⢛⡏⠐⠀⠂⣴⠟⠁⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⡟⠀⠀⡈⠛⣹⣿⢻⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⠿⣧⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠑⢐⠛⢽⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⢈⠟⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡿⣿⣿⣿⢿⣿⣿⠷⠠⠀⠐⠈⠂⠀⢠⠶⢈⠅⠀⠀⠀⠀⠀⠀⠠⠤⠶⠂⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⡷⣾⢆⣿⣾⢀⣾⣶⣷⣷⣿⣿⣶⣷⡗⣸⣾⣾⣿⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠲⣶⠎⢶⠄⢴⡾⣿⡿⠃⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠌⠁⠈⠀⠁⠈⠀⣶⣿⣾⣾⣾⣾⣾⣶⣷⣾⣾⣦⡅⠁⠀⣡⡥⣬⡀⠀⡾⠅⠀⠀⠈⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⢌⠱⡭⡻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣦⡄⠀⠀⠀⠀⡠⠂⢈⠑⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣾⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠿⣿⣿⣷⣿⣶⠀⠀⠀⠰⠓⣎⠌⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀

⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣯⣠⣿⡋⢹⡊⢀⣈⣥⣪⢲⣭⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢼⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⡦⡀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡿⡑⢸⣿⣿⣿⣦⠣⠯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⣲⠾⠿⠛⢿⣿⣿⣿⣿⣿⡿⣿⣿⣏⣀⣽⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣷⡆⠀⢀⣤⣶⡿⠀⠙⣿⣿⡿⡿⠣⢰⣾⣿⣿⣿⣿⣿⣺⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡝⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣟⡙⡋⠉⠀⠁⠟⣿⡿⡉⠠⡶⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠸⣿⣾⣿⣏⡤⠀⠀⠈⠀⠀⠀⠀⠘⣿⣿⡌⠀⢀⣹⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⢼⣿⣿⣿⣷⣾⣧⡄⠀⣼⣿⣿⣿⣿⣿⡟⣿⣛⣵⠃⣠⣿⢰⣟⡱⡏⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄⢸⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⠁⠀⠿⠿⡿⢿⣿⣿⣷⡟⢰⠋⢀⡿⢋⢿⣟⣤⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠘⣿⡿⢳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄⢻⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠘⠛⠂⠛⡆⠆⠀⠃⠘⠺⠟⠘⠌⠈⠀⢸⡇⡘⠋⠀⠀⠀⠂⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⢸⣿⢈⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢀⡃⠀⢷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣶⣶⣿⡂⠀⢹⣿⣿⣿⣿⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⢿⠃⡆⠀⠀⡾⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⠃⢀⣿⠀⣴⣏⢏⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡺⢿⡆⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢀⡠⠘⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠙⢬⠿⢿⠟⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣇⢈⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠒⠒⠊⠁⠀⣤⠄⠨⠃⠀⠀⠀⠀⠀⠀⠠⠴⠶⠂⠀⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⣷⣾⢆⣿⣾⢀⣾⣶⣷⣷⣿⣿⣶⣷⡟⣸⣿⣾⣿⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠲⣶⠎⢶⠄⢴⣾⣿⡿⠁⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⠀⣶⣿⣾⣾⣾⣾⣾⣶⣷⣾⣾⣦⠁⠁⠀⣡⡥⠈⠀⢠⠌⠁⠁⠈⠈⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⢠⢀⠁⢀⢌⠱⡯⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢎⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣦⡄⠀⠄⠀⠄⣑⠠⠈⠙⠿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡷⣾⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠿⣿⣿⣷⣾⣮⠐⠐⠒⠈⠠⢀⡈⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀

⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⣤⣿⡋⢹⡚⠁⣨⣵⣎⣾⣾⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡿⡁⠈⣿⣿⣿⣧⢛⣅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⣶⠾⠟⠻⢿⣿⣿⣿⣿⣿⡿⢿⢿⢛⣤⣽⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠘⣿⣾⣿⣿⡆⠀⣠⣤⣶⡿⠀⠙⣿⣿⡿⡿⠇⢮⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡏⠀⠀⠀⢀⣿⣟⡿⣿⣿⣿⣿⡛⡛⠁⠁⠀⡟⣿⡿⡋⢀⡦⠄⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⡤⠀⠈⠉⠀⠀⠀⠀⠘⢿⣿⡜⠄⢀⣸⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣷⣾⣧⡀⢠⣾⣷⣿⣿⣿⣿⣿⣿⣛⣥⠃⣴⣿⢰⣟⠹⡎⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡟⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⢿⣿⣄⠸⣿⣿⣿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⡟⠁⠘⣿⢟⡛⠻⠿⢿⣿⡿⢰⠇⢰⡿⢋⣿⣟⣥⠄⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠸⣿⡿⢳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄⢻⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠘⠋⠪⠓⢴⠌⠁⠀⠀⠚⠘⠉⠑⠈⠀⢸⠇⡸⠋⠀⠀⠀⡂⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⢸⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⣐⠀⠀⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣶⣶⣿⡂⠀⢘⡿⣿⢿⣿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡋⣿⣿⠁⠆⠀⢠⡟⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⠃⢄⣼⡇⣠⣆⢃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣶⡞⢻⡄⠀⠀⠀⠀⠀⠄⠘⠀⠀⠀⠀⠀⠀⠀⠀⢨⣄⠀⠀⢀⣀⠒⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠙⢷⠶⠿⠟⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣯⠸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠒⠓⠋⠁⠀⡄⠀⠨⠂⠀⠀⠀⠠⠄⠀⠠⠶⠞⠃⠀⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⣷⣾⢆⣿⣾⢀⣾⣶⣷⣷⣿⣿⣶⣷⡗⣸⣿⣾⣿⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠲⣶⠎⢶⠄⢴⣿⡿⡿⠁⠀⠈⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⠈⣶⣿⣾⣾⣾⣾⣾⣶⣷⣾⣾⡄⠁⠁⠀⣡⠅⠈⠀⠉⠨⠁⠁⠈⠈⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⢈⠹⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⠇⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀

⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣦⡄⠀⢀⠀⠄⠑⣠⠻⡽⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⣶⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀

⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠿⣿⣯⣴⣾⣯⠀⠀⠄⠉⡸⠠⠊⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⠧⠀⠀⠀⠀⠀

⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣠⣿⡋⢹⡲⠀⣄⣴⣎⡗⣶⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⢿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢠⣤⣶⣶⢄⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡿⠑⠁⣿⣿⣿⣷⡶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⢲⠾⠟⠛⢿⣿⣿⣿⣿⣿⣿⢿⣿⣻⣥⢸⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠘⣿⣶⣿⣾⡆⠀⣠⣤⣶⡿⠀⠙⣿⣿⡿⡿⠇⢤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠀⠀⠀⢈⣿⣟⣿⣿⣿⣿⣿⣛⣻⠉⠁⢀⡟⣿⣿⡋⠀⡤⠄⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⣯⡄⠀⠀⠈⠀⠀⠀⠀⠘⢿⣿⡌⠄⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣷⣾⣧⡀⢀⣼⣷⣿⣿⣿⣿⣿⢻⣛⣵⠇⣼⣿⢰⣿⡓⡆⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣄⢺⣿⣿⣿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡁⠘⣿⣿⠻⠿⣿⣿⣿⡿⢠⠏⢼⡿⢏⣟⣟⣧⡄⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠹⣿⡟⢳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄⢹⣿⣿⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠛⠃⠛⢳⠰⠈⠁⠄⠀⠛⠛⠁⠁⠈⠀⣽⠇⣘⠋⠀⠀⠀⡰⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠸⣿⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡆⠀⠀⣀⠀⠘⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⣶⣶⣿⡆⠀⢩⣿⢿⡿⣿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⢹⢿⣿⢁⠀⠀⢠⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⠃⢄⣿⣿⣌⣼⢇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⢿⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣀⠀⠀⢀⣀⠘⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⢳⡶⠾⠟⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠿⠿⢸⡇⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⣿⣿⣿⣿⣿⠿⠇⠐⠒⠃⠋⠀⢠⠠⠄⠝⠀⠀⠀⠀⠸⠆⠀⠀⠶⠛⠃⠈⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⡶⣾⢆⣿⣾⢀⣾⣶⣷⣷⣿⣿⣶⣷⡟⣸⣿⣾⣿⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠲⣶⠆⢶⠄⢴⣿⣿⠿⠀⠀⠈⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⠈⣶⣿⣾⣾⣾⣾⣾⣶⣷⣾⣬⡄⠁⠁⢀⢡⠅⠈⠀⡁⠈⠁⠁⠈⠈⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢌⠰⠬⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢈⠅⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀

⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣦⡄⠀⠀⠈⢄⣀⠠⢸⠽⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⡚⢰⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀

⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠿⢿⣧⣴⣾⣯⢐⠂⠀⡂⡱⣠⡪⠜⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀

⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣤⣿⣏⢹⡢⡂⢔⣉⣥⣢⣙⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⢿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢠⣤⣶⣶⢄⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⠁⠈⢸⣿⣿⣿⣦⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⠔⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣸⣿⣿⣿⣿⣿⡖⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠸⣿⣾⣷⣾⡆⠀⢀⣴⣶⣷⠀⠙⣿⣿⡿⡿⠫⠄⢲⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⣿⣿⣿⣟⣿⣿⣿⣛⣻⠉⠑⣀⡟⣿⣿⡋⢀⢠⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢧⡄⠀⠀⠈⠁⠀⠀⠀⠈⢿⣿⡌⠀⢀⣠⣿⣿⣿⣷⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣟⣿⣿⣾⣧⠀⢀⣾⣿⣭⣶⣿⣿⣿⢻⡟⣯⢏⣼⣿⢰⣿⡇⡀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄⢻⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣿⣿⡿⣿⣿⣏⠀⠘⣽⢟⣿⠻⢿⣿⠿⡾⡃⠏⣼⡿⢏⣟⣟⣦⠤⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢹⣿⠟⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠛⠃⠙⢳⠰⠈⢋⠅⠀⠸⠋⠁⢩⠁⠀⣿⠃⡸⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠸⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⡀⠀⠸⡕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠠⢰⣶⣶⣿⡇⠀⢸⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠏⢿⣿⣿⢰⠀⠀⢨⠂⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠙⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⡿⠃⢤⣿⣿⣿⣀⡶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣻⠀⠀⠀⠀⠀⠠⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣅⡄⠀⠀⠀⠤⠔⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉⠹⡶⠶⠾⠈⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⡟⡿⠿⢿⢻⡇⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣷⣄⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠐⠚⠋⠉⠀⢠⠀⠀⠝⠀⡂⠀⠀⠠⠀⠀⠐⠾⠛⠃⠘⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⣶⣾⢆⣿⣾⢀⣾⣾⣷⣷⣿⣿⣶⣷⡗⣸⣷⣾⣿⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠲⣶⠎⢶⠄⣴⢿⣿⠿⠀⠀⠈⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⡌⣶⣿⣾⣾⣾⣾⣾⣶⣷⣾⣮⠀⠁⠁⢀⠥⠁⠈⠀⡅⠈⠁⠁⠈⠈⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢌⠸⢯⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠹⠇⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀

⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣾⣿⣶⣶⠄⠀⠀⢈⠀⢐⠠⠸⡳⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢴⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀

⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠛⢿⢧⣾⣿⣧⠀⠀⠐⡊⣐⠘⠲⢞⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣾⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀

⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⣤⣿⣏⣹⡕⢄⣆⣁⣤⣜⡇⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⢿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢠⣤⣶⡶⢄⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⠌⠀⠀⣿⣿⣿⣧⢱⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⠔⠿⠿⢿⣿⣿⣿⣿⣿⣻⣿⣟⣿⣧⣸⣿⣿⣿⣿⣿⡖⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠸⣷⣾⣷⣾⡄⠀⢀⣤⣶⣷⠀⠙⢿⣿⣟⣟⠁⡄⠲⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣿⣿⣿⣿⣷⣿⣿⣛⣻⠉⠁⢠⡟⣿⣿⡋⠀⢠⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣣⡄⠀⠀⠈⠀⠀⠀⠀⠈⢻⣿⡌⠀⢀⣠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣾⣧⠀⢀⣼⣿⣾⣿⣿⣿⣿⢹⡟⣯⣿⣼⣿⢰⣿⠧⠂⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣄⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣏⠀⠙⣿⣿⣿⠿⣿⣿⡿⡾⡃⠏⢾⡿⢧⢟⣟⣤⠤⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢹⣿⠿⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆⢹⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠛⠑⠙⢱⡲⠈⢙⠇⠀⠙⠙⠁⢨⠁⠀⣿⢁⡜⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠘⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⠀⠀⢀⡀⠀⢸⡅⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶⣶⣿⡇⠀⢰⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠧⠿⣿⣿⠀⠀⠀⢨⠂⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠙⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⠃⢤⣿⣿⣿⡅⣰⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣻⠀⠀⠀⠀⠀⠠⠀⠃⠀⠀⠀⠀⠀⠀⠀⢸⣯⡀⠀⠀⠠⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠑⡶⠾⠿⠈⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⡛⡿⠿⣿⢻⠃⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡤⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⡿⣿⣿⣿⣿⣿⠿⠅⠀⠚⠋⠈⠀⠤⠄⠀⠕⠀⣃⠀⠀⠠⠀⠀⠐⠾⠛⠂⢺⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⡶⣾⢆⣿⣾⢀⣾⣶⣷⣷⣿⣿⣶⣷⡟⣸⣷⣾⣿⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠲⣶⠎⢶⠤⣴⢿⣿⠷⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⢨⣶⣿⣾⣾⣾⣾⣾⣶⣷⣬⣮⠄⠁⠁⡀⣥⠁⠈⠀⠁⠈⠁⠁⠈⠈⠀⠀⠁⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠰⠬⡻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠈⢀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀

⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⣿⣶⠀⠀⠀⠀⡀⢀⠀⠈⠵⢟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡕⣴⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀

⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⢛⡿⠃⣿⣿⣇⠀⠀⠐⠂⡠⢄⡌⢚⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡊⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀

⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣾⣿⣦⣾⢆⢠⠈⣀⣼⣽⡞⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢻⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣤⣴⠶⢄⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡏⠀⠀⠁⣿⣿⣿⣷⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⠔⠿⠻⢿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣧⣨⣿⣿⣿⣿⣷⡶⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠸⣷⣾⣷⣾⡄⠀⢀⣤⣶⡧⠀⠙⢿⣿⣟⣍⠅⡦⠐⣶⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⡁⠀⠀⠀⣻⣿⣻⣿⣷⣿⣿⣛⣻⠉⠑⣀⡟⣿⣿⠋⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⢧⡄⠀⠀⠈⠀⠀⠀⠀⠈⢻⣿⡌⠀⠀⣀⣸⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣾⣧⠀⢀⣼⣾⣻⣿⣿⣿⣿⢻⡟⣯⣾⣼⣿⣸⣿⠣⠀⠂⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣏⠀⠘⣿⣛⡿⠟⣿⣿⣿⡾⠃⠯⣾⡿⢳⢿⣟⣤⠄⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢹⣿⠿⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡆⢹⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠛⠁⠙⢱⡒⠀⠉⠉⠀⠊⠛⠁⠠⠁⠀⣿⠀⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠛⠀⠀⢀⡀⠀⢸⡇⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣼⡇⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠧⠿⣿⣿⠐⠀⠀⢨⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠙⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⡇⠤⣾⣿⣿⡇⢠⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣥⠀⠀⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠲⠾⠿⠈⠙⣹⣿⣿⣿⣿⣿⣿⣿⣿⠛⡿⠿⣿⢻⠁⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠿⠄⠁⠒⠋⠉⠀⠄⠄⠀⠇⠀⣀⠀⠀⠢⠄⠀⠐⠿⠋⠀⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⡷⣾⢆⣿⣾⢀⣾⣾⣷⣷⣿⣿⣶⣷⡟⣸⣷⣾⣿⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠲⣶⠎⢶⠤⣴⢿⡿⠗⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠌⠁⠈⠀⠁⠈⢸⣶⣿⣾⣾⣾⣾⣾⣶⣷⣮⣬⠀⠁⠁⡠⣥⠁⠈⢀⠁⠈⠁⠁⠈⠈⠀⠀⠁⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠡⠀⢌⠰⠬⡛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠈⣇⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀

⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⢛⣿⣅⠀⠀⠀⠀⠀⡀⠠⣨⠹⢟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣄⣐⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀

⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠙⣻⡿⢹⣿⠿⡄⡀⡀⢀⠀⣂⣤⡁⠷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⡎⣸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀

⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣷⣿⠫⠆⣠⢄⣭⣌⡝⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢻⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠠⣤⣶⠶⢄⠀⠀⠀⠀⠀⠀⠠⣼⣿⣿⣿⣿⡇⠄⡨⠁⢸⣿⣿⣿⡤⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⡔⠿⠿⠿⣿⣿⣿⣿⣿⣻⣿⣿⣟⣧⣨⣿⣿⣿⣿⣿⡦⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠸⣷⣾⣿⣾⡄⠀⢀⣤⣶⣧⠀⠙⢿⣿⣟⡌⠂⡧⢰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⠋⡁⠀⠀⠀⣿⣿⣿⣿⣷⣿⣿⣝⣻⠉⠑⣀⡟⣿⣿⠋⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣧⡄⠀⠀⠈⠁⠀⠀⠀⠀⢻⣿⣌⠀⠉⣀⣨⣿⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢀⣼⣿⣚⣿⣽⣿⣿⢻⡟⣷⣯⣼⣿⣼⣟⠏⡀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣺⣿⣿⡿⣿⣿⣏⠀⠙⣿⣿⣿⠛⢿⣿⣿⡾⡂⢯⣾⡿⣱⣯⣿⣤⠄⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠸⣿⡿⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠛⠁⠙⢱⡒⠈⠋⠇⠀⠂⠙⠁⢠⠀⠘⡟⢀⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠈⠿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⣿⠟⠀⠀⢀⡀⠀⢸⡇⠀⠈⠀⠀⠀⠀⠀⠈⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣾⣷⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠓⠿⣿⡽⠀⠀⠀⢨⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⡟⠰⣸⣿⣿⡇⢨⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣴⣿⣧⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣿⡥⠀⠀⡀⠤⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠶⠿⠿⢀⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⠛⡿⠿⣿⢺⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣤⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠿⠄⠂⠒⠋⠁⠀⠤⠄⠨⠃⠀⡀⠀⠀⠶⠀⠀⠒⠛⠋⠘⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⡶⣾⢆⣿⣾⢀⣾⣶⣷⣷⣿⣿⣶⣷⡟⣸⣷⣾⣿⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠲⣶⠎⢶⠤⣴⢿⡿⠗⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⢨⠁⠈⠀⠁⠈⢸⣶⣿⣾⣾⣾⣾⣾⣶⣷⣮⣬⠀⠁⠁⡠⡅⠁⠈⢠⠁⠈⠁⠁⠈⠈⠀⠀⠁⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⢀⠍⠠⠑⡴⠮⠟⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠭⣄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣭⣭⡀⠀⠠⢥⣄⡙⠠⠅⠂⠗⣙⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⠳⠭⣲⣾⣿⣿⣶⡄⠀⠀⠀⠀⠀

⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣽⣿⣏⣿⣿⢳⣀⠎⠥⠢⢰⣖⠏⢣⣋⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠕⠧⢱⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀

⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⠧⠄⠲⠐⣈⣞⣏⣅⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠺⣿⣿⣿⣿⡿⡏⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⢄⡀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⢿⡏⡀⢁⠤⠁⣿⣿⣿⣧⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⡦⠸⠿⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣁⠀⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢸⣷⣿⣷⣶⡇⠀⠀⢠⣶⡷⠀⠈⠻⣿⡟⡕⠁⠁⠠⢲⣶⣿⣿⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⠏⠁⠀⠀⠀⣹⣯⣻⣿⣷⣿⣿⣝⣻⠉⠁⠈⡿⣿⣿⠟⠁⠀⡀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣧⡅⠀⠀⠐⠈⠀⠀⠀⠀⠙⢿⣄⠀⠨⢀⣀⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢀⣰⣿⣽⣿⣿⣿⣿⢿⣻⣿⣧⣴⡿⣼⡿⠃⡀⠀⠈⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡁⠈⢿⣿⢻⠝⣿⣿⣿⡾⢡⢯⣿⠿⣽⣫⣿⡤⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠘⣿⡟⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠛⠃⠙⢑⡒⠀⠹⠗⠀⠟⠙⠃⢨⠈⣿⡏⢰⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⡀⠂⠸⡟⠀⠀⠀⠀⠀⠀⠀⠈⠀⡼⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣿⣿⣿⠀⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠑⠚⣿⡿⠰⠀⠀⢸⠈⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⡧⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠆⣙⣿⣏⢻⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣿⣣⠀⠀⠀⠐⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢸⣧⡄⠀⢀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠿⠾⠁⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⠿⣿⠺⠀⠀⠀⠀⡀⠀⡦⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⣿⣿⣿⡿⣿⠿⠄⠃⠒⠛⠀⠀⠤⠄⠨⠃⠀⡇⠀⠀⠶⠄⠀⠚⠛⠑⠿⣿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⣶⣾⢆⣿⣾⢀⣾⣶⣷⣷⣿⣿⣶⣷⡟⣸⣷⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠲⣶⠎⢶⠤⣴⢿⣿⠟⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⢈⢸⣶⣿⣾⣾⣾⣾⣾⣶⣷⣬⣬⠀⠁⠁⡤⡅⠁⠈⢠⠁⠈⠁⠁⠈⠈⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠍⠠⠕⣾⡮⣽⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠍⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣭⣭⡀⡀⠰⢭⡐⡁⠡⠥⠦⣝⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠪⠮⣲⣾⣿⣿⣶⡄⠀⠀⠀⠀⠀

⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣿⣿⣏⣿⣿⢳⣀⠦⠩⠠⢠⣐⣕⢣⡃⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠓⢱⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀

⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⠧⢄⢢⠀⠝⣯⣎⣼⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠺⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⢄⡀⠀⠀⠀⠀⠀⠰⣾⣿⣿⣿⠿⡻⡀⢀⠬⠀⣿⣿⣿⣧⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⡦⠸⠿⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣅⠀⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢸⣷⣿⣷⣶⣇⠀⠀⢠⣶⣷⠀⠈⠻⣿⡏⡝⠁⠅⠬⢲⣶⣿⣿⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠁⠀⠀⠀⣸⣿⣿⣿⣷⣿⣿⣟⣻⠉⠑⠈⡿⣿⣿⠟⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣧⡅⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⠀⠩⢄⣈⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢀⣰⣿⣿⣿⣿⣿⣿⢿⣻⣿⣧⣴⡿⣼⡿⡓⡀⠈⠀⠁⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣟⡁⠘⢿⣿⣿⠻⣿⣿⡿⡾⢡⢯⣿⡿⣹⣫⣿⡤⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠘⣿⡟⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠛⠃⠙⢑⡒⠈⢹⠝⠀⠉⠋⠁⢠⠈⢿⡏⣴⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⡀⠀⠸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⣿⣿⣿⠀⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠓⠚⣿⡟⠰⠀⠀⢨⠈⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠇⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠆⣹⣿⣏⢻⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣿⣣⠀⠀⠀⠐⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢸⣧⡄⠀⢠⡤⠄⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠿⠾⠁⣈⣽⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⠿⣿⢻⠀⠀⠀⠀⡀⠀⡦⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠄⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⣿⣿⣿⡿⡿⠿⠄⠃⠒⠛⠀⠀⠤⠄⠨⠃⠀⡇⠀⠀⠶⠄⠀⠚⠛⠑⠿⣿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⣶⣾⢆⣿⣾⢀⣾⣾⣷⣷⣿⣿⣶⣷⡟⣸⣷⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠲⣶⠎⢶⠤⣴⢿⣿⠟⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠁⠈⠈⠁⠈⠀⠁⢈⢸⣶⣿⣾⣾⣾⣾⣾⣶⣷⣬⣬⠀⠁⠁⡤⡅⠁⠈⢠⠁⠈⠁⠁⠈⠈⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠠⠀⠈⢑⢀⠼⠿⡭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣍⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡄⡀⠈⠀⡂⢔⢂⣼⡐⡕⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣺⡲⣼⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀

⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣯⣿⣿⣱⡀⠒⠀⠀⡢⡚⢏⠵⢞⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⡟⣹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀

⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⡷⠐⠀⡁⣀⣄⣷⣅⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠻⣿⣿⣿⣿⡿⠏⠁⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣄⡀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⠿⠓⠐⢘⡉⠀⣿⣿⣿⣧⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡔⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣯⣠⡰⢿⣿⣿⣿⣯⡄⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢸⣷⣿⣷⣾⡆⠀⠀⠠⡶⠷⠆⠀⠙⢿⣟⡀⢤⢑⠑⣲⣾⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⡁⠀⠀⢘⣿⣿⣿⣾⣿⣿⣻⠋⠉⠑⣲⢻⣿⡿⠋⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣥⡅⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠂⣀⣠⣼⣿⣿⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⡟⣤⣾⣧⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡹⣿⣿⣿⣿⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠀⢻⣿⣿⠻⣿⣿⣿⠃⡾⣼⡿⢏⣾⣽⡯⠤⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠈⢿⡟⣳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠘⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠛⠚⠟⡲⡂⠙⠝⠀⠇⠛⢠⠇⠹⣿⢃⡾⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⣀⠹⣿⣼⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡿⠁⠀⠀⢀⠐⠀⣿⠃⠀⠀⠀⠀⠀⠀⠁⠀⡏⠐⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠆⢿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠯⠀⣿⠃⠆⠀⠰⠕⠁⠀⢺⠀⠀⠀⠀⠀⠀⠀⣀⠀⠃⠀⠀⠀⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢣⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣿⣖⢻⡀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⣤⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠞⠻⠟⠋⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⡏⢿⣿⣿⡯⠡⠀⠀⠀⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣾⣿⡿⡿⣿⣿⠿⣿⠿⠇⠀⠍⠅⠁⠀⠠⢠⠂⠝⠀⠿⠀⠀⠤⠀⠐⠚⠛⠸⠿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⣷⣾⢆⣿⣾⢀⣾⣶⣷⣷⣿⣿⣶⣷⡟⣸⣷⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠲⣶⠎⢶⠄⣴⣿⣿⡿⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⢨⣶⣿⣾⣾⣾⣾⣾⣶⣧⣬⣬⡀⠁⠁⣠⡥⣥⠈⠀⡗⠈⠁⠁⠈⠈⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⢀⠢⠉⠈⠥⢸⠿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠩⡁⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣯⡄⠀⠀⠀⡆⠐⠅⠸⠸⣳⠝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣢⢇⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣹⣿⡙⡀⠀⠀⠀⣐⠥⠂⠐⠞⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠳⡃⣾⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀

⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢸⣿⣿⣿⣿⢟⠀⠠⡨⣦⣥⣷⣂⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⢿⣿⣿⣿⣿⠝⠉⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢤⣴⣶⣄⡀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⠿⠗⡀⢚⠁⣿⣿⣿⣿⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⣶⠽⠿⠻⣿⣿⡿⣿⣿⣿⣿⣅⣄⠼⢿⣿⣿⣿⣴⠄⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢸⣶⣿⣿⣾⣇⠀⠀⠠⠶⠷⠆⠀⠙⢿⣏⡄⠐⢀⡀⣶⣿⣿⣿⣯⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠂⠀⠀⣿⣿⣷⣿⣿⣟⣟⠙⠉⠃⢰⢻⣿⣟⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣡⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠒⣀⣃⣿⣿⣷⣦⣾⠿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢀⣼⣿⣿⣿⣿⣿⣿⣵⢋⣴⣾⣧⣿⣯⡅⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡹⣿⣿⣿⡗⢺⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⡁⠘⣿⡟⢏⣿⣿⢟⣰⢇⣾⣿⣟⣾⣽⣯⡤⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠘⢿⡿⡳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠘⣿⡿⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠙⠓⢻⠓⣖⠈⠙⠐⠉⠀⢸⠀⠪⣿⠇⣼⠿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣸⣀⢻⣷⠘⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢀⣀⠇⢱⡿⠀⠀⠀⠀⠀⠀⠀⠀⡞⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠇⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠄⢻⣼⣿⣿⣿⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⠋⢘⡇⠀⠀⢁⣾⠎⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡀⡇⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢤⠸⢻⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣶⠚⡆⠀⠀⠀⠀⠀⠀⡄⠃⠀⠀⠀⠀⠀⢀⣿⡄⠀⢀⣤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⠞⢻⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣠⠉⠀⠀⠀⣀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢸⣿⣧⡤⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡧⠈⠿⠿⠿⣿⣿⠿⣿⡿⠇⠈⠻⠿⠃⠀⠀⡔⠒⠉⠁⠨⠀⠀⠀⠀⠰⠟⠛⠀⠻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⣷⣾⢆⣿⣾⢀⣾⣶⣷⣷⣿⣿⣶⣷⡗⣸⣷⣾⣿⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠆⠲⣶⠎⢶⠄⢰⣶⣿⡿⠃⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⢀⣶⣿⣾⣾⣾⣾⣾⣶⣥⣬⣬⡄⠁⠁⢠⣥⢥⡌⠁⢱⠊⠁⠁⠈⠈⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⢄⠠⠉⠈⠥⠼⠿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠼⡁⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣯⡄⠀⠀⠀⠀⠐⠷⠪⠸⡳⠝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡚⡀⢇⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀

⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣹⣿⡙⡀⡀⠀⠐⣐⡭⢂⡑⠚⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⢓⠇⣾⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀

⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢸⣿⣿⣿⣿⡟⠀⠠⡨⣆⣥⣥⣂⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠘⢿⣿⣿⣿⣿⠝⠉⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢤⣴⣶⣄⡀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⠿⠗⡀⢚⠁⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⡶⠽⠿⠿⣿⣿⡿⣿⣿⣿⣿⣅⣄⠼⢿⣿⣿⣿⣴⠄⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢸⣶⣿⣿⣾⣇⠀⠀⠰⡶⠷⠆⠀⠙⢿⣟⡄⠐⢀⣀⣶⣿⣿⣿⣯⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠂⠀⠀⣿⣿⣿⣿⣿⣿⣟⠙⠉⠇⢰⢻⣿⣟⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣡⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠂⣁⣀⣽⣿⣷⣦⣾⠿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢀⣼⣿⣿⣿⣿⣿⣿⣵⢋⣴⣾⣧⣿⣯⡅⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡹⣿⣿⣿⡗⢺⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⡁⠘⣿⡿⢟⣿⣿⢟⣰⠇⣾⣿⣏⣾⣽⣯⡤⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠘⢿⡿⡳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠘⣿⡿⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠙⠓⢻⠓⣖⠈⠑⠀⠋⠁⢸⠀⠪⣿⠇⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣸⣀⠹⣷⠘⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢀⣀⠇⢱⡿⠀⠀⠀⠀⠀⠀⠀⠀⡞⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠅⠀⠘⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢿⣿⣿⠄⢻⣼⣿⣿⣿⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⡋⢘⡇⠀⠀⢁⣾⠎⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡀⡇⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢤⠲⢻⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣶⠒⡆⠀⠀⠀⠀⠀⠀⡄⠃⠀⠀⠀⠀⠀⢰⣯⡄⠀⢀⣤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡳⠞⢻⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢹⣿⣿⣠⠉⠀⠀⠀⣀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢸⣿⣧⡤⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠿⠿⠿⣿⣿⠿⣿⡿⠏⠈⠻⠿⠃⠀⠀⡔⠒⠉⠁⠨⠁⠀⠀⠀⠰⠟⠛⠀⠻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠆⠲⣶⠎⢶⠄⢰⣶⣿⡿⠃⠀⠀⠀⠁⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⢀⣶⣿⣾⣾⣾⣾⣾⣶⣥⣬⣬⡄⠁⠁⢠⣥⢥⡌⠀⢱⠊⠁⠁⠈⠈⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠰⠾⡾⡛⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣭⣅⠀⠁⠠⠗⢔⣀⠆⠂⡙⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠰⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢿⣟⣸⣿⡛⡆⠀⠀⠀⢀⡣⡖⠡⡝⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢸⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢸⣿⣿⣿⣿⠟⠀⢠⢐⣤⣷⡠⢆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠺⣿⣿⣿⣿⡋⡃⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⢄⡀⠀⠀⠀⠀⠀⠐⢾⣿⣿⣿⡿⡗⢘⠋⢸⣿⣿⣿⡄⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⢵⠶⠟⠛⢿⣿⣿⢾⣿⣿⣿⣯⣠⣄⠾⢿⣿⣿⣷⣷⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠠⣶⣿⣿⣶⣇⠀⠀⡠⠶⠷⡆⠈⠙⣿⣏⠄⠄⠠⢱⣾⣿⣿⣿⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠀⠀⠀⢸⣿⣿⣽⣿⣿⣻⠋⠉⠉⠢⢸⢿⣿⡟⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣬⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣎⢂⣈⣸⣿⣿⣦⣴⣿⢽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣄⢀⣼⣿⣿⣿⣿⣿⢻⡾⠁⣴⣾⡇⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣮⠻⣿⣿⣿⠒⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⢋⠈⢿⡯⢹⣿⡇⢇⠰⠁⣼⣿⡟⣸⣿⣛⣅⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠈⢻⣿⠛⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢹⣿⢿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⠙⠛⠺⡟⢒⡂⠉⠀⠈⠀⠃⠀⠀⢈⡟⢠⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠈⢿⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢿⡆⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⢀⡸⠈⣿⡏⠀⠀⠀⠀⠀⠀⠀⢰⠃⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⣿⣿⣿⠘⣷⣢⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣟⡀⠉⠸⠀⠘⣴⡟⠁⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣄⢿⡹⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢰⣿⠖⠃⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⣯⠀⠀⠀⣀⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡶⠖⠯⣿⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⡃⠀⡄⠀⠀⢀⡀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢘⣿⣄⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡄⠀⠻⠿⠿⣿⡿⠿⣿⡿⠏⠈⠿⠿⠃⠀⠀⢦⠶⠪⠁⠀⠸⠀⠀⠀⠴⠶⠂⠀⠀⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢦⡏⣾⣷⣶⣷⣿⣾⢆⣿⣾⢀⣾⣶⣷⣷⣿⣿⣶⣷⡟⣸⣷⣾⣿⠈⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠲⣶⠎⢶⠄⠰⣶⣿⣿⠛⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⠀⣶⣿⣾⣾⣾⣾⣾⣶⣷⣬⣬⣄⠁⠁⢠⣥⣕⣮⠄⠀⣾⠁⠁⠈⠈⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠁⠄⢄⢤⢌⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣟⣿⣿⣭⣅⠀⠀⠀⠀⠐⠤⠼⡰⢐⢬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡥⢴⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣟⣻⣿⠛⡆⠀⠀⡀⠠⠄⢲⡠⢝⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢹⣿⣿⣿⣿⡟⠱⡄⢂⣷⣠⡑⡱⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⡿⣿⣿⣿⣟⡗⠅⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣤⣀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⠿⠗⡸⠃⣿⣿⣿⣷⣔⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⡽⢶⠛⠛⠛⣿⣿⣿⡿⣿⣛⣿⣭⣤⠀⣿⣿⣿⣿⣯⡿⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⣶⣮⠀⠀⠴⠾⠿⠆⠈⠙⣿⣯⠄⠅⠀⣶⣿⣿⣿⣯⣥⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠍⠀⠀⠀⣸⣿⣟⣿⣯⣟⡿⠉⠉⠈⢂⢸⢿⣿⡟⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣇⣬⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⢂⣃⣸⣿⣿⣦⣴⠿⢿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣀⠀⣿⣿⣿⣿⡟⣟⣿⡞⠀⣴⣿⡇⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣎⢻⣿⣿⣿⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⠀⢻⡏⢹⣿⠧⠇⡾⠀⢼⣿⡿⣰⣯⣟⣁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢻⣿⠟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⢹⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠘⠙⠛⠺⠿⢰⢂⠀⠀⠍⠀⠃⠀⠀⠸⡿⢀⠯⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⣿⡈⠋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⠀⠀⠀⢀⣀⠁⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢻⣿⣿⡷⠙⣃⢠⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢻⣏⡀⠉⠸⠀⠐⢠⡿⠃⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠯⡀⣿⣸⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣸⣿⡖⠃⠀⠀⠀⠀⠀⠄⠀⠀⠇⠀⠀⠀⠀⠀⠀⣲⡀⠀⠀⠀⣀⠐⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡶⢟⠿⣿⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠄⠀⠀⠀⡀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢿⣧⡀⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡄⠀⠹⠿⠿⣿⡿⠿⣿⠿⠏⠘⠿⠿⠋⠀⠀⠠⢰⢊⠅⠀⠀⠅⠀⠀⠴⠶⠂⠀⠀⢹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢦⡏⣾⣷⣶⣷⡷⣾⢆⣿⣾⢀⣾⣶⣷⣷⣿⣿⣶⣷⡟⣸⣷⣾⣿⠀⠙⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠆⠲⣶⠎⢶⠄⠰⣶⣾⣿⠿⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠅⠈⠀⠁⠈⠀⣶⣿⣾⣾⣾⣾⣾⣶⣧⣬⣬⡄⠁⠁⠀⣡⡕⣾⡴⠠⣼⡇⠀⠀⠈⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠀⠆⢆⢤⣍⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣃⠀⠀⠀⠀⢠⣤⡼⣸⢠⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢼⣴⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⣿⣟⣹⣿⠿⡆⠀⠂⠂⣐⠀⠀⣯⣁⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢤⣿⣿⣿⣿⣿⡿⡦⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢻⣿⣿⣿⣷⡷⠠⠀⣝⣿⣕⡑⡣⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠈⣿⣿⣿⣿⣟⣻⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⣄⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⡤⢰⠀⣿⣿⣿⣧⠒⡲⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⠵⡾⠛⠛⢿⣿⣿⡿⢿⣿⣻⣿⣥⣤⠠⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣶⣾⡀⠀⠴⠾⠿⠂⠈⠻⣿⡏⡐⢐⡰⣾⣿⣿⣿⣭⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⠁⠀⠀⢸⣿⣿⢿⣿⣿⣟⡟⠘⠁⠰⢁⣹⢿⣿⡟⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣏⣨⠀⠀⠀⠈⠀⠀⠀⠀⠙⢿⡕⠰⣀⣸⣿⣷⣤⡾⡿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣦⡀⢠⣿⣿⣿⣿⡟⡟⣷⠏⢠⣾⣿⡗⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣌⢿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⠁⠈⠿⡘⠝⣿⠹⠃⠎⠀⢼⣿⡿⢱⢯⣞⣀⡀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠙⣿⣟⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⢻⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠈⠘⠋⠺⣷⢘⢳⠀⠀⠉⠀⠀⠀⠀⠚⣿⠁⠏⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢸⣷⠘⠼⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⠀⠀⠀⢀⣀⠁⠙⡼⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⣿⣿⣿⡆⢫⡆⢀⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⣏⡁⠉⠘⠀⠐⢢⡾⠏⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⢧⡸⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣽⣿⡖⠃⠀⠀⠀⠀⠀⠤⠀⠀⡇⠀⠀⠀⠀⠀⠀⣰⡁⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⡾⣟⠿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⢠⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡄⠀⠽⠿⠿⣿⡿⢿⣿⠿⠃⠘⠿⠿⠋⠀⠀⠠⡔⣖⡩⠀⠀⠀⠀⠀⠴⠶⠂⠀⠀⠈⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢦⡏⣾⣷⣶⣷⡷⣾⢆⣿⣾⢀⣾⣾⣷⣷⣿⣿⣶⣷⡟⣸⣷⣾⣿⠀⠙⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠲⣶⠎⢶⠄⠰⢶⣶⣿⡿⠂⠀⠀⠁⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⠀⣶⣿⣾⣾⣾⣾⣾⣶⣧⣬⣬⡄⠁⠁⠀⣡⣵⢪⣠⡅⢼⣷⠁⠈⠈⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣡⢼⠡⣄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⡷⡖⠀⠀⠠⠠⠄⣰⢐⢁⢿⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⣾⣿⣿⣶⠂⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢽⣿⠟⣿⣿⣿⡇⠀⠀⢀⠰⡓⢃⡯⢁⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⣿⣿⣿⣿⣿⣷⡂⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣿⣤⣧⠀⠠⣦⣤⣄⠸⢿⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⢹⣿⣿⣿⣿⣿⣝⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣄⡀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠃⢨⢨⣿⣿⣿⣧⢶⢑⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⡹⣿⠻⠛⠙⣿⣿⣿⠿⣿⣟⣿⣯⣤⠀⠙⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣷⣶⡇⠀⢴⡶⣿⠀⠙⢿⣿⡛⠉⣄⢰⣾⣿⣿⣿⣭⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣧⡨⠀⠀⠀⣿⣿⣿⣿⣿⣽⣻⠙⠉⠀⠐⢉⣽⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⣟⣩⡍⠀⠀⠀⠀⠀⠀⠀⢻⣿⡐⠈⣀⣿⣿⣿⣧⢾⡟⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣄⡀⣿⣿⣿⣿⣿⢻⣯⣴⠁⠀⣼⣿⡇⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣯⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡈⢿⣿⣿⡟⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⠀⡌⠏⠨⠟⡿⠜⢰⠃⠀⣼⣿⣿⢱⠟⣞⣀⡀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠈⢿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠂⠸⠻⠐⣠⠘⡗⡀⠀⠂⠐⠀⠀⠀⠙⣿⠁⡜⠎⠉⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⢸⣇⠙⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⣈⠄⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣾⣷⠀⠿⡀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣟⡁⠋⠀⠄⠠⠂⣼⠟⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣏⣄⠸⡆⢸⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⡯⠃⠀⠀⠀⠀⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢰⣂⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣿⡷⣽⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⢿⡀⠀⠴⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠈⠓⠩⠁⠙⠿⠿⠿⢿⣿⢿⢿⠿⠃⠽⣿⡿⠋⠀⠀⠀⠤⠲⣖⠄⠀⠀⠀⠀⢠⠴⠂⠀⠀⠀⢱⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢦⡏⣾⣷⣶⣷⡿⣾⢆⣿⣾⢀⣾⣾⣷⣷⣿⣿⣶⣷⡟⣸⣶⣾⣿⠀⠈⠻⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠲⣶⠎⢶⠄⠰⢶⣶⣿⡿⠃⠈⠀⠁⠁⠀⠈⠀⠀⠈⠈⠀⠈⢨⠁⠈⠀⠁⠈⠈⣶⣧⣾⣾⣾⣾⣾⣶⣧⣬⣬⠀⠁⠁⠀⠁⢁⣬⣤⣴⠈⢱⣷⠈⠈⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⡨⠄⢀⣴⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣷⣶⣦⡀⠀⠠⡀⠀⡂⠰⠽⢞⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣾⣷⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠯⣶⣶⣶⣦⠀⠀⠀⠂⠯⣐⢃⢆⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⣿⡋⢛⡿⠀⠠⣵⣴⣍⠬⢱⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠘⢻⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀⠀⠀⠀⢀⢠⣿⣿⣿⣿⣿⠇⡈⢀⣿⣿⣿⣆⢾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣛⠿⣿⠟⠛⢻⣿⣿⣷⢿⣟⣿⣿⣥⡄⠘⢻⣿⣿⣿⣿⣾⠇⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇⢰⣶⡾⡟⠀⠙⣿⣿⣿⣛⠀⢴⣾⣿⣿⣿⣭⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⡃⠀⠀⢸⣿⣿⣿⣿⣻⣛⡛⠉⡁⠐⠊⢉⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⣟⠩⠁⠀⠀⠀⠀⠀⠀⠘⢿⣿⡙⠈⣀⣿⣿⣿⣧⣿⠟⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣧⣀⠸⣿⣿⣿⣿⡟⣏⣠⡾⠀⠠⣾⣿⡇⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡀⢼⣿⣿⡟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⡟⠀⣝⠇⠙⠛⢁⠇⠼⠁⠀⣴⣿⣿⢱⠏⡾⣀⡀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⢷⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⣿⣷⠘⢻⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠁⠹⡋⠀⠠⠈⡕⠀⠀⠀⠀⠀⠀⠀⠍⢿⠁⡼⠌⠛⠉⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⢸⣧⠙⠸⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣐⡁⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠐⠀⣶⣤⣬⣿⠀⠈⢿⡀⢀⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⠟⢻⠃⠀⡄⢠⡆⣰⡿⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⡟⠰⣤⡨⣇⢸⣿⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣽⣷⣦⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠙⡾⢿⣿⣿⡷⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠉⠀⠘⠿⢿⡿⣿⣿⣿⠿⠿⠿⢿⣿⣿⡿⠋⠀⠀⠀⠠⠰⢤⡤⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⢲⣿⣖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⣿⣾⢆⣿⣾⢀⣾⣾⣷⣷⣿⣿⣶⣷⡟⣸⣶⣾⣿⠀⠀⠹⢿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠲⣶⠎⢶⠄⠰⣶⣶⣿⠛⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠨⠈⠁⠈⠀⠁⠈⢸⣶⣽⣾⣾⣾⣾⣾⣶⣧⣬⡌⠀⠁⠁⠀⠁⠁⣈⣄⣄⡌⠁⣷⠈⠈⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⢃⠁⠀⣢⣞⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣷⣶⣤⡀⠀⠀⠈⠌⡀⠓⡷⢪⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣶⣾⣷⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡹⢧⣾⣯⣶⣦⠀⠁⢀⡀⣾⣳⠭⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣼⣟⠛⢻⡷⠀⠀⣷⣧⣽⠺⢷⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠹⢻⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⠀⠀⠀⠀⢀⠠⣿⣿⣿⣿⣿⠋⠈⢀⣿⣿⣿⣆⡶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡛⢿⡿⠟⠛⣿⣿⣿⡿⢿⣛⣿⣯⣤⡄⠙⢻⣿⣿⣿⣿⣾⠇⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣾⡁⢴⣶⠿⠟⠀⠙⣿⣿⣿⣟⡁⢰⣾⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⠁⠀⠀⢹⣿⣿⣿⣿⣿⣻⠉⢈⠀⠒⠈⣩⡿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣏⡉⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡜⠁⠀⣿⣿⣿⣦⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣦⣀⢸⣿⣿⣿⣿⡟⣏⣴⡟⠀⢠⣾⣿⡇⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡟⠀⠀⠠⠀⠀⠀⠀⠀⠀⠹⣿⣿⡄⠀⣿⣿⡏⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣝⠇⠛⠟⢰⠇⡞⠀⠀⢼⣿⣿⢰⢯⡾⣀⡀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠸⣿⣟⠇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⢻⡿⣅⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠱⠻⡋⠂⠀⠈⡕⠀⠀⠁⠀⠃⠀⠀⠙⢿⠁⡼⠌⠛⠉⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣇⠘⠸⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠁⣐⡁⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠄⣤⣤⣤⣼⡇⠀⠈⢿⡄⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠁⠀⡄⢠⡖⢰⡿⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⣿⠃⠀⠷⣜⢧⣾⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⠤⣄⣿⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠛⣿⡿⠻⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⣻⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠤⠀⠀⠙⢿⣿⡿⡿⣿⣿⠿⣿⣿⣿⡿⠛⠛⠛⠀⠀⠀⠀⠰⢤⡤⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠲⣿⣖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢦⡏⣾⣷⣶⣷⣷⣾⢆⣿⣾⢀⣾⣾⣷⣷⣿⣿⣶⣷⡟⣸⣷⣾⣿⠀⠀⠹⢿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠲⣶⠎⢶⠄⠰⣶⣶⣿⠟⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⡬⠈⠁⠈⠀⠁⠈⣾⣶⣿⣾⣾⣾⣾⣾⣶⣷⣾⣬⠀⠁⠁⠀⠁⠁⣈⡄⣄⠌⠁⣷⠈⠈⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⢈⡋⡈⡸⡷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣦⣄⣀⠀⠀⠀⡄⣀⣒⡗⣯⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣦⣶⣶⣷⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣩⣯⣭⣭⡇⡀⠠⡠⢈⡟⡥⣬⠟⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄⣿⡿⠿⣿⡇⠀⠠⣛⣿⣽⠻⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠻⣿⣿⣿⣿⣿⣏⠇⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣤⣀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣶⣿⠁⠀⠀⣿⣿⣿⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢯⡿⠿⠻⣿⣿⣿⡿⣿⣿⣿⣧⢤⠀⠙⣻⣿⣿⣿⣿⣼⠇⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣶⣾⠀⢴⡶⡿⠏⠀⢻⣿⣿⣿⣏⡂⣱⣿⣿⣿⣿⣽⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⠁⠀⠀⣿⣿⣿⣿⣟⣟⡟⠉⣉⠀⠂⠈⣭⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⡋⠁⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡘⠁⠀⢿⣿⣿⣧⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣄⠀⢸⣿⣿⣿⣿⢛⣃⣴⠃⠀⢠⣿⣿⢧⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⡀⠀⢸⣿⡛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⡉⠀⠻⡏⡾⢠⠇⠀⠀⣾⣿⡟⢸⢯⡆⣀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢻⣿⠛⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⠐⢺⡿⣇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠄⢿⡟⠂⢀⢹⡃⠀⠀⠁⠘⠀⠀⠀⠙⣿⠁⡏⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡟⠀⢸⣷⠈⠚⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢁⠐⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⣈⣿⠀⠀⠀⣿⣷⣦⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⡀⢀⡤⢠⡟⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠆⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠇⠀⠀⠐⣿⠛⣸⣿⡟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡟⠀⠀⠁⠈⠁⠈⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠀⠀⠀⠀⠐⠀⠟⠋⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⣿⣿⣿⠿⢿⢿⢿⠿⠉⠛⠃⠀⠀⠀⠀⠐⠦⠤⠄⠀⠀⠀⠠⠄⠀⠀⠀⠀⢣⣿⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⣶⣾⢆⣿⣾⢀⣾⣾⣷⣷⣿⣿⣶⣷⡟⣸⣶⣾⣿⠀⠈⠻⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠲⣶⠎⢶⠄⠰⣶⣾⡿⠇⠀⠈⠀⠀⠁⠀⠈⠀⠀⠈⠈⠁⣬⠎⠁⠈⠀⠁⠈⣾⣶⣿⣾⣾⣾⣾⣾⣶⣷⣬⡌⠀⠁⠁⠀⠁⠁⣈⡅⣥⡌⠁⣥⠈⠈⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢄⣡⡟⣭⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣶⣶⣤⡄⠀⠀⠀⠄⠀⠀⠑⢃⠌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⡖⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣯⢱⣿⣾⡀⠀⠀⠀⡀⠮⠱⡒⣃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣀⣽⣟⢉⡇⠀⠀⢀⣴⣵⡉⢬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠁⠓⣿⣿⣿⣿⡿⡓⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢤⡀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⡁⠠⠀⢸⣿⣿⣷⣜⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣦⣹⠟⠛⢿⣿⢿⣿⣿⣿⡅⣤⠀⠉⣿⣿⣿⣿⣷⡿⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣶⣏⢠⣴⡶⠿⠃⠹⣿⣿⡿⢿⡛⠠⠆⣾⣿⣿⣿⣯⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣻⣟⡏⠉⡁⠀⠁⢉⣽⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⡋⠁⠀⠀⠀⠀⠀⠀⠘⣿⣿⣇⡁⠀⢀⣼⣿⣿⣿⣾⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣾⣧⠀⢼⣿⣿⡿⢛⣡⡾⠁⠀⢴⣿⣿⣸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣆⠀⢸⣿⣿⣟⢳⣾⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⠆⢀⡁⠘⠇⡿⢸⠁⠀⠀⣿⣿⢇⡿⡠⣀⡀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠹⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠙⣿⡿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠱⠸⣿⠀⢤⡶⢯⠀⠈⠀⠀⠀⠀⠀⢹⠏⠸⠈⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠁⠀⢻⣿⣈⣾⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡀⠀⠀⠚⠉⢦⣩⠀⠘⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣄⣿⠀⠀⠀⢿⣿⣿⣏⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠁⠠⠀⡶⢠⡿⠃⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⡛⠀⠀⢀⠘⠟⢻⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠐⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣶⣧⣌⠛⠛⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⢸⣇⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠀⢸⣿⣿⣿⡿⣿⣤⡟⠛⣛⠉⠉⠀⠘⠋⠀⠀⠀⠀⠀⠘⢴⡤⠀⠀⡄⠀⠐⠀⠀⠀⠀⠀⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢦⡏⣾⣷⣶⣷⡶⣾⢆⣿⣾⢀⣾⣾⣷⣷⣿⣿⣶⣷⡗⣸⣶⣾⣿⠀⠹⢿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠲⣶⠎⢶⠄⢰⣶⣾⡿⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠨⠌⠁⠈⠀⠁⠈⣾⣶⣿⣾⣾⣾⣾⣾⣶⣷⣾⣮⡄⠁⠁⠀⠁⠁⡈⡄⡀⠈⠁⢥⢨⡎⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠇⢀⣩⣟⣫⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠎⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣦⡄⠀⠀⠂⠀⠢⢁⡹⢻⣬⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⣴⣾⣷⠀⠀⠀⠠⠂⡾⢑⡷⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⡟⡇⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣄⣼⣏⣩⡆⠀⠀⠀⣚⣾⣷⠨⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠙⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⣿⠀⠀⠆⢠⣿⣿⣿⣦⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣎⠻⠛⠹⣿⣿⣿⣿⣿⡥⡤⠀⠈⣿⣿⣿⣿⣷⡿⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣇⣠⣴⣶⠟⠈⠻⣿⣿⡟⡟⡻⠶⠆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⣿⣿⣿⣛⡏⠉⡁⠈⠀⣠⣾⢿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠉⠁⠀⠉⠀⠀⠀⠀⠙⣿⣿⣄⠀⠀⣤⣼⣿⣿⣿⢾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⡄⢸⡿⣿⡿⢛⣡⡾⠁⠀⣾⣿⡇⣾⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣆⠀⣿⣿⣿⣟⢻⣶⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⡿⠕⠀⣁⠛⠃⡟⢰⠁⠀⠰⣿⣿⢱⢏⣖⣀⡀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡄⠹⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠑⠃⣿⡅⠴⡗⢯⠁⠀⠀⠀⠀⠀⠀⢻⠁⡎⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠂⠀⣿⣿⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡀⠀⠀⠞⠁⢚⣬⠀⢘⡂⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣿⠄⠀⠙⢻⡖⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠁⠠⠀⠾⢃⡾⠃⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⡟⠀⠀⠀⠉⠇⣛⠻⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢸⣶⣄⠘⠒⠃⠀⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⠿⠛⢿⡝⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⢸⡀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠩⢺⣿⣿⣿⡿⣿⣿⣿⣿⣿⣷⡦⠜⠛⠁⠀⠀⠀⠀⠀⠘⣔⡤⠀⠀⡆⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⣶⣾⢆⣿⣾⢀⣾⣶⣷⣷⣿⣿⣶⣷⡟⣸⣶⣾⣿⠈⠟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠆⠲⣶⠎⢶⠄⢰⣶⣶⡿⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠌⠁⠈⠀⠁⠈⣼⣶⣿⣾⣾⣾⣾⣾⣶⣷⣾⡮⡄⠁⢁⠀⠁⢁⡈⠀⠀⠈⠁⢱⣼⠈⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡆⠀⠠⠃⠀⣩⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠋⢂⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⠷⣦⡀⠀⠀⠄⠀⠈⠈⠽⠿⣍⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⠿⢺⣿⣏⠀⠀⢀⠠⠀⡜⣁⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣤⣾⣯⣼⠄⢀⠀⠁⣚⣾⣽⡂⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠛⢿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢠⣴⣦⣄⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⡿⢀⠦⡄⠀⣿⣿⣿⣷⢨⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡼⡟⠙⣿⣿⣟⣿⣿⣭⣤⠨⡀⢿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡄⣠⣶⣶⡏⠈⢻⣿⣟⡻⣫⠥⣬⠤⠻⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢊⡀⠀⣿⣿⣽⣛⡿⠉⡉⠀⠀⣠⡼⢿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⠀⠀⠀⠃⠀⠀⠀⠀⠹⣿⣿⣄⠀⣤⣴⣴⣿⣿⣿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡆⢠⣿⣿⣿⢛⣡⡾⠁⠀⣾⣿⡇⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣆⢸⣿⣿⣿⣿⢛⣷⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⠳⠀⣘⡿⠏⠞⠰⠁⠀⠰⣿⡟⡸⣣⣊⣀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠈⢻⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠀⢹⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠐⠃⠃⣻⣅⠒⠿⠟⡅⠀⠀⠀⠀⠀⠀⡻⠀⠇⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⢸⣿⣿⠈⠻⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡀⠀⠀⡞⠓⢚⣭⠃⢰⡅⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣿⡄⠈⠙⣿⡷⠄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠁⠁⠀⠹⢋⡾⠋⠀⠀⡇⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⢿⣯⠁⠀⠀⠈⠃⠀⠸⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠠⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢲⣦⡀⠀⠀⠸⡆⢥⣽⣿⣯⣿⣿⣿⣿⣿⡿⠛⢛⠟⡏⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⣧⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠞⠛⠁⠀⠀⠀⠀⠄⠞⣒⠶⠀⠀⡇⠀⠀⠀⠀⠀⠐⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⣷⣾⢆⣿⣾⢀⣾⣶⣷⣷⣿⣿⣶⣷⡟⣸⣷⣾⣿⠈⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠲⣶⠎⢶⠄⣰⣶⣾⠿⠀⠀⠈⠀⠁⠁⠀⠈⠀⠀⠈⠈⠀⠈⠎⠁⠈⠀⠁⠈⣼⣶⣿⣾⣾⣾⣾⣾⣶⣷⣾⠘⡄⠁⡩⠀⠁⢁⡈⠀⠀⠈⠁⣇⡞⠈⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⣆⠈⡑⢥⣥⡵⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣋⣁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡆⢀⠀⠄⢀⡄⢈⣈⢽⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣃⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⢿⢛⣿⠿⡀⢀⠀⢙⠆⣤⣸⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣶⠷⠀⡀⣊⠈⢟⣿⣽⡫⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠚⡙⣿⣿⣿⣿⣿⣁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣠⣴⡤⡀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⠆⠜⠼⡟⠁⣿⣿⣿⣷⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣸⠟⠙⣿⣿⣟⣻⣿⣭⣤⠰⡃⠿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⡀⣠⣴⣶⡇⠈⢿⣿⣿⡫⣭⣧⣼⣼⠻⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⡀⠀⣼⣾⣽⣛⡿⠋⢉⠈⠁⢠⡼⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠰⣾⣿⣿⡧⡴⠀⠈⡏⠉⠀⠀⠀⠙⣿⣷⡄⢠⣤⣤⣴⣿⣿⣿⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣿⣿⣿⢛⣩⡾⠃⠀⣶⣿⢷⡿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣄⢿⣿⣿⣿⣿⠉⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠣⠀⣙⡿⠟⠞⠰⠁⠀⢸⡿⢏⣞⣵⣥⠄⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠘⣿⢟⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠀⢹⣿⣿⢿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠙⠋⠃⣻⣇⠒⡻⠛⡅⠀⠀⠀⠀⠀⠘⠇⠸⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠸⣿⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⢸⣿⣿⠈⠻⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⡀⠂⣾⢗⠚⣥⠆⠀⡧⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣾⣦⠘⠻⣿⣷⠄⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠁⠈⠀⠹⣋⡾⠋⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⡅⠀⠀⠈⠃⠀⠘⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⠀⠀⠀⠀⢠⠀⠀⠀⣀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠦⠀⠀⠀⠘⠀⢭⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⢙⢷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣸⣄⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠉⠀⠀⠀⠀⠀⡄⠞⠒⠖⠀⢠⡇⠀⠀⠀⠀⠀⠿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⣷⣾⢆⣿⣾⢀⣾⣶⣷⣷⣿⣿⣶⣷⡟⣸⣷⣾⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠲⣶⠎⢶⠄⣴⣾⡿⠗⠀⠀⠈⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⢸⣶⣿⣾⣾⣾⣾⣾⣶⣷⣾⠘⡆⠁⡍⠀⠁⢡⡌⠀⠀⠈⠡⣱⠊⠈⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⢁⡁⠸⣧⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢄⢀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⡀⠀⠀⠀⠀⠓⠀⡌⠉⠅⠺⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡛⢂⣼⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⡿⣿⣟⣿⣟⡀⠀⠀⠀⠚⡾⡼⢨⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢶⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣹⣿⣿⣿⣏⠁⠀⠀⠀⣈⣙⢷⣫⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⣟⡇⣿⣿⣿⣿⣿⡝⠉⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⢴⣦⣄⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣧⠀⠠⢃⠁⠠⠃⣾⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡿⠛⢻⡿⣿⣿⣿⣿⣧⡀⡟⠾⢿⣿⣿⣿⣯⠇⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢰⣾⣿⣿⣿⡄⠀⠀⣀⣴⣤⠈⠙⢿⣿⣇⡠⠀⠒⠐⠀⢀⣿⣿⡿⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⡁⠀⢸⣾⣿⣟⣿⣿⠛⠀⠴⣤⡸⢻⣿⠟⡁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢾⣿⣿⣯⣤⡄⠀⠀⠉⠉⠁⠀⠀⠀⢻⣿⣖⢀⣤⣤⣶⣴⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣸⣿⣿⠟⣿⣿⠞⢀⣴⣿⣷⣿⣿⠾⡆⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢸⣿⣿⣧⡭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡻⣿⣿⣿⣿⣿⠁⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠏⠀⣙⡿⣿⡼⢩⠋⠀⣾⡿⣳⣻⣯⠥⠄⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢻⡿⡻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠘⣿⣿⣿⢿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⣏⠇⣸⡟⡀⡛⠿⢫⠀⠫⠐⠀⠀⡿⢰⠷⠙⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢻⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣀⢸⣿⣿⣄⠛⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⡣⣀⠃⣾⢟⠚⣩⠆⠘⣿⠀⠀⠀⠀⠀⠃⠎⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣻⣿⣿⡆⢺⡿⢏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠁⠨⡀⠸⣾⡶⠋⠀⢸⢱⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢻⣿⣷⣎⠀⠸⠇⡼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢾⠆⠀⠀⢠⠀⢀⠤⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠀⠸⠿⠧⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⠀⠀⢀⣽⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⢠⠀⠀⠀⢀⠤⠋⠚⠗⠀⠀⠎⠀⠀⠀⠘⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⡷⣾⢆⣿⣾⢀⣾⣾⣷⣷⣿⣿⣶⣷⡟⣸⣷⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠆⠲⣶⠎⢶⢴⡿⡿⠷⠆⠀⠀⠈⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠃⠈⠀⠁⠈⢨⣶⣿⣾⣾⣾⣾⣾⣶⣷⣾⣬⡄⢁⡅⠀⠁⣱⡈⢰⠀⠈⣁⣡⠈⠈⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⢁⠁⠸⣧⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢄⢀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⡀⠀⠀⠀⠀⠓⠀⡌⠉⠅⠸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡓⢂⣼⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⡿⣿⣟⣿⣟⣀⠄⠀⠀⠊⡾⡨⢨⣾⢟⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢶⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⣹⣿⣿⣿⣟⠁⠀⠀⠅⠈⣙⢷⣫⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⣗⡇⣿⣿⣿⣿⣿⡝⠉⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⢴⣦⣄⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣧⠀⠢⠀⠀⠐⠃⣾⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡿⠛⢻⡿⣿⣿⣿⣿⣣⡀⡾⠿⢿⣿⣿⣿⣯⠇⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢰⣾⣿⣿⣿⡄⠀⠀⣀⣴⣤⠈⠙⢿⣿⣍⡠⠂⢒⠠⠀⢀⣿⣿⡿⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡁⠀⢸⣿⣿⣟⣿⣿⠛⠀⠦⣤⡸⢻⣿⠟⡁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢶⣿⣿⣯⣤⡄⠀⠀⠈⠉⠉⠀⠀⠀⢻⣿⣖⢀⣤⣤⣶⣴⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣸⣿⣿⡟⣿⣿⠞⢀⣴⣿⣷⣿⣿⠾⡆⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢸⣿⣿⣯⡭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡻⣿⣿⣿⣿⣿⠁⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠏⠀⣙⡿⣿⡼⣩⠋⠀⣾⡿⣳⣻⣯⠥⠄⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢻⡿⡻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠘⣿⣿⣿⢿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⣏⠇⣸⡛⡀⡛⠿⢫⠀⠋⠐⠀⠀⡿⢰⠷⠉⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢻⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣀⢸⣿⣿⣄⠛⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⡣⣀⠃⣾⢟⠚⢩⠆⠘⣿⠀⠀⠀⠀⠀⠃⠏⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⣿⣿⣿⣿⡻⣿⣿⠆⢸⡿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠁⠨⡀⠸⣾⡶⠋⠀⢸⢳⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢻⣿⣶⣎⠀⠸⠇⡼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢾⠆⠀⠀⢀⠀⢀⠤⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠀⠸⡿⠧⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⠀⠀⢀⣼⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⣶⣾⢆⣿⣾⢀⣾⣾⣷⣷⣿⣿⣶⣷⡟⣸⣷⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠠⠘⢣⢩⣿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾⣿⣆⠀⠀⠀⠀⠀⠀⢈⠠⡀⠐⠝⠊⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢀⡀⢀⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣻⣿⣿⣻⣿⡃⡀⠀⠀⠀⠐⠉⠈⢚⠍⠶⠮⢋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠞⢱⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠘⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢃⢿⣙⣥⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⢿⠙⢸⣿⣿⣿⣿⣛⠙⠃⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⡇⢀⠀⠁⠀⠀⠤⢠⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣴⠿⠻⢿⣿⢿⣿⣿⣿⣧⡀⠨⡆⠝⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⣼⣿⣿⣿⡅⠀⠀⠀⣀⣤⣄⠉⠹⣿⣿⡁⠀⠈⠀⠀⠀⠀⢰⣿⣿⢿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣹⣿⣻⣿⣿⣿⠟⠁⠰⣄⡸⣻⣿⡟⡁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⣶⣿⣿⣯⣤⡄⠀⠀⠀⠈⠉⠉⠀⠀⠀⠻⣿⡤⣁⣴⣤⣤⣤⣼⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣾⡿⣻⣷⡞⠁⣴⣿⣷⣿⣿⢿⠖⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠈⣿⣿⣯⣝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣮⠿⣿⣿⣿⣿⣿⠅⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⣿⣿⠃⠈⡹⡿⣿⡴⣣⠏⠀⣾⡿⣿⣿⠿⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠙⣿⠟⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠙⣿⣿⣿⡻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⠇⠘⠙⢒⠚⢯⠋⠀⠏⠘⠀⠐⡏⠺⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠹⣿⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣤⣿⣿⣿⣷⡉⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⢻⣅⠇⣤⠄⠂⠈⠄⢸⣻⡀⠀⠀⠀⠐⠠⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠈⠫⠅⣼⣤⡿⠜⠀⠀⡏⡇⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⣿⣯⠉⠀⢻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠙⠃⠙⠃⠀⠀⠁⠀⠸⡷⠀⠀⡄⠀⣤⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⣾⣿⣿⣽⣿⣿⣿⣿⡿⠟⠻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⡀⠀⣴⣶⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⡄⠀⠀⠁⠀⠤⠆⠨⠓⠀⠀⠙⠁⠀⠀⠹⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⡷⣾⢆⣿⣾⢀⣾⣶⣷⣷⣿⣿⣶⣷⡗⣸⣶⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠲⣶⠎⣶⡶⢿⠷⠶⠆⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⠀⣴⣿⣾⣾⣾⣾⣾⣶⣷⣾⣮⠀⢡⡁⠀⠁⢁⡈⠀⡄⠈⠁⣤⣬⡈⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠄⡰⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⢶⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢩⢷⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠄⠀⠄⣀⣴⣾⣿⣶⣄⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣟⣻⣿⡃⠀⠀⠀⠀⡀⠀⠁⠰⠍⠶⣲⢭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠈⠈⣸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠨⣷⣝⣲⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⣿⡻⢌⣿⣿⣿⣿⣟⣟⠿⠀⠀⠀⠀

⠀⠀⠀⠀⢀⣠⣦⣤⡀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠁⠂⣾⣿⣿⣧⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡤⣾⠿⣿⣿⣿⢿⣿⣿⣿⣗⡄⢘⠙⠪⣻⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠠⣾⣿⣿⣿⣧⠀⠀⠀⢀⣤⣄⡈⠙⢿⣿⡁⢀⠐⠆⠀⠀⠀⢴⣾⣿⡿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠨⣿⣾⣿⣿⣿⣿⡟⠃⠸⢠⡞⣹⣿⣟⡁⢀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⣾⣿⣧⣥⣧⠄⠀⠀⠀⠀⠉⠉⠀⠀⠀⠻⣿⡍⣄⣤⣴⣶⣦⣾⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⠀⢸⣿⣿⣿⡿⡻⣳⡶⢡⣴⡿⣿⢿⣿⢿⠟⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠈⣿⣿⣭⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣮⠿⣿⣿⣿⣿⣿⡏⣸⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⣿⣿⠀⢙⣻⢿⣿⡡⢧⠝⢠⣿⡿⣿⣽⠗⠛⠂⡀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠘⣿⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠹⣿⣿⣿⡟⣇⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠇⠙⠙⢞⠛⢯⡇⠀⡾⠻⢋⢿⠏⡟⠋⠏⠀⠀⡀⠃⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣤⣷⣿⣿⡇⡏⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⢻⣏⠇⠀⠀⠀⣨⠀⢸⢻⡀⠀⠀⠀⠸⡰⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠿⠇⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢚⡯⢧⣼⣦⣼⠅⠀⠀⡿⡇⠀⠀⠀⠆⠀⠀⢀⠤⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠻⡿⠿⠟⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠙⠳⠛⠋⠀⠀⠂⠀⠁⠿⠀⠀⠄⢀⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡏⢰⣼⣭⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠄⠀⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⣿⣿⣿⢿⣿⣿⣿⡿⠀⠈⠀⠀⠁⠀⠤⠆⠐⠏⠀⠀⠁⡄⠀⠀⠸⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⡶⣾⢆⣿⣾⢀⣾⣶⣷⣷⣿⣿⣶⣷⡗⣸⣶⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠆⠲⣶⢎⣶⣶⣾⠷⠶⠆⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⠀⣴⣿⣾⣾⣾⣾⣾⣶⣷⣾⣾⡆⢱⠁⠀⠁⠁⠈⠄⣤⠈⠁⠀⣬⣬⡄⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠄⠱⢽⣯⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣷⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠶⢿⡗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡒⡐⠀⠀⠀⣠⣴⣶⣤⡀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣟⣛⣿⡗⠀⠀⠀⠀⠀⠀⠁⢐⠁⠀⠀⡈⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⠇⠰⣰⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠘⢿⣿⣿⣿⡏⠀⠀⠠⠀⠀⠀⠐⡔⢄⣀⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣦⡛⢕⣿⣿⣿⣿⠿⠿⢿⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣠⢦⣤⣀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⡇⠀⠀⠀⠀⠠⠀⠆⣾⣿⣿⣧⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡤⣼⠿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠳⠌⣿⣿⣿⣿⡃⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⣶⣿⣿⣿⣿⠀⠀⠀⢀⣤⣤⡈⠙⢿⣿⡁⢀⠀⡀⠀⠀⠀⠰⣾⣿⡿⢿⣯⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠁⠀⢹⣹⣿⣻⣿⣻⣿⡟⠋⠐⢠⡰⣻⣿⡟⡋⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢤⣽⣧⣵⡧⠄⠀⠀⠀⠀⠀⠀⠐⠀⠀⠙⣿⡅⡀⣤⣤⣴⣤⣘⣿⣿⣷⣾⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⠀⢺⣿⣿⣿⡿⡻⣳⡶⢃⣴⣿⣿⣿⣿⢿⠷⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠈⢹⣿⣭⣥⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣮⠿⣿⣿⣿⣿⣿⡏⢸⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⣿⣿⠀⣙⣻⢿⣿⡠⢇⡝⢠⣾⡿⣽⣿⡿⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠈⣿⡋⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠹⣿⣿⣿⡿⣇⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠃⠟⠑⠞⠛⢫⡇⠀⡼⠪⠋⢼⡏⡿⠙⠁⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣤⣿⣿⣿⡧⡋⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠈⢻⣇⠇⡀⠀⠀⣨⠀⢸⢿⡀⠀⠀⠀⠸⢠⠁⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢹⡏⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣯⡷⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢛⡯⢧⣾⣦⡼⠅⠀⠀⣿⣇⠀⠀⠀⡐⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⢿⠿⣿⠿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠑⠳⠛⠋⠀⠀⠂⠀⠁⠳⠀⠀⡀⠀⣠⠶⠎⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡏⢰⣭⣭⣭⣿⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⠈⠁⢠⣶⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣾⣿⡿⣿⣿⣿⢶⣿⣿⣿⠟⠀⠈⠀⠀⠁⠀⠤⠄⠐⠏⠀⠀⠁⠀⠀⠀⠸⠿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⡶⣾⢆⣿⣾⢀⣾⣶⣷⣷⣿⣿⣶⣷⡟⣸⣾⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠲⣶⢦⢶⡶⣿⠷⠶⠆⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⠀⣴⣿⣾⣾⣾⣾⣾⣶⣷⣾⣾⡆⢰⠁⠀⠀⠁⡎⠄⢠⠈⠁⠀⢀⣬⣄⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠅⡑⢭⣯⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢅⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠅⠓⠾⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⡶⡀⣀⠀⣀⣤⣶⣦⣀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡿⣿⣋⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⡢⠍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡢⠀⢠⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢻⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠈⣐⣴⣀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢾⡆⢁⣾⣿⣿⣿⠿⠿⢻⠁⠀⠀⠀

⠀⠀⠀⠀⠀⣀⠴⣤⣀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⡇⠀⠀⠀⠄⢀⡠⠆⣾⣿⣿⣧⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⡤⣼⠿⣿⣿⣿⡿⣿⣿⣿⣿⣀⠀⠗⠀⣿⣿⣿⣿⡏⠉⠀⠀⠀⠀⠀

⠀⠀⠀⠀⣴⣿⣿⣿⣿⡇⠀⠀⢀⣤⣤⡌⠙⢿⣿⡍⠀⠀⠀⠀⠄⠀⠲⣶⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠁⠀⣽⣝⣷⣿⣿⣟⣿⡿⠛⠀⢠⡜⣻⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢠⣽⣧⣴⡧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⢿⣍⡀⣠⣤⣶⣦⣐⣿⣿⣷⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⡇⠀⢿⣿⣿⣿⣿⠛⣿⣷⢋⣴⣾⣿⣿⣿⢿⠗⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢩⣿⣽⣥⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠿⣿⣿⣿⣿⣿⡯⢹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⣿⡿⠀⣙⣻⣿⣿⣣⠇⡽⢡⣾⡿⣽⣿⠿⠶⠀⡈⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢻⡏⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠙⣿⣿⣿⡟⡧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⠃⠟⠑⢞⠛⢫⣇⠈⢰⢽⠏⢭⡏⡽⠛⠃⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣤⣯⣿⣿⡧⡝⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡠⠘⢿⣇⠇⡀⠀⠀⣨⠀⢸⢿⡀⠀⠀⠈⢸⢠⠁⠀⠀⠀⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢸⡟⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢿⣿⣿⣿⣿⣿⣿⡷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢛⡯⢧⣾⣦⣼⠅⠀⠀⣿⣇⠀⠀⠀⡐⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡘⢿⢿⢿⠿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠑⠳⠛⠋⠀⠀⠂⠀⠁⠿⠀⠀⠀⠀⣠⠶⠖⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡇⢸⣯⣭⣭⣽⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⢀⠁⢠⣶⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢡⣾⣿⡿⣿⣿⣷⣶⣿⣿⣿⠏⠀⠈⠀⠀⠁⠀⠤⠄⠐⠏⠀⠀⠉⠀⠑⠀⠸⠿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠲⣶⠦⢶⣶⣿⠷⠶⠆⠀⠀⠀⠀⠁⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⠀⣶⣿⣾⣾⣾⣾⣾⣶⣷⣾⣾⡄⢱⠁⠀⠁⠁⡎⠄⢠⠈⠁⠀⠀⢈⣄⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡀⠷⡁⠽⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣖⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢂⠾⠢⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡐⠄⠀⠀⣠⣴⣿⣶⣤⡀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡿⣿⣋⣿⣟⠂⠀⠀⠀⠀⠀⠀⠀⡐⠉⡃⠉⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠈⡀⢣⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢹⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠄⠀⢒⣁⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡗⠫⠌⣸⣿⣿⣿⣿⣿⡫⠇⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣠⣤⣄⣀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣷⠀⢂⠀⠀⠀⡀⡆⣴⣿⣿⣷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣥⢄⣾⠿⣿⣿⣿⣿⢿⣿⣿⣿⡃⡀⠁⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⣠⣦⡌⠉⢻⣿⡏⠀⠀⡀⠀⠈⠀⠀⣶⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⣝⡟⣍⣿⣿⣿⣻⣿⠿⠃⢠⢜⣿⣿⣯⠁⣀⡀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣼⣥⣿⣥⡝⡉⠀⠀⠀⠁⠁⠀⠀⢹⢿⣇⠄⣀⣲⣴⣀⣂⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⡇⠀⣿⣿⣿⣿⣿⣟⢻⣿⣖⣤⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠉⣯⣿⣠⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡻⣿⣿⣿⣿⣿⣿⢹⣯⣽⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣾⣿⢿⣿⡟⠀⣙⣿⣿⣿⡟⣼⢨⠏⣾⠿⣹⣿⣯⠯⠌⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢻⠟⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠙⣿⣿⣿⡟⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠀⠋⠳⡛⠻⣿⡅⠘⠀⡧⣿⣟⡿⢸⡿⠝⠀⠀⢰⠄⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠘⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣤⣭⣿⣿⣿⡸⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠻⢿⡀⢀⠀⠀⢀⠅⠀⣽⠣⠀⠀⠍⠀⠁⠇⠄⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠠⠐⣻⠽⣄⣶⣤⠧⠀⠀⢸⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉⠻⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠀⠈⠻⠆⠛⠁⠀⠀⠀⠀⢀⠀⠀⠀⣦⠀⠀⡠⠴⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠘⣿⣿⢀⣶⣶⣿⣭⣿⣿⣿⣿⡿⠟⠛⡅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠀⠀⠀⣹⡤⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⣴⣿⣿⡿⣿⣿⣶⢾⣿⣿⡶⠂⠀⠐⠀⠀⠁⢀⠤⠄⠸⠁⠀⠀⠁⠸⠀⠀⠀⠿⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠲⣶⠆⢶⣴⣶⣾⡶⠆⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⣼⣶⣿⣾⣾⣾⣾⣾⣶⣷⣾⣮⠀⢠⠁⠀⠁⠁⠨⢀⡄⠈⠁⠀⠀⢨⣾⡆⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡀⠿⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢅⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢤⠀⣠⣶⣿⣿⣷⣤⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⢿⣛⣻⣿⠂⠀⠀⠀⠀⠀⠀⠀⣡⡟⢇⡛⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠇⣺⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠸⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⡐⠘⢢⣉⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠳⠂⣻⣿⣿⣿⣛⡫⠵⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠀⠀⠀⠀⠠⠀⡄⣶⣿⣿⣧⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣯⡤⣾⡿⣿⣿⣿⣿⢿⣿⣿⣿⣇⡀⠀⢻⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⣿⣶⣿⣿⣗⠀⠀⣠⣦⣄⠉⢻⣿⡏⠁⠀⠀⠀⠀⡀⠀⣶⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢘⣏⣞⣿⣿⣿⣿⣿⡿⠋⢠⢞⣿⣿⣫⠂⣠⡄⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢨⣉⣽⣉⡙⠋⠀⠀⠀⠀⠀⠀⠀⠜⢿⣆⠀⣐⣠⣄⣐⣀⣿⣿⣷⣤⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⠀⣼⣿⣿⣿⣾⣟⡻⣻⣶⣤⣿⣿⣿⣿⢿⠿⠃⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠈⢻⣿⣊⡟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡹⣿⣿⣿⣿⣿⣿⢋⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⢿⣿⡿⠀⣙⣻⣿⣿⣿⡸⣩⡝⣾⠟⣹⣿⣯⠭⠄⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠸⡿⢻⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠈⣿⣿⣿⣿⢿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⣿⡿⣿⠀⠋⠳⡛⠻⢿⡇⠘⠀⠨⢼⣿⣿⠸⡷⢽⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢻⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣇⣬⡻⣿⣿⡮⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠀⠹⣾⡀⢀⠀⠀⠀⠅⠀⣿⠃⠀⠀⠃⠀⠄⡇⡰⠀⠀⠀⢀⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⢻⣿⣿⣿⣿⣿⣿⡷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠐⠻⠽⢀⣦⣼⠇⠀⠀⠹⠀⠀⠀⠀⠀⠀⡇⠀⠂⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠘⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⡁⠙⢧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠘⠿⠂⠛⠁⠀⠀⠀⠀⡀⠀⠀⠀⣠⠄⠀⢀⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⢹⣿⣟⢰⣶⣾⣯⣽⣿⣿⣿⣿⡿⠛⠋⡅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢈⣇⡤⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢩⣼⣿⣿⡿⣿⣿⣷⣾⣾⣶⡖⠀⠀⠛⠀⠈⠀⠠⠤⠀⠪⠃⠀⠀⠁⡇⠀⠀⠀⠹⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⡾⣾⢆⣿⣾⢀⣾⣶⣷⣷⣿⣿⣶⣷⡗⣸⣶⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠲⣶⠎⢶⣤⣴⣶⣶⠆⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⣾⣶⣿⣾⣾⣾⣾⣾⣶⣷⣾⡎⠀⢡⠁⠀⠁⡁⠨⢠⠀⠈⠁⠀⠀⢸⣾⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡀⠧⡭⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡠⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣂⠀⠀⠀⠀⠀⠀⠀⠀⡀⢐⢁⢿⠣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣘⠂⣴⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⢿⣟⣹⣿⡃⠀⠀⠀⠀⠀⠀⠀⢠⠓⠇⠱⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠋⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⠊⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠨⠀⢣⣁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⢽⣿⣿⣿⣏⡉⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠀⠀⠀⠀⠐⢀⠈⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣠⣭⣿⣿⣿⡿⣿⣿⣿⣿⣀⡈⢿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢸⣷⣶⣿⣿⠀⠀⣠⣤⣤⠉⠻⣿⣏⠁⠀⠀⠀⠀⠁⢪⣶⣿⣿⣿⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣻⣛⢽⣛⣿⣿⣿⣿⠟⢁⢏⣿⣿⠏⡀⣀⡄⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢉⣻⣉⣛⠟⠁⠀⠀⠁⠁⠀⠄⢌⢿⣧⠀⢀⣀⣀⣀⣄⣿⣿⣷⣬⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⠀⢰⣿⣿⣿⣷⣟⣻⣻⣶⣷⣟⣿⣿⣿⠷⠿⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠸⣿⣎⡿⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡹⣿⣿⣿⣿⣿⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢽⡟⣿⣿⠀⢘⢻⣿⣿⣿⡧⣏⣼⢷⡿⢁⣯⣟⣯⡍⠐⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢹⢛⣵⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡈⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣻⣿⢿⡿⢿⠃⠟⠁⠞⠺⠯⡅⠘⠁⠀⡇⠽⢽⠃⠺⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠈⣳⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣇⣤⣭⣿⣿⣇⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⡀⠈⢺⣀⢀⢀⠀⠀⡈⠀⢸⡏⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⡇⠀⢛⠿⡄⣤⣼⡯⠀⠀⠘⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠘⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠀⠹⣷⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠧⠀⠀⠘⠆⠛⠃⠀⠀⠀⠀⡆⠀⠀⠀⠀⣤⠀⠀⣀⡠⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡏⢩⢬⣿⣟⣛⡿⣿⣿⣿⣿⡿⠛⠛⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⣀⠀⠀⢹⣂⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣩⣼⣿⣿⡿⣿⣿⣿⢯⣿⣤⠆⠁⠁⡏⠀⠀⠁⠀⠤⠄⠨⠛⠀⠀⢸⠀⠀⠁⠀⠀⠿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⡾⣾⢆⣿⣾⢀⣾⣶⣷⣷⣿⣿⣶⣷⡗⣸⣶⣾⣿⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠆⠲⣶⠂⢶⣤⣴⣶⣶⠆⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⣾⣶⣿⣾⣾⣾⣾⣾⣶⣷⣾⡌⠀⣤⠁⠀⠀⠁⠈⢠⠀⠈⠁⢠⢨⣾⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢐⠁⣉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠂⠀⠫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣧⣶⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⢿⣟⣘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⣲⡀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⡄⠀⠀⠀⠀⢀⠈⣾⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠋⣿⣿⣿⣷⣄⣿⣿⢻⡿⣇⣿⣯⣿⣿⣽⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣿⣶⣾⣿⡗⠀⢀⣤⣤⠈⠻⣿⣿⠃⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣶⣿⣿⣿⣿⢸⣿⣶⣯⡏⣿⣿⣿⣟⢋⢉⡟⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢈⣩⣋⣛⣟⠋⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⢀⣂⣀⣁⣄⣿⣿⣯⣽⣿⣷⠿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡿⣿⡣⣿⣿⣿⣀⢹⣿⣿⣭⡟⣴⣿⣿⣿⣿⣿⢹⡤⣶⣿⣿⣰⣿⡫⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢿⣿⣻⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡙⢿⣿⣿⣿⣿⣿⡛⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡿⣿⣻⣹⣿⣿⡿⣿⠀⣝⠒⠈⠉⠙⠋⠘⠐⣿⣿⡟⢸⢻⣍⣀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠈⡟⣫⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡌⢻⣿⣿⣿⡿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡿⠿⠛⠋⠈⢿⠀⡃⣤⡙⡁⠰⠀⠀⠀⠀⠀⠁⣿⠁⡇⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣼⣭⠻⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⠝⠀⠀⣄⠀⣠⢸⡿⢿⢋⡏⢸⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⠁⠀⠀⢿⡀⠐⠀⣠⣃⠊⠀⠈⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⣿⣿⡿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠀⠀⠘⠀⠀⠀⠐⠔⠉⠀⠀⠐⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡱⠂⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠃⣇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⡀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣿⣿⡿⣿⣿⡟⠻⠿⠿⠏⠉⠁⠏⠀⠀⠀⣨⠀⠀⠂⠀⠀⠀⠀⠀⠀⠃⠈⠁⠀⠠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣶⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣗⣞⣶⣷⣿⣾⣷⢻⣷⣷⢆⡏⣾⣷⣶⣷⡶⣾⢆⣿⣾⢀⣾⣶⣷⣷⣿⣿⣶⣷⡗⣸⣶⣾⣿⠀⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠲⣶⠊⢶⣶⣶⣶⣶⠆⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⣾⣶⣷⣾⣾⣾⣾⣾⣶⣷⣬⠈⠀⢰⡟⠀⠀⢱⡎⠀⢰⠈⠁⡄⠀⠈⠀⢀⣁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠩⢘⠉⡫⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣒⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⠄⣈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣿⣟⣋⣿⡗⠀⠀⠀⠀⠀⠠⡀⠐⠲⠀⢈⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠅⣻⣿⣿⣿⡟⠀⠀⠀⢀⠀⠀⢅⡊⢞⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠐⣤⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠉⣾⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣷⣌⣻⣿⣿⣿⡿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠐⣿⣶⣿⣿⣷⠀⣠⣤⣤⠈⠙⣿⣿⠁⠀⠐⠀⠀⠪⣠⣴⣿⣿⣿⣏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⡯⢰⣶⣿⣿⣿⣿⢸⣿⣿⣿⣮⣻⣿⣽⣟⢉⢉⡟⣿⣿⠏⠀⠀⢀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠈⣉⣏⣙⣻⠛⠀⠀⠈⠉⠀⠀⠘⡻⣧⡀⠀⠀⢀⡣⢨⣿⣿⣯⣽⣿⣶⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⢻⣿⣿⣭⠿⢼⣿⣿⣿⣿⣿⢯⡤⣴⣿⣿⣡⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢿⣿⣻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡝⢿⣿⣿⣿⣿⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⠀⣝⠛⠁⠀⠈⠁⠸⠁⣾⣿⣿⢹⢏⢿⣀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠈⡿⣻⣾⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡌⢻⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⠯⣗⠛⠊⢻⠃⠊⠀⢌⡃⠰⠀⠀⠀⠀⠀⠑⢿⠃⡌⠌⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣸⣯⠻⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⡏⠀⣤⢠⡀⢲⡄⣵⠿⠃⠹⠀⠆⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠺⣁⠠⠀⢀⣜⡜⠀⠈⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⢸⣿⡿⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠂⠀⠀⠀⠢⠋⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢈⠆⠁⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⢸⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠃⠀⠀⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⣿⣿⣿⡿⠻⠿⠟⠓⠀⢸⠀⠀⠀⣬⡲⠀⠐⠀⠂⠀⠀⠀⠀⠀⠡⠐⠀⠘⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢆⡏⣶⣷⣶⣷⡶⣾⢆⣿⣾⢀⣿⣶⣷⣷⣿⣿⣶⣷⡗⣸⣾⣾⣿⠀⠙⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠲⣶⠎⢶⣦⣴⣶⣶⠖⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⢸⣶⣿⣾⣾⣾⣾⣾⣶⣷⣦⡌⠀⠀⣯⠆⠀⠁⣬⡄⠀⠈⠁⢠⠀⠈⠀⠀⠁⣭⣄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡋⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣶⣶⣒⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠆⠈⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⣾⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣋⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠅⣻⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⡼⡊⢚⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⡀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣾⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣷⣎⢻⣿⣿⣿⣛⣾⣯⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠐⣿⣶⣿⣿⣷⠀⣀⣤⣤⠈⠙⢿⣿⠉⠀⠀⠀⠀⢀⣤⣴⣿⣿⣿⣟⢚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡗⠰⣶⣿⣿⣿⣿⣙⠿⢿⣿⡛⢻⣾⣽⡏⢉⡉⡟⣿⣿⠏⠀⠀⠄⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢈⣉⣟⣉⣻⡛⠀⠀⠈⠀⠀⠀⠀⡻⣷⡀⠀⠀⠠⠈⠠⣿⣿⣯⣽⣿⣷⡿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣷⣀⢻⣿⣿⣯⡿⣴⣼⣿⠿⣿⣿⠯⡤⣴⣿⣿⡃⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢿⣿⣻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡜⢿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡟⢿⠀⣝⠚⠁⠀⠀⠀⠰⠃⣾⣿⣿⢱⣏⡖⣀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢸⡿⣻⣾⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡎⢻⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣻⠿⣷⠛⠆⠹⠇⠘⠀⢄⣃⠐⠀⠀⠀⠀⠀⠉⢻⠊⡘⠈⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠈⣯⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⣸⣭⢻⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡏⠁⣤⠡⠀⢠⣄⣠⠶⡀⡸⠀⡀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢼⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⢿⣯⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⡡⠀⠀⠳⣇⣀⠄⠀⣰⡔⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠺⣿⠿⠟⠫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠂⠙⠀⠀⠀⠘⠂⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡠⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢸⡆⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠒⡆⡀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⡿⣿⣿⣿⢿⠿⠿⠿⠋⠂⠸⠇⠀⠀⣤⣗⠊⠀⠀⠐⠀⠀⠀⠀⠀⠈⠆⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣶⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢆⡏⣶⣷⣶⣷⡶⣾⢆⣿⣾⢀⣾⣶⣷⣷⣿⣿⣶⣷⡟⣸⣶⣾⣿⠀⠈⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠆⠲⣶⠎⢶⣦⣴⣶⣶⠆⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⢸⣶⣿⣾⣾⣾⣾⣾⣶⣷⣾⡌⠀⠀⢹⡤⠁⠁⡌⣤⠀⠈⠁⠀⠀⠈⠀⠀⠁⠉⢨⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠈⢈⢟⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣖⡂⠀⠀⠀⠀⠀⠀⠀⠘⠠⠒⠌⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⣶⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣿⣛⣻⣿⠆⠀⠀⠀⢀⠀⠀⠀⠀⠠⢄⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠅⣹⣿⣿⣿⣿⠂⠀⠀⠀⠀⠐⢫⢏⢌⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⠀⠂⠀⠀⠀⠀⣾⣿⣿⣆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⡏⢻⠿⣺⣿⣷⣝⣿⢿⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢐⣷⣿⣿⣿⣇⠀⠀⣠⣴⣦⠀⠙⢿⣿⡋⠀⠀⠀⢀⡀⣄⣤⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⠀⢺⣷⣿⣿⣿⣿⣿⣷⣿⡟⢽⣿⣯⣏⠛⡛⡻⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢨⣩⣽⣉⣍⠋⠀⠀⠀⠉⠀⠀⠀⠐⠛⣷⡄⠀⠄⠠⠈⠠⣿⣿⣯⣭⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣆⢀⣿⣿⣿⣿⢷⣿⣾⢻⣿⣿⡏⣥⢤⣿⣿⡃⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠈⢻⣿⣋⡏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣌⢿⣿⣿⣿⣿⣿⡟⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⣿⣿⠿⡇⠘⠚⠃⠀⠀⠈⠀⠇⢰⢿⡿⢣⣟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢸⡿⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⢹⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣯⡭⢔⠃⠛⣿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⠇⠸⠘⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣸⣍⢻⣿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡟⠀⠨⣿⡳⠆⢆⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⣿⣿⣿⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇⠀⠀⠻⡇⠀⢠⠃⠀⣬⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠁⢿⡿⢿⡟⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠉⠊⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠁⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣒⠀⠀⠈⢢⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⣿⣿⣿⢿⣿⠿⠿⠟⠒⠀⠆⠀⠀⣄⠃⠂⠀⠀⠲⠀⠀⠀⠀⠀⠘⠀⠀⠀⢪⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣶⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢇⡏⣾⣶⣶⣷⡶⣾⢆⣿⣾⢀⣿⣶⣷⣷⣿⣿⣶⣷⡟⣸⣶⣾⣿⠀⠘⢿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠆⠲⣶⠎⢶⣶⣶⣾⡷⠆⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⢸⣶⣿⣾⣾⣾⣾⣾⣶⣷⣾⣬⠀⠀⠁⢦⠁⠁⠈⣤⠀⠈⠁⠀⠀⠈⠀⠀⠁⠉⢈⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠜⠌⠟⠬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣒⡀⠀⠀⠀⠀⠀⠀⣄⠰⠁⠘⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⢸⣿⠷⠀⠀⠀⡀⠐⣐⠂⣔⣂⢁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿⣿⣶⠷⠀⠀⠀⢀⠑⣄⣒⣫⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠀⠤⠁⠂⢘⠀⣿⣿⣿⣦⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠿⠟⢺⣶⣦⡿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡀⠀⠀⣠⣴⣦⡄⠙⢿⣿⡏⠀⠀⠀⠀⠀⠌⣶⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⢺⣶⣾⣿⣿⣏⣿⣿⣿⠝⢿⣯⣟⢹⣿⣻⣿⣿⠃⠀⠀⠦⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢤⣿⣥⣭⡥⠌⠀⠀⠀⠀⠈⠀⠀⠀⠀⢙⢿⡄⡀⠀⠠⠀⠸⣽⣿⣯⣭⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢸⣿⣿⣿⣻⢿⣿⣿⡿⡿⣾⢩⢤⣾⣿⢁⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠈⢹⣯⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⢻⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣻⢿⣿⣿⢿⠙⠛⠟⠁⠀⠀⠀⠞⢰⣿⡿⢻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠘⣿⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⢹⣿⣿⣿⣿⡅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⣟⡁⢤⠘⢻⡟⠰⠀⠁⠆⠀⠀⠀⠀⠀⠘⠺⠇⠘⠐⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢹⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣈⡫⢿⣿⣇⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⡇⠀⠀⣤⢰⣣⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠘⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⢶⣿⣿⣿⣿⣾⣽⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡐⠀⠀⠰⢿⠀⠈⡫⢀⠀⡀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠁⠹⣿⢿⡿⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠂⠁⠀⢈⠀⠀⠐⠁⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠊⠁⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠃⠀⠀⠀⢠⠻⠱⢠⠀⠀⠄⠀⠀⠀⢶⠀⠒⠂⠀⠀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢆⡏⣾⣷⣶⣷⡿⣾⢆⣿⣾⢀⣾⣶⣷⣷⣿⣿⣶⣷⡗⣸⣶⣾⣿⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠆⠲⣶⠎⣶⣶⣶⣾⠶⠆⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⢨⣶⣷⣾⣾⣾⣾⣾⣶⣷⣼⡌⠀⠁⠁⠀⠁⠁⠈⠀⠀⠈⠁⠁⠈⠈⠀⠀⠁⡉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠜⠌⠟⠬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣒⡀⠀⠀⠀⠀⠀⠀⣄⠰⠁⠸⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣟⢸⣿⠷⠀⠀⠀⡀⠐⢘⠒⢘⡂⠥⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿⣿⣶⠷⡀⠀⠀⠀⠙⢄⣚⣹⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠀⠄⠀⠀⠘⠀⣿⣿⣿⣦⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢿⠟⢺⣷⣦⡿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡀⠀⠀⣠⣴⣦⡀⠉⢿⣿⡏⠁⠀⠀⠀⡈⠬⣶⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⢺⣦⣾⣿⣿⣏⣾⣿⣿⣟⢿⣿⣟⢻⣻⣻⣿⣿⠃⠀⠀⠦⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢴⣿⣥⣭⡤⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⢿⡄⡀⠄⠀⠈⢸⣽⣿⣯⣭⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢸⣿⣿⣿⣻⢿⣿⣿⣿⡿⣾⢩⢤⣾⣿⢁⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠈⢹⣯⣿⣤⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠻⣿⣿⣿⣿⣿⡟⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣻⢿⣿⣿⢿⠉⠛⠟⠁⠀⠀⠀⠞⢰⣿⡿⢻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠘⣿⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⢹⣿⣿⣿⣿⡅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⣟⡁⢤⠚⢻⡟⠰⠀⠁⠆⠀⠀⠀⠀⠀⠘⠺⠇⠘⠐⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢹⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣈⡙⢿⣿⣇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⡆⠀⠀⣤⢰⣷⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠘⣿⡿⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂⢶⣿⣿⣿⣿⣾⣽⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡐⠀⠀⠰⢿⠀⠈⡫⢀⠀⡀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠁⠹⣿⢿⣿⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠊⠁⠀⠈⠀⠀⠐⠁⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠊⠁⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠃⠀⠀⠀⢠⠻⠱⢠⠀⠀⠀⠀⠀⠀⢶⠀⠒⠂⠀⠀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢦⡏⣾⣷⣶⣷⣿⣾⢆⣿⣾⢀⣾⣶⣷⣷⣿⣿⣶⣷⡗⣸⣶⣾⣿⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠲⣶⠎⣶⣶⣶⣾⠶⠆⠀⠀⠈⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⢨⣶⣿⣾⣾⣾⣾⣾⣶⣷⣶⡌⠀⠁⠁⠀⠁⠁⠈⠀⠀⠈⠁⠁⠈⠈⠀⠀⠁⡉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠛⠘⢝⢾⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⡿⠷⠶⠀⠀⠐⠀⢀⣀⠁⢸⠃⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢉⣿⣿⣿⣿⣿⡄⠀⠀⡄⠐⣔⣋⠗⢌⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢿⣿⣾⣿⣄⣷⠀⠀⠠⢁⢚⣂⣃⡬⠷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠁⠤⠄⠠⣌⠀⣿⣿⣿⣆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢹⡿⢻⣷⣶⣿⣿⣿⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⣴⣿⣿⣿⣿⡀⠀⠀⠀⣤⣶⣦⠄⠙⢿⣿⡟⠉⠀⠠⠀⢪⢰⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢰⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣟⣿⣿⠏⠀⢐⣦⠀⠀⠀⠀⠀

⠀⠀⠀⢰⣿⣿⣏⣨⡍⠀⠀⠀⠀⢀⠈⠀⠀⠐⠀⡙⢿⣖⠄⣈⣂⣀⣑⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢰⣿⣿⣿⣿⢟⣻⣿⣿⣿⢿⢯⡧⣶⣿⡇⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢽⣿⣯⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠻⣿⣿⣿⣿⣿⡋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣻⣿⣿⢿⠛⡛⠻⠇⠀⠀⠀⠸⠁⡾⣿⢧⡟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠈⣿⠟⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠘⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣟⣋⡡⡖⢻⣿⠠⠀⠘⠆⠀⠀⠀⠀⠀⠀⠛⡇⠸⠐⠒⠓⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠻⣿⣿⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⡆⠀⢀⣦⢠⣷⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢻⡿⠀⠀⠛⠀⠀⠀⠀⠀⠀⠂⠀⠑⠂⣿⣿⣿⣿⣷⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠀⠐⣿⠄⠙⢻⠄⠀⢠⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠈⠻⢿⣎⠻⣽⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠃⠀⠀⠀⠀⠓⠉⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⠋⠂⠋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠗⠁⠀⠀⠀⢠⠨⠡⢄⠀⠀⠀⠀⠀⢸⠀⠰⠟⠃⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣿⣶⣷⣷⣾⢆⣿⣾⢀⣾⣾⣷⣷⣿⣿⣶⣷⡟⣸⣾⣾⣿⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠲⣶⢮⣶⣶⣾⡷⠶⠆⠀⠀⠀⠀⠁⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⢨⣶⣿⣾⣾⣾⣾⣾⣶⣷⣾⡌⠀⠁⠁⠀⠅⠁⠈⠀⠁⠈⠁⠁⠈⠈⠀⢠⠁⠉⠈⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⡨⢸⢽⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⡿⠷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⡿⣹⣿⣿⡄⠀⠀⠀⠀⢅⠀⠀⠠⠆⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⣿⣿⣠⣧⠀⠀⠀⠀⣀⣠⣤⡃⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡝⣿⣿⣿⣿⣿⣿⣷⣿⡀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣠⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠀⠀⠀⠂⡐⣿⣿⣿⣷⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢻⢿⣿⣿⣷⡿⣿⣿⣿⣟⢭⣿⣽⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠠⣴⣶⣶⣿⡅⠀⠀⠀⠀⣤⣶⡦⠀⠉⢿⣿⣋⠉⠀⠀⠀⠀⢲⣿⣿⠿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢶⣾⣿⣿⣿⡯⣽⣿⣿⣟⡺⣿⣿⡟⡋⣹⢿⣿⡟⠀⠀⡤⠀⠀⠀⠀⠀

⠀⠀⠠⣬⣿⣿⡏⣩⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣇⠐⣀⣀⣠⣾⣿⣷⣶⣿⡷⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⢸⣿⣿⣿⣛⣻⣿⣿⣿⡿⡿⡯⡧⢴⣿⡏⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢹⣿⣿⣽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⡙⣿⣿⣿⣿⣟⢸⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢿⣿⡿⢿⠉⠙⠻⠋⠀⠀⠀⠠⠃⡺⣿⢇⡟⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢻⡿⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠈⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣹⡭⠥⠶⠛⢻⡇⢸⠆⠀⠠⠄⠀⠀⠀⠀⠀⠃⡇⠸⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠈⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠛⣿⣿⣿⣟⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢈⠃⠋⣼⡗⠂⢺⡀⠀⡀⠊⠉⢰⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠸⣿⠃⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠆⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢺⠀⠀⠙⠆⢀⢈⠅⢀⢀⡗⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⢳⣤⣇⣹⣿⡏⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣿⣿⣻⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠾⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⠄⠉⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠿⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣿⣿⣿⡿⣿⣿⣿⣿⡿⠿⣿⣿⡿⠋⠸⠀⠀⣄⡒⠘⠄⠀⠠⠀⠀⠀⠀⠀⠀⠛⠁⠀⢠⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⡷⣾⢆⣿⣾⢀⣿⣶⣷⣷⣿⣿⣶⣷⡗⣸⣶⣾⣿⠀⠈⠿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠆⠲⣶⣪⢶⣶⣾⠶⠶⠆⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⠀⣶⣿⣾⣾⣾⣾⣾⣶⣷⣾⣬⠀⠀⠁⣤⠁⠁⠈⣄⠀⠈⠁⠀⠀⠈⠀⠀⡅⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⢄⡨⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⡿⠷⠦⠀⠀⠀⠀⠀⠀⠀⠈⠑⣸⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⡿⣻⣿⣿⡆⠀⠁⠈⠀⣥⠀⡀⢀⣒⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣶⣿⣿⣤⣧⠄⠀⠈⢀⣁⣠⣤⡃⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠀⠀⠀⠀⡐⣿⣿⣿⣷⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠻⢿⣿⣿⣷⣿⣿⣿⣿⣿⢯⣿⣽⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⣼⣷⣶⣿⡅⠀⠀⠀⠀⣤⣶⣦⠀⠉⢿⣿⣋⠉⠀⠀⠀⡄⣲⣿⣿⢿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢶⣾⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣟⣉⣹⢿⣿⡟⠀⠀⣶⠀⠀⠀⠀⠀

⠀⠀⠠⣬⣿⣿⡏⣩⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣏⠐⣀⣈⣪⣾⣿⣷⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢸⣿⣿⣿⣛⣻⣿⣿⣿⣿⡿⡿⡯⢴⣿⡇⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢹⣿⣿⣽⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⡙⣿⣿⣿⣿⣟⢸⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢿⣿⡿⢿⠉⠙⠛⠛⠀⠀⠀⠱⠣⡺⣿⢇⡿⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠈⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠛⣿⣿⣿⣟⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢈⠃⠃⣼⡗⠂⢻⡀⠀⡐⠎⠉⢰⢀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠸⣿⠃⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣿⣿⣿⣿⠆⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢺⠀⠀⠙⠆⢀⢈⠅⢤⢀⡗⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⢳⣬⣇⣹⣿⡟⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣿⣿⣻⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠾⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⣠⣄⠉⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⢿⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣿⣿⣿⡿⣿⣿⣿⣿⡿⠿⣿⣿⡿⠋⠸⠀⠀⣄⡚⠘⠄⠀⠠⠀⠀⠀⠀⠀⠀⠛⠁⠀⢰⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⣷⣾⢆⣿⣾⢀⣿⣶⣷⣷⣿⣿⣶⣷⡗⣸⣶⣾⣿⠀⠈⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠲⣶⣪⢶⣶⡾⡶⠶⠆⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠃⠈⠀⠁⠈⠀⣶⣿⣾⣾⣾⣾⣾⣶⣷⣾⣬⠀⠁⠁⣤⠁⠁⠈⣄⠀⠈⠁⠀⠈⠈⠀⠀⡅⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠂⢀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀

⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⡶⠦⠀⠀⠀⠀⠀⠀⠄⠈⠈⠁⠨⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡠⡉⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀

⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢻⣿⡹⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⡀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣇⣿⣵⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀

⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣦⣾⣿⣅⣽⡈⠀⠀⠀⠀⣀⡠⠤⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡅⠈⠀⠰⠄⣿⣿⣿⣤⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠹⢿⣿⣿⣶⡽⣿⣿⣿⣟⡏⣽⣯⣿⣿⡿⢿⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀

⠀⠀⠀⠀⣴⣶⣶⣾⠀⠀⠀⠀⠀⣠⣴⣶⠀⠉⢻⣿⣟⢉⠁⠀⠀⠁⣶⣿⣿⣛⣿⣤⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣶⣿⣿⣿⣿⣞⣿⣿⣿⣷⣧⣹⣿⣽⠏⠘⣉⢻⣿⡟⠁⠀⢀⠀⠀⠀⠀

⠀⠀⠠⣾⣿⣿⡏⣩⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⠀⠀⠠⣈⣺⣯⣁⣘⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢸⣿⣿⣧⣼⣹⣿⣿⣿⣿⣿⣿⢩⣥⣶⣿⡇⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢿⣿⣿⣽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡈⢿⣿⣿⣿⠍⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠻⣿⠀⢐⡺⠿⠁⠁⠀⠁⠞⢰⣿⠏⡼⢁⣠⡄⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠈⢿⡟⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠹⠿⠛⢋⠘⡟⢀⣷⣦⣀⠁⠐⠀⠀⠀⠀⠀⠀⠻⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠈⣧⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢸⣇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡿⠀⢀⠘⣀⡀⠈⠁⡁⠁⠀⡞⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠙⠋⠀⠀⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠢⣶⣾⣿⣿⡆⠀⣸⣻⣿⡟⠉⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁⠀⠸⣎⡤⠅⣶⣾⡀⠀⠀⠣⢰⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠀⠀⠙⠃⠻⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣶⣿⣿⡐⠀⠂⠀⠀⠀⠐⠃⠀⠀⠀⠁⠊⠀⠀⠀⠃⠀⠀⠀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢀⣀⢠⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠠⣾⣿⣿⡿⣿⣿⣿⣿⣿⣿⡿⢿⣿⠟⠀⠀⠀⠀⠂⠀⠂⠠⠀⠲⠀⠀⠀⠀⠘⠋⠀⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣶⣲⣷⡧⣴⣓⣾⣲⣶⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢇⡏⣾⣷⣶⣷⡿⣾⢆⣿⣾⢀⣾⣶⣷⣷⣿⣿⣶⣷⡟⣸⣶⣾⣿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠲⣶⢆⣶⣶⠷⠶⠶⠆⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⠀⣶⣿⣾⣾⣾⣾⣾⣶⣷⣾⣮⡄⠀⠁⠀⠀⠁⠈⠀⢠⠈⠁⠀⠀⣨⣄⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢁⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀

⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣾⣿⣶⡦⠀⠀⠀⠀⠀⠀⠄⠈⠌⢁⠸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡲⡍⡚⣽⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀

⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠂⠐⡼⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣯⣧⣸⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀

⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣧⣼⣿⣍⣽⡄⠀⠀⠀⠀⢀⡀⡀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⠿⣿⣿⣿⣿⣿⣿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⡇⠀⠀⠠⡠⣾⣿⣧⡄⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠹⢿⣿⣿⣶⣽⣿⣿⣿⣿⠓⣹⣿⣿⣿⣏⣽⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀

⠀⠀⠀⠀⣴⣷⣶⣿⠀⠀⠀⠀⠀⣀⣴⣖⡀⠉⢻⣿⣟⢋⠁⠀⠀⠀⣼⣟⣟⠟⣏⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣶⣾⣿⣿⣿⣟⣿⣿⣾⣦⣆⣹⣿⣽⠏⠑⠉⠞⣿⣿⠋⠀⠀⠀⠀⠀⠀

⠀⠀⢠⣾⣿⣿⡏⣩⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⠂⠀⠀⣀⣿⡛⠉⢻⠿⣿⣣⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢸⣿⣿⣷⡽⣱⣿⣿⣿⣿⣿⣿⢩⣅⣴⣿⡿⣼⣟⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢿⣿⣿⣙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡌⢿⣿⣿⣦⢿⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⢻⡿⠀⢘⠺⠿⠁⠀⠀⠉⠞⢰⣿⠏⡼⣳⣥⡤⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠈⣿⡟⢽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠈⠻⡿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⠿⠻⢉⢹⡏⢘⠅⠢⠘⠛⠀⠀⠀⠀⠀⠀⠈⠝⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠈⣧⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⣻⣿⣟⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠿⠀⢀⠸⢀⡀⠀⢀⠀⠂⠰⡇⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠙⠁⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣶⣾⣿⣿⡆⠀⣏⣿⣿⡏⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢨⣇⡜⠸⣷⣇⡀⠀⢰⡏⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠀⠀⠉⠈⠻⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣾⣿⣿⡐⠀⠀⠀⠀⠂⠘⠀⠀⠀⠈⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⣵⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⡄⠀⠀⠀⠀⣾⣿⣿⡿⣿⣿⣿⢿⣿⣿⠿⢿⣿⠟⠀⠀⠀⠀⠀⠐⠂⠠⠐⠖⠀⠀⠀⠀⠛⠋⠙⡿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⡿⣾⢆⣿⣾⢀⣾⣶⣷⣷⣿⣿⣶⣷⡟⣸⣶⣾⣿⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠆⠲⣶⠂⣶⣴⠷⠶⠶⠆⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⠀⣶⣿⣾⣾⣾⣾⣾⣶⣷⣾⣮⡄⠀⠁⠀⠀⠁⠈⠀⡅⠈⢡⠀⠀⣬⡄⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡠⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣿⣶⡦⠀⠀⠀⠀⠀⠀⠄⠈⠌⢁⢸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⢡⡢⡄⣨⣾⣿⣿⣿⣦⠀⠀⠀⠀

⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⠴⣾⣿⣷⠀⠀⠀⠂⢂⠀⠁⢠⡼⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣓⣂⡁⢰⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀

⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⣴⣿⣍⣹⡄⠀⠀⠐⠪⠅⡠⠆⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠙⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀

⠀⠀⠀⠀⠀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣇⠀⠀⠌⠄⣴⣶⡦⠉⢆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣦⣽⣿⣿⣿⣿⠟⣹⣿⣿⣿⡍⣠⢿⣿⣿⣿⣿⣥⠀⠀⠀⠀

⠀⠀⠀⠀⢨⣷⣶⣮⠀⠀⠀⠀⠀⢀⣤⣖⠀⠈⢻⣿⣟⠛⠁⠀⠀⢔⣀⣿⣿⣿⡆⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢴⣽⣿⣿⣿⣿⣿⣿⣿⣦⣾⢿⣾⣽⠏⠑⠉⠠⢻⣿⡿⠋⠁⠀⠀⠀⠀

⠀⠀⠠⣬⣿⣿⣟⢩⡅⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠙⢿⣷⡀⠀⠀⠘⡿⡧⣽⣽⣥⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣯⣽⢏⣿⣿⣿⣿⣿⣞⢻⣁⣴⣾⣶⣣⣿⡻⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢽⣿⣿⣇⠋⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣄⢻⣿⣷⡠⣄⡄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷⣿⠿⣿⠏⠙⠿⢿⠋⠉⠁⠉⢞⣰⣿⠏⣹⣫⣯⣤⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠈⢿⡟⢽⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⢹⣿⣷⣿⣗⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠾⡟⠛⣿⡟⠐⠇⠠⠀⠛⠂⠀⠀⠀⠀⠁⠋⡟⢰⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠈⢷⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡅⠀⠀⣿⣿⡟⣹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠘⠀⢨⣼⣀⠀⠀⣀⢀⡅⠀⡴⠀⠀⠀⠀⠈⠀⢁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⣶⣾⣿⣿⡆⠀⣛⣿⣿⡏⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠸⣃⠔⢸⣾⣧⡁⠁⢸⠃⠀⠀⠀⢠⠀⠐⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠀⠀⠀⠙⢿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⡀⠀⠀⠀⠼⠟⠙⠀⠀⠀⠈⠀⠀⠀⠀⡸⡄⢀⡤⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⢀⣀⣀⣶⡗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡀⠀⠀⠀⠀⣿⣿⣿⡿⣿⣿⣿⢿⣿⣿⣿⡿⣿⡿⠂⠀⠀⠈⠀⠈⠀⠂⠚⠔⢸⠃⠀⠘⠛⠁⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⡿⣾⢆⣿⣾⢀⣾⣶⣷⣷⣿⣿⣶⣷⡗⣸⣶⣾⣿⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠲⣶⠎⣶⣶⡿⠶⠶⠆⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⢠⣶⣿⣾⣾⣾⣾⣾⣶⣷⣾⣬⡀⠀⠁⠀⠀⠁⠈⠀⠀⢈⠁⠀⢸⣮⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠹⣟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⠿⠷⣖⠀⠀⠀⠀⠀⠁⠄⠉⠈⢡⢠⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢦⢥⣠⠤⢠⣶⣾⣿⣶⣤⠀⠀⠀⠀

⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠻⠿⠸⣿⣿⣧⠀⠀⠐⠀⡀⡔⠀⠁⡬⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣀⡐⢀⢁⣾⣿⣿⣿⣿⣿⡆⠀⠀⠀

⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣴⣿⣧⣼⠖⠀⠀⠃⠂⣉⢀⡂⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡗⠘⣿⣿⣿⣿⣯⠾⠁⠀⠀⠀

⠀⠀⠀⠀⠀⣤⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣇⠀⠀⠅⠢⢭⣦⣄⠁⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡿⣿⣿⣿⣯⣙⣿⣿⣿⣻⡟⣻⣿⣿⣿⡅⣀⢿⣿⣿⣿⣿⣅⠀⠀⠀⠀

⠀⠀⠀⠀⢩⣿⣶⣷⠀⠀⠀⠀⠀⣀⣤⣖⠀⠉⢿⣿⣛⡛⠁⠀⠀⠄⡁⣿⣿⣮⣤⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣮⣿⣿⣿⣿⣿⣿⣾⣿⣽⢿⣿⣽⠟⠓⠉⠀⢿⣿⣿⠟⠉⠀⠀⠀⠀

⠀⠀⠀⢤⣽⣿⣿⣋⣅⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠙⣿⣷⡁⠀⠐⢄⣿⣽⣹⣛⣃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⣿⣿⣿⣿⡄⢻⣿⣿⣽⡟⣽⡿⣿⣾⣿⣾⣻⣁⣴⣾⣴⢣⣿⡯⠀⠀⠐⠀⠀⠀⠀

⠀⠀⠀⢬⣿⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣄⢿⣿⣯⢠⣉⡉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣳⣿⡿⣿⡏⠂⠤⢻⠏⠉⠉⢣⢟⣰⣿⠟⣻⣻⣯⣤⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢻⣿⢻⠁⠀⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⢹⣿⣾⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣾⣛⣿⡿⠀⠋⠠⡀⠺⠆⠀⠀⠀⠀⠁⠓⡟⢰⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢹⡎⠀⠀⠀⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣆⠀⠉⣿⣿⡟⣹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⡿⠀⠀⢹⣿⣙⠁⠀⡀⢂⡭⠠⣤⠀⠀⠀⠀⠀⢠⠡⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⣶⣾⣿⣿⡇⠠⢻⣿⣿⡋⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠁⠸⣃⠚⢼⣾⣅⠁⠁⢰⠇⠀⠀⠀⢀⠀⠘⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠙⢿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⡀⠃⠀⠀⡿⠟⠘⠀⠀⠀⠈⠀⠀⠀⠀⣻⡄⣠⠔⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⢀⣀⣠⣾⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠃⠆⠀⠈⠀⠠⠰⠀⠚⠀⠰⠃⠀⠘⠋⠙⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢇⡏⣾⣷⣶⣷⡿⣾⢆⣿⣾⢀⣾⣶⣷⣷⣿⣿⣶⣷⡟⣸⣶⣾⣿⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠆⠲⣶⠂⣶⢴⡾⠶⠶⠆⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⢠⣶⣿⣾⣾⣾⣾⣾⣶⣷⣾⣮⡀⠀⠁⠀⠀⠁⠈⠀⠀⠈⠁⢀⣬⡈⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠈⠭⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠿⣻⣧⡀⠀⠀⠀⠀⠀⠀⠐⠀⢋⢀⠪⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢶⠀⠀⡀⠀⣰⣶⣶⣶⣤⠀⠀⠀⠀

⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⡿⠇⢻⣿⠛⡀⠀⠀⠀⠀⢀⠀⠀⠀⢂⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢵⡀⠐⠒⠀⣼⣿⣿⣿⣿⣿⣧⠀⠀⠀

⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣿⣿⣿⡟⠀⠀⠀⠀⠈⠁⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢳⣿⣿⣿⡇⠘⢿⣿⣿⣿⣿⡿⠋⠀⠀⠀

⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⠀⠁⠀⠀⢀⢣⣴⣆⠀⠁⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣟⠿⢿⣿⣗⣏⠏⣿⣿⣿⣿⡁⡀⢸⣿⣿⣿⣿⣄⡀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⣷⣾⣄⠀⠀⠀⠀⢀⣤⡖⠀⠉⢿⣿⣋⡩⠀⠀⠀⠀⠀⣾⣿⣬⣤⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⣅⣹⣿⣟⡿⠉⠟⠁⠀⠿⣿⣿⠟⠉⠀⠀⠀⠀

⠀⠀⠀⠀⣤⣿⣿⣿⢋⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠙⢿⣷⡁⠀⠀⠀⢻⣽⣻⣛⢃⣤⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣛⣿⡇⠀⣯⣿⣿⣿⡼⣛⣉⣤⣮⣴⢢⣿⣻⢁⡴⠀⠀⠀⠀⠀

⠀⠀⠀⠠⣼⣿⣿⡏⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⢻⣿⣇⢀⢉⠁⢹⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣽⣿⣿⡿⠀⢶⢿⠿⠯⠹⠧⡟⣼⣿⠟⣽⣿⠽⠤⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠙⣿⡏⠁⠶⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⢹⣿⣾⣿⠄⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣿⡿⠀⠿⣁⠠⠶⠬⠀⠀⠐⢐⠁⢳⠏⣼⠏⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠘⠞⠀⠀⠶⠿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⣤⠙⣿⣿⡟⣻⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⠃⠫⣿⣿⣹⡁⠀⠛⢛⠯⠀⣠⠀⠀⠀⠈⠁⡘⠐⢡⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠒⠰⣿⣿⣿⣿⡀⠺⣿⣿⡋⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠻⣿⣿⢀⣿⣟⠏⠀⢠⢿⠀⠀⠀⡠⠀⠁⠀⠀⣠⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡀⡀⠀⠻⣷⠃⠃⠀⠀⠀⢈⡀⠀⠀⠀⠗⢀⠴⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⠀⢀⠀⠀⠀⠀⠀⠀⢀⠞⠀⢀⣀⣴⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣿⣿⣿⢿⣿⣿⡿⢹⣿⣿⡿⠀⠀⠀⠀⠤⠂⠘⠏⠠⠀⠃⠀⠛⠁⠹⠟⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣶⣲⣷⡧⣴⣓⣾⣲⣶⣷⢰⣷⣞⣶⣶⣿⣾⣷⢻⣷⣷⢇⡏⣾⣷⣶⣷⡿⣾⢆⣿⣾⢀⣾⣾⣷⣷⣿⣿⣶⣷⡗⣸⣶⣾⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠲⣶⠂⢶⡤⣶⠶⠶⠆⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠀⠈⠀⠁⠈⢸⣶⣿⣾⣾⣾⣾⣾⣶⣷⣾⣬⠀⠀⠁⡄⠀⠁⢨⢐⣠⢈⣴⣧⠀⠈⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⠄⠀⠀⠀⠀⠀⢕⠁⠄⠠⠍⠭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣵⣿⣿⣦⠀⢀⠀⠀⡐⠀⢤⢠⣊⡰⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⠠⠀⠂⠀⣴⣾⣿⣿⣶⡀⠀⠀⠀

⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣯⣀⣿⣯⣨⣦⡀⠀⠀⠀⠄⣀⢐⠤⠢⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠀⠐⢆⠂⣼⣿⣿⣿⣿⣿⣷⠀⠀⠀

⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠃⣂⠀⠀⠀⣀⡇⣒⠤⠴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡇⠘⢿⣿⣿⣿⣿⡟⠉⠀⠀⠀

⠀⠀⠀⠀⢀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⣿⣿⣿⠿⠀⠅⠀⠀⣰⣿⣛⡛⠁⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣛⣻⣿⣿⡿⣿⡟⣿⣿⣿⣿⣇⡀⠼⣿⣿⣿⣿⣧⠄⠀⠀⠀

⠀⠀⠀⠀⠐⠉⣶⣶⣦⠀⠀⠀⠀⢠⠾⡅⠀⠀⠙⢿⣷⣔⡢⠄⠈⢰⢟⠿⣿⡃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠎⠉⠉⣿⣟⣧⢷⣿⣿⣿⢛⠽⠁⠀⢺⣿⡿⠋⠁⡀⠀⠀⠀

⠀⠀⠀⠀⢠⣼⣿⣿⡏⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠈⠙⠳⣾⣷⣏⣴⣟⡿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣷⣾⠀⠀⢿⣗⣿⣿⡹⡛⣿⣴⢖⣴⣶⣿⡿⠶⠿⠈⠀⠀⠀⠀

⠀⠀⠀⠀⢤⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠹⣿⡜⢻⣷⠀⢀⣰⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⠀⠬⠿⠟⣯⡿⢧⡏⡽⣿⢟⣿⣿⠛⠚⠀⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢻⡿⠍⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠨⣿⣾⣿⠯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⡍⣸⣟⡓⠲⠶⠆⠀⠈⠛⢸⡙⢹⢃⠟⡫⠁⠀⣠⠈⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠳⠀⠐⠲⣿⣦⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣤⣾⣿⣿⡝⣿⣿⡟⣻⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⡿⠏⣿⣟⠏⣾⠿⢛⣭⠅⣷⠂⠀⠀⠀⠈⠁⡌⠈⠌⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠎⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠛⠉⠉⠰⠺⣿⣿⡍⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠹⣯⢃⣈⣿⣯⠆⠀⡎⠀⠀⠀⠀⡴⠀⠀⢀⣠⠴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡁⠀⠂⠙⠀⠋⠀⠀⠀⢀⠀⠀⠀⠀⠀⣃⠠⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⠀⠠⠠⠀⠠⠀⠀⠀⡌⠀⠀⣀⡠⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣷⠇⠀⠀⠴⠆⠁⠸⠉⢸⠇⠀⠀⠋⠀⠹⠋⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢇⡏⣾⣷⣶⣷⡿⣾⢆⣿⣾⢀⣾⣶⣷⣷⣿⣿⣶⣷⡗⣸⣶⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠆⠲⣶⠊⢶⢤⣴⡶⠶⠆⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⢈⠾⣶⣿⣾⣾⣾⣾⣾⣶⣷⣾⣮⡄⠁⠉⠀⠁⠁⣌⢠⠀⠈⠁⣡⠈⠈⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠶⡀⠀⠀⠀⠀⠀⠐⠁⠠⠀⠉⠍⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡏⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⡨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣑⠰⡂⠀⠀⣴⣿⣿⣷⣶⠀⠀⠀⠀

⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣥⣾⣿⣦⣼⠆⠀⠠⡀⠀⡀⡠⢈⡢⣔⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣀⠸⠐⢡⣾⣿⣿⣿⣿⣿⣧⠀⠀⠀

⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣽⠀⠁⠁⠀⣠⣁⣤⣄⡄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠘⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀

⠀⠀⠀⠀⠀⣀⣠⣄⡀⠀⠀⠀⠀⠀⠀⡀⠐⠻⣿⣿⡿⠿⠀⠀⠄⣧⣿⣭⡍⠉⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣻⣿⣿⣿⣿⡯⣿⣿⣿⣿⣀⠀⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀

⠀⠀⠀⠀⠈⠉⢭⣶⣶⡀⠀⠀⠀⠰⠾⠟⠀⠀⠈⠻⣿⣾⠇⣅⠀⣻⣿⣿⣇⣠⠀⢸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠎⠀⠈⣽⣿⣿⢹⣿⣿⣿⣿⠿⠁⠠⣻⣿⢟⠉⠀⡀⠀⠀⠀

⠀⠀⠀⠀⠠⣬⣿⣿⣿⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄⢀⢻⡙⠛⠽⢿⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣷⣿⠀⠀⣽⣾⢧⣿⡹⡟⣏⣴⢆⣴⣴⣿⡿⠾⠓⠈⠀⠀⠀⠀

⠀⠀⠀⠀⢠⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡎⢻⣿⠁⣴⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⠀⠠⣿⠻⣯⡽⢣⠏⡽⣳⢛⣿⣿⠿⠆⠀⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢹⣿⢋⢁⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣇⢸⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⠍⣸⣿⣓⠲⣶⠆⠀⠉⠇⢸⢙⢽⠃⠟⡫⠃⠀⣠⠊⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠱⠂⠀⠲⢿⣧⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⡿⠿⠉⣿⣿⡟⣻⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⠋⣿⡟⣏⡾⠿⢋⣥⠀⡿⠀⠀⠀⠀⠅⠁⡈⠈⠌⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠁⠀⠀⠡⠞⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠻⣻⢁⢘⣿⣵⠁⠀⡇⠀⠀⠀⠀⠠⠂⠁⢀⣠⠼⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡅⠀⠆⠁⠀⠋⠀⠀⠂⢀⠀⠀⠀⠀⠀⡎⡠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣇⠀⡀⠦⠠⠄⠀⠀⠀⡘⠀⠀⣠⡄⣼⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢾⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠇⢻⣿⣷⠇⠀⢀⢤⠉⠰⠷⠀⢰⡇⠀⠀⠃⠀⠹⠛⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢇⡏⣾⣷⣶⣷⡾⣾⢆⣿⣾⢀⣾⣾⣷⣷⣿⣿⣶⣷⡗⣸⣶⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠆⠲⣶⠂⢶⢤⣴⡾⠶⠆⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠡⠬⣤⣶⣿⣾⣾⣾⣾⣾⣶⣷⣾⣮⡄⠁⠉⠔⠁⠡⡬⣤⠀⠈⠁⢡⠈⠈⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡄⠀⠀⠀⠀⠀⠀⠑⠁⠐⠠⠯⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣏⣿⣶⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⡠⠸⠠⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠎⡄⠀⠀⣼⣿⣿⣿⣶⡄⠀⠀⠀⠀

⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⢸⣿⣏⣉⣿⡀⠀⠀⠀⠀⠀⠄⢧⣧⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡐⣗⢀⣼⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀

⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⠀⠀⠀⢀⣀⣡⣖⣡⣸⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠜⢿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠀⠀⢰⣶⣶⣮⠉⠁⠙⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⠯⣿⢿⣿⡿⠀⠨⣿⣿⣿⣿⣧⠄⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠈⠉⣹⣥⣄⠀⠀⠀⢠⣶⡻⠀⠀⠙⢿⣿⣔⠦⡀⢸⣿⣿⣧⣤⡄⠀⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⠟⠉⠁⢹⣿⣧⣽⣿⣿⡟⢿⠾⠀⠘⣿⡿⠟⢁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢠⢴⣻⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣧⡄⠘⣿⣿⣿⣟⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡇⠀⢸⣿⣿⣇⠿⡟⣇⣤⢆⣤⣼⣿⡿⠄⠋⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠠⣬⣿⣿⡟⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡆⢻⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⠇⠠⡿⢿⣿⡯⣣⠇⣽⣱⢻⣿⡿⠧⠄⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠙⣿⡟⠃⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢻⣧⠈⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⡟⣸⣿⡓⠲⣶⠆⠀⠛⠁⣘⠚⢷⠇⡾⡣⠁⠀⡤⠈⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠘⠖⠀⠩⢭⣷⠀⠀⠀⠀⠀⡀⡀⢀⣠⣾⣿⡿⣿⠀⠘⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢹⡟⢏⡾⢟⢛⡩⢠⠗⠀⠀⠀⠀⠃⠀⠘⡘⡰⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠙⠀⠀⠀⠀⠀⠁⠀⠉⠿⠟⠉⠁⠀⠀⢠⡍⣿⣿⣟⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠹⡻⠀⢘⣿⡹⠁⢀⠂⠀⠀⠀⠀⠀⡀⠈⠈⢀⡠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠘⠛⠇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⡇⠀⠂⠀⠰⠃⠀⠀⠁⢀⠀⠀⠀⠀⠀⢸⠀⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢹⣿⣿⣷⠀⠠⠆⢤⠄⠀⠀⠀⡘⠀⠀⣠⠀⠀⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⠸⣿⣿⡎⠀⢠⠄⠃⢼⠆⠀⢰⠇⠀⠀⠁⠀⠘⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢇⡏⣾⣷⣶⣷⡿⣾⢆⣿⣾⢀⣾⣶⣷⣷⣿⣿⣶⣷⡗⣸⣶⣾⣿⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠆⠲⣶⠂⢶⣤⣴⣾⠶⠆⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠬⣤⣰⣿⣾⣾⣾⣾⣾⣶⣷⣾⣾⡄⠀⠙⣀⠃⠁⡌⡄⠀⠈⠡⢃⠊⠈⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⡀⠀⠀⠀⠀⠀⠑⢡⠀⠠⠭⠿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀

⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⣻⣽⣶⣿⡄⠀⠀⠠⠀⠀⠀⠀⠀⢎⡤⡻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⡧⣾⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀

⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢹⣿⠛⢻⣿⠀⠀⠀⠀⠀⢠⠈⡤⠈⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡐⢹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀

⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡿⢿⡇⠀⠐⢀⣀⣰⡎⣔⣤⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠀⠀⢰⣶⣶⣮⠙⠙⠳⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⢽⣿⣿⣿⣧⡸⢿⣿⣿⣿⡿⠓⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠚⢉⣽⣶⣦⠀⠀⠀⣠⣶⡿⠂⠀⠙⣿⣿⣧⠳⡀⢼⣿⣿⣧⣤⡄⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⡷⠋⠉⠉⣿⣇⣿⣿⣿⣿⡷⠃⠰⢻⣿⠏⣠⣄⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢰⢼⣽⣿⣯⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⡄⢸⣿⣿⣿⣿⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣶⡇⠀⠀⣿⣷⣺⣛⠻⣥⡶⣣⢦⣿⣿⡷⠟⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠠⣼⣿⣿⡿⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡎⠻⡟⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣿⣿⣿⡷⠀⣾⢿⣿⣟⣼⣨⠏⣸⢫⣿⣯⡥⠀⠂⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠘⣿⡟⡛⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡗⠀⢡⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⣩⣿⡛⠶⣶⠆⠙⢛⢡⡯⠃⠂⡇⡾⠫⠁⠀⡠⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠘⢦⠁⠨⢭⡇⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠙⡇⠀⠘⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢻⡟⠟⡾⠿⡛⡭⢡⠷⠀⠀⠀⠘⠀⠀⢠⠠⠁⠂⠀⣀⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠰⠀⠀⠀⠀⠀⢠⣾⣿⡿⠷⠀⠀⠀⠀⠀⢤⢿⣿⣿⣾⣿⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠸⠹⠁⢘⣿⢹⠁⠀⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠀⠀⠀⠀⠘⢿⡘⣿⣿⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠄⠀⠰⠃⠀⠀⠃⢠⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⡆⠤⠄⢤⠆⠀⡀⢀⡎⠀⠀⣀⠀⠀⠀⣍⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⠇⣿⣿⡧⠀⠠⠜⠃⣽⠆⠀⠼⠀⠀⠀⠁⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣶⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢇⡏⣾⣷⣶⣷⡷⣾⢆⣿⣾⢀⣿⣾⣷⣷⣿⣿⣶⣷⡗⣸⣶⣾⣿⠈⠐⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠲⣶⠊⢶⢤⣴⡾⡿⠆⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⢨⠄⢡⣾⣾⣾⣾⣾⣶⣷⣾⣾⣶⡁⠙⡲⠗⠁⠎⡀⠀⠈⠑⣡⠀⠈⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠁⠠⠀⠀⠬⠷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠢⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢛⣿⣭⣵⣆⠀⠀⠀⠀⠀⠀⠀⠀⠪⢄⢑⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢉⣴⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀

⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠸⣿⠿⢻⣿⠄⠀⠀⠂⠀⢀⢀⣰⡸⡕⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠆⠃⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀

⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⣷⣾⣿⡇⠀⠀⠀⢀⣂⣺⣕⣰⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣶⣿⠃⠀⠀⢰⣿⣿⣶⠉⠉⠣⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣿⣿⣿⠟⣿⣿⣿⣿⣅⣻⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠊⠋⣽⣷⣄⠀⠀⠀⣠⣴⣾⠃⠈⠻⣿⣿⣏⠶⠀⠀⣿⣿⣿⣷⣴⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⠏⠉⠙⣜⡐⣿⣟⣿⡻⠟⠁⠹⣿⣿⠋⢀⡄⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢰⢤⣿⣿⣟⡃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡄⠀⢻⣿⣿⣿⣿⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣷⡿⠀⠀⣷⣿⣘⢛⢻⣴⢞⣴⢠⣿⡷⡥⠞⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣤⣿⣿⡿⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⡌⠸⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⡿⠀⢸⢿⣿⢯⡞⣬⠋⣸⢣⣾⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠘⣿⡟⡛⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡧⠀⠋⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣣⣿⡛⠲⣶⠖⠈⢻⢸⡿⠁⠈⡎⢸⠃⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠘⢶⠁⠈⢭⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠐⢃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣿⠝⡹⠿⠛⣩⠁⡗⠀⠀⠀⠘⠀⠀⠀⠀⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⢀⣴⣦⡄⠀⠀⠀⠀⠀⠃⠀⠀⢺⣿⣿⣭⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⡿⠁⢘⣿⢺⠃⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠟⠟⠀⠀⠀⠀⠀⠀⠀⠀⠻⠉⢿⣿⡏⠁⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡇⠂⠀⠐⠋⠀⠀⠃⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠁⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⡧⠀⠦⢤⠄⠀⠀⢀⡎⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠈⢼⡿⣿⣿⣿⢿⣿⣿⣿⣿⡿⢸⣿⡿⠄⠠⠜⠃⠼⠆⠀⢸⠀⠀⠀⠁⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣶⣲⣷⡧⣴⣓⣾⣲⣶⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢇⡏⣾⣷⣶⣷⡿⣾⢆⣿⣾⢀⣾⣾⣷⣷⣿⣿⣶⣷⡗⣸⣶⣾⣿⠀⠛⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠆⠲⣶⠂⢶⠄⣴⣶⣿⠗⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⠨⢤⠁⣼⣾⣾⣾⣾⣶⣷⣾⣾⣶⣧⠉⢲⠡⠃⠊⡄⠀⠈⠁⣡⠀⠈⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠔⢮⢯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡶⢶⡄⠀⠀⠀⠀⠀⠀⠀⢛⣘⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀

⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⣾⣿⣿⣷⠀⠀⠀⠠⠄⠒⣤⠬⡘⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀

⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣼⣯⡉⣹⣿⣁⠀⠂⠀⢡⣤⣷⣜⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠇⡀⠀⢠⣿⣷⣦⡍⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢿⣿⣿⡿⢿⣿⣿⣿⣟⡻⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠢⢩⣿⣷⣦⡀⠀⠀⣀⣠⣶⡟⠀⢻⣿⣿⣿⠿⣀⠀⠀⣿⣿⣿⣿⣀⡀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⠏⠁⠉⢱⣿⣿⣻⣟⠟⠃⠉⡹⣿⣿⠃⢠⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢸⣿⣽⣿⡯⡄⠀⠀⠉⠉⠀⠀⠀⠀⢹⣿⣿⣧⡀⠀⠀⢿⣿⣿⣿⣿⣡⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣷⣿⠀⠀⣾⣿⣛⣫⣧⡾⠃⣼⢂⣿⡃⠀⠊⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢤⣿⣿⣿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧⠑⢀⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢴⢿⣿⢽⢣⡟⠀⢸⡏⣸⡽⣁⡀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠈⢻⡿⢉⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠘⢻⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠽⡾⢃⣿⡟⠺⣶⠖⠉⠋⡌⠘⠀⠀⢨⢁⠳⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢻⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠼⢩⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⠽⢱⢿⢛⣫⠁⡗⠀⠀⠀⠁⠀⠀⠀⠘⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠃⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⣼⣿⣏⣥⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠘⠟⠁⠘⣻⠵⠃⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠿⣿⣿⡟⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣧⠂⠀⠀⠊⠀⠀⠂⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠝⠋⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠀⠦⣠⡔⠀⠀⠀⡘⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣿⡿⡄⠀⠄⠋⢽⠦⠀⢰⠇⠀⠀⠉⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠿⢻⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣶⢻⣷⣷⢇⡏⣾⣷⣶⣷⡿⣾⢆⣿⣾⢀⣾⣶⣷⣷⣿⣿⣶⣷⡗⣸⣶⣾⣿⠀⠀⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠆⠲⣶⠊⢶⠄⢰⣶⢿⠿⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⢀⣠⣁⣸⣾⣾⣾⣾⣶⣷⣾⣾⣶⣷⡽⡒⡓⣡⡬⣄⠀⠈⠁⢁⠎⠈⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⣠⡶⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⣤⡀⠀⠀⣊⢀⠊⡔⢿⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣶⣢⠀⠀⠀⠀⠀⠀⠀⠀

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣍⣽⣭⣭⣿⠀⡁⠄⡆⣿⣦⣽⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀

⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣸⡿⠿⢿⣿⠄⠄⣥⣨⣾⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣶⣾⣿⠀⠀⣰⣯⣿⡿⠟⠯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣻⠿⣿⣿⣟⣿⣿⣯⣽⠻⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢉⣽⣿⣶⣆⠀⠀⢀⣠⣴⡶⠃⠘⣿⣿⣷⣾⠯⠄⠰⣿⣯⣯⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡁⠀⠀⣽⣿⣻⡛⠟⡉⠈⠉⣫⣿⣿⢏⢀⣠⣄⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣮⣿⣿⣿⣩⡄⠀⠙⠛⠁⠀⠀⠀⠸⣿⣶⣷⡀⠀⠀⢸⣿⣯⣄⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⣿⣟⣏⣵⡿⠃⠀⣴⡇⣾⡏⠄⠊⠉⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠠⣼⣿⣿⡏⠂⠀⠀⠀⠀⠀⠈⠀⠀⠀⢻⣿⣿⣧⠀⠀⢈⣿⡟⢥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⣿⣿⠟⠀⠿⣿⢷⡇⡾⠁⠀⠠⡿⢡⣏⠆⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠘⣿⠟⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡆⠰⢾⡏⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⡟⢡⣿⡛⡻⠿⠟⠈⠸⡄⠁⠀⠀⠀⡇⠘⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠈⣷⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠇⠀⠀⠰⠋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣷⠘⢰⢿⠛⣭⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠀⠀⠀⠀⢀⣠⣙⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠈⠟⠁⠘⣻⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢿⣿⣿⣿⠟⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣇⠢⠀⠀⠊⠀⠀⠊⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⡼⠋⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⣿⠀⠤⠀⡴⠀⠀⠀⡘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣼⣿⡧⠀⠀⠄⠚⢹⡷⠰⠀⡇⠀⠀⠁⠀⠀⠀⠀⠀⢰⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣶⢻⣷⣷⢧⡏⣾⣷⣶⣷⣿⣾⢆⣿⣾⢀⣾⣾⣷⣷⣿⣿⣶⣷⡟⣸⣶⣾⣿⠀⠀⠘⢷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠲⣶⠎⢶⠄⠰⣶⣶⣶⣤⣤⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⠈⠀⠁⢸⣾⣮⣾⣾⣶⣷⣾⣾⣶⣵⡿⠲⠃⢡⣼⢠⠀⠈⠁⠅⡜⠈⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢄⣰⡶⡍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⣤⡀⠀⠰⡂⠂⠊⠰⢿⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⡢⠀⠀⠀⠀⠀⠀⠀⠀

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣍⣽⣭⣭⣿⠀⠠⠤⡶⣿⣦⣽⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣶⣾⣿⠀⠀⣠⣮⣿⡿⠿⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣻⠿⣿⣿⣟⣿⣿⣿⣽⠻⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣋⣽⣿⣶⣆⠀⠀⢀⣠⣴⡶⠃⠘⣿⣿⣷⣾⡯⠄⠰⣿⣯⣯⡀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡁⠀⠀⣽⣿⣿⡟⠟⡉⠈⠉⢩⣿⣿⢏⠀⣤⣄⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣮⣿⣿⣿⣩⡄⠀⠙⠛⠁⠁⠀⠀⠹⣿⣶⣷⡀⠀⠀⢸⣿⣯⣀⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢠⣯⣟⣏⣥⡿⠃⠀⣴⡇⣾⠯⠄⠎⠋⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠠⣼⣿⣿⡏⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧⠀⠀⢈⣿⡏⢭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⣿⣿⠟⠀⠿⣿⢷⠇⡾⠁⠀⠠⡿⢣⣏⠏⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠘⣿⠟⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠰⢾⡏⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⡟⢡⣿⡛⡻⠿⠟⠈⠸⠂⠁⠀⠀⠀⡇⠘⠚⠛⠃⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠘⣷⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⢰⠋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣷⡘⢰⢿⠛⣭⠀⡗⠂⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠀⠀⠀⠀⢀⣠⣙⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠈⠟⠁⠘⣻⠖⠋⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢿⣿⣿⣿⠟⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣇⠂⠀⠀⠊⠀⠀⠊⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⡾⠋⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⣿⠀⠤⠀⡴⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣼⣿⡧⠀⠀⠄⠚⢹⡷⠰⠀⡗⠀⠀⠁⠀⠀⠀⠀⠀⢰⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠆⠲⣶⠎⢶⠄⠰⣶⣶⣶⣤⣤⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⠈⠀⠁⢸⣾⣾⣾⣾⣶⣷⣾⣾⣶⣵⡿⠲⠁⢡⣼⢠⠀⠈⠁⠅⡜⠈⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡤⠤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⡀⠀⠀⠁⢐⠂⣛⡍⣪⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⢿⠿⣿⠿⢧⠀⠂⠀⣻⡉⣏⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀

⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⣿⣿⣿⡆⠁⢬⣯⣿⡽⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⢹⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣿⣯⣉⣽⢅⠬⠽⣇⢼⣭⡷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⡿⠟⢿⣿⣿⣿⣿⣿⣧⢈⢹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠸⣽⣿⣿⣷⡄⠀⢀⣠⣤⣶⠒⠀⣿⣿⣿⣯⣽⠏⢶⣷⡾⠛⠴⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡀⠀⠈⣿⣿⣿⣿⡿⢋⠀⠁⠉⣍⢿⣿⡟⣀⣐⣄⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡧⣤⠀⠙⠛⠁⠀⠀⠀⢹⣿⣯⣽⡉⠀⠀⠀⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⠀⢸⣿⣿⣿⣥⣿⠋⠀⠀⣴⡿⣸⡟⠅⠘⠉⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⠀⠀⠀⣀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⢿⣿⠟⠀⡘⠿⡯⣟⢸⠃⠀⠀⢀⣾⠇⣞⡽⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠻⣿⠻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⢠⡄⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⠃⠸⢛⢚⠿⢿⠁⠀⠃⠁⠀⠀⠀⠈⠿⢰⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⡾⠻⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡄⡅⠠⠨⢛⡥⠀⠘⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡏⠀⠀⠀⠁⠀⠀⣡⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠸⢹⠀⠘⣻⠟⢃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠁⠀⠀⠀⠀⣼⣿⣿⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡀⠀⠀⠠⠆⠀⠀⠊⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⠛⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⠀⠀⠀⣠⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣿⣿⠋⠁⠀⠀⠘⢹⢷⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⣿⣾⢆⣿⣾⢀⣾⣾⣷⣷⣿⣿⣶⣷⡟⣸⣿⣾⣿⠀⠀⠘⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠲⣶⠎⢶⠄⠰⣶⣶⣶⣶⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠁⠈⠈⠁⠈⠀⠁⠈⠈⠀⠉⣾⣾⣾⣾⣾⣶⣷⣾⣾⣦⣷⣿⡖⠁⢁⣬⣦⡅⠈⠁⠡⢨⠈⠀⠀⠁⠉⠈⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢉⠯⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⣂⢁⢑⡂⣛⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣷⠀⡋⢳⣾⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀

⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢎⣿⣾⣷⠐⣲⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠿⣿⣿⣿⣿⣿⣟⡇⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⣾⣤⣼⣿⠋⣿⠆⢾⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⣿⣿⣿⣿⣿⣧⡀⠀⣠⢿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢸⣽⣿⣿⣿⡀⠀⣀⣤⣴⠞⠀⣶⣿⣿⣿⣟⡿⢽⣾⡿⠿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀⠀⠀⣿⣿⣿⣿⡿⠛⠁⠋⠉⠈⣍⣿⣿⡿⠁⣐⣤⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣬⣿⣿⣿⣋⠃⠛⠛⠁⠀⠀⠀⢸⣿⣯⣭⠉⠁⠀⠉⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢸⣿⣿⣟⣛⣿⡟⠀⠀⠀⣰⣿⢰⡿⡧⠀⠈⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣬⣿⣿⣟⠂⠀⠀⠀⠀⠀⠠⠀⢀⣿⣿⣿⣇⠀⠀⢀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⡈⣻⢿⡽⢧⡟⠁⠀⠀⠀⣾⠏⣾⡹⢀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇⢠⠔⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠑⠋⠘⠻⠒⠿⠿⡏⠀⠘⠘⠁⠀⠀⠀⠈⡿⢰⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⡿⠹⠛⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠣⢀⠀⠀⠀⣠⡅⠀⡇⠀⠆⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠈⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠿⡃⠀⠟⣰⠟⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠇⠀⠀⠀⠀⢠⣤⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣟⠀⠀⠀⠠⠀⠀⠀⠁⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠋⣿⠏⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⠀⠀⠀⠀⢀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠁⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠸⣿⡿⠟⠀⠀⠀⠰⠾⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⣿⣾⢆⣿⣾⢀⣾⣾⣷⣷⣿⣿⣶⣷⡟⣸⣿⣾⣿⠀⠀⠘⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠲⣶⠎⢶⠄⠰⣶⢶⣶⣤⡄⠈⠀⠁⠁⠀⠈⠀⠀⠈⠈⠁⠨⠈⠁⠈⠀⠁⠈⠈⠀⢹⣾⣾⣾⣾⣾⣶⣷⣾⣾⡄⣵⣿⣶⠁⠁⣪⡔⡅⠈⠁⠁⢈⠈⠀⠀⠁⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⡟⡻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠞⢁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠭⠍⣸⢁⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣿⣿⣷⡽⡴⢺⣴⡽⣮⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠙⢿⣯⣵⣾⣿⡌⣭⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⢿⣿⣷⢿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣦⣤⣿⠛⣻⣆⡸⣟⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣮⣿⠟⠿⣿⣿⣿⣿⣿⣿⣇⡀⠈⠁⡿⢟⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡂⠀⣀⣠⣴⡖⠀⣶⣾⣿⣿⣟⡿⣿⣿⢷⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⢸⣿⣿⣿⣿⣿⡷⠃⠒⠒⢙⡏⣈⡽⣿⣿⠋⢀⢀⡀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣏⠛⠚⠛⠋⠁⠀⠀⠘⣿⣯⣭⠉⠁⠠⣿⣿⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣧⠀⣽⣿⣿⣿⡟⣣⣶⠃⠀⠀⠈⣰⣿⢡⣿⠃⠀⠊⠉⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢬⣿⣿⣟⠛⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣄⠀⠀⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠈⠛⣿⢧⠏⣿⠃⠀⠀⠀⠀⣿⠟⡾⣿⣁⡀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡄⠠⣿⠇⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠈⠘⣟⠳⢰⠶⢟⠀⠉⠇⠃⠀⠀⠀⠀⠘⡏⢰⠝⠉⠉⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠇⠀⠉⠜⠀⠠⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠋⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠣⡀⢠⠆⣼⠇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣠⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢰⠂⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠹⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠰⠤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⣿⣾⢆⣿⣾⢀⣾⣾⣷⣷⣿⣿⣶⣷⡟⣼⣿⣾⣿⠀⠈⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠲⣶⠎⢶⠄⠰⣶⣶⣶⢀⣀⣬⡄⠁⠁⠀⠈⠀⠀⠈⠈⠁⠈⠈⠁⠈⠀⠁⠈⠈⠀⣿⣾⣾⣾⣾⣾⣶⣷⣾⣾⣶⣷⣿⣶⠁⠁⠘⣡⣥⠈⠁⠁⠈⠈⠀⠀⠁⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡟⣿⣞⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠇⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⣥⠍⠩⢆⢽⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣷⣤⠑⣺⣹⣿⣫⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⠙⢿⢿⣽⣾⣿⣨⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⣤⣿⡋⣹⣷⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⠿⠿⣿⣿⣿⣿⣿⡿⡀⠀⢛⡋⣗⠞⠿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠀⠀⢀⣠⣴⠞⠀⣶⣿⣿⣿⣟⡟⢻⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⣿⣿⣿⣿⣿⣿⠾⠀⠙⢩⡻⣇⣡⡼⣿⣿⠏⠀⢀⡀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⢟⠓⠚⠛⠋⠁⠀⠀⠘⣿⣯⣭⠉⠁⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⡀⢐⣿⣿⣿⣿⠫⣱⡾⠀⠀⠀⠨⢹⣿⢣⣿⡃⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⠎⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣄⠀⠈⣿⣿⣯⡭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠉⢻⣿⣿⠙⡿⠁⠀⠀⠀⢀⣿⢟⡾⣿⣃⡀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡆⠠⣿⡿⢡⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠊⢻⠟⠗⠀⢸⡗⠁⢻⠳⠃⠀⠀⠀⠀⠈⡏⢸⡋⠉⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠇⠀⠟⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠐⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⠀⠀⢀⠀⣼⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⠀⠀⠀⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⡤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⢰⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠓⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠰⡤⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⣿⣾⢆⣿⣾⢀⣾⣾⣷⣷⣿⣿⣶⣷⡟⣼⣿⣾⣿⠀⠙⠟⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠲⣶⠎⢶⠄⠰⣶⣶⣿⡇⢀⣈⣤⡅⠁⠀⠈⠀⠀⠈⠈⠁⠈⠈⠁⠈⠀⠁⠈⠈⣰⣿⣾⣾⣾⣾⣾⣶⣿⣼⣾⣦⠅⠉⠀⠁⠁⠘⣁⣥⠈⠁⠁⠈⠈⠀⠀⠁⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠟⣫⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠥⠁⡈⢆⢝⣻⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣿⢟⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣿⡿⣷⡦⡰⡚⣪⣾⣢⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⢻⠿⣷⣾⣿⣠⣺⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⣿⡿⢽⡽⢿⣿⣿⣿⣿⡟⡇⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣤⣿⡋⣹⡽⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⠘⠘⠛⠿⡔⢽⣿⣿⣿⣿⣿⡶⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⡇⠀⠀⢀⣠⣴⠞⠀⣶⣿⣿⣿⣿⡽⠁⢀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⠛⠉⠉⣿⣿⣿⣷⣿⣿⡷⠇⠘⡥⣅⣰⣲⣖⣠⢻⣿⡿⠉⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⣭⠀⠘⠛⠛⠉⠀⠀⠈⣿⣿⣭⠉⠀⠀⢹⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢁⡀⠀⠀⣿⣿⣿⣿⠿⣇⣵⡏⠀⠀⠉⠈⢸⣿⢃⣿⣯⠀⠀⠀⠁⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣆⠀⢰⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠐⠿⠛⢿⣿⣾⢙⡟⠀⠀⠀⠀⢀⣿⢫⣿⣻⣥⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡆⠰⣿⣿⠇⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠻⣿⣿⣧⠀⠰⣤⠿⢻⡳⡼⠁⠀⠀⠀⠀⢸⠇⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠇⠀⡿⢁⠌⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠘⠋⠁⠀⠀⢯⠀⠈⠀⠁⠀⠀⠀⠀⠀⠸⡐⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡀⠀⠈⠆⠀⠀⠀⠀⠀⠀⣀⠠⠂⠀⠀⣀⠐⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠰⠐⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⠊⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠸⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⣿⣾⢆⣿⣾⢀⣾⣶⣷⣷⣿⣿⣶⣷⡟⣸⣿⣾⣿⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠲⣶⠎⢶⠄⣰⣶⣿⡿⠁⠀⠈⢀⣥⣥⡀⠈⠀⠁⠈⠈⠁⠈⠈⠁⠈⠀⠁⠈⠈⢰⣿⣾⣾⣾⣾⣾⣶⣷⣾⣬⣤⠁⠁⠀⠁⠁⢨⠀⡅⣮⡥⠁⠈⠈⠀⠀⠁⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⡷⢮⢆⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⣀⠀⠠⣲⢎⣑⡙⠻⡮⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢼⡅⣰⣿⣿⣿⣷⡆⠀⠀⠀⠀

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢨⣿⣻⣿⣻⣷⡆⡤⡂⢮⡭⣬⣖⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣯⣹⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀

⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⣻⠿⣶⣿⣿⣬⢽⣿⣥⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⣿⣿⣻⠩⢻⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣴⣿⣉⣼⠷⡛⣿⣿⣿⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠈⠸⠋⢿⡕⠻⢿⣿⣿⣿⣿⡵⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠰⣾⣿⣿⣿⡅⠀⠀⢀⣠⣴⠞⠂⢷⣿⣿⣿⣿⡟⡈⡁⣤⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⠿⠛⠿⣿⣿⣿⣿⣿⣿⡷⠇⠐⡂⢼⢑⣑⠀⡠⢻⣿⡿⠋⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⡅⠀⠈⠛⠋⠁⠀⠀⠈⣿⣿⣥⠈⠀⠀⣇⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢁⠀⠀⠀⣽⣿⣿⣿⢿⣏⣴⡇⠀⠀⠀⠀⣰⣿⢏⡿⡿⠄⠔⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢾⣿⣿⣯⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣆⠀⢸⣿⣿⣿⢿⣛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⢠⡟⠛⢿⣿⣿⢹⡟⠀⠀⠀⠀⢠⡿⢣⣿⡿⠤⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠈⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄⠸⣿⣿⠗⡜⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⡇⠀⢀⠀⣿⢻⡱⡼⠁⠀⠀⠀⠀⢸⢃⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠇⠀⡿⢁⠔⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠿⠛⠁⠀⠼⡆⠀⠸⠀⠀⠀⠀⠀⠀⠀⠂⠌⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠏⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣅⠄⠁⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠀⠰⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⢟⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠟⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⣿⣾⢆⣿⣾⢀⣾⣶⣷⣷⣿⣿⣶⣷⡟⣸⣷⣾⣿⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠲⣶⠎⢶⢤⢴⣾⣿⠟⠀⠀⠈⢀⣠⣥⡄⠈⠀⠀⠈⠈⠁⠈⠈⠁⠈⠀⠁⠈⠈⢰⣿⣾⣾⣾⣾⣾⣶⣷⣾⣮⣦⡅⠁⠀⠁⠁⢨⠀⢥⣬⢵⠁⠈⠈⠀⠀⠁⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⡵⢮⠆⢹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⠄⠤⠲⠆⢱⣈⢹⠾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣫⢾⡄⢀⣶⣾⣷⣶⡦⠀⠀⠀⠀

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⠟⢿⢿⡖⠀⢠⣐⣸⣳⢸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⢩⣾⣿⣿⣿⣿⣿⣆⠀⠀⠀

⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡉⡿⠿⣿⣿⡷⠴⠵⠧⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⣿⣿⠿⣷⣾⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣴⣿⣤⣾⢳⠛⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠈⠻⡋⡁⡿⠀⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣇⠀⠀⠀⢀⣠⣴⠟⠀⢿⣿⣿⣿⣿⡏⣀⢈⣢⣷⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⠋⠉⠙⣿⣿⣿⣿⣿⡿⠃⠈⠄⡃⡀⢈⠂⠀⢿⣿⣿⠛⠁⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠰⣿⣿⣿⣏⣽⠀⠀⠈⠛⠋⠁⠀⠀⠀⢻⣿⣦⠀⠀⢘⣇⡏⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣄⠀⠀⠀⣾⣿⣿⢿⣯⣴⡇⠀⠀⠀⠈⢠⣶⢞⣾⣿⣷⠶⠈⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢰⣿⣿⣿⡝⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣇⠀⢸⣿⣿⣿⡿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣾⠉⢿⣟⣼⢹⡟⠀⠀⠀⠀⢠⡾⣻⣿⡿⠥⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢻⣿⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆⠸⣿⣿⡟⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⣿⣿⠇⠀⣠⡀⠽⢻⢳⠸⠁⠀⠀⠀⠀⡼⢱⠟⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⡏⡠⠊⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠉⠀⠀⠀⠛⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠣⠃⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠘⠟⠁⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⣿⠁⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⡇⠀⠁⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⡇⠀⠀⠀⠙⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆⣤⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⡿⢟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠿⠟⠋⠁⠀⠠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠸⠿⢇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⣿⣾⢆⣿⣾⢀⣾⣾⣷⣷⣿⣿⣶⣷⡟⣸⣿⣾⣿⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠲⣶⠎⢶⣤⢶⣾⡿⠖⠀⠀⠈⢀⣁⣥⣄⠈⠀⠀⠈⠈⠁⠈⠈⠁⠈⠀⠁⠈⠨⣶⣿⣾⣾⣾⣾⣾⣶⣷⣾⣾⣶⣧⠁⠀⠁⠁⠌⠀⠁⠈⠁⠁⠈⠈⠀⠀⠁⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⡷⢮⠆⢹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀⠀⠤⠖⠆⢱⡩⠵⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⡄⠀⣶⣾⣷⣶⣦⠀⠀⠀⠀

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣸⣿⣿⡿⠻⣿⡆⢀⢝⣶⣶⢮⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣪⠁⣾⣿⣿⣿⣿⣿⣇⠀⠀⠀

⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⣉⡟⠓⣿⣿⡷⢲⢷⣿⣯⢿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⢿⣿⣿⣿⣷⡻⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀

⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣷⣾⣿⣤⣧⣓⡳⡿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⡿⣿⢿⣿⣿⣠⠀⡏⣳⣈⡯⠀⢿⣿⣿⣿⣿⣥⠀⠀⠀⠀

⠀⠀⠀⠀⠐⣿⣿⣿⣾⡇⠀⠀⠀⠀⢀⣤⣶⠏⠀⢿⣿⣿⣿⣷⠯⡀⣛⡽⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠀⠈⢹⣿⣿⣿⣿⡿⢋⠀⠉⠂⠟⢵⢈⡄⢿⣿⣿⠛⠁⠀⠀⠀⠀

⠀⠀⠀⠀⢺⣿⣿⣿⣋⡇⠀⠀⠀⠈⠻⠛⠁⠀⠀⠀⢻⣿⣦⠁⠀⢸⣯⣗⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡇⠀⠀⣸⣿⣿⡟⣻⣷⡟⠀⠀⠈⠙⠀⣵⣾⣾⣿⣷⠞⠁⠈⠀⠀⠀

⠀⠀⠀⠀⢾⣿⣿⣯⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆⠀⣿⣿⣿⣿⣿⢯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠾⠉⢻⣿⣾⠇⡿⠁⠀⠀⠀⢀⣾⣿⣿⡯⠍⠀⠂⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠈⢿⡿⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡆⠹⣿⣿⣿⠏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⣿⠯⢒⠦⡴⠀⠘⣿⡏⠀⠁⠀⠀⠀⠀⡜⣸⢛⠎⠀⢠⠕⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠈⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢰⣿⣿⡇⡠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢾⠀⠀⠸⠀⠀⠀⠀⠀⠀⠰⡘⠡⠈⢀⣀⠉⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠘⣿⣿⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⠀⠀⡄⡀⠀⠸⠀⠀⠀⠀⠀⠀⠀⢀⡆⠊⠀⢀⣠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡇⠈⠀⠀⠙⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⣾⣃⣤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⠿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢰⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⡿⠿⠋⠁⠀⠀⠀⡀⢀⠀⠀⠀⠀⠤⠄⠀⠀⠹⠿⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⣿⣾⢆⣿⣾⢀⣿⣾⣷⣷⣿⣿⣶⣷⡟⣸⣷⣾⣿⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠲⣶⠎⢶⡴⣶⣿⠷⠖⠀⠀⠈⠀⢁⣥⣤⡌⠀⠀⠈⠈⠁⠈⠈⠁⠈⠀⠁⠈⠈⣰⣿⣾⣾⣾⣾⣾⣶⣷⣾⣾⣶⣧⠁⠀⠁⠡⣾⡇⠁⠈⠁⠁⠈⠈⠀⠀⠁⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠤⠢⢔⠹⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀⠀⠠⠒⠆⢰⠨⠽⡬⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡟⣤⠄⠀⣴⣾⣷⣶⡦⠀⠀⠀⠀

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣸⣿⣿⠻⠿⣷⠁⠀⠀⠑⣸⠣⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣫⠨⣁⣾⣿⣿⣿⣿⣿⣆⠀⠀⠀

⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣉⡟⠳⣿⡿⡇⠰⡂⣟⣅⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠻⣿⣟⢟⢖⠹⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀

⠀⠀⠀⠀⠀⣠⡴⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣷⣿⣷⣴⣧⠚⠺⡦⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣹⣿⣿⣿⣿⣿⢿⣿⣿⣿⣇⡀⣊⠀⡎⠫⠀⢿⣿⣿⣿⣿⣥⠀⠀⠀⠀

⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢀⣠⣶⠏⠈⢿⣿⣿⡿⣷⠇⡔⢸⡽⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠈⠉⣿⣿⣿⣿⣿⡿⠛⡁⠋⠈⢀⠄⡀⠀⢾⣿⣿⡋⠁⠀⠀⠀⠀

⠀⠀⠀⠸⣿⣿⣿⣧⣴⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⢻⣷⣦⠀⠀⡼⣷⣝⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠀⠀⢀⣿⣿⣿⡿⣛⣿⡾⠁⠀⠀⠙⠁⣴⣮⣿⡿⣾⠖⠉⠀⠀⠀⠀

⠀⠀⠀⠐⣿⣿⣿⣮⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣆⠀⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⡿⠉⠙⣿⢳⠏⣽⠃⠀⠀⠀⢀⣾⣿⣿⠯⠅⠀⠂⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠘⣿⡟⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡆⢻⣿⣿⣿⠏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⣿⠿⢺⢦⡤⠀⠨⡇⡟⠀⠃⠀⠀⠀⠀⡜⣼⢫⠚⠀⣠⠟⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠘⣿⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢰⣿⣿⢻⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡘⠑⠁⢀⣀⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠹⠁⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠘⢻⣿⡇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢠⣀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢀⡦⠈⠀⢀⡴⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⢹⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⠀⠀⠀⠀⠛⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⣾⣂⡴⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⣄⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⢸⣟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⡿⠿⠃⠀⠀⠀⠀⡀⢐⠀⠀⠀⠀⠶⠆⠀⠀⠹⠿⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣶⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⣷⣾⢆⣿⣾⢀⣾⣶⣷⣷⣿⣿⣶⣷⡟⣸⣶⣾⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠲⣶⠎⢶⡤⣶⣿⠷⠆⠀⠀⠀⠀⢀⣥⣴⣌⠀⠀⠈⠈⠁⠈⠌⠁⠈⠀⠁⠈⠈⣴⣿⣾⣾⣾⣾⣾⣶⣷⣾⣬⣶⣧⠁⠀⠁⡥⣾⡇⠁⠈⠁⠁⠈⠈⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⡴⠢⠆⠱⣞⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⡀⠀⠲⠆⢠⠌⠕⣬⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣎⣠⡆⢀⣶⣶⣷⣶⡦⠀⠀⠀⠀

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢸⣿⣿⠟⢛⣷⡁⡁⠀⢒⣗⡰⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⡿⠯⢁⣾⣿⣿⣿⣿⣿⡆⠀⠀⠀

⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⣈⡟⢙⣿⡿⡇⠐⠲⢓⣝⣳⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⢿⠟⣑⡛⠺⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀

⠀⠀⠀⠀⣠⣴⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣴⡧⢋⡳⠂⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣽⣿⣿⣿⣿⣿⢿⣟⣿⣿⣧⣤⠘⠀⣘⠣⠀⢿⣿⣿⣿⣿⣥⠀⠀⠀⠀

⠀⠀⠀⢸⣿⣿⣿⠿⠄⠀⠀⠀⠀⠀⢀⣤⡶⠏⠈⢿⣿⣿⢿⢷⠇⣀⢐⡢⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠈⠙⣿⣿⣿⣿⣿⣿⡛⣁⠈⠄⡠⠅⡀⠠⢾⣿⣿⡋⠁⠀⠀⠀⠀

⠀⠀⠀⢿⣿⣿⣿⣾⠇⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⢻⣿⣦⠀⢀⣘⣐⣾⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⠀⠀⣰⣿⣿⣿⣿⣛⣳⣾⠃⠀⠀⠀⠉⣴⣧⣿⣿⣿⠏⠁⠀⠀⠀⠀

⠀⠀⠀⠰⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣄⠈⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠰⠝⠉⠛⣿⣿⡿⢼⠃⠀⠀⠀⢀⣾⣿⣿⠿⠆⠐⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠙⣿⢟⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡆⢻⣿⣿⣿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢹⡿⠷⡲⢠⠦⠀⠠⠘⠙⠀⠃⠀⠀⠀⠀⡌⣼⢫⠊⠀⣰⠋⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠘⣿⡟⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⣿⣿⣽⠖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⠀⠀⠀⠀⠀⠁⠰⡆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⡑⠁⢀⡄⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠹⠁⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠘⠹⣿⡯⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢠⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡄⠈⠀⢀⡄⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣼⣿⡟⠀⠂⠀⠀⠛⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣾⢂⡴⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠠⡀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⢰⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⡿⠿⠃⠀⠀⠀⠀⡀⠰⡀⠀⠀⠀⠶⠂⠀⠀⠸⠿⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣶⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⣷⣾⢆⣿⣾⢀⣾⣶⣷⣷⣿⣿⣶⣷⡟⣸⣶⣾⣿⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠆⠲⣶⠎⢶⣤⢶⣿⡷⠆⠀⠀⠀⠀⢀⣥⣤⣬⠀⠀⠈⠈⠁⠈⠈⠁⠈⠀⠁⠈⠈⣴⣿⣾⣾⣾⣾⣾⣶⣷⣾⣬⣶⣧⠁⠀⠁⡥⣼⣦⠁⠈⠁⠁⠈⠈⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⡷⠦⢆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⡀⠀⠔⠆⢒⣸⠵⣮⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣶⣥⡄⢀⣶⣶⣷⣶⡦⠀⠀⠀⠀

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢸⣿⣽⠟⢻⣷⡓⢃⠀⢰⣷⣵⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⢁⣾⣿⣿⣿⣿⣿⡆⠀⠀⠀

⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⣈⠟⢙⣿⡿⣇⠐⡺⣾⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠻⠯⣛⢓⢻⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀

⠀⠀⠀⠀⣰⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣿⣷⣿⣷⣴⡯⣒⡙⠆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠃⣹⠫⠀⢿⣿⣿⣿⣿⣤⠀⠀⠀⠀

⠀⠀⠀⣶⣿⣿⡿⠳⠀⠀⠀⠀⠀⠀⢀⣤⣶⠏⠈⢿⣿⣿⣿⣷⠇⠴⠿⢝⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⢋⠀⠅⡑⠅⡀⠠⢿⣿⢿⣉⡀⠀⠀⠀⠀

⠀⠀⠘⢿⣿⣿⡿⣿⠃⠀⠀⠀⠀⠀⠹⠋⠁⠀⠀⠀⢻⣷⣦⠀⢀⣙⣮⣛⣳⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣇⠀⠀⣴⣿⣿⣿⣿⢻⣻⣷⠟⠀⠀⠀⠈⣵⣢⣿⣿⡿⠏⠀⠀⠀⠀⠀

⠀⠀⠀⠸⣿⣿⡿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣄⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠸⡟⠛⢛⢻⡟⡾⢠⡏⠀⠀⠀⢀⡾⣿⣿⠿⠌⠀⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠙⣿⢟⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⢹⠿⠕⠲⢲⡒⠀⠠⠝⠋⠑⠘⠀⠀⠀⠀⠞⡼⢋⠋⠀⣼⠋⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠘⣿⡟⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠈⣿⣿⣧⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠰⡆⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⡑⠁⢀⡀⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠹⠁⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠈⠘⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⠀⠀⠀⢤⣄⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢀⡦⠊⠀⢀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣇⣾⣿⡿⠀⠃⠀⠈⠋⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⣼⢂⣴⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠟⢛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠠⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢰⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠻⠿⠻⠃⠀⠀⠀⢀⠀⠢⣀⠀⠀⠰⠿⠃⠀⠀⠸⠿⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣶⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⣿⣾⢆⣿⣾⢀⣾⣶⣷⣷⣿⣿⣶⣷⡟⣸⣶⣾⣿⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠲⣶⠎⢶⡤⢲⣿⠷⠆⠀⠀⠀⠀⢁⣡⣤⣌⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⠈⣶⣿⣾⣾⣾⣾⣾⣶⣷⣾⣾⣶⡅⠁⠀⠁⠅⢈⠀⠁⠈⠁⠁⠈⠈⠀⠀⠁⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠨⠱⢌⢞⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣶⣤⣄⣀⠀⡀⠀⣀⣺⠟⢯⠝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣺⡇⢠⣾⣿⣿⣿⣶⠄⠀⠀⠀⠀

⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣿⣿⣏⣫⣿⣇⣈⠀⠠⡀⣠⢗⡗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣁⣾⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀

⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣜⢉⣿⠿⢻⠀⢐⣏⠗⡗⠅⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠛⠿⡚⢿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀

⠀⠀⠀⠀⠀⡠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣸⣿⣿⣿⣷⡾⡥⣼⢢⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡿⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⢤⠀⢓⢅⠸⣿⣿⣿⣿⣷⠄⠀⠀⠀⠀

⠀⠀⠀⠀⣤⣿⣿⣿⢷⠀⠀⠀⠀⠀⢀⣤⣶⠇⠈⢿⣿⡿⠿⠾⠁⣂⢬⠷⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⡀⠀⠀⢹⣿⣿⣿⣿⣟⣿⠟⢋⠀⠁⢂⠁⠽⣿⡿⢋⣤⠤⠀⠀⠀⠀

⠀⠀⠀⠀⣾⣿⣿⣷⣾⠆⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⢻⣷⡆⠀⢰⢰⣳⣞⣁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢠⣿⣿⣿⣿⣿⢻⣿⣷⠟⠀⠀⢀⣴⣷⣿⣿⠿⡋⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠸⣿⣿⣷⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⢏⣀⠹⡟⠫⢹⣿⡏⡞⢰⠏⠀⠀⠀⡞⣿⣯⠭⠀⠈⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠙⣿⡓⡆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠃⠛⠛⠻⡿⢻⠃⠀⠘⠛⠉⠀⠊⠀⠀⠀⠸⡸⢋⠃⢀⡼⠋⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠘⣿⡃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠡⠡⠁⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢼⣿⣩⠋⠀⡀⠀⠘⣶⡖⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣀⠐⠀⠀⣄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⢻⣽⣿⣿⣿⣿⣿⣿⢨⣵⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢀⡯⢀⡖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⠿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣏⣿⣿⠁⢀⠂⠀⠀⠀⠀⠀⠀⡆⠀⠀⣀⣀⠀⠀⠀⢸⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠇⠀⠃⠀⠀⢲⡮⡆⠀⠇⠀⠀⠛⠋⠀⠀⠀⠺⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣶⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⣿⣾⢆⣿⣾⢀⣾⣾⣷⣷⣿⣿⣶⣷⡗⣸⣷⣾⣿⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠲⣶⠎⢶⢄⣴⢶⣾⠗⠀⠀⠀⠀⠀⣁⣤⣬⡀⠀⠈⠈⠁⠈⠈⠁⠈⠀⠁⠈⢸⣶⣿⣾⣾⣾⣾⣾⣶⣷⣾⣮⡄⠁⠁⠀⠁⣡⠈⠀⠁⠈⠁⠁⠈⠈⠀⠀⠁⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠱⢜⣾⢭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣶⣤⣄⢄⠀⠀⠀⢀⢺⠟⠯⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣞⡄⢠⣾⣿⣿⣿⣶⠄⠀⠀⠀⠀

⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢿⣿⣽⣫⣿⣏⡘⠀⠤⠀⣩⢗⡗⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣾⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀

⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⣜⢉⣿⠿⢻⠀⢐⣋⠒⡞⢄⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠛⠿⡚⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣠⣤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣸⣿⣿⣿⣷⠾⡥⣰⢢⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡿⠿⠿⣿⣿⣿⣿⣿⣻⣿⣿⢤⠀⢻⠅⠸⣿⣿⣿⣿⣷⠄⠀⠀⠀⠀

⠀⠀⠀⠀⢤⣿⣿⣿⢷⠀⠀⠀⠀⠀⢀⣤⣶⠇⠈⢿⣿⡿⠿⠿⡀⡀⠪⡴⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⡀⠀⠀⢹⣿⣿⣿⣿⣟⣿⠿⢋⠀⠁⠦⠁⠽⣿⣿⢋⣤⠀⠀⠀⠀⠀

⠀⠀⠀⠐⣾⣿⣿⣷⣾⠆⠀⠀⠀⠈⠙⠛⠁⠀⠀⠀⢻⣿⡆⠀⢰⢸⣧⣟⣁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢠⣿⣿⣿⣿⣿⢻⣿⣷⠟⠀⠀⢀⣴⣷⣿⣿⠿⡋⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠸⣿⣿⣷⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢏⣀⠙⡻⠫⠹⣿⡋⡞⢰⠏⠀⠀⠀⡾⣿⣯⠭⠀⠈⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠙⣿⡓⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠃⠛⠛⠻⡿⢻⠃⠀⠨⠙⠁⠀⠊⠀⠀⠀⠸⠸⢛⠃⢀⡼⠋⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠘⣿⡃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠡⠡⠁⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⢩⠋⠀⡀⠀⠘⣶⡖⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣠⠐⠀⠀⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢻⣽⣿⣿⣿⣿⣿⣿⢨⣵⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢀⣯⢀⡖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣏⣿⣿⠁⢀⠂⠀⠀⠀⠀⠀⠀⡆⠀⠀⣀⣀⠀⠀⠀⢨⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠇⠀⠂⠀⠀⢺⡮⡆⠀⠇⠀⠀⠛⠋⠀⠀⠀⠺⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣶⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⣿⣾⢆⣿⣾⢀⣾⣾⣷⣷⣿⣿⣶⣷⡗⣸⣶⣾⣿⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠲⣶⠎⢶⢄⣴⢶⣾⠗⠀⠀⠀⠀⠀⣁⣤⣬⡀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⢸⣶⣿⣾⣾⣾⣾⣾⣶⣷⣾⣮⡄⠁⠁⠀⠁⣡⠈⠀⠁⠈⠁⠁⠈⠈⠀⠀⠁⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡊⠭⠿⠻⢽⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡩⡇⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀

⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⠦⠀⠠⠈⠮⢆⠎⣠⠭⣧⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⡇⢰⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀

⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⣿⣿⣿⡇⡀⢓⡈⠈⢄⣡⢅⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⣾⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀

⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣾⣿⣏⢉⣧⢀⢉⠐⡨⢯⣿⣢⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢛⢿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣤⡤⣄⡀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡫⠾⣦⣘⡉⠁⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⠿⠿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣤⠀⣈⢿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡇⠀⠀⠀⣠⣴⡾⠀⠙⣿⣿⡟⡛⠃⠎⣼⣌⡽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣅⠀⠀⢹⣿⣿⣿⣿⣿⣿⡿⡟⠋⠈⠅⢈⢿⣿⣟⣥⣤⡄⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢶⣿⣿⣿⣴⡦⠀⠀⠈⠉⠙⠀⠀⠀⠈⢿⣿⡄⠀⣓⣼⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣼⣿⣿⣿⣿⡿⣿⣱⣾⠃⠀⢀⣾⣾⣿⡿⢟⠃⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣿⣿⣿⣭⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⢁⣈⠛⢿⡽⢿⣿⣱⠃⡾⠁⠀⠀⡏⣾⣯⡭⠁⠈⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠘⣿⢋⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡇⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠘⠈⠛⠛⠿⠿⡏⠁⠀⠽⠏⠑⠘⠁⠀⠀⢸⢹⢋⠃⠀⡼⠇⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠘⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⢆⠃⠆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣹⠅⠸⠃⠀⠀⢱⡖⠁⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⡦⠂⠀⢀⠤⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢻⢻⣿⣿⣿⣿⣿⣿⣿⣼⣿⠷⠆⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⢸⡅⣠⡔⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠂⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣀⡀⠀⠀⠀⢸⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠿⠿⠂⠈⠂⠀⠠⢒⣮⠆⠀⠰⠀⠀⠘⠟⠁⠀⠀⠀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⣶⣾⢆⣿⣾⢀⣾⣾⣷⣷⣿⣿⣶⣷⡗⣸⣷⣾⣿⠈⠋⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠲⣶⠎⢶⠄⣰⣶⣶⣶⠂⠀⠀⠀⠁⠁⢠⣾⣾⡆⠈⠈⠁⠈⠈⡅⠈⠀⠁⠈⢸⣶⣿⣾⣾⣾⣾⣾⣶⣷⣾⣾⠀⠁⠁⠀⢁⣡⠌⢤⡇⠈⠁⡁⠈⠈⠀⠀⠁⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢚⡲⢬⢼⡭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀

⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⡷⠦⠀⠀⠈⠎⠻⠁⢒⣵⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱⣾⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀

⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠗⣿⣿⣿⣷⠀⠐⠀⠀⠠⣬⡶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀

⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣶⣿⣏⣈⣿⠀⠴⢍⢀⢰⠿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣄⡀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡿⢄⡰⠈⢀⠊⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡀⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣇⠀⢀⣠⣶⡮⠈⠻⣿⣿⡻⠓⣒⣖⡘⣗⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣁⠀⠀⢹⣿⣿⣿⣿⣿⣿⠿⠛⠁⢱⠹⢿⣿⣏⣤⣦⠄⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣴⡇⠀⠈⠙⠋⠀⠀⠀⠘⢿⣿⡁⠈⣿⣿⣿⣽⣿⣿⢷⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣾⣿⣿⣿⣿⢛⣛⣯⡞⠁⢰⣦⣿⣧⣿⠛⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠨⣿⣿⣷⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣁⡘⢿⣿⣿⣿⣏⡾⢠⠟⠀⠀⡞⡼⣟⣋⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢹⣿⠛⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡆⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠟⠁⠋⠸⠋⠻⢿⠿⡓⠀⠹⠟⠉⠆⠛⠀⠀⢸⢡⡟⡃⠀⢀⡞⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠹⣻⣗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⢋⣄⠐⠀⠀⠈⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠸⡘⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠘⢿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢨⣿⣿⣓⠀⠟⠀⠀⢈⡼⠊⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⢠⡔⠀⠀⢀⡙⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⡠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠃⣋⣻⣿⣿⣿⣿⣿⣿⣿⢿⠿⡿⣷⠀⠂⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣀⣀⠀⠀⠀⠀⣿⡴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠰⣿⣿⣿⡿⣿⣿⣿⢿⣿⡿⠤⠃⠉⠁⠀⠀⠀⡠⠞⣲⠆⠀⠀⠄⠀⠐⠛⠁⠀⠀⠀⠀⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⣶⣾⢆⣿⣾⢀⣾⣾⣷⣷⣿⣿⣶⣷⡟⣸⣿⣾⣿⠀⠙⠃⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠆⠲⣶⠎⢶⠄⠰⣶⣶⣶⡦⠀⠀⠀⠀⠁⠀⠸⣾⣿⣾⠈⠀⠈⠈⠁⠈⠀⠁⠈⠈⣶⣿⣾⣾⣾⣾⣾⣶⣷⣾⣾⡄⠁⠁⠀⣁⣥⣌⠀⠧⠈⠁⢡⠈⠈⠀⠀⠁⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡈⢭⢼⠩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾⠶⠄⠀⠀⠀⠀⠀⡀⠄⠐⡋⣃⢞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣶⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀

⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢾⣿⣿⣿⡆⠀⠀⠀⠐⣐⠦⣰⠄⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀

⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣾⣿⣅⣸⡇⠀⠀⠀⢀⡪⢿⣴⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡇⠀⠠⢥⣸⠂⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡝⣿⠿⢿⣿⣿⣿⡿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢤⣾⣿⣿⣾⡀⢀⣠⣶⠆⠙⢿⣿⣟⢏⠓⠀⢸⠹⡻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠈⣿⣿⣿⣿⣿⣿⣿⡿⠟⠹⠽⣿⣿⣃⣠⣤⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣏⣬⠀⠈⠉⠁⠀⠀⠀⠙⣿⣧⡃⠨⣯⣽⣿⣿⣿⣿⣮⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢀⣿⣿⣿⣿⡟⣛⣙⣶⠏⢰⢦⣿⣃⠼⠉⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠃⠸⡿⣿⣿⣿⢥⠏⡼⠃⠀⡞⣸⡿⣋⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⢫⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⠟⠳⠛⢸⡟⠳⣷⣷⡖⠉⠻⠏⠰⠙⠁⠀⢨⠇⡗⠛⠉⠀⡀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠻⣿⡇⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠹⣿⣿⣻⣿⢱⡄⠄⠀⠸⠿⢋⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠸⢀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⠇⠸⢻⠀⠾⢣⡾⠁⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⠛⠟⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢐⡞⠀⠀⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⡀⠈⠉⡀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⣛⣽⠀⠀⠀⠀⠀⡈⠀⠀⠀⢠⠛⠀⢀⣀⠀⠀⠀⠀⠈⡇⢀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠿⠟⠀⠀⠘⠛⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡷⡟⠉⠉⠀⠀⠀⣠⠎⢳⡦⠀⠀⠸⠀⠀⠘⠋⠀⠀⠀⠀⢀⣷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣵⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢦⡏⣾⣷⣶⣷⣶⣾⢆⣿⣾⢀⣿⣾⣷⣷⣿⣿⣶⣷⡟⣸⣷⣾⣿⠀⠀⠻⡆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠆⠲⣶⠎⢶⠄⠰⣶⣶⣦⣶⡄⠀⠀⠀⠁⠀⠈⠀⠐⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⠀⢰⣿⣾⣾⣾⣾⣾⣶⣷⣾⣾⡆⠁⢩⠀⣅⣡⢪⠀⠁⠈⠁⠁⡌⠈⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢭⠴⠘⣽⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣷⡶⠤⠀⠀⠀⠀⠠⠀⠂⢰⠛⢇⡖⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣵⣧⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⢠⣾⣿⣿⡄⠀⠄⢦⠰⠀⣊⠠⢄⠈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀

⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣰⣿⣏⢩⣧⠐⡉⠂⣠⠞⡩⣶⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⢀⣽⣿⣿⣿⣿⡇⠀⠀⠀⢔⠇⣸⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣶⣏⣀⣤⡶⠀⠙⣿⣿⣟⢟⡁⢠⢘⠙⠅⣷⣿⣿⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡚⠉⠀⡯⣿⣿⣿⣿⣿⣿⡿⠟⣿⣿⡿⠁⢀⣤⠄⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡉⠁⠉⡍⠁⠀⠀⠀⠻⣿⣷⡋⠀⣮⣦⣌⣿⣿⣷⣭⣿⣟⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡄⠀⣿⣿⣿⣿⡟⣛⣻⡶⣾⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣎⢻⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⢠⣿⣿⣿⡿⣰⡋⡽⠁⡟⢸⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠸⣿⣿⢿⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⢸⠿⠯⣤⣦⣭⠋⢟⡇⠘⠘⠐⠈⡇⡾⠢⠖⠂⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⢿⣿⣎⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠟⣿⡟⠏⣴⣷⠶⠷⠚⢭⡷⠈⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⢠⣄⣛⣯⣼⣿⣿⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢹⣿⣿⡟⠀⠻⢿⠉⠵⣶⡊⠊⠀⢻⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡟⢻⠻⠿⠟⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠜⠉⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣷⣄⠀⠀⠝⠀⠁⠀⠀⠁⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⣀⠀⠀⠀⠀⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⡿⣿⣿⣿⣿⣿⡿⠹⠏⠙⠀⠀⠀⢠⡖⠈⠰⠄⠀⠀⠀⡼⠀⠘⠋⠀⠀⠀⠀⠀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⣿⣾⢆⣿⣾⢀⣾⣶⣷⣷⣿⣿⣶⣷⡗⣸⣷⣾⣿⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠆⠲⣶⠎⢶⠄⠰⢶⣶⣶⣴⣤⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠁⠈⠈⠑⠈⠀⠁⠈⠈⠀⣽⣾⣾⣾⣾⣾⣶⣷⣾⣾⣶⡅⢡⠂⠡⣁⢨⣄⡄⠈⠁⠁⢨⣬⡆⠀⠁⠉⠈⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠅⠶⢠⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣷⣶⠤⠀⠀⠀⠀⠀⠀⠁⠰⠋⠭⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣥⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⢆⣷⣿⣿⡆⠀⠐⡀⢀⢀⣁⡰⠒⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀

⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣤⣿⣏⢉⣧⠀⢰⡀⠠⠐⣚⣫⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⢀⣽⣿⣿⣿⣿⠃⠀⠀⠄⡄⠖⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⣿⣀⣤⡶⠀⠙⢿⣿⣟⢟⣁⢠⢜⠙⢴⣷⣿⣿⣿⣯⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡑⠋⠁⢻⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⡿⠁⠀⣰⡀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡉⠉⠉⠟⠁⠀⠀⠀⠻⣿⣷⡉⢠⣮⣭⣧⣿⣿⣷⣬⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡄⠀⣸⣿⣿⣿⡟⣛⣳⣷⣿⢸⣿⠃⠀⠊⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣎⢹⣿⣿⣿⣿⠁⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡇⠠⡿⣿⣿⣿⢡⠏⡼⢡⡏⢸⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠘⣿⣿⢿⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢹⢿⠯⣤⣤⣬⠙⢻⡇⠐⠁⠹⠈⡇⣼⢸⡴⠆⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠿⣿⡆⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠟⣻⡟⡝⣰⣯⠶⠷⠶⢩⣽⠀⠈⠁⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⢠⣄⣛⢿⣴⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢹⣿⣿⡟⠀⠹⣻⠉⢭⣶⡞⠐⠃⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⢠⣤⣤⣄⠈⠻⠙⠛⡟⢿⣿⡏⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠟⠀⠀⠁⠀⠔⠉⠀⠀⠀⠘⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠙⠃⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⡇⠀⣀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡄⠀⠀⠀⠀⠀⣤⣿⡿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠀⠀⠀⢀⠶⠀⠐⠆⠀⠀⠀⢰⠀⠀⠉⠀⠀⠀⠀⠀⠠⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⣿⣾⢆⣿⣾⢀⣾⣾⣷⣷⣿⣿⣶⣷⡗⣸⣿⣾⣿⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠲⣶⠎⢶⠄⠰⢶⣶⣦⣴⣤⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⠈⠀⢹⣾⣾⣾⣾⣾⣶⣷⣾⣾⣶⣧⢁⠂⢡⢁⠈⡄⠀⠨⠁⠁⠈⢨⣪⡄⠁⠉⠈⠁⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀

[16A⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⡅⠬⣬⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣦⡤⠀⠀⠀⠀⠁⠀⠀⢘⢒⠽⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣥⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠯⣽⣷⣿⡆⠀⠀⠀⠀⠂⠀⣀⢐⣖⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀

⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣤⣼⣟⠉⣯⠀⢐⠀⢀⢈⣱⣱⣶⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⢀⣽⣿⣿⣿⣻⠏⠁⢀⣁⡁⠴⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⣿⣀⣤⣶⠀⠙⢿⣿⣟⢟⣇⢄⠕⠁⠤⣾⣾⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡱⠋⠉⢛⢻⣿⡿⣿⣿⣿⣿⢿⢿⣿⡿⠁⠀⣠⡄⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡅⠉⠉⠋⠁⠀⠀⠀⠻⣿⣷⡻⣀⣬⣦⣧⣽⣿⣷⣮⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡄⠀⣰⣿⣿⣿⡾⣻⢹⡼⣾⢸⣿⠇⠀⠈⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣎⢻⣿⣿⣿⣿⠃⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⡇⠀⣿⣿⣿⣿⢧⢟⣼⠃⡏⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠘⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⠿⣤⣤⢥⠙⢻⠟⠀⠇⠣⠊⡇⢸⢐⡤⠆⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⢿⣿⡌⠞⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠟⣻⣿⠟⢠⣫⠶⠳⠆⢩⣿⠀⠀⠁⠀⠀⠀⠀⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⢠⣈⠛⢏⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⡟⠀⠹⣿⠏⢫⣶⣞⠑⠃⢸⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣰⣿⣿⣷⡄⠻⣿⣾⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⡾⠀⠀⠁⠀⠕⡋⠀⠀⠀⠈⢹⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠀⣀⡈⠉⠉⠁⠉⠛⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠈⠁⡀⠀⠀⠀⠘⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡿⠀⠀⠀⠀⠀⢠⣿⡿⣿⣿⣿⣿⣿⣿⢿⣿⡿⠟⠁⠀⠀⢀⠶⠒⠀⠆⠀⠀⠠⠂⡇⠀⠘⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⣿⣾⢆⣿⣾⢀⣾⣾⣷⣷⣿⣿⣶⣷⡟⣸⣶⣾⣿⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠆⠲⣶⠊⢶⠄⠰⢶⣶⣶⣴⣦⠀⠀⠁⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⠈⠀⢹⣾⣾⣾⣾⣾⣶⣷⣾⣾⣶⣥⢁⠂⢡⢁⠈⡄⢠⣬⠁⠁⠈⠈⢠⣢⠁⠉⠈⠁⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀

                ䷩ 𝚕𝚒𝚗𝚎 6570

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

Gemini_version_available_♊︎

✐ Links_8/2/2022:_Fragments_2.0_and_Comparing_Various_GNU/Linux_Distros

Online⠀✐

Posted in News_Roundup at 7:30 pm by Dr. Roy Schestowitz

🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈

§ Contents⠀➾

* GNU/Linux

      o Distributions

      o Devices/Embedded

* Free_Software/Open_Source

* Leftovers

* § GNU/Linux⠀➾

      o § Desktop/Laptop⠀➾

            # ⚓ 5_Reasons_to_Install_Linux_on_an_Old_Computer⠀⇛

                   Short on cash to upgrade your PC? Installing Linux

                   is a great way to breathe new life into your aging

                   computer and save money.

                   A lot of people like to use Linux on older

                   machines. The reasons for doing so obviously vary

                   from person to person. Some may want to save money

                   by not upgrading to a new computer, whereas others

                   may wish to avoid e-waste. And yes, you’ll also

                   find many people who think running Linux is fun.

                   If you’re struggling to find a solid excuse, we’ll

                   list out various reasons why you should consider

                   installing Linux on your old computer.

      o § Audiocasts/Shows⠀➾

            # ⚓ WP_Briefing:_Episode_24:_Three_Goals_in_2022⠀⇛

                   In episode 24 of the WordPress Briefing, the

                   Project’s Executive Director reviews three big-

                   picture goals for the year: Increased Gutenberg

                   adoption, support of all open source alternatives,

                   and stewarding the open source ethos.

            # ⚓ Late_Night_Linux_–_Episode_163_–_Late_Night_Linux⠀⇛

                   Why FOSS is unlikely to gain traction in education,

                   what’s great about Discourse, Linux gaming, the

                   uncertain future of Termux, our thoughts on Snap

                   and Flatpak, and more.

            # ⚓ Middle_Mouse_On_Linux_Is_Incredibly_Powerful_–_Invidious⠀⇛

                   I rarely touch my middle mouse button but it turns

                   out it has a lot more power than I ever knew,

                   there’s the obvious autoscroll feature in browsers

                   which I didn’t know worked on Linux but there’s so

                   much more

            # ⚓ If_you’re_not_using_Flatpaks,_you’re_doing_Linux_wrong._–

              Invidious⠀⇛

                   They’re the future of Linux app distribution.

                   Distros like Elementary, Pop, and even Steam OS

                   support them by default. So here’s what they are,

                   how they work, and a bit of their history!

      o § Applications⠀➾

            # ⚓ Flatpak_App_of_the_Week:_Fragments_–_Modern_BitTorrent

              Client_for_the_GNOME_Desktop⠀⇛

                   Fragments is an easy-to-use BitTorrent client based

                   on the well-known Transmission BitTorrent client

                   (uses transmission-daemon), which is used as a

                   backend for transferring data. The app is written

                   in GTK and it’s designed specifically for use with

                   the GNOME desktop environment.

                   You’re probably already using Fragments since it is

                   being developed for a few years now. But the latest

                   release, Fragments 2.0, caught my attention as it

                   brings lots of new features and improvements, and

                   it’s completely rebuilt using Rust, GTK4, and the

                   libadwaita library.

            # ⚓ GNOME_BitTorrent_Client_Fragments_2.0_Released!_GTK4,

              Libadwaita_&_Remote_Control⠀⇛

                   The Fragments BitTorrent client finally released

                   version 2.0. It’s now uses Rust, GTK4 and the new

                   Libadwaita library to provide a stylish user

                   interface for those running Linux with GNOME

                   desktop.

                   For those never heard of Fragments, it’s a free

                   open-source torrent app that uses Transmission as

                   backend for transferring data. With it, user may

                   starting downloading via…

            # ⚓ BitTorrent_Client_‘Fragments_2.0′_for_Linux_is_Here,

              Rebuilt_Using_Rust_with_a_New_UI⠀⇛

                   Fragments is one of the best torrent clients for

                   Linux.

                   The latest Fragments 2.0 is a significant upgrade,

                   completely rewritten from scratch using Rust, GTK

                   4, and Libadwaita.

                   In addition to the technical improvements, you will

                   also find some new features and an improved user

                   interface.

            # ⚓ The_road_to_Fragments_2.0⠀⇛

                   It was a bit quiet around Fragments, many had the

                   fear that Fragments will no longer be maintained.

                   These rumors I can proudly counter, and can now

                   announce that Fragments 2.0 is now available after

                   about a year of development!

            # ⚓ Twine:_Open_Source_Tool_for_Making_Games_with_Words,_aka

              Interactive_Fiction⠀⇛

                   Everyone has a game inside them waiting to come

                   out, just like a chestburster. Unfortunately, not

                   everyone has the skills to create a game,

                   especially one complete with graphics. Thankfully,

                   there is a way to create a fun game using only

                   words. Let me share an application that could help

                   you with it.

                   As I alluded to above, Twine allows anyone to

                   create a game without needing to know how to write

                   code. Remember those Choose-Your-Own-Adventure

                   books? That’s essentially how Twine works.

                   You create a series of passages, which can be one

                   sentence or a wall of text. You named each of these

                   passages, so you can keep track of them. After

                   that, you connect these passages and create several

                   paths for the player to follow based on their

                   decisions.

      o § Instructionals/Technical⠀➾

            # ⚓ Metasploit_Tutorial_for_Beginners_–_Basics_to_Advanced⠀⇛

                   Metasploit, one of the most widely used penetration

                   testing tools, is a very powerful all-in-one tool

                   for performing different steps of a penetration

                   test.

                   If you ever tried to exploit some vulnerable

                   systems, chances are you have used Metasploit, or

                   at least, are familiar with the name. It allows you

                   to find information about system vulnerabilities,

                   use existing exploits to penetrate the system,

                   helps create your own exploits, and much more.

                   In this tutorial, we’ll be covering the basics of

                   Metasploit Framework in detail and show you real

                   examples of how to use this powerful tool to the

                   fullest.

            # ⚓ Running_unit_tests_in_Jenkins_–_Octopus_Deploy⠀⇛

                   Verifying code changes with unit tests is a

                   critical process in typical development workflows.

                   Jenkins provides a number of plugins to collect and

                   process the results of tests allowing developers to

                   browse the results, debug failed tests, ignore some

                   test failures, and generate reports on the history

                   of tests over time.

                   In this post, you learn how to add unit tests to a

                   Jenkins project and configure plugins to process

                   the results.

            # ⚓ Running_end-to-end_tests_in_Jenkins_–_Octopus_Deploy⠀⇛

                   End-to-end (E2E) tests represent the final stages

                   of automated testing. E2E tests are long-running,

                   especially compared to unit tests which can

                   complete thousands of checks in seconds. They are

                   typically executed by external tools which interact

                   with the application under test, through public

                   interfaces like web pages or HTTP APIs.

                   In this post, you learn how to run E2E tests with

                   Cypress to validate interactions with web pages and

                   with Newman, the command-line test runner for

                   Postman, to validate HTTP APIs.

            # ⚓ Install_Facebook_Messenger_On_Ubuntu_22.04_LTS_[Update]⠀⇛

                   No doubt Facebook is one of the most popular social

                   media networks these days. Now under Meta, Facebook

                   has a massive userbase with a high volume of usage.

                   1.93 billion people use Facebook on daily basis.

                   You can access Facebook from the web browser or

                   from its official mobile application. Meanwhile,

                   there are plenty of third-party apps available

                   these days from where you can access and manage

                   your Facebook account. In this tutorial post, we

                   are going to show you the process to Install

                   Facebook Messenger on Ubuntu 22.04 LTS.

            # ⚓ How_to_Setup_Django_with_Postgres,_Nginx_and_Gunicorn_on

              Ubuntu_20.04_–_RoseHosting⠀⇛

                   Django is an open-source web framework written in

                   Python. It is a popular all-in-one web framework

                   and one of the top choices for many developers.

                   Django offers many advantages, such as MVT (Model

                   View Template) architecture, automatic admin panel,

                   and powerful ORM (Object Relational Mapping)

                   database support. It also offers awesome debugging

                   tools for developers. In this tutorial, we will

                   show you how to install Django with PostgreSQL as

                   the database storage instead of the default SQLite,

                   Nginx as the reverse proxy, and Gunicorn as the

                   application server on Ubuntu 20.04.

            # ⚓ How_to_Install_Angular_on_Ubuntu_–_VITUX⠀⇛

                   Angular is a free and open-source JavaScript-based

                   framework for developing single-page applications,

                   it is the successor of the AngularJS framework. It

                   is maintained by Google, the same company that

                   created JavaScript and made Angular a household

                   name. According to Google Developers, it can be

                   used on top of “MongoDB, Node.js by IBM, Express by

                   Nodejitsu”, etc., which makes it possible for you

                   to develop an app without having to worry about

                   what technologies will power your application.

                   If you’re looking to get started with Angular, one

                   of the best ways to do that is to install it on

                   your own Ubuntu server. This will allow you to test

                   your app on different browsers like Google Chrome

                   and Mozilla Firefox.

                   In this guide, we’ll show you how to install

                   Angular on Ubuntu 20.04. The same procedure works

                   on Ubuntu 22.04 as well. We’ll also cover some

                   basic steps for getting started with Angular

                   development. So, whether you’re a beginner or an

                   experienced developer, this guide is for you!

            # ⚓ How_to_Set_Up_Nginx_with_Google_Pagespeed_Module_on_Debian

              11⠀⇛

                   Google Pagespeed Module is an open-source module

                   for optimizing your websites under the Nginx and

                   Apache web-server. The Pagespeed module is a

                   server-level module installed alongside the Nginx

                   and Apache webserver.

                   The Pagespeed module improves the performance and

                   speed of your website by optimizing static files on

                   your websites. The Pagespeed module optimizes

                   images on your websites, minify static files such

                   as HTML, CSS, and JavaScript, and optimize file

                   caching.

                   In this tutorial, we will show you how to build the

                   Nginx Pagespeed module on the latest Debian 11

                   Bullseye. This guide can be applied to the current

                   of your Nginx installation because you just build

                   the Nginx module.

            # ⚓ Linux_for_freshers:_How_to_Install_ranger_in_Ubuntu

              18.04?⠀⇛

                   Ranger is a free and open-source command-line file

                   manager for Linux. It comes with a minimalistic

                   text-based user interface and VI key bindings

                   support. The main design goal of this file manager

                   is switch directories and browse files in a quick

                   and easy way. Some of the main features are preview

                   the selected file or directory and automatically

                   determining file types and running them with

                   correct programs. It supports VIM like hotkeys,

                   UTF-8, multi-column display, mouse support, builds

                   in Tabs, and bookmarks support.

            # ⚓ How_to_Install_Lighttpd_with_PHP_in_Ubuntu_20.04⠀⇛

                   The concept of web servers has crossed the minds of

                   most, if not all, Linux enthusiasts; especially the

                   ones interested in pursuing web-based projects and

                   careers. Due to the numerous web servers offered to

                   the Linux community, you might feel like tossing a

                   coin or rolling a dice to find the one that ‘might’

                   suit your web-based needs.

                   Lighttpd is best attributed as a compatible, very

                   flexible, fast, and secure web server. It is

                   therefore optimized for high performance on

                   whichever operating system environment hosts it.

                   Also, this web server is indeed light such that it

                   needs very few resources to run or execute its

                   functional objectives like handling AJAX

                   applications. This web server is BSD licensed,

                   open-source, with flawless compatibility on UNIX-

                   like systems.

                   This article seeks to walk you through the

                   installation and configuration of Lighttpd as an

                   ideal web server for your Ubuntu 20.04 operating

                   system.

            # ⚓ How_To_Install_MySQL_Workbench_on_AlmaLinux_8_–_idroot⠀⇛

                   In this tutorial, we will show you how to install

                   MySQL Workbench on AlmaLinux 8. For those of you

                   who didn’t know, MySQL Workbench is a graphical

                   user interface tool for general administration and

                   maintenance of MySQL/MariaDB database systems

                   available in a free and a commercial edition. For

                   detailed features differences among MySQL Workbench

                   Edition have been described on MySQL Workbench

                   features.

                   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 through the step-by-

                   step installation of the MySQL Workbench on an

                   AlmaLinux 8. You can follow the same instructions

                   for CentOS and Rocky Linux.

            # ⚓ How_To_Install_Anaconda_on_Fedora_35_–_idroot⠀⇛

                   In this tutorial, we will show you how to install

                   Anaconda on Fedora 35. For those of you who didn’t

                   know, Anaconda is an open-source package and

                   environment manager that houses thousands of

                   predictive analysis, machine learning, and data

                   science packages. It is written in Python and R

                   programming language by data scientists, for data

                   scientists. It includes the packages related to

                   data science for various platforms like Linux,

                   Windows, and macOS.

                   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 Anaconda on a Fedora 35.

            # ⚓ How_to_Use_Hadolint_to_Lint_Your_Dockerfiles_–_CloudSavvy

              IT⠀⇛

                   Dockerfiles define the content of Docker images as

                   a set of instructions in a text file. The

                   Dockerfile syntax is generally straightforward but

                   there are some gotchas to avoid. Adhering to best

                   practices while writing complex Dockerfiles in a

                   team setting can be tricky unless you’re

                   automatically validating your file’s content.

                   Hadolint is a Dockerfile linter that can spot

                   common issues for you. It uses an abstract syntax

                   tree (AST) to parse your Dockerfile against

                   predefined rulesets. Hadolint also incorporates

                   ShellCheck so it can lint the shell scripts in your

                   Dockerfile’s RUN instructions too.

            # ⚓ How_to_get_the_directory_size_using_the_Linux_command_line

              –_PragmaticLinux⠀⇛

                   With the help of your desktop environment’s file

                   manager, you can easily obtain the size of a

                   directory’s contents. Right-click the directory and

                   select Properties from the pop-up menu. When

                   working on the command line in the terminal, it’s a

                   different story. For example, when interacting with

                   a server over SSH. This article explains who to get

                   the size of a directory using the Linux command

                   line, while working in the terminal.

            # ⚓ How_to_create_a_custom_image_from_a_Docker_container_|

              TechRepublic⠀⇛

                   Your containers are all based on images, most of

                   which you probably pull from DockerHub or some

                   other public repository. But why not create your

                   own custom images? After all, it’s easier for you

                   to not only get the exact image you need to work

                   with, it’s also a better route to security. It’s

                   also a great way to create a base image you can use

                   for a repeatable development environment (so, it

                   has exactly the tools you need).

            # ⚓ How_to_install_Friday_Night_Funkin_on_a_Chromebook_–

              Windows_64_Bit_version⠀⇛

                   Today we are looking at how to install Friday Night

                   Funkin, the 64 bit Windows version, on a

                   Chromebook. Please follow the video/audio guide as

                   a tutorial where we explain the process step by

                   step and use the commands below.

            # ⚓ How_to_install_Friday_Night_Funkin_on_a_Chromebook_–

              Windows_64_Bit_version⠀⇛

            # ⚓ How_to_install_YubiKey_Manager_GUI_on_Linux⠀⇛

                   One can use a hardware security key such as YubiKey

                   for OTP or FIDO2 for additional security on Linux

                   to protect disks, ssh keys, password manager, web

                   applications and more. Since I am a full-time Linux

                   desktop user, I thought today I would document how

                   to install the YubiKey GUI Manager to configure

                   functionality on your YubiKey on a Linux desktop.

            # ⚓ How_to_install_whois_on_Ubuntu_/_Debian_Linux⠀⇛

                   While working on the client’s system, I found that

                   the whois client was missing. So I used that in one

                   of my deployment scripts. I should add that to

                   cloud-init or Ansible, but the Ubuntu server was

                   already running.

                   The whois command searches an object in an RFC 3912

                   database without using online websites. For

                   example, you can find out who is the owner of an IP

                   address or domain name from your Debian Linux

                   command-line. You can automate stuff in your shell

                   script. Here is how to install whois client on your

                   Debian or Ubuntu Linux.

            # ⚓ Install_Kate_Text_Editor_on_Ubuntu_22.04_LTS_–

              LinuxCapable⠀⇛

                   Kate is a powerful and intuitive editor that may be

                   the perfect fit for you. With its robust yet

                   straightforward interface, Kate offers everything

                   from word processing to development tools in one

                   place – which saves time! And with 200+ languages

                   available on-board alongside plugins galore (think

                   code hooks), this tool will help maximize

                   productivity, whether it’s coding or content

                   creation.

                   In the following tutorial, you will learn how to

                   install Kate Text Editor on Ubuntu 22.04 LTS Jammy

                   Jellyfish.

            # ⚓ Install_Fragments_2.0_On_Ubuntu_/_Rocky_Linux_&_Fedora_|

              Tips_On_UNIX⠀⇛

                   Fragments is an open-source BitTorrent client for

                   Linux systems and developed by the GNOME desktop

                   environment.

                   This tutorial will be helpful for beginners to

                   install fragments 2.0 on Ubuntu 20.04 LTS, Rocky

                   Linux 8, AlmaLinux 8, and Fedora 35.

                   It is used to transfer huge files like videos,

                   Installation media images and it uses BitTorrent

                   protocol. Fragments 2.0 is the major update with

                   many new features and improvements. Fragments now

                   use the GTK4 and the new GNOME Libadwaitaa Library

                   under the hood.

            # ⚓ Install_7-Zip_on_Debian_11_Bullseye_–_LinuxCapable⠀⇛

                   7-Zip is a free, open-source file archiver software

                   used to compress files into archive containers or,

                   in more popular terms, zip files into archive

                   containers that can beat most other forms of

                   compression by 2 to 10% and strong AES-256

                   encryption in 7z and ZIP formats.

                   7-Zip isn’t as famous as some of the other

                   archives, but it is capable of having multi archive

                   format support across most known software. Another

                   benefit is that it supports all cross-platforms,

                   making it efficient to use amongst different

                   operating systems.

            # ⚓ Install/Upgrade_GNOME_Subtitles_on_Ubuntu_20.04_LTS_–

              LinuxCapable⠀⇛

                   GNOME Subtitles is an easy-to-use subtitle editor

                   for Linux. It allows you to add subtitles and

                   captions with preview, timing synchronization

                   capabilities (including language translation),

                   spell-checking support, and more options that are

                   only possible in this simple tool!

                   The interface of GNOME Subtitles includes emphasis

                   styles such as bold/italic or underline applied

                   automatically when needed alongside multi-level

                   undo & redoes, making it the perfect choice if

                   minimalism isn’t really what matters most here…

                   In the following tutorial, you will learn how to

                   install or upgrade your existing GNOME Subtitles

                   using PPA for Pedro Castro, endorsed by the GNOME

                   Subtitles team.

            # ⚓ Install_WhatsApp_Client_On_Ubuntu_22.04_LTS/_Ubuntu_20.04

              LTS_|_Itsubuntu.com⠀⇛

                   WhatsApp is one of the most popular messaging apps

                   right now in the World. Facebook bought WhatsApp in

                   February 2014, for $16 billion. WhatsApp is

                   currently available for Android, iOS, and Windows

                   operating systems. Sadly it is not available for

                   Linux-based operating systems. WhatsApp’s official

                   client app is not available to install on Linux but

                   doesn’t worry we are here to help you in this

                   process.

                   In this post, we are going to show you the way to

                   use the WhatsApp clients on Ubuntu. Thanks to the

                   third-party tool WhatsDesk that lets us use

                   WhatsApp client on Ubuntu. Whatsdesk is an

                   unofficial WhatsApp client for Linux and is

                   available as a Debian package. You can also get it

                   on the snapcraft repository.

            # ⚓ Install_RPM_Packages_on_Ubuntu_22.04_LTS_–_LinuxCapable⠀⇛

                   The Ubuntu repositories contain thousands of deb

                   packages that can be installed from the Software

                   Center or by using the apt command line. Deb is an

                   installation package format used in all Debian-

                   based distributions, including Ubuntu, but some

                   aren’t available through these methods; alternative

                   sources such as existing RPM repositories may

                   contain these.

                   RPM package format is used by Red Hat and its forks

                   such as Almalinux, CentOS Stream, and Rocky Linux,

                   to name a few. For Ubuntu users, an application

                   called alien allows you to install RPM packages on

                   Ubuntu or convert an RPM package into a Debian

                   (.deb) file for Ubuntu.

                   In the following tutorial, you will learn how to

                   install RPM packages and convert a Debian package

                   into an RPM package on Ubuntu 22.04 LTS Jammy

                   Jellyfish.

            # ⚓ Install_Neofetch_on_Debian_11_Bullseye_–_LinuxCapable⠀⇛

                   Neofetch is a free, open-source command-line system

                   information tool written in bash 3.2+. Neofetch

                   displays system information in a beautiful

                   aesthetic way, such as system, software, memory

                   resources, kernel version, and much more.

                   In the following tutorial, you will learn how to

                   install Neofetch and some basic commands on Debian

                   11 Bullseye desktop or server.

      o § Games⠀➾

            # ⚓ FEX-Emu_is_a_promising_project_for_gaming_on_64bit_Arm_|

              GamingOnLinux⠀⇛

                   Want to play more games on Arm devices? Projects

                   like Box86 and Box64 do already exist but is there

                   a better option? FEX-Emu sounds like it’s going to

                   be another great open source way to do what you

                   want.

                   The problem is that most games and software aren’t

                   really built for Arm, games especially of course

                   since we’re not exactly swimming in powerful Arm

                   hardware market for gaming on Linux (or Windows).

                   Emulation and translation layers once again to the

                   rescue then. FEX-Emu is getting quite advanced now,

                   and it’s even able to run Wine / Proton too.

            # ⚓ Top_10_New_Games_You_Can_Play_on_Linux_with_Proton_–_Feb

              2022_Edition_–_Boiling_Steam⠀⇛

                   We are back with our usual monthly update! Boiling

                   Steam looks at the latest data dumps from ProtonDB

                   to give you a quick list of new games that work

                   (pretty much?) perfectly with Proton since January

                   2022 – all of them work out of the box or well

                   enough with tweaks…

            # ⚓ Steam_Deck_Previews_are_up,_plus_dbrand_announce_Project

              Killswitch_|_GamingOnLinux⠀⇛

                   The flood gates are beginning to open around the

                   Steam Deck with a few big YouTube channels doing a

                   hands-on preview now live. Plus, dbrand poke fun at

                   Nintendo with their upcoming Steam Deck accessory

                   kit.

            # ⚓ Building_a_Retro_Linux_Gaming_Computer_–_Part_11:_Forgotten

              Heresies_|_GamingOnLinux⠀⇛

                   Almost from the very start Raven Software and id

                   Software had a symbiotic relationship. Raven would

                   use id tech to power their games for years, but one

                   of their deepest collaborations was on Heretic,

                   with then id Software designer John Romero even

                   acting as producer. Given the Linux friendly

                   atmosphere at id, it is no surprise that some of

                   that would start to rub off on Raven, culminating

                   in Loki Software negotiating to make a port of

                   Heretic II.

            # ⚓ RPG_game_engine_Flare_gets_improved_gamepad_support,_fonts

              and_more_in_v1.13_|_GamingOnLinux⠀⇛

                   Flare is a free and open source game engine for

                   creating RPGs, plus it also has its own Empyrean

                   Campaign to play through and it continued to get

                   enhanced to be a bit more modern. Version 1.13 was

                   just recently release, bringing with it some pretty

                   major enhancements.

                   A big one is improved gamepad support that was

                   overhauled. They’ve moved from using the

                   SDL_Joystick API to using the SDL_GameController

                   API, along with improved gamepad mapping and fixes

                   to some deadzone issues. Navigating the UI is also

                   quite a bit easier now too, as various actions give

                   you a pop-up now to easily pick what to do.

            # ⚓ Heroic_Games_Launcher_for_Epic_Games_on_Linux_gets_some

              more_fixes_|_GamingOnLinux⠀⇛

                   Readying up for the onslaught of users on the Steam

                   Deck who will probably want to play some of their

                   Epic Store loot, the free and open source Heroic

                   Games Launcher has a new bug fix release up.

                   An application that has only become more important

                   with the Steam Deck, since it ships with Linux and

                   Epic Games don’t support Linux with their store.

                   This at least gives Linux desktop gamers and Steam

                   Deck users a really easy way to get all their games

                   in one place.

            # ⚓ Linux_Kernel_getting_prepped_for_the_Steam_Deck_|

              GamingOnLinux⠀⇛

                   While it’s already known that the Steam Deck will

                   ship with Valve’s own SteamOS 3 based on Arch

                   Linux, what about running more standard Linux

                   distributions? It will get easier in a future

                   version of the Linux Kernel.

                   Since it’s open source, Linux gives Valve a lot of

                   true control on what they can do and tweak for the

                   Steam Deck and that’s a big part of the reason they

                   went with Linux instead of Windows. At release it

                   will likely be using a good number of Valve special

                   patches, many of which will be upstreamed to

                   various projects and we’re starting to see part of

                   that now.

            # ⚓ Indie_store_itch.io_comes_out_swinging_against_NFTs_|

              GamingOnLinux⠀⇛

                   Not only has Valve banned NFT games from Steam but

                   another store has come out clearly against them,

                   with the official itch.io Twitter account releasing

                   a very clear statement.

            # ⚓ Open_source_evolution_sim_Thrive_adds_a_new_cell_to_grow

              with_|_GamingOnLinux⠀⇛

                   Currently in Early Access, Thrive is an impressive

                   scientific evolution sim developed in Godot Engine

                   that continues to mature with a new version up.

                   Sounds like a pretty fun release too, adding in a

                   “chemoreceptor organelle” cell you can evolve your

                   creature with. This will allow you to sniff-out

                   needed resources from quite a distance so you won’t

                   get as lost once you manage to acquire it through a

                   little basic exploration and growth. There’s also

                   now a timeline tab in the reports screen, which

                   allows you to view the current history of the

                   microscopic world you’ve been exploring and

                   surviving in. Plus, lots of bug fixes and

                   optimizations and a Godot Engine upgrade too.

            # ⚓ Online_multiplayer_for_OpenMW_(Morrowind)_TES3MP_is_alive

              again_|_GamingOnLinux⠀⇛

                   OpenMW is a fantastic open source game engine

                   reimplementation for Morrowind, plus there’s the

                   online fork of TES3MP which has sprung back to life

                   with a new release. A project that should

                   eventually merge with OpenMW officially, for now

                   it’s a separate fork until OpenMW hits the big 1.0.

                   TES3MP 0.8.0 is now out and based on the latest

                   OpenMW 0.47.0 release, and the developer said it

                   “fixes a large part of the remaining gameplay

                   problems and also adds some major features”. It

                   took a little while, as the developer explained how

                   they “lost my motivation for TES3MP during the

                   pandemic, but I’ve been regaining it recently

                   because I want to look back on this project as one

                   that I ended up finishing instead of one that I

                   just got very far on”.

            # ⚓ Yacht_Club_Games’_newest_title_is_the_upcoming_Mina_the

              Hollower_|_GamingOnLinux⠀⇛

                   Yacht Club Games, know for the popular Shovel

                   Knight series has a new game in development called

                   Mina the Hollower, and it’s currently crowdfunding

                   on Kickstarter with it being a clear early success.

                   “Descend into a frightful world of action-adventure

                   in Mina the Hollower. Take control of Mina, a

                   renowned Hollower hurtled into a desperate mission

                   to rescue a cursed island. Burrow beneath hazards

                   and monsters, whip foes into oblivion, and gear up

                   with an arsenal of sidearms and trinkets. Explore a

                   vast world filled with pixel-perfect graphics,

                   masterful gameplay, beastly bosses, and infectious

                   music. Encounter a cast of bizarre characters,

                   search out secrets in an array of exotic locales,

                   and illuminate the omnipresent darkness in Mina the

                   Hollower, a brand new game from the developers who

                   brought you Shovel Knight!”

      o § Distributions⠀➾

            # ⚓ Zorin_OS_16_Educational_Spin_Now_Available⠀⇛

                   Zorin OS 16 Education is a Linux distribution aimed

                   at pre-schools as well as primary and secondary

                   schools. Building on their already-fantastic

                   desktop experience, the developers have added a few

                   tools to help educational institutions prepare

                   students with the skills they need to navigate the

                   waters of an ever-growing complicated world.

                   One of the key pieces of software added is Kolibri,

                   which aims to bridge the educational divide by

                   giving access to an enormous library of educational

                   content. Even better, an internet connection isn’t

                   required to use the tool. With Kolibri, school

                   administrators can either create their own

                   curriculum or download materials from educational

                   leaders such as Khan Academy, Open Stax, MIT, TED-

                   Ed, and Sikana. Once downloaded, the content can be

                   shared, peer to peer, over a local network.

            # ⚓ Qubes_OS_4.1.0_released⠀⇛

                   Version 4.1.0 of the secure-desktop-oriented Qubes

                   OS distribution has been released. “The culmination

                   of years of development, this release brings a host

                   of new features, major improvements, and numerous

                   bug fixes”. New features an experimental GUI domain

                   separate from dom0, the “Qrexec” policy system,

                   progress toward a reproducible build, and more. See

                   below and this article for more information.

            # ⚓ How_to_Test_Various_Linux_Distros_Online⠀⇛

                   Most Linux aficionados switch and test distros as

                   often as they change their socks. However,

                   searching and downloading your distro, creating a

                   bootable USB drive, and installing and configuring

                   the distro is time-consuming and oft-times an

                   exercise in futility. DistroTest.net allows you to

                   test drive 373 operating systems with 782 different

                   versions, so you can “test it before you hate it.”

            # § Slackware Family⠀➾

                  # ⚓ Hello_Slackware,_our_old_friend:_Veteran_Linux

                    distribution_releases_version_15.0_at_last⠀⇛

                         It’s been a long time coming but version 15

                         of Slackware finally showed up at the

                         weekend.

                         Fans of the distro, which debuted in 1993,

                         have waited since 2016′s 14.2 for the full

                         fat update. Now, nearly a year after the beta

                         turned up, “the Slackhog emerged from its

                         development den, did *not* see its shadow,

                         and Slackware 15.0 has been officially

                         released,” according to Benevolent Dictator

                         For Life Patrick Volkerding.

                         The release is a big one; after all – it’s

                         been nearly six years since the previous,

                         which came after 2013′s 14.1. Version 14 goes

                         all the way back to 2012. Hopefully the next

                         iteration will not take quite so long,

                         although Volkerding warned that he would be

                         taking “a bit of a breather” after the

                         lengthy gestation period of version 15.

            # § IBM/Red Hat/Fedora⠀➾

                  # ⚓ Best_Free_and_Open_Source_Alternatives_to_IBM_Maximo

                    Application_Suite⠀⇛

                         International Business Machines Corporation

                         (IBM) is an American multinational technology

                         corporation headquartered in Armonk, New

                         York. They sell computer hardware, middleware

                         and software employing over 370,000 people.

                         IBM acquired Red Hat in 2019. But you can

                         trace IBM’s history of open source far

                         further back. They were one of the earliest

                         champions of open source, backing influential

                         communities like Linux, Apache, and Eclipse,

                         advocating open licenses, open governance,

                         and open standards.

                  # ⚓ This_New_Linux_Distro_Combines_Fedora_With_Great

                    Gaming_Software⠀⇛

                         What happens when a senior engineer at Red

                         Hat, a member of the Lutris development team,

                         and the creator of Proton-GE decides to

                         create a Linux distribution? Well, the

                         aforementioned titles belong to the same

                         person, Thomas Crider (aka “Glorious

                         Eggroll). And what you get is the promising

                         Nobara Project, a distro powered by Fedora

                         and targeted squarely at gamers and content

                         creators.

                         “Fedora is a very good workstation OS,

                         however, anything involving any kind of 3rd

                         party or proprietary packages is usually

                         absent from a fresh install,” Crider says.

      o § Devices/Embedded⠀➾

            # ⚓ Qualcomm_IPQ8076A_WiFi_6E_access_point_offers_dual_10GbE,

              supports_PoE++⠀⇛

                   Lanner LWR-X8460 is an enterprise-grade 12-stream,

                   tri-band Wi-Fi 6E access point powered by Qualcomm

                   IPQ8076A quad-core Cortex-A53 processor also

                   equipped with two 10GbE multi-speed ports, and four

                   additional Gigabit Ethernet ports.

                   The access point also supports IEEE 802.3bt

                   standard for the PoE++ power delivery, Bluetooth

                   5.1 for IoT management, and its features set makes

                   it suitable for remote video conferencing,

                   telehealth, distance learning, public safety

                   monitoring, IoT applications, as well as general

                   connectivity in any crowded and dense Wi-Fi

                   environments.

            # ⚓ Add_four_PCIe_x1_slots_to_Raspberry_Pi_CM4_IO_with

              Waveshare_PCIe-Packet-Switch-4P_board⠀⇛

                   The 1-lane PCIe Gen 2 interface in Broadcom BCM2711

                   processor is exposed in Raspberry Pi CM4, and most

                   carrier boards are exploiting the interface

                   including the official Raspberry Pi Compute Module

                   IO carrier board.

                   But if you ever wanted to connect multiple PCIe

                   cards to the CM4 IO board, Waveshare has got you

                   covered with the PCIe-Packet-Switch-4P that

                   provides four PCIe x1 slots through an ASMedia

                   ASM1184e PCIe switch.

            # ⚓ RPi_HAT_features_high-frequency_RFID_reading_at_up_to_200

              tags/sec.⠀⇛

                   SB Components is Kickstartering a “UHF HAT for

                   Raspberry Pi” with high-frequency UFC RAIN RFID

                   technology for reading up to 200 tags per second.

                   If you read this before noon PST, you have a few

                   minutes left to get the Kickstarter early bird

                   special for the UHF HAT for Raspberry Pi at 199 UK

                   Pounds ($269). Otherwise, it goes to 225 Pounds

                   ($304), with shipments due in April. The

                   Kickstarter packages ship with 5x UHF RFID tags.

                   The UHF HAT is an RFID add-on for the Raspberry Pi

                   that uses Ultra High Frequency (UHF) RFID

                   technology operating over the 865MHz to 870MHz and

                   915MHz to 928MHz ranges. The UFC HAT offers

                   adjustable RF output range of 0 dBm to +27 dBm with

                   0.01 dB increments and supports the reading of up

                   to 200 tags per second.

            # § Mobile Systems/Mobile Applications⠀➾

                  # ⚓ Is_Google_Play_Store_Not_Working?_Here_Are_Some

                    Possible_Fixes⠀⇛

                  # ⚓ Video:_Top_5_Must-Have_Android_Apps_For_February_2022

                    |_NDTV_Gadgets_360⠀⇛

                  # ⚓ Nokia_G21_Android_smartphone_leaked_–_Geeky_Gadgets⠀⇛

                  # ⚓ New_CapraRAT_Android_Malware_Targets_Indian

                    Government_and_Military_Personnel⠀⇛

                  # ⚓ Android_12_February_security_patch_OTA_for_Pixel

                    rolling_out_–_9to5Google⠀⇛

                  # ⚓ Tecno_Pop_5S_goes_official_with_5.7″_LCD_and_Android

                    10_Go_–_comments⠀⇛

                  # ⚓ What_is_Android_Auto_and_what_can_it_do?_–

                    SlashGear⠀⇛

                  # ⚓ Tecno_Pop_5S_goes_official_with_5.7″_LCD_and_Android

                    10_Go_–_GSMArena.com_news⠀⇛

                  # ⚓ How_to_free_up_space_on_Android_–_Geeky_Gadgets⠀⇛

                  # ⚓ How_to_see_deleted_notifications_on_Android

                    smartphones⠀⇛

                  # ⚓ Here’s_An_Easy_Way_To_Block_Websites_On_Android⠀⇛

                  # ⚓ YouTube_For_Android_Is_Reportedly_Testing_“Listen

                    With_YouTube_Music”_Button⠀⇛

                  # ⚓ Truecaller_teams_up_with_global_Android_smartphone

                    manufacturers_to_preload_app_in_key_mkts_|_Business⠀⇛

                  # ⚓ PinePhone_call_quality⠀⇛

                         I bought a PinePhone a couple of months ago,

                         mainly for the opportunity to play with it

                         and see what it could do. Since I work for a

                         company that does voice call quality testing,

                         the first thing I wanted to do was figure out

                         how to play back our audio quality test files

                         and then do some call audio quality tests.

                         When doing call audio quality testing, it’s

                         very important that the audio you’re playing

                         back not be transcoded or even resampled, so

                         using PulseAudio or PipeWire was completely

                         out of the question. Figuring this process

                         out turned out to be far harder than I

                         expected, so I thought I should document how

                         I made it work. My background is in IT

                         infrastructure, and I am not an audio

                         engineer or a telephony expert, so I wouldn’t

                         be surprised if there are better ways of

                         doing things. Suggestions are very welcome on

                         Twitter or via email.

      o § Free, Libre, and Open Source Software⠀➾

            # § Productivity Software/LibreOffice/Calligra⠀➾

                  # ⚓ LibreOffice_ecosystem_interview:_Caolán_McNamara_at

                    Red_Hat⠀⇛

                         We try and do a lot of different things, from

                         integration with the GNOME desktop, Calc and

                         UNO work, and porting to architectures such

                         as aarch64 and ppc64le, but I can highlight

                         some of the efforts we make in detecting

                         flaws close to when they get introduced into

                         LibreOffice.

                         We maintain the regular crashtesting

                         infrastructure, where we import and export

                         120,000+ documents and typically fix, or

                         identify the triggering commit, any new

                         import/export failures as they are

                         discovered.

                  # ⚓ Improving_LibreOffice’s_network_file_access⠀⇛

                         Thanks to a tender by The Document

                         Foundation, we have been able to implement a

                         new and much improved curl-based HTTP/WebDAV

                         UCP for LibreOffice 7.3.

                         This is the technology that sits under almost

                         every public network file access LibreOffice

                         can do, like loading and saving from a

                         NextCloud instance, or working on a file

                         sitting on a SharePoint server.

                         Please read on for how we implemented that.

* § Leftovers⠀➾

      o ⚓ What_are_sparse_files_and_how_to_tell_if_a_file_is_stored

        sparsely⠀⇛

             Sparse files are files stored in a file system where

             consecutive data blocks consisting of all zero-bytes

             (null-bytes) are compressed to nothing. There is often no

             reason to store lots of empty data, so the file system

             just records how long the sequence of empty data is

             instead of writing it out on the storage media. This

             optimization can save significant amounts of storage

             space for other purposes.

             On most file systems, programs don’t need to do anything

             special to take advantage of sparse files when it’s

             supported by the file system. It all depends on how

             individual programs use the lower-level operating system

             application programming interfaces (API) to save the data

             to a storage medium. Some programs might write out

             consecutive blocks of null-bytes to the disk. These

             programs are non-sparse-aware.

      o § Internet Policy/Net Neutrality⠀➾

            # ⚓ School_exams_and_morning_TV_shows_behind_the_latest_raft_of

              internet_shutdowns_–_Coda_Story⠀⇛

                   Cutting off the internet has become a go-to

                   strategy for governments eager to disrupt

                   expressions of dissent. Entire regions and even

                   countries have gone offline, ripped clean from the

                   internet from one day to another. This happened

                   during a coup a year ago in Myanmar, large-scale

                   opposition protests in India, or elections in

                   Uganda, Democratic Republic of the Congo and Chad.

                   [...]

                   1) In January, Kazakhstan made headlines because of

                   its mass anti-government protests and the total

                   internet blackout that followed. The Kazakh

                   government has been in the habit of throttling the

                   internet for a while though. For example, on May 9,

                   2019, the presidential election day, authorities

                   cut off internet access coinciding with detentions

                   of activists and journalists participating in the

                   demonstrations at the time. In 2012, Kazakhstan’s

                   parliament amended a national security law allowing

                   the government to shut down internet and mobile

                   connections during riots or anti-terrorist

                   operations.

      o § Monopolies⠀➾

            # § Patents⠀➾

                  # ⚓ The_boundaries_of_causing_loss_by_unlawful_means:

                    Secretary_of_State_for_Health_v_Servier [Ed: EPO

                    patents versus human lives or public health]⠀⇛

                         Servier obtained a UK patent for a drug

                         “perindopril”, upheld by the European Patent

                         Office (“EPO”). It defended the validity of

                         the UK patent in English court proceedings,

                         obtaining an interim injunction preventing

                         the sale of generic perindopril.

                         Subsequently, the patent was held invalid on

                         the basis it lacked novelty (with the

                         decision upheld on appeal). In 2009, the EPO

                         revoked the patent.

                         The NHS claimed that in obtaining, defending

                         and enforcing its patent, Servier had

                         deliberately deceived (the unlawful means)

                         the EPO and/or the English courts (the third

                         parties) with the intention of profiting at

                         the expense of the NHS. Further, but for this

                         deceit, the NHS claimed other manufacturers

                         of generic perindopril would have entered the

                         market sooner and driven down the price the

                         NHS had to pay.

                         Servier applied to strike out the NHS’s

                         claim. For the purposes of the application,

                         the allegations were assumed to be true

                         (notwithstanding that Servier disputed the

                         basis of the claim).

                         The claim was struck out at first instance on

                         the basis that following OBG Ltd v Allan, the

                         unlawful means must have interfered with a

                         third party’s ability to deal with the

                         claimant. It was common ground that here, it

                         had not (the NHS had not dealt with the EPO

                         or the courts). The decision was upheld by

                         the Court of Appeal and was referred to the

                         Supreme Court to determine whether…

                  # ⚓ Montenegro_Ratifies_EPC,_Amends_Patent_and_Copyright

                    Laws [Ed: Montenegro ratifies something which does not

                    even exist because_it_is_being_violated_routinely

                    without_any_consequences_to_the_violators]⠀⇛

                         On December 29, 2021, Montenegro adopted the

                         Law on Ratification of the Convention on the

                         Grant of European Patents, commonly known as

                         the European Patent Convention (EPC), as well

                         as amendments to the Patent Law and the Law

                         on Copyright and Related Rights.

                ䷩ 𝚕𝚒𝚗𝚎 7921

Gemini_version_available_♊︎

✐ Links_7/2/2022:_OpenMandriva_Lx_4.3_Released_and_Lots_About_Patents⠀✐

Posted in News_Roundup at 6:03 am by Dr. Roy Schestowitz

🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈

§ Contents⠀➾

* GNU/Linux

      o Distributions

      o Devices/Embedded

* Free_Software/Open_Source

* Leftovers

* § GNU/Linux⠀➾

      o ⚓ 9to5Linux_Weekly_Roundup:_February_6th,_2022⠀⇛

             This week has been generous in Linux week as we got lots

             of cool stuff, starting with the launch of the

             LibreOffice 7.3 office suite, the end of life of the

             Linux 4.4 LTS kernel series, Education editions of Zorin

             OS 16, 64-bit edition of the official Raspberry Pi OS,

             major Slackware and Peppermint OS releases, and a new

             Linux laptop from System76.

             We also got new releases of the Linux Lite, Trisquel GNU/

             Linux, and Escuelas Linux distributions, as well as new

             updates to the KDE Falkon, NVIDIA graphics driver, KDE

             Gear, Raspberry Pi Imager, Inkscape, and GStreamer

             software.

      o § Audiocasts/Shows⠀➾

            # ⚓ Much_Ado_About_Ubuntu_|_LINUX_Unplugged_444⠀⇛

                   There’s just something off about Ubuntu these days,

                   this week we put it all together.

            # ⚓ Josh_Bressers:_Episode_309_–_The_bright_future_of_open

              source_secuirty⠀⇛

                   Josh and Kurt talk about NPM requiring 2FA for the

                   top 100 packages. We discuss the new Alpha and

                   Omega projects from the OpenSSF and what it could

                   mean for the future of open source security. Then

                   we end on a note about the new Samba critical

                   vulnerability.

      o § Kernel Space⠀➾

            # ⚓ Kernel_prepatch_5.17-rc3⠀⇛

                   The 5.17-rc3 kernel prepatch is out for testing.

                   Linus says: “Things look fairly normal so far, with

                   a pretty average number of commits for an rc3

                   release”.

            # § Graphics Stack⠀➾

                  # ⚓ NVIDIA_Adds_GeForce_RTX_2050,_MX570_&_MX550_Laptop

                    GPU_Support_To_Linux_Through_Latest_Drivers⠀⇛

                         Last December, NVIDIA launched three new

                         mobility GPUs, the RTX 2050, MX550, and

                         MX570. While the MX550 is a Turing variant

                         for NVIDIA, the RTX 2050 and MX570 utilize

                         identical GA107 cores, similar to the RTX

                         3050. Laptop manufacturers will use these new

                         chips in their notebooks during this first

                         quarter of 2022.

                         [...]

                         A new Linux driver (470.103.01) for the RTX

                         2050, MX570, and MX550 is available, offering

                         more compatibility and capability in the

                         open-source operating system.

      o § Instructionals/Technical⠀➾

            # ⚓ How_To_Install_Gnome_Tweak_on_Ubuntu_20.04_LTS_–_idroot⠀⇛

                   In this tutorial, we will show you how to install

                   Gnome Tweak on Ubuntu 20.04 LTS. For those of you

                   who didn’t know, The Gnome Tweak Tool is a utility

                   used to customize the overall look and behavior of

                   elements on the Gnome Desktop Environment. Some of

                   the things you can do with GNOME Tweaks are edit

                   font colors and scaling, disable animations for

                   desktop speed improvement, change themes, manage

                   GNOME extensions, bar changes, and much more.

                   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 through the step-by-

                   step installation of the Gnome Tweak on Ubuntu

                   20.04 (Focal Fossa). You can follow the same

                   instructions for Ubuntu 18.04, 16.04, and any other

                   Debian-based distribution like Linux Mint.

            # ⚓ Centralized_log_management_by_installing_rsyslog_on_Debian

              11!⠀⇛

                   Hello, friends. In this post, we will talk a little

                   about rsyslog on Debian 11. Besides that, we will

                   show you how to install it and set it up, so you

                   can work from the clients. Let’s get started.

            # ⚓ Introduction_to_Powerline_the_statusline_plugin_for_VIM⠀⇛

                   Vim is one of most used and famous text editors on

                   Linux and other Unix-based operating systems. It is

                   free and open source software, based on the

                   original Vi editor (Vim stands for Vi IMproved) and

                   mainly developed by Bram Moolenaar. The editor can

                   be setup by editing the ~/.vimrc configuration

                   file, and by using a vast range of plugins. In this

                   article we see how to improve and customize the Vim

                   status bar by installing Powerline, a nice plugin

                   written in Python which can be also used to

                   customize the Bash and Zsh shell prompts.

            # ⚓ Ubuntu_mirrors⠀⇛

                   People all over the world use Ubuntu Linux. In

                   order to accommodate users from different regions

                   of the world that wish to install updates or new

                   software from Ubuntu’s official repositories,

                   Canonical has “mirrors” all over the world.

                   For example, if all the software is hosted on

                   servers in North America, that will provide a fast

                   connection for some users, but users in Asia will

                   have much higher latency to the servers and their

                   downloads will take longer. Therefore it is

                   necessary to have the content hosted on multiple

                   servers in multiple regions.

                   On your Ubuntu system, your Ubuntu mirror should be

                   selected automatically, but it is possible to

                   change it manually. This can be useful if you

                   notice that your system is connecting to a location

                   that is far away, or your downloads are taking a

                   long time. Let’s dive into the tutorial and see how

                   this is configured via command line and GUI.

            # ⚓ How_To_Move_and_Rename_Files_in_Linux⠀⇛

                   Moving and renaming files in the Linux terminal is

                   quick and painless, but first you need to

                   understand how to do it. Whether you are sat at the

                   machine, or remotely connected via SSH, these are

                   the commands that will move files around your

                   machine.

                   In this how-to we’ll learn the basics of mv, an

                   command that moves, and renames files. We will also

                   learn a few advanced arguments for this command,

                   arguments which will enhance its use and make our

                   lives easier.

            # ⚓ How_To_Create_A_Bash_Script,_With_Example_Code_•_Python

              Land_Tutorial⠀⇛

                   With bash scripts, you can run sequences of

                   commands. They prevent you from repeating yourself

                   and allow you to store long and tedious to type

                   commands for later usage. In this article, you’ll

                   learn how to create a Bash script. You’ll also

                   learn how to read arguments, use variables, and

                   create for-loops to repeat actions.

                   Before you start creating scripts, make sure you

                   are familiar with the basic Linux commands.

      o § Desktop Environments/WMs⠀➾

            # ⚓ JWM_documentation_now_builtin⠀⇛

                   I have started work on a radical change to the

                   desktop user interface.

                   ROX-Filer is more than just a file manager, in Easy

                   it is also used to manage the icons on the desktop

                   and the wallpaper. I am interested in taking that

                   responsibility away from ROX, and reduce it to just

                   being a file manager.

                   The experiment is that the desktop icons will now

                   be in the JWM (Joe’s Window Manager) systray.

                   Hopefully, without the systray becoming too

                   crowded.

      o § Distributions⠀➾

            # § Reviews⠀➾

                  # ⚓ Review:_PlagueOS_R3_and_Ultramarine_Linux_35⠀⇛

                         This week I decided to dive into the

                         DistroWatch waiting list and try out two

                         projects selected at random. The first

                         project my mouse pointer jumped to was

                         something called PlagueOS. According to the

                         project’s website, PlagueOS “Is designed to

                         run as a hypervisor and launch guest virtual

                         machines (VMs). The OS is designed to be a

                         minimal build and have a restricted

                         userspace. The guests are launched from virt-

                         manager.”

                         The PlagueOS documentation lists a number of

                         security features the project provides. These

                         include kernel hardening, driver

                         blacklisting, hiding process IDs, locking the

                         root account, using doas in place of sudo,

                         randomized MAC addresses, more restrictive

                         file permissions, and encrypted DNS. While

                         other open source projects may provide many

                         of these security options, most do not enable

                         them out of the box.

                         The ISO download for PlagueOS R3 is 959MB.

                         This download can be verified using both a

                         SHA512 checksum and a signature. The steps

                         for fetching the verification key and

                         checking the ISO file are laid out in detail

                         and it’s nice to see this attention paid to

                         security.

                         I tested PlagueOS in a VirtualBox instance

                         and on my laptop. In Legacy BIOS mode the

                         operating system failed to boot with an error

                         which read: “Failed to load ldlinux.c32″.

                         When trying to start in UEFI mode the system

                         began by displaying a GRUB prompt and was

                         unable to continue.

                         It’s difficult to argue against the security

                         of an operating system which fails to boot on

                         my test systems. However, it’s also difficult

                         to accomplish anything with it, so I moved on

                         to another project.

            # § PCLinuxOS/Mageia/Mandriva/OpenMandriva Family⠀➾

                  # ⚓ OpenMandriva_Lx_4.3_released_–_OpenMandriva⠀⇛

                         OpenMandriva Lx is a unique and independent

                         linux distribution, a direct descendant of

                         Mandriva Linux and the first Linux

                         distribution utilise the LLVM compiler. This

                         release keeps using the entire LLVM toolchain

                         which completes the work that began in 2015.

                         We hope that you find that this link time

                         optimised desktop and its supporting

                         applications to be bright and responsive in

                         use. You can find out more about link time

                         optimisation here: https://llvm.org/docs/

                         LinkTimeOptimization.html

                         The OpenMandriva Lx 4.3 operating system

                         distribution is FREE and provides the user

                         with all the software funtionality that is

                         available on a proprietary system and then

                         some. All this is supported by the world

                         class KDE Plasma Desktop, a desktop user

                         interface that provides comprehensive access

                         to all the installed software toools. The

                         Plasma desktop offers advanced feature such

                         as multiple task based desktops, and a

                         collection of desktop widgets that support a

                         wide range of information gathering and

                         display.

                         We provide an OpenMandriva utility Desktop

                         Presets (om-feeling-like) which offers a

                         quick way to customize the appearance of your

                         OpenMandriva Plasma desktop to look and feel

                         similar to other systems you may be used to.

                         We hope that this will help those who are new

                         to OpenMandriva to feel at home with our

                         desktop.

                         We also provide an improved ‘OM-Welcome’

                         utility which guides you through initial

                         setup and suggests some useful additional

                         applications that you may wish to install

                         other than those distributed of the iso.

                         A third utility Software Repository Selector

                         (om-repo-picker), to enable additional

                         repositories with thousands of additional

                         Free Software packages, updated and greatly

                         improved.

                  # ⚓ OpenMandriva_Lx_4.3_Released_with_Linux_Kernel_5.16,

                    PipeWire_by_Default,_and_More⠀⇛

                         Almost a year in the works, OpenMandriva Lx

                         4.3 is powered by a Clang-compiled Linux 5.16

                         kernel to provide users with top-notch

                         hardware support, and ships with the PipeWire

                         low-level multimedia framework as default

                         sound server and a replacement for

                         PulseAudio.

                         OpenMandriva Lx 4.3 features the latest (at

                         the moment of writing) KDE Plasma 5.23

                         desktop environment, namely Plasma 5.23.5,

                         which is accompanied by the KDE Frameworks

                         5.90 and KDE Gear 21.12.2 software suites,

                         all compiled against Qt 5.15.3 with all

                         patches proposed by the KDE Project.

* § Leftovers⠀➾

      o ⚓ Making_Something_Gorgeous_From_Framing_Lumber_|_Hackaday⠀⇛

             Here at Hackaday, we typically cover things that blink,

             bleep, and occasionally they might even bloop. However,

             the name of the site is Hackaday. We’re about being

             clever, reusing things in new ways, and most importantly

             celebrating interesting projects. While not a traditional

             project that would grace the front page, we would argue

             that this nightstand made from framing lumber clearly

             belongs.

      o § Hardware⠀➾

            # ⚓ The_next_microchip_crisis_will_be_bigger⠀⇛

                   What’s happening: Right now, no U.S. company can

                   manufacture the most advanced leading edge chips

                   used in smartphones, laptops, servers,

                   supercomputers, gaming consoles and other products.

                   Instead, most of the supply for those chips are

                   made by Taiwan Semiconductor Manufacturing Company

                   (TSMC), and is concentrated in Asian countries.

      o § Health/Nutrition/Agriculture⠀➾

            # ⚓ U.S._considers_lengthening_gap_between_first_2_COVID_shots

              to_8_weeks⠀⇛

            # ⚓ European_Commission_calls_for_evidence_on_anti-counterfeit

              toolbox_initiative [Ed: Disguising protection of monopolies

              as a matter of "public health" or "safety" is not a new

              trick/lie]⠀⇛

                   In the 2020 Commission IP Action Plan, the European

                   Commission (‘EC’) announced that it would establish

                   an EU Toolbox against counterfeiting. The EU

                   Toolbox is part of the EU Strategy to tackle

                   Organised Crime 2021-2025. The EC reports that

                   despite efforts to battle counterfeit goods, the

                   market is still thriving, with an increase of

                   detained articles at EU borders. In 2019, the

                   imports of counterfeit goods equaled 5.8 % of total

                   EU imports, with a value of EUR 119 billion. The EC

                   furthermore notes a surge in counterfeit COVID-19

                   related goods such as face masks, protective

                   equipment and even vaccines.

                   [...]

                   Furthermore, the EC hopes that the toolbox will

                   stimulate the use of new technologies to battle

                   counterfeiting, such as data mining, AI powered

                   image recognition and blockchain based solutions.

            # ⚓ [Older]_US_legislators_call_for_screws_to_be_tightened_on

              pharma_patent_strategies [Ed: When patents needlessly kill

              people for profit]⠀⇛

                   New report issued by Democrats in the House of

                   Representatives indicates a change of tack in

                   approaching potential reforms may be on the cards

      o § Integrity/Availability⠀➾

            # § Proprietary⠀➾

                  # ⚓ [Crackers]_hit_Fortune_500_service_provider,_data_of

                    over_500k_people_leaked⠀⇛

                         The incident began on August 1, 2021, when

                         Morley’s data became unavailable.

                         Michigan-based Morley thereafter began

                         collecting contact information needed to

                         provide notice to potentially affected

                         521,046 individuals, which was completed in

                         early 2022, the company said last week.

                  # ⚓ European_Oil_And_Port_Facilities_Suffer_Cyberattacks

                    [iophk: Windows TCO]⠀⇛

                         Oiltanking GmbH and Mabanaft GmbH, an oil

                         supplier, were impacted, both of whom are

                         subsidiaries of the Marquard & Bahls group.

                         Oiltanking GmbH supplies the 1,995 Shell gas

                         stations in Germany, but local officials have

                         stressed there are no fuel shortages.

                  # ⚓ Oil_terminals_disrupted_after_European_ports_hit_by

                    cyberattack_Access_to_the_comments [iophk: Windows

                    TCO]⠀⇛

                         Port facilities in Belgium, Germany, and the

                         Netherlands have been targeted by a large-

                         scale cyberattack, authorities say.

                         Officials say the hack began several days ago

                         and has primarily disrupted operations at oil

                         terminals, preventing tankers from delivering

                         energy supplies.

                  # § Security⠀➾

                        # ⚓ More_than_1,000_malware_packages_found_in_NPM

                          repository [Ed: Microsoft (NPM) serves malware,

                          and not just to Windows]⠀⇛

                        # § Privacy/Surveillance⠀➾

                              # ⚓ ‘No_ordinary_IT_department’_–_spy

                                agencies_seek_tech_strategy_chief⠀⇛

                                     The post as director of strategy,

                                     portfolio and partnerships sits

                                     within a shared IT organisation

                                     that was established within GCHQ

                                     in 2019 to serve not only the

                                     cyber and signals intelligence

                                     outfit, but also the UK’s two

                                     other intelligence and security

                                     agencies: MI5 and MI6. The tech

                                     unit also offers support to “many

                                     other government departments

                                     where there is a requirement for

                                     operating at Top Secret”.

                              # ⚓ Meta_threatens_to_pull_Facebook_and

                                Instagram_from_Europe_if_it_can’t_target

                                ads⠀⇛

                                     Meta states in an SEC filing it

                                     is considering leaving Europe if

                                     it can no longer exchange data

                                     from European users with the

                                     United States, following the

                                     Schrems II decision.

                              # ⚓ Google_is_turning_search_history_tracking

                                on_for_all_Google_Workspace_customers⠀⇛

                              # ⚓ Facebook_stock_plummets:_What_it_means

                                for_antitrust⠀⇛

                              # ⚓ Microsoft_Edge_may_be_running_on_your

                                Windows_PCs,_even_if_you_don’t_use_the

                                browser⠀⇛

                              # ⚓ NSO_Group_Reportedly_Offered_‘Bags_of

                                Cash’_for_Access_to_U.S._Networks⠀⇛

      o § Defence/Aggression⠀➾

            # ⚓ Wisconsin_Is_Ground_Zero_for_the_MAGA_Effort_to_Steal_the

              Next_Election⠀⇛

                   Nowhere is this crusade to subvert the 2020

                   election result more on display than in Wisconsin.

                   Even though Republicans there do not control all

                   the levers of power — the governor, Tony Evers, is

                   a Democrat — they have launched a multifront effort

                   to cast doubt on the 2020 election, intimidate

                   local officials, and, in Ramthun’s case, throw out

                   the state’s presidential-election result.

                   Lawyers aligned with the Republican Party have

                   filed suit after suit seeking to roll back reforms

                   that made it easier to vote in the pandemic. A

                   secretive investigation run by a conservative

                   former judge with a controversial past has issued

                   dozens of expansive subpoenas, demanded closed-door

                   testimony of mayors and clerks, and sought jail

                   time for those who didn’t cooperate. GOP candidates

                   and elected officials have gone so far as to demand

                   the elimination of the state’s bipartisan election

                   commission — a body that Republicans created seven

                   years ago — and potentially give the GOP-led

                   Legislature the power to control elections.

                   “Wisconsin is the ground zero for the fights over

                   elections right now,” says Paul Nolette, a

                   political-science professor at Marquette

                   University.

            # ⚓ Man_Who_Attempted_to_Provide_Material_Support_to_ISIS

              Sentenced_to_16_Years_in_Federal_Prison⠀⇛

                   In 2019, law enforcement officers learned that

                   Guerra Blanco was following widely distributed

                   instructions from ISIS directing adherents to — on

                   their own — publish ISIS propaganda, fundraising

                   requests, recruitment material, justification for

                   attacks on the United States, and all manner of

                   material helpful to ISIS. Guerra Blanco attempted

                   to provide material support to ISIS by translating

                   the group’s materials into Spanish for his target

                   audience. In addition, Guerra Blanco produced

                   videos that he intended to use to recruit Spanish

                   speakers to ISIS’s cause, as well as to terrorize

                   regular citizens of Spain. Many of the videos that

                   Guerra Blanco produced and distributed from his two

                   ISIS media networks glorified the terrorist group’s

                   violence and called for attacks on Spanish

                   authorities.

            # ⚓ Christian_apologist_beaten_unconscious_in_Kampala,_Uganda⠀⇛

                   A resident of a town east of Kampala undisclosed

                   for security reasons, Kamya on January 24 had

                   debated Muslims in Jinja after going to the mosque

                   there to buy a Quran on January 21, accompanied by

                   a Muslim convert to Christianity, he said. He used

                   the Koran in the January 24 debate, he said.

            # ⚓ Who_Is_the_ISIS_Leader_Killed_in_the_U.S._Raid?_Here’s_What

              to_Know⠀⇛

                   Al-Qurayshi’s death may disrupt the group’s

                   momentum in the short term, but is unlikely to hurt

                   its operations in the long term.

                   “It’s an organization not focused on charismatic

                   leadership, but ideas, which is why its leaders

                   have been pretty low-profile,” Aaron Y. Zelin, a

                   senior fellow at the Washington Institute for Near

                   East Policy, said. “I think the IS machine will

                   continue with whoever the new leader is.”

                   Al-Qurayshi’s real name was Amir Mohammed Saeed

                   Abdul-Rahman al-Mawla. He was an Iraqi in his mid-

                   40s, born in 1976 and believed to be an ethnic

                   Turkman from the northern Iraqi town of Tel Afar.

                   He held a degree in Islamic law from the University

                   of Mosul.

            # ⚓ How_US-born_Allison_Fluke-Ekren_went_from_science_teacher

              to_ISIS_radical⠀⇛

                   As a high-ranking member of ISIS, who trained in

                   Egypt, Libya and Iraq before heading to Syria in

                   2012, Allison Fluke-Ekren planned to detonate

                   explosives at an unidentified US college campus and

                   “fantasized” about bombing a shopping mall,

                   according to court records.

            # ⚓ The_Washington_Post’s_Public_Relations_For_CAIR⠀⇛

                   The Council on American-Islamic Relations (CAIR),

                   which calls itself a “civil rights organization,”

                   though it is much more, in a sinister vein, than

                   that, has been the beneficiary of journalistic

                   malpractice. A recent example of this, at the

                   Washington Post, is reported on here: “The

                   Washington Post Gives CAIR a Boost,” by Sean Durns,

                   Algemeiner, January 24, 2022: [...]

      o § Environment⠀➾

            # ⚓ Opinion_|_It’s_Time_to_Overhaul_the_Chemical_Industry⠀⇛

                   Climate change is quickly evolving into climate

                   catastrophe, and there’s a narrow window of time to

                   do something about it. While the world works on

                   solutions, there’s surprisingly little focus on the

                   chemical industry, which accounts for roughly 7% of

                   global greenhouse gas emissions — as well as other

                   environmental harms.

            # § Energy⠀➾

                  # ⚓ Finland_unveils_plan_for_electric_aircraft_routes

                    across_Lapland_region⠀⇛

                         An experimental project operating out of

                         Enontekiö Airport in the northwest corner of

                         Finland is set to test the viability of using

                         electric airplanes to fly routes across the

                         wider Lapland region.

                  # ⚓ New_Study:_Gas_and_Oil_Drilling_Doesn’t_Create_Very

                    Many_Jobs⠀⇛

                         According to a new analysis by the corporate

                         watchdog Food and Water Watch, the actual

                         number of people directly employed by the

                         fossil fuel industry is only about half a

                         million. Moreover, the Food and Water Watch

                         report shows that the fossil fuel industry

                         has been shedding jobs for years, even with

                         oil and gas output at record levels.

                  # ⚓ Botswana_passes_[cryptocurrency]_bill,_unlike_Zim

                    they_want_to_stop_the_scams⠀⇛

                         Botswana’s push for a [cryptocurrency] bill

                         comes after it was removed from the Financial

                         Action Task Force’s (FAFT) list for countries

                         that need more monitoring in relation to

                         money laundering and terrorist financing. A

                         little sidenote, Zimbabwe is, as I am sure

                         you have already guessed, on the list with

                         the organisation stating that: [...]

                  # ⚓ El_Salvador_Has_Ambitious_Plans_for_Cryptocurrency⠀⇛

                         “It’s not like an entire nation has been

                         Bitcoin-ized and in two years everyone will

                         be using Bitcoin,” says cryptocurrency expert

                         Jeff Gallas, the founder of fulmo, a Berlin,

                         Germany-based Bitcoin Lightning network

                         startup. Still, he considers it to be a

                         successful start, “considering how little

                         time there was.” He says the government now

                         needs to show that it can deliver on all its

                         promises and fix the bugs in Chivo.

                         Security flaws in the software allowed scam

                         artists to collect the credit balances of

                         hundreds of citizens. Sometimes, money

                         transfers haven’t worked, either.

                  # ⚓ [Cryptocurrency]_Has_a_Climate_Problem⠀⇛

                         Bitcoin—the world’s oldest and most popular

                         form of cryptocurrency, with a total market

                         value that topped $1.3 trillion—now eats up

                         half a percentage point of all the

                         electricity consumed in the world. That puts

                         it on par with the usage of the entire

                         country of Sweden. In fact, Google could

                         power all of its global operations on that

                         amount of energy, seven times over. In

                         comparison with more traditional online

                         banking, a single bitcoin has the same carbon

                         footprint as 330,000 credit card

                         transactions.

            # § Wildlife/Nature⠀➾

                  # ⚓ Shipping_industry_needs_to_do_more_to_lessen

                    underwater_noise_in_Arctic,_say_NGOs⠀⇛

                         “The workplan put in place at SDC 8 must be

                         ambitious in scope and reflect the urgency

                         needed to address underwater noise from ships

                         as it continues to increase at alarming

                         rates”, Bobbe said.

                         “Advancements in new technologies such as

                         quieter propellers have already been

                         developed and can be installed on new ships

                         and retrofitted on existing ships when in

                         drydock for repairs. There are also very

                         simple ways to reduce noise, like slowing

                         ships down. This will bring co-benefits of

                         reduced fuel use and emissions.”

      o § Finance⠀➾

            # ⚓ Opinion_|_Labor_Win_in_Mexico_Augurs_Greater_Equality_for

              Workers_on_Both_Sides_of_the_Border⠀⇛

                   The U.S. labor movement, after a depressing

                   January, needed some encouraging news. That

                   encouraging news has just come — from Mexico.

            # ⚓ Flood_Insurance_Premiums_in_Louisiana_Are_Rising._Help_Us

              Investigate.⠀⇛

                   Sweeping changes are coming to the National Flood

                   Insurance Program, which will result in premium

                   increases for many Louisiana policyholders starting

                   April 1, 2022.

                   ProPublica and The Times-Picayune | The Advocate

                   could use your help in understanding how these

                   changes affect homeowners, other property owners

                   and the real estate market in Louisiana. If you’ve

                   explored purchasing flood insurance in Louisiana in

                   recent months, if you plan to, or if you are in the

                   real estate, mortgage or insurance fields, we may

                   have some questions as our reporting continues. If

                   you’re willing to help, please sign up here by

                   answering a few questions below.

            # ⚓ Credit_Monitoring_services_are_mostly_a_scam.⠀⇛

                   Have you seen an offer from your bank, credit card

                   company, or Lifelock about credit monitoring?

                   Are you thinking about buying it?

                   Well, the good news is you can ignore their pushy

                   sales tactics, and decline it when dark pattern

                   dialog boxes pop up, and prevent fraud yourself.

                   A while back, I was talking about using strong

                   randomly generated passwords and an authenticator

                   program, such as Google Authenticator and GNOME

                   Authenticator to manage one time codes.

                   It’s unlikely that anyone will sign into your

                   accounts and rip you off if you do that, but there

                   are still other ways to bilk you, like credit

                   fraud.

                   The truth is, the credit reporting bureaus are

                   required by federal and state laws to allow you to

                   manage fraud alerts and credit file freezes on your

                   own, but they don’t want you to know that because

                   they were hoping you’d buy it from them.

      o § AstroTurf/Lobbying/Politics⠀➾

            # ⚓ Trump’s_Political_Depravity_Sank_to_a_New_Level_This_Past

              Week⠀⇛

            # ⚓ Joe_Manchin_Gives_New_Reason_for_Why_He_Torpedoed_BBB⠀⇛

                   As progressive activists continue to push for the

                   stalled social and climate spending package, Sen.

                   Joe Manchin claimed Sunday that his biggest

                   opposition to his party’s Build Back Better

                   legislation was that it didn’t go through

                   committee.

                   Manchin’s (D-W.Va.) remark came in an interview

                   with CNN’s “State of the Union” in which he

                   endorsed Republican Sen. Lisa Murkowski and brushed

                   off the idea that he wouldn’t get the backing of

                   Senate Majority Leader Chuck Schumer (D-N.Y.) if he

                   faced a primary challenge.

            # ⚓ Manchin’s_Likely_Backing_of_Biden_SCOTUS_Pick_Reflects

              Court’s_Conservative_Role⠀⇛

            # ⚓ Claims_Over_Broken_Promises_About_NATO_Simmer_at_the_Heart

              of_the_Ukraine_Crisis⠀⇛

            # ⚓ Opinion_|_19_Facts_About_the_Poverty-Busting_Expanded_Child

              Tax_Credit⠀⇛

                   Date when the expanded child tax credit, which

                   Congress approved last year as part of the American

                   Rescue Plan pandemic stimulus, expired because the

                   closely divided U.S. Senate failed to renew it as

                   part of the Build Back Better Act: 12/31/2021

            # ⚓ The_Movement_Grows:_Jayapal_Heralds_Record_120_Medicare_for

              All_Co-Sponsors⠀⇛

                   Rep. Pramila Jayapal on Sunday welcomed a new

                   record number of co-sponsors—120—for her Medicare

                   for All legislation.

                   The latest support came from Rep. Sheila Cherfilus-

                   McCormick (D-Fla.), who was sworn in just two weeks

                   ago.

            # ⚓ Metamorphosis:_Facebook_and_big-tech_competition⠀⇛

                   Since listing in 2012 Meta has exemplified big

                   tech’s prowess and pitfalls. For a glimpse of the

                   caricature, consider the American government’s

                   antitrust case against it first launched in 2020.

                   It describes an invincible company in a world where

                   technology is perpetually frozen in the 2010s:

                   “this unmatched position has provided Facebook with

                   staggering profits,” America’s Federal Trade

                   Commission wrote in its lawsuit.

            # ⚓ Navalny_ally_in_Murmansk_flees_Russia_as_aides_face

              ‘terrorist’_labels⠀⇛

                   Another activist linked to jailed Kremlin critic

                   Alexei Navalny has fled Russia, Reuters reported

                   Thursday as the authorities’ year-long campaign to

                   dismantle his network and label its leading figures

                   “terrorists” showed little sign of slowing.

                   Violetta Grudina, 32, was blocked from running for

                   local office in the Arctic port city of Murmansk

                   last year after being forcibly hospitalized despite

                   testing negative for coronavirus. Grudina has said

                   she faced an intimidation campaign that included

                   several years of hefty fines and unknown people

                   shooting at her office.

            # ⚓ 20_Million_Dollar_Saudi_Festival_Organized_by_Vice_Media⠀⇛

                   Vice’s name was not used in any public marketing

                   materials as the company’s name was kept out as

                   much as possible. Both sides seem to be a good

                   match, as Saudi Arabia is desperately attempting to

                   whitewash its human rights abuses with

                   entertainment and Vice is dealing with allegations

                   of sexual harassment.

            # ⚓ In_the_Netherlands,_it’s_‘Civilized’_to_Empower

              Terrorists⠀⇛

                   Not until January 18 of this year did Sahla’s past

                   become a problem. On that day, during a discussion

                   in the Tweede Kamer, the lower house of the Dutch

                   parliament, Wilders, who since 2006 has been head

                   of the PVV (Freedom Party) and who since 2004 has

                   had to live with round-the-clock security owing to

                   jihadist death threats, raised the subject of

                   Sahla, saying that someone who’d been issued a gun

                   with which to kill him and Ayaan Hirsi Ali had no

                   business in a leading position in the country’s

                   ruling party. Wilders also mentioned Sahla’s sister

                   Fonda, who, as it happens, is a politician for the

                   centrist D66 and a colleague of Wilders’s in the

                   Tweede Kamer, where she routinely wears a hijab.

            # ⚓ Ankara_demanded_the_impossible_from_the_US_for_my_release,

              pastor_Brunson_says⠀⇛

                   Andrew Brunson, an American pastor who was jailed

                   for two years in Turkey before his release in 2018,

                   has said in a recent interview that Turkey’s

                   demands from the US in exchange for his release

                   were beyond what Washington could do, with the

                   Turkish government using him as a bargaining chip

                   to get its way on a number of issues.

            # ⚓ Islam:_Wave_of_the_Future?⠀⇛

                   “Islamism is the sole growing, developing, and

                   truly popular populist ideology in the Middle

                   East,” wrote House Taskforce on Terrorism and

                   Unconventional Warfare Director Yossef Bodansky in

                   1999. His book, Bin Laden: The Man Who Declared War

                   on America, documented the enduring appeal in

                   Muslim-majority societies of Islam as a political

                   system as opposed to other ideological

                   alternatives.

      o § Misinformation/Disinformation⠀➾

            # ⚓ Austria:_Left-wing_Turks_attack_a_mosque_and_Muslims_and

              Leftists_blame_it_on_Islamophobes⠀⇛

                   In a statement, the chairman of the Austrian

                   Freedom Party (FPÖ) in the Vienna district of

                   Favoriten, Stefan Berger, considers the radical

                   left-wing and foreign PKK attack on the ATIB mosque

                   to be proven on the basis of the video of the

                   confession. Berger said: [...]

            # ⚓ How_a_Butterfly_Refuge_at_the_Texas_Border_Became_the

              Target_of_Far-Right_Lies⠀⇛

                   When people began showing up at the butterfly

                   center, the nonprofit decided it needed to do more

                   to provide security for staff members and visitors.

                   It would remain closed, he said, until a plan could

                   be developed for how to do so.

            # ⚓ Ilhan_Omar’s_Husband_Accuses_Iranian_Dissident_of

              ‘Islamophobia’⠀⇛

                   It all started last Tuesday, when human rights

                   activist Masih Alinejad took to the Washington

                   Post, of all places, to point out some of the risks

                   involved in Omar’s “Islamophobia” bill. Alinejad,

                   who was recently the target of a kidnapping plot

                   launched by the Islamic Republic of Iran, wrote: “I

                   should make clear: I have nothing against Omar

                   personally. Like her, I have many relatives who are

                   pious Muslims I love and respect.” Alinejad added:

                   “My mother is a devout Muslim who wears hijab all

                   the time. I, on the other hand, challenged clerical

                   rule with my journalism until I was thrown out of

                   Iran. I launched a campaign against compulsory

                   hijab, demanding that Iranian women be given the

                   freedom of choice to decide their own destiny. Will

                   such criticism of compulsory hijab be labeled as

                   Islamophobia?”

      o § Censorship/Free Speech⠀➾

            # ⚓ ‘Message_is_clear,_Turkey_must_release_Osman_Kavala’⠀⇛

                   Amnesty International has released a statement

                   about the infringement proceedings brought against

                   Turkey by the Committee of Ministers of the Council

                   of Europe over rights advocate and businessperson

                   Osman Kavala’s continued detention despite the

                   European Court of Human Rights (ECtHR) judgment of

                   rights violation and immediate release.

            # ⚓ Three_Philippine_media_outlets_face_latest_in_a_string_of

              cyberattacks⠀⇛

                   All three sites have been openly critical of the

                   Duterte regime. The National Union of Journalists

                   of the Philippines released a statement condemning

                   the attacks and called for an investigation.

            # ⚓ UK:_British_citizen_found_guilty_of_conspiring_to_kill

              exiled_Pakistani_blogger⠀⇛

                   RSF representatives monitored the two-week trial

                   both in-person and remotely. The defendant, who had

                   been hired as a “hitman” by a middleman referred to

                   as “MudZ,” who appeared to be based in Pakistan,

                   refuted claims that he had intended to kill Goraya.

                   The defence argued that Khan had only planned to

                   extract money from MudZ while maintaining the

                   appearance that he would carry out the killing.

                   Khan created multiple false identities to give the

                   appearance of a larger team, allowing him to bill

                   £5,000 for operational expenses, which he received

                   in advance. A total fee of £100,000 was agreed for

                   the job, with Khan to receive £80,000 and £20,000

                   to go to MudZ after Goraya was killed. They also

                   discussed the possibility of future jobs contingent

                   on the successful completion of this one.

            # ⚓ Tibetan_monks_sent_to_labor_camps_for_spreading_news_of

              Buddhist_statue’s_destruction⠀⇛

                   Eleven Tibetans beaten and arrested by Chinese

                   authorities in January for spreading news of the

                   destruction of a 99-foot-tall Buddha statue and

                   dozens of prayer wheels in southwestern China’s

                   Sichuan province have been sent to labor camps in

                   the region, Tibetans with knowledge of the

                   situation said Friday.

                   Monks Tashi Dorjee, Tsering Samdup, Nyima Lhamo,

                   and Abbot Pelga, along with Pelga’s assistant

                   Nyima, and six other unidentified Tibetans were

                   arrested following the destruction of the statue

                   and 45 traditional prayer wheels in Drago (Luhuo)

                   county of Kardze (in Chinese, Ganzi) Tibetan

                   Autonomous Prefecture in December 2021, said a

                   Tibetan in exile who declined to be named for

                   safety reasons.

            # ⚓ Original_‘Fight_Club’_Ending_Restored_in_China_After

              Censorship_Backlash⠀⇛

                   But it would appear that the backlash has been

                   deemed more troublesome than the fictional film’s

                   ending, as Tencent has now restored 11 of the 12

                   minutes it originally cut from the 137-minute

                   movie. The minute still missing is mostly comprised

                   of brief nude sex scenes between Pitt’s and Bonham

                   Carter’s characters.

                   A spokesperson at Tencent didn’t respond to a

                   request for comment.

                   Reversals of censorship actions are extremely rare

                   within China’s entertainment industry — but cuts to

                   Hollywood movies are not.

      o § Freedom of Information/Freedom of the Press⠀➾

            # ⚓ Iowa,_Kansas_lawmakers_bar_media_from_Senate_floors,

              stymieing_newsgathering⠀⇛

                   CPJ interviewed Erin Murphy, the Des Moines bureau

                   chief for the Cedar Rapids Gazette and president of

                   the Iowa Capitol Press Association, and Sherman

                   Smith, the editor in chief of the Kansas Reflector,

                   a non-profit news website focused on Kansas

                   politics, about the changes. The interviews have

                   been edited for length and clarity.

            # ⚓ Taliban_forces_detain_2_journalists_in_undisclosed

              location⠀⇛

                   On Monday, men who identified themselves as members

                   of the Taliban arrested Hijab, a reporter, and

                   Hasrat, manager of political programs and a

                   political presenter, both with the independent

                   broadcaster Ariana News TV, at the entrance of

                   outlet’s headquarters in District 3 of Kabul, the

                   capital, according to former Ariana News Director

                   Sharif Hasanyar, who spoke to CPJ in a phone

                   interview, and a statement by the independent press

                   freedom group Free Speech Hub.

                   The Taliban has not disclosed where the journalists

                   are being held or any allegations against them,

                   Hasanyar said. Ahmadullah Wasiq, a Taliban deputy

                   spokesperson in Afghanistan, did not respond to

                   CPJ’s request for comment sent via messaging app.

            # ⚓ Afghan_journalists_increasingly_harassed_by_Taliban

              intelligence_and_new_ministry⠀⇛

                   The Istikhbarat is not just directly involved in

                   arresting journalists. RSF has learned that several

                   media outlets have received threatening phone calls

                   and summonses for questioning from Istikhbarat

                   officials. Javad Sargar, the senior Istikhbarat

                   official in charge of Department 53, which handles

                   the media, recently horrified journalists by

                   “inviting” them to stop covering certain subjects

                   and stop asking certain journalists to participate

                   in TV discussions, “if you don’t want me to rip

                   your tongue out.”

            # ⚓ Convoy_protesters_threatened,_harassed_journalists_at

              Friday’s_demo⠀⇛

                   Yle’s reporter and cameraperson on the scene say

                   they were continually threatened verbally and

                   physically. Some protesters attempted to prevent

                   reporters from moving around freely.

                   Journalists were abused and threatened, and one

                   protester attempted to steal a bag containing the

                   camera operator’s equipment.

            # ⚓ Malian_journalist_who_disappeared_six_years_ago_is_very

              likely_dead,_RSF_says⠀⇛

                   After registering his upcoming marriage at Bamako’s

                   city hall and spending the afternoon with his

                   family, Touré, set off for home on his motorcycle

                   on the night of 29 January 2016. None of his

                   friends and relatives has seen him since then. Six

                   years later, RSF is in a position to affirm not

                   only that he was secretly detained at a clandestine

                   prison run by Mali’s General Directorate for State

                   Security (DGSE) but also that he most likely died

                   as a result of being mistreated and tortured there,

                   according to damning new testimony obtained in

                   recent months.

            # ⚓ French_parliament_votes_against_handing_asylum_to_Wikileaks

              founder_Assange⠀⇛

                   After a long and intense debate, MPs in France’s

                   national assembly (lower house) voted 31 against

                   and 17 in support of a proposed text brought

                   forward by MP Jennifer de Temmerman, from the

                   opposition group known as Libertés et Territoires.

                   According to the document, which is not legally

                   binding, “Assange’s crime is that he told the truth

                   and was engaged in journalism.”

      o § Civil Rights/Policing⠀➾

            # ⚓ Opinion_|_Not_Retreat_But_Resistance_and_Resilience:_When

              Faced_With_Doomsday,_Look_to_Community⠀⇛

                   Sometimes at second hand books stores I find myself

                   with an armful of books, thinking “These will come

                   in handy if … If the internet goes away, if there

                   is no more electricity, if there aren’t grocery

                   stories anymore.” I cling to the books, push the

                   nightmare scenarios out of my head and make for the

                   cashier.

            # ⚓ Uber_Got_a_Sweetheart_Deal_With_One_of_Canada’s_Biggest

              Unions⠀⇛

                   Close inspection of the agreement reveals that the

                   deal is not the victory for workers that it

                   initially appeared to be. It is a victory for Uber

                   and other platform apps. Under the agreement, Uber

                   drivers will not actually become UFCW members; they

                   will simply be able to access some representation

                   in the case of disputes about pay and deactivation.

                   Uber drivers will have no say in electing their

                   representation. This violates the commitment to

                   democracy fundamental to all trade unionism.

            # ⚓ We_must_listen_to_Iranian_feminists_who_protest_forced

              hijab_–_opinion⠀⇛

                   In response, Alinejad launched the #LetUsTalk

                   campaign, which pushes back against the censorship

                   of Middle Eastern women fighting for women’s

                   equality. However, despite the fact that Alinejad

                   showed up to the Women’s March five years ago in

                   solidarity, none of the women there would join her

                   in her fight for freedom of choice. “I found that

                   hardly anyone was willing to support my campaign

                   against compulsory hijab, lest they be accused of

                   promoting Islamophobia,” she wrote in The

                   Washington Post.

      o § Digital Restrictions (DRM)⠀➾

            # ⚓ Spotify_CEO_Daniel_Ek_confirms_removal_of_Joe_Rogan

              episodes_after_n-word_video_resurfaces⠀⇛

                   Spotify CEO Daniel Ek addressed staff in a late

                   night memo addressing Joe Rogan’s use of the n-word

                   and the mysterious removal of 70 podcast episodes

                   earlier this week. The total number of deleted Joe

                   Rogan Experience episodes is now 113, according to

                   the website jremissing.com.

            # ⚓ Spotify_CEO_Apologizes_to_Staff_Over_Joe_Rogan_N-Word

              Controversy⠀⇛

                   According to Ek, Spotify has had conversations

                   “with Joe and his team about some of the content in

                   his show, including his history of using some

                   racially insensitive language. Following these

                   discussions and his own reflections, he chose to

                   remove a number of episodes from Spotify. He also

                   issued his own apology over the weekend.”

            # ⚓ Spotify_CEO_Addresses_Joe_Rogan’s_N-Word_Use,_Doubles_Down

              on_Keeping_Podcaster_on_Platform⠀⇛

                   In a letter sent to staff, obtained by The

                   Hollywood Reporter, Ek acknowledged that Rogan’s

                   comments were “incredibly hurtful” and confirmed

                   that Rogan decided to remove multiple past episodes

                   from Spotify but said he did not believe in

                   removing the podcast from Spotify.

            # ⚓ Disney,_Netflix,_Apple:_is_anyone_winning_the_streaming

              wars?⠀⇛

                   As revenue growth slows, costs swell. Media firms

                   will spend more than $230bn on video content this

                   year, nearly double the figure a decade ago,

                   forecasts Ampere Analysis, a research firm.

                   Netflix’s weak results came despite what it billed

                   as its “strongest content slate ever”, including

                   “Squid Game”, its most popular series, and “Red

                   Notice”, its most successful film. Disney+ is doing

                   far better than the company ever dreamed—but it is

                   costing more, too. Three years ago Disney said it

                   would spend about $2bn on streaming content in

                   2024. Mr Chapek recently said the figure would be

                   more than $9bn.

      o § Monopolies⠀➾

            # ⚓ Microsoft’s_Activision_Blizzard_Acquisition_Won’t_Save_the

              Games_Industry⠀⇛

                   Over the decades, Microsoft’s bid to consolidate

                   more of the games industry for itself has only

                   intensified. On January 18, 2022, Microsoft

                   announced it will be acquiring Activision Blizzard.

                   This deal — struck for a record-setting $68.7

                   billion — will give Microsoft control of some of

                   the most popular gaming franchises in the world:

                   StarCraft, Warcraft, Diablo, Call of Duty, and

                   Candy Crush.

                   This acquisition is good for Microsoft, which will

                   now be the third-largest firm in games behind Sony

                   and Tencent. But it’s bad for game workers at

                   Activision Blizzard, who are fighting for their

                   rights at a company that is synonymous with

                   workplace abuse in the games industry.

            # ⚓ UK:_Tarilian_Laser_Technologies_–_A_Case_Study_In_Due

              Diligence [Ed: HGF Ltd promoting the fiction of “Intellectual

              Property” [sic]; companies that lack actual products cannot

              compensate with supposed exclusivity, but lawyers stand to

              benefit from the myths (selling false dreams)]⠀⇛

                   When deciding whether to invest in a company, an

                   investor will inevitably have to decide the value

                   of the company.

                   Taking a simplified view, a company’s valuation can

                   be considered to be made up of tangible assets

                   (e.g. cash, inventory and fixed assets such as

                   plant/machinery) and intangible assets (e.g.

                   Intellectual Property (IP) and the skills and

                   knowledge of the founders and key staff (Human

                   Capital)). While it can be easier to place a

                   monetary value on tangible assets, there is much

                   more uncertainty regarding the monetary value of

                   intangible assets. However, to decide on the value

                   of a company, a monetary value must nonetheless be

                   placed on these assets, in particular the IP

                   portfolio of the company.

            # ⚓ Swedish_court_applies_C-762/19_CV-Online_Latvia_in_parking

              app_battle⠀⇛

                   Content and service aggregation is big business in

                   2022. Why having seven different newspapers

                   clogging up your mailbox, when you can have that

                   content carefully selected and curated for you

                   according to your interests and taste? Why having

                   seven different apps for ordering takeout if you

                   can aggregate all that sushi into one app? This

                   dynamic is not lost on entrepreneurs and innovators

                   around the world, sensing and opportunity to create

                   value for users and perhaps birthing a unicorn in

                   the process.

                   But digital aggregation often involves the use of

                   different data sets, including the use of data

                   protected as databases, and the makers of databases

                   often want to protect their own investment against

                   aggregators that are perceived as free riders.

                   Since one person’s entrepreneurial aggregator is

                   often another person’s parasitical competitor,

                   balancing these interests is no easy task for

                   national courts.

                   [...]

                   The argument that the aggregator app created an

                   additional layer between the claimant and its

                   customers seems in principle to be applicable to

                   most situations when a database maker battles a

                   content or service aggregator, whether it is a

                   parking app, an online CV database (CV-Online

                   Latvia) or a meta search engine (C-202/12 Innoweb).

                   To this author, it is not clear how a litigant

                   could quantify the adverse effect of this

                   “additional layer” on the database maker’s ability

                   to recoup its investment, and it is therefore not

                   obvious that this circumstance by itself motivates

                   a finding of infringement under the principles set

                   out in CV-Online Latvia. The court’s conclusion

                   that the aggregator app resulted in the claimant

                   selling less additional services to its customers

                   through its parking app on the other hand seems to

                   be a stronger argument in this regard, and one that

                   can in practice more easily be substantiated by

                   evidence. It will be interesting to see whether

                   this balancing of interests between makers of

                   databases and content and service aggregators is

                   confirmed on appeal or by other national courts in

                   future litigation.

            # ⚓ Sunday_Surprises [Ed: These events promote the_lie_of

              “IP”]⠀⇛

                   On February 3, 2022, the European Commission

                   formally closed its investigation under the EU

                   Trade Barriers Regulation (TBR) into Mexican

                   measures against the export of “Tequila” after

                   successfully resolving the matter. The complaint

                   had been filed by Brewers of Europe, which argued

                   that Mexico’s refusal to issue export certificates

                   for “Tequila” was incompatible with WTO rules and

                   caused significant economic harm to an EU company

                   that relies on “Tequila” as an input. In the course

                   of its investigation, the Commission expressed

                   concerns to the Mexican authorities about the WTO

                   compatibility of the measure. The measure was also

                   challenged by the exporter concerned in domestic

                   courts in Mexico. In October 2021, the complainant

                   informed the Commission that the EU company

                   concerned had reached a solution with the Mexican

                   authorities that would allow the removal of the

                   alleged trade barrier. As a result of this

                   development, Brewers of Europe has withdrawn its

                   TBR complaint. Read more about the background and

                   the TBR complaint by the TechieKat here.

            # § Patents⠀➾

                  # ⚓ Guest_Post:_Assessing_Responses_to_the_PTO’s_2021

                    Patent_Eligibility_Study [Ed: "It should be no surprise

                    to readers of Patently-O that many are unhappy with the

                    Supreme Court’s jurisprudence regarding patent

                    eligibility under Section 101 of the Patent Act," it

                    says. Because they're patent litigation profiteers, not

                    scientists. This is lobbying, funded by the litigation

                    fanatics.]⠀⇛

                         It should be no surprise to readers of

                         Patently-O that many are unhappy with the

                         Supreme Court’s jurisprudence regarding

                         patent eligibility under Section 101 of the

                         Patent Act. In response to various calls for

                         “reform” of patent eligibility jurisprudence,

                         on March 5, 2021, Senators Thom Tillis (R-

                         NC), Mazie Hirono (D-HI), Tom Cotton (R-AR),

                         and Christopher Coons (D-DE) requested that

                         the US Patent and Trademark Office (PTO)

                         conduct a study regarding public views on

                         “how the current jurisprudence has adversely

                         impacted investment and innovation in

                         critical technologies like quantum computing,

                         artificial intelligence, precision medicine,

                         diagnostic methods, and pharmaceutical

                         treatments.” The Senators also asked the PTO

                         to evaluate the responses and provide a

                         detailed summary of its findings by March 5,

                         2022. The PTO released its public request for

                         information (RFI) on July 9, 2021. The

                         original deadline for response was September

                         7, 2021, which the PTO extended until October

                         15, 2021. A total of 145 comments were

                         submitted before the deadline. In advance of

                         the official assessment, we have reviewed and

                         tallied these public comments for those who

                         are eager for the results in advance of the

                         official release.

                  # ⚓ Multinationals_and_renewable_energy:_boosting

                    innovation_through_foreign_direct_investments [Ed: In

                    spite of EPO corruption and crimes, LSE uses “European

                    Patent Office” as a source, citing greenwashing_fluff

                    designed_to_distract_from_the_crimes]⠀⇛

                  # ⚓ Sisvel_suing_Ford_Motor_Company_over_two_4G_standard-

                    essential_patents_in_Munich;_Ford’s_answer_to_Delaware

                    complaint_due_tomorrow [Ed: The so-called ‘media’ ain’t

                    talking about it, but Europe already has its share of

                    malicious, aggressive patent trolls like Sisvel [1,

                    2]]⠀⇛

                         The case numbers indicate that both Sisvel v.

                         Ford cases in Munich have been assigned to

                         the new 44th Civil Chamber under Presiding

                         Judge Dr. Anne-Kristin Fricke, who replaced

                         Presiding Judge Dr. Georg Werner yesterday as

                         he moved on to head the court’s equally

                         patent-specialized 21st Civil Chamber.

                         In mid-December, Sisvel’s patent enforcement

                         action against Ford Motor Company in the

                         District of Delaware became known. The

                         parties stipulated to an extension of time

                         until tomorrow (February 3, 2022) for Ford to

                         answer, or otherwise respond to, the

                         complaint.

                         It would have been out of character for

                         Sisvel to enforce SEPs only in the U.S. and

                         not also in Europe, and there, above all, in

                         Germany, where it has already made history

                         with two Sisvel v. Haier cases–case law that

                         will come into play here as well unless they

                         settle.

                         In another case brought by an Avanci

                         licensor–in that case, Japan’s IP Bridge–the

                         Munich court will hold a hearing in three

                         weeks unless the Federal Patent Court of

                         Germany annulled the patent two weeks ago

                         (haven’t been able to find out yet, but will

                         know soon).

                  # ⚓ Neurim_v._Mylan–_the_Illiad_was_shorter [Ed: Peddling

                    this bogus, phony, misleading narrative that "parent

                    patent was attacked on various grounds" is inversion of

                    roles; the patents themselves are the attacks; those

                    who challenge them act in self defence; Frantzeska

                    Papadopoulou is either deeply brainwashed/indoctrinated

                    or dishonest]⠀⇛

                         The Neurim v. Mylan saga, which started two

                         years ago, is still going strong. The latest

                         was a ruling by the High Court on 24 January

                         2022 (2022) EWHC 109 (Pat) (read here).

                         The ups and downs, and the turns this dispute

                         have taken, remind one of a rollercoaster. A

                         year ago, Neurim was successful in the UK

                         trial ([2020] EWHC 3270 (Pat)) when its

                         claims of infringement were accepted by the

                         court and counterclaims on the invalidation

                         of its patent were rejected, only to shortly

                         thereafter see its patent invalidated in the

                         EPO (patent EP 1 441 702). For the sake of

                         precision, the invalidity of the patent was

                         the result of Neurim withdrawing its appeal

                         to the Technical Board of Appeal (TBA), this

                         in order to avoid an unfavorable decision.

                         Some months ago, the court gave Neurim a new

                         chance at obtaining injunctive relief against

                         Mylan by agreeing that Neurim could have a

                         expediated preliminary issue trial ([2021]

                         EWHC 2198 (Pat)). On 24 January 2022, the

                         court then ruled on preliminary issues of the

                         case ((2022) EWHC 109 Pat).

                  # ⚓ Hungary_Amends_Patent_Act [Ed: But the_corruption_at

                    HIPO_will_prevail]⠀⇛

                         Amendments to the Hungarian Patent Act

                         entered into force on January 1, 2022,

                         introducing changes regarding the Bolar

                         exemption and affecting the bifurcation

                         system and the grant of preliminary

                         injunctions.

                  # ⚓ Patenting_AI:_the_nature_of_inventorship_and_the

                    mechanics_of_ownership [Ed: Corrupt and (recently very)

                    disgraced patent litigation firm uses buzzwords like

                    “Hey Hi” to mislead people and push patent law into

                    sheer_fantasy_world]⠀⇛

                         On 21 December 2021, the Boards of Appeal of

                         the European Patent Office (EPO) released its

                         latest decision on the “Dabus” cases relating

                         to identification of artificial intelligence

                         as an inventor of a patentable invention.

                         Adopting a similar approach to that taken by

                         the UK Court of Appeal in September 2021, the

                         EPO decided that “AI cannot be named as

                         inventor on patent applications… under the

                         European Patent Convention (EPC) an inventor

                         designated in a patent application must be a

                         human being”[i].

                  # ⚓ Description_amendments:_Will_the_EPO_change_its

                    examination_practice? [Ed: These_tribunals_are

                    rigged.]⠀⇛

                         In the recent decision T 1989/18 one of the

                         Boards of Appeal of the European Patent

                         Office (EPO) ruled that there is no legal

                         basis for requiring amendment of the

                         description to be in line with the allowed

                         claims.

                         This is in contrast to what is stated in the

                         2021 Guidelines for Examination in the EPO,

                         which are non-legally binding instructions

                         for Examiners working at the EPO as well as

                         parties interacting with the EPO.

                         BACKGROUND

                         For many years it has been common practice

                         for Examiners at the EPO to require

                         applicants to adapt the description to be in

                         line with the amended claims. In particular,

                         the applicant is required to prepare and file

                         an adapted description which is in line with

                         the allowed claims.

                  # ⚓ Progress_and_promise_for_green_plastics [Ed: The

                    greenwashing oxymoron of “green plastics” [oil], citing

                    the corrupt EPO with its_PR_strategy, looking to

                    distract from the EPO’s crimes]⠀⇛

                         In 2021, the European Patent Office (EPO)

                         released a study investigating trends in

                         plastic recycling and alternative plastics

                         technologies. The report draws on the latest

                         patent information available (particularly

                         using patent filing data from 2010 to 2019)

                         as well as the expertise of EPO Examiners to

                         provide an analysis of the ways in which

                         innovators are driving the transition towards

                         a circular economy for plastics. In view of

                         the global importance of the development of

                         green technologies, Appleyard Lees (AL) has

                         also recently produced its inaugural Inside

                         Green Innovation: Progress Report 2021, which

                         investigates patent trends in bioplastics and

                         plastic recycling, as well as other green

                         technologies including renewable energy

                         storage and food production. The AL report

                         reviews the impact of industrial activities

                         on the environment and highlights how

                         development of, and investment in, innovation

                         can be used to tackle these serious problems.

                         Here, we discuss the findings of these two

                         reports.

                  # ⚓ [Older]_PTO_Will_Transition_to_Electronic_Issuance_of

                    Patents_and_Trademarks [Ed: It is going to get a lot

                    easier to lose your patents; digital systems rot a lot

                    faster than paper]⠀⇛

                         The US Patent & Trademark Office (PTO)

                         announced on December 10, 2021, that it

                         intends to transition to electronic issuance

                         of patents and trademarks in 2022. Under the

                         current rule (37 C.F.R § 1.315), the PTO must

                         deliver or mail a patent “upon issuance to

                         the correspondence address of record.” The

                         PTO will soon issue a notice of proposed

                         rulemaking to seek public feedback on

                         revising the rules of practice to issue

                         patents electronically. Under the proposed

                         changes, the PTO would no longer mail patents

                         to the applicant. Instead, the PTO would

                         issue patents electronically via the Patent

                         Center and Patent Application Image

                         Retrieval, from which the patents could be

                         downloaded and printed.

                         While no changes to the trademark rules are

                         necessary, the PTO will also issue a public

                         request for comments on replacing paper

                         registration certificates with digital

                         versions.

                         The PTO believes that electronic issuance

                         will reduce the time it takes for a patent or

                         trademark to issue by about two weeks.

                         Once the transition is complete, applicants

                         can still receive a paper copy of the issued

                         patents and trademark registration

                         certificates with an embossed gold seal and

                         the director’s signature (i.e., a ribbon

                         certificate) for a fee of $25 per copy.

                  # ⚓ [Older]_A_Whole_Lot_of_“Cobbl[e]”-ty_Gook_After

                    Wertheim⠀⇛

                         Holding: In Indivior UK Ltd. v. Dr. Reddy’s

                         Laboratories S.A., No. 20-2073 (Fed. Cir.

                         2021), the Federal Circuit issued an opinion

                         (“Majority Opinion”) affirming a decision of

                         the Patent Trial and Appeal Board (“PTAB”)

                         holding all but one of the challenged claims

                         unpatentable in IPR2019-00329. Judge Linn

                         concurred-in-part and dissented-in-part

                         (“Linn Opinion”).

                  # ⚓ Huawei_inks_its_first_Wi-Fi_6_patent_licence_with_an

                    overseas_implementer [Ed: Wi-Fi is another sort of

                    patent cartel and writers_sponsored_by_this_cartel say

                    “patent [sic] owners spy monetisation [sic]

                    opportunities”]⠀⇛

                         Latest patent deals related to the next-gen

                         wireless internet standard suggest patent

                         owners spy monetisation opportunities

                  # ⚓ UK:_Why_Does_My_Start-Up_Need_Patents? [Ed: It does

                    not need that. The_litigation_firms (like this liar)

                    want any startup to be misled about a system designed

                    to enrich those who are already rich and rip off the

                    rest]⠀⇛

                         A patent is a legal monopoly granted by a

                         government in return for public disclosure of

                         an invention. A granted patent gives the

                         proprietor the right to prevent others using

                         the invention in the territory to which the

                         patent applies.

                  # ⚓ Battery_Innovation_Enhances_EV_Technology,_Generates

                    Worldwide_Patent_Boom [Ed: The EPO’s_greenwashing,

                    designed to glorify monopolies and distract from the

                    EPO’s crimes, keeps getting cited by patent profiteers

                    and fanatics]⠀⇛

                         Consider information from the joint study,

                         “Innovation in batteries and electricity

                         storage – a global analysis based on patent

                         data,” published in 2020 by the European

                         Patent Office (EPO) and the International

                         Energy Agency. From 2005 through 2018,

                         patents for electric storage technologies –

                         primarily for lithium-ion batteries –

                         increased annually by 14% worldwide. That’s

                         four times as much as the average patent hike

                         in all other technology industries.

                  # ⚓ Serbia_Amends_Patent_Law [Ed: Bending over to

                    monopolies that rip off ill people.]⠀⇛

                         Amendments to the Serbian Law on Patents

                         entered into force on December 23, 2021

                         introducing important changes relating to

                         Supplementary Protection Certificates (SPCs)

                         and utility models.

                  # ⚓ Supplementary_Protection_Certificates_For_Medicinal

                    Products [Ed: A timely reminder that big pharmaceutical

                    monopolies not only write the law but also pass the law

                    to protect themselves using "the law"; they even make

                    up new concepts and terms like "SPCs", quickly

                    exacerbating inequality by their own design]⠀⇛

                         A Supplementary Protection Certificate (SPC)

                         is an intellectual property right available

                         for active ingredients of human and

                         veterinary medicinal products requiring

                         marketing authorisation.

                  # ⚓ Introduction_To_Supplementary_Protection_Certificates

                    For_Plant_Protection_Products [Ed: They’re going for

                    monopolies on plants; these villanelles lawyers want

                    you_to_think_humans_“invented”_and_“own”_nature]⠀⇛

                         Plant protection products protect crops or

                         desirable or useful plants. They are

                         primarily used in the agricultural sector,

                         but also in forestry, horticulture, amenity

                         areas and in home gardens. Plant protection

                         products are defined as active substances, or

                         preparations containing one or more such

                         active substances, put up in the form in

                         which they are supplied to the user, which

                         are intended to:

                  # ⚓ MediciNova_nabs_new_patent_in_Korea_for_MN-001_for

                    treatment_of_blood_cholesterol⠀⇛

                         Recently, MNOV secured Canadian and European

                         patent for MN-001 for hepatic ballooning.

                  # ⚓ New_Referral_To_The_EPO_Enlarged_Board_Of_Appeal_On

                    The_Entitlement_To_Priority [Ed: EPO management sends a

                    case to a kangaroo court, which it_clearly_controls_in

                    direct_and_obvious_violation_of_the_EPC]⠀⇛

                         The Board of Appeal in consolidated cases T

                         1513/17 and T 2719/19 has referred two new

                         questions to the Enlarged Board of Appeal on

                         the issue of priority entitlement, in

                         particular relating to the “joint applicants”

                         approach to claiming priority.

                  # ⚓ USPTO_Tells_Fed._Circ._Only_Humans_Can_Be_Inventors

                    [Ed: Provocateur Stephen Thaler should be spurned based

                    on obviousness -- the obviousness that patents are not

                    for bots]⠀⇛

                         The U.S. Patent and Trademark Office has

                         urged the Federal Circuit to uphold a

                         Virginia federal judge’s ruling that

                         artificial intelligence cannot be listed as

                         an inventor on a patent application.

                         The USPTO’s Thursday brief formally opposed

                         AI researcher Stephen Thaler’s challenge to

                         U.S. District Judge Leonie Brinkema’s

                         September decision that shut down his suit

                         against the U.S. Patent and Trademark Office.

                         The USPTO said that Thaler was trying “to

                         rewrite the Patent Act” and added that “the

                         plain language Congress chose to incorporate

                         in the Patent Act unequivocally resolves this

                         question — only a human being can be an

                         ‘inventor.’”

                  # ⚓ Federal_Circuit:_Did_you_get_their_digits? [Ed:

                    Patent litigation-funded Dennis_Crouch still looking to

                    defend defunct patents]⠀⇛

                         In December 2021, the Federal Circuit sided

                         with the accused-infringer Mylan on claim

                         construction of the term “0.001%” — vacating

                         the judgment of infringement. See Crouch,

                         Rounding Errors in Patent Law, Patently-O

                         (Dec 8, 2021). Now Astrazeneca has petitioned

                         for en banc reconsideration–seeking

                         “consistent precedent regarding significant

                         digits.”

                  # ⚓ EU_set_to_put_spotlight_on_essentiality_in_new_SEP

                    policy [Ed: Patent extortion agenda in EU and based on

                    their support of EPO corruption it's clear whose side

                    they will take]⠀⇛

                         In-house sources from both sides of the SEP

                         licensing fence expect a new policy

                         initiative to introduce further transparency

                         in portfolios

                  # ⚓ PTAB_Procedural_Decisions_Report:_Non-Merits_Based

                    Decisions_Rise,_Denials_Fall_—_Unified_Patents⠀⇛

                         It was another year of hundreds of procedural

                         denials at the PTAB, as many as any other

                         previous year, save 2020’s record high. At

                         the same time, the Board ruled on Fintiv and

                         discretionary issues in almost half of all

                         decisions. The dip in the number of

                         discretionary denials in 2021 from 2020’s

                         record high likely reflects parties adjusting

                         to the recent requirements by filing so-

                         called Sotera stipulations, devoting petition

                         space to briefing the Fintiv factors, and

                         shifting to file ex parte reexaminations over

                         IPRs (which increased by half, as shown

                         below).

                         And while grants were down and it is

                         difficult to measure how much time, money,

                         and effort have been expended responding to

                         Fintiv, data shows the Board considered

                         discretionary issues in approximately 500 of

                         the institution decisions issued in 2021, or

                         roughly more than a third of all the 1,249

                         decisions it made. In short, Fintiv affected

                         at least half the cases on the Board’s docket

                         in 2021.

                         2021 saw 179 institution decisions denied on

                         procedural grounds, compared to 228 in 2020

                         and 162 in 2019.

                         [...]

                         Over the same period, companies began to

                         revive ex parte reexaminations–an old, but

                         nonetheless effective, tool. From 2020 to

                         2021, the number of reexaminations increased

                         by 47%. Over 300 reexaminations were filed in

                         2021, as parties occasionally forwent IPRs

                         that raised discretionary or stay-related

                         issues.

                  # ⚓ Patent_Litigation_2022_in_Turkey [Ed: Just looking to

                    profit by attracting patent trolls and such to

                    Turkey]⠀⇛

                         Under Article 90 of the Constitution, in the

                         event of a conflict between international

                         agreements and national legislation relating

                         to fundamental rights and freedoms, the

                         provisions of international agreements

                         prevail.

                  # ⚓ Broad_Files_Substantive_Preliminary_Motion_No._1_to

                    Substitute_the_Count [Ed: Hard to believe this is still

                    going; the patent fanatics (profiteers) want to own or

                    monopolise life itself through patents and "gene

                    editing"]⠀⇛

                         On December 3rd, Junior Party the Broad

                         Institute, Harvard University, and MIT

                         (collectively, Broad) filed its Substantive

                         Preliminary Motion No. 1 in Interference No.

                         106,133 (which names Sigma-Aldrich as Senior

                         Party), asking the Patent Trial and Appeal

                         Board to substitute the interference Count,

                         pursuant to the provisions of 37 C.F.R. §§

                         41.121(a)(1)(i) and 41.208(a)(2). Broad’s

                         Proposed Substitute Count takes the

                         “McKelvey” format (comprising in the

                         alternative a claim from one of each Party’s

                         applications in interference); the proposed

                         change is in the portion of the Count

                         reciting Broad’s claims…

                  # ⚓ FOSS_Patents:_Apple_opposes_Ericsson_motion_to_amend

                    FRAND_complaint_in_Eastern_District_of_Texas,_says_its

                    own_FRAND_case_was_first_properly_filed_one⠀⇛

                         The procedural tussle between Ericsson and

                         Apple in the Eastern District of Texas over

                         whether and how to go forward with their

                         mutual complaints continues. There’s even a

                         meta-procedural question–relating to

                         procedures related to defining the actual

                         procedures–they disagree on: whether Judge

                         Rodney S. Gilstrap should hold an early case

                         management conference, which Apple insists

on.

                         It’s interesting and a first achievement for

                         Ericsson (owing to its strategy of forging

                         ahead in the fall with a first FRAND action)

                         that the discussion is all about the

                         structure of their litigation in the Eastern

                         District of Texas–as opposed to the usual

                         venue fight over whether that district court

                         has jurisdiction over any case targeting

                         Apple, which even closed its local Apple

                         Stores to have a stronger case for a

                         transfer. If not for Ericsson’s early filing,

                         Apple would already have requested a transfer

                         to the Northern District of California.

                  # ⚓ Third_Party_Submissions [Ed: For the sake of money

                    the USPTO runs in auto-pilot, not even checking with

                    the public is something is novel; just grant, grant,

                    grant...]⠀⇛

                         In a prior post, I wrote about third party

                         prior art submissions, but that post was only

                         looking at issued patents. I have gone back

                         and pulled-in data from all publicly-

                         available applications, including those that

                         have been abandoned or are still pending. The

                         results: third parties have submitted prior

                         art in about 7,000 applications over the past

                         decade. This is about 0.2% of all the

                         applications in my dataset.

                  # ⚓ FOSS_Patents:_EPICSSON:_Apple_makes_public_interest

                    statement_in_Ericsson_patent_case_that_supports_Epic’s

                    antitrust_market_definition⠀⇛

                         What Apple is telling the ITC there is this:

                         even if patent infringements are identified,

                         the iPhone can’t be banned because it’s a

                         product category of its own. There’s nothing

                         else quite like it. Android smartphones may

                         also be smartphones, but they are not

                         iPhones, so they are not “like” articles

                         (which would count as a potential replacement

                         under the ITC’s rules).

                         In the Epic Games v. Apple App Store

                         antitrust case, however, Apple argued that

                         there was a broad market for game

                         distribution. So, according to Apple, if

                         Fortnite wasn’t available on the iPhone, who

                         cares? It could still be played on an Xbox, a

                         Windows PC, or a Samsung phone.

                         The district court didn’t adopt that same

                         market definition, but it did reject–as did

                         Apple–Epic’s single-brand market definition,

                         according to which there is a foremarket

                         (mobile operating systems) and an aftermarket

                         (app distribution for the iPhone). Single-

                         brand markets are a rare exception, but this

                         is such a case.

                         Interestingly, when the question is whether

                         iPhone imports could be excluded from the

                         U.S. market (limited exclusion order, or

                         colloquially “import ban”), Apple itself

                         advances a single-brand market definition,

                         claiming that the iPhone is a product

                         category and Android phones are not capable

                         of replacing any supply shortages or

                         disruptions affecting the iPhone.

                  # ⚓ Status_of_US_Utility_Patent_Applications.⠀⇛

                         David Kappos quickly reset expectations. And,

                         since then we have seen a steady rise in

                         allowance rate.

                  # ⚓ FOSS_Patents:_Ericsson_seeking_preliminary_injunction

                    against_Apple_distributor_in_Brazil,_filed_second_case

                    in_Belgium;_Apple_wants_December_trial_in_Texas,_now

                    challenging_10_Ericsson_patents⠀⇛

                         Ericsson keeps up the pressure on Apple. A

                         filing made by Apple in the Eastern District

                         of Texas on Monday (January 31) mentions that

                         “[i]n Brazil [...], in addition to targeting

                         Apple in a previous injunction request,

                         Ericsson [...] filed for a second preliminary

                         injunction on January 17 against Allied

                         Tecnologia S.A., based on Ericsson’s claimed

                         4G cellular SEPs and merely because Allied

                         resells Apple cellular products.” Apple is

                         now intervening to protect its wholesaler.

                         When I previously wrote about the preliminary

                         injunction Ericsson is seeking against Apple

                         itself in Brazil, I used the plural form

                         “injunctions” though it appears to be a

                         single motion for preliminary injunction

                         involving three SEPs. And now there’s another

                         such motion, also over three SEPs, targeting

                         Allied Tecnologia because of its distribution

                         of accused Apple products.

                  # ⚓ CVC_Files_Responsive_Preliminary_Motion_No._1_for

                    Priority_Benefit [Ed: The utter lunacy of patents on

                    life and nature does not end; these patent extremists

                    won't rest until everything -- including breathing air

                    -- gets monopolised, with lawsuits they stand to profit

                    from]⠀⇛

                         Pursuant to the Patent Trial and Appeal Board

                         Order issued November 29, 2021, Junior Party

                         the University of California, Berkeley; the

                         University of Vienna; and Emmanuelle

                         Charpentier (collectively, “CVC”) on December

                         17, 2021 filed its Responsive Preliminary

                         Motion No. 1 in Interference No. 106,132

                         (which names Sigma-Aldrich as Senior Party),

                         asking the Board for benefit of priority to

                         U.S. Provisional Application No. 61/652,086,

                         filed May 25, 2012 (“P1″), or in the

                         alternative either U.S. Provisional

                         Application No. 61/716,256, filed October 19,

                         2012 (“P2″); U.S. Provisional Application No.

                         61/757,640, filed January 28, 2013 (“P3″);

                         U.S. Application No. 13/842,859, filed March

                         15, 2013; U.S. Application No. 14/685,504,

                         filed April 13, 2015; or U.S. Application No.

                         15/138,604, filed April 26, 2016, pursuant to

                         37 C.F.R. §§ 41.121(a)(1)(ii) and 41.208(a)

                         (3) and Standing Order ¶ 208.4.1, contingent

                         on the Board granting Sigma-Aldrich’s

                         Substantive Preliminary Motion No. 1 to

                         Substitute the Count.

                  # ⚓ Patent_Docs:_Sen._Tillis_Asks_ACUS_to_Conduct_Study

                    on_Creation_of_U.S._IP_Office⠀⇛

                         Last month, Sen. Thom Tillis (R-NC), the

                         Ranking Member of the Subcommittee on

                         Intellectual Property of the Senate Committee

                         of the Judiciary, wrote to the Administrative

                         Conference of the United States (ACUS) to

                         request that the agency “conduct a study on

                         whether Congress should create a unified,

                         stand-alone, and independent Intellectual

                         Property Office.” ACUS is an independent

                         agency of the U.S. government, which was

                         established in 1964 by the Administrative

                         Conference Act, and which conducts research

                         and issues reports concerning various aspects

                         of the administrative process and, when

                         warranted, makes recommendations to the

                         President, Congress, particular departments

                         and agencies, and the judiciary concerning

                         the need for procedural reforms.

                         Stating that “[t]he current fractured

                         approach to intellectual property (IP) in the

                         federal government, with multiple IP

                         functions housed in different agencies, leads

                         to conflicting policy agendas and unnecessary

                         bureaucracy,” Sen. Tillis (above right) noted

                         that he was exploring the possibility of

                         creating an independent agency that would

                         unite the U.S. Patent and Trademark Office

                         (USPTO) and the U.S. Copyright Office (USCO),

                         and perhaps also the Intellectual Property

                         Enforcement Coordinator and other relevant IP

                         functions located in other agencies. The

                         Senator indicated that he believed that “a

                         single, Senate-confirmed, presidentially

                         appointed Director should lead such an office

                         and that it should have, at a minimum,

                         separate Commissioners for Patent, Trademark,

                         Copyright, and Policy Coordination that would

                         report to the Director.” Before pursuing

                         legislation to create a single agency,

                         however, Sen. Tillis suggested that ACUS

                         should contract with the USPTO and USCO to

                         study the issue.

                  # ⚓ Tillis_Floats_Idea_To_Consolidate_USPTO,_Copyright

                    Office [Ed: Tillis has long been the mole or the

                    "Manchin" of patent and copyright fanatics, in effect

                    helping them ram policies that harm the public; but

                    media in the pockets of those same fanatics won't

                    describe him as such]⠀⇛

                         The top Republican on the U.S. Senate

                         Subcommittee on Intellectual Property says

                         there’s too much “unnecessary bureaucracy” in

                         the federal government’s approach to patents,

                         trademarks and copyright law and wants a

                         study done on how to combine the agencies to

                         create a “one stop shop.”

                         In a letter dated Jan. 26, Sen. Thom Tillis,

                         R-N.C., asked the Administrative Conference

                         of the United States to launch an

                         investigation into “whether Congress should

                         create a unified, stand-alone and independent

                         Intellectual Property Office.” The ACUS is an

                         independent federal agency that makes process

                         recommendations to the government.

                  # ⚓ PCT_Direct_Procedure_–_Opportunity_To_Comment_On

                    International_Application [Ed: EPO_is_not_for_Europe

                    but for multinationals and oligarchs; PCT a reminder of

                    this]⠀⇛

                         If a new PCT application fulfils both of

                         these criteria, the Applicant may file a “PCT

                         Direct letter” providing informal comments

                         with the application. The Search Examiner is

                         obliged to consider those comments when

                         preparing the International Search Report and

                         the Written Opinion on patentability.

                  # ⚓ UPC:_Is_it_finally_here? [Ed: No, UPC is not legal

                    and these loaded headlines are their fake_news_lobbying

                    strategy]⠀⇛

                         The European Patent Office (EPO) issued 3 new

                         notices on 19 January 2022 about the Unitary

                         Patent.

                  # ⚓ [Older]_Shots_Fired:_Challenger_Must_Have_Requisite

                    Standing_Before_Appealing_Unfavorable_IPR_Decisions

                    [Ed: More obstacles against removal of fake patents in

                    the US]⠀⇛

                         The US Court of Appeals for the Federal

                         Circuit found, in the context of an appeal

                         from an inter partes review (IPR) decision,

                         that the appellant had Article III standing

                         and affirmed a Patent Trial & Appeal Board

                         (Board) decision, holding the challenged

                         claims unpatentable as obvious. ModernaTX,

                         Inc. v. Arbutus Biopharma Corporation, Case

                         No. 20-2329 (Fed. Cir. Dec 2, 2021) (Lourie,

J.)

                         Arbutus owns a patent pertaining to “stable

                         nucleic acid-lipid particles (SNALP)

                         comprising a nucleic acid (such as one or

                         more interfering RNA), methods of making the

                         SNALP, and methods of delivering and/or

                         administering the SNALP.” Moderna petitioned

                         for IPR of the patent, asserting three

                         grounds…

                  # ⚓ European_Union:_UPC:_Costs_And_Fees [Ed: Herbert

                    Smith Freehills wants you to think UPC exists even

                    though it does not, it’s moreover_illegal and will be

                    challenged (lawyers lying to people does harm to the

                    profession)]⠀⇛

                         Following a lengthy consultation, the

                         Preparatory Committee for the Unified Patent

                         Court (UPC) published its Rules on Court fees

                         and recoverable costs (the Rules) along with

                         Guidelines for the determination of value-

                         based Court fees and the ceiling of

                         recoverable costs of the successful party

                         (the Guidance).

                  # ⚓ Parties’_Duty_To_Keep_The_Patents_Court_Informed

                    About_EPO_Proceedings [Ed: The convicted corrupt firm

                    Marks & Clerk, lecturing us about law, even in relation

                    to EPO (whose_corruption_it_actively_supports), is

                    quite a howler]⠀⇛

                         Mr Justice Meade recently handed down

                         judgment in the ongoing Neurim v Mylan (now

                         named Viatris) saga. This judgment followed

                         an expedited three-day trial of preliminary

                         issues (see “Neurim v Mylan: Take Two”).

                         Dealing predominately with the principles of

                         issue estoppel, abuse of process and

                         competition law issues, this judgment is also

                         notable for imposing a new duty on parties to

                         litigation before the Patents Court to keep

                         it informed about scheduling issues and

                         changes to hearing dates in parallel EPO

                         proceedings, regardless of whether they

                         intend to make case management applications

                         themselves.

                  # ⚓ Should_AI_Systems_Be_Eligible_For_Patents? [Ed:

                    Misframing the debate or situation by interjecting

                    meaningless and misleading_terms_such_as_“Hey_Hi”]⠀⇛

                         The line between artificial intelligence

                         (“AI”) and pure human innovation has blurred

                         as technology continues to evolve at a rapid

                         pace. Technological advances and the parallel

                         progress of AI has resulted in several key

                         innovations: robots can double as

                         radiologists and have the ability to

                         interpret CT scans and other imaging,

                         vehicles can drive themselves with automated

                         technology, and algorithms have the ability

                         to create written and artistic bodies of

                         work.

                         AI advances have been front and center during

                         the COVID-19 pandemic. Algorithms were

                         established to determine which patients could

                         be discharged from the hospital, unique

                         symptoms like loss of smell were identified

                         as a distinguishing factor from the flu, and

                         future outbreaks could be predicted using AI.

                         A human vaccine was exclusively generated by

                         an AI program called SAM, and clinical trials

                         recently began in the United States.

                  # ⚓ Competition_Law_Aspects_of_Patent_Licensing_&

                    Enforcement_in_Israel⠀⇛

                         The Supreme Court of Israel recently held

                         that Sanofi intentionally deceived and failed

                         to provide material information to the

                         Israeli Patent Office during the prosecution

                         of a patent application in respect of

                         Sanofi’s drug Plavix (Clopidogrel

                         Bisulfate)1. Though Sanofi eventually

                         withdrew the patent application, the Supreme

                         Court held that such deception and failure to

                         provide material information were not

                         consistent with fair competition in the

                         marketplace, since Sanofi’s actions

                         significantly impacted how Sanofi’s

                         competitors brought generic alternatives to

                         market. As such, the Supreme Court held

                         Sanofi liable under claims of unjust

                         enrichment.

                  # ⚓ Printed_Publication_Proof_–_Cross_T’s_And_Dot_I’s⠀⇛

                         On November 30, the PTAB entered its final

                         written decision in Unified Patents, LLC v.

                         2BCom, LLC on the patentability of the claims

                         of U.S. Patent No. 7,127,210 (the ‘210

                         patent). The claims in question were directed

                         to a wireless communication apparatus,

                         reciting a method by which a wireless

                         communication apparatus, after establishing a

                         connection with at least a first wireless

                         communication device, is inhibited from

                         establishing a connection with a second

                         wireless communication device. The

                         petitioner, Unified Patents, LLC, challenged

                         the claims as obvious in view of a number of

                         articles, one of which was a Fall 2000 IEEE

                         article, Bluetooth-based wireless

                         connectivity in an automotive environment

                         (the Nüsser reference).

                  # ⚓ [Older]_Design_Patent_Prior_Art_Must_Be_From_Same_or

                    Analogous_Field_as_Claimed_Article_of_Manufacture [Ed:

                    Well, design_patents_ought_not_even_exist_at_all; it’s

                    misuse of patent law]⠀⇛

                         Finding that the Patent Trial & Appeal Board

                         (Board) applied an erroneous interpretation

                         of claim scope, the US Court of Appeals for

                         the Federal Circuit reversed a Board

                         decision, upholding an examiner’s rejection

                         of a lip implant design patent as anticipated

                         by a non-analogous art tool. In re: SurgiSil,

                         Case No. 20-1940 (Fed. Cir. Oct. 4, 2021)

                         (Moore, C.J.)

                  # ⚓ [Older]_Ex_Parte_Reexamination_Not_Allowed_After

                    Failed_IPR_Challenge⠀⇛

                         The US Court of Appeals for the Federal

                         Circuit found that ex parte reexamination was

                         unavailable to a challenger who repeatedly

                         tried and failed to raise the same arguments

                         for the same patent in a prior inter partes

                         review (IPR) proceeding. In re: Vivint, Inc.,

                         Case No. 20-1992 (Fed. Cir. Sept. 29, 2021)

                         (Moore, C.J.)

                         Vivint sued Alarm.com in 2015 for

                         infringement of several patents. In response,

                         Alarm requested that the Patent Trial &

                         Appeal Board (PTAB) institute “a litany of

                         post-issuance review proceedings,” including

                         three separate IPR petitions directed to one

                         of the patents. The PTAB refused to institute

                         two of the petitions because Alarm failed

                         show to a reasonable likelihood that it would

                         prevail on at least one challenged claim and

                         also refused to institute the third petition

                         because it represented an example of

                         “undesirable, incremental petitioning.”

                         According to the PTAB, Alarm had “used prior

                         Board decisions as a roadmap to correct past

                         deficiencies” and allowing such “similar,

                         serial challenges to the same patent” by the

                         same challenger risked, not only harassment

                         of patent owners, but also frustration of

                         congressional intent behind the America

                         Invents Act (AIA).

                  # ⚓ UK_IPO_announce_new_IP_Counter-Infringement_strategy

                    [Ed: Latest brainwash campaign from the oligarchs’

                    protectors_at_UK-IPO]⠀⇛

                         The new strategy represents a step change in

                         the IPO’s drive to protect IP rights. By

                         partnering with others to set a global gold

                         standard, it aims to make UK IP rights – and

                         rights owned by UK businesses internationally

                         – the best protected in the world.

                         The strategy seeks to establish how

                         enforcement agencies, government and industry

                         can work together to build upon and improve

                         current structures, ensuring that IP

                         infringement is tackled coherently as a

                         strategic economic and social threat – at

                         home and internationally. It will be

                         underpinned by a strong research plan, and

                         the findings will be shared widely with

                         partner organisations to build a robust

                         evidence base to support and inform work.

                  # § Software Patents⠀➾

                        # ⚓ [Older]_Analysis_indicates_that_Access_Advance

                          is_currently_the_top_HEVC_patent_pool [Ed:

                          |Software_patents_cartel boosted by IAM]⠀⇛

                               Licensees get access to higher-quality

                               rights via the platform than those

                               available through Velos Media and MPEG-

LA

            # § Trademarks⠀➾

                  # ⚓ NFTs_and_new_tech_to_shake_up_domain_disputes_in_2022

                    [Ed: And once again legitimising scams like "NFT"]⠀⇛

                         Sources explain how disruptive tech such as

                         NFTs, blockchain and the metaverse will

                         affect domain name protection and enforcement

                         this year

                  # ⚓ TTABlog_Test:_Is_“CRC_BAKERY”_Confusable_with_the

                    “CRC”_Kosher_Certification_Mark,_Both_for_Food

                    Products?⠀⇛

                         The USPTO refused to register the proposed

                         mark CRC BAKERY for various bakery products

                         (Class 30), for wholesale food

                         distributorship services (Class 35), and for

                         bakery services (Class 40) [BAKERY

                         disclaimed], finding confusion likely with

                         the registered certification mark CRC &

                         Design (shown below) for “fresh and processed

                         foods for human consumption.” Applicant

                         argued, inter alia, that the cited mark –

                         used to certify rabbinical approval of food

                         products as being kosher – limits the classes

                         of consumers for those foods to sophisticated

                         and discerning consumers. How do you think

                         this came out? In re CRC Packaging, LLC,

                         Serial No. 88696519 (January 28, 2022) [not

                         precedential] (Opinion by Judge Elizabeth A.

                         Dunn).

                         The cited certification mark is owned by the

                         Chicago Rabbinical Council, and states that

                         the mark is “used by persons authorized by

                         the certifier to certify a reliable

                         rabbinical approval of food products as being

                         kosher.”

                         The Section 2(d) likelihood-of-confusion

                         analysis does not change when the cited

                         registration is for a certification mark;

                         however, because the owner of a certification

                         mark does not itself use the mark, the

                         determination of likelihood of confusion is

                         based on use of the cited mark by the

                         certification mark users.

                  # ⚓ Additional_“GARANIMALS”_Evidence_Yields_District

                    Court_Reversal_Of_TTAB’s_“MANIMAL”_Opposition

                    Dismissal⠀⇛

                         The United States District Court for the

                         District of Oregon reversed the Board’s

                         decision dismissing an opposition to

                         registration of the mark MANIMAL for a wide

                         variety of clothing, including “children’s

                         clothing.” [TTABlogged here]. The Board found

                         that opposers failed to establish a

                         likelihood of confusion with its registered

                         mark GARANIMALS for children’s shirts and

                         pants. Reviewing de novo the TTAB record as

                         well as substantial additional evidence, the

                         court granted the plaintiffs’ motion for

                         summary judgment on its cause of action for

                         review under Section 1071 of the Trademark

                         Act. Garan, Incorporated and Garan Services

                         Corporation v. Manimal, LLC, Case No. 3:20-

                         cv-00623-IM (D. Oregon January 25, 2022).

                         Plaintiffs’ new evidence focused on

                         establishing the fame of the GARANIMALS mark,

                         including evidence of substantial media

                         recognition. Plaintiffs also placed their

                         sales and advertising figures in marketing

                         context, “showing that it is the second

                         largest children’s clothing brand by market

                         share, second only to Carter’s and ahead of

                         brands including Children’s Place, Old Navy,

                         Gerber, OshKosh, Circo, Hanes, Wrangler, and

                         Healthtex.”

                  # ⚓ New_UAE_Patent_Law:_What_do_you_need_to_know?⠀⇛

                         The UAE has issued Federal Law no. 11 of 2021

                         (“the Law”) concerning the regulation and

                         protection of Industrial Property Rights. The

                         Law will repeal the former Patent Law, Law

                         No. 17 of 2002 and covers patents, industrial

                         designs, integrated designs, undisclosed

                         information and utility certificates. It was

                         published in Official Gazette no. 703 on 31

                         May 2021 and is expected to come into force

                         when the Executive Regulations publish.

                  # ⚓ UAE_Joins_Madrid_Protocol_International_Trade_Mark

                    System [Ed: UAE in the monopolists' hegemony, now

                    celebrated by convicted corrupt firm Marks & Clerk,

                    which is inciting public officials to break the law by

                    lying to them]⠀⇛

                         The Madrid Protocol allows businesses located

                         in one member country of the Madrid Protocol

                         system to obtain trade mark protection in any

                         of the other 108 member countries through the

                         filing of a single trade mark application.

                         The Madrid Protocol currently extends to many

                         countries of general commercial importance,

                         including the UK, EU, US, Japan and China. It

                         is also possible for owners of Madrid

                         Protocol trade mark registrations to extend

                         their trade mark protection to other member

                         countries within the system as their business

                         needs change. Due to the flexibilities of the

                         system, using the Madrid Protocol to obtain

                         trade mark protection overseas can be a very

                         cost-effective mechanism, and can also

                         simplify management of the trade mark

                         portfolio moving forward.

                  # ⚓ The_Dark_Pictures_developer_trademarks_five_future

                    titles [Ed: This writer has no clue what he's writing

                    about; he thinks trademarks are obtained via "European

                    patent office"]⠀⇛

                         Supermassive Games, developer of Until Dawn

                         and the ongoing The Dark Pictures anthology

                         series, has trademarked logos and titles for

                         five future projects.

                         All five appear to be upcoming releases in

                         The Dark Pictures series, are styled with the

                         franchise’s logo, and were registered via the

                         European patent office yesterday, 31st

                         January (thanks, Gematsu).

                  # ⚓ The_Dark_Pictures_Series_Developer_Trademarks_Five

                    More_Games [Ed: Another clueless writer who thinks EPO

                    does trademarks]⠀⇛

                         It seems more titles are coming to The Dark

                         Pictures franchise as it got trademarked just

                         recently. There were registered via the

                         European Patent office.

            # § Copyrights⠀➾

                  # ⚓ Breaking:_UKIPO_outlines_five-year_IP_enforcement

                    plan [Ed: UKIPO ramps up its attack_on_the_interests_of

                    the_British_public]⠀⇛

                         The office will rely on intelligence sharing

                         and educational campaigns as it looks to

                         highlight the human impact of IP crime

                  # ⚓ Metaverse_could_spark_C-suite_IP_investment,_say

                    brands [Ed: Max Walters again pushing buzzwords and

                    nonsense; the quality of so-called 'journalism' has

                    fallen so sharply over the past 2 decade]⠀⇛

                         In-house counsel in the fashion, science and

                         drinks industries say that, despite

                         uncertainties, the metaverse may encourage

                         top-level investment in IP

                  # ⚓ Piracy_Icon_ETTV_Officially_Shuts_Down_Due_to_a_Lack

                    of_Funds⠀⇛

                         ETTV has shut down and will not be coming

                         back. The operator of the site informs

                         TorrentFreak that he doesn’t have the funds

                         to keep the site and upload bots going. The

                         domain names are still registered for now but

                         these won’t be renewed either. It’s the end

                         of an era.

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